[    {        "title": "0707.0746v1.The_current_spin_on_manganites.pdf",        "content": "The current spin on manganites  \n \nC. Israel1, M. J. Calderón2 and N. D. Mathur1* \n 1Department of Materials Science, University of Cambridge, Cambridge CB2 3QZ, UK  2Instituto de Ciencia de Materiales de Madrid (CSIC), Cantoblanco,  28049  Madrid, \nSpain.  \n*E-mail: ndm12@cam.ac.uk  \n \nSTANDFIRST:  \nManganites are pseudo -cubic  oxides of manganese  that show extremes of \nfunctional behavior . Diverse magnetic and electronic phases coexist on a wide \nrange of length scales even within single crystals. This coexistence demo nstrates \na complexity that inspires ever deeper study . Yet even the basic  nature of the \ncoexisting  phases remain s controversial. Can the ferromagnetic metallic phase  \nprovide fully spin -polarized electrons  for spin electronics ? Does the superlattice \nin the high ly insulating phase represent charge order?  Here we highlight recent \nresults that demonstrate  a coexistence of opinions about a  field in rude health.  \n \nABSTRACT:  \nIn a material, the existence and co existence of phases with very different ma gnetic \nand electro nic properties is both unusual and surprising. Manganites in particular \ncapture the imagination because they demonstrate  a complex ity that  belies  their \nchemically single -phase nature . This  complexity  arises because the magnetic, \nelectronic and crystal stru ctures interact with one another to deliver exotic magnetic \nand electronic phases that coexist. This coexistence is self-organized and yet  readily \nsusceptible to external perturbation s, permitting subtle and imaginative \nexperiments  of the type  that we desc ribe here . Moreover, t hese experiments reveal \nthat each competing phase itself remains an incompletely solved  mystery.  \n \nManganites were known to show pronounced magnetoresistance1,2 and phase separation3 \neffects in the 1950s , but they really hit the heights during the 1990s for three reasons. \nFirst, magnetoresistance took prominence  between  the 1988 discovery4 of giant \nmagnetore sistance  (GMR)  in metallic multilayers , and the first shipment  of GMR disc-\ndrive heads by IBM in 1998 . Second, great advances in laboratory infrastructure  \npermitted  new approaches, e.g. the fabrication  of high-quality thin films , the advent of \nsuperconduct ing magnets,  and the imaging of magnetic and electronic texture via e.g. \nscanning probe techniques . Third, this infrastructure  had been very productive in the \nstudy of the high-temperature cuprate superconductors , and scientists were therefore  \nimmediately able to accept the new challenges presented by the manganites.  \n \nThe manganites are a family of perovskite oxides in which the composition of the A-\nsite cations  may be varied using mixtures of divalent rare-earth and trivalent alkaline -\nearth  elements . The m ost immediate consequence  of this variation  is to alter the charge \ndoping  of the magnetic and electronic  structures that reside  in the  sublattice formed by  \nthe B-site manganese and intervening oxygen  atoms . Significantly charge disorder on the A-sites has little effect on  physical properties5,6, suggesting that it is screened.  However, \nthe average size of the A -site cations plays a strong role in determining physical \nproperties, as does size disorder7. This is because the A -site cations are relatively small \nsuch that  the surrounding MnO 6 octahedra are tilted. Physical properties are  also strongly \ninfluenced when these octahedra undergo Jahn-Teller distortions due to  the presence of \nvalence electron s. And e xtrinsic and intrinsic strain  are so significant8 that epitaxial films, \nsingle crystals, powders and polycrystalline samples all have the potential to behave quite \ndifferently.  \n \nA suitable mix of similarly sized cations makes it favorable  for Mn valence electrons  \n(in 3d eg levels)  to delocalize  and magnetically link Mn 3mB core spins, i.e. three highly \nlocalized 3d t2g electrons that are strongly Hund cou pled to each other  and on-site valence \nelectrons. Thus, for example, La 0.7Ca0.3MnO 3 is a ferromagnetic metal (FMM) below a \nCurie temperature9 of TC~260 K.  Above this temperature  the system is a paramagnetic \ninsulator (PMI)  because  the Mn core spin directions are random , and the valence \nelectrons  are bound to lattice distortions to form polarons that are n ot very mobile . Near  \nTC, an applied magnetic field aligns the core spins and recovers the metallic state. This \nnegative magnetoresistance (MR) was found to be colossal (~105%) in a strained \nannealed film10, the term colossal magnetoresistance (CMR) was coined , and the field of \nmanganites was born again . \n \nEven larger values of MR (~1012% in Pr0.67Ca0. 33 MnO 3) are recorded  if the magnetic \nfield is applied to the more highly insulating phase s11 of manganites  that result from the \nuse of  small A -site cations such as Pr3+. The traditional cartoon  of charge order (CO) \nused to describe these  insulating states involves  planes of Mn3+ interspersed with planes \nof Mn4+, and antiferromagnetic core -spin order.  As we discuss later, the appearance of a \nsuperlattice  in the CO phase is unambiguous  in a range of diffraction experiments , but the \nunderlying source of the modulation is controv ersial . However, we will persist  with the \nCO epithet since it is unlikely that charge modulation  is completely absent  in the \nsuperlattice , and in any case the label is familiar.  \n \nCertain manganites such as (La,Pr,Ca)MnO 3 show phase separation between the \nFMM and CO phases . The spatial distribution of these phases  was first visualized12 using \ntransmission electron microscopy  (TEM) to reveal th e extent  of the CO phase. Later, a \ncombination of TEM probes13 sensitive to  each of the coexisting phases  revealed  a phase \nthat was unexpectedly both  FMM and CO.  This hints at how subtly the manganites can \nbehave, a trait reflected in the controversy  regarding the CO phase itself.  Many further \nstudies have revealed phase coexistence phenomena on length  scales that are so short that \nit is questionable  whether each coexisting region truly represents a thermodynamic \nphase14. \n \nIn th is review  we comment on a snapshot of  recent manganite results, passing over \nthe earlier discoveries that are described elsewhere15-22, and recent work on  “layered” \nmanganites23-25 in which rocksalt layers separate the perovskite manganite blocks . Recent \nreview  article s26-31 to which  the manganites  are relevant  cover  oxide spin electronics \n(spintronics); the coexistence of  magnetic and electrical order  (multiferroic s); and  magnetoelectric coupling between magnetic and electrical order parameters.  This \ndiversity of contexts  epitomizes  the multifarious  nature of the manganites.  \n \nPhase separation  \nPhase separation is anticipated between ordered phases (e.g. the FMM and CO phase12,13) \nthat form below temperatures as high as  room temperature , and atomically sharp phase \nboundaries have been observed in scanning tunneling microscopy (STM)  experiments on \na single crystal32. Coexistence between  one of the se ordered phases and the PMI , seen in \nthin films  by STM33,34, does not23 occur in every manganite, and could be an extrinsic \neffect  due to thin -film strain or methodology35. To address this issue , Steffen Wirth  and \ncolleagues constructed zero-bias STM conductance maps35 for a Pr0.68Pb0.32MnO 3 single \ncrystal . They found  a nanoscale phase separation  (Fig. 1)  that appears to be intrinsic \nbecause (i)  it only occurred  at temperatures near the metal -insulator transition,  and (ii) it \nis far smaller than the length scales associated with twinning . The phase distribution \nshould therefore vary at least from run to run, but this was not confirmed . \n \n \n  \nFig. 1 (a) Schematic zero -bias STM conductance map  for a Pr0.68Pb0.32MnO 3 single crysta l at a \ntemperature near the metal -insulator transition (typical pixel resolution ~1 nm).  (b) The \ncorresponding conductance values are represented on this histogram. Two peaks are apparent, \nreflecting a phase separation that appears to be intrinsic because  at higher (lower) temperature the \nsample is significantly more homogeneous such that (i) the conductance map is mainly blue (green) \nand (ii) the histogram displays only a single blue (green) peak. Images courtesy of Steffen Wirth, \nbased on [ 35]. \n \nMagnetic force microscopy ( MFM) has previously revealed36 that the FMM \ncomponent in a phase -separat ed (La,Pr,Ca)MnO 3 film adopts  a pattern that varies a s the \ntemperature is changed.  This fluidity was  somewhat  surprising , since  long -range strain \narising from  the nucleation of FMM  regions had the  potential  to globally  lock the pattern  \nof phase separation . A more recent surprise from the same laboratory was the discovery37 \nthat although (La,P r,Ca)MnO 3 show s glassy magnetic behavior38, it is not a spin-cluster  \nglass39: variable-field MFM studie s37 found that  sample  magnetization  was determined  by \nFMM phase fraction rather than  cluster alignment12. Interestingly, this experiment \nrecorded correlations between magnetic phase changes and twin boundaries  (Fig. 2) , \nconsistent with the influence of the crystal structure, and strain,  on physical properties.   \n  \nFig. 2 MFM images of a (La,Pr,Ca)MnO 3 single crystal showing the conversion of the CO phase \n(bright) to the FMM phase (dark) under (a) the influence of an increasing magnetic field B at 7 K, \nand ( b) increasing temperature T at 1 T. Twin boundaries (black dashed lines) serve as both \nnucleation sites and boundaries for phase conversion. Images are (a) 7 ´7 µm2 and (b) 6 ´6 µm2. After \n[37]. \n \nTEM  has been very valuable in the study of manganites over the last decade12,13, and \ncontinues to produce important results. Recently, polycrystalline  (La,Ca)MnO 3 that \nnominally assumes an orthorhombic CO phase was found to contain micron -sized \nmonoclinic needle twins with no CO modulation40,41. It is instructive to compare with the \nafore -mentioned STM studies35 that report intrinsic phase separation in single crystal  \nPr0.68Pb0.32MnO 3. In polycrystalline (La,Ca)MnO 3, the monoclinic phase app ears to be \nextrinsic since x -ray diffraction reveals it to be absent in powders that are nominally \nstrain free42. \n \nPhase coexistence in manganites can produce  distinctive electrical and magnetic \nmemory effects43. The changes  observed  under the influence of an applied magnetic field \nsuperficially resemble  the sharp switches  associated with  the reorientation of FMM \ndomains at discontinuities such as grain boundaries44-46 and tunnel barrier s47-49. However, \njust like the original CMR effect10, memory effects43 in phase -separated manganites \ninvolve such a pronounced  continuous response  that even small magnetic fields result in \na significant change.  And if the se small magnetic field s are  turned on quickly, the \nresponses  they generate can appear  sharp  on a suitable  timescale . Electric  rather than \nmagnetic  fields can produce switch ing in various transition metal oxides  due to  the \ninfluence  near current contacts  of charge injectio n/extraction on sample oxygenation. A \npronounced  electrical pulse -induced resistance -change (EPIR) ha s been  seen in \nmanganite s that are prone to phase separation50,51, but also those that are not52,53. Local53 \nswitching and imaging seems a particularly promising route to probe further  the nature of  \nthis distinction.  \n Phase separation vis-à-vis CMR  \nThese beautiful recent results demonstrating  phase separation build on the earlier \nexcitement regarding CMR. It is therefore interesting to consider not just why phase \nseparation arises in the manganites, but how it relate s to CMR.  \nPhase separation may be considered to arise  in connection with the comp lexity that is \nreflected in the manganite Hamiltonian , which  should include:  \n• the kinetic energy of the conduction electrons plus Hund coupling (double \nexchange54), \n• a direct antiferromagnetic coupling between the core spins,  \n• electron -phonon coupling between octahedral deformations and the eg orbitals,  \n• on-site and long -range Coulomb interactions, and  \n• diagonal (on -site) and off -diagonal (hopping) disorder.  \nGiven this complexity, it is not surprising that the energy landscape has several local \nminima lying at similar energy levels. Each minimum  corresponds to a different phase, \nand experimentally it is easy to take the system from one minimum to another using \nvarious control parameters such as temperature.  \n \nExtrinsic phase separation is commonly observed near either first - or second -order \ntransi tions  as a consequence of  the local energetics being  modified by defects or strain, \ni.e. nucleating agents that render  phase distribution s similar from run to run.  Even i n the \nabsence of such agents,  intrinsic phase separation  near first -order transitions is expected \nin principle55 and arises in practice unless kinetically prevented ; the new phase is \nnucleated by intrinsic features such as m agnetic fluctuations, and the phase distribution \nvaries from run to run.  Although phase separation is pronounced in the manganites, it  \ndoes not require all the ingredients of manganite physics, and can indeed arise from a \nsimple double -exchange model55, or strain in a model where the electronic and magnetic \ndegrees of freedom are not taken into account56. But the richness of man ganite physics is \nsignificant because it sometimes produces  phase separation on such a short length scale \nthat the result is a new thermodynamic phase displaying magnetic a nd el ectronic \ntexture14. \n \nAlthough it is believed that  phase separation typically underpins CMR57, and it is true \nthat phase separation strongly influences CMR, phase separation is not in fact formally \nrequired for CMR. A CMR response arises when a magneti c field interconverts two \nphases which are very different , and thus separated by a first -order boundary near which \nphase separation is expected . However,  in principle , a CMR response could arise in a \nhomogenous system , and indeed the layered manganite La 1.4Sr1.6Mn2O7 shows a \nunimodal distribution of zero -bias conductances, indicating no phase separation23. \nTherefore the role of phase separation  in CMR is circumstantial and not c ausal . That said,  \nphase separation will strongly influence e.g. current pathways and therefore CMR.  \n \nDevices  \nElectronic and magnetic devices are of course widely used  to great effect  in an industr ial \ncontext , e.g. transistors  in computer chips , and magneti c sensors for anti -lock brakes in \nautomobiles . Thin -film devices also represent scientific tool s for manipulat ing and \nmonitor ing the manganites.  For example, lithographic patterning on some  length scale can indicate the presence58,59 or absence60 of phase separation on that length scale. In \nanother example, devices designed to  trap magnetic domain walls in the FMM phase61,62 \nhint at current -induced domain wall deformation63, but clear evidence for the proposed14 \nphase separation  at wall centre s remains elusive . \n \nMagnetic tunnel junctions made fro m traditional magnetic metals are currently \nstarting to find their way into data storage applications64. Some of the first manganite \ndevices were epitaxial tunnel junctions47 made from  FMM electrodes  of (La,Sr)MnO 3 or \n(La,Ca)MnO 3 with an  ultra -thin SrTiO 3 barrier . Subsequent improvements48,49 were both \nqualitative and quantitative , producing reports of  clean low-field MR switching with a \nmagnitude  on the order of 1000%.  Recent improvements in performance  (Fig. 3) are \nbased on reducing  interfacial charge discontinuities65 by interface engineering66. This \napproach could b e relevant to following through on the  interesting suggestion24 that a \nself-organized barrier forms at the free surface of a layered manganite . Separ ately, it \nwould  be interesting to fully explore  in manganite tunnel junctions the role of  symmetry \nfiltering26,27,67 by crystalline barriers , a phenomenon  that has been very successful ly \nexploited  to produce large room -temperature MR  using  MgO barriers  with CoFe68 or Fe69 \nelectrodes.  \n \n  \nFig. 3 MR data at 10 K for magnetic tunnel junctions with (La,Sr)MnO 3 (LSMO) electrodes. An \nSrTiO 3 (STO) barrier (bottom panel) was used for the original manganite tunnel junctions47. \nReplacing it with a trilayer  that also  involves  LaMnO 3 (LMO) is designed to increase the MR (middle \npanel) by compensating interfacial charge transfer. Using instead an LaAlO 3 (LAO) barrier is \ndesigned to prevent charge transfer, and this produces an even larger MR (top panel). After [ 66]. \n MR devices may also be obtained  without explicitly incorporating a tunnel barrier  by \ngrowing a bilayer  comprising a mangan ite and some other FMM material such as \nmagnetite70 or permalloy71. Magnetic decoupling is thought to be the result of interfacial \neffects associated with e.g. structural disco ntinuities or oxygenation.  Alternatively, MR \ndevices may be obtained using FMM manganite electrodes separated over relatively large \ndistances by  organic materials. This is because carbon has a low atomic number and \ntherefore weak  spin -orbit coupling, which  means  that traveling  spin -polarized  electrons \ndo not lose their magnetic information . Sub-micron organic layers of 8 -hydroxy -\nquinoline aluminum  (Alq3) between (La,Sr)MnO 3 and Co electrodes are the basis for \ndevices72 that show  a large low -field MR~30% . Moreover,  hysteretic current -voltage \ncharacteristics in similar devices73 produce  memory effects reminiscent of those due to \nelectric fields at m anganite contacts51. \n \nCarbon nanotubes are not taxonomically  considered to be long to the  organic family , \nbut exploiting their high Fermi velocity74 (0.8 ×106 m s-1) as well as weak spin -orbit \ncoupling permits the transport of spin information over micron -scale distances between \n(La,Sr)MnO 3 electrodes75. The associated conversion of magnetic information into large \nelectrical signals corresponds to an MR of 61%  (Fig. 4), and represents the basis for a \nspin transistor if the nanotube can be suitably gated. The innate  advantage of a spin \ntransistor is that t he use of a magnetic gate would permit non -volatile information \nstorage, unlike today’s fast silicon transi stors. And the surprising success with nanotubes \nand manganites is particularly significant75 given that the relevant  figure of merit for spin \ntransistor -like devices based on semiconductors76 is an MR  of only ~1%. Note that \nnanotubes of manganites77,78 (Fig. 5) have yet to be incorporated in spintronic devices . \n \n  \nFig. 4  (a) Scanning electron microscopy image of a 20 nm diameter multiwall carbon nanotube \n(CNT) running between epitaxial La0.7Sr0.3MnO 3 (LSMO) electrodes.  (b) The MR of this two -\nterminal device at 5 K under 25 mV bias, with the arrows showing the magnetic orientations of the manganite electrodes. The large MR persists up to a higher bias of 110 mV, permitting magnetic \ninformation to be converted to large el ectrical signals. CNTs could therefore make an impact in \nspintronics, e.g. as the non -magnetic channel in spin transistors. After [ 75]. \n \n  \nFig. 5 TEM images of (a) a (La,Sr)MnO 3 nanotube synthesized via a pore -wetting proce ss with liquid \nprecursors77, and (b) a MgO -(La,Sr)MnO 3 core -shell nanowire fabricated by the pulsed laser \ndeposition of (La,Sr)MnO 3 onto single -crystalline MgO nanowires78. \n \nThe devices discussed above require the magnetic electrodes to be switched using an \napplied magnetic field. For commercial  applications using traditional magnetic metals, \nthere is currently widespread interest in magnetic switching using the torque delivered by  \nspin-polarized currents79. Demonstrating the efficacy of using manganites as a test -bed \nfor novel effects , Jonathan Sun of IBM (Yorktown Heights) first reported80 spin torque in \na manganite structure  via the observation of asymmetric current -voltage characteristics.  \nThe magnetically  switched object was an intergrowth betwe en FMM manganite \nelectrodes in a  device  similar to the tunnel junctions he pioneer ed47. The architecture  \nemployed for th is report  of spin torque  is somewhat ironic  given that  defects in tunnel \nbarriers  are normally associated with device failure . But, asymmetric current -voltage \ncurves attributed to spin torq ue have now81 been reported in planar nanoconstrictions61-63 \nin a (La,Ba)MnO 3 film . \n \nThe related effect of s witching a magnetization using an electric field , rather than a \ncurrent, is currently a popular goal in manganite device  studies . This is primarily because \nit mimics the attractive electric -write process in ferroelectric random access memory \n(FeRAM)  without mimic king the less  attractive magnetic -write processes associated with \nmagnetic MRAM.  One effective  strategy  is to  apply a voltage between the surface of a \nmanganite film and the underside of an underlying  ferroelectric substrate , in order to  \nexploit strain coupling at the interface.  This strategy requires the ferroelect ric to also be \nferroelastic  so that it will deform when the ferroelectric domains are electrically \nswitched.  In the well -know n relaxor ferroelectric perovskite Pb(Mg,Nb)O 3-PbTiO 3 \n(PMN -PT), A-site cationic disorder reduces the ferroelectric domain  size to t he \nnanoscale . PMN -PT can  generate , in epitaxial manganite films , weakly hysteretic  \nchanges  in magnetization82 (Fig. 6a) that are also seen in electrical  resistivity83,84. To \nachieve e lectrically driven  switching  in the resistivity85 and magnetization86 that is sharp \nand non -volatile , the relaxor should  be replaced with the more traditional ferroelectric  \nBaTiO 3 (Fig. 6b). \n   \nFig. 6 Magnetoelectric strain -mediated coupling betw een a ferromagnetic manganite film and its \nferroelectric substrate. ( a) Weak hysteresis in magnetization M versus electric field E applied across \na (La,Sr)MnO 3 film and relaxor Pb(Mg,Nb)O 3-PbTiO 3 substrate82. (b) Sharp non -volatile switching \nin M for three samples across which E was ramped until the transition was observed86. Each s ample \ncomprised a (La,Sr)MnO 3 film on a BaTiO 3 substrate. The black lines indicate when E was switched \noff. \n \nThe heterostructures discussed above82-86 are multiferroic insofar as  three  ferroic \norders  are present between the film and the substrate , and we class86 the electrically \ninduced magnetic changes  they display  as “converse ” magnetoelectric effects . For \ncompleteness, we note that “direct” magnetoelectric effects , i.e. magnetically  induced \nchanges in an electrical polarization,  could in principle be used for room -temperature \nmagnetic field sensors87 to replace low -temperature SQUIDs . Strong  interest in direct \nmagnetoelectric effects in the manganites remains  purely scientific  because it is a low -\ntemperature phenomenon , and the ferroelectric polarization s (e.g.  0.08 µC cm-2 in88 \nmultiferroic  TbMnO 3) are typically three orders of magnitude smaller than the best \nferroelectrics . \n \nRecently the themes of tunnel junctions and multiferroics were combined89 in an all-\nmanganite spin-filter device  that displays four -state resistance  behavior . Charge carriers \nthat enter  the device from an upper gold contact are spin pola rized as they tunnel through  \nan ultra -thin insulating ferromagnetic layer of (La,Bi)MnO 3. The  magnetization s of this \nspin filter and an underlying  FMM (La,Sr)MnO 3 analyzer may be switched independently by an applied magn etic field, yielding two states of r esistance . The spin -filter device  is \ntherefore comparable to the tunnel junctions discussed above , but with the magnetic spin-\nfilter layer replacing both the barrier and the upper FMM electrode of the tunnel junction.  \nWhat makes the present device89 novel is that the spin filter is multiferroic, i.e. not just \nferro magneti c but also  (excitingly  for a manganite)  robustly  ferroelectric. Since the \nferroelectric spin filter lies between dissimilar materials, device resistance depends on its \npolarization90. Consequently,  the two magnetically encoded states become four  (Fig. 7). \nInterestingly, exploiting this electroresistance phenomenon89 is simpler than  the FeRAM  \nmethod of reading the ferroelectric polarization by cycling a voltage . \n \n  \nFig. 7 (a) For a (La,Sr)MnO 3/(La,Bi)MnO 3 (2 nm)/Au spin -filter device89, each MR trace displays \nstates of resistance R that are high (at the pea ks) and low (away from the peaks). As indicated on the \nfigure, the electrical history of the device changes the absolute resistance, thus yielding a total of four \nstates.  (b) Device schematic showing the magnetizations (white arrows) and electrical polariz ations \n(red arrows)  for the four states.  \n \nThis section has served to indicate that many manganite device applications have \nbeen suggested based on the diverse properties of the mangan ites. In other examples, \nmanganite diodes91-93 have been improved by integrating a single manganite layer with a \nferroelectric and a cuprate94 (Fig. 8), a MR >1000%  has been achieved by exploiting the \nproximity effect in manganite -cuprate trilayers95, and polycrystalline MR sensors  have \nbeen exploited in an electromagnetic device that launches projectiles96. Given this \ndiversity  of performance , the continuing scientific endeavors  skimmed over here justify \nthe continued study of manganite devices even if they never find commercial success.  \n   \nFig. 8 (a) High -resolution TEM cross -sectional image of a heterostructure comprising a manganite \n(hole -doped LSMO, La 0.67Sr0.33MnO 3), a ferroelectric (BST, Ba 0.7Sr0.3TiO3), and a cuprate (electron -\ndoped LCCO, La 1.89Ce0.11CuO 4). (b) Current -voltage cur ves show excellent rectification over a wide \nrange of temperatures. After [ 94]. \n \nFaults in charge order  \nThe beguiling s ubtlety of the ma nganites is clear at time of writing, but it was not always \nso. In the highly insulating CO phase, the superlattice periodicity recorded in electron97, \nneutron98,99 and x -ray98 diffraction experiments has traditionally been associated with Mn \n3d eg valence  electrons residing on only those Mn atoms that lie in certain pseud o-cubic \n(110) planes. This simple cartoon was strongly supported by TEM cross -sectional \nobservations97 of “stripes”, but the interpretation of such image contrast is non -trivial \nbecause the electrons from the TEM beam interact strongly with the  sample causing \nmultiple scattering (dynamical diffraction)100. Moreover, dark-field images  showing \nnearly commensurate order101 (where the periodicity of the superlattice is only just \ngreater than double the periodicity of the parent lattice ) are liable100,102 to show  \ninterf erence fringes that do not represent real phenomena such as discommensurations  \n(where the periodicity changes from one region to another ). \n \nVarious re -interpretations involve the Wigner crystallization  of charge103,104, or \ndistortions  that are primarily structural105 in which the pairing  of Mn atoms  has been \nargued106. However, controversy persists given that even the most sophisticated tools \ncannot probe the CO state with the precision required for unambiguous interpretation . \nThis is apparent from the ability  to fit neutron powder diffraction patterns equally well to \nmore than one of the competing models107. Periodicity information in diffraction studies remains a far safer  animal . A local TEM probe demonstrates in (La,Ca)MnO 3 that the \nsuperlattice possesses a pe riod that  remains uniform below a key length scale  such that it \ncannot100 be explained in term s of two species  of pseudo -cubic (110) plane s, e.g. with \ndifferent Mn valences.  \n \nThe complete separation of integer electronic charge across even one unit cell (to \nyield Mn3+ and Mn4+) is coulombically very expensive.  Given this, and the above \nexperimental  evidence,  it has now been established that the original CO picture should be \nreplaced with a charge modulation that varies by only a small percentage from the \nnominal doping108-110. The superlattices observed in CO phases could even arise in the \nabsence  of any charge modulation due to orbital ordering, where broken symmetry due to \nantiferromagnetic order3 opens a gap and stabilizes lattice distortions.  \n \nCurrently , an open debate rages on whether whatever charge modulation  is pre sent in \nthe CO phases is strongly coupled to the lattice or not. The original strong -coupling \npicture is based on an electron -phonon interaction that  produces regions with a specific \ntype of commensurate order (where the superlattice period is an integer multiple of the \nparent latti ce period) separated by discommensurations97,111. Tight -binding models \nalways give a charge/orbital modulation that is tied to the lattice, but the superlattice \nperiods can be so large110 that they cannot be experimentally distinguished from non-\ninteger modulations. Alternatively a charge -density -wave scenario100,112,113 with weaker \n(but non -zero) coupling may be more realistic. Ginzburg -Landau theory supports this \npicture through a complex scenario in which new thermodynamic phases114 permit \nincommensurability, even at commensurate doping, due to the presence of \nferromagnetism.  \n \nAdded value  \nWhy ha ve manganite  devices  not enjoyed  commercial success ? There are several well-\nknown potential factors connected with  low Curie temperatures, temperature -dependent \nresponses , high electrical resistivities and difficulties  of int egration with silicon \ntechnology . An extrinsic but instructive obstacle  is that manganite surfaces115 and \ninterfaces116-118 behave very differently from the bulk ; for example , at a free surface of \nthe FMM phase, (i) the spin polarization  falls fast with inc reasing temperature115 due to  \nweak double exchange at surfaces119, and (ii) a ferrodistortive behavior  has recently been  \npredicted120. This surface frailty is a manifestation of the subtle competing interactions \nlisted  earlier , and yet it is these interactions that generate the richne ss. \n \nThis richness inspires a question: c an we use a single complex material to define a \ncomplete set of technol ogical building blocks that mirror t he vast array of single -purpose  \nmaterials that we have at our disposal tod ay? These blocks could be defined using  \nscanning probe  lithography60 in a top -down process , but it would be more  radical to \ncontrol nan oscale phase separation in a manganite film without removing or adding \nmaterial121. A more extreme phase change  (between crystalline and amorphous phases)  is \ncommercially exploited  in chalcogenides for CD s, DVD s, and the up-and-coming122 all-\nsolid -state phase -change memory (PC -RAM).  In the manganites , the changes between \nmetallic and insulating phases involve only small structural changes and far less energy.   \nManganites demonstrate the potential of complex materials for device application s, \nand if we a re ever to go beyond silicon we require basic research in as many diverse \nfields as possible.  The manganites are excellent catalysts for interdisciplinary activity  as \nthey continue to encroach  on other areas of research . For example, f erroelectricity , \nreferred to  earlier,  has fallen prey to their advances  and various candidate mechanisms  \ncan produce an electrical polarization123-126. The recent demonstration127 that \nLa2/3Ca1/3MnO 3 possesses a negative refractive index  at GHz frequencies shows that the \nmanganites are full of surprises.  In this respect the manganites are excellent drivers to  \nadvance knowledge in a range of directions  with unknown future consequences.  \n \nAcknowledgements  \nFor helpful discussions we thank J Paul Attfield, Manuel Bibes, Luis Brey , Alex de \nLozanne , Thomas Fix,  Vincent Garcia,  Leticia Granja, Luis Hueso, Harold Hwang, Pablo \nLevy , Peter Littlewoo d, Juan Salafranca , Steffe n Wirth  and Weida Wu . C. I. is supported \nby the EU FP6 STRP CoMePhS.  M. J. C. acknowledges support from MAT2006 -03741 \nand Programa Ramón y Cajal (MEC, Spain).  \n \n1. Jonker, G . H. and Santen, J. H. V., Physica  (1950) 16, 337  \n2. Van Santen, J. H. and Jonker, G. H., Physica (1950) 16, 599  \n3. Wollan, E. O. and Koehler, W. C., Phys. Rev.  (1955) 100, 545  \n4. Baibich, M. N., Broto, J. M., Fert, A., Dau, F. N. V., Petroff, F., Eitenne,  P., \nCreuzet, G., Friederich, A., and Chazelas, J., Phys. Rev. Lett. (1988) 61, 2472  \n5. Williams, A. J., Sobotka, B. M., and Att ?eld, J. P., J. Solid State Chem.  (2003) 173, \n456 \n6. Palanisami, A., Warusawithana, M., Eckstein, J. N., Weissman, M. B., and Mathur, \nN. D., Phys. Rev. B  (2005) 72, 024454  \n7. Rodríguez -Martínez, L. M. and Attfield, J. P., Phys. Rev. B  (2000) 63, 024424  \n8. Millis, A. J., Nature (1998) 392, 147  \n9. Cheong, S. -W. and Hwang, H. Y., In Colossal Magnetoresistive Oxides , Tokura, \nY., (ed.), Gordon and Breach, Amsterdam, (2000)  \n10. Jin, S., Tiefel, T. H., McCormack, M., Fastnacht, R. A., Ramesh, R., and  Chen, L. \nH., Science  (1994) 264, 413  \n11. Anane, A., Renard, J. P., Reversat, L., Dupas, C., Veillet, P., Viret, M., Pinsard, L., \nand Revcolevschi, A., Phys. Rev. B  (1999) 59, 77 \n12. Uehara, M., Mori, S., Chen, C. H., and Cheong, S. -W., Nature  (1999) 399, 560 \n13. Loudon, J. C., Mathur, N. D., and Midgley, P. A., Nature  (2002) 420, 797  \n14. Mathur, N. D. and Littlewood, P. B., Solid State Commun.  (2001) 119, 271  \n15. Ramirez, A. P., J. Phys.: Condens. Matter  (1997) 9, 8171  \n16. Rao, C. N. R. and Raveau, B., Colossal Magnetoresistance, Charge Ordering and \nRelated Properties of Manganese Oxides , World Scientific, Singapore, (1998)  \n17. Coey, J. M. D., Viret, M., and von Molnar, S., Adv. Phys. (1999) 48, 167  \n18. Tokura, Y., Colossal Magnetoresistive Oxides , Gordon a nd Breach, Amsterdam, \n(2000)  \n19. Rao, C. N. R., Arulraj, A., Cheetham, A. K., and Raveau, B., J. Phys.: Condens. \nMatter  (2000) 12, R83  20. Salamon, M. B. and Jaime, M., Rev. Mod. Phys.  (2001) 73, 583  \n21. Dagotto, E., Hotta, T., and Moreo, A., Phys. Rep.  (2001) 344, 1 \n22. Mathur, N. and Littlewood, P., Phys. Today  (2003) 56, 25 \n23. Rønnow, H. M., Renner, C., Aeppli, G., Kimura, T., and Tokura, Y., Nature (2006) \n440, 1025  \n24. Freeland, J. W., Gray, K. E., Ozyuzer, L., Berghuis, P., Badica, E., Kavich, J., \nZheng, H., and Mitchell, J. F., Nat. Mater.  (2005) 4, 62 \n25. Tokunaga, Y., Lottermoser, T., Lee, Y., Kumai, R., Uchida, M., Arima, T., and \nTokura, Y., Nat. Mater.  (2006) 5, 937  \n26. Bibes, M. and Barthélémy, A., IEEE Trans. Electron Dev.  (2007) 54, 1003  \n27. Bibes, M., Herranz, G., and Barthélémy, A., manuscript in preparation  \n28. Dorr, K., J. Phys. D: Appl. Phys.  (2006) 39, R125  \n29. Eerenstein, W., Mathur, N. D., and Scott, J. F., Nature  (2006) 442, 759  \n30. Fiebig, M., J. Phys. D: Appl. Phys.  (2005) 38, R123  \n31. Prellier, W., Singh, M. P., and Murugavel, P., J. Phys.: Condens. Matter  (2005) 17, \nR803  \n32. Renner, C., Aeppli, G., Kim, B. G., Soh, Y. A., and Cheong, S. W., Nature  (2002) \n416, 518  \n33. Fäth, M., Freisem, S., Menovsky, A. A., Tomioka, Y., Aarts, J., and  Mydosh, J. A., \nScience  (1999) 285, 1540  \n34. Becker, T., Streng, C., Luo, Y., Moshnyaga, V., Damaschke, B., Shannon, N., and \nSamwer, K., Phys. Rev. Lett.  (2002) 89, 237203  \n35. Rößler, S., Ernst, S., Padmanabhan, B., Elizabeth, S., Bhat, H. L., Steglich, F. , and \nWirth, S., http://www.arxiv.org/abs/0705.4243v1  \n36. Zhang, L., Israel, C., Biswas, A., Greene, R. L., and de Lozanne, A., Science (2002) \n298, 805  \n37. Wu, W., Israel, C., Hur, N., Park, S., Cheong,  S.-W., and de Lozanne, A., Nat. \nMater.  (2006) 5, 881  \n38. Sharma, P. A., Kim, S. B., Koo, T. Y., Guha, S., and Cheong, S. W., Phys. Rev. B  \n(2005) 71, 224416  \n39. Dagotto, E., Science  (2005) 309, 257  \n40. Tao, J., Niebieskikwiat, D., Salamon, M. B., and Zuo, J. M., Phys. Rev. Lett.  (2005) \n94, 147206  \n41. Loudon, J. C. and Midgley, P. A., Phys. Rev. B  (2005) 71, 220408  \n42. Sagdeo, P. R., Anwar, S., and Lalla, N. P., Phys. Rev. B  (2006) 74, 214118  \n43. Levy, P., Parisi, F., Granja, L., Indelicato, E., and Polla, G ., Phys. Rev. Lett.  (2002) \n89, 137001  \n44. Hwang, H. Y., Cheong, S. -W., Ong, N. P., and Batlogg, B., Phys. Rev. Lett.  (1996) \n77, 2041  \n45. Gupta, A., Gong, G. Q., Xiao, G., Duncombe, P. R., Lecoeur, P., Trouilloud, P., \nWang, Y. Y., Dravid, V. P., and Sun, J . Z., Phys. Rev. B  (1996) 54, R15629  \n46. Mathur, N. D., Burnell, G., Isaac, S. P., Jackson, T. J., Teo, B. S., \nMacManusDriscoll, J. L., Cohen, L. F., Evetts, J. E., and Blamire, M. G., Nature  \n(1997) 387, 266  \n47. Sun, J. Z., Gallagher, W. J., Duncombe, P. R ., Krusin -Elbaum, L., Altman, R. A., \nGupta, A., Lu, Y., Gong, G. Q., and Xiao, G., Appl. Phys. Lett.  (1996) 69, 3266  48. Jo, M. H., Mathur, N. D., Todd, N. K., and Blamire, M. G., Phys. Rev. B  (2000) 61, \n14905  \n49. Bowen, M., Barthélémy, A., Bibes, M., Jac quet, E., Contour, J. -P., Fert, A., \nCiccacci, F., L. Duò, and Bertacco, R., Phys. Rev. Lett.  (2005) 95, 137203  \n50. Liu, S. Q., Wu, N. J., and Ignatiev, A., Appl. Phys. Lett.  (2000) 76, 2749  \n51. Quintero, M., Levy, P., Leyva, A. G., and Rozenberg, M. J., Phys. Rev. Lett.  (2007) \n98, 116601  \n52. Dong, R., Wang, Q., Chen, L. D., Shang, D. S., Chen, T. L., Li, X. M., and Zhang, \nW. Q., Appl. Phys. Lett.  (2005) 86, 172107  \n53. Chen, X., Wu, N. J., Strozier, J., and Ignatiev, A., Appl. Phys. Lett.  (2006) 89, \n063507  \n54. Zener, C., Phys. Rev.  (1951) 82, 403  \n55. Guinea, F., Gomez -Santos, G., and Arovas, D. P., Phys. Rev. B  (2000) 62, 391  \n56. Ahn, K. H., Lookman, T., and Bishop, A. R., Nature  (2004) 428, 401  \n57. Dagotto, E., Nanoscale Phase Separation and Colossal Magne toresistance , \nSpringer, (2002)  \n58. Wu, T. and Mitchell, J. F., Phys. Rev. B  (2006) 74, 214423  \n59. Zhai, H. Y., Ma, J. X., Gillaspie, D. T., Zhang, X. G., Ward, T. Z., Plummer, E. W., \nand Shen, J., Phys. Rev. Lett.  (2006) 97, 167201  \n60. Hirooka, M., Yanagis awa, Y., Kanki, T., Tanaka, H., and Kawai, T., Appl. Phys. \nLett. (2006) 89, 163113  \n61. Mathur, N. D., Littlewood, P. B., Todd, N. K., Isaac, S. P., Teo, B. S., Kang, D. J., \nTarte, E. J., Barber, Z. H., Evetts, J. E., and Blamire, M. G., J. Appl. Phys.  (199 9) \n86, 6287  \n62. Wolfman, J., Haghiri -Gosnet, A. M., Raveau, B., Vieu, C., Cambril, E., Cornette, \nA., and Launois, H., J. Appl. Phys.  (2001) 89, 6955  \n63. Arnal, T., Khvalokvskii, A. V., Bibes, M., Lecoeur, P., Haghiri -Gosnet, A. -M., and \nMercey, B., http://arxiv.org/abs/cond -mat/0610338v1  \n64. Sealy, C., Mater. Today  (2006) 9, 10 \n65. Kumigashira, H., Chikamatsu, A., Hashimoto, R., Oshima, M., Ohnishi, T., \nLippmaa, M., Wadati, H., Fujimori, A., Ono, K., K awasaki, M., and Koinuma, H., \nAppl. Phys. Lett.  (2006) 88, 192504  \n66. Ishii, Y., Yamada, H., Sato, H., and Akoh, H., Appl. Phys. Lett.  (2006) 89, 042509  \n67. Butler, W. H. and Gupta, A., Nat. Mater.  (2004) 3, 845  \n68. Parkin, S. S. P., Kaiser, C., Panchula, A., Rice, P. M., Hughes, B., Samant, M., and \nYang, S. -H., Nat. Mater.  (2004) 3, 862  \n69. Yuasa, S., Nagahama, T., Fukushima, A., Suzuki, Y., and Ando, K., Nat. Mater.  \n(2004) 3, 868  \n70. Singh, M. P., Carvello, B., and Ranno, L., Appl. Phys. Lett.  (2006) 89, 022504  \n71. Ruotolo, A., Oropallo, A., Granozio, F. M., Pepe, G. P., Perna, P., and di Uccio, U. \nS., Appl. Phys. Lett.  (2006) 88, 252504  \n72. Xiong, Z. H., Wu, D., Vardeny, Z. V., and Shi, J., Nature  (2004) 427, 821  \n73. Hueso, L. E., Bergenti, I., Riminucci,  A., Zhan, Y., and Dediu, V., Adv. Mater. \nDOI: 10.1002/adma.200602748  \n74. Buitelaar, M. R., Bachtold, A., Nussbaumer, T., Iqbal, M., and Schönenberger, C., \nPhys. Rev. Lett.  (2002) 88, 156801  75. Hueso, L. E., Pruneda, J. M., Ferrari, V., Burnell, G., Valde s-Herrera, J. P., Simons, \nB. D., Littlewood, P. B., Artacho, E., Fert, A., and Mathur, N. D., Nature  (2007) \n445, 410  \n76. Jonker, B. T. and Flatté, M. E. F., in Nanomagnetism , Mills, D. L. and Bland, J. A. \nC., (eds.), Elsevier, (2006)  \n77. Curiale, J., Sanch ez, R. D., Troiani, H. E., Leyva, A. G., and Levy, P., Appl. Phys. \nLett. (2005) 87, 043113  \n78. Lei, B., Han, S., Li, C., Zhang, D. H., Liu, Z. Q., and Zhou, C. W., Nanotechnology  \n(2007) 18, 044019  \n79. Myers, E. B., Ralph, D. C., Katine, J. A., Louie, R. N. , and Buhrman, R. A., Science  \n(1999) 285, 867  \n80. Sun, J. Z., J. Magn. Magn. Mater.  (1999) 202, 157  \n81. Pallecchi, I., Pellegrino, L., Caviglia, A., Bellingeri, E., Canu, G., Gazzadi, G. C., \nSiri, A. S., and Marre, D., Phys. Rev. B  (2006) 74, 014434  \n82. Thiele, C., Dörr, K., Bilani, O., Rödel, J., and Schultz, L., Phys. Rev. B  (2007) 75, \n054408  \n83. Thiele, C., Dorr, K., Schultz, L., Beyreuther, E., and Lin, W. M., Appl. Phys. Lett.  \n(2005) 87, 162512  \n84. Zheng, R. K., Chao, C., Chan, H. L. W., Choy, C. L., a nd Luo, H. S., Phys. Rev. B  \n(2007) 75, 024110  \n85. Dale, D., Fleet, A., Brock, J. D., and Suzuki, Y., Appl. Phys. Lett.  (2003) 82, 3725  \n86. Eerenstein, W., Wiora, M., Prieto, J. L., Scott, J. F., and Mathur, N. D., Nat. Mater.  \n(2007) 6, 348  \n87. Dong, S., Zh ai, J., Li, J., and Viehland, D., Appl. Phys. Lett.  (2006) 89, 252904  \n88. Kimura, T., Goto, T., Shintani, H., Ishizaka, K., Arima, T., and Tokura, Y., Nature  \n(2003) 426, 55 \n89. Gajek, M., Bibes, M., Fusil, S., Bouzehouane, K., Fontcuberta, J., Barthelemy, A. \nE., and Fert, A., Nat. Mater.  (2007) 6, 296  \n90. Zhuravlev, M. Y., Sabirianov, R. F., Jaswal, S. S., and Tsymbal, E. Y., Phys. Rev. \nLett. (2005) 94, 246802  \n91. Mitra, C., Raychaudhuri, P., Kobernik, G., Dorr, K., Muller, K. H., Schultz, L., and \nPinto, R. , Appl. Phys. Lett.  (2001) 79, 2408  \n92. Susaki, T., Nakagawa, N., and Hwang, H. Y., Phys. Rev. B  (2007) 75, 104409  \n93. Xiong, C. M., Zhao, Y. G., Zhao, Z. H., Kou, Z. Q., Cheng, Z. H., Tian, H. F., \nYang, H. X., and Li, J. Q., Appl. Phys. Lett.  (2006) 89, 143510  \n94. Yuan, J., Wu, H., Cao, L. X., Zhao, L., Jin, K., Zhu, B. Y., Zhu, S. J., Zhong, J. P., \nMiao, J., Xu, B., Qi, X. Y., Qiu, X. G., Duan, X. F., and Zhao, B. R., Appl. Phys. \nLett. (2007) 90, 102113  \n95. Peña, V., Sefrioui, Z., Arias, D., Leon, C., San tamaria, J., Martinez, J. L., te \nVelthuis, S. G. E., and Hoffmann, A., Phys. Rev. Lett.  (2005) 94, 057002  \n96. Schneider, M., Schneider, R., Stankevic, V., Balevicius, S., and Zurauskiene, N., \nIEEE Trans. Magn.  (2007) 43, 370  \n97. Mori, S., Chen, C. H., and Cheong, S. -W., Nature  (1998) 392, 473  \n98. Radaelli, P. G., Cox, D. E., Marezio, M., and Cheong, S. -W., Phys. Rev. B  (1997) 5, \n3015  99. Fernández -Díaz, M. T., Martínez, J. L., Alonso, J. M., and Herrero, E., Phys. Rev. B  \n(1999) 59, 1277  \n100. Loudon, J. C., Cox, S., Williams, A. J., Attfield, J. P., Littlewood, P. B., Midgley, \nP. A., and Mathur, N. D., Phys. Rev. Lett.  (2005) 94, 097202  \n101. Chen, C. H. and Cheong, S. W., Phys. Rev. Lett.  (1996) 76, 4042  \n102. Eaglesham, D. J., Bird, D., Withers, R. L., and St eeds, J. W., J. Phys. C: Solid State \nPhys.  (1985) 18, 1 \n103. Radaelli, P. G., Cox, D. E., Capogna, L., Cheong, S. -W., and Marezio, M., Phys. \nRev. B  (1999) 59, 14440  \n104. Wang, R., Gui, J., Zhu, Y., and Moodenbaugh, A. R., Phys. Rev. B  (2000) 61, \n11946  \n105. García, J., Sánchez, M. C., Blasco, J., Subías, G., and Proietti, M. G., J. Phys.: \nCondens. Matter  (2001) 13, 3243  \n106. Rodríguez -Carvajal, J., Daoud -Aladine, A., Pinsard -Gaudart, L., Fernández -Díaz, \nM. T., and Revcolevschi, A., Physica B  (2002) 320, 1 \n107. Rodriguez, E. E., Proffen, T., Llobet, A., Rhyne, J. J., and Mitchell, J. F., Phys. Rev. \nB (2005) 71, 104430  \n108. van den Brink, J., Khaliullin, G., and Khomskii, D., Phys. Rev. Lett.  (1999) 83, \n5118  \n109. Ferrari, V., Towler, M., and Littlewood, P. B.,  Phys. Rev. Lett.  (2003) 91, 227202  \n110. Brey, L., Phys. Rev. Lett.  (2004) 92, 127202  \n111. Brey, L. and Littlewood, P. B., Phys. Rev. Lett. (2005) 95, 117205  \n112. Cox, S., Rosten, E., Chapman, J. C., Kos, S., Calderon, M. J., Kang, D. J., \nLittlewood, P. B ., Midgley, P. A., and Mathur, N. D., Phys. Rev. B  (2006) 73, \n132401  \n113. Cox, S., Singleton, J., McDonald, R. D., Migliori, A., and Littlewood, P. B., \nhttp://arxiv.org/abs/0705.4310v1  \n114. Milward, G. C., Calderón, M. J., and Littlewood, P. B., Nature (2005) 433, 607  \n115. Park, J. -H., Vescovo, E., Kim, H. -J., Kwon, C., Ramesh, R., and Venkatesan, T., \nPhys. Rev. Lett.  (1998) 81, 1953  \n116. Lin, C. W., Okamoto, S., and Millis, A. J., Phys. Rev. B  (2006) 73, 041104  \n117. Salafranca, J. L., Calderón, M. J., and Brey, L., manuscript in preparation  \n118. Niebieskikwiat, D., Hueso, L. E., Borchers, J. A., Mathur, N. D., and Salamon, M. \nB., http://arxiv.org/abs/c ond-mat/0702350v1  \n119. Calderón, M. J., Brey, L., and Guinea, F., Phys. Rev. B  (1999) 60, 6698  \n120. Pruneda, J. M., Ferrari, V., Littlewood, P. B., Spaldin, N. A., and Artacho, E., \nhttp://arxiv.org/abs/070 5.0335v1  \n121. Mathur, N. and Littlewood, P., Nat. Mater.  (2004) 3, 207  \n122. Ball, P., Nature (2007) 445, 362  \n123. Seshadri, R. and Hill, N. A., Chem. Mater.  (2001) 13, 2892  \n124. Sergienko, I. A. and Dagotto, E., Phys. Rev. B  (2006) 73, 094434  \n125. Mostovo y, M., Phys. Rev. Lett.  (2006) 96, 067601  \n126. Efremov, D. V., van den Brink, J., and Khomskii, D. I., Nat. Mater.  (2004) 3, 853  \n127. Pimenov, A., Loidl, A., Gehrke, K., Moshnyaga, V., and Samwer, K., Phys. Rev. \nLett. (2007) 98, 197401  \n  "    },    {        "title": "0708.1462v1.Structural_Characterization_of_Magnetic_Nano_particles_Suspensions__Using_Magnetic_Measurements.pdf",        "content": "ENS’06 Paris, France, 14-15 December 2006  \n©TIMA Editions/ENS 2006 -page- ISBN:   \nSTRUCTURAL CHARACTERIZATION OF MAGNETIC NANO-PARTIC LES \nSUSPENSIONS, USING MAGNETIC MEASUREMENTS \n \nNicolae Calin POPA  1 , Ali SIBLINI  2 , Jean Jacques ROUSSEAU  2 ,  \nMarie-Françoise BLANC-MIGNON  2 , and, Jean Pierre CHATELON  2   \n \n1 Center for Advanced and Fundamental Technical Research (CAFTR), Rom anian Academy – \nTimisoara Branch, Bd. Mihai Viteazul nr 24, 300223 Timisoara, Romania ,  \nPhone: + 4 0256 403703, Fax: + 4 0256 403700,  \nE-mail: ncpopa@acad-tim.tm.edu.ro, or, ncpopa@flumag2.mec.utt.ro. \n2 DIOM, Dispositifs et Instrumentation en Optoélectronique et Micro -ondes, Université Jean Monnet, \n23 rue du Dr. P. Michelon, 42023 Saint - Etienne, Cedex 2, France,  \nPhone (33) 0477 485079, Fax: (33) 0477 485039,  \nE-mail: Ali.Siblini@univ-st-etienne.fr, or, rousseau@univ-st-etie nne.fr. \n \nABSTRACT \n \nThe paper describes some characteristics of the “P”  \ncurves for structural characterization of magnetic nano-\nparticles suspensions (complex fluids, complex powd ers, \ncomplex composite materials, or living biological \nmaterials having magnetic properties). In the case of these \nmaterials, the magnetic properties are conferred to  various \ncarrier liquids by artificially integrating in thei r structure \nferromagnetic particles of different sizes. The mag netic \nproperties are usually shown by the hysteresis curv e. The \nstructure can be seen on (electronic) micrography. The P \ncurves offer another possibility to determine the s tructure \nof the magnetic component of a complex fluid by \nnumerical analysis of the magnetization curve \nexperimentally obtained. The paper presents a detai led \napproach of the P curves and some limitations in th eir use. \n \n1. INTRODUCTION \n \nUsually, magnetizable fluids include nano-magnetic fluids \n(called also magnetic fluids or ferrofluids, [1 - 1 1]), \nmagneto – rheological fluids ([12 - 14]), or other fluids \nobtained mixing the first two categories. In all th ese \ncomplex fluids (suspensions), their magnetic proper ties \nare obtained by artificially integrating, in the ma ss of \ndifferent carrier liquids, ferromagnetic particles (of \ndifferent sizes and/or materials). The magnetic pro perties \nof these complex fluids are shown by the hysteresis  curve, \nand, their structure can be seen on the (electronic ) \nmicrography. In a previous paper ([15]), we defined  the \n“P” (peak) curves, which can deliver information \nconcerning the structure of magnetizable fluids, by  numerical derivation (relative to the magnetic fiel d \nstrength H) of the magnetization curves relative to  the \nsaturation magnetizations: \n \n( )() [ ]\ndH MHMdHPS= ,   (1) \n \nwhere P is the P value, H is the magnetic field strength, M \nis the fluid magnetization, and, the subscript S de notes the \nsaturation point from the magnetization curve. We d efined \nalso the “P shape factor” (PSF) for the P curves in  solid \nmatrix: \n \n()\n( )perp par \n0P0P\nPSF = ,   (2) \n \nwhere the subscript par  or perp  denotes that we \ndetermined the P curves with the measurement of \nmagnetic field respectively parallel or perpendicul ar to the \nsolidification magnetic field.  \nWe showed ([15]) that, for the same type of magneti c \nnano-particles (the same magnetic material and the same \ntechnology to obtain the particles), the height of the P \ncurves is greater when the magnetic particles are s maller, \nand, the spread of the P curves is wider when the m agnetic \nparticles are of greater dimensions. We showed also  that \nthe P curves are the same if we use the volume \nmagnetization or the mass magnetization; the P curv es do \nnot depend on the accuracy of the magnetometer y-ax is \ncalibration, and on the accuracy of sample mass or volume \nmeasurement. From all these, we get the most intere sting \napplication for P curves, the possibility to invest igate the \nliving biological material (from magnetic point of view) \nwithout extracting a sample.  N.C. POPA, A. SIBLINI, J.J. ROUSSEAU, Marie-Françoise BLAN C-MIGNON, J.P. CHATELON \nStructural Characterization of Magnetic Nano-particles Suspensions, Using Magneti c Measurements  \n \n©TIMA Editions/ENS 2006 -page- ISBN:  Fig. 1 presents a typical hysteresis curve \n(experimentally obtained using a Vibrating Sample \nMagnetometer VSM 880, ADE Technologies, USA) for a \nnano-magnetic fluid. The fluid (Ferrofluidics, USA)  has \nthe saturation magnetization M S = 15.9 kA/m, and the \nparticles diameter 8.5 nm (ferrite). As it is known , the \nnano-magnetic fluids have not hysteresis loop. Fig.  2 \nshows the P curve for the nano-magnetic fluid from Fig. 1.  \nThe paper presents a detailed approach of the P cur ves. \nWe tried to find mathematical equations to approxim ate \nthe P curves, and, to establish some limitations in  the use \nof these P curves.  \n \n2. DETAILED APPROACH OF “P” CURVES \n \nTo better understand the theoretical and practical \npossibilities offered by the P curves, some of thei r \ncharacteristics will be presented.  \nI. From the hysteresis curve of magnetizable fluids , \nwhere () ()H M HM − −=  ( 0H, 0 M ≥ ≥ ), we can see \nthat the P curves are symmetrically versus the Oy a xis, \nthat meaning ()()HP HP −=  ( 0H, 0 P ≥ ≥ ) (Figs. 2 and \n7). We can observe that, \n \n( ) ( ) dH HP 2 dH HPSH\n0⋅ ⋅= ⋅∫ ∫+∞ \n∞−.  (3) \n \nII. For an arbitrary point denoted by the subscript  X, \n \n( )\nSXH\n0MMdH HPX\n= ⋅∫.   (4)  \nIII. If the arbitrary point is the saturation point , \n \n( ) 1 dH HPSH\n0= ⋅∫.   (5) \n \nThis means that for any P curve, the area between t he P \ncurve, and, the Oy and Ox axis is always 1. With ot her \nwords, the amplitude and the spread of a P curve ar e not \nindependent. In this situation, the question is if a P curve \ncan be theoretically defined through a mathematical  \nequation which use several parameters, or through a  \nmathematical relation having one parameter only (th is \nparameter being P(0)). The P curve defines, in some  \nlimits, the nano-magnetic particles. If we can expr ess the \nP curve using one parameter only, than, having a P curve \n(experimentally obtained), from this P curve we can  \nobtain information about only one parameter of the nano-\nmagnetic particles. This parameter can be a physica l \nparameter (e.g. the most frequent dimension of the \nparticles), or can be a mathematical relation (e.g.  a ratio, a \nsum, etc.) between other physical characteristics o f the \nnano-particles.  \nIV. Because the P values are the result of numerica l \nderivation of some experimental measurements, the \ncalculus of these values is performed with certain \napproximation. In an arbitrary point, we can calcul ate the \nderivative to the left, to the right, or their arit hmetical \nmean (center derivative). Fig. 3 presents the diffe rence \nbetween these three situations (P values for a ferr ofluid, \n[3], having M S = 15.6 kA/m, and, the particles diameter of \n10.5 nm).  For a general view of P curves (Figs. 2 and 7), \nusually we used the center derivative. Further, for  a \n \nFig. 1: Typical hysteresis curve for a nano-magneti c \nfluid (experimentally measured).  \n \nFig. 2: P curve for the nano-magnetic fluid from Fi g. 1.  \n N.C. POPA, A. SIBLINI, J.J. ROUSSEAU, Marie-Françoise BLAN C-MIGNON, J.P. CHATELON \nStructural Characterization of Magnetic Nano-particles Suspensions, Using Magneti c Measurements  \n \n©TIMA Editions/ENS 2006 -page- ISBN:  theoretical approximation of the P curves, it is pr eferable \nto use the derivative to the right.  \nV. At the first sight, we have a great temptation t o \napproximate the P curve, using the theoretical rela tion:  \n( ) ( )*HH\nt e0P HP−\n⋅ = .   (6) \n \nwere, the subscript “t” denotes a theoretical curve . \nIf we admit this approximation (for SH H0 ≤ ≤ ), than  \n \n( ) ( ) ( ) [ ] 0P HP*H dH HPX tH\n0tX\n− ⋅ −= ⋅∫. (7) \n \n In fact, at the saturation point ()0 HPS=, so we can \nwrite \n \n( ) ( ) 0P*H dH HPSH\n0t ⋅ = ⋅∫ .  (8) \n \nTaking into consideration the equalities (8) and (5 ),  \n \n( )0P1H*= ,    (9) \n \nand, the approximation (6) becomes  \n \n()()H)0 ( P\nt e0P HP⋅ −⋅ = .  (10) \n This means that, if we admite the approximation (6) , \nthe P curves are completely determined by the value  P(0) . \nIn this situation, the P curves can deliver informa tion \nabout only one parameter of the magnetizable nano-f luid \n(this parameter could be the most frequent dimensio n of \nthe particles). \n \n3. THEORETICAL APPROXIMATIONS OF “P” \nCURVES \n \nAfter many experimental measurements and theoretica l \napproximations, we concluded that, the approximatio n \ngiven by relation (6) (or its particular case given  by \nequation (10)) is not good enough for the P curves.  Fig. 4 \nshows a P curve and its theoretical approximation \nobtained using one exponential function only (relat ion (6) \nfor H* = 30).  \nI. The same figure presents the approximation (of t he P \ncurve) obtained using a sum of two exponential func tions, \nE1(H) and E2(H) . \n \n( ) ( ) , e0E HE*\n1HH\n1 1−\n⋅ =   (11) \n \n( ) ( ) , e0E HE*\n2HH\n2 2−\n⋅ =   (12) \n \n() () ()HE HE HP2 1 t + = . (13) \n \nIn this case, the theoretical curve (for: E1(0) = 0.75P(0) , \nH* 1 = 10 kA/m , E2(0) = 0.25P(0) , and, H* 2 = 85 kA/m ) is \nalmost superposed to the experimental curve. We \n \nFig. 3:  Three different possibilities to calculate the \nderivative in an arbitrary point: derivative to the  left, \nto the right, and, the arithmetical mean of the fir st two \n(center derivative). \n \nFig. 4:  P curve (for the nano-magnetic fluid from Fig. \n1) and its theoretical approximations. N.C. POPA, A. SIBLINI, J.J. ROUSSEAU, Marie-Françoise BLAN C-MIGNON, J.P. CHATELON \nStructural Characterization of Magnetic Nano-particles Suspensions, Using Magneti c Measurements  \n \n©TIMA Editions/ENS 2006 -page- ISBN:  determined these four parameters for the equation ( 13) \nusing numerical investigations.  \nII. We get a very good theoretical (analytical) \napproximation of P curves using exponential functio ns \ndefined for the interval between two successive \nexperimental points. So, we take into consideration  the \nvalues Ho (=0), H 1, H 2, …, H n, and, Hn+1 , of magnetic \nfield, where, for the P curve, we experimentally ob tained \nrespectively the values vo (=P(0)), v 1, v 2, …, v n (for i = 1  \nto n, all vi > 0 ), and,  vn+1 =0 .  \nWe define the function Fi(H) , \n \n( )\n1i ii 1i *\ni1i iHHH\ni1i i\ni\nvln vln H HH: where HH H for evH H,HH for 0\nHF\n*\nii\n+++−−+\n−−=\n<≤ ⋅≤ <\n=\n . \n(14) \n \nThe expression for Hi* results from the condition (15). \n \n( )1iHH H\ni i\nHHH Hv ev HF lim *\nii 1i\n1i1i+−−\n<→= ⋅=+\n++.  (15) \n \n(This means, the sum of n consecutive functions, gi ves a \ncontinuous function.) For the continuity, we remark  that \n \n()i i i v HF =.   (16) \n \nWe define also the linear interpolation function Gi(H) , \n \n( ) ( )\ni 1i i i 1i i1i i\nii i\ni1i i\ni\nH H H,and ,v vv : where H H H,for ,HH HvvH H,HH,for , 0\nHG\n− = − =\n< ≤−+≤ <\n=\n+ +++\n∆ ∆∆∆\n. \n(17) \n \nWith these from above, the approximation of P curve  is \n \n( ) ( ) ( ) HG HF HPn1n\n0ii t + =∑−\n=.  (18) \n \nIII. We get also an acceptable approximation using the \nrelation \n ( ) ( )∑\n==n\n0ii t HG HP .   (19) \n \nIV. Another way to obtain a good analytical \napproximation of P curve is to approximate the P cu rve \nusing the sum of two exponential functions, this su m \npassing through four experimental points (relations  (11), \n(12), and (13), but, the four parameters will be \nanalytically determined). For that we use four equa tions \nhaving the form \n \n() ()i i 2 i 1 v HE HE = + ,  (20) \n \nwhere, i = 1 to 4, H0 = 0 , and, vi = P(H i).  \nThe obtained equations system is \n \n() ()\n( ) ( )\n( ) ( )\n( ) ( ) \n\n\n= ⋅ + ⋅= ⋅ + ⋅= ⋅ + ⋅= +\n− −− −− −\n3HH\n2HH\n12HH\n2HH\n11HH\n2HH\n10 2 1\nv e0E e0Ev e0E e0Ev e0E e0Ev 0E 0E\n*\n23\n*\n13*\n22\n*\n12*\n21\n*\n11\n. (21) \n \nTo solve the system, we note \n \nx e*\n11\nHH\n=−\n, and, y e*\n21\nHH\n=−\n. (22) \n \nIt doesn’t mater which four experimental points we \nconsider to belong to the sum of the two exponentia l \nfunctions. So, we consider an arbitrary H1, and,  \n \n,H2 H1 2 ⋅=  and, 1 3 H3 H ⋅= . (23) \n \nWe get the system \n \n() ()\n( ) ( )\n( ) ( )\n( ) ( )\n\n\n= ⋅ +⋅= ⋅ +⋅= ⋅ +⋅= +\n33\n23\n122\n22\n11 2 10 2 1\nv y0E x0Ev y0E x0Ev y0Ex0Ev 0E0E\n    (24) \n \nFrom the first equation of the system (24) \n \n() ()0E v0E1 0 2 − = .   (25) \n \nWe replace the value of E2(0)  in the other equations, \nand, from the second equation N.C. POPA, A. SIBLINI, J.J. ROUSSEAU, Marie-Françoise BLAN C-MIGNON, J.P. CHATELON \nStructural Characterization of Magnetic Nano-particles Suspensions, Using Magneti c Measurements  \n \n©TIMA Editions/ENS 2006 -page- ISBN:  ( )yxyv v0E0 1\n1−⋅ −= .    (26) \n \nOn the same way, from the third equation we can sti ll \nobtain a unique analytical expression for x, \n \nyv vyv vx\n0 11 2\n⋅ −⋅−= .   (27) \n \nThe last equation of the system (24) becomes an \nequation where y has exponent up to 4, \n \n( )\n( )\n( )312\n22 03202\n21 32\n1 130 211 232\n03\n1 210 3202\n10 44\n0ii\ni\nvv vv avvv vv 3 vv 2 avv vvv 3 avv v 2 vvv avv vv a0ya\n− =+ − =− =+ − =− ==⋅∑\n=\n. (28) \n \nThe problem is that, even the equation (28) exists for \nany four points from the plane (the first point hav ing \nabscissa 0, the second having an arbitrary abscissa , and, \nthe next two abscissas respecting the relation (23) ), not \nthrough any four points from the plane we can pass the \nsum of the same two exponential functions. Therefor e, the \nequation (28) has real solutions for some “four poi nts” \n(vi), which must respect some conditions. It is very \ndifficult to analytically express these conditions.  It is \neasier to find numerically the real solutions of th e \nequation (28). After many experiments, we concluded  that \nif the four points belong to a P curve, the equatio n (28) has real solutions. We replace these solutions of e quation \n(28) in (27), and than consecutively we solve (26) and \n(25). From (22) we get   \n \nxln HH1 *\n1−= ,  and, yln HH1 *\n2−= . (29) \nFig. 5 presents a general aspect of the function \ndescribed by equation (28), and, Fig. 6 shows a det ailed \naspect (of the same function) where we can see the real \nsolutions of this equation. For these two figures, we \nconsidered four points of the P curve from Fig. 1. ( H0 = 0  \nkA/m, H1 = 40  kA/m, H2 = 80  kA/m, H3 = 120  kA/m, v0 \n= 2.627385x10 -2 m/kA, v1 = 5.278942x10 -3 m/kA, v2 = \n2.379331x10 -3 m/kA, and, v3 = 1.412452x10 -3 m/kA.) \n \n4. SOME LIMITATIONS IN THE USE OF “P” \nCURVES \n \nBy experimental measurements, we concluded that the  \napplicability superior limit for P curves in magnet ic \nsuspensions is for the particles having diameters o f about \n20 - 25 µm. Over this limit, the P curves (of the complex \nfluids having different particles dimension) have t he same \naspect. The applicability inferior limit is at the dimension \nwhere the particles lose their magnetic properties.   \nAll the magnetizable fluids presented above, for th e \nmagnetic particles, have a dimensional distribution  curve \nwith only one maximum. Using two different complex \nfluids of this type (further on denoted as the firs t and the \nsecond fluid), we prepared a new magnetizable fluid  \nhaving two maximums in its dimensional distribution  \ncurve.  \nThe first fluid had the particles diameter of about  10.5 \nnm (nano-magnetic fluid with ferrite particles), MS = 15.6 \nkA/m ([3]), and, P(0)  = 0.022. The second fluid had the \nparticles diameter of about 25 µm (Fe particles), MS = 723 \nkA/m (Hoeganaes Europe, Romania), and, P(0)  = 0.004.  \n \nFig. 5: General aspect of the function described by  \nequation (28).  \nFig. 6: Detail of Fig. 5. \n N.C. POPA, A. SIBLINI, J.J. ROUSSEAU, Marie-Françoise BLAN C-MIGNON, J.P. CHATELON \nStructural Characterization of Magnetic Nano-particles Suspensions, Using Magneti c Measurements  \n \n©TIMA Editions/ENS 2006 -page- ISBN:   \nFor the new fluid, we used about 97 % from the firs t \nfluid, and, 3 % from the second fluid. The new flui d has \nMS = 50.3 kA/m and P(0)  = 0.02. \nFig. 7 presents the P curves for the first and for the \nnew fluid. We can observe that the two P curves fro m Fig. \n7 are very close. From the P curve of the new fluid , we \ncan’t conclude that it belongs to a fluid having tw o \nmaximums in the dimensional distribution curve.  \nWe can conclude that, the application of the P curv es \nis recommended at the magnetizable complex fluids \n(powders, suspensions, etc.) having only one maximu m in \nthe dimensional distribution curve of magnetic part icles. \n \n5. ACKNOWLEDGEMENTS \n \nWe are thankful to “Hoeganaes Europe S.A. - Buzau \nPlant / Romania”, for the ferromagnetic powders use d in \nour experiments, and, to “National Center for Compl ex \nFluids Systems Engineering, Politehnica University of \nTimisoara, Romania”, where the magnetic measurement s \nwere performed. \n \n6. REFERENCES \n \n[1] R. E. Rosensweig, “ Ferrohydrodynamics ”, Cambridge \nUniversity Press, Cambridge, 1985.  \n \n[2] B. Berkovski, V. Bashtovoi (Editors), “ Magnetic fluids and \napplications handbook ”, Begell House, 1996.  \n \n \n [3] Doina Bica, “Preparation of magnetic fluids for  various \napplications”, Romanian Reports in Physics , Vol. 47, Nos. 3 – 5, \n1995, pp. 265 - 272. \n \n[4] K. Raj, and, R. Moscowitz, “Commercial applicat ions of \nferrofluids”, J. Magn. Magn. Mater. , 85 (1990) pp. 233 - 245.  \n \n[5] N. C. Popa, A. Siblini, and, L. Jorat, “Influen ce of the \nmagnetic permeability of materials used for the con struction of \ninductive transducers with magnetic fluid”, J. Magn. Magn. \nMater. , 201 (1999) pp. 398 - 400.  \n \n[6] N. C. Popa, I. De Sabata, I. Anton, I. Potencz,  and, L. Vékás, \n“Magnetic fluids in aerodynamic measuring devices”,  J. Magn. \nMagn. Mater. , 201 (1999) pp. 385 - 390. \n \n[7] R. Nasri, A. Siblini, L. Jorat, and, G. Noyel, “Magneto \ndielectric behavior of the magnetic fluid manganese  ferrite in \ncarbon tetrachloride”, J. Magn. Magn. Mater. , 161 (1996) pp. \n309 - 315.  \n \n[8] A. Siblini, L. Jorat, and, G. Noyel, “Dielectri c study of a \nferrofluid Fe 2CoO 4 in dibutyl phthalate or diethylene glycol in the \nfrequency range 1 mHz – 10 MHz”, J. Magn. Magn. Mater. , 122 \n(1993) pp. 182 - 186.  \n \n[9] N. C. Popa, and, I. De Sabata, “Numerical simul ation for \nelectrical coils of inductive transducers with magn etic liquids”, \nSensors and Actuators A  59 (1997) pp. 272 - 276. \n \n[10] N. C. Popa, A. Siblini, and, L. Jorat, “Magnet ic fluids in \nflow meters network for gases”, International Journal of Applied \nElectromagnetics and Mechanics , 19 (2004) pp. 509 - 514.  \n \n[11] N. C. Popa, A. Siblini, and, C. Nader, “Magnet ic sensors \nnetwork controlled by computer. Influence of the se nsors reply \ntime”, Phys. stat. sol. (c)  1, No. 12 (2004) pp. 3608 - 3613.  \n \n[12] J. D. Carlson, D. M. Catanzarite, and, K. A. S t. Clair, \n“Commercial magneto-rheological fluid devices”, International \nJournal of Modern Physics B , Vol. 10, Nos. 23 & 24 (1996) pp. \n2857 - 2865. \n \n[13] I. Bica, “Damper with magnetorheological suspe nsion”, J. \nMagn. Magn. Mater. , 241 (2002) pp. 196 – 200.  \n \n[14] M. Lita, N. C. Popa, C. Velescu, and, L. Vékás , \n“Investigation of a Magnetorheological Fluid Damper ”, IEEE \nTransactions on Magnetics , 40 (2), (2004) pp. 469 – 472. \n \n[15] N. C. Popa, A. Siblini, and, C. Nader, “ “P” c urves for \nmicro-structural characterization of magnetic suspe nsions”, J. \nMagn. Magn. Mater. , 293  (2005) pp. 259 - 264.  \n \n \nFig. 7: P curves for the first fluid (denoted on th e \nfigure by 1 and having only one maximum in the \ndimensional distribution curve), and, for the new f luid \n(denoted on the figure by 2 and having two maximums  \nin the dimensional distribution curve). "    },    {        "title": "0709.1323v2.Reducing_the_magnetic_susceptibility_of_parts_in_a_magnetic_gradiometer.pdf",        "content": "arXiv:0709.1323v2  [cond-mat.mtrl-sci]  7 Jan 2008Reducing the magnetic susceptibility of parts\nin a magnetic gradiometer\nAndrew Sunderlanda,∗, Li Jua, Wayne McRaea,b,\nDavid G Blaira\naSchool of Physics, University of Western Australia, Perth, WA, Australia\nbGravitec Instruments, Perth, WA, Australia\nAbstract\nIn this paper we report a detailed investigation of a number o f different materials\ncommonly used in precision instrumentation in the view of us ing them as critical\ncomponents in the magnetic gradiometer. The materials requ irement inside a mag-\nnetic gradiometer is stringent because the presence of magn etic susceptible material\nwill introduce intrinsic errors into the device. Many comme rcial grade non-magnetic\nmaterials still have unacceptably high levels of volume mag netic susceptibility be-\ntween 10−3and 10−4. It is shown here that machining with steel tools can further\nincrease the susceptibility by up to an order of magnitude. T he ability of an acid\nwash to remove this contamination is also reported. Washing in acid is shown to\nreduce the variation of volume susceptibility in several co mmercial grade plastics\nwhich already have low values of susceptibility.\nKey words: magnetic properties, magnetometer, metals, polymers\nPACS:07.55.Yv\n1 Introduction\n1.1 Magnetic Gradiometers\nA major application for magnetic gradiometers is measuring the grad ient of\nthe magnetic field produced by nearby geological targets at distan ces of 30 m\nto 100 m[1]. Magnetic material may also be present inside the gradiome ter,\n∗Corresponding author. Tel.: +61 422 282 438.\nEmail address: asund@physics.uwa.edu.au (Andrew Sunderland).\nPreprint submitted to Elsevier 2 November 2018inside attached equipment and cables, or inside the vehicle used to de ploy the\ngradiometer. All of these pieces of equipment will produce their own magnetic\ngradients. Whereas magnetic fields from far field dipole sources sca le as the\ninverse third power of distance, magnetic gradients scale as the inv erse fourth\npower and are particularly sensitive to close objects.\nRecently, a Direct String Magnetic Gradiometer (DSMG) has been de veloped,\nwhich employs a single ”string” as the sensing element[2]. The use of a lo ng\nand thin sensing element in the DSMG means that a significant number o f\ninstrument components are near the sensor string where even re latively small\nlevels ofmagneticcontaminationcanleadtofalsesignaturesmanytim eslarger\nthan the signal from the distant geological target.\nThe magnetic material inside the sensor generates both induced an d remanent\nmagnetisation. The later produces a constant magnetic gradient t hat can be\nsubtracted from the signal without impeding the operation of the m agnetic\ngradiometer whereas induced magnetisation aligns in the Earth’s mag netic\nfield. If the sensor is rotated while being deployed in a moving vehicle, t he\nmagnetic gradient produced by induced magnetisation will vary. This varying\ndistortion in the measured magnetic gradient is called heading error. Here\nwe report an investigation of reducing susceptibilities of different ma terials\nwith a view to reducing the amount of heading error in this particular t ype of\nmagnetic gradiometers.\n1.2 Reasons for measuring the magnetic susceptibility\nFor small values of magnetic field, the magnetisation rises linearly with ap-\nplied magnetic field strength. This means that the induced magnetisa tion per\nunit volume from a component is equal to the volume susceptibility of t he\nmaterial multiplied by the strength of the applied field (which in this cas e is\nthe Earth’s 30 000 nT to 60 000 nT field). The magnetic field in the spac e\nsurrounding a magnetised object scales as the inverse third power of distance.\nThereforeinduced magnetisationwill produceaheadingerrorthat will depend\non the distance of the component from the sensing element of the m agnetic\ngradiometer, the volume of the component, any anisotropy in the s hape of the\ncomponent, and the volume magnetic susceptibility of the componen t.\nThere is more data in the literature on the remanent magnetic momen t of acid\nwashed samples (see below). Nevertheless, in this paper volume sus ceptibility\nis required to quantify the amount of heading error a material will pr oduce.\n21.3 Prior work\nMeasurements of the magnetic susceptibility before and after an a cid wash\nhave been well known in the literature, see for example Spencer and John[3].\nSpencer and John washed their samples in hydrochloric acid to remov e pos-\nsible traces of iron and repeated until a constant value was obtaine d for the\nsusceptibility. The acid wash was incidental to Spencer’s paper and t he actual\nsusceptibility values were not reported. Much advice about avoiding magnetic\neffects in industry is based on oral tradition (for example use phosp hor bronze\nand there will be no problem).\nHonda measured the mass magnetic susceptibility of various pure me tals, in\ndifferent forms such as ingot, wire or cast[4]. Honda also recorded t he concen-\ntration of iron and the chemical form that the iron impurity takes ins ide the\nbase metal. Honda found only insignificant variation in susceptibility be tween\ndifferent metal forms.\nConstant and Formwalt measured the remanent magnetic moment o f a series\nof metals[5]. Measurements were taken of both the commercial gra de metal\nand the chemically pure metal. Commercial brass was reported to ha ve the\nhighest magnetic moment, followed by commercial copper and silver. More\nrecently Keyser and Jefferts[6] measured the magnetic susceptib ility of a wide\nvariety of laboratory construction materials.\nMeasuring the volume magnetic susceptibility is not theoptimum way to iden-\ntify small amounts of ferromagnetism because the magnetic susce ptibility in\nthe material could be due to diamagnetism, paramagnetism as well as fer-\nromagnetism. On the other hand, measuring a non-zero remanent magnetic\nmoment when the external field is zero is a definite indication of ferro mag-\nnetism (although soft iron ferromagnets can have high susceptibilit y and near\nzero remanence). Remanent magnetic moment measurements are the princi-\npal method of checking a sample for magnetic contamination, see fo r example\nMatsubayashi et al[7] or Wang et al[8].\n2 Typical magnetic materials\nThe three ferromagnetic elements (Fe, Ni and Co) have very high s uscepti-\nbilities, the highest being the initial relative magnetic permeability of 99 .9%\npure iron µr= 25000[9]. When trying to reduce the magnetic contamination\nit is not enough to merely avoid the use of pure iron, nickel or cobalt p arts\nbecause other nonferrous metals of commercial grade are often less than 99%\npure and usually contain iron as an impurity.\n3Brass is often used as a nonmagnetic substitute to replace iron in pa rts that\nrequire high strength or density[10], but the magnetic volume susc eptibility\nof brass varies considerably and care must be taken when choosing a supplier.\nGenerally volume susceptibility will increase with increasing iron conten t, al-\nthough the susceptibility will be higher if the iron impurity is concentra ted in\nsmall clumps[11] or if precipitation of iron occurs during heat treatm ent[12].\nSmall amounts of iron ( <0.05%) can alloy with the copper in brass to produce\nan alloy with a volume magnetic susceptibility proportional to the squa re of\nthe iron concentration[13].\nThe complete analysis of the susceptibility of brass is quite complicate d as\nother factors such as heat treatment, cold working and oxygen c oncentration\ncan have a large effect, see for example Fickett and Sullivan[14]. Par ts inside\nthe DSMG are expected to be exposed to large temperature extre mes during\nconstruction andoperation. Relying ona heat treatment to lower t he suscepti-\nbility of a magnetic gradiometer is not sufficiently robust for all enviro nments.\nFor this reason the susceptibility values of prior work quoted in this p aper are\nall referring to the susceptibility of the material as cast or formed which tend\nto be higher than textbook values. Fig. 1 shows some previous work onvolume\nsusceptibility vs. iron concentration for yellow brass (60-70% Cu, 3 0-40% Zn).\nThe graph shows a good fit with the square law at low iron concentrat ions.\nIf an isotropic very low magnetic susceptibility is required then metals with\nmore than 0.01% iron should not be used. Unreinforced plastics are t he best\nmaterials to use in extreme nonmagnetic conditions since they have v ery low\nlevels ofimpurities[15]. Thethree unreinforced plastics (Torlon4203 ,PET and\nPTFE) in Table 1 all have less than 0.0001% iron. The composite materia ls\n(Torlon 4301 and G10) and the ceramic (macor) have higher impurity levels\nalthough not as high as the impurity levels of the metals. The exceptio n is\n99.95%pureoxygen freehighly conductive copper. Pure metals can have lower\nimpurity levels than commercially available alloys[15].\n3 Hacksaw contamination\nIn addition to the volume susceptibility of the bulk of the material, the re can\nalso exist residual contamination from the machining of parts that p roduces a\nsignificant surface contribution to induced magnetisation. To inves tigate this\nsurfacecontribution,14samplesof7different materialswerecutt odimensions\n12 mm x 16 mm x 16 mm with a high carbon steel hacksaw. In addition two\nM3 holes were tapped with a tap made from tool steel. Depending on t he\nabrasiveness of the sample in question, some of the steel on the to ols will be\ndeposited intothesurfaceofthesamples during machining. Table2s hows that\nthe initial relative magnetic permeability of a hacksaw blade can be as h igh\n4asµr= 11 compared to magnetic susceptibilities of χdiamagnet≈ −10−5for a\ntypical diamagnet. This meansthateven small amountsofsteel co ntamination\ncan produce unacceptably high heading error.\nTo remove any surface magnetism, the samples were immersed in 3% c oncen-\ntrated hydrochloric acid. Low field volume susceptibility readings wer e taken\nbefore and after immersion using a Bartington MS2b susceptibility me ter for\nthe metal samples and a ZH Instruments SM-30 susceptibility meter for the\nplastic andceramic samples. The DSMG operates at room temperatu re, hence\nall susceptibility measurements in this paper were taken at room tem perature.\nAll susceptibility values are volume susceptibility in SI (MKS) units. Con cen-\ntrations in samples are stated by mass.\nFig. 2 shows the change in volume susceptibility before and after acid treat-\nment for each of the plastic and ceramic samples. The graph shows a slight\ndecrease in the volume susceptibility of the plastic and ceramic sample s after\na 24 hour acid wash. There is very little contamination to remove from any\nof the plastic and ceramic samples, with the exception of G10 (G10 is s ig-\nnificantly more abrasive than the other plastics and removes more ir on from\ntools during machining). The advantage of immersing the plastic samp les in\nacid was that the volume magnetic susceptibility had less variation aft er the\nacid wash and that the magnetisation was more isotropic. The volume sus-\nceptibility of samples as machined varied ±2×10−6when rotated to different\norientations whereas the volume susceptibility of acid washed sample s var-\nied only±10−6. Hydrochloric acid removes surface iron from all samples, but\nwhen it is applied to metallic samples hydrochloric acid may also corrode t he\nsurface of the metal. To evaluate the rate that hydrochloric acid c orroded the\nmetal samples, each of the samples was immersed in hydrochloric acid for du-\nrations of 10 minutes, 70 minutes, and 24 hours. Table 3 shows some loss of\nmass from acid washing. In particular the corrosion in the aluminum sa mple\nafter 24 hours produced a significant 7% reduction in the mass.\nFig. 3 shows that immersing the metallic samples in acid for only 10 minute s\nremoves nearly all the surface contamination and reduces the volu me suscep-\ntibility by an order of magnitude. An acid wash of 70 minutes produces no\nfurther reduction in the volume susceptibility. From this result it can be in-\nferredthattheremaining inducedmagnetismiscausedbysmallbuts ignificant\nconcentrations of iron in the body of the sample. A 10 minute acid was h is\ntherefore optimal for reducing heading error from brass and alum inium parts\nbecauseimmersing partsinacidforlongerdurationsoftimemaycorr odeparts\nto the extent that they cease to be within design tolerances.\nThe volume susceptibility of the metallic samples before acid washing ar e\napproximately 3 orders of magnitude higher than the plastic samples before\nacid washing. This indicates that the more abrasive metal samples ar e more\n5easily contaminated with the high carbon steel in the hacksaw.\nThe value of the volume magnetic susceptibility of the acid washed alum inium\n6061 sample measured by the authors does not agree with previous work by\nKeyser andJefferts[6].This couldbeduetodifferent amountsofmag neticcon-\ntamination between samples or an erroneous response of the Bart ington MS2\nto electrical conductivity in the sample as shown in Benech and Marme t[16].\nHowever, for the purpose of this paper, in order to avoid any poss ible ambi-\nguity in getting samples with different contamination levels, the use of such\nmaterials should be avoided. The red brass susceptibility value recor ded by\nthe authors does agree with previous work as shown in Fig. 1.\n4 Lathe contamination\n10 samples of 5 different materials, were cut on a lathe with a tool bit m ade\nfrom high speed steel. The samples were machined on the lathe to mak e cylin-\nders of diameter 5 mm and length 5 mm in order to fit in a Vibrating Sample\nMagnetometer (VSM). A single M3 hole was tapped along the axis with a tool\nsteel tap. The 8 metal samples were immersed in acid for 10 minutes a nd the\n2 Torlon samples were immersed for 24 hours. Volume susceptibility me asure-\nments were taken before and after immersion following the same pro cedure\nused for the larger samples.\nFig. 4 shows the change in volume susceptibility before and after acid treat-\nment for each of the samples. The smaller cylindrical samples should h ave a\nhigher relative surface contamination due to the large surface to v olume ra-\ntio. However, the volume susceptibility of the unwashed aluminium cylin drical\nsample is a factor of three less than its hacksawed counterpart. T his is most\nlikely because the relative permeability of the lathe tool bit is only 1 .4 com-\npared to a relative permeability of 11 for the hacksaw blade. Anothe r factor\nis that the lower hardness of the carbon steel hacksaw blade listed in Table 2\nwill allow the blade to deposit more steel onto the surface of the sam ple\nThe unwashed red brass and copper cylindrical samples have almost the same\nvalue for volume susceptibility of 2 .2×10−4. This value is two orders of magni-\ntude lower than the hacksaw contaminated brass sample. This indica tes that\ncopper and copper alloys are difficult to contaminate with high speed s teel.\nThe yellow brass samplehas avery highbulk susceptibility andtheperc entage\nchange after an acid wash was unmeasurably small. The volume susce ptibility\nof the washed cylindrical samples was lowest for the materials with th e least\namount of iron. The OFHC copper sample with 0.0002% Fe has a volume\nsusceptibility of 3 ×10−5and Torlon 4301 with 0.0002% Fe has a volume\n6susceptibility of 2 ×10−5.\nThere is a discrepancy between the volume magnetic susceptibility of OFHC\ncopper measured using theVSM and thetextbook value of −1×10−5[17]. This\ncould be due to an imperfect acid wash or the limited accuracy of the V SM\nof±10−5for samples of this size. Despite this inaccuracy, the results of the\nVSM are show that an acid wash can reduce the volume suspectibility b elow\n10−4which is sufficient for reducing heading error.\n5 Varying applied field measurements\nIn addition to the low field volume susceptibility measurements, a comp lete\nscan of the magnetisation at different applied fields up to 1 T was pref ormed\non the two 5 mm diameter Torlon cylinders. Two additional measureme nts\nwere made at −7 T and 7 T to check the diamagnetic contribution. The\nmeasurements were taken using a Quantum Design MPSM-7 Superco nducting\nQuantum Interference Device (SQUID) before and after immersio n in acid.\nFrom the gradient at the origin (low field case) in Fig. 5, the volume sus cep-\ntibility of the unwashed and washed samples are both positive with valu es of\n3.6×10−5and2.0×10−5respectively. Whenthe appliedmagnetic fieldexceeds\nµ0H >0.1 T the magnetisation has saturated and the volume susceptibility\nbecomes negative. The high applied field susceptibilities for the unwas hed and\nwashed samples are −1.4×10−5and−1.7×10−5respectively. These values\nindicate that Torlon is diamagnetic so that a pure sample with no iron co n-\ntamination should have a volume susceptibility near −1.7×10−5in both low\nand high applied fields. The presence of a positive susceptibility that s aturates\nin a modest applied magnetic field indicates the presence of a small amo unt\nof ferromagnetism.\nImmersing the sample in acid reduced the low field volume susceptibility f rom\n3.6×10−5downto2 .0×10−5.Theacidwashremovedallsurfacecontamination\nand reduced the ferromagnetic contribution of the entire sample b y 30%. The\nremaining ferromagnetism in the washed sample is produced by the bu lk of\nthe sample.\nAfter subtracting the diamagnetic contribution to magnetisation, what is left\nis the magnetisation from ferromagnetic sources alone. Fig. 5 show s that this\nferromagnetic contribution in the washed Torlon saturates at a ma gnetisation\nofµ0M= 4.1µT. By comparison pure iron saturates at a magnetisation of\nµ0M= 2.15 T, nickel saturates at µ0M= 0.69Tand cobalt saturates at\nµ0M= 1.79 T[18]. Assuming the ferromagnetic contribution is all due to Fe,\nthe ferromagnetic iron in this Torlon 4301 sample is about 10 parts pe r million\n7by mass. The result of 0.086% Fe from elemental analysis suggests t hat almost\nalloftheironisinaparamagneticstate,aconsequence oftheironb eingevenly\ndissolved into the Torlon.\nThere is a discrepancy between the low field susceptibilities of the was hed 5\nmm diameter Torlon cylinder and the susceptibility of the washed large r 12\nmm x 16 mm x 16 mm prism. Possible causes could be a large anisotropy\nin the induced magnetism or that the acid is not removing all of the sur face\nferromagnetism which is more significant in the smaller samples. Despit e the\ndiscrepancy, the change in volume susceptibility after an acid washe d was\nnegligible for both the cylinder and the prism.\n6 Conclusion\nWith regard to minimizing heading error in a magnetic gradiometer, plas -\ntics and ceramics parts that were measured had the lowest values f or volume\nsusceptibility χplastic∼10−5. In addition the effect of machining plastic with\nsteel tools produced negligible contamination. Metallic parts may how ever be\nrequired for their high conductivity or strength. Metals with less th an 0.01%\niron, which have been acid washed can also have susceptibilities below 1 0−4,\ncomparable with plastics. Machining metals with high speed steel is pre ferred\ntohighcarbonsteel asit produces less contamination. Metallic samp les should\nbe immersed in 3% concentrated hydrochloric acid for an optimum time of 10\nminutes.\nWashing plastic or ceramic parts in acid will reduce the volume suscept ibility\nby only a insignificant amount. Out of the acid washed samples, the vo lume\nmagnetic susceptibility closest to zero was −6×10−6from PTFE. Suscep-\ntibilities significantly lower than that of PTFE in solid parts can only be\nachieved by using specially designed alloys that offset paramagnetism with\ndiamagnetism. Nevertheless using expensive alloys is not necessary since even\nassuming maximum asymmetry, volume susceptibilities of order 10−5will pro-\nduce heading error in the DSMG of order 10 nT/m peak which is less tha n\nthe typical heading error of 20 nT/m peak from the vehicle used to d eploy\nthe gradiometer. The anisotropy in the volume susceptibility of acid w ashed\nplastics is only ±10−6. A reduction in the anisotropy of magnetic impurities\ncoupled with symmetry in the sensor could reduce heading error. We intend\nto investigate this in future work.\n8Acknowledgements\nTheauthorswouldliketothankDr.AlexeyVeryaskinandMr.Howard Golden\nof Gravitec Instruments for many useful discussions and sugges tions, A/Prof.\nTim St Pierre of the BioMagnetics and Iron BioMineralisation group at U WA\nfor the use of the wet acid laboratory, Dr. Robert Woodward of th e Nano-\nmagnetics and Spin Dynamics Group at UWA for the SQUID and VSM mea -\nsurements, Prof. Li of the Tectonic Special Research Center at UWA for the\nuse of a MS2b susceptibility meter, Mr. Barry Price of the Chemistry Centre\nof WA for elemental analysis and Mr. Mads Toft of Alpha Geoscience f or the\nuse of a SM-30 susceptibility meter. Work on the DSMG project is fun ded in\npart by a linkage grant from the Australian Research Council.\nReferences\n[1] M.F. Mushayandebvu, J. Davies, The Leading Edge 25 (2006 ) 69.\n[2] H. Golden, W. McRae, A. Sunderland, A.V. Veryaskin, D.G. Blair, L. Ju, in:\nAustralian Institute of Physics 17th National Congress, Sy dney, 2006.\n[3] J.F. Spencer, M.E. John, Proceedings of the Royal Societ y A 116 (1927) 61.\n[4] K. Honda, Annalen der Physik 337 (1910) 1027.\n[5] F.W. Constant, J.M. Formwalt, Physical Review 56 (1939) 373.\n[6] P.T. Keyser, S.R. Jefferts, Review of Scientific Instrumen ts 60 (1989) 2711.\n[7] K. Matsubayashi, M. Maki, T. Tsuzuki, T. Nishioka, N.K. S ato, Nature 420\n(2002) 143.\n[8] W. Wang, Y. Hong, M. Yu, B. Rout, G.A. Glass, J. Tang, Journ al of Applied\nPhysics 99 (2006) 08M117.\n[9] R.A. McCurrie, Ferromagnetic materials, Academic Pres s, London, 1994, p. 42.\n[10] P. Webster, The Brasses - Properties & Applications, Co pper Development\nAssociation, Hemel Hempstead, 2005, p. 5.\n[11] F.B. Huck, W.R. Savage, J.W. Schweiter, Physical Revie w B 8 (1973) 5213.\n[12] A. Butts, P.L. Reiber, Journal of Geophysical Research 54 (1949) 303.\n[13] H.E. Ekstrom,H.P. Myers, Zeitschriftf¨ urPhysikBCondensedMatter 14(1972)\n265.\n[14] F.R. Ficket, D.B. Sullivan, Journal of Physics F Metal P hysics 4 (1974) 900.\n9[15] 2002 Goodfellow Catalog of Metals & Materials, Goodfel low Cambridge,\nHuntingdon, 2002.\n[16] C. Benech C, E. Marmet, Archaeological Prospection 6 (1 999) 31.\n[17] J.R. Davis (Ed.), ASM Specialty Handbook: Copper and Co pper Alloys, ASM\nInternational, Materials Park, 2001, p 487.\n[18] S. Zhou, Electrodynamics of Solids and Microwave Super conductivity, John\nWiley & Sons, New York, 1999, p 90.\n[19] J.R. Barker, Journal of Scientific Instruments 25 (1948 ) 363.\n[20] J. Gattacceca, P. Eisenlohr, P. Rochette, Geophysical Journal International 158\n(2004) 42.\n[21] P. Havrey (Ed.), Engineering Properties of Steel, ASM I nternational, Materials\nPark, 1982.\n0.001% 0.01% 0.1% 1%10−410−310−210−1100\nFe concentration, XSusceptibility, χSusceptibility of Brass\nBarker et al.\nASM\nButts et al.\nYellow Brass\nRed Brass\nFig. 1. The susceptibility of yellow brass rises rapidly wit h increasing iron concen-\ntration. The data is compiled from a paper by Barker et al[19] , a book by ASM\nInternational[17], a paper by Butts et al[12] and measureme nts performed by the\nauthors on yellow and red brass samples. The line is a best fit a t low Fe concentra-\ntions using a square law χ∝X2.\nG10 Torlon 4301 PET Macor PTFE−2−1.5−1−0.500.511.52Susceptibility, χ (10−5)Susceptibility of nonmetallic samples cut with a hacksaw\nAs machined\nAfter 24 hrs acid wash\nFig. 2. Low field ( <50µT) susceptibility of plastic and ceramic samples before\nand after a acid wash. Data taken using a ZH Instruments SM-30 susceptibility\nmeter which has uncertainty of ±10−6for samples of this size. An adjustment for\nsample volume in the SM-30 was done using a formula derived by Gattacceca et\nal[20] which has an uncertainty of ±20%.\n10Aluminium 6061 Red Brass10−410−310−210−1Susceptibility, χSusceptibilty of metallic samples cut with a hacksaw\nAs machined\nAfter 10 minutes acid wash\nAfter 70 minutes acid wash\nFig. 3. Low field ( <250µT) susceptibility of metallic samples before and after\nacid washes. Data taken using a Bartington MS2b susceptibil ity meter which has\nuncertainty of ±10−5for samples of this size.\nAluminium 6061 Red Brass Yellow Brass OFHC Copper Torlon 430110−410−310−210−1100Susceptibility, χSusceptibilty of samples machined on a lathe\nAs machined\nAfter 10 minutes acid wash\nAfter 24 hrs acid wash\nFig. 4. Low field ( <0.02 T) susceptibility of cylindrical samples before and af ter\nacid washes. Data taken using a Aerosonic 3001 Vibrating Sam ple Magnetometer\nwhich has uncertainty of ±10−5for samples of this size.\n−1−0.8 −0.6 −0.4 −0.2 00.2 0.4 0.6 0.8 1−15−10−5051015\nApplied Field, µ0H (T)Magnetisation, µ0M (µT)Magnetisation of Torlon\nAs machined\nFerromagnetic only\nAfter 24 hrs acid wash\nFig. 5. Magnetisation of Torlon sample 2 in applied fields fro m -1 T to 1 T before\nand after acid washes. The dashed line is an inferred curve of the ferromagnetic\ncontribution to the magnetisation of the acid washed sample s. Data taken using a\nQuantum Design MPSM-7 SQUID. The SQUID has a precision of ±0.2 nT mag-\nnetisation for samples of this size although the accuracy is ±5% due to imperfect\nalignment of the samples.\n11Sample material Nominal concentrations\n(ppm) Elemental analysis \n(ppm) \n Fe Ni Co Fe Ni Co \nG10        26.     <0.2     <0.1\nTorlon 4203 0.1    <0.1    <0.1    \nTorlon 4301      860.       4.5       1.1 \nPET    <0.1    <0.1    <0.1     <5.     <0.2       0.4 \nMacor      700.       7.   590. \nPTFE    <0.1    <0.1    <0.1     <5.     <0.2     <0.1\nRed Brass  <3000 <10000 <10000   680.   180.       0.7 \nYellow Brass  <5000  <5000  <5000 1700. 1500.       7.5 \nAluminium 6061  <7000  <5000  <5000 1700.     45.     <0.1\nOFHC Copper       2.     <1.     <1.     <5.       1.3     <0.1\nTable 1\nNominal concentrations were taken from material datasheet s. Elemental analysis\nwas performed by the Chemistry Centre of Western Australia u sing a Inductively\nCoupled Plasma - Atomic Emission Spectrometer (ICP-AES).\nTool Materal Relative \nPermeability  Hardness\nRockwell C \nLathe tool bit High speed steel           1.4        64 to 65 \nM3 Tap Tool steel           3.7        61 to 62 \nHacksaw blade High carbon steel         11.        59 \nTable 2\nThe permeability measurements were made with a Bartington M S2b susceptibility\nmeter. The permeability of the tools varied ±30% when rotated. Hardness values\nare from a book by ASM International[21].\nMetal Mass as \nmachined(g) Mass after 10 \nminutes(g) Mass after 70 \nminutes(g) Mass after \n24 hours(g) \nBrass      24.68      24.68      24.68      24.67 \nAl        8.05        8.05        8.04        7.46 \nTable 3\nThe mass reduction of metal samples in acid increases with lo nger immersion times,\nuncertainty is ±0.01g.\n12"    },    {        "title": "0710.2980v2.A_generalization_of_Snoek_s_law_to_ferromagnetic_films_and_composites.pdf",        "content": "Crit_skin_LL31.doc p. 1 28/11/2007 A generalization of Snoek’s la w to ferromagnetic films and \ncomposites \n \nO. Acher*, S. Dubourg  CEA Le Ripault, BP16, 37260 Monts, France Received () PACS 75.40.Gb ; 76.50.+g ; 77.84.Lf ; 84.40.-x   \nAbstract: \n \nThe present paper establishes characteristics of the relative magnetic permeability \nspectrum µ(f) of magnetic materials at microwave frequencies. The integral \n∫∞\n0.).('' dfffµ  of \nthe imaginary part of µ(f) multiplied with the frequency f gives remarkable properties. A \ngeneralisation of Snoek’s law c onsists in this quantity be ing bounded by the square of the \nsaturation magnetization multiplied with a cons tant. While previous results have been \nobtained in the case of non-c onductive materials, this work  is a generalization to \nferromagnetic materials and ferromagnetic-based co mposites with significant skin effect. The \ninfluence of truncating the summation to fi nite upper frequencies is investigated, and \nestimates associated to the finite summation are pr ovided. It is established that, in practice, the \nintegral does not depend on the damping m odel under consideration. Numerical experiments \nare performed in the exactly solvable case  of ferromagnetic thin films with uniform \nmagnetization, and these numerical  experiments are found to conf irm our theoretical results. \nMicrowave permeability measurements on soft  amorphous films are reported. The relation \nbetween ∫GHz\ndfffµ6\n0.).(''  andsMπ4  is verified experimentally, a nd some practical applications \nof the theoretical results are introduced. The in tegral can be used to determine the average \nmagnetization orientation in materials with co mplex configurations of the magnetization, and \nfurthermore to demonstrate the accuracy of microwave measurement systems. For certain \napplications, such as electromagnetic compatibility  or radar absorbing materials, the relations \nestablished herein provide useful  indications for the design of ef ficient materials, and simple \nfigures of merit to compare the properties measured on various materials. \n \nI. INTRODUCTION \n \nThe microwave permeability µ of magnetic materials is a qua ntity of interest both with \nrespect to applied and fundamental point s of views. High frequency inductors,1 magnetic \nrecording write heads, broadband skin antennas,2 microwave filters,3,4 noise suppressors5 and \nRadar Absorbing materials6,7 require high broadband permeability levels at elevated \nfrequencies. However, it has been  known since the work of Snoek8 that there exist tradeoffs \nbetween high permeability levels and operation at  elevated frequencies, i.e. the higher the \nresonance frequency F0, the lower is the low frequency permeability µ’0. In a bulk \npolycrystalline material, S noek’s law is written as  \n ()sM F µ πγ4321'0 0 = −  (1) Crit_skin_LL31.doc p. 2 28/11/2007 where 4 πMs is the saturation magnetization, and Oe MHz / 3 2/≈ = πγγ  the gyromagnetic \nfactor. The tradeoffs between the permeability level and the resonance frequency depend on \nthe shape of the magnetic domains or particles9,10 For soft thin films with uniform uniaxial in-\nplane anisotropies, the equation becomes  \n () ( )2 2\n0 0 4 1'sM F µ πγ= − . (2) \nThese relations are easily established from the gyromagnetic permeability of a saturated \nellipsoid. However, they become invalid for he terogeneous magnetic materials, or in the case \nof composites. In addition, they provide no clue to the linewidth of the permeability.  \nRecently11,12 another expression of the tradeoffs betw een permeability levels and frequency \nhas been established13  \n ()2\n042.).(''s A M k dfffµ πγπ= ∫∞\n, (3) \nHere, kA is a dimensionless factor associated with  the distribution of the orientation of the \nmagnetization in the sample. This sum law finds its  root in the causality principle, associated \nwith the fundamental equation of gyromagnetic  motion. For uniform soft thin films, kA=1. For \nbulk sintered ferrites, kA=1/3. For isotropic composite materials with a volume fraction τ of a \nmagnetic filler, 3/τ≤Ak . In any case, 1≤Ak . The ratio kA is easily determined from \nexperimental data, and can be used to quan tify the quality of thin films for microwave \napplications13 and to guide their design.14 Eq. (3) has also been found useful as an indication \nfor the conception of microwave absorbers.15 In this case, µ’’ is a quantity of direct interest. \nEq. (3) has a different form as compared to the original Snoek’s law given by Eq. (1) and \nits extension to thin films given by Eq. (2). Ho wever, strong connecti ons exist between these \nidentities. According to Eq (3), the higher the resonance frequency (generally corresponding \nto the peak of µ’’), the lower is the bandw idth multiplied by the maximum µ’’ levels.  \nFor materials with a permeability that coinci des with the gyromagnetic permeability of a \nsaturated ellipsoid, Snoek’s law in its discrete form (i.e. Eqs. (1), (2)) may be a more straightforward expression of the balance between high permeability levels and operation at high frequencies as opposed to Eq. (3).\n16 However, in many cases, Snoek’s law does not apply \nin its discrete form whereas Eq. (3) remains valid. As a consequence, Eq. (3) can be considered as a generalization of Snoek’s law. Hexagonal ferrites used in microwave \napplications are not soft materials in the sens e that their out-of-plane anisotropy field is \ncomparable or larger than the saturation ma gnetization. Thus, Eq. (3) does not apply to \nhexagonal ferrites, but a more general integral  relation has been proposed and verified \nexperimentally.\n17  \nThe purpose of this paper is to provide signific ant extensions for Eq. (3). In its original \nderivation,12 the effect of the conductiv ity on the permeability has b een neglected. This is a \nsignificant limitation, since skin effect due to fi nite conductivity may substantially affect the \npermeability of ferromagnetic materials. An importan t result reported in this paper is that the \nintegral of µ’’(f).f  is hardly affected by moderate skin effect, and slightly decreases when the \nskin effect becomes larger. Another limitation of Eq. (3) concerns the m odel used to describe \nthe magnetic damping. This identity was esta blished assuming a damping mechanism used in \nthe equations of Bloch-Bloembergen. The presen t study demonstrates that it also holds true \nwhen the Gilbert description of the magnetization relaxation is employed. \nWhen the integral in the left-hand side of Eq. (3) is determined from experimental \npermeability measurements, it has to be truncated to a finite upper frequency within the measurement range. This paper provides estimat es of upper integration frequencies that can \nbe used with negligible error, as well as simple estimates for the truncation error.  \nThe paper is organized as follows. In part II, the theoretical approach is outlined and \ngeneral results are presented. Anal ytical details are given in the appendix. In part III, results Crit_skin_LL31.doc p. 3 28/11/2007 are formulated for particular cases, namely thin films, multilayers, and composite materials. \nIn part IV, the relevancy of the approximations  is verified through numerical experiments on \nan exactly solvable case. In part V, our theore tical findings are confront ed with experimental \nvalues of permeabilities measured on thin films.  Ultimately, the potential applications of our \nfindings are discu ssed in part VI. \n \nII. THEORETICAL APPROACH \n \n A. Permeability of an ellipso id with uniform magnetization  \n \nThe magnetic susceptibility tens or of an ellipsoid with a uniform magnetization is well \nknown.18 Several models have been proposed for the damping mechanism. The Landau-\nLifschitz-Gilbert expression figuring the dimensionless damping parameter α is one of the \nmost popular. The full expression of µG is given in the appendix, see Eq. (A1). It depends on \nthe saturation magnetization 4 πMs of the material, on the demagnetizing coefficients of the \nellipsoid Nx, Ny, Nz, and on the resonance frequency F0. It is convenient to introduce the \nquantity s M M F πγ4= which has the dimension of frequency.  \n \n B. Influence of skin effect on the permeability  \n \nThe permeability of a conductive inclusion depends on its condu ctivity, shape and \ndimensions, and of course on the permeability of the constitutive material. It has been derived within many independent studies, and for numer ous shapes. The permeability of the inclusion \ncan be written as\n6,19,20,21,22 \n ) (.kaAµµG= , (4) \nwhere µG is the intrinsic permeability of the material, k the wavevector associated to the \nmicrowave excitation inside the inclusion, and a the radius of the inclusion (in the case of a \nsphere and a cylinder) or its half thickness (in the case of a plate). k depends implicitly on the \npermeability µG and the conductivity σ of the material. The expression of A(ka)  for various \ninclusion shapes is presented in Fig. 1. Though the expressions may appear dissimilar at first \nsight, their first order development in ka has the same form \n ()\npakkaA2.1)( +=  + higher order terms  (5) \nHere, p is a number that depends on the shape of the inclusion. It can be seen in Fig. 1 that \np is larger for a sphere ( p=10) than for a plate ( p=3), and for a cyli nder, its value is \nsomewhere in between. This suggests that Eq. (5) can be extended to a variety of regular shapes, and that it is fairly general. \n \n \nC. Derivation of the integral bound \n \nAs a consequence of the causali ty principle, the permeability µ function of the complex \nvariable f is analytic in the lower half of the f-plane.23 The Cauchy theorem is applied to the \nquantity f.µ(f) on a closed contou r consisting in the [- F, +F] segment of the real axis and the \nhalf circle C- defined by F.exp(j θ), θ  ranging from 0 to π. This yields  \n 0 .).( .).( = +∫ ∫\n−− CF\nFdfffµ dfffµ . (6) \nThe first term in Eq. (6) can be tr ansformed using the general properties )( )( fµ fµ =− , \nwhere the bar corresponds to the conjuga te. This yields an integral of µ’’(f).f. The second term Crit_skin_LL31.doc p. 4 28/11/2007 can be transformed into an inte gral on the angular coordinate θ of the semicircle C-. This is \nrelatively easy to calculate provided that F is large enough, but not too large, and is a result of \ngood approximations of µ being available at high frequencies F. Detailed calculations are \nshown in the appendix. One finds \n \n []2\n0''( ). . . 12F\nyM µff d f N F tseπ≈ −−± ∫, (7) \nwhere t and s are small positive numbers, and t corresponds to the fini te truncation whereas \ns is related to skin effect. The term e is the error induced by the measurement and Δµ the \nuncertainties with respect to µ. \n ( )FFN N tM\ny x+ = 22απ (8) \n \n FFNpaµsM\ny2 2\n04 σ=  (9) \n 2\n⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛Δ≤\nM yFF\nNµeπ. (10) \nHere, µ0 is the permeability of vacuum. The validity  of Eqs. (7) through (10) requires that \nthe upper summation frequency F verifies the conditions in the first 4 lines of Table I. For \nmost microwave magnetic materials, the permeab ility can be measured in the appropriate \nspectral range using conventional measurement syst ems, as will be evidenced in sections IV \nand V. Table I also indicates under which conditions the corrective terms t, s or e are \nnegligible. In the case where they are small but not negligible, they can be determined from \nthe analytical expression above. \n \nD. A generalization to magnetic materials with complex magnetization states and to \ncomposites \nLet us now deal with materials in demagnetiz ed states. For this purpose, we consider \nmagnetic matter constituted of a collection of magnetic domains  with various shapes. Each \nmagnetic domain can be described as a sa turated ellipsoid, with possibly differing \ndemagnetizing coefficients and internal fields . Let us also allow some non-magnetic matter. \nAll the inclusions are su pposed to be much smaller than th e wavelength. The permeability of \nthis complex matter can be determined thr ough an appropriate hom ogenization law. In \npractice, the difficulty is that the homogeniza tion law depends not only on the permeability of \neach domain, but also on the details of their ge ometries and arrangement. In cases where only \nthe permeabilities of the constitu ents are known, but not the exact  topology, it is not possible \nto precisely determine the permeability µeff of the homogenized medium. It is nevertheless \npossible to know certain bounds on the complex values of µeff. Different sets of bounds, \nknown as Wiener, Hashin-Shtrikman and Milton-Bergman bounds,24,25,26,27 have been \nderived, depending on the partial information available. At very high frequencies, the \npermeability µi(F) of each constituent is close to unity. In this case, all bounds converge to a \nsingle value of µeff that is independent of the composite topology: 12,28  \n )( )(. )( Fµ Fµ Fµi\niii eff = ≈∑τ , (11) \nwhere τi designates the volume fracti on of each domain labelled i, and  corresponds to a \nvolume average. Eq. (11) is also valid fo r any complex frequency on the semicircle C-. Using \nthis result in Eq. (6), one finds: Crit_skin_LL31.doc p. 5 28/11/2007  ∫∑ ∫=F\ni\niiF\neff dfff µ dfff µ\n0 0.).('' .).('' τ . (12) \nThis identity is similar to Eq. (20.6) in ref. [24], and constitutes a very important result: the \nintegral associated to the composite medium is  simply the linear average of the integral \nassociated to each constituent. \n \n E. Isotropic composites made of ferro magnetic loads in a dielectric matrix \n \nIn an isotropic material, 3/) (z y x eff µ µ µ µ + + = . The integral 3 /) (, , , iz iy ix µ µ µ + +  can be \neasily calculated for each ellipsoid, and then averaged on the whole sample by using Eq. (12). \nThe volume fraction of magne tic particles is denoted  τ, and the average of the demagnetizing \ncoefficients of the domains al ong their magnetization is denoted //N. //N is expected to \nbe small as compared to unity, since the magnetization tends to be aligned in the elongation \ndirection in soft materials. The demagnetizing coefficient in the elongation direction of an \nellipsoid is close to zero for large aspect ratios,18 and it will therefore be treated as a first order \ncorrection. We obtain from Eqs. (7) and (12): \n () ()2\n//\n0''( ). . 4 16F\ns µff d f M N t s eπτγπ≈− − − ± ∫ (13) \n \nwith \n ()FFtMη απ+ = 12 (14) \nwhere z xNN. 2=η  is the average of the product of the demagnetizing coefficients \nnormal to the magnetization. This term is comprised between 0 and ½.  \nIt is important to note that s does not depend on the internal fields, which suggests that for \na multi-domain particle with half radius a and shape parameter p, Eq. (9) is still the \nappropriate expression for s, provided that an averaging on Ny is performed. In  practical cases, \nthere may be a significant dispersion in radius a within the magnetic filler, while its \nconductivity σ remains constant. It thus follows that \n ()()\nFF\npa µ\nsM2 2\n014\nησ\n− = . (15) \nThe absolute error due to meas urement uncertainties is bounded by 2\n2FµΔ, and a \nmajoration of the relative error e can be written as : \n 23\n⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛Δ≤\nMFFµeτπ. (16) \n \nIII. RESULTS \n \nEqs. (13) to (15) are very general and onl y valid when the upper integration frequency F is \nchosen in the proper range as summarized in the f our first lines in Table I. It is useful to \nrewrite these equations for a few cases of particul ar interest, in order to  provide ready-to-use \nexpressions.  \n  Crit_skin_LL31.doc p. 6 28/11/2007  A. Application to soft thin films with uniform magnetization \n \nIn the case of a uniaxial th in film magnetized along the z direction with in-plane \norientation, the demagnetizing coefficient normal to the film plane Ny is unity. The hard axis \npermeability (along x) has the following properties: \n () [] est M dfffµsF\n±−− ≈ ∫1. 42.).(''2\n0πγπ, (17) \nwith \n FMtsπγαπ4 2= , (18) \n \n ( )\nFM aµss2 2\n0 4.34 πγσ= , (19) \n 2\n4⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛Δ≤\nsMF µeπγπ, (20) \n \nwhere 2 a it the thickness of the film. When measur ement errors are neglected, it follows in \na straightforward manner that : \n ()2\n042.).(''sF\nM dfffµ πγπ≤ ∫. (21) \nThis generalizes previous results11,12 to the case where a significan t skin effect is present, \nprovided that the summation is performed up to a reasonably high frequency. This \ndemonstrates that skin effect can not increase the factor of merit13 kA defined in Eq. (3). \nIndeed, the presence of skin  effect tends to decrease kA, but only as a first order correction. \nThis appears in Eq. (17) where - s is a negative corrective term associated to skin effect.  \nThe integral in Eqs. (17) and (21) can be eas ily evaluated from expe rimental results. The \nupper integration frequency F should be chosen significan tly larger than the resonance \nfrequency, but smaller than sMπγ4.   \nThe integral is expressed in Hz2, and yields a number that is expected to have a limited \nsignificance to people working on magnetic mate rials. It is not easy to know whether the \nintegral is large or small as compared to values  observed on other microw ave materials if it is \nexpressed in Hz2. One way to transform the integral in to an easily interpreted number is to \nnormalize the integral by ()242sMπγπ. This quantity has been in troduced in Eq. (3) as the \ndimensionless parameter kA. As aforementioned, this paramete r is convenient to use, but does \nhowever require a prior determination of the saturation magnetization. Another solution is to turn the integral into a quanti ty that has the dimension of ma gnetization. This can be carried \nout very easily by taking the square root of the integral, and multiplying it by an appropriate \nconstant. Let us define ) (FM\nµ  by: \n \n ∫=F\nµ dfffµ FM\n0.).(''21)(πγ (22) \n \nThis quantity can be deduced from the permeability measurements with no other \nknowledge of the magnetic material. For a film  with perfect orient ation and limited skin Crit_skin_LL31.doc p. 7 28/11/2007 effect, this quantity represents the saturation magnetization : Mµ(F)=4 πMs. Thus, Mµ(F) \nshould be a number with an intu itive signification to people involved in magnetic materials. In \nthe general case: \n \n s µ M FM π4)(≤  (23)  \n \nSince the quantity Mµ(F) has the dimension of a magnetizat ion and is obtained purely from \ndynamic measurements, it may be termed “effi cient dynamic magnetization”. It is also \npossible to estimate the saturation magnetization from the integral of the imaginary part of the permeability \n \n⎟\n⎠⎞⎜\n⎝⎛±++ =2 21)( 4estFM Mµ sπ  (24) \nwhere s, t and e can be easily computed  from Eqs. (18)-(20).  \n \n B. Application to soft films with m agnetization dispersion and multilayers \n \nLet us consider a multilayer made of thin films with in-plane magnetization, but with the \npossibility of non-uniformities along its thickn ess. Such non-uniformities may arise from \ndifferences in anisotropy between the layers,29 from antiferromagnetic coupling,30 or from \nexchange coupling, provided that these fiel ds are much smaller than the saturation \nmagnetization. Non-uniformities may also arise from unwanted phenomena31, or interfacial \nanisotropies. Let us also allow a certain non-uniformity within th e film plane, provided that \nthe demagnetization coefficient normal to the film plane remains close to unity. The angle \nbetween the x direction in the film plane and the magnetization is denoted φ. Then, neglecting \nmeasurement errors, the permeability µx along x has the following properties: \n () [] st M dfff µsF\nx −− = ∫1 4. sin2.).(''2 2\n0πγφπ. (25) \nIt follows that the integral of µ’’ can be a very useful tool to  obtain insights regarding the \norientation of the magnetization within multilayers. In the case where sMπ4 is uniform within \nthe film but the orientation fluctuates, it is possible to get information on the orientation from \npermeability measurements along the x and z directions in the film plane: \n \n∫∫\n=F\nzF\nx\ndfff µdfff µ\n00\n22\n.).(\".).(\"\ncossin\nφφ\n. (26) \nThough the permeability spectra along different dire ctions are expected to be significantly \ninfluenced by the detailed topology of the ma gnetization dispersion, th e ratio of integrals \nprovides simple numerical indica tions on the average values of φ2sin  and φ2cos . This ratio \nhas already been used in order to assess the eff ect of field annealing on the orientation of the \nmagnetization.32 The result presented here ex tends the validity of the method to thicker films. \nMultilayers have also been de signed to provide both magne tic softness and high saturation \nmagnetization, by alternating materials with di fferent saturation magnetization but with the \nsame uniaxial in-plane orientation.29 In this case \n () [] es t M dfff µ\nnns nF\nx ± − − =∑ ∫1 42.).(''2\n,\n0πγτπ. (27) Crit_skin_LL31.doc p. 8 28/11/2007 where τn is the volume fraction of material  with a saturati on magnetization of nsM, 4π . The \ncorrective terms can be easily expressed from Eqs.  (8)-(10), or neglected in the case where the \nsummation is performed up to a sufficiently high frequency. \n \nC. Application to isotropic composites cons tituted of a magnetic load in a dielectric \nmatrix  \nMicrowave composites made of a magnetic s pherical powder dispersed in a dielectric \nmatrix are widely used as microwave materials33,34,35 and magnetic absorbers.6,7,15 In most \ncases, the radius of the particles is significan t as compared to the skin depth. Eq. (13) \nestablishes that  \n ()2\n046.).(''sF\nM dfffµ πγτπ≤ ∫. (28) \nThis result has already been theoretically obtained for composites made up of insulating \nmaterials such as ferrite powders, as well as verified experimentally.12 The present work \nfurther established that this result remained largely unaffected by finite  frequency summation, \nand by skin effect.  \nEq. (15) (where p=10 is used for a sphere) provides useful guidelines for choosing an \nappropriate granulometry < a2> of the particles in order to obtain a small or negligible loss of \ndynamic permeability in the range of interest. The quantity \n ()⎥⎦⎤\n⎢⎣⎡=∫2\n03, 46/.).(''sF\nDA M dfffµ k πγτπ (29) \nis a dimensionless figure of merit for isotropi c composites. The closer it is to unity, the \nbetter is the material.  \n \nIV. NUMERICAL VALIDATION \n The aim of this numerical validation was to es tablish with confidence the exactitude of the \nestimates of the corrective terms  -t, –s. Confirmation was also desired that the terms  +S’ and \n+g from Eq. (A17) could be neglected. Th e validation was performed on conducting thin \nmagnetic films with uniform in-plane magnetiza tion. This case was numerically simple, and \nalso quite representati ve of typical measurements on soft  ferromagnetic films. The numerical \nexperiments were carried out with  a precision that could not be at tained in real experiments.  \nThe thin film was described by the following parameters: 4\nπMs=10 kG, Hk=16 Oe, \nγ=3 GHz/kOe, α=2%, σ=[130 µ Ω.cm]-1, Ny=1, which are common values for thin soft \nferromagnetic films. The resonance frequency was F0=1.2 GHz. The relative permeability \ncould be calculated using the La ndau-Lifschitz Gilbert equation (Eq. (A1)) a nd the skin effect \ncorrection (Eq. (4), with the expression of A(ka) for a plate according to Fig. 1). The \nimaginary part of the permeability is presented in Fig. 2 for thicknesses 2 a ranging from \n0.1 µm up to 2 µm. The broadening observed on the spectra of the 1 and 2 µm thick samples \nwas due to skin effect. The numerical integration of µ’’(f).f could be easily performed using \nthese spectra. \nTable II provides relevant lower and uppe r frequency bounds on the upper integration \nfrequency in the case of the 2 µm thick film. It appears that F=6 GHz is in the adequate range. \nThe values of ∫GHz\ndfffµ6\n0.).(''  obtained both numerical ly and analytically are displayed, and \nthe numerical integration was performed on the spectra shown in Fig. 2. The analytical \nestimate for the integral was obtained using Eq. (17), and the corrective terms were evaluated, Crit_skin_LL31.doc p. 9 28/11/2007 both numerically, and analytically using Eq. (18 )-(20) and (A18), (A21). It appeared that the \ncorrections g and s’ were extremely small, and they coul d thus be neglected in the following. \nThe effect of the truncation –t was to underestimate the integral by approximately 6%, and \nour analytical estimate agreed well with th e numerical determination. The skin effect \ncorrection -s was -19% according to our analytical es timates, which was close to the -23% \ndetermined in our numerical experiment. In c onclusion, the value of the integral predicted \nusing our model displayed a devi ation of less than 5% from the experimental value, for \nF=6GHz.  \nThe influence of the upper integration frequency F was also investigated in this numerical \nexperiment. The “efficient dynamic magnetization” Mµ(F) defined by Eq. (22) is represented \nin Fig. 3. Though the expression of Mµ(F) may appear less friendly than the integral \n∫F\ndfffµ\n0.).('' , it is very easy to calculate. Moreover , its value has an intuitive interpretation \nand can be compared directly to the satura tion magnetization of the material. Numerical \nresults were obtained by numerical  integration of the permeability  calculated using Eqs. (A1) \nand (4), whereas analytical results were esta blished from the saturation magnetization using \nEq. (24) and the values of s, t and e as computed from Eqs. (18)-(20). The analytical and \nnumerical results were in excellent agreement, thus validating our results. For the 0.1 µm thick layer, the skin effect was negligible, and as illustrated in the graph, the truncation effects \ndecreased when F was increased.  \nThe effect of measurement uncertainties was also explored. At fr equencies much higher \nthan the resonance frequency, µ’’ was weak, but could be  affected by significant \nmeasurement uncertainties. On most permeability measurement systems for thin films, errors \ndecrease when the thickness of the material increases as a re sult of a larger amount of \nmagnetic material in the cell. For the 0.1 µm thick sample, a typical error \nΔµ=10 was \nassumed, for the 1 µm thick film, Δµ=2, whereas Δµ=1 for the 2 µm film. The error bar \nassociated with the integration is represented in Fi g. 3. It can be seen that for the thinner film, \nthe upper integration bound should not exceed F=6 GHz to a great ex tent, in order for Mµ(F) \nnot to be significantly affected by the measurem ent uncertainties. On the thicker films, higher \nupper integration frequencies were  possible with a satisfactory pr ecision, but they may not be \nnecessary. It was remarkable to see that the integral provided the value of the saturation \nmagnetization within 10% if F>3.5 GHz for the 1 µm thick film, and if F>8 GHz for the 2 µm \nthick film. Behind the profound changes in the magne tic losses due to skin effect that can be \nevidenced in Fig. 2, it appear s that the integral quantity ∫dfffµ .).(''  was nearly an invariant.  \n \nV. EXPERIMENTAL VALIDATION \n \nAmorphous CoZr thin films were sputter-depos ited onto continuously transported 12 µm \npolyethylene teraphtalate substrat es. The base pressure inside the chamber before deposition \nwas less than 10-6 mbar, and during the process, th e Ar pressure was fixed at 5.10-3 mbar. The \nresidual magnetron field induced a uniaxial anisotropy para llel to the transportation direction. \nFour samples with various thicknesses, i.e. 0. 3, 1.3, 1.7 and 2.1 µm, were fabricated. The \nsaturation magnetization 4 πMs was measured using a Vibrating Sample Magnetometer, and \nwas found to be 11.3 kG ± 0.5 kG. The permeab ility was determined using a thin film \npermeameter described elsewhere.36 The typical error Δµ was estimated to approximately 20 \nfor the thinnest film, and to 2 for the thicker ones. Crit_skin_LL31.doc p. 10 28/11/2007 The imaginary part of the permeability measured  on the 4 films is presented in Fig. 4. The \nthinnest film displayed a highl y resonant permeability, and e xhibited a secondary peak at \nhigher frequency. This peak could be attributed  to certain inhomogeneities and the excitation \nof a higher frequency mode.31 The thicker film exhibited a permeability with a very damped \nbehaviour, and permeability le vels down by a fact or up to 4. The “efficient dynamic \nmagnetization” Mµ(F) obtained from the experimental spect ra using Eq. (22) is represented in \nFig. 5. As expected, this quantity was close to  the saturation magnetization at high frequency. \nBetter estimates of the saturation magnetizati on can be obtained using Eq. (24) with the \ncorrections s and t computed from Eqs (18)-(19). These refined estimates are also shown in \nthe graph, with their associated  error bars. It can be seen that all estimate ranges were \ncomprised within the experiment al error of the measured 4 πMs. A larger measurement \nuncertainty for the thin film permeability as evidenced in Fi g. 4 was responsib le for a larger \nuncertainty on the integral quantity. This proves that the integral relation on thicker films may be very useful in order to obtai n more precise experimental data. It is remarkable that, despite \nthe strong difference in the four spectra presented in Fig. 4, all the estimates derived using Eq. \n(24) coincided within the experimental errors.  \n  \nVI. DISCUSSION AND CONCLUSION \n Previous studies\n11,12 have established that, for a give n set of assumptions, the quantity \n∫∞\n0.).('' dfffµ  displays remarkable properties. The pres ent work demonstrates that this is a \nvery general result. In additi on, it shows that the finite frequency band on which microwave \npermeability measurements are performed generally suffices in order to obtain a good estimate of this integral. For materials with magnetic responses significantly influenced by \nskin effect, one may wonder whether it would not  be easier to first determine the intrinsic \npermeability from measured permeabilities with sk in effect, and subsequently determine the \nintegral of the imaginary part of the permeabil ity. Though this procedure is possible, it should \nbe underlined that, for magnetic particles constitu ted of different layers and/or domains with \nvarying permeabilities, the intrinsic permeability  cannot be rigorously obtained from the \nmeasurements. In contrast, the estimate of s for the skin effect correction on the integral is \nindependent on the detailed magnetic pa rameters. It depends only on the a\n2σ product for the \nparticle, and as a consequence it is a much more robust parame ter. In the cas e of composites \nmade of ferromagnetic powders, there is often a significant size distri bution with respect to \nthe particles. As a consequence, the intrinsi c permeability as determined by the inversion of \nEq. (4) with an averaged value of a, may have a limited validity, while the integral quantities \ncan be exploited. In this case, the averaged value of the corrective term s is directly related to \n< a2>, as expressed by Eq. (15). \n \nThe particular properties of ∫F\ndfffµ\n0.).(''  derived in this work may be useful for at least \nthree purposes: microwave measurement, microw ave design, and material characterization. \nDepending on personal likings, one may prefer to wo rk either with the integral, expressed in \nHz2; with the dimensionless ratio kA defined in Eq. (3); or with the efficient dynamic \nmagnetization Mµ(F) defined by Eq. (22). All properties es tablished for the integral can be \neasily translated into the two other quantities.  \n For microwave measurements, the upper bound of th e integral (Eq. (21), (28)) can be used \nto verify the consistency of the measured perm eability spectra. This can be done very simply. Crit_skin_LL31.doc p. 11 28/11/2007 It is not necessary for the measurement system  to cover a large band since the majoration is \nvalid for any integration range. This is very useful, especially for supporting experimental \nresults claiming large permeability levels, si nce microwave magnetic measurements are \nknown to be tricky. In the case of thin f ilm permeameters that cover a broad enough \nbandwidth, the relations µ M FM π4)(≈  can be used to assess or to demonstrate the \nmeasurement precision of the apparatus. In most  cases, the uncertainty on the right member is \nessentially due to the gyromagnetic ratio γ, which is generally considered to be comprised \nbetween 2.8 and 3 GHz/kOe, and to some ex tent to the measurement precision of the \nsaturation magnetization and of the film thickness.  \n The results established in this work are usef ul also for the design of magnetic microwave \nmaterials. The sum laws (21), (27), (28) ex press certain tradeoffs between high permeability \nlevels and operation at high fre quencies. As a consequence, thes e sum laws may be viewed as \ngeneralisations of Snoek’s law. The integral qua ntity can easily be experimentally determined \non many materials. Simple figures  of merit deduced from this  integral may be used to \ncompare microwave materials. In some applications, f.µ’’(f)  is a quantity of direct interest. \nThis is the case when magnetic losses are desi red for microwave attenuation, either for \nmicrowave filtering, electromagnetic compatibility or for Radar Absorbing Materials. The first order approximation of the refl ection or transmission losses are in f.µ’’(f) . It has been \nshown that in the thin absorb er limit, the performance of a magnetic absorber is bounded by \nthe integral.\n12 As a consequence, it is an important re sult that moderate skin effect maintain \nthe integral losses unaffected, ev en though their freque ncy distribution is much affected. For \nsomewhat larger skin effect, the correction factor –s may become significant. This leads to a \ndecrease in the integrated losses.  \n Last but not least, th is study shows that micr owave permeability m easurements can be a \ntool for obtaining information on the magnitude and the orient ation of the magnetization \nwithin samples. The integral is related to a few magnetic parameters even in cases where µ’’ \ncannot be described by simple models because of some heter ogeneities or magnetic coupling. \nThis is very appealing for the study of unsaturated materials. In the case of multilayers, Eqs. (25) and (26) show that the in tegral provides an i ndication on the average orientation of the \nmagnetization within the sample thickness. The microwave field is indeed a probe of the \nmagnetization normal to the excitation, with th e ability to penetrate into relatively thick \nsamples. The integral \n∫F\ndfffµ\n0.).('' provides quantitative informati on on the magnitude of the \nmagnetization normal to the probe field.  \n  \n \nAPPENDIX \n \nThe dependence of the fields with time is assumed to be exp(+ jωt), which is consistent \nwith permeabilities that take the form µ’-jµ’’ , µ’’>0. The expression of the permeability of a \nuniformly magnetized ellips oid can be written as: \n ( )\n2 2\n0 ) (1ffF Fj Ffj FFµ\ny xy M\nG− + +++=αα (A1a) \nwith \n y xFF F .0=  (A1b) Crit_skin_LL31.doc p. 12 28/11/2007  s M M F πγ4= ; ) (intH MN Fs x x + =γ ; ) (intH MN Fs y y + =γ   (A1c) \n s z k MN H H − =int  ; α<<1 (A1d) \n \n4πMs is the saturation magnetization of the material, Nx, Ny, Nz are the demagnetizing \ncoefficients of the ellipsoid, and Hk is the external field (or anis otropy field) that saturates the \nellipsoid along +z. πγγ 2/=  is close to 3 MHz/Oe. F0 is the resonan ce frequency. The \norientation conventions are similar to those in  ref [12], the permeability  given by (A1a) being \nin the x direction. In the case of soft magnetic materials under microwave excitation, and for \nnull or moderate external fields, the different cont ributions to the Hk field will be small as \ncompared to the saturation magnetization. The internal field Hint must be positive for the \nmagnetization to be stable in the + z direction, and as a consequence Hint is also small. \nFollowing Eq. (6), a central issu e is to estimate the quantity  \n () ∫π\nθ θθ\n02. ). (21d Fe Feµj j  \nfor a frequency F much larger than the resonance frequency F0. It is convenient to \nintroduce the reduced frequency \n \n0FFejθ\nν=  (A2) \nthereby giving \n () ∫ ∫=π π\nθ θθνπχνπχ θ\n02\n02\n00\n02..4)(421. ). (21dµF d Fe Feµj j (A3) \n \n The permeability from Eq. (A1) can thus be  expressed as a function of the reduced \nfrequency \nν: \n () νανβ νπχ' 1.2 14120jjµG ++−+= , (A4a) \nwhere 4 πχ0 is the initial susceptibility,  \n 2\n00.4FFF\nFF y M\nxM= =πχ ; (A4b) \n \n02FF Fy x+=αβ  ; \nyFF0'αα= . (A4c) \n \nThis is valid provided that the internal fields are small \n s k M HH π4 ,int<<  (A4d) \n \nThe development in 1/ ν of the susceptibility can be written as: \n \n () ναν νβ\nν πχν πχ' 11 211\n4)( 41\n2 2\n0jjG+⎥⎦⎤\n⎢⎣⎡− −−=−\n  \n ⎟\n⎠⎞⎜\n⎝⎛+ +−≈νβναν'2' 11\n2jj  (A5) \nwith Crit_skin_LL31.doc p. 13 28/11/2007  \n02'2FF Fy x+=αβ . (A6) \nThe terms in α’.β have been neglected in the a bove expression si nce the damping \nparameter is small and the terms in α2 are negligible. It should be noted that when the Bloch-\nBlombergen damping parameter is used inst ead of the Gilbert damping parameter, the \nexpression of the susceptibility Bπχ4  has the same form as Eq. (A1), with α’=0 and β=1/T, \nwhere T is the characteristic damping time. \nIt is thus necessary to obtain an appropriate development of the factor A(ka)  that accounts \nfor the skin effect. The wavevector inside th e ferromagnetic inclusion can be expressed as: \n cµ k /.ωε= , (A7) \nwhere ω=2πf is the pulsation corres ponding to the frequency f, c the celerity of light, and ε \nthe permittivity of the inclusion.  \n \n0.εωσεj−= , (A8) \nHere, ε0 is the dielectric constant of void and σ the conductivity. When a skin effect is \npresent but not overwhelming, it is possibl e to use the low order development of A(ka)  \naccording to Eq. (5). In the case where the upper integration frequency F is significantly \nlarger than the gyromagnetic resonan ce frequency, but not too large,  \n σ π2\n0021\naµF F << << , (A9) \nwe obtain  \n \n ( ))( 41.. 1)( ν πχ ν νB jb A + −≈ , (A10) \n \nwith  \n paFµbσ π2\n0 0 2= . (A11) \nThe set of assumptions (A 9) can be written as:  \n )./(1 1 pb << <<ν , (A12) \nThe permeability in the presence of  skin effect can be written as \n \n [ ] ν ν πχν ν ν πχ ν . )( 4.. .21).( 41)( jb jb jb µB G − − − +≈ . (A13) \n \nKeeping only the most significant terms leads to  \n \nν νανβννπχβνπχν . ''2 24'41.41)(0\n20jb j j jb b µ −⎥⎦⎤\n⎢⎣⎡+ +⎟\n⎠⎞⎜\n⎝⎛− + + −≈ . (A14) \nThe integration of µ(ν).ν on the semi-circle C- can be expressed as the linear combination \nof integrals of νn with different powers n. These in tegrals are easily calculated using: \n ∫ ∫=\n−π\nθθ ν θν\n0.21.21de djn n\nCn. (A15) \nOne finds Crit_skin_LL31.doc p. 14 28/11/2007 ()2\n0 00\n00\n0\n0.23'2 '42 421..2.).('' FFbF\nFF\nFF\nFF\nFFb FF dfffµy MF\n⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛+⎥\n⎦⎤\n⎢\n⎣⎡+ −⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛+ − ≈ ∫απ πβπχππ. (A16) \nEq. (A16) can be written in the following form \n () [] ' 1. 42.).(''2\n0Sgts M N dfffµs yF\n++−− ≈ ∫πγπ, (A17) \nwhere s, S’, t and g are small corrective terms, with positive signs. s and S’ are related to \nskin effect; t corresponds to the finite truncation; g corresponds to a small contribution when \nthe Gilbert damping model is considered, bu t becomes zero when the Bloch-Bloembergen \ndamping model is employed. Each of these terms will be discussed in the following sections. \n \n A. Corrections associated with the magnetic damping \nPrevious work11 has been conducted assuming a magnetic damping described by the \nBloch-Bloembergen equations. When the damp ing is described according to the Landau-\nLifshitz-Gilbert model, the integral up to infini te frequencies diverges. The corrective terms in \nEq. (A17) are: \n \nMy y FNF\nFF\nFFg απαπαπ2 2'2\n0= = = . (A18) \nCases where Ny is null or small are of no interest  since the dominating factor in the \nexpression of the integral is proportional to  Ny. As the upper integration bound, F is expected \nto be lower than FM, and since α is small (from a few percent dow n to a fraction of a percent), \ng<<1. This establishes that for a practical case, the theoretical results obtained for \n∫F\ndfffµ\n0.).(''  are independent of the damp ing model under consideration. \n \n B. Skin effect corrections \nLet us examine in more detail the corrective te rms associated with skin effect in Eq. (A17). \nThe term S’ is independent of the ma gnetization of the sample.  \n 2\n0.23' FFbFS⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛= . (A19) \nIt is well known that conductive particles ma y exhibit non-unit permeability as a result of \neddy currents. Although the integral of µ’’(f).f diverges at infinity, it should be noted that if \nthe integral is performed only up to a frequency F that is not too large, then S’<<F2 according \nto Eq. (A9). In the case of ferromagneti c materials, it is convenient to express S’ as a \nperturbation of the main term in Eq. (A17): \n '.2'2sFN SMyπ= . (A20) \nThe expression for s’ is: \n 22 3\n0\n2\n06 3'. .\nyM Mµa bF F FsNF F p Fσ\nπ⎛⎞ ⎛⎞== ⎜⎟ ⎜⎟\n⎝⎠ ⎝⎠. (A21) \n \nand s’ is negligible provided that (A9) is met and F<FM. Let us now examine the s \ncorrective term in Eq. (A17), \n FFNpaµ\nFF\nFFb sM\ny2 2\n0\n00\n042 42 σπχπ≈⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛+ = . (A22) Crit_skin_LL31.doc p. 15 28/11/2007 It is straightforward that s is positive, which means that skin effect tends to decrease the \nvalue of the integral.  \n \n C. Finite frequency summation correction \nStopping the integration at a certain finite upp er frequency would aff ect the value of the \nintegral, even if no skin effect is present. The t term in Eq. (A17) accounts for this truncation \neffect. It can be expressed as: \n ( )FFN NFFtM\ny x+ ≈ = 22 '40απ πβ. (A23) \nThis correction factor is far below unity provided that \n ( )s M M F F πγα α 4 = >> . (A24) \nEven for a material with a very large saturation magnetization such as CoFe with \n4πMs=24k Oe, for a typical value of α=2%, Eq. (A24) requires th at the upper integration \nfrequency is such that F>>1.4 GHz. This is an easily met condition. \n \n D. Effect of experimental measurement errors  \nWhen using experimental permeability data, th e error on the sum increases when the upper \nintegration bound is extended. An error term ha s to be added to the right member of Eq. \n(A17). In order to be able to directly compare the error ±e to the other terms –s and –t, it is \nconvenient to write this additional term as \n eFNMy.22 π.  \nIt can thus be shown in a straightforward manner that \n 2\n⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛Δ≤\nM yFF\nNµeπ, (A25) \nwhere Δµ is the maximum error on the measured permeability. The relative error is small \nprovided that \n ( ) µ M FsΔ << / 4πγ . (A26) \n Crit_skin_LL31.doc p. 16 28/11/2007 Figure Caption \n \n \n \nFIG. 1. Various inclusion shapes , with the associated functions A(ka)  used for the \nexpression of the permeability in the presen ce of skin effect according to ref [19]; k is the \nwavevector inside the inclusion, and a is its radius (or half thic kness in the case of a plate). \nThe expression of the 2nd order approximation of A(ka)  is also given.  \n     \n \n   Crit_skin_LL31.doc p. 17 28/11/2007 \n \n \nFIG. 2 The imaginary part of the permeability µ’’ computed for films with a thickness 2 a \nranging from 0.1 µm to 2 µm, using the Land au-Lifschitz-Gilbert model and taking into \naccount skin effect. \n  Crit_skin_LL31.doc p. 18 28/11/2007 \n \nFIG 3. The efficient dynamic magnetization ) (FMµ associated with the calculated \npermeabilities represented in Fig. 2, obtained ei ther by numerical integration (symbols), or by \nanalytical estimates (lines). The error bars represent typical experi mental errors and the \ndashed line corresponds to the saturation magnetization. \n    Crit_skin_LL31.doc p. 19 28/11/2007 \n \n \nFIG. 4. The imaginary part of the perm eability µ’’ measured on CoZr amorphous thin \nfilms of varying thicknesses. \n  Crit_skin_LL31.doc p. 20 28/11/2007 \n \nFIG. 5. The efficient dynamic magnetization ) (FMµ  associated with the measured \npermeabilities represented in Fig. 4, and a comparison with the saturation magnetization \nvalues (dashed line with error bars). The extr apolation of the satura tion magnetization from \nMµ(F) using analytical estimates is also represented, with appropriate error bars. \n Crit_skin_LL31.doc p. 21 28/11/2007 Table Caption \n  \nLower bound Upper bound Eq. Comment \nF0<<F \n  1 2\n0 ) 2(−<< σ πaµ F  \n \n (A9) \n \n(A4d) Required for the validity of the whole \napproach \ns k M HH π4 ,int<< also required  \n F <<FM/ α. (A18) Effect of Gilbert damping +g is small \n F <FM (A21) Skin effect term s’ is small \nF p FaµM <</ 42 2\n0σ   (A22) Skin effect term -s is small \nα.FM<<F   (A24) Truncation term -t is small \n µ F FM Δ << /  (A25) Experimental error ± e is small \nTable I. Guidelines for choosing the upper integration frequency F on ∫F\ndfffµ\n0.).('' , as a \nfunction of the gyromagne tic resonance frequency F0, s M M F πγ4= , and other parameters. \n \n   \nLower bound Upper bound Parameter Eq. Analytical \nValue Numerical \nvalue \nF0=1.2 GHz 21\n0 (2 ) 165 GHzµaπσ−=\n ∫F\ndfffµ\n0.).(''  1.05 103 GHz2 0.99 103 GHz2 \n FM/ α.=1500 GHz +g (A18) 0.3% 0.4% \n FM=30 GHz +s’ (A21) 0.05% <<0.1% \n22\n041.2 GHzM µa F\npσ=   -s (19) -19% -23% \nα.FM=0.6 GHz  -t (18) -6.4% -6.5% \n /3 0  G H zMFµ Δ=  ±e (20) ±1.3%  \n \nTable II. The numerical estimation of the lower and upper frequency bounds for F associated \nwith Table I in the case of a 2 µm thick film; for F=6 GHz, values of the different corrective \nterms accounting for the relative difference between \n0''( ). .F\nµff d f∫ and ()242sMπγπ obtained \nboth analytically and numerically.  Crit_skin_LL31.doc p. 22 28/11/2007  \n \n* olivier.acher@cea.fr \n1 B. Viala, A. S. Royet, R. Cuchet, M. Aid, P. Gaud, O. Valls, M. Ledieu, O. Acher, IEEE Trans. Magn. 40, \n1999 (2004). \n2 P. M. T. Ikonen, K. N. Rozanov, A. V. Osipov, P.  Alitalo, and S. A. Tr etyakov, IEEE Trans. Antennas Propag. \n54, 3391 (2006). \n3 B. K. Kuanr, D. L. Marvin, T. M. Christensen,  R. E. Camley, and Z. Celinski, Appl. Phys. Lett. 87, 222506 \n(2005). \n4 A. L. Adenot, O. Acher, T. Taffary, P.  Queffelec, and G. Tanne, J. Appl. Phys. 87, 6914 (2000). \n5  K. H. Kim and M. Yamaguchi, J. Appl. Phys. 99, 08M902 (2006). \n6 D. Rousselle, A. Berthault, O. Acher, J. P. Bouchaud and P. G. Zérah, J. Appl. Phys.  74, 475 (1993). \n7 L. X. Lian, L. J. Deng, L. J., M. Han, W. Tang, S. D. Feng, J. Appl. Phys.  101, 09M520 (2007). \n8 J.L. Snoek, Physica 14, 207 (1948). \n9 R.M. Walser, W. Win, P.M. Valanju, IEEE Trans. Magn. 34, 1390 (1998). \n10 G. Perrin, J. C. Peuzin and O. Acher, J. Appl. Phys. 81, 5166 (1997). \n11 G. Perrin, O. Acher, J.C. Peuzin, N.  Vukadinovic, J. Magn. Magn. Mater. 157/158 , 289 (1996). \n12 O. Acher and A. L. Adenot, Phys. Rev. B 62, 11324 (2000). \n13 I. T. Iakubov, A. N. Lagarkov, S. A. Maklakov, A. V. Osipov, K. N. Rozanov, I. A. Ryzhikov, N. A. Simonov, \nS. N. Starostenko, J. Magn. Magn. Mater. 258–259 , 195 (2003). \n14 A. N. Lagarkov, I. T. Lakubov, I. A. Ryzhikov, K. N. Rozanov et al. Physica B 394, 159 (2007). \n15 M. Abe, J. Kuroda and M. Matsumoto, J. Appl. Phys. 91, 7373 (2002). \n16 K. N. Rozanov, Z. W. Li, L. F. Chen and M. Y. Koledintseva, J. Appl. Phys. 97, 013905 (2005). \n17 A. L. Adenot, O. Acher, T. Taffary, and L. Longuet, J. Appl. Phys. 91, 7601 (2002). \n18 A.G. Gurevich and G. A. Melkov, Magnetization Oscillations and waves , CRC Press, New York (2000). \n19 L. Lewin, Proc. Inst. Elec. Eng. 94, 65 (1947). \n20 A.N. Lagarkov, A.K. Sarychev, Y. R. Smychkovich. and A. O. Vinogradov, J. Electromagn. Waves Applic. 6, \n1159 (1992). \n21 E. van de Riet and F. Roozeboom, J. Appl. Phys. 81, 350 (1997). \n22 O. Acher, S. Dubourg, F. Duverger and N. Malléjac, J. Magn. Magn. Mater. 310, 2319 (2007). \n23 J. D. Jackson, Classical Electrodynamics , 2nd edition, Wiley, New York (1975). \n24 D. J. Bergman and D. Stroud, Solid State Phys. 46, 147 (1992). \n25 Z. Hashin and S. Shtrickman, J. Appl. Phys. 33, 3125 (1962). \n26 D. J. Bergman, Phys. Rev. Lett. 44, 1285 (1980 ). \n27 G. W. Milton, Appl. Phys. Lett. 37, 300 (1980). \n28 D. Stroud, Phys. Rev. B 19, 1783 (1979). \n29 A. Gerber, J. McCord, C. Schmutz,  and E. Quandt, IEEE Trans. Magn. 43,  2624  (2007). \n30 O. Acher, S. Queste , K.-U. Barholz and R. Mattheis, J. Appl. Phys. 93, 6668 (2003).  \n31 S. Dubourg, S. Queste, O. Acher, J. Appl. Phys. 97, 10F903 (2005) \n32 G. de Temmerman, H. Pages, O. Acher, S. Dubourg,  F. Schoenstein, S. Queste, M. Ledieu, J. Magn. Magn. \nMater 290, 1580-1583 (2005). \n33 P. Toneguzzo, O. Acher, G. Viau, F. Fi évet-Vincent and F. Fi évet, J. Appl. Phys. 81, 5546 (1997). \n34 C. Brosseau, S. Mallégol, P. Quéffelec and J. Ben Youssef, Phys. Rev. B 70, 092401 (2004). \n35 C. Brosseau and P. Talbot, J. Appl. Phys. 97, 104325 (2005). \n36 D. Pain, M. Ledieu, O. Acher, A.-L. Adenot, and F. Duverger, J.Appl. Phys. 85, 5151 (1999). "    },    {        "title": "0710.4043v3.Observation_of_magnetization_reversal_and_negative_magnetization_in_a_double_perovskite_compound_Sr2YbRuO6.pdf",        "content": "Observation of magnetization reversal and negative mag-\nnetization in Sr 2YbRuO 6 \n \nRavi P. Singh and C. V. Tomy \nDepartment of Physics, Indian Institute of Technology Bombay, Mumbai 400 076, INDIA \ntomy@phy.iitb.ac.in \n \n \nABSTRACT \n \nDetailed magnetic properties of the compound Sr 2YbRuO 6 are presented here. The compound \nbelongs to the family of double perovskites form ing a monoclinic structure. Magnetization meas-\nurements reveal clear evidence for two components of magne tic ordering aligned opposite to \neach other, leading to a magnetization reversal,  compensation temperature (T* = 34 K) and neg-\native magnetization at low temperatures and low magnetic fields. Heat capacity measurements \ncorroborate the presence of two components in  the magnetic ordering and a noticeable third \nanomaly at low temperatures (~15 K) which cannot be  attributed the Schottky effect. The calcu-\nlated magnetic entropy is substantially lower than that expected for the ground states of the or-\ndered moments of Ru5+ and Yb3+, indicating the presence of large crystal field effects and/ or in-\ncomplete magnetic ordering and/or  magnetic frustrations well abo ve the magnetic ordering. An \nattempt is made to explain the magnetization reversa l within the frameworks of available models. \n \n \nPACS : 75.60.Jk, 75.50.Ee, 74.70.Pq 1. INTRODUCTION \n \nThe subject of magnetization reversal in oxid es and intermetallic compounds has received con-\nsiderable attention recently. The magnetization reve rsal is usually achieved by applying a large \nmagnetic field in a direction opposite to the aligned moments or by changing the temperature in \nmoderate fields. The temperature induced magnetiza tion reversal, which is quite rare, is found to \noccur in systems having two or more different types of magnetic ions, positioned at different \ncrystallographic sites [1]. A few ferrimagnetic compounds have shown the temperature induced \nmagnetization reversal effect [2] when the tw o antiferromagnetically coupled magnetic sublat-\ntices exhibited different temperature dependence of  the magnetization. Interestingly, there are a \nfew other oxides and intermetallic compounds wh ich show temperature induced magnetization \nreversal such as LnVO 3 (Ln = Y, La, Sm, Nd, etc.) [3-8], (Sm,Gd)Al 2 [9], LnCrO 3 (Ln = Gd, \nLa0.5Pr0.5) [10-12], etc. The origin of magnetization re versal in the above compounds is found to \nbe entirely different compared to that of the ferrimagnetic compounds. For example, LaVO 3 \nshows magnetization reversal due to the combined  effects of Dzyaloshinsky-Moriya (D-M) inter-\naction [13, 14] and a magnetostrictive distortion induced by orbital moments [15] whereas the \nmagnetization reversal in YVO 3 is caused by the competition between single ion anisotropy and \nD-M interaction [5]. At the same time, the observation of magnetization reversal in NdVO 3 and \nSmVO 3 is explained on the basis of N-type ferrimagnetism arising from the imbalance of the \nquenching rate of the orbital moments of V3+ ions [7,8]. (Sm,Gd)Al 2 causes magnetization rever-\nsal due to the compensation between the spin a nd the orbital parts of the ordered moments [9]. In \nLnCrO 3, this effect is attributed to the polarization of the paramagnetic moments of the Ln ions \nwhich align opposite to the canted Cr moments [10] . Here we report the magnetization reversal in \na new compound Sr 2YbRuO 6. \nSr2YbRuO 6 belongs to the family of double perovskite ruthenates [16] having the general \nformula Sr 2LnRuO 6 (Ln = Y or rare earth). These compounds form in a monoclinic structure be-\nlonging to the space group P21/n [17]. The structure of these antiferromagnetic insulators can be \nformed from the perovskite structure of SrRuO 3 by replacing the alternate Ru atoms by rare earth \natoms [18]. Due to the monoclinic distortion of the perovskite structure, these compounds are known to exhibit interesting magnetic properties at  low temperatures due to the canting of the Ru \nmoments resulting from the Dzyaloshinsky-Mori a (D-M) interaction among the antiferromagneti-\ncally ordered moments. Even though the magnetic ordering is primarily due to the Ru\n5+ moments \n(4d3, J = 3/2), the rare earth moments also show magnetic ordering in compounds having mag-\nnetic rare earths at temperatures close to  the ordering of the Ru moments [19]. 151Eu Mössbauer measurements [20,21] in Sr 2EuRuO 6 have indicated the presence of a large exchange field at the \nrare earth site (~280 kOe) due to the ordered Ru moments. 99Ru Mössbauer measurements in \nSr2YRuO 6 [22] have also shown the presence of a large exchange field (595 kOe) below the mag-\nnetic ordering temperature. The presence of this la rge exchange field is assumed to be responsible \nfor forcing the rare earth moments to order simulta neously with the Ru moments. Doi et al [23] \nhave reported the magnetization for most of the Sr 2LnRuO 6 compounds. They have also reported \nthat the zero field-cooled (ZFC) magnetization in Sr 2YbRuO 6 was higher than the field-cooled \n(FC) magnetization. Neutron diffraction measuremen ts at 10 K in this compound [24] have indi-\ncated the existence of antiferromagnetic ordering of both the Ru and Yb moments. Since no de-\ntailed magnetization studies exist for this com pound, we have performe d detailed magnetization \nand heat capacity measurements on this compound. Our magnetization results show clear evi-\ndence for a magnetization reversal, resulting in negative magnetization for low fields ( ≤ 2 kOe) at \nlow temperatures in the FC measurements. Heat capacity measurements show two well defined peaks that can be attributed to the two magnetic  orderings along with a prominent anomaly at low \ntemperatures (~15 K) that cannot be fitted to the usual Schottky anomaly. No other member of \nthis double perovskite family of compounds is  known to show magnetization reversal/negative \nmagnetization. The results are analyzed within the frameworks of the available models which \nexplain the magnetization reversal.  \n \n2. EXPERIMENTAL DETAILS \n \nSamples of Sr\n2YbRuO 6 were prepared in air by the standard solid state reaction method with the \nstarting materials SrCO 3, Yb 2O3 and Ru metal powder. The initial mixture was well ground and \nheated at 960 °C for 24 hours. The final sintering of th e pelletized powder was carried out at \n1285° C for 24 hours after two intermediate heat treatments followed by grindings. The samples \nwere examined by powder x-ray diffraction using an X’pert PRO diffractometer (PANalytical, \nHolland) having Cu- Kα radiation. The magnetization measurem ents were carried out as a function \nof temperature and magnetic field using a vibr ating sample magnetometer (Quantum design, \nUSA). The magnetization measurements were carried  out in both the zero field-cooled (ZFC) and \nfield-cooled (FC) modes. In ZFC measurements, the sample was cooled in zero applied fields to \n5 K, the required magnetic field was applied and the data were then taken while warming. For FC measurements, the sample was cooled from the paramagnetic state to 5 K in an applied field and the data were recorded while heating the sample. The heat capacity measurements using the re-laxation method were performed in a physical property measurement syst em (Quantum design, \nUSA) in the temperature range 1.8-300 K.  \n 3. RESULTS AND DISCUSSION \n \nThe x-ray diffraction pattern was refined by th e Reitveld analyses using the Fullprof software. \nThe analyses showed that the compound forms in the required phase. The pattern could be in-\ndexed to a monoclinic structure with space group P2\n1/n (see Fig. 1). The lattice parameters ob-\ntained from the analyses are, a = 5.723(2) Å, b = 5.719(2) Å, c  = 8.09(3) Å and β = 90.2(1)°,  \n \nFigure 1. Reitveld analysis of the XRD pattern of Sr 2YbRuO 6. The bottom line shows the differ-\nence plot between the observed and calculated x-ray intensities. \n \nwhich are in good agreement with those reported earlier [24]. Figure 2 (main panel) illustrates the magnetization of Sr\n2YbRuO 6 as a function of temperature in the ZFC and FC modes measured in \nan applied field of 50 Oe. No difference be tween the ZFC and FC ma gnetization is observed \ndown to ~46 K. The bifurcation between them then starts and the magnetization curves follow \nentirely different paths below this temperature. In the ZFC mode, the magnetization shows a maximum at ~44 K (see the lower inset of Fig. 2), goes through a minimum at ~39 K and then increases as the temperature is decreased. This minimum occurs with a negative magnetization if the applied fields are small. However, for higher fields ( ≥ 500 Oe), the ZFC magnetization is en-\ntirely positive with the maximum at ~44 K becoming sharper, as shown in the upper inset of Fig. \n2. In contrast, the FC magnetization increases below 44 K, goes through a maximum at 39 K, \n \nFigure 2. Magnetization of Sr 2YbRuO 6 as a function of temperature in the ZFC and FC modes in \n50 Oe. Insets show the expanded version of the ZFC mode near the magnetic transitions for \n50 Oe (lower) and 1 kOe (upper).  decreases and then passes through a zero value of magnetization ( M = 0) at the compensation \ntemperature ( T\n*). Below this compensation temperature,  the magnetization is negative down to \nthe lowest temperatures (5 K). No hysteretic behaviour was observed whether the FC magnetiza-\ntion was measured while cooling or warming th e sample. Figure 3 shows the FC magnetization \ncurves (normalized to the measuring field) for different applied fields. As the applied magnetic \nfield is increased, T* shifts to lower temperatures and the negative component of the magnetiza-\ntion decreases. Upper inset of Fig. 3 shows the T* vs H plot. The actual compensation temperature \n(T* = 34 K) is taken as the extrapolated value at H = 0. For fields H ≥ 3 kOe, one can observe on-\nly positive FC magnetization, even though a mini mum occurs at temperatures corresponding to \nT*. Lower inset of Fig. 3 shows additional eviden ce for the magnetization reversal. For obtaining \nthis data, the sample was field cooled in 10 kOe down to 5 K and the applied field was removed. The remnant magnetization was then measured in zero field while warming the sample. The sud-\nden increase in magnetization before attaining the paramagnetic state can be attributed to the magnetization reversal. Thus the magnetization data (Figs. 2 and 3) clearly show evidence for the \nmagnetic ordering as well as the magnetization reversal/ negative magnetization. In order to ver-\nify the reproducibility of the anomalous behaviour, the compound was prepared in two different \nbatches and both showed similar stru ctural and magnetic properties.  \nFigure 3. Field-cooled (FC) magnetizations normalized to the measuring fields ( M/H) as a func-\ntion of temperature ( T) at different fields. Upper inset shows the plot of compensation tempera-\nture T* as a function of measuring field H. Lower inset shows the warm up data (FCW) in zero \nfield. The sample was field-cooled in 10 kOe magnetic field down to 5 K and the field was switched off before taking the data. \n \nIn order to explore the magnetic behaviour in detail, magnetic isotherms were measured \nat different temperatures between 5 K and 50 K. Figure 4 shows the magnetization curves for \nsome selected temperatures in the ZFC mode. A clear hysteresis is observed at low temperatures \nin low fields. The magnetization does not saturate even at high fields (90 kOe) and shows only a \nlinear variation with H as expected for an antiferromagnet (Fig. 4(h)). As the temperature in-\ncreases, the hysteresis loop shrinks and the coercive field H\nc decreases. A small increase in Hc is \nobserved in the region of 39-44 K (see Fig. 4(e) and (g)). This temperature range corresponds to \nthe onset of the two magnetic anomalies. The magne tic isotherms were also measured in the FC  \n mode which gave similar hysteresis behaviour and Hc variation. Some of the Hc values from the \nFC loops are also plotted in Fig. 4(g). The above  observations clearly indicate the presence of two  \n \n \n   \n \n    \n \n   \n \n    \n \n   \n \nFigure 4. (a) – (f) Magnetization ( M) as a function of field ( H) at different temperatures  in zero \nfield cooled mode. (g) Coercivity ( H\nc) as a function of temperature. (h) The magnetization ex-\ntended to high fields at 5 K.  \ncomponents in the magnetic ordering, one starting at 44 K and the other at 39 K. The maximum at \n44 K and the minimum at 39 K in ZFC magnetiza tion as well as the maximum at 39 K in the FC \nmagnetization correspond to the two components mentioned earlier. From the magnetization be-\nhaviour in the FC and ZFC modes, it is clear th at the two magnetic components align opposite to each other. Since the magnetic ordering of both the Yb and Ru moments is inferred from the neu-\ntron diffraction measurements at 10 K [24], one can  attribute the anomalies in the magnetization \nto the magnetic ordering of Ru and Yb. As the te mperature variation of the intensity of the mag-\nnetic peaks is not reported in the neutron diffrac tion measurements [24], it will be difficult to as-\nsign the actual ordering temperatures for Yb and Ru. However, since Ru is seen to be ordering \nfirst in all the reported compounds of this series [19] and the rare earth moments are forced to \norder due to the large exchange field [20-22] resulting from the ordered Ru moments, we also \nassert that the first transition at 44 K is due to the magnetic ordering of the Ru moments. \n100\n80\n60\n40\n20\n0C (J/mole K)\n100 80 60 40 20\nT (K) Cexp\n fit5\n4\n3\n2\n1\n0Smag (J/mole K)\n60 50 40 30 20 10T (K)6\n4\n2\n0Cmag (J/mole K) Cmag\n Smag\n SSch\n \nFigure 5. Total heat capacity ( C) of Sr 2YbRuO 6  measured as a function of temperature (lower \npanel). The solid line represents the phonon contri bution calculated using the Debye and Einstein \ncontributions (see text). The upper panel shows the magnetic contribution to the heat capacity \n(Cmag) and magnetic entropy ( Smag). The dashed line is the calcula ted Schottky contribution to the \nheat capacity for a simple two-level conf iguration (ground state and excited state). \n There are no reports about the heat capacity of this compound in the literature. The result \nof heat capacity measurements for Sr 2YbRuO 6 is presented in the lower panel of Fig. 5. Two \npeaks can be identified, one at T  = ~44 K and the second at T  = ~39 K. As inferred from the mag-\nnetization measurements, one can attribute the two peaks in heat capacity to the magnetic order-\ning of the Ru and Yb moments. In order to separate the magnetic contribu tion to the heat capac-\nity, the phonon contribution needs to be removed from the total measured heat capacity. Since no \nobvious nonmagnetic analogue is available for this compound, an approximate phonon contribu-\ntion was calculated using the combined Debye and Einstein terms [25] from the equation, \n() ()\n() () ⎪⎭⎪⎬⎫\n⎪⎩⎪⎨⎧\n−⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛\n−+\n− −= ∫ ∑−\n=D\nii ix\nxx\nD D EE En n\ni Elattice dx\nee x\nx T TT T\nTR C\n0243\n22 3\n1 11\n19\n1 ) / exp(/ exp /\n11\nα θθ θ\nα  (1)  \nwhere α’s are the anharmonicity coefficients, θD and θE are the Debye and Einstein temperatures, \nrespectively and T xD D/θ=\n3001=E. We have used one Debye and three Einstein frequencies for the cal-\nculations along with a single αE. The calculated lattice heat capacity is shown as a solid line in the \nlower panel of Fig. 5. A reasonably good agreemen t with the experimental data is observed at \nhigh temperatures (above the magnetic ordering). Th e values of the parameters obtained from the \nfit are: θ  K, 5292=Eθ  K, 7003=Eθ  K, 189=Dθ  K,  K-1 \nand  K-1. The values obtained for the Debye and Einstein temperatures are compa-\nrable with those obtained under similar treatment of the heat capacity for YVO 3 which also shows \nmagnetization reversal, compensa tion and negative magnetization [2 6]. The contribution of the \nmagnetic heat capacity, Cmag was obtained by subtracting the calculated phonon contribution from \nthe total heat capacity and is shown in the upper panel of Fig. 5 along with the magnetic en-\ntropy410 0 . 1−× =Eα\n410 4 . 8−× =Dα\n∫=2\n1T\nTmag\nmag dTTCS . The magnetic heat capacity Cmag clearly shows two peaks one at ~41 K \nand the second at ~36 K corroborating the presen ce of two long range orderings as deduced from \nthe magnetization measurements (even though there is a slight mismatch between the correspond-\ning temperatures in the two measurements). The small hump observed at low temperatures \n(~15 K) was treated as the Schottky anomaly arisin g from the thermally populated excited levels \nof Yb (such a peak is absent in the heat capacity of Sr 2YRuO 6 [27], isostructural compound with \nnonmagnetic rare earth) due to the removal of the ground state degeneracy when the crystal field effects are present. First we assumed a simple two level system for Yb energy levels and calcu-lated the total heat capacity by thermal population using the equation ()\n[]2\n1 01 02\n) / exp( ) / ( 1) / exp( ) / ( /\nT g gT g g T RCSchΔ +Δ Δ=                      (2) \nwhere R is the gas constant, Δ is the energy difference between the ground state and the excited \nstate (in units of temperature), and g0 (g1) is the multiplicity of the ground (excited) state. For \nsimplicity, we have assumed g0 = g 1 = 1. The Schottky curve obtained using the above equation is \nshown as the dashed line in the upper panel of Fig. 5 for Δ = 35 K. The large mismatch of the \nheat capacity values between the calculated and observed curves (the observed anomaly is nearly \nhalf the expected value) indicates that the low temperature hump in Cmag may not be due to the \nSchottky anomaly.  \nMagnetic entropy saturates nearly to a value of ~5.7 J mole−1 K−1 above 45 K which is \nless than the entropy expected for the ordered Ru5+ moments with a ground state of J = 3/2 \n( 52 . 11 ) 1232 ln( = + × = R Smag  J mole−1 K−1). However, if the crystalline electric field effects \nare present, then the four-fold degenerate ground state of Ru5+ can transform into a Kramer’s \ndoublet, giving rise to a multiplicity of only two [2 4]. This will reduce the magnetic entropy of \nthe compound from 11.52 J mole−1 K−1 to 76 . 5 2 ln= R  J mole−1 K−1. However, the magnetic \nmoment value of Ru5+ deduced from the neutron diffraction data at 10 K (3.0 μB/Ru5+) in \nSr2YbRuO 6 [24] corresponds well with the expected value of the moment with a ground state J = \n3/2. The exact reason for such a reduction in the entropy is not very clear at present. If the en-\ntropy of the ordered Yb moments is also taken into account (magnetic ordering of Yb3+ is inferred \nfrom the neutron diffraction data at 10 K [24]), then  the discrepancy in entropy is even more seri-\nous. A similar entropy reduction was reported in a related compound Ba 2YbRuO 6 [24]. In this \ncompound also, the calculated entropy was only 7.0 J mole−1 K−1 even though both the Ru and Yb \nmoments show magnetic ordering at 10 K. After deducting the magnetic entropy observed \n(3.9 J mole−1 K−1) for the isostructural compound with nonmagnetic rare earth, Ba 2YRuO 6, where \nonly the Ru moments show magnetic ordering, the remaining entropy (3.1 J mole−1 K−1) was at-\ntributed to the crystal field split ground state doublet Γ6 of Yb3+ ions. If we do a similar treatment \nhere and deduct the observed magnetic entropy (2.6 J mole−1 K−1) of Sr 2YRuO 6 [27] from the to-\ntal entropy of Sr 2YbRuO 6, then we obtain 3.1 J mole−1 K−1 as the magnetic entropy of Yb3+ in our \ncompound also. Even though this value is still smaller than the required value (5.7 J mole−1 K−1) \nfor the crystal field split doublet ground state Γ6 of Yb3+ (under the assumption that the crystal \nfield splitting will be almost similar in the distorted cubic structure of Sr 2YRuO 6), we consider \nthis as the best possibility and attribute the discrepancy (2.66 J mole−1 K−1) to the non saturation of the ordered magnetic moments of Yb3+ (46%). The reduction in entropy of Ru ordering can be \ncompared to the reduction in entropy of the V3+ moments in YVO 3 that has been attributed to the \nfrustrations of V3+ moments at high temperatures (above magnetic ordering) which decreases the \neffective contribution of the entropy to the magnetic ordering [26]. In a similar manner, we can \nattribute the frustration effects of the Ru5+ moments at high temperatures for the effective reduc-\ntion of the entropy associated with the Ru ordering in Sr 2YRuO 6. In fact, the presence of frustra-\ntions among the Ru5+ moments has been inferred as the reason for the reduction in TN in \nSr2YRuO 6 even though the compound has a large value of the exchange integral [28]. This will \nimply that similar frustrations also exist among the Ru moments at high temperatures in \nSr2YbRuO 6. \nTwo distinct magnetic anomalies can be inferred in the compound from both the mag-\nnetization and heat capacity measurements, one at ~44 K and the second at ~39 K. The net result \nof these anomalies is to give rise to a compensation temperature ( T* = 34 K)  and a negative mag-\nnetization in the FC measurements at low fields ( ≤ 2 kOe). This is possible only if one of the \ncomponents of the magnetization aligns itself agai nst the applied fields. Since the FC magnetiza-\ntion goes through a positive maximum before goi ng through the compensation point, it is clear \nthat the first component of the magnetic ordering at ~44 K aligns parallel to the field and the sec-\nond component at ~39 K antiparallel to the magnetic field. \n The presence of hysteresis in the magnetization data substantiates the presence of a fer-\nromagnetic component in the magnetic ordering. In compounds with low structural symmetry \nsuch as Sr 2LnRuO 6 (monoclinic structure), weak ferromagne tic interactions can exist among the \nantiferromagnetically ordered moments due to canting of the spins resulting from the D-M inter-\nactions. In fact, the presence of such ferroma gnetic component is well documented in compounds \nof this series with the nonmagnetic rare earth, Sr 2YRuO 6 [22, 29] and Sr 2LuRuO 6 [23] resulting \nfrom the canting of the antiferromagnetically ordered Ru moments. If we consider the same effect to be present in Sr\n2YbRuO 6 also, then the increase in magnetiza tion below 44 K can be attributed \nto the effect of the canting of Ru moments. This  brings in the possibility that the second magnetic \nordering (Yb moments, as we have assumed) also starts with a canting and as a result, a ferro-magnetic component. How this component aligns itself against the field uniquely in the Yb com-pound is not clear now, since no other compounds in  this family show negative magnetization. \nThe large value of negative magnetization at low temperatures and small values of H\nc in the tem-\nperature range of 39-44 K clearly demonstrate that the second canted component (resulting from \nthe Yb moments) is much larger than the firs t component (from the Ru moments). The possibility \nof canting is inferred from the presence of a weak  (001) magnetic reflection in the neutron dif-fraction measurements in Sr 2YbRuO 6 [24]. The absence of the same weak reflection in the neu-\ntron diffraction data in Sr 2TmRuO 6 [24]  and the presence of a ferromagnetic component in the \nmagnetization data clearly affirm the larger magnitude of the ferromagnetic component in \nSr2YbRuO 6.  \nThe second possibility that can be considered as the reason for the magnetization reversal \nis the competing effects of D-M interaction and th e single ion anisotropy of Ru moments, as in \nthe case of YVO 3 in the temperature range of 75-110 K [5,6]. In this assumption, the magnetic \nordering of the Yb moments can be considered to be purely antiferromagnetic without any canted \ncomponent. If we compare the observation of negative magnetization in Sr 2YbRuO 6 with that of \nLaVO 3 compound, then other mechanisms have to be brought in. In LaVO 3, the D-M vector ro-\ntates against the magnetic field at the structur al transition resulting from the first order magne-\ntostrictive distortion [15]. Since the structure of Sr 2YbRuO 6 remains the same at 10 K (as de-\nduced from the neutron diffraction measurements [24], the possibility of any structural transition and hence the rotation of the D-M vector against the field can be ruled out. However, whether such a rotation can be initiated by the magnetic or dering of the Yb moment needs further investi-\ngation. \nAnother possibility for negative magnetization is the polarization of the paramagnetic \nmoments in a direction opposite to the direction of the applied magnetic field, as observed in \nsome LnCrO\n3 compounds [10-12]. However, if we assume  the magnetic ordering of Yb moments \nto take place at ~39 K and the Ru moments at~39 K as inferred from the peak  in the heat capacity \nmeasurements (Fig. 5), then this possibility can  be ruled out since no other paramagnetic mo-\nments exist in the compound. But if we take th e discrepancy between the observed magnetic mo-\nment of the ordered Yb moments [24] in neut ron diffraction measurements at 10 K (0.98 μB) to \nthat of the expected valu e even for the ground state Γ6 with the lowest moment value (1.33 μB), \nthen we can assign nearly 26% of the Yb moment s not to be ordered. Th is paramagnetic moment, \narising from the large fraction of unordered Yb mo ments, can polarize against the canted field of \nRu moments as in the case of LnCrO 3 compounds. If we consider this polarization as the cause of \nmagnetization reversal, then the measured magnetization M should follow the equation [10] \n) /( ) (Yb Ru θ− + + = T H H C M Ma I        ( 3 )  \nwhere MRu is the canted moment of Ru, HI is the internal field due to the canted Ru moments, Ha \nis the applied field, CYb is the Curie constant and θ is the Weiss constant. The limitation of this \nanalysis is the assumption of MRu and HI to be independent of   temp erature, which is usually true \nif . In the present case, this may not be true  and hence the values obtained will only be NT T<<an approximation. The solid line in Fig. 6 shows the fit to the magnetization curve ( H = 100 Oe) \nusing the above equation. The parameters obtained from the fit are MRu = 222 emu/mole, H I = \n−7690 Oe and θ = −55 K. These values are comparable to those obtained for GdCrO 3 [11] and \nLa0.5Pr0.5CrO 3 [12]. The value of C Yb (= 2.575) used in the analys is was obtained from the free ion \nYb3+ paramagnetic susceptibility above TN . The goodness of the fit to Eqn. (3) in Fig. 6 indicates \nthe presence of a considerable fraction of Yb moments that are paramagnetic and contributing to \nthe polarization against the canted Ru moments. Under these circumstances, one can attribute the \nlow temperature anomaly in the heat capacity measurements  \nFigure 6. FC magnetization of Sr 2YbRuO 6 for 100 Oe. The solid line is the fit to the equation (3) \nin the text. Variation of the canted Ru moment ( MRu) (lower panel) and the internal field due to \nordered Ru moments ( HI) (upper panel) obtained from the fit fo r different applied fields are given \nas insets.  (T~15 K) to the completion of the magnetic ordering of the Yb moments. That is, the Yb mo-\nments start ordering at ~39 K due to the large internal field from the ordered Ru moments, but \ncomplete the ordering at ~15 K. The negative value of the internal field H\nI highlights its direction \nagainst both the applied field and the canted Ru mo ments. We could obtain good fits for magneti-\nzation curves with other field values also. The inset of Fig. 6 shows the variation of MRu (lower) and HI (upper). The variation of these components is in good agreement with the observed mag-\nnetization behaviour. The internal field shows an initial increase with the field, but decreases and \nchanges over to positive values consistent with positive magnetization at high fields. The initial \nincrease is consistent with the increase in ne gative magnetization for low magnetic fields.  \nIn conclusion, we have shown that the antiferromagnetic double perovskite compound \nSr2YbRuO 6 shows magnetization reversal, compensation temperature ( M = 0) and negative mag-\nnetization below the magnetic ordering temperatures if the applied magnetic fields are low \n(≤ 2 kOe). Both the magnetization and heat capac ity measurements clearly indicate the presence \nof two components of the magnetic orderi ng, which are assumed to be due to Ru5+ and Yb3+ mo-\nments. Magnetization reversal is explained using the available models. In order to provide an ex-\nact explanation for the observed anomalous beha viour, detailed neutron diffraction measurements \nare necessary.  REFERENCES \n[1] Neel L 1948 Ann. Phys . 3 137  \n[2] Menyuk N, Dwight K and Wickham D G 1960 Phys. Rev. Lett . 41 119  \n[3]  Shirakawa N and Ishikawa M 1991 Jpn. J. Appl. Phys.  30 L755 \n[4 ] Mahajan A V, Johnston D C, Torgeson D R and Borsa F 1992 Phys. Rev. B  46 10966  \n[5] Ren Y, Palstra T T M, Khomskii D I, Pe llegrin E, Nugroho A A, Menovsky A A and Sa-\nwatzky G A 1998 Nature 396 441 \n[6] Ren Y, Palstra T T M, Khomskii D I, Nugr oho A A, Menovsky A A and Sawatzky G A 2000 \nPhys. Rev. B  62 6577 \n[7] Kimishima Y, Chiyanagi Y, Shimizu K and Mizuno T 2000 J . Magn. Magn. Mater . 210 244  \n[8] Kimishima Y, Uehara M and Saitoh T 2002 Solid State Commun . 133  559  \n[9] Adachi H and Ino H 1999 Nature 401 148  \n[10] Cooke A H, Martin D M and Wells M R 1974 J. Phys. C: Solid State Phys . 7 31333  \n[11] Yoshii K 2001 J. Solid State Chem.  159 204  \n[12] Yoshii K, Nakamura A, Ishii Y and Morii Y 2001 J. Solid State Chem . 162 84  \n[13] Dzyaloshinsky I 1958 J. Phys. Chem. Solids  4 241 \n[14] Moriya T 1960 Phys. Rev . 120 91 \n[15] Ngueyen H C and Gooodenough J B 1995 Phys. Rev. B  52 324  \n[16] Donohue P C and McCann E L 1977 Mat.  Res. Bull.  12 519  \n[17] Battle P D and Macklin W J 1984 J. Solid State Chem . 54 245  \n[18] Ovchinnikov S G 2003 Physics – Uspekhi  46 21  \n[19] Sakai C, Doi Y, Hinatsu Y and Ohoyama K 2005  J. Phys.: Condens. Matter 17 7383 \n[20] Gibb T C and Greatrex R 1980 J. Solid State Chem  34 279  \n[21] Nowik I, Felner I 2001 J. Magn. Magn. Mater . 237  1 \n[22] Greatrex R, Greenwood N N, Lal M and Fernandez I 1979 J. Solid State Chem . 30 137  \n[23] Doi Y and Hinatsu Y 1999 J. Phys.: Condens. Matter  11 4813 \n[24] Doi Y, Hinatsu Y, Nakamura A, Ishii Y and Morii Y 2003 J. Mater. Chem . 13 1758  \n[25] Martin C A 1991 J. Phys.: Condens. Matter  3 5967 \n[26] Blake G R, Palstra T T M, Ren Y, Nugroho A A and Menovsky A A 2002 Phys. \nRev. B  65 174112  \n[27] Singh R. P. et al (unpublished).  Singh R P and Tomy C V 2008  Anomalous Mag-\nnetic Properties of Sr 2YRuO 6 Preprint arXiv:0802.2953  \n[28] Kuz’min E V, Ovchinnikov S G and Singh D J 2003 Phys. Rev. B  68 024409 \n[29] Cao G, Xin Y, Alexander C S and Crow J E 2001 Phys. Rev. B  63, 184432  "    },    {        "title": "0711.1101v1.Magnetic_properties_of_bi_phase_micro__and_nanotubes.pdf",        "content": "arXiv:0711.1101v1  [cond-mat.mtrl-sci]  7 Nov 2007Magnetic properties of bi-phase micro- and nanotubes\nJ. Escrig1, D. Altbir1, and K. Nielsch2\n1Departamento de F´ ısica, Universidad de Santiago de Chile, USACH, Av. Ecuador 3493, Santiago, Chile\n2Max-Planck-Institut of Microstructure Physics, Weinberg 2, 06120 Halle, Germany\n(Dated: November 2, 2018)\nThe magnetic configurations of bi-phase micro- and nanotube s consisting of a ferromagnetic in-\nternal tube, an intermediate non-magnetic spacer, and an ex ternal magnetic shell are investigated\nas a function of their geometry. Based on a continuum approac h we obtained analytical expressions\nfor the energy which lead us to obtain phase diagrams giving t he relative stability of characteristic\ninternal magnetic configurations of the bi-phase tubes.\nPACS numbers: 75.75.+a,75.10.-b\nI. INTRODUCTION\nThe fabrication of ultra-highly magnetic recording me-\ndia has become one of the great challenges in the field of\nmagnetism. It is well known that in conventional record-\ning media, composed of weakly coupled magnetic grains,\nthe areal density is limited by the so-called superparam-\nagnetic effect, [1] which arises as the grain size is reduced\nbelow 10 nm. In such a case, thermal fluctuations in the\nmagnetic moment orientation may lead to loss of infor-\nmation. In order to increase the recording densities, new\nmagnetic elements need to be proposed.\nPatterned magnetic media consisting of regular ar-\nrays of magnetic layered nanodots [2] or nanorings [3]\nhave been considered as providing the basis for extend-\ning magnetic storage densities beyond the superparam-\nagnetic limit. In such systems, a single dot or ring with n\nmagnetic layers, whose volume is much larger than those\nofthegrainsinconventionalrecordingmedia, mightstore\nupto2nbits, beatingthermalfluctuationsandincreasing\nthe recording density by a factor of 2n−1.\nRecently, magnetic nanotubes can be (chemically)\nfunctionalized on the in- and outside, [4, 5, 6] motivat-\ning a new field of research. Nanotubes exhibit a core-\nfree magnetic configuration leading to uniform switching\nfields, guaranteeing reproducibility [6, 7] and have been\nproposed to be used as bi-directional sensors by Lee et\nal. [8] Also due to their low density they can float in so-\nlutions, making them suitable for biological applications\n(see [4] and references therein). Numerical simulations\n[6, 9] and analytical calculations[7, 9] on such tubes have\nidentified two main ideal magnetic configurations: a fer-\nromagnetic state with all the magnetic moments point-\ning parallel to the axis of the tube ( c= 1) and an in-\nplane magnetic ordering, namely the flux-closure vortex\nstate (c= 2). However, in tubes with low aspect ratio\n(L/R≤10), another state with two opposite directed\nvortices with a domain wall between them can appear.\n[6, 8] Similar nano-objects, bi-phase microwires consist-\ning of two metallic layers, a cylindrical nucleus and an\nexternal magnetic microtube, separated by an interme-\ndiate nonmagnetic microlayer, have been introduced by\nPirotaet al. [10] .\nThe synthesis of bi-phase microwires and magneticnanotubes opens the possibility of fabricating bi-phase\nmicro- and nanotubes, where new magnetic phases can\nappear. Because of the geometry, the internal and exter-\nnal tubes can be close enough to interact via a strong\ndipolar coupling. This interaction can produce new\nmagnetic states of the cylindrical particle as a whole,\n[11] which can be used for particular applications. Be-\nsides, we can expect the appearance of new magnetic\nproperties, like the dipolar magnetic bias responsible for\nthe giant magnetoimpedance behavior of amorphous mi-\ncrowires. [12] The possibility of achieving such a, spin-\nvalve-like, hysteresis loop is very attractive because of\npotential applications to sense magnetic fields in mag-\nnetic recording systems.\nFIG. 1: (a) Geometrical parameters and (b) characteristic\nmagnetic configurations of a bi-phase micro- and nanotube.\nThepurposeofthispaperistoinvestigatethemagnetic\nordering of bi-phase tubes. Our cylindrical particle, of\nlengthL, consists of two magnetic tubes separated by\na nonmagnetic spacer. The internal (external) tube is\ncharacterized by its outer Ri(Re) and inner ai(ae) radii,\nas illustrated in figure 1(a). Magnetic configurations of\nthebi-phasetubes canbeidentified bytwoindices[ ci,ce],\nwhereci,ce= 1 or 2 denote the magnetic configurations\nof the internal and external magnetic tubes, respectively\n(see figure 1(b)).2\nII. TOTAL ENERGY CALCULATIONS\nWe adopt a simplified description of the system, in\nwhich the discrete distribution of magnetic moments is\nreplaced by a continuous one characterized by a slowly\nvarying magnetization density /vectorM(/vector r). The total energy\nE[ci,ce]\ntotis generally given by the sum of three terms,\nthe magnetostatic E[ci,ce]\ndip, the exchange E[ci,ce]\nex, and the\nanisotropy contributions. Here we are interested in soft\nor polycrystalline magnetic materials, in which case the\nanisotropy contribution is usually disregarded. [4, 6]\nThe total magnetization can be written as /vectorM(/vector r) =\n/vectorMi(/vector r) +/vectorMe(/vector r), where /vectorMi(/vector r) and/vectorMe(/vector r) denote the\nmagnetization of the internal and external tubes, re-\nspectively. In this case, the magnetostatic potential\nU(/vector r) splits up into two components, Ui(/vector r) andUe(/vector r),\nassociated with the magnetization of each individual\ntube. Then, the total dipolar energy can be written\nasE[ci,ce]\ndip=E[ci]\nd+E[ce]\nd+ 2E[ci,ce]\nd,whereE[cp,cq]\nd=\n(µ0/2)/integraltext/vectorMp(/vector r)∇Uq(/vector r)dv, withp,q=i,e. The diag-\nonal terms, E[cp,cp]\nd≡E[cp]\nd, correspond to the dipolar\ncontributions to the self-energy of the individual mag-\nnetictubes, whereastheoff-diagonalterm, E[cp,cq]\nd, corre-\nsponds to the dipolar interaction between the two tubes.\nThe exchange energy E[cp,cq]\nexalso has three contri-\nbutions, two coming from the direct exchange interac-\ntion within the magnetic tubes, and the other one from\nits indirect interaction mediated by the non-magnetic\nspacer. We focus on systems in which the thickness of\nthe intermediate tube, ds=ae−Ri, is large enough\nto make negligible the indirect exchange interaction be-\ntween the two magnetic tubes across the non-magnetic\none. A good estimate of the range of the indirect\nexchange interaction can be obtained from results for\nmultilayers.[13] In general the interlayer exchange cou-\npling vanishes for spacer thicknesses greater than a few\nnanometers. Here we focus our attention on those cases\nin which dsis bigger than 5 nm, thus, to a good ap-\nproximation, E[cp,cq]\nexcan be written as E[ci]\nex+E[ce]\nex,\nwithE[cp]\nex=A/integraltext/bracketleftBig\n(∇mpx)2+(∇mpy)2+(∇mpz)2/bracketrightBig\ndv,\n[14]/vector mp= (mpx,mpy,mpz) =/vectorMp/M0is the magneti-\nzation of tube pnormalized to the saturation magnetiza-\ntionM0andAis the stiffness constant of the magnetic\nmaterial.\nThe total energy of the multilayered structure can be\nwritten in the form E[ci,ce]\ntot=E[ci]\nself+E[ce]\nself+E[ci,ce]\nint,\nwhereE[cp]\nself=E[cp]\nd+E[cp]\nexis the self-energy of each\nmagnetic tube, and E[ci,ce]\nint= 2E[ci,ce]\ndis the (dipolar) in-\nteraction energy between them. We now proceed to cal-\nculate the energy terms in the expressionfor E[c1,c2]\ntot. Re-\nsults are given in units of µ0M2\n0l3\nex, i.e,˜E=E/µ0M2\n0l3\nex,\nwherelex=/radicalbig\n2A/µ0M2\n0.\nIn order to perform the integrals in the above expres-\nsions, it is necessary to specify the functional form of themagnetization density for each configuration. For c= 1,\n/vectorMp(/vector r) can be approximated by M0ˆz, where ˆzis the unit\nvector parallel to the axis of the tube. In this case, we\nfind that the reduced self-energies take the form\n˜E[1]\nself(p) =πR2\np\nl3ex∞/integraldisplay\n0dq\nq2/parenleftbig\n1−e−qL/parenrightbig\n(J1(qRp)−βpJ1(qap))2,\nwithJ1(z)aBesselfunction offirst kind. In this case, the\nexchange contribution to the self-energy vanishes. For\nc= 2,/vectorMp(/vector r) can be approximate by M0ˆφ, where ˆφ\nis the azimuthal unit vector. In such case the dipolar\ncontribution to the self-energy turns out to be equal to\nzero, and ˜E[2]\nself(p) =−(πLlnβp)/lex. We have defined\nβp=ap/Rp.\nRegardingthe interaction between the magnetic tubes,\nthe only non-zero terms correspond to the case in which\nbothtubesareinthe c= 1configuration. Duetothecon-\ndition of perfect flux closure in the vortex configuration,\na magnetic tube in such a configuration does not interact\nwith another, independently of the magnetic configura-\ntion of the latter. Thus, we end up with just\n˜E[1,−1]\nint=−2πRiRe\nl3ex∞/integraldisplay\n0dq\nq2/parenleftbig\n1−e−qL/parenrightbig\n(J1(qRi)−βiJ1(qai))(J1(qRe)−βeJ1(qae)).\nThe minus sign in the superscript of ˜E[1,−1]\nintindicates\nthat the relative orientation of the magnetization of the\ninternal and external tubes is antiparallel. We remark\nthat, due to the dipolar interaction between the tubes,\nthe total energyofthe [1 ,1] configurationis alwayslarger\nthan the total energy of [1 ,−1].\nIII. RESULTS AND DISCUSSION\nWe are now in position to investigate the relative sta-\nbility of the various [ ci,ce] configurations. We consider\nnickel(lex= 8.225nm) andcobalt ( lex= 2.849nm) mag-\nnetic bi-phase tubes. However, to properly describe this\ngeometry we need to deal with five different geometri-\ncal parameters. In order to simplify the illustration of\nour results, we present phase diagrams in terms of di/de,\nwheredi=Ri−aiis the thickness of the internal mag-\nnetic tube and de=Re−aerepresents the thickness of\nthe external magnetic shell, as illustrated in figure 2.\nWe start by investigating systems with fixed ai= 10\nnm andds= 50 nm. Figure 3 illustrates the phase dia-\ngrams, giving the regions within which one of the [ ci,ce]-\nconfigurations is of lowest energy for different nanotube\nlengths. The diagrams show the existence of only three\nphases, correspondingto the configurations [1 ,−1], [1,2],\nand [2,2]. The absence of the [2 ,1] phase can be under-\nstood from the work by Escrig et al. [3] By inspecting\nthe phase diagram for magnetic tubes presented in that3\nFIG. 2: Geometrical parameters and limits of a bi-phase\nmicro- and nanotube.\nwork we can see that, for fixed length, it is easier to find\na vortex state for bigger external radius. Then it will be\nmuch difficult to find a bi-phase tube with the inner tube\nin the vortex phase and the external tube, which has a\nbigger radius than the internal one, in the ferromagnetic\nphase. The [2 ,1] phase is even less probable in this inter-\nacting regime, because the dipolar interaction between\nthe tubes will favor the antiferromagnetic-like coupling.\nBy inspecting the energy equation we observe that the\n[2,1] phase appears only in the limit di/de→ ∞. Be-\nsides, we observe that a shorter bi-phase tube favors the\nappearance of vortex configurations. It is worth men-\ntioning that in our model the [2 ,−2] configuration, cor-\nresponding to a vortex and an anti-vortex, and the [2 ,2]\none have the same energy, since in both cases the mag-\nnetic nanotubes do not interact. In what follows we shall\nrefer to both as [2 ,2]-configurations. By comparing our\nresults for Ni and Co we observe differences in the be-\nhavior of the triple point as a function of L. By looking\nto phase diagrams for isolated tubes, [3] we observe that\na vortex phase appears at smaller external radii of a Co\ntube than in a Ni one because lex(Co)≈3lex(Ni). This\neffect is also present in bi-phase tubes, where the triple\npoint occurs for smaller Rein Co. Because lexis bigger\nin Ni than in Co, by varying the geometry of the sys-\ntem, the triple point will experience stronger effects in\nCo than in Ni.\nThe dependence of the whole diagram on dsis illus-\ntrated in figure 4. In a first inspection of the figures it\nseems that the main role in this case is played by the\nmaterial specified in our calculations by lex. However it\nis important to recallthat the ordinate is given by a com-\nposed parameter, which makes it complex to determine\nfrom the figure the magnetic behavior of the system. Be-\ncause the interaction between the tubes contributes to\nstabilize the [1 ,−1] phase, the decay of the dipolar in-\nteraction between the tubes as a function of dsincreases\nthe energy of the [1 −1] phase, leading to the appear-\nance of the other phases. We illustrate this point with\nan example. Let us consider a bi-phase Ni tube defined\nbyai= 10 nm, di= 30 nm, de= 150 nm and L= 6\nµm. In this case di/de= 0.2. If the cylindrical particle\nis defined by ds= 5 nm, Re= 195 nm, and from figure/s48 /s50/s48/s48 /s52/s48/s48 /s54/s48/s48 /s56/s48/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54\n/s67/s111 /s78/s105\n/s91/s49/s44/s50/s93/s91/s50/s44/s50/s93\n/s82\n/s101/s32/s40/s110/s109/s41/s91/s50/s44/s50/s93/s91/s49/s44/s45/s49/s93\n/s91/s49/s44/s45/s49/s93\n/s82\n/s101/s32/s40/s110/s109/s41/s32/s32/s100\n/s105/s32/s47/s32/s100\n/s101\n/s48 /s50/s48/s48 /s52/s48/s48 /s54/s48/s48 /s56/s48/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54\n/s91/s49/s44/s50/s93\n/s32/s32\nFIG. 3: (color online) Variable tube length. Phase diagrams\nfor bi-phase nanotubes with ai= 10 nm, ds= 50 nm and\nL= 1µm (dashed lines), 6 µm (solid lines), and 10 µm\n(dotted lines).\n/s48 /s50/s48/s48 /s52/s48/s48 /s54/s48/s48 /s56/s48/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54\n/s91/s49/s44/s50/s93\n/s82\n/s101/s32/s40/s110/s109/s41 /s82\n/s101/s32/s40/s110/s109/s41/s78/s105\n/s91/s50/s44/s50/s93/s91/s49/s44/s45/s49/s93\n/s32/s32\n/s48 /s50/s48/s48 /s52/s48/s48 /s54/s48/s48 /s56/s48/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54\n/s91/s49/s44/s50/s93/s100\n/s105/s32/s47/s32/s100\n/s101/s67/s111\n/s91/s50/s44/s50/s93/s91/s49/s44/s45/s49/s93\n/s32/s32/s32\nFIG. 4: (color online) Variable thickness of the spacer laye r.\nPhase diagrams for bi-phase nanotubes with ai= 10 nm,\nL= 6µm andds= 5 nm (dashed lines), 50 nm (solid lines),\nand 100 nm (dotted lines).\n4 we observe that the nano-object will exhibit a [1 ,−1]\nphase. But if for the same geometry we chose ds= 100,\nthenRe= 290 and the cylindrical particle will be in the\n[1,2] phase.\nWe now turn our attention to the case in which ai\nis the variable (see figure 5). Here, a strong shift of the\ntransitionlinesisevidenced asvaryingthe internalradius\nof the nano-object. In particular, for geometries defined\nby parameters inside the dark region, the system can\nexhibit any of three ideal phases, depending on the value\nofai. Then a clear determination of aiis fundamental\nwhen a particular magnetic phase is searched for. In\nthese figures, a clear predominance of the [1 ,−1] phase\nappears while increasing ai. By increasing aiwith fixed4\nRe,dsanddi/de,Riandaenecessarily increase. In this\nway, both tubes havelesscross-sectionarea, and then the\nsystem prefers the ferromagnetic phase [1 ,−1].\n/s48 /s50/s48/s48 /s52/s48/s48 /s54/s48/s48 /s56/s48/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54\n/s91/s49/s44/s50/s93/s91/s50/s44/s50/s93/s91/s49/s44/s45/s49/s93/s78/s105\n/s32/s32\n/s48 /s50/s48/s48 /s52/s48/s48 /s54/s48/s48 /s56/s48/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54\n/s91/s49/s44/s50/s93\n/s82\n/s101/s32/s40/s110/s109/s41/s82\n/s101/s32/s40/s110/s109/s41/s100\n/s105/s32/s47/s32/s100\n/s101\n/s91/s50/s44/s50/s93/s91/s49/s44/s45/s49/s93/s67/s111\n/s32/s32/s32\nFIG. 5: (color online) Variable internal radius ai. Phase di-\nagrams for bi-phase nanotubes with ds= 50 nm, L= 6µm\nandai= 10 nm (solid lines), 30 nm (dotted lines), and 60 nm\n(dashed lines). Inside the dark region, the system can exhib it\nany of three ideal phases, depending on the value of ai.\n/s50/s48 /s51/s48 /s52/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54\n/s97/s41\n/s91/s50/s44/s50/s93/s91/s49/s44/s45/s49/s93\n/s32/s32\n/s50/s48 /s51/s48 /s52/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54\n/s98/s41\n/s91/s50/s44/s50/s93/s91/s49/s44/s45/s49/s93\n/s82\n/s101/s32/s40µ /s109/s41/s100\n/s105/s32/s47/s32/s100\n/s101\n/s82\n/s101/s32/s40µ /s109/s41\n/s32/s32\nFIG. 6: (color online) Phase diagrams for bi-phase microtub es\nwith a)ai= 5µm,L= 1 cm and ds= 1µm (dashed lines), 5\nµm (solid lines), and 10 µm (dotted lines) and b) ds= 5µm,\nL= 1 cm and ai= 3µm (dashed lines), 5 µm (solid lines),\nand 7µm (dotted lines).\nWe also look to the phase diagrams of bi-phase mi-\ncrotubes. In this case, for the range of diameters and\nlengths considered, the transition lines are almost inde-\npendent of the magnetic material. Our results are sum-\nmarized in figure 6, describing the phases for any mag-\nnetic material. Figure 6(a) illustrates the dependence\nof the phase diagram on ds, and figure 6(b) shows the\nbehavior of the whole diagram with ai. The diagramspresent only two regions, corresponding to the phases\n[1,−1] and [2 ,2]. The [1 ,2] phase is suppressed for di-\nameters in the range of the micrometers, as expected\nfrom previous figures. Pirota et al. [10] and V´ azquez\net al.[15] have investigated the magnetic behavior of\ndifferent multilayer microwires. Hysteresis loops clearly\nexhibit two Barkhausen jumps, each related to the re-\nversal of one of the tubes. For small values of di/de,\nthey observe that these Barkhausen jumps are smooth,\nshowing the existence of non-homogeneous states during\nthe reversal of each tube. This qualitative observation is\nin agreement with our phase diagrams, which show that\nthe [2,2] configurations, which exhibit non-homogeneous\nreversion, appear preferably for small di/de. By compar-\ning our results for nano- and microtubes we observe that\nthe [2,2] phase appears preferably in cylindrical particles\nwith large diameters.\nInourcalculationsweconsideredsoftorpolycrystalline\nmaterialsandthen anisotropywasdisregarded. However,\nin crystalline materials anisotropy plays a fundamental\nrole, as shown by Escrig et al.[16] In fact, the existence\nofastronguniaxialanisotropy,asinCo, favorsthe[1 ,−1]\nphase,decreasingtheothertwophases, speciallythe[2 ,2]\none. Nickel has a weak cubic anisotropy with K <0,\nwhich will enhance the [2 ,2] phase.\nIV. CONCLUSIONS\nIn conclusion, we have studied the relative stability\nof ideal configurations of magnetic bi-phase micro- and\nnanotubes composed by an internal magnetic tube, an\nintermediate non-magnetic spacer and an external mag-\nneticshell. Insuchsystemsweinvestigatedthe sizerange\nof the geometric parameters for which different config-\nurations are of lowest energy. Results are summarized\nin phase diagrams which clearly indicate that the mag-\nnetic behavior of such structures can be tailored to meet\nspecific requirements provided a judicious choice of such\nparameters is made. This includes not just the control\nover the number of magnetic configurations the system\nmightexhibits, butalsothepossibilityofsuppressingspe-\ncific phases. The lines separating the magnetic phases\nand, in particular, the triple point, are very sensitive to\nthe geometry of the bi-phase tube. Results in nanotubes\nstrongly depend on the material, defined by its exchange\nlength. However, in microtubes the [1,2] phase is sup-\npressed and the phase diagrams are almost independent\nof the material. For magnetic bi-phase tubes with di-\nameter of less than 100 nm, the [1 ,−1] configuration is\nalways present. Besides, we can conclude that for multi-\nlayertubes where total Mi≥Mewe always find the anti-\nferromagnetic alignment. The phase diagrams presented\ncan provide guidelines for the production of nanostruc-\ntures with technological purpose such as the fabrication\nof sensor devices.5\nAcknowledgments\nThis work has been partially supported in Chile by\nFONDECYT 1050013,Millennium Science Nucleus Con-\ndensed Matter Physics P02-054F and a CONICYT PhD\nProgramFellowship. Financialsupportfromthe GermanFederal Ministry for Education and Research (BMBF,\nProject No 03N8701) is gratefully acknowledged. JE is\ngrateful to the Max-Planck-Institut for Microstructure\nPhysics, Halle, for its hospitality. We thank M Daub\nand P Landeros for useful discussions.\n[1] C. A. Ross, Annual Review of Materials Science 31, 203\n(2001).\n[2] M. Albrecht, G. Hu, A. Moser, O. Hellwig, and B. D.\nTerris, J. Appl. Phys. 97, 103910 (2005).\n[3] J. Escrig, P. Landeros, D. Altbir, M. Bahiana, and J.\nd’Albuquerque e Castro, Appl. Phys. Lett. 89, 132501\n(2006).\n[4] K. Nielsch, F. J. Castano, C. A. Ross, and R. Krishnan,\nJ. Appl. Phys. 98, 034318 (2005).\n[5] Kornelius Nielsch, Fernando J. Castano, Sven Matthias,\nWoo Lee, and Caroline A. Ross, Adv. Eng. Mat. 7, 217-\n221 (2005).\n[6] Z. K. Wang et al, Phys. Rev. Lett. 94, 137208 (2005).\n[7] J. Escrig, P. Landeros, D. Altbir, E. E. Vogel, and P.\nVargas, J. Magn. Magn. Mater. 308, 233-237 (2007).\n[8] J. Lee, D. Suess, T. Schrefl, Oh K. Hwan, and J. Fidler,\nJ. Magn. Magn. Mater. 310, 2445-2447 (2007).\n[9] P. Landeros, S. Allende, J. Escrig, E. Salcedo, D. Altbir ,and E. E. Vogel, Appl. Phys. Lett. 90, 102501 (2007).\n[10] K. Pirota, M. Hernandez-Velez, D. Navas, A. Zhukov,\nand M. V´ azquez, Adv. Funct. Mater. 14, 266-268 (2004).\n[11] Q. Xiao, R. V. Krotkov, and M. T. Tuominen, J. Appl.\nPhys.99, 08G305 (2006).\n[12] J. P. Sinnecker, A. de Araujo, R. Piccin, M. Knobel, and\nM. V´ azquez, J.Magn. Magn.Mater. 295, 121-125(2005).\n[13] P. J. Bloemen, M. T. Johnson, M. T. H. van de Vorst, R.\nCoehoorn, J. J. de Vries, R. Jungblut, J. van de Stegge,\nA. Reinders, and W. J. M. de Jong, Phys. Rev. Lett. 72,\n764 (1994).\n[14] A. Aharoni, Introduction to the Theory of Ferromag-\nnetism(Oxford: Clarendon Press, 1996) p 135.\n[15] M. V´ azquez, K. Pirota, J. Torrej´ on, G. Badini, and A.\nTorcunov, J. Magn. Magn. Mater. 304, 197-202 (2006).\n[16] J. Escrig, P. Landeros, D. Altbir, and E. E. Vogel, J.\nMagn. Magn. Mater. 310, 2448-2450 (2007)."    },    {        "title": "0711.1978v1.Magnetic_nanowires_as_permanent_magnet_materials.pdf",        "content": " 1Magnetic nanowires as permanent magnet materials. \n \nT. Maurer, F. Ott, G. Chaboussant,  \nLaboratoire Léon Brillouin CEA/CNRS UMR12 , Centre d’Etudes de Saclay, 91191 Gif sur Yvette, \nFrance \n \nY. Soumare, J.-Y. Piquemal,  \nITODYS Université Paris 7- Denis Diderot, UMR CNRS 7086 2, place Jussieu 75251 cedex05 Paris, \nFrance \n \nG. Viau,  \nLaboratoire de Physique et Chimie des Nano-Objets, INSA de Toulouse, UMR CNRS 5215,  135 av. \nde Rangueil 31077 Cedex 4 Toulouse, France \n \n \n \nAbstract : \nWe present the fabrication of metallic magnetic nanowires using a low temperature chemical process. \nWe show that pressed powders and magnetically oriented samples exhibit a very high coercivity (6.5 \nkOe at 140K, 4.8 kOe at 300K). We discuss the magnetic properties of these meta-materials and show \nthat they have the suitable properties to realize “high-temperature magnets” competitive with AlNiCo \nor SmCo permanent magnets. They could also be used as recording media for high density magnetic \nrecording. \nKeywords : permanent magnets, nanowires, composite \n \n \n \n \n \n \n \nIn the 1960’s, magnets made of elongated single domain (ESD) particles were commercialized under \nthe name of Lodex [1-3]. However their performances were limited and they were superseded in the \n70’s by Rare-Earth (RE) magnets. In this letter, we revisit the subject and present an original way of \nsynthesizing ESD particles which could be used to fabricate materials with a high remanence and a \nhigh coercivity. These ESD particles are nanowires made of 3d transition metals with potentially high \nCurie temperature. One interesting aspect is that they are produced using a low temperature chemical \nroute enabling large scale fabrication. Moreover, the key advantage of these objects is their very large \nshape anisotropy which provides a high intrinsic coercivity to the material.  \n \nCo80Ni20 nanowires are synthesized by reduction in liquid polyol according to a procedure previously \nreported [4-5]. After synthesis, the black magnetic metal powder is collected by centrifugation and \nwashed several times with ethanol. TEM observations show nanowires with a mean diameter dm of 6.8 \nnm and a mean length Lm of 240 nm (Fig. 1). The standard deviation on the diameter distribution σd is \nsmall (σd/dm = 10%) and the length distribution is broader with a standard deviation σL = 55 nm \n(σL/Lm = 23%). X-ray diffraction patterns show mainly the metallic hcp phase and cobalt oxide CoO \nas a minor phase. High resolution electron microscopy shows very well crystallized wires with the \ncrystallographic c-axis parallel to the wires. The overall composition of Co80Ni20 is evidenced by \nchemical analysis on powders. \n \nThe magnetic properties were characterized by standard magnetometry (SQUID and VSM). Dried \npowders were compressed. The density of the pressed powders was 4.4 g.cm-3. A typical hysteresis \ncycle is presented on Figure 2. The sample exhibit a relatively high coercive field: Hc = 286 kA/m = \n3.6 kOe. The saturation magnetization of the powder is in the range 8.2x10-5 – 10.7x10-5 T.m3/kg (65 -  285 emu.g-1). If normalized by the bulk density of the material, one obtains M = 581 – 758 kA/m (4πM \n= 7.3 - 9.4 kG). This is lower than the bulk values for Co80Ni20 alloys M = 1230 kA.m-1 (4πM = 15.4 \nkG). This reduced magnetization is attributed to superficial oxidation of the nanowires (observed \nalready with high resolution TEM). The Curie temperature TC of our nano-objects is expected to be \nrelatively high since the magnetization is reduced by only 10% at 240°C (Fig 2). We estimate that TC \nis thus at least above 600°C. \n \nSince the most interesting property of these nano-objects is their shape anisotropy (Lm/dm>20), we \ntried to align the wires in order to increase the overall anisotropy of the material. In a first process, the \nparticles were dispersed in liquid toluene. A magnetic field of 10 kOe was applied during the freezing \nof the solution (Tf = 180 K). The magnetization was measured at 140K (see Figure 3). The square \nshape of the hysteresis loop suggests that the particles are well aligned in the solid toluene matrix. The \ncharacteristics of the sample are significantly improved: the coercive field is increased to 517 kA/m \n(6.5 kOe), compared to 286 kA/m for powder samples while the remanence is 0.974 Ms. Therefore, the \nnanowires alignment has significantly enhanced the anisotropy effects. This process however requires \nto work at low temperatures to freeze the particles solvent. \n \nIn order to produce solid samples at room temperature, a second process was devised. The particles \nwere dispersed in a polymer solution (PMMA + toluene) and we let the material solidify under a \nmagnetic field while the solvent was evaporating. The nanowires are expected to align along the \nmagnetic field direction. We will refer to this direction as the easy axis while the perpendicular axis is \nreferred to as the hard axis. Results obtained at T=300K are presented on Figure 4. Due to a partial \nalignment of the particles, the magnetic characteristics have been improved compared to the bulk \nsamples. The remanence has increased to 0.85 Ms for the nanowires aligned along the easy axis \n(compared to 0.65 Ms for powder samples). Similarly, the coercive field has increased from 286 kA/m \n(3.6 kOe) to 381 kA/m (4.8 kOe).  \n \nThe two different processes discussed above show that a significant coercivity increase can be \nachieved through nanowire alignment at either low temperature (140K) or room temperature. A direct \ncritical comparison of these techniques should however consider the significant effect of temperature \non the magnetocrystalline anisotropy [6]. Here, we are in the regime T<<TC and thus the shape \nanisotropy, which depends on the saturated magnetization Ms and the demagnetising factor N like K ∼ \n(1-N)Ms2, is virtually temperature-independent. \n \nTo extract quantitative information about the ordering of the particles in the frozen solution and in the \npolymer matrix, we considered the Stoner-Wohlfahrt model [7]. This model is well suited since our \nnanowires are a limiting case of very elongated ellipsoids, almost monodispersed and with excellent \ncristallinity. The diameter of the wires is sufficiently small to ensure that we have single domain states \nin our wires [7,8] and we make the assumption that the wires do not interact one with the others. We \nconsider three magnetic energies: the magnetostatic energy, the magneto-crystalline energy  and the \nZeeman energy. The free parameters of the model are the angular distribution of the wire directions \nwhich is assumed to be Gaussian and the magneto-crystalline anisotropy field. The magnetization \nmeasurement on Figure 3 has been modelled with a reasonable accuracy by considering a dispersion of \nthe nanowires orientation of σθ = 10° (HWHM) and by introducing a magneto-crystalline anisotropy \nfield HMC=3 kOe. The distribution of the wires orientations was chosen so as to fit the measured \nremanence. The magneto-crystalline anisotropy was chosen to fit the coercive field. This leads to the \nconclusion that the observed coercivity HC=6.5 kOe is the sum of two equivalent contributions: a \nmagnetocrystalline anisotropy HMC=3 kOe (which is very close to the value for bulk hexagonal cobalt) \nand a shape anisotropy which contributes to Hshape=3.5 kG. The contribution of the shape anisotropy is \nrather disappointing since, for perfectly aligned nanowires, one would expect Hshape = Ms/2 ≈ 7.5 kG. \nHowever, these results must be put in perspective with results obtained on arrays of nanowires grown \nby electrochemical routes [8] which are perfectly aligned but never exhibit coercivities higher than 3 \nkOe even for Fe where the theoretical value could be as high as 10 kOe. We think that these good \nresults are due to the mono-crystalline quality of the wires. The surface defects are very limited  3especially compared to nanowires grown in nanoporous alumina templates for which surface defects \nare often imprinted into the metallic wires.  \n \nWe argue that these composite nanomaterials exhibit very promising magnetic properties, suggesting \nthat they could be used in the fabrication of permanent magnets. Firstly, their single crystal structure \nprovides an extra magneto-crystalline anisotropy and the use of 3d transition metals provides high \nremanence and high TC. Most important, through their strong shape anisotropy, they provide a large \ncoercivity, almost temperature-independent far below TC, so that these nanowires could potentially be \nused as high temperature permanent magnets as are AlNiCo magnets. However, we still have to assess \nthe magneto-crystalline anisotropy contribution at high temperature.  Finally, the low temperature \nsynthesis process can be easily scaled to large volumes. \n \nIn order to fabricate permanent magnets, it is necessary to keep the nanostructuring of the material \nwhich means that it would not be possible to reach a packing density of 1. We estimate that a density \nabout half the bulk value can be used while keeping the shape anisotropy properties. This would lead \nto a magnetization of about 7.5 kG for the bulk material. For such a material, the energy product \nwould be of the order of (BH)max = 3.5kOe x 3.5kG ≈ 12 MGOe. Such energy products are not \ncompetitive with high performances NdFeB permanent magnets [9]. However, preliminary high \ntemperature measurements show a good stability up to 250°C (Fig. 2), thus we think that these \nmaterials could be serious contenders for permanent magnet applications at high temperatures. As \nshown in Figure 5, they could fill a gap between RE magnets like SmCo [9] and  AlNiCo magnets \n[10]. RE magnets have higher coercivities but they show stronger softening upon warming while \nAlNiCo magnets exhibit much lower coercivities in the whole temperature range of interest. In \naddition, the fabrication method is a low temperature chemical process which does not need any \nadvanced metallurgical skills. Another potential application of these materials is their use in magnetic \nrecording media. Their properties are already twice as good as existing materials used for magnetic \ntape recording [11-12].  \n \n \n \nAcknowledgment \nWe are grateful to J.B. Moussy for his help during the VSM measurements, M. Viret for the SEM \npictures and F. Herbst for the TEM images. \n \n \nReferences \n \n \n[1] L.I. Mendelsohn, F.E. Luborsky, T.O. Paine, J. Appl. Phys. 26 (1955), R1274-R1280. \n[2] R.B. Falk, J. Appl. Phys., 37 (1966), R1108-R1112. \n[3] D.J. Craik, R. Lane, J. Appl. Phys., 18 (1967), R1269-R1274. \n[4] D. Ung, G. Viau, C. Ricolleau, F. Warmont, P. Gredin, and F. Fiévet, Adv. Mater., 17 (2005) 338. \n[5] D. Ung, Y. Soumare, N. Chakroune, G. Viau, M.-J. Vaulay, V. Richard, F. Fiévet, Chem. Mater., \n19 (2007) 2084. \n[6] W.J. Carr, Phys. Rev., 109 (1958), R1971-R1976 \n[7] R.C. O’Handley, Modern Magnetic Materials, Principles and Applications, Wiley-Interscience \nPublication. \n[8] D.J. Sellmyer, M. Zheng and R. Skomski, J. Phys.: Condens. Matter,  13 (2001) R433. \n[9] O. Gutfleisch, J. Phys. D: Appl. Phys., 33 (2000) R157-R172 \n[10] E.R. Cronk , J. Appl. Phys, 37 (1966), R1097-R1100 \n[11] L.T. Nguyen, Tichelaar FD, Lodder JC, J. Magn. Magn. Mater., 290–291 (2005) R1294-R1297.  \n[12] C.Wang,Y.Hou, J.Kim and S.Sun, Angew. Chem. Int . Ed. 46 (2007) R1-4 \n[13] J. Degauque, Matériaux à propriétés magnétiques dures : matériaux industriels  M4601 \n(Techniques de l’Ingénieur, Paris, 2001). \n  4 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure 1 :  Co80Ni20 nanowires (TEM image). \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure 2 :  Magnetization (VSM) of a pressed powder sample (T=300K). (Inset) Variation of \nsaturation magnetization with temperature.  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure 3 : Magnetization (SQUID) of the nanowires dispersed in a frozen toluene matrix (solid line).  \nHysteresis cycles calculated using a Stoner-Wohlfahrt model with and without magneto-crystalline \nanisotropy (dashed lines).  \n \n \n \n \n 5 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure 4 : Magnetization of nanowires dispersed in PMMA (along the hard axis and the easy axis) at \nT=300K. \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure 5: Remanence and coercivity for the usual permanent magnets materials at 20°C. The values at \n120°C are indicated as dotted/hashed surfaces. Nanowires, as AlNiCo or ferrites are not very \ntemperature sensitive contrary to rare-earth magnets. Adapted from [13]. \n "    },    {        "title": "0711.2896v1.Room_Temperature_Magnetocaloric_Effect_in_Ni_Mn_In.pdf",        "content": "arXiv:0711.2896v1  [cond-mat.mtrl-sci]  19 Nov 2007Room Temperature Magnetocaloric Effect in Ni-Mn-In\nP. A. Bhobe and A. K. Nigam\nTata Institute of Fundamental Research,\nHomi Bhabha Road, Mumbai-400 005 India.\nK. R. Priolkar\nDepartment of Physics, Goa University,\nTaliegao-Plateau, Goa-403 206 India.\n(Dated: November 30, 2018)\nAbstract\nWe have studied the effect of magnetic field on a non-stoichiome tric Heusler alloy Ni 50Mn35In15\nthat undergoes a martensitic as well as a magnetic transitio n near room temperature. Temperature\ndependent magnetization measurements demonstrate the infl uence of magnetic field on the struc-\ntural phase transition temperature. From the study of magne tization as a function of applied field,\nwe show the occurrence of inverse-magnetocaloric effect asso ciated with this magneto-structural\ntransition. Themagnetic entropy change attains a value as h igh as 25 J/kg-K (at 5 T field) at room\ntemperature as the alloy transforms from the austenitic to m artensitic phase with a concomitant\nmagnetic ordering.\nPACS numbers: 75.30.Kz; 75.30.Sg; 75.40.-s; 75.50Cc\n1Inrecent years, therehasbeenanincreasing awareness toward sincorporatinganalternate\ntechnology for refrigeration that would replace the conventional gas compression/expansion\ntechnique. In this respect, the promising candidates are the magn etic materials that ex-\nhibit an inherent magnetocaloric effect (MCE). With its potential impact on energy saving\nand environment-friendly applicability these magnetic materials are a lso looked up as eco-\nnomically viable option for domestic and industrial refrigeration. Fun damentally, MCE is\na process in which an isothermal variation in the magnetic entropy ta kes place with an\nadiabatic temperature change of the system on the application of m agnetic field. In this\nregard, many rare-earth and transition-metal based alloys have found to show promising re-\nsults. These include the alloys like MnFeP 1−xAsx, Gd5(SiGe) 4, MnAs 1−xSb, La(Fe xSi1−x)13\n[1, 2, 3, 4, 5]. The research for the development of such MCE mater ials is made primarily\nwith two objectives: high MCE around room temperature, low-cost production. Ferromag-\nnetic Heusler alloy, Ni 2MnGa which pertains to the class of shape memory alloy have been\nattracting much attention in view of the giant MCE effect [6]. The fact or responsible for\nthe large entropy change is the first-order structural and conc omitant magnetic transition\ntaking place in the non-stiochiometric composition of this material, als o giving rise to the\npossibility of a magnetic control of shape memory effect. The latest candidates in the field\nof such materials has been alloys with composition Ni 50Mn50−xZxwith Z = Sn, In, Sb [7].\nThese materials share a number of features with Ni-Mn-Ga alloys and also display inter-\nesting magnetic properties [8, 9]. Being rich in Mn content (as compar ed to the Heusler\ncomposition Ni 2MnZ), there are two crystallographic sites occupied by Mn atoms giv ing\nrise to competing antiferromagnetic (AF) exchange along with the u nderlying ferromagnetic\n(FM) order [10]. A certain composition of the Ni-Mn-Sn and Ni-Mn-In a lloys are shown to\nexhibit an inverseMCEeffect inthevicinity ofmartensitic toaustenitic structural tra nsition\n[11, 12]. However, the temperatures where such a phenomenon is o bserved are much below\nthe room temperature. In this paper we present one such compos ition of Ni-Mn-In alloy\nthat undergoes a martensitic as well as a magnetic transition, both occurring in a narrow\ntemperature interval very close to the room temperature. Owing to this fact, an appreciable\nchange in the magnetic entropy is observed at the transformation temperature. The alloy\nhas been thoroughly investigated for its magnetic properties and t he order of the sequential\nphase transitions have been clearly determined.\nPolycrystalline ingot of Ni-Mn-In was prepared by arc-melting the st arting elements\n2(99.99% purity) under argon atmosphere. To attain a good compos itional homogeneity,\nthe ingots were re-melted 4-5 times with a weight loss of ≤0.5% and annealed at the tem-\nperature of 900 K for 48 h in an evacuated quartz ampoule followed b y quenching in cold\nwater. The precise composition of the alloy was determined from ene rgy dispersive x-ray\n(EDX) analysis to be Ni = 50.4 at. %; Mn = 34.5 at. %; and In = 15.1 at. %. Magnetiza-\ntion (M) measurements were performed on a superconducting qua ntum interference device\nmagnetometer (Quantum Design, MPMS-5S) in the temperature ra nge 5 K to 330 K and\nmagnetic field H = 0.01T and 5T. M(H) up to 5T was measured at various temperatures\nnear the region of both, the martensitic and the magnetic transfo rmations with an interval\nof 2 K between each temperature value.\nMagnetization as a function of temperature measured in low magnet ic field of 0.01 T, is\npresented in Fig. 1(a). The sample was initially cooled in the absence of field and data was\ncollected on warming from 5 to 330 K (ZFC), followed by cooling (FC) ba ck to 5 K and\nagain during warming in the presence of field (FW). The ferromagnet ic transition is marked\nby the sharp rise in magnetization at T C= 305 K. Below the magnetic ordering temperature\na sudden drop in magnetization takes place at 302 K with value almost c lose to zero. This\nsignature marks the formation of the new structural phase. The drop in magnetization can\nbe conjectured to be due to the variants of the new crystallograp hic phase being formed that\ntemporarilydisturbsthelocalferromagneticorientation. This arg umentisfurthersupported\nby the large hysteresis in the temperature range of 265-310 K obs erved in ZFC, FC and FW\nmagnetization curves. Though the difference in ZFC and FC curves c an also be interpreted\nto be due to the nonzero coercivity of the ferromagnetic material, the hysteresis between\nFC and subsequent FW curves strongly suggests the presence of a first-order structural\ntransition within this temperature interval. Thus the initial rise and t he subsequent fall in\nmagnetizationwithdecreasing temperaturearesignaturesofthe magnetic(T C=305K)and\nconcomitant martensitic (T M≈302 K) phase transformations that the present Ni-Mn-In\nsystem undergoes. Below 150K, an irreversible behaviour between the ZFC and FC curves is\nobserved with ZFC response lying below the FC. Such irreversibility is a n indication of some\ndegreeoffrustratedspinalignment. Thefrustrationofspinsmay result fromthecompetition\nbetween the underlying ferromagnetic coupling and an incipient antif erromagnetic coupling\nbetween Mn atoms present at two different crystallographic positio ns [10]. The subsequent\nFW curve is seen to retrace the FC curve over this temperature ra nge.\n3Another striking feature in the magnetization curves is the decrea se in intensity of the\npeak-like signature in the vicinity of T M- TCfor the FW curve. This curve also shows\na considerable splitting in the narrow temperature interval. Such a s ignature dictates the\ninfluence ofmagneticfieldonthemartensitictransformation. Prior totheFWmeasurement,\nthe sample undergoes a cooling in some magnetic field (0.01 T in the pres ent case) that\ncauses the T Mto shift to a lower temperature value (295 K) whereas the T Cremains\nunchanged. This gives rise to the observed splitting of the peak-like feature associated with\nmartensitic and magnetic transition in the M(T) curve. Fig. 1(b) tha t represents the FW\nM(T) measurement in magnetic field of 5 T, further supports this ob servation. It is seen\nthat the splitting of peak observed at 295K in the FW curve, shifts t o a lower value of 285\nK in the magnetic field of 5 T. Thus an overall shift in T Mof about -17 K is observed from\nthe initial value of 302 K upon the application of 5 T magnetic field. The lo wering of T M\nin Ni-Mn-In system implies that the magnetic field favors the formatio n of the austenitic\nphase.\nTo further investigate the magnetic properties of this alloy, magne tization isotherms were\nmeasured for different temperatures with an interval of 2 K, both above and below the two\ntransitiontemperatures. Themeasurements were carried out by cooling thesample from330\nKdowntotherequired temperatureofinterest andthenvaryingt hefieldfrom0-5T.Atthe\nsecond order magnetic transition, the magnetization isotherms pr esented in the Fig. 2 show\nBrillouin-like dependence, with a slope that decreases monotonically w ith increasing field.\nWhiletheM(H) inthetemperature interval between 302Kand296Ks how prominent meta-\nmagnetic like characteristics that implies the first order austenite t o martensite structural\nphase transition. The M(H) recorded at very low temperatures sh ow a typical ferromagnetic\nnature. In order to further assess the occurrence of first ord er martensitic and second order\nmagnetic transition in this sample, the Arrott plots were plotted in th e temperature range\nof 280 K≤320 K as shown in Fig. 3. For temperatures around T C= 305 K; the slopes are\npositive throughout, confirming the second-order continuous na ture of the transition in this\nsample. As the T Mis approached, the corresponding Arrott plots exhibit negative slo pes.\nThis criterion has been perviously employed to determine the order o f sequential transitions\nin Ni-Mn-Ga alloys [13] and confirms the first-order nature of the ma rtensitic transition at\n302 K in the present Ni-Mn-In sample.\nFinally, the magnetic entropy change ∆S Mhas been evaluated from the magnetization\n4isotherms using the Maxwell equation:\n∆SM(T,∆H) =/integraldisplayH\n0/parenleftbigg∂M(T,H)\n∂T/parenrightbigg\nHdH (1)\nThe values of the magnetic entropy changes corresponding to the average temperature\nbetween two consecutive M(H) isotherms, calculated by numerical integration using the\nabove expression over the field span of 1 - 5 T are shown in Fig. 4. A sh arp peak, with\na ∆SMvalue of 25 J/Kg-K is found at the temperature of ∼301 K for the magnetic\nfield variation from 1 to 5 T. The obtained value of the maximum in ∆S Mis an excellent\nfeature particularly because it has been observed at room temper ature. This makes the\nNi50Mn35In15alloy a potential candidate for practical applications. This propert y emerges\nas a consequence of spontaneous magnetization at room tempera ture followed by the clear\nmartensitic transition in the narrow temperature interval.\nIn conclusion, we have observed a large magnetic entropy change t aking place at room\ntemperatureinNi 50Mn35In15alloy. Acompletecharacterizationofthemagneticpropertiesof\nthis important material aids to the understanding required for the technological exploitation\nof such materials. Especially, the narrow difference ( ∼2 K) between the structural and\nmagnetic transition temperature and alteration of T Mby magnetic field are remarkable\nproperties that the present alloy exhibits.\n5[1] O. Tegus, E. Br¨ uck, K. H. Buschow and F. R. de Boer, Nature 415, 150 (2002).\n[2] H. Wada, Y. Tanabe, Appl. Phys. Lett. 793302 (2001).\n[3] V. K. Pecharsky and K. A. Gschneidner, Jr., Phys. Rev. Let t.78, 4494 (1997).\n[4] X. X. Zhang, G. H. Wen, F. W. Wang, W. H. Wang, C. H. Yu, G. H. W u, Appl. Phys. Lett.\n773072 (2000).\n[5] S. Fujieda, A. Fujita, K. Fukamichi, Appl. Phys. Lett. 811276 (2002).\n[6] L. Pareti, M. Solzi, F. Albertini and A. Paoluzi, Eur. Phy s. J. B.32, 303 (2003).\n[7] Y. Sutou, Y. Imano, N. Koeda, T. Omori, R. Kainuma, K. Ishi da and K. Oikawa, Appl. Phys.\nLett.85, 4358 (2004).\n[8] T. Krenke, M. Acet, E. F. Wassermann, X. Moya, L. Manosa an d A. Planes, Phys. Rev. B,\n72, 014412 (2005).\n[9] T. Krenke, M. Acet, E. F. Wassermann, X. Moya, L. Manosa an d A. Planes, Phys. Rev. B,\n73, 174413 (2006).\n[10] P. J. Brown, A. P. Grandy, K. Ishida, R. Kainuma, T. Kanom ata, K-U Neumann, K. Oikawa,\nB. Ouladdiaf and K. R. A. Ziebeck, J. Phys.:Condens. Mater., 182249 (2005).\n[11] T. Krenke, E. Duman, M. Acet, E. Wassermann, X. Moya, L. M anosa and A. Planes, Nat.\nMater.4, 450 (2005).\n[12] A. K. Pathak, M. Khan, I. Dubenko, S. Stadler and N. Ali, A ppl. Phys. Lett. 90, 262504\n(2007).\n[13] X. Zhou, W. Li, H. P. Kunkel and G. Williams, Phys. Rev. B, 73, 012412 (2006).\n6FIG. 1: Thermal variation in magnetization of Ni 50Mn35In15measured in an applied field of (a)\n0.01 T. (b) 5 T. Hysteresis between the FC, FH and sudden rise i n ZFC, FC, FH near 300 K are\nsignatures of structural and magnetic transitions respect ively. The influence of magnetic field on\nthe structural transition is evident through the shift obse rved in T M(shown in the inset).\nFIG. 2: Magnetization isotherms measured above and below th e magnetic and structural phase\ntransition in Ni 50Mn35In15. Some of the low temperature isotherms are shown separately in the\nupper panel of the figure.\nFIG. 4: Magnetic entropy change associated with the structu ral and magnetic transition for\nNi50Mn35In15. A large value of 25 J/kg-K is observed at 301 K for 5 T magnetic field.\n/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48 /s51/s48/s48 /s51/s53/s48/s48/s49/s50/s51/s52/s48/s56/s49/s54/s50/s52/s51/s50\n/s50/s54/s48 /s50/s56/s48 /s51/s48/s48 /s51/s50/s48/s48/s46/s48/s52/s56/s49/s50/s49/s54\n/s32/s90/s70/s67\n/s32/s70/s67\n/s32/s70/s87 \n/s32/s32/s77/s97/s103/s110/s101/s116/s105/s122/s97/s116/s105/s111/s110/s32/s40/s101/s109/s117/s47/s103/s109/s41\n/s84/s101/s109/s112/s101/s114/s97/s116/s117/s114/s101/s32/s40/s75/s41/s72/s32/s61/s32/s48/s46/s48/s49/s32/s84/s40/s97/s41/s72/s32/s61/s32/s53/s32/s84\n/s32/s32\n/s40/s98/s41\n/s72/s32/s61/s32/s53/s84/s32 /s32/s32\n/s32/s72/s32/s61/s32/s48/s46/s48/s49/s84\nFIG. 3: Arrott Plots indicating the second order magnetic an d first order structural transition in\nNi50Mn35In15.\n70\r 1\r 2\r 3\r 4\r 5\r0\r10\r20\r30\r40\r50\r0\r 1\r 2\r 3\r 4\r 5\r0\r5\r10\r15\r20\r25\r30\r\n 302 K\r\n 300 K\r\n 298 K\r304 K\r\n320 K\r\n \r \rMagnetization (emu/gm)\r\nMagnetic Field (T)\r\n \r \rMagnetization (emu/gm)\r 10 K\r\n 100 K\r\n 170 K\r\n/s48 /s53/s48/s48 /s49/s48/s48/s48 /s49/s53/s48/s48 /s50/s48/s48/s48 /s50/s53/s48/s48 /s51/s48/s48/s48/s48/s53/s48/s48/s49/s48/s48/s48/s49/s53/s48/s48\n/s32/s51/s50/s48/s32/s75\n/s32/s51/s49/s55/s32/s75\n/s32/s51/s49/s52/s32/s75\n/s32/s51/s49/s48/s32/s75\n/s32/s51/s48/s56/s32/s75\n/s32/s51/s48/s54/s32/s75\n/s32/s51/s48/s52/s32/s75\n/s32/s51/s48/s50/s32/s75\n/s32/s51/s48/s48/s32/s75\n/s32/s50/s57/s56/s32/s75/s32\n/s32/s72/s47/s77/s32/s40/s79/s101/s32/s103/s109/s47/s101/s109/s117/s41\n/s77/s50\n/s40/s101/s109/s117/s47/s103/s109/s41/s50\n8/s50/s55/s53 /s50/s56/s48 /s50/s56/s53 /s50/s57/s48 /s50/s57/s53 /s51/s48/s48 /s51/s48/s53 /s51/s49/s48/s45/s49/s48/s45/s53/s48/s53/s49/s48/s49/s53/s50/s48/s50/s53\n/s32/s32/s83\n/s77/s40/s74/s47/s75/s103/s45/s75/s41\n/s84/s101/s109/s112/s101/s114/s97/s116/s117/s114/s101/s32/s40/s75/s41/s32/s53/s32/s84\n/s32/s51/s46/s53/s32/s84\n/s32/s50/s32/s84\n9"    },    {        "title": "0712.1281v1.Polar_Behavior_in_a_Magnetic_Perovskite_Via_A_Site_Disorder.pdf",        "content": "arXiv:0712.1281v1  [cond-mat.mtrl-sci]  8 Dec 2007Polar Behavior in a Magnetic Perovskite Via A-Site Size Diso rder\nD.J. Singh\nMaterials Science and Technology Division, Oak Ridge Natio nal Laboratory, Oak Ridge, Tennessee 37831-6114\nChul Hong Park\nResearch Center for Dielectric and Advanced Matter Physics ,\nPusan National University, Busan 609-735, Korea\n(Dated: November 1, 2021)\nWe elucidate a mechanism for obtaining polar behavior in mag netic perovskites based on A-site\ndisorderanddemonstratethismechanismbydensityfunctio nal calculations forthedoubleperovskite\n(La,Lu)MnNiO 6with Lu concentrations at and below 50%. We show that this mat erial combines\npolar behavior and ferromagnetism. The mechanism is quite g eneral and may be applicable to a\nwide range of magnetic perovskites.\nPACS numbers: 77.84.Dy,75.50.Dd\nThere is great interest in materials that combine mag-\nnetism and polar behavior, especially multiferroics with\nboth ferromagnetism and ferroelectricity.1,2,3,4,5,6While\nthere are many ferromagnets and many ferroelectrics,\nthere remarkably few materials combining the two prop-\nerties. Arguments have been made explaining this ap-\nparent incompatibility in the case of perovskite ABO3\noxides.5In essence, it is because the best perovskite\nmagnets have magnetic ions on the Bsite, while fer-\nroelectrics, such as BaTiO 3, usually have Bsite ions\nwith no delectrons. Here we elucidate a mecahanism\nfor inducing polar behavior in magnetic perovskites and\ndemonstrate this mechanism by density functional cal-\nculations for a ferromagnetic Ni-Mn double perovskite.\nThis mechanism is quite general and may be applicable\nto a wide range of magnetic perovskites.\nPerovskitelattice instabilities are often understood us-\ning the tolerance factor t= (rO+rA)/√\n2(r+rB),\nwhererO,rA, andrBare the O, A-site and B-site ionic\nradii, respectively.18Ferroelectrics, such as BaTiO 3and\nKNbO 3, havet >1, indicating the that Bsite ion is too\nsmall for its site in the ideal cubic structure. In the ferro-\nelectric ground state of these so-called B-site driven ma-\nterials, this ion off-centers, aided by hybridizationwith O\nstates. There is another important class of ferroelectric\nperovskites, so called A-site driven materials. In these, t\nisnormallylessthanunity, andtheferroelectricityisfrom\noff-centeringof A-siteions. Thisfamilyincludesthe tech-\nnologicallyimportantPbbasedpiezoelectricsand relaxor\nferroelectrics. The essential physics is lone pair stere-\nochemistry, specifically hybridization of Pb and Bi 6 p\nstateswith O pstates.8This classincludes thefew known\nmagnetic ferroelectrics with strong ferroelectric proper-\nties,e.g.BiFeO 3, BiMnO 3,andPbVO 3.9,10,11,12,13With-\nout Pb or Bi, t <1 perovskite structures generally derive\nfromBO6octahedral tilts and not A-site off-centering.\nIons with delectrons are generally larger than d0ions.\nThe majority of magnetic perovskites have t <1, with\nlatticestructuresbasedontilts ofthe BO6octahedraand\nnot ferroelectricity. However, first principles calculations\nhaveshownthat, while thesematerialshavetiltedgroundstates, if the octahedra are prevented from tilting, strong\nferroelectricity may result, with an energy intermedi-\nate between the ideal cubic perovskite structure and the\nground state structure, but closer to the later.14,15,16,17\nThe role of Pb and Bi is then to shift the balance be-\ntween these states to yield ferroelectricity. Here we use\na different approach to shift the balance between these\nstates based on A-site size disorder.15,16,17This is ap-\nplied rare-earth double perovskites, R2MnNiO 6where\nwe obtain polar behavior combined with ferromagnetism\nfor mixtures of large and small rare earth ions. The\nmotivation for this choice is that the charge difference\nδQ=2 between Mn4+and Ni2+and their size difference\n(Shannon radii,18rMn4+=0.67˚A,rNi2+=0.83˚A) indicates\nB-site ordering into the double perovskite structure,19\nand that La 2MnNiO 6and Bi 2MnNiO 6are known to\nform and to be ferromagnetic.20,21,22,23,24,25These two\ncompounds were previously studied by first principles\ncalculations.26,27\nWe used the local density approximation (LDA) in\nthe general potential linearized augmented planewave\n(LAPW) method,28with well converged basis sets in-\ncluding local orbitals.29The LAPW sphere radii were 2.0\na0for La and Lu, 1.9 a0for Ni and Mn and 1.55 a0for\nO.30Mn and Ni atoms were placed in supercells with the\ndouble perovskite (rock-salt) ordering, and various or-\nderings of the A-site ions. The primary results reported\nhere were done with 40 atom supercells. However, the\nlattice parameter was determined by relaxation of a 10\natom cell of compositions LaLuMnNiO 6. No symmetry\nwas imposed, either for the 10 atom or 40 atom cells, but\nfor the 40 atom cells the lattice parameters were held\nfixed at their pseudocubic values as determined from the\nrelaxation of the 10 atom ferromagnetic cell, which as\nshown in Fig. 1 was 3.75 ˚A. For both the parallel and\nantiparallel spin alignments, relaxation of the 10 atom\ncells yielded structures with off-centering of the Lu ions,\ni.e.polar structures, even though perovskite R25type\ntilts are allowed in this cell.\nOur electronic structure for (La,Lu)MnNiO 6is sim-\nilar to those previously found for the Bi and La2\n 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7\n 3.65  3.7  3.75  3.8  3.85  3.9E(eV/f.u.)\na/2(Ang)AF\nFM\nFIG. 1: Energy of 10 atom LaLuMnNiO 6cells vs. pseudocu-\nbic lattice parameter ( a/2) for parallel (FM) and antiparallel\n(AF) Ni and Mn moments. Note that the FM alignment is\nstrongly favored.\n-20-15-10-5 0 5 10 15 20\n-8-6-4-2 0 2 4N(E)\nE(eV)Total\nMn d\nNi d\nFIG. 2: (color online) Electronic densityof states of a10 at om\nferromagnetic LaLuMnNiO 6cell (a=3.77˚A). The peaks at ∼\n-3.7 eV and ∼3.7 eV are the Lu and La fstates, respectively.\nThe projections are onto LAPW spheres.\nanalogues,26,27and show high spin Mn4+and Ni2+. The\nLDAdensityofstatesfortherelaxedferromagneticstruc-\nture ata=3.77˚A is shown in Fig. 2, and schematically\nin Fig. 3. For the various supercells we find either very\nsmall gaps or small band overlaps in the LDA depending\non the exact crystal structure. We also performed some\nLDA+U calculations (not shown). These yield insulat-\ning band structures, with gaps depending on U. Near\nmetallicity is highly unfavorable for ferroelectricity, as\nit means strong electronic dielectric screening that will\nweaken the Coulomb interactions. Nonetheless, we use\nthe LDA to avoid the ambiguity associated with an ad-\njustable parameter ( U) and expect that the prediction of\npolar behavior will be robust.\nThe ferromagnetism is due to the fact that with par-\nallel alignments of the Mn and Ni spins there is a strongMn4+(d3r=0.67Å) Ni2+(d8r=0.83Å)\nt2g(3)eg(2)\nminorityt2g(3)eg(2)\nt2g(3)eg(2)t2g(3)eg(2)\nminority majority majorityEF\nFIG. 3: (color online) Schematic depiction of the electroni c\nstructure of LaLuMnNiO 6showing the dominant superex-\nchange coupling by the arrow.\nTABLE I: Lu displacements for the various supercells. |<\nδ >|is the magnitude of the average Lu displacement, and\n<|δ|>is the average magnitude.\nnLanLu |< δ >|<|δ|>|< δ >|/ <|δ|>\n4 4 “G” 0.243 ˚A 0.396 ˚A 0.61\n4 4 “A” 0.405 ˚A 0.414 ˚A 0.98\n4 4 “C” 0.013 ˚A 0.396 ˚A 0.04\n4 4 “P” 0.201 ˚A 0.403 ˚A 0.48\n5 3 0.379 ˚A 0.379 ˚A 1.00\n6 2 0.331 ˚A 0.331 ˚A 1.00\ncross-gap hybridization of the unoccupied egmajority\nstates of Mn4+with the occupied majority egstates\nof Ni2+, leading to a ferromagnetic coupling consis-\ntent also with the Goodenough-Kanamori rules.31,32,33\nThis ferromagnetic superexchange is particularly strong\nbecause in perovskites the strongest coupling through\nthe near linear B-O-Bbonds is via eg-pσhopping.\nThe strength of this coupling is evident from the siz-\nable crystal field splittings34of both the Mn and Ni d\nstates (Fig. 2). Thus the hybridization between oc-\ncupied and unoccupied egorbitals, allowed for ferro-\nmagnetic alignment, but not for antiferromagnetic align-\nment, strongly favorsferromagnetism. Since the hopping\nis mediated by O this is not direct exchange, like the\nweak ferromagnetic coupling generally associated with\ntheGoodenough-Kanamoriferromagnetism,but isacon-\nventional strong superexchange.33,35,36\nWhile our relaxed structure for the 10 atom cell is po-\nlar, this size supercell favors ferroelectricity (ferroelec-\ntricity arises from a zone center instability, while the\ncompeting tilt modes occur at the zone boundary and\na 10 atom cell restricts tilts to the R-point). We there-\nfore performed supercell calculations with a 2 ×2×2 40\natom supercell. This cell is doubled along the [001], [011]\nand [111] directions and so allows arbitrary mixtures of3\nG(Å) G(Å) G(Å) G(Å)50-50 G\n50-50 A\n50-50 C\n50-50 P\nFIG. 4: (color online) Cation displacements with respect to\ntheir O cages in a 40 atom relaxed supercells of composition\n(La0.5Lu0.5)MnNiO 6.tilt instabilities and accommodates the observed Glazer\npatterns of perovskite tilt systems.37\nAs mentioned, all supercells were for the double per-\novskite structure, i.e.rock-salt ordering of the B-site Ni\nand Mn ions. For the A-site, we considered four arrange-\nments of the Lu and La at a 50–50 composition as well\nas one supercell each for 5/8–3/8 and 3/4–1/4 composi-\ntions. The specific cells at the 50–50 composition were\n(1) rock-salt ordering of La and Lu (“G” in the follow-\ning), (2) (001) layers of La and Lu (“A”), (3) lines of\nLa and Lu along [001] and ordering c(2×2) in plane\n(“C”) and (4) a cell maximizing like near neighbors (La\nat corner and edge centers, Lu at face and body centers,\ndenoted “P”). The 5/8–3/8supercell was constructed by\nreplacing one Lu by La in the cell “G”, while the 75–25\nsupercell was made by substitution of two Lu by La in\nthe same “G” supercell.\nFig. 4 shows the cation positions in the lowest energy\nrelaxed structures for the 50% Lu supercells with respect\nto the centers of their nearest neighbor O cage (nearest\n12 O atoms for the A-site atoms, and nearest 6 O for the\nB-sites ions). The average displacements of the Lu for\nthe various cells are sumarized in Table I. As may be\nseen, in all cases Lu strongly off-centers, by on average\n∼0.4˚A for the 50–50 supercells and slightly less for the\nlower concentration cells. Interestingly, unlike other A-\nsite driven perovskite ferroelectrics,38there is very little\noff-centering of the B-site ions. In fact the largest off-\ncentering aside from Lu are of the La ions and depending\non the supercell these may or may not be parallel to the\nLu.\nThe individual Lu off-centerings tend to avoid [111]\nand equivalent directions, and also tend to be non-\ncollinear with each other for 50% Lu concentration, e.g.\nin the “G” ordering (nominally the highest symmetry\ncase), three of the Lu displace along different Cartesian\ndirections, while the fourth has a smaller displacement\nnear [111]. A preference for Cartesian directions was\nnoted in (K,Li)NbO 3,16and understood from the fact\nthat the square faces of the cage (the faces with the most\nroom for the Li ion) are along these directions. Turning\nto the question of polar behavior, both of the cells at less\nthan 50% Lu concentration show polar structures. At\n50% the cells “G”, “P” and “A” have polar structures,\nmost strongly so for “G”, while “C” is nearly antifer-\nrodistortive, with tilts that avoid compressing the O -\nLa bonds. Of the four supercells investigated the relaxed\n“G”structure had the highest energy. Takingthis energy\nasthezero,thecalulatedenergieswere-0.43eV,-0.36eV,\nand -0.42 eV, for “A”, “C” and “P”, repectively on a per\nformula unit (10 atom) basis. The similarity of the en-\nergies other than “G” show that the A-site ions will be\ndisordered in material made by conventional methods,\nin agreement with what would normally be expected in\nperovskites with chemically similar, same charge, ions.\nWhileintheordered“C”structurestructurealongrange\ntilt pattern of this type is allowed, this will not be the\ncase in general for disordered A-site ions.4\nAssuming that the A-sites are disordered in the al-\nloy, this dependence of polar behavior on chemical order-\ning is more consistent with relaxor ferroelectric behav-\niorthannormalferroelectricity.39,40,41However,it should\nbe kept in mind that the relaxations reported here were\nperformed within the LDA, which also predicts zero or\nvery small band gaps, while in reality larger, but un-\nknown gaps may be present. Larger gaps would lower\nthe electronic dielectric constant favoring ferroelectric-\nity and stronger coupling between the Lu off-centerings.\nWhile actualferroelectricitymayoccur, what canbe con-\ncludedhereisthatpolarbehaviorwilloccurindisordered\n(La,Lu)MnNiO 6for Lu concentrations at or below 50%.\nThis may be ferroelectricity or relaxor ferroelectricity.\nThis polar behavior arises because of frustration of the\ntilt instabilities due to the mixture of A-site cation sizes\nand the fact that the coherence length for off-centering\nofA-site ions is shorter than that for the tilt instabili-\nties. Thismechanismisquitegeneralinprinciple, maybe\nuseful in producing polar behavior in other perovskites.Qualitatively, this is related to the rigidity of the BO6\noctahedra. This condition is often but not alwaysmet, as\nforexample, while often tilt instabilities arestrengthened\nby pressure, there are cases where this does not hold.42\nIt may be difficult to synthesize perovskite\n(La,Lu) 2MnNiO 6due to phase separation43or compet-\ning phases, e.g.tungsten bronze as often occurs with\nmismatched A-sites. These issues can sometimes be\novercome using thin film techniques, such as pulse laser\ndeposition, or by high pressure synthesis, which favors\nthe high density perovskite structure. Further, polar\nbehavior is predicted over a wide composition range.\nThis may help in finding specific compositions amenable\nto synthesis. In any case, the proposed mechanism is\nquite general, and should apply to other mixtures of\nA-site ions with different size, e.g.La with other small\nrare earths.\nThisworkwassupportedbytheDepartmentofEnergy,\nDivision of Materials Science and Engineering and the\nOffice of Naval Research.\n1D.N. Astrov, JETP 11, 708 (1960).\n2V.J. Folen, G.T. Rado, and E.W. Stalder, Phys. Rev. Lett.\n6, 607 (1961).\n3M. Fiebig, Th. Lottermoser, D. Frohlich, A.V. Goltsev,\nand R.V. Pisarev, Nature (London) 419, 818 (2002).\n4W. Eerenstein, N.D. Mathur, and J.F. Scott, Nature 442,\n759 (2006).\n5N.A. Hill, J. Phys. Chem. B 104, 6694 (2000).\n6N.A. Spaldin and M. Fiebig, Science 309, 391 (2005).\n7G.A. Samara, T. Sakudo, and K. Yoshimitsu, Phys. Rev.\nLett.35, 1767 (1975).\n8R.E. Cohen, Nature 358, 136 (1992).\n9R.T. Smith, G.D. Achenbach, R. Gerson, and W.J. James,\nJ. Appl. Phys. 39, 70 (1968).\n10G.A. Smolenskii, and I. Chupis, Sov. Phys. Usp. 25, 475\n(1982).\n11H. Chiba, T. Atou, and Y. Syono, J. Solid State Chem.\n132, 139 (1997).\n12R.V. Shpanchenko, V.V. Chernaya, A.A. Tsirlin, P.V.\nChizhov, D.E. Sklovsky, E.V. Antipov, E.P. Khlybov, V.\nPomjakushin, A.M. Balagurov, J.E. Medvedeva, E.E. Kaul\nand C. Geibel, Chem. Mater. 16, 3267 (2004).\n13A.A. Belik, M. Azuma, T. Saito, Y. Shimakawa, and M.\nTakano, Chem. Mater. 17, 269 (2005).\n14S.V. Halilov, M. Fornari, and D.J. Singh, Appl. Phys. Lett.\n81, 3443 (2002).\n15D.J. Singh, M. Ghita, S.V.Halilov andM. Fornari, J.Phys.\nIV (Paris) 128, 47 (2005).\n16D.I. Bilc and D.J. Singh, Phys. Rev. Lett. 96, 147602\n(2006).\n17D.J. Singh, M. Ghita, M. Fornari, and S.V. Halilov, Fer-\nroelectrics 338, 73 (2006).\n18R.D. Shannon, Acta Cryst. A32, 751 (1976).\n19M.T. Anderson, K.B. Greenwood, G.A. Taylor, and K.R.\nPoeppelmeier, Prog. Solid State Chem. 22, 197 (1993).\n20J.B. Goodenough, A. Wold, R.J. Arnott, and N. Menyuk,\nPhys. Rev. 124, 373 (1961).21G. Blasse, J. Phys. Chem. Solids 26, 1969 (1965).\n22M. Azuma, K. Takata, T. Saito, S. Ishiwata, Y. Shi-\nmakawa, and M. Takano, J. Am. Chem. Soc. 127, 8889\n(2005).\n23H. Hughs, M.M.B. Allix, C.A. Bridges, J.B. Claridge, X.\nKuang, H. Niu, S. Taylor, W. Song, and M.J. Rosseinsky,\nJ. Am. Chem. Soc. 127, 13790 (2005).\n24N.S. Rogado, J. Li, A.W. Sleight, and M.A. Subramanian,\nAdv. Mater. 17, 2225 (2005).\n25M. Sakai, A. Masuno, D. Kan, M. Hashisaka, K. Takata,\nM. Azuma, M. Takano, and Y. Shimakawa, Appl. Phys.\nLett.90, 072903 (2007).\n26Y. Uratani, T. Shishidou, F. Ishii, and T. Oguchi, Physica\nB383, 9 (2006).\n27S.F. Mater, M.A. Subramanian, A. Villesuzanne, V. Ey-\nert, and M.H. Whangbo, J. Magn. Magn. Mater. 308, 116\n(2007).\n28D.J. Singh and L. Nordstrom, Planewaves, Pseudopoten-\ntials and the LAPW Method, 2nd. Ed. (Springer, Berlin,\n2006).\n29D. Singh, Phys. Rev. B 43, 6388 (1991).\n30Smaller radii of 1.53 a0for O and 1.88 a0for theB-site ions\nwere used insome relaxations toavoid overlappingspheres.\nThe results for different radii were cross-checked.\n31J.B. Goodenough, Phys. Rev. 100, 564 (1955); J. Phys.\nChem. Solids 6, 287 (1958).\n32J. Kanamori, J. Phys. Chem. Solids 10, 87 (1959).\n33J.B. Goodenough, Magnetism and the Chemical Bond (Wi-\nley, New York, 1963).\n34Crystal field splittings are mainly from hybridization of\nmetaldand Opstates in perovskites, i.e.the nominal d\nbands are anti-bonding combinations of dandpstates so\nsince the hybridization is stronger for the eg-pσthan for\nthet2g-pπcombination, the egstates are higher in energy.\nLarge crystal field splittings show strong hybridization.\n35Note the exchange splitting of O pbands (Fig. 2), which\nshows the involvement of O via hybridization.5\n36P.W. Anderson, Phys. Rev. 115, 2 (1959).\n37A.M. Glazer, Acta Cryst. B 28, 3384 (1972).\n38M. Ghita, M. Fornari, D.J. Singh, and S.V. Halilov, Phys.\nRev. B72, 054114 (2005).\n39G.A. Smolenski and V.A. Isupov, Dokl. Akad. Nauk. SSR\n97, 653 (1954).\n40G. Burns and F.H. Dacol, Phys. Rev. B 28, 2527 (1983).41G.A. Samara, J. Phys. Condens. Matter 15, R367 (2003).\n42R.J. Angel, J. Zhao, and N.L. Ross, Phys. Rev. Lett. 95,\n025503 (2005).\n43S. Park, N. Hur, S. Guha, and S.W. Cheong, Phys. Rev.\nLett.92, 167206 (2004)."    },    {        "title": "0802.2953v2.Anomalous_Magnetic_Properties_of_Sr2YRuO6.pdf",        "content": "Anomalous Magnetic Properties of Sr 2YRuO 6\nRavi P. Singh and C. V . Tomy\nDepartment of Physics, Indian Institute of Technology Bombay, Mumbai 400 076, INDIA\nAnomalous magnetic properties of the double perovskite ruthenate compound Sr 2YRuO 6are reported here.\nMagnetization measurements as a function of temperature in low magnetic fields show clear evidence for two\ncomponents of magnetic order ( TM1\u001832 K and TM2\u001827 K) aligned opposite to each other with respect to\nthe magnetic field direction even though only Ru5+moments can order magnetically in this compound. The\nsecond component of the magnetic order at TM2\u001827 K results only in a magnetization reversal, and not\nin the negative magnetization when the magnetization is measured in the field cooled (FC) mode. Isothermal\nmagnetization ( M-H) measurements show hysteresis with maximum coercivity ( Hc) and remnant magnetization\n(Mr) atT\u001827 K, corroborating the presence of the two oppositely aligned magnetic moments, each with a\nferromagnetic component. The two components of magnetic ordering are further confirmed by the double peak\nstructure in the heat capacity measurements. These anomalous properties have significance to some of the earlier\nresults obtained for the Cu-substituted superconducting Sr 2YRu 1\u0000xCuxO6compounds.\nPACS numbers: 75.60.Jk, 75.50.Ee and 74.70.Pq.\nI. INTRODUCTION\nSr2YRuO 6belongs to the family of double perovskite in-\nsulators, Sr 2LnRuO 6(Ln=rare earth or Y)1, where the Ru\nions exist in the pentavalent state (Ru5+) with a high-spin state\n4A2gand 4 d3configuration ( J=3=2).Even though the struc-\nture of these compounds can be derived from the well known\nperovskite structure of SrRuO 3by replacing alternate Ru ions\nwith Lnions2, these compounds do not show any similarity\nto their parent compound SrRuO 3, which is a ferromagnetic\nmetal. The layered structure, consisting of alternate LnRuO 4\nand SrO planes, accommodates both the Ru and rare earth\natoms in the same LnRuO 4plane and hence both the atoms\nshare the same site symmetry ( B-site of the perovskite struc-\nture ABO 3). The alternating positions of the Ru and Lnatoms\nin the unit cell result in two type of interactions between the\nRu atoms; (i) direct interaction of Ru-O-O-Ru and (ii) indi-\nrect interaction through the rare earth atoms, Ru-O- Ln-O-Ru.\nSince the compounds having nonmagnetic Lnions (Y and\nLu) are also found to order magnetically2,3, the direct inter-\naction is assumed to be stronger than the indirect interaction\nthrough the rare earth atoms. Among the Sr 2LnRuO 6com-\npounds, Sr 2YRuO 6has captured additional interest due to the\noccurrence of superconductivity when Ru is partially ( \u001415%)\nreplaced by Cu4–9. Cu is found to get substituted at the Ru site\nin the YRuO 4planes and thus the structure of the substituted\ncompounds remains the same as that of the parent compound,\nwithout creating any additional Cu-O planes6.\nThe parent compound Sr 2YRuO 6is known to be an antifer-\nromagnetic insulator with the Ru moments ordering at TN=\n26 K2. The magnetic ordering temperature ( TN) was inferred\nas 26 K from the position of the peak in the magnetization\nmeasurements. Neutron di \u000braction measurements at 4.2 K\nhave confirmed the magnetic ordering of the Ru moments,\nconsisting of a type I AFM structure. Due to the monoclinic\ndistortion of the structure, the compound is expected to show\ncanting of the Ru moments resulting from the Dzyaloshinsky-\nMoriya (D-M) interactions10,11among the antiferromagneti-\ncally ordered spins. How such a compound becomes a metal-\nlic magnetic superconductor without creating Cu-O planes isstill a puzzling question. There are still many unanswered\nquestions regarding the origin of magnetism and supercon-\nductivity in the Cu-substituted Sr 2YRuO 6compounds. At\nthe same time, there are no detailed magnetization studies\navailable for the parent compound itself, except for one re-\nport on Sr 2YRuO 6single crystals12which confirms the mag-\nnetic ordering and weak ferromagnetism. In addition, the re-\nsistivity of Sr 2YRuO 6single crystals12shows anomalous be-\nhaviour below TNfollowed by a Mott-like transition at 17 K\nwhereas the magnetoresistance becomes negative below 30 K.\nThe band structure calculations13have indicated the compe-\ntition between the antiferromagnetic and ferromagnetic fluc-\ntuations among the Ru moments. We present here some ad-\nditional evidence for the competition between antiferromag-\nnetic and ferromagnetic coupling in this compound. Detailed\nmeasurements of magnetization and heat capacity show some\nanomalous properties exhibited by Sr 2YRuO 6. Both the mea-\nsurements unfold clear evidence for two magnetic orderings\n(TM1\u001832 K and TM2\u001827 K), even though the magnetic\nordering in this compound can occur only by Ru moments.\nThe magnetization measurements corroborate that both the\nmagnetic ordering occurs with ferromagnetic components and\nthese two components align opposite to each other with re-\nspect to the magnetic field direction, resulting in a magneti-\nzation reversal. The results presented here have relevance to\nthe magnetic properties exhibited by the Cu-substituted super-\nconducting Sr 2YRu 1\u0000xCuxO6compounds4–9.\nII. EXPERIMENTAL DETAILS\nPolycrystalline samples of Sr 2YRuO 6were prepared by the\nstandard solid state reaction method by mixing stoichiometric\namounts of SrCO 3, Y 2O3and Ru metal powder and heating\nat 960\u000eC for 12 hours. The final sintering of the pelletized\npowder was carried out at 1360\u000eC for 24 hours after several\nintermediate heat treatments followed by grindings. X-ray\ndi\u000braction pattern of the samples was recorded on an X’pert\nPRO di \u000bractometer (PANalytical, Holland). The magnetiza-\ntion as a function of temperature and magnetic field was mea-arXiv:0802.2953v2  [cond-mat.str-el]  18 Sep 20102\n2.5\n2.0\n1.5\n1.0\n0.5M (10−3emu)\n50 40 30 20 10T(K)/s32/s53/s48/s32/s79/s101\n/s32/s53/s48/s48/s32/s79/s101\n/s32/s50/s48/s48/s48/s32/s79/s101FC\n1.5\n1.0\n0.5\n0.0\n-0.5M (10−3emu)\n50 40 30 20 10\nT (K)ZFC  50 Oe\n 500 Oe\n 1500 Oe\n 2000 Oe\nFIG. 1: (Color online) Magnetization vs temperature for Sr 2YRuO 6\nin zero field-cooled (ZFC) and field-cooled (FC) modes under vari-\nous applied fields.\nsured using a vibrating sample magnetometer (Quantum de-\nsign, USA). The heat capacity measurements using the relax-\nation method were performed using a physical property mea-\nsurement system (Quantum design, USA) in the temperature\nrange 1.8-300 K.\nIII. RESULTS AND DISCUSSION\nThe Rietveld analyses of the x-ray di \u000braction patterns us-\ning Fullprof software showed that the compound forms in sin-\ngle phase with a monoclinic structure (space group P21=n).\nThe lattice parameters obtained from the analyses are, a=\n5:769 Å, b=5:772 Å and c=8:159 Å along with \f=90:18\u000e\nwhich are in good agreement with those reported earlier2. Fig-\nure 1 illustrates the magnetization of Sr 2YRuO 6as a function\nof temperature in zero field-cooled (ZFC) and field-cooled\n(FC) modes. In the ZFC measurements the sample was cooled\nin zero applied field to 2 K, the required magnetic field was ap-\nplied and then the data were taken while increasing the tem-\nperature. For the FC measurements, the sample was cooled\nfrom the paramagnetic state to 2 K in an applied field and\nthe data were recorded while heating the sample. In order to\nminimize the remnant field in the superconducting magnet be-fore the ZFC measurements, the magnetic field was reduced\nto zero from a large field value in the oscillating mode. This\nmade sure that the remnant field was within \u00062 Oe. The lower\npanel shows the ZFC measurements for various applied field\nvalues. For low field values, the magnetization is negative at\nlower temperatures. As the temperature is increased, the mag-\nnetization remains independent of temperature till \u001820 K and\nthen surprisingly decreases to go through a minimum. As the\ntemperature is further increased, the magnetization increases,\ngoes through a positive maximum and then shows the nor-\nmal paramagnetic behaviour. For H=1:5 kOe, the ZFC\nmagnetization starts with a positive value at low temperatures,\nbut goes through negative value at the minimum. For higher\nfields, the magnetization is always positive, even though it\ngoes through a minimum. The width of the peaks at the max-\nimum and minimum as well as the temperature at which they\noccur depends slightly on the applied fields; both decrease\nwith increasing field. The upper panel of Fig. 1 shows the\nFC measurements at various applied fields. The FC magneti-\nzations show a broad peak and the temperature at which the\npeak occurs shows a weak temperature dependence on the ap-\nplied fields.\nIn order to ascertain that the anomalies observed in the ZFC\nmagnetization is not entirely due to e \u000bects of negative rem-\nnant magnetic field in the superconducting coils, we have car-\nried out FC measurements in smaller field values, both posi-\ntive and negative. Figure 2 shows the FC measurements for\nan applied field of \u000610 Oe. It is clear that the FC magneti-\nzation remains negative whether the field is positive or neg-\native. Such e \u000bects are seen upto 25 Oe above which the FC\ncurves switch over to the positive side. Neutron di \u000braction\nstudies at 4.2 K2had indicated only an AFM ordering of the\nRu moments. It was also proposed that the distorted mon-\noclinic structure can give rise to a small canting of the Ru\nmoments and hence a small ferromagnetic component in this\ncompound resulting from the D-M interactions between the\nantiferromagnetically ordered Ru moments. This, however,\ncannot explain the observed magnetization behaviour in this\ncompound. A simple ferromagnetic component due to cant-\n-1.0-0.8-0.6-0.4-0.20.0M (10−3emu)\n40 35 30 25 20 15 10\nT (K)15\n10\n5\n0\n-5\n-10M (10−3emu)\n5040302010\nT (K)ZFC\n FC H = 50 Oe\n −10 Oe\n +10 OeFC\nFIG. 2: (Color online) Magnetization for Sr 2YRuO 6in FC mode at\n\u000610 Oe. Inset shows the FC and ZFC curves for MnCO 3.3\n-2.0-1.00.01.0M (10−3emu)\n-4-2024\nH (kOe) 23.5 K\n(c)2\n1\n0\n-1\n-2M (10−3emu)\n420-2-4\nH (kOe) 26 K\n(e)\n2\n1\n0\n-1\n-2M (10−3emu)\n-4-2024\nH (kOe) 27 K\n(f)2\n1\n0\n-1\n-2M (10−3emu)\n420-2-4\nH (kOe) 30 K\n(h)\n2\n1\n0\n-1\n-2M (10−3emu)\n-4-2024\nH (kOe) 32 K\n(i)2\n0\n-2M (10−3emu)\n400020000-2000-4000\nH (kOe) 28 K\n(g) -1.00.01.0M (10−3emu)\n-4-2024\nH (kOe) 25 K\n(d)\n-1.00.01.0M (10−3emu)\n-4-2024\nH (kOe) 22 K\n(b)-1.5-1.0-0.50.00.51.0M (10−3emu)\n-4-2024\nH (kOe) 5 K\n(a)\nFIG. 3: (Color online) Isothermal magnetization curves for\nSr2YRuO 6at di\u000berent temperatures.\ning can make the magnetization negative in the ZFC mode\nif the remnant field is negative. But then the magnetization\nwill monotonically decrease as the temperature is increased\nand will cross over to the positive side before completing the\nmagnetic order. A typical example for such a behaviour is\nshown in the inset of Fig. 2 for MnCO 3, which is a well\nknown canted antiferromagnet having D-M interactions14. We\nhave also made sure that the compound does not contain any\nSrRuO 3impurities (not detected in x-ray di \u000braction patterns)\nby taking the ZFC and FC data for small field values in the\ntemperature range 100-200 K (even a small trace of SrRuO 3\nimpurity will give a thermal hysteresis around its ferromag-\nnetic ordering temperature (150-160 K) between the ZFC and\nFC measurements).\nIn order to further corroborate that there exists more than a\nsimple canting in this compound, we have carried out detailed\nmagnetization measurements as a function of magnetic field\n10\n5\n0\n-5\n-10M (10−3emu)\n-30 -20 -10 0 10 20 30\nH (kOe)2.0\n1.5\n1.0\n0.5\n0.0Coercivity (kOe)\n3530252015105\nT (K)1.2\n0.8\n0.4\n0.0Remanence (10−3emu) Coercivity\n Remanence\nT = 26 K\nFIG. 4: (Color online) High field magnetization as function of field\nat 26 K. Inset shows the temperature variation of coercivity ( Hc) and\nremnance ( Mr)at di\u000berent temperatures. Figure 3 depicts the low field mag-\nnetic isotherms at some selected temperatures. At low tem-\nperatures, well below the magnetic anomalies, the magnetiza-\ntion curves are almost linear with a small value for coerciv-\nity (Hc). As the temperature crosses 22 K, the magnetization\nshows significant hysteresis and the magnetization loops open\nup. The opening of the loop increases until the temperature\nreaches \u001827 K and then decreases as the temperature is fur-\nther increased. Even at 32 K, the hysteresis is much more than\nthe same at 5 K. At 35 K, we see only a linear behaviour ex-\npected for a paramagnet. Even though the hysteresis loops are\nnot closed at some temperatures (Fig. 3(d), 3(e)), they show\na normal behaviour when the applied fields are extended to\nhigher values (see main panel of Fig. 4). No other anomalies\nare observed in the high field magnetization curves. The co-\nercivity and the remnant magnetization plotted as a function\nof temperature in the inset of Fig. 4 show a maximum near\n27 K and decrease on either side of this temperature. This\nclearly demonstrates that some sort of magnetization reversal\nhappens at 27 K.\nThere are no reports about the heat capacity of this com-\npound in the literature. The result of our heat capacity mea-\nsurements for Sr 2YRuO 6is presented in Fig. 5(a). Two peaks\nare obvious, one at T=\u001830 K and the other at T=\u001826 K,\nwhich correspond well to the anomalies observed in the mag-\nnetization. There is only a minor e \u000bect by the magnetic field\non the heat capacity of the sample even at 50 kOe (Fig. 5(a)),\neven though a small decrease in the temperature dependence\nof the peak positions were observed in the magnetization mea-\nsurements. In order to have an estimate of the approximate\nmagnetic heat capacity, the phonon contribution needs to be\nsubtracted from the total measured heat capacity. Since there\nare no nonmagnetic analogues available for this compound,\nthe phonon contribution was calculated from the combined\nDebye and Einstein equations15,\nCph=R0BBBBBB@1\n1\u0000\u000bD\u0012\u0012D\nT\u00133Zx\n0x4ex\n(ex\u00001)2dx+3n\u0000nX\ni=11\n1\u0000\u000bEy2ey\n(ey\u00001)21CCCCCCA\n(1)\nwhere\u000bEand\u000bDare the anharmonicity coe \u000ecients,\u0012Dis the\nDebye temperature, \u0012Eis the Einstein temperature, x=\u0012D=T\nandy=\u0012Ei=T. The best possible fit was obtained when the\ncalculations were performed by using one Debye and three\nEinstein frequencies along with a single \u000bE. The solid line in\nFig. 5(b) represents the fit to the phonon contribution, which is\nin good agreement with the experimental data at high tempera-\ntures (above the magnetic ordering). The parameters obtained\nfrom the best fit are: \u0012D=200 K,\u0012E1=300 K,\u0012E2=529 K,\n\u0012E3=615 K,\u000bE=1:0\u000210\u00004K and\u000bD=1:0\u000210\u00004K. The\nDebye and Einstein temperatures obtained for Sr 2YRuO 6are\ncomparable with those obtained for YVO 3where the phonon\ncontribution was obtained in a similar fashion, but with only\ntwo Einstein frequencies along with one Debye frequency16.\nThe magnetic heat capacity, Cmag, obtained by subtracting the\ncalculated phonon heat capacity from the total heat capacity,\nis shown in the Fig. 5(c) along with the magnetic entropy\n(Smag=RT2\nT1Cmag\nTdT). The two peaks become more obvious4\nin the magnetic heat capacity. In Sr 2YRuO 6, the magnetic\ntransition can occur only due to the ordering of Ru5+mo-\nments. In that case, the exact reason for the observed dou-\nble peak behaviour is not very clear at present. Magnetic\nentropy ( Smag) increases with temperature and saturates to\na value of \u00182.6 J mole\u00001K\u00001above 30 K. If we consider\nthe ground state of Ru5+ions as J=3=2, then the expected\nmagnetic entropy is 11.52 J mole\u00001K\u00001(S=Rln[2J+1]),\ncorresponding to the four-fold degenerate ground sate. How-\never, the crystalline electric fields, if present, can split this\nground state into two doubly degenerate states, giving rise to\na ground state multiplicity of only two17. This will reduce\nthe magnetic entropy of the compound to 5.76 J mole\u00001K\u00001\n(S=Rln 2). The observed entropy, however, is even less than\nhalf of this value. In fact, neutron di \u000braction measurements\nhad estimated a value of 1.8 \u0016B/Ru5+at 4 K (instead of the ex-\npected value of 3 \u0016B/Ru5+) in the magnetically ordered state2.\nThis moment value corresponds well with the doubly degen-\nerate ground state. If we compare the reduction in entropy\nof Sr 2YRuO 6to that observed for YVO 316, frustrations of Ru\nspins at high temperatures (above the magnetic ordering) can\nbe attributed as the reason for the reduction in entropy. The\ncorrelation between the frustrated moments at high tempera-\ntures reduces the contribution of the entropy to the magnetic\nordering. Such a frustration among the Ru moments is in-\nferred in Sr 2YRuO 6as the possible reason for the reduction\ninTNeven though the compound possesses a large exchange\nintegral value13.\nIt is clear that Sr 2YRuO 6exhibits two anomalies, the first at\n\u001832 K ( TM1) and the second at \u001827 K ( TM2) even though the\nmagnetic ordering in this compound can come only from the\nRu5+moments. If we assume that the two anomalies are as-\nsociated with the magnetic ordering of the Ru moments, then\nthe observed behaviour is very interesting. The isothermal\nmagnetization curves at di \u000berent temperatures (Fig. 3) clearly\ndemonstrate that the first magnetic order starts at TM1\u001832 K\nwith a ferromagnetic component resulting in the increase of\nhysteresis and Hcas the temperature is lowered. This ferro-\nmagnetic component is expected from the canting of the an-\ntiferromagnetically ordered Ru moments because of the D-M\ninteractions. However, the decrease of hysteresis and Hcbe-\nlow 27 K indicates that a second component of the magnetic\norder also develops with a ferromagnetic component ( TM2),\nbut aligns itself opposite to the first component and hence op-\nposite to the applied field. This component almost cancels\nthe first component and hence the hysteresis is negligible at\nlow temperatures ( <20 K). These anomalies are further con-\nfirmed in the zero field remnant magnetization measurements\nas shown in Fig. 6(a). Here the sample was cooled (FC) in a\nfield of 5 kOe down to 10 K. The field was then removed and\nthe remnant magnetization was measured in zero field while\nwarming the sample. The remnant magnetization shows a nor-\nmal decrease upto \u001820 K, but then increases, goes through a\nmaximum at \u001827 K and then decreases to zero above 32 K.\nThis clearly demonstrates that the magnetic ordering consists\nof two components and they are aligned opposite to each other\nwith respect to the magnetic field direction. While cooling the\nsample in magnetic field, the first component orders and aligns\n5\n4\n3\n2\n1\n0Cmag (J/mole-K)\n50403020100T (K)2.0\n1.5\n1.0\n0.5\n0.0Smag (J/mole-K)    Cmag\n Smag(c)\n80\n60\n40\n20\n0C (J/mole-K)\n10080604020T (K) Cexp\n fit\n(b)\n25\n20\n15\n10C (J/mole-K)\n34323028262422T (K)(a)\n H = 0 Oe\n H = 50 kOeFIG. 5: (Color online) (a) Measured total heat capacity ( Cv) of\nSr2YRuO 6in applied fields H=0 Oe and 5 kOe. (b) Heat capacity\nwith the fit (solid line) for phonon contribution. (c) Magnetic con-\ntribution to heat capacity ( Cmag) (left scale) and calculated magnetic\nentropy ( Smag) (right scale) as a function of temperature.\nparallel to the field at \u001832 K, but the second component aligns\nantiparallel to the field at \u001827 K, decreasing the net magne-\ntization. However, this antiparallel component is not strong\nenough to make the magnetization negative as in the case of\nsome LnVO 3compounds. As the sample is warmed up in zero\nfield, the remnant magnetization increases when the antipar-\nallel component relaxes and completes its disordering.\nIn order to verify the thermodynamic reversibility of the FC\nstate, we have measured the remnant magnetization by field-\ncooling the sample down to two pre-selected temperatures ( T1\nandT2) on either side of the maximum in the FC magnetiza-\ntion curve as shown in Fig. 6(a). In the first case, the sample\nwas field cooled to 28 K ( TM2<T1<TM1), where only the\nfirst magnetic component would have ordered, and the field5\n4\n3\n2\n1\n0M (10−3emu)\n3020100\nT (K)T2 T1 \nH = 5 kOe\nFCC\n H = 0 Oe(a)2.0\n1.5\n1.0\n0.5\n0.0\n-0.5M (10−3 emu)\n3020100\nT (K)FCW, H = 2.2 kOe(b)\nFIG. 6: (Color online) (a) FC data while cooling the sample in an\napplied field of 5 kOe (top curve) and the zero field warm up data\n(bottom curves) after switching o \u000bthe applied magnetic field at T\n=10 K, 23.5 K and 28 K. (b) FC warm up data in an applied field\nof 2.2 kOe after cooling the sample in a negative applied field of\n\u000050 Oe.\nwas removed. In the second case, the sample was field cooled\nto 23.5 K ( T2<TM1;TM2), where both components would\nhave undergone magnetic ordering, before removing the field.\nIn both cases, the remnant magnetization follows exactly the\noriginal remnant curve which was obtained by switching the\nfield o \u000bat 10 K, proving the thermodynamic reversibility of\nthe magnetically ordered states. Further evidence for the op-\nposite alignments of the two components of magnetic order-\ning is evident from the data in Fig. 6(b). Here the sample\nwas cooled in a negative field ( \u000050 Oe) so that the magnetiza-\ntion at 5 K is negative. At 5 K, the field was increased in the\npositive direction ( \u00182:2 kOe) until the magnetization became\npositive. Magnetization shows normal behaviour upto 20 K,\nbut shows a sudden dip to go through a negative minimum\nat\u001827 K. Thus it is clear that whether the sample is cooled\nin positive or negative field, the two components of magnetic\norder align always opposite to each other.\nNeutron di \u000braction measurements in this compound at\n4.2 K2had indicated that the nuclear structure of the com-pound remains unchanged at 4.2 K, ruling out the possibil-\nity of any structural changes. On the other hand if we as-\nsume that one of the anomalies is due to a possible structural\nchange, then the changed structure should again revert back\nto the original structure at low temperatures. From the posi-\ntion of the magnetic di \u000braction peaks, magnetic ordering of\nthe Ru moments was deduced to be antiferromagnetic with\na type I structure2. However, the temperature variation of\nthe intensity of magnetic peak(s) was not reported and hence\nthe exact temperature at which the Ru moments order is not\navailable. The TNof\u001826 K was assigned to this compound\nsimply from the position of the peak in the high field mag-\nnetization measurements2. Even though there are no detailed\nexperimental observations in Sr 2YRuO 6, many experimental\nresults including neutron di \u000braction exist for Cu-substituted\nSr2YRu 1\u0000xCuxO6compounds6–9. Assuming that the magnetic\nproperties associated with the ordering of the Ru moments are\nnot drastically altered, we can analyze the results of the \u0016SR\nmeasurements in the Cu-substituted compounds7,9. Both the\nprecession frequency and relaxation rate show anomalies at\n\u001830 K for muons trapped in the two possible sites; oxygen\nin the YRuO 4layers (\u0016O(1;2)) and oxygen in the SrO layers\n(\u0016O(3)). The authors assigned this anomaly to the fluctuation\nof the Ru moments which order in a spin-glass state. This\nis exactly the same temperature range at which the first com-\nponent of magnetic ordering starts in our studies for the par-\nent compound ( TM1). The variation of the power exponent\nat the\u0016O(1;2)site as a function of temperature9almost resem-\nbles the mirror image of our temperature variation of the co-\nercivity and remnant magnetization (inset of Fig. 4). It was\nalso proposed that the fluctuations of the Ru moments stop at\nT=23 K and order antiferromagnetically. We have identified\nthis temperature in our studies as the temperature at which\nthe second component of magnetic moments completes its or-\ndering.99Ru M ¨ossbauer measurements in Sr 2YRu 1\u0000xCuxO6\n(x=0:05)7,8have confirmed the magnetic ordering of Ru\nmoments. Both the isomer shift and the hyperfine field val-\nues are consistent with the pentavalent nature of the Ru mo-\nments. From the temperature variation of the M ¨ossbauer\nspectra8, it was concluded that that the magnetic ordering\nof the Ru moments persists upto 30 K, which is consistent\nwith the magnetic ordering temperature TM1in our measure-\nments. Additional support for the Ru ordering as high as 30 K\ncomes from the neutron di \u000braction measurements reported for\nSr2YRu 1\u0000xCuxO6(x=0:15) where the intensity of the mag-\nnetic peak due to the ordering is Ru moments is evident upto\n\u001830 K6.\nIn ZFC measurements, the sample is always cooled in a\nnominal remnant field ( \u0018 \u00062 Oe in our case). This may result\nin the negative magnetization at low temperatures. When the\nmagnetic field is applied, the magnetization remains negative\nfor low fields (Fig. 1) but changes over to positive values for\nsu\u000eciently large fields. Even then a magnetization reversal\nhappens and the magnetization goes though a negative mini-\nmum in between the two transitions. This behaviour may be\ncaused by the fact that the large fields flip (to orient parallel\nto the field) some, but not all, of the spins oriented against\nthe field. As the field value increases, majority of the spins,6\noriented antiparallel to the field, align parallel to the field, re-\nsulting only in a small minimum at TM2. In FC magnetization\n(H\u001550 Oe), the first component of the magnetic transition\naligns along the field at TM1, resulting in a positive magne-\ntization. However, at TM2, the second component aligns an-\ntiparallel to the first component, resulting in the reduction in\nmagnetization. When this alignment is over, the magnetiza-\ntion remains constant, as in the case of FC measurements in\nsmaller fields.\nThe reason for the two components of the magnetic order-\ning reminiscent of ferrimagnetic ordering in this compound\nis not clear. In the ordered double perovskite Sr 2LnRuO 6\ncompounds, the B-site of the perovskite structure ABO 3is\nuniquely occupied either by Ru or the rare earth metal ions\ndue to the lower coordination number compared to Sr. Since\nRuthenium is considered to be in the oxidation state of 5 +\nin these compounds, the chances of ferrimagnetic ordering\nof Ru5+/Ru4+moments are very rare. We have repeated the\nmeasurements with samples annealed in air, oxygen or argon\nand all of them showed the same behaviour. In fact, the iso-\nmer shift values from the99Ru M ¨ossbauer measurements in\nSr2YRuO 6had confirmed the pentavalent oxidation state of\nRu moments7,18. Even if the spin-glass state is assumed as\nsuggested by Harshman et al9, the observed properties - the\nmagnetization reversal, thermodynamic reversibility of mag-\nnetization and two peaks in heat capacity - cannot be ex-\nplained. The magnetic interactions among the ordered Ru mo-\nments can take place in two ways; (i) the \u001b-super exchange in-\nteraction between nearest neighbour (nn) Ru5+ions via Ru-O-\nO-Ru pathway and (ii) the \u0019-super exchange between the next\nnearest neighbour (nnn) Ru5+ions via Ru-O-Y-O-Ru pathway.\nThe relative strengths of these two interactions will determine\nthe type of magnetic ordering at low temperatures. Since Yis a nonmagnetic ion, it is not expected to take part in the ex-\nchange interaction and hence the second interaction between\nthe nnn is assumed to be negligible. This assumption can fur-\nther be supported by the fact that the relaxation rate at the\n\u0016O(3)site for the muons is very much smaller than the relax-\nation rate at the \u0016O(1;2)site7,9since the Ru-O-Y-O-Ru pathway\nincludes the oxygen at the O(3) sites only. Whether the com-\npetition between these two interactions, however, can give rise\nto the observed double peak behaviour needs further investi-\ngations. It is possible that the stronger interaction orders the\nRu moments at TM1and the weaker interaction realigns some\nof the Ru moments in the opposite direction at TM2. It is pos-\nsible that the second component of the magnetic order at TM2\nis not strong enough to bring the magnetization down to neg-\native values even though it gets reduced. However, why the\nsecond component aligns the moments against the first com-\nponent and hence the magnetic field is not clear now. Detailed\nneutron di \u000braction measurements are needed as a function of\ntemperature to explain the reason for the observed anomalies.\nIn conclusion, we have reported some of the anomalous\nproperties exhibited by SrYRuO 6deduced from the detailed\nmagnetic and heat capacity measurements. Two distinct mag-\nnetic orderings are evident in the compound even though only\nRu moments can order in this compound. The two compo-\nnents of the magnetic order align always opposite to each\nother and to the magnetic field. Observation of hysteresis and\ncoercivity in magnetic isotherms below the magnetic order in-\ndicates the presence of ferromagnetic component associated\nwith the magnetic ordering. The presence of two well de-\nfined peaks in the heat capacity indicates that the two mag-\nnetic components have large entropy change associated with\nthe ordering.\n1P. C. Donohue and E. L. McCann, Mat. Res. Bull. 12, 519 (1977).\n2P. D. Battle and W. J. Macklin, J. Solid State Chem. 52, 138\n(1984).\n3P. D. Battle and C.W. Jones, J. Solid State Chem. 78, 108 (1989).\n4M. K. Wu, D. Y . Chen, D. C. Ling, and F. Z. Chien, Physica B\n284, 477 (2000).\n5D. R. Harshman,W. J. Kossler, A. J. Greer, C. E. Stronach, E.\nKoster, B. Hitti, M. K. Wu, D. Y . Chen, F. Z. Chien, H. A. Black-\nstead and J. D. Dow, Physica B 289, 360 (2000).\n6H. A. Blackstead, J. D. Dow, D. R. Harshman, W. B. Yelon, Ming\nXing Chen, M. K. Wu, D. Y . Chen, F. Z. Chien and D. B. Pulling,\nPhys. Rev. B 63, 214412 (2001).\n7H.A. Blackstead, J. D. Dow, D.R. Harshman1, M.J. DeMarco,\nM.K.Wu, D. Y . Chen, F. Z. Chien, D. B. Pulling, W. J. Kossler,\nA. J. Greer, C. E. Stronach, E. Koster, B. Hitti, M. Haka and S.\nToorongian, Eur. Phys. J. B 15, 649 (2000).\n8M. D. Marco, H. A. Blackstead, J. D. Dow, M. K. Wu, D. Y .\nChen,5, F. Z. Chien, M. Haka, S. Toorongian, and J. Fridmann,\nPhys. Rev. B 62, 14301 (2000).9D. R. Harshman,W. J. Kossler, A. J. Greer, D. R. Noakes, C. E.\nStronach, E. Koster, M. K. Wu, F. Z. Chien, J. P. Franck, I. Isaaac\nand J. D. Dow, Phys. Rev. B 67, 054509 (2003).\n10I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241(1958).\n11T. Moriya, Phys. Rev. 120, 91(1960).\n12G. Cao, Y . Xin, C. S. Alexander and J. E. Crow, Phys. Rev. B 63,\n184432 (2001).\n13E. V . Kuz’min, S. G. Ovchinnikov and D. J. Singh, Phys. Rev. B\n68, 024409 (2003)\n14S. B. Romanova and M. P. Orlova, Zh. Eksp. Teor. Fiz. 31, 579\n(1956).\n15C. A. Martin, J. Phys.: Condens. Matter 3, 5967 (1991).\n16G. R. Blake, T. T. M. Palstra, Y . Ren, A. A. Nugroho and A. A.\nMenovsky, Phys. Rev. B 65, 174112 (2002).\n17Y . Doi, Y . Hinatsu, A. Nakamura, Y . Ishii and Y . Morii, J. Mater.\nChem. 13, 1758 (2003)\n18R. Greatrex, N. N. Greenwood, M. Lal and I. Fernandez, J. Solid\nState Chem. 30, 137 (1979)."    },    {        "title": "0803.2660v1.Magnetic_Graphene_Nanohole_Superlattices.pdf",        "content": "arXiv:0803.2660v1  [physics.comp-ph]  18 Mar 2008Magnetic Graphene Nanohole Superlattices\nDecai Yu, Elizabeth M. Lupton, Miao Liu, Wei Liu and Feng Liu∗\nDepartment of Materials Science and Engineering,\nUniversity of Utah, Salt Lake City, UT 84112\nAbstract\nWe investigate the magnetic properties of nano-holes (NHs) patterned in graphene using first\nprinciples calculations. We show that superlattices consi sting of aperiodicarray of NHs forma new\nfamily of 2D crystalline ”bulk” magnets whose collective ma gnetic behavior is governed by inter-\nNH spin-spin interaction. They exhibit long-range magneti c order well above room temperature.\nFurthermore, magnetic semiconductors can be made by doping magnetic NHs into semiconducting\nNH superlattices. Our findings offer a new material system for f undamental studies of spin-spin\ninteraction and magnetic ordering in low dimensions, and op en up the exciting opportunities of\nmaking engineered magnetic materials for storage media and spintronics applications.\nPACS numbers: 75.75.+a, 73.21.Cd, 81.05.Uw, 72.80.Rj\n1Magnetic materials have a wide range of applications, such as being us ed for storage\nmedia. Magnetism is commonly associated with elements containing loca lizeddorfelec-\ntrons, i.e. the itinerant ferromagnetism1,2. In contrast, the elements containing diffuse sp\nelectrons are intrinsically non-magnetic, but magnetism can be induced in sp-element ma-\nterials extrinsically by defects and impurities. There have been cont inuing efforts in search-\ning for new magnetic materials, and much recent interest has been d evoted to magnetism\nof carbon-based3,4,5,6,7, especially graphene-based structures8,9,10,11,12,13,14,15,16,17,18such as\ngraphene nanoribbons8,9,11,18and nanoflakes16,17. Here, we predict a new class of graphene-\nbased magnetic nanostructures, the superlattices of graphene nanoholes (GNHs), using first-\nprinciples calculations.\nGraphene nanoribbons8,9,11,18and nanoflakes16,17with zigzag edges have been shown to\nexhibitmagnetism. Theirmagnetizationisoriginatedfromthelocalized edgestatesthatgive\nrise to a high density of states at the Fermi level rendering a spin-p olarization instability1.\nThen, for the same reason, if nanoholes (NHs) are made inside a gra phene sheet with zigzag\nedges they may also exhibit magnetism. Furthermore, by making an a rray of NHs, we may\nexpect collective ”bulk” magnetism because inter-NH spin-spin interactions are introduced\nin addition to the intra-NH spin coupling. This allows us to go beyond the current scope\nlimited to the spins within a single nanoribbon or nanoflake. In effect, s uperlattices consist-\ning of a periodic array of NH spins form a family of nanostructured ma gnetic 2D crystals\nwith the NH acting like a ”super” magnetic atom.\nWe have investigated magnetic properties of GNHs, using first-prin ciples pseudopotential\nplane-wave calculations within the spin-polarized generalized gradien t approximation19. We\nused a rhombus supercell in the graphene plane with the cell size ran ging from 14 ×14˚A to\n41×41˚A and a vacuum layer of ∼10˚A. We used a 2 ×2×1 k-point mesh for Brillouin zone\nsampling and a plane wave cutoff of 22.1 Rd. The systems contain up to a maximum of 530\natoms. The dangling bonds on the edge atoms are saturated with hy drogen. The system is\nrelaxed until the force on each atom is minimized to less than 0.01 eV/ ˚A.\nConsidering first a single zigzag NH by examining the intra-NH spin-spin interaction, we\nfoundthatindividual NHcanbeviewedasan”inversestructure”of nanoflakeornanoribbon,\nlike an anti-flake or anti-ribbon, with similar spin behavior. We determin e the ground-state\nmagnetism of three typical NH shapes: triangular (Fig.1a), rhombu s (Fig.1b) and hexagonal\n(Fig.1c), by comparing the relative stability of ferromagnetic (FM), antiferromagnetic (AF)\n2and paramagnetic (PM) configuration as a function of NH size. Our c alculations show\nthat the ground state is FM for triangular NHs, but AF for rhombus and hexagonal NHs,\nand their corresponding spin densities are shown in Fig.1a, 1b and1c , respectively. The\nmagnetic moments are highly concentrated on the edges and decay quickly away from the\nedge, as shown in Fig.1d. Similar decaying behavior has been seen in na noribbons9,11and\nnanoflakes16,17. The edge moment increases with increasing NH size (see inset of Fig.1 d).\nThe triangular NHs have a metastable ferrimagnetic state with two e dges having one\nspin and the other edge having the opposite spin (see supplementar y Fig.1). For a 4-atom\ntriangular NH (Fig.1a), the FM state is 52 meV lower in energy than the ferrimagnetic state,\nand the latter is 13 meV lower than the PM state. For a 32-atom rhom bus NH (Fig.1b),\nthe AF state is 89.2 meV lower than the PM state; for a 54-atom hexa gonal NH (Fig.1c), it\nis 164.4 meV. The energy difference increases with increasing NH size. The triangular NHs\nfavor FM at all sizes, whereas rhombus and hexagonal NHs only bec ome AF when the edge\ncontains more than five atoms, i.e. they are PM if the NH is too small. So , the triangular\nNHs have a stronger tendency toward magnetization.\nThe magneticordering within asingle NH isconsistent with boththethe orem of itinerant\nmagnetism in a bipartite lattice20and the topological frustration model of the π-bonds17\ncounting the unpaired spins in the nonbonding states2,17. For a system like graphene con-\nsisting of two atomic sublattices, each sublattice assumes one spin a nd the total spin S of the\nground state equals1\n2|NB−NA|where N B(NA) is the number of atoms on B (A) sublattice.\nBecause of the honeycomb lattice symmetry, atoms on the same zig zag edge belong to the\nsame sublattice; while atoms on two different zigzag edges belong to t he same sublattice if\nthe two edges are at an angle of 0oor 60o, but different sublattices if at an angle of 120oor\n180o. Consequently, the triangular NH are FM, because all three edges are 60oto each other\non the same sublattice; the rhombus and hexagonal NHs are AF, be cause one-half the edges\nare on the A-sublattice and another half on the B-sublattice as the two types of edges are\n120oto each other. This same argument can be applied to nanoribbons9and nanoflakes16,17.\nNext, we consider GNH superlattices (a periodic array of NHs) by ex amining the inter-\nNH spin-spin interaction. In principle, one can generate four out of five possible 2D Bravais\nlattices of NHs (see supplementary Fig.2). Here, we focus on the ho neycomb superlattices of\ntriangular NHs (Fig.2a and 2b), in which each NH possesses a net mome nt acting effectively\nas ”one” spin. The superlattice contains two sublattices of NHs, su perimposed on the\n3FIG. 1: The ground-state magnetic configurations of different shapes of NHs. (a) FM triangular\nNH; (b) AF rhombus NH; (c) AF hexagonal NH. In (a-c), white and red balls indicate the up- and\ndown-spin density isosurface at 0.02e/ ˚A3, respectively; blue and white sticks represent C-C and\nC-H bonds respectively. (d) The average local magnetic mome nt (µB) per atom in the triangular\nNH (Fig.1a) as a function of distance moving away from the cen ter of NH, measured in atomic\nshells with the edge atoms as the first shell. The inset shows µBon the edge vs. NH size ( l).\nbackground of graphene containing two sublattices of atoms. We r ealize that the NHs on\nthe same sublattice will be FM-coupled because their corresponding edges are at 0oto each\nothersothattheiredgeatomsareonthesameatomicsublattice. O ntheotherhand, theNHs\nondifferent sublattices will beFM-coupled if they arein a parallel confi guration (Fig.2a) but\n4AF-coupled if they are in an antiparallel configuration (Fig.2b) when t heir corresponding\nedges are at 180oto each other so that their edge atoms are on different atomic subla ttices.\nThese have indeed been confirmed by our first-principles calculation s. Independent of NH\nsize and supercell dimension, the FM state is favored for parallel co nfigurations but the AF\nstate is favored for antiparallel configurations. In both cases, t he spin-polarization splits the\nedge states opening a gap at the Fermi energy9,17. The total spin S in one unit cell equals\nto1\n2|NB−NA|; it increases linearly in the FM parallel configuration but remains zero in the\nAF antiparallel configuration with increasing NH size.\nThe collective magnetic behavior of a GNH superlattice depends on int er-NH spin-spin\ninteraction. Particularly, there exists super exchange interactio n between the NH spins, in\naddition to the spin coupling defined by the underlying bipartite lattice (i.e., the relative\nangle between the zigzag edges of GNHs). In Fig.2c, we plot ∆ Epc=E(FM)−E(PM) for\nthe FM parallel configuration and ∆ Eac=E(AF)−E(PM) for the AF antiparallel con-\nfiguration as a function of cell dimension ( L), i.e., the NH-NH separation. |∆Epc|increases\nwhile|∆Eac|decreases with decreasing L. This indicates that as the NHs getting closer, the\nFM state becomes relatively more stable than AF state in both config urations, i.e. the FM\ncoupling is favored by the super exchange interaction. Also plotted in Fig.2c are magnetic\nmoments on the NH edges, which are found to increase in the FM but d ecrease in the AF\nconfiguration with decreasing L. This again reflects that the edge magnetization on the\nneighboring NHs is enhanced with the same spin when they are FM coup led but suppressed\nwith the opposite spin when they are AF coupled by the super exchan ge interaction.\nThe above results show that long-rangeferromagnetic ordering c an be created by employ-\ning the parallel configuration of triangular NHs in different lattice sym metries, as illustrated\nin supplementary Fig. 2. The next important question is what Curie te mperature ( Tc) they\ncan have. We have estimated Tcusing the mean-field theory of Heisenberg model21,22,23,\nTc=2∆\n3kB(1)\nWhere ∆ is the energy cost to flip one ”NH spin” in the FM lattice, which h ave been\ncalculated directly from first principles for the honeycomb lattices ( Fig.2a). Figure 2d shows\nthatTcincreases from 169 K to 1388 K when NH size ( l) increases from 0.738 to 1.476\nnm with cell dimension ( L) fixed at 2.982 nm, and decreases from 586 K to 169 K when L\nincreasesfrom1.704nmto2.982nmwith lfixedat0.738nm. Thesetrendsareexpectedsince\n5FIG. 2: (a) Ground-state spin configurations in a FM honeycom b NH superlattice. (b) Same as\n(a) in an AF superlattice. All the symbols and notations for b onds and spin densities are the same\nas Fig.1. Yellow dashed lines mark the primitive cell. (c) ∆ Epc=E(FM)−E(PM) of the FM\nsuperlattice (red solid squares) and ∆ Eac=E(AF)−E(PM) of the AF superlattice (blue solid\ntriangles) versus cell dimension ( L); Edge magnetic moments, µBin the FM lattice with fixed hole\nsize (l=1.476 nm) (red open squares) and in the AF lattice ( l=0.738 nm) (blue open triangles)\nversusL. (d) Curie temperature of the FM superlattice as a function o f NH size ( l) andL.\nmagnetization is stronger for larger NH size and higher NH density. L imited by computation\ntime, someofourcelldimensionsarepossiblyunrealisticallytoosmall( NHdensitytoohigh),\nwhich gives rise to a very high Tc. Still, it is important to point out that our calculations\nsuggest that it is possible to make FM GNH superlattices with Tcabove room temperature\nby using a NH size of 50 nm and a density of 10−4nm−2, achievable by today’s lithographic\npatterning technology. We note that a recent experiment24has shown a Tc≥350 K in FM\n6FIG. 3: Illustration of DMS made from GNH superlattice. (a) A semiconductor GNH hexagonal\nlattice (L= 8√\n3a,a= 2.46˚A is the lattice constant of graphene.) consisting of an arra y of rhombus\narmchair NHs ( L= 8√\n3a). (b) GGA Band structure of (a), the inset shows the Brilloui n zone.\n(c) TB band gap of (a)-type structures as a function of NH size (l) and cell dimension ( L). (d)\nMagnetic semiconductor made by doped (a) with triangular zi gzag NHs. All the symbols and\nnotations for bonds and spin densities are the same as Fig.1.\ngraphite made by proton bombardment.\nSince graphene-based nanostructures hold great promise for fu ture electronics25,26,27,28,\nour discovery of GNH magnetism offers the exciting prospect of com bining magnetic and\nsemiconducting behavior in one material system. Here, we demonst rate the possibility of\nmaking diluted magnetic semiconductors (DMS) by exploiting GNHs with two different\nkindsofedges. SimilartosuperlatticesofzigzagNHs, wecancreate superlattices ofarmchair\nNHs, which constitute a class of 2D semiconductors. Figure 3b show s the band structure\n7of a superlattice of rhombus armchair NHs (Fig.3a) having a direct ba nd gap of 0.43 eV,\nas obtained from first-principles calculations. Figure 3c shows the b and gap as a function\nof NH size ( l) and cell dimension ( L), from tight-binding calculations29. The gap increases\nwith increasing lbut decreases with increasing L.\nDMS can be made by adding triangular zigzag NHs into the semiconduct or superlat-\ntice, as illustrated in Fig. 3d. To ensure the ferromagnetism, all tria ngular NHs must be\nparallel with each other acting like magnetic dopants. Usually DMS are synthesized by mix-\ning two different materials, typically III-V semiconductors and tran sition-metal magnetic\nelements30,31. The main challenge is to increase the magnetic dopant concentratio n in order\nto raise the Curie temperature, because the two types of materia ls are usually not miscible.\nHere, we introduce an ”all-carbon” DMS, in which combined semicondu ctor and magnetic\nbehavior are achieved by structural manipulation. Consequently, room-temperature DMS\nare possible because the dopant concentration can be increased w ithout the miscibility prob-\nlem. One might also consider doping other magnetic elements into the s emiconducting GNH\nsuperlattice.\nIt is very exciting to consider making engineered magnetic materials w ith NHs for various\napplications. For example, it is possible to directly pattern NHs into en gineered magnetic\nstorage media (see Fig. 4). The ground state of rhombus NHs is AF ( Fig. 1b and Fig.4,\nlower-left inset) and their first excited state is FM (Fig. 4, up-right inset) when the NH size\nis larger than 14.6 ˚Aaccording to our calculation. Taking each NH as one bit, we can assign\nthe ground state with ”S=0” and the excited state with ”S=N” to re present the ’0’ and\n’1’, respectively. The switching between ’0’ to ’1’ can be done by apply ing a local magnetic\nfield or energy pulse to convert between the ground and the excite d state. Using a NH size\nof 50 nm and a density of 10−4nm−2, a storage density about 0.1 terabit per square inch\nwould be achieved, much higher than the current density in use. One interesting topic of\nfuture study is the magnetocrystalline anisotropy around individua l NHs, which must be\nlarger than kBTfor the proposed storage media to work.\nWe thank DOE-NERSC and Center for High Performance Computing ( CHPC) at the\nUniversity of Utah for providing the computing resources. This wor k was supported by\n8FIG. 4: Schematic Illustration of a magnetic storage medium consisting of a patterned array of\nrhombus GNHs. The insets show the detailed structure of ”0” a nd ”1” bit, represented by the\nground-state AF configuration (S=0) and the excited FM config uration (S=N), respectively. Red\nand green balls show the spin-up and spin-down density at an i sosurface value of 0.02 e/˚A3.\nDOE.\n∗Electronic address: fliu@eng.utah.edu\n1J. C. Slater, Phys. Rev. 49, 537 (1936).\n2F. Liu, S. N. Khanna, and P. Jena, Physical Review B 42, 976 (1990).\n3Y. Shibayama, H. Sato, T. Enoki, et al., Physical Review Lett ers84, 1744 (2000).\n4P. Esquinazi, D. Spemann, R. Hohne, et al., Physical Review L etters91, 227201 (2003).\n5P. O. Lehtinen, A. S. Foster, Y. C. Ma, et al., Physical Review Letters93, 167202 (2004).\n6H. Lee, Y. W. Son, N. Park, et al., Physical Review B 72, 174431 (2005).\n97J. M. D. Coey, M. Venkatesan, C. B. Fitzgerald, et al., Nature 420, 156 (2002).\n8K. Kusakabe and M. Maruyama, Physical Review B 67, 092406 (2003).\n9Y. W. Son, M. L. Cohen, and S. G. Louie, , Nature 444, 347 (2006).\n10K. Nomura and A. H. MacDonald, Physical Review Letters 96, 256602 (2006).\n11L. Pisani, J. A. Chan, B. Montanari, et al., Physical Review B 75, 064418 (2007).\n12L. Brey, H. A. Fertig, and S. Das Sarma, Physical Review Lette rs99, 116802 (2007).\n13K. S. Novoselov, Z. Jiang, Y. Zhang, et al., Science 315, 1379 (2007).\n14D. E. Jiang, B. G. Sumpter, and S. Dai, Journal of Chemical Phy sics127, 124703 (2007).\n15O. V. Yazyev and L. Helm, Physical Review B 75, 125408 (2007).\n16J. Fernandez-Rossier and J. J. Palacios, Physical Review Le tters99, 177204 (2007).\n17W. L. Wang, S. Meng, and E. Kairas, J. Appl. Phys. Nano Letters 8, 241 (2007).\n18B. Huang, F. Liu, J. Wu, et al., http://arxiv.org/abs/0708. 1795v1.\n19G. Kresse and J. Hafner, Physical Review B 47, 558 (1993).\n20E. H. Lieb, Physical Review Letters 62, 001201 (1989).\n21T. Hynninen, H. Raebiger, and J. von Boehm, Physical Review B 75, 125208 (2007).\n22K. Sato, P. H. Dederics, and H. Katayama-Yoshida, Europhysi cs Letters 61, 403 (2003).\n23I. Turek, J. Kudrnovsky, G. Bihlmayer, et al., Journal of Phy sics-Condensed Matter 15, 2771\n(2003).\n24J. Barzola-Quiquia, P. Esquinazi, M. Rothermel, et al., Phy sical Review B 76, 161403(R)\n(2007).\n25K. S. Novoselov, A. K. Geim, S. V. Morozov, et al., Science 306, 666 (2004).\n26K. S. Novoselov, A. K. Geim, S. V. Morozov, et al., Nature 438, 197 (2005).\n27B. Ozyilmaz, P. Jarillo-Herrero, D. Efetov, et al., Physica l Review Letters 99, 166804 (2007).\n28Q. M. Yan, B. Huang, J. Yu, et al., Nano Letters 7, 1469 (2007).\n29Our tight-binding band structure calculations for semicon ductor armchair GNH superlattices\nwere performed using the nearest-neighbor π-band model with the hopping parameter = 3.0\neV.\n30T. Jungwirth, J. Sinova, J. Masek, et al., Reviews of Modern P hysics78, 809 (2006).\n31A. H. Macdonald, P. Schiffer, and N. Samarth, Nature Materials 4, 195 (2005).\n10Supplementary Fig.1 The spin-density plot of the ferrimagn etic configuration of a 4-atom\ntriangular NH. White and red balls indicate the up- and down- spin density isosurface at 0.02e /˚A3\nrespectively; blue and white sticks represent C-C and C-H bo nds respectively.\n11Supplementary Fig.2 Schematic illustration of four possib le types of Bravais lattice of GNHs that\ncan be patterned in graphene. Solid arrows and lines mark the primitive cells. (a) hexagonal\nlattice; (b) rectangular lattice; (c) centered rectangula r lattice; the dashed lines mark the\nconventional cell; (d) oblique lattice. Note that the squar e lattice is not possible.\n12"    },    {        "title": "0803.3779v1.The_commensurate_phase_of_multiferroic_HoMn2O5_studied_by_X_ray_magnetic_scattering.pdf",        "content": "arXiv:0803.3779v1  [cond-mat.mtrl-sci]  26 Mar 2008The commensurate phase of multiferroic HoMn 2O5\nstudied by X-ray magnetic scattering\nG. Beutier,1,∗A. Bombardi,1C. Vecchini,2P. G. Radaelli,2S. Park,3S-W. Cheong,3and L. C. Chapon2\n1Diamond Light Source, OX11 0DE, United Kingdom\n2ISIS, Rutherford Appleton Laboratory - STFC, OX11 0QX, Unit ed Kingdom\n3Department of Physics and Astronomy, Rutgers University, P iscataway, New Jersey 08854, USA.\n(Dated: October 30, 2018)\nThecommensuratephaseofmultiferroicHoMn 2O5was studiedbyX-raymagneticscattering, both\noff resonance and in resonant conditions at theHo- L3edge. Below 40 K,magnetic ordering at the Ho\nsites is induced by the main Mn magnetic order parameter, and its temperature dependence is well\naccounted for by a simple Curie-Weiss susceptibility model . A lattice distortion of periodicity twice\nthat of the magnetic order is also evidenced. Azimuthal scan s confirm the model of the magnetic\nstructure recently refined from neutron diffraction data for both Mn and Ho sites, indicating that\nthe two sublattices interact via magnetic superexchange.\nPACS numbers: 75.25.+z, 75.50.Ee, 77.80.-e, 78.70.Ck\nThere has been very significant recent interest in\nmagnetoelectric multiferroics, in particular magnetically\nfrustrated transition-metal oxides such as TbMnO 3[1],\nNi3V2O8[2], RMn 2O5(R=rare-earth, Bi) [3, 4, 5, 6, 7, 8]\nand more recently RbFe(MoO 4)2[9]. In this class of\nmaterials, the onset of ferroelectricity coincides with the\ntransition to a magnetically ordered state characterized\nby a complex spin configuration. While the spontaneous\nelectric polarization is much weaker than for proper fer-\nroelectrics, the magneto-electric coupling is strong, lead-\ning to giant effects in the physical properties upon ap-\nplication of an electric or a magnetic field. Some key\nfacts about these materials have been established unam-\nbiguously: acentric magnetic ordering on the transition-\nmetal sites is clearly the main factor in inducing ferro-\nelectricity, and the direction of the electrical polarization\ncan be well explained by the Landau phenomenological\nanalysis of the magneto-electric coupling or by more gen-\neral symmetry arguments [10]. Other aspects are much\nless clear: the microscopic origin of ferroelectricity is\nstill much debated, in particular in the RMn 2O5and\ntriangular-lattice systems, where more than one mech-\nanism has been proposed. In addition, there is presently\nvery little understanding of the role played by the mag-\nnetic rare earths. Rare earth magnetism not only leads\nto spectacular magneto-electric effects at low tempera-\ntures, but can increase greatly the value of the electrical\npolarization even at high temperature, as recently shown\nfor DyMnO 3[11].\nMostRMn2O5become ferroelectric below ∼40 K[3],\ndriven by magnetic ordering to a commensurate state\nwith propagation vector k=(1/2,0,1/4) for R=Y,Ho,Tb\n[5, 6] and k=(1/2,0,1/2) for Bi [8]. At around 20K,\nthe R=Y, Ho, Tb analogues show a second magnetic\ntransition to an incommensurate structure, with much\nsmaller spontaneous electric polarization. Neutron\n∗Electronic address: guillaume.beutier@diamond.ac.ukdiffraction studies of the ferroelectric/commensurate\nphase on powder[4, 5, 6] and more recently single crystal\nspecimens[7, 12], have evidenced a small moment on the\nmagnetic rare-earth sites well above the main ordering\ntemperature of the rare earth sublattice ( ∼10 K),\nsuggesting that this moment is induced by the complex\nMn magnetic ordering. For HoMn 2O5, the magnitudes\nand directions of the Ho moments has been established\nindependently by two groups [7, 12], but there cannot\nbe absolute confidence in these results, since Ho’s\noverall contribution to the magnetic neutron scattering\nintensities is very small (the Ho moments are between\n0 and 1µBon different lattice sites compared with an\nalmost fully ordered Mn sublattice). More importantly,\nthe nature of the interplay between Mn and Ho order —\nin particular the induced nature of the Ho moments —\nare impossible to address with neutron diffraction, since\nthe Ho and Mn contributions cannot be separated at\ntemperature close to T N\nIn the present Communication, we report on resonant\nandnon-resonantX-raymagneticdiffractionexperiments\nperformed on the commensurate phase of HoMn 2O5.\nUnlike neutron diffraction, this technique allows one\nto probe the Ho and Mn ordering independently. The\nmagnetic structure of the Ho sublattice was confirmed\nby fitting azimuthal scans in resonant conditions at\nthe Ho L 3edge, while off-resonance scans can be\nwell reproduced with the overall magnetic structure\ndetermined by neutron diffraction. By studying the\ntemperature dependence of both signals, the Ho and\nMn sublattice magnetic order parameters are extracted,\nclearly showing that the Ho and Mn magnetic transitions\nare simultaneous and that the former is induced by\nthe latter. The evolution of the Ho order parameter\nis well explained by a simple model accounting for the\npolarization by the Mn sublattice. Weak charge super-\nlattice peaks with k L=2kM=(0,0,1/2) are also observed\nin the same temperature range; we find that the order\nparameter of the charge superstructure is proportional\nto the square of the Mn staggered magnetization, as2\npredicted by Landau theory.\nSynchrotron X-ray experiments were performed at\nDiamond Light Source, on Beamline I16 - Materials\n& Magnetism, dedicated to X-ray diffraction in the\nenergy range 3-25 keV. The horizontally polarized beam\ndelivered by a linear undulator was tuned either to the\nL3edge of Holmium ( ∼8.078 keV) or at 6.4 keV below\ntheKedge of Manganese ( ∼6.55 keV), and monochrom-\natized by a Si (111) double-crystal monochromator. The\nbeam was focused to 120 ×32µm in the horizontal and\nvertical directions. A single crystal of HoMn 2O5, with\nsize approximately 1 ×1×3 mm3and faces along the\n(110), (1 ¯10) and (001) crystallographic directions was\nused. The crystal was attached to a copper platform\nwith QuickFill and mounted on the Kappa-geometry\ndiffractometer of the beamline, in a Displex type cry-\nofurnace. When necessary, a polarization analysis of the\ndiffracted beam was performed with the (022) reflection\nof a copper crystal. Its efficiency at 6.4 keV was about\n1/4 and the cross-talk between polarization channels\nwas found to be negligible. The intensity was recorded\neither with an Avalanche Photo-Diode (APD) or with\nan energy-resolving Silicon-drift diode detector to reject\nthe fluorescence. Further details of the beamline are\navailable on [13].\nAll measurements were performed in the commensu-\nrate phase on two strong magnetic reflections, indexed\n(5\n231\n4) and (7\n241\n4) and on the (4 4 0.5) ”charge” Bragg\npeak.The first set ofmeasurementswereconducted at 6.4\nkeV, i.e. at an energy far below any absorption edges of\nthe sample. In these conditions, the magnetic scattering\nis not element specific and measures contributions from\nboth Mn and Ho sites. The low fluorescence, combined\nwith the high efficiency of the analyzer and the low noise\nof the APD, allowed us to measure in non-resonant con-\nditions with good statistics (typically 1000 counts/sec)\nand low background (about 250 counts/sec in the σ→σ\nchannel and nearly 0 counts/sec in the σ→πchannel).\nNoresonancewasfoundatthe K-edgeofManganese(not\nshown), confirming that its orbital moment is quenched\nby the crystalline electric field (at a K-edge, one actu-\nally measures the orbital contribution of the specific ion\nto the total magnetization, which is related to the spin\ncomponent by the spin-orbit coupling). A second set of\nmeasurements was conducted in resonant conditions in\nthe vicinity of the Ho L3-edge. A strong dipole-dipole\nenhancement, due to the resonance of the 2 p3/2electrons\nwith the empty 5 dshell, was observed at 8.076 keV (Fig.\n1). A quadrupolar contribution was also found at 8.068\nkeV.\nFigure 2 shows the temperature dependence of the\nmagnetic reflection (5\n2, 3,1\n4), off resonance and at the\nHo-L3edge. The non-resonant measurement indicates\nthat the transition temperature is ∼40K, in agreement\nwith previous neutron diffraction [6] and magnetization\nmeasurements. Around 18 K, the compounds under-8 8.05 8.1 8.15050010001500200025003000\nEnergy (keV)Intensity (counts/s)\n  \nT = 25 K[2.5 3 0.25]\n[2.51 3 0.25]\nfluorescence\nFIG. 1: (Color online) Energy dependence of the magnetic\nreflection (2.5 3 0.25) (red line) and of the fluorescence back -\nground (green line) around the Ho L3resonance energy. The\nquadrupoleanddipole contributionat theresonance occurs at\n8.068 and 8.076 keV, respectiviely. At higher energy, oscil la-\ntions of the signal are observed, probably related to magnet ic\nEXAFS, not studied here.\nFIG. 2: Integrated intensities of various Bragg peaks as a\nfunction of temperature. The intensity of the magnetic refle c-\ntion (2.5 3 0.25), collected on warming, is shown off resonanc e\n(energy of 6.4 keV) and at the Ho L3edge (energy of 8.076\nkeV)with filled triangle and open circle symbols, respectiv ely.\nThe superstructure charge reflection (4 4 0.5), measured off\nresonance at 7.96 keV, is shown as open square symbol. Lines\nare guide to the eyes. The inset shows the intensity of the (4\n4 0.5) superstructure peak against the intensity of the (2.5\n3 0.25) peak, for the temperature range 25-40 K. The line\ncorresponds to a fit with a quadratic law.\ngoes a first order transition (not studied here) to an\nincommensurate magnetic order with propagation vector\nk=(0.48, 0, 0.28) [6], splitting the (5\n2, 3,1\n4) peak and\ncausing the accidents observed around 18K in Fig. 2.\nNear the transition, the peak intensity in non-resonant\nconditions is essentially proportional to the square of the\nMn magnetic moment, since here the Ho contribution\nis negligible. Its temperature dependence is consistent\nwith the neutron data [5] and confirms that Mn ordering\nis the primary order parameter. In the Landau free\nenergy expansion, the magnetic order parameter Mcan3\nbe coupled not only to the gamma-point ferroelectric dis-\ntortions, but also to an additional structural modulation\n(L) of double wave-vector, k L=(0,0,0.5). Time-reversal\nsymmetry invariance requires L∝M2at the leading\nterm, so we also expect the charge peak intensity to\nbe proportional to the squareof the magnetic peak\nintensity. This is illustrated in the temperature depen-\ndence of the superlattice reflection (4 4 0.5), measured\noff resonance at 7.96 keV and shown in Figure 2. Its\nintegrated intensity is proportional to the square of the\nintegrated intensity of the (5\n2, 3,1\n4) magnetic reflection\n(inset of Figure 2). This result is similar to what was\nrecently derived from non-resonant X-ray scattering at\ntheMn L 3edge for the analog compound TbMn 2O5\n[14]. The underlying structural distortion minimizes the\nmagnetic energy, most likely through a modulation of\nthec-axis distances (and coupling), responding to the\nalternation of FM and AFM configuration across the\nrare earth layers.\nFIG. 3: Intensity of the resonant magnetic Bragg peak (2.5 3\n0.25) as a function of temperature (open symbols). The line\ncorresponds to a fit with a modified low-field Brillouin (Curie -\nWeiss) function dependingon the Mn molecular field (see text\nfor details). The inset shows the dependence for other Bragg\npeaks at the Ho L3edge and illustrates that the same overall\nbehavior, with some deviations, is observed irrespective o f the\nscattering vector or azimuth angle.\nIn sharp contrast to the off-resonance data, the (5\n2,\n3,1\n4) magnetic peak shows an unusual variation with\ntemperature at the Ho- L3resonance. The peak appears\nbelow 40K, clearly showingthat magnetic orderingof the\nHo moments coincides with the magnetic ordering of the\nMn sublattice but its intensity is marked by the absence\nof critical behavior at T N. Irrespective of the nature of\nthe Mn-Ho coupling, discussed later, one can postulate\nthat the Ho ordering is induced by the molecular field\narising from the Mn sublattice. This field can be taken\nto be directly proportional to the magnetic moment onMn sites, as estimated from the root-squared intensity\nof the non-resonant peak. The resonant intensity is then\nsimply calculated using a Curie-Weiss function diverging\natθ=10 K — the ordering temperature of the Ho\nsublattice — as Ires=κInr\n(T−θ)2. There is one adjustable\nparameter, κ, allowing the relative intensities of the\ntwo peaks to be scaled. Fig. 3 shows the resonant (5\n2,\n3,1\n4) integrated intensity together with the best fit to\nthe molecular field model. While the model reproduces\nrelatively well the overall temperature dependence, there\nis clearly a discrepancy between the two curves. This\nis likely to be due to a relative reorientation of the two\nsublattices as a function of temperature, as confirmed\nby the fact that different resonant peaks have some-\nwhat different temperature dependencies (inset of Fig 3).\n−150 −100 −50 0 50 100 1500246810Intensity (arb. units)\n  \nEnergy = 6.4 keV\nQ = [2.5 3 0.25]\n−150 −100 −50 0 50 100 15010203040\nψ (o)Intensity (arb. units)Energy = 8.076 keV\n  \nQ=[2.5 3 0.25]\nQ=[3.5 4 0.25]σ→πσ→σ\nFIG. 4: (Color online) Azimuthal dependence of the mag-\nnetic Bragg peak intensities at 25 K. The azimuth ψvalue\nis given with respect to a reference in the [0 0 1] direction.\nUpper panel: (2.5 3 0.25) reflection, in non-resonant condi-\ntion at 6.4 keV, in the σ→σ(green) and σ→π(light\nblue) channels, respectively. Lower panel: (2.5 3 0.25) (re d)\nand (3.5 4 0.25) (blue) reflections at 8.076 keV (Ho L3edge).\nSymbols with associated error bars shows the experimental\ndata points. Straight lines are calculations performed wit h\nthe model of the magnetic structure from [7].\nThe azimuthal dependence of the magnetic cross-\nsection in the commensurate phase has been measured in\nthe full angular range both off-resonance at 6.4 keV and\nat the Ho-L3edge (Fig. 4). For each azimuthal scan,\nthe intensity was integrated over a rocking curve. In the\nnon-resonant case, magnetic scattering appears in both\ntheσ→σandσ→πchannels. AttheL 3edge, magnetic\nscattering was observed only in the σ→πchannel, as\nexpected. The azimuthal scans are shown in Fig. 4. The\nscattering cross sections are proportional to the squared\nmodulus of the scattering amplitude [15, 16], f, written4\nas:\nfσσ\nnr(Q,ψ)∝(k×k′)·S(Q,ψ) (1)\nfσπ\nnr(Q,ψ)∝(1−k·k′)k·S(Q,ψ) (2)\nfσπ\nr(Q,ψ)∝k′·SHo(Q,ψ) (3)\nwhere the subscript nr and r refer to the non-resonant\nand resonant cases and the superscript refers to the scat-\ntering channel. k and k’ are unit vectors in the direction\nof the incident and scattered wave-vectors, respectively,\nandSare the unit-cell magnetic structure factors. Off\nresonance, we considered Mn and Ho spin moments with\ntheir appropriate form factors and neglected the orbital\nmoments. In the resonant case, only Ho sites withoutthe\nusualmagneticformfactorneedtobetakenintoaccount.\nNote that we consider only the dipole-dipole scattering,\nwhich is dominant at 8.076 keV (Fig. 1).The calculated\nintensities have been corrected for self-absorption, mul-\ntiplying them by the factor:\nA(Q,ψ) =1\nµ/bracketleftbigg\n1+sinα(Q,ψ)\nsinβ(Q,ψ)/bracketrightbigg−1\n(4)\nwhereα(Q,ψ) andβ(Q,ψ) are respectively the inci-\ndent and exit angles with respect to the crystal surface\n([1 1 0]) and the linear absorption coefficient µdoes not\ndepend onψ.\nIn the non-resonant case, the scattering intensities\nhave been calculated using the model of magnetic struc-\nture for HoMn 2O5recently derived by single-crystal neu-\ntron diffraction at 25K [7]. The agreement between ex-\nperimental data and calculations is excellent in both the\nσ→σandσ→πchannels as illustrated in Figure 4. In\nthis model, the manganese ions form antiferromagnetic\nzig-zag chains along the a-axis, with the main compo-\nnents of the moment in the ab-plane and pointing about\n14◦with respect to the a-axis. A small out-of phase com-\nponent along the c-axis gives rise to a cycloidal modula-\ntion along the Mn4+chains. The azimuthal dependence\nat the HoL3edge is also consistent with the neutron re-\nsults, and confirms unambiguously that the Ho moments\npoint mainly in the ab-plane. This is consistent with the\nHo single ion anisotropy: in fact, a point charge calcu-\nlation of the Ho crystal field with the program McPhas\n[17], takinginto accountneighboringchargesat distancesup to 50 ˚A, shows that the ground state multiplet is\nmade of two nearly degenerated singlets. Only the ma-\ntrix element JxandJyhave non vanishing components.\nThis is in contrast with calculations for ErMn 2O5, which\nshow that the ground state doublet has very strong easy-\naxis anisotropy, as expected from the opposite sign of the\nStevens equivalent operator B2\n0with respect to Ho, and\nalso compatible with neutron diffraction study showing\nthat the Er moments are aligned mainly along the c-axis\n[18]. There is a residual degeneracy in the patterns of\nin-plane moments that can be consistent with the reso-\nnant data; however, the neutron data strongly discrimi-\nnate between these alternatives. Two mechanisms, both\nleading to weak interactions, can account for the induced\nmoment on the Ho site: dipole-dipole interaction on one\nhand and magnetic superexchange interactions between\nthe Ho and first-neighbor Mn ions. The dipolar inter-\naction energy, taking into account the full paramagnetic\nHo moment M=10 µB(gJ=1.25,J=8), and the short-\nest Ho3+-Mn4+distance, is 0.4K. Calculations show that\nthe dipolar field induced by the ordering of the Mn ions\nis almost orthogonal to the Ho moments, which invali-\ndates this model. The super-exchange interaction medi-\natedthroughtheHo4(f)-O(p)-Mn4(d)orbitalpathisalso\nweak given the short extension of the 4f shell. However,\nthis mechanism is consistent with the observedstructure,\nas already pointed out in [7], since the Ho moment is ori-\nented antiparallel to the resultant magnetic moment of\nfirst-neighbor Mn4+ions.\nIn summary, we have studied the magnetic structure\nof HoMn 2O5in the commensurate/ferroelectricphase by\nmagneticX-rayscatteringoffresonanceand at the Ho-L 3\nresonance. Our study clearly established that magnetic\nordering of the Ho sublattice exists even at temperature\nclose to T Nand is induced by the magnetic ordering of\nthe Mn sites. The azimuthal dependence of the mag-\nnetic scattering is in agreement with the overall mag-\nnetic structure derived by single-crystal neutron diffrac-\ntionandprovideanindependentconfirmationofthemag-\nnetic ordering on the Ho sites at 25 K. The magnetic\nconfiguration on the Ho sites is only consistent with cou-\npling to the Mn4+moments through superexchange in-\nteractions, and agrees with the Ho easy-plane anisotropy\nderived from a point-charge model.\n[1] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima,\nand Y. Tokura, Nature 426, 55 (2003).\n[2] G. Lawes, A. B. Harris, T. Kimura, N. Rogado, R. J.\nCava, A. Aharony, O. Entin-Wohlman, T. Yildirim,\nM. Kenzelmann, C. Broholm, et al., Phys. Rev. Lett.\n95, 087205 (2005).\n[3] N. Hur, S. Park, P. A. Sharma, J. S. Ahn, S. Guha, and\nS.-W. Cheong, Nature 429, 392 (2004).\n[4] L. C. Chapon, P. G. Radaelli, G. R. Blake, S. Park, and\nS.-W. Cheong, Phys. Rev. Lett. 96, 097601 (2006).[5] L. C. Chapon, G. R. Blake, M. J. Gutmann, S. Park,\nN. Hur, P. G. Radaelli, and S.-W. Cheong, Phys. Rev.\nLett.93, 177402 (2004).\n[6] G. R. Blake, L. C. Chapon, P. G. Radaelli, S. Park,\nN. Hur, S.-W. Cheong, and J. Rodriguez-Carvajal, Phys.\nRev. B71, 214402 (2005).\n[7] C. Vecchini, L. C. Chapon, P. J. Brown, T. Chatterji,\nS. Park, S.-W. Cheong, and P. G. Radaelli, Cond-mat\narXiv:0710.2065 (2007).\n[8] A. Mu˜noz, J. A. Alonso, M. T. Casais, M. J. Mart´ ınez-5\nLope, J. L. Mart´ ınez, and M. T. Fern´ andez-D´ ıaz, Phys.\nRev. B65, 144423 (2002).\n[9] M. Kenzelmann, G. Lawes, A. B. Harris, G. Gasparovic,\nC. Broholm, A. P. Ramirez, G. A. Jorge, M. Jaime,\nS. Park, Q. Huang, et al., Phys. Rev. Lett. 98, 267205\n(2007).\n[10] P. G. Radaelli and L. C. Chapon, Phys. Rev. B 76,\n054428 (2007).\n[11] O.Prokhnenko, R.Feyerherm, E. Dudzik, S.Landsgesell ,\nN. Aliouane, L. C. Chapon, and D. N. Argyriou, Phys.\nRev. Lett. 98, 057206 (2007).\n[12] H. Kimura, S. Kobayashi, Y. Fukuda, T. Osawa, Y. Ka-\nmada, Y. Noda, I. Kagomiya, and K. Kohn, J. Phys.\nSociety Japan 76, 074706 (2007).[13] http://www.diamond.ac.uk/Beamlines/Beamlineplan /I16.\n[14] J. Koo, C. Song, S. Ji, J. S. Lee, J. Park, T. H.\nJang, C. H. Yang, J. H. Park, Y. H. Jeong, K. B.\nLee, et al., Non-resonant and resonant x-ray scat-\ntering studies on multiferroic TbMn2O5 (2007), URL\nhttp://www.citebase.org/abstract?id=oai:arXiv.org:0 704.0533 .\n[15] M. Blume and D. Gibbs, Phys. Rev. B 37, 1779 (1988).\n[16] J. P. Hill and D. F. McMorrow, Acta Cryst. A52, 236\n(1996).\n[17] http://www.mcphas.de.\n[18] P. P. Gardner, C. Wilkinson, J. B. Forsyth, and B. M.\nWanklyn, J. Phys. C: Solid State Phys. 21, 5653 (1988)."    },    {        "title": "0805.2706v1.Effect_of_spin_diffusion_on_spin_torque_in_magnetic_nanopillars.pdf",        "content": "arXiv:0805.2706v1  [cond-mat.mtrl-sci]  18 May 2008Effect of spin diffusion on spin torque in magnetic nanopillar s\nSergei Urazhdin and Scott Button\nDepartment of Physics, West Virginia University, Morganto wn, WV 26506\nWe present systematic magnetoelectronic measurements of m agnetic nanopillars with different\nstructures of polarizing magnetic layers. The magnetic rev ersal at small magnetic field, the onset\nof magnetic dynamics at larger field, and the magnetoresista nce exhibit a significant dependence\non the type of the polarizing layer. We performed detailed qu antitative modeling showing that the\ndifferences can be explained by the effects of spin-dependent electron diffusion.\nPACS numbers: 72.25.Ba, 72.25.RB, 75.47.De\nAccording to the spin torque (ST) model1, current-\ninduced magnetic switching (CIMS) in magnetic multi-\nlayers is caused by angular momentum transfer from the\nconduction electrons to the magnetic layers. ST is be-\nlieved to occur within atomic distances from the mag-\nnetic interfaces. Nevertheless, theories have shown that\nelectron diffusion in the layers has an important effect\non ST.2,3,4As a simple example, an electron scattering\nbetween two ferromagnets transfers angular momentum\nupon each reflection. However, this transfer is not neces-\nsarily associated with a net charge current I. Therefore,\nefficient utilization of electron scattering can result in re-\nducedIrequired to manipulate magnetic devices with\nST. In a more subtle manifestation, spin-dependent elec-\ntron diffusion causes an asymmetry between the ST in\nantiparallel (AP) and parallel (P) configurations of the\nmagnetic layers.5In an extreme case of such asymmetry,\nST can change direction, resulting in anomalous current-\ninduced behaviors.6\nDespite extensive theoretical work, few experiments\naddressed the effects of diffusion on ST.6,7,8,9,10The\nmain difficulty stems from the limited knowledge about\nthe transport properties of individual layers in magnetic\nnanostructures. Different deposition and measurement\ntechniques yielded significantly different values.11On the\nother hand, both the Magnetoresistance(MR) and CIMS\ndepend onthe samespin-dependent transportproperties.\nTherefore,simultaneousmeasurementsofMRandCIMS,\nand their analysis within the same theoretical framework\ncan lead to better understanding of the electron diffusion\nand its effect on ST.\nWe report systematic measurements of MR and CIMS\nin nanopillar spin valves F 1/N/F2with identical free lay-\ners F2=Py(5), Py=Ni 80Fe20, and different polarizers F 1\nincorporating Co. Thicknesses are given in nm. Large\nspin diffusion length lsf,Comakes Co ideal for studying\nthe effects of diffusion. We used F 1=Co(20) in samples\nlabeledCo20. To separatethe contributions ofthe Coin-\nterfaces and its bulk, we tested samples with F 1=Co(3),\nlabeledCo3, in which the scattering in the bulk of Co(3)\nwas negligible. To eliminate the spin diffusion in the\nsample contacts, we inserted a strongly spin flipping bi-\nlayer Fe 50Mn50(1)/Cu(1) between Co(3) and the bottom\ncontact in samples labeled FeMnCo 3.\nThe multilayers Cu(50)/F 1/Cu(10)/F 2/Cu(200) were/s48 /s49/s48/s48 /s50/s48/s48 /s51/s48/s48/s48/s50/s52/s54/s56\n/s48 /s49/s48/s48 /s50/s48/s48 /s51/s48/s48/s48/s52/s56/s32/s73\n/s67/s32/s40/s109/s65/s41\n/s84/s32/s40/s75/s41/s40/s100/s41 /s67/s111/s50/s48\n/s70/s101/s77/s110/s67/s111/s51/s67/s111/s51/s45/s50 /s48 /s50 /s52/s50/s46/s50/s50/s46/s51/s50/s46/s55\n/s49/s32/s107/s79/s101/s51/s48/s48/s32/s79/s101/s100/s86/s47/s100/s73/s32/s40Ω /s41\n/s73/s32/s40/s109/s65/s41/s53/s48/s32/s79/s101/s40/s97/s41/s84/s61/s50/s57/s53/s32/s75\n/s48 /s53 /s49/s48/s49/s46/s53/s50/s46/s48/s50/s46/s53/s51/s46/s50\n/s49/s32/s107/s79/s101/s51/s54/s48/s32/s79/s101/s53/s48/s32/s79/s101/s100/s86/s47/s100/s73/s32/s40Ω /s41\n/s73/s32/s40/s109/s65/s41/s40/s98/s41/s84/s61/s53/s32/s75\n/s32/s73/s43\n/s44/s32/s73/s45\n/s32/s40/s109/s65/s41\n/s84/s32/s40/s75/s41/s40/s99/s41\n/s73/s43\n/s73/s45\nFIG. 1: (a) dV/dIvsIat labeled HandT= 295 K. Curves\nare offset for clarity. (b) same as (a), at T= 5 K. (c) I+,I−\nvsTfor aCo20 sample. (d) ICvsTmeasured at H= 500 Oe\nfor the three types of samples as labeled.\ndepositedatroomtemperature295K(RT)bymagnetron\nsputtering at base pressure of 5 ×10−9Torr, in 5 mTorr\nof purified Ar. F 2and part of the Cu(10) spacer were\npatterned into an elliptical nanopillar with approximate\ndimensions 130 ×60 nm. We measured dV/dIwith four-\nprobes and lock-in detection. Positive Iflowed from F1\ntoF2. Magnetic field Hwas in the film plane and along\nthe nanopillar easy axis. At least three nanopillars of\neach type were tested with similar results.\nFigs. 1(a),(b) show dV/dIvsIfor aCo20 sample, ac-\nquired at RT and 5 K, respectively. The data at small\nH= 50 Oe are characterized by hysteretic jumps to\nthe P state with low resistance RPatI−<0, and to\nthe AP state with high resistance RAPatI+>0. At\nH= 300/360 Oe in Figs. 1(a)/(b), the jumps are re-\nplaced by large peaks caused by the reversible transition\nbetween the P and AP states.12The onset of the mag-\nnetic dynamics starting at I=ICappears as a sharp\nincrease of dV/dInearly independent of H(1 kOe data\nin Figs. 1(a),(b)). The approximate equality IC≈I+\nshown with a dashed line indicates that the reversal oc-2\n/s48 /s49/s48/s48 /s50/s48/s48 /s51/s48/s48/s48/s46/s48/s54/s48/s46/s48/s56/s48/s46/s49/s48\n/s48 /s49/s48/s48 /s50/s48/s48 /s51/s48/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52\n/s82\n/s65/s80/s45/s82\n/s80/s32/s40Ω /s41\n/s84/s32/s40/s75/s41/s67/s111/s50/s48\n/s67/s111/s51\n/s70/s101/s77/s110/s67/s111/s51/s40/s98/s41\n/s32/s32/s32/s32/s32/s32/s32 /s32/s67/s111/s50/s48\n/s32/s32/s32/s32/s32/s32/s32/s32/s32 /s32/s67/s111/s51\n/s32/s70/s101/s77/s110/s67/s111/s51\n/s32/s82\n/s112/s40/s84/s41/s45/s82\n/s80/s40/s53/s75/s41/s32/s40Ω /s41\n/s84/s32/s40/s75/s41/s40/s97/s41\nFIG. 2: (a) P-state resistances RPoffset by values at 5 K,\nand (b) MR vsTfor the three types of samples as labeled.\ncurs when large-amplitude dynamics is excited by ST.\nThe 5 K data exhibit significantly increased reversal cur-\nrents and IC. Fig. 1(c) summarizes the temperature de-\npendence of I+andI−. Both are nearly constant above\n130 K, below which they dramatically increase. Similar\nbehaviors of Co/Cu/Co nanopillars indicate their intrin-\nsic origin from the spin-dependent transport in Co.8\nOnemayattributesomeofthe dependenceon Tshown\nin Fig. 1(c) to the effects of thermal activation. Indeed,\nI+≤ICat RT because thermal fluctuations result in\nreversal slightly before the onset of large-amplitude dy-\nnamics. In contrast, I+≥ICat 5 K because current-\ninduced dynamics can occur before the reversal occurs.\nThe fundamental quantity predicted by the models of ST\nisIC. It is insensitive to thermal fluctuations and sam-\nple shape imperfections, and can be directly determined\nfrom the sharp increase of dV/dIatHlarge enough to\nsuppress hysteretic reversal. Fig. 1(d) summarizes ICvs\nTfor all three different sample structures. FeMnCo 3\ndata are approximately independent of T, whileICfor\nCo3 andCo20 increase when Tis decreased. Compar-\ning panels (c) and (d) reveals that ICclosely follows I+.\nIt is not possible to measure a similar excitation onset\ncurrentI−\nCin the AP state, because transition to the P\nstate is not suppressed at any H. Below, we use I−as\nan approximation for I−\nC.\nSince F 2is identical in all samples, the different be-\nhaviors of ICmust be attributed to the different spin-\ndependent transport properties of F 1. The difference be-\ntweenCo3 andFeMnCo 3 is due to the spin flipping\nin FeMn, which eliminates spin diffusion in the bottom\nCu(50) contact. The difference between the Co20 and\nCo3 data indicates that the effects of spin diffusion in\nCo are stronger than those in Cu. Despite a significant\nincrease of ICinCo20, it does not diverge as would be\nexpected if the sign of ST was reversed.6\nFigs. 2(a),(b) show temperature dependence of RP−\nRP(0) and MR= RAP−RP.RPincreased with Tdue\nto magnon and phonon scattering, and were surprisingly\nconsistent among the samples. Interestingly, there is a\nclear correlation between the variations of MR and ICin\nall samples. As Tdecreasesfrom RT, all MRs increase at\na similar rate, while ICslightly increase. At lower T, the\ntrends for Co3 andFeMnCo 3 remain the same, while/s48 /s49/s48/s48 /s50/s48/s48 /s51/s48/s48/s49/s48/s50/s48\n/s48/s46/s48/s48 /s48/s46/s48/s52 /s48/s46/s48/s56/s49/s48/s50/s48\n/s32/s84/s32/s40/s75/s41ρ /s32/s40µΩ /s32/s99/s109/s41/s80/s121\n/s67/s111\n/s67/s117/s40/s97/s41\n/s80/s121\n/s67/s111ρ /s32/s40/s84/s61/s53/s75/s41/s32/s40 µΩ /s32/s99/s109/s41\n/s49/s47/s100/s32/s40/s110/s109/s45/s49\n/s41/s67/s117/s40/s98/s41\nFIG. 3: (a) Resistivities of 40 nm thick Py, Co, and Cu films\nmeasuredin VanderPauwgeometry. The CoandCudataare\nfitted with the Bloch-Gruneisen approximation, with Debye\ntemperatures θCo= 373 K and θCu= 265 K. The Py data\nare fitted with a quadratic dependence. (b) Dependencies of\nresidual resistivities on inverse film thickness (symbols) , with\nlinear fits shown.\na decrease of MR in Co20 atT <130 coincides with a\nsharp increase of IC.\nTo understand the dependencies of MR, CIMS, and\nICon the sample structure, we performed simultaneous\ncalculations of spin-dependent transport and ST. Our\nmodel combines a diffusive approximation for the ferro-\nmagnets and outer sample contacts with a ballistic ap-\nproximationfor the Cu(10) spacer between the ferromag-\nnets.5This approximation is consistent with calculations\nbasedontheBoltzmannequation.14Wecombinethecon-\ntinuity conditions for spin currents and spin accumula-\ntion in the spacer between F 1and F 2derived by Slon-\nczewski5(Eqs. (13),(14)) with a small-angle expansion of\nEq. (28) for ST. The resulting expression for ST in terms\nof the spin current Is=I↑−I↓and spin accumulation\n∆µ=µ↑−µ↓in the Cu(10) spacer near the collinear\nmagnetic configuration is\nτ=¯hsin(θ)\n4e(AG∆µ−IS) (1)\nwhereeis the electron charge, ¯ his the Planck’s constant,\nGis twice the mixing conductance introduced in the cir-\ncuit theory,2Ais the area of the nanopillar, and θis\nthe angle between the magnetic moments. At I=IC,τ\ncompensates the damping torque, yielding\nIC=αeγS22πM2\nτ, (2)\nwhereα≈0.03 is the Gilbert damping parameter,15\nγis the gyromagnetic ratio, τis ST determined from\nEquation (1) at I= 1 in appropriate units, and S2=\nM2V/2µBis the total spin of the Py(5) nanopillar. Here,\nVis the volume of F 2, andµBis the Bohr magneton.\nThe magnetization M2of Py varied from 730 emu/cm3\nat 20K to 675emu/cm3at 300K, asdetermined by mag-\nnetometry of Py(5) films prepared under the same con-\nditions as the nanopillars. These values are lower than\nexpected for bulk Py, but consistent with the published\nresults for Py films.163\n/s48/s46/s53 /s49/s46/s48 /s49/s46/s53 /s50/s46/s48/s45/s50/s48/s50\n/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48/s48/s53/s49/s48/s49/s53/s50/s48\n/s48 /s53/s48 /s49/s48/s48/s45/s50/s48/s50/s52/s54\n/s48 /s49/s48/s48 /s50/s48/s48 /s51/s48/s48/s51/s52/s53/s54/s55/s56/s73\n/s67/s44/s32/s73/s45\n/s67/s40/s109/s65/s41\n/s71/s32/s40/s102Ω/s45/s49\n/s109/s45/s50\n/s41/s40/s97/s41\n/s71/s61/s48/s46/s56/s55/s32/s102 Ω/s45/s49\n/s109/s45/s50\n/s73\n/s67/s32/s44/s32/s73/s45\n/s67/s32/s40/s109/s65/s41\n/s116\n/s67/s117/s32/s40/s110/s109/s41/s40/s98/s41\n/s116\n/s67/s117/s61/s53/s53/s32/s110/s109\n/s32/s73\n/s67/s32/s44/s32/s73/s45\n/s67/s32/s40/s109/s65/s41\n/s108\n/s115/s102/s44/s67/s111/s32/s40/s110/s109/s41/s40/s99/s41\n/s108\n/s115/s102/s44/s67/s111/s61/s52/s50/s32/s110/s109\n/s84/s32/s40/s75/s41/s32/s73\n/s67/s32/s40/s109/s65/s41/s40/s100/s41\n/s50/s48/s110/s109/s52/s48/s32/s110/s109/s54/s48/s32/s110/s109\nFIG. 4: (a) Calculated IC,I−\nCvsGforFeMnCo 3. (b) Same\nvstCuforCo3. (c) Same vslsf,CoforCo20, (d) same vsT\nforCo20 samples, for the residual values of lsf,Coas labeled.\nEquations (1) and (2) express ICin terms of ∆ µand\nIS, the same quantities that determine MR in magnetic\nmultilayers. We calculated ∆ µandISself-consistently\nusing a one-dimensional diffusive approximation employ-\ning the standard MR parameters: spin asymmetries β,\nrenormalized resistivities ρ∗=ρ/(1−β2), spin diffusion\nlengthslsfin the layers, and similarly defined parame-\ntersAR∗,γ, andδfor the interfaces.17We estimate these\nparameters from a combination of the published values11\nand our own measurements, as described below.\nThe resistivityofeach layerin oursamples provideses-\nsential information about electron diffusion. Because of\nvariations among published resistivities, we instead de-\ntermined their values from measurements of thin films\nprepared under the same conditions as the nanopillars,\nwith thicknessesverifiedby x-rayreflectometry. Fig. 3(a)\nshowsρ(T)for40nmthickPy,Co,andCufilms,together\nwith fittings for Co and Cu with the Bloch-Gruneisen\napproximation. We obtained better fitting for Py data\nwith a quadratic dependence, indicating that electron-\nmagnon scattering may dominate electron-phonon scat-\ntering.18The dependence of the residual resistivity on\nfilm thickness wasconsistentwith the Fuchs-Sommerfield\napproximation(Fig.3(b)), allowingustoextractthebulk\nresidual values ρPy(0) = 11.3µΩcm,ρCo(0) = 4.4µΩcm,\nandρCu(0) = 1.1µΩcm. We used the extracted bulk\nρ(T) to model all the extended layers in the nanopillars.\nThe effect oflateralconfinement in Py(5) nanopillarswas\napproximated by using the resistivity of a Py(40) film.\nTo estimate lsf(T), we used its empirical inverse re-\nlationship with ρ, along with the bulk residual values\nlsf,Py(0) = 6 nm, and lsf,Cu(0) = 300 nm based on pub-\nlished measurements,11scaled by the somewhat different\nresidual resistivities of our films. If scattering by thermal\nexcitations does not flip electron spins, a weaker depen-/s48 /s49/s48/s48 /s50/s48/s48 /s51/s48/s48/s50/s52/s54/s56/s49/s48\n/s48 /s49/s48/s48 /s50/s48/s48 /s51/s48/s48/s48/s46/s49/s50/s48/s46/s49/s52/s48/s46/s49/s54/s48/s46/s49/s56/s73\n/s67/s32/s40Ω /s41\n/s84/s32/s40/s75/s41/s40/s97/s41\n/s67/s111/s50/s48\n/s67/s111/s51\n/s70/s101/s77/s110/s67/s111/s51\n/s82\n/s65/s80/s45/s82\n/s80/s32/s40Ω /s41\n/s84/s32/s40/s75/s41/s40/s98/s41\n/s67/s111/s50/s48/s70/s101/s77/s110/s67/s111/s51\n/s67/s111/s51\nFIG. 5: (a) Calculated ICvsT, and (b) calculated MR vsT\nfor three sample types as labeled.\ndencelsf(T)∝/radicalbig\n1/ρ(T) is possible. However, we show\nbelow that a dependence even stronger than 1 /ρis more\nlikely. We use βPy=γPy/Cu= 0.7,γCo/Cu= 0.8,βCo=\n0.36 for spin asymmetries, AR∗\nCo/Cu= 0.55fΩm2,\nAR∗\nPy/Cu= 0.5fΩm2for renormalized interface resis-\ntances, and δCo/Cu= 0.2,δPy/Cu= 0.25 for spin flip-\nping coefficients.8,11Their dependence on Tis neglected\ndue to the dominance of the band structure and impurity\nscattering far from the Curie temperature. For FeMn, we\nusedlsf,FeMn ≈0.5 nm, and ρFeMn= 87µΩcm. Scat-\ntering at its interfaces was modeled by adding 0 .5 nm\nto the nominal thickness of FeMn. To account for the\nCu contacts, the calculation included outer Cu layers of\nthickness tCu, determined as described below. These lay-\ners were terminated with fictitious spin sinks.\nTo demonstrate that CIMS is extremely sensitive to\nthe effects ofdiffusion, we now describe how our5 K data\ncan be fitted by appropriate choice of three parameters\nwhose values have the largest uncertainty: conductance\nGin Equation (1), effective MR-active thickness tCuof\nthe Cu contacts, and spin diffusion length lsf,Co. Calcu-\nlations for FeMnCo 3 were significantly affected only by\nG, which controls the asymmetry of CIMS. The values\nofIC/|I−|in mA measured at 5 K for three FeMnCo 3\nsamples were 2 .3/0.8, 1.6/0.6, and 3.1/1.5, giving an av-\nerage ratio IC/|I−|= 2.6. The calculated value increases\nfrom1.46atG= 0.5fΩ−1m−2to6.1atG= 2fΩ−1m−2\n(Fig. 4(a)). The best values IC/|I−\nC|= 3.34/1.27 are ob-\ntained at G= 0.87fΩ−1m−2, in reasonable agreement\nwith band structure calculations.5,19\nSpin diffusion in the bottom Cu layer has little effect\nonCo20 andFeMnCo due to the spin relaxation in Co\nand FeMn, respectively. To determine tCu, we use the ra-\ntiosIC/|I−|of the three Co3 samples, 3 .55/1.0, 4.6/1.5,\nand 4.2/1.2, giving an average ratio IC/|I−|= 3.4. The\ncalculated IC/|I−\nC|increases from 1 .9 fortCu= 0 to 14\nfortCu= 140 nm (Fig. 4(b)), and eventually diverges at\ntCu= 200nm. The best agreementwith data is obtained\nfortCu= 55 nm, resulting in IC/|I−\nC|= 4.4/1.3.\nLastly, diffusion in Co significantly affects CIMS in\nsamplesCo20, but not in Co3 andFeMnCo 3. We deter-\nminelsf,Cofrom the ratio IC/|I−|of fiveCo20 samples,\n8.9/2.1, 7.3/1.6, 9.0/2.0, 8.5/2.0, 8.0/1.7, giving an av-\nerage ratio IC/|I−|= 4.4. Fig. 4(c) illustrates that the4\ncalculated ratio IC/|I−\nC|increases from 1 .0 forlsf,Co= 0\nto 5.2 forlsf,Co= 100 nm. The best agreement with the\ndata is obtained for lsf,Co= 42 nm consistent with the\npublished values.11\nDespite the ability to model the 5 K data, the cal-\nculations did not reproduce the dramatic dependence of\nIConTin Fig. 2 (see below). Therefore, one can at-\ntempt to determine lsf,Cofrom the dependence of ICon\nT. Fig. 4(d) shows calculations for the residual values\nlsf,Co= 20 nm, 40 nm, and 60 nm. Large lsf,Coresults\ninICdecreasing with T, which is inconsistent with the\ndata. Small lsf,Cogives decrease of ICwithTin better\nqualitative agreement with data, but gives unreasonably\nsmallICat 5 K. Consequently, we return to the value\ndetermined from Fig. 4(c).\nFig. 5(a) shows the calculated ICvsTfor the three\nsample types. To interpret these results, we note that\nFigs. 4(b)-(d) exhibited an increase of ICwhen the ef-\nfective MR-active resistance of F 1determined by ρlsf\nwas increased. This relationship was also established an-\nalytically.5,20The experimental correlation between the\ndecreases of MR and increases of ICin Figs.1, 2 is of\nthe same origin. The lack of temperature dependence for\nFeMnCo 3isthereforeconsistentwith negligiblespin dif-\nfusion effects in F 1. In calculations for Co3, the increase\nofICwithTis caused by the increased contribution\ntCulsf,Cuto the effective resistance of F 1. Calculations\nforCo20 show a competition between the contribution of\nthe bulk Co resistivity, which increases with T, and the\ncontributionsfromthe Cu(50) layerandthe outerCo/Cu\ninterface, whichdecreasewith Tduetotheincreasedspin\nflipping in Co. However,both Co3 andCo20 calculations\ndo not reproduce the data, suggesting that the effects of\nthermal scattering should be re-examined.\nThe calculated dependence of MR on Twas in over-all agreement with data for Co3 andFeMnCo 3, but did\nnot reproduce the decrease at T <130 K seen in Co20\ndata (Fig. 5(b)). The calculations overestimated the val-\nues, suggestingthat oursamples maybe largerthan their\nnominal size. However, this seems to contradict the cal-\nculated temperature dependence of RPconsistent with\nthe data(not shown), and the values of ICthat arelarger\nthan the measured 5 K values. This discrepancy can be\nreduced e.g. by decreasing lsf,Py, which results in a de-\ncreased MR without significantly affecting CIMS.\nThe failure of Co20 calculations to capture the de-\ncrease of MR and the increase of ICatT <130 K in-\ndicates that lsf,Codecreases with Tmore rapidly than\nthe accepted lsf∝1/ρ, resulting in the reduction of\nthe effective MR-active resistance ρColsf,Co. One pos-\nsible mechanism for such a strong dependence may be\nelectron-magnon scattering which can result in electron\nspin flipping without significant momentum scattering.\nWe leave more detailed and perhaps alternative explana-\ntions to future studies.\nTo summarize, we performed magnetoelectronic mea-\nsurements of nanopillars with three different polarizing\nmagneticlayers. The samplesexhibited differentcurrent-\ninduced behaviors, attributed to the spin diffusion in the\npolarizing layer. The calculations reproduced the lower\ntemperature behaviors with reasonable values of trans-\nport parameters. However, temperature dependencies\nofmagnetoresistanceandcurrent-induced switchingindi-\ncate that the effects of thermal scattering on spin trans-\nport are more significant than presently believed.\nWe thank Mark Stiles, Jack Bass and Norman Birge\nfor helpful discussions. This work was supported by NSF\nGrant DMR-0747609 and a Research Corporation Cot-\ntrell Scholar Award. SB acknowledges support from the\nNASA Space Grant Consortium.\n1J. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996).\n2A.A. Kovalev, A. Brataas, and G.E.W. Bauer, Phys. Rev.\nB 66, 224424 (2002).\n3S. Zhang, P.M. Levy, and A. Fert, Phys. Rev. Lett. 88,\n236601 (2002).\n4A. Shpiro, P.M. Levy, and S. Zhang, Phys. Rev. B 67,\n104430 (2003).\n5J. Slonczewski, J. Magn. Magn. Mater. 247, 324 (2002).\n6O. Boulle, V. Cros, J. Grollier, L.G. Pereira, C. Deranlot,\nF. Petroff, G. Faini, J. Barnas, andA. Fert, Nature Physics\n3, 492 (2007).\n7S.Urazhdin, N.O.Birge, W.P. PrattJr., andJ. Bass, Appl.\nPhys. Lett. 84, 1516 (2004).\n8T. Yang, A. Hirohata, M. Hara, T. Kimura, and Y. Otani,\nAppl. Phys. Lett. 89, 252505 (2006).\n9M. AlHajDarwish, H. Kurt, S. Urazhdin, A. Fert, R.\nLoloee, W. P. Pratt, Jr., and J. Bass, Phys. Rev. Lett.\n93, 157203 (2004).\n10N. Theodoropoulou, A. Sharma, W.P. Pratt Jr., and J.\nBass, Phys. Rev. B 76, 220408(R) (2007).\n11J. Bass and W.P. Pratt Jr., JMMM 200, 274 (1999) andJ. Phys.: Condens. Matter 19, 183201 (2007).\n12S.Urazhdin, N.O.Birge, W.P. PrattJr., andJ. Bass, Phys.\nRev. Lett. 91, 146803 (2003).\n13S.D. Steenwyk, S.Y. Hsu, R. Loloee, J. Bass, and W.P.\nPratt Jr., J. Magn. Magn. Mater. 170, L1 (1997).\n14J. Xiao, A. Zangwill, and M.D. Stiles, Phys. Rev B 70,\n172405 (2004).\n15I.N. Krivorotov, N.C. Emley, J.C. Sankey, S.I. Kiselev,\nD.C. Ralph, and R.A. Buhrman, Science 307, 228 (2005).\n16I.N. Krivorotov, N.C. Emley, A.G.F. Garcia, J.C. Sankey,\nS.I. Kiselev, D.C. Ralph, and R.A. Buhrman, Phys. Rev.\nLett.93, 166603 (2004).\n17T. Valet and A. Fert Phys. Rev. B 48, 7099 (1993).\n18D.A. Goodings, Phys. Rev. 132, 542 (1963).\n19K. Xia, P.J. Kelly, G.E.W. Bauer, A. Brataas, and I.\nTurek, Phys. Rev. B 65, 220401R (2002).\n20S. Urazhdin, R. Loloee, and W. P. Pratt Jr., Phys. Rev. B\n71, 100401 (2005).\n21J. Bass and W.P. Pratt Jr., private communications."    },    {        "title": "0805.3191v2.Energetic_Analysis_of_Magnetic_Transitions_in_Ultra_small_Nanoscopic_Magnetic_Rings.pdf",        "content": "arXiv:0805.3191v2  [cond-mat.other]  22 May 2008Energetic Analysis of Magnetic Transitions in Ultra-small Nanoscopic Magnetic Rings\nDeepak K. Singh1, Robert Krotkov1, and Mark T. Tuominen1∗\n1Department of Physics, University of Massachusetts, Amher st, MA 01003\n(Dated: October 30, 2018)\nIn this article, we report on experimental and theoretical i nvestigations of magnetic transitions\nin cobalt rings of size (diameter, width and thickness) comp arable to the exchange length of cobalt.\nMagnetization measurements were performed for two sets of m agnetic ring arrays: ultra-small mag-\nnetic rings (outer diameter 13 nm, inner diameter 5nm and thi ckness 5 nm) and small thin-walled\nmagnetic rings (outer diameter 150 nm, width 5 nm and thickne ss 5 nm). This is the first report\non the fabrication and magnetic properties of such small rin gs. Our calculations suggest that if\nthe magnetic ring’s sizes are comparable to, or smaller than , the exchange length of the magnetic\nmaterial, then only two magnetic states are important - the p ure single domain state and the flux\nclosure vortex state. The onion-shape magnetic state does n ot arise. Theoretical calculations are\nbased on an energetic analysis of pure and slightly distorte d single domain and flux closure vortex\nmagnetic states. Based on the analytical calculations, a ph ase diagram is also derived for ultra-small\nring structures exhibiting the region for vortex magnetic s tate formations as a function of material\nparameter.\nPACS numbers: 75.75.+a, 81.16.-c, 75.60.Ej\nI. INTRODUCTION\nIn recent times, the magnetic ring geometry has been\nextensively studied, mostly because of its possible ap-\nplications in magnetic memory devices. The application\nin memory devices is mostly driven by the fact that near\nzerofield value, a narrownanoscopicmagnetic ring forms\naflux closurevortexmagneticstate.1,2,3A magneticring\nin vortex state has zero total magnetization and there-\nfore each ring in an array acts like an individual memory\nelement. Ring geometry is used in atleast one current\ndesign of magnetic random access memory (MRAM).4\nIn addition to the vortex magnetic state, a small mag-\nnetic ring also forms two other stable magnetic states:\n”onion state”, characterized by the presence of two head-\nto-head domain walls, and single domain (SD) state, as\nshown in Fig. 1.5However, we have found that if the\nring sizes are sufficiently small then onion magnetic state\nhas higher energy and does not arise. Therefore, mag-\nnetictransitionprocessesinsuchultra-smallringsinvolve\nonly two magnetic states: saturating SD state and flux\nclosure vortex state. These conclusions are based on the\ncalculation of total magnetic energies for various possible\nmagnetic states and on the measurement of magnetiza-\ntion as a function of applied field.\nBecause of the circular geometry of rings, shape\nanisotropy is absent and also if the parent magnetic ma-\nterial is of polycrystalline origin then magnetocrystalline\nanisotropy is limited to random grains and can be ig-\nnored also.6Therefore in zero field the only competing\nenergyterms in the caseofpolycrystallinemagneticrings\nare magnetostatic energy and quantum mechanical ex-\nchange energy.7,8. Exchange energy favors the parallel\nalignment of spins while the magnetostatic energy favors\nthe circular magnetization.\nIf the ring’s sizes (diameter, thickness and width) are\ncomparabletothecharacteristiclength(exchangelength)(a) (b) (c)\nFIG. 1: (color online) Magnetic states of nano-rings. (a) Vo r-\ntex magnetic state. (b) Onion magnetic state, with domain\nwalls. (c) Single domain magnetic state.\nof the parent magnetic material then the magnetic tran-\nsition processes areexpected to be different from those in\nrelativelylargersizenanoscopicrings( ∼100nm). In this\nnew geometrical regime, it is reasonable to assume that\nthe magnetization vector remains confined in the plane\nof the ring. In this article, we are presenting the study\nof magnetization and magnetic transitions in ultra-small\npolycrystalline magnetic, Co, rings of sizes comparable\nto the exchange length of Co ( lex= 3.8 nm).9For the\nfirst time, magnetic rings are studied at such an unprece-\ndented small length scale.\nThe magnetic rings are fabricated using copolymer\ntemplate, angular metal evaporation and ion-beam etch-\ning technique. Using this fabrication technique, we have\nbeen able to fabricate arrays of rings at two geometri-\ncal scales: ultra-small rings with outer diameter 13 nm,\nring width 4 nm and thickness ∼5 nm and small rings\nwith outer diameter 150 nm, ring width 5 nm and thick-\nness∼5 nm. The latter are small rings with a thin\nwall. Magnetization measurements are carried out for\narrays of both ultra-small and small rings. Experimen-\ntal dataareexplained by detailed theoreticalcalculations\nfor these rings. The theoretical calculations are based on\ntheenergeticanalysisofpossiblemagneticstateswiththe\nunderlying assumption that only the lowest energy mag-2\nnetic states will be excited. Different magnetic states in\na ring structure are obtained using reasonable models of\nmagnetization distortion on the ring’s circumferences.10\nII. FABRICATION PROCEDURE\nRecently small ferromagnetic rings have been fabri-\ncated by electron beam lithography,1,11evaporation over\nspheres12and other methods.13,14Our nanoring fab-\nrication technique is described in detail in an earlier\nwork.15The fabrication process for both ultra-small and\nsmall rings with thin wall (arms) involve the creation\nof nanoporous polymer templates, angular deposition of\ndesired material, Co, onto the wall of the pores and ion-\nbeam etching technique to remove undesired material\nfrom the top as well as bottom of the template. In the\ncase of ultra-small rings, the template is created from a\nself-assembled diblock copolymer film16while for small\nrings, the template is created by electron-beam lithog-\nraphy technique17out of the 40 nm thick copolymer\nfilm PMMA [poly(methyl-metha-acrylate)]. The diblock\ncopolymer film has the pore size of 13 nm on the av-\nerage and thickness 36 nm. The lattice separation be-\ntween pores is about 28 nm. In the case of copolymer\nPMMA film, the pore size is 150 nm and the separation\nbetween pores (center-to-centerdistance) is 350 nm. The\nangular deposition of desired material onto the wall of\nthe nanopores is the most critical step of this fabrication\nscheme and it depends on the critical deposition angle,\nθc. In our experiment w= 13 nm and h= 36 nm for the\nfabrication of ultra-small rings and w= 150 nm and h=\n40 nm for small rings, resulting in the critical angles of\nθc∼20oand 75orespectively. Angles of θ= 23oand 75o\nwere chosen for the fabrication of ultra-small and small\nrings respectively. The thickness of deposited Co mate-\nrial on nanopores varies in the range of 4-5 nm (based\non QCM reading). After material deposition, calibrated\nion-beam etching is used to get the desired thickness of\nboth ultra-small and small rings. The desired resulting\nthicknesses of both ultra-small and small rings are ∼5\nnm.\nAfter ion-beam etching, the small ring samples are\nrinsed in acetone solvent to remove the remaining poly-\nmerresiduesandarecharacterizedbyfield emissionscan-\nning electron microscope (FESEM) (Figure 2). Struc-\ntural characterization of ultra-small rings is done using\ntunneling electron microscope (TEM) (Figure 2). Sam-\nple preparation of ultra-small rings for TEM imaging in-\nvolved the transfer of ring templates onto an electron\ntransparent substrate. It is a difficult process and can be\nfound in detail somewhere else15. For the magnetic mea-\nsurement process, ultra-small rings were not transferred\non electron transparent substrate.\n(a) (b)\nFIG. 2: (color online) Images of rings. (a) TEM image of\nultra-small rings and some empty diblock pores (rings came\nout of these pores during sample preparation for imaging).\n(b) FESEM images of small rings with thin wall.\nIII. MAGNETIZATION MEASUREMENTS AND\nDATA ANALYSIS\nMagnetic measurements of ultra-small and small ring\narrays were carried out in a SQUID magnetometer with\nbase temperature 1.8 K and field applied in-plane of the\nring. Figure 3 and 4 shows magnetization measurements\nfor arrays of ultra-small and small rings respectively, af-\nter the subtraction of a linear diamagnetic background.\nAs we can see in the low temperature in-plane magne-\ntization data for both ultra-small and small rings, the\nwidth of the hysteresis curve is smaller near zero field\nvalue than near the saturation which is similar to the\nmagnetic transition in nanoscopic narrow rings.18In rel-\nativelylargersizenanoscopicrings, itisobservedthatthe\nmagnetic state is single domain (SD) state at saturating\nfield value and as the field is decreased, the ring’s mag-\nnetic state forms an ”onion-shape”, near zero field value,\nand finallytransformstoflux closurevortexstate (Figure\n1).3,4It also depends on the ring’s width, diameter and\nferromagnetic exchange length.19\nTo have a complete understanding of these magnetic\ntransition phenomena, one needs to solve the following\nintegro-differential equation:20,21\nl2\nexd2β\nd2φ+cos(β)ρ2hM−sin(β)ρ2hM−sin(β)ρ2hax= 0\nhM(ρ,φ) =/integraldisplay\ndφ′σ(β,φ′)K(ρ,φ,φ′) (1)\nwhereρis the radial co-ordinate, σis magnetic pole den-\nsity (depending on azimuthal position φ′), the kernel K\nis an explicit but complicated function involving ρand\nφandXis the direction of applied magnetic field. By\nsolving these integro-differential equations, we can get\nthe functional β(h,φ) and since m(h) =cosβ, explained\nlater, (here we have taken m= 1 just for the sake of sim-\nplicity), so we can get m(magnetization) as a function\nofh(dimensionless magnetic field). This is not an easy\ntask. Another approach is reverse approach.\nIn this approach, a reasonable model for magnetiza-\ntion distribution on ring’s circumference is assumed in3\n-1.0-0.50.00.51.0M / Ms\n-4000 0 4000\nField (Oe)T = 2 K\n1.0\n0.5\n0.0\n-0.5M / Ms\n-4000 0 4000\nField (Oe)T = 300 K(a)\n(b)\nFIG. 3: (color online) In-plane magnetization measurement s\nfor an array of ultrasmall Co rings. (a) Measurements at 2 K.\n(b) Measurement at 300 K.\nzero field value and total energy is calculated for dif-\nferent possible magnetic states, starting from the first\nprinciple. For any shape of body, those magnetic config-\nurations which are energetically favored are dominant in\ndeterminingthemagneticbehavior.5Ingeneral,themag-\nneticstateofaringwillbedeterminedbythecompetition\nbetween exchange energy, magnetostatic energy, Zeeman\nenergy and magneto-crystalline energy. The exchange\nenergy contribution favors the parallel alignment of the\nlocal magnetization mover the entire body while mag-\nnetostatic energy favors configurations where the magne-\ntization follows a closed path inside the body, so that no\nnet magnetic moment is produced.\nBefore considering the magnetization distributions on1.0\n0.5\n0.0\n-0.5\n-1.0M/Ms\n-4000 0 4000\nField (Oe)T = 2 K\n1.0\n0.5\n0.0\n-0.5\n-1.0M/Ms\n-2000 0 2000\nField (Oe)T = 300 K(a)\n(b)\nFIG. 4: (color online) (a) Magnetization measurements data\nfor thin wall small rings at 2 K. (b) Magnetic measurement\nat 300 K.\nthe ring’s circumference in detail, we first calculate the\nenergies of the uniformly magnetized SD, flux closure\nvortex and onion states near zero field (Figure 1). For\nthis purpose, first we consider ultra-small ring. Since the\nthickness (5 nm) and width (4 nm) of the ultra-small\nring are comparable to the exchange length of Co mate-\nrial (lex= 3.8 nm),9magneto-crystalline anisotropy can\nbe ignored for simplicity. For an ultra-small ring, the\nenergetic analysis described below shows that only sin-\ngle domain and vortex states are of significance at fields\nnear zero; the energy of the onion state lies far above.\nAn important underlying assumption in the calculation\nof energy is that since the thickness and width of the\nring are comparable to the exchange length for cobalt,4\nthere is no variation of magnetization along the symme-\ntry axis (easy axis), of the ring i.e. magnetization pat-\ntern is purely two-dimensional in nature. Recently other\nauthors22,23have found that the variation of magnetiza-\ntion along the symmetry axis in the relatively larger size\nmagnetic rings leads to triple point behavior, separating\nSD,vortexandonionmagneticstatesasafunctionofma-\nterial’s properties, in phase diagram. We have discussed\nthese results later in the discussion section.\nIn dimensionless form, the free energy for a magnetic\nsystem of volume Vis given by,24\nE=Eex+Ean+Em+Ezeeman\n=1\nV/integraldisplay\n(l2\nex\n2(∇m2)+κf(m)−1\n2(hm•m)−ha•m)d3r\nHerehm=HM/Msandha=Ha/Msare dimension-\nless magnetic fields. Hais the applied magnetic field,\nandHMis the magnetic field produced by the magne-\ntization of the sample, which has saturation magnetiza-\ntionMs.κ= 2K1/µ0Ms2=Han/Ms, where K1is\nthe first crystalline anisotropy constant (which will be\ntaken to be zero for simplicity). The exchange length\nlex=√(2A/µ0Ms2), where Ais the exchange stiffness\nconstant. For the uniformly magnetized SD state, the\nexchange energy is zero and the total energy is the sum\nof the magnetostatic and Zeeman contributions.\nESD=Em+Ezeeman (2)\n= 0.2−ha (3)\nIn the above equation, the dimensionless magneto-\nstatic energy Em= 0.20 was obtained by numerical inte-\ngration. Numerical integration for magnetostatic energy\nis carried out by assuming the ring’s inner and outer sur-\nfaces as two oppositely magnetic charged ribbons sepa-\nrated from each other by the width of rings. Thickness\nof that ribbon is 5 nm (ring’s thickness). We write the\nmagnetostatic potential at an arbitrary point, in the re-\ngion between ribbons, and then numerically integrate it\nover the volume of the ring.\nFor the vortex state, the magnetostatic, domain wall\nandZeemanenergycontributionsareallzero,sothe total\nenergy is solely exchange energy.\nEvortex=Eex (4)\n=l2\nex\nR2\n2−R2\n1[lnR2\nR1] (5)\nTo calculate the energy of the onion configuration, we\nseparate it into two parts: the ring arms and the domain\nwalls(DW). Thecontributingenergytermsareexchange,\nZeeman and magnetostatic. Exchange energy is propor-\ntional to ∇m2, so the vortex and the ring arms of the\nonion state have the same exchange energy. The energy\nof onion magnetic state is\nEonion=Eex+Ezeeman+Em(ringarms )+EDW\n=l2\nex\nR2\n2−R2\n1ln(R2\nR1)−2\nπ[ha]+Em(ringarms )+EDW0.8\n0.6\n0.4\n0.2\n0.0\n-0.2E / P0Ms2V\n-0.5 0.0 0.5\nha Vortex curve\n Onion curve\n SD curve\nFIG. 5: (color online) Magnetic energies of ultra-small rin gs.\nEnergies of SD, vortex and onion states as functions of dimen -\nsionless applied field ha. (The onion curve is a lower limit -\nsee text.)\nwhereR1is the innerradius, R2is the outerradius. Both\nEm(ringarms )andEDWare positive: each increases the\ntotal energy of the onion state.\nTheenergiesoftheSDandvortexstates, togetherwith\na lower limit of the onion state energy, are plotted as\nfunctions of the dimensionless applied field hain Figure\n5. The lower limit is obtained by neglecting the domain\nwall and magnetostatic terms. This figure suggests that\nthe energy landscape has three local minima and that\nthese three magnetic states have locally minimal ener-\ngies. According to this energy plot, it is inferred that\nSD state is always lowest in energy. Vortex and onion\nmagnetic state does not excite. Hence the corresponding\nmagnetic hysteresis curve would be a one step transi-\ntion, from one SD state to another SD state of opposite\npolarity. This is not exactly the experimental data for\nultra-small magnetic rings (Fig. 3).\nAs mentioned previously, rings are made of polycrys-\ntalline Co material. In the case of polycrystalline mate-\nrial, random anisotropies of grains play a crucial role in\ndetermining the intergranular interaction. If the grains\nare small then intergranular interactions becomes more\ndominating than interatomic exchange interaction and\nthus lower the exchange length values. As a result, the\nenergy of vortex magnetic state would be smaller. In\nthat case, a transition from saturating SD state to vor-\ntex state, near zero field value, is quite likely.\nDepending upon the polycrystalline exchange length\nof Co, magnetic transition in ultra-small ring can oc-\ncur from SD state to vortex state via the distortion of\npure SD state, or from the pure vortex state to pure SD\nstate via the distortion of vortex state. An important5\n(a) (b) (c)Saturating\nfield valueIntermediate\nfield valueNear zero\nfield valueField value\nreducingh\nFIG. 6: (color online) (a) At very high field value, the mag-\nnetic state of ring is single-domain, (b) when the field is re-\nduced then possible magnetic state may be a distorted SD\nstate and (c) near 0 field value, the magnetic state of ring\nbecomes vortex state.\nquestion arises then: are these intermediate (distorted)\nmagnetic states stable i.e. lower in energy compared to\npure SD and vortex states respectively. It is found that\nsmall distortions of the SD state increases its energy. In\nthe following section, detail calculation and results are\nexplained for distorted SD and vortex state.\nIV. DISTORTED SINGLE DOMAIN AND\nVORTEX STATES\nFor an ultra-small ring, at very high field the magnetic\nstate is saturated single domain. When the field is re-\nduced from the saturation value, SD state is supposed\nto distort and eventually attains a vortex configuration\nnear zero value of field, depending on the polycrystalline\nexchange length of Co material. A schematic descrip-\ntion of this phenomenon is shown in Figure 6. In this\nfigure, we call the magnetic state at intermediate field\nvalue as the ”distorted single domain state”. If the dis-\ntorted SD state is unfolded into one dimension, then the\nenvelop over magnetic spin shows an oscillatory charac-\nter, as shown below in Figure 7a.\nIn Figure 7a, βis the angle between an arbitrary spin\nand the applied field axis. An arbitrary spin is repre-\nsented by the angle φon the circumference of ring. So\nφvaries between 0 and 2 π. The very important under-\nlying assumption in this model is the slow variation of\nangleβover the circumference of ring in the distorted\nsingle domain magnetic state. Now we seek a function\nβ=f(φ), which will give us magnetization distribution\nas shown in the profile in Figure 7a. By keeping in mind\nthat the profile of magnetic spins shows oscillatory be-\nhavior, we make an assumption for the variation of angle\nβas a function of φas:\nβ=εsin2φ (6)\nmx=cosβ (7)\n=cos(−εsin2φ) (8)\nwhereεis the distortion coefficient and Xis the direction\nof externally applied magnetic field. Figure 7b shows the1.0\n0.8\n0.6\n0.4\n0.2\n0.0Mx\n-3 -2 -1 0 1 2 3\nM\u0003(in radians)\n(a)\n(b)\nFIG. 7: (color online) (a) One dimensional profile of magneti c\nspins of distorted SD state. Magnetic spins are represented\nby the azimuthal angle φand angle between one arbitrary\nspin and the applied field axis is β. In this model angle ?\nis supposed to be slowly varying through the circumference\nof ring. (b) In this picture variation of mxis plotted as a\nfunction of φfor two different values of distortion parameters\nε= 0.2 (Blue curve) and 0.5 (Red curve)\nvariations of mxas a function of φfor two different dis-\ntortion parameters of ε= 0.2 and 0.5. It is a reasonably\ngood approximation (if not exact) for magnetization dis-\ntribution. For different values of distortion coefficients,\nthe distortion of magnetic spins on the circumference of\na ring is shown in Figure 8.\nIn single domain state, β(φ) = 0, so ε= 0, which is\nsame as in Figure 8. On the other hand if ε= 1 then not\nall the spins are aligned along the magnetic field. Spins\nwhich are not aligned along the magnetic field appear\nto be distorted from their original direction while other\nspins are still aligned along the magnetic field direction.\nWe call this state as distorted SD magnetic state. At6\nPure SD \nstate\n(İ= 0.0)Distorted SD \nstate\n(İ= 0.2)Distorted SD \nstate\n(İ= 1.0)\nFIG. 8: (color online) (a) In this picture we see that for the\nvalue of distortion coefficient ε= 0, all the spins are aligned\nin along the magnetic field direction and thus creating a SD\nmagnetic state. (b) For the value of distortion coefficient ε\n= 0.2, not all the spins are aligned along the magnetic field\ndirection and therefore creating a distorted SD state. (c)\nHighly distorted SD state, ε= 1.0.\nzero applied field, the total dimensionless energy, g( ε), of\ndistorted SD state is the sum of two terms:\ng(ε) = gex(ε)+gms(ε)\nAs mentioned in the previous section, we reasonably\nignore crystalline anisotropy term in total energy calcu-\nlation.\nStarting from the first principle (as described in previ-\nous section), exchange energy and magnetostatic energy\nare calculated as a function of distortion coefficient ( ε)\nfor ultra-smallringgeometry. All the three energyterms,\nexchange energy, magnetostatic energy and total energy\nare plotted in Figure 11 as a function of distortion co-\nefficient ε. In this figure, if all the spins are aligned in\none direction i.e. no distortion ( ε= 0) and thus creating\na SD state then exchange energy is minimum (zero) but\nmagnetostatic energy is maximum. As the distortion is\nincreased so that spins are not aligned in one direction\nand therefore it is no longer a pure SD state then ex-\nchange energy also increases for increasing values of ε\nbut magnetostatic energy shows different trend. Magne-\ntostatic energy starts decreasing for increasing values of\ndistortion coefficient but for higher distortions ( ε≥1.2)\nthe magnetostaticenergystartsincreasingagain. Theto-\ntal energy of distorted SD state increases with increasing\nvalue ofε.\nAlthough magnetostatic energy decreases for increas-\ning values of εbut it does not affect the overall increase\nof total energy. This happens because of larger exchange\nenergy contributions as the pure SD state becomes more\nand more distorted. Thus we conclude that for perturba-\ntions ofthis particularform, the minimum energystate is\nstill of pure SD state. It means, for this model function\n(β=f(φ)), pure SD state has lower energy than dis-\ntorted single domain states in zero field. Since exchange\nand magnetostatic energies are independent of field, so\nevenin the presenceoffieldpure SDstateisstill oflowest\nenergy as compared to distorted SD states. For different\nvalues of ε(pure SD and perturbed SD states), total en-\nergy of an ultra-small ring are plotted in Figure 10 as a\nfunction of applied magnetic field. Here it is important1.5\n1.0\n0.5\n0.0Energy g ( H\f\n1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0\nDistortion coeff. ( H\f Total energy\n Magnetostatic energy\n Exchange energy\nFIG. 9: (color online) Energies of pure SD state and distorte d\nSD state for an ultra-small magnetic ring are plotted in this\nfigure as a function of distortion coefficient ε.\n2\n1\n0\n-1Energy (dimensionless)\n-1.0 -0.5 0.0 0.5 1.0\nha Pure S D state\n Distorted SD state ( H\u0003 \u0003\u0013\u0011\u0017\f\n\u0003Distorted SD state ( H\u0003 \u0003\u0010\u0013\u0011\u0017\f\n\u0003\nFIG. 10: (color online) Inthis figure, energies of pureSDsta te\nand distorted SD states are plotted as a function of field.\nto mention that the distorted SDstate with ε=1.0is not\nan ”onion” magnetic state. The onion state will have ex-\ntra energy as a result of formation of domain walls. Our\ncalculations suggest that distorted states with εgreater\nthan zero are higher in energy than the pure SD state,\neven though states with different εhave different sensi-\ntivities to applied field (i.e. Zeeman energy depends on\nε). Perhaps the magnetization does distort, but to some\nother shape, that we did not take into account.\nAnotherpossiblemagnetictransitioninvolvesthemag-\nnetic state of ultra-small ring is already a vortex state7\nPure vortex state\n(İv= 0)\nDistorted vortex state\n(İv= 0.5)\nFIG. 11: (color online) (a) In this picture we see that for\nthe value of distortion coefficient εv= 0, magnetization spins\nform a circular vortex magnetic state. (b) For the value of\ndistortion coefficient εv, all magnetization spins are not along\nthe tangential direction on a circle’s periphery inside the ring\nand therefore do not form a pure vortex state. We call this\nstate a distorted vortex state.\nnear zero value of field and it makes transition to sat-\nurating single domain state via some intermediate mag-\nnetic state. For this purpose, we consider another realis-\ntic model that involves a vortex distortion constant, εv.\nIn this model, vortex magnetization state is given by,\nmx=cosβ\nβ(φ) =π\n2+φ−εvcosφ (9)\nonce again β(φ) is the angle between the direction of the\nmagnetization and the field direction (applied along the\nx-axis). Different vortex states are shown in Figure 11\nfor the vortex distortion constants, εv, of 0 and 0.5. For\nthe vortex distortion constant value of εv= 0 means no\ndistortion and in that case, β(φ) =π/2 +φ. We see\nthat forεv= 0, magnetization configuration is indeed of\npure vortex state. Again, the total energy of the ultra-\nsmall ring in zero field consists of exchange and magne-\ntostatic energy terms (ignoring the magneto-crystalline\nanisotropy energy term in the total energy calculation).\nThe first principle calculation of exchange energy for dis-\ntorted vortex states as a function of εvis given by the\nfollowing equation:\ngex(εv) =(1/2)l2\nex\nπ(R2\n2−R2\n1)π(2+ε2\nv)lnR2\nR1(10)\nMagnetostatic energies for distorted vortex states are\ncalculated by numerical integrations (as explained pre-\nviously). The energies for distorted vortex states as a\nfunction of vortex distortion constant εvare plotted in\nFig. 12, in zero applied field. In this figure, the pure vor-\ntex state is indeed the lowest energy state in zero field\nbecause of the dominance of exchange energy term in\nthe total energy. However as we will see in the following\nparagraph, this is not the case in the presence of field.\nIn the presence of field, the total energy consists of\nthree terms:0.7\n0.6\n0.5\n0.4\n0.3\n0.2\n0.1\n0.0g(dimensionless)\n-1.0 -0.5 0.0 0.5 1.0\nHv Exchange energy\n Magnetostatic energy\n Total energy\nFIG. 12: (color online) Energies of pure and distorted vorte x\nstates, in zero field, are plotted in this figure as a function o f\ndistortion coefficient εv.\ng(εv) = gex(εv) + gms(εv) + gzeeman(εv)\nThe calculated Zeeman energies for distorted vortex\nstates is given by:\ngzeeman(εv) =−ha\n2/π2πBesselJ [1,abs(εv)]sign[εv]\nTheZeemanenergyisproportionaltothe appliedfield ha\n. Soatfirstinstanceitappearsthat purevortexstatewill\nalways remain the magnetic state of lowest energy but at\nthe same time we see from the Zeeman energy expression\nthat the slope of the Zeeman energy curve depends on\nthe distortion parameter εv. Total energy, including the\nZeeman energy, for pure as well as distorted vortex states\n(distortionparameters εv=0.2,0.3)areplottedinFigure\n13 as a function of applied field. Some very interesting\nbehaviors are observed in this figure.\nNear zero field values, pure vortex state is still the\nlowest energy state. At a field of 0.2 or so the state\nwith distortion εv= 0.2 crosses over to become lower\nthan the state with distortion εv= 0.0. At a somewhat\nhigher field the green state with distortion parameter εv\n= 0.3 becomes the one with lowest energy. This is not\nexactly the case for distorted SD states (Figure 10), as\ndiscussedearlier. Inthecaseofsingledomainstates,pure\nSD state remains lowest in energy as the applied field is\nchanged. Thereforedistorted single domain states can be\nignored in considering the magnetic transition for ultra-\nsmall rings. Thus there are three important states to\nconsider: pure SD state, pure vortex state and distorted\nvortex state. In Figure 13 we have plotted all these en-\nergies as a function of applied field. It is observed that\npure SD state is always the lowest energy state. In this\nfigure, an additional vortex state, arising for a lower ex-\nchange length value ( lex= 2.7 nm) of polycrystalline Co8\n0.6\n0.4\n0.2\n0.0\n-0.2E / P0MsV2\n-1.0 -0.5 0.0 0.5 1.0\nha Pure VORTEX state (lex = 3.8 nm)\n Pure SD state\n Pure VORTEX state (lex = 2.7 nm)\n Distorted VORTEX state ( Hv = 0.2)\n D istorted Vortex state (0.3)\nFIG. 13: (color online) This plot shows total magnetic en-\nergies of pure and perturbed vortex magnetic configurations\n(red, light blue and green lines), together with the energy o f\nthe pure SD state (dark blue line) as a function of applied\nfield. Pure SD state is always the lowest energy state.\nmaterial, is also plotted. This vortex curve intercepts\nthe pure SD curves at dimensionless ha=±0.01. The\nimplications are explained in the following section.\nV. DISCUSSION\nBased on the above analysis and crystalline exchange\nlength value ( lex= 3.8 nm), the magnetization hysteresis\ncurve for ultrasmall ring would be one step transition at\nzero field which is not quite the experimental data (Fig-\nure 3). The experimental hysteresis curve shows zero\nmagnetization at ha=±0.01 (equivalent to ±90 Oe of\napplied magnetic field). Now, as mentioned previously,\nthe rings are poly-crystalline, resulting in an effective ex-\nchange length that is smaller than the 3.8 nm bulk value\nused in the calculations. For a given geometry, the en-\nergy of a vortex at zero field is proportional to the square\nof the exchange length, while the energy of an SD state\nis independent of the exchange length. If we consider an\nexchange length of 2.7 nm for the polycrystalline Co ma-\nterial then the vortex state has the lowest energy at zero\nfield and is degenerate with an SD state at fields ofabout\nha=±0.01 (Figure 13). Theoretically, the correspond-\ning hysteresis curve would be two steps separated by a\nshort plateau of width about 0.02, as shown in Figure\n13. This provides a qualitative explanation of the exper-\nimental magnetization data of ultra-small magnetic rings\natT= 2 K.\nFromthis analysiswecanconcludethat nearzerofield,\nultra-small rings will be in either a single domain state0.20\n0.15\n0.10\n0.05\n0.00\n-0.05E/P\u00130\u0015\nsV\n0.10 0.00 -0.10\nha Vortex state energy curve\n Onion state energy curve\n Single-domain state energy curve\nFIG. 14: (color online) Energy plot for thin wall small ring\nof diameter 150 nm, width 5 nm and thickness 5nm is shown\nin this figure. In the case of small ring of thin walls, the\nmagnetic transition occurs via the formation of vortex stat e,\neven for the exchange length value of lex= 3.8 nm.\nor a vortex state, depending upon the polycrystalline ex-\nchange length value. The onion state is not expected to\nplay a role.\nNow we check the validity of above analysis for ultra-\nsmall magnetic rings in relatively longer geometrical\nregime of small ring of thin wall (outer diameter 150\nnm). Asmentionedinthefabricationsection,smallring’s\nwidth and thicknesses are comparable to that of ultra-\nsmall rings and therefore to the characteristic length of\nCo. However, the outer diameter of small rings are an\norder of magnitude larger than the diameter of ultra-\nsmall rings. The vortex energy and magnetostatic en-\nergy depends on the outer diameter of the ring geometry.\nBased on the first principle calculation, the three possi-\nble energy terms SD, onion and vortex magnetic state\nare plotted as a function of magnetic field in Figure 14.\nAs inferred from Fig. 14, in this case also the onion\nstate does not arise and the magnetic transition occurs\nbetween two SD states via the formation of vortex mag-\nnetic state. Interestingly, in the case of thin wall small\nrings vortex magnetic state arises even for the exchange\nlength value of lex= 3.8 nm. The reason behind this\nis the dominance of magnetostatic energy term in the\noverall energy counting. Therefore as the lateral size of\na ring increases, magnetostatic energy starts dominat-\ning over the exchange energy term. The experimental\n(in-plane) magnetization data (at 2 K) for small rings,\nFigure 4, does not seem to be in good agreement with\nFig. 14. Although the magnetic transition starts occur-9\n7\n6\n5\n4\n3\n2\n1\n0lex (nm)\n14 12 10 8 6 4 2 0\nW (nm) R1 = 1.25 nm\n R1 = 2.5 nm\n R1 = 4 nm\n R1 = 5 nm\nSD regime\n VORTEX regime\nFIG. 15: (color online) This figure represents the phase-\ndiagram for ultra-small magnetic rings with in-plane (2-D)\nmagnetization pattern. It also shows that whether SD or vor-\ntex state is lowest at zero field for a given size ring.\nring around ∼1000 Oe of field value but the curvature of\nmagnetic transition is very large, in terms of field, indi-\ncating that the magnetic transition process in small rings\nmay not be as simple. As the overall ring size increases,\nthe magnetostatic energy of the distorted SD states start\ndominatinginthe totalenergycountingandthereforeen-\nhances the possibility of interaction between individual\nring elements. It leads to magnetocrystalline anisotropy\nin the ring arrays that we have not taken into account in\nthe calculation. Someauthorshavecalculatedanisotropy\nenergy for relatively thicker magnetic rings.25More gen-\neral first principle calculation would be necessary to un-\nderstand the magnetization reversal in thin wall small\nrings.\nMagnetic measurements at room temperature for both\nultra-small and small rings do not show any magnetic\nhysteresis. At high temperature, thermal fluctuations\nplay dominant role, as compared to the magnetic energy\nof these rings. This cancels out any remnant magneti-\nzation at zero field. Weakly noticeable asymmetricity ofmagnetization loops for positive and negative fields, in\nthe low temperature magnetic hysteresis curve of ultra-\nsmall ring arrays (Fig. 3a), is possibly due to the weak\nexchange bias phenomena. On the surface of the ring,\npartial oxidization of Co material into CoO creates an\ninterface of FM (Co) / AFM (CoO) layer, resulting into\nvery weak exchange bias phenomena. A similar behavior\nhas recently been reported in the caseof magnetic disk.26\nNow we summarize the above analysis for ultra-small\nring geometry. Rings made of polycrystalline Co mate-\nrialcanhavesmallerexchangelength than the crystalline\nvalue. This exchange length, along with the ring’s geo-\nmetrical parameters, decides which magnetic state has\nthe lowest energy at zero field. Increasing the diame-\nter reduces both the magnetostatic and exchange ener-\ngies but the exchange energy decreases more rapidly and\ntherefore magnetostatic energy starts dominating as the\noveralldiameter ofthe magnetic ringincreases. Forgiven\ninner and outer radii difference, there is a value of the\nexchange length at which the vortex and SD states are\ndegenerate at zero field. We have also drawn a phase-\ndiagram in Figure 15 that shows the value of exchange\nlength,lexas a function of ring width w(R2-R1). If the\nring’s exchange length is larger than the ordinate of that\npoint, the SD states will be lowest at zero field, otherwise\navortexstatewillbethelowest. Thisphasediagrammay\nnot be valid for larger size nanoscopic rings. As there is\na strong underlying assumption in the above analysis is\nthat the magnetization pattern in the case of ultra-small\nmagnetic ring is purely 2-D. Magnetization vector does\nnot cant-out of the ring’s plane. For an ultra-small ring\nwith width and thicknesses comparable to the charac-\nteristic length (exchange length) of the parent magnetic\nmaterial, this assumption is quite reasonable. As a con-\nsequence, we do not observe the ”triple point” – defined\nas the point where the energies for onion, vortex and uni-\nform out-of-plane magnetization are same – as recently\nreported by other authors based on theoretical calcula-\ntions for the ring geometry.22,23.\nAcknowledgements\nThis project was supported by NSF Grants DMR-\n0531171, DMR-0306951 and MRSEC.\n1Y. G. Yoo , et al., Appl. Phys. Lett. 82, 2470 (2003).\n2M. Klaui , et al., J. Phys.: Cond. Matt. 15, R985 (2003).\n3M. Natali , et al., Phys. Rev. Lett. 88, 157203 (2002).\n4J. G. Zhu , et al., Jour. Appl. Phys. 87, 6668 (2000).\n5J. Rothman , et al., Phys Rev Lett 86, 1098 (2001).\n6R. Skomsky, Chapter 10, Spin Elctronics, Springer Pub-\nlishing Group (2000).\n7R. P. Cowburn , et al., J. Phys.D: Appl. Phys. 33, R1\n(2000).\n8A. Aharoni , et al., Phys. Rev. B 45, 1030 (1992).9J. M. D. Coey, Chapter 12, Spin Elctronics, Springer Pub-\nlishing Group (2000).\n10Deepak Kumar Singh, Ph. D. Thesis 2006, Uni-\nversity of Massachusetts Amherst, Available at:\nhttp://scholarworks.umass.edu/dissertations/AAI3242 328/.\n11L. J. Heyderman , et al., Jour. Appl. Phys. 93, 10011\n(2003).\n12F. Q. Zhu , et al., Advanced Materials 16, 2155 (2004).\n13K. L. Hobbs , et al., NanoLetter 4, 167 (2004).\n14A. Kosiorek , et al., SMALL 1, 439 (2005).10\n15D. K. Singh et al., Nanotechnology 19, 245305 (2008).\n16T. Albretch et al., Advanced Materials 12, 787 (2004).\n17M. Balet al., Appl. Phys. Lett. 81, 3479 (2002).\n18M. Klaui et al., Appl. Phys. Lett. 85, 5637 (2004).\n19S. P. Li, et al., Phys Rev Lett 86, 1102 (2001).\n20”Micromagnetics”, Interscience Publishers (1963).\n21A. Aharoni, Theory of Ferromangetism, Oxford Science\nPublication (2000).22V. P. Kravchuk , et al., J. Mag. Mag. Mat. 310, 116 (2006).\n23P. Landeros , et al., Jour. Appl. Phys. 100, 044311 (2007).\n24M. Bertotti, Hysteresis and magnetism, Academic Press\n(1998).\n25F. Q. Zhu , et al., Phys. Rev. Lett. 96, 027205 (2006).\n26J. Sort, et al., Phys. Rev. Lett. 97, 067201 (2005).\n*email: tuominen@physics.umass.edu"    },    {        "title": "0805.3922v2.Magnetic_field_induced_incommensurate_resonance_in_cuprate_superconductors.pdf",        "content": "arXiv:0805.3922v2  [cond-mat.supr-con]  1 Sep 2008Magnetic field induced incommensurate resonance in cuprate superconductors\nJingge Zhang and Li Cheng\nDepartment of Physics, Beijing Normal University, Beijing 100875, China\nHuaiming Guo\nDepartment of Physics, Capital Normal University, Beijing 100037, China\nShiping Feng∗\nDepartment of Physics, Beijing Normal University, Beijing 100875, China\nThe influence of a uniform external magnetic field on the dynam ical spin response of cuprate\nsuperconductors in the superconducting state is studied ba sed on the kinetic energy driven su-\nperconducting mechanism. It is shown that the magnetic scat tering around low and intermediate\nenergies is dramatically changed with a modest external mag netic field. With increasing the external\nmagnetic field, although the incommensurate magnetic scatt ering from both low and high energies\nis rather robust, the commensurate magnetic resonance scat tering peak is broadened. The part of\nthe spin excitation dispersion seems to be an hourglass-lik e dispersion, which breaks down at the\nheavily low energy regime. The theory also predicts that the commensurate resonance scattering at\nzero external magnetic field is induced into the incommensur ate resonance scattering by applying\nan external magnetic field large enough.\nPACS numbers: 74.25.Ha, 74.25.Nf, 74.20.Mn\nI. INTRODUCTION\nThe intimate relationship between the short-range an-\ntiferromagnetic (AF) correlation and superconductiv-\nity is one of the most striking features of cuprate\nsuperconductors1. This is followed an experimental\nfact that the parent compounds of cuprate supercon-\nductors are Mott insulators with the AF long-range or-\nder (AFLRO)1. However, when holes or electrons are\ndoped into these Mott insulators2, the ground state of\nthe systems is fundamentally altered from a Mott in-\nsulator with AFLRO to a superconductor with persis-\ntent short-range correlations1,3. The evidence for this\nclosed link is provided from the inelastic neutron scatter-\ning (INS) experiments4,5,6,7,8,9that show the unambigu-\nous presence of the short-rangeAF correlationin cuprate\nsuperconductors in the superconducting (SC) state.\nAt zero external magnetic field, the dynamical spin\nresponse of cuprate superconductors exhibits a number\nof universal features4,5,6,7,8,9, where the magnetic exci-\ntations form an hourglass-like dispersion centered at the\nAF ordering wave vector Q= [π,π] (in units of inverse\nlattice constant). At the saddle point, the dispersing\nincommensurate (IC) branches merge into a sharp com-\nmensurate feature, which is dramatically enhanced upon\nentering the SC state and commonly referred as the mag-\nnetic resonance scattering4,5,6,7,8,9. In particular, it has\nbeen argued that this commensurate magnetic resonance\nplays a crucial role for the SC mechanism in cuprate su-\nperconductors, since the commensurate magnetic reso-\nnance with the magnetic resonance energy scales with\nthe SC transition temperature forming a universal plot\nfor all cuprate superconductors10. To test the connec-\ntion between the commensurate magnetic resonance phe-\nnomenon and SC mechanism, it is desirable to perform\nfurther characterization. Since a uniform external mag-\nnetic field can serve as a weak perturbation helping to\nprobe the nature of the short-range AF correlation andsuperconductivity, therefore the dynamical spin response\nofcupratesuperconductorsintheSCstatehasbeenstud-\nied experimentally by application of a uniform external\nmagnetic field11,12,13,14,15. However, there is no a general\nconsensus. Some experimental results show that apply-\ning a uniform external magnetic field enhances the am-\nplitude of the IC magnetic scattering already present in\nthe system11,12. On the other hand, other experiments\nindicate that the intensity gain of the IC magnetic scat-\ntering is suppressed by application of a uniform external\nmagnetic field13. In particular, the influence of a uniform\nexternal magnetic field has been investigated on the res-\nonance scattering peak by using INS technique14,15. The\nearly INS measurement14shows that under a modest ex-\nternal magnetic field ( ∼11 Tesla), the resonance scat-\ntering peak remains almost unaffected, i.e., although a\nline broadening occurs without change of the resonance\nscattering peak amplitude, no shifting of the resonance\nscattering peak energy is observed. However, the later\nINS experiments15show that a modest external mag-\nnetic field applied to cuprate superconductors in the SC\nstate yields a very significant reduction in the commen-\nsurate magnetic resonance scattering. To the best of our\nknowledge, there are no explicit microscopic predictions\naboutthe effect ofauniformexternalmagneticfield large\nenough on the magnetic resonance scattering.\nForthecaseofzeroexternalmagneticfield, thedynam-\nical spin response of cuprate superconductors has been\ndiscussed16based on the framework of the kinetic energy\ndriven SC mechanism17, and all main features of the INS\nexperiments are reproduced, including the doping and\nenergy dependence of the IC magnetic scattering at both\nlow and high energies and commensurate magnetic reso-\nnance at intermediate energy4,5,6,7,8,9. In this paper, we\nstudy the influence of a uniform external magnetic field\non the dynamical spin response of cuprate superconduc-\ntors in the SC state along with this line. We calculate\nexplicitly the dynamical spin structure factor of cuprate2\nsuperconductorsunder auniformexternalmagneticfield,\nandshowthatthemagneticscatteringaroundlowandin-\ntermediate energies is dramatically changed with a mod-\nest external magnetic field. With increasing the external\nmagnetic field, although the IC magnetic scattering from\nboth low and high energies is rather robust, the commen-\nsurate magnetic resonance scattering peak is broadened.\nThe part of the spin excitation dispersion seems to be\nan hourglass-like dispersion, which breaks down at the\nheavily low energy regime.\nThe rest of this paper is organized as follows. The ba-\nsic formalism is presented in Sec. II, where we general-\nize the calculation of the dynamical spin structure factor\nfrom the previous zero external magnetic field case16to\nthe present case with a uniform external magnetic field.\nWithin this theoretical framework, we discuss the influ-\nence of a uniform external magnetic field on the dynam-\nical spin response of cuprate superconductors in the SC\nstateinSec. III,wherewepredictthatthecommensurate\nmagnetic resonance scattering at zero external magnetic\nfield is induced into the IC magnetic resonance scatter-\ning by an applied external magnetic field large enough.\nFinally, we give a summary and discussions in Sec. IV.\nII. THEORETICAL FRAMEWORK\nIn cuprate superconductors, the characteristic feature\nis the presence of the CuO 2plane1,3. It has been shown\nfrom ARPES experiments that the essential physics of\nthe doped CuO 2plane is properly accounted by the t-J\nmodel on a square lattice3,18. However, for discussions of\nthe influence of a uniform external magnetic field on the\ndynamical spin response of cuprate superconductors in\ntheSCstate, the t-Jmodelcanbe expressedbyincluding\nthe Zeeman term as,\nH=−t/summationdisplay\niˆησC†\niσCi+ˆησ+t′/summationdisplay\niˆτσC†\niσCi+ˆτσ+µ/summationdisplay\niσC†\niσCiσ\n+J/summationdisplay\niˆηSi·Si+ˆη−εB/summationdisplay\niσσC†\niσCiσ, (1)\nwhere ˆη=±ˆx,±ˆy, ˆτ=±ˆx±ˆy,C†\niσ(Ciσ) is the elec-\ntron creation (annihilation) operator, Si= (Sx\ni,Sy\ni,Sz\ni)\nare spin operators, µis the chemical potential, and εB=\ngµBBis the Zeeman magnetic energy, with the Lande\nfactorg, Bohr magneton µB, and a uniform external\nmagneticfield B. Thist-Jmodelwith auniformexternal\nmagnetic field is subject to an important local constraint/summationtext\nσC†\niσCiσ≤1 to avoid the double occupancy19. The\nstrong electron correlation in the t-Jmodel manifests it-\nself by this local constraint19, which can be treated prop-\nerly in analytical calculations within the charge-spin sep-\naration (CSS) fermion-spin theory20,21, where the con-\nstrainedelectron operatorsaredecoupled as Ci↑=h†\ni↑S−\ni\nandCi↓=h†\ni↓S+\ni, with the spinful fermion operator\nhiσ=e−iΦiσhirepresents the charge degree of freedom\ntogether with some effects of spin configuration rear-\nrangements due to the presence of the doped hole itself\n(chargecarrier), while the spin operator Sirepresentsthe\nspin degree of freedom (spin), then the t-Jmodel with auniform external magnetic field (1) can be expressed in\nthis CSS fermion-spin representation as,\nH=−t/summationdisplay\niˆη(hi↑S+\nih†\ni+ˆη↑S−\ni+ˆη+hi↓S−\nih†\ni+ˆη↓S+\ni+ˆη)\n+t′/summationdisplay\niˆτ(hi↑S+\nih†\ni+ˆτ↑S−\ni+ˆτ+hi↓S−\nih†\ni+ˆτ↓S+\ni+ˆτ)\n−µ/summationdisplay\niσh†\niσhiσ+Jeff/summationdisplay\niˆηSi·Si+ˆη−2εB/summationdisplay\niSz\ni,(2)\nwithJeff= (1−x)2J, andx=/an}bracketle{th†\niσhiσ/an}bracketri}ht=/an}bracketle{th†\nihi/an}bracketri}htis\nthe hole doping concentration. It has been shown that\nthe electron local constraint for the single occupancy is\nsatisfied in analytical calculations in this CSS fermion-\nspin theory20,21.\nWithin the framework of the CSS fermion-spin\ntheory20,21, the kinetic energy driven superconductivity\nhas been developed17. It has been shown that the inter-\naction from the kinetic energy term in the t-Jmodel (2)\nis quite strong, and can induce the d-wave charge car-\nrier pairing state by exchanging spin excitations in the\nhigher power of the doping concentration, then the d-\nwave electron Cooper pairs originating from the d-wave\ncharge carrier pairing state are due to the charge-spin re-\ncombination, and their condensation reveals the d-wave\nSC ground-state. Moreover, this SC-state is controlled\nby both d-wave SC gap function and quasiparticle co-\nherence, which leads to that the SC transition tempera-\nture increases with increasing doping in the underdoped\nregime, and reaches a maximum in the optimal doping,\nthen decreases in the overdoped regime16. Furthermore,\nfor the case of zero external magnetic field, the dop-\ning and energy dependent dynamical spin response of\ncuprate superconductors in the SC-state has been dis-\ncussed in terms of the collective mode in the charge car-\nrier particle-particle channel16, and the results are in\nqualitative agreement with the INS experimental data\non cuprate superconductorsin the SC state4,5,6,7,8,9. Fol-\nlowing their discussions16, the full spin Green’s function\nin the presence of a uniform external magnetic field is\nobtained as,\nD(k,ω) =1\nD(0)−1(k,ω)−Σ(s)(k,ω), (3)\nwith the mean-field (MF) spin Green’s function,\nD(0)(k,ω) =Bk\n2ωk/parenleftBigg\n1\nω−ω(1)\nk−1\nω+ω(2)\nk/parenrightBigg\n=/summationdisplay\nν=1,2(−1)ν+1Bk\n2ωk1\nω−ω(ν)\nk,(4)\nwhereBk= 2λ1(A1γk−A2)−λ2(2χz\n2γ′\nk−χ2),λ1=\n2ZJeff,λ2= 4Zφ2t′,γk= (1/Z)/summationtext\nˆηeik·ˆη,γ′\nk=\n(1/Z)/summationtext\nˆτeik·ˆτ,Zis the number of the nearest neigh-\nbor or next nearest neighbor sites of a square lattice,\nA1=ǫχz\n1+χ1/2,A2=χz\n1+ǫχ1/2,ǫ= 1+2tφ1/Jeff, the\nchargecarrier’sparticle-holeparameters φ1=/an}bracketle{th†\niσhi+ˆησ/an}bracketri}ht\nandφ2=/an}bracketle{th†\niσhi+ˆτσ/an}bracketri}ht, and the spin correlation functions\nχ1=/an}bracketle{tS+\niS−\ni+ˆη/an}bracketri}ht,χ2=/an}bracketle{tS+\niS−\ni+ˆτ/an}bracketri}ht,χz\n1=/an}bracketle{tSz\niSz\ni+ˆη/an}bracketri}ht,χz\n2=3\n/an}bracketle{tSz\niSz\ni+ˆτ/an}bracketri}ht, and the MF charge carrier excitation spec-\ntrum,ξk=Ztχ1γk−Zt′χ2γ′\nk−µ. Since a uniform exter-\nnal magnetic field is applied to the system, the MF spin\nexcitation spectrum has two branches, ω(1)\nk=ωk+2εB\nandω(2)\nk=ωk−2εB, withωkis the MF spin excitation\nspectrum at zero external magnetic field, and has been\nevaluated as16,\nω2\nk=λ2\n1[(A4−αǫχz\n1γk−1\n2Zαǫχ1)(1−ǫγk)\n+1\n2ǫ(A3−1\n2αχz\n1−αχ1γk)(ǫ−γk)]\n+λ2\n2[α(χz\n2γ′\nk−3\n2Zχ2)γ′\nk+1\n2(A5−1\n2αχz\n2)]\n+λ1λ2[αχz\n1(1−ǫγk)γ′\np−1\n2αǫ(C3−χ2γk)\n+1\n2α(χ1γ′\nk−C3)(ǫ−γp)+αγ′\nk(Cz\n3−ǫχz\n2γk)],(5)whereA3=αC1+(1−α)/(2Z),A4=αCz\n1+(1−α)/(4Z),\nA5=αC2+ (1−α)/(2Z), and the spin corre-\nlation functions C1= (1/Z2)/summationtext\nˆη,ˆη′/an}bracketle{tS+\ni+ˆηS−\ni+ˆη′/an}bracketri}ht,Cz\n1=\n(1/Z2)/summationtext\nˆη,ˆη′/an}bracketle{tSz\ni+ˆηSz\ni+ˆη′/an}bracketri}ht,C2= (1/Z2)/summationtext\nˆτ,ˆτ′/an}bracketle{tS+\ni+ˆτS−\ni+ˆτ′/an}bracketri}ht,\nandC3= (1 /Z)/summationtext\nˆτ/an}bracketle{tS+\ni+ˆηS−\ni+ˆτ/an}bracketri}ht,Cz\n3=\n(1/Z)/summationtext\nˆτ/an}bracketle{tSz\ni+ˆηSz\ni+ˆτ/an}bracketri}ht. In order to satisfy the sum\nrule of the correlation function /an}bracketle{tS+\niS−\ni/an}bracketri}ht= 1/2 in\nthe case without AFLRO, the important decoupling\nparameter αhas been introduced in the MF calculation,\nwhich can be regarded as the vertex correction22. The\nspin self-energy function Σ(s)(k,ω) in the SC-state is\nobtained from the charge carrier bubble in the charge\ncarrier particle-particle channel as16,\nΣ(s)(k,ω) =1\nN2/summationdisplay\np,q,ν=1,2(−1)ν+1Λ(q,p,k)Bq+k\nωq+kZ2\nhF\n8¯∆(d)\nhZ(p)¯∆(d)\nhZ(p+q)\nEpEp+q/parenleftBigg\nF(ν)\n1(k,p,q\nω−(Ep−Ep+q+ω(ν)\nq+k)\n+F(ν)\n2(k,p,q)\nω−(Ep+q−Ep+ω(ν)\nq+k)+F(ν)\n3(k,p,q)\nω−(Ep+Ep+q+ω(ν)\nq+k)−F(ν)\n4(k,p,q)\nω+(Ep+q+Ep−ω(ν)\nq+k)/parenrightBigg\n,(6)\nwhere Λ( q,p,k) = (Ztγk−p−Zt′γ′\nk−p)2+(Ztγq+p+k−\nZt′γ′\nq+p+k)2,¯∆hZ(k) =ZhF¯∆h(k), the charge carrier\nquasiparticle spectrum Ehk=/radicalBig\n¯ξ2\nk+|¯∆hZ(k)|2,\n¯ξk=ZhFξk,¯∆h(k) =¯∆hγ(d)\nkis the effective\ncharge carrier gap function in the d-wave symme-\ntry with γ(d)\nk= (coskx−cosky)/2,F(ν)\n1(k,p,q) =\nnB(ω(ν)\nq+k)[nF(Ep)−nF(Ep+q)]−nF(−Ep)nF(Ep+q),\nF(ν)\n2(k,p,q) = nB(ω(ν)\nq+k)[nF(Ep+q)−nF(Ep)]−nF(Ep)nF(−Ep+q),F(ν)\n3(k,p,q) =\nnB(ω(ν)\nq+k)[nF(−Ep)−nF(Ep+q)]+nF(−Ep)nF(−Ep+q),\nF(ν)\n4(k,p,q) =nB(ω(ν)\nq+k)[nF(−Ep)−nF(Ep+q)]−\nnF(Ep)nF(Ep+q), while the charge carrier quasiparticle\ncoherent weight ZhFand effective charge carrier gap\nparameter ¯∆hare determined by the following two\nself-consistent equations16,\n1 =1\nN3/summationdisplay\nk,p,q[Ztγk+q−Zt′γ′\nk+q]2γ(d)\nk−p+qγ(d)\nkZ2\nhF\n2EhkBpBq\nωpωq/parenleftbiggL1(k,p,q)\n(ωp−ωq)2−E2\nhk−L2(k,p,q)\n(ωp+ωq)2−E2\nhk/parenrightbigg\n,(7a)\n1\nZhF= 1+1\nN2/summationdisplay\np,q(Ztγp+k0−Zt′γ′\np+k0)2ZhFBpBq\n4ωpωq/parenleftbiggR1(p,q)\n(ωp−ωq−Ehp−q+k0)2+R2(p,q)\n(ωp−ωq+Ehp−q+k0)2\n+R3(p,q)\n(ωp+ωq−Ehp−q+k0)2+R4(p,q)\n(ωp+ωq+Ehp−q+k0)2/parenrightbigg\n, (7b)\nwherek0= [π,0],L1(k,p,q) = (ωp−ωq)[nB(ω(1)\nq)−\nnB(ω(1)\np) +nB(ω(2)\nq)−nB(ω(2)\np)][1−2nF(Ehk)] +\nEhk[nB(ω(1)\np)nB(−ω(1)\nq) + nB(ω(1)\nq)nB(−ω(1)\np) +\nnB(ω(2)\np)nB(−ω(2)\nq) + nB(ω(2)\nq)nB(−ω(2)\np)],\nL2(k,p,q) = ( ωp+ωq)[nB(−ω(1)\np)−nB(ω(1)\nq) +nB(−ω(2)\np)−nB(ω(2)\nq)][1−2nF(Ehk)] +\nEhk[nB(ω(1)\np)nB(ω(2)\nq) + nB(−ω(1)\np)nB(−ω(2)\nq) +\nnB(ω(2)\np)nB(ω(1)\nq) + nB(−ω(2)\np)nB(−ω(1)\nq)],\nR1(p,q) = nF(Ehp−q+k0){U2\nhp−q+k0[nB(ω(1)\nq)−\nnB(ω(1)\np)] + V2\nhp−q+k0[nB(ω(2)\nq) −4\nnB(ω(2)\np)]} − U2\nhp−q+k0nB(ω(1)\np)nB(−ω(1)\nq)−\nV2\nhp−q+k0nB(ω(2)\np)nB(−ω(2)\nq), R2(p,q) =\nnF(Ehp−q+k0){U2\nhp−q+k0[nB(ω(2)\np) −\nnB(ω(2)\nq)] + V2\nhp−q+k0[nB(ω(1)\np) −\nnB(ω(1)\nq)]} − U2\nhp−q+k0nB(ω(2)\nq)nB(−ω(2)\np)−\nV2\nhp−q+k0nB(ω(1)\nq)nB(−ω(1)\np), R3(p,q) =\nnF(Ehp−q+k0){U2\nhp−q+k0[nB(ω(2)\nq) −\nnB(−ω(1)\np)] + V2\nhp−q+k0[nB(ω(1)\nq)−\nnB(−ω(2)\np)]}+U2\nhp−q+k0nB(ω(1)\np)nB(ω(2)\nq) +\nV2\nhp−q+k0nB(ω(2)\np)nB(ω(1)\nq), R4(p,q) =\nnF(Ehp−q+k0){U2\nhp−q+k0[nB(−ω(1)\nq) −\nnB(ω(2)\np)] + V2\nhp−q+k0[nB(−ω(2)\nq)−\nnB(ω(1)\np)]}+U2\nhp−q+k0nB(−ω(2)\np)nB(−ω(1)\nq) +\nV2\nhp−q+k0nB(−ω(1)\np)nB(−ω(2)\nq), with U2\nhp−q+k0=(1 +¯ξp−q+k0/Ehp−q+k0)/2,V2\nhp−q+k0= (1 −\n¯ξp−q+k0/Ehp−q+k0)/2, and nB(ω) and nF(ω) are\nthe boson and fermion distribution functions, respec-\ntively. These two equations (7a) and (7b) must be solved\nsimultaneously with other self-consistent equations, then\nall order parameters, decoupling parameter α, and chem-\nical potential µare determined by the self-consistent\ncalculation16. In this sense, our above self-consistent\ncalculation for the dynamical spin structure factor\nunder a uniform external magnetic field is controllable\nwithout using adjustable parameters, which also has\nbeen confirmed by a similar self-consistent calculation\nfor the dynamical spin structure factor in the case\nwithout a uniform external magnetic field16.\nWith the help of the full spin Green’s function (3), we\ncan obtain the dynamical spin structure factor of cuprate\nsuperconductors under a uniform external magnetic field\nin the SC-state as,\nS(k,ω) =−2[1+nB(ω)]ImD(k,ω) =−2[1+nB(ω)]B2\nkImΣ(s)(k,ω)\n[(ω−2εB)2−ω2\nk−BkReΣ(s)(k,ω)]2+[BkImΣ(s)(k,ω)]2,(8)\nwhere ImΣ(s)(k,ω) and ReΣ(s)(k,ω) are the imaginary\nand realparts of the spin self-energyfunction (6), respec-\ntively.\nIII. MAGNETIC FIELD INDUCED\nINCOMMENSURATE MAGNETIC RESONANCE\nWe are now ready to discuss the influence of a uniform\nexternal magnetic field on the dynamical spin response\nof cuprate superconductors in the SC state. For cuprate\nsuperconductors, the commonly used parameters in this\npaper are chosen as t/J= 2.5 andt′/t= 0.3 with a\nreasonably estimative value of J∼120 meV23. At zero\nexternal magnetic field ( B= 0), we have reproduced the\nprevious results16. Furthermore, we have also performed\nthe calculation for the dynamical spin structure factor\nS(k,ω) inEq. (8) with auniformexternalmagneticfield,\nand the results of S(k,ω) in the ( kx,ky) plane for dop-\ningx= 0.15 with temperature T= 0.002Jand Zeeman\nmagnetic energy εB= 0.01J= 1.2 meV (then the corre-\nsponding external magnetic field B≈20 Tesla) at energy\n(a)ω= 0.08J= 9.6 meV, (b) ω= 0.31J= 37.2 meV,\nand (c)ω= 0.59J= 70.8 meV are plotted in Fig. 1. In\ncomparison with the previous results without a uniform\nexternal magnetic field16, our present most surprising re-\nsults involve the external magnetic field dependence of\nthe resonance scattering form, i.e., with increasing the\nexternalmagneticfield B, althoughtheICmagneticscat-\ntering from both low and high energies is rather robust,\nthe commensurate magnetic resonance scattering peak\nis broadened, and is shifted from the AF ordering wave\nvectorQto the IC magnetic scattering peaks with the\nincommensurability δr. The main difference is that theresonance response occurs at an IC in the presence of a\nuniform external magnetic field, rather than commensu-\nrate in the case of zero external magnetic field. In this\nsense, we call such magnetic resonance as the IC mag-\nnetic resonance. Experimentally, the growth of the low\nenergy IC magnetic resonance scattering due to the pres-\nenceofanexternalmagneticfield hasbeen observedfrom\nthe cuprate superconductor La 2−xSrxCuO413, which is\nqualitatively consistent with our theoretical predictions.\nFor cuprate superconductors, the upper critical magnetic\nfield at which superconductivity is completely destroyed\nis 50 Tesla or greater around the optimal doping24.\nTherefore the present result is remarkable because the\nmagnitude of the applied external magnetic field is much\nless than the upper critical magnetic field of cuprate su-\nperconductors. It has been shown that the magnetic res-\nonance scattering is very sensitive to the SC pairing, and\nthe external magnetic field induced the IC magnetic res-\nonance scattering is always accompanied with a breaking\nof the SC pairing15, this leads to a reduction of the SC\ntransition temperature in cuprate superconductors.\nHaving shown the presence of the IC magnetic reso-\nnance scatteringunder a uniform external magnetic field,\nit is importantto determineits dispersionas the outcome\nwill allow a direct comparison of the magnetic excitation\nspectra with and without a uniform external magnetic\nfield. In Fig. 2, we plot the evolution of the magnetic\nscattering peaks with energy for x= 0.15 inT= 0.002J\nwithεB= 0.01J= 1.2 meV (B≈20 Tesla) (solid line).\nFor comparison, the corresponding result for x= 0.15 in\nT= 0.002Jwith the same set of parameters except for\nεB= 0 (B= 0) is also shown in Fig. 2 (dashed line).\nAs in the previous work16, the dispersion of the magnetic\nscattering in the case of zero external magnetic field has5\nFIG. 1: The dynamical spin structure factor S(k,ω) in the\n(kx,ky) plane at x= 0.15 with T= 0.002JandεB= 0.01J\nfort/J= 2.5 andt′/t= 0.3 at energy (a) ω= 0.08J, (b)\nω= 0.31J, and (c) ω= 0.59J.\nkx0.40 0.45 0.50 0.55 0.60Energy (J)\n00.00.20.40.60.801.0\nFIG. 2: The evolution of the magnetic scattering peaks with\nenergy at x= 0.15 inT= 0.002Jfort/J= 2.5 andt′/t= 0.3\nwithεB= 0.01J(solid line) and εB= 0 (dashed line).H%00.000 0.002 0.004 0.006 0.008 0.010Gr\n00.0000.0050.0100.0150.020\nFIG. 3: The incommensurability of the incommensurate res-\nonance scattering at x= 0.15 inT= 0.002Jfort/J= 2.5\nandt′/t= 0.3 as a function of the external magnetic field.\nan hourglass shape. However, under a modest external\nmagnetic field B≈20 Tesla, although there is no strong\nexternal magnetic field induced change for the IC mag-\nnetic scattering at higher energy ω∼0.7J, the magnetic\nscattering around both intermediate and low energies is\ndramatically changed, in qualitative agreement with the\nINS experiments13,14,15. In particular, although the part\nabove 0.16J≈19 meV seems to be an hourglass-like\ndispersion, this hourglass-like dispersion breaks down at\nlower energy ω <0.16J≈19 meV. These are much dif-\nferent from the dispersion in the case of zero external\nmagnetic field.\nNow we turn to discuss that how strong external mag-\nnetic field can induce the IC resonance scattering in\ncuprate superconductors in the SC state. We have made\na series of calculations for the resonance energy at dif-\nferent external magnetic fields, and the result of the in-\ncommensurability of the IC resonance scattering δrfor\nx= 0.15 inT= 0.002Jas a function of a uniform ex-\nternal magnetic field Bis plotted in Fig. 3. Obviously,\nthe incommensurability δrincreases with increasing the\nexternal magnetic field. For a better understanding of\nthe influence of a uniform external magnetic field on the\nresonance scattering, we plot the dynamical spin struc-\nture factor S(k,ω) in the ( kx,ky) plane for x= 0.15 and\nT= 0.002Jwith (a) εB= 0.002J= 0.24 meV (then the\ncorresponding external magnetic field B≈4 Tesla) and\n(b)εB= 0.005J= 0.6 meV (then the corresponding ex-\nternal magnetic field B≈10 Tesla) at ω= 0.31J= 37.2\nmeV in Fig. 4. In comparison with Fig. 1(b), we there-\nfore find that there are two critical values of the Zeeman\nmagnetic energy ε(c)\nB1≈0.002J= 0.24meV (the corre-\nsponding critical external magnetic field Bc1≈4 Tesla)\nandε(c)\nB2≈0.005J= 0.6meV (the corresponding critical\nexternal magnetic field Bc2≈10 Tesla). When B > B c2,\nthe external magnetic field is strong enough to induce\nthe IC resonance scattering. On the other hand, when\nBc1< B < B c2, the commensurate resonance scatter-\ning peak is broadened, and remains at the same energy\nposition as the zero external magnetic field case with a\ncomparable amplitude, which is furthermore in qualita-\ntive agreement with the INS experiments14,15.6\nFIG. 4: The dynamical spin structure factor S(k,ω) in the\n(kx,ky) plane in x= 0.15 andT= 0.002Jfort/J= 2.5\nandt′/t= 0.3 with (a) εB= 0.002Jand (b)εB= 0.005Jat\nω= 0.31J.\nThe physical interpretation to the above obtained re-\nsults can be found from the property of the spin excita-\ntion spectrum. In contrast to the case of zero external\nmagnetic field, the MF spin excitation spectrum has two\nbranches, ω(1)\nk=ωk+ 2εBandω(2)\nk=ωk−2εB, in\nEq. (4) under a uniform external magnetic field as men-\ntioned in Sec. II. Since both MF spin excitation spectra\nω(1)\nkandω(2)\nkand spin self-energy function Σ(s)(k,ω) in\nEq. (6) are strong external magnetic field dependent,\nthis leads to that the renormalized spin excitation spec-\ntrum (Ω k−2εB)2=ω2\nk+ ReΣ(s)(k,Ωk) in Eqs. (3)\nand (8) also is strong external magnetic field dependent.\nAs in the case of zero external magnetic field16, the dy-\nnamical spin structure factor S(k,ω) in Eq. (8) under a\nuniform external magnetic field has a well-defined reso-\nnance character, where S(k,ω) exhibits peaks when the\nincoming neutron energy ωis equal to the renormalized\nspin excitation, i.e.,\nW(kc,ω)≡[(ω−2εB)2−ω2\nkc−BkcReΣ(s)(kc,ω)]2\n∼0, (9)\nfor certain critical wave vectors kc=k(L)\ncat low energy,\nkc=k(I)\ncat intermediate energy, and kc=k(H)\ncat high\nenergy, then the weight of these peaks is dominated by\nthe inverse of the imaginary part of the spin self-energy\n1/ImΣ(s)(k(L)\nc,ω) at low energy, 1 /ImΣ(s)(k(I)\nc,ω) at in-\ntermediate energy, and 1 /ImΣ(s)(k(H)\nc,ω) at high en-\nergy, respectively. In this sense, the essential physicsof the external magnetic field dependence of the dynam-\nical spin response is almost the same as in the case of\nzero magnetic field. However, as seen from Eqs. (6),\n(8), and (9), a modest external magnetic field mainly ef-\nfects the behavior of the dynamical spin response around\nlow and intermediate energies, and therefore leads to\nsome changes of the dynamical spin response around\nlow and intermediate energies. This is followed by a\nfact that the magnitude of the applied uniform exter-\nnal magnetic field is much less than the upper critical\nmagnetic field of cuprate superconductors, i.e., the Zee-\nman magnetic energy 2 εB/J= 0.02≪1 in Eqs. (6),\n(8), and (9), then the renormalized spin excitation spec-\ntrum at high energy can be reduced approximately as\n(ω−2εB)2=ω2\nk+ReΣ(s)(k,ω)≈ωin Eqs. (6), (8), and\n(9). This is why there is only a small influence of a mod-\nest external magnetic field on the IC magnetic scattering\nat hight energy. However, around low and intermediate\nenergies, this small Zeeman magnetic energy εBin Eqs.\n(6), (8), and (9) plays an important role that reduces the\nrange of the IC magnetic scattering at low energy and\nsplits the commensurate resonance peak at zero exter-\nnal magnetic field into the IC resonance peaks, then the\nIC magnetic resonance scattering appears. Furthermore,\nat the heavily low energy regime ω≪0.16J, the mag-\nnitude of the Zeeman magnetic energy 2 εB= 0.02Jis\ncomparable with these incoming neutron energies, where\nboth incoming lower neutron energy and Zeeman mag-\nnetic energy dominate the IC magnetic scattering, then\nthe hourglass-like dispersion breaks down.\nIV. SUMMARY AND DISCUSSIONS\nIn summary, we have discussed the influence of a uni-\nform external magnetic field on the dynamical spin re-\nsponse of cuprate superconductors in the SC state based\non the kinetic energy driven SC mechanism. Our results\nshow that the magnetic scattering around low and inter-\nmediate energies is dramatically changed with a mod-\nest external magnetic field. With increasing the ex-\nternal magnetic field, although the IC magnetic scat-\ntering from both low and high energies is rather ro-\nbust, the commensurate magnetic resonance scattering\npeak is broadened14,15. In particular, the part above\n0.16J≈19 meV seems to be an hourglass-like disper-\nsion, which breaksdown at the heavily low energyregime\nω <0.16J≈19 meV. The theory also predicts that the\ncommensurate magnetic resonance scattering at zero ex-\nternalmagneticfieldisinducedintotheICmagneticreso-\nnancescatteringbyapplyingauniformexternalmagnetic\nfield largeenough, which shouldbe verifiedby further ex-\nperiments.\nFrom the INS experimental results, it is shown that\nalthough some of the IC magnetic scattering properties\nhave been observed in the normal state, the magnetic\nresonance scattering is the main new feature that ap-\npears into the SC state4,5,6,7,8,9,10. In particular, apply-\ning a uniform external magnetic field large enough to\nsuppress superconductivity would yield a spectrum iden-\ntical to that measured at normal state25. Incorporating7\nthese experimental results, our present result seems to\nshow that the external magnetic field causes the behav-\nior of the dynamical spin response to become more like\nthat of the normal state. Moreover, in our present dis-\ncussions, the magnitude of an applied external magnetic\nfield is much less than the upper critical magnetic field\nfor cuprate superconductors as mentioned above, and\ntherefore we believe that both commensurate magnetic\nresonance scattering at zero external magnetic field and\nIC magnetic resonance scattering at an applied modest\nexternal magnetic field are universal features of cuprate\nsuperconductors.Acknowledgments\nThe authors would like to thank Professor P. Dai for\nthe helpful discussions. This work was supported by\nthe National Natural Science Foundation of China under\nGrant No. 10774015, and the funds from the Ministry\nof Science and Technology of China under Grant Nos.\n2006CB601002 and 2006CB921300.\n*To whom correspondence should be addressed (E-mail:\nspfeng@bnu.edu.cn).\n1See, e.g., the review, M.A. Kastner, R.J. Birgeneau, G.\nShiran, and Y. Endoh, Rev. Mod. Phys. 70(1998) 897.\n2J. G. Bednorz and K. A. M¨ uller, Z. Phys. B 64(1986) 189\n; Y. Tokura, H. Takagi, and S. Uchida, Nature 337(1989)\n345.\n3See, e.g., the review, A. Damascelli, Z. Hussain, and Z.-X.\nShen, Rev. Mod. Phys. 75(2003) 475.\n4See, e.g., the review, J. M. Tranquada, in Handbook of\nHigh-Temperature Superconductivity , edited by J. R. Schri-\neffer and J. S. Brooks (Springer, New York, 2007), p. 257.\n5P. Dai, H. A. Mook, R. D. Hunt, and F. Do˜ gan, Phys. Rev.\nB63(2001) 54525; M. Arai, T. Nishijima, Y. Endoh, T.\nEgami, S. Tajima, K. Tomimoto, Y. Shiohara, M. Taka-\nhashi, A. Garret, and S. M. Bennington, Phys. Rev. Lett.\n83(1999) 608.\n6K. Yamada, C.H. Lee, K. Kurahashi, J. Wada, S. Waki-\nmoto, S. Ueki, H. Kimura, Y. Endoh, S. Hosoya, G. Shi-\nrane, R. J. Birgeneau, M. Greven, M.A. Kastner, and Y.\nJ. Kim, Phys. Rev. B 57(1998) 6165; S. Wakimoto, H.\nZhang, K. Yamada, I. Swainson, H. Kim, and R.J. Birge-\nneau, Phys.Rev.Lett. 92(2004)217004; N.B.Christensen,\nD.F. McMorrow, H.M. Rønnow, B. Lake, S.M. Hayden, G.\nAeppli, T.G. Perring, M. Mangkorntong, N. Nohara, and\nH. Tagaki, Phys. Rev. Lett. 93(2004) 147002.\n7P. Bourges, B. Keimer, S. Pailh´ es, L.P. Regnault, Y. Sidis,\nand C. Ulrich, Physica C 424(2005) 45; P. Bourges, Y.\nSidis, H.F. Fong, L.P. Regnault, J. Bossy, A. Ivanov, and\nB. Keimer, Science 288(2000) 1234.\n8H. He, Y. Sidis, P. Bourges, G.D. Gu, A. Ivanov, N.\nKoshizuka, B. Liang, C.T. Lin, L.P. Regnault, E. Schoen-\nherr, and B. Keimer, Phys. Rev. Lett. 86(2001) 1610; R.\nJ. Birgeneau, C. Stock, J. M. Tranquada, and K. Yamada,\nJ. Phys. Soc. Jpn. 75(2006) 111003.\n9S.M. Hayden, H.A. Mook, P. Dai, T.G. Perring, and F.\nDo˜ gan, Science 429(2004) 531; V. Hinkov, S. Pailh´ es, P.\nBourges, Y. Sidis, A. Ivanov, A. Kulakov, C.T. Lin, D.P.\nChen, C. Bernhard, and B. Keimer, Nature 430(2004)\n650; C. Stock, W.J. Buyers, R.A. Cowley, P.S. Clegg, R.\nColdea, C.D. Frost, R. Liang, D. Peets, D. Bonn, W.N.\nHardy, and R.J. Birgeneau, Phys. Rev. B 71(2005) 24522.\n10Stephen D. Wilson, Pengcheng Dai, Shiliang Li, Songxue\nChi, H. J. Kang and J. W. Lynn, Nature 442(2006) 59.\n11B. Khaykovich, R. J. Birgeneau, F. C. Chou, R. W. Er-\nwin, M. A. Kastner, S.-H. Lee, Y. S. Lee, P. Smeibidl, P.\nVorderwisch, and S. Wakimoto, Phys. Rev. B 67(2003)\n054501; B. Khaykovich, Y. S. Lee, R. W. Erwin, S.-H.Lee, S. Wakimoto, K. J. Thomas, M. A. Kastner, and R.\nJ. Birgeneau, Phys. Rev. B 66(2002) 014528.\n12B. Lake, H. M. Ronnow, N. B. Christensen, G. Aeppli, K.\nLefmann, D. F. McMorrow, P. Vorderwisch, P. Smeibidl,\nN. Mangkorntong, T. Sasagawa, M. Nohara, H. Takagi and\nT. E. Mason, Nature 415(2002) 299.\n13J. M. Tranquada, C. H. Lee, K. Yamada, Y. S. Lee, L.\nP. Regnault, and H. M. Ronnow, Phys. Rev. B 69(2004)\n174507.\n14P. Bourges, H. Casalta, L.P. Regnault, J. Bossy, P. Burlet,\nC. Vettier, E. Beaugnon, P. Gautier-Picard, R. Tournier,\nPhysica B 234-236 (1997) 830.\n15P. Dai, H. A. Mook, G. Aeppli, S. M. Hayden and F. Doan,\nNature406(2000) 965.\n16Shiping Feng, Tianxing Ma, and Huaiming Guo, Physica\nC436(2006) 14; Shiping Feng, Tianxing Ma, and Xin-\ntian Wu, Phys. Lett. A 352(2006) 438; Shiping Feng\nand Tianxing Ma, in Superconductivity Research Horizons ,\nedited by Eugene H. Peterson (Nova Science Publishers,\nNrw York, 2007) chapter 5, p. 129.\n17Shiping Feng, Phys. Rev. B 68(2003) 184501.\n18C. Kim, P.J. White, Z.X.Shen, T. Tohyama, Y.Shibata, S.\nMaekawa, B.O. Wells, Y.J. Kim, R.J. Birgeneau, and M.A.\nKastner, Phys. Rev.Lett. 80(1998) 4245; B.O. Wells, Z.X.\nShen, A. Matsuura, D.M. King, M.A. Kastner, M. Greven,\nand R.J. Birgeneau, Phys. Rev. Lett. 74(1995) 946.\n19See, e.g., thereview, P.W.Anderson,in Frontiers and Bor-\nderlines in Many Particle Physics , edited by R. A. Broglia\nand J. R. Schrieffer (North-Holland, Amsterdam, 1987), p.\n1; P. W. Anderson, Science 235(1987) 1196.\n20Shiping Feng, Jihong Qin, and Tianxing Ma, J. Phys. Con-\ndens. Matter 16(2004) 343; Shiping Feng, Tianxing Ma,\nand Jihong Qin, Mod. Phys. Lett. B 17(2003) 361.\n21See, e.g., the review, Shiping Feng, Huaiming Guo, Yu\nLan, and Li Cheng, Int. J. Mod. Phys. B, in press,\narXiv:0710.5258.\n22J. Kondo and K. Yamaji, Prog. Theor. Phys. 47(1972)\n807.\n23S. Shamoto; M. Sato; J. M. Tranquada; B. J. Sternlib and\nG. Shirane, Phys. Rev. B 48(1993) 13817.\n24Yayu Wang, S. Ono, Y. Onose, G. Gu, Yoichi Ando, Y.\nTokura, S. Uchida, and N. P. Ong, Science 299(2003) 86.\n25G. S. Boebinger, Yoichi Ando, A. Passner, T. Kimura,\nM. Okuya, J. Shimoyama, K. Kishio, K. Tamasaku, N.\nIchikawa, and S. Uchida, Phys. Rev. Lett. 77(1996) 5417;\nX. F. Sun, Kouji Segawa, and Yoichi Ando, Phys. Rev.\nLett.93(2004) 107001."    },    {        "title": "0808.3922v1.Inhomogeneous_ferrimagnetic_like_behavior_in_Gd2_3Ca1_3MnO3_single_crystals.pdf",        "content": "Inhomogeneous ferrimagnetic-like behavior in Gd 2/3Ca 1/3MnO 3\nsingle crystals\nN.Haberkorn\nComisión Nacional de Energía Atómica, Centro Atómico Bariloche, S. C. de Bariloche, 8400 R. N., \nArgentina. and\nInstituto Balseiro, Universidad Nacional de Cuyo and Comisión Nacional de Energía Atómica, S. C. de \nBariloche, 8400 R. N., Argentina\nS. Larrégola\nFacultad de Química, Bioquímica y Farmacia, Universidad Nacional de San Luis, Chacabuco y Pedernera, \nSan Luis 5700, Argentina.\nD. Franco\nFacultad de Ciencias Químicas, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina\nG. Nieva\nComisión Nacional de Energía Atómica, Centro Atómico Bariloche, S. C. de Bariloche, 8400 R. N., \nArgentina. and\nInstituto Balseiro, Universidad Nacional de Cuyo and Comisión Nacional de Energía Atómica, S. C. de \nBariloche, 8400 R. N., Argentina\nWe present a study of the magnetic properties of Gd 2/3Ca1/3MnO 3single crystals at low temperatures. We \nshow that this material behave as an inhomogeneous ferrimagnet. In addition to small saturation \nmagnetization at 5 K, we have found history dependent effects in the magnetization and the presence of \nexchange bias. These features are compatible with microscopic phase separation in the clean Gd 2/3Ca1/3MnO 3\nsystem studied.PACS numbers: 75.50.Gg; 75.30.Kz\nnhaberk@cab.cnea.gov.ar\n  TE / FAX: 542944445171 / 2944445299* ManuscriptTransition metal oxides with perovskite structure have generated great interest due to the rich variety \nof their electrical and magnetic properties. These include, for example, high temperature superconductivity \nand colossal magnetorresistance (CMR).1, 2 In hole-doped perovskites R1í[AxMnO 3 (RA xMO R: Rare earths, \nand A: Ca, Sr) showing CMR, the electrical and magnetic properties are known to be very sensitive to the \nlattice parameters, the Mn3+ / Mn4+ ratio and the oxygen content.1 By modification of these parameters it is \npossible to obtain complex phase diagrams that include ferromagnetism (FM), antiferromagnetism (AF), \nweak FM, spin canting and, in some cases, spatial inhomogeneity related to multiphase coexistence.1,3The\nphenomenon of multiphase coexistence or phase separation corresponds to the simultaneous existence of \nmutually penetrating submicrometer sub-phases with slightly different electronic density giving rise to\ndifferent magnetic behavior. This electronic phase separation is associated with spatial inhomogeneity which \nin turn is related to local crystalline distortion. The mismatch between the size of different ions could be \nexpressed by the values of the tolerance factor,\n) (2;\nO MnO AR\nr rr rt\n\u000e\u000e²¢ , and size disorder at the R,A-site, \n¦ ²¢\u00102 2 2\ni ii r rxV , where ²¢ARr, corresponds to the average size of the R,A-site cations, and, x i and r i are \nthe fractional occupancies and ionic radii of the i cations.4, 5 In GdCa xMO for x § 1/3, we can estimate t and \nV2, 0.891 and 0.0025 A2, respectively, a result quite similar to YCa 1/3MO (t §0.884,V2§0.0014 A2).\nWhereas YCa 1/3MO shows short ferromagnetic order and a spin glass-like (SGL) behavior at low \ntemperatures (T < 30 K),6 in GdCa 1/3MO a ferrimagnetic behavior was reported, associated with the \nantiferromagnetic (AF) order of the Gd and Mn sublattices at low temperatures.7, 8 The presence of a SGL \nbehavior in YCa 1/3MO could be related to the large local lattice distortion and associated with phase \ncoexistence,3,6 similar to that found in PrCa 1/3MO.9 The GdCa 1/3MO compound presents ferrimagnetic \nbehavior with Curie temperatures of around 50 and 80 K, for the Gd and Mn sublattices, and a compensation \ntemperature (T comp) of § 15 K.7,8 At T comp, the rare-earth and transition metal sublattice magnetizations at zero \nfield exactly cancel.\nIn this work, we analyze the magnetic behavior at low temperatures of GdCa 1/3MO single crystals.\nThe samples were grown by the floating zone technique from isostatically pressed and pre-sintered rods of the \nsame nominal composition. The phase purity of the single crystals was probed by x-ray diffraction, and the composition was checked by energy dispersive spectroscopy (EDS). Magnetic properties were measured in a commercial SQUID magnetometer. Curie temperature (T c) was estimated from the inflection point of the \nfield-cooled (FC) magnetization ( M) versus T curves at low applied magnetic fields. In the FC procedure the \nsamples were cooled from 150 K, under an applied field between 0 and 5 T. Cooling (FCC) and warming \n(FCW) M versus Tmeasurements were performed. The results that will be presented correspond to the same \ncrystal, being representative of all measured crystals.\nPowder x-ray diffraction patterns obtained by grinding several GdCa 1/3MO single crystals show \nsingle phase orthorhombic Pbnm(n°62) structure. Two crystalline directions were identified in the single \ncrystal used in the magnetic measurements. Figure 1 shows a schematic picture of the crystalline axis and its \nrespective x-ray diffraction pattern. The (020) and (200) orthorhombic reflections are equivalent to the family \nof (110) reflection expected for the pseudo orthorhombic or pseudo cubic (p-cub) lattice formed by the \ncations. The lattice parameters are b/2§\u00030.393 nm, a/2§ 0.381 nm. Taking these into consideration, a \nface rotated 90° from those is equivalent to the (100) axis (see figure 1).\nFigure 2a shows M versus T curves for field H = 7.5 kOe applied along different crystal orientations\nof GdCa 1/3MO single crystal. The results show an inflection of the magnetization at approximately 80 K \nassociated with the ferromagnetic order of the Mn cations. Below 50 K the magnetization decreases due to the \ncompensation originated by the magnetic order of the Gd sublattice (Gd-Mn interaction). Depending on the \napplied magnetic field the magnetization goes to negative values (H < 2.5 kOe, not shown) or begins to \nincrease at T comp§ 16 K.7, 8 Figures 2b and 2c show the hysteretic M versus T behavior around Tcomp for two \ndifferent applied magnetic fields in the (100) p-cub axis. The differences in cooling and warming measurements \ncould be associated with a change in the domain size. This fact is also manifested in the coercive field. \nHysteresis loops at the same temperature range present different coercive fields when the temperature is\nreached by cooling or warming (not shown). Hysteresis in magnetization was previously reported in YCa\n1/3MO,6 and it was associated with a spin glass like (SGL) behavior. In this case, as in our experiments a \ndynamic phase coexistence could be present since long local distortions are present in both materials.3 As we \nwill show later, a possible phase separation is also supported by two different facts: the low Ms at low \ntemperatures, and the presence of exchange bias ( EB) near Tcomp. Different curves in figure 2a make evident \nthe crystalline anisotropy effect. This anisotropy is also manifested in the hysteresis loops presented in figure \n3. At 60 K it is easier to magnetize the Mn along the (020) direction than along (100) p-cub axis (see figure 3a). While at the lowest measured temperatures, where the Gd influences the magnetization, the easier axis \ncorresponds to the (100) p-cub axis(see figures 3b and 3c). Although more studies are necessary to clarify this \npoint, the anisotropy difference of the Mn and Gd sublattices could produce canting between them.\nFigure 4 shows the saturation magnetization ( Ms) obtained from hysteresis magnetic loops like those \nshown in figure 3. In the Ms estimated a paramagnetic signal was subtracted. The possible phase coexistence \nis supported by the low Ms value at 5 K § 80 emu / cm3. This value is approximately half of the expected \nvalue considering ferrimagnetic order. The saturation magnetization per mole of GdCa 1/3MO expected from \nthe Gd3+ s = 7/2, l = \u0013\u0003LV\u0003ȝ\u0003 \u0003\u000b\u0015\u0012\u0016\u0003[\u0003\u0015\u0003[\u0003\u001a\u0012\u0015\f ȝ%  \u0003\u0017\u0011\u0019\u001a\u0003ȝ%\u000f\u0003ZKLOH\u0003KLJK -VSLQ\u0003PDQJDQHVH\u0003JLYHV\u0003VSLQ\u0003RQO\\\u000f\u0003ȝ\u0003 \u0003\nJVȝ%\u000f\u0003 J\u0003  \u0003 \u0015\u0003 VR\u0003 ȝ\u0003  \u0003 \u0015\u0003 ȝ%>\u0015\u0012\u0016[\u0015\u0003 \u000bIRU Mn3+)+ 1/3x3/2 (from Mn4+\f@ \u0003 \u0016\u0011\u0019\u001a\u0003 ȝ%\u00117 Considering these \nmagnetizations, we expect a Ms§\u0003\u0014\u0011\u0013\u0013\u0003ȝ%\u0003§  160 emu/cm3.7 Magnetic hysteresis loops also show a high \nparamagnetic like signal at different temperatures (see figure 3). Although at low temperatures it could be \nassociated with sublattice rotation due to canting,7 it could also be associated with phase coexistence. It is \nimportant to remark that the contribution of paramagnetic Gd moment alone can not explain the high\nparamagnetic signal, because in this case a high Ms should be expected from the non compensated\nferromagnetic Mn moments. Figure 5 shows the temperature dependence of the coercive field, \nHc =| Hc1íHc2 | /2, where Hc1 and Hc2are the fields for zero magnetization at both branches of the hysteresis \nloops for field excursions up to 1 and 3 T. The Hctemperature dependence shows a non monotonic decrease\nwhen the temperature is raised, resulting quite different to the continuous and smooth decrease measured by \nO. Peña et al.8 We observe a drop of Hc around Tcomp, which is a consequence of the superposition of two \nsignals: a ferrimagnetic one, responsible for the loops, and a paramagnetic one.10 As we discuss previously, \nthe paramagnetic like behavior could be a consequence of weakly coupled sublattices,7 or phase coexistence. \nThe coercive field also makes evident the crystalline anisotropy (see figure 5). We observe that the differences in H\nc for the (100) p-cub and (020) axis are more important at temperatures lower than 30 K, in this \ntemperature range the Gd sublattice magnetization starts to play a more important role. However, in our case, \nconsidering a possible phase coexistence, the shape anisotropy of the small domains could be affecting the Hc\nvalues.11Another feature in the hysteresis loops (see inset figure 3b) is the shift with respect to zero field of \nthe magnetization, i. e. exchange bias (EB). The presence of EB, associated to the presence of FM / AF \nmagnetic interfaces is usually found in artificially designed materials like FM / AF multilayers or more recently, in manganite with phase coexistence.12, 13 Materials with AFM / ferrimagnetic and FM / \nferrimagnetic interfaces also could show EB.14 The magnitude of the effect depends on a number of \nparameters including AF and FM domain size, interfacial roughness, AF and FM anisotropy, etc.\nFigure 6 shows the T dependence of the EB field ( Heb =| Hc1+Hc2 | /2), obtained from hysteresis loops \nat different FC field, H = 1 and 3 T, in two crystalline directions. The exchange bias fields show a sharp increase and change sign around T\ncomp. This behavior is similar to that found in ferrimagnetic / FM \nmultilayer.10, 15 Since we are measuring a single crystalline sample we expect a homogeneous ferrimagnet \ndue to the absence of interfaces. However the presence of EB should be associated in our case with a very \nsmall domain size distribution with different Tcomp. This is supported by the suppression of the Heb when the \nmagnetic fields excursions in the loops are increased. For example, loops in a range -1 T < H < 1 T show Heb \nseveral times higher than loops in a range -3 T < H < 3 T, and the EB effect disappear for loops in a range -5\nT < H < 5 T. The change of sign in Heb near of Tcomp is a consequence of domain rotation when the Gd\nsublattices dominates the magnetization.\nIn summary, we studied the magnetic properties of GdCa1/3MO single crystals. This cleans system, \nhighly locally distorted, shows characteristics typically found in inhomogeneous ferrimagnets. Several \nfeatures are compatible with phase coexistence in the single crystals: the Ms at 5 K is approximately half of \nthe expected value considering a ferrimagnetic order; hysteric behavior on cooling and warming M versus T\ncurves; and the presence of exchange bias near Tcomp.\nAcknowledgments\nThis work was partially supported by CONICET PIP5251 and ANPCYT PICT PICT00-03- 08937. N. H. and \nG. N. are member of CONICET.\n.\n1Lev P. Gor’kov, and Vladimir Z. Kresinc. Physics Reports 400, 149 (2004).\n2Patrick A. Lee, Naoto Nagaosa, and Xiao-Gang Wen. Rev. Mod. Phys. 77, 721 (2005).\n3 Weida Wu, Casey Israel, Namjung Hur, Soonyong Park, Sang-Wook Cheong and Alex De Lozanne. Nature \nMaterials, 5, 881 (2006).4 J. P. Zhou, J. T. McDevitt, J. S. Zhou, H. Q. Yin, and J. B. Goodenough, Y. Gim and Q. X. Jia. Appl. Phys. \nLett., 75, 1146 (1999).\n5 A. Maignan, C. Martin, G. Van Tendeloo, M. Hervieu, and B. Raveau. Phys. Rev . B, 60, 15214 (1999).\n6 R. Mathieu, P. Nordblad, D. N. H. Nam, N. X. Phuc, and N. V. Khiem. Phys. Rev. B, 63, 174405 (2001).\n7 G. J. Snyder, C. H. Booth, F. Bridges, R. Hiskes, S. DiCarolis, M. R. Beasley and T. H. Geballe. Phys. Rev. \nB,55, 6453 (1997).\n8 Octavio Peña, Mona Bahout, Karim Ghanimi, Pedro Duran, Dionisio Gutierrez, and Carlos Moure. J. Mat \nChem. 12, 2480 (2002).\n9 P. G. Radaelli et al.Phys. Rev. B 63, 172419 (2001); V.N. Smolyaninova et al. Phys. Rev. B 65, 104419 \n(2002); D. Saurel et al. Phys. Rev. B 73, 094438 (2006).\n10 D. J. Webb, A. F. Marshall, Z. Sun, T. H. Geballe, and Robert M. White. IEE Trans. Magn. 24, 588 (1988).\n11 J. Tao, D. Niebieskikwiat, M. B. Salamon, and J. M. Zuo. Phys. Rev. Lett. 94, 147206 (2005).\n12 T. Qian, G. Li, T. Zhang, T. F. Zhou, X. Q. Xiang, X. W. Kang, and X. G. Lia. Appl. Phys. Lett. 90, 12503 \n(2007).\n13 D. Niebieskikwiat and M. B. Salamon. Phys. Rev B 72, 174422 (2005).\n14 J. Nogués and I. K. Schuller. J. Magn. Magn. Mater. 192, 203 (1999).\n15 David J. Webb, F. Marshall, Arnold M. Toxen, T. H. Geballe, Robert M. White. IEE Trans. Magn. 24, 2013 \n(1988).Figure 1. X-ray diffraction patterns for different crystalline axis in the studied GdCa 1/3MO single crystal.\nArrows indicate the equivalent crystalline orientations in the pseudo cubic structure given by the cations\nsublattices.\nFigure 2. (a) Magnetization ( M) versus Temperature ( T) at 7500 Oe for different crystalline axis in a\nGdCa 1/3MO single crystal. Open Circle: (020); Close square: (200); and, Open triangle: (100) p-cub. (b) and (c) \nMagnetization ( M) versus Temperature ( T) in the (100) p-cub axis at 2500 and 5000 Oe, respectively. Close \ncircle: cooling; Open circle: warming.\nFigure. 3: Magnetization ( M) versus magnetic field ( H) at different temperatures: (a) 60 K; (b) 30 K; and (c) 5 \nK. The inset in (b) shows the presence of exchange bias at 18 K for a magnetic loop in a magnetic field range \n-1 T < H < 1 T.\nFigure 4. Saturation magnetization ( MS) versus Temperature ( T) obtained from magnetic hysteresis loops in a \nGdCa 1/3MO single crystal. Dashed line is guide by to the eye.\nFigure 5. Coercive field ( Hc) vs Temperature ( T) for different crystalline axis in a GdCa 1/3MO single crystal.\nFigure 6. Exchange bias field ( Heb) vs Temperature ( T) for different crystalline axis in a GdCa 1/3MO single\ncrystal.30 40 50 60 70(400)\n69.8 °I [arb. units]\n2T\u0003>q@(200)\n33.3 °(020)\n20 30 40 50 60 70(040)67.2 °I [arb. units]\n2T\u0003>q@(020)32.1 °(200)(100) p-cubFigure0 20 40 60 80 100 1200255075100M[emu / cm3]\nT [K](a)\n10 20 3004080\n10 20 30(b)M[emu/cm3]\nT [K](c)\nT [K]Figure0 5 10 15 200255075100M[emu/cm3]\nH [kOe] (020)\n (100) p-cub(a)\n(b)\n-30 -20 -10 0 10 20 30-120-80-4004080120\n-30 -20 -10 0 10 20 30-180-120-60060120180M[emu/cm3]\nH [kOe] (020)\n (100)p-cub(c)-0.3 0.0 0.3-202M[emu/cm3]\nH [kOe] (020)\n (100)p-orth\nM [emu/cm 3]\nH [kOe]Figure0 1 02 03 04 0020406080MS[emu/cm3]\nT[ K ]Figure10 20 30 40 50 6001000200030004000Hc[Oe]\nT[ K ](020) H = 3T\n(020) H = 1 T\n(100)p-cubH=3 T\n(100)p-cubH=1 TFigure5 1 01 52 02 53 0-900-600-3000300600900Heb[Oe]\nT[ K ](020) H = 3T\n(020) H = 1T\n(100)p-cubH= 1 TFigure"    },    {        "title": "0809.1657v1.Magnetic_Properties_of_Ni_Fe_Nanowire_Arrays__Effect_of_Template_Material_and_Deposition_Conditions.pdf",        "content": "Magnetic Properties of Ni-Fe Nanow ire Arrays: Effect of Template Material \nand Deposition Conditions \n \nShyam Aravamudhan1*a), John Singleton2, Paul A. Goddard3, Shekh ar Bhansali1,b) \n \n1Departm ent of Electrical Engineering, Nanom aterials and Nanom anufactur ing Research Center \n(NNRC), University of Sout h Florida, Tam pa, FL 33620 \n2National High Magnetic Field La boratories (NHMFL), Los Alam os National Laboratory, Los \nAlam os, NM  \n3Clarendon Laboratory, Departm ent of Physics, University of Oxford, Oxford, United Kingdom  \n \na)Email: saravam u@gate ch.edu , b)Email: bhansali@eng.usf.edu , Tel: 1-813-874-3593, Fax: 1-\n813-974-5250. \n \n*Now with Microelectronics Rese arch Center (MiRC), Georgia In stitute of Technology, Atlanta, \nGA 30332. \n \n \nAbstract \n The objective of this work is to study th e magnetic properties of arrays of Ni-Fe \nnanowires electrodeposited in different tem plate materials such as por ous silicon, polycarbonate \nand alum ina. Magnetic properties were studied as a function of template m aterial, applied \nmagnetic f ield (parallel and perpendicular) during deposition, wire length, as well as m agnetic \nfield orientation during m easure ment. The resu lts show that app lication of m agnetic field during \ndeposition strongly influences the c-axis preferre d orientation growth of Ni-Fe nanowires. The \nsamples with m agnetic f ield perpen dicula r to te mplate plan e during de position  exhibits strong  \nperpendicular aniso tropy with greatly enhanced  coerciv ity and squaren ess ratio, particularly in \nNi-Fe nanowires deposited in po lycarbonate templates. In case of polycarbonate tem plate, as \nmagnetic field during deposition increases, both coer civity and squaren ess ra tio a lso incre ase.  \nThe wire length dependence was also m easured for polycarbonate templates. As wire length \nincreases, coercivity and squareness ratio decr ease, but saturation field increases. Such m agnetic \nbehavior (dependence on tem plate material, m agnetic field, wire length) can be qualitatively \n 1explained by preferential gr owth phenom ena, dipolar inte ractions among nanowires, and \nperpendicular shape anisotropy in individual nanowires.  \n \nKeyw ords : Electrodeposition, nanostructures, silicon, alum ina, polycarbonate. \n \nI. INTRODUCTION \n \n In re cent y ears the in creasing inte rest in highly-ordered  artificial m agnetic nanostructures  \nhas been driven not only by a de sire to understand the fundam ental properties of these m aterials \nbut also by the diversity of thei r potentia l app lications. Such  applic ation s range f rom magnetic \nrecording to sensors and to bio-m agnetism .1-3 Nanoscale m agnetic array s are a ttractive as u ltra-\nhigh density storage m edia. The m agnetic density  in conventional longi tudinal recording is \ntypica lly less than  50 Gb/in2, lim ited by  thermal instability.35 Howe ver, nanoscale m agnetic \narrays have the potential to  produce recording up to 100 tim es greater than existing random  \naccess m emories.4-6 The other field of extrem ely prom ising applications is bio-m agnetism , as the \nmagnetic nanowires can be m anipulated and probed by m agnetic  interactions.7 The spectrum  of \napplic ation s in bio-m agnetism  inclu des cell s eparation,9 bio-sensing,10 cellu lar stu dies,11,12 and a  \nvariety of other ther apeutic applications.7,8 Holmgren et al.13 perform ed both high yield (> 90%)  \nand high purity single  step  cell separations  on NIH-3T3 m ouse fibrobl ast cells  by app lying \nmagnetic forces through nanowires. These nanostru ctures have also been explored for use in \ndrug delivery and gene therapy.  Further, as nanowires are qua si-one-dim ensional, high-aspect \nratio (> 100) structures they have a large surf ace to volum e ratio. Thus, nanowire-based sensors \nallow for higher sensitivity, higher capture efficiency and  faster re spon se time, due to  their larg e \n 2adsorption s urface and sm all diffusion tim e.14 Many types of m agnetic nanowire arrays (m etals, \nalloys, o r multi- layer  struc tures) have been previous ly investig ated.15-17 Amongst the various \nmaterials studied, Ni-F e is attractive because of its superior ferro magnetic properties, high \nmagnetization behavior and invar effect in certain com positions.18,19\n  \nOne-dim ensional nanostructures can be produc ed by a variety of techniques such as \nmolecular beam  epitaxy, nanolithography, vapor-li quid-solid growth, and electrodeposition. \nElectrodepo sition  of metals into the  pores  of nanoscale  templates (such as alum ina m embranes, \nnuclear track-etched polym er m embranes, m esoporous silica or porous silicon) has been \nparticularly attractive 20,21 because: (a) it is a simple, low- cost, high -throughput technique for \nfabricating large arrays of nanowires with m onodispersive diam eter and length; (b) it provides \nthe ability to tailor s ize, length, sh ape and m orphology of the m aterial deposited b y contro lling \nthe tem plate m orphology and the synthesis param eters; and (c) it provides th e ability to introduce \ncomposition m odulation along the wire length, wh ich in turn enables precise control on \narchitecture and magnetic propertie s. For exam ple, Reich et al.1 showed s elective binding of two \ndifferent ligands onto two-com ponent Ni/Au nanowires, thus enabling spatially m odulate d \nfunctionalization schem es. Such properties can poten tially give rise to improved perform ance i n \nbio-m agnetic applications. \n \nTo date, m ost of the resear ch work has focused on studying the m agnetic properties by \nchanging the electrodeposition param eters or temp late param eters such as pore diam eter, inter-\npore spacing.22, 23 In this work, we present a comparat ive study of magnetic nanowires deposited \nin different tem plates. The m agnetic properties of  nanowire arrays are direc tly re lated to the  \n 3template properties - pore dim ensions, relative pore orientation, pore size distri bution and pore  \nsurface roug hness. In ad dition to tra ditional tem plates such a s porous alu mina and polycarbon ate, \nmagnetic properties of nanowires de posited in porous silicon are also  investig ated. In a previous \nwork, we have dem onstrated the ability to cont rol the porous silicon dim ensions (pore diam eter, \n40-290 nm  and length, up to 240 µm ) and then succe ssfully electroplated metal io ns into the \npores.24 In order to investigate the m agnetostatic coupling e ffect on the overall m agnetic \nproperties, nanowires with differe nt wire lengths were prepared  by controlling the electroplating \ntime. W e also investigate d the influen ce of a pplied m agnetic field during electrodeposition of Ni-\nFe nanowires on their crystallogr aphic and m agnetic properties.  \n  \nII. EXPERI MENTAL DET AILS \n Magnetic nanowire arrays are prepared by electropla ting Ni-Fe into the pores  of \nAnopore® alum ina m embranes,26 Nuclepore P olycarbon ate track -etch ed membranes,26 and in-\nhouse prepared porous silic on templates. The alum ina a nd polycarbonate m embranes are \nthoroughly cleaned in de-ionized water and subse quently dried prior to use. The porous silicon \ntemplate is  prepared in -house by electro chem ical etching  of silicon  substrate.24,25 N-type 2” \nsilicon substrate (resistivity: 0.4-0.6 ohm -cm) is etch ed in a m ixture of 1:1::49% HF:ethanol at a \nconstant current density of 35 m A/cm2. Ethanol is added to the HF solution to (a)  incre ase the \nwettability o f porous silicon surface and (b) to remove hydrogen evolved during etching.  \n \nA fil m of alum inum  (~ 1 µm ) is evaporated on one side of  all tem plates to serve as  the \nworking ele ctrode.  This  is followed  by electroc hemical dep osition  of Ni-Fe into th e tem plates \nfrom  a sul fate based electroplating bath (200g/L NiSO 4.6H 2O, 8g/L FeSO 4.6H 2O, 5g/L \n 4NiCl 2.6H 2O, 25 g/L H 3BO 3, 3g/L Saccharin). As the s toichio metry of the Ni-Fe nanowires is \nsignif icantly affected by plating tem peratu re, pH, agita tion co nditions, cu rrent, and ad ditives, all \nthe param eters have b een m aintained constan t, excep t for the electroplating tim e. In the \npolycarbonate tem plate, varying lengths of nanow ire are deposited (u p to 5 µm ) so that the \nlength dependent m agnetic properties can be studi ed. Ni foil is used as anode to m aintain \nconstan t metal-ion composition and  the electrop lating is perfor med under a current density of 3 \nmA/c m2 at room  temperature (20 ºC ). The app lied magnetic field during electroplating can be \noriented either perpendicular or parallel to the templa te plane. Note that throughout the paper the \norientation of applied m agnetic fiel ds will be d escrib ed with respec t to the tem plate plane r ather \nthan the nanowire axis. This is because, althoug h in general the wires ar e perpendicular to the \nplane of  the tem plate, som e samples exhib it a degree o f misalignment. This p oint will be \ndiscussed in detail later. \n \nThe structure and m orphology of the nanowir es are analyzed under a Scanning Electron \nMicroscope (SEM). Energy Dispersive Spectro scopy (EDS) and X-ray diffraction are used to \ninvestigate the com position and crystallographic st ructure of the electrodeposited Ni-Fe (after \netching Al). The X-ray diffraction is perform ed using an X’Pert PR O X-diffraction syste m \n(XRD) from Philips Analytical with a m onoc hrom atized Cu K α (λ = 15.4 nm ) radiation in a \nBragg-Brentano arrang ement. A Physical Property Measurem ent System  (PPMS) and \nSuperconducting Quantum  Interference Device (SQUID) magnetom eter from  Quant um Design \nare used to m easure the m agnetic properties of the nanowires em bedded within the templates.  \n \n \n 5III. EXPERIMENTAL RESULTS AND DISCUSSION \nA. Microscopy and Structural Characterization \nFigure 1(a) shows an S EM m icrograph of a cr oss-sec tion of the silico n tem plate af ter \nelectrochem ical etching for 100 m inutes. The av erage pore diam eter is 300±10 nm  with a n \ninterpore distance of 850±50 nm . The pores are 145 µm in length and suffer from  irregular walls \nand branching.24 Figure 1(b) and 1 (c) show th e SEM micrographs  of the top su rface of the \nalum ina and polycarbonate tem plates of thicknesses 60 µm  and 6 µm  respectively. T he pores are  \n190±10 nm in diam eter and have an interpor e distance of 285±15 nm  in the alum ina and \n520±125 nm  in the polycarbonate tem plate. Table 1 summ arizes the tem plate/pore  \ncharacteristics, as  measured with  the SEM. It is  evident f rom the table  that the lattic e par ameter, \nor inter-pore spacing, of polycarbonate and porous sili con tem plates are m uch larger than that of \nalum ina.  \n \nFigures 2(a) and 2(b) show the SEM im ages of Ni-Fe nanowires electrodeposited in the \nporous silicon, alum ina and polycarbonate tem plates respectively after rem oval of t he tem plate. \nThe nanowires deposited in porous  silicon are found to be 275±25 nm in diam eter, while those \ndeposited in both the alum ina a nd polycarbonate are 190±10 nm  in diam eter. The length of the \nnanowire, which is in itially es timated f rom the deposition ch arge and time, is la ter ve rified usin g \nthe SEM .  The Ni-Fe nanowires deposited in porous silic on exhibit a textured  and highly faceted \nwire surface with m ultiple grain boundaries, wire br eakage and branched  growth of wires. This is  \nprobably du e to the natu re of  the porous silicon e tching.24,29 In contrast, the nanowires deposited \nin the alum ina and  polycarbonate tem plates have sm ooth and uniform  surface morphology. \nHowever, those wires deposited in the commercia lly available polycarbonate tem plates are found \n 6have an ang le between the wire/pore axis and th e norm al to the plane ty pically between 0 º and \n34º.26-28 \n \nA quantitative EDS spectrum  was taken to dete rmine the elem ental composition o f the \nNi-Fe nanowires deposited in th e silicon, alum ina and polycarbona te tem plates and the results \nare shown in Table 2. EDS analysis dem onstrates that the  atom ic ratios of  Ni an d Fe in the \nnanowires f ormed in porous silicon, alum ina a nd polycarbonate tem plates are close to 77:13,  \n85:14 and 84:15 respectively. A small am ount of oxyge n is seen in all the spectra, indicating a \nmodicum of absorption  from air. Lower elem ental com position of Ni-Fe in porous silicon \ntemplate is due to f ormation Si im purity ph ases, whose crystallographic st ructure is investigated \nby the XRD technique. \n \nFigure 3 shows the x-ray diffraction patterns from  the Ni-Fe nanowires (a) deposited in \nsilicon without m agnetic field, a nd (b) deposited in polycarbonate in  the presence of a m agnetic  \nfield (320 Oe) applied perpendicular to the tem plate plane during electrodeposition. Significant \ndifferences in cry stallin e structu re are obs erved. The diffraction patterns  further confirm  the \nelectrodeposition of Ni-Fe alloy al ong with pure Ni. In absence of  magnetic f ield, the patte rn \n(Figure 3a) shows a strong peak for (111) FeNi 3 and (111) Ni along w ith other lesser peaks a t \n(200), (211) for FeNi 3 and Ni. There is also evidence for form ation of Ni-Si im purity phases  \nfrom  the silicon tem plate. A strong peak at (111) for Ni-Fe  and Ni ind icates  grain orientation \nalong the p referred (111 ) direction, but the oth er peaks  sugg est an  overall po lycry stallin e nature. \nThe peak for Al m ay be due the alum inum sa mple stage, in  case of the porous silicon sam ple.24 \nSimilar XRD dif fractio n peak in tensities a re obtained with alum ina and polycarbonate tem plates \n 7electrodeposited in the absence of magnetic f ield. Note th at all the sam ples m easure d have th e \nsame mass of Ni-Fe electrodeposits. \n \nWhen the nanowires are deposited with a perp endicular m agnetic field (F igure 3b), along \nwith Ni-Fe (111), Ni-F e grains with (200) text ure also becom e dom inant. This indicates a \ndifference in crystal structure fo r nanowires grown in polycarbonate  with applied magnetic field. \nFurtherm ore, SEM im ages (figure 2c) shows significant m orphological changes such sm oother \nwalls for th is type of nanowires. Th is is in acco rdance with the earlier re ported d ata of unifor m \nmorphology of the electrodeposited film s obtained in applied m agnetic field.33 Importan tly, the  \napplied m agnetic field seem s to have enhanced th e growth of Ni-Fe (200) textures com pared to \n(200) textures, when no m agnetic field wa s applied. As suggested by Devos e t al.30 and \nTabakovic et al.,33 this m ay be a consequence of indu ced convective solution flow due to \nmagnetohydrodynam ic effect near the tem plate’s vici nity. This is turn m ay cause decrease in the \nthickness of the diffusion layer and therefore an increase in the mass transport of active species. \nFurtherm ore, in the presence of applied m agnetic field, enhanced Ni-Fe ( 200) texturing indicates \ntowards forced growth of Ni-Fe grains with their c-axis parallel to the orientation of the applied \nfield.30 This result is c onsisten t with publish ed results f or Co nanowire arr ays.28 It seems \nhowever, that the applied field is not strong enough to totally force the Ni-Fe c-axis to alig n \nperpendicular to the plane of the template. Ther efore, Ni-Fe (111) textures do not disappear.  \n \nB. Magnetic Characterization \nNext, we compare the magnetic prop erties of the Ni-Fe nanowires deposited in the three \ndifferent templates (porous silicon, alum ina and polycarbonate) with/without  a magnetic field of \n 8320 Oe applied perpendicular to the plane of  the template during electrodeposition. The  \nsaturation m agnetizations of Ni-Fe were m easur ed to be about 1 T. Magnetization hysteresis \nloops, which display the m agnetic response of a m aterial to an external field have been used to \ncharacterize Ni-Fe nano wires. The hysteresis  loops m ay generally depend on the material, size \nand shape, m icrostructure and the orientation of applied m agnetic f ield with re spect to the  \nsample. In case of nanowires, the key depende nt property is m agnetic anisotropy, which is the  \nsum of different contributing factors such as shape anisotropy, m agnetocr ystalline anisotropy, \nmagnetostatic coupling and other morphological characteristics. It should be noted that in \nnanowires with no preferential orientation, the m agnetocrystallin e anisotropy can compete with \nthe shape anisotropy. However, if the easy axis is aligned along the wire axis both shape and \nmagnetocrystalline an isotropies will add up. Last ly, m agnetostatic coupling will alw ays reduce \nboth coercivity and effective pe rpend icular m agnetic aniso tropy.34  \n \nFigure 4 depicts typical m agnetic  hysteresis curves of Ni-Fe nanowires deposited without \nmagnetic field in (a) porous silicon, (b) alum ina and (c) polycarbonate tem plates. The \nmagnetization curves both parallel and perpendi cular to the  tem plate p lane a re sho wn. Quasi-\none-dim ensional structu res such as Ni-Fe nanowires  might reasonably be e xpected to behave like \ninfinitely long, m agnetic cylinders. If so, they  should exhibit strong anisotropy, with the \nmagnetic easy-axis aligning parallel to the wires.31 In addition, if the m agnetocrystalline  \nanisotropy is sm all compared to shape anisotrop y, square hysteresis curv es are expected when \nthe m agnetization  is m easured alon g the cy lindrical axis.31 However, it is clear from  Figure 4 \nthat these nanowires exhibit little or no m agnetic anisotropy. This is in agreem ent with our \nearlier publication in which we suggested that  (a) the presence of branched and rough wire \n 9surfaces m ay reduce th e shape aniso tropy term  and (b) com petition between this ‘red uced’ shap e \nanisotropy and m agnetocrystallin e anisotropy (with no preferen tial orientation along the easy \naxis, as seen in figure 3a) m ay resu lt in zero overall magnetic anisotropy.24\n \nThe coerciv ity and squar eness ra tio (defined as r atio of  the r emnant m agnetiz ation to  the \nsaturation m agnetization) are in  the range of 50-100 Oe and 0.1- 0.18 respectivel y for all the  \nsamples deposited in the absence of a m agnetic fiel d (see Table 3). W e note that a similarly wea k \nmagnetic anisotropy is shown by na nowires deposite d in sm all m agnetic field of 320 Oe applied \nparallel to th e tem plate p lane. \n \n A very diffe rent behavior is exhibited by th e nanowires electrodeposited in the presence \nmagnetic field of 320 Oe applied perpendicular to the tem plate plane. Figure 5 shows the typical \nmagnetic hystere sis curv es for these  sam ples in  the three different template s. The  coerc ivities \nand squareness ratios are tabulated in Table 3.  It is  seen that for all the sam ples, the  magnetic \nanisotropy is enhanced com pared to those deposite d in zero field. In all cas es, the coercivity and \nsquarenes s ratio is larg er for the m agnetiz ation  measured  perp endicular to the tem plate plane (i. e. \nroughly parallel to the nanowire ax is), but the precise value of these param eters depends on the  \ntemplate m aterial.  \n \nFigure 5a and Table 3a show the data for wi res deposited in the porous silicon tem plate. \nAlthough there is enhancem ent of the perpendicu lar squareness ratio and coercivity when the \nsample is deposited in a n applied f ield, this inc rease is sm aller com pared to other two tem plates. \nGiven the discussion about wire m orphology above and by A ravam udhan et al.,24 it seems likely \n 10that further enhancem ent of these param eters is hindered by the imperfections and surface \nroughness inherent in nanowires form ed using the silicon templates.  \n \nIn case of the alum ina tem plate (fi gure 5b and table 3b), b ecause of sm all \nmagnetocrystalline anisotropy (both Ni-Fe (111) a nd (200) textures equally being dom inant), the \nnet m agnetic anisotropy is m ainly due to tw o term s: (a) shape anisotropy induced due to \nmagnetic easy axis pa rallel to wir e axis, (b ) magnetostatic coupling between wires, which \ndevelops an  easy axis perpendicular to wire axis. Becaus e of higher pore density  in alum ina \ntemplate (about 109 pores/cm3) compared to polycarbon ate or porou s silic on (le ss than 108 \npores/cm3), the net contribution from di pole field (aligned perpendicula r to wire ) is to  reduc e the \neffective anisotropy field given by22, 23\n323.62dLrMM Hs\ns k−=π ,                                                  \n(1)   \nwhere, M s is the saturation m agnetization, r is the wire  diam eter, L is the length and d is the \ninterpore distance. The squarenes s ratios and co ercivities in this case (f or 3 different sam ples) \nwere, however, slightly im proved to 0.25-0.2 8 and 200-220 Oe respectively from  greater \noriented growth of nanowires. Finally, in the case of polycarbonate, (figure 5c and table 3c), a \nremarkable perpendicular anisotrop y is exhib ited. It can be seen that the m aximum squareness \nratio of 0.58-0.60 and coercivity  of 400-425 Oe were observed (from 3 sa mples) when the \nmeasuring m agnetic f ield is perpendicula r to te mplate p lane. This  suggests tha t applica tion of \nperpendicular m agnetic field during electrodepos ition in  polycarbon ate tem plate results in \nhighest perpendicular m agnetic anisotropy. However,  the slight shearing of the hysteresis curve \nis mainly due to th e 34º (maximum) devia tion between th e pore ax is and surface norm al,26-28 \n 11along with the dipole interactions  between the wires (interpore di stance is 520±125 nm ). Even  \nthough the average interpore distan ce in polycarbonate is much larger com pared to alum ina, \naccord ing to  Maeda et al.,32 wire interactions will still occu r for spacings up to 1.5 µm . This \ndipole wire interaction tends to al ign perpend icular to wir e axis, resulting in a decrease in both \nsquareness ratio and coercivity. \n \n Next, the effect of varying the m agneti c field perpendicular (270-1060 Oe) to the  \npolycarbonate tem plate during electrodeposition pr ocess was investigated. Figure 6 and table 4 \nshow the m easured average coercivity and  squareness  ratio (M r/Ms) as a function of \nperpendicular m agnetic field during electrodepos ition. W ith increase in applied magnetic field \nduring electrodeposition both coerci vity and  squareness  ratio in crease s ignifican tly. Squareness  \nratio of about 0.76 was observed for perpendicula r magnetic field of 1060 Oe, indicating greater \nNi-Fe growth with c-axis parall el to nanowire axis and hence enhanced perpendicular m agnetic \nanisotropy. However, this is stil l a lower squareness ratio than th e expected theoretical values \nbecause of the above stated reasons.  \n \n Lastly, th e length effect was exam ined by depositing Ni-Fe nanowires  of varying lengths \n(2-5 µm ) in polycarbon ate tem plate in presen ce of perpendicular m agnetic field of 320 Oe during \ndeposition. Figure 7 and table 5 sh ow the m easured average coerci vity and squareness ratio as a \nfunction of wire length. For m agnetic field applied perpend icular to tem plate plane, as the wire \nlength is in creased, acco rding to infi nite long magnetic cylinders m odel,31 the shape anisotropy \nshould also increase. But our experim ents s how that both coercivity and squareness  \n 12monotonically decreases, with increase in wi re length. T his m ay be  caused by the length \ndependence of dipole interactions am ong wires, given as22,23  \n322.4\ndLrMHs\nd=  ,                                                              \n(2) \nwhere, M s is the saturation m agnetization, r is the wire  diam eter, L is the length and d is the \ninterpore distance. In addition, as  wire length increases, saturati on m agnetization also increases.  \n \nIV. CONCLUSIONS \n In summ ary, in this work, a system atic investigation was pe rform ed to study the \nstructural and m agnetic propertie s of Ni-Fe nanowires as a func tion of  (a) tem plate m aterial \n(porous silicon, alum ina and poly carbonate), (b) applied m agnetic field during electrodeposition \n(0-1060 Oe), (c) wire length (2-5 µm ) and (d) field orientation (parallel/perpendicular to \ntemplate plane) during m easure ment. The appl ied m agnetic field durin g electrodeposition was \nshown to have strong influence on crystallographi c and m agnetic properties of Ni-Fe nanowires, \nin particular, in the case of polycarbonate tem plate, Ni-Fe nano wires of diam eter 190±10 nm  and \nlength 2 µm fabricated in polyc arbonate tem plate with 1060 Oe  applied m agnetic field showed \nthe highest coercivity of 530 Oe and squareness ratio of 0.74.  The applic ation of m agnetic field \nperpendicular to the template plane during depositi on tend s to force the Ni-Fe grains with c-ax is \nalong the orientation of applied field, thereby resulting in perpendicular shape anisotropy. \nFurther, the influence of app lied m agnetic field strength a nd nanow ire length on m agnetic \nproperties was also studied. It was shown that with increase in m agnetic field during deposition \nboth coercivity and squareness ratio increased  significan tly, while co erciv ity and  squareness  \nmonotonically decreased, with in crease in wire length because of the length dependency on \n 13dipole interactions. The prom ising aspect of this  work was the ability to  tailo r the magnetic and \nstructural properties of Ni-Fe nanowires by application of strong m agnetic fi eld during \nelectrodeposition and by selection of template m aterial. Optim ization of  fabricatio n process to \ncreate h igh-density,  isolated and  vertical fe rromagnetic nanowire arr ays com parable to th e \ntheoretical expectations (based on coherent rotati on theory ) for coer civity and squar eness ratio is  \ncurrently underway. This is a key requirem ent for applications in ultra-high density m agnetic \nstorage and bio-m agnetics. \n \nACKNOWLEDGEME NTS \n This work was supported the National Science Foundation (NSF) NER award no. ECS-\n0403800. P.A.G. thanks the Glasstone Foundation for financial support. \n \nReferences  \n \n1D. H.  Reich, M. Tanase, A. Hultg ren, L. A. Ba uer, C. S. Chen, G. J. Meyer, J. Appl. Phys. 93  \n7275 (2003). \n \n2A. Fert, L. Piraux, J. Magnetism  Mag. Mater. 200 338 (1999). \n \n3I. Safarik, M. Safarikova, J Appl. Bacteriol. 78  575 (1995). \n \n4S. S. P. Parkin, M. Hayashi, L. Thom as, Science 320  190 (2008) . \n \n5T. Thurn-Albrecht, J. Schotter, G. A. Kästle, N. Em ley, T. Shibauchi, L. Krusi Elbaum , K. \nGuarini, C. T. Black, M. T. Tuom inen, T. P. Russell. Science 290  2126 (2000). \n \n6Q. Zhan, Z. Chen, D. Xue, F. Li, H. Kunkel, X. Zhou, R. Roshko, and G. W illiam s, Phys. Rev. \nB 66, 134436 (2002). \n \n7M. Tanase, D. M. Silevitch, A. Hultgren, L. A. Ba uer, P. C. Searson, G. J. Meyer, D .   H Reich, \nJ. Appl. Phys. 91  8549 (2003).  \n \n8D. R. Baseli, G. L. Le e, M. Natesan, S. W. Metzger, P. E. Sheehan, R. J. Colton, Biosens. \nBioelectron. 13  731 (1998). \n 14 \n9A. Hultgren, M. Tanase,  F. J. Felton, K. Bhad riraju, A. K. Salem, C. S. Chen, D. Rei ch \nBiotech Pro g. 21  509 (2005). \n \n10D. R. Baselt, G. L. Lee, M. Natesan, S. W . Metzger, P. E. Sheehan, and R. J. Colton, Biosens. \nBioelectron. 13 731 (1998).  \n \n11F. C. MacKintosh, C. F. Schm idt, Curr. Opin. Colloid In terface Sci.  4 300 (1999). \n \n12F. J. Alenghat, B. Fabry, K. Y. Tsai, W . H. Goldm ann, D. E. Ingber, Biochem . Biophys. Res. \nCommun. 277 273 (2000). \n \n13A. K. Salem, P. C. Sea rson, K. W . Leong, Nature Mater. 2  668 (2003). \n \n14E.C. W alter, F. Favier, R.M. Penner, Anal. Chem. 74  1546 (2002). \n \n15L. Sun, P. C. Searson, C. L. Chien, Appl. Phys. Lett. 79  4429 (2001). \n \n16D. J. Sel meyer, M. Zhang, R. Skom ski, J. Phys. Condens. Matter 13  R433 (2001). \n \n17A. Blondel, J. P. Meier, B. Boudin, J.-Ph. Anserm et, Appl. Phys. Lett. 65  3019 (1994). \n \n18H. R. Khan, K. Petrikowski, J Magn Magn Mater 213 526 (2000). \n \n19H. Zhu, S. G. Yang, G. Ni, S. L. Ta ng, Y. W . Du, J Phys: Condens Matter 13 1727 (2001). \n \n20C. R. Martin, Science, 266 1961 (1994). \n \n21J. Hu, T. W. Odom, C. M. Lieber, Acc. Che m. Res. 32 435 (1999). \n \n22G. J. Strijkers, J. H. J. Dalderop, M. A. A. Broe ksteeg, H. J. M. Swagten, W . J. M. De Jonge, J . \nAppl. Phys. 86 5141 (1999). \n \n23G. C. Han, B. Y. Zong,  Y. H. Wu, IEEE Tran. Magn. 38 2562 (2002). \n \n24S. Arava mudhan, K. Luongo, S. Bhansali, P. Poddar, H. Srikanth, Appl. Phys.A 87 773 (2007). \n \n25V. Lehm ann, Appl. Phys. Lett. 58 856 (1991). \n \n26Alum ina and Polycarbonate m embranes were  manufactured by Whatman Inc., NJ, USA \n \n27R. Ferre, K. Ounadjela, J. M. George, L. Piraux, S. Dubois, Phys. Rev. B 56 14066 (1997). \n \n28S. Ge, C. Li, X. Ma, W. Li, L. Xi , C. X. Li  J Appl. Phys. 90 509 (2001). \n \n 1529M. Christophersen, J. Cartensen, S. Ronnebeck, C.  Jager, W . Jager, H. Foll, J Electrochem . \nSoc., 148 E267 (2001). \n \n30I. Tabakovic, S. Riem er, V. Vas’ko, V. Sapozbuikov, M. Kief, J Electrochem . Soc., 150 C635 \n(2003). \n \n31A. Aharoni, S. Shtrikm an, Phys. Rev. 109 1522 (1958). \n \n32A. Maeda, M. Kum e, T. Ogura, K. Kuroki, T.  Yamada, M. Nishikawa, Y. Harada, J. Appl. \nPhys. 76 6667 (1994). \n \n33O. Devos, A. Olivier, J. P. Chopart, O. Aa bobi, and G. Maurin, J. E lectrochem . Soc., 145 401 \n(1998). \n \n34G. Sorop, K. Nielsch, P. Göri ng, M. Kröll, W. Blau, R. B. Wehrspohn, U. Gös ele, L. J. de \nJongh, J. Magn. Magn.  Mater. 272-276  1656 (2004). \n \n35S. Charap, P. L. Lu, Y. He, IEEE Trans. Magn. 33 978 (1997). \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 16 \n(a) \n \n \n \n \n \n \n \n(b)                                               (c) \nFigure 1 : SEM im ages of  the star ting tem plates.  (a) Cross-section of the n- type silicon substrate \nshowing the 290±10 nm dia meter and 145 µm d eep nanopores created using electrochem ical \netching. View of the pores in (b) the alum ina template (diam eter = 200 nm , separation = 285±15 \nnm), and (c) the polycarbonate tem plate (diam eter = 200 nm, separation = 520±125 nm ). \n 17 \n(a) \n \n(b) \n 18 \n \n \n \n \n \n \n \n \n \n \n(c) \n \nFigure 2 : (a) SEM im age of a cluster of 275±25 nm  Ni-Fe nanowires released from  the porous \nsilicon template, (b) SEM view of released nanowires  electrodeposited in perpendicular \nmagnetic f ield in alum ina tem plate, (c) SEM view of released na nowires electrodeposited in \nperpendicular m agnetic field in p olycarbon ate tem plate. The alumina and po lycarbon ate \nnanowires w ires are 190±10 nm  in diam eter, regular and uniform . \n \n \n 19 \n(a) \n \n(b) \nFigure 3:  X-ray diffraction pattern of Ni-Fe nanowires deposited in: (a) porous silicon tem plate \nwith no applied m agnetic field, (b) polycarbonate tem plate with a m agnetic field of 320 Oe  \napplied perpendicular to the plane of the tem plate during electrodeposition. \n \n \n 20 \nFigure 4 : Typical m agnetic hysteresis curves of Ni -Fe na nowire a rrays electrodepos ited in the  \nabsence of m agnetic field in (a) porous silicon, (b) alum ina, and (c) polycarbonate tem plates \n(average of 3 sa mples measured).  Magnetization m easured both para llel and perpend icular to the \ntemplate plane are show n. \n \n 21 \n \n \nFigure 5 : Typical m agnetic hysteresis curves of Ni -Fe na nowire a rrays electrodepos ited in the  \npresence of a sm all magnetic field (320 Oe) in (a) porous silicon, (b) alum ina, and (c) \npolycarbonate tem plates (average of 3 sam ples measured ). Magnetization  measured both parallel  \nand perpendicular to the tem plate plane are show n. \n 22 \nFigure 6 : Dependence of coercivity and squareness ra tio on applied perpendicular magnetic field \nduring Ni-F e electrodeposition in po lycarbon ate tem plate.  \n \n \n \n \n 23 \nFigure 7 : Dependence of coercivity and squareness ratio on Ni-Fe wire length, deposited in \npolycarbonate tem plate.  \n \n \n \n \n \n \n \n \n \n \n \n \n 24Table 1 : Template par ameters and charac teristics \n \nParam eters Porous silicon Polycarbonate Alum ina \n \nPore size (nm ) 300±10 190±10 190±10 \nInter-pore distance (nm ) 850±50 520±125 285±15 \nPore density (pores/cm2) about 107about 108about 109\n \n \nTable 2 : EDS elem ental com position of Ni-Fe wires \n \n \nNi-Fe Nanowires \n(Elem ent) In Porous Silicon \nAt % In Alum ina \nAt % In Polycarbonate \nAt % \n \nO K 9.77   1.21 1.03  \nFe K 12.93 14.23 14.85 \nNi K 77.30 84.56 84.12 \nTotal 100.0 100.0 100.0  \n \n \n \n \n \n \n \n \nTable 3 : Magnetic char acterization param eters f or Ni-Fe nanowires in  different te mplate and  \nmagnetic field during deposition (Data s howed is from  3 samples each). \n \n(a) Template: Porous Silicon \nWire length (µm ) Magnetic field during \ndeposition (Oe) \n Coercivity (Oe) Squareness ratio \n2 - 3 0 80-100 0.18 \n2 - 3 320 100-130 0.2-0.22 \n \n(b) Tem plate: Alum ina \nWire length (µm ) Magnetic field during \ndeposition (Oe) \n Coercivity (Oe) Squareness ratio \n2 - 2.3 0 60-80 0.15 \n2 - 2.3 320 200-220 0.25-0.28 \n \n(c) Tem plate: Polyca rbonate \nWire length (µm ) Magnetic field during \ndeposition (Oe) \n Coercivity (Oe) Squareness ratio \n2 - 2.2 0 50-65 0.12 \n2 - 2.2 320 400-425 0.58-0.60 \n \n 25Table 4 : Magnetic characterization param eters fo r Ni-Fe nanowires of length 2-2.2 µm in \npolycarbon ate tem plate with vary ing magnetic field during deposition \n \nMagnetic field during depos ition (Oe) Coercivity (Oe) Squareness ratio \n \n270 379 0.52 \n320 400-425 0.58-0.60 \n650 460 0.63 \n1060 530 0.74 \n \n \nTable 5 : Magnetic characterization param eters fo r Ni-Fe nanowires of varying length in \npolycarbonate tem plate with fixed ma gnetic field (320 Oe) during deposition \n \nNanowire length (µm ) Coercivity (Oe) Squareness ratio \n \n2-2.2 400-425 0.58-0.60 \n2.5-2.75 387 0.54 \n3-3.2 370 0.5 \n4-4.25 360 0.48 \n5-5.3 350 0.47 \n \n \n 26"    },    {        "title": "0809.2005v1.Ferromagnetic_ordering_in_dilute_magnetic_dielectrics_with_and_without_free_carriers.pdf",        "content": " Ferromagnetic ordering in dilute magnetic dielectrics with and \nwithout free carriers \nK. Kikoin  \nSchool of Physics abd Astronomy, Tedl-Avi v Universiy, Tel-Aviv, 69978, Israel \n \n \nAbstract \nThe state of art in the theoretical and experimental studies of transition metal doped oxides (dilute magnetic \ndielectrics) is reviewed.  The available data show th at the generic non-equilibrium state of oxide films \ndoped with magnetic impurities may either favor ferrom agnetism with high Curie temperature or result in \nhighly inhomogeneous state without long-range magnetic order. In both case concomitant defects \n(vacancies, interstitial ions play crucial part.  \n \n \n1. Introduction \nThe available experimental information and existing theoretical considerations about \nthe nature of ferromagnetic ordering in dilute magnetic dielectrics (DMD) (mostly, \noxides doped with transition metal ions) [1] clearly demonstrate essential differences \nbetween these wide-gap materials and dilute magnetic semiconductors (DMS) [2]. In this \npaper we summarize the inherent features of  DMD, which allow treating these materials \nas a separate family of dilute magnetic materials. In the most of DMD with high Curie \ntemperature T C, the room-temperature ferromagnetism (FM) is apparently not related to \nhigh concentration of free carriers [1,3]. This implies that the carrier-mediated exchange \nmechanism responsible for FM order in DM S [2,4] is ineffective in DMD. These \nmaterials are characterized by extreme sensitivity to the growth and annealing conditions [5], and practically in all cases one may c onclude that the indir ect exchange between \nmagnetic transition metal ions is medi ated by complex def ects involving oxygen \nvacancies, shallow impurities or other imperfections [1,3,5,6].   We review the experimental a nd theoretical situation with materials, in which the role \nof magnetic inclusions is ruled out (II-VI oxides and some dioxides diluted with \nimpurities of iron group) and discuss in some details possible mechanisms of indirect \nferromagnetic exchange specific for the wi de gap materials. Among possible complex \ndefects, which may mediate th e indirect ferromagnetic exchange between transition metal \n(TM) impurities in oxides, one may menti on oxygen vacancies (both isolated and bound \nwith impurities), defect magnetic polarons and bound excitons.  \n \n2. Basic Experimental Facts  \n \n \nIt is generally recognized in current lite rature that the structural and magnetic \nproperties of TM-doped oxide films are extrem ely sensitive to sample preparation and \nthermal processing methods [5,6]. Availabl e methods (ion implantation, pulsed laser \ndeposition, reactive magnetron sp uttering, etc) produce imperf ect films, which are far \nfrom thermodynamic equilibrium. These materials are unstable against various \nheterogeneities (see, e.g., [7]), namely, precipitation of other crystallographic phases, \nphase separation in host material, spinodal decomposition of dopant, diffusion and implantation profiles, etc. Even in carefully  checked conditions, where the precipitation \nof parasitic phases and aggregation of superparamagnetic clusters with excessive \nconcentration of TM ions are prevented or at least controlled, one cannot get rid of this \ngeneric feature of oxide DMD materials. We have chosen for our review two families of \nDMD, namely ZnO and TiO\n2 doped with iron group ions (V, Cr, Mn, Fe, Co). The reason \nfor this choice is a consensus within the ex perimental community about intrinsic nature \nof long range FM order in these materials, at least in the best samples, although the \nnotion “best” demands additional specification, which will be given below.  One of the most salient featur es of TM doped oxide films is stabilization of FM order at \nroom temperature already in  relatively weakly doped n-type materials with concentration \nx of magnetic impurities well below the percolation threshold  xc for disordered \nmagnetism [1]. To resolve this discrepancy, the authors of the review [1] proposed the \nconcept of weakly bound magnetic polarons: these are the donor electrons near the \nbottom of conduction band, which are captured into a spin-split impurity band by means \nof s-d exchange with TM impurities. The radius of polaron orbitals is large enough to \nprovide the indirect exchange between magnetic ions via the states in the partially filled \npolaronic band even at  x< x c  . This approach may explain appearance of FM order in n-\ntype samples with metallic-type conductiv ity like  (Zn,Mn)O  and (Zn,Co)O codoped \nwith Al [8]. However, FM order is observed  also in highly insula ting samples of oxygen \ndeficient TM doped ZnO [3,9] and TiO 2 [5,10,11], so the concept of magnetic polaron \nshould be modified in order to interpret these data. The most exhaustive data about \ndependence of FM order on the degree of im perfection and codoping le vel in n-type ZnO \ndoped with Ti, V, Mn and Co are published in [3]. In the experiment both oxygen \npressure and codoping level were varied. Thus, the wide range of sa mples from strongly \nnon-stoichiometric oxygen-deficien t films to overcompensated n-type metallic-type films \nwas investigated. The data for (Zn,Co)) codope d with Al are presented in Fig.1. Three \ndifferent transport and magnetizat ion regimes were identified. In the insulating regime (1) \nof low carrier concentration the films are ma gnetic at room temperature, and the electron \ntransport arises from a variable range hopping,  where the resistivity  obeys Mott’s law, \nρ(T)=A  exp( T0 /T)1/4 . The samples are strongly magnetic only if T 0>104\n K, i.e. if hopping \nkinetic energy is small enough. In the intermed iate regime (2) magnetization disappears, but with growing donor concentration it aris es again and magnetization in metallic phase \n(3) has a sharp maximum as a function of car rier density. Evolution of magnetization and \nthe carrier density with decreasing temperat ure from 295 K to 5 K for three samples \na,b,c  is also shown. Similar effect, i.e. exis tence of FM order bot h in insulating and \nmetallic phases was observed in (Ti,Co)O 2 films [5,12]. Appare ntly, existence of \nmagnetism both in metallic and highly resistiv e films is the generic property of dilute \nmagnetic oxides, which should be explained within a framework of microscopic theory. \n Although the most of concise expe rimental data are related to n-type samples, one \nshould mention the peculiar observation of polarity dependent ferromagnetism in TM \ndoped ZnO [13]. It was shown that ferro magnetism in quite perfect (Zn,Co)O and \n(Zn,Mn)O nanocrystalline films prepared by di rect chemical synthe sis, have opposite \ncarrier polarities. FM order is observed in p-type (Zn,Mn)O and in n-type (Zn,Co)O. \nChanging the type of polarity by means of  nitrogen codoping  from p- to n-type in the \nfirst case and from n- to p-type in the second case result ed in disappearance of the FM \norder. This remarkable result is worth of attention because these chemically prepared \nsamples are relatively free from stru ctural defects and inclusions.  \n \n3. Basic Theoretical concepts \n \nTo interpret the above experimental data , one should have in mind the generic \ninhomogeneity of thin films containing both intrinsic defects (oxygen vacancies), TM \nions in concentration well above the solubi lity limit, and uncontrollable concomitant \ndefects. Additional source of inhomogeneity  is the film surface [6]. Any thermal treatment induces the diffusion of vacancies, magnetic ions and other defects and \nformation of complexes. Even in the samples, where the spinodal decomposition and \naccumulation of defects near the film surf ace do not make the film heterogeneous, and \nthe FM order is formed in a bulk of the sample ,  one may be sure that the complex defects \nare responsible for this order rather than is olated TM ions. Such picture is accepted in \nmany recent theoretical models [14-17].   \nThe complex defects involving magnetic ions in  substitution or inte rstitial positions, \noxygen vacancies and adjacent ions from host cation sublattice are formed in the course of migration of these defects under thermal processing. An example of such complex is \nthe double defect [Co\nTi,VO] in (Ti,Co)O 2 discussed in [14]. When Co impurity substitutes \nfor a Ti ion in the vicinity of oxygen vacancy V O, the bound state is formed in accordance \nwith “reaction” \nCo4+(d5) + V O(p2) → Co2+(d7) + V O(p0)                                                                       (1) \nIn accordance with this reacti on two electrons from double donor p-orbital level εt of O \nvacancy in the upper part of the forbidden gap of TiO 2 move to the 3 d shell of \nsubstitution Co ion, to the energy level determined by the addition energy [18,19] \n   ε(n/n-1)=E (dn) – E(dn-1) –  ε t                                                                                     (2) \n(n=7) in the lower part of the energy gap. The binding energy of the complex [Co Ti,VO] \nis determined by the charge transfer energy εt - ε(n/n-1) and the energy of Coulomb \nattraction between negatively charged impur ity and positively charged vacancy. Such \nsituation is common for TM-doped oxides, beca use of the universal trend in the position \nof addition energies (2) rela tive the center of gravity of the continuum of host valence \nand conduction bands.  In II-VI oxides the levels  ε(n/n-1) corresponding to the neutral substitution position of \nTM ion in the cation sublattice form the mid- gap states between the top of the valence \nband εt and the bottom of conduction band εb [19-21]. Neutral Mn2+(d5) is the only \nexclusion: its ε5/4 d-level D(0/+) falls deep in the valence band of ZnO [21]. \nCorresponding universal trend for TM-doped TiO 2 is more complicated [19,22]: several \ncharged donor states D(-/0), D(--/-) above εt may arise for each TM impurity. As a result, \ndifferent TM ions may enter the impurity-vaca ncy complex in different charge states, \nTM2+ or TM3+ [23].   \nEventually the thermally treated film ma y be considered as a non-equilibrium \nensemble of oxygen vacancies partially free and partially bound with  magnetic ions in a \nform of complexes. As is known [16], V O orbitals form a band of relatively shallow \ndefects states slightly below cb .  If the distribution of va cancies and magnetic ions is \nhomogeneous enough after thermal treatment, then the overlap between the weekly \nbound p-orbitals of oxygen vacancies play the same part as the donor states in the \npolaronic model of Ref. [1]. In the film s codoped with other shallow donors [3,8], second \npolaronic band of donor origin appears. The resulting ener gy level scheme is presented in \nFig. 2. Evolution of this spect rum corresponding to effective carrier concentration shown \nin Fig.1, is presented at the upper panel.  In undoped samples double donors tates V O(p2) \nare partially compensated by acceptor impurities Co Ti in accordance with  (1),  so  that  \nthe V O-related  band is partially filled and magnetized due to the indirect exchange \nbetween magnetic impurities [14]. Donor impurities compensate [V O-Co Ti] complexes. In \nthe intermediate phase the va cancy band is filled and the donor  band is nearly empty. \nWith further increase of donor concentration this band gradually fills up, and magnetizes respec tively in a ccorda nce with  the pola ronic mechanism [1]. W hen the b and filling  \nprocess is com pleted, the film  returns into nonmagnetic stat e. Evolution of m agnetization \nis shown in the lower panel of Fig. 2.  \n  Similar situation should be realized in TM doped ZnO with one im portant reservation. \nTM Zn substitution im purities  are isoelectron ic acc eptors  TM2+, so th e charge transfer f rom \nVO states is possible only provided the energy level TM+/2+ is belo w or at lea st in \nresonance with V O related band states. This is the case of Cr and Co ions [10], and just \nfor these impurities the dependence M(nc) observed experim entally [3] c orresponds to the \nqualitative picture of Fig. 2. Microscopic calculation of this dependence m ay be done \nwithin a fram ework of generalized A lexander-A nderson m odel [14] with the Ham iltonian  \n,,mj b d hyb\njb cv d sHH H H H\nκ ===+ ++ ∑∑ ∑                                                                     (3) \nThis Ham iltonian in cludes im purity term s Hmj describing TM ions in the sites j, band \nHam iltonian s Hb with term s describing  mobile electrons in the valence (b=v)  and \nconduction (b=c ) bands, defect Ham iltonian describing the V O related band (d=κ)  of \nweakly localized electrons and the set of shallow donor states (d=s) near the botto m of \nconduction band. The last term  descri bes the hybridization between 3 d of TM im purities \nand all band states, both conducting and locali zed. If the concentration of TM ions is \nbelow the p ercolation lim it for direct exchan ge and indirect exch ange via valence and \nconduction bands, then its sing le-site part m ay be taken into account by m eans of exact \ncanonical transform ation [24]. Then the superexchange via em pty states in the bands Hc \nwhich has the FM character [14], i s respons ible for long-range order in hom ogeneous  \nfilms. The Curie tem perature is propo rtion al to th e strength of  the ef fective inter -impurity \ncoupling, w hich has the for m Jjl F(µ). Here the constant           J jl ~|V j|2\n |Vl|2 /ρc|∆dc|2                                                                                                (4) \ncontains parameters of hybridization Vj(l) between the TM impurity in the site j(l), and the \nstates in the defect band  c with average density of states ρc and the charge transfer energy \n∆dc between defect level and the level En+1/n  . The function F(µ) depends on the position \nof chemical potential µ in the defect band which is regulated by the occupation degree. \nThis function with a maximum around the half-fill ing of the defect ba nd is shown in Fig. \n3. It correlates with experimentally found vari ation of magnetization as a function of the \ncarrier deficiency [3,8] (see the upper panel of  Fig.1 for comparison). This trend reflects \nthe obvious fact that the maximum energy gain due to indirect  exchange via empty states \nin the mediating subsystem is achieved when the band of these stat es is half-filled. \nSimilar trend was predicted for the indirect exchange via an impurity band split from the \nvalence band due to magnetic im purity scattering in DMS [25]. \nThe explanation of the dependence of ma gnetic ordering on the carrier polarity in \nnanocrystalline chemically synthesized film s [13] is based on the idea of indirect \nexchange via bound exciton states. Such st ates in TM doped II-VI materials were \ndiscovered experimentally and discussed theo retically in 80-es [26,27]. An electron-hole \npair may be captured by a neutral magnetic impurity in two ways in accordance with \n“reactions” \n           dn + [e,h] = [dn+1h]                                                                                      (5a) \nor \n           dn + [e,h] = [dn-1e],                                                                                       (5b) \nwhere either electron or hole is captured in the unfilled 3d sh ell of TM ion, whereas the \nsecond carrier (hole or electron) is retain ed on the loosely bound hydrogen-like orbit by the attractiv e Coulom b force. Then the indir ect exchange b etween ad jacent TM  ions  via \nvirtual excitation of such elec tron-hole pairs nam ely,    \n11\n11[] [] , (6\n[] [] , (6nn n n n n nn\nij i j i j ij\nnn n n n n nn\nij i j i j ijdd de d dde dd\ndd dhd ddh dd−−\n↑↑\n++\n↓↓→→→\n→→→a)\nb) \nis possib le. The f irst of  thes e pro cesses is realized in p-type (Zn,Mn)O with n=5, and the \nsecond one m ay be realized in n-type (Zn,Co)O with n=7. The loosely bound hydrogen-\nlike ch arge carriers play  the sam e part in the excitonic m echanism  of indirect exchang e as \nthe vacancy -related carriers in (4 ) or spin-p olaron states in the m echanism proposed in  \n[1]. It is worth to em phasize  that the Hund rule, which is responsible for the high spin \nstate of the 3d-electron s in the configurations d n\n and d n-1 plays the decisive part in the \nferrom agnetic type of indirect ex change in these m aterials [14]. \nConcluding remarks \nThe m ain m essage conveyed in this review is that the ferrom agnetic ordering in TM \ndoped oxide film s is intim ately connected with the non-equilibrium state of these \nmaterials. L ong range order m ay arise due to balance between the distribution of \nsubsitu tion m agnetic impurities and  native def ects like vac ancies, inte rstitial impurities \nets. Great s catter of m agnetic characteristic s is an unavoidable pr operty of DMD.  In \nmany sa mples the inhomogeneous distribution of all com ponents in th is ensem ble is \ndetrim ental for the FM orde ring. Imperfections responsible for form ation of loosely \nbound defect states in the ener gy gap of host m aterial medi ate an indire ct exchange \nbetween T M impuritie s, and the  careful con trol of these  defects is a key to s table FM \nordering with high Curie tem perature in DMD.   \nAuthor is indebted to V. Fleurov an d A. Rogalev for valuable discussions. References \n[1] J.M.D. Coey, M. Venkatesan, and C.B.  Fitzgerald, Nat. Mater. 4 (2005) 173  \n[2] T. Jungwirth, et al., Rev. Mod. Phys. 78 (2006) 809 \n[3] AJ. Behan, et al, Ph ys. Rev. Lett. 100 (2008) 047206 \n[4] T. Dietl, Nat. Mater. 5 (2006) 673 \n[5] K.A. Griffin, et al, Phys. Rev. Lett. 94 (2005) 157204 \n[6] B.K. Roberts, et al, Appl. Phys. Lett. 92 (2008) 162511 \n[7] T. Dietl, J. Appl. Phys. 103 (2008) 063918 \n[8] X.H. Xu et al, J. Appl. Phys. 101 (2007) 07D111 \n[9] C.B. Fitzgerald et al, Appl. Surf. Sci. 247 (2005) 493 \n[10] T. Dietl, Semicond. Sci. Technol. 17 (2002) 377 \n[11] T.C. Kaspar et al, Phys. Rev. Lett. 95 (2005) 217203 \n[12] T. Fukumura, et al , New J. Phys. 10 (2008) 055018 \n[13] K.R. Kittilstved, et al, Nat. Mater. 5 (2006) 291 \n[14] K. Kikoin and V. Fleurov, Phys. Rev B 74 (2006) 174407 \n[15] H. Weng, et al, Phys. Rev. B 69 (2004) 125219 \n[16] V.I. Anisimov, et al, J. Phys.: Cond. Mat. 18 (2006) 1695 \n[17] A.L. Rosa and R. Ahuja, J. Phys.: Cond. Mat. 19 (2007) 386232 \n[18] A. Zunger, in Solid State Physics, eds.D. Turnbull and H. Ehrenreich,  \n       (Academic Press, Orlando, 1986), Vol. 39, p. 276 \n[19] K. Kikoin and V. Fleurov, Trans ition Metal Impurities in Semiconductors,  \n        World Sci. (1994) \n[20] V.I. Sokolov, Sov. Phys. – Solid State 29 (1987) 1061   \n[21] T. Dietl, Semicond. Sci. Technol. 17 (2002) 377 \n[22] K. Mizushima, M. Tanaka, and S.  Iida, J. Phys. Soc. Jpn (1972) 1519 \n[23] K. Kikoin and V. Fleu rov, J. Magn. Magn. Mat. (2007) 2097 \n[24] G. Cohen, V. Fleurov, and K. Ki koin, J. Appl. Phys., 101 (2007) 09H106   \n[25] A. Chattopadhyay, S. Das Sarma, and A.J.Millis, Phys. Rev. Lett. 87 (2001) 227202 \n[26] V.N.Fleurov and K.A.Kikoin, Solid State Commun. 42 (1982) 353  \n[27] V.I. Sokolov and K.A. Kikoin, Sov. Sci. Rev. A 12  (1989) 147  \n Figure captions \n \nFig. 1. Experimental dependence of the room temperature magnetization on the \ncarrier density in (Zn,Co)O [3].  \n \nFig. 2. Upper panel: evolution of ener gy spectrum of oxygen deficient (Ti,Co)O 2 \n(n=7) with changing degree of disorder. From  left to right: insulating phase with \npartially filled V O related band; intermediate phase with filled vacancy band; n-doped \nmetallic phase with partially occupied donor  impurity band; metallic  phase with filled \ndonor band. Lower panel: Change of Curi e temperature from insulating phase to \nintermediate and metallic phases.   \n \nFig. 3. Theoretical dependence of Curie temperature on the filling of defect-related \nband. \n  \nFig. 1  \n \n \n \n \n     \nn−doping degreeCT\n \n \nFig. 2 \n \n  \n \n                      Fig.3 "    },    {        "title": "0810.5215v2.Contrasting_the_magnetic_response_between_magnetic_glass_and_reentrant_spin_glass.pdf",        "content": "arXiv:0810.5215v2  [cond-mat.mtrl-sci]  9 Feb 2009Contrasting the magnetic response between magnetic-glass and\nreentrant spin-glass\nS. B. Roy and M. K. Chattopadhyay\nMagnetic and Superconducting Materials Section,\nRaja Ramanna Centre for Advanced Technology, Indore 452013 , India.\n(Dated: November 3, 2018)\nAbstract\nMagnetic-glass is a recently identified phenomenon in vario us classes of magnetic systems un-\ndergoing a first order magnetic phase transition. We shall hi ghlight here a few experimentally\ndetermined characteristics of magnetic-glass and the rele vant set of experiments, which will enable\nto distinguish a magnetic-glass unequivocally from the wel l known phenomena of spin-glass and\nreentrant spin-glass.\nPACS numbers: 75.30.Kz\n1It has been shown recently that in many magnetic systems a kinetic a rrest of the first\norder ferromagnetic (FM) to antiferromagnetic (AFM) phase tra nsition leads to a non-\nequilibrium magnetic state with a configuration of FM and AFM clusters frozen randomly\nin experimental time scale1,2,3,4,5,6,7. The dynamics of this non-equilibrium magnetic state is\nvery similar to that of a structural glass8, and analogically this new magnetic state is named\nmagnetic-glass2,7,9. The results emerging from disparate classes of magnetic systems start-\ning from alloys and intermetallic compounds1,2,3,6,7,9to manganite systems showing colossal\nmagnetoresistance (CMR)3,4,5suggest that this magnetic-glass phenomenon is independent\nof the underlying microscopic nature of magnetic interactions. Ana logous to the structural\nglasses, the magnetic-glass (MG) canundergo devitrification with t he change intemperature\n(T)10,11.\nCompetition between AFM and FM interactions plays the central role in spin-glass (SG)\nand reentrant spin-glass (RSG)12,13. In SG this competition is so strong that none of the\nlong rangemagnetic orders isestablished, instead it gives rise to a ra ndomspin configuration\nfrozen in time13. In RSG long range magnetic order (FM or AFM) appears in certain T\nregime. However, the competing interactions introduce some frus tration amongst the set of\nspins, which ultimately leads to the partial or total breakdown of th e higher T FM or AFM\nstate to a SG like state at the lowest T12,13. The spin-configuration of this lower T RSG\nstate consists of individual spins (or small spin-clusters) frozen r andomly in the microscopic\nscale with14or without15a trace of long-range FM order along the direction of the applied\nmagnetic field (H).\nThe onset of both of these non-trivial MG and RSG state is accompa nied by distinct H\nand T history dependence of bulk magnetic response i.e. thermomag netic irreversibilities\n(TMI) and metastability, which at first sight can appear to be quite s imilar in nature.\nSuch TMI and metastability are very well studied experimental obse rvables in SG and RSG\nsystems12,13, and they are regularly used for initial identification of SG and RSG be haviour\nin a new magnetic system. The main aim of the present work is to caref ully study and\ncompare the TMI and metastability associated with the MG and RSG be haviour. We shall\nthen highlight the identifiable features in such experimental observ ables, which will enable\nto distinguish a MG unequivocally from RSG.\nFor our comparative study we have chosen a well studied MG system Ce(Fe 0.96Ru0.04)22,16\nand a canonical RSG system Au 82Fe18alloy12,13. The FM-RSG transition in AuFe alloys\n2/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48 /s50/s48/s48/s48/s50/s52/s54/s56/s49/s48/s49/s50/s77/s40/s101/s109/s117/s47/s103/s109/s41\n/s84/s32/s40/s75/s41/s90/s70/s67/s70/s67/s67/s32/s38/s32/s70/s67/s87 /s32\n/s72\n/s77/s101/s97/s115/s117/s114/s101/s61/s32/s53/s48/s48/s32/s79/s101/s65/s117\n/s56/s50/s70/s101\n/s49/s56\n/s48 /s50/s48 /s52/s48 /s54/s48 /s56/s48/s57/s46/s48/s57/s46/s53/s49/s48/s46/s48/s49/s48/s46/s53/s49/s49/s46/s48/s77/s32/s40/s101/s109/s117/s47/s103/s109/s41\n/s84/s32/s40/s75/s41/s72\n/s67/s111/s111/s108/s61/s48/s32/s79/s101/s72\n/s67/s111/s111/s108/s61/s49/s48/s48/s32/s79/s101/s72\n/s67/s111/s111/s108/s61/s51/s48/s48/s32/s79/s101/s72\n/s67/s111/s111/s108/s61/s53/s48/s48/s32/s79/s101/s72\n/s67/s111/s111/s108/s61/s49/s32/s107/s79/s101\n/s72\n/s67/s111/s111/s108/s32/s61/s32/s55/s48/s48/s32/s79/s101\nFIG. 1: (Color online):M vs T plot for Au 82Fe18obtained with ZFC, FCC and FCW protocol with\nH=500 Oe. The inset shows M vs T plot obtained under an experim ental protocol of ’cooling and\nheating in unequal field’ with H Measure=500 Oe. See text for details.\nabove the percolation concentration of 15% Fe has been studied in g reat details through\nboth bulk properties and microscopic measurements17. Various theoretical models have\nbeen proposed to understand these experimental results14,15. In Ce(Fe 0.96Ru0.04)2the low\nT state is AFM in zero and relatively low ( ≤10 kOe) applied H2,16. In the presence of\nan applied field H >10 kOe the first order FM-AFM transition in Ce(Fe 0.96Ru0.04)2gets\nkinetically arrested giving rise to a MG state2. We shall now present below the contrasting\nTMI and metastablities associated with the RSG behaviour in Au 82Fe18, and MG behaviour\nin Ce(Fe 0.96Ru0.04)2.\nThe details of the preparation and characterization of the Ce(Fe 0.96Ru0.04)2and Au 82Fe18\nsamples used here can be found in references16and18respectively. The Au 82Fe18sample,\nhowever, was freshly annealed at 8000C for 6 hours and quenched in liquid nitrogen be-\nfore starting the present experimental cycle. Bulk magnetization measurements were made\nwith a commercial vibrating sample magnetometer (VSM;Quantum Des ign, USA). We use\nthree experimental protocols, zero field cooled (ZFC), field cooled cooling (FCC) and field\ncooled warming (FCW), for magnetization (M) measurements. In th e ZFC mode the sam-\nple is cooled to the lowest T of measurement before the applied H is swit ched on, and\nthe measurement is made while warming up the sample. In the FCC mode the applied\nH is switched on in the T regime above the FM-AFM transition temperat ure in the case\n3/s48 /s50 /s52 /s54 /s56 /s49/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s48/s46/s56/s49/s46/s48/s77 /s32\n/s72/s32/s40/s107/s79/s101/s41/s65/s117\n/s56/s50/s70/s101\n/s49/s56/s48 /s49/s48 /s50/s48 /s51/s48 /s52/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s48/s46/s56/s49/s46/s48/s77 /s32\n/s72/s32/s40/s107/s79/s101/s41/s67/s101/s40/s70/s101\n/s48/s46/s57/s54/s82/s117\n/s48/s46/s48/s52/s41\n/s50\n/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48/s48/s53/s49/s48/s49/s53/s77/s32/s40/s101/s109/s117/s47/s103/s109/s41\n/s84/s32/s40/s75/s41/s40/s98/s41/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48/s48/s49/s48/s50/s48/s51/s48/s52/s48/s53/s48/s77/s32/s40/s101/s109/s117/s47/s103/s109/s41\n/s84/s32/s40/s75/s41/s90/s70/s67/s70/s67/s67/s40/s97/s41\nFIG. 2: M vs T plots for (a) Ce(Fe 0.96Ru0.04)2(b) Au 82Fe18obtained with H= 5 kOe. Insets of Fig.\n2(a) ( 2(b) ) show the difference ∆M between M FCC(T) and M ZFC(T) (normalized with respect\nto MFCC(T)) as a function of H for Ce(Fe 0.96Ru0.04)2(Au82Fe18).\nof Ce(Fe 0.96Ru0.04)2and FM-RSG transition temperature in the case of Au 82Fe18, and the\nmeasurement is made while cooling across the transition temperatur e to the lowest T of\nmeasurement. After completion of measurement in the FCC mode, t he data points are\ntaken again in the presence of same applied H while warming up the samp le. This is called\nFCW mode. A fixed rate of T variation 1K/Min has been used all throug hout the present\nstudy.\nThe main frame of Fig. 1 presents the M versus T plot of Au 82Fe18alloy in H=500\nOe, obtained under the ZFC, FCC and FCW mode. The value of Curie te mperature (T C\n≈155K) estimated from the point of inflection in the M-T curve matche s well with the\nearlier reported value in the literature17. The onset of the FM-RSG transition is marked\nby a small but distinct maximum in the M-T curve at a temperature T M≈50K. Then at a\nfurther lower temperature (T irrv) there is a sharp drop in the ZFC M-T curve accompanied\nby a clear bifurcation of the ZFC and FC M(T) curves. This maximum in M (T) and the\nonset of strong TMI at T irrvare the hallmarks of RSG behaviour12. Both these features\nare explained within a mean field theory of second order phase trans ition14. There is also\nan alternative viewpoint, where the maximum at T Mis envisaged as due to the onset of\nrandom freezing of isolated Fe-clusters in Au 82Fe18, which in turn creates a random internal\n4field acting onthe infinite FM cluster and leading to a complete breakdo wn of the long range\nFM order into a spin-glass state at a lower T15. Note that in the main frame of Fig. 1 the\nM-T curves obtained under the FCC and FCW protocol completely ov erlap, and this is in\nconsonance with both the types of theoretical pictures14,15. With the increase in H, T irrv\ndecreases and the M-T curve with H= 5 kOe (see the mainframe of Fig . 2(b)) resembles\nthat of a standard FM with no trace of FM-RSG transition at least do wn to 2K.\nThe main frame of Fig. 2(a) presents the M versus T plot of Ce(Fe 0.96Ru0.04)2in H=5\nkOe, obtained under the ZFC, FCC and FCW mode. Note that here th e MZFC(T) merges\nwith M FCW(T) at all T of measurement. A sharp rise (fall) in M in ZFC (FCC) path ( see\nFig. 2(a))at temperatures T NW(TNC) around65Kmarks theonset of AFM-FM(FM-AFM)\ntransition while warming (cooling)16. The distinct thermal hysteresis between M FCC(T)and\nMZFC(T)(or M FCW(T)) in the transition region arises due to the first order nature of the\nFM-AFM phase transition in Ce(Fe 0.96Ru0.04)2. The end point of the thermal hysteresis\nwhile cooling (warming) represents the limit of supercooling T* (super heating T**) across\nthe first order phase transition16. Below (above) T* (T**) the system is in the equilibrium\nAFM (FM) state.\nIn the FCC mode above a critical applied H of 10 kOe, the FM-AFM tran sition gets\nkinetically arrested leading to the formation of the MG state2. This behaviour is shown\nin the mainframe of Fig.3 in the M vs T plot of Ce(Fe 0.96Ru0.04)2in a field of 20 kOe.\nThe conversion to low T AFM state is not completed in the FCC mode. Wh ile warming\nup part devitrification of the MG state (to equilibrium AFM state) occ urs and the system\neventually reaches back to the higher T FM state. In contrast, in t he ZFC mode the applied\nH is switched on at the lowest T of measurement, and since in H ≤10 kOe there is no\nformation of MG, the equilibrium AFM state can be reached and subse quently transformed\nwith the increase in T to the FM state. All these effects give rise to int eresting TMI where\nMFCC(T)∝negationslash= MFCW(T) (and M ZFC(T)) over a large T regime (see mainframe of Fig. 3). This\nonset of the MG state in an applied H, can be compared with the recen t observation of the\nformation of glassy sate in liquid Ge under external pressure19.\nInstriking contrast totheTMIintheRSGstateofAu 82Fe18, theTMI associatedwiththe\nMGbehaviour inCe(Fe 0.96Ru0.04)2appearsonlyaboveacertaincriticalH,anditsmagnitude\nincreases with H. To highlight this difference in TMI we plot in the inset of Fig.2(a) and\n2(b) ∆M = (M FCC(T)- M ZFC(T))/MFCC(T) measured at 5 K, as a function of applied H\n5/s48 /s50/s48 /s52/s48 /s54/s48 /s56/s48 /s49/s48/s48 /s49/s50/s48 /s49/s52/s48 /s49/s54/s48 /s49/s56/s48/s48/s49/s48/s50/s48/s51/s48/s52/s48/s53/s48/s54/s48/s77/s40/s101/s109/s117/s47/s103/s109/s41\n/s84/s40/s75/s41/s90/s70/s67/s70/s67/s67\n/s70/s67/s87 /s72\n/s77/s101/s97/s115/s117/s114/s101/s32/s61/s32/s50/s48/s32/s107/s79/s101 /s67/s101/s40/s70/s101\n/s48/s46/s57/s54/s82/s117\n/s48/s46/s48/s52/s41\n/s50\n/s48 /s50/s48 /s52/s48 /s54/s48 /s56/s48 /s49/s48/s48/s49/s48/s50/s48/s51/s48/s52/s48/s53/s48/s77/s40/s101/s109/s117/s47/s103/s109/s41\n/s84/s32/s40/s75/s41/s72\n/s67/s111/s111/s108/s32/s61/s32/s49/s55/s32/s107/s79/s101/s72\n/s67/s111/s111/s108/s32/s61/s32/s49/s57/s32/s107/s79/s101\n/s72\n/s67/s111/s111/s108/s32/s61/s32/s48/s32/s107/s79/s101/s72\n/s67/s111/s111/s108/s32/s61/s32/s50/s48/s32/s107/s79/s101/s72\n/s67/s111/s111/s108/s32/s61/s32/s50/s53/s32/s107/s79/s101/s72\n/s67/s111/s111/s108/s32/s61/s32/s50/s56/s32/s107/s79/s101\nFIG. 3: (Color online):M vs T plot for Ce(Fe 0.96Ru0.04)2obtained with ZFC, FCC and FCW\nprotocol with H=20 kOe. The inset shows M vs T plot obtained un der an experimenatl protocol\nof ’CHUF’ with H Measure=20 kOe. See text for details.\nboth for Ce(Fe 0.96Ru0.04)2and Au 82Fe18. In Au 82Fe18∆M falls to zero rapidly as H increase\nto 5 kOe, while in Ce(Fe 0.96Ru0.04)2∆M acquires non-zero value only above H=10 kOe, and\nincreases thereafter with the further increase in H.\nThe quenched disorder in the concerned magnetic systems influenc es the FM-AFM first\norder transition process, andintroduces a landscape of transitio n temperature T N20. In such\nsystems the H-T phase diagram consists of the bands of transition temperature (T N), super-\ncooling and superheating limit (T* and T**) and a kinetic arrest tempe rature band (T K)\nbelow which the system enters a MG state1,3,10,21. The correlation between the characteristic\ntemperatures T N, T* (T**) and T Kand its experimental consequences have been studied\nwith a newly introduced experimental protocol, where the system is cooled across the tran-\nsition temperature in certain applied H Cooland the magnetization studies are made while\nwarming and after changing this H Coolisothermally to a different H Measure( higher or lower\nthan H Cool) at the lowest T of measurement22. This experimental protocol is in contrast\nwith the standard field cooling protocols FCC and FCW, where the H Cooland the H measure\nwhile warming is the same. This technique of ’cooling and heating in unequ al field (CHUF)’\nhas been used to investigate the MG phenomenon in various CMR-man ganite systems22. It\nhas been shown clearly that in a kinetically arrested FM-AFM transitio n, while warming\nwith H Measure>HCool(HMeasure<HCool) under the CHUF protocol, one observes only one\n6sharp structure (two sharp structures) in M(T)22. We use this key result here to discern\nbetween a MG and RSG. The inset of Fig. 3 shows the results of M(T) m easurements in\nCe(Fe 0.96Ru0.04)2obtained under CHUF protocol with H Measure=20 kOe. With H Measure>\nHCool, there is only one sharp rise in M(T) leading to the FM state. On the ot her hand,\nwhen H Measure<HCoolthe M(T) drops sharply and flattens before rising sharply again to\nreach the FM state. With a higher value of H Coolthe state prepared at the lowest T has a\nlarge fraction of the FM component in the MG state, and in the FCW mo de M(T) drops\nsharply with rising T due to the devitrification of this non-equilibrium FM component. For\na more detailed explanation of the origin of such distinct characteris tic features associated\nwith the MG phenomenon, the reader is referred to the Ref.22.The c hange in sign of the\ninequality between H Measureand H Cooldoes not lead to such distinctive characteristic fea-\ntures in the RSG system Au 82Fe18, and this is shown experimentally in the M(T) study with\nHMeasure=500 Oe (see the inset of Fig.1). The algebraic value of TMI around T irrvchanges\nmonotonically with the change in sign of the inequality.\nWe shall now discuss the characteristic metastable behaviour asso ciated with the RSG\nand MG state. The metastable response of SG and RSG systems con tinues to remain a\nsubject of active interest23. The ZFC state of these systems show strong relaxation in\nmagnetization, while the field cooled state does not12,13. These behaviors are exemplified in\nFig. 4 (a), which shows M versus time (t) plots for Au 82Fe18at T=14K and H=100 Oe in\nthe ZFC and FCC state. The M(t) data in the ZFC state can be filled wit h the equation\nM(t)= -1 +2tγ,whereγindicates the extent of relaxation. Higher value of γmeans a greater\ndegree of relaxation in the same t interval. This equation has earlier b een shown to apply to\nthe relaxation of ferromagnetic dots which interact through long r ange dipolar interaction24.\nThe obtained value of exponent γin the present case is 0.004. Since the ZFC state in MG\nis an equilibrium state, no relaxation of M is observed there. On the ot her hand, entrance\nin to the MG state along the FCC path introduces distinct glass-like re laxation and the\ndivergence of the relaxation time with lowering in T2,7,9. To contrast such metastabilty\nwith that observed in the RSG state, we present in Fig. 4(b) M vs time plot obtained for\nCe(Fe 0.96Ru0.04)2at T=18K and H=20 kOe in the ZFC state and FCC state. The M(t)\ndata in the FCC state can be filled with the Kohlrausch-Williams-Watt (K WW) stretched\nexponential function M(t) ∝exp[-(t/τ)β, whereτis the charactteristic relaxation time and\nβis a shape parameter2. The obtained value of exponent βhere is 0.65.\n7/s48 /s49/s48/s48/s48 /s50/s48/s48/s48 /s51/s48/s48/s48 /s52/s48/s48/s48 /s53/s48/s48/s48 /s54/s48/s48/s48/s49/s46/s48/s48/s49/s46/s48/s49/s49/s46/s48/s50/s49/s46/s48/s51/s49/s46/s48/s52/s49/s46/s48/s53/s77/s32/s40/s78/s111/s114/s109/s97/s108/s105/s122/s101/s100/s41\n/s116/s32/s40/s115/s101/s99/s41/s90/s70/s67\n/s70/s67/s67/s65/s117\n/s56/s50/s70/s101\n/s49/s56/s40/s97/s41\n/s48 /s49/s48/s48/s48 /s50/s48/s48/s48 /s51/s48/s48/s48 /s52/s48/s48/s48/s48/s46/s56/s53/s48/s46/s57/s48/s48/s46/s57/s53/s49/s46/s48/s48/s77/s32/s40/s78/s111/s114/s109/s97/s108/s105/s122/s101/s100/s41\n/s116/s32/s40/s115/s101/s99/s41/s90/s70/s67\n/s70/s67/s67/s67/s101 /s40/s70/s101\n/s48/s46/s57/s54/s82/s117\n/s48/s46/s48/s52/s41\n/s50/s40/s98/s41\nFIG. 4: (Color online):M vs time plots for (a)Au 82Fe18at T=14K (b)Ce(Fe 0.96Ru0.04)2at T=18K\nobtained under ZFC and FCC protocols. M is normalized with re spect to the initial M 0value\nobtained after 1 second of stabilizing at the respective T of measurement, which is reached with a\ncooling rate of 1K/min in the ’temperature no-overshoot’ mo de of the instrument. The relaxation\ndata for Au 82Fe18(Ce(Fe 0.96Ru0.04)2) are fitted with the eequation M(t)= -1 +2tγ(stretched\nexponential function M(t) ∝exp[-(t/τ)β)\nThe metastable nature of the FCC state in systems showing MG beha viour can be sup-\nported further by showing that this state is susceptible to any ene rgy fluctuation introduced\nby a T or H cycling2,7,9. Similar extensive T cycling in the FCC state of the present Au 82Fe18\nsample failed to reveal any such signature of metastablity25.\nSummarizing the above experimental results, we identify four distin ct experimental fea-\nturesinbulkmagnetizationmeasurements, whichcanbeusedtodist inguishamagnetic-glass\nfrom a reentrant spin-glass:\n(i) MG arises out of the kinetic arrest of a first order FM-AFM phase transition. This\nfirst order transition will give rise to a distinct thermal hystersis be tween the FCC and FCW\nmagnetization. No such thermal hysteresis is expected in the case of FM (or AFM)-RSG\ntransition, since this is considered to be a second order phase tran sition14or a gradual phase\ntransformation15.\n8(ii)The TMI decreases with the increase in applied H in RSG systems. Th is is just the\nopposite in MG, where TMI appears only above an critical applied H (th e value of which\nwill depend on the system under consideration) and increases with t he increase in H.\n(iii) A newly introduced experimental protocol ’cooling and heating in u nequal field\n(CHUF)’ reveals distinct features in the T dependence of magnetiz ation in MG, which\ndepend on the sign of inequality between the fields applied during coolin g and heating. No\nsuch features are expected for a RSG system.\n(iv) ZFC state of RSG shows distinct relaxation in magnetization, while the FC state\ndoes not. The behaviour observed in the MG systems is just the opp osite.\nIn conclusion the newly observed magnetic-glass phenomenon in diffe rent magnetic sys-\ntems is distinctly different from the well known spin-glass and re-ent rant spin-glass phenom-\nena. While the existence of a new magnetic-glass systems will finally be established through\nmicroscopic studies like magnetic imaging, the experimental criteria d escribed in this work\ncan definitely be used for regular identification of a magnetic-glass.\nThe authors thank P. Chaddah for useful discussion.\n1M. A. Manekar, S. Chaudhary, M. K. Chattopadhyay, K. J. Singh , S. B. Roy and P. Chaddah,\nPhys, Rev. B64104416 (2001).\n2M. K. Chattopadhyay, S. B. Roy and P. Chaddah Phys. Rev. B72180401R (2005).\n3K. Kumar A. K. Pramanik, A. Banerjee, P. Chaddah, S. B. Roy, S. Park, C. L. Zhang, and\nS.-W. Cheong, Phys.Rev. B 73,184435 (2006).\n4W. Wu, C. Israel, N. Hur, P. Soonyong, S.-W. Cheong, and A. De L ozane, Nat. Mater. 5, 881\n(2006).\n5A. Banerjee, K. Mukherjee, Kranti Kumar, and P. Chaddah, J. P hys. :Condens. Mater. 18, L605\n(2006); A. Banerjee, K. Mukherjee, Kranti Kumar, and P. Chad dah,,Phys. Rev. B74, 224445\n(2006); Z W Ouyang,H. Nojiri and S. Yoshii, Phys. Rev. B78104404 (2008)\n6K. Sengupta and E. V. Sampathkumaran, Phys. Rev. B73, 020406R (2006); P. Kushwaha, R.\nRawat and P. Chaddah, J. Phys.:Condens. Matr. 20, 022204 (2008).\n7S. B. Roy, M. K. Chattopadhyay, P. Chaddah,J. D. Moore, G. K. P erkins, L. F. Cohen, K. A.\nGschneidner, Jr. and V. K. Pecharsky, Phys. Rev. B74, 012403 (2006).\n98P G Debenedetti and F H Stillinger, Natur 410, 259 (2001).\n9V K Sharma, M. K. Chattopadhyay and S B Roy, Phys. Rev. B76, 140401(2007).\n10S. B. Roy, M. K. Chattopadhyay, A. Banerjee, P. Chaddah, J. D. Moore, G. K. Perkins, L.\nF. Cohen, K. A. Gschneidner Jr., and V. K. Pecharsky, Phys Rev .B75, 184410 (2007); M.\nK. Chattopadhyay, S. B. Roy, K. Morrison, J. D.Moore, G. K. Pe rkins, L. F. Cohen, K. A.\nGschneidner Jr., and V.K. Pecharsky, Euro.Phys. Lett. 8357006 (2008).\n11P. Chaddah, Kranti Kumar and A Banerjee, Phys. Rev. B67, 100402(R) (2008).\n12K. H. Binder and A. P. Young, Rev. Mod. Phys. 58801 (1986).\n13J A Mydosh, Spin Glasses (Taylor and Francis, 1992).\n14M. Gabay and G. Toulouse, Phys. Rev. Lett. 47, 201 (1981).\n15S. Nidera and F. Matsubara, 2007, Phys. Rev. B75144413 (2007).\n16S B Roy, G. K. Perkins, M. K. Chattopadhyay, A. K. Nigam, K. J. S . Sokhey, P. Chaddah, A.\nD. Caplin and L. F. Cohen, Phys. Rev. Lett. 92, 147203 (2004).\n17B. R. Coles, B. V. B. Sarkissian and R. H. Taylor, Philos. Mag. B37, 489 (1978); B. V. B.\nSarkissian, J. Phys. F 11, 2191 (1981);I. A. Campbell, D. Arvanitis and A. Fert, Phys. Rev.\nLett.5157 (1983).\n18A. K. Gangopadhyay, S. B. Roy and A. K. Majumdar, Phys. Rev. B33, 5010 (1986).\n19M H Bhat,V Molinero, E Soignard E, V C Solomon, S Sastry and J L Y arger, Nature 448,787\n(2007).\n20Y Imry and M Wortis, Phys. Rev. B19, 3580 (1979).\n21P Chaddah, A. Banerjee and S. B. Roy Cond-Mat arXiv:0601095 ( 2006).\n22A. Banerjee, K. Kumar and P. Chaddah, J. Phys.: Condens. Matt er21026002(2009);S Dash,\nA. Banerjee and P. Chaddah, Solid. St. Commun. 148336 (2008)\n23K. Hioki and K. Motoya, J. Phys. Soc. Japan, 74, 1830 (2005) (and references within).\n24L. C. Sampaio,R. Hyndman,F. S. de Menezes, J. P. Jamet, P. Mey er, J. Gierak,C. Chappert,\nV. Mathet and J. Ferre , Phys. Rev. B64, 18440 (2001).\n25S B Roy and M K Chattopadhyay (unpublished results).\n10"    },    {        "title": "0811.3493v2.Grounded_Uniaxial_Material_Slabs_as_Magnetic_Conductors.pdf",        "content": "arXiv:0811.3493v2  [physics.class-ph]  21 Aug 2009Machine Copy for Proofreading, Vol. x, y–z, 2004\nGROUNDED UNIAXIAL MATERIAL SLABS AS\nMAGNETIC CONDUCTORS\nO. Luukkonen, C. R. Simovski, and S. A. Tretyakov\nDepartment of Radio Science and Engineering/SMARAD CoE\nTKK Helsinki University of Technology\nP.O. 3000, FI-02015 TKK, Finland\n(email:olli.luukkonen@tkk.fi,csimovsk@cc.hut.fi,serge i.tretyakov@tkk.fi)\nAbstract —The objective of this paper is all-angle artificial magneti c\nconductor, i.e. artificial magnetic conductor that has stab le magnetic-\nwall effect with respect to the incidence angle. Furthermore, we\nseek for a design that would be easy for manufacturing. In ord er\nto achieve this we use grounded uniaxial material slabs and w e do\nnot constrict ourselves to naturally available materials. Instead, we\nassume that the desired parameters can be synthesized using the\nemerging artificial electromagnetic materials. It is found that it\nis possible to have an all-angle magnetic-wall effect for both TE\nand TM polarization. Especially for the TM fields the structu re\nwould be easily manufacturable. The proposed structure has similar\nappearance as more well-known artificial impedance surface s, but the\ndesignparametersandthephysicalpropertiesbehindthema gneticwall\neffect are novel. The performance of the proposed artificial ma gnetic\nconductorisverifiedwithnumericalsimulations. Thispape rintroduces\na new approach how to obtain a magnetic-wall effect. It is possi ble to\nuse this this approach also together with other ways of obtai ning the\nmagnetic-wall effect for dual-band operation.\n1. INTRODUCTION\nArtificial magnetic conductors (AMC) have been studied wide ly in the\nliterature after the seminal paper of D. Sievenpiper et al. p ublished\nin 1999 [1]. Especially, the use of these surfaces for loweri ng the\nheight of horizontal wire antennas has attracted much atten tion.\nIn [1, 2, 3, 4, 5, 6, 7, 8, 9] artificial magnetic conductors hav e\nbeen realized as a certain resonant structure, not involvin g resonant\nmagnetically or electrically polarizable particles. In th e vicinity of the2 Luukkonen, Simovski, and Tretyakov\nstructure resonance the surface impedance becomes very hig h in the\nabsolutevalue, makingtheuseofthesesurfacesasmagnetic conductors\npossible. Incorrugated surfacesthequarter-wavelength r esonances can\nbe utilized in a similar way (see e.g. [10]). In addition to re sonant\nstructures, also more conventional materials (in the sense of magnetic\nor electric polarizations excited by magnetic or electric s timuli) have\nbeen studied [11, 12, 13, 14]. In these cases the materials ha ve been\nconsidered without paying attention to the possible anisot ropy. In [13]\nit was shown that the radiation properties of a horizontal di pole can be\nimproved by a substrate implemented as a grounded slab with n early\nzero permittivity. Such a substrate operates as a magnetic c onductor\nfor all angles of incidence of TM-polarized electromagneti c waves.\nTheuniaxialsymmetryofthestructureisthemostgeneralal lowed\nsymmetry, if the magnetic-wall effect should be isotropic in t he surface\nplane. Thus, wewill studythemost general approach tothere alization\noftheall-angle magneticwallsusingmaterial layers. Thef ullyisotropic\nlayers are a special case covered by this theory, but we expec t that\nallowing uniaxial anisotropy will make the actual realizat ion much\nsimpler. Indeed, to engineer, for example, passive ε≈0 materials\none needs inclusions which are inherently anisotropic. Nat urally, it is\npossible to manufacture isotropic materials from anisotro pic inclusions\nby grouping and orienting the particles in such a way that an e lectric\nor a magnetic stimuli along all of the orthogonal direction w ill create\nthe same response. This is, however, a troublesome and most l ikely\nimpractical way, if electrically thin realizations are nee ded. The\npossibility to avoid the requirement of full 3D isotropy wou ld greatly\nsimplify the structure and its manufacturing.\nIn this paper we systematically study what uniaxial materia l\nproperty can allow us to realize all-angle magnetic conduct ors. We\nwill not restrict ourselves to the naturally available mate rials but\nassume that the desired parameters can be synthesized using emerging\nmetamaterials (e.g., [15]). In a uniaxial material, the rel ative\npermittivity or permeability have different values along the transversal\nand normal axes (defined with respect to the surface of the mat erial\nslab). Uniaxial materials provide hence an extra degree of f reedom\ncompared to the conventional materials. As we will see, the u se of\nartificial materials with extreme parameters offers a possibi lity for\ndesign of structures with superior performance, not achiev able with\nconventional materials.\nIn the following section II we derive the needed analytical m odels\nfor the analysis of the grounded uniaxial material slabs. In sections III\nand IV we use these models to study what kind of material param eter\nvalues are needed for all-angle magnetic conductors for the TM andGrounded Uniaxial Material Slabs as Magnetic Conductors 3\nFigure 1. An illustrative picture of the grounded uniaxial material\nslab. Index tcorresponds to the direction tangential to the interfaces,\nand index nmarks the components along the unit vector n.\nTE fields, respectively. The study reveals that for the TM fiel ds it is\nsufficient to have just the normal component of the permittivi ty to be\nclose to zero. This can be done by using wire medium at its plas ma\nfrequency and suppressing its spatial dispersion. In secti on V we will\ndiscuss the issue of suppression of the spatial dispersion i n the wire\nmedium. An example of the structure is given in section VI in w hich\nwe also verify our result by simulations.\n2. SURFACE IMPEDANCE OF A GROUNDED\nUNIAXIAL MATERIAL SLAB\nIn Fig. 1 a schematic picture of a grounded uniaxial material slab\nis shown. The properties of the material slab are described b y\nthe effective transverse and normal permittivities ( εtandεn) and\npermeabilities ( µtandµn), respectively. It is convenient to model\nthe structure shown in Fig. 1 with a surface impedance at the t op\ninterface of the structure. This surface impedance can be ca lculated\nthrough the transmission-line model illustrated by Fig. 2 [ 9]. For this\nwe need both the wave impedance and the normal component βof the\nwave number in the uniaxial material of the substrate.\nThe wave impedances in the uniaxial material read for TE- and\nTM-polarized incident plane waves, respectively, as [16]:\nZTE=ωµt\nβTE, (1)4 Luukkonen, Simovski, and Tretyakov\nZTM=βTM\nωεt, (2)\nHere, the normal components of the wave vectors in the uniaxi al slab\nread [16]:\nβ2\nTE=ω2εtµt−k2\ntµt\nµn, (3)\nβ2\nTM=ω2εtµt−k2\ntεt\nεn, (4)\nwherektis the transverse wave number. Using the transmission-line\nmodel in Fig. 2 and 1–4, we can write the surface impedances fo r both\npolarizations as (see also [17]):\nZTE\ns=jωµt\nβTEtan(βTEh), (5)\nZTM\ns=jβTM\nωεttan(βTMh). (6)\nIn order to realize a magnetic conductor, the absolute value s of these\nexpressions need to be maximized.\nLet us next look more closely into the cases of TM and TE\npolarizations separately. Our goal for both polarizations is to realize a\nmagnetic conductor whose performance would not be affected by the\nincident angle nor by the finite electrical thickness of the s lab.\n3. MAGNETIC CONDUCTORS FOR TM\nPOLARIZATION\nThemain problemsfor artificial magnetic conductors arethe frequency\nand angular dependencies of the magnetic wall effect. A ground ed\ndielectric slab with the quarter-wavelength electrical th ickness serves\nas a good example here. The magnetic wall effect due to the λ/4-\nthickness of the slab is clearly highly dependent on the freq uency. In\nthe case of low relative permittivity of the substrate the effe ct is also\nhighly dependent on the incidence angle. The magnetic wall e ffect\nmoves to higherfrequencies astheincidenceangle grows. It is desirable\nto decrease both frequency and angular dependencies of the m agnetic\nwall effect.\nWe first study the properties of uniaxial material slabs for w hich\nthe transverse and normal components of the relative permea bility are\nboth positive and the components of the permittivity are arb itrary\nchosen. We will then study the inverse case when the transver se\ncomponent of the permeability is arbitrary chosen. For simp licity of\nthe analysis we neglect the losses in the structure.Grounded Uniaxial Material Slabs as Magnetic Conductors 5\nFigure 2. Transmission-linemodelforthegroundeduniaxial materia l\nslab.\nLet us first consider reducing the periodical dependency of t he\nsurface impedance on the frequency by designing an imaginar yβTM.\nThis would mean that the waves propagating along the normal t o the\nsurface in the uniaxial material slab would be evanescent. I n the\ncase when εn→(+0) we approach the singularity of 4 and we can\napproximately write the normal component of the wave vector in the\nuniaxial material slab for obliquely incident plane waves a s\nβTM≈jkt/radicalBigg\nεt\n|εn|. (7)\nFor the normal incidence ( kt= 0) the incident plane wave has no\nelectric field component along the normal and therefore the n ormal\ncomponent of the permittivity has no effect. We can now write th e\nsurface impedance of the grounded uniaxial slab for oblique incidence\nusing 6 and 7 as:\nZTM\ns=−jkt\nω/radicalbig\nεt|εn|tanh/parenleftBigg\nkt/radicalBigg\nεt\n|εn|h/parenrightBigg\n. (8)\nFor TM polarization inductive surfaces support surface wav es, because\nthe surface impedance for the evanescent TM-polarized plan e wave in\nfree space is −jη0γn\nk0, whereγn=/radicalBig\nk2\nt−k2\n0andη0is the free-space\nwave impedance. We see from 8 that in this case the surface doe s not\nsupport TM-polarized surface waves, and its surface impeda nce is not\na periodic function of the frequency. More importantly, we s ee that\nasεnapproaches zero, the surface impedance for the TM polarizat ion\nZTM\nstends to ( −j∞).\nFor the case when εn→(−0) we can write the surface impedance6 Luukkonen, Simovski, and Tretyakov\n6 as:\nZTM\ns=jkt\nω/radicalbig\nεt|εn|tan/parenleftBigg\nkt/radicalBigg\nεt\n|εn|h/parenrightBigg\n. (9)\nWe see that when εn→(−0) the waves do not become evanescent\nin the uniaxial material slab and the surface impedance 9 bec omes a\nquickly oscillating function of ω. The surface operates as a magnetic\nconductor either for a narrow frequency band or for a limited range of\nincidenceangles. However, wecan overcome thisdrawback by choosing\nthe tangential component of the permittivity to be negative instead\nofε0and make the fields propagating along the normal of the surfac e\nevanescent in the material slab. For negative values of the p ermittivity\nand in cases when |εt| ≫ |εn|, we can replace the tangent with the\nhyperbolic tangent and εtwith its absolute value in 9.\nLet us next look at the case of electrically thin material sla bs.\nIn this case we can replace the tangent function by its argume nt.\nChoosing |εt| →0 andεn=ε0we make the uniaxial material slab\nelectrically thin. In this case a near-zero value of the tran sversal\npermittivity is not needed for realization of a high surface impedance:\nZTM\ns≈jωµth−jk2\nt\nωεnh. (10)\nInstead a high- µtor a low- εnmaterial is needed. In terms of\nsurface wave suppression, the latter choice outperforms th e former.\nUnfortunately, the latter choice will lead to a situation wh ere the\nperformance of the magnetic conductor deteriorates in the v icinity of\nthe incidence angle defined by\nsin2(θ1) =µtεnc2\n0, (11)\nwhereθ1is the angle of incidence and c0is the speed of light in free\nspace. In the case µt→ ∞the approximation of the electrically\nthin substrate results in the following conditions for the t ransverse\ncomponents of the permittivity:\nεt\nε0≪µ0\nµt, ε t≪εn. (12)\nThese conditions are difficult to satisfy because of the compl exity\nof the needed uniaxial grounded material slab structure. Fi rst, we\nwould need to have metallic wires (for near-zero values of th e relative\npermittivity) in all three directions. Secondly, we would n eed to add\nsplit-ring resonators or similar inclusions (for high valu es of relative\npermeability). We can conclude that the regime of electrica lly thinGrounded Uniaxial Material Slabs as Magnetic Conductors 7\nsubstrate leads to the situation where either the performan ce of the\nmagnetic conductor deteriorates at a certain incidence ang le or the\nrealization of the magnetic conductor is difficult.\nIn the case of a very high µt(the normal component of µhas no\neffect on the incident wave in the TM case), most of the incident wave\npower is refracted along the normal. Then the response of the slab\nbecomes weakly dependent on the incidence angle, since\nZTM\ns≈j/radicalbiggµt\nεttan(ω√εtµth). (13)\nIn addition to this, the slab becomes electrically thick whi ch results in\nquickly oscillating (with respect to the frequency) surfac e impedance.\nFrom the discussion above we see that it is possible to realiz e\nartificial magnetic conductors for TM polarization by havin g one of\nthe components of εclose to zero. εn→(+0) is a suitable choice if\nwe tolerate the loss of the magnetic wall effect at the angle θ1= 0.\nRealization of the high surface impedance over a wide freque ncy band\nor over a wide range of incidence angles otherwise is not poss ible\nwithout specially adjusting the value of one of the three rem aining\nmaterial parameters.\n4. MAGNETIC CONDUCTORS FOR TE\nPOLARIZATION\nFor theTE polarization the case of the groundeduniaxial mat erial slab\nbecomes different than for its counterpart TM polarization di scussed\nin the previous section. The surface impedance in 5 is more de pendent\non the permeability rather than permittivity. In order to re alize\na magnetic conductor from an isotropic material, the value o f the\npermittivity needs to be minimized and the value of the perme ability\nmaximized (see also 5 and 6). For this reason the singularity of 3 does\nnot play so significant role as it does for the TM polarization . Instead,\nwe concentrate on the regime µ≫1.\nIn order to minimize the angular dependency of the magnetic\nconductors, we should have µn≫1. Then we have from 3 and 1:\nZTE\ns≈j/radicalbiggµt\nεttan(ω√εtµth). (14)\nFor a high surface impedance we still need to maximize µt, which\nunfortunately leads to quick oscillations of ZTE\nsalong the frequency\naxis. We can overcome this drawback by decreasing the transv erse\npermittivity and thus complicating the layer structure.8 Luukkonen, Simovski, and Tretyakov\n(a) (b)\nFigure 3. (a) A side and (b) a top view of the spatially dispersive\nwire medium slab. The metallic vias having a diameter 2 r0are\nseparated from each other by a period a. The vias are embedded in a\ndielectric substrate. The height of the structure is hand the substrate\npermittivity is εh.\nWe can also decrease the angular dependency of the surface\nimpedance by having the transverse permittivity approach z ero:εt→\n0. In this case the surface impedance of TE polarized inciden t waves\nreads\nZTE\ns≈jω√µtµn\nkttanh/parenleftbigg\nkt/radicalbiggµt\nµnh/parenrightbigg\n. (15)\nObviously we still need to maximize the transverse permeabi lity in\norder to realize a magnetic conductor.\nThe magnetic wall effect realized by using grounded uniaxial\nmaterial slabs for the TE polarization does not seem to offer su ch\nadvantages as for the TM polarization. For the TM polarizati on it\nis sufficient to engineer only the normal component of the effect ive\npermittivity correctly in order to realize a magnetic condu ctor. The\ncase of the TE polarization is not so simple; for the TE polari zation\nat least two effective material parameters need to be engineer ed in\nthe transverse direction. Practically this means orientin g two different\ntype of particles (magnetic and electric) in two orthogonal directions.\n5. PRACTICALLY REALIZABLE UNIAXIAL\nMAGNETIC CONDUCTORS\nThe wire medium serves as a good example of a uniaxial\nelectromagnetic crystalthatcanpossessnearzerovalueso ftheeffective\npermittivity. Based on the discussion in the previous secti ons the most\npromising case is to use this feature for realizing magnetic conductorsGrounded Uniaxial Material Slabs as Magnetic Conductors 9\nfor TMpolarization. In this case the wires shouldbeoriente d normally\nto the surface. For TE-polarized incident fields these wires have no\neffect. This type of grounded wire medium slab structures, or ” Fakir’s\nbed of nails”, have been studied earlier in [18, 19] (see Fig. 3). In [18]\nthe wire medium slab comprised densely packed wires, and the height\nof the slab was large compared to the period of the wire medium . The\nsurface impedance for such a structure reads:\nZTM\ns=j/radicalbiggµt\nεttan(ω√εtµth), (16)\nas was shown also in [19]. For this type of structures we see th at\nthe near-zero value of the normal component of the permittiv ity\ntensor has no effect on the surface impedance, but the TEM\nmodes of the wire medium become dominant (see, e.g. [16],\np. 231). Furthermore, structures with densely packed metal lic vias are\nexpensive to manufacture. Instead, thin slabs with rather s parse wires\nare preferred in practical applications. In this case also t he TM modes\nexcited in the wire medium slab become significant. In the fol lowing,\nwe will discuss the structure needed for realizing the wide- angle and\nwide-band magnetic conductors for the TM polarization. How ever,\nin practical applications the bandwidth of the magnetic con ductor is\nreduced by the limited frequency band for which the wire medi um\nposses near-zero values for the effective permittivity.\nThe wire medium is known to be strongly spatially dispersive\nmaterial whose effective permittivity can be described for ou r case\nas [20, 21, 22]:\nεn=ε0εh/parenleftBigg\n1−k2\np\nk2−β2/parenrightBigg\n, (17)\nwhereεhis the relative permittivity of the host medium, kpis the\nplasma wave number, k=k0√εhis the wave number in the host\nmedium, and βis thez-component of the wave vector. This non-\nlocal homogenization model predicts that in the case of TM-p olarized\nincident waves two modes can be excited in the wire medium wit h\ndifferent values for βz. In this case the definition of the εnfor the wire\nmedium slab becomes non-explicit and the reflection propert ies of such\nslabs need to be solved by calculating the fields of both modes in the\nslab[19]. Inadditiontothis, thestudyintheprevioussect ionsbecomes\nnot applicable in the spatially dispersive case. For these r easons we\nneed to suppress the spatial dispersion in the wire medium sl ab.\nSuppression of the spatial dispersion in wire medium has bee n\nstudied recently in [23, 25, 24, 26]. In [23] the spatial disp ersion\nwas suppressed by connecting the parallel wires capacitive ly to each10 Luukkonen, Simovski, and Tretyakov\n(a) (b)\nFigure 4. (a) A side and (b) a top view of the non-spatially\ndispersive wire medium slab. The metallic vias having a diam eter\n2r0are separated from each other by a period aand each via is\ngalvanically connected to a metallic patch. The spacing bet ween the\nadjacent patchesis g. Theheightof thestructureis handthesubstrate\npermittivity is εh.\nother. This is similar to the situation in [25, 24, 26] where i t was first\nnoticed that the spatial dispersion in the wire medium slab c overed\nwith metallic patches is suppressed when choosing the heigh t and the\nlattice constant of the wire medium slab properly. In these c ases the\nlocal (non-spatially dispersive) model is valid for the effec tive value of\nthe normal component of the permittivity, and it reads:\nεn=ε0εh/parenleftBigg\n1−k2\np\nk2/parenrightBigg\n. (18)\nThe plasma wave number kpcan be estimated as [21]:\nk2\np=2π\na2/parenleftBig\nln/parenleftBig\na\n2πr0/parenrightBig\n+0.5275/parenrightBig, (19)\nwhereais the lattice constant of the wire medium and r0is the radius\nof the vias (see Fig. 4).\nThe explanation of the suppression of spatial dispersion in the\nwire medium is simple. The presence of patches makes the curr ents\ninduced in the wires by the incident TM-polarized waves prac tically\nuniformovertheheight h. Itissoif h < a, sinceinthiscasetheinduced\ncharges arepractically concentrated atthepatches’ edges . Theabsence\nof charge accumulation on the wires ensures the practical un iformity\nof currents. Though mathematically the currents along the w ires can\nstill be presented as a sum of the TEM and TM modes, the smallne ssGrounded Uniaxial Material Slabs as Magnetic Conductors 11\n8101214161820−1−0.500.511.52\nFrequency, [GHz]εn/ε0\nFigure 5. The normal component of the relative permittivity of the\nwire medium slab calculated using 18.\nof the current variation across the wire medium slab means th at the\npropagation effect of these modes over the height his negligible. Since\nthe waves in thewiremedium slab can propagate only in the hor izontal\nplane, one can consider the wire medium slab as a uniaxial die lectric\nwith negative εnbelow the plasma frequency.\n6. AN EXAMPLE AND NUMERICAL VALIDATION\nHere we concentrate on validating our results for the TM pola rization\nusing an example that follows the design of [25, 24, 26]. In ou r\nexample shown in Fig. 4 we have included metallic patches on t op of\nthe wire medium slab so that each patch is galvanically conne cted to\njust one via. The structure has similar appearance to the mus hroom\nstructure. However, here we do not utilize the structure res onance.\nInstead, we utilize the near-zero value of the normal compon ent of the\npermittivity of the wire medium slab in order to create a magn etic\nconductor. To demonstrate that the magnetic conductor effect of the\nsurface relates to the near-zero value of the normal compone nt of the\npermittivity we have used qualitatively the design equatio ns of [8].\nThese equations allow us to design the resonance frequency o f the\nstructure (the mushroom type of high-impedance surfaces) f ar away\nfrom the frequency region where we would have εn→0.\nWehavechosentheparametersofthenon-spatiallydispersi vewire\nmedium slab to be the following: a= 4mm, g= 0.5mm,h= 0.5mm,\nεh= 2, and r0= 0.05mm. Fortheseparametersthenormalcomponent12 Luukkonen, Simovski, and Tretyakov\n10 15 20 25 30 35−150−100−50050100150\nFrequency [GHz]Reflection phase [deg]\n(a)\n11 12 13 14−150−100−50050100150\nFrequency, [GHz]Reflection phase, [deg]Analytical, θ=10°\nHFSS, θ=10°\nAnalytical, θ=30°\nHFSS, θ=30°\nAnalytical, θ=50°\nHFSS, θ=50°\nFigure 6. (a) Thesimulated reflection phasefor the normal incidence.\n(b)Thereflectionphaseforobliqueincidencesof10, 30, and 50degrees.\nThe analytical results are calculated using 2. For the norma l incidence\nthe vias do not have any effect on the plane wave response of the\nstructure.\nof the effective permittivity tends to zero approximately at 1 2.2GHz\nand the mushroom structure resonance is approximately at 23 GHz as\nshown in Figs. 5 and 6(a), respectively. For the normal incid ence the\nvias donot have any effect on the plane-wave responseof the str ucture,\nand the resonance shown in Fig. 6(a) is solely due to the other\nstructural properties of the wire medium slab, that is, the e ffective\ncapacitance between the adjacent patches and the inductive responseGrounded Uniaxial Material Slabs as Magnetic Conductors 13\n(a)\n (b)\n (c)\nFigure 7. The magnitude of the normal component of the electric\nfield magnitude, En, over one unit cell at 12GHz for the incidence\nangles of (a) 10, (b) 30, and (c) 50 degrees. The magnitudes ha ve been\nplotted on a surface 0.25mm above the ground plane.\n(a)\n (b)\n (c)\nFigure 8. The magnitude of the tangential component of the electric\nfield magnitude, Et, over one unit cell at 12GHz for the incidence\nangles of (a) 10, (b) 30, and (c) 50 degrees. The magnitudes ha ve been\nplotted on a surface 0.25mm above the ground plane.\nof the grounded dielectric slab. The results for the reflecti on phase\nhave been verified using Ansoft’s High Frequency Structure S imulator\n(HFSS) [27]. We can therefore explicitly distinguish the ma gnetic\nconductor effect dueto εn→0fromtheknownparallel circuit response\nof a high-impedance surface [1, 2, 8].\nFor oblique incidence the wiremedium is excited by incident plane\nwaves. The main result which we obtain using this descriptio n of the\nmetasurface is the dramatic reduction of the resonance freq uency for\noblique incidence starting from very small angles. In Fig. 6 (b) the\nreflection phase for the incidence angles of 10, 30, and 50 deg rees\ncalculated using2isshown. Weseeclearlythatthesurfaceb ehavesasa\nmagnetic conductor (reflection phase equals to zero) at appr oximately\n12.2GHz for all of the incidence angles because εn→0 as predicted\nby 8. The HFSS simulations agree well with our analytical res ults.\nHowever, for the incidence angle of 10 degrees the difference b etween\nthe analytical and the simulated results is somewhat larger than for\nmore oblique angles. Furthermore, Eq. 18 implies that the el ectric14 Luukkonen, Simovski, and Tretyakov\nfields inside the wire medium slab are mainly oriented along t he\nmetallic vias. Indeed, thiscanbeconfirmedbylookingatthe simulated\nmagnitudes of the normal and transverse components of the el ectric\nfield shown in Figs. 7 and 8, respectively, for different angles of\nincidence at 12GHz. The magnitudes of the electric field comp onents\nhave been plotted at 0 .25mm above the ground plane. We see also\nthat for the incidence angle of 10 degrees the electric field l ines are not\nas parallel to the metallic vias as they are for the other case s. Because\nof this, the frequency for which εn= 0 is not exactly that predicted\nby 18. This explains the larger difference between the analyti cal and\nsimulated results for the incidence angle of 10 degrees comp ared to the\nlarger incidence angles in Fig. 6(b).\n7. DISCUSSION AND CONCLUSIONS\nIn this paper we have studied the possibility to use grounded uniaxial\nmaterials as magnetic conductors for both TE and TM fields. We have\nfirst studied the properties of such surfaces through the der ived surface\nimpedance expressions. Attention has been paid especially to the TM\npolarization which is more promising in view of practical re alizations.\nBased on the results of the theoretical studies we have desig ned an\nartificial magnetic conductor having the appearance of a Sie venpiper\nmushroom structure based on wire-medium slab, but operatin g in a\ndifferent regime. The epsilon-near-zero resonance which we u se here\nto create the magnetic conductor effect takes place at a freque ncy\nwhich is approximately twice as lower as the resonant freque ncy of\nthe same structure at the conventional parallel resonance. This offers\na possibility for significant reduction of the layer thickne ss or for a\ndual-frequency design, as proposed in [28]. The magnetic wa ll effect is\nvery little affected by the incidence angle (excluding θ1≈0). We have\nverified our results with simulations.\nThepresent studyof the properties of grounded uniaxial mat erials\nrelates closely to the recent studies on the electromagneti c boundary\nconditions for anisotropic metamaterials [29, 30], where i nstead of\ntreating the transversal components of the incident fields, the authors\nproposeboundaryconditionsforthenormalcomponentsofth eincident\nfields. In [29, 30] the authors arrive to the same conclusion a s the\nresults of this paper, that the perfect magnetic boundaryco ndition can\nbe achieved for the TM field by having n·D= 0. In the present paper\nthis is proposed to realize with wire medium at its plasma fre quency.\nIt is clear that this boundary condition differs considerable from the\nconventional boundary condition for the perfect magnetic c onductors\nn×H= 0.Grounded Uniaxial Material Slabs as Magnetic Conductors 15\nThe magnetic wall effect realized for the TM-polarization usi ng\nthe wire medium is limited to the vicinity of the plasma frequ ency\nof the wire medium. Because of this, the bandwidth of the magn etic\nwall effect is small, especially for small incidence angles. H owever, in\nsome applications, such as GPS or GALILEO, this does not impo se\nany limitations as the needed frequency band for these appli cations is\nrather small. In other applications the proposed novel way o f realizing\nthe surface resonance can be used to create a secondary reson ance\nin the vicinity of the primary resonance [28]. Also, the surf ace does\nnot operate as an AMC for the normal incidence. In a practical\nenvironment this should not be a problem as the waves impingi ng\nto the surface are seldom just normally oriented. Further, i n AMC\nantenna applications, where the primary radiator lies very close to the\nAMC surface, most of the power from the primary radiator is ra diated\nin the angular spectrum practically excluding the normal in cidence.\nAcknowledgements\nThe discussions with Prof. Igor Nefedov are warmly acknowle dged.\nOlli Luukkonen wishes to thank the Nokia Foundation, Jenny a nd\nAntti Wihuri Foundation, Emil Aaltonen Foundation, and the Finnish\nSociety of Electronics Engineers for financial support.\nREFERENCES\n1. D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexopoulos , and\nE. Yablonovich, “High-impedance electromagnetic surface s with a\nforbiddenfrequencyband,” IEEETrans. Microwave Theory Tech. ,\nVol. 47, pp. 2059–2074, 1999.\n2. A. Monorchio, G. Manara, and L. Lanuzza, “Synthesis of art ificial\nmagnetic conductors by using multilayered frequency selec tive\nsurfaces,” IEEE Antennas and Wireless Propagation Letters ,\nVol. 1, Issue 11, pp. 196–199, 2002.\n3. S. Clavijo, R. E. D´ ıaz, and W. E. McKinzie, III, “High-imp edance\nsurfaces: An artificial magnetic conductor for a positive ga in\nelectrically small antennas,” IEEE Trans. Antennas Propagat. ,\nVol. 51, No. 10, pp. 2678–2690, 2003.\n4. D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and\nM. J. Wilhelm, “The design synthesis of multiband artificial\nmagnetic conductors using high impedance frequency select ive\nsurfaces,” IEEE Trans. Antennas Propagat. , Vol. 53, No. 1, pp. 8–\n17, 2005.16 Luukkonen, Simovski, and Tretyakov\n5. A. P. Feresidis, G. Goussetis, W. Shenhong, and J. C. Varda x-\noglou, “Artificial magnetic conductor surfaces and their ap plica-\ntion to low-profile high-gain planar antennas,” IEEE Trans. An-\ntennas Propagat. , Vol. 53, No. 1, pp. 209–215, 2005.\n6. C. R. Simovski, P. de Maagt, and I. V. Melchakova, “High-\nimpedance surface having stable resonance with respect to\npolarization and incidence angle,” IEEE Trans. Antennas Prop.,\nVol. 53, No 3, pp. 454–460, 2005.\n7. G. Goussettis, A. P. Feresidis, and J. C. Vardaxoglou, “Ta iloring\nthe AMC and EBG characteristics of periodic metallic arrays\nprinted on grounded dielectric substrate,” IEEE Trans. Antennas\nPropag., Vol. 54, No. 1, pp. 82–89, 2006.\n8. O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Li-\noubtchenko, A. V. R¨ ais¨ anen, and S. A. Tretyakov, “Simple a nd\naccurate analytical model of planar grids and high-impedan ce sur-\nfaces comprising metal strips or patches,” IEEE Trans. Antennas\nPropagat. , Vol. 56, No. 6, pp. 1624–1632, June 2008.\n9. O. Luukkonen, C. Simovski, A. V. R¨ ais¨ anen, and S. A. Tret yakov,\n“An efficient and simple analytical model for analysis of\npropagation properties in impedance waveguides,” IEEE Trans.\nMicrow. Theory Tech. , Vol. 56, No. 7, pp. 1624–1632, July 2008.\n10. P.-S. Kildal, “Artificially soft and hard surfaces in ele ctromag-\nnetics,” IEEE Trans. Antennas Propagat. , Vol. 38, No. 10,\npp. 15371544, Oct. 1990.\n11. R. W. Ziolkowski and A. D. Kipple, “Application of double\nnegative materials to increase the power radiated by electr ically\nsmall antennas,” IEEE Trans. Antennas Propag. , Vol. 51, No. 10,\npp. 2626-2640, 2003.\n12. A. Erentok, P. L.Luljak, and R.W. Ziolkowski, “Characte rization\nof a volumetric metamaterial realization of an artificial ma gnetic\nconductor for antenna applications,” IEEE Trans. Antennas\nPropagat. , Vol. 53, No. 1, pp. 160–172, 2005.\n13. M. Hirvonen, and J. C.-E. Sten, “Power and Q of a horizonta l\ndipole over a metamaterial coated conducting surface,” IEEE\nTrans. Antennas Propagat. , Vol. 56, No. 3, pp. 684–690, 2008.\n14. M. Hirvonen and S. A. Tretyakov, “Near-zero permittivit y\nsubstratesforhorizontal antennas: Performanceenhancem ent and\nlimitations,” Microw. and Optical Techn. Lett. , Vol. 50, No. 10,\npp. 2674-2677, 2008.\n15. A. Sihvola, S. Tretyakov, and A. de Baas, Metamaterials\nwith extreme material parameters, Journal of Communications\nTechnology and Electronics, Vol. 52, No. 9, pp. 986990, 2007.Grounded Uniaxial Material Slabs as Magnetic Conductors 17\n16. S. A. Tretyakov, Analytical Modeling in Applied Electromagnetics ,\nArtech House: Norwood, MA, 2003.\n17. P.Ikonen, M.Lapine, I.Nefedov, andS.Tretyakov, “Vect or circuit\ntheory for spatially dispersive uniaxial magneto-dielect ric slabs,”\nProgress In Electromagnetics Research , PIER 63, pp. 279–294,\n2006.\n18. R. J. King, D. V. Thiel, and K. S. Park, “The synthesis of su rface\nreactance using an artificial dielectric,” IEEE Trans. Antennas\nPropag., Vol. 31, No. 3, pp. 471–476, May 1983.\n19. M. G. Silveirinha, C. A. Fernandes, and J. R. Costa,\n“Electromagnetic characterization of textured surfaces f ormed by\nmetallic pins,” IEEE Trans. Antennas Propag. , Vol. 56, No. 2,\npp. 405–415, Feb. 2008.\n20. G. Shvets, Photonic approach to making a surface wave\naccelerator, AIP Conference Proceedings, Vol. 647, 371, 2002.\n21. P. A. Belov, R. Marqu´ es, S. I. Maslovski, I. S. Nefedov,\nM. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong\nspatial dispersion in wire media in the very large wavelengt h\nlimit,”Physical Review B , Vol. 67, 113103, 2003.\n22. C. R. Simovski, and P. Belov, “Low-frequency spatial dis persion\nin wire medium,” Physical Review E , Vol. 70, 046616, 2004.\n23. A. Demetriadou and J. Pendry, “Taming spatial dispersio nin wire\nmetamaterial,” J. Phys.: Condens. Matter , Vol. 20, 2008, 295222.\n24. A. B. Yakovlev, O. Luukkonen, C. R. Simovski, S. A. Tretya kov,\nS. Paulotto, P. Baccarelli, and G. W. Hanson, “Analytical mo d-\neling of surface waves on high impedance surfaces,” Metamaterials\nand Plasmonics: Fundamentals, Modelling, Applications (Eds.\nS. Zouhdi, A. Sihvola, and A. P. Vinogradov), NATO Science fo r\nPeace and Security Series B, pp. 239–254, 2009.\n25. O. Luukkonen, M. G. Silveirinha, A. B. Yakovlev, C. R. Sim ovski,\nI. S. Nefedov, and S. A. Tretyakov, “Homogenization models\nfor the analysis of reflection properties of mushroom struct ures,”\nProc. 2nd International Congress on Advanced Electromagneti c\nMaterials in Microwaves and Optics, Pamplona, Spain , September\n21–26, pp. 208–210, 2008.\n26. A. B. Yakovlev, M. G. Silveirinha, O. Luukkonen, C. R. Sim ovski,\nI. S. Nefedov, and S. A. Tretyakov, “Homogenization models\nfor the analysis of surface waves on analysis of surface wave s\non mushroom structures” Proc. 2nd International Congress on\nAdvanced Electromagnetic Materials in Microwaves and Opti cs,\nPamplona, Spain , September 21–26, pp. 310–312, 2008.18 Luukkonen, Simovski, and Tretyakov\n27. Ansoft’s homepage: http://www.ansoft.com/\n28. O. Luukkonen, F. Costa, A. Monorchio, and S. Tretyakov, “ A\nthin electromagnetic absorber for wide incidence angles an d both\npolarizations”, to appear in IEEE Trans. Antennas Propag. ,\npreprint available at http://arxiv.org/abs/0807.4831v3 .\n29. I. V. Lindell and A. H. Sihvola, “Electromagnetic bounda ry and\nits realization with anisotropic metamaterial,” Physical Review E ,\nVol. 79, 026604, 2009.\n30. I.V.LindellandA.H.Sihvola, “UniaxialIB-mediuminte rfaceand\nnovel boundary conditions,” to appear in IEEE Trans. Antennas\nPropag.."    },    {        "title": "0811.3728v1.New_Samarium_and_Neodymium_based_admixed_ferromagnets_with_near_zero_net_magnetization_and_tunable_exchange_bias_field.pdf",        "content": "New Samarium and Neodymium based admixed ferromagnets \nwith near-zero net magnetization and tunable exchange bias field \nPrasanna D. Kulkarni1, U. V. Vaidy a1, S. K. Dhar1, P. Manfrinetti2 and A. K. Grover1 \n \n1Depart ment of Condensed Matter Phy sics and Materi als Science, Tata Institute of Fundam ental Research, \nColaba, Mumbai-4000 05.  \n2INFM and Dipartimento di Chim ica e Chim ica Industria le, Universitá di Genova, Via Dedecaneso 31, Gen ova \n1614 6, Ital y \ne-mail: prasanna@tifr.res.in \n \nAbstract \n             Rare earth based interm etallics, SmScGe and NdSc Ge, are shown to exhibit near zero net \nmagnetizatio n with substit utions of 6 to 9 atom ic % of Nd and 25 atom ic % of Gd, respectively . The notion \nof m agnetic compensation in them  is also elucidated by the  crossover of ‘zero m agnetizati on’ axis at low \nmagnetic fields (< 103 Oe) and field-induced reversal in the orientation of th e magnetic moments of the \ndissimilar rar e earth ions at higher m agnetic fields. These magnetically  ordered material s with ‘no-net’ \nmagnetizatio n and appreciable conduction electron polari zation display  an at tribute of an  exchange bias \nfield, which can be tuned.  The attractively  high m agnetic orderin g temperatures of ~ 270 K, underscore th e \nimportance of these materials for potentia l applications in spintronic s.  \n \nPACS n umbers : 71.20.Lp, 75.50.Ee, 85.75.-d \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 11. Introduction \n  \n    The interest in tailoring Samariu m based f erromagnets , having near-zero net magnetizati on along with large \nconduction el ectron polarization, for applications in spin tronics has gained momentu m with the realization of \nSm 1-xGd xAl2 alloy s (0.01 ≤ x ≤ 0.032), in the thin film form  [1,2]. These ad mixed alloy s undergo m agnetic \nordering at  ~ 125 K. Adachi and Ino [ 3] had pointed out  that am ongst rare earth based s ystems, the Samarium  \nalloy s are particularly  suitable for conceiving m aterial s having seemingl y incom patible properties of large spin  \npolarization and no net m agnetization. From  applicati on poi nt of view, it would be fruitful to sear ch for other \nferro magneti c Samariu m and rare eart h (R) based i ntermetallics,  which have magnetic ordering tem peratures  \nabove or close to the am bient tem peratu re and drive th em towards the near zero magnetizatio n lim it by suitable \nadmixing. In the present work, we ide ntify two such ma gneticall y ordered syste ms, which  sustain near -zero \nmagnetizatio n values up to tem peratures much higher than 200 K. Ty pically, the zero magnetizatio n state \namongst the metallic systems is achieved in adm ixed rare ea rth alloy s with the t wo R ions belonging to t he two  \ndifferent halves of the 4 f-rare earth s eries (such that the S-state ( L = 0) Gd3+ ions ( S = 7/2) are counted along  \nwith the R3+ ions belong ing to second h alf of the 4 f-series). In suc h adm ixed sy stems, the magnetic m oments of \ndissim ilar R ions belongi ng to the different halves of the 4 f n series (for  which J = L-S/L+S in the ground \nmultiplet of the first half /  second half)  get antiferromagne tically  linked via the indirect exchange interaction \nmediated by the conduction electrons. In an isoelectronic R-series of alloys, which display  ferrom agnetic \nordering, the  indirect exchange interaction m aintains ferro magnetic coupling between the “spins” of the 4 f-\nseries of R3+ ions under all circu mstanc es [4,5]. However, the magnetizations of the “m agnetic moments” of \ndissimilar R ions occupy ing the sa me cr ystallographic site in a given matrix evo lve differe ntly with tem perature,  \nand specific stoichiometries in the admixed rare ea rth alloy s are well known [ 4,6] to y ield magnetic \ncompensation behaviour. In recent y ears [3,7], it has been anticipated that the magnetizatio n (M) response per \nSamarium ion, aided by a contributi on from conduction el ectron polarization, in a given Samariu m intermetallic \ncan either be orbital-surplus or spin-surplus and it can be induced to the zer o magnetizati on lim it either on  \nsubstitution of Sm3+ ions b y Gd3+ or Nd3+ ions, as alre ady reported in SmAl 2 [3,9-13]  and S mCd sy stems [7,14] , \nrespectively .  \n    Several interm etallic compounds in the two ferro magnetic rare earth ( R) series, RScG e and RScSi, have  \nordering temperatures well above 200 K [15]. We are ab le to tune the magnetization of two co mpounds o f \nSmScGe and NdScGe across the M = 0 axis b y 9 at. %  substitution of Sm3+ by Nd3+ ions and b y 25 at. % \nreplacement of Nd3+ by Gd3+, respect ively. The characte ristic re sults of magnetization me asure ments i n Sm 1-\nxNd xScGe ( x = 0.06 an d 0.09) and Nd 0.75Gd 0.25ScGe, having Tc ~ 270 K and  ~ 240 K, resp ectively  have  been  \nchosen for presentation here. The M values in Sm 0.94Nd 0.06ScGe r emain very  close to zero even in very large \nfield (50  kOe) and t his co mposition would be particularly  suitable for applications, where self-stray  field is of \nconcern. We  are also r eporting here on the attribute of  exchang e bias fi elds in these allo ys on the ba sis of \ndetailed magnetization hysteresi s studies in them . The exch ange bias, which can be tuned in the present series of \nalloy s, enhance the potential use of these material s in m agnetic m ulti-lay er composites f or specific device  \napplications.  \n \n2. Experim ental \n     \n    Pol ycrystalline samples of Sm1-xNd xScGe ( x = 0.06, 0. 09) were prepared by  melting together  the \nstoichiom etric amounts of S mScGe an d NdScGe. I n the case of  Nd 1-xGd xScGe ( x = 0.25), the stoichiometric \namounts of t he pure elements were melted together in an arc fur nace. The characterization of the powdered  \nsamples by  x-ray diffracti on confirm ed their CeScGe ty pe tetrag onal structure. The magnetization data were \nobtained usin g Quantum  Design Inc. SQUID Magne tometers (Model MPMS 5 an d SVSM).    \n \n3. Results and Discussion s \n \nFigures 1 (a) and 1 ( b) show the field cool ed cool-down (FCC) magnetization curves ( MFCC) in \nSm 0.94Nd 0.06ScGe and Sm 0.91Nd 0.09ScGe at low and high applied fields, respecti vely. The shapes of the MFCC(T) \ncurves in Fig s. 1(a) and 1( b) displa y a non-m onoton ic behaviour,  and the low values (< 0.15 µB/form ula unit) \nimply the existence of a co mpetition between magne tic responses from different possible constituents \n 2contributi ng to the total M signal. The magnetic moments per form ula unit (f.u.) in the or dered state in the \npristine ferromagnets RScGe ( R = Sm , Nd and Gd) h ad been reported to be ~ 0. 2, 2 and  7 µB [15]. \nThe onset of magnetic ordering near 270 K associ ated with  the host S m-matrix in the two stoichiometries ( x \n= 0.06,  0.09) can be easily identified f rom their low field MFCC(T) curves in Fig. 1(a). Bo th the curves in Fig. \n1(a) displa y a similar pea k like response below Tc, however, there is one significant difference. The MFCC(T) \ncurve for x = 0.09 can be seen to crossover to the metast able neg ative values below com pensation tem perature \n(Tcomp) of about 88 K, whereas in the MFCC(T) curve for x = 0.06, t he values reach a minim um lim it at about 50  \nK, and therea fter the curve  flattens out. The MFCC(T) curve in 50 kOe in x = 0.06 allo y in Fig. 1(b) sho ws a \nturnaroun d in magnetizatio n response at about 90 K (identified as T*), thereby elucidating the com pensation \nbehaviour bet ween the two  competing contri butions at this co mposition as well. The MFCC(T) curve for x = 0.09 \nin H = 50 kOe shows a shallower minimum and a change  in curvature at about  180 K (being marked as T* in \nFig. 1( b)). M values in x = 0.06 alloy just var y from  ~ 0.0 15 µB / f.u. to ~ 0.05 µB / f.u. fr om 300 K down  to zero \ntemperature, this attests to its enhanced potential for applications, when stray  field due to sam ple magneti zation \nis of particular concern.  \nFig. 2 shows the MFCC(T) curves in 50 Oe and 50 kOe in Nd 0.75Gd 0.25ScGe. The low fiel d MFCC(T) curve \ndisplay s a Tc near 240  K and zero crossover at Tcomp ~ 105 K, whereas in a higher fiel d of 50 kOe, the \nturnaround behaviour is w itnessed at  T* of ~ 120 K. Both the characteristics are akin to those observed in the \nSm 1-xNd xScGe series alloys described above. However, the M values in 50 kO e in Fig. 2 are so mewhat l arger as  \ncompared to those in Fig. 1(b). \n     A subtle difference in the magnetic compensation behaviour in  Nd 0.75Gd 0.25ScGe and Sm 0.91Nd 0.09ScGe can  \nbe further hig hlighted by comparing the warm  up of the rem anent magnetizatio n (MRem) in them  (see Figs. 3(a) \nand 3(b)). MRem is initially  obtained by  cooling the sam ple to 5 K in a field of 5 0 kOe and th en reducing the field  \nto 50 Oe. Note that in Fig. 3(a), MRem(T) and MFCC(T) curves in the Nd 0.75Gd 0.25ScGe co mpound  have m irror \nimages like  appearances f rom 5 K upto ~ Tc, the two curves intersect at T ≈ 120 K (close to the T* value in Fig. \n2). On the other hand, i n Fig. 3( b), for  Sm 0.91Nd 0.09ScGe, prima facie , there does not appear any correspondence \nbetween the MRem(T) and MFCC(T) curves. The t wo curves do, however, inters ect at  T ≈ 188 K, and abo ve this \ntemperature  MRem(T) curve lies below MFCC(T) curve. The two curves eventual ly merge into  each  other as  T  \nT→\nc (≈ 270 K). In fact, a so mewhat similar feature of  merger into each other while approaching Tc value can be \nnoted for MRem(T) and MFCC(T) curves in Fig. 3(a) as well. The o bservations in Fig. 3 can be rationalize d by \nstating that Nd moments in the remanent state at 5 K are oriented along the field direction and su ch an  \norientation re mains sustain ed nearly  upto the respective Tc values. The magnetiz ation values at the tem peratures \nof intersection of  the MRem(T) and MFCC(T) curves in Fi g. 3(a) and Fi g. 3(b) are close to the respective \nmagnetizatio n values at  the temperatures of merger  of two curv es ne ar (re spective) Tc values. MRem(T) values \nbetween the t emperature  of intersection and te mperature of merger of two curves in Fig. 3(a) and Fig. 3(b) are in  \na metastable region in  the sense that they are lower than the correspondin g MFCC values. Similarly , the MFCC(T) \nvalues below  intersection temperature  are also in the  metastable region. The collection of h igher of the set of \ntwo M values at a given tem perature would constitute  a quasi -equilibrium  M-T curve in a field of 50 Oe. Such a  \ncollection would displa y a mini mum at a temperature, close to its T* value, determined from  high field.  \n     The net magnetizatio n has contributions from  three constituents, viz., the magnetic moments of two rare \nearth ions an d the con duction electron polarization (CEP) . The CE P contrib ution (exchanged  coupled  to the rare \nearth spins) is expected to undergo a phase rever sal as the rare earth m oments undergo a fie ld induced reversal  \nacross a given T*. The CEP contributi on is expected to be of the order of 0.1 µB / f.u. in bo th the co mpounds,  \nhowever, the net offset values fro m the t wo local moments in S m0.91Nd 0.09ScGe would be m uch lower than those  \nin the Nd 0.75Gd 0.25ScGe, as the former involves competition betw een smaller moment valu es (i.e., contribution \nfrom  91%  of Sm  moments and 9%  of N d moments) as co mpared to those i n the latter adm ixed com pound. This \nprobabl y accounts for the  larger difference between  the values of T* and Tcomp in the S m based co mpound as \ncompared to that in the Nd based co mpound. At Tcomp, the net magnetizatio n from  all th e three contributions  \nequals z ero (at low fi elds) , wherea s, T* perhaps repr esents a limit, where  the c ontributions (at high fields) fro m \nthe two local m oments bala nce out prior to reaching the Tcomp value.  \n     In the rare earth based f erromagnets with near zer o net magnetization, one can i magine that the CEP part i s \nakin to  a soft  com ponent which is exchange couple d to a pseud o-antiferromagnet m ade up of  dissim ilar rare \nearth moments. In Sm 0.98Gd 0.02Al2, Chen et al. [16] discovered the presence of t he exchange bias field ( Hexch = -\n(H+ + H-)/2), as characterized by  the asy mmetric shift in the magnetization hy steresis loop below its Tcomp, \nwhere H+ and H- represen t the fields at which the M cross es th e zero value in a M-H loop. The tem perature \nvariations of Hexch and the effective coercive field (de fined as half width of the hy steresis loo p, Hceff = (H+ - H-\n 3)/2) in S m0.98Gd 0.02Al2 imbibes a complex non-m onotonic beha vior. While Hceff(T) appeared to display  a \ndivergence as  T  T→ comp from low/high temperature ends, the Hexch(T) display s a peak, followed by  an increas e, \nas te mperature was low ered below Tcomp (see Fig .2 in Ref. 16). We show in Fig. 4 the M-H loops i n \nSm 0.94Nd 0.06ScGe  alloy  recorded betwee n ± 70 kOe  alloy at three representativ e temperature s, viz., 5 K, 50 K  \nand 80 K below its no minal T* of 90 K (cf. M(T) in 50 kOe in Fig. 1(b)). The shifts in the centre of gravity  of \nthe hy steresis loop in the horizontal as well as ver tical directions are well apparent. Suc h shifts have  been  \nreported in the magnetic multi-la yer com posit es comprising ferromagnetic and antiferro magnetic lay ers as well  \nas in other ad mixed magnetic sy stems [17,18 ]. The i nsets (a ) and (b) in Fig. 4 show the temperature variations  \nof Hexch and Hceff in Sm 0.94Nd 0.06ScGe. While the sha pe of Hexch(T) curve in the inset (a) bears rese mblance to its  \nshape in S m0.98Gd 0.02Al2 [16] , the Hceff(T) has a perplexing n on-monotonic r esponse, co mprising two peaks \ncentered around 100 K and 20 K, resp ectively , and with a minimum in between at ~ 70 K. The values o f the \nexchange bias field in t he inset (a) of  Fig. 4 are an  order m agnitude larger  than the cor responding  values \nreported in t he Sm 0.98Gd 0.02Al2 alloy  [16]. The effe ctive coercive  field values, likewise, are  also significantly \nlarger in the alloy  under study . The com position Sm 0.94Nd 0.06ScGe th us emerges as an exa mple of a magnetic ally \nordered material having (i) ‘no-net’ m agnetization, (ii) large spin p olarization, (iii) high exchange bias field  and \n(iv) m oderat e to large effec tive coercive field.  \nThe change of stoichiometry  from  Sm 0.94Nd 0.06ScGe to S m0.91Gd 0.09ScGe allows the possibility  of exploring \nsmaller values of the exch ange bias field. Fig.  5 sh ows the magnetization h ysteresis loops recorded between ± \n10 kOe at fe w sel ected te mperatures  in S m0.91Gd 0.09ScGe. The asymmetry in the shape of t hese loops is well \nevident at T ≤ 160 K, it is seen to rapidly enhance as the sam ple is cooled down below 50 K.  It can be noted that \nwhile the m agnetization values in this sample are higher than the earlier one, the exchange bias fields (i.e., the \nasymmetric shifts) are sign ificantly  lowe r. The insets ( a) and (b) in Fig. 5 show the plots of Hexch(T) and Hceff(T), \nrespectively . A co mparison of the inset  (b) in Fig. 4 with  that in Fig. 5 shows how the effec tive coercive field \nvalues differ in the two com positions. The shapes of Hexch(T) curves in the insets (a) of Fig. 4 and Fig. 5 are not \ntoo different.  It is apparent that  the com position variation in the  Sm 1-xNd xScGe (0.06 ≤ x ≤ 0.09) series would  \nperm it a wide range of selection of the values of ex change field and effective coercive field in ferromagnets \nwith ‘no net ’ magnetizatio n and large sp in polarizatio n.  \nTo gain some co mprehension of the behavior presented in the insets (b) of  Fig. 4 and Fig. 5, we reca ll the  \nbehavior of effective co ercive field reported in the literature [19,20 ] in ferromagnetic materials co mprising 4 f-\nrare earth an d 3d-transition m etals in which m agnetic moments of the rare earth and transiti on elements couple  \nantiferro magnetically . In particular, Webb et al.  [20] had found that multilay er com posites of Gd and Co \nprepared in t wo different way s yielded nearly the  same compensation te mperature but display ed different  \ntemperature  dependences  for the eff ective coer cive field. The effective  coe rcive field ( Hceff) is a material  \nattribute, whi ch is kn own to depend i n a com plex wa y on the details of t he composition m odulation s and  \nmultilay ering in the Gd-C o com posites [ 19]. In ideal ferri magnets, the coercive field ( Hc) is considered to \ninversely  relate to the (extrapol ated) spontaneous magnetization ( Ms) and is ex pected to diverge as  T  T→ comp \n[20,21 ] to co nform  with the collapse i n Ms at Tcomp, where the contributions from  the two different sublattices \nbalance out and the M versus H plot becomes linear, like, in antiferromagnets. Webb et al. [20] found that in the  \ncase of (unifor m) amorphous phase of Gd-Co co mposite, the Hc showed a diver gence, where as in the case of (an  \ninhom ogeneous) lay ered Gd-Co com posite, Hceff(T) display ed a m inimum value at Tcomp. It wa s argued [20 ] that \nM-H loop in the latter case co mprised two parts, one of  which switched direction like a soft magnetization  \ncontributi on having uni directional anis otrop y and th e other gave a linear M-H response. Su ch a superposition \ncan give effective coercive field to  be lower th an the ‘true ’ coercive fi eld, where the ‘spontane ous’ \nmagnetizatio n switches direction. Webb et al. [20]  provided a phenom enological descripti on to encompass the \nobservations ranging fr om divergence t o minimum in Hceff(T) in a variety  of ferri magnets in term s of the  \nstrength of (a ntiferromagnetic) coupling  between the two compensating com ponents of a ferrimagnet. In such a \ndescription, it is conceivable that at an inter mediat e strength (i n between th e strong to weak coupling), the  \neffective  coercive field can yield com plex behavior, co mprising a divergence  as well  as a minimum in the \nHeff(T) curve. In the adm ixed rare eart h alloy s display ing com pensation tem perature, the t wo dissi milar rare  \nearth ele ments occupy ing the sa me crystallographic site are, prime facie , strong ly coupled , however, they d o \nindeed respon d as if the m olecular field of one does no t strongl y influence the molecular field of the other an d in \nthis sense they  should be considered  as weakly  coupl ed. In the case of Sm 0.94Nd 0.06ScGe, the minimum in the \nHceff(T) is close to its T* value of ~ 70  K (cf. inset (b), Fig. 4).  The t emperature d ependence of the (extrapolated)  \nspontaneous magnetizatio n (data not s hown here) in this sam ple yielded  a shallow minimum  at about 70 K , \nwhich is satisfactory  (cf. Fi g. 5, Re f 20 in Gd-Co composite as well).  \n 44. Conclusions \n \n    To conclude, we have illustra ted the magnetic b ehaviour of the rare  earth based zero magnetizatio n “spin \nferro magnets” in Sm 1-xNd xScGe ( x = 0.06 and 0.09) and Nd 1-xGd xScGe ( x = 0.25) havi ng or dering tem peratures \nclose to the am bient tem perature. The fact that magne tic co mpensation in Sm ScGe happens on substitut ion of \nSm3+ ions by Nd3+ ions, instead of that by  Gd3+ ions, confirms the spin-surplus character of the (Sm ) \nmagnetizatio n in i t. The e xistence of appreciable conduc tion electron p olarization and  a tun able exchange bias \nfield conco mitant with the negligible stray  field due to sam ple magnetization in the doped SmScGe and Nd ScGe \ncompounds a re attractive attributes for applications in  spintronics.  \n \nRefe renc es \n \n[1] Avisou K, Dumesnil K and Dufour C  2007 J. Magn. Magn. M ater. 316 31 7 \n[2] Avisou K, Dufour C,  Dumesnil K, Rogalev A, Wilhelm  F an d Snoeck E  2008 J. Phys.: Condens. M atter 20 \n2650 01 \n[3] Adachi H and Ino H 1 999 Nature  401 148  \n[4] Williams H J, Wernick J H, Nesbitt E A and Sherwood R C 1962 J. Phys. Soc. of Jpn.  17 B-1 91 \n[5] Grover A K, Malik S K, Vijay aragha van R and Sh imizu K 1979  J. Appl. Phys.  50 7501 \n[6] Swift W M and Wallace W E 1968 J. Phys. Chem. Solids  29 2053 \n[7] Adachi H, Ino H and M iwa H 1997 Phys. Rev. B  56 34 9 \n[8] Adachi H, Ino H and M iwa H 1999 Phys. Rev. B  59 11 445  \n[9] Grover A K, Ram babu D, Dhar S K, Malik S K, Vijay araghavan R, Hilscher G and Kirch mayr H 1983  \nProceedings of Annual (1983) Depart ment of Atomic  Energy ( DAE) Nuclea r Physi cs & Solid State Physics \nSymposium (India) 26C 2 52  \n[10] Grover A K and Dha r S K in Experimental & Theoretical aspects of Valence Fluctuati ons edited b y Gupta \nL C and Malik S K (Plenum  Press, New York, U.S.A. 1987) p. 481  \n[11] Taylor J W, Duffy  J A, Bebb A M, Lees M  R, Bouchenoire L, Brown S D and Cooper M J 2002 Phys. Rev.  \nB 66 1 61319(R)  \n[12] Adachi H, Kawata H, Hashim oto H,  Sato Y, Matsu moto I and Tanaka Y 2001 Phys. Rev. Lett.  87 1 27202 \n[13] Wu A H,  Luo J L, Che n Z J, G T Li u, P, Yu and Wang N L 2005 J. Phys. D: Appl. Phys.  38 3 567 \n[14] Li G F, Su J R and Z hu C F 2 007 Appl. Phys. L ett. 90 1 72503  \n[15] Singh S, Dhar S K, Manfrinetti P, Palenzona A and Mazzone D 2004 J. Magn. M agn. Mater. 269 113  \n[16] Chen X H, Wang K Q, Hor P H, Xue Y Y an d Chu C W 2005 Phys. Rev. B  72 054 436 and references \ntherein. \n[17] Nogues J and Schuller I K 1999  J. Magn. M agn. Mater. 192 2 03  \n[18] Koga S and Narita K 1982 J. Appl. Phys.  53 16 55 \n[19] Webb D  J, Walmsley  R G, Parvin K, Di cknson P H, Geballe T H and W hite R M 19 85 Phys. Rev. B  32 \n4667 \n[20] Webb D J, Marshall A F, Sun Z, Geballe T H and White R M 1 988 IEEE Tr ans. Magn.  24 588 \n[21] Morrish A H, The Physical P rinciples of Magnetism , John-W illey & Sons,  Inc. (New York, \nU.S.A. ), 1965. \n \nFigure captions \n \nFig. 1. Tem perature variations of m agnetization ( M) values in Sm 1-xNd xScGe ( x = 0.06 and 0.09) durin g field \ncool cooldow n (FCC) proc ess in (a) 50 Oe and (b) 50 kOe. Tcomp of 88 K in panel (a) identifies the t emperature \nof crossover of M = 0 axis towards negative m etastable values in x = 0.09 alloy . T* in panel (b) identifi es the  \nturnaroun d in magnetizatio n values at hi gh fields in x = 0.06 allo y.  \nFig. 2. MFCC curves in H = 50 Oe and 50 kOe in Nd 0.75Gd 0.25ScGe alloy . Tc, Tcomp and T* values have been  \nmarked.  \nFig. 3. Plots of warm up of remanent magnetization ( MRem) from 5 K to 300 K alongwith the MFCC(T) curve in a \nfield of 50 Oe in (a) Nd 0.75Gd 0.25ScGe and (b) S m0.91Nd 0.09ScGe. The te mperatures of inters ection of the two  \ncurves in pan els (a) and (b) have been id entified, and t he Tcomp values have been marked as w ell.  \n 5Fig. 4.  Magn etization h ysteresis loops in Sm 0.94Nd 0.06ScGe at thre e temperatur es, as indicated. Sam ples wer e \ncooled to a given tem perature in a field of 70 kOe be fore recording the loop. The insets (a) and (b) show \ntemperature variations of Hexch (= -( H+ + H-)/2) and  Hceff (= ( H+ - H-)/2). A re presentative pair of H+ and H- \nvalues are marked for the M-H curve at 5 K.  \nFig. 5. Magn etization hy steresis loops in Sm 0.91Nd 0.09ScGe at 80 and 160 K, recorded after an initial cooling in \n10 kOe to a g iven te mperature. The inset s (a) and (b) show tem perature variation of Hexch and Hceff. T* (≈ 180 K) \nhas also been marked in the both insets.  \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 6 \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 \nFig. 1.  \n \n \n \n \n \n 7 \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 \nFig. 2.  \n \n \n \n \n \n \n \n \n \n \n 8 \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 \nFig. 3.  \n \n \n \n \n \n \n \n \n \n \n 9 \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 \nFig. 4.  \n \n \n \n \n \n \n \n \n \n \n \n 10 \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 \nFig. 5.  \n \n \n \n \n 11"    },    {        "title": "0812.3160v2.Evidence_for_reversible_control_of_magnetization_in_a_ferromagnetic_material_via_spin_orbit_magnetic_field.pdf",        "content": "arXiv:0812.3160v2  [cond-mat.mtrl-sci]  14 Jul 2009Evidence for reversible control of magnetization in a ferro magnetic material via\nspin-orbit magnetic field\nAlexander Chernyshov,∗Mason Overby,∗Yuli Lyanda-Geller, and Leonid P. Rokhinson†\nDepartment of Physics and Birck Nanotechnology Center,\nPurdue University, West Lafayette, Indiana 47907 USA\nXinyu Liu and Jacek K. Furdyna\nDepartment of Physics, University of Notre Dame, Notre Dame , Indiana 46556 USA\nConventional computer electronics creates a di-\nchotomy between how information is processed\nand how it is stored. Silicon chips process infor-\nmation by controlling the flow of charge through\na network of logic gates. This information is then\nstored, most commonly, by encoding it in the ori-\nentation of magnetic domains of a computer hard\ndisk. The key obstacle to a more intimate integra-\ntion of magnetic materials into devices and circuit\nprocessing information is a lack of efficient means\nto control their magnetization. This is usually\nachieved with an external magnetic field or by the\ninjection of spin-polarized currents [1, 2, 3]. The\nlatter can be significantly enhanced in materials\nwhose ferromagnetic properties are mediated by\ncharge carriers [4]. Among these materials, con-\nductors lacking spatial inversion symmetry cou-\nple charge currents to spin by intrinsic spin-orbit\n(SO) interactions, inducing nonequilibrium spin\npolarization [5, 6, 7, 8, 9, 10, 11] tunable by local\nelectric fields. Here we show that magnetization\nof a ferromagnet can be reversibly manipulated\nby the SO-induced polarization of carrier spins\ngenerated by unpolarized currents. Specifically,\nwe demonstrate domain rotation and hysteretic\nswitching of magnetization between two orthogo-\nnal easy axes in a model ferromagnetic semicon-\nductor.\nIn crystalline materials with inversion asymmetry, in-\ntrinsic spin-orbit interactions (SO) couple the electron\nspin with its momentum ¯ hk. The coupling is given\nby the Hamiltonian Hso=¯h\n2ˆσ·Ω(k), where ¯ his the\nPlanck’s constant and ˆ σis the electron spin operator\n(for holes ˆ σshould be replaced by the total angular\nmomentum J). Electron states with different sign of\nthe spin projection on Ω(k) are split in energy, anal-\nogous to the Zeeman splitting in an external magnetic\nfield. In zinc-blende crystals such as GaAs there is a\ncubic Dresselhaus term[12] ΩD∝k3, while strain in-\ntroduces a term Ωε=C∆ε(kx,−ky,0) that is linear in\nk, where ∆ εis the difference between strain in the ˆ z\nand ˆx,ˆydirections[13]. In wurzite crystals or in mul-\ntilayered materials with structural inversion asymmetry\nthere also exists the Rashba term[14] ΩRwhich has a\ndifferent symmetry with respect to the direction of k,ΩR=αR(−ky,kx,0),where ˆ zisalongtheaxisofreduced\nsymmetry. In the presence of an electric field the elec-\ntronsacquireanaveragemomentum¯ h∆k(E), whichleads\nto the generation of an electric current j= ˆρ−1Ein the\nconductor, where ˆ ρis the resistivity tensor. This current\ndefines the preferential axis for spin precession ∝angb∇acketleftΩ(j)∝angb∇acket∇ight.\nAs a result, a nonequilibrium current-induced spin polar-\nization∝angb∇acketleftJE∝angb∇acket∇ight∝ba∇dbl∝angb∇acketleftΩ(j)∝angb∇acket∇ightis generated, whose magnitude ∝angb∇acketleftJE∝angb∇acket∇ight\ndepends on the strength of various mechanisms of mo-\nmentum scattering and spin relaxation[5, 15]. This spin\npolarization has been measured in non-magnetic semi-\nconductors using optical[7, 8, 9, 11, 16] and electron spin\nresonance[17] techniques. It is convenient to parameter-\nize∝angb∇acketleftJE∝angb∇acket∇ightin terms of an effective magnetic field Hso. Dif-\nferent contributions to Hsohave different current depen-\ndencies ( ∝jorj3), as well as different symmetries with\nrespect to the direction of j, as schematically shown in\nFig. (c,d), allowing one to distinguish between spin po-\nlarizations in different fields.\nIn order to investigate interactions between the\nSO-generated magnetic field and magnetic domains\nwe have chosen (Ga,Mn)As, a p-type ferromagnetic\nsemiconductor[18, 19] with zinc blende crystalline struc-\nture similar to GaAs. Ferromagnetic interactions in this\nmaterial are carrier-mediated[20, 21]. The total angu-\nlar momentum of the holes Jcouples to the magnetic\nmoment Fof Mn ions via antiferromagnetic exchange\nHex=−AF·J. This interaction leads to the ferro-\nmagnetic alignment of magnetic moments of Mn ions\nand equilibrium polarization of hole spins. If additional,\nnon-equilibrium spin polarization of the holes ∝angb∇acketleftJE∝angb∇acket∇ightis in-\nduced, the interaction of the hole spins with magnetic\nmomentsofMnionsallowsonetocontrolferromagnetism\nby manipulating J. Magnetic properties of (Ga,Mn)As\nare thus tightly related to the electronic properties of\nGaAs. For example, strain-induced spin anisotropy of\nthe hole energy dispersion is largely responsible for the\nmagnetic anisotropy in this material. (Ga,Mn)As, epi-\ntaxially grownon (001) surface of GaAs, is compressively\nstrained, which results in magnetization Mlying in the\nplane of the layer perpendicular to the growth direction,\nwith two easy axes along the [100] and [010] crystallo-\ngraphic directions[22, 23]. Recently, control of magneti-\nzation via strain modulation has been demonstrated[24].\nIn this paper we use SO-generated polarization ∝angb∇acketleftJE∝angb∇acket∇ightto2\n] 110 [\n[110]jxjy\n] 110 [\n[110]jxjya) b) \nc) d) a) a) ] 100 [\n] 100 [\n6  m] 100 [\n] 100 [\n] 100 [\n] 100 [\n6  m+I Heff\nHeff-I ] 010 [\n] 100 [] 110 [] 10 1 [\n] 00 1 [MH\n M\n H\n+I -I \nHeffHeff] 0 1 0 [a) \n3344\n221155\n887766\nFIG. 1: Layout of the device and symmetry of the\nSO fields. a) AFM image of sample A with 8 non-magnetic\nmetal contacts. b) Diagram of device orientation with re-\nspect to crystallographic axes, with easy/hard magnetizat ion\naxes marked with blue/red dashed lines. Measured direction s\nofHefffield are shown for different current directions. c,d)\nOrientation of effective magnetic field with respect to cur-\nrent direction for c) strain-induced and d) Rashba SO inter-\nactions. Current-inducedOersted field underthe contacts h as\nthe same symmetry as the Rashba field.\nmanipulate ferromagnetism.\nWe report measurements on two samples fabricated\nfrom (Ga,Mn)As wafers with different Mn concentra-\ntions. The devices were patterned into circular islands\nwith 8 non-magnetic Ohmic contacts, as shown in Fig. a\nand discussed in Methods. In the presence of a strong\nexternal magnetic field H, the magnetization of the fer-\nromagnetic island is aligned with the field. For weak\nfields, however, the direction of magnetization is primar-\nily determined by magnetic anisotropy. As a small field\n(5< H <20 mT) is rotated in the plane of the sample,\nthe magnetizationisre-alignedalongtheeasyaxisclosest\nto the field direction. Such rotation of magnetization by\nan external field is demonstrated in Fig. . For the cur-\nrentI||[1¯10], the measured Rxyis positive for M||[100]\nand negative for M||[010]. Note that Rxy, and thus also\nthe magnetization, switches direction when the direction\nofHis close to the hard axes [110] and [1 ¯10], confirm-\ning the cubic magnetic anisotropy of our samples. The\nswitching angles ϕH=/negationslashHIwhereRxychanges sign are\ndenoted as ϕ(i)\nHon the plot.\nIn the presence of both external and SO fields, we\nexpect to see a combined effect of Hso+Hon the di-\nrection of magnetization. For small currents (few µA)\nHso≈0, andRxydoes not depend on the sign or\nthe direction of the current. At large dc currents the\nvalue of ϕ(i)\nHbecomes current-dependent and we define/s52/s53 /s57/s48/s45/s49/s48/s48/s49/s48/s57/s48 /s49/s56/s48 /s50/s55/s48 /s51/s54/s48/s45/s49/s48/s48/s49/s48\n/s51/s49/s53 /s51/s54/s48\n/s49/s51/s53 /s49/s56/s48/s45/s49/s48/s48/s49/s48/s50/s50/s53 /s50/s55/s48 /s49/s51/s53 /s49/s56/s48/s32/s32/s82 \n/s120/s121/s32/s40 /s41/s91/s48/s49/s48/s93 /s32/s32/s32/s32/s32/s32/s32 /s91/s49 /s49/s48/s93 /s32/s32/s32/s32/s32/s32/s32/s32 /s91/s49 /s48/s48/s93 /s32/s32/s32/s32/s32/s32/s32 /s91/s49/s49 /s48/s93 /s32/s32/s32/s32/s32/s32/s32 /s91/s48/s49 /s48/s93 /s32/s32/s32/s32/s32/s32/s32 /s91/s49/s49 /s48/s93 /s32/s32/s32/s32/s32/s32/s32 /s91/s49/s48/s48/s93 /s32/s32/s32/s32/s32/s32/s32 /s91/s49/s49/s48/s93 /s32/s32/s32/s32/s32/s32/s32 /s91/s48/s49/s48/s93\n/s72/s32/s40/s100/s101/s103/s41\n/s98/s41/s82 \n/s120/s121/s32/s40 /s41\n/s32/s32\n/s73/s32 /s124/s124/s32/s91/s49/s49 /s48/s93/s97/s41\n/s49/s51/s53 /s49/s56/s48/s48/s46/s48/s49/s32/s109/s65\n/s32 /s32/s32\n/s48/s46/s50/s53/s32/s109/s65\n/s48/s46/s53/s48/s32/s109/s65/s48/s46/s55/s53/s32/s109/s65\n/s49/s51/s53 /s49/s56/s48\n/s32\n/s32/s32\n/s49/s51/s53 /s49/s56/s48\n/s32\n/s32/s32\n/s73/s32 /s124/s124/s32/s91/s49/s49/s48/s93/s32\n/s40/s52/s41\n/s72/s32\n/s40/s51/s41\n/s72/s32\n/s40/s50/s41\n/s72\n/s32/s32\n/s32/s32\n/s40/s49/s41\n/s72\n/s99/s41\n/s32/s32/s82 \n/s120/s121/s32/s40 /s41\n/s32/s40/s100/s101/s103/s41\n/s32/s32/s32\n/s32/s32/s32\n/s72/s32/s40/s100/s101/s103/s41/s73/s32 /s124/s124/s32/s91/s49/s49/s48/s93/s48/s46/s55/s32/s109/s65\n/s48/s46/s55/s32/s109/s65\nFIG. 2: Dependence of transverse anisotropic magne-\ntoresistance on current and field orientation a,b)Trans-\nverse anisotropic magnetoresistance Rxyis plotted as a func-\ntion of external field direction ϕHforH= 10 mT and current\nI=±0.7 mA in Sample A. The angles ϕ(i)\nHmark magnetiza-\ntion switchings. In c) magnetization switching between [ ¯100]\nand [0¯10] easy axes is plotted for several values of the current.\n∆ϕ(i)\nH(I) =ϕ(i)\nH(I)−ϕ(i)\nH(−I). Specifically, for I||[1¯10]\nthe switching of magnetization [010] →[¯100] occurs for\nI= +0.7 mA at smaller ϕ(1)\nHthan for I=−0.7 mA,\n∆ϕ(1)\nH<0. For the [0 ¯10]→[100] magnetization switch-\ning, the I-dependence of switching angle is reversed,\n∆ϕ(3)\nH>0. There is no measurable difference in switch-\ning angle for the [ ¯100]→[0¯10] and [100] →[010] tran-\nsitions (∆ ϕ(2,4)\nH≈0). When the current is rotated by\n90◦(I||[110]), we observe ∆ ϕ(2)\nH>0, ∆ϕ(4)\nH<0, and\n∆ϕ(1,3)\nH≈0. In Fig. (c) we show that ∆ ϕ(2)\nH(I) decreases\nas current decreases and drops below experimental reso-\nlution of 0 .5◦atI <50µA. Similar data is obtained for\nSample B, see Fig. S4 in Supplementary Information.\nThe data can be qualitatively understood if we con-\nsider an additional current-induced effective magnetic\nfieldHeff, as shown schematically in Fig. b. When an\nexternal field Haligns the magnetization along one of\nthe hard axes, a small perpendicular field can initiate\nmagnetization switching. For I||[110], the effective field\nHeff||[¯110] aids the [100] →[010] magnetization switch-\ning, while it hinders the [ ¯100]→[0¯10] switching. For\nϕ(1)\nH≈90◦andϕ(3)\nH≈270◦, where [010] →[¯100] and\n[0¯10]→[100] magnetization transitions occur, Heff||H\ndoes not affect the transition angle, ∆ ϕ(2,4)\nH= 0. For\nI||[1¯10] the direction of the field Heff||[110] is reversed\nrelative to the direction of the current, compared to the\nI||[110] case. The symmetry of the measured Heffwith\nrespect to Icoincides with the unique symmetry of the\nstrain-related SO field, Fig. (c).\nThe dependence of ∆ ϕ(i)\nHon various magnetic fields3\n/s48/s46/s51 /s48/s46/s54/s45/s49/s48/s45/s53/s48/s53/s49/s48\n/s48/s46/s51 /s48/s46/s54 /s48/s46/s48 /s48/s46/s53 /s49/s46/s48 /s49/s46/s53/s48/s46/s48/s48/s46/s51/s48/s46/s54/s48/s46/s57\n/s32\n/s40/s50/s44/s52/s41\n/s32/s32/s72\n/s32\n/s40/s52/s41\n/s72/s32\n/s40/s50/s41\n/s72\n/s32/s72 /s32/s40/s100/s101/s103/s41/s32/s32\n/s73/s32 /s124/s124/s32/s91/s49/s49/s48/s93/s32/s40/s109/s65/s41/s32\n/s40/s49/s44/s51/s41\n/s32/s32/s72/s32\n/s40/s50/s41\n/s72/s40/s50/s41\n/s72\n/s72/s101/s102/s102\n/s40/s45/s73/s41/s73/s32 /s124/s124/s32/s91/s49/s49/s48/s93/s32/s40/s109/s65/s41\n/s73/s32 /s124/s124/s32/s91/s49/s49 /s48/s93/s32/s40/s109/s65/s41\n/s73\n/s40/s49/s41\n/s72/s72/s72/s101/s102/s102\n/s40/s43/s73/s41/s40/s49/s41\n/s72\n/s100/s41/s97/s41\n/s98/s41/s32\n/s40/s49/s41\n/s72/s40/s51/s41\n/s72\n/s73/s32 /s124/s124/s32/s91/s49/s49 /s48/s93/s32/s40/s109/s65/s41/s99/s41/s32/s72/s115/s111\n/s177/s72/s79/s101\n/s32/s72/s115/s111\n/s72/s32/s101/s102/s102\n/s32/s32/s40/s109 /s84/s41\n/s83/s97/s109/s112/s108/s101/s32/s66/s32\n/s60/s106/s62/s32/s120/s32/s49/s48/s54\n/s32/s40/s65/s47/s99/s109/s50\n/s41/s83/s97/s109/s112/s108/s101/s32/s65\nFIG. 3:Determination of current-induced effective SO\nmagnetic field. a,b) Difference in switching angles for oppo-\nsite current directions ∆ ϕ(i)\nHas a function of Iare plotted for\nSample Afor differentexternal fields Hfor orthogonal current\ndirections. Inc)themeasured effectivefield Heff=Hso±HOe\nis plotted as a function of average current density /angbracketleftj/angbracketrightfor Sam-\npleA(triangles) andSampleB(diamonds). Ind)weschemat-\nically show different angles involved in determining Heff:ϕH\nis the angle between current Iand external magnetic field\nH; ∆ϕHis the angle between total fields H+Heff(+I) and\nH+Heff(−I), andθis the angle between IandHeff(+I).\nand current orientations is summarized in Fig. 3(a,b).\nAssuming that the angle of magnetization switching de-\npends only on the total field Heff+H, we can extract\nthe magnitude Heffand angle θ=/negationslashIHefffrom the mea-\nsured ∆ϕ(i)\nH, thus reconstructing the whole vector Heff.\nFollowing a geometrical construction depicted in Fig. 3d\nand taking into account that ∆ ϕ(i)\nHis small, we find that\nHeff≈Hsin(∆ϕ(i)\nH/2)/sin(θ−ϕ(i)\nH),\nandθcan be found from the comparison of switching at\ntwo angles. We find that θ≈90◦, orHeff⊥IforI∝ba∇dbl[110]\nandI∝ba∇dbl[1¯10]. In order to further test our procedure we\nperformed similar experiments with small current I= 10\nµA but constant additional magnetic field δH⊥Iplaying\nthe role of Heff. The measured δH(∆ϕH) coincides with\nthe applied δHwithin the precisionofourmeasurements.\n(see Fig. S5 of Supplementary Information).\nIn Fig. 3(c), Heffis plotted as a function of the av-\nerage current density ∝angb∇acketleftj∝angb∇acket∇ightfor both samples. There is a\nsmall difference in the Heffvs∝angb∇acketleftj∝angb∇acket∇ightdependence for I∝ba∇dbl[110]\nandI∝ba∇dbl[1¯10]. The difference can be explained by con-\nsidering the current-induced Oersted field HOe∝Iin\nthe metal contacts. The Oersted field is localized under\nthe pads, which constitutes only 7% (2.5%) of the total\narea for samples A (B). The Oersted field has the sym-\nmetry of the field depicted in Fig. (d), and is added to\nor subtracted from the SO field, depending on the cur-/s48 /s50/s48/s48 /s52/s48/s48 /s54/s48/s48 /s56/s48/s48/s45/s53/s48/s53/s45/s49 /s48 /s49\n/s45/s49/s48/s49/s45/s49/s46/s48 /s45/s48/s46/s53 /s48/s46/s48 /s48/s46/s53 /s49/s46/s48\n/s45/s53/s48/s53\n/s52/s53 /s57/s48/s45/s53/s48/s53\n/s98/s41/s97/s41\n/s32/s82 \n/s120/s121/s32/s40 /s41\n/s116/s105/s109/s101/s32/s40/s115/s101/s99/s111/s110/s100/s115/s41/s99/s41/s60/s106/s62/s32/s183/s49/s48/s54\n/s32/s40/s65/s47/s99/s109/s50\n/s41/s77/s73/s32\n/s77/s73/s73/s32/s40/s109 /s65/s41\n/s32 /s32/s32/s73/s32/s40/s109/s65/s41\n/s72/s32/s40/s100/s101/s103/s41\n/s32/s32/s82 \n/s120/s121/s32/s40 /s41\n/s77/s73/s77/s73\nFIG. 4: Current-induced reversible magnetization\nswitching a)ϕH-dependence of Rxynear the [010] →[¯100]\nmagnetization switchingis plottedfor I=±0.7mAinSample\nA forI/bardbl[1¯10]. b)Rxyshows hysteresis as a function of current\nfor a fixed field H= 6 mT applied at ϕH= 72◦. c) Mag-\nnetization switches between [010] and [ ¯100] directions when\nalternating ±1.0 mA current pulses are applied. The pulses\nhave 100ms duration and are shown schematically above the\ndata curve. Rxyis measured with I= 10µA.\nrent direction. Thus, Heff=Hso+HOeforI∝ba∇dbl[110] and\nHeff=Hso−HOeforI∝ba∇dbl[1¯10]. Weestimatethefieldstobe\nas high as 0.6 mT under the contacts at I= 1 mA, which\ncorrespondsto HOe≈0.04mT(0.015mT) averagedover\nthe sample area for samples A (B). These estimates are\nreasonably consistent with the measured values of 0.07\nmT (0.03 mT). Finally, we determine Hsoas an average\nofHeffbetween the two current directions. The SO field\ndepends linearly on j, as expected for strain-related SO\ninteractions: dHso/dj= 0.53·10−9and 0.23·10−9T\ncm2/A for samples A and B respectively.\nWe now compare the experimentally measured Hso\nwith theoretically calculated effective SO field. In\n(Ga,Mn)As, the only term allowed by symmetry that\ngenerates HsolinearintheelectriccurrentistheΩ εterm,\nwhich results in the directional dependence of Hsoonj\nprecisely as observed in experiment. As for the mag-\nnitude of Hso, for three-dimensional J= 3/2 holes we\nobtain\nHso(E) =eC∆ε\ng∗µB(−38nhτh+18nlτl)\n217(nh+nl)·(Ex,−Ey,0),\nwhereEis the electric field, g∗is the Luttinger Land´ e\nfactor for holes, µBis the Bohr magneton, and nh,land\nτh,lare densities and lifetimes for the heavy (h) and light\n(l) holes. Detailed derivation of Hsois given in Sup-4\nplementary Information. Using this result, we estimate\ndHso/dj= 0.6·10−9T cm2/A assuming nh=n≫nl\nandτh=mh/(e2ρn), where ρis the resistivity mea-\nsured experimentally, and using ∆ ε= 10−3,n= 2·1020\ncm−3. The agreement between theory and experiment\nis excellent. It is important to note, though, that we\nused GaAs band parameters[25] mh= 0.4m0, wherem0\nis the free electron mass, g∗= 1.2 andC= 2.1 eV·˚A.\nWhile the corresponding parameters for (Ga,Mn)As are\nnot known, the use of GaAs parameters appears reason-\nable. We note, for example, that GaAs parameters ad-\nequately described tunnelling anisotropic magnetoresis-\ntance in recent experiments[26].\nFinally, we demonstrate that the current-induced ef-\nfective SO field Hsois sufficient to reversibly manipu-\nlate the direction of magnetization. In Fig. 4a we plot\ntheϕH-dependence of Rxyfor Sample A, showing the\n[010]→[¯100] magnetization switching. If we fix H= 6\nmT atϕH= 72◦,Rxyforms a hysteresis loop as cur-\nrent is swept between ±1 mA.Rxyis changing between\n±5 Ω, indicating that Mis switching between [010] and\n[¯100] directions. Short (100 msec) 1 mA current pulses of\nalternating polarity are sufficient to permanently rotate\nthe direction of magnetization. The device thus performs\nas a non-volatile memory cell, with two states encoded\nin the magnetization direction, the direction being con-\ntrolled by the unpolarized current passing through the\ndevice. The device can be potentially operated as a 4-\nstate memory cell if both [110] and [ ¯110] directions can\nbe used to inject current. We find that we can reversibly\nswitch the magnetization with currents as low as 0.5 mA\n(current densities 7 ·105A/cm2), an order of magnitude\nsmaller than by polarized current injection in ferromag-\nnetic metals[1, 2, 3], and just a few times larger than\nby externallypolarizedcurrentinjection in ferromagnetic\nsemiconductors[4].\nMethods\nThe (Ga,Mn)As wafers were grown by molecular beam\nepitaxy at 265◦C and subsequently annealed at 280\n◦C for 1 hour in nitrogen atmosphere. Sample A was\nfabricated from 15-nm thick epilayer with 6%Mn, and\nSample B from 10-nm epilayer with 7% Mn. Both\nwafers have Curie temperature Tc≈80 K. The de-\nvices were patterned into 6 and 10 µm-diameter cir-\ncular islands in order to decrease domain pinning.\nCr/Zn/Au (5nm/10nm/300nm) Ohmic contacts were\nthermally evaporated. All measurementswere performed\nin a variable temperature cryostat at T= 40 K for Sam-\nple A and at 25 K for Sample B, well below the temper-\nature of (Ga,Mn)As-specific cubic-to-uniaxial magnetic\nanisotropy transitions[27], which has been measured to\nbe at 60 K and 50 K for the two wafers. Temperature\nrise for the largest currents used in the reported experi-\nments was measured to be <3 K.\nTransverse anisotropic magnetoresistance Rxy=\nVy/Ixis measured using the four-probe technique, whichinsures that possible interfacial resistances, e.g., those\nrelated to the antiferromagnetic ordering in the Cr wet-\nting layer[28], do not contribute to the measured Rxy.\nThe DC current Ixwas applied either along [110] (con-\ntacts 4-8 in Fig. a) or along[1 ¯10] (contacts 2-6) direction.\nTransverse voltage was measured in the Hall configura-\ntion, e.g., between contacts 2-6 for Ix∝ba∇dbl[110]. To ensure\nuniform magnetization of the island, magnetic field was\nramped to 0.5 T after adjusting of the current at the\nbeginning of each field rotation scan. We monitor Vx\nbetween different contact sets (e.g. 1-7, 4-6 and 3-5) to\nconfirm the uniformity of magnetization within the is-\nland.\nIn order to determine the direction of magnetization\nM, we use the dependence of Rxyon magnetization[29]:\nRxy= ∆ρsinϕMcosϕM,\nwhere∆ρ=ρ/bardbl−ρ⊥,ρ/bardbl< ρ⊥aretheresistivitiesformag-\nnetization oriented parallel and perpendicular to the cur-\nrent, and ϕM=/negationslashMIis an angle between magnetization\nand current. In a circular sample the current distribu-\ntion is non-uniform and the angle between the magneti-\nzationandthelocalcurrentdensityvariesthroughoutthe\nsample. However, the resulting transverse AMR depends\nonly onϕM. For the current-to-current-density conver-\nsion,wemodeloursampleasaperfectdiscwithtwopoint\ncontacts across the diameter. The average current den-\nsityinthedirectionofcurrentinjectionis ∝angb∇acketleftj∝angb∇acket∇ight= 2I/(πad),\nwhereais the disk radius and dis the (Ga,Mn)As layer\nthickness. In a real sample the length of contact over-\nlap with (Ga,Mn)As insures that jchanges by less than\nfactor of 3 throughout the sample. A detailed discussion\nof the current distribution and of measurements of Joule\nheating can be found in Supplementary Information.\n∗These authors contributed equally to the project\n†To whom correspondence should be addressed. E-mail:\nleonid@purdue.edu\n[1] Slonczewski, J. C. J. Magn. Magn. Mater. 159, 1 – 7\n(1996).\n[2] Berger, L. Phys. Rev. B 54(13), 9353 – 8 (1996).\n[3] Myers, E. B., Ralph, D. C., Katine, J. A., Louie, R. N.,\nand Buhrman, R. A. Science285, 867 – 70 (1999).\n[4] Chiba, D., Sato, Y., Kita, T., Matsukura, F., and Ohno,\nH.Phys. Rev. Lett. 93(21), 216602 (2004).\n[5] Aronov, A. G. and Lyanda-Geller, Y. B. JETP Lett. 50,\n431 – 4 (1989).\n[6] Edelstein, V.M. Solid State Commun. 73, 233 –5(1990).\n[7] Kalevich, V. K. and Korenev, V. L. JETP Lett. 52, 230\n– 5 (1990).\n[8] Kato, Y., Myers, R. C., Gossard, A. C., and Awschalom,\nD. D.Nature427, 50–53 (2004).\n[9] Silov, A.Y., Blajnov, P.A., Wolter, J. H., Hey,R., Ploog ,\nK. H., and Averkiev, N. S. Appl. Phys. Lett. 85, 5929–\n5931 (2004).5\n[10] Ganichev, S. D. Int. J of Mod. Phys. B 22(1-2), 1–26\n(2008).\n[11] Meier, L., Salis, G., Shorubalko, I., Gini, E., Schoen, S.,\nand Ensslin, K. Nat. Phys. 3, 650–654 (2007).\n[12] Dresselhaus, G. Phys. Rev. 100, 580 – 586 (1955).\n[13] Bir, G. L. and Pikus, G. E. Symmetry and strain-induced\neffects in semiconductors . Wiley, New York, (1974).\n[14] Bychkov, Y. A. and Rashba, E. I. J. Phys. C: Solid State\nPhys.17, 6039–6045 (1984).\n[15] Aronov, A. G., Lyanda-Geller, Y. B., and Pikus, G. E.\nSov. Phys. JETP 73, 537 – 41 (1991).\n[16] Golub, L. E., Ganichev, S. D., Danilov, S. N., Schnei-\nder, P., Bel’kov, V. V., Wegscheider, W., Weiss, D., and\nPrettl, W. J. Magn. Magn. Mater. 300, 127 – 31 (2006).\n[17] Wilamowski, Z., Malissa, H., Schaffler, F., and Jantsch,\nW.Phys. Rev. Lett. 98, 187203 (2007).\n[18] Ohno, H., Shen, A., Matsukura, F., Oiwa, A., Endo, A.,\nKatsumoto, S., and Iye, Y. Appl. Phys. Lett. 69, 363 –\n5 (1996).\n[19] Ohno, H. Science281, 951 – 6 (1998).\n[20] Dietl, T., Ohno, H., Matsukura, F., Cibert, J., and Fer-\nrand, D. Science287, 1019 – 22 (2000).\n[21] Berciu, M. and Bhatt, R. N. Phys. Rev. Lett. 87, 107203(2001).\n[22] Welp, U., Vlasko-Vlasov, V. K., Liu, X., Furdyna, J. K.,\nand Wojtowicz, T. Phys. Rev. Lett. 90, 167206 (2003).\n[23] Liu, X., Sasaki, Y., and Furdyna, J. K. Phys. Rev. B 67,\n205204 (2003).\n[24] Overby, M., Chernyshov, A., Rokhinson, L. P., Liu, X.,\nand Furdyna, J. K. Appl. Phys. Lett. 92, 192501 (2008).\n[25] Chantis, A. N., Cardona, M., Christensen, N. E., Smith,\nD. L., van Schilfgaarde, M., Kotani, T., Svane, A., and\nAlbers, R. C. Pys. Rev. B 78(7), 075208 AUG (2008).\n[26] Elsen, M., Jaffres, H., Mattana, R., Tran, M., George, J. -\nM., Miard, A., and Lemaitre, A. Phys. Rev. Lett. 99(12),\n127203 SEP 21 (2007).\n[27] Chiba, D., Sawicki, M., Nishitani, Y., Nakatani, Y., Ma t-\nsukura, F., and Ohno, H. Nature455, 515–518 (2008).\n[28] Smit, P. andAlberts, H. L. J. Appl. Phys. 63(8), 3609–10\n(1988).\n[29] Tang, H. X., Kawakami, R. K., Awschalom, D. D., and\nRoukes, M. L. Phys. Rev. Lett. 90, 107201 (2003).\n[30] Rokhinson, L. P., Lyanda-Geller, Y., Ge, Z., Shen, S.,\nLiu, X., Dobrowolska, M., and Furdyna, J. K. Phys.\nRev. B76, 161201 (2007).6\nSupplementary Information\nEvidence for the reversible control of magnetization in a fe rromagnetic material via spin-orbit\nmagnetic field\nA. Chernyshov, M. Overby, X. Liu, J. K. Furdyna, Y. Lyanda-Ge ller, and L. P. Rokhinson\nJOULE HEATING\n(Ga,Mn)As is a magnetic semiconductor with strong temperature de pendence of resistivity, see Fig. 5(a). The\nenhancement ofresistivityat 80Kis due to the enhancementofspin scatteringin the vicinity ofthe Curie temperature\nTC. Inelastic scattering length in these materials is just a few tenths o f nm, and we expect holes to be in thermal\nequilibrium with the lattice[30]. Thus resistivity can be used to measure the temperature of the sample.\n/s48/s46/s48 /s48/s46/s51 /s48/s46/s54/s49/s46/s55/s48/s49/s46/s55/s49/s49/s46/s55/s50/s97/s41\n/s100/s41 /s99/s41/s32/s32\n/s32/s43/s32/s73\n/s32/s45/s32/s73/s82 \n/s120/s120/s32/s40/s107 /s41\n/s73/s32/s40/s109/s65/s41/s84/s32/s61/s32/s52/s48/s32/s75\n/s98/s41\n/s52/s48 /s52/s49 /s52/s50 /s52/s51/s73\n/s97/s99/s32/s61/s32/s53/s48/s32/s110/s65\n/s32\n/s84/s32/s40/s75/s41/s48/s46/s48 /s48/s46/s51 /s48/s46/s54/s48/s49/s50/s51/s84/s32/s40/s75/s41/s32/s32\n/s73/s32/s40/s109/s65/s41/s32/s43/s32/s73\n/s32/s32/s45/s32/s73/s84/s32/s61/s32/s52/s48/s32/s75/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48 /s51/s48/s48/s50/s46/s48/s50/s46/s53/s51/s46/s48/s51/s46/s53\n/s32/s32/s32/s40/s109 /s32/s99/s109 /s41\n/s84/s32/s40/s75/s41/s83/s97/s109/s112/s108/s101/s32/s65\n/s73\n/s97/s99/s32/s61/s32/s53/s48/s32/s110/s65\nFIG. 5: Current-induced heating a) Temperature dependence of resistivity for sample A; b) cu rrent and c) temperature\ndependence of sample resistance in the vicinity of 40 K; d) sa mple heating as a function of dc current.\nIn Fig. 5(b,c) we plot temperature and current dependences of th e sample resistance in the vicinity of 40 K. This\ndata is combined in (d), where the sample temperature change ∆ Tdue to Joule heating is plotted as a function of dc\ncurrent. The maximum temperature rise does not exceed 3 K at I= 0.7 mA in our experiments. This small heating\nensures that the sample temperature stays well below the Curie te mperature ( ≈80 K) and the (Ga,Mn)-specific\ncubic-to-uniaxial magnetic anisotropy transition ( ≈60 K for sample A and ≈50 K for sample B) when experiments\nare performed at 40 K and 25 K for samples A and B, respectively. Ob servation of different angles for magnetization\nswitching for + Iand−I(Fig. 2) further confirms that heating is not responsible for the re ported effects (Joule heating\nis∝J2and does not depend on the current direction).\nCURRENT DISTRIBUTION IN CIRCULAR SAMPLES\nMagnetization-dependent scattering in (Ga,Mn)As results in an anis otropic correction to the resistivity tensor ˆ ρ\nwhich depends on the angle ϕmbetween magnetization Mand local current density j[29]:\nρxx=ρ⊥+(ρ/bardbl−ρ⊥)cos2(ϕm),\nρxy= (ρ/bardbl−ρ⊥)sin(ϕm)cos(ϕm), (1)7\nwhereρ/bardbl(ρ⊥) are the resistivities for j||M(j⊥M), and we assumed that both jandMlie within the plane of the\nsample. Theoff-diagonalresistivity(transverseanisotropicmagn etoresistance) ρxycanbenon-zeroevenintheabsence\nof the external magnetic field. The difference ( ρ||−ρ⊥)/ρ⊥≈0.01 and we first calculate the local potential φ0(x,y)\ninside the sample by approximating it as a disk of radius aand thickness dwith isotropic resistivity ρ0= (ρ/bardbl+ρ⊥)/2:\nφ0=ρ0I\nπdln/bracketleftBig(a−x)2+y2\n(a+x)2+y2/bracketrightBig\n, (2)\nwhere current Iis injected along the ˆ x-axis. Current density j=∇φ0/ρ0is plotted in Fig. 6(a). Metal contacts have\na radius of ≈0.5µm in our samples, which limits the current density near the current inj ection regions. Integrating\njover the sample area we find average current density\n∝angb∇acketleftjx∝angb∇acket∇ight=2I\nπad,∝angb∇acketleftjy∝angb∇acket∇ight= 0. (3)\n+0.1 \n-0.1 Hj\n⊥\nHj\n⊥\n(mT)\na) c) jM\nφM\n-φj\nx0y\nx\nb) a0\n-a0xy\nI I\nFIG. 6: Current distribution a) Vector plot of local current density j(x,y) distribution in the sample; b) angles between\nj(x,y), magnetization Mand current I/bardblˆxare defined; c) Color map plot of Oersted field ( Hj\n⊥) distribution in a disk-shaped\nsample.\nWe find the transverse voltage Vyas a correction to the φ0potential due to the anisotropic resistivity ρ||−ρ⊥∝negationslash= 0:\nVy(x0) =/integraldisplaya0\n−a0/bracketleftbig\n−ρxy·jx(y)+ρxx·jy(y)/bracketrightbig\ndy. (4)\nThe current distribution is non-uniform, and the local electric field d epends on the total angle ϕm=ϕM−ϕj, where\nϕM=/hatwidestMIandϕj=/hatwidejI, see Fig. 6(b). This integral can be evaluated analytically, and the t ransverse anisotropic\nmagnetoresistance (AMR) Rxyis found to be the same as for an isotropic current flow, independen t of the distance\nx0of the voltage contacts from the center of the disk:\nRxy=Vy/I= (ρ/bardbl−ρ⊥)cos(ϕM)sin(ϕM). (5)\nThe magnetization angle ϕMcan therefore be directly calculated from the measured transver se resistance Rxy.\nCURRENT-GENERATED OERSTED MAGNETIC FIELDS\nIn this section we estimate conventional current-generate magn etic fields in our device that are not related to spin-\norbit interactions. There are two contributions to the Oersted ma gnetic fields: a magnetic field due to non-uniform\ncurrent distribution within the sample, and a field generated by high c urrents in the vicinity of the metal contacts.\nWe can calculate the Oersted field inside (Ga,Mn)As by using the Biot-S avart formula:\nH=µ0\n4π/integraldisplayj׈ r\nr2dV, (6)8\nspin-orbit field contact Oersted field ] 110 [\n[110]jxjy\n] 110 [\n[110]jxjy\nb) c)Hso HOe \nI(Ga,Mn)As Contact \nHOe \na) \nFIG. 7: Oersted field a) schematic illustration of the origin of the in-plane Oers ted field HOeunder gold contact pads; b,c)\nsymmetry of HsoandHOefields.\nwhereµ0is the permeability of free space, and the integral is taken over the volume of the disk. The most significant\nHj\n⊥normal component of the field is shown in Fig. 3(c). The largest Hj\n⊥≤1 Oe, which is negligible compared to the\n2000 Oe anisotropy field that keeps the magnetization in-plane.\nThe second contribution to the Oersted field originates from conta ct pads, see Fig. 7. The conductivity of gold\ncontacts is much higher that of (Ga,Mn)As, and the current flows p redominantly through the metal within contact\nregions, thus generating both in-plane ( HOe\n/bardbl) and out-of plane ( HOe\n⊥) magnetic fields in (Ga,Mn)As underneath and\nat the edges of the contact pads. The maximum value of the field can be estimated as HOe\n⊥≈HOe\n||=µ0I/2w, where\nIis the total current and w= 1µm is the width of the contact pad. This field can be as high as 6 Oe for I= 1 mA.\nThe field is localized under the pads, which constitute only 1/12th of t he sample area.\nTheHOe\n⊥field does not induce in-plane magnetization rotation. The HOe\n/bardblfield and the effective spin-orbit field have\ndifferentsymmetrieswithrespecttothe currentrotation, seeFig .3(b,c), andthuscanbe experimentallydistinguished.\nThe two fields point in the same direction for I||[110], but in the opposite direction for the current rotated by 90◦,\nI||[1¯10]. Experimentally, we observe an effective field which corresponds to the symmetry of the SO effective field.\nHowever, there is a small difference in the slopes of ∆ φHvsIcurves for the two orthogonal current directions,\nFig. 3(a,b), because the contact field is added to the SO field for I||[110] and subtracted from SO field for I||[1¯10].\nBoth fields ∝I. From the ratio of the slopes ( ≈1.2) we can calculate the strength of the contact field, HOe\n⊥≈0.1Hso.\nThis experimentally found ratio is consistent with the above estimate if we average the contact Oersted field over the\nsample area.\nDEPENDENCE OF TRANSVERSE ANISOTROPIC MAGNETORESISTANCE O N CURRENT AND\nFIELD ORIENTATION\n/s45/s49/s48/s48/s49/s48\n/s56/s48 /s57/s48 /s49/s48/s48/s45/s49/s48/s48/s49/s48\n/s49/s57/s48 /s50/s48/s48 /s50/s53/s48 /s50/s54/s48 /s51/s54/s48 /s51/s55/s48/s32\n/s32/s32/s82 \n/s120/s121/s32/s40 /s41\n/s73/s32 /s124/s124/s32/s91/s49/s49 /s48/s93\n/s73/s32 /s124/s124/s32/s91/s49/s49/s48/s93/s48/s46/s55/s109/s65\n/s48/s46/s55/s109/s65/s97/s41\n/s32/s32/s32\n/s32\n/s32/s32/s32\n/s32/s32/s32\n/s32/s82 \n/s120/s121/s32/s40 /s41/s98/s41\n/s32\n/s72/s32/s40/s100/s101/s103/s41/s32 /s32/s32/s32\n/s32/s32\n/s32/s32/s32\n/s32\nFIG. 8: Dependence of transverse anisotropic magnetoresistance o n current and field orientation for Sample\nB.Transverse anisotropic magnetoresistance Rxyis plotted for current I||[1¯10] (a) and I||[110] (b) for I=±0.75 mA with\nconstant magnetic field H= 20 mT as a function of field angle ϕH.\nIn order to test the procedure of the effective field mapping, we pe rformed control experiments where a small9\nconstant external magnetic field δH⊥Iwas playing the role of spin-orbit field. In these experiments the cur rent was\nreduced to I= 10µA. The results, shown in Fig. 9, are quantitatively similar to the effect of the spin-orbit field.\n/s45/s49/s48/s48/s49/s48\n/s32/s82 \n/s120/s121/s32/s40 /s41/s32\n/s32/s97/s41\n/s32/s32/s32\n/s32\n/s32/s32/s32\n/s72/s32/s40/s100/s101/s103/s41/s32 /s72/s32/s61/s32/s48\n/s32 /s72/s32/s61/s32/s48/s46/s56/s32/s109/s84\n/s32/s32/s32\n/s32\n/s49/s56/s48\n/s32\n/s32/s32\n/s52/s53 /s57/s48/s45/s49/s48/s48/s49/s48/s82 \n/s120/s121/s32/s40 /s41\n/s32\n/s32/s32\n/s98/s41\n/s50/s50/s53 /s50/s55/s48/s32/s73/s32/s61/s32 /s48/s46/s53/s32/s109/s65\n/s32/s73/s32/s61/s32 /s48/s46/s53/s32/s109/s65\n/s32\n/s32/s32\n/s51/s49/s53 /s51/s54/s48\n/s32\n/s32/s32\nFIG. 9: Control experiment with additional external field a)Rxyis plotted for Sample A with Htotal=δH+H, where\nδH⊥IandI= 10µA,δH= 0,0.8 mT. For comparison, in b) similar data are plotted for δH= 0 but I=±0.5 mA.\nCALCULATION OF THE EFFECTIVE SPIN-ORBIT FIELD INDUCED BY TH E ELECTRIC CURRENT\nManipulation of localized spins, electronic, nuclear or ionic, can be ach ieved via manipulation of free carrier spins.\nThe free carrier spins can be manipulated by the external magnetic field, by the Oersted magnetic field of the\ncurrent, and by the electric current via intrinsic spin-orbit interac tions. The intrinsic spin-orbit interactions arise in\ncrystalline systems, in which axial vectors, such as spin polarization , and polar vectors, such as the electric current,\nbehave equivalently with respect to the symmetry trasformations of a crystal. The crystal symmetry then allows\nthe transformation of the electric current into a spin polarization o f charge carriers. In this work, Mn ions of the\nferromagnetic semiconductor (Ga,Mn)As, and thus its ferromagn etic properties, are affected by the electric current\nvia the intrinsic spin-orbit interactions.\nIn (Ga,Mn)As, charge carriers are holes with an angular momentum J= 3/2. In contrast to electron systems, the\nhole system is defined by a very strong coupling of the total angular momentum Jto the hole momentum p, which\nincludes both terms quadratic in pand independent of p. These terms are quadratic in J, and they are not present\nfor electrons with spin 1/2. The Luttinger-Pikus Hamiltonian quadra tic inJis[13]\nHh=A0p2+A1/summationdisplay\niJ2\nip2\ni+A2/summationdisplay\ni,j/negationslash=iJiJjpipj+B1/summationdisplay\niεiiJ2\ni+B2/summationdisplay\ni,j/negationslash=iJiJjεij, (7)\nwherei,j=x,y,z. Despite the presence of a very strong spin-orbit coupling, which le ads to the spectral splitting of\nholes into two pairs of states, this Hamiltonian on its own cannot resu lt in a spin polarization of holes induced by\nthe electric current. Terms capable of generating spin polarization in systems characterized by the absence of center\nof symmetry in the crystal and by a corresponding additional lower ing of the crystalline symmetry in the presence of\nstrain, read\nH′=γv/summationdisplay\niJipi(p2\ni+1−p2\ni+2)+C/summationdisplay\ni[Jipi(εi+1,i+1−εi+2,i+2)+(Jipi+1−Ji+1pi)εi,i+1], (8)\nwhere cyclic permutation of indices is implied. The first term is cubic in th e hole momentum, and it can lead only\nto the polarization of hole spins cubic in the electric current (and only when the current direction is away from the\nhigh symmetry axes). For effects linear in electric current this term is only relevant insofar as it contributes to the\nspin relaxation of the holes. The third term contains off-diagonal co mponents of the strain tensor, and is negligible\nin (Ga,Mn)As crystals under study. In this system, strain originate s from doping by Mn ions, and constitutes\ntension along the growth axis z||[001] defined by the component εzzand ∆ε=εzz−εxx=εzz−εyy. Thus only\nthe second term results in a current-induced spin polarization. The symmetry of the corresponding effective field,\nΩ(p) =C∆ε(px,−py,0), depends markedly on the crystallographic orientation. When an electric field is applied, the\ndirection of the generated hole spin polarization with respect to the orientation of the electric current is the same as10\nthe direction of the SO effective field with respect to the hole moment um. Such peculiar symmetry differs from the\nsymmetry of the Oersted magnetic field, and thus allows one to distin guish between these effects.\nWe consider now the approximation linear in strain, when only the stra in-dependent term proportional to Cis\ntaken into account, and strain-dependent terms in Hhare omitted. In this case the hole spectrum given by Hhsplits\ninto heavy ( h) and light ( l) hole branches. The mechanism of generation a spin polarization by t he effective SO\nfield in the presence of an electric current is simply a shift in the distrib ution functions for heavy and light holes in\nmomentum space. In contrast low symmetry electron systems[15 ], where spin polarization is associated entirely with\nthe relaxation of spins, in case of holes the spin relaxation occurs on the time scale of momentum relaxation and plays\nno role in the current-induced spin polarization. At low temperature s the hole angular momentum density is given by\n∝angb∇acketleftJ(E)\ni∝angb∇acket∇ight= (−1)ieEiC∆ε\nEF/parenleftBig−38\n35nhτh+18\n35nlτl/parenrightBig\n, (9)\nwherei= 1,2 correspond to principal axes xandy, characteristic times τh,lare defined by mobilities of holes in the\ncorresponding bands, and nh(l)are densities of holes in these bands. At room temperatures EFin the denominator\nis to be replaced by 3 /2kBT,Tbeing the lattice temperature and kBthe Boltzman constant. Estimates show that\nthe negative term in brackets of Eq. 9 is dominant.\nWe note that in the case of very strong deformations the spin relax ation of holes occurs on the times scale longer\nthan that of momentum relaxation. Then simple shift of hole distribut ion functions in momentum space is no longer\nsufficient for generating spin polarization by current, and the mech anism of the effect becomes analogous to that for\nelectrons[15]. We will present the results for hole spin polarization ge nerated by electric current at arbitrary value of\nstrain elsewhere.\nThe spin polarization given by Eq. 9 leads to an effective magnetic field a cting on the Mn ions. In order to calculate\nwhat external magnetic field would result in the same polarization as t hat generated by the current, we calculate the\naverage spin density induced by an external magnetic field:\n∝angb∇acketleftJ(H)\ni∝angb∇acket∇ight=31g∗µBH(nh+nl)\n5EF(10)\nThe ratio of polarizations ∝angb∇acketleftJ(E)\ni∝angb∇acket∇ightand∝angb∇acketleftJ(H)\ni∝angb∇acket∇ightgives the electric field polarization measured in units of magnetic field.\nWe note that while the SO field affects Mn ionsonly viathe exchangeinte raction, the Oerstedorthe external magnetic\nfield also acts on the ions directly. However, the magnitude of the ex change interaction, A=−5 meV is quite large,\nmaking the exchange interaction dominant. We will therefore omit th e discussion of direct polarization of Mn by\nexternal fields."    },    {        "title": "0901.2812v1.Toroidal_moments_as_indicator_for_magneto_electric_coupling__the_case_of_BiFeO_3_versus_FeTiO_3.pdf",        "content": "arXiv:0901.2812v1  [cond-mat.mtrl-sci]  19 Jan 2009Toroidal moments as indicator for magneto-electric coupli ng: the case of BiFeO 3\nversus FeTiO 3\nClaude Ederer\nSchool of Physics, Trinity College, Dublin 2, Ireland∗\n(Dated: October 31, 2018)\nIn this paper we present an analysis of the magnetic toroidal moment and its relation to the\nvarious structural modes in R3c-distorted perovskites with magnetic cations on either the perovskite\nAorBsite. We evaluate the toroidal moment in the limit of localiz ed magnetic moments and\nshow that the full magnetic symmetry can be taken into accoun t by considering small induced\nmagnetic moments on the oxygen sites. Our results give a tran sparent picture of the possible\ncoupling between magnetization, electric polarization, a nd toroidal moment, thereby highlighting\nthe different roles played by the various structural distort ions in multiferroic BiFeO 3and in the\nrecently discussed isostructural material FeTiO 3, which has been predicted to exhibit electric field-\ninduced magnetization switching.\nThe concept of magnetic toroidal moments in solids\nhas recently received increased attention due to its po-\ntential relevance in the context of multiferroic mate-\nrials and magneto-electric coupling.1,2,3,4,5A magnetic\ntoroidal moment represents a vector-like electromagnetic\nmultipole moment which breaks both space and time re-\nversal symmetries simultaneously. It can be represented\nby a current flowing through a solenoid bent into a torus,\nor alternatively, by a ring-like arrangement of magnetic\ndipoles.6The toroidal moment has been proposed as the\nprimary order parameter for the low-temperature phase\ntransitionfromaferroelectricintoasimultaneouslyferro-\nelectricandweaklyferromagnetic,i.e. multiferroic,phase\nin boracites.7In addition, the observation of toroidal do-\nmains in LiCoPO 4has recently been reported.2This sug-\ngeststhatferrotoroidicityisafundamentalformofferroic\norder, equivalent to ferromagnetism, ferroelectricity, and\nferroelasticity.8\nThe practical relevance of ferrotoroidic order stems\nfrom the fact that the presence of a magnetic toroidal\nmoment also leads to the appearance of an antisymmet-\nric magneto-electric effect.7,9This is particularly inter-\nesting considering the extensive current research efforts\naimed at finding novel multiferroic materials which ex-\nhibit strong coupling between magnetization and elec-\ntric polarization.10,11,12,13As suggested in Ref. 3, the\ntoroidal moment concept can offer useful guidance in or-\nder to identify possible new candidate systems and to\nanalyze the specific nature of the magneto-electric cou-\npling. At the moment, however, it is not fully clear how\nthis has to be done in practice. It is therefore the pur-\npose of this work to present an instructive analysis of the\ntoroidal moment for an important class of multiferroics,\nandtoillustratehowsuchananalysiscanprovideinsights\ninto possible coupling between the various order param-\neters. Specifically, here we evaluate the toroidal moment\nfor the case of the R3c-distorted perovskite BiFeO 3and\nthe recently proposed isostructural system FeTiO 3(see\nRef. 14).\nBiFeO 3is probably the most studied multiferroic to\ndate, whereas R3cFeTiO 3has only recently been pro-\nposedasamaterialthatexhibitsferroelectrically-inducedweak ferromagnetism, and thus offers the possibility\nof electric-field controlled magnetization switching.14,15\nFirst principles calculations show weak ferromagnetism\nfor both BiFeO 3andR3cFeTiO 3.14,16The net mag-\nnetization in these systems is due to a slight cant-\ning of the mainly antiferromagnetically ordered Fe\nspins. This canting is induced by the Dzyaloshinskii-\nMoriya interaction.17,18A small magnetization has in-\ndeed been observed experimentally in thin film samples\nof BiFeO 3,19,20whereas in bulk BiFeO 3this effect is can-\nceled out by the presence of an additional cycloidal ro-\ntation of the antiferromagnetic order parameter.21As\nwas shown by both symmetry analysis and explicit first\nprinciples calculations, the weak magnetization is lin-\nearly coupled to the spontaneous electric polarization in\nFeTiO 3, but not in BiFeO 3.14,15,16The analysis of the\ntoroidal moment presented in the following confirms this\nfact while in addition providing a complementary per-\nspective.\nThe toroidal moment /vectortof a system of localized mag-\nnetic moments /vector miat sites/vector rican be written as:4,5,6\n/vectort=1\n2/summationdisplay\ni/vector ri×/vector mi. (1)\nAs described in Ref. 4, the presence ofthe position vector\ninEq.(1) togetherwiththe periodicboundaryconditions\nencountered in bulk systems lead to a multivaluedness of\nthe toroidal moment, in close analogy to the case of the\nelectric polarization.22,23As a result only differences in\nthetoroidalmoment(induced forexamplebyastructural\ndistortion) are well defined quantities, and the multival-\nuedness has to be taken into account when evaluating\nsuch toroidal moment differences. A toroidal state is\nrepresented by a spontaneous toroidal moment /vectorts∝negationslash= 0,\nwhere/vectortsis evaluated as the change in toroidal moment\nwith respect to a non-toroidal reference configuration.\nOn the other hand, a non-toroidal state corresponds to a\n“centrosymmetric” ensemble of toroidal moment values,\nbut does not necessarily imply that the straightforward\nevaluation of Eq. (1) for one unit cell leads to /vectort= 0.4\nAs already discussed in Ref. 4, the toroidal moment of2\nTABLE I: Coordinates of all ions iwithin the rhombohedral unit cell of the R3c ABO3structure, /vector ri=a1/vector a1+a2/vector a2+a3/vector a3.\nWithout loss of generality we define the origin to coincide wi th the position of the first Acation.\niA1A2 B1 B2 O1 O2 O3 O4 O5 O6\na101\n2(1\n4+δB) (3\n4+δB)(1\n2+u) w v (1\n2+w) (1\n2+v) u\na201\n2(1\n4+δB) (3\n4+δB) v (1\n2+u) w (1\n2+v) u (1\n2+w)\na301\n2(1\n4+δB) (3\n4+δB) w v (1\n2+u) u (1\n2+w) (1\n2+v)\nBiFeO 3evaluated in the limit of localized magnetic mo-\nments vanishes if one takes into account magnetic mo-\nments only on the nominally magnetic Fe sites. This is\ndue to the fact that the antiferromagnetically ordered\nFe cation sublattice in BiFeO 3represents a simple rhom-\nbohedral lattice, with inversion centers located on each\ncation site, and thus /vectorts= 0. The same holds true for R3c\nFeTiO 3. The symmetry-breaking required for a nonva-\nnishing toroidal moment in these systems is due to the\nstructural distortions exhibited by the oxygen network\nsurrounding the magnetic cations. In the following we\nwill therefore assume that small induced magnetic mo-\nments are located on the anion sites in both BiFeO 3and\nFeTiO 3, and we will evaluate the toroidal moment cor-\nresponding to these induced magnetic moments on the\noxygen sites. Note that if the full magnetization den-\nsity would be taken into account when evaluating the\ntoroidal moment, then the full magnetic symmetry of the\nsystem would automatically be included in the calcula-\ntion. A formalism for calculating the toroidal moment\ndirectly from the quantum mechanical wavefunction has\nbeen suggested recently.24\nInthiswork,weareconsideringperovskite-derivedsys-\ntems with structural R3csymmetry,25i.e. the crystal\nstructure found experimentally for BiFeO 3at ambient\nconditions.26,27R3cFeTiO 3(and MnTiO 3) can be syn-\nFIG. 1: a) Unit cell definition used in this work. To better\nvisualize the orientation of the coordinate system and rhom -\nbohedral basis vectors /vector ai, the rhombohedral unit cell is in-\nscribed into two cubes of the underlying perovskite structu re.\nOnly ions within one rhombohedral unit cell are shown. The\ndepicted atomic positions correspond to the undistorted ca se.\nb) Orientation of the three glide planes c1,2,3, and of the 12\nequivalent directions for the antiferromagnetic order par ame-\nter/vectorL(arrows) in the x-yplane.thesized at high pressure, and remains metastable at\nambient conditions, even though the equilibrium crys-\ntal structure in this case is the illmenite structure (space\ngroupR¯3).28,29\nWe use a rhombohedral setup with lattice vectors de-\nfined as: /vector a1=/parenleftig√\n3\n2a,1\n2a,1\n3c/parenrightig\n,/vector a2=/parenleftig\n−√\n3\n2a,1\n2a,1\n3c/parenrightig\n,\n/vector a3=/parenleftbig\n0,−a,1\n3c/parenrightbig\n(see Fig. 1a). With this choice of coor-\ndinate system, the electric polarization is oriented along\nthezdirection, whereas the magnetic order parameters\nwill be oriented within the x-yplane.\nThe positions of all ions within the unit cell are listed\nin Table I. The oxygen anions occupy Wyckoff positions\n6bof theR3cspace group. It can easily be seen that u=\nv=w=δB= 0 corresponds to the undistorted “ideal\nperovskite” case (but in our case with R¯3msymmetry,\ndue to the rhombohedral distortion of the lattice vectors\nforc/a∝negationslash= 3√\n2). In the following it will be convenient to\nexpress the oxygen coordinates in a somewhat different\nform using u=δO+2\n3ǫ,v=δO−1\n3ǫ+1√\n3φ, andw=\nδO−1\n3ǫ−1√\n3φ. In this notation, the oxygen positions\nare:\n/vector rO1=1\n2/vector a1+\n√\n3\n2aǫ−1\n2aφ\n1\n2aǫ+√\n3\n2aφ\nδOc\n, (2a)\n/vector rO2=1\n2/vector a2+\n−√\n3\n2aǫ−1\n2aφ\n1\n2aǫ−√\n3\n2aφ\nδOc\n, (2b)\n/vector rO3=1\n2/vector a3+\naφ\n−aǫ\nδOc\n, (2c)\n/vector rO4=1\n2(/vector a1+/vector a2)+\n−aφ\n−aǫ\nδOc\n, (2d)\n/vector rO5=1\n2(/vector a1+/vector a3)+\n−√\n3\n2aǫ+1\n2aφ\n1\n2aǫ+√\n3\n2aφ\nδOc\n,(2e)\n/vector rO6=1\n2(/vector a2+/vector a3)+\n√\n3\n2aǫ+1\n2aφ\n1\n2aǫ−√\n3\n2aφ\nδOc\n.(2f)\nIt can be seen that φ,ǫ, andδOdefine three distinct\ndistortions of the oxygen network: δOrepresents the dis-3\nFIG. 2: (Color online) Displacement vectors corresponding to\nφ(blue/dark grey) and ǫ(green/light grey) for the six oxygen\nanions in the R3cunit cell, viewed along the zdirection.\nplacement of the oxygen anions along the polar axis rel-\native to the Asite cations, φrepresents the counter-\nrotation of the oxygen octahedra around this axis (in-\ncluding a breathing, i.e. an overall volume change of the\noctahedra), and ǫrepresents an additional deformation\nof the octahedra, which compresses one side of the octa-\nhedron while expanding the opposing side (see Fig. 2).\nAs stated above, for the completely undistorted struc-\nture with δO=δB=ǫ=φ= 0 the crystallographic\nsymmetry of the system is R¯3m. In this case (and if\nwe for now do not consider magnetic order) two primi-\ntive cells are included in our unit cell definition. On the\nother hand, for φ∝negationslash= 0 (but otherwise ǫ=δO=δB= 0)\nthe resulting symmetry is R¯3c, with doubled primitive\ncell compared to φ= 0, whereas either ǫ∝negationslash= 0,δO∝negationslash= 0 or\nδB∝negationslash= 0 (while all other distortion parameters are zero)\nleads to polar R3msymmetry (again with two primitive\ncells contained in our unit cell definition if we neglect\nmagnetic order).\nThus, only φ∝negationslash= 0 leads to a crystallographic unit cell\ndoubling compared to the undistorted case (and unre-\nlated to the magnetic order), whereas both δOandǫ\nbreak space inversion symmetry and therefore represent\npolar distortions. In the case of δOthis is intuitively\nclear, whereas ǫis perhaps not immediately recognized\nas polar. However, ǫdoes indeed destroy the inversion\nsymmetry ofthe system, and it can easilybe verifiedthat\nǫalso creates an electric polarization /vectorP=/summationtext\niZ∗\ni∆/vector riif\nthe full Born effective charge tensor (see Ref. 30) is used\nforZ∗\ni. (Here, ∆ /vector riis the change in the position ofoxygen\nionidue toǫ∝negationslash= 0.)\nIt has been correctly pointed out in Ref. 31 that three\nindependentparametersarerequiredtodescribethecom-\nplete distortion of the oxygen network within R3csym-\nmetry. In our notation these three parameters are ǫ,ω,\nandδO. However, in Ref. 31 the distortion ǫwas in-\ncorrectly classified as non-polar, which leads to incorrect\nconclusions about possible magneto-electric coupling in\nBiFeO 3, as will become clear in the following. In fact, as\npointedoutinRef.32, thetwodisplacementpatternsrep-\nresented by ǫandδO(andδBas well) correspond to thesameirreducible representationΓ−\n4ofthe original Pm¯3m\nspace group, i.e. they have the same symmetry proper-\nties, and can therefore be viewed as two components of\nthe same polar distortion.\nWe now evaluate the toroidal moment resulting from\ninducedmagneticmomentsontheoxygenpositionslisted\nin Eqs. (2a)-(2f). For this we first have to discuss the\nsymmetry of the magnetically ordered state. First prin-\nciples calculations suggest that for both BiFeO 3andR3c\nFeTiO 3the preferred orientation of the Fe magnetic mo-\nments, and thus the weak magnetization, is perpendicu-\nlar to/vectorP.14,16This results in 12 energetically equivalent\norientations for the antiferromagnetic order parameter\n/vectorL=/vector mFe1−/vector mFe2within the x-yplane, either parallel or\nperpendicular to any of the three c-type glide planes of\nthe underlying R3cstructure (see Fig. 1b). (Here, /vector mFe1\nand/vector mFe2arethe magneticmomentsofthetwoFecations\nwithin the crystallographic unit cell.) The magnetic or-\nder thus breaks the threefold symmetry around the polar\nzaxis and reduces the crystallographic R3csymmetry to\nthe magnetic symmetry groups CcorCc′, depending on\nwhether the Fe magnetic moments are parallel or per-\npendicular to the remaining c-type glide plane. (Here, C\nindicates a base-centered monoclinic Bravais lattice and\nc′a glide plane combined with time reversal.) In the fol-\nlowing we will consider the two representative cases with\n/vectorLaligned either along the xdirection ( Cc′symmetry) or\nalong the ydirection ( Ccsymmetry).\nIf the antiferromagnetic order parameter defined by\nthe Fe magnetic moments is directed along the xdirec-\ntion, i.e. the magnetic symmetry is Cc′, then the y-z\nplane is a c-type glide plane combined with time reversal.\nThis symmetry operation poses the following restrictions\non the magnetic moments /vector mi(i= 1,...,6) at the oxy-\ngen sites: m6x=−m2x,m6y/z=m2y/z,m5x=−m1x,\nm5y/z=m1y/z,m4x=−m3x,m4y/z=m3y/z. Evaluat-\ning Eq.(1) using these relationstogetherwith the oxygen\npositions (2a)-(2f), and considering the multivaluedness\naccording to Ref. 4, results in the following xcomponent\nof the spontaneous toroidal moment:\nt(Cc′)\ns,x=a\n2/braceleftig√\n3φ(m1z−m2z)+3ǫ(m1z+m2z)/bracerightig\n.\n(3)\nHere, we have imposed the additional constraint that\nm3z=−m1z−m2z, to ensure that/summationtext\nimiz= 0. This\ncorresponds to a decomposition of the full moment con-\nfigurationinto compensated and uncompensated partsto\nensure independence of the calculated toroidal moment\nfrom the choice of origin (see Ref. 4). We note that both\ntyandtzare vanishing if appropriate multiples of lattice\nvectors are added to the atomic positions of the oxygen\nanions. This means that the components of the spon-\ntaneous toroidal moment along these directions are zero\n(see Ref. 4).\nThecorrespondingexpressionfor Ccsymmetry, i.e. for\norientation of the antiferromagnetic vector /vectorLalong the y4\ndirection, is:\nt(Cc)\ns,y=a\n2/braceleftig\nφ(m1z+m2z−2m3z)−√\n3ǫ(m1z−m2z)/bracerightig\n.\n(4)\nIn this case the symmetry restrictions for the oxygen\nmagnetic moments are: m6x=m2x,m6y/z=−m2y/z,\nm5x=m1x,m5y/z=−m1y/z,m4x=m3x,m4y/z=\n−m3y/z, and there is also a nontrivial zcomponent of\nthe toroidal moment. However, since this component of\nthe toroidal moment does not contribute to the coupling\nbetween /vectorPand/vectorM(see below), we only consider ty.\nIt can be seen that in general the toroidal moment\ninR3cBiFeO 3and FeTiO 3is nonzero for both possi-\nble magnetic symmetries, and that it is related to the\nstructural distortions of the oxygen network ( /vectorts= 0 for\nǫ=φ= 0). However, the full functional dependence\nof/vectortsonφ,ǫ, andδOcan not be seen from Eqs. (3)\nand (4), since in general the values of the oxygen mag-\nnetic moments will also depend on these structural pa-\nrameters (including also δB). To gain further insight\ninto possible magneto-electric coupling we now consider\nthe case ǫ= 0,φ∝negationslash= 0, i.e. the paraelectric reference\nphase with crystallographic R¯3csymmetry. As has been\npointed out in Refs. 33, 14, and 15, the presence of a lin-\near magneto-electric effect in the paraelectric reference\nphase will lead to a linear coupling between the sponta-\nneousorder parameters /vectorMsand/vectorPs. In contrast, a linear\nmagneto-electriceffect inthe multiferroicphasedescribes\nthe coupling of an additional inducedcomponent of po-\nlarization or magnetization to the corresponding recipro-\ncal fields (e.g. /vectorM(/vectorE) =/vectorMs+α/vectorE). It is therefore very\nimportant to clearly distinguish between the presence of\na linear magneto-electric effect in the para-phase (where\n/vectorMs=/vectorPs= 0) and in the multiferroic phase ( /vectorMs∝negationslash= 0 and\n/vectorPs∝negationslash= 0).\nWe first consider the case /vectorL∝bardblx. For BiFeO 3this re-\nsults in magnetic C2′/c′symmetry, which leads to the\nadditional constraint m2z=m1zand thus vanishing\ntoroidal moment t(C2′/c′)\ns,x= 0. For FeTiO 3the resulting\nsymmetryis C2/c′, which requires m2z=−m1zandthus\nt(C2/c′)\ns,x=√\n3aφm1z. The difference between BiFeO 3and\nFeTiO 3in this case results from the different site sym-\nmetries of the magnetic Fe sites within R¯3csymmetry.\nInR¯3cBiFeO 3the Fe cation is located on a site with in-\nversion symmetry, whereas in R¯3cFeTiO 3the inversion\ncenters are located in between the magnetic cations (see\nalso Ref. 15). For the case /vectorL∝bardblythe resulting symme-\ntry isC2/c(BiFeO 3) orC2′/c(FeTiO 3). The additional\nconstraints on the oxygen magnetic moments are m2z=\n−m1zandm3z= 0 forC2/csymmetry and m1z=m2z\nforC2′/csymmetry, leading to toroidal moment compo-\nnentst(C2/c)\ns,y= 0 and t(C2′/c)\ns,y=aφ(m1z−m3z), respec-\ntively. The calculated spontaneous toroidal moments for\nthe various cases are summarized in Table II.\nIt can be seen that in the paraelectric R¯3cphase (i.e.\nforǫ= 0) only FeTiO 3, but not BiFeO 3, has a nonva-TABLE II: Calculated values of the spontaneous toroidal\nmoment and corresponding magnetic symmetry groups for\nBiFeO 3and FeTiO 3in the paraelectric R¯3cstructure ( ǫ= 0)\nfor different orientation of the antiferromagnetic order pa ram-\neter.\nBiFeO 3 FeTiO 3\n/vectorL/bardblˆxC2′/c′/vectorts= 0C2/c′ts,x=√\n3aφm1z\n/vectorL/bardblˆyC2/c/vectorts= 0C2′/c t s,y=aφ(m1z−m3z)\nnishing toroidal moment, and that the toroidal moment\nin paraelectric FeTiO 3is related to the counter-rotations\nof the oxygen octahedra represented by φ. The presence\nof this toroidal moment causes a linear magneto-electric\neffect/vectorM=α/vectorEwithα∝/vectortvia the free-energy invariant\nETPM∝/vectort·/parenleftig\n/vectorP×/vectorM/parenrightig\n(see e.g. Ref. 4). This means that\nonce the polarization in R¯3cFeTiO 3becomes nonzero\n(which of course reduces the crystallographic symmetry\ntoR3c),itwillinduceaweakmagnetizationviathelinear\nmagneto-electric effect, consistent with the design crite-\nria outlined in Ref. 14. Such “ferroelectrically-induced\nferromagnetism” via the linear magneto-electric effect\nhas been originally suggested in Ref. 33.\nOn the other hand, paraelectric R¯3cBiFeO 3is non-\ntoroidal and does not exhibit a linear magneto-electric\neffect. Therefore, the weak magnetization in BiFeO 3\nis not ferroelectrically-induced and there is no linear\ncoupling between /vectorMsand/vectorPsin the multiferroic phase.\nThis is also consistent with first principles calculations,\nwhere for BiFeO 3weak ferromagnetism occurs in both\nthe ferroelectric R3cand the paraelectric R¯3cstructures,\nwhereasfor FeTiO 3it occurs onlyin the ferroelectric R3c\nstructure.14,16\nNote that in the multiferroic R3cphase both FeTiO 3\nandBiFeO 3exhibit atoroidalmoment (accordingtoEqs.\n(3) and (4)) and thus a linear magneto-electric effect.\nThis means that an external electric field will induce\nchanges in both polarization and magnetization, linear\nin the external field, but only in FeTiO 3the correspond-\ning spontaneousorder parameters /vectorMsand/vectorPsare linearly\ncoupled. Such linear coupling between /vectorPsand/vectorMsis re-\nquired to achieve full electric-field control of the weak\nmagnetization. As outlined in Refs. 14 and 15 a rever-\nsal of/vectorPsin FeTiO 3induced by an external electric field\nwill result in a corresponding reversal of /vectorMsprovided\nthe antiferromagnetic order parameter (or equivalently\nthe toroidal moment) is fixed by a large enough mag-\nnetic anisotropy. On the other hand, such electric field\ncontrolled switching of the weak magnetization is not ex-\npected to occur in BiFeO 3.\nTheevaluationofthetoroidalmomentpresentedabove\nallowsto clearly identify which structuralmodes, in com-\nbination with the antiferromagnetic order, lead to the\nappearance of a toroidal moment and a linear magneto-\nelectric effect. In contrast to the antiferromagnetic order\nparameter, which generally depends only on the orienta-5\ntion of the individual magnetic moments, it follows from\nEq. (1) that the toroidal moment contains information\nabout where the magnetic moments are located as well\nas on how they are oriented. Furthermore, the toroidal\nmoment is a macroscopic multipole moment that is re-\nlated to the (magnetic) point group symmetry, whereas\na proper symmetry analysis of antiferromagnetic order\nrequires a treatment based on the full space group sym-\nmetry. In particular, antiferromagnetic order is not con-\nnected to any particular macroscopic symmetry break-\ning, i.e. all 90 magnetic point groups are compatible\nwith the existence of antiferromagnetic order. On a mi-\ncroscopic space group level, antiferromagnetic order of\ncourse always breaks time reversal symmetry. However,\nfor systems where the magnetic unit cell is a multiple\nof the crystallographic unit cell, a primitive translation\nof the original nonmagnetic lattice can be combined with\ntime reversal, and as a result the correspondingmagnetic\npoint group still contains time reversal as a symmetry\nelement.34In contrast, a toroidal moment always breaks\nspace and time reversal symmetries on the macroscopic\nlevel, i.e. the corresponding magnetic point group does\nnot contain neither space inversion ¯1 nor time reversal 1′\n(whereasthe combinedoperation ¯1′can still be a symme-\ntryelement). Sinceallmacroscopicpropertiesofapartic-\nularcrystalaredeterminedbyitspointgroupratherthan\nspace group symmetry,34the toroidal moment appears\nto be a more appropriate quantity to classify macro-\nscopic symmetry properties compared to the antiferro-\nmagnetic order parameter. In particular, the toroidal\nmoment is ideally suited to discuss magneto-structural\nor magneto-electric coupling. For a given structural and\nmagnetic configuration the toroidal moment can be eval-\nuated straightforwardly, applying the procedure outlined\ninRef.4. Usingtherelationbetweenthetoroidalmoment\nandthemagneto-electrictensor α, thisallowstocorrectly\nidentify which quantities determine the magneto-electricproperties of the system. The same can of course also\nbe achieved by a group theoretical analysis of the sym-\nmetry properties of the various structural modes and of\nthe antiferromagnetic order parameter. The straightfor-\nward evaluation of the toroidal moment should therefore\nbe considered as an alternative (or complementary) way\nto discuss magneto-electric symmetry that does not nec-\nessarily require the application of group theoretical con-\ncepts.\nFinally, we point out that the toroidal moment is only\nrelated to the antisymmetric part of the linear magneto-\nelectric tensor α, whereas the symmetric part of αis\nconnected to other electromagnetic multipole moments\n(see Ref. 5). However, for the present case where weak\nferromagnetism is caused by the Dzyaloshinskii-Moriya\ninteraction, the antisymmetric component related to the\ntoroidal moment is indeed the crucial part of α.\nIn summary, we have shown that by evaluating the\ntoroidal moment in the limit of localized magnetic mo-\nments, a clear picture of the different roles played by\nthevariousstructuraldistortionsforthemagneto-electric\nproperties in BiFeO 3andR3cFeTiO 3can be achieved.\nThe toroidal moment can be used to characterize the\nmagneto-electricpropertiesinantiferromagneticsystems.\nIts usefulnessstems fromthe fact that isdepends on both\nposition and orientation of the magnetic moments and\nfrom its well-defined macroscopic symmetry properties,\nwhich allow to use point groups instead of space groups,\nincontrasttoadiscussionbasedontheantiferromagnetic\norder parameter.\nAcknowledgments\nThis work was supported by Science Foundation Ire-\nland under Ref. SFI-07/YI2/I1051.\n∗Electronic address: edererc@tcd.ie\n1H. Schmid, in Magnetoelectric interaction phenomena in\ncrystals, edited by M. Fiebig, V. Eremenko, and I. E.\nChupis (Kluwer, Dordrecht, 2004), pp. 1–34.\n2B. B. Van Aken, J. P. Rivera, H. Schmid, and M. Fiebig,\nNature449, 702 (2007).\n3K. M. Rabe, Nature 449, 674 (2007).\n4C. Ederer and N. A. Spaldin, Phys. Rev. B 76, 214404\n(2007).\n5N. A. Spaldin, M. Fiebig, and M. Mostovoy, J. Phys.: Con-\ndens. Matter 20, 434203 (2008).\n6V. M. Dubovik and V. V. Tugushev, Physics Reports 4,\n145 (1990).\n7D. G. Sannikov, J. Exp. Theo. Phys. 84, 293 (1997).\n8H. Schmid, Ferroelectrics 252, 41 (2001).\n9A. A. Gorbatsevich, Y. V. Kopaev, and V. V. Tugushev,\nSov. Phys. JETP 58, 643 (1983).\n10N. A. Spaldin and M. Fiebig, Science 309, 391 (2005).\n11W. Eerenstein, N. D. Mathur, and J. F. Scott, Nature 442,759 (2006).\n12S.-W. Cheong and M. Mostovoy, Nature Materials 6, 13\n(2007).\n13R. Ramesh and N. A. Spaldin, Nature Materials 6, 21\n(2007).\n14C. J. Fennie, Phys. Rev. Lett. 100, 167203 (2008).\n15C. Ederer and C. J. Fennie, J. Phys.: Condens. Matter 20,\n434219 (2008).\n16C. Ederer and N. A. Spaldin, Phys. Rev. B 71, 060401(R)\n(2005).\n17I. E. Dzyaloshinskii, Sov. Phys. JETP 5, 1259 (1957).\n18T. Moriya, Phys. Rev. 120, 91 (1960).\n19W. Eerenstein, F. D. Morrison, J. Dho, M. G. Blamire,\nJ. F. Scott, and N. Mathur, Science 307, 1203a (2005).\n20H. Bea, M. Bibes, S. Petit, J. Kreisel, and A. Barthelemy,\nPhilos. Mag. Lett. 87, 165 (2007).\n21I. Sosnowska, T. Peterlin-Neumaier, and E. Streichele,\nJ. Phys. C 15, 4835 (1982).\n22R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47,6\nR1651 (1993).\n23R. Resta, Rev. Mod. Phys. 66, 899 (1994).\n24C. D. Batista, G. Ortiz, and A. A. Aligia, Phys. Rev. Lett.\n101, 077203 (2008).\n25Depending on the amount of distortion, the correspond-\ning structure is sometimes referred to as the “ferroelectri c\nLiNbO 3structure”.This distinction betweendistortedper-\novskite and LiNbO 3structure is purely quantitative and\nthus not relevant in the present context.\n26C. Michel, J.-M. Moreau, G. D. Achenbach, R. Gerson,\nand W. J. James, Solid State Commun. 7, 701 (1969).\n27F. Kubel and H. Schmid, Acta Crystallogr. Sect. B 46, 698\n(1990).28J. Ko and C. T. Prewitt, Phys. Chem. Miner. 15, 355\n(1988).\n29L. C. Ming, Y.-H. Kim, Y. Uchida, Y. Wang, and\nM. Rivers, Am. Mineral. 91, 120 (2006).\n30P. Ghosez, J.-P. Michenaud, and X. Gonze, Phys. Rev. B\n58, 6224 (1998).\n31R. de Souza and J. E. Moore, arXiv:0806.2142 (2008).\n32C. J. Fennie, arXiv:0807.0472 (2008).\n33D. L. Fox and J. F. Scott, J. Phys C 10, L329 (1977).\n34R. R. Birss, Symmetry and Magnetism (North Holland\nPub., Amsterdam, 1966)."    },    {        "title": "0902.0091v2.Neutron_Studies_of_the_Iron_based_Family_of_High_TC_Magnetic_Superconductors.pdf",        "content": "Neutron Studies of the Iron -based Family of High T C Magnetic Superconductors  \n \nJeffrey W. Lynn NIST Center for Neutron Research, National Institute of Sta ndards and Technology, \nGaithersburg, MD 20899-6102 \n  \nPengcheng Dai  \nDepartment of Physics and Astronomy, Univ ersity of Tennessee, Knoxville, TN 37996-1200 \nand Neutron Scattering Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6393  ABSTRACT \n \nWe review neutron scattering investigations of the crystal structures, magnetic structures, and \nspin dynamics of the iron-based RFe(As,P)O ( R=La, Ce, Pr, Nd), (Ba,Sr,Ca)Fe\n2As2, and \nFe1+x(Te-Se) systems.  On cooling from room temperature all the undoped materials exhibit \nuniversal behavior, where a tetr agonal-to-orthorhombic/monoclinic  structural transition occurs, \nbelow which the systems become antiferromagnets.  For the first two classes of materials the \nmagnetic structure within the a-b plane consists of chains of parallel Fe spins that are coupled \nantiferromagnetically in the orthogonal direction,  with an ordered moment  typically le ss than one \nBohr magneton.  Hence these ar e itinerant electron magnets, with  a spin structure that is \nconsistent with Fermi-surface nesting and a very energetic spin wave bandwidth ~0.2 eV.  With \ndoping, the structural and magnetic transitions are suppressed in favor of superconductivity, with \nsuperconducting transition temperatures up to ≈55 K.  Magnetic correlations are observed in the \nsuperconducting regime, with a magnetic resona nce that follows th e superconducting order \nparameter just like the cuprates .  The rare-earth moments orde r antiferromagnetically at low T \nlike ‘conventional’ magnetic-superc onductors, while the Ce crystal field linewidths are affected \nwhen superconductivity sets in.  The application of pressure in CaFe 2As2 transforms the system \nfrom a magnetically ordered orthorhombic mate rial to a ‘collapsed’ non-magnetic tetragonal \nsystem.  Tetragonal Fe 1+xTe transforms to a low T monoclinic st ructure at small x that changes to \northorhombic at larger x, which is accompan ied by a crossover from  commensurate to \nincommensurate magnetic order.  Se dopi ng suppresses the magnetic order, while \nincommensurate magnetic correlations ar e observed in the superconducting regime. \n PACS:  74.25.Ha, 74.70.Dd, 75.25.+z, 75.30.Ds Keywords:  Iron Superconductors;  neutron scattering;  crys tal & magnetic structures;  \nspin dynamics 1. Introduction \n \nThe nature of the magnetic or der and spin fluctua tions in superconducto rs has had a rich \nand interesting history, and has been a topic of speci al interest ever since the parent materials of \nthe high T C cuprates were found to be antiferroma gnetic Mott insulators that exhibit huge \nexchange energies within the Cu-O planes [1].  These energetic spin correlations persist into the \nsuperconducting regime, often developing a ‘magnetic resonance’ whose energy scales with T C \nand whose intensity exhibits a superconducting order-parameter-like behavi or [1].  The newly \ndiscovered iron oxypnictide superconductors possess a number of similarities to the cuprates, \nwhich naturally has led to strong parallels being drawn between the two classes of materials.  \nThere are, though, important differences as well.  The basic properties are reviewed in detail \nelsewhere in this volume [2-4], so we simp ly highlight a few asp ects that are key to \nunderstanding the magnetic properties exhibited by th ese materials.  The iron-based systems are \nlayered like the cuprates, although they are not nearly as two-dimensi onal in character (an \nimportant advantage for applica tions).  The parent (undoped) materials exhibit long range \ncollinear antiferromagnetic order, but are metallic rather than Mott insulators.  Indeed all five iron d-bands are partially occupied and cross th e Fermi surface, clearly classifying these \nmaterials as itinerant electron in character.  Thus a multi-orbital theoretical description is \nnecessary rather than the single orbital approa ch for the cuprates.  The magnetic energies are \nvery large, with a spin wave bandwidth ~0.2 eV.  Moreover, in the superconducting regime, a ‘magnetic resonance’ excitation ha s been observed, just like for ma ny of the cuprates.  Here we \nreview the neutron studies of the structure and magnetic transitions of the undoped materials, and \nhow these progress with doping into the superc onducting regime.  We also discuss the spin \ndynamics that have been investigated, and the ma gnetic resonance that has been observed in the \nsuperconducting state.  We note that  all the properties discussed here have been corroborated by \na variety of techniques such as resistivit y, specific heat, magnetiz ation, x-ray diffraction, \nMössbauer spectroscopy, muon spin  rotation measurements, and NMR, as described elsewhere \nin this review volume. \n2.  Crystal and Magnetic Structures \n \n There are four different classes of ir on-based superconductors typified by LaFeAsO \n(1:1:1:1), SrFe\n2As2 (1:2:2), LiFeAs (1:1:1), and Fe 1+x(Te-Se) (1:1).  The (known) crystal \nstructures at room temperature are all tetragonal [5-9], and are shown in Fig. 1.  The important \ncommon aspect is that the Fe2+ ions form square-planar sheet s, where the direct iron-iron \ninteractions render the d-electrons metallic in nature.  The LiFeAs system is superconducting and \ndoes not order magnetically nor does the structure di stort at low temperatures [7,8], as is the case \nfor the related LaFePO systems [10].  The ba sic crystallographic information for these two \nsystems is presented in Table 1, and we will not di scuss them any further in this review.  All the \nother undoped systems undergo a subtle structural distortion below room temperature that breaks \nthe tetragonal symmetry.  This transition is th ought to be magnetically driven to relieve the \nmagnetic frustration [3,4], and indeed long range magnetic order develops in the distorted state for all these materials.  The structural phase transition temperatures ar e given in Table 2, along \nwith the iron magnetic ordering temperatures, magnetic structures, and ordered moments in the \nground state.  Doping reduces and eventually completely suppresses these transitions as \nsuperconductivity develops. \n 2 \nFig. 1.  Crystal structures for the four classes of superconductors:  a) LaFeAsO, b) SrFe 2As2, c) LiFeAs, and d) \nFe1+xTe.  Below the tetragonal to orthorhombic structural transition the undoped materials can order magnetically, \nand the commensurate magnetic structures are also indicated in a) and b), where the spins are parallel along the \northorhombic b axis, antiparallel along the a axis, and with the spin direction along a.  LiFeAs does not distort, \nwhile the magnetic structure for Fe 1+xTe is discussed below. \n \nTable 1.  Basic crystal structure of LaFeAsO and related ma terials.  Above the structural transition the symmetry is \ntetragonal ( P4/nmm ), with Fe and O at special positions [2b, (3/4,1 /4,1/2) and O 2b, (3/4,1/4,0), respectively], La \n[2c, (1/4,1/4,0.1417)], and As [2c, (1/4,1/4,0.6507)].  The internal coordinates are quite similar for the other 1:1:1:1 \nmaterials.  At low T the structure is orthorhombic ( Cmma ), described by an a-b plane rotated by ≈45° and the lattice \nparameters unequal and multiplied by ≈2.  The special positions for the Fe and O can be generalized by employing \nthe P112/n  monoclinic space group which allows these atoms to shift along the c-axis.  The crystal structure of \nSrFe 2As2 is I4/mmm, with the Sr and Fe at the 2a (0,0,0) and 4d (1 /2,0,1/4) special positions, respectively.  The As \noccupies the 4e site, (0,0,0.3541).  Below the structural distortion the 1:2:2 structure is orthorhombic Fmmm .  \nLiFeAs is tetragonal P4/nmm  at all T, Fe (2b, (3/4,1/4,1/2)), As (2c, (1/4,1/4,0.2635)), Li (2c, (1/4,1/4,0.8459).  \nFe1+x(Te,Se) is tetragonal P4/nmm  at elevated temperatures, Te (2a, (1/4,1 /4,0.2829)) and two iron sites, Fe(1) (2b, \n(3/4,1/4,0)) and the partially occupied Fe(2) site, (2a, (1/4,1/4,0.7350)).  Superconducting compositions remain \ntetragonal, while the non-superconducting ones distort at low T to monoclinic P21/m for smaller x, or orthorhombic \nfor larger x. \nSystem a (Å)  b(Å)  C(Å) Ref. \nLaOFeAs (175 K) 4.0301 ≡a 8.7368 [11-15] \n(4 K) 5.7099 5.6820 8.7265  \nCeOFeAs (175 K) 3.9959 ≡a 8.6522 [16] \n(30 K) 5.6626 5.6327 8.6382  \nPrOFeAs (175 K) 3.977 ≡a 8.6057 [19,20] \n(5 K) 5.6374 5.6063 8.5966  \nNdOFeAs (175 K) 3.9611 ≡a 8.5724 [17,18] \n(0.3 K) 5.6159 5.5870 8.5570  \nCaFe 2As2 (175 K) 3.912 ≡a 11.667 [24-26] \n 5.542 5.465 11.645  \nSrFe 2As2 (300 K) 3.920 ≡a 12.40 [21-23] \n(150 K) 5.5695 5.512 12.298  \nBaFe 2As2 (175 K) 3.9570 ≡a 12.9685 [27-29] \n(5 K) 5.61587 5.57125 12.9428  \nLiFeAs (215 K) 3.7914 ≡a 6.3639 [7,8] \nFe1.068Te (80 K) 3.81234 ≡a 6.2517 [9,30-33]\n(5 K) 3.83435 3.78407 6.2571  \n   β=89.212°  \n \n 32.1.  LaFeAsO and SrFe 2As2 type systems \n \nNeutron diffraction measurements have been  carried out on the undoped La [11-15], Ce \n[16], Nd [17,18], and PrFeAs O [19,20] (1:1:1:1) mate rials, as well as th e Sr- [21-23], Ca- [24-\n26], and BaFe 2As2 [27-29] (1:2:2) systems.  The crystal structure consists of single Fe-As layers \nthat are separated by a single la yer of (for example) LaO or Ba, respectively.  They are all \ntetragonal at room temperature as already indi cated, and undergo an orthorhombic distortion at \nlower temperatures.  For the 1:2:2 materials the structural transition is clearly first-order in \nnature, and is directly accompanied by antiferr omagnetic order.  For the 1:1:1:1 systems the \nstructural component of the orde ring also appears to be first order, but the antiferromagnetic \norder generally develops at a lower temp erature and appears to be second order. \nThe basic crystallographic information for th e undoped materials of the four classes of \nsystems is given in Table 1.  The lattice paramete rs are given for the high temperature tetragonal \nphase and for the low temperature di storted structure.  For atoms th at are not at special positions, \nthe internal coordinates quoted in the caption are for the prototype systems, namely LaFeAsO, SrFe\n2As2, LiFeAs, and Fe 1.068Te, in the tetragonal (higher T) phase.  These internal coordinates \nare representative and do not va ry substantially between high and low temperature, or for \ndifferent cations.  If more detailed crystallogra phic information is needed then the references \nshould be consulted. \nThe crystallographic distortion breaks the tetr agonal symmetry, and the materials become \northorhombic.  In this crystallographic description, the Fe and O ions  remain at special positions.  \nThe refinements from the initial study [11] sugge sted that the O ion might be shifted, which can \nbe described by the monoclinic P2/c space group, allowing the Fe and O ions to have a \ndisplacement along the c-axis.  Most powder diffraction studies do not indicate that this \nadditional degree of freedom is necessary, and higher precision si ngle crystal diffraction studies \nwould be desirable to determine whic h description is best.  But this is a rather subtle feature, and \nat the present level of precision either description can be employed. \nThe structural distortion is t hought to be driven by the magne tic interactions , as the lower \nsymmetry relieves the magnetic frustration and allo ws the system to order [3,4].  The observed \nmagnetic structure within the a-b plane is identical for both classe s of materials and consists of \nchains of Fe spins that are para llel to each other along the (short) b-axis of the distorted \ntetragonal cell, while along the longer a-axis the spins are coupled antiferromagnetically, with \nthe spin direction along the a-axis as shown in Fig. 2.  Note that this type of magnetic structure is \nforbidden in tetragonal symmetry.  The observed spin structure is consistent with Fermi-surface nesting, although the calculated orde red moment based on first-princi ples theory is much larger \nthan observed [3,4].  This is another indication that these metals are it inerant electron magnets, \nwhich simply means that the electrons which are unpaired and magnetically active occupy \nenergy bands that cross the Fermi energy.  Along the c-axis the nearest-neighbor spins can be \neither antiparallel as for the La and Nd 1:1:1:1 sy stems, or parallel like Ce  and Pr.  For the three \n1:2:2 materials neares t neighbors along the c-axis are antiparallel.  The magnetic configurations \nare all simple commensurate structures. \nFor the 1:2:2 materials sizable single crystals are available that enable more detailed \ninvestigations of the structural and magnetic pha se transitions, such as shown in Fig. 3.  The \nintensity of the tetragonal peak for SrFe\n2As2 is followed as the structural transition is traversed, \nand the sudden change in intensit y shows that the structural tran sition is clearly abrupt (first \norder).  In the distorted phase, the T dependen ce of the (1,0,1) magnetic peak shows that the \n 4magnetic order develops at the same temperature as  the structural distorti on.  On first inspection \nthe magnetic order parameter looks continuous (second order),  but it is actually  truncated just at \nTN, and the lack of any significant  critical scattering also reveal s the first order nature of the \nmagnetic transition. \n \n \nFig. 2.  Magnetic structure for the iron spins in the 1:1:1:1 and 1:2:2 systems.  The in-plane spin configuration and \nspin direction are identical for a ll these materials, where the spins are parallel along the orthorhombic b  axis, \nantiparallel along the a axis, and with the spin direction along a .  Along the more weakly coupled c-axis the \narrangement can be either parallel (ferro) or antiparallel (antiferro).  All the struct ures are simple commensurate \nmagnetic structures.  \n \nTable 2.  Structural phase transitions for undoped mate rials, together with the ordering temperatures, spin \nconfiguration, and ordered moment for the iron spins.  As a function of doping, all studies so far have found that \nboth the structural and iron magnetic phase transitions decrease with increasing doping level.  We note that some \nsamples have been found to be unintentionally doped, and low transition temperatur es for the nominally undoped \nmaterials have been reported.  Here we list the higher T observations.  The magnetic rare earth ions in the 1:1:1:1 \nmaterials order at low temperatures in  commensurate magnetic structures, a nd the ordering temperature, magnetic \nmoment and ordering wave vector are also given. \nMaterial TS \n(K) TN(Fe) \n(K) μFe \n(μB) qFe Spin \ndirection TN(R) \n(K) μR \n(μB) qR Spin direction Ref \nLaOFeAs 155 137 0.36 101 likely  a -    [11-14]  \nCeOFeAs 158 140 0.8 100 a 4.0 0.94 101 a,b,c  [16]  \nPrOFeAs 153 127 0.48 100 a 14 0.84 100 c [19]  \nNdOFeAs 150 141 0.25 101 likely  a 1.96 1.55 100 a,c [17,18]  \nCaFe 2As2 173 173 0.80 101 a -    [24-26]  \nSrFe 2As2 220 220 0.94 101 a -    [21-23]  \nBaFe 2As2 142 143 0.87 101 a -     [27]  \nFe1.068Te  67 67 2.25 100 b -     [32]  \n  \nFor both classes of materials where it has been  determined, the easy axis (spin direction) \nis along a as indicated in Table 2.  This determin ation rests on the ability to distinguish a from b  \nfor the magnetic peaks.  The size of the ordered moment is typically one μ\nB or considerably less, \nand recalling that the magnetic intensity is propor tional to the square of the ordered moment, the \nmoment direction has not yet been determined fo r some of the smaller-moment 1:1:1:1 materials \nbecause of the weak magnetic scattering in the powders.  For the three 1:2:2 materials, it is \n 5straightforward to distinguish a from b  on the available single crystals, and the spin \nconfiguration is the same as fo r the 1:1:1:1 systems, with th e spins parallel along the shorter b-\naxis, antiparalle l along the longer a-axis within the a-b plane, and with the spin direction along a \nas shown in Fig. 1.  It is lik ely that all these materials have the spin direction along a. \n \n \nFig. 3.  Peak intensity of the tetragonal (220) peak in a single crystal of SrFe 2As2 as a function of temperature (solid \ncircles).  The crystallographic distortion splits the peak into the (400) and (040) orthorhombic peaks, which causes \nthe intensity in between to rapidly decrease.  At the same temperature the development of the (101) magnetic peak signals the onset of long range magnetic order [21]. \n \n \nFig. 4.  Magnetic structure for Fe 1.068Te, which is commensurate with the underlying lattice.  The magnetic \nconfiguration and spin direction differ from the 1:1:1:1 and 1:2:2 magnetic structures [32]. \n \n2.2.  Fe 1+x(Te-Se) system \n For the Fe\n1+x(Te-Se) system [9, 30-33], crystallogra phically there are two iron sites, one \nof which is partially occupied, while the (Te, Se ) site is fully occupied.  Hence the composition \nshould be indicated as Fe 1+x(Te,Se).  This material is tetragonal  at elevated temperatures.  For the \npure Te system the structure distorts into  a monoclinic phase, where commensurate \nantiferromagnetism abruptly sets in at the same temperature.  Thus the magnetic and structural transitions occur simultaneously in a first-order transition.  In addition, the two inequivalent Fe \nsites are both active magnetically.  The magnetic st ructure is shown in Fi g. 4, and the nature of \nthe distortion as well as the magne tic structure the system exhibits are different than the 1:1:1:1 \nand 1:2:2 systems.  This contrasts with theoreti cal expectations based on a 1:1 stoichiometry, but \nthe difference may be due to the additional iron site.  Interestingly, at higher Fe content (for \nexample Fe\n1.141Te [31]) the magnetic order b ecomes incommensurate, and the \nincommensurability wave vector is strongly depe ndent on the Fe content.  With Se doping the \nstructural distortion changes from monoclinic to orthorhombic while the magnetic order is \nsuppressed in favor of superconductivity.  Howeve r, incommensurate spin fluctuations survive \n 6into the superconducting regime [31].  The pure FeSe superconducting phase  is stoichiometric \n(x=0) [33]. \n \n2.3.  CaFe 2As2 under pressure \n \nThe application of modest pressure (a few kbars) was found to cause CaFe 2As2 to go \nsuperconducting [34].  Pressure de pendent neutron diffraction measur ements revealed a dramatic \nchange in the crystal structure— a strongly first-order phase transi tion to a “collapsed” tetragonal \nphase [25,26].  By collapsed we mean that there is a huge decrease in the c- axis lattice \nparameter, by 10%, and an overall decrease in the volume of the unit cell by 5%;  the a-b plane \nundergoes a smaller expansion.  The region of superconductivity appeared  to occur in this \ncollapsed phase.  However, th e initial reports of superconductivity were carried out on a single \ncrystal with a solid medium pr oviding the pressure, before the large changes in the crystal \nstructure were discovered.  Because of the huge anisotropic change in  the lattice as the system is \ntransformed into the collapsed tetragonal phase, the pressure ap plied using a solid medium to \nproduce the superconductivity is also hugely anisotropic.  S ubsequent measurements under \nhydrostatic pressure revealed that the supercon ducting phase was complete ly or nearly absent \nunder these conditions [35].  The detailed origin of the superc onductivity is now not resolved, \nbut it appears to occur in a mixed-phase region.  It would be interesting to investigate the \nsuperconductivity using epitaxially grown thin film s where the appropriate stress can be applied. \nOne of the very interesting aspects of this  collapsed phase is that first principles \ncalculations using the observed cr ystal structure indicate that the Fe moment itself collapses \n[3,4,25,26].  Indeed, the neutron di ffraction measurements do not find any evidence for magnetic \norder in the tetragonal collapsed phase [25,26], and inelastic scatteri ng data do not find any \nevidence for spin correlations [36].  If the co llapsed phase is actually  superconducting, it’s very \nlikely that magnetic fluctuations cannot be the origin  of the pairing.  It will be interesting to see \nif spin correlations do exist when anisotropic pressure is applied, and in what crystallographic phase the superconductivity is present.  These ma y be particularly difficult measurements for \nneutron scattering on single crys tals, however, because the pressure has to be applied in the a-b \nplane. \n \n2.4.  Rare Earth Magnetic Ordering \n For the 1:1:1:1 systems, the rare earth ordering has been studied for the Ce [16], Nd [18], \nand Pr [19,20] materials.  They  all order at low T like “conventional” magnetic superconductors;  \nT\nN(Ce) = 4 K, and T N(Nd) = 2 K.  It is interesting, however , that the ordering temperature for Pr \nis much higher than the other rare earth ions, T N(Pr) = 14 K, much like what happens in the 1:2:3 \ncuprate superconductors where T N(Pr) = 17 K [37].  The Pr spins order in the rather complicated \nmagnetic structure as shown in Fig. 5, where tr ios of spins above and below the plane that \ncontains the oxygen ions are coupled ferro magnetically, while adjacent trios align \nantiferromagnetically.  The spin direction is simply along the c-axis, and adjacent planes of spins \nare identical along the c-axis so that the magnetic unit cell is the same as the nuclear unit cell.  \nThen the ordering wave vector is [1,0,0] in the orthorhombic system.  The Nd system exhibits \nthe same type of spin configuration, but with  components of the ordered moment along all three \naxes rather than just along c.  The Ce magnetic structure, on the other hand, has moments \nprimarily in the a-b  plane, with a chain-like structure sim ilar to the iron, but with adjacent chains \n 7with their spin direction approxima tely orthogonal rather than antipar allel.  The Ce ions may also \nhave a small component of the moment along the c-axis.  The direction of the spins for nearest \nneighbors along the c-axis is also (approximately) orthogonal rather than paralle l, so that the \nmagnetic unit cell is doubled and the ordering wave vector is [ 1,0,1].  The rare earth magnetic \nordering temperatures, ordered magnetic moments,  and ordering wave vectors are given in Table \n2. \n \n \n \nFig. 5  Low temperature magnetic structures for the rare earth and iron moments in a) CeFeAsO, b) NdFeAsO, c) \nPrFeAsO.  In each, the iron magnetic structure is assu med not to change when the rare earth moments order. \n \n \nIt should be noted that the rare earth and ir on spins interact with each other, which can \nalter both magnetic structures an d correlate the moments obtaine d in the refinements.  In \naddition, there are a limited number of magnetic peaks with two relatively small moments to \nrefine.  Hence in the refinements the spin structure for the iron s ublattice was assumed to be the \nsame as found above the rare earth ordering, while the size of the moment was allowed to vary.  In the case of the Ce and Nd systems this produc ed iron moments substantially larger than found \nabove T\nN (rare earth), but it is not clear at this stage whether this is a real increase or an artifact \nof the limited magnetic data and concomitant assumptions.  Data on larger samples/longer \ncounting times might be helpful to clarify this i ssue, but it’s final resolution may have to await \nthe availability single crystals large enoug h for neutron diffraction (or resonant x-ray \ndiffraction). \nThe rare earth ordering of the Ce has also been investigated  systematically for the doped \nsystem.  Interestingly, as the iron transition temp erature approaches zero with increasing fluorine \ncontent (discussed below), the Ce moment rotates from the a-b plane to being along the c-axis.  \nThere is little effect on the transition temperatur e for the Ce order, which contrasts with the Pr \nsystem both as a function of F doping and oxyge n depletion, where no Pr magnetic order is \nobserved down to 5 K.  Thus the Pr ordering  temperature has decreased dramatically with \ndoping. \n  \n 82.5  Doping Dependence of the Structural and Magnetic Transitions \n \nInitial studies revealed that the structural distortion and long range magnetic order were \nabsent in the optimally doped LaFeAsO 1-xFx material [11], and this wa s found to be the case for \nall the 1:1:1:1  and 1:2:2 materials inve stigated to date [11,12,14,16,19,38,39].  The doping  \n  \n \n \nFig. 6.  Phase diagram for CeFeAsO 1-xFx as a function of fluorine doping.  Both the structural and magnetic phase \nboundaries decrease with increasing x.  The magnetic lo ng range order is suppressed before superconductivity \ndevelops, while the superconductivity is able to develop in the orthorhombic as well as th e tetragonal structure [16]. \n \ndependence of the structural and magnetic transitions has been investigated in detail for the La \n[14] and Ce [16] 1:1:1:1 materials, and the phase diagram for CeFeO 1-xFx is shown in Fig. 6.  \nThe structural and magnetic temperatures both d ecrease with increasing doping content, with the \niron Néel temperature decreasing more rapidly.  Fo r the Ce system [16], it is apparent that the \nlong range order for the iron vani shes before superconductivity a ppears.  Therefore these two \norder parameters appear to fully compete with  each other.  For the La 1:1:1:1 system the \ntransition as a function of doping may be first orde r or there could be coex istence [14], while for \nthe Ba 1-xKxFe2As2 there is evidence of coexistenc e of antiferromagnetic order and \nsuperconductivity [39].  On the other hand, it is cl ear that the orthorhombic structural phase \noverlaps into the superconducting regime for thes e systems, so that the superconductivity can \noccur in both the tetragonal and orthorhombic structures. \nOne trend that has become a pparent in the crystallographic studies is a systematic \ndecrease in the Fe–As/P–Fe bond angle for Fe-based superconductors with higher T C as shown in \nFig. 7 [16], indicating that lattice effects play an  important role in the superconductivity.  Indeed \nthe highest T C is obtained when the Fe–As/P–Fe angle reaches the ideal valu e of 109.47° for the \nperfect FeAs tetrahedron.  This suggests th at the most effective way to increase T C in Fe-based \nsuperconductors is to decrease th e deviation of the Fe–As/P–Fe bond angle from the ideal Fe-As \ntetrahedron.  It also explains  in a pedagogical manner that we have reached the maximum T C≈55 \nK for these single-layer iron arsenide materials. \n 9 \n \nFig. 7.  The Fe-As(P)-Fe bond angle is found to vary systematically with T C for the Fe-based superconductors.  a) \nSchematic illustration of what happens to th e Fe-As-Fe tetrahedron as a function of T c.  b,c) Dependence of the \nmaximum-T c on the Fe-As(P)-Fe angle and Fe-Fe/ Fe-As(P) distance.  The maximum T c is obtained when the Fe-\nAs(P)-Fe bond angle reaches the ideal value of 109.47° for the perfect FeAs tetrahedron [16]. \n \n \n3.  Inelastic Scattering Studies \n \n For the cuprate superconducto rs, the undoped materials are Mo tt insulators where the Cu \nS=1/2 spins are two-dimens ional in nature, with a spin wave ba ndwidth that is typically ~0.2-0.4 \neV [1].  The undoped iron-base d superconductors are also magnetically ordered, and the \nmagnetic exchange interactions are only somewhat smaller than the cuprates.  More interestingly, the spin correlati ons in both systems su rvive into the superc onducting regime, with \na magnetic resonance that is clearly linke d to the superconducting order parameter. \n 3.1.  Iron Spin Waves  \nSingle crystals are available for the 1:2:2 mate rials (and for the 1:1 systems) that are not \nonly large enough for neutron diffraction studies, but  inelastic studies as  well.  For the undoped \nmaterials the spin wave dispersion rela tions have been measured for the SrFe\n2As2 [40], CaFe 2As2 \n[41,42], and BaFe 2As2 [43,44] systems, and the overall spin dynamics for the three systems are \nquite similar as shown in Table 3.  These st udies reveal that the spin dynamics are quite \nenergetic, with a spin wave bandwidth ~0.2 eV as shown in Fig. 8 for SrFe 2As2.  This energy \nscale is comparable to the energy scale of the S= 1/2 Cu spins in the Mott insulating cuprates.  In \ncontrast to the cuprates, though, there is significant spin wave  dispersion along the c-axis, \nalthough the overall dispersion is  still anisotropic.  Hence thes e materials are not strictly two-\ndimensional like the cuprates, but ar e better described as anisotropi c three-dimensional materials.  \nAll three materials also have a significant spin gap in the antiferromagnetic spin wave spectrum of the parent material, and the origin of this gap has not been established yet. \n \n 10Table 3.  Low temperature spin dynamics results, using Eq. (1), for the undoped 1:2:2 materials, obtained on \npowders (pwd) and single crystals (xtl).  For the Ba velocitie s, the data were obtained just above the spin wave gap, \nand hence it is likely that the actual values of the velocitie s will be larger when more complete data are available. \nMaterial va-b (meV-Å)  vc (meV-Å)  \n v v\nb - ac Band width (meV)  Gap (meV)  Reference\nSrFe 2As2 xtl 560±110 280±56 0.5 170 6.5(2) [40] \nCaFe 2As2 xtl 420 ±70 270±100 0.4 200 6.9(2) [41,42] \nBaFe 2As2 xtl 280±150 57±7 0.2  9.8(2) [44] \nBaFe 2As2 pwd  -  175 7.7(2) [43] \n \n \n \n \nFig. 8.  Calculated spin wave dispersion relations for SrFe 2As2 based on inelastic neutron scattering measurements \ntaken in the low energy regime [40].  The bandwidth of the spin waves is ≈0.2 eV for all three materials. \n \n These materials are itinerant electron system s and consequently the usual description of \nthe spin excitations would be in terms of the dynamic susceptibility χ(q,ω) of the electron \nsystem.  However, because of the large overall ba ndwidth of the spin wave excitations the higher \nresolution measurements have been taken at relatively small wave vectors and a simple \nparameterization of the dispersion relations in terms of a Heisenbe rg model and linear spin wave \ntheory can be used, employing the empirical relation \n \nqvq q vc c y x abq E2 2 2 2 2 2) ( +⎟⎠⎞⎜⎝⎛+ + Δ =→\n      ( 1 )  \n \nwhere the energy E(q) and the spin wave gap Δ  are in meV, the vab and v c are the in-plane and c -\naxis spin wave velocities in units of meV-Å, and the wave vectors are in Å-1.  The results for the \n 11three materials are given in Table 3, where we see that the basic description is quite similar for \nthe three in terms of the spin wave dispersion and overall bandwidth of the spin waves.  \nObviously these first experimental  results will be refined as th e measurements are extended, but \nthe basic energetics are now known.  At high ener gies the spin waves are reported to be heavily \ndamped [42], as can occur for itinerant electron sy stems where the collective excitations interact \nwith the single-particle density of states.  We would also expect that the overall spin dynamics \nfor the 1:1:1:1 systems will be similar, but at the present time sizable single crystals are not available and little work has been carried out [15].  However, spin dynamics work is now \nongoing for the Fe(Se-Te) materials.  3.2.  Superconducting Regime  \nThe initial search for magnetic correlations in the superconducting regime carried out on \na small polycrystalline sample of LaFeAsO\n0.87F0.13  was unsuccessful [18].  A subsequent \nmeasurement on a very large polycrystalline sample of Ba 0.6K0.4Fe2As2 observed magnetic \ncorrelations, and the development of a magnetic re sonance in the superconducting state [45], and \nthis work was quickly followed by single crystal measurements [46-48] as shown in Table 4.  The observation of a magnetic resona nce that is directly associated with the formation of the \nsuperconducting state, analogous to the magnetic re sonance phenomena first discovered in the \ncuprates, makes it clear that magnetic fluctuations  play an intimate role  in the superconductivity \nof both classes of high T\nC superconductors. \n \nTable 4.  Inelastic neutron scattering results for the magnetic resonance E r that develops in the \nsuperconducting phase of the 1:2:2 materials. \n \nMaterial E r(meV) T C(K) E r/kBTC Reference \nBa0.6K0.4Fe2As2 pwd 14 38 4.3 [45] \nBaFe 1.84Co0.16As2 xtl 9.6(3) 22 5.1 [46] \nBaFe 1.9Ni0.1As2 xtl 9.1(4) 20 5.3 [47,48] \n \nThere have not been any measurements of the dispersion of th e rare earth magnetic \nexcitations in any of these materials, but there have been detailed measurements of the energies \nand linewidths of the 18 meV Ce crysta l field level in su perconducting CeFeAsO 0.84F0.16, with \nsome interesting results [49].  Below the superconducting transition a substantial change in the \nenergy and increase in the intrinsi c linewidth of the level was observed.  This can be understood \nas the coupling of superconducti ng electrons with the crystal field levels.  When the \nsuperconducting gap opens an energy renormalizatio n can be expected, along with a decrease in \nthe linewidth for any excitation below the gap, because the electrons form a bound (Cooper) pair \nand there is not enough energy to break the pair.  On the other hand, an increase in linewidth \nwould be expected for excitations above the ga p, due to a ‘piling-up’ of the available one-\nelectron states.  This energy reno rmalization and linewidth behavior have been observed for both \nphonons [50] and crystal field leve ls [51] in conventional elect ron-phonon superconductors.  In \nthe present case the 18 meV level should be above the gap, and hence an increase in the linewidth would be expected, as observed.  A dramatic splitting of the crystal field levels has also been observed for the undoped system when the magnetic system orders. \n \n 124.  Future Directions  \n \nThis is a very young field as far as the superco nductivity is concerned, but the pace of \nresearch has been extremely rapid.  At this point the basic physics of the undoped (parent) \n1:1:1:1 and 1:2:2 materials is fa irly well established in terms of the structure, magnetic order, \nand spin dynamics, and in terms of how these overall properties comp are with expectations \nbased on first-principles theoretical calculations.  Of course, there are many issues still to be \nquantified and resolved.  The spin waves need to be measured to higher energies for all three of \nthe 1:2:2 materials, and determine if the damping is from single-particle (Stoner) excitations as might occur for itinerant electron systems, while little work on the spin dynamics of the 1:1:1:1 materials is available yet.  Much progress also has been made  on the doping dependence of the \nproperties, in that it is clear that the structural and magnetic phase transitions are reduced and eventually disappear as the superconductivity deve lops.  It appears that the magnetic order does \nnot overlap with the superconductivity in some syst ems, but it apparently does in others.  This \ncoexistence could be macroscopic in origin, or it could be intrinsic, and this issue will only be \nresolved when the question of inhomogeneity is fully addressed; the question is whether these \ntwo order parameters are mutually exclusive.   Magnetic correlations do persist into the \nsuperconducting regime, and the elucidation of the magnetic fluctuation spectrum in the \nsuperconducting regime is one of the most important  areas to explore.  Th e magnetic fluctuations \nare the present frontrunner among possible pairing mechanisms, as is the case for the cuprates;  \nboth systems are highly correlated electron materials—the cuprat es more so.  However, the \npairing mechanism is by no means settled for eith er system;  one only has to recall that the \npairing mechanism in the cuprates is still elus ive after more than tw o decades of intensive \nresearch.  There may be some surprises fo r the community, and perhaps the iron-based \nsuperconductors will provide the key to understanding both classes of materials. \nThe discovery of high temperature superconduc tivity in these iron-based materials has \nfocused the attention of the c ondensed matter physics community  on these new superconductors.  \nAlthough the superconductivity is ne w, they belong to an enormous class of systems with a wide \nvariety of properties.  This will enable the physical properties to be tailored both to investigate the fundamental properties of thes e systems as well as for applicati ons.  This flexibility provides \na vast potential that will stimulate the field for the foreseeable future. \nAcknowledgments \n \nThe authors would like to express their sincere grat itude to all of their collaborators, as listed in \nthe references, who have shared the research excitement  of this new family of superconductors.  \nP.D. is supported by the US Depa rtment of Energy, Division of\n Materials Science, Basic Energy \nSciences, through DOE DE-FG02-05ER46202; a nd by the US National Science Foundation \nthrough DMR-0756568. This work is also supported in part by the US De partment of Energy, \nDivision of Scientific User  Facilities, Basic Energy  Sciences. \n \nReferences \n \n[1] P. A. Lee, N. Nagaosa, and X-G. Wen, Rev. Mod. Phys. 78, 17 (2006); M. Eschrig, Adv. \nPhys. 55, 47 (2006). \n[2] Hosono Review, Physica C \n 13[3] Singh Review, Physica C \n[4] Yildirim Review, Physica C \n[5] B. I. Zimmer, W. Jeitschko, J. H. Albering, R. Glaum, M. Reehuis, J. Alloys and \nCompounds 229, 238 (1995);  R. Pottgen and D. Johrendt, Z. Naturforsch 63, 1135 \n(2008). \n[6] M. Pfisterer and G. Nagorsen, Z. Naturforsch. B 35, 703 (1980). \n[7] Joshua H. Tapp, Zhongjia Tang, Bing Lv, Kalyan  Sasmal, Bernd Lorenz, Paul C.W. Chu, \nArnold M. Guloy, Phys. Rev. B 78, 060505(R) (2008). \n[8] Michael J. Pitcher, Dinah R. Parker, Paul  Adamson, Sebas, Chemical Communications \n5918, 2008. \n[9] D. Fruchart, P. Convert, P. Wolfers, R. Mada r, J. P. Senateur, and R. Fruchart, Mater. \nRes. Bull. 10 , 169 (1975). \n[10] T. M. McQueen, M. Regulacio, A. J. Williams, Q. Huang, J. W. Lynn, Y. S. Hor, \nD.V. West, and R. J. Cava, Phys. Rev. B 78, 214305 (2008). \n[11] C. de la Cruz, Q. Huang, J. W. Lynn, J. Li, W. Ratcliff II, J. L. Zarestky, H. A. \nMook, G. F. Chen, J. L. Luo, N. L. Wang, and P. Dai, Nature 453, 899 (2008). \n[12] C. H. Lee, A. Iyo, H. Eisaki, H. Kito, M. T. Fernandez-Diaz, T. Ito, K. Kihou, H. \nMatsuhata, M. Braden, K. Yamada, J. Phys. Soc. Jpn. 77, 083704 (2008). \n[13] M. A. McGuire, A. D. Christianson, A. S.  Sefat, B. C. Sales, M. D. Lumsden, R. \nJin, E. A. Payzant, and D. Mandrus, Y. Luan  and V. Keppens, V. Varadarajan and J. W. \nBrill, R. P. Hermann, M. T. Sougrati a nd F. Grandjean, G. J. Long, Phys. Rev. B 78, \n094517 (2008). \n[14] Q. Huang, J. Zhao, J. W. Lynn, G. F. Chen, J. L. Lou, N. L. Wang, and P. Dai, \nPhys. Rev. B 78, 054529 (2008). \n[15] M. Ishikado, R. Kajimoto, S. Shamoto, M.  Arai, A. Iyo, K. Miyazawa, P. M. \nShirage, H. Kito, H. Eisaki, S.-W. Kim, H. Hosono, T. Guidi, R. Bewley, S. M. \nBennington, arXiv:0809.5128v2. \n[16] J. Zhao, Q. Huang, C. de al Cruz, S. Li, J. W. Lynn, Y. Chen, M. A. Green, G. F. \nChen, G. Li, Z. C. Li, J. L. Luo, N. L. Wang, and P. Dai, Nature Materials 7, 953 (2008). \n[17] Y. Chen, J. W. Lynn, J. Li, G. Li, G. F. Chen, J. L. Luo, N. L. Wang, P. Dai, C. \ndela Cruz, and H. A. Mook, Phys. Rev. B 78, 064515 (2008). \n[18] Y. Qiu, W. Bao, Q. Huang, T. Yildirim, J. M. Simmons, M. A. Green, J.W. Lynn, \nY.C. Gasparovic, J. Li, T. Wu, G. Wu, and X.H. Chen, Phys. Rev. Lett. 101, 257002 \n(2008). \n[19] J. Zhao, Q. Huang, Clarina de la Cruz, J.  W. Lynn, M. D. Lumsden, Z. A. Ren, J. \nYang, X. Shen, X. Dong, Z. Zhao, and P. Dai, Phys. Rev. B 78, 132504 (2008). \n[20] S. A. J. Kimber, D. N. Argyriou, F. Yoka ichiya, K. Habicht, S. Gerischer, T. \nHansen, T. Chatterji, R. Klingeler, C. Hess,  G. Behr, A. Kondrat, and B. Buchner, Phys. \nRev. B 78, 140503 (2008). \n[21] J. Zhao, W. Ratcliff-II, J. W. Lynn, G. F.  Chen, J. L. Luo, N. L. Wang, J. Hu, and \nP. Dai, Phys. Rev. B 78, 140504( R) (2008). \n[22] K. Kaneko, A. Hoser, N. Caroca-Canales, A.  Jesche, C. Krellner, O. Stockert, C. \nGeibel, Phys. Rev. B 78, 212502 (2008). \n[23] A. Jesche, N. Caroca-Canales, H. Rosner, H. Borrmann, A. Ormeci, D. \nKasinathan, H. H. Klauss, H. Luetkens, R.  Khasanov, A. Amato, A. Hoser, K. Kaneko, \nC. Krellner, and C. Geibel, Phys. Rev. B 78, 180504 (2008). \n 14[24] A. I. Goldman, D. N. Argyriou, B. Ouladdi af,, T. Chatterji, A. Kreyssig, S. Nandi, \nN. Ni, S. L. Bud’ko,, P. C. Canfield, and R. J. McQueeney, Phys. Rev. B 78, 100506(R) \n(2008). \n[25] A. Kreyssig, M. A. Green, Y. B. Lee, G.  D. Samolyuk, P. Zajdel, J. W. Lynn, S. \nL. Bud’ko, M. S. Torikachvili, N. Ni, S. Nandi , J. Leão, S. J. Poulton, D. N. Argyriou, B. \nN. Harmon, P. C. Canfield, R. J. McQu eeney, and A. I. Goldman, Phys. Rev. B 78, \n184517 (2008). \n[26] A. I. Goldman, A. Kreyssig, K. Prokes, D.  K. Pratt, D. N. Argyriou, J. W. Lynn, \nS. Nandt, S. A. Kimber, Y. Chen, Y. B. Lee,  G. Samolyuk, J. Leao, S. J. Poulton, S. L. \nBud’ko, N. Ni, P. C. Canfield, B. N. Harmon, and R. J. McQueeney, Phys. Rev. B 79, \n024513 (2009). \n[27] Q. Huang, Y. Qiu, W. Bao, J.W. Lynn, M. A. Green, Y.C. Gasparovic, T. Wu, G. \nWu, and X. H. Chen, Phys. Rev. Lett. 101, 257003 (2008). \n[28] M. Kofu, Y. Qiu, Wei Bao, S.-H. Lee, S. Chang, T. Wu, G. Wu, X. H. Chen, New \nJ. Phys. (accepted) arXiv:0901.0738v1 . \n[29] Y. Su, P. Link, A. Schneidewind, Th. Wolf , P. Adelmann, Y. Xiao, M. Meve, R. \nMittal, M. Rotter, D. Johrendt, Th. Brueckel, M. Loewenhaupt, Phys. Rev. B 79, 064504 \n(2009). \n[30] S. Margadonna, Y. Takabayashi, M. T. McDonald, K. Kasperkiewicz, Y. \nMizuguchi, Y. Takano, A. N. Fitch, E. Suar de and K. Prasside s, Chem. Commun. 5607 \n(2008). \n[31] W. Bao, Y. Qiu, Q. Huang, M.A. Green, P. Zajdel, M.R. Fitzsimmons, M. \nZhernenkov, M. Fang, B. Qian, E.K. Vehstedt, J. Yang, H.M. Pham, L. Spinu, Z.Q. Mao \narXiv:0809.2058v1. \n[32] S. Li, C. de la Cruz, Q. Huang, Y. Che n, J. W. Lynn, J. Hu, Y-L Huang, F-C. Hsu, \nK-W. Yeh, M-K. Wu, and P. Dai, Phys. Rev. B 79, 054503 (2009). \n[33] T. M. McQueen, Q. Huang, V. Ksenofontov, C. Felser, Q. Xu, H. W. Zandbergen, \nY. S. Hor, J. Allred, A. J. Williams, D. Qu, J. Checkelsky, N. P. Ong, R. J. Cava, Phys. Rev. B 79, 014522 (2009). \n[34] M. S. Torikachvili, S. L. Bud’ko, N. Ni , and P. C. Canfield, Phys. Rev. Lett. 101, \n057006 (2008). \n[35] W. Yu, A. A. Aczel, T. J. Williams, S. L.  Bud’ko, N. Ni, P. C. Canfield, and G. \nM. Luke, Phys. Rev. B 79, 020511 (2009). \n[36] D.K. Pratt, Y. Zhao, S.A.J. Kimber, A.  Hiess, D.N. Argyriou, C. Broholm, A. \nKreyssig, S. Nandi, S.L. Bud' ko, N. Ni, P.C. Canfield, R. J. McQueeney, A.I. Goldman, \nhttp://arxiv.org/abs/0812.4056\n. \n[37] Neutron Scattering Studies of Lanthanide  Magnetic Ordering, J. W. Lynn and S. \nSkanthakumar, Handbook on the Physics and Chemistry of Rare Earths , Chap. 199, Vol. \n31, pg. 315-350, ed. by K. A. Gschneidner, Jr., L. Eyring, and M. B. Maple (North Holland, Amsterdam, 2001). \n[38] Y. Qiu, M. Kofu, Wei Bao, S.-H. Lee, Q. Huang, T. Yildirim, J. R. D. Copley, J. \nW. Lynn, T. Wu, G. Wu, and X. H. Chen, Phys. Rev. B 78, 052508 (2008). \n[39] H. Chen, Y. Ren, Y. Qiu, W. Bao, R. H. Liu, G. Wu, T. Wu, Y. L. Xie, X. F. \nWang, Q. Huang, X. H. Chen, Europhys. Lett. 85, 17006 (2009). \n 15 16[40] J. Zhao, D-X. Yao, S. Li, T. Hong, Y. Ch en, S. Chang, W. Ratcliff II, J. W. Lynn, \nH. A. Mook, G. F. Chen, J. L. Luo, N. L. Wang, E. W. Carlson, J. Hu, and P. Dai, Phys. \nRev. Lett. 101 , 167203 (2008). \n[41] R. J. McQueeney, S. O. Diallo, V. P. Antropov, G. D. Samolyuk, C. Broholm, N. \nNi, S. Nandi, M. Yethiraj, J. L. Zarestky, J. J. Pulikkotil, A. Kreyssi g, M. D. Lumsden, B. \nN. Harmon, P. C. Canfield, and A. I. Goldman, Phys. Rev. Lett. 101, 227205 (2008).  \n[42] S. O. Diallo, V. P. Antropov, C. Broholm, T. G. Perring, J. J. Pulikkotil, N. Ni, S. \nL. Bud’ko, P. C. Canfield, A. Kreyssig, A. I. Goldman, and R. J. McQueeney, arXiv:0901.3784. \n[43] R.A. Ewings, T.G. Perring, R.I. Bewley, T. Guidi, M.J. Pitcher, D.R. Parker, S.J. \nClarke, A.T. Boothroyd, Phys. Rev. B 78, 220501(R) (2008). \n[44] K. Matan, R. Morinaga, K. Iida , and T. J. Sato, Phys. Rev. B 79 (in press) \narXiv:0810.4790v1. \n[45] A. D. Christianson, E. A. Goremychkin, R. Osborn, S. Rosenkranz, M. D. \nLumsden, C. D. Malliakas, I. S. Todorov, H. Cl aus, D. Y. Chung, M. G. Kanatzidis, R. I. \nBewley, and T. Guidi, Nature 456, 930 (2008). \n[46] M. D. Lumsden, A. D. Christianson, D. Parshall, M. B. Stone, S. E. Nagler, H. A. \nMook, K. Lokshin, T. Egami, D. L. Abernathy, E. A. Goremychkin, R. Osborn, M. A. McGuire, A. S. Sefat, R. Jin, B. C. Sales, and D. Mandrus, \nhttp://arXiv.org/abs/0811.4755v1\n. \n[47] S. Chi, A. Schneidewind, J. Zhao, L. W. Harriger, L. Li, Y. Luo, G. Cao, Z. Xu, \nM. Loewenhaupt, J. Hu, and P. Dai, Phys. Rev. Lett. (accepted) arXiv:0812.1354  . \n[48] S. Li, Y. Chen, S. Chang, J. W. Lynn, L.  Li, Y. Luo, G. Cao, Z. Xu, and P. Dai, \narXiv:0902.0813  . \n[49] S. Chi, D. T. Adroja, T. Guidi, R. Be wley, Shliang Li, Jun Zhao, J. W. Lynn, C. \nM. Brown, Y. Qiu, G. F. Chen, J. L. Lou, N. L. Wang, and Pengcheng Dai, Phys. Rev. \nLett. 101, 217002 (2008). \n[50] See, for example, S. M. Shapiro, G. Shirane, and J. D. Axe, Phys. Rev. B12, 4899 \n(1975). \n[51] See, for example, R. Feile, M. Loewenha upt, J. K. Kjems, and H. E. Hoenig, \nPhys. Rev. Lett. 47, 610 (1981). \n "    },    {        "title": "0902.0531v2.Tuning_Magnetic_Avalanches_in_Mn12_ac.pdf",        "content": "arXiv:0902.0531v2  [cond-mat.mtrl-sci]  7 Apr 2009Tuning magnetic avalanches in Mn 12-ac\nS. McHugh, Bo Wen, Xiang Ma, and M. P. Sarachik∗\nDepartment of Physics\nCity College of New York, CUNY\nNew York, New York 10031, USA\nY. Myasoedov and E. Zeldov\nDepartment of Condensed Matter Physics\nThe Weizmann Institute of Science\nRehovot 76100, Israel\nR. Bagai and G. Christou\nDepartment of Chemistry\nUniversity of Florida\nGainesville, Florida 32611, USA\nUsing micron-sized Hall sensor arrays to obtain time-resol ved measurements of the local magneti-\nzation, we report a systematic study in the molecular magnet Mn12-acetate of magnetic avalanches\ncontrollably triggered in different fixed external magnetic fields and for different values of the initial\nmagnetization. The speeds of propagation of the spin-rever sal fronts are in good overall agreement\nwith the theory of magnetic deflagration of Garanin and Chudn ovsky [1].\nPACS numbers: 75.45.+j, 75.40.Gb, 47.70.Pq\n1. INTRODUCTION\nMn12-acetate is a crystal composed of magnetic\nmolecules, each of which behaves as a high-spin, high-\nanisotropy magnet [2, 3]. At low temperatures, the 12\nMn atoms are strongly coupled via superexchange to\nform a ferrimagnet with a net (rigid) spin S= 10. Mag-\nnetic interactions between the molecules are thought to\nbe negligible so that Mn 12can be modeled by an effective\nspin Hamiltonian:\nH=−DS2\nz−AS4\nz−gµBSzBz+H⊥,(1)\nwhereBzis a magnetic field applied along the c-axis of\nthe crystal, Szis thezcomponent of the spin, D= 0.548\nK,A= 1.17×10−3K,g= 1.94, andH⊥represents small\nsymmetry-breakingtermsthat allowtunneling acrossthe\nanisotropy barrier [4, 5, 6]. The energy barrier against\nmagnetic reversal, U, is easily calculated from Eq. 1.\nThe magnetic relaxation rate for an individual molecule\nbecomes sufficiently slow at low temperatures ( <2 K)\nthatthemagnetizationofthecrystalcanbepreparedand\nmaintained in a metastable state for time periods well in\nexcessoftheexperimentaltimes. Oncein thismetastable\nstate, the magnetization may relax as an abrupt ( <1ms)\n“magnetic avalanche,” an exothermic process involving\nthereleaseofZeemanenergy[7]. Thesespatiallyinhomo-\ngeneous reversals proceed as a traveling “front” between\nregions in the crystal with opposing magnetization and\nhave been described as magnetic deflagration in analogy\nwith chemical deflagration [1, 8].\n∗Electronic address: sarachik@sci.ccny.cuny.eduIn general, the speed of a deflagration front is gov-\nerned by two parameters: the thermal diffusivity, κ,\nwhich specifies the rate at which heat diffuses through\nthe medium, and the reaction rate of the constituents,\nΓ(Tf), where Tfis the “flame temperature” produced\nby the reactants near the front. Combining these pa-\nrameters gives an approximate expression for the speed,\nv∼√\nκΓ [9]. In the case of magnetic deflagration, the\nmedium through which heat flows is the crystal, and Γ is\nthe relaxation rate of the metastable spins, which obeys\nan Arrhenius law,\nΓ = Γ0exp[−U(B)/T], (2)\nwith Γ 0= 3.6×107s−1[10, 11]. The relaxation rate can\nbe increased by lowering the barrier with an increasing\nexternal magnetic field or by increasing the temperature,\nT. Although κhas not been measured for Mn 12-ac, a\nvalue ofκ∼10−5m2/s was deduced from the avalanche\ndatainRef. [12]. Suzukiet al. [8] showedthat thespeeds\nofmagneticavalanchescanbemodeledapproximatelyas,\nv∼√κΓ0exp[−U/(2Tf)], where Tfis the temperature\nat or near the propagating front associated with the en-\nergy released by the reversing spins. The theory of mag-\nnetic deflagration stands in qualitative agreement with\nexperiments, yet more precise quantitative confirmation\nremains an open experimental challenge [1, 8, 12, 13, 14],\nwhich is undertaken here.\nThere are two parameters under experimental control\nwhenperformingmagneticavalanchestudies onMn 12-ac:\nthe external magnetic field and the initial magnetization\nwhich tunes the metastable spin density and thus the\navailable “fuel”. Varying the external magnetic field af-\nfectsboththebarrieragainstspinreversalandtheenergy\nreleased which determines the temperature Tfproduced2\nby the reversing spins. The variation of the metastable\nspin density affects primarily the energy released and\ntherefore, Tf. By varying these parameters indepen-\ndently, we areableto explorethe wide rangingconditions\nin which avalanches may be triggered. In particular, we\nreport systematic studies for three classes of avalanche\npreparations. The first class (I) contains avalanches trig-\ngered at various external fields with fixed (maximum)\ninitial magnetization. For these avalanches, both Uand\nTfvary. The second class (II) contains avalanches trig-\ngered at a fixed external field, but with various initial\nmagnetizations. Avalanches of this class differ primarily\nthrough Tf, withUvarying only through the internal\nfields. And the final class (III) contains avalanches trig-\ngered with various initial magnetizations and external\nfields, such that Tfis approximately constant while U\nvaries (details below).\nWe report the speeds of propagation of the fronts for\nthese three classes of avalanches, allowing us to make a\nthorough comparison with the theory of magnetic defla-\ngration. Our results are in overall agreement with the\ntheory. With certain simplifying assumptions detailed\nbelow, we obtain temperatures between 5 and 16 K and\nthermal diffusivities ranging from κ= 1.2×10−5to\n8.7×10−5m2/s, consistent with the value of κestimated\nin Ref. [12].\nFIG. 1: The initial magnetization, Mz, as a function of ap-\nplied cooling field. Msatis defined as the magnetization with\nall the spins aligned in the positive direction. The change\nof magnetization during an avalanche is ∆ M=Msat−Mz.\nThe same curve is found for all crystals measured. The inset\nshows the energy levels biased with a +0.3 T field.\n2. EXPERIMENT\nThe magnetization dynamics were studied with an ar-\nray of 30 ×30µm2Hall sensors spaced apart by 80 µmcenter-to-center [15]. Crystals of Mn 12-acetate with di-\nmensions about 1 .0×0.2×0.2mm3were attached to the\narraywith Apiezon M grease. The crystal was encased in\ngreasealong with a constantan wire placed near the sam-\nple for use as a heater in an arrangement similar to that\nused in Ref. [14]. The entire assembly was immersed in\n3He at temperatures down to <300 mK.\nPrior to triggering an avalanche, the sample was pre-\npared in a metastable magnetic state. To do this, the\nsamplewascooledfromahightemperature( ≈6K)down\nto 300 mK in the presence of a small external magnetic\n“cooling” field between ±0.3 T. The inset of Fig. 1 is\na schematic of the energy levels biased with a +0.3 T\ncooling field; as shown in Fig. 1, the magnetization of\nthe sample, Mz, depends on the magnetic field in which\nit was cooled. At 0.3 K, only the Sz=±10 states are\nappreciably occupied. Mzreflects the ratio of these oc-\ncupied states. Oncethe sample is well belowthe blocking\ntemperature, the external field can be changed without\nchanging the magnetization (the system is blocked). The\nfield is then increased to a predetermined value ( ≥+1.25\nT) [16]. When the field has stabilized ( ∼1 min), a cur-\nrent is passed through the wire heater gradually raising\nthe temperature and triggering the avalanche. For more\ndetails on triggering avalanches with this method, see\nRef. [14].\nAll avalanches reported here were triggered in a posi-\ntive field. The amount of metastable magnetization that\nreverses during an avalanche is given by ∆ M=|Msat−\nMz|, whereMzis the initial magnetization and Msatis\nthe magnetization with all spins aligned in the positive\ndirection. For full magnetization reversal, ∆ M= 2Msat.\nFor convenience, we introduce the parameter ∆ M/2Msat\nas a dimensionless measure ofthe initial metastable mag-\nnetization density. As an example, cooling the sample in\nzero field leads to Mz= 0, or ∆ M/2Msat= 0.5.\nWe prepared the three classes of avalanches by varying\nthe initial magnetization, Mz, and the external magnetic\nfieldHz. Variation of Hztunes the barrier, U, as well\nas the average energy released per molecule during an\navalanche,\n∝angbracketleftE∝angbracketright= 2gµBSBz/parenleftbigg∆M\n2Msat/parenrightbigg\n, (3)\nwhereBz=µ0(Hz+Mz). Avalanches of class I are\nthose with initial magnetization Mz=−Msat, i.e.,\n∆M/2Msat= 1, and Hzis varied. Class II avalanches\nare triggered at a fixed external field, with various ini-\ntial magnetizations. Finally, class III avalanchesare trig-\ngered at various HzandMz, such that ∝angbracketleftE∝angbracketrightremains con-\nstant.\nWe collected avalanche data on four different crystals\nwith dimensions 1 .00×0.20×0.20 mm3(Sample A),\n1.20×0.10×0.10mm3(Sample B), 0 .80×0.15×0.15mm3\n(Sample C), and 1 .00×0.25×0.25mm3(Sample D). We\nreport detailed data on crystal A. Although the absolute\nvalues of the avalanche speeds differed for different crys-\ntals (as discussed in detail later in this paper), similar3\nFIG. 2: The time response of five equally spaced Hall sensors\nplaced along the length of the crystal. The peak indicates\nthe arrival of the magnetization interface (avalanche fron t).\nThe inset shows the traveling front that separates spin-up\nand spin-down regions. Note the transverse magnetic field\nlines at the position of the spin-reversal front.\nbehavior was obtained for all crystals as a function of\nthe experimental parameters.\n3. RESULTS\nAs was shown by Suzuki et al. [8], the avalanche pro-\ngresses through the crystal in a similar fashion to that of\na domain wall in a ferromagnet [17]. There is an inter-\nface separating regions of opposing magnetization, which\nproduces a large transverse magnetic field, Bxnear the\nfront, as shown schematically in the inset of Fig. 2. Fig-\nure 2 shows the time response of five equally spaced Hall\nsensors produced by a zero field cooled avalanche. At\ntimet= 0, the magnetization is zero. At t≈0.32 ms,\nthe magnetization begins to reverse near the first sen-\nsor as the avalanche front approaches. At t= 0.41 ms,\nthe signal on the first sensor is maximum indicating the\navalanche arrival at position 0 µm. Byt= 0.65 ms all\nspins have reversed and the sample is completely magne-\ntized. The avalanche speed is deduced from the arrival\ntime of the peak at each sensor and the known spacing\nbetween the sensors.\nFigure 3 shows the avalanche speed for class I\navalanches triggered at various fields, all with the same\ninitial metastable magnetization, ∆ M/2Msat= 1. The\nspeeds of the avalanches increase as the field is increased.\nThis is expected since increasing the field both lowersthe\nbarrier and increases ∝angbracketleftE∝angbracketright. There are local maxima at\nfields corresponding to the tunneling resonances, which\nFIG. 3: Propagation speed as a function of applied magnetic\nfield for Class I avalanches in crystal A for Class I avalanche s,\n∆M/2Msat= 1\nFIG. 4: Propagation speed as a function of ∆ M/2Msatfor\nClass II avalanches in crystal A. The field was fixed at 2 .50 T\nand 2.20 T, while ∆ M/2Msatwas varied between about 0 .10\nand 1.00.\nare denoted with vertical dotted lines. This tunneling\nenhancement of the avalanche speed is consistent with\npreviously reported results [12, 13, 14]. It is also an in-\ndication that the flame temperatures are low enough to\npreserve the effective Hamiltonian, Eq. 1, and the rigid\nspin (S= 10) approximation.\nFigure 4 shows the speed for class II avalanches trig-\ngered at fixed values of the external field. In particular,4\nFIG. 5: Propagation speed as a function of applied magnetic\nfield for Class III avalanches in crystal A. The initial magne -\ntization and external field are adjusted to hold the average\nenergy released per molecule constant at ∝angbracketleftE∝angbracketright= 32.6 K and\n18.3 K. The vertical lines indicate the fields at which quantum\ntunneling occurs for Mn 12-ac. Note that the avalanche speed\ndisplays clear oscillations as a function of magnetic field, with\nhighervalueson-resonancethanoff-resonanceduetoquantu m\ntunneling. This can also be seen in Fig. 7.\nFIG. 6: Speed of propagation of Class II avalanches triggere d\nin four different crystals at µ0Hz= 2.5 T for various initial\nmagnetizations.\nFIG. 7: Avalanchespeed vs. the ratio U/Tmax, whereUis the\ncalculated barrier and Tmaxis the maximum flame tempera-\nture. The inset shows Tmaxcalculated from the heat capacity\nat 2.5 T as a function of ∝angbracketleftE∝angbracketright.\ndata are shown for µ0Hz= 2.50 T and µ0Hz= 2.20 T.\nBy keeping the field fixed and varying the initial magne-\ntization, only ∝angbracketleftE∝angbracketrightvaries while Uremains approximately\nfixed. As ∆ M/2Msatdecreases, so does the speed.\nFigure 5 shows the speed for class III avalanches trig-\ngered at various external fields. The initial magnetiza-\ntions were also varied such that ∝angbracketleftE∝angbracketrightremained approx-\nimately constant. Presumably, the flame temperature\nis also nearly constant for all avalanches so prepared.\nTherefore, the variation in avalanche speeds should be\ndue to variation in the field-dependent barrier U. Again,\nthe vertical dotted lines drawn on Fig. 5 denote the lo-\ncation of the resonant fields for Mn 12-ac.\nFigure 6 compares the class II avalanche speeds for all\nfour crystals. The speed of the avalanche varies consid-\nerably from sample to sample; however, any dependence\non the sample dimensions is not immediately obvious.\n4. COMPARISON WITH THEORY AND\nDISCUSSION.\nGaranin and Chudnovsky [1] developed a comprehen-\nsive theory of magnetic deflagration describing the ig-\nnition and propagation of the deflagration front. For a\nplanar front, the avalanche speed is given over a broad\nrange of parameters by the simple approximate expres-\nsion [18]:\nv=/radicalBigg\n3κTfΓ(B,Tf)\nU(B), (4)5\nFIG. 8: (a) Avalanche speed vs. the ratio ( U∗/Tf), where the scaled barrier U∗= (1−α∆M\n2Ms)Uwithα= 0.13, and the\nflame temperature Tf= 0.67×Tmaxwithκ= 1.2×10−5m2/s. The inset illustrates that a data collapse can be obtaine d\nby adjusting U∗, (hereκ= 2.4×10−6m2/s); however, numerical agreement with the measured data re quires the additional\nscaling parameter Tf. (b) Data collapse obtained using αcalculated from the measured transverse field during the ava lanche,\nsettingT=Tmax, and allowing the thermal diffusivity to vary with temperatu re. The fit yields κ= (1.8×10−8) T2.9m2/s.\nwhereTfis the temperature at the front (flame tem-\nperature), κis the thermal diffusivity, U(B) is the field-\ndependent barrier in units of Kelvin, and Γ( B,Tf) is the\nrelaxation rate of the metastable spins (Eq. 2).\nRef. [19] established the importance of the dipolar\nfields in Mn 12-ac, as a fully magnetized sample adds (or\nsubtracts) µ0Mz=±52 mT to the applied external field,\nµ0Hz. We account for the initial magnetization, Mz,\nwhen calculating the various field dependent quantities\nusingBz=µ0(Hz+Mz), where −52 mT≤Mz≤52\nmT (see Fig. 1). The barrier U(Bz=µ0Hz+µ0Mz) is\ncalculated from the effective spin Hamiltonian (Eq. 1).\nThe average magnetic energy released by the relaxing\nspins(Eq. 3)leadstoanincreaseinthe temperaturenear\nthe front. Assuming no heat loss, the maximum possible\ntemperature, Tmax, can be calculated using the experi-\nmental heat capacity reported in Ref. [11]. The heat ca-\npacity of Mn 12-ac depends on the magnetic field. There-\nfore, wesubtractthe calculatedzero-fieldspin (Schottky)\ncontribution from the measured zero-field heat capacity\nfrom the data reported in Ref. [11]. To this we add the\ncalculated spin contribution at a specified field, Bz, for\nthe total field dependent heat capacity Ctot(Bz,T). By\nequating the integral of this heat capacity to the aver-\nage energy released per molecule, ∝angbracketleftE∝angbracketright, we can calculate\nTmax,\n∝angbracketleftE∝angbracketright=/integraldisplayTmax\n0Ctot(Bz,T)dT. (5)\nWe assume the initial (ignition) temperature is much lessthanTmax. This is a reasonable approximation, as the\nignition temperatures for avalanches triggered above 1T\nare below 1 K (see ref. [14]) compared with values calcu-\nlated for Tmaxbetween 7 and 18 K (depending on ∝angbracketleftE∝angbracketright).\nTmax(forµ0Hz= 2.5 T) is shown as a function of ∝angbracketleftE∝angbracketright\nin the inset of Fig. 7 (a).\nWe now proceed to compare our data with the theory\nof Garanin and Chudnovsky [1] as given by Eq. 4. If we\nassume that the thermal diffusivity κis a constant (or\na weak function of temperature), then the speeds for all\navalanches should lie on a single curve when plotted as\na function of U/Tmax. Figure 7 shows avalanche speeds\nfor crystal A for the three different experimental proto-\ncols shown in Figs. 3, 4, and 5 plotted as a function\nofU/Tmax. Although the overall behavior for the three\ntypes of avalanches is similar, the data do not lie on one\ncurve.\nThe deviations could arise from severalfactors. (1) We\nhaveused an Arrhenius form for the magnetic relaxation;\ndepartures from Arrhenius law behavior are unlikely to\nbe responsible for the deviations as it has been found\nexperimentally to hold reasonably well in the range of\ntemperature of our experiment [10, 11]. (2) The thermal\ndiffusivity is known to depend on temperature, while we\nhave assumed it to be constant. (3) The flame temper-\nature may be lower than the value calculated from the\nspecific heat, as some of the energy may escape the sam-\nple, or be distributed ahead of the front. (4) The barrier\nUmaybe reduced by the transversecomponent of the in-\nhomogeneous field, Bx, established at the traveling front6\nby the reversing spins (see inset to Fig. 2). The effects\nofBxcan be included in the calculation of Uby includ-\ning an additional Zeeman term ( −gµBSxBx) in Eq. 1.\nIn addition, Bxprovides a symmetry-breaking term that\nincreases the tunneling rate [20, 21].\nWe note that the deviations shown in Fig. 7 are espe-\ncially pronounced at high values of U/Tmax. In particu-\nlar, the class I avalanches with ∆ M/2Msat= 1 (shown\nas filled diamonds) have the highest speeds. This sug-\ngests that reduction of the potential barrier Ufor large\n∆M/2Msatplays an important role.\nItisunclearhowtoincorporatetheeffectsofaspatially\ninhomogeneous transverse field component into the ana-\nlytical theory of magnetic deflagration (Eq. 4). Instead,\nwe include the effects of Bxon the relaxation rate by\nintroducing an effective barrier:\nU∗≡/parenleftbigg\n1−α∆M\n2Msat/parenrightbigg\nU, (6)\nwhereαis determined empirically [22]. Although the\nscaling factor α∆M/2Msatexplicitly contains Mz(thus\nappearing to be used twice), it is used here only to ac-\ncount for the size of Bx. This is justified by our exper-\niment, since the maximum value of Bxmeasured by the\nHall sensors during an avalanche is found to be propor-\ntional to ∆ M/2Msat.\nThe inset to Fig. 8 (a) demonstrates that a collapse\nonto a single curve is obtained for α= 0.13±0.01. How-\never, the collapsed curve does not agree with the theory,\nshown by the dashed curve. An additional step can bring\nthem into line, as described below.\nAs pointed out earlier, due to possible heat loss\nthrough the edges of the crystal and/or heat diffusion\nahead of the front, the flame temperature Tfmay well\nbe less than Tmax. Assuming that Tfis proportional to\nTmax, the constantofproportionalityis deduced from fit-\nting the data in the inset of Fig. 8 (a) with Eq. 4. The\ndiffusivity, still assumed to be temperature-independent,\nis also treated as a fitting parameter. As shown in the\nmain part of Fig. 8 (a), agreement with theory is ob-\ntained for crystal A for Tf= (0.67±0.02)×Tmaxand\nκ= 1.2×10−5m2/s . Using this analysis, all crystals\nshow similar dependence on the barrier U∗and the flame\ntemperature Tfand yield Tf≈0.67×Tmax. However, we\nfind that the thermal diffusivity ranges from 1.2 ×10−5\nto 8.7×10−5m2/s from crystal to crystal.\nThe fact that Tfis the same fraction, 0 .67×Tmax,\nfor all crystals is a puzzle. The rate at which heat es-\ncapes the crystal during an avalanche must affect Tf.\nThe rateofheatlossis controlledprimarilybythe crystal\ncross section, surface roughness, and the thermal mount-\ning conditions. Variations in the mounting conditions\ninevitably occur (e.g., thickness of insulating grease), al-\nthough every effort was made to use similar conditions\nfrom crystalto crystal. There wereno obviousvisible dif-\nferences in surface quality of the crystals. The cross sec-\ntions, however, were deliberately varied from 0 .10×0.10\nto 0.25×0.25 mm2. One expects that the crystals withsmaller cross sections should lose more heat through the\nboundaries and should consequently have lower flame\ntemperatures and, according to Eq. 4, smaller speeds.\nFigure 6 shows that the maximum speeds vary by ap-\nproximately a factor of 2.5 from crystal to crystal, but\nwithout the expected dependence on cross section. This\nimplies that the widely different avalanche speeds in the\nfour crystals (see Fig. 6) are unlikely to be due primarily\nto heat loss. Instead, we suggest that the variation of the\navalanche speeds are attributable to variations of κ. The\nthermal diffusivity of dielectric crystals (like Mn 12-ac) at\nlow temperatures is known to be strongly dependent on\nthe defects, surface roughness, and dislocations in the\ncrystal [23].\nAn additional puzzle is the large amount by which the\npotential barrier needs to be reduced to obtain a fit by\nthe above analysis. From our data, we deduce a bar-\nrierU∗that is 87% of the classically calculated barrier,\nU. A straightforward calculation implies that a trans-\nverse field of ≈0.4 T is required to reduce the barrier by\nthat amount. The largest Bxfield recorded by the Hall\nsensors during an avalanche is only ∼0.05 T, an order\nof magnitude smaller. Although it may contribute to it,\nthe measured transverse field cannot by itself account for\nthe large reduction of the barrier.\nIn the analysis presented above, the thermal diffusiv-\nity was assumed to be independent of temperature. We\nnow relax this condition. We assume that the barrier U∗\nis reduced by a much smaller amount corresponding to\nthe measured transverse field, we set Tf=Tmax, and\nwe allow κto assume a temperature dependence that\nyields the best fit. The result of this alternate fitting\nprocedure, shown in Fig. 8 (b), yields a collapse that is\nacceptable within the experimental uncertainties of the\nmeasurements.\nRemarkably, the latter method of analysis yields a\nthermal diffusivity that increases with increasing tem-\nperature approximately as κ∝T3. This form seems\nquite unphysical, as the thermal diffusivity normally de-\ncreases as the temperature is raised. We suggest that\nthis unexpected behavior may be associated with a spin-\nphonon bottleneck.\nA number of experiments have provided evidence that\na spin-phonon bottleneck strongly affects the spin dy-\nnamics and energy relaxation at low temperatures in\nmolecular magnets such as V 15[24], Fe 8[25, 26] and Ni 4\n[27]. In this process, the Zeeman energy generated by\nthe reversing spins does not find a sufficient number of\nphononmodesat lowtemperaturestoallowdirectenergy\nrelaxation and equilibration, so that thermal equilibrium\nisestablishedslowlywhilethe energyis“bottlenecked”in\nthe spin system. This bottleneck is lifted as the temper-\nature increases, so that the number of available phonon\nmodes increases and the energy is able to relax by direct\nspin-phonon processes. The effect of the bottleneck can\nfind expression within our analysis as either a departure\nfrom Arrhenius Law behavior(which we haveassumed to\nbe valid), or as an anomalous temperature dependence of7\nthe thermal diffusivity. Within this scenario, κwouldnot\ndisplaythe sametemperature dependence when obtained\nby the standard method of measurement where one de-\ntermines the time of propagation of a heat pulse, since in\nthis case the energy is deposited into the phonon system\ndirectly.\n5. CONCLUSION\nWe have presented the results of a thorough investiga-\ntion in Mn 12-ac of the behavior of magnetic avalanches -\nthe rapid reversal of magnetization that spreads through\nthe crystal at subsonic speeds as a narrow interface be-\ntween regions of opposite spin. A controlled set of mea-\nsurements in which some parameters were held fixed\nwhile others were varied provided systematic informa-\ntion, enabling a rigorous comparison with the theory.\nTwo different methods were applied to fit data to the\ntheory of magnetic deflagration of Garanin and Chud-\nnovsky [1]. In the first, we suggest that the internal\ntransverse field produced by the avalanche front affects\nthe speed of the front itself. We model this effect with\na reduced barrier, U∗, that varies with the size of the\ntransverse field, Bx, produced by the avalanche front.\nAssuming a constant, temperature-independent thermal\ndiffusivity, a reduced barrier U∗allows a collapse of all\nthe data onto a single curve. However, the transverse\nfield measured at the front is not sufficiently strong to\naccount for the large barrier reduction needed to obtain\na good fit. A barrier reduction of this magnitude, if cor-\nrect, defies a simple classicalanalysisand maybe asignal\nthat quantum effects are important in the deflagration\nprocess for all values of µ0Hz, not just those associatedwith the tunneling resonances [5, 12, 13, 14].\nAn alternative method of analysis that assumes a\nsmaller barrier reduction commensurate with the mea-\nsured values of transverse field yields a temperature de-\npendent κ∝T3. We speculate that this rather surpris-\ning temperature dependence may be real and due to a\nphonon bottleneck that becomes less effective asthe tem-\nperature is raised.\nTo summarize, we find overall agreement between our\nmeasurements and the theory of magnetic deflagration of\nGaranin and Chudnovsky[1]. However, detailed compar-\nisonyieldseither(A)astrongerreductionofthepotential\nbarrier than can be justified by the measured transverse\nfields; or (B) a thermal diffusivity that unexpectedly in-\ncreases with increasing temperature, perhaps due to a\nphonon bottleneck; or (C) a combination of these (and\npossibly other) factors. Further confirmation of the the-\nory and a better understanding of the avalanche process,\nwould be provided by a detailed theoretical analysis of\nbottleneckeffects, andindependent measurementsofvar-\nious parameters such as the flame temperature and the\nthermal diffusivity.\n6. ACKNOWLEDGEMENTS\nWe are grateful to Eugene Chudnovsky, Dmitry\nGaranin,andYosiYeshurunformanyhelpfuldiscussions.\nWethank HadasShtrikmanforprovidingthewafersfrom\nwhichthe Hallsensorswerefabricated. S. M. thanksLiza\nMcConnell for assistance with the data analysis. This\nwork was supported at City College by NSF grant DMR-\n00451605. E. Z. acknowledges the support of the Israel\nMinistry of Science, Culture and Sports. Support for G.\nC. was provided by NSF grant CHE-0414555.\n[1] D.A. Garanin and E.M. Chudnovsky,Phys. Rev. B 76,\n054410 (2007).\n[2] T. Lis, Acta Cryst. B 36, 2042 (1980).\n[3] R. Sessoli, D. Gatteschi, A. Caneschi, and M. A. Novak,\nNature (London) 365, 141 (1993).\n[4] R. Sessoli, H.-L.Tsai, A. R. Schake, S. Wang, J. B. Vin-\ncent, K. Folting, D. Gatteschi, G. Christou, and D. N.\nHendrickson, J. Am. Chem. Soc. 115, 1804 (1993)\n[5] J. R. Friedman, M. P. Sarachik, J. Tejada, and R. Ziolo,\nPhys. Rev. Lett. 76, 3830 (1996).\n[6] S. Hill, J. A. A. J. Perenboom, N. S. Dalal, T. Hathaway,\nT. Stalcup, and J. S. Brooks, Phys. Rev. Lett. 80, 2453\n(1998), I.Mirebeau etal., Phys.Rev.Lett. 83, 628(1999)\n[7] C. Paulsen and J.G. Park, in Quantum Tunneling of\nMagnetization-QTM’94 , edited by L. Gunther and B.\nBarbara (Kluwer, Dordrecht, The Netherlands, 1995),\npp. 189-207.\n[8] Yoko Suzuki, M. P. Sarachik, E. M. Chudnovsky, S.\nMcHugh, R. Gonzalez-Rubio, Nurit Avraham, Y. Mya-\nsoedov, E. Zeldov, H. Shtrikman, N.E. Chakov, and G.\nChristou , Phys. Rev. Lett. 95, 147201 (2005).\n[9] L. D. Landau and E. M. Lifshitz, Fluid Dynamics, (Perg-amon, New York 1987).\n[10] M. A. Novak, R. Sessoli, A. Caneschi, and D. Gatteschi,\nJ. Magn. Magn. Mater. 146, 211 (1995), F. Luis, J. Bar-\ntolom´ e, J. F. Fern´ andez, J. Tejada, J. M. Hern´ andez,\nX. X. Zhang, and R. Ziolo, Phys. Rev. B. 55, 11448\n(1997), B. Barbara, L. Thomas, F. Lionti, I. Chiorescu,\nA. Sulpice, J. Magn. Magn. Mater., 200, 167-181 (1999)\n[11] A. M. Gomes, M. A. Novak, R. Sessoli, A. Caneschi, and\nD. Gatteschi, Phys. Rev. B 57, 5021(1998).\n[12] A. Hernandez-Minguez, F. Macia, J. M. Hernandez, J.\nTejada, and P. V. Santos, J. Magn. and Magn. Matt.,\n1457-1463, 320 (2008).\n[13] A. Hernandez-Minguez, J. M. Hernandez, F. Macia, A.\nGarcia-Santiago, J. Tejada, and P. V. Santos, Phys. Rev.\nLett.95, 217205 (2005).\n[14] S. McHugh, R. Jaafar, M. P. Sarachik, Y. Myasoedov,\nA. Finkler, H. Shtrikman, E. Zeldov, R. Bagai, and G.\nChristou , Phys. Rev. B 76, 172410 (2007).\n[15] Nurit Avraham, Ady Stern, Yoko Suzuki, K. M. Mertes,\nM. P. Sarachik, E. Zeldov, Y. Myasoedov, H. Shtrikman,\nE. M. Rumberger, D. N. Hendrickson, N. E. Chakov, and\nG. Christou, Phys. Rev. B. 72, 144428 (2005).8\n[16] In order to avoid complications with the fast-relaxing mi-\nnor species in Mn 12-acetate, the external field is chosen\nto be above +1 .25 T, at which point, the minor species\nhas already relaxed to the stable state and is uninvolved\nin the avalanche.\n[17] Mn 12-ac is a superparamagnet at the temperatures\ngreater than ≈3 K, which are produced during an\navalanche. This precludes the possibility of a ferromag-\nnetic domain wall.\n[18] TheexpressionderivedinRef. [1] fortheavalanchespe ed,\nv, contains afactor√\n4rather thanthe√\n3usedhere. The\nfactor√\n4 was derived assuming the heat capacity is of\nthe the form C∝T3; however, a fit to the heat capacity\nof Ref. [11] yields C∝T2in the temperature range of\ninteresthere. Usingtheexperimental temperaturedepen-\ndence in the derivation for vgives the appropriate factor√\n3.\nThis expression for vis correct for relatively slow relax-\nation rates, i.e., U/Tf>>1 [1], which we find is approx-\nimately satisfied by the avalanche data presented here\n(see Fig. 7).\n[19] S. McHugh, R. Jaafar, M. P. Sarachik, Y. Myasoedov, H.\nShtrikman, E. Zeldov, R. Bagai, and G. Christou, Phys.\nRev. B79, 052404 (2009).\n[20] Jonathan R. Friedman, Phys. Rev. B 57, 10291 - 10294\n(1998)\n[21] E. del Barco, A.D. Kent, S. Hill, J.M. North, N.S. Dalal,E. Rumberger, D.N. Hendrikson, N. Chakov, and G.\nChristou, J. Low Temp. Phys. 140, 119 (2005).\n[22] It should be mentioned that the data can also be\ncollapsed by scaling the temperature, T∗= [1 +\nα(∆M/2Ms)]Tmax, rather than the barrier U∗. We can\nfind no physical justification for this, as the flame tem-\nperature is determined by the Zeeman energy released\nand not by the height of the barrier.\n[23] C. Enss and S. Hunklinger, Low-temperature Physics,\n(Springer-Verlag, Berlin, 2005).\n[24] I. Chiorescu, W. Wernsdorfer, A. Muller, H. Bogge, and\nB. Barbara, Phys. Rev. Lett. 84, 3454 (2000).\n[25] M. Bal, J. R.Friedman, E. M.Rumberger, S.Shah, D.M.\nHendrickson, N. Avraham, Y. Myasoedov, H. Shtrikman,\nand E. Zeldov, J. Appl. Phys. 9908D103 (2006); M. Bal,\nJ. R. Friedman, W. Chen, M. T. Tuominen, C. C. Beedle,\nE. M. Rumberger, and D. M. Hendrickson, Europhys.\nLett.82, 17005 (2008).\n[26] K. Petukhov, S. Bahr, W. Wernsdorfer, A.-L. Barra, and\nV. Mosser, Phys. Rev. B 75, 064408 (2007); S. Bahr, K.\nPetukhov, V. Mosser, and W. Wernsdorfer, Phys. Rev.\nB77, 064404 (2008).\n[27] G. de Loubens, D. A. Garanin, C. C. Beedle, D. N. Hen-\ndrickson, and A. D. Kent, Europhys. Lett. 83, 37006\n(2008)."    },    {        "title": "0904.4490v1.Magnetically_induced_electric_polarization_in_an_organo_metallic_magnet.pdf",        "content": "arXiv:0904.4490v1  [cond-mat.mtrl-sci]  28 Apr 2009Magnetically-induced electric polarizationinanorgano- metallicmagnet\nV. S. Zapf1, M. Kenzelmann2, F. Wolff-Fabris1,∗, F. Balakirev1, Y. Chen3,4,5\n1National High Magnetic Field Laboratory (NHMFL), Los Alamo s National Lab (LANL), Los Alamos, NM\n2Laboratory for Developments and Methods, Paul Scherrer Ins titute, CH-5232 Villigen, Switzerland\n3Department of Physics and Astronomy, Johns Hopkins Univers ity, Baltimore, Maryland 21218, USA\n4NIST Center for Neutron Research, National Institute of Sta ndards and Technology, Gaithersburg, MD 20899\n5Department of Materials Science and Engineering, Universi ty of Maryland, College Park, MD 20742\n†Now at Dresden Hoch-feld Labor, Dresden, Germany, D-01328\n(Dated: September 1, 2021)\nThecouplingbetweenmagneticorderandferroelectricityh asbeenunderintenseinvestigationinawiderange\nof transition-metal oxides. The strongest coupling is obta ined in so-called magnetically-induced multiferroics\nwhereferroelectricityarises directlyfrommagnetic orde r thatbreaks inversion symmetry. However, ithasbeen\ndifficult to find non-oxide based materials in which these eff ects occur. Here we present a study of copper\ndimethyl sulfoxide dichloride (CDC), an organo-metallic q uantum magnet containing S= 1/2Cu spins, in\nwhichelectricpolarization arisesfrom non-collinear mag netic order. Weshow that the electricpolarization can\nbe switched in a stunning hysteretic fashion. Because the ma gnetic order in CDC is mediated by large organic\nmolecules,ourstudyshowsthatmagnetoelectricinteracti onscanexistinthisimportantclassofmaterials,open-\ning the road to designing magnetoelectrics and multiferroi cs using large molecules as building blocks. Further,\nwe demonstrate that CDC undergoes a magnetoelectric quantu m phase transition where both ferroelectric and\nmagnetic order emerge simultaneously as a functionof magne tic fieldatverylow temperatures.\nPACS numbers:\nKeywords:\nMagnetoelectric multiferroics are compounds with mag-\nneticandelectricordersthatcoexistandarecoupledviama g-\nnetoelectric interactions [1, 2, 3, 4]. Research in this fiel d is\nmotivated by the promise of devices that can sense and cre-\natemagneticpolarizationsusingelectricfieldsandviceve rsa,\nthereby creating new functionality as well as improving the\nspeed, energy-efficiencyand size of existing circuits. A ne w\nclassofinducedmultiferroicshasbecomethetopicofinten se\nstudyinthepastfewyears,inwhichamagneticorderinduces\nan electric polarization [5, 6, 7, 8, 9, 10, 11, 12, 13]. These\nmaterials are either low-dimensionalor frustrated magnet s in\nwhich competinginteractionsgive rise to non-collinearor der\nthat breaks inversion symmetry. This inversion symmetry-\nbreakingmagnetismcouplestothelatticemostlikelyviasp in-\norbit interactions that attempt to lower magnetic entropy a nd\ninthe processcreateelectricpolarization.\nMost magnetoelectrics and multiferroics are transition-\nmetal oxides or fluorides where the magnetoelectric interac -\ntions are mediated via superexchange through the oxide and\nfluoride anions. Magnetoelectric interactions can also be e x-\npected in other materials such as organo-metallic solids bu t\nhavenotyetbeenclearlyestablished[14,15,16]. Inthispa per\nwepresentfield-inducedmultiferroicbehaviourinanorgan o-\nmetallicquantummagnet,CuCl 2·2[(CH3)2SO](CDC)where\nthe Cu spins adopt non-collinear magnetic order that create s\nanelectricpolarizationinthepresenceofmagneticfields. Un-\nlike most magnetically-induced multiferroics, the magnet ic\nspins do not form a spiral in order to break inversion sym-\nmetry.\nCDC crystallizes in an orthorhombiccrystal structure with\nspace group Pnma (see Fig. 1a) [17]. The Cu spins form\nzig-zag chains in the crystallographic a-c plane, along whi chthe Cu spinsare antiferromagneticallycoupledvia a supere x-\nchange interaction J = 1.46 meV mediated by Cl ions [18].\nPerpendicular to the chains, the Cu atoms are separated by\ndimethyl sulfoxide groups (Fig. 1b) and it is this weaker an-\ntiferromagnetic interaction that sets the energy scale for 3-\ndimensional long-range antiferromagnetic order with a N ´ eel\ntemperature T N= 0.9K [18]. Fig. 1c shows the evolu-\ntion of the Cu spins with applied magnetic fields along the\nc-axis. At zero magneticfield H, the magneticorderconsists\nof a collinear antiferromagnetic arrangement with the mag-\nnetic moments pointing along the c-axis. For magnetic fields\napplied along the c-axis, the spins undergo a first-order spi n-\nflop transition into the b-axis at 0.3 T. As His increased fur-\nther, spin-orbit couplings produce a staggered g-tensor an d a\nDzyaloshinskii-Moriya interaction that create effective local\nmagnetic fields on the Cu sites whose magnitude is propor-\ntional to the external magnetic field and whose direction al-\nternates from one site to the next. These are only shown in\nthe final panel of Fig. 2c for clarity. In response to these\nstaggered fields, the spins gradually rotate from the b-axis to\nthe a-axis and become non-collinearin the process [19]. Be-\ntweenH= 0.3Tand3.8T,themagneticstructureisthusde-\nscribedbytwoantiferromagneticorderparameters,onedue to\ntheantiferromagneticsuperexchangeinteractionsbetwee nthe\nCuspinsandtheotherduetothespin-orbit-inducedstagger ed\nfields. Finally, the spins align with the staggered fields alo ng\nthe a-axis for Hc>3.8T. In addition to the behaviour de-\nscribedso far,the spinsalso increasinglycant alongthe ma g-\nnetic field direction with increasing field. The non-colline ar\nstate between 0.3 and 3.8 T (AFM B) where the two order\nparameters are competing with each other breaks inversion\nsymmetry and thereby allows an electric polarization to oc-2\nFIG. 1: a) Crystal structure of CDC showing the Cu-Cl chains. b)\nStructure showing the organic molecules mediating exchang e along\nthe b-axis. c) Effect of applied magnetic fields on the spins ( shows\nas arrows) of the Cuatoms (shown as balls)for one unit cell.\ncur along the b-axis. In this work we present measurements\nof the electric properties of CDC and we show that the mag-\nneticandelectricpolarizationscoexistandarecloselyco upled\nforHcbetween0.3and3.8T.\nSingle-crystal samples of CDC were grown by a flux\nmethod[19]. Forelectricpolarizationmeasurements,thes am-\nples were coated on the a-c faces with silver paint and leads\nwere attached, permitting the magnetoelectric current to b e\nrecordedwithaStanfordResearch570currenttovoltagecon -\nverteralongtheb-axis. Measurementswereperformeddurin g\nmagnetic field pulses with applied magnetic fields along the\nc-axis. The samples were cooled by immersionin liquid3He\nwhile rapid 10 T magnetic pulses with dB/dt up to 3.8 kT/s\nwere applied using a short-pulse capacitatively-driven ma g-\nnet at the National High Magnetic Field Laboratory in Los\nAlamos,NM.Alarge dB/dtincreasesthesignaltonoiselev-\nels and thus only the upsweep data with a larger dB/dtis\nshown. The dielectric constant was measured capacitativel y\ninthe liquidmixingchamberofa3He-4He dilutionrefrigera-\ntor. Inordertoruleoutpossiblemagnetostrictionaffecti ngthe\ndielectric constantmeasurements,magnetostrictionwas m ea-\nsured separately using a titanium dilatometer in the vacuum\nmixingchamber[20,21]. Nosignaturesofthe3.8Ttransitio n\nwere observed with a sensitivity to magnetostriction effec ts\n10xgreaterthanthat ofthe dielectricconstantmeasuremen ts.\nThe electric polarization of CDC along the b-axis and the\nmagnetoelectriccurrent fromwhich it was derivedare shown\nin Fig. 2a and b. The data are shown for a series of mag-\nnetic field pulses along the positive and negative c-axis (A\nthrough G) applied at T= 0.5K while the electric polariza-\ntion is measured along the b-axis. The electric polarizatio n\nhasadomeshapeforappliedmagneticfieldsbetween0.3and\n3.8T,indicatinganelectricpolarizationthatcoexistswi ththe\nFIG. 2: a) Electric polarization P along the b-axis vs magnet ic field\nH along the c-axis collected during a sequence of seven magne tic\nfieldpulses (A-G)at 0.5 K.(Data is shown only for risingfield s.) b)\nMagnetoelectric current I vs H. A first-order-like transiti on into the\nferroelectricphaseisevidentat0.3Tandabroaderpeakocc ursat3.8\nT. c) Comparison of the electric polarization and the non-co llinear\nmagneticorder,whichistheproduct ofthelong-range antif erromag-\nnetic order and the field-induced staggered local fields meas ured by\ninelasticneutron diffraction [16, 17].\nAFM Bphase. Inthe magnetoelectriccurrentdataofFig. 2b,\nthe onset of electric polarization at 0.3 T is sharp and first-\norder like, whereas the transition near 3.8 T appears to be\nsecond order. As shown in Fig. 2c, the field dependence of\nthe electric polarization is proportional to a measure of no n-\ncollinearity, namely the productof the two-antiferromagn etic\norderparameters,whicharedeterminedfromneutronscatte r-\ningdata[16,17]. Thisprovidesfirmevidencethattheelectr ic\npolarizationisgeneratedbynon-collinearmagneticorder .\nThe direction of the electric polarization can switch de-\npending on the history of the magnetic field pulses, which\ndemonstrates that it is ferroelectric polarization. When t wo\nconsecutive magnetic field pulses are applied along the same\ndirectioninthe c-axis(e.g. D followedbyE orF followedby\nG in Fig. 2a),the resultingmagneticpolarizationforE andG\nis ”positive”along b. (The definition of positive and negati ve3\n-60 -40 -20 020 40 60 80 \n0.52 K \n0.89 K 0.77 K 0.65 K \n0 1 2 3 4 5Magnetoelectric current ( µA/m 2)b) \nH (T) 0.22 K \n1.11 K 0.46 K 0.08 K \n-0.004 -0.002 00.002 0.004 Δε  (%) a) \n0123\n0 2 4 6 8 10  dB/dt (kT/s) \nH (T) \nFIG.3: a)Percentagechangeinthedielectricconstantduet oapplied\nmagneticfield. b)Magnetoelectriccurrentmeasurementsvs . applied\nmagneticfieldshowingthetransitionsintoandoutofthefer roelectric\nphase. Inset: Rate of change of magnetic field as a function of field\nduring a 10Tpulse.\nis arbitrary). On the otherhand,whentwo consecutivepulse s\nare applied in opposite directions along the c-axis (A and B,\nB and C, C and D, E and F), the resulting polarization for B,\nC, D andF isswitchedintothe”negative”directionalongthe\nb-axis. These measurements were repeated for three samples\nand found to be reproducible. This type of switching behav-\nior, where the direction of the electric polarization depen ds\nboth on the direction of the present magnetic field pulse and\nthe previousone, is unique as far as we know amongmagne-\ntoelectrics. We note that in addition to the sample being in-\ntrinsicallyhysteretic,theremustalsobeasymmetry-brea king\nelectric field along the b-axis in order for the behavior de-\nscribed above to occur. This is further supported by the fact\nthat no electric field poling is required to observe the elect ric\npolarization. Wespeculatethatthiscouldresultfromthei nflu-\nence of Schottky voltages where the capacitor plates contac t\nthe sample. These do not contribute a background signal to\nthe data since they are magnetic field-independent, however\nthey can subject the crystal to a symmetry-breaking electri c\nfield along b. The absence of electric-field poling required t o\nobserve electric polarization has previously been reporte d in01234\n0 0.2 0.4 0.6 0.8 1Magnetoelectric \nMagnetoelectric \nNeutrons and specific heat \nDielectric constant \nT (K) AFM B and Ferroelectricity \nAFM A Phase C H (T) \nFIG.4: H-TphasediagramofCDCshowingregionsofcollinear and\nnon-collinear antiferromagnetism (AFM A and B), ferroelec tricity,\nand the aligned staggered paramagnetism (phase C) that occu rs at\nhigh fields for H along [001]. Data are obtained from peaks in t he\ndielectric constant and magnetoelectric current (this wor k), neutron\ndiffraction[18] and specific heat [19].\nthemultiferroiccompoundsLiNiPO 4andLiCoPO 4[22].\nThe existence of a phase transition in the electric polariza -\ntion is confirmed by dielectric constant measurements along\nthe b-axis(Fig. 3a). The signatureof the phase transitioni s a\npeakinthedielectricconstantnearH=3.8T.Theevolutiono f\nthepeaksinthedielectricconstant(Fig. 3a)andthemagnet o-\nelectric current (Fig. 3b) with temperature are plotted in t he\nphase diagram in Fig. 4 along with previous neutron scatter-\ningandspecificheatresults[18,19]. Theexcellentagreeme nt\nbetween the region of long-range magnetic order (AFM B)\nandelectric polarizationinFig. 4areevidenceforthe coex is-\ntenceandintimatecouplingbetweentheelectricandmagnet ic\npropertiesofCDC.\nOur measurements show that at the upper boundary of the\nH-T phase diagram in Fig. 4, magnetic order and electric\npolarization are suppressed simultaneously in a continuou s\nphase transition as a function of magnetic field. This tran-\nsition is not driven by temperature fluctuations, as it occur s\nat very low temperatures where temperature fluctuations are\nbasically absent. Instead, the transition is the result of m ag-\nneticfield-tunedquantumfluctuationsthatareassociatedw ith\na quantum phase transition at H = 3.8 T [19] where both a\nmagnetic and electric order parameter are critical. This su p-\npression occurs due to a competition between the long-range\nantiferromagneticcouplingsbetweenCuionsandtheeffect ive\nstaggeredmagneticfieldscreatedbyspin-orbitcouplings. The\nresulting quantum fluctuations create a continuous quantum\nphase transition that is magnetic field-induced. The presen ce\nof a peak in the dielectric constant confirms that the electri c\npolarizationundergoesanactualphasetransitionwhoseor der\nparameteris coupledto that of the magnetic phase transitio n.\nThis identifies this transition as a magneto-electric quant um\nphasetransition.4\nThe significance of the observed magnetoelectric quan-\ntum phase transition goes well beyond the field of magneto-\nelectricsandmultiferroics. Quantumcriticalpointshave been\nwell-investigatedforcaseswhereoneorderparametersisc rit-\nical,butmulti-orderquantumphasetransitionsareonlypo orly\ninvestigated at best. The simultaneity and coupling of the\nelectric and magnetic phase transitions add a new dimension\nto the field of quantum phase transitions. Investigations of\nthe magnetic component of this quantum critical point using\nspecific heat [19] have shown critical exponentsapproachin g\nthose of a 3-dimensional Ising magnet with effective dimen-\nsionality D = d + z = 4, where d = 3 is the spatial dimension\nand z = 1 is the dynamical exponent. This is contrast to an\nordinarythermalIsingphasetransitionwith D= d= 3.\nIn summary, we demonstrate that magnetoelectric inter-\nactions mediated via large molecules produce magnetically -\ninduced ferroelectricity. The ferroelectric polarizatio ncan be\nswitched by short magnetic field pulses in an unusual hys-\nteretic fashion. Our study opens the road towards molecule-\nbased designer magnets based on a wider range of organic\nligandswith which desired magnetoelectricpropertiescan be\nfine-tuned. Finally,theobservationofamagnetoelectricq uan-\ntum phase transition illustrates the scope of novel physics to\nbestudiedinorganicmagnets.\nWork at the National High Magnetic Field Laboratorywas\nsupported by the U.S. National Science Foundation through\nCooperative Grant No. DMR901624, the State of Florida,\nand the U.S. Department of Energy. Work at Johns Hopkins\nUniversitywassupportedbytheNationalScienceFoundatio n\nthroughGrantNo. DMR-0306940.\n[1] M.Fiebig, J.Phys. D 38, R123 (2005).\n[2] D.I.Khomskii, J. Magn. Magn. Mater 306, 1(2006).\n[3] W. Eerenstein, N. D. Mathur, and J. F. Scott, Nature 442, 759\n(2006).[4] N. Hill,J. Phys.Chem. B 104, 6694 (2000).\n[5] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, an d Y.\nTokura, Nature 426, 55(2003).\n[6] T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and Y. Tokura,\nPhys. Rev. Lett. 92, 257201 (2004).\n[7] N. Hur, S. Park, P. A. Sharma, J. S. Ahn, S. Guha, and S.-W.\nCheong, Nature 429, 392(2004).\n[8] G. Lawes, A. B. Harris, T. Kimura, N. Rogado, R. J. Cava,\nA. Aharony, O. Entin-Wolhman, T. Yildirim, M. Kenzelmann,\nC. Broholm, and A. P. Ramirez, Phys. Rev. Lett. 95, 087205\n(2005).\n[9] H. Katsura, N. Nagaosa, and A. V. Balatasky, Phys. Rev. Le tt.\n95, 057205 (2005).\n[10] S.Cheong andM. Mostovoy, Nature Materials 6, 13(2007).\n[11] M. Kenzelmann, G. Lawes, A. B. Harris, G. Gasparovic, C.\nBroholm, A. P. Ramirez, G. A. Jorge, M. Jaime, S. Park, Q.\nHuang, A. Y. Shapiro, and L. A. Demianets, Phys. Rev. Lett.\n98, 267205 (2007).\n[12] T. Arima,J. Phys.Soc.Japan 76, 073702 (2007).\n[13] T. Kimura, Annu. Rev. Mater. Res. 37, 387 (2007).\n[14] H.-B. Cui, Z. Wang, K. Takahashi, Y. Okano, H. Kobayashi ,\nand A.Kobayashi, J.Am. Chem.Soc. 128, 15074 (2006).\n[15] Q.Ye,D.-W.Fu,H.Tian,R.-G.Xiong,P.W.H.Chan,andS. D.\nHuang, Inorg. Chem. 47, 772 (2008).\n[16] J. F.Scott,J.Phys.: Condens. Matter 20, 021001 (2008).\n[17] R.D.WilletandK.Chang,InorganicChem.Act. 4,447(1970).\n[18] M.Kenzelmann,Y.Chen,C.Broholm,D.H.Reich,andY.Qi u,\nPhys. Rev. Lett. 93, 017204 (2004).\n[19] Y. Chen, M. B. Stone, M. Kenzelmann, C. D. Batista, D. H.\nReich, and C.Broholm, Phys.Rev. B 75, 214409 (2007).\n[20] V. S. Zapf, V. F. Correa, P. Sengupta, C. D. Batista, M.\nTsukamoto, N. Kawashima, P. Egan, C. Pantea, A. Migliori,\nJ. B. Betts, M. Jaime, and A. Paduan-Filho, Phys. Rev. B 77,\nR020404 (2008).\n[21] G.M.Schmiedeshoff,A.W.Lounsbury,D.J.Luna,S.J.Tr acy,\nA. J. Schramm, S. W. Tozer, V. F. Correa, S. T. Hannahs, T. P.\nMurphy, E. C. Palm, A. H. Lacerda, S. L. Bud’ko, P. C. Can-\nfield,J.L.Smith,J.C.Lashley,andJ.C.Cooley,Rev.Sci.In st.\n77, 123907 (2006).\n[22] I. Kornev, M. Bichurin, J.-P. Rivera, S. Gentil, H. Schm id,\nA.G.M.Jansen,,andP.Wyder,Phys.Rev.B 62,12247(2000)."    },    {        "title": "0906.4979v1.Relaxation_Mechanism_for_Ordered_Magnetic_Materials.pdf",        "content": "arXiv:0906.4979v1  [cond-mat.mtrl-sci]  26 Jun 2009Relaxation Mechanism for Ordered Magnetic Materials\nC. Vittoria and S.D. Yoon\nCenter for Microwave Magnetic Materials and Integrated Cir cuits\nECE Department, Northeastern University, Boston MA. 02115 USA\nA. Widom\nPhysics Department, Northeastern University, Boston MA. 0 2115 USA\nWe have formulated a relaxation mechanism for ferrites and f erromagnetic metals whereby the\ncoupling between the magnetic motion and lattice is based pu rely on continuum arguments con-\ncerning magnetostriction. This theoretical approach cont rasts with previous mechanisms based\non microscopic formulations of spin-phonon interactions e mploying a discrete lattice. Our model\nexplains for the first time the scaling of the intrinsic FMR li newidth with frequency, and1\nMtemper-\nature dependence and the anisotropic nature of magnetic rel axation in ordered magnetic materials,\nwhereMis the magnetization. Without introducing adjustable para meters our model is in reason-\nable quantitative agreement with experimental measuremen ts of the intrinsic magnetic resonance\nlinewidths of important class of ordered magnetic material s, insulator or metals.\nPACS numbers: 76.50.+g\nINTRODUCTION\nSince the discovery of magnetic resonance, the physics\ncommunity has been fascinated with possible mecha-\nnisms to explain the absorption linewidth or the relax-\nationtimeinmagneticmaterials. Itwasandstillisavery\nchallengingproblem. Magneticrelaxationissoimportant\ntounderstandbecauseitaffectsanumberoftechnologies,\nincludingcomputer,microwave,electronics,nanotechnol-\nogy, medical, etc.. Ultimately, the physical limitation of\nany technology which incorporates magnetic materials of\nany size, shape and combinations thereof comes down to\nprecise knowledge of the relaxation time of the magnetic\nmaterialbeing utilized. Thebackgroundofvariouscalcu-\nlationsorformulationsofmagneticrelaxationforthepast\nsixty years or so can be summarized briefly as follows:\n(i) The relaxation times in paramagnetic materials [1]\nis characterized by two parameters, T1andT2, wherein\nT−1\n2describes the magnetic resonance linewidth and T1\ndescribes the time taken for the external magnetic field\nZeemann energy density −Hext·Mto relax into thermal\nequilibrium. These times have been modeled in terms\nof various coupling schemes, i.e. spin-spin and/or spin-\nlattice interactions [2]. Since the coupling between spins\nisrelativelyweak,asitshouldbeinaparamagneticmate-\nrial, the coupling to the lattice involvesdiscrete spin sites\nrather than a collective cluster of spins. As such, param-\nagnetic coupling is necessarilymicroscopic in nature. For\nexample, a microscopic coupling scheme was formulated\n[3] whereby a spin Hamiltonian was modulated by the\nlattice motion. Variants to this approach have been very\nsuccessful in explaining relaxation in paramagnetic ma-\nterials. (ii) The magnetic relaxation of ferrimagnetic or\nferromagnetic resonance (FMR) linewidth is character-\nized by the Gilbert parameter [4] α, or equivalently by\nLandau-Lifshitz parameter [5] λL. A distinguishing fea-tureofthe collectivecoherentmagneticmomentsinFMR\nis that the magnitude of the magnetization, M=|M|re-\nmainsfixedwhichrequiresamagneticresonanceequation\nof the simple form\ndM\ndt=γM×Htot=γM×(H+H′),(1)\nwherein the gryomagnetic ratio γ=ge/2mc. Thetotal\nmagnetic intensity Htothas a thermodynamic part H\ndetermined by the energy per unit volume u,\ndu=Tds+H·dM, (2)\nand a dissipative part H′determined by the Gilbert lin-\near operator ˜ α,\nH′=/bracketleftbigg1\nγM/bracketrightbigg\n˜α·dM\ndt. (3)\nEqs.(1) and (3) imply that all components of the magne-\ntization must relax simultaneously in a way which con-\nserves the magnitude of the magnetization. Much of the\nsuccessful microscopic approaches or formulations uti-\nlized in paramagnetic materials were transferred over to\nmodels [6] which attempted to explain Eqs.(1) and (3).\nIn some sense this presented a contradiction or paradox\nwhich was conveniently ignored. As it is well known that\ncollective excitations in a ferri or ferromagnetic state can\nbe adequately described in classical continuum termi-\nnologies, although microscopic descriptions remain per-\nhapsmoreaccurate[7]. Toourknowledgeveryfeworany\nmicroscopicmodelshavebeensuccessfulinexplainingthe\norigin of Eq.(3). For example, much attention was given\nin the seventies to explain the FMR linewidth in YIG\n(Y3Fe5O12), since its linewidth was the narrowest ever\nmeasured in a ferrimagnetic material [8]. Clearly, there\nwas less to explain, and perhaps spin-lattice interactions2\ncould be treated at discrete spin sites as in paramagnetic\nmaterials. These calculations[8]containedmanyapprox-\nimations and predicted an FMR linewidth about 1/10 to\n1/100 of the measured linewidth. We believe that this\nis the best agreement between theory and experiment on\nrelaxation in an ordered magnetic material. The pur-\npose of this work is to improve upon the predictability\nof a theoretical model not only on a given material but\nin general for any ordered magnetic materials without\nrestoring to any approximations and assumptions.\nWe have adopted a conventional continuum magneto-\nmechanical description of the magnetic and elastic states\nof the ferri or ferromagnetic crystal [9, 12]. The ad-\nvantage of this description is that the microscopic spin-\nlattice coupling need not be formulated, since it has al-\nready been included in the continuum model which has\nbeenprovedtobeexperimentallycorrect. Weintroducea\nthermodynamic argument stating that the heat exchange\nbetween the magnetic and elastic systems must be the\nsame. Assuch, Eq.(3) maybe directlyrelatedtotheelas-\ntic sound wave relaxation time and the coupling strength\nbetween the magnetic and elastic systems. Specifically,\nwe will show that αis proportional to the square of the\nmagnetostriction constant. i.e. λ2and inversely propor-\ntional to γMτwherein τthe elastic relaxation time. In\naddition, the model predicts that ˜ αcannot be presumed\nto be a scalar as it has been done in the past; i.e. ˜ α\nis predicted to be anisotropic a second rank tensor in a\nsingle crystal material.\nIt is clear that one needs an interaction between\nphonons and electron spins to account for Gilbert damp-\ning parameter α. Suhl [10] and more recently Hickey\nandMoodera[11]haveconsideredsuchcouplingschemes.\nThe Gilbert damping parameter can be thought of as a\ntransport coefficient in much the same way as conduc-\ntivity and/or viscosity are transport coefficients. Such\ntransportcoefficientsdescribeheatingprocessesbywhich\notherwise long lived modes are damped. One can in\nfact relate the Gilbert damping parameter to conduc-\ntivity and/or viscosity. For metallic ferromagnetic mate-\nrials, conductivity as well as electron viscosity produces\nconsiderable amount of magnetic damping via eddy cur-\nrent heating. For magnetic insulators it is the viscos-\nity which determines the magnetic damping. As it is\nwell known, conductivity and viscosity can be non zero\neven in zero frequency limit. Hence, the implied Gilbert\ndamping parameter is also non zero at zero frequency. In\nSuhl and Hickey and Moodera’s papers they find, in the\nlimit of zero frequency and zero wave number, that the\nreal part of αis zero. This limiting case suggests that\nthey have not included the zero frequency transport co-\nefficients consistently in their theory. In our derivation\nthe expected result at zero frequency occur naturally in\nour formalism. In general, we believe the very nature of\ndiscreteness (as in paramagnetic materials) gives rise to\nrelatively long magnetic relaxation times. However, themagnetic relaxation time of a coherent collection of spins\n(as in FMR) implies shorter relaxation times, since it in-\nvolvescollectiveacousticwavesinthe interactionscheme.\nOur present theoretical treatment takes this into account\nvia the continuum magneto-mechanics.\nTHEORETICAL MODEL\nFrom Eq.(3), it is evident that the heating rate per\nunit volume due to the dissipative magnetic intensity H′\nobeys\n˙Q=dM\ndt·H′\n˙Q=/bracketleftbigg1\nγM/bracketrightbiggdM\ndt·˜α·dM\ndt\n˙Q=M\nγ˙Niαij˙Njwherein N=M\nM, (4)\nand ˜αis a second rank tensor\n˜α=\nαxxαxyαxz\nαyxαyyαyz\nαzxαzyαzz\n. (5)\nThe crystaldisplacement uyields in elasticity theory [13]\nthe strain tensor\neij=1\n2(∂iuj+∂jui) (6)\nIn virtue of the magneto-elastic effect [14], a chang-\ning magnetization dM/dtwill produce a changing strain\nde/dt. In detail, in terms of third rank magneto-elastic\ntensor Λ ijklone finds\neij= ΛijklNkNl,\n˙eij= 2λijklNk˙Nl. (7)\nFinally, the fourth rank crystal viscosity tensor, ηijkl\ndtermines the heating rate per unit volume due to the\ntime dependent strain\n˙Q=˙eijηijkl˙ekl. (8)\nEmploying Eqs.(7) and (8) and comparing the result to\nEq.(4) yields the central result of our model.\nFor any crystal symmetry the Gilbert damping tensor\ndue to magnetostriction coupling is rigorously given by\nαij=/bracketleftbigg4γ\nM/bracketrightbigg\n(ΛnmpiNp)ηnmrl(ΛrlqjNq).(9)\nThe following properties of the Gilbert damping tensor\nEq.(9) are worthy of note: (i) The Gilbert damping ten-\nsor ˜αis inversely proportionalto the magnetization mag-\nnitudeM. (ii) The Gilbert damping tensor ˜ αis propor-\ntional to the squares of the magnetostriction tensor el-\nements. (iii) The tensor nature of ˜ αdictates that the3\nmagnetic relaxation is anisotropic . To a sufficient degree\nof accuracy, one may employ an average of the form\nα=1\n3tr{˜α}=/bracketleftbiggαxx+αyy+αzz\n3/bracketrightbigg\n(10)\ndefining a scalar function α. (iv) The crystal viscosity\ntensorηnmrlmay be employed to describe the acoustic\nwave damping [15]. For a mode label a, e.g. a longitudi-\nnal (a=L) or a transverse ( a=T) mode, the acoustic\nabsorption coefficient at frequency ωis given by [15]\nτ−1\na=ω2ηa\n2ρv2a, (11)\nwherein vais the acoustic mode velocity and ρis the\nmass density. Finally, for a cubic crystal, there are only\ntwoindependent magneto-elastic coefficients which may\nbe defined\nΛxxxx=3\n2λ100and Λ xyxy=3\n2λ111 (12)\nwherein the Cuachy three index magneto-elastic coeffi-\ncients are λijk.\nCOMPARISON WITH EXPERIMENT\nThe Gilbert damping factor αmay be deduced from\nthe measurement of the intrinsic FMR linewidth. How-\never, the measurement of the intrinsic linewidth is, in-\ndeed, very difficult. The reason for this conclusion is\nthat there are too many extrinsic effects that influence\nthe measurement. For example, in ferromagnetic metals\nlike Ni, Co and Fe the intrinsic linewidth contribution to\nthe total linewidth measurement [16, 17] may be between\n10% and 30%. The rest of the linewidth [18] may be due\nto exchange-conductivity effects.\nHowever, there may be other contributions, such as\nmagnetostatic excitations, surface roughness, volume de-\nfects [19], crystal quality, interfaces [20], size, etc.. Sim-\nilar conclusions apply to ferrites except there are no\nexchange-conductivity effects [18]. Thus, the reader\nshould be mindful that when we quote or cite an intrinsic\nvalue of the linewidth it represents a maximum value for\nthere can be some hidden extrinsic contributions in an\nexperiment. However, we have relied on data well estab-\nlished over the years. The criteria that we have adopted\nin choosing an ensemble of intrinsic linewidth measure-\nments are the ones exhibiting the narrowest linewidth\never measured in single crystal materials. In addition,\nwe required full knowledge of their elastic, magnetic and\nelectrical properties [16, 17, 18, 21]. The objective is not\nto introduce any adjustable parameters.\nThe experimental value of Gilbert damping parameter\nαexpmay be deduced from the FMR linewidth ∆ Hatfrequency fas\nαexp=√\n3\n2/parenleftbiggγ∆H\n2πf/parenrightbigg\n. (13)\nThefactor√\n3/2assumesLorentzianlineshapeoftheres-\nonance absorption curve. The theoretical Gilbert damp-\ning parameter αthvalue is expressed in terms of known\n[17] parameters so that there are no adjustable parame-\nters in our comparison to experiments, as shown in TA-\nBLE I. The theoretical prediction for the Gilbert damp-\ning paramter is that\nαth=36ργ\nMτ/bracketleftbiggλ2\n100\nq2\nL+λ2\n111\nq2\nT/bracketrightbigg\n, (14)\nwhereinρis the mass density, qT≈vTM\n2γAis the trans-\nverse acoustic propagation constant, qLis the longitudi-\nnal acoustic propagation constant, v Tis the transverse\nsound velocity, Ais the exchange stiffness constant, λ100\nandλ111are magnetostriction constants for a cubic crys-\ntal magnetic material. The transverse acoustic propaga-\ntion constant, was approximatedon the basisthat the re-\nlaxationprocessconservedenergyandwavevector. Since\nthe acoustic frequency is fixed in the process the longi-\ntudinal propagation constant may be also calculated to\nbeqL=qT(vT/vL) for magnetic materials, wherein v L\nis the longitudinal sound wave velocity.\nIn FIG.1, we plot the experimental and theoretical val-\nues Gilbert damping constants as given by Eqs.(13) and\n(14). We note that the agreement between theory and\nexperiment is remarkable in view of the fact that any\nof the cited parameters could differ from the ones listed\nin TABLE I by as much as 20-30%. For example, the\nlinewidth reported in TABLE I may not be on the same\nsample where the elastic or magnetic parameters were\ncited. In a few cases we needed to extrapolate the value\nofA, since there was no published value. In FIG.1, we\ndid not present data on the ferromagnetic metals for lack\nof confidence on the linewidth data. For example, mag-\nnetostatic mode excitations have a deleterious effect on\nthe dependence of the FMR linewidth on size. Most, if\nnotall, previousFMRlinewidthmeasurementshavebeen\nperformed on slabs, wiskers, etc.. whcih can indeed sup-\nportmagnetostaticmode excitations. Additional compli-\ncations arise as a result of exchange-conductivity excita-\ntions in the linewidth data. Nevertheless, the agreement\nbetween theory and experiment is quite satisfctory.\nCONCLUSION\nQualitative and quantitatively our model is in agree-\nment with experimental observations of the intrisic FMR\nlinewidth reported over the years. Speciafically, experi-\nmentallythe mostimportant characteristicsofthe intrin-\nsic FMR linewidth, ∆ H, measured on ordered magnetic4\nTABLE I: Calculated and measured Gilbert damping ( α) parameters\nqT λ100λ111 M A ∆H f τ α thαexp\nMaterials (10−6cm−1) (10−6) (10−6) (G/4 π) (10−6erg/cm) (Oe) (GHz) (10−13sec) (10−5) (10−5)\nY3Fe5O12a3.8 1.25 2.8 139 0.40 0.33 9.53 4.4 5.56 9.0\nY3Fe4GaO12a1.46 −1−1 36 0.28 3.0 9.53 4.4 51 76\nLi0.5Fe2.5O4b8.6 −8 + 0 310 0.40 2.0 9.50 1.5 26 50\nNiFe2O4b7.49 −63−26 270 0.40 35 24.0 710 26 350\nMgFe2O4b9.30 −10−1 90 0.1 2.3 4.9 1.5 120 120\nMnFe 2O4b6.6 −30−5 220 0.4 238 9.2 1.5 930 1040\nBaFe12O19c9.6 15 350 0.4 6 55 1.5 18 26\nNid6.3 −46 25 484 0.75 102 9.53 1.8 770 2600\nFed8.75 20 −20 1690 1.9 9 9.53 1.8 30 220\nCod5.1 80 1400 2.78 15 9.53 1.8 530 370\naGarnetsbSpinelscHexagonal FerritedFerromagnetic Materials\n(Note: Longitudinal acoustic wave constant is qL= (vT/vL)qT)\n/s49/s48/s45/s53\n/s49/s48/s45/s52\n/s49/s48/s45/s51\n/s49/s48/s45/s50\n/s49/s48/s45/s49/s49/s48/s45/s53/s49/s48/s45/s52/s49/s48/s45/s51/s49/s48/s45/s50/s49/s48/s45/s49/s101/s120/s112\n/s116/s104\nFIG. 1: Shown are the experimental and theoretical values of\nthe Gilbert damping constants as given by Eqs.(13) and (14).\nmaterials (metal or insulator) for the past fifty years are\nthat ∆Hscales with frequency and1\nM[16, 22, 23]. In-\ndeed, these arethe predictions of our theory. In addition,\n∆Hscales with the magnetostriction constant squared,\nsee FIG.1. FIG.1 was plotted in a logarithmic scale only\nto be able to include all ofthe datain TABLE I. Another\nprediction of our theoretical work is that the Gilbert\ndamping parameter ˜ αis not simply a scalar parame-\nter but a tensor quantity. This implies that the FMR\nlinewidth is intrinsically anisotropic in single crystals of\nferri-ferromagnetic materials. There was much contro-\nversy in the seventies about whether or not the intrin-\nsic linewidth should be anisotropic or not. Poor qualityof samples seemed to have incited the controversy. Im-\nproved or more accurate angular linewidth data [18, 19]\nsupports the notion of an anisotropic linewidth in or-\ndered magnetic materials in agreement with our model.\nIn summary, we believe that the comparison between\ntheory and experiment is very encouraging in terms of\ncontinuing this continuum approach to explain intrinsic\nlinewidths in ordered magnetic materials.\nAcknowledgement\nWe wish to thank to Prof. V.G. Harris and A. Geiler for\nstimulus discussions about magnetic materials and their\nrelaxation.\n[1] F. Bloch, Z. Physik, 74, 295 (1932).\n[2] H.B. Callen, Fluctuation, Relaxation, and Resonance in\nMagnetic Systems , Editor D. ter Haar, p 176, Oliver &\nBoyd Ltd., London (1962).\n[3] R. Orbach, Proc. Phys. Soc., 77, 821 (1961).\n[4] T.L. Gilbert, IEEE Trans. Mag., 40, 3443 (2004).\n[5] L.D. Landau and E.M. Lifshitz, Phys. Z. Sowjet., 8, 153\n(1935).\n[6] C. Kittel, J. Phys. Soc. Japan Suppl., 17(B1), 396\n(1962).\n[7] M. Sparks, Ferromagnetic Relaxation Theory , McGraw-\nHill Book Co., New York, (1970).\n[8] R.C. LeCraw and E.G. Spenser, J. Phys. Soc. Japan,\nSuppl.,17(B1), 401 (1962).\n[9] S. Chikazumi, Physics of Magnetism John Wiley and\nSons, Inc., New York (1964).\n[10] H. Suhl, IEEE Trans. Mag., 34, 1834 (1998).\n[11] M. C. Hickey and J. S. Moodera, Phys. Rev. Letts., 102,\n137601 (2009).\n[12] L.D. Landau, L.P. Pitaevskii, and E.M. Lifshitz, Elec-\ntrodynamics of Continuous Media , Elsevier Butterworth-\nHeinemann, Oxford, (2000).5\n[13] L.D. Landau and E.M. Lifshitz, Theory of Elasticity ,\nButterworth-Heinemann, Oxford, (1986).\n[14] L.D. Landau, L.P. Pitaevskii, and E.M. Lifshitz, op. cit.\npp 144-146.\n[15] L.D. Landau and E.M. Lifshitz, op. cit., Chapt. V.\n[16] S.M.BhagatandP.Lubitz, Phys.Rev., B 10, 179(1974).\n[17] G.C. Bailey and C. Vittoria, Phys. Letts., 37A, 3, 261\n(1972).\n[18] W.S.AmentandG.T.Rado, Phys.Rev., 97, 1558(1955).\n[19] A.M.Clogston, H.Suhl, L.R.WalkerandP.W.Anderson,\nJ. Phys. Chem. Solids, 1, 129 (1956).\n[20] C. Vittoria and J.H. Schelleng, Phys. Rev., B 16, 4020\n(1977).[21] Landolt-Bornstein. Numerical Data and Functional Rela-\ntionships in Science and Technology , Editors K.-H. Hell-\nwege and A.M. Hellwege, Magnetic and Other Prop-\nerties of Oxide and Related Compounds ,4part-a,b\n(Spring-Verag, Berlin, Heidelberg, New York, 1970); 12\npart-a,b,c (Spring-Verag, Berlin, Heidelberg, New York,\n1980).\n[22] P.Roschmann, IEEETrans.Mag., 11, 1247(1975); IEEE\nTrans. Mag., 20, 1213 (1984).\n[23] C. Vittoria, P. Lubitz, P. Hansen, and W. Tolksdorf, J.\nAppl. Phys., 57, 3699 (1985)."    },    {        "title": "0906.5340v2.A_Magnetization_Sensitive_Potential_at_Garnet_Metal_Interfaces.pdf",        "content": "A Magnetization Sensitive Potential at Garnet-Metal Interfaces\nL. R. Hunter, K. A. Virgien, A. W. Bridges, B. J. Heidenreich,\u0003and J. E. Gordon\nDepartment of Physics, Amherst College, Amherst, MA 01002\nA. O. Sushkov\nYale University, Department of Physics,\nP.O. Box 208120, New Haven, CT 06520-8120\n(Dated: July 27, 2021)\nAbstract\nWe investigate a magnetization-dependent voltage that appears at the interface between garnets\nand various metals. The voltage is even in the applied magnetic \feld and is dependent on the\nsurface roughness and the pressure holding the surfaces together. Large variations in the size, sign\nand magnetic dependence are observed between di\u000berent metal surfaces. Some patterns have been\nidenti\fed in the measured voltages and a simple model is described that can accommodate the\ngross features. The bulk magnetoelectric response of one of our polycrystalline YIG samples is\nmeasured and is found to be consistent with a term in the free energy that is quadratic in both\nthe electric and magnetic \felds. However, the presence of such a term does not fully explain the\ncomplex magnetization dependence of the measured voltages.\nPACS numbers: 75.80.+q, 75.70.Cn, 75.50.Gg\n\u0003Present address: Department of Physics, Cornell University\n1arXiv:0906.5340v2  [cond-mat.mtrl-sci]  8 Jul 2010I. INTRODUCTION\nSurface magnetoelectric e\u000bects are of considerable interest and have been the subject of\na number of recent investigations.[1, 2] Enhanced magnetoelectric couplings have been ob-\nserved in bilayers of yttrium iron garnet (YIG) and lead magnesium niobate-lead titanate.[3]\nLarge magnetoelectric couplings have been studied in new multiferroic materials.[4, 5] Much\nof the renewed interest in the magneto-electric e\u000bect has been driven by the possibility of\nusing this e\u000bect for controlling magnetic data storage with an electric \feld.[6, 7]\nAn e\u000bort to measure the electron electric dipole moment (edm) using gadolinium doped\nYIG is underway.[8] Presently, the experimental precision is limited by an unanticipated\nelectrical potential, dubbed the \\ M-even e\u000bect\", that is predominantly symmetric in H, the\napplied magnetic \feld. With the hope of overcoming this obstacle, we have launched an\ninvestigation into the characteristics of this potential. The e\u000bect is observed to be highly\nsensitive to the roughness of the garnet surfaces and the pressure applied to hold these\nsurfaces together. A complex magnetic dependence is observed that varies dramatically\nwith the composition of the metallic electrode or epoxy in immediate contact with the garnet\nsurface. Overwhelmingly, the evidence suggests that the e\u000bect is a surface magnetoelectric\ne\u000bect.\nII. OBSERVATIONS IN GdIG TOROIDS\nWe \frst observed the M-even e\u000bect in the magnetic toroid designed to search for the\nelectron edm (Fig. 1). The sample was assembled from two \\C\"s of gadolinium-yttrium-\niron-garnet (Gd xY(3\u0000x)Fe2Fe3O12) that were geometrically identical. \\C1\" had x= 1:35\nwhile \\C2\" had x= 1:8 wherexrepresents the average number of Gd ions per formula unit.\nCopper foil electrodes were bonded between the two \\C\"s using silver epoxy. A coil wrapped\non the outside of a copper Faraday cage was used to produce Hin the toroidal direction.\nThe voltage on each electrode was monitored using a detector built with a Cascode pair of\nBF 245 JFETs. The detector has an input impedance of 1013\n and an input capacitance\nof about 4 pF.\nA hysteresis curve inferred from coils wrapped on the toroid is shown in Figure 2. It is\nimportant to keep this curve in mind when viewing the subsequent data, which are generally\n2(1.35Gd, 1.65Y)IG\nJFET(1.8Gd, 1.2Y)IG\nMFIG. 1. The GdIG toroid. The applied \feld and magnetization circulate around the toroid.\n-320 -240 -160 -80 0 80 160 240 320 -120 -80 -40 0 40 80 120 4πM (G) Applied field (Oe) \nFIG. 2. A magnetic hysteresis curve obtained from the GdIG toroid at 127 K.\nplotted as a function of the applied magnetic \feld. In the toroid, the magnetization is nearly\nsaturated at applied \felds of only a few tens of Oersted.\nTo investigate the M-even e\u000bect we monitor the electrode voltages and the sample mag-\nnetization as a function of the applied \feld H, which is varied using a triangular wave. A\ntypical trace is shown in Fig. 3. The bumps in the triangle wave at approximately t=\u00001:2 s\nandt= 0 s are due to the back emf associated with the reversal of the YIG magnetization.\nWe \fnd that such traces are best understood by splitting them into \\even\" and \\odd\"\ncomponents. Denoting the electrode voltage by a function V(t) with period T, we de\fne\nthe even and odd components of V(t) to be\nVEVEN (t) =1\n2(V(t) +V(t+T=2))\n3-900 -600 -300 0 300 600 900 \n-120 -80 -40 0 40 80 120 \n-1.25 -0.75 -0.25 0.25 0.75 1.25 Electrode Voltage (µV) Applied Field (Oe) Time (s) Applied Field Electrode Voltage FIG. 3. The observed electrode voltage and applied magnetic \feld as a function of time. These\ndata are taken at 127 K with an 0.41 Hz triangle wave.\nVODD(t) =1\n2(V(t)\u0000V(t+T=2))\nIt is clear that V(t) is completely speci\fed over its entire period Tby specifying VEVEN (t)\nandVODD(t) over a half-period T=2. The process of computing the even and odd components\nof the electrode voltage is illustrated graphically in Figure 4.\nThe primary bene\ft of analyzing the data in this fashion is that the current in the driving\ncoil has a vanishing even component, and consequently inductive voltages on the electrodes\nshould show up in the odd component only. Figure 5 shows the even and odd components\nof the trace analyzed above plotted as a function of the applied \feld, as well as the voltage\nmeasured by a pickup coil wound around the toroidal Faraday cage enclosing the sample,\nand the sample magnetization inferred from integrating the pickup coil voltage.\nTransient induction pulses due to dB=dt appear clearly in the odd component of the\nelectrode voltage. They quickly approach a constant value associated with dH=dt after the\nreversal of the magnetic domains. As Figure 5 demonstrates, this behavior also appears in\nthe voltage measured across the pickup coil, suggesting that the odd component is primarily\nor entirely inductive in nature. As one expects, the magnitude of the odd component grows\nlinearly with increasing scan frequency.\n4-1.25 -0.75 -0.25 0.25 0.75 1.25Time (s)Electrode Voltage (200 µV/tick)V(t)V(t+T/2)VEVEN (t) VODD (t) FIG. 4. An example of how the even and odd components of the electrode voltage are extracted.\nThe \frst trace is the same as that shown in Fig. 3, whereas the second is o\u000bset by half a period.\nThe third trace (the even component) is obtained by averaging the \frst two traces, and the fourth\n(the odd component) is obtained by taking one half of their di\u000berence. The \frst trace can be\nrecovered by adding the third and fourth together.\nThe even component behaves di\u000berently, changing rapidly with the reversal of the sample\nmagnetization and then falling o\u000b roughly as 1 =Hat higher \felds. We refer to this voltage\nas the \\M-even e\u000bect\" since it appears in the even component of the voltage and is clearly\nassociated with the reversal of the sample magnetization. In our toroidal geometry the M-\neven e\u000bect is nearly identical for the two electrodes. Unlike the odd component of the signal,\ntheM-even voltage is not appreciably modi\fed by changing the frequency of the triangle\n5-700-600-500-400-300-200-1000100200300400\n-120 -80 -40 0 40 80 120\nApplied Field (Oe)Electrode Voltage ( µV)\n-700-600-500-400-300-200-1000100200300400\n4M (G)\nEven Component Odd Component Pickup Coil (Arb. Units) MagnetizationFIG. 5. The even and odd components of the electrode voltage shown in Fig. 3, plotted over a half-\nperiod as a function of applied \feld. These data are acquired as the applied \feld is increased (left to\nright), and so, because of magnetic hysteresis, the even component is not symmetric about H= 0.\nAlso plotted are the voltage measured by a pickup coil, rescaled to match the odd component of the\nelectrode voltage, and the magnetization of the sample, as inferred from integrating this voltage\nand correcting for the e\u000bects of the driving coil.\nwave. The persistence of the M-even voltage with the increasing applied \feld is particularly\nproblematic for the edm measurement. Though the e\u000bect appears to be strongly dependent\non the sample magnetization, we \fnd it more illuminating to plot the voltage as a function\nof the applied magnetic \feld as this more clearly displays the problematic 1 =Hdependence.\nAfter the submission of ref. [8] we disassembled our sample and repaired several \raws.\nA small chip that had been present on C2 was removed by grinding down the top surfaces.\nThis reduced the toroid height by 3/16\". The epoxy was baked o\u000b, the electrodes were\nremoved and the interstitial garnet surfaces were ground \rat. New electrodes with more\nsecure connections were then bonded to the sample with a new silver epoxy. Following the\nreassembly we again measured the M-even e\u000bect. Somewhat surprisingly, the reassembled\nsample exhibited an M-even e\u000bect that was smaller by about a factor of 5 (Fig. 6). This\nsuggested that the e\u000bect was likely not a bulk e\u000bect but was rather associated with the\n6    2005 data\n-700-600-500-400-300-200-1000100\n0 20 40 60 80 100 120Applied Field (Oe)V (µV)\n040801201602002402803204πM (Gauss)MagnetizationNew dataFIG. 6. The M-even voltage ( V) observed on our GdIG sample in our 2005 data and after re-\nassembling the toroid (new). Only the half of the cycle with increasing magnitude of His shown.\nThe half of the cycle with decreasing magnitude of His essentially \rat. The solid lines are the\nasymptotic \ft of the high-\feld part of the electrode voltages to the function V=a=H+b=H2. The\nmagnetization of the sample as a function of His also shown on the secondary axis. The M-even\nvoltage has an onset that coincides with the rising of the magnetization. These data were taken at\n127 K.\nsurface between the garnet and the electrode.\nIII. EXPERIMENTAL STUDY OF THE M-EVEN EFFECT ON YIG CYLINDERS\nFollowing this observation, we launched an e\u000bort to characterize the e\u000bect. First, we\nestablished that the M-even e\u000bect is present at room temperature in an electrode sandwiched\nbetween two cylindrical samples (1.25\" diameter, 2\" long) of YIG (Fig. 7). This is important\nin that these cylindrical samples can be easily inserted into a solenoid magnet to study their\nbehavior. Hence, it is not necessary to wrap a new coil for every test. In addition, operation\nat room temperature eliminates the time-consuming process of cycling the temperature\nbetween tests. These advantages have allowed us to study the e\u000bect in a wide variety of\n7Electrode Wire\nBrass Top\nBrass BottomSS Rods\nElectrodeFIG. 7. Schematic of the assembly used to study the M-even e\u000bect. The stainless steel (SS) rods\nand the brass caps are connected to circuit ground. This entire assembly is easily mounted within\na magnetic solenoid. The bore of the solenoid forms a complete Faraday cage once the ends are\nclosed o\u000b with metal plates.\nelectrode con\fgurations and to replace our cascode-pair detector with an instrumentation\nampli\fer (Burr-Brown INA116).\nA typical trace of the M-even voltage taken in this new geometry is shown in Fig. 8\nalong with a plot of the sample magnetization. In this \fgure and in most of the reported\ntraces the data are an average of several independent and reproducible measurements taken\non di\u000berent days. The trace is essentially the signal you would observe if you scanned the\napplied magnetic \feld from -600 Oe up to 600 Oe with the odd part of the signal removed.\nNote that the shape of the M-even potential is di\u000berent from that observed in the toroid.\nThis is primarily due to the demagnetizing \felds that are present in the solenoid but absent\nin the toroid. In the cylindrical geometry, the magnetic domains begin to relax as the\nmagnitude of magnetic \feld is reduced whereas in the toroidal geometry some coercive \feld\nis required in the opposing direction before signi\fcant reduction and then reversal of the\nmagnetization is observed. For this reason, we now display the entire plot rather than just\nthat for increasing \feld as was done in Figure 6.\nWe \frst studied the pressure-dependence of the M-even e\u000bect for metallic electrodes\n8-2000 -1500 -1000 -500 0 500 1000 1500 2000 \n-200 -150 -100 -50 0 50 100 150 200 \n-600 -400 -200 0 200 400 600 4πM (G) Even Voltage ( µV) \nH (Oe) Even V oltage Magnetization Field Sweep Direction FIG. 8. A plot of the observed M-even voltage and magnetization in the new apparatus with a cop-\nper electrode between YIG cylinders. The magnitude of the applied \feld is increasing (decreasing)\nfor positive (negative) values of H.\nplaced between the two YIG cylinders. The pressure is varied by adjusting the tension on\nthe 4 stainless-steel rods that hold the assembly together (Fig. 7). Reproducible pressures\ncan be achieved by plucking these rods and tuning their response to a particular frequency.\nWe have determined the pressure that corresponds to each frequency both empirically and by\ncalculation. All samples have been observed at multiple pressures. We \fnd that for modest\npressures (less than 300 psi), the magnitude of the M-even voltage generally decreases as\nthe pressure increases. However, we observe only modest change in the M-even e\u000bect at\nhigher pressures (300 psi { 800 psi). A typical variation in this pressure regime is shown in\nFig. 9.\nWe also studied the e\u000bect as a function of the roughness of the YIG surfaces facing the\nelectrode and discovered that the e\u000bect diminishes in size as the surfaces become rougher,\nat least up to a point (Fig. 10).[9] We speculate that in the process of roughening the\nsurface, certain crystal orientations may be more likely to be removed from the surface. The\nremaining, more durable crystal orientations might then dominate the surface magneto-\nelectric and magneto-mechanical e\u000bects. Alternatively, it may simply be that the size of\nthe e\u000bect is proportional to the fraction of the surface that is in direct contact with the\n9-40 -20 0 20 40 60 80 \n-600 -400 -200 0 200 400 600 Even Voltage (µV) \nApplied Field (Oe) 760 psi 320 psi FIG. 9. The M-even voltage observed with a nickel electrode at 320 psi and 760 psi. The voltage\nat high, positive (increasing) magnetic \felds is signi\fcantly reduced at the higher pressure.\nelectrode. However, no clear trends emerged in the data when the metallic electrodes were\nsimilarly roughened. The M-even voltage also shows no dependence on the thickness of the\nelectrode for thicknesses between 0.05 mm and 0.5 mm.\nWe found signi\fcantly di\u000berent M-even responses in more recently fabricated YIG sam-\nples. The manufacturer investigated and found that the newer samples had grain sizes\nof about 12 microns while the older samples had grain sizes of about 8 microns.[10] We\nchose to use only the older samples with smaller grain size in this investigation. Most of\nour subsequent M-even observations have been standardized to relatively rough surfaces\n(Ra\u0019170 microinches) and relatively high pressure (about 490 psi).\nWe measure the voltages produced on a variety of metallic electrode materials and \fnd\na wide range of di\u000berent M-even responses. Copper and palladium yield M-even curves\nthat are virtually identical (Fig. 11). Stainless steel and tantalum produce curves of similar\nshape but di\u000berent amplitude (Fig. 12). They both exhibit a characteristic \\blip\" as the\nmagnetization approaches saturation. Silver has a large central maximum, but exhibits an\nabrupt change of sign as the magnitude of Mis increased, followed by a large negative tail\nas the sample approaches saturation (Fig. 13). The \\poor metals\" (aluminum, indium and\ntin) produce M-even voltages that have the same shape as silver, but with the opposite sign\n10-50 0 50 100 150 \n-600 -400 -200 0 200 400 600 Even Voltage ( µV) \nApplied Field (Oe) 150 microinch 170 microinch FIG. 10. The M-even voltage observed on YIG samples with di\u000berent surface roughness. The\nsamples were ground with 120 (80) grit abrasive which resulted in an average surface roughness\nRaof 150 (170) microinches. The surface roughness was measured using a Mitutoyo Surftest { 402\nsurface roughness tester. In both cases copper electrodes were bonded to the YIG surfaces using\nsilver epoxy.\n(Fig. 14).\nFerromagnetic electrodes (Fe, Ni and Co) tend to produce M-even voltages that have\nsharper low \feld peaks and more modest amplitudes, especially at higher applied \felds\n(Fig. 15). Cobalt clearly displays additional structure that is only suggested in the other\nplots.\nOther hard non-magnetic electrodes (Nb, Mo, Ti and W) produce small low-\feld peaks\nand rather complex shapes similar to cobalt (Fig. 16). However, the voltage amplitude\ntends to decay slowly as the applied \feld is increased. The high-\feld M-even signals for\nthese metals are strikingly similar.\nFurther evidence that the e\u000bect is primarily produced at the garnet-metal interface is\nprovided by measurements with plated electrodes. Fig. 17 shows the M-even e\u000bect observed\non tin-plated nickel and tin-plated copper. While there is signi\fcant variation in the ampli-\ntude of the signals, the sign and general shape of the signal is similar to that of tin and is\nclearly di\u000berent from that obtained from both copper and nickel.\n11-50 0 50 100 150 200 \n-600 -400 -200 0 200 400 600 Even Voltage ( µV) \nApplied Field (Oe) Pd Cu FIG. 11. Palladium (0.1 mm, 99.9%) and copper (0.05 mm, 99.98%) M-even curves.\n-50 -30 -10 10 30 50 70 90 110 130 \n-600 -400 -200 0 200 400 600 Even Voltage (µV) Applied Field (Oe) Ta SS \nFIG. 12. Stainless steel (0.05 mm) (\fne) and tantalum (0.127 mm, 99.9%) (bold) M-even curves.\nWe have studied the e\u000bect of bonding various metals to the YIG using di\u000berent epoxies.\nFigure 18 shows the M-even signals associated with four di\u000berent metals bonded with silver-\nimpregnated epoxy (Epo-Tek EE129-4). The 4 curves are remarkably similar, providing\nfurther evidence that the e\u000bect is dominated by the surface in immediate contact with the\n12-200 -150 -100 -50 0 50 100 150 200 250 \n-600 -400 -200 0 200 400 600 Even Voltage ( µV) \nApplied Field (Oe) Ag FIG. 13. The M-even voltage observed with silver (0.05 mm, 99.9%).\nYIG.\nThe epoxy composition can play an important role in the observed M-even signal. The\ndi\u000berence between nickel electrodes bonded with nickel epoxy (Epo-Tek N20E) and with\nnon-conductive epoxy (Epo-Tek 377) is shown in \fgure 19. It is interesting to note that\nthe nickel impregnated epoxy is more sharply peaked at the center, similar to the results\nobtained from the unbonded magnetic electrodes (Fig. 15).\nWe note that the signal observed for unbonded aluminum (Fig. 14) has the opposite\nsign to that observed with nonconductive epoxy (Fig. 19). In the hope of minimizing the\nM-even e\u000bect, we mixed various fractions of aluminum \rake into the non-conductive epoxy\nand recorded the associated M-even voltages. The results are shown in Figure 20. Note that\nat about 60% aluminum by weight that the resulting signal achieves a minimum size. The\ncancellation is, however, not complete and results in a rather complex magnetic dependence.\nIV. PHENOMENOLOGY\nBased upon these studies we conclude that the M-even e\u000bect is a magnetically dependent\npotential generated at the interface between the garnet and the surface in immediate contact\nwith it. Unfortunately, we have not yet been successful at formulating a theoretical model\n13-300 -200 -100 0 100 200 -600 -400 -200 0 200 400 600 Even Voltage ( µV) \nApplied Field (Oe) Al In Sn FIG. 14. The M-even voltages observed for aluminum (0.1 mm, 99.99%), indium (0.127 mm,\n99.99%) and tin (0.05 mm, 98.8%).\nthat can account for all of the rich behavior observed. However, we have identi\fed an\ninteresting pattern in the data. All of the curves can be approximately reproduced by\nsuperposing two distinct signals. The \frst is a potential that is quadratic in the observed\nmagnetization (Fig. 8) evaluated at a \feld shifted by Hshiftwith respect to the applied \feld\nH:\nV=Ah\nM2(H\u0000Hshift)\u0000M2\nsati\n(1)\nHereAis a constant and the term Msatreferences the potential to zero at saturation.\nHshiftis a \ft parameter that displaces the center of the quadratic distribution. This quadratic\nterm generally accounts for the large and smooth central features of the observed curves.\nSuch an e\u000bect may be linked to the magnetostriction of the sample, or more generically\nto the presence of an E2B2term in the free energy, as discussed below. Once this e\u000bect\nis removed from the data, two symmetric \\wings\" remain (Fig. 21). These have a sharp\nonset at a particular value of the applied \feld and then decay away at higher applied \feld.\nThis part of the potential may be associated with the surface of the garnet transitioning\ninto modes II and III of the magnetization (or demagnetization) process [11] where further\nalignment (or depolarization) of the magnetization requires rotating the local moment away\n14-75 -50 -25 0 25 50 75 100 \n-600 -400 -200 0 200 400 600 Even Voltage (µV) \nApplied Field (Oe) Co Ni Fe FIG. 15. The M-even response of iron (0.1 mm, 99.99%), nickel (0.1 mm, 99.5%) and cobalt\n(0.1mm, 99.95%).\nfrom (or toward) the easy axis of the crystal.\nSimilar decompositions can largely accommodate all of our data. Pd, Ag and stainless\nsteel result in \ft parameters with the same sign as copper. Ta is nearly entirely accounted\nfor by the voltage quadratic in M. The poor metals (In, Al and Sn) have the opposite signs\nof both contributions. The narrow and sharp features of the magnetic electrodes (Co, Ni and\nFe) can be accounted for with relatively small quadratic parts and sizable \\wings\" which\nhave their onset at much smaller applied \felds. This suggests that the magnetization of the\nYIG's surface at an interface with a magnetic electrode requires more modest coercive \felds\ndue to the better \rux match at the interface.\nV. A SIMPLE MODEL\nBulk magnetoelectric e\u000bects have been observed in single-crystal YIG [12] and GdIG.[13]\nBecause these Garnet crystals are centro-symmetric, no linear magnetoelectric e\u000bect is pos-\nsible. Legg and Lanchester have suggested that the bulk magneto-electric e\u000bects observed\nin YIG can be accounted for by electrostriction and inverse magnetostriction.[14] This e\u000bect\n15-80 -60 -40 -20 0 20 -600 -400 -200 0 200 400 600 Even Voltage (µV) \nApplied Field (Oe) Nb Mo Ti W FIG. 16. The M-even response of niobium (0.05 mm, 99.8%), molybdenum (0.1 mm, 99.5%),\ntitanium (0.127 mm, 99%) and tungsten (0.05 mm, 99.95%).\ncan be parameterized by introducing a term in the free energy\nF=\rE2B2(2)\nwhereB(E) is the total magnetic (electric) \feld and the tensor indices have been omitted.[15]\nNotice that this free energy is fully allowed from symmetry considerations. Di\u000berentiation\nwith respect to Eyields the electric displacement, D:\nD=dF\ndE= 2\rEB2(3)\nHence, the electric \feld associated with the magneto-electric e\u000bect is\nEME=D\n\u0014=2\rEB2\n\u0014(4)\nwhere\u0014\u001915 is the dielectric constant for YIG. We imagine that the presence of the metal\nelectrode at the YIG surface can induce a contact \feld Eand an associated contact potential\nV=Ed, wheredis the distance that the contact \feld penetrates into the YIG surface. In\nturn, the magneto-electric \feld will induce a magneto-electric voltage at the surface\nVME=dEME=2\rdEB2\n\u0014=2\rVB2\n\u0014(5)\n16-500 -400 -300 -200 -100 0 100 200 -600 -400 -200 0 200 400 600 Even Voltage (µV) \nApplied Field (Oe) Sn plated Ni Sn plated Cu FIG. 17. The observed M-even voltage for copper and nickel electrodes plated with tin.\n-40 -20 0 20 40 60 80 100 120 \n-600 -400 -200 0 200 400 600 Even Voltage (µV) Applied Field (Oe) Cu Ti Al Ni \nFIG. 18. The M-even signal from four di\u000berent electrodes bonded with silver impregnated epoxy.\nHence, this simple model predicts a magneto-electric voltage at the electrode surface that is\nlinear in the contact potential and quadratic in B. SinceBis dominated by Min the YIG,\nthis term would qualitatively agree with the part of the M-even voltage that appears to be\napproximately quadratic in M. In this model, the observed variation of the magnitude and\n17-40 0 40 80 120 160 200 \n-600 -400 -200 0 200 400 600 Even Voltage (µV) \nApplied Field (Oe) noncondutive epoxy nickel epoxy FIG. 19. The M-even e\u000bect observed for nickel electrodes bonded with either a nonconductive\nepoxy or a nickel-impregnated epoxy.\n-60 0 60 120 180 \n-600 -400 -200 0 200 400 600 Even Voltage (µV) \nApplied Field (Oe) 60% Al 30% Al No Al \nFIG. 20. The M-even signal obtained from nickel electrodes bonded with non-conductive epoxy im-\npregnated with aluminum \rake. The fraction is the relative mass of the added aluminum compared\nwith the epoxy.\n18-100 -50 0 50 100 150 200 \n-600 -400 -200 0 200 400 600 Even Voltage (µV) \nH (Oe) M-even V oltage V oltage quadratic in M residual voltage FIG. 21. The decomposition of the observed M-even voltage into a part that is quadratic in M\nand a residual. This particular sample was an unbonded copper electrode. The quadratic part has\nbeen shifted by 28 Oe to the left in order to achieve the \ft ( Hshift=\u000028 Oe). Notice that the\ncentral part of the curve is well accounted for and that the residual \\wings\" appear to have an\nabrupt onset at about 100 Oe.\nsign of the M-even e\u000bect is attributed to di\u000berent values of the contact potential between\nthe YIG and the adjacent surface.\nTo investigate this possibility further we observe the YIG's bulk magneto-electric re-\nsponse. To do this, we apply a voltage to the center electrode while the two exterior ends\nof the cylinder, which have been coated with conductive silver paint, are held at ground.\nThe signal from the center electrode is AC coupled to our detector using a 47 pF blocking\ncapacitor and is isolated from the supply voltage by a 2 \u00021011\n resistor. The applied\nmagnetic \feld is modulated at about 1 Hz using a triangle wave. The H-even potentials\nobserved in our polycrystalline samples are shown in Figure 22.\nThe magneto-electric response of our sample appears to be approximately quadratic in\nthe sample magnetization and linear in the applied electric \feld (Fig. 23). The ratio of the\nmaximum magneto-electric voltage change (between the magnetization of zero and satura-\ntion) and the applied voltage is 2 :4\u000210\u00005. We estimate the calibration uncertainty in this\nratio to be about 10%. This ratio is a little less than half of the value reported by O'Dell\n19-15 -10 -5 0 5 10 15 -600 -400 -200 0 200 400 600 Even Voltage (mV) Applied Field (Oe) - Diff +Diff FIG. 22. The magnetoelectric voltage even in the applied \feld observed on a polycrystaline YIG\nsample. The curve +Di\u000b ( \u0000Di\u000b) is the di\u000berence between two traces, one taken with the center\nelectrode at +500 V ( \u0000500 V), and one taken with the center electrode at 0 V. The Faraday cage\nsurrounding the sample and the electrode painted on the outer ends of the YIG pieces are held\nat earth ground. These smooth signals represent the contribution to the voltage due to the bulk\nmagnetoelectric e\u000bect.\nfor a single crystal along the 110 axis.[16]\nOur bulk magnetoelectric measurements suggest that to produce an e\u000bect comparable\nin size to the quadratic part of our observed M-even voltages (typically 100 \u0016V) would\nrequire a potential drop at the YIG surface of about 4 Volts. This seems a bit large for\na surface contact potential but is not completely unreasonable. We conclude that this\nattractively simple model may be adequate to account for the part of the observed M-even\ne\u000bect quadratic in M. TheM-even \\wings\" remain unexplained. Further, we are not able\nto account for the various magnitudes and signs of the contact potential di\u000berences required\nto match the di\u000berent electrode materials. Clearly, a more rigorous and detailed model,\nperhaps one that considers some of the additional mechanisms outlined in ref. [1], will be\nrequired to achieve a quantitative understanding of the M-even e\u000bect.\n20-15 -10 -5 0 5 10 15 -600 -400 -200 0 200 400 600 Even Voltage (mV) Applied Voltage (V) FIG. 23. The di\u000berence between the electrode voltage when the magnetization is saturated and\nwhen the magnetization is zero. The slope of the line is 2 :38\u000210\u00005.\nACKNOWLEDGMENTS\nWe thank Dr. Daniel Krause, Jr., Norman Page, Robert Bartos and Robert Cann for\ntechnical support and Prof. Jonathan Friedman for important discussions. This work was\nfunded by NSF grant PHY-0555715 and Amherst College. LRH would also like to thank\nProf. David DeMille, Prof. Steven Lamoreaux and Yale University for their hospitality\nduring part of this work.\n[1] C.-G. Duan, J. P. Velev, R. F. Sabirianov, Z. Zhu, J. Chu, S. S. Jaswal, and E. Y. Tsymbal,\nPhys. Rev. Lett., 101, 137201 (2008).\n[2] C.-G. Duan, C.-W. Nan, S. S. Jaswal, and E. Y. Tsymbal, Phys. Rev. B, 79, 140403 (2009).\n[3] G. Srinivasan, C. P. D. Vreugd, M. I. Bichurin, and V. M. Petrov, Applied Physics Letters,\n86, 222506 (2005).\n[4] S.-W. Cheong and M. Mostovoy, Nature Materials, 6, 13 (2007).\n[5] R. Ramesh and N. A. Spaldin, Nature Materials, 6, 21 (2007).\n[6] T. Zhao et al. , Nature Materials, 5, 823 (2006).\n21[7] F. Zavaliche, T. Zhao, H. Zheng, F. Straub, M. P. Cruz, P. L. Yang, D. Hao, and R. Ramesh,\nNano Letters, 7, 1586 (2007).\n[8] B. J. Heidenreich, O. T. Elliott, N. D. Charney, K. A. Virgien, A. W. Bridges, M. A. McKeon,\nS. K. Peck, D. Krause, J. E. Gordon, L. R. Hunter, and S. K. Lamoreaux, Phys. Rev. Lett.,\n95, 253004 (2005).\n[9] This observation may partially explain why the M-even e\u000bect was reduced after the edm toroid\nwas reassembled. In the 2005 experiment the electrode surfaces of the garnet were polished\n\rat by the manufacturer while in our most recent measurements we ground them with 600\ngrit abrasive, creating a rougher surface.\n[10] D. Fleming, Private communication, Paci\fc Ceramics, http://pceramics.com/.\n[11] M. Mercier, Magnetism, 6, 77 (1974).\n[12] T. H. O'Dell, Philosophical Magazine, 16, 487 (1967).\n[13] G. R. Lee, Ph.D. thesis, University of Sussex (1970).\n[14] G. J. Legg and P. C. Lanchester, Journal of Physics C: Solid State Physics, 13, 6547 (1980).\n[15] A. O. Sushkov, S. Eckel, and S. K. Lamoreaux, Phys. Rev. A, 79, 022118 (2009).\n[16] Note that O'Dell appears to correct his plotted data by a factor of 3 to accommodate capacitive\nlosses.\n22"    },    {        "title": "0907.0956v1.Magnetic_Charge_Transport.pdf",        "content": "Magnetic Charge Transport\nS. T. Bramwell1\u0003, S. R. Giblin2\u0003, S. Calder1, R. Aldus1, D. Prabhakaran3and T. Fennell4\n1. London Centre for Nanotechnology and Department of Physics and Astronomy, University\nCollege London, 17-19 Gordon Street, London, WC1H OAH, U.K.\n2. ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, U.K.\n3. Clarendon Laboratory, Department of Physics, Oxford University, Oxford, OX1 3PU, U.K.\n4. Institut Laue-Langevin, 6 rue Jules Horowitz, 38042 Grenoble, France.\nIt has recently been predicted that certain magnetic materials contain mobile\nmagnetic charges or `monopoles'1. Here we address the question of whether these\nmagnetic charges and their associated currents (`magnetricity') can be directly\nmeasured in experiment, without recourse to any material-speci\fc theory. By\nmapping the problem onto Onsager's theory of weak electrolytes, we show that\nthis is possible, and devise an appropriate method. Then, using muon spin\nrotation as a convenient local probe, we apply the method to a real material:\nthe spin ice Dy 2Ti2O7. Our experimental measurements prove that magnetic\ncharges exist in this material, interact via a Coulomb interaction, and have\nmeasurable currents. We further characterise deviations from Ohm's Law, and\ndetermine the elementary unit of magnetic charge to be 5 \u0016B\u0017A\u00001, which is equal\nto that predicted by Castelnovo, Moessner and Sondhi1using the microscopic\ntheory of spin ice. Our demonstration of magnetic charge transport has both\nconceptual and technological implications.\n1arXiv:0907.0956v1  [cond-mat.other]  6 Jul 20091 Introduction\nThe transport of electrically charged quasiparticles (based on electrons, holes or ions) plays\na pivotal role in modern technology as well as determining the essential function of bio-\nlogical organisms. In contrast, the transport of magnetic charges has barely been explored\nexperimentally, mainly because magnetic charges are generally considered to be, at most,\nconvenient macroscopic parameters2rather than sharply de\fned quasiparticles. However,\nthe recent proposition of emergent magnetic monopoles in spin ice materials1may change\nthis point of view. It is of great interest to investigate the transport of such atomic-scale\nmagnetic charges, as the resulting `magnetricity' could have potential technological signif-\nicance. Furthermore, the direct observation of magnetic charge and current would a\u000bord\nthe strongest case for believing in their reality. Thus, in the analogous case of electrical\ncharge transport (electricity), the fact that both current Iand the elementary charge ecan\nbe directly measured emphasises that these quantities are `real', rather than just convenient\nparameters in a model.\nSpin ices are frustrated magnets, a class of magnetic material that is well known for sup-\nporting exotic excitations, both in experiment3and in theory4,5. The spin ice family6,7,8,9\nis predicted to support sharply de\fned magnetic monopole excitations and o\u000bers the pos-\nsibility of exploring the general properties of magnetic charge transport in an ideal model\nsystem1. There is signi\fcant experimental evidence to support the existence of spin ice\nmagnetic monopoles1,10, but this evidence does not include the direct observation of charge\nor current and relies strongly on interpretation via the microscopic theory of spin ice. In the\nanalogous electrical case, charge and current may be directly measured, with only the basic\nknowledge that the sample is say a semiconductor or a metal. It therefore seems realistic to\nseek a method of measuring magnetic charge and current that is similarly direct and robust.\nAs spin ices are magnetic analogues of water ice, the magnetic charges of spin ice are\npredicted to be directly analogous to water ice's mobile ionic defects. Water ice in turn may\nbe classi\fed as a weakly dissociated electrolyte, for which there exist a variety of general\n2experimental methods to prove the existence of unbound ions and to estimate their charge\nand mobility. Although most of the relevant methods have no possible magnetic analogy,\nwe have identi\fed one that does. The `second Wien e\u000bect' describes the nonlinear increase\nin dissociation constant K(or equivalently the conductance) of a weak electrolyte (solid or\nliquid) in an applied electric \feld E11,12. In a seminal work of 1934 Onsager12derived a\ngeneral equation for the second Wien e\u000bect. This equation provides an excellent description\nof experimental conductivity measurements, and remarkably for a thermodynamic relation,\nenables the determination of the elementary charge e.\nThe aim of the current Article is to present a theory for the direct characteristion of\nmagnetic currents via the Wien e\u000bect, and to test it experimentally. The principal theoretical\npredictions are that the magnetic conductivity is proportional to the \ructuation rate \u0017of\nthe magnetic moment, and that the `elementary' magnetic charge Q(which should depend\non material) may be derived from the initial slope and intercept of the \feld dependence of\n\u0017(B) via the equation:\n~Q= 2:1223m1=3T2=3: (1)\nHerem= slope=intercept is the \feld gradient of the relative magnetic conductivity, Tis the\ntemperature and the tilde means that Qis measured in units of \u0016B\u0017A\u00001(SI units are used\nelsewhere). Eqn. 1 is valid for a su\u000eciently weak magnetic electrolyte and assumes a small\nrelative permeability of the material (although this assumption is not strictly necessary: see\nbelow).\nThus we predict a speci\fc data collapse of \u0017(B;T) over the range of \feld and temperature\nwhere the theory is valid. As the charge depends only on the ratio \u0017(B)=\u0017(0), we simply\nrequire an experimental quantity that is proportional to\u0017(B) in the weak \feld limit. This use\nof relative quantities obviates the need for absolute measurements, which makes the method\nparticularly robust and \rexible. In the case of the spin ice Dy 2Ti2O77,9, we have found that\ntransverse \feld muon spin rotation13a\u000bords a convenient probe. We have therefore used\nthis technique to test the theory and to determine the elementary magnetic charge in the\n3spin ice Dy 2Ti2O7.\nThe Article is organised as follows. In the \\Theory of the Magnetic Wien E\u000bect\" Section,\nwe describe the magnetic equivalent of the second Wien e\u000bect, and derive Eqn. 1. In the\n\\Application to a Real Material\" Section we describe our muon spin rotation ( \u0016SR) exper-\niments on Dy 2Ti2O7. Finally, in the \\Discussion and Conclusions\" Section, we summarise\nour main \fndings and discuss the broader implications of the work.\n2 Theory of the Magnetic Wien E\u000bect\nThe dissociation of a weak electrolyte may generally be represented by two successive equil-\nlibria, the \frst representing the formation of an associated or bound ion pair and the second\nthe dissociation into free ions. For example, in the speci\fc case of water ice, the equilibria\nmay be represented:\n2H2O = [H 3O+OH\u0000] = H 3O++ OH\u0000; (2)\nwhere [:::] represents the bound pair. Here the unbound ions interact according to a (pos-\nsibly screened) Coulomb law. A physical picture of the Wien e\u000bect is that an applied \feld\naccelerates the free ions and, opposed by Brownian motion, in some cases does enough work\nto overcome the Coulomb potential barrier that binds the ions together. The result is an\nincrease, with \feld, of the rate of dissociation and hence of the corresponding equilibrium\nconstant. The \feld acts only on the forward reaction of the second (dissociation) equilibrium\nvia the electrical force F=\u0000eE. Onsager's theory12is valid under the condition that the\nconcentration of unbound defects is su\u000eciently small for the Debye screening length to be\nmuch greater than the association distance12,14. His main result may be approximated by\nthe following form in the weak \feld limit:\nK(E) =K(0) \n1 +b+b2\n3:::!\n; (3)\n4valid forb<3, wherebis the dimensionless group\nb=e3E\n8\u0019\u000fk2T2: (4)\nHere the symbols have their usual meaning and \u000fis the permittivity of the solvent. The\nquantity\u0000kTp\n8bmay be interpreted as the Coulombic barrier to ion pair dissociation, at\nwhich the \feld energy \u0000eErbalances the force of Coulomb attraction14(note that here the\nzero of potential energy is measured at in\fnite separation).\nOnsager's theory would be expected to be very general and realistic. It should be appli-\ncable, by analogy, to emergent magnetic charges and their transport. In analogy with Eqn.\n2, the formation of magnetic charges may be represented by the successive equilibria:\n[solvent] = [bound charges] = [free charges] (5)\nWith the correspondence e!Q;E!B;\u000f 0!\u0016\u00001\n0, we \fnd that the dissociation equilibrium\ninto free magnetic monopoles is then characterised by Eqn. 3 with\nb=\u00160Q3B\n8\u0019k2T2\u0016r(6)\nwhere\u0016ris the relative permeability of the magnetic `solvent'. A pictorial representation of\nthe physical content of the theory is shown in Fig. 1.\nWe de\fnenb;nuas the number of bound and unbound pairs respectively, n0=nb+nuas\nthe total pair concentration and \u000b=nu=n0as the degree of dissociation. The dissociation\nconstant is given by\nK=n0\u000b2\n1\u0000\u000b: (7)\nThe increase in this equilibrium constant with increasing magnetic \feld (the Wien e\u000bect)\n5de\fnes a corresponding change in magnetic moment per unit forward reaction:\n @lnK\n@B!\nT;N= @\u0001G0=kT\n@B!\nT;N=\u0001\u0016\nkT; (8)\nwhere \u0001G0is the change in Gibbs energy per atom. Using Eqn. 3 we \fnd, for the weak\n\feld limit,\n\u0001\u0016=kTb\nB; (9)\nwhich is \feld-independent.\nFollowing Onsager we now assume that the reaction rates of the \frst equilibrium are much\nfaster than those of the second equilibrium, in which case all molecules may be considered\nas bound pairs12. Recalling that \u000b\u001c1, we see that n0\u0019nb\u0019N, so the total number\nof defects is approximately constant at a given temperature. Following a small disturbance,\nthe relaxation of \u0001 \u000bback to its equilibrium value is determined by charge recombination.\nOnsager showed that the decay is exponential with time constant \u0017= 2\u00160\u0014:where\u0014is the\nconductivity, which is proportional to the equilibrium \u000b. Following Eqn. 9 a \ructuation in\n\u000bcauses a proportionate \ructuation in magnetic moment, which decays at the same rate\n\u0017. Thus, measurement of the magnetic moment \ructuation rate as a function of \feld is\nequivalent to the observation of the magnetic conductivity, and gives direct access to the\nWein e\u000bect:\n\u0017(B)\n\u0017(0)=\u0014(B)\n\u0014(0)=\u000b(B)\n\u000b(0)=vuutK(B)\nK(0)= 1 +b\n2+b2\n24+:::; (10)\nwherebis linear in \feld (eqn. 6). This equation should be valid provided that both \u000band\nits change in \feld \u0001 \u000bare su\u000eciently small. It may be used to derive Eqn. 1 in the case\nthat\u0016r= 1.\n63 Application to a Real Material\nIn spin ice materials like Ho 2Ti2O7and Dy 2Ti2O7, the magnetic charges or monopoles are\npredicted to be a consequence of the many body nature15of the dipole-dipole interactions in\nthese materials1. In detail, the Ising-like Ho or Dy moments (`spins') are equivalent to proton\ndisplacement vectors in water ice8. The spins populate the vertices of a lattice of linked\ntetrahedra, pointing either `in' or `out' of any particular tetrahedron. The con\fguration\n`two spins in, two out' corresponds to a water molecule, H 2O. At low temperature, magnetic\ninteractions of mainly dipolar character ensure a ground state consisting only of such `two\nin, two out' con\fgurations: the magnetic system is governed by an ice rule and shares with\nwater ice the Pauling zero point entropy7. The elementary excitation out of the spin ice state\nis a single spin \rip, which breaks the ice rule on neighbouring tetrahedra to create a pair\nof defects, `three in one out plus one in three out'. The equivalent water ice con\fguration\nis a closely bound ion pair H 3O+OH\u000016,17. Castelnovo et al.1predicted that defects should\nunbind and behave as free magnetic monopoles (in the H-\feld) that interact via the magnetic\nCoulomb law. This interaction is determined only by fundamental constants except that the\ncharge takes the value \u0006Qtheoretical = 2\u0016=a, where\u0016\u001910\u0016Bis the rare earth moment\nandad= 4:3356\u0017A is the distance between tetrahedron centres. The formation of magnetic\ncharges in spin ice is thus directly analogous to Eqn. 2. As water ice shows a Wien e\u000bect18,\nit seems valid to test for one in spin ice.\nWe studied Dy 2Ti2O7by the technique of transverse \feld muon spin rotation, with the\naim of testing the theory of Section 2, and of measuring the `elementary' charge Q. In\u0016SR,\nmuons implanted into a sample precess around the sum of the local and applied \felds, and\ntheir decay characteristics give information on the time dependence of these \felds. In an\napplied transverse \feld the muon relaxation function has an oscillatory form, resulting from\nthe uniform muon precession about the applied \feld. However this uniform precession can\nbe dephased by \ructuating local \felds that arise from the sample magnetization M(r;t).\nIn the low temperature limit of slowly \ructuating magnetization the dephasing may lead\n7to an exponential decay envelope of the muon relaxation function in which the decay rate\n\u0015depends only on the characteristic rate \u0017of the magnetic \ructuations. By dimensional\nanalysis\u0015/\u0017, so the key property \u0017(B)=\u0017(0) =\u0015(B)=\u0015(0) can be directly measured (see\nEqn. 10). In the opposite (high temperature) limit of fast \ructuations, \u0015also depends\non the width of the \feld distribution \u001band the muon gyromagnetic ratio \r. Here, one\nexpects\u0015/(\u001b\r)2=\u0017(Ref.13), with\u001bindependent of temperature, so \u0015is proportional to\nthe relaxation timescale \u001c=\u0017\u00001.\nThe muon relaxation rate \u0015(B) was measured as a function of \feld and temperature\nafter zero \feld cooling of the sample to 60 mK (see Methods). Selected experimental results\nthrough the region of interest are shown in Fig. 2. To compare with theory it is useful to\nde\fne an e\u000bective magnetic charge by ~Qe\u000b\u00112:1223m1=3\nexperimentalT2=3(see Eqn. 1), clearly\ndemonstrating that only relative changes in\u0015are required to obtain an absolute measurement\nof~Qe\u000b. Here we set \u0016r= 1, which is appropriate to spin ice under the conditions of interest\n(see Methods).\nWe would expect ~Qe\u000bto approximate the true Qonly in a \fnite range of temperature.\nAt too low temperature (say b= 2mB\u001d3) the theory breaks down because \u0001 \u000bbecomes\nlarge, while at too high temperature, it breaks down because \u000bbecomes large. These limits\non the range of validity can be estimated experimentally.\nWe \frst consider the temperature dependence of \u0015(B= 2mT), as shown in Fig. 3. The\nhigh temperature behaviour mirrors the known behaviour of the magnetic relaxation time,\ndecreasing with temperature as econstant=T(Ref.10,19). At low temperature \u0015increases with\ntemperature, consistent with the expected \u0015/\u0017/\u000b. From the graph we can determine\nthat the crossover from the presumed unscreened regime to the screened regime with rapidly\nincreasing\u000bis atTupper\u00190:3 K. The inset of Fig. 3 shows the temperature dependence of\n\u0015(B= 2mT;1mT): the apparent irregularity of the measurements below T <T upper is in fact\nconsistent with the data collapse predicted by theory (see below), and naively demonstrates\nthat the current is dependent on B. By measuring bwith Eqn. 10, we estimate that the\n8theory starts to break down below Tlower = 0:07K. Thus 0:3< T < 0:07 K is the range\nwhere the theory should be valid (it should be emphasised that this represents a large range\nin the more physically relevant parameter 1 =T).\nBy \ftting the experimental \u0015(B) to extract slope and intercept, we estimate the e\u000bective\nchargeQe\u000b(T), as described above. In the regime of validity, the value of Qe\u000bsaturates\nat\u00185\u0016B=\u0017A, even though both slopes and intercepts depend quite strongly on temperature\n(Fig. 2). The (inverse) temperature dependence of Qe\u000bis illustrated in Fig. 4, where the\ne\u000bective charge can be seen to increase rapidly above Tupper = 0:3K, and to decrease slightly\nbelowTlower= 0:07 K. This direction of this slight deviation is consistent with the theory.\n4 Discussion and Conclusions\nWe now compare these results with the properties, known and predicted, of Dy 2Ti2O7. As\nmentioned above, the predicted monopole charge for this material is Qtheoretical = 2\u0016=a 0=\n4:6\u0016B=\u0017A1. Fig. 4 illustrates how the experimentally measured charge very closely ap-\nproaches this value in the temperature range Tlower< T < T upper. The actual value of\nTupper may be rationalised on the basis of our expectations for spin ice. Thus the monopole\nconcentration should increase as c\u0002e\u00002J=T, withc\u001c1 meaning that in the above tem-\nperature range it should vary between, at most, 10\u000014and 10\u00004. This is indeed a typical\ndegree of dissociation for a weak electrolyte that obeys Onsager's theory (i.e. screening is\nnegligible)12,14.\nThe success of the method is impressive. For example, regarding Fig. 2, this data may\nbe collapsed over a signi\fcant range of temperature and \feld using a single parameter that\nis in excellent agreement with that calculated by a microscopic theory. However, even more\nremarkably, the method produces precisely the same data collapse (modulo the value of the\ncharge) over a range of experimental data on a broad variety of liquid and solid electrolytes12.\nThus using Onsager's theory, we have demonstrated a perfect equivalence between electricity\nand magnetism. It is further a testament to Onsager's genius that his theory is not only\n9correct and universal, but also robust, in that it may be applied to straightforward experi-\nmental measurements of only modest precision12. As already mentioned, the robust quality\nof the method stems from the fact that it deals with relative rather than absolute quanti-\nties. In our case, this means that the muon spin rotation measurements are not subject to\ninterpretation: many di\u000berent analysis protocols would yield essentially the same result.\nOur\u0016SR measurements are in full agreement with other \u0016SR studies of Dy 2Ti2O720as\nwell as bulk relaxation measurements9. Using ultra low \feld magnetization measurements\nwe have independently veri\fed that a spin ice freezing occurs at around T= 0:7K. Below\nthis temperature the bulk magnetization responds only extremely slowly to an applied \feld,\nbut there are dynamics arising from the magnetic charges. Here we have proved the detailed\norigin of the dynamical response discussed in Ref.20.\nWe have thus established overwhelming evidence that decon\fned magnetic charges exist\nin a spin ice material, that they interact by Coulomb's law and are accelerated by an applied\n\feld. Our experimental results are consistent with those discussed in Refs.1,10, but more\ndirectly probe the quantities of interest in the regime of temperature and \feld where a dilute\ngas of magnetic monopoles can be interrogated. We have also measured relative changes\nin the magnetic conductivity (Fig. 2), and proved that monopole currents exist. This\ndemonstration raises an interesting question. As discussed by Jaubert and Holdsworth10,\nthe dynamics of spin ice monopoles are to some extent constrained by their Dirac strings,\nand this almost certainly precludes a direct current. It is therefore notable that di\u000busion\ncurrents do exist, as this would suggest that macroscopic alternating currents may also be\nachievable in spin ice.\nIn the broader context, it has been suggested that non Ohmic transport characteristics of\nthe Wien e\u000bect make it important in biological systems11. Therefore one might imagine that\nthere could be novel technological applications for the magnetic equivalent. This is clearly a\nlong way o\u000b as the temperature scales are low, but it would be interesting to establish proofs\nof principle in this regard, and search for other systems (perhaps micromagnetic arrays21)\n10that show similar e\u000bects. In this context, we note the universality of the current method,\nand recommend it as a diagnostic tool in the study of magnetic charge transport.\nAcknowledgements\nIt is a pleasure to thank C. Castelnovo, M. J. P. Gingras, P. C. W. Holdsworth, L.\nJaubert, D. F. McMorrow and R.Moessner for useful discussions.\n5 Methods\nHigh quality single crystals of Dy 2Ti2O7were grown using the \roating zone method, and\naligned using an X-ray Laue camera. In the experiment, the crystals were aligned with the\ninitial spin polarisation of the muons along the [110] axis, with the magnetic \feld applied\nat right angles to this axis. In \u0016SR experiments, one measures the asymmetry of the muon\nbeta decay as a function of time A(t), which is proportional to the time evolution of the\nmuon spin polarization. A(t) depends on the distribution of internal magnetic \felds and\ntheir temporal \ructuations.\nOur experiment was performed on the MuSR spectrometer at the ISIS facility in the UK.\nAll data was taken upon warming after zero \feld cooling ( <10\u0016T) from 4K to 60 mK, the\ntemperature dependence being repeated twice as a control. Transverse \feld spectra were\n\ftted out to long times using A(t) =Aexp(\u0000[\u0015t]) cos(2\u0019\u001dt). The frequency of oscillations\n(\u001d) can be expressed by \u001d=\r\u0016jBj=2\u0019, whereBis the average magnitude of the local \feld at\nthe muon site and \r\u0016is the muon gyromagnetic ratio. A constant, quick gaussian relaxation\n(\u0015= 3\u0016S\u00001) was required for all the data, as expected for spin ice materials20. The \ftting\nprocedure allowed the slow oscillatory relaxation \u0015(B), and the applied \feld to vary, meaning\nwe are directly reporting the relative change in \u0015. Fig. 5 shows the time evolution of data\ntaken at 100mK in \felds of both 1 and 2 mT along with the \fts to the data; the envelope\n11of the relaxation is also shown. Background measurements have also been performed on a\nbackground silver plate to test for the \feld inhomogeneity in the coils: here the observed\nrelaxation was an order of magnitude slower than in the Dy 2Ti2O7sample.\nWhen zero \feld cooled below 0 :7 K, the susceptibility of Dy 2Ti2O7is su\u000eciently small\nto approximate \u0016r= 1 and to ignore demagnetizing e\u000bects.\nReferences\n1. Castelnovo, C, Moessner, R and Sondhi, S. L. Magnetic monopoles in spin ice. Nature\n451, 42-45 (2007).\n2. Morrish, A. H. The Physical Principles of Magnetism (John Wiley and Sons, 1965).\n3. Lee, S.-H. et al. Emergent excitations in a geometrically frustrated magnet, Nature 418,\n856-858 (2002).\n4. Moessner, R and Chalker, J. T. Properties of a classical spin liquid: The Heisenberg\npyrochlore antiferromagnet. Phys. Rev. Lett. 80, 2929-2932 (1998).\n5. Hermele, M, Fisher, M. P. A and Balents, L. Pyrochlore photons: The U(1) spin liquid\nin a S=1/2 three-dimensional frustrated magnet, Phys. Rev. B 69, 064404 (2004).\n6. Harris, M. J., Bramwell, S. T., McMorrow, D. F., Zeiske, T and Godfrey, K. W. Ge-\nometrical Frustration in the Ferromagnetic Pyrochlore Ho 2Ti2O7.Phys. Rev. Lett. 79,\n2554-2557 (1997).\n7. Ramirez, A. P., Hayashi, A., Cava, R. J., Siddharthan, R. B. and Shastry, S. Zero-point\nentropy in spin ice. Nature 399, 333-336 (1999).\n8. Bramwell, S. T. and Gingras, M. J. P. Spin ice state in frustrated magnetic pyrochlore\nmaterials. Science 294, 1495-1501 (2001).\n129. Snyder, J. et al. Low-temperature spin freezing in the Dy 2Ti2O7spin ice. Phys. Rev. B\n69, 064414 (2004).\n10. Jaubert, L. D. C. and Holdsworth, P. C. W. Signature of magnetic monopole and Dirac\nstring dynamics in spin ice. Nature Phys. 5, 258-261 (2009).\n11. Moore, W. J. Physical Chemistry (Longman, London, (1978)).\n12. Onsager, L. Deviations from Ohm's law in weak electrolytes. J. Chem. Phys. 2, 599-615\n(1934).\n13. Uemura, Y. J. \u0016SR relaxation functions in magnetic materials. Muon Science: Muons\nin Physics, Chemistry and Materials , edited by S. Lee, S. Kilcoyne, and R. Cywinski\n(SUSSP and Institute of Physics, Bristol, 1998).\n14. Bass, L. Wien dissociation as a rate process. Trans. Faraday. Soc. 64, 2153-2159 (1968).\n15. den Hertog, B. C. and Gingras, M. J. P. Dipolar interactions and origin of spin ice in\nising pyrochlore magnets. Phys. Rev. Lett. 84, 3430?3433 (2000).\n16. Bramwell, S. T and Harris, M. J. Frustration in Ising-type spin models on the pyrochlore\nlattice. J. Phys.: Condens. Matter 10, L215-L220 (1998).\n17. Ryzhkin, I. A. Magnetic relaxation in rare-earth oxide pyrochlores. J. Exp. Theor. Phys.\n101, 481-486 (2005).\n18. Eigen, M. and de Maeyer, L. Self-Dissociation and Protonic Charge Transport in Water\nand Ice. Proc. Roy. Soc. (London) A 247, 505-533 (1958).\n19. Orend\u0013 a\u0014 c, M., Hanko, \u0014Ci\u0014 zm\u0013 ar, E., Orend\u0013 a\u0014 cov\u0013 a, Shirai, A. M. and Bramwell, S. T. Mag-\nnetocaloric study of spin relaxation in dipolar spin ice Dy 2Ti2O7.Phys. Rev. B. 75,\n104425 (2007).\n1320. Lago, J, Blundell S. J. and Baines, C. \u0016SR investigation of spin dynamics in the spin-ice\nmaterial Dy 2Ti2O7.J. Phys.: Condens. Matter 19, 326210 (2007).\n21. Wang R. F. et al. , Arti\fcial `spin ice' in a geometrically frustrated lattice of nanoscale\nferromagnetic islands, Nature 439, 303-306 (2006).\n14Figure 1: Illustration of the magnetic Wien e\u000bect, and the detection of magnetic charge by\nimplanted muons. (a) In zero \feld magnetic charges occur mainly in tightly bound pairs,\nbut some thermally dissociate to give a magnetic moment (green arrow) that \ructuates due\nto Brownian motion. (b) The competition of Coulomb potential energy ( V\u00181=r) and\n\feld energy\u0000QBr creates a \fnite energy barrier to dissociation: the stronger the \feld, the\nlower the barrier and more dissociation occurs. (c) On application of a transverse \feld, many\npairs dissociate as individual charges are accelerated by the \feld. (d) After applying the \feld\nthe pairs remain separated while more bound pairs form to restore equilibrium. Magnetic\nmoment \ructuations due to free charges (green arrows) produce local \felds that are detected\nby an implanted muon ( \u0016+).\n150.00 .51 .01 .52 .00.020.040.060.080.100.120.14λ(B) (µS-1)F\nield (mT) 100mK \n250mK \n350mK0.00 .51 .01 .52 .00\n.020.040.060.080.100.120.14Figure 2: A quantity that is proportional to magnetic charge conductivity, illustrating a\nnon-Ohmic increase in conductivity with \feld. The measured muon relaxation rate \u0015(B) is\nplotted as a function of \feld at selected temperatures. Linear \fts to the data (lines) are\nshown, from which it is possible to obtain the intercept, slope and consequently the e\u000bective\nchargeQe\u000b(T).\n160.51.01.52.02.53.03.54.04.55.00.050.100.150.200.250.30λ (µs-1)T\nemperature (K)0.11 1 00.1λ (µS-1)T\nemp (K) 1mT  \n2mT0.51.01.52.02.53.03.54.04.55.00\n.050.100.150.200.250.30Figure 3: The temperature dependence of the muon relaxation rate \u0015measured at an\napplied magnetic \feld of 2 mT. The high temperature regime follows the expected activated\nbehaviour as described in the text (\ft is shown as a solid line). At low temperature \u0015is\nproportional to the monopole concentration. Its rapid increase above Tupper = 0:3Kmarks\na crossover from the regime of weak screening to strong screening of the charges. The inset\nshows the main \fgure on a logarithmic scale along with data taken in 1mT. The fact that\nthe apparently irregular behaviour at low temperature is encompassed by the theory helps\ndemonstrate that we are indeed measuring magnetic charge transport.\n170246810121416182005101520253035404550Qeff (µBA-1)1\n/T (K-1)Theory02 4 6 8 1 012141618200\n5101520253035404550T\nupperTlowerFigure 4: Experimentally measured `elementary' magnetic charge Qe\u000bin Dy 2Ti2O7. On-\nsager's theory is valid in the regime Tlower<T <T upper where the magnetic charges are un-\nscreened. The horizontal green line marks the theoretical prediction of Castelnovo, Moessner\nand Sondhi1.\n1805 1 01 5-15-10-5051015Asymmetry (%)T\nime (µS) 1mT \n2 mT 05 1 01 5-\n15-10-5051015Figure 5: The muon relaxation as a function of time at 100 mK in an applied \feld of\n1mT (solid circles) and 2 mT (open circles), along with the respective \fts to the data. The\nenvelope of each function is also shown, clearly showing a di\u000berence in relaxation at long\ntime.\n19"    },    {        "title": "0908.1278v1.Tunnel_magnetoresistance_of_magnetic_junctions_with_cubic_symmetry_of_the_layers.pdf",        "content": "arXiv:0908.1278v1  [cond-mat.mtrl-sci]  10 Aug 2009Tunnel magnetoresistance of magnetic junctions\nwith cubic symmetry of the layers\nS. G. Chigarev, E. M. Epshtein∗, P. E. Zilberman\nV.A. Kotelnikov Institute of Radio Engineering and Electronics\nof the Russian Academy of Sciences, 141190 Fryazino, Russia\nJanuary 7, 2019\nAbstract\nA tunnelmagnetic junction is considered with magnetic hard andmag-\nnetic soft layers of cubic symmetry. The magnetic switching is analyzed of\nthe layers by a magnetic field perpendicular to the initial ma gnetizations.\nIn such a situation, an additional peak of the TMR ratio appea rs at the\nmagnetic field value lower substantially than the anisotrop y energy of the\nsoft layer.\n1 Introduction\nThe tunnel magnetoresistance (TMR) is one of the most import ant effects\nin modern spintronics. It attracts interest as a beautiful p henomenon as\nwell as a basis of promising spintronic devices such as magne tic random\naccess memory (MRAM), magnetic sensors, and magnetotunnel transis-\ntors (see, e.g., [1, 2]).\nRecently, interest has revived to the magnetic junctions wi th magnetic\nlayers ofthe cubic-symmetrical materials, suchas well-kn own iron [3, 4, 5].\nThin iron films of (001) orientation have two in-plane easy ax es, [100] and\n[010], with equal anisotropy energy. This fact allows switc hing magneti-\nzation by magnetic field between different easy axes, so that a possibility\noccurs of creating a memory with more than two stable states, that may\nbe laid to the basis of many-valued logic devices. Moreover, very high\nTMR ratio, from 170% at room temperature to 318% at 10 K, has be en\nobservedinepitaxial Fe/MgO/Fe magnetic tunneljunctions [5] (note, that\nsuch high TMR ratios were predicted theoretically [6, 7]). A ll this makes\nsuch structures to be very attractive objects of study.\nIn this work, we consider a magnetic junction with magnetic h ard and\nmagnetic soft layers of iron-type cubic symmetry. Switchin g such systems\nby external magnetic field was studied under various relativ e magnetic\nconfigurations of the layers [4, 8]. Here, a different situati on is analyzed,\n∗E-mail: eme253@ms.ire.rssi.ru\n1when the magnetic field is applied perpendicularly, rather t han collinearly,\nas usual, to the initial collinear magnetization direction s of the layers.\nIt is shown, that a new Π-shaped resistance peak occurs under these\nconditions at the magnetic field lower substantially than th e anisotropy\nfield, while the peak height is lower significantly than the re sistance peaks\ncorresponding to the conventional collinear configuration s. Therefore, the\nsystem in study obeys more than two resistive states switcha ble by an\napplied magnetic field.\nIn Sec. 2 we describe the structure in study and introduce a ph e-\nnomenological model. In Sec. 3 the layer magnetization dire ctions are\ncalculated as functions of the magnetic field perpendicular to the initial\ndirections. In Sec. 4 the results obtained are used to calcul ate the corre-\nsponding resistances. In Sec. 5 the results are discussed.\n2 The model and main equations\nLet us consider a magnetic tunnel junction with magnetic har d (1) and\nmagnetic soft (2) layers of iron-type cubic symmetry. The di fferent val-\nues of the magnetic anisotropy of the layers may be ensured wi th larger\nthickness or pinning of layer 1. The layers have (001) orient ation with\nin-plane easy axes [100] and [010]. The layer magnetization vectors are\ndirected along the [100] easy axis originally, such paralle l configuration\ncorresponds to minimal resistance RPof the junction when the current\nflows perpendicular to the layer planes (CPP mode). Under mag netiza-\ntion switching by applied magnetic field, the junction resis tance changes;\nthis is well-known TMR effect.\nThe conductance of the tunnel junction is [9]\nG(χ) =GPcos2χ\n2+GAPsin2χ\n2, (1)\nwhereχis the angle between the layer magnetization vectors, GPand\nGAPare the conductances corresponding to parallel ( χ= 0◦) and an-\ntiparallel ( χ= 180◦) configurations of the junction, respectively. The\nangular dependence of the TMR ratio F(χ) defined as\nF(χ) =R(χ)−RP\nRP, R(χ)≡1\nG(χ)(2)\ntakes the form\nF(χ) =f(1−cosχ)\n2+f(1+cosχ), (3)\nwheref=F(180◦) = (RAP−RP)/RPcoincides with the conventional\ndefinition of the TMR ratio [10].\nTo obtain the TMR ratio as a function of the external magnetic field,\nit is necessary to find the dependence of the χangle on the value and\ndirection of the magnetic field.\nThemagnetization orientationofthemagneticlayerisdete rminedwith\nthe minimum condition of the magnetic energy, which takes th e following\nform under cubic symmetry [11]:\nU(θ) =−MHcos(θ−α)+1\n2MHasin2θcos2θ, (4)\n2whereMis the saturation magnetization, His the external magnetic\nfield,Hais the anisotropy field, αandθangles determine directions of\nthe external magnetic field and magnetization vector, respe ctively; the\nangles are counted off from [100] axis.\nLet the magnetic field be applied along [010] axis ( α= 90◦). The\nextremum condition dU(θ)/dθ= 0 takes the form\n[(1−2sin2θ)sinθ−h]cosθ= 0, (5)\nwhereh=H/Hais the dimensionless magnetic field.\nThe roots θ= 90◦≡θ1andθ=−90◦≡θ2of Eq. (5) correspond to\ntwo equilibrium positions of the magnetization vector; wit hα= 90◦, the\nlatter state becomes unstable ( d2U(θ)/dθ2<0) ath >1.\nThe other equilibrium states are determined by the cubic equ ation\nwith respect to sin θ\n2sin3θ−sinθ+h= 0. (6)\nAth <√\n6/9≡h0≈0.272, the equation has three real roots, of which\nonly one corresponds to a stable state, namely,\nθ= arcsin r\n2\n3cos„\n60◦+1\n3arccosh\nh0«!\n≡θ3. (7)\nAth > h 0, the stable solution θ3disappears (the only real root of Eq. (6)\ncorresponds to an unstable state), and only θ1= 90◦andθ2=−90◦\nstable states remain.\nThese results are used below to analyze magnetic configurati on of the\nmagnetic junction.\n3 Layer magnetization direction\nLet us trace behavior of the magnetization vector of a magnet ic layer ori-\nented originally along [100] easy axis in the magnetic field d irected along\nanother easy axis [010]. With the field increasing from zero, the magneti-\nzation vector deflects gradually from the former easy axis to the latter one\nin accordance with Eq. (7), until hreachesh0value (the corresponding\nvalue ofθangle isθ= arcsin(1 /√\n6)≈24◦) andθ3state disappears. Then\nthe vector turnsabruptlyto θ1position (along themagnetic field and [010]\neasy axis) and remains in this state with further increase of the magnetic\nfield. It remains in that state, also, when the magnetic field d ecreases to\nzero and further to negative value h=−1. Then the magnetization vector\nswitches abruptly from the θ1position antiparallel to the magnetic field\nto the parallel one θ2position. Under subsequent cycling of the magnetic\nfield between h=−1 andh= +1 values, the magnetization switches\nabruptly between θ1andθ2states without returning to the initial state\nθ= 0◦. The return may be realized by the magnetic field h=h0along\n[100] axis.\nSuch a behavior of the system with transitions from one energ y min-\nimum to another one may be traced also by means of Fig. 1 where t he\nmagnetic energy U(θ) is shown in various magnetic fields.\n3-180 -135 -90 -45 0 45 90 135 180\n-1.5-1.0-0.50.51.01.5 \n  h = 0\n h = 0.1\n h = 0.272\n h = 0.5\n h = 0.7\n h = 1.0\n h = 1.5\n h = - 0.1\n h = - 0.272\n h = - 0.5\n h = - 0.7\n h = - 1.0\n h = - 1.5U(θ)/MHa\nθ, deg\nFigure 1: The (dimensionless) magnetic energy of a magnetic layer wit h cubic\nsymmetry as a function of θangle between the magnetization vector and the\neasy axis at various dimensionless magnetic fields h=H/Hadirected along\n[010] axis ( θ= 90◦). The minimum θ= 0◦disappears at h= 0.272 so that the\nsystem being in that minimum comes to another minimum θ= 90◦. The latter\nexists under subsequent field changes until h=−1, when the system switches\ntoθ=−90◦minimum. Under subsequent cycling the magnetic field between\nh=−1 andh= 1, the system switches between θ=−90◦andθ= 90◦positions\nwithout returning to the initial θ= 0◦position.\n4-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0\n-90-75-60-45-30-15153045607590\n1 2θ, deg\nH/Ha212\nIII21\nI II\nFigure 2: The dependence of the magnetic hard (1) and soft (2) lay er orienta-\ntions on the magnetic field along [010] axis ( θ= 90◦) referred to the soft layer\nanisotropyfield Ha2. The layer anisotropyfield ratio Ha1/Ha2is supposed to be\nequal to 2, as example. Three subsequent stages of the whole swit ching cycle,\n0◦→90◦, 90◦→ −90◦, and−90◦→90◦, are marked with Roman numerals I,\nII and III, respectively. The arrows show directions of the layer m agnetization\nswitching.\nNow we consider the magnetic junction described in Sec. 2 ins tead of\na single magnetic layer. The each of two layers behaves indep endently of\nthe other, so that the magnetization direction dependence o n the applied\nmagnetic field is to be found as above for both layers, but with differ-\nent anisotropy energies. We assume, as an example, that the a nisotropy\nenergy of the magnetic hard layer is twice as many as that of th e soft\nlayer.\nBecause of larger anisotropy energy, the hard layer lags beh ind the soft\none and switches from one position to another at larger magne tic field.\nThe results are shown in Fig. 2. Three subsequent stages of th e whole\nswitching cycle, 0◦→90◦, 90◦→ −90◦, and−90◦→90◦, are marked\nwith Roman numerals I, II and III, respectively, the Arabic n umerals 1\nand 2 refer to the hard and soft layers, respectively.\n4 Tunnel magnetoresistance\nThe TMR ratio is determined with the difference χof the corresponding\nθangles for two layers in accordance with Eq. (3). Using Eqs. ( 3), (7), we\nobtain the results shown in Fig. 3. The Roman numerals have th e same\n5-3 -2 -1 0 1 2 30.00.10.20.30.40.5 (R - RP)/RP\nH/Ha2III III\nFigure 3: The TMR ratio as a function of the magnetic field along [010] a xis\n(θ= 90◦) referred to the soft layer anisotropy field Ha2atHa1/Ha2= 2,\n(RAP−RP)/RP= 0.5. The Roman numerals and the arrows have the same\nmeaning as in Fig. 2.\nmeaning as in Fig. 2. It is seen, that a new peak I appears besid es the\nstandard TMR ratio peaks II and III corresponding to the swit ching from\nparallel configuration to antiparallel one and vise versa. T his new peak is\nlower substantially because it corresponds to the angle bet ween the layer\nmagnetization vectors smaller than 90◦(this angle tends to 90◦when the\nhard layer anisotropy energy is large in comparison with tha t of the soft\nlayer; in that case, the TMR ratio is half of the standard valu e). This\npeak corresponds to the magnetic field value lower considera bly (almost\n4 times) than the soft layer anisotropy field.\n5 Conclusion\nIt follows from the results that using magnetic junctions wi th cubic rather\nthan uniaxial symmetry of the layers opens additional possi bilities in ap-\nplications of the TMR effect. The switching with a perpendicu lar mag-\nnetic field allows to lower significantly the corresponding m agnetic field,\nthat may improve sensibility of the magnetic sensors based o n TMR. The\nextra peak of the TMR ratio as a function of the applied magnet ic field\nmeans existence of an additional stable equilibrium state o f the system in\nstudy. This fact may be used to create memory devices with mor e than\ntwo stable states and multi-valued logic devices.\n6Acknowledgment\nThe work was supported by the Russian Foundation for Basic Re search,\nGrant No. 08-07-00290.\nReferences\n[1] G.A. Prinz, J. Magn. Magn. Mater. 200, 57 (1999)\n[2] A. Fert, Rev. Mod. Phys. 80, 1517 (2008)\n[3] J. Grabowski, M. Przybylski, M. Nyvlt, J. Kirschner, J. Appl. Phys.\n104, 113905 (2008)\n[4] R. Lehndorff, M. Buchmeier, D.E. B¨ urger, A. Kakay, R. Her tel, C.M.\nSchneider, Phys. Rev. B 76, 214420 (2007)\n[5] S.G. Wang, R.C.C. Ward, G.X. Du, X.F. Han, C. Wang, A. Kohn ,\nPhys. Rev. B 78, 180411 (2008)\n[6] W.H. Butler, X.-G. Zhang, T.C. Schulthess, J.M. MacLare n,Phys.\nRev. B63, 054416 (2001)\n[7] J. Mathon, A.Umerski, Phys. Rev. B 63, 220403 (2001)\n[8] A.A. Leonov, U.K. R¨ oßler, A.N. Bogdanov, J. Appl. Phys. 104,\n084304 (2008)\n[9] Y. Utsumi, Y. Shimizu, H. Miyazaki, J. Phys. Soc. Japan 68, 3444\n(1999)\n[10] M. Guilliere, Phys. Lett. A 54, 225 (1975)\n[11] K.H.J. Buschow, F.R. De Boer, Physics of Magnetism and Magnetic\nMaterials (Kluwer Academic Publ., New York, 2003)\n7"    },    {        "title": "0908.3153v1.Quantitative_Observation_of_Magnetic_Flux_Distribution_in_New_Magnetic_Films_for_Future_High_Density_Recording_Media.pdf",        "content": "arXiv:0908.3153v1  [cond-mat.mtrl-sci]  21 Aug 2009Quantitativeobservationofmagneticflux\ndistributionin newmagneticfilmsforfuturehigh\ndensityrecording media.\nAurélienMasseboeuf,∗,†,§AlainMarty,†PascaleBayle-Guillemaud,†Christophe\nGatel,‡andEtienneSnoeck‡\nCEA,INAC, Grenoble(FR), and CEMES-CNRS, Toulouse(FR)\nE-mail: aurelien.masseboeuf@cemes.fr\nAbstract\nOff-axiselectronholographywasusedtoobserveandquanti fythemagneticmicrostructure\nof aperpendicular magnetic anisotropic (PMA)recording me dia. Thinfoilsof PMAmaterials\nexhibitaninteresting UpandDowndomainconfiguration. The sedomainsarefoundtobevery\nstable and were observed at the same time with their stray fiel d, closing magnetic flux in the\nvacuum. The magnetic moment can thus be determined locally i n a volume as small as few\ntens of nm3.\n†CEA,InstitutNanoscienceset Cryogénie-SP2M,17ruedesMa rtyrs,38054GrenobleCedex09,France\n‡CEMES-CNRS, BP 94347,29rueJeanneMarvig,31055ToulouseC edex,France\n§New ad. : CEMES-CNRS,Toulouse,France\n1AurélienMasseboeufet al. Quantitativemagneticobservat ionofPMA alloysat thenanoscale\nFrom the first desktop (5.25 inch diameter) hard disk drive (H DD) in the early 1980’s, with\n5 MegaBytes storage capacity, to the 1 TeraByte hard drive di stributed now by Hitachi, funda-\nmental improvments have been achieved in HDD technology. Th e main evolutionnary step in the\ndata storage history happened certainly before the first HDD -integrated Personal desktop Com-\nputer(Seagatein1980)whentheperpendicularrecordingid eawasfirstintroducedin1977.1Now,\nall improvements in new memory capacity are expected to be re ached thanks to perpendicular\nrecording. Whileimportantstudies are publishedon new mat erialsdesign,2,3studieson magnetic\ninteraction between the recording head and the data bits are mostely concerned about the tip field\nleakagecharacterization.4,5Hereweshowthatitisalsopossibletoobtainnanometricand quantita-\ntivemagneticinformationsofstrayfieldandmagneticinduc tionatthesametimeonperpendicular\nmagneticanisotropic(PMA)materials.\nDue to the strong stray fields perpendicular to their surface , PMA materials have been exten-\nsivelystudied by MagneticForce Microscopy (MFM),6,7micro-magneticsimulations,8and other\nmagneticcharacterizationtechniques.9,10Howeverthesetechniqueswerenotsuitabletostudythe\ninnermagneticconfiguration of materials and innermagneti zationat thesame time. Thus, forma-\ntionofstrayfielddistributionwithrespectinnermagnetic parametersofthematerialhavenotbeen\nyet confirmed by experimental results.11This could be of great importance to evaluate the ability\nofareading head toflip abit.\nElectron Holography (EH) in a Transmission Electron Micros cope (TEM) is a powerful tech-\nniquewhichenablesobservationofelectrostaticandmagne ticfieldsatthenanoscalebyaelectron\nwave phase retrieval process.12Through the so-called Aharonov-Bohm effect,13it is known that\nan electron wave is sensitive to the electric and magnetic po tential. As a consequence, it can be\nused to investigate magnetic properties of materials. Elec tron holography has thus been used to\nstudy many magnetic materials, for example, the analysis of stray fields around a MFM tip,14or\nthe study of the magnetic configuration of magnetic nanopart icles,15magnetic films,16magnetic\n2AurélienMasseboeufet al. Quantitativemagneticobservat ionofPMA alloysat thenanoscale\ntunnel junctions,17or even magnetitecore of magnetotacticbacteria.18The phase shift of theexit\nelectron wave, Δφ, travelling along the zdirection across the sample, which interacted with the\nelectromagneticfield (electrostaticand magneticpotenti alsfromthesample)can beexpressesas:\nΔφ(x,y)=CE/integraldisplay\nVint(x,y,z)dz−e\n¯h/integraldisplay\nAz(x,y,z)dz (1)\nwhereV(x)intrepresents the electrostatic contribution to the phase shi ft (in the case of a material\nit is mainly its Mean Inner Potential or MIP), and Azis thez-component of the magnetic vector\npotential describing the magnetic induction distribution in a plane (for a given z) pendicular to\nthe optic axis. Azis related to the magnetic induction /vectorBby means of the Maxwell’s equation :\n/vectorB=(Bx,By)=(∇yAz,−∇xAz).CEis an electronenergy related constant.\nThe keypointis the separation of the magnetic and electrost atic contributions in the reconstructed\nphaseshiftand isextensivelydiscussedelsewhere.19\nWe have used for our purpose a method consisting of recording two holograms before ( Δφ+)\nand after ( Δφ−) removing and inverting the sample. The electrostatic cont ribution to the phase\nshift remains similar in the two holograms while the magneti c contribution changes in sign. The\nmagneticcontribution( Δφmagn.)canthusbeobtainedbyevaluatinghalfofthedifferenceof thetwo\nphase images calculated from the two holograms. The MIP cont ribution ( ΔφMIP) is then half of\nthesum. Toaccountforthesamplereversal,itisnecessaryt oreverseoneofthetwophaseimages\nand alignthem.\nΔφmagn.=1\n2∗[Δφ+−Δφ−] =e\n¯h[AzΔt(x,y)]\nΔφM.I.P.=1\n2∗[Δφ++Δφ−] =CEV(x,y)intΔt(x,y)(2)\nEH has been used to study the magnetic configuration and measu re the remanent magnetization\nofaFePd L10/FePddisord.stack,grownonMgO(001),whichexhibitsastrongPMA.Thete tragonal\naxis of the chemically ordered FePd L10crystalline structure lies along the growth direction cor-\nresponding to an alternate stacking of pure Iron and Palladi um planes. This chemical anisotropy\nalongthe z-axisinducesaneasymagneticaxisinthesamedirectionwhi chgivesrisetotheupand\n3AurélienMasseboeufet al. Quantitativemagneticobservat ionofPMA alloysat thenanoscale\ndownmagneticdomainconfiguration.6Themainpurposeofthesecond\"soft\"layer,havingavan-\nishinganisotropy,is usuallydescribed as themainfactorf orincreasingtherecording efficiency.20\nTheexpectedmagneticconfigurationoftheFePd L10/FePddisord.bilayerispresented inFigure1-A.\nDomains in the FePd L10layer are separated by Bloch walls where the magnetization l ies in the\nplaneofthefoil,surroundedbyaNéelCapinwhichthemagnet izationrunsaroundtheBlochwall\naxis. ThebottomFePd disord.layergivesrisetoin-planecomponentsallowingafluxclosu rewithin\nthebilayer,andenablesthedomainstobealignedinaparall elstripesconfiguration. Thismagnetic\nconfiguration is confirmed by studying the external stray fiel d by MFM experiment as shown in\nFigure1-B.\nFigure1: A.Magneticconfigurationexpectedforthefoil. B.MFMviewofthesampleinitsstripe\nconfiguration. Black contrast is down domains, bright contr ast is up ones. Thedashed area shows\nthe geometry used for TEM sample preparation, across magnet ic orientation. C.Fresnel view of\nthesampleshowingblack andwhitecontrastwherethebeam ar eoverlaping.\nOur purpose is to analyse in more detail the inner magnetic co nfiguration with higher resolu-\ntion. Figure 1-C shows a Fresnel TEM micrograph21of the sample. The thin foil used for TEM\nexperiments has been prepared in cross-section in order to o bserve the magnetic structure by the\nside instead of the top in the MFM geometry. In this micrograp h, domains are clearly defined,\nseparated from one another by a bright or dark line localised at the positionof domain walls. The\ndomain periodicity is 100 nm which fully agree with MFM measu rement. EH experiments were\ncarried out onthesameareaofthePMA magneticfilm.\n4AurélienMasseboeufet al. Quantitativemagneticobservat ionofPMA alloysat thenanoscale\nFigure2: MeanInnerPotential( A)andmagnetic( B)contributiontothephaseoftheelectronwave.\nThe color scale used here is a temperature scale described ne ar each picture. The contour lines\nare for equi-phase lines and represent 1 radian for MIP contr ibution and 1/4 radian for magnetic\ncontribution.\nFigure 2-A showsthededuced MIPcontributionto thephasesh ift,and themagneticcontribu-\ntionisshowninFigure2-B.Theiso-phasecontoursdisplaye donbothphaseimagesdirectlyrelate\nto thickness variations (in the MIP phase image) and to magne tic flux (in the magnetic one). The\nvariation of the MIP contribution, exhibits that the TEM sam ple increases uniformly in thickness\nwhile magnetic contribution highlights vortices correspo nding to the Bloch walls. Between these\nvorticesareareaswherethemagneticfluxisparalleloranti -paralleltothegrowthdirection. These\ncorrespond to the \"up\" and \"down\" magnetic domains. Stray fie lds close the flux in the vacuum\nand inside the stack. However, the vortices appear to be flatt er at the bottom (close to the FePd\ndisordered layer) than at the top (close to the vaccum). This asymmetrical shape of the vortices is\ndue to the disordered FePd layer which forces the magnetic in duction to lie within the foil plane.\nFromequation2,quantitativevaluesofmagneticinduction canbeextractedprovidedthattheMIP\n5AurélienMasseboeufet al. Quantitativemagneticobservat ionofPMA alloysat thenanoscale\northethicknessofthedifferentlayers are known:\nΔt(x) =ΔφM.I.P.\nCEV(x)int\nB⊥=¯h\ne·Δt(x)∇[Δφmagn.](3)\nFigure 3: Mean Inner Potential contribution to the phase ana lysis. This is a plot profile along the\ndashedlineinFigure2-A.Right(yellow)labelandsolidlin eisthephaseprofileusedtodeducethe\ndifferent layers in the foil. Dashed lines present linear in terpolation variations for each different\nlayers. Thicknessprofileispresented inthecolored(blue) area and islabeled ontheleft.\nFigure 3 showsinyellowtheexperimentalprofileof theelect rostaticcontributionto thephase\nextractedalongthedashedlineinFigure2. Todeducethethi cknessprofile(inblue),wehavefirst\ncalculated themean innerpotentialvaluesforthePd, FePd L10and FePd disord.layers.\nAccording to Equation 3, this thickness profile is used to cal culate the BxandByinside the layer\n(Figure 4, A and B). Neglecting the demagnetizing field withi n the material, the measured mag-\nnetic induction is directly related to the magnetization in the material. The value of the magnetic\ninductionmodulusintheFePd L10region(i.e.insidethedomains)givesrisetoamagneticinduction\nof 1.3±0.1 T while same measurements performed on the FePd disord.area (under domain walls)\ngives an aeeeveraged values of 1 .2±0.1 T. Values measured for the µ0Msof the FePd L10layer\nare the same as those expected for FePd.6The variations observed in the different domains come\nfrom a variation in the evaluation of the local thickness, du e to small deformation of the crystal,\noramorphizationduringionmilling. Thedifference foundb etween thetwolayers is negligible. It\nshould comes from the smaller area of magnetization purely p erpendicular to the electron path in\n6AurélienMasseboeufet al. Quantitativemagneticobservat ionofPMA alloysat thenanoscale\nthesoftlayerunderthedomainwall. Thisimpliesavariatio nofthemagnetizationdirectiondueto\nthepresence ofthedomainwalland thein-planemagnetizati onunderthedomains. Themeasured\nvalueis thenno longerapuremagneticmomentbutaprojectio nofit.\nMoreaccuratemeasurementsoftheFePdmagneticproperties canbedoneperformingmicromag-\nFigure 4: AandBare the X and Y components (left and right respectively) of th e magnetic\ninduction deduced from phase gradients. Profile for quantit ativeinterpration is displayed on each\nfigure.Cis a zoomed view of Fig. 2-B compared with a micro-magneticsi mulationin D. In both\nimages,iso-phaselinesrepresent 0 .08radand thecolorscaleusedis described.\nneticsimulations. WehaveusedacodebasedonLLGtemporali ntegration,GL_FFT,8tosimulate\nthe magnetic flux (i.e. the iso-phase contours) observed by E H. Calculated magnetic phase shift\n(usingbulkvalues6)and experimentaldataare comparedin Figure4, Cand D.\nIt is seen that the Bloch walls are much wider in the experimen tal data which could be explain by\na slight decrease of the thickness due to the thinning proces s (see also Supporting Informations).\nThe magneticflux can be quantitativelymeasured, both in and outsidethe sample. The stray field\ncan then berelated to themagnetizationmomentinthedomain s. Thisis potentiallyofgreat inter-\nest forthedesignofareader ofthiskindofmaterial.\nElectron holographywas used to highlightthemagneticstru cture of FePd L10-FePddisord.mag-\n7AurélienMasseboeufet al. Quantitativemagneticobservat ionofPMA alloysat thenanoscale\nneticbilayerexhibitingPMA, witha resolutionclosed to th e nanometerand an accurate measure-\nmentofthelocalmagneticinduction. Themagneticconfigura tionwasthensuccessfullycompared\ntomicromagneticcalculations. Moreover,thequantitativ einformationsgivenbythetechniquecan\nbedirectlyrelatedtothestrayfieldofthematerials,which arethebitinformationforreadingheads\ninhard drives.\nAcknowledgement\nThanksare duetoDr. P. Cherns forcriticsand usefulldiscus sionsaboutthismanuscript.\nSupporting InformationAvailable\nThe samplewas grown on MgO (001) substrate by Molecular Beam Epitaxy (MBE) according to\nthefollowingsequence: Cr(2.5nm)inordertoinitiatethee pitaxialgrowth,Pd(48nm),FePd(15\nnm) co-deposited at room temperature, FePd (37 nm) co-depos ited at 450◦Cand a 1.5 nm caping\nofPt was added toavoidoxydation.\nThesamplehasbeenpreparedforelectronmicroscopyusingm echanicalpolishingandionmilling.\nThelayeristhusexhibitingadoublewedgegeometryalongth eobservationplane. Themicroscope\nusedfortheholographyexperimentsis aFEITecnai F20 field- emission-gunTEMfitted withaCs\ncorrector(CEOS).AFEITitanFEGTEMfittedwithadedicatedL orentzlenswasusedforFresnel\nimaging. A Gatan ImagingFilterwas alsoused forzero lossfil teringfortheFresnel images.\nHologramsare recorded usingoff-axiselectron holography witha rotatablebiprismlocatedin the\nSA aperture. The biprism is aligned along the foil direction x. The fringe spacing is 1.8 nm,\nthe fringe contrast is 12 %. For calculating the phase image w e perform a Fourier transform of\nthe hologram and apply a mask of 0.25 nm−1on the side-band spot before calculating an inverse\nFouriertransform.\nTo separate the electrostatic and magnetic contributions t o the phase shfit, two holograms were\nrecordedbeforeandafterinvertingthesample. Imagecalcu lationswerethenperformedtoaligned\nthe two images. The phase images have been digitally flipped f or accordance with the physical\n8AurélienMasseboeufet al. Quantitativemagneticobservat ionofPMA alloysat thenanoscale\ninversion of the sample. After data acquisition, an accurat e correction of the drift, rotation and\nscalingbetween thetwoimageshas been performed usingrece ntly developpedscripts.\nMean Inner Potentials have been calculated using the Doyle a nd Turner scattering amplitude cor-\nrected withtheRossandStobbsequation(seechapter12of.22)Wecalculate: VFePdL1o=21.73V,\nVFePddis.=22.67V,VPd=22.37V.\nMicro-magnetical simulation has been carried out using the bulk FePd following parameters :\nExchangeconstant A=6.910−12J.m−1,UniaxialAnisotropyK=1 .03106J.m−3,SaturatedMag-\nnetization µ0MS=1.294Tesla. Thecellsare0 .781nm×0.625nmandinfinitealongthe zdirection\n(considered as invariant).\nReferences\n(1) Iwasaki,S.; Y. Nakamura, K. IEEETransactionsonMagnetics 1977,13, 1272–1277.\n(2) Kryder, M. H.; Gustafson, R. W. Journal of Magnetism and Magnetic Materials 2005,287,\n449–458.\n(3) Richter, H. J. JournalofPhysicsD:AppliedPhysics 2007,40, R149.\n(4) Signoretti, S.; Beeli, C.; Liou, S.-H. Journal of Magnetism and Magnetic Materials 2004,\n272-276,2167–2168.\n(5) Kim, J. J.; Hirata, K.; Ishida, Y.; Shindo, D.; Takahashi , M.; Tonomura, A. Applied Physics\nLetters2008,92, 162501.\n(6) Gehanno, V.; Samson, Y.; Marty, A.; Gilles, B.; Chambero d, A.Journal of Magnetism and\nMagneticMaterials 1997,172, 26–40.\n(7) Attane,J.P.;Samson,Y.;Marty,A.;Halley,D.;Beigne, C.AppliedPhysicsLetters 2001,79,\n794–796.\n9AurélienMasseboeufet al. Quantitativemagneticobservat ionofPMA alloysat thenanoscale\n(8) Toussaint, J. C.; Marty, A.; Vukadinovic, N.; Youssef, J . B.; Labrune, M. Computational\nMaterialsScience 2002,24, 175–180.\n(9) Dürr, H. A.; Dudzik, E.; Dhesi, S. S.; Goedkoop, J. B.; van der Laan, G.; Belakhovsky, M.;\nMocuta,C.; Marty,A.;Samson,Y. Science1999,284,2166–2168.\n(10) Beutier, G.; Marty, A.; Chesnel, K.; Belakhovsky, M.; T oussaint, J. C.; Gilles, B.; der\nLaan, G.V.; Collins,S.; Dudzik,E. Physica B 2004,345,143–147.\n(11) Hubert,A.; Shäfer, R. MagneticDomains ; Springer, 1998.\n(12) Gabor, D. Nature1948,161, 777–778.\n(13) Aharonov,Y.; Bohm,D. PhysicalReview 1959,115, 485–491.\n(14) Streblechenko, D. G.; Scheinfein, M. R.; Mankos, M.; Ba bcock, K. IEEE Transactions on\nMagnetics 1996,32,4124–4129.\n(15) Hytch, M. J.; Dunin-Borkowski, R. E.; Scheinfein, M. R. ; Moulin, J.; Duhamel, C.; Maza-\nleyrat,F.; Champion,Y. PhysRevLett 2003,91,257207.\n(16) McCartney, M. R.; Smith, D. J.; Farrow, R. F. C.; Marks, R . F.Journal of Applied Physics\n1997,82,2461–2465.\n(17) Snoeck, E.; Baules, P.; BenAssayag, G.; Tiusan,C.; Gre ullet,F.; Hehn, M.; Schuhl, A. Jour-\nnalofPhysics: CondensedMatter 2008,20,055219–.\n(18) Dunin-Borkowski, R. E.; McCartney, M. R.; Frankel, R. B .; Bazylinski, D. A.; Pósfai, M.;\nBuseck, P. R. Science1998,282, 1868–1870.\n(19) Dunin-Borkowski,R. E.; Kasama, T.; Wei, A.; Tripp, S. L .; Hytch, M. J.; Snoeck, E.; Harri-\nson,R. J.;Putnis,A. MICROSCOPY RESEARCHAND TECHNIQUE 2004,64,390–402.\n(20) Khizroev,S.;Litvinov,D. PerpendicularMagneticRecording ; KluwerAcademicPublishers,\n2004; p174.\n10AurélienMasseboeufet al. Quantitativemagneticobservat ionofPMA alloysat thenanoscale\n(21) Chapman,J. N. Journalof PhysicsD :AppliedPhysics 1984,17,623–647.\n(22) Edgar Volkl, E.; Allard, L. F.; Joy, D. C. Introduction to Electron Holography ; Kluwer\nAcademic/PlenumPublishers: New York,1999; p 354.\n11"    },    {        "title": "0909.4645v1.Probing_punctual_magnetic_singularities_during_magnetization_process_in_FePd_films.pdf",        "content": "arXiv:0909.4645v1  [cond-mat.mtrl-sci]  25 Sep 2009Probing punctual magnetic singularities during magnetiza tion\nprocess in FePd films\nAur´ elien Masseboeuf,∗Thomas Jourdan,†Fr´ ed´ eric\nLan¸ con, Pascale Bayle-Guillemaud, and Alain Marty\nCEA, INAC, SP2M, F-38054 Grenoble-, France\n(Dated: October 26, 2018)\nAbstract\nWe report the use of Lorentz microscopy to observe the domain wall structure during the magne-\ntization process in FePd thin foils. We have focused on the ma gnetic structure of domain walls of\nbubble-shapedmagnetic domains near saturation. Regions a re found along the domain walls where\nthe magnetization abruptly reverses. Multiscale magnetic simulations shown that these regions are\nvertical Bloch lines (VBL) and the different bubble shapes obs erved are then related to the inner\nstructure of the VBLs. We were thus able to probe the presence of magnetic singularities as small\nas Bloch points in the inner magnetization of the domain wall s.\n1It has been shown that alloys with perpendicular magnetic anisotrop y (PMA) are good\ncandidates for applications in new recording media with high density st orage capacity or\nin magneto-logical devices1. Recently such materials, namely iron palladium (FePd) alloys\nhave been used in spin-valves where they act as the polarizer and th e free layer2. These\ndevices are believed to work through the nucleation of a reversed d omain followed by the\npropagation of a domain wall3. Numerous studies have advanced the knowledge of the\nmagnetic configuration of FePd alloys by means of MFM imaging4,5, X-ray scattering6,\nor numerical simulations7. Moreover it has been shown recently that it is possible, using\nLorentz Transmission Electron Microscopy (LTEM) to image the mag netic distribution in\nPMA thin foils at the domain wall scale8. This method enables quantitative information\nto be obtained with a spatial resolution below ten nanometers couple d to the opportunity\nof applying magnetic field during imaging. Here we show that it is also pos sible to probe\nthe micromagnetic configuration inside the domain wall enabling the de tection of defects\nsmaller than the expected spatial resolution.\nAlonga domainwall onecanfindsome regionswhere thechirality abrup tly switches. The\narea where the magnetization reverses is called a Bloch line, which can be either horizontal\nor vertical. An horizontal Bloch line is parallel to the magnetization ins ide the domain wall\nwhile the vertical Bloch line is perpendicular to the magnetization. Dom ain walls in PMA\nmaterials are Bloch-like walls and the in-plane magnetization inside the d omain wall can\nthus be oriented in one or the other direction of the wall plane and de fines its chirality.\nWe can thus expect some vertical Bloch lines in FePd delimiting two differ ent chirality\nof the domain wall. Vertical Bloch lines were extensively studied in the 8 0s in garnets.\nExperimental9,10,11and numerical12,13,14,15approaches have helped us to understand these\ntypes of magnetic defects. Observations were possible using magn eto-optical microscopy\ndue to the large width of domain walls in garnets ( δ≈0.1µm). This large value has to be\ncompared with the domain wall width in FePd of around 8 nm16, well below the resolution of\nopticalmethods. Thesimulationofthemagneticstructureingarne tsisalsomucheasierthan\nfor FePd. Indeed, in garnets the very high quality factor Q= 2K/(µ0M2\ns)≈8, where Kis\nthe anisotropy constant and Msthe saturation magnetization, enables local approximations\nfor the computation of the demagnetizing field13. This assumption is a priori not valid in\nthe case of FePd, which exhibits smaller values of Qin the order of 1.6.\nThe aim of this letter is to show that new magnetic modeling coupled to r ecent develop-\n2ments in LTEM enables the observation of such small magnetic defec ts as VBL in domain\nwalls ofless than 10nm width. We focus inthis work on VBL which aretra pped in magnetic\nbubbles appearing in FePd thin foils near the saturation state.\nA thin layer of L1 0-FePd (37 nm) has been deposited on a “soft” layer of chemically\ndisordered FePd 2layer, grown on a MgO (001) substrate by Molecular Beam Epitaxy17.\nThe soft layer is used to enhance the recording efficiency in perpend icular recording hard\ndrives (see for example the section 2.4 of 18). The sample for LTEM h as been then prepared\nusing classical method by mechanical polishing and ion milling. The micros cope used is\na JEOL 3010 fitted in with a Gatan imaging filter for contrast enhance ment by zero-loss\nfiltering19. Thein-situmagnetization is performed with the objective lens while imaging is\nrealized with the objective mini lens traditionally used for low magnifica tion imaging. The\nfield produced by the objective lens has been carefully calibrated by inserting a dedicated\nsample holder mounted with a Hall probe before the experiment.\nWe measured the half hysteresis loop of the film in Fresnel mode20. For a field of 775 mT,\njust before the complete saturation of the magnetic layer, a foca l series has been performed.\nThecompletedescriptionofthismagnetizationprocesscanbefoun delsewhere8. Fig.1shows\nthe focal series reconstruction using the Transport-of-Inten sity Equation21. The magnetic\ninformation is originally mixed with an electrostatic contribution22which has been removed\nby considering a constant variation of the thickness of the sample16. Due to the Lorentz\nforce, the LTEM is sensitive to magnetic induction integrated along t he electron beam\ndirection in the TEM. However, assuming that stray fields on both sid e of the layer are\nantiparallel, the integrated induction may be considered approximat ely the same as the\nintegrated magnetization. In the following we will discuss about simula tion on integrated\nmagnetization.\nIn Fig. 1 we can clearly see two types of magnetic bubbles. On the upp er left corner one\ncan see a magnetic bubble where the magnetization swirls continuous ly along the domain\nwall between the residual magnetic domain (indicated as down in Fig. 1 ) and the reversed\ndomain. On the bottom right corner, one finds a magnetic bubble whe re the magnetization\nexperiences tworotationsof180◦resulting intwo “different”domainwallspointing insimilar\ndirections.\nAt this point of the hysteresis loop a lot of bubbles are present in the film and both kinds\nof bubbles can be easily found. The two switching points observed in t he second bubble\n3type are supposed to be vertical Bloch lines (VBL)23. It must be noticed that the geometric\ndeformation observed for the bubble with two VBL (the bubble show ing alemonshape) is\nfully reproducible.\nIn order to investigate the internal structure of these lines, we h ave performed magnetic\nsimulations on bubbles with and without VBL. Due to the large range of scale needed to\nmodel these objects, we developed and used a multiscale efficient me thod. This method\nuses an adaptive mesh refinement technique to achieve both compu tational efficiency and\nnumerical accuracy (details on the method can be found in Ref. 24) . This is particularly\nuseful in the case of bubbles as the inner and outer part of the bub ble can be loosely\nmeshed, whereas the domain wall and the VBL must be densely meshe d25. Moreover, the\ncode we used has the particularity to take into account the atomic s tructure of the material\nwhich is ignored in standard micromagnetic codes. The size of the micr omagnetic mesh is\nthen automatically adapted and switch to atomistic mode to keep a go od precision when\nnecessary. This ensures that all magnetic configuration is correc t as the micromagnetic\nfundamental assumption of low spatial variations is fulfilled (see 26 f or more details and\ncomparisons with traditional code) and at the same time decrease d rastically the number\nof mesh (thus decreasing the calculation time). The following calculat ion would have cost 8\ntimes more mesh with a traditional micromagnetic parallel code.\nIn these simulations the saturation magnetization is Ms= 106A.m−1, the anisotropy\nconstant is K= 106J.m−3and the exchange stiffness constant27isA= 7×10−12J.m−1.\nWith these parameters the exchange length, Λ =/radicalbig\n2A/(µ0M2\nS) = 3.3 nm. Two different\nthicknesses have been considered : 15 and 20.7 nm. In Fig. 2 the inte grated magnetization\nalong the thickness obtained from the simulations is shown for a bubb le without VBL (A)\nand two bubbles with VBL for thicknesses of 15 (B) and 20.7 nm (C) in a field of 0.25 and\n0.3 T respectively.\nItcanbeseen thatforathickness of15nm(Fig.2B)thebubble isde formed inagreement\nwith the LTEM observations, whereas for a thickness of 20.7 nm its s hape remains circular\n(Fig. 2 C).\nThe modification of the shape canbe explained by analysing precisely t he structure of the\nVBL,depending ofthethickness. TwokindsofVBLcanthusbefoun d. Inthecaseofasmall\nthickness, the magnetization is uniform along the VBL (Fig. 3 A), whe reas it reverses along\nthe VBL in the second case (large thickness), which leads to a magne tic singularity called\n4a Bloch point (BP) (Fig. 3 B). The reason for the transition is a compe tition between the\nexchange and demagnetizing energies: the presence of a Bloch poin t leads to an increase in\ntheexchange energy, whereas thedemagnetizing energy decrea ses because themagnetization\nin the two segments of the line is aligned along the stray field generate d by the domains.\nSuch a transition as a function of the thickness, hhas been reported by Hubert to\nbeh= 7.3 Λ with an analytical model for a straight domain wall28. According to our\nsimulations for the particular geometry considered here, the tran sition is found between\n4.5 and 6.3 Λ. Given the thickness, h= 11.2 Λ of the films observed by LTEM, the VBL\nshould contain a Bloch point, which is not consistent with the deforme d states observed.\nHowever, the soft layer under the L1 0FePd film changes the magnetic configuration and\nalters the respective contributions of the exchange and demagne tizing terms to the energy.\nAs described in a previous article29, the main role of the soft layer on the domain wall is an\nenhancement of the size (and as a consequence, the thickness) o f the bottom N´ eel cap of the\nBloch walls. This vertical dissymmetry could thus favours the config uration with no BP by\nincreasing the dipolar energy.\nThe deformation observed in the absence of a BP gives rise to a redu ction of magnetic\ncharges25: it is analogous to the small buckling of the magnetization identified in s traight\ndomain walls in garnets15. In these materials, the buckling reduces the so-called “dipolar” π\ncharges which are related to the variation of the magnetization per pendicular to the domain\nwall. In the case of FePd, the lower quality factor, Qreduces the lateral extension of the\nVBL, which leads to large “monopolar” σcharges. A far larger buckling than could be\nexpected following the studies on garnets is obtained, beside a redu ction ofπcharges, it\nalso reduces σcharges by a compensation of these two types of charges. It is wo rthy to note\nthat the magnetization is oriented in the same direction in both VBL, s o that the 360◦-like\ndomain walls are located on opposite surfaces. To compensate thes e charges, a different\norientation in the VBL would lead to a “heart”-shape bubble, which is n ot found to be\nstable in our simulations.\nTo conclude, in this letter we have highlighted the very high resolution obtained by com-\nbiningLorentzTransmissionElectronMicroscopyandmultiscalesimula tions. Theresolution\nwe achieved by conventional electron microscopy enables us to pro be magnetic singularities\nwell below the LTEM spatial resolution. Furthermore a main advanta ge of the multiscale\ncode was its rapidity and its low memory requirements. In that partic ular case we decrease\n5the number cells thanks to a factor 8 regarding traditional parallel code. The successful\ncomparison of the two methods shown that it is possible to determine the inner magnetic\nconfiguration of a VBL, namely the presence or the absence of Bloc h points in them.\n∗New ad. : CNRS, CEMES, F-31055 Toulouse Cedex, France\n†New ad. : CEA, DEN, Service de Recherches de M´ etallurgie Phy sique, F-91191 Gif-sur-Yvette,\nFrance\n1D. Weller, A. Moser, L. Folks, M. E. Best, W. Lee, M. Toney, M. S chwickert, J.-U. Thiele, and\nM. Doerner, IEEE Transaction on Magnetics 36, 10 (2000).\n2T.Seki, S.Mitani, K.Yakushiji, andK.Takanashi, AppliedP hysicsLetters 88, 172504 (pages 3)\n(2006).\n3T. Seki, S. Mitani, and K. Takanashi, Physical Review B (Cond ensed Matter and Materials\nPhysics) 77, 214414 (pages 8) (2008).\n4A. Asenjo, J. Garcia, D. Garcia, A. Hernando, M. Vazquez, P. C aro, D. Ravelosona, A. Ce-\nbollada, and F. Briones, Journal of Magnetism and Magnetic M aterials 196, 23 (1999),\nISSN 0304-8853, 7th European Magnetic Materials and Applic ations Conference (EMMA 98),\nZARAGOZA, SPAIN, SEP 09-12, 1998.\n5Y. Samson, A. Marty, R. Hoffmann, V. Gehanno, and B. Gilles, in J. Appl. Phys. (AIP, 1999),\nvol. 85, pp. 4604–4606.\n6M. Mulazzi, K. Chesnel, A. Marty, G. Asti, M. Ghidini, M. Solz i, M. Belakhovsky, N. Jaouen,\nJ. M. Tonnerre, and F. Sirotti, Journal of Magnetism and Magn etic Materials 272-276 , E895\n(2004), proceedings of the International Conference on Mag netism (ICM 2003).\n7J. C. Toussaint, A. Marty, N. Vukadinovic, J. B. Youssef, and M. Labrune, Computational\nMaterials Science 24, 175 (2002).\n8A. Masseboeuf, C. Gatel, A. Marty, J. C. Toussaint, and P. Bay le-Guillemaud, in Journal of\nphysics: conference series (Institute of Physics Publishing, 2008), vol. 126, p. 01205 5.\n9A. Thiaville and J. Miltat, Journal of Applied Physics 68, 2883 (1990).\n10A. Thiaville, J. B. Youssef, Y. Nakatani, and J. Miltat, 35th annual conference on magnetism\nand magnetic materials 69, 6090 (1991).\n11A. Thiaville, J. Miltat, and J. Ben Youssef, European Physic al Journal B 23, 37 (2001).\n612A. Hubert, AIP Conference Proceedings 18, 178 (1974).\n13J. C. Slonczewski, AIP Conference Proceedings 24, 613 (1975).\n14Y. Nakatani and N. Hayashi, Magnetics, IEEE Transactions on 24, 3039 (1988).\n15J. Miltat, A. Thiaville, and P. Trouilloud, Journal of Magne tism and Magnetic Materials 82,\n297 (1989).\n16A. Masseboeuf, C. Gatel, J. C. Toussaint, A. Marty, and P. Bay le-Guillemaud, Ultramicroscopy\nIn press , doi:10.1016/j.ultramic.2009.08.006 (2009).\n17G. Beutier, A. Marty, K. Chesnel, M. Belakhovsky, J. Toussai nt, B. Gilles, G. Van der Laan,\nS. Collins, and E. Dudzik, Physica B 345, 143 (2004).\n18S. Khizroev and D. Litvinov, Perpendicular Magnetic Recording (Kluwer Academic Publishers,\n2004).\n19J. Dooley and M. De Graef, Micron 28, 371 (1997).\n20J. Chapman, Journal of Physics D : Applied Physics 17, 623 (1984).\n21D. Paganin and K. Nugent, Physical review letters 80, 2586 (1998).\n22Y. Aharonov and D. Bohm, Physical Review 115, 485 (1959).\n23A. Hubert and R. Sh¨ afer, Magnetic Domains (Springer, 1998).\n24T. Jourdan, A. Marty, and F. Lan¸ con, Physical Review B 77, 224428 (2008).\n25T. Jourdan, A. Masseboeuf, F. Lan¸ con, P. Bayle-Guillemaud , and A. Marty, submitted to\nJournal of Applied Physics (2009).\n26T. Jourdan, Ph.D. thesis, Universit Joseph Fourier (2008).\n27V. Gehanno, A. Marty, B. Gilles, and Y. Samson, Physical Revi ew B55, 12552 (1997).\n28A. Hubert, Journal ofMagnetism andMagneticMaterials 2, 25 (1976).\n29A. Masseboeuf, F. Cheynis, J. C. Toussaint, O. Fruchart, C. G atel, A. Marty, and P. Bayle-\nGuillemaud, in Materials Research Society Symposium Proceedings (2007), vol. 1026, pp. 1026–\nC22.\n7FIG. 1: (Colour online) Magnetic induction mappingof the Fe Pd thin film usingTIE solving at 775\nmT. The colour scale used here is explained by the colour whee l (colour for the magnetic induction\ndirection and colour intensity for the induction modulus). Arrows are also used to emphasize the\nmagnetic induction. Perpendicular induction ( i.e.magnetization inside the domains) is deduced\nfrom the whole magnetization process (saturation state sho uld be up).\n8FIG. 2: Magnetic multi-scale simulations of three different m agnetic bubbles. The magnetization\nhas been integrated along the observation direction to corr espond to LTEM measurements. (A) A\nmagnetic bubble with no VBL. (B) A magnetic bubble with two VB L, both VBL contain no Bloch\npoint. (C) A magnetic bubble with two VBLs, each VBL contains a Bloch point.\n9FIG. 3: (A) Vertical Bloch line without Bloch point. The uppe r N´ eel Cap of the Bloch wall is\nexperiencing a swirl of 360◦. (B) Vertical Bloch Lines with a Bloch point. The N´ eel Caps o n each\nsurface remain antiparallel.\n10"    },    {        "title": "0912.2612v1.Magnetic_Faraday_rotation_in_lossy_photonic_structures.pdf",        "content": "arXiv:0912.2612v1  [physics.optics]  14 Dec 2009Magnetic Faraday rotation in lossy photonic\nstructures\nA. Figotin and I. Vitebskiy\nAbstract. Magnetic Faraday rotation is widely used in optics and MW. In\nuniform magneto-optical materials, this effect is very weak . One way to enhance\nit is to incorporate the magnetic material into a high-Q opti cal resonator. One\nproblem with magneto-optical resonators is that along with Faraday rotation, the\nabsorption and linear birefringence can also increase dram atically, compromising\nthe device performance. Another problem is strong elliptic ity of the output light.\nWe discuss how the above problems can be addressed in the case s of optical\nmicrocavities and a slow wave resonators. We show that a slow wave resonator\nhas a fundamental advantage when it comes to Faraday rotatio n enhancement in\nlossy magnetic materials.Magnetic Faraday rotation in lossy photonic structures 2\n1. Introduction\nMagnetic materials play a crucial role in optics. They are essential in n umerous\nnon-reciprocal devices such as optical isolators, circulators, ph ase shifters, etc. A\nwell-known example of nonreciprocal effects is magnetic Faraday ro tation related to\nnonreciprocal circular birefringence. Nonreciprocal effects only occur in magnetically\nordered materials, such as ferromagnets and ferrites, or in the p resence of bias\nmagnetic field [1, 2]. At optical frequencies, all nonreciprocal effec ts are very weak,\nand can be further obscured by absorption, linear and/or form bir efringence, etc.\nA way to enhance a weak Faraday rotation is to incorporate the mag neto-optical\nmaterial into a resonator, which can be a complex nanophotonic str ucture with\nfeature sizes comparable to the light wavelength [3, 4, 5, 6, 7, 8, 9 , 10]. An intuitive\nexplanation for the resonance enlacement invokes a simple idea that in a high-Q\noptical resonator filled with magneto-optical material, each individu al photon resides\nmuch longer compared to the same piece of magnetic material taken out of the\nresonator. Sincethenonreciprocalcircularbirefringenceisindep endentofthedirection\nof light propagation, one can assume that the magnitude of Farada y rotation is\nproportional to the photon residence time in the magnetic material. With certain\nreservations, the above assumption does provide a hand-waving e xplanation of the\nresonance enhancement of magnetic Faraday rotation, as well as many other light-\nmatter interactions.\nResonance conditions can indeed result in a significant enhancement of\nnonreciprocal effects, which in our case is a desirable outcome. On t he other hand,\nthe same resonance conditions can also enhance absorption and line ar birefringence\nin the same magnetic material, which would be undesirable. Indeed, line ar and/or\nform birefringence, if present, can significantly suppress the Far aday rotation, or any\nother manifestation of nonreciprocal circular birefringence. Eve n more damaging can\nbe absorption. In uniform magneto-optical materials, the absorp tion contributes to\nthe ellipticity of propagating electromagnetic wave by causing circula r dichroism.\nIn low-loss uniform magnetic materials those effects are insignificant . Under the\nresonance condition, though, the role of absorption can change d ramatically. Firstly,\nthe enhanced absorption reduces the intensity of light transmitte d through the optical\nresonator. Secondly, evenmoderateabsorptioncanlowerthe Q- factoroftheresonance\nby several orders of magnitude and, thereby, significantly compr omise its performance\nas Faraday rotation enhancer. Finally, enhanced absorption, alon g with spatial\nnonuniformity, contributes to deviation of the transmitted light po larization from\nlinear, making it difficult to measure the amount of Faraday rotation.\nWe explore the idea of composite magneto-photonic structures ha ving enhanced\nnonreciprocal characteristics associated with magnetism but, at the same time,\nsignificantly reducing the light absorption. In other words, we want to enhance the\nuseful characteristics of a particular magnetic material, while dras tically reducing its\ncontribution to the energy dissipation. The possibility of appreciable enhancement of\nFaraday rotation or other nonreciprocal effects is particularly imp ortant at infrared\nand optical frequencies, where all light-matter interactions are v ery weak. In those\ncases, the use of photonic structures instead of uniform magnet ic materials can\nalso dramatically reduce the size of the respective optical compone nts, without\ncompromising their performance.\nWe alsocomparetwoqualitativelydifferent approachestoresonanc eenhancement\nof light-matter interactions. The first one is based on a magnetic mic rocavityMagnetic Faraday rotation in lossy photonic structures 3\nsandwiched between a pair of Bragg reflectors, as shown in Fig. 1. T he second\napproachisbasedonaslowwaveresonanceinamagneticphotoniccr ystal,anexample\nof which is shown in Fig. 2. In either case, one can simultaneously enha nce the useful\ncharacteristics of a particular magnetic material, while reducing its c ontribution to\nthe energy dissipation. Yet, the above two approaches are qualita tively different,\nand which one is preferable depends on specific circumstances. For instance, if the\nabsorption of light by the magnetic material is an issue, the slow wave resonance is\ndefinitely preferable. Otherwise, if the light absorption is insignifican t and the only\ngoal is to enhance the magnetic Faraday rotation, then the microc avity resonance can\nbe a better choice.\n2. Absorption suppression in composite structures\nHow is it possible to enhance Faraday rotation produced by the lossy magnetic\ncomponent of composite structure, while reducing the losses caus ed by the same\nmagnetic material? Following [14], we can use the fact that the absorp tion and\nthe useful functionality of the particular magnetic material are re lated to different\ncomponents of its permittivity and/or permeability tensors ˆ εand ˆµ. Specifically, the\nabsorption is determined by the anti-Hermitian parts ˆ ε′′and ˆµ′′the permittivity and\npermeability tensors\nˆε′′=−i\n2/parenleftBig\nˆε−ˆε†/parenrightBig\n,ˆµ′′=−i\n2/parenleftBig\nˆµ−ˆµ†/parenrightBig\n, (1)\nwhile the nonreciprocal circular birefringence responsible for the F araday rotation is\ndetermined by the Hermitian skew-symmetric parts of the respect ive tensors\nˆεa=i\n2Im/parenleftBig\nˆε+ˆε†/parenrightBig\n,ˆµa=i\n2Im/parenleftBig\nˆµ+ ˆµ†/parenrightBig\n, (2)\nwhere†denotesHermitianconjugate. Therelations(1)and(2)suggestt hattherateof\nenergy absorption by the lossy magnetic material can be functiona lly different from its\nusefulfunctionality(nonreciprocalcircularbirefringenceinourc ase). Suchadifference\nallows us to adjust the physical and geometric characteristics of t he periodic structure\nso that the electromagnetic field distribution inside the photonic str ucture suppresses\nthe energy dissipation by the lossy magnetic component, while even e nhancing its\nuseful functionality. The way to address the problem essentially de pends on the\nfollowing factors.\n(i) The physical mechanism of Faraday rotation.\n(ii) The dominant physical mechanismofabsorption. Forinstance, e nergydissipation\ncaused by electric conductivity requires a different approach, com pared to the\nsituation where the losses are associated with the dynamics of magn etic domains,\nor some other physical mechanisms. In each individual case, the st ructure of the\nanti-Hermitian part (1) of the permittivity and/or permeability tens ors can be\ndifferent, and so can be the optimal configuration of the composite material.\n(iii) The frequency range of interest. A given photonic structure c an dramatically\nenhance Faraday rotation at some frequencies, while sharply redu cing it at\ndifferent frequencies. The same is true with absorption, which can b e either\nsuppressed, or enhanced, depending on the frequency range.Magnetic Faraday rotation in lossy photonic structures 4\nSince our goal is to enhance Faraday rotation while reducing absorp tion, the\nsame photonic structure can be either effective or counterprodu ctive, depending on\nthe frequency range and the dominant physical mechanism of elect romagnetic energy\ndissipation. Fortunately, in some important cases, the photonic st ructure can be\nengineered in such a way that it only enhances the useful light-matt er interaction,\nwhile limiting or even suppressing the absorption. Usually, it can be don e if the\nuseful functionality and the absorption are associated with differe nt components\nof electromagnetic field. An impressive example of the kind is consider ed in [14],\nwhere a simple layered structure provides significant enhancement of Faraday rotation\nproduced by a lossy magnetic component, while dramatically reducing absorption\ncaused by the same magneto-optical material.\nUnder what circumstances can we not only suppress the absorptio n but also\nhave the size of the periodic composite structure much smaller than that of the\nuniform (magnetic) slab with similar performance? When considering t his question\nwe should keep in mind that within the framework of the photonic appr oach the\ncharacteristic length Lof the the structural components is always comparable to that\nof the electromagnetic wavelength in the medium. Therefore, for a given frequency\nrange and for a given set of the constitutive materials, we cannot s ignificantly change\nthe length L. Nor can we substantially reduce the number Nof unit cells of the\nperiodic structure without loosing all the effects of coherent inter ference. All we can\nachieve by adjusting the configuration of the periodic array compr ising as few as\nseveral periods is to suppress the losses and/or to enhance the F araday rotation. The\nreal question is: what is the thickness DUof the uniform slab producing Faraday\nrotation comparable to that of the optimized photonic structure? Indeed, if such a\nuniform slab turns out to be much thicker than the layered structu re, then we can\nclaim that not only the periodic array dramatically reduces the losses , but it also has\nmuchsmallerdimensions. Thelatterisonlypossibleifthethickness DUofthe uniform\nslab with desired functionality is much greater than the electromagn etic wavelength\nin the medium. Otherwise, all we can achieve by introducing periodic inh omogeniety\nwould be a reduction of losses. At optical frequencies, due to the w eakness of light-\nmatter interactions, the thickness of the uniform slab producing s ignificant Faraday\nrotation is indeed much greater than the light wavelength. Therefo re, in optics we\ncan simultaneously suppress the losses, while reducing the size of th e nonreciprocal\noptical device.\n>>>>>>>>>>>>>>\nIf the resonance Q-factor is high enough, the acquired ellipticity be comes so\nsignificant that the very term ”Faraday rotation” becomes irrelev ant. Indeed, one\ncannot assign a meaningful rotation angle to a wave with nearly circu lar polarization.\nThe above circumstance, though, does not diminish the practical im portance of the\nnonreciprocal effect, which now reduces to the conversion of linea r polarization of the\nincident wave to nearly circular polarization of transmitted and/or r eflected waves.\n3. Notations, definitions, and physical assumptions\n3.1. Transverse electromagnetic waves in stratified media\nOur analysis is based on the time-harmonic Maxwell equations\n∇×/vectorE(/vector r) =iω\ncˆµ(/vector r)/vectorH(/vector r),∇×/vectorH(/vector r) =−iω\ncˆε(/vector r)/vectorE(/vector r), (3)Magnetic Faraday rotation in lossy photonic structures 5\nwhere the second rank tensorsˆ ε(/vector r) and ˆµ(/vector r) are coordinate dependent. In a stratified\nmedium\nˆε(/vector r) = ˆε(z),ˆµ(/vector r) = ˆµ(z),\nwhere the Cartesian coordinate zis normal to the layers. We also assume that\nthe dielectric permittivity and magnetic permeability tensors in each la yer has the\nfollowing form\nˆε=\nεxxεxy0\nεyxεyy0\n0 0 εzz\n,ˆµ=\nµxxµxy0\nµyxµyy0\n0 0 µzz\n, (4)\nin which case the layered structure support transverse electrom agnetic waves with\n/vectorE(/vector r) =/vectorE(z)⊥z,/vectorH(/vector r) =/vectorH(z)⊥z, (5)\npropagating along the zdirection. The Maxwell equations (3) in this case reduce to\nthe following system of four ordinary differential equations\n∂\n∂zΨ(z) =iω\ncM(z)Ψ(z), (6)\nwhere\nΨ(z) =\nEx(z)\nEy(z)\nHx(z)\nHy(z)\n, (7)\nand\nM(z) =\n0 0 µ∗\nxyµyy\n0 0 −µxx−µxy\n−ε∗\nxy−εyy0 0\nεxxεxy0 0\n. (8)\nThe 4×4 matrix M(z) is referred to as the (reduced) Maxwell operator.\nSolutions for the reduced time-harmonic Maxwell equation (6) can b e presented\nin the following form\nΨ(z) =T(z,z0)Ψ(z0), (9)\nwherethe4 ×4matrix T(z,z0)isthetransfer matrix . Thetransfermatrix(9) uniquely\nrelatesthevaluesofelectromagneticfield(7)atanytwopoints zandz0ofthestratified\nmedium.\nIn a uniform medium, the Maxwell operator Min (8) is independent of z. In this\ncase, the transfer matrix T(z,z0) can be explicitly expressed in terms of the respective\nMaxwell operator M\nT(z,z0) = exp/bracketleftBig\niω\nc(z−z0)M/bracketrightBig\n. (10)\nIn particular, the transfer matrix of an individual uniform layer mis\nTm= exp/parenleftBig\niω\nczmMm/parenrightBig\n, (11)\nwherezmis the thickness of the m-th layer.Magnetic Faraday rotation in lossy photonic structures 6\nThe transfer matrix TSof an arbitrary stack of layers is a sequential product of\nthe transfer matrices Tmof the constituent layers\nTS=/productdisplay\nmTm. (12)\nIn the following subsection we specify the form of the material tens ors (4),\nwhich determine the transfer matrices of the individual layers and t he entire periodic\nstructure. In this paper, we use the same notations as in our prev ious publication\n[12, 13, 14] related to magnetic layered structures.\n3.2. Permittivity and permeability tensors of the layers\nWe assume that the permittivity and permeability tensors of individua l layers have\nthe following form\nˆε=\nε+δ iα 0\n−iα ε−δ0\n0 0 εzz\n,ˆµ= 1, (13)\nwhereαis responsible for nonreciprocal circular birefringence and δdescribes linear\nbirefringence. In a lossless medium, the physical quantities ε,α, andδare real. If the\ndirection of magnetization is changed for the opposite, the parame tersαalso changes\nits sign and so will the sense of Faraday rotation [1, 2]. The absorptio n, is accounted\nfor by allowing ε,α, andδto be complex.\nSubstitution of (13) into (8) yields the following expression for the M axwell\noperator\nM=\n0 0 0 1\n0 0 −1 0\niα−ε+δ0 0\nε+δ iα 0 0\n. (14)\nThe respective four eigenvectors are\n\n\n1\n−ir1\nin1r1\nn1\n\n↔n1,\n\n1\n−ir1\n−in1r1\n−n1\n\n↔ −n1,\n\n−ir2\n1\n−n2\n−in2r2\n\n↔n2,\n\n−ir2\n1\nn2\nin2r2\n\n↔ −n2.\n(15)\nwhere\nn1=/radicalBig\nε+/radicalbig\nδ2+α2, n2=/radicalBig\nε−/radicalbig\nδ2+α2, (16)\nr1=α/radicalbig\nδ2+α2+δ, r2=/radicalbig\nδ2+α2−δ\nα, (17)\nCompared to [6], we use slightly different notations.\nThe explicit expression for the transfer matrix ˆT(A) of a single uniform layer of\nthickness Ais\nˆT(A) =ˆW(A)ˆW−1(0), (18)\nwhere\nˆW(A) =\neiφ1e−iφ1 −ir2eiφ2−ir2e−iφ2\n−ir1eiφ1−ir1e−iφ1eiφ2 e−iφ2\nir1n1eiφ1−ir1n1e−iφ1−n2eiφ2n2e−iφ2\nn1eiφ1−n1e−iφ1−ir2n2eiφ2ir2n2e−iφ2\n,(19)Magnetic Faraday rotation in lossy photonic structures 7\nand\nφ1=ω\ncAn1, φ2=ω\ncAn2.\nThe eigenvectors (15) correspond to elliptically polarized states. T here are\ntwo important particular cases corresponding to linearly and circula rly polarized\neigenmodes, respectively.\n3.2.1. Non-magnetic medium with linear birefringence In the case of a non-magnetic\nmedium\nα= 0, r1= 0, r2= 0. (20)\nThe respective eigenmodes are linearly polarized\n\n\n1\n0\n0\nn1\n\n↔n1,\n\n1\n0\n0\n−n1\n\n↔ −n1,\n\n0\n1\n−n2\n0\n\n↔n2,\n\n0\n1\nn2\n0\n\n↔ −n2.(21)\nwhere\nn1=√\nε+δ, n2=√\nε−δ.\n3.2.2. Magnetic medium with circular birefringence Another important limiting case\ncorresponds to a uniaxial magnetic medium with\nδ= 0, r1= 1, r2= 1. (22)\nThe respective eigenmodes are circularly polarized\n\n\n1\n−i\nin1\nn1\n\n↔n1,\n\n1\n−i\n−in1\n−n1\n\n↔ −n1,\n\n−i\n1\n−n2\n−in2\n\n↔n2,\n\n−i\n1\nn2\nin2\n\n↔ −n2.(23)\nwhere\nn1=√\nε+α, n2=√\nε−α.\n3.3. Numerical values of material tensors\nOur objectives include two distinct problems associated with Farada y rotation\nenhancement.\nOne problem can be caused by the presence of linear birefringence d escribed by\nthe parameter δin (13). Linear birefringence δcompetes with circular birefringence\nα. At optical frequencies, the former can easily prevail and virtually annihilate any\nmanifestations of nonreciprocal circular birefringence. If linear b irefringence occurs in\nmagnetic F layers in Fig. 2, it can be offset by linear birefringence in the alternating\ndielectric A layers. Similarly, in the case of a magnetic resonance cavit y in Fig. 1,\nthe destructive effect of the linear birefringence in the magnetic D la yer can be offset\nby linear birefringence in layers constituting the Bragg reflectors. In either case, the\ncancellation of linear birefringence of the magnetic layers only takes place at one\nparticular frequency. Therefore, the layered structure should be designed so that\nthis particular frequency coincides with the operational resonanc e frequency of theMagnetic Faraday rotation in lossy photonic structures 8\ncomposite structure. The detailed discussion on the effect of linear birefringence and\nways to deal with it will be presented elsewhere.\nIn the rest of the paper we will focus on the problem associated with absorption.\nThis problem is unrelated to the presence or absence of linear birefr ingence and,\ntherefore, can be handled separately. For this reason, in our num erical simulation we\ncan setδ= 0 and use the following expressions for the dielectric permittivity te nors\nof the magnetic F-layers and dielectric A-layers in Fig. 2\nˆεF=\nεF+iγ iα 0\n−iα ε F+iγ0\n0 0 ε3\n, (24)\nˆεA=\nεA0 0\n0εA0\n0 0 εA\n, (25)\nwhereεF,εA, andγare real. Parameter γdescribes absorption of the magnetic\nmaterial.\nIn the case of photonic cavity in Fig. 1 we use similar material paramet ers. The\npermittivity tensorofthe magneticD-layeristhesameasthat ofth emagneticF-layers\nin Fig. 2\nˆεD= ˆεF (26)\nˆεFis defined in (24). The permittivity tensors of the alternating dielect ric layers A\nand B constituting the Bragg reflectors in Fig. 1 are chosen as follow s\nˆεB=\nεBo0\n0εB0\n0 0 εB\n,ˆεC=\nεC0 0\n0εC0\n0 0 εC\n. (27)\nIn either case, only the magnetic layers F or D are responsible for ab sorption,\nwhich is a realistic assumption.\nIn the case of periodic stack in Fig. 2 we use the following numerical va lues of\nthe diagonal components of the permittivity tensors\nεF= 5.37, εA= 2.1. (28)\nSimilar values are used in the case of photonic microcavity in Fig. 1\nεD=εC= 5.37, εB= 2.1.\nThe numerical values of the gyrotropic parameter α, as well as the absorption\ncoefficient γof the magnetic layers F and D, remain variable. We also tried different\nlayer thicknesses dA,dF,dB,dC, anddD. But in this paper we only include the\nresults corresponding to the following numerical values\ndA=dC= 0.8L, dF=dC= 0.2L, dD= 0.4L, (29)\nwhereLis the length of a unit cell of the periodic array\nL=dF+dA=dB+dC.\nThe thickness dDof the defect layer in Fig. 1 is chosen so that the frequency of the\ndefect mode falls in the middle of the lowest photonic band gap of Brag g reflectors.Magnetic Faraday rotation in lossy photonic structures 9\n3.4. Scattering problem for magnetic layered structure\nIn all cases, the incident wave Ψ Ipropagates along the zdirection normal to the\nlayers. Unless otherwise explicitly stated, the incident wave polariza tion is linear with\n/vectorEI∝ba∇dblx. Due to the nonreciprocal circular birefringence of the magnetic m aterial, the\ntransmitted and reflected waves Ψ Pand Ψ Rwill be elliptically polarized with the\nellipse axes being at an angle with the xdirection.\nThe transmitted and reflectedwaves,as wellthe electromagnetic field distribution\ninside the layered structure, are found using the transfer matrix approach. Let us\nassume that the left-hand and the right-hand boundaries of a laye red arrayare located\natz= 0 anda=d, respectively. According to (9) and (12), the incident, transmitt ed,\nand reflected waves are related as follows\nΨP(d) =TS(ΨI(0)+Ψ R(0)). (30)\nKnowing the incident wave Ψ Iand the transfer matrix TSof the entire layered\nstructure and assuming, we can solve the system (30) of four linea r equations and,\nthereby, find the reflected and transmitted waves. Similarly, using the relation (9), we\ncan also find the field distribution inside the layered structure.\nThe transmissionand reflectioncoefficientsofthe slab (either unifo rm, orlayered)\nare defined as follows\nt=SP\nSI, r=−SR\nSI, (31)\nwhereSI,SP, andSRare the Poynting vectors of the incident, transmitted, and\nreflected waves, respectively. The slab absorption is\na= 1−t−r. (32)\nIf the incident wave polarization is linear, the coefficients t,r, andaare\nindependent of the orientation of vector /vectorEIin thex−yplane, because for now,\nwe neglect the linear birefringence δ. Due to nonreciprocal circular birefringence, the\npolarization of the transmitted and reflected waves will always be ellip tic.\nBy contrast, if the incident wave polarization is circular, the coefficie ntst,r, and\nadepend on the sense of circular polarization. The polarization of the transmitted\nand reflected waves in this case will be circular with the same sense of rotation as that\nof the incident wave.\nThe effect of nonreciprocal circular birefringence on transmitted wave can be\nquantified by the following expression\n∆ΨP=1\n2/bracketleftbig\n(ΨP)α−(ΨP)−α/bracketrightbig\n(33)\nwhere (Ψ P)αand (Ψ P)−αrespectively correspond to the wave transmitted through\nthe original periodic structure and through the same structure b ut with the opposite\nsign of circular birefringence parameter α. If the incident wave polarization is linear\nwith/vectorEI∝ba∇dblx, the vector-column (33) has the following simple structure\n∆ΨP=/parenleftBig\n/vectorEP/parenrightBig\ny\n0\n1\n1\n0\n,Magnetic Faraday rotation in lossy photonic structures 10\nimplying that the ycomponent/parenleftBig\n/vectorEP/parenrightBig\nyof the transmitted wave has ”purely”\nnonreciprocal origin and, therefore, can used to characterize t he magnitude of\nnonreciprocal circular birefringence on transmitted wave. Indee d, in the absence of\nmagnetism, the parameter αin (13), (24), and 26) vanishes and the transmitted wave\nis linearlypolarizedwith /vectorEP∝ba∇dblx. Theabovestatement followsdirectlyfromsymmetry\nconsideration and remains valid even in the presence of linear birefrin genceδin (13).\nFurther in this paper will use the ratio\nρ=(EP)y\n(EI)x,where|ρ|<1. (34)\nto characterize the effect circular birefringence on transmitted w ave.\nGenerally, the transmitted wave polarization in the situation in Figs. 2 and 1 is\nelliptical, rather than linear. Therefore, the quantity ρin (34) is not literally the sine\nof the Faraday rotation angle. Let us elaborate on this point. The e lectromagnetic\neigenmodes of the layered structures in Figs. 2 and 1 with permittivit y tensors given\nin (24) through (27) are all circularly polarized. This implies that if the polarization\nof the incident wave is circular, the transmitted and reflected wave s will also be\ncircularly polarized. On the other hand, due to the nonreciprocal ( magnetic) effects,\nthe transmission/reflection coefficients for the right-hand circula r polarization are\ndifferent from those for the left-hand circular polarization. This is t rue regardless\nof the presence or absence of absorption. Consider now a linearly p olarized incident\nwave. It can be viewed as a superposition of two circularly polarized w aves with equal\namplitudes. Since the transmission/reflection coefficients for the r ight-hand and left-\nhand circular polarizations are different, the transmitted and refle cted waves will be\nelliptically polarized. Such an ellipticity develops both in the case of a unif orm slab\nand in the case of a layered stack, periodic or aperiodic, with or witho ut absorption.\nNote, though, that at optical frequencies, the dominant contrib ution to ellipticity of\nthe wave transmitted through a uniform slab is usually determined by absorption,\nwhich is largely responsible for circular dichroism. Without absorption , the ellipticity\nof the wave transmitted through a uniform magnetic slab would be ne gligible. This\nmight not be the case for the layered structures in Figs. 2 and 1 at f requencies of the\nrespective transmission resonances. In these cases, the ellipticit y of transmitted and\nreflectedwavescanbesignificantevenintheabsenceofabsorptio n. Moreover,iftheQ-\nfactor of the respective resonance is high enough, the transmitt ed wave polarization\nbecomes very close to circular and, therefore, cannot be assigne d any meaningful\nangle of rotation. The numerical examples of the next section illustr ate the above\nstatements.\nTo avoid confusion, note that a linear polarized wave propagating in a uniform,\nlossless, unbounded, magnetic medium (24) will not develop any elliptic ity. Instead, it\nwill display a pure Faraday rotation. But the slab boundaries and the layer interfaces\nwill produce some ellipticity even in the case of lossless magnetic mater ial. The\nabsorption provides an additional contribution to the ellipticity of tr ansmitted and\nreflected waves. The latter contribution is referred to as circular dichroism.\nFor simplicity, in further considerationwe will often refer to the qua ntityρin (34)\nas the amount of (nonreciprocal) Faraday rotation, although, du e to the ellipticity, it\nis not exactly the sine of the Faraday rotation angle.\nIn all plots, the frequency ωand the Bloch wave number kare expressed in\ndimensionless units of cL−1andL−1, respectively. In our computations we use aMagnetic Faraday rotation in lossy photonic structures 11\ntransfer matrix approach identical to that described in Ref. [12, 1 3].\n4. Resonance enhancement of magnetic Faraday rotation\n4.1. Cavity resonance: Lossless case\nLet us start with the resonance enhancement based on microcavit y. The magnetic\nlayer D in Fig. 1 is sandwiched between two identical periodic stacks pla ying the role\nofdistributedBraggreflectors. TheD-layerisalsoreferredtoas adefectlayer,because\nwithout it, the layered structure in Fig. 1 would be perfectly periodic . The thickness\nof the defect layer is chosen so that the microcavity develops a sing le resonance mode\nwith the frequency lying in the middle of the lowest photonic band gap o f the adjacent\nperiodic stacks. This resonancemode is nearlylocalized in the vicinity o fthe magnetic\nD-layer.\nA typical transmission spectrum of such a layered structure in the absence of\nabsorption is shown in Fig. 3. The stack transmission develops a shar p peak at the\ndefect mode frequency. The respective transmission resonance is accompanied by a\ndramatic increase in field amplitude in the vicinity of the magnetic D-laye r. The large\nfield amplitude implies the enhancement of magnetic Faraday rotation produced by\nthe D-layer, as clearly seen in Fig. 4.\nIf the Q-factor of the microcavity exceeds certain value and/or if the circular\nbirefringence of the magnetic material of the D-layer is strong eno ugh, the resonance\nfrequency ofthe defect mode splits intotwo, asshownin Fig. 4(c) a nd (d). Eachofthe\ntwo resonances is associated with left or right circular polarization. The transmitted\nlight will also display nearly perfect circular polarization with the oppos ite sense of\nrotation for the twin resonances. Formally, the above nonrecipro cal effect cannot be\nclassified as Faraday rotation, but it does not diminish its practical v alue.\n4.2. Slow wave resonance: Lossless case\nThe second approach to Faraday rotation enhancement is based o n the transmission\nband edge resonance in periodic stacks of magnetic layers alternat ing with some\nother dielectric layers, as shown in Fig. 2. A typical transmission spe ctrum of\nsuch a layered structure is shown in Fig. 7. The sharp peaks in trans mission\nbands correspond to transmission band edge resonances, also kn own as Fabry-Perot\nresonances. The resonance frequencies are located close to a ph otonic band edge,\nwhere the group velocity of the respective Bloch eigenmodes is very low. This is why\nthe transmission band edge resonances are referred to as slow wa ve resonances. All\nresonance frequencies are located in transmission bands – not in ph otonic band gaps,\nas in the case of a localized defect mode. The resonance field distribu tion inside the\nperiodic stack is close to a standing wave composed of a pair of Bloch m odes with\nequal and opposite group velocities and nearly equal large amplitude s\nΨT(z) = Ψk(z)+Ψ−k(z), (35)\nThe left-hand and right-hand photonic crystal boundaries coincid e with the standing\nwavenodes, wherethe forwardandbackwardBlochcomponentsin terferedestructively\nto meet the boundaryconditions. The most powerfulslow waveres onancecorresponds\nto the transmission peak closest to the respective photonic band e dge, where the waveMagnetic Faraday rotation in lossy photonic structures 12\ngroup velocity is lowest. At resonance, the energy density distribu tion inside the\nperiodic structure is typical of a standing wave\nW(z)∝WIN2sin2/parenleftBigπ\nNLz/parenrightBig\n, (36)\nwhereWIis the intensity of the incident light, Nis the total number of unit cells\n(double layers) in the periodic stack in Fig. 2.\nSimilarly to the case of magnetic cavity resonance, the large field amp litude\nimplies the enhancement ofmagneticFaradayrotationproducedby magnetic F-layers,\nas demonstrated in Fig. 9. Again, if the Q-factor of the slow wave re sonance exceeds\ncertain value and/or if the circular birefringence αof the magnetic material of the F-\nlayers is strong enough, each resonance frequency splits into two , as shown in Fig. 10.\nEach of the two twin resonances is associated with left or right circu lar polarization.\nTo demonstrate it, let us compare the transmission dispersion in Fig. 10, where the\nincident light polarization is linear, to the transmission dispersion in Figs . 11 and 12,\nwhere the incident wave is circularly polarized. One can see that the c ase in Fig. 10\nof linearly polarized incident light reduces to a superposition of the ca ses in Figs. 11\nand 12 of two circularly polarized incident waves with opposite sense o f rotation.\n4.3. The role of absorption\nIn the absence of absorption, the practical difference between c avity resonance and\nslow wave resonance is not that obvious. But if the magnetic materia l displays an\nappreciable absorption, the slow wave resonator is definitely prefe rable. The physical\nreason for this is as follows.\nIn the caseofaslowwaveresonance, the reductionofthe transm itted waveenergy\nis mainly associated with absorption. Indeed, although some fractio n of the incident\nlight energy is reflected at the left-hand interface of the periodic s tack in Fig. 2, this\nfraction remains limited even in the case of strong absorption, as se en in Fig. 8(b). So,\nthe main source of the energy losses in a slow wave resonator is abso rption, which is a\nnatural side effect of the Faraday rotation enhancement (some im portant reservations\ncan be found in [14]).\nIn the case of magnetic cavity resonance, the situation is fundame ntally different.\nIn this case, the energy losses associated with absorption cannot be much different\nfrom those of slow wave resonator, provided that both arrays dis play comparable\nenhancement of Faraday rotation. What is fundamentally different is the reflectivity.\nAninherentproblemwithany(localized)defectmodeisthatanysignifi cantabsorption\nin defect layer makes it inaccessible. Indeed, if the D-layer in Fig. 1 dis plays\nan appreciable absorption, the entire structure becomes highly re flective. As a\nconsequence, a major portion of the incident light energy is reflect ed from the stack\nsurface and never even reaches the magnetic D-layer. Such a beh avior is illustrated\nin Fig. 6, where we can see that as soon as the absorption coefficient γexceeds\ncertain value, further increase in γleads to high reflectivity of the layered structure.\nIn the process, the total absorption areduces, as seen in Fig. 5, but the reason for\nthis reduction is that the light simply cannot reach the magnetic layer . There is no\nFaraday rotation enhancement in this case.\nAcknowledgments: Effort of A. Figotin and I. Vitebskiy is sponsored by the\nAir Force Office of Scientific Research, Air Force Materials Command, USAF, under\ngrant number FA9550-04-1-0359.Magnetic Faraday rotation in lossy photonic structures 13\n[1] L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii. Electrodynamics of continuous media . (Pergamon,\nN.Y. 1984).\n[2] A. G. Gurevich and G. A. Melkov. Magnetization Oscillations and Waves . (CRC Press, N.Y.\n1996).\n[3] M. Inoue, et all. Magnetophotonic crystals (Topical Review) . J. Phys. D: Appl. Phys. 39, R151–\nR161 (2006).\n[4] I. Lyubchanskii1, N. Dadoenkova1, M. Lyubchanskii1, E. Shapovalov, and T. Rasing. Magnetic\nphotonic crystals . J. Phys. D: Appl. Phys. 36, R277–R287 (2003)\n[5] M. Inoue, K. Arai, T. Fuji, and M. Abe. One-dimensional magnetophotonic crystals . J. Appl.\nPhys. 85, 5768 (1999).\n[6] M. Levy and A. A. Jalali. Band structure and Bloch states in birefringent onedimensi onal\nmagnetophotonic crystals: an analytical approach . J. Opt. Soc. Am. B, 24, 1603-1609 (2007).\n[7] M. Levy and R. Li. Polarization rotation enhancement and scattering mechani sms in waveguide\nmagnetophotonic crystals . Appl. Phys. Lett. 89, 121,113 (2006)..\n[8] S. Khartsev and A. Grishin. High performance magneto-optical photonic crystals . J. Appl. Phys.\n101, 053,906 (2007).\n[9] S. Kahl and A. Grishin. Enhanced Faraday rotation in all-garnet magneto-optical p hotonic\ncrystal. Appl. Phys. Lett. 84, 1438 (2004).\n[10] S. Erokhin, A. Vinogradov, A. Granovsky, and M. Inoue. F ield Distribution of a Light Wave\nnear a Magnetic Defect in One-Dimensional Photonic Crystal s. Physics of the Solid State, 49,\n497 (2007).\n[11] Vol. 49\n[12] A. Figotin, and I. Vitebsky. Nonreciprocal magnetic photonic crystals . Phys. Rev. E63, 066609\n(2001).\n[13] A. Figotin, and I. Vitebskiy. Electromagnetic unidirectionality in magnetic photonic c rystals.\nPhys. Rev. B67, 165210 (2003)\n[14] A. Figotin and I. Vitebskiy. Absorption suppression in photonic crystals . Phys. Rev. B77, 104421\n(2008)Magnetic Faraday rotation in lossy photonic structures 14\nBCBCBCBCDBCBCBC\nΨIΨR\nΨP\n L\nFigure 1. (Color online) Magnetic resonance cavity composed of magne tic layer\nD sandwiched between a pair of identical periodic non-magne tic stacks (Bragg\nreflectors). The incident wave Ψ Iis linearly polarized with E/bardblx. Due to\nthe nonreciprocal circular birefringence of the magnetic m aterial of D-layer, the\nreflected wave Ψ Rand the transmitted wave Ψ Pare both elliptically polarized.Magnetic Faraday rotation in lossy photonic structures 15\nAFAFAFAF\nΨIΨR\nΨP\n Lzx\ny\nFigure 2. (Color online) Periodic layered structure composed of alte rnate\nmagnetic (F) and dielectric (A) layers. The F-layers are mad e of the same lossy\nmagnetic material as the D-layer in Fig. 1. Lis the unit cell length. The incident\nwave Ψ Iis linearly polarized with E/bardblx. Due to the nonreciprocal circular\nbirefringence of the magnetic material of the F-layers, the reflected wave Ψ Rand\nthe transmitted wave Ψ Pare both elliptically polarized.Magnetic Faraday rotation in lossy photonic structures 16\n1.41.61.822.200.20.40.60.81\nFrequencyTransmissiona) γ = 0\n1.91.911.921.931.9400.20.40.60.81\nFrequencyTransmissionb) γ = 0\n1.91.911.921.931.9400.020.040.060.080.1\nFrequencyTransmissionc) γ = 0.1\n1.91.911.921.931.9402468x 10−3\nFrequencyTransmissiond) γ = 0.5\nFigure 3. (Color online)Transmissiondispersion ofthe layered arra y in Fig. 1 for\ndifferent values of absorption coefficient γof the D-layer. Circular birefringence α\nis negligible. Fig. (b) shows the enlarged portion of Fig. (a ) covering the vicinity\nof microcavity resonance.Magnetic Faraday rotation in lossy photonic structures 17\n1.91.911.921.931.9400.0050.010.0150.02\nFrequency| Ey|a) α = 10−3\n1.9 1.92 1.9400.050.10.150.2\nFrequency| Ey|b) α = 10−2\n1.9 1.92 1.9400.20.40.6\nFrequency| Ey|c) α = 0.1\n1.9 1.92 1.9400.20.40.6\nFrequency| Ey|d) α = 0.2\nFigure 4. (Coloronline)Frequency dependence ofpolarization compo nent|Ey|of\nthe wave transmitted through layered array in Fig. 1 fordiffe rent values of circular\nbirefringence αof the D-layer and zero absorption. When circular birefring ence\nαis strong enough, the cavity resonance splits into a pair of t win resonances,\ncorresponding to two circularly polarized modes with oppos ite sense of rotation.\nThe incident wave is linearly polarized with /vectorE/bardblx.Magnetic Faraday rotation in lossy photonic structures 18\n1.91.911.921.931.9400.20.40.6\nFrequencyAbsorptiona) γ = 0.01\n1.91.911.921.931.9400.20.40.6\nFrequencyAbsorptionb) γ = 0.2\n1.91.911.921.931.9400.20.40.6\nFrequencyAbsorptionc) γ = 0.5\n1.91.911.921.931.9400.20.40.6\nFrequencyAbsorptiond) γ = 1.0\nFigure 5. (Color online) Frequency dependence of absorption of the la yered\narray in Fig. 1 for different values of absorption coefficient γof the D-layer.\nCircular birefringence αis negligible. The frequency range shown covers the\nvicinity of microcavity resonance. Observe that the stack a bsorption decreases\nafter coefficient γexceeds certain value, which is in sharp contrast with the ca se\nof a periodic stack, shown in Figs. 8.Magnetic Faraday rotation in lossy photonic structures 19\n1.91.911.921.931.9400.20.40.60.81\nFrequencyReflectivitya) γ = 0.01\n1.91.911.921.931.9400.20.40.60.81\nFrequencyReflectivityb) γ = 0.2\n1.91.911.921.931.9400.20.40.60.81\nFrequencyReflectivityc) γ = 0.5\n1.91.911.921.931.9400.20.40.60.81\nFrequencyReflectivityd) γ = 1.0\nFigure 6. (Color online) Frequency dependence of the reflectance rof the layered\narray in Fig. 1 for different values of absorption coefficient γof the D-layer.\nCircular birefringence αis negligible. The frequency range shown covers the\nvicinity of microcavity resonance. Observe that if the abso rption coefficient γof\nD-layer increases, the stack reflectivity also increases ap proaching unity. Such a\nbehaivior is line with frequency dependence of the stack abs orption shown in Fig.\n5. It is in sharp contrast with the case of a periodic stack, sh own in Figs. 8.Magnetic Faraday rotation in lossy photonic structures 20\n1.4 1.6 1.8 2 2.2 2.400.20.40.60.81\nFrequencyTransmission\n  \n1.4 1.6 1.8 2 2.2 2.400.20.40.60.81\nFrequencyTransmission\n  γ = 0\nγ = 0.01\nγ = 0.1\nγ = 0.2a)\nb)\nFigure 7. (Color online) Transmission dispersion of periodic layere d structure\nin Fig. 2 for different values of absorption coefficient γof the F-layers. Circular\nbirefringence αis negligible.Magnetic Faraday rotation in lossy photonic structures 21\n1.4 1.6 1.8 2 2.2 2.400.20.40.60.81\nFrequencyAbsorption\n  \n1.4 1.6 1.8 2 2.2 2.400.20.40.60.81\nFrequencyReflection\n  γ = 0.1\nγ = 0.2\nγ = 0.5\nγ = 0.1\nγ = 0.2\nγ = 0.5a)\nb)\nFigure 8. (Color online) Frequency dependence of (a) absorption and ( b)\ntransmission of periodic layered structure in Fig. 2 for diff erent values of\nabsorption coefficient γof the F-layers. Circular birefringence αis negligible.Magnetic Faraday rotation in lossy photonic structures 22\n11.21.41.61.822.22.42.62.800.0050.010.015\nFrequency| Ey|a) α = 10−3\n11.21.41.61.822.22.42.62.800.050.10.15\nFrequency| Ey|b) α = 10−2\nFigure 9. (Color online) Frequency dependence of polarization compo nent|Ey|\nof the wave transmitted through the periodic layered struct ure in Fig. 2 for\ndifferent values of circular birefringence αof the F-layers and zero absorption.\nThe incident wave is linearly polarized with /vectorE/bardblx.Magnetic Faraday rotation in lossy photonic structures 23\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissiona) α = 0.01\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissionb) α = 0.1\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissionc) α = 0.5\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissiond) α = 1.0\nFigure 10. (Color online) Transmission dispersion of periodic layere d structure\nin Fig. 2 for different values of circular birefringence αof the F-layers and zero\nabsorption. When circular birefringence αis large enough, each transmission\nresonance splits into a pair of twin resonances, correspond ing to two circularly\npolarized modes with opposite sense of rotation. The incide nt wave polarization\nis linear.Magnetic Faraday rotation in lossy photonic structures 24\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissiona) α = 0.01\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissionb) α = 0.1\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissionc) α = 0.5\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissiond) α = 1.0\nFigure 11. (Color online) The same as in Fig. 10, but the incident wave\npolarization is circular with positive sense of rotation.Magnetic Faraday rotation in lossy photonic structures 25\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissiona) α = 0.01\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissionb) α = 0.1\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissionc) α = 0.5\n1.5 1.6 1.7 1.800.20.40.60.81\nFrequencyTransmissiond) α = 1.0\nFigure 12. (Color online) The same as in Figs. 10 and 11, but the incident wave\npolarization is circular with negative sense of rotation."    },    {        "title": "0912.5487v1.Voltage_induced_control_and_magnetoresistance_of_noncollinear_frustrated_magnets.pdf",        "content": "arXiv:0912.5487v1  [cond-mat.mtrl-sci]  30 Dec 2009Voltage induced control and magnetoresistance of noncolli near frustrated magnets\nA. Kalitsov,1M. Chshiev,1B. Canals,2and C. Lacroix2\n1SPINTEC, UMR 8191 CEA/CNRS/UJF, 38054 Grenoble, France\n2Institut N´ eel, CNRS-UJF, BP 166, 38042 Grenoble Cedex 9, Fr ance\n(Dated: October 2, 2017)\nNoncollinear frustrated magnets are proposed as a new class of spintronic materials with high\nmagnetoresistance which can be controlled with relatively small applied voltages. It is demonstrated\nthat their magnetic configuration strongly depends on posit ion of the Fermi energy and applied\nvoltage. The voltage induced control of noncollinear frust rated materials (VCFM) can be seen as a\nway to intrinsic control of colossal magnetoresistance (CM R) and is the bulk material counterpart of\nspin transfer torque concept used to control giant magnetor esistance in layered spin-valve structures.\nPACS numbers: 72.15.Eb, 72.15.Gd, 75.10.Lp, 75.10.Jm, 75. 47.-m, 75.47.Pq\nThe discoveryofgiant magnetoresistance(GMR) [1, 2]\nin magnetic multilayered structures has generated a new\nfield of spin-based electronics [3, 4], or spintronics, which\ncombines two traditional fields of physics: magnetism\nand electronics. A spin-valve concept [5] used in GMR\nstructures allows controlling the magnetic configuration\nof its ferromagnetic layers by (i) application of relatively\nsmall magnetic fields or (ii) passing spin polarized cur-\nrents using spin transfer torque (STT) [6, 7]. These fac-\ntors made them ideal systems for spintronic applications\nsuch as magnetic random access memories (MRAM) and\nmagnetic field sensors used in read heads.\nThe advent of GMR has considerably increased an in-\nterest in related phenomenon in bulk materials, colossal\nmagnetoresistance (CMR) [8, 9], which is several orders\nhigher than GMR and unlike the latter, can be viewed\nas an ”intrinsic” property of material itself. To date,\nthe CMR is typically observedin certain manganite com-\npounds with the bulk magnetic configuration controlled\nby applying the magnetic field (similar to method (i)\nmentioned above for spin valves) but requires character-\nistic magnetic fields of several Tesla [9]. Such high fields\nmake them inappropriate for use in spintronic applica-\ntions where appropriate scale should be about Oersteds.\nHowever, one may expect the possibility of controlling\nthe intrinsic magnetic configuration of the bulk materi-\nals (and thus of CMR) by passing spin polarized currents\nthrough them similar to STT mechanism (ii) mentioned\nabove for spin-valves. Since the STT in the latter orig-\ninates from non-collinearity of their adjacent magneti-\nzations, the same requirement should hold for the bulk\nmaterials.\nHere we promote for the first time magnetically frus-\ntrated bulk materials as a new paradigm for spintronic\napplications with high magnetoresistance which can be\ncontrolledwith relatively small applied voltagesand does\nnot require spin polarized currents. This novel phe-\nnomenon may be viewed as the ”bulk” counterpart of\nSTT in layered spintronic structures (spin valves) and\nmay represent a crucial interest both from applications\nand fundamental points of view. Below we demonstratecurrent1 12 23 3\n4 4(a) (b)\ncurrent1 12 23 3\n4 4(a) (b)\nFIG. 1: (a) ”4in” and (b) ”2in2out” configurations for square\nlattice\nthat the magnetic configuration of the bulk frustrated\nmaterial is changed under applied voltage leading to the\nstrong variation of its conductance.\nThekeymechanismatstakeisasomewhatmicroscopic\nequivalent of spin torque, allowing for local spin flips\nwithin the microscopic spin texture. Those local moves\nrequires non collinearity of the spin configuration, which\nwould otherwise be insensitive to the current. Further-\nmore, in order to avoid a continuous response of the spin\nconfiguration, we require the ground states to be well\ndefined minima, such that the switching from one to the\notherlookslikealogicaloperation. Thesetwoaspectsare\nwell taken into account as soon as the underlying local-\nized moments possess strong multiaxial anisotropies, in\norder to behave bitwise like and fulfill the non collinear-\nity criterion. Several Rare-Earth-transition metal inter-\nmetallics systems are relevant candidates : in these sys-\ntems frustration arises due to the competition of crystal\nfield anisotropy, exchange and quadrupolar interactions\n(for a review see Ref. [10]). These intermetallics systems\noften show a non-collinear magnetic structure: this is\nthe case for example of TbGa 2[11], HoGe 3[12] or Ura-\nnium compounds[13]. Naturally, pyrochlores in which\nfrustration is due to the crystal structure are also rele-\nvant candidates, as it is well known that in such exotic2\n0.0 0.5 1.0 1.5 2.0-7-6-8-7\n  \nEF=-2.5 eVEtot (eV)\nVoltage (V) 4in\n 2in2out\n  \nEF=-2 eVEtot (eV) 4in\n 2in2out(a)\n(b)\n0.0 0.5 1.0 1.5 2.0-7-6-8-7\n  \nEF=-2.5 eVEtot (eV)\nVoltage (V) 4in\n 2in2out\n  \nEF=-2 eVEtot (eV) 4in\n 2in2out(a)\n(b)\nFIG. 2: (a) and (b): total energy as a function of applied\nvoltage for EF=-2 eV and EF=-2.5 eV, respectively, shown\nby arrows in Fig. 3.\nsystems, non collinear low temperature magnetic phases\nare often stabilized[14], among those, few metallic com-\npounds have been identified like Pr 2Ir2O7[15, 16] and the\nfamily of the pyrochlore Molybdates, R 2Mo2O7[17].\nFor argument’s sake, we have used a two-dimensional\nsquare lattice model in order to focus on the driving\nmechanism that is at stake and to describe its qual-\nitative behavior. Realistic realizations would involve\nmore complicated structures, like the one in the 3-D py-\nrochlores [14]. We consider a square lattice of classical\nlocalized moments Siwith strong local on-site uniaxial\nanisotropy ( D0) along square diagonals (represented by\nunit vector ni) and coupled through intersite exchange\nIij. Inaddition, moments Siarecoupledwithconduction\nelectrons through the local exchange ( J0) described here\nquantummechanicallyusingtight-bindingmodel. Unlike\ncollinear systems, non-collinearity provided by magnetic\nfrustration is a key ingredient for switching phenomenon\nproposed here since its origin is due to STT mechanism\nacting locally by conduction electrons on localized mo-mentsSi. The Hamiltonian of the system has the form:\nˆH=−/summationdisplay\ni,jIijSi·Sj−D0/summationdisplay\ni(ni·Si)2+\nt/summationdisplay\ni,j,σ/parenleftBig\nˆc†σ\niˆcσ\nj+H.c./parenrightBig\n−J0/summationdisplay\niˆc†α\ni(σαβ·Si)ˆcβ\ni,(1)\nwhereIijandJ0are the intersite and the local exchange\nconstants respectively, D0is the uniaxial anisotropy con-\nstant, t is the hopping integral between two neighboring\nsites, ˆc†σ\niand ˆcσ\niare the creation and annihilation oper-\nators of the conduction electron with the spin σon site\niandσαβis the vector of Pauli matrices. For the cho-\nsen model, nearest neighbor interactions I1are irrelevant\n(becausenearestneighborspinsarealwaysorthogonal)so\nthat only the second nearestneighborone I2is takeninto\naccount. We emphasize that dealing with longer ranges\ninteraction does not affect further results reported here\nsince only energy differences between magnetic configu-\nrations matter.\nIn the limit of low temperature and D0→ ∞the lo-\ncalized moments Siare strictly collinear with ni(Si/bardblni)\nand the total energy ofthe system within a constant shift\nbecomes\nEtot=−I2/summationdisplay\ni,jSi·Sj+Tr[ˆHˆρ] =\n=−I2/summationdisplay\ni,jSi·Sj−i\n2π/summationdisplay\nj/integraldisplay\nEG<\njj(E)dE, (2)\nwhereG<and ˆρrepresent the ”lesser” non-equilibrium\nGreen function and density matrix respectively [18], and\nthe Green function indices include spin index as well.\nWe adoptaconventionaltransportapproachwherethe\nsystem is considered to consist of three regions: semi-\ninfinite left ( L) and right ( R) regions connected to the\nmiddle scattering region ( M) which is assumed to be\nvery long. Despite of all three regions being identical,\nsuch a subdivision is chosen in order to consider all non-\nequilibrium processes occuring in the scattering region\nMwhile the left and right regions are in thermodynam-\nical equilibrium described with Fermi-Dirac distribution\nfunctionsfL(R)=f(E−µL(R)), whereµL(R)is the chem-\nicalpotentialintheleft(right)region. The”lesser”Green\nfunction can be written as\nG<\nij=i(fLψL\niψL∗\nj+fRψR\niψR∗\nj), (3)\nwhereψL(R)\njis the single-electron wave function on site\nj∈Mincident from the left (right). It is straightforward\nfrom the definition of retarded and advanced Green func-\ntions that\nGa\njj−Gr\njj=i(ψL\njψL∗\nj+ψR\njψR∗\nj). (4)\nSince the middle regionis assumedto be verylong, the fi-\nnite potentialdrop eV=µL−µRresultsintoinfinitesmal3\nchange from one unit cell to another within the middle\nregionM. In this case the reflections from the L|Mand\nR|Mboundaries are negligible and one can write for the\nleft(right) wave functions ψL(R)\nj=cL(R)exp(+(−)kxaj),\nwherekxis the wave vector along x-axis andais the lat-\ntice constant. One can show that the expression for the\ncharge current which is proportional to ( fL−fR) [19] is\nsatisfied when |ψL\nj|2=|ψR\nj|2. Indeed, the charge current\ncan be expressed using the lesser Green function as [20]:\nI∼/integraldisplay\n[(G<\nj+1,j−G<\nj,j+1)]dE.\nUsingEq.(3)andaforementionedwavefunctionsityields\nthe following form:\nI∼/integraldisplay\nsinkxa/bracketleftbig\nfL|cL|2−fR|cR|2/bracketrightbig\ndE\nwhichisproportionalto( fL−fR)onlywhen |cL|2=|cR|2\n(and consequently |ψL\nj|2=|ψR\nj|2).\nThen, it straightforwardly follows from Eq. (3) and\nEq. (4) that\nG<\njj(E) =i(fL+fR)ℑ(Gr\njj(E)) (5)\nwhereℑnotation for imaginary part is used. The total\nenergy given by expression (2) of the system per a unit\ncell yields:\nEtot=−I2/summationdisplay\ni,jSi·Sj−\n1\n2π/integraldisplay\n(fL+fR)/summationdisplay\njℑ(Gr\njj(E))EdE, (6)\nwhereGr\njj(E) is calculated as jth diagonal element of\nthe matrix [ E−ˆH+iδ]−1. Thus, the magnetic config-\nuration corresponding to the minimum of the total en-\nergy is resulting from the interplay of intersite exchange\ninteraction between localized moments on the next near-\nest neighbour sites (the first term in Eq. (6)) and the\nexchange interaction between the localized moment and\nthe conduction electron described by the second term in\nEq. (6).\nFor simplicity, among the possible magnetic configura-\ntions of the system ( Si/bardblni) we select ”4in”and ”2in2out”\noneswhicharethe twoconfigurationswith the largesten-\nergy separation in this example (see Fig. 1). We choose\nfor parameters J0= 2eV,t= 1eVandI2= 0.1t[21].\nIn Fig. 2 we show the dependence of the total energy\nfor the two aforementioned selected configurations as a\nfunction of applied voltage. First, one can note that Etot\nstrongly depends on the Fermi level position which is\nused to represent different materials. Indeed, when the\nsystem isin equilibrium, its ”2in2out”(”4in”)state is en-\nergetically more favorable for EF=−2eV(−2.5eV) as\nshown in Fig. 2(a) and (b), respectively. Furthemore, the-6 -4 -2 0036\n  DOS (States/eV)\nE (eV) 4in\n 2in2out\nFIG. 3: Total density of states for ”4in” (black solid) and\n”2in2out” (red dashed) configurations represented in Fig. 1 .\nstrong variation of the total energy as a function of ap-\nplied voltagecausesthe system to switch from anequilib-\nrium state to another one at certain critical voltage (see\nFig. 2). Moreover, further increase of the applied volt-\nage may again reverse the state of the system (Fig. 2a).\nThis demonstratesthat the magnetic configurationofthe\nsystem can be controlled by the applied voltage.\nThe mechanism of these dependences may be under-\nstood from the corresponding total density of states\n(DOS) [23] for ”2in2out” and ”4in” configurations repre-\nsented in Fig. 3 where for convenience purposes only neg-\native energy range is shown since DOS( E)=DOS(−E).\nThe DOS for both magnetic states have sharp peaks and\nband gaps causing strong dependence of the preferable\nconfiguration on the Fermi level EFboth in and out of\nequilibrium. Indeed, as on can see from the second term\nin Eq. (6), the total energy is defined by the sum of two\nproducts of the DOS with Eintegrated till µLandµR.\nIn the absence of applied voltage, Etotis calculated with\nµL=µR=EF, i.e. defined by the position of the Fermi\nlevel indicated by black arrows in Fig. 3 corresponding\nto two values −2eVand−2.5eVused in Fig. 2(a) and\n(b), respectively.\nOne might expect that the conductances of two afore-\nmentioned magnetic configurations may strongly dif-\nfer due to significant differences in their DOS, thereby\nleading to high magnetoresistance values defined as\n(σ2in2out\nxx−σ4in\nxx)/σ4in\nxx), whereσ4in\nxxandσ2in2out\nxxare the\nconductances for ”4in” and ”2in2out” magnetic config-\nurations, respectively. We calculate the linear response\nconductance using the Kubo formula [22]\nσxx=πe2/planckover2pi1\nLTr/bracketleftBig\nˆvxδ(E−ˆH)ˆvxδ(E−ˆH)/bracketrightBig\n,\nwhere ˆvxis the electron velocity operator along the ap-\npliedvoltagedirection, L→ ∞isthelengthofthesystem4\n/s45/s54 /s45/s52 /s45/s50 /s48/s48/s51\n/s32/s32/s67/s111/s110/s100/s117/s99/s116/s97/s110/s99/s101 /s32/s40 /s101/s50\n/s47/s104 /s41\n/s69/s110/s101/s114/s103/s121/s32/s40/s101/s86/s41/s32/s52/s105/s110\n/s32/s50/s105/s110/s50/s111/s117/s116\nFIG. 4: Conductance as a function of the Fermi level.\nand\nδ(E−ˆH) =−1\nπℑ(ˆGr(E)) =i\nπ(ˆGr(E)−ˆGa(E))\nThe calculated conductance of the system for ”4in”\nand”2in2out”magneticconfigurationsarerepresentedin\nFig. 4. As one can see, both σ4in\nxxandσ2in2out\nxxstrongly\ndepend on position of the Fermi energy EFand strongly\ncorrelate with DOS picture (see Fig. 3). For the two\nvalues of the Fermi energy used above, the MR ratio is\nfoundtobeabout336%forthecasewhen EF=−2.5eV\nand becomes infinite for EF=−2eV.\nOne can note that similar behavior is expected to oc-\ncurin systemswith collinearantiferromagneticstructure:\ndepending on the band structure and the band filling,\nthe ferromagnetic state can be close in energy with the\nAF one, and an applied voltage could stabilize the fer-\nromagnetic state. However in such a case, there is no\nspin torque since the structure is colinear, and no mech-\nanism for spin reversal (except through spin waves). On\nthe contrary, the mechanism proposed here neither re-\nquire any defect, spin wave nor a fine tuning of any kind.\nThe noncollinear nature of the magnetic configurations\nconsidered provides a robust mechanism for microscopic\nmagnetic switching. Furthermore, this mechanism does\nnot require spin polarized current injection.\nIn conclusion, we have shown that magnetoresistance\nof noncollinear frustrated bulk magnets may reach ex-tremely high values and their magnetic configuration\nmay be controlled by applied voltage. The proposed\nphenomenon is the bulk material analog of spin trans-\nfer torque used in layered spin-valve structures. The\nmodelchosenhereused toprovethe concept, incombina-\ntion with inverse approach of designing the crystal struc-\nture from predefined electronic structure properties [24],\nopens the way towards experimental realization of the\nproposed phenomenon.\nThis work was supported by Chair of excellence Pro-\ngram of the Nanosciences Foundation in Grenoble.\n[1] M. Baibich et al, Phys. Rev. Lett. 61, 2472 (1988)\n[2] G. Binasch, P. Gr¨ unberg, F. Saurenbach and W. Zinn,\nPhys. Rev. B 39, 4828 (1989)\n[3] A. Fert et al, Mat. Sci. Eng. B, 84, 1 (2001)\n[4] S. Wolf, Science, 294, 1488 (2001)\n[5] B. Dieny et al, Phys. Rev. B 43, 1297 (1991)\n[6] J. Slonczewski, JMMM 159, L1 (1996)\n[7] L. Berger, Phys. Rev. B 54, 9353 (1996)\n[8] R. von Helmolt, J. Wecker, B. Holzapfel, L. Schultz, and\nK. Samwer, Phys. Rev. Lett. 71, 2331 (1993)\n[9] S. Jin et al, Science, 264, 413 (1994)\n[10] D. Gignoux and D. Schmitt, J.Magn. Magn. Mater, 100,\n99 (1991) and J. Alloys and Comp. 326, 143 (2001).\n[11] I. Auneau et al, Physica B 212, 351 (1995)\n[12] P. Schobinger-Papamantellos et al, J. Phys. : condens\nMatter20, 195202 (2008)\n[13] P. Burlet et al, Sol. St. Comm. 39, 745 (1981)\n[14] J. Gardner, M. J. P. Gingras, J. E. Greedan,\narXiv:0906.3661; to appear in Rev. Mod. Phys\n[15] S. Nakatsuji et al, Phys. Rev. Lett. 96, 087204 (2006)\n[16] Y. Machida et al, Phys. Rev. Lett 98, 057203 (2007)\n[17] I. K´ ezsm´ arki et al., Phys. Rev. Lett. 93, 266401 (2004))\n[18] E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics,\nCourse of Theoretical Physics (Pergamon, Oxford, 1981),\nVol. 10\n[19] Y. Meir and N. S. Wingreen, Phys. Rev. Lett. 68, 2512\n(1992)\n[20] C. Caroli and R. Combescot and P. Nozieres and D.\nSaint-James, J. Phys. C: Solid St. Phys., 4, 916 (1971)\n[21] I. V.Solovyev, Phys. Rev. B 67, 174406 (2003)\n[22] R. Kubo, J. Phys. Soc. Jpn, 12, 570 (1957)\n[23] The Density of States is equal to −1/πP\njℑGR\njj(E),\nwhere summation includes all atoms in the unit cell and\nspins.\n[24] A. Franceschetti and A. Zunger, Nature 402, 60 (1999)"    },    {        "title": "1001.1328v1.Self_organized_synthesis_of_patterned_magnetic_nanostructures_with_in_plane_and_perpendicular_to_the_plane_magnetization.pdf",        "content": "Self-organized synthesis of patterned magnetic nanostructures with in-plane and\nperpendicular to the plane magnetization\nH. Krishna1,\u0003A. K. Gangopadhyay1, J. Strader2, and†R. Kalyanaraman2,3\n1Department of Physics and Center for Materials Innovation, Washington University in St. Louis, MO 63130\n2Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996\n3Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996\nAbstract\nPatterned arrays of ferromagnetic nanoparticles of Co, Ni, and Fe 50Co50have been synthesized from\ntheir ultrathin metal films on SiO 2substrate by nanosecond laser-induced self-organization. The mor-\nphology, nanostructure, and magnetic behavior of the nanoparticle arrays were investigated by a com-\nbination of electron, atomic force, and magnetic force microscopy techniques. Transmission electron\nmicroscopy investigations revealed a granular polycrystalline nanostructure, with the number of grains\ninside the nanoparticle increasing with their diameter. Magnetic force measurements showed that the\nmagnetization direction of the Co and Ni nanoparticles was predominantly out-of-plane while those for\n\u0003Contact author: anup@wuphys.wustl.edu\n†Contact author:ramki@utk.edu\n1arXiv:1001.1328v1  [cond-mat.mtrl-sci]  8 Jan 2010the Fe 50Co50alloy was in the plane of the substrate. This difference in behavior is due to the dominating\ninfluence of magnetostrictive energy on the magnetization as a result of residual thermal strain follow-\ning fast laser processing. Since the magnetostriction coefficient is negative for polycrystalline Co and\nNi, and positive for Fe 50Co50, the tensile residual strain forces the magnetization direction of the neg-\native magnetostriction materials out-of-plane and the positive magnetostriction materials in-plane. This\ndemonstrates a cost-effective non-epitaxial technique for the fabrication of patterned arrays of magnetic\nnanoparticles with tailored magnetization orientations.\n1. Introduction\nFabrication of patterned nanostructures consisting of discrete nanoparticles whose physical properties ( e.g.\nmagnetic, semiconducting, optical) can be reliably controlled by shape, size, and spacing, in conjunction\nwith processing parameters, is of prime importance in the field of nanotechnology. Arrays of magnetic\nnanoparticles can be used for many applications, including high density magnetic data storage [1] to non-\nvolatile and high speed magnetic random access memories (MRAM) [2], opto-electronics [3], and biological\nsensor applications [4, 5]. One of the important challenges in the applications of magnetic nanoparticles is\nthe control of magnetic orientation of each nanoparticle, which can provide additional advantages. For\nexample, particles with perpendicular to the plane anisotropy enable higher density for the same signal-to-\nnoise ratio [6] and lower read and write errors [7], compared to particles with in-plane magnetization. In\nthe absence of an external magnetic field, the magnetic moment of a ferromagnetic material aligns sponta-\nneously along a preferred direction. This direction corresponds to the minimum magnetic energy, which is\ndetermined by intrinsic material parameters such as crystalline anisotropy, as well as extrinsic parameters\nrelated to the processing conditions, such as shape, size, and strain. Therefore, achieving desired magnetic\norientation and switching behavior requires control of magnetic energy through the choice of materials and\n2processing parameters. For instance, epitaxial thin film growth technique can be used to synthesize single\ncrystal magnetic nanodots, where the magnetocrystalline anisotropy uniquely determines the magnetization\ndirection [8].\nIn this work, we demonstrate magnetic orientation control in polycrystalline nanoparticles through non-\nepitaxial means. We have synthesized ordered magnetic nanoparticle arrays with the magnetization direction\ntailored either in-plane or perpendicular to the plane. The magnetic nanoparticle arrays were produced on\namorphous SiO 2surfaces by nanosecond (ns) laser-induced self organization of nm thick ferromagnetic\nmetal films. In this process, the ns laser pulse melts the film, which then undergoes a spontaneous change in\nmorphology. Application of multiple pulses leads to self-organized nanoparticles with predictable particle\nsize and interparticle spacing. The self-organization is a result of spinodal dewetting [9–11] or thermocap-\nillary driven flow [12–14]. We have used this approach previously to synthesize single-domain Co [15] and\nFe nanoparticles [16], which showed particle size-dependent magnetic anisotropy behavior. Here we have\napplied this technique to orient the magnetization direction of the nanoparticles either in-plane or perpen-\ndicular to the substrate plane. We have chosen two elemental ferromagnets with negative magnetostriction\ncoefficient, lS, (lS= -30 ppm for Co and lS= -34 ppm for Ni) and one alloy, Fe 50Co50, with positive magne-\ntostriction coefficient ( lS= +84 ppm) [17–19]; the quoted values of lSare for polycrystalline materials. The\nensuing investigations of magnetic properties show that single-domain nanoparticles of Co and Ni have pref-\nerential perpendicular (out-of-plane) magnetic orientation, while those of FeCo have preferential in-plane\norientation. The reason for this difference was attributed to the coupling of strain (tensile), generated within\nthe nanoparticles by the substrate during rapid thermal processing, to the magnetostriction. The opposite\nsign of the magnetostriction coefficients for Co and Ni compared to FeCo is responsible for their different\norientations.\n32. Experimental Details\nA thin film of Co ( \u00184 nm) was deposited using electron beam evaporation (e-beam), while Ni ( \u00185 nm),\nand Fe 50Co50(\u00184 nm) films were deposited using pulsed laser deposition (PLD) technique on commer-\ncially available optically smooth SiO 2/Si(100) substrates under ultra high vacuum ( \u00181\u000210\u00008Torr). The\nthermally grown oxide (SiO 2) layer was 400 nm thick. Prior to evaporation, the samples were cleaned in\nan ultrasonic bath with acetone, followed by methanol and de-ionized water. The ingot for PLD used for\nFeCo alloy was made by repeated arc-melting of a stoichiometric mixture of Co and Fe (4N pure, Alfa\nAesar). The arc-melting was performed in a water-cooled copper hearth under a high purity TiZr-gettered\nargon atmosphere. The thicknesses of the films were determined by in-situ quartz crystal thickness moni-\ntor and calibrated electron dispersive x-ray spectroscopy (EDS) measurements. The films were irradiated\nwith a Nd:YAG pulsed laser beam (266 nm wavelength, 9 ns pulse width, and 50 Hz repetition rate) under\nhigh vacuum. The energy density of the laser pulses ( \u0018100 mJ/cm2) was chosen to be slightly above the\nmelt threshold [20]. Approximately 3000 laser pulses were required to achieve the pattern with arrays of\nnanoparticles. Two types of laser irradiation experiments were performed. For the case of Ni and FeCo,\na spatially uniform single beam was incident perpendicular to the substrate surface to produce nanoparti-\ncle arrays by spinodal dewetting [9–11]. For Co, two beam laser-interference irradiation was performed to\nproduce a 1-dimensional ordered nanoparticle array [12].\nThe resulting nanoparticle arrays were characterized by scanning electron microscopy (SEM, Hitachi\nS-4500) and by transmission electron microscopy (TEM, JEOL 2100F) using a 200 KeV beam. The TEM\nsamples were prepared by a chemical etching method [21]. Tapping mode atomic force microscopy (AFM)\nand zero-field magnetic force microscopy (MFM), using a Digital Instruments Dimension 3000 instrument,\nwere performed on the nanoparticle arrays to obtain the topographic image, and magnetization direction,\nrespectively. A silicon cantilever, coated with a few tens of nm thick CoCr alloy (Asylum Research, ASY),\nwas used in the MFM measurements at a scan height of 50 nm. To rule out any influence of the MFM-tip\n4on the measurement, MFM was performed in different directions (0oand 90o) and at different heights (20,\n50 and 100 nm) from the sample. The orientation of the magnetization of individual nanoparticles was\ndetermined by comparing the MFM image contrast of the nanoparticles with simulated images [15].\nTo determine the residual thermal strain, finite element simulations were performed on 20 - 100 nm\ndiameter hemispherical nanoparticle on top of 400 nm thick SiO 2substrate under the processing conditions.\nThis was accomplished using the COMSOL software package for a 2-D axi-symmetric geometry, where\nthe particle is perfectly adhesed to the substrate. The model is set to be stress-free at the melting point of\nthe nanoparticle, and the stresses and strains generated during cooling to room temperature due to thermal\ncontraction are determined. The substrate is assumed to be elastic, and the particle is modeled as both\na purely elastic (in which case the yield stress is infinite) and elastic-perfectly plastic (in which case the\nstandard yield strength, sy, of the material is used) solid [22]. The yield strength, sy, of annealed pure Co\n(400 MPa) and pure Ni (300 MPa) was determined by converting large depth hardness data by means of the\ntabor relation, Hardness = 3 sy[23–25]. The average stresses within the particle were converted to elastic\nstrain by Hooke’s law, resulting in two tensile in-plane principal elastic strains, corresponding to the radial\nand hoop strains (in cylindrical geometry) [22]. The various materials parameters used and results obtained\nare tabulated in table 1.\n3. Results\nThe microstructural studies on the arrays of Co, Ni and Fe 50Co50particles are shown in Fig.1. Figure1(a)\nis the bright field (BF) TEM micrograph of Co nanoparticles. Detailed microstructural analysis for Co\nparticles, published in ref. [15], revealed a granular microstructure with random orientation of the grains\ninside the nanoparticles. The number of grains increased with increasing nanoparticle size from 1 grain\n(i.e. single crystal) for the smaller particles ( <40 nm) to 20-30 grains for the bigger particles ( \u0018120 nm),\nwith small statistical variation when different similar size particles were compared. Figure1(b) is the BF\n5TEM image for the array of Ni nanoparticles. These also indicate a granular nanostructure with random\ngrain orientation. Similar to Co, the very small Ni particles ( \u001815 nm) are single grained while the bigger\nparticles have multiple grains ( e.g.,\u001840 nm particles show nearly 20 grains). The TEM image of Fe 50Co50\nnanoparticles [shown in Fig.1(c)] also showed similar granular behavior. The main difference was the large\nstatistical variation in the number of grains from particle to particle, even when the size was similar ( e.g., a\nsmall fraction of \u0018150 nm size particles had only 2-5 grains, while the majority had more than 15 grains).\nFigure2 shows the AFM (2(a)) and zero-field MFM (2(b)) images of an array of Co nanoparticles pro-\nduced by two beam irradiation. The separation between the rows of particles is 400 nm, consistent with the\nseparation of the interference fringes from the two beams. The regular 1D pattern of the nanoparticles along\nthe lines is clearly evident. A 2D pattern can also be formed using three beam irradiation [14]. The average\nparticle diameter was measured to be 110 \u000634 nm. The corresponding MFM image in Figure 2(b) shows\nthat the image contrast of the particles is either uniformly dark with a bright periphery or uniformly bright\nwith a dark periphery. When compared with the simulated MFM image contrast of single domain particles\nwith different magnetization directions (Fig.3), it is clear that all particles in Fig.2(b) are single domain and\nhave their magnetization oriented perpendicular to the substrate plane; the exactly opposite image contrast\nof the two groups is due to their magnetization pointing either up or down. The single domain behavior\nof such large diameter particles, exceeding that of theoretically calculated single domain size of 60 nm for\nsingle crystal Co particles [17, 26], is possibly due to strong exchange coupling among the grains in these\npolycrystalline nanoparticles.\nThe AFM and MFM images for the Ni array produced by a single beam irradiation, is shown in Fig-\nure4(a) and 4(b), respectively. Due to self-organization by spinodal dewetting, the particles have a character-\nistic interparticle spacing (~ 615 nm) and a fairly narrow particle size distribution (176 \u000637 nm). Compared\nto the two beam irradiation, the spatial distribution of these particles do not follow any pattern, however.\nSimilar to Co, the contrast in the MFM image [Fig.4(b)] indicates that almost all particles (similar in size\n6to that marked as # 3) have their magnetization perpendicular to the substrate plane, either up or down. A\nfew particles ( e.g.marked as 2 in Figure4(a)) have their magnetization at an angle <90oto the plane; only\nthe smallest particle (marked as 1) of about 75 nm in diameter is oriented at a small angle to the plane.\nAgain, the nanoparticles have a multi-grained microstructure, but are single domain up to about 220 nm\ndiameter, which is slightly larger than the previously reported value of ~ 180 nm for spherical single grain\nNi nanoparticle [27].\nThe AFM and the MFM images on an array of Fe 50Co50nanoparticles, produced by a single beam\nirradiation of a \u00184 nm film are shown in Figures5(a) and (b), respectively. The average particle diameter\nis 113\u000632 nm with about ~ 580 nm separation. The particles with diameters 50 nm and 150 nm, indicated\nas 1 and 2 in the AFM and MFM images, show in-plane (0o) magnetization. In stark contrast to Co and Ni\nnanoparticles, most of the Fe 50Co50nanoparticles (around 70 %) show in-plane magnetization while the rest\n(e.g.number 3) are at a small angle ( \u001445o) to the plane. These multigrain particles remain single domain up\nto about 175 nm in diameter. These results clearly show a difference in the orientation of the magnetization\nof the nanoparticles with respect to the substrate plane when the magnetostriction coefficient changes sign.\nThe average in-plane elastic thermal strains determined from the finite element simulations were found\nto be independent of particle size since the only length scale present in the problem is the ratio of particle\ndiameter to the size of the SiO 2substrate, which is sufficiently large. The larger of the two (radial versus\nhoop strain) average in-plane elastic strains is given in Table1, along with the material parameters used in\nthe simulation [28]. Only the average elastic component of strain is reported due to its contribution to the\nmagnetostrictive energy. With no mechanism to relieve internal stresses, the elastic solutions (corresponding\nto the columns with ¥yield stress in table 1) represent an upper bound on the average elastic strains. The\naverage elastic strain is found to be lower for the elastic-perfectly plastic simulations (corresponding to the\ncolumns with finite values of yield stress in table 1) due to the presence of large plastic deformations. The\nyield strength chosen and the nature of the elastic-perfectly plastic simulations neglects any size, strain hard-\n7ening and cooling rate affects, which may significantly reduce plastic deformations consequently increasing\naverage stresses and elastic strains within the particle [22,29]. For this reason, the elastic-plastic simulations\nare assumed to be a lower bound of the resulting average elastic strain.\n4. Discussion\nTo understand this difference, we now focus on the various contributions to the magnetic energy of a\nnanoparticle. The magnetocrystalline anisotropy, which depends on the crystal structure, is significant\nonly for single crystal or polycrystalline particles with preferred crystallographic orientation of the grains.\nFor random crystallographic orientation of the grains, such as the case here, the contribution of crystalline\nanisotropy scales inversely with the number of grains [30]. We have estimated that the crystalline anisotropy\nis at least one to two orders of magnitude smaller than the single crystal value for nanoparticles that contain\nmore than 20 grains (see Fig.6 and [15]). Because of the large interparticle separation (400 to 600 nm), dipo-\nlar interaction energy is also small ( \u001410 J/m3). The shapes of these nanoparticles are nearly hemispherical\nas has been determined by the AFM measurements. The estimated contact angles were 104 \u000622o, 106\u000626o,\nand 103 \u000620o, for Co, Ni, and Fe 50Co50, respectively. For the average particle size and separations, using the\nknown saturation magnetizations (1400, 485, and 1922 Gauss for Co, Ni, and Fe 50Co50, respectively [17]),\nthe demagnetization energy was estimated to be \u00181:8\u0002103,\u00182:3\u0002102, and\u00183:6\u0002103J/m3for Co,\nNi, and Fe 50Co50, respectively (see horizontal lines in Fig.6(a-c)). To estimate the magnetostrictive en-\nergy, we have used the maximum theoretical elastic strain value of 0.1% for both Co and Ni, and 0.24%\nfor Fe 50Co50, obtained from simulation (see Table1). In addition, the magnetostrictive energy contribution\n(EMS) was calculated as a function of strain (%) in the particles. Fig.6 show such plots for Co, Ni, and\nFe50Co50, along with the magnetocrystalline energy, E MC, and demagnetization energy, E DM, as a function\nof number of grains in the nanoparticles. The calculated values of E MSfor maximum strain present in Co,\nNi and Fe 50Co50particles are, 7 :7\u0002103, 1:1\u0002104and 3 :3\u0002104J/m3, respectively. It clearly shows that,\n8EMSdominates over other energy terms (E MCor E DM), even when a very small amount of strain ( \u00180:1%)\nis present in these magnetic particles. The dominance of the magnetostrictive energy, therefore controls the\nmagnetization direction of the nanoparticles.\nWith this reasoning, the difference in the behavior of magnetization direction for the nanoparticles of Co\nand Ni versus Fe 50Co50can be understood. Melting under the 9 ns laser pulse and the subsequent solidifica-\ntion during cooling is associated with large cooling rates, of the order of \u00181010K/s [20]. One consequence\nof this quenching is a residual intrinsic biaxial tensile strain within the nanoparticles because of the ther-\nmal expansion mismatch between the metal and the SiO 2substrate [15]. For an in-plane tensile strain, the\nmagnetization will be perpendicular to the substrate plane when the lSis negative, as is the case for Co\nand Ni. On the other hand, for positive values of lS, the magnetization will be in-plane, as is the case for\nFe50Co50. One point needs to be clarified, however. A fairly significant number of Fe 50Co50nanoparticles\n(about 30%), also show slightly out of plane (0 \u000045o) magnetization. Interestingly, as mentioned above,\nthe TEM analysis of Fe 50Co50showed large statistical variations in the number of grains in the same diam-\neter nanoparticles. The magnetocrystalline anisotropy contribution cannot be completely neglected when\nthe number of grains is small. For example, the magnetocrystalline anisotropy energy for 2 grains was\ncalculated to be \u00181\u0002104J/m3, compared to an order of magnitude smaller value of \u00141\u0002103J/m3for\n15 grains (anisotropy constant K1=4:8\u0002104J/m3[17]). The magnetocrystalline energy, therefore, may\ncompete with the magnetostrictive energy for particles containing smaller number of grains and orient the\nmagnetization slightly off from the in-plane direction. The same argument may be applied to the in-plane\nmagnetization of smaller Ni nanoparticles. Moreover, some statistical variation in the amount of strain in\nparticles of the same size, or a variation due to the different number of grains in the particles, may also be\npartly responsible for the above observations.\n95. Conclusion\nIn conclusion, we have synthesized magnetic nanoparticle arrays of Co, Ni, and Fe 50Co50using nslaser-\ninduced self-organization from ultrathin films deposited on SiO 2surfaces. The resulting nanoparticles are\nhemispherical in shape with polycrystalline microstructure. An extensive study of the orientation of the\nmagnetization as a function of nanoparticle size was performed using zero-field MFM. This revealed that\nthe single-domain magnetic nanoparticles of Co and Ni were primarily oriented out-of-plane. On the other\nhand, nanoparticles of Fe 50Co50were primarily oriented in-plane. The reason for this difference was at-\ntributed to the difference in the sign of magnetostriction coefficients. Magnetic energy arguments showed\nthat the magnetostrictive energy dominates among all other contributions, when some residual tensile strain\nis present in the nanoparticles due to the fast cooling process following the ns pulsed laser irradiation.\nAs a result, metals with negative magnetostriction coefficient (Co, and Ni) show out-of-plane magnetiza-\ntion while, positive magnetostriction coefficient materials (Fe 50Co50) showed in-plane magnetization. This\ndemonstrates a cost-effective, non-epitaxial, laser-based processing technique for the production of one- and\ntwo-dimensional arrays of magnetic nanoparticles with controlled magnetization directions.\nAcknowledgments\nRK acknowledges support by the National Science Foundation through CAREER grant NSF-DMI-0449258,\nand NSF-CMMI-0855949, while RK and AKG acknowledge grant NSF-DMR-0856707. AKG and HK also\nacknowledge support from CMI . HK would also like to acknowledge Vanessa Ramos for her inputs in the\npreparation of this manuscript.\nReferences\n[1] M. Todorovic, S. Schuttz, J. Wong, and A. Scherer Appl. Phys. Lett. , vol. 74, p. 2516, 1999.\n10[2] S. Y . Chou, P. R. Krauss, and L. Kong J. Appl. Phys. , vol. 79, p. 6101, 1996.\n[3] M. Saleno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. R.\nAussenegg Opto-Electron. Rev. , vol. 10, p. 217, 2002.\n[4] S. R. Dave and X. Gao Wiley Interdisciplinary Reviews: Nanomedicine , 2009.\n[5] R. S. Molday and D. MacKenzie J. Immunol. Methods , vol. 52, p. 353, 1982.\n[6] H. N. Bertram and M. Williams IEEE Trans. Magn. , vol. 36, p. 4, 2000.\n[7] M. Albrecht, S. Ganesan, C. T. Rettner, A. Moser, M. E. Best, R. L. White, and B. D. Terris IEEE\nTrans. Magn. , vol. 39, p. 2323, 2003.\n[8] H. M. Hwang, S. W. Shin, J. H. Kang, J. Lee, J. H. Lee, J. H. Song, J. Y . Choi, H. H. Lee, and H. S.\nLeeJ. Korean Phys. Soc. , vol. 49, pp. 1016–1019, 2006.\n[9] H. Krishna, N. Shirato, C. Favazza, and R. Kalyanaraman Phys. Chem. Chem. Phys. , vol. 11, p. 8136,\n2009.\n[10] C. Favazza, J. Trice, H. Krishna, R. Kalyanaraman, and R. Sureshkumar Appl. Phys. Lett. , vol. 88,\np. 1531181, 2006.\n[11] C. Favazza, R. Kalyanaraman, and R. Sureshkumar Nanotechnology , vol. 17, p. 4229, 2006.\n[12] C. Favazza, J. Trice, R. Kalyanaraman, and R. Sureshkumar Appl. Phys. Lett. , vol. 91, p. 043105, 2007.\n[13] J. Trice, C. Favazza, D. Thomas, H. Garcia, R. Kalyanaraman, and R. Sureshkumar Phys. Rev. Lett. ,\nvol. 101, no. 1, p. 017802, 2008.\n[14] A. K. Gangopadhyay, H. Krishna, C. Favazza, C. Miller, and R. Kalyanaraman Nanotechnology ,\nvol. 18, p. 485606, 2007.\n11[15] H. Krishna, C. Miller, L. Longstreth-Spoor, Z. Nussinov, A. K. Gangopadhyay, and R. Kalyanaraman\nJ. Appl. Phys. , vol. 103, no. 7, p. 073902, 2008.\n[16] H. Krishna, N. Shirato, A. K. Gangopadhyay, and R. Kalyanaraman Proc. SPIE , vol. 7039, p. 703909,\n2008.\n[17] B. D. Cullity, Introduction To Magnetic Materials . Addison-Wesley Publishing Company, 1972.\n[18] R. C. Hall J. Appl. Phys. , vol. 30, p. 816, 1959.\n[19] B. E. Lorenz and C. D. Graham IEEE Trans. Magn. , vol. 40, p. 2751, 2004.\n[20] J. Trice, D. Thomas, C. Favazza, R. Sureshkumar, and R. Kalyanaraman Phys. Rev. B , vol. 75,\np. 235439, 2007.\n[21] L. Longstreth-Spoor, J. Trice, H. Garcia, C. Zhang, and R. Kalyanaraman J. Phys. D: Appl. Phys. ,\nvol. 39, p. 5149, 2006.\n[22] G. F. Dieter, Mechanical metallurgy (3rd ed.) . McGraw Hill, New York, 1986.\n[23] A. A. Karimpoor, U. Erb, K. T. Aust, and G. Palumbo Scripta Mat. , vol. 49, pp. 651–656, 2003.\n[24] Z. Zong, J. Lou, O. O. Adewoye, A. A. Elmustafa, F. Hammad, and W. O. Soboyejo Mat. Sci. and Eng.\nA, vol. 434, pp. 178–187, 2006.\n[25] D. Tabor, The Hardness of Metals . Clarendon Press, Oxford, 1951.\n[26] C. Kittel Phys. Rev. , vol. 70, p. 965, 1946.\n[27] X. Liu, U. Meridor, P. Zhao, G. Song, A. Frydman, and A. Gedanken J. Magn. Magn. Mat. , vol. 301,\np. 13, 2006.\n[28] G. A. Alers, J. R. Neighbours, and H. Sato J. Phys. Chem. Solids , vol. 13, p. 40, 1960.\n12[29] Q. Ma and D. Clarke J. Mater. Res. , vol. 10, p. 853, 1995.\n[30] R. M. H. New, R. F. W. Pease, and R. L. White IEEE Trans. Magn. , vol. 31, p. 3805, 1995.\n13Property SiO 2 Cobalt Nickel Fe50Co50\nThermal expansion coeff. a\u000210\u000060.55 13 13.4 12.4\nMelting temperature Tm(K) 1768 1728 1748\nYoung’s modulus E (GPa) 72 209 200 82.7\nPoisson’s ratio n 0.17 0.31 0.31 0.31\nYield strength sy(MPa) ¥ ¥ 400 ¥ 250 ¥\nAvg. in-plane elastic strain e(%) 0.10 0.04 0.11 0.5 0.24\nTable 1: List of material parameters used for finite element simulation and the average in-plane elastic\nstrain values obtained from the simulation. The strain reported is the larger of the radial and hoop in-plane\nprincipal strains averaged over the volume of the particle. The yield strength corresponding to ¥values\ndenote the purely elastic calculations while the columns with the finite numerical values of sycorrespond\nto the elastic-perfectly plastic calculations. Since the syfor the Fe 50Co50alloy was note available, only the\nelastic result is presented.\n14(a)\n(b)\n(c)\nFigure 1: Representative bright field TEM micrographs for nanoparticle arrays synthesized by the laser-\ninduced self-organization; (a) Co nanoparticles, (b) Ni nanoparticles, and (c) Fe 50Co50nanoparticles. The\ncontrast within each nanoparticle arises from random crystallographic orientation of multiple grains. Such\nimages were used to generate statistics on the number of grains as a function of nanoparticle size.1516(a)\n (b)\nFigure 2: AFM (a) and zero field MFM (b) images of one dimensional patterned Co nanoparticles produced\nby 2-beam pulsed laser interference irradiation of a 4 nm Co film.\n17Figure 3: The simulated contrast in the MFM images of a single domain ferromagnetic particle with (a)\nin-plane (0o), (b) at an angle of 45oand (c) perpendicular to the plane (90o) (taken from ref. [15]).\n18(a)\n (b)\nFigure 4: AFM (a) and zero field MFM (b) images of Ni nanoparticles produced by single beam pulsed laser\nirradiation of a 5 nm Ni film. The nanoparticles marked as #s 1, 2, and 3 in the AFM image (Fig. (a)) are\n75 nm, 135 nm and 200 nm diameter, respectively. The corresponding MFM image [Fig. (b)] indicates the\nmagnetization directions with respect to the substrate plane at 0o, 45oand 90o, respectively.\n19(a)\n (b)\nFigure 5: AFM (a) and the zero-field MFM (b) images of Fe 50Co50nanomagnets produced from a 4 nm\nfilm by pulsed laser irradiation. The nanoparticles indicated as #s 1 and 2 in the AFM image (Fig. (a)) are\nnm and 150 nm diameters; the corresponding MFM image (Fig. (b)) indicates that both have magnetization\ndirection in the substrate plane (0o), while another 150 nm diameter particle ( # 3) is aligned at \u001845oto the\nsubstrate. The bold arrows in Fig. (b) indicate the in-plane random orientations of the other nanoparticles.\n20(a)\n(b)\n(c)\nFigure 6: The comparison of different magnetic energies for the three different materials. The magnetocrys-\ntalline energy (E MC) is shown as a function of number of grains ,and the magnetostrictive energy (E MS) as\na function of strain (%). The demagnetization energy (E DM) is also shown. Fig (a) corresponds to Co, Fig.\n(b) to Ni and, Fig. (c) to Fe 50Co50. In each of the three cases a small amount of residual strain (~0.1%) is\nsufficient to make the E MSdominate over E MCand E DM.\n2122"    },    {        "title": "1003.3309v1.On_effective_electromagnetic_parameters_of_artificial_nanostructured_magnetic_materials.pdf",        "content": "arXiv:1003.3309v1  [physics.optics]  17 Mar 2010On effective electromagnetic parameters of artificial\nnanostructured magnetic materials\nC.R. Simovski and S.A. Tretyakov\nDepartment of Radio Science and Engineering / SMARAD Center of Excellence, Aalto\nUniversity, School of Science and Technology, 00076, Aalto , Finland\nAbstract\nIn this paper we discuss effective material parameter description o f new\nnanostructures designed to perform as artificial magnetic mater ials for vis-\nible light. Among these structures there are various split-ring reso nators,\ndual-bar structures, fishnet layers and other geometries. Artifi cial magnetic\nresponse in these structures appears due to weak spatial disper sion effects,\nand it is important to study the conditions under which the magnetic r e-\nsponse can be adequately measured with effective permeability tens or. On\nthe examples of dual bars and split rings we show that this is possible o nly\nunder some quite restrictive conditions. In the general case, mor e compli-\ncated constitutive relations with more effective material paramete rs need to\nbe developed.\nKeywords: metamaterial, electromagnetic characterization, effective\nmaterial parameters, permeability, spatial dispersion, multipole me dia,\nbianisotropic media\n1. Introduction\nConventionally, the electromagnetic properties of bulk materials ar e de-\nscribed by their permittivity ( ε) and permeability ( µ) tensors. There are no\nmeansforthedirectmeasurement oftheseelectromagneticpara meters, which\nare for this reason dependent on the model used for their extrac tion from the\nmeasurement data. Approaches to measurements of even these fundamental\nelectromagneticcharacteristics ofmaterialsvarydramaticallyfor electromag-\nnetic waves of different frequencies, e.g. radio waves and light, and require\nPreprint submitted to Photonics and Nanostructures Novemb er 19, 2018specialized measurement techniques. These difficulties are dramatic ally es-\ncalated in electromagnetic characterization and metrology of nano structured\nmaterials with complex geometries of unit cells and exotic electromagn etic\nresponse. For example, let us consider a device that operates at t he wave-\nlength of 500-600 nm, with the structural periodicity of artificial m aterial in\nthe range of 50-100 nm, while the sizes of resonant inclusions are ab out 30-70\nnm. Such structures, if they are bulk (3D) lattices, can still be des cribed in\nterms of effective parameters (permittivity and permeability) of an equiv-\nalent homogeneous medium. However, the conventional models bas ed on\nquasi-static homogenization procedures normally applied at the ato mic level\nare not applicable here, and the resulting effective phenomenologica l param-\neters (like permittivity and permeability) often have quite different p hysical\nmeaning as compared with conventional materials – natural ones an d com-\nposites of non-resonant inclusions.\nThe bulk material parameters εandµof an effective medium (isotropic\nor anisotropic) are classically defined so that they relate vectors DandBof\nthe electromagnetic field in a medium with macroscopic (averaged) ve ctors\n/angb∇acketleftE/angb∇acket∇ightand/angb∇acketleftH/angb∇acket∇ight, respectively:\nD=ε0/angb∇acketleftE/angb∇acket∇ight+P≡ε0ε·/angb∇acketleftE/angb∇acket∇ight,B=µ0(/angb∇acketleftH/angb∇acket∇ight+M)≡µ0µ·/angb∇acketleftH/angb∇acket∇ight(1)\nHerePandMarethebulkelectric andmagneticpolarizationsresulting from\nmicroscopic electric and magnetic dipole moments of particles averag ed over\nthe same volume as the electric and magnetic fields. For regular arra ys of\natoms, molecules or inclusions this is usually the volume Vof the lattice unit\ncell. Parameters defined by formulas (1) are applicable for solving bo undary\nproblems with the Maxwell boundary conditions [1, 2, 3].\nPhysically sound local material parameters should satisfy the follow ing\nbasic requirements:\n•Passivity (for the temporal dependence e−iωtit implies Im( ε)>0 and\nIm(µ)>0 simultaneously at all frequencies; for the ejωttime depen-\ndence convention the sign of bothIm( ε)and Im(µ) should benegative).\nViolation of this condition in passive media (no sources of electromag-\nnetic energy at frequency ω) means the violation of the second law of\nthermodynamics;\n•Causality (for media with negligible losses it corresponds to conditions\n∂(ωε)/∂ω >1 and∂(ωµ))/∂ω >1. This also means that in the fre-\n2quency regions where losses are small, material parameters grow v ersus\nfrequency: ∂(Re(ε))/∂ω >0 and∂(Re(µ))/∂ω >0 );\n•Absence of radiation losses in electrically dense arrays with uniform\ndistribution of particles. This means that in lossless arrays the elect ro-\nmagnetic parameters should take real values.\nThe first two requirements (passivity and causality) are most know n and can\nbe mathematically expressed through the Kramers-Kronig relation s (see e.g.\nin [1, 2, 4]). These basic physical requirements must be satisfied to e nsure\nthat the use of the effective medium description does not lead to non physical\nresults. Furthermore, locality of the model implies that the parame ters\n•are independent of the spatial distribution of fields excited in the ma -\nterial sample,\n•are independent of the geometrical size and shape of the sample.\nThis ensures independence of material parameters on the wave ve ctorq, if\none uses a plane wave as a probe field to determine the material para meters.\nFor a given frequency this means independence of effective parame ters on\nthe wave propagation direction [4]. These two requirements are diffic ult to\nsatisfy for many nanostructures, in part because the samples us ually contain\nonly a few (or even one) layers of inclusions or patterned surfaces across the\nsample thickness. This introduces limitations on the applicability area o f the\neffective parameters and demands the use of alternative descript ions in terms\nof surface impedance or grid impedance. If the last two conditions a re not\nsatisfied, the material parameters can be used basically only for th e same\nexcitation environment as in the characterization experiment.\nRecently, considerable effortshave beendevoted tothedesignan drealiza-\ntion of nanostructures behaving as artificial magnetic materials at terahertz\nand optical frequencies, with the main motivation to create double- negative\nmaterials (e.g., [5, 6, 7]). These structures are usually characteriz ed using\na probe plane electromagnetic wave normally incident at planar sample s.\nThen, the classical Nicolson-Ross-Weir method [8, 9] is used to extr act the\neffective permittivity and permeability of the sample. However, in man y\nsituations one can observe that the resulting parameters do not s atisfy the\nbasic physical requirements of local material parameters (param eters have\nnonphysical signs of the imaginary parts in some frequency regions , do not\n3satisfy the Foster theorem (e.g., [10]) in low-loss regions, depend on the in-\ncidence angle of the probing wave, etc.) In a recent paper [11] is was shown\nthat for typical optical fishnet structures the effective medium d escription in\nterms of permeability is not valid in the whole range where the backwar d-\nwave regime is observed. While these parameters still correctly res tore the\nreflection and transmission coefficients for plane waves which were u sed in\nthe characterization, they fail to describe the material for othe r excitations\nand sample shapes. This dramatically reduces their value in the design of\napplications which would utilize the effective magnetic properties of th e new\nmaterials. Thus, it is of scientific and practical importance to under stand\nthe limitations of the effective parameter models and study the reas ons for\nnonphysical behavior of extracted parameters. In this paper we make a step\nin this direction analyzing magnetic response of some simple inclusion ge -\nometries, conventionally used in the design of artificial magnetics.\n2. Effective medium description of bulk optically dense meta ma-\nterials\nIn this paper we concentrate on effective-parameter character ization of\noptically dense bulk nanocomposites formed by electrically small scat terers.\nEven in this case the homogenization is a difficult task that obviously imp lies\nanswering to the following questions:\n•How to introduce (define) material parameters of composite media ,\nwhat is the physical meaning of them and in which electrodynamic\nproblems such material parameters are applicable?\n•What are frequency bounds in which these material parameters ke ep\ntheir physical meaning and applicability?\n•What are the physical limitations that should be imposed on these\nmaterial parameters and can be used as a check of calculations, me a-\nsurements, and, finally, in practical applications?\nFrequency dispersion in metamaterials formed by electrically (optica lly)\nsmall inclusions can be strong when particles are excited in a vicinity of their\nresonant frequencies. This implies dramatic shortening of the wave length\ninside the composite, which means that spatial dispersion effects ca n appear\neven in optically dense metamaterials. If the effective wavelength λ/neff,\n4whereneffis the effective refraction index, is close to or smaller than the\nlattice period, the local material parameters cannot be introduce d. This\nsituation can be easily detected experimentally or numerically, becau se in\nthis case the nonlocality in response is visible also in the properties of t he\neffective refraction index neffand wave impedance Zeff. In the following, we\nassume that the lattice period is electrically small, and concentrate o n the\nanalysis of the influence of the inclusion shape on the effective prope rties.\n2.1. Artificial magnetism in composites of nanodimers\nIt has been known since early fifties [12] that composites containing elec-\ntrically small conductive inclusions of complex shapes can exhibit prop erties\nof artificial magnetics, usually described by magnetic polarizability of inclu-\nsionsαmm. This parameter is defined as\nm=αmm·H (2)\nwheremis the induced magnetic moment and His the local magnetic field\nat the center of the particle. After appropriate averaging, magn etic response\nof individual inclusions defines the effective permeability of the compo site.\nThis magnetic response is a manifestation of spatial dispersion effec ts, be-\ncause the response to magnetic field basically means the response t o the\nnonuniform component of the electric field (in form of ∇×E) [13, 14]. The\nkey pre-requisite for the validity of the effective permeability model is that\nthe response to other combinations of spatial derivatives of Ecan be ne-\nglected [15, 16] (see also Chapter 2-1 of [17]). Also, electric quadru pole as\nwell as other higher-order polarization moments should be negligibly s mall\nas compared with the magnetic dipole [16]. This very much depends of t he\ninclusion shape. In fact, only for some specific shapes these condit ions can\nbe satisfied.\nLet us, for example, consider arrays of dual plasmonic nanopartic les\n(dimers): dual spheres, dual bars or other nanostructures in w hich the res-\nonant magnetic response of a unit cell is related with the phase shift of the\nexciting wave over the distance abetween two plasmonic elements. In one\nof the resonant modes of such pairs the electric polarizations induc ed in two\nparticles are out of phase, which corresponds to high magnetic mom ent of\nthe pair. Usually, composites formed by many such inclusions are mod elled\nby effective permeability and permittivity, as in [18]–[25] and a number o f\nother papers. However, we will see from the following that in this cas e the\n5xy\napA\npBpAq=q x\nxy\nq=qyHH\nE(-d/2)dE(d/2) E(d/2)\nE(-d/2)\nFigure 1: (Color online) A unit cell of a lattice of pairs of plasmonic sphe res. If the\nwave propagates along x, the magnetic field induces a resonant magnetic moment (and\nan electric quadrupole moment). If the wave propagates along y, the same magnetic field\nat the same frequency induces only an octupole moment, which is neg ligible for optically\ndense lattices. Such a lattice cannot be described only in terms of εandµ.\nphysical meaning of the permeability introduced via averaging of the induced\nmagnetic moments is different from the conventional definition, whic h limits\nthe possible use of this effective parameter.\nFig. 1 represents a plasmonic nanodimer. Let this nanopair be a unit c ell\nof a nanostructured metamaterial. The magnetic moment of the me dium\nunit cell of volume Vis defined as [2, 4]\nm=1\n2/integraldisplay\nVJ×rdV (3)\nHereris the radius-vector referred to the particle center, and J=−iωε0(ε−\nεh)Eis thepolarizationcurrent density (inour case that inside theplasmo nic\nspheres). Metal nanospheres are non-magnetic, and their perm ittivity is\ndenoted as ε.εhis the permittivity of the host medium. The response\nof the pair of nanopsheres to the time-varying magnetic field is in fac t the\nresponse of the nanopair to spatially varying electric field [13, 14]. W hen the\nlocal electric field Eacting on different nanospheres is different, the dimer\ncan acquire magnetic moment. Since for the centers of two nanosp heres\nthe radius vector is equal to r=±(a/2)x0, magnetic moment mof the\nnanopair given by (3) is always z-directed and for any direction of the wave\npropagation equals to m=mz=−(iωa/2)[py(B)−py(A)]. The action of the\nlocal magnetic field Hto the nanopair is in this way represented as action of\nelectric fields E(A) andE(B) to nanospheres A and B.\n6To quantify the magnetic effect, we assume that the dimer is probed\nby a pair of plane waves that form a standing wave. This allows us to\nposition the dimer center at the point where the incident electric field is zero\nand this way find the response to quasi-uniform magnetic field [13, 1 4]. If\nthe exciting waves propagate along x(q=qxin Fig. 1), the local electric\nfield isy-polarized, E(B) =−E(A), andp(B) =−p(A). Respectively,\nm=−iωap(B)/2. The local magnetic field H=Hzat the nanopair center\nis related to the electric fields E(A) andE(B) through Maxwell’s equations:\niωµ0Hz=∂Ey\n∂x−∂Ex\n∂y=∂Ey\n∂x≈E(B)−E(A)\na=2E(B)\na(4)\nIn (4) we have taken into account the small optical size of the nano pair\n(|k|a<1). The nanopair magnetic polarizability αmm=αzz\nmmis then equal\nto\nαmm≡m\nH=Z0(ka)2pB\nE(B)=Z0(ka)2α (5)\nwhereZ0isthefree-spacewaveimpedanceand α=E(B)/p(B) =E(A)/p(A)\nis the electric dipole polarizability of the individual plasmonic particle. Th e\nmagnetic polarizability in this special case of propagation turns out t o be\nresonant at the same frequency as the plasmon resonance of an in dividual\nparticle. Actually, the magnetic resonance is slightly red-shifted wit h respect\nto that of the single sphere (our simplistic model does not take into a ccount\nthe mutual coupling of spheres), but it is not important for our pur poses.\nOn the other hand, if the probing waves propagate along y(q=qyin\nFig. 1), the response of the nanopair to the same magnetic field Hat the\ndimer center corresponds to zero induced magnetic moment. In th is case we\nhave\niωµ0Hz=∂Ey\n∂x−∂Ex\n∂y=−∂Ex\n∂y(6)\nThe magnetic moment of the unit cell induced by the magnetic field is ze ro\nbecauseExis zero at the centers of nanopsheres and their electric dipole\nmoments vanish. Magnetic field Hinduces opposite electric polarizations of\ntheupperandlower halvesofbothspheresasitisshowninFig. 1. This effect\nis practically negligible and has nothing to do with magnetic polarization,\ni.e., in this case αmm= 0.\nWe observe a dramatic dependence of the magnetic polarizability αmm\non the direction along which the incident field is changing. For example, in\npaper [25] this effect is treated as that of strong spatial dispersio n, resulting\n7inbothpermittivity andpermeability stronglydependent ontheprop agation\ndirection. However, the optical size of the dimers and the lattice pe riod are\nassumed to be optically very small, and there are no physical reason s for\nstrong spatial dispersion in the effective medium response. The abs ence of\nstrong spatial dispersion means that the permeability tensor µ(as well asε)\ncannot depend strongly on the direction of the vector q.\nThe answer to this paradox is given in the theory of multipole media,\nalso called media with weak spatial dispersion [15, 16, 17, 26]. Multipole me-\ndia depend on higher-order multipole response accompanying the ma gnetic\ndipole response of complex particles. In the present case this highe r-order\nmultipole response is the electric quadrupole susceptibility. In [25] it was\ncorrectly noticed that the quadrupole polarization of plasmonic dime rs is as\nessential as their electric and magnetic dipole polarizations. In gene ral, me-\ndia with resonant quadrupole moments as any other multipole media ca nnot\nbe described only in terms of εandµ. Physically sound material equations\nfor multipole media contain besides macroscopic fields EandHalso spa-\ntial derivatives of E[15, 16, 26]. Respectively, more material parameters\nare required. In this theory the unit cell magnetization can be prop erly\ndescribed without involving spatially dispersive permittivity ε(q) and per-\nmeabilityµ(q), which describe only excitation by plane waves traveling along\none particular direction.\nFor a medium formed by dimers we can write for any direction of the\nwave propagation\nm=mz=−iωapy(B)−py(A)\n2=−iωa2α\n2Ey(B)−Ey(A)\na≈2ν∇xEy(7)\nwhereν=iωa2α/4. This relation is more adequate than the proportionality\nbetweenmandH, which is only a special case of (7). We can present (7) as\nthe sum of the symmetric and antisymmetric derivative forms:\nmz=ν(∇xEy−∇yEx)+ν(∇xEy+∇yEx) (8)\nor, in the index form,\nmα= ΓαβHβ+καβγ∇βEγ (9)\nIn (9) indices α, β, γ correspond to the Cartesian coordinates and we use\nthe notations\nΓzz=−iνωµ0, κzxy=κzyx=ν (10)\n8Components with all the other combinations of indices α, β, γ equal zero.\nFrom (9) it is clear that the magnetic polarization contains two parts . The\nfirst part is the magnetic moment of the dimer induced by the magnet ic\nfield which results in the resonant effective permeability of the compo site\nmedium. The second partdescribes the magneticmoment ofthedime r which\nis proportional to all the other combinations of spatial derivatives of the\nelectric field. When the wave propagates along y, the second term cancels\nout with the first one and the induced magnetic moment vanishes. Th e\ndependence of the magnetic moment on the propagation direction is not\na feature of strong spatial dispersion because the polarizability tensors Γ αβ\nandκαβγdo not depend on the propagation direction. This feature of weak\nspatial dispersion was discussed in books [15, 16]. The material equ ation for\nthemagneticfieldresulting from(9)andthequasi-staticaveraging procedure\ncan be written in the index form as\nBα≡µ0Hα+Mα=µ0µαβHβ+χαβγ∇βEγ (11)\nHere tensor µαβresults from Γ αβand tensor χαβγresults from καβγ.\nA similar consideration can be done for the quadrupole moment of the\ndimer. The vectors of the electric dipole and magnetic dipole moments of the\ndimer and the tensor of its quadrupole moment are resonant. This m eans\nthat the electric displacement vector Dessentially includes the contribution\nof the electric quadrupole polarization Qαβ. This evolves one more material\nparameter in the material equation which takes the form [15, 16, 1 7, 26]:\nDα≡ε0Eα+Pα+1\n2∇βQαβ=ε0εαβEβ+ξαβγδ∇β∇γEδ(12)\nMaterial equations (11) and (12) corresponds not only to dimers. They refer\nto all composites whose inclusions possess resonant quadrupole po larization\nin the absence of bianisotropy, see e.g. [30, 31, 32].\nIn this formalism the boundary conditions should be revised as com-\npared to the formalism of initial equations (11) and (12), because t he set of\nMaxwell’s boundary conditions is not enough to solve boundary proble ms for\nsuch media. Additional boundary conditions should be derived as it wa s ex-\nplained in books [15, 16]. However, to our knowledge, for media descr ibed by\nequations (11) and (12) boundary conditions have not been derive d. In the\nknown papers composites of dimers and other multipole media are des cribed\nby onlyεandµ. That description implies the use of Maxwell’s boundary\n9conditions, but can be applied only to the plane-wave incidence at the angle\nused in the extraction of the effective parameters.\n2.2. Artificial magnetism in bianisotropic composites\nNext we will discuss the artificial magnetism in composites based on sp lit\nrings(SRR),withtheemphasisontheeffectofbianisotropy. Inpar ticular, we\nconsider an array of U-shaped metal SRRs experiencing plasmonic r esonance\nin the optical range. Similarly to the previous section, we use a pair of plane\nwaves to probe the particle response to external magnetic fields. First, let us\nshow that magnetic polarizabilities are different for the two cases: w hen the\nwaves propagate with vector q=qx0alongxand the electric field associated\nto the local magnetic field Hisy-polarized, and when q=qy0and the same\nmagnetic field is related to x-polarized electric fields.\nThe following consideration is based on the method of induced electro mo-\ntive force (IEF) as it was formulated in [27] for conducting wire scat terers.\nA formula for the IEF more appropriate to the case of a plasmonic SR R is\nmore involved and corresponding derivations are cumbersome, whe reas the\nresult will be definitely similar to that obtained below.\nLet us choose the coordinate system as shown in Fig. 2 and locate an\nimaginary port in the origin. The electromotive force induced by the lo cal\nelectromagnetic field at this imaginary port is equal to [12, 27]\nE=1\nI0/integraldisplay\nlElIrad(l)dl (13)\nHereElisthecomponentofthelocalelectricfieldtangentialtothescatte rer’s\ncontour,Iradis the complex amplitude of the linear current distributed over\nthis contour in the radiation regime, when an external voltage sour ce is con-\nnected to the port, and I0=Irad(0). In the case q=qxfrom Maxwell’s\nequation (4) we obtain\nEl=±Ey|x=±d\n2=±iωµ0Hd\n2(14)\nSince the U-shaped scatterer isoptically small and thecurrents at the ends of\nthe stems vanish, the distribution of the induced current over the scatterer’s\ncontourIrad(l) can be approximated as a linear function of the contour coor-\ndinatel:\nIrad(l) =I0b+d\n2−l\nb+d\n2(15)\n10x\nqqHz Hz\ndEyx\nEPort Portby\nFigure 2: (Color online) A sketch of U-shaped SRRs for two cases of the wavepropagation.\nThe incident magnetic field at the particle center is the same in both ca ses. Introducing\nan imaginary port at the center of the horizontal bar and applying t he method of induced\nelectromotive force we prove the strong difference of the particle magnetic polarizabilities\non the propagation direction for these two cases.\n11wherel= 0 at the port, l=|x|for−d/2<x<d/ 2, y= 0 andl=y+d/2\nforx=±d/2, y < b. Upon substitution of (14) and (15) formula (13) can\nbe rewritten in the case q=qxas\nE=iωµ0Hd\nb+d\n2b/integraldisplay\n0(b−y)dy=iωµ0Hb2d\n2b+d(16)\nThesameelectromotiveforce Ecanbeexpressedthroughtheinputimpedance\nZinof thescatterer referredto theimaginaryport: E=I0Zin. Equating these\ntwo representations one can express the ratio ( I0/H) throughZin:\nI0\nH=iωµ0Hb2d\nZin(2b+d)(17)\nWhen we calculate αmm, we use the definition (3), and take into account\nthat the current distribution induced by the local field is different fr om the\ndistribution of the current excited by an external voltage in the po rt. There-\nfore, instead of (15) we use a more adequate approximation which is smooth\nat the coordinate origin:\nI(l)≡I0F(l) =I0/parenleftbig\nb+d\n2/parenrightbig2−l2\n/parenleftbig\nb+d\n2/parenrightbig2(18)\nUsingthedefinitionofthemagneticmoment(3)andthedistributionf unction\nF(l) we can write the magnetic polarizability of the SRR in the form:\nαmm=m\nH=µ0I0\n2H\nb\n2d/2/integraldisplay\n−d/2F(x,y= 0)dx+2d\n2b/integraldisplay\n0F/parenleftbigg\nx=d\n2,y/parenrightbigg\ndy\n(19)\nSubstituting relation (18) for function F(l) into (19) we finally obtain\nαmm=iωµ2\n0b3d2(6b+d)\n2Zin(2b+d)2(20)\nIn the case q=qyfrom Maxwell’s equation (6) we find\nEl=Ex(y= 0) =±iωµ0Hb\n2(21)\n12Substituting (21) and (15) into the main formula (13) we obtain\nE=iωµ0Hb\nb+d\n2d/2/integraldisplay\n0/parenleftbiggd\n2+b−x/parenrightbigg\ndx=iωµ0Hbd(4b+d)\n8(2b+d)(22)\nOnly the horizontal bar gives contribution into the induced electrom otive\nforce, while the integrals over the stems vanish. For the ratio I0/Hwe have\nin this case\nI0\nH=iωµ0bd(4b+d)\n8Zin(2b+d)(23)\nSubstituting (23) into formula (19) we obtain\nαmm=iωµ2\n0b2d2(6b+d)(4b+d)\n16Zin(2b+d)2(24)\nThis result clearly differs from (20). The ratio of magnetic polarizabilit ies\ncorresponding to the two cases of propagation is as follows:\nα(q=qx)\nmm\nα(q=qy)\nmm=8b\n4b+d(25)\nForb=dthese magnetic polarizabilities differ by the factor of 1 .6. Though\nin both cases of the wave propagation direction the magnetic polariz abil-\nity is nonzero, this example clearly shows that the magnetic polarizab ility\nαmmof a U-shaped SRR is an ambiguous value, similarly to the case of a\ndimer. Respectively, one should take into account the electric quad rupole\npolarization.\n2.3. Bianisotropic material relations for nanostructured metamaterials\nWhen some local magnetic field acts on a U-shaped SRR, the same po-\nlarization current which forms dipole moments of the stems (whose v ector\nsum vanishes) also creates some noncompensated resonant dipole moment of\nthe horizontal bar. Thus, local magnetic field in this case creates r esonant\nmagnetic dipole moment, resonant electric quadrupole moment, and reso-\nnant electric dipole moment. The effect of electric dipole polarization o f the\nmedium unit volume by magnetic field can be expressed as the second t erm\nin the right-hand side of the equation\nPα= ΛαβEβ+ΨαβHβ (26)\n13This effect in reciprocal media is complemented by the effect of the ma gnetic\npolarization of the medium by electric fields:\nMα= ΘαβHβ+Ψ′\nαβEβ+καβγ∇βEγ (27)\nThis couple of effects (tensors Ψ and Ψ′are uniquely related: Ψ′\nαβ=−Ψβα)\nis well known in the electromagnetic theory and engineering (e.g., [15]) and\nis called bianisotropy. Media formed by parallel U-SRR particles posse ss\nresonant bianisotropy. Even dual SRRs introduced in [28] are bianis otropic,\nand their bianisotropy was widely discussed in the literature after th e publi-\ncation of paper [29]. The bianisotropy of dual SRRs is an important fa ctor\nthat can suppress the backward-wave regime in metamaterials [29]. More-\nover, U-shaped particles show stronger bianisotropic effects tha n dual SRRs.\nSince bianisotropy is a stronger effect than artificial magnetism (fir st- and\nsecond order effects in terms of ka), characterization of such metamaterials\nonly by two parameters εandµis clearly not adequate.\nFrom (26) and (27) it is clear that two additional material paramete rs\nshould be introduced compared to multipole media without bianisotrop y.\nMaterial equations (11), (12) for bianisotropic multipole media gene ralize to\nthe form:\nBα=µ0µαβHβ+ψαβEβ+χαβγ∇βEγ (28)\nDα=ε0εαβEβ−ψβαEβ+ξαβγδ∇β∇γEδ (29)\nThe material parameter describing the bianisotropic effect in equat ions (28)\nand (29) is tensor ψ, calledmagnetoelectric coupling parameter in the theory\nof reciprocal bianisotropic media (e.g. in [15, 16, 33]).\nTwo special cases of bianisotropic media are well known: chiral media\nwhen tensor ψis symmetric, and omega media when tensor ψis antisym-\nmetric. According to the classification [34, 15] arrays of parallel U- SRRs\nbelong to the class of omega media. The known theory of omega media (see\ne.g. in [15, 35, 36, 37]) was developed for the special case when tens orsχ\nandξin (28) and (29) are negligible. Fabrication of nanostructured arra ys\nof U-SRRs [38] will hopefully motivate researchers to develop the th eory of\nmultipole bianisotropic media, and the first task should be the derivat ion of\nboundary conditions for media described by equations (11) and (12 ) and for\nmedia obeying equations (28) and (29).\n2.4. Artificial magnetism without resonant multipole polar ization\nFinally, letusdiscusswhichinclusionshapescanpotentiallyofferartific ial\nmagnetism property without strong excitation of higher multipoles. If the\n14ring shown in Fig. 2 were closed, the electric dipole moments in each side\nwouldbeinallcasesofthewavepropagationcancelledbythatintheo pposite\narm. In an electrically small closed loop with uniform current distribut ion,\ntheinducedelectromotiveforceisthesameforanydirectionofpro pagationof\nincident waves. This inducedelectromotive forceisequal totheneg ativetime\nderivative of the applied magnetic flux. No bianisotropy and no quadr upole\nmoment arise, and the array of closed rings (at enough low frequen cies, of\ncourse) behaves an effective diamagnetic medium.\nIf the open part of the ring is very small compared to its perimeter, the\ndependence of the induced magnetic moment on the propagation dir ection\nis also small and, respectively, quadrupole moments are negligible. Ho wever,\nthe bianisotropy remains strong and resonant, since the induced c urrent dis-\ntribution is not uniform, which results in both electric and magnetic dip ole\nmoments of the loop. The bianisotropy of the array related to the o pen part\nof the loop can be suppressed in two ways. The first way is to prepar e the\nunit cell from at least two SRRs so that the bianisotropy of the unit c ell\nis compensated. That way was suggested in [29]. A similar approach wa s\ndeveloped in [39, 40] where a practically isotropic doubly-negative co mpos-\nite was designed. The unit cell in these works was formed by six prope rly\narranged Ω-shaped metal particles. A dense stack of split rings wit h inter-\nmitting positions of splits was introduced in [41]. In all these design the\ngoverning idea is to realize uniform distribution of induced current alo ng the\ninclusion perimeter.\nHowever, the above designs refer to the microwave range. Realist ic ap-\nproaches to the artificial magnetism without strong spatial disper sion, high-\norder multipoles and bianisotropy in the optical range were suggest ed more\nrecently. Suitable design solutions are, for example, as follows: fou r-split\noptical SRRs suggested in [42] and effective nanorings of plasmonic s pheres\n[43]. In [43] an effective ring is formed by plasmonic nanospheres loca ted at\nthe corners of a regular polygon. The minimal number of nanospher es when\nthe higher mutlipoles can be (with a qualitative accuracy) neglected is four.\nIn [42] each of four plasmonic scatterers forming the effective ring is a planar\nL-shaped nanoparticle. In [43] these four plasmonic scatterers a re spheres.\nIt is clear that in both these design solutions the physical mechanism of the\nartificial magnetism is the same.\nNotice, that the concentration of these effective rings should be v ery high\nin order to obtain a strong resonance of permeability. Results pres ented\nin [43] correspond to almost touching nanorings. Therefore the ma gnetism\n15of such nanorings can be realized only in the anisotropic variant. The re-\nquirement of the high concentration makes a composite of randomly oriented\neffective rings of nanospheres hardly feasible (the same concerns three mutu-\nally orthogonal arrays of effective rings). The fully isotropic solutio n based\non core-shell magnetic nanoclusters [44] is probably more practica l.\n3. Conclusion\nIn this paper we have considered the problem of effective medium des crip-\ntion of nanostructures designed to emulate properties of magnet ic materials\nin the visible range. The artificial magnetic effect can be achieved due to\nspecific shapes of nanoinclusions and results from weak spatial disp ersion in\nthe composite. In general, spatial dispersion produces a variety o f effects,\nincluding resonant bianisotropy, and the artificial magnetism is only o ne of\nthem. Care should be taken in introducing effective permeability in suc h a\nway that it indeed measures the averaged magnetic polarization and can be\nused in solving boundary problems for composite samples. If the inclu sion\ngeometry is such that bianisotropic effects are allowed, appropriat e terms\nshould be added to the material relations: bianisotropic effects are usually\nstronger thanthe artificial magnetism. Except some very specific geometries,\ninduced electric quadrupoles are of the same order as magnetic mom ents and\nthey must be included in the analysis. Furthermore, not only the res ponse\nto the curl of electric field (that is, to magnetic field), but also to all other\ncombinations of the first-order spatial derivatives of electric field should be\nincluded for adequate description of the effective material proper ties. In\nother words, characterizing bulk optically dense nanostructured metamate-\nrials starts from the analysis of multipoles and bianisotropy. The insig ht\non adequate material equations for particular nanocomposite is ma ndatory\nfor physically sound characterization. Unfortunately, the effect ive medium\ntheory of weakly dispersive media is not complete at this stage, and f urther\ninvestigations arenecessary (especially inwhatconcerns boundar yconditions\nat interfaces), before we will be able to use the effective paramete rs in the\ndesign of optical devices.\nAcknowledgement\nThis work has been partially funded by the Academy of Finland throug h the\nCenter-of-Excellence program and supported by the FP7 CSA ECONAM .\n16References\n[1] M. Born and Kun Huang, Dynamic Theory of Crystal Lattices , Oxford\nPress: Oxford, 1954.\n[2] J.D. Jackson, Classical Electrodynamics, 3rd edition, New York: J. Wi-\nley and Sons, 1999\n[3] V.M. Agranovich, Y.N. Gartstein, Spatial dispersion and negative re-\nfraction of light, Physics Uspekhi ,49(2006) 10\n[4] L.D. Landau and E.M. Lifshits, Electrodynamics of Continuous Media,\n2nd edition, Oxford, England: Pergamon Press, 1984\n[5] G.Dolling,C.Enkrich, M.Wegener, C.M.Soukoulis, S.Linden, Low- loss\nnegative-index metamaterial attelecommunication wavelengths, Science\n312, 892, 2006.\n[6] T. F. Gundogdu, N. Katsarakis, M. Kafesaki, R. S. Penciu, G. Ko nstan-\ntinidis, A. Kostopoulos, E. N. Economou, andC. M. Soukoulis, Negat ive\nindex short-slab pair and continuous wires metamaterials in the far in -\nfrared regime, Opt. Express 16(2008) 9173\n[7] M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Souk oulis,\nand E. N. Economou, Left-handed metamaterials: The fishnet str ucture\nand its variations, Phys. Rev. B 75(2007) 235114\n[8] A.M. Nicolson and G.F. Ross, The measurement of the intrinsic prop -\nerties of materials by time-domain techniques, IEEE Trans. Instrum.\nMeas.,17(1968) 395\n[9] W.W. Weir, Automatic measurement of the complex dielectric const ant\nand permeability at microwave frequencies, Proc. IEEE ,62(1974) 33.\n[10] R.E. Collin, Field theory of guided waves , New York: IEEE Press, 1991\n[11] C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, a nd F. Led-\nerer, Validity of effective material parameters for optical fishnet meta-\nmaterials, Phys. Rev. B, 81(2010) 035320\n[12] S.A. Schelkunoff, H.T. Friis, Antennas: Theory and Practice , New York:\nJohn Wiley and Sons, 1952\n[13] S.A. Tretyakov, C.R. Simovski, and A.A. Sochava, The Relation be -\ntween Co-and Cross-Polarizabilities of Small Conductive Bi-Anisotro pic\nParticles, Advances in Complex Electromagnetic Materials, Priou, A.,\net al., (eds.), NATO ASI Series High Technology, Vol. 28, pp. 271-280 ,\nDordrecht, the Netherlands: Kluwer Academic Publishers, 1997.\n[14] S. Tretyakov, Analytical Modeling in Applied Electromagnetics, Nor-\nwood, MA: Artech House, 2003\n17[15] A.N. Serdyukov, I.V. Semchenko, S.A. Tretyakov, A. Sihvola, Electro-\nmagnetics of bi-anisotropic materials: Theory and applica tions,Ams-\nterdam: Gordon and Breach Science Publishers, 2001.\n[16] C.R. Simovski, Weak spatial dispersion in composite media , St. Peters-\nburg: Politekhnika, 2003 (in Russian).\n[17]Metamaterials Handook. Volume 1. Theory and phenomena of me tama-\nterials,F.Capolino, Editor, BocaRaton-London-NewYork: CRCPress,\n2009.\n[18] V.A. Podolskiy, A.K. Sarychev, and V.M. Shalaev, Plasmon modes a nd\nnegative refraction in metal nanowire composites Optics Express, 11\n(2003) 735\n[19] J. Zhou, L. Zhang, G. Tuttle, Th. Koschny and C. M. Soukoulis, Neg-\native index materials using simple short wire pairs, Phys. Rev. B 73\n(2006) 041101.\n[20] S. Linden, C. Enkrich, G. Dolling, M.W. Klein, J. Zhou, T. Koschny,\nC.M. Soukoulis, S. Burger, F. Schmidt, M. Wegener, Photonic Metam a-\nterials: Magnetism at Optical Frequencies, IEEE Journal Of Selected\nTopics In Quantum Electronics 12(2006) 1097\n[21] G. Dolling, C. Enkrich, M. Wegener, J.F. Zhou, C. M. Soukoulis, S.\nLinden, Cut-wire pairs and plate pairs as magnetic atoms for optical\nmetamaterials, Optics Lett. 30(2005) 3198.\n[22] H.-K. Yuan, U.K. Chettiar, W. Cai, A.V. Kildishev, A. Boltasseva, V .P.\nDrachev, V.M. Shalaev, A negative permeability material at red light,\nOptics Express 15(2007) 1076\n[23] V.P. Drachev, U.K. Chettiar, A.V. Kildishev, H.-K. Yuan, W. Cai, V.M .\nShalaev, The Ag dielectric function in plasmonic metamaterials, Optics\nExpress16(2008) 1186\n[24] U.K. Chettiar, S. Xiao, A.V. Kildishev, W. Cai, H.-K. Yuan, V.P.\nDrachev, and V.M. Shalaev, Optical Metamagnetism and Negative-\nIndex Metamaterials, MRS Bulletin 33(2008) 921\n[25] J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tnner mann,\nF.Lederer, andT.Pertsch, MultipoleApproachtoMetamaterials, Phys.\nRev. A78(2008) 043811\n[26] R.E. Raab and O.L. De Lange, Multipole Theory in Electromagnetism ,\nOxford: Clarendon Press, 2005\n[27] S.A. Schelkunoff, Theory of antennas of arbitrary size and sha pe,Proc.\nIRE29(1941) 493\n[28] J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J. Stewart, Magne tism\n18from conductors and enhanced nonlinear phenomena, IEEE Trans. Mi-\ncrow. Theory Tech. 47(1999) 2075\n[29] R. Marqu´ es, R. Media, R. Rafii-Edrissi, Role of bianisotropy in ne gative\npermeability and left-handed metamaterials, Phys. Rev. B 65(2002)\n144440\n[30] H. Chen, L. Ran,J. Huangfu, X.M. Zhang, K. Chen, T.M. Grzegor czyk,\nand J.A. Kong, Left-handed materials composed of only S-shaped r es-\nonators, Phys Rev E 70(2004) 057605.\n[31] K. Aydin, I. Bulu, K. Guven,M. Kafesaki, C.M. Soukoulis, E. Ozbay ,\nInvestigation of magnetic resonances for different split-ring reso nator\nparameters and designs, New J. of Physics 7(2005) 168.\n[32] B. Kante, A. de Lustrac, J.-M. Lourtioz, B. Burokur, Infrar ed cloaking\nbased on the electric response of split ring resonators, Optics Express\n16(2008) 9191\n[33] C.R. Simovski, On the averaging of induced multipoles in media with\nweak spatial dispersion, International Journal of Electronics and Com-\nmunications 54(2000) 271\n[34] S.A. Tretyakov, A.H. Sihvola, A.A. Sochava, C.R. Simovski, Magne to-\nelectric interactions in bi-anisotropic media, Journal of Electromagnetic\nWaves and Applications 12(1998) 481\n[35] C.R. Simovski, S.A. Tretyakov, A.A. Sochava, B. Sauviac, F. Mar iotte,\nT.G.Kharina, Antennamodelforconductiveomegaparticles, J. of Elec-\ntromagnetic Waves and Applications ,11(1997) 1509\n[36] A.A. Sochava, C.R. Simovski, S.A. Tretyakov, Chiral effects and eigen-\nwaves inbi-anisotropic omega structures, in: Advances in Complex Elec-\ntromagnetic Materials (Edited by A. Priou, A. Sihvola, S. Tretyakov,\nandA. Vinogradov), NATO ASISeries HighTechnology, vol. 28, Kluwe r\nAcademic Publishers: Dordrecht/Boston/London, pp. 85-102, 1 997\n[37] T.G. Kharina, S.A. Tretyakov, A.A. Sochava, C.R. Simovski, S. Bo li-\noli, Experimental studies of artificial omega media, Electromagnetics 18\n(1998) 423\n[38] N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, Thre e-\ndimensional photonic metamaterials at optical frequencies, Nature Ma-\nterials7(2008) 31\n[39] C.R. Simovski, S. He, Frequency range and explicit expressions f or neg-\native permittivity and permeability of an isotropic medium formed by a\nlattice of perfectly conducting Omega-particles, Physics Letters A 311\n(2003) 254\n19[40] E. Verney, B. Sauviac, C.R. Simovski, Isotropic Metamaterial E lectro-\nmagnetic Lens, Physics Letters A 331(2004) 244\n[41] S. Maslovski, P. Ikonen, I. Kolmakov, S. Tretyakov, and M. Ka unisto,\nArtificial magnetic materials based on the new magnetic particle: Met a-\nsolenoid, Progress in Electromagnetics Research 54(2005) 61\n[42] J. Zhou, Th. Koschny, M. Kafesaki, E.N. Economou, J.B. Pendr y, C.M.\nSoukoulis, Saturation of the magnetic response of split-ring reson ators\nat optical frequencies, Phys. Rev. Lett. 95(2005) 223902\n[43] A. Alu, A. Salandrino, N. Engheta, Negative effective permeabilit y and\nleft-handedmaterialsatopticalfrequencies, Opt. Express 14(2006)1557\n[44] C.R. Simovski, S.A. Tretyakov, Model of isotropic resonant mag netism\nin the visible range based on core-shell clusters, Phys. Rev. B 79(2009)\n045111\n20"    },    {        "title": "1003.5242v1.Temperature_effects_on_the_magnetization_of_quasi_one_dimensional_Peierls_distorted_materials.pdf",        "content": "arXiv:1003.5242v1  [cond-mat.str-el]  26 Mar 2010Temperature Effects on the Magnetization of Quasi-One-Dime nsional\nPeierls Distorted Materials\nHeron Caldas1,∗\n1Departamento de Ciˆ encias Naturais. Universidade Federal de S˜ ao Jo˜ ao del Rei,\n36301-160, S˜ ao Jo˜ ao del Rei, MG, Brazil\nIt is shown that temperature acts to disrupt the magnetizati on of Peierls distorted quasi-one-\ndimensional materials (Q1DM). The mean-field finite tempera ture phase diagram for the field theory\nmodel employed is obtained byconsidering both homogeneous and inhomogeneous condensates. The\ntricritical points of the second order transition lines of t he gap parameter and magnetization are\nexplicitly calculated. It is also shown that in the absence o f an external static magnetic field the\nmagnetization is always zero, at any temperature. As expect ed, temperature does not induce any\nmagnetization effect on Peierls distorted Q1DM.\nPACS numbers: 71.30.+h,36.20.Kd,11.10.Kk\nI. INTRODUCTION\nThe recent experimental observation of a signature of one-dimen sional (1D) transport in 30 nm wide graphene\nribbons [1] certainly motivated the theoretical investigation of 1D s ystems. A very interesting class of Q1DM are\nthe ones where a lattice distortion develops spontaneously with the appearance of a gap ∆ 0, rendering the material\nan insulator. This is the mechanism of the Peierls transition , which has been observed experimentally in various\nQ1DM. Probably, one of the most well-known Q1DM that exhibits this p henomenon is trans-polyacetylene (TPA).\nThis polymer is a 1D chain of CH groups with alternating single and double bonds, having one electron per site. In\nthe tight binding approximation, TPA would be a metal. However, the in teraction of the electrons with the lattice\n(also known as the spontaneous Peierls dimerization) is such that th e energy gain in the system is always larger that\nthe energy investment for distorting the lattice. As a consequenc e, polyacetylene is an insulator. After doping, and\nthe consequent vanishing of the gap at an experimentally measured critical doping concentration yc∼=6% [2], the\nconductivity of TPA is enormously increased, presenting metal-like p roperties [3].\nAlthough we shall refer to trans−CHxthroughout the paper, due to the large amount of data on this mat erial,\nthe main results obtained here are robust and can be applied to any Q 1DM possessing the same dimerized structure\noftrans−CHxfor which a field theory model is suitable to be employed [4, 5]. The elect ron-phonon interaction\nintrans−CHxis described by the discrete Su-Schrieffer-Heeger (SSH) Hamiltonia n [6], and its continuum version,\nthe Takayama–Lin-Liu–Maki (TLM) Hamiltonian [7]. The TLM model is a relativistic field theory with two-flavor\nDirac fermions that, with a doping equal to or greater than yc, have linear dispersion relations with a Fermi velocity\nvF≈106m/s, which is of the order of the velocity of the Dirac fermions in graphen e [8]. Employing the Gross-Neveu\n(GN) model [9], that can be properly identified with the TLM model, as a n effective field theory model for describing\nthe insulator-metal phase transition in polyacetylene [10–12], ther e has been found a very good agreement with the\nexperimental value, yc=N\nπ¯hvFaµc∼=6% [11, 12], where N(=2 for TPA) is the number of spin degrees of freedom of\nthe (delocalized) πelectrons, ¯his the Planck’s constant divided by 2 π,vF=kF¯h/m,kFis the Fermi wavenumber,\nm≡¯h2/2toa2, anda(∼=1.22˚A for TPA) is the lattice (equilibrium) spacing between the xcoordinates of successive\nCH radicals in the undimerized structure, and µc=∆0√\n2(∆0≈0.7eV for TPA) is the critical chemical potential at\nwhich the GN model undergoes a first-order phase transition to a s ymmetry restored (zero gap) phase [13].\nRegarding our choice of using a continuum model, a few comments are pertinent here. The TLM model can be\nderived from the SSH model by expanding its Hamiltonian about the Fe rmi surface and keeping terms only to lowest\norder ina/ξ, whereξ≡¯hvF/∆ is the electronic correlation length. This is fulfilled for the materials w e are interested\nin and will be described by the TLM (GN) model, for which ξ >> a. Besides, the clear advantages of employing\ncontinuum models such as the TLM (or GN) are the analytical solution s that they provide and the fact that field\ntheory methods are suitable for the calculation of the effective pot ential, which is appropriate for the analysis of the\nphase structure of the model, as in this work. On the other hand, t he disadvantages are that continuum models with\nrelativistic dispersion relations have an electronic spectrum that is u nbounded below, and that the acoustic modes\n∗Electronic address: hcaldas@ufsj.edu.br2\nare lost in the continuum limit. The first problem is resolved by adopting a certain energy cutoff, and the second, if\nonly terms to next order in a/ξare kept [3].\nIn [14] the zero temperature phase diagram of 1D TPA under asymm etric doping, defined as an imbalance between\nthe chemical potentials of the electrons with the two possible spin or ientations (“up” ≡↑, and “down” ≡↓) introduced\nin the system by the doping process, has been studied. As emphasiz ed in [14], the chemical potentials asymmetry\nbetween the ↑and↓electrons can be achieved experimentally by the actuation of an ext ernal static magnetic field B0\non the polyacetylene wire, which breaks the spin-1/2 SU(2) symmetry. In [14], the continuous model that describes\nthe electron-phonon interactions in TPA has been introduced and t he magnetization, the critical magnetic field B0,c\nat which there is a quantum phase transition to a fully polarized (magn etized) phase, and the magnetic susceptibility\nat zero temperature, within the field theory approach, have been obtained.\nIn this paper, we study the thermal effects on the magnetic prope rties of Peierls distorted Q1DM and verify the\npossibility of the existence of this fully polarized phase at finite tempe rature. The mean-field finite temperature phase\ndiagram for the field theory model employed is obtained. The tricritic al points of the second-order transition curves of\nthe gap parameter and magnetization are explicitly calculated by con sidering both homogeneous and inhomogeneous\n∆(x) condensates. One of the main results of this paper is the demonst ration of the “stationarity” of the tricritical\npoint ofthe second-ordertransitionline ofthe gap parameterund er the the influence of an external (constant) Zeeman\nmagnetic field. In other words, in a Peierls distorted Q1DM under the influence of an external Zeeman magnetic field,\nthe tricritical point obtained consideringhomogeneouscondensat es remains at the same location when inhomogeneous\n∆(x) condensates are taken into account.\nThe paper is organized as follows. In Section II we introduce the mod el Lagrangian describing polyacetylene. In\nSection III the temperature dependent renormalized effective po tential is presented. In this section we obtain an\nanalytical expression for the effective potential at high temperat ure, as well as the chemical potentials dependent gap\nequation and the critical temperature at which the gap vanishes. B esides this, the tricritical points of the second-\norder transition lines of the gap parameter and magnetization are e xplicitly calculated. The temperature dependent\nmagnetic properties of Peierls distorted Q1DM are also obtained in th is section. In the Summary we present the\nconclusions.\nII. MODEL LAGRANGIAN\nFor the benefit of the reader, let us reproduce from [14] the mod el Lagrangian and the basic definitions necessary\nto describe polyacetylene and equivalent Peierls distorted Q1DM. As we mentioned already, the electron-phonon\ninteraction in TPA is represented by the SSH model [6], which has a co ntinuum version known as the TLM model [7].\nThe TLM Lagrangian density in the adiabatic approximation (consider ing static configurations for which ∂∆/∂t= 0)\nis given by\nLTLM=N/summationdisplay\nj=1ψj†(i¯h∂t−i¯hvFγ5∂x−γ0∆(x))ψj−1\n2π¯hvFλTLM∆2(x), (1)\nwhereψis a two component Dirac spinor ψj=/parenleftbigg\nψj\nL\nψj\nR/parenrightbigg\n, representing the “left moving” and “right moving” electrons\nclose to their Fermi energy, respectively, and jis an internal symmetry index (spin) that determines the effective\ndegeneracy of the fermions. We define 1 = ↑, and 2 = ↓. The gamma matrices are given in terms of the Pauli matrices,\nasγ0=σ1,γ5=−σ3, and ∆(x) is a (real) gap related to lattice vibrations. λTLM=2α2\nπt0Kis a dimensionless\ncoupling, where αis theπ-electron-phonon coupling constant of the original SSH Hamiltonian , andKis the elastic\nchain deformation constant. The equivalence between the TLM and the Gross-Neveu (GN) model [9], is established\nby settingλTLM=λGN\nNπ. Note that the electron-phonon interaction term in Eq. (1) is an an alog of the fermion-\nboson interaction in the field theory context, which appears in differ ent models and dimensions. In four space-time\ndimensions, for example, this interaction has been investigated in th e framework of the linear sigma model at finite\ntemperature [15].\nThe GN model has been investigated earlier at finite temperature an d density several times (see for instance\nRefs.[13,16,17]), andrecentlyconsideringalsofinitecorrections totheleadingorderinthelarge Napproximation[12].\nHowever, these approximations did not consider the effects of an e xternal Zeeman magnetic field applied on the\nsystem, which is of fundamental importance in many physical situat ions, as in the investigation of metal-insulator\ntransitions [18] and magnetization in 2D electron systems [19].\nInordertoconsidertheapplicationofanexternalZeemanmagnet icfieldtothesystemanditseffects, itisconvenient\nto start by writing the grand canonical partition function associat ed withLGN,3\nZ=/integraldisplay\nD¯ψDψ exp/braceleftBigg/integraldisplayβ\n0dτ/integraldisplay\ndx[LGN]/bracerightBigg\n, (2)\nwhere¯ψ≡ψ†γ0,β= 1/kBT,kBis the Boltzmann constant, and LGNis the Euclidean GN Lagrangian density:\nLGN=/summationdisplay\nj=1,2¯ψj[−γ0¯h∂τ+i¯hvFγ1∂x−∆(x)+γ0µj]ψj−1\n¯hvFλGN∆2(x), (3)\nwhereµ↑= ¯µ+δµ,µ↓= ¯µ−δµ. The Zeeman splitting energy is given by ∆ E=SzgµBB0[20], where Sz=±1/2,g\nis the effective g-factor and µB=e¯h/2m≈5.788×10−5eV T−1is the Bohr magneton, giving δµ=g\n2µBB0. In [14]\nwe also have chosen ¯ µ=µc.\nIntegrating over the fermion fields leads to\nZ=exp/braceleftbigg\n−β\n¯hvFλGN/integraldisplay\ndx∆2(x)/bracerightbigg\nΠ2\nj=1detDj, (4)\nwhereDj=−γ0∂τ+i¯hvFγ1∂x+γ0µj−∆(x) is the Dirac operator at finite temperature and density. Since ∆( x)\nis static, we can transform Djto theωnplane, where ωn= (2n+1)πTare the Matsubara frequencies for fermions,\nyieldingDj= (−iωn+µj)γ0+i¯hvFγ1∂x−∆(x). After using an elementary identity ln( det(Dj)) = Trln(Dj), one\ncan define the bare effective action for the static ∆( x) condensate\nSeff[∆] =−β\n¯hvFλGN/integraldisplay\ndx∆2(x)+2/summationdisplay\nj=1Trln(Dj), (5)\nwhere the trace is to be taken over both Dirac and functional indice s. The condition to find the stationary points of\nSeff[∆] reads\nδSeff[∆]\nδ∆(x)= 0 =−2β\n¯hvFλGN∆(x)+δ\nδ∆(x)\n2/summationdisplay\nj=1Trln(Dj)\n. (6)\nThe equation above is a complicated and generally unknown functiona l equation for ∆( x), whose solution has been\ninvestigated at various times in the literature [21–26]. Its solution is not only of academic interest, but has direct\napplication in condensed matter physics as, for example, in [3, 25], a nd in the present work.\nIII. THE RENORMALIZED EFFECTIVE POTENTIAL AT FINITE TEMPER ATURE\nA. Homogeneous ∆(x)Condensates\nFor a constant ∆ field the Dirac operator reads Dj= (−iωn+µj)γ0+i¯hvFγ1p−∆, so the trace in Eq. (5) can\nbe evaluated in a closed form for the asymmetrical ( δµ/negationslash= 0) system [14]. From Eq. (4) one obtains the “effective”\npotentialVeff=−kBT\nLlnZ, whereLis the length of the system:\nVeff(∆,µ↑,↓,T) =1\n¯hvFλGN∆2−kBT/integraldisplay+∞\n−∞dp\n2π¯h/bracketleftBig\n2βEp+ln/parenleftBig\n1+e−βE+\n↑/parenrightBig\n+ln/parenleftBig\n1+e−βE−\n↑/parenrightBig\n(7)\n+ ln/parenleftBig\n1+e−βE+\n↓/parenrightBig\n+ln/parenleftBig\n1+e−βE−\n↓/parenrightBig/bracketrightBig\n,\nwhereE±\n↑,↓≡Ep±µ↑,↓,Ep=/radicalbig\nv2\nFp2+∆2.\nThe first term in the integration in p, corresponding to the vacuum part ( µ↑,↓=T= 0), is divergent. Introducing\na momentum cutoff Λ to regulate this part of Veff, we obtain, after renormalization, a finite effective potential4\nVeff(∆) =∆2\n¯hvF/parenleftbigg1\nλGN−3\n2π/parenrightbigg\n+∆2\nπ¯hvFln/parenleftbigg∆\nmF/parenrightbigg\n, (8)\nwheremFis an arbitrary renormalization scale, with dimension of energy. The m inimization of Veff(∆) with respect\nto ∆ gives the well-known result for the non-trivial gap [9]:\n∆0=mFe1−π\nλGN. (9)\nFrom this gap equation we see that with the experimentally measured ∆0andα,t0andKwhich enters λTLM, one\nsets the value of mF. Equation (8) can be expressed in a more convenient form in terms o f ∆0as\nVeff(∆) =∆2\n2π¯hvF/bracketleftbigg\nln/parenleftbigg∆2\n∆2\n0/parenrightbigg\n−1/bracketrightbigg\n, (10)\nwhich is clearly symmetric under ∆ → −∆, which generates the discrete chiral symmetry of the GN model. A s has\nbeen pointed out before [21], this discrete symmetry is dynamically b roken by the non-perturbative vacuum, and thus\nthere is a kink solution interpolating between the two degenerate min ima ∆ = ±∆0of (10) atx=±∞:\n∆(x) = ∆0tanh(∆ 0x). (11)\nIn the next subsection we discuss the effects of space dependent ∆(x) condensates.\nWe can rewrite Veff(∆,µ↑,↓,T) as\nVeff(∆,µ↑,↓,T) =Veff(∆)+Veff(µ↑,↓,T), (12)\nwhere\nVeff(µ↑,↓,T) =−kBT/integraldisplay∞\n0dp\nπ¯h/bracketleftBig\nln/parenleftBig\n1+e−βE+\n↑/parenrightBig\n+ln/parenleftBig\n1+e−βE−\n↑/parenrightBig\n+ln/parenleftBig\n1+e−βE+\n↓/parenrightBig\n+ln/parenleftBig\n1+e−βE−\n↓/parenrightBig/bracketrightBig\n.(13)\nSince we can not calculate expression (13) in a closed form, we shall u se a high temperature expansion to evaluate it.\nUsing the function\nI(a,b) =/integraldisplay∞\n0dx/bracketleftBig\nln/parenleftBig\n1+e−√\nx2+a2−b/parenrightBig\n+ln/parenleftBig\n1+e−√\nx2+a2+b/parenrightBig/bracketrightBig\n, (14)\nwherea= ∆/kBT, andb=µ/kBT, which can be expanded in the high temperature limit, a <<1 andb <<1,\nyielding, up to order a4andb2[27],\nI(a<<1,b<<1) =π2\n6+b2\n2−a2\n2ln/parenleftBigπ\na/parenrightBig\n−a2\n4(1−γE)−7ξ(3)\n8π2a2/parenleftbigg\nb2+a2\n4/parenrightbigg\n+186ξ(5)\n128π4b2a4+O/parenleftbig\na2b4/parenrightbig\n,(15)\nwhereγE≈0.577...is the Euler constant and ξ(n) is the Riemann zeta function, having the values ξ(3)≈1.202, and\nξ(5)≈1.037. With the equation above, together with Eq. (8), the high temp erature asymmetrical effective potential\nis written as\nVeff(∆,µ↑,↓,T)≡Veff=∆2\nπ¯hvF/bracketleftbigg\nln/parenleftbiggπkBT\n∆0/parenrightbigg\n−γE/bracketrightbigg\n−π\n3¯hvF(kBT)2(16)\n−1\n2π¯hvF/bracketleftbigg\nµ2\n↑+µ2\n↓−7ξ(3)\n8π2∆4\n(kBT)2−7ξ(3)\n4π2(µ2\n↑+µ2\n↓)∆2\n(kBT)2+186ξ(5)\n64π4(µ2\n↑+µ2\n↓)∆4\n(kBT)4/bracketrightbigg\n.\nThe equation above may be rearranged in the form of a Ginzburg-La ndau (GL) expansion of the grand potential\ndensity, which is appropriate to the analysis of the phase diagram in t he region near the tricritical point,5\nVeff=α0+α2∆2+α4∆4, (17)\nwhere\nα0(µ↑,↓,T) =−1\n2π¯hvF/bracketleftbig\nµ2\n↑+µ2\n↓/bracketrightbig\n−π\n3¯hvF(kBT)2, (18)\nα2(µ↑,↓,T) =1\nπ¯hvF/bracketleftBigg\nln/parenleftbiggπkBT\neγE∆0/parenrightbigg\n+7ξ(3)\n8π2(µ2\n↑+µ2\n↓)\n(kBT)2/bracketrightBigg\n,\nα4(µ↑,↓,T) =−1\n32π3¯hvF(kBT)2/bracketleftBigg\n−14ξ(3)+186ξ(5)\n4π2(µ2\n↑+µ2\n↓)\n(kBT)2/bracketrightBigg\n. (19)\nExtremizing Veffwe find the trivial solution (∆ = 0) and the chemical potential and tem perature dependent gap\nequation\n∆(µ↑,↓,T)2=−α2\n2α4, (20)\nwhich has meaning only if the ratioα2\nα4is negative. Besides, a stable configuration (i.e., bounded from below ) requires,\nup to this order, α4>0. At the minimum Veffreads\nVeff,min=α0−α2\n2\n4α4. (21)\nThe critical temperature Tcis, by definition, the temperature at which the gap vanishes. Thus, atTcwe have\nα2= 0 or\nln/parenleftbiggπkBTc\neγE∆0/parenrightbigg\n+7ξ(3)\n8π2(µ2\n↑+µ2\n↓)\n(kBTc)2= 0, (22)\nwhereTc=Tc(µ↑,µ↓). Aswillbecomeclearbelow, theequationabovedefinesasecond-o rdertransitionlineseparating\nthe non-metallic (∆ /negationslash= 0) and metallic phases (∆ = 0). At µ↑=µ↓= 0, we recover the well-known result for the\ntemperature at which the discrete chiral symmetry is restored [28 ]:\nTc(µ↑=µ↓= 0)≡Tc(0) =eγE\nπ∆0\nkB. (23)\nIn order to find Tc(µ↑,µ↓) we define dimensionless variables η=7ξ(3)\n8π2(µ2\n↑+µ2\n↓)\n(kBTc(0))2andt=T\nTc(0), and with the help of\nEq. (23) we rewrite the L.H.S. of Eq.(22) as\ny(t) = ln(t)+η\nt2. (24)\nThe zeros of y(t) for a given η, i.e., for a given µ2\n↑+µ2\n↓, are the respective Tc. This defines the (second-order) Tcversus\nµ2\n↑+µ2\n↓phase diagram. As can be seen in Fig. 1, the graphical analysis of y(t) shows that there is no solution for this\nfunction for ηabove certain value, that we define ηtc. Besides, at ηtcwe havey=y′= 0. These two equations give\nttcandηtcfor the tricritical point Ptc= (ηtc,ttc). Strictly speaking, yandy′are associated with the coefficients of\nthe second-order and forth-order terms of the effective poten tial expanded in powers of ∆ [29]. Solving the equations\ny= 0 andy′= 0 self-consistently (which is equivalent to solve α2=α4= 0), we obtain\nηtc=7ξ(3)\n8π2(µ2\n↑+µ2\n↓)tc\n(kBTc(0))2=1\n2e, t tc=Ttc\nTc(0)=/radicalbig\n2ηtc=1√e. (25)6\nForηabovecertainvalue and less than ηtc, the function ypresentstwo solutions(not shown in Fig. 1) for Tc. However,\nthe lower of these always corresponds to unstable solutions. The s econd-order transition curve, defined as the line\nstarting at the point (0 ,Tc(0)) and ending at the point (( µ2\n↑+µ2\n↓)tc,Ttc), comes simply from the solution of the\ngap equation. This curve, shown in Fig. 2, represents a system at fi nite temperature where the chemical potentials\nµ2\n↑+µ2\n↓= 2(¯µ2+δµ2) start from zero and increases until ( µ2\n↑+µ2\n↓)tc. Note that ¯ µ2+δµ2is zero if and only if ¯ µ2\nandδµ2are both zero. It is well known that below the tricritical point one ha s to properly minimize the effective\npotential rather than using the gap equation as the transition bec omes first order. Thus Eq. (22) cannot be used for\nfindingTcbelowPtcsince this equation is valid only for the second-order transition. In t his caseTchas to be find\nnumerically, through the equality Veff(µ↑,µ↓,∆ = ∆ min,Tc) =Veff(µ↑,µ↓,∆ = 0,Tc), where ∆ minis the non-trivial\nminimum of Veff.\nFIG. 1: The function y(t), as a function of t=T\nTc(0), for different values of η. The bottom curve is for η= 0.01, the second\ncurve is for η=ηtc=1\n2e≈0.184, and the top curve (with no solution) is for η= 0.4.\nThe number densities n↑,↓=−∂\n∂µ↑,↓Veff(∆,µ↑,↓,T) read\nn↑,↓=/integraldisplay∞\n0dp\nπ¯h/bracketleftBig\nnk(E−\n↑,↓)−nk(E+\n↑,↓)/bracketrightBig\n, (26)\nwherenk(E+,−\n↑,↓) =1\neβE+,−\n↑,↓+1is the Fermi distribution function. The density difference\nδn=n↑−n↓ (27)\nis zero ifδµ=g\n2µBB0= 0, at any temperature, since in this case we have the equalities nk(E+\n↑) =nk(E+\n↓), and\nnk(E−\n↑) =nk(E−\n↓). The physical meaning of these results is that at zero external Z eeman magnetic field, the ↑(up)\nand↓(down) electrons of the conduction (+) band have the same densit y, and the same for the electrons of the\nvalence ( −) band.\nIn the high temperature regime, the number densities are given by\nn↑,↓(T) =1\nπ¯hvF/bracketleftbigg\n1−7ξ(3)\n4π2∆2\n(kBT)2/bracketrightbigg\nµ↑,↓. (28)7\nFIG. 2: The phase diagram t=T\nTc(0)as a function of η=7ξ(3)\n8π2(µ2\n↑+µ2\n↓)\n(kBTc(0))2, from Eq. (22). The small dot at the end of the\nsecond order transition line represents the tricritical po intPtc= (1\n2e,1√e). Below this point the transition is of first order.\nIn the high temperature limit the total number density, nT(T) =n↑(T)+n↓(T), is independent of the applied field\nnT(T) =2\nπ¯hvF/bracketleftbigg\n1−7ξ(3)\n4π2∆2\n(kBT)2/bracketrightbigg\n¯µ, (29)\nand for the density difference we obtain\nδnhigh T(T,δµ) =2\nπ¯hvF/bracketleftbigg\n1−7ξ(3)\n4π2∆2\n(kBT)2/bracketrightbigg\nδµ, (30)\nthat, as we have observed before, is clearly zero if B0=δµ= 0. Since the densities have to be evaluated at the\nminimum of the effective potential, we use Eq. (20) in the equation abo ve and find the temperatures at which the\ndensities and, consequently, the density difference vanish. These temperatures are the solutions of\nγE−1\n2+ln/parenleftbigg∆0\nπkBT∗c/parenrightbigg\n−7ξ(3)\n8π2(µ2\n↑+µ2\n↓)\n(kBT∗c)2= 0, (31)\nwhereT∗\nc=T∗\nc(µ↑,µ↓). As for the gap parameter, the equation above defines the seco nd-order line for the densities\nand the density imbalance. At µ↑=µ↓= 0, we get\nT∗\nc(µ↑=µ↓= 0)≡T∗\nc(0) =eγE−1\n2\nπ∆0\nkB. (32)\nIt is very easy to see that T∗\nc(0) =Tc(0)√e, which coincides with Ttc, whereTtcis given by Eq. (25). Proceeding as\nbefore we find\nη∗\ntc=7ξ(3)\n8π2(µ2\n↑+µ2\n↓)tc\n(kBT∗c(0))2=1\n2e2, t∗\ntc=T∗\ntc\nT∗c(0)=/radicalbig\n2η∗\ntc=1\ne, (33)8\ndefining the tricritical point for the densities, total density and de nsity imbalance second order curves.\nLet us nowverify the possibility of afully polarized state at finite temp erature. It wouldbe possible with a magnetic\nfield with a intensity such that n↓in Eq. (28) vanishes. In this case µ↓= ¯µ−δµc=µc−g\n2µBB0,c= 0, or\nB0,c=2µc\ngµB, (34)\nyielding, for TPA (for which µc=∆0√\n2andg≈2) a critical magnetic field\nB0,c≈8.6 kT, (35)\nwhich is, as the critical magnetic field found in [14] at zero temperatu re (≈4.6 kT), a magnetic field of very high\nmagnitude, compared to the maximum current laboratory values [3 0].\nB. Inhomogeneous ∆(x)Condensates\nSince we consider the addition of a chemical potential (i.e., doping) in t he theory representing Peierls distorted\nQ1DM, and the effects of a Zeeman magnetic field on these materials, some important remarks are in order. It\nis well-known that doping in conducting polymers with degenerate gro und states results in lattice deformation, or\nnon-linear excitations, such as kink solitons and polarons, meaning t hat ∆(x) can vary in space [3, 31, 32]. Therefore,\none may expect not only homogeneous-like configurations (as cons idered in the previous subsection), but also that\nthe inclusion of these excitations in any theoretical calculation in this model should be considered. In this context,\nwithin the GN field theory model that we are considering, by taking int o account kink-like configurations in the large\nNapproximation, the authors of Refs. [23–26] found evidence for a crystalline phase that shows up in the extreme\nT∼0 and large µpart of the phase diagram, while the other extreme of the phase dia gram, for large Tand smallµ,\nseemed to remain identical to the usual large Nresults for the critical temperature and tricritical points, which a re\nwell-known results [13] for the GN model.\nTo take into account the effects of inhomogeneousconfigurations in the GL expansionof the grandpotential density,\nlet us write Eq. (17) in terms of ∆( x) and its derivatives up to α4[23–26]:\nVeff(x) =α0+α2∆(x)2+α4[∆(x)4+∆(x)′2], (36)\nwhere ∆(x)′≡d∆(x)/dx. A straightforwardvariational calculation gives the following condit ion for the minimization\nof the free energy E=/integraltext\nVeff(x)dx:\n∆(x)′′−2∆(x)3−α2\nα4∆(x) = 0. (37)\nThe general solution of an equation of the form\n∆(x)′′−2∆(x)3+(1+ν)∆2\n0∆(x) = 0, (38)\ncan be written as [26]\n∆(x) = ∆0√νsn(∆0x;ν), (39)\nwhere sn is the Jacobi elliptic function with the real elliptic parameter 0≤ν≤1. The sn function has period 2 K(ν),\nwhereK(ν)≡/integraltextπ/2\n0[1−νsin2(t)]−1/2dtis the complete elliptic integral of first kind. ∆( x) in (39) represents an array\nof real kinks. When ν= 1 Eq. (39) is reduced to the single kink condensate given in Eq. (11) . By comparing Eqs. (37)\nand (38) one can identify the scale parameter ∆ 0as\n∆2\n0=/parenleftbigg\n−α2\nα4/parenrightbigg/parenleftbigg1\n1+ν/parenrightbigg\n. (40)9\nGiven that1\n1+ν>0, the solution for inhomogeneous condensates has physical mean ing only if the ratioα2\nα4is negative,\nas in the case of homogeneous condensates. In terms of Eq. (39) it can be shown that the xdependent grand potential\ndensity can be written as\nVeff(x) =α0+α2∆(x)2+α41\n3/bracketleftbig\n(1+ν)∆2\n0∆(x)2+ν∆4\n0/bracketrightbig\n. (41)\nAveraging over one period, it is found [26] that <∆(x)2>=/parenleftBig\n1−E(ν)\nK(ν)/parenrightBig\n∆2\n0, whereE(ν) is the complete elliptic\nintegral of second kind. The ratio E(ν)/K(ν) is a smooth function of νinterpolating monotonically between 0 and 1.\nThus we can write\n<Veff(x)>=α0+A2∆2\n0+A4∆4\n0, (42)\nwhere\nA2=α2/parenleftbigg\n1−E(ν)\nK(ν)/parenrightbigg\n, (43)\nA4=α41\n3/bracketleftbigg\nν+(1+ν)/parenleftbigg\n1−E(ν)\nK(ν)/parenrightbigg/bracketrightbigg\n.\nThe interesting results obtained considering inhomogeneous conde nsates are:\n(1.) Forν= 1,E(ν=1)\nK(ν=1)= 0, so the grand potential density is that of the homogeneous cas e, Eq. (17), at the\nnon-trivial minimum.\n(2.) Forν= 0,E(ν=0)\nK(ν=0)= 1, so the grand potential density is that of the metallic phase, for which ∆ = 0 and\nVeff=α0.\n(3.) The tricritical point is still found for α2=α4= 0. These coefficients are µ↑,↓andTdependent and were not\naffected by the space dependence of the condensate ∆( x). Then the location of the tricritical point in a Peierls\ndistorted Q1DM under the influence of an external Zeeman magnet ic field is unaltered even considering a xdependent\ngrand potential density. This happens because in the high tempera ture limit the influence of the Zeeman field is not\nsufficient to change the position of the tricritical point. This same co nclusion has been obtained for the symmetric\ncase (δµ=B0= 0) [23–26].\nC. Magnetic Properties\nThe Pauli magnetization of the chain in the high temperature limit has t he following expression:\nMhigh T(T) =µBδnhigh T(T) =2µB\nπ¯hvF/bracketleftbigg\n1−7ξ(3)\n4π2∆2\n(kBT)2/bracketrightbigg\nδµ\n=2gµ2\nB\nπ¯hvF/bracketleftBigg\nln/parenleftbiggT\nT∗c(0)/parenrightbigg\n+7ξ(3)\n8π2(µ2\n↑+µ2\n↓)\n(kBT)2/bracketrightBigg\nB0, (44)\nwhere we have made use of Eq. (20) to leading order in(µ2\n↑+µ2\n↓)\n(kBT)2. The second-order line where the magnetization\nvanishes is the same as the one given by Eq. (31). Finally, we obtain th e magnetic susceptibility in this regime\nχhigh T(T) =∂Mhigh T(T)\n∂B0=χ(0)+χ(T), (45)\nwhere\nχ(0) =gµ2\nB\nπ¯hvF, (46)10\nand\nχ(T) =2gµ2\nB\nπ¯hvF/bracketleftbigg\nln/parenleftbiggT\nTc(0)/parenrightbigg\n+7ξ(3)\n4π2(kBT)2/parenleftbigg\n¯µ2+3\n4g2µ2\nBB2\n0/parenrightbigg/bracketrightbigg\n. (47)\nχ(0) is the well known zero temperature contribution for the Pauli e xpression of the magnetic susceptibility for nonin-\nteractingelectrons. The function χhigh T(T)alsobehavesat finite temperature asthe densities and the magne tization,\nwith a second-order transition up to a tricritical point given by Eq. ( 33). Below this point the transition is again of\nfirst order.\nNote that in spite of the fully polarization, at B0,cthe magnetization is given by exactly the same expression shown\nin Eq. (44). With the help of Eq. (28) we find:\nMhigh T,c(T) =µBn↑(T) =µB\nπ¯hvF/bracketleftbigg\n1−7ξ(3)\n4π2∆2\n(kBT)2/bracketrightbigg\n(µc+δµc)\n=2gµ2\nB\nπ¯hvF/bracketleftBigg\nln/parenleftbiggT\nT∗c(0)/parenrightbigg\n+7ξ(3)\n8π2(µ2\n↑+µ2\n↓)\n(kBT)2/bracketrightBigg\nB0,c. (48)\nThis shows that this function is indeed continuous for 0 ≤B0≤B0,c.\nIV. SUMMARY\nWe have investigated the mean-field finite temperature phase diagr am of Q1DM under the influence of an external\nZeeman magnetic field. We found that the gap parameter and the ma gnetization (as well as the densities and\ndensity imbalance, and the magnetic susceptibility) of asymmetrically doped Q1DM have a similar second-order\nbehavior until their respective tricritical points are reached. Belo w these points the transitions are of first order.\nWe found these two tricritical points analytically. He have shown tha t the location of the tricritical point in the\nt/parenleftBig\n=T\nTc(0)/parenrightBig\nversusη/parenleftBig\n=7ξ(3)\n8π2(µ2\n↑+µ2\n↓)\n(kBTc(0))2/parenrightBig\nphase diagram stays at the same place by considering both homogen eous\nand inhomogeneous condensates, as occur in symmetric δµ=B0= 0 systems [23–26]. We have shown that for\nthe particular case of TPA, in order to have a fully polarized organic c onductor at finite temperature it would be\nnecessary to have a very high critical magnetic field, namely B0,c. However, for a given magnetic field below B0,c,\npartial polarizations (magnetizations) can be realized experimenta lly, provided the temperatures are kept outside the\n“non−metallic” region of Fig. 2. It is worth noting that, according to Eq. (34), fo r other 1D systems with a smaller\ncritical chemical potential or with a greater effective g-factor, a smaller (attainable) critical magnetic field necessary\nfor a fully polarization of the Q1DM would be found. As a final remark, it would also be very interesting to study the\ntransport properties of the asymmetrically doped Peierls distorte d Q1DM at zero and finite temperature, employing\nthe field theory approach. We intent to address these topics elsew here.\nV. ACKNOWLEDGMENTS\nThe author acknowledges partial support by the Brazilian funding a gencies CNPq and FAPEMIG. I am grateful to\nA. L. Mota and R. O. Ramos for stimulating conversations.\n[1] Yu-Ming Lin, V. Perebeinos, Z. Chen, and P. Avouris, Phys . Rev. B 78, 161409, (2008).\n[2] J. Chen, T. -C. Chung, F. Moraes and A. J. Heeger, Solid Sta te Commun. 53, 757 (1985); F. Moraes, J. Chen, T. -C.\nChung and A. J. Heeger, Synth. Met. 11, 271 (1985).\n[3] A. J. Heeger, S. Kivelson, J. R. Schrieffer and W. P. Su, Rev . Mod. Phys. 60, 781 (1988).\n[4] David K. Campbell, Synth. Met. 125, 117 (2002).\n[5] A. Zee Quantum Field Theory in a Nutshell , Chapter V. 5, Princeton University Press, New Jersey, (2003).\n[6] W. P. Su, J. R. Schrieffer and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979); Phys. Rev. B 22, 2099 (1980).\n[7] H. Takayama, Y.R. Lin-Liu and K. Maki, Phys. Rev B 21, 2388 (1980).11\n[8] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. K atsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A.\nFirsov, Nature 438, 197 (2005); R. S. Deacon, K-C. Chuang, R. J. Nicholas, K. S. N ovoselov, and A. K. Geim, Phys. Rev.\nB76, 081406(R) (2007).\n[9] D. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974).\n[10] S. A. Brazoviskii and N. N. Kirove, JETP Lett. 33, 4 (1981); Pis’ma ZhETF 33, 6 (1981); D. K. Campbell and A. R.\nBishop, Phys. Rev. B24, 4859 (1981); Nucl. Phys. B200, 297 (1982).\n[11] A. Chodos and H. Minakata, Phys. Lett. A191, 39 (1994); Nucl. Phys. B490, 687 (1997).\n[12] H. Caldas, J.-L. Kneur, M. B. Pinto and R. O. Ramos, Phys. Rev.B 77, 205109 (2008).\n[13] U. Wolff, Phys. Lett. B157, 303 (1985).\n[14] H. Caldas, Nucl. Phys. B 807, 651 (2009); H. Caldas, Physica B 404, 3159 (2009).\n[15] H. Caldas, Nucl. Phys. B 623, 503 (2002).\n[16] T. F. Treml, Phys. Rev. D 39, 679 (1989).\n[17] K. G. Klimenko, Theor. Math. Phys. 75, 487 (1988).\n[18] P. J. H. Denteneer and R. T. Scalettar, Phys. Rev. Lett. 90, 246401 (2003), and references therein.\n[19] H. Caldas and R. O. Ramos, Phys. Rev. B 80, 115428 (2009).\n[20] C. Kittel, Introduction to Solid State Physics , sixth ed., John Wiley & Sons, New York, (1986).\n[21] R. F. Dashen, B. Hasslacher and A. Neveu, Phys. Rev. D 12, 2443 (1975).\n[22] J. Feinberg, Ann. Phys. 309, 166 (2004), and references therein.\n[23] O. Schnetz, M. Thies and K. Urlichs, Ann. Phys. (NY) 314, 425 (2004).\n[24] M. Thies and K. Urlichs, Phys. Rev. D 72, 105008 (2005).\n[25] M. Thies, J. Phys. A39, 12707 (2006).\n[26] G. Basar, G. v. Dunne, and M. Thies, Phys. Rev. D 79, 105012 (2009).\n[27] J.-L. Kneur, M. B. Pinto, R. O. Ramos, Phys. Rev. D 74125020 (2006), and references therein.\n[28] L. Jacobs, Phys. Rev. D 10, 3956 (1974); B. Harrington and A. Yildiz, Phys. Rev. D 11, 779 (1975).\n[29] H. Caldas and A. L. Mota, JSTAT, P08013 (2008).\n[30] S Hansel, H -U Muller, T. T. Anh, B. Richter, H. Rossmann a nd M von Ortenberg, Journal of Physics: Conference Series\n51, 639 (2006).\n[31] B. Horovitz, Solid State Comm. 34, 61 (1980).\n[32] J. A. Krumhansl, B. Horovitz, A. J. Heeger, Solid State C omm. 34, 945 (1980)."    },    {        "title": "1004.0972v1.Frontiers_of_Condensed_Matter_Physics_Explored_with_High_Field_Specific_Heat.pdf",        "content": "1\nFrontiers of Condensed Matter Physics Ex plored with High-Field Specific Heat \nMarcelo Jaime \nMPA-CMMS, Los Alamos National Labor atory, Los Alamos, NM 87545, USA.  \n \nAbstract \nProduction of very high magnetic fields in the laboratory has rele ntlessly increased in \nquantity and quality over the last five decades, and a shift occurred from research focused in \nmagnet technology to studies of the fundamental physics of novel materials in high fields. New \nstrategies designed to understand microscopic mech anisms at play in materials surfaced, with \nmethods to extract fundamental energy scales  and thermodynamic properties from thermal \nprobes up to 60 tesla. Here we summarize developmen ts in the area of specific heat of materials \nin high magnetic fields, with focus in the or iginal study of the K ondo Insulator system Ce 3Bi4Pt3. \n KEYWORDS\n: Specific Heat, Magnetocaloric Eff ect, High Magnetic Fields, Correlated \nElectron Systems, Quantum Magnets. \n \n \n1. Introduction \n  One of the most remarkable features of the present times, from the standpoint of the \nbalance between basic science and technology applic ations, is that while magnetic materials and \nmagnetism have central roles in a large part of our life, ubiquitous to motor generators, \ntransportation, electr onic devices, medical diagnostics tool s, and industrial pr ocesses of many \nsorts, we have yet to fully understand the origin  of magnetism and the consequences of a strong \ninterplay between magnetic, charge and lattice de grees of freedom in materials. High magnetic \nfields are instrumental to tackle this challeng e. Indeed, the effect of high magnetic fields on \nmaterials includes favoring exotic magnetic states  in detriment of non-magnetic ones, inducing \nchanges in electronic band structure throu gh manipulation of sp in-orbit coupling and 2\nmagnetostriction, suppression of superconductivit y, inducing metal-insulator phase transitions, \ndriving charge and spin excitations through di mensional crossovers and quantum limits, tilting \nthe balance between competing ground-states, and tuning quantum  fluctuations near quantum \ncritical points, among a number of other effects.  A handful of experimental techniques have \nhistorically been the tools-of-choi ce for the study of these phenomena, i.e. mostly conventional \nand quantum Hall effect, magnetoresistance, magnetization, ESR/EPR, de Haas-van Alphen \neffect, Suvnikov-de Haas effect, and NMR. Howeve r, thermal properties remained largely out of \nthe radar screen of experimentalists due to some significant technical obstacles, such as reliable \nthermometry in high fields and fast varying magnetic  fields during experiments. In this work we \nsummarize our strategy to overcome technical obstac les and achieve some degree of maturity in \nthe field of measurement of thermal properties and specific heat in magnetic fields to 60 tesla. \nWe have done so by removing some low-temp erature-physics experi mental taboos, and by \nshedding light on poorly understood thermal processe s. During this quest we benefited from the \ntalent of numerous material scientists that produced samples of extraordinary quality and fascinating physics. In many of the case studies, a significant theo retical effort served as the \nintellectual driving force for progres s, with solid interpretations a nd encouraging predictions.     \n \n2. Specific heat at high magn etic fields: a brief recount \n Specific heat at constant pressure (C\np) measurements in elements and compounds has \nbeen used for more than half a century to und erstand their properties, approximately since the \ntime when Brown, Zemansky and Boorse1) first measured the low temperature C p(T) of the \nsuperconducting and field-induced normal states of pure Niobium down to T = 2K, in a magnetic \nfield of 6000 gauss. This development was, not su rprisingly, tied to the serendipitous discovery \nof negligible magnetoresistance in what would b ecome the thermometry of choice for decades to \ncome: radio carbon resistors (also known as carbon-glass ) manufactured by Allen-Bradley Co. \nWhile there are probably thousands of publications of specific heat in the presence of man-made \nmagnetic fields, a comprehensive discussion of all contributions is both impossible and out of the \nscope of this work. Having said so, a quick bibl iographic search indicates that by 1958 standard \nmagnetic fields available increased to 10,000 gauss2), and soon were cranked up to 70,000 gauss \nto study the robust superconducting state in V 3Ga, when Morin et al. estimated that fields as high 3\nas 300,000 gauss (30 tesla) were necessary to completely suppress s uperconductivity in V 3Ga3), a \ndevelopment that would take several decades. As  a matter of fact, as late as 1980 standard \nlaboratory fields achieved with s uperconducting coils remained close to  10 tesla, as discussed for \ninstance by Ikeda and Gschneidner4) among others. By these times the calorimetry methods of \nchoice were the adiabatic method2) or heat-pulse5) method with relatively large samples (several \ngrams), and thermometry had migrated to light ly doped germanium. The development of AC \ncalorimetry6) and the thermal relaxation time technique7) made calorimetry a real option for small \nhigh-quality single crystalline samples in the mid 70’s, allowing for the first measurements up to 18 tesla\n8), but optimal thermometry was still limited. The development of much smaller RuO 2 \nresistive-paste thermometry and 24-26 tesla hybrid resistive/superconducting magnets opened \nthe window to the first specific heat and magnetocal oric effect studies of  the metamagnetic phase \ntransition in UPt 39), that shows a critical field µ 0Hc = 20.3 tesla. With the commissioning of the \n60 tesla long pulse magnet (see Fig 2 Top) at  the National High Ma gnetic Field Laboratory \n(NHMFL) in 1998 the evolution of magnetic fiel ds suitable for speci fic heat experiments \nwitnessed a significant step up with the measurements of the Kondo insulator Ce 3Bi4Pt310), using \na quasi-adiabatic technique in a setup fu rbished with calibrated bare-chip Cernox thermometry \n(Fig 2 Bottom), a record that  still holds unchallenged. The c onstruction and operation of the \nworld class 45 tesla hybrid magnet at the NHMF L was, especially for calorimetrists, truly \nrevolutionary. Indeed, since the first measurements that eluc idated a evasive (H,T) phase \ndiagram in URu 2Si2 done in 200211), approximately more than a dozen different specific heat \nexperiments were run by several groups. Closer to our interest are a number of studies of \nquantum magnetism, heavy fe rmions and superconductors12,13) that, using various technique \ndevelopments14,15) topped this year with so me re-exploration of AC-C p and magnetocaloric effect \nin pulsed field magnets16). The next technical frontier for speci fic heat in high magnetic fields is \nthe full development of a method suitable for 20 msec long pulses that can reach the 100 tesla \nterritory, but it will requir e significant improvements ove r presently known techniques. \n \n3. Specific heat in pul sed magnetic fields 4\nThere are enough technical challenges in th e field of pulsed magnets to initially \ndiscourage most condensed matter physics experi mentalists, and number one in the list of \nobstacles is the short duration of magnetic field pulses. Following in importance is the \ngeneralized perception that Eddy- current heating induced by rapidl y changing magnetic fields in \nthe samples under study inevitably leads to poor  data quality. Some other popular reasons for \naversion to pulsed-fields incl ude electromagnetic noise, thermo metry, mechanical vibrations, \nreduced sample space, magnetocaloric effect (expe riments are usually adiabatic, not isothermal \nlike in DC magnetic fields), lack of equilibrium between sample and magnetic fields and, last but \nnot least, the concerns relate d to catastrophic failure of th e magnets and cryogenic equipment \nwith the concomitant irreversible loss of the spec imens.  In what follows we describe how these \nobstacles are solved or circumvent in the case of specific heat measurements. \nDealing with short duration magnetic field pulses in calorimetry requires several \nconsiderations, regarding principally thermal equilibrium between sample and thermometry, and measurement techniques for resistive temperature sensors. The first point, thermal equilibrium \nwithin the duration of the field pulse, is addresse d with the miniaturizati on of the specific heat \nstage. In our case we used a 6x6x0.25 mm\n3 platform Si (single crystal) platform, onto which we \nglued a 1x1x0.25 mm3 heater made of amorphous-metal film on  a Si substrate, a 1x0.5x0.25 \nmm3 bare chip Cernox  thermometer, and the sample under study. To minimize Eddy-current \nheating during magnetic field pulse s we mounted all elements pa rallel to the a pplied magnetic \nfield, and used 25 micrometer resistive-alloy el ectrical wires for connections. The samples, \nweighting typically 1-50 mg depending on availa bility and expected contribution to the total \nspecific heat, were polished into slabs as thin  as the material would allow (typically 200-400 \nmicrometers) with the largest su rface glued to the Si platform to minimize the internal thermal \ntime constant in the calorimeter platform, and al so to minimize the sample  cross section in the \ndirection of the applied field. Extensive experience with state- of-the-art high frequency AC \ntechniques in our lab indicates that meas urement of electrical resistances between 1 ohm and \n103 ohm are relatively easy to accomplish in a s ub-millisecond timeframe, and that resistances \nbetween 10-3 ohm and 105 ohm are detectable, with anythi ng smaller or la rger requiring \nsomewhat extraordinary measures a nd highly skilled experimentalists. 5\nThe first calorimeter used for experiment in pul sed fields to 60 tesla is  displayed in Fig 3. \nThe picture shows a non-metallic frame made of  epoxy embedded fiberglass (G-10), and used to \nattach the nylon strings holding a Si platform. On the top of the platform it is possible to see the \nresistive film heater, th e opposite side holds the bare-chip th ermometer. Electrical connections \nare made with 5 inches-l ong NiCo alloy (Constantan ) minimizing open electrical loops. The \ncopper coil at the fa r left end is used to lo cally measure the voltage induced by the time-varying \nmagnetic field during the pulse. The main thermometer, an un-encapsulated Cernox  resistor is \nlocated at the far right and glue d directly on the Si block. This setup sits in vacuum during the \nexperiment, and the vacuum can was made of StyCast  1266 epoxy resin manufactured in-\nhouse with a conical seal. \nEssential to the proper functioning of any calorimeter in high magnetic fields is the \navailability of calibrated ther mometers. In our case we choose a bare chip CX-1030 Cernox  \nthermometer having a resistance of  approximately 900 ohm at 4 ke lvin. The calibration of this \nchip was done in a 25 msec 60 tesla pulsed magnet, immersed in liquid/gas 4He, with the \nmagnetic field applied in the plane of the re sistive film, perpendicular to contact pads, i.e. \nperpendicular to the applied AC current (see Fi g 3 bottom panel). We choose the quasi-adiabatic \nmethod to measure the specific heat in pulsed fiel ds with our setup. In this method a pulse of \ncurrent is delivered to the heater on the specific heat platform, and the temperature of the entire \nensemble (platform + sample + thermometer + h eater) is recorded as a function of time.   \n \n4. Specific heat of Ce 3Bi4Pt3 at high magnetic fields \nKondo insulator materials (KIM), such as Ce 3Bi4Pt3, are intermetallic compounds that \nbehave like simple metals at room temperature but an energy gap opens in the conduction band \nat the Fermi energy when the temperature is reduced17). The formation of the gap in KIM is not \nyet completely understood, and has been proposed to be a consequence of  hybridization between \nthe conduction band and the f-electron levels in Ce18). We used an external magnetic field (H) to \nclose the charge/spin gap in Ce 3Bi4Pt3, and observed a significant in crease in the Sommerfeld \ncoefficient (H), consistent with a magnetic field-induced  metallic state. Ind eed, here we present \nspecific-heat measurements of Ce 3Bi4Pt3 in pulsed magnetic fields up to 60 tesla. Numerical 6\nresults and the analysis of our data usin g the Coqblin-Schrieffer model demonstrated \nunambiguously a field-induced in sulator-to-metal transition10). \nThe raw unprocessed data collected duri ng the experiment using a 44.85 mg single \ncrystal sample are displayed in Fig 4, where the color-coded plots show the temperature of the \ncalorimeter (black), the magnetic field measured with the Cu-coil near to the sample (red), and \nvoltage across the sample heater (blue) vs time. Data for four different pulses are plotted in Fig \n4A, where two specific heat data points are obtaine d per pulse. The specific heat is calculated in \nthe calorimeter simply as the energy in joul es delivered by the heater, calculated as E = \nV(t).I(t)dt, where V(t) and I(t) are the time  dependent voltage and current in the heater \nrespectively, divided by the temperature change T. Fig 4B shows eight sp ecific heat data points \ncollected in a single 41.5  tesla pulse, when the voltage in the heater is  programmed conveniently. \nA compilation of data obtained with the calorime ter is shown in Fig 5. In the top panel the \nspecific heat of Ce 3Bi4Pt3 divided by the temperature (C p/T) is plotted vs temperature square, \nafter subtraction of the empty calorimeter (a ddenda) contribution. The bottom panel contains \ndata for a 300 mg Silicon sample, without subtracting the addenda. The simplest expression for \nthe specific heat of a metal is C p/T =  +T2, where  is the Sommerfeld coefficient due to free \nelectrons,  is the lattice contribution, and T is the te mperature. While in the case of Silicon \nneither the slope ( ) nor the small T →0 extrapolation are affected by a field of 60 tesla within \nthe experimental scattering of the data, in the case of Ce 3Bi4Pt3 the electronic contribution (H) \nis a strong function of the magnetic field.  \n The sample measured here shows a finite (H=0) = 18.6 mJ/molK2 that is roughly 2/3 of \nthe value observed in the metallic system La 3Bi4Pt3. This value, high for an insulator, has an \nunclear origin. While extrinsic effects such as impurities, vacancies and CeO surface states can \ncertainly contribute, a recent proposal suggests that in-gap states could be magnetic-exciton \nbound states intrinsic to KIM19,20). Magnetocaloric effect (MCE) results obtained during this \nexperiment can provide additional evidence to this effect.  Fig 6 Top shows the extracted  vs H \nfor Ce 3Bi4Pt3, and the bottom panel displays the MCE traces recorded during the experiment.   \nIn order to tell whether our results indicate the recovery of the metallic Kondo state in \nhigh fields, the increase in (H) observed in Ce 3Bi4Pt3 needs to be put in perspective. Using an 7\nestimate for the Kondo temperature of T K0= 240-320 K, the Sommerfeld coefficient for a metal \nwith such T K can be estimated using the expr ession for a single-impurity Kondo21) to be K = 53 - \n70 mJmol-1K-2. This provides an upper bound for the high field (H) in Ce 3Bi4Pt3, as it is \nexpected that an external field will suppress correlati ons and induce a reduction in (H). Taking \ninto account the effect of the applied ma gnetic fields within a single impurity model22), our \nestimate of the Sommerfeld coefficient at 60T is (60T) = 51-66mJ mol-1K-2. Hundley et al.23) \nhave measured the compound La 3Bi4Pt3 in zero field, and obtained La = 27mJmol-1K-2. This \nvalue in La 3Bi4Pt3, an isostructural metal where electroni c correlations are absent, should be our \nlower bound limit on (60T) in the high field metallized state of Ce 3Bi4Pt3. \nThe upper panel in Fig 6 shows (H) for Ce 3Bi4Pt3 in applied magnetic fields up to 60 T. \nThe values were obtained from a singl e-parameter fit of the form C(T) = T + T3, with the \ncoefficient  of the lattice term fixed to its zero -field value. We see a sharp rise in (H) between \nH = 30T and 40T. The result of the fit suggests a saturation at a value of sat(H) = 62-63mJmol-\n1K-2 above 40 T. The strong enhancement of (H) from its zero-field value, and the quantitative \nagreement with the estimate based on T K for a metallic ground state of Ce 3Bi4Pt3, prove that we \nindeed crossed the phase boundary between the Kondo insulator and the Kondo metal.  \nAdditional evidence for a significant change of regime induced by magnetic fields in \nCe3Bi4Pt3 is found in the ma gnetocaloric effect, i.e the changes in sample temperature when the \nmagnetic field is swept in adia batic conditions. The lower panel of Fig 6 shows the temperature \nvs magnetic field (same as T vs time curves in Fi g 4) for all magnetic fiel ds used to determine \nCp(T,H).  The curves show an initial increase ( ) that could be due to alignment of paramagnetic \nimpurities, then a decrease of the temperature ( ) consistent with the increase in (H) displayed \nin the top panel. At top field ( ) the temperature increases due to the heat pulses delivered to the \nplatform. Finally, when the magnetic field decreases the temperature of the sample reversibly \nincreases ( ) as (H) drops to the low field value, to then decrease in the impurity zone ( ). \nOne important observation from this drop is that the initial (low field) temperature change in \nT(H) decreases in magnitude as the initial sample temperature rises from 1.8 K to 4.5 K. On \nthe other hand the temperature change obs erved in the high field region, where (H) is a strong \nfunction of H, is roughly temperature independent (parallel MCE curves). A quick analysis of the 8\nMCE effect curves reveals that  the low field region (0 < µ 0H < 16T) has a much stronger \ntemperature dependence than the high field region (16T < µ 0H <60T). Fig 7 displays the absolute \ntemperature change | T| extracted from the curves in Fig 6 lower panel. The high field region \n(red circles), clearly linked to (H) and hence linked to the char ge gap, depends only slightly on \ntemperature likely due to relative changes be tween electronic and phononic contributions as the \ntemperature is increased. Indeed as the phon on contribution increase s the entropy change \nobserved upon closing of the charge gap, which remains the same, causes a gradually smaller \n|T|. On the other hand, the temperature change observed at low fields (blue triangles) changes \nmuch more rapidly with temperature,  in a region of magnetic field where (H) changes little. The \nrapid change resembles the temperature dependen ce of the magnetic susceptibility and leads us \nto conclude that in this region | T| is dominated by free magnetic moments. Indeed, \nparamagnetic magnetic moments in external fiel ds produce positive MCE.  The origin of the \nmagnetism is unclear, but we feel that impuriti es alone cannot explain the magnitude of the \nobserved effect, and that some type of intr insic phenomenon must play an important role20).   \n \n5. Determination of Phase Diagrams in High Fields \n Since the first measurements of specific heat in the 60 tesla long pulse magnet at \nNHMFL-Los Alamos many interesting materials su rfaced that have strong correlations between \ncharge, spin and lattice degrees of freedom. High magnetic fields can  be used to tilt the balance \nbetween competing mechanisms, just like in the case of Ce 3Bi4Pt3, to study phases of matter that \ndo not otherwise occur. Fig 8 s hows a compilation of data for al l materials and systems where \nstrong magnetic fields were us ed to change the ground state12). Figure 8 Top displays phase \ndiagrams for strongly correlated me tals, including the superconductor La 2CuO 4.11 where H//c-\naxis, the valence transition material YbInCu 4, the hidden order-parameter compound URu 2Si2, \nand AFM metals CeIn 3 and CeIn 2.75Sn0.25. Note that all these materials present a low temperature \nstate (different in nature) that can be suppr essed with a strong enough magnetic field, and that \nthe energy scale of the zer o-field phase transition (T c, T V, T N) does not correlate in a simple \nmanner with the magnetic field re quired to change the ground stat e. The reason for this is, \nclearly, the diversity of zero-fi eld ground states observed and the spread in magnitude in the 9\ncoupling between order para menter and magnetic field12). Ce 3Bi4Pt3, which does not show phase \nboundaries but a crossover, is not displayed here. \n Fig 8 Bottom displays (T,H) phase diagrams  for a collection of classical and quantum \nmagnets (insulators). The magnetic system RbFe(MoO 4)2 presents a in-plane AFM phase in zero \nfield that turns into a multiferroic phase as a mode st magnetic field of a few tesla is applied.  The \nrest of the materials displayed do not show ma gnetism in zero field, but a XY-type AFM state is \ninduced by the applied magnetic field. The strengt h of the exchange interactions, the always \npresent geometrical frustration, and the magnetic lattice dimensionality play together, or against \neach other, to determine the magnitude of magne tic fields necessary to  induce a change of \nground state. These materials, also known as qua ntum magnets, can under special circumstances \nbe approximated with a mode l that describes Bose-Einst ein condensation of magnons 12,24). The \ninsulator-to-metal crossover in Ce 3Bi4Pt3 is displayed for co mparison purposes.   \nSpecific heat studies in high magnetic field have been instrumental to understand the \nmechanisms and physics at play in correlated electron systems and quant um magnets, and we do \nexpect to continue finding new materials that will help us u nderstand many physics puzzles that \nstill exist in these topical areas. Some of these outstanding puzzles include the nature of magnetic \nstates in Ce 3Bi4Pt3, the pairing mechanisms in cuprate su perconductors, the nature of the order \nparameter in URu 2Si2, and the effects of geometrical frustr ation, quantum fluctu ations and lattice \ncoupling in quantum magnets. In pa rticular, one area of development for the near future will be \nthe implementation of AC specific heat to determine the shape of the phase boundary and \nrelevant physics of quantum magnets  in the high magnetic field region, i.e. for fields µ 0H > 45T \nand temperatures below 4 kelvin. \nAcknowledgements:  Work at the National High Magnetic Field Laboratory was \nsupported by the US National Science Foundation, the State of Florida and the US Department of \nEnergy through Los Alamos National Laboratory. 10\nReferences  \n1) A. Brown, M.W. Zemansky, H.A. Boorse; Phys. Rev.  84, 1050 (1951); idem  Phys. Rev.  86, \n134 (1952).      \n2) A. Berman, M. W, Zemansky, H.A. Boorse, Phys. Rev.  109, 70 (1958). \n3) F.J. Morin, J.P. Maita, H.J. Williams, R. C. Sherwood, J.H. Wernick, J. E. Kunzler, Phys. Rev. \nLett. 8, 275 (1962).  \n4) K. Ikeda, K.A. Gschneidner Jr., Phys. Rev. Lett. 45, 1341 (1980). Also W.E. Fogle, J.D.  \nBoyer,  R.A. Fisher, N.E. Phillips,  Phys. Rev. Lett. 50,1815 (1983). \n5) J.C. Lasjaunias, B. Picot, A. Ravex, D. Thoulouze, M. Vandorpe,  Cryogenics  17, 111 (1977).  \n6) P. F. Sullivan, G. Seidel, Phys. Rev. 173, 679 (1968). \n7) R. Bachmann, F.J.  DiSalvo, T.H. Geballe, R.L. Greene, R.E. Howa rd, N.C. King, H.C. \nKirsch, K.N. Lee, R.E. Schwall, H.-U. Thomas,  R.B. Zubeck, Rev. Sci. Inst.  43, 205 (1972).  \n8) G.R. Stewart, B.  Cort, G.W. Webb,  Phys. Rev. B 24, (1981) \n9) T. Muller, W. Joss, L. Taillefer, Phys. Rev. B  40, 2614 (1989). idem  Phys.  B 163, 155 (1990). \nAlso H. P. van der Meulen, Z.  Tarnawski, A. de Visser, J.J.M.  Franse, J.A.A.J. Perenboom, D. \nAlthof, H. van Kempen,   Phys. Rev. B 41, 9352 (1990). \n10) M. Jaime, R. Movshovich, G.R.  Stewart,  W.P. Beyermann, M.G. Berisso, M.F. Hundley, \nP.C. Canfield, J.L. Sarrao, Nature  405, 160 (2000). \n11) M. Jaime, K.H. Kim, G. A. Jorge, S. McCall, J. Mydosh, Phys. Rev. Lett.  89 287201 (2002). \nAlso  J.S. Kim, D. Hall, P. Kumar, G.R.  Stewart, Phys. Rev. B 67, 14404 (2003).  \n12) M. Jaime, et al., Phys. Rev. Lett . 93, 087203 (2004). G.A. Jorge,  et al.,  Phys. Rev.  B 69, \n174506 (2004). G.A. Jorge, et al.,  Phys. Rev. B 71, 092403 (2005). A. V. Silhanek, et al.,   Phys. \nRev. Lett. 96, 136401 (2006). A.V. Silhanek et al.,  Phys. B 378–380 , 90 (2006). A.V. Silhanek et \nal., Phys Rev. Lett.  96, 206401 (2006).V. Zapf et al., Phys. Rev. Lett.  96, 077204 (2006). M. \nKenzelmann, et al.,  Phys. Rev. Lett.  98, 267205 (2007). E.C. Samulon,  et al.,  Phys. Rev. B  77, \n214441 (2008). A. Aczel, Phys. Rev.  B 79, 100409 (2009). E.C. Samulon,  et al.,    Phys. Rev. \nLett. 103, 047202 (2009). 11\n13) H. Tsujii,  et al., Jou. Mag. Mag. Mat.  272-276 , 173-4 (May 2004). C.R. Rotundu,  et al.,   \nPhys. Rev. Lett. 92, 037203 (2004). J.S. Kim,  et al.,   Phys. Rev. B 69, 2440 (2004). C. R. \nRotundu,  et al.,  Jou. Appl. Phys.  97, 10A912 (2005). H. Tsujii,  et al.,   Phys. Rev. B 71, 14426 \n(2005). M. Hagiwara,  et al.,  Phys. Rev. Lett. 96, 147203 (2006). H. Tsujii,  et al.,  Phys. Rev. B \n76, 060406 (2007), among others. \n14) S. Riegel and G. Weber, J. Phys. E: Sci. Inst. 19, 790 (1986).  \n15) H. Wilhelm, T. Luhma nn, T. Rus, F. Steglich,  Rev. Sci. Inst.  75, 2700 (2004). \n16) A. Aczel, Y. Kohama, C. Marcenat, F. We ickert, M. Jaime, O. E. Ayala-Valenzuela, \nR. D. McDonald, S. D. Selesnic, H. A. Dabkowska, and G. M. Luke, Phys. Rev. Lett. to be \npublished (2009). Also Y. Kohama, C. Marcenat, A. Aczel, G.M. Luke, M. Jaime; in preparation   \n17) G. Aeppli and Z. Fisk, Kondo insulators. Comments Cond. Mat. Phys.  16, 155 (1992). \n18) M. F. Hundley, et al.; Phys. Rev.  B 42, 6842 (1990). Also Thompson, J. D. in Transport and \nThermal Properties of f-Electron Systems  (eds Fujii, H., Fujita, T. & Oomi, G.) 35 (Plenum, New \nYork, 1993). \n19) P. Schlottmann, Phys. Rev.  B 46, 998 (1992). \n20) P. S. Riseborough, Phys. Rev.  B 68, 235213 (2003). \n21) V.T. Rajan, Phys. Rev. Lett.  51, 308 (1983). \n22) K.D. Schotte, U. Schotte, Phys. Lett.  A 55, 38 (1975). \n23) M. F. Hundley, M. F. et al.; Phys. Rev.  B 42, 6842 (1990). \n24) T. Giamarchi, A. M. Tsvelik, Phys. Rev.  B 59, 11398 (1999). Also T. Giamarchi, C. Ruegg, \nO. Tchernyshyov, Nature Phys. 4, 198 (2008). \n \n   12\n\n \nMarcelo Jaime  \nMPA-CMMS, Los Alamos National Labor atory, Los Alamos, NM 87545, USA.  \nTEL. +1-505-667-7625 FAX. +1-505-665-4311 e-mail: mjaime@lanl.gov\n  \nResearch area: Specific heat of materials at very high magnetic fields and low temperatures.  \n \n  13\nFigure Captions  \nFig. 1  A selection of representative  specific heat experiments pe rformed in man-made magnetic \nfields, plotted as strength of ma gnetic field vs year of publicat ion. Bracketed numbers indicate \nreferences.  \nFig. 2 Top:  from right to left D. Rickel, J. Schil lig, R. Movshovich and the author standing in \nfront of the first motor generator-driven 60 tesla Long Pulse Magnet, equipped with a 4He \ncryostat. Bottom:   magnetic field pulses. The purple line  in the center is a pulse produced by a \nstandard capacitor bank-dr iven pulsed magnet. \nFig. 3 Top:  first functional calorimete r for pulsed magnetic fields10), consisting of a frame made \nof G10 attached to a Si block. Bottom:  electrical resistance vs magnetic field for the Cernox  \nbare chip thermometer.  \nFig 4.  Color coded plot of sample Temperature (bl ack), applied Magnetic field (red) and sample \nHeater voltage (blue) vs time recorded during a C p experiment in the 60 tesla Long Pulse \nMagnet. A) Cp measurement in 42 a tesla pulse B) Cp measurements in 60 tesla pulses. \nFig. 5  Top:  specific heat divided by the temperature C p/T vs T2 for C 3Bi4Pt3  for magnetic fields \nup to 60T as indicated in the label. A sudden change is observed between H = 30 tesla and 40 \ntesla. Bottom:  Cp (T,H) results for Silicon in  H = 0 and H = 60T  \nFig. 6 . Top: Sommerfe ld coefficient  vs. field for Ce 3Bi4Pt3. The value observed in La 3Bi4Pt3 is \nindicated as comparison. Bottom: temperature of the specific heat platform + sample vs field, as \nrecorded during the specific heat experiment. \nFig. 7  Absolute value of the temperature change observed in Ce 3Bi4Pt3 when the magnetic field \nis swept. Blue triangles correspond to the low fi eld region. Red circles, were extracted at high \nfields. \nFig. 8 Top:  (T,H) phase diagrams determined from C p(T) for La 2CuO 4.11, YbInCu 4, URu 2Si2, \nCeIn 3 and CeIn 2.75Sn0.25. Bottom: (T,H) phase diagrams determined from C p(T,H) and MCE \nexperiments for RbFe(MoO 4)2, NiCl 2-4SC(NH 2)2, Ba 3Mn 2O8, Ba 3Cr2O8, BaCuSi 2O6 and \nSr3Cr2O8. Star symbols ( ) from magnetization vs field. Fo r more details see ref. (12) 14\n\n \n \n   Figure 1  15\n\n \n \n Figure 2 16\n\n \n \nFigure 3 17\n\n \nFigure 4 18\n\n \n \n \nFigure 5 19\n\n \n \nFigure 6 20\n\n \n   \nFigure 7 21\n\n \nFig 8 \n            \n      "    },    {        "title": "1006.3415v1.Recent_progress_in_exploring_magnetocaloric_materials.pdf",        "content": " 1 Recent progress in exploring magnetocaloric materials  \n \nB. G. Shen, * J. R. Sun, F. X. Hu , H. W. Zhang, and Z. H. Cheng  \nState Key Laboratory for Magnetism , Institute of Physics , Chinese Academy of Sciences ,  \nBeijing 100190 (China)  \n \nAbstract  \nMagnetic refriger ation based on the magnetocaloric effect (MCE) of materials is a potential technique \nthat has prominet  advantages over the currently used gas compression -expansion technique in the sense of  \nits high efficiency and environment friendship. In this article, our recent progress in exploratin g effective \nMCE materials is review ed with the emphasis on the MCE in the LaFe 13-xSix–based alloys  with a first \norder magnetic transition  discovered by us . These alloys  show large entropy changes in a wide \ntemperature range near room temperature . Effects of magnetic rare -earth doping, interstitial atom, and \nhigh pressure on the MCE have been systematically studied. Special issues such as appropriate  \napproaches to determin ing the MCE associated with the first -order magnetic transition , the depression  of \nmagnetic  and thermal hystereses, and the key factors determin ing the magnetic  exchange in alloys of this \nkind are discussed. The applicability of the giant MCE materials to the magnetic r efrigeration near \nambient temperature is evaluated. A brief review of other materials with significant MCE  is also presented \nin the article .  \n \n \nKeywards: Magnetocaloric effect , magnetic property, thermal and magnetic hystereses , LaFe 13-xSix–based \ncompound s \n \n \n[*] E-mail: shenbg@g203.iphy.ac.cn  \n \n \n \n  2 1. Introduction  \nMagnetocaloric effect (MCE) provides a unique way of realizing the refrigeration from ultra -low \ntemperature to room temperature. With the increase of applied field, magnetic entropies decrease and heat \nis radiated  from the magnetic system  into the environment through  an isothermal process , while  with the \ndecrease of applied field, magnetic entropies increase and heat is absorbed from the lattice system into the \nmagnetic system through  an adiabatic process. Both the large isothermal entropy  change and the adiabatic \ntemperature change characterize the prominent MCE.  \nThe MCE was first discovered by Warburg in 1881.[1] Debye in 1926[2] and Giauque in 1927[3] \nindependently pointed out that ultra -low temperatures could be reached through the reve rsible temperature \nchange of paramagnetic (PM) salts with the alternation of magnetic field and first foresaw the \ntechnological potential of this effect. The first experiment o n magnetic refrigeration was performed by \nGiauque and MacDougall in 1933.[4] With the use of this technology, the te mperatures below 1 K were \nsuccessfully achieve d. Nowadays, magnetic refrigeration has become one of the basic technologies ge tting \nultra-low temperatures.  \nAlong with  the success in the ultra -low temperature range, this t echnique in lifted temperature ranges \nsuch as ~1.5 K ~20 K  for the range of liquid helium, and ~20 K ~80 K  for the range of liquid hydrogen \nand liquid nitrogen, is also appli ed. The mature refrigerants for the rang from ~1.5 K to ~20 K are the \ngarnets of  the R 3M5O12 (R=Nd, Gd, and Dy, M=Ga and Al), Gd 2(SO 4)3.8H 2O,[3,4] Dy3Al5O12 (DAG).[5] \nThe most typical material is Gd 3Ga5O12 (GGG),[6] which has been successfully applied  to the precooling \nfor the preparation of liquid helium. As for the temperature range  ~10 K ~80 K,  the modest refrigerants \nare Pr, Nd, Er, Tm, RAl 2 (R=Er, Ho, Dy and Dy 0.5Ho0.5, R=DyxEr1-x 0<x<1, GdPd  ) and RNi 2 (R=Gd,  Dy \nand Ho).[7]  \nMagnetic refrigeration near room temperature is of special interest because of its great social effect \nand economical benefit. Compared with the refrigeration technology based on the \ngas-compression/expansion, which has been  widely used today, magnetic refrigeration is environment \nfriend ly and energy saving. Due to the significant increase of heat capacity ne ar the ambient temperature, \nthe heat transferred by each magneti zing-demagnetizing cycling of the refrigerator should be considerably \nlarge to guarantee refrigeration efficiency. As a result, most of the materials working at low temperatures \ncannot be dire ctly utilized, and new materials with great entropy change around the ambient temperature \nmust be explored. Brown in 1968 observed a large MCE of Gd (TC=293 K ).[8] However, the entropy \nchange s of magnetocaloric materials reported  subsequently are much smal ler than that of Gd. In 1997 , it \nwas found by Gschneidner and his colleagues[9] that the entropy change of Gd 5Si2Ge2 with a fist order \nphase transition  is ~18 J/kgK around  TC=278 K  for a field change of 0 5 T, which is significantly larger \nthan that of Gd (~10 J/kgK) under a similar condition. Du and his colleagues[10] found that La1-xCaxMnO 3 \n(x = 0.2)  has a large entropy change of 5.5 J/kgK at  230 K for a field change of 0 1.5 T. Subsequently, \nsome n ew magnetocaloric  materials with a first-order magnetic t ransition  such as LaFe 13-xSix,[11,12] \nMnAs 1-xSbx,[13] and MnFeP 0.45As0.55[14] were found  to have  entropy changes from 18 J/kgK to 30 J/kgK. \nThese achievements arous ed a new wave of MCE r esearch.    3 A common feature of the giant MCE is that it usually occurs being  accompan ied by  a first -order \nmagnetic transition. However, several basic problems involved in the MCE , arising from the first -order \nphase transition , must be solved , such as , the determination of MCE, the contributions other than \nmagnetic entropy to MCE, and the effects of magnetic/thermal hysteresis as far as practical application \nbeing concerned. Detailed review s of the magnetic refrigeration technology and corresponding materials \nhave been given by Tishin,[15] Gschneidner[16] and Bruck.[17] In th e present  paper, we give a brief review \nof the development in exploring magnetocaloric materials, mainly on our recent progress in typical \nmagnetic materials with giant MCE.  \n \n2. Thermodynamics of magnetocaloric effect  \nAccording to the standard thermodynamics ,[15] the total differential of Gibbs free energy G of a \nsystem under volume V, magnetic field H, pressure P, and at temperature T is given by  \ndG=VdP-SdT-MdH. Based on this equation, t he well -known Maxwell relation can be o btained  as  \n dHTMP HTSPHTS PHTSH\nPH\n\n\n   \n0 \n,,0 , ,, ,,\n                          (1) \nif the pressure and temperature are fixed, where M is the magnetization. Eq uation  (1) gives an approach to \ncalculat ing entropy change from magnetic data. In practice , an alternative formula is us ually used for \nnumerical calc ulation,  \n \n\nii\ni ii iHT TM MS\n11\n .                                                    (2) \nThe following formula is also used : \ndTTC CPHTST P PH  \n0 ,0 ,,,\n,                                              (3) \nwhere CH,P and C0,P are the heat capacities in the field s of H and 0, respectively, under constant pressure P. \nAccording to the standard the rmodynamics, the differential entropy has the following form :  \ndPPSdHHSdTTSdS\nHT PT PH , , ,\n\n\n\n\n\n\n\n\n\n.                                    (4) \ndS=0 under the adiabatic condition, then the adiabatic temperature change will be  \ndHTM\nCTdT\nPH PH , ,\n\n\n\n,                                                   (5) \nwhere CH,P=T(S/T)H,P denotes heat capacity. Integrating Eq . (5) over H=0-H yields  the adiabatic \ntemperature change Tad. This is an indire ct technique for the determination of Tad. \n  4 3. Magnetic and magnetocaloric properties of LaFe13-xSix-based compounds  \nLaFe 13 does not exist because of its positive formation enthalpy. To obtain  a LaFe 13-based alloy, a \nthird element has to be introduced. Th e first stable LaFe 13-xMx compound was obtained by Kripyakevich \net al .[18] in 1968 after partially replacing Fe with Si or Al. The compound crystallizes in the cubic \nNaZn 13-type structure with a space group of\ncFm3 . The incorporation of S i/Al causes no change in crystal \nstructure but lattice shrinkage s because of the small atomic size of Si/Al compared with that of Fe. We \nmeasured the lattice constant for LaFe 13-xSix as shown in Fig ure 1a. The lattice constant was found to \ndecrease with Si  content increasing from ~1.14 75 nm for x=1.2 to ~1.14 50 nm for x=2. 5. Although the \nchange is not very large, it has dramatic effects on magnetic property.  \nThe study showed that LaFe 13-xSix is PM near the ambient temperature, and undergoes a n FM \ntransitio n upon cooling at a temperature between 200 and 250 K, depending on Si content. The Curie \ntemperature TC obtained from  our measurement s increases linearly from ~1 75 K for x=1. 17 to ~2 54 K for \nx=2.5 (Fig. 1a) in conformity  with the result reported by Palstr a et al.[19] We and Palstra et al.[19] also \nobserved a  monotonic decrease of saturation magnet ization, respectively, at a rate of 0.286 B for each Si, \nwith the increase of Si content (Fig.  1b). This is a rate much more rapid than that expected for a simp le \ndilution effect , and therefore  indicat ing the change of electronic structure due to the incorporation of Si. A \nfirst-principle s calculation conducted by Wang et al.[20] indicated the occurrence of hybridization between \nthe Fe -3d and Si -2p electrons and the change of the density of state below Fermi surface after the \nintroduction of Si, which could be the cause  for the change of Fe magnetic moment.  \n \n3.1 Magnetocaloric effect in LaFe 13-xSix \nThe study  by Palstra  et al.[21] indicated that LaFe 13-xSix compou nds were stable in the  cubic NaZn 13 \nstructure in a concentration region  1.5  x  2.5. We found that Si content c ould be further lowered down \nto x=1.2 through improving preparation arts , while  the cubic NaZn 13 structure remain ed unchanged.  \nAccompan ied with  the FM to PM transition, the LaFe 13-xSix compounds exhibit an obvious lattice \ncontraction, especially for the samples with low Si content. Sizable thermal or magnetic hysteresis was \nobserved for the temperature/magnetic field ascending -descending cycling.  These results reveal the \nfirst-order nature of the phase transition. An evolution of the phase transition from first -order to \nsecond -order takes place as x increases, and a typical second -order transition appears when x > 1.8.  For \nLaFe 13-xSix compounds wi th Si content x  1.6, an external field can induce metamagnetic transition from \nPM to FM state at temperatures near but above TC, which is the so -called itinerant -electron metamagnetic \n(IEM) transition.[22,23] The FM state becomes more stable than the PM state under an applied field due to \nthe field -induced change in the band structure of 3 d electrons. The IEM transition is usually indicat ed by \nthe appearance of “S” -shaped  M2-H/M isotherms (Arrott plot). For the LaFe 13-based compounds, the \nlower the Si con tent is, the stronger the first -order nature of the magnetic transition will be .[24]  \nAlthough the magnetic property of LaFe 13-xSix had been intensively studied before, the \nmagnetocaloric property did not come into the vision of peo ple until the work by Hu et al.[11] in 2000 , they \nobserved an entropy change as high as ~20 J/kgK , for a field change of 0 5 T, in LaFe 13-xSix with lower Si  5 concentration. In 2001 further study by Hu et al .[12] found that the large entropy change |S| in LaFe 13-xSix \nis associated  with negative lattice expansion and metamagnetic transition behavio ur. Figure  2a shows  the \nmagnetization isotherms of LaFe 11.4Si1.6 as field increase s and decrease s at different temperatures  around \nits Curie temperature TC=208 K . It is evident that e ach isotherm shows a reversible behavio ur. Almost no \ntemperature and magnetic hysteresis  accompan ied with  the magnetic transition is observed, although the \nSi content of x=1.6 is located near the critical boundary from first -order to second -order transition. The \ncompletely reversible magnetization indicate s that |S| should be fully reversible on temperature and \nmagnetic field. Figure  2b exhibits Arrott plots of LaFe 11.4Si1.6. The existence  of the inflection point \nconfirms the occurrence of a metamagnetic transi tion from the paramagnetic to ferromagnetic ordering \nabove the TC. The S of LaF 11.4Si1.6 as a function  of temperature  is shown in  Figure 2c and t he maximal  \nvalues of |S| under  fields of 1, 2, and 5 T are 10.5, 14.3, and 19.4 J/kg K,  respectively . Another  \ninteresting feature is that the S peak broadens asymmetrically to higher temperature with field increas ing. \nDetailed analysis indicate s that the field -induced metamagnetic transition above TC contributes to the \nasymmetrical broadening of S.  \nThe x -ray d iffraction measurements at different temperatures reveal that the LaFe 11.4Si1.6 remain s \ncubic NaZn 13-type structure but the cell parameter changes dramatically with TC. The negative expansion \nof lattice parameter reaches 0.4% with appearance of FM ordering  for LaFe 11.4Si1.6, while only a small \nchange of lattice parameter is observed for LaFe 10.4Si2.6 (see Fig. 3a). The occurrence  of the large |S| in \nLaFe11.4Si1.6 is attributed to the rapid change of magnetization at TC, which is caused by a dramatic \nnegati ve lattice expansion. For comparison, Figure 2c also presents an entropy change of LaFe 10.4Si2.6, and \nits value is much smaller than that of LaFe 11.4Si1.6. The saturation magnetization s of LaFe 11.4Si1.6 and \nLaFe 10.4Si2.6 were determined to be  2.1 and 1.9 μ B/Fe from the M–H curves at 5 K. The influence of the \nsmall difference in saturation magnetization between the two samples on the |S| should be very small , \nand the large negative lattice expansion at T C should be the key reason for the very large |S| in \nLaFe 11.4Si1.6. \nAs mentioned above,  the first -order nature of  the phase transition is strengthened with Si content \nlowering in LaFe 13-xSix, and an evolution  of the transition from second -order to first-order can take place . \nFor the samples with x  1.5, the rmal and magnetic hysteresis appears inevitably  because of the f irst-order \nnature of the transition. Details about hysteres is loss can be seen in the following  sections. Figure  3b \ndisplays  the typical S as a function of temperature under a field change of 05 T for LaFe 13-xSix with \ndifferent Si content  x.[24] The maximal |S| is ~29 J/kgK when x=1.2.  However, from  a simple analysis it \ncan be concluded that the max imal |S| for LaFe 13-xSix will be ~40 J/kgK. It is easy to see that there \nshould be a one -to-one correspondence between the field -induced ma gnetization change ( ) and S. By \ncomparing the data of different compounds, a S- relation can be obtained, and the utmost entropy \nchange will be the result corresponding to =1. A remarkable feature is th e rapid drop in S with x for \nlower Si content, while slow  variation with x for higher Si content  as shown in the inset of Fig ure 3b. The \nnegative lattice expansion  near TC increases  rapidly with Si content reducing (see Fig. 3a). It is a signature  6 of the crossover of the magnetic transition from second -order to first-order. Th ese result s reveal a fact that \nlarge entropy changes occur always accompan ied with  the first -order phase trans ition. \n \n3.2 Neutron diffraction and Mö ssbauer  studies on  LaFe 13-xSix \nThe detailed investigation of magnetic phase transition driven by temperature and magnetic field can \ngive an insight into the mechanism of large magnetic entropy change in these compounds. It is well \nknown that neutron diffraction is a powerful and direct tech nique to investigate the phase transition, \nespecially for magnetic phase transition. Wang et al .[25] carried out neutron diffraction  investigations on \nLaFe 11.4Si1.6. Rietveld refinements of powder diffraction patterns showed that the occupancy of Fe atoms \nare 90.5(±1.7) and ∼87.0(±1.8)% for FeI and FeII sites, respectively. Thus Si atoms are almost randomly \ndistributed on these two Fe sites. It is noted that the diffraction profiles at 2K and 300 K can be fitted by \none cubic NaZn 13-type lattice, whereas that at 191 K (very cl ose to the Curie temperature) must be fitted \nby two cubic NaZn 13-type lattices with different lattice parameters (Fig.  4). The onset of the ferromagnetic \nordering results in a large volume expansion, exerting  no influence on the symmetry of the atomic latt ice. \nThe volume changes discontinuously and the large volume ferromagnetic phase coexist with a small \nvolume paramagnetic phase at 191 K. The refinement shows that at 191 K, the sample is composed  of \n12% of the large volume phase and 83% of the small one  (the rest i s 5% α-Fe). Th e coexistence of \ntwo phases implies that the first -order magnetic phase transition and strong interplay between lattice and \nmagnetism  take place , which is in agreement with the observation s in La (Fe0.88Si0.12)13 from the  x-ray \ndiffraction.[26] \nIt was  also found[25] that the lattice parameter is strongly correlated with the Fe moment. With \ntemperature  decreasing  from 300 to 250 K, the compound displays a normal thermal contraction resulting \nfrom the anharmonic vibrations of atoms. Since the Invar effect is caused by the expansion resulting from \nthe spontaneous magnetostriction which cancels the normal thermal contraction, one may infer that the \nshort -range magnetic correlation appear s far above the Curie temperature in LaFe 11.4Si1.6. With a further \nreduction in temperature, the effect of the spontaneous magnetostriction increases and the lattice \nparameter shows a large jump with a long-range ferromagnetic ordering. Even below the Curie \ntemperature, the contribution of magnetic therma l expansion is still related to the increase of the magnetic \ncorrelation as the temperature is lowered.  \nAlthough several papers about x -ray diffraction,[26] neutron diffraction,[25] as well Mö ssbauer \nstudies[27,28] have confirmed two -phase coexistence in L aFe 11.44Si1.56 in a narrow temperature region of \nTc± 2 K, the detailed phase ev olution s driven by temperature and magnetic field around TC, especially the \nindividual characteristic feature of these two phases , are not yet well understood. In the case of \nLa(Fe1-xSix)13 compounds, a large number  of iron atoms provide a unique opportunity to investigate the \nmagnetic phase transition by using  57Fe Mö ssbauer spectroscopy. Cheng et al .[29] and Di et al .[30] carried \nout Mö ssbauer  studies on  LaFe 13-xSix. Figure s 5a and 5b show mö ssbauer spectra in various applied fields \nfor LaFe 11.7Si1.3 at 190 K and LaFe 11.0Si2.0 at 240 K, respectively. Zero -field Mö ssbauer spectra collected \nabove TC show a paramagnetic doublet , owing to the quadrupole splitting. With external field  increasing  7 up to 10 kOe, no evidence of a magnetically split sextet is detected in the spectrum of LaFe 11.7Si1.3, but the \npresence of a sextet is evident in spectrum of LaFe 11.0Si2.0. With external field further increasing over 20 \nkOe, sharp well -split pa irs of sextets are observed, and their areas increase rapidly at the expense of the \ndoublets. Direct evidence of a field -induced magnetic phase transition in LaFe 13−xSix intermetallics with a \nlarge magneticaloric effect was provided by 57Fe Mö ssbauer spect ra in externally applied magnetic fields. \nMoreover, Mö ssbauer spectra demonstrate that a magnetic structure collinear to the applied field is \nabruptly achieved in LaFe 11.7Si1.3 compound once the ferromagnetic state appears, showing a \nmetamagnetic first -order phase transition. In the case of LaFe 11.0Si2.0, the Fe magnetic moments rotate \ncontinuously from a random state to the collinear state with applied field  increasing , showing that a \nsecond -order phase transition is predominant. The different types of pha se transformation determine the \nmagnetocaloric effects in response to temperature and field in these two samples.  \nIn the case of Fe -based alloys and intermetallic compounds, 57Fe hyperfine field is Hhf roughly \nproportional to the Fe magnetic moment μFe, and consequently, the temperature dependence of the average \nhyperfine field for the compounds LaFe 13-xSix with x=1.3, 1.7 and 2.0 can be  fitted with Brillouin function \n(BF) according to the e xpression   \n),/)(( )0( )(2/1 tThB H THhf hf hf\n                                        (6) \nwhere \n) coth() coth(2)(2/1 x x x B   is the Brillouin function, and t= T/TcBF. TcBF is the temperature of \nHhf(TcBF)=0 obtained from mean field model.  \nThough the curves can be well fitted at low temperatures, the BF relation fails to fit the Hhf(T) near \nthe TC[20] As in the mean field theory the magnetic phase transition at TC is presumed to be of the \nsecond -order, in the compound LaFe 11.7Si1.3, the significant deviation of the BF relation from the \ntemperature dependence of Hhf(T) near TC suggests that th e magnetic phase transition is of the first-order \nin nature. With Si concentration  increasing , the second -order magnetic phase transition is predominant \nand leads to a smaller magnetic entropy change.  \n \n3.3 MCE in Co, Mn and magnetic R doped  LaFe 13-xSix \nAlthough the LaFe 13-xSix compounds exhibit a giant MCE, the S peak usually appears at low \ntemper atures (< 210 K). For the purpose of practical application s, it is highly desired that the maximal \nentropy change can take place near the ambient temperature. Acc ording to Figure 3b, unfortunately, the \nMCE weakens ra pidly as TC increases. It is therefore an important issue about how to shift TC toward  high \ntemper atures without significantly affecting S. \nHu et al.[11,31] found that the best effect c ould be obtained  by replacing Fe with an appropriate amount \nof Co. An entropy change  value of  11.5 J/kgK in LaFe 10.98Co0.22Si1.8 at 242 K  for a field change of 5 T  \nwas observed in 2000 .[11] Further study[31] found that the maxim al value of  ΔS in LaFe 11.2Co0.7Si1.1 near \nthe Curie temperature TC of 274 K  for a field change of 05 T is  20.3 J/kgK, which exceeds that of Gd by \na factor of 2 and is  nearly as large as th ose of Gd 5Si2Ge2[9] (see the i nset of Fig.  6a) and MnFeP 0.45As0.55[14] \nwhereas there was no obvious magnetic  hysteresis in the sample, which is highly desired in the sense of  \npractical application. Figure 6a displays the entropy change as a function of temperature for  8 La(Fe 1-xCox)11.9Si1.1. It is very significant  that in the La(Fe 1-xCox)11.9Si1.1 (x=0.04, 0.06 and 0.08) the Curie \ntemperature increases from  243 K to 301 K as x increases from 0.04 to 0.08, while |S| only slow ly \ndecrease s from ~23 J/kgK to ~15.6  J/kgK for a field change of 0-5T.[32] The study on the MCE  of \nLa0.5Pr0.5Fe11.5-xCoxSi1.5 (0≤x≤1.0)  was performed  by Shen et al.[33] The substitution of Co in the \nLa0.5Pr0.5Fe11.5Si1.5 causes the order of phase transition at TC to change from first -order to second -order at \nx = 0.6. Although t he magnetic entropy change decreases with increasing Co concentration, TC increases \nfrom 181 K for x = 0 to 295 K for x = 1.0  and the hysteresis loss at TC also reduces remarkably from 94.8 \nJ/kg for x = 0 to 1.8 J/kg for x = 0.4 because an increase of Co content can weaken the itinerant electron \nmetamagnetic transition. For the sample of x = 1.0, i t is not eworthy  that the maximum values of |S| at TC \n= 295 K for a magnetic field change of 0 -2 T and 0 -5 T respectively are 6.0 and 11.7  J/kgK, which are \n20% higher than those of Gd. The MCE  of La 1-xPrxFe10.7Co0.8Si1.5 was also stu died.[34] As x grows from 0 \nto 0.5, the maximal value of entropy change increases from 13.5 to 14.6 J/kgK for a field change of 0 5 T, \nwhile TC, which is near room temperature, exhibits only a small change.  The effect s of substituting Fe by \nCo on the MCE in LaFe 11.7-xCoxSi1.3,[35] LaFe 11.9-xCoxSi1.1,[35] LaFe 11.8-xCoxSi1.2[36] and LaFe 11.4-xCoxSi1.6[37] \nwere also studied and similar effects to those described above w ere observed.  \nThe study on the MCE of La0.7Pr0.3Fe13-xSix (x=1.5, 1.6, 1.8 and 2.0) exhibite d an increase in TC and a \nreduction in S due to  the substitution of Si for Fe,[38] which is similar to  the case of LaFe 13-xSix. Although \nboth the Si -doping and the Co -doping drive TC to high temper atures, the reduction of S is much slower \nin the latter c ase. The maximal |S| is ~24 J/kgK ( H=5T) for La 0.5Pr0.5Fe11.5-xCoxSi1.5 (x=0.3) and ~11 \nJ/kgK (H=5T) for La 0.7Pr0.3Fe13-xSix (x=2.0) while TC takes nearly the same value of ~218 K. Therefore, \nreducing the Si co ntent in LaFe 13-xSix and partial replacing Fe by Co is a promising way to get \nroom -temperature giant MCE.  \nIn an attempt to find out a way to depress TC while effectively retain the large |∆S|, Wang et al.[39,40] \nstudied the effect of substituting Fe by Mn, which may have a n AFM coupling with adjacent Fe. The Mn \ncontent in La(Fe 1-xMn x)11.7Si1.3 is x=0, 0. 01, 0.02, and 0. 03.[40] The cubic NaZn 13-type structure keeps \nunchanged except when  the minor -Fe phase (<5 wt%) for x  > 0.02 appears . A decrease in saturation \nmagnetization much larger than that expected due to  a simple dilution e ffect is observed, which is \nconsistent with the anticipated antiparallel arrangements of Fe and Mn. The Curie te mperature was found \nto decrease at a rate of ~174 K for 1% Mn. A large |S| was gained in a wide temperature range, though a \ntendency toward degeneration appears as y increases. It is ~17 J/kgK for TC=130 K and ~25 J/kgK for \nTC=188 K  (Fig. 6b), for a field  change of 0 -5 T. The temper ature span of S increases  obvious ly. It is \n~21.5 K for x=0 and ~31.5 K for x=0.03 (H=5 T). For La(Fe 1-xMn x)11.4Si1.6,[39] when the content of Mn \nis high enough ( x > 0.06), long -range FM order will be destroyed, and typical spi n glass behavior a ppears.  \nEffects of Nd substitution on MCE were studied  by Anh et al.,[41] who declared an i ncrease of TC and \na decrease of MCE in La 1-xNdxFe11.44Si1.56 (x=0 -0.4) with the i ncorporation of Nd. However, these results \nare inconsistent with t hose subsequently obtained by other groups. Fujieda et al .[42,43] performed a \nsystematic study on the effect of Ce -doping for the co mpounds LaFe 13-xSix with x  = 1.3, 1.56, and 1.82. It \nwas observed that the substitution of Ce cause  TC to reduce and the ent ropy and adiabatic temperature  9 changes  to increase . Shen et al.[44] studied systematically effects of substituting Fe with R on magnetic \nproperties and MCEs  of La 1-xRxFe13-xSix. It was found that the substitution of R for La  in La 1-xRxFe11.5Si1.5 \n(R = Ce, Pr and Nd)  leads to a monotonic  reduction in TC due to the  lattice contraction  as shown in F igure \n7a. The TC exhibits  a linear reduction  with the decrease of unit-cell volume  at a rate of 2990 K/nm3 for R \n= Ce, 1450 K/nm3 for R = Pr and 800  K/nm3 for R = Nd. Partially replacing La with R causes an \nenhancement of the field-induced  itinerant electron metamagnetic transition, which leads to a remarkable \nincrease in Δ S. The S as shown in  Figure 7b for a field change of 0 5 T, varie s from 23.7 J/kgK for x=0 \nto 32.4 J/kgK for La 1-xPrxFe11.5Si1.5 (x=0.5) and to 32.0 J/kgK for La 1-xNdxFe11.5Si1.5 (x=0.3), but keeps at \n~24 J/kgK for La 1-xCexFe11.5Si1.5 (x=00.3).  \nFrom these results above it is concluded that the substitution of magnetic rare earth R causes a shift of \nTC towards low temperature s, and strengthen s the first -order n ature of the phase transition. Sometimes a \nsecond -order phase transition becomes of the first-order after the introduction of R. The MCE is enhance d \nwith the increase of R content.  \n \n3.4 Interstitial effect in La(Fe 1-xSix)13 \nFor the purpose of practical applic ations, as mentioned in the previous se ctions, the giant MCE \noccurr ing near the  ambient temperature is required. It is therefore highly desired to find out an effective \napproach to push ing S to high temperatures without reducing its value.  In 2002, Chen et al.[45] and Fujita  \net al.[46] indepen dently  found that the incorporation of i nterstitial hydrogen in to LaFe 13-xSix shifts TC to \nhigh te mperatures while a large MCE still a ppears. For example, the entropy change is as large as 17 \nJ/kgK (H = 5 T) in LaFe 11.5Si1.5H1.3 even at a temperature of 288 K .[45] The hydrogen concentration was  \ndetermined by both gas chromatograph and gas fusion analyses. By changing either hydrogen pressure or \nannealing temperature, under which the sample was processed, Fujieda  et al .[47] controlled  the \nconcentration of interstitial hydrogen . In contrast,  Chen et al .[45,48] tuned the content of hydrogen by \ncarefully reg ulating the desorption of absorbed hydrogen. The Curie temperature  TC of LaFe 13-xSixHδ was \nfound to increase linearly with the increase of hydrogen content  δ, while the magnetic transition remain ed \nto be of the  first-order. This is completely different from the effect of Si - and/or Co -doping, which causes \nan evolution of magnetic transitio n from the first order to the second o rder. In this way, the giant MCE \nthat usually appears at low temperatures can be pushed towards high temperatures. The entropy changes \nof LaFe 11.5Si1.5Hδ (δ=0-1.8)[48] as a function of temperature are shown in Figure 8a. The values of |S| are \n24.6 and 20.5 J/kgK ( H = 5 T) at 195 and 340 K, respectively. Due to the broadening of ma gnetic \ntransition caused by hydrogen desorption, the S value in LaFe 11.5Si1.5Hδ is somewhat lower in an \nintermediated hydrogen concentr ation range. However, the maximum value of |S| for LaFe 11.44Si1.56Hδ \n(δ=0-1.5) keeps at ~23 J/kgK ( H = 5 T) as TC increases from ~195 K to ~330 K.[47]  \nWang et al.[49] studied the MCE of hydrides  La(Fe 1-xMn x)11.7Si1.3Hy. Although the antiferromagnetic \ncoupli ng between Fe and Mn causes a decrease of the Curie temperature, TC still can be tuned around \nroom temperature by controlling the hydrogen absorption and has the values of 287K, 312K and 337K for \nx=0.01, 0.02 and 0.03, respectively. The effect of hydrogen atoms on TC is similar to that of the La(Fe,  10 Si)13H hydrides , for which lattice expansion caused by interstitial atoms depresses the overlap between \nFe-3d electrons, thus lead ing to an increase of TC. The first order phase transition nature weakens after  Mn \ndoping, however, the IEM transition remains, which results in a large entropy change  (Fig. 8b). The \nmaximal  value s of |S| are 23.4, 17.7 and 15.9  J/kgK under a magnetic field change from 0 to 5T for \nx=0.01, 0.02 and 0.03, respectively.   \nThe hydrides a re usually chemically unstable above 150 C, which could be a fatal problem to \npractical applications. It is therefore necessary to obtain chemically stable interstitial compounds with \nhigh TCs and great |S| values . Chen et al .[50,51] studied the e ffects of interstitial carbon for the \nLaFe 13-xSixCδ carbides, which are stable up to the melting point. The LaFe 11.6Si1.4Cδ (δ=0, 0.2, 0.4, and 0.6) \ncarbides were prepared by the solid -solid phase reaction tec hnique, that is, arc melting Fe -C intermediate \nalloy t ogether with La, Fe and Si. X -ray diffraction analyses indicate that the cubic NaZn 13-type structure \nremains unchanged after the introduction of carbon atoms, but minor -Fe phase appears when the carbon \nconcentration is δ 0.6.The lattice  expansion s caused  by the interstitial carbon atoms are 0.29%, 0.75%, \nand 0.93% for δ=0.2, 0.4 and 0.6, respectively. Compared with hydrides, carbides have much strong \nlattice expansion.[52] The Curie te mperatures grows  from 195 K for δ=0 to 250 K for δ=0.6.  \nFigure  8c show s the entropy change as a function of temperature for LaFe 11.6Si1.4Cδ.[50] The entropy \nchange is nearly constant when x is below 0.2, but decreases rapidly for x > 0.4. The maximal values of \n|S|, for a field change of 0 5 T, are 24.2 J/kgK for δ=0.2, 18.8  J/kgK for δ=0.4, and 12.1 J/kgK for x=0.6 , \nrespectively . The decrease of |S| for x > 0.4 could be due to impurity phase, which broadens the phase \ntrans ition. A slightly different carbides LaFe 11.5Si1.5Cδ was also studied,[51] and similar effects were \nobserved.  \nJia et al.[52] studied the effect of interstitial  hydrogen  on lattice  volume of the hydrides LaFe 11.5Si1.5Hδ \n(=0, 1.2, and 2), based on the Rietveld analyses of powder x -ray di ffraction spectra. It was found that the \nincorporation of interstitial h ydrogen causes a lattice expansion while the structural symmetry remains \nunchanged. Accompanying the lattice expansion, Fe -Fe bond exhibits a concomitant vari ation. Four of the \nfive Fe -Fe bonds show a tendency towards  expansion. The largest elongation occu rs for the shortest \ninter-cluster bond (B 4), and the relative change is as large as ~2.37% as  increases from 0 to 2. In contrast, \nthe longest Fe -Fe bond (B 2) shrinks consi derably (0.53%). The e ffect of Ce -doping was also studied[52] \nfor comparison. It i s fascinating that the increase in Ce content produces essentially the same effect on \nFe-Fe bonds as the decrease of hydrogen content, though inte rstitial atoms occupy different \ncrystallographic sites from rare -earths. A linear i ncrease of Curie temperatur e with the increase of lattice \nconstant  is observed , to be at a rate of ~1779 0 K/nm for LaFe 11.5Si1.5H/La 1-xCexFe11.5Si1.5 and ~1089 0 \nK/nm for LaFe 11.5Si1.5C. This is a signature of the strengthening of magnetic co upling. It was found that \nthe change of the shortest Fe -Fe bond dominates the magnetic co upling in the LaFe 1s-xSix-based \nintermetallics. A relation between e xchange integral and Fe -Fe distance has been proposed to explain the \nvolume effects observed.  \nIn Table I we give a summary of the magnetic transition temperature TC and isothermal entropy \nchange |S| for LaFe 13-xSix and related compounds .  11  \n3.5 Magnetic exchanges in hydrogenised, pressed and magnetic R-doped LaFe 13−xSix  \nA remarkable feature of the LaFe 13-xSix compound is the strong dependence of Curie temperature on \nphase vo lume. It has been reported that the incorporation of interstitial hydrogen causes a significant \nincrease in TC, while the hydrostatic pre ssure leads to a reduction in TC. For example, the typical change \nof the Curie te mperature is ~150 K when ~1.6 hydrogen / f.u. is absorbed and ~  −106 K as the pressure \nsweeps from 0 to 1 GPa.[55] The most remarkable result is the presence of a universal relatio n between \nCurie temperature and phase volume: the former linearly grows with the i ncrease of lattice constant. This \nresult implies the exclusive depen dence of the magnetic coupling in LaFe 13−xSix on Fe–Fe distance  and no \neffect of interstitial hydr ogen on the electronic structure of the compounds.  \nThe x -ray diffraction  measurements for LaFe 11.5Si1.5H reveal that  the introduction of interstitial \nhydrogen causes a considerable lattice expansion , though the crystal structure r emains unchanged. The \nmaximum la ttice constant change is ~3.4%. Subsequent magnetic measurement s reveal the stabilization of \nthe FM state  by interstitial hydrogen , as shown by the increase  of TC from ~190 K to ~356 K.   \nThe direct effect of high pressure or interstitial hydrogen is on pha se volume. It is therefore \ninteresting to check the relation between TC and phase volume. Based on the XRD data collected at the \nambient temperature, the lattice constant at TC (PM phase) varies according to  the relation \na(TC)=a0−(296 − TC) for Tc  296 K and a(TC)=a0+(TC−296)−Δ a for TC 296 K, where a0 is the lattice \nconstant at ~296 K, Δ a is the lattice expansion accompan ying the FM -PM transition, and /a08.2× 10−6 \nK−1 is the linear expansivity of LaFe 13-xSix. Δa can be derived from the rigid shift of th e TC-a0 curve along \nthe a0 axis when TC exceeds 296 K and it is found to be ~0.044 Å, essentially independent of Si co ntent.  \nTo compare with the results of hydrogenation, information on pressure induced volume change is \nrequired. The crystal structure of LaFe 11.5Si1.5 was an alyzed by synchrotron radiation XRD conducted \nunder the pressures of up to 4.1 GPa. The compressibility obtained is =−V−1dVdP8.639× 10−3 GPa−1, \nwhere P is pressure and V is the volume. The volume under high pressure has the form V =V0(1−P), \nwhere V0 is the volume under ambient pressure. Based on these results, the TC-a relation under pressures \ncan be obtained (solid c ircles in Fig. 9). Results of hydrogen ation and Ce doping for La 1−yCeyFe11.5Si1.5 \n(y=0 –0.3) are also presented for comparison ( open  triangles in Fig. 9). It can be seen that the slope s of the \nTC-a relations are essentially the same in the cases of hydrogen ating and Ce substitution, but considerably \nlarge under pressures. This result reveals the exclusive effect  of Fe -Fe distance on magnetic coupling.  \nTo improve the magnetic and the magnetocaloric properties, sometimes lanthanum in the materials is \npartiall y replaced by magnetic rare earths. In this case the magnetic exchange can also occur between R \nand Fe. It has been reported that both the MCE and the Curie temperature of La1-xRxFe11.5Si1.5 compounds \ncould be greatly modified by magnetic rare earths  as sh own in Figure 7. We have found that a magnetic \ninteraction compar able with that among Fe atoms exists between R and Fe.[56] It can cause the Curie \ntemperature to enhance up to ~11% when ~30% of the La atoms are replaced by R. Further, t he R–Fe \ncoupling is found to be strongly dependent o n the species of rare earths, and mon otonically grows as R \nsweeps from Ce to Nd. This could be a consequence of the lanthanide contraction, which causes an  12 enhanc ement of the intra -atomic magnetic coupling.  \nThe XRD patterns of La 0.7R0.3Fe11.5Si1.5 were measured . Similar XRD spectra are obtained for all of \nthe samples, suggesting the similar structures of di fferent samples. However, a close view of the XRD \npatterns shows a continuous, yet considerable, high -angle shift of the Bragg reflection as R sweeps from \nLa to Pr, and Nd. This is a signature of lattice contraction. The max imal and minimal lattice constants are, \nrespectively, ~11.468 Å obtained in LaFe 11.5Si1.5 and ~11.439 Å obtained in La 0.7Nd0.3Fe11.5Si1.5.  \nIt was found that t he Curie temperatures are ~194, ~17 3, ~18 5, and ~18 8 K, corresponding to La, Ce, \nPr, and Nd  for La0.7R0.3Fe11.5Si1.5, respectively. As expected, obvious decreases of TC occur after the pa rtial \nsubstitution of R for La. A remarkable result is the stro ng dependence of the do ping effects on the R \nspecies. Different from the lattice parameter, which displays a monotonic contra ction as R goes from La to \nCe, Pr, and Nd, TC decreases along the sequence from La to Nd, Pr, and Ce. The max imal Δ a appears in \nLa0.7Nd0.3Fe11.5Si1.5, whereas the maximal Δ TC occurs in La 0.7Ce0.3Fe11.5Si1.5. This feature remains for \nother R contents, and a simple anal ysis shows that TC decreases with x at a rate of ~20.8 K/atom for R=Nd, \n~32.3 K/atom for R =Pr, a nd ~85.9 K/atom for R=Ce.  \nAlthough the doping effect of R varies from sample to sample, the generic tendency is clear: it yields \na considerable depression of TC. This result implies the presence of additional factors that affect the Curie \ntemperature by considering the fact that the R–T coupling may have a positive contribution to TC. As \ndemonstrated by the data in  Figure 10, the incorporation of smaller R atoms leads to significant lattice \nshrinkage. This, according to our previous work, will cause a depr ession of the exchange integral between \nFe atoms due to the reduction of Fe –Fe distance. From the systematic investigation of the magnetic \ncoupling under high pressure, which yield s a lattice contraction without changing sample composition, it \nhas been fou nd that the decrease of phase volume leads to a TC reduction at a rate of ~3.72 K/ Å (marked \nby solid circles in Fig. 10). The Curie temperature s of the LaFe 13−xSix compound s, with Si content \nbetween 1.3 and 1.9, are also presented in Fig ure 10 for comparison (open circles). A similar TC–V \nrelation to that of the LaFe 11.5Si1.5 compound under pressure is obtained if only the lattice effects caused \nby the Si -doping are considered. These results indicate the universality of the TC–V (V=a3) relation for the \nsamples with only the Fe –Fe interaction. It can be clearly seen that the incorporatio n of R results in a \nsignificant change of the TC–V relation (solid squares and triangles in Fig. 10). Although TC linearly \nreduces with the decrease o f lattice constant, (i.e.  the increase of R content), the decrease rate is less rapid \nthan that of LaFe 11.5Si1.5. This fe ature becomes increasingly obvious as R goes from Ce to Nd, and a \nsimple calcul ation gives the TC–V slopes of ~85 0, ~147 0, and ~352 0 K/nm3, respectively, for the Nd -, Pr-, \nand Ce -doped compounds. All of these values are smaller than that of  LaFe 11.5Si1.5 (~372 0 K/nm3) for \ndifferent extents, and indicate the presence of magnetic coupling between R and Fe.  \n \n3.6 MCE in the vicinity of the first -order phase transition  \nFor an idealized first -order transition, that is, the magnetization is a step  function of temperature, we \nshowed that the Maxwell relation and the Clausius -Clapeyron equation gave similar results.[57] Based on \nthe integrated Maxwell relation, entropy change can be expressed as   13 \ndHTMTS\nPH\n\n\nH \n0 \n,)( \nCC PHC\nCTMHdTdHdTTTM \n\n\n(H)T \n)0( T ,1\nC\nC) (       \n,                       (7) \nwhere the equalities ( M/T)H,P= Mδ(T-TC) and d TC/dH=TC/H have been used. The right side of \nEquation  (7) is exactly the entropy change predicted by the Clausius -Clapeyron equation. It reveals a \nconstant entropy change in a temperature range between TC(0) and TC(H) whereas null otherwise,  without \nthe effects from the variation of magnetic order parameter. This work proves the applicability of the \nMaxwell relation to first -order phase transition.  \nIn reality,  a first -order phase transition occurs in a finite temperature range, and two phase s may \ncoexist in the trans ition process. We found[58-61] that in this case the Maxwell relation c ould yield a \nspurious S peak in the vicinity of the Curie temperature TC(H=0). Besides the phase coexistence, some \nother important factors may have great infl uence on the MCE evaluation in the vicinity of first -order \nphase transition. For example, the magnetic domains and the discrepancy between macroscopic \nmagnetization and magnetic order are usually ignored, which may lead to revaluating the results \ndetermine d by Maxwell relation in the vicinity of a first -order phase transition.[61]  \nThe origin and physical meaning of spike -like entropy -change curves can be revealed by a \ncomparison between the Maxwell relation and heat capacity methods. As an example, Figure 11a shows \nthe magnetization isotherms of La0.7Pr0.3Fe11.5Si1.5 measured in the field ascending process. A stepwise \nmagnetic behavior appears at TC (critical temperature under zero applied magnetic field), signifying the \ncoexistence of FM and PM phases. The  first steep increase of magnetization marks the contribution of the \nFM phase, while the subsequent stair -like variation signifies the filed -induced FM transition of the PM \nphase. The corresponding entropy change calculated by the Maxwell relation is shown  in Figure 11b \n(H=5 T). In addition to the flat Δ S plateau, an extra spike -shaped peak appears at exactly the same \ntemperature where stepwise magnetic behaviors appear. The heat capacit ies of the two samples w ere also \nmeasured under the fields of 0 and 5 T, and the entropy change indicates the absence of the spike S peak.  \nThese results show the failure of the Maxwell relation, which cannot give a correct result for the \nentropy change near TC. Considering the fact that magnetic field affects only the magne tic state of PM \nphase, which coexists with the FM phase near TC, only the PM phase contri butes to thermal effect. With \nthis in mind, a modified equation for calculati ng S can be established. Figure 11c is a schematic diagram \nshowing the determination of S for the system with an idealized stepwise behavior. Denoting the area \nsurrounded by the two M-H curves at T1 and T2 as 1+2, the Maxwell relation gives S=(1+2)/(T1-T2). \nConsidering the fact that the field -induced metamagnetic transition takes place i n the PM phase, only 1 \ncontributes to S. This implies S= 1/(T1-T2). \nStepwise magnetic behaviors widely exist in magnetic materials such as MnAs 1-xFex[62] and \nGd5Si4-xGex.[63] It was also observed in MnAs[64] and Mn 1-xCuxAs[65] under high pressure. It c ould be a \ngeneral feature of the first -order phase transition because the finite temperature width of the phase \ntransition. In this case, S should be handled car efully. It is worthy not ing that the applied field drives  14 both magnetic moments and magnetic d omains toward the applied field before reaching the saturat ion \nmagnetization. In fact, magnetization is a measure of magnetic moment in the direction of applied field. \nIts change in field direction does not inevitably reflect the change in magnetic order o f the materials. Only \nwhen the magnetization really gives a description of the magnetic order, the Maxwell relation predicts the \ncorrect entropy change. The Maxwell relation does not distinguish the FM and PM phases. As a result, \nwhen magnetic hysteresis o ccurs and two phases coexist, the area bounded by two adjacent magnetization \nisotherms could be large, giving rise to the spike -like S peak . In contrast, when FM materials are under a \nsaturated field, the applied field can drive the magnetic moments direc tly, and the domain effect is \nnegligible approximately. Therefore, the Maxwell relation may be applicable when the magnetic moments \nare manipulated by the applied field freely.  \n \n3.7 Thermal and magnetic hysteres es in La(Fe 1-xSix)13-based  alloys  \nAs mentione d before , significant MCE appears to be usually accompan ied with  a first -order magnetic \ntransition. A typical feature of the first -order transition is thermal and magnetic hystereses. This \nphenomenon is especially obvious in R -doped LaFe 13-xSix,[44,59] Gd5(Si1-xGex)4,[63] and MnAs -based[62] \ncompounds. The study  by Shen et al .[44] have  show n that t he M–T curve  of La 1-xRxFe11.5Si1.5 has a thermal  \nhysteresis , which  enhances with the increase of R concentration. The thermal hysteresis is about 1.4 K , 3.2 \nand 5 K for LaFe 11.5Si1.5, La 0.7Nd0.3Fe11.5Si1.5 and La 0.5Pr0.5Fe11.5Si1.5, respectively. This result implies that \nthe substitution of R for La  in LaFe 11.5Si1.5 can enhance thermal -induced first -order magnetic transition. \nFigure s 12a, b and c  presents the magnet ization isotherms of La 1-xPrxFe11.5Si1.5 (0, 0.2 and 0.4) , \nrespectively,  obtained for the field descending -ascending cycling.[59] Two features can be clearly seen \nfrom these figure s. The first one is the enhancement of magnetic hysteresis with the increase  of Pr content \nand the second one is the growth of hys teresis as temperature approaches TC from above. This result \nreveals the intensifying of the first -order nature of the phase transition after introduc ing Pr. \nDefining the hysteresis loss  as the area enc ircled by the two magnetization isotherms obtained in the \nfield ascending -descending cycling, Shen et al.[44] obtained the temperature dependent hysteresis loss es as \nshown in  Figures 12d and e  for the La 1-xRxFe11.5Si1.5 compounds (R=Nd or Pr). The hysteres is loss is \nmaximal near TC, reaching a value of ~100 J/kg for R=Pr. With the increase of temperature,  it decreases \nrapidly, and vanishes above ~210 K. This means the weakening of the first -order nature of the phase \ntransition as TC grows. When temperature is fixed, hysteresis loss  increases with the increase of R content. \nThe hysteresis  losses are, for instance, ~20 J/kg in LaFe 11.5Si1.5 and ~70 J/kg in La 0.7Pr0.3Fe11.5Si1.5, under \nthe same temperature of 195 K. Similar effects are observed in the cases of Pr and Nd doping. These \nresults are different from th ose of Fujieda et al.,[42] who claimed a depression of hysteresis  loss after the \nincorporation of magnetic rare earth Ce.  \nMagnetic hysiteresis can depress the efficiency of magnetic refrigeration. Among  other requirements, \ntwo basic demands for practical refrigerants are strong MCE and small hysteresis loss. Although the \nfirst-order materials have obvious advantages over the second -order ones as far as the entropy change is \nconcerned, they usually exhibi t considerable thermal  and magnetic hysteres es. By partially replacing Ge  15 with Fe, Provenzano et al.[66] depressed the hysteresis loss in the Gd 5Ge2Si2 compound. Our studie s have \nalso show n that appropriate substitution of Co for Fe in LaFe 13−xSix can cause the weakening of the \nfirst-order character of the phase transition, in addition to the high temperature shift of TC, thus a \nreduction of thermal/magnetic hysteresis.[33,54,67 ] However, the improvement of the hysteresis behavior \nalways acc ompan ies the weakening of the magnetocaloric property of the materials. It is therefore highly \ndesired to find an approach to depress magnetic hysteresis without considerably spoiling the MCE.  \nRecently Shen et al .[53] found that the hysteresis can be si gnificantly depressed by introducing \ninterstitial carbon atoms into the compound. Figure 12f displays the hysteresis loss of \nLa0.5Pr0.5Fe11.5Si1.5Cδ. The hysteresis loss  decreases from 9 4.8 J/kgK to 2 3.1 J/kgK when δ increases from \n0 to 0.3. In the meantime, the entropy change, obtained for a field change of 0 -5 T, varies from 3 2.4 J/kgK \nto 27.6 J/kgK. This result indicates that the introduc tion of interstitial carbon atoms could be a promising \nmethod of depressing hysteresis loss while maintain ing MCE. Gao et al .[68] also investigated the entropy \nchange and hysteresis loss in LaFe 11.7(Si1-xCux)1.3. With Cu content  increasing  from x = 0 to 0.2, TC \nincreases from 185K to 200K, metamagnetic behavior becomes weaker, and magnetic entropy change S \ndrops  off. However, S remains a large value, ~20 J/ kgK, when x reaches 0.2. Both thermal and \nmagnetic hysteres es are reduced by introducing Cu. The maximal hysteresis loss at TC drops  off from 74.1 \nJ/kg to zero when the Cu  content x  increases from 0 to 0.2. \nTo get a deep understanding of the effect of magnetic hysteresis, the magnetic isotherms of the \nLa1-xRxFe11.5Si1.5, La0.7Pr0.3Fe13-xSix, La0.5Pr0.5Fe11.5Si1.5C and La0.5Pr0.5Fe11.4Si1.6N intermetallics were \nfurther studied. Based on these data the relation between the maximum entropy change and hysteresis loss \nwas established  as shown in Figure 13. ΔS and hysteresis loss  exhibit a simultaneous  change, the former \ndecreases as the latter vanishes. Fortunate ly, the variation of hysteresis loss  is much more rapidly than ΔS, \nand the latter can be as high as ~20 J/kgK when the former is negligibly small. According to the standard \nthermodynamics, for the nucleation and the development of the second phase in the background of the \nfirst phase, a driving force is required to overcome energy barrier between two phases. These results \nindicate that the driving fo rce of the phase transition is similar in the LaFe 13-based intermetallics, \nregardless of their composition s. The main reason for the reduction of hysteresis loss  could be the high \ntemperature shift of TC. The strong thermal flu ctuation at a high temperatur e provides the driving force \nrequired by the phase transition.  \n \n3.8 Direct measurement of MCE for La(Fe,Si) 13 based compounds  \nAs an alternative characterization of the MCE, the adiabatic  temperature change of La(Fe,Si) 13 was \nmeasured  by Hu et al .[32,69,70 ]. Figure 14a displays the temperature -dependent Tad obtained in both \nheating and cooling processes for sample LaFe 11.7Si1.3 (TC 188K ). The peak value of Tad reaches 4 K \nupon the field chang ing from 0 to 1.4 T. The field -dependent Tad collected at diffe rent temperatures in \nthe vici nity of TC is shown in  Figure 14b. One can find that Tad collected above 183.2 K has a nearly \nlinear dependence on applied field in a region of 0.4 T < H < 1.4 T.[69,70] Most curves (except for those at \n182.5 and 183.2 K) do n ot display a saturation behavior. It means that adiabatic temperature change  16 would increase noticeably with field increasing. Based on the linear dependence, Tad value can reach \n5.8K for a 0 -2T field change. Similarly, we measured Tad for La(Fe 0.94Co0.06)11.9Si1.1 with TC=274K. The \nobserved Tad reaches 2.4 K upon the field chang ing from 0 to 1.1 T.[32,70] Tad also has a nearly linear \ndependence on applied field at temperatures near TC. In this way, the estimated value of Tad can be 3.2K \nfor a 0 -2T fiel d change.  \nWe also calcul ated Tad for La(Fe,Si) 13-based compounds from the heat capacity measurements.  \nFigure 14c displays the Tad as a function of temperature for LaFe 13-xSix under different magnetic fields. \nThe maximal  value of Tad as a function of Si content x  is shown in Fig ure 14d. One can find that with the \nevolution from first -order to second -order transition, Tad decreases from 11.4 K for x=1.4 to 3.5 K for \nx=2.2  for a field change of 0 5T. It was also observed that the values of Tad for LaFe 11.7Si1.3 and \nLaFe 11.1Si1.9 are 9.4 and 2.6 K for a field change of 0 2T, respectively.  \nBecause of the  discrepanc y amon g thermal measurements, the Tad data reported by different groups \nare not identical . Fujieda et al.[71] made both indirect and direct Tad measurements on the same sample, \nLaFe 11.57Si1.43. The directly measured Tad value was 6  K at TC = 188K for a field change of 02 T while \nthe indirect Tad calculated from heat capacity measurement was 7.6  K. The directly measured Tad for \nLaFe 11.57Si1.43H1.6 was 4 K at TC = 319 K for a 02 T field change, which is probably lower than the \nindirect value by 2 to 3 K. Despite the discrepance among  different experiments, all these data  verified the \npotential application of La(Fe,Si) 13-based compounds as magnet ic refrigerants.  \n \n3.9 Progress in practical applications  \nSince Brown proposed to use Gd for the room temperature magnetic cooling in 1976, a number of \ninteresting magnetocaloric materials with tunable Curie temperatures and attractive  magnetocaloric \nproper ties have been discovered in recent years, such as G dSiGe, La(Fe,Si,Al) 13, MnFePAs, NiMn(Ga,  Sn, \nIn), etc. which have opened the way  to improve temperature span and efficiency for a refrigerant device. \nThe synthesis of La(Fe,Si,Al) 13 is friendly and does n ot require extremely high -purity and costly raw \nmaterials, thus La(Fe,Si,Al) 13-based materials are considered to have  high potential application s near \nroom temperature. Several groups have tested the cooling effect in devices near room temperature. Zimm \net al.[72] carried out a preliminary test by using irregular La(Fe 0.88Si0.12)13H1.0 particles of 250∼500 μm in \nsize as refrigerants in a rotary magnetic refrigerator (RMR) and found that cooling capacity of \nLa(Fe 0.88Si0.12)13H1.0 compares favorably with that of Gd. Fujita et al .[73] tested the hydrogenated \nLa(Fe 0.86Si0.14)13 spheres with an  average diame ter of 500μm  in an AMR -type test module, and observed a \nclear difference in temperature  between  both the ends of the AMR bed. The temperature span of 16K was \nachieved in a steady state.  \nOur prototype test with using various La(Fe,Si,Al) 13-based particles as refrigerants in an AMR \nmodule  is being performed. La(Fe,Si,Al) 13 material is brittle and easily pulverized. Their poor corrosion \nresistance also restricts  their applications. C orrosive characteristics of La(Fe 0.94Co0.06)11.7Si1.3 with minor \n-Fe were in vestigated  by Long et al.[74] It was found that the random pitting corrosion appears first in the  17 phase of 1:13, resulting in products of La 2O3, γ-Fe(OOH), Co(OH) 2 and H 2SiO 3. Further studies have \nrevealed that a hybrid inhibitor can prevent  the materials from being eroded. Sample tests showed that the \nbest inhibition efficiency was nearly 100% by using the corrosion inhibitor. No corrosion product s were \nfound after sample had been  immersed in the inhibitor for 7776 h . La(Fe 0.92Co0.08)11.9Si1.1 spheres through  \na rotating electrode process  was also fabricated . The test in an AMR module is under way.  \n \n4. MCE in La (Fe,Al )13-based compound s \nLaFe 13-xAlx compounds possess rich magnetic properties  compared with LaFe 13-xSix compounds . For \nthe substitutions of Si for Fe atoms, the stable concentration region is only 1.2 < x < 2.6 and the obtained \npseudobinary compounds exhibit ferromagnetic characteristics.[21,24] By substituting Al for Fe atoms, the \nconcentration region becomes much wider, 1.0 < x < 7.0, and the stabilized LaFe 13-xAlx compounds \nexhibit complicated magnetic properties.[19] The systems will be in favor of the LaFe 4Al8 structure if the \nAl concen tration is too large, and a large amount of -Fe will  appear if the Al content is too small. \nLaFe 13-xAlx compounds with NaZn 13-type structure exhibit three types of magnetic order s with the \nvariation of  Al concentration. Mictomagnetic states were found for  a high Al concentration from x = 4.9 to \n7.0, originating from a competition between antiferromagnetic Fe -Al-Fe superexchange and ferromagnetic \nFe-Fe direct exchange. For the Al concentration ranging from x=1.8 to 4.9, the system manifests soft \nferromagnet ic properties. At the minimum  permitted Al concentration s from x=1.0 to 1.8, they show weak \nantiferromagnetic coupling, which can be overcome even by applying a small field of a few Testa and \ncause a spin -flip transition to ferromagnetic state. Our studies  have revealed that a small doping of Co can \nmake the antiferromagnetic coupling collapse, resulting in a ferromagnetic state.  \n \n4.1 Room temperature MCE in Co -doped La(Fe,Al )13 \nIn 2000, Hu et al .[11,75] firstly studied magnetic entropy change in Co -doped La(Fe,Al )13. \nLa(Fe 0.98Co0.02)11.7Al1.3 and LaFe 11.12Co0.71Al1.17 exhibit ferromagnetic behavio urs with a second -order \nmagnetic transition at TC198K and 279K, respectively. The magnetic entropy change is about 5.9 and \n10.6 J/kgK for La(Fe 0.98Co0.02)11.7Al1.3, and 4.6 and 9.1 J/kgK for LaFe 11.12Co0.71Al1.17 under field change s \nof 02 T and 05 T, respectively. Our experiments have confirmed the antiferromagne tic nature of \nLaFe 11.7Al1.3 and LaFe 11.83Al1.17, and found that Co doping can convert the antiferroma gnetic coupling to a \nferromagnetic one. TC shifts to ward  higher temperature s with Co content  increasing .[76] Figure 15 displays \nmagnetic entropy change of La(Fe 1-xCox)11.83Al1.17 (x=0.06 and 0.08). The S of La(Fe 1-xCox)11.83Al1.17 has \nnearly the same magn itude as that of Gd near room temperature. The calculated S in the molecular field \napproximation is also shown  in Fig ure 15. The theoretical result is in qualitative agreement with the \nexperimental one. Since the highest magnetocaloric effect involving a second order magnetic transition \nnear room temperature is produced by Gd, and most intermetallic compounds which are ordered \nmagnetically near or above room temperature show significantly lower | S| than Gd,[7] obviously, these \nresults are very attractive.   \nThe high magnetization of Co -doped La(Fe,Al )13 is considered to be responsible for the large | S|.[76]  18 From M-H curves measured at 5 K, the values of 2.0 and 2.1μ B/Fe(Co) were determined for \nLa(Fe 1-xCox)11.83Al1.17 (x=0.06 and 0.08), respectively. Usuall y, a small substitution  of Co can shift TC \ntoward  high temperatures without affecting the saturation magnetization considerably. As a result, | S| \nremains nearly unchanged upon increasing the substitution of Co for Fe.  \n \n4.2 Nearly constant magnetic entropy  change in La(Fe, Al )13  \nAn ideal magnetic refrigerant suitable for use in an Ericsson -type refrigerator should have a constant \n(or almost constant) magnetic entropy change through the thermodynamical cycle range.[77] A good choice \nfor a suitable Ericsson -cycle refrigerant would be a single material with an appropriate | S| profile. \nTypical materials with such properties are those of the series (Gd , Er)NiAl,[78] in which the suitable \nworking temperature range is from 10 to 80K. However, at relatively high  temperatures, rare materials \nwere reported to show a table -like S. We investigated  magnetic entropy change around phase boundary  \nin LaFe 13-xAlx compounds. A table -like S from 140K to 210 K involving two successive transitions \nwas found in a LaFeAl sam ple at phase boundary.[79] \nHu et al . tuned Al content from x = 1.82 to x = 1.43 in LaFe 13-xAlx and a gradual change from \nferromagnetic (F M) to weak antiferromagnetic (AF M) state was observed. A completely F M ground state \nat x=1.82 is followed by the emerge nce of AF M coupling at x=1.69 and 1.56, in which two spaced \ntransitions appear, one at T0 from F M to AF M and the other at TN from AF M to paramagnetic state. The \ntransition nature at T0 and TN are of first -order and second -order, respectively. Continuously reducing Al \nto x=1.43 results in a completely AF M ground state.[80] X-ray diffraction measurements at different \ntemperatures were performed to monitor the change of crystal structure. We found that the samples \nremain cubic NaZn 13-type structure when the ma gnetic state changes with temperature, but the cell \nparameter changes dramatically at the first -order transition point T0.[79] \nFrom the  magnetic entropy change S as functions of temperature and magnetic field for LaFe 13-xAlx \n(x=1.82, 1.69, 1.56, and 1.43)  compounds , it was found  that with the emergence and enhancement of AF \ncoupling, the S profile evolves from a single -peak shape at x=1.82 to a nearly constant -peak shape at \nx=1.69 and 1.56, and then to a two-peak shape at 1.43.  The nearly temperature inde pendent |S| over a \nwide temperature range (an about 70 K span from 140 to 210 K) in the sample with x=1.69 is favorable \nfor application in an Ericsson -type Refrigerator working in a corresponding temperature range.  \n \n4.3 Interstitial Effect  in La(Fe,Al )13  \nWang et al.[81] investigated interstitial effect  on magnetic properties and magnetic entropy change  in \nLa(Fe, Al )13 alloys. Carbonization brings about an obvious increase in lattice parameter, thus an \nantiferromagnetic to ferromagnetic transition. In LaF e11.5Al1.5, a considerable increase of Curie \ntemperature from 191 to 262 K was observed with carbon concentration increasing from 0.1 to 0.5, \nhowever, only a slight increase in saturation magnetization is accompanied. The magnetic transition is of \nsecond -order in nature and thus the magnetization is fully reversible on temperature and magnetic field. \nOne can find that all the LaFe 11.5Al1.5 carbides exhibit a considerable magnetic entropy change,  19 comparable with that in Gd around the Curie temperature. Thus,  one can get a large reversible magnetic \nentropy change over a wide temperature range by controlling the carbon concentration.  \n \n5. Magnetic and magnetocaloric properties in Mn -based Heusler a lloys  \nMn-based Heusler a lloys are well -known for their shape -memo ry effect, superelasticity, and \nmagnetic -field-induced strain. In stoichiometric Ni 2MnGa alloys, the nearest neighboring distance \nbetween Mn atoms is around 0.4 nm. Ruderman -Kittel -Kaeya -Yo (RKKY) exchange through conductive \nelectrons leads to a ferromagne tic ordering. The magnetic moment is mainly confined to Mn atoms, 4.0 \nB, while Ni has a rather small m oment . Ni–Mn–Ga undergoes a marte nsitic-austenitic transition. \nAlthough both the martensite and au stenite phases are usually ferromagnetic , their magnet ic behaviors are \nsignificantly different. The marte nsitic phase is harder to be magnet ically saturated because of its large \nmagnetocrystalline anisotropy. The simultaneous change s in structure and magnetic propert y at the phase \ntransition yield significant  entropy changes.  \nIn 2000, Hu et al. firstly reported on entropy change S associated with the stru cture transition in a \npolycrystalline Ni 51.5Mn 22.7Ga25.8 (Fig.  16a).[82] The marte nsitic-austenitic transition, which is of first order \nin nature with a ther mal hysteresis about 10K, takes place at 197K. A positive entropy change, 4.1J/kgK \nfor a field change of 00.9 T, appear s, accompanying the field-induced changes in magnetization and \nmagnetic anisotropy. A positive -to-negative crossover of the entropy cha nge[83] and subsequent growth in \nmagnitude were  further observed as magnetic field increases, and a  negative S of ~ 18 J/kgK (300K) \nfor the field change of 0 5 T was obtained in single crystal Ni52.6Mn 23.1Ga24.3 (Fig.  16b).[84] For the \nNi52.6Mn 23.1Ga24.3 single crystal, the thermal hysteresis around marte nsitic transition is about 6  K, and the \nmagnetic hysteresis is negligible.  \nSince the first report of large entropy change in Ni 51.5Mn 22.7Ga25.8,[82] numerous investigations on the \nmagnetic properties and  magnetocaloric effect (MCE) in various f erromagnetic shape memory Heusler  \nalloys (FSMAs) have been carried out.[16] Typical reports are about the great | S| obtained in a \npolycrysta lline Ni 2Mn 0.75Cu0.25Ga[85] and a single crystal Ni55.4Mn 20.0Ga24.6,[86] in which the structural and \nthe magnetic transition s are tuned to coincide with each other. Ho wever, the large entropy change usually \nappears in a narrow temperature range, for example  15 K. As is well know n, a real magnetic refrigerator \nrequires not only a large MCE but also a wide temperature span of the MCE. Although the | S| in these \nconventional  Heusler alloys can be very large, the narrow temperature span of the S may restrict  their \napplications.  \nA recent discovery of metamagnetic shape memory alloy s (MSMAs) has arouse  the intens ive interest \nbecause of huge shape memory effect and different mechanism from th at of traditional alloys.[87] In these \nGa-free Ni -Mn-Z Heusler alloys (where Z can be a n element of group III or group IV , such as In, Sn  or \nSb), an excess of Mn causes a fundamental change of magnetism for parent and product phases. A strong \nchange of magnetization across the martensitic transformation results in a large Zeeman energy 0MH. \nThe enhanced Zeeman energy  drives the structural transf ormation and causes a field -induced \nmetamagnetic behavior, which is responsible for the huge shape memory effect. The simultaneous  20 change s in structure and magnetism , induced by magnetic field , should be accompanied by a large MCE . \nSeveral groups studied m agnetic properties and MCE, and inverse MCE with a relative wide temperature \nspan has been observed.[88-92] \nThe composition s of Ni50Mn 34In16 belong  to the so -called MSMAs, which is the only one that exhibits \na field -induced transition in Ni 50Mn 50-yIny.[93] Several groups investigated its shape memory effect and \nmagnetocaloric effect. The reported ΔS with a considerable large temperature span  reaches 12J/kgK under \na magnetic field of 5T,[92] which is larger than that of Gd. However, the large ΔS takes place around 180  K, \nwhich is still far from room temperature. Furthermore, a large hysteresis is accompanied even for the \nmetamagnetic shape memory alloys. The reported thermal hysteresis can be as large as 20 K for \nNi-Mn-Sn[89] and 10K for Ni -Co-Mn-In alloys.[87] For Ni50Mn 34In16, the thermal hysteresis even reaches \n20 K, and more seriously it becomes further wider with external field  increasing .[92] Our recent studies \nreveal ed that a little more increase of Ni content not only increases Tm and but also signif icantly enhances \nthe magnetic entropy change. More importantly, it can remarkably improve the thermal hysteresis.[94]  \nThe zero -field-cooled (ZFC) and field -cooled (FC) magnetization s were measured under 0.05 T, 1 T, \nand 5 T for Ni51Mn 49-xInx (x = 15.6, 16 .0, and 16.2) .[94] One can find that all alloys show a very small \nthermal hysteresis, < 2 K, around martensitic  transition. More importantly, an increase in magnetic filed \ndoes not enlarge the hysteresis for all samples. The frictions from domain rearrange ments and phase \nboundary motions are considered to be a main factor affecting the hysteresis gap.[95,96] The gap of thermal \nhysteresis may characterize the strength of frictions during the transformation. In these systems, the small \nhysteresis indicates th at the friction to resist the transformation is small. Anyway, t he small thermal \nhysteresis is an aspiration of engineer s to apply MCE materials to a refrigerator. These features guarantee \nthat the magnetocaloric effect is nearly reversible on temperature even a high magnetic field is applied.  \nOur study showed  that the entropy change  ΔS of Ni 51Mn 49-xInx is positive, peaks at Tm and gradually \nbroadens to lower temperature, which is a result of the field induced metamagnetic transition from \nmartensitic to austenitic state at temperatures below Tm. The maxim al value s of ΔS reach 33, 20, and 19 \nJ/kgK at 308 K, 262 K, and 253 K for compositions x = 15.6, 16.0, and 16.2, respectively. In comparison \nwith ΔS (12 J/kgK,  at 188 K) observed in Ni 50Mn 34In16 alloys, not  only the Tm, at which ΔS peaks, goes \nmuch nearer to room temperature but also the size of ΔS is remarkably enhanced. ΔS span could reach \n20 K under a field of 5T. Such a large temperature span should be attractive compared with the \ntraditional Heusler al loys.  \nThe Δ S shows a table -like peak under 5T for Ni51Mn 49-xInx. The flat plateau of ΔS should reflect the \nintrinsic nature of magnetocaloric effect . In some first -order systems, such as LaFeSi, ΔS peak usually \nexhibits a peculiar shape, an extremely high  spike followed by a flat plateau. Detailed studies[58] suggested \nthat the extremely high peak dose not reflect the intrinsic entropy change but a spurious signal . However, \ncareful investigations based on specific heat measurements verified that the flat p lateau does reflect the \nintrinsic nature of ΔS. Similar to the case of the first -order systems La -Fe-Si,[58] the broad plateau of ΔS \nshould reflect the intrinsic nature of magnetocaloric effect . As is well  know n, a plateau -like ΔS is \nspecially desired f or Ericsson -type refrigerators.   21 We also investi gated magnetic properties and entropy change in Co -doped NiMnSn alloys , and  found \nthat t he incorporation of Co enhances ferromagnetic exchange for parent phases, while the magnetic \nexchange of martensitic phase keeps nearly unchanged. An external magnetic field can shift Tm to a lower \ntemperature at a rate of 4.4 K/T in Ni43Mn 43Co3Sn11 and a field -induced structural transition takes place . \nAssociated with the metamagnetic behaviors, a large positive entropy change, 33 J/kgK ( ΔH=5 T, at 188 \nK), is observed. T he ΔS also displays a table -like peak under 5 T.  \n \n6. MCE in other materials  \nCompared with the first -order  materials,  the second -order  ones can have comparable  or even larger  \nrefrigerant capacity ( RC) though they sometimes  exhibit relatively low ΔS. Moreover, the absence s of \nmagnetic and thermal hystereses are also promising features of the materials of this kind. As mentioned \nabove, the hysteresis loss, which makes magnetic refrigeration less efficient , usually  happened \naccompanying a first -order transition. It is therefore of significance to search for efficient magnetic \nrefrigerants with the second -order characters.  \n \n6.1 MCE in R6Co1.67Si3  \nIn the previous studies,  a family of ternary silicides R 6Ni2Si3 with R =  La, Ce, Pr and Nd was \ndiscovered .[97] Recently, a ferromagnetic silicide  Gd6Co1.67Si3 derived from the Ce 6Ni2Si3-type structure \nwas reported .[98] The compound exhibits a high saturation magnetization and a reversible second -order \nmagnetic transition at a  temperature  of 294 K.  Thus, large values of |ΔS| and RC of R 6Co2Si3 \ncompounds around room temperature could be expected. Shen et al.[99-101] studied the magnetic properties \nand MCE s of the R6Co1.67Si3 compounds  with R = Pr, Gd and Tb . The MCE  of R6Co1.67Si3 (R = Gd a nd \nTb) and Gd6M5/3Si3 (M = Co and Ni) were also studied by Jammalamadaka  et al.[102] and Gaudin  et al. ,[103] \nrespectively.  \nR6Co1.67Si3 (R = Pr, Gd and Tb)  have a single phase with a  hexagonal Ce 6Ni2Si3-type structure (space \ngroup P63/m). The TCs are determ ined to be 48, 298 and 186 K, respectively. The TC of Gd 6Co2Si3 is \nnearly  as large as that of Gd. Figure  17a shows the magnetization isotherms  of R6Co2Si3 (R = Pr, Gd and \nTb) around the Curie temperature.[99-101] It is evident that each isotherm near TC shows a reversible \nbehaviour between the increasing field and decreasing field. Moreover, neither inflection nor negative \nslope in the Arrott plot of R6Co1.67Si3 is observed as a signature of metamagnetic transition above the TC, \nindicating a characteristic of second -order magnetic transition. The Δ S as a function of temperature for the \nR6Co1.67Si3 compounds with R = Pr, Gd and Tb is shown in Fig ure 17b.[99-101] It is found that both the \nheight and the width of ΔS peak depend on the applied field, increasing  obviously with the increas e of \napplie d filed. T here is n o observed  a visible change in peak temperature of ΔS. The Δ S–T curve  shows a \n“”-type as displayed  in typical second -order  magnetocaloric  materials . For the R6Co1.67Si3 (R = Pr, Gd \nand Tb) , the maximal values of |ΔS| are 6.9, 5.2 and 7. 0 J/kgK, respectively, for field chang ing from 0 to \n5T. \nIn general, the refrigeration  capacity  (RC) is an important characteri stic of the magnetocaloric  22 materials, providing an accepted criterion to evaluate the refrigeration efficiency  which is of special ly \nimportance in practical application. The RC value, obtained by  integrating numerically the area under the \nΔS-T curve  using the temperature  at half maximum  of the ∆S peak as the integration limits ,[104] is 440 J/kg \nfor Gd6Co1.67Si3 for a field change of 05 T, much larger than those of some magnetocaloric materials  for \na field change of 0 5 T, such as Gd5Ge1.9Si2Fe0.1 (355 J/kg at 305 K),[66] Gd5Ge1.9Si2 (235 J/kg at 2 70 \nK),[66] and Gd5Ge1.8Si1.8Sn0.4 ribbons prepared at 15 45 m/s (305335 J/kg at 260 K).[105] For the RC \nvalue, it is necessary to take into account the hysteresis loss. However the study on th e isothermal field \ndependence of magnetization  for Gd6Co1.67Si3 reveals no hysteresis loss . It is very important to \nGd6Co1.67Si3 that the large |∆S| and the enhanced RC are observed to occur around 298  K, thereby \nallowing room -temperature magnetic refrigeration. This result is of practical importance, because the \nGd6Co1.67Si3 can be a good working material for magnetic refrigeration at the ambient temperature . \n \n6.2 MCE in CdCr 2S4 \nAB 2X4-type sulfospinels have attracted much attention due to their colossal magnetocapacity \neffects[106] and large magnetoresistance effects.[107] Many of sulfospinels, e.g.  (Cd,Hg)Cr 2(S,Se) 4, have \nferromagnetic spin config uration and large spontaneous magnetization.[108] CdCr 2S4 is a member of the \nchalcogenide ACr 2S4 spinels with ferromagnetically coupled Cr3+ spins ( S=3/2). Recently, Yan et al.[109] \nstudied the magnetocaloric effects of CdCr 2S4. A polycrystalline CdCr 2S4 sample was fabricated by using  \nthe solid -state reaction method. The sample is a normal spinel structure of space group Fd3m with Cr3+ \noctahedrally and Cd2+ tetrahedrally surrounded by sulfur ions , and its lattice parameter and Curie \ntemperature are 1 .0243(4) nm and = 87 K, respectively. The saturation moment is about 5.96 B per \nformula unit , in agreement with ferromagnetically ordered Cr3+ spins due to the superexchange interaction \nbetween Cr –S–Cr atoms.[110] Magnetic entropy change versus temperature  is shown in Fig ure 18(a). Near \nthe Curie temperature, the maxim al entropy change is 3.9 and 7.0 J/kg K for the field changes of 2 and 5 T , \nrespectively . The Arrott plot of CdCr 2S4 shows a characteristic of second -order magnetic transition. This \nlarge magnetic e ntropy change can be attributed to a sharp drop in magnetization with temperature \nincreasing near Curie temperature. Yan et al  also performed the measurements of the heat capacity in the \nfields of H=0, 2, and 5 T. An applied field broadens th e peak and rou nds it off in high field s, which \nfurther indicates a second -order phase transition.[9] The isothermal magnetic entropy change ΔSheat \ncalculated from the heat capacity data exhibits a similar behavior to ΔS. The adiabatic temperature change \nΔTad is presente d in Fig. 18(b). The maxim al values of ΔTad are about 1.5 and 2.6 K for magnetic field \nchanges of 2 and 5 T, respectively. Shen et al.[111] further  studied the magnetocaloric effects  in spinels (Cd, \nM)Cr 2S4 with M = Cu or Fe. It is found that t he partial r eplacement of Cd by Cu can exert a little \ninfluence on the magnetic coupling, and only a small shift of T C from 86 K to 88 K was observed. In \ncontrast, a significant increase of TC from 86 K to 119 K was observed, which stems from the substitution \nof Fe fo r Cd. The maxim al values of m agnetic entropy change ΔS were  found to be 5.1 and 5.4 J/kgK for \nCd0.8Cu0.2Cr2S4 and Cd 0.7Fe0.3Cr2S4 for a field change from 0 to 5T , respectively . \n  23 6.3 MCE  in amorphous alloys  \nAmorphous magnetic materials, in spite of their relatively small magnetic entro py change compared \nwith that of crystalline  materials, usually have a large refrigerant capacity. Recently, magnetic entropy \nchange and refrigerant capacity (RC)  of Gd -based amorphous Gd 71Fe3Al26 and Gd 65Fe20Al15 alloys were \ninvestigated by Dong et al.[112] The values of TC are 114 K for Gd 71Fe3Al26 and 180 K for Gd 65Fe20Al15, \nrespectively, which can be easily tunable by adjusting the composition. Furthermore, scarcely any thermal \nhysteresis can be observed in the vicinity of TC. The maximal  value of | magn etic entropy change  S| (7.4 \nJ/kgK for Gd 71Fe3Al26 and 5.8 J /kgK for Gd 65Fe20Al15, H=05T) is not very large, however, the values \nof RC reach 750 J /kg and 726 J /kg for Gd 71Fe3Al26 and Gd 65Fe20Al15, respectively, which are much larger \nthan those of other  magnetocaloric materials ever reported. Such a  high RC is due to the glassy structure \nthat extends the large MCE into a broad  temperature range.   \nWang et al.[113] studied the magnetic properties and MCE s of amorphous Ce2Fe23−xMn xB3 (1 ≤ x ≤ 6) \nalloys. It was found that t he magnetic state is sensitive to the Mn content  due to the competition between \nthe Fe-Fe ferromagnetic coupling and the Fe–Mn antiferromagnetic coupling. A spin glass behavior at \nlow temperature s was observ ed in the samples of x   4. Typical ferromagnetism appears  for the samples \nwith x  3, and their TC almost linearly decreases from 336 to 226 K as x increases  from 1 to 3. The \nmagnetization has a sharp drop around TC without thermal hysteresis , suggest ing a second order phase \ntransition resulting from their amorphous nature. In spite of the relatively small |S|, the value of RC for \namorphous Ce 2Fe22MnB 3 alloy is found to be ~225 J/kg  (H=0–5 T), which is comparable with that of \nsome good crystalline materi als with TC around room temperature.  \n \n7. Summary and outlook  \nInvestigations on magnetocaloric effect (MCE) are of great importance for not only fundamental \nproblems but also technological applications. Over the past decade, we have investigated the MCE  and \nrelevant physics in several kinds of materials, including La(Fe,  M)13-based compounds with M=Si and Al, \nNiMn -based Heulser alloys, Ce6Ni2Si3-type R6Co1.67Si3 compounds , AB 2X4-type sulfospinels CdCr 2S4, \netc. Among these materials, the La(Fe,  M)13-based co mpounds have received most attention. We have  \nfound  a large entropy change (|S| > 19 J/kgK , at TC < 210 K ) for a field change of 0 5 T in La(Fe,  Si)13 \nwith a low Si concentration , which is associated with negative lattice expansion and metamagnetic \ntransi tion behaviour. Partially replacing La with magnetic R atoms in La(Fe,  Si)13 leads to a remarkabl e \nincrease in entropy change , a reduction in TC and an increase  in magnetic hysteresis . A strong MCE and \nzero hysteresis loss  are obtained near room temperatur e in Co -doped La(Fe,  Si)13 alloys. By introducing \ninterstitial  hydrogen  atoms, we have found that the large MCE can remain at  room temperature.  The \nmaximal value of |S| for LaFe 11.5Si1.5Hδ attains to  20.5 J/kgK at  340 K for a field change of 0 5 T, which \nexceeds that of Gd by a factor of 2 . Introduc ing interstitial carbon atoms is found to be  a promising \nmethod of depressing hysteresis loss while the large MCE  is kept unchanged . To understand the nature of \nthe large MCE, the detaile s of phase volume and ma gnetic exchanges are studied  in hydrogenised, pressed \nand magnetic R-doped LaFe 13−xSix alloys . The most remarkable result we have obtained is the presence of  24 a universal relation between Curie temperature and phase volume: the Curie temperature  linearly g oes up \nwith the increase of lattice constant. This result implies the exclusive dependence of the magnetic \ncoupling in LaFe 13−xSix on Fe –Fe distance.  \nLa(Fe,  M)13-based materials have attracted worldwide attention  in recent years . Several hundred \nscientific papers dealing with these materials have been publishe d since  the advent of the  first report o n \ntheir large entropy change in 2000. The low cost, easy and friendly preparation, and large magnetocaloric \neffect  near room temperature make La(Fe,  M)13-based compounds more attractive as candidates for \nmagnetic refrigerants, especially the  potential application near room temperature. La(Fe,  M)13-based \ncompounds  may be a good candidate that can replac e Gd metal as a room temperature refrigera nt. Up to \nnow, over 30 related patents have been published all over the world. Several groups have te sted the \ncooling effect of La(Fe, M)13-based  materials in principle -of-proof experiments of refrigerators. The \ncooling capacity near room temperature has been verified. All these efforts and achievements give us \nfresh  hope that the magnetic refrigerators based on La(Fe,  M)13-based refrigerants may come ture in \nindustry and daily life in the near future.  \n \nAcknowledgements  \nThis work was supported by the National Basic Research Program of China, the National Natural \nScience Foundation of China and the Knowledg e Innovation Project of the Chinese Academy of Sciences . \n  25 References  \n \n[1] E. Warburg, Ann. Phys.  1881 , 13, 141.  \n[2] P. Debye, Ann. Phys.  1926 , 81, 1154.  \n[3] W. F. Giauque, J. Amer. Chem. Soc.  1927 , 49, 1864.  \n[4] W. F. Giauque, I. P. D. McDougall, Phys. Rev. 1933 , 43, 768.  \n[5] R. Li, T. Numazawa, T. Hashimoto, A. Tomoyiko, T. Goto, S. Todo, Adv. Cryog. Eng.  1986 , 32, 287.  \n[6] R.D McMichael, J. J. Ritter, R. D. Shull, J. Appl. Phys.  1993 , 73, 6946.  \n[7] V. K. Pecharsky, K. A. Gschneidner Jr., J. Magn. Magn. M ater. 1999 , 200, 44.  \n[8] G. V. Brown, J. Appl. Phys.  1976 , 47, 3673.  \n[9] V. K. Pecharsky and K. A. Gschneidner, Jr., Phys. Rev. Lett.  1997 , 78, 4494.  \n[10] Z. B. Guo, Y. W. Du, J. S. Zhu, H. Huang, W. P. Ding, D. Feng, Phys. Rev. Lett.  1997 , 78, 1142.  \n[11] F. X. Hu, B. G. Shen, J. R. Sun, X. X. Zhang, Chin. Phys.  2000 , 9, 550.  \n[12] F. X. Hu, B. G. Shen, J. R. Sun, Z. H. Cheng, G. H. Rao, X. X. Zhang, Appl. Phys. Lett.  2001 , 78, \n3675 . \n[13] H. Wada, Y. Tanabe, Appl. Phys. Lett.  2001 , 79, 3302.  \n[14] O. Tegus, E . Bruck, K. H. J. Buschow and F. R. de Boer, Nature  2002 , 415, 150.  \n[15] A. M. Tishin and Y. I. Spichkin, The Magnetocaloric effect and its application  ( IOP Publishing Ltd \n2003 ). \n[16] K. A. Gschneidner Jr, V. K. Pecharsky and A. O. Tsokol, Rep. Prog. Phys . 2005 , 68, 1479.   \n[17] E. Bruck, Handbook of Magnetic Materials  Vol. 17, edited by K. H. J. Buschow (North -Holland, \nAmsterdam, 2008 ). \n[18] P. I. Kripyakevich, O. S. Zarechnyuk, E. I. Gladushevsky, O. I. Bodak, Z. Anorg. Chem.  1968 , 358, \n90. \n[19] T. T. M. Palstra, G. J. Nieuwenhuys, J. A. Mydosh, K. H. J. Buschow, Phys. Rev. B  1985 , 31, 4622.  \n[20] G. J. Wang, F. Wang, N. L. Di, B. G. Shen, and Z. H. Cheng, J. Magn. Magn. Mater.  2006 , 303, 84.  \n[21] T. T. M. Palstra, J. A. Mydosh, G. J. Nieuwenhuys, A. M. va n der Kraan, K. H. J. Buschow, J. Magn. \nMagn. Mater.  1983 , 36, 290.  \n[22] H. Yamada, Phys. Rev. B  1993 , 47, 11211.  \n[23] A. Fujita, Y. Akamatsu, and K. Fukamichi, J. Appl. Phys.  1999 , 85, 4756.  \n[24] F. X. Hu, Magnetic properties and magnetic entropy change o f Fe-based La(Fe,M) 13 compounds and \nNi-Mn-Ga alloys , Ph. D thesis, Institute of Physics, Chinese academy of Sciences, 2002 . \n[25] F. W. Wang, G. J. Wang, F. X. Hu , A. Kurbakov, B. G . Shen, Z. H. Cheng, J. Phys.: Condense Matter.  \n2003 , 15, 5269.  \n[26] A. Fuji ta, S. Fujieda, K. Fukamichi, Phys. Rev. B  2001 , 65, 014410.  \n[27] X. B. Liu, Z. Altounian, D. H. Ryan, J. Phys.: Condens. Matter  2003 , 15, 7385.  \n[28] H. H. Hamdeh, H. Al -Ghanem, W. M. Hikal, S. M. Taher, J. C. Ho, D. T. K. Anh, N. P. Thuy, N. H. \nDuc, P. D.  Thang, J. Magn. Magn. Mater.  2004 , 269, 404.  26 [29] Z. H. Cheng, N. L. Di, Q. Q. Li, Z. Q. Kou, Z. Luo, X. Ma, G. J. Wang, F. X. Hu , B. G.. Shen, Appl. \nPhys. Lett.  2004 , 85, 1745.  \n[30] N. L. Di, Z. H. Cheng, Q. A. Li, G. J. Wang, Z. Q. Kou, X. Ma, Z. Luo, F. X. Hu , B. G. Shen, Phys. \nRev. B  2004 , 69, 224411.   \n[31] F. X. Hu, B. G . Shen, J. R. Sun, G. J. Wang, Z. H. Cheng, Appl. Phy. Lett.  2002 , 80, 826.  \n[32] F. X. Hu, J. Gao, X. L. Qian, Max Ilyn, A. M. Tishin, J. R. Sun, B. G. Shen , J. Appl. Phys.  2005 , 97, \n10M303.  \n[33] J. Shen, Y. X. Li, F. X. Hu, J. R. Sun, J. Appl. Phys.  2009 , 105, 07A901.  \n[34] J. Shen , B. Gao, Q. Y. Dong, Y . X. Li, F. X. Hu, J. R. Sun, B. G. Shen, J. Phys. D: Appl. Phys.  2008 , \n41, 245005.  \n[35] M. Balli, D. Fruchart, D. Gignoux, J. Phys.: Condens. Matter  2007 , 19, 236230.  \n[36] A. Yan, K. H. Muller, O. Gutfleisch, J. Alloys Compd.  2008 , 450, 18.  \n[37] X. B Liu, X. D Liu, Z. Altounian, J. Appl. Phys.  2005 , 98, 113904.  \n[38] J. Shen, Y. X. Li, Q. Y. Dong, J. R. Sun, J. Magn. Magn. Mater.  2009 , 321, 2336 .  \n[39] F. Wang, J. Zhang, Y. F. Chen, G. J. Wang, J. R. Sun, S. Y . Zhang, B. G. Shen, Phys. Rev. B  2004 , 69, \n094424.  \n[40] F. Wang, Y.F. Chen, G.J. Wang, B.G .Shen, J. Phys. D: Appl. Phys.  2003 , 36, 1.  \n[41] D.T. Kim Anh, N.P. Thuya, N.H. Duc, T.T.  Nhien, N.V . Nong, J. Magn. Magn. Mater.  2003 , 262, \n427. \n[42] S. Fujieda, A. Fujita and K. Fukamichi, Mater. Trans.  2004 , 45, 3228.  \n[43] S. Fujieda, A. Fujita, K. Fukamichi, N. Hirano, S. Nagaya, J. Alloys Compd.  2006 , 408, 1165.  \n[44] J. Shen, Y. X. Li, J. R. Sun, B. G. Shen, Chin. Phys.  2009 , 18, 2058 .  \n[45] Y. F. Chen, F. Wang, B. G. Shen, F. X. Hu, Z. H. Cheng, G. J. Wang, J. R. Sun, Chin. Phys.  2002 , 11, \n741. \n[46] A. Fujita , S. Fujieda , K. Fukamichi, Y. Yamazaki, Y . Iijima, Mater. Trans.  2002 , 43, 1202.  \n[47] A. Fujita, S. Fujieda, Y. Hasegawa, K. Fukamichi, Phys. Rev. B  2003 , 67, 104416.  \n[48] Y. F. Chen, F. Wang, B. G. Shen, F. X. Hu, J. R. Sun, G . J. Wang, Z. H. Cheng, J. Phys.: Co ndens. \nMatter  2003 , 15, L161.  \n[49] F. Wang, Y.F. Che n, G.J. Wang, J.R. Sun, B.G. Shen, Chin. Phys.  2003 , 12, 911.  \n[50] Y. F. Chen, F. Wang, B. G. Shen, F. X. Hu, J. R. Sun, G. J. Wang, Z. H. Cheng, J. Appl. Phys . 2003 , 93, \n1323.  \n[51] Y.F. Chen, F. Wang, B.G. Shen, J.R. Sun, G.J. Wang, F.X .Hu, Z.H. Cheng, T . Zhu, J. Appl. Phys.  \n2003 , 93, 6981.  \n[52] L. Jia, J. R. Sun, J. Shen, B. Gao, T. Y. Zhao, H. W. Zhang, F. X. Hu, B. G. Shen, to be published.  \n[53] J. Shen, B. Gao, H. W. Zhang, F. X. Hu, Y. X.  Li, J. R. Sun, B. G. Shen, Appl. Phys. Lett.  2007 , 91, \n142504 . \n[54] J. Shen, Y. X. Li, J. Zhang, B. Gao, F. X. Hu, H. W. Zhang, Y. Z. Chen, C. B. Rong, J. R. Sun, J. \nAppl. Phys.  2008 , 103, 07B317.   27 [55] L. Jia, J. R. Sun, F. W. Wang, T. Y. Zhao, H. W. Zha ng, B. G. Shen, D. X. Li, S. Nimori, Y. Ren, Q. \nS. Zeng, Apppl. Phys. Lett.  2008 , 92, 101904.  \n[56] L. Jia, J. R. Sun, J. Shen, Q. Y. Dong, F. X. Hu, T. Y. Zhao, B. G. Shen, Appl. Phys. Lett.  2008 , 92, \n182503.  \n[57] J. R. Sun, F. X. Hu, B. G. Shen, Phys. Rev . Lett. , 2000 , 85, 4191.  \n[58] G. J. Liu, J. R. Sun, J. Shen, B. Gao, H. W. Zhang, F. X. Hu, B. G. Shen, Appl. Phys. Lett.  2007 , 90, \n032507 . \n[59] J. Shen, B. Gao, L. Q. Yan, Y. X. Li, H. W. Zhang , F. X. Hu, J. R. Sun, Chin. Phys.  2007 , 16, 3848.  \n[60] H. W. Zhang, J. Shen, Q. Y Dong, T. Y. Zhao, Y. X. Li, J. R. Sun, B. G. Shen, J. Magn. Magn. \nMater.  2008 , 320, 1879.  \n[61] J. D. Zou, B. G. Shen, B. Gao, J. Shen, J. R. Sun, Adv. Mater.  2009 , 21, 693.  \n[62] A. de Campos, D. L. Rocco, A. M. G. Carvalho, L. Caron, A. A. Coelho, S. Gama, L. M. D. Silva, F. \nC. G. Gandra, A. O. D. Santos, L. P. Cardoso, P. J. von Ranke, N. A. de Oliveira, Nat. Mater.  2006 , \n5, 802.  \n[63] V . K. Pecharsky, K. A. Gschneidner Jr., Appl. Phys. Lett.  1997 , 70, 3299.  \n[64] S. Gama, A. A. Coelho, A. de Campos, A. M. G. Carvalho, F. C. G. Gandra, P. J. von Ranke, N. A. \nde Oliveira, Phys. Rev. Lett.  2004 , 93, 237202.  \n[65] D. L. Rocco, A. de Campos, A. M. G. Carvalho, L. Caron, A. A. Coelho , S. Gama, F. C. G . Gandra, A. \nO. dos Santos, L. P. Cardoso, P. J. von Ranke, N. A. de Oliveira, Appl. Phys. Lett.  2007 , 90, 242507.  \n[66] V. Provenzano, A. J. Shapiro, R. D. Shull, Nature  (London) 2004 , 429, 853. \n[67] Q. Y. Dong, H. W. Zhang, T. Y. Zhao, J . R. Sun, B. G. Shen, Solid State Commun.  2008 , 147, 266.  \n[68] B. Gao, F. X. Hu, J. Wang, J. Shen, J. R. Sun, B. G. Shen, J. Appl. Phys.  2009 , 105, 07A916.  \n[69] F. X. Hu, Max Ilyn, A. M. Tishin, J. R. Sun, G. J. Wang, Y. F. Chen, F. Wang, Z. H. Cheng, B. G . \nShen, J. Appl. Phys.  2003 , 93, 5503.  \n[70] Max Ilyn, A.M. Tishina, F.X. Hu, J. Gao, J.R. Sun, B.G. Shen, J. Magn. Magn. Mater.  2005 , 290, \n712. \n[71] S. Fujieda, Y. Hasegawa, A. Fujita, K. Fukamichi, J. Magn. Magn. Mater.  2004 , 272, 2365.  \n[72] C. Zimm, A. B oeder, J. Chell, A. Sternberg, A. Fujita, S. Fujieda, K. Fukamichi , Int. J. Refrig . 2006 , \n29, 1302.  \n[73] A. Fujita, S. Koiwai, S. Fujieda, K. Fukamichi,  T. Kobayashi, H. Tsuji, S. Kaji, A. T. Saito , Japan. J. \nAppl. Phys.  2007 , 46, L154. \n[74] Y. Long et al.  to be published.  \n[75] F. X. Hu, B. G . Shen, J. R. Sun, Z. H. Cheng, X. X. Zhang, J. Phys.: Condens . Matter  2000 , 12, \nL691.  \n[76] F. X. Hu, B. G . Shen, J.R.Sun, Z. H. Cheng, Phys. Rev. B  2001 , 64, 012409.  \n[77] T. Hashimoto, T. Kuzuhura, M. Sahashi, K. Inoma ta, A. Tomokiyo, H. Yayama, J. Appl. Phys.  1987, \n62, 3873.  \n[78] B. J. Korte, V. K. Pecharsky, K. A. Gschneidner Jr, J. Appl. Phys.  1998 , 84, 5677.   28 [79] F. X. Hu, X. L. Qian, G. J. Wang, J. Wang, J. R. Sun, X. X. Zhang, Z.H. Cheng, B. G . Shen, J. Phys.: \nCondens. Matter  2003 , 15, 3299.  \n[80] F. X. Hu, B. G. Shen, J. R. Sun, G. J. Wang, J. Gao, J. Appl. Phys.  2007 , 101, 09C525.  \n[81] F. Wang, Y. F. Chen, G. J. Wang, J. R. Sun, B. G. Shen, J. Phys.: Condens. Matter  2004 , 16, 2103.  \n[82] F. X. Hu, B.G.Shen, J.R.Sun , Appl. Phys. Lett.  2000 , 76, 3460.  \n[83] F. X. Hu, J. R. Sun, G. H. Wu, B.G. Shen, J. Appl. Phys.  2001 , 90, 5216.  \n[84] F. X. Hu, B.G. Shen, J. R. Sun, G. H. Wu, Phys. Rev. B  2001 , 64, 132412.  \n[85] S. Stadler, M. Khan, J. Mitchell, N. Ali, A. M. Gomes, I. D ubenko, A. Y . Takeuchi, A. P. Guimarã es, \nAppl. Phys. Lett.  2006 , 88, 192511.  \n[86] M. Pasquale, C. P. Sasso, L. H. Lewis, L. Giudici, T. Lograsso, D. Schlagel, Phys. Rev. B 2005 , 72, \n094435 . \n[87] R. Kainuma, Y. Imano, W. Ito, Y. Sutou, H. Morito, S. Okamoto , O. Kitakami, K. Oikawa, A. Fujita, \nT. Kanomata, K. Ishida, Nature  2006 , 439, 957.  \n[88] T. Krenke, E. Duman, M. Acet, E. F. Wassermann, X. Moya, L. Mañ osa, A. Planes, Nat. Mater.  \n2005 , 4, 450.  \n[89] Z. D. Han, D. H. Wang, C. L. Zhang, H. C. Xuan, B. X. Gu,  Y. W. Du, Appl. Phys. Lett.  2007 , 90, \n042507 . \n[90] V. K. Sharma, M. K. Chattopadhyay, R. Kumar, T. Ganguli, P. Tiwari,  S. B. Roy , J. Phys. Condens. \nMatter  2007 , 19, 496207.  \n[91] X. Moya, L. Mañ osa, A. Planes, Phys. Rev. B  2007 , 75, 184412 . \n[92] T. Krenke,  E. Duman, M. Acet, E. F. Wassermann, X. Moya, L. Mañ osa, A. Planes, E. Suard, B. \nOuladdiaf, Phys. Rev. B  2007 , 75, 104414 . \n[93] T. Krenke, M. Acet, E. Wassermann, X. Moya, L. Mañ osa, A. Planes, Phys. Rev. B  2006 , 73, \n174413.  \n[94] F. X. Hu , J. Wang, J. Sh en, B. Gao, J. R. Sun, B. G. Shen, J. Appl. Phys.  2009 , 105, 07A940.  \n[95] Y. Deng, G. S. Ansell, Acta Metall. Mater.  1990 , 38, 69. \n[96] W. H. Wang, J. L. Chen, Z. H. Liu, G. H. Wu, W. S. Zhan, Phys. Rev. B  2001 , 65, 012416 . \n[97] O. I. Bodak, E. I. Gladyshe vskii, and O. I. Kharchenko, Kristallografiya  1974 , 19, 80.  \n[98] B. Chevalier, E. Gaudin, and F. Weill, J. Alloys Compd.  2007 , 442, 149.  \n[99] J. Shen, F. Wang, Y. X. Li, J. R. Sun, B. G. Shen, Chin. Phys.  2007 , 16, 3853.  \n[100] J. Shen , Y. X. Li, Q. Y. Dong , F. Wang, J. R. Sun, Chin. Phys. B  2008 , 17, 2268.  \n[101] J. Shen , F. Wang, Y. X. Li, J. R. Sun, B. G.  Shen,  J. Alloys Compd.  2008 , 458, L6. \n[102] S. N. Jammalamadaka, N. Mohapatra, S. D. Das, K. K. Iyer, E. V. Sampathkumaran, J. Phys.: \nCondens. Matter  2008, 20, 425204.  \n[103] E. Gaudin, S. Tencé , F. Weill, J. R. Fernandez, B. Chevalier, Chem. Mater.  2008 , 20, 2972.  \n[104] K. A. Gschneidner Jr., V. K. Pecharsky, A. O. Pecharsky, C. B. Zimm, Mater. Sci. Forum  1999 , \n315, 69. \n[105] T. B. Zhang, Y. G. Chen, Y. B.  Tang, J. Phys. D: Appl. Phys.  2007 , 40, 5778.   29 [106] J. Hemberger, P. Lunkenheimer, R. Fichtl, H. A. Krug von Nidda, V. Tsurkan, A. Loidl, Nature  2005 , \n434, 364.  \n[107] H. W. Lehmann, M. Robbins, J. Appl. Phys.  1966 , 37, 1389.  \n[108] P. K. Baltzer, H. W. Leh mann, M. Robbins, Phys. Rev. Lett.  1965 , 15, 493.  \n[109] L. Q. Yan, J. Shen, Y. X. Li, F. W. Wang, Z. W. Jiang, F. X. Hu, J. R. Sun, B. G. Shen, Appl. Phys. \nLett. 2007 , 90, 262502.  \n[110] P. K. Baltzer, P. J. Wojtowicz, M. Robbins, E. Lopatin, Phys. Rev.  1966, 151, 367.  \n[111] J. Shen, L. Q. Yan, J. Zhang, F. W. Wang, J. R. Sun, F. X. Hu, C. B. Rong, Y. X. Li, J. Appl. Phys.  \n2008 , 103, 07B315.  \n[112] Q. Y . Dong, B. G. Shen, J. Chen, J. Shen, F. Wang, H. W. Zhang, J. R. Sun, J. Appl. Phys.  2009 , 105, \n053908.  \n[113] F. Wang, J. Shen, J. Zhang, J. R. Sun, B. G. Shen, J. Appl. Phys.  2009 , 105, 07A944 . \n \n \n  30 Table 1 Magnetic transition temperature TC and isothermal entropy change | S| for LaFe 13-xSix and related \ncompounds  \n \ncompounds  TC (K) S (J/kgK)  \n02 T S (J/kgK)  \n05 T Refs.  \nLaFe 11.83Si1.17 175 21.2 27.8 This work  \nLaFe 11.8Si1.2  25.4 29.2 This work  \nLaFe 11.7Si1.3 183 22.9 26.0 This work  \nLaFe 11.6Si1.4 188 20.8 24.7 This work  \nLaFe 11.5Si1.5 194 20.8 24.8 This work  \nLaFe 11.5Si1.5 194 21.0 23.7 [44] \nLaFe 11.5Si1.5 195 21.9 24.6 [48] \nLaFe 11.4Si1.6 199 14.2 18.7 This work  \nLaFe 11.4Si1.6 209 14.3 19.3 [11] \nLaFe 11.4Si1.6 208 14.3 19.4 [12] \nLaFe 11.3Si1.7 206 11.9 17.6 This work  \nLaFe 11.2Si1.8 210 7.5 13.0 This work  \nLaFe 11.0Si2.0 221 4.0 7.9 This work  \nLaFe 10.6Si2.4  2.8  [24] \nLaFe 10.4Si2.6  2.3  [14] \nLa0.9Pr0.1Fe11.5Si1.5 191 24 26.1 [44] \nLa0.8Pr0.2Fe11.5Si1.5 188 26 28.3 [44] \nLa0.7Pr0.3Fe11.5Si1.5 185 28 30.5 [44] \nLa0.6Pr0.4Fe11.5Si1.5 182 29 31.5 [44] \nLa0.5Pr0.5Fe11.5Si1.5 181 30 32.4 [44] \nLa0.9Nd0.1Fe11.5Si1.5 192 23 25.9 [44] \nLa0.8Nd0.2Fe11.5Si1.5 190 24 27.1 [44] \nLa0.7Nd0.3Fe11.5Si1.5 188 29 32.0 [44] \nLa0.7Ce0.3Fe11.5Si1.5 173  23.8 [44] \nLa0.7Pr0.3Fe11.4Si1.6 190 25.4 28.2 [38] \nLa0.7Pr0.3Fe11.2Si1.8 204 14.4 19.4 [38] \nLa0.7Pr0.3Fe11.0Si2.0 218 6.2 11.4 [38] \nLaFe 11.5Si1.5H0.3 224  17.4 [48] \nLaFe 11.5Si1.5H0.6 257  17.8 [48] \nLaFe 11.5Si1.5H0.9 272  16.9 [48] \nLaFe 11.5Si1.5H1.3 288 8.4 17.0 [45,48]  \nLaFe 11.5Si1.5H1.5 312  16.8 [48] \nLaFe 11.5Si1.5H1.8 341  20.5 [48] \nLa(Fe 0.99Mn 0.01)11.7Si1.3H 336 16.0 23.4 [49] \nLa(Fe 0.98Mn 0.02)11.7Si1.3H 312 13.0 17.7 [49] \nLa(Fe 0.97Mn 0.03)11.7Si1.3H 287 11.0 15.9 [49] \nLaFe 11.5Si1.5C0.2 225 18.0 22.8 [51]  31 LaFe 11.5Si1.5C0.5 241 7.4 12.7 [51] \nLa0.5Pr0.5Fe11.5Si1.5C0.3 211 25.2 27.6 [53] \nLa(Fe 0.96Co0.04)11.9Si1.1 243 16.4 23.0 [32] \nLa(Fe 0.94Co0.06)11.9Si1.1 274 12.2 19.7 [32] \nLa(Fe 0.92Co0.08)11.9Si1.1 301 8.7 15.6 [32] \nLaFe 11.2Co0.7Si1.1 274  20.3 [31] \nLaFe 10.7Co0.8Si1.5 285 7.0 13.5 [34] \nLaFe 10.98Co0.22Si1.8 242 6.3 11.5 [11] \nLa0.8Pr0.2Fe10.7Co0.8Si1.5 280 7.2 13.6 [34] \nLa0.6Pr0.4Fe10.7Co0.8Si1.5 274 7.4 14.2 [34] \nLa0.5Pr0.5Fe10.7Co0.8Si1.5 272 8.1 14.6 [34] \nLa0.5Pr0.5Fe10.5Co1.0Si1.5 295 6.0 11.7 [33] \nLa0.7Nd0.3Fe10.7Co0.8Si1.5 280 7.9 15.0 [54] \nLaFe 11.12Co0.71Al1.17 279 4.6 9.1 [11] \nLa(Fe 0.98Co0.02)11.7Al1.3 198 5.9 10.6 [11] \nGd 293 5.0 9.7 [34] \n \n  32 Figure captions  \n \nFigure 1. a) Curie temperature TC, lattice constant a and b) magnetic moment of Fe atoms as a function of \nSi content x for LaFe 13-xSix. Data indicated by the open circles were obtained  from Ref. 19. \n \nFigure 2. a) Magnetization isotherms and b) the Arrott plots of LaFe 11.4Si1.6 on field increase and decrease. \nTemperature step is 2 K in the region of 200 –230 K, and 5 K in 165 –200 K and 230 –265 K , and c) \nentropy change S as a fun ction of temperature for LaFe 11.6Si1.6 and LaFe 10.4Si2.6 (Ref. 12) .  \n \nFigure 3. a) Lattice parameter a and b) entropy change S as a fun ction of temperature under a field \nchange of 0 5 T for LaFe 13-xSix. Inset plot shows S as a fun ction of Si content for LaFe 13-xSix under a \nfield change of 0 2 T (Ref. 24). \n \nFigure 4. Observed (dot), calculated (line) neutron diffraction patterns and their difference for LaFe 11.4Si1.6 \nat T = 2 , 191 and 300 K  (Ref. 25) . \n \nFigure 5. a) Mö ssbauer spectra of LaFe 11.7Si1.3 at 190 K and b)  Mö ssbauer spectra of LaFe 11.0Si2.0 at 240 \nK in various external magnetic fields  (Ref. 29) . The dotted lines are paramagnetic subspectra.  \n \nFigure 6. a) Temperature dependence of e ntropy change S for a) La(Fe 1-xCox)11.9Si1.1 (Ref. 32) and b) \nLa(Fe 1-xMn x)11.7Si1.3 (Ref. 40) under field changes of 0 2 T and 0 5 T. Inset plot is the S of \nLa(Fe 1-xCox)11.9Si1.1 with x=0.06 compared with that of Gd and Gd 5Si2Ge2 for a field change of 0 –5 T \n(Ref. 31) .  \n \nFigure 7. a) Curie temperature TC and b) e ntropy change S as a function of R concentration for \nLa1-xRxFe11.5Si1.5 (R = Ce, Pr and Nd)  (Ref. 44). \n \nFigure 8. Temperature dependence of e ntropy change S for a) LaFe 11.5Si1.5Hδ under a field change of 0 5 \nT (Ref. 48), b) La(Fe 1-xMn x)11.7Si1.3Hδ under field changes of 02 T and 0 5 T (Ref. 49) and c) \nLaFe 11.6Si1.4Cδ under a field change of 0 5 T (Ref. 50). \n \nFigure 9. Curie temperature TC as a function of lattice constant for the hydrogenised and pressed \nLaFe 11.5Si1.5 and Ce -doped LaFe 11.5Si1.5. The open circles show the  pure volume -effects while the solid \ncircles the as -detected TC under pressures. Solid lines are guides for the eyes  (Ref. 55) . \n \nFigure 10. Phase volume dependence of the Curie temperature TC for La0.7R0.3Fe11.5Si1.5 (solid symbols). \nThe TC-V relation of t he LaFe 13-xSix compounds is also presented for comparison (open circles). Inset \nplot shows the TC/TC-x relation, where TC is the difference of the Curie temperatures of the  33 La1-xRxFe11.5Si1.5 and LaFe 11.5Si1.5 compounds under the same phase volume. Solid  lines are guides for \nthe eye  (Ref. 56) . \n \nFigure 11. a) Magnetization isotherm s measured by ascending ma gnetic field , b) temperature -dependent \nentropy change calculated from Maxwell relation (MR) and heat capacity (HC) for La 0.7Pr0.3Fe11.5Si1.5, \nand c) a schematic diagram showing the calculation of e ntropy change when stepwise magnetic \nbehaviors o ccur (Ref. 58) . \n \nFigure 12. Magnetization isotherms of La 1-xPrxFe11.5Si1.5 (x = a) 0, b) 0.2 and c) 0.4) in the field ascending \nand descending processes  (Ref. 59), and t emperature -dependent hysteresis loss of d) La1-xNdxFe11.5Si1.5 \n(x = 0, 0. 1, 0.2  and 0. 3), e) La1-xPrxFe11.5Si1.5 (x = 0.1, 0.2,  0.3, 0.4  and 0.5) (Ref. 44)  and f) \nLa0.5Pr0.5Fe11.5Si1.5Cδ (δ=0 and 0.3)  (Ref. 53) , respectively.  \n \nFigure 13. Relation bet ween entropy change and hysteresis loss for LaFe 13-xSix-based compounds with \ndifferent compositions.  \n \nFigure 14. a) Adiabatic temperature change Tad as a function of temperature obtained by direct \nmeasurements under a field change from 0 to 1.4 T , b) Tad as a function of applied magnetic field at \ndifferent temperatures  for LaFe 11.7Si1.3 (Refs. 24 and 69), c) Tad calculated  from the heat capacity \nmeasurements as a function of temperature and d) Tad as a function of Si content under different fields  \nfor LaFe 13-xSix.  \n \nFigure 15. Entropy change S of La(Fe 1-xCox)11.83Al1.17 (x=0.06  and 0.08), compared with that of Gd for \nmagnetic field changes of 0 2 and 05T (Ref. 76) . Solid lines  show the theoretical results calculated in \nthe molecular field approximation  for a field chang ing from 0 to 5 T.  \n \nFigure 16. Temperature dependence of  entropy change S for a) polycrystalline Ni 51.5Mn 22.7 Ga25.8 (Ref. 82) \nand b) single crystal Ni 52.6Mn 23.1Ga24.3 (Ref. 84) under different field changes.  \n \nFigure 17. a) M agnetization  isotherms  and b) entropy change S as a function of temperature for R6Co2Si3 \n(R = Pr, Gd and Tb)  (Refs. 99, 100 and 101) .  \n \nFigure 18. a) Entropy change S and b) adiabatic temperature change Tad as a function of temperature \nfor CdCr 2S4 under different f ield changes  (Ref. 109) . \n \n \n \n  34 \n180210240270\n1.1451.1461.1471.148\n1.2 1.6 2.0 2.41.82.02.2\n  TC (K)\nLaFe13-xSix  \na (nm) \n a) Magnetic moment ( B/Fe)\nSi content xb) \nFigure 1 by Shen et al.  \n0 1 2 3 4 5 6050100150\n0.00 0.02 0.04 0.0601000020000\n175 210 245 28005101520 field increase\n field decrease255K165K\n  M(emu/g)\nH(T)\n field increase\n field decrease\nT=2 K\n230K200K\n  M2(emu2/g2)\nH/M(T g/emu)\n 2T 2T\n 5T\nLaFe10.4Si2.6 LaFe11.4Si1.6 -S (J/kgK)\nT (K)a)\nb)\nc)\n  35 Figure 2 by Shen et al.  \n0 60 120 180 240 3001.1461.1481.1501.1521.1541.156\n160 200 240 2800102030\n1.2 1.8 2.401020\n  a (nm)\nT (K)X=1.2\n1.6\n1.8\n2.0\n2.4\n2.6LaFe13-xSix–S (J/kgK)\nT (K) x=1.2     x=1.6\n x=1.3     x=1.7\n x=1.4     x=1.8\n x=1.5     x=2.0\n  -S (J/kgK)\nSi content a)\nb)\n \nFigure 3 by Shen et al.  \n20 40 60 80 100 120 140020000400000200004000002000040000\nT = 2 K \n  \n2(deg.)RWP=8.83%\nRe=4.39%\nRm=4.18%T = 191 K\n \n  Neutron CountsRWP=7.10%\nRe=4.19%T = 300 K\n  \n  \nRWP=7.65%\nRe=4.19%LaFe11.4Si1.6\n \nFigure 4 by Shen et al.  \n  36 \n-15 -10 -5 0 510 15 -15 -10 -5 0 510 15Absorption \n80 kOe60 kOe10 kOe\n20 kOe\n40 kOeH=0 kOe \n  \n  \n  \n  \n  \n  \nvelocity(mm/s)a) b)\nAbsorption \n80 kOe60 kOe10 kOe\n20 kOe\n40 kOeH=0 kOe \n  \n  \n  \n  \n  \n  \nvelocity(mm/s) \nFigure 5 by Shen et al.  \n \n200 240 280 320 360081624\n250 300 35001020\n100 125 150 175 200 22508162432x=0.08x=0.06 x=0.04 \n S (J/kgK)\nT (K) 5T\n 2T\na)La(Fe1-xCox)11.9Si1.1Gd5Si2Ge2\nGd \n S (J/kgK)\nT (K)x=0.06\n  S (J/kgK)\nT (K) 2T\n 5Tx=00.01\n0.02\n0.03La(Fe1-xMnx)11.7Si1.3b)\n \nFigure 6 by Shen et al.   37 \n0.0 0.1 0.2 0.3 0.4 0.5168176184192\n0.0 0.1 0.2 0.3 0.4 0.524273033\n  TC (K)\n R content xR = CeR = Nd\nR = PrLa1-xRxFe11.5Si1.5\na)\n  –S (J/kgK)\nR content  x R = Nd\nR = Pr\nLa1-xRxFe11.5Si1.5\nb) \n \n \nFigure 7 by Shen et al.  \n  38 \n150 200 250 300 35006121824\n270 300 330 36006121824\n180 210 240 270 30006121824\n  –S(J/kgK)\nT(K)LaFe11.5Si1.5H\n0.3 0.6\n0.91.31.51.8a)–S (J/KgK)\nT (K) 2 T\n 5 Tx=0.01 x=0.02x=0.03La(Fe1-xMnx)11.7Si1.3H b)\n  –S (J/kgK)\nT (K)=0\n0.2\n0.4\n0.6LaFe11.6Si1.4Cc) \nFigure 8 by Shen et al.  \n1.140 1.144 1.148 1.152 1.156075150225300375\n  TC (K)\na (nm)Hydrogenized\nPressedCe-doped\nSimple \nvolume-effect\n \nFigure 9 by Shen et al.   39 \n1485 1490 1495 1500 1505 1510120135150165180195210\n0.0 0.2 0.4 0.6\n051015\n  TC (K)\nV (Å3)LaFe11.5Si1.5LaFe13-xSixR=Nd\nR=PrR=Ce\nTC\n \n R content xTC/TC (%)\nCePrNd \n \nFigure 10 by Shen et al.  \n \n  40 \n0 1 2 3 4 50246810165 180 195 2100306090\n 5T MR\n 5T HCLa0.7Pr0.3Fe11.5Si1.5\n  \n –S (J/kgK)\nb)0 1 2 3 4 5050100150\n \n  M (emu/g)184\n185190192\nT (K)\nH (T)a)\n1\n  M (Arb. Units)\nH (Arb. Units)TCT1 T2\n2\nc) \n \nFigure 11 by Shen et al.  \n  41 \n060120\n060120\n0 1 2 3 4 5060120\n180 190 200 210 22004080  \n M (emu/g)182K\n226K a)\n  \n  \n175K\n220Kb) \n  \nH (T)211K166K\nc)04080\n \n  \n X = 0\n X = 0.1\n X = 0.2\n X = 0.3La1-xNdxFe11.5Si1.5\nd)\n04080\n  Hysteresis loss (J/kg) \n X = 0.1\n X = 0.2\n X = 0.3\n X = 0.4\n X = 0.5\n La1-xPrxFe11.5Si1.5\ne)\n  = 0\n  = 0.3\n  \nT (K)La0.5Pr0.5Fe11.5Si1.5C\nf) \n \nFigure 12 by Shen et al.  \n \n0 20 40 60 80 100 120101520253035\n La0.5Pr0.5Fe11.5Si1.5C\n La0.7Pr0.3Fe11.5-xSix\n La1-xPrxFe11.5Si1.5\n La1-xNdxFe11.5Si1.5\n La0.5Pr0.5Fe11.4Si1.6H\n  -S (J/kg K)\nHysteresis loss (J/kg)\n \nFigure 13 by Shen et al.  \n  42 \n175 180 185 19001234\n0.0 0.4 0.8 1.201234180 210 240 27004812\n1.2 1.5 1.8 2.104812 \n T (K)\nH (T) heating\n coolingLaFe11.7Si1.3\nH=1.4 T\n T (K)\nH (T) 182.5 K\n 183.2 K\n 184 K\n 184.6 K\n 185 K\n 186 KLaFe11.7Si1.3\n  T (K)\nT (K)LaFe13-xSixx=1.4\n1.6\n1.8\n2.2\n 2 T\n 5 T\n  T (K)\nSi content xa)\nb)c)\nd)\nLaFe13-xSix \nFigure 14 by Shen et al.  \n \n200 240 280 3200246810\n240 280 320 3600246810\n–S (J/kgK)Gdx=0.06 \n –S (J/kgK)\nT(K) 2T\n 5T 2T\n 5T x=0.08\n  \nT(K)\n \nFigure 15 by Shen et al.  \n \n  43 \n185 190 195 200 205012345\n296 300 304 30805101520Ni51.5Mn22.7Ga25.8\n0.9 T \n S (J/kgK)\nT(K)Ni52.6Mn23.1Ga24.3 \n  5T\n 4T\n 3T\n 2T\n 1T\n 0.65T\n 0.5T\n 0.4T\n 0.25T\n 0.2T–S (J/kgK)\nT(K)a) b) \nFigure 16 by Shen et al.  \n \n0 1 2 3 4 50204060\n0 1 2 3 4 504080120\n0 1 2 3 4 505010015020015 30 45 60 7502468\n200 250 300 3500246\n50 100 150 200 25002468 \n  M (emu/g)\n73K20K R=Pr\n \n  M (emu/g)211K\n342KR=Gd\n  M (emu/g)\nH (T)70 K\n240 KR=Tb  1T\n 2T\n 3T\n 4T\n 5T\n  –S (J/KgK)R=Pr\nT (K) \n 2T\n 3T\n 4T\n 5T 1T\n 2T\n 3T\n 4T\n 5T\n  –S (J/kgK)R=Gd\n \n  –S (J/KgK)R=Tba) b)\n \nFigure 17 by Shen et al.  \n \n  44 \n02468\n50 75 100 125012\n  –S (J/kgK)  1T\n  2T\n  3T\n  4T\n  5T(a)\n T (K)\nT (K) 2T\n 5T(b)\nCdCr2S4 \n \nFigure 18 by Shen et al.  \n \n \nTable 1 Magnetic transition temperature TC and isothermal entropy change | S| for \nLaFe 13-xSix and related compounds  \n \ncompounds  TC (K) S (J/kg  K) \n02 T S (J/kg  K) \n05 T Refs.  \nLaFe 11.83Si1.17 175 21.2 27.8 This work  \nLaFe 11.8Si1.2  25.4 29.2 This work  \nLaFe 11.7Si1.3 183 22.9 26.0 This work  \nLaFe 11.6Si1.4 188 20.8 24.7 This work  \nLaFe 11.5Si1.5 194 20.8 24.8 This work  \nLaFe 11.5Si1.5 194 21.0 23.7 [44] \nLaFe 11.5Si1.5 195 21.9 24.6 [48] \nLaFe 11.4Si1.6 199 14.2 18.7 This work  \nLaFe 11.4Si1.6 209 14.3 19.3 [11] \nLaFe 11.4Si1.6 208 14.3 19.4 [12] \nLaFe 11.3Si1.7 206 11.9 17.6 This work  \nLaFe 11.2Si1.8 210 7.5 13.0 This work  \nLaFe 11.0Si2.0 221 4.0 7.9 This work  \nLaFe 10.6Si2.4  2.8  [24] \nLaFe 10.4Si2.6  2.3  [14] \nLa0.9Pr0.1Fe11.5Si1.5 191 24 26.1 [44]  45 La0.8Pr0.2Fe11.5Si1.5 188 26 28.3 [44] \nLa0.7Pr0.3Fe11.5Si1.5 185 28 30.5 [44] \nLa0.6Pr0.4Fe11.5Si1.5 182 29 31.5 [44] \nLa0.5Pr0.5Fe11.5Si1.5 181 30 32.4 [44] \nLa0.9Nd0.1Fe11.5Si1.5 192 23 25.9 [44] \nLa0.8Nd0.2Fe11.5Si1.5 190 24 27.1 [44] \nLa0.7Nd0.3Fe11.5Si1.5 188 29 32.0 [44] \nLa0.7Ce0.3Fe11.5Si1.5 173  23.8 [44] \nLa0.7Pr0.3Fe11.4Si1.6 190 25.4 28.2 [38] \nLa0.7Pr0.3Fe11.2Si1.8 204 14.4 19.4 [38] \nLa0.7Pr0.3Fe11.0Si2.0 218 6.2 11.4 [38] \nLaFe 11.5Si1.5H0.3 224  17.4 [48] \nLaFe 11.5Si1.5H0.6 257  17.8 [48] \nLaFe 11.5Si1.5H0.9 272  16.9 [48] \nLaFe 11.5Si1.5H1.3 288 8.4 17.0 [45,48]  \nLaFe 11.5Si1.5H1.5 312  16.8 [48] \nLaFe 11.5Si1.5H1.8 341  20.5 [48] \nLa(Fe 0.99Mn 0.01)11.7Si1.3H 336 16.0 23.4 [49] \nLa(Fe 0.98Mn 0.02)11.7Si1.3H 312 13.0 17.7 [49] \nLa(Fe 0.97Mn 0.03)11.7Si1.3H 287 11.0 15.9 [49] \nLaFe 11.5Si1.5C0.2 225 18.0 22.8 [51] \nLaFe 11.5Si1.5C0.5 241 7.4 12.7 [51] \nLa0.5Pr0.5Fe11.5Si1.5C0.3 211 25.2 27.6 [53] \nLa(Fe 0.96Co0.04)11.9Si1.1 243 16.4 23.0 [32] \nLa(Fe 0.94Co0.06)11.9Si1.1 274 12.2 19.7 [32] \nLa(Fe 0.92Co0.08)11.9Si1.1 301 8.7 15.6 [32] \nLaFe 11.2Co0.7Si1.1 274  20.3 [31] \nLaFe 10.7Co0.8Si1.5 285 7.0 13.5 [34] \nLaFe 10.98Co0.22Si1.8 242 6.3 11.5 [11] \nLa0.8Pr0.2Fe10.7Co0.8Si1.5 280 7.2 13.6 [34] \nLa0.6Pr0.4Fe10.7Co0.8Si1.5 274 7.4 14.2 [34] \nLa0.5Pr0.5Fe10.7Co0.8Si1.5 272 8.1 14.6 [34] \nLa0.5Pr0.5Fe10.5Co1.0Si1.5 295 6.0 11.7 [33] \nLa0.7Nd0.3Fe10.7Co0.8Si1.5 280 7.9 15.0 [54] \nLaFe 11.12Co0.71Al1.17 279 4.6 9.1 [11] \nLa(Fe 0.98Co0.02)11.7Al1.3 198 5.9 10.6 [11] \nGd 293 5.0 9.7 [34] \n \n "    },    {        "title": "1006.4075v2.Dynamics_of_magnetic_charges_in_artificial_spin_ice.pdf",        "content": "arXiv:1006.4075v2  [cond-mat.mtrl-sci]  24 Aug 2010Dynamics of magnetic charges in artificial spin ice\nPaula Mellado, Olga Petrova, Yichen Shen, and Oleg Tchernyshyov\nDepartment of Physics and Astronomy, The Johns Hopkins Univ ersity, Baltimore, Maryland 21218, USA\nArtificial spinice hasbeenrecentlyimplementedintwo-dim ensional arrays ofmesoscopic magnetic\nwires. We propose a theoretical model of magnetization dyna mics in artificial spin ice under the\naction of an applied magnetic field. Magnetization reversal is mediated by domain walls carrying\ntwo units of magnetic charge. They are emitted by lattice jun ctions when the the local field exceeds\na critical value Hcrequired to pull apart magnetic charges of opposite sign. Po sitive feedback from\nCoulomb interactions between magnetic charges induces ava lanches in magnetization reversal.\nSpin ice [1] shares some remarkable properties with\nwater ice [2]: both possess a very large number of low-\nenergy, nearly degenerate configurations satisfying the\nBernal-Fowler ice rules. In water ice, an O2−ion has\ntwo protons nearby and two farther away; in spin ice,\ntwo spins point into and two away from the center of ev-\nery tetrahedron of magnetic ions. Because the ice rules\nare satisfied by a large fraction of states, the system re-\ntains much entropy down to very low temperatures [3].\nLow-frequencydynamicsin ice is associatedwith the mo-\ntion of defects violating the ice rules. In water ice, these\ndefects carry fractional electric charges of ±0.62e(ionic\ndefects) and ±0.38e(Bjerrum defects) [2]. Fractionaliza-\ntion takes an even more surprising form in spin ice: while\nthe original degrees of freedom are magnetic dipoles, the\ndefects are magnetic monopoles [4–8].\nThe charge of an ice defect is defined in terms of the\nnet flux of electric field Eor magnetic field Hemerging\nfrom the defect. On the atomic scale, the flux is obscured\nby the fields of background ionic charges or magnetic\ndipoles. Coarse graining is required to reveal the field\nflux of a defect on longer length scales [5]. An alternative\napproach is to alter the model by stretching point-like\nspin dipoles into dumbbell magnets until they touch one\nanother, while keeping their dipole moments fixed [4]. At\nthe expense of a slight change in the Hamiltonian, the\nmagnetic charge of a defect becomes well defined even on\nthe microscopic scale. It equals ±2q≡ ±2µ/a, whereµ\nis the dipole moment and ais the length of a dumbbell.\nThe dumbbell model is realized in artificial spin ice, a\nnetwork of submicron ferromagnetic islands [9] or wires\n[10–12]. Each element represents a spin whose mag-\n+\n(a) (c)−++−+\n−H\n(b)−+++−\nFIG. 1: (a) A configuration of square spin ice with no mag-\nnetic charges. (b) Honeycomb spin ice always has magnetic\ncharges. (c) Magnetized honeycomb spin ice.netic dipole moment is aligned with the wire by shape\nanisotropy, Fig. 1. The magnetostatic energy is a posi-\ntive definite quantity Edip= (1/8π)/integraltextH2dV, where the\nintegral is taken over the entire space. It is minimized\nwhen the magnetic field H= 0.Edipcan be expressed as\nthe Coulomb interaction of magnetic charges with den-\nsityρ(r)≡ ∇·H/4π=−∇·M. The field is zero, and the\nenergyisminimized, when therearenomagneticcharges.\nThis yields the ice rule: a network node with zero mag-\nnetic charge has zero influx of magnetization. The zero-\nflux rule can be satisfied in square ice, Fig. 1(a), but not\nin honeycomb ice, Fig. 1(b), also known as kagome ice,\nwhere the allowed values of magnetic charge Qon a site\nare±qand±3qin units of q≡MA, whereMis the\nmagnetization of the magnetic wire and Ais its cross\nsection. Minimization of magnetic charge restricts Qto\nthe values of ±q, yielding the modified ice rule for this\nlattice: two arrows in and one out, or vice versa [10, 11].\nThe presence of residual magnetic charges in honey-\ncomb ice even at low temperatures may result in a se-\nquence of two phase transitions as its temperature is\nlowered: magnetic charge order appears first, spin order\narises later [13, 14]. Unfortunately, thermal fluctuations\nare virtually absent in artificial spin ice: reversing the\ndirection of magnetization in a single wire requires going\nover an energy barrier of a few million kelvins [9]. Left to\nitself, the system remains forever in the same magnetic\nmicrostate. Wang et al.suggested a way to introduce\nmagnetization dynamics into artificial spin ice by plac-\ning the system in a rotating magnetic field of an oscillat-\ning magnitude [15, 16], the analog of fluidizing granular\nmatter through vibration. It has been suggested [17, 18]\nthat such induced dynamics of magnetization effectively\ncreate a thermal ensemble with an effective temperature.\nIn this Letter we present an entirely different approach\nto the dynamics of artificial spin ice that incorporates\nthe physics of magnetization reversal in ferromagnetic\nnanowires, a process mediated by the creation, propaga-\ntion, and annihilation of magnetic domain walls [19, 20].\nIt is inherently dissipative [21, 22]: as a domain wall\npropagates, magnetic energy is transferred to the lattice.\nLike fluidized granular matter, artificial spin ice is a sys-\ntem far out of equilibrium and it is not obvious that it\ncan be described in the framework of equilibrium ther-2\nmodynamics [23]. Mesoscopic degrees of freedom of spin\nice tend to move downhill in the energy landscape until\nthey come to rest at a local energy minimum. We use\nthis approach to describe the dynamics of magnetization\nobserved in honeycomb spin ice [11] in an applied field.\nIn static equilibrium, artificial spin ice is fully de-\nscribed by specifying the direction of the magnetization\nvector in every link of the lattice. These are Ising vari-\nables because magnetization is aligned with the wire.\nSites of the lattice carry magnetic charge of ±qor±3qas\nexplained above. Site charges can be deduced from mag-\nnetization variables because the magnetic charge equals\nthe net influx of magnetization. The converse is not true\nbecause the number of links exceeds the number of sites\nby a factor of 3/2, so the magnetic state of artificial spin\nice cannot be described in terms of charges alone [11].\nSpin variables must be specified for a complete descrip-\ntion.\nTransitions between static states, triggered by the ap-\nplication of an external magnetic field, involve intermedi-\natestatesinwhichthe magnetizationofoneormorelinks\nis being reversed. At the mesoscopic level of our theory,\nsuch links are pictured as having two sections uniformly\nmagnetized in opposite directions separated by a domain\nwall of magnetic charge Q=±2q[21]. The reversal of\nmagnetization in a link begins with the creation of a do-\nmain wall at one of the link ends. The process conserves\nmagnetic charge: when a site with magnetic charge −q\nemits a domain wall of charge −2q, the charge of the site\nchanges to + q, Fig. 2. The Zeeman force −2qµ0Hthen\npushes the domain wall to the opposite end of the link.\nThe critical field required to initiate the reversal can\nbe estimated as follows. A site of charge + qand a do-\nmain wall −2qattract each other with a Coulomb force\nF∼µ02q2/(4πr2) at distances rexceeding the charac-\nteristic size of the charges a. The attraction weakens for\nshort distances r<∼awhen the two charges merge. The\nmaximum attraction is thus Fmax≈µ02q2/(4πa2). To\npull the charges apart, the Zeeman force 2 qBfrom the\napplied field must exceed Fmax, giving the critical field\nHc=q/(4πa2) =Mtw/(4πa2). (1)\nDomain walls in nanowires of submicron width whave\nthe characteristic size a≈0.6w[24]. For the permalloy\nhoneycomb network of Qi et al.[11] with magnetization\nM= 8.6×105A/m, width w= 110 nm and thickness\nt= 23 nm, µ0Hc≈50 mT.\nWhen the magnetic field is applied at an angle θto a\nlink, the Zeeman force comes from the longitudinal com-\nponentHcosθ. For this reason we expected the reversal\nto occur at a higher field H(θ) =Hc/cosθ. A similar\nangular dependence has been observed in magnetic wires\nwith submicron width [25].\nTotestthisphenomenologicalmodel, weperformednu-\nmerical simulations of magnetization reversal in a single(g)+1 +1H\n−2 (b) +1 +1H\n−2 (c)\n+1 −1H\n(d) +1 +1H\n(e)−2−1 +1H\n(a)\n+1 −1H\n−2 (h) +1 +1H\n−2 (i)\n−2\n+1 +1H\n(j) −2 +1H\n(k) −1+1 +1H\n(f)\n+1 −1H\n−2\nFIG. 2: Magnetization reversal in honeycomb spin ice. (a-\nd) A domain wall is emitted at one end of a link, travels to\nthe other end, and gets absorbed at the junction. (e-f) If\nthe applied field is sufficiently strong, a new domain wall can\nbe emitted into an adjacent link triggering its magnetizati on\nreversal. (g-k) When a domain wall encounters a site with\nlike magnetic charge, it induces the emission of a new domain\nwall into an adjacent link.\nµ0H, mT\n 90\n 80\n 70\n 60\n 50\nθ, deg 30 15 0−15−30−45−60−75Link 1\nLink 2\nbest fit\nFIG. 3: The reversal field Hof two out of three magnetic\nwires forming a junction vs. the angle between the field and\nthe axis of the wire whose magnetization is being reversed.\nThe lines are fits to Eq. (2) with µ0Hc= 52.0 and 55.3 mT.\njunction of three ferromagnetic nanowires using micro-\nmagnetics software package OOMMF [26] with the cell\nsize of 2 nm ×2 nm×23 nm. The dependence H(θ) is\nnot symmetric, Fig. 3, and is fit well by the function\nH(θ) =Hc/cos(θ+α), (2)\nwhere the offset α= 19◦reflects an asymmetric distribu-\ntion of magnetization at the junction, as we will discuss\nelsewhere [27]. The critical-field parameter Hcvaried\nslightly between links reflecting small random variations\nof the width caused by lattice discretization. Two links\nof the same junction exhibited slightly different critical\nfieldsHc, Fig. 3.\nWe use these phenomenologicalconsiderations and mi-\ncromagnetics simulations to build a discrete mesoscopic3\nmodel of magnetization dynamics in artificial spin ice.\nWe start with a fully magnetized state in which links of\nthe same orientation have the same direction of magne-\ntization and magnetic charges form a staggered pattern.\nSuch a state can be obtained by placing the system in a\nstrong magnetic field, Fig. 1(c). In this state, each mag-\nnetic wire has uniform magnetization pointing along the\nwire’s axis and each junction contains a magnetic charge\nof±1 in the units of q=Mtwdetermined by the flux\nof magnetization into the junction. The external field is\nthenappliedintheoppositedirectionwithagraduallyin-\ncreasing magnitude. Magnetization reversal begins when\nthe net field Hnetat one of the junctions exceeds a crit-\nical value determined by Eq. 2. The net magnetic field\nHnetis a superposition of the applied field Happand of\nthe demagnetizing field of the sample Hdem. The latter\nis computed as a sum of Coulombic fields of individual\njunctions, H=Qr/(4πr3). The junction, initially con-\ntaining charge ±1, emits a domain wall with charge ±2\nand changes its own charge to ∓1. The emitted domain\nwall is pushed by the magnetic field to the other end\nof the link, reversing the link magnetization in the pro-\ncess, Fig. 2 (b-c). Quenched disorder, inevitably present\nin real samples, is modeled by setting at random slightly\ndifferent critical fields Hcin individual wires with a mean\n¯Hcand a distribution width ∆ Hc.\nAs the domain wall with charge ±2 reaches the other\nend of the link, its further fate depends on sign of the\nmagnetic charge it meets at the junction. If the charge\nis of opposite sign, ∓1, then the domain wall is absorbed\nby the junction, Fig. 2(c-d), whose charge reverts to ±1.\nIf the net field is strong enough to stimulate the emission\nof a new domain wall of charge ±2 out of this junction,\nFig. 2(e), one of the adjacent links reverses its magneti-\nzation, Fig. 2(f). Otherwise, the evolution stops at the\nstage shown in Fig. 2(d).\nAlternatively, if the domain wall comes to a junction\nwith the same sign of charge, Fig. 4(a-b), it stops dis-\ntanceashort of the junction thanks to magnetostatic\nrepulsion. While this could be a new equilibrium posi-\ntion, the charged domain wall creates a field of strength\n2Hcat the junction, so that the net field at the junc-\ntion is close to 3 Hc. Its projection onto an adjacent link,\n1.5Hc, is sufficient to stimulate the emission of a new\ndomain wall of charge ±2 into that link, Fig. 4(c). The\njunction, now carrying charge of the opposite sign, ∓1,\npulls in the original domain wall and settles down in a\nstate with charge ±1, Fig. 4(d).\nThe sequence illustrated in Fig. 4 explains why ice rule\nviolations are hard to find in honeycomb ice of Qi et al.\n[11]. Unless variations of the critical field are so strong\nthatHcat some junctions exceeds 1 .5¯Hc, triply charged\njunctions, Fig. 4(b), are unstable and decay via the emis-\nsion of a new domain wall, Fig. 4(c-d). Permalloy sam-\nples of Qi et al.exhibit a Gaussiandistribution ofcritical\nfields with a standard deviation ∆ Hc= 0.04¯Hc[28], so(g)H\n+1\n−2+1(c)H\n+1 −1(a)H\n(b)−3 +1 +2\nH\n+1 +1\n(d)H\n+1+2−1\n(e)H\n−1+2\n+2−1\n(f)H\n+1 −1\nFIG. 4: Magnetization reversal in uniformly magnetized spi n\nice. (a-b)Inthebulk, thereversal inalinkmagnetized agai nst\nthe field would lead to the formation of triple charge, which\ncan only happen when the field is of order 3 Hc. (c) Instead,\nthe reversal occurs first in links magnetized at 120◦to the\nfield when H≈2Hc. (d-g) At the edge, the reversal begins\nwhenH≈Hcand propagates into the bulk.\nthat states with charge ±3 are only transients. Much\nstronger disorder exists in cobalt samples of Ladak et\nal.[12] who observed magnetization reversal in a field\nrange between H= 50 and 75 mT. Thus some of the\ndomain walls encounter junctions whose critical field ex-\nceeds 1.5H, which explains the presence of charges ±3.\nIn the limit of weak disorder, ∆ Hc≪¯Hc, there is\nanother characteristic scale of the field that becomes im-\nportant. The new scale set by the demagnetizing field\nof the sample Hdem, is the strength of the field created\nby a unit magnetic charge, Q=Mtw, at a neighboring\njunction distance Laway,H0=Mtw/(4πL2). When\n∆Hc≫H0, the reversal of magnetization is controlled\nmostly by the effects of quenched disorder, with links re-\nversinginalargelyindependent fashionintheorderofin-\ncreasing critical field Hc. Conversely, when ∆ Hc≪H0,\nthe reversal proceeds in a correlated fashion because of\na positive feedback: the reversal of magnetization in one\nlink redistributes magnetic charges at its ends, which in\nturnincreasesthe netfield at adjacentjunctions andthus\ntriggers the emission of domain walls there. In samples\nof Qiet al.,H0= 0.87 mT, which is comparable to the\nwidth of their reversal region, ∆ Hc= 2 mT.\nWe simulated magnetization reversal in this model\nwith the critical fields uniformly distributed in an in-\nterval of width ∆ Hc= 5 mT around the mean ¯Hc= 50\nmT and the Coulomb field scale H0= 0.87 mT. For sim-\nplicity we set the offset angle α= 0. A sample contain-\ning 937 links was initially magnetized along one subset\nof links, Fig. 1(c). Subsequently, the field was switched\noff and a reversal curve M(H) was measured in field ro-\ntatedthroughangle θfromtheinitialdirection. For120◦,\nquenched disorder dominates so that magnetization re-\nversals occur largely independently, in two stages. Links\nmagnetizedagainstthefieldswitchwhentheappliedfield\nis within the range ¯Hc±∆Hc/2, whereas links magne-\ntized at 120◦to the field switch in the range 2 ¯Hc±∆Hc.\nThe net magnetization Mxgrows in an approximately\nlinear fashion in both ranges, Fig. 5, as expected for4\nMx\n 600\n 400\n 200\n 0\n−200\n−400\n−600\nH, mT 100 90  80  70  60  50θ = 180°\nθ = 120° 0.001 0.01 0.1\ns 30 20 10 0θ = 180°\nθ = 120°\nFIG. 5: Simulated magnetization reversals. A sample is ini-\ntially magnetized in a strong field directed as in Fig. 1(c).\nSubsequently, the field is switched off and reapplied at angle s\nθ= 120◦and 180◦to the initial direction. Vertical dashed\nlines are at ¯Hc±∆Hc/2 and 2¯Hc±∆Hc. Inset: Distribution\nof avalanche lengths D(s) in the range of fields near ¯Hc. De-\nviations near the bottom of the graph are due to statistical\nnoise.\nlinks with a uniform distribution of Hc. Links do not\nreverse completely independently from one another: as\nnoted previously, the redistribution of magnetic charges\ninduced by the reversal of magnetization in one link may\ntrigger another reversal nearby. We observed that re-\nversals often involves small groups of links. As can be\nseen in the inset of Fig. 5, the distribution of the num-\nber of links sreversing in a single event is Gaussian,\nD(s)∝exp(−s2/2ξ2), withξ= 4.6.\nAn entirely different process is observed when the field\nis rotated through θ= 180◦. In this case, Coulomb in-\nteractions play a major role and the reversal proceeds\nthrough avalanches evidenced by steps in Mx(H), Fig. 5.\nWhen the field is near ¯Hc, the reversal cannot begin in\nthe bulk because links parallel to the applied field have\nthe wrong sign of magnetic charges at the ends and will\nreverse only in a much higher field (of order 3 Hc). Links\nat the edges have no such problem and the reversalstarts\nwhen a site at the edge emits a domain wall, Fig. 4(d-e).\nWhen the domain wall reaches the other end of the link,\nit encounters a site with like magnetic charge and trig-\ngersthe emission ofa new domain wall, Fig. 4(f), and the\nreversal of magnetization in an adjacent link, Fig. 4(g).\nThis triggers an avalanche of reversals that stops when\nthe traveling domain wall is absorbed by a junction with\na large critical field Hcorruns into already reversedlinks\n[12, 29]. The distribution of avalanche lengths (Fig. 5)\nfits a power law, D(s)∝s−τ, with the exponent τ= 1.6,\nindicative of self-organized criticality [30]. Chain rever-\nsals involving 3 links have been reported by Ladak et al.\n[12] in this geometry; avalanches involving up to 39 links\nhave been observed by Daunheimer et al.[28].We havepresentedadiscretemodel ofartificialspinice\nwhere magnetization dynamics is mediated by domain\nwalls carrying magnetic charge. Interactions between\nmagnetic charges compete with the effects of quenched\ndisorder. In samples with low disorder, positive feed-\nback from charge redistribution is responsible for mag-\nnetic avalanches that have been observed in some exper-\nimental situations.\nWe thank John Cumings for numerous discussions and\nfor sharing his unpublished data. This work was sup-\nported in part by the NSF Grant No. DMR-0520491.\n[1] S. T. Bramwell and M. J. P. Gingras, Science 294, 1495\n(2001).\n[2] V. F. Petrenko and R. W. Whitworth, Physics of ice\n(Oxford University Press, 1999).\n[3] A. P. Ramirez, A. Hayashi, R. J. Cava, R. Siddharthan,\nand B. S. Shastry, Nature 399, 333 (1999).\n[4] C. Castelnovo, R. Moessner, and S. L. Sondhi, Nature\n451, 42 (2008).\n[5] L. D. C. Jaubert and P. C. W. Holdsworth, Nat. Phys.\n5, 258 (2009).\n[6] D. Morris et al., Science 326, 411 (2009).\n[7] T. Fennell, P. Deen, A. Wildes, K. Schmalzl, D. Prab-\nhakaran, A. Boothroyd, R. Aldus, D. Mcmorrow, and\nS. Bramwell, Science 326, 415 (2009).\n[8] S. T. Bramwell, S. R. Giblin, S. Calder, R. Aldus,\nD. Prabhakaran, and T. Fennell, Nature 456, 956 (2009).\n[9] R. F. Wang et al., Nature 439, 303 (2006).\n[10] M. Tanaka, E. Saitoh, H. Miyajima, T. Yamaoka, and\nY. Iye, Phys. Rev. B 73, 052411 (2006).\n[11] Y. Qi, T. Brintlinger, and J. Cumings, Phys. Rev. B 77,\n094418 (2008).\n[12] S. Ladak, D. E. Read, G. K. Perkins, L. F. Cohen, and\nW. R. Branford, Nat. Phys. 6, 359 (2010).\n[13] G. M¨ oller and R. Moessner, Phys. Rev. B 80, 140409\n(2009).\n[14] G.-W. Chern, P. Mellado, and O. Tchernyshyov (unpub-\nlished), arXiv:0906.4781.\n[15] R. P. Cowburn, Phys. Rev. B 65, 092409 (2002).\n[16] X. Ke, J. Li, C. Nisoli, P. E. Lammert, W. McConville,\nR. F. Wang, V. H. Crespi, and P. Schiffer, Phys. Rev.\nLett.101, 037205 (2008).\n[17] C. Nisoli, R. Wang, J. Li, W. F. McConville, P. E. Lam-\nmert, P. Schiffer, and V. H. Crespi, Phys. Rev. Lett. 98,\n217203 (2007).\n[18] L. A. M´ ol, R. L. Silva, R. C. Silva, A. R. Pereira,\nW. A. Moura-Melo, and B. V. Costa, J. Appl. Phys. 106,\n063913 (2009).\n[19] A. Thiaville and Y. Nakatani, in Spin Dynamics in Con-\nfined Magnetic Structures III (Springer, 2006), vol. 101\nofTopics in applied physics , pp. 161–205.\n[20] M. Hayashi, L. Thomas, C. Rettner, R. Moriya, and\nS. S. P. Parkin, Nat. Phys. 3, 21 (2007).\n[21] O. A. Tretiakov, D. Clarke, G.-W. Chern, Y. B. Baza-\nliy, and O. Tchernyshyov, Phys. Rev. Lett. 100, 127204\n(2008).\n[22] C. H. Wong and Y. Tserkovnyak, Phys. Rev. B 81,\n060404 (2010).5\n[23] G. M¨ oller and R. Moessner, Phys. Rev. Lett. 96, 237202\n(2006).\n[24] A. Kunz, J. Appl. Phys. 99, 08G107 (2006).\n[25] W. Wernsdorfer, B. Doudin, D. Mailly, K. Hasselbach,\nA. Benoit, J. Meier, J. P. Ansermet, and B. Barbara,\nPhys. Rev. Lett. 77, 1873 (1996).\n[26] M. J. Donahue and D. G. Porter, Tech. Rep. NISTIR\n6376, National Institute of Standards and Technology,Gaithersburg, MD (1999), http://math.nist.gov/oommf.\n[27] P. Mellado et al., manuscript in preparation.\n[28] S. Daunheimer, Y. Qi, and J. Cumings (unpublished).\n[29] O. Tchernyshyov, Nat. Phys. 6, 323 (2006).\n[30] P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. A 38,\n364 (1988)."    },    {        "title": "1007.3531v3.Inhomogeneous_Magnetoelectric_Effect_on_Defect_in_Multiferroic_Material__Symmetry_Prediction.pdf",        "content": " \n \n \n \n \n \nInhomogeneous Magnetoelectric Effect on Defect in \nMultiferroic Material: Symmetry Prediction \nB Tanygin 1 \nTaras Shevchenko Kyiv National University, Radiophy sics Faculty, Kyiv, Ukraine \nE-mail: b.m.tanygin@gmail.com \nAbstract. Inhomogeneous magnetoelectric effect in magnetizati on distribution heterogeneities \n(0-degree domain walls) appeared on crystal lattice  defect of the multiferroic material has been \ninvestigated. Magnetic symmetry based predictions o f kind of electrical polarization \ndistribution in their volumes were used. It was fou nd that magnetization distribution \nheterogeneity with any symmetry produces electrical  polarization. Results were systemized in \nscope of micromagnetic structure chirality. It was shown that all 0-degree domain walls with \ntime-noninvariant chirality have identical type of spatial distribution of the magnetization and \npolarization. \n1.  Introduction \nCoupling mechanism between magnetic and electric su bsystem in multiferroics [1] is of considerable \ninterest for fundamentals of condensed matter physi cs as well as for their application in the novel \nmultifunctional devices [2]. Magnetically induced f erroelectricity is caused by homogeneous [3-6] or \ninhomogeneous [7-10] magnetoelectric interaction. T he last appears in spiral multiferroics [11] or \nmicromagnetic structures like domain walls (DWs) [7 ,12-17] including cases of magnetization \ndistribution heterogeneities (0-degree DWs). Ferroe lectricity developed from micromagnetic structure \ncan appear in any magnetic material even in centros ymmetric one [18]. It was shown that \ninhomogeneous magnetoelectric effect is closely rel ated to the magnetic symmetry of the system that \nhad been demonstrated for specific cases of DWs [12 ]. Building of symmetry classification of 0°-DWs \nleads to determination of the type of electric pola rization rotation in volume of any magnetic 0°-DW. \nBuilding of complete symmetry classification of one -dimensional magnetic heterogeneities and \nqualitative description of induced ferroelectricity  in their volume is the aim of this report. \n \n \n \n \n \n \n \n \n                                                      \n1  B.M. Tanygin, 64 Vladimirskaya str., Taras Shevch enko Kyiv National University, Radiophysics Faculty . \nMSP 01601, Kyiv, Ukraine.  \n \n \n \n \n \n2.  Magnetoelectric effect on crystal lattice defect \nLet us describe the magnetoelectric effect in the m agnetization distribution heterogeneity (i.e. 0°-DW ). \nSuch micromagnetic structure appears on the crystal  lattice defect according to the localized change o f \nthe magnetocrystalline anisotropy. Most general exp ression for the free energy ME F of the \nmagnetoelectric interaction is produced from symmet ry analysis. All following analysis is \nphenomenological (no specific types of the microsco pic interactions were considered). According to \nthe Neumann’s principle, the ME F terms must be the invariant of the crystal crystal lographic class \n∞\nPG(magnetic point symmetry of paramagnetic phase). Th e well known homogeneous linear \nmagnetoelectric coupling term is given by  [3-6]: \n ()()\nbaiab iMMPfF00 \n,00 \nME =  (1) \nFor the case of the polarization produced by the in homogeneous magnetization it should be \nsupplemented by the terms with magnetization deriva tes [7,12] : \n ()()\nkbai ab ik xMMPfF ∂∂ = /10 \n,10 \nME  (2) \nThe produced polarization distribution is inhomogen eous as well. Consequently, the following \nterms can be introduced: \n ()()\nlibaab il xPMMfF ∂∂ = /01 \n,01 \nME  (3) \n ()()()likbaab ikl xPxMMfF ∂∂∂∂ = //11 \n,11 \nME  (4) \nThe terms with higher derivates are next in order o f magnitude [12]. The structures of the tensors \n()00 ˆf, ()10 ˆf, ()01 ˆf, and ()11 ˆf are  defined by the crystal symmetry. The terms (1-4) re lates to the local \n(short-range) magnetoelectric interactions [7,12]. The non-local interactions between magnetization \nand electric polarization distributions can be coup ling via the spatially distributed stress tensor [1 9]. \nThe free energy term ()() { }r PrM,loc non −F  of the non-local interactions is not the invariant  of the \ncrystal crystallographic class ∞\nPG in general case. This peculiarity of the Neumann’s  principle relates \nto the fact that crystallographic class does not co mpletely describe symmetry of the medium. \nSymmetry of the crystal surface (crystal shape with  magnetic point group SG) restricts the symmetry \nof the medium in case of the non-local interactions  which strongly depends on the boundary \nconditions. Consequently, the actual magnetic point  symmetry of paramagnetic phase for non-local \ninteractions is [20]: \n ()∞ ∞⊆∩=P S P P GGGG  (5) \nThe term ()() { }r PrM,loc non −F  should be invariant of the group (5). Total free e nergy describing the \nmagnetoelectric coupling in the 0°-DW is determined  by the: \n ()()()()()() { }r PrM,loc non 11 \nME 01 \nME 10 \nME 00 \nME ME −++++= FFFFFF  (6) \nSolving the variational problem using the free ener gy term (6) allows obtaining of the function \n()r P produced by the magnetoelectric effect as it was s hown in [21]. In the case of the one-\ndimensional model (planar DW) this function ()zP can be described based on the symmetry analysis \nonly [7,12]. Here Z axis is directed along the DW p lane normal. It was shown [22] that there are 42 \nmagnetic point groups of 0°-DW (table 1-3) which we re systemized depend on their chirality (based \non the novel chirality definition [23-26]). Specifi c component type (A) labels the odd function, (S) \nlabels the even function and (A,S) labels the sum o f odd and even ones. Relation between the \nmagnetic point group of the DW and these order para meter component types is described in [22].  \n \n \n \n \n \nTable 1.  Types of spatial distribution of electric polariza tion induced by the inhomogeneous \nmagnetoelectric effect in volume of magnetic 0°-DWs  with the time-invariant chirality.  \nMagnetic \npoint group   \n()zMx \n  \n()zMy  \n()zMz  \n()zPx  \n()zPy  \n()zPz \nz y x' 2 2 ' 2 A S 0 0 0 A \nz' 2 A,S A,S 0 0 0 A,S \nx' 2 A S S S A A \ny2 A S A A S A \n1 A,S A,S A,S A,S A,S A,S \nz2 0 0 A,S 0 0 A,S \nz3 0 0 A,S 0 0 A,S \nz4 0 0 A,S 0 0 A,S \nz6 0 0 A,S 0 0 A,S \ny x z' 2 ' 2 2 0 0 S 0 0 A \nx z' 2 3 0 0 S 0 0 A \ny x z' 2 ' 2 4 0 0 S 0 0 A \nyx z' 2 ' 2 6 0 0 S 0 0 A \n     \nTable 2.  Types of spatial distribution of electric polariza tion induced by the inhomogeneous \nmagnetoelectric effect in volume of magnetic 0°-DWs  with the time-noninvariant chirality.  \nMagnetic \npoint group   \n()zMx \n  \n()zMy  \n()zMz  \n()zPx  \n()zPy  \n()zPz \nxm' 0 A,S A,S 0 A,S A,S \ny z x2m'm'  0 S A 0 S A \nzm' S S A S S A \nz y x2m'm'  0 0 A,S 0 0 A,S \nxzm'3  0 0 A,S 0 0 A,S \nxy xzm'm'4  0 0 A,S 0 0 A,S \nyxzm'm'6  0 0 A,S 0 0 A,S \n \n \n     \n \n \n \n \n \n  \n \n \n \n \n \nTable 3.  Types of spatial distribution of electric polariza tion induced by the inhomogeneous \nmagnetoelectric effect in volume of magnetic achira l 0°-DWs.  \nMagnetic point \ngroup  \n()zMx \n  \n()zMy  \n()zMz  \n()zPx  \n()zPy  \n()zPz \nzxy' 2mm'  A,S 0 0 0 0 A,S \nym A,S 0 0 0 A,S A,S \nx y z' 2m'm  A 0 S S 0 A \nzm A A S S S A \nzxym'm'm  0 S 0 0 0 A \n x z y' 2m'm  0 S 0 S 0 A \nyy/m 2 0 S 0 A 0 A \nzz/m'' 2  S S 0 0 0 A \nxx/m'' 2  0 S S 0 A A \n1 S S S A A A \nzz/m 2 0 0 S 0 0 A \nyxzm'm'm  0 0 S 0 0 A \nz6 0 0 S 0 0 A \nx y z' 2m'6  0 0 S 0 0 A \nxzm'3  0 0 S 0 0 A \nzz/m 4 0 0 S 0 0 A \nxy xzzm'm'/m 4  0 0 S 0 0 A \nz4 0 0 S 0 0 A \nxy x zm'' 2 4  0 0 S 0 0 A \nzz/m 6 0 0 S 0 0 A \nyxzzm'm'/m 6  0 0 S 0 0 A \nz3 0 0 S 0 0 A \n3.  Conclusions \nThus, the magnetic point groups allow determining k ind of distributions of electrical polarization in \nmagnetization distribution heterogeneities appeared  on crystal lattice defect. Spontaneous polarizatio n \nproduced by the inhomogeneous magnetoelectric effec t can be realized in crystal with arbitrary \nsymmetry. The zero degree domain walls with non-pol ar magnetic point group have odd electrical \npolarization distribution. Any zero degree domain w alls have coupled electric charge in their volume. \nThus, their magnetoelectric properties can be detec ted using the homogeneous electric field. All zero \ndegree domain walls with time-noninvariant chiralit y have identical type of spatial distribution of th e \nmagnetization and polarization. \n  \n \n \n \n \n \nReferences \n[1] Khomskii D 2009 Physics  2 20  \n[2] Bibes M and Barthelemy A 2008 Nature Materials  7 425  \n[3] Landay L and Lifshitz E 1965 Electrodynamics of Continuous Media  (Oxford: Pergamon Press)  \n[4] Smolenskii G and Chupis I 1982 Uspehi Fiz. Nauk  137  415  \n[5] Dzyaloshinskii I 1959 JETP  37  881  \n[6] Neronova N and Belov N 1959 Dokl. Akad. Nauk SSSR  120  556  \n[7] Bar'yakhtar V, L'vov V and Yablonskiy D 1983 JETP Lett.  37  673   \n[8] Smolenskii G and Chupis I 1982 Sov. Phys. Usp.  25(7)  475  \n[9] Vitebskii I and Yablonski D 1982 Sov. Phys. Solid State  24  1435  \n[10] Sparavigna A, Strigazzi A and Zvezdin A 1994 Phys. Rev. B  50  2953  \n[11] Kimura T et al. 2003 Nature  426  55  \n[12] Bar'yakhtar V, L'vov V and Yablonskiy D 1984 Problems in solid-state physics ,  \n ed A M Prokhorov and A S Prokhorov (Moscow: Mir Pu blishers) p 56  \n[13] Pyatakov A et al. 2010 Ferroelectricity of Nee l-type magnetic domain walls \n arXiv:1001.0672v1 [cond-mat.mtrl-sci]  \n[14] Logginov A et al. 2008 JETP Lett.  86  115 (2007)  \n[15] Pyatakov A and Zvezdin A 2010 Spin flexoelectr icity in multiferroics  \n arXiv:1001.0254v2 [cond-mat.mtrl-sci]  \n[16] Pyatakov A et al. 2010 Journal of Physics: Conference Series  200  032059  \n[17] Pyatakov A and Meshkov G 2010 Electrically sta bilized magnetic vortex and antivortex states \n in magnetic dielectrics arXiv:1001.0391 [cond-mat. mtrl-sci]  \n[18] Dzyaloshinskii I 2008 EPL  83  67001  \n[19] Eerenstein W, Mathur N and Scott J 2006 Nature  442  759  \n[20] Tanygin B and Tychko O 2010 Acta Physic. Pol. A.  117  214  \n[21] Mostovoy M 2006 Phys. Rev. Lett.  96  067601  \n[22] Tanygin B and Tychko O 2009 Physica B: Condensed Matter  404  4018  \n[23] Barron L 1986 J. Am. Chem. Soc.  108  5539  \n[24] Barron L 2000 Nature  405 895  \n[25] Barron L 2002 Chirality in Natural and Applied Science , ed W J Lough and I W Wainer \n (Oxford: Blackwell Publishing) p 53  \n[26] Barron L 1991 New developments in molecular chirality  (Dordrecht: Kluwer Acad. Publishers)  "    },    {        "title": "1008.1041v1.Anisotropic_magnetocaloric_effect_in_all_ferromagnetic__La0_7Sr0_3MnO3_SrRuO3__superlattices.pdf",        "content": " 1 \nAnisotropic magnetocaloric e ffect in all-ferromagnetic \n(La 0.7Sr0.3MnO 3/SrRuO 3) superlattices \n \nS. Thota, Q. Zhang, F. Guillou, U. Lüders, N. Barrier, W. Prellier* and A. Wahl \nLaboratoire CRISMAT, CN RS UMR 6508, ENSICAEN, \n6 Boulevard du Maréchal Juin, F-14050 Caen Cedex, France \n \nP. Padhan \nDepartment of Physics, Indian Institut e of Technology Madras, Chennai-600036, India \n \n                                                                       Abstract We exploit the magnetic interlayer coupling in La\n0.7Sr0.3MnO 3/SrRuO 3 superlattices to realize a \ncrossover between inverse and c onventional magnetic entropy change s. Our data reveal a strong \nanisotropic nature of the magneto caloric effect due to the magnetic anisotropy of the superlattice. \nTherefore, artificial superlattices built from ferro magnetic materials that can  be used to alter the \nmagnetic structure as well as the magnetic anis otropy, could also be ut ilized for tuning the \nmagnetocaloric properties, which may open a cons tructive approach for magnetic refrigeration \napplications.    \n* Author to whom any corres pondence should be addressed   2 In the recent years, magnetocaloric effect (MCE) in mixed-valency manganese-oxides1 \nhave been extensively studied owing to the fact that some of them exhibit fairly large entropy \nchange (ΔSM values) comparable with Gd- based all oys. Of particular interest are “AMnO 3” type \nstructures where  “A” is trivalent rare-earth ion mixed w ith divalent alkaline-earth element (e.g. \nLa1-xSrxMnO 3) because they exhibit a rich variety of magnetic and electronic properties.2 \nHowever, the main drawback in these system s is large heat capacities leading to small \ntemperature change ( │∆T│~2K for a field change, ∆H of 2T).3,4 On the other hand, a wide range \nof transition temperatures (100 K ≤ TC ≤ 375 K) together w ith large MCE values  (associated with \nthe sharp rise of the magnetization) for small fiel d changes are the positive features which makes \nthem useful in magnetic refrigiration.5 Most of today’s research activity in this field is limited to \nbulk materials. Little literature is ava ilable on the MCE properties of thin films6-8, although \nprincipally they will be easier to integrate into electronic structures for applications. Nevertheless, the concept of using magnetic superl attices for magnetic cooling has been recently \nillustrated by Mukherjee et al. in Co/Cr superlattices.\n7 They suggested that the interlayer \nantiferromagnetic coupling between two ferromagnetic constituents-(Co) separated by a non magnetic layer (Cr) in their case-can be used to tune the MCE properties, and found that Co/Cr \nsuperlattices exhibit a maximu m entropy change of >-0.4 J kg\n-1 K-1, at 330 K. Apart from \ninterlayer coupling, superlatti ces can show strong magnetic interface coupling when two \nferromagnetic materials are in close contact w ith each other resulti ng in antiferromagnetic \ncoupling9,10 which would lead to the gr owth of magnetic structures comparable to those proposed \nby Mukherjee et al.7 In this direction, we ha ve explored the magnetocal oric properties in all-\nferromagnetic (FM) La 0.7Sr0.3MnO 3/SrRuO 3 (LSMO/SRO)  artificial  superlattices. Our results \nindicate (i) the presence of interfacial antiferromagnetic (AFM) coupling between the FM  3materials SrRuO 3 and (La,Sr)MnO 3,11 and (ii) an inverse (negativ e) and conventional (positive) \nanisotropic-MCE, below and above the temperat ure at which this AFM coupling appears.  \nA multitarget pulsed laser deposition system operating at 248 nm wavelength has been \nused. The bottom layer LSMO (20 unit cells) is  directly grown on the [001]-oriented SrTiO 3 \nsubstrate followed by ‘n’ unit cells of SRO layer (in the present ca se ‘n’ = 6). The above bilayer \nis repeated 15 times and finally covered with 20 unit cells of LSMO. The details of preparation \nconditions and their structural analys is have been reported elsewhere.12 A superconducting \nquantum interference device ba sed magnetometer (Quantum Desi gn MPMS) with magnetic field \n(H) up to 50 kOe and temperature (T) 5-340 K has been used to perform the magnetization (M) \nmeasurements.  \nFig. 1 shows the M(T) plots measured in th e presence of a 50 Oe magnetic field applied \nalong the out-of-plane (H//[001]) and in-plane (H//[100]) directions u nder zero-field-cooling \n(ZFC) and 50 Oe field-cooling (FC) conditions. A good estimation of the transition temperatures \ncan be drawn from the [ ∂M/∂T] versus T plot shown in the inse t of Fig. 1(a). Fo r both in-plane \nand out-of-plane configurations, the first tran sition at 325 K and th e corresponding magnetic \nmoment are coherent with  the Curie temperature (T CLSMO) and bulk magnetic moment of \nLa0.7Sr0.3MnO 3, respectively.13 The T C of SrRuO 3 (TCSRO) is not clearly visi ble in Fig. 1(a) and \n1(b) as expected at 145 K where an enhancement of magnetization ( ΔM ≈ 50 emu cm-3) is \nobserved with decreasing the temperature. This ΔM value is lower than the bulk due to the small \nvolume fraction of SrRuO 3. In the case of in-p lane configuration the enhancement of the \nmagnetization value within the temperature range T*<T<T CSRO is consistent with the onset of \nferromagnetic coupling arising from the ordering of the SrRuO 3 magnetic moment as \nemphasized in Ref. 14 (where T* is the onset of the decrease in the magnetization in the ZFC  4mode associated with the occurrence of the inte rfacial magnetic coupling). Further, the in-plane \nmagnetization curves exhibit higher values than that measured in the out-of-plane (~12 times \nlarger at 5K) configuration. This indicates that th e easy axis orientation in  these superlattices is \nalong (100) direction in c ontrast to thicker SrRuO 3 coherently grown on SrTiO 3 substrates which \nexhibit typically an easy axis  normal to the surface due to  the strong magnetocrystalline \nanisotropy of this material.15  \nBelow 100 K the decrease  in the in-plane M FC and splitting between the M FC and M ZFC \nindicates the presence of a third magnetic tr ansition with an antiferromagnetic character \n(indicated by T* in the inset of Fig. 1(b)). This featur e suggests that there is a coupling between \nSrRuO 3/La 0.7Sr0.3MnO 3 yielding to a partial compensation of  the overall magnetic moment of the \nsuperlattice for both in-plane a nd out-of-plane configuration.6,12 The value of this compensation, \nalong the easy axis , of around 100 emu cm-3 is consistent with a scenario, where the SrRuO 3 \nlayer couples antiferromagnetically to the La 0.7Sr0.3MnO 3.12 In general, field cooling from a \nparamagnetic (disordered) state to a lower temperat ure gives preferential or ientation to the spins, \nwhereas in zero field cooling no preferred orienta tion is induced. Thus, cooling the sample in the \npresence of a small magnetic field prevents th e antiferromagnetic interlayer coupling between \nthe La 0.7Sr0.3MnO 3 and SrRuO 3.  \nFig. 2(a) shows the magnetic hysteresis loops  recorded at 70 K applying the magnetic \nfield along [001] (i.e. out-of-plane) and the [100] (i.e. in-plane) directions after subtracting the  \nsubstrate diamagnetic contribution (which is estimated from extrapolating the high field data) . \nThe values of the remanent magnetization (M r) and coercive fields (H C) under the in-plane \ndirection are 441 emu cm-3 and 198 Oe, respectively; where as for the out-of-plane direction M r \nand H C being 48 emu cm-3 and 400 Oe, respectively (clearly show n in the inset of Fig. 2(a)). The  5above observations confirm that th e [100]-direction is an easy axis, the [001] is a hard axis. As \nstated before, the magnetic moments of the SrRuO 3 are thus forced into the sample plane. In \nthese superlattices, the small thickness of the laye rs (6 unit cells) and strain at the interfaces \ncould significantly modify the magnetic anisotropy in SrRuO 3 films15.  \nFig. 2(b) shows the in-plane magnetizatio n at low magnetic fields at different \ntemperatures. Prior to each measurement, the temperature was raised above the T CLSMO, in order \nto ensure a perfect demagnetization. The value of  in-plane magnetization per unit volume in each \nof the isotherms increases gradually until a transition magnetic field (H T), where it rises rapidly \nwith the applied magnetic field, an d then saturates (See Fig. 2(b)). The transition field (H T) \ncorresponds to the point of maximum slope in the magnetization isotherm.  First the magnitude of \nthe magnetization step ( ΔM) has been estimated using the difference between the linear \nextrapolations of M(H) curve above and below the transition region. Th e field corresponding to \nthe midpoint of the ‘ ΔM’ gives the rough estimation of H T. This can be understood on the basis \nof the AFM coupling of the SRO/LSMO film s. The spontaneous magnetization at H = 0 \ncorresponds to a partially co mpensated overall moment (M LSMO-MSRO), and the application of a \nthreshold magnetic field leads to the alignment of the magnetic moment of SrRuO 3 in the field \ndirection and therefore, sa turates at a value of (M LSMO+M SRO). Such behavior closely resembles a \nmetamagnetic-like transition, where a jump in the magnetization value ( δM) results from the \nsuppression of AFM-like coupling at the interface.  This feature is induced by changing the field \nstrength in the vicinity of this first order tr ansition (either in M versus H or M versus T).16 The \ntemperature-dependence of ‘H T’ is shown in the inset of Fig. 2(b). With increasing the \ntemperature, ‘H T’ gradually decreases and approaches zero near T N where AFM coupling is \ntotally suppressed. H T is a measure of the strength of the antiferromagnetic coupling. The low  6values of H T indicate a weak antiferromagnetic interlayer/interfacial coupling at low \ntemperatures. This particular lo w field behavior was only observed  in the virgin M-H curves, and \nnot in the hysteresis loops, due to this extrem ely small coupling strength. The application of a \nhigh magnetic field destroys the interface coupli ng, so these hysteresis loops have the same \nshape as for a typical ferromagnet. The M(H) measurements recorded in the out-of-plane \nconfiguration are shown in Fig 2(c) . Due to its hard axis nature, a stronger field is necessary to \nbreak the interfacial  coupling and, to align the ma gnetic moment of the SrRuO 3 in the field \ndirection. This is the reason why one does not observe this feature at low temperature within the \ninvestigated field range. \nFrom the isothermal M(H)  curves (Figs. 2(b,c)), the change of magnetic entropy, [- ΔSM] \nis estimated at various magnetic field changes ( ΔH) using both Maxwell’s [ ∂S(T,H)/∂H]T = \n[∂M(T,H)/∂T]H  and Clausius-Clape yron (CC) equations = ΔS(T)\n = δM×[∂T/∂HT]-1.17,18 In the \npresent case ‘ δM’ occurs under the applicatio n of a small magnetic field ( ≤ 400 Oe) in each \nisotherm which in turn causes variation in the magnetic entropy. This is an important aspect \nsince such significant variation in the entropy by means of moderate magne tic fields will indeed \nbe more appropriate than bulk fo r magnetic refrig eration technology.17,19 \nThe behavior of [- ∆SM] (Figs. 3(a,b)) strongly depends on  field orientations, temperature \nand the magnitude of field change ( ΔH). In the in-plane configura tion (easy magnetic axis), we \nobserve small negative values in [- ∆SM] for a broad range of investigated temperatures for lower \napplied magnetic fields (at least up to 1T). In this low field regime one can see a crossover of [-∆S\nM] to positive values for temperatures beyond T*. When the field change is sufficiently high, \npositive values in [- ∆SM] are observed over the whole range of temperatures due to the complete \nfield induced suppression of AFM aligned spins at  interface. It is worth pointing out that under  7high field change the in-plane [- ∆SM] values reach  0.85 and 1.3 mJ cm-3 K-1 for ∆H = 1T and 2T, \nrespectively around T C of SRO. For the bulk SRO, the reported [- ∆SM] value around T C is ~ 3.83 \nmJ cm-3 K-1 for ∆H = 1.5 T20 in agreement with the reported bulk data 0.87 mJ cm-3 K-1 \n(considering the fact that SrRuO 3 occupies 23 % of total volum e in the superlattices).  \nThese results provide convincing evidence that  below 150 K the main contribution to the \ntotal entropy change comes from the SrRuO 3. Furthermore, the magnetic entropy changes \nobtained from Maxwell method are in good agreem ent with that of CC equations around the \nmetamagnetic transition, up to the field change  of 0.5 kOe. In th e case of out-of-plane \nconfiguration, [- ∆SM] reaches a maximum value of -0.6 mJ cm-3 K-1 at T = 100 K, for a field \nchange of ΔH = 2.2 T (Fig. 3(c)). This field configur ation is the hard axis direction of \nmagnetization and consequently; the magnetization saturates at much higher fields than in the in-\nplane direction, making difficult any comparison with [- ∆SM] values at low fields.  However, \nabove 2T, small [- ∆SM] values are observed for the in-pla ne configuration, whereas negative \nvalues in [- ∆SM] have been observed in out-of-plane c onfiguration. The magnitude of entropy \nchanges determined under easy -axis orientation below T CSRO is greater than that of hard-axis \norientation whereas an opposite  trend is observed beyond T CSRO. All these results reveal strong \nanisotropic nature of magnetocaloric properties.  \nIn summary, we have demonstrated that La 0.7Sr0.3MnO 3/SrRuO 3 superlattices exhibit both \ninverse and conventional magnetocaloric effect s associated with the antiferromagnetic and \nferromagnetic coupling, respectively. The sign of the magnetic entropy change depends strongly \non the temperature. Furthermore, due to very  high magnetic anisotropy of the superlattices, \nentropy change also depends on the magnitude a nd direction of applied field strength. Thus, \nthese results reveal strong anisotropic nature of  magnetocaloric properties . This may introduce a  8more efficient way of tuning the magnetocalori c properties through a moderate applied magnetic \nfield (≤400 Oe).  \nThis work is done in the frame of th e LAFCIS. Support of the CEFIPRA/IFPCAR  (3908-\n1), the C’Nano Nord Ouest (GDR 2975) a nd STAR (21465YL), ENERMAT (2009-1/086) and \nSOPRANO (PITN-GA-2008-214040)  projects are acknowledged. We also thank J. Lecourt, L. \nGouleuf, V. Hardy and C. Mcloughlin. \nReferences \n1K. A Gschneidner Jr, V. K. Pechar sky and A. O. Tsokol, Rep. Prog. Phys. 68, 1479 (2005); M. \nH. Phan and S.C. Yu, J. Magn. Magn. Mater. 308, 325 (2007). \n2W. Prellier, Ph. Lecoeur and B. Me rcey, J. Phys.: Condens. Matter 13, R915 (2001). \n3V. K. Pecharsky and K. A Gschneidner Jr, J. Appl. Phys.  90, 4614 (2001). \n4H. Terashita, J. J. Garbe, and J. J. Neumeier, Phys. Rev. B.  70, 094403 (2004). \n5C. Zimm, A. Jastrab, A. Sternbe rg, V. K. Pecharsky, K  Gschneidner Jr, M. Osborne and I. \nAnderson, Adv. Cryog. Eng. 43, 1759 (1998). \n6 T. Mukherjee, S. Sahoo, R. Skomski, D.  J. Sellmyer, and Ch. Binek, Phys. Rev. B. 79, 144406 \n(2009) \n7C.W. Miller, D. V. Williams, N. S. Bingham, and H. Srikanth, J. Appl. Phys. 107, 09A03 \n(2010). \n8D.T. Morelli, A.M. Mance, J. V. Mant ese and A.L. Micheli, J. Appl. Phys. 79, 373 (1996). \n9R. E. Camley, Phys. Rev. B 39, 12316 (1989). \n10K. R. Nikolaev, A. Bhattacharya, P. A. Krau s, V. A. Vas'ko, W. K. Cooley and A. M. \nGoldman, Appl. Phys. Lett. 75, 118 (1999).  911 M. Ziese, I. Vrejoiu, E. Pippe l, P. Esquinazi, D. Hesse, C. Etz, J. Henk, A. Ernst, I.V. \nMaznichenko, W. Hergert, and I. Mertig, Phys. Rev. Lett. 104, 167203 (2010). \n12P. Padhan ,W. Prellier and R. C. Budhani, Appl. Phys. Lett.  88, 192509 (2006). \n13M. Huijben, L. W. Martin, Y.-H . Chu, M. B. Holcomb, P. Yu, G.  Rijnders,  D. H. A. Blank, \nand R. Ramesh,  Phys. Rev. B 78, 094413 (2008). \n14G. Cao, S. McCall, M. Shepard, J. E. Crow, and R. P. Guertin, Phys. Rev. B 56, 321 (1997). \n15C. U. Jung, H. Yamada, M. Kawasaki, and Y. Tokura, Appl. Phys. Lett. 84, 2590 (2004). \n16C. Triguero, M. Porta, and A. Planes, Phys. Rev. B 76, 094415 (2007). \n17V. K. Pecharsky, K. A. Gschneidner, Jr. A. O. Pecharsky, and A. M. Tishin, Phys. Rev. B 64, \n144406 (2001). \n18L. Caron, Z. Q Ou, T.T. Nguyen, D. T. C. Thanh, O. Tegus and E. Bruck, J. Magn. Magn. \nMater. 321, 3559 (2009) \n19A. M. Tishin and Y. I. Spichkin 2003 The Magnetocaloric Effect and its Applications  (Bristol: \nInstitute of Phys ics Publishing). \n20X. Y. Zhang, Y. Chen and Z. Y. Li, J. Alloys and Compd. 459, 51 (2008).  10 \nFigure captions:  \nFigure 1. (Color online) Temperature dependence of magnetization measured at 50 Oe applied \nfield along (a) In-plane and (b) Out-of-plane di rection under ZFC [open circles] and FC [filled \ncircles] conditions. Inset in (a) shows the firs t derivative of magnetizat ion versus temperature \nwhere T* corresponds to the Néel  temperature, and T SRO and T LSMO being, Curie temperatures of \nSrRuO 3 and La 0.7Sr0.3MnO 3, respectively.      \n Figure 2. (Color online) (a): Magne tic hysteresis loops recorded at 70 K in in-plane (circles) and \nout-of-plane (squares) orie ntation [The low field regime is cl early shown in the inset], (b) and \n(c): Isothermal magnetization curv es at different temperatures unde r (b) In-plane and (c) Out-of-\nplane configurations. Inset of Fi g. (b) shows the variation of H\nT as a function of temperature.  \n \nFigure 3. (Color online) Temperature de pendence of magnetic-entropy change (- ΔSM ) under (a) \nIn-plane and (b) Out-of-plane configurations, calculated from magnetization isotherms in the \ntemperature range 50-165 K. The arrow mark shows that ΔS = 0.  \n "    },    {        "title": "1012.3869v1.Phenomenology_of_magnetically_active_superconductors.pdf",        "content": "arXiv:1012.3869v1  [cond-mat.supr-con]  17 Dec 2010Phenomenology of magnetically active superconductors\nby\nDOMINIK ROGULA∗and MA/suppress LGORZATA SZTYREN†\nNovember 10, 2018\nSummary: The thermodynamical phenomenological theory of magnetically act ive superconducting\nmaterialsandmagnetic-superconductingheterostructuresis pr esented. The materialsmayexhibit arbitrarily\nstrong anisotropy, parametric or structural. Exact anisotropic similarity transformations are found for both\nthe continuum and layered hybrid systems.\nKeywords: Ginzburg-Landau theory, variational principles, superconducto rs, magnetic order, anisotropy,\nheterostructures, hybrid systems\n1 Introduction\nA formulation of thermodynamical theory of magnetically active, an isotropic materials ad-\nmitting coexistence of the superconductivity and magnetic order h as been proposed in [1].\nThe theory is based on the Ginzburg-Landau approach extended t o multi-component order\nparameters and the states of thermodynamic quasi-equilibrium far from the superconduct-\ning phase transition. The field equations are derived under assumpt ion of theU(1) gauge\ninvariance. The nonlinearity with respect to the order parameter, magnetic field, and other\nphysical quantities is assumed reasonably general, without any par ticular restrictions of its\nfunctional form.\nIn the present paper we give an improved version of that theory co mplemented with the\nexact anisotropic similarity transformations for layered hybrid sys tems [23].\n2 Background\nA material medium is considered magnetically active if its magnetic prop erties differ (sub-\nstantially) from those of the physical vacuum. Although the super conductivity itself is\na magnetic phenomenon, the superconducting materials need not b e magnetically active.\nThis circumstance justifies disregarding the magetic activity of a su perconducting material\nin heuristic or didactic considerations, but not in a more complete the ory. Due to orbital\npolarizability and/or spin degrees of freedom, the effects of magne tic activity of superconduc-\ning materials are practically always present, and in many instances sig nificant. In particular\n∗Polish Academy of Sciences, Institute for Fundamental Technolog ical Research, ul. Pawi´ nskiego 5B,\nPL-00-106 Warsaw, E–mail: dominikrogula@op.pl\n†Department ofMathematics and Information Science, WarsawUniv ersityof Technology, Pl. Politechniki\n1, PL-00-661 Warsaw, E–mail: emes@mech.pw.edu.pl\n1it concerns the heterostructures which involve interactions betw een superconducting and\nferromagnetic components [6, 18]. One may also notice that, on the background of some\ncontroversial views [4, 8] concerning coexistence of supercondu ctivity and ferromagnetism,\nmaterials which combine these phenomena were found experimentally [3, 11, 14, 15]. More-\nover, it seems that, in accordance with earlier theoretical predict ions, the superconductivity\nof such materials is magnetically mediated [12].\nIn order to describe the superconducting state of condensed ma tter, the Ginzburg-\nLandau theory [9] introduces a phenomenological quantity, called the orde r parameter, rep-\nresented by a complex scalar field ψ(x) with properties quite analogous to the microscopic\nquantum-mechanical single-particle wave function. Contrary, ho wever, to the microscopic\nwave function, the GL order parameter describes the macroscop ic condensate of the super-\ncurrent carriers and enters as an independent variable into the th ermodynamical free energy\nfunctional. This approach turned out to be extremely succesful.\nIn the original GL paper the functional was given a simplest form suit able for description\nof the states of a superconducting material near the phase tran sition. In this form, the\ntheory was confirmed afterwards by Gorkov [10] through rederivation from the microscopic\ntheory. Its range of applicability turned out, however, severely r estricted by the condition of\nproximity to the transition point.\nTo cope with broader ranges of real situations, the GL theory has been extended in\nvarious directions, including multicomponent order parameters, mo re elaborate forms of\nthe free energy functional, time-dependent phenomena, and het erostructures. Any such\nmodification, as long as it respects the idea of a (possibly generalized ) superconducting\norder parameter as a thermodynamical variable, is referred to as belonging to the framework\nofextended Ginzburg-Landau phenomenology [21, 22, 23].\nThe theory under consideration admits arbitrary (in a reasonable s ense) functional forms\nof the GL thermodynamical potential. We intend to include in this way a lso the thermody-\nnamical states which are far from the superconducting phase tra nsition. We admit multiple\norder parameters, anisotropy, and material inhomogeneities, bu t, for simplicity, we retain\nthe assumptions of stationarity, thermodynamical quasi-equilibriu m, and charge neutrality.\nThe assumption of charge neutrality refers to the resultant elect ric charge density of all\ncharged components, such as the superconducting carriers (Co oper pairs), normal electrons,\nand the ionic substrate. It restricts our considerations to the ca se of bulk superconductivity\nin good (quasi-metallic) superconductors. To include ”bad” superc onductors and interface\neffects one would need a further extension of the model, which is bey ond the scope of the\npresent paper and will be given elsewhere.\nWe shall focus our attention on superconducting materials which ca n be (a) strongly\nanisotropic, (b) inhomogeneous at the macro- and micro-scale, an d (c) magnetically active.\nBelow we shall comment briefly on the above marked specific assumpt ions.\n(a) The idea of isotropic superconductor, due to its simplicity and he uristic power, at-\ntracts much attention as a tool in theoretical investigations. It s uffices here to note examples\nof most outstanding and successful classic theories of supercon ductivity such as Ginzburg-\nLandau, Bardeen-Cooper-Schriefer, and Abrikosov’s ones, eac h of them based on an appro-\npriate isotropic model. On the other hand, the real superconduct ing materials exhibit, as a\nrule, some anisotropy of physical properties. In particular, the a nisotropy of high Tccuprate\noxides is rather high [5, 7]: e.g. the ratio of penetration depths λc/λabfor YBa 2Cu3O7−y\n2and Bi 2Sr2CaCu2O8+ylies in the range 5 ÷7 and 50 ÷200, respectively; it corresponds to\nestimated values of the ratio of flux line tensions Uc/Uabranging from 20 to 40000.\n(b) To describe heterogeneous superconducting materials or dev ices, the theory must\nadmit material inhomogeneities of various – macroscopic, microscop ic, and intermediate –\nscales of length. The inhomogeneities can be smooth or abrupt, tec hnological or natural.\nMany high T csuperconducting materials exhibit a distinct layered structure at t he atomistic\nlevel. The spacings between atomic layers, such as Cu-O planes in cup rate-oxide supercon-\nductors, can be relatively large as compared with the in-plane distan ces what, besides the\nstructural anisoptropy, can result in a natural micro-scale inhom ogeneity of those materials\nin the out-of-plane direction. The Lawrence-Doniach model [13] and its generalization\n[22, 23] can be considered an extreme case of such a natural micro -inhomogeneity. On the\nother hand, due to the recent progress in nanotechnology it is pos sible to fabricate diverse\nnano-scale technological heterostructures.\n(c) Apart from magnetic activity originating from physical factors , we found it also ex-\npedient to introduce its equivalent at the level of theoretical mode lling. We refer here to the\nanisotropic similarity transformations - a useful tool in the study o f anisotropic supercon-\nductors, discussed in Section 8.\n3 Notation\nWhenever appropriate, we use implicit tensor notation with supress ed indices; the indices are\nexposed only when otherwise the expressions would be equivocal or illegible. For instance, a\npoint in the physical space (as well as the corresponding material p oint when the distinction\nmakes no difference) is denoted simply by x, which is to be developed to ( x1,x2,x3) in typical\n3D situation.\nBasically, the standard notation from recent literature on phenom enology of supercon-\nductivity [20] is employed throughout the paper. The effective mass m∗of the supercurrent\ncarriers is tensorial; in the case of transversally isotropic superco nducting materials (e.g. lay-\nered oxides, in good approximation) the relevant mass tensor comp onents aremab(in-plane)\nandmc(out-of-plane).\nThe complex conjugate of the order parameter ψis denoted by ¯ψ. The symbols ∂and∇\nare employed in a somewhat non-standard way. The partial derivat ive operator is denoted\nby∂, while the symbol ∇is reserved for the electromagnetic U(1)-covariant derivative. Both\noperators∂and∇act from the left. We found it expedient to introduce also the conju gate\noperators ¯∂and ¯∇which act from the right.\nDue to a bug in the routine translating from TeX to PDF, in the final pr inted form of\nthe reference [1] a repeated typographic error occured. The er ror consisted in the fusion of\ntwo consecutive short overbars into a longer one. It resulted in er roneous replacement of the\nexpressions ¯ψ¯∂withψ∂and ¯ψ¯∇withψ∇. The present text contains terms counteracing\nthose faults.\n34 The reference model\nTo fix the point of departure for construction of extended models we start from the reference\nmodel which, excepting the details of notation, almost exactly coinc ides with the original\nGL model [9]. It is also convenient to develop the notation adapted in t his paper.\n1. The superconducting state of the superconductor is describe d with the aid of the order\nparameter represented by a single-component complex scalar fun ctionψ=ψ(x).\nThe gauge transformation for this parameter is defined as\n\n\nA→A+∂Λ,\nψ→eie∗\n¯hcΛψ,\n¯ψ→¯ψe−ie∗\n¯hcΛ,(1)\nwheree∗denotes the electric charge of the supercurrent carriers. The c orresponding covariant\nderivatives ∇and ¯∇are given by\n∇=∂−ie∗\n¯hcA, (2)\nand\n¯∇=¯∂+ie∗\n¯hcA. (3)\n2. The free energy of the superconductor is given by the function al\nF[T;ψ,A] =/integraldisplay\nd3xFS (4)\nwith an appropriate free energy density FSof the superconducting state.\n3. The free energy density FSequals\nFS=FN+α|ψ|2+β\n2|ψ|4+¯h2\n2m∗¯ψ¯∇∇ψ, (5)\nwhereFNrefers to the normal state and m∗represents the effective mass of the supercurrent\ncarriers. The coefficients αandβare given as\nα=a(T−Tc), a =const, β =const. (6)\nThe normal state free energy density FNdoes not depend on the order parameter.\nThe expression (5) ensures the already required invariance with re spect to the gauge\ntransformations (1).\n5 Local first order functional\nThe reference model sketched in the previous section relies upon m any intentional simplifi-\ncations, including isotropy, homogeneity, and proximity to the N-S t ransition point. Some of\nthese drawbacks are direct consequences of the particular form of the free energy density FS\nand can be eliminated simply by admitting, in place of (5), more general functionals defined\non the same space of the field variables. In this way one can success fully take into account\n4many realistic features of superconductors. As examples one can mention such properties\nas high anisotropy or more subtle thermodynamical behaviour of hig hTcsuperconductors\n[16, 5, 20].\nThe range of applicability of such models is, however, severely restr icted by the singlet\nnature of the order parameter. From the microscopic point of view a singlet order parameter\nis justified, first of all, for superconductors with dominating isotro pics-pairing. Also other\ntypes of pairing can be treated in this way, provided that a single pair ing mode, corresponding\nto a one-dimensional representation of the internal symmetry gr oup, is strongly dominating.\nMany superconding materials require, however, multiple order para meters. One can men-\ntion here the heavy fermion unconventional superconductors [1 7] which exhibit anisotropic\nspin triplet p-pairing, possibly mixed with spin singlet s-pairing. Another typical example is\ndelivered by the coexistence of spin singlet s- andd-pairings in orthorombic high Tcmaterials\n[19].\nIn the present section we shall briefly discuss an extension of the G L phenomenology\nwhich avoids the above mentioned drawbacks.\n1. First of all we modify the assumption stated in item 1 of Section 1. I n place of the\nsinglet order parameter, represented in the reference model by a complex-valued scalar field,\na more general multi-component order parameter is introduced. F or brevity, this order pa-\nrameter will also be denoted by the single symbol ψ=ψ(x). In geometrical interpretation\nthe admissible values of ψwill be considered as organized into a differential manifold. When-\never a particular component will be referred to, an indexed symbol likeψA=ψA(x) will be\nused and interpreted as an appropriate – real or complex – coordin ate in the corresponding\nlocal map. The index Awill take integer values from 1 to N, with arbitrary fixed N. The\nreal dimension of the order parameter manifold may, due to the pre sence of complex-valued\ncoordinates, differ from N.\n2. From the physical point of view the multiplet order parameter rep resents generally\na mixture of charged fields. In contrast to the reference model, s uch a mixture can not be\ncharacterized by a single scalar charge. To characterize the coup ling of the multiplet order\nparameterψwith the electromagnetic field we must specify an adequate gauge tr ansforma-\ntion. To that end, in place of the scalar charge e∗we introduce a real symmetric matrix\ne∗= (e∗\nAB) (7)\nsuch that the gauge transformation is defined by the correspond ing matrix reinterpretation\nof the old formula (1). In this way also the gauge covariant derivativ es (2) and (3) retain\ntheir graphic form with reinterpreted meaning.\nIn general, the charge matrix e∗need not be diagonal. However, being real and sym-\nmetric, it can be diagonalized by an appropriate orthogonal transf ormation of the order\nparameters ψA. The eigenvalue 0, if present, corresponds to electrically neutral subspace of\norder parameters which carries no supercurrent; in spite of this p roperty such order param-\neters can seriously affect the thermodynamical properties of a su perconducting system. The\nremaining eigenvalues of e∗determine the spectrum of charges of supercurrent carriers.\nIn most cases the supercurrent carriers are experimentally ident ified as electrically equiv-\nalent to pairs of electrons or holes. Then the spectrum of the matr ixe∗simplifies to at most\n3 eigenvalues: ±2eand 0.\n53. We accept the assumption formulated in item 2 of Section 4, so tha t the free energy\nfunctional retains the local form (4). We, however, modify item 3.: instead of the particular\nform (5) we assume\nFS=F[ψ,A] =F(T,x,ψ, ¯ψ,∂ψ, ¯ψ¯∂,A,∂A ). (8)\nThe explicit dependence on xis intended to reflect natural or artificial inhomogeneities\nof the materials, such as inhomogeneous doping, structure defec ts, etc., including possible\nheterostructural properties of the system. Implicit dependenc e on some external control\nparameters (such as mechanical deformation) is admitted; the imp licit parameters can also\ndepend on the position x.\nApart from reasonable mathematical properties and the gauge inv ariance, no particular\nrestrictions will, in general, be imposed upon the function (8). The sy mbole∗stands here\nfor the matrix (7).\n4. The requirement of gauge invariance results in the following relatio ns\n∂F\n∂ψe∗ψ−¯ψe∗∂F\n∂¯ψ+∂F\n∂(∂ψ)e∗∂ψ−¯ψ¯∂e∗∂F\n∂(¯ψ¯∂)= 0, (9)\n∂F\n∂A+i\n¯hc(∂F\n∂(∂ψ)e∗ψ−¯ψe∗∂F\n∂(¯ψ¯∂)) = 0, (10)\nand∂F\n∂(∂jAk)+∂F\n∂(∂kAj)= 0 (11)\nto be satisfied identically by the function (8).\nThe conditions (10) and (11) can be integrated in a straightforwar d way. As a result,\none obtains the functional dependence\nFS=F[ψ,A] =F(T,x,ψ, ¯ψ,∇ψ,¯ψ¯∇,B) (12)\nwith the vector potential Aentering indirectly through the gauge covariant derivatives ∇,¯∇\nand the (gauge invariant) magnetic induction field B= curlA. The gauge invariance condi-\ntions for the function (12) reduce to\n∂F\n∂ψe∗ψ−¯ψe∗∂F\n∂¯ψ+∂F\n∂(∇ψ)e∗∇ψ−¯ψ¯∇e∗∂F\n∂(¯ψ¯∇)= 0. (13)\n5. Taking into account the functional dependence (12), the func tional derivatives of FS\nwith respect to the field variations δψ,δ¯ψ, andδAcan be represented in the form\nδF\nδψ=∂F\n∂ψ−∇∂F\n∂(∇ψ), (14)\nδF\nδ¯ψ=∂F\n∂¯ψ−∂F\n∂(¯ψ¯∇)¯∇, (15)\nandδF\nδA=i\n¯hc(¯ψe∗∂F\n∂(¯ψ¯∇)−∂F\n∂(∇ψ)e∗ψ) + curl∂F\n∂B. (16)\n66. In consequence, one obtains the generalized Ginzburg-Landau equation\n∂F\n∂¯ψ−∂F\n∂(¯ψ¯∇)¯∇= 0, (17)\nand the magnetic field equation\ncurlH=4π\ncj (18)\nwith the intensity of magnetic field\nH= 4π∂F\n∂B(19)\nand the supercurrent density\nj=−i\n¯h(¯ψe∗∂F\n∂(¯ψ¯∇)−∂F\n∂(∇ψ)e∗ψ). (20)\n7. Taken literally, the above equations are derived for sufficiently sm ooth fields. As a\nrule, such degree of differetiability can not be guaranteed at abrup t interfaces, in particular\nat the heterostructural ones. However, the integral form of t hose equations is valid under\nmuch weaker differentiability conditions, sufficient for the derivation of boundary conditions.\nThe standard procedure applied to the equation (14) leads to the b oundary conditions, which\nin index notation take the form of continuity equation across the int erface\n∂FI\n∂(¯ψA¯∇k)nk=∂FII\n∂(¯ψA¯∇k)nk(21)\nwherenkrepresents the normal vector of the surface demarcating the r egions I and II. In\nconsequence of this equation the normal component of the super current (20) is continuous.\n6 Layered hybrid model\nThe free energy functional for higher-grade hybrid model [23] ha s the following form\nF=F0+FS+/integraldisplay\ng(B)d3x. (22)\nThe last term represents the contribution of magnetic field to the f ree energy. In the standard\nparticular case of magnetically inactive material the function g(B) reduces to B2/8π. The\ntermF0describes the normal state, while FSthe superconducting one. The supercoducting\nterm is composed of two parts:\nFS=FP+FJ, (23)\nwhere the part\nFP=s/summationdisplay\nn/integraldisplay\ndxdyF n (24)\ndescribes the contribution of atomic planes, while FJcorresponds to interplanar Josephson’s\nbonds.Fnhas the Ginzburg-Landau form (5), with 2D operator ∇and the coefficients\ndependent, in general, on the plane n.\n7The form of the functional FPalready ensures its invariance with respect to the gauge\ntransformation (1), understood this time in the 2D sense.\nThe Josephson term in the free energy functional for the hybrid m odel of grade K has\nthe form\nFJ=s/summationdisplay\nn/summationdisplay\nq/integraldisplay\ndxdyε qn. (25)\nThe quantity εqndenotes the energy of J-link between n-th and (n+q)-th planes an d is given\nby\nεqn=1\n2{ζq(|ψn|2+|ψn+q|2)−γq(¯ψnψn+qe−ipqn+c.c.)}, (26)\nwith the coupling parameters ζqandγqvanishing for q > K . The exponent pqnis defined\nby the formula\npqn=e∗\n¯hc/integraldisplay(n+q)s\nnsAzdz. (27)\n7 Structured order parameters, nonlocal and higher\norder models\nIn the extension of GL phenomenology discussed in Section 5 we rest ricted our attention\nto superconductors which can be described by local first order fu nctionals with multiplet\norder parameters. Such a restriction greatly simplifies the theore tical considerations. On\nthe other hand, it eliminates some physical phenomena which are kno wn to be present in\nsuperconductors. It concerns, in particular, the nonlocal effec ts and nonparabolic dispersion\ncurves. Such phenomena can, however, be taken into account by admitting yet more general\n– nonlocal and/or higher order – free energy functionals.\nThe microscopic theories of superconducting materials of complex a tomic and electronic\nstructure indicate various possible mechanisms of superconductiv ity [2]. To cope with the\ndiversity of those mechanisms, the phenomenological description c an be further generalized\nby introducing the structured order parameter. Instead of the customary order parameter\nrepresented by a (possibly multicomponent) function ψ(x), we introduce a generalized one,\nrepresented by a function of ψ(x,ξ), where the new variable ξruns over a certain internal\nspace Σ. The space Σ serves as a mathematical stage on which the in ternal structure of\nsuperconducting carriers (such as Cooper pairs) appears.\nThe space Σ depends on the material under consideration and, par ametrically, on the\ntemperature, doping, and other control parameters such as ex ternal mechanical deformation.\nIn the case of uniform material samples the space Σ is the same for a ll material points; in the\ncase of heterostructures and inhomogeneous material samples it can become x-dependent.\nThe concept of structured order parameter offers tighter boun d between the phenomenol-\nogy and the microscopic theories. Apart from more accurate quan titative description it al-\nlows also to study possible topological transitions relalated to chang es in the deep topological\nstructure of the space Σ. The detailed discussion of those effects is, however, beyond the\nscope of the present paper.\n88 Anisotropic similarity and scaling\nAssume now that the order parameter space is endowed with a linear structure and consider\na linear transformation x→x′,ψ→ψ′,A→A′of the following form\n\n\nx′=Qx,\nψ′=Rψ,\nA′=˜QA,(28)\nwhereQ,R, and ˜Qare linear matrices; the matrices are real except Rwhich can be, totally\nor partially, complex. The transformation rule\n∂′=∂Q−1(29)\nis an immediate consequence of (28).\n1. The transformation (28) in its general form violates the U(1) gauge structure. If\nwe request that, under (28), the depart gauge covariant deriva tive be transformed into the\ntarget gauge covariant derivative, ∇ψ→ ∇′ψ′, the transformation (28) must be adequately\nresticted. It follows that the relation ¯Q=Q−1must hold. Such a transformation will be\ncalled a (gauge covariant) anisotropic similarity. The resulting trans formation rules for the\ngauge covariant derivatives of ψ(x) and ¯ψ(x) take the form\n∇′ψ′=RQ−1T∇ψ, ¯ψ′∇′=¯ψ¯∇Q−1R+, (30)\nwhere the superscriptsTand+stand for the matrix transposition and Hermitian conjugation,\nrespectively.\n2. Consider two material systems, say the dashed and the undash ed ones, described by\nthe thermodynamical functionals (4) with the densities F′(.) andF(.), respectively. We shall\nsay that those systems are anisotropically similar if\nF′(T,x,ψ, ¯ψ,∂ψ, ¯ψ¯∂,A,∂A ) =F(T,x′,ψ′,¯ψ′,∂′ψ′,¯ψ′¯∂′,A′,∂′A′). (31)\nDue to the gauge covariance this is equivalent to\nF′(T,x,ψ, ¯ψ,∇ψ,¯ψ¯∇,B) =F(T,x′,ψ′,¯ψ′,∇′ψ′,¯ψ′¯∇′,B′). (32)\n3. To justify this conclusion let us examine the behaviour of the field e quations (17 – 20)\nunder the trasformations (28). Taking into account the transfo rmation rules (28 - 30) we\nobtain from eqn. (32)\n∂F′\n∂¯ψ′=R−1+∂F\n∂¯ψ, (33)\n∂F′\n∂(¯ψ′¯∇′)=R−1+Q∂F\n∂(¯ψ¯∇). (34)\nIn consequence, from the expression (20) one obtains\nj′=Qj. (35)\n9Further,\nB′= (detQ)−1QB (36)\nand\nH′= (detQ)Q−1H. (37)\nThe relations (33 – 37) guarantee the covariance of the field equat ions (17) and (18) with\nrespect to the anisoptropic similarity transformations.\nIn the layered hybrid model a straightforward calculation shows th at the energy of the\nJosephson’s coupling (26) is invariant with respect to transformat ion\n\n\nψ′\nn= (−1)nψn,\nA′=A,\nγ′\nq= (−1)qγq,(38)\nwith all the remaining quantities kept fixed.\nThis transformation switches between systems with all the consta ntsγqtransformed\naccording to the parity of q: the constants remain identical for even q’s and change sign\nfor oddq’s; in particular γ′\n1=−γ1andγ′\n2=γ2. At the same time the order parameter\nψnis transformed by the sign-alternating factor; in particular the st ates of uniform order\nparameter are transformed into alternating ones, and vice versa .\nIn consequence the energy of the Josephson’s coupling is invariant with respect to trans-\nformation (38). This invariance extends to the Josephson part of the total free energy func-\ntional (25). Two hybrid systems related by the transformation (3 8) have identical ground\nstate energies, excitation energy spectra, and all the thermody namical properties, including\nTc. The shapes of the corresponding ground states are, however, substantially different.\nThe usefulness of the above transformations stems from the fac t that they allow to ob-\ntain a solution valid for one system from a solution valid for another – a nisotropically similar\n– system. Analogous transformations, known as anisotropic scalin g, have been defined in\nreference [5]. However, although very useful as a tool for gettin g approximate estimations,\nthey do not imply exact invariance. In opposition to that, our anisot ropic similarity trans-\nformations are exact. In consequence, transformed exact solu tions for the depart system are\nalways guaranteed to be also exact solutions for the target syste m.\nReferences\n[1] D. Rogula, Extended Ginzburg-Landau theory of magnetically active an isotropic super-\nconductors , Journal of Technical Physics 45(2004), p.243\n[2] P. W. Anderson, The theory of superconductivity in the high– Tccuprates, Princeton\nUniversity Press 1997\n[3] D. Aoki et al. ,Coexistence of superconductivity and ferromagnetism in UR hGe, Nature\n413, 613(2001)\n[4] N. F. Berk and J. R. Schrieffer, Effect of ferromagnetic spin correlation on superconduc-\ntivity , Phys.Rev.Lett. 17, 433-436(1966)\n10[5] G. Blatter, M. V. Feigel’man, V. B. Geshkenbein, A. I. Larkin and V . M. Vinokur, Vor-\ntices in high–temperature superconductors, Reviews of Modern Physics 66, 1125(1994)\n[6] O. Bourgeois, P. Gandit, A. Sulpice, J. Chaussy, J. Lesueur and X. Grison, Transport\nin superconductor/ferromagnet/superconductor junction s dominated by interface resis-\ntance, Physical Review B 63, 064517-8(2001)\n[7] M. Cyrot and D. Pavuna, Introduction to Superconductivity an d High–T cMaterials,\nWorld Scientific 1992\n[8] V. L. Ginzburg, Ferromagnetic superconductors , Sov. Phys. JETP 4, 153-161(1957)\n[9] V. L. Ginzburg and L. D. Landau, Towards the theory of superconductivity, Journal of\nExperimental and Theoretical Physics (in Russian) 20, 1064(1950)\n[10] L. P. Gorkov, Microscopic derivation of Ginzburg–Landau equations in th e theory of\nsuperconductivity, Journal of Experimental and Theoretical Physics (in Russian) 36,\n1918(1959)\n[11] A. Huxley, I. Shelkin, E. Ressouche, N. Kernavanois, D. Brath waite, R. Calemczuk and\nJ. Floquet, UGe2: A ferromagnetic spin triplet superconductor, Physical Review B 63,\n144519-13(2001)\n[12] N. Karchev, Magnon-mediated superconductivity in itinerant ferromag nets, Journal of\nPhysics Condensed Matter 15, L385-L391(2003)\n[13] W. E. Lawrence and S. Doniach, Theory of layer structure superconductors, in Proceed-\nings of the Twelfth International Conference on Low Temperatur e Physics, Kyoto, ed.\nE.Kanda, Academic Press of Japan 1971, p.361\n[14] C. Pfeiderer et al. ,Coexistence of superconductivity and ferromagnetism in th ed-band\nmetal ZrZn 2,Nature412, 58(2001)\n[15] S. Saxena et al. ,Superconductivity on the border of itinerant ferromagneti sm in UGe 2,\nNature406, 587(2000)\n[16] L. N. Shehata, The modified Ginzburg-Landau theory for anisotropic high te mperature\nsuperconductors, ICTP Report IC/89/45\n[17] M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconducti vity,\nReviews of Modern Physics 63, 239(1991)\n[18] N. Stefanikis and R. M´ elin, Transport properties of ferromagnet-d-wave superconduc-\ntor ferromagnet double junctions, Journal of Physics Condensed Matter 15, 4239-\n4248(2003)\n[19] M. B. Walker, Orthorhombically mixed s– anddx2−y2–wave superconductivity and\nJosephson tunneling, Physical Review B 53, 5835(1996)\n[20] J. B. Ketterson and S. N. Song, Superconductivity, Cambridg e Univ. Press 1999\n11[21] D. Rogula, Dynamics of magnetic flux lines and critical fields in high T csuperconduc-\ntors, Journal of Technical Physics 40(1999), p.383\n[22] D. Rogula, M. Sztyren, Long-range Josephson couplings in superconducting system s,\nJournal of Technical Physics, 47, 3, 73(2006)\n[23] M. Sztyren, Layered superconductors with long-range Josephson coupli ngs,\narXiv.org.cond-mat/0606521\n12"    },    {        "title": "1103.1069v1.Physics_and_measurements_of_magnetic_materials.pdf",        "content": "Physics and measurements of magnetic materials S. Sgobba CERN, Geneva, Switzerland Abstract  Magnetic materials, both hard and soft, are used extensively in several components of particle accelerators. Magnetically soft iron–nickel alloys are used as shields for the vacuum chambers of accelerator injection and extraction septa;  Fe-based material is widely employed for cores of accelerator and experiment magnets; soft spinel ferrites are used in collimators to damp trapped modes; innovative materials such as amorphous or nanocrystalline core materials are envisaged in transformers for high-frequency polyphase resonant convertors for application to the International Linear Collider (ILC). In the field of fusion, for induction cores of the linac of heavy-ion inertial fusion energy accelerators, based on induction accelerators requiring some 107 k g  o f  m a g n e t i c  m a t e r i a l s ,  n a n o c r y s t a l l i n e  materials would show the best performance in terms of core losses for magnetization rates as high as 105 T / s  t o  1 07 T / s .  After a review of the magnetic properties of materials and the different types of magnetic behaviour, this paper deals with metallurgical aspects of magnetism. The influence of the metallurgy and metalworking processes of materials on their microstructure and magnetic properties is studied for different categories of soft magnetic materials relevant for accelerator technology. Their metallurgy is extensively treated. I n n o v a t i v e  m a t e r i a l s  s u c h  a s  i r o n  p o w d e r  c o r e  materials, amorphous and nanocrystalline materials are a l s o s t u d i e d .  A  section considers the measurement, both destructive and non-destructive, of magnetic properties. Finally, a section discusses magnetic lag effects.    1 Magnetic properties of materials: types of magnetic behaviour The sense of the word ‘lodestone’ (waystone) as magnetic oxide of iron (magnetite, Fe3O4) is from 1515, while the old name ‘lodestar’ for the pole star, as the star leading the way in navigation, is from 1374.  Both words are based on t h e  o r i g i n a l  ‘lode’ s p e l l i n g  o f  ‘load’, issued from the old (1225) English ‘lad’, guide, way, course [1]. According to tradition, the mariner Flavio Gioia of Amalfi, born 1302, first discovered the ‘power of the lodestone’ enabling the manufacture of the first compass and replacing t h e  l o d e s t a r  i n  navigation. Nevertheless m a g n e t i t e, known according to tradition t o  the Chinese since 2600 B.C., is cited first in Europe by Homer, relating that lodestone was already used by the Greeks to direct navigation at the time of the siege of Troy [2].  Magnetic properties of several materials are discussed in the text by Bozorth [3]. Conventional soft and hard magnetic materials are treated i n  Ref. [4]. The volume of O’Handley [5] c o v e r s  a  number of advanced materials, including amorphous and nanocrystalline materials. A general introduction to magnetic properties of materials can be found in the recent textbook by Cullity and Graham [6]. The comprehensive Handbook of Magnetism and Advanced Magnetic Materials [ 7] systematically covers very novel materials of technological and scientific interest in volume 4, including advanced soft magnetic materials for power applications.  Diamagnetism is due to induced currents opposing an applied field resulting in a small negative magnetic susceptibility !. Diamagnetic contributions are present in all atoms, but are generally negligible in technical materials, except superconducting m a t e r i a l s  under some conditions. Monoatomic rare gases such He are diamagnetic, as well as most polyatomic gases such as N2 (that might show nevertheless a net paramagnetic behaviour because of O2 c o n t a m i n a t i o n ) .  Since He is repelled by magnetic fields, operation of superconducting magnets in a weightless environment during orbital flights imposes a significant difficulty not present in laboratory experiments, already discussed and quantified in 1977 [8]. This concern is still present today: the effect of a magnetic field on diamagnetic liquid helium w i l l  b e  s t u d i e d  i n  the v e r y  n ear f u t u r e  i n  t h e  c r y o g e n i c  s y s t e m  o f  t h e  cryomagnet of the Alpha Magnetic S p e c t r o m e t e r  ( A M S )  experiment, foreseen on the International Space Station (ISS) [9].   Paramagnetism, corresponding to a positive susceptibility, is observed in many metals and substances including ferromagnetic and antiferromagnetic materials above their Curie (Tc) and Néel (TN) temperature, respectively [10]. Particular care should be taken for some Ni-basis superalloys for non-magnetic application at very low T. Incoloy 800 (32.5Ni-21Cr-46Fe) features a  m a g n e t i c  permeability as low as 1.0092 at room temperature (annealed state, under a field of 15.9 kA/m). Nevertheless, due to a Tc = -115 °C, the alloy is ferromagnetic at cryogenic temperatures. Ferromagnetism is due to the ordered array of magnetic moments, caused by the interaction of atomic spin moments occurring in certain conditions. Field-dependent permeability a n d p e r s i s t e n t  magnetization after the removal of magnetic field are observed for hysteretic ferromagnetic materials.  Ordered ferromagnetic phase occurs for ferromagnets at T < Tc. Here Tc is the temperature above which spontaneous magnetization ‘vanishes’ [6]. The Tc of Fe, Ni and Co are 1043 K, 631 K and 1394 K, respectively. In general, ferrous alloys with body centred cubic (bcc) crystalline s t r u c t u r e  a r e  ferromagnetic, while face centred cubic (fcc) are not. Nevertheless, rapidly solidified metastable alloys such as Fe-Cu alloys can show ferromagnetism in a wider composition range than expected, even in the fcc phase formed below 70% Fe content [11].  Antiferromagnetism corresponds to an antiparallel arrangement with zero net magnetic moment at T < TN. ‘Non-magnetic’ a u s t e n i t i c  s t a i n l e s s  s t e e l s  s u c h  a s  AISI 304L, 316L, 316LN, high Mn – high N stainless steels are antiferromagnetic under TN and paramagnetic above TN, where they obey a Curie–Weiss law (! =  C/(T-!), where ! is a negative critical temperature and C i s  a  c o n s t a n t  (Fig. 1a).  Magnetic susceptibility of high Mn – high N grades such as P506 (approx. 0.012%C, 19%Cr, 11%Ni, 12%Mn, 0.9%Mo, 0.33%N) and UNS 21904 (approx. 0.028%C, 20%Cr, 7%Ni, 9%Mn, 0.35%N), particularly at 4.2 K, is lower than any traditional steel of the 300-series. As known, this is essentially due to the higher Mn content of the alloys ( P 5 0 6 ,  M n  =  1 2 %; UNS21904, Mn = 9%), stabilizing austenite (fcc ‘non-magnetic’ phase), and increasing TN. Higher TN allows for lower values of ! (<3!10-3) at 4.2 K. Measured values of TN are in agreement with the Warnes [12] law:     . (1) As an example, for steel P506, predicted TN  = 121.5 K, measured TN is 125.7 K. Owing to the absence of precipitated \"-ferrite (bcc magnetic phase) in the weld, the presence of a laser weld has no measurable influence on the magnetic susceptibility of P506 (Fig. 1b). On the other hand, in welds of UNS21904, \"-ferrite contributes a significant increase of susceptibility in the whole T range [13].  Diamagnetism and paramagnetism can be considered as mainly due to the magnetic contribution of isolated atoms or molecules (in reality the existence of a Curie temperature Tc i s  e x p l a i n e d  b y  interaction of elementary moments i n  t h e  p a r a m a g n e t i c  r a nge). Ferromagnetism and antiferromagnetism are due to a larger order arrangement of electron spins and/or magnetic moments.  \n Fig. 1a:  Magnetic susceptibility of different steels of the AISI 300 series, compared to high Mn – high N steels P506 and UNS 21904. Maximum allowed limit at CERN for non-magnetic applications is 5!10-3. P e a k s  a r e  a t  t h e  r e s p e c t i v e  N é e l  t e m p e r a t u r e s  TN. Above TN, susceptibility obeys a Curie–Weiss law ! = C/(T-!). \n Fig. 1b:    Compared magnetic susceptibility of steels P506 (base metal and weld) and UNS 21904 (idem). Maximum allowed limit at CERN in the welds for non-magnetic applications is 5!10-3. 2 Soft ferromagnetic materials of interest for accelerator technology 2.1 Some definitions and units Working in SI, we define the flux density or magnetic induction B (measured in T) and the magnetic field strength H (A !m-1). The permeability µ (H !m-1) is defined by  B = µ · H   (2) The magnetization M (A m-1) is defined as  B = µ0 ! (H + M)    (3) where µ0 (H  m-1) is the permeability of free space. The susceptibility ! (dimensionless) is the ratio M/H. From the above  µ = µ0 ! (1 + !)    (4) The relative permeability is defined as µr = µ / µ0. From the above relationships, µr = 1 + !. A relative permeability of 1.005 corresponds to a susceptibility of 5!10-3. The relative permeability µr and susceptibility ! are material properties, frequently reported for both magnetic and ‘non-magnetic’ materials. 2.2 Magnetization curves of soft ferromagnetic materials A magnetization curve is the plot of the intensity of magnetization M or the magnetic induction B against the field strength H.  \n Fig. 2: Magnetization curve and hysteresis loop of iron (from Bozorth [3]) In the example of Fig. 2, the values of the field strength Hm and the magnetic induction Bm at the tip of the loop are defined. In the hysteresis loop, are also defined the residual induction Br for which H = 0 (called retentivity if the tip corresponds to saturation) and the coercive force Hc for which B = 0 (called coercivity if the tip corresponds to saturation). For ferromagnetic materials, permeability is strongly dependent on field and tends to 1 for saturation. The initial and maximum permeability are easily identified in the curve. The magnetic properties of f e r r o m a g n e t i c  m a t e r i a l s  a r e  s i g n i f i c a n t l y  \naffected by their purity, the metalworking processes applied to the material ( h o t  a n d  c o l d  wo r k i n g ,  subsequent annealing), and the resulting microstructure. Anisotropy effects due to texture can occur (effect of rolling, extrusion). By definition, soft ferromagnetic materials are easily magnetized and demagnetized (materials for transformer cores, for shielding of magnetic fields, magnetically soft ferrites for ac shielding applications, etc.). They have narrow hysteresis loops (low values of Hc), high permeability, low eddy-current losses, high magnetic saturation inductions.  2.3 High-purity iron Iron is referred to as ‘high purity’ when the total concentration of impurities (mainly C, N, O, P, S, Si and Al) does not exceed a few hundred ppm. Otherwise it is rather referred to as low carbon steel or non-alloyed steel [14]. Very pure Fe features!\" high electrical conductivity and is unsuitable for ac applications.  Typical impurity contents of different grades of iron are shown in Table 1. Table 1: Impurity content of different iron grades. So-called ‘Armco irons’ can correspond to very different purity grades (from Ref. [15]). \n  Table 2 summarizes magnetic properties of various grades of iron. Saturation magnetization (# 2.15 T) is not strongly influenced by purity, while coercivity Hc and achievable magnetic permeability d o  s t r o n g l y  d e p e n d  o n  p u r i t y  a n d  c r y s t a l l o g r a p h i c  f e a t u r e s .  Values of i n i t i a l  a n d  maximum permeability drop for cold worked material. I n  o r d e r  t o  r e s t o r e  magnetic properties, annealing cycles are required, allowing internal strains to be reduced, grain size to be increased, as well as the annealing of dislocations. Iron has various phases with different stability domains: $- and \"-iron, corresponding to the ferromagnetic ferritic phase of bcc structure, which are present up to 912°C (T\",# ) and in the ranges between 1394°C and 1538°C, respectively, and %-iron, corresponding to the austenitic phase of fcc s t r ucture, in the range between 912°C and 1394°C. This phase is non-ferromagnetic. For this reason, there are two classes of anneals used commercially [16]: 1) Anneals below 900°C  2) Anneals at or about 925°C or higher to promote grain growth and to further improve magnetic properties.  These anneals, particularly the high T ones, should be followed by slow cool. Higher maximum permeability is obtained by exceeding T\",#, al l owi ng t he mat er i al  t o enter the # st abi l i t y domai n and subsequently revert # by slow cooling. F o r  h i g h  maximum permeability, a n n e a ling should be performed at between 925°C and 1000°C (above T\",#) followed by cool i ng at a rate < 5°C/min. For high permeability at B & 1.2 T, it is advisable to anneal at a maximum of 800°C and to cool slowly [17].  Table 2: Magnetic properties of various grades of iron (from Ref. [14]). \n 2.4 Low-carbon steels  For applications that require ‘less than superior magnetic properties’ [4], low-C steels are frequently used, including i n  m a g n e t c o n s t r u c t i o n  w h e r e  in several cases they are purchased to magnetic specification.   One of the most common grades is the structural–constructional steel 10101 used for the VINCY cyclotron, in the OPERA and ATLAS experiments, and recently proposed for the CLIC main beam quadrupole prototypes. Owing t o  l a r g e  r a n g e s  a n d  a l l o w e d  i m p u r i t y  c o n t e n t s ,  the composition of a specific grade of low-C steel is not sufficiently reproducible between different producers and heats to closely guarantee magnetic properties. For the 1010 steel, Si varies in different possible content ranges depending even on the form of the product (bars, rods, etc.). This explains the large spread in m a g n e t i z a t i o n  c u r v e s  f o r  different heats of the same grade of steel (Fig. 3). The recommended magnetic annealing cycle for this steel is at 815°C \"  T \" 9 8 0°C, for a duration of between 1 h and 6 h followed by furnace cooling [4]. As for pure Fe, lower values of T are intended for stress relief, and higher range for full annealing. During cooling, particularly in the critical temperature range (between 849°C and 682°C), slower cooling rates should be applied (for 1010 steel at a rate of 28°C/h).   Contrary to high-purity irons (for C concentrations less than 20 ppm), low-C steels are subject to magnetic ageing. An increase of coercivity occurs with time, due to formation of cementite precipitates giving rise to domain wall pinning. For magnetic cores that may operate at between 50°C                                                         1 Roughly equivalent to European grades 1.1121, 1.0301, 1.0308, 1.0032. and 100°C, ageing can be an issue. Ageing is mainly due to C, but also to N (due to formation of AlN precipitates), and S. In order to avoid ageing, C, N, S should be reduced below the range 20 ppm to 30 ppm. This reduction is possible by degassing of the melt followed by a final purification of the steel under pure hydrogen, at a T as high as 1475°C. Indeed, at high T, H2 reacts with the C present in the steel through the reaction Fe + C + 2H2 = Fe + CH4 and with other impurities such as oxygen, sulfur, nitrogen by forming H2O, H2S, NH3, r e s p e c t i v e l y ,  t h u s  r e d u c i n g  t h e i r  content under critical concentrations.   \n Fig. 3:  Magnetization curves of different heats of 1010 constructional steels used as magnetic steel in different experiments (courtesy A. Vorozhtsov) 2.5 Non-oriented silicon steels The Fe-Si alloys (phase diagram in Fig. 4) were accidentally discovered by Hadfield in 1882 (1.5% Si content). Magnetic properties were reported in 1900. Properties of earlier alloys (Hopkinson, 1885) were hindered by an excessive C content. Industrial production started in Germany in 1903 (2–2.5% Si). Their commercial use started in the US in 1905 and in England in 1906 [3].  Alloying with Si allows for an increase in permeability and decrease in hysteresis loss. Also thanks to additions of Al and Mn, eddy current losses decrease due to higher resistivity. With A l  addition that reacts with N to form AlN, no ageing is experienced by silicon steels. On the other hand, with respect to pure Fe, saturation magnetization decreases with increasing Si content (2 T for 3.5% Si). Silicon steels, also called electrical steels, are industrially produced in casting-hot rolling lines. Hot-rolled strips are subsequently pickled, cold rolled, continuous annealed ( a n n e a l e d  p r o d u c t s  a r e  called ‘fully processed’), coated and slitted on line to the required width [19]. Coatings play an important role for the adhesive bonding of magnet laminations. They provide electrical insulation in addition to m e c h a n i c a l  b o n d i n g .  Coatings a r e  d e s i g n a t e d  a c c o r d i n g  t o t h e I E C  6 0 4 0 4-1-1 standard [20], can be organic, inorganic with organic components, can be applied on one or both sides. Advanced coatings based on active organic bonder lacquers such as STABOLIT 70® require a delicate curing operation at a later stage, after stacking of the laminations. This coating can reach a mean shear strength above 22 MPa when cured at 190°C for 15 min [21], which stays above 20 MPa for doses up to 108 rad. Fully processed non-oriented silicon steels can be easily specified according to EN 10106 [22]. \nFig. 4:  Phase diagram of the Fe-Si system (from Ref. [18]) and detail of the austenitic ‘% loop’ (from Ref. [14]). Si content of 3.5% (vertical arrow) represents an upper industrial limit (limited ductility for higher contents). 2.6 Oriented silicon steels Iron single crystals exhibit minimum coercivity and maximum permeability when magnetized along one of the <001> axes. Fe-Si is also most easily magnetized in this direction. The so-called ‘Goss’ texture (110)[001] (Fig. 5) can be developed in silicon steels by a controlled sequence of cold rolling and annealing steps.  \n Fig. 5: Prevalent orientation of grain crystal axes with respect to rolling direction (RD) in grain oriented sheets of silicon steels (from Ref. [14]) \nControl of the texture, achievement of a large grain size and low impurity content will allow coercive fields as low as 4 A/m to 10 A/m and maximum permeability around 5 # 104 to be achieved in grain-oriented (GO) alloys. These figures are approximately 10 times higher than in non-grain-oriented (NGO) silicon steels. Conventional GO (7° dispersion of the [001] axes around RD) sheets represent 80% of the market, 1 M ton/y and some 1500 M EUR/y. High permeability GO (HGO, 3° dispersion) s t e e l s c a n  a c h i e v e  e v e n  h i g h e r  p r o p e r t i e s .  Since very large domains are detrimental, scribing the sheet surface (a series of parallel lines arrayed perpendicular to RD, spaced a few mm apart, obtained through mechanical scratching or laser irradiation) allows multiplication of domains oriented along the [001] axis in HGO sheets [14]. Surface coatings capable of exerting a tensile stress of 2 MPa to 10 MPa improve magnetic performance further.  The industrial processing of oriented silicon steels includes several steps [23]: starting from hot-rolled strip, surface descaling is performed in shot-blasting and pickling lines. Heavy cold rolling (CR) is followed by an intermediate annealing and final cold rolling (strips may be cold rolled twice on special cold rolling mills with an intermediate annealing in a continuous annealing furnace). Total CR exceeds 50%. A decarburization step is performed on strips that are coated with an annealing separator (magnesium oxide) to prevent the windings of the coiled strips from adhering to each other during subsequent high-temperature annealing. A further high-temperature box annealing at a T up to 1200°C for a treatment lasting 5 d to 7 d under a protective atmosphere, allows Goss-texture to be developed. Individual grains up to 5 mm and 20 mm can be grown. Material, further refined by diffusion annealing, is stress relief annealed and coated with insulation and t h e r m a l l y  f l a t t e n e d. Stress relief annealing is performed in c o n t i n u o u s  annealing furnaces. Final steps are side trimming and slitting.  Power losses due to eddy currents can be minimized by reducing the sheet thickness d. Indeed, the ‘classical’ e d d y  c u r r e n t  p o w e r  l o s s e s  a r e  p r o p o r t i o n a l  t o  d2 f o r  a  c o n s t a n t  permeability a n d complete flux penetration. Nevertheless, for very thin sheets the domain wall spacing is reduced. The presence of concentrated electric fields at domain boundaries and of supplementary domain structure in thin sheets, limit the beneficial effect of reducing sheet thickness under a few tenths of mm [24,25]. For this reason, the industrial thinner sheets usually have d = 0.23 mm. 2.7 Fe-Ni alloys This family of alloys, before their use as magnetic materials, was already known for the low thermal expansion coefficient of Invar, an Fe-36%Ni alloy, discovered by C. E. Guillaume in 1896 [26]. The ferromagnetic % phase can be retained by a suitable choice of annealing T, cooling rates, addition of other alloying elements such as Mo, Cu, Cr. F o r  N i  c o n t e n t s  a b o v e  3 5 % ,  t h e  %'$ t r a n s i t i o n  s t i l l  exists, but it occurs at T < 500 °C and is therefore limited because of low diffusion rates (Fig. 6). Two main families of alloys for magnetic applications have been developed: the ‘low-Ni’ F e N i  a l l o y s ,  containing 47% to 50% of Ni, featuring higher saturation fields (1.6 T) and maximum permeabilities up to 60 000, and the ‘high Ni’ alloys including mumetal and containing approximately 80% of Ni, with lower saturation fields (0.8 T) but higher maximum permeability (up to 800 000).  High-Ni alloys were the first to find commercial applications: Elmen’s w o r k  i n  1913 was aimed at finding a material superior to Si-steels for ‘use in telephone apparatus operating at less than a few hundred gausses’.  Low-Ni alloys are prepared as strongly textured (110)[001] sheets by means of severe CR and annealing at T # 1000 °C. Magnetic annealing is usually applied. These alloys, and in  particular 45 Permalloy, also found early applications in telephone apparatus, since they featured higher saturation than any of the other permalloys and could be operated at higher induction.     Fig. 6: Fe-Ni phase diagram (from Bozorth [3]), showing the two main compositions of alloys of this family for magnetic applications \nFig. 7: Between 65% and 85% Ni crystalline anisotropy K1 (the relevant coefficient of the first order expansion of the crystal anisotropy energy for a given angle of misorientation [6]) vanishes and magnetostriction $ as well, b u t  n o t  s i m u l t a n e o u s l y .  Addition of other elements (Mo, Cu, Cr, etc.) allows the two parameters to be reduced simultaneously and a very high permeability to be achieved (from Ref. [27]). \nAs already mentioned, the highest permeability in this alloy family is featured by alloys containing approximately 80% of Ni. Indeed, between 65% and 85% Ni crystalline anysotropy vanishes and magnetostriction as well (but not simultaneously, see Fig. 7). The addition of other elements (Mo, Cu, Cr, etc.) reduces simultaneously the two parameters, while increasing the resistivity (relevant for ac applications).  Vacuum chambers for the circulating beams in the LHC injection and extraction septa [28] were manufactured from a 77Ni-5Cu-4Mo-Fe mumetal [29] produced by Imphy /FR. Because of very limited solubility of N in mumetal, mumetal tubes should be welded to AISI 304L or AISI 316L flanges depending on the application, in order to avoid gross porosity unavoidable in mumetal/AISI 316LN autogeneous welds [30]. Internal stresses, plastic deformation induced during f o r m i n g a n d w e l d i n g  all degrade the magnetic performance of mumetal (Fig. 8). A high-temperature annealing treatment allows restoration of magnetic properties. Nevertheless, in order to achieve t h e  best magnetic properties of mumetal (max. permeability as high as 100 000, coercivity as low as 0.05 Oe), the final annealing treatment should be performed under hydrogen at 1120°C.   \nFig. 8: Evolution of coercivity and maximum permeability of mumetal with fabrication steps. Sample machined from the as-delivered material (‘initial state’), sample containing TIG welds (‘after welding’), idem after annealing u n d e r  v a c u u m  a t  1 0 7 0°C for 1 h (‘after annealing’). Coercivity, which was 8.0 A/m in the initial state, increased due to the presence of the welds (11.5 A/m) and was considerably reduced by annealing (1.2 A/m). Permeability, approximately 21 800 in the as delivered state, decreased about 60% due to the presence of the welds, to a value of around 12 570. After the annealing treatment, the permeability reached 92 000 [30]. Material delivered by Telcon Ltd. /UK. For some Fe-Ni alloys, particular care has to be paid to cooling conditions from an ‘ordering temperature’ (( 500°C). Heat treatment in a magnetic field, discovered by Kelsall in 1934 [31] can cause a large increase in permeability (#10) o f  s o m e  F e-Ni alloys. Taking as an example 65 Permalloy, the presence of the field during cooling from Tc t o  4 0 0°C i s  e s s e n t i a l. Magnetic annealing is based on non-random diffusion of atoms and preferential alignment of like-atom pairs. It is explained on the basis of a ‘directional-order’ t h e o r y  [32–34]. At a temperature T ) Tc, but high enough for diffusion to occur, like-atom pairs tend to be aligned in the direction of the local magnetization. As temperature is lowered during cooling, since diffusion constants become too low for further diffusion to occur, the ‘freezing’ in place of like-atom pairs produces a uniaxial anisotropy in the material [35]. \n2.8 Compressed powdered iron and iron alloys Iron-based products produced by powder metallurgy (PM) techniques have the advantage of featuring isotropic 3-D properties. For application in the medium frequency (kHz) range, cores of compacted iron are often used. PM pr oduct s can be near-net shaped to close dimensional tolerances and show satisfactory T stability due to limited internal stresses. Designers can exploit 3-D flux paths [36]. For some components (claw pole, brushless motor) use of laminations would not be applicable. Coated iron powders (of a typical size 50 µm to 100 µm) are mixed with some 1% of binding material, compressed as cores of the desired shape and then sintered. The cores are coated by protective painting. Fe, Fe-Si and other Fe powders can be compacted. The maximum achievable permeability is controlled by grain size, sintering T and degree of porosity. The dc properties of hot-pressed high-purity Fe are considered as good as or better than conventional Fe. Electromagnetic actuators of complex core shapes for use in transport, electrical rotating machines are produced through this technology. The usual field of compressed powdered irons are dc and medium frequency applications (ferrites dominate in very high frequencies). Two components of core losses are identified in powder metallurgy irons: a classical hysteresis contribution and an eddy current one [37].  Powder metallurgy cores exhibit larger hysteresis contributions than steel sheets, but (particle to particle) eddy current contributions are much smaller already at 60 Hz (estimated at 5% of the total in the example of Fig. 8). Eddy currents b e c o m e  d o m i n a n t  a t  h i g h e r  f r e q u e n c i e s, where, d u e  t o  l o w e r  e d d y  c u r r e n t  contributions, p r e s s e d  m a t e r i a l s  a r e  c o m p e t i t i v e  i n  p e r f o r m a n c e  w i t h  l a m i n ated steels (Fig. 9). In powder materials, two kinds of eddy current are identified, circulating within the insulating particles and around clusters of particles. This explains size effect contributions to the total losses [38], and the advantage of the use of insulating coatings on powder particles, respectively.  \n Fig. 9: Comparison of a pressed material with 0.64 mm thick ‘Cold Rolled Motor Lamination’ (CRML) steel and 0.061 mm thick ‘M-19’ NGO silicon steel. At 60 Hz, the total core loss of the pressed material is d o m i n a t e d  b y  h y s t e r e s i s  c o n t r i b u t i o n s ,  w h i le the eddy current contribution is estimated at only 5% of the total losses. The pressed material has lower performance than conventional steels. At higher frequencies, the total loss for the pressed material is less than for laminated steels (from Ref. [37]).  2.9 Soft spinel ferrites Ferrites are largely applied in the high-frequency range up to few hundred MHz. Their composition is MO•Fe2O3 where M is a divalent metal (M = Fe2+, Mg2+, Mn2+, Ni2+, Zn2+; lodestone FeO•Fe2O3 = Fe3O4 i s  a  p a r t i c u l a r  c a s e  o f  a ferrite). They are ceramics featuring very high resistivity, between 106 $ m and 1012 $ m. They are used at frequencies where eddy current losses for metals become excessive. At very high frequencies, they are ideal soft magnetic materials. Disadvantages are low magnetic saturation ( t y p i c a l  r a n g e  0 . 1 5 T to 0.6 T), low Tc ( 3 3 0°C t o  5 8 5°C) p o o r  m e c h a n i c a l  properties, hardness and brittleness. Since they are practically unmachinable, close dimensional tolerances are achieved by grinding. \n  Fig. 10: Collimator jaw equipped with BPM buttons and ferrite blocks (courtesy of A. Dallocchio) Ferrites are used as cores for electromagnetic interference suppression, to control transmission or adsorption of electromagnetic waves. One example of the application of ferrites in accelerators is the LHC collimators, where ferrite blocks are used to damp trapped modes (Fig. 10).  \n  Fig. 11: Properties of FERROXCUBE 4S60 ferrite. Maximum absorption occurs where µr matches the dielectric constant %r (from Ref. [39]) The ferrite FERROXCUBE 4S60 is used for the TCLIA collimators in the LHC at CERN. This ‘NiZn’ ferrite is of a mixed type. The proportions of Ni and Zn are tailored for the specific application. While MnZn ferrites show the highest permeability, NiZn, shows a  b r o a d b a n d  o p e r a t i o n  u p  t o  1000 MHz and features higher resistivity (Fig. 11).  Ferrites are prepared through a powder metallurgy process. After mixing and weighing the base oxides in the form of fine powders, the powder is heated to between 900°C and 1200°C (pre-firing in air) to produce flakes of a few cm3. During this stage, the spinel structure is formed by the reaction of Fe2O3 with MO. This material is ball milled in water and mixed with a binder. A spray drying step results in balls of few mm3. The powder is then mechanically pressed in a mould by die punching or hydrostatic pressing. The green (filling factor 50% to 60%) is batch sintered in a kiln at T between 1200°C and 1400°C, with or without external pressure, in an oxidizing atmosphere (filling factor 95% to 98%). Shape is conferred by a final grinding [14,40]. 2.10 Innovative materials: amorphous alloys Amorphous alloys (metallic glasses) a r e  m a t e r i a l s  devoid of long-range atomic order. They are produced by rapid solidification from the liquid or gaseous state. Generally they are in ribbon form and obtained by rapid solidification from the liquid state. Metastable sputtered amorphous thin-films of Co-Au were produced by Mader and Nowick in 1965 [41]. Today, ribbons up to 100 mm or 200 mm wide of a thickness of 10 &m to 40 &m can be produced. In order to develop the amorphous structure, cooling rates of 105°C/s to 106°C/s have to be obtained. Amorphous wires are also produced. The preparation of amorphous magnetic materials by rapid quenching from the melt is generally performed through planar flow casting on metallic wheels or drums in air, shielding with atmosphere or vacuum (Fig. 12).   \n Fig. 12: Rotating drum. A jet of molten metal is ejected into a rotating water layer (from Ref. [42]). In order to guarantee rapid quenching, drum velocities are as high as 3 m/s to 10 m/s. Reported range of peripheral velocities of metallic wheels for the production is 10 m/s to 40 m/s [14]. Amorphous alloys are generally of the type T70-80M30-20, where T is a transition metal (Fe, Co, Ni) and M is a combination of metalloids (B, Si, P, C, etc.). Amorphous ribbons of 25 &m thickness in Fe78B13Si9, compared to a conventional GO Fe-3Si of 0.23 mm of thickness, show a coercive field of 2 A/m after annealing (5 A/m for the latter) and a maximum relative permeability of 2 105 (8·104, idem). Annealing allows for a local crystallization. These materials are hard and show ductility l i m i t e d  t o  some 2.5% elongation at failure. Alloy glass ribbons have an excellent magnetic softness. Magnetization curves have an ideal loop with a precise ‘cut’ at a specific value of B (see the example of the loop of a commercial Vitrovac material in Fig. 13a). This behaviour, c o m b i n e d  with a high magnetomechanical coupling, makes them ideal materials for sensors for electronic article surveillance in the so-called ‘harmonic-electromagnetic systems’: glass ribbons are used for security tags in libraries and stores [43, 44]. In order to be conveniently activable and deactivable and not to be demagnetized by the fields in the interrogation zone, materials should show Hc between 1600 A/m and b 8000 A/m [43]. Permalloys could also be used for the purpose illustrated in Fig. 13, but their ductility would imply a risk of degradation of their magnetic properties by handling.      \n \n  Fig. 13: a) Ideal loop of a commercial amorphous material ( f r o m  V a c u u m s c h m e l z e [45]). When applied in security tags, a length of amorphous alloy is packaged together with a hard magnet strip. The tag i s  a c t i v a t e d  b y  u n m a g n e t izing the permanent magnet, and deactivated at the cash register by magnetizing (saturating) the strip. b) Activated labels respond to an electromagnetic field generated by a pedestal at the store exit with specific frequencies detected by the receiver, since the material is periodically driven into saturation. c) Response to a periodic excitation H: U0, unactivated label, U a c t i v a t e d  label: high permeability at fields below saturation induces high attenuation w h e n  t h e  label is activated, while above saturation spikes are present during the transmission time (from G. Herzer [43]). 2.11 Innovative materials: nanocrystalline alloys Nanocrystalline alloys consist of small ferromagnetic crystallites of bcc FeSi with grains of 10 nm to 15 nm embedded in an amorphous matrix, coupled to each other by exchange interaction. Crystallites are separated by 1–2 nm for interaction. These materials show very low coercivity (0.4 A/m to 8 A/m), high initial permeability (up to 150 000), low losses and magnetostriction and high saturation up to 1.3 T.  They are available in ribbons of few tens of &m thickness. Compared to conventional Fe-Si steels and amorphous materials, they show exceptionally low core losses, specially at very high magnetization rates (Fig. 14). For this reason, they are envisaged for application to heavy-ion inertial fusion-energy, based on induction accelerators where s o m e  3 0 000 tons of magnetic material are necessary for induction cores [46]. For this application, nanocrystalline materials would show the best performance in terms of core losses at the required magnetization rates between 105 T/s and 107 T/s. \na b c They are commercially applied in low-loss high-frequency transformers, such as the one foreseen by the Linac group of the Spallation Neutron Source (SNS) of the Los Alamos National Laboratory for application in high-frequency polyphase resonant converters for the ILC (International Linear Collider) [47]. These materials are interesting for both high-energy physics and accelerator applications, but a drawback is their cost (between $20 and $150 per kilogram).   \n Fig. 14: a) In heavy-ion inertial fusion-energy accelerators some 30 000 tons of magnetic material are necessary for induction cores in order to accelerate heavy-ion energies in the GeV range and deliver several MJ per pulse to a target (from Ref. [46]). b) Nanocrystalline materials are the highest performing ferromagnetic materials as induction core alloys. They form the lowest loss group at the very high magnetization rates required for this application (from Ref. [48]). 3 Methods of measurement 3.1 Characterization of soft magnetic materials  Characterization of the magnetic properties of soft magnetic materials is generally based on the measurement of a transient voltage induced on a secondary winding by a step-like field variation applied on a primary winding. The two coils are generally wound together on a toroid sample. The \na signal is integrated over a time interval for complete decay of eddy currents, since every recorded point should correspond to a stable microscopic configuration of the system. Since flux variations are measured, providing a discrete sequence of field values, a reference condition is needed, that is generally the saturated or demagnetized state. A ‘split-coil’ p e r m e a m e t e r  (Fig. 15) is available at CERN, facilitating the exchange of samples, and not requiring a prior winding contrary to the wound toroid methods [49]. For a careful assessment of the magnetic properties through t h e s e  m e t h o d s ,  a  precise measure of the cross sectional areas of the samples is necessary, which should not be estimated from sample mass and density.  The technique of the split-coil permeameter has recently been u s e d  f o r  t h e  e l e c t r o m a g n e t i c  characterization of the steels used for the OPERA magnets [50].  \n Fig. 15: Split-coil permeameter. The flux measuring and excitation coils are not wound directly onto the samples. The advantage of the system is the rapid exchange of samples (rings, or pile up of rings), an automatic measurement of the relevant parameters of the hysteresis curve, making it adapted to the evaluation of large series. A drawback is the cumulative contact resistance between the two split parts of the coils (two contacts per turn), making this method inadequate for measurements in liquid He (excessive power dissipation). CERN owns s p e c i a l  coercimeters aimed at measuring t h e  c o e r c i v i t y  d i r e c t l y  o n  s t e e l  s h e e t s  without having to cut samples. The instrument was used to perform the coercivity measurements needed during the production of the 11000 t of steel sheets for the LEP dipole magnets and to measure their permeability. The coercimeter is based on a main excitation and detector coil, and auxiliary coils used to estimate the air gap of the yoke contacts (Fig. 16). The yokes are pressed against the sheets that are introduced through a system of rollers in the coercimeter. The sequence of measurements is automatic. After demagnetizing the yokes, a stable hysteresis cycle is assessed. Four flux variations \"#i (i = 1 to 4) are measured along the cycle and the remanent flux #r is calculated as #r = ' [|\"#1| - |\"#2| + |\"#3| - |\"#4|]. The current Ic, necessary to cancel #r i s  me a s u r e d  o n  b o t h  s i d e s  o f  t h e  c y c l e ,  allowing the coercive field to be calculated from the mean absolute value of Ic taking also into account the coercive field of the yoke (from Ref. [51]).  \n  Fig. 16: a) The coercimeter is based on a main excitation and detector coil. b) hysteresis cycle (from Ref. [51])  3.2 Measurement of feebly magnetic materials Measurement of permeability of feebly magnetic materials (materials with permeability in the range µr = 1.00001 to 2 or 4) is possible through several techniques. Portable magnetometers are adapted to non-destructive measurement of materials of complex shape but having a radius of curvature not less than 40 mm or a flat area not less than 20 mm in diameter. The material should be thicker than 8 mm. Measurements of materials thinner than 8 mm can be performed by stacking two pieces or applying corrections. The air gap between two pieces should be as small as possible; otherwise permeability less than actual value will be estimated.  \n  Fig. 17: Gradient probes allow measurement of t h e  d i s p l a c e m e n t  o f  t h e  z e r o  f i e l d  l i n e  o f  t h e  permanent magnet towards the feebly magnetic material to be measured. T h e  f i e l d  strength of the probes generally used to assess permeability of austenitic stainless steels is approximately 80 kA/m. a b Probes of portable magnetometers are based on a permanent cylindrical magnet (Fig. 17). A permanently built-in field sensor, sensitive to the field emanated from the sample, is placed on either side of the cylindrical magnet in the plane perpendicular to t h e  c y l i n d e r  a x i s  a t  t h e  c e n t r e  o f  t h e  permanent magnet. Since t he per meabi l i t y of t he feebly magnetic material t o be measured is larger than 1, the zero field line of the cylindrical magnet will be displaced towards the sample. This displacement allows the permeability of the material to be assessed [52].  Magnetic balance measurements are suitable for measurement of materials with µ < 1.05. This destructive test method is applicable to the evaluation of semifinished products or welds before fabrication of parts. Samples measurable at CERN are cylinders with a diameter of 3 mm and a height of 2 mm. Larger samples are measurable according to relevant standards. After several reverses of the current to delete the effects of the hysteresis in the core, a n  i n c r e a s i n g  c u r r e n t is turned on in an electromagnet, p r o d u c i n g  s t e p-by-step increasing field strength u p  t o  m o r e  t h a n  450 kA/m. The sample should not be overheated. The sample is suspended from the balance and positioned above the centreline of the air gap of the electromagnet (Fig. 18). The permeability is calculated from the apparent change in mass of the specimen [53].  \n  Fig. 18: a) Magnetic balance built up at CERN. b) Magnetic permeability is assessed for different fields from the apparent change of mass of the sample. \na b Magnetic Field Microscopy (MFM) techniques allow identification of a  m a g n e t i c  c o n t r a s t  between magnetic and non-magnetic phases on a very local scale (Fig. 19). More recently, MOKE (Magneto-Optical Kerr Effect) techniques have been associated to MFM and used to quantify locally the magnetic properties of phases in the samples, including measurement of hysteresis loops [54].   \n   Fig. 19: Atomic Force Microscopy (AFM) and MFM measurements of a sample of an austenitic stainless steel including a longitudinal laser weld, after tensile testing at 4.2 K. While AFM images are only sensitive to the topographical contrast of the surface (grain boundaries and dendrite boundaries are visible in AFM images of the base metal and the weld, respectively), MFM allows qualitative identification of the presence of a magnetic contrast between magnetic and non-magnetic phases possibly present in the weld.  4 Magnetic lag The two main sources of magnetic lag are discussed: lag due to eddy currents, and the so-called magnetic ‘after-effect’ (Nachwirkung), which is material dependent. 4.1 Lag due to eddy currents When one applies a magnetizing current to a bar, eddy currents develop whose direction is opposite to that of the applied current. This current flow has both an effect in DC (the field cannot penetrate immediately into the interior of the material) and in AC (set-up of field gradient between surface and interior). Lag due to eddy currents should be taken into account when measuring the magnetization curves of soft magnetic materials (see Section 3.1). Indeed, the sudden application of a field to a cylinder of field-dependent permeability of diametre d requires a time $ to reach a field B:     (5) where b = 1 - B/B0, B0 is the ultimate field and % is the resistivity [3]. For a constant permeability, a variation o f f i e l d  a p p l i e d  t o a  l a m i n a t i o n  o f  r e l a t i v e p e r m e a b i l i t y  &r, conductivity %, thickness d implies a decay time of eddy-current-generated counterfield $ & &0 &r % d2 [14]. For a 10 mm sheet of a 1010 steel, $ is approximately 3 s [55]. Undesirable effects due to lag induced by eddy currents were identified in CERN SPS magnets, when measuring in multicycles the influence of the 450 GeV proton cycle on the following positron cycle [56].   4.2 Magnetic ‘after-effect’ The application of a magnetic field requires a given time to reach the final induction value in a magnetic material. A p a r t  f r o m  t h e  c o ntribution to the lag due to eddy currents discussed in Section 4.1, additional delayed effects have a metallurgical origin (impurities such as C and N in Fe, dislocations, etc.) and are mainly due to a time-dependent microstructural redistribution associated with s t r a i n  i n d u c e d  b y  m a g n e t o s t r i c t i v e  e f f e c t s .  T h e  c o m m o n a l t y  o f  p h e n o m e n a  b e t w e e n  m a g n e t i c  (Fig. 20a) and anelastic (Fig. 20b) after-effect suggests a common origin. The time constant of magnetic after-effects can be appreciable. The effect is strongly dependent on temperature (faster for higher temperatures) and on material purity. A d e t a i l e d  d i s c u s s i o n o f  t h e  d i f f e r e n t  c o n t r i b u t i o n s  t o  magnetic after-effect is found in Ref. [57].    \n Fig. 20: Analogy between magnetic (a, from Ref. [6]) and anelastic (b, from Refs. [58, 59]) after effect. In Fig. 20a, the field strength in a demagnetized sample is increased suddenly from zero to a constant value H. The induction B, apart from the delay due to eddy currents, rises immediately to a value Bi, and then at a finite rate to the final value B that is associated to H in the magnetization curve. In Fig. 20b, the sudden application of a stress '0 to a sample suddenly induces an elastic strain (el, followed by an elastic after-effect (time-delayed deformation), composed of r e v e r s i b l e  a n e l a s t i c  ((an) and irreversible viscoelastic ((irr) contributions. Delayed effects are observed as well on removal of the field (magnetic or elastic).  \n(a) H 5 Conclusions Magnetic materials are key elements of magnet technology. They should be procured on the basis of careful selection and adapted specifications, since their primary and secondary metallurgy, chemical composition, purity, applied thermal treatments, and microstructure will have a significant influence on their final properties. Low-carbon steel laminations, but also general-purpose constructional steels, such as type 1010, generally used for applications that require ‘less than superior’ magnetic properties [4], are often applied as yoke materials for accelerator and experiment magnets. They are not always purchased to magnetic specifications. Soft ferromagnetic materials of better controlled composition and impurity limits, properties and metallurgy might be considered for specific applications, such as fast magnet systems. On the other hand, innovative materials such as nanocrystalline and amorphous alloys a r e  being considered or are already used for an increasing number of devices, including for high-energy physics and fusion-related applications. Examples are high-frequency transformers for the International Linear Collider a n d  i n d u c t i o n  c o r e s  o f  heavy-ion inertial fusion-energy accelerators, respectively. In 2007 nanocrystalline materials represented a production of 1000 t. The importance and use of powder metallurgy is also increasing for application to structural components of magnets, soft magnetic materials, a n d  m a t e r i a l s  f o r  p e r m a n e n t  m a g n e t s. In 2003, powder-based soft ferrites represented 5% of the world market of magnetic materials, i n c l u d i n g  s e m i h a r d  a n d h a r d  m a t e r i a l s ,  compared to 27% covered by conventional steels [60].  Acknowledgement The author wishes to thank L. Walckiers and D. Brandt for their invitation to contribute to the special CERN Accelerator School, D. Tommasini for f r u i t f u l  exchanges, G. Peiro and J. Garcia Perez for helpful discussion on testing facilities available at CERN, F. Caspers for the expertise provided on soft ferrites, and R. Veness for the final spell checking of the manuscript.  References [1] Online Etymology Dictionary, http://www.etymonline.com/. [2] P.F. Mottelay, Bibliographical History of Electricity and Magnetism (Charles Griffin, London, 1922). [3] R.M. Bozorth, Ferromagnetism (Van Nostrand, New York, 1951). [4] ASM Metals Handbook, 9th ed., vol. 3: Properties and Selection: Stainless Steels, Tool Materials and Special-Purpose Metals (American Society for Metals, Metals Park, OH, 1980). [5] R. C. O’Handley, Modern Magnetic Materials: Principles and Applications (Wiley, New York, 1999). [6] B.D. Cullity and C.D. Graham, Introduction to Magnetic Materials, 2nd ed. (Wiley, Hoboken, NJ, 2009). [7] Handbook of Magnetism and Advanced Magnetic Materials, vol. 4 – N o v e l  M a t e r i a l s ,  H .  Kronmüller and S. Parkin (eds.) (Wiley, Hoboken, NJ, 2007). [8] Fletcher et al., Low gravity phase separator, United States Patent 4027494 (1977). [9] Alpha Magnetic Spectrometer (AMS) Experiment Utilization Plan for Exploration Magnet Development, NASA AMS Project Office, Houston, Texas, Preliminary Draft March 24, 2005. [10] F.R. Fickett and R.B. Goldfarb, Magnetic properties, in: R i c h a r d  P .  R e e d  a n d  A l a n  F .  C l a r k  (eds.), Materials at Low Temperatures (American Society for Metals, Metals Park, OH, 1983), p. 209. [11] P.A. Serena and N. García, Ferromagnetism in FeCu metastable alloys, Phys. Rev. B 50 (1994) 944–948. [12] L.A.A. Warnes and H.W. King, Cryogenics, 16 (1976) 659–667. [13] S. Sgobba and G. Hochoertler, A new non-magnetic stainless steel for very low temperature applications, Proceedings of the International Congress Stainless Steel 1999: Science and Market, Chia Laguna, Italy, 1999 (Associazione Italiana di Metallurgica, Milan, 1999), vol. 2, pp. 391–401. [14] F. Fiorillo, Measurement and Characterization of Magnetic Materials (Elsevier, Amsterdam, 2004). [15] W. Fulkerson, J.P. Moore, a n d  D . L .  M c E l r o y, Comparison of the thermal conductivity, electrical resistivity, and Seebeck coefficient of a high-purity iron and an Armco iron to 1000°C, J. Appl. Phys. 37 (1966) 2639–2653. [16] A.J. Otter, Annealing cycles for magnet steel and variation in B-H characteristics, Tri-University Meson Facility, Design Note n °  T R I-DN-69-3, University of British Columbia, Vancouver, B.C. (1969). [17] Armco Magnetic Ingot Iron (The American Boiling Mill Co., Middletown, OH, 1945). [18] C.J. Smithells (ed.), Metals Reference Book, 4th ed., vol. 2 (Butterworths, London, 1967). [19] ThyssenKrupp Steel catalogue, Non Grain Oriented Electrical Steel Powercore® (2008). [20] IEC 60404-1-1 Magnetic materials Part 1-1: Classification surface insulations of electrical steel sheet, strip and laminations (2004). [21] S. Bates, D. Willis, and K. Sinram, IEEE Trans. Magn. 28 (1992) 964. [22] EN 10106:1996, Cold rolled non-oriented electrical steel sheet and strip delivered in the fully processed state. [23] PowerCore® grain oriented electrical steel, ThyssenKrupp Steel catalogue (2008). [24] T. Yamaguchi and K. Takeda, Effects of crystallographic misorientation on power loss in (110)[001] three percent Si-Fe sheets with low thickness, IEEE Trans. Magn. 21 (1985) 41–44. [25] S.D. Washko and R.F. Miller, Sheet thickness effects on energy loss in 3% silicon-iron, J. Magn. Mater. 19 (1980) 361–364. [26] G. Béranger, F. Duffaut, J. Morlet, and J.F. Tiers, The Iron-Nickel Alloys: A Hundred Years After the Discovery of Invar (Lavoisier Pub., Secaucus, NJ, 1996), translated from the French. [27] G. Couderchon, Techniques de l’Ingénieur, Alliages fer-nickel et fer-cobalt – Propriétés magnétiques (1994). [28] J.M. Jimenez and B. Henrist, Vacuum chambers for the circulating beams in the LHC injection and extraction septa, functional specification, CERN EDMS document n° 405734, 14/05/2004. [29] S. Sgobba, Tubes en Mumetal® 77Ni-5Cu-4Mo-Fe pour chambres spéciales LSS, fiche technique CERN n° 555 – rev. 0, 08/01/2004. [30] S. Sequeira Tavares and S. Sgobba, CERN Metallurgy report n° 98/10/06 (1998). [31] G.A. Kelsall, Physics, 5 (1934) 169–172. [32] L. Néel, J. Phys. Radium, 15 (1954) 225. [33] S. Taniguchi, Sci. Rep. Res. Inst. Tcihku Univ. A7 (1955) 269. [34] S. Chikazumi and T. Oomura, J. Phys. Soc. Jpn. 10 (1955) 842. [35] D.I. Gordon and R.S. Sery, A new magnetic-field electron-irradiation treatment for producing low-coercive-force rectangular hysteresis loops in Supermalloy, IEEE Trans. Nucl. Sci. NS-11 (1964) 105–110. [36] F.G. Hanejko, H.G. Rutz, and C.G. Oliver, Effects of processing and materials on soft magnetic performance of powder metallurgy parts, paper presented at the 1992 Powder Metallurgy World Congress, San Francisco, CA, 21–26 June 1992. [37] J.H. Bularzik, R.F. Krause, and H.R. Kokal, Properties of a new soft magnetic material for AC and DC motor applications, J. Phys. (Paris) IV, 8 (1998) Pr2-747–Pr2-753. [38] G. Nord, L.O. Pennander, and A.G. Jack, Loss calculation for soft magnetic composites, 16th ICEM Conference, Cracow, Sept. 2004. [39] Ferrite Absorber Tiles, FERROXCUBE catalogue (2003). [40] Ferrite Production, unpublished FERROXCUBE document. [41] S. Mader and A.S. Novick, Metastable CoAu alloys: example of an amorphous ferromagnet, Appl. Phys. Lett. 7 (1965) 57. [42] Y. Abe, K. Miyazawa, M. Nakamura, and T. Ohashi, The behavior of metal jet in the in-rotating-water spinning method, Trans. ISIJ, 27 (1987) 929. [43] G. Herzer, J. Magn. Magn. Mater. 254/255 (2003) 598–602. [44] T. Meydan, Amorphous materials in sensor applications, magnetic materials for sensors and actuators, in: Technical Digest, IEE Colloquium on New Magnetic Materials, London, UK, 11 October 1994. [45] Tape-Wound Cores for Magnetic Amplifier Chokes VITROVAC 6025 Z, Vacuumschmelze document n° PK-002 (1998). [46] W. Waldron, The Heavy Ion Fusion Virtual National Laboratory, hif.lbl.gov. [47] W.A. Reass, D.M. Baca, and D.E. Rees, Possibilities of high frequency polyphase resonant converters for ILC application, paper presented at the 2004 Power Modulator Conference, San Francisco, CA, 2004. [48] A.W. M o l v i k  a n d  A .  F a l t e n s, Induction core alloys for heavy-ion inertial fusion-energy accelerators, Phys. Rev. Spec. Top. Accel. Beams, 5 (2002) 080401.  [49] P. Haren, Magnetic permeability measurements, automatic testing of ring samples at cryogenic and ambient temperatures, CERN ISR-BOM/78-4A. [50] A. Cazes, A. Cecchetti, B. Dulach, F. Iungo, M. Incurvati, D. Orecchini, G. Peiro, C. Sanelli, F. Terranova, and M. Ventura, Electromagnetic characterization of the 990 ton gapless magnets for the OPERA experiment, technical report published by Institute of Physics Publishing and SISSA (2007). [51] J. Billan, Coercimeter for non-destructive measurement of the coercivity of steel sheets, J. Phys. Colloques, 45, C1 (1984) C1-965–C1-968. [52] Foerster Instruments Incorporated, documentation on portable MAGNETOSCOP® 1 . 0 6 9, (2008). [53] ASTM A342/A342M – 0 4  S t a n d a r d  T e s t  M e t h o d s  f o r  P e r m e a b i l i t y  o f  F e e b l y  M a g n e t i c  Materials.  [54] J. Sort, A. Concustell, E. Menéndez, S. Suriñach, M. D. Baró, J. Farran, and J. Nogués, Selective generation of local ferromagnetism in austenitic stainless steel using nanoindentation, Appl. Phys. Lett. 89 (2006) 032509. [55] A. Chao and M. Tigner, Handbook of Accelerator Physics and Engineering (World Scientific, Singapore, 1999).  [56] C. Arimatea and D. Jacquet, Mesure de l'influence magnétique du cycle proton 450 GeV sur le cycle positron, SL-Note-2001-013 MD 20, février 2001. [57] B. Hohler and H. Kronmüller, Magnetic after-effects in ferromagnetic materials, J. Magn. Magn. Mater. 19 (1980) 267–274. [58] S. Sgobba, PhD thesis EPFL n° 1215, 1994. [59] S. Sgobba, H.U. Künzi, and B. Ilschner, Acta Metall. Mater. 43 (1995) 1171–1181. [60] M. Vazquez, Materiales Magnéticos (COTEC Foundation, Madrid, 2003).   "    },    {        "title": "1103.1573v1.Permanent_magnets_including_undulators_and_wigglers.pdf",        "content": "Permanent magnets including undulators and wigglers  \nJ. Bahrdt  \nHelmholtzzentrum für Materi alien und Energie, Berlin, Germany  \nAbstract  \nAfter a few historic remarks on magnetic material s we introduce the basic \ndefinitions related to permanent magnets . The magnetic properties of the \nmost common materials are reviewed and the production processes are \ndescribed . Measurement t echniques for the characterization of macroscopic \nand microscopic properties of permanent magnets are presented . Field \nsimulation techniques  for permanent magnet devices are discussed. Today, \npermanent magn ets are used in many fields. This  article concentrates on the \napplications of permanent magnets in accelerator s starting from dipole s and \nquadrupoles on to wigglers and undulators.  \n1 History  \nPermanent magnets were already mentioned around 600 BC by Thales of Milet us. He attributed \nmagnets a soul because he observed that they attract small pieces of iron . People were always \nimpressed by permanent magnet phenomena as documented in an old anecdote : A long time ago a \nshoemaker walked through the beautiful countryside of Greece . After a while he was surprised that \nhis shoes started to fa ll apart. Finally, he noticed mysterious stones on his path  that pulled out the iron \nnails from his sandal s.  \nMagnetic material s were  discovered two and a half thousand years ago in the Greek area \nMagnesia, which gave this remarkable material its name — magnetite  (FeII(FeIII)2O4. In 200 B C the \nfirst scientific device called Si Nan (translation: pointing south) was built in China. A magnetic \n‘spoon ’ spins on a polished surface and once it comes to rest it points southwards. It is not known \nwhether this device ever worked reliabl y as a compass. The first European compass was mentioned in \n1200 AD . A piece of magnetite  sitting on a wooden piece in a bowl of water aligns after a while in the \nnorth –south direction. Around 1600 William Gilbert describe d how to magnetize iron by mechanical \ndeformation such as forging or drawing in the north –south direction. Also cooling do wn a r ed-hot iron  \nbar may freeze the earth magnetic field. In 1750 the first ferrites were fabricated by Gowan Knight. \nHe used the sintering technique which is still an essential step in today’s magnet production. In 1815 \nHans Oersted discovered that a current -carrying wire produces a magnet field. Following this \ninvention it took only six years to build the first  electromagnet  that w as capable of magnetiz ing steel \n(William Sturgeon). In 1867 a German handbook was publish ed that describes the fabrication  of \nmagne tic materials from non-magnetic components and vice versa.  \nThe twentieth  century saw a rapid development of various types of magnetic materials which \nwas always driven by the demand for higher remanence, higher stability with respect to reverse fields \nand temperature , and last but not least by a cost effective production which implied  the availability of \nthe constituents of the material. There are only a few chemical elements that show ferromag netic \nproperties. Those are the transition metals  Fe, Co, Ni with Curie temperatures of several 100°C and \nthe lanthanides Eu, Gd, Tb, Dy,  Ho, Er, Tm  with Curie temperature s below room temperature . All \nrelevant permanent magnets are alloys made of a large variety of components.  Over  the last 100 years \nthe energy product  of permanent magnets increased by several orders of magnitude (Fig. 1).     \nFig. 1: Development of the energy product of various magnet types over the last century  [1] \nBefore c oming  back in more detail later , we give here a brief overview of the b ig step s in \nmagnet technology in  the twentieth  century. In 1916 it was observed that the coercivity of normal \nsteel could be enhance d with Co  additions . AlNiCo, an alloy made of Al,  Ni and Co, played an \nimportant role for several decades. The grades AlNiCo 3 and 5 go back to 1931 an d 1938 , \nrespectively . In 1938 the production techniques of ferrites were  significantly improved in Japan. From \n1945 onwards  permanent magnets became  comparable  with electromagnets  in performance and cost. \nNew AlNiCo grades with improved  performance , AlNiCo 8 and 9,  were invented in 1956. Until 1970 \nAlNiCo was the prevalent permanent magnet material.  In 1970 the first rare earth alloy, SmCo 5, was \nproduced . Though rare earth s are generally  more abundant than copper or lead they are  not \nconcentrated in big mines and it is difficult to extract the rare earth s from the ore.  Most of the \nmaterial is located in China  and was not always accessible. Therefore, the r esearch on magnets \nwithout rare earths was still ongo ing, resulting in the productio n of FeCrCo in 1971. Owing  to the Co \ncrisis in the late 1970s the magnet suppliers started to look for alternatives with less Co content. Hard \nferrites were produced all the time since the constituents are plentiful and non strategic. In 1981 \nSm 2(Co,Cu,Fe, Zr) 17 was invented. Pure Sm is expensive , and with the elaboration of a Ca -reduction \nprocess Sm -oxides could be used as well , thus  reducing the cost significantly. W ith the invention of \nNd 2Fe14B in 1983 a high performing material became  available which doe s not require Co at all. Fe \nand B are p lentiful and Nd is a factor of ten more frequent than Sm. In the following years the \nNd 2FeB 14 production incr eased exponentially ( Fig. 2) and the price per kilogram dropped one order of \nmagnitude ( Fig. 3). It is worth  mentioning that the USA stopped production in 2004. In Europe only \none supplier is left. In 2001 China surpassed Japan in the production rate though most of the material \nis still used in China. Comparing the tonnage dedicated for export China and Japan ar e comparable. A \ntrend is observable that magnet suppliers in industr ialized  countries specialize in downstream \nproducts with a higher added value or in high -performance magnets for special applications.   \nFig. 2 : Production rate of Nd 2Fe14B [2]. For China the total magnet production and the production \ndedicated for export is plotted  \n \nFig. 3: Cost development of Nd 2Fe14B magnets  [2] \n2 Permanent magnet applications  \nToday, permanent magnets are used in many areas. A systematic classification of the applications  \nrelated to the underlying physical law is given by R . Parker (see bibliography) . \n– Coulomb law:  compass, magnetic bearing, magnetic coupling, fixing tool  for machining, \ntransportation  line, conveyer, hysteresis device, small MRI system for medical applicat ions. \n– Faraday law:  dynamo, ge nerators based on wind or water energy, microphone, eddy current \nspeedometer . – Lorentz force law:  loud-speaker, servo motor, voice coil motor (hard disk drive ), device where \nthe Lorentz force acts on free electrons such as: sputter facility, ion getter pump, accelerator \nmagnet including undulator  and wi ggler, Halbach type dipole  and higher order multipole . \nThe third class of applications will be discuss ed later in more detail. Figure 4 shows the developmen t \nof applications from 1 999 to 2003 . Today, industrialized  countries use about 50% of the magnets in \nvoice coil motors.  Table 1 gives an overview of permanent magnet applications in China.  \n \nFig. 4:  Applications of permanent magnets world wide in 2004 [3] \nTable 1: Magne t applicat ions in China in 2007  \nHigh -tech products (t)  Low -tech products (t)  \nMRI  1800  Loud speaker  11280  \nVCM  1300  Separator  3610  \nCD-pickup  2515  Magnetizer  900 \nDVD / CD -ROM  4060    \nMobile phone  3160    \nCord less tool  3180    \nElectric bike  5860    \nThere are several  advantages of permanent  magnets as compared to electro magnets: i) \nMachines such as motors can be built more compact ly with permanent magnet s. A permanent magnet \narray can be scaled in all three dimensions maintaining the magnet ic field level at the centre . This is \npossible since permanent magnets can be described as blocks that carry infinite thin layer s of surface \ncurrents with a constant s urface current density of the order of 10  kA/cm  (see Section  10). Scaling an \nelectromagnet to smaller dimensions whil e keeping the field constant requires a linear enhancement \nof the current density . The technical limit for water -cooled coils is about 500  A/cm2. ii) In principle, \ninfinitely high fi elds can be produced. Let us imagine a  magnet configuration that produces  a field B0. \nScaling this configuration by a factor of two in all three dimensions and adding it to the old \nconfiguration doubles the total field. Of course, the available spac e and price limit this procedure  \nrather soon. Nevertheless, there are many device s whose fields exceed the remanent field by large \nfactors, e.g. , Iwahita built a 3.9 T dipole  magnet [ 4]. iii) The power consumpt ion is zero and, thus, \nthere are no cooling problems.  iv) Permanent magnet devices are fail safe as long as they are operated \nbelow the Curie temperature.  3 Basic definitions  \nIn this article we use Gaussian units. The macroscopic property of magnetic material  is described by  \nthe dependenc e of magnetic induction and magnetization on  the external field. The zero crossing of \nthe inducti on or magnetization between the second and third quadrant is called coercive force (the \nabsolute value of the external field  as plotted in Fig. 5). The location of t his crossing can be \nsignificantly d ifferent fo r the induction ( Hc) and the magnetization ( Hcj). The BH-dependency is \nreproduced if the material is periodically driven to complete magnetization in one direction and \ncomplete magnetization in the opposite direction by tuning the external field.  A non -magnetized block \nshows a different dependency wh ich is called the initial magnetization curve. The local dep endence \nbetween B and H is described  by the permeability . Apart from the usual permeability \ndHdB/  \nwhich describes the linear part in the first and second  quadrant we differentiat e between the initial, \nthe differential or maximum , and the reversal or recoil permeability (Fig. 6). The reversal \npermeability describes the properties in the non -linear part close to the knee. For small field variations  \nthe BH-curve exhibits a small loop  around a straight line which is approximately parallel to the slope \nof the BH-curve above the knee.  Nd 2Fe14B magnets have a different permeability parallel and \nperpendicular to the easy axis of about  μpar = 1.04 and μperp = 1.17 . Depending on the working point of \nthe magnet, i.e. , the operating point on the hysteresis loop, the remanence can be lower than Br = \nB(H = 0) by a few per cent . \nH / kOe\nor\nu0H / 0,1TInduction B / kG or B / 0,1 T\nMagnetization 4piM / kG or 4piM / 0,1 T\n-Hc-HcjBr Hs\nlocation of the knee of B:\n- 2nd quadrant for ferrites\n- 3rd quadrant for RE magnetsHc< 200 Oe: soft material\nHc> 200 Oe: hard material\n \nFig.  5: Hystere sis loop of a magnetic material  \nH / kOeB / kG\nuiud\nur\n \nFig. 6: Initial permeability μ i, differential or maximum permeability μ d, and reversal or recoil \npermeability  μr We call a material hard magnetic if Hc > 200 Oe which is a bit arbitrary. The performance of a \nmagnet is related to the maximum energy product. It is equal to the largest rectangle which can be \nplotted under the BH-curve ( Fig. 7). Though modern magnets have a nearly rectangular BH-curve we \nhave always  \n2\nmax ( ) / .r BH B \n. \nlines of equal energy productB\nBHmax\nBHmaxBr\n \nFig. 7 : Two graphic representations of the m aximum energy p roduct  \nThe efficiency of an electric circuit is given by the conductivity = 1 / resistance = current / \nvoltage. In analogy the efficiency of a magnetic circuit is written as: permeance = 1 / reluctance = flux \n/ magnetomotive force difference. The magnetomo tive force is the magnetic potential as produced by \ncurrents or magnetized samples.  The permeance of a volume V is defined by  \n\n\n\nldHsdB\nP \n \nwhere the integral over B is taken at the plane B and the line integral over H is taken betwe en the \nplane s A and C ( Fig. 8) \nlines of magnetizing\nforce: H\nsurfaces of equal\nmagnetic potentialC\nB\nA\n \nFig. 8: For the definition of the permeance see text  Inside  a magnetized body  demagnetizing forces proportional to the magnetization are present. \nThe strength is given by the demagnetization factor D which varies between 0 and 4π depending on \nthe shape of the sample (small for pencil -like samples  with the easy axis pointing in the long direction \nand large for flat samples ). The working point of a material is given by  Bd and Hd where Bd / Hd is the \ncoefficient of demagnetiza tion or unit permeance. The line connecting the origin and the working \npoint is called the load line.  In a magnetic design the working point has to be chosen such that it is \nwell above the knee for all possible operation conditions. Knowing the demagnetiza tion factor the \nworking point can be derived according to:  \nD HBHDH BMD HM HB\nddd d dd\n\n4144\n\n  \n \nIn Cartesian  coordinates we always  have : Dx + Dy + Dz = 4π. For specific geometries the \nliterature provides tables and approximate d expressions  for the evaluation of demagnetization factor s \nD (see the book by R. Parker  in the bibliography ). More complicated geometries have to be evaluated \nnumerically or measured . Depending on the measurement method one gets either magnetometric or  \nfluxmetric (ballistic ) demagnetization factors. In the first case a long coil is placed along the complete \nsample yielding averaged values for the whole sample , in the second case a fla t coil is placed a round \nthe centr e cross section yielding a value average d over this  area. The magnetometric values are \nalways lar ger than the fluxmetric values.  \nAnalytic  expressions of demagnetization factor s are available for a generalized ellipsoid and for \na rectangular prism. Osborn  [5] gives values for a generalized ellipsoid with  the semi -axes a ≥ b ≥ c: \nkabackE DkF kE DkE kF D\nzyx\n \n\n\n \n\n\n   \n) sin(/) sin() sin(/ ) cos(/ ) cos(),() cos() cos() sin(\n)(cos)(sin) cos() cos(4) cos() cos() sin()(sin)(cos),( ),()(cos)(sin)(sin) cos() cos(4)),( ),(()(sin)(sin) cos() cos(4\n2 32\n2\n2 2 32 3\n\n\n \nF and E are elliptical integrals  of the first and second  kind with  k = modulus and θ = amplitude . It has \nto be emphasized tha t these values are exact and they are constant over the whole volume. Special \ncases are the sphere with Dx = Dy = Dz = 4π/3, the infinite long circular cylinder with Dpar = 0 and \nDperp = 2π or an in finite wide plane with Din-plane = 0 and Dperp-plane = 4π.  \nAveraged demagnetization  factor s for a parallel prism are derived  by Aharoni [6 ]. In reality the \nfactors vary over the volume.  \n2 22 22 22 2 23 3 3 2 2 23 3 32 2 2 2\n3 3232arctan2 ln2ln2ln2ln2ln2ln24/\nc b sbcc a sacb a sabc b a sabcabcsac sbc sabsbc sacabcsabcabcc b aabcc b a\nsabccab\na saca sac\nbc\nb sbcb sbc\nacb sabb sab\nca\na saba sab\ncb\nb sabcb sabc\nacc a\na sabca sabc\nbcc bDz\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n  \nIn analogy Dx and Dy can be derived. Special cases are a cube with Dx = Dy = Dz = 4π/3 and an infinite \nlong rectangular cylinder with  \nacpp p p pppDD\nperppar\n/)/1 arctan(2)ln( ) 1ln(214/0\n22\n\n \nFor more complicated geometries or if the demagnetization distribution over a rectangular block is \nneeded , analytic expressions do not exist and t he demagnetization factors have t o be evaluat ed \nnumerically . Figure 9  shows the variation of the demagnetization over rectangular blocks with \ndifferent shapes.  \n \nFig. 9: Magnetic induction, magnetic field , and magnetization for four bl ocks with different \ngeometries. The length in the easy axis direction is varied as indicated in the graph  4 Permanent magnet types  \nIn this section  the magnetic properties of the most common magnet types  are summarized . This \noverview will  give only a tast e of the diversity of magnet properties. The magnet materi al has to be \nchosen carefully according to the demands: Some applications need high remanence, others require \nhigh coercivity or high temperature stability. Some applications do not require high performance and \nonly the price counts. The properties of high -end grades  are listed  in Tables 2 –9. \nPermanent magnets are either of type I or type II  (Fig. 10). Type I magnets have a high leakage \nflux leaving the magnet  at the sides . The energy stored in these leakage fields is not usable. The \npermeability of these m aterials is large and Hcj is usually smaller than Br. Typical examples are \n35%Co Fe or AlNiCo. Type II magnets have a low leakage flux, the permeability is close to one and \nHcj is much larger than Br. Rare earth s based magnets as well as hard ferrites belo ng to this species.  \nSintered magnets are either isostatic pressed (IP), transversally pressed (TP) , or axially pressed (AP).  \n-Hc-HcjBr\n-Hc-HcjBr\nleakage flux\n \nFig. 10: Type I magnets (left) and type II magnets  (right)  \n4.1 Carbon steel or martensitic steel  \nPure carbon steel (up to one per cen t carbon) has a rather low energy product which can be \nsignificantly enhanced with the addition of Co  (Fig. 11). The performance can fur ther be improved \nwith other non -magnetic ingredients. Internal strain and lattice imperfections can also have a positive  \neffect  on the performance . \nTable 2: Magnetic properties of carbon steel  \nGrade  Remanence (kG)  Coercivity Hcj (kOe)  Energy product ( MGOe)  \n3.5 Cr 9.8 0.05 0.22 \n36.0 Co  9.6 0.24 0.94 -200\nH / Oersted-400412\n8\nB / kGauss\n35wt. % CoCoFe\n6wt. % Co \nFig. 11: Carbon steel  \n4.2 AlNiCo  \nThe ma gnets consist of an alloy of Al, Ni , Co and also Fe, Cu, Ti. The remanence is pretty high \nwhereas the coercivity is low which has to be taken into account  in the magnetic design . Some grades \ncan be operated at tem peratures up to 550°C. The energy product can be  enhanced when an \nanisotropy is deliberately introduced,  e.g., by cooling the blocks in a magnetic field. The material is \nextremely difficult  to machine and very brittle which requires a near to finish production. Better \nmechanic al properties have been achieved with sintered magnets. T he temperature coefficients are as \nlow as 0.02% for Br and -0.02% up to 0.01% for Hcj. \n \nTable 3: Typical m agnetic properties of  a few AlNiCo  grades  \nGrade  Remanence (kG)  Coercivity Hcj (kOe)  Energy product ( MGOe)  \nAlNiCo 5 cast  13.5 0.74 7.5 0 \nAlNiCo 9 c ast 10.6 1.5 10.0 \nAlNiCo 5 \nsintered  11.2 0.61 4.4 \nAlNiCo 8 \nsintered  8.0 1.60 4.5 \n4.3 FeCoCr  \nThe material  properties are  similar to those of AlNiCo 5 but this magnet requires less  Co. \nFurthermore, it has a higher ductility and it  can be oriented by mechanica l deformation.  \n Table 4: Magn etic properties of  FeCoCr  \nGrade  Remanence (kG)  Coercivity Hcj (kOe)  Energy product ( MGOe)  \nFeCoCr  13.0 0.55 5.0 4.4 MnCAl  \nThis material does not need Co at all. It has a higher ductility than AlNiCo. The magnet can be \noriented i n a warm extrusion process. The extrusion is, however, rather expensive.  \nTable 5: Magnetic properties of  MnCAl  \nGrade  Remanence (kG)  Coercivity Hcj (kOe)  Energy product ( MGOe)  \nMnCAl cast  3.0 0.95 1.0 \nMnCAl cast & exruded  6.0 2.5 7.0 \n4.5 Hard ferrites  \nThe c hemical composition is MO 6(F 2O3) or MFe 12O19 with M = Ba, Sr or Pb . The mag nets are \nsintered. They are either isotropic or oriented. The remanence is low but the coercivity is pretty high. \nThe material has la rge temperature coefficients of  0.2%  for the r emanence and  +0.1 up to 0.5%  for \nthe coercivity.  Hc and Hcj are similar and the knee is located in the second quadrant.  \nTable 6: Magne tic properties of hard ferrites  \nGrade  Remanence (kG)  Coercivity (kOe)  Energy product (M GOe)  \nHard ferrite  4.0 3.6 (4.0 ), Hc (Hcj) 4.0 \n4.6 SmCo 5 \nSamarium  based rare earth magnets hav e a high energy product. The high coercive grade is the \nfavourite material  in the presence of strong reverse fields or in an ionizing radiation environment. The \nmaximum operation temperature is 250° C. The temperature co efficients are as low as 0.045% / deg. \nand 0.22% / deg. ( Hcj). \n Table 7: Magnetic properties of SmCo 5 \nGrade  Typ. r emanence (kG)  Min. c oercivity  Hcj (kOe)  Typ. energy product ( MGOe)  \nIP 10.1 12.5 25.0 \nIP 9.0 25.0 20.0 \n4.7  Sm 2Co 17 \nThe material has a higher remanence than SmCo 5. The m aximum operation temperature is 350 –500°C \ndepending on the grade . The temperature coefficients are lower as compared to SmCo 5: 0.035% / \ndeg. and 0.12% / deg. ( Hcj). \nIn comparison  with Nd 2Fe14B magnets , SmC o5 and Sm 2Co17 magnets are brittle and the \nhandling is delicate. The temperature coefficients are lower as compared to Nd 2Fe14B which is \nadvantageous in temperature sensitive applications.  \n \n \n \n Table 8: Magnetic properties of  Sm 2Co17 \nGrade  Typ. remanence (k G) Min. coercivity H cj (kOe)  Typ. energy product (MGOe)  \nIP 11.0 20.0 28.0 \nTP 10.7 20.0 27.0 \nAP 10.4 20.0 25.0 \n4.8 Nd 2Fe14B \nThis material has the highest remanence among all rare earth based permanent magnets. The \ntemperature gradient s are higher than in  Sm based magnets:  0.09 to 0.11% / deg for Br and -0.45 \nto 0.6% for Hcj. Depending on the amount of added dysprosium the coercivity can be enhanced \nsignificantly sacrificing remanence.  The maximum operation temperature depends o n the grade and \nvaries betw een 8 0°C for material of highest remanence  and 230°C for material  with highest \ncoercivity.  \nTable 9: Magnetic properties of  Nd 2Fe14B  \nGrade  Typ. remanence (kG)  Min. coercivity  Hcj (kOe)  Typ. energy product (M GOe)  \nIP 14.7 11 53 \nTP 14.1 14 48 \nAP 13.4 14 43 \n5 Temperature dependence  \n5.1 Compensation of temperature dependent effects  \nCritical permanent magnet applications need  a compensation of the temperature dependent remanence \nchanges. This can be accomplished with various strategies:  \n– Curie alloys consisting of Ni and Fe have a negative temperature gradient of  the permeability. \nThey can be used as temperatur e sensitive flux shunts. With r ising temperature they shortcut \nless flux , and thus  compensate for the remanence loss of the permanent magnets. These \nmaterials  are used , for example , in speedometers. Other applications are accelerator magnets.  In \nthe 344 permanent magnet gradient dipole s of the 8.9 GeV antiproton recycler ring at Fermilab , \nthin Ni -Fe bars shortcut part of the magnetic material ( strontium ferrite ) between the  Fe pole \ntips and the iron yokes [7]. \n– The next Brazilian light source , LNLS II , will be based on 48 permanent magnet gradient \ndipole s made of hard ferrites  [8]. The gap of the magnets is passively readjusted with \ntemperature.  \n– Compared to Nd 2Fe14B material SmCo 5 has a small remanence temperature coefficient. It can \nfurther be reduced  by mixing the material with other compounds with a positive temperature \ngradient such as ErCo 5 and/or GdCo 5.  \n5.2 Curie temperature  \nThe temperature range for a safe ope ration depends on the Curie temperature. Above the Curie \ntemperature th e remanence and coercivity drop  to zero and the material becomes paramagnetic. The \nCurie temperatures of some magnetic materials are summarized in Table 10.  Table 10 : Curie temperatures  of typical elements a nd permanent magnets  \nGrade  Curie temperature (°C)  \nIron 770 \nCobalt  1130  \nNi 358 \nNd 2Fe14B 310 \nSmCo 5, Sm 2Co17 700–800 \n35% Co steel  890 \nCrFeCo  630 \nAlNiCo  850 \nHard ferrites  400 \nThe coercivity  of Nd 2Fe17B magnets can be enhanced wi th the addition of Dy ( Fig. 12). On the \nother hand, the Dy reduces the remanence. The maximum operation temperature of Sm 2Co17 grades \ncan be raised with a specific tempering procedure . In both cases the Curie temperature of the material \ngrows a bit but muc h less than the coercivity. Optimized permanent magnets can be used up to about \n75% of the Curie temperature.  \n0                    200               400          600     800                 1000600\n500\n400\n300\n200\n100\n0\nCurie Temperature in °CMaximum Operation Temperaturein °C\nhard ferrites\n(Nd, Dy)2(Fe,Co)14BSmCo5AlNiCoSm2(Co,Cu,Fe,Zr)17\n \nFig. 12: Temperature stability versus Curie temperature of various magnet materials [ 9]. The dotted \nlines connect different grades of the same magnet material (f or details see text)  \nOnly recently, Hitachi described a vapour deposition and diffusion process which enhances the \ncoercivity of Nd 2Fe14B magnet by about 4  kOe without sacrificing remanence. Alternatively, the \nremanence can be enhanced by  400 G withou t losing in coercivity [ 10]. The magnets are exposed to \ndysprosium vapour. The Dy atoms diffuse along the grain boundaries into the bulk material without \npenetrating into the grains. The penetration depth is only a few millimetres  which limits  this method \nto thin magnets . This material is of particular interest for in -vacuum undulators where the magnets are \nclose to a several GeV electron beam and the demagnetization stability is an important issue.  \n5.3 Reversible demagnetization  \nOperating permane nt magnets above the Curie temperature causes  a complete demagnetization. The \ncrystal structu re remains unchanged, and hence  the magnets can be remagnetized recovering full performance. Since the demagnetization factor varies over the magnet volume, certai n parts \ndemagnetize earlier than more stable regions. For critical applications the magnet supplier \ndeliberately ages the blocks, in order to avoid a remanence loss over the years. For this purpose the \nmagnets can either be heated well above the final operation temperature or they can be stabilized in a \nreverse field.  \nSynchrotron radiation light sources are based on periodic permanent magnet structures, so -\ncalled undulators , which are passed by relativistic electrons emitting photons in the VUV to X -ray \nregime (see Sections  12–14). If the magnets are hit by off -axis electrons they may get demagnetized. \nDemagnetization has been reported at the ESRF [ 11], the APS [ 12–13] (see Fig. 13) and DESY [ 14]. \nThough the remanence losses reached 10% the structures could be repaired in these cases by re -\nmagnetizing the blocks . If, however, the ionizing radiation changes the crystal structures , irreversible \nlosses may occur  [15].    \n \nFig. 13: History of sector 3 un dulator at the APS (left) and single block Hall probe scan s (right). \nThe damage is localized  at the surface close to the electron beam (courtesy of L. Moog , \nAPS) \n6 Permanent magnet fabrication  \n6.1 Sintered magnets  \nSumitomo developed the fabrication process for sintered rare earth magnets. The various ingredients \nare mix ed in the desired percentages, melt ed under vacuum conditions and cast to macroscopic pieces.  \nThe pieces are crushed and then milled in several steps down to particle sizes of a few micrometres . \nThe powder is highly reactive and has to be processed under i nert gas conditions. The powder is \npressed in the presence of a high field which aligns the magnetic domains. The pressed pieces are \nsintered at temperatures around 8 50°C which melts the surfaces of the grain s (so-called liquid phase \nsintering). The qualit y of the magnet depends on the type of pressing.  \nHighest remanence is achieved with isostatic pressing. Here, the powder is poured  into long \nrubber tubes which are placed into a liquid environment. The powder is compressed with equal \npressure from all dire ctions. The magnetic field is applied with a long coil surrounding the tube. \nThese magnets have rather large dipole orientation errors  whereas the  homogeneity is pretty good. \nAlternatively, the powder can be pressed in a die. Depending on the geometry , the pressing direction \ncan be parallel (axial pressing) or perpendicular to the field lines (transverse pressing). The latter \ngeometry yields a higher remanence but it can not be applied for block geometries with high aspect ratios. Die pressed magnets have v ery similar magnetic properties over the whole batch since they all \nsee the same magnetic environment during the pressing. The dipole errors are small but the \ninhomogeneities can be l arger than in isostatic  pressed magnets. Die pressing is preferred for la rge \nbatches because the die can be shaped close to the final geometry and the machining time afterwards \ncan be minimized  (near net -shape production) . More details on the development and the \ncharacteristics of sintered Nd 2Fe14B magnets are given in Ref. [16]. \n6.2 Melt spun magnets  \nIn 1984 General Motors developed another fabrication method for rare earth permanent magnets. The \nmelted ingredients are po ured into an induction heated container under Ar atmosphere. A liquid alloy \njet is quenched on a water cooled sp inning wheel  forming a 300 μm microcrystalline ribbon  (Fig. 14). \nThis material is further processed following one of three procedures : \n– Magnequench I: The ribbons are bonded to form a solid block which can further be machined. \nThe material is isotropic.  \n– Magnequench II: The ribbons are pressed under high temperature. The material is isotropic.  \n– Magnequench III: Starting with Magnequench II material the blocks are deformed under high \ntemperature resulting in an anisotropic grade. This material has the highest e nergy product \namong the three grades.  \nwatercooled\nspinningwheelliquid alloy\nin an induction\nheatedcontainer\nunderAr atmosphere\n300 m ribbon:\nmicrocrystalline\nstructurewith\nhigh anisotropyhigh pressure\nliquid alloyjet\n \nFig. 14: Magnet fabrication foll owing the Magnequench technique  \n7 Measurement techniques  for macroscopic properties  \nThe magnetic  hysteresis can be measured either in a closed loop or in an open loop geometry. At \nroom t emperature or higher temperatures a hysteresis graph can be used ( Fig. 15). Here, the sample is \nclamped between two  iron yokes which short -cut the magnetic flux. Powering a coil that is wound \naround the iron yoke the external field can be varied. The param eters B and H can be directly \nmeasured with pickup coils . Large samples (a few cubic centimetres ) can be characterized which \nminimizes the impact of surface effects.  \nAt low temperatures another method  has to be used, i.e., a vibrating sample spectrometer: In a \nHe cryostate a small sample vibrates back and forth inducing a voltage in a pickup coil. The signal is proportional to the dipole moment of the sample. Knowing the sample geometry , this value can be \nconverted to the remanence. Usually, the samples mus t be small (a few cubic millimetres ) and the \nsurface effects have to be taken into account  for the interpretation of the results . Furthermore, a \nprecise calibration of the set up is required which includes the demagnetization factor of the sample.  \nEllipsoid al samples with a constant demagnetization factor are preferable but difficult to fabricate and \nalign.        \nelectromagnet\npermanent magnet\nHall sensor for H-meas.\npickup coils for M-meas.\npickup coil for B-meas.motordrivesystem\npickupcoil\nvibratingmagnet\nHe bath cryostate\nSC solenoid\n \nFig. 15: Hysteresis  graph (left) and vibrat ing sample magnetometer (right)  \nUsually , the dipole moment is measured in a  Helm holtz coil with high a ccuracy. Th e geometry \nis optimized such that the measure ment is insensitive to a displacement of the magnet  and the magnet \nblock size . The magnetizing force of two coils  with winding N and current I is \n\n\n\n\n\n\n\n\n\n\n  5.1\n225.1\n22) 2/(1) 2/(12\nax d\nax d\naNIH\n \nwhere d = distance of the coil s and a  = radius of coil . \nIn the Helmholtz geometry, d = a, the quadratic terms disappear.  An automated rotation of the \nmagnet around all three axes and an averaging over several turns yields rms reproducibilities better \nthan 0.07 % for the main component and better than 0.04 ° for the easy axis orientation errors with \nrespect to a reference surface  (values of the BESSY II system ). \nThe dipole  moment can also be measured with a fluxgate sensor located at a large distance \n(typically 1 m) from  the sample. In th e far field only the dipole component contributes and higher \norders can be neglected. The signals are small and the magnet has to be flipped to get rid of \nenvironmental fields. This method is adequate for the main component but less accurate for the minor \ncomponents.   \nClose to the magnet surface (i.e., a few millimetres  for magnets with dimensions of a few \ncentimetres ) the magnet fields can n ot be described by the dipole moment only. Higher order \nmultipoles have to be included. These higher order t erms can  be measured with a set -up where the \nmagnet is moved with respect to a fixed wire. The rms reproducibility  of the BESSY II system , which \nuses a single fixed wire, is  summerized in Table 1 1. In other laboratories alternative fluxmetric \nmethods are applied : at SPRING -8 a multifilament rotating coil close to the magnet surface is used \n[17]. At the ESRF , modules of several magnets are continuously moved at a speed of 60  mm/s passing \na fixed multifilament wire (20 single wires) [18]. The modules include an equal  number of magnets \nwith the easy axis pointing to the wire an d into opposite direction. Thus  the modules are magnetically \ncompensated and the field integrals are below 100 G  cm. The rms error of a module measurement is 1 \nG cm.  The information on dipole er rors and magnet field inhomogeneities  can be used to sort the \nmagnets such that the fabrication errors cancel in the assembled structure.  \nTable 11 : Reproducibility of field integral measurements of single magnet blocks  (BESSY II system) . The \nblocks have a distance of 5 mm to the wire. The orientation of the easy axis is  given with respect \nto the wire  \nEasy axis  \norientation  Absolute  error  \n(rms values)  Relative  error  \n(rms values)  \nParallel  310-4 T mm 610-3 \nPerpendicular  1.510-3 T mm 2.510-4 \nThe capacity  of the  furnace crucible defines the size of a batch of magnets . Within a batch  the \nmagnet properties are similar , whereas the  dipole moment variations between batches can be as large \nas a few per cent . Magnets  from the same batch c an be sorted efficiently  resulting in  high-\nperformance structures. This strategy is limited to  typical batch size s of 1–2 tonnes. For larger \nundulators with a total weight of the magnet material of 20  tonnes and more (e.g. , undulator length  \n>100  m for FEL structures) other strate gies have to be employed. One of them is a sophisticated \nmixing scheme of the different powder batches before pressing the  blocks.  \n8 Microscopic p roperties  \n8.1 Microscopic s tructure of RE permanent magnets  \nRare earth (RE) based permanent magnets are either sinte red or melt spun . They consist of \nmonocrystalline grains with a diameter of a few micrometres  which are embedded in a RE -enriched \nmatrix. In the case of Nd 2Fe14B this matrix contains ingredients such as Nd, Co, Cu, Al, Ga, Dy and \nNd-oxides. The crystal str uctures of RE -based magnets are described in detail in Ref. [19]. The unit \ncell of SmCo 5 is hexagonal. Sm 2Co17 has a rhombohedral unit cell and Nd 2Fe17B is tetragonal. The \nmono crysta lline areas  are form ed when the melted phase is cooled down. They remain u ncha nged \nduring the crushing and milling process and they are oriented with respect to the external field during \nthe pressing. At typical sintering temperatures of about 850°C the matrix enclosing  the \nmonocrystalline particles melts whereas the crystallite s remain unchanged. This liquid phase sintering \nyields rather dense products.  The theoretical limit of  the energy product is given by  \n2\nmax\n0( ) /\n(20 C) (20 C) (1 ) ,r\nr r sat nonmagneticBH B\nB B V f\n\n\n      \n \nwhere \ncos( )f\n \nand \narctan 2r perp\nr parB\nB\n\n\n . \nTypical  values for Nd 2Fe14B ma gnets are as fo llows  [20]. Owing  to the liquid phase sintering \nthe density is close to the single crystal density : ρ/ρ 0 > 0.985 . An optimized pressing process yields alignment coefficients as high as  fφ > 0.98. The vacuum induction furnace and the conseque nt inert \ngas processing keep the amount of impurities (Nd oxides and others) below 2.5 weight per cent . The \noccurrence of o ther RE constituents is also below 2.5 weight per cent . Thus  the amount of \nnonmagnetic material is less than 5%. With these parameter s an energy product of 59  MGOe has been \nachieved which is close to the theoretical limit of 63  MGOe.  \nIt is worth noting  that Nd 2Fe14B magnets are sensitive to hydrogen decrepitation:  Nd + H 2O >> \nNdOH + H , H + Nd >>  NdH . The hydrogen  decrepitation can have fatal consequences for magnets \noperated in a sensitive environment (e.g. , undulators of an accelerator ). During magnet fabrication \nspecial care is needed to cope with these effects. Appropriate chemical constituents between the grain \nboundaries minimize  the hydrogen decrepitation  and an appropriate surface passivation or coating \n(Al, TiN and others) protect s the magnets in a humid environment . On the other hand , the \ndecrepitation process may be interesting for a final decomposition of permanent magnet mater ial and \na RE recovery  [21, 22]. \n8.2 Coercivity  \nThe potential existence of Bloch walls in a magnetic particle depends on the size of th e particle.  \nEnergy considerations show that Bloc h walls can not exist below a certain grain size. For example, \nthis critical s ize is 0.01  μm for Fe and 1  μm for Ba f errites. Below these limits the particles behave \nlike a single domain. For larger grains Bloch walls may show up. The typical grain size of a RE-\nmagnet of a few micrometres  is a bit larger than the single domain size. Usually, th e magnetization \nvector rotates in  the plane o f the boundary between  two magnetic domains. Exceptions are t hin films \nwhere the rotation occurs  perpendicular to the boundary plane (N éel wall).  \nThe coercivity  can be enhanced by various methods:  \n– intentio nal ad dition  of imperfections  which impede the Bloch wall movement in large grains \n(e.g, carbides in steel magnets) ; \n– preparation of single domain grains which can be switched only completely requiring  high \nfields ; \n– implementation or enhancement of the magnet anisotropy  (shape or crystal anisotropy) . \nOriented  AlNiCo 5 is a n example of a magnet with shape anisotropy . When cooling down the \nmolten components a spinodal decomposition into the magnetic phase FeCo and the less magnetic \nphase FeNiAl occurs. The spinodal d ecomposition as described by the Cahn –Hilliard equation is a \ndiffusion process which results in a periodic and crystallographic oriented structure of the phases. The \nsize of the segregated phases and the width of the boundaries  (it is described by a tanh f unction ) is a \nfunction of time.  \nWhen  AlNiCo 5 is cooled  down i n the presence of a magnetic field the two phases get oriented \nand a strong shape anisotropy evolves [23]. As a consequence the energy product along the easy axis \nis about a factor of ten large r than in  the perpendicular direction.  \nRE-based permanent magnets exhibit a  large crystal anisotropy. These magnets are either of the \nnucleation type or the pinning type. Nucleation type magnets are SmCo 5, Nd 2Fe14B, and ferrites. \nPinning type magnets are Sm(Co,Fe,Cu,Hf) 7, SmCo 5+Cu precipitation , and Sm 2Co17+SmCo 5 \nprecipitation of the size of domain wall thickness . \nThe Bloch walls of nucleation type magnets move easily within one grain  and are stopped only \nat the grain boundaries. After heating , many domain  walls exist within each grain. They are easily \npushed out of the grain bulk to the boundaries with rather low fie lds (high initial permeability). Then , \nthe domain walls are fixed to the grain boundaries. Once the magnet is fully magnetized , high reverse \nfields are needed to switch the domains. Most grains switch the magnetization in a single step w ithout \nforming new Bloch walls.  Pinning type magnets  have pinning centres within the grains which impede the Bloch wall \nmotion. These can be impurities or precip itations. The two magnet types show a different initial \nmagnetization after  complete demagnetization by heating as plotted in Fig. 16. \n \nFig. 16: Initial magnetization of nucleation type magnets (solid lines) and pinning type \nmagnets  (dashed lines)  \nPartial  repla cement of neodymium  with dysprosium  enhances the crystal anisotropy and, hence, \nthe coercivity.  Simultaneously, the remanence is reduced.  Nd 2Fe14B magnet suppliers provide various \ngrades of one material which differ in the Dy  content . Depending on th e specific application the \nappropriate material can be chosen. Dy sprosium  is rather expensive , so much effort has been spent in \nthe maximization of the coercivity without using additional Dy. A correlation between  the coercivity \nand the grain size was discussed by Mager  in 1952 [24]. Systematic studies show  a decrease of the \ncoercivity with growing grain size within the range of the final grain size of 3.8  to 7.6  μm (Table 1 2): \nTable 12: Coercivity dependence on grain size [ 25] \nGrain s ize before \nsintering (μm) Final g rain \nsize (μm)  Hcj (20°C)  \nkA/m  Hcj (100°C)  \n kA/m  \n1.9 3.8 1178  581 \n2.2 4.3 1162  573 \n2.6 4.9 1090  525 \n3.0 6.0 971 462 \n3.5 7.6 883 414 \nThe exper imental data can be fitted with \n 0.44(20 C) final_grain_size .cjH  The grain size grows \nduring sintering  according to\nntktR/1)( . \nThe pa rameter n depends  on the material. For  pure metals we find n = 2–4. In sintered \nNd 2Fe14B the gra in growth rate depends on the B concentration. It is about n = 16–20 for B \nconcentrations below 5.7 at.  % and  decreases  to n = 7.5 for B concentrations above 5.7 at.  %. Also the \nRE-rich constituents have an impact on the grain growth rate. For magnets with RE-rich constituents \n< 4 wt. % we have n = 30–40. For higher fractions of RE -rich constituents n decrea ses to n = 10 [26]. \nThe sintering time has to be adjusted appropriately, to get an optimum grain size of 3 –5 μm and to \navoid giant grain growth. Usually, the grain size is measured according to the standard methods as \ndefined in ASTEM E112.  Another figure of merit during  sintering is the number of corners per grain (looking in the easy \naxis direction). Owing  to the crystal struct ure of Nd 2Fe14B six corners indicate an unper turbed crystal \nstructure. Hence  the number of six -corner grains should be maximized  [26].  \nThe coerc ivity depends also on the alignment factor fφ. With increasing fφ the remanence grows \nbut the coercivity diminish es (Fig. 17) [20].  \n \nFig. 17: Remanence and coercivity versus alignment factor  [20] \nThe coercivity is a function of the direction of the  applied external field [ 27]. It increases with \nthe angle between the field and the easy axis . For angles smaller than 45° the dependence is roughly \ndescribed by  \n1.cos( )cjH\n \nIn certain cases this enhanced coercivity can be used in a magnetic design.  \n9 Observation of mag netic domains  \nAn effective  development of magnetic materials is based on detailed microscopic information of the \nmaterial. A large variety of techniques is  used for the observation of magnetic domains. In the \nfollowing we can give only a brief overview  of the most common methods and a few new methods . \nFor more details we refer to the book by Schaefer (see bibliography) . \nBitter elaborated a simple procedure to visualize magnetic domain boundaries by strewing  \nferromagnetic powder onto a magnetic surface . The ferromagnetic particles mo ve to the areas of \nstrong field gradients which are equivalent to the domain boundaries. The pictures are called Bitter \npatterns . Today, ferrofluids are used which are colloidal suspensions containing small ferromagnetic \nparticles of the size of a few tens of nano metres . The reso lution of this method is 100  nm. It is \nrestricted to stationary measurements . \nFast processes can be studied  by making use of various magneto -optical effects. All magneto -\noptical effects are described with a generalized permittivity tensor. For a cu bic crystal it has the form  \n\n\n\n\n\n\n\n\n\n\n2\n31 32 2 31232 22\n21 212312 2122\n11\n1 21 32 3\n111\nmB mmB mmBmmB mB mmBmmB mmB mB\nmiQ miQmiQ miQmiQ miQ\nv vv vv V\n \nSimilarly, a magnetic permeability tensor can be set up. The matrix elements, however, are two orders \nof magnitude smaller and are usually neglected. Inserting this tensor in the Fresnel e quations , all of \nthe magneto-optical effects can be described  quantitatively . In magneto -optical spectroscopy a  \nmagnetic sample is irradiat ed with linear ly polarized light. The rotation of the polarization vector in \ntransmission geometry is called the Fara day effect and the rotation in reflection geometry is called the \nKerr effect. The linear polari zed light introduces vibrations of the charged particles  in the sample . In \nthe presence of a magnetic field the moving charges experience a Lorentz force. The mo dified \nvibration introduces perpendicular electric field components in the reflected or transmitted beam.  \nFigure 1 8 shows the geometries of all magneto -optical effects.  \n \nFig. 18: Magneto-optical effects.  From left to right: (i) Polar magnetization, in pla ne polarization: \nclockwise rotation of polarization in reflection and transmission.  (ii) Longitudinal \nmagnetization, in plane  polarization : anticlock wise rotation of polarization in reflection and \ntransmission. (iii) Longitudinal magnetization, polarizatio n perpendicular to p lane of \nincidence: clockwise rotation of polarization in reflection and anticlock wise rota tion in \ntransmission. (iv) Transverse magnetization, in plane polarization : in reflection no rotation \nbut amplitude variation, no effect in transm ission.  \nAll these  methods are not element specific. With the development of synchrotron radiation light \nsources the element specific investigation of magnetic samples in the soft X -ray regime  has evolved to \na large research field  where the 2p–3d transitio ns of Fe, Co, Ni and the 3d –4f transitions of the rare \nearth metals  are of particular interest . The s amples are irradiated with circular polarized photons as \nproduced by circular undulators in a storage ring. The d ifferent absorption coefficient  of right a nd left \ncircular po larized light is used to identify the magnetic domains  (XMCD: X -ray Magnetic Circular \nDichroism) . Photoelectrons emitted by the sample can be used i n a photoelectron micro scope (PEEM) \nto visualize  the local distribution of the domains ( Fig. 19). It has to be emphasized that this type of \nexperiment goes far beyond the usual Kerr  effect measurement  with visible light since the \ninvestigation of layered magnetic samples requires tuneable monochromatic light of variable \npolarization in the sof t X-ray regime which is only available at modern synchrotron radiation light \nsources.    \nFig. 19:  Measurement of  a system consisting of a Co layer on a Ni substrate separated by a wedged \nCu layer making use of a photoelectron microscope at BESSY II.  Here  the exchange \ncoupling between the Co and the Ni layer is studied in dependence of the thickness of the \nnonmagnetic Cu layer.  At large dista nces the Ni atom s orient verti cally, at small distances \nthe Ni atoms tilt in the direction of the Co magnetic moment s [28].  \nMagnetic  domains can be imaged also with a soft X-ray hologr aphic technique . A pinhole in \nthe radiation cone of a circular ly polarizing undulator prepares  a coherent photon beam  which \nilluminates the sample.  Simultaneously, a small pinhole (100 –350 nm) is irradiated with the same \nbeam. Both transmitted beams are superimposed on a CCD camera. With  the geometry of the \nreference pinhole known, the hologram can be inverted yielding the real structure of the magnetic \ndomains of the sample [ 29]. No lense s, mirrors or zone plates are needed for this technique  thus \nstress ing the potential of this method . So far, a resolution of 50  nm h as been demonstrated ( Fig. 20). \n \nFig. 20: Soft-X-ray holography using the circular ly polarized undulator radiation . The mag netic \nsample is irradiated with right - and left -handed circular polarized light and the varying \nabsorption strength depicts the orientation  of the magnetization  [29]. \nThe bulk of thick magnetic samples can not be studied with photon beams on account of  the \nlimited penetration depth. Neutrons penetrate thick samples in the centimetre  range. Neutron \ndecoherence imaging is suited to detect magnetic domains  of such samples [30].  The neutrons of a \nnuclear reactor hit a source grating.  Each slit of the grating represents a coherent line source whereas \nthe different line sources are mutually incoherent.  A proper choice of the grating line density \nprovides a coherent superposition of the fringes of all line sources in the image plane.   After a few \nmetres  of free propagation the neutrons are scattere d at the magnetic domains of a sample .  A phase grating behind the sample imprints a periodic phase modulation onto the wavefront. During further \npropagation the phase modulation transforms into a density modulation (Ta lbot imaging) which can \nbe detected with a sliding detection grating in front of a detector. An undistorted neutron beam \nproduces a periodic intensity modulation. The modulation amplitude decreases for a distorted beam \nand gives information on the scatteri ng process (Fig. 21). The resolution demonstrated so far is  50 –\n100 μm. \n \nFig. 21: Neutron decoherence imaging  [30] \nIn plane magnetic domains thin layers can be detected with a transmission electron microscope \nacting as a Lorentz force microscope. Several 100 MeV electrons hit the magnetic film with \nmagnetization vectors o riented perpendicular to the electron beam. The Lorentz force deflect s the \nelectrons and from their distribution behind the sample the magnetic domains can be reconstructed \n(Fig. 22). The resolution of this method is 10  nm. If the domains are oriented perp endicular to the film \nthe sample has to be tilted to produce a deflection of the electrons. The resolution is reduced in these \ncases.  \n \nFig. 22: Lorentz force  microscope . For other domain geometries a tilting of the sample may be necessary  \n10 Simulation meth ods for permanent magnet devices   \nThere are many codes on the market which solve Maxwell’s equation s in the presence of permanent \nmagnets and current carrying wires , e.g., Refs.  [31, 32]. In the following we concentrate on an \nalgorithm which is very effici ent for pure permanent magnet structures but also applicable to \ngeometries i ncluding iron though it is significantly slower in these cases. The algorithm is widely \nused for the design of undulators and wigglers. Th e algorithm is implemen ted in the code RAD IA [33, \n34] which is freely available from the ESRF [35]. 10.1 3D fields  \nMagnetic fields of pure permanent magnet structures can be simulated with an accuracy of a few per \ncent using the current sheet or charge sheet equivalent model (CSEM). These method s assum e a \npermeability of one , hence  the fields of individual blocks can be linearly superimposed. A magnet \nblock is represented by current sheet s at the magnet surfaces parallel to the easy axis or charge sheets \nat the surface perpendicular to the easy axis. Th e current sheets or charge sheets are assumed to be \ninfinitely thin ( Fig. 23). \n \nFig. 2 3: Charge sheet (left) and current sheet (right) equivalent method  \nThe magnetic induction of a current carrying wire is evaluated from the equation of  Biot–\nSavart : \n0\n0 3\n0' 1( ) .\n'rrB r Idlc rr\n\n \nIn analogy in the current sheet equivalent method the magnetic induction is derived  via integration \nover the surface current density\nnM jM\n : \n00\n0 33\n00''( ) ( ') ' ' .\n''M\nsurfacer r r r jB r M r dV dSc r r r r    \n \n \nFollowing the charge sheet equivalent model a scalar pot ential is established by integrating over the \nsurface charge density \n)'('rMnM  at the pole faces.  The derivative of the scalar potential yields  \nthe magnetic field.  \n0\n00\n00' ' ( ')( ) '''\n( ) grad( ( ))M\nsurfacedS Mrr dVr r r r\nH r r   \n  \n \nFor rectangular blocks and a homoge neous magnetizatio n the integration  can be done analytically.  In \nthis specific case t he magnetic induction is given by  \n \n2/ ),( ),( ),(lnarctan )1()( )(\n),( 0 0 0 2,1 2,1 2,12\n1)1(2 2 22\n12 2 210 0\nzyx c c cijkk j i k xyijk\nk j i ikj kji\nxx\nw zyx zyx zyxz y x z Qz y xxzyQMrQ rB\nkji\n  \n\n\n \n\n\n\n\n\n\n\n and similar for the other Qij. The parameter s xc, yc, zc define the cent re of the magnet, wx, wy, wz are the  \nmagnet dimensions , and x0, y0, z0 are the coordinates of the observation point.  \nSimilarly, the magnetic induction B and the field integral of an y (plane) p olygon  can be \nevaluated [ 33, 34]. Based on these expressions the magnetic induction and field integrals of an \narbitrary po lyhedron can be evaluated:  \n'\n'' ')()( )(\n3\n00\n00 0\nrd\nrrn rrrQMrQ rB\nsurfacesurface\n\n\n \n \n'\n'' '2),(),( ) ( ),(\n2\n00\n00 0 0\nrd\nvrrn vvrrvrGMvrGdlvrB vrI\nsurfacesurface\n \n\n\n\n \nQ and G are 3  × 3 matrices describing the geometric shape of the magnetic cell,  \ndenotes a dyadic \nproduct  and \nis the integration directi on. These equations are based on the assumption of a \npermeability of μ = 1. Fields evaluated under this assumption are a few per cent  higher than in reality. \nA higher accuracy is achieved with a  realistic susceptibility\n0  with \n1 . The permeability \nof RE  based permanent magnets is higher than one and it is different when parallel to or  \nperpendicular to the easy axis. Typical values are μpar = 1.06, μperp = 1.17. The values depend slightly \non the fabrication procedure  and the magnet grade. For example μpar = 1.05 for axially pressed  and \nμpar =1.03 for isostatic pressed magnets. μpar shows no correlation with coercivity whereas μperp \ndecreases with increasing coercivity ( 1.17 for Hcj = 18 kOe and 1.12 for Hcj = 32 kOe [ 27]). \nTo include a realistic permeability , iterative simulation strategies  must be employed . The \nmagnet configuration h as to be segmented into individual cells where the cell size depends on the \ndesired accuracy. Then, the ge ometry factors Q and G for the cells are evaluated . In a first run the \nmagnetic induction and magnetic field Hi at the centr e of each cell  is evaluated assuming a \nmagnetization of M0 = M(Hi = 0) in each cell. In the following iterations the parallel and perpendicular \nmagnetization is co rrected and new values for the magnetic induction and magnetic field are derived:  \nperpi perp perpipari par r parii i ii ii kN\nikkik i\nH MH B MM B HMQ M Q B\n  \n\n)1 ()1 (4141,\n   \n . \nA linear dependence of the magnetization on the magnetic field is assumed : \nperp perp perp perppar par r par par\nH H MH M H M\n\n\n) () (\n . \nFor reverse fields H approaching  Hcj the magnet ization does not change linear ly anymore with \nH and irreversible losses may occur. These cases  can be simulated with a non -linear  approach for the magnetization  which includes also the temperature  [36]. The t emperature depende nce of Mr, Hcj and \nχperp can be parametriz ed as  \n...)) ( ) ( 1()( )(...)) ( ) ( 1()( )(...)) ( ) ( 1()( )(\n2\n0 2 0 1 02\n0 2 0 1 02\n0 2 0 1 0\n \nTTa TTa T TTTb TTb TH THTTa TTa TM TM\nperp perpcj cjr r\n \n \nwhere ai and bi are extracted from the d ata sheet of the magnet supplier . The non -linear behaviour of \nthe magnetization for a given temperature T is expressed by  \n\n\n\n\n 3\n1))( ( tanh )( ),(\nicj\nsii\nsi THHMM T THM\n . \nMsi, χi are der ived from a fi t of the M(H) curve from the magnet supplier at T = T0 and α(T) is \ndetermined from  \n)( ),0 ( TM T HMr\n . \nThis model has been tested at a real undulator structure and excellent agreement between simulation \nand measurement has been found [36]. \nIt is worth noting that the operation of a permanent magnet in the third quadrant ( still above the \nknee) does not imply  that the magnet does not contribute to the field.  \n10.2 Complex notation of 2D field \nThe magnet geometry can be approximated with a two -dimensional model if the magnet is long \ncompared to the end sections . Then, it is convenient to express t he magnetic induction in complex \nnotation:  \n0\n0 0 0 00*)(\niy x\ner iyx ziB B zB\n\n\n . \nThe complex conjugate\n*B  is used instead of \nB  because \n*B  is an analytic function whereas \nB  is not. \nExtremely useful tools for a magnet field optimization such as conformal  mapping can be applied in \nthis case (see next section ). In complex notation the fi eld of a current flow ing into the plane is given \nby \ndydxzzja zBz\n00*)(\n . \nAny iron -free permanent magnet distribution can be expressed as [37]: \n*\n0 2\n0( ) ,\n()\n.r\nr rx ryBB z b dx dy\nzz\nB B iB  \n\n\n \nThis equation expresses  an important rule: If the easy axis vector of all magnet s of a complex two-\ndimensional configuration is  rotated by the same angle (+φ) this adds a factor of eiφ on the right -hand \nside. In consequence, the total field vector at a given point rotates by (–φ): This behaviour is known \nas the easy axis rotation theorem .  Any source -free two -dimensional field distribution can be expanded in terms of multipoles. \nUsing the complex notation  we have a compact form with an and bn being the regular  and skew \nmultipoles.  \n1\n1*) ( )(\nn\nnn n ziba zB \n . \n10.3 Conformal mapping  \nThe technique of conformal mapping can be extremely useful in solving Maxwell’s equations in  \ncomplicated 2D -magnet arrangements [38–40]. Using a conformal map t he complete configuration is \ntransformed to a simpler geometry where Maxwell’s equations are solved. Then, the  results are \ntransformed back to the old variables. One might argue that the techn ique of conformal mapping is no \nlonger  necessary when  high performance multiprocessor computers are cheap and available \neverywhere. This is, however, only half the truth. For  many problems the solution in transformed \ngeometry provides higher accuracy for less effort, and , even more important, the conformal mapping \ntechnique provides  a deeper insight into the properties of magnet systems . This understanding helps in  \na fast and efficient design.  \nConformal  maps  preserve both  angles and shapes of infinitesimal  small figures, whereas the \nsize of the se figures usually  change s. The intersection angle between any two curves in the original \nand the transformed geometry is identical.  \nAny analytic function represents a conformal map in the regions of non -zero derivatives.  Let \n)(zwF\n be a complex function with   \n),( ),( yxivyxuw   where u and v are real functions. F is \nanalytic if and only if the Cauchy –Riemann  (C–R) relations are fulfilled:  \nyu\nxvyv\nxu\n\n \nu and v also obey the Laplace equation  which is proven by differentiating the C –R equations : \n00\n22\n2222\n22\n\nyv\nxvyu\nxu\n \nWithin a source -free region (no currents , no magnetic charges) the complex magnetic field strength \ny xiH H H*\n satisfies the C –R relations which are identical to Maxwell’s equations in two \ndimensions. \n*H is an analytic function  and an integration yields the complex potential F: \nzFizHyxiVyxAF\n\n\n)(),( ),(\n*\n \nV(x,y)  is the  scalar potential and A(x,y)  the z component of the vector potential  in the usual sense , \nwhere Ay and Ax can be set to zero without lo sing generality (2 -dimensional fields).  As an example we \nwill derive the conformal map  that transforms a multipole into di pole geometry : For F being the \ncomplex potential of \n*H  we have  zwwHzw\nwFizFizH \n\n\n )( )(* * . \nThe field strength of an ideal regular octupole is given by  \n3 *)( zozH\n  whereas a dipole is \ndescribed by\n*( ) const.Hw\n  Thus  we have \n3' / constw o z\n  and the conformal map that transforms \nthe octupole to  dipole geometry is  given by\n4( ) ( ) / (4 const).w z o z  \n  \n11 Permanent magnet multipoles  \nAccelerators are built of d ipole  magnet s for the deflection of the relativistic particles, q uadrupoles  for \na strong focusing  of the electron be am, and sextupoles and higher or der multipoles which cope  with \nnon-linear effects. Usually, the magnets are constructed as electromagnets since they provide \nflexibility in terms of the machine parameters. There are, however, cases where the flexibility is not \nneeded and permanent magnets are the better choice. In the previous section  we presented the fields \nof ideal multipoles.  Now, we will discuss the layout of permanent magnet multipoles.   \n11.1 Fixed-strength multipoles  \nHalbach proposed segmented permanent magnet multipoles which approximate ideal multipoles to an \naccuracy limited by the number of magnets M to be used per period [ 37]:  \n)/ ln( 11/)/ sin()/(cos11)(\n1 2\n11\n2101\n211\n1*\nrrrr\nnnM NnMnM nM KKrr\nnn\nrzB zB\nnnn\nnnn n\nr\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n . \nHere, N is the order of the  multipole ( N = 1: dipo le, N = 2: quadrupole etc .), v is the harmonic where \nv = 0 is the fundamental, r1 and r2 are the inner and outer radius, and ε  is the stacking factor. \nΑ = (N + 1)2π/M  is the relative angle  of the easy ax es of neighbouring magnet segments.  A few \nexamples a re given in Fig. 24. \n \nFig. 24: Halbach -type multipoles. F rom left to right: 1: N = 0, at the centr e of the disk the field is \nzero according to the easy axis rotation theorem.  2: Dipole ( N = 1, M = 6). 3: Quadrupole \n(N = 2, M = 4).  4: Sextupole ( N = 3, M = 3). Halbach -type permanent magnet quadrupoles ( M = 6) with gradients of 500 T/mm in a 6  mm, 20 mm \ninner/ outer diam eter have been built [ 41, 42]. The higher order content of the quadrupoles could be \nsignificantly reduced by adjusting the individual magnet  segments. Halbach multipoles can be \nimproved with respect to the peak field when a fraction of the permanent magnets at the pole tips is \nreplaced with soft iron ( Fig. 25). A field gradient of 300 T/mm in a 14  mm inner diameter has been \nrealized [ 43].  \n \n \nFig. 25: Left: Modified Halbach dipole w ith iron pole tips. Right: Modified Halbach quadrupole \n(300 T/m m in the 14 /100 mm inner/ outer diameter ) [43].  \n11.2 Variable strength m ultipoles  \nPermanent magnet quadrupoles are needed if the geometric constraints do not permit the use of bulky \nelectromagnets such as at the final focus section of the ILC. The quadrupoles have to be placed close \nto the interaction point but must not block the other beam. A certain tuning range of the focusing  \nstrength is desirable which req uires a specific design. Gluckstern proposed a continuously adjustable \nquadrupole consisting of five individual discs, each of them individually  rotatable [44]. The linear \neffect of a rotated quadruple is given by a symplectic 4  × 4 matrix with  \n\n\n\n\n\n001 00001100 0010 0\nM MT\n \nThe off -diagonal elements characterize the coupling between the horizontal and vertical plane. With \nfive individual discs with three rotation angles α and three quadruple strength q (thicknesses) the \ncoupling can be compensated and an arbitra ry focusing  can be realized: disc 1: α1, q1;  disc 2: α2, q2;  \ndisc 3: α3, q3; disc 4:  α2, q2;  disc 5: α1, q1  (Gluckstern singlet , Fig. 26, left ). Prototypes with \ninner/ outer diameter s of 12/ 36 mm, respectively,  and a gradient of 140 T/m have been built  [45, 46]. \nAnother design is the binary stepwise permanent magnet quadrupole [ 47] consisting of two \nlayers of quadrupoles. The inner quadrupole is fixed in strength. The outer quadrupole is made of a \nseries of rings with relative thicknesses of powers of t wo. Thus, a discrete (bitwise) adjustment is \npossible via rotating specific rings by m ultiples of π/2. The resolution is limited by the strength of the \nthinnest ring  (Fig. 26, right ).  \n  \nFig. 26: Gluckstern singlet for continuous adjustment of quadrupole strength (left)  [44] and \nbinary step wise adjustable quadrupole (right)  [47] \n12 Permanent magnet u ndulators  and wigglers  \nUndulators and wigglers are period magnetic structures which force the electrons  on a sinusoidal \npath. High field wigglers are used for electron beam damping to achieve low emittance in ultimate \nstorage rings such as PETRA II I [48] or NSLS II [49]. The main purpose of these devices, however, is \nthe production of synchrotron radiation from the infrared to the hard X -ray region. First -generation \nsynchrotron radiation light sources were storage rings which were shared betwee n hig h-energy \nphysics and sync hrotron radiation users. Second -generation light sources were dedicated machines for \nthe synchrotron radiation us er community. Undulators and wigglers were still rarely used and bending \nmagnet s were the normal radiation sources . Third-generation synchrotron radiation light  sources a re \nexplicitly built for the use of undu lators and wigglers. The lattice s have a high symmetry with several \ntens of straight sections to adapt as many undulators or wigglers as possible.  \nThe brightness of photon beams as emitted by typical  storage ring undulators is three to four \norders of magnitude  higher than that of dipole radiation  (see Section  13). The photon energy is related \nto the undulator period length , and short -wavelength photons require short p eriods which can not be \nrealized with electromagnets. Usually, permanent magnet undulators are chosen.  \nIn 1973 Mallinson published a magnet design under the title: ‘One-sided fluxes - A magnetic \ncuriosity? ’. The article describes a linear array of magnets  where the easy axis orientation is rotated \nbetween succeeding mag nets. This array has a remarkable  characteristic : At one side a significant \namount of flux leaves the array where as much less flux is detected at  the opposite side. The high flux \nside is det ermined by the sense of rotation of the magnetization . \nHalbach recognized the potential  of this effect. He combined two of these arrays facing the \nhigh flux sides to each other. This array is called a pu re permanent magnet undulator or Halbach I \nundulator  [50] (Fig. 27).  M=4 g xy \nFig. 2 7: Pure permanent magnet undulator (Halbach  I) \nThe two -dimensional field of such an array can be expressed analytically:  \n002/ *\n/21/)/ sin() 1( ) cos( 2)(\n\n\n \n \nkM nyixzMnM ne eznk BizBnkL nkg\nr\n \n \nHere λ0 is the period length, ε is the filling factor, g is the distance of the arrays  (magnetic gap), M is \nthe number of magnets per period , and n is the field harmonic. Note  that the higher order field \nharmonic content is related to M. In most cases , four magne ts per period are used. A larger  M \nenhances the field only by a few per cent . Higher fields can be produced with hybrid undulators , so-\ncalled Halbach II devices [51],  where soft iron material is used to  concentrate the flux ( Fig. 28). For \nhigh performance applications the iron poles can be replaced by CoFe pieces with a saturation \nmagnetization of 2.4 T to boost the peak magnetic field further.  \ng\n \nFig. 2 8: Hybrid undulator (Halbach II)  \nThere is no analytic  field expression for a hybrid undulator and the field has to be parametrized \nbased on numerical field simulations : \n\n\n\n\n\n\n\n2\n0 0expgcgb a By\n . \nFor a hybrid undulator Elleaume derives the parameters a = 3.69, b = 5.07, c = 1.52 [ 52]. Parameters \nfor other undulator designs are also presente d in Ref. [52]. 13 Spectral properties of undulators and w igglers  \n13.1 Ideal s ources  \nThe spectral properties  of undulators and wigglers are described only briefly. For details we refer you \nto the books and CAS  proceedings listed in the bibliography. The electromagnetic properties of \nrelativistic particles are given by the Lienard –Wiechert potentials which are th e solution of the \ninhomogeneous Maxwell equations  (Gauss ian units) : \nretret\nRnetxARnetx\n\n\n\n\n\n\n\n) 1(),() 1(),(\n\n\n\n \n)(rett\nis the particle trajectory at the retarded time\n( ) / ,ret rett t R t c  \n)(rettn is the vector pointing \nfrom the particle to the  observer , and \n)(rettR is the distance between the particle and the observer.  \nThe acceleration and velocity terms of the electric field are derived from these potentials and the \npointing vector\nS describes the emitted pow er: \n \n   \n\nBEcSEnBn R netEn R n ncet E\nretretvelretacc\n   \n\n\n\n\n  \n4) 1( ) ( )() 1( ) ( )(\n3 2 23\n \n\nis the Lorentz factor. A Fourier transform and a far field approximation deliver  the spectral content \nof the radiation:  \n2\n) ( 2\n22 2\n) 1( ) (4\n\n\n dt en n nce Irnti\n \nIn a vertical dipole field a charged particle describes a hor izontal circle with a radius ρ. The radiation \nis giv en by the analytic expression  \n   \n)2/()3(/))(1(2)( ))(1()( )( ))(1(43\n32/322\n3/12 2 2\n3/222 22\n22 2\n    \ncyyK K yce I\nccy\n   \n \nThe first and the second part in rectangular brackets describe  the contributions from the horizontal \nand vertical electric field component, respective ly. In plane the radiation is horizontally polarized. Off \nplane a circular component shows up which is opposite  in sign  above and below the midplane.  Wigglers  and undulators are periodic magnetic structures where the particles employ an \noscillating trajec tory. The devices are characterized by the undulator parameter\n0 04.93 B K   \nwhere \n0  and \n0B  are the period length and the maximum field, respectively. Devices with K >> 1 are \ncalled wigglers. The  emitted radiation can be evaluated as a sum of dipole spectra emitted at each \nindividual pole. In undulators the K parameter and hence  amplitudes of the oscillation are smaller and \nthe radiation beams emitted at each of the poles  overlap coherently.  In planar undu lators constructive \ninterference is observed at the odd harmonics ( n = 1, 3, 5…):  \n 22 2\n202/ 12  Knn\n \nNeglecting end pole effects, the undulator radiation in the far field close to the harmonics can be \napproximated with  \n \n )(/ sin)(/ sin),,,(\n12 212 2 22 2\n\n  \nNNKKFcNe I\ny x n\n \nwhere F is an infinite sum over Bessel functions.  \n13.2 Real s ources  \nWigglers have a low brightness and today they are used only for the production of high -energy \nphotons which are not accessible with undulators. Wigglers are insensitive to field errors since the \ndipole  spectra are spatially and spectrally broad and coherence effects can be ignored . \nIn contrast , undulators  are based on a coherent overlap of the radiation contributions from the \nwhole undulator. The spectral performance of an undulator is characterized by the phase error which \ndescribes the jitter in time between the electron beam and the emitted light:  \n' ' ' '\n22\n0 0 0 0 0 022'' '' ' 0.5 '' '' '\n( ) ( )z z z z z z\nfit res res res\ny y y yB dz B dz dz B dz B dz dz\nBB\n                  \n        \n . \nField errors produce p hase errors which reduce the on -axis flux density of the odd harmonics \napproximately by \n 2 2 2 2/ ) exp( )) exp(1( M M M R      where M is the number of poles  \n[53]. Though the magnet quality of commercially available blocks has improved a lot during the last \nfew years , it is still impossible to build high-quality permanent magnet undulator s without applying \nspecific techniques such as magnet sorting and undulator shimming  (see Section  15). Phase errors \nbelow  2° can be achieved for devices with up to 100 periods. This limits the brightness reduction in \nthe 15th harmonic  to values well below 20% . Thus  magnet field errors can be efficiently compensated \nand today the spectral performance of an undulator is only limited  by the electron beam parameters , \nemittance , and energy spread . \n14 Undulator  and w iggler designs  \nThere is a large variety of undu lator and wiggler designs optimized for sp ecific  purposes . The device \nparameters can be grouped in four categories: tuning range, polarization, spectral purity, and on -axis-\npower density.  \n14.1 Tuning r ange: out-of-vacuum versus in -vacuum devices  \nIn-vacuum undulators  permit smaller period lengths than c onventional devices for a fixed  vertical \nvacuum aperture and K parameter  and, t herefore , they provide higher photon energies . Planar in-vacuum devices rely on a mature technology and today many in -vacuum undulators are in operation \nall over the world [54]. \nAs already mentioned , the negative temperature coefficients of the remanence and the \ncoercivity of Nd 2Fe14B favour an operation at lower temperatures. Between 300  K and 150  K the \nremanence increases by 16%. The coercivity grows even more and thus another magnet grade with \nhigher remanence and less coercivity can be used since the magnets gain stability at low er \ntemperatures. Tanaka et al. proposed a cryogenic undulator to be operated at 150  K [55, 56]. \nMeanwhile, a cryogenic undulator is in operation at th e ESRF [ 57–60], a 2  m device to be installed at \nthe PSI [ 61] has been built at SPRING -8, and more devices are under consideration.  \nAt 150  K Nd 2Fe14B features  a spin reo rientation [62, 63] and the remanence decreases below \nthis temperature.  By replacing  the Nd2Fe14B magnets with Pr-Fe-B magnets even lower temperatures \ncan be used [ 55]. Temperatures below 80  K are of particular interest because textured dysprosium can \nbe used as pole material which has an even higher saturation magnetization than CoFe. Furth ermore, \nthe temperature sensitivity of the magnetic performance decreases at lower temperatures. Recently , \nVAC in collaboration with Helmholtz -Zentrum Berlin (HZB) and Ludwig -Maximilian -Universitaet \nMuenchen (LMU) developed a new (Pr,Nd) 2Fe14B grade with a n energy product of 65.3 MGOe at \n85 K [64] (Fig. 29). A (Pr,Nd) 2Fe14B based undulator is currently  under construction at HZB [65] and \na short prototype Pr-Fe-B undulator has been measured recen tly in a vertical bath cryostat  at the \nNSLS [ 66]. Tanaka et al.  proposed to place passive high temperature superconducting loop s around \nthe pole tips of a cryogenic undulator. Closing the gap to 0  mm at a high temperature, cooling down \nand opening the gap again  to the operation gap induces permanent current s in the lo ops which \nenhance  the peak field further [ 67]. \n \nFig. 29: Performance of (Pr,Nd) 2Fe14B material [ 64] \n14.2 Variable p olarization  \nThe first wiggler for the production of linearly and elliptically polarized light, an asym metric wiggler,  \nwas proposed in 1987 [68]. Positive and negative poles have different field amplitudes  where the field \nintegrals are compensated to zero. In the energy regime above the cut -off frequency of the weaker \npoles circularly polarized light is observed off plane just as in a bending magnet . The brightness of \nsuch sources is low due to the depth -of-field effect  which increases with the angle of observation. \nHowever, high  photon energies can be reached  which are inaccessible with  undulators.  Asymmetric \nwigglers are being operated at seve ral facilities [69 –72]. At the ESRF an asymmetric wiggler with a \npeak field exceeding 3 T is in operat ion [73]. \nThe brightness  of an elliptical wiggler is significantly higher than that of  an asymmetric \nwiggler since the on -axis beam is used [74 ]. Elliptical wi gglers consist of individual magnet arrays for the horizontal and vertical magnetic fields where one of the field components is significantly larger \nthan the other one. The electrons move on an elliptical trajectory producing elliptically polarized light \non-axis. The helicity can be switched by  moving one of the arrays longitudinally. Elliptical wigglers \nwith variable helicity have been installed at the accumulator ring of the TRISTAN ring, at the Photon \nFactory [75, 76], and at SPRING -8 [77, 78]. \nIn third -generation storage rings helical undulators are favour ed on account of  their higher \ndegree of circular polarization and the higher brightness. Various helical undulator designs have been \ndeveloped  and implemented . The APPLE II design [79 ] provides the high est fields among all helical \nundulators and APPLE II undulators have become the work -horse in many light sources. The magnet \narrays are split longitudinally and the individual magnet rows can be moved independently. In the \nelliptical mode (shifting two row s in the same direction) the horizontal and vertical fields are 90° out \nof phase whereas in the inclined mode (shifting two rows in opposite direction) they are in phase \nproducing linearly polarized light at arbitrary angles. By m oving three rows , any stat e of polarization \ncan be produced and with an appropriate undulator setting polarizing effects of the be amline optical \ncomponents in particular below 100  eV can be compensated [ 80, 81]. \nIn the ESRF design [82 ] vertical and horizontal fields are produced by  the upper and lower \nmagnet girder , respectively. A ny state of polarization can be realized  and the good field region is \nlarge . However, the fields are lower than those of  an APPLE II, the two beams have to be moved \nindividually and the  electron beam is st eered vertically . The ELETTRA design [ 83] allows for a \ncombined movement of both beams with one motor. This undulator provides only circularly polarized \nlight (independent o f gap setting) , the fields are lower than in an APPLE II and the good field region \nis small. The SPRING -8 design [ 84] employs three magnet rows, the central one producing vertical \nfields and the side rows the horizontal fields. The good field region is large but the field levels are \neven lower than in the other designs.  \n14.3 Spectral purity: undulator periodicity  \nUsually, undulators have a periodic structure to achieve highest brightness at the fundamental and at \nhigher harmonics . In the low -energy regime  higher undulator harmonics may spoil the spectrum \nbecause they are efficiently  transmitte d through the monochromator together with the first  harmonic . \nHelical devices produce only the first harmonic and higher harmonics are suppressed with the use of \nan appropriate pinhole . If the higher harmonics are needed and the spectral purity is essentia l, quasi -\nperiodic structure s as proposed by Sasaki et al. can help. The quasiperiodicity zm is derived from the \nprojection of the grid points of a quadratic [85, 86] or rectangular lattice [87 ] with a grid parameter \nratio of r onto a tilted straight line w ith a tilt angle =  α: \ntan( )( tan( ) 1) 1 .tan( ) tan( )mdZ m r mrr           \n \nIn the first design (Halbach I undulator  with M = 2) the quasiperiodicity was realized with two \ndifferent air gaps between the poles [ 88]. In a Halbach I M = 4 design t he quasiperiodicity can also be \nintroduced by completely rem oving longitudinally magnetized blocks, replacing these blocks with \nblocks of a reduced height [89, 90] or by retracting them [ 91]. Specific higher harmonics ca n be \nmaximized with an appropri ate choice of the amount of magnet retraction or height  reduction . A \nsuccessful suppression o f higher harmonics has been demo nstrated by measurements [ 92, 93]. A \nquasiperiodic hybrid undulator (Halbach II) has been installed at BESSY II [94]. The quasiperiodic \nscheme has also been applied to an electromagnet ic undulator  [95].  \n14.4 On-axis power d ensity  \nAll helic al undulators have a reduced on -axis power density. This is a comfortable side effect, though  \nthese rather expensive devices are built for another purpose. A device emitting linearly polarized light with a reduced on-axis power density i s the figure -eight un dulator [96 –99]. It consists of independent \nmagnet arrays for the horizontal and vertical fields, respectively. One array has half the period length \nof the other one. In this way the projected electron trajectory ha s the shape of an eight. Such devices \nhave been bui lt at SPRIN G-8 [100 –102] and at ELETTRA [ 103–105]. If an a symmetry is added to the \nfigure -eight motion of the electrons the right - and left -handed circularly polarized light components \nno longer  cancel and  elliptically  polarized light is emitted [106 –108]. \nIn 1990  Tatchyn [109] proposed a  variable -period undulator because of the  better performance \nas compared to a fixed -period undulator. If the photon wavelength could be tuned by changing the \nperiod length while keeping the un dulator parameter K constant (\n1K ), highest brightness could be \nachieved without producing too much un desirable  power in the higher harmonic s. A variable -period \nundulator based on the stagg ered pole design [110 ] was proposed at the APS [111] but it was not \nbuilt, finally, because of  the mechanical complexity , even though  the design has no permanent \nmagnets . A variable -period ppm -undulator would be even more complicated. For an electromagnetic \nundulator a period doubli ng by rewiring has  been  demonstrated [ 112] and a superconducting \nundulator with the potential of period tripling has been propose d [113].  \n15 Shimming c oncepts  for permanent magnet structures  \nToday’s permanent magnet quality (dipole errors and magnetization homogeneity) is sufficient for \nmost  applications. There are , however, products which need  a much better field performance and they \nrequire a sophisticated field tuning and optimization.  \n– Permanent magnet NMR spectrometers for medical applications require  field homogeneities in \nthe 10-6 regime which can be achieved only by shimming.  \n– A precise, smooth (low vibrations) and dynamic operation of a linear motor is essential for \nspecial applications. A homogeneous field quality can be achieved via magnet sorting.  \n– Sputtering facilities require a good field quality to provide homogeneous depositions. Magnet \nsorting and shimming help to reach the field accuracy.  \n– Permanent magnet based accelerator devices for third and next generation light sources such as \nmultipoles or undulators need a sophisticated magnet sorting and shimming prior to installation.  \nIn the following we concentrate on the shimming of undulators. The field optimization has to \nmeet two targets: i) the spectral properties must not be deteriorated by magnet field errors, ii) the \nmultipoles have to be sufficiently small to permit a transparent operation of the devices. The first goal \ncan easily be achieved with well elaborated techniques whereas the second one needs more effort, in \nparticular in the case of va riably polarizing devices.  \n15.1 Static m ultipoles  \nField errors of planar undulators are usually minimized (i.e., shimmed) with small soft iron sheets \nwhich are put on top of the magnets facing the electron beam. Trajectory errors are reduced with \nshims on trans versely  magnetized blocks whereas phase errors are minimized with shims on \nlongitudinally mag netized blocks [114 –117]. Another method developed by Pflueger varies the pole \nheight for trajectory strai ghtening [118 ]. \nConventional shim ming can not be applied in APPLE II undulators. Iron shims change their \nresponse when the magnet rows are phased and, furthermore, the air gap between the rows does not \npermit the application of conventional shims at the centre close to the electron beam. A combination \nof sever al techniques has to be applied to achieve a field quality comparable to planar devices. In the \nfollowing we describe the technique as applied to the BESSY II de vices [119 ]. Prior to assembly  the three dipole components are measured in an automated Helmholtz  coil \nsystem and  the magnet block inhmogeneities are measu red in a stretched wire set -up. Based on these \ndata the magnets are  sorted with a simulated annealing algorithm where the figure of merit is a \ncombination of the transverse field integral distributi on and the phase error. An excellent agreement \nbetween the pred iction of the field integrals based on single block measurements and Hall probe \nmeasurements of the com plete device is observed ( Fig. 30).  \n \nFig. 30 : Vertical (left) and horizontal (right) fie ld integrals of the BESSY II UE49 APPLE undulator at \nvarious transverse positions. Thin line s: prediction from single block measurements. Thick lines: \nHall probe scans of the complete device.  The periodic part has been removed for a better \nvisibility of th e errors.  \nThe pre -sorted and assembled st ructure is measured with a Hall probe , and trajectory and phase \nerrors are removed via virtual shimming [ 120]. Here, the magnet blocks are moved transvers ely in the \nhorizontal and vertical direction by up to 0.1  mm. Owing  to the finite susceptibility of the magnetic \nmaterial the field integrals change when phasing the magnet rows. This effect is minimized with iron \nshims which are placed on the vertically and longitudinally magnetized blocks. In the final step the \nphase independent field integrals are compensated with magic fingers at either end of the device. The  \nmagic fingers  are array s of small magnets with a cross -section of 4  × 4 mm2 and variable  thickness in \nthe longitudinal direction . The thicknesses are derive d from field integral measurements and the \nresponse functions of the magnets via a matrix inversion.    \n15.2 Dynamic m ultipoles  \nUndu lators feature  complicated three -dimensiona l magnetic fields which cause e -beam focusing  (so-\ncalled edge focusing ) and  higher ord er dynamic effects which can not be described in terms of two -\ndimensional multipoles (the straight line integrals are zero). They do not obey two -dimensional \nMaxwell ’s equation s and, sometimes, they are called pse udo-multipoles. The terms as derived in \nRef. [121] have the form  \ndzdzyxBdzB dzyxBdzBBy\nyx\nx yx\n\n  '/' '/')(1\n2 /\n \nwhich for an undulator structure reduces to \n\n yxBByxBBBL y\nyx\nx yx/ / )2()(20\n00\n0\n22\n0\n2 /\n . \nThe pseudo -multipoles scale quadratic ally with the period length, the maximum field , and the inverse \nof the energy. Choosing too-small a  pole width of a high field wiggler may result in beam dynamic \neffects which reduce the injection efficiency [ 122]. APPLE II undulators show strong horizontal field \ngradients , and hence  high pseudo -multipoles . In the elliptical mode the terms can be compensate d \npassively with L -shaped iron shims [ 123, 124]. In the inclined mode active compensa tion schemes \nhave to be adopted. The low electron energy of BESSY II (1.7 GeV) requires an active compensation \nof the pseudo -multiples of the UE112 APPLE II undulator (112  mm period length). Twenty -eight  flat \nwires are glued onto the vacuum chamber. They are powered individually and arbitrary transverse  \nfield integral distributions can be produced with a high accuracy [125, 126]. It is worth mentioning \nthat the wires produc e two-dimensional multipoles which , by principle , can not compensate the \npseudo -multipoles. The wires or L-shims  minimize the effects only in the midplane while adding non-\nlinear terms out of plane. Here, they  are less harmful if the vertical betatron func tion is smaller  than \nthe horizontal one . \n16 Next -generation light s ources  \nToday , many storage ring based third -generation light sources are in operation all over the world \nserving thousands of users every year. The fields of research include protein crystallo graphy  (aiming \nfor an understanding of the function of large biological relevant molecules  from its structure) ; \ninvestigation of magnetic materials  employing magnetic circular dichroism (MCD)  in the soft X -ray \nregime ; element -specific microscopy on the nanometre  scale;  time-dependent spectroscopy down to \nthe picosecond regime with low alpha optics ; non-destructive 3D investigation of matter with respect \nto the chemical composition, morphol ogy, internal stress and strain;  high-pressure study  of matter; \ninves tigation of electron cor relation phenomena such as high -temperature superconductivity; \narcheometry;  and many more topics.  \nIn storage  rings t ime-dependent studies can be extended down to the 100 –200 fs using the \nfemtosecond  slicing technique  [127]. A high -power infrared fs laser interacts with the electron bunch \nwithin an undulator (modulator) which is resonant to the laser . The energy of the particles in the \ninteraction region is modulated. In a dispersive sectio n the off -energy electrons are transvers ely \ndisplaced or deflected with respect to the unperturbed beam which permits a spatial separation of the \ntwo photon beams as produced in  the next undulator (radiator).  The polarization of the fs pulses is \ndefined by the radiator. Femto second slicing facilities  have been built at the ALS  [128, 129], at \nBESSY II [ 130–132], and at the SLS [ 133]. At the ALS and the SLS  the fs photon beam is linearly \npolarized whereas at BESSY II the polarization is variable (APPLE II).  \nThe next-generation light sources are free electron lasers (FEL). They provide a high peak \nbrightness, short pulses in the tens of fs regime , and longitudinal and transverse coherent light  beams . \nThese properties open new research  areas . Currently, t wo soft X -ray FELs are in operation. FLASH at \nDESY p rovides photons up to 200  eV [134] and the SPRING -8 Compact SASE Source (SCSS) test \naccelerator [135 ] delivers photons up to 50 eV. FLASH uses fixed -gap undulators (the energy has to \nbe tuned with the electron energy) whereas the SPRING -8 facility  operates  variable -gap in -vacuum \nundulators. In spring 2009 the first X -ray FEL, the Linac Coherent Light Source  (LCLS) , went into \noperation lasing at 0.15  nm [136]. The fixed -gap device has a transverse canting of the poles for a \nfine-tuning of the energy. Further  X-ray FELs are under construction or are planned at DESY [137 ], \nat the SPRING -8 site [138], and at PSI  [139]. These facilities will have several undulator beamlines \nwith typical lengths of 100  m each. The total length of the first three European X -FEL und ulator lines \nadds up to 555 m. The weight of the magnetic material of the three devices is 60  tonnes.  Another challenging  linac -based light source concept  is the energy recovery linac. A high-\nquality low -emittance beam as generated in an rf gun is injecte d into a circular machine an d serves \nmany users in parallel. Before the electron bunch is damped , which would be accompanied with \ngrowth of emittance and bunch length , it is recovered and replaced by a fresh bunch. E RLs provide a \nhigh averaged photon flux,  a low emittance with a round beam , and short pulses in the 200  fs regime.  \nApart from the Jefferson Lab ERL [ 140], the existing and planned soft X -ray ERLs have a pr ototype \ncharacter [141 –146]. They are operated for the development and investigation of rel evant \ntechnologies which are needed in X -ray ERLs. X -ray ERLs are planned at Cornell University [ 147], at \nthe APS [ 148], and at KEK JAEA [ 149–150].  \nThe new light sources  require  new und ulator concepts. The period length s of the undulators \ndetermine the el ectron energy and shorter period length s permit shorter linacs, which reduces the total \ncosts. Following this argument , in-vacuum undulators are planned at the SPRING -8 X-FEL and the \nPSI X-FEL. Circularly  polarizing devices covering the  regime up to 3  keV are under consideration. \nStudies on crossed undulators [151–153] predict a power which is o ne order of magnitude lower as \ncompared to an APPLE  II. The degree of polarization is only 80% whereas it is close to 100% for an \nAPPLE  II. Most challenging are vari able polarizing devices operated under ultra high vacuum \nconditions. T emnyk h built a 30  cm prototype of an in -vacuum Delta -magnet un dulator [154 ]. The \nfixed -gap, variable polarization device has a four -fold symmetry without any access from t he side. \nThis i s affordable in l inac-based machines which do not require side access for injection. For similar \ngap-to-period length ratios t he peak fields are comparable to the APPLE III design (Fig. 31) [155]. \n \nFig. 31: Field comparison of  a Delta undulator and an APP LE III  \nNew acceleration  concepts are used in so -called table-top FELs where electrons are accelerated \nup to the GeV regime within a l ength of a few centimetres  [156]. A high-power laser ionizes the \nhydrogen atoms in a region of about 30 μm generating extre mely high field gradients  which accelerate \nthe electrons . These devices are optimize d for small dimensions , and short -period permanent magnet \nundulators as well as permanent magnet quadrupoles are essential. The small vertical apertures \nrequire  magnets wit h high radiation stability. It is expected that in -vacuum undulators based on Pr -Fe-\nB material operated at low temperatures will play a key role in this field .     References  \n[1] Product leaflet of Vacuumschmelze  2007,  http://www.Vacuumschmelze.com  \n[2] Y. Luo, 20th Workshop on Rare Earth Permanent Magnets , Crete, Greece, 2008 . \n[3] Y. Kaneko,  18th Workshop on HPMA, Annecy, 2004.  \n[4] Y. Iwashita  et al. , Proc. of  the PAC, Portland, OR, USA (200 3) 2198 –2200.  \n[5] J. Osborn, Phys. Rev . 67 (1945) 351 –357. \n[6] A. Aharoni, J. Appl. Phys.  83 (1998) 3432 –343. \n[7] K. Bertsche et al., Proc of PAC , Dallas, TX, USA (1995) 1381 –1383.  \n[8] P. F. Tavares et al ., LNLS -2, Preliminary Conceptual Design Report, Campinas, Brazil, April \n2009 . \n[9] W. Rodewald  et al.,  Hage ner Symposium für Pulvermetallurgie, Band 18 (2002) 225–245. \n[10] Hitachi Metals Ltd., private communication, 2009.  \n[11] P. Colomp et al., Machine Technical Note 1 -1996/ID, 1996 . \n[12] M. Petra  et al., Nucl. Instrum.  Methods . Phys. Res. , A 507 (2003) 422 –425.  \n[13] S. Sasaki e t al., Proc. of the PAC, Knoxville, TN, USA, 2005, 4126 –4128.  \n[14] H. Delsim -Hashemi et al., Proc. of the PAC, Vancouver , BC, Canada (2009 ). \n[15] R. Qiu  et al., Nucl. Instrum. Methods  Phys. Res. , A 594 (2008)  111. \n[16] J. F. Herbst, Rev. Mod. Phys. 63  (1991)  819.  \n[17] T. Tan aka et al. , Rev. Sci. Instrum.  71 (2000) 3010 –3015.  \n[18] J. Chavanne, contribution to IMME 14, CERN, Geneva, Switzerland (2009).  \n[19] J. F. Herbst  et al., Annu. Rev. Mater. Sci. 16  (1986)  467.  \n[20] W. Rodewald  et al.,  IEEE Trans. Magn. 36 (2000) 3279 –3281.  \n[21] M. Zakotnik  et al., J. Iron Steel Res., International, 13 (2006) 289 –295. \n[22] M. Zakotnik  et al., J. Alloys Comp.  450 (2008) L1 –L3. \n[23] J. Cahn , J. App.  Phys.  34 (1963) 3581 –3586.  \n[24] A. Mager, Ann. Phys (Leipzig) , 446 (1952)  15–16. \n[25] K. Üstün er et al., IEEE Trans. Magn. 42 (2006) 2 897. \n[26] W. Rodewald  et al.,  IEEE, Trans. Magn. 39 (2003) 2932 –2934.  \n[27] M. Katter, IEEE Trans. Mag n. 41 (2005) 3853 –3855.  \n[28] W. Kuch et al., Phys. Rev. B  65 (2002) 0064406 . \n[29] S. Eisebitt et al ., Phys. Rev. B 68 (2003) 104419 . S. Eisebitt et al., Nature 432 (2004) 885 –888. \n[30] F. Pfeiffer et al., Phys. Rev. Let t. 96 (2006) 215505 . C. Grünzweig et al., Phys. Rev. Let t. 101  \n(2008) 025504.  \n[31] OPERA 2D and 3D:  http://www.c obham.com/about -cobham/avionics -and-surveillance/about -\nus/technical -services.aspx   \n[32] MAXWELL:  http://www.ansoft.com/products/em/maxwell/  [33] O. Chubar  et al., J. Synchr.  Rad. 5 (1998) 481 –484.  \n[34] P. Ell eaume  et al., Proc. of the PAC , Vancouver, BC, Canada  (1997) 3509 –3511.  \n[35] RADIA:  http://www.esrf.eu/Accelerators/Groups/InsertionDevices/Software  \n[36] J. Chavanne et al., Proc. of the EPAC, Vienna, Austria (2000) 2316 –2318.  \n[37] K.Halbach, Nucl. Instrum. Methods , 169 (1980) 1 –10. \n[38] K. Halbach Nucl. Instrum. Methods , 64 (1968) 278.  \n[39] K. Halbach, Nucl. Instrum. Methods , 74 (1969) 147.  \n[40] K. Halbach, Understanding modern magnets through conformal  mapping, Proc. Symposiu m on \nConductivity and Magnetism:  the Legacy of Felix Bloch , Stanford, C A, USA, 1989 , Ed. \nW. A. Little (World Scientific, Singapore, 1990), pp. 1201 –1222.  \n[41] T. Eichner et al.  Phys. Rev. ST Accel. Beam s, 10 (2007)  082401.  \n[42] S. Becker et al. Phys. Rev. ST Accel. Beams , 12 (2009) 102801 . \n[43] Y. Iwashita, Proc. of the PAC, Portland, OR, USA  (2003)  2198 –2200.  \n[44] R. Gluckstein et al., Nucl. Instrum. Methods , 187 (1981) 119 –126. \n[45] T. Sugimoto et al., Proc. of the EPAC, Genoa, Italy (2008) 583 –585. \n[46] Y. Iw ashita et al., Proc of the PAC, Vancouver, BC, Canada  (2009 ). \n[47] Y. Iwashita et al., Proc. of the EPAC, Edinburgh, Scotland (2006) 2550 –2552.  \n[48] PETRA III Technical Design Report, DESY 2004 -035. http://petra3.desy.de/  \n[49] NSLS  II Conceptual Design Report : http://www.bnl.gov/nsls2/project/CDR/  \n[50] K. Halbach, Nucl. Instrum. Methods , 187 (1981) 109 –117. \n[51] K. Halbach, J. Phys.  Colloques , 44 (1983) C1-211–C1-216. \n[52] P. Elleaume et al., Nucl. Instrum. Methods  Phys. Res. , A 455 (2000) 503 –523. \n[53] R. Walker, Nucl. Instrum. Methods  Phys. Res. , A 335 (1993) 328 –337. \n[54] T. Tanaka et al., Proc of the FEL Conference, Stanford, CA, USA (2005) 370 –377. \n[55] T. Hara  et al., Phys. Rev. ST Accel. Beams, 7 (2004) 050702.   \n[56] T. Tanaka et al., J. Synchr.  Rad. 14 (2007) 416 –420. \n[57] C. Kitegi et al ., Proc. of the EPAC, Edinburgh, Scotl and (2006) 3559 –3561.   \n[58] J. Chavanne et al., Proc. of the EPAC, Genoa, Italy (2008) 2243 –2245.  \n[59] J. Chavanne et al. , Synchr.  Rad. News  22 (2009)  34–37.  \n[60] J. Chavanne et al., Proc. of the SRI Conference, Melbourne , Australia  (2009)  to be published \nby the AIP.  \n[61] T. Tanaka et al. , Phys. Rev. ST Accel. Beams , 12 (2009) 120702 . \n[62] J. Hu  et al., Phys. Stat. Sol. b  188 (1995) 807.  \n[63] L. M. Garci a et al., Phys. Rev. Lett. 85  (2000) 429 and references therein.  \n[64] K. Üstüner  et al., 20th Conference on Rare Earth Permanent Magnets, Crete (2008 ). \n[65] J. Bahrdt et al., Proc. of the SRI Conference, Melbourne , Australia  (2009) , to be published by \nthe AIP.  [66] T. Ta nabe et al., Proc. of the SRI Conference, Melbourne , Australia  (2009) , to be published by \nthe AIP.  \n[67] T. Tanaka et al., New J. Phys.  8 (1006) 287 –303. \n[68] J. Goulon, et al., Nucl. Instrum.  Methods  Phys. Res. , A 254 (1987) 192 –201. \n[69] J. Pflueger et al., Nucl. Instru m. Methods  Phys. Res., A 289 (1990 ) 300 –306.  \n[70] J. Pflueger , Rev. Sci. Instr um. 63 (1992) 295 –300.  \n[71] P. Elleaume et al. , IEEE Trans. Magn. 28 (1992) 601.  \n[72] J. Chavanne et al., R ev. Sci. Instrum. 66 (1995) 1868 –1871.  \n[73] J. Chavanne  et al., Nucl. Instrum. Methods  Phys. Res. , A 421 (1999) 352 –360. \n[74] S. Yamamoto et al., Jpn. J. Appl. Phys. 26 (1987) L1613 –L1615.  \n[75] S. Yamamoto et al., Rev. Sci. Instrum.  60 (1989) 1834 –1837.   \n[76] S. Ya mamoto et al., Phys. Rev. Lett.  62 (1989) 2672 –2675.  \n[77] X. Marechal et al., Rev. Sci. Instrum.  66 (1995)1937 –1039.  \n[78] X. Marechal et al., J. Synchr. Rad. 5 (1998) 431 –433.  \n[79] S. Sasaki, Nucl. Instrum. Methods  Phys. Res., A 347 (1994) 83 –86. \n[80] J. Bahrdt et al., Proc of the PAC, Vancouver, BC, Canada  (2009) , to be published.  \n[81] J. Bahrdt et al., Proc. of the SRI  Conference, Melbourne , Australia  (2009) , to be published by \nthe AIP.  \n[82] P. Elleaume , Nucl. Instrum. Methods  Phys. Res., A 291 (1990) 371 –377. \n[83] B. Diviacco et al ., Nucl. Instrum. Methods  Phys. Res., A 292 (1990) 517 –529. \n[84] T. Hara et al., J. Synchr. Rad.  5 (1998 ) 426 –427. \n[85] S. Sasaki et al., Rev. Sci. Instrum.  66 (1995) 1953 –1955.  \n[86] S. Hashimoto et al., Nucl. Instrum. Methods  Phys. Res.,  A 361 (1995) 611 –622.  \n[87] S. Sasaki, Technical Report ELETTRA, Trieste, Italy, ST/M–TN–98/24 (1998).  \n[88] M. Kawai et al., Proc. of the EPAC, Sitges (Barcelona), Spain (1996) 2549 –2551.   \n[89] B. Diviacc o et al., Proc. of the EPAC, Stockholm, Sweden (1998) 2216 –2218.   \n[90] S. Sasaki et al. , Proc. of the EPAC, Stockholm, Sweden (1998)  2237 –2239.  \n[91] J. Chavanne et al., Proc. of the EPAC, Stockholm, Sweden ( 1998) 2213 –2215.  \n[92] J. Chavanne et al., Proc. of the PAC, New York, NY, USA (1999) 2662 –2664.  \n[93] B. Diviacc o et al., Proc. of the EPAC, Vienna, Austria (2000) 2322 –2324.  \n[94] J. Bahrdt et al., Nucl. Instrum. Methods  Phys. Res. , A 467 –468 (2001) 130–133.  \n[95] T. Schmidt e t al., Proc. of the EPAC, Paris, France (2002) 2631 –2633.  \n[96] H. Kitamura, Rev. Sci. Instrum.  66 (1995) 2007 –2010.  \n[97] T. Tanaka  and H. Kitamura,  Nucl. Instrum. Methods  Phys. Res. , A 364 (1995)  368–373.  \n[98] T. Tanaka and H. Kitamura,  J. Synch r. Rad. 3 (1996) 47.  \n[99] T. Tanaka  and H. Kitamura,  J. Electron Spectrosc . Rel. Phenom . 80 (1996)  441–444.  [100]  T. Tanaka  et al., J. Synch r. Rad. 5 (1998) 459 –461. \n[101]  T. Tanaka et al., Rev. Sci. Instrum.  70 (1999) 4153.  \n[102]  T. Tanaka et al., J. Appl. Phys. 88 (2000 ) 2101.  \n[103]  B. Diviacco et al., Pr oc. of the PAC, Chicago, IL, USA (2001) 2468 –2470.  \n[104]  B. Diviacco et al., Proc. of the  EPAC, Paris, Fr ance (2002) 2610 –2612.  \n[105]  D. Zangrando et al., Proc. of the PAC, Portland, OR, USA (2003) 1050 –1052.  \n[106]  T. Tanaka  et al. , Nucl. Instrum. Methods   Phys . Res., A 449 (2000) 629 –637.  \n[107]  T. Tanaka et al., Rev. Sci. Instrum.  73 (2002) 1724 –1727 .  \n[108]  K. Shirasawa et al., Phys. Rev. ST Accel. Beams , 7 (2004)  020702 . \n[109]  R. Tatchyn et al., IEEE Trans . Magn.  26 (1990) 3102 –3123.  \n[110]  J. W. Lewellen et al.,  Nucl. Instrum. Methods  Phys. Re s., A 358 (1995) 24 –76. \n[111]  G. K. Shenoy, J. Synchr. Rad. 10 (2003) 205 –213. \n[112]  R. Klein  et al., J. Synchr . Rad. 5 (1998) 451–452. \n[113]  A. Bernhard et al., Proc. of the EPAC, Genoa, Italy (2008) 2231 –2233.  \n[114]  D.C. Quimby  et al., Nucl. Instrum. Methods  Phys. Res., A  285 (1989) 281.  \n[115]  S.C. Gottschalk  et al., Nucl. Instrum. Methods  Phys. Res., A 296 (1990) 579 .  \n[116]  B. Diviacco  et al.,  Nucl. Instrum. Methods  Phys. Res., A 368  (1996) 522.  \n[117]  P. Elleaume  et al. , Synchr . Rad. News 8 (1995) 18.  \n[118]  J. Pflüger  et al., Nucl. Instrum. Methods  Phys. Res. , A429 (1999) 368.  \n[119]  J. Bahrdt et al ., Nucl. Instrum. Methods  Phys. Res. , A 516 (2004) 575 –585. \n[120]  S. Marks  et al., Proc. of the PAC , New York, NY, USA  (1999) 162–164. \n[121]  P. Elleaume, Proc . of the EPAC, Berlin, Germany (1992) 661 –663. \n[122]  J. Safranek et al. , Proc. of the EPAC, Vienna , Aus tria (2000) 295 –297. \n[123]  J. Chavanne et al. , Proc of the EPAC, Vienna , Austria (2000) 2346 –2348.  \n[124]  J. Bahrdt et al., Proc. of the  SRI Conferenc e, Daegu, South Korea, AIP Con ference \nProceedings 879 (2006) 315–318. \n[125]  J. Bahrdt et al. , Proc of the EPAC, Geno a, Italy  (2008) 2222 –2224.   \n[126]  J. Bahrdt et al. , Proc. of the PAC , Vancouver, BC, Canada  (2009) . \n[127]  A. A. Zholents  et al., Phys. Rev. Lett.  76 (1996) 912 –915. \n[128]  R. W. Schoenlein et al., Science, 287 (2000) 2237 –2240.  \n[129]  R. W. Schoenlein, Appl . Phys. B 71 (2000) 1 –10. \n[130]  K. Holldack et al., Phys. Rev. ST Accel. Beams , 8 (2005)  040704.  \n[131]  K. Holldack et al.,  Phys. Rev. Lett. 96 (2006)  0548 01. \n[132]  S. Khan et al., Phys. Rev. Lett. 97 (2006)  074801 .   \n[133]  P. Beaud et al., Phys. Rev. Lett. 99 (2007) 174801 . [134]  http://flash.desy.de/  \n[135]  T. Tanaka et al., Proc. of the FEL Conference, Gyeongju, Korea (2008) 537 –542. H. Tanaka et \nal., Proc. of the FEL Conference, Liverpool, UK (2009) 758 –765. \n[136]  http://lcls.slac.stanford.edu/  \n[137]  http://www.xfel.eu/de/  \n[138]  http://www.riken.jp/XFEL/  \n[139]  http://fel.web.psi.ch  \n[140]  G. R. Neil et al., Nucl. Instrum. Methods  Phys. Res.,  A 557 (2006) 9 –15.  \n[141]  L. Merminga, Proc. of the PAC, Albuquerque, NM, USA (2007) 22 –26. \n[142]  E. Minehara et al., Nucl. Instrum. Methods  Phys. Res. , A 557 (2006) 16 –22. \n[143]  V. P. Bolotin et al., Nucl. Instrum. Methods  Phys. Res. , A 557, (2006 ) 23–27. \n[144]  S. L. Smith, Proc. of the PAC, Albuquerque, NM, USA (2007) 1106 –1108.  \n[145]  V. Litvinenko et al., Proc. of the PAC, Albuquerque, NM, USA (2007) 1347 –1349.  \n[146]  M. Abo -Bakr, Proc. of the SRF Conference , Berlin, Germany (2009) 223 –227. \n[147]  D. Bilderback  et al., Sy nchr. Rad. News, 19, No. 6 (2006)  30–35. G.H. Hoffstaette r et al., Proc. \nof the PAC , Albuquerque, NM, USA  (2007)  107–109. \n[148]  M. Borland et al., Proc. of the PAC , Albuquerque, NM, USA  (2007) 1121 –1123 . N. Sereno et \nal., Proc.  of the PAC , Albuquerque, NM, USA (2007) 1145 –1147.  \n[149]  T. Kasuga et al., Proc. of the PAC , Albuquerque, NM, USA  (2007)  1016 –1018 .  \n[150]  S. Sakanaka et al., Proc. of the EPAC, Genoa, Italy (2008) 205 –207. \n[151]  Y. Ding  et al. , Phys. Rev. ST Accel. Beams , 11 (2008)  030702.  \n[152]  Y. Li et al., Proc of the EPAC, Genoa, Italy (200 8) 2282 –2284.  \n[153]  Y. Li  et al. , Nucl. Instrum. Methods  Phys. Res ., A (2009)  accepted.  \n[154]  A. Tem nykh, Phys. Rev. ST Accel. Beams , 11 (2008)  120702 . \n[155]  J. Bahrdt et al., Proc. of FEL Conf erence, Trieste, Italy (2004)  610–613. \n[156]  F. Grüner  et al. , Appl.  Phys ., B 86  (2007)  431–435. \nBibliography  \n \nR. J. Parker, Advances in Permanent Magnetism  (Wiley, New York, 1990 ) ISBN 0 –471–82293 –0. \n \nA. Huber t and R. Schäfer, Ma gnetic Domains: The Analysis of Magnetic Microstructures  (Springer, \nBerlin, 1998 ). \n \nH. Onuki an d P. Elleaume, editors,  Undulators, Wiggle rs and their  Applications (Taylor and Francis, \nLondon, 2003)  ISBN 0 –415–28040 –0. \n \nJ. A. Clarke, The Science and Technology of Undulators and Wigglers (Oxford U niversity Press, New \nYork, 2004)  ISBN 0 -19-850855 -7. \n R. Walker , Proceedings of CERN Accelerator School, Fifth Advanced Accelerator  Physics Course , \nRhodes, Gr eece, 1993,  CERN 95 -06 v2, editor S. Turner.  \n \nR. Walker, Proceedings of CERN Accelerator School, Synchrotron Radiation and Free Electron \nLasers , Grenoble , France, 199 6, CERN  98-04, editor S. Turner.  \n \nP. Elleaume , Proceedings of CERN Accelerator School, Synchrotron Radiation and Free Electron \nLasers , Brunnen, Switzerland , 2003, CERN -2005 -012, editor D. Brandt.  \n \nJ. Bahrdt , Proceedings of CERN  Accelerator Sc hool, Intermediate Accelerator Physics, DESY \nZeuthen , Germany , 2003 , CERN -2006 -002, editor D. Brandt.   "    },    {        "title": "1105.3962v1.Ultra_fast_spin_avalanches_in_crystals_of_molecular_magnets_in_terms_of_magnetic_detonation.pdf",        "content": "arXiv:1105.3962v1  [cond-mat.mtrl-sci]  19 May 2011Ultra-fast spin avalanches in crystals of molecular magnet s in terms of magnetic\ndetonation\nM. Modestov, V. Bychkov, and M. Marklund\nDepartment of Physics, Ume˚ a University, SE-901 87 Ume˚ a, S weden\nRecent experiments (Decelle et al., Phys. Rev. Lett. 102, 027203 (2009), Ref. [1]) discovered\nan ultra-fast regime of spin avalanches in crystals of magne tic magnets, which was three orders of\nmagnitude faster than the traditionally studied magnetic d eflagration. The new regime has been\nhypothetically identified as magnetic detonation. Here we d emonstrate the possibility of magnetic\ndetonation in the crystals, as a front consisting of a leadin g shock and a zone of Zeeman energy\nrelease. We study the dependence of the magnetic detonation parameters on the applied magnetic\nfield. Wefindthat themagnetic detonation speed only slightl y exceeds the soundspeed in agreement\nwith the experimental observations.\nPACS numbers: 75.50.Xx 75.60.Jk 47.70.Pq 47.40.Rs\nMolecular magnetism is a rapidly developing interdis-\nciplinaryresearchareawithin materialscience[2, 3]. One\nof the widely investigated materials in the subject is\nMn12-acetate, with a high spin number ( S= 10) and\nstrongmagneticanisotropy[2–6]. Atsufficientlylowtem-\nperature all the spins of the molecules become oriented\nalong an applied external magnetic field, thus occupying\nthe ground state (e.g. Sz= 10); in this state the magne-\ntization reaches its saturation value. When the magnetic\nfield direction is switched to the opposite one, the for-\nmer ground state becomes metastable with an increased\npotential energy (the Zeeman energy) and a barrier sep-\narating it from the new ground state. Active research\non the subject demonstrated that spin-relaxation from\nthe metastable to the ground state often happens in the\nform of a narrow front spreading in a sample with ve-\nlocity of a few meters per second [7–13]. Still, all these\nworks focused on magnetic deflagration, i.e. a front of\nenergy release propagating due to thermal conduction at\nvelocities much smaller than the sound speed.\nHowever, in contrast to other studies, recent experi-\nments by Decelle et al., Ref. [1], discovered a new fast\nregime of the magnetic avalanches in Mn 12-acetate with\na front velocity estimated to be (2000-3000) m/s, which\nexceeds the typical magnetic deflagration speed by three\nordersofmagnitude. Thoughalimited numberofsensors\nled to rather large uncertainty in measuring the front ve-\nlocity, the experiments still indicated clearly that it was\ncomparable to the sound speed in the crystals. Further-\nmore, Decelle et al. [1] hypothetically interpreted the\nnew regime as magnetic detonation . Although this hy-\npothesis looked reasonable, it still required much theo-\nretical work to be justified. In particular, detonations in\ncombustion problems demonstrate a propagation veloc-\nity larger than the sound speed by order of magnitude\nand destructively high pressure [14, 15]. Besides, even in\ncombustion science, the phenomenon of deflagration-to-\ndetonation transition has remained one of the least un-\nderstood processes for more than seventy years, despite\nits extreme importance [15, 16]. It is only recently thata quantitative theoretical understanding of this process\nhas been achieved [17–20].\nIn this Letter we demonstrate the possibility of mag-\nnetic detonation, in the form of a front with a leading\nshock and a zone of Zeeman energy release. We study\nthe dependence of the magnetic detonation parameters\non the applied magnetic field. We find that the magnetic\ndetonation speed is only slightly greater than the sound\nspeed, in agreement with experimental observations.\nIn line with the experiments [1], we consider magnetic\navalanches in Mn 12-acetate with the Hamiltonian\nH=−βS2\nz−gµBHzSz, (1)\nsuggested in [11]. Here Szis the spin projection, β≈\n0.65Kis the magnetic anisotropy constant, g≈1.94\nis the gyromagnetic factor, µBis the Bohr magneton,\nandHzis the external magnetic field. The Hamiltonian\n(1) determines the Zeeman energy release and the en-\nergy barrierof the spin transition (in temperature units),\nwhich depend on the magnetic field as\nEa=βS2\nz−gµBHzSz+g2\n4βµ2\nBH2\nz,(2)\nQ= 2gµBHzSz, (3)\nrespectively, with Sz= 10. The energy barrier decreases\nwith the field while the Zeeman energy increases linearly.\nNext, we consider a stationary magnetic detonation in a\ncrystal of molecular magnets. Similar to the theory of\nshocks in solids [21], we adopt the reference frame of the\ndetonation front and find the conservation laws of mass,\nmomentum and energy according to\nρ0D=ρu, (4)\nP0+ρ0D2=P+ρu2, (5)\nε0+P0\nρ0+1\n2D2+Q=ε+P\nρ+1\n2u2+Qa,(6)\nwhere the label 0 designates the initial state, Dis the\ndetonation speed, uis velocity produced by the deto-\nnation,εis thermal energy per molecule, and ais the2\nfraction of molecules in the metastable state. Here we\nneglect the thermal conduction, since this is a compar-\natively slow process. In the theory of shock waves one\nintroduces the volume per unit mass V≡1/ρinstead of\ndensity. The conservation laws Eqs. (4)–(6) have to be\ncomplemented by an equation of state. Following Ref.\n[21], we represent the pressure and energy of condensed\nmatter at low temperature as a combination of elastic\nand thermal components according to\nP=c2\n0\nV0n/bracketleftbigg/parenleftbiggV0\nV/parenrightbiggn\n−1/bracketrightbigg\n+Γ\nVAkBTα+1\n(α+1)Θα\nD,(7)\nε=c2\n0\nn/braceleftBigg\n1\nn−1/bracketleftBigg/parenleftbiggV0\nV/parenrightbiggn−1\n−1/bracketrightBigg\n+V\nV0−1/bracerightBigg\n+AkBTα+1\n(α+1)Θα\nD,\n(8)\nwherec0is the sound speed (we take c0≈2000 m/s in\naccordance to [1]), the power exponent n≈4 as sug-\ngested in [21], Γ ≈2 is the Gruneisen coefficient, Θ Dis\nthe Debye temperature with Θ D= 38Kfor Mn 12,kBis\nthe Boltzmann constant, A= 12π4/5 corresponds to the\nsimple crystal model, α= 3 is the problem dimension.\nThus, in Eqs. (4)–(8) we have a complete system for\ndescribing magnetic detonation in molecular magnets.\nThe properties of shocks and detonations are repre-\nsented by the Hugoniot/detonation curve P=P(V), see\nRef. [14, 15, 21]. We also introduce the scaled density\nratior=ρ/ρ0=V0/Vwhich characterizes the matter\ncompression. Using Eqs. (4)-(8), we derive the following\nimplicit form for the detonation relation\n/parenleftbigg1\nΓ−r−1\n2/parenrightbiggP\nρ0=rQ(1−a)+/parenleftbigg\nr+r−1\n2Γ/parenrightbigg\nε0\n+c2\n0\nn−1/bracketleftbigg\nr−1−/parenleftbigg\n1−n−1\nΓ/parenrightbiggrn−1\nn/bracketrightbigg\n. (9)\nIn the case ofzeroenergyrelease( a= 1), Eq. (9) reduces\nto the Hugoniot equation for a shock wave (which we de-\nnote by the subscript s). In the detonation, the leading\nshock compresses the sample, increases temperature and\nhencefacilitatesthespinreversalwiththeZeemanenergy\nrelease. The released Zeeman energy provides expansion\nof the medium, which acts like a piston and supports the\nleading shock. In the case of the completed spin rever-\nsal (a= 0), Eq. (9) describes the final state behind the\ndetonation front (which we denote by the subscript d).\nThe insert of Fig. 1 shows the Hugoniot and detonation\ncurves found using Eq. (9) for H= 4 T. We assume that\nthere is no external atmospheric pressure and the initial\ntemperature is negligible, which corresponds to the ini-\ntial point ( V=V0;r= 1;P= 0). Because of the energy\nrelease, the detonation curve is always above the Hugo-\nniot one. In the case of Mn 12we find that the elastic\ncontribution to the pressure and energy dominates over\nthe thermal one, which leads to a rather weak detonation-1000 -500 0500 1000 1500 2000 \n0.975 0.98 0.985 0.99 0.995 1P-Pt(Pa) \nV/V 0Ps-PtPd-Pt\nChapman-Jouguet point Shock point tangent 01234\n0.92 0.94 0.96 0.98 1P (atm) \nV/V 0PtPs, P d\nFIG. 1: The insert: Traditional presentation of the Hugonio t\nand detonation curves and the tangent line to the detonation\ncurve in Mn 12-acetate for the external magnetic field Hz=\n4T. The main plot: The Hugoniot and detonation curves with\nthe tangent line extracted; label ”t” stands for tangent.\nwith the shock and detonation curves almost coinciding\nasshown at the inset ofFig. 1. A self-supportingdetona-\ntion corresponds to the Chapman-Jouguet (CJ) regime,\nfor which velocity of the products in the reference frame\nof the front is equal to the local sound speed [14]. The\nCJ point at the detonation curve is determined by the\ntangent line connecting the initial state and the detona-\ntion curve. Since the detonation and Hugoniot curves\nare extremely close at the insert of Fig. 1, the intersec-\ntion of the tangent line cannot be seen in the traditional\nrepresentation of the curves. In order to make the fig-\nure illustrative, we subtract this tangent line from the\nHugoniot and detonation curves in Fig. 1. In the new\nrepresentation, the tangent line corresponds to the zero\nline, while the Hugoniot and detonation curves may be\ndistinguished quite well. The CJ point in Fig. 1 corre-\nspondstothefinalstatebehindthedetonationfront. The\nshock point indicates the strength of the leading shock\nas determined by the Zeeman energy release for the CJ\nregime; the density and the pressure acquire maximum\nvalues at the shock front. The Zeeman energy release\nbehind the shock produces expansion of matter with an\nensuing pressure reduction.\nWe notice from Fig. 1 that the Mn 12crystal is com-\npressed by few percents in the detonation wave, which\nmakes an analytical theory for the detonation front pa-\nrameters possible using expansion r= 1+δwithδ≪1.\nThen, to leading order in δ, Eqs. (7), (9) reduce to\nP=ρ0/bracketleftbig\nΓQ(1−a)+c2\n0δ/bracketrightbig\n, (10)\nTα+1= (α+1)Θα\nD\nAkB/bracketleftbigg\nQ(1−a)+n+1\n12c2\n0δ3/bracketrightbigg\n.(11)\nWefindthefinalcompressionbehindthedetonationfront3\nas\nδd=1\nc0/radicalbigg\n2ΓQ\nn+1. (12)\nThe compression behind the leading shock is larger by a\nfactor of 2, δs≈2δd, as may be seen from the parabolic\nshape of the Hugoniot and detonation curves in Fig. 1.\nThe detonation speed may be found from Eq. (4) as\nD=c0/parenleftbigg\n1+n+1\n4δs/parenrightbigg\n, (13)\nwhich means that the magnetic detonation speed slightly\nexceeds the sound speed in agreement with the experi-\nmental observations [1]. Substituting δs,δd, anda= 1; 0\ninto Eqs. (10), (11), we find the analytical formulas for\npressure and temperature at the shock and behind the\ndetonation front, respectively. Taking into account Eq.\n(3), these formulas specify the dependence of the detona-\ntion parameters on the external magnetic field. In Fig. 2\nwe compare the analytical theory to the numerical solu-\ntiontoEq. (9). ThecurvesofFig. 2ashowthe densityat\nthe shockwaveand behind the detonationfront, when all\nthe spins have been aligned along the magnetic field. We\nsee that the density at the shock increases by less than 3\npercents if the magnetic field is below 10 T. Because of\nthis small compression, the analytical theory (12) is in a\nvery good agreement with the numerical solution. The\nmaximum value of shock pressure is about 1.2 atm for 10\nT. Thus, due to the small compression and the moder-\nate pressure increase, the magnetic detonation does not\ndestroy the magnetic properties of the crystals.\nAt the same time, the crystal temperature increases\nconsiderably because of the shock, and this stimulates\na fast spin reversal and a further temperature increase.\nFig. 2b illustrates the temperature increase at the shock\nwaveand behind the detonation front. Again, we observe\nvery good agreement between the analytical theory and\nthe numerical solution. The temperature at the leading\nshock is comparable to that expected for the magnetic\ndeflagration [7–10], which also makes the reaction time\ncomparable in both processes. In classical combustion,\nthe temperature at the leading shock in the detonation\nwaveis still quite small in comparisonwith the activation\nenergy of the chemical reactions, so that the active reac-\ntion zone lags considerably behind the shock [15]. The\nsituation may be quite different in magnetic detonation.\nWhen the magnetic field is stronger than 2 −3 T, the\nshock temperature is relatively high ( Ea/Ts<5) so that\nactivespin reversalstarts rightat the shockwave. Figure\n2bpresentsalsothe energybarrierasafunction oftheex-\nternal magnetic field. The energy barrier decreases with\nthegrowthofthemagneticfield, Eq. (2), asshowninFig.\n2b. When the magnetic field exceeds 10 T, the energy\nbarriervanishes, themetastablestateturnsunstable, and\nthe molecules may settle down freely to the ground state.11.005 1.01 1.015 1.02 1.025 1.03 \n0 2 4 6 8 10 12 14 16 ρ/ρ0\nH(Tesla) ρsa) \nρd\n0510 15 20 25 \n0 2 4 6 8 10 12 14 16 Ts, T d, E a(K) \nH (Tesla) Td\nTsEab) \nFIG. 2: Density ratio (a) and temperature (b) at the leading\nshock and behind the detonation front versus the external\nmagnetic field. Solid lines show exact numerical solution; t he\ndashed lines stand for the analytical theory.\nHence, one may interpret magnetic avalanches as deto-\nnation or deflagration only for the fields below 10 T.\nFinally, we describe the internal structure of the mag-\nnetic detonationfront. In the referenceframeofthe mov-\ning front, the molecule fraction with the spin opposite to\nthe field direction is determined by [11]\nu∂a\n∂x=a\nτRexp/parenleftbigg\n−Ea\nT/parenrightbigg\n, (14)\nwhereτRis a constant of time dimension characterizing\nthe spin reversal. We integrate Eq. (14) numerically to-\ngether with Eqs. (4) and (7) along the tangent line in\nFig. 1, from the shock to the CJ point; the obtained pro-\nfiles are depicted in Fig. 3 for H= 3 T. The background\nshading represents the energy release due to the spin re-\nversal; the temperature and the pressure are scaled to\ntheir maximal values. The coordinate is scaled by the\ncharacteristic length L0=c0τR≈2·10−4m, where we\ntakeτR≈10−7s as obtained in several experiments [7–\n10]. Using this value we can estimate the characteristic4\nFIG. 3: Stationary profiles of the scaled temperature, pres-\nsure, and fraction of molecules in the metastable state for\nHz= 3 T. The background shading shows the energy release.\nwidth of the stationary detonation wave to a few mil-\nlimeters. The applied magnetic field influences strongly\nthe reaction rate and thus the front width. For mag-\nnetic fields higher than 5 T, the detonation width is <1\nmm, while for a weaker field the width may increase con-\nsiderably. For this reason, the detonation mechanism in\nmolecular magnets may only be observed in experiments\nutilizing high enough magnetic fields, since the typical\nsample size is of order of several millimeters. The typical\nscales in the experiments of Ref. [1] were also about a\nfew millimeters. Thus the experimentally observed fast\navalanche regime was, presumably, a non-stationary det-\nonation in the process of developing.\nTo summarize, in this Letter we have developed a the-\nory of magnetic detonation in molecular magnets, which\nexplains a new regime of ultra-fast spin avalanches dis-\ncovered recently in the experiments of Ref. [1]. The det-\nonation regime is two to three orders of magnitude faster\nthan the magnetic deflagration observed before [7–10].\nWe have shown that the leading shock triggers the spin\nreversalinthesemagneticsystems,andthatthemagnetic\ndetonation propagateswith velocities slightly largerthan\nthesoundspeed. In contrasttotraditionaldetonationsin\ncombustion, which are characterized by strongly super-\nsonic velocities and ultra-high pressure, magnetic deto-\nnations involve rather moderate pressure increase, which\nis about 1 atm even for considerable magnetic fields. For\nthis reason, magnetic detonation does not destroy mag-\nnetic properties of the crystals, a very important conclu-\nsioninviewofpossibleapplicationsofmolecularmagnets\nto, e.g., quantum computing.\nThis work was supported by the Swedish Research\nCouncil and by the Kempe Foundation. The authorsthank Petter Minnhagen, Bertil Sundqvist, Thomas\nW˚ agberg, Sune Pettersson, Tatiana Makarova and Va-\nleria Zagainova for useful discussions.\n[1] W. Decelle, J. Vanacken, V. V. Moshchalkov, J. Tejada,\nJ. M. Hernandez, and F. Macia, Phys. Rev. Lett. 102,\n027203 (2009).\n[2] D. Gatteschi and R. Sessoli, Angew. Chem., Int. Ed. 42,\n268 (2003).\n[3] E. del Barco, A. D. Kent, S. Hill, J. M. North, N. S.\nDalal, E. Rumberger, D. N. Hendrikson, N. Chakov, and\nG Christou, J. Low Temp. Phys. 140, 119 (2005).\n[4] R. Sessoli, D. Gatteschi, A. Caneschi, and M. A. Novak,\nNature (London) 365, 141 (1993).\n[5] J. R. Friedman, M. P. Sarachik, J. Tejada, and R. Ziolo,\nPhys Rev. Lett. 76, 3830 (1996).\n[6] L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli ,\nand B. Barbara, Nature (London) 383, 145 (1996).\n[7] Y. Suzuki, M. P. Sarachik, E. M. Chudnovsky, S.\nMcHugh, R. Gonzalez-Rubio, N. Avraham, Y. Myasoe-\ndov, E. Zeldov, H. Shtrikman, N. E. Chakov, and G.\nChristou, Phys. Rev. Lett. 95, 147201 (2005).\n[8] A. Hernandez-Minguez, J. M. Hernandez, F. Macia, A.\nGarcia-Santiago, J. Tejada, and P. V. Santos, Phys. Rev.\nLett.95, 217205 (2005).\n[9] S. McHugh, R. Jaafar, M. P. Sarachik, Y. Myasoedov,\nA. Finkler, H. Shtrikman, E. Zeldov, R. Bagai, and G.\nChristou, Phys. Rev. B 76, 172410 (2007).\n[10] A. Hernandez-Minguez, F. Macia, J. M. Hernandez, J.\nTejada, and P. V. Santos, J. Magn. Magn. Mater. 320,\n1457 (2008).\n[11] D. A. Garanin and E. M. Chudnovsky, Phys. Rev. B. 76,\n054410 (2007).\n[12] D. Villuendas, D. Gheorghe, A. Hernandez-Minguez, F.\nMacia, J. M. Hernandez, J. Tejada, R. J. Wijngaarden,\nEPL (Europhysics Letters) 84, 67010 (2008).\n[13] M. Modestov, V. Bychkov, and M. Marklund, accepted\nin Phys. Rev. B.\n[14] L. Landau and E. Lifshitz, Fluid Mechanics , Pergamon\nPress, Oxford, 1989.\n[15] C.K. Law, Combustion Physics , Cambridge University\nPress, NY, 2006.\n[16] S. Dorofeev, Proc. Combust. Inst. 332161 (2011).\n[17] V. Bychkov, A. Petchenko, V. Akkerman, L.-E. Eriksson,\nPhys. Rev. E 72, 046307 (2005).\n[18] V. Akkerman, V. Bychkov, A. Petchenko, L.-E. Eriksson,\nCombust. Flame 145, 206 (2006).\n[19] V. Bychkov, D. Valiev, L.-E. Eriksson, Phys. Rev. Lett.\n101, 164501 (2008).\n[20] D. Valiev, V. Bychkov, V. Akkerman, C. K. Law, L.-E.\nEriksson, Combust. Flame 157, 1012 (2010)\n[21] Ya. B. Zeldovich and Yu. P. Raizer, Physics of Shock\nWave and High-Temperature Hydrodynamic Phenomena ,\nDover Publications, Inc. Mineola, New York (2002)."    },    {        "title": "1106.3009v1.Monte_Carlo_simulation_of_magnetic_phase_transitions_in_Mn_doped_ZnO.pdf",        "content": "Monte Carlo simulation of magnetic phase transitions  \nin Mn doped ZnO  \n \n \nL.B Drissi1,2 * , A. Benyoussef  1,3 , E.H Saidi1, 4, 5 , M. Bousmina1 \n \n1. INANOTECH, Institute of Nanomaterials and Nanotechnology  (MAScIR) , Rabat, Morocco,  \n2. International Centre for Theoretical Physics, ICTP, Trieste, Italy  \n3.   Lab Magnetisme et PHE , Faculté des Sciences, Univ Mohammed V, Rabat, Morocco,  \n4.  LPHE, Modelisation et Simulation, Faculté des Sciences, Univ Mohammed V, Rabat, Morocco  \n5. CPM, Centre of Physics and Mathematics -Rabat, Morocco.  \n \n    \n \nAbstract  \nThe magnetic properties of  Mn-doped ZnO semi -conductor  have been investigated using  the \nMonte Carlo method within the Ising mo del. The temperature dependences  of the spontaneous \nmagnetization, specific heat and magnetic susceptibility have been constructed for different \nconcentrations of magnetic d opant Mn and different carrier  concentration s. The  exact values \nof  Mn concentration and carrier  concentration  at which high temperature  transition occurs are \ndetermined. An alternative for the explanation of some controversies  concerning the existence \nand the nature of magnetism in Mn diluted in ZnO systems is given.  Other features are also \nstudied.  \n \nKeywords:  MC simulation s, DMS,  ZnO, Magnetic property, RKKY, TCurie, Carrier mediated \nferro magnetism  \n                                                           \n* e-mail  : ldrissi@ictp.it  Introduction  \nIn the recent years, a great interest has been devoted to Diluted Magnetic Semiconductors \n(DMS) doped with a small concentration of magnetic impurities inducing ferromagnetic \nDMSs.  In particular, DMS based on III -V and II -VI semiconductors doped with transition \nmetal are deeply investigated by both theoretical and experimental scientists  [1-11] in order to \nuse them for spintronic devices such as spin -valve transistor, spin light emitting diodes, \noptical isolator, non -volatile memory . \nTheoretical studies have revealed interesting results. Dietl et al. [1] predicted high \ntemperature ferromagnetism in some p -type doped semiconductors such as ZnO, GaN, GaAs \nand ZnTe. Later, this room temperature ferromagnetism was reported for the case of \npolycrystalline Zn 1-xMn xO samples in [2] and [3]. Consequently, this oxide DMS has become \none of the promising candidates for room temperature ferromagnetic DMSs.  \nZnO based DMSs offer other desirable features as a semiconductor host.  It has a direct wide -\nband gap (~3.4 eV), large exciton binding energy at room temperature (~ 60 meV). \nFerromagnetic doped ZnO is a transparent piezoelectric ferromagnet with promoting \napplications in spintronics.  \nThe study of these magnetic systems features by numerical simulation techniques has \nattracted great attention. This has, lead to several results. The ferromagnetic properties have \nbeen predicted in the work [4] using First -principle calculations and proved later by several \nexperiments [5-9]. \nThe incorporation of Mn into ZnO not only causes the introduction of magnetic moments but \nalso increases the band gap. With co -doped concentration, the band gap decreases because a \nlarge hy bridization between p-d orbitals was observed [6], so the p-d exchange not only plays \nthe key role in the ion -ion ferromagnetic d -d exchange but also decreases the band gap.  \nFrom experimental point of view, there is a controversy  concerning the existence and the \nnature of magnetism in Mn -doped ZnO  systems. There exists some  data where no  \nferromagnetism has been found [12]. While there is also other  data on many systems  which \nexhibit ferromagnetism with Curie temperature higher than room temperature [13]. However, \nthis ferromagnetism is non conventional and seems to be a strange sort of 'intrinsic' \nferromagnetism [14, 15 ]. Coey [16] has shown that the origin of the ferro magnetism is \nintrinsic; it is due to defects [17]. Indeed, sample without defects are paramagnetic, while \nthose containing defects may be ferromagnetic. Ab initio calculations of transition metal \ndoped ZnO, without defects, show that the ferromagnetic phase is stable (except for Mn, \nwhich is paramagnetic ) [18]. Using LDA functional, t he paramagnetic phase in Mn -doped \nZnO has been confirmed by introducing self interaction correction , however, it has been \nstabilized for other transition metal doped ZnO [19]. The necessity to insert carriers, \nespecially hole s, into the system to stabilize the ferromagnetic phase was reported in details in \n[1]. Moreover, codoping (Zn, Mn)O system with N can change the ground state from spin \nglass to ferromagnetic as investigated in [17]. Depending on the functional used, the D FT \nresults seem  also controversial  as showed in details in the two recent works  [20, 21] for the \ncase of Co -doped ZnO that is very well investigated in the literature1. \nAdditionally, these conflicting results also exist concerning the distribution of Mn in ZnO as \nreported in the experimental results of [22] where Mn is distributed homogeneously and in  \n[23] that reports clustering of Mn atoms  or in [24] that studies dense nanograined Mn doped \nZnO polycrystals.  Thus, inconsistent phenomena and conclusions have been obtained, \n                                                           \n1 The authors thank the reviewer for pointing out this idea.  showing that the intrinsic ferromagnetism of Mn -doped ZnO systems remains an open \nquestion. It is hence of vital importance to clari fy the correlation, i f any, between carriers and \nthe mechanism of ferromagnetism inherent to this  class of diluted magnetic oxides.  \nTo overcome these discrepancies, ZnO have been well investigated employing  ab-initio  \ncalculations  as reported previously  [4], [18-25], however  Monte Carlo simulations are rarely \nexamined for general diluted semiconductors , such the work highlighting the study of Co \n[26], and we are not aware of any studies for Mn -doped ZnO. I n this work, we study in  the \nframework of Monte Carlo  simulations ZnO diluted by Mn to shed more light on the  \nambiguities concerning reports of ferromagnetism . In our model, the hole concentration is \nconsidered globally and it is introduced in the RKKY coupling via Fermi wave number as it is \ngiven explicitly  in section 2. Amongst our results,  spontaneous  magnetization, specific heat, \nmagnetic susceptibility and the Curie temperature TC have been evaluated for different \nconcentrations of magnetic impurities and carrie rs of Mn-doped ZnO .  This lead s us to  study \nthe effect of both magnetic impurities and hole carriers on the existence and nature of \nferromagnetism in Zn1-xMn xO and to give the values of concentration of carriers  that could \nperform its magnetic order and those that must be avoided.  Other results are also investigated.  \nModel description  \n ZnO has wurtzite crystal  structure (P63mc) , where each atom of Zinc is surrounded by four \ncations of oxygen at the corners of a  tetrahedron and vice versa.  This tetrahedral coordination \nis typical of sp3 covalent bonding  and some of the divalent sites Zn substituted by the \nmagnetic ions Mn.  In the wurtzite  structure, the two lattice constants of the hexagonal unit \ncell are a=3.27A and c=5.26A as reported for (Zn,Mn)O in [27]. \nZnO system is n -type doped with free electrons in the conduction band or p -type with free \nholes  carriers in the valance band. Based on the Hund’s rule, we know that Mn2+ with his half \nfilled 3d shell  has S = 5/2 ground state.  So Mn2+ introduce  d levels in the band gap of ZnO \nsemiconductor   According to the Zener model approach, ferromagnetism in ZnO originates \nfrom  the RKKY –like interaction between the localized Mn spins  via the  delocalized  holes  \ncarriers’ spins [1].  The system is described by the Hamiltonian  \n         jifor               J H\n, Z\njZ\niji ij\njiSSnnr\n(1) \nwhere r ij is the separation between moments  at the two sites  i and j in the hexagonal structure  \nand ni is the magnetic impurity occupation number.  In H, the RKKY range function  J(rij)=\nr JRKKY\n is given as follows  \n   rK rK rK reJr JF F Flr\nRKKY2cos 2 2sin4\n0  \n (2) \nwhere the Fermi wave number \nFK  =\n )n31(1/3\nc2 depends on the  hole density  \ncn. The positive \ncoefficient  J0  is related to the local Zener coupling Jpd  between the Mn local moments and the \nhole spins.  As we are concerned with short ranged RKKY coupling, we assume that the \ndamping scale  l, in the damped factor\nlr\ne , is exactly  the distance  D1 between the first nearest \nneighbors . For long range, the scale l corresponds to the distance D3 between the third nearest \nneighbors . We employ the above approach to estimate magnetic interactions in DMSs [28], \n[29].   \nFor a site i, the spin \nz\niS  introduced in eq(1)  takes the values ±1/2, ±3/2, ±5/2. The \ncorresponding energy E i is defined as follow s:  z\njj\njijRKKY z\nii i Snr J SnE )( .  (3) \nIn our calculations , the concentration ni of Mn dopants in ZnO takes  values in the interval\n0.35-0.15 \n, as  solubility of Mn in the ZnO matrix is relatively high (x≤0.35) as showed in \n[30] by pulsed laser deposition (PLD).  Moreover, it was reported in [31] that co -doping (Zn, \nMn)O system with N can change the ground state from spin glass to ferromagnetic . For p-type \nZnO, the us e of co-doping method could pave the way for a promising potential of Mn  doped  \nZnO but this depends on the hole s mediated ferromagnetism. This is why we are interested , in \nthe current work,  in investigating the carrier -induced ferromagnetism in the ZnO -based \nDMSs . So notice that the hole concentration that we consider globally are introduced in the \nRKKY coupling via Fermi wave number (eq. 2).  following some previous works such as [31] \nthat gives a generalized RKKY description of DMS , and  going beyond [33] that uses effective \nfield theory, with a Honmura -Kaneyoshi differential operator technique,  to calculate the \ntransition  temperature as a function of the carrier (hole) n c and impurity  ni concentrations for \np-type ZnO diluted magnetic semiconductors.  Recall that t he Hamiltonian employed there \ncontains a damped and undamped  Ruderman -Kittel -Kasuya -Yosida (RKKY) interaction \nmodel to describe the  exchange coupling constants J ij between the local moments Mn i and \nMn j. The method used is an effective field theory taking into account  self correlations, but \nstill neglecting correlations. It is well known  that this approximation over estimates the  \ntransition temperature. As we mention ed before, in this  present work we will go beyond this \napproximation, by using Monte Carlo simulation  which gives more precise results. In this \nsense, our results are more  precise than those obtained by effective field theory  [33]. Indeed, \nas it is showed in the following  sections , for [0- 0.2] we obtained lower transition \ntemperature. Moreover, we  investigated a larger domain of parameter than that investigated in  \n[33]; in the region [0.52 - 0.65] we obtained highest value of T C, while in the  intermediate \nregion [0.2 - 0.52] the system is nonmagnetic.  \n \nComputational  details  and Results  \nWe perform Monte Carlo simulations for the Ising  model  described above . The supercell, \nemployed in these calculations , consists of  319-atom s, namely it represents 2×2×2 primitive \nunit cell.  The periodic boundary condition is applied . We have also used the supercell s 3×3×3 \nand 4×4× 4, which  corresponds  respectively to 612 and 1270 atoms , to determine the size \neffect . A specific number of nonmagnetic Zn atom s are replaced  by the  Mn impurities \nrandomly .  \nThe calculations need  some input. As a first step, we determine the nearest neighbors . We \nrestrict our calculations to the third first ones to take account of competition between \nferromagnetic and antiferromagnetic interactions.  Then, we use eq(2) to compute  J(r ij) for \neach distance r ij . This step is crucial  as this RKKY range function is required to calculate the \ntotal energy  E of the system  by using eq (3). It is also important  to determine both the values \nof the hole density  nc for which  strong ferromagnetic coupling take place and the values  \ncorresponding to  frustration phenomena  as depicted in figure1 .   \nFigure 1 :  Variation of  RKKY  function J(r ij)  in terms of hole density nc  for the three distances D1, D2 \nand D3 of the third first  nearest  neighbors   \nWith these ingredients at hand, we build our program where t he thermal average of \nmagnetization M and energy E are calculated by means of the Metropolis algorithm [34]. In \nthis algorithm  the Monte Carlo steps are 20000 per site using every 10 -th step for averaging.  \nWe average over at least 100 different random configurations  of magnetic sites of the \ndisordered system for the quenched disorder  average . \nIn this current work, we stu dy the series of the system Zn 1-xMn xO. The data got from Monte \nCarlo simulations (MC) lead to the following results. We get the magnetization M and the \nenergy E as function of temperature for different magnetic cations concentrations , ni, and hole \nconcentrations, nc, for short ranged  RKKY interaction. In figure2  we display the \nmagnetization  M versus temperature for a fixed carrier concentration n c=0.18 and varied Mn \nimpurity concentrations ni. When  T increases the magnetization M decreases and goes to zero.  \nAnd it increases as  ni increases 0. 15, 0.25, 0.3 and 0.35  which is due to the alignment of spins \nthat are antiferromagnetic as it is clearly shown in figure1  for nc=0.18 . \n \nFigure 2 :  Magnetization versus temperature for some different impurity concentrations ni  , at n c=0.18  \nWe also get the temperature dependence of the susceptibility.  Indeed, correspondingly to M, \nthe associated magnetic susceptibility \n M- M1 2 2\nT  is represented in figure 3  for \nni=0.2, 0.25 and 0.3. The three curves peak for different values of T that decreases as the \nconcentration ni reduces. These computations are done as previously for a fixed carrier \nconcentration n c=0.18 . The \nT  peaks suggest that thermal fluctuation are driven phase \ntransition from FM to paramagnetic that is  in agreement with standard results.   \nFrom the three  graphs  of figure 3 , we estimate the Curie temperatures of Mn -doped ZnO as a \nfunction of the Mn substitutional concentration  ni for the specific nc = 0.18.  Notice that  we \nplot here the results only for nc = 0.18, however we have done the calculations for different \nvalue s of  nc as we will show in what follows.  \n \nFigure 3 : Temperatute dependence of  susceptibility for the 3 magnetic impurity concentrations n i  0.20, \n0.25 and 0.3 at n c=0.18  \nTo focus in this direction, we vary values of n i in the large interval [0.2 -0.9] for the above \nmentioned and other  holes density values n c , namely  0.14, 0.18  and 0.55, 0.64 , the obtained  \nresults of this study  are presented here below in figure 4  where T C is depicted vs different \nvalues of n i for some  fixed  nc. One sees T C  increasing linearly with impurity concentration for \nthe choosen four values of n c. Generally, t his behavior of   TC  is similar whatever  nc is. \nHowever, from figure 4 , it is obvious that hole density has also an effect. To understand it let \nus project the four  values of nc in figure 1  that describes the short ranged  RKKY coupling . We \nlearn that , as ni is fixed, the highest and lowest transition temperature values depends on the \nnature of coupling. So, it is high in the region where the third first nearest  neighbors coupling \nare ferromagnetic  and it is low where only the first and second nearest neighbors  coupling are \nferromagnetic  (see figure 1  for more details) .  \n \nFigure 4 : The transition temperature, Tc , as function of the impurity concentrations ni for four different \nvalues of  n c. \nMore information explaining the choice of these  numbers will be given  here below.  \nAt fixed n c =0.18 , TC as function of Mn concentrations but for different range; namely short \nand long range  that correspond respectively to damping scale l =D 1 and D 3, shows no \ndeviation from strictly linear behavior  as plotted in figure 5 . \n \nFigure 5: the Curie temperature versus the impurity concentrations ni  for the short and long range \ncase,  for n c=0.18  \n Since the transition temperature increase s monotonically with magnetic impurities \nconcentration n i for both long and short ranged RKKY coupling, then we will concentr ate on \nthe effect of carriers as well as the size of the cell on the variation of T C for fixed value s of Mn \nconcentrations. This is accomplished through  collecting data from temperature de pendence \nsusceptibility by fixing the impurity concentration at a fixed  value ni and varying the holes \ndensity. For the case2 ni =0.30 ,  we get the variation in the T C of Zn0,7Mn 0,3O versus carriers \nconcentration n c  as shown in figure 6.   \n \nFigure 6:  The transition temperature, Tc , as function of the carriers concentration, n c , for the specific Mn \nconcentration 30% . \nThe evolution of t he C urie temperature  in this figure  reveals that we have four main different \nregions.  Region  I where T C  peaks for nc=0.14 and then decline. After, the transition \n                                                           \n2 The result can be generalized for any  value n i  ≤0.35 . \ntemperature vanish es for n c taking values in the interval\n0.42-0.21  that coincides with \nRegion II .  In t his last region we have competition between ferromagnetic and \nantiferromagnetic coupling that destabilize s ferromagnetism , leading to frustration . After this \nregion  the Curie temperature increases  about 2 times as compared to that for low carrier \nconcentrations  (namely Region I)  to maximize for n c=0.58 and declines to vanish , for \n82.0n c\n that co rresponds again to the frustrated R egion  IV. In order to shed more light on \nthis data, it is necessary to focus  on (eq 2). According to the study of the variation of \nr JRKKY  \nin term  of n c  as showed in figure 1 , we learn that region I corresponds to the case where the \nfirst and second near neighbors are ferromag netic and the third one is anti ferromagnetic while \nin region III all the three neighbors are FM. On the other hand, in both region II and IV the \nfrustration is due to th e dominant  of AF mechanism . This confirm s that in orde r to stabilize \nthe FM phase in Zn1-xMn xO system, it is necessary to insert carriers with concentration n c \nbelonging to the regions I or much better to region III.  So, the various experimental and \ntheoretical investigations of the magnetic order in Zn1-xMn xO doesn’t give contradictory \nresults. The ferromagnetism in (Zn,Mn)O systems reported in [2] or the anti -ferromagnetic or \nspin-glass behavior observed  in [12], [17] could be now explained. The region I and region III \nagree with the results  exhibiting ferromagnetism with Curie temperature higher than room \ntemperature [13]. While the region II and IV correspond  both to the experimental study [35] \nshowing there is no e vidence f or magnetic order for some low t emperature.    \nOn the other hand, t o take into account the effect of size, we consider two lattice size  2×2×2 \nprimitive unit cell  (319 Zn atoms)  and 4×4×4 supercell ( 1270 Zn atoms ). We plot the \ntemperature dependence of the susceptibility introduced previously and the specific heat \n E-E1 2 2\n2TCV\n for different cell sizes of the system Zn 0,7Mn 0,3O at n c=0.18.   \n  \nFigure 7:  At fixed nc=0.18 and ni=0.3 and for different cell size, (a) Scusceptibility versus \nTemperature. (b) Specific heat C v as a function of temperature   \n \nIn figure 7a,  the three curves depicting magnetic susceptibility for 1×1×1, 2×2×2 and 4×4×4 \nprimitive peak for different values of T . In figure 7b  the two curves corresponding to 2×2×2 \nprimitive unit cell and 4×4×4 supercell peaks at specific value of temperature T and then \ndrops to vanish. We observe that the specific heat is large for the biggest cell (1270 a toms), \nand becomes smaller as the size decreases.   \n \nFigure 8: Temperature vs holes density for 30% of Mn diluted in ZnO containing 319 Zn atoms (small \ncell) and 1270  Zn atoms  (big cell).  \n \nMotivated by the subsequent discussion and because of the interesting results got in the region \nIII , we restrict on n c varying in the range from 0.42 to 0.75.  As shown in figure 8 , the two \ncurves of the temperature T C increases with n c  and reach their maximum a t 0.58; then they \nsharply drop as a function of (–nc)  for higher values.  This maximum incre ases as the cell size \nis bigger which agrees very well with literature.  \n \nConclusion  \nIn thi s paper, we have studied  Zn1-xMn xO with concentration  ni of Mn dopant  ranging  from \n0.15 to 0.35 and for different values of the carrier  concentration s nc. The Monte Carlo \nsimulations are performed to determine TC of those systems. We find that the thought \ncontroversy concerning magnetic  order can be understood on the basis of investigating the \neffect of carriers in the system. The present study offers a specific example of how carriers \ncan induce and control magnetic order.  \nSo from this study we learn that T C is function of many paramet ers as magnetic cation  \nconcentrations  ni , cell size, short or long range , holes density n c.  This last parameter is very \ncrucial because as we have showed  the region III -that corresponds to the case where three \nneighbors are FM - gives the highest value of TC, however the critical temperature has lower \nvalues in the region I where the first and second near neighbors are ferromagnetic but the \nthird one is antiferromagnetic. So this  work showed us that , for th e case of Zn 1-xMn xO, to get  \nthe FM phase with high T C, the concentration of carriers should belong to the range [0.52-\n0.65] . And  we give explicitly the regions of the values of nc. that must be avoided.   \nComments  and Discussion s \nSeveral models have been proposed to explain the nature of the exchange interaction in DMS; \ndouble exchange, Bound magnetic polaron and Ruderman -Kittel -Kasuya -Yosida (RKKY) \ninteraction. The ab intio calculation of doped ZnO with defects, show that a domina nt \ninteraction is RKKY [33,36]. It belongs to one of the most important and frequently discussed  \ncouplings between the localized magnetic moments in solids. Where indirect exchange \ncoupling is applied to localize inner d -electron of transition metal spins via conduction \nelectrons. Such a coupling between the distant magnetic moments can also be a sour ce of \ndecoherence [37]. Our results here show that the transition temperature depends on the \nmagnetic cation concentrations n i, and  holes density n c. For low n c , the region where the first \nand second near neighbors are ferromagnetic and the third one is antiferromagnetic, the \nsystem exhibit low transition temperature. For intermediate value of n c concentration, where \nthe frustration is dominant, the system is paramagnetic. While for enough high n c \nconcentration, one obtain high transition temperature. Thi s confirms that in order to stabilize \nthe FM phase in Zn 1-xMn xO system, it is necessary to insert carriers with concentration n c \nbelonging to the regions I or much better to region III. So, the various experimental and \ntheoretical investigations of the mag netic order in Zn 1-xMn xO doesn’t give contradictory \nresults as now we can explain the ferromagnetism in (Zn,Mn)O systems reported in [2] or the \nanti-ferromagnetic or spin -glass behavior observed in [12],  [17].  \n \nAcknowledgement s: Lalla Btissam Drissi would  like to thank ICTP (Trieste)  for the \njunior associate ship scheme . L.B. Drissi would like also to thank P. Ghosh for discussion s. \nReferences  \n[1] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science 287 (2000) 1019.  \n[2] P. Sharma, et al, Nature materials 2, 673 (2003).  \n[3] D. Milivojevi c, et al, Solid State  Commun. 141 (2007) 641.  \n[4] K. Sato, H. K. Yoshida, Physica B 308 -310 (2006) 904.  \n[5] K. Ueda, H. Tabata, T. Kawai, Appl. Phys. Lett. 79 (2001) 988.  \n[6] G. T. Thaler, et al, Appl. Phys. Lett. 80 (2002) 3964.  \n[7] M.A. Garcia , et al, Phys Rev Lett. 94 (2005) 217206 . \n[8] S. A. Chambers, et al, Appl. Phys. Lett. 82 (2003) 1257.  \n[9] J. H. Kim, et al. , J.Appl. Phys. 92 (2002)  6066.  \n[10] A.M. Nazmul, et al, Physica E 21 (2004) 937.  \n[11] O.D. Jayakumar, et al, Physica B 381 (2006) 194.  \n[12] Qingyu Xu , et al, Appl. Phys. Lett. 92, 082508 (2008).  \n[13] Pan et al, Materials Science and Engineering R 62 (2008) 1 –35 \n[14] M. Venkatesen, C. B. Fitzgerald, J.M.D. Coey , Nature 430 (7000): 630 -630 (2004)  \n[15] M. Venkatesen, C. B. Fitzgerald, J. G. Lunney, J.M.D. Coey, Phys. Rev. Lett., 93,  177206 (2004)  \n[16]  J.M.D. Coey, Current Opinion in Solid State and Materials Science 10 (2006) 83 –92 \n[17] A. Tiwari, et al, Solid State Commun. (2002).121,371  \n[18] K. Sato, H. Katayama -Yoshida, Jpn. J. Appl. Phys. 40 (2001) L485.  \n[19] M. Toyoda, H. Akai,  K. Sato, and H. Katayama -Yoshida, Physica B 376 -377, 647 (2006).  \n[20] C. D. Pemmaraju, R. Hanafin, T. Archer, H. B. Braun, S. Sanvito, Phys. Rev. B 78, 054428 (2008)  \n[21] S. Lany, H. Raebiger, A. Zunger, Phys. Rev. B 77, 241201(R) (2008)  \n[22] X.M.Cheng , C.L. Chien , J. Appl. Phys. 93(2003) 7876.  \n[23] Z. Jin, et al, Appl. Phys. Lett. 83 (2003) 39.  \n[24] B. B . Straumal,.et al., J. Appl. Phys. 108 (2010) 073923.  \n[25] H. Wu, A. Stroppa, S. Sakong , S. Picozzi,  M. Scheffler, P . Kratzer ., Phys Rev Lett  105, 267203 (2010)  \n[26] A. F. Jalbout, H. Chen, S. L. Whittenburg, APPL. Phys. Lett  81,   2217 (2002)  \n[27]  T. Fukumara,   Z. Jin,  A. Ohtomo,  H. Koinuma, M. Kawasaki, Appl.Phys.Lett.75 (1999) 3366  \n[28] I. Turek, et al, Phys. Stat. Sol. (b) 236, 318 (2003).  \n[29] G. Bouzerar, et al.,  Rev. B 68, 081203  (2003).  \n[30] T. Fukumura, et al ., Appl.Phys.Lett. (2001)78,958.  \n[31] D. Maouche, P. Ruterana, L. Louail, Physics Letters A 365 (2007) 231 –234. \n[32] A. Singh, A. Datta, S. K. Das,  V. A. Singh, Phys. Rev. B 68, 235208 (2003)  \n[33] O. Mounkachi, A. Benyoussef, A. El Kenz, E.H. Saidi, E.K. Hlil, Physica A 388 (2009) 3433.   \n[34] K. Binder, D. W. Heermann, MC  Simulation in Statistical Physics (Springer, Germany, 2002).  \n[35] G. Lawes, A. P. Ramirez, A. S. Risbud,  Ram Seshadri, Phys. Rev. B 71, 045201 (2005)  \n[36] T. Dietl, A. Haury, and Y. M. dA ubigné, Phys. Rev. B 55, R3347, 1997 . \n[37] Y. Rikitake and H. Imamura, Phys. Rev. B 72, 033308 , 2005 . "    },    {        "title": "1107.1647v1.Antimagnets__Controlling_magnetic_fields_with_superconductor_metamaterial_hybrids.pdf",        "content": "Antimagnets: Controlling magnetic \felds with\nsuperconductor-metamaterial hybrids\nAlvaro Sanchez\u0003, Carles Navau, Jordi Prat, and Du-Xing Chen\n1Grup d'Electromagnetisme, Departament de F\u0013 \u0010sica,\nUniversitat Aut\u0012 onoma de Barcelona,\n08193 Bellaterra, Barcelona, Catalonia, Spain\nAbstract\nMagnetism is very important in science and technology, from magnetic recording\nto energy generation to trapping cold atoms. Physicists have managed to master\nmagnetism - to create and manipulate magnetic \felds- almost at will. Surprisingly,\nthere is at least one property which until now has been elusive: how to 'switch o\u000b'\nthe magnetic interaction of a magnetic material with existing magnetic \felds without\nmodifying them. Here we introduce the antimagnet, a design to conceal the magnetic\nresponse of a given volume from its exterior, without altering the external magnetic\n\felds, somehow analogous to the recent theoretical proposals for cloaking electro-\nmagnetic waves with metamaterials. However, di\u000berent from these devices requiring\nextreme material properties, our device is feasible and needs only two kinds of avail-\nable materials: superconductors and isotropic magnetic materials. Antimagnets may\nhave applications in magnetic-based medical techniques such as MRI or in reducing\nthe magnetic signature of vessels or planes.\n1arXiv:1107.1647v1  [cond-mat.supr-con]  8 Jul 2011I. INTRODUCTION\nCloaking a region in space from electromagnetic waves seemed something scienti\fcally\nimpossible until very recently. Pendry et al and Leonhardt [1, 2], using the concepts of\nmetamaterials and transformation optics, theoretically designed an electromagnetic cloak,\nwhich would render a given volume 'invisible' to electromagnetic waves. Such a device\nrequired extreme values of magnetic permeability \u0016and electrical permittivity \". Although\nsome experimental results presented partial cloaking in special cases [3{5], no complete\nbroadband cloak has been experimentally achieved until now [6].\nIn 2007 Wood and Pendry introduced the concept of magnetic cloaking [7]. They showed\nthat in the dc case (electromagnetic waves in the limit of zero frequency), for which the\nelectrical and magnetic e\u000bects decouple, a magnetic cloak for concealing static magnetic\n\felds without disturbing the external \feld needed a material with anisotropic and position-\ndependent\u0016values, smaller than 1 in one direction and larger than 1 in the perpendicular one\n(see Fig. 1a and Eq. (1) for the case of a cylinder). A \u0016<1 could be achieved by arrays of\nsuperconducting plates [7{9], whereas \u0016>1 could be obtained with ferromagnetic materials.\nHowever, no method has been presented to achieve in a real case the required position-\ndependent values in perpendicular directions simultaneously. Because of these di\u000eculties a\nmagnetic cloak has never been designed nor fabricated until now.\nThis eventual magnetic cloaking would have not only scienti\fc interest but also important\ntechnological applications since magnetic \felds are fundamental to many everyday technolo-\ngies and in many of them it is necessary to have a precise spatial distribution of the magnetic\n\feld, which should not be perturbed by magnetic objects - not only by magnets but by any\nmaterial containing iron or steel, for example. Is it therefore possible to build a cloak for\nstatic magnetic \felds with - very important- using only ingredients that are practical and\navailable? In this work we will demonstrate the a\u000ermative answer to this question, by\nexploiting the properties of two worlds: metamaterials and superconductors.\nII. DEFINITION OF THE ANTIMAGNET\nAt this point we want to rede\fne our goal into a more precise and even more ambitious\none: instead of a magnetic cloak -null interior \feld and external \feld una\u000bected-, we want\n2to design here an antimagnet, de\fned as a material forming a shell that encloses a given\nregion in space while ful\flling the following two conditions:\ni) The magnetic \feld created by any magnetic element inside the inner region - e. g. a\npermanent magnet - should not leak to outside the region enclosed by the shell.\nii) The system formed by the enclosed region plus the shell should be magnetically unde-\ntectable from outside (no interaction -e. g. no magnetic force- with any external magnetic\nsources).\nIn this work we will consider the case of a cylindrical cloak; results can be extended to\nother geometries. It was demonstrated in [1, 7, 10] that di\u000berent sets of radially dependent\nvalues of radial and angular permeabilities, \u0016\u001aand\u0016\u0012, yield a magnetic cloak behavior. An\nexample is\n\u0016\u001a=\u001a\u0000a\n\u001a;\u0016\u0012=\u001a\n\u001a\u0000a; (1)\nrepresented in Fig. 1a, with the resulting \feld pro\fle shown in Fig. 1b. Materials with\nsuch \fne-tuned values of anisotropic permeabilities do not exist. It is easily seen from Eqs.\n(1) that\u0016\u0012=1and at the same time \u0016\u001a= 0 at the inner layer ( \u001a=a). This makes any\npractical implementation very di\u000ecult [1]. In particular, condition (i) could not be ful\flled\nbecause the \feld from any internal source would leak to the exterior. Therefore a strong (or\nan exact) validation of condition (i) for our antimagnet requires a radically new approach.\nThis is what we present in this work. Two important new ideas would be required to achieve\nthe design of a practical antimagnet ful\flling conditions (i) and (ii): \frstly, the introduction\nof a new scheme for cloaking, requiring homogeneous (although anisotropic) parameters,\nwhich would involve a new transformation of space, and, secondly, the addition of an inner\nsuperconducting layer, which in the static case considered here would ensure \u0016= 0. In a\n\fnal step we will present a general way of implementing the antimagnet design in practical\ncases.\nIII. A CLOAKING DESIGN WITH HOMOGENEOUS PARAMETERS\nAs a \frst step, we want to study whether the values of \u0016derived for the magnetic cloak,\nwhich are impractical because they involve a \fne-tuned continuous variation of anisotropic\npermeabilities, can be modi\fed into a simpli\fed scheme. Can a cloaking behaviour (in\nparticular no \feld distortion in an exterior region) be produced with simpler permeabil-\n3ity arrangements -even with a homogeneous permeability value? In the following, we will\ndemonstrate that a whole family of homogeneous magnetic systems exist with the property\nthat they produce a null e\u000bect on an externally applied magnetic \feld. Each of these systems\n-we call them homogeneous cloaks - is a cylindrical shell composed of an homogeneous (i.\ne., properties are the same in all the material points) anisotropic material.\nConsider one of such cylinders in\fnitely long along the zaxis with radius R2and a\ncentral coaxial hole of radius R1< R 2. This cylinder is made of a magnetic material with\nhomogeneous radial and angular relative permeabilities, \u0016\u001aand\u0016\u0012respectively. A uniform\nexternal \feld Hais applied along the ydirection. We want to \fnd the analytical expression\nfor the \feld Hin all regions with the condition that the applied \feld is not modi\fed by the\npresence of the cylinder, in the region outside it.\nInside the material there are neither free charges nor free currents. Then, r\u0001B= 0 and\nr\u0002H= 0 and given that neither \u0016\u001anor\u0016\u0012depend on position, we obtain\n\u0016\u001a\u001a@H\u001a\n@\u001a+\u0016\u001aH\u001a+\u0016\u0012@H\u0012\n@\u0012= 0; (2)\n\u001a@H\u0012\n@\u001a+H\u0012\u0000@H\u001a\n@\u0012= 0: (3)\nThe boundary conditions for these equations are set by considering that both BandH\nequal the applied \feld values at \u001a=R2and that there is a uniform \feld inside the hole.\nThen, by imposing continuity of the normal component of Band the tangential component\nofH, we get\nH\u001a(R2) =Ha1\n\u0016\u001asin\u0012; (4)\nH\u0012(R2) =Hacos\u0012; (5)\nThe solution for the magnetic \feld inside the ring ( R1\u0014\u001a\u0014R2) is found to be\nH\u001a(\u001a;\u0012) =Ha\u0016\u0012\u0012\u001a\nR2\u0013\u00001+\u0016\u0012\nsin\u0012; (6)\nH\u0012(\u001a;\u0012) =Ha\u0012\u001a\nR2\u0013\u00001+\u0016\u0012\ncos\u0012: (7)\nIt is important to remark that this solution is valid only when the condition \u0016\u001a\u0016\u0012= 1 is\nful\flled; otherwise, the problem has no solution. Therefore, we demonstrate that the condi-\ntion of null external distortion of magnetic \feld is directly ful\flled as long as permeabilities\n\u0016\u001aand\u0016\u0012are the inverse of each other ( \u0016\u001a\u0016\u0012= 1).\n4It is interesting to notice that the presented scheme for a homogeneous cloaking implicitly\ninvolves a space transformation di\u000berent from that of Wood and Pendry [7], which involved\nexpanding a zero-dimensional point into a \fnite sphere corresponded (in our cylindrical\ncase, expanding a central one-dimensional line into a cylindrical region, that from \u001a0= 0 to\n\u001a0=a). This transformation basically consists on, \frst, compressing the space from \u001a=R0\nto\u001a=binto the space occupied by \u001a0=aand\u001a0=busing a radially symmetric function,\nand, second, expanding the space from \u001a= 0 to\u001a=R0into the space from \u001a0= 0 to\u001a0=a,\nusing another radially symmetric function. R0is a positive constant ( R0< a). A detailed\ndescription and discussion of the transformation (which may also be used in the case of\nelectromagnetic waves) will be presented elsewhere.\nAn example of such homogeneous cloak is shown in Fig. 1c, with the values \u0016\u0012=6 and\n\u0016\u001a=1/6=0.1667 (solid lines in \fg. 1a), and in Fig. 1d, with \u0016\u0012= 10 and\u0016\u001a=1/10 is\nshown; in both, the condition \u0016\u001a=1/\u0016\u0012is enough to ensure no distortion of the magnetic\n\feld outside the shell. Interestingly, it can be demonstrated that the null distortion is also\nobtained for a non-uniformly applied magnetic \feld. As to the \feld in their interior, we see\nthat increasing \u0016\u0012while maintaining the ratio \u0016\u001a\u0016\u0012=1 causes the magnetic \feld lines to be\nconcentrated nearer the external surface of the shell. This means that such homogeneous\ncloaks do not have exactly zero magnetic \feld inside, although they do so approximately -\nthe larger the value of \u0016\u0012the closer to zero the internal \feld.\nIn spite of achieving magnetic cloaking, these homogeneous cloaks are not antimagnets,\nbecause the magnetic \feld created by a source in its interior will leak to the exterior. To avoid\nthis, we introduce the second key step in our idea: placing a superconducting layer at the\ninner surface of the cloak. Because \u0016= 0 for an ideal superconductor, it directly follows from\nthe magnetostatic boundary conditions at the inner boundary of the superconductor that\ncondition (i) is ful\flled. Introducing such a superconducting layer does not substantially\nmodify the property of cloaking, as long as \u0016\u0012is su\u000eciently larger than 1, because in\nthis case, as seen in Figs. 1c and 1d, magnetic \feld is excluded from the central part so\na superconducting layer would not practically interact with the \feld created by external\nsources. In this way an antimagnet design is being outlined: an inner superconducting layer\nand an outer homogeneous shell. However, this scheme alone cannot yet solve our goal of\na feasible antimagnet, because the material in the outer shell, even though it would have a\nconstant permeability, would require \fne-tuned anisotropic values (with \u0016\u001a= 1=\u0016\u0012); such\n5materials are not available.\nIV. ANTIMAGNET DESIGN AND DEMONSTRATION OF ITS PROPERTIES\nTherefore, another important step is needed, and again help from metamaterials con-\ncepts will be used. Can we transform our homogeneous cloak with uniform and anisotropic\nparameters into one made with realistic materials? We have attained this by modifying the\nhomogeneous shell with constant anisotropic permeability into a discrete system of alter-\nnating layers of two di\u000berent kinds: one type consisting simply of a uniform and isotropic\nferromagnetic material with constant permeability ( \u0016FM\n\u001a=\u0016FM\n\u0012>1) and a second type\nhaving a constant value of radial permeability \u0016SC\n\u001a(\u0016SC\n\u001a<1) and\u0016SC\n\u0012= 1. The \frst\n(isotropic) kind of layers could be a superparamagnet (i. e. ferromagnetic nanoparticles\nembedded in a non-magnetic media [11]). The second kind could be realized with arrays of\nsuperconducting plates (the precise value tunable by changing distances between the plates)\n[7{9]; one of such arrays has actually been constructed and tested [9]. Now we need to \fnd\nthe values of permeability for the two kinds of layers. To do this, we start with the values\nfor a homogeneous cloak described above (for example, that in Fig. 1c) and then apply the\nfollowing method: we select the value of the angular permeability ( \u0016\u0012=6) for the isotropic\nlayers (\u0016FM\n\u0012=\u0016FM\n\u001a=6) and then reduce the value of \u0016SC\n\u001ain the superconducting layers to\na lower value than 1 =\u0016FM\n\u001a(1/6) to compensate for the larger value of \u0016FM\n\u001ain the isotropic\nlayers.\nTo demonstrate the validity of the method, we show in Fig. 2e the calculated response for\na system with an inner superconducting layer surrounded by 10 outer alternating layers half\nof them with \u0016FM\n\u0012=\u0016FM\n\u001a= 6 and the other half with \u0016SC\n\u001a=0.104 (and \u0016SC\n\u0012=1); the scheme\ncloaks a uniform static magnetic \feld with an impressive quality (as can be visualized in\nFig. S1). This means that our goal of using only realistic material is ful\flled. It is only left\nto con\frm that the resulting scheme acts indeed as an antimagnet and it does so for any\napplied \feld. This is demonstrated on the panels in Fig. 2, where we show the magnetic\n\feld of a single small magnet (basically a dipole \feld), the \feld of two such magnets (now\nthe \feld has changed very much because of the interaction), and, \fnally, how surrounding\none of the magnets with the antimagnet makes the \feld outside it una\u000bected - i. e. equal to\nthe \feld of a single magnet. Besides the constant \feld and two dipole cases, we also show in\n6Fig. 2d another example corresponding to the \feld created by a current line. In all cases the\nantimagnet is the same. We thus con\frm that the antimagnet performs as a such for any\napplied \feld con\fguration. We also show in Fig. 2f that even when there is missing portion\nof the antimagnet, a reasonable shielding inside with a small \feld modi\fcation outside can\nbe obtained.\nV. DISCUSSION\nThe presented solution with 10 layers and \u0016FM\n\u0012= 6 is not unique; starting from a\ndi\u000berent\u0016FM\n\u0012=\u0016FM\n\u001avalue (10, for example, as in Fig. 1d) and even with a di\u000berent\nnumber of layers one can follow the described method and obtain similarly good antimagnet\nproperties. Actually, although a good behavior is obtained for 10 layers as shown above,\nincreasing the number of layers may be convenient when there is an applied \feld very\nspatially inhomogeneous or when we require a certain practical tolerance in the values of\nthe permeabilities (more on this in Figs. 3 and S2).\nWe would like to make some remarks with practical consequences. First, we have con-\nsidered that the superconductor is characterized by \u0016= 0, which is a good approximation\nfor superconductors in the Meissner state. This would limit in principle the applicability of\nthe antimagnet to applied \felds less than the (thermodynamic or lower) critical \feld of the\nsuperconductor. However, a type-II superconductor (like most high-temperature ones) with\na high critical-current density can produce a response very similar to a Meissner response\n(with currents circulating mainly in a thin layer at the surface) up to much larger \felds [12].\nFinally, constructing the described antimagnet with 10 layers may be feasible but di\u000ecult\nin practice. However, the same strategy can be applied to a much more simple design, by\nsubstituting all superconducting layers (except the central one) with layers with \u0016= 1\n(the permeability of air or any non-magnetic material such as plastic). This change requires\ntuning the value of \u0016in the magnetic layers to a di\u000berent value. An example of that is shown\nin Fig 4. This simpli\fed scheme works equally well than the described antimagnet when\nthere is a uniform magnetic \feld, whereas its response gets worse with increasing applied \feld\ninhomogeneity. Moreover, in the latter case, increasing the number of layers does not bring\na signi\fcant improvement of the antimagnet properties. Therefore, this simpli\fed scheme\nwith only a central superconducting layer and layers with homogeneous \u0016alternated with\n7air may work well for applications in which the applied \feld has a small spatial variation.\nVI. CONCLUSIONS\nIn summary, we have presented a method to design hybrid superconductor-metamaterial\ndevices that prevent any magnetic interaction with its interior while keeping the external\nmagnetic \feld una\u000bected. Two important key ideas have been needed for achieving our\ngoal: the design of a simpli\fed cloak with homgeneous parameters, corresponding to a new\nspace transformation, and the placement of a superconducting layer at the inner surface.\nSuch an antimagnet would be passive and, provided that the superconductors are in the\nMeissner state [8] and that the isotropic layers have a negligible coercivity (as if using\nsuperparamagnetic materials), also lossless. The strategy for antimagnet design presented\nin this work can be adapted to other geometries (e.g. spheres) or even to other forms of\nmanipulating magnetic \felds, such as magnetic \feld concentrators [10, 13]. Antimagnet\ndevices may bring important advantages in \felds like reducing the magnetic signature of\nvessels or in allowing patients with pacemakers or cochlear implants to be allowed to use\nmedical equipment based on magnetic \felds, such as magnetic resonance imaging MRI [14] or\ntranscraneal magnetic stimulation [15]. Moreover, by tuning one parameter like the working\ntemperature of the device - below or above the critical temperature of the superconductor,\nfor example - one could 'switch o\u000b and on' magnetism in a certain region or material at will,\nopening up room for some novel applications.\nMethods\nThe simulations have been performed with Comsol Multiphysics software, using the elec-\ntromagnetics module (magnetostatics). All the presented results correspond to an in\fnitely\nlong cylinder (with translational symmetry) with outer radius equal twice the inner radius\n(b= 2a). We have checked that other dimensions yield similar results. Except when oth-\nerwise indicated, we have considered 10 outer layers plus an inner superconducting layer,\nall with the same thickness. The outest layer is of the magnetically isotropic type. The\nsuperconductor has been simulated assuming \u0016= 0. All permeabilities are understood to\nbe relative permeabilities. The pink region in Figs. 3 and 4 denoting the region in which\n8the magnetic induction Bdi\u000bers from the externally applied magnetic induction Bextis\ncalculated as the points in space following the condition\nvuut(Bx\u0000Bx;ext)2+ (By\u0000By;ext)2\n(Bx;ext)2+ (By;ext)2>0:01 (8)\nAcknowledgements\nWe thank Spanish Consolider Project NANOSELECT (CSD2007-00041) for \fnancial\nsupport.\n[1] Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic \felds. Science 312,\n17801782 (2006).\n[2] Leonhardt U. Optical conformal mapping. Science 312, 1777-1779 (2006).\n[3] Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314 ,\n977 (2006).\n[4] Ergin T., Stenger N., Brenner P., Pendry, J. B., Wegener M. Three-Dimensional Invisibility\nCloak at Optical Wavelengths. Sience 328, 337 (2010).\n[5] Chen X., Luo Y., Zhang J., Jiang K., Pendry J. B., and Zhang, S. Macroscopic invisibility\ncloaking of visible light. Nat. Commun. 2, 176 (2011).\n[6] Leonhardt U. To invisibility and beyond. Nature 471, 292-293 (2011).\n[7] Wood, B. & Pendry, J. B. Metamaterials at zero frequency. J. Phys. Condens. Matter 19,\n076208 (2007).\n[8] Navau, C., Chen, D.-X., Sanchez, A. and Del-Valle, N. Magnetic properties of a dc metama-\nterial consisting of parallel square superconducting thin plates. Appl. Phys. Lett. 94, 242501\n(2009).\n[9] Magnus, F. et al. A d.c. magnetic metamaterial. Nature Materials 7, 295 - 297 (2008).\n[10] Yaghjian, A. D. and Maci ,S. Alternative derivation of electromagnetic cloaks and concentra-\ntors. New Journal of Phys. 10, 115022 (2008).\n[11] Goya, G. F., Berquo, T. S., Fonseca, F. C., and Morales, M. P.. Static and dynamic magnetic\nproperties of spherical magnetite nanoparticles. J. Appl. Phys. 94, 3520 (2003).\n9[12] F. M. Araujo-Moreira, C. Navau, and A. Sanchez. Meissner state in \fnite superconducting\ncylinders with uniform applied magnetic \feld. Phys. Rev. B 61, 634 (2000).\n[13] Rahm, M. et al. Design of electromagnetic cloaks and concentrators using form-invariant\ncoordinate transformations of Maxwell's equations. Photon. Nanostruct.: Fundam. Applic. 6,\n87 (2008).\n[14] Roguin, A. Magnetic Resonance Imaging in Patients With Implantable Cardioverter-\nDe\fbrillators and Pacemakers. J. Am. Coll. Cardiol. 54, 556 (2009).\n[15] Kobayashi, M. and Pascual-Leone, A. Transcranial magnetic stimulation in neurology. Lancet\nNeurology 2, 145 (2003).\n10FIG. 1: Magnetic permeabilities and behavior of exact and approximate magnetic\ncloaks . In panel ( a) radial dependence of radial and angular permeability for a cylinder of inner\nradiusaand outer radius b= 2a; curves are the values for the exact cloak [Eq. (1)] and straight\nlines are the approximate constant values in panel ( c). In the rest of the panels, magnetic \feld lines\nfor the ( b) exact cloak, ( c) approximate cloak with constant values \u0016\u0012=6 and\u0016\u001a=1/6=0.1667, and\n(d) approximate cloak with constant values \u0016\u0012=10 and\u0016\u001a=1/10.\n11FIG. 2: Display of the antimagnet behavior. The magnetic properties of an antimagnet\nare visualized as follows. First, we show in panel ( a) the magnetic \feld lines for one uniformly\nmagnetized cylindrical magnet. When a second magnet is added ( b) the magnetic \feld is distorted\nowing to the magnetic interaction between both magnets. When one of the two magnets is covered\nby the antimagnet ( c), then the magnetic \feld outside the region enclosed by the antimagnet is\nthe same as that for a single magnet (as in panel a), demonstrating the two antimagnet properties:\nthe \feld of the inner magnet does not leak outside the antimagnet shell and the \feld external to\nthe antimagnet remains unperturbed independently of what it is contained in its interior. In panel\n(d) and ( e) the same antimagnet is shown to behave as such in the \feld of a current carrying\nwire and a uniformly applied magnetic \feld, respectively. Panel ( f) shows that a rather good\nantimagnet behavior is maintained even when the shell is not closed. The antimagnet is composed\nof an inner superconducting layer ( \u0016= 0) and 10 alternating outer layers of two kinds: one with\n\u0016FM\n\u0012=\u0016FM\n\u001a= 6 and the other with \u0016SC\n\u001a=0.104.\n12FIG. 3: Optimizing the number of layers for the antimagnet. Response of antimagnets\nwith -from left to right- 10, 20, and 30 layers to the \feld created by a near uniformly magnetized\ncylindrical magnet. The permeabilities of the magnetic layers are in all cases \u0016FM\n\u0012=\u0016FM\n\u001a= 6\nwhereas the superconducting ones are \u0016SC\n\u001a=0.104, 0.128, and 0.136, for the 10, 20, and 30 layer-\ncases, respectively. The light pink region indicates the zones for which the di\u000berence between the\ntotal \feld and the dipole \feld exceeds 1% and the darker pink region when they exceed 3%.\n13FIG. 4: Simpli\fed antimagnet with air ( \u0016= 1) layers. Response of the antimagnet of 10\nlayers (as in Fig. 1) for a uniform applied \feld, a dipole-like \feld and the \feld of a current-carrying\nwire (top row, form left to right). For comparison, the same results are plotted in the bottom row\nfor the simpli\fed antimagnet case in which the permeability \u0016SC\n\u001aof the superconducting layers\n- except the central one, which has \u0016= 0- has been set as 1 (and \u0016FM\n\u0012=\u0016FM\n\u001a=2.405 in this\ncase). The pink regions indicate the zones for which the di\u000berence between the total \feld and the\nexternally applied \feld exceeds 1%. Both antimagnet and simpli\fed designs work well for uniform\napplied \feld, but the region of distortion of the external \feld is large in the latter.\n14"    },    {        "title": "1108.1990v1.Proximal_magnetometry_of_monolayers_of_magnetic_moments.pdf",        "content": "Physics Procedia 00 (2021) 1–6Physics Procedia\nProximal magnetometry of monolayers of magnetic moments\nZ. Salmana,\u0003, S. J. Blundellb\naLaboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5 232 Villigen PSI, Switzerland\nbClarendon Laboratory, Department of Physics, Oxford University, Parks Road, Oxford OX1 3PU, UK\nAbstract\nWe present a method to measure the magnetic properties of monolayers and ultra-thin films of magnetic material.\nThe method is based on low energy muon spin rotation and \f-detected nuclear magnetic resonance measurements. A\nspin probe is used as a “proximal” magnetometer by implanting it in the substrate, just below the magnetic material.\nWe calculate the expected magnetic field distribution sensed by the probe and discuss its temperature and implantation\ndepth dependencies. This method is highly suitable for measuring the magnetic properties of monolayers of single\nmolecule magnets, but can also be extended to ultra-thin magnetic films.\nKeywords: Single molecule magnets, ultra-thin magnetic films, monolayer, proximal magnetometry\n1. Introduction\nRecent developments of low energy muon spin rotation (LE- \u0016SR) [1, 2] and \f-detected nuclear magnetic reso-\nnance (\f-NMR) [3, 4], provide unique local spin probe tools for measurements in thin films and multilayers. However,\nthe application of these methods is limited by a minimal thickness of films, which provides su \u000ecient stopping power\nfor the implanted probes. For typical density materials a minimal 1-2 nm thickness is required at the lowest available\nimplantation energy (1-2 keV). Therefore, these methods are generally not suitable for studies of monolayers and\nultra-thin films. Nevertheless, for magnetic materials it is possible to perform a “proximal” measurement by implant-\ning the probe in the substrate (or an under-layer) of the material, and sensing the dipolar magnetic fields from the layer\nof interest [5, 6].\nTo date, measurements of the magnetic properties of monolayers of single molecule magnets [7] (SMMs) have\nbeen mostly performed using X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichorism (XMCD)\n[8, 9]. These are typically limited to high magnetic fields and provide information regarding the average static mag-\nnetic properties of the irradiated portion of the monolayer. In contrast, LE- \u0016SR and\f-NMR provide local probe\nmeasurements with important advantages; sensitivity to a large range of spin fluctuations and dynamics and applica-\nbility in zero or any applied magnetic field. However, a detailed interpretation of the measured spectra using LE- \u0016SR\n[6] or\f-NMR [5] when implanting the probe just below the monolayer is still absent. In this paper we calculate the\nmagnetic field distribution in a non-magnetic substrate due to a monolayer of SMMs. This distribution can be used\nto fit LE-\u0016SR and\f-NMR measurements, providing information regarding the magnetic and geometric properties of\nthe monolayer. The calculations can be easily generalized for the case of ultra-thin magnetic films by considering the\ndomains as individual magnetic moments with a given average size.\n\u0003Tel.+41-56-310-5457\nEmail address: zaher.salman@psi.ch (Z. Salman)arXiv:1108.1990v1  [cond-mat.mes-hall]  9 Aug 2011Z. Salman et al. /Physics Procedia 00 (2021) 1–6 2\n2. Uniformly Magnetized Sheet Approximation\nAs a simple approximation, a monolayer of magnetic moments (or a thin film) can be viewed as a uniformly\nmagnetized sheet. Assuming magnetic moment Mper unit area, located in the plane z=0 (see inset of Fig. 1) with\nthe magnetization aligned along \u0000ˆz. The magnetic scalar potential from an annular region of radius \u001aand width d\u001ais\nd\u001eM(\u001a;z)=\u0000Mz\u001ad\u001a\n2(z2+\u001a2)3=2: (1)\nThe contribution of such a region to the magnetic field at a distance zfrom its center is\ndBz(\u001a;z)=\u0000\u00160@(d\u001eM)\n@z=\u00160M\n2\u001a(\u001a2\u00002z2)\n(\u001a2+z2)5=2d\u001a; (2)\nwhere\u00160is the permeability of the vacuum. We plot this contribution as a function of \u001a=zin Fig. 1. Integrating the\n/s48/s50 /s52 /s54 /s56 /s49 /s48/s45/s48/s46/s54/s45/s48/s46/s52/s45/s48/s46/s50/s48/s46/s48/s48/s46/s50\n/s32\n/s32/s100/s66/s122/s32/s91/s97/s46/s117/s46/s93/s61554\n/s47/s122\nFigure 1: The contribution dBzof one annular region as a function\nof\u001a=z. The inset shows a uniformly magnetized sheet divided into\nannular regions.\nFigure 2: The zcomponent of the field, sensed by a spin probe at\nz=a=2, as a function of position. The color scale represents the\nstrength of the field.\ncontributions from all annuli gives a magnetic field zero as expected.\nHowever, this approximation fails when looking at the microscopic structure of the sheet, i.e., as a collection of\nindividual magnetic moments or even randomly oriented magnetic domains. This is the case when measuring the field\ndue to such sheet using a local spin probe, which is positioned at a distance smaller than the microscopic details of the\nsheet (distance between moments or size of domains). For example, if we have a monolayer of moments with average\nspacing abetween them, then the magnetic field sensed by a spin probe at a distance z<afrom the monolayer is\nnon-zero.\n3. Monolayer of Magnetic Moments\nIn order to adequately account for the microscopic structure of a monolayer of magnetic moments, ~\u0016i, one needs\nto sum the contribution of all moments in the monolayer. The dipolar field from ~\u0016iat~ri=xiˆx+yiˆy+ziˆzis\n~Bi(~ri)=\u00160\n4\u00193~ri(~\u0016i\u0001~ri)\u0000~\u0016ir2\ni\nr5\ni: (3)\nA typical NMR or transverse field \u0016SR measurement is sensitive to the field distribution of one component of the field.\nIn what follows we will restrict ourselves to the Bzcomponent, where zis normal to the monolayer surface. Working\nin polar coordinates with ~\u0016i=\u0016i\n\u001aˆ\u001a+\u0016i\nzˆzand~ri=\u001aiˆ\u001a+ziˆzwe can write\nBi\nz(\u001ai;zi)=\u00160\n4\u00193zi\u001ai\u0016i\n\u001a+2z2\ni\u0016i\nz\u0000\u001a2\ni\u0016i\nz\n(\u001a2\ni+z2\ni)5=2: (4)Z. Salman et al. /Physics Procedia 00 (2021) 1–6 3\nTherefore the field distribution, n(z;B), can be obtained by summing the contribution from all magnetic moments.\nFor simplicity, we start by considering a monolayer of moments ~\u0016i=\u0016ˆzin the plane z=0, arranged on a triangular\nlattice with lattice constant a. For example, taking \u0016=\u0016B, a spin probe at z=a=2 will sense dipolar fields as shown\nin Fig. 2. The resulting field distribution is shown in Fig. 3(a), where di \u000berent curves are results of summation of a\ndi\u000berent number of moments, such that Nis the radius (in units of a) of the considered “patch”. In order to sample a\nfield distribution as in Fig. 2, it is su \u000ecient to sample only a unit cell of an equilateral ( a) triangular area between 3\nmoments1. Note that the qualitative shape of the distribution is almost independent of N. However, due to the finite\nnumber of considered moments, we find a strong shift which decreases as a function of N.\n/s48/s49/s53/s51/s48/s52/s53/s48\n/s49 /s53/s51 /s48/s52 /s53/s54 /s48/s45/s51/s45/s50/s45/s49/s48/s45\n/s53/s48 /s53 /s49 /s48/s48/s49/s53/s51/s48/s52/s53/s32/s78/s61/s51/s32/s32/s32/s32/s32/s32/s32/s32/s32 /s78/s61/s50/s48/s32\n/s78/s61/s53/s32/s32/s32/s32/s32/s32/s32/s32/s32 /s78/s61/s52/s48/s32\n/s78/s61/s49/s48/s32/s32/s32/s32/s32/s32/s32 /s78/s61/s54/s48/s32\n/s32/s110/s110/s99/s40/s122/s44/s66/s41/s32/s91/s37/s93/s40/s97/s41/s32\n/s78\n/s32/s66/s109/s97/s120/s32/s97/s51/s91/s84/s197/s51/s93/s40/s98/s41/s32\n/s32/s110/s40/s122/s44/s66/s41/s32/s91/s37/s93/s66\n/s97/s51/s32/s91/s84/s197/s51/s93\nFigure 3: The distribution of Bzsensed by a spin probe due to a patch of moments with radius N(a) before and (b) after the correction in Eq. 6.\nThe inset shows the most probable field as a function of Nbefore (full symbols) and after (empty symbols) correction.\nIn order to correct for this “artifact” we need to account for all the moments in the infinite monolayer. However,\nsince the moments outside the patch satisfy the criterion of a uniformly magnetized sheet, i.e. ri\u001da, their contribution\ncan be calculated as an infinite sheet of uniform magnetization with a hole of radius \u001a0=aNaround the origin. This\ncan be calculated by integrating dBz(Eq. 2) between \u001a=\u001a0and infinity,\n\u0001Bz=Z1\n\u001a0dBz(\u001a;z)=\u00160M\n2\u001a0(1+\u00102)3=2; (5)\nwith\u0010=z=\u001a0. In contrast to the case of a uniformly magnetized sheet, \u0001Bzhere does not vanish for finite \u001a0. Note\nthat when the spin probe is far from the monolayer, such that \u001a0\u001dz, then \u0001Bz\u0019\u00160M\n2\u001a0. This is quite di \u000berent from\nthe three dimensional case, where the remaining contribution is\u00160M\n3(where in this case Mis the three-dimensional\nmagnetization, i.e. the magnetic moment per unit volume), independent of how far we integrate out to.\nAssuming uniform magnetization due to moments \u0016=\u0016B, ordered on a triangular lattice with lattice constant a,\nthe magnetic moment per unit area is M=\u0016B=(p\n3a2=4). Using N=\u001a0=awe arrive at,\n\u0001Bz=2\u00160\u0016Bp\n3a3N(1+\u00102)3=2: (6)\n1Due to the symmetry of the lattice the sampling can also be done on 1 /6 of this areaZ. Salman et al. /Physics Procedia 00 (2021) 1–6 4\nThis is the cause of shift seen in Fig. 3(a), and should be subtracted from the dipolar field of the patch of moments\nto correct for its finite size e \u000bect. Comparison between the field distribution before (Fig. 3(a)) and after (Fig. 3(b))\nthe correction shows clearly how well it works. Taking into consideration a patch with N=10 is already su \u000ecient to\naccurately calculate the field distribution. Note that without the correction, even a patch with N=60 exhibits a small\nartificial shift (inset of Fig. 3).\nThe field distribution has a similar shape to that in the vortex state of a superconductor [10]. The high field cut-\no\u000bis due to probes stopping exactly below a magnetic moment, while the low field cusp is due to probes stopping\nin middle between three neighbouring moments. However, one important di \u000berence between this case and a vortex\nlattice is that in the former the field distribution depends strongly on the stopping depth of the probe while in a\nsuperconductor the depth dependence is much weaker [11, 12]. As we show below, this strong depth dependence will\nalter the shape of the field distribution entirely in a real measurement. Nevertheless, it is important to point out here\nthat the shape of n(z;B) is determined by the lattice constant aand and the size of magnetic moment \u0016. Hence, these\nparameters can, in principle, be extracted directly from a measurement of the field distribution. Also, the details of\nthe lattice, e.g. triangular or other, do not alter the qualitative shape of n(z;B) dramatically.\n4. Measured Field Distribution\nIn a LE-\u0016SR or\f-NMR measurements, the implanted probes stop in the sample at a distribution of depths, D(z),\nrather than a unique single depth. This distribution can be simulated accurately [13, 14] using Trim.SP Monte-Carlo\ncode [15]. Therefore, the calculated n(z;B) should be averaged over D(z). Moreover, since the probe stops in the\nsubstrate of the monolayer, its intrinsic line shape (field distribution) has to be convoluted with the depth averaged\nfield distribution. Finally, disorder in the monolayer, e.g. deviations from a perfect triangular lattice, can be taken\ninto account by convoluting the depth averaged distribution with a Gaussian of width that represents the degree of\ndisorder. In practice, one can simply convolute the calculated distribution with a single Gaussian or Lorentzian that\nincludes both substrate and disorder e \u000bects. The resulting field distribution is then\nL(B)=I(B)\u0003Z1\nz0D(z)n(z;B)dz; (7)\nwhere I(B) is the broadening due to the substrate and disorder, and z0is the distance between the magnetic cores in\nthe monolayer and the surface of the substrate. In the case of SMMs, z0is due to the ligands used to graft the magnetic\ncorse of a SMM to the substrate. In Fig. 4, we plot a typical field distribution due to a monolayer of 1 \u0016Bmoments,\nwith a\u00185 nm, z0\u00181 nm and a stopping profile as shown in the inset. Both, the distribution with (solid line) and\n/s45/s50/s48/s48 /s50 /s48/s48/s46/s48/s48/s48/s46/s50/s53/s48/s46/s53/s48/s48/s46/s55/s53/s49/s46/s48/s48/s48\n/s46/s48/s48 /s46/s53/s49 /s46/s48/s49 /s46/s53/s50 /s46/s48/s32\n/s32/s76/s40/s66/s41/s66\n/s97/s51/s32/s91/s84/s197/s51/s93/s32/s32\n/s122\n/s47/s97/s68/s40/s122/s41/s32/s91/s97/s46/s117/s93/s122\n/s48/s47/s97\nFigure 4: The field distribution L(B) sensed by a spin probe due to\na monolayer of moments at z=0. The dashed and solid lines are\ncalculated with and without broadening, respectively. The inset\nshows a typical stopping profile of implanted probes in the sub-\nstrate (shaded area).\n/s48/s50 /s53/s53 /s48/s55 /s53/s49 /s48/s48/s48/s52/s48/s56/s48/s49/s50/s48/s49/s54/s48/s48\n/s53 /s49 /s48/s48/s53/s49/s48/s49/s53/s32\n/s32/s97/s51/s40/s60/s66/s50/s62/s45/s60/s66/s62/s50/s41/s49/s47/s50/s32/s91/s84/s197/s51/s93/s40\n/s97/s47/s122/s41/s50/s32/s32Figure 5: The square root of the second moment of the field dis-\ntribution as a function of distance from the monolayer (circles and\nsolid line in inset). The inset is an expanded view of the shaded\narea. The dashed line is the fit described in the text.\nwithout (dashed line) the broadening I(B) are shown. Surprisingly, the asymmetry of the distribution after averaging\nover depth is opposite to that of a single depth, i.e. we find a low field instead of the high field tail in Fig. 3. This is\ndue to a larger near-zero field contribution of probes implanted deeper into the substrate, far away from the magneticZ. Salman et al. /Physics Procedia 00 (2021) 1–6 5\ncores in the monolayer. Note that unlike Fig. 3, the most probable field in L(B) is much closer to B=0, and therefore\nin a real measurement we do not expect to see a considerable shift in the precession frequency of the probe, instead\nonly some broadening can be measured [5, 6].\nNow we turn to the depth dependence of the field distribution. As we mentioned earlier, we expect that for a depth\nz\u001dathe dipolar field of the magnetic moment vanishes as in the case of a uniformly magnetized infinite sheet. The\ndepth dependence can be very useful in measurements as a tool for identifying (I) the nature of the sensed magnetic\nfields by the probe, dipolar or other, and (II) to estimate the characteristic length scale, a, in the monolayer [5]. In\nFig. 5 we plot the second moment of the field distribution as a function of depth. The dashed line is a linear fit of the\nsecond moment as a function of ( a=z)2in the range 50-100. Clearly, the second moment is inversely proportional to\nz2. This is in contrast to the 1 =z3dependence of the dipolar field from a single moment. A very small deviation from\nthe (a=z)2behaviour can be seen for z\u0015a=3 (see inset of Fig. 5). Note also that the second moment vanishes at z\u0018a,\nas expected.\n5. Information Drawn from an Experiment\nConsidering actual measurements, in LE- \u0016SR we measure the time dependence of the polarization of the im-\nplanted muons in an applied transverese field. This is proportional to the Fourier transform of field distribution sensed\nby the muons, so that the average precession frequency is propotional to the average field and damping rate is propor-\ntional to the width of field distribution. In a \f-NMR experiment we measure the8Li nuclear magnetic resonance line\nwhich directly proportional to the field distribution. In both cases it is, in principle, possible to fit the measured spec-\ntra. However, the asymmetry of the field distribution is quite small, and therefore hard to detect within the uncertainty\nof the measurement. Usually it is su \u000ecient to approximately fit the data assuming a simple Lorentzian field distribu-\ntion. As we mentioned above, there is no detectable shift in the average field as a function of depth and temperature.\nIn contrast, the width of the distribution depends strongly on these parameters. In fact, the width is proportional to\nh\u00162i. Therefore, its temperature dependence can be obtained by measuring the temperature dependence of the field\ndistribution width at a fixed depth (implantation energy). From this one should subtract the additional broadening due\nto the substrate. This can be easily evaluated by a measurement of the field distribution as a function of temperature\ndependence at large depths (high implantation energy). Finally, we point out that since we are dealing with local probe\nmeasurements, the averaging in h\u00162i, is on individual moments during the lifetime of the probe. This is di \u000berent from\nthe case of a XMCD measurement, where the averaging is done on the absorption signal from all molecules.\n6. Conclusions\nWe have presented a detailed calculation of the properties of the magnetic field distribution, measured in the\nsubstrate, due to a monolayer near its surface. This distribution and its depth dependence can be used to infer the\nproperties of the monolayer, such as the size of magnetic moment and the average distance between neighbouring\nmoments. Although we restricted our calculations to oriented moments on a triangular lattice, they can be easily\ngeneralized for di \u000berent systems. Nevertheless, the depth dependence of the width of the distribution (i.e. relaxation\nrate of the muon spin precession) and its temperature and depth dependencies should not be a \u000bected by the geometric\ndetails of the lattice.\nReferences\n[1] E. Morenzoni et al., Phys. Rev. Lett. 72 (1994) 2793.\n[2] T. Prokscha et al., Nucl. Instr. and Meth. A 595 (2) (2008) 317–331.\n[3] Z. Salman, E. P. Reynard, W. A. MacFarlane, K. H. Chow, J. Chakhalian, S. R. Kreitzman, S. Daviel, C. D. P. Levy, R. Poutissou, R. F. Kiefl,\nPhys. Rev. B 70 (2004) 104404.\n[4] G. D. Morris et al., Phys. Rev. Lett. 93 (2004) 157601.\n[5] Z. Salman et al., Nano Lett. 7 (2007) 1551.\n[6] Z. Salman et al., arXiv:0909.4634v1.\n[7] D. Gatteschi, R. Sessoli, J. Villain, Molecular Nanomagnets, Oxford University Press, 2006.\n[8] M. Mannini et al., Nature Mater. 8 (3) (2009) 194–197.\n[9] M. Mannini et al., Nature 468 (7322) (2010) 417–421.Z. Salman et al. /Physics Procedia 00 (2021) 1–6 6\n[10] E. H. Brandt, J. Low. Temp. Phys. 73 (5-6) (1988) 355–390.\n[11] C. Niedermayer et al., Phys. Rev. Lett. 83 (1999) 3932.\n[12] Z. Salman et al., Phys. Rev. Lett. 98 (2007) 167001.\n[13] E. Morenzoni et al., Nuc. Inst. Meth. Phys. 192 (2002) 254.\n[14] T. A. Keeler et al., Phys. Rev. B 77 (14) (2008) 144429.\n[15] W. Eckstein, Computer Simulation of Ion-Solid Interactions, Springer, Berlin, Heidelberg, New York, 1991."    },    {        "title": "1108.2105v1.A_route_towards_finding_large_magnetic_anisotropy_in_nano_composites__application_to_a_W___1_x__Re__x__Fe_multilayer.pdf",        "content": "A route towards \fnding large magnetic anisotropy in nano-composites: application to\na W 1\u0000xRex/Fe multilayer\nSumanta Bhandary,1Oscar Gr\u0017 an as,1Laszlo Szunyogh,2Biplab Sanyal,1Lars Nordstr om,1and Olle Eriksson1\n1Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden\n2Department of Theoretical Physics, Budapest University of Technology\nand Economics, Budafoki u. 8, H-1111, Budapest, Hungary\n(Dated: September 25, 2021)\nWe suggest here a novel nano-laminate, 5[Fe]/2[W xRe1\u0000x] (x=0.6-0.8), with enhanced magnetic\nhardness in combination with a large saturation moment. The calculated magnetic anisotropy of\nthis material reaches values of 5.3-7.0 MJ/m3, depending on alloying conditions. We also propose\na recipe in how to identify other novel magnetic materials, such as nano-laminates and multilayers,\nwith large magnetic anisotropy in combination with a high saturation moment.\nI. INTRODUCTION\nThe search for new materials with tailored proper-\nties for speci\fc applications is a vital e\u000bort in the\nrealization of novel and improved technologies. Re-\ncent developments in the ability to perform theoretical\nsimulations with predictive power are just starting to\nshow potential in this regard. An example here is the\npredicted huge tunneling magneto-resistance (TMR) of\nFe/MgO/Fe trilayers,1,2which subsequently was veri\fed\nexperimentally.3Most read-heads in modern disc-drives\nactually make use of this huge TMR e\u000bect.\nMagnetic materials are found in many applications.\nAn example are permanent magnets, where the large en-\nergy product of Nd 2Fe14B is utilized,4e.g. in electri-\ncal machines and generators. The materials properties\nwhich are relevant in Nd 2Fe14B is the large magnetic\nanisotropy energy (MAE) combined with a large satu-\nration moment (M s). Recently the risk of only a limited\naccess to rare-earth elements has been discussed, with a\npotential threat for manufacturing permanent magnets\nlike Nd 2Fe14B.5Other classes of materials, which do not\ncontain rare-earth elements, but with similar magnetic\nproperties, are hence in high demand.\nTo identify materials with a large saturation moment\nonly, is a subject of interest in its own right, with sev-\neral challenges, e.g. as discussed recently.6The wish of\ncombining a large saturation moment with a high MAE\nbecomes even more complicated, since the physical in-\nteractions responsible for one property do not necessar-\nily correlate with those determining the other. To date\nno material has been identi\fed with magnetic properties\nsuperior to rare-earth based compounds, where SmCo 5\nand Nd 2Fe14B stand out in particular. Several new ma-\nterials have however been considered, where the tetrag-\nonal compound FePt is one of the most recently studied\nmaterials.7\nTheory based on density functional theory has proven\naccurate in reproducing measured saturation moments,\nand the di\u000berence between observations and measure-\nments is seldom larger than 5-10 %. As regards the\nmagnetic anisotropy it is signi\fcantly more di\u000ecult,\nsince the accuracy needed is very high. However, somedevelopments have recently been made.8As an exam-\nple we mention the predicted large MAE of a tetrago-\nnally strained FeCo-alloy9which subsequently was veri-\n\fed experimemtally.10\nIn this communication we use \frst principles theory\nand focus on the magnetic anisotropy energy (MAE) and\nsuggest a novel nano-laminate with enhanced magnetic\nhardness in combination with a large saturation moment.\nIn addition to identifying this new material, we propose\nhere a recipe in how to identify other novel magnetic\nmaterials, such as nano-laminates and multilayers, with\nlarge magnetic anisotropy in combination with a high\nsaturation moment.\nII. GEOMETRY AND COMPUTATIONAL\nDETAILS\nIn a similar spirit as that used in Ref.9 we wish to inves-\ntigate the MAE as a function of electron concentration,\nbut in the present study it is the electron concentration\nof the ligand atoms, W and Re, which are under focus,\nnot the atoms carrying the magnetic moment(Fe). The\nadvantage of tuning the electron concentration of the lig-\nand states, is that they can be chosen with a large spin-\norbit coupling, which via hybridization with the Fe 3d\nstates are expected11to in\ruence the anisotropy of the\nwhole multilayer. We considered multilayers of di\u000ber-\nent thickness of the Fe and W-Re layer, and the chosen\ncomposition, 5[Fe]/2[W xRe1\u0000x] (x=0.6-0.8), is the one\nthat gives a suitable strain of the W-Re layer, as well as\nan optimized electron concentration, as described below.\nThe \fnal geometry was obtained via force minimization\nusing the VASP package. This resulted in essentially a\ntetragonal structure with an e\u000bective c/a ratio of the W-\nRe layers (and of the Fe layers), i.e. the ratio between\natomic distances of the W-Re layer in the out-of-plane\nand in-plane direction. As we shall see below this ratio\nis a crucial parameter determining the MAE.\nUsing the geometry optimized structure we then used\ntwo all electron methods to calculate the MAE, which are\ndescribed in detail below. The two methods are below re-\nferred to as FPLMTO-VCA12and KKR-CPA.13In thesearXiv:1108.2105v1  [cond-mat.mtrl-sci]  10 Aug 20112\ncalculations we also varied, within limits, the c/a ratio\nof the W-Re layer, and as we shall see below, this causes\ndrastic changes in the MAE. An experimental realiza-\ntion of modifying the e\u000bective c/a ratio of multilayers is,\nin general, readily done by varying the thickness of the\nindividual layers.\nAs mentioned, from the geometry optimized structure\nwe used an all electron, full-potential linear mu\u000en-tin\norbital (FPLMTO) method12to evaluate the MAE. This\ncalculation used the simple virtual crystal approximation\n(VCA) to treat the alloying between W and Re. In these\nsubsequent calculations we also varied, within limits, the\nc/a ratio of the W-Re layer, and as we shall see below,\nthis causes drastic changes in the MAE. An experimental\nrealization of modifying the e\u000bective c/a ratio of the W-\nRe layers can be done by tuning the relative amount of\nFe and W-Re layers, i.e. by considering the superlattice\nm[Fe]/n[W xRe1\u0000x], with m6= 5 and n6= 2.\nIn order to give further credit to our theoreti-\ncal study we repeated the MAE calculations for the\n5[Fe]/2[W xRe1\u0000x] superlattice in terms of the fully\nrelativistic screened Korringa-Kohn-Rostoker (SKKR)\nmethod13. This method can combine a full relativistic\ndescription with the more advanced coherent-potential\napproximation (CPA) to tackle the chemical disorder in\nthe W xRe1\u0000xlayers (where x=0.79). We used the lo-\ncal spin{density approximation of the density functional\ntheory as parametrized by Vosko et al.14, the e\u000bective po-\ntentials and \felds were treated within the atomic sphere\napproximation (ASA) with an angular momentum cut{\no\u000b of`max = 3. To calculate the MAE we used the\nso-called magnetic force theorem15in which the previ-\nously determined self-consistent e\u000bective potentials and\n\felds are kept \fxed and the change of total energy of\nthe system with respect to the direction of the magne-\ntization, ^n, is approached by that of the single-particle\n(band) energy. In these calculations the energy integra-\ntions were performed by sampling 20 points on a semi-\ncircular path in the upper complex semi-plane and, for\nthe energy point closest to the real axis, nearly 10.000\nk-points were selected in the surface Brillouin zone that\nensured a numerical error not exceeding about 5% of the\ncalculated MAE values.\nIII. RESULTS\nWe show in Fig.1a the calculated MAE of\n5[Fe]/2[W xRe1\u0000x] as a function of the local c/a ra-\ntio of the W-Re layers. The starting concentration\nwhich was considered was x=0.8. In the \fgure we show\nboth results from FPLMTO-VCA as well as KKR-CPA.\nFrom the \fgure it is clear that the two methods give\nsimilar overall behavior, but that the KKR-CPA calcu-\nlations result in a maximum of \u00184 meV/f.u., whereas\nthe FPLMTO-VCA results have a maximum of \u00183\nmeV/f.u. This is comforting since the KKR-CPA treats\nthe disorder better while the FPLMTO-VCA handlesthe relaxed structure more accurately. The two methods\ngive both a similar shape of the MAE curve with respect\nto c/a ratio of the W-Re layer, and the maximum of\nthe curves occur at similar c/a. The maximum value\nof the KKR-CPA results can be compared to the MAE\nof FePt, which from theory is \u00183 meV/f.u.,16whereas\nexperiment results in 1.2 meV/f.u.17The MAE of\n5[Fe]/2[W 0:8Re0:2] is hence very comparable to that of\nFePt. A further tuning of the magnetic anisotropy can\nbe done by modifying the amount of alloying between\nW and Re in the multilayer, while keeping the c/a ratio\nthe same as that giving the maximum MAE value in\nFig.1, i.e. 1.34. Calculations based on FPLMTO-VCA\nare shown in Fig.1b, and we note that the MAE can be\nmade\u001830 % larger by tuning xto 0.6.\nAs to the magnetic moments they are rather constant\nfor the di\u000berent values of x considered, and we obtain\nvalues of 1.65 \u0016Bper interface atom and 2.4 \u0016Bfor the\nsub-interface Fe atoms, and 2.2 \u0016Bfor the Fe atom in\nthe middle of the Fe slab. The moment on W-Re is -0.1\n\u0016B, resulting in a total moment just above 10 \u0016B/f.u.\nFor comparison we note that for FePt this value is 3.3\n\u0016B/f.u.\nSo far we have only considered calculated values\nper formula unit, whereas for practical applications\nit is with respect to volume one should compare the\n5[Fe]/2[W xRe1\u0000x] system with e.g. FePt. As concerns\nthe MAE we obtain a maximum value 5.3-7.0 MJ/m3\n(depending on concentration or computational method)\nwhich should be compared to a measured value of \u0018\n7 MJ/m3for FePt7. For the moments we obtain 0.11\n\u0016B/\u0017A3which is to be compared to 0.12 \u0016B/\u0017A3for FePt.\nA \fnal note on the comparison to the properties of FePt,\nis that this material often exhibits partial chemical dis-\norder on the Fe and Pt sublattices, which drastically re-\nduces the MAE.18\nIn order to obtain a more detailed, microscopical un-\nderstanding for why the MAE of Fig.1 obtains a maxi-\nmum at c/a close to 1.3 we show \frst of all that the large\nMAE is caused by the large spin-orbit coupling of the\nW-Re atoms. As a second step we will illustrate that it\nis a delicate detail of the energy bands of the W-Re layer,\nwhich take a special structure for a c/a ratio close to 1.3,\nwhich determine the large MAE. We start however, with\nanalyzing the spin-orbit e\u000bect of the W-Re atoms.\nAs a direct way to illustrate the dominant role of the\nWxRe1\u0000xlayers in the formation of the high perpendic-\nular MAE of this system, we varied the spin-orbit cou-\npling strength at these layers for the optimal c=aratio\n(c=a= 1:3) and concentration (for x= 0:8, other val-\nues of x give a similar picture). Here we employed the\ntechnique developed by Ebert et al. within the KKR for-\nmalism.19The corresponding MAE values are shown in\nFig. 2 for SOC strengths ( \u0018) scaled from 0 to 1. Remark-\nably, for\u0018= 0, i.e. when SOC is considered just in the\nFe layers, the MAE is slightly negative preferring thus\nan in-plane orientation of the magnetization. Increasing\n\u0018in the W xRe1\u0000xlayers the MAE starts to increase as3\n1.15 1.2 1.25 1.3 1.35 1.4\nc/a01234MAE (meV/f.u.)FPLMTO-VCA\nKKR-CPA\nFPLMTO-VCA\n1234(a)(a)\n(b)MAE (meV/f.u.)\n40 50 60 70 80 90\nW % (x)\nFIG. 1: (Color online) (a) Calculated magnetic anisotropy of\n5[Fe]/2[W xRe1\u0000x] (x=0.8) as a function of e\u000bective c/a ratio\nof the W-Re layers. (b) Calculated magnetic anisotropy of\n5[Fe]/2[W xRe1\u0000x] as a function of W concentration, x, for a\nc/a ratio of 1.34 of the W-Re layers. The MAE is shown per\nformula unit.\na quadratic function: this behavior is well understood in\nterms of the second order perturbation theory, discussed\nbelow. For about 0 :5<\u0018 < 1, however, the MAE seems\nto follow a linear behavior implying that in this regime\nSOC can not be regarded as a small second order per-\nturbation to the scalar-relativistic spin-polarized band\nstructure. Overall, the data of Fig.2 demonstrate that\nthe large MAE is indeed caused by the large spin-orbit\ncoupling of the W-Re atoms.\n-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5\n 0  0.2  0.4  0.6  0.8  1MAE  (meV/f.u.)\nSpin-orbit scaling factor[Fe]  [W(0.79)Re(0.21)]   \n5 2\nFIG. 2: Calculated MAE (circles) within the KKR-CPA ap-\nproach with SOC strength scaled between 0 and 1. The\noptimal setup, c=a = 1:3 and x= 0:8, is \fxed for the\n5[Fe] 2[W xRe1\u0000x] superlattice. Solid line serves as a guide\nfor the eye.We now turn to investigating why an e\u000bective c/a ratio\nof the W-Re layer close to 1.3 causes a maximum value\nof the MAE. The MAE of a nano-composite material can\nbe expressed as\n\u0001ESO=X\nqq0\u0001Eqq0=X\nqq0[Eqq0(^n1)\u0000Eqq0(^n2)];(1)\nwhereqis the atomic species and ^ niare two spin-\nquantization axis, one out of plane and one in plane.\nEach of the Eqq0(^n) can now, according to second order\nperturbation theory, be written as\nEqq0(^n) =\u0000X\nkijX\nfsgX\nfmgnkis;qm;q0m0nkjs0;q0m00;qm00\n\u0002hqmsjHSO(^n)jqm000s0ihq0m00s0jHSO(^n)jq0m0si\n\u000fkj\u0000\u000fki;(2)\nwhere krepresents the sampling points in the Bril-\nlouin zone, i,jis the occupied and unoccupied states,\nfsg=fs;s0grun over the spin components and fmg=\nfm;m0;m00;m000grun over the magnetic quantum num-\nbers. The basis functions jqlmsiare speci\fed through the\natomic site q, thel,mandsquantum numbers, i.e. the\nazimuthal, magnetic and spin component quantum num-\nbers. Note that the band character nkis;qm;q0m0includes\nhybridization, i.e. mixing of di\u000berent basis functions at\ne.g. di\u000berent atomic sites q. The contributions from Eqn.\n2 are seen to become large if the energy di\u000berence be-\ntween occupied and unoccupied electron states is small\nto permit a strong coupling of the spin-orbit interaction,\nespecially if this happens for a large fraction of the BZ.\nThis fact is further enhanced if the states that couple\nvia the spin-orbit coupling have a signi\fcant contribu-\ntion from the states residing on the heavy W-Re atom,\nsince this guarantees that at least one of the spin-orbit\nmatrix elements in Eqn. 2 is then large.\nIt is in such an analysis that the e\u000bective c/a ratio of\nW-Re close to 1.3 becomes clear. Inspection of a W-Re\nalloy reveals that as a function of c/a ratio, conspicu-\nous features of the band structure explain the enhanced\nMAE. To illustrate this we show in Fig. 3 the energy\nbands along \u0000\u0000M\u0000G\u0000P\u0000Y\u0000M0\u0000\u0000\u0000X (of the bct\nBZ) of a W-Re alloy (calculated in this case by virtual\ncrystal approximation - VCA - for simplicity, and with\nx=0.8). From the \fgure one may note a spin-degenerate\nband situated very close to the Fermi level ( EF) between\nM0and \u0000 and X. As a function of changing the c/a ratio\nthis band moves from being completely occupied to be-\ncome unoccupied, and for c/a=1.3 it is situated right at\nEF. When put in contact to Fe, in the 5[Fe]/2[W xRe1\u0000x]\nmultilayer, the narrow band discussed in Fig.3 will be-\ncome exchange split, due to the induced moment of the\nW-Re layers. In order to illustrate this e\u000bect in a simple\nway, we have performed a \fxed spin moment calculation\nof W-Re, with the same induced moment on the W-Re\nsite as for the 5[Fe]/2[W xRe1\u0000x] multilayer. The result-\ning dispersion relationship is also shown in Fig.3 (bottom\npanel). Here we note a breaking of the spin-degeneracy4\nclose toEF, and the \rat band is split into up- and down-\nbands, which for a substantial part of the BZ are situ-\nated on each side of EFin a large part of the in-plane\nBrillouin zone. Spin-orbit coupling via the l+s\u0000+l\u0000s+\nterms ofHSOin Eqn.2 then provides a large contribu-\ntion to the magnetic anisotropy. A modi\fcation of the\nc/a ratio away from this value moves the \rat bands away\nfromEF, which reduces the MAE.\n-10E-EF [Ry]-0.1\n00.1E-E F [Ry]updown\nΓ\nΓM\n0ΓM GP YM0XX\nFIG. 3: (Color online) Non spin-polarized bands (upper\npanel) and spin-split bands (lower panel) of W-Re for bct\nc/a ratio 1.3.\nIV. CONCLUSION\nWe have here presented theoretical evidence for that\na non-laminate involving W-Re layers in contact to Fe,\ncan result in a magnetic material with a substantial mag-\nnetic moment and a large magnetic anisotropy. The new\nmaterial compares in performance to the well known ma-\nterial FePt, both in terms of saturation moment as well\nas anisotropy. One advantage with the present system is\nthe possibility to tune the MAE by tuning the local c/a\nratio of the W-Re layer, which can be done by introduc-\ning more Fe layers. This simultaneously also increases\nthe saturation moment per volume.\nOur analysis points to a general route to \fnd materials\nwith a large magnetic anisotropy. A strong ferromagnetic\nmaterial, preferably based on Fe or an FeCo alloy, should\nbe in contact with a heavier material with large spin-orbit\nsplitting. Most crucially, the electronic structure of the\nheavy material should be similar to the schematic energy\nband plot of Fig.4. Here bands which are dominated by\nstates on the heavy atom are drawn to be exchange split,\ndue to the interaction (hybridization) of the ferromag-\nnetic material. If a large fraction of the BZ has majoritybands below the Fermi level, and a large fraction of the\nEnergy\nWave vector}∆x\nFIG. 4: (Color online) Schematic picture of the electronic\nstructure of bands projected on heavy atoms, having possi-\nbility of inducing a large magnetic anisotropy. Majority spin\nstates in red, minority states in blue, and the Fermi level a\ndashed horizontal line. The exchange splitting is marked as\n\u0001x.\nBZ has minority states above (as Fig.4 is drawn), then\nthe spin-orbit coupling of the heavy atom will give rise to\na large contribution to the MAE for many wave vectors\n(as Eqn.2 shows).\nThe situation shown in Fig.4 corresponds to a set of\nnarrow bands close to the Fermi level, which corresponds\nto a system with a large value of the density of states\nat the Fermi level (DOS( EF)). Hence, a large value of\nDOS(EF) is also a requirement when searching for novel\nmaterials with a large MAE. Unfortunately a large value\nof DOS(EF) is often associated with an unstable or meta-\nstable crystal structure,20which points to that it is meta-\nstable systems, such as multilayers and nano-laminates,\nwhich one should consider, when searching for novel ma-\nterials with a large MAE.\nV. ACKNOWLEDGEMENT\nWe gratefully acknowledge \fnancial support from the\nSwedish Research Council (VR), Swedish Foundation for\nStrategic Research (SSF), G oran Gustafssson Founda-\ntion, Carl Tryggers Foundation, STEM and STINT. O.E.\nis in addition grateful to the ERC (project 247062 -\nASD) and KAW foundation for support. Support from\neSSENCE and STANDUP acknowledged. We also ac-\nknowledge Swedish National Infrastructure for Comput-\ning (SNIC) for the allocation of time in high performance\nsupercomputers. Partial \fnancial support was provided\nalso by the Hungarian Research Foundation (contract\nno. OTKA K68312, K77771 and IN83114) and by the\nNew Szechenyi Plan of Hungary (Project ID: T \u0013AMOP-\n4.2.1/B-09/1/KMR-2010-0002).5\n1W.H. Butler, X.G. Zhang, T.C. Schultess, J.M. MacLaren,\nPhysical Review B 63, 54416 (2001).\n2J. Mathon, A. Umarski, Physical Review B 63, 220403\n(2001).\n3S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki,\nK. Ando, Nature Materials 3, 868 (2004).\n4J.M.D. Coey, Rare-earth Iron Permanent Magnets Ox-\nford, (1996).\n5D. Kramer, Physics Today, May, 22, (2010).\n6B. Sanyal, C. Antoniak, B. Krumme, A. Warland,\nF. Stromberg, K. Fauth, H. Wende, O. Eriksson, Physi-\ncal Review Letters 104, 156402 (2010).\n7S. Sun, C.B. Murray, D. Weller et al., Science 287, 1989\n(2000).\n8L. Szunyogh, B. Ujfalussy, P. Weinberger, Physical Review\nB51, 9552 (1995).\n9T. Burkert, L. Nordstr om, O. Eriksson and O. Heinonen,\nPhysical Review Letters 93, 27203 (2004).\n10G. Andersson, T. Burkert, P. Warnicke, M. Bj ork,\nB. Sanyal, C. Chacon, C. Zloeta, L. Nordstr om, P. Nord-\nblad and O. Eriksson, Physical Review Letters 96, 37205\n(2006).\n11C. Andersson, B. Sanyal O. Eriksson et al., Physical Re-\nview Letters 99, 177207 (2007).12J.M.Wills, M.Alouani, P.Andersson, A.Delin, O.Eriksson,\nA.Grechnev, \\Full-Potential Electronic Structure Method,\nEnergy and Force Calculations with Density Functional\nand Dynamical Mean Field Theory\" (Springer Series in\nSolid-State Sciences, Volume 167, 2010).\n13J. Zabloudil, R. Hammerling, L. Szunyogh, and P. Wein-\nberger, Electron Scattering in Solid Matter, Springer Se-\nries in Solid- State Sciences Vol. 147 (Springer, Heidelberg,\n2005)\n14S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58,\n1200 (1980).\n15H. J. F. Jansen, Phys. Rev. B 59, 4699 (1999).\n16G. H. O. Daalderop, P. J. Kelly, and M. F. H. Schuurmans,\nPhys. Rev. B 44, 12054 (1991).\n17S. Okamoto, N. Kikuchi, O. Kitakami, T. Miyazaki, Y. Shi-\nmada, and K. Fukamichi, Phys. Rev. B 66, 024413 (2002).\n18J.B. Staunton, S. Ostanin, S.S.A. Razee, B.L. Gyor\u000by, L.\nSzunyogh, B. Ginatempo, and E. Bruno, J. Phys. Cond.\nMatt. 16, S5623 (2004).\n19H. Ebert, H. Freyer and M. Deng, Phys. Rev. B 56, 9454\n(1997).\n20H.L.Skriver, Phys. Rev. B 31, 1909 (1985)."    },    {        "title": "1110.1123v1.Giant_Magnetoresistance_Effect_in_Organic_Material_and_Its_Potential_for_Magnetic_Sensor.pdf",        "content": "Giant Magnetoresistance Effect in Organic Material \nand Its Potential for Magnetic Sensor  \n \nMitra Djamal 1, Ramli 2, Sparisoma Viridi 3 and Khairurrijal 4 \n1Department of Physics, Institut Teknologi Bandung, Bandung, Indonesia \n(Tel : +6288218165981960; E8mail: mitra@fi.itb.ac.i d) \n2Department of Physics, Universitas Negeri Padang, P adang, Indonesia \n(Tel : +6288138210289889; E8mail: ramlisutan@ymail. com) \n3Department of Physics, Institut Teknologi Bandung, Bandung, Indonesia \n(Tel : +6288128211184973; E8mail: dudung@fi.itb.ac. id) \n4Department of Physics, Institut Teknologi Bandung, Bandung, Indonesia \n(Tel : +628812821287181; E8mail: krijal@fi.itb.ac.i d) \n \nAbstract-Giant magnetoresistance (GMR) material has  great \npotential as next generation magnetic field sensing  devices, have \nmagnetic properties and high electrical potential t o be developed \ninto various applications such as: magnetic field s ensor \nmeasurements, current measurements, linear and rota tional \nposition sensor , data storage, head recording, and  non-volatile \nmagnetic random access memory (MRAM). Today, the ne w GMR \nmaterials based on organic material obtained after allowing for \nOrganic Magnetoresistance (OMAR) was found in OLEDs  \n(organic light-emitting diodes). This organic mater ial is used as a \nspacer layer in GMR devices with spin-valve structu res. \nTraditionally, metals and semiconductors are used a s a spacer \nlayer in spin-valve. However, several factors such as spin \nscattering caused by large atoms of the spacer mate rial and the \ninterface scattering of ferromagnetic with a spacer , will limit the \nefficiency of spin-valve. In this paper, we describ e a new GMR \nmaterials based on organic material that we have de veloped.  \nKeyword: giant magnetoresistance, magnetic sensor, organic \nmagnetoresistance, spin valve, spintronics. \n \nI. I NTRODUCTION  \n \nThe discoveries of giant magnetoresistance (GMR) [1 ] \nand tunneling magnetoresistance (TMR) [2] in metall ic spin \nvalves (SVs) and magnetic tunnel junctions (MTJ) ha ve \nalready found widespread applications in magnetic r ecording \nand memory. The GMR material promises some importan t \napplications, among others as magnetic sensor. The GMR \nsensor has many attractive features, for example: r eduction \nsize, low8power consumption, low price as compared to other \nmagnetic sensors and its electric and magnetic prop erties can \nbe varied in very wide range [3]. \nGMR materials show benefit compare to other low8\nmagnetic sensor technology such as high sensitivity , low cost, \nlow power and small size (see Fig. 1). Because of t hese \nbenefits compare to other magnetic materials, techn ically it is \nnot very complicated and the technique is rather ne w in the \nworld. Recently, we has been successfully to deposi tion of \nGMR thin film based on inorganic material with sand wich \nstructure, and we have found that about 70 % MR val ue in \nNiCoFe/Cu/NiCoFe sandwich [4, 5]. In this paper, we  would \nlike to describe a new giant magnetoresistance base d on organic material by Opposed Target Magnetron Sputte ring \n(OTMS) method. \n \nFig. 1. Comparison of power, price and size of some  \nmagnetic sensors [3]. \n \nOrganic magnetoresistance (OMAR) is a recently \ndiscovered, which magnetoresistance (MR) values up to 10% \nat room temperature and at fields of only a few mil litesla have \nbeen reported in various organic materials [6]. Org anic \nmagnetoresistance effect also was found in organic thin films \nsandwiched between two conductive electrodes. \nCurrently, organic spintronics is a new and promisi ng \nresearch field where organic materials are applied to mediate or \ncontrol a spin8polarized signal. One of the most wi dely studied \norganic systems in this context is the spin valve c onsisting of \nan organic layer sandwiched between two ferromagnet ic \nelectrodes. Fig 2 shows the typical configuration o f organic \nspin valve device. \nA spin valve is a layered structure of two ferromag netic \n(FM) electrodes separated by a nonmagnetic spacer. The spacer \ndecouples the two FM electrodes and allows spin pol arized \ncarriers to travel through it without much relaxati on. \nTraditionally, metals and inorganic semiconductors are used as \nthe spacer material in SVs. However, a few factors like the spin \nscattering due to large atomic radii of the spacer materials and \nscattering from the FM/spacer interface, limit the efficiency of \nsuch SVs to a certain level. One solution to the fi rst problem \ncould be the introduction of spacer materials made from lighter \nelements, e.g. carbon, that will also have spin8tra nsporting capabilities. The weak spin–orbit and hyperfine int eractions of \norganic semiconductor small molecules and π8conjuga ted \npolymers lead to the possibility of preserving spin –coherence \nover times and distances much longer than the conve ntional \nmetals or semiconductors. These which are the succe ss of π8\nconjugated polymers and organic materials for comme rcial \nelectronic applications, they were considered a pro mising \nalternative for spin transport [7]. \nThe advantages of organic materials include chemica l tuning \nof electronic functionality, easy structural modifi cations, ability \nof self8assembly and mechanical flexibility. These \ncharacteristics are exploited for large8area and lo w8cost \nelectronic applications. For spintronics applicatio ns, organic \nspin valves are particularly attractive because of its flexibility \nand low cost.  \n \nFig. 2. Schematic picture of an organic SV device a nd \nmagnetoresistance experiment. \n \n \nII. E XPERIMENTAL METHOD  \n \nGrowth of spin valve of NiCoFe/Alq3/NiCoFe (see Fig  2) \nthin film performed at the Laboratory for Electroni c Material \nPhysics, Department of Physics, Institut Teknologi Bandung \nusing dc8Opposed Target Magnetron Sputtering (dc8OT MS) \nmethod. Scheme of reactor dc8OTMS shown in Fig. 3. \nSputtering target is NiCoFe as ferromagnetic materi al and Alq3 \n{(tris8(88hydroxyquinoline) aluminum}  as an organi c material. \nMaking the target NiCoFe performed by solids reacti on with a \nmolar ratio Ni:Co:Fe = 60:30:10. Alq3 target also m aking by \nsolid reaction of Alq3 powder. The NiCoFe/Alq3/NiCo Fe thin \nfilm was grown onto Si (100) substrate. \nSamples of the NiCoFe/Alq3/NiCoFe were deposited in  \nseveral different time of growth, so that they had different \nthickness of layers. Other deposition parameters ar e fixed. \nThese parameters are: flow rate of Argon gas is 100  sccm, the \ngrowth pressure is 0.52 torr, dc Voltage is 600 vol t, and the \ntemperature is 100 0C. The samples were characterized by using \nSEM (Scanning Electron Microscope) type JEOL JSM863 60 \nLA and magnetoresistance measurements were made by using \na linear four8point probe method with current8perpe ndicular to8\nplane. \n \nIII. R ESULT AND DISCUSSION  \n \nGiant magnetoresistance ratio can be calculated by the \nequation MR (%) = {(R maks  8 R min ) / R maks } x 100%. The  GMR \nratio of NiCoFe/Alq3/NiCoFe thin film are shown in Fig. 4.  \n \n \nFig. 3. Schematic picture of dc8OTMS reactor. \n \n840 830 820 810 010 \n88 86 84 82 0 2 4 6 8GMR Ratio (%) \n \n840 830 820 810 010 \n88 86 84 82 0 2 4 6 8GMR Ratio (%) \n \n840 830 820 810 010 \n88 86 84 82 0 2 4 6 8\nH (kOe) GMR Ratio (%) \n \nFig. 4. The GMR ratio curve of NiCoFe/Alq3/NiCoFe a t \nroom temperature with time of growth: 10 minutes (t op), \n15 minutes (middle), and 20 minutes (bottom).  \nFor the growth time of 10, 15 and 20 minutes, we fo und the \nGMR ratio respectively; 10.5%, 35.0% and 12.0%. The  \nthickness of each layer for growth time of 10, 15, and 20 \nminutes are; NiCoFe (100 nm) / Alq3 (48 nm) / NiCoF e (100 \nnm); NiCoFe (137 nm) / Alq3 (72 nm) / NiCoFe (137 n m); \nNiCoFe (175 nm) / Alq3 (96 nm) / NiCoFe (175 nm), \nrespectively. The maximum GMR ratio of about 35.5% at \nroom temperature obtained at 15 minutes old growth.  \nAs seen in the Fig.4, the GMR ratio is not monotoni c \ndecreasing to the thickness of the each layers of \nNiCoFe/Alq3/NiCoFe nor the spacer thickness as repo rted in \n[8]. It can be caused by variation of applied volta ge in the \nlayers growing process. In this experiment, for gro wth time 10, \n15 and 20 minutes the average applied voltage are 7 8.4, 154.1, \nand 95.2 mV, respectively. It seems that the differ ent applied \nvoltage in layers growing process accidentally enha nces the \nGMR ratio, as it is used in electrical conditioning  [9]. We have \nfound that as the applied voltage increasing, the G MR ratio is \nalso increasing as shown in Fig 5. \n \n010 20 30 40 \n0 25 50 75 100 125 150 175 \nV (mV)GMR Ratio (%)\n \nFig. 5. Influence of applied voltage V to GMR ratio. \n \nIt seems that the influence of spacer thickness is overridden \nby applied voltage that acts accidentally as electr ical \nconditioning. Further investigation to merge both i nfluences to \nGMR ratio is interesting but it is out of scope of this work. \nThe hysteresis loop of GMR spin valve is shown in F ig. 6. \nThe shape of hysteresis loop shows a drop magnetiza tion and \nindicates that there is a magnetic phases with the same \ncoercivity. \n \nIV. C ONCLUSION  \n \nWe have been successfully grown a new GMR sensor \nmaterials based organic materials with a spin valve  structure \nNiCoFe/Alq3/NiCoFe using Opposed Target Magnetron \nSputtering (OTMS) onto Si (100) substrate. Magnetor esistance \nratio of the sample are affected by time of growth.  In this \nresearch, the maximum GMR ratio of 35.5% at room \ntemperature obtained on time of growth is 15 minute s, where \nthis maximum value of GMR ratio is caused mainly du e to \napplied voltage about 154.1 mV during the layers gr owing \nprocess. From this results it was concluded that a sandwich \nNiCoFe/Alq3/NiCoFe that have been developed, has th e \npotential to be used as magnetic field sensors.  \n \n \n \nFig. 6. Room8temperature hysteresis loop organic GM R spin \nvalve, NiCoFe/Alq3/NiCoFe. \n \n \nACKNOWLEDGMENT  \nThis work was (partially) supported by the Director ate for \nResearch and Community Service, The Ministry of Nat ional \nEducation Republic of Indonesia through Competency Grant \nunder contract No: 407/SP2H/PP/ DP2M/VI/2010.  \n  \nREFERENCES  \n \n[1].  Baibich M, Broto J M, Fert A, Nguyen Van Dau F, Petroff F, Eitenne P, \nCreuzet G, Friederich A and Chazelas, Giant Magneto resistance of (001) \nFe/(001) Cr Magnetic Superlattices, J Phys. Rev. Le tt. 61. (1988). 2472.  \n[2]. Moodera J S, Kinder L. R, Wong T M and Meserve y R, Large \nMagnetoresistance at Room Temperature in Ferromagne tic Thin Film \nTunnel Junction. Phys. Rev. Lett. 74. (1995). 32738 3276. \n[3].  Robert Kelsall. W., Lan W. Hamley, Mark Geogh egan, (2005): Nanoscale \nScience and Technology, John Wiley & Sons, LTD., Be llason and Ed \nGrochowski, The era of Giant Magnetoresisistive hea d, at:  \nwww.storage.ibm.com/hdd/tecnologi/gmr/gmr.  \n[4]. Ramli, Mitra Djamal, and Khairurrijal, “Effect  of Ferromagnetic Layer \nThickness on the Giant Magnetoresistance Properties  of \nNiCoFe/Cu/NiCoFe Sandwich” Proceeding 3rd Asian Phy sic Symposium \n(APS) 2009 ISBN: 97889798980108580,  Bandung, 22 – 23 July 2009. pp \n65 – 67. \n[5]. Mitra Djamal, Ramli, Yulkifli, and Khairurrija l, “Effect of Cu Layer \nThickness on Giant Magnetoresistance Properties of NiCoFe/Cu/NiCoFe \nSandwich” Proceeding ICCAS8SICE 2009 Fukuoka, Japan , August 18821, \n2009, pp. 3958398. \n[6]. Bobbert. P.A, Nguyen. T.D, van Oost. F.W.A., K oopmans. B, and \nWohlgennt. M, Bipolaron Mechanism for Organic Magne toresistance, \nPhysical Review Letters, 99, (2007) 216801. \n[7].  Taliani, C, Dediu.V, Biscarini. F, Cavallini.  M, Murgia. M,and Nozar. P. \nOrganic8inorganic hybrid spin8valve: A novel approa ch to spintronics. \nPhase Transit. 75, (2002). 1049–1058. \n[8]. Xiong, Z. H., Wu, D., Vardeny, Z. V., and Shi,  J., \"Giant \nmagnetoresistance in organic spin8valves\", Nature 4 27 (2004), 8218824 \n[9]. Niedermeier, U., Vieth, M, Pätzold, R., Safert , W., and von Seggern, H., \"  \nEnhancement of organic magnetoresistance by electri cal conditioning\", \nApplied Physics Letters 92 (2008), 193309 \n "    },    {        "title": "1110.5737v1.Nanostructured_exchange_coupled_hard___soft_composites__from_the_local_magnetization_profile_to_an_extended_3D_simple_model.pdf",        "content": "arXiv:1110.5737v1  [cond-mat.mtrl-sci]  26 Oct 2011Nanostructured exchange coupled hard / soft composites: fr om the\nlocal magnetization profile to an extended 3D simple model\nV. Russier, K. Younsi and L. Bessais\nICMPE, UMR 7182 CNRS and University UPEC,\n2 rue Henri Dunant, 94320 Thiais, France.\nIn nanocomposite magnetic materials the exchange coupling between phases plays a central role\nin the determination of the extrinsic magnetic properties o f the material: coercive field, remanence\nmagnetization. Exchange coupling is therefore of crucial i mportance in composite systems made of\nmagnetically hard and soft grains or in partially crystalli zed media including nanosized crystallites\nin a soft matrix. Ithas been shown also tobe a key point in the c ontrol of stratified hard / soft media\ncoercive field in the research for optimized recording media . A signature of the exchange coupling\ndue to the nanostructure is generally obtained on the magnet ization curve M(H) with a plateau\ncharacteristic of the domain wall compression at the hard/s oft interface ending at the depinning of\nthe wall inside the hard phase. This compression / depinning behavior is clearly evidenced through\none dimensional description of the interface, which is rigo rously possible only in stratified media.\nStarting from a local description of the hard/soft interfac e in a model for nanocomposite system we\nshow that one can extend this kind of behavior for system of ha rd crystallites embedded in a soft\nmatrix.\nI. INTRODUCTION\nA simple model in order to understand the relation between the nano scale structure and the\nextrinsic magnetization curves in partly crystallized rare earth tra nsition metal alloys (Re-M), can\nbe built as an assembly of nanosized crystallites embedded in an amorp hous matrix. Such a model\nis based upon experimental caracterization of the samples obtaine d from an amorphous precur-\nsior, obtained either by high energy milling or a melt spun technique for instance, followed by an\nappropriate annealing which induces the re-crystallization [1–4]. The crystallites and the matrix\nmust be characterized by hard and soft magnetocrystalline anisot ropy respectively. One key point\nconcerning the extrinsic magnetic properties of the system is then the exchange coupling between\nthe crystallites and the matrix or between the crystallites viathe matrix. In other words, since one\ndeals with nanocomposite including magnetic hard and soft phases, s uch models can enter in the\nso-called exchangespring magnet (ES) systems [5–11]. Exchange c oupling between different phases\nofnanostructredcompositematerialshavebeenwidelystudied aft erthe pioneeringworkofAharoni\n[12] mainly through the behavior of the average magnetization curv e in terms on the applied field,\nM(H) [4, 10, 13–17]. On the other hand the nucleation field correspondin gto the verybeginning of\nthe magnetization reversalin the soft phase has been determined semi-analytically in different situ-\nations from the linearization of the micromagnetic energy with respe ct to the deviation of the local\nmagnetization from the direction imposed by the hard phase easy ax is [14, 16, 18, 19]. Conversely,\nthe local magnetization m(r) in the vicinity of the interface between phases in nanocomposites h as\nnot been investigated in details but in continuous film geometry (layer ed systems) [20–22], where\nfurthermore the effect of the hard and soft layers thickness has been investigated through the mag-\nnetic phase diagram representing the reversal mode of the demag netization, namely rigid mode2\nversus ES-coupled mode, [13–16] viathe analytical determination of the magnetic susceptibility.\nIn the works devoted to the magnetization reversal in ES layered s ystems through the behavior\nof the local magnetization in terms of the distance, z, normal to the interface the solvation of the\nEuler equations relative to the micromagnetic energy minimization is ma de tractable because of\nthe symmetry parallel to the surface according to which the local m agnetization depend only on\nz[20–22]. This makes the nucleation, domain wall (DW) compression and depinning process at\nthe hard / soft interface a well established theoretical result [6, 9 , 17, 21] which moreover has been\nexperimentally observed [6, 23, 24]. In the case of nanocomposites made of true 3D grains either\nsimply juxtaposed or separated by grain boundaries, the situation is not so clear and as a general\nrule one refers to the similarity in the M(H) curve to map the magnetization reversal process to\nthe one indeed obtained for the ES layered system.\nIn the present work, we deal with a model made of hard inclusions em bedded in a soft matrix\nwith the purpose to exploit the above mentioned theoretical result s on the magnetization reversal\nin magnetically hard/soft composite systems. More precisely our aim is to bridge the gap between\nthe stratified media, for which the reversal process is well unders tood, and our system of magnet-\nically hard material inclusions embedded in the soft matrix. We investig ate the way according to\nwhich one can map the well-known nucleation, DW compression and dep inning process of the mag-\nnetization reversal characteristic of the exchange coupled stra tified media to the exchange coupled\ninclusion / matrix system. We will use both analytical results for the a ngle profile at the planar\ninterface in a one dimensional approximation and numerical results f or true 3-D systems obtained\nfrom a micromagnetism finite element based code (MAGPAR) [25].\nInafirststep,wecomparethe1-Dprofiletothesimulatedresultfo ronecubicinclusionembedded\nin a prismatic matrix. The easy axis of the inclusion is parallel to the inte rface (parallel recording\nmedia type of geometry). The variation of M(H) in the plateau region characteristic of layered\nES media is very well reproduced, and the accuracy obtained for th e magnetization profile, shows\nthat the nucleation, domain wall compression and depinning process is valid for isolated inclusions\nembedded in a very soft matrix.\nIn order to investigate the effect of the finite value taken by the ed ge to edge separation ∆\nbetween the crystallites in the actual system, we consider a model made of two cubic inclusions\nin the soft matrix. The magnetization profile behavior in terms of the applied field shows that\nthe magnetization reversal follows the nucleation, domain wall comp ression and depinning process\nwhen ∆ is larger than the exchange length lexof the soft material whereas when ∆ gets smaller\nthanlexthe magnetization reverses in a coherent way in the whole system wh ich corresponds to\nthe strong coupling regime, or the rigid composite magnet of Refs. [ 13, 14], where the system\nbehaves as a single phase.\nThen, we consider the effect of the misallignment between the easy a xes of the neighboring inclu-\nsions. In this case, the domainwallwhich wasofBlochtype for the pa rallelorientedinterface, takes\nclearly a N´ eel character, with nevertheless at the qualitative leve l, the same type of magnetization\nreversal processes.3\nII. ONE DIMENSIONAL MODEL\nIn this section, we first recall the basic equations concerning the o ne dimensional description for\nthe magnetization profile accross the hard soft interface. We con sider the planar sharp interface\nbetween a uniaxial hard material and an ultra soft material. The inte rface, normal to the ˆ zaxis, is\ndefinedby z=z0andtheeasyaxisofthehardmaterial,thislatterbeinglocatedat z > z0,coincides\nwith the ˆ xaxis. The micromagnetic characteristics of the media will be denoted Ks,h,As,h,Js,h\nwhere the subscript s(h) refers to the soft (hard) phase and K,A,Jdenote the magnetocrystalline\nanisotropy constant, the exchange stiffness and µ0times the saturation magnetization respectively.\nHere we shall consider the limiting case of an ultra soft phase, with Ks= 0. Then the properties\nof the one dimensional model are totally determined by the reduced parameters ǫA=As/Ah,\nǫJ=Js/Jh, the reduced distance z∗=z/δB,δBbeing the Bloch DW thickness in the hard phase,\nδB=π/radicalbig\nAh/Khand the reduced field h=−Ha/HKwhereHaandHK= 2Kh/Jhare the applied\nand the hard-phase anisotropy field respectively. The minus sign in t he definition of his only for\nconvenience in order to deal with h >0 in the second quadrant Ha<0. We consider the case of\nan external field Hain the ˆxdirection. Starting from the energy functional where we explicitly\nassume the magnetization profile to lie in the plane (ˆ x,ˆy) and to depend only on z\nE[ˆm(z)] =S/integraldisplay/bracketleftBigg\nA(z)/parenleftBigg/parenleftbigg∂mx(z)\n∂z/parenrightbigg2\n+/parenleftbigg∂my(z)\n∂z/parenrightbigg2/parenrightBigg\n+K(z)(1−mx(z)2)−J(z)mx(z)Ha/bracketrightBigg\ndz\nX(z) =XsΘ(z0−z)+XhΘ(z−z0); X=K,AorJ. (1)\nwhere Θ( z) is the Heavyside step function. The minimization of the functional E[ˆm(z)] with\nrespect to ˆ m(z) leads to the well known Euler equations [13, 14, 20–22] which, writ ten in terms of\nthe angular profile ϕ(z) = (ˆm(z),ˆx) reads\n∂ϕ(z)\n∂z=±1/radicalbig\nAh,s[∆Uh,s(ϕ(z))]1/2\nwith ∆Uh,s(ϕ(z)) =K(z)/parenleftBig\nsin2(ϕ(z))−sin2(ϕ(z(h,s)\nb))/parenrightBig\n−J(z)Ha/parenleftBig\ncos(ϕ(z))−cos(ϕ(z(h,s)\nb))/parenrightBig\n(2)\nThe singularity of the interface leads to the boundary condition at z=z0\nǫA∂ϕ\n∂z/bracketrightbigg\nz−\n0=∂ϕ\n∂z/bracketrightbigg\nz+\n0(3)\nIn equation (2) the choice for the ±sign depends on the boundary conditions far from the interface,\nrepresented by the values taken by ϕ(s,h)\nb=ϕ(zs,h\nb) where z(s,h)\nbdenote the location of either\nthe soft or the hard layer center. In the case of the hard / soft in terface with z(s,h)\nb→ ±∞ we\nshall asume in equation (2) that far from the interface, z∼zb, the magnetization ˆ mis alligned\nto the easy axis and that either Kh,s>0 orKh>0 andKs= 0 (sin ϕb= 0). Starting from\nan external field applied in the x >0 direction, where ˆ m(z) = ˆxin the whole system, the field\nis decreased and then the first step in the magnetization reversal is the so-called nucleation field\nh=hnuclcorrespondingto the reversalin the soft phase. hnuclcan be obtained from the expansion\nofE[ˆm(z)] in terms of the small deviations δ/vector m= (ˆm(z)−ˆx) at second order in |δ/vector m|[18]. In the4\nfollowing we limit ourselves to a hard layer thick enough for zh\nbto be considered as infinite. Let\nus first consider the case z(s)\nb→ ∞. As usual, we consider the situation where the magnetization\nin the soft phase, far from the interface is along the field, namely ˆ m(z∼z(s)\nb) =−ˆx. The profile\nϕ(z) can be easyly obtained from the numerical inversion of\nz−z0=/integraldisplayϕ(z)\nϕ0∂z\n∂ϕdϕ=−/integraldisplayϕ(z)\nϕ0/radicalbig\nA(z)[∆Uh,s(ϕ)]−1/2dϕ (4)\nwhich can be integrated, with the result\nz∗−z∗\n0=/radicalbig\nǫA/ǫJ\nπln/parenleftbigg1−tan(ϕ/4)\n1+tan(ϕ/4)/parenrightbigg/bracketrightBiggϕ(z)\nϕ0; forϕ > ϕ 0\nz∗−z∗\n0=−1\n2π√\n1−hln/parenleftbigg∆−cos(ϕ/2)\n∆+cos( ϕ/2)/parenrightbigg/bracketrightbiggϕ(z)\nϕ0with ∆ =/radicalBigg\n1−sin2(ϕ/2)\n1−h; forϕ < ϕ 0\n(5)\nHere we implicitly asumed that the profile ϕ(z) is a monotonous function of zand accordingly\nwithϕ(s,h)\nb=π,0 the soft ( z < z0) and the hard ( z > z0) phases correspond to π > ϕ(z)> ϕ0and\nϕ0> ϕ(z)>0 respectively. The value ϕ0ofϕatz=z0is obtained from the boundary condition\n(3) [21]\ncos(ϕ0) =1\n(1−ǫAǫK)/bracketleftBig\nh(1−ǫAǫJ)\n+/bracketleftbig\nh2(1−ǫAǫJ)2+(1−ǫAǫK)[(1−ǫAǫK)−2h(1+ǫAǫJ)]/bracketrightbig1/2/bracketrightBig\n(6)\nwhich is defined up to a critical value which defines the depinning field, i.e.the largest value of\nϕ0which can be accomodated by the hard phase, and coincides with the coercive field hcsince we\nexpect the nucleation field of the soft phase to be smaller. hcis given by [21]\nhc=1−ǫAǫK\n(1+√ǫAǫJ)2(7)\nWhenz(s)\nbtakes a finite value and then coincides with the half thickness of the s oft layer, ϕb=\nϕb(z(s)\nb) in equation (2) is considered as a parameter. The profile in equation (4) is numerically\nintegrated and ϕbis determined from the fulfillment of\nz(s)\nb−z0=−/integraldisplayϕb\nϕ0/radicalbig\nAs[∆Us(ϕ,ϕb)]−1/2dϕ≡I(ϕb)\nwith cos( ϕ0) =h(1−ǫAǫJ)+/bracketleftbig\nh2(ǫAǫJ−1)2+1−2h(1−ǫAǫJcosϕb)/bracketrightbig1/2(8)\nfrom a Newton-Raphson procedure by solving : I(ϕb)−(z(s)\nb−z0) = 0.\nLet us now consider the case where the easy axis of the hard inclusio n is not oriented parallel to\nthe interface, (ˆ n,ˆz) =θh/ne}ationslash=π/2, still with (ˆ n,ˆy) =π/2. As a general rule, for ( θh−π/2) not\ntoo small, the numerical simulations lead to a N´ eel domain wall at the in terface, and accordingly\nwe consider only this situation in the one dimensional model. The magne tization is therefore in\nthe (ˆx,ˆz) plane and is totally determined by the angle ϕ(z) = (ˆm,ˆz). As a consequence of the5\nlongitudinal nature of the domain wall at the soft / hard interface t he demagnetizing field in the\nsoft phase must be introduced. We still do not introduce the demag netizing field in the hard phase,\nsince we aim in fineto model a system where this latter concerns a cubic inclusion chara cterized\nbyNx=Ny=Nz. The soft phase is enclosed in an ellongated shaped prism, whose long axis, ˆz,\nis normal to the interface. In the following we shall consider the 1-D model in the infinitelly long\nprism geometry with demagnetizing coefficients Nx=Ny= 1/2;Nz= 0. In the bulk soft phase\nand ifz(s)\nb→ ∞, the equilibrium value ϕ(z(s)\nb) is determined from the minimum of the energy\ndensity\nEb=−JsHasin(ϕ(s)\nb)+1\n2∆NJ2\ns\nµ0sin2(ϕ(s)\nb); with ∆ N= (Nx−Nz) =1\n2(9)\nwith the result\nsin(ϕ(s)\nb) =−inf/parenleftbigg\n1,kh\nǫJ/parenrightbigg\n; with : Ha=−HKh (10)\nIn the bulk hard phase, the equilibrium value, ϕ(h)\nbofϕ(z) is determined in a similar way and can\nexpanded in the vicinity of θhbecause of the high value of HKand we get\nϕ(h)\nb=θh−hcosθh\n1+hsinθh(11)\nIn the present geometry, ∆ Uh,s(ϕ(z)) are now given by\n∆Uh(ϕ(z)) =Ah/parenleftbiggπ\nδB/parenrightbigg2/parenleftBig\nsin2(θh−ϕ(z))+2h/parenleftBig\nsin(ϕ(z))−sin(ϕ(h)\nb)/parenrightBig/parenrightBig\n∆Us(ϕ(z)) =As/parenleftbiggπ\nδB/parenrightbigg2ǫ2\nJ\nkǫA/parenleftbigg\nsin2(ϕ(z))+2kh\nǫJsin(ϕ(z))−sin2(ϕ(s)\nb)−2kh\nǫJsin(ϕ(s)\nb)/parenrightbigg\n(12)\nwhere we have introduced the hardness factor k= 2µ0HK/Jh. In a similar way to what have\nbeen done for the parallel oriented interface we get the profile ϕ(z) from the solvation of\nz∗−z∗\n0=1\nπ(ǫAk)1/2\nǫJ/integraldisplayϕ0\nϕ(z)dϕ\n/parenleftBig\nsin2(ϕ)+(2kh/ǫJ)sin(ϕ)−sin2(ϕ(s)\nb)−(2kh/ǫJ)sin(ϕ(s)\nb)/parenrightBig1/2\n(13)\nin the soft phase and\nz∗−z∗\n0=1\nπ/integraldisplayϕ(z)\nϕ0dϕ\n/parenleftbig\nsin2(ϕ−θ)+2h(sin(ϕ)−sin(θ))/parenrightbig1/2\n(14)\nin the hard phase. The value ϕ0ofϕ(z=z0) is determined from the boundary condition and6\nresults from the numerical solvation of\nǫAǫ2\nJ\nk/bracketleftBig\nsin(ϕ0)2+2h(k/ǫJ)sin(ϕ0)−sin(ϕ(s)\nb)2−2h(k/ǫJ)sin(ϕ(s)\nb)/bracketrightBig\n−/bracketleftBig\nsin(ϕ0−θh)2−sin(ϕ(h)\nb−θh)2+2h(sinϕ0−sinϕ(h)\nb)/bracketrightBig\n(15)\nAs in the preceding case, when z(s)\nbtakes a constant value, the value of ϕ(s)\nbis no more taken from\nthe equilibrium condition (10) but is determined from the fulfillment of z(ϕ(s)\nb) =z(s)\nbwithz(ϕ(s)\nb)\nnumerically calculated from equation (13).\nFurthermore, we also introduce a way to fit the value of the field, sa yh(fit), at which the 1-D\nprofile is calculated in order to enhance the accuracy with the 3-D sim ulated profile: instead of\nusing the actual value of h, we fix the value of ϕ(s)\nbto that obtained in the simulation. Hence,\nh(fit)satisfies\nϕ(s)\nb(h(fit)) = ˜ϕ(s)\nb(h), (16)\n˜ϕbbeing the 3-D micromagnetic simulation result for ϕb.\nThe angular profile across the interface can be used to understan d the behavior of the demag-\nnetization process in exchange coupled media. This has been done in d ifferent situations in the\nliterature [6, 16, 17, 26], especially in the framework of recording me dia optimisation although the\nmagnetization profile accross the interface is generally not explicite d. Here, our purpose is to make\nthe link with the situation of a lattice of magnetically hard inclusions in a m agnetically soft matrix.\nMore precisely, we now compare the ϕ(z) profile calculated from equations (5), (13, 14) with the\none extracted from the 3-D micromagnetic simulation in two simple situ ations.\nIII. FEM SIMULATION OF THE GRAIN / MATRIX INTERFACE\nThe numerical simulation of the magnetization in terms of the applied fi eldHais performed\nby the micromagnetic code MAGPAR [25], based upon a finite elements numerical scheme. The\nembedded hard grain is a cube of edge length a= 2R, withR= 17nmbeing the length scale\nfixed at a convenient value for nanostructured rare earth - tran sition metal intermetallics [1–4].\nWe have chosen to keep fixed the magnetic parameters of the hard phase and consequently the\nBloch domain wall thickness, δBtakes a constant value, δB= 5nm(see section IV below). In the\nmodel including only one such embedded grain in order to represent t he case of isolated crystallites\nin the soft matrix this latter is a parallepipedic prism of total length Lz= 6R, and lateral width\nLx=Ly= (2R+δ), withδ= 0.40δBand the embedded grain is located at its center. In the\nmodelwith twocrystallitesintroducedinordertostudythe influenc eof∆/lexonthemagnetization\nprofile, we use a fixed edge to edge distance ∆ = 2 δBand the ratio ∆ /lexis varied through the\nvalue of lex=/radicalbig\n2µ0As/J2s≡δB/π/radicalbig\nµ0(HK/Jh)(ǫA/ǫ2\nJ) as a function of ǫAandǫJ. The local\nmagnetization profile is extracted along a line parallel to the ˆ zdirection, cutting the grain / matrix\ninterface at its center. A particular attention is paid to the quality o f the mesh, which must be\nsuperior to what is necessary for the average magnetization curv e,M(Ha) over the whole system.\nHere the quality of the mesh has been controlled through the fulfillme nt of the unitary condition7\nofm(r) which is exactly satisfied only on the nodes. The typical size of the m esh tetraedra is\nsharply peaked at 0.10 δB, the maximum edge length for more than half of the tetraedra is less\nthan 0.20 δBleading to a mesh for our (2 R+δ)×(2R+δ)×6Rmodel including about 8.5 105\nfinite elements.\nBefore going further we have to note that because in our system t he soft phase surrounds the\nwhole hard grain, we have to take into account not only the interfac e we are interested in, normal\nto ˆz, but also the other sides of the embedded cubic grain. By symmetry , only the top and bottom\nones are to be considered. This is important especially for the nuclea tion field determination. To\nestimate the effect of the additional interface, we divide the soft p hase domain into the prism\nbased on the side normal to ˆ zlocated at z=z0namely bounded by ( x,y) =±R, and the top\nand bottom layers ( |x|> R) for which the hard/soft interface is perpendicularly oriented. Fo r\nthese additional layers, the demagetizing factors are Ny=Nz≃0 andNx≃1 and we must add\nto the energy density a term due to the corresponding demagnetiz ing field and proportional to\nthe volumic fraction say αoccupied by these layers in the total soft phase domain. Then, in th e\ncase of the Bloch wall parallel to the interface, the implicit equation f rom which hnuclis obtained\n[14, 15, 18],\nλhtanh(λhLh/2) =ǫAλstan(λsLs/2) (17)\nstill holds but with modified definitions of the parameters λhandλs\nλ2\nh=/parenleftbiggπ\nδB/parenrightbigg2\n[1−h]\nλ2\ns=/parenleftbiggπ\nδB/parenrightbigg2/parenleftbiggǫJ\nǫA/parenrightbigg/bracketleftbigg\nh+αNxJs\nµ0HK−ǫK/ǫJ/bracketrightbigg\n(18)\nSinceλhLh>1 forLh> δBthe value of hnuclis nearly independent of Lh, and therefore,\nwe can estimate the effect of the surrounding layers by solving equa tion (17) for the field h′≃\nh+αNzJs/µ0HK. The nucleation field is thus approximately given by hnucl=h0−αNzJs/µ0HK\nwhereh0is the solution ofequ. (17) with α= 0, and may be negativecorrespondingto a nucleation\nof the soft phase in the first quadrant. For the same geometrical reason, we do not expect the\ncoercive field to be given by the analytical result of the 1-D model (s ee equ. (7)).\nIn the following, we mainly focus on the local magnetization profile in te rm ofzfor different\nvalues of the reduced external field, h.\nIV. RESULTS AND DISCUSSION\nWe first focus on the magnetization profile obtained at the interfac e between a cubic grain\nof magnetically hard material and the soft matrix. We consider a mag netically hard material\ncharacterized by Kh= 3.05 106Jm−3,Ah= 7.7 10−12J/m−1andJh= 1T, typical values for the\nRe-Fe compounds [4], leading to δB= 5nm, the soft matrix being characterized by Ks= 0 and the\nother parameters defined through the values of ǫAandǫJ. We first compare the demagnetization\ncurves given by the true 3-D model to that one should get from the 1-D profile as calculated\nfrom equation (5). The latter is obtained analytically from the magne tization profile and the8\ngeometrical average weighted by the respective volumes of the ha rd and soft phases in the 3D\nmodel. The result is displayed in figure (1) for 3 characteristic sets o f values of ( ǫA,ǫJ). As\ncan be seen, the agreement is qualitatively correct, the main discre pancy being the values of the\nnucleation and coercive fields. This stems from shape and finite size e ffect as as been discussed for\nthe nucleation field above. On the other hand, the characteristic p lateau in between hnuclandhc\nis very well reproduced especially concerning its h−dependence. Then, in figure (2) we compare\nthe magnetization profile mz(z) = cos(ϕ(z)) as calculated in the 1-D description corresponding\ntoz(s)\nb=∞to the one obtained from the 3-D simulation. This is done for a set of v alues\nofhcorresponding to characteristic points on the demagnetization pla teau (hnucl< h < h c).\nWe see that on the one hand the compression process of the domain wall in the soft side of the\ninterface is clearly evidenced and on the other hand the agreement between the 3-D simulated\nprofile and the 1-D anaytical one is quite satisfactory. The only cas e where the calculated 1-D\nmagnetization profile deviates from the simulation result at large valu es of|z|corresponds to a\nsituation ( ǫA= 0.75;ǫJ= 0.325 and lex= 2.345δB) where the plateau mx(z) = -1 is not reached\nattheboundaryofthesystem(seefigure(2c))becausethe valu eofthe fieldistoosmalltocompress\nthe profile in the limits of the micromagnetic model. We note that the bo undary of the system\ncorresponds to |z/δB|= 6.8. As can be seen in figure (2) the fitting procedure introduced thr ough\nequation (16) definitely solves the problem. We conclude that the 1- D model leads to a rather good\napproximation for the magnetisation curve, and a very good appro ximation for the angular profile\nat the hard/soft interface. Accordingly the local demagnetizatio n process at the hard grain / soft\nmatrix interface follows the one deduced from the 1-D layered mode l. In particular, we emphasize\nthat the strong reduction of the coercive field due to the exchang e coupling is reproduced although\nthe value of hcdiffers due to the mentioned shape and size effects resulting from th e embedding\ngeometry.\nNow we focus on the influence of the edge to edge distance ∆ betwee n two inclusions, still\nin the parallel orientation, namely ˆ n= ˆxfor the two inclusions. The 1-D angular profile is\ncalculated by using the numerical determination of ϕ(s)\nbas described in section II, equation (8).\nThe magnetization profile mx(z) for the value of the field closest to the depinning point of the 3-D\nsimulation is displayed in figure (3). As ǫAincreasesfrom ǫA= 0.162to 0.75, the ratio (∆ /2)/lexof\nthe distance between the mid-plane and the interface to the excha nge length decreases from 2.115\nto 0.983; hence the flexibility of the profile mx(z) in the soft phase is sufficient for this latter to\nreach a plateau at mx(z) = -1 in between the two hard inclusions only in the first case. Moreov er\nwhen (∆ /2)/lex≤1.0 the two inclusions become exchange coupled viathe soft phase, and the\nmagnetization reversal occurs as a whole with a one phase like behav ior, as can be seen in figure\n(4) where the corresponding demagnetization curve is displayed. T his means that in this case,\na strong coupling regime is reached. This is in qualitative agreement wit h the magnetic phase\ndiagram of Ref. [13] since we clearly evidence the three phases name ly the decoupled magnet\nfor (∆/2)/lex>2, the ES coupled magnet for 2 >(∆/2)/lex>1 and the rigid magnet for\n(∆/2)/lex<1.\nThesameconclusionsasaboveholdforthecasewhenoneeasyaxisis notparalleltotheinterface;\nHere we have chosen as an exemple θh=π/4; the 3-D simulation has been performed only in the\ntwo inclusions model with θh/ne}ationslash= 0 for one of the inclusions. The results for the angular profile ϕ(z)\nand the magnetization profiles mx(z) andmz(z) are given in figures (5), (6) and (7) respectively.9\nOne important difference with the case θh= 0 is that the magnetization of the hard phase in the\nθh/ne}ationslash= 0 grain presents a reversible variation of mxbefore switching as is the case in Stoner Wolfarth\nspherical particles when the easy axis does not coincide with the ext ernal field direction. The other\ndifference as already mentioned is the fact that the hard / soft inte rface for h < hcis a longitudinal\n(N´ eel) domain wall instead of transverse (Bloch) one as it is evidenc ed from the figure (7).\nNow as we have shown from the local magnetization profile across th e interface that the process\nforthedemagnetizationatthelayeredsystemholdsatthehard/s oftinterfaceof3Dhardinclusions\nin a soft matrix at least for one or two finite sized objects, we relate the demagnetization curve\nof the two inclusions model to an extended one. We consider a lattice including Np= 256 cubic\ninclusions located on the nodes of a simple cubic lattice made of 4 (8 ×8) planes and is an\nextended version of the preceding two grains model. The edge to ed ge distance between nearest\nneighbors in each plane is ∆ = 2 δBas above and the external field is along ˆ x. Two different easy\naxes distributions have been used; in the first one all the easy axes are close to the ˆ x-axis, with\nΣi(|(ˆni.ˆx)|)/Np= 0.94 and in the second one the axes are randomly distributed on the un it sphere\n(Σi(|(ˆni.ˆx)|)/Np= 0.5). We haveconsideredthesetofparametersasinfig. (4). Since2 /3−rdofthe\ninterfacesareparalleltoboththepreferentialorientationofth e{ˆni}andthedirectionoftheapplied\nfield, the comparison with the preceding model for the parallel inter face is meaningful. As we can\nseeonfigure(8 a), atthequalitativelevel, thedemagnetizationcur vefortheeasyaxespreferentially\ndistributed along ˆ xisclosethe that obtainedfor the 2-inclusions’toy’model. Thedemag netization\ncurve calculated with the randomly distributed easy axes is displayed on figure (8 b), and leads\nto the same type of conclusion but only at a qualitative level. Given the results we have got on\nthe two inclusions ’toy’ model, we conclude that the caracteristic pla teau in the demagnetization\ncurve is indeed the signature of the local magnetization profile comp ression / depinning process.\nHowever, considering a mesh of the required quality for extracting the magnetization profile in\nthe 256 inclusions model would lead to prohibitively heavy simulations. I ndeed, our analysis of\nthe local magnetization profile is based upon a continuous function f or the later and its behavior\nwith respect to the external field. Such a requirement from the fin ite element simulation results,\nwhere the profile is obtained from an interpolation between the mesh nodes, can be reached only\nwith a very fine mesh. Nevertheless, on the physical point of view, in spite of its continuous\nnature the magnetization profile resulting either from an analytical calculation or a finite elements\ninterpolation cannot be interpreted at an infinitely small length scale since the micromagnetic\nformalism remains a continuous medium type of approach valid beyond some characteristic lenght\nscale, say ∼1 nm.\nWe conclude that as is the case on the small local model, the rigid magn et, exchange spring and\ndecoupled magnet regimes are reached on the extended model for roughly ∆ /(2lex)<1, 1<\n∆/(2lex)<2and ∆/(2lex)≥2 respectively. In this case, these boundaryvalues can be related to\nthe volumic fraction ϕvof the embedded cristallites through ∆ /(2lex) = (ϕ−1/3\nv−1)(R/lex) with\nthe simple cubic geometry. This extended model provides a link with a m ore realistic modelling of\nan actual experimental system as was shown in ref. [3]. Thus, the results displayed in figure (8)\nshow that the local demagnetization process explicited at the single inter-grains soft layer can be\nqualitatively transfered to a realistic situation.10\nV. CONCLUSION\nIn this work, focusing on the well established mecanism of exchange coupling between phases\nin hard / soft composite systems, we made the connection between the demagnetization behavior\nat the layered system where a 1-D description holds and a fully 3-D co mposite system. The\nconnection has been done through the local magnetization profile a nd we have shown that locally\nat the hard/ soft interface this profile can be transfered from th e layeredto the 3-Dsystems. While\nit is well known that the distance between hard objects in a soft mat rix as measured w.r.t. the\nsoft phase exchange length is one of the most relevant parameter s driving the coupling, this point\non the one hand has been made more quantitative and on the hand illus trated by the behavior\nof the simulated local magnetization profile in a small 3-D model. This lat ter play the role of an\nintermediate between the 1-D description of the interface and the true 3-D model.\nAcknowledgements\nThe numerical micromagnetic simulations were performed using HPC r esources from GENSI-\nCINES (grant number 2011-096180).\n[1] Z. Chen, X. Meng-Burany, and G. C. Hadjipanayis, Applied Physics Letters 75, 3165 (1999).\n[2] Z. Chen, X. Meng-Burany, H. Okumura, and G. C. Hadjipanay is, Journal of Applied Physics 87, 3409\n(2000).\n[3] K. Younsi, V. Russier, and L. Bessais, Journal of Applied Physics107, 083916 (2010).\n[4] G. C. Hadjipanayis, Journal of Magnetism and Magnetic Ma terials200, 373 (1999).\n[5] E. Kneller and R. Hawig, IEEE Trans. Magn. 27, 3588 (1991).\n[6] E. E. Fullerton, J. S. Jiang, M. Grimsditch, C. H. Sowers, and S. D. Bader, Phys. Rev. B 58, 12193\n(1998).\n[7] R. Victora and X. Shen, IEEE Trans. Magn. 41, 2828 (2005).\n[8] R. Skomski, T. A. George, and D. J. Sellmyer, Journal of Ap plied Physics 103, 07F531 (2008).\n[9] D. Suess, Applied Physics Letters 89, 113105 (2006).\n[10] D. Suess, Journal of Magnetism and Magnetic Materials 308, 183 (2007).\n[11] A. Goncharov, T. Schrefl, G. Hrkac, J. Dean, S. Bance, D. S uess, O. Ertl, F. Dorfbauer, and J. Fidler,\nApplied Physics Letters 91, 222502 (2007).\n[12] A. Aharoni, Phys. Rev. 119, 127 (1960).\n[13] G. Asti, M. Solzi, M. Ghidini, and F. M. Neri, Phys. Rev. B 69, 174401 (2004).\n[14] G. Asti, M. Ghidini, R. Pellicelli, C. Pernechele, M. So lzi, F. Albertini, F. Casoli, S. Fabbrici, and\nL. Pareti, Phys. Rev. B 73, 094406 (2006).\n[15] M. Ghidini, G. Asti, R. Pellicelli, C. Pernechele, and M . Solzi, Journal of Magnetism and Magnetic\nMaterials 316, 159 (2007).\n[16] R. Pellicelli, M. Solzi, V. Neu, K. H¨ afner, C. Perneche le, and M. Ghidini, Phys. Rev. B 81, 184430\n(2010).\n[17] A. Y. Dobin and H. J. Richter, Applied Physics Letters 89, 062512 (2006).\n[18] R. Skomski and J. M. D. Coey, Phys. Rev. B 48, 15812 (1993).\n[19] R. Skomski, Journal of Applied Physics 76, 7059 (1994).11\n[20] T. Leineweber and H. Kronmuller, Journal of Magnetism a nd Magnetic Materials 176, 145 (1997).\n[21] H. Kronm¨ uller and D. Goll, Physica B: Condensed Matter 319, 122 (2002).\n[22] K. Y. Guslienko, O. Chubykalo-Fesenko, O. Mryasov, R. C hantrell, and D. Weller, Phys. Rev. B 70,\n104405 (2004).\n[23] F. Casoli, F. Albertini, L. Nasi, S. Fabbrici, R. Cabass i, F. Bolzoni, and C. Bocchi, Applied Physics\nLetters92, 142506 (2008).\n[24] J.-L. Tsai, H.-T. Tzeng, and B.-F. Liu, Thin Solid Films 518, 7271 (2010).\n[25] W. Scholz, J. Fidler, T. Schrefl, D. Suess, R. Dittrich, H . Forster, and V. Tsiantos, Comp. Mat. Sci.\n28, 366 (2003).\n[26] A. Y. Dobin and H. J. Richter, Journal of Applied Physics 101, 09K108 (2007).12\n-1-0.5 0 0.5 1\n-0.4 -0.3 -0.2 -0.1  0M/Ms\nH/HK\nFigure 1: Demagnetization curve as calculated by using the p rofile calculated on the 1-D model (lines)\nand compared to the results of the 3-D micromagnetic simulat ions (symbols). ( ǫA,ǫJ) = (0.75, 0.325) open\nsquares and solid line; (0.325, 0.75) open circles and dotte d line; (1.00, 1.00) triangles and dashed line.13\n-1-0.5 0 0.5 1\n-5-4-3-2-1 0 1mx(z)\nH/HKa)\n-1-0.5 0 0.5 1\n-5-4-3-2-1 0 1mx(z)\nH/HKb)\n-1-0.5 0 0.5 1\n-6-5-4-3-2-1 0 1mx(z)\nz/δBc)\nFigure 2: Magnetization profile, mx(z) in terms of z/δBacross the hard/soft interface along the normal\ncutting the center of the cubic inclusion. The hard (soft) ph ase is located at z >0 (z <0). Solid line:\nresult of the 1-D model; Symbols: 3-D micromagnetic simulat ion.Ks= 0;Kh= 3.05 106Jm−3;\na) :ǫA= 1, ǫJ= 1h= 0.0328, squares; 0.0740, circles; 0.1150, upward triangl es; 0.1760, downward\ntriangles. b) : ǫA= 0.325, ǫJ= 0.75h= 0.0123, squares; 0.1352, circles; 0.2580, triangles. c) : ǫA=\n0.75, ǫJ= 0.325h= 0.0165, squares; 0.0492, circles; 0.1230, upward triangl es; 0.2295, downward triangles;\n0.3320, diamonds. Dash-dotted line : result of the 1-D model calculated with z(s)\nb/δB= 7.0 and a fitted\nvalue of the field h(fit)= 0.0240, according to equation (16).14\n-1-0.5 0 0.5 1\n-2 -1.5 -1 -0.5  0mx(z)\n z/δBa)\n-1-0.5 0 0.5 1\n-2 -1.5 -1 -0.5  0mx(z)\n z/δBb)\nFigure 3: Magnetization profile, mx(z) between the two cubic inclusions in the soft matrix. ∆ = 2 δB. The\ncenter of soft layer is located at z/δB=−1.0. Symbols: 3-D micromagnetic simulation; Solid line: profi le\nas calculated from the 1-D model.\na)ǫJ= 0.75 and : ǫA= 0.75 and h= 0.1475, triangles; ǫA= 0.325 and h= 0.2295, squares; ǫA= 0.162\nandh= 0.2622, circles. For ǫA= 0.75, the 1-D model profile is calculated with the fitted valu e of the field,\nh(fit)= 0.1874, according to equation (16). In each case, the value of the field is close to the depinning\nfield of the 3-D micromagnetic simulation.\nb)ǫJ= 1.50 ; ǫA= 0.1623 and h= 0.0697, circes; 0.1885, squares. The larger value of the fie ld is close\nto the depinning field of the 3-D micromagnetic simulation.15\n-1-0.5 0 0.5 1\n-0.35-0.3-0.25-0.2-0.15-0.1-0.05  0 0.05M/Ms\nH/HK\nFigure 4: Demagnetization curve of the two cubic inclusions model.ǫJ= 0.75 ; ǫA= 0.162, open squares;\n0.325, open circles; 0.75 open triangles. Dashed line : dema gnetization curve of the 1-D model for the\nhard/soft interface with ǫJ= 0.75 and ǫA= 0.162.16\n-1.5-1-0.5 0 0.5 1 1.5\n-2 -1.5 -1 -0.5  0φ(z)\n z/δB \nFigure 5: Angular profile accross the soft phase between the t wo hard cubic inclusions located at\nz/δB<−2 andz/δB>0 respectively with (ˆ n,ˆz) =π/4 for the latter. Symbols: 3-D micro-\nmagnetic simulations for h= 0.0655, triangles; 0.1311, circles and 0.3440, squares. 1 -D profile for the\nfitted values of the field h(fit)= 0.130, solid lines; 0.2020, dashed lines and 0.3080, dash- dotted lines\nrespectivelly. h(fit)is determined using equation (16) to fit ϕ(z=z(s)\nb) on the simulated result where\nz(s)\nb/δB=−1 is the location of the soft layer mid plane.\n-1-0.5 0 0.5 1\n-2 -1.5 -1 -0.5  0mx(z)\n z/δB \nFigure 6: Same as figure (5) for the x−component of the magnetization ˆ m(z).17\n 0 0.2 0.4 0.6 0.8 1\n-2 -1.5 -1 -0.5  0mz(z)\n z/δB\nFigure 7: Same as figure (5) for the z−component of the magnetization ˆ m(z).18\n-1-0.5 0 0.5 1\n-0.4 -0.3 -0.2 -0.1  0 M/Ms\nH/HKa)\n-1-0.5 0 0.5 1\n-0.4 -0.3 -0.2 -0.1  0  0.1 M/Ms\n H/HKb)\nFigure 8: Demagnetization curve obtained from a micromagne tic simulation on the system including 256\ncubic particles located on the nodes of a simple cubic lattic e.\na) Preferentially oriented easy axes in the direction of the field with Σ i(|(ˆni.ˆx)|)/Np= 0.94 ;ǫJ= 0.75\nandǫA= 0.162, dashed line; 0.325, solid line and 0.75 dotted line.\nb) Random distribution of easy axes; ǫJ= 0.75 and ǫA= 0.162, solid line; 0.75, dashed line."    },    {        "title": "1111.2506v1.Magnonic_band_structure_of_a_two_dimensional_magnetic_superlattice.pdf",        "content": "arXiv:1111.2506v1  [cond-mat.mtrl-sci]  10 Nov 2011Magnonic band structure of a two-dimensional magnetic\nsuperlattice\nGlade Sietsema∗and Michael E. Flatté†\nDepartment of Physics and Astronomy and Optical Science and Technology Center,\nUniversity of Iowa, Iowa City, Iowa 52242, USA\n(Dated: October 10, 2018)\nAbstract\nThe frequencies and linewidths of spin waves in a two-dimens ional periodic superlattice of mag-\nnetic materials are found, using the Landau-Lifshitz-Gilb ert equations. The form of the exchange\nfield from a surface-torque-free boundary between magnetic materials is derived, and magnetic-\nmaterial combinations are identified which produce gaps in t he magnonic spectrum across the\nentire superlattice Brillouin zone for hexagonal and square -symmetry superlattices.\n1I. INTRODUCTION\nAdvances in the control of spin-wave propagation and dynami cs1have led to the demon-\nstration of magnonic bose condensation2and coupling of electronic spin currents to spin\nwaves in hybrid systems3. Such effects, along with theoretical proposals to electric ally-\ncontrol spin-wave properties4, and theoretical suggestions of high-temperature operati on\nwith small switching energies, may provide the foundation f or an information-processing\ntechnology based on spin waves5,6. Any such technology would benefit from magnetic ma-\nterials with designed spin-wave dispersion relations, gro up velocities, and linewidths. A\ncommon method of designing such features is the fabrication of a superlattice of different\nconstituent materials, used to design electronic band stru ctures in semiconductor superlat-\ntices, and photonic band structures in dielectric superlat tices.\nHere we focus on the effect of a two-dimensional superlattice of magnetic materials on\nthe magnonic frequencies and linewidths, obtained from a re ciprocal-space solution to the\nLandau-Lifshitz-Gilbert (LLG) equation7. Infinite cylinders of one magnetic material are\nembedded in a second magnetic material in a periodic arrange ment corresponding to a two-\ndimensional square lattice or hexagonal lattice. Large gap s within the spin-wave spectrum\nare obtained when the exchange constants and saturation mag netization of the two materials\ndiffer greatly; thus the gaps are considerably larger for cyl inders of iron embedded within\nyttrium iron garnet (YIG) than within nickel. For iron embed ded in YIG we demonstrate\nthe existence of a gap throughout the superlattice Brilloui n zone in the magnon spectrum for\nboth square and hexagonal-symmetry magnonic crystals. In p hotonic crystals such a feature\nforms an essential element of photonic band gap materials8,9, and permits the control of\nspontaneous emission of emitters embedded within the photo nic crystal; here similarly the\nspontaneous emission of magnons from a source such as a spin- torque nano-oscillator could\nbe suppressed by embedding this spin-wave emitter in a fully -gapped magnonic crystal.\nCentral to the accurate calculation of dispersion curves as sociated with a superlattice is\nthe proper treatment of the boundaries between the two magne tic materials. For a magnonic\nsuperlattice the exchange field that enters into the LLG equa tions is discontinuous at the\nboundary, and that discontinuity strongly influences the sp in wave dynamics. Two distinct\nforms for this exchange field have been described in the liter ature10–12, although to our\nknowledge it has not been pointed out that these two forms pro vide dramatically-different\n2solutions to the LLG equation. In Section II we present an exp licit derivation of the correct\nform of the exchange field, followed by spin wave frequencies and linewidths for various\nmagnetic material combinations in Section III. In Section I V we show that solutions to\nthe LLG equations for the incorrect form of the exchange field differ greatly from those for\nthe correct form, and furthermore the incorrect solutions a re incompatible with the spatial\nsymmetry of the lattice.\nII. LLG FORMALISM FOR A QUASI-TWO-DIMENSIONAL MAGNONIC CRYS-\nTAL\nWe consider a magnonic crystal composed of an array of infinit ely long cylinders of\nferromagnetic material A embedded in a second ferromagneti c material B in a square or\nhexagonal lattice; the structures are shown in Fig. 1, and ha ve lattice constant aand cylinder\nradiusRcyl. The cylinders are aligned parallel to a static external mag netic field H0=H0ˆz,\nand the magnetization of both materials is assumed to be para llel toH0. The equation of\nmotion for this system is the Landau-Lifshitz-Gilbert (LLG ) equation7:\n∂\n∂tM(r,t) =γµ0M(r,t)×Heff(r,t)+α(r)\nMs(r)M(r,t)×∂\n∂tM(r,t). (1)\nHereγis the gyromagnetic ratio, Ms(r)is the spontaneous magnetization, α(r)is the\nGilbert damping parameter, and ris the three dimensional position vector. The effective\nmagnetic field\nHeff(r,t) =H0+h(r,t)+Hex(r,t) (2)\nacting on the magnetization M(r,t)consists of three terms: the external field H0, the\ndynamic dipolar field h(r,t), and the exchange field Hex(r,t).\nA. Derivation of the Effective Electric Field\nWe wish to derive the correct form of Heff(r,t)to use in Eq. (1) for our magnonic\ncrystal. As shown by Gilbert7, the exchange field can be obtained by taking the functional\nderivative of the exchange energy. For a homogeneous materi al, the exchange energy is13\nUex[M(r)] =A\nM2sˆ/bracketleftbig\n(∇mx(r))2+(∇my(r))2+(∇mz(r))2/bracketrightbig\ndr, (3)\n3where A is the exchange stiffness constant. This yields the fo llowing exchange field:\nHex(r) =−1\nµ0δUex[M(r)]\nδM(r)=2A\nµ0M2s∇2M(r). (4)\nFor the inhomogeneous crystal considered here, the values o f the exchange constant and\nthe spontaneous magnetization will differ for the two ferrom agnets, so AandMsbecome\nspatially dependent quantities:\nA(r) =AB+Θ(r)(AA−AB),\nMs(r) =MsB+Θ(r)(MsA−MsB),(5)\nwhereΘ(r) = 1 in material A and Θ(r) = 0 in material B. The exchange energy for this\ninhomogeneous situation is\nUex[M(r)] =ˆ\nA(r)/braceleftBigg/bracketleftbigg\n∇/parenleftbiggmx(r)\nMs(r)/parenrightbigg/bracketrightbigg2\n+/bracketleftbigg\n∇/parenleftbiggmy(r)\nMs(r)/parenrightbigg/bracketrightbigg2\n+/bracketleftbigg\n∇/parenleftbiggmz(r)\nMs(r)/parenrightbigg/bracketrightbigg2/bracerightBigg\ndr,(6)\nBy approximating the energy with Uexwe have neglected non-exchange terms that would\ngive rise to a surface torque (such as terms in the energy asso ciated with surface-induced\nmagnetic anisotropy).\nThe total magnetization will consist of both a time-depende nt term and a time-\nindependent term: M(r,t) =Ms(r)ˆz+m(r,t).Using the linear magnon approximation we\nassume that the time-dependent magnetization is small comp ared toMs(r)and therefore\nwe only keep terms up to first order in m(r,t).With these assumptions, the inhomogeneous\nexchange field derived from Eq. (6) is\nHex(r,t) =2\nµ0/parenleftbigg\n∇·A(r)\nM2s(r)∇/parenrightbigg\nM(r,t)+2M(r,t)\nµ0Ms(r)(∇·A(r)∇)1\nMs(r)\n−2m(r,t)\nµ0M2\ns(r)·/bracketleftbigg\n(∇·A(r)∇)m(r,t)\nMs(r)/bracketrightbigg\nˆz.(7)\nThe exchange field enters the LLG equation only as a cross prod uct with the magnetization\nM(r,t). The second term is parallel to M(r,t)and thus will not contribute to Eq. (1).\nThe third term of Eq. (7), which is proportional to m(r,t)and parallel to Ms(r), will only\nproduce terms of second order in m(r,t)in Eq. (1) and can safely be dropped. Therefore,\nwe can approximate\nHex(r,t) =2\nµ0/parenleftbigg\n∇·A(r)\nM2\ns(r)∇/parenrightbigg\nM(r,t), (8)\nwhich produces a LLG equation from Eq. (1) that is correct to fi rst order in m(r,t).\n4We now have the following equation for the effective field:\nHeff(r,t) =H0ˆz+h(r,t)+2\nµ0/parenleftbigg\n∇·A(r)\nM2s(r)∇/parenrightbigg\nM(r,t). (9)\nThis form is a generalization of the boundary condition obta ined at the interface between a\nferromagnet and vacuum14, in the absence of any surface torque, and later derived for t he\nboundary condition between dissimilar magnetic materials15,16. It is also the form used in\nRef. 11.\nB. Plane-Wave Solution to LLG Equation for Quasi-Two-Dimens ional-Magnonic\nCrystal\nWhen solving for magnons of a specific frequency ωwe write m(r,t) =m(r)exp(−iωt)\nand the dipolar field, h(r,t) =−∇Ψ(r)exp(−iωt), withΨ(r)the magnetostatic potential.\nWith the form of the effective field in Eq. (9), the LLG equation (Eq. (1)) can be written\niΩmx(R)+Ms(R)∇·(Q(x)∇my(R))−my(R)∇·(Q(R)∇Ms(R))\n−my(R)−Ms(R)\nH0∂Ψ(R)\n∂y+iΩα(R)my(R) = 0,(10)\niΩmy(R)−Ms(R)∇·(Q(R)∇mx(R))+mx(R)∇·(Q(R)∇Ms(R))\n+mx(R)+Ms(R)\nH0∂Ψ(R)\n∂x−iΩα(R)mx(R) = 0,(11)\nwhereΩ =ω/(|γ|µ0H0)andQ(R) = 2A(R)/(µ0H0M2\ns(R)). Additionally, since there is\nnozdependence in the above equations, the three dimensional po sition vector rhas been\nreplaced with the two dimensional position vector, R= (x,y).\nThis system of equations can be efficiently solved with a plane -wave method10–12. We take\nadvantage of the crystal’s periodicity and use Bloch’s theo rem to write the magnetization\nand magnetostatic potential as an expansion of plane waves:\nm(R) =eik·R/summationdisplay\nimk(Gi)eiGi·R, (12)\nΨ(R) =eik·R/summationdisplay\niΨk(Gi)eiGi·R. (13)\nHereGirepresents a two dimensional reciprocal lattice vector of t he crystal and kis a wave\nvector in the first Brillouin zone. The magnetostatic potent ial can be rewritten in terms of\nthe magnetization by using one of Maxwell’s equations:\n∇·(h(R)+m(R)) = 0. (14)\n5Replacing h(R)with−∇Ψ(R), substituting in Eqs. (12) and (13), and solving for the\npotential yields\nΨ(G) =−imx,k(G)(Gx+kx)+my,k(Gy+ky)\n(G+k)2. (15)\nNext, we need to be able to write the material properties Ms(R),Q(R), andα(R)in\nreciprocal space. Since these have the same periodicity as t he crystal lattice, this can be\ndone with a Fourier series expansion:\nMs(R) =/summationdisplay\niMs(Gi)eiGi·R,\nQ(R) =/summationdisplay\niQ(Gi)eiGi·R,(16)\nα(R) =/summationdisplay\niα(Gi)eiGi·R.\nThe Fourier coefficients are obtained by an inverse Fourier tr ansform:\nMs(G) =1\nSˆ\nSMs(R)e−iG·Rd2R. (17)\nwhere S is the area of the two-dimensional unit cell. Perform ing the integration for G= 0\ngives the average\nMs(G= 0) =MsAf+MsB(1−f), (18)\nwherefis the fractional space occupied by a cylinder in the unit cel l. ForG/negationslash= 0, we have\nMs(G/negationslash= 0) = (MsA−MsB)2fJ1(|G|Rcyl)\n|G|Rcyl. (19)\nHereJ1is a Bessel function of the first kind, and Rcylis the radius of the cylinders. The\nfollowing infinite system of equations in reciprocal space i s obtained by substituting Eqs.\n(12)-(16) in Eqs. (10) and (11):\niΩ/summationdisplay\nj(mx,k(Gi)δij+α(Gi−Gj)my,k(Gj)) =\n/summationdisplay\nj/braceleftBigg\nMs(Gi−Gj)(Gx,j+kx)(Gy,j+ky)\nH0(Gj+k)2mx,k(Gj)+/bracketleftBigg\nδij+Ms(Gi−Gj)(Gy,j+ky)2\nH0(Gj+k)2\n+/summationdisplay\nl(Ms(Gi−Gl)Q(Gl−Gj)((k+Gj)·(k+Gl)−(Gi−Gj)·(Gi−Gl)))/bracketrightBigg\nmy,k(Gj)/bracerightBigg\n(20)\n6iΩ/summationdisplay\nj(my,k(Gi)δij−α(Gi−Gj)mx,k(Gj)) =\n−/summationdisplay\nj/braceleftBigg\nMs(Gi−Gj)(Gx,j+kx)(Gy,j+ky)\nH0(Gj+k)2my,k(Gj)+/bracketleftBigg\nδij+Ms(Gi−Gj)(Gy,j+ky)2\nH0(Gj+k)2\n+/summationdisplay\nl(Ms(Gi−Gl)Q(Gl−Gj)((k+Gj)·(k+Gl)−(Gi−Gj)·(Gi−Gl)))/bracketrightBigg\nmx,k(Gj)/bracerightBigg\n.\n(21)\nWe solve this by limiting the number of reciprocal lattice ve ctors in the sum and expressing\nit as a matrix equation:\niΩ\nδijα(Gi−Gj)\nα(Gi−Gj)δij\n\nmx,k(G1)\n...\nmx,k(GN)\nmy,k(G1)\n...\nmy,k(GN)\n=\nBxx\nijBxy\nij\nByx\nijByy\nij\n\nmx,k(G1)\n...\nmx,k(GN)\nmy,k(G1)\n...\nmy,k(GN)\n(22)\nBxx\nij=−Byy\nij=Ms(Gi−Gj)(Gx,j+kx)(Gy,j+ky)\nH0(Gj+k)2(23)\nBxy\nij=δij+Ms(Gi−Gj)(Gy,j+ky)2\nH0(Gj+k)2\n+/summationdisplay\nlMs(Gi−Gl)Q(Gl−Gj)[(k+Gj)·(k+Gl)−(Gi−Gj)·(Gi−Gl)](24)\nByx\nij= =δij+Ms(Gi−Gj)(Gx,j+kx)2\nH0(Gj+k)2\n+/summationdisplay\nlMs(Gi−Gl)Q(Gl−Gj)[(k+Gj)·(k+Gl)−(Gi−Gj)·(Gi−Gl)].(25)\nThe LLG equation is now reduced to finding the eigenvalues and eigenvectors for the above\nequation.\nIII. RESULTS\nFrom Eq. (22) we calculate the complex eigenvalues Ωcorresponding to the frequencies\nof magnons in the two-dimensional magnetic superlattices o f Fe, Co, Ni, and YIG. The real\npart ofΩn(k)is the magnon frequency of branch nfor the wave vector kand the imaginary\n7part is the inverse spin wave lifetime. To focus on the depend ence of these properties on\nmagnetic material combinations we consider superlattices with a lattice constant a= 10nm,\nan external field µ0H0= 0.1T, and a filling fraction f= 0.5. The material properties, Ms,\nA, andα, are listed in Table I.\nFigures 2 and 3, show the empty-lattice band structures obta ined from the LLG equation\nfor homogeneous crystals of Fe, Co, Ni, and YIG. As the empty- lattice features are governed\nby the lattice symmetry and the material’s spin wave velocit y, these plots depend on material\nonly in setting the frequency scale of the features.\nFigs. 4 and 5 show the results for when Fe is combined with Co, N i, or YIG. The change\nin band structure from the homogeneous case is more substant ial when there is a greater\ndifference in the spontaneous magnetization between the two materials. For example, the\nmagnetics properties of Fe and Co are fairly similar, and so f or a crystal composed of these\nmaterials, the band structure differs little from the homoge neous case, with only some small\nsplittings of the spin wave dispersion curves occurring. Ho wever, when for a crystal of Fe\nand YIG, whose magnetizations differ by more than a factor of t en, the magnonic modes\nare almost completely different from the homogeneous crysta l. Furthermore, the opening of\nband gaps in these structures is more easily attainable when the magnetization is larger in\nthe cylinders than it is in the host. With Fe cylinders embedd ed in YIG in a square lattice,\nthere are four gaps occurring within the lowest nine spin wav e modes, while YIG cylinders\nin Fe shows only one small gap between the first and second spin wave modes.\nFigs. 6-9 show the detailed dispersion curves and spin wave r elaxation rates for a hexag-\nonal superlattice of Fe cylinders in Ni. Plotted are the lowe st nine spin wave modes ( Re(Ω) )\nin the entire first Brilllouin zone as well as the correspondi ng inverse spin wave lifetimes\n(Im(Ω) ). Quality factors for these modes, corresponding to the rat io of the relaxation rate\nto the mode frequency, can exceed 100 for such spin waves, esp ecially for the lowest-frequency\nmodes.\n8IV. COMPARISON WITH ALTERNATE EFFECTIVE FIELD\nSome recent calculations of magnonic crystals dispersion c urves used a different exchange\nfield10,12than the one derived in Sec. II. The alternate form,\nHex(r,t) =2\nµ0Ms(r)/parenleftbigg\n∇·A(r)\nMs(r)∇/parenrightbigg\nM(r,t). (26)\ndiffers by the positioning of one factor of Ms(r)−1outside the gradient operators. A com-\nparison of the band structures obtained for the two different exchange fields is shown in\nFig. 10. An examination of the band structure for a homogeneo us material composed of\nFe or Ni (Fig. 2) indicates that the results for the derived ex changed field (Eq. (8)) pro-\nduce a band structure that is appreciably different from the h omogeneous case, whereas the\nband structures produced by the alternate exchange field ( Eq . (26)) are very similar to the\nhomogeneous crystal.\nIn Fig. 11 we show the lowest spin wave mode and corresponding relaxation rate obtained\nfor Fe cylinders in Ni when using Eq. (26) as the exchange field . When looking at these\ncontours, we would expect them to have the same symmetries as the real space lattice.\nFor a square lattice, that would be symmetry under rotations of90◦and symmetry under\nreflections about either axis. All symmetries are present fo r the spin wave modes of Fig.\n11, however, the spin wave lifetimes are lacking the reflecti on symmetries. Comparison with\nFigs. 6 and 7 shows that the use of Eq. 8 for the exchange field ke eps the symmetries of\nthe lattice preserved in the contours. A very slight asymmet ry in Figs. 7 and 9 is caused by\nterminating the infinite summation of the reciprocal lattic e vectors in the LLG equation (Eq.\n(22)), and disappears as the number of reciprocal lattice ve ctors is increased; the asymmetry\nin Fig. 11 does not.\nThus the consequences of using the exchange field of Eq. (26) i nstead of the correct\nform, Eq. (8), include a dramatic underestimate of the split tings in the magnonic crystal\ndispersion relations, as well as flawed rotational symmetry of the spin wave relaxation rate.\nV. CONCLUSION\nSpin wave dispersion curves and relaxation rates have been c alculated for hexagonal and\nsquare two-dimensional superlattices of magnetic cylinde rs embedded in another magnetic\n9material. The correct form of the exchange field at the bounda ry between these two magnetic\nmaterials has been found, and the difference from another for m used in the literature has been\nshown to be significant. Full-zone magnonic gaps are obtaine d for superlattice materials that\ndiffer substantially in their saturation magnetization, su ch as Fe and YIG. Quality factors\nfor spin waves can exceed 100, especially for the lowest-fre quency spin mode. These results\nshould assist in the design of magnonic crystals that can foc us or redirect spin waves due to\ntheir effective band structure.\nAcknowledgments\nWe acknowledge helpful conversations with A. D. Kent and F. M acia and support from\nan ARO MURI.\n10∗Electronic address: glade-sietsema@uiowa.edu\n†Electronic address: michael_flatte@mailaps.org\n1A. A. Serga, A. V. Chumak, and B. Hillebrands, J. Phys. D 43, 264002 (2010).\n2S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A . Serga, B. Hillebrands, and\nA. N. Slavin, Nature 443, 430 (2006).\n3K. Ando, S. Takahashi, J. Ieda, H. Kurebayashi, T. Trypiniot is, C. H. W. Barnes, S. Maekawa,\nand E. Saitoh, Nature Materials 10, 655 (2011).\n4T. Liu and G. Vignale, Phys. Rev. Lett. 106, 247203 (2011).\n5M. P. Kostylev, A. A. Serga, T. Schneider, B. Leven, and B. Hille brands, Appl. Phys. Lett. 87,\n153501 (2005).\n6A. Khitun, M. Bao, and K. L. Wang, J. Phys. D 43, 264005 (2010).\n7T. L. Gilbert, IEEE Trans. Magn. 40, 3443 (2004).\n8E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).\n9S. John, Phys. Rev. Lett. 58, 2486 (1987).\n10J. O. Vasseur, L. Dobrzynski, B. Djafari-Rouhani, and H. Pusz karski, Phys. Rev. B 54, 1043\n(Jul 1996).\n11M. Krawczyk and H. Puszkarski, Phys. Rev. B 77, 054437 (Feb 2008).\n12R. P. Tiwari and D. Stroud, Phys. Rev. B 81, 220403 (Jun 2010).\n13C. Kittel, Rev. Mod. Phys. 21, 541 (Oct 1949).\n14G. T. Rado and J. R. Weertman, J. Phys. Chem. Solids 11, 315 (1959).\n15F. Hoffmann, A. Stankoff, and H. Pascard, J. Appl. Phys. 41, 1022 (1970).\n16F. Hoffmann, Phys. Stat. Sol. 41, 807 (1970).\n17R. Skomski and D. Sellmyer, Handbook of Advanced Magnetic Materials: Vol 1. Nanostruct ural\nEffects (Springer, New York, 2006) p. 20.\n18M. Oogane, T. Wakitani, S. Yakata, R. Yilgin, Y. Ando, A. Saku ma, and T. Miyazaki, Jpn. J.\nAppl. Phys. 45, 3889 (May 2006).\n19J. C. Slonczewski, A. P. Malozemoff, and E. A. Giess, Appl. Phy s. Lett. 24, 396 (Apr 1974).\n20Z. Zhang, P. C. Hammel, and P. E. Wigen, Appl. Phys. Lett. 68, 2005 (Jan 1996).\n11Ms(A/m)A(pJ/m) α\nFe1.711·1068.30.0019\nCo1.401·10610.30.011\nNi0.485·1063.40.064\nYIG0.14·1064.150.0014\nTable I: Properties of the different materials considered fo r the magnonic crystals17–20.\n12Figure 1: Physical structure of the magnonic crystals studi ed here. The ferromagnetic material B\nis the host for infinitely long cylinders of a different ferrom agnetic material A arranged in either\na square (left) or hexagonal (right) lattice. The lattice co nstant of the superlattice is aand the\ncylinder radius is Rcyl.\n012Re(ω)\n0123Re(ω)\nΓ MXΓ0123Re(ω)\nΓ MXΓ0510Re(ω)\nFigure 2: Empty square lattice band structure obtained from the LLG equation for a homogeneous\ncrystal of Fe (upper left), Co (upper right), Ni (lower left) , and YIG (lower right) with lattice\nconstant a= 10nm. Frequencies are in units of THz.\n13012Re(ω)\n01234Re(ω)\nΓ MK Γ0123Re(ω)\nΓ MK Γ0510Re(ω)\nFigure 3: Empty hexagonal lattice band structure obtained f rom the LLG equation for a homoge-\nneous crystal of Fe (upper left), Co (upper right), Ni (lower left), and YIG (lower right) with lattice\nconstant a= 10nm. Frequencies are in units of THz.\n14012Re(ω)\n012Re(ω)\nΓ MXΓ0123Re(ω)012Re(ω)\n012Re(ω)\nΓ MXΓ0123Re(ω)\nFigure 4: Magnonic band structures for a square lattice magn onic crystal with lattice spacing\na= 10nm and filling fraction f= 0.5. On the left is Fe cylinders embedded in Co (top), Ni\n(middle), and YIG (bottom). The right is for an Fe host with Co (top), Ni (middle), and YIG\n(bottom) cylinders. Frequencies are in units of THz.\n150123Re(ω)\n0123Re(ω)\nΓ MK Γ0123Re(ω)0123Re(ω)\n0123Re(ω)\nΓ MK Γ01234Re(ω)\nFigure 5: Magnonic band structures for a hexagonal lattice m agnonic crystal with lattice spacing\na= 10nm and filling fraction f= 0.5. On the left is Fe cylinders embedded in Co (top), Ni\n(middle), and YIG (bottom). The right is for an Fe host with Co (top), Ni (middle), and YIG\n(bottom) cylinders. Frequencies are in units of THz.\n160.20.30.4Re(ω)\n0.50.60.7Re(ω)\n0.60.70.8Re(ω)\n0.811.2Re(ω)\n1.21.41.6Re(ω)\n1.41.61.8Re(ω)\n1.71.81.9Re(ω)\n22.12.2Re(ω)\n22.252.5Re(ω)\nFigure 6: (Color online) The lowest nine spin wave frequenci es (in THz) for a square lattice magnonic\ncrystal composed of Fe cylinders in Ni with a filling fraction off= 0.5, and a lattice constant of\na= 10nm. These results were obtained using the exchange field in Eq . (8).\n2.533.54Im(ω)\n101112Im(ω)\n7.510Im(ω)\n303540Im(ω)\n2030Im(ω)\n20304050Im(ω)\n20304050Im(ω)\n405060Im(ω)\n405060Im(ω)\nFigure 7: (Color online) The spin wave relaxation rate (in un its of GHz) corresponding to the lowest\nnine spin wave modes from Fig. 6.\n170.20.3Re(ω)\n0.50.75Re(ω)\n0.60.8Re(ω)\n1.21.31.4Re(ω)\n1.41.51.6Re(ω)\n1.51.752Re(ω)\n1.7522.25Re(ω)\n2.252.52.75Re(ω)\n2.52.753Re(ω)\nFigure 8: (Color online) The lowest nine spin wave frequenci es (in THz) for a hexagonal lattice\nmagnonic crystal composed of Fe cylinders in Ni with a filling fraction of f= 0.5, and a lattice\nconstant of a= 10nm. These results were obtained using the exchange field in Eq . (8).\n33.54Im(ω)\n81012Im(ω)\n1012.5Im(ω)\n3032.535Im(ω)\n202530Im(ω)\n 3040Im(ω)\n506070Im(ω)\n4060Im(ω)\n6080100Im(ω)\nFigure 9: (Color online) The spin wave relaxation rates (in u nits of GHz) corresponding to the\nlowest nine spin wave modes from Fig. 8\n18Γ MXΓ012Re(ω)\nΓ MXΓ012Re(ω)\nFigure 10: Magnonic band structure of Fe cylinders embedded in Ni calculated from the LLG\nequation using exchange field in Eq. (8) (left) and Eq. (26) (r ight). Frequencies are in units of\nTHz.\n0.10.20.30.4Re(ω)\n1020Im(ω)\nFigure 11: (Color online) The lowest spin wave mode (in THz) a nd the corresponding relaxation\nrate (in units of GHz) for a square lattice magnonic crystal c omposed of Fe cylinders in Ni with a\nfilling fraction of f= 0.5, and a lattice constant of a= 10nm. These results were obtained using\nthe exchange field in Eq. (26).\n19"    },    {        "title": "1111.5636v1.Converse_Magnetoelectric_Experiments_on_a_Room_Temperature_Spirally_Ordered_Hexaferrite.pdf",        "content": "Converse Magnetoelectric Experiments on a Room Temperature Sp irally Ordered \nHexaferrite \n \n \nKhabat Ebnabbasi and Carmine Vittoria \nDepartment of Electrical and Computer Engineering, Northe astern University, Boston MA 02115 \n \nAllan Widom \nPhysics Department, Northeastern University, Boston MA 02115 \n \n \nExperiments have been performed to measure magnetoelectr ic properties of room temperature \nspirally ordered Sr 3Co 2Fe 24 O41  hexaferrite slabs. The measured properties include the ma gnetic \npermeability, the magnetization and the strain all as a function of the electric field E and the \nmagnetic intensity H. The material hexaferrite Sr 3Co 2Fe 24 O41  exhibits broken symmetries for \nboth time reversal and parity. The product of the two sym metries remains unbroken. This is the \ncentral feature of these magnetoelectric materials. A simple physical model is proposed to \nexplain the magnetoelectric effect in these material s. \n  \n \nINTRODUCTION \n \nThere has been considerable recent interest in the nat ure of magnetoelectric materials[1]. Of \npresent interest are spirally ordered hexaferrites[2-5] which have strong magnetoelectric effects at \nroom temperature. Neutron scattering experiments performe d in [5,6] revealed a spiral spin \nconfiguration responsible for the magnetoelectric effec t at room temperature in Sr 3Co 2Fe 24 O41  \nhexaferrite.  Sr 3Co 2Fe 24 O41  is identified as a Z-type hexaferriteconsisting of S,R  and T \"spinel\" \nblocks (see [4,5] for details of the crystal structure). It was further revealed that in the T block the \nFe-O-Fe bond angles were slightly deformed to affect t he super-exchange interaction between the \nFe ions and induce the spiral spin configuration in Sr 3Co 2Fe 24 O41 . The magneto-electric coupling \nparameter, α, was measured to be ~ 0.5x10 -2 (CGS) at room temperature which is more than 50 \ntimes larger than the α measured in Cr 2O3. This is a significant result in terms of the practic al \nimplications at room temperature. Most magnetoelectric m aterials operate at low temperatures, \nsuch as TbMnO 3, CuO, Cr 2O3, etc.. The magnetoelectric effect in Sr 3Co 2Fe 24 O41  was confirmed \npreviously [5] by conventional measuring techniques whereby a mag netic field, H, was applied to \ninduce electric polarization, P, and changes in the dielec tric constant , εr, at low frequencies (~ \n100KHz). We have adopted an unconventional technique of measuri ng the magnetoelectric effect \nin these materials by applying an electric field, E, inst ead and induce changes in magnetization, \npermeability and strain. We refer to these measurements as the \"converse\" magnetoelectric \nmeasurements. Although previous authors [1-5] have establish ed a strong correlation between the \nspiral configuration and the magnetoelectric effect, we  provide a physical picture or model for the \neffect. Our measurments reveal that Sr 3Co 2Fe 24 O41  is electrostrictive. As such, the application of \nE strains the material and , therefore, changing the phy sical structure of the spiral spin \nconfiguration. It is this physical motion of the spiral w ith respect to E that induces a change in \nmagnetization. We refer to this model as the \"Slinky\"  helix model. Our model should be contrasted with the model for the magnetoelectric effec t in ferromganetic metal films whereby \nthe band energies of the up and down spin are modified by the electric fields at the interface \nbetween ferromagnetic and ferroelectric films. The ch ange in the splitting of the bands leads to \nchanges of magnetization at the surface. [7].  \n \nThe thermodynamic enthalpy per unit volume ω(s,E,H,σ) determines all of the spirally ordered \nhexaferrite thermodynamic equations of state[8] via \n  \ndω = Tds - P .dE -M. d H- e : dσ           (1) \nHere, T, P, M, and e represent, respectively, the temp erature, polarization, magnetization and \nstrain, while s, E, H, and σ represent, respectively, the entropy per unit volume, e lectric field, \nmagnetic intensity and stress. Other thermodynamic quant ities of interest include the adiabatic \ndielectric constant tensor \nε=1+4 π/g4666/g3105/g3017\n/g3105/g3006/g4667 s,H, σ = 1+4 πχ  P,          (2) \n \nthe adiabatic permeability tensor \nµ=1+4 π/g4666/g3105/g3014\n/g3105/g3009/g4667 s,E,σ = 1+4 πχ  M,         (3) \n \nand the adiabatic magnetoelectric tensor \nα= /g4666/g3105/g3014\n/g3105/g3006/g4667 s,H, σ =/g4666/g3105/g3017\n/g3105/g3009/g4667 s,E,σ                    (4) \n \nConventional experiments probing magnetoelectric effects , measure elements of the \nmagnetoelectric tensor αij  = ( ∂Mi=∂Ej) s,H, σ. In the converse experiments reported in this work, t he \nmagnetoelectric effect is probed by measuring elements of  the magnetic permeability tensor µ \nand the strain tensor e, while noting the manner in which these tensors depend on E and H. Direct \nmeasurements of the magnetization M were also employ ed.  \n \n  \nEXPERIMENTAL RESULTS \n \n   Experimental Material Growth \nWe have adopted similar procedure in preparing single phase of Sr 3Co 2Fe 24 O41  except for the \nfollowing preparation steps. In order to prevent formation of other impurity phases, including W-, \nM- and/or Y- types phases, it was found most favorable t o quench the sample immediately to \nroom temperature after annealing. The resulting X-ray di ffraction pattern is shown in FIG.1. \nAlso, for the magnetoelectric measurements it is impo rtant to minimize conductance current flow \nor heating effects through the sample in the presence of  high electric fields. As such, the \nresistivity was increased by annealing the samples at 600 oC in an oxygen atmosphere for another \nsix hours. \nThe resistivity estimated from the experimental linear  V- I characteristic was ρ= 1.43x10 9 Ω-cm \nfor samples with 1 millimeter thickness. The preparati on in oxygen leads to Fe ++  concentration \nreduction which then lowered the hopping of electrons betw een Fe ++  and Fe +++  ions[5, 9]. \nSince we are proposing here a set of converse experim ents such as the measurment of \npermeability with frequency, it called for unconventional measuring techniques. Typically, coaxial lines are used to measure permeability and dielect ric constants as a function of frequency, \nbut never FIG. 2: Real and imaginary parts of the polycr ystalline Sr Z-type permeability versus \nfrequency. in the presence of an electric field or a D C voltage as high as 1-2000 VDC. The risks \nto instrumentation are too high. We have developed a coaxi al line technique whereby the inner \nand outer conductors are coupled at RF fields, but not at DC voltages. This technique will be \ndescribed elsewhere. The microwave experiments were per formed under the following \nconditions: For a given direction of remanence magneti zation, Mr the electric field was applied \nparallel, opposite and perpendicular to M r. Prior to the experiments the remanence direction wa s \npoled with a permanent magnet. In FIG.2 we exhibit the co mplex relative magnetic permeability \nµ(ω+i0+) for low microwave frequencies on the scale of the fe rromagnetic resonant frequency. In \nthe limit of f /g13720, we expect the permeability, µ(0), to be in the order of [10] \n \nµ(0)=1+( /g2872/g3095/g3014/g3293\n/g3009/g3349)            (5) \nwhere 4 πMr is the remanence magnetization and H φ is the six fold magnetic anisotropy field. We \nmeasured 4πMr=105 G and ,therefore, H φ ≈ 40 Oe, see Fig.2.  \n \n \nFIG. 1: X-ray di_raction pattern of the polycrystalline Sr 3Fe 24 Co 2O41 at room temperature. The black lines represent the ref erence \npeak positions for the Ba Z-type hexaferrite \n    \n \n \nFIG. 2: Real and imaginary parts of the polycrystalline S r Z-type permeability versus frequency. \n \n \n \n \n \nExperimental Magneto-Electric Measurements  \n \nShown in FIG.3 is the change in permeability when an ele ctric field is applied parallel or anti-\nparallel to the magnetization. Under a change in parity  E /g1372 -E and M r /g1372 Mr. Under time reversal, \nE /g1372 E and M r /g1372 -M r. The data indicates both a broken parity and a broken t ime reversal \nsymmetry with the product of the symmetries unbroken. Thi s represents the fundamental \nsymmetry expected of magnetoelectric effects. The mea surements in FIG.3 correlate very well \nwith the vibrating sample measurements (VSM) whereby M r scales as E, changing polarity with \nthe direction of E. Thus, in the limit as f /g1372 0, ∆µ r may be explained simply in terms of changes in \nMr with E. However, at high frequencies dynamical magneto electric interaction between the RF \nmagnetization and electric fields must be considered, si nce, for both directions of E, ∆µ r decrease \nmonotonically with frequency. For contrast we exhibit in  FIG.4, the change in permeability for \nelectric fields perpendicular to the magnetization. The  permeability shift for this case is a \nfunction only of |/g1831/g2884|2. For either case E anti-parallel or perpendicular to M  the change in \npermeability, ∆µ r, decreased precipitously with frequency. Simple arguments would say that ∆µ r \nto be approximately constant up to FMR frequency in zero fiel d.   \n \nf/g34042.8/g3493/g1834/g3101/g46664/g2024/g1839/g3045/g3397/g1834/g3087/g4667             (6) \n \nwhereHφ=40 Oe, 4 πMr=105 G, H≈20 KOe and as a result f ≈3 GHz. However, this is not the \ncase. Clearly, there are dynamic magnetoelectric effe cts that need to be accounted for in order to \nexplain the monotonic decrease of ∆µ r with frequency. For proper discussion of the monotonic \ndecrease of ∆µ r with frequency one must include magnetic and electric re laxation effects in the \nLandau and Khalatnikov [11] equation pertaining to dynamic inte ractions in magnetoelectric \nmaterials. We will address these effects in a future publ ication. Finally, in FIG.5 the strain \ninduced by an electric field is exhibited as a function of t he electric field. The strain is quadratic \nin the electric field strength which indicates that Sr 3Co 2Fe 24 O41  is neither ferroelectric or \npiezoelectric material. Hence, the material exhibits electrostriction. \n \n \nFIG. 3: The magnetic permeability change versus electric f ield is exhibited over a microwave frequency range when M  is parallel \nand anti-parallel to E. \n \nFIG. 4: The magnetic permeability change versus electric f ield is exhibited over a microwave frequency range when M  is \nperpendicular to E. \n \n \nFIG. 5: The electrostriction strain of poly-crystalline  Sr Z-type depends on the electric field. \n \n \n \nCONCLUSIONS AND DISCUSSIONS \n \nIn general terms, the magnetoelectric effect implies  the following: the application of a magnetic \nintensity H induces a change in electric polarization P and the application of an electric field E \ninduces a change in magnetization M. In the majority of the previous works on magneto-electric \neffect, the change in material parameters including the  electric polarization have been measured \nversus magnetic field intensity only. The material hex aferrite Sr 3Co 2Fe 24 O41  exhibits broken \nsymmetries for both time reversal and parity. The product  of the two symmetries remains \nunbroken. This is the central feature of these magnetoele ctric materials. Measurements have been \nmade in order to verify this feature but in a novel manner.  The measurements involve the \nmagnetic permeability, magnetization, and strain all a s a function of the electric field E and the \nmagnetic field H. The field dependence on strain indicate s that the material is electrostrictive. In \nour so called converse experiments we have reversed the roles of E and H whereby \nmagnetoelectric effects were measured with the applica tion of E rather than H. As such from \npractical considerations it simplifies the design of d evices and applications. For example there \nwould be less of a need for permanent magnets in microwav e device applications. \n \n \n[1] M. Fiebig. J. Phys. D 38, R123 (2005). \n[2] G. Srinivasin, V. Zavislyak and A.S. Tatarenko Appl. Phys . Lett. 89, 152508 (2006). \n[3] T. Kato, H. Mikami and S. and S. Noguchi, J. Appl. Phys. 108, 033903 (2010). \n[4] M. Soda, T. Ishikara, H. Nakamura, Y. Wakabayashi, and T . Kimura, Phys. Rev. Lett 106, \n087201 (2011). \n[5] Y. Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Naka mura and T. Kimura, Nature Mater. \n9, 797 (2010). \n[6] Y. Takada, T. Nakagawa, M. Tokunaga, Y. Fukuta, T.Tanaka an d T. A. Yamamoto, J. Appl. \nPhys. 100, 043904 (2006). \n[7] Chun-Gang Duan, Julian P. Velev, R. F. Sabirianov, Z iqiang Zhu,Junhao Chu, S. S. Jaswal, \nand E. Y. Tsymbal \"Surface Magnetoelectric E_ect in Ferro magnetic Metal Films\", Phys. Rev. \nLett 101, 137201 (2008). \n[8] L.D. Landau and E.M. Lifshitz, Electrodynamics of Con tinuous Media, Pergamon Press, \nOxford (1984). \n[9] O. Kimura, M. Matsumoto and M. Sakakura,. J. Am. Ceram.  Soc. 78, 2857 (1995). \n[10] C. Vittoria, \"Magnetics, dielectrics, and wave propaga tion with MATLAB codes\", (CRC \npress, New York (2011). \n[11] L. D. Landau and I. M. Khalatnikov, Dokl. Akad. Nauk SSSR 96, 469 (1954). \n "    },    {        "title": "1111.6753v2.Low_magnetic_field_reversal_of_electric_polarization_in_a_Y_type_hexaferrite.pdf",        "content": "\n1\nLow magnetic field reversal of electric polarization in a Y-type \nhexaferrite \nFen Wang, Tao Zou, Li-Qin Yan, Yi Liu, and Young Sun  \nBeijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China Correspondence and requests for materials should be addressed to Y .S. (E-mail: youngsun@iphy.ac.cn) . \n \nAbstract \nMagnetoelectric multiferroics in  which ferroelectricity and magnetism coexist have attracted \nextensive attention because they provide grea t opportunities for the mutual control of \nelectric polarization by magnetic fields and m agnetization by electric fields. From a practical \npoint view, the main challenge in this field is  to find proper multiferroic materials with a \nhigh operating temperature and great magnetoele ctric sensitivity. Here we report on the \nmagnetically tunable ferroelectricity and the giant magnetoelectric sensitivity up to 250 K in \na Y-type hexaferrite, BaSrCoZnFe 11AlO 22. Not only the magnitude but also the sign of \nelectric polarization can be effectively contro lled by applying low m agnetic fields (a few \nhundreds of Oe) that modifies the spiral magn etic structures. The magnetically induced \nferroelectricity is stabilized even in zero magn etic field. Decayless re producible flipping of \nelectric polarization by oscill ating low magnetic fields is shown. The maximum linear \nmagnetoelectric coefficient reaches a high value of ~ 3.0×103 ps/m at 200 K.  \n \nIn the past several years, spiral magnetic order induced multiferroics and magnetoelectric \n(ME) effects have been observed in a number of transition metal oxides such as TbMnO 3, RMn 2O5, \nCoCr 2O4, and others1-3. In these spiral magnets, the magne tic order and ferr oelectricity are \ninherently coupled and thus pronounced ME effects could be expected.4,5 The microscopic \nmechanism has been well described with the spin current model6 or the inverse \nDzyaloshinskii-Moriya (DM) interaction model7. However, the ME effects in these spiral magnets \nare not useful for practical applications because th ey occur at low temperatures and require a large \nmagnetic field of several tesla. Recently, the hexaferrites with helical spin order have been suggested as promising candidates for high temperature multiferroics. It was reported that some Y-type hexaferrites, such as (Ba,Sr)\n2Zn2Fe12O22 and Ba 2Mg 2Fe12O22, can show magnetically \ninduced ferroelectricity and pronounced ME effects due to modifications of spiral magnetic structures by applying magnetic fields\n8-11. Although the magnetic ordering temperatures of these \nY-type hexaferrites are above room temperature, their ME effects are observable only below ~ 130 K. Subsequently, ME effects were also observed in Z-type\n12,13, M-type14, and U-type15 hexaferrites. \nEspecially, the low field ME effect in a Z-type hexaferrite, Sr 3Co2Fe24O41, happens at room \ntemperature, representing a big step towards practical applications12. Nevertheless, there are still \nsome critical problems to be overcome. For in stance, although magnetic control of electric \npolarization at room temperature has been achiev ed, the reversal of electric polarization by \nmagnetic fields has been realized only at low temperatures10,11,14. The stabilization of the \nmagnetically induced ferroelectric phase at zero magnetic field is another important issue for \n2\nmemory device applications11. In this communication, we demonstrate low magnetic field reversal \nof polarization up to 250 K in a Y-type hexaferrite, BaSrCoZnFe 11AlO 22. The extreme sensitivity \nof polarization to external magnetic fields yields a giant ME coefficient of 3.0×103 ps/m at 200 K.  \n \nResults  \nCharacterization of BaSrCoZnFe 11AlO 22 samples.  The fundamental structure of the Y-type \nhexaferrite system consists of alternate stacks of superposition of spinel blocks (S) and the \nso-called T-blocks with space group of R3_\nm, as illustrated in Figure 1a. Denotation Me denotes for \nFe, Co, Zn and Al, Me(t) and Me(o) denote for Me in tetrahedral and octahedral sites, respectively. \nWe prepared the Y-type hexaferr ites by solid state reaction in oxygen. The as-sintered samples are \nnot insulating enough at high temperatures, and thus a post-annealing in oxygen atmosphere is performed to enhance the resistivity of the samp le. Figure 1b presents powder X-ray diffraction \npatterns of the BaSrCoZnFe\n11AlO 22 sample at room temperature. All the diffraction peaks can be \nindexed with the Y-type hexaferrite structure. The result suggests a clean single phase of the Y-type hexaferrite in the prepared samples. Figure 1c shows temperature dependence of the magnetization measured in 0.01 T after zero-fi eld cooling (ZFC) and fi eld cooling (FC). The \nparamagnetic to ferrimagnetic transition temperature of this compound is above 400 K. Both the ZFC and FC magnetization exhibit a sharp peak at 365 K, which is likely to correspond to the transition from the collinear ferrimagnetic to the spiral magnetic phase. We note that the XRD patterns and magnetization are almost the same after annealing, but the resistivity is greatly increased so that the ME effects can be tested up to 250 K.   \nMultifrroics and magnetoelectric effects. Figure 2 displays the magnetic field dependence of \nmagnetization ( M), dielectric constant (\n), and electric polarization ( P) of BaSrCoZnFe 11AlO 22 at \nvarious temperatures between 30 and 350 K. For measurements of ε and P, the direction of electric \nfield was perpendicular to that of magnetic fi eld. At all temperatures the magnetization of \nBaSrCoZnFe 11AlO 22 shows similar field dependence. With increasing magnetic field, the \nmagnetization rises rapidly at low fields, and then increases slowly with several kinks to the saturation magnetization. This stepwise feature of magnetization has also been observed in several other Y-type hexaferrites and evidences the magne tic-field-driven transitions between different \nmagnetic order structures\n9-11,16-18. Another important feature is that the magnetization loops exhibit \nnegligible hysteresis. Only a small hysteresis can be observed at low temperatures. This is \nsomewhat different from other Y-type hexaferrites which usually show apparent magnetization hysteresis\n16. \nThe dielectric constant of BaSrCoZnFe 11AlO 22 shows a strong dependence on magnetic field, \ni.e., the magnetodielectric effect, suggesting the ME  coupling at all the temperatures studied. \nEspecially, as shown in Figure 2b, the magnetic field dependence of the relative change in dielectric constant, defined as Δε(H)/ε(7 T)=[ε(H)-ε(7 T)]/ε(7 T), exhibits two distinct peaks below \n~ 250 K, one sharp peak around zero field and another broad peak at high magnetic fields. The high-field peak with apparent hysteresis shifts to higher fields with decreasing temperature. The \nmagnetodielelctric ratio shows a maximum (~ 4%) at ~ 200 K. The dielectric loss tangent tan δ \n(not shown) is less than 10\n-2 at 30 K and ~0.36 at 300 K. These dielectric peaks/anomalies imply \nthe ferroeletric phase transitions driv en by applied magnetic fields.  \n3\nFigure 2c displays the magnetic-field dependence of electric polarization, obtained from \nintegrating the magnetoelectric current, at select ed temperatures between 30 and 250 K. At low \ntemperatures, the polarization develops and evolves in a wide range of magnetic field between -4 and 4 T. Even at 250 K, a finite polarization is seen between -2 and 2 T. More importantly, the polarization is reversed as the magnetic field sc ans from positive to negative. This is in strong \ncontrast to the Z-type hexaferrite showing room temperature ME effects\n12 where the polarization \ncan not be reversed by magnetic fields. It should be noted that the polarization has a finite value without magnetic field, in contrast to most other hexaferrites in which no spontaneous polarization appears at zero magnetic field\n9,10,12,14,15. These results indicate that  the magnetically induced \nferroelectricity sustains even in zero magnetic field.  \nFigure 3 illustrates the close correlation betwee n the magnetic structure and the ferroelectric \nphase. Taking T=200 K for example, three magnetic transitions at ~ 0.1 T, ~ 0.85 T, and ~ 2 T can \nbe determined from the M-H  curve (Fig. 3a). Corresponding to the magnetic transitions, several \ndielectric anomalies appear. Especially, the dielectri c peak at ~ 2 T marks clearly a paraelectric to \nferroelectric phase transition. These magnetic tran sitions are similar to those observed in other \nY-type hexaferrites9-11, and separate the magnetic phase diagram of BaSrCoZnFe 11AlO 22 into four \ndistinct phases; three of them (FE1, FE2, and FE3) are ferroelectric and the one in high magnetic fields is paraelectric (PE). In phase FE1, the polarization grows rapidly with increasing magnetic field. In phase FE2, the ferroelecricity is stabiliz ed with a high polarization. In phase FE3, the \npolarization decays rapidly with increasing magne tic field and disappears above ~ 2 T. In high \nmagnetic fields, the system with a high magnetization is believed to be in the collinear ferromagnetic phase which does no t generate the ferroelectricity\n16. The magnetic structures of \nBaSrCoZnFe 11AlO 22 in the three low-field phases are stil l unclear. According to recent studies in \nseveral Y-type hexaferrites, the application of moderate magnetic fields induces the transverse conical spin structures and yields a finite polarization\n16-18. However, distinct from other Y-type \nhexaferrites, BaSrCoZnFe 11AlO 22 exhibits a spontaneous polarization at zero magnetic field, \nwhich suggests that the magnetic structure in zero magnetic field is not in a perfect proper-screw or longitudinal conical configuration. Based on the correlation between magnetic structures and ferroelectricity at various temperatures, we then  obtained the magnetoelectric phase diagram of \nBaSrCoZnFe\n11AlO 22 shown in Figure 4c. The phase boundaries are determined by the magnetic \ntransitions obtained in the M-H  curves. We note that the transition between phase FE2 and FE3 is \nclearly seen at high temperatures but becomes faint at low temperatures.  \n \nLow magnetic field reversal of polarization.  To check the ME sensitivity in \nBaSrCoZnFe 11AlO 22, we carried out detailed measurements at 200 K. Figure 4a-4c show the \nmagnetization, ME current ( IME), and polarization in the low field range between -0.1 and 0.1 T. \nCorresponding to the M-H  loop, a P-H hysteresis loop is observed. The sign of IME and P depends \non the directions of both magnetic field and the poling electric field. As the magnetic field scans from positive to negative (or reversely),  I\nME exhibits a remarkable peak only at a negative (or \npositive) field. Consequently, the polarization does not go to zero at zero magnetic field but changes its sign at a coercive field (~ 80 Oe). Although magnetic field reversal of polarization has been found at low temperatures in some hexaferrites, the polarization usually goes to zero at zero magnetic field. The spontaneous polarization without magnetic field is one of the most important steps for the device applications. Since the polariz ation changes rapidly around the coercive fields, \n4\nthe linear magnetoelectric coefficient α, defined as α=dP/dH, becomes huge. The maximum \nmagntoelectric coefficient αmax of our sample is ~ 3×103 ps/m at 200 K. For comparison, the αmax \nreported in Ba 0.5Sr1.5Zn2(Fe 0.92Al0.08)12O22 single crystal is 2×104 ps/m at 30 K9, and the αmax in the \nZ-type hexaferrite12 Sr3Co2Fe24O41 is 2.5×102 ps/m.  \nFor practical applications, the magnetic reversal of electric polarization should be \nreproducible and decayless with time. We then demonstrate a sequ ential flipping of polarization \nby an oscillating magnetic field between 0.2 T at 200 K. As shown in Fig. 5, the magnetoelectric \ncurrent IME and the electric polarization P vary periodically with a sign change as the magnetic \nfield oscillates. The amplitudes of IME and P do not decay even after many rounds.  This \nreproducible low-magnetic-field reversal of electr ic polarization provides a great potential for new \ntype non-volatile memory devices.  \n \nDiscussion We have demonstrated low magnetic field reversal of electric polarization in the \nY-type hexaferrite, BaSrCoZnFe 11AlO 22. This composition is carefully selected based on the \nfollowing concerns. Previous studies on hexaferri tes indicate that the symmetry breaking can be \ninduced by partial substitution of Fe ions as well as the simultaneous presence in the oxygen \nplanes of ions having different ionic radius such as Sr and Ba19. The partial replacement of Ba \nwith Sr modifies the superexchange interaction of the Fe-O-Fe bonds and may stabilize the spiral magnetic state. Moreover, the presence of nonmagnetic ion such as Zn in the octahedral sites of T-block might cause a drastic change in the magnetic order\n19. In addition, it has been recognized \nthat the weak planar magnetic anisotropy is very important for the realization of magnetically controllable ferroelectricity\n9,17,18. For example, the substitution of Zn stabilizes the easy-plane \nanisotropy and consequently destabilizes the longitudinal conical spin structure17. The substitution \nof Al ions into octahedral Fe sites with nontrivial orbital moment can finely modify the magnetic \nanisotropy and thus tune the ME coupling9,18. The above factors are all integrated in the present \ncompound BaSrCoZnFe 11AlO 22. The experimental results turn out a peculiar and amplified ME \ncoupling with notable advantages such as the high working temperature, low magnetic field \nreversal of polarization, the giant ME coefficient, and the stabilization of polarization without magnetic field. The only problem of the present compound is that the working temperature is still a little below room temperature. This may require further tailoring of the composition and the synthesis conditions. Nevertheless, our study opens up a route toward high-temperature magnetoelectric multiferroics with excellent performance.  \nMethods \nPolycrystalline samples of BaSrCoZnFe 11AlO 22 were prepared by conventional solid-state reaction \nmethod. Stoichiometric amounts of SrCO 3, BaCO 3, Co 3O4, ZnO and Fe 2O3 were thoroughly \nmixed and ground together, calcinated at 940 ℃ in air for 10 hours. The resulting mixture were \nreground, pressed into pellets, and fired at 1200 ℃ for 24 hours in oxygen atmosphere. \nSubsequently, as-sintered samples were annealed in a flow of oxygen at 900 ℃ for 72 hours and \nthen slowly cooled down at a rate of 40 ℃/h. The phase purity was checked by powder X-ray \ndiffraction (XRD) at room temperature using a Rigaku X-ray diffractometer. The magnetic and \ndielectric properties were performed using a superconducting quantum interference device magnetometer (Quantum Design MPMS-XL). For the measurement of dielectric constant and magnetoelectric current ( I\nME), the electrodes were made with silver paste onto the opposite faces \n5\nof the sample. Magnetoelectric current IME was measured with an elect rometer (Keithley 6517B) \nand a superconducting magnet (Quantum Design PPMS), while sweeping magnetic field at constant rates. Electric polarization ( P) value was obtained  by integrating I\nME with respect to time. \nBefore each measurement of P, an electric field of 500 kV/m was applied to the sample. The \npoling electric field was removed before each measurement.  \nAcknowledgments \nThis work was supported by the Natural Science Foundation of China and the National Key Basic Research Program of China.   References \n1. Kimura, T. et al. Magnetic control of ferroelectric polarization. Nature  426, 55-58 (2003) \n2. Hur, N.  et al .Electric polarization reversal and memory in a multiferroic material induced by \nmagnetic fields. Nature  429, 392-395 (2004). \n3. Yamasaki, Y. et al.  Magnetic reversal of the ferroelectric polarization in a multiferroic spinel \noxide. Phys. Rev. Lett.  96, 249902 (2006). \n4. Cheong, S. W. & Mostovoy, M. Multiferroics: a magnetic twist for ferroelectricity. Nat. Mater.  \n6, 13-20 (2007). \n5. Kimura, T. Spiral magnets as magnetoelectrics. Annu. Rev. Mater. Res.  37, 387-413 (2007). \n6. Katsura, H., Nagaosa, N., & Balatsky, A. V . Spin current and magnetoelectric effect in \nnoncollinear magnets. Phys. Rev. Lett.  95, 057205 (2005). \n7. Sergienko, I. A. & Dagotto, E. Role of the Dzyaloshinskii-Moriya interaction in multiferroic \nperovskites. Phys. Rev. B  73, 094434 (2006). \n8. T. Kimura, G. Lawes, and A. P. Ramirez, Electric polarization rotation in a hexaferrite with \nlong-wavelength magnetic structures. Phys. Rev. Lett.  94, 137201 (2005). \n9. Chun, S. H. et al.  Realization of giantmagnetoelectricity in helimagnets. Phys. Rev. Lett.  104, \n037204 (2010). \n10. Ishiwata, S. et al.  Low-magnetic-field control of electric polarization vector in a helimagnet. \nScience  319, 1643-1646 (2008). \n11. Taniguchi, K. et al. Ferroelectric polarization reversal by a magnetic field in multiferroic \nY-type hexaferrite Ba\n2Mg 2Fe12O12. Appl. Phys. Express.  1, 031301 (2008). \n12. Kitagawa, Y . et al.  Low-field magnetoelectric effect at room temperature. Nat. Mater.  9, 797 \n(2010). \n13. Soda, M. et al.  Magnetic ordering in relation to the room-temperature magnetoelectric effect \nof Sr 3Co2Fe24O41. Phys. Rev. Lett.  106, 087201 (2011). \n14. Tokunaga, Y . et al.  Multiferroic M-type fexaferrites with a room-temperature conical state and \nmagnetically controllable spin helicity. Phys. Rev. Lett.  105, 257201 (2010). \n15. Okumura, K. et al.  Magnetism and magnetoelectricity of a U-type hexaferrite Sr 4Co2Fe36O60. \nAppl. Phys. Lett.  98, 212504 (2011). \n16. Sagayama, H. et al. Two distinct ferroelectric phases in the multiferroic Y-type hexaferrite \nBa2Mg 2Fe12O22. Phys. Rev. B  80, 180419(R) (2009). \n17. Ishiwata, S. et al. Electric polarization induced by transverse magnetic field in the \nanisotropy-controlled conical helimagnet Ba 2(Mg 1−xZnx)2Fe12O22. Phys. Rev. B  79, 180408(R) \n6\n(2009). \n18. Lee, H. B. et al. Field-induced incommensur ate-to-commensurate phase transition in the \nmagnetoelectric hexaferrite Ba 0.5Sr1.5Zn2(Fe 1−xAlx)12O22. Phys. Rev. B  83, 144425 (2011). \n19. Albanese, G. et al.  Influence of the cation distribution on the magnetization of Y-type \nhexagonal ferrites.  Appl. Phy.  7, 227 (1975). \n  \n7\nFigure 1 Characterization of BaSrCoZnFe 11AlO 22 samples.  (a) Schematic crystal structure of \nBaSrCoZnFe 11AlO 22, Me denotes for Fe, Co, Zn and Al, Me(t) and Me(o) denote for Me in \ntetrahedral and octahedral site, respectively. (b) Powder X-ray diffraction patterns at room \ntemperature. The red lines represent the peak  positions for Y-type he xaferrite structure. (c) \nMagnetization as a function of temperature under  0.01 T after the zero-field cooling (ZFC) and \nfield cooling (FC) process.  \n \nFigure 2 Multiferroics and magnetoeletric effects in BaSrCoZnFe 11AlO 22. Magnetic field \ndependence of (a) magnetization, (b) magnetodielectric and (c) polarization at various \ntemperatures. To pole the sample, E=500 kV/m was applied at H>3.5 T, and then H was reset to \ndrive the system to a range of intermediate phases. After these procedures, the poling E was \nremoved, and the magnetoelectric current was measured during the H increasing or decreasing \nruns.  \n-40040\n04\n- 6 - 4 - 2 0246-20020 30 K\n 150 K\n 200 K\n 250 K\n 300 K\n 350 K\n  M (emu/g)\n (H)/(7 T)-1 (%)\n \n P (C/m2)\nMagnetic field (T) (a)\n(b)f=10 kHz\n350 KHE\n300 K\n250 K\n200 K150 K\n30 K\nH\nE\n 30 K\n 150 K\n 200 K\n 250 K \n(c)E=500 kV/m\n \n20 30 40 50 60 70\n0 100 200 300 400012\n Intensity (a. u.)\n2 (degree)\n ZFC\n FC\n  M (emu/g)\nT (K)H=100 OeT\nTS\nS\nS\nTMe(t) Me(o)\nBa, SrO\nS(a) (b)\n(c)c-axis\n8\nFigure 3 Correlation between magnetic phase and ferroelectricity.  (a) M-H  curve showing \nthree magnetic transitions at 200 K. (b) Dielectric anomalies corresponding to the magnetic \ntransitions at 200 K. (3) Magnetoelectric phase diagram of BaSrCoZnFe 11AlO 22. The phase \nboundaries are determined by the critical magnetic fields in the M- H curves.  \n02550\n43.544.044.5\n01020\n0.1 10200400  M (emu/g)200 Ka\n200 K\n  \n \nb\n200 K\n  P (C/m2)\nc  T (K)\nMagnetic field (T)PE\nFE1FE2FE3Pmax\nd\n \nFigure 4 Low magnetic field reversal of electric polarization . (a) The M-H  loop in the low field \nrange at 200 K. (b) The magnetoelectric current ( IME) as a function of low magnetic field at 200 K. \n(c) The P-H loop at 200 K. The data in b and c were obtained after poling in a positive or negative \nelectric field. The finite polarization at zero magnetic field suggests that the magnetically induced \nferroelectricity is stabilized without magnetic field. \n-20020\n-1500150\n-1000 -500 0 500 1000-30030(b)\n-500 kV/mT=200 K M (emu/g)(a)\n500 kV/m\n-500 kV/m IME (pA)\n500 kV/m\n(c) P (C/m2)\nH (Oe) \n9\nFigure 5 Reproducible polarization switching at 200 K.  (a) Oscillating magnetoelectric current \nas a function of time. (b) Reproducible decayless flipping of the electric polarization. (c) \nPeriodically changing magnetic field between -0.2 and 0.2 T.  \n-1000100\n-20020\n0 500 1000 1500-0.20.00.2  IME (pA)(a)\n(b)\n  P (C/m2)\n(c) H (T)\nTime (s)\n "    },    {        "title": "1201.0831v1.Origin_of_training_effect_of_exchange_bias_in_Co_CoO_due_to_irreversible_thermoremanent_magnetization_of_the_magnetically_diluted_antiferromagnet.pdf",        "content": "arXiv:1201.0831v1  [cond-mat.mtrl-sci]  4 Jan 2012Origin of training effect of exchange bias in Co/CoO due to\nirreversible thermoremanent magnetization of the magneti cally\ndiluted antiferromagnet\nS. R. Ali,∗M. R. Ghadimi, M. Fecioru-Morariu, B. Beschoten, and G. G¨ unther odt\nII. Institute of Physics, RWTH Aachen University, 52056 Aac hen, Germany\n(Dated: November 10, 2018)\nAbstract\nThe irreversible thermoremanent magnetization ( mirr\nTRM) of a sole, magnetically diluted epitaxial\nantiferromagnetic Co 1−yO(100) layer is determined by the mean of its thermoremanent magneti-\nzations ( mTRM) at positive and negative remanence. During hysteresis-lo op field cycling, mirr\nTRM\nexhibits successive reductions, consistent with the train ing effect (TE) of the exchange bias mea-\nsured for the corresponding Co 1−yO(100)/Co(11 ¯20) bilayer. The TE of exchange bias is shown to\nhave its microscopic origin in the TE of mirr\nTRMof the magnetically diluted AFM.\nPACS numbers: 75.70.-i, 75.30.Et, 75.50.Ee, 75.60.Nt\n∗rizwan@physik.rwth-aachen.de\n1The phenomenon of exchange bias (EB) originates from the interfa cial exchange coupling\nbetween an antiferromagnet (AFM) and a ferromagnet (FM).[1–3 ] This interaction results\nfor the magnetic hysteresis loop of the FM layer in a field offset from t he origin by the\nEB field, BEB. EB has been in the focus of intense research activities because of its po-\ntential applications in spintronics devices where it stabilizes a refere nce FM magnetization\nin magnetic read heads, sensors and nonvolatile memory devices [4, 5 ]. It has been shown\nexperimentally that field cooling of an AFM stabilizes pinned uncompens ated moments near\nthe AFM/FM interface, which are responsible for the EB effect.[6–1 1] A domain state de-\nvelops upon field cooling of the AFM, which carries an irreversible surp lus thermoremanent\nmagnetization, mirr\nTRM. The crucial role of mirr\nTRMat the AFM/FM interface for the EB effect\nhas been demonstrated both experimentally [8–11] and by Monte Ca rlo simulations.[12] At\nthe surface and in the bulk of the AFM there may be structural and substitutional defects\n[13], giving rise to domain wall pinning and thus leading to metastable dom ain structures\nwhose evolution with field cycling is responsible for the training effect ( TE). The latter is a\ncrucial feature associated with the fundamentals and applications of EB due to the reduc-\ntion inBEBduring successive field cycles in hysteresis loops.[1, 3] The TE plays an essential\nrole in the reliable performance of devices based on EB. The microsco pic origin of the TE\nremains under intensive debate (see, e.g., Refs. [1–3, 12, 14–18]) a nd raises the question\nabout the involvement of, e.g., mirr\nTRMat the AFM/FM interface. However, the smallness of\nmirr\nTRM[19, 20] remains a serious difficulty in answering this question.[21] A sim ple approach\nmight be to consider a sole AFM layer with a dilution enhanced mTRM, i.e.mirr\nTRM, such\nthat its role for the TE could unambiguously be investigated by magne tometry.\nHere, we utilize nonmagnetic dilution throughout the bulk of an epitax ially grown\nCo1−yO(100) layer ( y→0) to significantly enhance its mTRM. This in turn also yields\nan enhanced BEBfor the corresponding Co 1−yO(100)/Co(11 ¯20) bilayer. The mirr\nTRMof a\nsole AFM layer is then determined by the difference of its enhanced mTRMat positive and\nnegative remanence. The measured mirr\nTRMexhibits systematic reductions during successive\nfield cycling. Detailed analysis of the data using Binek’s model [14] show s that the TE of\nBEBof the AFM/FM bilayer has its origin in the TE of mirr\nTRMof the sole AFM.\nDiluted ( y/negationslash= 0) and undiluted ( y→0) sole epitaxial AFM samples with the layer\nsequence: MgO(100)/Co 1−yO(100)/Au(5nm)andepitaxialAFM/FMbilayerswiththelayer\nsequence: MgO(100)/Co 1−yO(100)/Co(11 ¯20)/Au(5 nm) were deposited by molecular beam\n2epitaxy (MBE) on MgO(100) substrates. The samples were capped by a 5 nm thick Au\nlayer and the thicknesses of CoO and Co are 30 nm and 8 nm, respect ively. We have chosen\nCoO as a model AFM for the present study because it allows us to intr oduce conveniently\nnonmagnetic defects at the Co sites by just controlling the partial pressure of oxygen ( p(O2))\nduring the growth of the CoO layer. The over-oxidation of CoO unde r highp(O2) yields\na Co2+-deficient layer, Co 1−yO. Thus the (intentionally) diluted sample ( y/negationslash= 0) contains a\nCoO layer which was grown at a high p(O2) (= 5×10−6mbar). On the other hand, the\nCoO layer in the (nominally) undiluted ( y→0) sample was grown at low p(O2) (= 4×10−7\nmbar). These pressures were carefully chosen after a number of tests and were found to yield\nrepresentative values of mTRMandBEBfor the respective diluted and undiluted samples.[13]\nThe epitaxy of our samples has been established in-situ by reflection high energy electron\ndiffraction (RHEED). The RHEED patterns of an undiluted Co 1−yO (y→0) layer and a\ndilutedCo 1−yO(y/negationslash=0)layergrownontheMgO(100)substratearepresentedinthein sets(a)\nand (b) of Fig. 1, respectively. The electron beam was parallel to th e [010] direction of the\nMgO(100) substrate. For all the samples the growth of the CoO dir ectly on the MgO(100)\nsubstrate leads to untwinned Co 1−yO(100) layers in this system.[13] For the diluted Co 1−yO\nlayers (y/negationslash= 0)(grownat p(O2)=5×10−6mbar), thedestructive interference ofthefcclattice\nis removed due to some empty lattice sites caused by the over-oxida tion (dilution). Hence,\nadditional diffraction spots become visible which correspond to a cry stalline structure with\na lattice constant in the real space about twice as large as that of t he undiluted CoO (grown\natp(O2) = 4×10−7mbar). This structure is identified as the Co 3O4phase which is formed in\nthe diluted sample due to overoxidation of Co. For AFM/FM bilayers th e Co layer grew in\nan hcp lattice structure with (11 ¯20)-orientation (not shown). Magnetic characterization was\nperformed by superconducting quantum interference device (SQ UID) magnetometry after\nthe samples were field cooled (FC) from 340 K through the N´ eel tem perature ( TN= 291 K)\nto 5 K in a field of +7 T oriented parallel to the plane of the CoO film along it s easy [010]\naxis. For AFM-only samples the mTRMwas recorded as a function of Tduring the heating\nof the sample from 5 K to 340 K in the absence of an external field. Fo r AFM/FM bilayers\nTwas increased in steps (from 5 K to 340 K) and a hysteresis-loop was measured between\n±1 T for each step. The coercive fields of the hysteresis cycles BC1for descending and BC2\nfor ascending field branches were used to determine BEB= (BC1+BC2)/2.\nFigure1shows the Tdependence of BEBfor bothundiluted anddiluted AFM/FMbilayer\n30 100 200 300 400 04812 IBEB I (mT) \nT (K)undiluted\ndiluted(a) undiluted \n(b) diluted\nFIG. 1. (color online) Exchange bias field |BEB|of MgO(100)/Co 1−yO(100)/Co(11 ¯20)/Au vs T\nfor undiluted (circles) and diluted (squares) samples. The inset shows RHEED patterns of (a) the\nundiluted CoO layer and (b) the diluted Co 1−yO layer grown on an MgO(100) substrate. The\nelectron beam direction is parallel to [010] of the MgO(100) substrate.\nsamples. A distinct enhancement of BEBupon dilution is evident below 291 K. However, no\nchange in the blocking temperature, TB(at which BEB= 0), due to dilution was noticed.\nThisisconsistentwithanupto5%dilutionofCo2+byMg2+inCo1−xMgxO.[8]Theconstant\nTBwe attribute to the high anisotropy of CoO ( ∼2×107J/m3, see, e.g., Ref. [22]) which\nis an Ising-type AFM, making it more robust against magnetic degrad ation upon dilution.\nThis is in contrast to, e.g., metallic EB systems with low [23] or intermedia te anisotropy [9]\nAFMs which show a more strongly reduced TBupon dilution.\nFigure2showsthe Tdependence of mTRMforbothFCdiluted(curveI)andFCundiluted\n(curve II) sole AFMsamples. The reference level is set by the zero field cooled (ZFC) diluted\nsample (curve III). As expected, a strong dilution-induced enhan cement (∼400% at 5 K) is\nobserved in the mTRMof the FC diluted sample in comparison to the FC undiluted one. The\noverallTdependence of the FC mTRMof the diluted sample compared to the undiluted one\nexhibits two distinct features withdecreasing T: (i) a monotonically increasing enhancement\nbetween 370 K and 100 K and (ii) an abrupt increase in mTRMforT <50 K. The dilution-\ninduced enhancement of the FC mTRMof sole-CoO layers above 50 K is roughly similar to\nthe one observed for BEBof diluted CoO/Co bilayers in Fig. 1. It is in agreement with\nthe domain state model.[8, 12] However, as opposed to mTRMthe entire Tdependence of\n40 100 200 300 010 20 30 mTRM  (10 -7  emu) \nT (K)I\nII \nIII  I : diluted-FC = 7 T\n II : undiluted-FC = 7 T\nIII : diluted-ZFC\nTN = 291 K \nFIG. 2. (color online) Thermoremanent magnetization of fiel d cooled sole-AFM\nMgO(100)/Co 1−yO(100)/Au as a function of Tfor undiluted(solid circles, II)and diluted (squares,\nI) samples. The zero field cooled (stars, III) curve of the dil uted sample is shown for reference.\nBEBis monotonic and it lacks the abrupt increase below 50 K. The differenc e ofBEB(T)\nandmTRM(T) forT <50 K (Figs. 1 and 2, respectively) is attributed to the low anisotropy\nof the uncompensated AFM spins [6], which is insufficient to pin the FM lay er. This is\nevidenced by the missing strong increase of the EB field below 50 K (Fig . 1). The ”isolated”\nuncompensated AFM spins freeze in a Bfield at low temperatures ( T <50 K), since they\nare weakly exchange coupled to neighboring spins within the core of t he AFM CoO due\nto missing or frustrated exchange bonds. The magnetic field stabiliz es the uncompensated\nspins, whereas zero-field cooling does not exhibit any mTRM(see Fig. 1).\nWe now focus on the cycle number dependence of mirr\nTRM. A sole diluted Co 1−yO(100)\nsample was cooled from 340 K to 5 K in an external field of +7 T. Subseq uently, at 5 K the\nhysteresis loops were measured by cycling Bbetween -7 T and +7 T. The overall procedure\nis similar to the measurement of a usual hysteresis loop of an FM. How ever, during each\nfield cycle, we stop the measurement at B= 0 for some time in both the decreasing and\nincreasing field branches. The remanent value of mTRMwas then measured (Fig. 3) as a\nfunction of time ( t) for both ascending (lower curves) and descending (upper curve s) field\nbranches. It is evident from Fig. 3 that the mTRMis not constant but that it decreases both\nas a function of time and cycle number nespecially for the descending field branches.\nFor a given cycle number nthe mean of the values of mTRMof the upper and lower curves\nin Fig. 3 characterizes the vertical shift of the hysteresis loop of the AFM layer.[12, 18] The\n50 10 20 30 40 50-10122830\n     # 1\n   # 2\n   # 3\n   # 4\nt (min)mTRM (10 -7  emu) \nFIG. 3. Thermoremanent magnetization at 5 K of the diluted so le-AFM\nMgO(100)/Co 1−yO(100)/Au sample vs time at B= 0 (in remanence) for both ascending\n(lower curves) and descending (upper curves) field branches of successive hysteresis loop cycles\n(indicated by #1 - 4). Details about the measurement procedu re are described in the text.\nvertical shift can be attributed to an additional effective field on th e FM, thus yielding EB.\nWe have calculated this meanfor t= 0, i.e. forthe time when the field was set to zero during\ntheAFMhysteresis loopmeasurement. This quantity measures the irreversible domainstate\nmagnetization mirr\nTRMin the whole AFM layer [9, 23] and is plotted as a function of cycle\nnumbernin Fig. 4 (open circles). Clearly, the mirr\nTRMis not constant during successive field\ncycles; instead it decreases monotonically during each cycle.\nIn order to identify the origin of the EB effect we have also plotted th e TE ofBEBat 5\nK (open squares) in Fig. 4. This was recorded for a diluted Co 1−yO(100)/Co bilayer after\nfield cooling at +7 T from 340 K to 5 K. As a reference for our SQUID me asurement, we\nhave tested undiluted CoO in a field cooled CoO/Co bilayer at 5 K by expo sing it to a\nreversed field of -0.5 T during waiting times of 0 min. and 60 min. No time d ependence of\nthe hysteresis loop was observed. In Fig. 4 a good qualitative agree ment is clearly visible\nbetween the cycle dependences of BEBand ofmirr\nTRMat 5 K. The maximum decrease in both\nquantities occurs between the first and second field cycle and they asymptotically approach\nconstant values for the remaining cycles. The following empirical for mula has been widely\nused to describe the TE, [24]\nBEB(n)−BEB(∞) =k√n, (1)\n61 2 3 410.811.2 11.6 12.012.4\n14.014.515.0\n14.0 14.5 15.0 11 12 1\n432\n \n   \nirr mTRM(10 -7  emu) IBEB I(mT) \n mirr\nTRM \nBEB \n2% 1.2% 9.6%6% \nCycle number ( n)\n mirr \nTRM  (10 -7  emu)  IBEB I (mT) \nFIG. 4. (color online) Training effect of exchange bias field, |BEB|, of a diluted CoO/Co bilayer\n(open squares) and of the cycle dependence of mirr\nTRMof a diluted sole CoO layer (open circles) at\n5 K. The solid lines show fits by Eq. (1) to the data for n >1. Solid squares are the respective\ncalculated data points generated from Eq. 2. The inset shows |BEB|vsmirr\nTRMat 5 K; the solid\nline is a fit to the data points marked by their respective cycl e number n.\nwherekis a material dependent constant and BEB(∞) is the EB field in the limit of an\ninfinite number of loops. The solid lines in Fig. 4 show the best fits to BEBandmirr\nTRM\ndata using Eq. 1 for n >1. The resulting parameters obtained from the fit for BEB(n) are\nBEB(∞) = 10.2mTand k= 0.8mT.Similarlyfor mirr\nTRM(n)thefittingparameters mirr\nTRM(∞)\nandk′were found to be 13 .5×10−7emu and 0 .6×10−7emu, respectively. The fits clearly\nshow a good agreement with the data for n >1. It should be noted that the experimental\ndata points at n= 1 significantly exceed the values obtained by simple extrapolation of the\nfits ton= 1 (not shown). The strong TE of BEBbetween the first andsecond hysteresis loop\nhas been attributed to some initial nonequilibrium arrangement or me tastable state of the\nAFM spins.[18, 25–29] The exact mechanism for the initial AFM spin arr angement is still\nsubject to debate. Hoffmann [28] has pointed out that due to biaxia l anisotropy axes in the\nAFM a noncollinear arrangement of the AFM (sublattice) spins can init ially be stabilized\nafter field cooling. This leads for perpendicular spin arrangements t o a sharp drop in the\ndescending field branch of the first hysteresis loop as the AFM spins relax into a collinear\narrangement. Beckmann et al.[26]haveshownthatamisalignment betweenthecoolingfield\ndirection and the easy axis of the AFM can result in a nonequilibrium arr angement of the\nAFM spins with a net mirr\nTRMoriented in a direction determined by the relative orientations\n7between the cooling field and AFM easy axis. During the field cycling mirr\nTRMtends to find an\nenergetically most favourable orientation via irreversible rearrang ements in the AFM spin\nconfiguration. This leads to a partial loss of mirr\nTRMand thus of BEBduring each cycle, with\nthe maximum decrease taking place during the first cycle.\nAlthough the above dependence of the TE (Eq. 1) has been widely ob served, it lacks\na physical basis. Alternatively, Binek [14] has considered the TE of AFM/FM bilayers in\nthe thermodynamic framework of spin configurational relaxation a t the AFM surface. This\nspin relaxation is activated by the consecutive cycling of the extern al field. The following\nrecursive formula is obtained for describing the TE of BEBandmirr\nTRM,\nF(n+1)−F(n) =−γ[F(n)−F(∞)]3(2)\nwithFdescribing BEB(usingγ) ormirr\nTRM(usingγ′). Taking the respective initial values\n(forn= 1) ofBEBandmirr\nTRMas obtained from the experiment (Fig. 4), the calculated data\n(solid squares in Fig. 4) are obtained from the recursive formula in Eq . 2. ForBEB,γand\nBEB(∞) are 0.05 (mT)−2and 9.26 mT, respectively. Similarly, for mirr\nTRMthe parameters γ′\nandmirr\nTRM(∞) are 0.08 (10−7emu)−2and 12.8 (10−7emu), respectively. Clearly, Eq. 2 (2)\ndescribes the TE of BEBand ofmirr\nTRMfairly well, not only for n >1 but also for n= 1.\nThe inset of Fig. 4 shows a direct correlation between mirr\nTRMandBEBfor the respective\nfield cycles marked by their number. The solid line represents the bes t linear fit. The\nobserved correlation between the TE of mirr\nTRMand that of BEBsuggests that TE of BEB\nis due to the loss of mirr\nTRM, i.e. due to irreversible changes in the AFM domain state\nmagnetization during the field cycles. It should be noted that during each cycle the percent\nreductions (see labelings in Fig. 4) in the respective values of mirr\nTRMandBEBdo not\nagree quantitatively. For example during the first field cycle BEBshows 9.6 % reduction in\ncomparison to the 6.0 % reduction of mirr\nTRM. These differences are due to some experimental\nlimitations. First, for the case of AFM/FM bilayers the interfacial AF M spins experience\nin addition to the external field a strong molecular field exerted by th e magnetized FM.\nThis results in different strengths of the effective cycling fields on th e sole AFM and on the\nAFM/FMbilayer. Since the molecular fields are typically much stronger (∼100 T) [30] than\nexternally applied fields the AFM spins in the AFM/FM bilayer will experien ce a stronger\neffective cycling field. This gives rise to a relatively larger percentage of decrease in BEB\nof CoO/Co bilayers in comparison to that of mirr\nTRMof the sole CoO sample. Second, our\n8measured mirr\nTRMincludes both volume as well as surface parts of the pinned uncompe nsated\nAFM moments, whereas BEBis primarily determined by the pinned AFM moments near\nthe FM/AFM interface. Another factor is the uncertainty in deter mining the zero of the\ntime scale ( t= 0) with high accuracy, i.e. when the magnetic field is just switched off and\nmTRMstarts to decay. Significant time (1 - 2 min) was required to reduce t he field to zero\nbefore the decay of mTRMcould be recorded.\nIn conclusion, our investigation has shown that irreversible thermo remanent magneti-\nzation of the sole diluted Co 1−yO(100) AFM layer exhibits systematic reductions during\nsuccessive magnetic field cycling which is consistent with the TE of the exchange bias mea-\nsured for the corresponding Co 1−yO(100)/Co(11 ¯20) bilayer. Detailed analysis shows that\nthe TE of the exchange bias field of the AFM/FM bilayer has its origin in t he TE of mirr\nTRM\nof the sole AFM layer.\nS.R.A. is grateful for funding by the Higher Education Commission (HE C), Government\nof Pakistan.\n[1] J. Nogu´ es and I. K. Schuller, J. Magn. Magn. Mater. 192, 203 (1999).\n[2] A. E. Berkowitz and K. Takano, J. Magn. Magn. Mater. 200, 552 (1999).\n[3] J. Nogu´ es et al., Phys. Rep. 422, 65 (2005).\n[4] B. Dieny et al., Phys. Rev. B 43, 1297 (1991).\n[5] J. C. S. Kools, IEEE Trans. Magn. 32, 3165 (1996).\n[6] K. Takano et al., Phys. Rev. Lett. 79, 1130 (1997).\n[7] P. Milt´ enyi et al., Phys. Rev. Lett. 84, 4224 (2000).\n[8] J. Keller et al., Phys. Rev. B 66, 014431 (2002).\n[9] M. Fecioru-Morariu et al., Phys. Rev. Lett. 99, 097206 (2007).\n[10] L. C. Sampaio et al., Europhys. Lett. 63, 819 (2003).\n[11] R. Morales et al., Phys. Rev. Lett. 102, 097201 (2009).\n[12] U. Nowak et al., Phys. Rev. B 66, 014430 (2002).\n[13] M. R. Ghadimi, B. Beschoten, and G. G¨ untherodt, Appl. P hys. Lett. 87, 261903 (2005).\n[14] C. Binek, Phys. Rev. B 70, 014421 (2004).\n[15] S. Brems, K. Temst, and C. Van Haesendonck, Phys. Rev. Le tt.99, 067201 (2007).\n9[16] P. Y. Yang et al., Appl. Phys. Lett. 92, 243113 (2008).\n[17] A. G. Biternas, U. Nowak, and R. W. Chantrell, Phys. Rev. B80, 134419 (2009).\n[18] A. G. Biternas, R. W. Chantrell, and U. Nowak, Phys. Rev. B82, 134426 (2010).\n[19] P. Kappenberger et al., Phys. Rev. Lett. 91, 267202 (2003).\n[20] H. Ohldag et al., Phys. Rev. Lett. 91, 017203 (2003).\n[21] A. Hochstrat, C. Binek, and W. Kleemann, Phys. Rev. B 66, 092409 (2002).\n[22] J. Kanamori, Prog. Theor. Phys. 17, 197 (1957).\n[23] C. Papusoi et al., J. Appl. Phys. 99, 123902 (2006).\n[24] D. Paccard et al., Phys. Status Solidi 16, 301 (1966).\n[25] D. Suess et al., Phys. Rev. B 67, 054419 (2003).\n[26] B. Beckmann, U. Nowak, and K. D. Usadel, Phys. Rev. Lett. 91, 187201 (2003).\n[27] F. Radu et al., Phys. Rev. B 67, 134409 (2003).\n[28] A. Hoffmann, Phys. Rev. Lett. 93, 097203 (2004).\n[29] T. Hauet et al., Phys. Rev. Lett. 96, 067207 (2006).\n[30] C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996).\n10"    },    {        "title": "1202.3381v2.Ferroelectricity_induced_by_interatomic_magnetic_exchange_interaction.pdf",        "content": " 1Ferroelectricity induced by interato mic magnetic exchange interaction \n \nXiangang Wan,1† Hang-Chen Ding,2 Sergey Y. Savrasov3 and Chun-Gang Duan2,4‡ \n1Department of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China \n2Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200062, \nChina \n3Department of Physics, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA \n4National Laboratory for Infrared Physics, Chinese Academy of Sciences, Shanghai 200083, China \n \n† Electronic addres s: xgwan@nju.edu.cn \n‡ Electronic address: wxbdcg@gma il.com or cgduan@clpm.ecnu.edu.cn \n \nMultiferroics, where two or more ferroic order parameters coexist, is one of the hottest fields in condensed \nmatter physics and materials science1-9. However, the coexistence of magnetism and conventional \nferroelectricity is physically unfavoured10. Recently several remedies have been proposed, e.g., improper \nferroelectricity induced by specific magnetic6 or charge orders2. Guiding by these theories, currently most \nresearch is focused on frustrated magnets, which us ually have complicated magnetic structure and low \nmagnetic ordering temperature, consequently far from th e practical application. Si mple collinear magnets, \nwhich can have high magnetic transiti on temperature, have never been considered seriously as the candidates \nfor multiferroics. Here, we argue that actually simple  interatomic magnetic exchange interaction already \ncontains a driving force for ferroelectricity, thus pr oviding a new microscopic mechanism for the coexistence \nand strong coupling between ferroelectricity and magnetism. We demonstrate this mechanism by showing \nthat even the simplest antiferromagnetic (AFM) insulator MnO, can display a magnetically induced  \nferroelectricity under a biaxial strain. \n \nThe combination of different ferroic properties, \nespecially ferroelectricity and (anti)ferromagnetism, \nprovides additional degree of freedom to control \nmagnetic and dielectric properties of the material. Such \nfunctionality is of great potential in applications to \nnext-generation fast, portable and low-energy \nconsumption data storage and processing devices. \nUnfortunately, magnetism and ferroelectricity tend to be \nmutually exclusive, as conventional ferroelectric \nperovskite oxides usually require transition metal (TM) \nions with a formal configuration d0, whereas magnetism, \nin contrast, needs TM ions with partially filled d shells10. \nAs a consequence, simultaneous occurrence of \nferromagnetism and ferroelectricity is hard to be \nachieved, especially at room temperature. There are \nindeed some exceptions in Bismuth related magnetic oxides, e.g., BiFeO\n3 and BiMnO 3. In these compounds, \nhowever, the magnetism and ferroelectricity are widely \nbelieved to have different origins, rendering that the \nmagnetoelectric coupling rather weak9.  \nTo gain a strong magnetoelectric coupling, vast \nefforts have been devoted to search the improper \nferroelectricity where electri c dipoles are induced by \nmagnetism6. Phenomenological theory suggests that \nspatial variation of magnetization is essential for the \nmagnetically induced electric polarization11. Several \nmicroscopic mechanisms12-14, all emphasizing the \nimportance of spin-orbital coupling, have also been proposed to explain the ferroelectricity in magnetic spiral \nstructures. Electric polarization can also be induced by \ncollinear spin order in  the frustrated magnet  with several \nspecies of magnetic ions6,15-17. There are also proposals to \nrealize multiferroic state in composite systems or \nmaterials with nanoscale inhomogeneity18,19. \nNevertheless, currently all of the known magnetically \ndriven single-phase multiferroics require either \nDzyaloshinskii-Moriya interaction (DMI)20,21, which is \nsmall in strength, or competing exchange interactions in \nreal space. Therefore, they generally have complex \nmagnetic order, low trans ition temperature (below \nseveral ten K) and small elec tric polarization (generally \ntwo to three orders of magnitude smaller than typical \nferroelectrics), making them still far away from practical \napplications. Therefore searching new mechanism for multiferroicity is of both fundamental and technological \ninterest. \nIn this Letter, we demonstrate that regardless the \nspin-orbit coupling, simple interatomic magnetic \nexchange interaction already provides a strong driving \nforce to break the inversion symmetry of the system, \nwhich is necessary for the occurrence of ferroelectricity. \nIt is therefore a new microscopic mechanism for the \ncoexistence and strong coupling between ferroelectricity \nand magnetism, and all of the  magnetic insulators with \nsimple magnetic structure need to be revisited. Using \nband structure calculations, we numerically confirm  this  2new mechanism by illustrating that even simplest \nantiferromagnets, i.e. MnO, can display a magnetically \ninduced ferroelectricity under biaxial strain. \n \nFigure 1 | Illustration of ferroelectricity induced by indirect magnetic exchange interaction between \nanion-mediated magnetic cations.  Here  M\n1 and M 2 are \nmagnetic cations, O is oxygen anion. When O atom, \nwhich originally sits in the middle of M 1 and M 2 ions, is \nshifted along the M 1(2)-O bond direction ( x) by a small \ndisplacement u, the magnetic exchange interactions of \nthe system will increase and may support the O off-center \nmovement. An electric dipole is then formed, as shown by an arrow in the picture. \nTo study the interatomic magnetic exchange \ninteraction and the associated magnetic ordering energy, \nwe consider a three atoms case, where a diamagnetic ion \nsuch as oxygen ion sits be tween two transition metal \nions, as shown in Fig.1. As revealed by Sergienlo and \nDagotto\n13, DMI provides a driving force for the oxygen \nion to shift perpendicularly to the spin chain. Due to the \nsmall strength, however, the energy gain from DMI is \nusually less than the ordinary elastic energy, consequently only a few compounds show magnetically induced ferroelectricity\n6. Here, we consider the effect of \nlongitudinal displacement of diamagnetic ions (shown by \nthe dot line in Fig.1) on the magnetic ordering energy. As \nis well known, in the above case, the distance between \nmagnetic ions usually is much larger than the radii of d/f \norbital which carry magnetic moments, thus the direct \nexchange is negligible, and  the hybridization between \nmagnetic and diamagnetic ions is essential for the \nindirect magnetic exchange coupling. Therefore, we first \ndiscuss the hopping integrals in this system. For simplicity, here we only show the case of one orbital per \nion, and it is easy to generalize our results to multi-orbital cases. The kinetic energy then can be written as: \n11 2 2\n12 12           ( . .) ( . .)       (1)kin d d d o o o d d d\ndo d oHc cc c c c\ntc c h c tc c h cσσ σ σ σσ\nσσ σ\nσσεε ε++ +\n++=+ +\n++ ++∑∑ ∑\n∑∑ \nwhere the operator \n11()ddccσσ+, \n22()ddccσσ+, ()ooccσσ+ \ncreates (annihilates) a spin σ electron at M 1, M 2 and O \nsite, respectively. dεand oεare the on-site energies for M 1/M2 and O site. t1/t2 are the hopping integrals \nbetween M 1/M2 and O. Based on the standard \nSchrieffer-Wolff transformation22, we can eliminate the \nO orbital and obtain the effective hopping integral \nbetween M 1 and M 2 site: \n12                               (2)eff\ndotttεε∝− \nIt is well known that the hopping integral is inversely \nproportional to the bond-length:11ytr−∼ , 22ytr−∼ , where \nr1(2) is the bond length of M 1(2)-O, y is a positive value \nand strongly depends on both the bond type and the \nparticipated orbital23. A longitudinal displacement of O \nion u will then change the effective hopping to \n011 1=C    (3)() () () ()eff yy yy\ndtru ru ru ruεε∝−+− +− \nwhere C is a parameter and not sensitive to u, r is the \ndistance between magnetic ion and center O-site. It is interesting to notice that regardless the parameter C and \nthe superscript y in Eq.  (3), a displacement u which \nbreaks inversion symmetry always increases the effective \nhopping between the magnetic ions. \nTo see the effect of u on the magnetic ordering \nenergy, we take the superexchange, which is one of the \nmost common mechanisms in magnetic insulators, as an \nexample. It is well known that for superexchange the \ninteratomic exchange interaction can be written as\n24: \n24                                     (4)efftJU=−  \nwhere U is the Coulomb interaction for the magnetic \norbital. Thus, an off-center displacement of O ion can \nenhance the interatomic exchange interaction. Usually \nthe magnetic ordering energy has the form of \nij i jijJSS−⋅∑, thus for the AFM case, the energy gain up \nto the second order of the longitudinal displacement of O \nions u is  \n2\n22 4 4 211 2       (5)() ()yy y yyEuru ru r r+Δ∝ − + ≈ −+− \nThus we prove that regardless the exact formula for the \nhopping dependence on distance, an off-center distortion \ncan definitely lower the total energy by an amount2u∼.  \nAbove we have discussed the superexchange in \none-band case. Fo r multi-band superexchange and even \ndouble exchange mechanism25, the exchange coupling J \nis also proportional to the effective hopping, just the relationship between J and t\neff in these mechanisms may \nnot be as simple as shown in Eq. (4). Keeping in mind \nthat the effective hopping is a function of 221( )ru− , an \noff-center distortion will therefore always lower the \nmagnetic energy. Moreover, regardless the specific form  3\nFigure 2 | Energy difference as a function of O offcenter displacement. a , Calculated energy differences between \nzero-temperature AFM and FM state of MnO for a series of O off-center displacement at different biaxial strains: no strain (red square), -3% (blue triangle), -5% (green circle). b, Calculated lattice instabilities of MnO under different \nbiaxial strains at zero-temperature AFM and high-temperature PM states (magenta open star). Zero-temperature results \ncome from DFT+ U calculations with U=3.0 eV, and high-temperature result is from LDA+DMFT simulation with \nU=3.0 eV  and T=300 K. \nof J (t\neff), the corresponding energy gain is still ～ u2, \nas in the case of the single band superexchange. This is \na nontrivial conclusion, since now we see that both the \nmagnetic exchange energy change and the ordinary \nelastic energy change (22 Ku∼ ) are of the second order \nof the off-center displacement. Therefore, when the \nanion located between magnetic ions is shifted away \nfrom the center-symmetric point, the increase in elastic energy may be compensated by the decrease of magnetic exchange energy, consequently, forming an \nelectric dipole and resulting in ferroelectricity, as Fig. 1 \nshows. \nThe ferroelectricity is lo ng believed to originate \nfrom a delicate balance between the short-range forces \nfavoring the undistorted paraelectric structure and the long range Coulomb interactions favoring the \nferroelectric phase\n26,27.  Now we see that indirect \nmagnetic exchange, which is short-range in nature, \nprovide another driving force for the off-center atomic \nmotion. To numerically prove the above conclusion, \nwe then carried out a series of first-principles calculations (see Methods). For the purpose of avoiding the complication due to complex  magnetic \norder and achieving an unambiguous result, we choose \nthe simple insulator MnO with rock-salt structure, which is AFM at low temperature (~ 120 K)  and \nparamagnetic (PM) under normal conditions, as the \ndemonstrating system. \nAlthough cannot deal with the high-temperature \nPM state of MnO, DFT+ U scheme is adequate for the \nzero-temperature  magnetic ally ordered insulating state\n28.  Thus we utilize the DFT+ U method to check \nwhether a reasonable biaxial strain can induce \nferroelectricity in the ground state of MnO.  Here, we \nconcern the off-center (001)-direction motion of O ions. Our numerical results show that regardless the values of U and O-displacement, the ground state of MnO is \nalways AFM. One important parameter relevant to the \nmagnetic ordering energy is the energy difference \nbetween AFM and FM state ( ΔE=E\nFM-EAFM). For  U \n= 3 eV29, the results are shown in Fig. 2a. It is clear \nfrom the figure that ΔE enhances with increasing O \ndisplacement, which directly supports our conclusion: \noff-center motion of the anion between two magnetic \ncations would enhance the magnetic exchange interaction. As clearly show n in Fig.2b, at strain-free \nstate (0%), the curve for total energy change with the O \noff-center displacement is parabolic, which indicates a paraelectric state. When the compressive strain applies, the bottom of the curve becomes flat. Then, at a \nreasonable strain, e. g., -3%, ferroelectricity is induced \nin the ground state of MnO. At even larger compressive strain (-5%), the energy curve is clearly in \nthe shape of double-well －the symbol of \nferroelectricity. The calculated polarization is about \n0.38 C/m\n2, which is comparative to that of typical \nperovskite ferroelectrics. Furthermore, our numerical \nresults show that enlarging U will suppress the \nmagnetic ordering energy, and consequently the critical strain for the occurrence of ferroelectricity will \nincrease. This is expected from our theory [see Eq. (4)], \nand again demonstrates the importance of magnetic  4ordering energy for the ferroelectricity. \nTo confirm  that the above ferroelectric instability is \nof magnetic origin instead of other mechanism30, \nLDA+DMFT calculations are then carried out. We use \nthe highly accurate continue time quantum Monte \nCarlo (CT-QMC) as the impurity solver31. For low \ntemperature, CT-QMC would be  very demanding on \nthe computer resource, we thus only consider the high \ntemperature PM phase of MnO by LDA+DMFT. All of \nour calculations, regardless the temperature (T=200, \n300 and 400 K) and U,  give the same qualitative \nconclusion: losing the magnetic ordering will suppress \nthe off-center displacement, and even a large strain \n(-5%) can no longer induce the ferroelectric instability \nfor PM phase (see line with star symbols in Fig. 2b, \nwhich is the result of T=300 K and U=3.0 eV). Thus \nwe unambiguously demonstrate that here the magnetic interaction is essential for the onset of ferroelectricity.  \nSpeaking solely from the point of view of magnetic \nexchange interaction, antiferroelectric phases are also \npossible states to lower the magnetic energy of the \nsystem. We show here that these states are not \nenergetically favored by considering the electrostatic \nenergy. This is confirmed by our phonon frequency \ncalculation on the paraelectric phase of a 2 ×2×2 \nsupercell of MnO (64 atoms) under different in-plane \nstrains. We find that only the A\nu mode (vibration of \nMn and O ion along z-axis) has been gradually softened when the compressive epitaxial strain increases. No lattice instability corresponds to an \nantiferroelectric phase. Therefore, the off-center O \nmovement will result in ferroelectricity instead of antiferroelectricity. \nOur finding, that magnetic exchange interaction \ncould induce ferroelectricity even in simple magnetic \noxide insulators, is unexpected and exciting. As shown in the above analysis, the bonus coming with the \ninduced ferroelectricity would be the enhancing of the \nmagnetic transition temperat ure. In addition, this \nmechanism is ubiquitous, i.e., not confined in \nantiferromagnets. Therefore various magnetic systems could be potential multiferroics.  \nIn summary, we have confirmed both analytically \nand numerically that indirect magnetic exchange, \ncontrary to what people previously thought, favors ferroelectricity even in collinear magnetic systems. Our research provides a new way to explain the coexistence \nof ferroelectricity and magnetism and might be useful \nto the search of novel multiferroics suitable of practical use.   \n \nMethods For the zero-temperature magnetically ordered \ninsulating state, we use the projector augmented wave \n(PAW) method implemented in the Vienna Ab-Initio  \nSimulation Package (VASP)\n32. The exchange-correla-\ntion potential is treated in the generalized gradient \napproximation (GGA). We use the energy cut-off of \n500 eV for the plane wave expansion of the PAWs and \na 10 x 10 x 10 Monkhorst-Pack grid for k-point \nsampling in the self-consistent calculations. We vary \nthe onsite Coulomb energy U from 1 to 6 eV and \nconfirm its value do not change our qualitative \nconclusions. The epitaxial strain is defined as ( a − \na0)/a0, where a is the in-plane lattice parameter and a0 \nis the theoretical equilibrium lattice constant in cubic \nsymmetry. The out-of-plane lattice parameter c is \noptimized at every strain.  The Berry phase technique is \nused to calculate ferroelectric polarizations. We use the LDA+DMFT method\n28,31 to calculate the \nhigh temperature PM state. We use continue time quantum Monte Carlo as the impurity solver\n31, and \ncrossing check our results by the non-crossing \napproximation. Calculations are fully self-consistent in \ncharge density, chemical potential,  impurity level and \ntotal energy . The line with star symbol in Fig.2b shows \nthe LDA+DMFT results for -5% strain with \ntemperature equal to 300K and U equal to 3.0 eV. \n \nAcknowledgements XW thanks Kristjan Haule for \nuseful discussion. The work was supported by the \nNational Key Project for Basic Research of China \n(Grant no. 2011CB922101 and 2010CB923404), \nNSFC (Grant No. 91122035, 61125403, 50832003); \nPCSIRT, NCET, Shanghai ShuGuang. Computations were performed at the ECNU computing center. S.Y.S \nwas supported by DOE Computational Material \nScience Network (CMSN) and DOE SciDAC Grant \nNo. SE-FC02-06ER25793. \n \nCorrespondence and requests for materials should be \naddressed to X. W or C.G. D. \n References \n1. Kimura, T.  et al.  Magnetic control of ferroelectric \npolarization. Nature  426, 55-58 (2003). \n2. Efremov, D. V., Van den Brink, J. & Khomskii, D. \nI. Bond-versus site-centred ordering and possible ferroelectricity in manganites. Nat. Mater.  3, \n853-856 (2004). \n3. Fiebig, M. Revival of the magnetoelectric effect. J. \nPhys. D: Appl. Phys.  38, R123-R152 (2005). \n4. Eerenstein, W., Mathur, N. D. & Scott, J. F. \nMultiferroic and magnetoelectric materials. Nature  \n442, 759-765 (2006).  55. Duan, C.-G., Jaswal, S. S. & Tsymbal, E. Y. \nPredicted magnetoelectric effect in Fe/BaTiO 3 \nmultilayers: Ferroelectric control of magnetism. \nPhys. Rev. Lett.  97, 047201 (2006). \n6. Cheong, S.-W. & Mostovoy, M. Multiferroics: a \nmagnetic twist for ferroelectricity. Nat. Mater.  6, \n13-20 (2007). \n7. Ramesh, R. & Spaldin, N. A. Multiferroics: \nprogress and prospects in thin films. Nat. Mater.  6, \n21-29 (2007). \n8. Wang, K. F., Liu, J. M. & Ren, Z. F. Multiferroicity: \nthe coupling between magnetic and polarization \norders. Adv. Phys.  58, 321-448 (2009). \n9. Spaldin, N. A., Cheong, S. W. & Ramesh, R. \nMultiferroics: Past, present, and future. Phys. Today  \n63, 38-43 (2010). \n10. Hill, N. A. Why are there so few magnetic \nferroelectrics? J. Phys. Chem. B  104, 6694-6709 \n(2000). \n11. Mostovoy, M. Ferroelectricity in Spiral Magnets. \nPhys. Rev. Lett.  96, 067601 (2006). \n12. Katsura, H., Nagaosa, N.  & Balatsky, A. V. Spin \ncurrent and magnetoelectric effect in noncollinear \nmagnets. Phys. Rev. Lett.  95, 057205 (2005). \n13. Sergienko, I. A. & Dagotto, E. Role of the \nDzyaloshinskii-Moriya interaction in multiferroic \nperovskites. Phys. Rev. B  73, 094434 (2006). \n14. Hu, J. Microscopic Origin of Magnetoelectric \nCoupling in Noncollinear Multiferroics. Phys. Rev. \nLett. 100, 077202 (2008). \n15. Chapon, L. C.  et al.  Structural Anomalies and \nMultiferroic Behavior in Magnetically Frustrated \nTbMn 2O5. Phys. Rev. Lett.  93, 177402 (2004). \n16. Aliouane, N.  et al.  Field-induced linear \nmagnetoelastic coupling in multiferroic TbMnO 3. \nPhys. Rev. B  73, 020102 (2006). \n17. Sergienko, I. A., Şen, C. & Dagotto, E. \nFerroelectricity in the Magnetic E-Phase of \nOrthorhombic Perovskites. Phys. Rev. Lett.  97, \n227204 (2006). \n18. Pirc, R., Blinc, R. & Scott, J. F. Mesoscopic model \nof a system possessing both relaxor ferroelectric \nand relaxor ferromagnetic properties. Phys. Rev. B  \n79, 214114 (2009). \n19. Kleemann, W., Shvartsman, V. V., Borisov, P. & \nKania, A. Coexistence of Antiferromagnetic and Spin Cluster Glass Order in the Magnetoelectric \nRelaxor Multiferroic PbFe 0.5Nb0.5O3. Phys. Rev. \nLett. 105, 257202 (2010). \n20. Dzyaloshinskii, I. A thermodynamic theory of \n“weak” ferromagnetism of antiferromagnetics. J. \nPhys. Chem. Solids  4, 241-255 (1958). \n21. Moriya, T. Anisotropic Superexchange Interaction \nand Weak Ferromagnetism. Phys. Rev.  120, 91-98 \n(1960). \n22. Schrieffer, J. R. & Wolff, P. A. Relation between \nthe Anderson and Kondo Hamiltonians. Phys. Rev.  \n149, 491-492 (1966). \n23. Harrison, W. A. Electronic Structure and the \nProperties of Solids: The Physics of the Chemical \nBond .  (Dover Publications, 1989). \n24. Anderson, P. W. New Approach to the Theory of \nSuperexchange Interactions. Phys. Rev.  115, 2-13 \n(1959). \n25. White, R. M. Quantum Theory of Magnetism: \nMagnetic properties of Materials . 3rd edn,  \n(Springer-Verlag, 2007). \n26. Cochran, W. Crystal stability and the theory of \nferroelectricity. Adv. Phys.  9, 387-423 (1960). \n27. Cohen, R. E. Origin of fe rroelectricity in perovskite \noxides. Nature  358, 136-138 (1992). \n28. Kotliar, G.  et al.  Electronic structure calculations \nwith dynamical mean-field theory. Rev. Mod. Phys.  \n78, 865-951 (2006). \n29. Kulik, H. J. & Marzari, N. Systematic study of \nfirst-row transition-metal diatomic molecules: A \nself-consistent DFT plus U approach. J. Chem. \nPhys.  133, 114103 (2010). \n30. Bousquet, E., Spaldin, N. A. & Ghosez, P. \nStrain-Induced Ferroelectricity in Simple Rocksalt \nBinary Oxides. Phys. Rev. Lett.  104, 037601 \n(2010). \n31. Haule, K., Yee, C.-H. & Kim, K. Dynamical \nmean-field theory within th e full-potential methods: \nElectronic structure of CeIrIn 5, CeCoIn 5, and \nCeRhIn 5. Phys. Rev. B  81, 195107 (2010). \n32. Kresse, G. & Furthmüller, J. Efficiency of ab-initio \ntotal energy calculations for metals and \nsemiconductors using a plane-wave basis set. \nComput. Mater. Sci.  6, 15-50 (1996). \n "    },    {        "title": "1203.3840v1.Magnetic_domain_structure_of_epitaxial_Ni_Mn_Ga_films.pdf",        "content": "1 Magnetic domain structure of epitaxial Ni-Mn-Ga fil ms \nAnett Diestel a,b,* , Anja Backen a,b , Volker Neu a, Ludwig Schultz a,b  and Sebastian Fähler a \n \na IFW Dresden, Institute of Metallic Materials, P.O.  Box 270116, 01171 Dresden, Germany \nb Dresden University of Technology, Institute of Mat erials Science, 01062 Dresden, Germany \n* Corresponding author: a.diestel@ifw-dresden.de, Tel .: +49 (0)351 4659-259  \n \nFor the magnetic shape memory effect, knowledge abo ut the interaction \nbetween martensitic and magnetic domain structure i s essential. In the case \nof Ni-Mn-Ga bulk material and foils, a staircase-li ke magnetic domain \nstructure with 90°- and 180°-domain walls is known for modulated \nmartensite. In the present paper we show that the m agnetic domain pattern \nof thin epitaxial films is fundamentally different.  Here we analyze epitaxial \nNi-Mn-Ga films by atomic and magnetic force microsc opy to investigate the \ncorrelation between the twinned martensitic variant s and the magnetic stripe \ndomains. The observed band-like domains with partia lly perpendicular out-\nof-plane magnetization run perpendicular to the mic rostructure domains \ndefined by twinning variants. These features can be  explained by the finite \nfilm thickness, resulting in an equilibrium twinnin g period much smaller than \nthe domain period. This does not allow the formatio n of a staircase domain \npatter. Instead the energies of the magnetic and ma rtensitic microstructures \nare minimized independently by aligning both patter ns perpendicularly to \neach other. By analyzing a thickness series we can show that the observed \nmagnetic domain pattern can be quantitatively descr ibed by an adapted band \ndomain model of Kittel. \n \n \n \n \n \n \n 2 1 Introduction \nMagnetic shape memory (MSM) single crystals reach h uge strains up to 10 %, induced \nby an external magnetic field [1]. This effect is o bserved in modulated martensite and \noriginates from magnetically induced reorientation (MIR) of differently oriented \nmartensitic variants. The huge strain makes these a lloys of particular interest for \nactuators or sensors in micro-mechanical systems [2 ]. While the preparation of epitaxial \nfilms [3], cantilevers [3,4,5] and freestanding fil ms [6] is well established, little is known \nabout the correlation of magnetic and martensitic m icrostructure in these microscaled \nsystems. Since coupling of magnetic and martensitic  microstructure is the key \nrequirement for MIR, a better understanding of poss ible finite size effects is necessary \nfor the functionalization of these microstructures.  For this, bulk single crystals [7,8,9]  \nand foils [10] can be considered as a reference sys tem. The variants in multivariant state \nof bulk Ni-Mn-Ga typically run through the complete  sample. Within one single variant \nthe formation of antiparallel domains separated by 180°-domain walls (DW) is observed. \n90°-DW form at twin variant boundaries and enable t he magnetization to follow the \nmagnetic easy c-axis. With the formation of a typical staircase pa ttern consisting of 90°- \nand 180°-DW the magnetic flux can be closed [7-10] (see Fig. 1c). In addition to this \nfundamental pattern domain mirroring at twin bounda ries [11] and branching at slightly \nmiscut surfaces [12] have been analyzed in single c rystals. \nUntil now the magnetic domain pattern of thin films  has only been analyzed in \npolycrystalline Ni-Mn-Ga [13]. Magnetic force micro scopy micrographs reveal a strong \nmagnetic out-of-plane contrast produced by band dom ains forming a maze like pattern. \nA thickness series revealed that the domain period DW Λ  depends on the film thickness d \nas predicted by Kittel ( 2 / 1\nDW ~dΛ ) [14]. However, the physical origin of the prefact or in \nKittel’s relation is missing and due to the polycry stalline nature of these films a \ncorrelation of magnetic domains and martensitic var iants was not possible [13]. \nIn the present paper we use the advantage of epitax ial films, which allow a local \nidentification of the martensitic microstructure by  atomic force microscopy (AFM) \n[15,16]. Magnetic force microscopy (MFM) measuremen ts reveal a correlation of \nmagnetic and martensitic microstructure of 14M mart ensite, which is fundamentally \ndifferent compared to bulk. We show that these diff erences originate from the finite film \nthickness and the reduced martensitic variant perio dicity. We analyze the thickness \ndependency of the magnetic domain period and compar e it with the qualitative prediction 3 of Kittel’s theory for magnetic band domains [14]. Furthermore we demonstrate that a \nmodified band domain theory leads to a full quantit ative explanation of the thickness \ndependency without any free parameter. \nOur domain model benefits from the fact, that Ni-Mn -Ga is a well characterized system. \nDirect measurements of the spin wave stiffness cons tant 2meVÅ 100 =W  [17] allow \ncalculating the exchange constant 32aNSWA⋅⋅=  by using the atomic moment BSµ8 . 3=, \nthe number N of Mn atoms per unit cell and the corresponding la ttice parameter a of Ni-\nMn-Ga. The uniaxial anisotropy coefficient for the present 14M martensite is \n3 5Jm 10 9 . 0−⋅=uK  [18]. \n \n2 Experimental \nWe prepared a series of epitaxial Ni-Mn-Ga films wi th thicknesses d ranging from \n125 nm to 2 µm by DC magnetron sputtering, as descr ibed in detail in our previous work \n[15]. In order to improve the film quality and enab le freestanding Ni-Mn-Ga films, we \nfirst deposited a sacrificial chromium layer on the  single crystalline MgO(100) substrate \n[6]. Film composition was probed by means of energy -dispersive X-ray spectroscopy \n(EDX) with an accuracy of 0.5 at.% using a Ni 50 Mn 25 Ga 25  standard. The valence electron \ndensity ( e/a -ratio) was determined to be about 7.61 (±0.06) by these measurements. \nMartensitic and magnetic microstructure were invest igated by AFM and MFM, \nrespectively, using a digital instrument dimension 3100. Topography was imaged by \nheight contrast in tapping mode. Magnetic micrograp hs were obtained in lift mode with a \nstandard magnetic tip (Co-alloy coating, magnetizat ion along tip axis). The lift scan \nheight ranges from 50 to 100 nm depending on the fi lm thickness.  \n \n3 Results and Discussion \n3.1 Magnetic domain configuration in 14M martensite  \nCrystallographic and magnetic microstructures were measured by AFM and MFM and \nare exemplarily shown for a 2 µm thick Ni-Mn-Ga fil m in Fig. 1. Due to the epitaxial \nfilm growth, the crystallographic orientation of th e austenitic Ni-Mn-Ga unit cell is \nknown [15]. It is rotated about 45° with respect to  the substrate and image edges. The \nAFM micrograph in Fig. 1a shows a periodically modu lated waved topography with a \nrhombus-like superstructure. This pattern represent s traces of mesoscopic c-a-twin 4 boundaries of the modulated 14M martensitic phase [ 15]. Due to the four-folded \nsymmetry of the epitaxial (001) oriented film two c rystallographic equivalent \norientations of twin boundary traces along MgO ]011 [ and MgO ] 110 [  are possible. In \nboth cases the traces of twin boundaries are rotate d about 45° with respect to the \nsubstrate edges [16]. \nWith the knowledge about twinned 14M martensite and  the presented AFM micrographs \nthe crystallography can be sketched schematically a s top view and cross section in \nFig. 1b. The diagonal, black lines illustrate the t races of mesoscopic c14M -a14M -twin \nboundaries (TB) and the double arrows are equivalen t to the crystallographic short and \nmagnetic easy c14M -axis. The top view displays the alternating in- an d out-of-plane \nc14M -axes of adjoining martensitic variants. The cross section cut along MgO[011] \ndirection (Fig. 1b, dotted line) sketches the tilte d run of the twin boundaries within the \nfilm.  \nBy transferring the magnetic domain structure of bu lk Ni-Mn-Ga [7] onto the given \narrangement of martensitic variants a proposed doma in structure can be sketched in \nFig. 1c. The c14M -axis is equivalent to the preferential direction o f magnetization m, \nwhich is illustrated by red arrows. According to th e findings on bulk Ni-Mn-Ga, the \ncross section along MgO[011] should exhibit a stair case domain pattern of 90°- and \n180°-domain walls (DW, red dashed lines). 90°-DW co incide with the tilted twin \nboundaries, whereas 180°-DW separate oppositely mag netized domains within one \nmartensitic variant. This typical structure minimiz es the magnetic stray field and closes \nthe magnetic flux within the sample. The staircase domain structure inside the sample \nwould cause a domain pattern on the film surface as  sketched in the top view (Fig. 1c). A \nband like out-of-plane contrast along the twin boun daries should be observed by MFM.  \nIn contrast to these expectations, the experimental ly observed domain pattern (Fig. 1d) \npresents a lamellar bright-dark-contrast perpendicu lar to the twin boundaries, which \nsuggests the formation of magnetic band domains wit h antiparallel out-of-plane \nmagnetization. Within the dark domains a finer cont rast is visible. This contrast \ncoincides exactly with the topography contrast in t he AFM micrograph, which cannot be \nexcluded completely during MFM measurements for lar ger film thicknesses ( d ≥ 1 µm). \nDue to branching and bending the magnetic domains d o not run perfectly parallel to each \nother, though we could not find any correlation bet ween topographic features and these \ndiscontinuities.  5 In Fig. 1e the entire data obtained from AFM and MF M micrographs are summed up. \nThe schematic top view and cross section explain th e visible contrast by means of a \npossible domain configuration. From AFM measurement s the crystallography and the \norientation of twin boundaries and c14M -axes are known. For the interpretation of the \nmagnetic configuration we consider that the magneti zation m follows the magnetic easy \nc14M -axis in every segment of the band domains, which a lternates from in- to out-of-\nplane between neighboring variants. In the followin g we discuss the possible alignments \nof magnetization (up, left, down, right) within the  magnetic domains. Instead of \npermutation of all four possible magnetization dire ctions within each band domain, only \ntwo magnetic directions occur within each band doma in (e. g. up and left in the dark \nband domain, Fig. 1e cross section). In the case of  not-observed permutation of all four \ndirections every second 90°-DW would be charged (Fi g. 1f). So this configuration is \nenergetically unfavorable.  \nWe observe only little magnetic contrast within eac h band domain. This indicates for \ncoupling effects, which brings magnetization even m ore parallel. In particular \nmagnetostatic coupling favors a more parallel align ment of magnetization within one \nband domain, which is illustrated by the slightly t ilted magnetizations in the cross section \nof Fig. 1e. The same parallel alignment would be al so favored by exchange coupling \nacross twin boundaries. However, the exchange lengt h with nm 3 . 81\nex =⋅=−\nuKAL  is \nquite low in comparison to the twin variant width i n our films. Exchange coupling \ntherefore should only play a role in very thin film s with a short twinning period.  \nCoupling results in an out-of-plane component of ma gnetization. To minimize stray field \nenergy antiparallel magnetized band domains form, w hich are divided by 180°-DW (Fig. \n1e). For band domains the equilibrium domain period  ΛDW  is an optimum balance \nbetween total domain wall energy, which increases w ith ΛDW , and stray field energy, \nwhich reduces with ΛDW  [14]. As we will describe in detail in 3.3, the ex perimentally \nobserved ΛDW  agrees well with the calculated one. Since ΛDW  is substantially larger than \nthe twinning period ΛΤΒ  the formation of domains along the direction of th e twin \nboundaries does not allow reaching their optimum pe riod. For a domain wall orientation \nperpendicular to the twin boundaries this restricti on does not exist and every domain \nwidth can be formed to adjust the equilibrium domai n configuration. This magnetic 6 domain structure is visualized by MFM as bright and  dark stripes perpendicular to the \ntwin boundaries (see Fig. 1d).  \nTo understand why this domain configuration is more  favorable in thin films compared \nto the bulk staircase pattern we estimate the domai n wall energies in both configurations \n(Fig 1c, e). When comparing the total domain wall e nergy, it is sufficient to compare the \nareas of 180°-DWs only, since in both cases the are a of the 90°-DW is identical and \ndetermined by the twin boundary area.  For the stai rcase pattern sketched in Fig. 1c the \nratio of DW area per film surface area is at least 6 .10 2TB =Λd  (or a multiple) for the \npresented 2 µm thick film. For the experimentally o bserved magnetic band domain \npattern this ratio depends on film thickness d (since the DWs are perpendicular to the \nsubstrate) and their period ΛDW . The ratio DW 2Λd gives a value of 3.3. This illustrates \nthat the total domain wall energy is substantially lower for band domains compared to a \nstaircase domain pattern.  7 \n \n \nFIG. 1. (Color online) (a) The AFM micrograph of a 2 µm thick Ni-Mn-Ga film shows \ndiagonal traces of mesoscopic c14M -a14M -twin boundaries. (b) The crystallographic \norientation is sketched as top view and cross secti on, where the black lines illustrate the \ntwin boundaries (TB) with the twinning period ΛTB  and the double arrows picture the \ncrystallographic short and magnetic easy c14M -axis. (c) Following the known magnetic \ndomain pattern of bulk materials and the crystallog raphy from the AFM image, a \nhypothetical magnetic domain structure can be sugge sted. For the cross section a \nstaircase pattern of 180°-domain walls (DW, red das hed lines) is sketched, where the \nmagnetization (arrows) follows the c14M -axis and the 90°-DW coincide with the TB. (d) \nIn contrast to this, the experimental MFM micrograp h shows a high out-of-plane \nlamellar contrast perpendicular to the TB. (e) The corresponding domain structure with \nthe domain width period ΛDW  is sketched schematically as top view and cross se ction. \n(f) The cross section shows the energetically unfav ourable, experimentally not observed \ndomain configuration with charged 90°-DWs.  8 3.2 Film thickness dependency \nThe change of the magnetic domain pattern as a func tion of the film thickness d in the \nrange of 125 nm to 2 µm was determined by analyzing  MFM micrographs shown in \nFig. 2. The corresponding AFM images are not shown here, but they reveal a similar \ntopography caused by mesoscopic c14M -a14M -twin boundaries imaged in Fig. 1a. \n \n \n \nFIG. 2. (Color online) MFM micrographs of Ni-Mn-Ga films with thicknesses d of \n(a) 125 nm, (b) 250 nm, (c) 500 nm and (d) 1 µm sho w an increasing domain width \nperiod ΛDW . For d ≥ 1 µm fine lines originating from the topographic c ontrast of twin \nboundaries become visible.  \n \nIn analogy to magnetic band domains proposed by Kit tel [14] the equilibrium twinning \nperiod can be described by minimization of the sum of elastic volume energy and twin \nboundary energy. Accordingly the twinning period ca n be described with the power law \nνdad⋅=Λ)(TB . A non-linear fitting of ΛTB versus d results in the parameters \n)04 . 0(87 . 0±=ν  and ν−±=1nm )16 . 0(53 . 0a  (Fig. 3). In our previous work we analyzed \na similar film series and obtained a different para meter 21=ν [16]. The exponent \nallows distinguishing different solutions to minimi ze both, twin boundary energy and \nelastic energy [19]. While 21=ν describes a constant twin boundary density through  \nthe film thickness, 32=ν is expected when branching of twin boundaries occu rs. The \nclear difference between both film series becomes a lso evident by different shapes of the 9 mesoscopic c14M -a14M -twins on the surface. The present topography shows  a sharp \nrhombus-like superstructure whereas the previous on e exhibits a meandering pattern \n[16]. This indicates a different relaxation mechani sm, which will be analyzed in detail \nelsewhere. In the present paper we take the twin bo undary periodicity as given and focus \non the correlation with the magnetic domain pattern . \nFor the magnetic domain structure the non-linear fi tting of the domain width period \nνdad⋅=Λ)(DW   results in the parameters )04 . 0(46 . 0±=ν  and ν−±=1nm ) 7 . 8( 1 .37 a  \n(Fig. 3). This demonstrates that the observed magne tic domain structure obeys the \ntheoretical thickness dependency of magnetic band d omains predicted by Kittel [14]. By \nfixing 21=ν the dependency of )nm ( nm 7 .27 (nm) 2/ 1 2/ 12/ 1\nDW d⋅ = Λ  is obtained. To \nestimate the thickness for which the magnetic domai n pattern should change from the \nthin film configuration towards the bulk staircase pattern the different thickness \ndependencies of domain and variant periodicity is u sed. A crude extrapolation of both \ncases depicted in Fig. 3 suggests a crossover for f ilm thicknesses in the millimeter range. \n \n \nFIG. 3. (Color online) Double-logarithmic plots of periodicity versus film thickness d to \ndetermine the exponent ν in the film thickness dependency νdad⋅=Λ)(  is shown. For \nthe twinning period ΛTB  (triangle) an exponent of 04 . 087 . 0±=ν  is obtained. For the \ndomain width period ΛDW (square) an exponent of 04 . 046 . 0±=ν  is obtained, which \nallows using a square-root thickness dependency )nm ( nm 7 .27 (nm) 2 / 1 2 / 12 / 1\nDW d⋅ = Λ . \n 10 3.3 Quantitative description according to the Kitte l model \nMaterials with an uniaxial anisotropy and out-of-pl ane magnetic easy axis often show a \nband domain structure. This domain configuration wa s theoretically studied by Kittel and \napplies for materials with a quality-factor \ndu\nKKQ= larger than one [14]. \n02\n2µS\ndJK= \ndenotes the magnetostatic energy density with the s aturation magnetization T6 . 0=SJ . \nUnder these conditions Q is 0.64, which is smaller than one  and  the application of the \nKittel model is not valid.  \nAs described in 3.1 magnetostatic coupling results in an averaged, tilted magnetization. \nThen the effective saturation magnetization )(∗\nSJ is reduced and as projection to the \nfilm normal S SJ J\n21=∗ is obtained (Fig. 4a). In this case the correspond ing quality \nfactor ∗Q is 1.29,  which allows the comparison with the band domain th eory.  \nAccording to Kittel the band domain structure is fo rmed by minimizing the total energy \nas sum of magnetic domain wall and stray field ener gy. The equilibrium domain width  D  \ncan be determined by \n*3\n8dw\nKdD⋅⋅=γπ.      (1) \nWith 180° Bloch domain walls exhibiting an energy o f u w KA⋅=4γ , the film \nthickness dependence of the domain width can be det ermined with Eq. 1. The domain \nwidth periodicity ΛDW  represents the sum of two adjoining domain widths D and was \ncalculated: ) nm ( nm 8 .25 )nm (2 / 1 2 / 12 / 1\nDW d⋅ = Λ . Fig. 4b shows the relation of the \nexperimentally determined domain width period (squa res) and the calculated ΛDW  \n(graph) as function of the film thickness d. The deviation of the experimental data from \nthe calculated function is only minor and may be du e to the simplification of the complex \nmagnetic domain structure. The high conformity betw een experimental data and theory \nindicates that no additional domain walls are embed ded parallel to the film surface.   11 \n \n \nFIG. 4. (Color online) (a) Three dimensional sketch  images the simplified magnetic \ndomain structure of thin epitaxial Ni-Mn-Ga films. The short twinning period TB Λ \nresults in exchange coupling of the magnetization mr between adjoining variants. The \nresulting exchange coupled magnetization Rmr exhibits an out-of-plane component. To \nreduce their stray field energy band domains with t he periodicity DW Λ form. \n(b) Comparison of experimentally determined domain width period DW Λ (black squares) \nand calculated values from Kittel’s theory of magne tic band domains (red line) as a \nfunction of film thickness d. \n \n4 Conclusions \nThe finite film thickness and twin variant width do es not allow the formation of a \nstaircase pattern known for Ni-Mn-Ga bulk materials . Due to the high aspect ratio of \nthin films, stray field energy has an impact on the  magnetic domain pattern and band \ndomains are formed. Their microscopically analyzed width can be described \nquantitatively without any free parameter by Kittel ’s theoretical model of magnetic \nband domains. In the analysed thin films the equili brium magnetic band domain period \nexceeds the twin boundary period. In agreement with  our experiments the energies of \nmagnetic as well as martensitic microstructure can be minimized independently, when \ndomain and twin boundaries are aligned perpendicula r to each other.  \n 12 5 Acknowledgments \nWe acknoledge Rudolk Schäfer and Ulrich K. Rößler f or helpful discussions. This work \nwas funded by the German research Foundation (DFG) via the Priority Programme \nSPP1239. \n \n6 References \n                                                 \n[1] Sozinov A, Likhachev AA, Lanska N, Ullakko K. A ppl Phys Lett 2002; 80:1746. \n[2] Kohl M, Yeduru SR, Khelfaoui F, Krevet B, Backe n A, Fähler S, Eichhorn T, Jakob \nG, Mecklenburg A. Mater Sci Forum 2010;635:145. \n[3] Dong JW, Chen LC, Palmstrom CJ, James RD, McKer nan S. Appl Phys Lett \n1999;75:1443. \n[4] Jenkins CA, Ramesh R, Huth M, Eichhorn T, Pörsc h P, Elmes HJ, Jakob G. Appl \nPhys Lett 2008;93:234101. \n[5] Eichhorn T, Hausmanns R, Jakob G. Acta Mater 20 11;59:5067. \n[6] Backen A, Yeduru SR, Kohl M, Baunack S, Diestel  A, Holzapfel B, Schultz L, \nFähler S. Acta Mater 2010;58:3415. \n[7] Lai YW, Scheerbaum N, Hinz D, Gutfleisch O, Sch äfer R, Schultz L, McCord J. \nAppl Phys Lett 2007;90:192504. \n[8] Ge Y, Heczko O, Soderberg O, Lindroos VK. J App l Phys 2004;96:2159.  \n[9] Venkateswaran SP, Nuhfer NT, Graef MD. Acta Mat er 2007;55:5419. \n[10] Heczko O, Soroka A, Hannula SP. Appl Phys Lett , 2008;93:022503. \n[11] Lai YW, Schäfer R, Schultz L, McCord J. Appl P hys Lett, 2010;96:022507. \n[12] Scheerbaum N, Lai YW, Leisegang T, Thomas M, L iu J, Khlopkov K, McCord J, \nFähler S, Träger R, Meyer DC, Schultz L,  Gutfleisc h O. Acta Mater 2010;58:4629. \n[13] Chernenko VA, Lopez Anton R, Barandiaran JM, O rue I, Besseghini S, Ohtsuka \nM, Gambardella A. IEEE Trans Magn 2008;44:3040. \n[14] Kittel C. Rev Mod Phys 1949;21:541. \n[15] Buschbeck J, Niemann R, Heczko O, Thomas M, Sc hultz L, Fähler S. Acta Mater \n2009;57:2516. \n[16] Diestel A, Backen A, Rößler UK, Schultz L, Fäh ler S. Appl Phys Lett \n2011;99:092512. \n[17] Runov V, Stuhr U. J Magn Magn Mater 2011;323:2 44.  \n[18] Straka L, Heczko O, Ullakko K. J Magn Magn  Ma ter 2004;272-276:2049. \n[19] Kohn RV, Müller S. Philos Mag A 1992; 66:697. "    },    {        "title": "1203.6886v1.Field_induced_changes_in_cycloidal_spin_ordering_and_coincidence_between_magnetic_and_electric_anomalies_in_BiFeO3_multiferroic.pdf",        "content": " 1Field induced changes in cycloidal spin ordering an d coincidence \nbetween magnetic and electric anomalies in BiFeO 3 multiferroic \n \nB. Andrzejewski 1, A. Molak 2, B. Hilczer 1, A. Budziak 3, R. Bujakiewicz-Koro ńska 4  \n \n1Institute of Molecular Physics, PAN, Smoluchowskiego 17, PL-60179 Pozna ń, Poland \n2University of Silesia in Katowice, Institute of Physics,  Bankowa 14, PL-40007 Katowice, \nPoland \n3The H. Niewodnicza ński Institute of Nuclear Physics, PAN, Radzikowskiego 152, PL -31342 \nCracow, Poland \n4Pedagogical University in Cracow, Institute of Physics, Podc hor ąż ych 2, PL-30084 Cracow, \nPoland \nCorresponding author : B. Andrzejewski, e-mail: Bartlomiej.Andrzejewski@if mpan.poznan.pl  \n \nPACS: 75.85.+t; 75.25.-j; 71.38.Ht \n \nAbstract \nThe ZFC and FC magnetization dependence on temperature wa s measured for BiFeO 3 \nceramics at the applied magnetic field up to µ0H = 10 T in 2 K ÷ 1000 K range.  \nThe antiferromagnetic order was detected from the hyster esis loops below the Neel \ntemperature TN = 646 K. In the low magnetic field range there is an a nomaly in M(H), \nprobably due to the field-induced transition from circular cy cloid to the anharmonic cycloid. \nAt high field limit we observe the field-induced transiti on to the homogeneous spin order. \nFrom the M(H) dependence we deduce that above the field Ha the spin cycloid becomes \nanharmonic which causes nonlinear magnetization, and abov e the field Hc the cycloid \nvanishes and the system again exhibits linear magnetization M(H). The anomalies in the \nelectric properties, ε’(T) , tan δ(T) , and σ(T) , which are manifested within the 640 K ÷ 680 K \nrange, coincide to the anomaly in the magnetization M(T) dependence, which occurs in the \nvicinity of TN = 646 K. We propose to ascribe this coincidence to the cri tical behaviour of the \nchemical potential µS, related to the magnetic phase transition.   21. INTRODUCTION \nBismuth ferrite BiFeO 3 (BFO) belongs to multiferroic compounds. It exhibits a  \ncoexistence of antiferromagnetic and ferroelectric or dering that attracts attention due to \npossible applications in sensors and multi-state memory devices [1-5]. The intrinsic properties \nof the BFO have been determined for single crystal samp les [4, 6]. It shows a rhomboedrally \ndistorted perovskite cell with space group R3c  at room temperature.  \nThe G-type antiferromagnetic (AFM) order below temper ature TN = 643 K with \nsuperimposed long-range incommensurate cycloidal spiral struct ure was reported [7]. \nHowever, there are controversial reports also, e.g. a  lack of cycloidal structure influence on \nAFM susceptibility was noticed in the literature. Despite  the weak ferromagnetism was \ndetected in bismuth ferrite [8], actually it may be also ascribed to magnetic properties of the \nprecipitated impurity phase since this type of ordering vanishe d in the pure BFO [4, 9].  \nThe magnetic order in BFO is a subject to several trans itions manifesting in magnetic \nproperties near the temperatures 140 K, 200 K and 643 K. The last and most distinct one is \nthe transition between antiferromagnetic and paramagn etic order (AFM-PM transition).  \nThe transition at 140 K is interpreted in terms of spin- glass [10] and the anomaly about 200 K \nis ascribed to magnon softening [10].  \nThe transitions in magnetic ordering can be also induced by  means of an external \nmagnetic field. A homogeneous AFM spin state with no s uperimposed cycloidal spin ordering \nin bismuth ferrite can be obtained under the influence of  a very strong magnetic field \nexceeding 20 T and at room temperature [9]. \nThe ferroelectric features, with the Curie temperature  TC = 1143 K, were confirmed by \nthe P-E hysteresis loop measurement with a remnant polarisatio n Pr ≈35 µC cm -2 at room \ntemperature [4]. The measured ferroelectric remnant polar isation Pr ~35 µC cm -2 is close to \nthe value estimated from first-principles calculations  [11, 12]. Moreover, this quantity value \nand the electric polarisation P(E)  hysteresis loop depend markedly on the oxygen vacancies \ncontent [13].  \nThe coexistence and interaction of the antiferromagne tic and ferroelectric phases is \nconfirmed both in crystals and ceramics BFO [4, 14]. The  influences of the applied electric \nfield E on the magnetic magnetisation M and the applied magnetic field H on the electric \npolarization P have been reported. However, the significant differenc e between the phase \ntransition temperatures, i.e. TN ≈ 643 K for the AFM-PM transition and the TC ≈ 1143 K for  3the FE -PE transition, suggest that direct interaction between the magnetic and electric \nsubsystem might be week.  \nThe stoichiometric BiFeO 3 is a highly resistive material and exhibits the resistivi ty of the \nGΩm order at room temperature [4]. The calculated energy ga p in the electronic structure is \nequal to 2.8 eV [15]. The optical energy gap was estimate d as 2.7 eV [16]. However, the \nelectric conduction activation energy Ea of the BFO ceramics was reported as varying e.g. \nfrom 0.2, 0.3, 0.58, 0.9, to 1.1 eV [17-19], dependably on tempera ture range. Hence, the \nelectric conduction depends on the crystal lattice defect s, both the oxygen vacancies and \ndoping, e.g. with Nb [17], La and Mn [20, 21] which influence t he electrical conductivity \nvalue by several orders in magnitude. It is worthwhile to note that the transition from states \n~0.3 eV below the band gap were related to the oxygen vacanc ies, basing on the refractivity \nmeasurements [16]. \nThe aims of the work were: (1) to determine the magneti sation M(H) and cycloidal spin \nordering dependence on strong magnetic fields; (2) to determ ine whether the magnetic AFM-\nPM phase transition can be detected by means of the ele ctrical measurements.  \n \n2. EXPERIMENTAL METHODS \n2.1. Sample preparation \nThe BiFeO 3 ceramics were obtained by the hot pressing method. The B i 2O3 and Fe 2O3 \nstarting materials were mechano-activated when milled f or 24 h in a ball mill filled with \nethanol, then calcined at 923 K. The product was crushed, grin ded, and then sintered at  \n1123 K. The proper composition was confirmed with the EDS te st [22].  \n \n2.2 Magnetic test \nThe magnetometric measurements were performed by means o f Quantum Design PPMS \nSystem (Physical Property Measurement System). Two mag netometer probes fitted to PPMS \nwere used. The first one was extraction magnetometer (ACMS) probe allowing both DC \nmagnetic moment and AC susceptibility measurements and t he second was VSM (Vibrating \nSample Magnetometer) probe equipped additionally with high temperature set. The BiFeO 3 \nsample, for magnetic test, was cut to proper dimensions ( about 3x3x5 mm 3). It was mounted \nin a standard PTFE straw when the ACMS probe was used and it was mounted in a bronze \nsample support for the measurements performed by means of V SM probe. For high  4temperature measurements the thin slab (about 3x3x1mm 3) was cut from BiFeO 3 sample to \navoid of any temperature gradients. \n \n2.3 X-ray diffraction test  \nX-ray diffraction (XRD) studies have been carried out us ing an X’Pert PRO \n(PANalytical) diffractometer with the Cu K α radiation and a graphite monochromator. \nTemperature of a sample has been stabilized (accuracy ±1 K) with the high-temperature oven-\nchamber HTK 1200N supplied by an Anton Paar Co. The BiFeO 3 powder sample was placed \nin a ceramic container (the diameter of 16 mm and the dept h of ca. ~0.8 mm). No specimen \nwas added to the sample to stick it to the container. Be fore the measurement, the chamber was \npumped-out to pressure about 1 mbar. The measurements have bee n performed during \nheating. After each heating stage the sample has been held about 10 min to obtain \nequilibrium. A profile-fitting program FULLPROF [23] based on the Rietveld method was \nused to analyze and fit the XRD patterns. \n \n2.4 Electrical test \nA sample in the form of parallelepiped (about 2x3x1 mm 3) was cut from the sintered \nceramic pellets. The surfaces were polished with a diamo nd paste, grade 2000. The samples \nfor electric measurements were polished and Ag paste (Leit silber 200, Hans Wolbring GmbH) \nelectrodes were painted and fired. The Cp(T,f)  and G(T,f)  was measured with a use of a \nHP4263B LCR meter. The effective quantities ε’(T) , tan δ(T) , and σ(T)  were evaluated \nassuming a standard dielectric capacitor model. Temperature  was varied within the range  \n290 ÷ 700 K, at a rate ±3 K/min.  \n \n3. RESULTS AND DISCUSSION \n3.1 Magnetic properties \nThe magnetization dependence on temperature M(T) for BiFeO 3 sample studied for the \napplied magnetic field µ0H = 1 T is shown in Figure 1. The magnetization curves me asured \nafter zero field cooling (ZFC) and after field cooling (F C) in the field µ0H = 1 T are exactly \nthe same which proves that there irreversible processes  in the sample are negligible. This  5observation is in contradiction to the results presen ted in a work of Singh et al. [10] who \nreported substantial irreversibility between ZFC and FC magnetization for the same applied \nmagnetic field value as in our case. They explained this irreversible effect in terms of spin-\nglass behavior.  \nThe magnetization M(T)  rapidly decreases on heating in the low temperature ran ge (2 K ÷ \n∼50 K), it exhibits a plateau within a range 50 K ÷ 150 K, and it gradually increases at higher \ntemperatures (150 K ÷ ∼640 K). This type of M(T) dependence is consistent with the previous \nreports [10, 24, 25]. The maximum in M(T) observed in the low temperature range cannot be \nexplained in terms of changes in population or domain reorien tations because no sudden \nchanges in domain structure occur at this temperature range [ 24]. Hence, we deduce that the \nmarked decrease in the M(T)  value within the low temperature range results from sma ll \namounts of ferromagnetic contaminations.  \nThe AC susceptibility measurement, shown in Fig. 2, confi rms the magnetization \nmeasurement result, i.e. the real part of susceptibilit y χ'(T) is identical to magnetization \ndependence on temperature M(T). The values of the imaginary part χ“(T) are too low to \ndeduce any conclusions. However, this observation once a gain proves that the irreversible \nmagnetization mechanisms are absent in our sample.  \nFigure 3 presents several magnetization loops M(H) obtained for the BiFeO 3 ceramics, \nrecorded for chosen temperatures from 4 K to 300 K range. The y exhibit no magnetic \nirreversibility in agreement with ZFC-FC magnetization and AC measurements, and almost \nthe linear dependence of magnetization M(H) on the applied magnetic field (-2T< µ0H< +2T). \nSuch behavior of magnetization is consistent with the antiferromagnetic ordering in bismuth \nferrite [26-29].  \nSignificant results of magnetometric measurements appea r in the high temperature range, \nclose to the Néel temperature, at the transition to pa ramagnetic state, which are shown in  \nFig. 4. The magnetic moment M(T) increases with temperature and exhibits a marked peak \nascribed to the phase transition temperature. The phase t ransition occurs at TN = 646 K (when \nmeasured in the middle of the magnetization maximum) and its width is 8 K. The behavior of \nthe magnetization near the Néel temperature TN can be explained in terms of changes in ratio \nof the population of the in-plane magnetic domains to th e out-of-plane ones. It has been \nreported that this ratio decreases rapidly from almost constant value equal to 1.6 in a wide \ntemperature range to about 1.0 near the AFM phase transi tion and can be related to a strong  6increase in the magnetization [24]. In our case, the ra tio value by which the magnetization \ndrops at the Néel temperature is equal to 1.4 that seems to  be comparable to the literature \nreport change in ratio of the populations of domains which is 1.6.  \nTwo magnetization curves vs. magnetic field M(H) obtained at temperature 304 K and \n577 K are shown in Fig. 5. For the temperature equal to 304 K,  the M(H) exhibits the \nnonlinearity in a very narrow field range when the µ0H value  is  close to zero. Then, the M(H)  \nincreases linearly when the magnetic field increases an d finally the M(H)  deviates from linear \ndependence above a field Ha (noted in Fig. 5). Another dependence occurs in the M(H) curve \nrecorded for temperature equal to 577 K. Neglecting the low m agnetic fields close to zero, the \nmagnetization increases linearly. It exhibits non-line ar changes in the intermediate field range, \ni.e. between the fields Ha (i.e. anharmonic) and Hc (i.e. critical), and it increases once again \nlinearly at high fields above Hc.  \nKadomtseva et al. [30] proposed to interpret the origin of  the field Hc followed by the \nlinear M(H) magnetization in high magnetic field in terms of the f ield induced phase \ntransitions. Namely, at low magnetic fields the spi n cycloid is nearly circular (Fig. 6a), at \nintermediate fields the cycloid becomes anharmonic due t o interaction of spins system with \nthe magnetic field (Fig. 6b), and at high fields H > Hc there is a transition to the homogeneous \nspin order (Fig. 6c). Therefore, in the field strong en ough, H > Hc, the system of spins in the \ncycloid is aligned with magnetic field direction and exhi bits a linear magnetization. Such a \ntransition has been already observed in magnetization, dielectric and ESR investigations [25, \n30-33]. We assume that, for the room temperature, the Hc appears in too high magnetic fields \n(estimated as about 15 T) to be recorded by PPMS System equi pped with 9 T magnet, that \nexplains the absence of this transition in M(H) curve measured at 304 K.  \nThe temperature dependence of the magnetization M(H) is related to the cycloidal order of \nFe spins and has been already modeled by Kadomtseva et al. [30] and by Popov et al. [33].  \nIn the case of the field applied in [001] c direction, the component of the magnetization \nM[001] (H) along the field is as follows [30]: \n \n ( )\nλ λSθ Hχ Hχθ M H M2sin sin ⊥ ⊥+ + =31\n32\n001 001 ][][   (1) \nwhere θ is the angle between antiferromagnetic vector and t he vector of the spontaneous \nmagnetization Ps (hexagonal c-axis or cubic [111] c direction).   7For the low magnetic fields we have <sin θ>λ ≈ 0, and <sin 2θ>λ ≈ ½, hence  M [001] (H) \ntakes the form M[001] (H) = 5/6 χ⊥H dependence. Above the critical field Hc, the spin cycloid \ndisappears and homogeneous magnetic ordering is established,  which corresponds to  \n<sin θ>λ ≈ 1, <sin 2θ>λ ≈ 1, and the eq. (1) transforms to M = MS\n[001] +χ⊥H [30].  \nThe mean magnetization of the polycrystalline sample 〈M(H)〉 along magnetic field, i.e. in \nour case measurement, is obtained from average of eq. (1) taken over all orientations of the \napplied magnetic field H with respect to Ps vector of each individual crystalline grain, \ntherefore: 〈M(H)〉=2/ πM[001] (H).  \nIt has been observed and reported that the model equation ( eq.1) roughly fitted \nexperimental data for single crystals of BiFeO 3 [30, 34]. The identical disagreement is visible \nin Fig. 5, which shows magnetization data for the ceramic,  polycrystalline BiFeO 3 sample. \nThe following values of parameters: µ0Hc = 8.25 T, χ⊥ = 1.28 10 -5 emu/g·Oe, Ms = 0,199 \nemu/g has been obtained with the best numerical fitting procedure. These values can be \ncompared to the values of parameters determined for the si ngle crystal: µ0Hc ≈ 20 T, χ⊥ ≈ 0,6 \n10 -5 emu/g·Oe, and Ms ≈ 0,25 emu/g [35]. However, our measurements were performed at \nmuch higher temperature T = 577 K than in the case of the single crystals, which we re \ninvestigated at T = 10 K [35]. At high temperature as in our case one can ex pect that the \ncritical field Hc and the spontaneous magnetization Ms decreases but the susceptibility χ⊥ \nincreases because of the lower “stiffness” of the spin c ycloid. The increased value of χ⊥ at the \nhigh temperature corresponds also well to the rise of m agnetization observed close to the Neel \ntemperature at the AFM-PM transition (see Fig. 4).  \nThe discrepancy between the model eq. 1 and the experimen tal data are much more \nevident in Fig. 7.  The deviation from linearity ∆M was obtained after subtraction of the linear \npart M = 5/6 χ⊥H from the experimental data and from the fit data, res pectively, (drawn as the \nblack line in Fig. 5). Moreover, it is clear that the linea r section in M(H) data recorded for 577 \nK, which extends from 0 to 1.9 T, is a few times longer than the linear part of the fit covering \nrange from 0 to 0.5 T. Therefore we deduce that the model e quation (eq.1) is correct for the \nintermediate field range. On contrary, for the low fi elds there probably exists another \nmechanism or a different energy barrier for spin reor ientations that stabilizes the spin cycloid. \nHowever, the exact nature of this field-induced transiti on is unknown. In case of the \nmeasurement carried out at 577 K, a deviation of the ∆M experimental data from linear \ndependence appears above the field Ha which means that the spin-cycloid starts to be  8anharmonic (Fig. 6.b) leading to a nonlinear magnetization. Thus we deduce that magnetic \nfield induces the following sequence of the transitions: in low field there is the circular spin-\ncycloid and BiFeO 3 compound exhibits the linear magnetization on the applied f ield; above \nthe field Ha the spin cycloid becomes anharmonic which causes the no nlinear magnetization \nand above the field Hc almost all spins are aligned according with field direc tion and the \nsystem once again exhibits the linear magnetization M(H).  \nThe measurements of M(H) magnetization curves and the anomalies taking place at Hc \nand Ha for various temperatures allowed us to propose the diagra m presented in Fig. 8. \nCompared to the previous report by Tokunaga et al. [31] this dia gram contains data from \nmagnetization measurements close to TN and the additional line Ha(T) associated probably \nwith field-induced transformations of the cycloid. In the  diagram, Hc(T) and Ha(T) lines \nseparate different regimes in the spin arrangements rel ated to the circular, the anharmonic and \nthe homogeneous spin order.  \nHowever, the diagram proposed by us and the exact mechanis m of the field-induced \ntransition taking place at Ha needs both experimental confirmation by means of various \ntechniques (for example EPR, NMR and neutron diffraction ) and also theoretical studies.  \nSo far, neutron diffraction experiments were performed at zero magnetic field for which the \nspin system exhibits the circular cycloid order in a who le temperature range. The same \nproblem occurs in NMR measurements [36-38] performed in absenc e of an applied magnetic \nfield because only the circular cycloid order is tested in this case. On the other hand, the EPR \nspectra recorded by Ruette et al. [32] in the wide magnetic field range (0-25 T) reveal a \ncomplex structure with few anomalies. Unfortunately, t hese authors have not analyzed the \nlow-field anomaly, which could correspond to the possible  transition from the circular to \nanharmonic spin order suggested by us. \n \n3.2 Crystal structure and thermal lattice expansion \nThe analysis of X-ray diffraction of the sample of B FO ceramics preserved the \nrhombohedral (space group R3c ) in accord to literature data [4]. This symmetry remain s \nunchanged in the wide range of temperature, from 300 K up to 900 K. The X-ray pattern of \nthe BFO obtained at room temperature is shown in Fig. 9. In addition to the main phase, \ntraces of impurities are observed (noted by asterisks in Fig. 9). This impurity has been \nidentified as Bi 2O3. The content of this precipitation is about 4 %, est imated from the formula:  9() ( )T Tσ TσB akEexp 1\n0−= \n(2) \n \nwhere Iprec  and IBFO  denote the most intensive lines belonging to the precipi tation phase and to \nthe main phase spectra, respectively. The relative volum e expansion of the cell within the \ntemperature range 300-900 K estimated, as ( ∆V/V0)·100 % ≈ 2 % is quite small. One can see \nin Fig. 10 that increase of the lattice parameter a is insignificant since the relative expansion \n(∆a/a0)·100 % ≈ 0.08%, while the lattice constant c changes markedly ( ∆c/c0)·100 % ≈0.8%. \nIt indicates that lattice parameter c is mainly responsible for expansion of the unit cell. T here \nis no structural anomaly in vicinity of the magnetic AF M-PM phase transition occurring at TN. \nHowever, one can distinguish a slight change in the rat e of the crystal lattice expansion \n(∆c/c0). This structural transformation corresponds to the appea rance of the magnetic phase \ntransition in BFO (see Fig. 4).  \n \n3.3 Electrical properties \nThe effective dielectric permittivity ε’(T,f)  (Fig. 11.a) and the dielectric loss coefficient \ntan δ(T,f)  (Fig. 11.b), show slight anomalies in vicinity of the t emperature TN where the \ntransition between the AFM and PM phases occur. The ε’(T,f)  increases markedly in the high \ntemperature range, i.e. above the temperature TN where the magnetic transition exists.  \nThe dielectric loss coefficient value varies from ab out tan δ  ≈1 at room temperature that \nremains in agreement with literature data [13] and reaches  tan δ~100 in the 650-700 K range. \nMoreover, the ε’(T)  and tan δ(T)  exhibit dispersion in the whole temperature range  \n(300-700 K).  \nThe ac electric conductivity σ(T,f=100Hz)  (Fig.12.a) temperature dependence is shown in \nthe Tσ vs.  T-1 plot, according to the small polaron model proposed for the BiFeO 3 [18, 19]: \n \n(3) \n \nThe small polaron dependence (eq.3) is fulfilled below th e temperature TN (see straight-\nline segment in Fig. 12.a). One can distinguish a change i n the slope of the electric \nconductivity plot in vicinity of the magnetic phase trans ition TN temperature and the Tσ(T -1) ( )BFO prec prec I I Ic + = 10 curve deviates from the presumed dependence above the  TN (Fig. 12.a). However it should be \nnoted, that the thermally activated dependence, i.e. σ ~T-1 did not also fit the conductivity \nwithin this temperature range.  \nHence, the derivative d(ln(Tσ))/ d(T-1) was calculated (Fig. 12.b). The horizontal part of \nthe plot visible in the temperature range below ~640 K and  above ~670 K confirms the small \npolaron mechanism of the electric conduction described wi th the formula (3). Therefore, the \nestimated activation energy equals to Ea = 0.81 eV below TN. One can estimate Ea ≈ 0.54 eV \nabove 670 K, when assuming the small polaron model is sati sfactorily approximated in the \nhigh temperature range.  \nThe steep change in the d( ln(Tσ))/d(T -1) value occurs within a several degrees range and \nthe minimum in this plot anomaly occurs at TA = 650 K. This anomaly in the electric \nconduction temperature dependence corresponds to the anomali es in the dielectric permittivity \nε’(T)  and tan δ(T) , which occur within the 640-660 K range. Moreover, both the di electric \npermittivity and the dielectric loss coefficient tan δ(T,f)  show dispersion. Such effects \nindicates an existence of the electric charge carriers,  or space charge subsystem. Hence, the \nthermally generated charge carriers contribute to the m easured values of the Cp(T,f)  and G(T,f)  \nquantities. Therefore we deduce that the anomaly in the electric properties, which manifest \nwithin the 640-660 K range, corresponds to the anomaly in the ma gnetic properties, which \noccur in the vicinity of TN = 646 K (compare Figs 11 and 12 to Fig. 4).  \nOn the other hand, the magnetic phase transition, ma nifested by the magnetization M(T)  \npeak detected near the Néel temperature occurring within sever al degrees i.e. TN ±8 K range \n(Fig. 4), corresponds to a lack of structural, or crysta l lattice parameters, and anomaly in this \nrange. However, it worthwhile to note that a smooth chan ge in the thermal expansion can be \ndiscerned (see Fig. 10). Hence, concerning the multiferroic  features of the BiFeO 3 there is no \ndirect interaction between the ferromagnetic and ferro electric ordering that would lead to the \nmulti-ferroic phase transition at the same critical  temperature, since the values of TN = 646 K \nand TC = 1143 K are different.  \nWe propose to ascribe the detected coincidence, between the magnetic and electric \nanomalies in vicinity of the Néel temperature TN in the BiFeO 3, to the contribution of the \nelectric charge carrier subsystem. This effect can be described using the chemical potential \napproach [39, 40]. The possibility to register kinks in the te mperature dependence of the \nconductivity of the investigated sample is a consequence o f the chemical potential critical  11 behaviour. The thermodynamic equilibrium condition requi res that the chemical potentials of \nthe sample µs and the chemical potential of the electrodes µe, which are attached to enable the \nelectrical measurement should be equal µs = µe. It has been shown [39, 40] that the chemical \npotential of a solid state material exhibits critical be haviour in the case of second order phase \ntransitions. Therefore, the critical behaviour of the  chemical potential µs, related to the \nmagnetic phase transition, should influence the flow of  the electron gas in the electrode-\nsample-electrode system, when the electric conduction temperature dependence is measured. \nThis is due to the fact that the chemical potential ent ers the theoretical Kubo formula [41] for \nthe electrical conductivity. Consecutively, the change in the activation energy value reflects \nthe transformation in the electronic structure when the  phase transition between the \nferromagnetic and the paramagnetic phases occurs in th e BiFeO 3. Hence, the observed \ncorrespondence can be ascribed to the electronic subsystem and chemical potential features \nhowever a detailed discussion needs further studies. \n \n4. CONCLUSIONS \nTo summarize, we report on the magnetic and dielectric measurements of the properties of \nthe hot-pressed BiFeO 3 ceramic.  \nIn magnetic properties, behavior of this sample is simi lar to that one exhibited by several \nsingle crystals [24] with negligible irreversible process es and the almost identical \nmagnetization dependence on temperature M(T) and hysteresis loops M(H). Near the Néel \ntemperature TN = 646 K there appears a pronounced jump in a magnetic moment,  which is \nfound in single crystals also [24]. The reason for this  feature is still unknown.  \nIn the low magnetic field range there is an anomaly i n  M(H) , probably due to the field-\ninduced transition from circular cycloid to the anharmonic  cycloid. Some evidence for such \ntransition in the form of low-field anomaly can be fo und also in the report by Ruette et al. [32] \non EPR measurements but it was not analyzed and explaine d yet. At high field limit we \nobserve the field-induced transition to the homogeneous spi n order [25, 30, 33]. Therefore, we \npropose possible H-T diagram of the magnetic order in the bismuth ferrite,  which contains the \ncycloidal, anharmonic and homogeneous magnetic orders. We s uggest that magnetic field \ninduces the following sequence of the transitions: (1) at low  field there is a circular spin-\ncycloid and BiFeO 3 compound exhibits the linear magnetization on the applied field \ndependence; (2) above the field Ha the spin cycloid becomes anharmonic which causes  12 nonlinear magnetization, and (3) above the field Hc almost all spins are aligned according \nwith the field direction and the system once again exhibi ts linear magnetization M(H). This \nproposal however, ought to be confirmed by other experimen tal methods and explained \ntheoretically. \nThe anomalies in the electric properties, ε’(T) , tan δ(T) , and σ(T) , which are manifested \nwithin the 640-680 K range, coincide to the anomaly in the magn etization M(T)  dependence, \nwhich occurs in the vicinity of TN = 646 K. We propose to ascribe this coincidence to the \ncontribution of the electric charge carriers subsyste m. This effect in the BiFeO 3 material can \nbe described using the chemical potential formalism since  the critical behaviour of the \nchemical potential µs, related to the magnetic phase transition.  \n \nAcknowledgements \nThis project has been founded by National Science Centre  (project No. N N507 229040).  \nThe discussion with dr. A. Rachocki from Institute of  Molecular Physics PAN is kindly \nacknowledged. \n  13 REFERENCES \n[1]  G. Smolenskii, V. Yudin, E. Sher, Y. E. Stolypin,  Sov. Phys. JETP, 16 , 622, (1963). \n[2]  M. Fiebig J. Phys. D: Appl. Phys,. 38 , R123-R152, (2005).  \n[3]  A.M. Kadomtseva, Yu.F. Popov, A.P. Pyatakov, G.P.  Vorobev, A.K. Zvezdin,  \nD. Viehland, Phase Transit., 79 , 1019-1042, (2006).  \n[4]  D. Lebeugle, D. Colson, A. Forget, M. Viret, P. B oville, J.F. Marucco, S. Fusil, Phys. \nRev. B, 76 , 024116-1-8, (2007). \n[5]  T. Choi, S. Lee, Y.J. Choi, V, Kiryukhin, S.-W. Ch eong, Science, 324 , 63-66, (2009).  \n[6]  J. R. Teague, R. Gerson, W. J. James, Solid State Commun., 8, 1073, (1970). \n[7]  I. Sosnowska, T. Peterlin-Neumaier, E. Steichele , J. Phys. C: Solid State Phys, 15,  \n4835, (1982). \n[8]  M. Ramazanoglu, M. Laver, W. Tatcliff II, S. M. Watson, W. C. Chen, A. Jackson,  \nK. Kothapalli, Seongsu Lee, S.-W. Cheong, V. Kiryukhin, Phys.  Rev. Lett., 107 , \n207206 (2011). \n[9]  Yu. F. Popov, A. M. Kadomtseva, A. K. Zvezdin, G. P. Vorob’ev, and A. P. Pyatakov, \nMagnetoelectronic Phenomena in Crystals, M. Fiebig, V. V. Eremenko, I. E. Chupis \nEd., (Kluwer Academic, Boston 2004), p. 277. \n[10]  M. K. Singh, W. Prellier, M. P. Singh, R. S. Kat iyar, J. F. Scott, Phys. Rev. B, 77,  \n144403 (2008). \n[11]  A. Lubk, S. Gemming, N.A. Spalin, Phys. Rev. B, 80 , 104110, (2009). \n[12]  C. Ederer, N. A. Spaldin, Phys.Rev. B, 71 , 224103, (2005).   \n[13]  M. Kumar, K.L. Yadav, G.D. Varma, Materials Lett . 62 , 1159-1161, (2008).  \n[14]  Z.H. Chi, C.J. Xiao, S.M. Feng, C.Q. Jin, X.H. Wa ng, R. Z. Chen, L.T. Li, J. Appl. \nPhys. 98 , 103519, (2005).  \n[15]  S.J. Clark, J. Robertson, Appl. Phys. Lett. 90 , 132903, (2007).   14 [16]  A.J. Hauser, J. Zhang, L. Mier, R.A. Ricardo, P.M.  Woodward, T.L. Gustafson,  \nL.J. Brillson, F.Y. Yang, Appl. Phys. Lett. 92 , 222901, (2008). \n[17]  Y.-K. Jun, W.-T. Moon, Ch.-M. Chang, H.-S. Kim, H.  S. Ryu, J. W. Kim, K. H. Kim, \nS.-H. Hong, Solid St. Commun., 135 , 133-137 (2005). \n[18]  R. Mazumdar, S. Ghosh, P. Mondal, D. Bhattacharya,  S. Dasgupta, N. Das, A. Sen, \nA.K. Tyagi, M. Sivakumar, T. Takami, H. Ikuta, J. Appl. Phys., 100 , 033908, (2006).  \n[19]  S. Hunpratub, P.Thongbai, T. Yamwong, R. Yimnirun, S.  Maensiri, Appl. Phys. Lett., \n94 , 062904, (2009). \n[20]  Y.-H. Lee, J.-M. Wu, and C.-H. Lai, Appl. Phys. Let t., 88 , 042903, (2006). \n[21]  D. K. Pradhan, R. N. P. Choudary, C. Rinaldi, R. S . Katiyar, J. Appl. Phys., 106 , \n0241102, (2009).  \n[22]  R. Bujakiewicz-Koro ńska, Ł. Hetma ńczyk, B. Garbarz-Glos,A. Budziak, J. Koro ński,  \nJ. Hetma ńczyk, M. Antonova, A. Kalvane, Ferroelectrics, 417 , 63-69, (2011).  \n[23]  J.Rodrigues-Carvajal, FullProf.2k Ver.4.7, ILL, 2010, \nhttp://www.ill.eu/sites/fullprof/php/programs.httml \n[24]  M. Ramazanoglu,  W. Ratcliff II,  Y. J. Choi,  Seongsu Lee,  S.-W. Cheong,  V. Kiryukhin, \nPhys. Rev. B, 83 , 174434, (2011). \n[25]  G. Catalan, F. Scott, Adv. Mater., 21, 2463, (2009). \n[26]  S. V. Kiselev, R. P. Ozerov, G. S. Zhdanov, Sov.  Phys.-Dokl., 7, 742, (1963). \n[27]  C. Blaauw and F. van der Woude, J. Phys. C: Solid Sta te Phys, 6,  1422, (1973). \n[28]  J-M. Moreau, C. Michel, R. Gerson, and W. James, J. Phys. Chem. Solids, 32  1315, \n(1971). \n[29]  I. Sosnowska, T. Peterlin-Neumaier, E. Steichele , J. Phys. C: Solid State Phys., 15 , \n4835, (1982). ] \n[30]  A. M. Kadomtseva, A. K. Zvezdin, Y. F. Popov, A. P. Pyatakov, G. P. Vorob’ev, JETP \nLett., 79 , 571, (2004).  15 [31]  M Tokunaga, M Azuma, and Y Shimakawa, Journal of Physics : Conference Series, 200, \n012206, (2010). \n[32]  B. Ruette, S. Zvyagin, A. P. Pyatakov, A. Bush, J.  F. Li, V. I. Belotelov, A. K. Zvezdin, \nD. Viehland, Phys. Rev. B, 69 , 064114, (2004). \n[33]  Yu. F. Popov, A. K. Zvezdin, G. P. Vorob’ev, A. M. Kadomtseva, V. A. Murashev,  \nD. N. Rakov, JETP Lett., 57 , 69, (1993). \n[34]  A. K. Zvezdin, A. M. Kadomtseva, S. S. Krotov, A .P. Pyatakov, Yu. F. Popov,  \nG. P. Vorob’ev, J. Magn. Magn. Mater., 300 , 224–228, (2006). \n[35]  Yu. F. Popov, A. M. Kadomtseva, A. K. Zvezdin, G.  P. Vorob’ev, A. P. Pyatakov, \nMagnetoelectronic Phenomena in Crystals, M. Fiebig, V. V. Eremenko, I. E. Chupis \nEd., (Kluwer Academic, Boston 2004), p. 277 \n[36]  A. V. Zalesskii, A. A. Frolov, A. K. Zvezdin, A . A. Gippius, E. N. Morozova,  \nD. F. Khozeev, A. S. Bush, V. S. Pokatilov, JETP 95 , 101, (2002). \n[37]  A. V. Zalesskii, A. K. Zvezdin, A. A. Frolov, A.  S. Bush, JETP Lett.,  71 , 465, (2000). \n[38]  A. A. Gippius, D. F. Khozeev, E. N. Morozova, A. V. Zalessky, Phys. Stat. Sol. (a), \n196 , 221–224, (2003). \n[39]  M. Matlak, A. Molak, M. Pietruszka, Phys. Stat. Sol.  (b), 241 , R23–R26, (2004). \n[40]  M. Matlak, A. Molak, M. Pietruszka, and A. Ślebarski, phys. stat. sol. (b) 242 , 461–462, \n(2005). \n[41]  R. Kubo, J. Phys. Soc. Jpn., 12 , 570, (1957).  16 FIGURE CAPTIONS \nFig. 1 ZFC and FC magnetization dependence on temperature M(T) recorded for the applied \nmagnetic field µ0H = 1 T. \n \nFig. 2 Real χ’ and imaginary χ” components of magnetic susceptibility measured for AC \nmagnetic field at amplitude Hac =3 Oe and frequency f = 1000 Hz.  \n \nFig. 3 Antiferromagnetic hysteresis loops recorded for seve ral temperatures: 4, 50, 100, 200, \nand 300 K.  \n \nFig. 4 Magnetization peak showing a maximum which occurs nea r the Neel temperature  \nTN  = 646 K ( TN value has been determined at the half of the maximum ampl itude).  \n \nFig. 5 Magnetization dependence vs. magnetic field M(H)  for two chosen temperatures 304 \nand 577 K. Ms is the spontaneous magnetization extrapolated from high- field range, denoted \nwith a dashed line. Hc is the critical field. The solid lines represent the be st fits to the linear \nregimes occurring in the low field.  \n \nFig. 6 The magnetic order in the spin cycloid. (a) the c ycloid is: circular for low fields; (b) the \ncycloid becomes anharmonic in the intermediate fields ab ove Ha field; (c) the cycloid is \ndestroyed above the critical field Hc, and the homogeneous order is established. Ps denotes \nhere the vector of electric spontaneous polarization a nd q the propagation vector of the \ncycloid.  \n \nFig. 7. Experimental data and the fit within the model equat ion (eq.1) after the subtraction of \nthe linear part of the magnetization characteristic f or the low field range. The Ha denotes the \ntransition field to the anharmonic order and the Hc the critical field and transition to the \nhomogeneous order.  \n  17 Fig. 8 The proposed H-T diagram for the magnetic order wit hin the spin cycloid.  \n \nFig.9. The XRD pattern of the BiFeO 3 ceramics at 300 K. \n \nFig.10. Lattice parameters a and  c of BiFO 3 vs. temperature. \n \nFig.11. (a) The dielectric permittivity temperature dependence  ε’(T)  measured at f = 0.10, \n0.12, 1, 10, 20, and 100 kHz. (b) The dielectric loss coefficien t tan δ(T,f)  shown in vicinity of \nthe magnetic phase transition temperature TN = 646 K.  \n \nFig 12. (a) The electric conduction dependence Tσ vs. T -1 plotted according to the assumed \nsmall polaron model. (b) The electric conductivity deriva tive d(ln (Tσ))/d(T -1) plot, the \nhorizontal straight-line segments indicate the ranges proper for evaluation of the activation \nenergy value.  18 Figures  \n0 50 100 150 200 250 300 350 400 0,03 0,06 0,09 0,12 \n  M (emu/g) \nT (K)  ZFC \n FC µ0H=1 T \n \nFig. 1  \n0 50 100 150 200 250 300 350 400 -3 036912 \n  \nHac =3 Oe \nf=1000 Hz \nχ (emu/g*Oe) x 10 -6 \nT (K)  χ'\n χ\"\n \nFig. 2 \n  19  \n-2 -1 0 1 2-0,20 -0,15 -0,10 -0,05 0,00 0,05 0,10 0,15 0,20 \n  M (emu/g) \nµ0H (T)  4K \n 50K \n 100K \n 200K \n 300K \n \nFig. 3 \n300 400 500 600 700 800 900 0,05 0,06 0,07 0,08 0,09 0,10 \n  M (emu/g) \nT (K) TN=646 K µ0H=1 T \n \nFig. 4 \n  20 0 2 4 6 8 10 0,0 0,2 0,4 0,6 0,8 1,0 \nHa\nHa\n  M (emu/g) \nµ0H (T)  304 K \n 577 K \nMsHc\n \n \nFig. 5  \n \n \nFig. 6 \n \n  21 0 2 4 6 8 10 -0,02 0,00 0,02 0,04 0,06 0,08 0,10 \nHa\n  \n304 K \n577 K \n  fit \n∆M (emu/g) \nµ0H (T) HaHc\n \nFig. 7 \n \n0 10 20 30 40 300 400 500 600 700 800 0246810 12 \nhomogeneous \norder \nanharmonic cycloid \n  \nµ0H (T) \nT (K)  Ha\n Hc\ncircular cycloid \n \nFig. 8  22  \n20 40 60 80 100 0900 1800 \n(101)                  \n(012)                  \n(104) (110)              \n(015)                   (021) \n(202)                  \n(024) (205) (211)                  (116) (122)                  (214)                  (300) \n009                  (303) (208) (220)                  \n(119) (131)                  (306) (312)                  \n(128) (134)                  \n(111) (315)                  (401) (226)                  (042) \n(137)                  (045) (232) \n(318)                  (324) \n407                  (235) \n  Intensity (count) \n2 θ (deg) T = 300 K \nSG: R3C \n \nFig 9. XRD pattern of the BiFeO 3 ceramics, obtained at  300 K \n \n \n \nFig.10 Lattice parameters of BiFO vs.  temperature  23  \n \nFig. 11.(a) and (b) \n \n \n \nFig. 12.(a) and (b) \n "    },    {        "title": "1205.3528v3.Probing_the_Interplay_between_Quantum_Charge_Fluctuations_and_Magnetic_Ordering_in_LuFe2O4.pdf",        "content": "1 \n Probing the Interplay between Quantum Charge Fluctuations \nand Magnetic Ordering in LuFe 2O4 \nJ. Lee1*, S. A. Trugman1,2, C. D. Batista2, C. L. Zhang3, D. Talbayev4,  X. S. Xu5, S. – W. \nCheong3, D. A. Yarotski1,  A. J. Taylor1, and R. P. Prasankumar1# \n1Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, NM 87545  \n2Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545  \n3Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, \nPiscataway, NJ 08854  \n4Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118  \n5Oak Ridge National Laboratory, Oak Ridge, TN 37831 \n*Email: kjindda@naver.com   \n#Email: rpprasan@lanl.gov  \n \nFerroelectric and ferromagnetic m aterials possess spontaneous electric and magnetic  order , \nrespectively, which can be switched by  applied electric and magnetic  fields. Multiferroic s \ncombine  these properties in a single material, providing an avenue for controlling electric \npolarization wi th a magnetic field and magnetism with an electric field. These materials \nhave been intensively studied in recent years, both  for their fundamental scientific interest \nas well as  their  potential applications in a broad range of magnetoelectric devices [ 1, 2, 3, 4]. \nHowever, the m icroscopic origins of magnetism and ferroelectricity are quite different,  and \nthe mechanism s producing  strong coupling between them are not always well  understood.  \nHence, gaining  a deeper understanding of magnetoelectric coupling in  these materials is  the \nkey to their rational design. Here, we use ultrafast optical spectroscopy to show that the \ninfluence  of magnetic o rdering on quantum charge fluctuations via the double -exchange \nmechanism can govern the interplay between electric pol arization and magneti sm in the \ncharge -ordered multiferroic LuFe 2O4.  2 \n Recently, the iron -based multiferroic LuFe 2O4 has attracted much attention because it exhibits \nmagnetoelectric coupling close to room temperature [5 ~21]. The unique layered structure of \nLuFe 2O4 consists of double layers of Fe ions connected in a triangular lattice in the ab- plane \n(Figure 1(a)) [ 14].  The  average valence of Fe ions is Fe2.5+, with Fe2+ and Fe3+ ions occupying  \nequivalent sites in different layers with equal densities. The corresponding spin values are S=2  \n(Fe2+) and S=5/2 (Fe3+), with the spin structure shown in Figure 1(b) [ 15,16].  A simple \ndescri ption based on nearest -neighbour interactions between Fe ions leads to the characterization \nof this material as a spin and charge frustrated system [5, 17 ]. Bulk ferroelectricity was observed \nbelow the charge ordering temperature, T CO~ 320 K, resulting in a spontaneous electric \npolarization that further increased upon the appearance of ferrimagnetic spin order below the \nNeel temperat ure, TN~240 K  [5]. Ferroelectricity in each bilayer is thus induced by electronic  \ncharge ordering, although the stacking of adjacent bilayers (i.e., in an antiferroelectric or ferroelectric arrangement) is still controversial [ 11,12,15,18].   Regardless, in  each bilayer, the \nelectric polarization P  is coupled to the magnetic degree s of freedom in LuFe\n2O4, but a \ncomprehensive understanding of the mechanism underlying this magnetoelectric coupling has eluded researchers to date. Knowledge of this mechanism cou ld potentially allow researchers to \noptimize both the strength of this coupling and its operating temperature to address the general goal of developing multiferroic materials with strong magnetoelectric coupling at room temperature.  \n Theoretical studies have linked the magnetoelectric coupling in LuFe\n2O4 to both thermal [ 19] \nand quantum [ 20, 21] charge fluctuations. In general, magnetic ordering can modify the effective \nhopping amplitude between two ions via the well -known double -exchange mechanism [ 20~23 ], 3 \n in which hopping is governed by  the angle between the two core spin s, as shown in Figure 1(b).  \nThis change in the hopping amplitude will necessarily affect the quantum fluctuations of any \ncharge ordered state of electronic origin . The corresponding change  in charge ordering will \nnecessari ly modify P. In other words , if electronic charge ordering leads to a net electric \npolarization, the value of P  should be modified by the presence of magnetic ordering ( Figure \n1(b)). Moreover, if the magnetic ordering redu ces (on average) the effective hopping amplitude, \nthe corresponding suppression of quantum charge fluctuations leads to an increase of P below TN. \nSince the same mechanism should affect optically induced charge fluctuations , we use \nfemtosecond optical pump- probe spectroscopy, which has been extensively used to shed light on \nthe properties of correlated electron materials [ 24~31, to directly photoexcite and probe the \nFe2+→Fe3+ charge transfer channel in LuFe 2O4. Then, by varying the temperature T above and \nbelow TN, we can shed light on the role of these fluctuations in governing the coupling between \nspin and charge order in a single LuFe 2O4 bilayer, regardless of whether the bilayers are stacked \nferroelectrically or antiferroelectrically. We find that the in terlayer hopping matrix element \ndescribing these fluctuations depends strongly on their local core spin alignment via the double -\nexchange mechanism, making charge delocalization (in real space, as shown in Figure 1(b)) and hence the electric polarization extremely sensitive to the spin structure evolution over a broad temperature range. Therefore, although magnetoelectric coupling in various multiferroic materials has been studied using many different techniques [ 32], to the best of our knowledge, \nthis is the first experimental evidence of magnetoelectric coupling mediated by  the double -\nexchange mechanism in an insulator . \n 4 \n We begin by developing a model for electronic hopping between two atomic sites, governed by \nthe double exchange mechanism, which shows that the transition rate (i.e., charge transfer rate) between the ground and the excited state induced by an external driving electromagnetic field is \nproportional to the effective hopping matrix, t\nij2, according to  the Fermi Golden rule [ 33], as \ndescribed i n the M ethod s section . Furthermore, the amount of delocalized charge δq is \nproportiona l to t ij2, 2)(∆=δijtq , where Δ is the energy difference between the ground and excited \nstates. This simple observation establishes our ability to probe quant um charge fluctuations \nbetween two atomic sites using optical spectroscopy (see Methods for more detail). In LuFe 2O4, \nthese fluctuations are due to charge transfer between Fe2+ and Fe3+ ions (as revealed by optical \nspectroscopy [ 34] and band structure calc ulations [ 19]). We can consider four different charge \ntransfer channels  in the bilayer crystal structure of LuFe 2O4,: interlayer charge transfer from the \nFe2+ rich bottom layer to the Fe3+ rich top layer (E ↑) or from the top to the bottom layer ( E↓), and \nintralayer charge transfer within the top layer (E t→) and within the bottom layer ( Eb→), as shown \nin Figure 1(a). We can gain insight on the relative energies of these different charge transfer \nchannels by c onsidering the Coulomb energy between Fe ions in the Hamiltonian,  \n∑επε=\n)( 0 4ij ij rz\njz\ni\nVrQQ\nH ,        (1)  \nwhere the pseudospin operators Qiz\n and Qjz are 1/2 or - 1/2 for Fe3+ or Fe2+, respectively, and \n0ε,rε and ijrare the permittivity of free space, the relative permittivity and the distance between \nsites i and j, respectively. Considering only the largest three interaction terms, we find that E↑ \nhas the lowest excitation energy, E t→ and Eb→ have intermediate excitation energies, and E ↓ has \nthe highest excitation energy. T he interlayer transitions can be distinguished by noting that  the 5 \n bottom layer is rich in Fe2+ while the top layer is rich in  Fe3+. It is clear that if the top layer has a \npositive  charge density σ >0 per unit area, the bottom layer must have the opposite  charge density , \n–σ, to ensure charge neutrality. E↓ increases with  σ while  E↑ decreases, so it is reasonable  to \nassume that  E↓ >>E↑ in LuFe 2O4.  We can also distinguish the intralayer transitions by noting \nthat the configuration of in- plane oxygen ions around Fe ions in both layers leads to a higher in-\nplane charge transfer excitation energy for E b→ than that of E t→. The optical conductivity \nmeasurements described in ref. [ 34] show two distinct charge transfer excitation channels at ~1.1 \neV and ~1.5 eV, which should thus correspond to E ↑ and Et→, respectively . To further confirm \nthis, we performed angle -dependent reflectivity measurements (not shown), which agreed well \nwith the data in ref. [ 34] and allowed us to verify that E ↑ ~1.1 eV and E t→ ~1.5 eV by tracking \nthe strength of these absorption peaks as a function of angle and polarization. It is worth noting \nthat both in our meas urements and in the data of ref. [ 34], no spectral signatures corresponding to \nEb→ and E↓ were observed. This is likely because there are many different possible transitions \nthat overlap at higher energies , which obscure the peaks corresponding to Eb→ and E↓. Therefore , \nwe used photon energies of 1.1 ( E↑) and 1.5 ( Et→) eV in our experiments to examine inter - and \nintralayer quantum charge fluctuations in LuFe 2O4. This is actually advantageous, since the \ndirection of P  in LuFe 2O4 is nearly parallel to the c -axis with a small angle (Fig. 1), directly \nlinking it to the 1.1 eV interlayer charge fluctuations [ 20, 21].  \n We propose that magnetic order and charge flu ctuations in LuFe\n2O4 are linked through the \ndouble exchange mechanism [20, 21 ], which leads to an effec tive hopping matrix element t ij (see \nMethods) between the ions i  and j that is determined by the angle θij between the spins \n Si and \n Sj: \n tij=tcos(θij/2) [23]. Thermal fluctuation s prevent any preferred spin ori entation in the 6 \n paramagnetic phase ( T>T N). Within an Ising spin model, in the paramagnetic phase  the hopping \nmatrix element t ij will 0 (if the Fe2+ and Fe3+ core spins are antiparallel) or t (if they are parallel) \nand  thus its average value will be t  /2 fo r this transition , and  similarly, the average value of t ij2 \nis tij2/2. However, in the magnetically ordered state  (T<T N), tij=t if the nearest neighbour spins \nare aligned ferromagnetically (FM), while t ij=0 if they are antiferromagnetically (AFM) aligned \n(Fig. 1(b) and Fig. 2).  This can then be applied to the four charge transfer channels discussed \nabove (considering electron hopping from a given Fe2+ ion to its nearest neighbour Fe3+ ions) to \nfind the total steady -state absorption (proportional to t ij2) for each transition above and below T N. \nWe find that the development of magnetic order does not affect the total  tij2 for E↑ and Et→. This \ncan straightforwardly be seen by consider ing the E↑ transition above T N (Figure 1(a)) , where the \nspins do not have a preferred direction  and below T N . . Because there are two possible charge \ntransfer channels for E↑(Figure 1(a))  , we obtai n a total transition amplitude of  t2/2×2= t2 above \nTN with average value of t2 /2 as described  in above . Below TN, there is only one possible \ntransition with an amplitude  of t2 (Figure 1(b)), so the transition amplitudes above and below T N \nare the same . In the same manner, if we consider the E t→ transition above TN (Figure 1(a)), there \nare six charge transfer channels, giving a transition amplitude of  t2/2×6=3t2. Below TN, there are  \nonly three possible transition s, each  with amplitude t ij2, so the transition amplitudes above and \nbelow T N are th e same, as for the int erlayer transition.  \n \nThis agrees with the data in ref. [34] , which shows that the absorption for the E↑ and Et→ \ntransitions does not significantly change with temperature. In contrast, the total tij2 is reduced \nthrough the double exch ange mechanism for E b→ and E↓ below TN; therefore, as described in the \nintroduction, the corresponding suppression of quantum charge fluctuations should increase P . A 7 \n simple test of the influence of the double exchange mechanism on magnetoelectric coupling in \nLuFe 2O4 would thus be to track the expected changes in the steady -state optical absorption at \nEb→ and E↓ as the temperature T  is varied across T N. However, as described above, this is not \npossible since the energies of these transitions are unknown and couldn't find any specific peaks  \nrelated with these transitions  in the absorption spectrum as shown in ref. [34].   \n \nOne can circumvent this limitation by performing a non-equilibrium  experiment; i.e., \nphotoexciting the known E ↑ and Et→ transitions and examining the resulting changes in the \noptical absorption at the E ↑ transition (which is proportional to P ). Photoexcitation changes the \ncharge configuration, which in turn changes both the total t ij2 and the E ↑ charge transfer energy \nthrough equation (1), l eading to a transient change in the reflectivity that can be measured in our \nexperiments (see Methods for more detail). The development of magnetic order below T N can \nthen further modify the absorption at E↑ through the double exchange mechanism in the sam e \nmanner as in the steady state, potentially causing an additional change in the photoinduced \nreflectivity. In short, our ultrafast optical experiments (described in more detail in Methods) \nallow us to examine the effect of photoexciting either intralayer or interlayer charge transfer \ntransitions (in effect externally driving charge fluctuations) on the interlayer charge transfer energy as a function of temperature. Tuning the temperature above and below T\nN then allows us \nto determine the effect of magnetic ordering on charge fluctuations. In this way, we can test if \nthese fluctuations are indeed responsible for the magnetoelectric coupling measured in LuFe 2O4. \n Figure 3(a) shows the temporal profile of the normalized photoinduced reflectivity change, ΔR/R (t), in LuFe\n2O4 at several different temperatures for a degenerate 1.1 eV pump -probe 8 \n measurement.  Immediately after photoexcitation, ΔR/R  decreases to its minimum value within \n<0.5 picoseconds (ps) (Figure 3(b)) and returns to equilibrium while exhibiting c oherent acoustic \nphonon oscillations with a period of ~40 ps (Fig. 3(a)). These coherent phonons are generated by \nthe dynamic stress on the sample induced by absorption of the pump pulses and are commonly observed in ultrafast optical experiments on correl ated electron materials [ 30], as well as non -\ncorrelated materials described by a simple band structure [ 35].  In this paper, we will focus on \nthe variation of the maximum amplitude of the transient reflectivity signal (ΔR/R\nmax) with \ntemperature, which gives insight into the influence of intra - and interlayer charge fluctuations on \nmagnetoelectric coupling in LuFe 2O4.  \n Figure 3(c) depicts ΔR/R\nmax (1.1 eV) after 1.1 eV photoexcitation as a function of temperature \nnear TN. As described above, photoexcitation changes the charge distribution in LuFe 2O4, \naltering the energy required to transfer a charge from the bottom to the top layer ( E↑) (and thus \nthe absorption/reflectivity probed at 1.1 eV) (Figure 2 (a)). We calculated ∆ E↑, the difference in \nenergy before and after photoexcitation, for T<T N and T>T N, using equation (1) (and using rε=2 \nfrom [ 34]) (see Methods). This  calculation  reveals that there is no change in the ΔR/R max signal \nas T is varied across T N, which is consistent with our experimental observation (Figure 3(c)); \nfundamentally, although the specific allowed charge transfer transitions change s after \nphotoexcitation and give ∆E↑ or dR/R  signal as shown in figure 3(a) and (b), absorption change \ndue to double exchange mechanism(Fig. 2(a)) across  TN is very small and thus undetectable  in \nour experiment. The negative sign of the signal is also expected since photoexcitation reduces the absorption at 1.1 eV.   9 \n Figure 4(a) shows the transient reflectiv ity change for the 1.1 eV interlayer transition after \nphotoexciting the intralayer ( Et→) charge transfer channel at 1.5 eV. The time -dependent \ndynamics  are similar to those observed after photoexciting E↑, but the variation of ΔR/R max with \ntemperature is quite different (Figure 4(b)); in particular, a significant increase in the amplitude  \nis clearly observed as the temperature rises above T N.  As described above, the steady state \nabsorption for the  1.1eV  (E↑) interlayer transition does not change across T N; however, the probe \nabsorption at this transition can change after 1.5 eV photoexcit ation  as T is varied across T N. To \nunderstand this, we calculated the effect of the photoinduced intralayer charge transfer at 1.5 eV \non E↑ in the same manner as described above for E ↑ (see Methods). Our calculation  shows that \nthe ratio of the maximum phot oinduced change in reflectivity between T<T N and T>T N is ~0.9, \nwhich agrees very well with our experimental results (~0.87) (Figure 4). From this experimental observation, we deduce that the ferrimagnetic order influences the fluctuations of the charge ordered state that is  responsible for the electric polarization in LuFe\n2O4 through the double \nexchange interaction.  This result  indicates that the interplay between charge fluctuations and \nmagnetic ordering can result in strong magnetoelectric coupling at the  Neel temperature. Finally, \nit is worth noting that this mechanism will generate an electric polarization in each bilayer, regardless of whether the ground state consists of layers stacked with ferroelectric or antiferroelectric order.  \n In summary, we used  femtosecond optical pump- probe spectroscopy to investigate the role of  the \ndouble exchange mechanism  in the magnetoelectric coupling observed in LuFe\n2O4. Our \nexperiments revealed that optically induced charge fluctuations are affected by magnetic order in  \na manner  that is consistent with this mech anism . Importantly, this result opens an alternative 10 \n route for finding strong magnetoelectric effects: charge  ordering in transition metal oxides can \nnaturally lead to electric polarization that is coupled to the magnetic degree of freedom vi a the \ndouble -exchange interaction .   \n \nAcknowledgments:  \nThis work was performed at the Center for Integrated  Nanotechnologies, a US Department of \nEnergy, Office of  Basic Energy Sciences (BES) user facility and under the auspices of the \nDepartment of Energy, Office  of Basic Energy Sciences, Division of Material Sciences . Los \nAlamos National Laboratory, an affirmative action equal opportunity employer, is operated by \nLos Alamos National Security, LLC, for the National  Nuclear Secur ity administration of the U.S. \nDepartment of  Energy under contract no. DE -AC52 -06NA25396. \nReferences:  \n1. Eeren stein, W., Mathur, N. D. & Scott, J. F. Multiferroic and magnetoelectric materials.  \nNature  442, 759 (2006).  \n2. Chu, Y.- H., Martin, L. W., Holcomb, M. B . & Ramesh, R. Controlling magnetism with \nmultiferroics. Mater. Today  10, 16 (2007)  \n3. Cheong, S.- W. & Mostovoy, M. Multiferroic: a magnetic twist for ferroelectricity. \nNature. Mater. 6, 13 (2007).   \n4. Khomskii, D. Classifying multiferroics: Mechanisms and eff ects. Physics 2, 20 (2009). \n5. Ikeda, N. et. al.  Ferroelectricity from iron valence ordering in the charge -frustrated \nsystem LuFe 2O4. Nature  436, 1136 (2005).  11 \n 6. Subramanian, M.A. et. al. Giant room -temperature magnetodielectric response in the \nelectronic ferroe lectric LuFe 2O4.  Adv. Mater.  18, 1737 (2006). \n7. Niermann, D., Waschkowski, F. de Groot, J., Angst, M., and Hemberger. Dielectric \nProperties of Charge -Ordered LuFe 2O4 Revisited:  The Apparent Influence of Contacts. \nPhys. Rev. Lett . 109, 016405 (2012)  \n8. de Groot, J. et. al . Competing Ferri - and Antiferromagnetic Phases in Geomet rically \nFrustrated LuFe 2O4. Phys. Rev. Let t. 108, 037206 (2012)  \n9. Lee, C., Kim, J.- Y., and Cheong, S. W. Infrared optical response of LuFe 2O4 under dc \nelectric field. Phys. Rev. B  85, 014303 (2012)  \n10. Mulders, A. M., Bartkowiak, M., Hester, J. R., Pomjakushina, E., and Conder, K. Ferroelectric charge order stab ilized by antiferromagnetism in multiferroic. Phys. Rev. B  \n84, 140403(R) (2011)  \n11. Xu, X. S. et. al . Lattice dynamical probe of charge order and antipolar bilayer stacking in \nLuFe\n2O4. Phys. Rev. B  82 014304 (2010)  \n12. Vitucci, F. M. et. al . Infrared study of the charge -ordered multiferroic LuFe 2O4. Phys. \nRev. B  81 195121 (2010)  \n13. Ishihara, S. Electric Ferroelecricity and Frustration . J. Phys. Soc. Jpn. 79, 011010(2010)  \n14. Iida, J. et. al. Magnetization and spin correlation of two- dimensional triangular \nantiferromagnet LuFe 2O4. J. Phys. Soc. Jpn. 62 1723 (1993). \n15. Ko, K. –T. et. al. Electronic origin of giant magnetic anisotropy in multiferroic LuFe 2O4. \nPhys. Rev. Lett . 103, 207202 (2009).  12 \n 16. Xiang, H. J., Kan, E. J., Wei, S.- H., Whangbo, M. –H.  & Yang, J. Origin of the Ising \nferrimagnetism and spin -charge coupling in LuFe 2O4. Phys. Rev. B  80, 132408 (2009). \n17. Yamada, Y., Nohdo, S. & Ikeda, N. Incommensurate charge ordering in charge -frustrated \nLuFe 2O4 system.  J. Phys. Soc. Jpn. 66 3733 (1997). \n18. Angst, M. et. al. Charge order in LuFe 2O4 : Antiferroelectric ground state and coupling to \nmagnetism.  Phys. Rev. Lett . 101, 227601 (2008) . \n19. Xiang, H. J. & Whangbo, M.- H. Charge order and the origin of giant magnetocapacitance \nin LuFe 2O4. Phys. Rev. Lett . 98, 246403 (2007).  \n20. Watanabe, T. & Ishihara, S. Quantum fluctuation and geometrical frustration effects on \nelectric polarization. J. Phys. Soc. Jpn. 78 113702 (2009).  \n21. Watan abe, T. & Ishihara, S. Quantum dielectric fluctuation in electronic ferroelectricity \nstudied by variational Monte -Carlo method. J. Phys. Soc. Jpn. 79 114714 (2010).  \n22. Tokura, Y. Colossal Magnetoresistive O xides. (Gordon and Breach Science, Amsterdam, \n2000)  \n23. Khomskii, D. Electronic structure, exchange, and magnetism in oxides. In Lecture Notes \non Physics, ed. Thornton, M. J. & Ziese, M. (Springer -Verlag,  Berlin,  2001)   \n24. Eichberger, M. et. al . Snapshot of cooperative atomic motions in the optical suppression \nof charge density waves. Nature  468, 802 (2010).  \n25. Möhr -Vorobeva, E. et. al . Nonthermal melting of a charge density waves in TiSe 2. Phys. \nRev. Lett . 107 , 036403 (2011). 13 \n 26. Prasankumar, R. P. et. al . Coupled Charge -Spin Dynamics of the Magnetoresistive \nPyrochlore Tl 2Mn 2O7 Probed Using Ultrafast Midinfrared Spectroscopy. Phys. Rev. Lett . \n95, 267404 (2005) . \n27. Talbayev, D.  et. al . Detection of Coherent Magnons via Ultrafast Pump- Probe \nReflectance Spectroscopy in Multiferroic Ba 0.6Sr1.4Zn2Fe12O22.. Phys. Rev. Lett . 101, \n97603 (2008) . \n28. Först, M. et. al .Nonlinear photonocs as an ultrafast route to lattice control. Nature Phys. 7 \n854 (2011)  \n29. Matsubara, M., Kaneko, Y. He, J.- P., Okamoto, H., and Tokura, Y. Ultrafast polarization \nand magnetization response of multiferroic GaFeO 3 using time -resolved nonlinear optical \ntechniques. Phys. Rev. B  79 140441(R) (2009).  \n30. Ren, Y. H. et. al. Generation and detection of coherent longitudinal acoustic phonons in \nthe La 0.67Sr0.33MnO 3 thin films by femtosecond light pulses. Appl. Phys. Lett . 90, 251918 \n(2007).  \n31. Gong, T. et. al . Femtosecond optical response of Y -Ba-Cu-O films: The dependence on \noptical frequency, excitation intensity, and electric current. Phys. Rev. B  47, 14495 \n(1993).  \n32. Brink, Jeroen van den, and Khomskii, Daniel I. Multiferroicity due to charge ordering. J. Phys.: Condens. Matter  20, 434217 (2008). \n33. Liboff, R. L. Introductory Quantum Mechanics . (Addison Wesley, Reading, 1992). \n34. Xu, X. S. et. al. Charge order, dynamics, and magnetostructural transition in multiferroic LuFe\n2O4. Phys. Re v. Lett . 101, 227602 (2008).  14 \n 35. Liu R. et. al . Femtosecond pump- probe spectroscopy of propagating coherent acoustic   \nphonons in In xGa1-xN/GaN heterostructures.  Phys. Rev. B  72, 195335 (2005). \n \n \n \nFigure 1. Charge and spin ordering in LuFe 2O4 above and below T N. (a) For T>T N, charge \nordering results in a finite polarization P .  The top layer is displaced from the bottom layer by an \nangle shown by the black straight dashed line, which shows an iron atom in the upper plane \ndirectly above the center of a triangle  in the lower plane.  Quantum fluctuations between Fe2+ \nand Fe3+ ions (depicted by blue dashed lines) can reduce P by delocalizing charges, with an \neffective matrix element for hopping between two sites given by t 12=t/2. Red arrows show the \npossible charge  transfer routes between Fe2+ and Fe3+, as defined in the text. (b) For  T<T N, 15 \n ferrimagnetic spin ordering increases P  by decreasing the average hopping through the double \nexchange mechanism; t 12=t when spins at both sites are ferromagnetically aligned (blue dashed \nline), and t 12=0 when both spins are antiferromagnetically aligned (red dashed lines).  \n \n \n \nFigure 2.  Possible interlayer and intralayer charge transfer transitions for T<T N. Both \nfigures show the spin structure of LuFe 2O4 for T<T N. Big and smal l solid circles correspond to \natoms in the top and bottom layers, respectively. The black arrows show the local spins along the \nc axis at 220 K, from refs. [ 15] and [ 16]. Red solid and broken arrows represent allowed and \nforbidden interlayer (a) and intral ayer (b) charge transfer channels, respectively, when \nconsidering the double exchange mechanism. After 1.1 eV excitation, one electron from an Fe2+ \nion in the bottom layer moves to an Fe3+ ion in the top layer, while after 1.5 eV excitation, one 16 \n electron f rom an Fe2+ site in the top layer moves to an Fe3+ site in the same layer.  \n \n \n \n0 50 100 150-200-1000\n0 2 4-200-1000\n200 250 300-400-200\n Time(ps)\nTemperature(K) Time(ps)\n   200K\n 250K\n 300K\n∆R/R\n (c)(b)\n   (a)\n(×10-6)(×10-6)\n ∆R/Rmax∆R/R   (×10-6)\n \nFigure 3. Temperature -dependent transient reflectivity change after 1.1 eV \nphotoexcitation. (a) Temperature -dependent transient reflectivity change after photoexciting and \nprobing the Fe2+Fe3+ interlayer charge transfer excitation at 1.1 eV. The open circles are the \nexperimentally obtained data points and the solid lines are the results of fitting the data with \nexponential and oscillating terms. (b) The data from (a) at earl y times. (c) The amplitude of the \nnegative peak as a function of temperature. The red vertical line shows the magnetic transition \ntemperature, TN~240 K, and the blue horizontal line is parallel to the x  axis, which indicates that \nthere is no significant variation in  max/RR∆ (1.1 eV) across T N. We note that the high signal -to-17 \n noise ratio of our experiment resulted in error bars that are comparable to the size of the data \npoints.  \n \n0 1 2 3 4-400-300-200\n200 250 300-400-200\n Temperature(K) Time(ps)\n  \n 300K\n 200K∆R/R∆R/Rmax(×10-6)\n \n   (×10-6)\nRatio between two lines:0.87 (b) (a)\n \nFigure 4. Pe ak amplitude of the transient reflectivity change near TN after 1.5 eV \nexcitation.  Temperature- dependent transient reflectivity change at 1.1 eV after photoexciting the \nFe2+Fe3+ intralayer charge transfer excitation at 1.5 eV.  \n 18 \n Methods  \nExperimental set up and sample preparation. Our femtosecond optical pump- probe \nspectroscopy system is based on a 75 femtosecond (fs), 250 kHz repetition rate Ti:sapphire \nchirped pulsed amplifier operating at 800 nm (~1.5 eV) and seeding an optical parametric amplifier (OPA ) that allows us to tune the photon energy. A delay line allows us to vary the \noptical path difference between the pump (200 µ m diameter) and probe (100 µ m diameter) \nbeams, which are then focused to the same spot on the sample. Temperature- dependent transient \nreflectivity changes were obtained  in reflection with cross -polarized pump and probe beams in a \n>10:1 power ratio (the pu mp fluence is 76 µ J/cm\n2, which photoexcites ~0.007 electrons/unit cell), \nincident at an angle of less than 10o to the hexagonal c  axis of the crystal.  The probe photon \nenergy was 1.1 eV in all experiments (examining E↑), and the pump photon energies were 1.1 \nand 1.5 eV (photoexciting E↑ andEt→, respectively). It is worth mentioning that pump fluence -\ndependent measurements revealed that only the amplitude of the ΔR/R  signal changes linearly  \nwith fluence, with no changes in the measured dynamics, for both 1.1 and 1.5eV excitation. Furthermore, at the fluence used here, the maximum temperature increase due to laser heating is <8 K, which should not significantly affect the measured dynamics, a nd the sample completely \nrecovers in the 4 µ s time interval between amplifier pulses.  Finally, t he LuFe\n2O4 single crystal \nused in this study was grown by the floating zone method as described in ref. [15] , with its \nsurface normal to the c- axis.  \n Theoretical  background .  Quantum charge fluctuations  originate from hopping of an electron \nbetween two spatially separated potential minima. When an electron is localized in one potential well, the system becomes electrically polarized [ 20, 21]. If we consider two energetically non -19 \n degenerate states localized at two  different  lattice sites and include the double exchange \ninteraction in the system, the Hamiltonian can be expressed as  \n \n H0=ε1C1+C1+ε2C2+C2−t12C1+C2−t21C2+C1,                                  ( M1) \nwhere εiis the atomic energy, +\niCand iCare creation and annihilation operators at the ith site \n(i=1, 2) , and t ij= tji is a effective hopping matrix element accounting for the hopping between \nsites. This matrix element is governed by the double exchange mechanism, which relates the \nprobability of an electron hopping between two atoms to the angle θij between the local core \nspins \n Siand \n Sj [22, 23]. This mechanism has most frequently been used to explain the metallic \nproperties of colossal magnet oresistive  manganites [ 22], but  also applies here to LuFe 2O4, since \nthe ferrimagnetic spin order existing below T N influence s electron hopping (and therefore charge \nfluctuations  of the charge -ordered state ), which can in turn change the dielectric properties of  the \nsystem.  In other words, since  the electronic charge is never com pletely localized in insulators, \nthe degree o f delocalization depends  on the effective hopping amplitude  given by the double \nexchange mechanism . Since magnet ic ordering suppresses this  hopping amplitude for the E b→ \nand E↓ transitions , we expect electrons in LuFe 2O4 to be more localized, stabilizing  charge order . \n \nFor small t ij values ( tij<<Δ, where ∆≡ε−ε1 2 and t 12=t21) andε2>ε1, most of the charge will be \nlocalized at site 1, with a small fraction \n  of delocalized charge remaining at site 2. \nBecause the electric polarization P  is proportional to the difference of charge densities between \nsites, ρ2−ρ1 (where 2ρand 1ρ are the electron densities at sites 2 and 1, respectively), any \nchange in the delocalized charge at site 2 causes a change in P.  20 \n  \nWhen an external electromagnetic field ( t E ωcos0 ) is applied to the system, it will introduce a \nsmall perturbation t exE H ω = cos01 into the Hamiltonian, inducing a site -to-site transition \n(where e is the electron charge and x  is the distance between the two sites). We can use Fermi’s \ngolden rule [ 33] to calculate the probability of transitions between both sites (corresponding to \nquantum charge fluctuations), which is found to be proportional to the delocalized charge on site \n2, δq, through qtH H δ∆Ψ Ψ= ~)(~2 122\n11\n22\n12  ( where 1Ψand 2Ψ are the ground and \nexcited states of H0, respectively). Note that the transition rate is proportional to the extent of \ncharge delocalization in the ground state of the system. Since the photoinduced change in \nreflectivity at the absorption peak is proportional to changes in the absorption under the \nconditions of our experiment [ 31], which, in turn, is proportional to 2\n12H and \n , we can relate \nour transient reflectivity measurements to the amount of delocalized charge and thus the \npolarization P.  This then establishes that we can use our ultrafast optical measurements to \nreliably photoexcite and probe quantum charge fluctuations in LuFe 2O4.  \n \n We first calculate ∆E↑ , i.e. the pump- induced difference in the interlayer charge transfer energy \nbased on the new Coulomb ener gy after exchanging Fe2+ and Fe3+ ions, using equation (1) and \nonly considering four ions : two excited by the pump and two examined by the probe after \nexcitation (Figure 2 in our manuscript). This was done by exchanging a Fe2+ and a Fe3+ ion either \nbetween the bottom and top layers (corresponding to absorption of a 1.1 eV pump photon( figure \n2(a)) ) or between two sites in the top layer (corresponding to absorption of a 1.5 eV pump \nphoton(figure 2(b) ).  This result was then used to calculate the change in absorption as described 21 \n above , from which we calculated the variation of ΔR/R max with temperature after both 1.1 eV and \n1.5 eV photoexcitation for comparison to our experimental data. It is worth noting that if either \nof the ions that absorb a pump photon is involved in the subsequent absorption of a probe photon, \nwe find that the resulting Δ E↑ is much larger than the probe bandwidth (~13 meV) and thus does \nnot contribute to the observed absorption change. Finally, including more than 47 Fe2+ electrons \nin this calculation resulted in an insignificant reflectivity change, since there is almost no change \nin E↑ due to Fe2+ ions far from the Fe2+ and Fe3+ sites that participate in the photoinduced \ntransition.  \n ,   \n "    },    {        "title": "1206.0402v1.Electric_dipoles_on_magnetic_monopoles_in_spin_ice.pdf",        "content": "arXiv:1206.0402v1  [cond-mat.str-el]  2 Jun 2012Electric dipoles on magnetic monopoles\nin spin ice\nD. I. Khomskii\nII. Physikalisches Institut, Universit¨ at zu K¨ oln,\nZ¨ ulpicher Str. 77,\n50937 K¨ oln, Germany\nAbstract\nThe close connection of electricity and magnetism is one of t he cor-\nnerstones of modern physics. This connection plays crucial role from\nthe fundamental point of view and in practical applications , including\nspintronics and multiferroic materials. A breakthrough wa s a recent\nproposal that in magnetic materials called spin ice the elem entary ex-\ncitations haveamagnetic charge andbehaveas magnetic mono poles. I\nshow that, besides magnetic charge, there should be an elect ric dipole\nattached to each magnetic monopole. This opens new possibil ities\nto study and to control such monopoles by electric field. Thus the\nelectric–magnetic analogy goes even further than usually a ssumed:\nwhereas electrons have electric charge and magnetic dipole (spin),\nmagnetic monopoles in spin ice, while having magnetic charg e, also\nhave electric dipole.\nIntroduction\nSpin ice materials present a very interesting class of magnetic mater ials [1].\nMostly these are the pyrochlores with strongly anisotropic Ising-lik e rare\nearth such as Dy or Ho [2], although they exist in other structures, and\none cannot exclude that similar materials could also be made on the bas is\nof transition metal elements with strong anisotropy, such as Co2+or Fe2+.\nSpin ice systems consist of a network of corner-shared metal tet rahedra with\n1effective ferromagnetic coupling between spins [3, 4], in which in the gr ound\nstate the Ising spins are ordered in two-in/two-out fashion. Artifi cial spin ice\nsystems with different structures have also been made [5, 6, 7, 8].\nSpin ice systems are bona fide examples of frustrated systems, and they\nattract now considerable attention, both because they are inter esting in their\nown right and because they can model different other systems, inc luding real\nwater ice [9]. A new chapter in the study of spin ice was opened by the\nsuggestion that the natural elementary excitations in spin ice mate rials —\nobjects with 3-in/1-out or 1-in/3-out tetrahedra — have a magne tic charge\n[10] and display many properties similar to those of magnetic monopole s [11].\nEspecially the last proposal gave rise to a flurry of activity, see e.g. [12], in\nwhich, in particular, the close analogy between electric and magnetic phe-\nnomena was invoked. Thus, one can apply to their description many n otions\ndeveloped for the description of systems of charges such as elect rolytes; this\ndescription proves to be very efficient for understanding many pro perties of\nspin ice.\nUntilnowthelargestattentionwaspaidtothemagneticproperties ofspin\nice, both static and dynamic, largely connected with monopole excita tions\n[13, 14, 15, 16, 17, 18], and the main tool to modify their properties was\nmagnetic field, which couples directly to spins or to the magnetic char ge\nof monopoles. I argue below that the magnetic monopoles in spin ice ha ve\nyet another characteristic which could allow for other ways to influe nce and\nstudy them: each magnetic monopole, i.e. the tetrahedron with 3-in /1-out or\n1-in/3-out configuration, shall also have an electric dipole localized a t such\ntetrahedron. This demonstrates once again the intrinsic interplay between\nmagnetic and electric properties of matter.\nIt is well known that some magnetic textures can break inversion sy mme-\ntry – a necessary condition for creating electric dipoles. This lies at t he heart\nof magnetically-driven ferroelectricity in type-II multiferroics [19 ]. There ex-\nists, in particular, a purely electronic mechanism for creating electr ic dipoles.\nI demonstrate that a similar breaking of inversion symmetry, occur ring in\nmagnetic monopoles in spin ice, finally leads to the creation of electric d i-\npoles on them.\n2Results\nThe appearance of dipoles on monopoles\nTheusualdescriptionofmagneticmaterialswithlocalizedmagneticmo ments\nis based on the picture of strongly correlated electrons with the gr ound state\nbeing a Mott insulator, see e.g. Ch. 12 in [20]. In the simplest cases, ign oring\norbital effects etc., one can describe this situation by the famous H ubbard\nmodel\nH=−t/summationdisplay\n/angbracketleftij/angbracketright,σc†\niσcjσ+U/summationdisplay\nini↑ni↓, (1)\nwheretis the matrix element of electron hopping between neighbouring\nsites/angbracketleftij/angbracketrightandUis the on-cite Coulomb repulsion. For one electron per site,\nn=Ne/N= 1, and strong interaction U≫tthe electrons are localized, and\nthere appears an antiferromagnetic nearest neighbour exchang e interaction\nJ= 2t2/Ubetween localized magnetic moments thus formed (which acts\ntogether with the usual classical dipole-dipole interaction). Depen ding on\nthe type of crystal lattice there may exist different types of magn etic ground\nstate, often rather nontrivial, especially in frustrated lattices co ntaining e.g.\nmagnetic triangles or tetrahedra as building blocks.\nOne can show [21, 22] that, depending on the magnetic configuratio n,\nthere can occur a spontaneous charge redistribution in such a mag netic tri-\nangle, so that e.g. the electron density on site 1 belonging to the tria ngle\n(1,2,3) is\nn1= 1−8/parenleftbiggt\nU/parenrightbigg3/bracketleftBig\nS1·(S2+S3)−2S2·S3/bracketrightBig\n(2)\n(inother spintextures theremay appearspontaneous orbitalcu rrents [21,22]\nin such triangles.) From this expression one sees, in particular, that there\nshould occur charge redistribution for a triangle with two spins up an d one\ndown, Fig. 1, which would finally give a dipole moment\nd∼S1·(S2+S3)−2S2·S3 (3)\nshown in Fig. 1 by a broad green arrow.\nA similar expression describes also an electric dipole which can form on\na triangle due to the usual magnetostriction. One can illustrate this e.g. on\nthe example of Fig. 2, see e.g. [23], in which we show the triangle (1,2,3)\nmade by magnetic ions, with intermediate oxygens sitting outside the tri-\nangle and forming a certain angle M–O–M. For 3-in spins, Fig. 2( a), all\n31\n2 3d\nFigure 1: Electronic mechanism of dipole formation. The formation of\nan electric dipole (green arrow) on a triangle of three spins (red arr ow).\nthree bonds are equivalent, and all M–O–Mangles are the same. However,\nin a configuration of Fig. 2( b) (which, according to Eq. (2), would give a\nnonzero dipole moment due to electronic mechanism), two bonds bec ome\n“more ferromagnetic”, and the oxygens would shift as shown in Fig. 2(b),\nso as to make the M–O–Mangle in the “antiferromagnetic” bond closer to\n180 degrees, and in “ferromagnetic” bonds closer to 90 degrees; according to\nthe Goodenough–Kanamori–Anderson rules this would strengthen the corre-\nsponding antiferromagnetic and ferromagnetic exchange and lead to energy\ngain. As one sees from Fig. 2(b), such distortions shift the centre of gravity\nof positive ( M) and negative (O) charges and thus would produce a dipole\nmoment similar to that of Fig. 1. A similar effect would also exist in a mono-\npole configuration of spin ice, in which on some bonds the spins are orie nted\n“ferromagnetic-like” (e.g. on bonds with 2-in spins), and on other b onds the\nspins are “more antiferromagnetic” (bonds with 1-in and 1-out spin s).\nThe expression (3) is the main expression, which gives the “dipole on\nmonopole” in spin ice. Indeed, when one considers three possible con figura-\ntion of a tetrahedron in spin ice, Fig. 3( a) (4-in or 4-out state), the monopole\nconfiguration of Fig. 3( c,d) (3-in/1-out or 1-in/3-out), and the basic spin ice\nconfigurations 2-in/2-out, Fig. 3( b), then, applying the expressions (2), (3)\nto every triangle constituting a tetrahedron, one can easily see th at there\nwould be no net dipole moments in the cases of Fig. 3( a) (4-in or 4-out) and\nFig. 3(b) (2-in/2-out), but there will appear a finite dipole moment in the\ncase of Fig. 3( c,d), i.e.there will appear an electric dipole on each magnetic\nmonopole in spin ice .\nThe easiest way to check this is to start from the case 3( a), with 4-in\nspins. The total charge transfer e.g. on site 1 is\nδn1∼2S1·(S2+S3+S4)−2(S2·S3+S2·S4+S3·S4).(4)\n4(b) (a)1\n2 31\n2 3\nFigure 2: Magnetostriction mechanism of dipole formation. Illustra-\ntion of magnetostriction mechanism of the formation of an electric d ipole\n(green arrow): the symmetric location of oxygens (green circles) for equiv-\nalent bonds ( a) changes to an asymmetric one for spin configuration (red\narrows) with different spin orientations on different bonds ( b).\nFor the 4-in state all the scalar products ( Si·Sj) are equal, i.e. the charge\nredistribution, and with it the net dipole moment of the tetrahedron is zero.\n(One can also use the condition S1+S2+S3+S4=0, valid in this case,\nto prove this; the fact that the dipole moment is zero also follows jus t from\nthe symmetry.)\nHowever when we reverse the direction of one spin, e.g. S1→ −S1,\ncreating a 3-in/1-out monopole configuration of Fig. 3( c), the first term in\nEq. (4) changes sign, and the resulting charge transfer from site s 2, 3 and 4\nto site 1 would be non-zero — and there will appear a dipole moment on s uch\na tetrahedron, directed from the centre of the tetrahedron to the site with\nthe “special spin”, in this case to site 1 — the broad green arrow in Fig . 3(c)\n(or in the opposite direction, depending on the specific situation — th e sign\nof the hopping tin Eq. (2), or the details of the exchange striction). This\nconclusion, shown in Figs. 3( c,d), is actually the main result of this paper.\nAs the expressions (2)–(4) for the charge redistribution and for the dipole\nmoment are even functions of spins S, the reversal ofall spins will not change\nthe results. Thus the magnitude and the direction of the electric dipole is\nthe same for both the monopole (3-in/1-out) and antimonopole (1- in/3-out)\nconfigurations, Fig. 3( c) and 3(d): in both cases the dipole points in the\ndirection of the “special” spin.\nSimilar considerations show that when we change the direction of one\n5(a)\n(d) (c)(b)2\n341\n2\n341\n2\n3412\n341\nFigure 3: Formation of dipoles on monopoles. Possible spin states (red\narrows) in spin-ice-like systems, showing the formation of electric d ipoles\n(broad green arrow) in monopole ( c) and antimonopole ( d) configurations\n(dipoles are absent in 4-in ( a) and 2-in/2-out ( b) states). Note that the\ndirection of dipoles in cases ( c), (d) is the same (in the direction of the\n“special” spin S1).\nmore spin, e.g. S2→ −S2, creating the 2-in/2-out configuration of Fig. 3( b),\nvarious terms in Eq. (4) again cancel, and such spin configurations d o not\nproduce electric dipole. Thus, electric dipoles appear in spin ice only on\nmonopoles and antimonopoles.\nSome consequences\nThe appearance of electric dipoles on monopoles in spin ice could have m any\nconsequences, some of which we now discuss. The main effect would b e the\ncoupling of such dipoles to the dc or ac electric field,\nE=−d·E. (5)\n6This would give an electric activity to monopoles, would allow one to influ-\nence them by external electric field, and would thus open a new way t o study\nand control such monopoles in spin ice. Due to this coupling the monop oles\nwould contribute to the dielectric function ǫ(ω). Actually such effect was\nobserved in [24], where it was found that the dielectric function has s trong\nanomalies in Dy 2Ti2O7in the magnetic field in the [111] direction when the\nsystem approaches a transition to the saturated state at H∼1T [25]. The\nmechanism of these anomalies was not discussed in [24], but one can co nnect\nit with the proliferation of monopoles and antimonopoles, with the cor re-\nsponding electric dipoles on each of them, in approaching this transit ion.\nThe saturated state in this situation, shown in Fig. 4, has the form o f\nstaggered monopoles–antimonopoles at every tetrahedron. Fro m our results\npresented above, we conclude that in this state there would also be electric\ndipoles at every tetrahedron, shown in Fig. 4 by thick green arrows . We\nsee thus that this saturated state in a strong enough [111] magne tic field\nwould simultaneously be antiferroelectric. Thus one can also associa te the\nanomalies observed in [24] in ǫ(ω) in approaching this state as the anomalies\nat the antiferroelectric transition.\nYet another consequence of the appearance of dipoles on monopo les could\nbe the possibility of changing the activation energy for creating suc h mono-\npoles by electric field: the excitation energy of a monopole, or the mo nopole–\nantimonopole pair would be\n∆ = ∆ 0−d·E. (6)\nCorrespondingly, depending on the relative orientation of dandE, the ex-\ncitation energy can both increase and decrease, but one can alway s find con-\nfigurations of monopoles for which the energy would decrease. One should\nthen be able to see this change of activation energy in thermodynam ic and\nmagnetic properties, such as specific heat, etc.\nThe orientation of electric dipoles depends on the particular situatio n.\nOne can easily see that in the absence of magnetic fields, for complet ely\n“free”, random spin ice, in general the orientation of dipoles on mon opole\nexcitations is random, in all [111] directions. But, for example, in str ong\nenough [001] magnetic field, in which the spin ice state is ordered, Fig. 5, the\nmonopoles and antimonopoles would have the z-components of dipoles re-\nspectively positive and negative, dz(monopoles) >0,dz(antimonopoles) <0,\nwhile the perpendicular projections of dwould be random. Similarly, in the\n7H\nFigure 4: Ordered spin configuration in spin ice in a strong [111]\nmagnetic field. Thisstructurecanbeseenasanorderedarrayofmonopoles\nand antimonopoles; simultaneously it is antiferroelectric (electric dip oles are\nshown by broad green arrows).\n[110] field [26] the xy-projection of dipole moments will be parallel to the\nfield,dxy/bardbl[110].\nYet another effect could appear in an inhomogeneous electric field, c re-\nated for example close to a tip with electric voltage applied to it, in an\nexperimental set-up shown in Fig. 6 (cf. e.g. the study of N´ eel do main walls\nin a ferromagnet, which also develop electric polarization and which ca n be\ninfluenced by inhomogeneous electric field [27]). As always, the electr ic di-\npoles would move in grad E, with positive dipoles e.g. being attracted to the\nregion of stronger field and negative ones repelled from it. One can u se this\neffect to “separate” monopoles from antimonopoles. Thus, as is cle ar from\nFig. 4, in a [111] magnetic field, e.g. in the phase of “kagome ice” [25], t he\n“favourable” monopoles would have dipole moments up, and antimono poles\ndown, so that the monopoles would be attracted to the tip, to the r egion\nof stronger electric field, and antimonopoles would be repelled from t he tip.\n8H\nFigure5: Possible monopole–antimonopole pair in strong [001] mag-\nnetic field. Thez-component of electric dipoles (broad green arrows) on\nmonopoles is pointing up, and on antimonopoles down. The perpendicu lar\ncomponentsof dpointinrandom[110]and[1 ¯10]directions. Bluearrowsshow\nspins inverted in creating and moving apart monopole and antimonopo le.\nSimilarly, the monopole–antimonopole separation could be reached in a [001]\nmagnetic field, in which, as we have argued above, Fig. 5, monopoles h ave\ndz>0, and antimonopoles have dz<0.\nThe magnitude of the dipoles created on monopoles, and the corres pond-\ning strengths of their interaction with electric field, depend on the d etailed\nmechanism of their creation and on the specific properties of a given mate-\nrial. One should think that in real spin ice materials, in which the hopping of\nf-electronsis rathersmall, itis themagnetostriction mechanism ofth edipole\nformationon monopoles and antimonopoles that would be the dominan t one.\nIn this case one could make a crude estimate based on the interactio n (5).\nIf the shifts of ions udue to striction would be e.g. of order 0 .01˚A, then\nthe change of the energy E=−d·E=−euEin a field E∼105V/cm\nwould be ∼0.1K — which would lead to measurable effects, as the typical\nexcitation energy of monopoles in spin ice is ∼1K [11, 1]. We would get\neffects of the same order of magnitude for the distortions u∼10−3˚A in a\n9Figure 6: Separation of monopoles and antimonopoles. The behaviour\nof monopoles and antimonopoles with respective electric dipoles (gre en ar-\nrows) in spin ice in [111] or [001] magnetic field in the inhomogeneous elec tric\nfield (dashed lines) created by a tip (brown) with electric voltage.\nfield∼106V/cm.\nDiscussion\nSummarizing, we demonstrated that there should appear real elec tric dipoles\non magnetic monopoles in spin ice. Creation of such dipoles may lead to\nmany experimental consequences, some of which were discussed a bove. They\ncan open new ways to study and to manipulate these exciting new obj ects —\nmagneticmonopoles ina solid. Wealso see thatthe closeconnection be tween\nelectric and magnetic phenomena, which lies at the hart of modern ph ysics,\nextends in this case even further than one thought: in these syst ems one can\nhave not only magnetic charges instead of electric ones, and “magn etricity”\ninstead of electricity, but, similar to electrons which have electric charge and\nmagnetic dipole (spin), magnetic monopoles in spin ice will have magnetic\n10chargeandelectric dipole .\nReferences\n[1] Bramwell, S. T. and Gingras, M. J. P. Spin ice state in frustrated\npyrochlore materials. Science294,1495–1501 (2001)\n[2] Gardner, J. S., Gingras, M. J. P. and Greedan, J. E. Magnetic py -\nrochlore oxides. Rev. Mod. Phys 82,53–107 (2010)\n[3] den Hertog, B. C. and Gingras, M. J. P, Dipolar interactions and o rigin\nof spin ice in Ising pyrochlore magnets. Phys. Rev. Lett 84,3430–3433\n(2000)\n[4] Yavors’kii, T., Fennell, T., Gingras, M. J. P. and Bramwell, S. T.\nDy2Ti2O7spin ice: A test case for emergent clusters in a frustrated\nmagnet. Phys. Rev. Lett 101,037204 (2008)\n[5] Wang, R. F. et al.Artificial “spin ice” in a geometrically frustrated\nlattice of nanoscale ferromagnetic islands. Nature439,303–306 (2006)\n[6] Tchernyshyov, O. Nolonger onthinice. Nature Phys. 6,323–324(2010)\n[7] Ladak, K. et al.Direct observation of magnetic monopole defects in an\nartificial spin-ice system. Nature Phys. 6,359–363 (2010)\n[8] Mengotti, E. et al.Real-space observation of emergent monopoles and\nassociated Dirac strings in artificial kagome spin ice. Nature Phys. 7,\n68–74 (2010)\n[9] Pauling, L. The structure and the entropy of ice and of other cr ystals\nwith some randomness in atomic arrangement. J. Am. Chem. Soc 57,\n2680–2684 (1935)\n[10] Ryzhkin, I. A. Magnetic relaxation in rare earth pyrochlores. JETP\n101,481–486 (2005)\n[11] Castelnovo, C., Moessner, R., and Sondhi, S. L. Magnetic monop oles\nin spin ice. Nature451,42–45 (2008)\n11[12] Gingras, M. J. P. Observing monopoles in a magnetic analog of ice.\nScience326,375–376 (2009)\n[13] Morris, D. J. P. et al. Dirac strings and magnetic monopoles in spin ice\nDy2Ti2O7.Science326,411–414 (2009)\n[14] Fennel, T. et al. Magnetic Coulomb phase in the spin ice Ho 2Ti2O7.\nScience326,415–417 (2009)\n[15] Kadowaki, H. et al. Observation of magnetic monopoles in spin ice.\nJourn. Phys. Soc. Jpn. 78,103706 (2009)\n[16] Jaubert, L. D. C. and Holdsworth P. C. W. Signature of magnet ic\nmonopole and Dirac string dynamics in spin ice. Nature Phys. 5,258–\n261 (2009)\n[17] Slobinsky, D. et al. Unconventional magnetization process and thermal\nrunaway in spin-ice De 2Ti2O7.Phys. Rev. Lett. 105,415–417 (2009)\n[18] Giblin, S. R. et al. Creation and measurement of long-lived magnetic\nmonopole current in spin ice. Nature Phys. 7,252–258 (2011)\n[19] Khomskii, D.I. Multiferroics: mechanisms andeffects. Physics (Trends)\n2,20 (2009)\n[20] Khomskii, D. I. Basic aspects of quantum field theory: Order and ele-\nmentary excitations . Cambridge Univ. Press (2010)\n[21] Bulaevskii, L. N., Batista, C. D., Mostovoy, M. V. and Khomskii, D. I.\nElectronic orbital currents and polarization in Mott insulators. Phys.\nRev.B 78,024402 (2008)\n[22] Khomskii, D. I. Spin chirality and nontrivial charge dynamics in fru s-\ntrated Mott insulators: spontaneous currents and charge redis tribution.\nJ. Phys.: Condens. Matter 22,164209 (2010)\n[23] Delaney, K. T., Mostovoy, M. and Spaldin, N. A. Superexchange -driven\nmagnetoelectricity in magnetic vortices. Phys. Rev. Lett. 102,157203\n(2009)\n[24] Saito, M., Higashinaka, R. and Maeno, Y. Magnetodielectric resp onse\nof the spin-ice Dy 2Ti2O7.Phys. Rev. B 72,144422 (2005)\n12[25] Aoki, H., Sakakibara, T., Matsuhira K. and Hiroi, Z. Magnetocalor ic\neffect onthepyrochlore spinicecompoundDy 2Ti2O7ina[111]magnetic\nfield.J. Phys. Soc. Jpn. 73,2851–2856 (2004)\n[26] Fennell, T. et al.Neutron scattering studies of the spin ice Ho 2Ti2O7\nandDy 2Ti2O7inappliedmagneticfield. Phys. Rev. B 72,224411(2005)\n[27] Logginov, A. S. et al.Room temperature magnetoelectric control of mi-\ncromagnetic structure in iron garnet films. Appl. Phys. Lett. 93,182510\n(2008)\nAcknowledgements\nI am grateful to C. D. Batista, S.-W. Cheong and M. J. P. Gingras fo r useful\ndiscussions. This work was supported by the German project SFB 6 08 and\nby the European project SOPRANO.\n13"    },    {        "title": "1206.1699v1.Room_temperature_magnetic_entropy_change_and_magnetoresistance_in_La__0_70__Ca__0_30_x_Sr_x_MnO_3_Ag_10___x___0_0_0_10_.pdf",        "content": "1 \n J. Magnetism & Magnetic Materials 324, 2849 -2853 (2012)  \n \nRoom temperature magnetic entropy change and magnetoresistance in La 0.70(Ca 0.30-\nxSrx)MnO 3:Ag 10% ( x = 0.0 -0.10)  \nR. Jha, Shiva Kumar Singh,* Anuj Kumar and V.P.S Awana† \nQuantum Phenomena and Applications, National Physical Laboratory (CSIR), New Delhi -\n110012, India  \nAbstract  \nThe magnetic and magnetocaloric properties of polycrystalline La 0.70(Ca 0.30-\nxSrx)MnO 3:Ag 10% manganite have been investigated. All the compositions are crystallized in \nsingle phase orthorhombic Pbnm  space group. Both, the Insulator -Metal transition temperature \n(TIM) and Curie temperature ( Tc) are observed at 298 K for x = 0.10 composition . Though both \nTIM and Tc are nearly unchanged with Ag addition, the MR is slightly improved . The MR at 300 \nK is fo und to be as large as 31% with magnetic field change of 1T esla, whereas it reaches up to \n49% at magnetic field of 3T esla for La0.70Ca0.20Sr0.10MnO 3:Ag 0.10 sample. The maximum entropy \nchange (∆S Mmax) is 7.6 J.Kg-1.K-1 upon the magnetic field change of 5T esla, near its Tc (300.5 K).  \nThe La0.70Ca0.20Sr0.10MnO 3:Ag 0.10 sample having good MR (31%1Tesla, 49%3Tesla) and reasonable \nchange in magnetic entropy ( 7.6 J.Kg-1.K-1, 5 Tesla) at 300 K can be a potential magnetic \nrefrigerant material at ambient temperature s.  \nPACS:  \nKey Words: Manganites; Magnetization; Magnetocaloric effect;  Magnetoresistance  \n*Corresponding Author’s singhsk@mail.nplindia.ernet.in   \nTel.: +91 11  45609357; Fax; +91 11 45609310   \n†awana@mail.nplindia.ernet.in  Web page - www.freewebs.com/vpsawana/  \n \nIntroduction  \nManganites are considered to be promising candidate for the technological applica tions such \nas bolometer and magnetic refrigeration [1 -7]. Along with the all other fascinating properties, the \npresence of magnetocaloric nature makes them more outstanding material. Practically one \ndesires to have higher Temperature coefficient of resistance ( TCR), MR and magnetic entropy \nchange near room temperature i.e. at around 300 K. It is seen that the maximum MR as well as \nTCR in hole -doped manganites occur near the insulator -metal ( IM) transition TIM being \naccompanied with ferromagnetic ( FM)-paramagnetic ( PM) transition  (Curie Temperature Tc). \nThe steep transition about IM crossover determines the sensitivity as well as active zone for these \nsensors. Since magnetic refrigeration has a lot of advantages over gas refrigeration, manganites \nhave been getting attention [ 4, 6 -7]. Also, since the magnetic properties of perovskite 2 \n manganites, Curie temperature and saturation magnetization, are strongly doping -dependent, \nthese typical materials are believed to be good candidates for magnetic refrigerat ion at various \ntemperatures [5-11].  \nThe magnetocaloric effect ( MCE ) is an isothermal magnetic entropy change or an \nadiabatic temperature change (∆ Tad) of a magnetic material caused by an applied magnetic field. \nThe adiabatic temperature change ∆ Tad is mai nly affected by the magnetic entropy change |∆ SM| \n[12]. The magnetic entropy change |∆ SM| induced by a magnetic field change is another \nimportant parameter to describe the magnetocaloric effect. A constant magnetic entropy change \nover the working temperatu re range is required in an ideal Ericsson refri geration cycle [13 ]. It \nhas been observed that heavy rare -earth and their compounds are good candidates for finding a \nlarge MCE , due to their large  magnetic moments  [14, 15]. The highest MCE  involving a secon d-\norder transition is found in g adolinium, which can be used to achieve cooling between 270 and \n310 K [14]. However, the cost of a magnetic refrigerant using gadolinium is quite expensive , \nwhich limits the usage of it as an active magnetic refrigerant ( AMR ) in magnetic refrigerators. \nFurther efforts to investigate new materials exhibiting large MCE  in relatively  low applied field \nare of significant importance [11, 15-16]. An AMR  material should have large magnetic entropy \nchange induced by low magnetic fiel d change. However higher resistivity of manganites is \nfavorable for reducing eddy current heating though their maximum entropy change is smaller \nthan rare earth compounds.  \nVarious attempt has been made to increase TCR and MR in La 2/3Ca1/3MnO 3:Ag y \ncomposite s [17-18]. Higher TCR with optimized reasonable MR at low fields is seen below room \ntemperature (< 265 K). Some of us found 30% MR at 1 T esla and TCR as high as 9 %/K above \n300K in La 0.70Ca0.20Sr0.10MnO 3:Ag 0.2 [5]. These values are quite reasonable in bulk  \npolycrystalline samples and can be used in the bolometric and infrared detectors. However there \nare scant reports on LCMO:Ag composites study for magnetic refrigeration or for magneto -\ncaloric applications.  In this report we have studied La 0.70Ca0.30-xSrxMnO 3:Ag 0.10 composites for \nMCE  and applications. Our results show that Ag addition improves MR and magneto -entropy \nchange. The occurrence of maximum entropy change (∆S Mmax) near its Tc (300.5 K) makes it \nmuch of practical importance and  it can be used for magnetic refrigeration .  \n \nExperimental  \nThe samples are synthesized in air by solid -state reaction route. The stoichiometric mixture \nof La 2O3, SrCO 3, CaO and MnO 2 are ground thoroughly, calcined at 1000ºC for 12h and then \npre-sintered at 1100  ºC, 1200  ºC, 1300  ºC and 1400  ºC for 20h with intermediate grindings. \nFinally, the powders are palletized and sintered at 1420  ºC for 20h in air. Samples are cooled \nvery slowly  (10C /minute)  from 1420ºC to room temperature. In Ag composite samples Ag 2O is \nmixed by weight percentage before final sintering. The phase formation is checked for each \nsample with powder diffractometer, Rigaku (Cu -Kα radiation) at room temperature. The phase \npurity analysis and lattice parameter refining are performed by Rietveld refinement  programme \n(Fullprof version). The resistivity and magnetization measurements of all samples are carried out 3 \n applying a field magnitude up to 5 T using Physical Properties Measurement system - Quantum \nDesigned PPMS -14 T.  \n1. Results and discussion  \nAll the sampl es are crystallized in single phase [Fig. 1(a) and (b)]. This is confirmed from the \nRietveld analysis of powder X -ray diffraction pattern s. All the compositions La 0.70Ca0.30-\nxSrxMnO 3 (x = 0.0, 0.05 and 0.10) are fitted in orthorhombic Pbnm  space group. Ion ic radii of \nCa2+ with coordination number (CN) VI is 1.0 Å and the ionic radii of Sr2+ with CN VI is 1.18 Å \n[19]. Increase in lattice parameters indicates that substitution by Sr at Ca site. Fitted parameters \nare shown in table 1.  In Ag composite samples,  it is possible for Ag to enter the manganite \nlattice, which would increase the Mn4+content [ 20]. Also, Ag is volatile above 1000  0C and it \nmay restrict presence of Ag less than the desired stoichiometry. To avoid these, Ag 2O is mixed in \nfinal sintering. The Rietveld refinement of Ag added samples shows that presence of Ag peak in \n[see Fig. 1(b)]. This clearly indicates that most of Ag is present at the grain boundary.   \n Fig. 2 depicts RTH  plot of La 0.70Ca0.30MnO 3:Ag 0.10 composition up to applied field of 7 T, \nwhich shows transition near 270 K in zero field. With increasing field transition shifts towards \nhigher temperature, which is attributed to enhancement in the ferromagnetic interactions with \nhigher applied fields. Inset of Fig. 2 shows MR of the same.  A maximum 58 % change of MR can \nbe seen with the change in applied field of 3 T at 270 K. Although it has better MR but the \nworking temperature is far below room temperature. Earlier it is reported [ 5, 7, 11 ] with doping \nof Sr at Ca site the transition te mperature increases and it is found around 308 K for Sr = 0.10. \nAlthough the Tc increases with Sr doping but it is at the cost of sharpness of transition. However, \nsynthesis condition and oxygen content, largely determine the Tc and sharpness of transition  [21-\n22].  In other reports [ 5, 11 ], Tc was found around 306 -308 K with Sr = 0.10. In the studied \nsamples the Tc is found to be 298 K with Sr content of 0.10. This is determined through \nderivative of the magnetization data ( M-T) in an applied field of 0.1 T [Fig. 3].  The observed \ndifference in Tc may be due to deficiency of oxygen content. I n earlier report  [5] samples are \noxygen annealed at 1200 C after being synthesized at 1400 C, whereas the studied samples are \nslowly cooled  in air from 1420 C to room temperature.  In any case working temperature of 298K \nis good enough for room temperature applications.    \n The large magnetic entropy change in manganites mainly originates from the \nconsiderable variation of magnetization near Tc. Also, the spin lattice coupling in the magnetic \nordering process plays an important role [ 8-11]. It is reported that with Ag addition in \nmanganites, though sharpness of transition improves , the TIM remains nearly invariant  [7, 23 -24]. \nFig. 4a and 4b show the MR of La 0.70Ca0.20Sr0.10MnO 3 and La 0.70Ca0.20Sr0.10MnO 3:Ag 0.10 \ncomposition respectively. It can be seen that maximum MR increases with Ag addition . The MR \nat 3 Tesla is 43 % and 49 % in Ag free and Ag added samples respectively. Contrasting \ninterpretations are argued about the mechanism of MR increase with Ag addition. Low melting \npoint silver segregates at the grain boundaries and lead to reduction in intergrain tunnel 4 \n resistance [ 5, 7]. Intergrain region offers more resistance i n conduction as it behaves as non \nmetallic and nonmagnetic region. Ag addition provides a conducting channel between the grains \nwhich leads to sharper transition. It is reported that Ag addition improves FM in nonmagnetic \nintergrain region [ 23]. A remarkab le improvement in the magnetic homogeneity is indicated by \nnarrower ferromagnetic resonance ( FMR ) line widths in thin films [ 23]. Thereby, a more abrupt \nreduction of magnetization  occurs, which results in a significant magnetic -entropy change near \nTc and thus a better MCE  can be obtained in manganites. In addition to this it is argued that Mn \nspin disorders occur at the phase interfaces due to which Mn -Mn magnetic exchange is \ninterrupted as Ag segregates at the grain boundaries [ 7]. This magnetic inho mogeneity leads to \nthe increase in resistivity [2 5-27]. With an external field applied, spin scattering is suppressed \nand thus enhanced MR is obtained. Considering the points given above, it is thus assumed that \nincrease in MR and sharpness of transition a t Tc/TMI is obvious for Ag added sample.  \nConsidering the fact that better MR is observed in Ag added sample and we are interested \nin near room temperature, the isothermal magnetization is done for La 0.70Ca0.20Sr0.10MnO 3:Ag 0.10 \nsample.  The magnetocaloric e ffect can be measured either by the adiabatic change of \ntemperature under the application of a magnetic field or through the measurement of isothermal \nmagnetization versus field at different temperatures [2 8]. We used the second one to avoid \ncomplications related with adiabatic measurement. Fig. 5 shows the representative isothermal \ncurves of magnetization with the applied field up to 5 T for La 0.70Ca0.20Sr0.10MnO 3:Ag 0.10 sample. \nIsothermal curves are obtained around Tc from 290 to 310 K at an interval of 1  and 2 K. The \nchange in magneto -entropy is related to the magnetization by the Maxwell relation [2 8]. \n \n \nThis equation can be rewritten as  \n \nIf the magnetization measurement is done at small temperature i nterval and discrete fields, this \nequation can be approximated as  \n \nHere, Mi and Mi+1 are the magnetization values measured at temperatures Ti and Ti+1 in an applied \nfield H, respectively. Thus the magneto -entropy change can be calculated through isothermal \nmagnetization curves.  5 \n  Fig. 6 shows the magnetic entropy change |∆S M| as a function of temperature for the \nLa0.70Ca0.20Sr0.10MnO 3:Ag 0.10 sample with different magnetic fi eld changes ∆H. In the same \nmagnetic field change, |∆S M| variation with temperature shows a peak near Tc (300.5 K).  Upon \nthe change of 5 T esla applied field, the highest value of |∆S M| is 7.6 J.Kg-1.K-1.  With the same \nfield change (5 T esla) the value of |∆S M| is 7.45 J.Kg-1.K-1 was found in single crystal of \nLa0.70Ca0.20Sr0.10MnO 3 [7]. It means Ag addition provides similar results to that of single crystals \nof non Ag added samples. At commercial level it is easy to synthesize bulk material than single \ncrystals. Thus Ag composites of bulk manganites could be the potential candidate for magnetic \nrefrigeration.  \n \nConclusion  \nImprovement in magnetic and magnetocaloric properties has been observed with Ag addition \nin polycrystalline manganites. Both, the Insulator -Metal transition and Curie temperature s areo \nobserved at 298 K for x = 0.10 composition. While TIM remains constant with Ag addition, ~ 6 % \nincrease of MR is observed with same. The MR at 300 K is found to b e as large as 31% with \nmagnetic field change of 1T in Ag added x = 0.10 composition. The maximum entropy change \n(∆S Mmax) is found to be 7.6 J.Kg-1.K-1 upon the magnetic field change of 5T, near its Tc. It shows \nthat Ag addition is competent  to that of sing le crystals of non Ag added samples. Thus Ag \ncomposites of bulk polycrystalline manganites could be the potential candidate for magnetic \nrefrigeration.  \n \nAcknowledgements   \nThe authors would like to thank DNPL Prof. R. C. Budhani for his constant support and \nencouragement. Authors S. K. Singh and A. Kumar would like to acknowledge CSIR , India, for \nproviding fellowships.  \n \nReferences  \n[1] R. von Helmolt, J. Wocker, B. Holzapfel, M.  Schultz, and K. Samver Phys. Rev. Lett. 71 \n(1993) 2331  \n[2]  S. Jin, T. H. Tiefel, M. McCormack, R. A. Fastnacht, R. Ramesh, and L. H. Chen, \nScience 264 (1994) 413  \n[3] A.-M. Haghiri -Gosnet and J. -P. Renard, J. Phys. D 36 (2003) R127  \n[4] A. F. Lacaze, R. Beranger, G.  Bon Mardion, G. Claudet, A. A. Lacaze Cryogenics 23 \n(1983) 427  \n[5] V. P. S. Awana, Rahul Tripathi, Neeraj Kumar, H. Kishan, G. L. Bhalla, R. Zeng, L. S. \nSharth Chandra, V. Ganesan, and H. U. Habermeier J. Appl. Phys 107 (2010) 09D723  \n[6] G. C. Lin, X. L. Yu, Q. W ei, J. X. Zhang Materials Letters 59 (2005) 2129  6 \n [7] Y-H Huang, C -H Yan, F. Luo, W. Song, Z -M. Wang, and C -S Liao Appl. Phys. Lett. 81 \n(2002) 76  \n[8] Z. B. Guo, Y. W. Du, J. S. Zhu, H. Huang, W. P. Ding, and D. Feng, Appl. Phys. Lett. \n78 (1997) 1142  \n[9] X. Bohigas, J. Tejada, E. del Barco, X. X. Zhang, and M. Sales, Appl. Phys. Lett. 73 \n(1998) 390  \n[10] A. Szewczyk, H. Szymczak, A. Wisniewski, K. Piotrowski, R. Kartaszynski, B. \nDabrowski, S. Kolesnik, and Z. Bukowski, Appl. Phys. Lett. 77 (2000) 1026  \n[11] M. H. Phan, S. C. Yu , and N. H. Hur, Appl. Phys. Lett. 86 (2005) 72  \n[12] X. Bohigas, J. Tejada, M. L. Marı´nez -Sarrio´n, S. Tripp, R. Black, J. Magn. Magn. \nMater. 208 (2001) 85  \n[13] T. Hashimoto, T. Kuzuhara, M. Sahashi, K. Inomata, A. Tomokiyo, H.Yayama, J. Appl. \nPhys. 62 (1987) 3873  \n[14] R. D. McMichael, J.J. Ritter, R.D. Shull, J. Appl. Phys. 73 (1993) 6946  \n[15] S. Yu. Dan’kov, et al., Phys. Rev. B 57 (1998) 3478  \n[16] V. K. Pecharsky, K. A. Gschneidner Jr., Phys. Rev. Lett. 78 (1997) 4494.  \n[17] H. Wada and Y. Tanabe, Appl. Phys. Lett. 79 (2001) 3302  \n[18] Tegus, E. Bruck, K. H. J. Buschow, and F. R. de Boer, Nature (London) 415 (2002) 150  \n[19] R. D. Shannon, Acta Crystallogr . Sect. A: Cryst. Phys. Diffr.  Theor. Gen. Crystallogr. \nA32, 751 1976  \n[20] T. Tang, Q. Q. Cao, K. M. Gu, H. Y. Xu, S. Y. Zhang, and Y. W. Du, Ap pl. Phys. Lett. \n77 (2000) 723  \n[21] B C Nam, W S Kim, H S Choi, J C Kim, N H Hur, I S Kim  and Y K Park J. Phys. D \nAppl. Phys. 34 (2001) 54 –59 \n[22] R. Tripathi, V. P. S. Awana, N. Panwar, G. L. Bhalla, H. U. Habermier, S. K. Agarwal, \nand H. Kishan, J. Phys. D 42 (2009) 175002  \n[23] R. Shreekala, M. Rajeshwari, S. P. Pai, S. E. Lofland, V. Smolyaninova, K. Ghosh, S. B. \nOgale, S. M. Bhagat, M. J. Downes, R. L. Greene, R. Ramesh, and T. Venkatesan, Appl. \nPhys. Lett. 74 (1999) 2857  \n[24] V. P. S. Awana, R. Tripathi, S. Balamurugan, H. Kishan, and E. Takayama -Muromachi, \nSolid State Commun. 140 (2006) 410  \n[25] L. Balcells, A. E. Carrillo, B. Martinez, and J. Fontcuberta, Appl. Phys. Lett. 74 (1999) \n4014  \n[26] D. K. Petrov, L. Krusin -Elbaum, J. Z. Sun , C. Field, and P. R. Duncombe, Appl. Phys. \nLett. 75 (1999) 995  \n[27] S. Gupta, R. Ranjit, C. Mitra, P. Raychaudhuri, and R. Pinto, Appl. Phys. Lett. 78 (2001)  \n362  \n[28] A. H. Morrish, The Physical Principles of Magnetism IEEE, New York, (2001)  \n \n 7 \n  \n \nFigure Caption  \n \nFig. 1: Rietveld fitted XRD  pattern of (a) La0.70(Ca 0.30-xSrx)MnO 3 (x = 0.00 and 0.05); (b) \nLa0.70(Ca 0.30-xSrx)MnO 3 (x = 0.10) and La0.70(Ca 0.30-xSrx)MnO 3:Ag (x = 0.10) with space group \nPbnm . In Fig 1(b) * represents peaks associated with Ag.  \nFig. 2: RTH  plot of La 0.70Ca0.30MnO 3:Ag 0.10 composition up to applied field of 7 T. Inset of Fig. \n2 shows MR of the same at various temperature.  \n Fig. 3:  Magnetization ( M-T) and its derivative in an applied field of 0.1 T of the La 0.70(Ca 0.30-\nxSrx)MnO 3:Ag (x = 0.10) sample . \nFig. 4:  MR of (a) La 0.70Ca0.20Sr0.10MnO 3 and (b) La 0.70Ca0.20Sr0.10MnO 3:Ag 0.10 composition with \nfield at various temperatures.  \n \nFig. 5: Representative isothermal curves of magnetization with the applied field up to 5 T for \nLa0.70Ca0.20Sr0.10MnO 3:Ag 0.10 sample. Isothermal curves are obtained around Tc from 290 to 310 \nK at an interval of 1 and 2 K.  \n \nFig. 6: T he magnetic entropy change |∆S M| as a function of temperature for the \nLa0.70Ca0.20Sr0.10MnO 3:Ag 0.10 sample with different magnetic field changes ∆H.  \n \nTable 1: Rietveld Refined lattice parameters  and unit cell volume of La 0.70(Ca 0.30-xSrx)MnO 3 (x = \n0.00, 0.05 and 0.10) . \nLa0.70(Ca 0.30-\nxSrx)MnO 3 Rp Rwp Chi2 a (Å)  b (Å)  c (Å)  Vol. (Å3) \nx  = 0.00  4.73 6.03 2.34 5.45 (4)  5.47 (1)  7.70 (9)  230.06 (6)  \nx  = 0.05  4.87 6.20 2.08 5.45 (8)  5.48 (2)  7.71 (1)  230.79 (6)  \nx  = 0.10  4.92 6.24 2.61 5.46 (4)  5.49 (5)  7.72 (2)  231.92 (1)  \n \n \n 8 \n Fig. 1(a) \n \nFig. 1(b) \n \n9 \n Fig. 2 \n \nFig.3 \n \n10 \n Fig. 4(a) \n \nFig. 4(b) \n \n11 \n Fig. 5 \n \nFig.6 \n \n"    },    {        "title": "1206.2805v1.Saturation_Magnetization_of_Inorganic_polymer_Nanocomposites_Higher_than_That_of_Their_Inorganic_Magnetic_Component.pdf",        "content": "1 \n Saturation Magnetization of Inorganic/polymer Nanocomposites \nHigher than That of  Their Inorganic Ma gnetic Component \nYang Liu*1, Makoto Takafuji2, Hirotaka Ihara 2,and Takeshi Wakiya 2 \n1 Beijing Key Lab of Special Elastomer Composite Materials, Department of Material Science and Engineering, \nBeijing Institute of Petrochemical Technology, 19 North Qingyuan Road, Beijing 102617, China. Tel: +86 10 \n81292129; *Corresponding author:  E-mail: blue_ocean3000@mail.dhu.ed u.cn, yang.liu@bipt.edu.cn  2  Department of Applied Chemistry and Biochemistry , Kumamoto University, Kumamoto 860-8555, Japan.  \n \nAbstract: Herein, some magnetic nanoparticles (MNP)/ clay/polymer nanocomposites have been \nprepared, whose saturation magnetization is highe r than that of pure oleic acid coated MNP \ncomponent. The existence of unique ‘nano-netw ork’ structure and ti ght three-phase nano-\ninterface in the nanocomposites contribute to the surprisi ng saturation magnetization. \n    Inorganic/polymer composites are widely us ed in daily life because  they exhibit both the \nfunctionality of inorganic compone nt and the properties of polymer substrate. It is convenient to \nendow the composites functionalities by introduci ng different inorganic fillers, such as carbon \nblack, carbon nanotube, graphene, clay, sili ca, quantum dot, polyhedral oligomeric \nsilsesquioxane, magnetic particles, and so on1-5. As for the magnetic inorganic/polymer \ncomposites, the saturation magnetization of the co mposites is proportional to the amount of their \nmagnetic components6-8, lower than that of pure magnetic inorganic components, which is \nnaturally believed to be true. However, the ‘tru e’ view is not right fo r all magnetic composites \nnow: herein, some magnetic na noparticles (MNP)/clay/polym er nanocomposites have been \nprepared, exhibiting ultrahigh saturation magnetiz ation with low content of oleic acid coated \nMNP (OA-MNP) (i.e. 10 wt% OA-MNP with respect to the total weight ), even stronger than that \nof pure OA-MNP component. The nanocomposite film s were prepared by casting the mixture of \nclay (Laponite XLG), poly(butyl acrylate) (PBuA) emulsion, and OA-MNP. This is a \nbreakthrough for the research of nanocomposites, which indicates that the functionality of the \nnanaocomposites can be better th an that of their pure functio nal components by forming unique \nnanostructure in nanocomposites.   \nThe preparation of the nanocomposites is shown in Scheme 1. First, the mixture of polymer \nemulsion and clay dispersion forms a system without  aggregations. Then, the mixture turns into a \ngel during the drying process because of the formati on of a “house of cards” of clay, as shown in \nScheme 1b. This ‘house of cards’ results fr om the electrical attr action among the opposite 2 \n charges of the surfaces and the edges of the cl ay platelets (i.e., negative charge and positive \ncharge, respectively) (inset of Sc heme 1b). At this stage, the mixt ure still contains a large amount \nof water; polymer particles and OA-MNP are separately fixed in the rooms of the house of cards. \nWith further drying, when polymer particles are sufficiently close, coalescence among \nneighboring polymer particles takes place. Fina lly, all polymer particles coalesce into a \nmacroscopic bulk film; clay platelets and OA-MNP are fixed in the polymer substrate. A unique \n‘nano-network’ structure forms in the nanoc omposites, shown in Scheme 1c. The obtained \nnanocomposite films are called B xGyMz, where B, G, and M stand for poly(butyl acrylate) \n(PBuA), Laponite XLG, and oleic acid coated magnetic nanoparticles ( OA-MNP) respectively, \nand x, y, z  stands for PBuA, clay, and OA-MNP conten t (with respect to the total weight). \nDetailed composition for film casting is shown in Table 1. The casting process is similar to the \ncasting process of clay/pol ymer composite latexes9-11, except that OA-MNP is  introduced as the \nthird component. As shown in Scheme 1c, OA-MN P disperse in clay/polymer nanocomposites, \nsimultaneously touching clay platelets and polymer.    \n \n  \n  \nScheme 1.  Preparation of magnetic nanoparticles (MNP )/clay/polymer nanocomposite films. a) \nMixture of emulsion, clay aqueous dispersi on, and oleic acid coated  MNP (OA-MNP); b) \nFixation of polymer nanospheres and MNP in the r ooms of ‘House of Cards’; c) Magnetic film \ncontaining ‘nano-network’ structure. \n \nTable 1.  Composition for BxGyMz nanocomposite films \nSample Name Emulsion \n(PBuA, 21 wt%)\n⎯⎯⎯⎯⎯  \ng Clay  Dispersion \n(2 wt%) \n⎯⎯⎯⎯⎯  \ng OA-MNP Slurry \n(4.2 wt%) \n⎯⎯⎯⎯⎯  \ng Water \n \n⎯⎯⎯  \ng \nB80G10M10 1.1 1.5 0.714 4.686\nB60G30M10 0.829 4.5 0.714 1.957\nB40G50M10 0.553 7.5 0.714 0\nB80M10 3.3 0 2.142 2.6\nG50M10 0 3.75 0.357 4a b c\n3 \n  \n \n  \n \nFigure 1.  TEM photos of BxGyMz. a) B80G10M10; b) B40G50M10. \n \nTEM photos confirm the existence of the nano-ne twork structure, shown in Figure 1 (or Figure \nS2: high resolution photos of TEM),  where intercalated clay platel ets play frames of the network \nand divide the nanocomposites into many nano- polyhedrons filled with polymers (i.e. PBuA). \nWith increasing clay content, the size ( ζ) of the nano-polyhedrons decreases and the frame a-1 \nb-1 a-2\nb-24 \n thickness (D) increases: ζ = 80–200 nm and D = 5–30 nm for B80G10M10, and ζ = 60–100 nm \nand D = 10–400 nm for B40G50M10. There are OA-MNP aggregates in both B80G10M10 and \nB40G50M10. Nano-interfaces of three phases ar ound the OA-MNP aggregates are found in the \nnanocomposites. The three phases are clay plat elets, MNP particles and polymers. The nano-\ninterfaces are believed to be tight because of the merging force of PBuA latexes during the \ncasting process.      BxGyMz nanocomposite films with such ‘nano-netw ork’ structure and ti ght three-phase nano-\ninterface exhibit surprising ultrahigh saturation ma gnetization, even higher than that of pure OA-\nMNP (i.e. 100 emu/g for B80G10M10, and 30 emu/ g for pure OA-MNP), while the saturation \nmagnetization of other two nanocomposites - B80M 10 (the mixture of PBuA and OA-MNP) and \nG50M10 (the mixture of Laponite XLG and OA-MNP) is much lower than that of pure OA-MNP, shown in Figure 2. There is no chemi cal reaction and no new component during the \ncasting process, which is confirmed by the FTIR  (Figure 3), so the surprising saturation \nmagnetization results from th e physical structure in B xGyMz films. Since the unique ‘nano-\nnetwork’ structure and the tight three-phase na no-interface, confirmed by TEM photos, can exist \nonly in the B xGyMz nanocomposites instead of the tw o-component nanocomposites (i.e. \nB80M10 and G50M10). Therefore, the ‘nano-networ k’ structure and the tight three-phase nano-\ninterface is the reason for th e surprising saturation magnetiza tion. In addition, the saturation \nmagnetization decreases with increasing clay  content: the saturation magnetization of \nB40G50M10 is lower than that  of B80G10M10, shown in Figure 2. The OA-MNP aggregates in \nB80G10M10 disperse uniformly in the polymer subs trate, generally near the plates of the nano-\npolyhydrons and surrounded by polymer and clay pl atelets; while most OA-MNP aggregates in \nB40G50M10 disperse in the fram e of the ‘nano-network’, surrounde d by more clay platelets and \nless polymer, shown in Figure 1b, which may make  the nano-interface looser because of the \ndecreasing number of polymer chains. The looser  three-phase nano-interfaces probably give rise \nto the decrease in sa turation magnetization.  5 \n -20 -10 0 10 20-120-100-80-60-40-20020406080100120\n  \n B80M10\n G50M10\n Pure OA-MNP\n B40G50M10\n B60G30M10\n B80G10M10Magnetization (emu/g)\nMagnetic Field (kOe)\n \nFigure 2 . Magnetic hysteresis loop of BxGy Mz, B80M10, G50M10, and pure OA-MNP. \n4000 3500 3000 2500 2000 1500 1000 Laponite XLG\n Oleic acid\n Pure OA-MNP\n B80G10M10\n B40G50M10\nWavenumber (cm-1)\nFigure 3 . FTIR of BxGyMz, oleic acid, OA-MNP and laponite XLG. 6 \n In conclusion, some magnetic nanoparticles (MNP) /clay/poly mer nanocomposites have been \nprepared, whose saturation magnetization is highe r than that of pure oleic acid coated MNP \ncomponent. The existence of unique ‘nano-netw ork’ structure and ti ght three-phase nano-\ninterface in the nanocomposites contribute to th e surprising saturation magnetization. Although \nthe detailed theoretical explanation for the surprising saturation magnetization in the nanocomposites needs to be further investigated in  future, the experimental discovery is believed \nto greatly promote both experimental and theore tical research in magnetism of nanocomposites \nand to widen the applications of magne tic nanocomposites. And perhaps the unique \nnanostructure will also improve the functionality of other functional clay/polymer nanocomposites, like quantum dot/c lay/polymer nanocomposites etc. \nExperimental  \nMaterials:  Butyl acrylate (BuA) (9 8%, Wako Co., Japan), Laponite XLG (Rockwood Co., \nU.S., Mg\n5.34Li0.66Si8O20(OH) 4Na0.66), sodium dodecyl sulfate (SDS ) (99%, Nacalai Tesque Inc., \nJapan), ammonium persulfate (A PS) (98%, Kanto Chemical Co., Inc., Japan). BuA were used \nafter removing inhibitors. Other re agents were used as received. \nPreparation of Polymer Emulsion: The emulsion was prepared by conventional emulsion \npolymerization using monomer (15.6 g; BuA), SDS (0.15 g) as the surfactant, APS (0.06 g) as \nthe initiator and water (57 g) . The reaction was run at 80 oC for 8 h under nitrogen atmosphere. \nThe average diameter of PBuA latex is 67.2 nm. \nPreparation of oleic acid coated magnetic nanoparticles (OA-MNP):  Preparation of OA-\nMNP nanoparticles was carried out according to the well-established co-precipitative reaction \nprotocol. Typically, FeCl 2·4H 2O (2.35 g) and FeCl 3·6H 2O (0.86 g) were disso lved in water (40 \nmL), and co-precipitated by adding con centrated ammonia (28%, 5 mL) under N 2 atmosphere at \n60 oC. Oleic acid (1g) was slowly dropped in to the reactor under vigorous stirring. The \ndispersion was heated to 90 oC, and was kept at 90 oC for 30 min. Then, it was cooled to room \ntemperature. The OA-MNP was poured  into a dialysized bag and was dialyzed with excessive \ndistilled water until the pH of the OA-MNP dispersion dropped to 7. The obtained OA-MNP \nslurry was stored for use. The content of OA-MNP and MNP are 4.2 wt% and 2.1 wt%, \nrespectively, shown in Figure S1. 7 \n Preparation of BxGyMz Nanocomposite Films: First, clay (0.6 g) wa s added into water (30 \ng) under stirring for 2 h to obtain a transparen t aqueous dispersion. Then, an amount of the \ndispersion (1.5–7.5 g) was diluted by water (0–4.686 g). The polymer emulsion (0.553–1.1 g) \nand the OA-MNP slurry (0.714 g) were added into  the diluted clay di spersion, respectively. \nFinally, the mixture was poured into a polyethy lene container and dr ied in an oven at 50 oC for \n30 h. For all samples, the total so lid content was fixate d at 0.3 g. Here, the samples are expressed \nas B xGyMz, where B, G, and M stand for poly(butyl  acrylate) (PBuA), Laponite XLG, and \nmodified magnetic nanoparticle s (OA-MNP) respectively, and x, y, z  stands for PBuA, clay, and \nOA-MNP content (with respect to the total weight).  \n     Measurement methods:  Transmission electron microsco py (TEM) (JEOL JEM2100): 50 nm \nthin film, 100 kV. Thermogravim etric analysis was performed on a Seiko Exstar 6000 TG/DTA \n6200 thermal analyzer (Seiko Instruments, Chib a, Japan) in static air from 30 to 600 oC with a \nheating rate of 10oC min-1. Vibrating sample magnetometer (VSM, Tamakawa Co., Japan) was \ncalibrated by nickel sheet. Nanocomposite films were cut as 5mm×10mm rectangles (thickness: \n40-100 μm; weight: 2.8-7 mg) for measurement. Fourier transform IR (FTIR): 40-100 μm film, \n400-4000 cm-1. \n100 200 300 400 500 600020406080100\n  Weight Loss (%)\nTemperature (oC) \nFigure S1. Thermogravity graph of OA-MNP slurry. 8 \n  \n \na-1 9 \n \na-2 10 \n \nb-1 11 \n \nFigure S2. High resolution photos of TEM of B xGyMz \nAcknowledgements \nThis research is financially supported by Beijing Natural Science Foundation(No.2122015), and \nthe Japan Society for the Promotion of Science for Foreign Researchers (P08043). \nNotes and references b-2 12 \n 1. P. Podsiadlo, A. K. Kaushik, E. M. Arruda, A. M. Waas, B. S. Shim, J. Xu, H. Nandivada, \nB. G. Pumplin, J. Lahann, A. Ramamoorthy and N. A. Kotov, Science , 2007, 318, 80-83. \n2. S. Sinha Ray and M. Okamoto, Prog. Polym. Sci. , 2003, 28, 1539-1641. \n3. T. Kuilla, S. Bhadra, D. Yao, N. H.  Kim, S. Bose and J. H. Lee, Progress in Polymer \nScience , 2010, 35, 1350-1375. \n4. N. Tomczak, D. Ja ńczewski, M. Han and G. J. Vancso, Prog. Polym. Sci. , 2009, 34, 393-\n430. \n5. J. Hu, M. Chen and L. M. Wu, Polym. Chem. , 2011, 2, 760-772. \n6. T. N. Gruji ć A., Stojanovi ć D., Stajić-Trošić J., Burzi ć Z., Balanovi ć Lj., Aleksi ć R., J. \nMin. Metall. B,  2010, 46, 7. \n7. Z. H. Guo, K. Shin, A. B. Karki, D.  P. Young, R. B. Kaner and H. T. Hahn , J Nanopar. \nRes., 2009, 11, 1441-1452. \n8. J. Martín, M. Hernández-Vélez, O. de Abr il, C. Luna, A. Munoz-Martin, M. Vázquez and \nC. Mijangos, Euro. Polym. J. , 2012, 48, 712-719. \n9. N. Negrete-Herrera, J.-L. Putaux, L. Davi d, F. D. Haas and E. Bourgeat-Lami, Macromol. \nRapid Commun. , 2007, 28, 1567-1573. \n10.T. Wang, P. J. Colver, S. A. F. Bon and J. L. Keddie, Soft Matter , 2009, 5, 3842-3849. \n11.C. J. G. Plummer, R. Ruggerone, E.  Bourgeat-Lami and J.-A. E. Månson, Polymer , 2011, 52, \n2009-2015. \n "    },    {        "title": "1206.5181v1.Reversible_Control_of_Magnetic_Interactions_by_Electric_Field_in_a_Single_Phase_Material.pdf",        "content": "1 \n Reversible Control of Magnetic Interactions by Electric Field in a Single Phase Material.  \n \nP. J. Ryan1, J. -W. Kim1, T. Birol2, P. Thompson3, J. -H. Lee1, X. Ke4, P. S. Normile5, E. Karapetrova1, P. \nSchiffer6, S. D. Brown3, C. J. Fennie2, D. G. Schlom7. \n \nIntrinsic magnetoelectric coupling describes the interaction between magnetic and electric polarization \nthrough a n inherent  microscopic mechanism  in a single phase material. This phenomenon has the \npotential to control the magnetic state of a material with  an electric field , an enticing prospect for \ndevice engineering. We demonstrate  ‘giant’  magnetoelectric cross -field control  in a single phase rare \nearth titanate film. In bulk form , EuTiO 3 is antiferromagnetic . However , both anti and ferromagnetic \ninteractions coexist betwe en different nearest neighbor europiu m ions. In thin e pitaxial films , strain can \nbe used to alt er the relative  strength of the magnetic  exchange constants . Here, w e not only show that \nmoderate biaxial compression precipitates loca l magnetic competition, but also demonstrate that the \napplication of an electric field at this strain state , switches the magnetic ground state. Using first \nprinciples density functional theory , we resolve the  underlying microscopic mechanism  resulting in the  \nEuTiO 3 G-type  magnetic structure and illustrate how it  is responsible for  the ‘giant’ cross -field \nmagnetoelectric effect . \n \n \n1 X-ray Science Division, Argonne National Laboratory, Argonne, Illinois, 60439, USA.2 School of Applied Engineeri ng Physics, \nCornell University, Ithaca, New York 14853 -1501, USA. 3 University of Liverpool, Dept. of Physics, Liverpool, L69 3BX, United \nKingdom & XMaS, European Synchrotron Radiation Facility, Grenoble, France.4 Quantum Condensed Matter Division, Oak Rid ge \nNational Laboratory, Oak Ridge, TN 37831, USA . 5Instituto Regional de Investigación Científica Aplicada (IRICA) and \nDepartamento de Física Aplicada, Universidad de Castilla -La Mancha, 13071 Ciudad Real, Spain.  6 Department of Physics and \nMaterials  Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, USA.  7Department of \nMaterials Science and Engineering, Cornell University, It haca, New York 14853 -1501, USA. Correspondence to:  \npryan@aps.anl.gov  \n 2 \n The magnetoelectric (ME) effect represents the coupling between the electric and m agnetic \nparameters in matter1. M ultiferroic (MF) materials with coexisting  ferromagnetism (FM) and \nferroelectricity  were  thought to offer the best prospect  of achieving a strong linear ME coupling \ncoefficient due to the combination of typically higher electric permittivity and magnetic permeability, \nboth of which combine as an upper limit to any potential coupling strength2. Unfortu nately, ME-MF \nmate rials are rare since ferroelectric materials need to be  robustly insulating while magnetic materials \nare typically conducting3. Although uncommon, such compounds have been the subject of intense \nresearch over the past decade1,2. The realization of this  phenomenon may lead to the dev elopment of \nmultistate logic, new  memory or advanced sensor technologies2. To integrate such characteristics into a \nfunctional device requires strong ME coupling between the ferroic properties, enabling the \nmanipulation of magnet ic order with an electric (E) field or electric polarity with a magnetic field. The \nintense search for materials exhibiting such functional ferroic control has centered on a number of \ncomplex oxide systems with a ps eudo -cubic perovskite structure2-5. Withi n these systems , the electronic \nband structure of the central B -site cation generally determines the ferroic properties. A completely \nempty d band is required for ferroelectricity, while partial occupation is ess ential for the double and \nsuper exchange (SE) magnetic interacti ons, typical of these materials3,6. One approach circumventing  this \nobstacle has been to engineer spatially segregated two phase systems which take advantage of electro - \nor magnetostriction mediated through strain or pr oximity to generate ME coupling7-12. However, finding \nan intrinsic single -phase  mechanism would evade the inherent disadvantages and complexities of \nmultiphase environments. In single -phase systems , the d band occupation issue is typically avoided  \nthrough geometric ( magnetic) frustration, where the ferroic properties arise from the D zyaloshinski -\nMoriya interaction13-16. In these cases, the ferroic properties are weak, relegating device application \nunlikely.   3 \n Alternatively , the ferroic functionalities may be carried se parately by the perovskite A and B site \ncations  as in the case of BiFeO 317. The rare earth tetravalent titanate,  EuTiO 3 (ETO)  is an  emerging multi -\ncation ferroic proto type , whereby magnetic spins are carried by the half -occupied Eu 4f7 spins and the \nunoccupied  Ti 3d0 band lends itself to potential ferroelectricity. Moreover, t he anomalous response  of \nthe dielectric constant to spin alignment  indicates  an inhere nt ME coupling mechanism in ETO18. It was \nthis effect that impelled  Fennie and Rabe to calcu late that, through strain engineering , one could c reate \nstrong multiferroicity  and additionally predict the exceptional strain -boundary state , allowing  cross -field \ncontrol capability19. Indeed, epitaxial films  of tensile strained ETO  showed  multiferroicity  with a large \nferromagnetic moment (7μ B/Eu) alongside spontane ous electric polarization (~10μCm-2)20. Furthermore , \nETO demonstrates a third order biquadratic ME coupling response (E2H2) allowing for circumvention of \nthe linear ME  susceptibility  boundary condition21. \nIn this article , we present  E-field  control of the full magnetic moment in the single phase ETO \nsystem . However , our findings do not match initial predictions. Instead, we find the dramatic ME effect \ndoes not require the proposed pol ar instability19 . Ra ther , the combination of tuning the relative \nstrengths of the intrinsic competing magnetic interactions under a moderate compressive strain state \nwith  the inherent paraelectric nature of the system is sufficient to generate complete ME control .  \nX-ray resonant magnetic scattering (XRMS) was used to confirm the magnetic structure  of the  \ncontrasting strained ETO film series a nd reveal  the emergence of competition between coexisting \nmagnetic interactions in a moderately (-0.9%) compressed state. First principles density functional \ntheory ( DFT) calculations identified  the third  nearest neighbor (NN) Eu interaction central to  the G-AFM \nstructure of ETO.  Finally , using in-situ (E-field) XRMS , we demo nstrate cross -field ME control by  \neliminating  long rang e AFM order and inducing a magnetic state of nanometer sized FM clusters. The \nunderlying intrinsic mechanism is illustrated  through simulations replicating the effect of E -field \napplication by calculating the energy difference between  the AFM and FM spin configurations.  4 \n  \nResults  \nX-ray scattering  is sensitive to both charge and magnetic distributions22. Typically, the magnetic \ncomponent is about 6 orders of magnitude lower than conventional charge scattering. H owever , \nthrough resonance  an enhanced magnetic response  in th e present  case at the Eu L II edge , whereby, \nthrough  the Eu 4f -5d exchange interaction , the Eu sublattice  magnetic structure  is probed by E1 (2p 1/2-\n>5d 3/2) electronic excitations. Additionally , due to the polarization  dependence of magnetic  scattering  a \npost  sample analyzer  can be used to preferentially suppress charge scattering  as illustrated in Fig. 1a. \nUnstrained , compressive and tensile strai n states were accomplished with 22nm of epitaxial cube on \ncube layered growth by ozone assisted molecular beam epitaxy on SrTiO 3(STO), (LaAlO 3)0.29-\n(SrAl ½Ta½O3)0.71(LSAT) , and DyScO 3(DSO)  single crystal substrates respectively20.  \nBoth ETO and STO share the same lattice parameter, thus when grown on the (001) surface , the \nfilm is nominally unstrained and exhibits bulk like G -AFM  order  with the emergence of  magnetic \nscattering  intensity at (1/2 1/2 5/2) ETO below T N at 5.25  K shown  in Fig. 1a . A -0.9 % compressive strain is \nimposed by the  LSAT (001)  substrate and as shown in Fig. 1b  also maintains  G-AFM  order with the onset \nof magnetic scattering at TN of 4. 96 K. Under 1.1 % tensile strain the ETO film grown on DSO(110) is \nhowever ferromagnetic, confirmed both by  the absence  of a resonant magnetic signature at the (1/2 1/2 \n5/2) ETO reflection shown in Fig. 2a  and with  the emergence of a resonant enhancement of the magnetic \nscattering at the (001) ETO reflection at the Eu L II edge shown in Fig. 2b, with a T C of 4.05  K. \nContrasting wit h the unstrained  (STO)  and tensile strain (DSO) conditions the temperature \ndependence of the magnetic scattering intensity of the compressive state  (LSAT)  shows a significantly \ndissimilar  and suppressed  critical behavio ur, presented in Fig. 3a. This charac ter is found in systems due \nto local competition between FM and AFM intera ctions exemplified by the mixed -magnetic crystal \nsystem Gd xEu1-xS 23. The temperature dependent magnetic scattering intensity  is fit to  the critical 5 \n behavio ur <m>2 ~ I = I0(1 - T/TCritical )2β, where < m> is the magnetic moment, I is the magnetic scattered \nintensity, T = sample temperature, TCritical  = magnetic transition temperature and β = the critical order \nexponent.  The AFM order of the ETO -STO film closely follows the 3 dimension al (D) Heisenberg  model \nwith a crit ical order exponent of β=0.385 , while a larger exponent, 0.496 , is found  in the compre ssively \nstrained ETO -LSAT film. The substantial magnetic suppression demonstrates  significant local magnetic \ncompetition.  Similar to the unstrained  G-AFM  state , the tensile strained ETO-DSO film in the FM phase  \nalso indicates  3-D Heisenberg behavio ur where the local FM exchange dominates t he AFM interacti ons \nwithout evidence of competing magnetic interactions .  \nClearly both local AFM and FM interactions coexist within the ETO. In order to describe the \nunderlying mechanism determining the G -AFM Eu spin structure, previous first principles DFT focused \non the 1st and 2nd NN Eu ion  interactions , illustrated in Fi g. 3a–inset24,25. Without significant volume \n(lattice)  expansion the calculatio ns found FM order preferential. However t o investigate the underlying \nfactor leading to the G -AFM magnetic structure, the issue of symmetry needed to be addressed, in order \nto best know  the structure at hand . This was accomplished through a combination of  DFT calculations \nand XRD measurements.  Until recently, bulk EuTiO 3 under zero stress boundary conditions was \ntraditionally believed to be in high symmetry cubic Pm -3m space group. H owever our first principles \ncalculations indicated that there were strong rotational instabilities  as recently discussed by \nRushanchinskii et al.26. \nThe full ionic relaxations show that the lowest energy structure was I4/mcm  or (a0a0c-) in Glazer \nnotation with the  emergence of antiferrodistortive (AFD) oxygen octahedral rotations27. Energy gain due \nto this distortion is 30 eV/f.u., but the energy difference between this state and another metastable \nstate, Imma, (a-a-c0) is less than an eV/f.u.. The competit ion between these two possible rotation \npatterns b ecomes evident when we consider the structures under strain. Geometric relaxations were \nperformed  keeping the in -plane lattice constant fixed but relaxing the out -of plane  lattice length  6 \n corresponding to  the films fixed biaxial strain boundary conditions. When we compare energies of \ndifferent rotation patterns under thes e conditions, we see that the two aforementioned patterns \ncompete. A s a result the (a-a-c0) pattern  is favored under tensile s train  and (a0a0c-) is favore d under \ncompressive strain.  In Fig. 3 b we present XRD results r efining  the AFD related  structure of the ETO film \non LSAT . The combination of  the non-zero H=L (1/2 5/2 1/2) ETO reflection with the absence of the H=K \n(1/2 1/2 5/2) ETO peak indicates  the emergence  of a pure in-plane AFD rotation  finding agreement with \nthe DFT calculations indicating  I4/mcm  or (a0a0c-) symmetry28. The biaxial compressive strain effect \ngenerating the octahedral rotations is illust rated in the pseudo -cubic perovskite cell in Fig. 3b -inset.  \nEngaging the AFD revised strain dependent DFT calculat ions invoked considerable differences  in \nthe strain -phonon response compared to the initial  calculations19. The competitive coupling between \nthe pol ar and rotational structural instabilities leads to the calculated suppress ion of the predicted  polar \nT01 phonon instability  state29. The biaxial compression drives the AFD in-plane rotation  in an attempt  to \nmaintain  the Ti -O bond length s, consequently  prevent ing the T01 phonon  from ‘freez ing’ out of the film \nplane  and thus  providing an alternate avenue to minimise bond length changes . While the previous \ncalculations without rotations (pm -3m) (a0a0c0) indicated a  ~-0.9% strain generat ing the polar instability,  \nour current calculations including  the AFD rotations require  ~-2.5% compressive strain  beyond what is \ncurrently achievable.  \nIn table 1  we present the calculated results of the magnetic exchange interactions (J) for the 1st, \n2nd and 3rd NN Eu ions for the ETO (a0a0c-) structure for both bul k (zero boundary conditions) and under -\n0.9% compressive strain, simulating epitaxial growth on the LSAT substrate. The exchange constants are \nbroken down further into in -plane  (xy) and out -of-plane  (z), with positive and  negative  values  indicating \nFM and AFM respectively.  We find that both the 1st and 2nd NN Eu atoms interact in aggregate  with FM \norder . The 3rd NN interaction  however is AFM  coupled . This diagonal exchange is most likely facilitated  \nby the central Ti 3d0 band coupled to the Eu 4f7 spins through a 180° SE mechanism mediated by the 7 \n intra -atomic hybridized 4f -5d orbitals , similar to the previously propose d 90° SE mechanism between \nthe 1st NN Eu ions24. As a result, t he G-AFM structure is  dependent upon this 3rd NN interaction. \nMoreover,  the strength of this SE coupling is reliant  upon the Eu -Ti-Eu bond alignment, thus sufficient \nangular distortion could significantly alter the magnetic structure of the entire system30. \nUpon  this premise, the paraelectric natur e of the ETO film  becomes central to the feasibility of  \nME control. In Fig. 4a, the cartoon illustrates how the 3rd NN interaction bond angle alignment is \ndistorted by the Ti displacement from its central position  under an applied E -field , reducing the efficacy \nof the interaction. Under biaxial compression the system is  expected to have  a preferential uniaxial \npolar anisotropy with the Ti displa cement out of the film plane. Thus in order  to examine the capability \nof ME cross -field control we measured the  magnetic signature  of the strained ETO-LSAT film where the \ncompetition between the magnetic interactions is prevalent and appl ied an E -field across the film  to \nfurther alter the magnetic balance , as illustrated in the sample schematic  in Figure 4b.  \nA seri es of reciproca l space scans through the G-AFM (1/2 1/2 5/2 )ETO magnetic reflection at 1.9  \nK versus E-field strength  is presented  in Fig. 4c . The suppression of the XRMS  intensity with E- field is \nclearly displayed and is ostensibly eliminated by  1.0×105 V/cm . The t ransitio n lacks hysteresis, is \ncontinuous , and reproducible. In F ig. 4d the resonant ma gnetic scattering amplitude at the  fixed  film Q \nposition is plotted w ith decreasing  E-field strength and  on the return the data is extracted from a series \nof L scans through the magnetic reflection at each field point . This plot exemplifies the reversibility and \ndemonstrates the stability of the transition with each  data point separated by 30 minutes on the return .  \nTo further establish  the proposed underlying  ME microscopic mechanism we performed  first principles \nDFT calculations to replicate  the response of the applied E -field  on the strained film . In Fig. 4d, the \ncalculated enthalpy difference between the G-AFM and FM spin configurations  is plotted against the \neffective polarization. The polarization is simulated by calculating the lowest frequency polar Eigen \nmode, and then forcibly and incrementally displacing the oxygen ions further from the face center  8 \n (a0a0c-)  in conjunction with the Ti shift to mainta in this frequency minimum. The resulting energy \ndifference s between  both magnetic states  are subsequently calculated. The system responds by  \nenergetically  trending from AFM towards FM order with increasing polar ization. Crucially it is the \nparaelectric gro und state which allows for the ability to displace the Ti atom. This shift affects the \nrelative strength of the local magnetic interactions reducing the 3rd NN exchange coupling . In order to \nreach a quantitative correlation between experiment and theory, w e have estimated the critical E-field \nby dividing the energy required to displace the ions by the polarization. To generate a polarization field \nof P = 18 μC/cm2, where AFM and FM states are degenerate, would require  ~ 5 x 105 V/cm. This is \ncomparable to  the experimental field found to extinguish the AFM state, ~1.0  x 105 V/cm.  \nTo explore  the resulting induced magnetic state by E -field, we employed x -ray resonant \ninterference scattering (XRIS)31. XRIS is sensitive to the magnetic moment aligned along one direction by \neither an internal FM interaction or an external magnetic field. Even in the AFM state, the magnetic \nmoments uniformly canting towards an external magnetic field direction result in c harge -magnetic \ninterference of the scattered intensity  illustrated in Fig. 5a. Here contrasting  energy scans through the \nEu L II edge at the (003) ETO reflection with opposing applied magnetic field directi ons ([110] ETO) at 1.2T in \nthe film plane  demonstrate  the interference effect. The measurements were made in horizontal \nscattering geometry which provide s for additional  charge scattering  suppression , illustrated in Fig. 5b -\ninset . In ETO the AFM coupling is generally weak  and as a result  1 T is sufficient to fully saturate the Eu \nmoments alo ng the magnetic field direction shown  by the magnetic field dependence of the \ninterference effect in Fig. 5b. This plot shows  the degree of magnetic moment canting by the external H -\nfield is proportion al to the field strength . \nFigure  5c-i presents the XRIS spectroscopic differ ence applying 0.1  T showing  that the magnetic \nmoments cant  towa rds the field direction with ~10% of the  full Eu moment . Once the electric field \n(1\n105 V/cm) is applied, the interfe rence effect is quenched , Fig5c -ii. This was  a surprising result 9 \n because an enhanced  XRIS effect  due to long range FM order  would be expected . Alternatively, i f the \nelectric field induced a true AFM -FM degenerate state, the magnetic ally frustrated moments would \nnevertheless align along the applied magnetic field direction resulting in an interference effect. Similarly, \nif the E -field c aused a paramagnetic state, 0.1  T is sufficient to align the magnetic moments producing \nan interference effect due to small  thermal fluctuations at this  temperature, 1.9 K. Consequently, the \nmagnetic state induced by the E -field is neither frustrated nor param agnetic . However to adequately  \nexplain both the XRIS and AFM order suppression  would require  the emergence of short rang e ordered \nnanometer sized FM clustering . This model disrupts the long range spin coherence of the AFM order \nwhile the emergence of FM interactions in short range cluster  formation  remain insufficiently large to \ncontribute to t he charge -magnetic interferenc e.  \nDiscussion  \nOur findings present conclusive evidence for direct single phase cross -field ME control in a \ncompressively strained EuTiO 3 film. Employing in-situ x-ray scattering measurements , we present \nreversible electric swit ching of magnetic order using a strong intrinsic coupling phenomenon. We have \ndirectly measured the microscopic magnetic structure of EuTiO 3 as G -AFM under low strain states (0.0% \n& 0.9%) and FM under 1.1%  tensile strain. The magnetic critical parameters s how  -0.9% compressive \nstrain  alters the relative strength s of coexisting AFM and FM magnetic interactions bringing them into \ncompetition . First principles DFT calculations indicate that the 3rd NN Eu ion  super exchange interaction \nmediated through the centr al Ti ion, ultimately determines the G -AFM spin periodicity along the <111> \ndirection. Moreover by  calculating the energy of the simulated ETO -LSAT film , we have replicated our \nexperimental findings by modeling the field induced polarization effect with co ntrolled Ti displacements. \nAs such, the energetic stability of the AFM order  dissipates leading to the  emergence  of FM interactions . \nThe underlying mechanism relies on bond alignment distortion suppressing the efficacy the  3rd NN Eu -Ti-10 \n Eu interaction. This novel ‘giant’ ME coupling phenomenon will likely offer intriguing prospects to \nexplore new types of ME functionality.  \nMethods  \nX-ray Resonant Magnetic Scattering (XRMS) . XRMS measurements were performed on the 6 ID -B \nbeamline at the Advanced Photon Sou rce and the XMaS beamline at European Synchrotron Radiation \nFacility. The sample was mounted on the cold finger of a Joule -Thomson stage closed cycle helium \ndisplex refrigerator. The incident x -ray energy at 6 -ID was tuned to the Eu L II edge by a liquid ni trogen \ncooled double crystal Si(111) monochromator source with a 3.3cm period undulator. The XMaS \nbeamline is a bending magnet source and the energy selection performed with a water cooled double \ncrystal Si(111) monochromator. All samples were oriented wit h respect to the substrate crystallographic  \naxis. The films are epitaxial to their substrates so that the  film diffraction peaks are easily found with \nrespect to the substrate reciprocal matrix. The incident x -ray is linearly polarized perpendicular to the  \nscattering plane (σ polarization). The resonant magnetic scattering , arising from electric dipole \ntransitions from the 2 p-to-5d states, rotates the polarization resulting in π polarized photons (parallel to \nthe scattering plane). A post sample pyrolytic g raphite analyzer at the (0 0 6) PG reflection was used to \nselect π -polarized radiation and suppress the background from charge scattering (σ polarized light).  \nMagnetic scattering is not frequently used to measure ferromagnetism with zero magnetic field bec ause \nthe magnetic reflection occurs at the same position in reciprocal space as the larger charge scattered \nintensity. In the rare -earth compound however, the magnetic scattering intensity can be comparable to \nthe final charge scattering by coupling the la rge resonant enhancement and suppression of the charge \nscatt ering by polarization analysis32. It is expedient to choose the optimum reflection to maximize the \nmagnetic to charge scattering ratio since the chemical structure factor is different from the magnetic \nstructure factor. The (0 0 Odd) ETO charge reflection is about 40 times smaller than the  (0 0 Even) ETO \nreflection, where the diffracted x -rays are in -phase enhancing the scattering amplitude due to the 11 \n structure factor of the ETO film. The magnetic structure factor, on the other hand, is the same for both \n(0 0 Even) ETO and (0 0 Odd) ETO reflec tions. Hence, we obtained the clear resonant behavio ur from the \ndifference between the intensity of the (001) ETO reflection above and below T C presented in Fig. 2b.  \nX-ray resonant I nterference Scattering, (XRIS).  Measurement of ferromagnetic order can also  be \nachieved from the interference between magnetic and charge s cattering at the resonant edge32.  \nNominally in the XRMS  process, the electric dipole resonance is dominant. The magnetic scattering (E1 \ntransition) from the moments out of the scattering plan e produce the same polarization as the charge \nscattering when the incoming polarization is parallel to the scattering plane (\n -polarization). Thus, the \ncharge scattering and magnetic scattering can interfere and con sequently the interference effect is \ndepe ndent on the magnetic moment direction. X -rays from synchrotron radiation are linearly polarized \n(in the plane of the synchrotron itself) so by using horizontal scattering geometry with the magnetic field \napplied in the vertical direction orthogonal to bot h the beam direction and beam polarization one may \nmeasure the interference change by  alternating the H -field direction (up and down).  \nFirst Prin ciple Density Functional Theory.  We performed Density Functional Theory calculations with \nprojector augmented w ave potentials in the GGA+U framework, using VASP code. We used a 8 x 8 x 8 k -\npoint grid for Brillouin zone integrals and a 500eV plane -wave energy cutoff. This cutoff has been \nincreased to 600eV in certain parts of the calculations for greater accuracy. G eometric relaxations are \ndone by keeping the in -plane lattice parameter ‘a’ fixed and relaxing the out -of-plane lattice parameter \n‘c’. Residual force threshold was decreased to 0.5 eV/Å where necessary in order to resolve differences \nbetween states close i n energy. An external stress has been applied along the c axis in order to \ncompensate for the over estimation of cell volume . Exchange parameters for an Ising model are fitted to \ntotal energy calculations done in a 2 x 2 x 2 perovskite supercell that consis ts of 40 atoms and 10 \ndifferent magnetic configurations. Standard deviations of these exchange parameters are not reported \nsince they are small and of no qualitative significance.  12 \n EuTiO 3 is predicted to be near a magnetic phase transition as a function of the on -site Hubbard repulsion \nparameter U25. In order to pick a best initial estimate of U, we calculate the Curie -Weiss constant and \nNeel temperature for bulk (under fixed stress boundary conditions) EuTiO 3, the results are presented in \nTable 2 . It is not  possible to reproduce the exact transition temperatures from first principles due to \nlimitations of the simple mean field theory we used, and also because of the very small energy \ndifferences under consideration. However, if we pick a U that gives a T N : TC ratio close to experiment (T C \nis extracted fr om susceptibility measurements  33), then we can get a good sense of the competition \nbetween FM and AFM states. We see that U = 5.7 eV, which is the value that was used in previous \nstudies works well when oxyg en rotatio ns were not taken into account (19) . However, once the \nrotations are taken into account and calculations are repeated in the relevant structure (I4=mcm), a U = \n5.7eV overestimates the T N : TC ratio. To better fix the deficiencies in DFT, we inste ad use U = 6.2 eV as \nstandard. Also, an intra -atomic exchange parameter J=1.0 eV is kept fixed.  \nAcknowledgments:  Work at Argonne and use of beamline 6 -ID-B at the Advanced Photon Source at \nArgonne was supported by the U. S. Department of Energy, Office of  Science, Office of Basic Energy \nSciences under Contract No. DE -AC02 -06CH11357. The EPSRC -funded XMaS beamline at the ESRF is \ndirected by M.J. Cooper, C.A. Lucas and T.P.A. Hase. P. S., X. K., J -H. L. and D.G. S were funded through \nPSU MRSEC, Grant DMR -0820404. T. B. and C. J. F. were supported by the DOE -BES under Grant No. DE -\nSCOO02334. P.J.R is grateful for fruitful discussions with Jonathon Lang, Steve May, John W. Freeland, \nAndreas Kreyssig and Yusuke Wakabayashi. Additional thanks to Michael Wieczorek  & Chian Liu and \nMichael McDowell & David Gagliano for sample processing and sample environment engineering, \nrespectively. We are grateful to O. Bikondoa, D. Wermeille, and L. Bouchenoire for their invaluable \nassistance and to S. Beaufoy and J. Kervin for additional XMaS support.  \n \n 13 \n References  \n1. Fiebig, M. Revival of the magnetoelectric effect. J. Phys. D 38, R123 -R152 (2005).  \n2. Eerenstein, W., Mathur, N. D. & Scott, J. F. Multiferroic and magnetoelectric materials. Nature  \n442, 759 -765 (2006).  \n3. Hill, N. A. Why are there so few magnetic ferroelectrics? J. Phys. Chem.  B. 104, 6694 –6709 \n(2000).  \n4. Cheong, S -W. & Mostovoy, M. Multiferroics: A magnetic twist for ferroelectricity. Nat. Mater . 6, \n13-20 (2007).  \n5. Spaldin, N. A., Cheong, S -W. & Ramesh, R . Multiferroics : Past, present, and future. Physics \nToday  63, 38-43 (2010).  \n6. Cohen, R. E. Origin of ferroelectricity in perovskite oxides. Nature  358, 136 -138 (1992).  \n7. Eerenstein, W., Wiora, M., Prieto, J. L., Scott, J. F. & Mathur, N. D. Giant sharp and persistent \nconverse magnetoelectric effects in multiferroic epitaxial heterostructures. Nat. Mater . 6, 348 -351 \n(2007).  \n8. Wu, S. M. et al.  Reversible electric control of exchange bias in a multiferroic field -effect device. \nNat.  Mater . 9, 756 -761 (2010 ). \n9. Chen, Y., Fitchorov, T., Vittoria, C. & Harris, V. G. Electrically controlled magnetization switching \nin a multiferroic heterostructure. Appl. Phys. Lett.  97, 052502 (2010).  \n10. Zavaliche, F. et al.  Electric Field -Induced Magnetization Switching in E pitaxial Columnar \nNanostructures. Nano Lett.  5, 1793 -1796 (2005).  \n11. Choi, Y. J., Zhang, C. L., Lee, N. & Cheong, S -W. Cross -Control of Magnetization and Polarization \nby Electric and Magnetic Fields with Competing Multiferroic and Weak -Ferromagnetic Phas es. Phys. Rev. \nLett.  105, 097201 (2010).  \n12. Tokunaga, Y. et al.  Composite domain walls in a multiferroic perovskite ferrite. Nat. Mater.  8, \n558-562 (2009).  \n13. Fiebig, M., Lottermoser, Th., Frohlich, D., Goltsev, A. V. & Pisarev, R. V. Observation of coup led \nmagnetic and electric domains. Nature  419, 818 -820 (2002).  \n14. Ueland, B. G., Lynn, J. W., Laver, M., Choi, Y. J. & Cheong, S. -W. Origin of Electric -Field -Induced \nMagnetization in Multiferroic HoMnO 3. Phys. Rev. Lett.  104, 147204 (2010).  \n15. Hur, N. et al. Electric polarization reversal and memory in a multiferroic material induced by \nmagnetic fields. Nature  429, 392 -395 (2004).  \n16. Kimura, T. et al.  Magnetic control of ferroelectric polarization. Nature  426, 55–58 (2003).  \n17. Wang, J. et al.  Epitaxial  BiFeO 3 Multiferroic Thin Film Heterostructures. Science  299, 1719 -1722 \n(2003).  \n18. Katsufuji, T. & Takagi, H. Coupling between magnetism and dielectric properties in quantum \nparaelectric EuTiO 3. Phys. Rev. B  64, 054415 (2001).  \n19. Fennie, C. J. & Rabe, K.  M. Magnetic and electric phase control in epitaxial EuTiO 3 from first \nprinciples. Phys. Rev. Lett.  97, 267602 (2006).  14 \n 20. Lee, J. H. et al.  A strong ferroelectric ferromagnet created by means of spin -lattice coupling. \nNature  466, 954 -958 (2010).  \n21. Shvar tsman, V. V., Borisov, P., Kleemann, W., Kamba, S. & Katsufuji, T. Large off -diagonal \nmagnetoelectric coupling in the quantum paraelectric antiferromagnet EuTiO 3. Phys. Rev. B 81, 064426 \n(2010).  \n22. Blume, M. Magnetic scattering of x -rays. J. Appl. Phys.  57, 3615 -3618 (1985).  \n23. Hupfeld, D. et al.  Element -specific magnetic order and competing interactions in Gd 0.8Eu0.2S. \nEurophys. Lett.  49, 92-98 (2000).  \n24. Akamatsu, H. et al.  Antiferromagnetic superexchange via 3 d states of titanium in EuTiO 3 as seen \nfrom hybrid Hartree -Fock density functional calculations. Phys. Rev.  B 83, 214421 (2011).  \n25. Ranjan, R., Nabi, H. S. & Pentcheva, R. First principles study of magnetism in divalent Eu \nperovskites. J. Appl. Phys.  105, 053905 (2009).  \n26. Rushchanskii, Konstantin Z., Spaldin, Nicola A. & Ležaić, Marjana.  First -principles prediction of \noxygen octahedral rotations in perovskite -structure EuTiO 3. Phys. Rev. B 85, 104109 (2012).  \n27. Glazer, A. M. The classification of tilted octahedra in perovskites. Acta C ryst.  B 28, 3384 (1972).  \n28. May, S. J. et al.  Quantifying octahedral rotations in strained perovskite oxide films. Phys. Rev. B \n82, 014110 (2010).  \n29. Zhong, W. & Vanderbilt, David. Competing Structural Instabilities in Cubic Perovskites. Phys. Rev. \nLett. 74, 2587 (1995).  \n30. Treves, D., Eibschütz, M. & Coppens, P. Dependence of superexchange interaction on Fe3+-O2-\nFe3+ linkage angle. Phys. Lett.  18, 216 -217 (1965).  \n31. Brown, S. D. et al.  Dipolar Excitations at the LIII X-Ray Absorption Edges of the Heavy Rare -Earth \nMetals. Phys. Rev. Lett.  99, 247401 (2007).  \n32. Kim, J. W. et al.  X-ray resonant magnetic scattering study of spontaneous ferrimagnetism. Appl. \nPhys. Lett.  90, 202501 (2007).  \n33. McGuire, T. R., Shafer, M. W. , Joenk, R. J., Alperin, H. A. & Pickart, S. J. Magnetic Structure of \nEuTiO 3. J. Appl. Phys. 37, 981 -982 (1966).  \n \n \n \n \n 15 \n  \nFigure  1. X-ray resonant magnetic scattering (XRMS) presenting G -AFM order in epitaxial ETO films  \ngrown on STO(001) and LSAT (001) substrates . (a) A series of reciprocal L -scans (film normal) through \nthe (1/2 1/2 5/2) ETO reflection of the nominally unstrained ETO on STO (001)  through a range of \ntemperatures crossing TN. Also seen  is a half order reflec tion from the STO substrate due to AFD order. \nThe measurements were taken in vertical scattering geometry with σ to π polarization  selection analysis  \n(inset) used to suppress charge and optimize the magne tic/charge scattering ratio. (b ) A similar \ntemperatu re dependence data  set for the compressively ( -0.9%) strained ETO on LSAT (001) . The \nencumbering substrate charge intensity originates from anti -phase boundary half order reflections \ntypical of LSAT.  The inset shows the resonant response with an energy scan  at 1.5K through the Eu L II \nedge.  \n \n16 \n  \n \nFigure  2: XRMS demonstrating both the absence of G -AFM order and the emergence of FM order in \nthe 1.1% tensile strained ETO on DSO(110) substrate.  a) An L -scan through the (1/2 1/2 5/2) ETO \nreflection at 1.6K below the TC mark of 4.05K. Some charge scattered leakage is detected, however an \nenergy scan through the Eu L II edge is presented in the inset showing no resonant (magnetic) response. \nThe finding demonstrates absence of long range G -AFM order of the Eu ions in the FM phase. The leaked \ncharge amplitude derives from the octahedral tilting pattern, (a-a-c0) (26). (b) Presents contrasting \nenergy scans through the Eu L II edge above and below TC at the integer (001) ETO reflection . Inset plots an \nL-scan through the same reflection . Due to the overlap of both charge and magnetic scattering at this \nreflection, suppression of the former is restricted . The onset of magnetic scattering below TC is shown \nwith the increase of scattered intensity through the edge  and indicates the spontaneous (zero field) FM \nlong range order. The magnetic scattering contribution was about 9 % of the total intensity . \n17 \n  \nFigure 3. Magnetic  critical behavio ur of the magnetic scattering intensities of the three strain states \nand XRD demonstrating  the oxygen octahedral rotations  in the ETO on LSAT . (a) The temperature \ndependence of the XRMS Eu L II amplitudes for all three strain states, STO - unstrained, LSAT - 0.9% \ncompressive and DSO - 1.1% tensile. The solid lines are fits of the critical behavio ur <m>2 ~ I = I0(1 - \nT/TCritical )2β, where < m> is the magnetic moment, I is the magnetic scattered intensity, T = sample \ntemperature, TCritical  = magnetic transition te mperature and β = the critical order exponent. Both the G -\nAFM order in the unstrained (STO) and FM order of tensile (DSO) film s show typical 3D Heisenberg \nbehavio ur while the compressively strained (LSAT) film shows significant suppression , a classic indicator \nof local magnetic competition. Inset -top, presents a log -log plot showing the near transition region.  Inset \nbottom illustrates the multiple coexisting magnetic interactions between the 1st, 2nd and 3rd NN Eu ions.  \n(b) The symmetry resp onse of the ETO film to t he biaxial compressive tetragonal distortion imposed by \nthe LSAT (001) substrate. Both the (1/2 5/2 1/2) ETO and (1/2 1/2 5/2) ETO reflections at 300  K are \npresented. The occurrence  of half order Bragg peaks  show the presence of  long  range AFD rotations in \nthe film. The combination of H=L allowed and H=K forbidden reflections indicate I4/mcm symmetry with \nthe oxygen octahedral pattern (a0a0c-) in Glazer notation27, illustrated in the bottom inset . Again the \nLSAT substrate generates substantial background from the anti -phase boundary half order reflections. \nThe top inset indicates the relative position of the (002) ETO reciprocal position with respect to the \nsubstrate (002) LSAT.  \n18 \n  \n \nFigure 4 : With th e application  of an E -field across the ETO film on LSAT we demo nstrate and model \nthe control of the magnetic  state.  (a) The response of the Ti atom to E -field is represented pictorially as \na displacement along the direction of the field distorting the Eu -Ti-Eu 3rd NN bond alignment. (b) \nPresents a schematic of the exp erimental sample environment for the  in-situ XRMS measurement. (c) A \nseries of L -scans through the G -AFM scattered (1/2 1/2 5/2) ETO reflection with incrementally increasing \nE-field strength sho wing the suppressive response of the AFM signature. (d) Presents a static Q plot of  \nthe magnetic scattering intensity (1/2 1/2 5/2) ETO vs. E -field with increasing and decreasing field \nstrength. (e) A plot of the f irst principles DFT  calculations  of the ene rgy differences between FM and G -\nAFM spin configuration s as a function of polarization modeled upon the ETO on LSAT with a compressive \nstrain state of -0.9 %, and (a0a0c-) oct ahedral symmetry27. The calculation replicates the suppression of \nthe AFM state in agreement wit h the experimental observation.  \n \n19 \n  \nFigure 5 : The response of Eu spin alignment with applied H -Field in the ETO film on LSAT with and \nwithout E -field using X-ray Magnetic Interference Scattering (XRIS).  (a) Energy scans through the Eu L II \nedge at the (003) ETO reflection with \n 1.2 T showing  the maximum interference effect at full saturation \nbetween the magnetic and charge scattering amplitudes. The sign of the magnetic amplitude switches \nwith the H -field direction altering  the interference effect . (b) The linear XRIS -H-field dependence is \npresented by plotting the scattering amplitude at the line indicated energy in (a). The arrows illustrate \nthe spin reorientation of the Eu ions with H-field and the inset shows the measurement (π -π) geometr y. \n(c) The e nergy dependence of the intensity difference between ±0.1  T across the resonance edge with \nand without E -field application (1 x 105 V/cm).  The solid line in the top panel is a scaled version of the \n1.2 T data set. The charge -magnetic interfere nce phenomenon is eliminated with E -field.  (c-Inset) A \nmicroscopic cartoon model of the Eu spin arrangement w ith and without E -field. Naturally th e G-AFM \nordered Eu spins coherently cant towards the external H -field direction, however w ith applied E-field , \nthe near magnetic degenerate states likely induce a collinear mixed AFM -FM phase devoid of long range \nmagnetic ordering. While t he FM regions  produce insufficient coherency themselves, by pining \n20 \n neighboring AFM spin orientations along the applied H -field  direction they inhibit spin canting and in \neffect mute the interference effect.  \n \nTable 1  \nETO-LSAT  J1xy J1z J2xy J2z J3 \nJ / K B(K)-Bulk  +0.075  -0.114  +0.062  +0.083  -0.031  \n#  Neighbors  4 2 4 8 8 \nJ / K B(K)-LSAT  +0.086  -0.147  +0.06  +0.087  -0.034  \nTable 1  lists the calculated exchange constants between the Eu ions within the unconstrained bulk \nI4/mcm ETO and the ETO (a0a0c-) structure under -0.9% compressive strain, including the 1st, 2nd, and 3rd \nNN Eu ions describing both the in -plane (xy) and out of pla ne (z) interactions. Positive indicates FM and \nnegative AFM coupling. The second row indicates the number of neighbors for each particular \ninteraction. The 1st and 2nd NN interactions are all FM bar the 1st NN out of plane J 1z exchange constant. \nThe calcul ations indicate the importance of J 3 in determining the G -AFM structure in ETO.  \n \nTable 2  \nU 5.7eV(Pm3m)  5.7eV(I4/mcm)  6.0eV  6.2eV  6.5eV  7.0eV  Exp.  \nTN (K) \nTC 12.0  \n10.5  17.9  \n5.6 13.9  \n7.0 11.4  \n7.7 8.8 \n8.3 4.0 \n9.4 5.5 \n3.8 \nTN/TC 1.14  3.2 1.99  1.48  1.06  .43 1.45  \n 21 \n Table 2  lists the Curie -Weiss constant, T C and T N from first principles for bulk ETO in space group \nI4/mcm. The last column extracts the T C from the positive magnetic susceptibility parameter in \nreferenc e 33 in order to use the ratio to estimate a best guess of an appropriate value of U.  \n "    },    {        "title": "1206.6929v2.Enhancement_of_critical_current_density_in_superconducting_magnetic_multi_layers_with_slow_magnetic_relaxation_dynamics_and_large_magnetic_susceptibility.pdf",        "content": "S. Z. Lin and L. N. Bulaevskii, Phys. Ref. B 86 , 064523 (2012).\nEnhancement of critical current density in superconducting /magnetic multi-layers with slow\nmagnetic relaxation dynamics and large magnetic susceptibility\nShi-Zeng Lin and Lev N. Bulaevskii\nTheoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA\n(Dated: August 3, 2021)\nWe propose to use superconductor-magnet multi-layer structure to achieve high critical current density by\ninvoking polaronic mechanism of pinning. The magnetic layers should have large magnetic susceptibility to\nenhance the coupling between vortices and magnetization in magnetic layers. The relaxation of the magnetiza-\ntion should be slow. When the velocity of vortices is low, they are dressed by nonuniform magnetization and\nmove as polarons. In this case, the viscosity of vortices proportional to the magnetic relaxation time is enhanced\nsignificantly. As velocity increases, the polarons dissociate and the viscosity drops to the usual Bardeen-Stephen\none, resulting in a jump in the I-V curve. Experimentally the jump shows up as a depinning transition and the\ncorresponding current at the jump is the depinning current. For Nb and proper magnet multi-layer structure, we\nestimate the critical current density Jc\u0018109A=m2at magnetic field B\u00191 T.\nPACS numbers: 74.25.Wx, 74.25.Sv, 74.25.Ha, 74.78.Fk\nI. INTRODUCTION\nOne fascinating property of superconductors is ability to\ncarry dissipationless current. With a transport current, vortices\nare induced inside the superconductor due to the magnetic\nfield generated by the current. These vortices are driven by the\nLorentz force exerted by the current and their motion causes\nvoltage and dissipation. In inhomogeneous superconductors,\nthe Lorentz force can be balanced by the pinning force due to\ndefects. The strength of pinning thus determines how much\ndissipationless current the superconductor can carry, which is\ndefined as the critical current. The random distributed point-\nlike defects where superconductivity are weakened, are im-\nportant for pinning of vortices.1One may also introduce arti-\nficially columnar pinning centers by heavy ion irradiation.2In\nthese cases, the pinning is caused by suppression of supercon-\nductivity.\nAn alternative approach to introduce pinning is to use mag-\nnetic moments, which interact strongly with vortex. Such op-\ntion may be present in magnetic superconductors.3,4The mag-\nnetic moments can also be introduced artificially in hybrid\nsystems consisting of superconducting and magnetic layers5.\nIt was proposed in Ref. 6 that the domain walls can provide\nstrong pinning with characteristic pinning energy \b0Md. Here\n\b0=hc=(2e) is the quantum flux and Mdis the magnetization\nat the wall. There are experimental attempts to enhance the\ncritical current by putting magnetic particles7, dots8,9or fer-\nromagnet with domain walls on top of superconductors.10\nReduction of dissipation can be also achieved by enhance-\nment of the vortex viscosity. At a given current J, the dis-\nsipation power for a superconductor without pinning due to\nquenched disorder is proportional to J2=\u0011where\u0011is the vor-\ntex viscosity. In nonmagnetic superconductors, \u0011is just the\nstandard Bardeen-Stephen (BS) drag coe \u000ecient accounting\nfor the dissipation in the normal vortex core. If one can in-\ncrease significantly the vortex viscosity, superconductors can\ncarry large current density with low dissipation, despite vor-\ntices are not pinned. It was shown that in magnetic supercon-\nductors, motion of vortex lattice excites magnons11. When the\nkinematic condition \n(G)=G\u0001vis satisfied, Cherenkov ra-diation of magnon occurs and the vortex viscosity is enhanced\ndue to transferring energy into the magnetic subsystem, where\nenergy is finally dissipated through magnetic damping. Here\nGis the lattice wave vector, vis the velocity of vortex lattice\nand\n(G) is the magnon spectrum. When the magnetic damp-\ning is weak, magnetic domain walls are created dynamically\ndue to the parametric instability and the viscosity is increased\nfurther.12\nRecently a polaronic mechanism of vortex pinning is pro-\nposed in Ref. 13 to explain the increase of critical current ob-\nserved in ErNi 2B2C below the incommensurate to commensu-\nrate spin density wave (SDW) transition at 2.3 K14. The tran-\nsition into the commensurate SDW phase leaves 1 /20 spins\nfree from molecular field15. These spins can be easily po-\nlarized by vortices. These spins are Ising spins and experi-\nence large crystal field splitting16, which results in slow re-\nlaxation dynamics17. When the velocity of vortex lattice is\nlow,a=v\u001d\u001c, the nonuniform component of free-spin magne-\ntization induced by vortex lattice follows the vortex motion,\nand the nonuniform magnetization and vortex form a polaron.\nHere ais the vortex lattice constant and \u001cis the relaxation time\nfor magnetizations. The e \u000bective viscosity of vortex lattice in-\ncreases with the relaxation time. For a large velocity, a=v\u001c\u001c,\nthe nonuniform magnetization cannot follow the motion of\nvortex lattice and they are decoupled from each other. The vis-\ncosity of the system recovers to the conventional BS one. The\ndecoupling or dissociation of polaron experimentally shows\nup as a depinning transition. The maximal critical current for\nErNi 2B2C is estimated as 1010A=m2at magnetic field B\u00190:1\nT. The polaronic mechanism is also at work in other borocar-\nbides, cuprate and iron-based superconductors with magnetic\nrear earth ions locating between superconducting layers.\nThe polaronic mechanism of pinning provides an additional\nroutine to achieve high critical current. To optimize such pin-\nning mechanism, we propose to use a multi-layer structure\nconsisting of superconducting (S) and magnetic (M) layers\nshown in Fig. 1, to achieve high critical current. For that\nthe magnetic layers should have high magnetic susceptibility\nat working magnetic field to ensure a strong coupling between\nmagnetic moments and vortices. Secondly, the relaxation timearXiv:1206.6929v2  [cond-mat.supr-con]  23 Aug 20122\nFIG. 1. (color online) Schematic view of multi-layer structure con-\nsisting of alternating magnetic (M) layers (green) with thickness dm\nand superconducting (S) layers (blue) with thickness ds. The distri-\nbution of the magnetic field is shown by red lines.\nof the magnetization should be long. Thirdly, the penetration\ndepth of the superconducting layers should be small.\nII. MODEL AND RESULTS\nUnder external magnetic fields, the vortex lattice is induced\ninside the S layers. With a transport current, vortex lattice\nmoves in response to the Lorentz force. In the quasistatic ap-\nproximation, the motion of vortex lattice is given by\n\u00152r\u0002r\u0002 B+B= \b 0X\ni\u000e[r\u0000ri(t)]ˆz; (1)\nwhere ri(t)=r0\u0000vtis the vortex coordinate, ˆzis the unit vec-\ntor along the zaxis and\u0015is the London penetration depth. In\nthe flux flow region, the quenched disorder is averaged out\nby vortex motion and the lattice ordering is improved18,19.\nThe magnetic field inside the M layers is determined by the\nMaxwell equations\nr\u0002(B\u00004\u0019M)=0;r\u0001B=0: (2)\nThe magnetization Mdepends on Band is determined by the\nmaterial properties. With a strong field and in static case, M\nis a nonlinear function of Band generally can be expressed as\nM(r)=R\ndr3f(r\u0000r0;B(r0)). The characteristic length of mag-\nnetic subsystem is much smaller than \u0015and we use a local ap-\nproximation f(r\u0000r0;B(r0))=\u000e(r\u0000r0)f(B(r0)).B(r) has com-\nponent uniform in space, B0, and the other component nonuni-\nform in space, ˜B(r), with B0\u001c¯B. Thus the spatially nonuni-\nform magnetization ˜M(r) is ˜M(r)\u0019@f(B0)=@B0˜B(r)\u0011\n\u001f0(B0)˜B(r). In the following we assume the magnetic subsys-\ntem is isotropic and is characterized by a susceptibility \u001f0(B0)\natB0in static case. The magnetic field inside the M layer isdetermined by the equation r2˜B=0. Since only the spatially\nnonuniform component ˜Mand ˜Bare responsible for pinning,\nwe will focus on the nonuniform components in the following\ncalculations. At the interface between the M and S layers, we\nuse the standard boundary condition for the field parallel to\nthez-axis Bzand field parallel to the interface Bjj\nBzjS=BzjM;BjjjS=(1\u00004\u0019\u001f0)BjjjM: (3)\nThen we can obtain the magnetic field inside the M layers\nBz\nm(G>0;z)=\u000bh\neGz0+e\u0000G(z0+dm)i\b0exp(\u0000iGxvxt)\n1+\u00152G2;(4)\nBjj\nm(G>0;z)=i\u000bh\neGz0\u0000e\u0000G(z0+dm)i\b0exp(\u0000iGxvxt)\n1+\u00152G2;(5)\n\u000b=\u0000edmG\u0010\n\u00001+edsks\u0011\n\u001f0\n(1\u0000\u001f0)(edsks\u0000eGdm)+(1+\u001f0)(1\u0000edmG+dsks);\nwith z0=z\u0000n(ds+dm),ks=p\n\u0015\u00002+G2, and\u001f0=(1\u0000\n4\u0019\u001f)\u00001ks=G. Here nis the layer index and the vortex motion\nis assumed to be along the xdirection. We consider square\nlattice G=(mx2\u0019=a;my2\u0019=a) with a=p\b0=B0the lattice\nconstant and mx,myintegers.\nWe assume a relaxational dynamics for the M layers,\nM(!)=\u001f(!)Bm(!), with a dynamic susceptibility\n\u001f(!)=\u001f0\n1+i!\u001c: (6)\nHere we have assumed that the relaxation dynamics is gov-\nerned by a single relaxation time. This assumption is not es-\nsential but just for convenience of calculations. In the steady\nstate, we have\nM(G;z;t)=Zt\n0exp[( t0\u0000t)=\u001c]\u001f0Bm(G;z;t0)\n\u001cdt0:(7)\nBecause of the relaxation, Mdepends on the history of vortex\nmotion. Due to slow relaxation of the magnetization, there is\nretardation between the time variation of induced nonuniform\nmagnetization and vortex motion. As a result, the magneti-\nzation exerts a drag force to the vortex which is opposite to\nthe driving force. The pinning force acting on a single vortex\ndue to the induced magnetization in one M layer is given by\nFp=@r0R\ndxdyR0\n\u0000dmdzM\u0001Bm, which yields\nFp=X\nG\u00021\u0000exp(\u00002Gdm)\u0003 2\u000b2\u001f0\u00001+\u00152G2\u00012a2Gv\u001c\b2\n0\n1+(Gv\u001c)2:(8)\nThe I-V curve is determined by the equation of motion for\nvortex ds\u0011BSv=dsFL\u0000Fpwith the electric field E=Bv=c\nand the Lorentz force FL=J\b0=c. Here\u0011BSis the BS vis-\ncosity\u0011BS= \b2\n0=(2\u0019\u00182c2\u001an) with\u001anthe resistivity just above\nTcand\u0018the coherence length. We consider a realistic case\nwhere a=(2\u0019)\u001cdm;ds. Taking into account only the domi-\nnant contribution Gx=2\u0019=aandGy=0 in the summation,\nwe obtain\nu=FL\u0000F pu\n1+u2; (9)3\n03 6 9 1 21 503691215r\netrapping(\nJr, Er)depinning(\nJc, Ec)2/s61552/s61556caE//s6151002\n/s61552J/s61556/s615100(dm+ds)/(/s61544ads) /s61510p=20 \n/s61510p=2\nFIG. 2. (color online) Calculated I-V curves for Fp=20 andFp=2.\nForFp=20 the system shows hysteresis in the I-V while for Fp=2\nno hysteresis is present. The green dotted line denotes the unstable\nsolution.\nFL=FL\n\u0011BSv0;Fp=2\u001c\n\u0011BSds 1\n2\u00004\u0019\u001f0!2\u001f0a\b2\n0\n\u00154(2\u0019)3; (10)\nwith u=v=v0andv0=a=(2\u0019\u001c).\nAt a small velocity u\u001c1, the velocity is given by u=\nFL=(1+Fp) which becomes inversely proportional to \u001cfor a\nlarge\u001c. For a large u\u001d1, we recover the conventional BS\nviscosity v=FL. The dependence of uonFLis shown in Fig.\n2. Hysteresis is developped when Fp\u00158. For typical param-\neters for Nb superconductor \u0018\u0019\u0015\u001940 nm,\u001an\u001910\u00006\n\u0001m\nanda=40 nm at B\u00191 T and\u001f0=0:05,Fp\u00158 requires\n\u001c > 1 ps. For the relaxation time of order \u001c\u00191\u0016s, the ef-\nfective viscosity is enhanced by a factor of 106compared to\nthe bare BS one at v<a=\u001c. Upon increasing the current,\nthe velocity increases and at a critical current (velocity), the\nsystem jumps at dFL=du=0 to the conventional BS branch\ndue to the dissociation of vortex polaron. The e \u000bective critical\ncurrent density for the whole system is given by\nJc\u0019 1\n2\u00004\u0019\u001f0!2\u001f0c\n(2\u0019)4\u00154\b0a2\nds+dm: (11)\nFords=dm=100 nm , we obtain Jc\u0019109A=m2. On the\nother hand, when one reduces the current from the conven-\ntional BS branch, the system jumps to the branches with high\nviscosity due to the formation of vortex polaron. We call this\nretrapping transition and the retrapping current Jris\nJr\u00191\n1\u00002\u0019\u001f0r\n\u001f0\u0011BSads\n\u0019\u001cac\n\u001524\u001921\nds+dm: (12)\nFor the parameters used before and \u001c=1\u0016s, we estimate\nJr\u00192\u0002106A=m2.III. DISCUSSIONS\nNow we discuss the optimal thickness of M and S layers.\nFordm\u001da, the magnetic induction and the magnetization\nis practically uniform in the lateral direction in the middle of\nthe M layer. This can be seen from Eqs. (4) and (5) that\nBm(G>0)\u0019exp(\u00002\u0019dm=a) when\u0000dm\u001cz0\u001c0. As a\nresult, the pinning force becomes practically dmindependent\nwhen dm\u001da. In other words, the pinning is e \u000bective only\nnear the boundaries between S and M layers in the area of\nthickness of the order a. On the other hand, the Lorentz force\nis proportional ds. Thus the e \u000bective critical current of the\nwhole system Jcis proportional to 1 =(ds+dm) as described by\nEq. (11). Therefore the thinner of both M and S layers, the\nhigher is the critical current of the system.\nLet us discuss the possible choice of S and M layers. The\ncritical current decreases as \u0015\u00004because the smaller \u0015, the\nmore nonuniform is the magnetic field distribution inside the\nM layers, hence stronger pinning. Thus superconductors with\nsmaller\u0015are preferred. The critical current does not depend\non\u001cfor su \u000eciently large \u001c, while the viscosity in the branch\nwith vortex polaron is proportional to \u001c. The slow magnetic\ndynamics can be realized in spin glasses. Their relaxation\nis described by a broad spectrum of time scale, with aver-\nage time of the order 0 :1\u0016s20,21. For CuMn 0:08,\u001f0\u00190:002\natB=1 T.22One may enhance \u001f0by tuning the concen-\ntration of magnetic metal in alloys.23One may use super-\nparamagnets with \u001cas large as 1 s and with huge \u001f0due to\nlarge magnetic moments in superparamagnets.24–26One may\nalso use the recently synthesized cobalt-based and rare-earth-\nbased single chain magnets with \u001f0\u00190:05 at B=1 T and\n10\u00006s<\u001c< 10\u00004s.27–30.\nNext we discuss the e \u000bect of quenched disorder. In the\npresence of quenched disorder, the vortex lines adjust them-\nselves to take the advantage of the pinning potential, which\ndestroys the long-range lattice order. Below a threshold cur-\nrent, vortices remain pinned (actually they creep between pin-\nning centers due to fluctuations). In this region, the polaronic\nmechanism does not play a role. When the current is high\nenough to depin the vortices from quenched disorder, vortices\nstart to move and the lattice ordering is enhanced. By for-\nmation of polaron with the nonuniformly induced magnetiza-\ntion, the vortex viscosity is enhanced. At a critical velocity\n(current), the polaron dissociates and the system jumps to the\nconventional BS branch. Pinning due to quenched disorder\nworks in the static region and polaronic pinning works in the\ndynamic region. The critical current of the whole system is\nthe sum of these two threshold currents. Note that magne-\ntostriction in combination with quenched disorder enhance the\npolaronic pinning mechanism.\nThe M /S multi-layer structure is naturally in some su-\nperconducting single crystals, such as RuSr 2GdCu 2O831and\n(RE)Ba 2Cu3O732,33, where RE is the rear earth magnetic\nions. In RuSr 2GdCu 2O8the magnetic moments order fer-\nromagnetically above Tcthus the dominant enhancement of\nvortex viscosity is due to the radiation of magnons11. For\n(RE)Ba 2Cu3O7, magnetic RE ions positioned between su-\nperconducting layers interact weakly with superconducting4\nelectrons and order at very low N ´eel temperatures of the\norder TN\u00181 K. The polaronic mechanism is important\nabove the magnetic ordering temperature, where spins are\nfree. The London penetration depth of cuprate supercon-\nductors is large \u0015\u0019200 nm, thus the critical current is re-\nduced significantly compared to that for Nb multi-layer struc-\nture, because Jcdrops as 1=\u00154. Another natural realization is\nthe recently discovered iron-based superconductors, such as\n(RE)FeAsO 1\u0000xFx, where RE ions ordered antiferromagneti-\ncally below TN\u00181K.34\nIV . CONCLUSION\nTo summarize, we have proposed superconductor-magnet\nmulti-layer structure to achieve high critical current densitybased on the polaronic pinning mechanism. The critical cur-\nrent is estimated to be 109A=m2atB\u00191 T for an optimal\nconfigurations of Nb and proper magnet multi-layer structure.\nIn the presence of quenched disorder, the polaronic pinning\nstarts to work when vortices depin from quenched potential.\nThus the total critical current of the system is the sum of de-\npinning current due to quenched disorder and depinning cur-\nrent due to the polaronic mechanism.\nACKNOWLEDGMENTS\nThe authors are indebted to Cristian D. Batista for helpful\ndiscussion. This publication was made possible by funding\nfrom the Los Alamos Laboratory Directed Research and De-\nvelopment Program, project number 20110138ER.\n1G. Blatter, M. V . Feigelman, V . B. Geshkenbein, A. I. Larkin, and\nV . M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994).\n2L. Civale, A. D. Marwick, T. K. Worthington, M. A. Kirk,\nJ. R. Thompson, L. Krusin-Elbaum, Y . Sun, J. R. Clem, and\nF. Holtzberg, Phys. Rev. Lett. 67, 648 (1991).\n3L. N. Bulaevskii, A. I. Buzdin, M. L. Kulic, and S. V . Panjukov,\nAdv. Phys. 34, 175 (1985).\n4A. I. Buzdin, Rev. Mod. Phys. 77, 935 (2005).\n5I. F. Lyuksyutov and V . L. Pokrovsky, Adv. Phys. 54, 67 (2005).\n6L. N. Bulaevskii, E. M. Chudnovsky, and M. P. Maley, Appl.\nPhys. Lett. 76, 2594 (2000).\n7Y . Otani, B. Pannetier, J. Nozires, and D. Givord, J. Magn. Magn.\nMater. 126, 622 (1993).\n8J. I. Mart ´ın, M. V `elez, J. Nogu ´es, and I. K. Schuller, Phys. Rev.\nLett. 79, 1929 (1997).\n9J. I. Mart ´ın, M. V `elez, A. Ho \u000bmann, I. K. Schuller, and J. L.\nVicent, Phys. Rev. Lett. 83, 1022 (1999).\n10V . Vlasko-Vlasov, U. Welp, G. Karapetrov, V . Novosad, D. Rosen-\nmann, M. Iavarone, A. Belkin, and W. K. Kwok, Phys. Rev. B 77,\n134518 (2008).\n11A. Shekhter, L. N. Bulaevskii, and C. D. Batista, Phys. Rev. Lett.\n106, 037001 (2011).\n12S. Z. Lin, L. N. Bulaevskii, and C. D. Batista, arXiv:1201.4195\n(2012).\n13L. N. Bulaevskii and S. Z. Lin, Phys. Rev. Lett. 109, 027001\n(2012).\n14P. L. Gammel, B. Barber, D. Lopez, A. P. Ramirez, D. J. Bishop,\nS. L. Bud’ko, and P. C. Canfield, Phys. Rev. Lett. 84, 2497 (2000).\n15P. Canfield, S. Bud’ko, and B. Cho, Physica C 262, 249 (1996).\n16U. Gasser, P. Allenspach, J. Mesot, and A. Furrer, Physica C 282,\n1327 (1997).\n17P. Bonville, J. A. Hodges, C. Vaast, E. Alleno, C. Godart, L. C.\nGupta, Z. Hossain, R. Nagarajan, G. Hilscher, and H. Michor, Z.\nPhys. B 101, 511 (1996).\n18A. E. Koshelev and V . M. Vinokur, Phys. Rev. Lett. 73, 3580\n(1994).19R. Besseling, N. Kokubo, and P. H. Kes, Phys. Rev. Lett. 91,\n177002 (2003).\n20Y . J. Uemura, T. Yamazaki, D. R. Harshman, M. Senba, and E. J.\nAnsaldo, Phys. Rev. B 31, 546 (1985).\n21K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986).\n22J. Prejean, M. Joliclerc, and P. Monod, J. Physique 41, 427\n(1980).\n23J. Kouvel, J. Phys. Chem. Solids 21, 57 (1961).\n24C. P. Bean and J. D. Livingston, J. Appl. Phys. 30, S120 (1959).\n25R. B. Goldfarb and C. E. Patton, Phys. Rev. B 24, 1360 (1981).\n26B. D. Cullity and C. D. Graham, Introduction to Magnetic Mate-\nrials, 2nd ed. (Wiley-IEEE Press, 2008).\n27A. Caneschi, D. Gatteschi, N. Lalioti, C. Sangregorio, R. Sessoli,\nG. Venturi, A. Vindigni, A. Rettori, M. G. Pini, and M. A. Novak,\nAngew. Chem. Int. Ed. 40, 1760(2001).\n28A. Caneschi, D. Gatteschi, N. Lalioti, C. Sangregorio, R. Sessoli,\nG. Venturi, A. Vindigni, A. Rettori, M. G. Pini, and M. A. Novak,\nEurophys. Lett. 58, 771 (2002).\n29L. Bogani, C. Sangregorio, R. Sessoli, and D. Gatteschi, Angew.\nChem. Int. Ed. 44, 5817 (2005).\n30K. Bernot, L. Bogani, A. Caneschi, D. Gatteschi, and R. Sessoli,\nJ. Am. Chem. Soc. 128, 7947 (2006).\n31A. C. McLaughlin, W. Zhou, J. P. Attfield, A. N. Fitch, and J. L.\nTallon, Phys. Rev. B 60, 7512 (1999).\n32P. H. Hor, R. L. Meng, Y . Q. Wang, L. Gao, Z. J. Huang, J. Bech-\ntold, K. Forster, and C. W. Chu, Phys. Rev. Lett. 58, 1891 (1987).\n33P. Allenspach, B. W. Lee, D. A. Gajewski, V . B. Barbeta, M. B.\nMaple, G. Nieva, S. I. Yoo, M. J. Kramer, R. W. McCallum, and\nL. Ben-Dor, Z. Phys. B 96, 455 (1995).\n34C. Wang, L. Li, S. Chi, Z. Zhu, Z. Ren, Y . Li, Y . Wang, X. Lin,\nY . Luo, S. Jiang, X. Xu, G. Cao, and Z. Xu, Europhys. Lett. 83,\n67006 (2008)."    },    {        "title": "1207.2331v1.Micromagnetic_simulation_of_magnetic_small_angle_neutron_scattering_from_two_phase_nanocomposites.pdf",        "content": "arXiv:1207.2331v1  [cond-mat.mes-hall]  10 Jul 2012Micromagnetic simulation of magnetic small-angle neutron scattering\nfromtwo-phasenanocomposites\nAndreasMichelsa,∗,SergeyErokhinb, DmitryBerkovb, NataliyaGornb\naLaboratory for the Physics of Advanced Materials, Universi ty ofLuxembourg, 162A Avenue dela Fa¨ ıencerie, L-1511 Luxe mbourg, Luxembourg\nbINNOVENTTechnology Development, Pr¨ ussingstraße 27B,D- 07745 Jena, Germany\nAbstract\nThe recent development of a micromagnetic simulation metho dology—suitable for multiphase magnetic\nnanocomposites—permitsthecomputationofthemagneticmi crostructureandoftheassociatedmagneticsmall-angle\nneutronscattering(SANS) crosssection ofthese materials . Inthis reviewarticle we summarizeresults onthe micro-\nmagnetic simulation of magnetic SANS from two-phase nanoco mposites. The decisive advantage of this approach\nresides in the possibility to srutinize the individual magn etization Fourier contributions to the total magnetic SANS\ncross section, rather than their sum, which is generally obt ained from experiment. The procedure furnishes unique\nandfundamentalinformationregardingmagneticneutronsc atteringfromnanomagnets.\nKeywords: small-angleneutronscattering,micromagnetism,nanocom posites\n1. Introduction\nSmall-angle neutron scattering (SANS) is one of the\nmost important techniques for microstructure determi-\nnationin soft andhard condensedmatter, materialssci-\nence,andinphysicalchemistry. SincemostSANSstud-\nies focus on nuclear rather than magnetic scattering, it\nis not surprising that the theoretical concepts behind\nnuclear SANS are rather well developped [1–9]. By\ncontrast, the understanding of magnetic SANS is still\nat its beginning, although magnetic SANS has previ-\nouslydemonstratedgreatpotentialforresolvingthespin\nstructures of various magnetic materials. For instance\n(inthelastdecade),magneticSANShasbeenemployed\nfor studying the microstructuresof magnetic nanocom-\nposites [10–19], amorphousalloys [20–23], and of ele-\nmental nanocrystalline bulk ferromagnets [24–35], the\nprocess of dynamic nuclear polarization [36], imaging\nof the flux-line lattice in superconductors[37, 38], pre-\ncipitatesinsteels[39],nanocrystallinerare-earthmeta ls\nwith random paramagnetic susceptibility [40], fractal\nmagnetic domain structures in NdFeB permanent mag-\nnets [41], spin structures of ferrofluids, nanoparticles,\nandnanowires[42–52],magnetostrictioninFeGaalloys\n∗Corresponding author\nEmailaddress: andreas.michels@uni.lu (Andreas Michels)[53], electric-field-induced magnetization in multifer-\nroics[54],magnetizationreversalinmagneticrecording\nmedia[55]andexchange-biasmaterials[56],andchiral\nandskyrmion-likestructuresinsinglecrystals[57–59].\nNecessary prerequisite for the quantitative analysis\nof elastic magnetic SANS data is the knowledge of\ntheFouriercomponentsofthestaticmagnetizationvec-\ntor fieldM(r) of the sample under study. The theory\nof micromagnetics [60–62] provides the proper frame-\nwork for the computation of M(r). However, the solu-\ntion of Brown’s equations of micromagnetics amounts\nto the solution of a set of nonlinear partial di fferen-\ntialequationswithcomplexboundaryconditions,atask\nwhich cannot be done analytically for most practically\nrelevant problems. Therefore, closed-form expressions\nfor the ensuing so-called spin-misalignment scattering\ncross section are limited to the approach-to-saturation\nregime [31, 63], in which the micromagnetic equations\ncanbelinearized.\nIn this review article we summarize our recentwork,\nin which we have used numerical micromagnetics for\nthecomputationofthemagneticSANS crosssectionof\ntwo-phase magnetic nanocomposites. The use of nu-\nmerical techniques allows us to solve the underlying\nequationsrigorously,without resortingto the high-field\napproximation (saturation regime). This approach pro-\nvidesinsightsintothefundamentalsofmagneticSANS.\nThe micromagnetic simulations are adapted to the mi-\nPreprintsubmitted to Elsevier November 6,2018crostructure of a two-phase nanocomposite from the\nNANOPERMfamilyofalloys[64].\nThe paper is organized as follows: in Sec. 2 we\nprovidethe details of our micromagneticmethodology,\nSec. 3 discusses the magnetic SANS cross sections for\nthe two most commonly used scattering geometries,\nSec. 4 presents and discusses the results of the micro-\nmagneticsimulationsforthemagneticSANScrosssec-\ntion, and in Sec. 5 we summarize the main findings of\nthisstudy.\n2. Micromagneticbackground\nMicromagnetism is a mesoscopic phenomenological\ntheorydesignedto computethe equilibriummagnetiza-\ntion state of an arbitrarily shaped ferromagnetic body,\nwhentheappliedfield,thegeometryoftheferromagnet\nand all materials parameters are known [60–62]. In or-\nder to find the equilibrium magnetization configuration\nMeq(r), the total magnetic free energy of a ferromag-\nnet should be considered as a functional of its magne-\ntization state, Etot=Etot[M(r)]. The state which de-\nlivers a (local) minimum to this functional corresponds\ntotherequiredequilibriummagnetizationconfiguration,\nso that the problem amountsto the minimizationof the\ntotal energy functional. In the most common case Etot\ncontains contributionsfrom the energy due to an exter-\nnal field, exchange, anisotropy and magnetodipolar in-\nteraction energies. Due to the nonlocal nature of the\nmagnetodipolarinteraction, almost all practically inter -\nesting problems can not be treated analytically, so that\nnumericalminimizationof Etot[M(r)]shouldbecarried\nout. Inthecontemporaryresearchlandscape,numerical\nmicromagneticsisalargeandstillcontinuouslyexpand-\ningfield. Recent reviewson the micromagneticstate of\nthe art can be found in the handbook Ref. [65]. In this\narticle we brieflydiscuss onlythosemethodicalaspects\nof numerical micromagnetics which are important for\nsimulationsofnanocompositematerials.\nFirst,wewouldliketoemphasizethatsuchmaterials\nare one of the most complicated objects from the point\nofviewofnumericalsimulations. Themaindi fficultyis\nthat they consist of at least two phases, and the bound-\naries between these phasesare complicated curvedsur-\nfaces; a typical example is a hard-soft nanocompos-\nite consisting of magnetically hard (i.e., having a large\nmagnetocystallineanisotropy)crystalgrainssurrounded\nby a magnetically soft matrix. Such a system is very\ndifficult to simulate for the following reasons. The\nmajority of modern numerical micromagnetic methods\ncan be subdividedinto two classes, the so-called finite-\ndifferenceandfinite-elementmethods(FDMandFEM)[65]. InFDM thesystemunderstudyisdiscretizedinto\na regular translationally invariant (usually rectangular )\ngrid. Suchadiscretizationallows,first,theevaluationof\nthe exchangefield by simple finite-di fferenceformulas,\nwhich are the finite-di fference approximations for the\ncorrespondingsecond-orderdi fferential operatoracting\non the magnetization field M(r) (see below). Second,\nthe translational invariance of a FDM grid enables the\nusageofthefastFouriertransformation(FFT)technique\nfor the computation of the long-range magnetodipolar\ninteraction field and energy. For a system discretized\nintoNcells, the FFT technique reduces the operation\ncount for this energy from ∼N2(for a direct summa-\ntion) to∼NlogN. However, a serious disadvantage\nof a regular grid is a pure approximationfor arbitrarily\ncurved surfaces and boundaries. This is an important\ndrawbackfor simulations of magnetic nanocomposites,\nbecause the adequate representation of the interphase\nboundariesforthe accurateevaluationofassociatedex-\nchangeandmagnetodipolarinteractionsbetweendi ffer-\nentphasesiscruciallyimportant.\nThesecondgroupofnumericalmethodswidelyused\nin micromagnetics—finite-element methods (FEM)—\nemploy the discretization of the system under study\ninto arbitrarily shaped tetrahedrons. The flexibility of\nthis discretization type allows one to represent curved\nboundaries(includingthose between magneticallyhard\ninclusions and the soft magnetic matrix) with any de-\nsired accuracy. However, the price to pay for this flex-\nibility is high. First, computation of the exchange field\nrequiresnow complicatedmethodsdesignedforthe ac-\ncuraterepresentationofsecond-orderdi fferentialopera-\ntors on irregular lattices. Second (and most important),\nitisnolongerpossibletouseFFTforthemagnetodipo-\nlarfieldevaluation. Forthisreason,highlysophisticated\nmethods for the computation of this field are used in\nFEM simulations. These methods, which are based on\nthedecompositionofmagneticpotentialsinsidethefer-\nromagnetandintheouterspace,andthesubsequentso-\nlution of the correspondingPoisson equationsfor these\npotentials on irregular grids [65] require a high pro-\ngramming effort and result in iterativealgorithms for\nthe evaluation of the dipolar field for a given magneti-\nzationconfiguration(incontrasttotheFFT technique).\nAnother important limitation of finite-element meth-\nods is that they can only be employed in simulations\nwithopenboundaryconditions(OBC), so that periodic\nboundaryconditions(orPBC,routinelyappliedinsimu-\nlationsofextendedthinfilmsandbulkmaterialsinorder\nto eliminate strong finite-size e ffects) can not be used.\nThe impossibility to apply PBC is a serious disadvan-\ntage in simulationsof SANS experimentson nanocom-\n2posites, whereby the scattering intensity is sensitive to\nmagnetization fluctuations in the bulk. Artificial sur-\nface demagnetizing e ffects arising in simulations with\nOBC might be very significant in this case, due to a\nrelatively small simulation volume a ffordable even for\nmoderncomputers. Inaddition,thesuppressionofthese\neffects is especially importantfor nanocompositescon-\ntaininga softmagneticphase.\nAnother undesirablefeature of a tetrahedronmesh is\nthat hard magnetic grains must also be discretized into\ntetrahedrons,althoughinmanycasesthemagnetization\nwithinasinglegrainisnearlyhomogeneous. Thisleads\ntoasignificantincreaseofthetotalnumberoffiniteele-\nmentsrequired,resultinginacorrespondingincreaseof\nthe computation time; we refer the reader to Ref. [66]\nforthediscussionofthisproblem.\nDue to all the reasons explained above, numerical\nmicromagnetic simulations of SANS experiments on\nnanocomposites are very rare [67, 68]. Corresponding\nfull-scalesimulationsofSANSmeasurementsonatwo-\nphasesystem havebeen reported,up to our knowledge,\nonlyinRef.[67],wherethemagnetizationconfiguration\nof a longitudinal magnetic recording media film was\nmodeled. Based on the experimental characterization\nof this material, the authors of [67] have built a two-\nphasemodelforthissystem,whereeachmagneticgrain\nconsisted of a hard magnetic grain core and an essen-\ntially paramagneticgrain shell, having a very high sus-\nceptibility. The OOMMF code employing the standard\nFDM has been used [69], so that a very fine discretiza-\ntion(0.3×0.3×0.3nm3cells)hadtobeappliedinorder\nto reproduce the spherical shape of grain cores with a\nrequiredaccuracy. Forthisreason,onlya ratherlimited\nnumber of grains ( ∼50) could be simulated. In addi-\ntion, the exchange interaction both between the grains\nandwithinthe softmagneticmatrix(representedbythe\nmerging grain shells) was neglected. Still, using sev-\neral adjustable parameters, a satisfactory agreement of\nthesimulatedSANS intensityprofilewithexperimental\ndatawasachieved.\nThe brief overview of the methodical problems pre-\nsented here clearly shows that both a qualitative im-\nprovement of the micromagnetic simulation methodol-\nogy and extensive numerical studies devoted to SANS\nexperimentsarehighlydesirable.\n2.1. New micromagnetic algorithm: mesh generation\nanditsregularrepresentation\nForthereasonsexplainedin theprevioussection and\ninordertoperformaccurateande fficientsimulationsof\ntwo-phasenanocomposites,weneedtogenerateapoly-\nhedronmeshwiththefollowingproperties: (a)itshouldallow to represent each hard magnetic crystallite as a\nsingle finite element (because the magnetization inside\nsuch a crystallite is essentially homogeneous), (b) the\nmesh should allow for an arbitrarily fine discretization\nof the soft magnetic matrix in-between the hard grains\n(toaccountforthe possiblelargevariationsof themag-\nnetizationdirectionbetweenthehardgrains),and(c)the\nshapeofthemeshingpolyhedronsshouldbeascloseas\npossible to spherical, in order to ensure a good quality\nof a spherical dipolar approximationfor the calculation\nof the magnetodipolar interaction energy, even for the\nnearestneighboringmeshelements.\nAmeshconsistingofpolyhedronssatisfyingallthese\nrequirementscanbegeneratedusingtwokindsofmeth-\nods. First, there exist various modifications of a purely\ngeometrical algorithm designed to obtain a random\nclosepackingofhardspheres[70]. Inthesealgorithms,\nthe initial distribution of sphere centers is completely\nrandom. Then, at each step the worst overlap between\ntwospheresiseliminatedbypushingthesespheresapart\nalong the line connecting their centers. This procedure\nusually introduces new overlaps; however, these over-\nlaps are usually smaller and are eliminated during the\nnext steps, so that on the average the packing quality\nimproves (the largest overlap present in the system de-\ncreases). The algorithm is robust and produces a ran-\ndom close packingof nonoverlappingspheres with any\ndesiredaccuracy(see Ref. [70] for furtherdetails). Un-\nfortunately, the computation time for this method in-\ncreaseswith the numberofelements Nas∼N2, so that\nthemaximalnumberofsphereswhichcanbepositioned\nwithina reasonablecomputationtime is N∼104.\nTherefore, in order to generate a mesh with a much\nlargernumberoffiniteelements( N>105),wehavede-\nvelopeda“physical”method,wherewemodelasystem\nofspheresinteractingviaashort-rangerepulsivepoten-\ntial:\nUi=N/summationdisplay\nj=1Apotexp/braceleftBigg\n−dij−(ri+rj)\nrdec/bracerightBigg\n. (1)\nHere, the constant Apotdetermines the value of our po-\ntential when the distance dijbetween the centers of in-\nteractingspheresisequaltothesumoftheirradii riand\nrj(to ensure small overlaps in the final configuration,\nit should be Apot≫1; in a typical case Apot=10).\nThe parameter rdecdefines the decay radius of the po-\ntential. Again, at the beginning of iterations, sphere\ncenters are positioned randomly. Then, we move the\nspheresaccordingtothepurelydissipative(i.e.,neglect -\ning the inertial term) equationof motion resulting from\ntheforcesobtainedfromthepotentialEq.(1). Thetime\n3step for the integration of this equation is adjusted to\nensure decrease of the total system energy after each\nstep. DuetotherepulsivenatureofthepotentialEq.(1),\nthis procedure leads also to the decrease of overlaps of\nthe spheres. To achieve the desired result, we movethe\nspheres until their maximum overlap does not exceed\nsome prescribed small value (we have found that for\nour purposesthe remainingoverlap ( ri+rj)/dij>0.95\nis good enough). The algorithm may be refined further\nto increase its efficiency; in particular, one might de-\ncrease the decay radius of the potential rdec, thus mak-\ning the potential “harder”, when the overlapping be-\ntween spheres decreases during the sphere motion. We\nalso note that due to the randomspatial arrangementof\nspheresobtainedinthisway,weavoidpossibleartifacts\ncausedbytheregularplacementoffiniteelements.\nAfter the spheres have been positioned using one of\nthe two algorithms described above, their centers are\nusedaslocationpointsofmagneticdipoles. Tocompute\nthemagnitudesµiofthesedipoles,wehavetodetermine\nthevolumeofeachcorrespondingmeshelement,which\nisinfactapolyhedron.Thisdeterminationismadeviaa\nregulargridrepresentationprocedurethatshouldsatisfy\nthe following requirements. First, we should conserve\nthe total sample volume. Second,the interfacebetween\nneighboringmesh elementsshouldbe flat asfar as pos-\nsible(apartfromgeometricalreasons). Thelastrequire-\nment is also supported by electron microscopy images\nofvariouspolycrystallinemagnets(e.g.,[71, 72]).\nIn order to satisfy both these requirements, we used\nthe following method: the sample is divided into cubi-\ncalcellswhichside ismuchsmaller(usuallyaboutfour\ntimessmaller) than the size of a finite element(polyhe-\ndron)of our disorderedmesh used to discretize the soft\nphase. For every cubical cell ( j,k,l), we calculate the\ndistances∆si\nj,k,lbetween the center of this cell and the\ncenters of neighboringpolyhedrons(labeled by i). The\nfunction\nmin{i}/bracketleftBig\n(∆si\nj,k,l)2−R2\ni/bracketrightBig\n(2)\nindicates to which polyhedron (with radius Ri) we at-\ntribute the current ( j,k,l) cube. The sum of cube vol-\numes ascribed to the given polyhedron is taken as its\nvolume. As a result of this procedure, the distribu-\ntionofmesh-elementvolumesforbothmagneticphases\ndemonstratesa nearlyGaussian behavior. To obtainthe\nmagnitudeofthedipolarmomentassignedtoeachpoly-\nhedron, its volume is multiplied by the saturation mag-\nnetizationofthematerialinsidewhichthepolyhedronis\nlocated (we remind that nanocompositesconsist of ma-\nterialswith differentmagnetizations).\nFigure 1: Schematical representation of the mesh-generati on method:\nspheres in the left image indicate the distribution of magne tic\ndipoles (blue—hard magnetic phase, yellow-orange-red—so ft mag-\nnetic phase). The corresponding regular grid representati on on the\nrightisusedforthemesh-elementvolumedetermination (se eSec.2.1\nfor details). Note that the actual “sample”, which is used fo r the mi-\ncromagnetic simulations, is featured in Fig. 3.\nThis method also allows for a very e fficient calcu-\nlation of the Fourier components of the magnetization\n(see Eqs. (17) and (18) below) for a disorderedsystem,\nusingFFTonthealreadycomposedregulargrid.\nSummarizing, the whole algorithm can be viewed as\na method to discretize a sample into polyhedrons hav-\ning nearly spherical shape (see Fig. 1). This is due to\nthe fact that polyhedrons “inherit” the spatial structure\nobtained by the positioning of closely packed spheres.\nThefactthattheshapeofthevolumewhichisoccupied\nby each magnetic moment is nearly spherical allows us\nto use the spherical dipolar approximation (equivalent\nto the point dipole approximation)for the evaluationof\nthemagnetodipolarinteractionbetweenthemoments.\nFinally, we point out that both algorithms allow for\ntheusageofpolyhedronswithdi fferentsizes,ifweneed\ndifferentmeshingondi fferentsystemlocations.\n2.2. New micromagnetic algorithm: energy contribu-\ntions\nIn our micromagnetic simulations we take into ac-\ncount all four standard contributions to the total mag-\nnetic free energy listed above: energy in the exter-\nnal magnetic field, energy of the magnetocrystalline\nanisotropy, exchange sti ffness and magnetodipolar in-\nteractionenergies.\n2.2.1. Externalfieldandmagnetocrystallineanisotropy\nenergies\nThesystemenergyduetothepresenceofanexternal\nmagneticfieldandtheenergyofthemagnetocrystalline\n4anisotropy(whichcanbeuniaxialand /orcubic)arecal-\nculatedinourmodelin thestandardway,namely\nEext=−N/summationdisplay\ni=1µiH, (3)\nEun\nan=−N/summationdisplay\ni=1Kun\niVi(mini)2, (4)\nEcub\nan=N/summationdisplay\ni=1Kcub\niVi/parenleftBig\nm2\ni,x′m2\ni,y′+m2\ni,y′m2\ni,z′+m2\ni,x′m2\ni,z′/parenrightBig\n,(5)\nwhereHis the external field, µi=µ(ri) andViare the\nmagnetic moment and the volume of the ith finite ele-\nment (polyhedron),and midenotes the unit magnetiza-\ntionvector. Boththeanisotropyconstants Kiandthedi-\nrectionsoftheanisotropyaxes nicanbesite-dependent,\nas required for a polycrystalline nanocomposite mate-\nrial. Forthecubicanisotropycase,thesymbols mi,x′etc.\nrepresentthe componentsof unitmagnetizationvectors\ninthelocalcoordinatesystemthatisattachedto thecu-\nbicanisotropyaxes.\n2.2.2. Exchangeenergy\nThe evaluation of this energy contribution in our\nmodel requires a much more sophisiticated approach\nthan in the standard FDM, because the continuous in-\ntegralversionof thisenergycontainsthe magnetization\ngradients,\nEexch=/integraldisplay\nVA(r)/bracketleftBig\n(∇mx)2+(∇my)2+(∇mz)2/bracketrightBig\ndV,(6)\nwhereAdenotes the exchange-sti ffness parameter and\nVis the sample volume. Finding an approximation to\nEq. (6) for a disordered system is a highly nontrivial\ntask.\nWeremindthatforaregularcubicgridwithacellsize\na(andcellvolume∆V=a3),itcanbeshownrigorously\n(see the detailed proof in Ref. [73]) that the integral in\nEq.(6)canbeapproximatedasthesum\nEexch=−1\n2N/summationdisplay\ni=1/summationdisplay\nj⊂n.n.(i)2Aij∆V\na2/parenleftBig\nmimj/parenrightBig\n.(7)\nHere,Aijdenotes the exchange-sti ffness constant be-\ntween cells iandj, and the notation j⊂n.n.(i) means\nthat the inner summation is performed over the nearest\nneighbors of the ith cell only. We note in passing that\nthis Heisenberg-like expression is valid only when the\nanglesbetweenneighboringmomentsare nottoolarge;asshowninRef.[73],neglectingthisconditioncanlead\ntocompletelyunphysicalresults.\nForadisorderedsystemoffiniteelementshavingdif-\nferentvolumes,differentdistancesbetweentheelement\ncenters, and different numbers of nearest neighbors for\neach element, the expression Eq. (7) obviously can not\nbe used. The most straightforwardway to compute the\nexchange interaction in such a system would be to em-\nploy a rigorous numerical approximation suitable for\nthe evaluation of the integral Eq. (6), where the inte-\ngrandvalues(magnetizationvectors m) are givenat ar-\nbitrarily placed spatial points. Derivation of such inte-\ngration formulas amounts to the approximation of the\nmagnetization projections mx,y,z(r) using some kind of\na polynomial interpolation of these functions between\nthe points where their values are defined (in our case,\npolyhedron centers). The integrand in Eq. (6) includes\nfirstspatialderivativesofthemagnetizationfield,sothat\ncorresponding polynomials for the energy evaluation\nshould deliver a continuous (and even better smooth)\nfirst derivative of m(r). For the effective field evalua-\ntion, where the continuousexpression involvessecond-\norder derivatives, the polynomial interpolation is even\nmore demanding. In addition, we should keep in mind\nthat the condition |m(r)|=1 must be fulfilled every-\nwhere,sothattheinterpolationofthemagnetizationan-\ngles,ratherthanthatofCartesianmagnetizationcompo-\nnentsshouldbeused. All these featureswouldresult in\nahighlycomplicatedalgorithmfortheexchangeenergy\nand field evaluation, which might be, in addition, sub-\nject to serious stability problems to usage of the angle\ninterpolation.\nFor these reasons, we have decided to developan al-\ngorithm for the exchange-energy evaluation based on\nthe summation of the nearest neighbors contributions\n[similar to the expression(Eq. 7)] and at the same time\ntake into accountthe di fferencesbetweena regulargrid\nand a disordered system mentioned above. To achieve\nthis goal, we modify the expression Eq. (7) in the fol-\nlowingway. First, fromthederivationoftheexpression\nEq. (7) presented in [73], it is clear that for the regular\nmeshconsistingofcubiccells,thevolume ∆Vinthenu-\nmeratorof this expressionis actually not the volume of\nthecell,butthevolumeenclosedbetweenthecentersof\nthecelliandtheneighboringcell j(foracubiclatticeor\nalatticeconsistingofrectangularprisms,thisvolumeis\nobviously equal to the cell volume, because it includes\ntwo halves of identical cells). Therefore, for a disor-\nderedsystem of arbitraryfinite elements, ∆Vshould be\nreplacedby Vij=(Vi+Vj)/2 , where ViandVjare the\nvolumesofthe ithandthe jth finiteelements.\n5The second adjustment of Eq. (7) to a finite element\nsystemisthe replacementofthedistance abetweenthe\ncell centers in a regular lattice by the distance ∆rijbe-\ntweenthecentersofcells iandj.\nThe third and most complicated correction is due to\nthe different number of nearest neighbors in a regular\nlattice and in a disorderedsystem of finite elements. In\naregularCartesianlattice,eachcellhasexactly Nnn=6\nnearestneighbors,andtheanglesbetweenthelinescon-\nnecting the cell center with the centers of its neighbors\ninx,yandzdirections are always 90◦. For this rea-\nson, the overlapping of volumes enclosed between the\ncenters of neighboring cells in, e.g., xandydirections\nis the same for all cells, what was taken into account\nby derivation of Eq. (7) (it is important to note, that\nthis overlapping should not be confused with the over-\nlappingof spheresmentionedin the discussionof algo-\nrithmsusedtocontructourdisorderedmeshinSec.2.1).\nIncontrasttothisnicefeatureofaregularCartesianlat-\ntice, in a disordered system of finite elements the num-\nber of nearest neighbors for di fferent finite elements\nmay be different, and the overlapping of volumes en-\nclosedbetweenthecentersofagivencell anditsdi ffer-\nent neighbors may also vary. For example, for the ele-\nmentwithmorethansixnearestneighbors,thevolumes\nenclosedbetweenitscenterandcentersofitsneighbors\nwould overlap more than for a cubic lattice. For such\nanelement, theexchange-sti ffnessenergyevaluatedus-\ning the sum Eq. (7) would be overestimateddue to this\nexcessive overlapping, even when the two corrections\nexplainedabovewouldbetakenintoaccount.\nThe simplest method to solve this problem is the in-\ntroduction of the correction factor 6 /nav, wherenavis\ntheaveragenumber of nearest neighborsfor the partic-\nularrandomrealizationofourdisorderedfinite-element\nsystem. This correction would compensate on aver-\nage the effect of the incorrect count of overlapping re-\ngions explained above. The accuracy of this simple\ncorrection method can be hardly estimated in advance,\nbut both simple tests performed in [74] and additional\nmuch more complicated tests discussed in Sec. 2.3 be-\nlow show that the accuracy provided by this correction\nmethodis surprisinglygood.\nSummarizing, for magnetic moments belonging to\nthesamephaseweproposethefollowingexpressionfor\ntheexchange-stiffnessenergy:\nEexch=−1\n2N/summationdisplay\ni=1/summationdisplay\nj⊂n.n.(i)2AijVij\n∆r2\nij/parenleftBig\nmimj/parenrightBig\n,(8)\nwhereVij=(Vi+Vj)/2,∆rijis the distance between\nthe centers of the ith and the jth finite elements withvolumesViandVj,andAijis theexchangeconstant.\nThelast pointtobediscussedisthechoiceofnearest\nneighbors,whichshouldbeusedintheinnersummation\nin Eq. (8). The choice whether two elements should\nbe considered as nearest neighborsis not unambiguous\nin disordered systems. We have adopted the following\nconvention: two magnetic moments are considered as\nnearest neighbors, if the distance between the centers\nof correspondingpolyhedronsis not larger than dmax=\n1.4(ri+rj). Thecut-offfactorfcut=1.4ischosensothat\nfor the overwhelming majority of finite elements those\ntwo of them which have a common face are treated as\nnearestneighbors.\nToevaluatetheexchange-interactionenergybetween\ntwofiniteelements(polyhedrons)belongingto different\nphases(hardandsoft),we usetheformula:\nEexch=−1\n2N/summationdisplay\ni=1/summationdisplay\nj⊂n.n.(i)2AijVsp/2\n(∆rij−Rhp)2(mimj).(9)\nHere,Vspisthevolumeofa soft-phaseelementand Rhp\nis the radius of the sphere corresponding to the hard\nphasepolyhedron. ThismodifiedexpressionEq.(9)ac-\ncounts for the fact that in this case the magnetization\nrotation occurs almost entirely within the polyhedron\ncorrespondingtothesoft phase.\n2.2.3. Magnetodipolarinteraction\nTheenergyofthelong-rangemagnetodipolarinterac-\ntion between magneticmomentsand the corresponding\ncontributiontothetotal e ffectivefieldarecomputedus-\ningthepoint-dipoleapproximationas\nEdip=−1\n2N/summationdisplay\ni=1µi/summationdisplay\nj/nequali3eij(eijµj)−µj\n∆r3\nij,(10)\ni.e., magnetic momentsof finite elements are treated as\npointdipoleslocatedatthepolyhedroncenters. Thisap-\nproximationisequivalenttotheapproximationofspher-\nicaldipoles,i.e.,itwouldbeexactforsphericalfiniteel-\nements. Hence,for ourdiscretizedsystem, this approx-\nimation introducessome computationalerrors, because\nourfinite elementsare polyhedrons. However,these er-\nrors are small, because the shape of these polyhedrons\nis close to spherical (see Fig. 3), due to the special al-\ngorithm employed for the generation of our mesh, as\nexplainedin Sec.2.1.\nThe summation in Eq. (10) is performed by the so\ncalled particle-mesh Ewald method. Didactically very\ninstructive and detailed introduction into Ewald meth-\nods can be found in Ref. [75]. The specific implemen-\ntationofthelattice-basedEwaldmethodforthemagne-\ntodipolarinteractionforregularanddisorderedsystems\n6ofmagneticparticlesisdescribedinourpapers[76,77].\nHere,webrieflyrepeatthebasicissuesofthisalgorithm\ntomakeourpaperself-containing.\nFirst we remind that the Ewald method [78] was ini-\ntially invented for evaluating conditionally converging\nlattice sums for the Coulomb interaction in ionic crys-\ntals. At present, it is a standard method to calculate\nany long-range interaction—including Coulomb sums,\ngravitation energy, dipole interaction, elastic forces in\ndislocation networks etc.—in systems with periodic\nboundaryconditions(PBC).Insuchsystemsdirectsum-\nmation over all field sources is impossible simply due\nto their infinite number. Hence, we must use a Fourier\nexpansion over the reciprocal lattice vectors kwhich\ncorrespondtotheinfinitelyrepeatedsimulationvolume.\nFor thepointsources of the long-range field, the cor-\nrespondingFouriercomponentsdecayrelativelyslowly\nwithincreasingmagnitudeofthewavevector kinrecip-\nrocal space. In numerical simulations we always have\nto our disposal only a finite number of such wave vec-\ntors, so that the Fourier spectrum of our long-rangein-\nteraction should be cut o ffat the maximal finite value\nkmax. As mentioned above, the Fourier harmonics de-\ncay slowly, so that at kmaxthey are by no means small.\nForthisreason,thespectrumcut-o ffduetotheelimina-\ntion of all Fourier components with k>kmaxis sharp,\nthus,leadingtolargeartificialoscillationsoftheintera c-\ntion potential after its inverse transformationto the real\nspace.\nAs with nearly all Ewald methods, the version de-\nscribed below for dipolar systems solves the problem\nbyaddingand subtractinga Gaussian dipoleat eachlo-\ncation of a point dipole µiin the initial system. Using\nthedefinitionofthegradientofthe δfunction,itiseasy\nto show that this operation corresponds to the addition\nandsubtractionofachargedistribution(withawidth σ)\nρG\ni(r)=−(r−ri)µi\n(2π)3/2σ5exp/parenleftBigg\n−(r−ri)2\n2σ2/parenrightBigg\n.(11)\nThen the magnetodipolar field Hdip=Hdip\nA+Hdip\nBis\nevaluatedas the sum of two contributionsfrom subsys-\ntemsA andB. Thefirst subsystemconsistsofGaussian\ndipolesEq. (11) and the secondone is composedof the\noriginalpointdipolesminusthese Gaussiandipoles,\nρB(r)=−N/summationdisplay\ni=1/bracketleftBig\nµi∇δ(r−ri)−ρG\ni(r)/bracketrightBig\n, (12)\nwhere the first terms in the sum on the right represent\nthe charge density of a point dipole located at ri. Thefieldcreatedbyacompositeobjectinsquarebracketsof\nEq.(12) is[76]\nHα\nB,i(r−ri)=3(α−αi)(µi∆ri)\n∆r5\ni−µα\ni\n∆r3\nifG(∆ri)+\n/radicalbigg\n2\nπ(α−αi)(µi∆ri)\n∆r5\niexp−∆r2\ni\n2σ2,\n(13)\nwhereα=x,y,z.\nIt is important to note that the function fG(r) decays\nwithdistanceasexp( −r2),\nfG(r)=1−erf/parenleftBiggr\nσ√\n2/parenrightBigg\n+√\n2r\nπaexp/bracketleftBigg\n−r2\n2σ2/bracketrightBigg\n.(14)\nThegoalofthisdecompositionoftheoriginalsystem\nofpointdipolesisthefollowing. ThefieldEq.(13)from\nthe second subsystem B is a short-range one, because\neachpointdipoleisscreenedbya Gaussiandipolewith\nthe same total moment,but with the opposite sign. The\ncomputation of such a short-range contribution takes\n∼Noperations for a system of Nparticles. The first\nsubsystemAconsistsofdipoleshavingasmoothGaus-\nsian charge distribution, so that its Fourier components\ndecay rapidly with increasing k. This fast decay allows\na painless cut-offof the Fourier spectrum at large wave\nvectors,sothatthecontributionfromthefirstsubsystem\nEq. (11) can be safely calculated using Fourier expan-\nsion. Moredetailedexplanationsconcerningthisproce-\ndurecanbefoundinRef. [76].\nAlreadytheabovemoststraightforwardimplementa-\ntion of the Ewald method allows for a reliable evalua-\ntionof the dipolarfield in systemswith PBC. However,\nfor disordered systems, this method has the same pro-\nhibitivelyhighoperationcount ∼N2,asadirectsumma-\ntion for systems with OBC. The reason is that particle\npositions in disordered systems do not form a regular\nlattice, so that the Fourier transformation for the cal-\nculation of the long-range contribution Hdip\nAcan not be\ndone via the fastFourier transformationtechnique: ex-\nponential factors exp(i kri) should be computed for all\nwave vectors kand all particle positions riseparately,\nleadingtothe operationcountgivenabove.\nIn order to decrease the computational costs, several\nlattice versions of the Ewald method have been devel-\noped (see the overview [79]). The general idea behind\nallthesemethodsistoemploysomemappingoftheini-\ntial disordered system onto a regular lattice, in order\nto enable the application of the FFT. Using this gen-\neral paradigm, we have implemented the following al-\ngorithm:\n7(i)First,wemapourdisorderedsystemofpointmag-\nnetic dipolesµi=µ(ri) onto a system of dipoles lo-\ncatedat lattice points rp(pisthe3D index)usingsome\nweightingfunction w3d(r),\n˜µ(rp)=N/summationdisplay\ni=1µ(ri)w3d(|ri−rp|)=\nMnb/summationdisplay\ni=1µiw(|xi−xp|)w(|yi−yp|)w(|zi−zp|).(15)\nWe emphasizethat thewholemethodmakesonlysense\nif the mapping function wis strongly localized, so that\nthe sum over all Ndipoles in Eq. (15) is actually re-\nstricted to a few nearest neighbors Mnbof the lattice\nnodep.\n(ii) Next, we add and subtract to each point lattice\ndipoletwoGaussiandipolesEq.(12),asinthestraight-\nforwardEwaldmethoddescribedabove.\n(iii) Further, we compute the dipolar field of this lat-\ntice system as described above, i.e., as the sum of the\nlong-range contribution from smooth Gaussian dipoles\npositioned on the lattice and the short-range contribu-\ntion Eq. (13) from the composite objects “point dipole\n−Gaussiandipole”,also placedonthelattice.\n(iv) Finally, the field obtained in this way on the lat-\nticepointsrpis mappedback onto the initial dipole lo-\ncationsriusingthesame functions wasinEq.(15).\nAsmentionedabove,the majoradvantageof thislat-\nticeEwaldversionisthepossibilitytouseFFTforcom-\nputing the long-range part of the total magnetodipolar\nfield. In addition, we can also accelerate the evalutaion\noftheshort-rangecontribution. Namely,wenotethat( i)\nthecontributionEq.(13)dependsonlyonthedi fference\n∆rbetween the source and target coordinates and ( ii)\nboth source and target points are located on the lattice.\nHence, this short-range contribution also is a discrete\nconvolution and as such can be also computed by the\nFFTtechnique. Usingthisnicefeature,wecanincrease\nthe numberof nearest neighborshells used by the eval-\nuation of the short-range interaction part without addi-\ntional time cost, making the corresponding truncation\nerror arbitrarily small. Keeping in mind that the evalu-\nation of the long-rangefield part via the FFT technique\nforthelatticesystemisexact,weconcludethattheonly\nsource of computational errors in our algorithm is the\nmapping of the initial disordered system onto a lattice,\nwhich can be easily controlled and reduced by choos-\ning the suitable mapping scheme [79]. We have found\nthat already the conventional first-order mapping used\ntogether with a lattice having a cell size equal to Rsp/2\n(hereRspis thesphere radiusused to generatethe meshfor the soft-phase discretization)ensuresby the evalua-\ntion ofHdipa relative error smaller than 0 .01, which is\ngoodenoughforourpurposes.\n2.3. New micromagnetic algorithm: minimization pro-\ncedureandnumericaltests\nFortheminimizationofthetotalmagneticenergy,ob-\ntained as the sum of all contributions described above,\nwe use the simplified version of a gradient method\nemploying the dissipation part of the Landau-Lifshitz\nequationofmotionformagneticmoments[65,80]. This\nmeansthatweupdatethemagnetizationconfigurationat\neachstepas\nmnew\ni=mold\ni−∆t/bracketleftBig\nmold\ni×/bracketleftBig\nmold\ni×heff\ni/bracketrightBig/bracketrightBig\n,(16)\nwheremidenotes the unit magnetization vector mi=\nMi/MSandheff\niis the reducedeffective field, evaluated\ninastandardwayasthenegativeenergyderivativeover\nthemagneticmomentprojections[65].\nSince we are looking for the energy minimum, the\ntime step in Eq. (16) is chosen and adapted using the\nmonitoringof this energy. If the total energy decreases\nafterthe iterationstep performedaccordingto Eq.(16),\nwe accept this step. If the energy increases, we restore\nthe previous magnetization state, halve the time step\n(∆t→∆t/2) and repeat the iteration. During the mini-\nmization procedure we may also increase the time step\nto avoid an unnecessary slow minimization: the time\nstep is doubled, if the last few steps (typically 5 −10\nsteps) were successful. For the termination of the min-\nimization procedure, we use the local torque criterion:\nwestoptheiterationprocess,ifthemaximaltorqueact-\ning on magnetic moments is smaller than some pre-\nscribed value, i.e., max i{|mi×heff\ni|}< ε. As is well\nknown,thisconditionismoreappropriatethanthealter-\nnativecriterionof a su fficientlysmall energydi fference\nbetween the two subsequent steps. In all tested cases\nthevalueε=10−3wassmallenoughtoensurethemin-\nimizationconvergence.\nThe new methodologyexplained in detail above was\ntested on two simple examplesin Ref. [74]. We remind\nthat we have first reproduced—using our disordered\nmesh—with a high accuracy the analytically known\nmagnetizationprofileofastandard3DBlochwall. Sec-\nond, for a trial 3D magnetic configuration defined via\nsimple trigonometricfunctionsof coordinates(we have\nused these functions to ensure a su fficiently slow spa-\ntialvariationofthesystemmagnetizationdirection),we\nhave obtained a very good agreement between the to-\ntalenergyandpartialenergycontributionsfoundbyour\nnew method and the FDM micromagneticpackage Mi-\ncroMagus[81].\n8Figure2: (a)Vortex (2Dcrosssection) and (b)flower (3Darro w plot) magnetization states obtained byournew methodolog y explained in Sec.2.3\nabove. Data taken from Ref. [82].\nHere, we would like to present two additional much\nmorecomplicatedtests, where we computethe equilib-\nrium magnetization configurations of a cubic magnetic\nparticle obtained using our new method and compare\nthese configurations with the results obtained for the\nsamesystembytheMicroMaguspackage.\nTheparticlesize waschosento be40 ×40×40nm3,\nandthemagneticmaterialsparametersweresetto MS=\n800kA/m,A=1.0×10−11J/m,andK=5.0×104J/m3\n(uniaxialanisotropy). Forthesimulationsusingournew\nmethod, the particle was discretized into N=9000\npolyhedrons with a typical size of d=2nm. For the\nMicroMagussimulations,acubiccellwithasidelength\nof2.5nmwasused.\nFor the test problems, we have chosen two well\nknown magnetization states typical for ferromagnetic\nparticles of this size [83]: the vortex state and the so-\ncalled flower state. To obtain the vortex state, we have\nstarted the minimization procedure from the state that\nis topologically equivalent to the vortex, the so-called\nclosed Landau domain configuration. The flower state\ncould be obtained by starting the energy minimization\nsimply from the homogeneous configuration with the\nmagnetizationdirectedalonga cubeside.\nTable 1 lists the total energies, partial energy contri-\nbutions and the reduced magnetization values for the\nequilibrium magnetization states shown in Fig. 2 ob-\ntained by the new method and by the standard FDM\nsimulations (MicroMagus package). Almost all energy\ncontributions obtained by the two methods agree very\nwell. The only significant relative di fference can be\nfoundfortheanisotropyenergyoftheflowerstate;how-\never, this significant relativedifference (∆E/E) arisesTable 1: Comparison of energies and reduced magnetizations for the\nvortex and flower magnetization states computed by the new me thod\nand by the standard finite di fference simulations (MicroMagus soft-\nware). Data taken from Ref. [82].\nVortex energies (×10−18J) New method MicroMagus\nEtot 8.225 8.270\nEan 1.361 1.385\nEexch 4.409 4.562\nEdip 2.455 2.324\nM/MS 0.400 0.406\nFlower energies (×10−18J) New method MicroMagus\nEtot 7.813 7.843\nEan 0.137 0.127\nEexch 0.434 0.441\nEdip 7.242 7.275\nM/MS 0.972 0.974\nsimply due to a very low value of this energy. All in\none,theagreementbetweenthenewandtheestablished\nmethodologiesforallcaseswherethestandardmethods\nareapplicableisfullysatisfactory.\n3. MagneticSANS crosssectionofunpolarizedneu-\ntrons\nInourmicromagneticsimulationsofelasticmagnetic\nSANS we have focussed on the two most commonly\nemployed scattering geometries where the wavevector\nk0of the incident neutron beam is either perpendicu-\nlar [case (i)] or parallel [case (ii)] to the external mag-\nnetic field H, which is applied along the z-direction of\na Cartesian coordinate system. ( ex,eyandezrepre-\nsent the unitvectorsalongthe Cartesian axes.) Further-\nmore, since the focus of the present study is on mag-\n9Figure 3: Sketch of the two scattering geometries and of the m icro-\nscopic structure of the nanocomposite sample (simulation v olume:\nV=250×600×600nm3). Blue polyhedrons—Fe particles; yellow-\norange-red polyhedrons—matrix phase. In the micromagneti c simu-\nlationsthesizesoftheFeparticles aredistributedaccord ing toaGaus-\nsianfunction centered atabout10nmandtheparticle volume fraction\nequals 40%, as in the experimental study Ref. [17].\nnetic spin-misalignment scattering, we have ignored\nthe nuclear SANS contribution. Note, however, that\nfor polycrystalline texture-free magnetic nanocompos-\nitesthenuclearSANSsignalisvirtuallyindependentof\nthe applied magnetic field and isotropic, and its mag-\nnitude is generally small compared to the here relevant\nspin-misalignmentscattering[31]. Furthermore,the re-\nstriction to unpolarized neutrons entails the neglect of\nscattering contributions from helical spin arrangments,\nwhichareofrelevance,e.g.,inFeCoSiandMnSisingle\ncrystals[58,59].\nAsketchoftheabovetwoscatteringgeometriesalong\nwith a schematic drawing of the microscopic structure\nofthenanocompositesamplecanbeseen inFig.3.\n3.1. Case(i): k0⊥H∝ba∇dblez\nFork0∝ba∇dblex, the elastic magneticSANS crosssection\ndΣM/dΩat momentum-transfervector qreads[31]\ndΣM\ndΩ(q)=8π3\nVb2\nH/parenleftBig\n|/tildewideMx|2+|/tildewideMy|2cos2θ\n+|/tildewideMz|2sin2θ−(/tildewideMy/tildewideM∗\nz+/tildewideM∗\ny/tildewideMz)sinθcosθ/parenrightBig\n,(17)whereV=250×600×600nm3is the scattering vol-\nume,bH=2.9×108A−1m−1,c∗is a quantitycomplex-\nconjugated to c, and/tildewideM(x,y,z)(q) are the Fourier trans-\nformsofthemagnetizationcomponents M(x,y,z)(r). Note\nthat in the small-angle limit and for this particular ge-\nometry the scattering vector qcan be expressed as q/simequal\nq(0,sinθ,cosθ), whereθdenotes the angle between q\nandH(Fig.3).\n3.2. Case (ii): k0∝ba∇dblH∝ba∇dblez\nForthisgeometry,onefinds\ndΣM\ndΩ(q)=8π3\nVb2\nH/parenleftBig\n|/tildewideMx|2sin2θ+|/tildewideMy|2cos2θ\n+|/tildewideMz|2−(/tildewideMx/tildewideM∗\ny+/tildewideM∗\nx/tildewideMy)sinθcosθ/parenrightBig\n,(18)\nwhereq/simequalq(cosθ,sinθ,0) andθis measured relative\ntoex(Fig.3).\nFor the micromagnetic simulations of magnetic\nSANS from two-phase nanocomposites, we used (un-\nless otherwise stated) the following materials param-\neters for hard (“h”) and soft (“s”) phases, which are\ncharacteristic for the Fe-based nanocrystalline alloy\nNANOPERM [64]: magnetizations Mh=1750kA/m\nandMs=550kA/m, anisotropy constants Kh=4.6×\n104J/m3andKs=1.0×102J/m3. As a value for the\nexchange-stiffnessconstantweused A=0.2×10−11J/m\nfor interactions both within the soft phase and between\nthehardandsoftphases.\n4. Resultsanddiscussion\nThe applied-field dependence of the total magnetic\nSANS cross sections dΣM/dΩ[computed,respectively,\nbymeansofEqs.(17)and(18)]isdisplayedinFig.4for\nboth scattering geometries, i.e., for the situations when\nthewavevector k0oftheincomingneutronbeamisper-\npendicular[case (i)]orparallel[case (ii)]tothe applied\nmagneticfield H,whichforbothcasesisassumedtobe\nparallelto ez. Thecorrespondingradially-averageddata\ncanbeseenin Fig.5.\nWhiledΣM/dΩfork0∝ba∇dblHis isotropic (i.e.,θinde-\npendent) over the whole field and momentum-transfer\nrange, it is highly anisotropic for k0⊥H(Fig. 4). At\na saturating applied magnetic field of µ0H=1.5T,\nwhere the normalized “sample” magnetization is (for\nboth geometries) larger than 99 .9%, the anisotropy of\ndΣM/dΩ[case(i)]isclearlyofthesin2θ-type,i.e.,elon-\ngated normal to H; this is because magnetic scattering\ndue to transversal spin misalignment is small close to\nsaturation and the dominating scattering contrast arises\n10Figure 4: Applied-field dependence of the total magnetic SAN Scross section dΣM/dΩfork0⊥H(Eq.(17), upper row) and for k0∝ba∇dblH(Eq. (18),\nlower row). The external magnetic field H∝ba∇dblezis applied horizontally in the plane of the detector for k0⊥H(qx=0, upper row) and normal to\nthe detector plane for k0∝ba∇dblH(qz=0, lower row). Materials parameters of NANOPERM were used (s ee text). Pixels in the corners of the images\nhaveq/simequal1.2nm−1. Logarithmic color scale is used.\n10−1100100101102103104\nq (nm−1)dΣM /dΩ (cm−1sr−1)\n10−1100100101102103104\nq (nm−1)dΣM /dΩ (cm−1sr−1)\nFigure 5: Solid lines: Radially-averaged dΣM/dΩas a function of scattering vector qfork0⊥H(left image) and for k0∝ba∇dblH(right image) (data\nhave been smoothed). Field values (in mT) from top to bottom, respectively: 30, 100, 290, 1500. Dashed lines in both image s:dΣM/dΩ∝q−4.\nSolid circles in both images represent part of the (squared) form factor of asphere with aradius of R=5.7nm.\nfrom nanoscale jumps of the longitudinal magnetiza-\ntion at phase boundaries. On decreasing the field, the\ntransversalmagnetizationcomponentsincreasein mag-\nnitude as long-rangespin misalignment developsat the\nsmallestq. The SANS pattern in case (i) essentially re-\nmainsofthesin2θ-typeatlowerfields,althoughamore\ncomplicatedanisotropy builds up at small q. As can be\nseen in Fig. 5, dΣM/dΩat smallqincreases by more\nthan one order of magnitude as the field is decreased\nfrom 1.5T to 30mT. Asymptotically, at large q, the\npower-lawdependenceof dΣM/dΩcanbedescribedbydΣM/dΩ∝q−4. Inagreementwiththenatureoftheun-\nderlying microstructure ( ∼10nm-sized single-domain\nFe particles in a nearly saturated matrix), one can de-\nscribe the oscillations of dΣM/dΩat largeqandHby\nthe form factor of a sphere with a radiusof R=5.7nm\n(solidcirclesinFig.5). Weremindthattheshapeofthe\nparticles in our micromagnetic algorithm is not strictly\nspherical.\nFigure 6 shows the projections of the magnetization\nFourier coefficients|/tildewideMx|2,|/tildewideMy|2,|/tildewideMz|2, and of the cross\ntermsCT=−(/tildewideMy/tildewideM∗\nz+/tildewideM∗\ny/tildewideMz) andCT=−(/tildewideMx/tildewideM∗\ny+\n11Figure 6: Results of the micromagnetic simulations for the F ourier coefficients of the magnetization. The images represent projecti ons of the\nrespective functions into theplane of the2D detector, i.e. ,qx=0 fork0⊥H(left image) and qz=0fork0∝ba∇dblH(right image). Fromleft column to\nright column, respectively: |/tildewideMx|2,|/tildewideMy|2,|/tildewideMz|2, andCT=−(/tildewideMy/tildewideM∗\nz+/tildewideM∗\ny/tildewideMz) (left image) and CT=−(/tildewideMx/tildewideM∗\ny+/tildewideM∗\nx/tildewideMy) (right image). In the first\nthree columns from left, red color corresponds, respective ly, to “high intensity” and blue color to “low intensity”; in the fourth column, blue color\ncorresponds to negative and orange-yellow color to positiv e values of the CT. Pixels in the corners of the images have q/simequal1.2nm−1. Logarithmic\ncolor scale is used.\n/tildewideM∗\nx/tildewideMy) into the plane of the 2D detector at the same\nexternal-field values as in Fig. 4. It can be seen in\nFig. 6 that in case (i) both |/tildewideMx|2and|/tildewideMz|2are isotropic\noverthe displayed( q,H) range,while the Fouriercoef-\nficient|/tildewideMy|2reveals a pronounced angular anisotropy,\nwith maxima that lie roughly along the diagonals of\nthe detector (the so-called “clover-leaf”anisotropy, see\nFig. 11 below). In case (ii), |/tildewideMx|2and|/tildewideMy|2are both\nstrongly anisotropic (with characteristic maxima in the\nplane perpendicular to H), while|/tildewideMz|2is isotropic.\nWhen [for case (ii)] all Fourier coe fficients are multi-\nplied by the correspondingtrigonometricfunctionsand\nsummed up [compare Eq. (18)], the resulting dΣM/dΩ\nbecomesisotropic(Fig.4,lowerrow).\nThe cross terms for both scattering geometries vary\nin sign between quadrants on the detector. The respec-\ntiveCTis positive in the upper right quadrant of the\ndetector(0◦<θ<90◦),negativeintheupperleftquad-\nrant (90◦<θ <180◦), and so on. When both CT’s\nare multiplied by sin θcosθ, the corresponding contri-\nbution to dΣM/dΩbecomes positive-definitefor all an-\nglesθ(compareFig.7). Thisobervationsuggeststhat—\ncontrary to the common assumption that the CTav-\nerages to zero for statistically isotropic polycrystallin e\nmicrostructures—the CTappears to be of special rele-vancein nanocompositemagnets.\nFigure 7: (left image) CT=−(/tildewideMy/tildewideM∗\nz+/tildewideM∗\ny/tildewideMz) fork0⊥H(µ0H=\n0.29T). Blue color corresponds to negative and orange-yellow color\nto positive values of the CT. (right image) CTsinθcosθ. Red color\ncorresponds to “high intensity” and blue color to “low inten sity”. All\nother settings areas in Fig.6.\nIn Fig. 8 we show for both scattering geometries\nthe radially-averaged total dΣM/dΩalong with the\nradially-averaged individual scattering contributions to\ndΣM/dΩ, i.e., the radial average of terms8π3\nVb2\nH|/tildewideMx|2,\n8π3\nVb2\nH|/tildewideMy|2cos2θ,8π3\nVb2\nHCTsinθsinθ, and so on [com-\npare Eqs. (17) and (18)]. At saturation ( µ0H=1.5T),\nboth transversal scattering contributions, i.e., terms ∝\n|/tildewideMx(q)|2and∝|/tildewideMy(q)|2, are for both cases (i) and (ii)\nsmall relative to the other terms and the main contribu-\ntion to the total dΣM/dΩoriginates from longitudinal\nmagnetization fluctuations, i.e., from terms ∝|/tildewideMz(q)|2.\nFork0∝ba∇dblH,bothtransversaltermsaresosmallthatthey\n120.10.2 0.7101102103104k0 ⊥ H; 1500 mT\nq (nm−1)dΣM /dΩ (cm−1sr−1)\n0.10.2 0.7101102103104\nq (nm−1)dΣM /dΩ (cm−1sr−1)k0 || H; 1500 mT\n0.10.2 0.7101102103104k0 ⊥ H; 290 mT\nq (nm−1)dΣM /dΩ (cm−1sr−1)\n0.10.2 0.7101102103104\nq (nm−1)dΣM /dΩ (cm−1sr−1)k0 || H; 290 mT\n0.10.2 0.7101102103104k0 ⊥ H; 30 mT\nq (nm−1)dΣM /dΩ (cm−1sr−1)\n0.10.2 0.7101102103104\nq (nm−1)dΣM /dΩ (cm−1sr−1)k0 || H; 30 mT\nFigure 8: Radially-averaged total magnetic SANScross sect ionsdΣM/dΩand radially-averaged individual contributions to dΣM/dΩas afunction\nof scattering vector qand applied magnetic field Hfork0⊥Handk0∝ba∇dblH(see insets). Black lines: total dΣM/dΩ; Blue lines:|/tildewideMz|2; Magenta\nlines:CT; Green lines:|/tildewideMy|2;Red lines:|/tildewideMx|2. In theabove notation, the prefactor8π3\nVb2\nHand the numerical factors that result from theaveraging\nprocedure have been omitted for clarity. Note that di fferent trigonometric functions may be involved in the averag ing procedure, compare, e.g.,\n8π3\nVb2\nH|/tildewideMx|2fork0⊥H[Eq.(17)] and8π3\nVb2\nH|/tildewideMx|2sin2θfork0∝ba∇dblH[Eq.(18)].\nare not visible within the displayed “intensity” range\nanddΣM/dΩpractically equals the |/tildewideMz(q)|2scattering\n(bothcurvessuperimpose). Notethatthe CTforcase(i)\nistheproductofatransversalandthelongitudinalmag-\nnetization Fourier coe fficient, whereas for case (ii) the\nCTcontains the two transversal components. This ex-\nplainswhythe CTforcase(ii)ismuchsmallerthanthe\nCTforcase(i)at fieldsclosetosaturation. Ondecreas-\ningthefield,the transversalFouriercoe fficientsandthe\nCT’s becomeprogressivelymore important,in particu-\nlarat small q.It is also important to note that the present simula-\ntions were carried out by assuming a quite large jump\nin the magnetization magnitude ∆Mat the interphase\nbetween particles and matrix, µ0∆M=1.5T. Conse-\nquently, the ensuing |/tildewideMz(q)|2scattering in both geome-\ntriesandthe CTscatteringincase(i)arerelativelylarge.\nFor∆M=0, theCTat saturation for case (i) becomes\nnegligible,since /tildewideMz(q)∝δ(q=0).\nFigures 6 and 8 embody the power of our approach:\nBy employing numerical micromagnetics for the com-\nputation of magnetic SANS cross sections, it becomes\n13possible to study the individual magnetization Fourier\ncoefficients and their contribution to dΣM/dΩ. This\nsheds light on the ongoing discussion regarding the\nexplicitq-dependence of dΣM/dΩ[56]. In particu-\nlar, the approach of combining micromagnetics and\nSANScomplementsneutronexperiments,whichgener-\nallyprovideonlyaweightedsumofFouriercoe fficients\n[compareEqs. (17) and (18)], a fact that often hampers\nthe straightforward interpretation of recorded SANS\ndata. Whileitisinprinciplepossibletodeterminesome\nFourier coefficients, e.g., through the application of a\nsaturating magnetic field or by exploiting the neutron-\npolarizationdegreeoffreedomviaso-calledSANSPOL\norPOLARISmethods(e.g.,Refs.[18,51,84]),itisdif-\nficult to unambiguously determine a particular scatter-\ning contribution without “contamination” by unwanted\nFourier components. For instance, when the applied\nfieldisnotlargeenoughtocompletelysaturatethesam-\nple, then the scattering of unpolarized neutrons along\nthe field direction does not represent the pure nuclear\nSANS, but containsalso the magneticSANS dueto the\nmisalignedspins[39].\nThe finding [for case (i)] that |/tildewideMx|2and|/tildewideMz|2are\nisotropicandthat|/tildewideMy|2=|/tildewideMy|2(q,θ)providesastraight-\nforward explanation for the experimental observation\nof the clover-leaf anisotropy in the SANS data of\nthenanocrystallinetwo-phasealloyNANOPERM [17].\nOur simulation results for the di fference cross section\n∝(|/tildewideMx|2+|/tildewideMy|2cos2θ+CTsinθcosθ) (seeFigs.9and\n10),wherethescatteringatsaturation( µ0H=1.5T)has\nbeen subtracted, agree qualitatively well with the ex-\nperimental data [74, 82]. Clover-leaf-type anisotropies\nindΣM/dΩhave also been reported for a number of\nother materials, including precipitates in steels [39],\nnanocrystalline Gd [32, 35], and nanoporous Fe [33].\nThe maxima in the di fference cross section [for\ncase(i)]dependon qandH,andmayappearatangles θ\nsignificantlysmaller than 45◦. This becomesevidentin\nFig. 11, where we show (for k0⊥H) polar plots of the\nsimulateddifferencecrosssectionat selected qandH.\nThe results of our previous work [82, 85] strongly\nsuggest that the magnetodipolar interaction plays a de-\ncisive role for the understanding of magnetic SANS of\nnanocomposites. In fact, it is this interaction which is\nresponsiblefortheanisotropy,i.e.,forthe θ-dependence\nof the magnetization Fourier coe fficients and, hence,\nofdΣM/dΩ. The impact of the dipolar interaction on\ndΣM/dΩcan be convenientlystudied, since our micro-\nmagneticalgorithmallowsoneto“switchon”and“o ff”\nthis energy term. Figure 12 shows results of micro-\nmagnetic simulations for |/tildewideMy|2and for both CT’s ob-\nFigure 9: Comparison between simulation (upper row) and exp eri-\nmental data (lower row) for the di fference cross section ∝(|/tildewideMx|2+\n|/tildewideMy|2cos2θ+CTsinθcosθ) at different external fields as indicated\n(k0⊥H). Pixels in the corners of the images have q/simequal0.64nm−1.\nLogarithmic color scale is used. Since the experimental dat a was not\nobtained in absolute units, we have multiplied it with a scal ing factor\nfor comparison with the simulated data. His horizontal in the plane.\nExperimental data weretaken from Ref. [17].\nFigure 10: (•) Radially-averaged experimental di fference cross sec-\ntions as a function of momentum transfer qandH(k0⊥H). Field\nvalues (in mT)from top to bottom: 30, 100, 290. Solid lines: R esults\nof the micromagnetic simulations (data have been smoothed) . Verti-\ncaldashedlinesindicate theregionwheretheclover-leaf a nisotropy is\nobserved. ExperimentaldataweretakenfromRef.[17]andmu ltiplied\nby ascaling factor (compare Fig. 9).\ntained with and without the dipolar interaction. When\nthe dipolar interaction is ignored in the micromagnetic\ncomputations,allFouriercoe fficientsareisotropicatall\nqandHinvestigated (data for |/tildewideMx|2and|/tildewideMz|2are not\n14Figure 11: Polar plots of the simulated di fference cross section ∝\n(|/tildewideMx|2+|/tildewideMy|2cos2θ+CTsinθcosθ)atdifferentcombinations ofmo-\nmentumtransfer qandappliedmagneticfield H(seeinsets)( k0⊥H).\nData have been smoothed. Dotted lines ( ∝sin2θcos2θ) serve as\nguides to the eyes.\nshown). This observation shows that for any realistic\ndescription of experimental magnetic SANS data this\ninteractionhastobetakenintoaccount.\nGenerally, the sources of the magnetodipolar field\nare nonzero divergencesof the magnetization ( ∇·M/nequal\n0). For magnetic nanocomposites, the most prominent\n“magneticvolumecharges”arerelatedtothenanoscale\nvariations in the magnetic materials parameters at the\nphaseboundarybetweenparticlesandmatrix,e.g.,vari-\nations in the magnetization, anisotropy or exchangein-\nteraction. Such jumps in the magnetic materials pa-\nrametersmaygiverisetoaninhomogeneousspinstruc-\nture which decorates each nanoparticle. Figure 13 dis-\nplays the real-space magnetization distribution around\ntwo nanoparticles. Note that the symmetry of the spin\nstructurereplicatesthesymmetryofthe CT(compareto\nFig.6). In thepresenceof anappliedmagneticfieldthe\nstray-field and associated magnetization configuration\naround each nanoparticle “look” similar (on the aver-\nage), thusgivingrise to dipolarcorrelations which add\nup to a positive-definite CTcontribution to dΣM/dΩ.\nNote, however, that for polycrystalline microstructures\nclover-leaf-type anisotropies may become only visible\nindΣM/dΩfork0⊥H.\nAs mentionedabove, not only variations in the mag-\nnetization magnitude, but also variations in the direc-\ntionand/ormagnitude of the magnetic anisotropy K\n(randomanisotropy)and variationsin the magnitudeof\nthe exchange coupling may give rise to dipolar corre-\nlations. The micromagnetic simulation package allows\nFigure 12: Influence of the dipolar interaction on the Fourie r co-\nefficients of the magnetization. |/tildewideMy|2and both cross terms CT=\n−(/tildewideMy/tildewideM∗\nz+/tildewideM∗\ny/tildewideMz) (k0⊥H) andCT=−(/tildewideMx/tildewideM∗\ny+/tildewideM∗\nx/tildewideMy) (k0∝ba∇dblH)\nwerecomputed fromareal-space magneticmicrostructure wi thanor-\nmalized magnetization of 99 .0%. Applied fields of 290mT (with\ndipolar interaction) and 7mT (without dipolar interaction Edip=0)\nwere required in order to achieve this magnetization value. The cor-\nresponding results for the Fourier coe fficient|/tildewideMx|2(fork0∝ba∇dblH) are\nanalogous tothedepicted resultsfor |/tildewideMy|2. Pixelsinthecornersofthe\nimages have q/simequal0.9nm−1. Logarithmic color scale is used.\nus to vary the magnetic materials parameters of both\nphases of the nanocomposite. Hence, it becomes pos-\nsible to study the impact of such situationson the mag-\nneticSANS.\nIn order to investigate variationsin K(which are, by\nconstruction,naturallyincludedintoourmicromagnetic\nalgorithm), we have computed the spin distribution for\nthe situation that Mh=Ms=M(i.e.,∆M=0), but for\ndifferent values of M. Figure 14 reveals that a clover-\nleaf-typepatternin |/tildewideMy|2developswithincreasingmag-\nnetization value M, i.e., with increasing strength of the\nmagnetodipolar interaction. As jumps in the magneti-\nzation at phase boundaries are excluded here as possi-\n15Figure 13: Results of amicromagnetic simulation for the 2D s pin distribution around two selected nanoparticles (blue c ircles), which are assumed\nto be in a single-domain state. The external magnetic field His applied horizontally in the plane ( µ0H=0.3T). Left image: Magnetization\ndistribution in both phases; note that µ0∆M=µ0(Mh−Ms)=1.5T. In order to highlight the spin misalignment in the soft ph ase, the right image\ndisplays the magnetization component M⊥perpendicular to H(red arrows). Thickness of arrows is proportional to the mag nitude of M⊥. Blue\nlines: Dipolar field distribution.\nble sources for perturbations in the spin structure, it is\nstraightforward to conclude that nanoscale fluctuations\ninKgive rise to inhomogeneous magnetization states,\nwhich decorate each nanoparticle and which look sim-\nilar to the structure shown in Fig. 13. This observation\nstrongly suggests that the origin of the clover-leaf pat-\ntern indΣM/dΩof nanomagnets is not only related to\nvariations in magnetization magnitude but also due to\nvariations in the magnitude and direction of the mag-\nneticanisotropyfield.\nFigure 14: Fourier coe fficient|/tildewideMy|2(q) atµ0H=0.3T and for Mh=\nMs=M(i.e.,∆M=0) (k0⊥H).Mincreases from left to right\n(see insets). Kh=4.6×104J/m3,Ks=1.0×102J/m3and random\nvariationsineasy-axisdirectionsfromparticletopartic leareassumed.\nData taken from Ref. [85].\n5. Summary andconclusions\nBy means of a recently developed micromagnetic\nsimulation methodology—especially suited for model-\ningmulti-phasematerials—wehavecomputedthemag-\nnetic small-angle neutron scattering (SANS) cross sec-\ntiondΣM/dΩof a two-phase nanocomposite magnet\nfromtheNANOPERM familyofalloys. Besidestaking\ninto account the full nonlinearity of Brown’s equationsof micromagnetics, the approach allows one to study\nthedependencyof the individual magnetizationFourier\ncoefficients /tildewideM(x,y,z)on the applied magnetic field H\nand, most importantly, on the momentum-transfervec-\ntorq. Thisideallycomplementsneutronexperiments,in\nwhich a weighted sum of the /tildewideM(x,y,z)is generally mea-\nsured. It is this particular circumstance, in conjunc-\ntion with the flexibility of our micromagnetic package\nin terms of microstructure variation (particle size and\ndistribution, materials parameters, texture, etc.), whic h\nmakes us believe that the approach of combining full-\nscale 3D micromagneticsimulations with experimental\nmagnetic-field-dependentSANS data will provide fun-\ndamental insights into the magnetic SANS of a wide\nrange of magneticmaterials. The micromagneticsimu-\nlations underline the importance of the magnetodipolar\ninteractionforunderstandingmagneticSANS.Inpartic-\nular,theso-calledclover-leaf-shapedangularanisotrop y\nindΣM/dΩ—which was previously believed to be ex-\nclusively related to nanoscale jumps in the magnetiza-\ntion magnitude at internal interphases—is of relevance\nforallbulknanomagnetswithspatiallyfluctuatingmag-\nneticparameters.\nAcknowledgments\nWe thank the Deutsche Forschungsgemeinschaft\n(Project No. BE 2464 /10-1) and the National Re-\nsearch Fund of Luxembourg (ATTRACT Project\nNo. FNR/A09/01 and Project No. FNR /10/AM2c/39)\nforfinancialsupport. Critical readingof themanuscript\n16by Jens-Peter Bick and Dirk Honecker is gratefully ac-\nknowledged.\nReferences\n[1] A. Guinier, G. Fournet, Small-Angle Scattering of X-ray s, Wi-\nley, New York, 1955.\n[2] O. Glatter, O. Kratky (editors), Small-Angle X-ray Scat tering,\nAcademic Press,London, 1982.\n[3] L. A. Feigin, D. I. Svergun, Structure Analysis by Small- Angle\nX-Ray and Neutron Scattering, Plenum Press, New York,1987.\n[4] S.-H.Chen, T.-L.Lin,in: D.L.Price, K.Sk¨ old (Eds.),M ethods\nof Experimental Physics–Neutron Scattering, Vol. 23-Part B,\nAcademic Press,San Diego, 1987, pp.489–543.\n[5] P. Lindner, T. Zemb (editors), Neutron, X-Ray and Light S cat-\ntering: Introduction to an Investigative Tool for Colloida l and\nPolymeric Systems, North Holland, Amsterdam, 1991.\n[6] J. S. Pedersen, in: P. Lindner, T. Zemb (Eds.), Neutrons, X-\nRaysandLight: Scattering MethodsApplied toSoftCondense d\nMatter, Elsevier, Amsterdam, 2002, pp. 391–420.\n[7] D.I.Svergun, M.H.J.Koch, Rep. Prog. Phys.66 (2003) 173 5.\n[8] H.B.Stuhrmann, Rep. Prog. Phys.67 (2004) 1073.\n[9] Y. B. Melnichenko, G. D. Wignall, J. Appl. Phys. 102 (2007 )\n021101.\n[10] A. Heinemann, H. Hermann, A. Wiedenmann, N. Mattern,\nK.Wetzig, J.Appl. Cryst. 33 (2000) 1386.\n[11] H. Hermann, A. Heinemann, N. Mattern, A. Wiedenmann, Eu -\nrophys.Lett. 51 (2000) 127.\n[12] A.Michels,R.N.Viswanath, J.Weissm¨ uller,Europhys .Lett.64\n(2003) 43.\n[13] A. Grob, S. Saranu, U. Herr, A. Michels, R. N. Viswanath,\nJ.Weissm¨ uller, Phys.Status Solidi A 201 (2004) 3354.\n[14] W. Wagner, J. Kohlbrecher, in: Y. Zhu (Ed.), Modern Tech -\nniques for Characterizing Magnetic Materials, Kluwer Aca-\ndemic Publishers, Boston, 2005, pp. 65–103.\n[15] A. Michels, C. Vecchini, O. Moze, K. Suzuki, J. M. Cadoga n,\nP.K.Pranzas, J. Weissm¨ uller, Europhys. Lett. 72 (2005) 24 9.\n[16] C.Vecchini, O.Moze, K.Suzuki, P.K.Pranzas, J.Weissm ¨ uller,\nA.Michels, Appl. Phys.Lett. 87 (2005) 202509.\n[17] A. Michels, C. Vecchini, O. Moze, K. Suzuki, P. K. Pranza s,\nJ.Kohlbrecher, J.Weissm¨ uller, Phys.Rev. B 74 (2006) 1344 07.\n[18] D. Honecker, A. Ferdinand, F. D¨ obrich, C. D. Dewhurst,\nA. Wiedenmann, C. G´ omez-Polo, K. Suzuki, A. Michels, Eur.\nPhys.J.B 76 (2010) 209–213.\n[19] A. Michels, D. Honecker, F. D¨ obrich, C. D. Dewhurst,\nK.Suzuki, A.Heinemann, Phys.Rev. B 85 (2012) 184417.\n[20] A. Bracchi, K. Samwer, P. Schaaf, J. F. L¨ o ffler, S. Schneider,\nMater. Sci. Eng.A 375–377 (2004) 1027.\n[21] E.Garc´ ıa-Matres, A.Wiedenmann,G.Kumar,J.Eckert, H.Her-\nmann, L.Schultz, Phys.B 350 (2004) e315.\n[22] R. Garc´ ıa Calder´ on, L. Fern´ andez Barqu´ ın, S. N. Kau l, J. C.\nG´ omez Sal, P. Gorria, J. S. Pedersen, R. K. Heenan, Phys. Rev .\nB 71 (2005) 134413.\n[23] K. Mergia, S. Messoloras, J. Phys.: Condens. Matter 20 ( 2008)\n104219.\n[24] A. Michels, J. Weissm¨ uller, A. Wiedenmann, J. G. Barke r, J.\nAppl. Phys.87 (2000) 5953.\n[25] A. Michels, J. Weissm¨ uller, A. Wiedenmann, J. S. Peder sen,\nJ.G.Barker, Philos. Mag. Lett. 80 (2000) 785.\n[26] A. Michels, J. Weissm¨ uller, U. Erb, J. G. Barker, Phys. Status\nSolidi A 189 (2002) 509.\n[27] A. Michels, J. Weissm¨ uller, R. Birringer, Eur. Phys. J . B 29\n(2002) 533.[28] A. Michels, R. N. Viswanath, J. G. Barker, R. Birringer,\nJ.Weissm¨ uller, Phys.Rev. Lett. 91 (2003) 267204.\n[29] J. Weissm¨ uller, A. Michels, D. Michels, A. Wiedenmann , C. E.\nKrill III, H. M. Sauer, R. Birringer, Phys. Rev. B 69 (2004)\n054402.\n[30] J. F. L¨ offler, H. B. Braun, W. Wagner, G. Kostorz, A. Wieden-\nmann, Phys.Rev. B 71 (2005) 134410.\n[31] A.Michels, J.Weissm¨ uller, Rep.Prog.Phys.71(2008) 066501.\n[32] A. Michels, F.D¨ obrich, M. Elmas, A.Ferdinand, J. Mark mann,\nM. Sharp, H. Eckerlebe, J. Kohlbrecher, R. Birringer, EPL 81\n(2008) 66003.\n[33] A. Michels, M. Elmas, F. D¨ obrich, M. Ames, J. Markmann,\nM. Sharp, H. Eckerlebe, J. Kohlbrecher, R. Birringer, EPL 85\n(2009) 47003.\n[34] D. Honecker, F. D¨ obrich, C. D. Dewhurst, A. Wiedenmann ,\nA.Michels, J. Phys.: Condens. Matter 23 (2011) 016003.\n[35] F. D¨ obrich, J. Kohlbrecher, M. Sharp, H. Eckerlebe, R. Bir-\nringer, A.Michels, Phys.Rev. B 85 (2012) 094411.\n[36] B. van den Brandt, H. Gl¨ attli, I. Grillo, P. Hautle, H. J ouve,\nJ.Kohlbrecher, J.A.Konter, E.Leymarie, S.Mango, R.P.May ,\nA. Michels, H. B. Stuhrmann, O. Zimmer, Eur. Phys. J. B 49\n(2006) 157.\n[37] M. Laver, E. M. Forgan, S. P. Brown, D. Charalambous,\nD. Fort, C. Bowell, S. Ramos, R. J. Lycett, D. K. Christen,\nJ. Kohlbrecher, C. D. Dewhurst, R. Cubitt, Phys. Rev. Lett. 9 6\n(2006) 167002.\n[38] M. R. Eskildsen, E. M. Forgan, H. Kawano-Furukawa, Rep.\nProg. Phys.74 (2011) 124504.\n[39] M. Bischof, P. Staron, A. Michels, P. Granitzer, K. Rump f,\nH.Leitner, C.Scheu, H.Clemens, Acta mater. 55 (2007) 2637.\n[40] G. Balaji, S. Ghosh, F. D¨ obrich, H. Eckerlebe, J. Weiss m¨ uller,\nPhys.Rev. Lett. 100 (2008) 227202.\n[41] A.Kreyssig, R.Prozorov, C.D.Dewhurst, P.C.Canfield, R.W.\nMcCallum, A.I.Goldman, Phys.Rev. Lett. 102(2009) 047204.\n[42] F. Gazeau, E. Dubois, J.-C. Bacri, F. Bou´ e, A. Cebers,\nR. Perzynski, Phys.Rev. E65 (2002) 031403.\n[43] T.Thomson,S.L.Lee,M.F.Toney,C.D.Dewhurst,F.Y.Og rin,\nC. J.Oates, S.Sun, Phys.Rev. B 72 (2005) 064441.\n[44] Y. Ijiri, C. V. Kelly, J. A. Borchers, J. J. Rhyne, D. F. Fa rrell,\nS.A.Majetich, Appl. Phys.Lett. 86 (2005) 243102.\n[45] A. Wiedenmann, U. Keiderling, K. Habicht, M. Russina,\nR. G¨ ahler, Phys.Rev. Lett. 97 (2006) 057202.\n[46] N. A. Grigoryeva, S. V. Grigoriev, H. Eckerlebe, A. A. El iseev,\nA.V.Lukashin,K.S.Napolskii, J.Appl.Cryst. 40(2007) s53 2.\n[47] K. S. Napolskii, A. A. Eliseev, N. V. Yesin, A. V. Lukashi n,\nY.D.Tretyakov,N.A.Grigorieva, S.V.Grigoriev,H.Eckerl ebe,\nPhysica E37 (2007) 178.\n[48] M. Bonini, A. Wiedenmann, P. Baglioni, J. Appl. Cryst. 4 0\n(2007) s254.\n[49] T.Oku,T.Kikuchi, T.Shinohara, J.Suzuki, Y.Ishii,M. Takeda,\nK. Kakurai, Y. Sasaki, M. Kishimoto, M. Yokoyama, Y. Nishi-\nhara, Physica B404 (2009) 2575.\n[50] S. V. Grigoriev, A. V. Syromyatnikov, A. P. Chumakov, N. A.\nGrigoryeva, K. S. Napolskii, I. V. Roslyakov, A. A. Eliseev,\nA.V. Petukhov, H.Eckerlebe, Phys.Rev. B 81 (2010) 125405.\n[51] K. L. Krycka, R. A. Booth, C. R. Hogg, Y. Ijiri, J. A. Borch ers,\nW. C. Chen, S. M. Watson, M. Laver, T. R. Gentile, L. R. De-\ndon, S.Harris, J. J. Rhyne, S.A. Majetich, Phys. Rev. Lett. 1 04\n(2010) 207203.\n[52] S. Disch, E. Wetterskog, R. P. Hermann, A. Wiedenmann,\nU. Vainio, G. Salazar-Alvarez, L. Bergstr¨ om, T. Br¨ uckel, New\nJ.Phys.14 (2012) 013025.\n[53] M.Laver,C.Mudivarthi, J.R.Cullen, A.B.Flatau,W.-C .Chen,\nS.M.Watson, M. Wuttig, Phys.Rev. Lett. 105 (2010) 027202.\n[54] B. G. Ueland, J. W. Lynn, M. Laver, Y. J. Choi, S.-W. Cheon g,\n17Phys.Rev. Lett. 104 (2010) 147204.\n[55] S. J. Lister, T. Thomson, J. Kohlbrecher, K. Takano,\nV. Venkataramana, S. J. Ray, M. P. Wismayer, M. A. de Vries,\nH.Do,Y. Ikeda, S.L.Lee, Appl. Phys.Lett. 97 (2010) 112503.\n[56] C. Dufour, M. R. Fitzsimmons, J. A. Borchers, M. Laver, K . L.\nKrycka, K. Dumesnil, S. M. Watson, W. C. Chen, J. Won,\nS.Singh, Phys.Rev. B 84 (2011) 064420.\n[57] C. Pappas, E. Leli` evre-Berna, P. Falus, P. M. Bentley,\nE.Moskvin,S.Grigoriev,P.Fouquet,B.Farago,Phys.Rev.L ett.\n102 (2009) 197202.\n[58] S. V. Grigoriev, D. Chernyshov, V. A. Dyadkin, V. Dmitri ev,\nS. V. Maleyev, E. V. Moskvin, D. Menzel, J. Schoenes, H. Eck-\nerlebe, Phys.Rev. Lett. 102 (2009) 037204.\n[59] S. M¨ uhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Ros ch,\nA.Neubauer, R.Georgii, P.B¨ oni, Science 323 (2009) 915.\n[60] W. F. Brown Jr., Micromagnetics, Interscience Publish ers, New\nYork,1963.\n[61] A.Aharoni, Introduction to theTheory of Ferromagneti sm, 2nd\nEdition, Clarendon Press,Oxford, 1996.\n[62] H. Kronm¨ uller, M. F¨ ahnle, Micromagnetism and the Mi-\ncrostructure of Ferromagnetic Solids, Cambridge Universi ty\nPress,Cambridge, 2003.\n[63] H.Kronm¨ uller,A.Seeger,M.Wilkens,Z.Phys.171(196 3)291.\n[64] K. Suzuki, G. Herzer, in: D. Sellmyer, R. Skomski (Eds.) , Ad-\nvanced Magnetic Nanostructures, Springer, New York, 2006,\npp.365–401.\n[65] H. Kronm¨ uller, S. Parkin, Handbook of Magnetism and Ad -\nvanced Magnetic Materials, John Wiley & Sons, Chichester,\n2007, vol.2,pp.795.\n[66] J. Fidler, P. Speckmayer, T. Schrefl, D. Suess, J. Appl. P hys. 97\n(2005) 10E508.\n[67] F. Y. Ogrin, S. L. Lee, M. Wismayer, T. Thomson, C. D. De-\nwhurst, R. Cubitt, S. M. Weekes, J. Appl. Phys. 99 (2006)\n08G912.\n[68] S.Saranu, A.Grob, J.Weissm¨ uller, U.Herr, Phys.Stat us Solidi\nA205 (2008) 1774.\n[69] M.Donahue,D.Porter,TheObject Oriented MicroMagnet ic Framework (OOMMF).\nURLhttp://math.nist.gov/oommf/\n[70] W.S.Jodrey, E.M. Tory,Phys.Rev. A32 (1985) 2347.\n[71] O. Gutfleisch, K.-H. M¨ uller, K. Khlopkov, M. Wolf, A. Ya n,\nR.Sch¨ afer, T.Gemming,L.Schultz, ActaMater.54(2006)99 7.\n[72] G.Hrkac, T.G.Woodcock, C.Freeman,A.Goncharov,J.De an,\nT.Schrefl, O.Gutfleisch, Appl. Phys. Lett. 97 (2010) 232511.\n[73] D. V. Berkov, N. L. Gorn, in Handbook of Advanced Mag-\nneticMaterials, Vol.2,SpringerVerlagandTsinghuaUnive rsity\nPress, 2005, pp. 421–507, edited by Y.Liu, D. Shindo and D.J.\nSellmyer.\n[74] S.Erokhin,D.Berkov,N.Gorn,A.Michels,IEEETrans.M agn.\n47 (2011) 3044.\n[75] P. Gibbon, G. Sutmann, in Quantum Simulations of Comple x\nMany-Body Systems: From Theory to Algorithms, Lecture\nNotes, edited by J. Grotendorst, D. Marx and A. Muramatsu 10\n(2002) 467–506.\n[76] D.V. Berkov, N.L.Gorn, Phys.Rev. B 57 (1998) 14332.\n[77] N.L.Gorn, D.V. Berkov, P.G¨ ornert, D. Stock, J. Magn. M agn.\nMat. 310 (2007) 2829.\n[78] R.W.Hockney,J.W.Eastwood,Computersimulationusin gpar-\nticles, McGraw-Hill, 1981.\n[79] M.Deserno, C.Holm, J.Chem.Phys. 109 (1998) 7678.\n[80] L.Landau, E.Lifshitz, Phys.Z.Sowjetunion 8 (1935) 15 3.\n[81] D. V. Berkov, N. L. Gorn,\nMicromagus: package for micromagnetic simulations.\nURLhttp://www.micromagus.de\n[82] S. Erokhin, D. Berkov, N. Gorn, A. Michels, Phys. Rev. B 8 5\n(2012) 024410.[83] W. Rave, K. Fabian, A. Hubert, J. Magn. Magn. Mater. 190\n(1998) 332.\n[84] A. Wiedenmann, Collection SFN 11 (2010) 219,\nhttp://www.neutron-sciences.org /.\n[85] S. Erokhin, D. Berkov, N. Gorn, A. Michels, Phys. Rev. B 8 5\n(2012) 134418.\n18"    },    {        "title": "1208.1493v1.Temperature_controlled_interlayer_exchange_coupling_in_strong_weak_ferromagnetic_multilayers__a_thermo_magnetic_Curie_switch.pdf",        "content": "1 \n Temperature -controlled interlayer exchange coupling in strong/weak ferromagnetic \nmultilayers : a thermo -magnetic  Curie -switch  \n \nA. Kravets1,2, A. N. Timoshevskii2, B. Z. Yanchitsky2, M. Bergmann1, J. Buhler1, S. Andersson1, \nand V. Korenivski1 \n1Nanostructure  Physics, Royal Institute of Tech nology, 10691 Stockholm, Sweden  \n2Institute of Magnetism, National Academy of Science, 03142 Kiev, Ukraine  \n \n  2 \n We investigate a novel  type o f interlayer exchange coupling  based on driving a \nstrong/weak/strong ferromagnetic tri -layer through the Curie point of the weak ly \nferromagnet ic spacer, with the exchange coupling between the strongly ferromagnetic outer \nlayers that can be switched , on and off, or varied continuously in magnitude by controlling the \ntemperature of the material . We use Ni-Cu alloy of varied composition as the spacer material \nand model the effect s of proximity -induced magnetism and the interlayer exchange coupling \nthrough the spacer from first principles, taking into account not only thermal spin -disorder but \nalso the dependen ce of the atomic moment of Ni on the nearest -neighbor concentration of the \nnon-magnetic Cu. We propose and demonstrate  a gradient -composition spacer, with a lower \nNi-concentration at the int erfaces, for greatly improved effective -exchange  uniformity and \nsignificantly improved thermo -magnetic  switching in the structure . The reported magnetic \nmultilayer materials can form the base for a variety of novel magnetic devices, such as sensors, \noscillators, and memory elements  based on thermo -magnetic Curie -switch ing in the device.  \nInterlayer exchange coupling is one of the key fundamental characteristics of magnetic multilayers \n[1, 2], important for  such large scale industrial applications as field sensors, magnetic recording, and \nmagnetic random access memory [3 -6]. In many cases it controls the magnetization switching in the \nsystem under the influence of external fields [7] or spin -polarized curren ts [8 -10]. The oscillatory \ninterlayer exchange coupling  (RKKY) [11-13] is due to the conduction electrons  mediating the spin \ntransfer between the ferromagnetic layers, and is fixed in fabrication to be positive or negative in \nmagnitude by selecting a suitable thickness of the nonmagnetic metal spacer. Once the coupling is set \nto antiparallel , an external switching field is necessary to change the state of the structure to parallel.  \nIt is highly desirable to design multilayer materials where the interlayer exchange coupling is not \nfixed but rather controllable, on and off, by varying an external physical parameter, such as 3 \n temperature. One such system is strong/weak/strong ferromagnetic sandwich (F/f/F) where the \nweakly ferromagnetic spacer (f) has a lower Curie temperature (TC) than that of the str ong \nferromagnetic outer layers (F)  [14,15]. Heating the structure through the  TC of the spacer exchange -\ndecouples the outer magnetic layers, so their parallel alignment below TC can be switched to \nantiparallel above TC. This switching is fully reversible on c ooling through the  TC, as the number of \nthermal magnons is reduced and the exchange spring in the spacer , aligning the outer F-layers , \nbecomes stronger. This action can provide a spin switch or oscillator with intrinsic thermo -electronic \ncontrol by the Joule heating of a transport current through the structure . \nThe key element in such an  F/f/F sandwich is the weakly ferromagnetic spacer  f, which should \nhave a tunable in fabrication but well defined in operation  TC and, preferably, a narrow fe rromagnetic \n(f) to paramagnetic (P) transition. Diluted ferromagnetic alloys, such as Ni -Cu, with the  TC in the \nbulk known to be easily tunable to near room temperature [16, 17] is the natural choice for the spacer \nmaterial. However, t he effects of thermal  disorder on the magnetization and exchange coupling in \nthin-film multilayers are practically unexplored. In particular, the strong excha nge at an F/P  interface \nshould be  expected to suppress the thermal magnons in the spacer, driving the para -to-ferro magn etic \ntransition  due to the magnetic proximity effect [18,19 ], there by result ing in a gradient of the effective \nmagnetization and interatomic exchange  in the spacer  [20,21 ], as well as critically affect ing the \ninterlayer exchange coupling  through the sp acer. In this work we indeed find a pronounced \nferromagnetic proximity effect at F/f(P) interfaces as well as  propose and demonstrate experimentally \na gradient spacer design  (f*/f/f*) , which significantly improves the thermo -magnetic switching \nbeha vior of the multilayer material and makes it attractive for technological applications . \nOur choice for the diluted ferromagnetic alloy to be used as the spacer material is Ni -Cu. It is \nconsidered to be a well known system, at least in the bulk [ 16,17 ]. Our recent de tailed studies o f 4 \n sputter -deposited Ni-Cu films confirmed the known general properties, but also revealed some \npecular properties, such as exchange -induced phase separation at high Ni concentration x, above 70% \nof atomic Ni  corresponding to the Curie tempera ture range above 100º C  [22]. In this work, the \nconcenration range of interest is x(Ni)≤70%, corresponding to the TC range of 100º C and below . In \nfact, the Ni -Cu concentrations with x<50% are non -magnetic at all temperatures in the bulk [16,17 ] \nor thick f ilms [23]. The situation is quite  different in thin film multilayers , as we show below.  \nFigure 1 shows the saturation magnetization of 60 nm thick NixCu100-x films of varied composition, \ndeposited at ambient temperature by dc magnetron sputtering on oxidized Si substrates, normalized \nto the saturation magnetization of pure Ni. The magnetization vanishes at room temperature for x≈62 \nat.%, where the Ni-Cu becomes paramagnetic in the bulk limit ( here single -layer , 60 nm thic k). \nFigure 1 also shows the saturation magnetization measured at 100º  C, which vanishes at x≈70%. The \nratio of the magnetization at these two temperatures, shown by the blue symbols in Fig.  1, has a sharp \nstep at 70 -74% Ni , indica ting the optim um composition interval for exploit ing the ferro -to-\nparamagnetic tr ansition in  the Ni -Cu alloy . We show, however, that this composition  range must be \nsignificantly shifted  to lower effective concentrations , if the Ni -Cu spacers are to be used for sharp \non/off  thermal switching in thin-film multilayer s. \nPerhaps the most informative way to investigate the properties of thin spacers as it relates to the \ninterlayer exchange is to integrate them into a spin -valve type structure , AF/F/f/F, where one of the \nouter str ongly ferromagnetic layers is pinned by an antiferromagnet (AF), and study the \ncoupling/decoupling of the outer ferromagnetic layers (F)  as a function of the spacer composition, \nthickness, and temperature. The method is not direct as to measuring the magnetization of  the spacer , \nbut is very sensitive and direct when it comes to the inter-layer exchange interaction of interest.  Our \nmaterial system is a Permalloy -clad spacer, with one of the P ermalloy (Py) layers exchange -pinned to 5 \n antiferromagnet ic IrMn . Specifically, Ir 20Mn 80(12 nm)/Co 90Fe10(2 nm)/Ni 80Fe20(2 nm) /Ni xCu100-x(t \nnm)/ Ni80Fe20(6 nm), henceforth  Fpin/Ni xCu100-x(t nm)/ F. \nFigure 2 shows the key magnetic parameters of the Fpin/Ni xCu100-x(t nm)/ F structure s, measured at \nroom temperature . Figure 2 a shows magnetization loops for the  NixCu100-x spacer thickness of 6 nm \nand x varied in the range from 0 to 72 at.%. For low Ni concentration s (x<35%), due to the absence \nof any significant magnetic coupling between the free and pinned F layers through the  spacer , the \nmagnetization loop consist s of two well -separated transitions at approximately zero field and -480 Oe \n(Fig 2a, green) , corresponding to switching of the free Py layer  and the pinned ferromagnetic layer, \nrespectively. With increasing Ni -concentration past x≈35%, the minor and major  loops  begin to \nmerge (Fig. 2a, blue ), indicating  the onset of exchange coupling between the free and pinned outer  \nlayers . The middle  points of the two magnetization transitions ( minor and major ) define the two \nexchange fields, H ex1 and H ex2, respectiv ely. As the spacer becomes fully non-magnetic at low Ni -\nconcentrations and does not mediate any exchange coupling, the unpinned Py layer becomes free to \nswitch and H ex1→0, while H ex2 characterizes solely  the strength of the AF -pining of the other \nferromagnetic layer. Already at x≈52%, the two transitions merge significantly, indicating a \nsubstantial exchange coupling across the spacer. Inte restingly, the x=52% composition for a single -\nlayer Ni -Cu is non -magnetic (paramagnetic) at room temperature ( TC~10 K) and normally would not \nbe expected to exchange couple the outer F -layers. These data indicate that a ferromagnetic order of \nsignificant strength is induced in the paramagnetic spacer on rather long length scales, several \nnanometers in this case. This induced ferromagnetism couples the outer layers, bringing together the \ntwo magnetic transitions, such that  Hex1 and Hex2 merge. Thus, for thi s geometry, Hex1 is a direct \nmeasure of the interlayer exchange coupling, while Hex2 additionally reflects the strength of the \nantiferromagnetic pinning. For x>70%, a composition ferromagnetic at room temperature  in the bulk , 6 \n the minor and major  loops  merg e into one  (Fig. 2a, red ). Fine -stepping through the low -concentration \nrange, illustrated by the  minor loops in Fig. 2b, shows that the onset of the interlayer exchange \nindeed is at x≈35%, which is due to the vanishing Ni atomic magnetic moment in the Cu matrix, as \ndetailed below.  \nThe dependence of the two exchange fields, Hex1 and Hex2, on the Ni -concentration in a 6 nm thick \nNi-Cu spacer is shown in Fig.  2c. The free and pinned ferromagnetic layers are fully decoupled up to \nx=35% (red symbols), at which point Hex1 begins to increase  in magnitude , first slightly and then \nsubstantially above x=50%, even though the spacer is still intrinsically paramagnetic at this \nconcentration. At x ≈70% the two exchange fields merge into one, which is expected since the sp acer \nis intrinsically ferromagnetic at 70% at RT.  \nFig. 2d shows the thickness dependence of the exchange fields for a nominally (in the bulk) \nparamagnetic spacer composition of x=56%. One can see that at 3 nm thickness the outer \nferromagnetic layers are fu lly coupled and behave as one. For this composition, the interlayer \nexchange vanishes at approximately 9 nm in the spacer thickness. This is much greater that the \ninteratomic spacing normally associated with direct exchange and indicates that the character istic \nlength scale for the induced ferromagnetic proximity effect under study is dictated by another \nmechanism, namely, thermally disordered lattice spins in the spacer by short -wave spin -waves on \nlength scales of at least several lattice units.  \nIn order t o understand the mechanism involved as well as optimize the performance  of the material  \nwe develop a full model of the F/f(P)/F multilayer from first principles, which takes into account the \nthermal spin disorder as well as the effect of Cu -dilution on the  atomic magnetic moment of Ni in the \nperformance -critical spacer layer.  7 \n Our model system is a Ni/Ni -Cu/Ni t hree-layer, in which the diluted magnetic alloy spacer is \nenclosed by bulk -like fcc Ni [001]  (for making the calculations time efficient; qualitatively same \nbehavior is obtained with Permalloy  outer layers ). Both Ni and Cu atoms in the t hree-layer structure \noccupy the sites of the fcc lattice , and are distributed randomly  within each monolayer in  the spacer . \nThe number of atomic monolayers in the spacer is denoted by Nf. The atomic concentration of Ni in i-\nth monolayer is denoted by ci. The Ni atoms interact magnetically by the standard  isotropic \nHeisenberg interaction. Cu -Cu and Ni -Cu exchange in teractions are neglected since the magnetic \nmoment of Cu is negligible (Cu does not polarize in Ni). The local atomic magnetic moment of Ni, \nmloc(z), is a function of the number of the nearest neighbor Ni atoms, z. For obtaining the effective \n(measurable) magnetic characteristics of the structure we use the mean field model and take the \naverage Ni -magnetic moment to be the same within one monolayer,  mi=m(zi). The effective magnetic \nfield is [ 24]: \ni j i j i j i j\njH J n c m  \n, \nwhere the sum is over monolayers , Ji  – the Ni -Ni exchange interaction, and  ni – the coordination \nnumber. The magnetization at a given temperature  T is given by [ 24]: mi=L(miHi/kBT), where L(x) is \nthe Langevin function and kB – the Boltzmann constant.  \nThe unknown exchange integrals  Ji were obtained for 2 coordination spheres of the fcc lattice . In \nthis the total energies of 3 superstructures of fcc Ni were calculated for the ferro - (F), antiferro - (AF), \nand antiferro -double (AFD) [25] types of magnetic ordering.   \nWith the magnetic energy in the Heisenberg  form  and assuming the magnetic moment of Ni \nindependent of its direction , the following expressions for the exchange interaction are obtained:  \nJ1=(E F-EAF)/8; J2=(E F+E AF-2EAFD)/4, where  EF, EAF, and EAFD are the full energies of the \nsuperstructures . 8 \n The total energ ies of the structures w ere obtained using DFT approach and the Wien2k FLAPW \ncode [ 26]. The GGA exchange -correlation potential was the same as in Ref. 27. The radiu s of the \nMT-spheres was 2.2 atomic length units. The electron density was computed for 63 k-point s in the \nirreducible parts of the first Brillouin zone. The obtained exchange integrals were: J1=-6.15 meV and \nJ2=-17.01 meV.  \nFor obtaining the mloc(z) dependence , the electronic structure of three special quasi -random \nsuperstructures [28], which model random bulk Ni -Cu alloy , were calculated. The stoichiometries of \nthe structures were : Ni25Cu75, Ni 50Cu50, and Ni 75Cu25. Figure 3a  (solid circles) shows the values of \nmloc calculated by  the FLAPW method. For calibration purposes, the slope of  the Curie temperature \nof bulk Ni -Cu alloy was calculated and agreed well with the experiment [ 17], as shown in the inset to \nFig. 3a. The interesting result in the obt ained mloc(z) is that Ni becomes essentially nonmagnetic in \nthe Ni -Cu alloy at concentration of approximately 30% -Ni. This has important implications for \noptimizing the spacer material, as discussed below.  \nThe key for efficient operation of a spin -thermo -electronic F/f/F valve is a small width of its Curie \ntransition. The green line in Fig. 3b shows the calculated magnetization per Ni atom of bulk Ni 80Cu20 \nalloy. The b lue curve show s the temperature dependen ce of the magnetization  of a homogeneous  Ni-\nCu spacer with Ni outer layers . The spacer consists  of 38  monolayers  (approx.  7 nm) and  is placed  \nbetween outer planes of fcc Ni. At T=0 K the magnetization is equal to  the local  moment of the Ni \natom  mloc for this  composition  (Fig.  3a). When the spacer is enclosed by strongly ferromagnetic outer \nelectrodes (Ni), the spacer’s ferromagnetic state greatly extends in temperature, vanishing completely \nonly above 0.9 TC (Ni) (Fig. 3b, blue) . This means that the outer electrodes are strongly exchange -\ncoupled at the nominal TC of the spacer alloy (0.58), marked as the inflection point, Mt (Tt). The \neffective transition extends over a broad interval of 0.3 -0.4 TC(Ni) above the effective transition point 9 \n of 0.58 . The  reason for this extended transition is the strong ferromagnetic order induced in the \nspacer in proximity to the interfaces, as shown by the open symbols in Fig. 3c, for two characteristic \ntemperatures. At Tt the moment at the interface is enhanced 4 -fold compared to that in the center of \nthe spacer, with a strong  variation in the effective TC across the thickness. The proximity length is an \norder of magnitude greater than the atomic spacing, so the induced ma gnetization penetrates through \nall of the spacer thickness. The result is non -zero magnetic exchange between the outer ferromagnetic \nlayers , well above the intrinsic Curie point of the spacer material. This proximity eff ect should be \nuniversal for F/f/F tri-layer s and sets a fundamental limitation on the width of the Curie transition of \nthe weak ferromagnet incorporated in the multilayer.  \nIt is highly desirable for device applications to narrow the magnetic transition in the spacer. Using  \nthe above detailed  understanding of the highly non -uniform magnetization profile at the F/f interface, \nwe have designed  a gradient -spacer , in which the magnetic -atom concentration is reduced at the \ninterfaces. This efficiently suppresses the proximity effect and makes the m agnetization distribution \nmuch more uniform, as shown in Fig. 3c with solid symbols for a gradient spacer with the interface \nNi concentration reduced from 80% to 65%.  \nThis change in the spacer layout has a dramatic effect on the simulated transition width , as shown \nin Fig. 3b (red). The magnetization at the inflection point is 5  times  smaller for the uniform -spacer \ndesign, which translates into an order of magnitude sharper Curie transition for the tri -layer, \ncomparable in width with that in the ideal spacer  (uniform, bulk -like; green  in Fig. 3b). \nIn order to experimentally demonstrate the gradient -spacer effect proposed above , we have \nfabricated a range of valves, in which the spacer itself had a tri -layer structure, f*/f/f*, with the buffer \nlayers f* of different thickness and Ni -content  compared to the inner spacer layer f . The inner layer f  \nhad a fixed thickness and concentration of 6 nm and 72%, respectively. This new layout is illustrated 10 \n in the inset to Fig. 4, which shows the phase map of the res ulting proximity effect. The vertical scale \ngives the thickness of the buffer layer f*  for a given concentration and temperature , at which the \nouter Py layers fully decouple, determined in  the same fashion as in Figs. 2 . The phase map thus \ngives the opera ting area for a Curie -valve based of the gradient -spacer design.  \nInteresting ly, the scaling is logarithmic and shows  that the thinnest layers decouple only below \nx=30%, where the Ni atoms become , in fact , nonmagnetic. We believe that this finding has high \nrelevance for the RKKY interaction in th is system in the thin -spacer limit studied previously [ 29, 30]. \nThe RKKY interlayer coupling through thin Cu spacer s was interpreted to withstand paramagnetic Ni \nimpurities up to approximately 35% Ni, vanishing at hi gher concentrations. We suggest that the \nmechanism behind the strong RKKY and its subsequent vanishing at higher Ni -content was instead \nthe loss of the atomic moment on Ni below 30% Ni in Cu , detailed in our simulation results above  \n(Fig. 3a).  \nHaving esta blished the key physical parameters of the new gradient spacer design, below we \ndemonstrate its greatly improved thermo -electronic characteristics. Figure 5  compares the \ntemperature dependence of the magnetization of the two spacer layouts, with uniform an d gradient -\ntype composition. The samples were heated to 100  ºC (to just above the bulk - TC of the inner spacer \nmaterial, but below any significant reduction in the AF pinning), after which a reversing field of 50 \nOe was applied in order to switch the free Py layer, and the temperature was gradually decreased to \nroom temperature while the magnetization was recorded.  As a result, the spacer acts as an exchange \nspring of increasing stre ngth, which rotates the free  Py la yer during the cooling . \nThe Curie transition ( para-to-ferromagnetic ) is very broad in the uniform -spacer multilayer. In fact, \nthe rotation of the free layer is far from complete at 100º  C, even for the relatively thick spacer (20 \nnm), due to the residual p roximity -induced interlayer exchange . In stark contrast, the gradient -spacer 11 \n sample fully exchange -decouples into the antiparallel state of the outer Py layers at 90 ºC (the Curie \npoint of the inner spacer material with x=72% ), and has a sharp transition i nto the parallel state of the \nmultilayer  at RT . The 20 -80% width of the transition is approximately 20 degrees, same as the full -\nwidth -at-half-maximum width, and several times narrower than that for the uniform spacer . This \nresult is in good agreement with  the theoretically predicted behavior.  \nIt is informative to note that the thermo -magnetic switching demonstrated herein can have \nsignificant advantages over the recently developed and very promising thermally -assisted switching , \nused in the memory technology, based on thermally  controlling antiferromagnetic exchange pinning \n[31]. One advantage  is the the Curie point o f a diluted ferromagnet can be easily varied in the desired  \nrange and is not fixed to the Neel (or blocking) temperature  of the antiferromagnet. Furthermore, the \nferro -to-paramagnetic  transition typically is fully reversible , does not involve spin “blocking ”, and \ntherefore should not suffer from training effects present at the exchange -biased  F/AF interface.  \nIn conclusion, we have investigated strong/weak/strong ferromagnetic tri -layer s where the \ninterlayer exchange coupling is controlled by driving  the material through the Curie point of the \nspacer . The  resulting exchange coupling between the strongly ferromagnetic outer layers can be \nswitched on and off, or varied continuously in magnitude by controlling the temperature of the \nmaterial. This effect is explained theoretically a s due to induced ferromagnetism at F/f (P) interfaces . \nIt is show n that the atomic magnetic moment and the effective interatomic exchange coupling are \nhighly non -uniform throughout the spacer thickness, especially in the proximity to the strongly \nferromagnetic interfaces. This critically affect s the interlayer exchange coupling and the ability to \ncontrol it thermo -electronically. We have propose d and demonstrate d a new, gradient -type spacer , \nhaving a significantly narrower  Curie transition  and distinct thermo -magnetic switching . The  12 \n demonstrate d multilayer material can form the base for a variety of novel magnetic devices based on \nspin-thermo -electronic switching.  \nWe gratefully  acknowledge financial support from EU -FP7-FET-Open  through project  Spin-\nThermo -Electronics . \n \nFigure caption s: \n1. Saturation magnetization of thick NixCu100-x alloy films normalized to that of pure Ni, as a \nfunction of Ni content, measured at room temperature (RT) and 100º C. The solid lines are \nguides to the eye.  Blue symbols show the ratio of the magnetiza tion at the two temperatures , \nwhich becomes zero at the boundary of the thermo -magnetic operating region.   \n2. (a) Magnetization loops of F pin/Ni xCu100-x(6 nm)/ F tri-layers having 35, 52 and 70 Ni at.% \ncontent. The exchange fields, Hex1 and Hex2, for the free and pinned ferromagnetic layers are \ndefined as the midpoints of the respective transitions. (b) Magnetization minor loops of \nFpin/Ni xCu100-x(6 nm)/F tri -layers with different Ni -Cu spacer compositions. Exchange fields of \nthe two outer ferromagnetic la yers versus  (c) nickel concentration in a 6 nm thick Ni -Cu spacer \nand (d) thickness of the Ni -Cu spacer for x=56 at.%. The solid lines are guides to the eye.  \n3. (a) Calculated local atomic magnetic moment of Ni atoms in Ni xCu100-x alloy as a function of \nthe n umber of the Ni atoms in the first coordination sphere, normalized to the moment of bulk \nfcc Ni of m0(Ni)=0.63µ B. The solid lines are guides to the eye. Inset shows the calculated and \nexperimental [17] slopes of TC in the bulk. (b) Calculated magnetization  per nickel atom versus \ntemperature for a bulk Ni 80Cu20 alloy (green), uniform Ni 80Cu20(7 nm) spacer (blue) and a \ngradient  composition spacer  Ni65Cu35(1 nm)/Ni 84Cu16(5 nm)/  Ni65Cu35(1 nm) (red) , the spacers \nenclosed by outer Ni layers. The inflection points, where the transition is steepest as defined by \nthe second derivative changing sign, are marked with Mt(Tt). (c) Calculated magnetization 13 \n profiles in a uniform Ni 80Cu20(38 ML) (open symbols) and gradient Ni 65Cu35(4 ML)/ \nNi84Cu16(30 ML)/ Ni 65Cu35(4 ML) (solid symbols) composition spacers for two different \ntemperatures near the respective Curie points.  \n4. Thickness of the interfacial buffer layer f* of the weak ly ferromagnetic spacer at which the \nouter Py layers decouple, a s a function of its Ni -content, for room temperature and 100º C. The \nthickness and Ni -concentration of the inner spacer layer f are 6 nm and 72 at.%, respectively.   \n5. Magnetization of two uniform Ni 72Cu28 spacer multilayers, with 10 nm (us1) and 20 nm (us2) \nthick spacers, and of a gradient Ni 50Cu50(4 nm)/Ni 72Cu28(6 nm)/Ni 50Cu50(4 nm) spacer \nmultilayer  (gs), normalized for a direct comparison . The solid lines are guides  to the eye. The \narrows in the illustrations of the right panel show the respective relative  orientation s of the \nmagnetic moments in the center  of the individual layers of the ex change coupled F/f/F \nmultilayer . \n  14 \n References  \n[1] S. S. P. Parkin. Systematic variation of the strength and oscillation period of indirect magnetic exchange coupling \nthrough the 3d, 4d, and sd transition metals. Phys. Rev. Lett.  67, 3598 -3601 (1991).  \n[2] A. Fert, P. Grünberg, A. Barthélémy, F. Petroff, an d W. Zinn. Layered magnetic structures: interlayer exchange \ncoupling and giant magnetoresistance. J. Magn. Magn. Mater.  140-144, 1-8 (1995).  \n[3] G. A. Prinz. Magnetoelectronics . Science  282, 1660 -1663 ( 1998).  \n[4] U. Hartmann. Magnetic multilayers and giant magnetoresistance: fundamentals and industrial applications; Springer: \nBerlin, Germany, 1999.  \n[5] P.  Grünberg. Layered magnetic structures: history, highlights, applications. Phys. Today  54, 31-37 (2001).  \n[6] C. Chappert, A. Fert, and F. Nguyen Van D au. The emergence of spin electronics in data storage nature materials. \nNature Mater.  6, 813 -823 (2007).  \n[7] J. M. Daughton. GMR applications. J. Magn. Magn. Mater.  192, 334 -342 (1999).  \n[8] J. S. Slonczewski. Current -driven excitation of magnetic multilaye rs. J. Magn. Magn. Mater . 159, L1–L7 (1996).  \n[9] E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman. Current -induced switching of domains in \nmagnetic multilayer devices. Science  285, 867-870 (1999).  \n[10] A. Brataas, A. D. Kent, and H. Ohno. Current -induced torques in magnetic materials. Nature Mater.  11, 372 (2012).  \n[11] P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sowers. Layered magnetic structures: evidence for \nantiferromagnetic coupling of Fe layers across Cr interlayers. Phys. Rev. Lett.  57, 2442 -2445 (1986).  \n[12] G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn. Enhanced magnetoresistance in Fe -Cr layered structures with \nantiferromagnetic interlayer exchange. Phys. Rev. B  39, 4828 -4830 (1989).  \n[13] M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen van Dau, F. Petr off, P. Etienne, G. Creuzet, A. Friederich, and J. \nChazelas. Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices. Phys. Rev. Lett. 61, 2472 -2475 (1988).  \n[14] S. Andersson and V. Korenivski. Thermoelectrically controlled spin -switch. IEEE Trans. Magn.  46, 2140 -2143 \n(2010).  \n[15] A. M. Kadigrobov, S. Andersson, D. Radić, R. I. Shekhter, M. Jonson, and V. Korenivski. Thermoelectrical \nmanipulation of nanomagnets. J. Appl. Phys . 107, 123706 (2010).   \n[16] C. G. Robbins, H. Claus, and P. A. Beck. Magnetism in Ni -Cu alloys. Phys. Rev. Lett.  22, 1307 -1310 (1969).  \n[17] D. J. Chakrabarti, D. E. Laughlin, S. W. Chen, and Y. A. Chang. Cu -Ni (Copper - Nickel). In Phase d iagrams of \nbinary copper alloys, edited by P. Subramanian, D. Chakrabarti, and D. Laughlin (ASM International, Materials Park, \nOH, 1994) pp. 276 – 286. \n[18] J. J. Hauser. Magnetic proximity effect. Phys. Rev.  187, 580 -583 (1969).  \n[19] M. G. Samant, J. Stöh r, S. S. P. Parkin, G. A. Held, B. D. Hermsmeier, F. Herman, M. van Schilfgaarde, L. -C. Duda, \nD. C. Mancini, N. Wassdahl, and R. Nakajima. Induced spin polarization in Cu spacer layers in Co/Cu multilayers. Phys. \nRev. Lett.  72, 1112 -1115 (1994).  15 \n [20] N. García and A. Hernando. Theory for coupling ferromagnets through paramagnetic layers: direct exchange \ncoupling plus a magnetic pump mechanism. J. Magn. Magn. Mater . 99, L12 -L19 (1991)  \n[21] I. Navarro, M. Ortuno, and A. Hernando. Ferromagnetic interactions in nanostructured systems with two different \nCurie temperatures. Phys. Rev. B  53, 11656 -11660 (1996).  \n[22] A. F. Kravets, A. N. Timoshevskii, B.Z. Yanchitsky, O.Yu. Salyuk, S.O. Yablonovskii, S. Andersson, and V. \nKorenivski. Exchange -induced phase separati on in Ni -Cu films. J. Magn. Magn. Mater.  324, 2131 -2135 (2012).  \n[23] I. Bakonyi, E. Tóth -Kádár, J. Tóth, T. Becsei, T. Tarnóczi, and P. Kamasa. Magnetic and electrical transport \nproperties of electrodeposited Ni -Cu alloys and  and Ni 81Cu19/Cu multilayers . J. Phys.: Condens. Matter. 11, 963 -973 \n(1999).  \n[24] R. E. Camley and D. R. Tilley. Phase transitions in magnetic superlattices. Phys. Rev. B  37, 3413 -3421 (1988).  \n[25] H. C. Herper, E. Hoffmann, and P. Entel. Ab initio full -potential study of the structural  and magnetic phase stability \nof iron. Phys. Rev. B  60, 3839 -3848 (1999).  \n[26] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz. WIEN2k, An augmented plane wave + local orbitals \nprogram for calculating crystal p roperties (Karlheinz Schwarz, Techn. Universität Wien, Austria), 2001. ISBN 3 -\n9501031 -1-2. \n[27] J. P. Perdew, K. Burke, and M. Ernzerhof. Generalized gradient approximation made simple. Phys. Rev. Lett.  77, \n3865 -3868 (1996).  \n[28] S. L. Shang, Y. Wang, D. E. Kim, C. L. Zacherl, Y. Du, a nd Z. K. Liu. Structural, vibrational, and thermodynamic \nproperties of ordered and disordered Ni 1-xPtx alloys from first -principles calculations. Phys. Rev. B  83, 144204 (2011).  \n[29] S. N. Okuno and K. Inomata. Dependence on Fermi surface dimensions of osc illatory exchange coupling in Co/Cu 1-x \nNix (110) multilayers. Phys. Rev. Lett.  70, 1711 -1714 (1993).  \n[30] S. S. P. Parkin, C. Chappert, and F. Hermann. Oscillatory exchange coupling and giant magnetoresistance via Cu -X \nalloys (X=Au, Fe, Ni). Europhys. Lett ., 24, 71-76 (1993).  \n[31] I. L. Prejbeanu, M. Kerekes, R. C. Sousa, H. Sibuet, O. Redon, B. Dieny, and J. P. Nozières. Thermally assisted \nMRAM. J. Phys.: Condens. Matter . 19, 165218 (2007).  \n  \n \n \n \n \nFIG. 1 \n  \n  \n \n \n \n \n \n \n \n \nFIG 2. \n \n  \n \n \n \n \n \n \nFIG. 3 \n \n \n \n \n \n \nFIG. 4 \n  \n \n \n \n \n \nFIG. 5  \n"    },    {        "title": "1211.3252v1.Giant_third_order_magneto_optical_rotation_in_ferromagnetic_EuO.pdf",        "content": "arXiv:1211.3252v1  [cond-mat.str-el]  14 Nov 2012Giant third-order magneto-opticalrotationin ferromagne ticEuO\nMasakazu Matsubara1,2,∗Andreas Schmehl3, Jochen\nMannhart4, Darrell G. Schlom5, and Manfred Fiebig1,2\n1Department of Materials, ETH Zurich,\nWolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland\n2HISKP, Universit ¨at Bonn, Nussallee 14-16, 53115 Bonn, Germany\n3Institut f¨ur Physik, Universit ¨at Augsburg, Augsburg 86135, Germany\n4Max Planck Institute for Solid State Research,\nHeisenbergstraße 1, 70569 Stuttgart, Germany and\n5Department of Materials Science and Engineering,\nCornell University, Ithaca, New York 14853-1501, USA\n(Dated: October 8, 2018)\nAbstract\nA magnetization-induced rotation in the third-order nonli near optical response is observed in out-of-\nplane-magnetized epitaxial EuOfilms. Wediscuss therelati on ofthisnonlinear magneto-optical rotation to\nthe linear Faraday rotation. It is allowed in all materials b ut, in contrast to the linear Faraday rotation, not\naffected by the reduction of the thickness of the material. T hus, the third-order magneto-optical rotation is\nparticularly suitable for probing the magnetization of fun ctional magnetic materials such asultra-thin films\nand multilayers.\nPACS numbers: 75.50.Pp,42.65.Ky,78.20.Ls,75.47.Lx\n1I. INTRODUCTION:NONLINEARMAGNETO-OPTICS\nMichael Faraday’s discovery of magnetically induced optic al activity in 18461constituted the\nfirst conclusive demonstration of an intimate connection be tween light and magnetism. This so-\ncalled Faraday effect exists in allmedia and has long been applied to study the magnetic and\nelectronic properties of materials and image magnetic doma in structures.2,3By controlling the\npolarization of light, a key functionality in modern opto-t echnology, the Faraday effect plays a\ncrucial roleinapplicationssuchas opticalrotators,isol ators,modulators,and circulators.2,3\nDuring the past two decades, nonlinear optical effects, suc h as sum and difference frequency\ngeneration, entered the realm of magneto-optics.4,5With nonlinear optics, unique information\nabout thecrystallographic,geometric, electronic, and ma gneticstructurecan beacquired. It often\naddresses states that are inaccessible by linear optics so t hat a search for the nonlinear analogues\noftheestablishedlinearmagneto-opticaleffects commenc ed.\nThusfar,thevastmajorityofinvestigationsisfocusedons econd-ordermagneto-opticaleffects\nlikemagneticallyinducedsecond-harmonicgeneration(SH G).4,5SinceSHGintheelectric-dipole\napproximationislimitedtosystemswithoutcenterofinver sion,itisparticularlyvaluableforinves-\ntigating the inherently noncentrosymmetric surface or int erface in centrosymmetric magnets.4A\nrotationofthepolarizationofareflectedSHGwavewithresp ecttothepolarizationoftheincident\nfundamental light wave, the so-called “nonlinear magneto- optical Kerr effect”, was reported.4,6–8\nThenonlinearKerrrotationcanbeordersofmagnitudelarge rthanthelinearKerrrotationsince,in\ncontrast to the linearcase, the magnetization-inducednon linearcontributionsto thesusceptibility\ntensorcan beofthesameorderofmagnitudeas themagnetizat ion-independentones.\nYet,theselectivityofSHGcanbeitsmajordeficiency,becau seinthemajorityofmagnetically\nordered compounds SHG is restricted or even forbidden by sym metry and hence inappropriate\nfor probing their magneto-optical performance. Instead, a nonlinear magneto-optical effect unre-\nstrictedby symmetry is called for. Here an extension of the linear Far aday rotation (LFR) into\nthe regime of harmonic generation is one possibility. Takin g third-harmonic generation (THG)\nas an example, the principle of such a higher-order effect is shown in Fig. 1(b) in comparison to\nthe LFR depicted in Fig. 1(a). Both effects correspond to a ro tation of the plane of polarization\nof the emitted light (frequency nωwithn=1,3) with respect to the polarization of the incident\nlight (frequency ω) by an angle θ(n). The rotation is generated by the spontaneous or magnetic-\nfield-inducedmagnetizationofthesamplealongthedirecti onoflightpropagation. Becauseofthis\n2similarityitisintuitivetoconsidertheprocessshowninF ig.1(b)ashigher-orderFaradayrotation.\nHowever,suchadenominationfirst needstobejustifiedbypla cingthenonlinearmagneto-optical\nrotationand theLFR ona commonbasis,macroscopicallyas we llas microscopically.\nII. MAGNETO-OPTICALROTATIONOFPOLARIZATION\nFor identifying a common macroscopic basis for the two proce sses depicted in Figs. 1(a) and\n1(b), we will first review the equations leading to the LFR. Th en the formalism will be expanded\nto the regime of harmonic generation. We will see that the thi rd-order rotation, i.e., the rotation\nof polarization of the frequency-tripled light wave with re spect to the polarization of the incident\nfundamental light wave (see Fig. 1(b)), has many properties in common with the LFR and can\ntherefore be interpreted as its nonlinear complement. For s implicity we restrict the discussion to\nisotropicanduniaxialmediaintheabsenceoflineargyrotr opyandabsorptionsothatthemagneto-\noptical rotation does not interfere with other dichroic and birefringence effects. The direction of\nthemagnetization Mischosen alongthehigh-symmetry zaxis.\nA. Linearmagneto-optical rotation: TheFaraday rotation\nThe LFR, expressed by the magneto-optical rotation of the li near polarization of light at the\nfrequency ωpropagating through a material in the direction parallel to that ofM, is derived by\ninsertingthelineardielectrictensor\nˆε=\nε/bardbl−ε⊥(M)0\nε⊥(M)ε/bardbl0\n0 0 ε′\n/bardbl\n(1)\nwithε/bardblandε⊥as purelyreal and imaginarycomponents,respectively,int othewaveequation\n/parenleftbiggˆε\nc2∂2\n∂t2−△/parenrightbigg\n/vectorE=0 (2)\nand solving it for a linearly polarized electromagnetic wav e/vectorE=/vectorE0exp{−iω(t−n\ncz)}.ε/bardbland\nε⊥(M)∝Mdenote the elements of the linear dielectric function descr ibing the propagation of\nlightpolarized parallel and perpendicular,respectively ,tothepolarizationoftheincidentlight. In\ngeneral, the off-diagonal component ε⊥is much smallerthan the diagonal component ε/bardbl. We ob-\ntain two eigenmodes, for theelectromagneticwave transmit tingthrough thematerial, represented\n3byn2\n±=ε/bardbl∓iε⊥withn+andn−as refractive index of light with right- and left-handed cir cular\npolarization, respectively. For the geometry in Fig. 1(a) t he plane of polarization of the incident\nlinearlypolarized lightis rotatedby theangle\nθF=−ω\ncΔnℓ, (3)\nwhereΔn= (n+−n−)/2 andℓis the length of the light path in the material along the direc tion\nofM. Thus, the LFR arises due to the magnetization-induced circ ular birefringence and θFis\nproportionalto thethicknessofthematerial.\nB. Non-linear magneto-optical rotation\nInanalogy tothedefinitionofthenonlinearmagneto-optica lKerreffect wecan nowintroduce\nthen-th-ordermagneto-opticalrotationasrotationoftheharm onicwaveat nωwithrespect tothe\npolarizationoftheincidentfundamentallightwaveat ω. Inthesimplestcasesthisisexpressedby\ntanθ(n)=iε(n)\n⊥(M)\nε(n)\n/bardbl,n≥2. (4)\nwithε(n)\n⊥∝Mandε(n)\n/bardblaselementsofthe n-thorderdielectricfunctiondescribingthepropagation\noflightpolarizedperpendicularand parallel,respective ly,tothepolarizationoftheincidentlight.\nByinsertingintoEq.(3)thedefinitionsof Δnandn±asgivenabove,Equations(3)and(4)can\nbecombinedintothegeneral expression\nfn(θ(n))=Re\na(n)iε(n)\n⊥(M)\nε(n)\n/bardbl\n,n∈N. (5)\nwithfnanda(n)as a function and a proportionality factor, respectively. W e havef1(u) =u,\na(1)= (ωn0/2c)·ℓwithn0= (n++n−)/2 andfn≥2(u) =tanu,a(n≥2)=1. Only for n=1 the\nfrequency of the ingoing and the outgoing light is the same wh ich explains the difference in the\nexpressionsfor n=1andn≥2. Inanycase,Eq.(5)emphasizesthatthemagneto-opticalr otation\nof any order is determined by the ratio between the off-diago nal and diagonal components of the\ndielectrictensorofthatorder. Notethatalthoughwenegle ctedabsorptionthusfar,thecomponents\nof the dielectric tensor can in general be complex. The rotat ion of the plane of polarization may\nbetherefore accompaniedby ellipticalcontributions.2In Eq.(5)thisis already taken intoaccount\nby distinguishingbetween real and imaginaryparts.\n4TABLE I: Nonzero elements of the linear and third-order susc eptibility tensor relevant to the LFR and\nthe TFR in ferromagnetic EuO. The components are derived by c onsidering 4 /mmmas magnetic point\nsymmetry. Only the experimentally relevant components for a magnetization parallel to the zaxis and an\nirradiation of x-polarized fundamental light incident along the zaxisarelisted.11Evencontributions couple\ntoM0,M2,etc.whereasoddcontributions coupleto M1,M3,etc. Ingeneral higher-order termsaresosmall\nthat only the leading terms coupling to M0(magnetization-independent) and M1(linear coupling) need to\nbe considered. A manifestation of higher-order terms will b ediscussed insection IV.\nEveninM OddinM\nLFR χxx=χyy χyx=−χxy\nTFR χxxxx(=χyyyy) χyxxx(=−χxyyy)\nWe now have to identify the nonlinear complement to the LFR by investigating the different\norders of n. The case n=1 leads to the LFR discussed above and shown in Fig. 1(a). As di s-\ncussed, the case n=2 (as well as n=4,6,8,...) is restricted or even forbidden by symmetry\nand therefore inappropriate for probing the magneto-optic al performance in general. The case\nn=3 is the leading-order nonlinear magneto-optical rotation process that is, like the LFR, al-\nlowed in materials of anysymmetry. The “nonlinear magneto-optical Kerr effect” des ignates the\nmagnetization-induced rotation of polarization of a reflec ted nonlinear (frequency-doubled) light\nwave; in exactly the same way we might now use the term “nonlin ear Faraday effect” for the\nmagnetization-inducedrotationofpolarizationofatrans mittednonlinear(frequency-tripled)light\nwave with respect to the incident light wave. However, the te rm “nonlinear Faraday effect” is\nalso usedfor thenonlineardependenceoftheLFR on theinten sityoftheincidentlightcaused by\nmulti-photon absorption.9For clarity we henceforth employ the term “third-order Fara day rota-\ntion” (TFR) for the effect discussed in our work. The most obv ious difference between the LFR\nand theTFR is thattheformerisproportionalto thethicknes softhematerialwhereas thelatteris\nthickness-independent. The experimental verification of t his striking difference will be the topic\nofsectionIV.\nForthegeometry inFigs. 1(a)and 1(b), nonzero elementsoft helinearand third-ordersuscep-\ntibility tensor relevant to the LFR and the TFR are summarize d in Table I. Here the third-order\n5susceptibilityis derivedfrom thegeneral expressionforT HG,\nPi(3ω)=ε0χ(3)\nijklEj(ω)Ek(ω)El(ω). (6)\nWithˆε(3)=ˆχ(3)in Eq.(4), weobtain\ntanθ(3)=Re(iχyxxx(M)/χxxxx). (7)\nDespitethepotentialof theTFR as universalmagneto-optic alprobe, only a singlestudyhas been\nreportedthusfar.10Inthatstudy,garnetfilmsrevealedarotationofabout4◦andneitherthespectral\ncharacteristicsnorthemicroscopicoriginoftheeffectwe reinvestigated,sothatthegeneralaspects\nofthenatureand potentialoftheTFR remained unclear.\nInthefollowingwewillshowthatthinepitaxialfilmsofthef erromagneticsemiconductorEuO\ndisplay a “giant” TFR. The rotation varies between zero in th e absence of a magnetic field and\nabout 80◦in a field of 2.5 T. Spectroscopy reveals its microscopic orig in. Based on an inherent\nrelationbetween theTFR andtheLFRwepointoutthegeneral f easibilityoftheTFR forprobing\nmagneticmatterandthinfilms inparticular.\nIII. SAMPLESANDMETHODS\nA. Ferromagnetic EuO\nEuO is attracting much attention from the point of view of bas ic science and application.12It\nhas a high potentialfor semiconductor-basedspintronics a pplications12–15due to its half-metallic\nbehavior with electron doping12–14and its structural and electronic compatibility with Si, Ga N,\nand GaAs.12,16At room temperature, stoichiometric EuO is a paramagnetic s emiconductor with\na band gap of ∼1.2 eV. It orders ferromagnetically at TC=69 K. The Eu2+ions have localized\n4f7electrons with8S7/2as the ground state, yielding a saturation magnetic moment a s large as\n7µB. A multitude of remarkable magneto-optical properties hav e been revealed in EuO, such as\na strong linear and circular birefringence and dichroism,17–20as well as a large well-investigated\nred-shift of the absorption edge associated to the magnetic ordering.17,21With a rotation of 5 ·\n105deg/cm, EuO shows one of the largest LFR.18Pronounced magnetization-induced SHG and\nTHG contributions have been observed on the binary Eu compou nds and the electronic origin of\nthe SHG and THG spectra has been discussed.21–24Hence, because of outstanding magnetic and\n6optical properties and their strong connection, EuO is an id eal compound for exploring the TFR.\nYet, as wewillsee, theresultsgainedon EuOare instructive for understandingTFR ingeneral.\nB. Samplepreparation andexperimental methods\nEpitaxialEuO(001)filmsprotectedbyanamorphoussilicon( a-Si)caplayerof10-20nmwere\ngrownbymolecular-beamepitaxyontwo-sidepolishedYAlO 3(110)substrates.12Formostofthe\nmeasurements, film with a thickness of 100 nm was used. Bulk-l ike crystallographic, transport,\nand linear optical properties12,21confirm the excellent quality of the epitaxial films. Samples\nwere mounted in an optical helium-operated split-coil cryo stat in which magnetic fields of up to\n±3.5 T applied along the zaxis induced the TFR. The TFR was measured with light inciden t\nperpendicularto theEuO surface. The setup fornonlineartr ansmissionspectroscopy is described\nin detail in Ref. 21. Light pulses were generated in an optica l parametric amplifier pumped by a\nregenerative Ti:sapphire amplifier system providing a cent ral wavelength of 800 nm (1.55 eV), a\npulse width of 120 fs, and a repetition rate of 1 kHz. The TFR wa s investigated at temperatures\nof 10−200 K in the spectral range 3 ¯hωof 1.85−3.50 eV. The nonlinear spectra of the EuO\nfilmswerenormalizedtothereferencesignalobtainedonawe dgedα-SiO2plate. Theywerealso\nnormalizedto thespectral responseofthedetectionsystem .\nIV. RESULTSANDDISCUSSION\nA. Verifying third-order Faraday rotation\nFigure 1(c) shows the intensity of the frequency-tripled li ght as a function of the angular po-\nsitionϕAof a polarization filter. Maximum intensity directly reveal s the direction of polarization\nat 3ω. Data were taken at 10 K and 3 ¯hω=2.0 eV for magnetic fields µ0Hzof 0 T and ±3 T.\nAtµ0Hz=0 T the sample possesses an in-plane magnetization, so that Mz=0 andθ(3)=0◦.\nAtµ0Hz= +3 T the situation changes entirely. The intensity of the freq uency-tripled light is\ngreatly enhanced and its maximum shows a large shift with res pect toϕA. Here the field induces\nan out-of-planemagnetization Mz/ne}ationslash=0 and withitalargerotationofabout70◦.\nInordertoexploretherelationofthisrotationtotheTFRav arietyoftestswasperformed. First,\nthe observed rotation agrees well with the symmetry analysi s. In- and out-of-plane magnetized\nEuO possesses the point symmetry 4 mmmand 4mmm, respectively, and only the latter allows the\n7magneticallyinduced frequency triplingthat can lead to aT FR.11Second, we notethereversalof\nthe rotation occurring with the reversal of Mzin Fig. 1(c). This is a property required for Faraday\nrotation of any order. Third, Fig. 2(a) shows the angular dep endence of the frequency-tripled\nsignal as in Fig. 1(c) for a variety of temperatures in the fer romagnetic and the paramagnetic\nstate. The extracted temperature variation of the rotation is indicated by triangles and entered in\nFig. 2(c) as open squares. We see that in the vicinity of TCthe rotation decreases drastically and\nreflectsthedecreaseof Mz. NotethattheonsettemperatureofthemagnetizationinEuO isstrongly\ninfluenced by external magnetic fields,15,25which explains the small signal remaining just above\nTC. ContributionsbytheLFRthatmayinterferewiththethird- orderrotationaresmall. At10Kwe\nfind thatθ(1)(ω)andθ(1)(3ω)are∼0◦and∼4◦, respectively,inagreement withearlierdata.18\nB. Temperature andmagnetic fielddependence\nWithreference toEq.(7),Fig.2(b)showsthetemperaturede pendenceofthefrequency-tripled\nsignalfor χyxxxandχxxxx. Wefind thatbothsusceptibilitieschangewithtemperature , inparticular\naroundTC, albeit in a different way. However, their magnetic-field de pendence at a fixed temper-\nature in Fig. 3(b) reveals that only χyxxxresponds to the applied field while χxxxxdoes not. With\nthe application of the magnetic field χyxxxincreases from zero for Mz=0 to its saturation value\nat≥2.5 T. In contrast, χxxxxis independent of the applied field and the associated reorie ntation\nofthespontaneousmagnetization. Wethereforeseethatthe variationof χxxxxwithtemperaturein\nFig. 2(b) is caused by the large temperature-dependent spec tral shift occurring around TC.17,21,26\nThecouplingtothemagnetizationisthereforeanindirectb and-structuraleffect. Becauseofthein-\ndependenceofthedirectionofthemagnetization,theband- structuralshiftmaybeparametrizedby\nan even-powerexpansion, yielding in total terms ∝M2\nsat,M4\nsat, etc. inχxxxxand terms ∝Mz·M2\nsat,\nMz·M4\nsat, etc. in χyxxx) (withMsatas saturation magnetization at a certain temperature). The\nrotationanglesarenotdirectlyaffectedbythisband-stru cturalshiftbecauseitentersbothsuscep-\ntibilities, χxxxxas well as χyxxx, in the same way (they are probed at the electronic transitio n, see\nsectionIVC).\nConsidering that the frequency-tripled signal Iforχyxxxis proportional to the square of Mz\nbecause of I∝|χ|2, the dependence of Mzon the applied field Hzis extracted. The magnetic-\nfield dependence of χyxxxin Fig. 3(c) reproduces the results of earlier measurements ofMz,15\nthus revealing that the coupling of χyxxxtoMzis indeed linear and in agreement with Table I.\n8At saturation, χyxxxsubstantially exceeds χxxxx. This notably contrasts the linear magneto-\noptical response, where the magnetization-induced suscep tibilityχyxis much smaller than the\nmagnetization-insensitivesusceptibility χxx.\nA noticeable difference distinguishing the TFR from the LFR is the proposed independence\nof the rotation angle of the thickness of the material. We scr utinized this claim by measuring the\nTFR for EuO(001) films with a thickness of 100, 34, and 10 nm. Fi gure 4 shows that within the\nstatistical error the same value θ(3)≈80◦is observed for all three samples. Thus, TFR can be\nparticularly useful for probing the magnetic properties of very thin films where θ(1)of the LFR\nwouldapproachzero. Anotherdistinctdifferencebetweent heLFRandtheTFRisthedependence\nof the rotation angle on the magnetization. Figure 3(a) show s the angular dependence of the\nfrequency-tripledsignalformagneticfieldsbetween0Tand ±2.5T.Theextractedmagnetic-field\nvariation of θ(3)entered in Fig. 3(c) differs from that of Mz. Unlike the LFR, which follows the\nrelationθ(1)∝Mz, the TFR is expressed by the relation θ(3)∝arctan(const·Mz)according to\nEq.(4).\nInFigs.2(c)and3(c)thevalueofarctan (|χyxxx|/|χxxxx|)isplottedandcomparedtotherotation\nangleθ(3)directlymeasuredinFigs.2(a)and3(a). Theagreementbetw eenthetwodatasetsisob-\nvious. ThissuggeststhattheapproximationofRe (iχyxxx/χxxxx)inEq.(7)by |χyxxx|/|χxxxx|,which\nneglects dichroic effects, is applicable for determining θ(3). Because of the excellent agreement\nbetween the two data sets, we henceforth use the convenient a pproximation of θ(3)via the third-\norder susceptibilities,instead of measuring it by an invol ved polarization analysis as in Figs. 2(a)\nand 3(a).\nC. Comparingthemicroscopy of LFRand TFR\nFinally,inordertodisclosethemicroscopicmechanismoft hegiantTFR,itsspectraloriginhas\nto be clarified. Therefore, Fig. 5(a) showsthe spectral depe ndence of thefrequency-tripled signal\nforthemagnetization-induced( χyxxx)andthemagnetization-insensitive( χxxxx)susceptibilitiesand\ntheestimatedrotation θ(3)at10Kinamagneticfield µ0Hz=+3T.Whiletheslopeofaresonance\ncentered at <1.9 eV is present in χyxxxbut not in χxxxx, a pronounced peak around 3.1 eV is\nobserved in both components. This corresponds to a specific r esonance of θ(3)at<1.9 eV, just\nlikeinthecaseoftheLFR,asshowninFig.5(b). TheLFRisatt ributedtothetransitionsfromthe\n4f7groundstatetothe4 f65d1(t2g)stateoftheEu2+ion.17–20Itiscausedbythespinpolarization\n9andthespin-orbitsplittingofthe fanddstatesinvolvedintheopticaltransition. Weassociatethe\nTFR to the same transition, yet as a three-photon-resonant excitation. This is reasonable because\nthe selection rules for a one-photon transition are include d in that of a three-photon transition. In\ncontrast,thepeaknear3.1eVseemstoinvolvea two-photon-resonant transitiontothe4 f65d1(t2g)\nstate followed by the transition via the third photon to the h igher lying 5 d/6smixing state,23as\nshown in the inset of Fig. 5(a). This excitation does not cont ribute notably to the TFR. It reflects\nthat the selection rules for the two-photon transition to th e 4f65d1(t2g)state are fundamentally\ndifferent from the selection rules of the LFR and also that th e 6sstate with less magneto-optical\nactivityis involvedintheexcitationprocess.\nV. SUMMARYANDCONCLUSION\nInsummary,agiantthird-ordermagneto-opticalrotationt ermedTFRwasobservedinepitaxial\nferromagneticEuOfilmswithamagnetic-field-inducedout-o f-planemagnetization. Itresultsfrom\nthelargespinpolarizationandthespin-orbitsplittingof thestatesinvolvedintheopticaltransition\nand reveals an inherent similarity to the LFR. However, the T FR is boosted by the ratio of the\nmagnetictothenonmagnetictensorelementsinthedielectr ictensorˆε. Thisratioismuchlargerfor\nthe nonlinear than for the linear contributions. The giant T FR is particularly suitable for probing\nthe magnetization of ultra-thin films and multilayers, beca use in contrast to the LFR, it is not\naffectedbythereductionofthethicknessofamaterial. Ina ddition,thethird-orderFaradayrotation\nand the second-order Kerr rotation (commonly referred to as “nonlinear magneto-optical Kerr\nrotation”)complementeachotherasprobesformagnetismbe causeoftheirdifferentsensitivityto\nthesymmetry.\nAcknowledgments\nThis work was supported by the Alexander von Humboldt Founda tion, by the SFB 608, the\nTRR 80 of the Deutsche Forschungsgemeinschaft, and by the AF OSR (Grant No. FA9550-10-1-\n0123).\n∗Electronic address: masakazu.matsubara@mat.ethz.ch\n101M. Faraday, Phil. Trans. Roy. Soc. 136, 1(1846).\n2A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Taylor and\nFrancis Group, New York, 1997).\n3Magneto-Optics , edited by S. Sugano and N. Kojima (Springer-Verlag, Berlin , Heidelberg, New York,\n2000).\n4Nonlinear Optics inMetals , edited by K.H.Bennemann (Clarendon Press, Oxford, 1998).\n5M. Fiebig, V. V.Pavlov, and R.V.Pisarev, J. Opt. Soc. Am.B 22, 96 (2005).\n6U.Pustogowa, W.H¨ ubner, and K.H.Bennemann, Phys. Rev. B 49, 10031 (1994).\n7B.Koopmans, M.G.Koerkamp, Th.Rasing, H. vanden Berg, Phys . Rev.Lett. 74, 3692 (1995).\n8Th. Rasing, J. Magn. Magn. Mater. 175, 35 (1997).\n9J. Frey, R.Frey, C.Flytzanis, and R.Triboulet, J.Opt. Soc. Am.B9, 132 (1992).\n10J. Shimura, S.Ohkoshi, and K.Hashimoto, Appl. Phys. Lett. 82, 3290 (2003).\n11R.R. Birss, Symmetry and Magnetism (North-Holland, Amsterdam, 1966).\n12A.Schmehl,V.Vaithyanathan, A.Herrnberger, S.Thiel,C.R ichter, M.Liberati, T.Heeg,M.R¨ ockerath,\nL. F. Kourkoutis, S. M¨ uhlbauer, P. B¨ oni, D. A. Muller, Y. Ba rash, J. Schubert, Y. Idzerda, J. Mannhart,\nand D.G. Schlom, Nature Mater. 6, 882 (2007).\n13P. G. Steeneken, L. H. Tjeng, I. Elfimov, G. A. Sawatzky, G. Ghi ringhelli, N. B. Brookes, and D.-J.\nHuang, Phys. Rev. Lett. 88, 047201 (2002).\n14T.S.Santos, J.S.Moodera, K.V.Raman, E.Negusse, J.Holroy d, J.Dvorak, M.Liberati, Y.U.Idzerda,\nand E.Arenholz, Phys. Rev. Lett. 101, 147201 (2008).\n15T. Mairoser, A. Schmehl, A. Melville, T. Heeg, L. Canella, P. B¨ oni, W. Zander, J. Schubert, D. E. Shai,\nE.J. Monkman, K.M. Shen, D.G.Schlom, and J. Mannhart, Phys. Rev. Lett. 105, 257206 (2010).\n16A. G. Swartz, J. Ciraldo, J. J. I. Wong, Yan Li, Wei Han, Tao Lin , S. Mack, J. Shi, D. D. Awschalom,\nand R.K. Kawakami, Appl. Phys. Lett. 97, 112509 (2010).\n17M. J. Freiser, F. Holtzberg, S. Methfessel, G. D. Pettit, M. W . Shafer, and J. C. Suits, Helv. Phys. Acta\n41, 832 (1968).\n18K.Y. Ahnand J. C.Suits, IEEETrans. Magn. MAG3,453 (1967).\n19J. Feinleib, W.J. Scouler, J. O.Dimmock, J. Hanus, T.B. Reed , and C. R.Pidgeon, Phys. Rev. Lett. 22,\n1385 (1969).\n20H.-Y.Wang, J.Schoenes, and E.Kaldis, Helv. Phys. Acta 59, 102 (1986).\n21M.Matsubara, A.Schmehl,J.Mannhart, D.G.Schlom,andM.Fi ebig,Phys.Rev.B 81,214447(2010).\n1122B.Kaminski,M.Lafrentz,R.V.Pisarev,D.R.Yakovlev,V.V. Pavlov,V.A.Lukoshkin,A.B.Henriques,\nG.Springholz,G.Bauer,E.Abramof,P.H.O.Rappl,andM.Bay er,Phys.Rev.Lett. 103,057203(2009).\n23M. Lafrentz, D. Brunne, B. Kaminski, V. V. Pavlov, A. B. Henri ques, R. V. Pisarev, D. R. Yakovlev, G.\nSpringholz, G.Bauer, E.Abramof, P.H.O. Rappl, and M.Bayer , Phys. Rev. B 82, 235206 (2010).\n24M. Matsubara, C. Becher, A. Schmehl, J. Mannhart, D. G. Schlo m, and M. Fiebig, J. Appl. Phys. 109,\n07C309 (2011).\n25K.Hayata, N.Iwata, Y.Hasegawa, and K.Sato, J. Magn. Soc. Jp n.25, 299 (2001).\n26T. Kasuya, CRCCrit. Rev. Solid StateSci. 3, 131 (1972).\n12E(Z)(a) Linear Faraday rotation (b) Third-order Faraday rotation \nT(1) \nx\ny z\nE(Z)Mz\nE\nM\nE(Z)\nT(3) \nx\ny z\nE(3 Z)Mz\nE\nM\n(c) \n(c)\nFIG. 1: (Color online) Schematic of (a) the linear Faraday ro tation (LFR) and (b) the third-order Faraday\nrotation (TFR). The plane of polarization of the outgoing wa ve atω(LFR) or 3 ω(TFR) is rotated with\nrespecttotheplaneofpolarization oftheingoinglightwav eatω. Therotationiscausedbythespontaneous\nor field-induced magnetization Mzparallel to the direction of light propagation z. (c) TFR in a EuO(001)\nfilmfor different Mz. Themeasurement showsthe intensity of the frequency-trip led light as function of the\nangular position ϕAof a linear polarization filter. The nonlinear rotation angl e is derived from the value\nofϕAat the maximum of the intensity of the frequency-tripled lig ht. The data for ±MzandMz=0 were\nobtained infieldsof ±3Tand 0Tapplied along the zaxisof the EuO(001) film. Thelines show sinusoidal\nfits. TheTFRisinvestigated for x-polarized incident light at 10K and 3 ¯hω=2.0eV.\n13-90 -45 045 90 \nAnalyzer angle (deg) 200 K 120 K 82 K 73 K 64 K 58 K 50 K 12 K (a) µ0H = ±3 T \n+Mz −Mz\n0Intensity (3 ω)(b) \nχxxxx χyxxx µ0H = +3 T \n90 \n60 \n30 \n0|θ (3) | and |θ (1) | (deg) \n100 50 0\nTemperature (K) 200 |θ (3) |\n \narctan(|χyxxx |/|χxxxx |) (c) \n|θ (1) | (0.66 eV) \n|θ (1) | (2.0 eV) Intensity (3 ω) \nFIG. 2: (Color online) Temperature dependence of the TFR of a EuO(001) film at 3 ¯hω=2.0 eV. (a)\nDetermination of the nonlinear rotation angle for temperat ures between 10K and 200 K. For µ0Hz=+3T\n(closed circles) and µ0Hz=−3 T (open circles) this angle is indicated by the respective t riangles. (b)\nTemperature dependence of the nonlinear susceptibilities χyxxxandχxxxxforµ0Hz=+3 T. (c) Comparison\nof the rotation angle derived from (a) (open squares) and (b) (open circles). Thehexagons refer to the LFR\nat 0.66 and 2.0 eV.\n14±2.5 T +Mz −Mz(a) T = 10 K \n±1.5 T \n±1.25 T \n±1 T \n±0.75 T \n±0.5 T \n±0.25 T \n±0.125 T \n-90 -45 045 90 \nAnalyzer angle (deg) 0 T 0Intensity (3 ω)T = 10 K (b) \nχxxxx χyxxx \n-90 -45 045 90 \nθ (3)  (deg) \n-3 -2 -1 0123\nMagnetic field (T) -1 01Mz (arb. unit) (c) \n± arctan(| χyxxx |/|χxxxx |) θ (3) \n \n \nMzIntensity (3 ω) \nFIG. 3: (Color online) Magnetic-field dependence of the TFR o f a EuO(001) film at 3 ¯hω=2.0 eV. (a)\nDetermination of the nonlinear rotation angle as in Fig. 2 fo r magnetic fields between 0 T and ±2.5 T.\n(b) Magnetic-field dependence of the nonlinear susceptibil itiesχyxxxandχxxxxat 10 K. Data represented\nby closed (open) symbols were taken with increasing (decrea sing) field. (c) Comparison of the rotation\nangle derived from (a) (open squares) and (b) (closed and ope n circles). The magnetic-field dependence\nof the out-of-plane magnetization Mzderived from (b) is shown by triangles. It agrees well with pu blished\nmagnetization measurements.15\n1590 \n60 \n30 \n0|θ (3) | and |θ (1) | (deg) \n120 100 80 60 40 20 0\nThickness of EuO film (nm) 10 K EuO \n|θ (3) |\n|θ (1) |\nFIG. 4: (Color online) Thickness dependence of the TFR measu red on EuO(001) films at 10 K and 3 ¯hω=\n2.0eV.DatawerecorrectedbythemeasuredTHGcontribution fr omthea-Sicaplayer. Theexpectedlinear\ndependence of the LFRat 2.0eV isalso plotted asareference.\n164f 7 w 3w 5d (t2g) T << TC \n6s \n0Intensity (3 w)10 K (a) \ncyxxxcxxxx\n90 \n60 \n30 \n0|q (3) | (deg) \n3.5 3.0 2.5 2.0 \nPhoton energy 3 w (eV) (b) 10 K \n9\n6\n3\n0q (1)  (deg) \n2.5 2.0 1.5 \nFundamental energy (eV) 5 K \nAhn et al .\nFIG. 5: (Color online) Spectral dependence of nonlinear sus ceptibilities and TFR of a EuO(001) film. (a)\nSpectrum of χyxxxandχxxxxat 10 K in a magnetic field µ0Hz= +3 T. The inset shows schematics of the\nspin-dependent electronicbandstructureofferromagneti cEuOandoftheopticaltransitions oftheLFRand\nthe TFRin the depicted spectral range. (b) Spectral dependa nce of the TFRderived from the data in (a) by\n|θ(3)| ≈arctan(|χyxxx|/|χxxxx|)(see text). Inset: Spectral dependence of the LFR at 5 K for a E uO film of\n153 nm, taken from Ref. 18.\n17"    },    {        "title": "1211.4400v1.Magnetically_controlled_accretion_onto_a_black_hole.pdf",        "content": "arXiv:1211.4400v1  [astro-ph.HE]  19 Nov 2012Journal of Physics: Conference Series, 2012\nProc. of AHAR2011 Conference “The Central Kiloparsec in Gal actic Nuclei”, Bad-Honnef,\nGermany, Aug. 29 – Sep. 2, 2011\nMagnetically controlled accretion onto a black hole\nN R Ikhsanov1, L A Pustil’nik2and N G Beskrovnaya1\n1Pulkovo Observatory, Pulkovskoe Shosse 65, Saint-Petersb urg 196140, Russia\n2Israel Space Weather and Cosmic Ray Center, Tel Aviv Univers ity, Israel Space Agency, &\nGolan Research Institute, Israel\nE-mail:ikhsanov@gao.spb.ru\nAbstract. An accretion scenario in which the material captured by a bla ck hole from\nits environment is assumed to be magnetized ( β∼1) is discussed. We show that the\naccretion picture in this case is strongly affected by the mag netic field of the flow itself. The\naccretion power within this Magnetically Controlled Accre tion (MCA) scenario is converted\npredominantly into the magnetic energy of the accretion flow . The rapidly amplified field\nprevents the accretion flow from forming a homogeneous Keple rian disk. Instead, the flow is\ndecelerated by its own magnetic field at alarge distance (Shv artsmanradius) from the black hole\nand switches into a non-Keplerian dense magnetized slab. Th e material in the slab is confined\nby the magnetic field and moves towards the black hole on the ti me scale of the magnetic field\nannihilation. The basic parameters of the slab are evaluate d. Interchange instabilities in the\nslab may lead to a formation of Z-pinch type configuration of t he magnetic field over the slab\nin which the accretion power can be converted into jets and hi gh-energy radiation.\n1. Introduction\nWe consider a black hole of the mass Mbh, surrounded by a gas of the average density ρ∞, which\nmoves in the frame of the black hole with a relative velocity vrel=/parenleftbig\nv2\ns+v2\nw/parenrightbig1/2, wherevsandvw\nare the sound speed and the velocity of the gas proper motion. A maximum distance at which\nthe black hole interacts with its environment through gravi tational potential is the Bondi radius\nRG= 2GMbh/v2\nrel. It is defined by equation vp(RG) =vrel, wherevp(r) = (2GMbh/r)1/2is the\nparabolic (free-fall) velocity at a distance r. The mass with which the black hole interacts in a\nunit time is ˙Mc=πR2\nGρ∞vrel. The mass capture rate by the black hole from its environment\nin general case is limited to ˙Ma≤˙Mc.\nThe structure of the accretion flow onto a black hole and the mo de by which the accretion\npower is released depends on the initial conditions in the ma terial captured by the black hole\nat the Bondi radius. A situation in which this material is slo wly moving, i.e. vw< vs, and non-\nmagnetized is discussedinthenextsection. Itcan beexpect ed iftheblack holecaptures material\nfrom a giant molecular cloud. If the material captured by the black hole is supplied by nearbystars its properties can significantly differ from those menti oned above. The velocity of stellar\nwind usually exceeds the sound speed in the outflowing materi al, i.e.vw≫vs, and the magnetic\npressure in the wind, E(0)\nm=Bw/8π, is comparable to its thermal pressure, E(0)\nth=ρ∞v2\ns. This\nis justified by studies of solar wind (see e.g. [17], and refer ences therein) and recent results on\nthe surface field of massive O/B-type stars (see e.g. [18], an d references therein). The accretion\npicture which is realized under these conditions is discuss ed in Sect.3. We show that accretion\npicture in this case is strongly affected by the magnetic field o f the flow itself. It prevents\nthe material from forming a Keplerian disk. Instead appeara nce of a dense magnetized non-\nKeplerian slab is expected. Formation of the slab can under c ertain conditions result in a strong\nelectric potential in the vicinity of the black hole which mi ght be responsible for powerful jets.\nOur conclusions are summarized in Sect.4.\n2. Non-magnetized accretion flow scenario\nAccretion scenario in AGNs is usually built around the assum ptions that the material\nsurrounding the black hole is non-magnetized and moves with a relatively small velocity, i.e.\nvrel∼vs. As this material is captured by a black hole it initially fol lows ballistic trajectories\nforming a quasi-spherical accretion flow. If the accreting m aterial possesses angular momentum\nthe flow can switch its geometry from quasi-spherical to a Kep lerian disk. For the disk to\nform the circularization radius, Rcirc=˙J2/GMbh˙M2\na, at which the angular velocity of the\nmaterial, ωen=ξΩ0(RG/r)2, reaches the Keplerian angular velocity, ωk=/parenleftbig\n2GMbh/r3/parenrightbig1/2,\nshould exceed a distance at which the ballistic trajectorie s of the material are truncated. Here\n˙J=ξj0˙Mais the angular momentum accretion rate, j0is the specific angular momentum of\nthe material captured by a black hole at the Bondi radius, and ξis the factor by which angular\nmomentum accretion rate is reduced due to inhomogeneities ( velocity and density gradients)\nand the magnetic viscosity in the accretion flow. The specific angular momentum carried by a\nmaterial captured by the black hole from turbulent Interste llar Medium (ISM) can be evaluated\nasj0=vt(Rt)R−1/3\ntR4/3\nG, wherevt(Rt) is the velocity of turbulent motions at the scale of Rt\nand the Kolmogorov spectrum of the turbulent motions is assu med (see e.g. [12], and references\ntherein). The circularization radius of the accretion flow i n this case can be expressed as\nRcirc=ξ2v2\ntR−2/3\ntR8/3\nG\nGMbh. (1)\nA formation of Keplerian accretion disk would be expected if Rcirc> κrRg, where Rg=\n2GMbh/c2is the gravitational radius of the black hole, κr=Rst/Rg, andRstis the radius\nof the last stable orbit around the black hole. Solving this i nequality for vrelyieldsvrel< v(0)\ncr,\nwhere\nv(0)\ncr≃690km/s×κ−3/16\nrm1/8\n6/parenleftbiggvt\n10km/s/parenrightbigg3/8/parenleftbiggRt\n1020cm/parenrightbigg−1/8\n. (2)\nHerem6isthemassoftheblackholeinunitsof106M⊙,andparameters vtandRtarenormalized\nfollowing [14]. The derived value of v(0)\ncrsignificantly exceeds the sound speed in ISM and thus,\na supermassive black hole within the non-magnetized accret ion flow scenario is expected to be\nsurrounded by a Keplerian accretion disk.\nAsablackholeisaccretingmaterialfromtheKepleriandisk itsgravitation energyisconverted\npredominantly into the kinetic and thermal energy of the acc reting material, which then can be\nconverted into the magnetic energy due to dynamo action. The pressure of the magnetic field\ngenerated in the disk? therefore, is limited to E(d)\nm(r)< ρ(r)v2\nk(r), where vk(r) = (GMbh/r)1/2\nis the Keplerian velocity. An influence of the field on the accr etion flow in this case is relatively\nsmall and does not lead to any significant changes in the flow dy namics. The disk remainsKeplerian and the accreting material approaches the black h ole on the viscous timescale. The\nscale of the magnetic field generated in the turbulent differen tially rotating Keplerian disk by the\ndynamoaction is limited tothe diskthickness (which repres ents thelargest scale of the turbulent\nmotions in the disk). The energy of the magnetic field is relea sed in the disk corona, which is\nformed as the field emerges from the disk due to the buoyancy in stability. The energy release\nprocess is associated with the magnetic reconnection which leads to heating and ejection of\nmaterial [5]. However, the kinetic luminosity of the ejecta is relatively small and the outflowing\nmaterial is non-collimated.\nExistence of collimated powerful jets cannot be explained w ithin this scenario unless some\nadditional assumptions are incorporated into the model. In particular, one can assume that the\njets are powered by the rotational energy of the black hole, w hich is released as the inner radius\nof the disk is approaching the last stable orbit. The ejected material can be self-collimated, or\n(which looks more reasonable) is collimated by the large-sc ale magnetic field of the disk. The\nfield in the latter case should be strong enough to collimate a powerful jet. This criterium is\ndifficult to satisfy if the large-scale field of the disk is prov ided by the small-scale magnetic\narches generated in the disk due to dynamo action. The pressu re of the magnetic field in this\nsituation is substantially smaller than the ram pressure of the accretion flow itself. It is more\nlikely that the large-scale field of the disk was initially pr esent in the material captured by the\nblack hole and has been amplified during the accretion proces s. In the next Section we show\nthat this assumption cannot be simply incorporated into the traditional accretion model. The\nmagnetic field in the spherical accretion flow increases rapi dly and prevents accreting material\nfrom forming a Keplerian disk.\n3. Magnetically controlled accretion scenario\nA situation in which vrel≈vwandβ=E(0)\nth/E(0)\nm∼1 can be realized if the material captured by\na black hole is supplied by the stellar wind of nearby stars. T he ram pressure of the material\nat the Bondi radius, E(0)\nr=ρ∞v2\nw, in this case significantly exceeds its thermal and magnetic\npressure and hence, the Alfv´ en velocity, vA=Bw/(4πρ)1/2, in the accreting material is much\nsmaller than the free-fall velocity. The time of the magneti c field annihilation in the accretion\nflow,\ntrec=r\nηmvA=η−1\nmtff/parenleftbiggvff\nvA/parenrightbigg\n, (3)\nunder these conditions significantly exceeds the dynamical (free-fall) time, tff=/parenleftbig\nr3/2GMbh/parenrightbig1/2,\nand the magnetic flux in the free-falling gas is conserved. He reBwis the field strength in the\naccretion flow and the efficiency parameter of the magnetic rec onnection ranges in the interval\n0.01–0.15 (see e.g. [11, 10]).\n3.1. Shvartsman radius\nThe magnetic field in the free-falling material is dominated by the radial component [19], which\nunder the condition of the magnetic flux conservation increa ses asBr(R)∼Bf(RG)(r/RG)−2\n[1]. The magnetic pressure in the accreting material, there fore, increases while approaching the\nblack hole as\nEm(r) =Em(RG)/parenleftbiggr\nRG/parenrightbigg−4\n, (4)\nand the ram pressure of the free-falling spherical flow is\nEram(r) =E(0)\nram/parenleftbiggr\nRG/parenrightbigg−5/2\n. (5)This indicates that the magnetic energy in the free-falling gas increases more rapidly than\nits kinetic energy, Em/Eram∝r−3/2, and hence, the gravitational energy of the black hole in\nthe scenario under consideration is converted predominant ly into the magnetic energy of the\naccreting material.\nA distance Rsh, at which the magnetic pressurein the accretion flow reaches its ram pressure,\ncan be evaluated by equating Em(Rsh) =Eram(Rsh). This yields [16]\nRsh=β−2/3/parenleftbiggVs\nVrel/parenrightbigg4/3\nRG=β−2/32GMbhV4/3\ns\nV10/3\nrel. (6)\nParameter Rsh(hereafter Shvartsman radius) represents a minimum distan ce from which the\naccretion process is fully controlled by the magnetic field o f the flow itself. The Alfv´ en velocity\nin the accretion flow at this distance reaches the free-fall v elocity. An accretion of homogeneous\ngas in which the magnetic flux is conserved inside Shvartsman radius is impossible. Otherwise,\nthe magnetic energy in the flow would exceed the gravitationa l energy, which contradicts the\nenergy conservation law (for discussion see [16]). Further accretion, therefore, can be realized\nonly on the timescale of the field dissipation, trec, which is significantly larger than the free-fall\ntime (see Eq. 3). This indicates that the initially free-fal ling accretion flow is decelerated by\nits own magnetic field at Rsh. The deceleration leads to formation of a shock in which the g as\nis heated up to a temperature Ts= (3/16)Tff(Rsh), where Tff(r) =GMbhmp/kBris the proton\nfree-fall temperature, mpis the proton mass and kBis the Boltzmann constant [9]. If cooling\nof the material in the region of flow deceleration is ineffectiv e a hot envelope surrounding the\nblack hole at the Shvartsman radius forms.\nRapid amplification of the magnetic field in the spherical flow as well as deceleration of the\nflow by its own magnetic field at the Shvartsman radius have bee n confirmed by the results of\nnumerical studies of magnetized spherical accretion onto a black hole [6, 7]. These calculations\nhave shown that the magnetized flow under the conditions of in terest is shock-heated at the\nShvartsman radius up to the adiabatic temperature. These au thors have considered further\naccretion under assumptions that the flow is radiatively ine fficient and heating of the flow\ndominates cooling. An overheating of material in this case c an lead to transition of the\naccretion flow into convective-dominated stage in which a po rtion of the accreting material\nis leaving the system in a form of turbulent jets and the mass a ccretion rate inside the region\nof the flow deceleration significantly decreases. Here we sho w, however, that MCA picture can\nbe constructed without these assumptions and a question abo ut the nature of energy source\nresponsible for the overheating of material (which is requi red for the flow to switch into the\nconvective-dominated phase) can be avoided.\n3.2. No Keplerian disk within MCA scenario\nBallistic trajectories of the free-falling spherical accr etion flow within MCA scenario are\ntruncated at the Shvartsman radius. The condition for the Ke plerian disk formation in this\ncase reads Rcirc≥Rsh. This inequality can be expressed using Eqs. (1) and (6) as vrel≤vmag\ncr,\nwhere\nvmag\ncr≃5×105cms−1β1/3ξ0.2m1/3\n6/parenleftBigvs\n10kms−1/parenrightBig−2/3/parenleftbiggVt\n10kms−1/parenrightbigg/parenleftbiggRt\n1020cm/parenrightbigg−1/3\n.(7)\nParameter ξ0.2=ξ/0.2 is normalized here to its maximum average value, which has b een derived\nin numerical studies of the accretion process within the non -magnetized spherical accretion flow\napproximation [13]. Since the derived value of vmag\ncris comparable or even smaller than the\nsound speed in the surrounding gas the angular momentum of th e accreting material at the\nShvartsman radius appears to be insufficient for the Kepleria n disk to form.3.3. Cooling of the accretion flow\nCooling of the accretion flow in the considered case is domina ted by the inverse Compton\nscattering of electrons on photons emitted in the vicinity o f the black hole. The Compton\ncooling time of the material at Rshcan be evaluated as [4],\ntc(Rsh) =3πmec2R2\nsh\n2σTLbh, (8)\nwheremeis the electron mass, σTis the Thomson cross-section and Lbhis the luminosity of the\nsource associated with the black hole. Cooling is dominatin g heating at the Shvartsman radius\niftc(Rsh)≤tff(Rsh). Solving this inequality yields vrel≥vccwhere\nvcc≃2×107β−1/5m3/5\n6L−3/5\n42/parenleftBigvs\n10kms−1/parenrightBig2/3\ncms−1, (9)\nandL42=Lbh/1042ergs−1. The value of vccis much smaller than typical wind velocity of\nmassive stars and is even comparable to the velocity of stell ar wind emitted by the red dwarfs.\nThis indicates that a stationary magnetically controlled a ccretion at the rate ˙Ma≈˙Mcis\nexpected if the material captured by the black hole is predom inantly supplied by the stellar\nwind of nearby stars. Compton cooling in this case prevents t he flow from switching into the\nconvective-dominated stage.\n3.4. Non-Keplerian slab\nThe accretion picture of a cold ( T < Ts) magnetized ( β <1) gas has been discussed in [2, 3]. It\nhas been shown that the material in this case tends to flow alon g the magnetic field lines and in\nthe region r≤Rshis accumulated in a dense non-Keplerian slab (see Fig.1 in [3 ]). The material\nin the slab is confined by the magnetic field of the flow itself an d its radial motion continues as\nthe field is annihilating. The accretion process in the slab, therefore, occurs on the timescale of\ntrec.\nThe magnetic pressure inside the Shvartsman radius increas es according to the energy\nconservation law as Em=Em(Rsh)(Rsh/r)5/2, where\nEm(Rsh) =˙Mc(2GMbh)1/2\n4πR5/2\nsh(10)\nis the magnetic pressure at the Shvartsman radius. This indi cates that the field strength in the\nvicinity of the black hole reaches the value\nB(Rg) = 20L1/2\n42m−1\n6kG. (11)\nSince the material is confined by the field in the slab its therm al pressure does not exceed\nthe magnetic pressure. The gas number density at the inner ra dius of the slab in this case can\nbe estimated as\nρsl≤1019cm−3L42m−2\n6T−1\n4, (12)\nwhereT4is the gas temperature at the inner radius of the slab in units of 104K. The thickness\nof the slab depends on the magnetic field configuration and in t he first approximation can be\nevaluated from continuity equation as\nhz(Rg)≃105cmη−1\n0.01m6T4, (13)\nwhereη0.01=ηm/0.01. It should be noted, that the thickness of the slab strongl y depends on\nthe field annihilation time, which can be evaluated from the s hortest timescale of the sourcevariability. Furthermore, we cannot discard a possibility that the slab is disintegrated by\ninterchangeinstabilitiesintoalargenumberoffilamentsc onnectedbythefieldlinesasitsketched\nin Fig.1 in [8]. Formation of jets in this case can be associat ed with interaction between the\nmagnetic arches connecting the filaments which leads to a Z-p inch field configuration over the\nslab. The process of energy release and plasma ejection in th is configuration will be discussed\nin a forthcoming paper.\n4. Conclusions\nBlack holes within the non-magnetized accretion flow scenar io are expected to be surrounded\nby Keplerian disks. The scale of the magnetic field generated in the disk due to dynamo\naction is comparable to the disk thickness and the magnetic p ressure associated with this field\ninsignificantly contributes the total power of the disk. A fo rmation of a strong large-scale\nmagnetic field in the accretion flow can be expected if the mate rial captured by the black hole\nis magnetized. The behavior of the accreting material in thi s case is strongly affected by its\nmagnetic field. The flow is decelerated by the magnetic field at the Shvartsman radius and\nmoves towards the black hole on the timescale of the magnetic field annihilation. Formation of\na homogeneous Keplerian disk within this Magnetically Cont rolled Accretion (MCA) scenario\ndoes not occur. Instead, the accreting material is accumula ted in a non-Keplerian dense slab.\nThe material in the slab is confined by its own magnetic field an d moves towards the black hole\nas the magnetic field is annihilating. Interchange instabil ities of the slab may lead to formation\nof the Z-pinch type configuration of the magnetic field in whic h the accretion power is released\nin the form of jets and high energy emission.\nAcknowledgments\nWe would like to thank G.S.Bisnovatyi-Kogan, M.V.Medvedev and P.L.Biermann for useful\ndiscussions. Nazar Ikhsanov is grateful to Alexander von Hu mboldt Foundation for support\nin attending the conference and Michael Kramer for useful di scussions and kind hospitality at\nMax-Planck Institute of Radio Astronomy in Bonn. The resear ch has been partly supported by\nthe Program of RAS Presidium N19, NSH-3645.2010.2, and by th e grant “Infrastructure” of\nIsrael Ministry of Science.\nReferences\n[1] Bisnovatyi-Kogan, G.S., Fridman, A.M., 1970, Soviet Astronomy ,13, 566–568\n[2] Bisnovatyi-Kogan, G.S., Ruzmaikin, A.A. 1974, Astrophys. and Space Sci. ,28, 45–59\n[3] Bisnovatyi-Kogan, G.S., Ruzmaikin, A.A. 1976, Astrophys. and Space Sci. ,42, 401–424\n[4] Elsner R.F., Lamb F.K. 1977, Astrophys. J. ,215, 897–913\n[5] Galeev, A.A., Rosner, R., Vaiana, G.S. 1979, Astrophys. J. ,229, 318–326\n[6] Igumenshchev, I.V., Narayan, R., Abramowicz, M.A. 2003 ,Astrophys. J. ,592, 1042–1059\n[7] Igumenshchev, I.V. 2006, Astrophys. J. ,649, 361–372\n[8] Ikhsanov, N.R., Pustil’nik, L.A. 1994, Astrophys. J. Suppl. ,90, 959–961\n[9] Lamb, F.K., Fabian, A.C., Pringle, J.E., Lamb, D.Q. 1977 ,Astrophys. J. ,217, 197–212\n[10] Noglik, J.B., Walsh, R.W., Ireland, J. 2005, Astron. Astrophys. ,441, 353–360\n[11] Parker, E.N. 1971, Astrophys. J. ,163, 279–285\n[12] Prokhorov, M.E., Popov, S.B., and Khoperskov, A.V. 200 2,Astron. Astrophys. ,3811000–1006\n[13] Ruffert, M. 1999, Astron. Astrophys. ,346, 861–877\n[14] Ruzmaikin, A.A., Sokolov, D.D., and Shukurov, A.M. 199 8,Nature,336, 341–347\n[15] Shakura, N.I. 1973, Soviet Astronomy ,16, 756–762\n[16] Shvartsman, V.F. 1971, Soviet Astronomy ,15, 377–384\n[17] Strumik, M., Ben-Jaffel, L., Ratkiewicz, R., Grygorczu k, J. 2011, Astrophys. J. ,741, 6\n[18] Walder, R., Folini, D., Meynet, G. 2011, Space Sci. Rev. ,125, in press\n[19] Zel’dovich, Ya.B., Shakura, N.I. 1969, Soviet Astronomy ,13, 175–183"    },    {        "title": "1211.5187v1.Hydrogenated_Bilayer_Wurtzite_SiC_Nanofilms__A_Two_Dimensional_Bipolar_Magnetic_Semiconductor_Material.pdf",        "content": " \n \nHydrogenated Bilayer Wurtzite Si C Nanofilms: A Two-Dimensional \nBipolar Magnetic Se miconductor Material \nLong Yuan, Zhenyu Li, Jinlong Yang* \n \nHefei National Laboratory for Physical Sciences at Microscale, University of Science and Technol ogy of China, Hefei, 230026, Ch ina 5 \n \nRecently, a new kind of spintronics materials, bipolar magnetic semiconductor (BMS), has been proposed.  \nThe spin polarization of BMS can be conveniently c ontrolled by a gate voltage , which makes it very \nattractive in device engineering. Now, the main challe nge is finding more BMS materials. In this article, \nwe propose that hydrogenated wurtzite SiC nanof ilm is a two-dimensiona l BMS material. Its BMS 10 \ncharacter is very robust under the effect  of strain, substrate, or even a st rong electric field. The proposed \ntwo-dimensional BMS mate rial paves the way to use this promising new material in an integrated circuit. \n \n1.  Introduction \nSemiconductor-based spintronics recently have attracted lots of 15 \nattentions, which seeks to utilize the spin degree of freedom of \nthe carriers and leads to a revolution in the current electronic \ninformation processing technology.1 There are two big challenges \nin spintronics. One is generating spin polarized carriers, and the \nother is manipulating it. The first challenge can be met if we have 20 \na kind of materials, where its one spin channel is metallic while \nthe other is semiconducting. This kind  of materials is called half \nmetal, and various half-metal lic nanostructures have been \nproposed in previous study.2-8 \nWith totally spin polarized carriers provided by half metallic 25 \nmaterials, to manipulate the spin polarization direction, typically \nan external magnetic field is required. However, we notice that an electric control of spin is more attractive, since electric field can \nbe easily applied locally. Recently,  such a goal has been realized \nin a newly proposed spintronic s material, bi polar magnetic \n30 \nsemiconductor (BMS).9 In BMS, the valence and conduction \nbands possess opposite spin polarization when approaching the \nFermi level. Therefore, completely spin-polarized currents with reversible spin polarization can be created and controlled simply \nby applying a gate voltage. A prototype one dimensional (1D) \n35 \nBMS material has been proposed previously.9 The remain open \nquestion is if the BMS character can widely exist, for example, in \ntwo dimensional (2D) materials. For applications in integrated \ncircuits, a two-dimensional (2D) BM S material is more desirable. \nHere, we report a study on hydroge nated wurtzite SiC nanofilm, 40 \nwhich is predicted to be a 2D BMS material. There are several \nmerits with this new BMS material . First of all, it is transition \nmetal (TM) free. Traitionally, magnetism in semiconductors is typically introduced by doping magnetic impurities,10 such as \nTMs. However, considering the spin-scattering problem in the 45 \nelectron transmission, TM-free mate rials are more promising. On \nthe other hand, compared with the extensively studied 2D material, graphene or silicon,\n11-17 SiC is attractive for spintronics \napplications due to the larger spin-orbit interaction of Si than \nC.18-20 Thirdly, the material proposed in this study is expected to 50 \nbe readily synthesized in expe riment. Actually , graphitic SiC \nsheet has been formed by sonication of wurtzite SiC, 21 and our \nfirst-principles molecular dyna mics (MD) simulations suggest \nthat the graphitic-like SiC bilaye r could be easily transformed \nback into the wurtzite structure via surface hydrogenation. 55 \nTherefore, we provide a feasible way to control the spin \npolarization of carriers in two-di mensional materials by electric \nmeans.  \n2.  Computational methods \nAll geometry optimizat ions and electronic structures calculations 60 \nwere performed by spin-polarized  density functional theory (DFT) \nas implemented in the Vienna ab initio  Simulation Package \n(VASP). The project-augmented wave method for core-valence \ninteraction and the ge neralized gradient a pproximation (GGA) of \nthe Perdew-Burke-Erzerhof (PBE) form for the exchange-65 \ncorrelation function was employed.22-25 A kinetic energy cutoff of \n500 eV was chosen in the plane- wave expansion.  A large value \n(15 Å) of the vacuum region was used to avoid the interaction \nbetween two adjacent periodic images. Reciprocal space was represented by Monkhorst-Pack  special k-point scheme.\n26 The 70 \nBrillouin zone was sampled by a set of 11×11×1 k-points for the \ngeometry optimization and 21×21× 1 k-points for the static total  \n \n \nFig 1. (a) Graphitic-like SiC bilayers with  three types of stacking orderings (A, B and C), (b) Total energy for the A, B, C st acking arrangements as a \nfunction of distance between the two layers, in eV/atom. \nenergy calculations. To investig ate the magnetic coupling of the \nhydrogenated nanofilms, we perfor med calculations using a 2×2 5 \nsupercell. The Monkhorst-Pack special k-point of 6×6×1 and \n11×11×1 were employed for the ge ometry optimizat ion and static \ntotal energy calculations. The structure was relaxed using \nconjugate gradient scheme with out any symmetry constraints and \nthe convergence of energy and force was set to 1×10-4 eV and 10 \n0.01 eV/Å. The accuracy of our methods was tested by calculating the C-Si bond length an d band gap of pristine SiC \nsheet. Our calculated results are 1.789 Å and 2.54 eV, in good \nagreement with previous theoretical results.\n19, 27 \nIt is well known that GGA usually fa ils to accurately describe the 15 \nvan der Waals (vdW) interactions. So, the empirical correction \nmethod of Grimme (DFT+D2) was employed for this part of \ninteraction.28, 29 Standard parameters of the dispersion \ncoefficients C 6 (0.14, 1.75, and 9.230 J nm6 mol-1, for H, C, and \nSi, respectively), vdW radii (1.001, 1.452, and 1.716 Å ), cutoff  20 \nradius (30.0 Å), global scaling factor (0.75 Å), and damping \nfactor d (20.0 Å) have been used. Local density approximation \n(LDA) was also used to compute bilayer distance and agreed well \nwith the PBE (with vdW correction) results. The external electric field, as implemented in VASP code, was \n25 \nintroduced by adding an planar dipole layer in the middle of \nvacuum part in the periodic supercell.30 Since GGA usually \nunderestimates band gap, we also  performed test calculations \nwith the hybrid Heyd-Scuseri a-Ernzerhof (HSE) functional.31, 32 \nAlthough band gap increased with  HSE functiona l, the main 30 \nresults reported here remained unchanged. \nMD simulations, as implemented in the VASP code, were \nemployed to study the transformation process and thermal stability of the hydrogenated wurt zite SiC nanofilms. A kinetic \nenergy cutoff of 400 eV and PBE functional (with vdW \n35 \ncorrection) were chosen. MD si mulations were performed in NVT ensemble with a 4×4 supercell.  2×2×1 k-points were used to \nsample the 2D Brillouin zone. MD simulations at 200K (or 450K) \nlasted for 2 ps (or 10 ps) with a time step of 1.0 fs (or 2.0 fs) were performed to investigate the transformation process (or thermal \n40 \nstability). The temperature was controlled by using the Nose-Hoover method.\n33 The climbing image nudged elastic band (CI-\nNEB) method was used for transition state search.34, 35 Four or \nfive images were inserted between the initial and final states. \nImages were optimized until the energy and force on each atom 45 \nwere less than 1×10-4 eV and 0.02 eV/Å. \n3. Results and discussion \nIn SiC sheets, hydrogenation can be completed by absorbing H \natoms on C site or Si site. A 2×2 supercell consisting of four unit \ncells in the SiC  monolayer  were constructed to investigate the 50 \nenergetically favorable absorbi ng site. For this purpose, we \ndefined the formation energi es of semihydrogenated SiC \nmonolayer as \nEf = (EH–SiC − ESiC − mμH)/N \nwhere EH–SiC, ESiC are the energies of the semihydrogenated SiC 55 \nsheet and pristine SiC sheet, respectively. We choose μH as the \nenergy of a H atom. m, N are the numbers of hydrogen atoms and \ntotal number of atoms in the supercell. The optimized bond \nlength of C-H and Si-H are 1.118 and 1.515 Å, respectively. The \nformation energies of the two semihydrogenated SiC sheets, 60 \nlabeled as H-CSi and H-SiC, are -0.565 and -0.440 eV/atom, \nrespectively. Our results are consistent with previous DFT \ncomputations.36 The formation energy of H-CSi is smaller than \nH-SiC, indicating that H atom prefers to absorb on the C site.  Next, we examine three types of stacking arrangements in the  \n65 \ngraphitic-like SiC multilayered structures: (A) C-Si ordering, (B)   \nTable 1  Calculated energies and distances for the  three types of stacking \norderings (A, B and C) by using PBE(with vdW correction) and LDA \nfunctional, respectively, in eV/atom, Å. \n PBE (with vdW correction) LDA \n Energy Bilayer distance Energy        Bilayer distance\nA -7.157  3.221 -7.714 3.205 \nB -7.142 3.396 -7.704 3.407 \nC -7.124 3.889 -7.687 3.981 \nSi-Si ordering, and (C) C-C ordering, as shown in Figure 1a. \nBased on our calculations, C-Si or dering is the most energetically 5 \nfavorable stacking arrangement, wh ich also agrees with previous \ntheoretical computations.37 The interlayer spacing value is 3.221 \nÅ. LDA calculations (Tab le 1) also leads to similar results, with \nan interlayer spacing of 3.205 Å, slightly smaller than the PBE \n(with vdW correction) result.  10 \nMD simulations are performed to study hydrogenation on the top layer at C sites of the bilayer SiC. Four snapshots in the 2 ps trajectory at 200 K are shown in Figure 2a. In the initial state, the \nSiC sheets remain planar structur es. At the intermediate stage (I), \nstrong σ-bond between C atom and H atom is formed and the \n15 \noriginal planar sp2-hybridized SiC structure is broken, leaving \nunpaired electrons on Si atoms. The hydrogenated top layer \nexhibits a buckling structure and the bottom layer remains intact. \nThen, at the intermediate  stage (II), due to in terlayer interaction, \nthe bottom layer gradually exhib its the buckling structure. The 20 distance between the two layers becomes shorter. At last, as \nshown in the final stage, the interlayer C-Si bond is formed and \nthe transformation is completed. The formed hydrogenated \nwurtzite nanofilms can be very stable during a subsequent 10 ps MD simulation at 450 K.  \n25 \nWe name the hydrogenated wurt zite SiC bilayer as H-(CSi) 2. The \noptimized structure at 0 K is s hown in Fig 2b. C atoms and Si \natoms in the first layer become fully sp3-hybridized. In the second \nlayer, only the C atoms are sp3-hybridized, the Si atoms remain \nsp2-hybridized. The optimized lattice  parameter is 3.102 Å, slight 30 \nlarger than the pristine SiC sheet. The length of C-H bond and \ninterlayer C-Si bond are 1.108 Å and 1.899 Å, respectively. The \nminimum energy path (MEP) of the hydrogenation is shown in Fig 2d. The system only need to overcome a small barrier of 0.03 \neV/atom to complete the transformation and the formed wurtzite \n35 \nnanofilm is more energetically favorable by about 0.27 eV/atom. \nTherefore, the hydrogenated wurtzite nanofilm should be feasible \nto be synthesized in experiment under mild conditions.  \nTo further investigate the structural stability of the hydrogenated nanofilms, another formation energy is defined as \n40 \nEf = (Enanofilm  − ESiC − mμH)/n \nwhere Enanofilm , ESiC are the energies of the hydrogenated \nnanofilms, pristine SiC multilaye rs, respectively. We choose μH \nas the energy of a H atom. m, n are the numbers of H atoms and \ntotal atoms in the supercell, respectively. The computed 45 \n \n \nFig 2.  Formation of the hydrogenated wurtzite na nofilm from the semihydrogenated SiC bilayer.  (a) Snapshots of th e initial, intermedi ate, and final stage \nof the transformation. (b) Op timized geometry of H-(CSi) 2 at 0 K. (c) Spin density distribution of H-(CSi) 2 (isosurface value: 0.05 e/Å3). (d) Calculated \nMEP of the transformation, insets show the atomic structures  of initial (I), transition (T), a nd final (F) states along the ene rgy path.  50 \n  \n \n \nFig 3.  (a) Ferromagnetic and (b) an tiferromagnetic configurations.  Green and pink are used to indicate the positiv e and negative signs of the spin density \n(isosurface value: 0.05 e/Å3), respectively. \nformation energy of H-(CSi) 2 nanofilm is -0.592 eV/atom. A \nnegative value indicates an exot hermic transformation process, 5 \nproviding more evidence for the thermodynamics stability.  \nAs we mentioned, the Si atoms in the second layer are still \nremaining sp2-hybridized, leaving the electrons in the \nunhydrogenated Si atoms locali zed and unpaired, which gives \nabout 1 μB magnetic moment per unit cell,  as shown in Fig 2c. In 10 \norder to identify the preferred magnetic coupling of these moments, three kinds of magnetic configurations were considered: \n(1) ferromagnetic (FM) coupling; (2) antiferromagnetic (AFM) coupling; (3) nonmagnetic (NM) c oupling. The first two cases are \nas shown in Figure 3. The calcul ated results show that the FM \n15 \nstate is energetically more favorable than the AFM and NM states. \nFM coupling is 21 and 273 meV per unit cell lower in energy \nthan AFM and NM coupling.  \n \n 20 \nFig 4. Electronic band structures of H-(CSi) 2 based on (a) PBE functional and (b) HSE func tional. The Fermi level is set at zero. \n \n Fig 5.  Band structures of H-(CSi) 2 with doping concentrations of (a) 0.02 electron per atom and (b) 0.03 hole per atom. The Fermi level is set at zero.  \n \nAs shown in Figure 4a, H-(CSi) 2 is a ferromagnetic \nsemiconductor with a small band gap of 0.834 eV. Our test \ncalculation with HSE functional also  gives similar band structure \n(Figure 4b), with an enlarged band gap of 1.874 eV. Importantly, the spin polarizations of H-(CSi)\n2 are different for the valence 5 \nband (VB) and the conduction band (CB). Therefore, it is a typical BMS material. Half-met allicity with opposite spin \npolarization can be obtained vi a electron or hole dopping, as \nshown in Figure 5. Take the do ping level of 0.03 hole per atom \nfor example, the Fermi level m oves down, crossing the VB. The \n10 \nspin-up channel becomes gapless, while the spin-down channel is \nstill insulating, with a band ga p about 2 eV. The FM coupling is \nstill energetically favorable under electron or hole doping. For example, the system with 0. 03 hole doping per atom favors the \nFM state by 16 meV per unit compared to the AFM state. The net \n15 \nmagnetic moment becomes 0.85 μB per unit cell, indicating that \nthe doped hole is mainly distri buted on the unhydrogenated Si \natoms.  \nAn electronic device may under an electric field. So, we first \ncheck the effect of external field to H-(CSi) 2. The electric field 20 \nwas added perpendicularly to th e nanofilm, with a strength \nranging from -0.8 to 0.8 V/angstr om. The positive direction of the electric field is defined along the z axis as shown in Figure 6. \nUnder an electric field as strong  as 0.4 V/angstrom, the band gap \nis only slightly affected by the field. Therefore, the H-(CSi) 2 is a 25 \nrobust BMS material even under strong electric field. We also \nobserved that the band gap of the spin-up channel decrease \nrapidly when the electric field is larger than 0.2 V/angstrom. This \nis an effect of the nearly free electron (NFE) state,38 which in \nmarked in blue in Figure 6. The NFE state exists widely in the 30 \nlow dimensional materials,39-42 and it can be easily shifted with \nelectrostatic potential. As a bypr oduct, an occupied NFE state is \nrealized in our system, which can be used as ideal transport \nchannels, when the electric field is larger than 0.6 v/angstrom.  \nOn the other hand, the hydrogenated wurtzite nanofilm should be 35 \non a suitable substrate in applic ations. A substrate can apply a \nstress on the material. Then, it is interesting to see if the BMS \nelectronic structure is robust under external strain. To answer this \nquestion, we applied external stress to H-(CSi) 2, which is defined \nas ε = (c 1 − c0)/c0, where c 1 and c 0 are the unit cell parameters 40 \nwith and without deformation. The tensile or compression strain \nis uniformly applied along both in-p lane lattice vectors. As shown \nin Figure 7, the BMS characters in H-(CSi) 2 are well survived \nunder external strains of ±3%. Besi des, we have also checked that  \n 45 \nFig 6.  (a) Electric field induced ener gy gap modulation of H-(CSi) 2, with the positive direction denoted by the red arrow. Band structures of H-(CSi) 2 \nunder an electric field of (b) 0.0 V/angstrom , (c) 0.4 V/angstrom, and (d ) 0.6 V/angstrom. The states in blue line are the near ly free electron states. The  \nFermi level is set at zero. \n \n \nFig 7.  Electronic band structures of H-(CSi) 2 under external strain. The Fe rmi level is set at zero. \n 5  \n \nFig 8. The initial and optimized geometry, the band structures of H-(CSi) 2 nanofilm on a hydrogenated (0001) SiC substr ate. The Fermi level is set at zero.  \n \nthe FM coupling is still the en ergetically favorable magnetic 10 \nconfiguration under these two st ress levels. For example, the \nenergy of FM state is 12 meV per unit cell lower than that of the AFM state at a stress level of +3%. The energy difference \nbecomes smaller compared to H-(CSi)\n2 without strain. This is \nreasonable, since the distance be tween two neighboring magnetic 15 \nSi atoms is increased under a tensile stress, and the exchange \ncoupling is thus efficiently weakened. \nWe have also tested the system of semihydrogenated SiC bilayer on a real substrate, the hydrog enated (0001) SiC surface. After \nDFT+D2 geometry optimization, the distance between the SiC \n20 \nbilayer and substrate is 3.01 Å. For this system, we still get 1 μB \nmagnetic moment per unit cell.  More importantly, the BMS \ncharacter of the electronic struct ure is still kept, as shown in \nFigure 8. On the substrate, th e band gap between the two spin \nchannel becomes very small (0.136 eV), which makes the gate  25 \n voltage based spin polarization control very feasible. \n4.  Conclusion In summary, based on first-princi ples calculations, we have \nproposed that hydrogenated SiC bi layer will keep the wurtzite 30 \nstructure and it is a 2D TM-fr ee BMS material, which could \nintroduce half-metallicity with  opposite spin polarization via \nelectron or hole dopping possibly realized by a simple gate \nvoltage control. This BMS mate rial is robust under moderate \nexternal electric  field and under relatively high level of external 35 \nstrain possibly induced by a substr ate. Our results thus pave the \nway to spintronics application of the promising new BMS \nmaterial. \nAcknowledgements.  \nThis work is partially suppor ted by the National Key Basic 40 \nResearch Program (2011CB921404), by NSFC (21121003, \n91021004, 20933006), and by USTCSCC, SCCAS, Tianjin, and Shanghai Supercomputer Centers.  \n \nNotes and references 45 \n1.   S. A. Wolf, D. D. Awschalom, R. Buhrman, J. Daughton, S. Molnar, \nM. Roukes, A. Chtchelkanova, D. Treger,  Science.  2001, 294, 1488.   \n2.    Y.-W. Son, M. L. Cohen, S. G. Louie, Nature. 2006, 444, 347. \n3.   H. J. Xiang, J. L. Yang, J. G. Hou, Q. S. Zhu,  J. Am. Chem. Soc.  \n2006, 128,  2310.  \n4.   E. J. Kan, Z. Y. Li, J. L. Yang, J. G. Hou,  J. Am. Chem. Soc.  2008, \n130, 4224.  5 \n5.   Z. H. Zhang and W. L. Guo,  J. Am. Chem. Soc.  2009, 131, 6874.  \n6.    W. Chen, Y. Li, G. Yu, S. Zhang, Z. Zhou, Z. Chen, J. Am.  Chem. \nSoc. 2010, 132, 1699.  \n7.    J. Zhou and Q. Sun, J. Am. Chem. Soc.  2011, 133, 15113.  \n8.    E. J. Kan, W. Hu, C. Y, Xiao, R. F. Lu, K. M. Deng, J.  L. Yang, H. B. 10 \nSu, J. Am. Chem. Soc. 2012, 134, 5718.  \n9.   X. X. Li, X. J. Wu, Z. Y. Li, J. L. Yang, J. G. Hou,  Nanoscale , 2012,4, \n5680. \n10.  K. Sato, L. Bergqvist, J. Kudrnovsky, P. H. Dederichs, O. Eriksson, I. \nTurek, B. Sanyal, G. Bouzerar, H. Katayama-Yoshida, V. A. Dinh, T. 15 \nFukushima, H. Kizaki, R. Zeller, Rev. Mod. Phys.  2010, 82, 1633.  \n11. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. \nV. Dubonos, I. V. Grigorieva, A. A. Filrsov, Science 2004,  306, 666.  \n12. K. S. Novoselov, A. K. Geim, S.  V. Morozov, D. Jiang, M. I. \nKatsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Filrsov,  Nature , 20 \n2005, 438, 197..  \n13. T. Morishita, S. P. Russo, I. K. Snook, M. J. S. Spencer, K. Nishio, \nand M. Mikami.  Phys. Rev. B. , 2010, 82, 045419.  \n14.  B. Feng, Z. Ding, S. Meng, Y. Yao, X. He, P. Cheng, L. Chen, and K. \nWu,  Nano Lett.  2012, 12, 3507. 25 \n15. L. A. Chernozatonskii, P. B. Sorokin, A. G. Kvashnin and D. G. \nKvashnin,  JETP Letters. , 2009, 90, 134. \n16.  D. K. Samarakonn and X.-Q. Wang, ACS Nano , 2010, 4, 4126. \n17.   L. Yuan, Z. Li, J. L. Yang  and J. G. Hou. Phys. Chem. Chem. Phys. , \n2012, 14, 8179. 30 \n18.  H. C. Hsueh, G. Y. Guo, S. G. Louie. Phys. Rev. B.  2011, 84, 085404 \n1 9 .   J .  C .  G a r c i a ,  D .  B .  d e  L i m a ,  L .  V .  C .  A s s a l i ,  J .  F .  J u s t o ,  J. Phys. \nChem. C.  2011, 115, 13242. \n20.   T. Lu, X. Liao, H. Wang, J. Zheng, J. Mater. Chem.  2012, 22, 10062.  \n21.   S. S. Lin,  J. Phys. Chem. C.  2012, 116, 3951. 35 \n22.   P. E. Blochl, Phys. Rev. B . 1994, 50, 17953.  \n23.   J. P. Perdew, Y. Wang,  Phys. Rev. B . 1992, 45, 13244.  \n24.   G. Kresse, D. Joubert, Phys. Rev. B . 1999, 59, 1758. \n25.   J. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett.  1996, 77, 3865. \n26.   H. J. Monkhorst, J. D. Pack,  Phys. Rev. B. 1976, 13, 5188.  40 \n27.   L. Sun, Y. Li, Z. Y. Li, Q. Li, Z. Zhou, Z. Chen, J. L. Yang, J. G. \nHou,   J. Chem. Phys.  2008, 129, 174114. \n28     S. Grimme, J. Comput. Chem.  2006, 27, 1787.  \n29.   T. Bucko, J. Hafner, S. Lebegue, J. G. Angyan, J. Phys. Chem. A . \n2010, 114, 11814.  45 \n30.    J. Neugebauer and M. Scheffler.  Phys. Rev. B . 1992, 46, 16067.  \n31.    J. Heyed, G. E. Scuseria,  J. Chem. Phys. 2004, 121, 1187.  \n32.   J. Heyed, J. E. Peralta, G. E. Scuseria, J. Chem. Phys. 2005, 123, \n174101.  \n33.   G. J. Martyna, M. L. Klein, M. E. Tuckerman,  J. Chem. Phys . 1992, 50 \n97, 2635.  \n34.   G. Henkelman and H. A. Jónsson,  J. Chem. Phys.  2000, 113, 9978.  \n35.   G. Henkelman, B. P. Uberuaga, H. A. Jónsson, J. Chem. Phys.  2000, \n113, 9901.  \n36.   B. Xu, J. Yin, Y. D. Xia, X. G. Wan and Z. G. Liu, Appl. Phys. Lett.  55 \n2010, 96, 143111. \n37.   M. Yu, C. S. Jayanthi and S. Y. Wu, Phys. Rev. B . 2010, 82, 075407.  \n38.   E. R. Margine, V. H. Crespi, Phys. Rev. Lett.  2006, 96, 196803.  \n39.  S. L. Hu, J. Zhao, Y. D. Jin, J. L. Yang, H. Petek and J. G. Hou,  \nNano Lett.  2010, 10, 4830.  60 \n40.   Z. H. Zhang  and W. L. Guo,  Phys. Rev. B . 2008, 77, 075403.  \n41.  Z. H. Zhang, X. C. Zeng and W. L. Guo, J. Am. Chem. Soc.  2011, \n133, 14831.  \n42.   N. Lu, Z. Y. Li and J. L. Yang, J. Phys. Chem. C. 2009, 113, 16741. \n 65 "    },    {        "title": "1212.4997v1.Magnetic_properties_of_the_RbNd_WO4_2_single_crystal.pdf",        "content": "Magnetic properties of the RbNd(WO 4)2 single crystal \n \nM.T.Borowiec1*, E.Zubov2, T.Zayarnyuk1, M.Barański1. \n1Institute of Physics, Polis h Academy of Sciences, al.L otników 32/46, 02-668 Warsaw, \nPoland. \n2A. A. Galkin Donetsk Physic-Techn ical Institute, Donetsk, Ukraine. \n \nAbstract   \nThe magnetic investigations as a function of temperature and ma gnetic field for the rubidium \nneodymium double tungstate RbNd(WO 4)2 single crystal have been performed. The \nmagnetization was measured in the temperature range from 4.2  to 100 K and for the magnetic \nfield up to 1.5 T. The crystal field and exchange parameters were found. \n \nPACS: 75.40.Cx; 75.50.Ee; 75.10.b Keywords:  rare earth double tungsta te, magnetization, anisotropy. \n \n* Corresponding author. \nE-mail: borow@ifpan.edu.pl  \n \n \n1. Introduction \n \nThe rubidium neodymium tungstate RbNd(WO 4)2 (RbNdW) is the representative of the \nfamily of alkaline (A) and rare ea rth (Re) double tungstates ARe(WO 4)2 (AReW). RbNdW \nbelongs to the monoclinic system with space group C2/c; which is isostructural with -\nKY(WO 4)2 [1]. This crystal is usually grown by high temperature solution method in order to \nobtain the low temperature monoclinic phase. At  present, the AReW tungstates having the \nlow-symmetric (e.g., monoclinic) cr ystalline structure and the atom arrangements in forms of \nchains or layers are intensively studied. Struct ural, optical and magnetic investigations of the \nKDyW, KHoW, KErW and RbDyW compounds were performed earlier [2]. Many of them \nshow complicated structural phase transitions  (SPT), caused by the cooperative Jahn–Teller \neffect (CJTE), and magnetic phase transitions.  \n The rubidium neodymium double tungstate, was also studied, especially its structural \nand spectroscopic properties [1].   In this paper, we show the new results of magnetization measurements for the \nrubidium neodymium double tungstate RbNd(WO 4)2 (RbNdW) single crystal. \n \n2. Magnetic properties of RbNd(WO 4)2 \n The temperature, magnetic field and a ngular magnetization dependences of the \nRbNd(WO 4)2 single crystal were inves tigated using the vibrating sample magnetometer (PAR \nModel 450) in a temperature range from 4.2 to 100 K for magnetic field up to 1.5 T. The field \nwas applied both in the ac plane and along the b-axis.  \nThe electron configuration of Nd3+ is 4f3. In the crystal field of monoclinic symmetry the \nground multiplet 4I9/2 splits into five Kramers doublets.  \nAn angular dependence of magnetization has allowed to determine the magnetic x and z-axes, \nwhich correspond to the directions of minimal and maximal values of magnetization in the ac \ncrystallographic plane,  respectively (fig. 1). The angle between c- and z-axes in clockwise \ndirection is equal to 86°  and the angle between a- and x-axes is equal to 46°. The third main y \nmagnetic axis is parallel to the second-order axis C 2 and coincides with the crystallographic b-\naxis perpendicular to the ac plane. \n \n0.000360.001890.00390.00650.008690.010230.01121\n0306090\n120\n150\n180\n210\n240\n2703003300.00036\n0.00189\n0.00390.0065\n0.00869\n0.010230.01121c\nRbNd(WO4)2\n \nFig. 1. The angular dependence of magnetization for RbNd(WO 4)2  single crystal.  \n \nThe magnetic field dependences of magnetization M i both along all magnetic axes and along \nthe x, y and z crystal directions do not display the magnetization saturation in temperature interval from 4.2 to 100 K and in magnetic field up to 1.45 T (fig. 2), that it is characteristic \nfor paramagnet.  \n-10 -5 0 5 10-3000-2000-10000100020003000\n  [emu/mol]\nH[ kOe] along x axis\n along y axis\n along z axis\n \nFig. 2. The magnetic field dependences of magnetiza tion along three magnetic axis at  T=6 K.  \n \nFor a weak magnetic field H we may use linear relation for susceptibility ( ) /iiTM H . The \nexperimental temperature dependences ( )iT  were analyzed using the Curie-Weiss law: \n0i\nii\niC\nT                              (1) \nGeneral fitting was used for finding the parameters : 0i(temperature independent part of \nsusceptibility), the Curie constant Ci = N A (Bgi)2J(J+1)/3k B  and i (paramagnetic \ntemperature)  (see table 1).  \n Table 1. The fittig parameters for the Curie-Weiss law. \n χ\n0i C i g i θi \nH||a H=0.125 T 2.7·10-3emu/mol 1.161 emu·K/mol 3.52 -105.13 K \nH||b H=0.1 T 1.06·10-3emu/mol 5.55 emu·K/mol 7.69 -101.1 K \nH||c H=0.1 T 3.03·10-3emu/mol 1.13 emu·K/mol 3.59 -0.654 K \n \n The results of fitting are also presented in  Fig. 3(a,b,c). The paramagnetic temperature \nhas a large value along the x and y directions. \n10 20 30 40 50 60 70 80 90 100020406080100120\n  \n experiment along axis x\n general fitting\na [mol/emu]\nT [K]\n  10 20 30 40 50 60 70 80 90 1000102030405060\n  \n experiment along axis y\n general fitting\nb [mol/emu]\nT [K]\n \n \n0 1 02 03 04 05 06 07 08 09 0 1 0 0010203040506070\n  \n experiment along axis z\n general fitting\nc [mol/emu]\nT [K]\n \nFig. 3 abc. The temperature dependences of inve rse susceptibility along three magnetic axes: \npoints (experiment) and line (theory).   The obtained values of paramagnetic Curie temperature were used to find the crystal \nfield parameters. For the C\n2 symmetry of Nd3+ site ˆ\ncrH involves 15 non-zero crystal field \nparameters because for the z-axis parallel to the C 2 axis the crystal field parameters with the \nodd q are equal to zero. Following to Ref. [3] we  shall restrict consideration only to second \norder crystal field parameters. Our system has the symmetry axis of the second order that excl udes in crystal field \nHamiltonian the Stevens operators with odd powers. Acording to that the Hamiltonian has the following form with the first nonvanishing terms:  \n                                     \n 02 2 2 2\n.2 2ˆ 3( 1 )cr z x yH BJJ J B JJ                                              (2) We attempted to estimate crystal field parameters 0\n2B and 2\n2B. At  high temperatures, the \nrelations between the crystal field parameters and crystal field contribution in paramagnetic \ntemperatures icr in the i direction have a form \n                                              \n.0 2\n22\n.0 2\n22\n.0\n21\n2\n1\n2cr\nx\ncr\ny\ncr\nzB B\nB B\nB\n\n\n\n      ,                                                 (3) \nwhere 121 ( 23 )5JJ [3]. For J = 9/2   = 96/5. In our case, the x, y and z axes \ncoincide with the c, a and b axes, respectively. Then the paramagnetic temperature i  can be \nexpressed  as [3] \n                                                   ..cr exch\nii i  ,                                                               (4) \nwhere the exchange contribution in pa ramagnetic temperature is equal to \n.23 3(1 ) ( 0 ) ( 0 )32exchJJ J J . The J(0)=z* J, where z -number of the nearest neighbours of \nthe rare-earth ion. J is the parameter of the pair exchange interaction. \nSince the contribution of crys tal field in sum of paramagnetic temperatures along the 3rd \ndirection is equal to zero, only the 3rd contribution from exchange remain.  \nFrom relation  99(0)2xyz J   we obtain J(0) = -4.18 K, and the crystal field \ncontribution in paramagnetic temperatures is equal to \n.68.3Kcr\nx , .-36.16Kcr\ny  and .-32.16Kcr\nz .  \nThen we obtain the following paramete rs of crystal field Hamiltonian 0\n21.68 B K , \n2\n2 5.44 B K . It gives five Kramers doublets with en ergies of 0, 85.4, 149.4, 191.9 and 213.9 \nK. \n In summary, we have found that the ma gnetization shows a strong anisotropy in  \ntemperature range studied. In the temperature range up to 100 K,  the experimental curves of \nsusceptibility follow to the Curie-Weiss law. By fitting the calculated susceptibility to the \nexperimental data, the crystal field and exchange  parameters and  g-factors along main crystal \ndirections  were calcula ted. The energies of Nd3+ spectra in a low symmetric crystal field \nwere estimated.  \nAcknowledgements This work was supported by EU project DT-CRYS, NMP3-CT-2003-505580,  of the Polish \nState Committee for Scientific Research (KBN)  (decision of project No. 72/E-67/SPB/6. \nPR/DIE 430/2004-2006)  , and by the European Regional Development Fund through the \nInnovative Economy grants POIG 01.03. 01-00-058/08 and POIG 01.01.02-00-108/09. \n \nReference  \n[1] M.T. Borowiec, A.D. Pr okhorov, I.M. Krygin, V.P. Dyakonov, K. Wozniak, L. \nDobrzycki, T. Zayarnyuk, M. Baranski, W. Domukhowski, H. Szymczak, Physica B 371, 205 \n(2006)  \nM.T.Borowiec, A.A.Prokhorov, A.D.Prokhorov, V.P.Dyakonov,  H.Szymczak  J. Phys., \nCondens. Matter 15, 5113 (2003) \nG. Leniec, T. Skibinski, S.M. Kaczmarek, P.  Iwanowski, M. Berkowski Cent.Eur.J.Phys. 10, \n500 (2012) \n[2]. M.T. Borowiec, A. Watterich, T. Zayarnyuk,  V.P. Dyakonov, A. Majchrowski, J. Zmija, \nM. Baranski, H. Szymczak, J. Appl. Spectrosc. 71, 888 (2004) \nM.T. Borowiec, I. Krynetsk i, V.P. Dyakonov, A. Nabia łek, T. Zayarnyuk, H. Szymczak, New \nJ. Phys. 8, 124 (2006) \nM.T. Borowiec, V.P. Dyakonov, K.Wozniak, L.  Dobrzycki, M. Berkowski, E.E. Zubov,  \nE. Michalski, A. Szewczyk, M.U. Gutowska, T. Zayarnyuk, H. Szymczak, J. Phys., Condens. \nMatter 19, 056206 (2007) \nM.T. Borowiec, Proc. SPIE 4412 , 196 (2001) \nM.T. Borowiec, A.D. Prokhorov, I. M. Krygin, V.P. Dyak onov, K. Wozniak, L. Dobrzycki, T. \nZayarnyuk, M. Baranski , W. Domukhowski, H. Szymczak, Physica B 371, 205 (2006)  \n[3] A.K.Zvezdin, V.M.Matveev, A.A.Mukhin, A.I.Popov, “Rare ea rth  ions in magnetically \nordered crystals”, Moscow, Nauka, 1985, p.120. \n "    },    {        "title": "1301.1200v1.Magnetic_domain_pattern_in_hierarchically_twinned_epitaxial_Ni_Mn_Ga_films.pdf",        "content": " 1 Magnetic domain pattern in hierarchically twinned epitaxial \nNi-Mn-Ga films  \n \nAnett Diestela,b,*, Volker Neua, Anja Backena,b, Ludwig Schultza,b and Sebastian Fählera \n \na IFW Dresden, Institute of Metallic Materials, P.O. Box 270116, 01171 Dresden, Germany  \nb Dresden University of Technology, Institute of Materials Science, 01062 Dresden, Germany  \n* Corresponding author: a.diestel@ifw -dresden.de , Tel.: +49 (0)351 4659 -259 \n \n \nMagnetic shape memory alloys exhibit a hierarchical ly twinned micro structure , \nwhich has been well examined in epitaxial Ni -Mn-Ga films . Here w e analyze  \nconsequences of this “twin within twins” microstructure on the magnetic domain \npattern. Atomic and magnetic force microscopy are used to probe  the correlation \nbetween the martensitic micro structure and magnetic domains.  We examine \nconsequences of different twin boundary orientations with respect to the substrate \nnormal as well as variant boundaries between differently aligned twinned \nlaminates. A detailed micromagnetic analysis is given which describes the \ninfluence of the finite film thickness on the formation of magnetic band domains  in \nthese multiferroic materials .  \n \n \nKeywords: magnetic shape memory alloy, magnetic force microscopy (MFM), twinni ng, \nmagnetic domains , 14M martensite  \n  2 1 Introduction   \n \nMagnetic Shape Memory (MSM) alloys are multiferroics which exhibit ferroelastic  and \nferromagnetic order . The coupling between martensitic microstructure and magnetic domains \ngives rise to the Magneticall y Induced Reorientation (MIR) of martensitic variants1, resulting \nin huge strains up to 10  % in moderate magnetic fields2. The martensitic and  the magnetic \nmicrostructures have  been examined in detail in bulk single crystals. The martensitic \nmicrostructure  of modulated martensite  (e.g. 10M and 14M)  exhibits a characteristic “twin \nwithin twins” microstructure , which involves  several generations and length scales .3,4 \nAccording to Roytbur d 5, each generation of twins form s in order to compensate the  type of  \nelastic energy, which was not minimized  by the finer twinning generation. The first \ngeneration in this hierarchy can be identif ied in  the modulated unit cell  itself.4 According to  \nthe adaptive concept of Khachat uryan  et al .6 the modulated unit cell is a  nano -twinned \nmicrostructure  of a simple tetragonal unit cell . The next generation of twinning occurs \nbetween differently aligned unit cells of the modulated structure. These twin boundaries are \noften called mesosc opic twin boundaries.4 As the  MIR effect is based on the  movement of this \nmesoscopic twins by a magnetic field , we will refer to  them as twin boundaries throughout \nthis paper . \nA martensitic microstructure commo nly contains r egions of parallel twin boundaries , so-\ncalled laminates.  There are different possibilities to orient laminates, which are \ncrystallographically equivalent. Thus , a further  generation of macroscopic twin boundaries \nforms, which connects  mesosco pic laminates of different orientations. To avoid confusion  \nwith the other twin generations , we will call  the twin boundaries between different oriented \nlaminates  variant  boundaries.  \nEach generation of twin boundaries differs by several orders of magnitude  in its twinning \nperiod, twin boundary energy7 and mobility4. Accordingly each generation should have a \ndifferent impact on the magnetic domain pattern. For the first generation , the twinning period \nis just a f ew unit cells, which is well below the magnetic exchange length8. Accordingly , \nmagnetization is completely coupled between nanotwins. Indeed one can calculate both the \nsign and absolute value of magnetocrystalline anisotropy of the modulated cell simply as  a \nmean average of the nanotwinned tetragonal building blocks. This approach also gives the \nappropriate temperature dependency of magnetocrystalline anisotropy .9 \nConsequences of the mesoscopic  twinning on the magnetic domain pattern s have been \nextensively examined in bulk single crystals, as the MIR effect  is based on this coupling . The \nfundamental pattern is a staircase  domain pattern .10-12 This pattern is possible due to  different  3 symmetr ies of the underlying  ferroelastic or ferromagnetic transformation , resulting in \nmartensit ic variants or  magnetic domains . While for a martensitic variant only the direction of \nthe magnetic  easy axis is important, for a magnetic domain also the direction  of \nmagnetization matters. Thus one can distinguish two different domai n walls : The 90°-domain \nwalls coincid ing with twin boundaries  and are form ed, since they allow magnetization to \nfollow the magnetic easy axis  to minimiz e magnetocrystalline anisotropy energy.  The 180° -\ndomain walls  can be form ed within one martensitic varia nt since there are two possible  \nmagnetization direction s follow ing the given  crystallographic easy axis . This additional \nfreedom  for the formation of  a magnetic domain pattern  is commonly used to  minimize \nmagnetostatic energy.  \nIn addition  to the fundament al staircase pattern , magnetic  domain mirroring  at twin \nboundaries13 and the formation of spike domains at 90° -domain walls to reduce the magnetic \nstray field at the surface14 were  observed  in single crystalline Ni -Mn-Ga. To our knowledge , \nthere is no report  on the domain pattern occurring at variant boundaries . \nAnother rarely analyzed  aspect  is the influence of the reduced symmetry of  thin films \ncompared to bulk. Up to now  magnetic domain pattern s of thin films ha ve mostly been \nexamined in polycrystalline fo rm.15 An increased magnetic domain period with increasing \nfilm thickness according to Kittel16 was observed , but the polycrystalline nature hinders  \nprobing a possible correlation between  magnetic and martensitic microstructure. In a previous \nwork17, we analyz ed the magnetic domain configuration in  a thickness series of epitaxial 14M \nmartensitic Ni-Mn-Ga films . As these findings represent one particular case of twin boundary \nalignment out of six possible orientations , another case of twin boundary alignment  is \nintroduced  in this paper . In addition,  a detailed micromagnetic analysis of th e type X  domain \npattern is given . We also analyz e the variant boundaries occurring between both different \norientations .  \nIn this paper we examine Ni-Mn-Ga films on a rigid substr ate only. The rigid substrate \ninhibits any macroscopic length change  and therefore no substantial changes of the \nmartensitic microstructure are possible. Furthermore , in the present films the martensitic \ntransition temperature is above the Curie temperatur e. Therefore one may consider the \nmartensitic microstructure as given and can reduce the investigation to the question of how \nthe magnetic domain pattern adapts to it. This is of advantage as the martensitic \nmicrostructure of epitaxial films ha s been exami ned in detai l.18-21 All measurements ha ve \nbeen performed in the as -deposited state at room temperature, which is below the ferroelastic \nand ferromagnetic order temperature.  We did not apply an external magnetic field during the  4 measurements. H ence, these measurements represent the starting point for a future field \ndependent reorientation.  \n \n2 Experimental  \n \nNi-Mn-Ga films  (sample X and Y) of different  film thickness es (dX = 2 µm; dY = 1.5 µm) \nwere prepared by  DC magnetron sputter deposition from an alloy ed target on a heated single \ncrystalline (100) -MgO substrate  (TX = 400 °C; TY = 300 °C), as described in detail in our \nprevious work22. The epitaxial rel ation MgO(100)[001]║Cr(100)[011]║Ni -Mn-Ga(100)[011] \ndescribes the film architecture.  All micrographs shown here are aligned with the MgO[001] \nsubstrate edges parallel to the picture edges and the austenitic Ni -Mn-Ga unit cell is rotated \nby 45° . The sacrifi cial chromium layer ( dCr = 100 nm) improves the film quality and enables \nthe preparation of freestanding Ni -Mn-Ga films.23 The film composition s (X: \nNi47.8Mn 32.5Ga19.7 and Y: Ni 48.5Mn 32.8Ga18.8) were determined by energy dispersive X -ray \nspectroscopy (EDX) with an accuracy of 0.5  at.% using a Ni 50Mn 25Ga25 standard . All \ninvestigated samples exhibit the 14M modulated martensitic structure, which ha s been \nexamined by X -ray diffraction and transmission electron microscopy measurements, which \nwill be published el sewhere.  \nMartensitic and magnetic microstructure was probed by atomic (AFM ) and magnetic force \nmicroscopy ( MFM ) using a digital instrument dimension 3100 . Topography was imaged by \nheight contrast in tapping mode  and m agnetic micrographs were scanned  in lif t mode by a \nstandard magnetic tip with a Co-alloy coating  and the  magnetization along the tip axis. The \nlift scan height ranges from 50 to 100 nm depending on the strength of the magnetic stray \nfield.  \n \n3 Magnetic properties of Ni -Mn-Ga \n \nDue to the technologi cal relevance of magnetic shape memory alloys, the magnetic properties \nof Ni -Mn-Ga are well examined. For the mi cromagnetic calculations , we use the following \nvalues of 14M martensite at room temperature :24,25 magnetostatic energy density \n3\n02\nS\nd MJm14.02JK\n with s aturation magnetization \nT6.0SJ , uniaxial anisotropy \ncoefficient \n3 5Jm109.0uK . The spin wave stiffness constant \n2meVÅ 100W   allow s \ncalculating the exchange constant \n1\n3pJm1.62aNSWA  using the magnit ude of atomic  5 moment \n8.3S  in units of \nB , the number N of Mn atoms per unit cell and the \ncorresponding lattice parameter a of austenitic  Ni-Mn-Ga. From these values the domain wall \nenergy  desity \n-2\n180 mJm9.2 4 uKA  of 180° -domain walls and \n2\n180 90 mJm9.0 3.0\n  \n of 90°-domain walls are obtained . The latter is calculat ed \nthrough integration of anisotropy and exchange energy density along the profile of a domain \nwall across a boundary with 90° easy axis orientation  (see Eq. 1 in Ref. 26). \n \n4 Results and discussion  \n \n4.1 Orientations of twin boundaries in epitaxial films: type X and Y  \n \nTwin boundaries (TB) are well defined crystallographic planes which connect different ly \noriented martensitic variants.  Six different orientati ons of {1 01}-type twin boundaries are \npossible which are sketched in Figure 1 with respect to the cubic austenite unit cell. Each of \nthese orientations  represents  mesoscopic  a-c-twin boundaries connect ing 14M marte nsitic \nvariant s with alternating a- and c-axis in plane . While in bulk all six possible orientations are \nequivalent, this is not the case for thin films. Due to the finite film thickness one has to \ndistinguish between two kinds of  twinning , which we call  type X and Y .  \nType X twinned martensite  exhibit s twin planes  inclined by 45° with respect to the substrate \nnormal  and their traces run 45° rotated  to the substrate edges at the film surface (see Figure 1, \norange  TB). The crystallographic short c-axis lies alternating  in- and out -of-plane.  Type Y \ntwinned martensite  show s twin planes  which are aligned  perpendicular to the substrate surface  \nwith traces  running  parallel to the substrate edges  at the film surfaces (see Figure 1, blue TB). \nThe c-axis is aligned in -plane, but alternat es between both equivalent  orientations 45° rotated  \nto the substrate edges . Type  X as well as type  Y twinned regions  consist of the same kind of \nmodula ted 14M martensite, however the b-axis and the a-c-twin boundaries run different ly \nwith respect  to the sample normal. Since the crystallographic c-axis coincides with the \nmagnetic easy axis in 14M martensite8, substantially different domain pattern  in both types of \ntwinning  are expected . Only for type X twinning  the magnetic easy axis points out -of-plane \nand stray field effects play a n important  role. This  should be negligible for type Y twinned \nvariants with in-plane magnetic easy axis.  \nTo understand the measurements  below  it is important to consider that the six different \norientations of twin boundaries sketched in  Figure 1 are a simplif ication . As these twin \nvariants  form at the irrational habit plane, connecting austenite and martensite, they are tilted  6 and rotated by a few degrees away from precise {101}-planes  of austenite.27 Instead of the six \nfundamental orientations, a multiple of 24 so -called habit plane variants exist. Th e slight tilt \nand rotation is elastically incompatible with the rigid substrate. This incompatibility is \ncompensated by alternating twin variants  with positive and negative angular deviations, \nresulting in a wavy or rhombus -like topographic  patter n on the film surface.  \nIn addition to a-c-twin boundaries also a-b- and b-c-twin boundaries are possible due to the  \northorhombic  distortion of  14M  martensite . First indications of these boundaries h ave recently \nbeen reported also for 10M  martensite in Ni -Mn-Ga.28 For the present films we have no \nindication of these types of boundaries , hence they will not be considered in the following .  \n \n4.2 Magnetic d omain pattern within t ype X twinning  \n \nThe correlation between magnetic and martensitic domain structures of typ e X twinned \nmartensite is explained in detail in our previous work17. The key points of this analysis are \nshortly summarized since they are the basics of the following sections.  \nThe martensitic microstructure of a 2  µm thic k Ni-Mn-Ga film (sample X) has been  mapped \nby AFM and is depicted in Figure 2a. A periodical , wavy surface topography with a rhombus -\nlike superstructure is visible. Since in  type X the mesoscopic a-c-twin boundarie s are inclined \nby 45°  towards the substrate normal , the magnetic easy c-axis lies alternat ely in- and out -of-\nplane  (Figure 1, orange TB) . The schematical  cross section s in Figure 6 illustr ate the typical  \nsurface  profile s of a c-a-twinned martensite22. Twinning results in a slight inclination between \nboth variants  connected by a twin boundary . Traces of twin boundaries  are therefore visible \non the surface topography as linear ridges and valleys . Due to the epitaxial film growth , the \norientation of the austenitic Ni -Mn-Ga unit cell is rotated about 45° in respect to the MgO -\nsubstrate edges.22  \nThe ex perimental ly observed corresponding magnetic domain pattern (see  Figure 2b) consists \nof magnetic band domains with domain walls (DW) perpendicular to the twin boundaries.17 \nFor the present 2 µm thick film a n additional  contrast within the band domains is visible, \nwhich resembles  the same  direction and  period of the twinning. This aspect is discussed in \ndetail in section 4.3.  \nIn Figure 2c the correlation between martensitic and magnetic information  is summarized  by \na schematical top view and cross section along MgO[0\n1 1]. The magnetic easy c-axes (black \narrows) o f neighboring variants lie alternat ely in- and out -of-plane. Due to the high \nmagnetocrystalline anisotropy of Ni -Mn-Ga the magnetization \nm  (orange arrows)  follows c.  7 For a given twin boundary orientation (e.g. Figure 2c, cross section : TBs are inclined to the \nleft) there are only two arrangements of magnetization directions  possible. The first one is \nillustrated by  orange  arrows , where the magnetization  alternates between up and right. In the  \nsecond one the direction s of magnetization are  reversed  to down and left . Any other \nconfigurations  of magnetization direc tions  (combining up and dow n or left and right)  result s \nin energetically unfavorably charged 90° -DWs .  \nSince both possible  arrangement s exhibit a perpendicular magnetization component, which \npoints either up or down, a band domain pattern will form  to minimize the magnetic stray \nfield energy.  \nThe same perpendicular alignment of twin boundaries and  band  domain walls was observed \nin a thick ness series17 ranging from 125 to 2000 nm. The observed domain period  \nDW  as a \nfunction of the film thickness  d follows a square root dependency , as expected from Kittels  \nlaw16: \n) nm( nm8.25)nm(2/1 2/1 2/1\nDW d  . Kittels law also predicts  appropriate absolute \nvalue s of \nDW when assuming that within each band domain magnetization is averaged \nbetween neighboring twin variants . The validit y of this assu mption is discussed in detail in \nsection 4.3. This agreement allows considering the observed band domain pattern as the \noptimum balance between the total domain wall energy and stray field energy. In contrast to \nthese magnetic energies , the twinning period is an optimum balance between  elastic energy \ncontributions:  total twin boundary energy and elastic energy.7 Since the  equilibrium  magnetic \ndomain peri od exceeds  the equilibrium  martensitic twinning period, the formation of \nmagnetic band domains parallel to  the martensitic variants does not allow  obtaining  their \noptimum width. For a perpendicular alignment the domain period does not need to match  the \ntwin period  and thus a domain period with minimum energy can form.17 This orthogonal \narrangement allows an  independent minimization of magnetic and elastic energies, \nrespectively.  \nA completely  different domain pat tern is known for bulk samples (staircase domain pattern) . \nThe absence of additional 180° -domain walls within the films  are due to the  unfavorable total \nmagnetic energy. In the following section the observed domain pattern in type X films was \nanalyzed in d etail in comparison with competing models.  \n \n4.3 Micromagnetic analysis of type X domains  \n \nIn order to explain the observed magnetic domain pattern more precisely , we will compare the \nmicromagnetism of three different patterns, which are sketched in Figure 3: a) a magnetic  8 domain pattern , which considers a homogeneous  and tilted magnetiz ation, irrespective of the \nlocal anisotropy axis in the underlying martensitic  variants, b) a refined model , where \nmagnetization follows the magnetic  easy axis within each  martensitic  variant , and c) a \nstaircase pattern adapted from bulk.   \nBy deriving  reasonable approximations for the total magnetic energy of these  domain \nscenarios , we can predict t he energetically favored domain state. Fo r discussing magnetostatic \nenergies , the Far aday picture of magnetization is applied . This means that  discontinuities in \nthe normalized magnetization vector \nsJJm  are sources of ma gnetic charges . There are  \neither surface charges  \nnm  (\nn as normal vector ) or volume charges \n)(divm , which \nby themselves are sources of stray fields.  \nIn case (a) the considered domain pattern consists of alternating band s with  homogeneous ly \ntilted magnetiz ation  in each domain , which results from averaging over the easy axis of two \nneighboring martensitic variants  (Figure 3a). The total energy consists of the wall energy of \n180° -DWs  (\n180 ), the mag netostatic energy (\nd) of the tilted parallel magnetic bands with \nthe given domain period (\nDW ) and the anisotropy energy  (\nani ) for rotating the \nmagnetization by 45° out of the local magneti c easy axis throughout the whole film  thickness \nd. The respective contributions per unit film area are: \n \n   180\nDW180 DW DW 1802#    d A     (1a) \nwith \nDW#  as number and \nDWA  as area of 180° -DWs per unit film surface . According to \nRef. 29 the magnetostatic energy of band domains is given by  \n \nDW d DW*\nd d48525.0\n4705.1 K K       (1b) \nwith \nd2\ns 0*\nd 5.0)()5.0(  K J K  , due to the 45° tilt of the magnetization . The anisotropy \nenergy does not depend on the domain wall period : \n \ndKu ani 5.0        (1c) \nThus \nDW  will be adjust ed to minimize the sum of the first two energy contributions only, \nwhich leads to the known equation for band d omains16,29: \n  \nd180 BD\nDW8525.08\nKd\n       (1d) \n (Note, that Eq. 1d differs by the factor 1.0517  from the equation used in Ref.  17. The factor  \narises from higher order harmonic terms in the calcul ation of the magnetostatic en ergy.) As \nani increases with the film thickness d, this contribution makes this model more unrealistic for  9 thicker films. The rotation of magnetic moments becomes undesirable and the more complex \ndomain pattern sketched in  Figure 3b has to be considered.  \nIn case  (b), the  magnetization follows the easy axis within each martensitic variant (Figure \n3b). The energy contributions of this model are:  \n  \n   180\nDW180 DW DW 1802#    d A     (2a) \n  \n) (DW df         (2b)  \nThe magnetostatic energy arising from the two-dimensionally modulated charges at the uppe r \nand lower film surface  will be evaluated below  with the twin boundary period \nTB . \n  \n   90\nTB90 DW DW 9022#    d A      (2c) \nDue to the same amount of 180° -DWs  as in the hom ogeneous band domain pattern , case (a), \n180\n is unchanged. The missing rotation of magnetization leads to the absence of an \nanisotropy term  (\n0ani ), however  on the cost of additional 90° -DWs  at each twin boundary. \nDespite of the a-c-twin boundaries no volume charg es appear, as the magnetization passes \neach twin boundary with constant perpendicular component, thus \n0)(mdiv . The \nmagnetostatic ene rgy density of the simple band domain pattern , case (a), is now replaced by \nthe energy of a periodic, two -dimensionally modulated cha rged surface as sketched in Figure \n3b with su rface charges on the rectangular uni t area \nTB DW  given by:  \n\n \n\nTB TB DW DWTB DW DWDW\ns*\n5.0 , 5.0, 15.0 0 , 5.0, 15.0 0 , 0\n),(\nx xy xx\nJyx\n (3) \nThis term can be analyzed through the standard micromagnetic approach29, namely the \ncalculation of the magnetostatic potential  \n  \n\nsurfaceextended0s\nd '')'(\n4)( dSrrr Jr  \n      (4) \nof the charged surface s, and subsequent  computation of the energy density  \n  \n\n \nTB DW SsdSr rJ\n'd\nTB DWd ')'( )'(      (5) \nIn Eq. 4 the surface integration has to be computed for the periodically extended surface \ncharge pattern \n)(r , in Eq. 5 the integration is sufficient on the unit area \nTB DW .   10 We developed a micromagnetic code which calculates the magnetostatic energy \nd  of an \narbitrary periodic two -dimensional charges pattern based  on Eq.  4 and 5. This was \nsuccessfully tested for the charged patterns of regular perpendicular band domains (BD) and \ncheckerboard domains (CB) and reproduced the known solutions of  \nDW dBD\nd4705.1 K  \nand \nDW dBD\nd4705.1 K  (see Ref. 16). Applying the code to analyze the charge pattern of \ncase (b) (Eq. 3) we derive again an equation of the form \nDW d d4 K , with \n9.0 . \nThe variance in  the factor  \n is a conseque nce of the small additional influence of the \ntwinning periodicity on \nd . Using  \n)5.01.0 (DW TB    as observed in the \nexperimental film series17, results in \n95.088.0 . \nAlso for the modulated band domain pattern  \nDW  affects  only the  first two energy terms \n(Eq. 2a/b), and the optimum domain wall period \nDW  is therefore again  proportional to  \n21d . \nThe similarity of \n9.0  with the factor \n8525.0  in case (a) (Eq. 1b) leads to a \nquantitatively almost identical  \n)(DWd  behavior, irrespective of the actual domain \nconfiguration. Which of the two domain sc enarios , case (a) or (b), is energetically favored, \ndepends on  the film thickness  d and the twin boundary period \nTB .  \nCase (c) is a staircase -like domain pattern  which is sketched in  Figure 3c. While in bulk the \nlarge martensitic variant period allows containing  many 180° -DWs , for thin films we consider \nonly one domain wall per martensitic variant, as a higher number would increase the domain \nwall energy further.  In case (c), 180° -DWs run with equal proportion horizo ntally and \nvertically through the film. They correspond in area to two vertical 180° -DWs  per \nTB  \nextending through the whole film thickness. As in case (b), the twin boundaries constitute \n90°-DWs . Internal charges are absent as the flux  is guided through the whole depth of the \nfilm, leaving only charges at the upper and lower surface s. These charges form a one -\ndimensional periodic pattern  of the type (+,0, -,0) (see Figure 3c), which gives rise to  a \nmagnetostatic energy term . In total we have the following contrib utions:  \n  \n  180\nTB1802  d        (6a) \n  \nTB d d425.3 K  with  \nDW TB 5.0    (6b) \nderived again through Eq . 4 and 5 with the appropriate surface charge pattern, a nd  11   \n   90\nTB90 DW DW 9022#    d A      (6c) \nThe energy terms are formally identical to those in case (b) and now depend solely on  the \ntwin boundary period , which  has no degree of freedom , but is a given function of the film \nthickness17: \nd 2.0TB.  \nFigure 4a summarizes the total energy for all three cases as a function of the film thickness. \nUp to a film thickness of 200 nm the homogeneous band domain pattern of completely \ncoupled domains in neighboring variants, case (a), has the lowest total energy \ntot  of all \nconsidered domain models. The roughly linear i ncrease in \ntot  is a result of the \nmagnetocrystalline anisotropy contr ibution and disfavors this domain pattern for larger \nthicknesses. Above 200 nm, magnetization prefers to follow the local anisotropy axis of the \ntwin variant , which results  in an additional , but moderate energy contribution from 90°-DWs \nand a two -dimension ally modulated charged surface. The magnetostatic energy of this \nmagnetization pattern compares quantitatively with the h omogeneous band domain pattern . \nAccordingly , the equilibrium domain width s of case (a) and (b) (Figure 4b) are essentially \nunaltered and describe the experimental period .17 The slight modulation within the band \ndomains observed only in thick films ( Figure 2b) indeed suggest s that a crossover from case \n(a) to case (b) occurs at a certain thickness . For a precise confirmation  detailed examinations, \ne.g. of the film cross section , would be required.  \nOver  the whole  film thickness range  the total energy of the staircase domain patte rn, case (c), \nis clearly above that one of case (b). This originates  from the small twin boundary period \nwhich introduces a large density of 180° - and 90° -DWs . The consequence  is an increased \nmagnetostatic contribution of the one -dimensionally modulated ch arged surface  (see Figure \n3c). An explanation for the latter fin ding can be found in  the separation of the charged bands \nof opposite polarity. Here, flux closure is less effective and the resulting strong stray fields \nlead to  increased magn etostatic energy. One should note that these results do not disagree \nwith the observed staircase d omain pattern in bulk material. In macroscopic samples the \nindividual twin variants reach a size which is large enough to contain  several magnetic \ndomains  for an effective flux closure.  \n \n  12 4.4 Variant boundar ies of two type X variants  rotated by 90° around the substrate \nnormal  \n \nFour crystallographic equivalent orientations of type X twinned variants  exist  (Figure 1, \norange TB ). Acco rdingly variant boundaries between them  are possible . They  occur at much \nlarger length scale compared to the twin boundaries within one twinned laminate . In this \nsection, the most obvious variant boundary between two martensitic type X  variants  is \nanalyzed . \nThe AFM micrograph in  Figure 5a shows the typical periodical  surface topography of  a 2 µm \nthick Ni -Mn-Ga film  (sample X) exhibit ing type X twinn ing. Two different ly oriented \nmartensitic variants are visible  and t heir traces run perpendicular to each other, along \nMgO[011] and MgO[0\n1 1]. As the traces of one twinned variant  can be transformed to the \nother one by a rotation of 90° around the substrate  normal , we call this type a 90° -variant \nbound ary. This variant bo undary is not a strict boundary, but is disturbed and splits up in \ndifferent segments . \nThe MFM micrograph in Figure 5b shows the corresponding magnetic band domain pattern, \nwhere magnetic band  domains run perpendicular to the twin boundary traces  within each \nmartensitic variant . Therefore also the magnetic band domains  in both variants are aligned \nperpendicular to each other. At the 90°-variant boundary no correlation between the magnetic \ndomain structures of both variants could be observed.  All information obtained from AFM \nand MFM micrographs are summarized schematically in Figure 5c.  \n \n4.5 Magnetic d omain mirroring at variant boundar ies of two type X twinne d variants \nrotated by 180° around the substrate normal  \n \nFor type X twinned martensitic variants  the orientation of traces on the surface is not \nsufficient for determin ing the twin boundary orientation, since there are two different ways to \ntilt the a-c-twin boundary from the substrate normal: plus and minus 45° ( Figure 1, orange \nTB). As both variants  are connected by a  rotation of  180° around the substrate normal  we call \nthe variant boundary a 180° -variant boundary.  \nBut how to identify 180° -variant boundaries in AFM measurements, when traces in both \nneighboring martensitic variants  run parallel? For this we first consider the sketch of cross \nsections through the Ni-Mn-Ga film. In Figure 6 two kinds of 180° -variant boundar ies are  \nsketched, which passes through a n out-of-plane  a-axis. In Figure 6a the twinning results in a \ntopography , where the variant boundary exhibits a maximum  along th e directions of twin  13 boundaries . Also a minimum is possible depending of the orientation of the (101) -twin \nboundaries  (sketched in Figure 6b). The t opography  of both types of  180° -variant boundar ies \ncan be identifi ed in the AFM micrograph s (marked as 1 and 2 in Figure 5a, zooms are shown \nin d and g ). The details of the AFM micrograph s reveal  a topographic ridge ( Figure 5d, bright \narea, corresponds to Figure 6a) and a topographic valley ( Figure 5g, dark area , corresponds to \nFigure 6b). Both 180° -variant boundaries run  along the picture diagona ls and disturb the \ntypical surface profile only ma rginally .  \nFor an unambiguous identification of variant boundaries the corresponding MFM \nmicrographs ( Figure 5e/h) can be used . In both regions  an abrupt inversion of the magnetic \ncontrast of the band domain  pattern  is observed . This inversion  can be attributed to domain \nmirroring at twin boundar ies. For bulk single crystals the domain mirroring effect at one twin \nboundar y had been already described by  Lai et al.13 He showed that a mirrored  magnetic \ndomain pattern  appears at both corresponding sample  surface s connected  by a twin boundary \nat macroscopic distances , but is inverted  in contrast. In the present thin films a sim ilar effect \noccurs, but involves two twin boundaries, which allows observing the pattern on the same \n(film) surface. As sketched exemplary in Figure 6a, the magnetization \nm  (dotted arrows) \nfollows the magnetic easy c-axis, which is mirrored at the first twin boundary  from out -of-\nplane to in -plane  direction . At the next twin boundary the magnetization is mirrored back to \nout-of-plane. The magnetization changes from pointing into the film surface  to out of the \nsurface on the other side of the twin boundary trace. At the surface an abrupt inversion of the \nmagneti c contrast within the magnetic band domains can be  observed. In addition to the both \npossibilities de picted in Figure 6 two more variant boundaries parallel to a c-axis exist  (not \nshown) . For these only a topographic contrast, but no mirroring of magnetic domain pattern is \nexpected.  \nThe origin of such 180° -variant boundaries  can be explained by multi ple transformation \nnucleuses  during the martensitic transformation , where d ifferent oriented m artensitic variants \ngrowth. To keep the crystallography precise, one has to note that the  sketches  in Figure 6 are \nsimpl ifications . A general variant boundary, as de scribed in the introductions, involves  a \nslight tilt and rotation of both variants . Accordingly the crystallographic lattice at a variant \nbound ary is expected to be disturbed, which is symbolized by the blue dot ted lines in Figure \n6. However, these small angular deviations result  just in a slight bending of the easy axis, \nwhich apparently does not disturb  the domain mirroring  effect . \n  14 4.6 Magnetic domain pattern within t ype Y twinning  \n \nIn add ition to  type X twinning another  solution for the orienta tion of {101}-twin boundaries  \nin thin  14M films is possible : The twin planes in type Y twinned martensite run perpendicular \nthrough  the film plane and parallel to the MgO -substrate edges (see Figure 1, blue TB). Two \nequivalent solutions for such twin boundaries are possible.  In the following the martensitic \nand magnetic domain  pattern  of a predominantly  type Y twinned epitaxial film  (sample Y)  is \nanalyzed .  \nThe AFM micrograph in Figure 7a show s a marquetry surface topogra phy. The type Y \ntwinned martensitic variants run as long bands of different  length and wid th parallel to the \nMgO -substrate edges and perpendicular to e ach other. Within the bands hardly any  \ntopographic contrast  is visible  (Figure 7c). This is expected for type Y twin boundaries, as for \nthis orientation the twinning angle connecting the c-axis of neighboring varia nts lies within \nthe film plane . Due to the perpendicularly aligned twin boundar ies the magnetic easy c-axis is \nalways in -plane  and just alternates between both substrate diagonals.  \nThe corresponding MFM micrograph  of type  Y twinned regions  in Figure 7b exhibits  very \nlow magnetic contrast . A network of lines with a dark magnetic  contrast  is obvious , which \nencloses rhombohedra l areas.  Based on the in -plane orientation of the magnetic easy axis , it is \nassumed that with in these areas no internal charges exist, and stray fields are only created at \nthe clearly visible domain boundaries. The enlarged MFM micrograph  (Figure 7d) offers a \nmore detailed picture and reveals on the right hand side of the image a pattern of regularly \nspaced vertical lines and horizontal zigzag -lines. The most likely corresponding domain \npattern is sketched in Figure 7e and displays a pattern of rhombohedral domains . The weaker \ncontrast lines are identified as 90°-DWs running parallel to the MgO -substrate edges , which \nallow the magnetization to follow the easy axes in each martensitic variant. The zigzag -like \ncontrast can be attributed to 180° -DWs , which are possible as there are two cases  for the \nmagnetizati on direction to fo llow the easy axis . The length ( l) of the rhombohedral pattern  \nexceed s their constant width (w) and varies  without exhibiting an y obvious  correlation with \ncrystallograph ic features . As the magnetization passes each domain boundary with co nstant \nperpendicular component, no charges are building  up and the c ontrast must originate  from the \nstructure of the domain walls itself. The overall domain pattern resembles the magnetic \nstaircase domain pattern in Ni -Mn-Ga bulk12. All in all t he staircase pattern  is just rotated  by \n45° with respect to the substrate edges  since for the thin film experiments the substrate edge is \ntaken as a reference , whereas domain images of bulk single crystals are  commonly  oriented \nwith respect to the austenitic unit cell. This similarity is plausible, as for the type Y  15 orientation the magnetic easy axis  is always in -plane and magnetic stray field effects are thus \nnegligible.  While in bulk the spacing of 180° -DWs (l) is common ly much shorter than that of \n90°-DWs (w), this is different for the present thin film. We attribute this to the substantial \nshorter twin boundary period  in films , which  fixes w, while a large l may minimize the total \ndomain wall energy.  \n \n4.7 Domain pattern at the  variant  boundary between type X and Y twinned variants  \n \nAfter the  detailed  analysis  of the correlation between the martensitic and magnetic domain \npattern  in type X and Y twinned 14M martensitic regions, it is interesting to probe the variant \nboundar ies between both types. As an example  AFM and MFM micrographs of a 2  µm thick \nNi-Mn-Ga film (sample X) containing both types of variants are shown in Figure 8. In the \nAFM micrograph ( Figure 8a) the type Y variants form two long bands  running in both \nequivalent orientations  parallel to the substrate edges . This T-shaped region of type Y is \nsurrounded by large type X areas . The presence of both types in one micrograph clearly \nreveals the subst antially different topography. W hile type X  exhibits  a pronounced periodical \nwavy surface topography, only a marginal  height contrast can be observed in type Y.  \nA similar strong  difference in contrast of both types is also  visible in the  corresponding  MFM \nmicrograph  (Figure 8b). While the type X twinned martensitic variants exhibit  magnetic band \ndomains with a high out -of-plane contrast  perpendicular to the  traces of twin boundaries  at the \nsample s urface , the type Y variants show only very little magnetic contrast . Indeed the \nmagnetic contrast within the type Y region  is sufficient to resolve  the weak zigzag -shape  of \n180°-DWs, but no additional contrast, which ha s been clearly visible  in the previou s enlarged \nMFM micrograph ( Figure 7d).  \nThis mapped  region allows analyz ing the consequences of variant boundaries between type X \nand Y  on the domain pattern . While within type  X regions the band domain period is mostly \nunaffected  when approaching the variant boundary , within the type Y regions  the length l \nbetween the zig zag-pattern s vary . From the MFM micrograph it is obvious that the zigzag-\npattern s usually  coincide with band domain boundaries within the type X  regions. This \nsuggests that the variability in l, described in section 4.6, is used to compensate some of the \nhorizontal component of the band domain s, which are fixed in their period (section 4.3). Since \ntype Y variants exhibit only in -plane magnetization, at their variant boundaries towards type \nX variants no boundary condition for the out -of-plane magnetization component exists. \nAccordingly two different configuratio ns of adjacent magnetic band domains can be observed \nin the MFM micrographs. When comparing magnetic band domains at opposite borders of  16 type Y regions both configurations are observed: bright/bright or dark/dark magnetic band \ndomains on both sides ( Figure 8b/c, region 2) or antiparallel  magnetized out-of-plane band \ndomains (region 1: bright/dark) . \n \n5 Conclusion   \n \nEpitaxial Ni -Mn-Ga films represent a prototype  to probe the correlation between martens itic \nand magnetic microstructure in  hierarchically twinned magnetic shape memory alloys. Due to \nthe finite film thickness one has to distinguish two different twin boundary orientations in \n14M martensite. In case of perpendicular twin boundaries (typ e Y) the easy axis alternates \nbetween bot h in-plane orientations. This results in a degenerated staircase -like domain \npattern, where the small twinning period and high 180° -domain wall energy inverts the period \nratio of 90° - and 180° -domain walls compared to bulk. In case of inclined twin boundar ies \n(type X) the  magnetic  easy axis alternates between in - and out -of-plane directions. To \nminimize stray field energy a magnetic band domain pattern  is form ed. Twin and domain \nboundaries are aligned orthogonal as this allows minimizing elastic and magneti c energies \nindependently.  \nMicromagnetic calculatio ns for type X twinned martensite  reveal that in agreement with \nexperiments a staircase pattern is not favorable at any film thickness. At thicknesses below \n200 nm a band domain pattern originating from a h omogeneous magnetization is expected, \nwhile above it is favorable for the magnetization to follow the local  magnetic  easy axis. \nDespite this expected crossover the domain period remains practically identical and agrees \nwith experiments.  \nAt much larger len gth scales compared to mesoscopic twinning one observes variant \nboundaries between laminates with different twin boundary orientations. While in some cases \n(90°-variant boundary) no correlation of magnetic and martensitic microstructure was \nobserved, domai n mirroring occurs at 180° -variant boundaries. At variant boundaries between \ntype X and Y some correlation of domain period is observed which we attribute to the in -\nplane magnetization components present in both types.  \nOur analysis reveals how multiferroi cs are affected by the reduced dimension of thin films. In \naddition to the increased re levance of magnetic stray field  the reduced twining period must be \nconsidered. It does not only result in different domain patterns compared to bulk , but also \nshrinks th e size of martensitic laminates. Hence variant boundaries are observable at a high er \ndensity and  thus are relevant for thin films.  \n  17 6 Acknowledgeme nts  \n \nWe acknowledge Sandra Kauffmann -Weiss, Christian Behler and Robert Niemann for helpful \ndiscussions. This w ork was funded by the German research foundation (DFG) via the Priority \nProgram SPP1239.  \n  18 Figures  \n \n \nFigure 1. (color online ) Six possible orientations of {110} -twin boundaries  (TB)  exist, which \nare sketched here with in the austenit ic Ni -Mn-Ga unit cell . In thin films t wo types of twinning \nhave to  be di stinguished : Type X TBs (orange) run inclined by 45° with respect to the \nsubstrate normal and type Y TBs (blue) run perpendicular to the substrate plane.  \n \n \nFigure 2. (color online) Twin and domain pattern of type X orientation. (a) The AFM \nmicrograph of a 2  µm thick Ni-Mn-Ga film  (sample X)  shows a twinned surface topography \nwhere the magnetic easy c-axis alternates between in-and out -of-plane  orientation . (b) The \ncorresponding MFM micrograph shows  magnetic  band domains which are aligned \nperpendicular to the twin boundaries. (c) The crystallographic and magnetic domain structures \nare sketched as top view and cross section along MgO[0\n1 1], wher e the magnetization \nm  \nfollows the magnetic easy c-axis.17 \n  19 \n \nFigure 3. (color online) Charge distributions and three -dimensional sketch es of three  possible \nmagnet ic domain structures  for type X  twinning : (a) homogenous band domain model, (b) \ntwo-dimensional surface  domain model for thin films,  (c) staircase -like model  for bulk. A \nmicromagnetic comparison  of all three cases is described  within the text (section  4.3). \n \n \nFigure 4. (color online)  (a) Total magnetic energy tot of three different domain models for \ntype X  twinning  as a function of film thickness d: case a) homogen eous band domain pattern  \n(dashed  line), case  b) two-dimensional surface pattern  of thin films  (solid  line), case c) \nstaircase -like domain pattern  (dotted  line). (b) The equilibrium  domain period DW calculated \nfrom model case a) (dashed  line) and b)  (solid  line) in compar ison with experimental data17 \n(squares) .   20 \n \n \nFigure 5. (colo r online)  Variant boundaries between different orientations of type X  \ntwinning . (a) The AFM and (b) MFM micrograph s of a 2  µm thick Ni -Mn-Ga film (sample \nX) show the crystallographic and magnetic domain structure at a variant connecting tw o type \nX variants  rotated by 9 0° around the substrate normal. The pattern  is summarized \nschematically in (c). The magnified details reveal  a (d) topographic ridge and (g) valley  \n(AFM) whereas in the magnetic contrast (MFM, e/h) an inversion is observed , sketched \nschematica lly in (f /i). Both, the topographic features and the domain mirroring, can be \nexplained by a variant boundary connecting  two type X variants  rotated by 180° around the \nsubstrate normal (see Figure 6). \n \n    \nFigure 6. (color online)  Origin of surface topography and domain mirroring at type X variant \nboundaries.  The cross -section s illustrate  two types of variant boundaries (blue dotted lines) \nconnecting two type X twinned variants  rotated by 180 ° around the substrate normal. In case \nthat the variant boundary  coincides with an a-axis (a) a maximum in topography or (b) a \nvalley occurs  depending of the twin boundary orientation . The mechanism for domain \nmirroring is sketched . The dotted arrows illus trate the magnetization direction following the \nmagnetic easy c-axis.   21 \n \n \nFigure 7. (color online) The (a) AFM and (b) MFM micrographs of a 1.5  µm thick Ni -Mn-Ga \nfilm (sample Y) show the crystallographic and magnetic domain structure  of the predominant \ntype Y twinned 14M martensite. Magnified details show a weak  (c) topographic (AFM) and \n(d) magnetic contrast (MFM) within the long variants. (e) Schematic sketch of the magnetic \nstaircase -like domain pattern with 180° - and 90° -domain wa lls (DW) .  22 \n \nFigure 8. (color online)  Variant boundaries between type X and Y variants . The (a) AFM and \n(b) MFM micrographs of a 2 µm thick Ni -Mn-Ga film (sample X) show the crystallographic \nand magnetic domain structure of type X and Y twinned 14M martensitic variants , which is \nsketched schematically  in (c). \n \n \nReferences  \n                                                 \n1 K. Ullakko, J.K. Huang , C. Kantner , R.C. O’Handley , and V.V. Kokorin,  Appl. Phys. Lett. \n69, 1966 (1996).   \n2 A. Sozinov, A.  Likhachev, N. Lanska, and K. Ullakko, Appl. Phys. Lett. 80, 1746 (2002).  \n3 P. Müllner and A.H. King,  Acta Mater. 58, 5242 (2010).  \n4 S. Kaufmann, R. Niemann, T. Thersleff, U.K Rößler, O. Heczko, J. Buschbeck, B. \nHolzapfel, L. Schultz, and S. Fähler, New J.  Phys.  13,  053029 (2011).  \n5 A.L. Roytburd, Phase Transitions 45, 1 (1993).  \n6 A.G. Khachaturyan, S.M. Shapiro, and S. Semenovskaya, Phys. Rev. B 43, 10832 (1991).  \n7 A. Diestel, A. Backen, U.K. Rößler, L. Schultz, and S. Fähler, Appl. Phys. Lett. 99, 092512  \n(2011).  \n8 O. Heczko, L. Straka, and K. Ullakko,  J. Phys. IV France 112, 959 (2003).  \n9 O. Heczko, L. Straka, N. Lanska, K. Ullakko, and J. Enkovaara, J. Appl. Phys. 91, 8228 \n(2002).  \n10 O. Heczko, K. Jurek, and K. Ullakko, J. Magn. Magn. Mater. 226-230, 996 (2001).  \n11 Y. Ge, O. Heczko , O. Söderberg , and V. K. Lindroos,  J. Appl. Phys. 96, 2159 (2004).  \n12 Y.W. Lai, N. Scheerbaum, D. Hinz, O. Gutfleisch, R. Schäfer, L. Schultz, and J. McCord, \nAppl. Phys. Lett. 90, 192504 (2007).  \n13 Y.W. Lai, R. Schäfer, L. Schultz,  and J. McCord, Appl. Phys. Lett. 96, 022507 (2010).   23                                                                                                                                                          \n14 N. Scheerbaum, Y.W. Lai, T. Leisegang, M. Thomas, J. Liu, K. Khlopko, J. McCord, S. \nFähler, R. Träger, D.C. Meyer, L. Schultz, and O. Gutfleisch, Acta Mat. 58, 4629 (2010).  \n15 V.A. Chernenko, R. Lopez A nton, J.M. Barandiaran, I. Orue, S. Besseghini, M. Ohtsuka, \nand A. Gambardella, IEEE Trans. Magn. 44, 3040 (2008).  \n16 C. Kittel, Rev. Mod. Phys. 21, 541 (1949).  \n17 A. Diestel, A. Backen, V. Neu, L. Schultz, and S. Fähler, Scripta Mater. 67, 423 (2012).  \n18 G.J. Mahnke , M. Seibt , and S.G. Mayr , Phys. Rev. B 78, 012101 (2008).  \n19 P. Leicht, A. Laptev, M. Fonin, Y. Luo, K. Samwer, New J. Phys.  13, 033021 (2011).  \n20 T. Eichhorn, R. Hausmanns, and G. Jakob, Acta Mater. 59, 5067 (2011).  \n21 M. Thomas, O. Heczko, J. Buschbeck, U.K. Rößler, J. McCord, N . Scheerbaum, L. Schultz, \nand S. Fähler, New J. Phys. 10, 023040 (2008).  \n22 J. Buschbeck, R. Niemann, O. Heczko, M. Thomas, L. Schultz, and S. Fähler, Acta Mater. \n57, 2516 (2009).  \n23 A. Backen, S.R. Yeduru, M. Kohl, S. Baunack, A. Diestel, B. Holzapfel, L. S chultz, and S. \nFähler, Acta Mater. 58, 3415 (2010).  \n24 L. Straka, O. Heczko, and K. Ullakko, J. Magn. Magn. Mater. 272-276, 2049 (2004).  \n25 V. Runov and U. Stuhr, J. Magn. Magn. Mater. 323, 244 (2011).  \n26 V. Neu, A. Hubert, and L. Schultz, J. Magn. Magn. Mate r. 189, 391 (1998).  \n27 S. Kaufmann, U.K. Rößler, O. Heczko, M. Wuttig, J. Buschbeck, L. Schultz, adn S. Fähler, \nPhys. Rev. Lett. 104, 145702 (2010).  \n28  L. Straka, O. Heczko, H. Seiner, N. Lanska, J. Drahokoupil, A. Soroka, S. Fähler, H. \nHänninen, and A. Soz inov, Acta Mater. 59, 7450 (2011).  \n29 A. Hubert and R. Schäfer, Magnetic domains – The analysis of magnetic microstructure  \n(Springer Verlag, Berlin, 1998).  \n \n "    },    {        "title": "1302.1636v1.Crystal_Structure_and_Magnetic_Properties_of_the_Ba3TeCo3P2O14__Pb3TeCo3P2O14__and_Pb3TeCo3V2O14_Langasites.pdf",        "content": "Krizan 1 Crystal Structure and Magnetic P roperties of the Ba3TeCo 3P2O14, Pb3TeCo 3P2O14, and Pb 3TeCo 3V2O14 \nLangasites  \nJ. W. Krizan1*, C. de la Cruz2, N. H. Andersen3, and R. J. Cava1 \n1Department of Chemistry, Princeton University, Princeton, NJ 08544, USA  \n2Quantum C ondensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -\n6393, USA  \n3Department of Physics, Technical University of Denmark, 2800 Kgs. Lyngby , Denmark  \n* Corresponding Author: jkrizan@princeton.edu  \nAbstract  \n We report the structura l and magnetic characterizations of Ba 3TeCo 3P2O14, Pb 3TeCo 3P2O14, and \nPb3TeCo 3V2O14, compounds that are based on the mineral Dugganite, which is isostructural to \nLangasites. The magnetic part of the structure consists of layers of Co2+ triangles. Nuclear and magnetic \nstructures were determined through a co -refinement of synchrotron and neutron powder diffraction \ndata. In contrast to the undistorted P321 Langasite structure of Ba 3TeCo 3P2O14, a complex structural \ndistortion yielding a large supercell is found  for both Pb 3TeCo 3P2O14 and Pb 3TeCo 3V2O14. Comparison of \nthe three compounds studied along with the zinc analog Pb 3TeZn 3P2O14, also characterized here, \nsuggests that the distortion is driven by Pb2+ lone pairs; as such, the Pb compounds crystallize in a \npyroelectric space group, P2.  Magnetic susceptibility, magnetization , and heat capacity measurements \nwere performed to characterize the magnetic behavior. All three compounds become antiferromagnetic \nwith Néel temperatures T N ≈ 21 K (Ba 3TeCo 3P2O14), ≈ 13 K ( Pb3TeCo 3P2O14), and ≈ 8 K (Pb 3TeCo 3V2O14), \nand they exhibit magnetic transitions at high  applied magnetic  fields, suggesting intrinsically complex \nmagnetic behavior for tetrahedrally coordinated d7 Co2+ in this structure type.  \nKeywords:  Langasite, Dugganit e, frustrated magnetism, neutron diffraction, structure determination, \nmagnetic structure, multiferroic, property measurements , co-refinement   Krizan 2 Introduction \nRecently, Langasites have been the focus of extensive research due to their  magnetic \nfrustratio n,1 multiferroic,2 non-linear optic al,3 piezoelectric ,4 ferroe lectric  and dielectric properties .4,5 \nMany of these  phenomena result from the non -centrosymmetric space group (P321) in which they \ncrystallize.  Ferroelectricity is not directly po ssible in the P321 space group, but  through the symmetry \nbreaking by  magnetic ordering  or a structural phase transformation to one of the polar sub -groups, this \nproperty can  be realized .6 Some Langasites are available commercially for use in surface acoustic wave \n(SAW) filters due to their exceptional piezoelectric properties. Hundreds of compounds with the \nLangasite crystal structure have been reported. The four crystallographic positions occupied by the \ncations are significantly d ifferent and tolerant to the accommodation of a wide variety of metals, which \nmakes the Langasites ideal for structure -property studies. Dugganite, Pb 3TeZn 3As2O14, is a mineral \nisostructural to Langasite, and is the inspiration for the compounds studied he re.7,8  \nThe prototypical Langasite, or Ca3Ga 2Ge 4O14 structure type ( typified by Ba 3TeCo 3P2O14, Figure  1), \npossess es two-dimensional lattices of ions which are  symmetry confined  by multiple independent \nthreefold rotation axes  to be in  equilateral  triangles. Occupied by the appropriate ions,9 these materials \nare ideal for the study of magnetic frustration  due to the high symmetry of the magnetic interactions. \nThe structure consists of two alternating layers of cations with triangle -based lattices: the first is  \ncomposed of AO 10 decahedra  and MO 6 octahedra , and the seco nd of larger M’O 4 and smaller M”O 4 \ntetrahedra. The large tetrahedra l site  can be popu lated by a magnetic ion,  forming a planar triangular \ncluster of M’O 4 tetrahedra sharing corners with the MO 6 octahedra in adjacent layers and the M”O 4 \ntetrahedra within the layer. This results in a magnetic lattice of two different size  triangles.  Alternat ively, \na magnetic rare earth can be plac ed in the decahedra to form a slightly puckered kagomé lattic e. \nInterest in the magnetism of the Langasites has been primarily focused on materials with praseodymium \nor neodymium on the kagomé net, or others with iro n in the triangular clusters  (in each case with the Krizan 3 other ions non -magnetic) .1,2,5,10– 14 With interplay between magnetic frustration and multiferroicity,  \nmaterials with cobalt in this structural motif are also currently of interest.15 \nHere we report our study of three compounds, Ba 3TeCo 3P2O14, Pb 3TeCo 3P2O14, and \nPb3TeCo 3V2O14 , whose existence was described in a broad chemical survey of Langasites7 - one of which \nhaving recently been characterized from a magnetic standpoint.15 We report the results of structural \ndeterminations based on co -refinement of high resolution synchrotron powder X -ray diffraction and \nneutron powder diffraction data of both the nuclear and magnetic structures. The Ba compound is \nessentially a normal Langasite, but structural distortions are found to give rise to a large supercell in the \nPb compounds, placing them in a pyroelectric space gr oup (indicating that multiferroicity would be \nallowed by symmetry in these materials ).6 Characterization includes the field and te mperature \ndependent magnetization and low temperature specific heat, which all suggest complex magnetic \nbehavior.  \nExperimental  \n Polycrystalline samples were prepared by typical solid state methods, with slight modifications \nfor each specific compound. Starting materials used for Pb 3TeCo 3V2O14 were PbO (Aldrich 99.999%), \nTeO 2 (99.995%), Co 3O4 (99.7%), and V 2O5 (Alfa >99.6%). Starting materials for Pb 3TeCo 3P2O14 and \nBa3TeCo 3P2O14 were PbO, BaCO 3, TeO 2, Co 3O4, and NH 4H2PO 4 (Fisher, HPLC Grade). The non -magneti c \nanalogues Pb 3TeZn 3P2O14, Pb 3TeZn 3V2O14 and Ba 3TeZn 3P2O14 were synthesized from PbO, BaCO 3, TeO 2, \nZnO (Alfa 99.99%), V 2O5, and NH 4H2PO 4 for use as background subtraction materials in the specific heat \nstudies. Stoichiometric (by metal) mixtures were groun d and placed in high density, covered alumina \ncrucibles and pre -reacted overnight at 550 ° C (Pb 3TeCo 3V2O14) or 450 °C under flowing oxygen. \nPb3TeCo 3V2O14 was fully reacted after subsequent heating at 625 °C in air. Pb 3TeCo 3P2O14 was \nsynthesized by addition al heating for 146 hours at 700 °C in a covered crucible under flowing oxygen \nwith intermittent grindings. Ba 3TeCo 3P2O14 was synthesized by subsequent heating at 800 °C for 120 Krizan 4 hours. The zinc analogues were synthesized under identical conditions except fo r Ba 3TeZn 3P2O14, which \nwas heated at 900 °C; all were heated until shown to be pure by laboratory X -ray powder diffraction \n(XRD). Laboratory diffraction experiments were carried out on Rigaku Miniflex II, and Bruker D8 Focus \ndiffractometers, both Cu Kα wit h graphite monochromator. Low temperatures and an oxidizing \natmosphere were critical in minimizing the volatilization of the starting materials and the formation of a \npure product. Pb 3TeCo 3P2O14 and Ba 3TeCo 3P2O14 powders are very bright indigo and purple r espectively. \nPb3TeCo 3V2O14 is a dull slate color with a hint of blue.  \n Bulk magnetic measurements were performed on powders of mass 75 – 140 mg using a \nCRYOGENIC Cryogen Free Measurement System (CFMS) V ibrating Sample Magnetometer (VSM). The \nmagnetic susce ptibility was recorded in a field of 0.1 T and temperatures between 2 and 300 K, using a \nscanning mode with a ramping rate of 2 K/min.  Magnetization measurements were performed at three \ntemperatures: 2 K, 11 K, and 23 K (Ba 3TeCo 3P2O14) or 30 K (Pb 3TeCo 3P2O14 and Pb 3TeCo 3V2O14), and fields \nup to 16 T using scanning sequences with a ramping rate of 0.2 T/min. Heat capacity measurements  \nbetween 2 K and 250  K were conducted in a Quantum Design Physical Property Measurement System \nusing the heat relaxation metho d. Dense polycrystalline pellets of 5 -10 mg were placed on the sapphire \nplatform using Apiezon N grease, of which the heat capacity was previously measured for subtraction.  \nSynchrotron X -ray powder diffraction (SXRD) data was collected at the Advanced Phot on Source at \nArgonne National Lab on beamline 11 -BM. The Pb -containing samples were loaded into 0.1  mm \ndiameter glass capillaries to reduce sample absorption. Ba 3TeCo 3P2O14 was loaded in a 0.8  mm Kapton \ntube due to its lower predicted absorption. The absor ption of the materials was calculated using the \nCromer & Liberman algorithm through the APS web interface.16 SXRD patterns were collected at a \nwavelength of 0.413159 Å over a 2θ  range of 0.5 to 50 degrees at 100 K to minimize the thermal \nparameters and match the temperature of the neutron diffraction data.  Krizan 5  Neutron powder diffraction (NPD) patterns for Ba 3TeCo 3P2O14 and Pb 3TeCo 3P2O14 were collected \nat the High Flux Isotope Reactor beam line HB- 2A at Oak Ridge National Laboratory. Diffraction patterns \nwere collected at both 100 K and 4 K with 2.41 Å and 1.54 Å wavelength neutrons,  as produced by \nGe[113] and Ge[115] reflections from a vertically focusing germanium wafer- stack monoc hromator . This \nresulted  in four NPD data sets for each compound. For all experiments, the collimation was set to 12’ -\nopen -6’ to increase the neutron flux but at the detriment of the resolution; this improved the statistics \nfor the determination of the magn etic structure and increased the visibility of the superstructure \nreflections. The magnetic structures were determined and refined through the use of the SARAh and \nFullProf software suites.17–19 \nBa3TeCo 3P2O14 Structural A nalysis  \nThe diffraction patterns for Ba 3TeCo 3P2O14 showed an ideal Langasite structure, space group \nP321. Peak sh apes were modeled with the Thompson -Cox-Hastings pseudo -Voight profile convoluted \nwith axial divergence asymmetry, but the high resolution SXRD pattern revealed an additional \nasymmetry for many of the peaks ( Figure  2). Using the prototypical Langasite stru cture, this resulted in a \ngood fit to the data. However , to account for the additional peak shape asymmetry which may be due to \nanisotropic strain arising at the grain boundaries ,20 the SXRD pattern was also modeled in FullProf as a \nconvolution of two identical phases wit h very slightly different cell parameters. There is no indication \nthat two distinct phases are actually present ; even at the highest angles in the high resolution SXRD \npattern there is a continuous distribution of intensity. For the final refinements of th e structure, five \ndiffraction patterns were co -refined simultaneously: four neutron diffraction patterns ( Figure  3; at 2.41 \nÅ and 1.54 Å at both 100 and 4 K) were simultaneously refined along with the SXRD data taken at 100 K, \nusing the same Debye -Waller factor for both temperatures.  All atomic positions were refined. For the 4 \nK data, the magnetic structure was also refined; this is described in a later section. The fit of the model Krizan 6 to the SXRD and NPD patterns is excellent (Figures 2 and 3). The results o f this refinement are presented \nin Table  1.  \nPb3TeCo 3P2O14 and Pb 3TeCo 3V2O14 Structural analysis  \nAnalysis of the SXRD patterns indicated that the basic Langasite structure with trigonal \nsymmetry could account for many of the peaks in the Pb -based compounds ,6 but that there were many \nsuperlattice peaks present ( Figure  4). Beginning with the nonisomorphic subgroups of space group P321 , \nand the subsequent subgroups, it was determined that the space group of the supercell is P2 for both \nPb3TeCo 3P2O14 and Pb 3TeCo 3V2O14.  \nFor Pb 3TeCo 3P2O14, iterative structure solutions using only the SXRD pattern were first \nperformed by varying only the p ositions of the cations, first in the prototypical P321 cell, then in the \nlarger, lower symmetry P2 cell. The very large unit cell and the number of independent atoms required that chemically reasonable constraints be imposed to facilitate the full superst ructure refinement. \nTellurium and phosphorous atoms were initially refined as the centers of octahedral TeO\n6 and \ntetrahedral PO 4 rigid body groups (RBG), respectively. RBG s are hard constraints on the positions of the \ncoordinating oxygen atoms in relation to the cations and to each other . These groups can then translate \nand rotate as a unit centered on the cation. In the octahedral TeO 6 RBG, the three oxygen atoms above \nthe tellurium are symmetry related to those below. This was initially set with a perfect  octahedral \norientation with one face of the octahedron parallel to the ab-plane and a fixed Te -O bond length of \n1.927 Å as determined from the initial refinements of Ba 3TeCo 3P2O14. The phosphorous -oxygen \ntetrahedron is well characterized in the literature  and is known to be fairly rigid in the solid state.21 The \nPO 4 tetrahedron was modeled after “orthophosphates proper” and adjusted for the apical oxyg en (O *) \ncorner sharing with the lead polyhedra, and for the base oxygens (O **) edge sharing with the lead \npolyhedra.21 This resulted in an initial model for the phosphate tetrahedron with the apical  P-O* \n(roughly parallel to the c -axis)  distance of 1.53045 Å and a base P -O** distance of 1.546 Å.  The bond Krizan 7 angles between the apex and the base (O *-P-O**) and within the base (O **-P-O**) were set as 111.2° \nand 106.3° , respectively.  \nThis model was implemented in a co -refinement of the supercell structure performed with the \nSXRD pattern at 100 K (0.413 Å ) and the NPD patterns at 100 K and 4 K  (both at 1 .54 Å and 2.41 Å ). Initial \nrefinements allowed for the translation of the PO 4 tetrahedra in three dimensions, and for the three \nsymmetry inequivalent oxygen atoms forming the octahedron  around tellurium to rotate as a unit in the \nab-plane. The fit was further improved by allowing for the tilting and twisting of the PO 4 tetrahedra. For \nthe co -refinement of the five diffraction patterns (four neutron diffraction patterns, at 2.41  Å and 1.54 Å \nat both 100 and 4 K and the SXRD data taken at 100 K) atomic positions and thermal parameters were \nconstrained to be the same fo r both the high temperature and low temperature neutron and SXRD data. \nTo account for thermal contraction of the unit cell, the a :b-ratio and the monoclinic β angle were held \nconstant in the neutron patterns since there was not sufficient resolution to distinguish the subtle \ndifferences in the temperature dependence of the metric distortion from trigonal symmetry. Careful \nanalysis of the individual patterns indicated that no significant structural changes occurred between 5 \nand 100 K. Thus the superstructure reported can be considered a thermal average of the 5 K and 100 K structures; any differences in the thermal parameters that may be present are beyond the scope of this study.  \nTo take full advantage of the better statistics of the 4 K neutron data, the magnetic contribution \nto the pattern needed to be modeled; alternating between refinement of the structural and magnetic components resulted in further improvements to the fit. The magnetic structure is described in a later \nsection of this report. The initially -employed  rigid body model for the P -O and Te -O polyhedra was \ndisabled after achieving a reasonable fit to the magnetic structu re and replaced by soft constraints on \nthe M -O bond lengths and O -O distances (Table 2). The final structural model for Pb\n3TeCo 3P2O14 is Krizan 8 presented in Table 3. The excellence of the fit of the model to the data can be seen in the SXRD pattern \nshown in figur e 4a, and in the NPD patterns shown in Figure 5.   \nIn the case of Pb 3TeCo 3V2O14, neutron diffraction data was not collected due to previous work15 \nand therefore only SXRD data was refined. The rigid body model developed for the full superstructure o f \nPb3TeCo 3P2O14 was carried over to the vanadate case with a slight modification to account for the size \ndifference between phosphorous -oxygen and vanadium -oxygen tetrahedra. The vanadium -oxygen bond \nlengths were changed to those typically observed ,22 but no changes in the orientation of the tetrahedra \nwere allowed other than simple translation. The oxygen coordination around the tellurium atoms was \nnot modified, but the position of the tellurium was refined. This yielded a stable  refinement and an \nexceptionally good fit to the synchrotron diffraction pattern ( Figure  4b) with few anomalous bond \nlengths.   Metal oxide bond lengths, especially the Co -O bond lengths, are not expected to be well \ndefined in this experiment.  \nThe crystal structure of Pb 3TeCo 3P2O14 is compared to Ba 3TeCo 3P2O14 in Figure s 6 and 7.  Atomic \npositions of the Pb compounds are given in Table  3 and 4 respectively. Selected bond lengths relating to \nthe Pb -O, Ba -O and Co -O coordination polyhedra in  Ba3TeCo 3P2O14 and Pb 3TeCo 3P2O14 are given in Table  \n5.  \nPb3TeZn 3P2O14 Structure Analysis  \nPb3TeZn 3P2O14, Pb 3TeZn 3V2O14, and Ba 3TeZn 3P2O14 were synthesized as non -magnetic analogs for \nsubtracting the lattice contribution in heat capacity measurements and were characterized using \nlaboratory PXRD. Pb3TeZn 3P2O14 was found to be isostructural to Pb 3TeCo 3P2O14. Using the atomic \ncoordinates obtained for the cobalt variant as a model result s in an excellent fit to the laboratory XRD \npattern for Pb 3TeZn 3P2O14 (see Figure 8).  Only the cell dimensions and a n overall Debye -Waller factor \nwere refined.  The monoclinic distortion puts the structure in space group P2 with unit cell parameters a \n= 14.51284(3), b  = 25.1385(2), c  = 5.1874(4), β = 90.0631 (β was fixed at the value found for Krizan 9 Pb3TeCo 3P2O14). The inset to Figure  8 shows details of the pattern in a region including superlattice \nreflections, which are visible in the laboratory powder XRD patterns, illustrating the quality of the fit.  \nFinal χ2 and R values are presented for the final structural model in Table  6. For quantitative \ndetermination of the structure of this phase, datasets and refinements similar to those performed here \nfor Pb 3TeCo 3P2O14 would be required.   \nResults – Bulk Mag netic Properties  \nFigure  9 shows the temperature dependent magnetic susceptibility and inverse susceptibility \nboth on heating and cooling with the results of a Curie -Weiss fit, for all three compounds. The Curie \nWeiss fits are to the data on heating and are  of the type 𝜒 =𝐶\n𝑇−𝜃 where C is the Curie constant, and θ \nthe Weiss temperature.  All three samples order antiferromagnetically, with ordering temperatures of  \n6.5(1)  K, 9.172(12) K , 12.9(1) K , and 20.9(4)  K, for Pb 3TeCo 3V2O14 (two transitions),  Pb3TeCo 3P2O14, and \nBa3TeCo 3P2O14 respec tively. These ordering temperatures were obtained from the maxima in a 𝑑𝜒𝑇\n𝑑𝑇 vs.𝑇 \nplot. For low applied  fields these materials act as traditional antiferromagnets; the Co2+ moments found \nin the fits to the susceptibility data above 150 K are 4. 46, 4. 73, and 4. 69 µB, respectively. These are \nhigher than the expected spin only value (3.87  µB) due to the presence of an incompletely quenched \norbital contribution  and agree with other experimental observations of Co2+. The Weiss temperatures \nare -21.05  K, -30.60  K and - 20.29 K, respectively . \nThe magnetic transitions were further characterized by the heat capacity, as shown in Figure  10. \nThe magnetic contribution to the heat capacity was determined by subtracting the lattice component \nestimated  by using non -magnetic Pb 3TeZn 3P2O14, Pb 3TeZn 3V2O14 and Ba 3TeZn 3P2O14 as standards. No \nscaling factor was employed , or necessary . Sharp ordering transitions were observed  and all are in \nagreement with susceptibility data . Though Pb 3TeCo 3P2O14 and B a3TeCo 3P2O14 exhibit  shoulders in the \nheat capacity at lower temperatures.  Pb3TeCo 3V2O14 exhibits two transitions in the heat capacity, in \nagreement with previously reported data,15 indicating the presence of two magnetically ordered phases Krizan 10 at zero applied field. In all cases, there is a significant amount of magnetic entropy released on cooling \nat temperatures above the 3D  ordering transition. The total entropy released approaches the amount \nexpected for spin 3/2, with the small differences from the expected value likely due to the inexactness \nof the lattice heat capacity subtraction.  \nFigure 11 shows the VSM measurements of the magnetizations at 3 K and 11 K for all three \nsamples, at 30 K for Pb 3TeCo 3P2O14 and Pb 3TeCo 3V2O14, and at 23 K for Ba 3TeCo 3P2O14, recorded in \nincreasing and  decreasing fields up to 16 T. The results for Pb 3TeCo 3P2O14 and Ba 3TeCo 3P2O14 show \npronounced hysteresis, and in particular Ba 3TeCo 3P2O14 displays a dramatic jump in the magnetizations \nat low temperatures, indicating first  order field induced phase transitions. The effect of field on the \nmagnetic states  of Ba 3TeCo 3P2O14 is particularly dramatic; there are clearly three different magnetic \nordering reg imes encountered before the 16 T  limit of the applied field. Although there  is no significant \nhysteresis in the Pb 3TeCo 3V2O14 sample, it displays an S -shape variation at low temperatures that also \nindicates a magnetic transition driven by the applied field.   \nResults – Magnetic S tructures  \nThe magnetic superlattice reflections of Ba 3TeCo 3P2O14 were indexed with a k -vector of (1/3, \n1/3, 1/2).  This k -vector was determined through an iterative search through the Brillouin zone focusing \non the high symmetry directions. The software package SARAh Refine was used for this purpose with a Reverse Monte Carlo algorithm to perform a rough fit to the data and determine the most likely k -\nvector. After successfully indexing the patterns, SARAh Representational Analysis was used to calculate the different symmetry allowed basis vectors ( ψ) and the irreducible representations ( Γ) that they could \nform.\n19 Using the FullProf Software suite, the irreducible representations were subsequently analyzed to \ndetermine which could most accurately model the magnetic structure peaks before proceeding with a \ncareful quantitative refinement.   Krizan 11 The magnetic structures of Ba 3TeCo 3P2O14 and Pb 3TeCo 3P2O14, as expressed in terms of the \nirreducible representation ( Γ) and basis vectors ( ψ) in the scheme used by Kovalev’s tabulated works ,23 \nare reported in Tables 7 and 8 respectively. For both Pb 3TeCo 3P2O14 and Ba 3TeCo 3P2O14 (Figure 12), the \nrefinements of the magnetic structu res at zero applied field indicate that there are ferromagnetic \ntriangular cobalt clusters that are coupled antiferromagnetically both in the ab- plane and along the c -\naxis by nature of the respective k- vectors.  \nPb3TeCo 3P2O14, however, exhibits another typ e of cluster behavior. T he cobalt atoms at a =1/2 \nmust have moments along the b -axis as a res ult of the symmetry constraints allowed  by Γ1. A symmetry \nanalysis places no restrictions on the direction of the adjacent (symmetry equivalent) moments in the \ntriad and  so to facilitate finding  a simple model that can be used to approximate the true magnetic \nstructure, these are assumed to be clusters with zero net spin. The model presented here in Figure 12 is the simplest model found that reasonably fits the data  using Γ\n1. While it is not immediately clear what \nwould lead to this behavior, the modulation of the moments improves the fit and this behavior is \nconsistent with the model presented here for Ba 3TeCo 3P2O14 and the model for Pb 3TeCo 3V2O14 in the \nliterature .15 \nBoth magnetic structures are consistent with the geometry of the oxygen sublattice. Looking at \nsuperexchange interactions within the triangular clusters, a  nearest -neighbor  ferromagnetic interaction \nis expected, and in the inter -triangle Co -O-O-Co case, super -superexchange interactions are mediated \nthrough a series of large bond angles that give the expected antiferromagnetic interaction. Interestingly \nhowever, both structures seem to illustrate mixed antiferromagnetic and ferromagnetic interact ions \nbetween adjacent triangular clusters within the ab- plane , suggesting a competition between the two \ninteractions . \nDiscussion  and Conclusion  Krizan 12 Ba3TeCo 3P2O14 displays an essentially prototypical  P321 Langasite structure. The phosphate \ntetrahedra display po sitional disorder in this compound, however, manifested in the split oxygen \npositions in the PO 4 units (Figure 1). In the refinement of Pb 3TeCo 3P2O14, the large cell posed a challenge \nfor obtaining an accurate full superstructure determination from the pow der data. With 78  unique \natoms in the unit cell of Pb 3TeCo 3P2O14, spanning from very heavy t o very light, co -refinement of \nneutron and X -ray data was needed for a successful determination of the full superstructure . Careful use \nof hard and soft constraints  on the atomic positions was employed to reach a final structural model. \nAfter lifting the RBG restraints and replacing them with soft bond length constraints, both TeO 6 and PO 4 \npolyhedra retained their shapes and did not distort significantly. In applying the superstructure model \nderived for Pb 3TeCo 3P2O14 to Pb 3TeCo 3V2O14, it was hypothesized that the oxygen sublattices are almost \nbut not quite identical. The st able  refinement and the exceptionally good fit to SXRD data support this \nhypothesis. Co -refineme nt of SXRD and NPD data would improve the details of our structural model for \nPb3TeCo 3V2O14, rectifying some of the anomalous M -O bond lengths. We note that complex structural \ndistortions of the La 3SbZn 3Ge 2O14 Langasite  have  also been reported, with an eve n larger unit cell than \nthat found here, but no structural solution was obtained.24  \n Comparing these three compounds shows the subtle effects of the stereochemical lone pairs on \nPb2+. The fact that both the Pb2+ variants (and the Zn analo gues) display a nearly identical metric \ndistortion from trigonal symmetry suggests that the cation in the decahedral site has a strong influence \non the rest of the structure.  The Pb lone pairs are the driving force, and result in a transition metal \nindepen dent effect on the crystal structure.  This effect is seen in the comparison of Pb 3TeCo 3P2O14 and \nBa3TeCo 3P2O14 (Figure  6); it is clear that the introduction of Pb has resulted in significant atomic \ndisplacements. With respect to the Ba analog, the Pb analo g displays its most significant deviations from \nthe higher symmetry in the ab- plane. The most notable shifts are those of the Pb and the phosphate \ntetrahedra: the phosphate tetrahedra predominantly rotate in the ab- plane and the Pb cations Krizan 13 immediately surrounding each tetrahedron rotate counter to this motion. The PO 4 tetrahedra share all \noxygen anions with the surrounding Pb polyhedra resulting in an intimate relationship between the two. \nDistortions of the phosphate groups and the Pb coordination are thus  likely both a result of the \nstereochemical lone pairs on Pb2+.25 Figure  7 compares the Pb -O coordination to the Ba -O coordination. \nWithin their coordination spheres,  the Pb and the Ba sit closer to the oxygens shared with the TeO 6 \noctahedra. However, this is significantly more exaggerated in the Pb -O coordination, in agreement with \nthe expected involvement of the lone pairs. The range of bond leng ths for the Pb -O coordination \npolyhedra are compared to those of the Ba- O polyhedra in Table  5. \n Structurally,  substituting Pb for Ba in  Pb3TeCo 3P2O14 and Pb 3TeCo 3V2O14 (and Pb 3TeZn 3P2O14) \npushes these materials over  a tipping point. The lone pairs on Pb2+ push the structures into a large \nsupercell that breaks the strict three- fold symmetry, with the consequence that some of the magnetic \nfrustration intrinsic to the Langasite structure is relieved. With respect to the corresponding dimension in the original P321 cell, the a -axis in the monoclinic cell is compressed, resulting in symmetry -confined \nisosceles triangle cobalt clusters. Additionally, in  both Pb\n3TeCo 3P2O14 and Ba 3TeCo 3P2O14, the cobalt \ncations are displaced towards the edges of their tetrahedra. T his can be considered as an overall \ncontraction of the cobalt clusters, suggesting strong magnetic interactions between cobalt cations within each discrete cluster.   \nDugganite and other structural analogues of Langasite with Pb\n2+ in the decahedral site are  likely \nto exhibit similar behavior, and should be further investigated by SXRD. (The previously reported structure of Pb\n3TeCo 3V2O1415 actually represents the substructure, determined without taking into \naccount the superlattice.) In the compounds reported here, even taking the supercell into account in the current refinements, the characterization of the phosphorous tetrahedra indicates that in all cases some residual disorder is present; the refinements suggest that there is room for the small PO\n4 tetrahedron to \nrattle in the cage formed by the rest of the structure and that the stereochemical lone pairs on the Pb2+ Krizan 14 help to direct the orientations of the tetrahedra. (The “disorder” of the tetrahedra could reflect the \npresence of a supercell that is  even larger than the one detected and  described here.)  \n The compounds all display typical Curie -Weiss behavior in low magnetic fields.  In the case of \nPb3TeCo 3V2O14, this is in agreement with a previous report.15 For each of the three materials st udied, the \nmagnetic transition is reasonably sharp. The index of frustration ( θ/Tn) is apparently low, but this is due \nto the low values of θ that artificially result from the competition between ferromagnetic and \nantiferromagnetic interactions in these compounds. Heat capacity data for all three compounds showed sharp transitions c orresponding to the antiferromagnetic ordering. Pb\n3TeCo 3V2O14 exhibited two sharp \ntransitions, as previously reported . The magnetic heat capacities (Figure 10) show that both \nPb3TeCo 3P2O14 and Ba 3TeCo 3P2O14 have anomalies below the sharp ordering peak that  could potentially \nbe representative of broad transitions. This is further corroborated by slight kinks in the high resolution magnetic susceptibility  (Figure 9)  at the corresponding temperatures. These transitions could be related \nto the second sharp tran sition observed in Pb\n3TeCo 3V2O14, though further work is needed to analyze this \ncomplex magnetic behavior.  All three compounds released  a significant amount of entropy at \ntemperatures above the 3D magnetic ordering transition. This suggests that short rang e ordering is \npresent above the 3D ordering temperatures. Of the three, the Ba analog is most interesting from this \nperspective – it releases half of the entropy before the 3D  ordering transition on cooling, suggesting the \npresence of much more substantial  short range order before the 3D T N than is exhibited by the other \ntwo compounds.  \n All three of the compounds display complex behavior in magnetic fields greater than 5 T . Up to \nthis point , the magnetization is linear. At higher fields, several magnetic st ates are observed. While none \nof these compounds has a fully saturated magnetization by 16 T  at 3 K, Ba 3TeCo 3P2O14 is nearly \nsaturated. This compound shows at least two distinct magnetic transitions and a large hysteresis . \nPb3TeCo 3P2O14 and Pb 3TeCo 3V2O14 behave similarly, with one distinct transition occurring far before Krizan 15 magnetization saturation; this suggests that there may be another transition in these compounds \nanalogous to the one at high field observed in Ba 3TeCo 3P2O14, but just outside of the measure ment \nrange. These measurements also suggest that the magnetic behavior is similar in all the materials, a \nproperty of Co2+ in this particular crystallographic environment and magnetic sublattice, but that the \nbehavior may be different in the Ba analog due to its higher symmetry.  \n The structural distortions observed in Pb 3TeCo 3P2O14 and Pb 3TeCo 3V2O14 and their novel \nmagnetic properties under applied field makes them of interest as potential multiferroics. Materials \nwith cobalt in the Ca 3Ga 2Ge 4O14 structure type appear to exhibit novel behavior under high magnetic  \nfields, and thus it is of interest to look for more Co2+ variants: few are reported compared to  those with  \nFe3+ on the same site. Further measurements of these materials will ideally involve single crystal \nmeasurements of both the crystal structure and the magnetism. The simple model of the magnetic structure reported here, while not unique and despite showing such a difference in the nature of the \nmagnetism in the cobalt triads, exhibits some fundam ental characteristics that are in agreement with \nthe nuclear structure and the magnetic properties; single crystal experiments are needed to determine the magnetic structure unambiguously. To date, the magnetic Langasites and Dugganite s have only been \nrepo rted in the noncentrosymmetric, trigonal space group P321; the two Pb variants reported here are \nthe first compounds with structures in one of the pyroelectric space groups, a necessary symmetry requirement for the rise of multiferroicity.  Further measurem ents would be of interest to determine \nwhether the materials studied here are indeed multiferroic.  \nAcknowledgements  \nThe authors would like to thank S. Dutton for helpful discussions. This research was supported \nby the U . S. Department of Energy, Division o f Basic Energy Sciences,  Grant DE -FG02 -08ER46544. The \nauthors thank the 11 -BM team for their excellent synchrotron diffraction data; u se of the Advanced \nPhoton Source at Argonne National Laboratory was supported by the U. S. Department of Energy, Office Krizan 16 of Science, Office of Basic Energy Sciences, under Contract No. DE -AC02 -06CH11357.  The research  \nperformed at the High Flux Isotope Reactor at the Oak Rid ge National Laboratory was  sponsored by the \nScientific User Facilities Division, Office of Basic Energy S ciences, U . S. Department of Energy.  \n  Krizan 17 References  \n(1)  Choi, K. Y.; Wang, Z.; Ozarowski, A.; Van Tol, J.; Zhou, H. D.; Wiebe, C. R.; Skourski, Y.; Dalal, N. S. Journal \nof Physics: Condensed Matter  2012, 24, 246001.  \n(2)  Zhou, H. D.; Lumata, L. L.; Kuhns, P. L.; Reyes, A. P.; Choi, E. S.; Dalal, N. S.; Lu, J.; Jo, Y. J.; Balicas, L.; Brooks, J. S.; Wiebe, C. R. Chem. Mater.  2009 , 21, 156– 159.  \n(3)  Heimann, R. B.; Hengst, M.; Rossberg, M.; Bohm, J. physica status solidi (a)  2003 , 195, 468 –474.  \n(4)  Mill, B. V.; Pisarevsky, Y. V. In Frequency Control Symposium and Exhibition, 2000. Proceedings of the \n2000 IEEE/EIA International ; IEEE, 2000; pp. 133 –144.  \n(5)  Marty, K.; Bordet, P.; Simonet, V.; Loire, M.; Ballou, R.; Darie, C. ; Kljun, J.; Bonville, P.; Isnard, O.; Lejay, \nP.; Zawilski, B.; Simon, C. Phys. Rev. B  2010 , 81, 054416.  \n(6)  Hahn, T. International Tables for Crystallography, Volume A: Space Group Symmetry ; 5th ed.; Wiley, \n2011.  \n(7)  Mill, B. V. Russ. J. Inorg. Chem. 2009, 54, 1205 –1209.  \n(8)  Anthony, J. W.; Bideaux, R. A.; Bladh, K. W. Handbook of Mineralogy ; Nichols, M. C., Ed.; Mineralogical \nSociety of America: Chantilly, VA 20151 -1110, USA., 2006.  \n(9)  Belokoneva, E. L.; Simonov, M. A.; Butashin, A. V.; Mill’, B. V.;  Belov, N. V. Soviet Physics Doklady  1980 , \n25, 954.  \n(10)  Bordet, P.; Gelard, I.; Marty, K.; Ibanez, A.; Robert, J.; Simonet, V.; Canals, B.; Ballou, R.; Lejay, P. Journal \nof Physics: Condensed Matter  2006, 18, 5147.  \n(11)  Ghosh, S.; Datta, S.; Zhou, H.; H och, M.; Wiebe, C.; Hill, S. J. Appl. Phys. 2011, 109, 07E137.  \n(12)  Marty, K.; Simonet, V.; Bordet, P.; Ballou, R.; Lejay, P.; Isnard, O.; Ressouche, E.; Bourdarot, F.; Bonville, \nP. Journal of Magnetism and Magnetic Materials  2009, 321, 1778 –1781.  \n(13)  Loire, M.; Simonet, V.; Petit, S.; Marty, K.; Bordet, P.; Lejay, P.; Ollivier, J.; Enderle, M.; Steffens, P.; \nRessouche, E.; Zorko, A.; Ballou, R. Phys. Rev. Lett. 2011, 106, 207201.  \n(14)  Lumata, L. L.; Besara, T.; Kuhns, P. L.; Reyes, A. P.; Zhou, H. D.; Wiebe, C. R.; Balicas, L.; Jo, Y. J.; Brooks, J. \nS.; Takano, Y.; Case, M. J.; Qiu, Y.; Copley, J. R. D.; Gardner, J. S.; Choi, K. Y.; Dalal, N. S.; Hoch, M. J. R. Phys. Rev. B  2010, 81, 224416.  \n(15)  Silverstein, H. J.; Cruz -Kan, K. C.; Hallas, A. M.; Zhou , H.; Donaberger, R. M.; Hernden, B. C.; Bieringer, M.; \nChoi, E. S.; Hwang, J. M.; Wills, A. S.; Wiebe, C. R. Chem. Mater.  2012.  \n(16)  Cromer, D. T.; Liberman, D. A. Acta Crystallographica Section A 1981 , 37, 267 –268.  \n(17)  Rodríguez- Carvajal, J. Newslette r of the Commission on Powder Diffraction  2001 , 26, 12–19. \n(18)  Rodríguez- Carvajal, J. Physica B: Condensed Matter  1993 , 192, 55–69. \n(19)  Wills, A. S. Physica B: Condensed Matter  2000 , 276, 680 –681.  \n(20)  West, D. V.; Davies, P. K. J. Appl. Crystallogr. 2011 , 44, 595 –602.  \n(21)  Baur, W. H. Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry  1974, 30, \n1195– 1215.  \n(22)  Shannon, R. D.; Prewitt, C. T. Acta Crystallographica Section B: Structural Crystallography and Crystal \nChemis try 1969, 25, 925 –946.  \n(23)  Kovalev Representation of Crystallographic Space Groups: Irreducible Representations, Induced \nRepresentation and Corepresentations ; CRC Press, 1993.  \n(24)  Mill, B. V.; Maksimov, B. A.; Pisarevsky, Y. V.; Danilova, N. P.; Markin a, M. P.; Pavlovska, A.; Werner S; \nSchneider, J. In Frequency Control Symposium and Exposition, 2004. Proceedings of the 2004 IEEE International ; IEEE, 2004; pp. 52–  60. \n(25)  Lam, A. E.; Groat, L. A.; Cooper, M. A.; Hawthorne, F. C. The Canadian Mineralogist  1994 , 32, 525 –532.  \n(26)  Bérar, J. F.; Lelann, P. Journal of Applied Crystallography  1991, 24, 1–5. \n Krizan 18 Figure s \nFigure  1: The crystal structure of Ba 3TeCo 3P2O14, which has  the prototypical Ca3Ga 2Ge 4O14 structure type. \nEach crystallographic site is differentiated by color (online) . Shown are the individual layers that \ncomprise the structure.  In the lower right image, shaded triangles join the magnetic cations to in the \nmagnetic sublattice and show the  two different types of cobalt triangles  present.  \nFigure  2: Rietveld refinement of synchrotron diffraction data for Ba 3TeCo 3P2O14 from 11 -BM. Upper inset \nshows fit at high angles.  Lower inset shows the peak  asymmetry that was modeled by the  inclusion of a \nsecond “dummy phase” in the refinement . \nFigure  3: Combined Rietveld refinements of Ba 3TeCo 3P2O14 using the 2.41 Å and 1.54 Å NPD data.  Inset \nhighlights the magnetic peaks in the 2.41 Å diffraction data.  \nFigure  4: Rietveld refinements of synchrotron diffraction data from 11 -BM. Top: Pb 3TeCo 3V2O14 Bottom: \nPb3TeCo 3P2O14 Upper insets highlight splitting of trigonal peaks that confirm the monoclinic distortion.  \nLower insets highlight the fit of the P2 supercell with six times increase in volume  over the standard \nLangasite cell.  \nFigure  5: Combined R ietveld refinements of Pb 3TeCo 3P2O14 using the 2.41 Å and 1.54 Å NPD data.  Inset \nhighlights the magnetic peaks in the 2.41 Å diffraction data.   \nFigure  6: Crystal Structures of Pb 3TeCo 3P2O14 and Ba 3TeCo 3P2O14 as viewed along the c -axis.  Arrows show \ndirection of ion displacement  in Pb 3TeCo 3P2O14 relative to the higher symmetry Ba 3TeCo 3P2O14. Also \nshown are the respective unit cells for spatial comparison (cells normalized for comparison).   \nFigure  7: Comparison of Pb -O and Ba -O coordination showing the effect of  Pb2+ stereochemical lone \npairs.  Two bond distances are given to account for the split oxygen position.  \nFigure  8: Rietveld refinement of the laboratory XRD data for Pb 3TeZn 3P2O14. Structural model is taken \nfrom Pb 3TeCo 3P2O14; the only changes made were the substitution of zinc for cobalt, the unit cell size, \nand t he overall Debye -Waller factor.  Similar peaks are found in Pb 3TeZn 3V2O14.  Krizan 19 Figure  9: Temperature dependent magnetic susceptibility (upper panel) and inverse susceptibility (lower \npanel) for Pb 3TeCo 3V2O14, Pb3TeCo 3P2O14, and Ba 3TeCo 3P2O14. Samples show distinct antiferromagnetic \nordering and minimal frustration as evidenced by index of frustration ( f=|θW|/TN). Inset of parameters \ndetermined by fitting the data on heating to the Curie -Weiss law.   \nFigure  10: Temperature dependent h eat capacity normalized per mole of cobalt.  Pb3TeCo 3V2O14 is the \nonly variant  that exhibits  two distinct  magn etic transitions in zero field.  The magnetic component of the \nheat capacity and the entropy release show that there is a significant amount of entropy released above \nTn in all cases.  Vertical lines are drawn to illustrate transition temperatures across all panels.  Inset sh ows \nheat capacity comparison of Ba 3TeCo 3P2O14 and nonmagnetic Ba 3TeZn 3P2O14. \nFigure  11: Field dependent magneti zation of compounds up to 16 T.  Each illustrates field driven \ntransitions suggesting that this is inherent to cobalt in this type of magnetic sub lattice.  Ba3TeCo 3P2O14 \nand Pb 3TeCo 3P2O14 exhibit large hysteresis.  Arrows indicate the direction of field change.  \nFigure  12: Magnetic s tructure  models  of Ba 3TeCo 3P2O14 and Pb 3TeCo 3P2O14. Both structures exhibit \nferromagnetic coupling within each triangle as well as antiferromagnetic coupling between triangles and \nlayers.  Structures are shown from the same perspective for ease of comparison.  \n  Krizan 20  \nFigure  1:   \nKrizan 21  \nFigure  2:  \nKrizan 22  \nFigure  3:  \nKrizan 23  \nFigure  4:  \nKrizan 24  \nFigure  5: \n  \nKrizan 25  \nFigure  6:  \nKrizan 26  \nFigure  7:  \nKrizan 27  \nFigure  8:  \nKrizan 28  \nFigure  9:  \nKrizan 29  \nFigure  10:   \nKrizan 30  \nFigure  11:  \nKrizan 31  \nFigure  12:  \nKrizan 32  \nTable  1: Crystal Structure of Ba 3TeCo 3P2O14† \nPrimary Phase  Space Group  100 K  a=8.44862(2)  Å b=8.44862(2)  Å c=5.313998 (13) Å \n   Z = 1 4 K a=8.44 64(6)  Å a=8.44 64(6)  Å c=5.31 46(5 ) Å \n   P 3 2 1   α=90 ° β=90°  γ=120°  \nAtom  Site X y z Biso  U11 U22 U33 U12 U13 U23 \nBa 3e 0.56161(5)  0 0 0.243  0.0013(2)  0.0009(3)  0.0020(4)  0.00045(13)  0.00 00(5)  0.000(1)  \nTe 1a 0 0 0 0.287  0.0016(5)  0.0016(5)  0.002(1)  0.00 8(3) 0.00  0.00  \nCo 3f 0.23437(5)  0 1/2 0.1934(5)        \nP 2d 2/3 1/3 0.53718(5)  0.184(2)        \nO1* 6g 0.6602(6)  0.3415(5)  0.25059(5)  0.065(6)        \nO2**  6g 0.5227(1)  0.71845(5)  0.3516(1)  0.200(2)  Occ. = 0.5       \nO3**  6g 0.51686(5)  0.69851(5)  0.3522(1)  0.200(2)  Occ. = 0.5       \nO4 6g 0.78546(5)  0.90707( 5) 0.79196(5)  0.240  0.00 15(16)  0.001(2)  0.000(2)  0.000(1)  0.00  0.00  \n† Estimated standard deviations (ESDs) were multiplied by 5.19 to account for the presence of \ncorrelated residuals.26 \n* Apical Oxygen  \n** Base Oxygen  \n \nTable  2: Soft constraints implemented in the refinement  of Pb 3TeCo 3P2O14 \nBond  Length  (Å)  Sigma  (Å)  \nCo-O 1.97  0.09  \nTa-O 1.93  0.05  \nP-O* 1.531  0.01  \nP-O** 1.546  0.01  \n* Apical Oxygen  \n** Base Oxygen  \n   Krizan 33 Table  3: Crystal Structure of Pb 3TeCo 3P2O14† \nMonoclinic   100 K  a=14.47600(6)  Å b=25.0579(1)  Å c=5.214222(16)  Å \n  4 K a=14.47371(5)  Å b=25.0378(4)  Å c=5.21340(9)  Å \nSpace Group P 1 2 1  Z = 6  α=90 ° β=90.0304(4)  ° γ=90°  \nType  Site x y z Biso Type  Type  x y z Biso \nPb1 1a 0 0.4686(17)  0 0.289(3)  Co4 1d 1/2 0.409(4)  1/2 0.17(1)  \nPb2 1c 1/2 0.9734(17)  0 0.289(3)  Co5 1b 0 0.248(4)  1/2 0.17(1)  \nPb3 1a 0 0.794(2)  0 0.289(3)  Co6 1d 1/2 0.752(4)  1/2 0.17(1)  \nPb4 1c 1/2 0.292(2)  0 0.289(3)  Co7 2e 0.114(5)  0.041(3)  0.497(18)  0.17(1)  \nPb5 1a 0 0.133(2)  0 0.289(3)  Co8 2e 0.632(5)  0.537(3)  0.523(17)  0.17(1)  \nPb6 1c 1/2 0.631(2)  0 0.289(3)  Co9 2e 0.119(5)  0.699(3)  0.510(18)  0.17(1)  \nPb7 2e 0.2941(15)  0.0953(15)  0.990(5)  0.289(3)  Co10  2e 0.626(5)  0.203(3)  0.485(5)  0.17(1)  \nPb8 2e 0.7848(15)  0.5940(15)  0.003(5)  0.289(3)  Co11  2e 0.120(5)  0.371(3)  0.488(18)  0.17(1)  \nPb9 2e 0.295(3)  0.7627(14)  0.009(7)  0.289(3)  Co12  2e 0.634(5)  0.871(3)  0.493(19)  0.17(1)  \nPb10  2e 0.800(2)  0.2630(14)  0.987(7)  0.289(3)  O19* 2e 0.166(9)  0.161(6)  0.253(5)  0.256(1)  \nPb11  2e 0.293(2)  0.4225(13)  0.013(6)  0.289(3)  P1 2e 0.1676(17)  0.166(9)  0.546(4)  0.256(1)  \nPb12  2e 0.806(2)  0.9288(13)  -0.002(7)  0.289(3)  O20** 2e 0.136(8)  0.111(2)  0.65(2)  0.256(1)  \nO1 2e 0.050(8)  0.716(4)  0.21(2)  0.17(1)  O21** 2e 0.104(7)  0.210(4)  0.65(2)  0.256(1)  \nTe1 1a 0 0.658(2)  0 0.17(1)  O22** 2e 0.262(5)  0.178(5)  0.67(2)  0.256(1)  \nO2 2e 0.899(7)  0.648(5)  0.23(2)  0.17(1)  O23* 2e 0.332(9)  0.662(6)  0.737(5)  0.256(1)  \nO3 2e 0.068(7)  0.604(4)  0.20(2)  0.17(1)  P2 2e 0.3351(17)  0.664(9)  0.44 3(4) 0.256(1)  \nO4 2e 0.541(9)  0.215(4)  0.21(2)  0.17(1)  O24** 2e 0.393(7)  0.712(3)  0.35(2)  0.256(1)  \nTe2 1c 1/2 0.154(2)  0 0.17(1)  O25** 2e 0.237(4)  0.670(5)  0.33(2)  0.256(1)  \nO5 2e 0.393(8)  0.154(5)  0.22(20)  0.17(1)  O26** 2e 0.377(8)  0.612(3)  0.34(2)  0.256(1)  \nO6 2e 0.569(8)  0.106(5)  0.21(20)  0.17(1)  O27* 2e 0.163(4)  0.828(3)  0.246(4)  0.256(1)  \nO7 2e 0.062(7)  0.054(4)  0.167(18)  0.17(1)  P3 2e 0.1608(16)  0.8261(9)  0.540(4)  0.256(1)  \nTe3 1a 0 0 0 0.17(1)  O28** 2e 0.095(7)  0.868(3)  0.66(3)  0.256(1)  \nO8 2e 0.057(6)  0.944(4)  0.19(20)  0.17(1)  O29** 2e 0.256(4)  0.837(5)  0.67(2)  0.256(1)  \nO9 2e 0.892(7)  0.992(5)  0.21(2)  0.17(1)  O30** 2e 0.122(8)  0.773(3)  0.64(2)  0.256(1)  \nO10  2e 0.548(8)  0.548(4)  0.22(2)  0.17(1)  O31* 2e 0.328(8)  0.325(6)  0.744(5)  0.256(1)  \nTe4 1c 1/2 0.491(2)  0 0.17(1)  P4 2e 0.3314(16)  0.3277(10)  0.450(4)  0.256(1)  \nO11  2e 0.402(7)  0.485(5)  0.23(2)  0.17(1)  O32** 2e 0.397(7)  0.371(4)  0.34(2)  0.256(1)  \nO12  2e 0.562(7)  0.440(4)  0.22(2)  0.17(1)  O33** 2e 0.232(4)  0.332(5)  0.34(2)  0.256(1)  \nO13  2e 0.047(8)  0.392(4)  0.22(2)  0.17(1)  O34** 2e 0.363(9)  0.273(3)  0.35(3)  0.256(1)  \nTe5 1a 0 0.336(2)  0 0.17(1)  O35* 2e 0.160(9)  0.487(4)  0.211(6)  0.256(1)  \nO14  2e 0.893(7)  0.326(5)  0.21(2)  0.17(1)  P5 2e 0.1667(17)  0.4960(9)  0.500(4)  0.256(1)  \nO15  2e 0.065(7)  0.285(4)  0.21(2)  0.17(1)  O36** 2e 0.078(3)  0.515(4)  0.637(14)  0.256(1)  \nO16  2e 0.539(8)  0.893(4)  0.21(2)  0.17(1)  O37** 2e 0.235(5)  0.539(3)  0.59(2)  0.256(1)  \nTe6 1c 1/2 0.832(2)  0 0.17(1)  O38** 2e 0.202(6)  0.4402(18)  0.577(18)  0.256(1)  \nO17  2e 0.397(7)  0.827(5)  0.22( 2) 0.17(1)  O39* 2e 0.322(8)  0.998(6)  0.754(5)  0.256(1)  \nO18  2e 0.567(8)  0.780(4)  0.20(2)  0.17(1)  P6 2e 0.3273(17)  0.9999(10)  0.460(4)  0.256(1)  \nCo1 1b 0 0.575(4)  1/2 0.17(1)  O40** 2e 0.392(7)  0.043(4)  0.34(2)  0.256(1)  \nCo2 1d 1/2 0.073(4)  1/2 0.17(1)  O41** 2e 0.236(4)  0.009(5)  0.312(18)  0.256(1)  \nCo3 1b 0 0.916(5)  1/2 0.17(1)  O42** 2e 0.369(8)  0.947(3)  0.36(2)  0.256(1)  \n† ESDs  were multiplied by 2.79 to account for the presence of correlated residuals.26 \n* Apical Oxygen  \n** Base Oxygen  \n \n  Krizan 34 Table  4: Crystal Structure of Pb 3TeCo 3V2O14† \nMonoclinic    a=14.81359(9)  Å b=25.64683(16)  Å c=5.21137(3)  \nSpace Group P 1 2 1  Z = 6  α=90 ° β=90.0631(8) ° γ=90°  \nType  Site x y z Biso‡ Type Site x y z Biso‡ \nPb1 1a 0 0.466(2)  0 0.55(2)  Co4 1d 1/2 0.416(4)  1/2 0.3 \nPb2 1c 1/2 0.972(2)  0 0.55(2)  Co5 1b 0 0.254(4)  1/2 0.3 \nPb3 1a 0 0.790(2)  0 0.55(2)  Co6 1d 1/2 0.756(4)  1/2 0.3 \nPb4 1c 1/2 0.287(2)  0 0.55(2)  Co7 2e 0.137(4)  0.044(3)  0.48(2)  0.3 \nPb5 1a 0 0.130(2)  0 0.55(2)  Co8 2e 0.617(5)  0.534(3)  0.52(2)  0.3 \nPb6 1c 1/2 0.626(2)  0 0.55(2)  Co9 2e 0.113(5)  0.696(3)  0.51(2)  0.3 \nPb7 2e 0.296(1)  0.096(2)  -0.009(5)  0.55(2)  Co10  2e 0.620(5)  0.200(3)  0.51(2)  0.3 \nPb8 2e 0.788(1)  0.594(2)  0.005(5)  0.55(2) Co11  2e 0.114(5)  0.378(3)  0.48(2)  0.3 \nPb9 2e 0.300(2)  0.764(2)  -0.001(6)  0.55(2)  Co12  2e 0.630(5)  0.867(3)  0.50(2)  0.3 \nPb10  2e 0.807(2)  0.265(2)  -0.009(6)  0.55(2)  O19  2e 0.16702  0.15831  0.19745  0.15  \nPb11  2e 0.298(1)  0.419(2)  0.022(4)  0.55(2)  V1 2e 0.17(1)  0.16 3(7) 0.53(3)  0.3 \nPb12  2e 0.818(1)  0.930(2)  -0.001(5)  0.55(2)  O20  2e 0.13098  0.10437  0.67756  0.15  \nO1 2e 0.04424  0.71084  0.2124  0.2 O21  2e 0.09285  0.21116  0.64382  0.15  \nTe1 1a 0 0.65 5(5) 0 0.4 O22  2e 0.27223  0.17712  0.6599  0.15  \nO2 2e -0.1059  0.649  0.2124  0.2 O23  2e 0.33201  0.66788  0.77637  0.15  \nO3 2e 0.06191  0.60482  0.2124  0.2 V2 2e 0.33(1)  0.66 7(7) 0.44(3)  0.3 \nO4 2e 0.53762  0.20884  0.2124  0.2 O24  2e 0.39797  0.71829  0.31304  0.15  \nTe2 1c 1/2 0.151 (5) 0 0.4 O25  2e 0.22724  0.67103  0.3042  0.15  \nO5 2e 0.39503  0.1413  0.2124  0.2 O26  2e 0.38254  0.60926  0.32078  0.15  \nO6 2e 0.5676  0.10374  0.2124  0.2 O27  2e 0.16047  0.83035  0.23667  0.15  \nO7 2e 0.04338  0.05618  0.2124  0.2 V3 2e 0.16(1)  0.827(7)  0.57(3)  0.3 \nTe3 1a 0 0 0 0.4 O28  2e 0.08486  0.87354  0.70568  0.15 \nO8 2e 0.06267  -0.04975  0.2124  0.2 O29  2e 0.26343  0.83764  0.71094  0.15  \nO9 2e -0.1058  -0.00642  0.2124  0.2 O30  2e 0.12095  0.76622  0.68305  0.15  \nO10  2e 0.55269  0.54555  0.2124  0.2 O31  2e 0.32659  0.32624  0.80969  0.15  \nTe4 1c 1/2 0.492(5)  0 0.4 V4 2e 0.32(1)  0.32 9(7) 0.47414  0.3 \nO11  2e 0.39362  0.49168  0.2124  0.2 O32  2e 0.39258  0.37835  0.35097  0.15  \nO12  2e 0.55395  0.43905  0.2124  0.2 O33  2e 0.21577  0.33966  0.3533  0.15  \nO13  2e 0.04189  0.39516  0.2124  0.2 O34  2e 0.3619  0.2705  0.33414  0.15  \nTe5 1a 0 0.339(5)  0 0.4 O35  2e 0.14618  0.49552  0.15067  0.15  \nO14  2e -0.10562  0.33124  0.2124  0.2 V5 2e 0.155(9)  0.50(3)  0.49(2)  0.3 \nO15  2e 0.06183  0.29107  0.20526  0.2 O36  2e 0.05265  0.51348  0.63317  0.15  \nO16  2e 0.54418  0.89283  0.2124  0.2 O37  2e 0.23405  0.54311  0.59176  0.15  \nTe6 1c 1/2 0.837(5)  0 0.4 O38  2e 0.18852  0.43732  0.61456  0.15  \nO17  2e 0.39411  0.83094  0.2124  0.2 O39  2e 0.30838  0.98915  0.79302  0.15  \nO18  2e 0.56197  0.78682  0.2124  0.2 V6 2e 0.32(1)  0.99 5(7) 0.46(3)  0.3 \nCo1 1b 0 0.572(4)  1/2 0.3 O40  2e 0.39234  1.04513  0.37054  0.15  \nCo2 1d 1/2 0.079(4)  1/2 0.3 O41  2e 0.21624  1.00683  0.30754  0.15  \nCo3 1b 0 0.923(4)  1/2 0.3 O42  2e 0.36186  0.93766  0.31964  0.15  \n† ESDs  were multiplied by 5.14 to account for the presence of correlated residuals.26 TeO 6 and VO 4 \npolyhedra are refined as rigid body groups.  ESDs are given for the refined position of the central atom \nonly.  Only SXRD refined . \n‡ Biso estimated and fixed at chemically reasonable values for the light elements.  \n \n  Krizan 35 Table  5: Bond Lengths Compared –  Ba3TeCo 3P2O14 and Pb 3TeCo 3P2O14: \nBa3TeCo 3P2O14 \n Average ( Å) Range ( Å) \nBa1-O1 2.83  2.62-3.02 \nCo1-O1 2.00  1.91 -2.04  \nPb3TeCo 3P2O14 \n Average ( Å) Range ( Å) \nPb1-O 2.79  2.33 -3.73  \nPb2-O 2.75  2.35 -2.95 \nPb3-O 2.68  2.36 -2.89  \nPb4-O 2.75  2.30-3.03  \nPb5-O 2.74  2.33 -3.05  \nPb6-O 2.77  2.47 -3.14  \nPb7-O 2.67  2.25 -2.91  \nPb8-O 2.75  2.38 -3.37  \nPb9-O 2.73  2.32 -3.17  \nPb10 -O 2.67 2.28 -2.94 \nPb11 -O 2.81  2.46 -3.75 \nPb12 -O 2.73  2.25 -3.18 \nCo1-O 2.00  1.98 -2.02  \nCo2-O 1.96  1.92 -2.01  \nCo3-O 1.98  1.93 -2.02  \nCo4-O 1.92  1.88 -1.96  \nCo5-O 1.97  1.95 -1.99  \nCo6-O 1.98  1.95 -2.01 \nCo7-O 2.00  1.91-2.15  \nCo8-O 1.98  1.90 -2.02 \nCo9-O 1.96  1.89 -2.08  \nCo10 -O 1.94  1.92 -1.97  \nCo11 -O 1.99  1.84 -2.15 \nCo12 -O 2.01  1.91-2.11  \n \nTable  6: R Value s for combined Rietveld r efinements   \n Ba3TeCo 3P2O14 Pb3TeCo 3P2O14 Pb3TeCo 3V2O14 Pb3TeZn3P2O14 \nPattern  Rp Rwp χ2 Rp Rwp χ2 Rp Rwp χ2 Rp Rwp χ2 \n100K,  0.41  Å 7.86  10.4  5.05  12.8  12.0  1.57  13.7  15 2.51     \n100 K , 1.54  Å 10.0  9.85  3.49  10.2  10.8  6.80        \n100 K,  2.41  Å 14.3  12.5  3.52  13.8  13.8  4.39       \n4 K, 1.54  Å 8.98  9.54  3.61  7.79  8.76 9.18       \n4 K, 2.41  Å 13.7  12.9  6.06  10.4  11.1  9.64       \n300 K , Cu K α          13.5  17.6  6.01  \n \n  Krizan 36  \nTable  7: Magnetic Structure of Ba 3TeCo 3P2O14  \nIrreducible Represen tation:  Γ1         k=(1/3, 1/3, 1/2)  \nCo1 Ψ1 Ψ2 C1 C2 \n(x,y,z)  (2 0 0)+i(0 0 0) (0 0 2)+i(0 0 0)   \n(-y, x-y, z) (-2 -1 0)+i(0 0 0) (0 0 2)+i(0 0 0) 0.856  1.660  \n(-x+y+1, -x+1, z)  (-0.5 -0.5 0)+i(0.866  -0.866  0) (0 0 -1)+i(0 0 1.732)    \nTwo types of cobalt  clusters exist in the structure; those which are comprised of 3.64 Bohr magneton \nmoments and opposing clusters of 1.82 Bohr magneton moments.  Irreducible representation and basis \nvectors used in the magnetic structure solution are listed.  Basis vectors ( ψ) are given in terms of the \ntrigonal axes.  Labeling follows the scheme used by Kovalev’s tabulated works .23 The magnetic moment \nfor atom j is given by 𝑚𝑗=𝐶1𝜓1+𝐶2𝜓2 \n \nTable  8: Irreducible representations, basis vectors, and m agnetic structure model  of Pb 3TeCo 3P2O14  \nIR: Γ1 k=(1/2 , 0, -1/2)  Γ2   \nAtom s Ψ1 Ψ2 Ψ3 mtotal μB Ψ1 Ψ2 Ψ3 \nCo1 (2 0 0) (0 0 2)  4.01  (0 2 0)   \nCo2 (0 2 0)   2.42  (2 0 0) (0 0 2)  \nCo3 (2 0 0) (0 0 2)  2.78  (0 2 0)   \nCo4 (0 2 0)   2.42  (2 0 0) (0 0 2)  \nCo5 (2 0 0) (0 0 2)  4.46  (0 2 0)   \nCo6 (0 2 0)   2.42  (2 0 0) (0 0 2)  \nCo7 (1 0 0) (0 1 0) (0 0 1) 3.76  (1 0 0) (0 1 0) (0 0 1) \n (-1 0 0) (0 1 0) (0 0 -1)  (1 0 0) (0 -1 0) (0 0 1) \nCo8 (1 0 0) (0 1 0) (0 0 1) 2.42  (1 0 0) (0 1 0) (0 0 1) \n (-1 0 0) (0 1 0) (0 0 -1)  (1 0 0) (0 -1 0) (0 0 1) \nCo9 (1 0 0) (0 1 0) (0 0 1) 4.90  (1 0 0) (0 1 0) (0 0 1) \n (-1 0 0) (0 1 0) (0 0 -1)  (1 0 0) (0 -1 0) (0 0 1) \nCo10 (1 0 0) (0 1 0) (0 0 1) 2.42  (1 0 0) (0 1 0) (0 0 1) \n (-1 0 0) (0 1 0) (0 0 -1)  (1 0 0) (0 -1 0) (0 0 1) \nCo11 (1 0 0) (0 1 0) (0 0 1) 3.10  (1 0 0) (0 1 0) (0 0 1) \n (-1 0 0) (0 1 0) (0 0 -1)  (1 0 0) (0 -1 0) (0 0 1) \nCo12 (1 0 0) (0 1 0) (0 0 1) 2.42  (1 0 0) (0 1 0) (0 0 1) \n (-1 0 0) (0 1 0) (0 0 -1)  (1 0 0) (0 -1 0) (0 0 1) \nPossible irreducible representation and basis vectors are listed.  Data modeled with Γ1, and moments on \nthe cobalt atoms range from 2.42 to 4.9 Bohr magnetons.  \n  Krizan 37 TOC – Image  \n \n \n"    },    {        "title": "1302.4869v1.Non_magnetic_doping_induced_magnetism_in_Li_doped_SnO2_nanoparticles.pdf",        "content": "1 \n Non-magnetic doping induced magnetism in  \nLi doped SnO 2 nanoparticles \n \nS. K.  Srivastava 1∗, P. Lejay 2,  A. Hadj-Azzem 2 and G. Bouzerar 2 \n \n1Institute of Condensed Matter and Nano-sciences, Un iversité Catholique de Louvain, \nLouvain-la-Neuve, Belgium-1348 \n2Institut Néel, CNRS Grenoble and Université Joseph Fourier, Grenoble, Cedex 9, \nFrance-38042 \n \nAbstract \n \nWe address the possibility of non-magnetic doping i nduced magnetism, in Li doped SnO 2 \nnano-particles. The compounds have been prepared by  solid state route at equilibrium  and were \nfound to be crystallized in single rutile phase. Th e magnetization measurements have shown that \nLi-doping induces magnetism in SnO 2 for a particular range of Li concentration. Howeve r, for \nother Li concentrations, including pure SnO 2, the samples exhibit diamagnetism. To investigate \nthe possible origin of the induced magnetism, we ha ve studied the variation of the magnetization \nas a function of the average nano-particle radius. Possible scenarios for the appearance of \nmagnetism in these compounds are discussed. \n \n \n \n \n \n \n \n \n \n                                                 \n*   E-mail:  sandeep.srivastava@uclouvain.be \n 2 \n I. INTRODUCTION \n \nOver the last decade, transition metal (TM) doped f erromagnetic semiconductors have \ndrawn a considerable interest as demonstrated by th e huge existing literature [1–4]. The main \ngoal of studying TM ferromagnetism is to incorporat e such material in devices where the spin \ndegree of freedom would be utilized to carry inform ation. This would lead to a reduction in the \npower consumption, as well as allow non-volatile st orage and data processing at or beyond room \ntemperature. However, there have been controversial  experimental reports on the magnetic \nproperties of TM doped oxides [5-6]. Despite TM dop ed ferromagnetism, unexpected \nferromagnetism known as d 0 has been reported or predicted in several oxides l ike HfO 2, CaO, \nZnO, ZrO 2 and even in CaB 6 [7-11]. Thus the d0 or intrinsic ferromagnetism was believed to \nprovide an alternative pathway to TM induced ferrom agnetism.  However, the origin of the \nferromagnetism in such materials is still controver sial for most of the cases. From ab initio  \nstudies, it has been shown that point defects such as cation vacancies could be the origin of the \nmagnetism in some of these materials such as; HfO 2 or CaO [8, 12-14]. In a recent model, which \nincludes disorder and electron-electron correlation  effects on equal footing, it has been proposed \nthat high Curie temperatures could be reached in ox ides such as A 1-xBxO2 (A=Ti, Zr, or Hf) \nwhere B is a monovalent cation of the group 1A [15] .  The non-magnetic dopant induces local \nmoments on the neighboring oxygen atoms which then interact with extended ferromagnetic \nexchange couplings. These findings have been follow ed by many ab initio  studies and they have \npredicted high T C ferromagnetism in several oxides such as; K-SnO 2 [16], Mg–SnO 2 [17], \nanatase Li-TiO 2 [18], rutile K–TiO 2 [19], V-TiO 2 [20], and K–ZrO 2 [11, 19]. From experimental \npoint of view, such non-magnetic doping induced mag netism has been observed in several \noxides such as; alkali metal doped ZnO [21-23]; Cu doped TiO 2 prepared in thin film form [24, \n25], carbon-doped TiO 2 prepared by solid state route [26], K: SnO 2 [27] and K: TiO 2 [28].  \nBecause of their potential interest for spintronic devices, the search for suitable oxides, \nappropriate non-magnetic dopants and optimal prepar ation procedure to obtain room temperature \nferromagnetism became really intense.  But, in most of the cases (for example, thin film);  \npreparation of materials is not yet very well contr olled. Therefore, it is imperative to prepare \nbulk materials at equilibrium  conditions, which will intrinsically diminish the u ncertainties and \ninaccuracies in characterization. SnO 2 is a wide band-gap material with a band gap of abo ut 3.6 3 \n eV, used as a transparent conduction electrode in f lat panel display and solar cells [29]. It has a \nrutile structure with distorted octahedral coordina tion. Experimentally, the possibility of \nmagnetism in Li doped SnO 2 has not been investigated yet. In this manuscript,  we have \ninvestigated the possibility of non-magnetic doping  induced magnetism in Li doped SnO 2. \n \nII. EXPERIMENTAL METHODS \nWe have prepared Sn 1−xLi xO2 compounds (0 ≤ x ≤ 0.12) by standard solid state route \nmethod by using high-purity SnO 2 (purity, 99.996%) and Li 2CO3 (99.998 %) compounds.  The \nfinal annealing in pellet form was carried out at 5 00 0C for 30 hours in air. Slow scan powder X-\nRay diffraction (XRD) patterns were collected by us ing Philips XRD machine with CuK α \nradiation. The recording of microstructure images h ave been carried out by using Zeiss-Ultra  \nScanning Electron Microscope (SEM) equipped with an  energy dispersive spectrometer (EDS). \nMagnetization measurements as a function of magneti c field (H) were carried out using a \ncommercial SQUID magnetometer (Quantum Design, MPMS ).  \n \nIII. RESULTS AND DISCUSSIONS \n \nThe X-Ray diffraction patterns for Sn 1-xLi xO2 compounds are shown in Figure 1. All the \ndiffraction’s peaks could be indexed on the basis o f the tetragonal rutile type-structure. No extra \ndiffraction peaks were detected showing that no cry stalline parasitic phases are present in the \nsamples within the limit of XRD. These XRD patterns  were refined with the help of the fullprof \nprogram by the Rietveld refinement technique [30]. A typical XRD pattern along with \nrefinement is shown in Figure 2 for Sn 0.97 Li 0.03 O2 compound. We can clearly see that the \nexperimental X-ray peaks are perfectly matching wit h power-diffraction software generated x-\nray peak. The lattice parameters for pure SnO 2 are found to be a = b = 4.7385 Å and c = 3.1871 \nÅ, and are comparable to those reported by Duan et al . [31]. However, we do not observe any \nsignificant change in the lattice parameters. This can be understood by the fact that Sn 4+  (0.71Å) \nand Li + (0.68 Å) have very similar ionic radii. To understa nd the microstructure, we have \nperformed observations by SEM. One typical SEM imag e of Sn 0.91Li 0.09O2 compound prepared \nat 500˚C is shown in Figure 3 (a). The morphology o f all samples was found to be uniform and it \nshowed conglomerates of nanometric grains.  Energy dispersive spectroscopy was carried out to 4 \n check the presence of any unwanted magnetic impurit y. EDS analyses confirm that there is no \ntrace of any kind of magnetic impurity in the compo unds within the instrumental limit as shown \nin the Figure 4.  Thus, from the X-ray and SEM analyses, we can concl ude that all compounds \nhave been crystallized to single phase of tetragona l rutile type-structure of SnO 2.  \n20 30 40 50 60 70 80 90  \n  2 θ  θ  θ  θ (( ((degree )) ))SnO 2Sn 0.97 Li 0.03 O2\n Intensity (arb. Unit) \nSn 0.94 Li 0.06 O2\n  \n410 222 400 321 202 301 112 310 002 220 211 210 111 200 101 110 Sn 0.91 Li 0.09 O2\n  \n  Sn 0.88 Li 0.12 O2\n  \n \n        Figure 1: X-Ray Diffraction patterns of Sn 1-xLi xO2 (0 ≤ x ≤ 0.12) compounds. \n \n         Figure 2: Refinement of XRD patterns for Sn 0.97 Li 0.03 O2 compound  5 \n    \n    \n \nFigure 3: SEM micrograph of Sn 0.91 Li 0.09 O2 compound (a) prepared at 500 0C  (b) prepared at \n800 0C. \n1 2 3 4 5 6 7 8 9 10 \nkeV 0123456789 cps/eV \nC-KA1 O-KA1 \n Fe  Fe  Co  Co \nSn-LA1 Sn-MZ2 \n \nFigure 4: Energy dispersive spectroscopy of Sn 0.91 Li 0.09 O2 compound prepared at 500 0C. The \nolive color curve represents all detected peaks. Th e expected positions for magnetic impurities \nlike Co and Fe are marked in the curve. It confirms  that there is no trace of any magnetic \nimpurity in these compounds.  6 \n The magnetic measurements for all samples were done  with SQUID magnetometer with \nutmost care and repeated in triplicate with differe nt pieces of samples to guarantee the \nreproducibility of results. The magnetic properties  of all the starting compounds; SnO 2 and \nLi 2CO 3 were also checked and they clearly exhibit diamagn etic behavior. The M-H \nmeasurements for Sn 1-xLi xO2 compounds show that both, pure SnO 2 and 3% Li doped compound \nexhibit a clear diamagnetic behavior at 3 K, as ill ustrated in Figure 5 (a). However, the 6% and \n9% doped compounds are surprisingly found to be mag netic. Their magnetization is found to \nincrease with Li concentration, as shown in Figure 5 (a). It approaches saturation for the 9% Li \ndoped compound with a magnetic moment of 0.0022 emu /gm at 3 K and 5 Tesla field. However, \nfor a larger concentration x=0.12, it again exhibit s diamagnetic behavior. Thus, to summarize, Li \ndoping in SnO 2 leads to magnetic moment formation only for a smal l window of Li-\nconcentration (0.03 ≤ x ≤ 0.12).  Nevertheless, within this concentration ra nge, the compounds \nexhibit weak paramagnetism, but no long-range ferro magnetic order. \nTo understand the origin of the observed magnetism in these compounds, we have \nfocused our attention on the 9% doped compound. Sev eral different samples were obtained by \nchanging the annealing temperature. The samples wer e systematically annealed for 20 hours \nafter pre-sintering them at 300 0C for about 30 hours in the air. The annealing temp erature ranges \nfrom 400˚C to 800 ˚C. The XRD patterns for all samp les have been refined by using the \ntetragonal rutile type-structure. All compounds wer e found to be in a single-phase form. Two \ntypical microstructural images obtained from SEM ar e shown in Figure 3a & 3b for samples \nprepared at 500 and 800 0C. The morphology obtained from SEM was found to be  quite uniform \nand it shows conglomerates of nano-sized grains. Th e average particles size of the grains was \nobtained by analyzing several frames of images. The  error of measurement was of the order of 2 \nnm. The average particle size ( D) obtained from the above analysis was 60, 90, 130,  160, 190 nm \nfor the compounds prepared at 400˚C, 500˚C, 600˚C, 700˚C and 800˚C respectively.  The M-H \nmeasurements for the series of Sn 0.91 Li 0.09 O2 compounds, prepared at various temperatures are \nfound to be quite interesting. The M-H measurement shows that the sample prepared at 400˚C \nexhibits a diamagnetic behavior at 3 K, as shown in  Figure 5 (b). However, the compounds \nprepared at higher temperature are found to be magn etic. Their magnetization increases sharply \nwith their average radii. The magnetization of the sample prepared at 500˚C is almost seven \ntimes to that of the compound prepared at 800˚C, as  seen in Figure 5 (c).  7 \n -5 -4 -3 -2 -1 0 1 2 3 4 5-0,015 -0,010 -0,005 0,000 0,005 0,010 0,015 \n 400° C \n 500° C \n 600° C \n 700° C \n 800° C \nField(Tesla) Magnetization (emu/gm) Sn 0.91 Li 0.09 O2\n  \nAt 3K (b) -5 -4 -3 -2 -1 0 1 2 3 4 5-0,0025 -0,0020 -0,0015 -0,0010 -0,0005 0,0000 0,0005 0,0010 0,0015 0,0020 0,0025 Magnetization (emu/gm)  SnO2 \n SnLi03 \n SnLi06 \n SnLi09 \n SnLi12 \nField(Tesla) Sn 1-x Li xO2\n  \nAt 3K (a) \n40 60 80 100 120 140 160 180 200 0,000 0,001 0,002 0,003 0,004 \n   \nDiamagnetic Magnetization ( µµµµB/Li)\nParticle Size (nm) (c) Sn 0.91 Li 0.09 O2\n \nFigure 5:  (a)  M-H loops recorded at 3 K for Sn 1-xLi xO2 compounds prepared at 500˚C ( b)  M-H \nloops recorded at 3 K for Sn 0.91 Li 0.09 O2 compounds prepared at various temperatures. (c) \nVariation of magnetic moment (at 3K, 5 Tesla) with average particle size for Sn 0.91 Li 0.09 O2 \ncompounds prepared at various temperatures. 8 \n Now, let us discuss the possible origin of magnetis m in these Li doped SnO 2 compounds \nin the light of existing first-principles calculati ons. We discuss three possible scenarios to explain  \nthe experimentally observed magnetism. \n(i) Bulk magnetism : In the case of a direct cationic substitution, theo retical studies [11, 15] have \ndemonstrated that three physical parameters are ess ential to explain induced d0 magnetism: (i) \nthe position of the induced impurity band which sho uld be located near the top of the valence \nband, (ii) the density of carrier per defect, and ( iii) the electron-electron correlations. The \nsubstitution of Sn 4+  by Li + in pure SnO 2 provides three holes in the present case. In a rec ent first-\nprinciples calculation for Li doped SnO 2, it has been shown that Li substitution induces \nmagnetism in SnO 2 [32]. A large magnetic moment of 3µ B has been obtained. The low-lying s \norbitals of Li are spin-polarized and strongly hybr idized with the p orbitals of O. The Fermi \nenergy is mainly dominated by the p orbitals of O, which indicates that magnetism is mainly \ninduced in the p orbitals, localized at the O atom.  Indeed, the oxygen atoms surrounding the Li \nion provide the dominant contribution to the total magnetic moment. Moreover, they have shown \nthat there is a very small (negligible) induced mag netic moment at the Li site, which suggests \nthat Li behaves as a spin polarizer in SnO 2 [32]. These results are consistent with the genera l \npicture provided in ref. [15] and discussed in ref.  [11] in the case of K and Na doped ZrO 2. From \nour experimental results, we have found much smalle r moments, (see Figure 5c). Indeed, the \nmoment found for the largest nano-particle was of t he order of 0.0035 µ B/Li.  \n \n (ii) Native defect induced Magnetism : While preparing the samples, the increase in prep aration \ntemperature causes an increase in particle size; th is may not be the only change that occurs. In \nparticular, defect formation/ vacancies in the bulk  may be temperature dependent; and it may be \nthose defects that are responsible for the magnetis m. These defects could be oxygen vacancies or \ncationic vacancies, for example refer [8, 12, 14, 1 5]. From ab initio  based studies (which have \ntheir own limitations), oxygen vacancies do not lea d to magnetic moment formation in most of \nthe cases. However cationic vacancies lead to large  moments. Thus, it would be of interest to \naddress these possibilities theoretically in SnO 2. From our data, we do not believe that this \nscenario is likely. \n \n 9 \n  (iii) Surface induced Magnetism:  If the observed moment was surface-induced, one wo uld \nnormally expect the magnetization (M) to be inverse ly proportional to the average particle radius \n(Ravg ). However, we observe an increase of M with respec t to Ravg from our experimental data. \nOur data seems to contradict this scenario. However , if one takes into account the fact that the \nparticle sizes obey a Gaussian distribution with a certain width and that below a certain radius \nRC, the nano-particles remain diamagnetic. Thereafter , one would get first an increase as a \nfunction of R and then a 1/R behavior, only for R>>  R C. Thus, this scenario appears to be a \npossible explanation. The calculated moment per Li( s) is found to vary from 0.1 to 2.6 µB for the \nlargest radius. Note that, similar results showing the crucial role played by the surface has been \nreported from ab initio  studies. More precisely, it has been shown that C induces a magnetic \nmoment at the surface only in the C: SnO2  compound [33]. The origin of the moment was \nattributed to surface bonding. Indeed, at the surfa ce, the numbers of bonds are reduced leading to \nunpaired electrons that follow the Hund’s rule to m inimize the Coulomb repulsion. As a result, \none finds a large induced moment of 2 µB/C.  \n \n \nIV. CONCLUSION \n \nTo conclude, we have prepared Sn 1-xLi xO2 (x=0-0.12) compounds by solid state route \nmethod. The X-ray diffraction and the detailed micr o structural analyses provide the evidence of \nsingle rutile phase. We have shown that 6% and 9% L i-doped compounds exhibit a magnetic \nphase at 3 K. However, other Li doped compounds, in cluding SnO 2 are diamagnetic. We have \nalso studied the effect of annealing temperature on  the magnetization in order to understand the \nobserved magnetism and we have speculated the possi ble origin of observed magnetism. \nHowever, further advanced study is required to know  the exact origin of magnetism in these \nsamples. The experimental tools such as X-Ray magne tic circular dichroism can help to probe \nlocal magnetism. We hope that our results will stim ulate further experimental studies in these \ncompounds. It would be exciting to find out whether  other cations with different valence such as \nZn 2+ or Mg 2+  with respective ionic radii 0.74 Å and 0.65 Å, cou ld also induce a magnetic moment \nin SnO 2 nano-particles. \n 10 \n References: \n1J. M. D. Coey, M. Venkatesan, and C. B. Fitzgerald,  Nature Mater. 4, 173 (2005). \n2S. J. Pearton, C. R. Abernathy, M. E. Overberg, G. T. Thaler, D. P. Noton, N. Theodoropoulou, \nA. F. Hebard, Y. D. Park, F. Ren, J. Kim, and L. A.  Boatner, J. Appl. Phys. 93 , 1 (2003). \n3Y. Matsumoto, M. Murakami, T. Shono, T. Hasegawa, T . Fukumura, M. Kawasaki, P. Ahmet, \nT. Chikyow, S. Koshihara, H. Koinuma, Science 291 , 854(2001). \n4T.C. Kaspar, T. Droubay, V. Shutthanandan, S.M. Hea ld, C.M. Wang, D.E. Mc- Cready, S. \nThevuthasan, J.D. Bryan, D.R. Gamelin, A.J. Kellock , M.F. Toney, X. Hong, C.H. Ahn, S.A. \nChambers, Phys. Rev. B 73  155327 (2006). \n5J.Y. Kim, J.H. Park, B.G. Park, H.J. Noh, S.J. Oh, J.S. Yang, D.H. Kim, S.D. Bu, T.W. Noh, \nH.J. Lin, H.H. Hsieh, C.T. Chen, Phys. Rev. Lett. 90,  017401 (2003). \n6S. K. Srivastava, P. Lejay, B. Barbara, O. Boisron,  S. Pailhes, and G. Bouzerar, J. Appl. Phys. \n110 , 043929 (2011).  \n7M. Venkatesan, C.B. Fitzgerald, J.M.D. Coey, Nature  430, 630 (2004). \n8J. Osorio-Guillen, S. Lany, S.V. Barabash, A. Zunge r, Phys. Rev. Lett. 96,  107203 (2006).  \n9H. Pan, J.B. Yi, L. Shen, R.Q. Wu, J.H. Yang, J.Y. Lin, Y.P. Feng, J. Ding, L.H. Van, J.H. Yin,, \nPhys. Rev. Lett. 99,  127201 (2007). \n10 D. P. Young, D. Hall, M. E. Torelli, Z. Fisk, J. L.  Sarrao, J. D. Thompson, H.-R. Ott, S. B. \nOseroff, R. G. Goodrich, R. Zysler, Nature 397,  412 (1999).  \n11 F. Maca, J. Kudrnovsky, V. Drchal, G. Bouzerar, App l. Phys. Lett. 92,  212503 (2008). \n12 C. Das Pemmaraju, S. Sanvito, Phys. Rev. Lett. 94,  217205 (2005). \n13 A. M. Stoneham, A. P. Pathak, and R. H. Bartram, J.  Phys. C 9,  73 (1976). \n14 S. Elfimov, S. Yunoki, and G. A. Sawatzky, Phys. Re v. Lett. 89,  216403 (2002). \n15 G. Bouzerar, T. Ziman, Phys. Rev. Lett. 96 , 207602 (2006). \n16 W. Zhou, L. Liu, P. Wu, J. of Magnetism and Magneti c Materials 321,  3356 (2009). \n17 C.W. Zhang, S.S. Yan, Appl. Phys. Lett. 95,  232108 (2009). \n18 J. G. Tao,  L. X. Guan, J. S. Pan, C. H. A.  Huan, L. Wang, J. L. Kuo, Physics Letters A, 374,  \n4451 (2010). \n19 F. Maca, J. Kudrnovsky, V. Drchal, G. Bouzerar, Phi los. Mag. 88 , 2755 (2008). \n20 J. Osorio-Guuillén, S. Lany, and A.  Zunger, Phys. Rev. Lett. 100 , 036601 (2008). \n21 S. Chawla, K. Jayanthi, R.K. Kotnala, Phys. Rev. B 79 , 125204 (2009). 11 \n 22 S. Chawla, K. Jayanthi, R.K. Kotnala, J. Appl. Phys . 106,  113923 (2009). \n23 J.B. Yi, C.C. Lim, G.Z. Xing, H.M. Fan, L.H. Van, S .L. Huang, K.S. Yang, X.L. Huang, X.B. \nQin, B.Y. Wang, T. Wu, L. Wang, H.T. Zhang, X.Y. Ga o, T. Liu, A.T.S. Wee, Y.P. Feng, J. \nDing, Phys. Rev. Lett. 104, 137201 (2010). \n24 D. L. Hou, H. J. Meng, L. Y Jia, X. J. Ye, H. J. Zh ou and X. L. Li, EPL, 78,  67001 (2007).  \n25 S. Duhalde  et al. Phys. Rev. B  72 , 161313(R) (2005). \n26 X.J. Ye, W. Zhong, M.H. Xu, X.S. Qi, C.T. Au, Y.W. Du, Physics Letters A 373,  3684 (2009).  \n27 S. K. Srivastava, P. Lejay, B. Barbara, S. Pailhès,  V. Madigou, and G. Bouzerar, Phys. Rev. B        \n82 , 193203 (2010). \n28 S. K. Srivastava, P. Lejay,  B. Barbara, O. Boisron , S. Pailhès and G. Bouzerar, J. Phys.: \nCondens. Matter 23 (2011) 442202. \n29 H. L. Hartnagel, A. L. Dawar, A. K. Jain, and C. Ja gadish, Semiconducting Transparent Thin \nFilms (Institute of Physics, Bristol, 1995). \n30 R. A. Young, 1996 The Rietveld Method International  Union of Crystallography (New York: \nOxford University Press). \n31 L. B. Duan, G. H. Rao, J. Yu, Y. C. Wang, G. Y. Liu , and J. K. Liang, J. Appl. Phys. 101 , \n063917 (2007). \n32 G. Rahman, N. Ud Din and V. M. García-Suárez, arXiv :1210.5602 [cond-mat.mtrl-sci] 2012 \n33G. Rahman and V. M. García-Suárez, App. Phys Letter  96 , 052508 (2010) "    },    {        "title": "1302.6886v1.When_metal_organic_frameworks_turn_into_linear_magnets.pdf",        "content": "When metal organic frameworks turn into linear magnets\nPieremanuele Canepa,1Yves J. Chabal,2and Timo Thonhauser1,\u0003\n1Department of Physics, Wake Forest University, Winston-Salem, NC 27109, USA\n2Department of Materials Science and Engineering,\nUniversity of Texas at Dallas, TX 75080, USA.\n(Dated: October 29, 2018)\nWe investigate the existence of linear magnetism in the metal organic framework materials MOF-\n74-Fe, MOF-74-Co, and MOF-74-Ni, using \frst-principles density functional theory. MOF-74 dis-\nplays regular quasi-linear chains of open-shell transition metal atoms, which are well separated. Our\nresults show that within these chains|for all three materials|ferromagnetic coupling of signi\fcant\nstrength occurs. In addition, the coupling in-between chains is at least one order of magnitude\nsmaller, making these materials almost perfect 1D magnets at low temperature. The inter-chain\ncoupling is found to be anti-ferromagnetic, in agreement with experiments. While some quasi-1D\nmaterials exist that exhibit linear magnetism|mostly complex oxides, polymers, and a few other\nrare materials|they are typically very di\u000ecult to synthesize. The signi\fcance of our \fnding is\nthat MOF-74 is very easy to synthesize and it is likely the simplest realization of the 1D Ising\nmodel in nature. MOF-74 could thus be used in future experiments to study 1D magnetism at low\ntemperature.\nPACS numbers: 75.10.Pq, 75.25.-j, 75.75.-c, 75.40.Cx\nThe continued quest for the development of non-\nvolatile memories and spintronic devices of smaller sizes\nrequires the full comprehension of \fnite-size e\u000bects. To\nthis end, over the last decade, exotic magnetic proper-\nties have received much attention in experimental and\ntheoretical studies.1{14Considerable emphasis has been\ngiven to the synthesis and prediction of materials show-\ning mono-dimensional magnetism,1{14also referred to as\n1Dorlinear magnetism. While 1D magnetism can be\nexplained with the well-understood Ising model (dating\nback to 1925),15a satisfactory physical realization of\nthis model in simple materials has not yet been found\nand 1D magnetism is only observed in a few|often\ndi\u000ecult8,10,14or dangerous9to synthesize|synthetic in-\norganic materials and polymers. Although, for example,\nCrSb 2is one of the few materials that shows naturally\n1D anti-ferromagnetism, this property remains di\u000ecult\nto control and tune.14In fact, theory has shown that\nstrong spin \ructuations induce ferromagnetic disorder\nof 1D-spin arrays at any temperature, independent of\nthe extent of exchange interactions between neighboring\nspins.15,16Thus, progress in the \feld of 1D magnetism\ncrucially depends on the availability of currently missing\nsimple-to-synthesize model systems and materials.\nThe main di\u000eculty in engineering good model systems\nexhibiting 1D magnetism are:2,10(i) to \fnd materials\nthat have quasi-1D chains of spins with signi\fcant in-\nteractions and large magnetic anisotropy, (ii) to \fnd ma-\nterials with a large ratio between intra and inter-chain\nmagnetic interactions, (iii) to \fnd materials in which fer-\nromagnetism is preserved at \\reasonable\" low temper-\natures, (iv) to \fnd materials with very few impurities,\nwhich tend to destroy ferromagnetism, and \fnally (v) to\n\fnd materials that are simple, safe, inexpensive to syn-\nthesize, and where linear magnetism is easy to control.\nHistorically, the engineering of 1D magnetic materialshas followed several routes. Attempts were made using\ninorganic materials such as Sr 2Cu(PO 4)2, Sr2CuO 3,4and\nBaCo 2V2O8,11along with non-periodic magnetic clusters\nor molecular magnets.10Another strategy is the combi-\nnation of organic molecules and transition metals (TM)\nto form regular polymer 1D magnets.2,8,10,13The latter\nstrategy o\u000bers a larger degree of freedom due to the high\ntunability of the diamagnetic organic separators, which\ncan promote spin localization on the central TM.2,8,10\nWe propose here that metal organic frameworks\n(MOFs), a novel class of nano-porus materials, o\u000ber a\nversatile platform for the realization of 1D magnets due\nto their high tailorability and tunability that results from\ntheir discrete molecular building-block nature.17{20For\nthis reason MOFs are already targeted in a large variety\nof applications such as gas-separation, gas-sensing, gas-\ncapture, catalysis, and drug-delivery.17{22In particular,\nin the following, we argue that the structural simplicity,\nlow cost, and ease of synthesis of MOF-74|together with\nthe already existing understanding of this material|\nful\fll the criteria mentioned above and thus make it\nan outstanding candidate for studying linear magnetism.\nNote that signatures of 1D-ferromagnetism in MOF-74-\nCo were already observed experimentally by Dietzel et\nal.in their pioneering work on this MOF.23From Fig. 1\nit is apparent that MOF-74-TM (with TM = Mn, Fe, Co,\nNi, and Cu) can be seen as 1D magnet since it displays\nregular pseudo-chains of transition metals aligned along\nthe basal plane. The helicoidal chains resulting from the\natomic-motif of Fig. 1a are interspaced by \\long\" organic\nlinkers, suggesting that the inter-chain interactions are\nquenched. In fact, MOF-74 shows a large structural ratio\n(\u00183) between the separation of spins in a chain compared\nto chain separation (see Fig. 1), establishing a required\ncondition for the construction of a 1D magnet.\nTo elucidate the 1D-like magnetic properties exhib-arXiv:1302.6886v1  [cond-mat.mtrl-sci]  27 Feb 20132\na)\nb)\nFIG. 1. a)Frontal view of MOF-74, helicoidal magnet\nchains are highlighted in green. b)side view of MOF-74, TM\natoms are represented by green balls. dNNanddNNN are the\nnearest-neighbor and next-nearest-neighbor intra-chain dis-\ntances, while dI\u0000Iis the inter-chain distance. The couplings\nJNN,JNNN, andJI\u0000I, are de\fned in parallel.\nited by MOF-74, we study the three isostructural\nmaterials MOF-74-Fe,24MOF-74-Co,23and MOF-74-\nNi.25To this end, we use density functional theory\n(DFT) with the PBE functional, as implemented in\nQuantumEspresso .26We employ ultrasoft pseudopo-\ntentials with wave-function and density cuto\u000bs of 680 eV\nand 6800 eV. The pseudopotentials used for the TM (i.e.\nFe, Co, and Ni) are also suitable for spin-orbit calcula-\ntions including relativistic corrections. The total energy\nis sampled with a 2 \u00022\u00022k-point mesh, resulting in en-\nergy di\u000berences converged to within less than 1 meV.\nProjected density of states onto selected atomic orbitals\nare performed on a denser k-point mesh, i.e. 4 \u00024\u00024. The\nSCF total energy convergence criterium is 1.4 \u000210\u000010eV.\nWe need such tight criteria to be able to accurately sam-\nple the delicate energy landscape originating from di\u000ber-\nent spin arrangements.\nAll calculations are performed on the experimental\nstructures of MOF-74-Fe,24MOF-74-Co,23and MOF-74-\nNi,25which crystallize in a rhombohedral primitive cell\nwith 54 atoms and space group R3. The calculation ofTABLE I. MOF-74-TM net atomic charges (in units of the\nelectronic charge), QOandQTM, and electron population of\npanddorbitals on O and TM atoms, qO(2p) andqTM(3d),\nrespectively. Magnetic moments, \u0016, are reported in units of\n\u0016B.\nTMQOqO(2p)QTMqTM(3d)\u0016\nFe {0.30 4.75 +0.50 6.35 3.625\nCo {0.95 5.35 +2.49 5.17 3.255\nNi {0.61 4.94 +1.24 8.33 1.567\nthe intra-chain J-coupling constants requires the freedom\nto have varying spin directions along a chain. But, the\nprimitive cell of MOF-74-TM contains only 6 TM atoms\nthat all belong to di\u000berent chains (1 per chain), which\ndoes not give the required freedom. Thus, we construct\na supercell extending the unit cell along the chain direc-\ntion, such that each unit cell now contains two chains\nwith 6 TM atoms per chain, and a total of 108 atoms.\nCoordinates and relative lattice constants of the super-\ncells are reported in the Supplementary Information.\nLinear magnetism relies on ferro- or antiferro-\nmagnetism that can only exist if the TM atoms have a\nnon-negligible magnetic moment. We therefore begin by\nanalyzing the localization of the magnetic moment on the\nTM atoms, combining the projected density of states and\nthe L odwin population analysis. The L odwin analysis,\nsimilarly to the Mulliken analysis is an intuitive (but not\nunique) way of re-partitioning the electron charge density\non each atom (and orbital), by projecting it onto indi-\nvidual orthonormalized atomic orbitals.27Table I shows\nthe L odwin charges, relative contribution, and magnetic\nmoments of the TM and O atoms in the three MOF-74\ninvestigated. The magnetic moments, \u0016, were computed\nby integrating the spin-densities di\u000berence ( \u001aup\u0000\u001adown)\nof the d-porbitals in the valence region of each TM. Al-\nthough it is inadequate to draw decisive conclusions from\nthe charge analysis of Table I, we observe that oxygen\natoms in MOF-74 assume an interesting covalent nature,\nhaving repercussions on the \fnal charges and magnetic\nmoment of the TM in MOFs. We further con\frm the\nlocal charge of Co in MOF-74-Co (+2.49), which was ex-\nperimentally assigned as 2+.23It is also interesting to see\nthat the local charge of Fe in MOF-74-Fe behaves almost\nlike the metallic case, thus increasing the local magnetic\nmoment. The experimental magnetic moment for Co is\n4.67\u0016B,23which is larger than our computed value; a\ndiscrepancy connected to the well-known unphysical de-\nlocalization of the electron charge density that is intro-\nduced by the exchange-correlation functional adopted in\nDFT simulations.28Note that orbital magnetism29{31is\nnot included in our calculations, as its e\u000bect is typically\nvery small.32\nFigure 2 shows the density of states of the valence\nbands projected onto the d-orbitals of the TM atoms\nand p-orbitals of oxygen atoms (pDOS). Here we see\nthat some of the electronic charge density of the TM3\n-6 -5 -4 -3 -2 -1 0\nTM (d)\nO (p)\n-6 -5 -4 -3 -2 -1 0\nEnergy  [eV]Fe\nCo\nNi\nFIG. 2. Projected density of states onto Fe, Co, and Ni\nd-orbitals (gray) and O p-orbitals (red) of the valence bands\nof MOF-74-TM. Energy is given in eV with respect to the\ntop of the valence band. Spin-up and spin-down densities are\nplotted above and below the zero line of each plot.\nspills-over (due to orbital hybridization) to the nearest-\nneighbor oxygen atoms. This diminishes the local mag-\nnetization on spin-carriers and thus their total magnetic\nmoment. Not surprisingly, the analysis of the pDOS to-\ngether with the charge analysis suggests that the mag-\nnetization originates from the d-electrons (spin-down,\nsee Fig. 2) of the TM atoms. Note that the angle\n6TM\u0000O\u0000TM\u001990\u000e\u00065\u000edoes not allow su\u000ecient over-\nlap between the relevant orbitals enforcing the intra-\nchain ferromagnetism according to the Goodenough and\nKanamori rules.33The above analysis clearly shows how\nthe tunability of the organic linkers in MOFs can be uti-\nlized to increase the spin localization on the TM, and a\nmore involved explanation can be found in Ref. 8. From\nthis analysis we conclude the existence of localized mag-\nnetic moments that can give rise to ferromagnetic cou-\npling among TM atom chains.\nAlthough we have clari\fed the existence of chains of\nspin carriers, we still need to understand if spin chains are\nindependent of each other (see Fig. 1) in order to produce\nisolated spin arrays acting as linear magnets. To this end,\na qualitative estimation of the magnetic independence of\nspin chains is obtained by performing calculations where\neach chain magnetization is assigned a random spatial\nstarting orientation, which thereafter is free to relax to-\nwards the most favorably energetic orientation. If there\nis some degree of inter-chain interaction, each chain spin-\nmagnetization will assume some preferred orientation.\nBut, our results show that only a small rearrangement\nof the spin directions occurs, i.e. only \u00062\u000efrom the ini-\ntial directions, supporting the idea that chains are only\nweakly coupled. However, a quantitative measurement\nof such chain-chain interactions can only be obtained byTABLE II. Intra-chain J-coupling constants JNNandJNNN\nand inter-chain JI\u0000Ifor MOF-74-TM in cm\u00001. For clarity\nwe report again the magnetic moment, \u0016, in\u0016B, from Ta-\nble I. The standard deviation of JNNandJI\u0000Iis not reported\nbecause below the accuracy limit.\nTM \u0016 J NN JNNN JI\u0000I\nFe 3.625 28.1 \u00060.4 6.0 {1.2\nCo 3.255 40.1 \u00062.9 4.9 {1.9\nNi 1.567 21.0 \u00063.5 6.9 {1.3\ncalculating the inter-chain J-coupling constants, which\nfollows next.\nHaving established that the TM spin-carriers exhibit\na substantial magnetization that can produce potential\nferromagnetic coupling, our investigation moves to the\ncalculation of the J-coupling interactions. Figure 1b\nshows the magnetic pathways and de\fnes the following J-\ncouplings: The intra-chain JNNandJNNN, origin of the\n1D linear magnet properties; and, the unwanted inter-\nchainJI\u0000Iinteractions. A complete structural analy-\nsis shows that the intra-chain TM-TM distance falls be-\ntween 2.8 \u0017A and 3.0 \u0017A for MOF-74-TM, whereas the\nintra-chain distance falls between 7.5 \u0017A and 8.8 \u0017A, giv-\ning reason to believe that the inter-chain J-coupling in-\nteractions are quenched. If each spin magnetization is\nconstrained along the z-direction,34the coupling interac-\ntion,Jij, described by the complex Heisenberg-Dirac-van\nVleck Hamiltonian simpli\fes to the 1D Ising Model15\n^H=\u00002nX\ni;jJij^Sz\ni\u0001^Sz\nj; (1)\nwhere ^Sz\niis the projection of the spin operator along the\nzdirection at site i. Due to the gyromagnetic factor, for\nthe expectation values of ^Sz\niwe use 1/2 of the magnetic\nmoments\u0016in Table I, i.e. 0.813 for Fe, 1.628 for Co, and\n0.784 for Ni. We now use DFT to map the real system\nonto this model Hamiltonian by computing the energy\ndi\u000berences of various ferro- and anti-ferromagnetic spin\ncon\fgurations, which in turn yields the J-couplings. Our\nsupercell contains 6 independent TM atoms per chain\n(see Fig. 1b), resulting in 26= 64 possible di\u000berent spin\ncon\fgurations, out of which only 16 combinations are\nlinearly independent and compatible with our periodic\nboundary conditions. The coupling constants Jijare\nthen obtained by solving an overdetermined system of\n16 equations with a least-square \ft. Table II reports our\ncalculated values for the nearest-neighbor coupling JNN,\nthe next-nearest-neighbor coupling JNNN, and the inter-\nchain coupling JI\u0000Ifor MOF-74-Fe, MOF-74-Co, and\nMOF-74-Ni. Note that these calculations are a partic-\nularly challenging task requiring high accuracy, as these\nenergy di\u000berences are tiny compared to the total energy\nof a 108 atom unit cell.\nFrom Table II we see that the intra-chain J-couplings\nare larger and more positive than the inter-chain ones,4\n0 50 100 150 200 250 300\nT  [ K ]0.000.020.040.060.080.100.120.14χM  [cm3 mol-1]Fe\nCo\nNi\n0 5 10 15 20 25 300.040.060.080.100.120.14\nFIG. 3. Computed magnetic susceptibility \u001fM(in cm3\nmol\u00001) as a function of temperature T(in K) for MOF-74-Fe,\nMOF-74-Co, and MOF-74-Ni. The inset shows an enlarge-\nment of the transition zone.\nsuggesting the existence of linear ferromagnetism. On\nthe other hand, the interaction among chains is very\nsmall and of anti-ferromagnetic nature. As expected,\nlonger range J-coupling interactions, such as JNNN, are\nof smaller magnitudes than the nearest-neighbor interac-\ntions and are expected to vanish at increasing distances.\nAlthough couplings for longer distances are in princi-\nple easily obtainable from Eq. (1), such results are not\npresented here since they fall below our accuracy limit.\nOverall, the trend of the magnetic constants is main-\ntained between the three TMs. From our simulations\nthe computed JNNfor MOF-74-Fe seems largely overes-\ntimated from the experimental value of 4.12 cm\u00001, which\nwas extrapolated by \ftting experimental magnetic sus-\nceptibility pro\fles.24On the other hand, our calculated\ninter-chain constant for MOF-74-Fe is in excellent agree-\nment with the experimental result of \u00001.12 cm\u00001.24In\nsummary, we conclude that the ferromagnetic intra-chain\ninteractions are one order of magnitude larger than the\nanti-ferromagnetic inter-chain ones|con\frming the pos-\nsibility of the existence of 1D-magnetic phenomena at\nlow temperature.\nWe \fnally move to calculating the temperature-\ndependent magnetic susceptibility \u001fM. Starting from our\ncomputedJ-coupling constants, we can predict the mag-\nnetic susceptibility, \u001fM, which is measurable experimen-\ntally. We use Fisher's model35\n\u001fM=Ng2\niso\u00162\n12kbT\u00021 +u(JNN)\n1\u0000u(JNN); (2)\nu(JNN) = coth\u0012kbT\n2JNN\u0013\n\u0000\u00122kbT\nJNN\u0013\n; (3)\nwhereNis the number of atoms in the chain, gisothe\ng-factor,kbthe Boltzman constant, and Tthe temper-\nature. Figure 3 shows our calculated \u001fMas a func-\ntion of temperature for the three MOF-74-TM investi-\ngated, using the JNN-coupling constants from Table II.The transition temperature corresponding to the phase\ntransition from ferromagnetic order to anti-ferromagnetic\norder along the chains is given by the peak position of\n\u001fM. Obviously, the transition temperature depends on\ntheJ-coupling strength: the larger the J-coupling con-\nstant is, the broader the peak becomes and the higher the\ntransition temperature. A similar dependence is found\nfor the\u001fMmagnitude itself, which decreases for increas-\ningJ-coupling constant. For MOF-74-Co, the tempera-\nture dependence of \u001fMwas measured experimentally,23\n\fnding a transition temperature of 8{10 K, in good\nagreement with our calculated transition temperature\nof 13 K. The experimental maximum of the peak is at\n\u00180.17 cm3mol\u00001, whereas our calculated maximum is\nonly at\u00180.06 cm3mol\u00001. However, this discrepancy is\na result of the fact that our DFT calculated Co dipole\nmoment of 3.255 \u0016Bis too small compared to the experi-\nmental one of 4.67 \u0016B(as mentioned above).23As can be\nseen from Eq. (2) the dipole moment \u0016enters the suscep-\ntibility as\u00162. If we simply use the experimental dipole\nvalue, our peak maximum would be at \u00180.13 cm3mol\u00001,\nin reasonable agreement with experiment. Furthermore,\nnote that according to the susceptibility model used, the\nJNNcoupling constant for MOF-74-Fe has to be larger\nthan the 4.12(6) cm\u00001found experimentally through \ft-\nting data by Bloch et al. ;24such a small value results in a\ntransition temperature too close to 0 K and below the ex-\nperimental conditions reported in their study (2{300 K).\nEquation (2) includes only the e\u000bect of JNN, making this\nmodel quite unsatisfactory. The e\u000bect introduced by in-\nterchainJI\u0000Icoupling constant in \u001fMcan be reintro-\nduced in Eq. (3) by replacing u(JNN) withu(jJNN=JI\u0000Ij),\nwith the e\u000bect of slightly shifting all curves by \u0018{3 K,\nbringing them in very good agreement with experimen-\ntal observation. Our estimated transition temperatures\nof all three investigated MOFs are clearly above the liq-\nuid He temperature, encouraging further experiments on\nlinear magnetism phenomena in MOF-74.\nIn summary, we have explored the existence of lin-\near magnetic phenomena in the metal organic frame-\nwork materials MOF-74-Fe, MOF-74-Co, and MOF-74-\nNi by using DFT calculations. Our results provide an\nunderstanding of the origins and magnitude of linear\nmagnetic e\u000bects in these materials. We verify the exis-\ntence of intra-chain ferromagnetism and quenched anti-\nferromagnetic coupling between chains, large enough to\nbe observed at liquid He temperatures. The signi\fcance\nof our \fnding is that MOF-74 is easily synthesized, safe,\nand inexpensive. As such, it is likely to be the simplest\nrealization of the 1D Ising model in nature and has the\npotential to provide simple means to study linear mag-\nnetism. Note that the MOFs studied here have not been\ntailored in any way to make them good 1D magnets. In\nview of the high tailorability and tunability of MOFs,\nexciting new opportunities open up, where especially de-\nsigned linkers and spin-centers decrease the spin-density\ndelocalization and maximize the spin moments, resulting\nin largerJ-couplings and higher transition temperatures.5\nThis work was entirely supported by the Department of Energy Grant No. DE-FG02-08ER46491.\n\u0003thonhauser@wfu.edu\n1M. Pratzer, H. J. Elmers, M. Bode, O. Pietzsch, A. Ku-\nbetzka, and R. Wiesendanger, Phys. Rev. Lett. 87, 127201\n(2001).\n2R. Cl\u0013 erac, H. Miyasaka, M. Yamashita, and C. Coulon, J.\nAm. Chem. Soc. 124, 12837 (2002).\n3P. Gambardella, A. Dallmeyer, K. Maiti, M. C. Malagoli,\nW. Eberhardt, K. Kern, and C. Carbone, Science 416, 301\n(2002).\n4M. D. Johannes, J. Richter, S. -L. Drechsler, and H. Ros-\nner, Phys. Rev. B 74, 174435 (2006).\n5G. Beobide, O. Castillo, A. Lunque, U. Garci\u0013 a-Couceiro,\nJ. P. Garci\u0013 a-Ter\u0013 an, and P. Rom\u0013 an, Dalton T., 2669 (2007).\n6S. Kimura, T. Takeuchi, K. Okunishi, M. Hagiwara, Z.\nHe, K. Kindo, T. Taniyama, and M. Itoh, Phys. Rev. Lett.\n100, 057202 (2008).\n7S. Kimura, M. Matsuda, T. Masuda, S. Hondo, K. Kaneko,\nN. Metoki, M. Hagiwara, T. Takeuchi, K. Okunishi, Z. He,\nK. Kindo, T. Taniyama, and M. Itoh, Phys. Rev. Lett.\n101, 207201 (2008).\n8M. Kurmoo, Chem. Soc. Rev. 38, 1353 (2009).\n9Y. Zhang, X.-T. Wang, X.-M. Zhang, T.-F. Liu, W.-G. Xu,\nand Song Gao, Inorg. Chem. 49, 5868 (2010).\n10H. -L. Sun, Z. -M. Wang, and S. Gao, Coordin. Chem. Rev.\n254, 1081 (2010).\n11Y. Kawasaki, J. L. Gavilano, L. Keller, J. Schefer, N. Chris-\ntensen, A. Amato, T. Ohno, Y. Kishimoto, Z. He, Y. Ueda,\nand M. Itoh, Phys. Rev. B 83, 064421 (2011).\n12J. Simon, W. S. Bakr, R. Ma, M. E. Tai, P. M. Preiss, and\nM. Greiner, Nature 472, 307 (2011).\n13L. M. Toma, C. Ruiz-P\u0013 erez, J. Pas\u0013 an, W. Wernsdorfer,\nF. Lloret, and M. Julve, J. Am. Chem. Soc. 134, 15265\n(2012).\n14M. B. Stone, M. D. Lumsden, S. E. Nagler, D. J. Singh, J.\nHe, B. C. Sales, and D. Mandrus, Phys. Rev. Lett. 108,\n167202 (2012).\n15S. Blundell, Magnetism in Condensed Matter. Oxford: Ox-\nford University Press (2001).\n16N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133\n(1966).\n17H. Furukawa, M. A. Miller, and O. M. Yaghi, J. Mater.\nChem. 17, 3197 (2007).\n18L. J. Murray, M. Dinc\u0015 a, and J. R. Long, Chem. Soc. Rev.\n38, 1294 (2009).\n19D. K. Britt, H. Furukawa, B. Wang, T. G. Glover, andO. M. Yaghi, Proc. Nat. Acad. Sci. USA 106, 20637 (2009).\n20J.-R. Li, R. J. Kuppler, and H.-C. Zhou, Chem. Soc. Rev.\n38, 1477 (2009).\n21N. Nijem, P. Canepa, L. Kong, H. Wu, J. Li, T. Thon-\nhauser, and Y. J. Chabal, J. Phys.: Cond. Mat. 24, 424203\n(2012).\n22P. Canepa, N. Nijem, Yves J. Chabal, and T. Thonhauser,\nPhys. Rev. Lett. 110, 026102 (2013).\n23P. D. C. Dietzel, Y. Morita, R. Blom, and H. Fjellv\u0017 ag,\nAngew. Chem. Int. Ed. 44, 6354 (2005).\n24E. D. Bloch, W. L. Queen, R. Krishna, J. M. Zadrozny,\nC. M. Brown, and J. R. Long, Science 335, 1606 (2012).\n25P. D. C. Dietzel, B. Panella, M. Hirsher, R. Blom, and H.\nFjellv\u0017 ag, Chem. Commun. 9, 959 (2006).\n26P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car,\nC. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni,\nI. Dabo, A. Dal Corso, S. Fabris, G. Fratesi, S. de Giron-\ncoli, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj,\nM. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R.\nMazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C.\nSbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A.\nSmogunov P. Umari, and R. M. Wentzcovitch, J. Phys.:\nCond. Mat. 39, 395502 (2009).\n27A. Szabo and N. S. Ostlund, Modern Quantum Chemistry:\nIntroduction to advanced Electronic Structure Theory. Mi-\nneola, New York: Dover Publications, Inc. (1996).\n28I. de P. R. Moreira and F. Illas, Phys. Chem. Chem. Phys.\n8, 1645 (2006).\n29R. Resta, D. Ceresoli, T. Thonhauser, and D. Vanderbilt,\nChemPhysChem 6, 1815 (2005).\n30T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta,\nPhys. Rev. Lett. 95, 137205 (2005).\n31D. Ceresoli, T. Thonhauser, D. Vanderbilt, and R. Resta,\nPhys. Rev. B 74, 024408 (2006).\n32T. Thonhauser, Int. J. Mod. Phys. B 25, 1429 (2011).\n33J. B. Goodenough, Magnetism and the Chemical Bond,\nNew York-London, J. Wiley and Sons (1963).\n34We have considered the more general case of truly non-\ncollinear spin, but our results show that all three MOF-74\nsystems indeed prefer collinear spin arrangements. We thus\nconstrain our calculations here to spin directions only along\nthez-axis.\n35M. E. Fisher, Am. J. Phys. 32, 343 (1964)."    },    {        "title": "1303.1607v1.Complex_Magnetic_Phase_Diagram_of_a_Geometrically_Frustrated_Sm_Lattice__SmPd2Al3_case.pdf",        "content": "Complex Magnetic Phase Diagram of a Geometrically Frustrated Sm \nLattice: SmPd 2Al3 case \n \nJ. Pospíšíl1*, G. Nénert2, S. Miyashita3, H. Kitazawa4, Y. Skourski5, M. Diviš1, J. Prokleška1 \nand V. Sechovský1 \n \n1Faculty of Mathematics and Physics, Department of Condensed Matter Physics,  \nCharles University, Ke  Karlovu 5, 121 16 Prague 2, The Czech Republic  \n2Institut Laue Langevin,  BP 156, 6 rue Jules Horowitz, 38042, Grenoble Cedex 9, France  \n3Department of Physics, School of Science, The University of Tokyo 7 -3-1 Hongo, Bunkyo -ku, \nTokyo, 113 -0033 Japan  \n4National Institute for Materials Science, Tsukuba, Ibaraki 305 -0047, Japan  \n5Dresden High Magnetic Field Laboratory, Helmholtz -Zentrum Dresden Rossendorf,  \nD-01314 Dresden,  Germany  \nAbstract  \nMagnetism in  SmPd 2Al3 was investigated on a single crystal by magnetometry and neutron \ndiffraction. SmPd 2Al3 represents a distinctive example of the Sm magnetism exhibiting \ncomplex magnetic behavior at low temperature s with four consecutive magnet ic phase \ntransitions at 3.4, 3.9 , 4.3 and 12.5 K. The rich magnetic phase diagram of this compound \nreflects  the specific features of the Sm3+ ion, namely the energy nearness of the ground -state \nmultiplet J = 5/2 and  the first excited multiplet J = 7/2 in conjunction with strong crystal field \ninfluence. Consequently, a significantly reduced Sm magnetic moment in comparison with the \ntheoretical Sm3+ free-ion value is observed. Despite the strong neutron absorption by natural \nsamarium and the small Sm magnetic moment (~ 0.2 µ B) we have successfully determined the \nmagnetic k -vector (1/3, 1/3, 0) of the phase existing in the  temperature interval 12. 5 - 4.3 K. \nThis observation classifies the SmPd 2Al3 compound as a magnetica lly frustrated system. The \ncomplex magnetic behavior of this material is further illustrated by kinetic effects of the  \nmagnetization inducing rather complicated magnetic structure with various metastable states .  \n \nKey words: SmPd 2Al3, Sm magnetism, neutron diffraction, magnetic frustration, Foehn \neffect,  \nPACS numbers: 75.10.Dg, 75.25 -j, 75.30. Gw,  Introduction  \nThe SmPd 2Al3 compound belongs to the class of the rare earth materials crystallizing in \nthe hexagonal crystal structure of the PrNi 2Al3-type (space group P6/mmm)1. The physical \nproperties of the rare earth counterparts with the composition REPd2Al3 (for RE= Ce, Pr, Nd \nSm and Gd) are  given mainly by the strong influence of the crystal field on the magnetic state \nof RE ions1, 2. This leads to various types of magnetic order (Ce, Nd, Sm and Gd)3-7 or \ncontrary paramagnetic ground state (Pr)8 and heavy fermion behavior (Ce).9 Finally, the Y \nand La compounds are superconductors10-12. The REPd2Al3 compounds are therefore  an \ninteresting play ground for theoreticians as they are modeling examples to study rare earth \nelements magnetism due to their high variability of the physical properties connected with a \nsimple and high symmetry crystal structure.10, 13-15 Although physical properties of all \ncompounds in the REPd2Al3 series were  subjected  to intensive research  activities , yet the two \nmost interesting cases - Gd and Sm compound s remain poorly understood despite the recent \nprogress within the last two years.13, 16 \nSmPd 2Al3 was described as a n antiferromagnet  with strong uniaxial anisotropy even in \nthe paramagnetic state with an easy -magnetization direction along the crystallographic axis c. \nFour successive magnetic transitions have been identified in the temperature dependence of \nthe specific heat at temperatures T3 = 3.4 K, T2 = 3.9 K, T1 = 4.3 K and TC = 12.5  K. The high \nnumber of the magnetic phase transitions and t he series of four magnetic field induced \ntransitions detected at 0.03, 0.35, 0.5, and 0.75 T, respectively , at 1.8 K yield a complex \nmagnetic phase diagram . \nGenerally, the compl exity of the Sm magnetism is giv en by anomalous magnetic ground  \nstate of the  Sm3+ ion.17 The Sm3+ ground -state multiplet J = 5/2 is radically influenced by first \nand second excited multiplets  J = 7/2 and J = 9/2 which have only an energy of 0.1293 eV \nand 0.2779 eV17 which results in distinctive features like multiple magneti c phase transitions \nand the susceptibility influenced via the temperature -independent Van Vleck term.18 \nNeutron scattering is usual ly a good tool to study magnetism on a microscopic scale. \nHowever , Sm containing materials are usually disregarded due to high thermal -neutron \nabsorption by of natural samarium. In addition to the absorption problem, another difficult y \narises from the usually low magnetic moment of Sm3+. The natural Sm consists of  7 isotopes \nwith abundances  shown in the Table 1.19, 20 \n \nTABLE I. Table summarized information about all isotopes presented in natural Samarium -their \natomic masses, natural abundance and their neutron absorption.  \nIsotope  Atomic mass (ma/u)  Natural abundance (atom. %)  Absorption (barn)  \n144Sm 143.911998 (4)  3.07 (7)  0.7 \n147Sm 146.914894 (4)  14.99 (18)  57 \n148Sm 147.914819 (4)  11.24 (10)  2.4 \n149Sm 148.917180 (4)  13.82 (7)  42080  \n150Sm 149.917273 (4)  7.38 (1)  104 \n152Sm 151.919728 (4)  26.75 (16)  206 \n154Sm 153.922205 (4)  22.75 (29)  8.4 \n The high thermal -neutron absorption of the natural samarium (natSm) is given mainly by \nisotopes 149Sm, 150Sm and 152Sm ( see Table I)  with total average absorption of the natSm 5922 \nbarn21-23. In order to overcome the problem of absorption, there are 2 possibilities. The first \none is to work with isotopic samarium, typically 154Sm which combines low neutron \nabsorption and high coherent scattering length. Unfortunately the cost of 154Sm isotope (99%) \nmetal is prohibitive. The second choice is to make use of the opportunity that the magnitude \nof the neutron absorption  can strongly depends o n neutron energy24. Consequently, high er \nenergy neutron s (\"hot\" neutrons25, 26) are  a good alternative. Therefore , we have carried out \nneutron single crystal experiment using the D9 high resolution diffractometer at hot source in  \nthe Institut  Laue Langevin, Grenoble, France.  \nIn this paper , we construct a detailed magnetic phase diagram of SmPd 2Al3 using \nSQUID magneto metry and investigate the nature of the first magnetic phase using single \ncrystal neutron diffraction on natural isotopic SmPd 2Al3.  \n \nExperimental and computational details  \nThe single crystal of the SmPd 2Al3 compound has been grown in a triarc furnace by \nCzochralski pulling method from stoichiometric amounts of elements. Pulling and single \ncrystal growth details and quality were  already described in Ref. [13]. The natural isotope of \nSm has been used.  \nThe samples of the appropriate shape for the magnetization and neutron experiment \nhave been cut by a wire saw (South Bay Technology Inc, type 810). The sample for the \nmagnetization m easurements had the following dimensions: 1x1x1.5 mm3 with rectangular \nplanes oriented perpendicular to the crystallographic axes a and c. A single crystal of size 1.9 \nx 1.8 x 2.2 mm3 was used for the neutron diffraction experiment. All the planes of the s amples \nwere gradually polished and clean using 6, 3 and 1 -micron diamond particles suspension. The \norientation o f each as -prepared sample was checked by backscattering Laue technique using \nCu white X -ray radiation before measurements.  \nThe magnetization mea surements were performed using a commercial Quantum Design \nMPMS (Magnetic Property Measurement System) device. To calculate magnetic isotherms , \nwe have employed crystal field model  introduced in our previous  work .13 The high -field \nmagnetization experiment was carried out with the extraction method using the 40 T  class \nhybrid magnet  in High Magnetic Field Laboratories of the  National Institute  for Materials \nSciences in Tsukuba, Japan . The pulse magnetic field experiment was realized in 60 T magnet \nin Dresden High Magnetic Field Laboratory (HZDR) in Germany.  \nSingle -crystal neutron diffraction data were collected on the high re solution four -circle \ndiffractometer D9 at the Institut  Laue -Langevin, Grenoble, using a wavelength of 0.5109(1) Å \nobtained by reflection from a Cu(220) monochromator. The wavelength was calibrated using \na germanium single crystal. D9 is equipped with a sma ll two -dimensional area detector ,27 \nwhich for this measurement allowed optimal delineation of the peak from the background. For \nall data, background corrections following Wilkinson et al. (1988) and Lorentz corrections \nwere applied .28 \n \nCrystal structure analysis  \nUsing single crystal neutron data  we have confirmed that  SmPd 2Al3 crystallizes in the \nspace group P6/mmm with cell param eters a = b = 5.3970(4) Å and c = 4.1987(5) Å at 20 K. \nThere are very similar to previously published cell parameters .1, 7 No crystal structure phase \ntransition has been observed from room temperature down to 2 K. The crystal structure refinement at 20 K was based on the data collection of 149 unique reflections. The data were \ncorrected f or absorption. The best data fit with R(F2) = 6.14 %  is presented in Fig. 1 . The  \ncorresponding atomic coo rdinates which are all in special Wyckoff positions and the \nanisotropic displacement parameters are given in Table II.   \nF2103\ncalc0 5 10 15 20F2103\nobs\n05101520\n \nFIG. 1. Calculated versus observed of the squared intensities for the data collected at 20 K .  \nTABLE II. Atomic coordinates and the anisotropic displacement parameters as determined at \ntemperature 20 K.  \n X Y Z U11 U22 U33 U12 U13 U23 \nAl 1/2 0(-) ½ 0.0028(7)  0.0021(7)  0.0028(9)  0.0011(7)  0(-) 0(-) \nPd 1/3 2/3 0(-) 0.0012(6)  0.0012(6)  0.0007(6)  0.0006(6)  0(-) 0(-) \nSm 0(-) 0(-) 0(-) 0.0081(8)  0.0081(8)  0.0084(11)  0.0040(8)  0(-) 0(-) \n \nMagnetic phase diagram study  \nFirst, we studied magnetization curves at low temperature T = 1.7 K and magnetic field \nup to 30 T using  a hybrid magnet  (at Tsukuba Magnet Laboratory) with field applied  along \nthe crystallographic axis c, a and the in-plane 210 direction. W e have found clear eviden ce of \nthe easy-axis type anisotropy with axis c as the direction of easy magnetization (see Fig. 2). If \none ass umes the constant slope of the magnetization curve for each axis  without any \nmetamagnetic transition, the magnetization along the hard axis in the ab plane  will attain  to \nthe magnetization along the c axis at 79.8 T.  T = 1.7 K\n0H (T)0 5 10 15 20 25 30\n (\nB/f.u.)\n0.000.050.100.150.200.25\n0H II c\n0H II a\n0H II 210 \nFIG. 2.  Magnetization curves measured with magnetic field applied along the a, c \ncrystallographic axis and also in the in -plane 210 direction  at 1.7 K .  \nThe behavior of the magnetization cu rves clearly denotes a  strong easy -axis-type \nmagnetic anisotropy . A small  discrepancy of magnetization curves for the hybrid magnet and \nthe SQUID magnetometer along the c -axis (discussed later) may come from the difference of \nthe temperature s of measurements  and/or a wrong estimation of background .  \nBefore exploring the t emperature and magnetic field dependence of the phase diagram  \nin more details , we have focused on the magnetic behavior  of the SmPd 2Al3 compound  \npublished in  previous works . Precise magnetization loops were measured exhibiting complex \nmagnetic features with complicated step -like shape .6, 13 \nThe heat capacity data published in Ref.[13] show four successive magnetic transitions at \nT3 = 3.4 K, T2 = 3.9 K, T1 = 4.4 K and TC = 12. 5 K in the zero magnetic field.  From the \npublished crystal field analysis, we may regard the system as  a spin S = 1/2 system . The \nenergy gap to the next spin doublet is about 100  K and it would not affect low temperature \nproperties below 1 2 K. The spin degree of freedom exhibits magnetic phase transitions  (see \nRef.[13]). \nFinally, t he magnetic phase diagram of the SmPd 2Al3 is complicated not only due to the \nfour successive magnetic transitions observed in the specific heat data  in zero magnetic fie ld \nbut furthermore by a series of field -induced magnetic transitions (see Refs. [6, 13]).  \nOn the ground of the heat capacity data (Ref.[13]), we have precisely investigated the \ntemperature evolution of  the magnetization loops by 0.1 K  temperature  steps  in the  \ntemperature  range 1.8 – 5 K while applying the magnetic field along the c axis. Another four \nmagnetization loops have been measured also in the temperature range 5 – 12 K. We present \nthese magnetization loops in Fig s. 3, 4 and 5.  \nIn Fig.  3a, we present  three representative loops for the interval between 1.9 and 2.9 K \nwhich  covers the region below T3. Three magnetic field -induced transitions can be identified \nin the magnetization curves with in this interval . In Figs. 3b and 3 c, we  present a zoom  into the \nmagnetic field regions where the phase transitions occur. The onset of the first transition is \nlocated at 0H C1 = 0.038  T. We call the phase defined by 0H < 0HC1 as P1. The second \nfield-induced transition is smooth. It starts to appear at a ma gnetic field of 0.35 T and is \ncompleted at 0.55 T where  it terminates. The onset of 0.55 T will be considered as a point for \nconstruction of the magnetic phase diagram. We will call this phase as P2. The determination \nof the third transition is rather tedi ous as it is quite broad. For simplicity, we will take into account the upper onset of 2.5 T that is also the point used for construction of the phase \ndiagram. The third phase will be called as P3. To study the hysteresis our attention has been \nalso focuse d on the second branches of the loops in the magnetic field decreasing from 5 T to \n0 T. The first drop of the magnetization has been found in the magnetic field of 1.9 T which \ndenotes the hysteresis of 0.6 T for the magnetic phase P3 (area of the hysteresis is marked as \nP3a - Fig. 6). The first drop of magnetization is followed by continuous decrease of the \nmagnetic moment, which ends in the magnetic field of –0.02 T by magnetization reversal. It \nmeans the hyst eresis of the P1 phase o f 0.018  T (area of the hysteresis is marked as P1a - Fig. \n6). The subsequent temperature increase from initial 1.9 K leads to reduction  of the hysteresis \nboth phases P1a and P3a and all field induced transitions are shifted to lower magnetic field \nas it is  marked by arrows in the panel B) of Fig. 3. B)\n0H (T)-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 (B/f.u.)\n-0.10.00.1\nC)\n0H (T)0.0 0.5 1.0 1.5 2.0 2.5 (B/f.u.)\n0.000.020.040.060.080.100.120.140.16A)\n0H (T)-5-4-3-2-1 012345 (B/f.u.)\n-0.170.000.17\nT = 1.8 K\nT = 2.4 K\nT = 2.9 K \nFIG. 3. A) Magnetization loops measured in the temperature interval between 1.8 – 2.9 K.  \nOnly three representative loops are displayed. B) Low magnetic field features of the loops. Gradual \nvanishing of the hysteresis and shifts of the jumps in the loops to lower magnetic fields is indicated by \narrows. C) Magnetic field loops in the positive field quadrant up to the saturation field.   A)\n0H (T)-5-4-3-2-1012345 (B/f.u.)\n-0.15-0.10-0.050.000.050.100.15\nT = 3.1 K\nT = 3.5 K\nT = 3.9 K\nB)\n0H (T)-0.1 0.0 0.1 0.2 0.3 0.4 (B/f.u.)\n0.00.1\n0H (T)-0.050 -0.025 0.000 0.025 0.050 (B/f.u.)\n-0.10.00.1 \nFIG. 4. A) The representative of magnetization loops measured in the temperature interval between \n3.1 – 3.9 K. B) Low magnetic field features of the loops. Gradual vanishing of the hysteresis and shifts \nof the jump s in the loops to lower field . Dramatic changes occurs in this temperature interval when \nhysteresis ( P3a) disappears at  3.5 K and also the jump of the P2 phase disappears at a temperature \nbetween 3.7 - 3.9 K.  \nThe other set of figures (Figs. 4a and 4b ) represents  the temperature evolution of the \nhysteresis loops in the temperature interval between 3.1 – 3.9 K. The first significant change \nof the loops is expected in this  interval because two magnetic transitions were predicted at \ntemperatures 3.4 and 3.9 K in specific  heat data.13 All magnetic field induced  transitions \ndescribed in Fig.  3 are conserved up to 3.4 K but dramatic suppression of t he transition (jump) \noriginally occurring in field interval 0.35 T - 0.55 T (marked as P2 phase) is evident. It is \nfollowed by fast reduction  of the hysteresis of the upper phase marked as P3a in the later \nconstructed phase diagram. The critical point appe ars at a temperature of 3.5 K where the \nhysteresis  of the upper phase P3a disappears. Th e second dramatic change is merging of the \nphases P2 and P3 at  a temperature between 3.7 - 3.9 K. Above the temperature of  3.8 K \nonly the hysteresis of the P1a phase appears in the low magnetic field and the common weak \nknee of the phases P2 and P3 appearing aro und magnetic field 0.2  - 0.3 T is conserved (Fig. \n4). The new phase rising from t he original P2 and P3 phases is newly called P4. \nThe third set of the lo ops (Fig s. 5a and  5b) comes from the temperature interval between \n4.1 – 4.9 K. This temperature interval is characterized by erase of the last of the phases P1 (including its hysteresis P1a) in the low  magnetic fields. The hysteresis and also P1 phase \nsimultaneously disappear at a temperature of 4.5 K (Fig. 5 panel B). The temperature \ninterval between temperatures 3.8 – 4.4 K is characterized by coexistence of the P4 and P1 \nphase with P1a hysteresis. Above 4.4 K only the P4 phase survives as a w eak knee up to 12 \nK where the loop has a paramagnetic like shape.  \nA)\n0H (T)-5-4-3-2-1012345 (B/f.u.)\n-0.15-0.10-0.050.000.050.100.15\nT = 3.1 K\nT = 3.5 K\nT = 3.9 K\nB)\n0H (T)-0.02 -0.01 0.00 0.01 0.02 (B/f.u.)\n-0.050.000.05\n \n \nFIG. 5. A) The group of magnetization loops measured in the temperature interval between 4.1 – 4.9 \nK. B) Low magnetic field features of the loops. Gradual vanishing of the hysteresis P1a and P1 phase \nis evident. Dramatic change occurs when the hysteresis (P1a) and P1 phase simultaneously disappear \nat the temperature of 4.5 K and only the P4 phase survive s up to 12 K.  \nTaking into account results of  the magnetization measurements , we have finally \nconstructed the phase diagram of SmPd 2Al3 compound (see Fig. 6 ). T (K)2 4 6 8 10 12 14 160H (T)\n0.00.51.01.52.02.53.0\nT (K)2 3 4 5 60H (T)\n0.00.51.01.52.02.53.0\nT (K)2 3 4 50H (mT)\n010203040\nP1a\nP3P3a\nP2P1\nP4P4\nP2P3P3a \nFIG. 6. Magnetic phase diagram of the SmPd 2Al3 compound constructed on the basis  of \nmagnetization data  in the magnetic field applied along the c -axis. \nMagnetic structures study  \nBased on the magnetization data, we have sketched the complex magnetic phase \ndiagram of SmPd 2Al3 as shown in Fig. 6. However , the natur e of the various magnetic phases \nremain ed unknown. Consequently , we have carried out single crystal neutron diffraction \nexperiment using  the D9 four cycle diffractometer with a short wavelength  = 0.511 Å. We \nhave cooled down the crystal below TC and carried out q-scans. Despite a weak magnetic \nsignal ( the saturated magnetic moment is only  of 0.16 µ B/f.u.) and the strong absorption, we \nwere able to observe magnetic reflections. One of the strongest magnetic reflections (5/3 5/3 0) \nis illustrated in Fig. 7. The  Miller indices of the magnetic reflections  are of the type  (h k 0) in \ngood agreement with magnetization data where the c-axis represents the easy magnetization \naxis; the k -vector of the ground state magnetic structure has been determined as k = (1/3, 1/3, \n0) and symmetry conditions given by P6/mmm space group. N o component of the magnetic \nmoment has been detected in other crystallographic directions  by magnetization \nmeasurement s. \n \nFIG. 7. Reflection (5/3 5/3 0) as observed at 3.6  K. A ) Filled contour plot showing the reflection as \nrecorded in the 2D detector. B) 3D plot of the reflection.  \nB) \n A) We could do acquisition at the top of a restricted number of magnetic reflections using the 2D \narea detector. Integrated intensities as functio ns of temperature using omega scans could not \nbe determined  due to the weakness of the magnetic reflections. We followed few reflections \nas function s of temperature. We present in Fig. 8 the temperature dependence of the (5/3 5/3 0) \nreflection  which appeared to be the strongest .  \nSmPd2Al3\nT (K)0 2 4 6 810 12 14 160200400600800100012001400\nI (5/3 5/3 0)\n12.4 K3.9 K\n4.3 K\n3.4 K ??\nT (K)2 3 4 5 6Intensity (arb. units)\n200400600800100012001400\n3.4 K ??4.3 K3.9 KA)\nB)\n \nFIG. 8. Temperature dependence of the (5/3 5/3 0) reflection.  In A), we show the temperature \nevolution in the whole temperature range. B) Zoom in the temperature range 2 to 6K. The red arrows \nmark the transition temperature s as determined from specific heat.  The presence of the last transition \nat temperature T3 = 3.4 K is disputable within the error bars .  \nWe can clearly see that the magnetic reflection (5/3 5/3 0)  emerges  at about 12. 4 K, \nwhich well corresponds to the critical temperature TC determined from specific heat \nmeasurements .4-7, 13 Further  decrease of temperature leads  to an increase of the (5/3 5/3 0) \nreflection intensity with a maximum around 4.5 - 5 K which  quite well  corresponds to T1.13 \nWhen further decreas ing temperature the intensity of the ( 5/3 5/3 0) reflection shows a drop \naround 4 K. This corresponds to the critical temperature T2.13 The expected anomalies at T1 \nand T3 are not so clearly visible. The presence of the last anomaly T3 at temperature 3.4 K is \nopen question when taking into account the error bars of the intensity. The sudden drop of the \nintensity at around 4.5 K is probably related to a change of the propagation vector as it goes \naway. However , the extremely weak magnetic signal  and the lack of resolution in q  due to \nshort neutron wavelength prevented confirm ation  of this hypothesis . \n \nDiscussion  Below TC, the intensity of the reflection (5/3 5/3 0) beh aves as an order parameter which \ncould be fitted to a power law as I = a  (TC – T). The resulting fit is presented in Fig. 9. The \nobtained critical exponent is close to 0.5 suggesting that the behavior of SmPd 2Al3 between  \nTC and T1 can be understood  within the  mean field theory . \nI = a(TC-T)\na = 391(15)\nTC = 12.44(3) K \n= 0.54(2)\nT (K)5.0 7.5 10.0 12.5 15.0Intensity (arb. units)\n0200400600800100012001400\nintensity of reflection\nmodel\n \nFIG. 9 . Fit of the intensity of the reflection (5/3 5/3 0) as function of temperature.  \nIn addition, we have inspected several  other measured magnetic reflections such as (4/3 \n1/3 0), (1/3 4/3 0), (1/3 1/3 0) and (2/3 2/3 0). No magnetic  reflection with l ≠ 0 has been \ndetected . This observation is consistent with the magnetic ordering of Sm magnetic moment s \nparallel to the c axis. Nevertheless,  we are aw are that a possible slight off the c-axis \ncomponent cannot give magnetic reflections detectable within our experiment and therefore \nwe can take the scenario with the Sm magnetic moments parallel to the c -axis only tentatively. \nTaking into account that the propagation vector between TC and T1 is k = (1/3, 1/3, 0) and \nthere is a p riori no magnetic component in ab plane, we can give a representation of this \nlikely magnetic structure ( see Fig. 1 0). The  magnetic unit -cell is 3 times larger along a and b, \nrespectively,  and is formed by 2 hexagonal sublattices which are interpenetrated and are \ncoupled antiferromagnetically. The coupling along the c-axis is ferromagnetic.  \n \nFIG. 10 . Likely magnetic structure of the phase stable between TC and T1 in SmPd 2Al3. \nThe magnetic structure between TC and T1 characterized  by k = (1/3, 1/3, 0) with a  \nhexagonal lattice can be  discuss ed in the scenario of magnetic frustration. As the model  \nexample the isostructural compound GdPd 2Al3 can be considered being  presented as a \nmagnetically frustrated Heisenberg triangular lattice antiferromagnet with weak Ising \nanisotropy .16, 29, 30 This can be a  key for understanding of the magnetic structures of the phases \nin the phase diagram of the  related  SmPd 2Al3. Both compounds , GdPd 2Al3 and SmPd 2Al3, \nhave many similar ities but also some different magnetic features. The main difference  \nbetween the Sm and Gd compounds comes from  the magnetic state and influence of the \ncrystal field on magnetic ions. The Gd3+ ion represents an exception among rare earth  ions \nbecause of  its zero angular  momentum . Due to this fact the multiplet J = 8S7/2 ground state \nremains fully degenerate in the crystal field.  In the absence of external magnetic field, only an \nexchange magnetic field can lift the (2J + 1) -fold degeneracy.31, 32 The Sm3+ ion represents a \ntotally  different case as it was suggested in the Introduction . The connecting point between \nthe two compounds is the same hexagonal crystal structure with magnetic k-vector (1/3, 1/3, 0) \n(temperature interval TC - T1) for SmPd 2Al3 and also for GdPd 2Al3 between TN1 and TN2.16 \nGenerally, the presence of magnetic frustration in solids is reveal ed by a few \nexperimental evidences in first simple approach. The first of them is the existence of plateaus \nin magnetization curves33-35 and anomalously low CW with respect to critical temperatures36, \n37. The empirical quantity f = -CW/TC> 1 corresponds to frus tration (2 for antiferromagnets). \nThe investigation of both parameters is pretty complicated for the Sm3+ magnetic state. The \nreciprocal susceptibility 1/  of SmPd 2Al3, which is affected by temperature -independent Van \nVleck  contribution due to the low -lying first excited multiplet J = 7/2 being populated13 does \nnot follow the Curie -Weiss law.  Despite of this fact the fitted CW = -21.3 K using a modified \nCurie -Weiss law1 and our found TC = 12.5 K give s f = 1.7 which is close to expected value for \nfrustrated antiferromagnets.37 The analysis of the magnetization plateaus is not \nstraightforward due to the missing saturated moment of the Sm3+ ion. For comparison, the \nisostructural compound GdPd 2Al3 is characterized by the well-define d wide 1/3 plateau on the \nmagnetizat ion curve in the magnetic field interval  between 6.2 and 11.8 T .29, 30 Such behavior \nis typical for triangular lattice antiferromagnet s with weak Ising like anisotropy.  \nThe saturated magnetization value of 0.16 µ B/f.u. deduced from the magnetization data \nis significantly less than the expected magnetic moment of gJB = 0.71 B for the Sm3+ free \nion. This 0.16 µ B/f.u. value of the saturated magnetic moment is comparable with value found \nin Ref.13. This considerably reduced saturated magnetic moment value by a factor of about \nfive motivated us to carry out high magnetic field experiment up to 60 T in the pulse field \nmagnet. The pulse field was applied along the easy magnetization c axis. Our high magnetic \nfield experiment up to 60 T did not show any additional features compared to our low er \nmagnetic field measurement. Especially no extra magnetic field induced phases were \nobserved either along the c axis or in ab plane.  \nIn order to gain some more insight into our system, we have carried out theoretical \ncalculations. To calculate the magnetic isotherms we have employed a crystal field model. \nThe microscopic crystal field Hamiltonian has the hexagonal symmetry and reasonable crystal \nfield parameters were found by first principles calculations  in our previous work13. The total \n(CF + Zeeman)  Hamiltonian has been diagonaliz ed and the obtained eigen -values and \neigenvectors has been used to calculate magnetic isotherms along the c- and a- axes, \nrespectiv ely. The result of the calculation is presented in Fig. 11 . 0H (T)0 1 2 3 4 5 6 7 (B/f.u.)\n0.00.10.20.30.40.50.6\n0H II c\n0H II a \nFIG. 11 . Figure represents magnetization isotherms calculated using crystal field model.  \nFirstly the calculation confirms the c-axis as the easy magnetization  axis but t he \nevolution of the saturated moment is not in reasonable agreement with the experimental data \nwhen significantly higher moment has been found – almost three times higher than \nexperimental result in the magnetic field of 5 T. Based on our model,  the theoretical field \nrequired to reach the saturated magnetic moment is 220 T. However such magnetic field is not \nexperimentally routinely available nowadays. On the basis  of the se calculations and \nexperimentally available magnetization data , we still ca nnot exclude any additional field \ninduced transition in magnetic field s higher than 60  T and the question regarding the value of \nthe saturated magnetic moment is still open.  \n \nT = 1.9 K\n0H (T)0 1 2 3 4 5 (B/f.u.)\n0.000.020.040.060.080.100.120.140.16\nvirgin curve\n+5 T - (-5) T\n-5 T - (5) T \n0.5 B/f.u. 1/3 plat.0.8 B/f.u.0.9 B/f.u.1/2 plat.\n0HC2 = 0.25 T 0HC1 = 0.06 T 0HC3 = 0.55 T0Hsat = 2.5 T\n \nFIG. 12 . First quadrant of the magnetization  loop of the SmPd 2Al3 measured at temperature 1.9 K.  \nPresent ly, we adopt 0.16 B/f.u. as the saturated value  (Fig. 12 ). Then, we find, in the \nfield-increasing process, a plateau around 1/3 of the saturated magnetization, and a jump to another plateau aroun d 1/2 of the saturated magnetization. The magnetization gradually \nincreases to the saturated magnetization. On the other hand, in the field -decreasing process, \nthe magnetization decreases to 1/2 of the saturated magnetization. Around zero magnetic field \nthe magnetization shows sharp change (almost jumps) to the opposite sign. But it shows a \nsmall hysteresis with 0H  0.01 T. The 1/3 plateau reminds us the magnetization process of \nantiferromagnets  in the triangular (hexagonal) systems. We may also regard the plateau of \n0.16 B as the 1/3 plateau and then we expect another jump to the saturated magnetization at \nhigher field.  However , the 1/2 plateau does not fit to this picture. Therefore  we cannot take \nthis scenario.  Some intermediate kinetic effects could cause the 1/2 plateau in hexagonal \nsystems .38 Here similar kinetic effect is expected for the ordered state. This type of plateau in \nthe increasing field process has been discussed as Magnetic Foehn effect39, 40 in single \nmolecular magnets, wh ich occurs as a kinetic effect.  The dependence on the time scale will be \nstudied later.   \nAcco rding to the simple triangular scenario of XXZ  antiferromagnetic model on the \nhexagonal lattice,  the magnetization at 0H is given by  Ref [33]. For the model of anisotropic \ncoupling  \n \n𝐻𝐴=  𝐽 𝑆𝑖𝑋𝑆𝑗𝑋+𝑆𝑖𝑦𝑆𝑗𝑦 +𝐽𝑧𝑆𝑖𝑧𝑆𝑗𝑧 −𝐻𝑧 𝑆𝑖𝑧\n𝑧  𝑖𝑗  \n \n \nthe magn etic field at the beginning of the 1/3 plateau is 0HC1 = 3J, and the end of the 1/3 \nplateau is  \n𝐻𝐶2=3𝐽 2𝐴−1+ 4𝐴2+4𝐴−7 \n2 \n \n with A = Jz/J. The magnetization at 0H = 0 T is given by  \n \n𝑀0= 𝐴−1 \n 𝐴+1  \n \nFrom the observation we find M 0   1/2. Thus we estimate A   3. From the value of 0HC1 in \nthe experiment, we estimate  J = 2T/3. From  these values, 0HC2 is estimated as \n \n𝐻𝐶2=2𝑇 5+ 41 ≈22𝑇 \n \nThus, we may expect another jump around 0H = 22 T. But we did not find this jump in Fig. 2.  \nNow we consider the shape of magnetization loop from the view point of  the kinetic \neffect. As we saw in the previous section, the magnetization curve of the SmPd 2Al3 at \ntemperature T = 1.9 K is characterized by two types of steps  (Fig. 1 2). The first on e appears \nas a jump to a plateau of 1/3 of the saturated moment at small value of the magnetic field. The \nplateau exists in the magnetic field interval 0HC1 = 0.0 45 T and 0HC2 = 0.25  T. Then the \nmagnetization increases and reaches 1/2 of saturated moment to full saturate d value at 0HC3 \n= 0.55 T. Then the magnetization curv e has a kink or a small plateau and t hen, the \nmagnetization gradually increase s to full saturate d value. I t reaches the saturated moment at \n0HC4 = 2.5  T. In the process of decreasing magnetic field, the magnetization begins to \ndecrease from the saturated value at 0HC5 = 1.9  T and decreases gradually to near 1/2 of \nsaturated moment and jump to the negative value around  0H = 0 T. Because of the hysteresis of the magnetization process, the magnetization curve cannot be considered in truth as a \nplateau.  \nThere  is also necessary to consider other effects that can lead to induction of the \nplateaus and jumps in magnetization curves.  Dynamical magnetic processes have been found \nin single molecular magnets and also magnetic rings. For example, a  phonon -bottleneck effect \nin V 1541 which was explained as a phenomenon due to lack of photon mode for the \nequilibration . Similar phenomenon was observed in [Fe(salen)Cl] 242\n and also Fe 1043\n. These \nphenomena can be regarded as adiabatic processes with small infl ow of heat. Such effect of \nthe influence of  kinetic effect of swee ping magnetic field is under stood as magnetic Foehn \neffect.34,35 Similar phenomena have been observed in macroscopic magnetization processes. \nFor example, Katsumata et al. has found it in FeCl 2.2H2O38 and also Narumi et al. in Kagome \nlattice44. \nIn the present case the step is found in a macroscopic change of magnetization. To \nclarify the influence of the sweeping magnetic field on magnetization we have measured \nmagnetiz ation loop both  with a  slow field rate in SQUID magnetometer and in pulse  field \nmagnet  where the maximum used field of 8 T was reached within few tens milliseconds . The \nresults are shown in the Fig. 1 3. \n0H II c\nT = 1.9 K\n0H (T)0 1 2 3 4 (B/f.u.)\n0.000.020.040.060.080.100.120.140.160.18\nSQUID magnetometer\npulse field \n \nFIG. 13. The virgin magnetization curves measured in various magnetic field sweep rates. All jumps \n(plateaus) have been shifted to higher field in the case of pulse field magnetization experiment. The \nred (full line) arrows mark the shift of the 1/3 plateau. The bl ue (dashed) arrows mark the shift of the \n1/2 jump.  \nThe original 1/3 plateau has been shifted to higher magnetic field (from original field \nregion 0HC1 = 0.06 T and 0HC2 = 0.25 T to 0HC1 = 0.35 T and 0HC2 = 0.70 T). In addition \nthe original 1/3 plateau has not conserved the 1/3 characteristic and has been suppressed to the \nlower magnetic moment. The 1/2 jump has been shifted from the original 0HC3 = 0.55 T to \n0HC3 = 1.35 T and saturation has been reached at a significantly higher magnetic field of  \n3.5 T. We have suggested a scenario of the kinetic effect on the magnetization of  SmPd 2Al3. \nThere, we find large change of the magnetization process where even the height of the plateau \nchanges. Thus, we have to consider that the ordered state has a rather complicated structure \nand various metastable states exist. In general, a plateau indicates  a collinear structure (e.g., \nup-up-down structure, etc .), while gradual increase indicates a non -collinear structure (e.g., \nthe Y shape structure). In Fig s. 3, 4 and 5 we find that the temperature  simply smear s the \nstructure, but in the Fig.  14, the spin structure at intermediate magnetic field seems different in the SQID measurement and the pulse field measurement.  Unfortunately, at this moment, \nwe cannot identify the structure, yet. Further detailed observations are expected.  \n \nConclusions  \nWithin the SmPd 2Al3 study we have established the magnetic phase diagram on the \nbasis of magnetization data. We have found rather complicated magnetic phase diagram \nwhere four different magnetic phases appear with pronounced hysteresis of two phases. We \nhave detected the rather reduced saturated magnetic moment (0.16 B/f.u.) then expected for \nSm3+ ion which is most probably given by  the strong crystal field effect. Eve n applied high \nmagnetic field of 60 T has not led to any significant increase of the saturated magnet ization. \nAlthough the constructed magnetic phase diagram brings considerable progress in knowledge \nof the Sm magnetism in SmPd 2Al3 compound the detail information regarding their magnetic \nstructures were still lacking of.  \nTherefore we have performed a neutron diffraction experiment of SmPd 2Al3 single \ncrystal and we have successfully observed magnetic reflection (5/3 5/3 0 ) and its equivalents \nin the temperature interval 12.4 - 4.3 K which denotes the magnetic k-vector (1/3 1/3 0) . \nConsequently SmPd 2Al3 material  can be considered as belonging to the group of magnetically \nfrustrated systems. Based on our observations, we  expe ct a triangular lattice antiferromagnet \nwith weak Ising like anisotropy as  the most suitable model for SmPd 2Al3 compound.  \nThe pulse d high magnetic  field magnetization experiment surprisingly points to  the \ninfluence of kinetic effect in magnetization process. The kinetic effect turns out to be the \npartially responsible effect for step like shape of magnetization curves at low temperatur es \nwhere  various rates of external field sweep lead to different metastable magnetic states .  \nOn the basis of our investigation, the SmPd 2Al3 compound represents a unique example \nof a complicated three dimensional phase diagram when not only the temperature and \nmagnetic field are external variables but also the field sweep rate plays an important role.  The \nrich magnetic phase diagram is given by  a unique interplay of the magnetic frust ration with \nkinetic effect of the sweeping magnetic field . \nAlthough many features of the Sm magnetism in SmPd 2Al3 have been conceived , there \nare still unresolved  questions regarding the magnetic structures of the low  temperature phases.  \nMainly the question and confirmation of the existence off -c-axis component of the magnetic \nmoment  seems to be most essential to understand the SmPd 2Al2 physic s well . Magnetic X -ray \nresonant scattering performed on Sm absorption edge , polarized neutron dif fraction and fine \ntorque magnetometry studies  are planned to reveal relevant  SmPd 2Al2 magnetic features.  \n \nAcknowledgements  \nThis work was supported by the Czech Science Foundation (Project # 202/09/1027) and  the \nCharles University grant UNCE 11. Experiments performed in MLTL (see: http://mltl.eu/ ) \nwere  supported within the program of Czech Research Infrastructures (project # LM2011025).  \nNeutron diffraction experiments in ILL Grenoble were performed within  the projec t # \nLG11024 financed by the Ministry of Education of the Czech Republic.  High -field \nmagnetization measurements were  supported by EuroMagNET under the EU contract \nn°228043.  \n \n \nReference List  \n 1 A. Dönni, A. Furrer, H. Kitazawa, and M. Zolli ker, Journal of Physics -Condensed \nMatter 9, 5921 (1997).  \n2 A. Dönni, A. Furrer, E. Bauer, H. Kitazawa, and M. Zolliker, Zeitschrift für Physik B -\nCondensed Matter 104, 403 (1997).  \n3 A. Dönni, H. Kitazawa, P. Fischer, T. Vogt, A. Matsushita, Y. Iimura, and M. Zolliker, \nJournal of Solid State Chemistry 127, 169 (1996).  \n4 K. Ghosh, S. Ramakrishnan, A. D. Chinchure, V. R. Marathe, and G. Chandra, \nPhysica B: Condensed Matter 223-224, 354 ( 1996).  \n5 K. Ghosh, S. Ramakrishnan, S. K. Malik, and G. Chandra, Physical Review B 48, \n6249 (1993).  \n6 K. Ghosh, S. Ramakrishnan, S. K. Malik, and G. Chandra, Physica B: Condensed \nMatter 199-200, 604 (1994).  \n7 H. Kitazawa, A. Mori, S. Takano, T. Yamadaya, A . Matsushita, and T. Matsumoto, \nPhysica B 188, 661 (1993).  \n8 G. Motoyama, T. Nishioka, and N. K. Sato, Journal of the Physical Society of Japan \n71, 1609 (2002).  \n9 S. A. M. Mentink, N. M. Bos, G. J. Nieuwenhuys, A. A. Menovsky, and J. A. Mydosh, \nPhysica B: Condensed Matter 186-188, 497 (1993).  \n10 J. Pospisil, M. Kratochvilova, M. Divis, J. Prokleska, J. Vejpravova Poltierova, and V. \nSechovsky, Journal of Alloys and Compounds 509, 1401 (2011).  \n11 A. M. Strydom and P. d. Du Plessis, Journal of Magnetism and Ma gnetic Materials \n226-230, 150 (2001).  \n12 V. S. Zapf, R. P. Dickey, E. J. Freeman, C. Sirvent, and M. B. Maple, Physical \nReview B 65, 024437 (2002).  \n13 J. Pospisil, M. Kratochvilova, J. Prokleska, M. Divis, and V. Sechovsky, Physical \nReview B 81, 024413 (20 10). \n14 Z. S. Liu, Physica B 262, 348 (1999).  \n15 Z. S. Liu, Physical Review B 64, 144407 (2001).  \n16 T. Inami, N. Terada, H. Kitazawa, and O. Sakai, Journal of the Physical Society of \nJapan 78, 084713 (2009).  \n17 G. H. Dieke, Spectra and Energy Levels of Rare Earth Ions in Crystals  (John Wiley & \nSons, USA, 1968).  \n18 H. W. Dewijn, A. M. Vandiepe, and K. H. J. Buschow, Physical Review 161, 253 \n(1967).  \n19 J. K. Böhlke, J. R. d. Leater, P. D. Bièvre, H. Hidaka, H. S. Peisar, K. J. R. Rosman, \nand P. D. P. Taylor, Journal of Physical and Chemical Reference Data 34, 57 (2005).  \n20 K. J. R. Rosman and P. D. P. Taylor, Pure and Applied Chemistry 70, 217 (1998).  \n21 F. V. Sears, Neutron News 3, 26 (1992).  \n22 A. J. Dempster, Physical Review 74, 505 (1948).  \n23 R. E. Lapp, J. R. Vanhorn, and A. J. Dempster, Physical Review 71, 745 (1947).  \n24 http://www -nds.iaea.org/ngatl as2/. \n25 K. A. Toukan, K. Debus, F. Kappeler, and G. Reffo, Physical Review C 51, 1540 \n(1995).  \n26 K. Wisshak, K. Guber, F. Voss, F. Kappeler, and G. Reffo, Physical Review C 48, \n1401 (1993).  \n27 M. S. Lehmann, W. Kuhs, G. J. McIntyre, C. Wilkinson, and J. A llibon, J. Appl. \nCrystallogr. 22, 562 (1989).  \n28 C. Wilkinson, H. W. Khamis, R. F. D. Stansfield, and G. J. McIntyre, J. Appl. \nCrystallogr. 21, 471 (1988).  29 H. Kitazawa, H. Suzuki, H. Abe, J. Tang, and G. Kido, Physica B: Condensed Matter \n259-261, 890 (1999).  \n30 H. Kitazawa, K. Hashi, H. Abe, N. Tsujii, and G. Kido, Physica B: Condensed Matter \n294-295, 221 (2001).  \n31 K. H. J. Buschow and F. R. de Boer, Physics of Magnetism and Magnetic Materials  \n(Kluwer Academic/Plenum Publisher, New York, 2003).  \n32 M. Bouvier, P. Lethuillier, and D. Schmitt, Physical Review B 43, 13137 (1991).  \n33 S. Miyashita, Journal of the Physical Society of Japan 55, 3605 (1986).  \n34 K. Penc, N. Shannon, and H. Shiba, Physical Review Letters 93 (2004).  \n35 H. Nishimori and S. Miyashit a, Journal of the Physical Society of Japan 55, 4448 \n(1986).  \n36 C. Lacroix, P. Mendels, and F. Mila, Introduction to Frustrated Magnetism: Materials, \nExperiments, Theory  (SPRINGER -VERLAG BERLIN, Berlin, 2011).  \n37 A. P. Ramirez, Annual Review of Materials S cience 24, 453 (1994).  \n38 K. Katsumata, Journal of the Physical Society of Japan 39, 42 (1975).  \n39 K. Saito and S. Miyashita, Journal of the Physical Society of Japan 70, 3385 (2001).  \n40 E. C. Yang, et al., Inorganic Chemistry 45, 529 (2006).  \n41 I. Chiorescu, W. Wernsdorfer, A. Muller, H. Bogge, and B. Barbara, Physical Review \nLetters 84, 3454 (2000).  \n42 Y. Shapira, M. T. Liu, S. Foner, C. E. Dube, and P. J. Bonitatebus, Physical Review B \n59, 1046 (1999).  \n43 H. Nakano and S. Miyashita, Journal of the Physical Society of Japan 70, 2151 (2001).  \n44 Y. Narumi, K. Katsumata, Z. Honda, J. C. Domenge, P. Sindzingre, C. Lhuillier, Y. \nShimaoka, T. C. Kobayashi, and K. Kindo, Europhysics Letters 65, 705 (2004).  \n \n "    },    {        "title": "1303.5262v1.Co_monolayers_and_adatoms_on_Pd_100___Pd_111__and_Pd_110___Anisotropy_of_magnetic_properties.pdf",        "content": "arXiv:1303.5262v1  [cond-mat.mtrl-sci]  21 Mar 2013Co monolayers and adatoms on Pd(100), Pd(111) and Pd(110): A nisotropy of\nmagnetic properties\nO.ˇSipr,1,∗S. Bornemann,2H. Ebert,2S. Mankovsky,2J. Vack´ aˇ r,1and J. Min´ ar2\n1Institute of Physics of the ASCR v. v. i., Cukrovarnick´ a 10, CZ-162 53 Prague, Czech Republic\n2Universit¨ at M¨ unchen, Department Chemie, Butenandtstr. 5-13, D-81377 M¨ unchen, Germany\n(Dated: September 16, 2018)\nWe investigate to what extent the magnetic properties of dep osited nanostructures can be influ-\nenced by selecting as a support different surfaces of the same substrate material. Fully relativistic\nab initio calculations were performed for Co monolayers and adatoms o n Pd(100), Pd(111), and\nPd(110) surfaces. Changing the crystallographic orientat ion of the surface has a moderate effect\non the spin magnetic moment and on the number of holes in the dband, a larger effect on the\norbital magnetic moment but sometimes a dramatic effect on th e magnetocrystalline anisotropy\nenergy (MAE) and on the magnetic dipole term Tα. The dependence of Tαon the magnetization\ndirection αcan lead to a strong apparent anisotropy of the spin magnetic moment as deduced from\nthe X-ray magnetic circular dichroism (XMCD) sum rules. For systems in which the spin-orbit\ncoupling is not very strong, the Tαterm can be understood as arising from the differences betwee n\ncomponents of the spin magnetic moment associated with diffe rent magnetic quantum numbers m.\nPACS numbers: 75.70.Ak,75.30.Gw,78.70.Dm,73.22.Dj\nKeywords: magnetism,anisotropy,nanosystems,XMCD\nI. INTRODUCTION\nThe magnetic properties of surface deposited nanos-\ntructures have been in the ongoing focus of many ex-\nperimental and theoretical investigations as they often\nexhibit interesting and sometimes unexpected phenom-\nena. One of the main features in this context is that the\nlocal magnetic moments and their mutual interaction as\nwell as the magnetocrystalline anisotropy energy (MAE)\nare in general different and often much larger in nanos-\ntructures than in corresponding bulk systems. Various\naspects of the magnetism of many different nanostruc-\ntures were studied in the past to identify the key fac-\ntors which could then be used to tune the properties of\nsuch systems in a desired way. It has been known for\nsome time that one such key factor is the coordination\nnumber, with smaller coordination numbers generally im-\nplying larger magnetic moments.1–3However, coordina-\ntion numbers alone do not fully determine magnetism of\nnanostructures. The chemical composition can play a\nsignificant role as well. An Fe monolayer, for instance,\nhas a larger spin magnetic moment when deposited on\nAu(111) than when deposited on Pt(111), whereas for a\nCo monolayer it is vice versa .3The situation is even more\ndiverse for the MAE where different substrates may lead\nto different properties of systems of otherwise identical\ngeometries. For example, Co 2and Ni 2dimers on Pt(111)\nhave out-of-plane magnetic easy axis but the same dimers\non Au(111) have an in-plane magnetic easy axis.3\nExperimental research on magnetism of nanostructures\nrelies heavily on the X-ray magnetic circular dichroism\n(XMCD) sum rules.4–6The strength of these sum rules\nis that they give access to spin magnetic moments µspin\nand orbital magnetic moments µorbseparately and in a\nchemically specific way.7,8However, the XMCD spin sum\nrule does not provide µspinalone but only its combinationµspin+ 7Tα, whereTαis the magnetic dipole term (for\nthe magnetization Mparallel to the αaxis,α=x,y,z ).7\nFor bulk systems, Tαcan be usually neglected but for\nsurfaces and clusters the Tαterm can have significant\ninfluence, as it has been demonstrated experimentally9,10\nand theoretically.11–13The anisotropy of the magnetic\ndipole term was predicted on general grounds14and some\nestimates concerning the magnitude of this anisotropy in\nnon-cubic bulk systems were given based on atomic-like\nmodel Hamiltonians14or onab initio calculations.15\nMagnetic nanostructures may be prepared by combin-\ning and arranging different magnetic elements on differ-\nent substrates. In this respect one can also address sur-\nfaces of different crystallographic orientations. Thus, it\nis important to know how the magnetic properties can be\ncontrolled by selecting for the substrate crystallographi-\ncally different surfaces of the same material and whether\none can expect different effects for complete monolayers\nand for adatoms. Connected with this is the question\nabout the effects on the Tαterm, because XMCD is per-\nhaps the most frequently used experimental technique in\nthis field and it is desirable to know how Tαcan influ-\nence the values of magnetic moments deduced from the\nXMCD sum rules. For planning and interpreting such\nexperiments, it would be very useful not only to know\ntheTαvalues from ab initio calculations but also to have\na simple intuitive interpretation of the Tαterm.\nIn order to learn more about this, we undertook a sys-\ntematic study of Co monolayers and adatoms on Pd(100),\nPd(111), and Pd(110) surfaces. Fully relativistic ab ini-\ntiocalculations were performed to obtain µspin,µorb, and\nTαfor different magnetization directions. The MAE was\ndetermined for all these systems as well. The accuracy of\nan approximative expression for the Tαterm was checked\nto see whether it captures the essential physics. It is\nshown in the following that monolayers and adatoms on2\ndifferent crystallographic surfaces may have indeed quite\ndifferent magnetic properties, especially as concerns the\nMAE. Moreover, it is also demonstrated how the depen-\ndence of the Tαterm on the magnetization direction leads\nto a surprisingly strong apparent anisotropy of µspinas\ndeduced from the XMCD sum rules.\nII. METHODS\nA. Investigated systems\nWe investigated Co monolayers on Pd(100), Pd(111)\nand Pd(110) and also Co adatoms on the same surfaces.\nThe corresponding structure diagrams are shown in Fig. 1\n(for adatoms, obviously only one Co atom is kept). Two\nhollow adatom positions are possible for the (111) sur-\nface, differing by the position of the adatom with respect\nto the sub-surface layer; we consider the fcc position in\nthis work (unless specified otherwise).\nThe Pd substrate has fcc structure with lattice con-\nstanta=3.89 ˚A. To determine the distances between the\nCo atoms and the substrate, we relied in most cases on\nthe “constant volume approximation”: the vertical Co–\nPd interplanar distance zCo-Pd is taken as an average\nbetween the interlayer distance in bulk Pd and the inter-\nlayer distance in a hypothetical pseudomorphically grown\nfcc Co film compressed vertically in such a way that\nthe atomic volume of Co is the same as in bulk Co.16\nIn addition we took also into account relevant experi-\nmental data and results of ab-initio geometry relaxations\nwhen available. For example, the constant volume ap-\nproximation yields zCo-Pd =1.70 ˚A for a Co monolayer on\nPd(100) while we took zCo-Pd =1.65 ˚A instead, following\nthe surface X-ray diffraction experiment of Meyerheim et\nal.17For the other two surfaces we used the constant vol-\nume approximation distances, namely, zCo-Pd =1.96 ˚A for\nCo on Pd (111) and zCo-Pd =1.20 ˚A for Co on Pd(110).\nIn the case of the (111) surface we can compare our\ndistance with an EXAFS-derived experimental distance\nzCo-Pd =2.02 ˚A (Ref. 18) and with an ab initio equilib-\nrium distance zCo-Pd =1.91 ˚A (Ref. 19). It follows from\nthis comparison that the constant-volume-approximation\nleads to reasonable distances.\nSystems with interplanar distances as given above will\nbe called systems with “optimized geometries”. Apart\nfrom that, we investigate for comparison also systems\nwhere the Co atoms are located in ideal positions of the\nunderlying Pd lattice. For this we use the designation\n“bulk-like geometry”. The interplanar distances are sum-\nmarized in Tab. I.\nFor adatoms we use the same zCo-Pd distances as for\nmonolayers. This is a simplification because the constant\nvolume approximation will work worse for adatoms than\nfor monolayers. For example the ab initiozCo-Pd dis-\ntance for a Co adatom on Pd(111) is 1.66 ˚A (Ref. 20)\nin contrast to our optimized geometry value of 1.96 ˚A.\nHowever, by using identical zCo-Pd distances for mono-TABLE I. Vertical distances zCo-Pd between the plane con-\ntaining Co atoms and plane containing Pd atoms for systems\ninvestigated in this study. The unit is ˚A.\nsurface optimized geometry bulk-like geometry\n(100) 1 .65 1 .95\n(111) 1 .96 2 .25\n(110) 1 .20 1 .38\nlayers and adatoms, the net effect due to the change in\nCo coordination can be studied. It will be shown that\nthe effect of varying the distances is in fact smaller than\nthe effect of monolayer-to-adatom transition.\nB. Computational scheme\nThe calculations were performed within the ab initio\nspin density functional framework, relying on the local\nspin density approximation (LSDA) with the Vosko, Wilk\nand Nusair parametrization for the exchange and corre-\nlation potential.21The electronic structure is described,\nincluding all relativistic effects, by the Dirac equa-\ntion, which is solved using the spin polarized relativis-\ntic multiple-scattering or Korringa-Kohn-Rostoker (SPR-\nKKR) Green’s function formalism22as implemented in\nthespr-tb-kkr code.23The potentials were treated\nwithin the atomic sphere approximation (ASA) and for\nthe multipole expansion of the Green’s function, an an-\ngular momentum cutoff ℓmax=3 was used.\nThe electronic structure of Co monolayers on Pd sur-\nfaces was calculated by means of the tight-binding or\nscreened KKR technique.24The substrate was modeled\nby slabs of 13–14 layers (i.e. a thickness of 17–27 ˚A, de-\npending on the surface orientation), the vacuum was rep-\nresented by 4–5 layers of empty sites. The adatoms were\ntreated as embedded impurities: first the electronic struc-\nture of the host system (clean surface) was calculated and\nthen a Dyson equation for an embedded impurity cluster\nwas solved.25The impurity cluster contains 135 sites if\nnot specified otherwise; this includes a Co atom, 50–60\nPd atoms and the rest are empty sites.\nIt should be stressed that the embedded clusters define\nthe region where the electronic structure and potential\nof the host is allowed to relax due to the presence of the\nadatom and notthe size of the considered system. In this\nrespect the Green’s function approach differs from the of-\nten used supercell approach: there is an unperturbed host\nbeyond the relaxation zone in the former approach while\nin the latter approach, the supercell is terminated either\nby vacuum or by another (interfering) relaxation zone\npertaining to an adjacent adatom. The sizes of the em-\nbedded clusters and the sizes of the supercells thus have\na different meaning and cannot be directly compared.\nThe magnetocrystalline anisotropy energy (MAE) is\ncalculated by means of the torque T(ˆn)\nˆuwhich describes\nthe variation of the energy if the magnetization direction3\n(100)\nxy(111)\nxy(110)\nxy\nFIG. 1. (Color online) Structure diagrams for a Co monolayer on Pd(100), Pd(111) and Pd(110). The blue and yellow circles\nrepresent the Co and Pd atoms, respectively. The orientatio n of the xandycoordinates used throughout this paper is also\nshown.\nˆnis infinitesimally rotated around an axis ˆ u. For uniaxial\nsystems where the total energy can be approximated by\nE(θ) =E0+K2sin2(θ) +K4sin4(θ),\nthe difference E(90◦)−E(0◦) is equal to the torque eval-\nuated forθ= 45◦.26The torque itself was calculated by\nrelying on the magnetic force theorem.27\nApart from the magnetocrystalline anisotropy induced\nby the spin-orbit coupling, the magnetic easy axis is\nalso determined by the so-called shape anisotropy caused\nby magnetic dipole-dipole interactions. The shape\nanisotropy energy is usually evaluated classically by a\nlattice summation over the magnetostatic energy contri-\nbutions of individual magnetic moments, even though\nit can be in principle obtained ab initio via a Breit\nHamiltonian.28In this paper, we always deal only with\nthe magnetocrystalline contribution to the magnetic\nanisotropy unless stated otherwise.\nIII. RESULTS\nA. Magnetic moments and magnetocrystalline\nanisotropy\nTo assess the effect of selecting different crystallo-\ngraphic surfaces and of going from a monolayer to an\nadatom, we calculated magnetic moments, numbers of\nholes in the Co dband and the MAE for all these sys-\ntems. The results are summarized in Tab. II. For each\nsystem, the data are shown first for the optimized geom-\netry and then for the bulk-like geometry (numbers in the\nbrackets). The x,y, andzsuperscripts in the column\nheader labels indicate the direction of the magnetization\nM.\nThe spin magnetic moment µspinand the number of\nholes in the dbandnhare shown only for M/bardblz, because\nthey are practically independent on the magnetization\ndirection: by varying it, µspincan be changed by no more\nthan 0.2 % and nhby no more than 0.1 %. On the\nother hand, for µorbthe differences can be quite large.\nThe second in-plane magnetization direction M/bardblywasinvestigated only for the (110) surface, because there is\nonly very small “intraplanar anisotropy” for the (100)\nand (111) surfaces (this issue is addressed in more detail\nin Sec. III C). For bulk hcp Co we get µspin=1.61µB,\nµorb=0.08µBandnh=2.48.\nChanging the surface orientation has a moderate effect\nonµspinandnh. The differences in µspinwhen going\nfrom one surface to another are at most 9 %. For nh\nthese differences are at most 5 %. However, the situation\nis quite different for µorbwhere the differences are 20–\n50 %. The sensitivity in µorbfinds its counterpart in\nthe sensitivity of the MAE. For example, the magnetic\neasy axis for a Co monolayer is in-plane for the (100) and\n(110) surfaces but out-of-plane for the (111) surface. For\nthe adatom, the easy axis is in-plane for the (110) surface\nbut out-of-plane for the (100) and (111) surfaces. So in\nthis respect the choice of the crystallographic surface can\nhave a dramatic influence.\nAnother finding emerging from Tab. II is that as\nconcernsµspin, the difference between monolayers and\nadatoms is only quantitative in most cases. A surpris-\ningly small difference in this respect is found for the (110)\nsurface. As the same Co–Pd distances have been used\nfor monolayers and adatoms, one observes here the net\neffect of the change in Co coordination. For µorb, the\ndifference between monolayers and adatoms is obviously\nmuch larger than for µspin. For the MAE this difference\ncan again be essential: The magnetic easy axis for a Co\nmonolayer on Pd(100) is in-plane while for a Co adatom\non the same surface it is out-of-plane. Similarly, the mag-\nnetic easy axis for a monolayer on Pd(110) is parallel to\nthey-axis while for an adatom it is parallel to the x-axis.\nChanging the distance between Co atoms and the sur-\nface clearly affects the magnetic properties (cf. the values\nwith and without brackets in Tab. II). However, it is note-\nworthy that the effect of geometry relaxation is smaller\nthan the effect of the transition from the monolayer to\nthe adatom.\nWe calculated also the magnetic shape anisotropy for\nthe monolayers (classically, via a lattice summation,\ntaking into account also moments on Pd atoms). As\nexpected, this contribution favors always an in-plane4\nTABLE II. Magnetic properties of Co monolayers and adatoms o n Pd(100), Pd(111), and Pd(110). The first column specifies\nwhether the values are for a monolayer or for an adatom, the se cond column contains spin magnetic moment for the Co atom\nforM/bardblz(in units of µB), the third column contains number of holes in the dband for M/bardblz. The fourth, fifth and sixth\ncolumns contain orbital magnetic moments for the Co atom for M/bardblz,M/bardblx, andM/bardbly, respectivelly. The last three columns\ncontain the MAE between indicated magnetization direction s (in meV per Co atom). Numbers without brackets stand for\nsystems with optimized Co–Pd distances, numbers in bracket s stand for systems with a bulk-like geometry (see Sec. II A).\nµ(z)\nspin n(z)\nh µ(z)\norb µ(x)\norb µ(y)\norb E(x)−E(z)E(y)−E(z)E(x)−E(y)\nCo on Pd(100)\nmonolayer 2 .09 2 .45 0 .132 0 .203 −0.73\n(2.07) (2 .39) (0 .190) (0 .241) ( −0.69)\nadatom 2 .29 2 .57 0 .299 0 .279 0 .26\n(2.32) (2 .53) (0 .610) (0 .473) (2 .69)\nCo on Pd(111)\nmonolayer 2 .02 2 .43 0 .135 0 .136 0 .36\n(1.99) (2 .41) (0 .154) (0 .176) (0 .21)\nadatom 2 .35 2 .62 0 .605 0 .355 5 .50\n(2.34) (2 .52) (0 .780) (0 .575) (6 .38)\nCo on Pd(110)\nmonolayer 2 .15 2 .50 0 .192 0 .183 0 .210 −0.15 −0.43 0 .28\n(2.18) (2 .54) (0 .215) (0 .220) (0 .289) ( −0.48) ( −0.97) (0 .49)\nadatom 2 .20 2 .49 0 .270 0 .347 0 .201 −1.51 1 .10 −2.61\n(2.25) (2 .47) (0 .349) (0 .472) (0 .255) ( −1.88) (2 .01) ( −3.89)\norientation of the magnetization. For Co monolayers\non Pd(100) and Pd(111), we get E(x)\ndip-dip−E(z)\ndip-dip=\n−0.1 meV. For Co monolayers on Pd(110), there is a\nsmall difference regarding the xandydirections: we get\nE(x)\ndip-dip−E(z)\ndip-dip=−0.07 meV and E(y)\ndip-dip−E(z)\ndip-dip=\n−0.09 meV. By comparing these values with the values\nshown in Tab. II, we see that the shape anisotropy en-\nergy is smaller in magnitude than the magnetocrystalline\nanisotropy energy and thus the shape anisotropy does not\nchange the orientation of the magnetic easy axis as de-\ntermined by the magnetocrystalline anisotropy.\nB. Induced magnetic moments\nPalladium is not magnetic as an element but it is quite\npolarizable.29,30Spin magnetic moments induced in the\nPd substrate by Co monolayers and adatoms are shown\nin Tab. III for all three surface orientations. In the case\nof Co monolayers, the induced moments are shown for\nthe first three atomic layers of Pd below the Co layer\n[denoted as Pd(1), Pd(2) and Pd(3) in Tab. III]. Note\nthat the interlayer distances are 1.95 ˚A, 2.25 ˚A and 1.38 ˚A\nfor the (100), (111) and (110) surfaces, respectively. The\nrelatively large µspinfor the Pd(2) and Pd(3) sites in\nthe case of the (110) surface reflects the relatively small\ninterlayer distance for this crystallographic orientation.\nIn the case of adatoms, the description is formally more\ncomplicated because Pd atoms belonging to the same co-\nordination shell around the Co atom are not all equiva-\nlent: some of them belong to the surface layer, some to\nthe sub-surface layer and so on. In order not be over-TABLE III. Spin magnetic moments for Pd atoms which are\nfirst, second and third nearest neighbors of Co atoms, in unit s\nofµB. As in Tab. II, the numbers without brackets stand for\nsystems with optimized geometry and the numbers in brackets\nstand for systems with bulk-like geometry.\nPd(1) Pd(2) Pd(3)\nCo on Pd(100)\nmonolayer 0 .29 0 .17 0 .11\n(0.25) (0 .16) (0 .10)\nadatom 0 .18 0 .06 0 .04\n(0.15) (0 .06) (0 .04)\nCo on Pd(111)\nmonolayer 0 .32 0 .16 0 .03\n(0.25) (0 .15) (0 .06)\nadatom 0 .16 0 .02 0 .04\n(0.12) (0 .02) (0 .03)\nCo on Pd(110)\nmonolayer 0 .29 0 .22 0 .17\n(0.29) (0 .24) (0 .19)\nadatom 0 .15 0 .04 0 .04\n(0.15) (0 .05) (0 .04)\nwhelmed by too much data, we display here only mo-\nments averaged over all atoms of a given coordination\nshell. Symbols Pd(1), Pd(2), and Pd(3) in Tab. III stand\nnow for the first, second, and third shell of Pd atoms\naround the Co adatom.\nMoreover, we also calculated the orbital magnetic mo-\nments for the Pd atoms in all systems and we found that\nµorbamounts to about 8–17 % of the corresponding µspin.5\nIn this section we deal only with magnetic moments\non those Pd atoms which are close to the Co atoms. The\nissue of more distant Pd atoms and of the total charge\ncontained in the polarization cloud is dealt with in the\nAppendix. Here, we would only like to stress that it fol-\nlows from the analysis outlined in the Appendix that our\nmodel system is clearly adequate to yield reliable values\nof induced magnetic moments for the Pd(1), Pd(2), and\nPd(3) sites.\nC. Azimuthal dependence of MAE\nIn general, the MAE defined as the difference between\ntotal energies for in-plane and out-of-plane orientation of\nthe magnetization will depend on the azimuthal angle φ.\nThis dependence is often ignored but may sometimes be\nsignificant. In our case, the intraplanar MAE E(x)−E(y)\nis quite comparable to E(x)−E(z)orE(y)−E(z)for\nthe (110) surface (see Tab. II). To get a more com-\nplete picture, we inspect the azimuthal dependence of\nE(/bardbl)(φ)−E(z), whereE(/bardbl)(φ) is the total energy if M\nis in the surface plane ( θ=0◦) with the azimuthal angle\nφ. Our results for a Co adatom on all three Pd surfaces\nare shown in Fig. 2. The data reported here were ob-\ntained for the bulk-like geometry but the trends would\nbe similar for any zCo-Pd distance.\nOne can see from Fig. 2 that the E(/bardbl)(φ)−E(z)curves\nfollow the symmetry of the appropriate surface, as ex-\npected. The amplitude of these curves is the most in-\nteresting information here. For high-symmetry surfaces,\nit is almost negligible: 0.008 meV or 3 % of the average\nvalue for Co on Pd(100) and 0.06 meV or 1 % of the\naverage value for Co on Pd(111). For the (110) surface,\nhowever, the amplitude is 2.6 meV and to speak about an\naverage MAE does not make sense in this case, as illus-\ntrated by the fact that the magnetic easy axis is in-plane\nforφ= 0◦and out-of-plane for φ= 90◦.\nD. Relation between magnetic dipole term and\nm-decomposed spin magnetic moment\nThe spin magnetic moment sum rule for the L2,3edge\nXMCD spectra can be written for a sample magnetized\nalong theαdirection as7\n3\nI/integraldisplay\n(∆µL3−2∆µL2) dE=µspin+ 7Tα\nnh,(1)\nwhere ∆µL2,3are the differences ∆ µ=µ(+)−µ(−)be-\ntween absorption coefficients for the left and right circu-larly polarized light propagating along the αdirection,I\nis the integrated isotropic absorption spectrum, µspinis\nthe local spin magnetic moment (only its dcomponent\nenters here), nhis the number of holes in the dband, and\nTαis the magnetic dipole term related to the delectrons.\nTαcan be written as31,32\nTα=−µB\n/planckover2pi1/angbracketleftˆTα/angbracketright,\n=−µB\n/planckover2pi1/angbracketleftBigg/summationdisplay\nβQαβSβ/angbracketrightBigg\n, (2)\nwhere\nQαβ=δαβ−3r0\nαr0\nβ (3)\nis the quadrupole moment operator and Sαis the spin\noperator. If zis the quantization axis, the eigenvalues of\nSzare±(1/2)/planckover2pi1.\nA more transparent expression for Tαcan be obtained\nif the spin-orbit coupling can be neglected. Then one can\nwrite32\nˆTx=/parenleftBig\n−µB\n/planckover2pi1/parenrightBig\nˆQxxˆS¯zforM/bardblx ,\nˆTy=/parenleftBig\n−µB\n/planckover2pi1/parenrightBig\nˆQyyˆS¯zforM/bardbly ,\nˆTz=/parenleftBig\n−µB\n/planckover2pi1/parenrightBig\nˆQzzˆS¯zforM/bardblz ,(4)\nwhere ˆQxx,ˆQyyand ˆQzzare quadrupole moment com-\nponents referred to the crystal (global) reference frame\nand ˆS¯zis the spin component with respect to the local\nreference frame in which ¯ zis identical to the spin quan-\ntization axis. We are interested in the expectation value\nof the ˆTαoperator acting on the dcomponents of the\nwave function in the vicinity of the photoabsorbing site.\nUsing for the sake of clarity a simplified two-component\nformulation instead of the full Dirac approach, the wave\nfunction can be expanded in the angular-momentum ba-\nsis as\nψEk(r) =/summationdisplay\nℓm/summationdisplay\nsa(s)\nEkℓm(r)Yℓm(ˆr)χ(s)(5)\nto obtain\nTα=/parenleftBig\n−µB\n/planckover2pi1/parenrightBig/integraldisplayEF\n−∞dE/integraldisplay\nBZdk/angbracketleftψEk|ˆQααˆS¯z|ψEk/angbracketright.(6)\nRestricting ourselves just to the ℓ= 2 component and\nomitting the corresponding subscript in a(s)\nEkℓm(r), we get6\n0.2550.260.265E(||)()-E(z)[meV]\n0/2 3/2 2\nazimuthal angle(100) 5.465.485.55.52\n0/2 3/2 2\nazimuthal angle(111)\n-2-101\n0/2 3/2 2\nazimuthal angle(110)\nFIG. 2. (Color online) Difference between total energies for in-plane and out-of-plane magnetization for a Co adatom on P d\n(100), (111), and (110) surfaces (bulk-like geometry). Poi nts are results of the calculation, dashed lines are sinusoi dal fits. The\norientation of the xandyaxes is as in Fig. 1.\nTα=/parenleftBig\n−µB\n/planckover2pi1/parenrightBig/integraldisplayEF\n−∞dE/integraldisplay\nBZdk/summationdisplay\nmm′/summationdisplay\nss′/integraldisplay\ndra(s)∗\nEkm(r)Y∗\n2m(ˆr)Qααa(s′)\nm′kE(r)Y2m′(ˆr)/angbracketleftχ(s)|ˆS¯z|χ(s′)/angbracketright\n=/parenleftBig\n−µB\n/planckover2pi1/parenrightBig/integraldisplayEF\n−∞dE/integraldisplay\nBZdk/summationdisplay\nmm′/integraldisplay\nr2dr/bracketleftBig\na↑∗\nEkm(r)a↑\nm′kE(r)−a↓∗\nEkm(r)a↓\nm′kE(r)/bracketrightBig\n×\n/angbracketleftY2m|ˆQαα|Y2m′/angbracketright1\n2/planckover2pi1\n=1\n2(−µB)/summationdisplay\nmm′/bracketleftBig\nN↑\nmm′−N↓\nmm′/bracketrightBig\n/angbracketleftY2m|ˆQαα|Y2m′/angbracketright, (7)\nwhere the spin-dependent number of states matrix N(s)\nmm′\nis defined as\nN(s)\nmm′=/integraldisplayEF\n−∞dE/integraldisplay\nBZdk/integraldisplay\nr2dra(s)∗\nEkm(r)a(s)\nm′kE(r).\nThe difference of the diagonal terms of N(s)\nmmis just\nthe spin magnetic moment decomposed according to the\nmagnetic quantum number m,\n(−µB)/parenleftbig\nN↑\nmm−N↓\nmm/parenrightbig\n=µ(m)\nspin,\nwith the sum of all the mcomponents giving the total\nspin magnetic moment (of the delectrons, in our case).\nTherefore, if it was possible to restrict the sum (7) just\nto the terms diagonal in m, one would have\nTα=1\n2/summationdisplay\nmµ(m)\nspin/angbracketleftY2m|ˆQαα|Y2m/angbracketright. (8)\nThe procedure we employed above is essentially the one\nsuggested by St¨ ohr,31,32but we present it here in a more\nexplicit way.TABLE IV. Diagonal components of the quadrupole opera-\ntor in the basis of real spherical harmonics. Non-diagonal\ncomponents are all zero except for the components given in\nEq. (9).\nQxx Qyy Qzz\n/angbracketleftYxy|ˆQαα|Yxy/angbracketright −2\n7−2\n74\n7\n/angbracketleftYyz|ˆQαα|Yyz/angbracketright4\n7−2\n7−2\n7\n/angbracketleftY3z2−r2|ˆQαα|Y3z2−r2/angbracketright2\n72\n7−4\n7\n/angbracketleftYxz|ˆQαα|Yxz/angbracketright −2\n74\n7−2\n7\n/angbracketleftYx2−y2|ˆQαα|Yx2−y2/angbracketright −2\n7−2\n74\n7\nThe coefficients /angbracketleftY2m|ˆQαα|Y2m′/angbracketrightcan be obtained by\nanalytic integration. If we use the basis of realspherical\nharmonics, the only “cross-terms” which are non-zero are\n/angbracketleftYx2−y2|ˆQxx|Y3z2−r2/angbracketright= (2/7)√\n3,\n/angbracketleftYx2−y2|ˆQyy|Y3z2−r2/angbracketright=−(2/7)√\n3.(9)\nOtherwise, only the diagonal terms /angbracketleftY2m|ˆQαα|Y2m/angbracketrightare\nnon-zero and we list them in Tab. IV (see also Refs. 14\nand 31). Therefore, in the absence of spin-orbit coupling,7\nEq. (8) presents an exact expression for Tzand an ap-\nproximate expression for TxandTy[due to the existence\nof non-diagonal terms (9)]. As argued by St¨ ohr,32the\nnon-diagonal terms drop out of the sum in Eq. (7) for\nhigh symmetry systems.\nEq. (8) together with Tab. IV illustrate the common\nstatement that the magnetic dipole term Tαis related\nto spin anisotropy: if the m-components of µspinare all\nidentical,Tαis zero (in the absence of spin-orbit cou-\npling). It is also evident from Eq. (8) and Tab. IV that\ntheTαterm will generally depend on the magnetization\ndirectionα.\nTo get a more quantitative feeling of how the various\ncontributions add together to generate Tα, we present in\nTab. V the m-decomposed magnetic moment µ(m)\nspinand\nindividual terms of the sum (8) for Co monolayers on\nPd surfaces. One can see that the Tαterm is formed by\na competition between those mcomponents which con-\ntain theαcoordinate and those which do not (they con-\ntribute with an opposite sign, as it can be seen also from\nTab. IV). In fact, this is what is meant by the statement\nthat theTαterm describes the anisotropy of µspin.\nEq. (8) gives an intuitive insight into Tαprovided that\nthe underlying approximations — the neglect of the spin-\norbit coupling and of the non-diagonal terms shown in\nEq. (9) — are not too crude. To check this, we com-\npare the values of Tαcalculated via the exact relation in\nEq. (2) and via the approximative Eq. (8). Special at-\ntention is paid to the differences between the Tαterms\nfor different orientations of M, because the 7( Tα−Tβ)\nquantities determine the apparent anisotropy of µspinas\ndeduced from the XMCD sum rule in Eq. (1). The out-\ncome for both monolayers and adatoms is summarized\nin Tab. VI. Let us recall that for bulk hcp Co, the mag-\nnetic dipole term is very small (we get Tz=−0.002µB).\nNote that all values presented in Tabs. V–VI were ob-\ntained from fully relativistic calculations, including the\nspin-orbit coupling.\nOne can see from our results that the approximative\nexpression for Tαworks quite well for the Co-Pd systems:\nquantitative deviations sometimes occur but the main\ntrend is well maintained. One can expect that for systems\nwith a strong spin-orbit coupling the deviations between\nEqs. (2) and (8) will be larger.\nThe last two columns of Tab. VI contain the values of\n7(Tx−Tz) and, for the case of the (110) surface, also of\n7(Ty−Tz). These values are comparable to µspinwhich\nmeans that even though µspinpractically does not depend\non the magnetization direction at all, its combination\nµspin+ 7Tαprobed by the XMCD sum rule may strongly\ndepend on the magnetization direction.\nIV. DISCUSSION\nWe investigated how the magnetic properties of Co\nadatoms and monolayers can be manipulated by select-\ning different supporting Pd surfaces. We found that thishas a moderate effect on µspinandnh, larger effect on\nµorband dramatic effect on the MAE and on the Tα\nterm. For the adatoms the effect is larger than for the\nmonolayers. Moreover, the transition from monolayers\nto adatoms has a larger effect than a moderate variation\nin the height of the Co layer above the substrate. If the\nspin-orbit coupling is not very strong, the Tαterm can be\nunderstood as arising from a competition between those\nm-decomposed components of µspinwhich are associated\nwith theαcoordinate and those which are not.\nIn the past, the influence of the orientation of super-\nlattices (multilayers) on magnetic properties was already\ninvestigated, however, the focus was mainly on the role\nof defects and interface abruptness.33Here, we deal with\nperfect monolayers and surfaces and investigate how sole\nselection of a different surface can affect various quanti-\nties related to magnetism. Likewise, the importance of\ntheTzterm for an XMCD sum rules analysis has been\nhighlighted before when it was found that the absolute\nvalue of 7Tzamounts to about 20 % of µspinfor some\nlow-dimensional systems12or that for atomic clusters\nµspincan show a different behavior with changing clus-\nter size when compared to µspin+ 7Tz.13In this study\nthe importance of the anisotropy of the magnetic dipole\nterm in nanostructures is stressed for the first time and\nit should be noted that the anisotropy of Tαwhich we\nhighlight here is primarily connected with the breaking\nof the crystal symmetry at the surface and occurs even\nwithout spin-orbit coupling.\nFor the monolayers, the changes in µspinwhen going\nfrom one surface to another reflect the corresponding\nchanges in the coordination numbers: µspinis largest for\nthe (110) monolayer where each Co atom has got only\ntwo nearest neighboring Co atoms, next comes the (100)\nmonolayer with four Co neighbors and the lowest µspin\nis obtained for the (111) monolayer with six Co neigh-\nbors. This complements an analogous trend found ear-\nlier for free1and supported clusters.2,3,34The magnetic\nmoments induced at individual Pd atoms are larger for\nCo monolayers than for Co adatoms, which reflects the\nfact that for monolayers, Pd atoms are polarized by more\nthan one Co atom.\nThe large amount of data gathered here for quite a\ncomplete set of systems allows a comprehensive look at\nthe relation between the MAE and the anisotropy of µorb.\nIn this respect Bruno’s formula35\nE(α)−E(β)=−ξ\n4/bracketleftBig\nµ(α)\norb−µ(β)\norb/bracketrightBig\n(10)\nconnecting the differences of total energies to the dif-\nferences of orbital magnetic moments for two orienta-\ntions of the magnetization, αandβ, proved to be very\nuseful36despite its limitations,37which become more se-\nvere in the case of multicomponent systems with large\nspin-orbit coupling parameter ξfor the non-magnetic\ncomponent.38,39To assess the situation for 3 d-4dalloys,\nwe compare the differences ∆ µorband ∆E, using all\nthe appropriate values given in Tab. II. The outcome is8\nTABLE V. Spin magnetic moment decomposed according to the ma gnetic quantum number mtogether with the corresponding\nT(m)\nα=1\n2µ(m)\nspin/angbracketleftY2m|ˆQαα|Y2m/angbracketrightterms of the decomposition (8) for Co monolayers on Pd (optim ized geometry). The sums of\nthese components are shown in the last row for each system and they correspond to the total µspin,Tz,Tx, andTyof thed\nelectrons [evaluated using the approximative expression ( 8) in the case of Tα].\ncomponent µ(m)\nspin T(m)\nz T(m)\nx T(m)\ny\nCo on Pd(100)\nxy 0.319 0 .092 −0.046 −0.046\nyz 0.465 −0.066 0 .133 −0.066\n3z2−r20.365 −0.104 0 .052 0 .052\nxz 0.465 −0.066 −0.066 0 .133\nx2−y20.449 0 .128 −0.064 −0.064\nsum 2 .062 −0.018 0 .009 0 .009\nCo on Pd(111)\nxy 0.339 0 .097 −0.048 −0.048\nyz 0.428 −0.061 0 .122 −0.061\n3z2−r20.490 −0.140 0 .070 0 .070\nxz 0.428 −0.061 −0.061 0 .122\nx2−y20.339 0 .097 −0.048 −0.048\nsum 2 .023 −0.069 0 .034 0 .034\nCo on Pd(110)\nxy 0.397 0 .113 −0.057 −0.057\nyz 0.346 −0.049 0 .099 −0.049\n3z2−r20.515 −0.147 0 .074 0 .074\nxz 0.527 −0.075 −0.075 0 .151\nx2−y20.343 0 .098 −0.049 −0.049\nsum 2 .128 −0.060 −0.009 0 .069\nTABLE VI. Magnetic dipole term for Co monolayers and adatoms on Pd(100), Pd(111) and Pd(110) (optimized geometries)\nfor different magnetization directions. For each system, th e first line (“exact”) contains values calculated using Eq. ( 2) and the\nsecond line (“approx.”) contains values calculated using E q. (8). The Tyterms were evaluated only for the (110) surface.\nTz Tx Ty 7(Tx−Tz) 7( Ty−Tz)\nCo on Pd(100)\nmonolayer exact −0.017 0 .010 0 .188\napprox. −0.018 0 .009 0 .184\nadatom exact −0.024 0 .015 0 .275\napprox. −0.026 0 .013 0 .276\nCo on Pd(111)\nmonolayer exact −0.066 0 .035 0 .707\napprox. −0.069 0 .034 0 .723\nadatom exact −0.146 0 .080 1 .577\napprox. −0.154 0 .077 1 .618\nCo on Pd(110)\nmonolayer exact −0.057 −0.008 0 .068 0 .339 0 .872\napprox. −0.060 −0.009 0 .069 0 .360 0 .904\nadatom exact −0.112 −0.020 0 .141 0 .644 1 .768\napprox. −0.117 0 .011 0 .106 0 .900 1 .566\nshown in Fig. 3, together with a straight line represent-\ning Eq. (10). Here we take 85 meV for the spin-orbit\ncoupling parameter ξ[which appears to be a rather uni-\nversal value for Co as our calculations yield ξof 85.4 meV,\n84.5 meV, 84.9 meV and 85.1 meV for bulk hcp Co and\nfor a Co monolayer on Pd(100), Pd(111) and Pd(110),\nrespectively]. It follows from Fig. 3 that Bruno’s for-\nmula Eq. (10) works quite well for adatoms (albeit withsome “noise”) but not so well for monolayers, where re-\nlying solely on Eq. (10) might even lead to a wrong sign\nof the MAE. This may be connected with the fact that\nfor monolayers, the MAE is generally not very large and\nhence small absolute deviations from the rule given in\nEq. (10) can lead to large relative errors.\nThe sizable intraplanar anisotropy E(x)−E(y)which\nwe get for a Co monolayer on Pd(110) had to be expected9\n0246MAE [meV]\n0.0 0.1 0.2 0.3\ndifference inorb[B]adatoms\nmonolayers\nFIG. 3. (Color online) Dependence of the MAE for Co mono-\nlayers and adatoms on the difference of orbital magnetic mo-\nments for respective magnetization directions. The dashed\nline represents Bruno’s formula in Eq. (10).\nas this system could be viewed as a set of Co wires which\nare surely anisotropic in this respect. However, we get a\nvery strong azimuthal dependence of the MAE also for\ntheadatom on the (110) surface which is quite surprising\nas this can be only caused by the underlying substrate.\nThe magnetic moments at Pd atoms are not very large\n(Tab. III), neither is the spin-orbit coupling parameter\nξfor Pd in comparison to, say, 5 delements. Thus, this\nseems to be yet another example of the extreme sensi-\ntivity of the MAE. At the same time, let us note that\nthe calculated azimuthal dependence of the MAE can be\naccurately fitted by smooth sinusoidal curves (see Fig.\n2) which indicates a very good numerical stability of the\ncomputational procedure.\nThe intraplanar anisotropy for a Co adatom on the\nPd(111) surface can be compared to similar systems in-\nvestigated in the past. In particular, for a Co adatom\non Pt(111) the amplitude of the E(/bardbl)(φ)−E(z)curve is\nabout 2 % of the average value,40i.e., similar to the cur-\nrent case. For a 2 ×2 surface supercell coverage of Fe on\nPt(111), this amplitude is 10–25 % (depending on the\ngeometry relaxation)41but this situation is already quite\ndistinct from the isolated adatom case.\nAccording to our calculations, a Co monolayer on\nPd(100) has an in-plane magnetic easy axis, a Co mono-\nlayer on Pd(111) has an out-of-plane magnetic easy axis\nand the difference between the respective MAE values is\nabout 1 meV, which can be seen as a measure of how\nmuch the out-of-plane magnetization is preferred by the\nCo/Pd(111) system in comparison with the Co/Pd(100)\nsystem. This is similar to what was calculated for Co/Pd\nmultilayers: both Co 1Pd3(100) and Co 1Pd2(111) mul-\ntilayers have an out-of-plane magnetic easy axis but theMAE per unit cell is by about 0.9 meV larger for the\n(111) multilayer than for the (100) multilayer.42\nThe theoretical values for the anisotropy of Tαshown\nin Tab. VI can be compared with experimental data for\na similar system, namely, a single Co(111) layer sand-\nwiched between two thick Au layers. By extrapolat-\ning results obtained via angle-dependent XMCD mea-\nsurements, Weller et al.43obtained 7Tx= 0.43µBand\n7Tz=−0.86µB. Our values for a Co monolayer on\nPd(111), 7Tx= 0.24µBand 7Tz=−0.46µB(see Tab.\nVI), are fully consistent with this.\nWe expect that our values for µorbwill be systemat-\nically smaller than experimental values because we rely\nin the LSDA which usually underestimates µorb.44,45The\nsame may be also true for the MAE. However, this does\nnot affect our conclusions.\nWe used potentials subject to the ASA which may limit\nthe numerical accuracy of our results, particularly as con-\ncerns the MAE. On the other hand, our results do not\ndiffer too much from results of full-potential calculations,\nespecially in the case of monolayers. For a Co monolayer\non Pd(100), we get an in-plane magnetic easy axis with\nan MAE of -0.73 meV per Co atom while Wu et al.46ob-\ntained for the same zCo-Pd distance (1.65 ˚A) a theoretical\nMAE of -0.75 meV. Magneto-optic Kerr measurements17\nas well as XMCD experiments47showed that the mag-\nnetic easy axis of ultrathin Co films on Pd(100) is indeed\nin-plane (the experiment includes also an in-plane con-\ntribution from the shape anisotropy). Note that the the-\noretical MAE of -0.18 meV given in Ref. 17 was obtained\nfor a partially disordered Co monolayer simulating the\ngrowth conditions, so it cannot be directly compared to\nour results obtained for an ideal monolayer.\nFor a Co monolayer on Pd(111), we get a µspinvalue of\n2.01µBin a Co ASA sphere with a radius of 1.46 ˚A while\nthe full-potential calculations of Wu et al.48led to aµspin\nvalue of 1.88 µBobtained within a Co muffin-tin sphere\nwith a radius of 1.06 ˚A — both calculations thus again\ngive consistent results. For Pd atoms just below the Co\nlayer, we get a µspinvalue of 0.32 µBin a sphere with a\nradius of 1.49 ˚A while the corresponding µspinvalue of\nWuet al.48obtained within a sphere having a radius of\n1.32 ˚A is 0.37µB. In this last case, one has to bear in\nmind that Wu et al.48used a thin slab of only five Pd\nlayers sandwiched between two Co layers which clearly\nfavors a larger Pd polarization in comparison with just a\nsingle Co-Pd interface considered in this work.\nFor adatoms, the ASA may be more severe than for\nmonolayers, nevertheless, the agreement between our cal-\nculations and the results obtained via a full potential cal-\nculation is pretty good (see the end of the Appendix). As\na whole, the accuracy of our calculations is sufficient to\nwarrant the conclusions which rely on comparing a large\nset of data and not only on results for a singular system.\nIt follows from our results that one can change the\nmagnetic easy axis from in-plane to out-of-plane direction\njust by using as a substrate another surface of the same\nelement. This could be used as yet another ingredient10\nfor engineering the MAE of nanostructures, which has\nbecome a great challenge recently.49We also showed that\nthe magnetic dipole Tαterm can mimic a large anisotropy\nofµspinas determined from the XMCD sum rules. Hence,\nthe anisotropy of Tαhas to be taken fully into account\nwhen analyzing XMCD experiments on nanostructures.\nV. CONCLUSIONS\nCo monolayers and adatoms adsorbed on different sur-\nfaces of Pd exhibit quite different magnetic properties.\nThe effect on µspinis moderate, the effect on µorbis larger\nwhile the effect on the MAE and on the magnetic dipole\ntermTαmay be crucial. A surprisingly strong azimuthal\ndependence of the MAE is predicted for a Co adatom on\nPd(110).\nThe dependence of Tαon the direction of the magne-\ntization can lead to an apparent anisotropy of the spin\nmagnetic moment as deduced from the XMCD sum rules.\nFor systems with small spin-orbit coupling, the Tαterm\ncan be related to the differences between components of\nthe spin magnetic moment associated with different mag-\nnetic quantum numbers.\nACKNOWLEDGMENTS\nThis work was supported by the Grant Agency of the\nCzech Republic within the project 108/11/0853, by the\nBundesministerium f¨ ur Bildung und Forschung (BMBF)\nVerbundprojekt R¨ ontgenabsorptionsspektroskopie\n(05K10WMA) and by the Deutsche Forschungsgemein-\nschaft (DFG) via SFB 689. Stimulating discussions with\nP. Gambardella are gratefully acknowledged.\nAppendix: Effect of the size of the relaxation zone\nWhen studying the magnetism of adatoms, one should\naddress the question to which extent the host around the\nadatom has to be allowed to polarize. Zeller showed29\nthat the polarization cloud around a magnetic impurity\nin bulk Pd extends at least up to 1000 atoms. ˇSipret al.50\nshowed that the convergence of the MAE with respect to\nthe slab thickness and/or with respect to the size of the\nsupercell which simulates the adatom is much slower than\nthe convergence of magnetic moments. In view of these\nfacts, it is desirable to explore more deeply the situation\nfor the systems considered in this work.\nAs a test case, we select a Co adatom on Pd(111).\nTo facilitate the comparison with calculations done by\nother methods, we put the Co adatom in an hcp hollow\nsite, with the vertical distance between the Co adatom\nand the Pd surface layer as zCo-Pd =1.64 ˚A. Our system\nis thus similar to the system investigated by B/suppress lo´ nski et\nal.20(the main difference with respect to Ref. 20 is that\nwe do not consider any buckling of the substrate). To2345totalspinin zone [B]\n0 2 4 6 8 10 12\nradius ofzone [A] Ê220 Pd atoms\n133 Pdatoms\n46 Pdatoms\n7 Pd atoms\nFIG. 4. (Color online) Sum of the spin magnetic moments at\nthe Co adatom and at those substrate Pd atoms which are\nenclosed in hemispherical zones of the given radii, for four\nembedded cluster sizes (identified by numbers of Pd atoms\ncontained in them).\ncheck the convergence with respect to the size of the zone\nwhere the electronic structure is relaxed, we probed a\nseries of embedded cluster sizes, starting with relaxing\nthe electronic structure just in three Pd atoms (i.e., up\nto the distance of 2.3 ˚A from the Co adatom) and ending\nwith relaxing it in 220 Pd atoms (up to 11.7 ˚A from the\nCo adatom). To safely accommodate this large embedded\nclusters, we model the Pd substrate by a slab of 19 layers\n[contrary to 13 layers used in other calculations involving\nthe Pd(111) surface in this work]. The largest embedded\ncluster with 220 Pd atoms contains Pd atoms located\nwithin the fith layer below the surface and comprises 329\nsites altogether.\nFirst we investigate the convergence of the spin mag-\nnetic moments. This can be achieved by inspecting the\ntotalµspincontained inside a hemisphere stretching from\nthe adatom up to a certain radius. The dependence of\nthis totalµspinon the radius of the hemisphere forms an\n“integral magnetic profile”. This is presented in Fig. 4\nfor four embedded cluster sizes containing 7, 46, 133, and\n220 Pd atoms, respectively. The total µspinfor a sphere\nwith zero radius is obviously just the µspinvalue of the\nCo adatom. With increasing sphere radius the spin mag-\nnetic moments of enclosed Pd atoms are added to it. If\nthe radius of the hemisphere becomes larger than the ra-\ndius of the embedded cluster, the total µspinobviously\ndoes not change any more because the Pd atoms outside\nthe embedded impurity cluster are nonmagnetic.\nIt follows from Fig. 4 that the spin magnetic moment\nof the adatom as well as magnetic moments induced in\nthe nearest Pd atoms are actually already well described\nby relatively small embedded clusters. However, the total11\n1.751.81.851.91.95E(x)- E(z)[meV]\n0 50 100 150 200\nPd atoms in embeddedcluster\nFIG. 5. The MAE of a Co adatom in an hcp position on\nPd(111) for different sizes of the embedded clusters.\nµspinconverges only very slowly with increasing size of\nthe relaxation zone because even quite distant Pd atoms\nstill contribute with their non-zero µspin. Our results sug-\ngest that the magnetic moments on all the Pd atoms do\nnot arise due to a direct interaction with the Co adatom.\nRather, the adatom induces a magnetization in its near-\nest neighbors, then these further induce magnetization in\nthe next coordination shell and so on. The emerging pic-\nture of how the magnetism spreads through the Pd host\nis thus consistent with the picture suggested by Polesya\net al.30in terms of an exchange-enhanced magnetic sus-\nceptibility (see Fig. 4 of Ref. 30 and the associated text).\nA plot analogous to Fig. 4 could also be drawn for µorb\nexhibiting the same features as seen in Fig. 4.\nOur results on the convergence of the magnetic mo-\nments may raise objections about the convergence of the\nMAE. If embedded clusters containing as much as 220Pd atoms still do not fully account for the host polariza-\ntion, can one get reliable results for the MAE, which is\nsensitive to the way the substrate is treated?50To check\nthis, we calculated the MAE for a series of embedded\ncluster sizes (Fig. 5). One can see that in fact the MAE\nconverges quickly with increasing size of the embedded\ncluster. Already with a relaxation zone including only\n46 Pd atoms, which corresponds to a radius of the hemi-\nsphere of 6.9 ˚A containing Pd from up to the third Pd\nlayer below the surface, the accuracy of the MAE is bet-\nter than 1 %. This means that all the results presented\nin this work are well converged.\nThe data in Fig. 5 demonstrate that it is sufficient\nto include a rather small polarization cloud within the\nPd host in order to get convergence in the MAE values.\nMore distant Pd atoms do not contribute to the MAE,\neven if they are magnetically polarized . This conclusion\nis not in contradiction with an earlier result that reliable\nvalues of the MAE can be obtained only if the host is\nrepresented by slabs of at least ten layers50because that\nresult concerned the total “physical” size of the model\nsystem while in this appendix we focus only on the size\nof the zone where the electronic structure is allowed to\nrelax to the presence of an adatom (or of an adsorbed\nmonolayer).\nTo complete this part, we should compare our results\nwith the results of B/suppress lo´ nski et al.20which were obtained\nby performing a plane-wave projector-augmented wave\n(PAW) calculation for a supercell comprising five-layers\nthick slabs and a 5 ×5 surface unit cell. As concerns the\nCo adatom itself, µspinandµorbfor the in-plane magneti-\nzation direction and µorbfor the out-of-plane magnetiza-\ntion direction are 2.48 µB, 0.15µB, and 0.27µBin this\nwork and 2.24 µB, 0.19µB, and 0.22 µBin B/suppress lo´ nski et\nal.20As concerns the MAE calculated via the magnetic\nforce theorem (torque method), it is 1.90 meV out-of-\nplane in this work and 0.72 meV out-of-plane in B/suppress lo´ nski\net al.20The value for the induced µspinin the nearest Pd\natoms is 0.28 µBin this work and 0.33 µBin B/suppress lo´ nski et\nal.20All these values are in good agreement, considering\nthe differences between both approaches.\n∗sipr@fzu.cz; http://www.fzu.cz/˜sipr\n1O.ˇSipr, M. Koˇ suth, and H. Ebert, Phys. Rev. B 70,\n174423 (2004).\n2P. Mavropoulos, S. Lounis, R. Zeller, P. H. Dederichs, and\nS. Bl¨ ugel, Appl. Physics A 82, 103 (2006).\n3S. Bornemann, O. ˇSipr, S. Mankovsky, S. Polesya,\nJ. B. Staunton, W. Wurth, H. Ebert, and J. Min´ ar,\nPhys. Rev. B 86, 104436 (2012).\n4P. Gambardella, A. Dallmeyer, K. Maiti, M. C. Malagoli,\nW. Eberhardt, K. Kern, and C. Carbone, Nature 416, 301\n(2002).\n5J. T. Lau, A. F¨ ohlisch, R. Nietubyc, M. Reif, and\nW. Wurth, Phys. Rev. Lett. 89, 057201 (2002).\n6P. Gambardella, S. Rusponi, M. Veronese, S. S. Dhesi,\nC. Grazioli, A. Dallmeyer, I. Cabria, R. Zeller, P. H. Ded-erichs, K. Kern, C. Carbone, and H. Brune, Science 300,\n1130 (2003).\n7P. Carra, B. T. Thole, M. Altarelli, and X. Wang,\nPhys. Rev. Lett. 70, 694 (1993).\n8B. T. Thole, P. Carra, F. Sette, and G. van der Laan,\nPhys. Rev. Lett. 68, 1943 (1992).\n9P. Gambardella, S. S. Dhesi, S. Gardonio, C. Grazioli,\nP. Ohresser, and C. Carbone, Phys. Rev. Lett. 88, 047202\n(2002).\n10S. Stepanow, A. Mugarza, G. Ceballos, P. Moras,\nJ. C. Cezar, C. Carbone, and P. Gambardella,\nPhys. Rev. B 82, 014405 (2010).\n11R. Q. Wu and A. J. Freeman, Phys. Rev. Lett. 73, 1994\n(1994).\n12M. Komelj, C. Ederer, J. W. Davenport, and M. F¨ ahnle,12\nPhys. Rev. B 66, 140407(R) (2002).\n13O. ˇSipr, J. Min´ ar, and H. Ebert,\nEurophys. Lett. 87, 67007 (2009).\n14J. St¨ ohr and H. K¨ onig, Phys. Rev. Lett. 75, 3748 (1995).\n15M. Komelj, C. Ederer, and M. F¨ ahnle,\nPhys. Rev. B 69, 132409 (2004).\n16P. Kr¨ uger, M. Taguchi, and S. Meza-Aguilar, Phys. Rev.\nB61, 15277 (2000).\n17H. L. Meyerheim, M. Przybylski, A. Ernst,\nY. Shi, J. Henk, E. Soyka, and J. Kirschner,\nPhys. Rev. B 76, 035425 (2007).\n18J. Miyawaki, D. Matsumura, A. Nojima, T. Yokoyama,\nand T. Ohta, Surf. Sci. 601, 95 (2007).\n19R. Wu, C. Li, and A. J. Freeman,\nJ. Magn. Magn. Materials 99, 71 (1991).\n20P. B/suppress lo´ nski, A. Lehnert, S. Dennler, S. Rusponi, M. Et-\nzkorn, G. Moulas, P. Bencok, P. Gambardella, H. Brune,\nand J. Hafner, Phys. Rev. B 81, 104426 (2010).\n21S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58,\n1200 (1980).\n22H. Ebert, D. K¨ odderitzsch, and Min´ ar,\nRep. Prog. Phys. 74, 096501 (2011).\n23H. Ebert and R. Zeller, The spr-tb-kkr package,\nhttp://olymp.cup.uni-muenchen.de (2006).\n24R. Zeller, P. H. Dederichs, B. ´Ujfalussy, L. Szunyogh, and\nP. Weinberger, Phys. Rev. B 52, 8807 (1995).\n25S. Bornemann, J. Min´ ar, S. Polesya, S. Mankovsky,\nH. Ebert, and O. ˇSipr, Phase Transitions 78, 701 (2005).\n26X. D. Wang, R. Q. Wu, D. S. Wang, and A. J. Freeman,\nPhys. Rev. B 54, 61 (1996).\n27J. B. Staunton, L. Szunyogh, A. Buruzs, B. L. Gyorffy,\nS. Ostanin, and L. Udvardi, Phys. Rev. B 74, 144411\n(2006).\n28S. Bornemann, J. Min´ ar, J. Braun, D. Koedderitzsch, and\nH. Ebert, Solid State Commun. 152, 85 (2012).\n29R. Zeller, Modelling Simul. Mater. Sci. Eng. 1, 553 (1993).\n30S. Polesya, S. Mankovsky, O. ˇSipr, W. Meindl, C. Strunk,\nand H. Ebert, Phys. Rev. B 82, 214409 (2010).\n31J. St¨ ohr, J. Electron. Spectrosc. Relat. Phenom. 75, 253\n(1995).\n32J. St¨ ohr, J. Magn. Magn. Materials 200, 470 (1999).\n33C. H. Lee, R. F. C. Farrow, C. J. Lin, E. E. Marinero, andC. J. Chien, Phys. Rev. B 42, 11384 (1990).\n34O. ˇSipr, S. Bornemann, J. Min´ ar, S. Polesya,\nV. Popescu, A. ˇSim˚ unek, and H. Ebert,\nJ. Phys.: Condens. Matter 19, 096203 (2007).\n35P. Bruno, Phys. Rev. B 39, 865 (1989).\n36H. A. D¨ urr, G. Y. Guo, G. van der Laan, J. Lee, G. Lauhoff,\nand J. A. C. Bland, Science 277, 213 (1997).\n37P. Ravindran, A. Kjekshus, H. Fjellv˚ ag, P. James,\nL. Nordstr¨ om, B. Johansson, and O. Eriksson,\nPhys. Rev. B 63, 144409 (2001).\n38C. Andersson, B. Sanyal, O. Eriksson, L. Nordstr¨ om,\nO. Karis, D. Arvanitis, T. Konishi, E. Holub-Krappe, and\nJ. Hunter Dunn, Phys. Rev. Lett. 99, 177207 (2007).\n39O.ˇSipr, J. Min´ ar, S. Mankovsky, and H. Ebert,\nPhys. Rev. B 78, 144403 (2008).\n40S. Bornemann, J. Min´ ar, J. B. Staunton, J. Hon-\nolka, A. Enders, K. Kern, and H. Ebert,\nEur. Phys. J. D 45, 529 (2007).\n41M. Tsujikawa, A. Hosokawa, and T. Oda, J. Phys.: Con-\ndens. Matter 19, 365208 (2007).\n42K. Kyuno, J. Ha, R. Yamamoto, and S. Asano, J. Phys.:\nCondens. Matter 8, 3297 (1996).\n43D. Weller, J. St¨ ohr, R. Nakajima, A. Carl, M. G. Samant,\nC. Chappert, R. M´ egy, P. Beauvillain, P. Veillet, and G. A.\nHeld, Phys. Rev. Lett. 75, 3752 (1995).\n44O. Hjortstam, J. Trygg, J. M. Wills, B. Johansson, and\nO. Eriksson, Phys. Rev. B 53, 9204 (1996).\n45S. Chadov, J. Min´ ar, M. I. Katsnelson, H. Ebert,\nD. Kdderitzsch, and A. I. Lichtenstein,\nEurophys. Lett. 82, 37001 (2008).\n46R. Wu, L. Chen, and A. J. Freeman,\nJ. Magn. Magn. Materials 170, 103 (1997).\n47M. Sawada, T. Tagashira, K. Furumoto, T. Ueno,\nA. Kimura, H. Namatame, and M. Taniguchi, J. Electron.\nSpectrosc. Relat. Phenom. 184, 280 (2011).\n48R. Wu, C. Li, and A. J. Freeman, J. Magn. Magn. Mate-\nrials99, 71 (1991).\n49S. Ouazi, S. Vlaic, S. Rusponi, G. Moulas, P. Buluschek,\nK. Halleux, S. Bornemann, S. Mankovsky, J. Min´ ar, J. B.\nStaunton, H. Ebert, and H. Brune, Nature Communica-\ntions3, 1313 (2012).\n50O.ˇSipr, S. Bornemann, J. Min´ ar, and H. Ebert,\nPhys. Rev. B 82, 174414 (2010)."    },    {        "title": "1303.6986v1.Possible_valence_bond_condensation_in_the_frustrated_cluster_magnet_LiZn2Mo3O8.pdf",        "content": "1 \n Possible v alence -bond condensation in the frustrated cluster \nmagnet LiZn 2Mo 3O8 \n \nJ.P. Sheckelton,  J.R. Neilson,  D.G. Soltan, and T.M. McQueen  \n \nDepartment of Chemistry, Department of Physics and Astronomy, and the Institute \nfor Quantum Matter, The Johns Hopk ins University, Baltimore, MD 21218  \n \nThe emergence of complex electronic behavio ur from simple ingredients has \nresulted in the discovery of numerous states of matter. Many examples are found in  \nsystems exhibiting geometric magnetic frustration , which  preve nts simultaneous \nsatisfaction of all  magnetic  interactions . This frustration  gives rise to  complex magnetic \nproperties such as  chiral spin structures1,2,3 orbitally -driven magnetism4, spin -ice behavior5 \nexhibiting Dirac strings with magnetic monopoles6, va lence bond solids7,8, and spin \nliquids9,10. Here we report the synthesis and characterization of LiZn 2Mo 3O8, a \ngeometrically frustrated antiferromagnet in which the magnetic moments are localized on \nsmall transition metal clusters rather than individual io ns11,12, 13. By doing so, first order \nJahn -Teller instabilities and orbital ordering are prevented, allowing t he strongly \ninteracting magnetic clusters in LiZn 2Mo 3O8 to probably  give rise to an exotic condensed \nvalence -bond ground state reminiscent of the proposed  resonating valence bond state14,15. \nOur results also link magnetism on clusters  to geometric magnetic frustration  in extended 2 \n solids , demonstrating a new approach  for unparalleled chemical control and tunability in \nthe search for collective, emerge nt electronic states of  matter16,17. \nNumerous materials possess a geometric ally frustrat ed arrangement of  magnetic atoms;  \nsuch materials have their magnetic moments arranged on frustrated topologies such as triangular \nlattices18,19, kagomé lattices20,21, hyper-kagomé lattices22, and edge sharing tetrahedra23,24. A rich \ndiversity of properties  result  depending on the magnitude of the per -site spin  and orbital \noccu pancies . Yet, the presence of local structural distortions25,26, and a degree of site mixing \nbetween non-magnetic and magnetic layers27 are still key limiters in the quest for new quantum \nstates of matter28. Here we show that these problems can be overcome  through the use of  clusters  \nin which a magnetic, unpaired electron is delocalized over a small number of transition metal \natoms , rather than individual magnetic ions, by demonstrating that the S = ½ cluster magnet \nLiZn 2Mo 3O8 is geometrically frustrated and likely possesses a condensed valence bond  ground \nstate. \nLiZn 2Mo 3O8 is built of discrete Mo 3O13 cluster units ( figure 1a), in which all Mo atoms \nare on equivalent crystallographic sites29. The average formal oxidation state of Mo is +3.67. \nEach cluster has seven  valence electrons. By a simple electron count , supported by molecular \norbital calculatio ns (figure 1b), six of these electrons localize into Mo -Mo bonds hold ing the \ncluster together. The seventh  electron  remains unpaired in a  totally symmetric (A1 irreducible \nrepresentation ) molecular orbital with equal contributions from all three Mo atoms . The result is \none S = ½ magnetic moment on each  Mo 3O13 cluster.  This cluster can then replace an atom as the \nbasic building block of a geometrically frustrated magnet ic system , when  appropriately  arranged . \nThere have been previous report s of systems built of magnetic clusters30. In those cases, the \nunpaired, magnetic electrons within  a cluster are still (just like the non -cluster cases) localized on 3 \n individual atom s. By contrast, i n LiZn 2Mo 3O8, the magnetism arises from a collective \ncontribution of all  three atoms in the Mo 3O13 cluster.  This gives rise to a S=  ½ moment \ndelocalized over three Mo atoms. This delocalized nature of the moment  contributes to the \nstability of the system and  renders the structure  impervious to first order Jahn-Teller distortions.   \nThese Mo 3O13 clusters in LiZn 2Mo 3O8 connect at corners , making a two -dimensional \nMo 3O8 layer (figure 1c). The  2.6 Å Mo-Mo distance within each cluster  is substantially shorter \nthan between clusters  (3.2 Å ) reflecting strong metal -metal bonding within each cluster. These \nMo 3O8 layers are separated by non -magnetic Li/Zn ions ( figure 1d) to form the full structure \nwith R3m symmetry. Consequently, LiZn 2Mo 3O8 contains two -dimensional layers in which S = \n½ Mo 3O13 clusters are arranged on the  geometrically frustra ted triangular lattice.  \nThe t emperature dependence of the magnetic susceptibility of  LiZn 2Mo 3O8 shows  \nunusual and unexpected behavior . At temperatures above 96 K, the inverse magnetic \nsusceptibility ( figure 2a) is well described by t he Curie -Weiss law for paramagnetic spins . A \nWeiss temperature of θ = -220 K indicates a net mean -field antiferromagnetic interaction \nbetween  unpaired spins on  Mo 3O13 clusters . A Curie constant of C = 0.24 emu·K·Oe-1·mol f.u.-1 \n(peff = 1.39)  is reduced fro m the ideal 0.3 75 value for a free S = ½ moment . This may be due to  a \nnumber of possibilities (see SI), but the most likely is a partial unquenched orbital contribution to \nthe moment,  due to spin -orbit coupling . It is not due to the formation of a metallic  state: \nresistivity data ( figure S6 ) shows that LiZn 2Mo 3O8 is electrically insulating at all accessible \ntemperatures . Further more, the molecu lar calculations predict a n on-site (cluster) Hubbard U of \n~1.2 eV , which, depending on bandwidth, could open a gap and  explain the insulating behavior . \nTogether , these data  imply  that the one unpaired electron per cluster in LiZn 2Mo 3O8 behaves as a  \nlocalized  effective S = ½ magnetic system  (with a partial unquenched orbital  contribution just 4 \n like Co2+ or Cu2+), and that t he magnetic interactions between clusters are strong and \nantiferromagnetic.  \nA change in the slope of the inverse magnetic susceptibility as a function of temperature \noccurs around  T = 96 K , with a  second linear region of χ(T) present below this transition  (or \ncrossover) . A fit to  the linear region  from T = 2 K to T = 96 K  gives a  Weiss temperature of θ = -\n14 K  and a Curie constant of  C = 0.08. This Curie constant  is one -third  that of the high \ntemperature value, indicating that two-thirds  of the spins  contribute negligibly to the magnetic \nsusceptibility  below  T = 96 K  as the Curie constant scales with the number of moments .   \nNeutron powder diffraction  experiments at T = 12 K indicate  that long-range magnetic \norder do es not develop below the T ≈ 96 K transition  (figure S1) . Instead, our results are \nconsistent with two-thirds  of the  effective  spins  condensing  into magnetic singlets. Although  our \ndata are not sufficient to unambiguously determine whether these singlets are static , making a \nvalence -bond solid, or dynam ic, making a resonating valence -bond  state, neutron powder \ndiffraction  data suggest that the singlets are indeed  dynamic : at T = 12 K, LiZn 2Mo 3O8 maintains \nthe trigonal  R3m symmetry  that exists at T = 300 K .  In most cases,  static singlets form a \nvalence bond network  and distort the lattice to a  lower  symmetry.   Unambiguous determination  \nof the ground state  warrants  further study , but  the ground state of LiZn 2Mo 3O8 is unusual and \nreflective of the  strong  geometric magnetic frustration .  \nChan ges in the experimentally measur ed heat capacity further elucidate  the unusual \nelectronic behavior in LiZn 2Mo 3O8 (figure 2b). LiZn 2Mo 3O8 does not undergo a transition to \nlong range magnetic order above T = 0.1 K: there is no sharp lambda transition  of the heat \ncapacity as a function of temperature . Instead  there is only an upturn in the specific heat capacity \ndata below T = 1 K . Applied magnetic fields of  μoH = 1 T and μoH = 9 T ( figure 2b inset) 5 \n radically modulate  the behavior  of the low temperature data . Such large change s from small \nmagnetic fields are surprising given the large Weiss temperature and  are likely  a result of \nmagnetic frustration in the sys tem.  Geometric f rustration prevents the formation of long range \norder and results in  low-lying magnetic excitations  perturbed by an applied field . Simple models, \nsuch as a  multilevel Schottky anomaly , do not  adequately  describe the low temperature data  (see \nSI); further studies are needed to examine and understand the behavior in detail . \nThe magnetic  entropy change of LiZn 2Mo 3O8, accounting for the extra lattice \ncontribution from lithium compared to Zn 2Mo 3O8 (figure 2c, figure S2) also indicates the \nconden sation of two -thirds of the available spins . The total expect ed magnetic entropy change \nfor S = ½ system is R·ln(2) (=  5.76 J·K-1·mol f.u.-1), compared to the experimental value of 8 (3) \nJ·K-1·mol f.u.-1 from T = 0.1 to  T = 400 K . On cooling from T = 400 K , we observe a gradual and \ncontinuous loss of entropy , approximately two-thirds  of the expected S=  ½ value from T = 400 K \nto T = 100 K . Critically, the change in the  linear regions of  magnetic susceptibility is not \naccompanied by a sharp transition in the entropy , supporting  the claim that these spins condens e \ninto singlets , rather than adopt long range magnetic order. Furthermore , the difference in  entropy \nbetween T = 0.1 K and  T = 100 K is approximately  31R·ln(2) , consistent with free zing out of  the \nremaining  one-third  of spins that did not condense into singlets at T = 96 K .  \nThe resulting magnetic phase diagram of LiZn 2Mo 3O8 is shown in figure  2d. Near  room \ntemperature, the system  is paramagnetic and the spins thermally randomize.  Cooling  below the \ncondensation temperature  (T ~ 96 K) , two-thirds  of the spins form  a condensed valence bond \nstate. The remaining one-third  spins are  still paramagnetic  and interacting antiferromagnetically  \nuntil lower temperatures, at which point they lose entropy  in a yet -to-be determined manner .   6 \n These results suggest  that LiZn 2Mo 3O8 exhibits geometric magnetic frustration between S \n= ½ magnetic clusters and two-thirds  of the spins condense into singlets  below  approximately  T \n= 96 K . Therefore  LiZn 2Mo 3O8 is a can didate for a resonating valence -bond state , as there is no \nevidence for static singlets . More generally , our results show how  an extended lattice of \nmagnetic clusters , in place of magnetic ions , produce s exotic physics while providing numerous \nadva ntages in the design and control of magnetically frustrated materials. This  approach opens a \nnew chemical frontier in the search for emergent phenomena in frustrated systems.  \n \nAcknowledgements  \nThis research is supported by the U.S. Department of Energy, Of fice of Basic Energy \nSciences, Division of Materials Sciences and Engineering under Award DE -FG02 -08ER46544. \nUse of the Spallation Neutron Source was supported by the Division of Scientific User Facilities, \nOffice of Basic Energy Sciences, US Department of  Energy, under contract DE -AC05 -\n00OR22725 with UT -Battelle, LLC.  J.P.S. acknowledges the  assistance of J . Hodges in \ncollecting and analyzing powder neutron data from  POWGEN/SNS.  TMM acknowled ges useful \ndiscussions with O . Tchernyshyov and C . Broholm.  \n \n  7 \n Methods  \nPhase -pure LiZn 2Mo 3O8 was synthesized from a mixture of Mo, ZnO, Li 2MoO 4, and \nMoO 2 (99+% purity) with an overall starting formula of LiZn 2Mo 3O8(Li2Zn2O3)0.2. Mo was used \nas received. ZnO and Li 2MoO 4 were dried at T = 160 °C overnight. MoO 2 was purified by \nheating overnight under flowing 5% H 2/95% Ar. The mixtures were pressed into pellets, placed \nin alumina crucibles, and double -sealed in evacuated, fused silica tubes. The reaction vessel was \nheated to T = 600oC for 24 hours, ramped to T = 1000oC at 10°C/hr, held for 12 hours, followed \nby a water quench. The sample was reground and heated again in the same manner. Zn 2Mo 3O8 \nwas synthesized in a similar manner, but with 3% excess ZnO, and a final temperature of T = \n1050  oC.  \nMagnetization measureme nts, heat capacities, and resistivities were measured on  a \nsintered pellet  in a Quantum Design Physical Properties Measurement System  (PPMS)  using a \ndilution refrigerator for T < 2 K measurements.  Heat capacities were measured three times at \neach temperat ure using the semi -adiabatic pulse technique, waiting for three time constants per \nmeasurement. Data were collected from T = 0.05 K to T = 400 K under magnetic fields of μoH = \n0 T, μoH = 1 T and μoH = 9 T. Magnetic susceptibilities were measured from T = 1.8 K to T = \n320 K under a μoH = 1 T field. Laboratory X -ray powder diffraction patterns were collected \nusing Cu Kα radiation (1.5418 Å) on a Bruker D8 Focus diffractometer with a LynxEye detector. \nPowder neutron diffraction data sets at T = 12 K with d-spacing of 0.2760Å ≤ d ≤ 3.0906 Å and \n1.6557Å ≤ d ≤ 8.2415 Å were collected at the Spallation Neutron Source POWGEN \ndiffractometer (BL -11A) at the Oak Ridge National Laboratory and analyzed with the Rietveld \nmethod using GSAS with EXPGUI31,32. Molecular orbital  calculations using density functional \ntheory  with the PBE0 functional at the UHF level of theory were performed with the GAMESS \nsoftware package33. 8 \n  \nAuthor Contributions  \nTMM supervised the project. JPS and DES prepared samples. JPS measured neutron \ndiffraction patterns. JPS an d TMM measured properties, and JPS, JRN, and TMM analyzed data \nand prepared the manuscript.  \n \n  9 \n  \n \nFigure 1 | LiZn 2Mo 3O8 structure. a, A single Mo 3O13 cluster  shows the local coordination of \neach Mo atom . b, A spin polarized  molecular orbital diagram for M o3O13H15 (C3v). There is one \nunpaired electron per cluster , distributed over all Mo atoms, with a large energy gap to the next \navailable state.  The hybrid functional produces an estimate of the on -site repulsion energy, U ~ \n1.2 eV.  A1, A2 and E are the irreducible representation labels for each orbital level from the C 3v \npoint group.  c, Top-down view of the Mo 3O8 layer showing the triangular network formed by the \nMo 3O13 S = ½ clusters.  d, A schematic representation of the magnetic Mo 3O8 layers  separated by  \nLiZn 2 in LiZn 2Mo 3O8.  \n10 \n  \nFigure 2 | Physical properties  of LiZn 2Mo 3O8.  a, Inverse magnetic susceptibili ty as a function \nof temperature for LiZn 2Mo 3O8. Curie -Weiss fits to the two distinct linear portions are shown . \nTwo-thirds of the spins ‘disappear’ upon cooling below T = 96 K.  The Curie constant C is in \nunits of emu·K·Oe-1·mol f.u.-1. b, Heat capacity divided by  temperature as a function of  \ntemperature . The inset shows a strong magnetic field dependence of the low temperature specific \nheat. Data for non -magnetic Zn 2Mo 3O8 is shown for comparison.  c, Integrated entropy as a \nfunction of  temperature . The lattice contribution was subtracted prior to integrating  (see SI) . \nError bars are calculated using standard analysis of error techniques for the propagation of the \nuncertainty in each C p measurement through the numerical integration. This is given by\n11 \n \nN\nii ii i\nN y yx xS\n12 2\n11)() (2   , where the error bars are given byNS, and iyis the \nuncertainty in the C p/T value of the ith point . d, Proposed magnetic phase diagram of \nLiZn 2Mo 3O8. Below T = 96 K the spins  enter a condensed  valence  bond  state. \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 12 \n References  \n \n \n(1) Bode, M. et al. Chiral magnetic order at surfaces driven by inversion asymmetry . Nature . \n447, 190 -193. (2007).  \n \n(2) Grohol, D. et al. Spin chirality on a two -dimensional frustrated lattice. Nature Materials . 4, \n323-328. (2005).  \n \n(3) Taguci, Y., Oohara, Y., Yoshizawa, H., Nagaosa, N., Tokura, Y. Spin chirality, berry phase, \nand anomalous Hall effect in a frustrated ferromagnet. Science . 291, 2573 -2576 . (2001).  \n \n(4) Chen, G. and Balents, L. Spin -orbit coupling in d2 ordered double perovskites. Phys. Rev. B . \n84, 094420. (2011).  \n \n(5) Fennell, T. et al. Magnetic coulomb phase in the spin ice Ho 2Ti2O7. Science . 326, 415 -417. \n(2009).  \n \n(6) Morris, D. J. P. et al. Dirac strings and magnetic monopoles in the spin ice Dy 2Ti2O7. \nScience . 326, 411 -414. (2009).  \n \n(7) Affleck, I., Kennedy, T., Lieb, E. H., Tasaki, H. Rigorous results on valence bond ground \nstates in antiferromagnets. Phys. Rev. Lett.  59, 799 -802. (1987)  \n \n(8) Matan, K. et al. Pinwheel valence -bond solid and tr iplet excitations in the two -dimensional \ndeformed kagome lattice. Nature Physics . 6, 865 -869. (2010).  \n \n(9) Pratt, F. L. et al. Magnetic and non -magnetic phases of a quantum spin liquid. Nature . 471, \n612-616. (2011).  \n \n(10) Anderson, P. W. The resonating va lence bond state in La 2CuO 4 and superconductivity. \nScience . 235, 1196 -1198 . (1987).  \n \n(11) Bramwell, S. T. and Gingras, M. J. P . Spin ice state in frustrated magnetic pyrochlore \nmaterials.  Science . 294, 1495 -1501 . (2001).  \n \n(12) Carlo, J. P. et al. Triplet a nd in -gap magnetic states in the ground state of the quantum \nfrustrated fcc antiferromagnet Ba 2YMoO 6. Phys. Rev. B . 84, 100404. (2011).  \n \n(13) Winterlink, J. et al. Exotic magnetism in the alkali sesquioxides Rb 4O6 and Cs 4O6. Phys. \nRev. B . 79, 214410. (2009 ). \n 13 \n (14) Anderson, P.W. Resonating valence bonds: a new kind of insulator? Mat. Res. Bull . 8, 153 -\n160. (1973).  \n \n(15) Anderson, P.W. On the ground state properties of the anisotropic triangular antiferromagnet. \nPhilosophical Magazine . 30, 423 -440. (1973).  \n \n(16) McCarley, R. E., Metal clusters and extended metal -metal bonding in metal oxide systems.  \nInorganic Chemistry: Toward the 21st Centu ry. 211, 273-290. (1983).  \n \n(17) King, R. B., Encyclopedia of Inorganic Chemistry , vol. 2 (Chichester, New York, 1994).  \n \n(18) Nakatsuji, S. et al. Spin disorder on a triangular lattice. Science . 309, 1697 -1700 . (2005).  \n \n(19) Yamashita, S., Yamamoto, T., Nakazawa, Y., Tamura, M. and Kato, R. Gapless spin liquid \nof an organic triangular compound evidenced by thermodynamic meas urements. Nature \nComm . 2, 1-6. (2011).  \n \n(20) Shores, M. P., Nytko, E. A., Bartlett, B. M., Nocera, D. G. A structurally perfect S= ½ \nKagome antiferromagnet. J. Am. Chem. Soc. 127, 13462 -13463 . (2005) . \n \n(21) Helton, J.S. et al. Spin dynamics of the spin -½  Kagome lattice antiferromagnet \nZnCu 3(OH) 6Cl2. Phys. Rev. Lett . 98, 107204. (2007).  \n \n(22) Okamoto, Y., Nohara, M., Aruga -Katori, H. and Takagi, H. Spin liquid state in the S= ½ \nhyperkagome antiferromagnet NA 4Ir3O8. Phys. Rev. Lett . 99, 137207. (2007).   \n \n(23) Castelnovo , C., Moessner, R., Sondhi, S.L. Magnetic monopoles in spin ice. Nature . 451, \n42-45. (2008).  \n \n(24) Benbow, E. M., Dalal, N. S., Latturner, S. E. Spin glass behavior of isolated, geometrically \nfrustrated tetrahedra of iron atoms in the intermet allic La 21Fe8Sn7C12. J. Am. Chem. Soc. 131, \n3349 -3354 . (2009).  \n \n(25) De La Cruz, C. et al. Magnetic order close to superconductivity in the iron based layered \nLaO 1-xFxFeAs systems. Nature . 453, 899 -902. (2008).  \n \n(26) Pene, K., Shannon, N., Shiba, H. Half -magnetization plateau stabilized by structural \ndistortion in the antiferromagnetic Heisenberg model on a pyrochlore lattice. Phys. Rev. \nLett. 93,197203. (2004).  \n 14 \n (27) Freedman, D. E. et al. Site specific X -ray anomalous dispersion of the geometrically \nfrustrated Kagome magnet, herbertsmithite, ZnCu 3(OH) 6Cl2. J. Am. Chem. Soc. 132, 16185 -\n16190 . (2010).  \n \n(28) Wang. R. F. et al. Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale \nferromagnetic islands. Nature . 439, 303 -306. (2006).  \n \n(29) Torardi, C. C. and McCarley, R. E. Synthesis, crystal structures, and properties of \nLiZn 2Mo 3O8, Zn 3Mo 3O8, and ScZnMo 3O8, reduced derivatives containing the Mo 3O13 \ncluster unit. Inorganic chemistry . 24, 476 -481. (1985).  \n \n(30) Bridges, C.A., Hansen, T., Wills,  A.S., Luke, G.M., Greedan, J.E., Frustrated magnetism \nand the effects of titanium substitution in the mixed valence oxide BaV 10-xTix015. Phys. Rev. \nB. 74, 024426. (2006).  \n \n(31) Larson , A.C. and Von Dreele , R.B. General Structure Analysis System (GSAS) , Los Alamos \nNational Laboratory Report LAUR , 86-748 (1994).  \n \n(32) Toby, B. H. EXPGUI, a graphical user interface for GSAS, J. Appl. Cryst . 34, 210 -\n213.(2001).  \n \n(33) Schmidt, M. W. et al. General atomic and molecular electronic structure system. J. Comput. \nChem. 14, 1347 -1363 . (1993).  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 15 \n Supp lementary information  \n \n \nPossible v alence bond condensation in the frustrated cluster \nmagnet LiZn 2Mo 3O8 \n \n \n \nJ.P. Sheckelton, J.R. Neilson, D.G . Soltan, and T.M. McQueen  \n \n \nDepartment of Chemistry, Department of  Physics and Astronomy, and the Institute \nfor Quantum Matter, The Johns Hopkins University, Baltimore, MD 21218  \n \nemail: mcqueen@jhu.edu  \n \nIndex\nFigure S1.  12 K powder neutron diffraction and Rietveld refinement.  16 \nHeat capacity analysis.  17-21 \nFigure S2.  Formula scaled Zn 2Mo 3O8 Cp·T-1 dataset.  17 \nFigure S3. Excess Heat capacity plots.  18 \nFigure S4. Integrated entropies.  19-20 \nFigure S5. Schottky anomaly analysis.  21 \nFigure S6.  Resistivity measurement from 50 K to 300 K.  22 \nMagnetism and spin -orbit co upling considerations.  23-26 \n         Figure S7.  Magnetic susceptibility analysis details.  24 \n         Figure S8. Magnetic Kotani behavior analysis.  25-26 \nTable S1. GAMESS input files.  27-28 \nTable S2. Crystallographic information.  29 \nSupplementary re ferences.  30 \n                                                               16 \n  \nFigure S1 | 12 K TOF neutron powder diffraction data for LiZn 2Mo 3O8 from POWGEN .  \na,b. Rietveld refinement of data show that LiZn 2Mo 3O8 remains in the R 3m spacegroup and \nmaintains its trigonal symmetry in the condensed valence bond state. The inset in a shows the \n(220) peak at both T = 12 K (open circles) and at T = 300 K (triangles), which are sharp and \nshow no indication of a distortion breaking trigonal s ymmetry. Attempts to fit the patterns to \nlower symmetry but trigonal models (R3m, R32, R3) did not result in better fits to the data. The \npatterns show no extra Bragg reflections or diffuse scattering due to magnetic ordering of any \nkind down to T = 12 K.  \nAs a test, a magnetic phase was added to the refinement to asses if scattering from a magnetic \nphase would be visible. The magnetic form factor in this material is not known, and there are \nmany possible magnetic orders. Thus to estimate our sensitivity to  magnetic order, we used a \n120° magnetic state with the Mo metal form factor. This resulted in an upper limit on the \nmagnetic moment of 0.2(2) μB per Mo. Together with the absence of an anomaly in the heat \ncapacity, these data suggest no magnetic ordering around T = 96 K.   \n \n17 \n Heat capacity analysis.  \nThe magnetic contribution to the heat capacity was extracted  by two methods. In the first \nmethod , the data  for non-magnetic Zn2Mo 3O8 was scaled to account for the expected change in  \nDebye temperature (compared to LiZn 2Mo 3O8) as well as for the change in the number of atoms \nper formula unit (=14/13). Subtraction gives the estimated magnetic heat capacit y shown in \nfigure S3(a).  \n \nFigure S2 | LiZn 2Mo 3O8 and formula scaled Zn 2Mo 3O8 Cp·T-1 datasets.  \n \n18 \n In the second method, the non -magnetic Zn 2Mo 3O8 data were not scaled for the change in the \nnumber of atoms per formula unit (paper Figure 2b) . Instead, a smooth  fit to the non -magnetic \nZn2Mo 3O8 Cp·T-1 was directly subtracted, giving the data in figure S3(b), which includes both the \nmagnetic contribution and the extra lattice contribution from the extra lithium atom per formula \nunit.   \n \n \nFigure S3 | Estimated ex cess heat capacity in LiZn 2Mo 3O8 computed by two methods. a,  In \nthe first method, the data for non -magnetic Zn 2Mo 3O8 was scaled to account for the expected \nchange in Debye temperature (compared to LiZn 2Mo 3O8) as well as for the change in the number \nof atom s per formula unit, leaving only an estimate of the magnetic entropy. Note the unphysical \ndip to negative heat capacity around T = 50 K. b, In the second method, the non -magnetic \nZn2Mo 3O8 data were not scaled for the change in the number of atoms per formu la unit, leaving \ncontributions from both magnetism and the extra lattice contribution from the extra lithium atom \nper formula unit. The extra lattice entropy of Li can then be accounted for by fitting to an \n19 \n Einstein (or Debye) oscillator mode (fit shown in  red). \n \nBoth methods give similar insights into the magnetic behavior for LiZn 2Mo 3O8. Method two \ngives a larger feature at T ≥ 100 K, which must (at least partly) the freezing out of the extra \nvibrational modes from Li in LiZn 2Mo 3O8. Figure S3(b) shows a fit of this feature to an Einstein \noscillator mode, with an Einstein temperature Θ = 403 K (a Debye mode fits equally well), \nwhich was subtracted to leave the magnetic contribution. In both cases, the magnetic entropy was \nthen extracted by computing dTTCTST\n0)(  . A comparison of the two are shown in figure S4.  \n \nFigure S4 | Estimated magnetic entropy by two methods . a, Integrated Cp·T-1 data from \nmethod one. Although the dip in entropy around T = 50 K is unphysical, the general result, of \ntwo di stinct regions of entropy loss - below and above T ≈ 100 K – is the same as that found by \nmethod two. b, Integrated Cp·T-1 from method two. This data is the same as paper figure 2c, and \nalso shows two distinct regions of entropy loss.  \n20 \n  \nIn both cases, the magnetic entropy contribution contains two discre te regions of entropy \ngain/loss, below and above T = 100 K. We note that the validity of fitting C p to an Einstein (or \nDebye) oscillator model for the lattice contribution at high temperature (rather than C v), is \njustified. We estimate that  Cv and Cp are the same to within approx. 1%  up to T = 400 K: t he \nrelation  TAC C Cp v P2  can be used to estimate Cv, where  TpCV A 2 2/ , \nPTVV\n\n\n1  is \nthe volume expansion coefficient and \nPTPVV\n\n\n1  is the isothermal compressibil ity34. \nLeBail  refinements of the neutron diffraction patterns from T=300 K to T=12 K were used to \nestimate β ( ≈ 10-5 K-1 ). The isothermal compressibility was estimated using a literature value \nfor another closest packed oxide ( MgO T= 7.2 Pa-1; virtually all oxides have isothermal \ncompressibilities within one order of magnitude of this value35).  \n \nIn both methods, there is a low temperature feature in the magnetic C p·T-1 data. Figure S5 shows \nan analysis indicating that the feature can not be adequately explained by simple Schottky \nanomaly models. Two or three level Schottky anomalies do not account for excess heat capacity \nin the data, even when other extra terms that might be present are also included.  \n \n 21 \n  \nFigure S5 | Low temperature Cp·T-1 Schottky anomaly analysis . a, μoH = 0 T data fit to a two \nlevel anomaly and b, μoH = 1 T fit for both a two (red) and three (blue) level Schottky anomaly. \nc, A fit to the μoH = 0 T data allowing for a γT electronic contribution (γ is in units of J·K-2·mol \nf.u.-1) and AT-2 nuclear contribution (A is in units of J·K·mol f.u.-1). Despite allowing for these \ncontributions (a γT term is unphysical considering the material is an insulator, see figure S6, \nalthough such a contribution could arise from spin -liquid behavior) the fit still does not \nadequately describe the data. In all cases, changing the degeneracy of the anomaly levels (g o/g1) \ndoes not resolve the fit, only changes the width by a small amount.  All figures show datasets \nfrom both methods of subt racting the lattice contribution of Zn 2Mo 3O8, but at these temperatures, \nthe difference is negligible.   \n \n \n \n \n22 \n  \nFigure S6 | LiZn 2Mo 3O8 resistivity. Resistivity as a function of temperature data measured on a \nsintered pellet of LiZn 2Mo 3O8. Measurements take n down to T = 50 K (where the voltmeter \nsaturated) show that LiZn 2Mo 3O8 is an electrical insulator and shows no obvious signs of \nelectronic transitions. This is as expected for the formation of a condensed valence bond state \n(which occurs as T = 96 K). The  high temperature data was fit to a model TK E\noB ge2/  giving \nan estimated band gap of Eg = 0.12 eV.  \n \n23 \n Magnetism and s pin-orbit coupling considerations.  \nIn 4d and 5d systems, spin orbit (SOC) contributions to magnetism can be significant. The spi n-\norbit coupling constant for Mo is ξ = 0.068 eV, similar to the value for Cu, ξ = 0.100 eV37. \nFurthermore, the crystal field splitting of adjacent states in a Mo 3O13 cluster is ~1.2 eV, on the \nsame scale as in Cu2+ compounds (~2.4 eV). Thus the effects of SOC are expected to be similar, \nwithin a factor of 2. To more quantitatively assess the expected effect of spin orbit coupling on \nthe observed magnetism, we calculated the expected deviation in the magnetic g -factor arising \nfrom a partial unquenched orbital contribution (from SOC) in a pert urbative manner. To second \norder36, the observed g -value, g m, is given by ) 1(EA g ge m where ge is the ideal value  (= \n2.0),  is the spin -orbit coupling constant, and E is the energy gap between electronic states \nfrom crystal field effects, and A is a constant dependant on the exact nature of the ground and \nlow-lying electronic states. The values of  are taken from the literature37 and values for A are \ntypically in the range of 2 -4. Performing calculations using the extremes of A, we see that gm \nranges from 1.55 to 1.77, consistent with a g -factor value extracted from the high -temperature \nCurie constant of 0.24  emu·K·Oe-1·mol f.u.-1 found in our data ( gm≈1.6). Performing this same \ntype of calculation on Cu yields a g -factor range of 2.18 to 2.37, consistent with experiment \n(gm≈2.2). This shows that spin -orbit coupling can be an explanation as to the reduced value of \nthe Curie constant (and hence μeff) obs erved in our inverse susceptibility data.  \n \nHowever, while spin -orbit coupling can itself give rise to interesting magnetic phases38, an \nanalysis carried out in the same way as Kotani show that, in this case, it does not explain the \nobserved trends in the magnetic data, notably the transition around T = 96 K.   \n 24 \n  \nFigure S7 | LiZn 2Mo 3O8 and Zn 2Mo 3O8 magnetic susceptibility. Magnetic susceptibility data \nas a function of temperature for LiZn 2Mo 3O8 and Zn 2Mo 3O8. DC magnetization was measured \non equimolar amoun ts (0.112 mmol) of each compound using the same sample container. This \nallowed for direct subtraction of the two datasets to determine the intrinsic response of the \nunpaired electrons in LiZn 2Mo 3O8. M(H) curves were linear up to μoH = 1 T, the applied fiel d \nused for the measurements, and thus the susceptibility was calculated assuming HM . The \nsmall Curie tail on Zn 2Mo 3O8 corresponds to 4.4% of paramagnetic impurity spins, mostly from \nthe sample holder.  \n25 \n  \n \nFigure S8 | LiZn 2Mo 3O8 temperat ure dependence of effective magnetic moments. \nCalculations of effective magnetic moments on LiZn 2Mo 3O8 as a function of thermal energy \n(kBT) divided by the spin orbit coupling constant ) 068.0 ( eV for molybdenum. The formula \n) )( (3\n2   TNk\no\nBAB\neff  is used to calculate the effective magnetic moment where is the \nmeasured magnetic susceptibility, ois the temperature independent contribution to the \nsusceptibility (in this case = 0 because of the subtraction of  Zn2Mo 3O8 and sample holder \nsusceptibility), T is temperature and is the Weiss temperature - indicative of the magnitude and \nsign of interactions between magnetic moments. effis in units of Bper f.u. The plots show the \ncalculated magnetic moment for a, no interactions (θ = 0 K), b, weak (θ = -14 K) or strong (θ = -\n220K) antiferromagnetic interactions uniform over all temperatures, and c, a change from strong \nto weak antiferromagnetic interactions  at  T ≈ 96 K. In a and b, the expected Kotani behaviors \nfor d2 ions, d1 ions, and a scaled (by one -third) combination of 2 d2 and 1 d3 ions are shown. The \nd1 case is similar to our proposed spin -½ degree of freedom magnetic molybdenum clusters, and \nthe li near combination of d2 and d3 case is what one would expect if each cluster were comprised \nof two Mo4+ and one Mo3+ distinct ions. The observed data are not consistent with any of these \n26 \n Kotani behaviors, as can be seen; the shape of the data is inconsisten t with a change in \nunquenched orbital contribution with temperature (which is the hallmark of SOC Kotani \nbehavior). In c, the extracted Weiss temperatures from fits to the inverse susceptibility data are \nused for the temperature ranges from which they are extracted. In this case the appearance of two \nflat regions above and below this transition indicates a loss of a large contribution to the effecti ve \nmagnetic moment around this temperature. This supports the argument that LiZn 2Mo 3O8 behaves \nas an isolated S=½ system with a partial unquenched orbital contribution that is temperature -\nindependent (just like Cu2+ compounds).  \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 27 \n  \n \nTable S1 | GAMESS input files:  \n \nGAMESS input files for calculations on a Mo 3O4(OH) 3(H2O)6 cluster using un restricted spin \ndensity functional theory with the PBE0 hybrid functional and Popel’s N -21 split valence basis \nset with 3 gaussians for Mo, the 6 -31G(d) basis for O and the 6-31G basis  for H39,40. \nMo 3O4(OH) 3(H2O)6 was chosen because it is a neutral molecul e, has the same electron count as \nthe Mo 3O13 clusters in LiZn 2Mo 3O8, and maintains the C 3v symmetry. Input file (a) uses \nHuzinaga’s minimal basis set to provide a suitable initial guess for the electron densities, which \nis then used as input for the full c alculation, using input file (b). Changes to the hybrid functional \nor basis sets used in (b) results in only minor changes to the calculated frontier orbitals. Spin -\norbit coupling effects are not included in these calculations.  \n \n a \n $CONTRL SCFTYP=UHF RUNT YP=energy MAXIT=200 ICHARG=0 MULT=2  \nCOORD=UNIQUE UNITS=ANGS EXETYP=RUN DFTTYP=PBE0 $END  \n $SYSTEM TIMLIM=525600 MEMORY=10000000 $END  \n $BASIS GBASIS=MINI $END  \n $GUESS GUESS=HUCKEL $END  \n $SCF DIRSCF=.TRUE. FDIFF=.FALSE. SOSCF=.TRUE. DAMP=.TRUE. $END  \n $DATA \nMo3O4(OH)3(H2O)6  \nCnv 3 \n0.0 0.0 0.0 0.0 0.0 1.0  \n1.0 0.0 0.0 'PARALLEL'  \nMo  42.0 1.48725 0.00000 0.00000  \nO4   8.0 0.00000 0.00000 -1.45412 \nO2   8.0 -1.61790 0.00000 1.2638  \nO3   8.0 3.35505 0.00000 1.0374  \nO1   8.0 2.57769 1.3475 -1.11802 \nH3   1.0 3.35505 0.0000 0 2.00706  \nH1_1 1.0 2.18474 1.17574 -1.98769 \nH1_2 1.0 2.66704 2.21202 -0.68806 \n $END \n \n \n \n 28 \n  \n \n \nb \n $CONTRL SCFTYP=UHF RUNTYP=energy MAXIT=200 ICHARG=0 MULT=2  \nCOORD=UNIQUE UNITS=ANGS EXETYP=RUN DFTTYP=PBE0 ISPHER=1 $END  \n $SYSTEM TIMLIM=525600 MEMORY=10000000 $EN D \n $BASIS BASNAM(1)=metal,metal,metal,ligO,  \n                  ligO,ligO,ligO,  \n                  ligO,ligO,ligO,  \n                  ligO,ligO,ligO,ligO,ligO,ligO,  \n                  ligH,ligH,ligH,  \n                  ligH,ligH,ligH,ligH,ligH,ligH,  \n                  ligH,ligH,ligH,ligH,ligH,ligH $END  \n $GUESS GUESS=RDMINI $END  \n $SCF DIRSCF=.TRUE. FDIFF=.FALSE. DIIS=.TRUE. DAMP=.TRUE. $END  \n $DATA \nMo3O4(OH)3(H2O)6  \nCnv 3 \n0.0 0.0 0.0 0.0 0.0 1.0  \n1.0 0.0 0.0 'PARALLEL'  \nMo  42.0 1.48725 0.00000 0.00000  \nO4   8.0 0.00000  0.00000 -1.45412 \nO2   8.0 -1.61790 0.00000 1.2638  \nO3   8.0 3.35505 0.00000 1.0374  \nO1   8.0 2.57769 1.3475 -1.11802 \nH3   1.0 3.35505 0.00000 2.00706  \nH1_1 1.0 2.18474 1.17574 -1.98769 \nH1_2 1.0 2.66704 2.21202 -0.68806 \n $END \n $metal \nn21 3 \n \n $end \n $ligO \nn31 6 \nd 1 ; 1 0.8 1.0  \n \n $end \n $ligH \nn31 6 \n \n $end \n  \n $VEC    \n \n \n \n \n 29 \n  \n \nTable S2 | Crystallographic information  \nLiZn 2Mo 3O8 refinement  \nChemical formula sum  Li1.2(1) Zn1.8(1) Mo3 O8  \nSpace group  R3തm \na (Å)  5.7956(3)  \nb (Å)  5.7956(3)  \nc (Å)  31.039(3)  \nZ 6 \nwR p 0.030 3 \nRp 0.0445  \nR(F2) 0.0846  \nχ2 8.356  \nLeBail χ2 2.705  \n \n LiZn 2Mo 3O8 structural parameters  \natom  x y z Wyck. pos.  Occ Uiso \nMo 0.18573(7)  0.81428(7)  0.08401(4)  18h 1.000  0.0033(1)  \nO1 0.84500(9)  0.15498(9)  0.04766(3)  18h 1.000  0.0012(1)  \nO2 0.49217(10)  0.50783(10)  0.12404(3)  18h 1.000  0.0060(1)  \nO3 0.0000  0.0000  0.11820(7)  6c 1.000  0.0052(2)  \nO4 0.0000  0.0000  0.37178(6)  6c 1.000  0.0029(2)  \nZn1 0.3333  0.6667  -0.64148(6)  6c 0.901(4)  0.0014(1)  \nZn2 0.0000  0.0000  0.18132(9)  6c 0.716(4)  0.0014(1)  \nLi1 0.3333  0.6667 -0.64148(6)  6c 0.099(4)  0.0014(1)  \nZn3 0.0000  0.0000  0.0000  3a 0.226(7)  0.0014(1)  \nLi2 0.0000  0.0000  0.18132(9)  6c 0.284(4)  0.0014(1)  \nZn4 0.0000  0.0000  0.5000  3a 0.143(6)  0.0014(1)  \nLi3 0.0000  0.0000  0.5000  3a 0.774(7)  0.0014(1)  \nLi4 0.0000  0.0000  0.5000 3a 0.857(6)  0.0014(1)  30 \n  \n \nSupplementary References  \n \n(34) Tari, A. The Specific Heat of Matter at Low Temperatures, Ch. 1  (Imperial College press, \nLondon, 2003)  \n \n(35) Washburn, E.W. (1926 - 1930;2003). International Critical Tables of Numerical Data, \nPhysics, Chemistry and Technology (1st Electronic Edition). Knovel. \nhttp://www.knovel.com/web/portal/browse/display?_EXT_KNOVEL_DISPLAY_bookid=7\n35&VerticalID=0  \n(36) Slichter, C.P., Principles of Magnetic Resonance, 3rd ed., Ch. 11 (Springer -Verlag, New \nYork, 1990)  \n(37) Vijayakumar, M. and Gopinathan, M.S. Spin -orbit coupling constants of transition metal \natoms and ions in density functional theory. J. Molecular Structure (Theochem) . 361, 15-19 \n(1996).  \n(38) Chen, G., Pereira, R., Balents, L., Exotic phases indu ced by strong spin -orbit coupling in \nordered double perovskites. Phys. Rev. B.  82, 174440. (2010).  \n(39) Binkley, J.S., Popel, J.A., Hehre, W.J. Self -consistent molecular orbital methods. 21. Small \nsplit-valence basis sets for first -row elements. J. Am. Che m. Soc. 102, 939 -947 (1980).  \n \n(40) Dobbs, K.D., Hehre, W.J. Molecular orbital theory of the properties of inorganic and \norganometallic compounds 5. Extended basis sets for first -row transition metals. J. Comput. \nChem.  8, 880-893. (1987).  \n \n "    },    {        "title": "1304.0137v1.Defect_Induced_Magnetism_in_Solids.pdf",        "content": "Defect-Induced Magnetism in Solids\nP. Esquinazia,1, W. Hergertb, D. Spemanna, A. Setzera, A. Ernstc\naInstitute for Experimental Physics II, University of Leipzig, Linn´ estraße 5, D-04103 Leipzig, Germany\nbinstitute of Physics, Martin Luther University Halle-Wittenberg, 06120 Halle, Germany\ncMax Planck Institute of Microstructure Physics, 06120 Halle, Germany\nAbstract\nIn the last years the number of nominally non-magnetic solids showing magnetic order induced by some kind of\ndefects has increased continuously. From the single element material graphite to several covalently bonded non-\nmagnetic compounds, the influence of defects like vacancies and /or non-magnetic ad-atoms on triggering magnetic\norder has attracted the interest of experimentalists and theoreticians. We review and discuss the main theoretical\napproach as well as recently obtained experimental evidence based on di \u000berent experimental methods that supports\nthe existence of defect-induced magnetism (DIM) in non-magnetic as well as in magnetic materials.\n1. Why Defect-Induced Magnetism was recognized\nso late?\nIn the original publication of Heisenberg, published\nin Leipzig in 1928 [1], about the basic concepts on the\norigin of magnetic order in solids, it is written at the end\nof the paper that the principal quantum number of the\nelectrons responsible for the magnetism must be n&3.\nIt took several decades till scientists started thinking that\nmagnetic order may exist beyond this n&3 condition.\nThe reason why magnetism based on sandpelectrons\nwas finally predicted, discovered and recognized so late,\nis mainly due to a mixture of three things, namely: The\nfirst reason is theoretical, since Heisenberg’s successful\ntheory on magnetic order promoted a kind of magnetic\nprejudice against magnetic signals coming from com-\npounds with full d- or f-bands or materials with only\nsandpelectrons. Second, the contribution of magnetic\nimpurities and their usually di \u000ecult characterization put\nalso hard constraints, which till now are not always\nremoved. Finally, the phenomenon of defect-induced\nmagnetism (DIM) in systems without usual magnetic\nions is based on the e \u000bect of di \u000berent kinds of defects\nupon the system. The production of samples with a ho-\nmogeneous distribution of defects at the right lattice po-\nsitions remains di \u000ecult. Therefore, the obtained mag-\nnetic signals are in some cases so small, that even tens of\nppm of magnetic Fe would be enough to produce similar\n1Corresponding author. Tel /Fax: +49 341 9732751 /69. E-mail\naddress: esquin@physik.uni-leipzig.de (P. Esquinazi)ones. Thus, the answer to the question of this section is\na mixture of technical capabilities to check for the im-\npurity contribution, scientific (over)skepticism and the\nnature of the DIM phenomenon itself.\nIn spite of these “di \u000eculties”, the DIM phenomenon\nhas been finally observed in a broad spectrum of mate-\nrials, from carbon-based to several oxides and the ob-\ntained evidence of the last ten years leaves little doubt\nabout its existence. In this contribution we do not try\nto review the huge amount of studies published but we\nwould like to emphasize a few new theoretical and ex-\nperimental results from di \u000berent groups as well as from\nus obtained in the last years that we believe should be\nof interest for all scientists working on this subject.\n2. Basic ideas and general theoretical approach to\nthe problem\nIn parallel to the experimental exploration of the un-\nusual magnetism, not based on dorfelectrons, theo-\nretical studies emerged. Theoretical investigations can\nbe based on model Hamiltonians to study basic physical\nfeatures of the problem [2, 3]. Detailed considerations\nof native defects, hydrogen or light impurities in car-\nbon or oxides require calculations on the ab initio level,\nbased on density functional theory (DFT). The appli-\ncation of sophisticated computer codes is not without\nproblems and the complete discussion of DIM demands\na multicode approach.\nAn intensive search for new routes to ferromagnetic\noxidic materials started with the investigation of Elfi-\nTo be published in IEEE Transactions on MagneticsarXiv:1304.0137v1  [cond-mat.mtrl-sci]  30 Mar 2013movet al. [4]. Using CaO as an example, it was demon-\nstrated that dilute divalent cation vacancies in oxides\nwith rocksalt structure lead to a ferromagnetic ground\nstate. The quite general result in [4] that the spin triplet\nstate is the ground state, is also applicable to other com-\npounds with vacancies in octahedral coordination. In\nterms of this somehow initiating paper an innumerable\nseries of papers appeared during the last 10 years in-\nvestigating the electronic and magnetic properties of va-\ncancies and non-magnetic impurities in di \u000berent oxides,\nwhereas especially MgO and ZnO attracted the attention\n[5, 6, 7].\nA consistent theoretical proof of a stable ferromag-\nnetic ground state consists of several steps. First, one\nhas to calculate the magnetic properties of the corre-\nsponding vacancies and impurities in the dilute limit.\nSecond, the mechanism of magnetic interaction as a re-\nquirement of long-range magnetic order has to be inves-\ntigated. Third, a calculation of the transition tempera-\nture has to predict the temperature range of ferromag-\nnetic order. All steps are connected with problems, as\ndiscussed by Zunger et al. [8]. Those problems and\nthe restricted knowledge of the nature and distribution\nof defects in experimental investigations, usually used\nas input of calculations, limit the predictive power of ab\ninitio calculations.\nAs a result of DFT calculations cation vacancies in\nZnO carry a magnetic moment of 1 :89\u0016B[9]. The mag-\nnetic interaction of such defects breaks down if localiza-\ntion corrections [8] are taken into account. Calculations\non Open-shell impurity molecules like C 2in ZnO seem\nto be a possible way for long-range ferromagnetic order\nin ZnO as calculations demonstrated [5].\nSurfaces provide another route to controlled ferro-\nmagnetism in an otherwise non-magnetic host material.\nWe studied room-temperature p-induced surface ferro-\nmagnetism at the oxygen-terminated ZnO(001) surface\n[10]. The pseudopotential code SIESTA was used to re-\nlax the structure. For a more adequate description of\nthe correlated electrons a multiple scattering Korringa-\nKohn-Rostoker code [11] was used. The code provides\nthe real space exchange coupling constants, which serve\nas an input to a Monte Carlo simulation in the frame-\nwork of a classical Heisenberg model to determine the\nCurie temperature. Finally it was shown, that the sur-\nface is thermodynamically stable and ferromagnetic at\nroom temperature [10].\n3. DIM in carbon\nAlready in 1968 the possibility to have magnetic or-\nder in hypothetical hydrocarbons was emphasized byMataga in a short paper [12]. Within the same line,\nin 1974 Tyutyulkov and Bangov proposed theoreti-\ncally the existence of unpaired electrons in hydrocar-\nbon molecules and nonclassical \u0019-conjugated polymers\n[13]. Ovchinnikov and coworkers followed a similar\nline [14, 15] and in 1991 they proposed a pure car-\nbon structure based on 50% graphite and 50% diamond\nbondings that could show magnetic order with a sat-\nuration magnetization above 200 emu /g [16], compa-\nrable to\u000b-Fe. Although this structure apparently was\nnot reproduced or realized, later experiments with dis-\nordered or amorphous carbon obtained by pyrolysis of\ncertain precursors indicated the existence of magnetic\norder with critical temperature above 500 K and satura-\ntion magnetization \u001810 emu /g at 4.3 K [17]. Further\ndetails of this early work can be seen in [18]. The main\nproblem of the early work is the unclear contribution of\nmagnetic impurities, basically due to insu \u000ecient char-\nacterization of their density and reproducibility of the\nreported phenomenon. In this section we discuss results\nrelated to the magnetic order mainly found and con-\nfirmed in graphite samples. Recent experimental stud-\nies did not provide clear evidence for the existence of\nthis phenomenon in single layer graphene [19, 20] and\ntherefore we will not discuss them here due to the avail-\nable space. The importance of the 3D lattice structure\nof graphite to trigger magnetic order through carbon va-\ncancies or bonded hydrogen has been emphasized in\n[21], see also [3].\n3.1. DIM in as-received graphite samples and the con-\ntribution of magnetic impurities: A never end story\nThe relatively small ferromagnetic moments obtained\nin most of the materials that show DIM due to the ac-\ntually “brute force” production methods used to trig-\nger this phenomenon, make the knowledge of the fer-\nromagnetic contribution from magnetic impurities un-\navoidable to assure that the measured phenomenon is\nintrinsic. In this section we discuss mainly the magnetic\ncontribution of impurities in the as-received state of the\nsamples. Whatever is the as-received state of the sample\nto be characterized, one should not forget that ultrasonic\ncleaning is nevertheless required to get rid of the edge\ncontamination graphite samples may have. The influ-\nence of defects or ion irradiation to the magnetism of\ngraphite will be discussed in the next section.\nThere are basically two main problems to character-\nize the magnetic response from impurities using only\nthe SQUID magnetometers. Firstly, the measurement of\ntheir concentrations. For concentration below 50 ppm\nthere are not too many experimental methods able to\nmeasure this content with enough certainty. Second, the\n2Figure 1: Remanent magnetization at zero field measured after field\ncooling the samples in a field of 1 T to 5 K. The data have been taken\nby warming to 300 K and cooling down to 5 K, see arrows. The results\nof two HOPG samples are shown: AC-ZYH (upper black data points)\nand AC-ZYB (lower red data points). The inset shows the same data\nbut in a semi logarithmic scale. The continuous black top line was\ncalculated using the 3D Bloch T3=2model with the following param-\neters: Curie temperature Tc=800 K, a ratio 2 JS=kB=210 K ( J\nthe exchange coupling and Sthe total spin). For the AC-ZYB sample\nthe remanence follows an anisotropic 2D spin waves model, contin-\nuous red line [22, 23], which follows a nearly linear decrease of the\nmagnetization with temperature. The continuous line was calculated\nusing the following parameters: Critical temperature Tc=600 K,\nspin-wave critical temperature due to low-energy spin-wave excita-\ntions TS W\nc=1950 K and anisotropy \u0001 = 0:001. For comparison we\nshow the theoretical (dashed) line obtained within the 3D Bloch T3=2\nmodel with the best parameters set to fit the data of sample AC-ZYB.\n/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48 /s51/s48/s48 /s51/s53/s48/s53/s46/s48/s53/s46/s50/s53/s46/s52/s53/s46/s54/s53/s46/s56/s54/s46/s48/s54/s46/s50/s54/s46/s52/s54/s46/s54\n/s48/s46/s50/s48/s48/s46/s50/s53/s48/s46/s51/s48/s48/s46/s51/s53/s48/s46/s52/s48/s32\n/s90/s89/s65/s82/s101/s109/s97/s110/s101/s110/s116/s32/s77/s97/s103/s110/s101/s116/s105/s122/s97/s116/s105/s111/s110\n/s77/s40/s49/s48/s45/s52\n/s32/s101/s109/s117/s47/s103/s41\n/s84/s101/s109/s112/s101/s114/s97/s116/s117/s114/s101/s32/s84/s40/s75/s41/s90/s89/s72\nFigure 2: Temperature dependence of the remanent magnetization,\nsimilar as in Fig. 1, for two HOPG samples after field cooling the\nsamples in a field of 1 T to 5 K. The continuous lines follow the 2D\nHeisenberg model with anisotropy [22, 23] and were obtained with\nthe following parameters for sample ZYH (ZYA): Critical temperature\nTc=550 K (750 K), spin-wave critical temperature due to low-energy\nspin-wave excitations TS W\nc=1700 K (830 K) and anisotropy \u0001 =\n0:001.knowledge of their concentration alone is not enough.\nOne needs to know at least the typical size of the impu-\nrity grains inside the material of interest, which requires\na method for elemental imaging that provides excel-\nlent detection limits in the ppm and sub-ppm range to-\ngether with reliable quantification, preferably in a non-\ndestructive way. The sole measurement of the magnetic\nmoment of a sample with a known amount of impurities\ndoes not provide always with a clear statement whether\nthe ferromagnetism is or is not due to impurities. In\nthis section we provide a simple example of this prob-\nlem using the magnetization data of four as-received\nHOPG samples of di \u000berent origins and impurity con-\ncentrations. A complete description of all measure-\nments done in as-received HOPG samples including the\nelemental analysis as a function of position inside the\nsamples using particle induced x-ray emission (PIXE,\nsee for example [24]) will be published elsewhere.\nFigure 1 shows the temperature hysteresis of the re-\nmanent (zero field) magnetization after cooling the sam-\nples in a field of 1 T, as a function of temperature of two\nHOPG samples with Fe concentration (the main mag-\nnetic impurity) 23 \u0016g/g ('5:8 ppm) for sample AC-\nZYH and 0:2\u0016g/g ('0:05 ppm) for sample AC-ZYB,\nwithin a relative error .10%. As shown in [24] the Fe\nis mainly distributed in spot-like regions of diameters\n.10\u0016m all over the sample interior (penetration depth\nof the PIXE analysis &30\u0016m). For the sample AC-\nZYH one recognizes a larger density of Fe atoms in the\nspots than in the spots of sample AC-ZYB, both samples\nappear to have similar density of spots. Therefore, the\ndi\u000berence in Fe concentration of a factor 115 between\nthe two samples is probably due to the di \u000berence in Fe\nconcentration within the spots and also a bit due to spot\nsize, because the spots (grains) appear larger for the AC-\nZYH sample. Both samples show the typical field hys-\nteresis with a ratio between saturation values at 5 K of\nMs(AC-ZYH)=M(AC-ZYB)'6\u000210\u00003=4\u000210\u00005=150\n(both values in emu /g). If allFe would be ferromag-\nnetic, from the ratio in concentration we would con-\nclude that the Fe concentration roughly explains the dif-\nference in magnetization at saturation values as well\nas the ratio of 102 in the remanent magnetization, see\nFig. 1. Taking into account that 1 \u0016g/g of ferromagnetic\nFe (Fe 3O4) in graphite would produce a magnetization\nat saturation of 2 :2\u000210\u00004emu/g (1:4\u000210\u00004emu/g), if all\nthe measured Fe concentration would be ferromagnetic\nwe would have the magnetization values at saturation\nof 5\u000210\u00003emu/g (3:2\u000210\u00003emu/g) for sample AC-\nZYH and 4:4\u000210\u00005emu/g (2:8\u000210\u00005emu/g) for sam-\nple AC-ZYB. From these estimated values it appears\nthat all the measured Fe, if ferromagnetic, would be\n3enough to explain the observations. It should be noted,\nhowever, that Fe in general is not homogeneously dis-\ntributed in the micron-sized impurity grains as revealed\nby PIXE elemental imaging. For example, the main im-\npurity contamination in these grains in AC-ZYB is Ti\nand V , but in AC-ZYH the Fe and V concentrations are\nsimilar whereas the Ti contamination can be neglected.\nConsequently, the impurity grains in both samples are\ndi\u000berent and cannot be considered to be of pure Fe (or\nFe3O4).\nFurthermore, Fe in graphite not always shows a fer-\nromagnetic behavior or induces one, upon grain size\nand distribution. For example, in [25] a sample with\nan inhomogeneous Fe concentration of up to 0.38%\n(in weight) shows no magnetic order at all. Moreover,\nno increase in the magnetic order, existing in the as-\nreceived state, was measured in HOPG samples after\nimplanting Fe up to concentrations of 4000 \u0016g/g [26].\nIn this last case, the obtained result appears reasonable\nbecause after implantation the Fe atoms reside as single\natoms randomly distributed in the (disordered) graphite\nlattice. The T\u0000dependence of the remanent magnetiza-\ntion suggests that not only Fe ferromagnetism is at work\nin the as-received samples. As shown in [24], to com-\npare quantitatively the T-dependence of the ferromag-\nnetic signal with appropriate models avoiding arbitrary\nbackground subtractions, we take the remanent magne-\ntization measured at zero applied field. The observed\nhysteresis between warming and cooling, see Fig. 1, is a\nclear evidence for the existence of a ferromagnetic state\nwith Curie temperature above 300 K.\nFor large enough 3D ferromagnetic Fe particles we\nexpect to see a T\u0000dependence of the remanent mag-\nnetization given by the excitation of spin waves fol-\nlowing the usual 3D Bloch T3=2model [27]. The\nsample with the largest Fe concentration (AC-ZYH)\nshows a T\u0000dependence for the remanent magnetiza-\ntion compatible with this law, see Fig. 1. However,\nfor the other sample with 0.05 ppm Fe concentration,\ntheT\u0000dependence deviates from this law but decreases\nquasi-linearly with T, the same dependence observed\nfor the magnetization of irradiated HOPG samples and\ninterpreted in terms of 2D Heisenberg model with a\nweak anisotropy [28, 29], see Fig. 1. We may con-\nclude that for the sample with the smaller Fe concen-\ntration a non-negligible part of the observed magnetic\norder comes from defects that induce a two dimensional\nanisotropic magnetism and is not due to ferromagnetic\nFe or other magnetic impurities.\nTo check the above correlation we did similar mea-\nsurements in two other samples of di \u000berent origin. Fig-\nure 2 shows the results for the samples ZYH and ZYAwith Fe concentrations (main impurity): 10 :2\u0016g/g and\n0:55\u0016g/g. The ratio between magnetizations at satura-\ntion at 5 K is Ms(ZYH)=Ms(ZYA)'2:3\u000210\u00003=2:8\u0002\n10\u00004=8:2 (values in emu /g). This ratio does not fol-\nlow the expected ratio (19) if allFe would contribute\nto the ferromagnetic signal. Whereas Ms(ZYH) ap-\npears to be compatible assuming that allFe concen-\ntration would contribute ferromagnetically, Ms(ZYA) is\na factor of 2.3 larger than the highest expected satu-\nration magnetization. From this we conclude that an\nextra contribution produces the observed magnetic or-\nder. Interestingly, both samples show a quasi-linear\ntemperature dependence for the remanence magnetiza-\ntion, see Fig. 2, which can be well fitted within the 2D\nHeisenberg anisotropic model. From all these studies\nwe may conclude that extra contributions, other than\nthose from magnetic impurities, to the observed ferro-\nmagnetic magnetization response exist in as-received\ngraphite samples. No general answer can be given, how-\never, even knowing the magnetic impurity concentra-\ntion, to the question whether magnetic impurities are or\nare not the reason for the observed magnetic response\nin a given sample. For samples with a relatively large\namount of magnetic impurities [30] it has little sense to\nspeculate whether the DIM phenomenon can be clearly\nobserved from the measurements.\n3.2. The role of vacancies and hydrogen\nThe existence of DIM in graphite, as-received sam-\nples of di \u000berent magnetic impurity contents [31, 25]\nas well as after inducing defects by ion irradiation\n[32], was later confirmed by independently done stud-\nies [33, 34, 29, 35, 36, 37, 3, 38, 39, 40]. The main idea\nto interpret the existence of magnetic order in graphite\n[21, 41, 42] (for reviews see [3, 43]) is based in the\nlong range interaction that appears between the nearly\nlocalized magnetic moments existing at carbon vacan-\ncies [44, 45], or when a proton is bonded to a carbon\np-electron normal to the graphene layer [46]. That sin-\ngle vacancies in graphite can trigger a magnetic moment\nhas been proved experimentally by STM spectroscopy\n[37] at the surface of a bulk graphite sample as well\nas by SQUID measurements of bulk samples irradiated\nwith di \u000berent ions and doses [38]. As expected, mag-\nnetic order was found only in samples in which a va-\ncancy density of several percents was achieved, i.e. a\ndistance between them of the order of 2 nm [38]. This\ndensity is necessary to get magnetic order in solids, in-\ndependently of the details of the structure or elements\nthat are in the lattice, provided that the vacancies or\nother defects in the lattice lead to nearly localized mag-\nnetic moments. Further recent studies on the magnetic\n4order in graphite triggered by proton and helium irradia-\ntion were done in [47]; the observed magnetic order ap-\npeared to be linked to defects in the graphite planes, like\nvacancies. Electron spin resonance studies on proton-\nirradiated HOPG samples at di \u000berent fluences indicated\nthe existence of metalliclike islands surrounded by insu-\nlatinglike magnetic regions [48] in agreement with pre-\nvious findings [49].\nThe intrinsic origin of the magnetic order triggered by\nproton irradiation on graphite has been backed by trans-\nmission x-ray magnetic circular dichroism (XMCD)\nstudies [33]. That study left no doubt that carbon can be\nmagnetic without the need of magnetic impurities. Fur-\nther XMCD studies in as-received as well as in proton\nirradiated HOPG samples [36] showed that not only the\ncarbon\u0019-band is spin polarized but hydrogen-mediated\nelectronic states also exhibit a net spin polarization with\nsignificant magnetic remanence at room temperature\n[36]. The obtained results showed that the magnetic sig-\nnals originated mostly from a \u001810 nm near-surface re-\ngion of the sample, where the saturation magnetization\nmay reach up to 25% of that of Ni. The results also in-\ndicated that hydrogen plays a role in the magnetic order\nbut it is not implanted by the irradiation but should come\nfrom dissociation of H 2molecules at the near surface\nregion of the HOPG sample [36]. These XMCD results\nsupport the findings from a low-energy muon spin rota-\ntion experiment on HOPG samples that indicated the ex-\nistence of a ferromagnetic surface of \u001815 nm thickness\n[50]. Further theoretical work showed that the magnetic\ncoupling becomes weaker when the hydrogen-hydrogen\ndistance increases [51, 41].\nAccording to [46] hydrogen absorption on a graphene\nsheet as well as hydrogen chemisorption in graphite\n[21], may lead to the formation of a spin-polarized band\nat the Fermi level and robust ferromagnetic order should\nappear. These theoretical studies are supported by the\nXMCD results referred above [36] and emphasize the\nneed for further studies on the role of hydrogen in the\nmagnetism of graphite. Searching for a simple method\nto trigger magnetic order in graphite samples of meso-\nscopic size through hydrogen doping, the authors in\n[52] treated graphite surfaces with sulfuric acid. It is\nknown that this kind of acid treatment leads to hydro-\ngen doping in the graphite structure. Indeed, the mag-\nnetization measurements of micrometer small graphite\ngrains treated with sulphuric acid showed clear signs for\nmagnetic order, which amount depends on the used di-\nlution of the acid as well as on the treatment time; it\ndecreased after mild annealing in vacuum [52]. Further\nevidence for the existence of magnetic order triggered\nby the acid treatment came from the anisotropic mag-netoresistance (AMR), defined as the dependence of the\nresistance on the angle between the direction of the elec-\ntric current and the magnetic field, both applied parallel\nto the main area of the sample [52]. The reported results\nindicated that the L\u0000Scoupling in graphite is not negli-\ngible when a magnetic moment is originated by hydro-\ngen doping (or due to vacancies). The observed rather\nlarge AMR values support a hydrogen-mediated mag-\nnetism in graphite in agreement with the XMCD results\nof [36].\n4. Evidence for DIM in Oxides\nNearly simultaneously with reports on magnetic or-\nder in graphite about 12 years ago, the search for fer-\nromagnetism in diluted magnetic semiconductors at-\ntracted the interest of a broad community. This was ba-\nsically due to the expectations of combining the advan-\ntages of semiconductors into spintronics applications,\nfor example. However, the early excitement after the\nfirst reports on magnetic order at room temperature ap-\npeared, was quickly overwhelmed by doubts on homo-\ngeneity issues as well as extra contaminations. On the\nother hand the broad research done afterwards helped\nto recognize that, as in graphite, defects, as vacancies\n(or added nonmagnetic ions) play a crucial role in the\nobserved magnetic order. For recent reviews on DIM\nin oxides the reader should refer to [53, 54, 43]. Here\nwe restrict ourselves to point out some results regarding\nDIM due to vacancies, hydrogen and surface states in\ncertain oxides reported recently.\nThe ground state of cation vacancies (0,V ,F centres)\nin oxides attracted attention already in the 60’s and 70’s\nand there are extensive studies of cation vacancies in\nsimple oxides like Al 2O3, MgO, SrO, CaO, BeO and\nZnO, for a review see, e.g., [55]. A high spin state of\nthe neutral Mg vacancy in MgO was reported in [56],\nbut probably the first observation of a high spin state\ndue to a cation vacancy was reported in a ZnO sample,\ni.e. due to a Zn vacancy, treated by electron irradiation\n[57]. In spite of that the possibility to have magnetic\norder through a minimum amount of vacancies was not\nrecognized at that time.\nFor undoped ZnO, probably the first hints on the pos-\nsible role of vacancies in the observed magnetic order\nwere obtained in thin films prepared by pulsed laser de-\nposition (PLD) under partial N 2atmosphere [58]. This\nrather preliminary result was confirmed a year later in\n[59], a study that concluded that neutral Zn vacancies,\nnot O vacancies, produced during the preparation of the\nfilm in the PLD chamber should play the main role in the\nobserved magnetic order. Characterization of the lattice\n5defects by x-ray absorption spectroscopy (XANES) at\nthe Zn K-edge in ferromagnetic, pure ZnO films, sup-\nported this conclusion [60]. We note that the absolute\nvalue of the magnetization of these ferromagnetic thin\nfilms (\u001810\u00002emu/g) suggests already that the amount\nof ferromagnetic mass in the films is certainly less than\n1%, an indication of the inhomogeneous distribution of\ndefects. Therefore one may still doubt whether bulk\ncharacterizations of the films would provide the prop-\nerties of the magnetic regions. New studies of un-doped\nZnO films prepared on silicon and quartz substrates\nsuggested, however, that the ferromagnetism is origi-\nnated from singly occupied oxygen vacancies, not Zn\nvacancies, reaching magnetization values of the order\nof 1 emu /g for\u0018100 nm thick films [61]. The con-\nclusion that oxygen vacancies in ZnO are the reason\nfor the observed magnetic order is at odd with several\nworks cited above. However, in that work [61] no clear\nanalysis of the magnetic impurities in the successive an-\nnealing steps was done. Therefore, the subject remains\npartially controversial.\nThe possibility of triggering magnetic order due to\nhydrogen adsorption at the surface of pure ZnO was\nstudied theoretically in [62, 63]. Evidence for surface\nmagnetism in pure ZnO films after hydrogen annealing\nat 100\u000e\u0000500\u000ewas found in [64] together with evidence\nof the importance of OH-terminated surfaces, support-\ning theoretical predictions. Interestingly, the FM could\nbe turn on and o \u000bafter annealing in hydrogen or ar-\ngon atmosphere. Further support to the possibility of\nusing hydrogen to trigger magnetic order in ZnO came\nfrom the change in magnetization [65] as well as in the\nmagnetotransport properties [66] after low energy pro-\nton implantation on ZnO single crystals. The obtained\nmagnetization at saturation was \u00185 emu /g and localized\nin a near surface region of thickness .20 nm [65, 66].\nThe measured anisotropic magnetoresistance (AMR) up\nto room temperature indicates a spin splitted band as\nwell as a finite spin-orbit coupling [66]. These works in-\ndicate that hydrogen should be a good candidate to trig-\nger magnetic order in a more systematic way than with\nsolely vacancies. If the e \u000bect is reproducible, triggering\nmagnetic order through hydrogenation of the surfaces\nof micro- and nanowires of ZnO should be possible.\nNot only in ZnO but in several other oxide structures\nlike MgO, SrTiO 3, MgAl 2O4, LaAlO 3, their surface and\nupon termination can show magnetic order at room tem-\nperature without extra doping. This is the conclusion\nthat was arrived in [67]. In particular the sensitivity of\nthe magnetic signals after acetone or ethanol cleaning\nof the surface of SrTiO 3substrates indicate a surface\norigin. The impact of these two liquids on the surfacemagnetism has been theoretically studied in [68]. Those\nresults indicate that Ti- as well as O-vacancies at the\nsurface play a role in the observed di \u000berence between\nethanol and acetone influence on the surface magnetism.\nThe studies in [69] showed that the observed room\ntemperature magnetic order in ZnO:Cu(2%) films can\nbe attributed the magnetic moments arising at the Cu\nion, i.e. the d10electronic state of Cu can decrease when\ncoupled to an O-vacancy originating a finite moment\ncoming from the Cu d\u0000band; the magnetic moments of\nO are found opposite oriented to the Cu ones. Actu-\nally, a similar explanation was proposed earlier in [70]\nto explain the ferromagnetism observed in TiO 2:Cu. All\nthese results indicate the important role that vacancies\nmay play after doping non magnetic oxides to trigger\nmagnetic order. Not only vacancies but also dislocations\nappear to provide a main contribution to the magnetic\nresponse of undoped and Mn-doped ZrO 2films [71].\nThe role of defects in the magnetic response of ox-\nides goes beyond the nominally nonmagnetic oxides\nbut can be also shown to play a role in magnetic ox-\nides stressing the fact that DIM is a quite general phe-\nnomenon. Recent experiments [72] provided evidence\nfor DIM in ZnFe 2O4samples grown under low O 2pres-\nsure, pointing at the role of oxygen vacancies in the ob-\nserved magnetism. This is further supported by recently\ndone XMCD measurements and ab initio calculations\nin the framework explained above [73]. All this work\ndemonstrates that a missing oxygen atom between two\nadjacent Fe3+atoms on B sites leads to a parallel align-\nment of the Fe moments and therefore a large magnetic\nmoment per unit cell.\nWe would like to end this section referring to photo-\nconductivity studies, a property that was hardly used in\nthe past to characterize the e \u000bects of DIM. The idea is\nto study the e \u000bects of a magnetic field on the photore-\nsistance, a property that depends on the lifetime of pho-\ntogenerated electrons and this on the particularities of\nthe energy centers inside the gap that are originated by\ndefects. If these defects play a role in DIM, then a mag-\nnetic field can influence the photoconductivity. Mea-\nsurements in magnetic ZnO films [74] revealed that a\nmagnetic field enhances the recombination time of pho-\ntoexcited carriers, increasing the photoconductivity. In\nprinciple this property may be used in the future as a\nmagnetic defect spectroscopy, studying the e \u000bect of a\nmagnetic field on the photoconductivity in a broad en-\nergy range.\n65. Evidence for DIM in other compounds\nWe note here two di \u000berent non-oxide materials that\nafter irradiation show a ferromagnetic response. Pro-\nton irradiation of MoS 2revealed magnetic ordering at\nroom temperature when exposed to a 2 MeV proton\nbeam (similar energy than in [32]). The temperature\ndependence of magnetization displays ferrimagnetic be-\nhavior with an remarkably high Curie temperature of\n895 K [75]. The authors suggest that not necessarily\na single kind of defect but the combination of mag-\nnetic moments arising from di \u000berent defects, like va-\ncancies, interstitials, deformation and partial destruction\nof the lattice structure may be necessary to understand\nthe triggered magnetic order. DIM was also observed\nafter neutron irradiation of SiC single crystals [76]. The\nauthors in that work demonstrated that mainly the pro-\nduced divacancies (V SiVC) appear to be responsible for\nthe observed magnetism. Theoretical studies revealed\nthat extended tails of the defect wave functions induce\nthe long-range coupling between the localized moments\ncaused by the divacancies [76], a further example of the\nrichness of the DIM phenomenon in solids.\n6. Perspectives and Conclusion\nMaximum magnetization can be achieved for a cer-\ntain vacancy concentration, beyond it, the magnetiza-\ntion will reduce and eventually vanishes. This limit pro-\nvides maximum magnetization values that would hardly\nsurpass that of usual strong ferromagnets. Therefore,\nthe production of large-mass homogeneous magnetic\nsamples with DIM will remain di \u000ecult and future activ-\nities should concentrate on inducing this phenomenon in\nrather small samples. Although vacancies will remain\nan important defect to take care, several studies dis-\ncussed here (see also [43]) already indicate that doping\nwith non-magnetic elements as H, C, N, etc., appears\nnowadays an interesting route to achieve high magne-\ntization values and homogeneous samples. Due to the\nrelatively small values of magnetization one tends to be-\nlieve that DIM is a weak phenomenon, however they\nare small because of the unidentified mass of the FM\nregions. Taking into account that \u00185% vacancies can\ntrigger magnetic order with TC>300 K, a comparison\nwith TC'150 K triggered by \u00185% Fe-magnetic ions\nin Pd [77] indicates that DIM is not a weak but an ex-\ntraordinarily strong phenomenon.\nAcknowledgment\nThis work was supported by the DFG within the Col-\nlaborative Research Center (SFB 762) ”Functionality ofOxide Interfaces.”\nReferences\n[1] W. Heisenberg, “Zur Theorie des Ferromagnetismus,” Z. Phys. ,\nvol. 49, pp. 619–636, 1928.\n[2] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, and D. Ferrand,\n“Zener model description of ferromagnetism in zinc-blende\nmagnetic semiconductors,” Science , vol. 287, no. 5455, pp.\n1019–1022, 2000.\n[3] O. V . Yazyev, “Emergence of magnetism in graphene materials\nand nanostructures,” Rep. Prog. Phys. , vol. 73, p. 056501, 2010.\n[4] I. S. Elfimov, S. Yunoki, and G. A. Sawatzky, “Possible path\nto a new class of ferromagnetic and half-metallic ferromagnetic\nmaterials,” Phys. Rev. Lett. , vol. 89, p. 216403, 2002.\n[5] H. Wu, A. Stroppa, S. Sakong, S. Picozzi, M. Sche \u000fer, and\nP. Kratzer, “Magnetism in C-or N-doped MgO and ZnO: A\ndensity-functional study of impurity pairs,” Phys. Rev. Lett. , vol.\n105, p. 267203, 2010.\n[6] I. Slipukhina, P. Mavropoulos, S. Bl ¨ugel, and M. Le ˇzai´c, “Fer-\nromagnetic spin coupling of 2p impurities in band insulators\nstabilized by an intersite coulomb interaction: Nitrogen-doped\nMgO,” Phys. Rev. Lett. , vol. 107, no. 13, p. 137203, 2011.\n[7] P. Mavropoulos, M. Le ˇzai´c, and S. Bl ¨ugel, “Ferromagnetism\nin nitrogen-doped MgO: Density-functional calculations,” Phys.\nRev. B , vol. 80, no. 18, p. 184403, 2009.\n[8] A. Zunger, S. Lany, and H. Raebiger, “The quest for dilute fer-\nromagnetism in semiconductors: Guides and misguides by the-\nory,” Physics , vol. 3, p. 53, 2010.\n[9] W. A. Adeagbo, G. Fischer, A. Ernst, and W. Hergert, “Mag-\nnetic e \u000bects of defect pair formation in ZnO.” J. Phys.: Con-\ndens. Matter , vol. 22, p. 436002, 2010.\n[10] G. Fischer, N. Sanchez, W. Adeagbo, M. L ¨uders, Z. Szotek,\nW. M. Temmerman, A. Ernst, W. Hergert, and M. C. Mu ˜noz,\n“Room-temperature p-induced surface ferromagnetism: First-\nprinciples study,” Phys. Rev. B , vol. 84, p. 205306, 2011.\n[11] M. L ¨uders, A. Ernst, M. D ¨ane, Z. Szotek, A. Svane,\nD. K ¨odderitzsch, W. Hergert, B. L. Gy ¨or\u000by, and W. M. Temmer-\nman, “Self-interaction correction in multiple scattering theory,”\nPhysical Review B , vol. 71, p. 205109, 2005.\n[12] N. Mataga, “Possible “ferromagnetic states” of some hypotheti-\ncal hydrocarbons,” Theoret. Chim. Acta (Berl.) , vol. 10, pp. 372–\n376, 1968.\n[13] N. Tyutyulkov and I. Bangov, “Electronic structure of some hy-\npothetical polymeric nonclassical hydrocarbons,” Compt. Rend.\nAcad. Bulg. Sci. , vol. 27, pp. 1517–1524, 1974.\n[14] A. A. Ovchinnikov, “Multiplicity of the ground state of large\nalternant organic molecules with conjugated bonds,” Theoret.\nChim. Acta (Berl.) , vol. 47, pp. 297–304, 1978.\n[15] A. A. Ovchinnikov and V . N. Spector, “Organic ferromagnets -\nnew results,” Synth. Metals , vol. 27, pp. B615–B624, 1988.\n[16] A. A. Ovchinnikov and I. L. Shamovsky, “The structure of\nferromagnetic phase of carbon,” J. of Molecular Structure\n(Theochem) , vol. 251, pp. 133–140, 1991.\n[17] K. Murata, H. Ushijima, H. Ueda, and K. Kawaguchi, “Mag-\nnetic properties of amorphous-like carbons prepared by tetraaza\ncompounds by the chemical vapour deposition (CVD) method,”\nJ. Chem. Soc., Chem. Commun. , pp. 1265–6, 1991.\n[18] P. Esquinazi, Magnetic Carbon, Handbook of Magnetism and\nAdvanced Magnetic Materials . H. Kronm ¨uller and S. Parkin\n(eds.), John Wiley & Sohn Ltd, Chichester, UK, 2007, vol. 4,\npp. 2256–2281.\n[19] M. Ricc `o, D. Pontiroli, M. Mazzani, M. Choucair, J. A. Stride,\nand O. V . Yazyev, “Muons probe strong hydrogen interaction\n7with defective graphene,” Nano Lett. , vol. 11, pp. 4919 – 4922,\n2011.\n[20] R. R. Nair, M. Sepioni, I.-L. Tsai, O. Lehtinen, J. Keinonen,\nA. V . Krasheninnikov, T. Thomson, A. K. Geim, and I. V . Grig-\norieva, “Spin-half paramagnetism in graphene induced by point\ndefects,” Nature Phys. , vol. 8, pp. 199–202, 2012.\n[21] O. V . Yazyev, “Magnetism in disordered graphene and irradiated\ngraphite,” Phys. Rev. Lett. , vol. 101, p. 037203, 2008.\n[22] A. P. Levanyuk and N. Garc ´ıa, “The two-dimensional Heisen-\nberg ferromagnet with various types of interactions: tempera-\nture dependence of magnetic parameters,” J. Phys.: Condens.\nMatt. , vol. 4, p. 10277, 1992.\n[23] P. A. Serena, N. Garc ´ıa, and A. P. Levanyuk, “Monte Carlo\ncalculations on the two-dimensional anisotropic Heisenberg\nmodel,” Phys. Rev. B , vol. 47, p. 5027, 1993.\n[24] P. Esquinazi, J. Barzola-Quiquia, D. Spemann, M. Rothermel,\nH. Ohldag, N. Garc ´ıa, A. Setzer, and T. Butz, “Magnetic order\nin graphite: Experimental evidence, intrinsic and extrinsic di \u000e-\nculties,” J. Magn. Magn. Mat. , vol. 322, pp. 1156–1161, 2010.\n[25] P. Esquinazi, A. Setzer, R. H ¨ohne, C. Semmelhack, Y . Kopele-\nvich, D. Spemann, T. Butz, B. Kohlstrunk, and M. L ¨osche,\n“Ferromagnetism in oriented graphite samples,” Phys. Rev. B ,\nvol. 66, pp. 024 429–1–10, 2002.\n[26] R. H ¨ohne, P. Esquinazi, V . Heera, H. Weishart, A. Setzer, and\nD. Spemann, “The influence of iron, fluorine and boron implan-\ntation on the magnetic properties of graphite,” J. Magn. Magn.\nMater. , vol. 320, pp. 966–977, 2008.\n[27] C. Kittel, Introduction to Solid State Physics, 7th ed. John\nWiley & Sons, Inc., 1996, p. 455.\n[28] J. Barzola-Quiquia, P. Esquinazi, M. Rothermel, D. Spemann,\nT. Butz, and N. Garc ´ıa, “Experimental evidence for two-\ndimensional magnetic order in proton bombarded graphite,”\nPhys. Rev. B , vol. 76, p. 161403(R), 2007.\n[29] H. Xia, W. Li, Y . Song, X. Yang, X. Liu, M. Zhao, Y . Xia,\nC. Song, T.-W. Wang, D. Zhu, J. Gong, and Z. Zhu, “Tunable\nmagnetism in carbon-ion-implanted highly oriented pyrolytic\ngraphite,” Adv. Mater. , vol. 20, pp. 4679–4683, 2008.\n[30] M. Sepioni, R. R. Nair, I.-L. Tsai, A. K. Geim, and I. V . Grig-\norieva, “Revealing common artifacts due to ferromagnetic inclu-\nsions in highly oriented pyrolytic graphite,” Europhysics Letters ,\nvol. 97, p. 47001, 2012, see comment to this article by D. Spe-\nmann et al., idem, vol. 98, p. 57006, 2012 and the reply by M.\nSepioni et al., arXiv:1204.2992.\n[31] Y . Kopelevich, P. Esquinazi, J. Torres, and S. Moehlecke,\n“Ferromagnetic- and superconducting-like behavior of\ngraphite,” J. Low Temp. Phys. , vol. 119, pp. 691–702,\n2000.\n[32] P. Esquinazi, D. Spemann, R. H ¨ohne, A. Setzer, K.-H. Han, and\nT. Butz, “Induced magnetic ordering by proton irradiation in\ngraphite,” Phys. Rev. Lett. , vol. 91, pp. 227 201–1–4, 2003.\n[33] H. Ohldag, T. Tyliszczak, R. H ¨ohne, D. Spemann, P. Esquinazi,\nM. Ungureanu, and T. Butz, “ \u0019-electron ferromagnetism in\nmetal-free carbon probed by soft x-ray dichroism,” Phys. Rev.\nLett., vol. 98, p. 187204, 2007.\n[34] Y . Zhang, S. Talapatra, S. Kar, R. Vajtai, S. K. Nayak, and P. M.\nAjayan, “First-principles study of defect-induced magnetism in\ncarbon,” Phys. Rev. Lett. , vol. 99, p. 107201, 2007.\n[35] X. Yang, H. Xia, X. Qin, W. Li, Y . Dai, X. Liu, M. Zhao, Y . Xia,\nS. Yan, and B. Wang, “Correlation between the vacancy defects\nand ferromagnetism in graphite,” Carbon , vol. 47, pp. 1399–\n1406, 2009.\n[36] H. Ohldag, P. Esquinazi, E. Arenholz, D. Spemann, M. Rother-\nmel, A. Setzer, and T. Butz, “The role of hydrogen in room-\ntemperature ferromagnetism at graphite surfaces,” New Journal\nof Physics , vol. 12, p. 123012, 2010.[37] M. M. Ugeda, I. Brihuega, F. Guinea, and J. M. G ´omez-\nRodriguez, “Missing atom as a source of carbon magnetism,”\nPhys. Rev. Lett. , vol. 104, p. 096804, 2010.\n[38] M. A. Ramos, J. Barzola-Quiquia, P. Esquinazi, A. Mu ˜noz\nMartin, A. Climent-Font, and M. Garc ´ıa-Hern ´andez, “Magnetic\nproperties of graphite irradiated with MeV ions,” Phys. Rev. B ,\nvol. 81, p. 214404, 2010.\n[39] Z. He, X. Yang, H. Xia, X. Zhou, M. Zhao, and Y . Song, “En-\nhancing the ferromagnetism of graphite by successice12C+ion\nimplantation steps,” Carbon , vol. 49, pp. 1931–1938, 2011.\n[40] X. Miao, S. Tongay, and A. F. Hebard, “Extinction of ferro-\nmagnetism in highly ordered pyrolytic graphite by annealing,”\nCarbon , vol. 50, pp. 1614–1618, 2012.\n[41] L. Pisani, B. Montanari, and N. Harrison, “A defective graphene\nphase predicted to be a room temperature ferromagnetic semi-\nconductor,” New Journal of Physics , vol. 10, p. 033002, 2008.\n[42] O. V . Yazyev and L. Helm, “Defect-induced magnetism in\ngraphene,” Phys. Rev. B , vol. 75, p. 125408, 2007, see also O. V .\nYazyev, Phys. Rev. Lett. vol. 101, p. 037203, 2008.\n[43] O. V olnianska and P. Boguslawski, “Magnetism of solids result-\ning from spin polarization of porbitals,” J. Phys.: Condens.\nMatter , vol. 22, p. 073202, 2010.\n[44] P. O. Lehtinen, A. S. Foster, Y . Ma, A. Krasheninnikov, and\nR. M. Nieminen, “Irradiation-induced magnetism in graphite: a\ndensity-functional study,” Phys. Rev. Lett. , vol. 93, pp. 187 202–\n1–4, 2004.\n[45] Y . Ma, P. O. Lehtinen, A. S. Foster, and R. M. Nieminen, “Mag-\nnetic properties of vacancies in graphene and single-walled car-\nbon nanotubes,” New Journal of Physics , vol. 6, pp. 68–1–15,\n2004.\n[46] E. J. Duplock, M. Sche \u000fer, and P. J. D. Lindan, “Hallmark of\nperfect graphite,” Phys. Rev. Lett. , vol. 92, pp. 225 502–1–4,\n2004.\n[47] T. L. Makarova, A. L. Shelankov, I. T. Serenkov, V . I. Sakharov,\nand D. W. Boukhvalov, “Anisotropic magnetism of graphite ir-\nradiated with medium-energy hydrogen and helium ions,” Phys.\nRev. B , vol. 83, p. 085417, 2011.\n[48] K. W. Lee, H. Kweon, J. J. Kweon, and C. E. Lee, “Electron\nspin resonance study of proton-irradiation-induced defects in\ngraphite,” J. Appl. Phys. , vol. 107, p. 044302, 2010.\n[49] K. Schindler, N. Garc ´ıa, P. Esquinazi, and H. Ohldag, “Insulat-\ning behavior of magnetic spots in proton-bombarded graphite,”\nPhys. Rev. B , vol. 78, pp. 045 433–1–7, 2008.\n[50] M. Dubman, T. Shiroka, H. Luetkens, M. Rothermel, et al.,\n“Low-energy \u0016SR and SQUID evidence of magnetism in highly\noriented pyrolytic graphite,” J. Magn. Magn. Mat. , vol. 322, pp.\n1228–1231, 2010.\n[51] X. Y . Pei, X. P. Yanga, and J. M. Dong, “E \u000bects of di \u000ber-\nent hydrogen distributions on the magnetic properties of hydro-\ngenated single-walled carbon nanotubes,” Phys. Rev. B , vol. 73,\np. 195417, 2006.\n[52] J. Barzola-Quiquia, W. B ¨ohlmann, P. Esquinazi, A. Schadewitz,\nA. Ballestar, S. Dusari, L. Schultze-Nobre, and B. Kersting,\n“Enhancement of the ferromagnetic order of graphite after sul-\nphuric acid treatment,” Appl. Phys. Lett. , vol. 98, p. 192511,\n2011.\n[53] S. B. Ogale, “Dilute doping, defects, and ferromagnetism in\nmetal oxide systems,” Adv. Mater. , vol. 22, pp. 3125–3155,\n2010.\n[54] M. Stoneham, “The strange magnetism of oxides and carbons,”\nJ. Phys.: Condens. Matter , vol. 22, p. 074211, 2010.\n[55] O. F. Schirmer, “O\u0000bound small polarons in oxide materials,”\nJ. Phys.: Condens. Matter , vol. 18, pp. R667–R704, 2006.\n[56] L. E. Halliburton, D. L. Cowan, W. B. J. Blake, and J. E.\nWertz, “Magnesium-25 hyperfine confirmation of the localized-\n8ground-state model of the V\u0000center in MgO,” Phys. Rev. B ,\nvol. 8, pp. 1610–1616, 1973.\n[57] D. Galland and A. Herve, “ESR Spectra of the zinc vacancy in\nZnO,” Phys. Lett. , vol. 33A, pp. 1–2, 1970.\n[58] Q. Xu, H. Schmidt, S. Zhou, K. Potzger, M. Helm,\nH. Hochmuth, M. Lorenz, A. Setzer, P. Esquinazi, C. Mei-\nnecke, and M. Grundmann, “Room temperature ferromagnetism\nin ZnO films due to defects,” Appl. Phys. Lett. , vol. 92, p.\n082508, 2008.\n[59] M. Khalid, M. Ziese, A. Setzer, P. Esquinazi, M. Lorenz,\nH. Hochmuth, M. Grundmann, D. Spemann, T. Butz, G. Brauer,\nW. Anwand, G. Fischer, W. A. Adeagbo, W. Hergert, and\nA. Ernst, “Defect-induced magnetic order in pure ZnO films,”\nPhys. Rev. B , vol. 80, p. 035331, 2009.\n[60] J. Haug, A. Chass ´e, M. Dubiel, C. Eisenschmidt, M. Khalid,\nand P. Esquinazi, “Characterization of lattice defects by x-ray\nabsorption spectroscopy at the Zn K-edge in ferromagnetic, pure\nZnO films,” J. Appl. Phys. , vol. 110, p. 063507, 2011.\n[61] P. Zhan, W. Wang, Z. Xie, Z. Li, Z. Zhang, P. Zhang, B. Wang,\nand X. Cao, “Substrate e \u000bect on the room-temperature ferro-\nmagnetism in undoped ZnO films,” Appl. Phys. Lett. , vol. 101,\np. 031913, 2012.\n[62] N. Sanchez, S. Gallego, J. Cerd ´a, and M. C. Mu ˜noz, “Tun-\ning surface metallicity and ferromagnetism by hydrogen adsorp-\ntion at the polar ZnO(0001) surface,” Phys. Rev. B , vol. 81, p.\n115301, 2010.\n[63] E. Liu and J. Jiang, “Magnetism of O-terminated ZnO(0001)\nwith adsorbates,” J. Phys. Chem. C , vol. 113, p. 16116, 2009.\n[64] T. Li, C. S. Ong, T. S. Herng, J. B. Yi, N. N. Bao, J. M. Xue, Y . P.\nFeng, and J. Ding, “Surface ferromagnetism in hydrogenated-\nZnO film,” Appl. Phys. Lett. , vol. 98, p. 152505, 2011.\n[65] M. Khalid, P. Esquinazi, D. Spemann, W. Anwand, and\nG. Brauer, “Hydrogen-mediated ferromagnetism in ZnO single\ncrystals,” New Journal of Physics , vol. 13, no. 6, p. 063017,\n2011.\n[66] M. Khalid and P. Esquinazi, “Hydrogen-induced ferromag-\nnetism in ZnO single crystals investigated by magnetotransport,”\nPhys. Rev. B , vol. 85, p. 134424, 2012.\n[67] M. Khalid, A. Setzer, M. Ziese, P. Esquinazi, D. Spemann,\nA. P ¨oppl, and E. Goering, “Ubiquity of ferromagnetic signals\nin common diamagnetic oxide crystals,” Phys. Rev. B , vol. 81,\nno. 21, p. 214414, 2010.\n[68] W. A. Adeagbo, G. Fischer, and W. Hergert, “First-principles\ninvestigations of electronic and magnetic properties of SrTiO 3\n(001) surfaces with adsorbed ethanol and acetone molecules,”\nPhys. Rev. B , vol. 83, p. 195428, 2011.\n[69] T. S. Herng, D.-C. Qi, T. Berlijn, J. B. Yi, K. S. Yang, Y . Dai,\nY . P. Feng, I. Santoso, C. S ´anchez-Hanke, X. Y . Gao, A. T. S.\nWee, W. Ku, J. Ding, and A. Rusydi, “Room-temperature fer-\nromagnetism of Cu-doped ZnO films probed by soft x-ray mag-\nnetic circular dichroism,” Phys. Rev. Lett. , vol. 105, no. 20, p.\n207201, 2010.\n[70] S. Duhalde, M. F. Vignolo, F. Golmar, C. Chiliotte, C. E. R.\nTorres, L. A. Errico, A. F. Cabrera, M. Renteria, F. H. Sanchez,\nand M. Weissmann, “Appearance of room-temperature ferro-\nmagnetism in Cu-doped TiO 2\u0000\u000efilms,” Phys. Rev. B , vol. 72,\np. 161313 (R), 2005.\n[71] J. Zippel, M. Lorenz, A. Setzer, G. Wagner, N. Sobolev, P. Es-\nquinazi, and M. Grundmann, “Defect-induced ferromagnetism\nin undoped and Mn-doped zirconia thin films,” Phys. Rev. B ,\nvol. 82, p. 125209, 2010.\n[72] C. E. R. Torres, F. Golmar, M. Ziese, P. Esquinazi, and\nS. P. Heluani, “Evidence of defect-induced ferromagnetism in\nZnFe 2O4thin films,” Physical Review B , vol. 84, p. 064404,\n2011.[73] C. E. R. Torres et al., “The role of O-vacancies in the enhance-\nment of the magnetic order in Zn ferrites,” to be published.\n[74] C. Zapata, M. Khalid, G. Simonelli, M. Villafuerte, S. P. Helu-\nani, and P. Esquinazi, “Magnetic field influence on the transient\nphotoresistivity of defect-induced magnetic ZnO films,” Appl.\nPhys. Lett. , vol. 99, p. 112503, 2011.\n[75] S. Mathew, K. Gopinadhan, T. K. Chan, X. J. Yu, D. Zhan,\nL. Cao, A. Rusydi, M. B. H. Breese, S. Dhar, Z. X. Shen,\nT. Venkatesan, and J. T. L. Thong, “Magnetism in MoS 2induced\nby proton irradiation,” Appl. Phys. Lett. , vol. 101, p. 102103,\n2012.\n[76] Y . Liu, G. Wang, S. Wang, J. Yang, L. Chen, X. Qin, B. Song,\nB. Wang, and X. Chen, “Defect-induced magnetism in neutron\nirradiated 6H-SiC single crystals,” Phys. Rev. Lett. , vol. 106, p.\n087205, 2011.\n[77] B.-H. Yeh and J. Chen, “Magnetization measurements of Pd-Fe\nalloys in the intermediate Fe concentration region,” CHINESE\nJOURNAL OF PHYSICS , vol. 13, pp. 1–5, 1975.\n9"    },    {        "title": "1304.2945v1.A_proposed_new_route_to_d0_magnetism_in_semiconductors.pdf",        "content": "arXiv:1304.2945v1  [cond-mat.mtrl-sci]  10 Apr 2013A proposed new route to d0magnetism in semiconductors\nJ. Berashevich\nThunder Bay Regional Research Institute, 290 Munro St., Thu nder Bay, ON, P7B 5E1, Canada and\nMax Planck Institute for the Physics of Complex Systems, Nth nitzer Str. 38, 01187 Dresden, Germany\nA. Reznik\nThunder Bay Regional Research Institute, 290 Munro St., Thu nder Bay, ON, P7B 5E1, Canada and\nDepartment of Physics, Lakehead University, 955 Oliver Roa d, Thunder Bay, ON, P7B 5E1\nHere we propose to induce magnetism in semiconductor utiliz ing the unique properties of the\ninterstitial defect to act as the magnetic impurity within t heα-PbO crystal structure. The Pb i\ninterstitial generates the p-localized state with two on-site electrons to obey the Hund ’s rule for\ntheir ordering. It is demonstrated that instead of Pb inters titial other non-magnetic impurities of\ns2pxouter shell configuration can be applied to induce d0magnetism with possibility to tune the\nlocal magnetic moments µBby varying a number of electrons 1 ≤x≤3. The magnetic coupling\nbetween such defects is found to be driven by the long-range o rder interactions that in combination\nwith highdefect solubility promises the magnetic percolat ion toremain above theroom temperature.\nSpintronics has recently emerged as a widely success-\nful technology that exploits the principles of magnetism,\nbut the classical metal ferromagnets are not applicable\nthere. That has led to the creation of a new branch of re-\nsearch directed at semiconductors exhibiting magnetism\nat room temperature [1]. The first success in this regard\nwas with the so-called ”diluted magnetic semiconduc-\ntors” created by doping semiconductors with magnetic\nions whose inner 3 dor 4fshells being partially filled that\nallows the ferromagneticspin alignment [2–5]. A keen in-\nterest on ferromagnetic semiconductors also arose when\n’non-magnetic’ materials were discovered to demonstrate\nmagnetism [6–9]. Origin of so-called d0magnetism was\nproposed to be due to localized spstates: vacancies cre-\nate a network of unpaired electrons and as interaction\nbetween such defects can demonstrate the long-range or-\nder, their magnetic coupling occurs [9].\nHere we propose to induce d0magnetism by form-\ning the interstitial defect Pb i(Pbi:6s26p2outer shell)\nwithin the crystal structure of the tetragonal lead ox-\nideα-PbO. It generates the state occupied by two p-\nunpaired electrons Pb i:6p2. Ordering of the localized\nelectrons Pb i:6p2obeys the first Hund’s rule thus result-\ning in formation of the stable local magnetic moment of\n2.0µB. The spin-polarization energy of such state is\nEM=EAFM−EFM=0.235 eV, where EAFMandEFM\nare the total energies of the anti-(AFM) and ferromag-\nnetic states (FM), respectively [10]. Therefore, other-\nwise than magnetism occurs due to the partially filled p\nshell instead of the 3 dor 4fshells, Pb iworks exactly\nas the magnetic impurity. It demonstrates the high on-\nsite spin stability, its pelectrons are localized on impu-\nrity site showing a weak perturbation with the host (an\ninteraction with the host occurs through Pb i:6s2elec-\ntrons) and in addition, the interstitial defect is almost\nnon-invasive to the electronic and crystal structures of\nthe host. We have established that any impurity of the\ns2p1≤x≤3outer shell embedded as the interstitial defect\ninto theα-PbO crystal structure would act as magnetic.\nThep-shell occupation, p1≤x≤3, can be used to controlthe spin ordering between impurities and also to tune\nthe local magnetic moments: x= 2 works for 2.0 µB,\nwhilex= 1 orx= 3 for 1.0 µB. From the technologi-\ncal point of view, the layered crystal structure of α-PbO\npromises the superior advantages in achievement of the\nmagnetic percolation and more importantly, a practical\nway for its control: i)the crystal structure of PbO type\ngrows in polycrystalline form whose large surface area\noffers enormous potential for doping (on surface the im-\npurities can be placed on the nearest-neighbours); ii)the\ndopant solubility and long-range order interactions can\nbe manipulated with the impurity atomic radius; iii)any\ncompounds of the tetragonal PbO type can be used as a\nsemiconductor matrix.\nIn our study we applied the generalized gradient ap-\nproximation (GGA) with the PBE parametrization [11]\nprovided by WIEN2k package for the density functional\ncalculations [12]. The supercell approach ( RKmax=7)\nwith sufficiently large supercell of 108-atom size (3 ×3×3\narray of the primitive unit cells) for single impurity and\nof 160-atom size (5 ×4×2) for two interacting impurities\nhave been used. The Pb:5 p,5d,6s,6pand O:2s,2pelec-\ntrons have been treated as the valence electrons. For\nintegration of the Brillouin-zone, the Monkhorst-Pack\nscheme using a (5 ×5×4) k-mesh was applied. The local-\nization of the impurity wavefunction has been addition-\nally examined with HF applied directly to the unpaired\nelectrons that allows to preserve accuracy provided by\nDFT but in the same time to correct the unpaired elec-\ntrons self-interaction [13].\nThe tetragonal lead oxide α-PbO possesses the layered\nstructure leading to formation of platelets upon com-\npound growth and each platelets is considered as a sin-\ngle crystal. The layers within such crystal are held to-\ngether by the interlayer interaction of Pb:6 s2electrons\n[14]. In terms of electronic properties, these interactions\ninduce adeeping ofthe conduction bandat M∗point [15]\nand the gap shrinks as interactions enhance. GGA tends\nto overestimate the interlayer separation in the layered\nstructures but in the same time it also well known to2\nunderestimate the band gap size. For α-PbO system it\nresults in compensation effect [17]: for the lattice param-\neters optimized with GGA the band gap is only slightly\nunderestimated as 1.8 eV against the experimental value\nof 1.9 eV [16] (application of the experimental value of\nthe lattice parameters causes the band gap to shrink by\n0.22 eV). The correct band gap size is important in in-\nvestigation of the magnetic impurities: when the band\ngap size is underestimated the hole-carrying impurity or-\nbital occurs closer to the the host conduction band in\nturn forcing a delocalization of the defect tails. In or-\nder to avoid the spurious long-range order interactions\n[5] all band structure calculations have been performed\nforthelatticeparametersoptimizedwithGGA.However,\nsince an incorporation of the interstitial becomes easier\nas interlayer distance increases, the interlayer distance\nhas also crucial impact on the defect formation energy.\nIn order to make correct evaluation of the formation en-\nergy, the experimentalvalue ofthe lattice parametershas\nbeen applied for those calculations.\nThe interstitial defects have never been considered in\norigin of d0magnetism because they do not belong to a\nclass of most common defects in crystalline materials as\nthey induce a significant perturbation of the host lattice\nresulting in their large formation energy [18]. The lay-\nered structure of α-PbO is different, as it allows the for-\neign atoms to squeeze between layers inducing a minimal\nlattice deformation to the host immediate neighborhood\n(see Fig. 1 (a)). As a result, the formation energy of\nPbiis not too high. For the Pb rich conditions/vacuum\nthe neutralchargestate is characterizedby the formation\nenergy of 1.23 eV (for methods see [17]).\nThe band diagram and the density of states (DOS)\nforα-PbO containing Pb iare presented in Fig. 1 (b)\nand (c), respectively. The Pb interstitial makes a bond\nwith Pb atom from the host generating the defect state\ninside the band gap. The defect-induced spin-up and\nspin-down bands (1uand 1din Fig. 1 (b) and (c)) both\nshow dominant Pb i:6px+ycharacter but demonstrate a\ndifferent behavior. The spin-up band is filled with two\nelectrons and appears just above the midgap at 0.99 eV\n+EV, where EVis a top of the valence band (VB).\nIn contrast, the spin-down band (1d) is unoccupied and\nappears at the edge of the conduction band (CB). In\norder to understand an asymmetry in filling of the spin-\nup and spin-down states, bonding of Pb iwith the host\nlattice has to be considered.\nThe integration of the Pb interstitial into the crystal\nlattice requires excitation of its ground state 6 s26p2to\n6s16p3. The Pb i:6s1and Pb i:6p1\nzelectrons participate in\nbond formation with the Pb atom from the host which\nshares its Pb:6 s2electrons (see Fig. 1 (c)). The bonding\norbital appears inside VB, while the antibonding forms\nthe CB bottom (see 2uand 2dbands and notations of\n’bonding’ and ’antibonding’ at B and C panels to DOS).\nThe length of the Pb i-Pb bond is fairly short, 2.9 ˚A, that\nis indicative of a double bond formation. An out-of-plane\ndisplacement of 0.54 ˚A occurs for the Pb atom involved\nFIG. 1: (a) The Pb interstitial in the layered crystal struct ure\nofα-PbO (b) Band diagram: 1uand 1dare for the defect\ninduced bands, while 2uand 2dare the antibonding orbitals\nof the Pb i-Pb bond. (c) Total and partial density of states for\nPbiand host Pb atoms (’top’ is referred to Pb atom forming\nthe Pb i-Pb bond, while ’bottom’ for Pb atoms in the bottom\nlayer). The ’bonding’ and ’antibonding’ in panels B and C\nare reffered to the Pb i-Pb bond.\nin bonding. Because participation of the host Pb:6 s2\norbitalsin bondinginterfereswith interlayerinteractions,\nit alters a behavior of the conduction bands near the CB\ntop: in analogy with the band behavior in a single layer\n[15], the band deeping at the M∗point is suppressed.\nTherefore, out of three Pb i:6p3electrons found in the\nexcited state (6 s16p3), only one Pb i:6p1\nzparticipates in\nbonding while the two others Pb i:6px+yare left at the3\ndefect site. The Hund’s rule dictates both unpaired elec-\ntrons to occupy the 1uspin-up band. The empty 1dspin-\ndown band is pushed up to CB that causes considerably\nlarge spin-exchange splitting of order 0.523 eV. The fer-\nromagnetically ordered Pb i:6px+yelectrons generate the\nlocal magnetic moment of 2.0 µB. The difference in to-\ntal energy between the AFM and FM states is found\nto beEM=EAFM−EFM=0.235 eV thus promising\nthe FM state to be stable well above the room tempera-\nture. An application of the HF approach to the unpaired\nelectrons induces further stabilization of the FM state to\nEM=0.490 eV due to stronger on-site localization of the\nimpurity wave function (the 1uorbital is shifted towards\nthevalencebandby0.5eVthusenhancingthesplittingof\nthe 1uand 1dorbitals). On the other hand, reduction of\nthe interlayer distance (the experimental lattice parame-\nters are applied) in opposite causes delocalization of the\nwave function due to stronger hybridization of impurity\nstate with the host lattice.\nThe 6s26p2electronic configuration is a key point for\nthe Pb interstitial to act as a magnetic impurity: filled s2\nouter shell is required for bonding with the host lattice\nwhile partially filled pshell contributes in development\nof the local magnetic moment. Following this principle,\nother chemical elements possessing s2p1≤x≤3outer shell\ncan be applied to induce d0magnetism. Indeed, several\nexamined impurities have shown a formation of the local\nmagnetic moment, impurity of x= 1 orx= 3 induces\nthe local magnetic moments of 1 µB, whilex= 2 pro-\nduces 2µB. The stability of the spin-polarized state is\nobserved to grow substantially with reduction of the im-\npurity atomic radius.\nOurstudiesoflocalizationoftheelectrondensityatthe\ndefect site has revealed a duality in its behavior. Since\noccupied band 1uis located deep inside the band gap,\nthe Pb i:6p2\nx+yelectrons shows strong localization on the\ndefect sitethus allowingtoformthe stablelocalmagnetic\nmoment of 2 µB(see Fig. 2 (a)). However, the long defect\ntails appear as well but due to bonding/hybridization of\nthe Pb i:6s1and Pb i:6p1\nzelectrons from the Pb intersti-\ntial and Pb:6 sand Pb:6 p, O:2pelectrons from the host\n(see partial DOS in Fig. 1 (c)). As a result, the electron\ndensity around the defect site is spin-polarized showing\nan anisotropyin its distribution: the defect tails aresym-\nmetrically polarized relative to Pb ithus contributing in\nstabilization of the ferromagnetic state.\nSince extension of the wave function tails to the host\nlattice seems to be of the long-range order, it is expected\nto induce effective defect-defect interactions. In this re-\nspect we have investigated an interaction of Pb iwith the\nO vacancy ( VO) which formation is also favored at the\nPb-rich/O-poor limit (oxygen deficiency). In its charge\nneutralstate, VOisoccupiedbytwoelectronsshowingthe\nstrong localization at the vacancy site [17]. Since the vir-\ntual hopping is allowedbetween the states formed by Pb i\nandVO, they can work as compensating centers to each\nother. Forthedefectsappearingatthenearest-neighbour\nsites, the FM ordering of the localized spins at Pb iis\nFIG. 2: Schematic band diagrams demonstrate a formation\nof FM (Pb i) and AFM (Pb i-VOpair) states. The energy\nvalues are appearance of the defect levels relative to EV. The\nelectron density map is plotted for isovalues of ±0.005 e/˚A3\nwith help of Xcrysden. (a) FM state at the Pb isite. The\ndensity map demonstrates the spin density calculated for th e\nenergyrange (1.0eV+ EV)±0.15 eV.(b)Aninteraction ofPb i\nwithVOdestroys the FM state at the Pb isite. The electron\ndensity is plotted for the energy range (0.9 eV+ EV)±0.4 eV.\nfound to be destroyed due to the strong interaction be-\ntween defects to be accompanied by hybridization. The\nPbi:6px+yelectrons from the interstitial and the Pb:6 s\nand Pb:6 pand O:2pelectrons from the host lattice, all\nhave been found to contribute equally in formation of\nboth defect states (see manifestation of the electron den-\nsity in the inter-defect region in Fig. 2(b)). The strong\ninteractions between defects contribute in lowering of the\nformation energy of defect pair by 0.84 eV in comparison\nto the non-interacting defects. With defect separation\nthe electronic interactions are suppressed leading to re-\ncoveryof the FM state: for distance of 6.2 ˚A between the\ndefects the local magnetic moment is 1.8 µB. However,\nbecause interaction of Pb iwithVOdo not vanish com-\npletely, the magnitude of the spin polarization energy is4\nfound to be considerably low EM=EAFM−EFM=0.06\neV. Therefore, the electronic interactions between Pb i\nandVOdemonstrate the long-rangeorder due to the long\ntails of the Pb iinterstitial.\nFor two interacting interstitial defects, as both defects\ncontributewith their tailsinto the long-rangeorderinter-\nactions, the magnetic coupling between them is expected\nto sustain over the larger distance. The 6 p2\nx+ystate is\nexactly half filled and, therefore, for two interacting im-\npurities the virtual hopping is allowed only in the AFM\nstate making it the ground state [5]. For two Pb intersti-\ntials placed on distance 4.1 ˚A we found that EM=-0.96\neV while for distance 12.5 ˚A it drops down to -0.0056eV.\nFor the C interstitial the interactions are lower as EM=-\n0.38 eV for distance 4.1 ˚A andEM=-0.0023 eV for 12.5\n˚A. An application of HF for the localized electrons sup-\npressesEMalmost twice. The AFM interaction between\nimpurities can be switched to FM for the impurity of p1\noccupation of outer shell (for example, In or Ga work for\nFM state) or for p2occupation by choosing the charged\nstate (1+).\nIn terms of the formation energies of the interstitials,\nit drastically drops down as the atomic radius decreases.\nThus, if the formation energy ofthe Pb interstitial is 1.23\neV for the Pb-rich/vacuum conditions, it is reduced al-\nmost to zerofor Ge, Si impurities and alreadyturns to be\nnegative for the C and O impurity (the formation energy\nof the O interstital is -0.26 eV) thus implying the higher\nsolubility limit with prospects of spontaneous defect ap-\npearance. Therefore, it is found that suppression in the\nmagnetic coupling between impurities to occur with re-\nduction of its atomic radius is compensated by simulta-\nneous shift of the impurity solubility limit to the higher\ndefect concentration. For defects appearing on surface,\nthedefectconcentrationcanreachanumberofsitesavail-\nable for doping ( ∼1022cm−3) as the formation energy is\nreduced further down (for example for the Pb interstitial\nit drops down by ∼1.0 eV such as the solubility limit is\n1020cm−3).\nIn summary, we propose to induce the plocal orbitalmagnetism by doping of α-PbO semiconductor with the\nnon-magnetic impurities to appear in layered structure\nofα-PbO as the interstitial defects. To create conditions\nfor partially filled pshell to act as 3 dor 4fshells\nof the magnetic ions, i.e. obeying the Hund’s rule\nfor the on-site ordering of the unpaired electrons, an\nimpurity of specific s2p1≤x≤3outer shell is required.\nThe combination of the outer shell with the PbO crystal\nstructure is unique because it allows doping to be almost\n’non-invasive’ to the host lattice and its electronic prop-\nerties. In particular, bonding between impurity and the\nhost involves only their s2outer shell electrons thereby\npreserving the original electronic configuration of the p\nshells. In this case, the partially filled p1≤x≤3-shell of\nimpurity generates the localized spins on-site of defect.\nThe main advantage of the defect-induced magnetism\nover the diluted magnetic semiconductors is duality\nin its state localization. Thus, the p-localized state\nformed on site of the Pb interstitial has the localized\nnature to form the stable local magnetic moment, but\nimpurity-host hybridization results in the extended de-\nfect tails. The manifesting long-range order interactions\nbetween defects in combination with their high solu-\nbilitycreateconditionsformagneticpercolationtooccur.\nI. ACKNOWLEDGEMENT\nWe would like to thank Prof. P. Fulde, Prof. T.\nChakraborty and Dr. L. Hozoi for their guidance and\nthoughtful insights in our work. This work was made\npossible by the computational facilities of Dr. O. Rubel\nandtheSharedHierarchicalAcademicResearchComput-\ning Network (SHARCNET:www.sharcnet.ca) and Com-\npute/Calcul Canada. Financial support of Ontario Min-\nistry of Research and Innovation through a Research Ex-\ncellence Program Ontario network for advanced medical\nimaging detectors is highly acknowledged.\n[1] K. Ando, Science 312, 1883 (2006).\n[2] W. Prellier, A. Fouchet, and B. Mercey, J.\nPhys.:Condens. Matter. 15, R1583 (2003).\n[3] J.M.D. Coey, Solid State Sciences 7, 660 (2005).\n[4] P. Mahadevan, A. Zunger, D.D. Sarma, Phys. Rev. Lett.\n93, 177201 (2004).\n[5] A. Zunger, S. Lany, H. Raebiger, Physics 3, 53 (2010).\n[6] Z. A. Khan and S. Ghosh, Appl. Phys. Lett. 99, 042504\n(2011).\n[7] M. Venkatesan, C.B. Fitzgerald, and J.M.D. Coey, Na-\nture430, 630 (2004).\n[8] R. Podila et al., Nano Letters 10, 1383 (2010).\n[9] P. Dev, Y. Xue, and P. Zhang, Phys. Rev. Lett. 100,\n117204 (2008).\n[10] Preliminary results: EPR measurements performed on\nPbO samples at room temperature have indicated an ap-pearance of several paramagnetic centers.\n[11] J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.\nLett.77, 3865 (1996).\n[12] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J.\nLuitz, Wien2k: An Augmented Plane Wave + Local Or-\nbitals Program for Calculating Crystal Properties: Karl-\nheinz Schwarz, Techn. Universit¨ at Wien, Austria, 2001.\n[13] M. d’Avezac, M. Calandra, F. Mauri, Phys. Rev. B. 71,\n205210 (2005).\n[14] H. J. Terpstra, R.A. de Groot, and C. Haas, Phys. Rev.\nB52, 11690 (1995); A. Walsh, D. J. Payne, R. G. Edgell,\nand G. W. Watson, Chem. Soc. Rev. 40, 4455 (2011).\n[15] J. Berashevich, O. Semeniuk, J.A. Rowlands, and A.\nReznik, EPL 99, 47005 (2012).\n[16] B. Thangaraju and P. Kaliannann, Semicond. Sci. Tech-\nnol.15, 542 (2000).5\n[17] J. Berashevich, O. Semeniuk, O. Rubel, J.A. Rowlands,\nand A. Reznik, J. Phys.: Condens. Matter 25, 075803\n(2013).\n[18] A. Janotti and C. G. Van de Walle, Rep. Prog. Phys. 72,126501 (2009)\n[19] Y. Gohda and A. Oshiyama, Phys. Rev. B 78, 161201\n(2008)."    },    {        "title": "1304.6156v2.Interfacial_tuning_of_perpendicular_magnetic_anisotropy_and_spin_magnetic_moment_in_CoFe_Pd_multilayers.pdf",        "content": "Interfacial tuning of perpendicular magn etic anisotropy and spin magnetic \nmoment in CoFe/Pd multilayers  \nD.-T. Ngo,1 Z. L. Meng,1 T. Tahmasebi,1,2 X. Yu,3 E. Thoeng,3,4 L. H. Yeo,4 A. Rusydi,3,4,a G. \nC. Han,2 and K.-L. Teo,1,b \n1Department of Electrical and Computer Engine ering, National University of Singapore, 4 \nEngineering Drive 3, Singapore 117576 \n2Data Storage Institute, A*STAR (Agency for Science Technology and Research), 5 Engineering \nDrive 1, Singapore 117608 \n3NUSNNI-NanoCore and Singapore Synchrotron Light Source, National University of Singapore, \n5 Research Link, Singapore 117603 \n4Department of Physics, National Un iversity of Singapore, Singapore 117542 \nAbstract \nWe report on a strong perpendicular ma gnetic anisotropy in [CoFe 0.4nm/Pd t]6 (t = 1.0-2.0 nm) \nmultilayers fabricated by DC s puttering in a ultrahigh vacuum chamber. Saturation magnetization, \nMs, and uniaxial anisotropy, Ku, of the multilayers decrease with increasing the spacing thickness, \nwith a Ms of 155 emu/cc and a Ku of 1.14×105 J/m3 at a spacing thickness of t = 2 nm.  X-ray \nabsorption spectroscopy and X-ray magnetic circular  dichroism measurements reveal that spin \nand orbital magnetic moments of Co  and Fe in CoFe film decrease  as function of Pd thickness, \nindicating the major contribution of surface/interfacial magnetism to the magnetic properties of \nthe film.  Keywords : Magnetic multilayers, Perpendicular ma gnetic anisotropy, Magnetic domains and \ndomain walls, Interfacial magnetism, X-ray magnetic ci rcular dischroism  \n \na Corresponding author: phyandri@nus.edu.sg   \nb Corresponding author: eleteokl@nus.edu.sg   1. Introduction \nPerpendicular magnetic anisotropy (PMA) films [1] have been drawn much intention \nbecause of their potential appl ications in magnetic recording technology and spintronics. The \nPMA films with high saturation magnetization ( Ms) have been used for perpendicular magnetic \nrecording, bit-patterned media r ecording technology [2-4]. In spintronics, the PMA films have \nbeen exploited in spin-transfer torque (STT)  technology, such as STT MRAM [5], nanowire \nracetrack memory [6], spin logic devices [7], etc.  with commitment to create spin-torque devices \noperating with low energy consumption. \nAmong the STT applications, the PMA films w ith unique magnetic properties have been \nextensively concentrated for spin-torque dom ain walls (DWs) nanowir e devices (non-volatile \nmemory, spin logic devices, etc) [6,7]. One of the most important issues of such devices is to \nreduce magnetization-switching current density, of which the critical current density is essentially \ngoverned by the intrinsic para meters of the films [8]: \n2\n01s\nc\nBeMjgPαγμβαΔ=−    ( 1 )  \nWhere, e is the electron charge, g is the gyromagnetic ratio, μB is the Bohr magneton, \nrespectively; α, β, M s, Δ and P are the Gilbert damping factor, non-adiabatic spin transfer \nparameter, saturation magnetization, domain wall thickness and spin polarization of the film, \nrespectively. In the PMA films, the Bloch-type  walls with narrower thickness form instead of \nNéel-type walls of very large wall thickness whic h normally exist in the thin films with in-plane \nanisotropy. The narrow Bloch wall is also favorable  for non-adiabaticity that is expected to \nenhance the wall motion [9], which is crucial for high-speed devices. Therefore, a PMA film with \nlow Ms, low damping constant, narrow DW and high spin polarization would be desirable for a \nspin-torque DW device working with low current density. In this article, we observe strong PMA on fcc-Co 70Fe30 multilayers with low Ms, high \nuniaxial anisotropy and spin polarization. The low Ms of the multilayers containing high- Ms \nCo70Fe30 as magnetic layers are realized using non- magnetic Pd spacing layers to modify the \ninterfacial magnetic moment proved by X-ray absorption spectroscopy (XAS) and X-ray \nmagnetic circular dichroism (XMCD) measurements. \n2. Experiments  \nThe CoFe/Pd-based multilayers with the st ructure of Ta 5.0 nm/Pd 5.0 nm[CoFe 0.4 \nnm/Pd t]6/Ta 2.0 nm ( t = 1.0, 1.2, 1.4, 1.6, 1.8 and 2.0 nm, respectively) were grown on thermally \noxidized Si substrates by using DC magnetron spu ttering in an ultrahigh vacuum chamber of an \nUHV Deposition Cluster. Composition of the CoFe layers was fixed at Co 70Fe30 (at.%). The base \npressure was better than 2.5×10-9 Torr whereas Ar working pressure was remained at 1.5 mTorr \nduring deposition. Magnetic  properties of the films at room te mperature were characterized using \nan alternating gradient force magnetometer (AGF M) with a maximum magnetic field of 20 kOe.  \nThe X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism \n(XMCD) at Co L3,2 and Fe L3,2 edges at room temperature were obtained by recording the sample \ncurrent (total yield mode) as a function of photon  energy at the SINS beam line of the Singapore \nSynchrotron Light Source (SSLS) [10]. Elliptically  polarized light with a degree of circular \npolarization (DCP) = 80 and an energy resolu tion of 0.25 eV was employed for the XMCD \nmeasurements. To measure the out-of-plane spin  and orbital magnetic moments, the light was \nincident at a normal angle from the sample su rface, with its propagat ion direction along the \nsample out-of-plane magnetisation direction. An external magnetic field of ±10 kOe was applied \nto magnetize the sample along the out-of-plane direction. The XCMD were done by changing the \ndirection of applied magnetic field while kept the helicity of the light. Thin films of Co and Fe \nwere used as the reference to normalize the XMCD  data. We intentionall y measured XMCD with spin polarization along out-of-plane magnetic moments to follow an easy-axis magnetization \nshown by the magnetometer measurements. Microm agnetic simulation of domain structure was \nperformed using LLG Micromagnetic SimulatorTM [11]. \n3. Results and Discussion \nFigure 1 shows a series of ma gnetic-hysteresis (M-H) loops m easured on two directions \nfor CoFe/Pd multilayers ( t = 1.0÷2.0 nm): parallel (dash curves) and perpendicular (solid-dot \ncurves) to the film plane. The M-H  loops for the field applied in th e film plane exhibit a hard axis \nbehavior with rotation mechanism of the magn etization reversal de noted by S-shape loops. \nWhilst the loops measured with th e perpendicular field show an eas y-axis behavior reflected as \nthe highly square M-H  loops. Smooth M-H  loops indicate that unique  magnetic properties occur \nover the film as the single-phase behavior du e to strong ferromagnetic coupling between the \nmagnetic CoFe layers. These prove the strong alignment of the magnetization of the films perpendicular to the film plane, or the existenc e of the PMA in the studied multilayers. It should \nbe note that the perpendicular loops are not pe rfectly 100% squareness which is ascribed to a \nsmall in-plane component existing in the films. This  in-plane component is attributed to the Néel \ncaps located in the Bloch walls, which will be  discussed detailed by looking into the domain \nstructure of the films in coming paragraphs. \nUsually, the Co-Fe alloy with a concentration of Fe above 15 at.% is favorable for the \nformation of body-centered cubic (bcc) crystal st ructure [12], and the magnetic anisotropy in \nsuch a film should appear in-plane. However, the thick Pd seed layer in face-centered cubic (fcc) \nwith a strong <111> texture normal to the film plane was proved in our pr evious report [13] to \ninduce the <111>-texture fcc stru cture in the CoFe that supporte d the out-of-plane anisotropy \n[12,14]. Hence, the Pd seed layer with <111> text ure normal to the film plane is effective to induce the PMA in ultra thin CoFe films [12,14],  including CoFe/Pd multila yers [13]. In recent \nreports, some authors proposed that the interfacial  anisotropy of the CoFe/Pd interface, in which \nthe CoFe layer was in <111>-textu re fcc, is possibly an importa nt factor governing the PMA of \nthe CoFe/Pd multilayers [15]. Following analysis of magnetic moments by XMCD in this paper \nallows confirming this prediction, and we prove th e minor contribution of th e crystal structure of \nthe layers to the PMA of these multilayers. \nIt is then important to understand the modi fication of magnetic properties of the CoFe/Pd \nmultilayers by varying Pd spacing layer thickne ss. Figure 2(a) illustrates the saturation \nmagnetization, Ms, of the CoFe/Pd multilayers as a function of Pd spacing layers thickness. \nObviously, Ms appears to decrease with the Pd sp acing layer thickness due to diluting the \nmagnetic interaction by the non-magnetic Pd layers. With Pd spacing layers of 1.0 nm thick, the \nMs value is measured to be 280 emu/cc, whereas  this value decreases  to 155 emu/cc as the \nthickness of the spacing layers incr eases to 2.0 nm. The reduction in Ms is in good agreement \nwith the function of 1/ t as it has been commonly seen in PMA multilayers [16]. Such Ms values \nare significantly lower than that in other co mmon Co-based PMA films used for spin-torque \ndomain wall applications, such as Pt/Co mu ltilayers (~900 emu/cc) [17] , Co/Ni multilayers (660 \nemu/cc) [6], perpendicular magnetized CoFeB f ilms (1200 emu/cc) [18,19], and comparable with \nlow-Ms ferrimagnetic TbFeCo film [20,21]. The Ms of the studied CoFe/Pd multilayers is \ndefinitely much lower than that of pure fcc-Co 70Fe30 alloy film (1200 emu/cc) [22].  This \nreduction is ascribed essentially to the presence  of the Pd layers (with weak induced magnetic \nmoments) and also as demonstrat ed in next section from the XMCD measurements to a decrease \nof the moments of Fe and Co atoms located at the interfaces. \nIn contrary to the tendency of the Ms, the anisotropy field, which is derived from the M-H \nloops as Hk = H s + 4πMs (Hs is the saturation field) [18], increas es as a linear function of the Pd layer thickness [see inset of Fig. 2(a)] from 12.6 kOe to 14.8 kOe. From Hk and Ms, the uniaxial \nanisotropy Ku is determined as Ku = H k.Ms/2 [18]. Figure 2(a) shows Ku as a function of the Pd \nspacing thickness. It is clearly seen that the in sertion of Pd space layers reduces the uniaxial \nanisotropy of the multilayers. As the thickness of th e Pd space layers increases from 1.0 nm to \n2.0 nm, the Ku decreases from 1.77×105 J/m3 to 1.14×105 J/m3 which is consistent with the 1/ t \nlaw.  Such a high Ku is comparable to other common multilayer PMA films used in spintronics \n(discussed in the previous paragraph). The uni axial anisotropy allows the domain wall thickness \nto be estimated using the relation: /u AKπΔ≈ with A is the exchange constant. Assuming A ~ \n10 pJ/m (typically for Co-based magnetic thin films), the domain wall thickness is about 20-25 \nnm in scale of that in the Co/Pd multilayers and other Co-based multilayers [23]. Additionally, \nthe exchange interaction length can be deduced from the Ms by using the \nrelation2\n0 2/ex slA M μ= . This value is in range of 7-12 nm, which is about the overall thickness \nof the multilayers, supporting the thin magnetic layers in the multilayers to ferromagnetically \ncouple to each other. \nTo understand the magnetic anisotropy in our  samples, micromagnetic simulations of \ndomain structure for out-of-plane and in-plane  induction components were performed using LLG \ncommercial simulator [11]. Figure 3 depicts simulated domain pattern in the multilayer with the Pd thickness of 1.0 nm at demagnetized state as a typical picture (the si mulated domain patterns \nof the other samples look similar to  this picture – data not shown) . A stripe-like domain structure, \nwhich looks similar to that of the PMA FePd film  reported previously [24]  is observed in all the \nmultilayer samples with a very well-defined peri od of about 400 nm, and mostly unchanged with \nthe Pd spacing thickness. This is also the size of the domains in some PMA multilayers based on Co [19,25]. For the stripe domains, it is important to take into account the quality factor which is \ngiven by [25]: \n2\n02u\nsKQMμ=       ( 2 )  \nIn our studied multilayers, the Q factor ranges from 3.5 to 7.6,  indicating that the anisotropy \nenergy term is dominant to form a sharply define d domain state as seen in Fig. 3(a) with the \nBloch-type domain walls extendi ng right up the surface of the f ilms with a weak Néel caps in \nsimilar size of the Bloch walls as described in previous reports [24,26]. The simulated results \nshown in Fig. 3 somehow affirm this suggestio n. Namely, perfectly perpendicular magnetization \nin the domains is obviously visibl e via the blue-red colo r whilst the Néel caps  are visualized as \nthe in-plane components located at the domain walls [Fig. 3(b)]. These in-plane Néel caps are \nsupposed to be the contribution to the less-squareness in the perpendicular loops as seen in Fig. 1. \nIn the application points of view, if the films are used in domain wall devices, the Néel caps \nwould help the walls to nucleate easier. \nThe final important aspect is to discuss about  the electronic structur e and spin polarization \nof the films revealed using XAS and XMCD. Fi g. 4(a,b) shows the XAS and XMCD at Fe L3,2 \n(i.e. Fe 2 p Æ Fe 3 d transitions) and Co L3,2 edges (i.e. Co 2 p Æ Co 3 d transitions). Thus, because \nof dipole selection rule, these transitions ar e element specific and extremely sensitive to \nelectronic structure and spin  polarization at the Co 3 d and the Fe 3 d bands. Due to strong core \nhole spin-orbit coupling, XAS at Co L3,2 edges show main two peaks, at ~778 eV for L3 and at \n~794 eV for L2, while XAS at Fe L3,2 edges shows main two strong peaks, at ~708 eV for L3 and \n~721 eV for L2 in the CoFe layers. In Fig. 4(a), we present XAS (using circ ular polarized light \nwith different direction of ma gnetic field with respect to th e normal surface of sample) and \nXMCD on CoFe layers of the multilayer film with a Pd spacing thickness of 1.0 nm as a typical example. A magnetic field of ±10 kOe is applie d out-of-plane direction and the XMCD signal is \ndeduced by subtracting two XAS signals at the opposite magnetic field directions, namely \npositive and negative fields. We have fabricated Co and Fe films (~200 nm thick) and used them as the reference samples to calibrate and compare XAS and XMCD signals [Figs. 4(c,d)]. In the XMCD signal, we observe strong ferromagnetic prope rties in the films, which can be referred as \ntwo well-defined peaks at both edges, L\n3 and L2 of Co and Fe. This is strong evidence that the \nintrinsic ferromagnetism in our CoFe/Pd multilayers results from the Co 3 d and Fe 3 d states, \nessentially. The enhancement of the normalized  peak in the XMCD signal of the CoFe/Pd \nmultilayer films comparing to those of Co and Fe reference signals [Figs. 4(c,d)] indicates the \nstrong ferromagnetic interaction between Co-Fe ions  in the CoFe lattice which is well-known as \nthe origin of the high magnetic moment  in the Co-Fe alloy system [27]. \nOne of great advantages of XMCD data is it s capability to reveal the spin and orbital \nmagnetic moments [28]. By applying the X-ray MC D sum rule [29,30], we have estimated spin \nmagnetic moment ( μS)  and orbital magnetic moment ( μL) based on the following equations: \n()6( ) 4 ( )71 33 210 13 cos ( ) 232ddT LL Lznsd CPD d S LLzμμω μμω\nμθμ μ ω⎛⎞ −− − ⎛⎞ ∫∫ + +− +−⎜⎟ ⎜⎟=− × × − +⎜⎟ ⎜⎟ ×+ ∫ ⎜⎟ ⎜⎟ ++−⎝⎠ ⎝⎠\n (3) \n()32\n3234( )110cos 3( )LL\nL d\nLLd\nnCPD dμμω\nμθ μμω+−+\n+−+⎛⎞ −⎜⎟=− × × −⎜⎟× +⎝⎠∫\n∫    (4) \nwhere n3d is the 3 d electron occupation number, < Tz> is the expectation va lue of magnetic dipole \noperator, < S > is equal to half of the mspin in Hartree atomic units, θ is photon incident angle \nwhich is 0o, and CPD  is circular polarization degree wh ich is 0.8. Based on band structure \ncalculations, the < Tz>/<Sz > is negligible. From the elementa ry magnetic moments of Co and Fe atoms, magnetic moments of the Co 70Fe30 composition in the CoFe/P d multilayers are calculated \nby combining those of Co and Fe. The results are shown in  Figures 4(e-g). \nThe spin magnetic moment observed in the XMCD signals [Figs. 4(e,g)] reveals that spin \npolarization  ( P), which is associated to the spin magnetic moment ( µs) [31] (() s PNN μ↑↓=− ), \nis evidenced. As a result, by normalizing the spin magnetic moment of the CoFe/Pd multilayer \nfilms to the reference Co and Fe films, the sp in polarization in the CoFe/Pd multilayer films can \nbe estimated. It is assumed that the spin polari zation of Fe is ~43-45% [22,27]. Then, the spin \npolarization in the studied CoFe/Pd-based multilaye rs can be qualitatively evaluated to be ~45-\n60%, and better than the spin polarization of the Co-based multilayers (e.g. 56% in Pt/Co multilayer) [32].\n It should make a note that the CoFe-based multilayer obtained in this study can \nbe competitive with the well-known Co-based  multilayers for the spin-transfer torque \napplications because of their controllably low Ms, high Ku, narrow Bloch wa ll and high spin \npolarization. From the techni cal point of view, using of alloy layers (in this case Co 70Fe30 ally \nlayers) would bring benef it in stabilization of device structur e and properties. Commonly, layers \nof the multilayers are in few Angstrom thick and the PMA would be logically threatened by heat \nreleased from the electrical current due to the diffusion between the layers. Close packed structure of the alloy magnetic la yers would help to prevent the diffusion to enhance the thermal \nstability of the devices.  \nInterestingly, Figs. 4(e,g) show that spin  magnetic moment and total magnetic moment \napparently decrease by varying the Pd spacing thickness. This is in good agreement with our \nAGFM result [Fig. 2(a,c)]. Because the thickness of  the CoFe magnetic layers is fixed, such \ndecreases can be assigned to the contribution of the in terfacial magnetic moment of the CoFe/Pd interfaces, which varies with Pd thickness. This is an evidence to prove that the interfacial \nanisotropy significantly affects the ma gnetic anisotropy of the films.  \n4. Conclusions \nIn conclusion, the Co 70Fe30/Pd multilayers with strong pe rpendicular magne tic anisotropy \nand modifiable magnetic properties have been fa bricated. Saturation magnetization as low as 155 \nemu/cc and narrow Bloch-wall type as thin as 20 -25 nm are obtained by increasing the Pd layer \nthickness to 2.0 nm to reduce the interlayer  exchange coupling. Using XAS and XMCD \nmeasurements, spin polarization is observed an d estimated (~43-60%) to be higher in the very \nthin CoFe layers than those in the thicker Co  and Fe films. Furthermore, the XAS and XMCD \nspectra reveal the modification of electronic st ructure of CoFe/Pd interfacial magnetic moments \nby changing the Pd spacing layer,  contributing to the magnetic properties of the films. These \nadvantages indicated that our studi ed CoFe/Pd multilayers are of s uperior characteristics for spin-\ntorque applications. \n \nACKNOWLEDGEMENTS \nThis work was completed by a financial support  from the A*STAR (SERC) Public Sector \nFunding (Grant No. 092 151 0087) . We also acknowledge MOE- AcRF-Tier-2 and CRP Awards \nNo. NRF-CRP 8-2011-06 and NRF-CRP 8-2009-024 for the works performed at Singapore \nSynchrotron Light Source. D.-T. Ngo would like to  thank Prof. Michael R. Scheinfein (Arizona \nState University in Tempe, Arizona) for his kind support in LLG simulation. \nReferences \n[1] M. T. Johnson, P. J. H. Bloemen, F. J. A. den Broeder, and J. J. de Vries, Rep. Prog. Phys. \n59 (1996) 1409. [2] M. De Santis, R. Baudoing-Savois, P. Dolle, a nd M. C. Saint-Lager, Phys. Rev. B 66 (2002) \n085412. \n[3] C. M. Günther, O. Hellwig, A. Menzel, B. Pfau, F. Radu, D. Makarov, M. Albrecht, A. \nGoncharov, T. Schrefl, W. F. Schlotter, R. Ri ck, J. Lüning, and S. Eisebitt, Phys. Rev. B 81 \n(2010) 064411. \n[4] H. Nomura, R. Nakatani, Appl . Phys. Express 4 (2011) 013004..  \n[5] C. Brombacher, M. Grobis, J. Lee, J. Fidler , T. Eriksson, T. Werner, O. Hellwig and M. \nAlbrecht, Nanotechnology 23 (2012) 025301 (2012).  \n[6] R. Sbiaa, H. Meng, and S. N. Piramanaya gam, Phys. Stat. Sol. (RRL) 5 (2011) 413.  \n[7] T. Koyama, D. Chiba, K. Ueda, K. Kondou, H. Tanigawa, S. Fukami, T. Suzuki, N. \nOhshima, N. Ishiwata, Y. Nakatani, K. Kobayash i, and T. Ono, Nat. Mater. 10 (2011) 194.  \n[8] H. Szambolics, J.-Ch. Toussaint, A. Marty, I. M. Miron, and L.D. Buda-Prejbeanu, J. Magn. \nMagn. Mater. 321 (2009) 1912. \n[9] C. Burrowes, A. P. Mihai, D. Ravelosona, J.-V . Kim, C. Chappert, L.  Vila, A. Marty, Y. \nSamson, F. Garcia-Sanchez, L. D. Buda-Prejbea nu, I. Tudosa, E. E. Fullerton, and J. -P.  \nAttané, Nat. Phys. 6 (2010) 21.  \n[10] X. J. Yu, O. Wilhelmi, H. O. Moser, S. V. Vidya rai, X. Y. Gao, A. T. S. Wee, T. Nyunt, H. \nQian, and H. Zheng, J. Electron Spec trosc. Relat. Phenom.144–147 (2005) 1031. \n[11] Available at: http://llgmicro.home.mindspring.com/  \n[12] S.N. Piramanayagam, M.J. Liau, J.Z. Shia, and B.C. Lim, J. Magn. Magn. Mater. 303 \n(2006) e152. \n[13] D.-T. Ngo, Z. L. Meng, and K.-L. Teo (submitted to IEEE Trans. Nanotech.). \n[14] S. Okamoto, O. Kitakami, and Y. Sh imada, IEEE Trans. Magn. 35 (1999) 3031. [15] J.-S. Ma, H.-C. Koo, J.-W. Eom, J.-Y. Chang, S.-H. Han, and C.-W. Kim, Elec. Mater. Lett. \n3 (2007) 87. \n[16] K. Shintaku, Y. Daitoh, and T. Shinjo, Phys. Rev. B 47 (1993) 14584. \n[17] P .  J .  M e t a x a s ,  J .  P .  J a m e t ,  A .  M o u g i n ,  M .  C o r m i e r ,  J .  F e r r é ,  V .  B a l t z ,  B .  R o d m a c q ,  B .  Dieny, and R. L. Stamps, Phys. Rev. Lett. 99  (2007) 217208.  \n[18]\n S. Fukami, T. Suzuki, Y. Nakata ni, N. Ishiwata, M. Yamanouchi, S. Ikeda, N. Kasai, and H. \nOhno, Appl. Phys. Lett. 98 (2011) 082504.  \n[19] M. Yamanouchi, A. Jander, P. Dhagat, S. Ik eda, F. Matsukura, and H. Ohno, IEEE Magn. \nLett. 2 (2011) 3000304.  \n[20] D-T. Ngo, K. Ikeda, and H. Awano, Appl. Phys. Express 4 (2011) 093002. \n[21] M. Tofizur Rahman, X. Liu, M. Matsumoto, and A. Morisako, IEEE Trans. Magn.41 (2005) \n2568.  \n[22] C.-X. Ji, Feng Lu, Y. Austin Chang, J. Josh ua Yang, and M. S. Rzchowski, Appl. Phys. \nLett. 92  (2008) 022504. \n[23] T. Kato, S. Tsunashima, and S. Iwata, IEEE Trans. Magn. 42 (2006) 2972.  \n[24] P. R. Aitchison, J. N. Chapman, V. Gehanno, I. S. Weir, M. R. Sche infein, S. McVitie, and \nA. Marty, J. Magn. Magn. Mater. 223 (2001) 138.  \n[25] C. H. Marrows, Adv. Phys. 54 (2005) 585.  \n[26] M. Viret, Y. Samson, P. Warin, A. Marty, F. Ott, E. Søndergård, O. Klein, and C. Fermon, \nPhys. Rev. Lett. 85 (2000) 3962.  \n[27] J. M. D. Coey: Magnetism and Magnetic Mate rials (Cambridge Univ ersity Press, 2010) \nISBN-13 978-0-511-67743-4. \n[28] A. Rusydi, S. Dhar, A. Roy Barman, Ariando , D.-C. Qi, M. Motapothula, J. B. Yi, I. \nSantoso, Y. P. Feng, K. Yang, Y. Dai, N. L. Yakovlev, J. Ding, A. T. S. Wee, G. Neuber, M. B. H. Breese, M. Ruebhausen, H. Hilgenka mp, and T. Venkatesan, Phil. Trans. R. Soc. \nA 370 (2012) 4927. \n[29] B. Thole, P. Carra, F. Sette, and G. van der Laan, Phys. Rev. Lett. 68 (1992) 1943. \n[30] P. Carra, B. Thole, M. Altarelli, and X. Wang, Phys. Rev. Lett. 70 (1993) 694. \n[31] T.-S. Choy, J. Chen and S. Hershfield, J. Appl. Phys. 86 (1999) 562. \n[32] A. Rajanikanth, S. Kasai, N. Ohshima, and K. Hono, Appl. Phys. Lett. 97 (2010) 022505. Figure captions \nFIG. 1. Magnetic hysteresis (M-H) loops of the CoFe/Pd multilayers with different Pd spacing \nthickness. The loops with circle dots were measured  out-of-plane of the films, and the dash plots \ndenoted the in-plane loops. FIG. 2. Linear dependence of the saturation magnetization, M\ns (a) and the uniaxial anisotropy, Ku \n(b) on the inversed thickness (1/ t) of Pd spacing layer. The inset shows anisotropy field, Hk, as a \nfunction of Pd spacing thickness. FIG. 3. Simulated domain pattern in the CoFe/Pd multilayer with a spacing thickness of 1.0 nm: (a) out-of-plane induction component and (b) in-p lane induction components. The images size is \n10 µm. FIG. 4. (a,b) X-ray absorption (XAS) and X-ray magnetic circular dichroism (XMCD) spectra of \nthe Fe and Co atoms in the CoFe/Pd multilayer with a spacing thickness of 1.0 nm. (c,d) XAS and XMCD spectra of the Fe and Co atoms in thic k reference Fe and Co films. (e,f) Particular \nelementary spin magnetic moment (\nμs), orbital magnetic moment ( μL) of Fe and Co atoms in the \nCoFe/Pd multilayers derived from XMCD spectr a. (g) Spin magnetic moment, orbital moment \nand total magnetic moment of Fe 70Co30 composition in the CoFe/Pd multilayers.  \n  \n \n  \nFIG. 1. \n \n  \n \n  \nFIG. 2. \n   \nFIG. 3. \n \n    \n  \nFIG. 4. "    },    {        "title": "1306.6451v1.Amorphous_GdFeCo_Films_Exhibiting_Large_and_Tunable_Perpendicular_Magnetic_Anisotropy.pdf",        "content": "1 \n Tunable perpendicular magnetic  anisotropy  in GdFeCo \namorphous films  \n \nManli Dinga) and S. Joseph Poona) \nDepartment of physics, University of Virginia, Charlotte sville, Virginia 22904, USA     \nAbstract  \n       We report  the compositional and temperature dependence  of magnetic compensation  in \namorphous ferrimagnetic Gd xFe93−xCo7 alloy  films. Magnetic compensation is  attributed to the \ncompeti tion between  antiferromagnetic coupling of rare-earth ( RE) with transition -metal ( TM) \nions and ferromagnetic interaction between the TM ions. The low-Gd region of x between 20 and \n34 was found to exhibit compensation phenomena characterized by a low saturation \nmagnetization  and perpendicular magnetic anisot ropy (PMA) near the compensation tempe rature . \nCompensation temperature  was not observed in previously unreported high-Gd region of x= 52-\n59, in qualitative agreement  with results from recent model calculations. However, low \nmagnetization was achieved  at room temperature , accompanied by a large PMA with coercivity \nreaching ~6.6 kOe . The observed perpendicular magnetic anisotropy of amorphous GdFeCo \nfilms probably ha s a structural origin consistent with certain aspects of the atomic -scale \nanisotropy.  Our findings have broadened the composition range of transition metal -rare earth \nalloy s for design ing PMA  films , making it  attractive for tunable magnetic anisotropy in  \nnanoscale devices.  \n \nKeywords  \nMagnetic Compensation; RE -TM ferromagnetic alloy; Perpendicular Magnetic Anisotropy  \n                                                           \na)Electronic mail: md3jx@virginia.edu , sjp9x@virginia.edu . \n 2 \n 1. Introduction  \n      Magnetic materials with perpend icular magnetic anisotropy (PMA)  have attracted large \ninterest over the past few years  from the viewpoint of both academic research and technological \napplications. It is predicted that magnetic tunnel junctions or spin valves with perpendicularly \nmagnetized electrodes are able to facilitate  faster and smaller data -storage magnetic bits, \ncompared with the normal in -plane ones  [1]. For device s, it is preferable to use a single film \nlayer with perpendicular magnetic anisotropy instead of multilayer in order to avoid complicated \nfabrication process and decrease the total thickness of the devices. One well -known candidate  is \namorphous rare -earth  transition -metal (RE –TM) thin films with strong perpendicular magnetic \nanisotropy  [2,3,4] . \nAmorphous  GdFeCo  films have been known to have a low saturation magnetization, \npreventing magnetization curling at the film edge. Furthermore, they possess Curie temperatures \nwell above room temperature for a wide range of compositions  [5].  Gd is a unique  member of \nthe lanthanide series in that its ground -state electronic configuration is 4 f 7(5d6s)3 with the \nhighest possible number of majority  spin electrons and no minority spin electron in its 4f state \naccording to Hund’s rule. In addition, because the 4 f states  of Gd are half filled , their orbital \nmoment and spin -orbit coupling are zero. This L=0 state of Gd provide s a favorable condition for \nlow Gilbert damping, which is preferable in spin -torque -transfer devices.  Amorphous GdFeCo \nalloys are ferrimagnets in which the Fe (Co) sublattice s are  antiferomagnetically coupled to the \nGd sublattice  in a collinear alignment , while the exchange coupling in the Fe (Co) sublattice  is \nferro magnetic  [6]. These f errimagnetic  GdFeCo alloys tend to exhibit magnet ic compensation  \nbehavior  characterized by a vanishing  magnetization below the Curie temp erature  [7]. Also , \ndepending on the composition, amorphous  GdFeCo  films generally possess a uniaxial anisotropy 3 \n with an anisotropy axis either perpendicular or parallel to the film plane .  \nIn this study,  we have obtained amorphous GdFeCo films for a wide range of Gd content  via \nthe combinatorial growth technique.  We have investigated the compositional and temperature \ndependence of magnet ization  compensation in these amorphous  ferrimagnetic Gd xFe93-xCo7 \nfilms  and demonstrated the tunability of perpendicular magnetic anisotropy . Possible \nmechanism s for the observed perpendicular magnetic anisotropy  are discussed.   \n2. Experimental procedure  \n       The GdxFe93-xCo7 (GdFeCo)  films were  prepared at ambient temperature on thermally \noxidized Si substrates using  rf magnetron sputtering . The base pressure of the sputtering c hamber \nwas ~ 7\n 10-7 Torr. GdFeCo alloy films were deposited by means of co -sputtering with the \nelemental targets under a processing Ar gas pressure around 5\n 10-3 Torr. The capping MgO  \nlayer was formed directly from a sintered MgO target to protect GdFeCo layer from oxidation. \nAll the samples de posited at room temperature had  a typical structure consisting  of \nSi(100)/SiO 2/Gd xFe93-xCo7(15   x   59 at. %)/MgO(6 nm) with a fixed thickness of GdFeCo \nlayer ~  50 nm. The film thickness  of all samples were measured by x -ray reflectivity, and film  \ncomposition s were  determined using inductively coupled plasma -mass spectrometry (ICP -MS) \nafter chemically dissolving the films, and confirmed by X -ray fluorescence (XRF) using peak \nratios.  The magnetic properties of the samples were inv estigated by  vibrating sample \nmagneto meter ( VSM ) and magneto -optic Kerr effect  (MOKE)  measurements, with a maximum \nfield of 20 kOe. Structural characterization of the films were performed by x -ray diffraction \n(XRD) with Cu Kα (λ = 1.541 Å) radiation (Smart -lab®, Rigaku Inc.) and tran smission electron \nmicroscopy ( TEM, FEI Titan ). Atomic Force Microscopy (CypherTM, Asylum Research Inc.) \nwas used to characterize surface morphology.  4 \n 3. Results and discussions  \n      The amorphous structure s of the as-deposited samples were  confirmed by TEM and XRD \nobservations . Fig. 1(a) shows a typical cross -sectional TEM image obtained from as -deposited  \nGd22Fe71Co7 film on the Si / SiO 2 substrate. The microstructure was  dense with no visible cracks \nor holes, and  all layers in the structure were  well adhered to each oth er. The uniform thickness of \nGd22Fe71Co7 film was  measured to be 52  nm in Fig.  1(a). The high resolution TEM image in Fig. \n1(b) revealed  the feature less nanoscale  structure  that indicated  the lack of long -range  order. The \nbroad ring pattern in the fast Fourier -transform  (FFT)  image  in the inset of Fig.  1(b) indicated  the \nlack of crystallinity . In addition, XRD scans  showed that there were no diffraction peaks other \nthan th ose from the substrate for Gd FeCo films with different compositions  (not shown here).  \nThe XRD results were consistent with the TEM, ind icating that all the as-deposited samples were  \namorphous  in nature , without the formation of a long -range structural order.  Atomic force \nmicroscopy (AFM) measurements show ed that the surfaces were free of pinholes and were flat \nwith roughness  less than  1 nm.  \n3.1. Low Gd -content films  \n       The magneti zation of GdFeCo films were characterized in the in -plane and out -of-plane \ndirections using the VSM option in Quantum Design VersaLab. Fig. 2 shows the temperature \ndependence of saturation magnetization of as -deposited GdFeCo films for several compositions.  \nSaturation magnetization ( Ms) was extracted from the hysteresis loop s measured as a function of \ntemperature between 100 K and 400 K.   Compensation temperature  (Tcomp) was defined as the  \ntemperature at which Ms(T) reached its minimum.  The saturation moment s at the compensation \ntemperature s were below 100 emu/cc. The observed small saturation moment  was due to the \nferrimagnetism of amorphous RE -TM alloys. The TM-TM ferromagnetic interaction aligns the 5 \n magnetic mom ents among Fe and Co ions, which are coupled antiferromagnetic ally with the \nmagnetic moments of Gd . As a result, the net moment is the differen ce between the magnetic \nmoment s of Gd and Co( Fe). At the compensation temperature, the moments  of the two magnetic  \nsublattices were  nearly equal, giving rise to a low saturation magnetization .  \n      Due to the different temperature dependence of the sublattice magnetizations, compensation \ntemperature can be varied, depending on the compositions. The variation of Ms with temperature  \n(Fig. 2)  resembled  the expected compensation  behavior when approaching the compensation \npoint. The GdFeCo films with x= 22,  27 and 30 at. % exhibit ed the compensation temperatures \nTcomp at 300 K, 350 K and 378 K, respectively . However, for several other compositions , there \nwas no compensation point  within the investigated temperature interval from 100 to 400 K . For \nGd35Fe58Co7 film, the compensation point was not obtained due to the limitation of the \nmeasurement temperature range. For the sample  Gd15Fe78Co7, the dependence of saturation \nmagnetization on T (not shown) indicated that the magnetization of the Fe(Co) sublattice s \nexceed ed the magnetization of the Gd sublattice in the whole temperature range. This was due to \nthe fac t that ferromagnetic exchange of the Fe (Co) sublattice s dominate s the magnetic behavior \nat low Gd content . As the Gd content increases  and Fe (Co) content decreases , there is a  \ncorresponding increase in the antiferromagnetic coupling relative to the ferromagnetic exchange , \nand magnetic compensation emerges.  Further increase in the Gd concentration resulted in the \nincrease in Tcomp, as shown in the inset to Fig. 2.  \n      According to magnetization measurement s, the perpendicular magnetic anisotropy in  \nGdFeCo films appeared near their compensation temperatures , whereas otherwise the magnetic \neasy axis was in -plane . Fig. 3(a) shows the typical normalized out -of-plane hysteresis loops of \nthe as -deposited Gd 27Fe66Co7 films at various temperatures . At 250K, far from Tcomp~350K, 6 \n magnetization was  dominated by in -plane anisotropy. Near the compensation point, \nperpendicular magnetic anisotropy was dominant, and a square hysteresis loop was established in \nthe out -of-plane direction with coercivity near 100 Oe .  \n       From the magnetization variation curve  (Fig. 2) , the Gd 22Fe71Co7 film had magnetic \ncompensation temperature at room temperature , which has particular technological importance  \n[8]. Fig. 3(b) shows the room -temperature  in-plane and out -of-plane hysteresis (M -H) loops of \nthe 50 nm Gd 22Fe71Co7 film, indicating that this composition has PMA with out -of-plane \ncoercivity of about  360 Oe. The total perpendicular anisotropy energy density ( Ku), which \ndetermin es the thermal stability, was  3.8 \n105 erg/cm3, as calculated by evaluating the area \nenclosed between the in -plane and perpendicular M -H cur ves [9].  The out -of-plane loop showed  \nsharp, square switching characteristics with a squareness of one (1). For Gd 22Fe71Co7 film, a \nrelatively small concentration of the high -moment RE magnetically compensate d the lower \nmoment TM  at room temperature . Since the tunneling current in spintronics devices is dominated \nby that from the highly polarized TM atoms, this material  would be very useful for device \napplications because it would eliminate magnetic dipole fields that can give rise to significant \nmagnetic coupling within and between devices.  \n       The above results underline d the fact that in GdFeCo system, the magnetization anisotropy  \nmay be easily tuned by adjusting the composition and/or the temperature. In the low-Gd region \nof x between 20 and 34 , the Gd sublattice dominated  the overall magnetization of the system  \nbelow the compensation  temperature. However, Above Tcomp the magnetization o f the Fe(Co) \nsublattice prevailed  and the total magnetization of the  system continuously increased  on further \nwarming. Since the magnetic anisotropy ca n vary around this temperature, Tcomp is an important \nparameter that ensures the stability of the stored information .  7 \n 3.2. High Gd -content films  \n      At room temperature , amorphous GdFeCo films with Gd concentrations varying between 52% \nand 59% were  found to exhibit low magnetization . Fig. 4 shows the temperature dependence of \nsaturation magnetization of as-deposited GdFeCo films for Gd concentrations at 54% and 57%.  \nThe magnetization decreased  precipitously  with increas ing temperature  and finally decreased to \nnear zero between 370 and 400 K . Magnetic compensation temperature was not observed in this \ncomposition  region , which was  consistent with some  recent ly reported  computational results  on \nGdFeCo  films [10]. The film compositions  with 54 and 57 at. % Gd exhibited  Curie \ntemperature s at 375 K and 400 K, respectively , much lower than 500 K of the composition with \n22 at. % Gd [11]. These  can be attributed to a stronger role of antiferromagnetic coupling at high \nGd content, which also tended to reduce the Curie temperature.   \n      In view of the  low magnetization , perpendicular magnetic anisotropy w as investigated at \nroom temperature  for Gd content between  52% to 59%. Fig. 5(a) shows the compositional \ndependence of out-of-plane  coercivity ( Hc) and saturat ion magnetization ( Ms) of 50 nm as -\ndeposited perpendicularly magnetized GdFeCo films for x between 52  and 59 . With the \nincreasing content of Gd, Ms decreased  from 100 to 55 emu/cc at x=57, then increas ed to 84 \nemu/cc at x=59. However, the out-of-plane  coerci vity showed  an opposite trend , which increased  \nwith increasing Gd concentration and was  greatest in the sample with  57 at. % Gd. Fig. 5(b) \nshows the typical hysteresis  loops of as -deposited Gd 57Fe36Co7 film with thickness of 50 nm. A \nclear perpendicular anisotropy was realized with out -of-plane coercivity Hc = 6.6 kOe. The total \nperpendicular anisotropy energy density Ku, which determined the thermal stability, was  2.6\n 105 \nerg/cc. Generally, the RE ions exhibit large local magnetic anisotropy due to its spin -orbit \ncoupling.  Gd is in the L=0 state , spin-orbit coupling is supposed to be small ; however, the 5d  8 \n electrons have finite spin -orbit coupling which can be partially responsibl e for this anisotropy. \nBecause of their large  out-of-plane coercivity, ferrimagnetic GdFeCo films in the composition \nrange 52 ≤ x ≤ 59 can be of technological  importance in the area of the thermomagnetic \nrecording devices. \n3.3. Discussion  \n      Perpendicular magnetic anisotropy at room temperature was found in the compositions near \n23 and 57 at. % Gd. Since  amorphous alloys  lack structural long-range  order , one might expect \nthat atomic -scale structure plays a n important  role in determining the pr operties of these  alloy s. \nStudies have attempted to correlate the magnetic anisotropy of amorphous RE-TM films with \nvarious structural characteristics ranging from columnar textures  [12] to microcrystallinity [13] to \nlocal magnetic anisotropy or/and  atomic -scale anisotropy [14,15,16] . Cross -sectional TEM  study  \n(Fig. 1)  failed to detect nanoscale columnar growth and microcrystallinity in the amorphous \nGdFeCo films. As discussed above, l ocal magnetic anisotropy of rare earth atoms does not play a \nrole in Gd -Fe-Co, unlike other rare e arth elements such as Tb and Dy;  and yet amorphous Gd -\nFe-Co films show robust PMA behavior with a large Hc comparable to that of amorphous Tb -Fe-\nCo films [17]. These findings suggest that the observed perpendicular magnetic anisotropy in \namorphous GdFeCo films probably has a structural origin involving atomic -scale anisotropy. \nThis atomic -scale  order can be anisotropic in as -grown films, which influences the short -range \nexchange interaction , leading to anisotropic  properties. The perpendicular anisotropy may arise \nfrom the change  in nearest neighbor distance and the coordination numbers for RE and TM \nsublattices  which can affect the short range order. \n \n 9 \n 4. Conclusion  \n      In summary, it  was shown that the magnet ic anisotropy  of amorphous ferri magnetic Gd xFe93-\nxCo7 films can be controlled by varying the composition as well as temperature. The low-Gd \nregion of x between 20  and 34  were  found to exhibit compensation phenomena characterized by \na low saturation magnetization and pe rpendicular magnetic anisotropy near the compensation \ntemperature.  Furthermore, l ow magnetization s and perpendicular magnetic anisotropy with large \ncoercivit y of 6.6 kOe were  observed at room temperature in previously unreported composition \nrange of 52-59 at. % Gd. No compensation temperature was measured in this range , which was \nconsistent with recent model calculations.  The observed perpendicular magnetic anisotropy in \namorphous GdFeCo films probably ha s a structural  origin consistent with certain aspects of the \natomic -scale anisotropy.  Our results have provide d a way to fabricate GdFeCo films  with tunable \nmagnetic anisotropy  by varying the composition or/and temperature , making these amorphous \nfilms attractive for future nanomagnetic  devices.  \n \n \n \nAcknowledgements     \n      We thank Dr. T. Paul Adl in Micron Techology for helpful composition measurements  and \nProf. Jiwei Lu (University of Virginia)  for stimulating discussions . This work was carried out \nunder the  financial support of DARPA through a subcontract with Grandis Inc.   \n \n \n 10 \n References  \n \n[1] A. D. Kent, B. Ozyilmaz, and E. del Barco,  Appl. Phys. Lett.  84, 3897 (2004) . \n[2] M. Nakayama, T. Kai, N. Shimomura, M. Amano, E. Kitagawa, T. Nagase, M. Yoshikawa, T. Kishi, \nS. Ikegawa, and H. Yoda, J. Appl. Phys.103, 07A710 (2008).  \n[3] Ching -Ming Lee, Lin -Xiu Ye, Jia -Mou Lee, Wan -Ling C hen, Chao -Yuan Huang, Gung Chern, and \nTe-Ho Wu, IEEE T rans. Magn. 45, 3808  (2009 ). \n[4] T. Hauet, F. Montaigne, M. Hehn, Y. Henry, and S. Mangin, Appl. Phys. Lett. 93, 222503 (2008).  \n[5] P. Hansen, J. Magn. Magn. Mater. 83, 6 (1990).  \n[6] O. S. Anilturk and A. R. Koymen, Phys. Rev. B 68, 024430 (2003).  \n[7] Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, and Y. Kushiro, J. Appl. Phys. 49, 1208 (1978).  \n[8] X. J. Bai, J. Du, J. Zhang, B. You, L. Sun, W. Zhang, X. S. Wu, S. L. Tang, and A. Hu, J. Appl. Phys. \n103, 07F305 (2008).  \n[9] M. T. Johnson, P. J. H. Bloemen, F. J. A. den Broeder, and J. J. de V ries, Rep. Prog. Phys. 59, 1409 \n(1996).  \n[10] Thomas A. Ostler , Richard F. L. Evans , and Roy W. Chantrell , Unai Atxitia , Oksana Chubykalo -\nFesenko , Ilie Radu , Radu Abrudan , Florin Radu , Arata Tsukamoto , A. Itoh , Andrei Kirilyuk , Theo Rasing , \nand Alexey Kimel , Phys. Rev. B 84, 024407 (2011).  \n[11] C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk and Th. Rasing, Phys. \nRev. B 73, 220402(R) (2006). \n[12] H. J. Leamy and A. G. Dirks,  J. Appl. Phys.  50 (4), 2871 (1979).  \n[13] Y. Takeno, K. Kaneko, and K. Goto,  Japanese Journal of Applied Physics Part 1 -Regular Papers \nShort Notes & Review Papers 30 (8), 1701 (1991).  \n[14] L. Néel,  J. Phys.  Radium  12, 339 (1951) ; 13, 249 (1952) . \n[15] V. G. Harris, K. D. Aylesworth, B. N. Das, W. T. Elam, and N. C. Koon,  Phys.  Rev. Lett. 69, 1939  \n(1992) . \n[16] X. Yan, M. Hirscher, T. Egami, and E. E. Marinero,  Phys.  Rev. B 43, 9300  (1991) . \n[17] R. Shan, J. Du, X. X. Zhang, L. Sun, W. W. Lin, H. Sang, T. R. Gao, and S. M. Zhou, Appl. Phys. \nLett. 87, 102508 (2005).  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 11 \n Figure Captions:  \n \n \nFig. 1. (a) Cross -sectional TEM image of a s-deposited Gd 22Fe71Co7 film on SiO 2/Si substrate. 6 \nnm MgO layer was used to cap the film; (b) high -resolution TEM image of the Gd 22Fe71Co7 film.  \nThe inset is a FFT pattern of the image.  \n \nFig. 2. Temperature dependence of the saturation magnetization of as-deposited GdFeCo films \nwith various Gd concentrations  (x = 22, 27, 30 and 35 ).  The inset in (b) shows the dependence \nof the  magnetization compensation temperature Tcomp on the Gd concentration.  \n \nFig. 3. (a) Normalized out -of-plane hysteresis loops of as-deposited Gd 27Fe66Co7 film measured \nat 250, 300, and 350 K. (b) In -plane (black square ) and out -of plane (red  circle ) hysteres is loops \nof 50 nm as -deposited Gd22Fe71Co7 film. \n \nFig. 4. Temperature dependence of the saturation magnetization of GdFeCo films with various \nGd concentrations (x = 54 and 57).   \n \nFig. 5. (a) Gd -content dependence of M s (black  triangle ) and H c (blue  circle ) for perpendicularly \nmagnetized GdFeCo  films between 52 and 59 at. % Gd . (b) In-plane and out-of-plane hysteresis \nloops of Gd 57Fe36Co7 film with thickness at 50  nm.  \n \n \n \n \n \n \n \n \n \n 12 \n Figure 1:  \n \n \n \nFigure 2:  \n100 150 200 250 300 350 40050100150200250300350400450500\n20 25 30 35280300320340360380400\n  Ms (emu/cc)\nTemperature (K) Gd22Fe71Co7\n Gd27Fe66Co7\n Gd30Fe63Co7\n Gd35Fe58Co7\n  Tcomp (K)\nx (at. %)\n \n \n \n \n13 \n Figure 3:  \n-15000 -10000 -5000 0 5000 10000 15000-1.0-0.50.00.51.0\n-10000 -5000 0 5000 10000-100-80-60-40-20020406080100  M/Ms \nH (Oe) 250 K\n 300 K\n 350 K\n(b)\n  M (emu/cc)\nH (Oe) In plane\n Out of Plane\n(a)\n \n \nFigure 4:  \n100 150 200 250 300 350 400050100150200250300350400450500 \n Ms (emu/cc)\nTemperature (K) Gd57Fe36Co7\n Gd54Fe39Co7\n \n \n \n \n \n \n \n \n \n \n \n \n \n 14 \n  \nFigure 5:  \n-15000 -10000 -5000 0 5000 10000 15000-80-60-40-20020406080\n51 52 53 54 55 56 57 58 59 606080100\n(a) (b) \nHc (Oe) Ms\n Hc\nGd concentration (x at. %)Ms (emu/cc)\n01000200030004000500060007000\n \n  M (emu/cc)\nH (Oe) In plane\n Out of plane\n "    },    {        "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": "1307.5164v1.X_ray_diffraction_by_magnetic_charges__monopoles_.pdf",        "content": "15/VII/2013 \nX-ray diffraction by magnetic charges (monopoles) \nS W Lovesey 1,2 and D D Khalyavin 1  \n1. ISIS Facility, STFC Oxfordshire OX11 0QX, UK  \n2. Diamond Light Source Ltd, Oxfordshire OX11 0DE, UK \nAbstract  Magnetic charges, or magnetic monopoles, may form in the electronic \nstructure of magnetic materials where ions are depr ived of symmetry with \nrespect to spatial inversion. Predicted in 2009, th e strange magnetic, pseudo-\nscalars have recently been found different from zer o in simulations of \nelectronic structures of some magnetically ordered,  orthorhombic, lithium \northophosphates (LiMPO 4). We prove that magnetic charges in lithium \northophosphates diffract x-rays tuned in energy to an atomic resonance, and to \nguide future experiments we calculate appropriate u nit-cell structure factors \nfor monoclinic LiCoPO 4 and orthorhombic LiNiPO 4. \n1. Introduction \n Absence of spatial inversion symmetry on a local s cale in the electronic \nstructure of a magnetic material allows the formati on of atomic magnetic \ncharge [1]. This unusual entity is a scalar (monopo le) magneto-electric multipole \nthat is parity-odd and time-odd [2]. Magnetic charg e contributes to resonant x-\nray Bragg diffraction but not the corresponding dic hroic signals [1, 3]. There is \nsolid experimental evidence for magneto-electric di poles (anapoles) in vanadium \nsesquioxide [4, 5] and haematite [6]. Evidence for magnetic charges in gallium \nferrate is less convincing [7], and the prediction for its existence in haematite \nis not tested [6]. Interest in magneto-electric mul tipoles, and counterpart polar \nmultipoles that are parity-odd and time-even, stems  from their practical \nimportance, in device design and demanding tests of  simulations of the \nelectronic structure of complex materials, and nove lty, of course. \n Observation of magneto-electric multipoles require s a test with matching \ndiscrete symmetries, and x-ray absorption and scatt ering are candidate tools. \nParity-odd absorption derived from electric dipole - magnetic dipole (E1-M1) and \nelectric dipole - electric quadrupole (E1-E2) event s give access to magneto-\nelectric and polar multipoles with rank 0 - 2 and 1  - 3, respectively [1, 8]. Thus, anapoles contribute in both E1-M1 and E1-E2 events,  whereas magnetic charge is \nfound in E1-M1 only [9, 10]. \n Lithium orthophosphates of divalent manganese (lit hiophilite), iron \n(triphylite), cobalt, and nickel are members of the  olivine family of structures \n(some minerals in the family of structures possess the colour olive-green), with \nmagnetic motifs indexed on the chemical unit cell ( Γ-point) [11]. Cell dimensions \nof lithium orthophosphates permit Bragg diffraction  at L-edges, which are 2p → \n3d dipole-allowed in the soft x-ray region with a w avelength λ ≈ 14 Å. X-ray \ndiffraction is strongly enhanced by L 2,3  edges of 3d transition metal ions and \nmay display a weak E1-M1 event and, in consequence,  magnetic charge [7, 12, 13]. \n In this communication, we report electronic struct ure factors for \ntransition metal ions in lithium orthophosphates th at describe diffraction, of \nboth neutrons and x-rays, and dichroic signals. Res ults make use of established \nchemical and magnetic symmetries. Our findings with  regard to magnetic charge \naccord with ab initio  simulations of electronic structure in orthorhombi c \ncrystals [14]. It is shown here that, x-ray diffrac tion by LiNiPO 4 can confirm \nmagnetic charge predicted in simulations of this co mpound. A second example of \nthis kind is LiCoPO 4. For this compound magnetic charge is allowed in t he \nmonoclinic structure proposed by Vaknin et al [15],  while it is forbidden by \nsymmetry in the undistorted, orthorhombic structure  used in [14]. \n Orthorhombic, magnetic lithium orthophosphates are  discussed in \nSections 2, 3 and 4. In the next section their poin t symmetries and multipoles, \nfollowed, in Section 3, by electronic structure fac tors for bulk properties, \nneutron diffraction and x-ray diffraction.  Resonan t x-ray Bragg diffraction is \nthe subject of Section 4. The same topics  are covered in Section 5 for the \nmonoclinic compound LiCoPO 4. Conclusions are gathered in Section 6. \n2. Orthorhombic space groups and point-symmetry \n The chemical structure is orthorhombic Pnma-type w ith metal ions using \nsites (4c) that are not centres of inversion symmet ry. Crystal class D 2h  (mmm) \nis centrosymmetric. \n There are three magnetic motifs of interest for li thium compounds \nLiMPO 4 with M = Mn, Fe, Co and Ni, and we label them by t he corresponding \nparity-odd, one-dimensional irreducible representat ions (irrep) that are Γ−\n1, Γ−\n2, and Γ−\n4. Here we list the motifs, space-groups, crystal cl ass, and point symmetry \nof sites (4c) used by metal ions. (Magnetic space-g roups are specified in terms \nof the Miller and Love and Belov-Neronova-Smirnova notations. [16, 17]) \n Γ−\n1 : (m a, 0, m c) ( −ma, 0, m c) ( −ma, 0, −mc) (m a, 0, m c) Mn ions,  \n Pn'm'a', m'm'm', m y' \n Γ−\n2 : (0, m b, 0) (0, −mb, 0) (0, −mb, 0) (0, m b, 0) Fe & Co ions,  \n Pnma', mmm', m y \n Γ−\n4 : (m a, 0, m c) (m a, 0, −mc) ( −ma, 0, −mc) ( −ma, 0, m c) Ni ions,  \n Pnm'a, mm'm, m y'.      (2.1) \nMagnetic crystal classes that appear here occur in the 58 classes that allow a \nlinear magneto-electric effect. \n Electronic degrees of freedom of the magnetic ions  are encapsulated in \nirreducible, spherical multipoles. Our notation for  a generic spherical multipole \nis 〈OK\nQ〉, with a complex conjugate 〈OK\nQ〉* = ( − 1) Q 〈OK\n−Q〉, where the positive \ninteger K is the rank and Q the projection, which s atisfies   − K ≤ Q ≤ K [8, 18]. \nAngular brackets 〈 ... 〉 denote the time-average of the enclosed quantum-\nmechanical operator, i.e., a multipole is a propert y of the electronic ground-\nstate. Parity-even multipoles are denoted by 〈TK\nQ〉 and they have a time \nsignature σθ = (− 1) K. In x-ray scattering, they arise in a description of Thomson \nscattering and resonant Bragg diffraction enhanced by a parity-even event, e.g., \nE1-E1 and E2-E2 events. They arise also in a descri ption of neutron diffraction \n[8]. In this case, K is odd, and for nd-ions K has has a maximum value 5 \n(triakontadipole) and for nf-ions K has a maximum v alue 7 \n(octaeicosahecatontapole). For parity-odd events in  x-ray diffraction our \nnotation for multipoles is 〈UK\nQ〉 for time-even, polar and 〈GK\nQ〉 for time-odd, \nmagneto-electric [8, 18]. The time-odd pseudo-scala r 〈G0\n0〉 is magnetic charge, \n〈G1〉 is an anapole (toroidal dipole), and the time-even  pseudo-scalar 〈U0\n0〉 is \nchirality (helicity). The five standard dichroic si gnals (linear, circular, natural \ncircular, magneto-chiral and non-reciprocal linear)  can be written in terms of \nmultipoles, and expressions for them are found in r eference [3]. Magnetic charge can be represented by the scalar pr oduct of spin, S, and \nposition, R, operators with 〈G0\n0〉 = 〈S●R〉 [3, 9]. It is allowed in an E1-M1 event, \nwhere it contributes to diffraction in which polari zation is rotated, namely, σ→π \nand π→σ (Figure 1) [1]. The physical content of multipoles  in resonant Bragg \ndiffraction is brought out in the sum-rules they ob ey. For diffraction enhanced \nby L-edges, parity-even dipoles (K = 1) satisfy, \n  〈T1〉 L2  + 〈T1〉 L3  = − 〈L〉3d /(10 √2),     \nwhere 〈L〉3d is orbital angular momentum in the 3d-valence state , and quadrupoles \n(K = 2) satisfy, \n  〈T2〉L2  + 〈T2〉L3 = 〈{L ⊗ L}2〉d/60,      \nwhere the tensor product { L ⊗ L}2 has for its diagonal component (Q = 0) a value \n{L ⊗ L}2\n0 = [3L 2\nz − L(L + 1)]/ √6, which demonstrates affinity to a standard, \nparity-even quadrupole operator. For magneto-electr ic dipoles one finds, \n  〈G1〉 L2   + 〈G1〉 L3  = − 〈[R x ( L + 2S)] 〉3d /(2 √2),    \nwhich demonstrates that 〈G1〉 is related directly to standard spin and orbital \nanapoles. \n2.1 consequences of point-group symmetry  \n There are two site symmetries to consider, namely,  m y and m y'. Site \nsymmetry is implemented using 2 y 〈OK\nQ〉 = ( − 1) K 〈OK\nQ〉*.  \n The identity m y 〈OK\nQ〉 = 〈OK\nQ〉 leads to the condition,  \n σπ (− 1) K + Q 〈OK\n−Q〉 = σπ (− 1) K 〈OK\nQ〉* = 〈OK\nQ〉,    (2.2) \nwhere σπ = ± 1 is the parity-signature of 〈OK\nQ〉. The magnetic dipole, σπ = + 1, 〈T1〉 \npoints along the b-axis, as expected. Parity-odd ( σπ = − 1) multipoles with K odd \nare purely real. In particular, the c-axis componen t of the anapole, 〈G1\n0〉, is \nallowed and magnetic charge is not allowed, 〈G0\n0〉 = 0, for point-group symmetry \nmy. \n The identity m y'〈OK\nQ〉 = 〈OK\nQ〉 leads to quite different physical properties. \nIn place of (2.2) we have,  \n σθ σπ (− 1) K + Q 〈OK\n−Q〉 = σθ σπ (− 1) K 〈OK\nQ〉* = 〈OK\nQ〉,   (2.3) where σθ  = ± 1 is the time-signature. Parity-even ( σπ = + 1) multipoles have σθ =   \n(− 1) K, and 〈TK\nQ〉 = 〈TK\nQ〉* from (2.3), i.e., all parity-even multipoles are purely real \nand the magnetic dipole is confined to the a-c plan e. The result σθ σπ = ( − 1)( − 1) \n= + 1 applies for magneto-electric multipoles, and the  requirement 〈GK\nQ〉 = ( − 1) K \n〈GK\nQ〉*, means magnetic charge is allowed while 〈GK\n0〉 = 0 for K odd, in point-group \nsymmetry m y'. \n3. Orthorhombic structure factors  \n Unit-cell structure factors for scattering are der ived from [8], \n ΨK\nQ = ∑d exp(id▪ττ ττ) 〈OK\nQ〉d,      (3.1)  \nwhere the sum is over the four magnetic ions at pos itions d in the unit cell, and \nthe Bragg wavevector ττ ττ = (h, k, l) with integer Miller indices. Using sit es (4c) at:  \nx, 1/4, z; − x +1/2, 3/4, z + 1/2; − x, 3/4, − z; x + 1/2, 1/4 , − z + 1/2; \n ΨK\nQ = exp(i ϕ)〈OK\nQ〉1 + (− 1) h + l exp( −iϕ') 〈OK\nQ〉2 \n    + exp( −iϕ)〈OK\nQ〉3 + (− 1) h + l exp(i ϕ') 〈OK\nQ〉4,  (3.2) \nwith spatial phase-factors ϕ = 2 π(hx + k/4 + lz) and ϕ' = 2 π(hx + k/4 − lz) [19]. \nEnvironments at sites 2, 3, and 4 are related to si te 1 by rotations by 180 o \nabout crystal axes, and they are 2 z, 2 y, and 2 x, respectively. In ensuing \ncalculations, we will use 2 z 〈OK\nQ〉 = ( − 1) Q 〈OK\nQ〉, and 2 x 〈OK\nQ〉 = ( − 1) Q 2y 〈OK\nQ〉. \n3.1 charge diffraction \n Pure charge diffraction by the magnetic ions is cr eated by parity-even \nand time-even multipoles, with σθ = ( − 1) K = + 1 for K even. Corresponding \nmultipoles are purely real for both sites symmetrie s and, \n  ΨK\nQ(charge) =  2 〈TK\nQ〉 [cos ϕ + (− 1) h + l + Q cos ϕ'],   (3.3) \nwhich is purely real, for the chemical structure is  centrosymmetric. Standard \nextinction rules for Miller indices satisfy Ψ K\n0(charge) ≠ 0, whereas Templeton & \nTempleton scattering, created by angular anisotropy  in electronic structure, is \nlabelled by Miller indices and Q ≠ 0. Thus, to avoid charge scattering from \northorhombic structures consider reflections (h, k,  0) with h odd that give \nΨK\n0(charge) = 0. \n 3.2 magnetic diffraction \n All three structure factors are proportional to 〈OK\nQ〉 which is subject to \neither (2.2) or (2.3). Structure factors for Γ−\n1 and Γ−\n2 are distinguished solely \nby point-group symmetry, i.e., properties of 〈OK\nQ〉, and for this reason we only \nwrite out Ψ K\nQ(Γ−\n1 ). From (3.2), \n ΨK\nQ(Γ−\n1) = 〈OK\nQ〉[exp(i ϕ) + σθ σπ exp( −iϕ)  \n  + (− 1) h + l + Q (σθ σπ exp(i ϕ') + exp( −iϕ'))] \n   = 〈OK\nQ〉[exp(i ϕ) + σθ σπ exp( −iϕ)] [1 − σθ σπ (− 1) Q]; (h, k, 0) with h odd,  (3.4) \n ΨK\nQ(Γ−\n4) = 〈OK\nQ〉[exp(i ϕ) + σθ σπ exp( −iϕ)  \n  + σθ (− 1) h + l + Q (σθ σπ exp(i ϕ') + exp( −iϕ'))] \n   = 〈OK\nQ〉[exp(i ϕ) + σθ σπ exp( −iϕ)] [1 − σπ (− 1) Q]; (h, k, 0) with h odd.   (3.5) \nTime-odd multipoles vanish in the paramagnetic phas e. Second equalities in (3.4) \nand (3.5) apply for x-ray reflections at which char ge scattering is forbidden, \nand describe Templeton and Templeton scattering in the paramagnetic phase.  \n The expressions (3.4) and (3.5) apply to bulk prop erties, x-ray \ndiffraction, and neutron diffraction.  By way of an  example of neutron \ndiffraction, we consider LiMnPO 4, illustrated in Figure 2, and find Ψ 1\n0(Γ−\n1 ) = 0 \n(c-axis) and  Ψ 1\n1(Γ−\n1 ) ≠ 0 (a-axis) for reflections (0, 1, 0), (0, 1, 2) an d (2, 3, 0), \nresults which agree with observations at 2 K [20]. Magnetic neutron diffraction \nis bound by a selection rule; if all electronic dip oles are parallel with the Bragg \nwavevector ττ ττ = (h, k, l) the intensity is zero, no matter what value the magnetic \nstructure factor takes. \n3.3 bulk properties  \n Bulk properties of magnetic ions are determined by  structure factors \nevaluated for Miller indices h = k = l = 0. For thi s condition, \n  ΨK\nQ(Γ−\n1) = ΨK\nQ(Γ−\n2) = 〈OK\nQ〉Γ [1 + σθ σπ] [1 + (− 1) Q], Bulk  (3.6) \nand the expressions applies to orthorhombic crystal s containing Mn, Fe or Co \nions. Magnetic dipoles, and all other parity-even a nd time-odd multipoles, \npossess σθ σπ = − 1 and make no contribution to bulk properties. The  same is true of magnetic charge for Γ−\n2, because 〈G0\n0〉 = 0 by virtue of the point-group \nsymmetry, m y. But there is a net magnetic charge for Γ−\n1, together with all \nother magneto-electric multipoles with Q even and n ot forbidden by 〈GK\n0〉 = 0 \nfor K odd in point-group symmetry m y'. Turning to Γ−\n4, \n ΨK\nQ(Γ−\n4) = 〈OK\nQ〉[1 + σθ σπ] [1 + σθ (− 1) Q], Bulk    (3.7) \nfor Ni ions. Here, also, magnetic moments fully com pensate, together with all \nother parity-even magnetic multipoles. There is no net magnetic charge, and a \nnet anapole moment resides along the b-axis [21, 22 ]. \n4. Orthorhombic unit-cell structure factors  \nUnit-cell structure factors for x-ray diffraction, F, are very easily \nderived using A K,Q  = A K,−Q = (ΨK\nQ + ΨK\n−Q)/2 with A K,0 = ΨK\nQ, and B K,Q  = − BK,−Q = \n(ΨK\nQ − ΨK\n−Q)/2 and B K,0  = 0. Unit-cell structure factors for E1-E1 and E1- M1 \nevents are found in references [1, 23]. A K,Q and B K,Q , are calculated relative to \nstates of polarization and a Bragg wavevector (h, k , l) shown in Figure 1; \nspecifically, the setting of the crystal at the ori gin of a rotation of the crystal \nby an angle ψ around the Bragg wavevector (azimuthal-angle scan) .  \nΓ−\n1 :  From (3.4) we see that diffraction at reflection s (h, k, 0) with h odd from \nmagneto-electric multipoles, σθ σπ = + 1, is allowed for Q odd. In consequence, \nmagnetic charge, 〈G0\n0〉, is not observed. \nΓ−\n2 : Site symmetry m y does not allow magnetic charge. In Section 5 we ex amine \nconsequences of a lower symmetry structure for LiCo PO 4 proposed by Vaknin et \nal [15] and find that magnetic charge is allowed an d contributes to diffraction \nat space-group forbidden reflections.  \nΓ−\n4 : Unit-cell structure factors for (h, k, 0) with h odd are derived from the \nsecond equality in (3.5). They are purely real for each of the four polarization \nchannels, which mean (a) diffraction is independent  of circular polarization in \nthe primary beam, and (b) unit-cell structure facto rs add coherently, unless \nmixing parameters are complex and depend on energy.  \n The Bragg angle is determined by sin θ = ( λ/2) (h, k, l) and λ ≈ 14.4 Å at \nthe Ni L 3 absorption edge (a = 10.02 Å, b = 5.83 Å, c = 4.66  Å [20]). Whence, \ndiffraction is allowed at (1, 0, 0). Chemical and m agnetic structures of LiNiPO 4 \nare depicted in Figure 2. The Bragg wavevector (h, k, 0) is aligned with − x in Figure 1 by rotation \nby an angle α about the c-axis (z-axis). We find, \nAK,Q  = (1/2) Ψ K\nQ(Γ−\n4 )[exp( −iQ α) + σθ σπ (− 1) K + Q exp(iQ α)] \nBK,Q  = (1/2) Ψ K\nQ(Γ−\n4 )[exp( −iQ α) − σθ σπ (− 1) K + Q exp(iQ α)].     (4.1) \nFor the particular case of (h, 0, 0) α = π. For this reflection, there is no \ndiffraction in channels with unrotated polarization , F π'π = F σ'σ = 0, while for the \nchannel with rotated polarization F π'σ = F σ'π and, \n F π'σ = 4 cos( ϕ) [sin( θ)tan( ϕ)〈T1\n+1〉 + cos( θ)cos( ψ)〈T2\n+1〉  \n+ (1/ √2) sin(2 θ) cos( ψ) tan( ϕ) 〈U1\n0〉 − (2/ √3) sin 2(θ)〈G0\n0〉  \n  − (1/2 √6) [2 + cos 2(θ)(1 + 3 cos(2 ψ))] 〈G2\n0〉   \n   + (1/2)[2 + cos 2(θ)(1 − cos(2 ψ))] 〈G2\n +2〉].    (4.2) \nThe contribution to diffraction from magnetic charg e does not change with \nrotation of the crystal about the Bragg wavevector by an angle ψ, as might be \nanticipated. The time-odd multipoles, 〈T1\n+1〉 and 〈GK\nQ〉, vanish in the absence of \nlong-range magnetic order, and Templeton and Temple ton scattering is created \nby the quadrupole 〈T2\n+1〉. \n Chemical and magnetic symmetry, together with disc rete symmetries of \nmultipoles, are the foundation of expression (4.2) for resonant x-ray Bragg \ndiffraction. Resonant energy denominators are consp icuous by their absence. \nThis is a singular benefit of the fast-collision ap proximation, which amounts to \nneglect of angular anisotropy in the wavefunction f or the intermediate state \nthat accepts the photon [8]. Loss of the benefit re sults in a vastly more \ncomplicated expression for the scattering length, t he starting point for an \nelectronic structure factor, that might not be just ified [24, 25]. \n Contributions in (4.2) depend on the x-ray wavelen gth and radial integrals, \nwhich are not made explicit. To create a meaningful  measure of relative \nstrengths of E1-E1 and E1-M1 contributions it is us eful to consider a \ndimensionless quantity ρ that includes q = 2 π/λ and atomic radial integrals. In \nthe case of an E1-M1 event, there is the familiar d ipole radial integral from the \nE1-event, namely, ( ΘRΞ) where Θ is a valence state, and Ξ is the intermediate \nstate which accepts the photon. The second radial i ntegral, ( Θ'Ξ), is the radial part of the matrix element of the magnetic moment, and the valence state Θ' \nand Ξ have identical orbital angular momentum, l', because the magnetic moment \noperator does not change angular momentum. With the se definitions, a value of \nρ(E1-M1) is, \n ρ(E1-M1) = q ( ΘRΞ) ( Θ'Ξ).        \nLikewise, for an E1-E1 event, \n ρ(E1-E1) = [( ΘRΞ)/a o]2(m∆a o2/ħ2), \nwhich has no explicit dependence on q. In the dimen sionless factor (m∆a o2/ħ2) \nthe Bohr radius is a o and ∆ is the energy of the resonance. \n5. LiCoPO 4 \nVaknin et al [15] show that in LiCoPO 4 the Co magnetic dipole departs \nfrom the b-axis and the appropriate magnetic space- group is monoclinic P2 1’11 \n(unique axis a), crystal class 2 x’, and not Pnma1’. Here, we demonstrate that \nmagnetic charge is allowed and contributes to diffr action for this monoclinic \nstructure. The chemical and magnetic structures ( Γ2) of LiCoPO 4 are depicted in \nFigure 3.  \nInitial positions (4c) in Pnma split using two non- equivalent groups;  \n \n(2a: 1) (x, 1/4, z; x + 1/2, 1/4, − z + 1/2),  \nand,  \n(2a: 2) ( − x + 1/2, 3/4, z + 1/2; − x, 3/4, − z).  (5.1) \n \nThe site symmetry 1 (identity) allows magnetic char ge, of course. Two \nenvironments inside (2a) are related by the 2 x' symmetry element. We go on to \nfind, \nΨK\nQ(1) = exp(i ϕ)[ 〈OK\nQ〉 + σθ (− 1) h + l + K exp( − 4πilz) 〈OK\n− Q〉],  (5.2) \nΨK\nQ(2) = exp( − iϕ)[( − 1) h + l exp(4 πilz) 〈OK\nQ〉 + σθ (− 1)  K 〈OK\n− Q〉],  (5.3), \nwhere ϕ = 2 π(hx + k/4 + lz), as before. Note the absence in (5.2) and (5.3 ) of an \nexplicit dependence on the parity of multipoles. As  in previous cases, the \nelectronic structure factors are appropriate for ne utron and x-ray scattering.  In the nominal setting of the crystal orthogonal a xes ( a, b, c*) match    \n(x, y, z) in Figure 1. Here, a = a (1, 0, 0), b = b (0, 1, 0), c = c (0, cos αo, sin αo) with \ncell volume v o = abc sin αo. For a reflection (h, k, 0) the Bragg wavevector            \nττ ττ = 2 π(h/a, k/b, − (k/b) cot αo). \n Bulk properties are determined by,  \n ΨK\nQ(1) = ΨK\nQ(2) = [〈OK\nQ〉 + σθ (− 1) K 〈OK\n− Q〉]. Bulk \nEvaluation of this quantity for the magnetic dipole , 〈T1〉, and the anapole, 〈G1〉, \nshow that both have net values in the b-c* plane. U nlike orthorhombic \nstructures, net magnetization can be different from  zero. A net polar dipole \nresides along the a-axis. There is no net magnetic charge. A linear magneto-\nelectric effect is allowed, and with 2'11 (unique a xis a) setting α12 , α13 , α21 , α31  \nare components of the tensor allowed different from  zero.  \n X-ray charge scattering is absent for h odd and l =  0, the same condition \nas in Pnma, and electronic structure factors reduce  to,  \n ΨK\nQ(1) = exp(i ϕ)[ 〈OK\nQ〉 − σθ (− 1)  K 〈OK\n− Q〉], (5.4) \nfor space-group reflections (h, k, 0) with h odd, w ith a similar expression for \nΨK\nQ(2). Applying (5.4) to parity-even (t), polar (u) a nd magneto-electric (g) \nmultipoles, \n ΨK\nQ(t) = − ΨK\n−Q(t) and Ψ K\n0(t) = 0,   (5.5) \n ΨK\nQ(u) = − (− 1)  K ΨK\n−Q(u) with Ψ K\nQ(u) = 0 for K even,  \n and Ψ 1\n+1(u) = −i√2 exp(i ϕ)〈U1\nb〉,    (5.6) \n ΨK\nQ(g) = ( − 1)  K ΨK\n−Q(g) with Ψ 1\n0(g) = 0,  \n and Ψ 1\n+1(g) = −√2 exp(i ϕ)〈G1\na〉.    (5.7) \nIt follows from (5.5) that the magnetic dipole para llel to the c*-axis does not \ncontribute to diffraction and charge scattering is absent, as expected. \nContributions from polar dipoles are parallel to th e b-axis and c*-axis, and the \nanapole contribution is parallel to the a-axis. \n We calculate A K,Q  and B K,Q  with an analogue of (4.1) and find,   \n A K,Q  = (1/2)[exp( −iQ π) Ψ K\nQ + exp(iQ π) Ψ K\n−Q],  B K,Q  = (1/2)[exp( −iQ π) Ψ K\nQ − exp(iQ π) Ψ K\n−Q],  (5.8) \nfor the class of reflection (h, 0, 0) with h odd. E xpression (5.8) is used in \nconjunction with (5.5), (5.6) and (5.7). Magnetic c harge contributes in the \nrotated channel of diffraction and we give the appr opriate structure factor, \n F π'σ = F σ'π = i sin( θ)B 1,1 (t) − cos( θ)cos( ψ)B 2,1 (t) + i cos( θ)sin( ψ)B 2,2 (t) \n− (i/ √2)sin(2 θ) cos( ψ)A 1,0 (u) − sin(2 θ) sin( ψ)A 1,1 (u)  \n− (2/ √3)sin 2(θ)A 0,0 (g) − (1/2 √6) [2 + cos 2(θ)(1 + 3 cos(2 ψ))]A 2,0 (g) \n + i cos 2(θ)sin(2 ψ)A 2,1 (g) + (1/2)[2 + cos 2(θ)(1 − cos(2 ψ))]A 2,2 (g).       (5.9) \nContributions in (5.9) not in (4.2) are permitted b y the absence of selection \nrules from sites (2c) used in P2 1’11. The anapole does not feature in F π'σ, even \nthough it is an allowed multipole, and magnetic cha rge contributes through \nA0,0 (g). \n6. Conclusions \n Magnetic properties of LiMPO 4 with M = Mn, Fe, Co and Ni have been \ndiscussed, with emphasis on properties visible in n eutron and x-ray scattering. \nParticular attention is given to magnetic charges, or magnetic monopoles, that \nwe predict in calculations of resonant x-ray Bragg diffraction amplitudes for \nLiCoPO 4 (monoclinic) and LiNiPO 4 (orthorhombic). Recent, independent ab initio  \nsimulations of the electronic structure of LiNiPO 4 support the existence of  \nmagnetic monopoles in this compound [14]. All being  well, resonant x-ray Bragg \ndiffraction experiments will soon be made on both t he monoclinic and the \northorhombic compounds.  \nAcknowledgement \nOne of us is grateful to Dr K S Knight and A Rodríg uez-Fernández for valuable \ndiscussions about the physical properties of lithiu m compounds with the olivine \nstructure. In 2012 Dr V Scagnoli contributed in an initial calculation for \nLiNiPO 4. \nReferences \n1] Lovesey S W and Scagnoli V 2009 J. Phys.: Condens. Matter  21  474214 2] Goldhaber A S 1977 Phys. Rev.  D16  1815 \n3] Lovesey S W and Balcar E 2010 Phys. Scr.  81  065703 \n4] Lovesey S W et al 2007 Phys. Rev . B 75  0144095 \n5] Fernández-Rodríguez J et al 2010 Phys. Rev.  B81  085107 \n6] Lovesey S W et al 2011 Phys. Rev.  B83  054427 \n7] Staub U et al 2009 Phys. Rev . B 80  140410(R) \n8] Lovesey S W et al 2005 Phys. Rep . 411  233 \n9] Lovesey S W and Balcar E 2010 J. Phys. Soc. Japan  79  074707 \n10] Lovesey S W and Balcar E 2010 J. Phys. Soc. Japan  79  104702 \n11] Santoro R P et al 1966 J. Phys. Chem. Solids  27  1192 \n12] Scagnoli V et al 2011 Science  332  69 \n13] Joly Y et al 2012  Phys. Rev . B 86  220101(R) \n14] Spaldin N A et al 2013 arXiv:submit/0744393 \n15] Vaknin D et al 2002 Phys. Rev . B 65  224414 \n16] Stokes H T, Hatch D M, and Campbell B J 2007 IS OTROPY, \n[stokes.byu.edu/isotropy.html] \n17] Campbell B J et al 2006 J. Appl. Crystallogr.  39  607 \n18] Lovesey S W and Balcar E 2013 J. Phys. Soc. Japan  82  021008 \n19] Abrahams I and Easson K S 1993 Acta. Cryatallog.  C49  925 \n \n20] Toft-Petersen R et al 2012 Phys. Rev.  B85  22441 \n21] Grimmer H 1994 Ferroelectrics  161  181 \n22] Gorbatsevich A A and Kopaev Yu V 1994 Ferroelectrics  161  3215 \n \n23] Scagnoi V and Lovesey S W 2009 Phys. Rev . B 79  035111 \n 24] Lovesey S W 1997 J. Phys.: Condens. Matter  9 7501 \n \n25] Lovesey S W and Balcar E 2012 J. Phys. Soc. Japan  81  014710 \n \nFigure  1. Cartesian coordinates (x, y, z) and x-ray polarizat ion and wavevectors.  \nThe plane of scattering spanned by primary ( q) and secondary ( q') wavevectors \ncoincides with the x-y plane.  Polarization labelled σ and σ' is normal to the plane \nand parallel to the z-axis, and polarization labell ed π and π' lies in the plane of \nscattering. \nPn 'm'a' Pnm 'a\nLi Li Mn Ni \nP P\n \nFig. 2 Orthorhombic crystal structure of LiMPO 4 (M = Mn and Ni) and magnetic \ndipole motifs associated with Γ−\n1 (left) and Γ−\n4 (right) irreducible \nrepresentations of the Pnma1' space group.  \n Pnma 'Li PCo \nP2 1'11 Li PCo 2\nCo 1\n \nFig. 3 Orthorhombic crystal structure of LiCoPO 4 and magnetic dipole motif \nassociated with Γ-\n2 irreducible representation of the Pnma1' grey-grou p (left). \nMonoclinic crystal structure of LiMPO 4 and magnetic dipole motif associated \nwith a Γ2 irreducible representation of the P2 111' grey-group (right). Two non-\nequivalent cobalt sites are denoted as Co 1 and Co 2, and symmetry places no \nconstraint on relative orientations of magnetic dip oles in the two pairs. \nHowever, magnetic dipole moments associated with Co 1 and Co 2 nearly \ncompensate, as shown in the cartoon, due to an anti ferro-magnetic exchange \nbetween the two sub-lattices. \n "    },    {        "title": "1308.6078v1.Static_magnetic_field_concentration_and_enhancement_using_magnetic_materials_with_positive_permeability.pdf",        "content": "Static magnetic field concentration and enhancement using  magnetic \nmaterials with  positive permeability  \nF. Sun1, 2 and S . He1, 2* \n \n1. Department of Electromagnetic Engineering, School  of Electrical Engineering, \nRoyal Institute of Technology  (KTH)  \n2. Centre for Optical and Electromagnetic Research,  JORCEP  \n  \nAbstract  \nIn this paper a  novel compressor for static magnetic field s is proposed based on \nfinite embedded transformation optics. When the  DC magnetic field passes through \nthe designed device, the magnetic field  can be compressed inside  the device . After it \npasses  through the device, one can  obtain an enhanced static magnetic field behind the \noutput surface of the device ( in a free space region) . We can also combine our \ncompressor with some other structures to get a higher static magnetic field \nenhancement  in a free space region . In contrast  with other devices based on \ntransformation  optics for enhancing static magnetic field s, our device is not a closed \nstructure  and thus  has some special applications (e.g ., for controlling magnetic \nnano- particles for gene and drag delivery ). The designed compressor can be \nconstructed  by using current ly available materials  or DC meta- materials  with positive \npermeability . Numerical  simulation verifies  good performance of our device. \n \n1. Introduction  \nThe static magnetic fields play an essential role in many applications, inclu ding \nmagnetic resonance imaging  [1], transcranial magnetic stimulation [ 2], controlling \nmagnetic nano- particles for gene and drag delivery [ 3, 4], magnetic sens ors [5] and so \non. Higher static magnetic fields can promote the  development of these applications. \nWe can classify the static magnetic field enhancement under  two types : one is for \nenhancing s tatic magnetic field s in a large free space region which may be applied for \ne.g. improving the spatial resolution in MRI; the other is for enhancing static \nmagnetic field s in a small region which can be used to improve the sensitivity of \nmagnetic sensors  and promote  the development of magnetic nano -particles for gene \nand drag delivery , etc.  \nMagnetic lens es are passive devices  which can cause an external magnetic field to \nconverge /focus  without consuming additional power . We can acquire an  enhanced DC \nmagnetic field without consuming power by using m agnetic lenses, and this  is \ndifferent from magnet s which need a power supply to acquire  a higher DC magnetic \nfield. A compact high field system (>10T) is an important trend in magnetic \nenhancement [ 6, 7]. Based  on the diamagnetism of the superconductor, people have \ndesigned various magnetic lenses composed of superconductor s to concentrate the  DC \nmagnetic field when applying a background magnetic field to the lenses [ 6-10]. However, magnetic lenses based on supe rconductor s have many disadvantages: the \ndegree of enhancement is very  low (e.g., magnification factor is only 1.82 by using \nNbTi/Nb/Cu superconducting multilayered sheets [ 8], and only  3.2 at the center by \nusing HTS bulk cylinders [ 9]), refrigeration  is required  and the performance is  often \ninfluenced by quenching and other factors.  \nTransformation optic s (TO) is a powerful tool, which is based on the invariance \nform of Maxwell's equations [ 10, 1 1]. A special medium ( often referred to as the \ntransformed medium), which can be used to control the trace of the electromagnetic \nwave and also the static electric or magnetic field, can be designed by TO. As the transformed medium is often complex, which may often not exist in nature, people \nhave  to design some artificial materials ( e.g., meta -materials) to create them. In the \ndevelopment of DC magnetic and electric meta -material s [12, 13], many DC magnetic \nand electric devices based on TO (e.g., DC magnetic or electric cloaking devices [13, \n14] a nd DC magnetic or electric energy concentrators [ 15-17]) have been studied in \nrecent years. In this paper, we design a novel magnetic compressor  which can \ncompress the DC  magnetic f ield and obtain a high  magnetic field in a free space  \nregion . Our device can be constructed with  natural materials or current DC magnetic  \nmeta -materials  [12, 18]  with permeability  μ>0. Note that it is not clear yet to this \ncommunity how to achieve a meta -material with  μ<0 at DC and fortunately  \npermeability  μ is always positive in our design . We will thoroughly describe the \ndesign method in section 2. We will also give numerical  simulation results based on \nthe finite element method (FEM), which shows good device performance. In section 3, \nwe combine our magnetic  compressor with some other structures  to get a further \ndegree of static magnetic field enhancement  in a free space. The summary will be \ngiven in section 4, where we also make a comparison between our compressor  and \nother devices which can also be used for enhancing the DC magnetic field.  \n \n2. The m ethod of designin g a compressor for static magnetic field s \nTraditional transformation s are often continuous , and thus the electromagnetic \nproperties of the incident waves are altered exclusively within a restricted region  and \nthe corresponding  devices are inherently invisible to observers outside of the \ntransformed region (e.g., invisible cloaks  and field rotator s). Finite embedded \ntransformation (FET) is a special kind of transformations, which is discontinuous  at \nthe output surface of the devices  [19]. FET can  transfer /manipulat e fields from the \ntransform ed medium to a n un-transformed  medium , which has been widely used to \ndesign light splitter s [20], polarization  controller s [21], light beam expander s or \ncompressor s [22], etc. In this paper, we will use FET to design a magnetic compressor \nfor the static magnetic field, which may have important applications in DC magnetic \nflux controlling and DC magnetic field enhancement.  \nFor simplicity we consider a two -dimensional  (2D) device ; the input surface of the \ndevice is x ’=0 and the output surface of the device is x ’=d. We use ( x’, y’, z’) and (x , y, \nz) to express the coordinate system s in the physical space and reference space,  \nrespectively. We can use the following transformation to concentrate magnetic flux at the output of the device:  ()'\n1' 1:\n'xx\nMy xyyd\nzzα=\n−= +=\n\n=                      (1)  \nwhere  d is the thickness of the device and M  (0<M<1) determines both the degree of \nthe enhancement  and the permeability distribution of the device . The smaller  the \nvalue of  M, the higher the concentration and also the larger  the field enhancement . \nThe Jacobean matrix of the  above transformation can be calculated  by \n()1 00\n10\n0 01MAydα\n−=\n\n                         (2)  \nAs the transformation optics is based on the invariant form of Maxwell’s equations, it \nstill holds for the static magnetic field cases for which only two of the Maxwell’s \nequations are involved [ 17]. We also assume that the ref erence space is free space. \nThe magnetic permeability  parameters corresponding to  the above transformation can \nbe given:  \n()\n()()2\n2\n00 211/ 0\n11/ det( ) 0\n0 0 1/TMyd\nMMAA A y yddαα\nµµ µ ααα\nα− \n\n\n−−= = + \n\n         (3) \nFor a 2D device, only μxx, μxy and μyy affect the magnetic field . We can rewrite Eq. (3) \nas: \n()\n()()0 2\n2\n211/\n:\n11xx xy\nxy yyMyd\nMMyyddαµµ αµµµµ\nααα− \n= =−− +            (4) \nFor fabricati on convenience of the compressor , it is preferable to denote the material \nparameters in their eigenbasis, where the permeability tensor  is diagonal. Due to the \nsymmetry of the  transformed medium, this can always be accomplished . We can \ndiagonalize  the permeability tensor in Eq. (4) as:  \n12 ( , ): ( , )22xx yy xx yydiag diagµµ µµµ κ κ µµ++= − +=\n           (5) \nwhere22 224\n2xx xy xx yy xyµ µ µµ µ\nκ+− +\n=  \nNext we use the finite element method (FEM) [23] to simulate the performance of the proposed device. As shown in Fig. 1( a), 1(d) and 1(g), when a uniformed \nbackground static magnetic field Bb=1T is imposed onto the device from left to right, \nthe magnetic field is compressed inside the device. At the ou tput surface of the device, \nwe get a concentrated DC magnetic field. We also verify that M  deter mines the rate of \nconcentration: In Fig. 1 (a), M=0.1 and the enhancement factor is about 4.7; In Fig. \n1(d), M=0.35  and the enhancement factor is about 1.65; I n Fig. 1 (g), M=0.01 and the \nenhancement factor is about 45. The corresponding permeability of these devices are \nalso shown in Fig. 1( b) and1( c) for M=0.1, Fig. 1 (e) and 1(f) for M=0.35, and Fig. 1( h) \nand 1(i) for M=0.01. Here t he p ermeability is always positive , which can be \nconstructed  with natural materials (e.g., diamagnetic substances  and paramagnetic  \nmaterials ) or current meta- materials for static magnetic field s [12, 18]. As M \napproaches  zero, the concentration degree and enhancement factor become larger. At \nthe same time the smallest value of μ1 approaches zero and the largest value of μ 2 \napproach es infinit y. If the concentration degree is not too high (e.g., M=0.35), we  can \nconstruct  the device through  the combination of diamagnetic materials  and \nparamagnetic materials without super -conductor s, which means that  we can avoid \nrefrigeration , quenching  and other drawbacks in super -conductor  devices [ 6-10]. If we \nwant to achieve a very large concentration degree (e.g., M=0.01), we can use the \ncombination of super -conductor and ferromagnetic materials [14, 16]  to construct  it. \nIn this case we can achieve a much higher enhancement , compared with traditional \nsuper -conductor  based magnetic lenses [ 6-10]. \n  As the role of our  device is to compress the magnetic field , we can simply add \nanother identical  device  behind the former one to further concentrate the magnetic \nfield (see Fig. 2) . The comparison between Fig. 1 and Fig. 2 reveals  that two adjacent  \nidentical  devices can achieve a better magnetic field enhancement at the final output \nof the structure  than a single device , though the improvement is slight . The reason for \nthis will be discussed in section 3. If we want to furth er increase the degree of the \nmagnetic  field enhancement, we will use some other structure s which will also be \ngiven in section 3.  \nFig. 1.2D F EM simulation results . The height  of the de vice is 0.8m  and the thickness  \nof the device is d= 0.5m . When a  uniformed background static magnetic field B b=1T is \nimposed onto the device from left to right,  the distribution of the  total magnetic flux \ndensity  is shown in  (a) for M=0.1, (d) for  M=0.35 and ( g) for M=0.01. The principal \nvalue s of the  permeability tensor distribution (μ1 and μ2) are shown for M=0.1 in (b) \nand (c); for M=0.35 in (e) and (f); for M=0.01 in (h) and (i). The black rectangle is the \ndesigned compressor and the  other regions are free space.  \n \nFig. 2. 2D F EM simulation result s. When  a uniformed background static magnetic \nfield Bb=1T is imposed onto the device from left to right, the distribution of the  total \nmagnetic flux density (B) for two adjacent identical compressors with the same size \nof Fig. 1  are shown in ( a) for M=0.1, (b) for  M=0.35 and ( c) for M=0.01. The \nenhancement factor in this case is about 5.3, 1.7 and 45.4 for ( a), (b) and (c), \nrespectively.  The two black rectangles  are identical compressor s and other regions are \nfree space.  \n \n3. Combination structure s for static magnetic field enhancement  \nWe have shown that a  single  compressor  based on FET can concentrate the static \nmagnetic field. In this section, we will combine the compressor with some other \nstructures to achieve  a further magnetic field enhancement . The reason why we can \nonly achieve a little improvement in magnetic  field enhancement by using two \nadjacent  identical  compressors  is that no matter how many compressor s we use, once \nthe DC magnetic field exits from the output surface of the last device, the DC field  \nwill diverge  very quickly  in free space. If we can add some other structure  which  can \nprevent the  DC magnetic f ield from diverging too quickly , we can achieve a better DC \nmagnetic field enhanc ement . As diamagnetic materials (0<μ <1) can exclude the DC \nmagnetic field, we can set up some diamagnetic structure s after the designed device to \nprevent the DC magnetic f ield from diverging once it gets out of the compressor . As \nshown in Fig. 3( a), we add two parallel  slabs with μ =0.3 after the compressor  (which  \nis the same as  the one in Fig. 1( a)). In this case, we get a better enhancement (the \nenhance ment factor is about 6 in the free space  region). For comparison , we also \nsimulate the case that a single structure  with two parallel  diamagnetic slabs (μ=0.3)  is \nused for static magnetic field enhancement (see Fig. 3 (b)). In this case the \nenhancement factor is only about 1.9 in the free space region.  \nA magnetic hose which can transport the static magnetic energy  to a long distance \nhas been proposed very recently  based on TO [ 24].A structure with a super -conductor \nshell whose permeability approaches zero) and an inner ferromagnetic core ( whose \npermeability  approaches infinit y) has been shown to be able  to guide the static \nmagnetic en ergy to an arbitrary distance.  We can combine our concentrator with the \nreduced magnetic hose to obtain a further magnetic  field enhancement. In order to \navoid using superconduc tors, as we have mentioned its drawbacks  in the introduction, \nwe can reduce the magnetic hose by using a diamagnetic shell whose permeability is \nsmaller than 1 but not necessar ily very close to zero and a paramagnetic core whose \npermeability is larger than 1 but not necessar ily infinite ly large . Then we can put our \ncompressor  (the same as  the one in Fig. 1( a)) before  the reduced magnetic  hose and \nremove some paramagnetic materials in the middle region of the reduced hose to get a \nhigher magnetic field enhancement in this empty /free region  (the enhance ment factor \nis about 8.5 in this  free space region; see  Fig. 3 (d)). For comparison, we also simulate \nthe case when  a single reduced magnetic hose structure  is used for static magnetic \nfield enhancement (see Fig. 3 (c)). In this case the enhancement factor is only about \n3.5 in the  middle  free space region. These combination structure s can  be utilized to \nenhance the sensitivity of magnetic sensors .   \nFig. 3.2D FEM simulation result s. When a uniformed background static magnetic \nfield Bb=1T is imposed onto the whole structure from left to right, the distribution  of \nthe total magnetic flux density  is shown in ( a) when t he structure is the combination \nof the compressor ( with the same size as Fig.1 (a)) and two parallel slabs with μ=0.3. \nThe height and thickness of each slab is 19cm and 5cm respectively. (b) when the \nstructure is only two parallel slabs with the same size and permeability as Fig. 3 (a). (c) \nwhen t he structure is only the reduced magnetic hose. ( d) when  the structure is the \ncombination of the compressor and the reduced magnetic hose. The reduced magnetic  \nhose is shown in detail in the inset of Fig. 3 (c). The white region means that the \nmagnetic field is larger than the largest value of the color bar.  \n \n4. Discussion and summary \nBased on FET, we have design ed a novel compressor  for static magnetic  field \nenhancement. A simulation based on FEM shows good performance  of our device. \nCompared with other devices based on TO for static magnetic field concentration [ 16, \n17], our device is not a closed structure , which has potential applications in some \nspecial cases. F or example, m agnetic nano -particles, attached by cytotoxic drugs for \ntargeted chemotherapy or therapeutic DNA to correct a genetic defect, have been \nutilized in vitro  and in animal experiment s in recent years [ 3, 4]. A m agnetic field with \nhigh strength and high gradient is needed in this case to allow magnetic nano- particles  \nto be captured and extravasated at the target. While this may be effective for targets \nclose to the body’s surface, as the magnetic field strength falls off rapidly with \ndistance, it is very difficult to send them to deeper targets within the body. A stronger  \nmagnetic field with high gradient can break through this barrier and acquire  better \ncontrol of magnetic nano -particles inside the human body. Our magnetic compressor \nis an open structure  and can  also achieve high magnetic  fields with high gradient, \nwhich  will have potential  applications for controlling magnetic nano -particles for \ngene and drag delivery .  \n  Our compressor can also be combined with other structure s to get a n even  higher \nmagnetic field enhancement. More important ly, the permeability values for all the  \nmaterials  used in our compressor are all larger than 0, which  means it can be realized \nby current ly available  materials  or DC meta -materials . We should also not e that some \nmeta -materials without magnetic materials can also achieve a magnetic response even \nfor DC magnetic field s. Those meta- materials , combined with high permeability \nmaterials (e.g., soft ferromagnetic materials [ 14, 16]) can be utilized  to construct  our \ndevice.  \n  \nReference  \n \n[1] M. A Brown and R. C. Semelka, MRI: basic principles and applications. (2010, Wiley -Blackwell).  \n[2] M. Kobayashi and A. Pascual -Leone, ‘Transcranial magnetic stimulation in \nneurology,’ Lancet Neurology 2, 145 (2003).  \n[3] O. Veiseh, J. W. Gunn, M. Zhang,  ‘Design and fabrication of magnetic \nnanopart icles for targeted drug delivery and imaging, ’ Advanced Drug Delivery \nReviews 62(3), 284- 304 (2010).  \n[4] J. Dobson,  ‘Magnetic micro - and nano- particle- based targeting for drug and gene \ndelivery, ’ Nanomedicine 1(1), 31- 37 (2006).  \n[5] P. Ripka and M. Janosek, ‘Advances in m agnetic field sensors,’ IEEE Sens. J. 10, \n1108 (2010).  \n[6] Z. Y . Zhang, S. Matsumoto, S. Choi, R. Teranishi and T. Kiyoshi, ‘Comparison of \ndifferent configurations of NbTi Magnetic lenses,’  Supercond. Sci. Technol. 24, \n105012 (2011).  \n[7] Z.  Y . Zhang, S. Choi, S. Matsumoto, R. Teranishi, G. Giunchi, A. F . Albisetti and T. \nKiyoshi, ‘Magnetic lenses using diffe rent MgB2 bulk superconductors,’  Supercond. \nSci. Technol. 25, 025009 (2012).  \n[8] Z. Y . Zhang, S. Matsumoto, S. Choi, R. Teranishi and T. Kiyoshi, ‘A new structure \nfor a magnetic field concentration using NiTb sheet superconductors,’  Physica C 471, \n1547- 1549 (2011).  \n[9] T. Kiyoshi, S. Choi, S. Matsumoto, T. Asano, and D. Uglietti, ‘Magnetic flux \nconcentratorusing Gd-Ba-Cu-O bulk superconduc tors,’ IEEE Transections on applied superconductivity 19(3), 2174- 2177 (2009).  \n[10] U. Leonhardt and T.G. Philbin, Geometry and Light: Science of Invisibility \n(Dover, 2010).  \n[11] J. B. Pendry, D. Schurig, and D. R. Smith, ‘Controlling electromagnetic field s,’ \nScience 312, 1780- 1782 (2006).  \n[12] F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, ‘A d.c. magnetic metamaterial,’ Nature Materials 7, 295 (2008). [13] F. Yang, Z. L. Mei, and T. Y . Jin, ‘ DCelectric invisibility cloak,’ Phys. Rev. \nLett.109, 053902 (2012).  \n[14] F. Gömöry, M. Solovyov, J. Šouc, C. Navau, J. Prat -Camps, A. Sanchez, \n‘Experimental Realization of a Magnetic Cloak,’ Science 335, 1466- 1468 (2012).  \n[15] W. X. Jiang, C. Y . Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, ‘Enhancement of \nCurrent Density by dc Electric Concentrator,’ Scientific Reports 2, 956 (1012). [16] C. Navau, J. Prat -Camps, and A. Sanchez, ‘Magnetic e nergy harvesting and \nconcentration at a distance by t ransformation optics,’ Phys. Rev. Lett.109, 263903 \n(2012).  \n[17] F. Sun and S. He, ‘ Create a uniform static magnetic field over 50T in a large free \nspcae region, ’ Prog.Electromagn.Res. V ol. 137, 149- 157 (2013).  \n[18] H. S. Chen, L. Huang, and X. X. Cheng, ‘ Magnetic properties of metamaterial \ncomposed of closed rings,’  Prog.Electromagn.Res. V ol. 1 15, 317- 326 (201 1). \n[19] Pu Zhang, Yi Jin, and Sailing He, ‘ Inverse transformation optics and reflection \nanalysis for two -dimensional finite -embedded coordinate tran sformation, ’ IEEE J. Sel. \nTop. Quant. Electron., 16, 427 (2010).  \n[20] M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, ‘Optical \ndesign of reflectio nless  complex media by finite embedded coordinate \ntransformations ,’ Phys. Rev. Lett. 100, 063903 (2008). \n[21] D. H. Kwon and D. H. Werner, ‘Polarization splitter and polarization rotator \ndesigns based on transformation  optics,’  Opt. Express 16(23), 18731- 18738 (2008).  \n[22] M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, ‘ Transformation -optical \ndesign of adaptive beam bends and beam expanders,’  Opt. Express 16(15), \n11555- 11567 (2008).  \n[23] The finite element simulation is conducted by using commercial software \nCOMSOL Multiphysics. \nhttp://www.comsol.com/ . \n[24] C. Navau, J. Prat -Camps, O. Romero- Isart, J. Ignacio, and A. Sanchez, ‘ Magnetic \nhose: routing and long -distance transportation of magnetic fields, ’ \narXiv:1304.6300v1.  "    },    {        "title": "1309.0022v1.Scaling_in_Modeling_of_Core_Losses_in_Soft_Magnetic_Materials_Exposed_to_Nonsinusoidal_Flux_Waveforms_and_DC_Bias.pdf",        "content": "arXiv:1309.0022v1  [cond-mat.mtrl-sci]  30 Aug 2013Scaling inModeling ofCoreLosses inSoftMagnetic Material sExposed to NonsinusoidalFlux\nWaveformsand DC BiasCondition\nAdam Ruszczyk∗\nABB Corporate Research, Starowi´ slna 13a, 31-038 Krak´ ow, Poland\nKrzysztof Sokalski†\nInstitute of Computer Science, Cze ¸stochowa University of Technology, Al. Armii Krajowej 17, 42-200 Cze ¸stochowa, Po land\nJan Szczygłowski‡\nInstitute of Power Engineering, Cze ¸stochowa University o f Technology, Al. Armii Krajowej 17, 42-200 Cze ¸stochowa, P oland\nAssuming thatcore loss data ofSoftMagnetic Materialsobey scalingrelations,models describing the power\nlossesinmaterialsexposedtononsinusoidalfluxwaveforms andDCBiasconditionshavebeenderived. Inorder\ntotestthesemodels, themeasurement datafor twomaterials havebeen collectedandthe corelosses calculated.\nAgreement between the experimental data andthe model predi ctions issatisfactory.\nINTRODUCTION\nTheusualwaveformsinpowerelectronicsaresquarewaves\nor a superposition of square waves rather than sine waves.\nSome magnetic components also operate under a DC bias,\nwhich has a significant influence on the core losses. During\nthe last two ldecades significant progressin modelingthe de -\npendencesof core losses both due to square wave parameters\nandDCbiashasbeenachieved. Thederivedmethodsforhan-\ndling the core losses in soft magnetic materials (SMM) ex-\nposed to nonsinusoidal flux waveforms have been based on\nthe Steinmetz Equation[1]. These methodsinclude the Mod-\nified Steinmetz Equation (MSE) [2], [3], Generalized Stein-\nmetz Equation (GSE) [4], Improved Generalized Steinmetz\nEquation(iGSE) [5] [6] andImproved-improvedGeneralized\nSteinmetz Equation (i2GSE) [7]. Methods and models ex-\nist, however, based on the assumption that the shape of the\nwaveform does not matter and as a result only look at peaks:\nScaling of power Losses in SMM [11],[12],[13] and Field-\nExtrema Hysteresis Model (FHM), [14]. Both do not capture\nthe effects of the waveform. Is this feature a disadvantage\nor an advantage? All the models we are talking about have\nbeen derived for prediction of losses for the designing pro-\ncesses. If one assumes that the waveform does not vary in\nsuch a processthen the modelis universalandcan be applied\nto any waveform possessing a constant period. Moreover, if\nexperimentaldata obeya scalinglaw thenthedata collapsei s\npossible. In practise the collapse leads to a reduction of th e\nnumber of independent variables [11] - [13] which makes a\nmodel or a method much simpler. For these reasons we will\napply the scaling theory in order to describe the core losses\nin softmagneticmaterialsexposedto anyperiodicfluxwave-\nform. In order to take into account DC Bias we apply the\nmethodderivedbyVandenBossche,etal. [6],[15].\nThis paper is organized in the following way. In Section I\n∗e-mail: adam.ruszczyk@pl.abb.com\n†e-mail: sokalski krzysztof@o2.pl\n‡e-mail: jszczyg@el.pcz.czest.plwe present the Scaling approach to modeling of core losses\nfor any periodic flux waveform. In order to take into account\nDC bias we combine the scaling with the Van den Bossche\nmethod. Section II is devoted to experiment, measurement\ndata, estimation of the model parameters and comparison of\ntheoreticalmodelwiththemeasurementdata. SectionIIIco n-\ntainsconclusions.\nI. APPROACHTOSCALINGOF CORELOSSESDATA\nInstead of an analysis based on Maxwell’s equations\n[18],[16] we have assumed that the SMM is a complex sys-\ntem in which the function of power losses obeys the scaling\nlaw. Thisassumptionleadstotheformulafortotalpowerlos s\nintheformofgeneralhomogenousfunction[9],[10]:\n∃a,b,c∈R: (1)\n∀λ∈R+Ptot(λaf,λb(△B))=λcPtot(f,(△B)),\nwherePtot- total loss of power’s density, f- frequency, △B\n- peakto peakmagneticinduction. Substituting λ=(△B)−1\nb\nwehavederivedthe generalformof Ptot:\nPtot(f,(△B))=(△B)βF/parenleftbiggf\n(△B)α/parenrightbigg\n, (2)\nwhereF(·)wasanarbitraryfunction, α=a\nb,andβ=c\nb. This\nfunction depends on the features of the phenomena to be de-\nscribed. Since our measurement data are unable to consider\nquasi-static losses we choose for F(·)the power series as a\nroughdescriptionofthepowerlosses Ptot[11]-[13]:\nPtot(f,△B)\n(△B)β=[Γ1f\n(△B)α+Γ2/parenleftbiggf\n(△B)α/parenrightbigg2\n+(3)\nΓ3/parenleftbiggf\n(△B)α/parenrightbigg3\n+Γ4/parenleftbiggf\n(△B)α/parenrightbigg4\n+...].\nNote that the left hand side of (3) is a function of the one\neffectivevariablef\n(△B)α. Itiseasytorecognizein(3)thehys-\nteresis losses Phand the eddy currentlosses Pcby the powers2\nfandf2, respectively. All highertermscorrespondto excess\nlossesPex. The formula (3) is the mathematical model, ready\nto apply. Values of α,βand amplitudes Γnhave been esti-\nmated for the ten selected soft magnetic materials [11]-[13 ].\nVeryrecently(3)hasbeenappliedtoSoftMagneticComposi-\nties [19]. Obtained results confirm the good quality of this\nmodel. Unfortunately, the model fails when a DC Bias is\npresent. In this situation we propose to keep (3) as a limit\nforHDC→0 and add the second term of a similar form to\n(3) withΓ-s dependenton HDC. These we take from Van den\nBossche,etal. [6],[15]. Theyhaveproposedmapping HDCto\nthe correspondingprimary magnetization curve which works\nvery well. In the case of a lack of appropriate experimental\ndata it is possible to use a mathematical model for HDC. For\ninstance:\nHDC→tanh(HDC·c), (4)\normoregenerally:\nHDC→{tanh(HDC·c1),tanh(HDC·c2),...,tanh(HDC·cp)},\n(5)\nwhereciarefreeparameterstobedetermined[6]. Bythisway\nwe derivethe finalmodel’sform:\nPtot(f,△B,HDC)\n(△B)β=Σ5\ni=1Γi/parenleftbiggf\n(△B)α/parenrightbiggi(1−x)\n+\nΣ3\ni=1Γi+5/parenleftbiggf\n(△B)α/parenrightbigg(i+4)(1−x)\ntanh(HDC·ci),(6)\nwherexis a small phenomenologicaltuning parameter. This\nparameter is derived in the following way. (3) arises as the\nMaclaurinseriesof(2). Thisiswhyexpansionof(3)possese s\nonly integer exponents. However, in nature this needs not be\nso. Thereforebythesmall xweintroduceanaturalcorrection\noftheseries’ exponents.\nEquation(6)hasbeensuccessfullyappliedtoSIFERRITN87,\nhowever playing with data for VITROPERM 500F 18K and\nmodel (6) we have got an expirence which suggested the fol-\nlowing modifications: 1) to split the xparameter into two in-\ndependenttuning parameters xandy, wherextunes the bias-\nindependentterm, whereas ytunes the part describing the in-\nfluenceofthebiasonthelosses,and2)todistributefunctio ns\n(5) along the HDCaxis. These requirements lead to the fol-\nlowingmodel:\nHDC→{tanh(HDC·c1−r1),...,tanh(HDC·cp−rp)},(7)\nPtot(f,△B,HDC)\n(△B)β=Σ4\ni=1Γi/parenleftbiggf\n(△B)α/parenrightbiggi(1−x)\n+\nΣ2\ni=0Γi+5/parenleftbiggf\n(△B)α/parenrightbigg(i+y)(1−x)\ntanh(HDCci+1−ri+1),(8)\nwhereridescribesthepositionofthe i-thfunction(5).\nII. EXPERIMENTALDATA ANDPARAMETERS'\nESTIMATIONS\nTheB-HLoopmeasurementshavebeenperformedfortwo\nmaterials: SIFERRIT N87andVITROPERM 500F18K.The\nFIG. 1. SIFERRIT N87. Projection of measurement points and\nscalingtheory points (6) in ((f/(△B)α)1−x,Ptot/(△B)β)plane.\nFIG.2. SIFERRITN87. Projectionof measurement points ands cal-\ningtheory points (6) in (tanh(HDC·c3),Ptot/(△B)β)plane.\nCore Losses per unit volum have been calculated as the en-\nclosed area of the B-H loop, multiplied by the frequency\nf. The following factors influence the accuracy of measure-\nments: 1) Phase Shift Error of Voltage and Current ≤4%,\n2) Equipment Accuracy ≤5,6%, 3) Capacitive Couplings\nnegligible (capacitive currents are relatively lower compared\nto inductive currents), and 4) Temperature ≤4%. For details\nof the applied measurement method and the errors of factors\nwereferto[7],[8]. Inordertoenablereaderstocomparethe ir\nown results with this work we enclose measurement data for\nSIFERRITN87(TABLEI).\nTheparametervaluesof(3)havebeenestimatedforeachsam-\nple’smeasurementdatabyminimizationof χ2usingtheSim-\nplex method of Nelder and Mead [20], see TABLE III and\nTABLEII.\nBoth measurement series consist of 30 points. All mea-\nsurementpointshavebeentakenintemperature27oC±0.5oC.\nStandarddeviationsperpointareequal12 [W\nm3Tβ]and15[W\nm3Tβ]\nfor VITROPERM 500F 18K and SIFERRIT N87, respec-3\nFIG.3. VITROPERM500F 18K. Projectionof measurement point s\nandscalingtheorypoints(8)in ((f/(△B)α)1−x,Ptot/(△B)β)plane.\nFIG. 4. VITROPERM500F 18K. Projection of measurement point s\nandscalingtheorypoints(8)in (tanh(Hc2−r2),Ptot/(△B)β)plane.\ntively. Applying the formulae (6) and (8) and the estimated\nvaluesof parameterswe havedrawnscatter plotswhichcom-\nparestimatedpointswiththeexperimentalones. Eachsampl e\nis presented in the two projections. Note that the estimated\nmodel parameters are universal, which means that they work\nfor each fand△B. Attention, in order to prevent genera-\ntionoflargenumbersintheestimationprocesstheunitoffr e-\nquencywaskHz while othermagnituteswereexpressedin SI\nunitsystem.III. CONCLUSIONS\nAgreement between the models of core losses ((6),(8))\nand the measurement data confirms the hypothesis that these\ndata obey scaling relations. Now we can construct esti-\nmators for core loss in soft magnetic materials exposed to\nnonsinusoidal periodic flux waveforms and DC Bias condi-\ntion. Moreover, thanking to data collapse the space of inde-\nTABLEI. Measurement data for SIFERRITN87\n△B[T]f[kHz]HDC[A\nm]Ptot[W\nm3]\n0,201 500,07013155,0\n0,202 504,69913384,6\n0,204 5010,7014043,9\n0,201 5014,7514338,9\n0,204 5019,8315295,3\n0,414 504,92052552,5\n0,411 509,9654106,4\n0,416 5015,1156641,6\n0,411 5020,1860464,5\n0,618 504,662118206\n0,600 5010121104\n0,619 5015,03127222\n0,613 5019,85135366\n0,807 14,810582,66\n0,814 110,29582,38\n0,812 115,29618,87\n0,804 119,81682,53\n0,810 125,26829,74\n0,804 20,0671127,81\n0,802 24,7801036,27\n0,805 210,041010,43\n0,805 214,781059,07\n0,803 219,811161,91\n0,808 54,8184066,07\n0,808 515,274098,72\n0,807 519,594418,86\n0,806 105,07712875,9\n0,806 1010,1612931,8\n0,805 1014,7813593,5\n0,806 1019,7014891,1\npendent variables is reduced from the three-dimensional on e\nspanedby [f,△B,HDC]tothetwo-dimensionalonespanedby\n[f\n(△B)α,tanh(HDC·ci)]. The consequence which results from\nthis reductionis very significant: both models(6) and (8) de -\nscribe the core loss problem completely(for each f, for each\n△Bandforeach HDC). Thequestionisthenhowmanymodel\nparametersmustoneintroduceinordertocompletelydescri be\nthecorelossinthe3-dimensionalspace.4\nTABLEII.The setof estimatedmodel’s parameters for VITROP ERM500F 18K, formula (8)\nα β x Γ1Γ2 Γ3 Γ4Γ5 Γ6\nΓ7 y c1 c2 c3 r1 r2 r3 -\n7,848601 13,40684 0,3529973 -101,7297 2390,43 -334,3942 121,0903 7,88E+00 1,29E+03\n-7,66917 9,77E-01 4,668659 9,52E-02 43,98191 0,2228664 3,042717 -2,016617 -\nTABLEIII.The setof estimatedmodel’s parameters for SIFER RITN87, formula (6)\nα β xΓ1Γ2Γ3Γ4\nΓ5 Γ6Γ7Γ8c1c2c3\n-7,7413 -11,375 -0,1712285,292 118,459 -27,1697 -2,2167\n-5,35E-01 -3,03E+01 5,8086-5,750-0,05529 8,0579 0,1102\n[1] C.P. Steinmetz, On the law of hysteresis, Trans. Amer. In st.\nElect.Eng., 9,3-64 (1892).\n[2] M. Albach, T. Durbaum, and A. Brockmeyer, Calculating co re\nlosses intransformers for arbitrarymagnetizingcurrents a com-\nparison of different approaches., IEEE Power Electronics S pe-\ncialistsConference, 1996, pp. 14638.\n[3] J.Reinert,A.BrockmeyerJ.Reinert,A.Brockmeyer,and R.W.\nDe Doncker, Calculation of losses in ferro- and ferrimagnet ic\nmaterials based on the modified Steinmetz equation, Annual\nMeetingof the IEEEIndustry Applications Society, 1999.\n[4] Jieli Li, T. Abdallah, and C. R. Sullivan, Improved calcu lation\nof core loss withnonsinusoidal waveforms, in Annual Meetin g\noftheIEEEIndustryApplicationsSociety,2001,pp.220322 10.\n[5] K. Venkatachalam, C. R. Sullivan, T. Abdallah, and H. Tac ca,\nAccurate prediction of ferrite core loss with nonsinusoida l\nwaveforms using only Steinmetz parameters IEEE Workshop\nonComputers inPowerElectronics (COMPEL),2002.\n[6] Alex Van den Bossche, Vencislav Valchev, Georgi Georgie v,\nMeasurement and loss model of ferrites in non-sinusoidal\nwaves,IEEEPower ElectronicsSpecialists Conference, 200 4.\n[7] Jonas M¨ uhlethaler, J¨ urgen Biela, Johann Walter Kolar and An-\ndreas Ecklebe, Improved Core-Loss Calculation for Magneti c\nComponents Employed in Power Electronic Systems, IEEE\nTRANSACTIONS ON POWER ELECTRONICS, 27, pp.964-\n973(2012).\n[8] J. M¨ uhlethaler, J. Biela, J.W. Kolar, A. Ecklebe, ”Core Losses\nUnder the DC Bias Condition Based on Steinmetz Parame-\nters,”IEEETransactionsonPowerElectronics, 27,pp.953-963,\n(2012).\n[9] H.E. Stanley, Introduction to Phase Transitions and Cri tical\nPhenomena, Oxford: Clarendon Press 1971.\n[10] H.E. Stanley, Scaling, universality, and renormaliza tion: Three\npillars of modern critical phenomena, Rev. Mod. Phys., 71,\nS358-S366(1999).\n[11] K. Sokalski, J. Szczygłowski, M. Najgebauer and\nW. Wilczy´ nski, Thermodynamical Scaling of Eddy CurrentLosses in Magnetic Materials, Proc. 12th IGTE Symposium, (\n2006) pp. 83-86.\n[12] K. Sokalski, J. Szczygłowski, M. Najgebauer and\nW. Wilczy´ nski, Losses scaling in soft magnetic materials,\nCOMPEL: Int. J. Comput. Math. Electr. Electron. Eng., 26,\n640-649 ( 2007).\n[13] K. Sokalski, J. Szczygłowski, and W. Wilczy´ nski, Scal ingcon-\nception of power loss’ separation in soft magnetic material s,\narXiv:1111.0939v1[cond-mat.mtrl-sci] 3Nov 2011.\n[14] J. Cale, S.D. Sudhoff, S. D. and R.R. Chan, A Field-Extre ma\nHysteresis Loss Model for High-Frequency Ferrimagnetic Ma -\nterials, IEEE Transactions on Magnetics, 44, issue 7, pp. 1728-\n1736 (2008).\n[15] A.VandenBossche, etal.,FerriteLossesofCoreswithS quare\nWave Voltage and DC bias, J. Appl. Phys., 99, p. 08M908\n(2006).\n[16] G. Bertotti, General Properties of Power Losses in Soft Ferro-\nmagnetic Materials, IEEETrans. Magn. 24, p.621 (1988).\n[17] G. Bertotti, F. Fiorillo and G. P. Soardo, THE PREDICTIO N\nOF POWER LOSSES IN SOFT MAGNETIC MATERIALS,\nJOURNAL DE PHYSIQUE, Colloque C8, Supplement au no\n12,49(1988).\n[18] G. Bertotti, A general statistical approach to the prob lem of\neddy current losses, J.Mag. Mag. Mater. 41, p.253 (1984).\n[19] B.´Slusarek, B. Jankowski, K. Sokalski, J. Szczygowski,\nCharacteristics of Power Loss in SMC a Key for De-\nsigning the Best Values of Technological Parameters, Jour-\nnal of Alloys and Compounds, 581, pp. 699-704 (2013),\nhttp://dx.doi.org/10.1016/j.jallcom2013.07.084.\n[20] W.H.Press, B.P.Flannery, S.A.Teukolsky, and W.T.Vet terling,\nNumerical Recipes. The Art of Scientific Computing , Cam-\nbridge Univ. Press 1987, pp. 289-293."    },    {        "title": "1309.0298v2.Recent_progress_in_perpendicularly_magnetized_Mn_based_binary_alloy_films.pdf",        "content": " \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  \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  \nRecent progress in perpendicularly \nmagnetized Mn-based binary alloy films \nZhu Li-Jun, Nie Shuai-Hu a, and Zhao Jian-Hua\n † \nState Key Laboratory of Superlattices and \nMicrostructures, Institute of Semiconductors, \nChinese Academy of Sciences, P. O. Box 912, Beijing \n100083, China \nIn this article, we review the recent progress in \ngrowth, structural characterization, magnetic \nproperties and related spintronic devices of \ntetragonal Mn\nx\nGa and Mn\nx\nAl thin films with \nperpendicular magnetic anisotro py. In the first part of \nthis review, we present a brief introduction to the \ndemands for perpendicularly magnetized materials in \nspintronics, magnetic recording and permanent \nmagnets applications, and the most promising \ncandidates of tetragonal Mn\nx\nGa and Mn\nx\nAl with \nstrong perpendicular anisotropy. Then, in the second \nand third parts, we focus on the recent progress of \nperpendicularly magnetized Mn\nx\nGa and Mn\nx\nAl, \nrespectively, including thei r lattice structures, bulk \nsynthesis, epitaxial growth, structural \nchracterizations, magnetic and other spin-dependent \nproperties, and spintronic devices like magnetic \ntunneling junctions, spin valves and spin injector into \nsemiconductors. Finally, we give a summary and a \nperspective of these perpendicularly magnetized \nMn-based binary alloy film s for future applications. \nKeywords: Spintronics, Magnetic material, \nPerpendicular magnetic anisotropy, Semiconductors \nPACS: 85.70.2w , 81.05.-t, 75.30.Gw, 85.30.2z \n1. Introduction \nFerromagnetic films with high perpendicular \nmagnetic anisotropy ( K\nu\n) have attracted much \nattention for their potential applications in nanoscale \nmagnetic devices with high thermal stability.\n[1-4]\n Spin \nvalves and magnetic tunneling junctions (MTJs) with \nhigh K\nu\n have been demonstrated to allow for \nrealization of high-sensitivity magnetoresistive \nsensors, spin-transfer-torque (STT) switching \nGbit-class magnetoresistive random access memory \n(MRAM) and high-power oscillators.\n[2-5]\n Magnetic \nmaterials which have high K\nu \nalong with high spin \npolarization ( P), high Curie temperature ( T\nc\n), flexible \nmagnetization ( M\ns\n) and low magnetic damping \nconstant ( α) are the most ideal combination for \nspin-transfer-torque applications to facilitate reliable \nswitching under the current density below 10\n5 \nA/cm\n2\n.\n[2-4]\n Moreover, ferromagnetic films with both \nhigh K\nu\n and good compatibility with semiconductor \nallow for not only the development of ferromagnetic \n* Project supported by NSFC 11127406 \n†\n Corresponding author: jh zhao@red.semi.ac.cn \nmetal/semiconductor hybrid devices including spin \nfield effect transistor, \n[6,7]\n spin Hall transistor,\n[8]\n light \nemitting diodes\n[9,10]\n and lateral spin valves\n[12]\n with \nperpendicular anisotropy, but also high-density \nintegration of metallic spintronics functional devices \nlike nonvolatile magneto-resistive random access \nmemory on semiconductor photonic and electronic \ncircuits.\n[12,13-17 ] \nThese approaches could also perform \nlogic, communications and storage within the same \nmaterials technology taking advantage of \nnonvolatility, increased integration density, increased \nspeed and decreased ener gy consumption compared \nwith conventional charge-based devices.\n[18] \nFurthermore, demand for increasing high-density \ndata storage leads to the replacement of in-plane \nmagnetic recording by perpendicular magnetic \nrecording. Perpendicular magnetic recording with \nareal density beyond 10 Tb/inch\n2\n requires films with \nhigh K\nu\n up to 10\n7 \nerg/cc and moderate magnetization \nM\ns\n.\n[19]\n Too high  M\ns \nmay result in strong coupling \nbetween adjacent bits, while too low M\ns\n brings about \nlow signal-noise ratio. Be sides, rare-earth magnets \nprovide the backbone of many products including \ncomputers, mobile phones, electric cars and \nwind-power generators. However, because of both \nthe increasing limited availability and high costs of \nmining and processing of rare-earth elements, new \nkind of rare-earth-free magnets are urgently \nneeded.\n[16, 20 ]\n Permanent magnets applications \nrequire materials that have large magnetic energy \nproduct, high intrinsic and extrinsic coercivities and \nlinear demagnetization cu rve in the second \nquadruple. \nAs the most outstanding representatives, \nperpendicularly magnetized Mn-binary alloys Mn\nx\nGa \n(MnGa) and Mn\nx\nAl (MnAl) have attracted much \nattention and have been studied intensively in the \npast couple of decades. L1\n0\n-MnGa (D0\n22\n-Mn\n3\nGa) \nalloys are theoretically expected to have K\nu \nof 26 (20) \nemu/cc,\n[16,21-23 ]\nMerg/cc,\n[21,22 ] \nM\ns\n of 845 (305) \n(BH)\nmax\n=(2πM\ns\n)\n2 \nof 28 (3.7) MGOe,\n[17,24 ] \nP of 71% \n(88%) at the Fermi level \n[17,21,24,25 ]\n and α of 0.0003 \n(0.001),\n[22]\n respectively. Moreover, L1\n0\n-MnAl are \ntheoretically predicted to have a K\nu \nof 15 Merg/cc, \nM\ns \nof 800 emu/cc (or 2.37 μ\nB\n/Mn) and \n(BH)\nmax\n=(2πM\ns\n)\n2\n of 12.64 MGOe.\n[26,27 ] \nThese \nfascinating magnetic properties make MnGa and \nMnAl promising in spintronics, ultrahigh-density \nmagnetic recording and economical permanent \nmagnets applications. Moreover, many experimental \nattempts have been made to the preparation and \ncharacterization of MnGa and MnAl bulks and films, \nand their related spintronic devices like magnetic \ntunneling junctions, spin valve and spin-injection \ndevices. In this article, we will present an overview \nof recent progress on the growth ， structural \ncharacterization, magnetic properties and some other \nproperties of perpendicularly magnetized Mn\nx\nGa and \nMn\nx\nAl alloys and their related spintronic devices. \n1 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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   2. Mn\nx\nGa with perpendicular magnetic anisotropy \n2.1 Lattice structure and synthesis of Mn\nx\nGa bulks \nAlloys of Manganese (Mn) and Gallium (Ga) \nhave quite complicated phase diagram (Fig. 1a) with \nseveral magnetically ordered phases.\n[28-30 ]\n This \nreview is mainly confined to two most interesting \ntetragonal phases with strong magnetism and high \nCurie temperature: the first is L1\n0\n-ordered ( γ\n3\n) \nthermal-dynamically ferromagnetic phase for 0.76 ≤ \n 1.8;\n[17,31,32 ]\nx ≤  the second is D0\n22\n-ordered ( ε) \nferrimagnetic phase, forming when 2 ≤ x <3.\n[25,33-36 ] \nThe lattice units of both L1\n0\n-MnGa and D0\n22\n-Mn\n3\nGa \nare outlined in Fig. 1(b). The lattice unit of \nL1\n0\n-MnGa consists of Mn and Ga monatomic layers \nstacked alternately along the c axis. The lattice \nconstants of L1\n0\n-MnGa bulk (space group  P4/mmm ) \nare a=3.88-3.90  Å and c=3.64-3.69 Å.\n[31,32 ]\n Bither et \nal. synthesized L1\n0\n-Mn\nx\nGa (1.2< x ≤ 1.5) \npolycrystalline bulks.\n[31]\n Lu et al.  systemically \ninvestigated the crystalline structures of Mn\nx\nGa \nbulks in a broad composition range of \n1.15< x<1.89.\n[32]\n For perfect stoichiometric \nL1\n0\n-MnGa ( x=1), each Mn atom is expected to \ncontribute a magnetic moment of 2.51 μ\nB \n(corresponding to magnetization of 845 emu/cc); the \nmagnetism of L1\n0\n-Mn\nx\nGa may also strongly be \ninfluenced by compositions and strains.\n[16,17,23,25,31,36 ] \nAs theoretically predicted, excess Mn atoms will \nalign antiparallel to the rest and result in \ncompensation, and strains will also induce a decrease \nof Mn moment.\n[23,31 ] \nFor D0\n22\n-Mn\nx\nGa bulk (space \ngroup  I4/mmm ), the lattice constants are a=3.90-3.94 \nÅ and c=7.10-7.17 Å.\n[33-35 ]\n Krén and Kádár obtained \nD0\n22\n-Mn\n2.5\nGa bulks by annealing hexagonal D0\n19\n-Mn\nx\nGa at 350-400 \no\nC for 1-2 weeks, and \nrevealed the ferrimagnetism with Mn atom magnetic \nmoment of 2.8 ± 0.3 μ\nB \nand 1.6 ± 0.2 μ\nB\n at site I and \nsite II, respectively, by neutron diffraction \nmeasurement.\n[33]\n Niida et al.  and Winterlik et al . \nsynthesized polycrystalline D0\n22\n-Mn\nx\nGa bulks in the \ncomposition range of 1.94 ≤ x ≤2.85\n[34]\n and 2≤ x \n≤ 3,\n[25]\n respectively, and revealed the \ncomposition-sensitive magnetization in the \nmagnetically frustrated ferrimagnets. With Mn \ncontent increasing, lattice constant a slightly \nincreases or keeps constant, while c always decreases \nmonotonically.\n[25, 31-36 ]\n Huh et al.  synthesized Mn\nx\nGa \nnano-ribbons with L1\n0\n (x=1.2, 1.4, 1.6) and \nD0\n22\n-ordering ( x=1.9) using arc-melting and \nmelt-spinning followed by a heat treatment and \ninvestigated their magnetic and transport \nbehaviors.\n[37]\n The Curie temperature of Mn\nx\nGa \nnano-ribbons are found to increase with increasing x. \nAll the ribbons are metallic transport behavior, in \nconsistent with MnGa films. \nThe magnetic properties of Mn\nx\nGa alloys, \nespecially giant perpendicular anisotropy, high spin \npolarization, high Curie temperature, flexible \nmagnetization and low magnetic damping constant \nare promising for applications of magnetic recording, \npermanent magnets and spintronics like magnetic \nsensors, memories and logics.\n[16,17 ]\n Reliable growth \nof smooth MnGa thin films and effective tailoring of \nthe magnetism are of particular importance for the \npossible practical applications in not only metal \nspintronics but also semicon ductor spintronics. In the \nfollowing, we will overview the recent progress in \nthe growth and characterizations of L1\n0\n-MnGa films. \nFig. 1. (a) Phase diagram of Mn-Ga alloys, based on [ 30]; (b) Lattice unit of MnGa with  L1\n0\n (left) and D0\n22\n (right), \narrows stand for magnetic moment directions of  Mn atoms (Reprinted with permission from [ 17]). \n2.2 Growth and magnetic properties of Mn\nx\nGa \nepitaxial films \nIn recent couple of decades, a great deal of effort \nhas been made on growth of L1\n0\n and D0\n22\n-Mn\nx\nGa \nfilms by magnetron sputtering or molecular-beam \nepitaxy (MBE). Since Krishnan and Tanaka et al. \nrespectively observed square perpendicular \nhysteresis of Mn\nx\nGa (1.2< x<1.5) grown on GaAs \n(001) by magneto-optical, magnetic and transportation measurements  in the early years of \n1990s,\n[38,39 ]\n the growth and characterizations of \nL1\n0\n-Mn\nx\nGa films have been intensively studied on \nmany kinds of substrates, such as GaN, GaSb, Si, \nAl\n2\nO\n3\n and MgO with different buffer layers (ScN \nand Cr).\n[36, 40-44 ]\n However, only a few of those films \non GaAs and MgO demonstrated magnetic \nperpendicular anisotropy. D0\n22\n-Mn\nx\nGa films have \nbeen prepared mainly on MgO (001) \n2 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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 \n \n   \n  \n \n substrates.\n[22,35,36,45-47 ]\n Wu et al.  reported magnetic \nand magneto-transport properties of Mn\nx\nGa ( x=2.5 \nand 2.0) epitaxial films on Cr-MgO (001) and even \nfound perpendicular anisotropy in 5 nm-thick \nfilms.\n[45,47 ]\n Kurt et al.  prepared stoichiometric \nD0\n22\n-Mn\n3\nGa films with perpendicular easy axis on \nMgO, Pt-MgO and Cr-MgO, and observed the spin \npolarization of 58% (40%) in Mn\n3\nGa (Mn\n2\nGa). \n[35,47 ] \nRecently, Nummy et al.  and Zha  et al. reported \nnanostructured Mn\nx\nGa films on Si/SiO\n2\n with \ncoercivity over 20 kOe and discussed the possibility \nfor permanent magnet applications, respectively.\n[48,49 ] \nMotivated by the great application potential and \ninspiring result of Mn\nx\nGa alloys, we prepared Mn\nx\nGa \nepitaxial films in a wide composition range (0.76 ≤ \nx≤ 2.60) on GaAs (001) substrates by MBE, and \ncarried out detailed studies on the tailoring of \nmagnetism in these films with giant perpendicular \nanisotropy, ultrahigh coer civity and large energy \nproduct.\n[16,17 ] \nTable1. Lattice constants of representative metals, \ninsulators and semiconductors and calculated misfit \nin respect to D0\n22\n-Mn\n3\nGa ( a=3.910 Å), L1\n0\n-MnGa \n(a=3.886 Å) and L1\n0\n-MnAl ( a=3.920 Å). * \nrepresents the lattice constants after 45\no\n in-plane \nrotation ( a*=a/√2). \nbuffer a \n(Å) f\nD022-Mn3Ga \n(%) \nf\nL10-MnGa \n(%) f\nL10-MnAl \n(%) \nCu 3.61 8.3 7.6 8.6 \nPd 3.89 0.5 -0.1 0.8 \nPt 3.92 -0.3 -0.9 0 \nAu 4.08 -4.2 -4.8 -3.9 \nAg 4.09 -4.4 -5.0 -4.2 \nAl 4.05 -3.5 -4.0 -3.2 \nCr 4.07* -4.0 -4.6 -3.8 \nSi 3.94* -0.8 -1.4 -0.5 \nSrTiO\n3\n 3.91 0 0.8 0.3 \nGaAs  4.00* -2.1 -2.7 -1.9 \nMgO  4.21 -7.2 -7.8 -7.0 \nInAs 4.28* -8.6 -9.1 -8.4 \nAlAs 4.00* -2.2 -2.7 -1.9 \nTo realize the practical applications, especially \nfor spintronics, it is essential to choose suitable \nsubstrates with small lattice misfit for epitaxial \ngrowth of Mn\nx\nGa films simultaneously with high \nmagnetic performance, good structural quality and \nsmooth surface. Table 1 summarizes the in-plane \nlattice constants of representative metals, insulators \nand semiconductors with (001) orientation and \ncalculated misfit f of D0\n22\n-Mn\n3\nGa ( a=3.910 Å) and \nL1\n0\n-MnGa ( a=3.886 Å). Simply in view of lattice \nmisfit, Pt (001), Pd (001), Si (001), SrTiO\n3\n (001) and \nGaAs (001) should be the best choices for epitaxial \ngrowth of both D0\n22\n and L1\n0\n films. To our best \nknowledge, the report of both L1\n0\n- and D0\n22\n- Mn\nx\nGa epitaxial films grown on Pd is still lacking. \nPerpendicularly magnetized L1\n0\n-Mn\nx\nGa was not \navailable on Si (001) probably due to strong reaction \nbetween metal layer and active silicon though f \nbetween  L1\n0\n-MnGa and Si (001) is only 1.4%.\n[43]\n So \nfar, only Pt, GaAs and SrTiO\n3\n buffers have been \nexperimentally confirmed to be good choice for \nepitaxial growth of Mn\nx\nGa films with flat surface \nand high crystalline quality.\n[16, 17, 35, 47 ] \nAs a recent \nreview outlined,\n[24]\n the surfaces of Mn\nx\nGa films on \nCr and MgO buffers appeared to be very rough with \ndiscontinuous islands,\n[47]\n whereas films on Pt and \nGaAs buffers exhibited very smooth surfaces, since \nthe misfit of D0\n22\n-Mn\n3\nGa is -7.2%, -4 .0%, -0.3% and \n2.2% in respect to MgO, Cr, Pt and GaAs buffers, \nrespectively. Therefore, it seems difficult to directly \nprepare smooth Mn\nx\nGa films on MgO or sharp \nMn\nx\nGa-MgO interface for high-TMR MTJ due to the \nlarge misfit.\n[50-53 ]\n Recently, Glas et al. also reported \nsmooth Mn\nx\nGa (x=2.9) films with ro ot mean square \n(RMS) even below 0.25 nm on SrTiO\n3\n.\n[54] \nZhu et al. \nreported Mn\nx\nGa samples ( 0.76≤x≤2.60) grown on \nGaAs with good homogeneity and abrupt \ninterfaces\n[16,17 ]\n as revealed by the low-magnification \nTEM image in the inset of Fig. 2(a). \nThe structural and magnetic properties of \nMn\nx\nGa films could be tailored effectively by several \nreliable methods, such as by controlling growth \ntemperature ( T\ns\n),\n[16]\n tuning composition ( x),\n[17, 36 ] \n[17]\nchanging annealing conditions  and selecting \ndifferent substrates.\n[42,43 ]\n In the following paragraphs, \nwe will show in detail how T\ns\n and x influence the \nstructure and magnetism, taking Mn\nx\nGa films grown \non GaAs (001) as examples. \n3 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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  \n  \n  \n \n \n \n    \n  \n \n \n Fig. 2. (a) TEM image of MnGa films ( x=1.5) grown \non GaAs (001). The inset shows low-magnification \nTEM image. (b) XRD patterns of MnGa films ( x=1.5) \ngrown at 100, 150, 200, 250 and 300 \no\nC, respectively. \nReprinted with permission from [ 16]. \nFigure 2(a) shows representatively a \nhigh-resolution cross-sectio nal transmission electron \nmicroscopy (TEM) image of Mn\nx\nGa films grown on \nGaAs,\n[16]\n indicating a well-textured Mn\nx\nGa layer \nwith c-axis perpendicular to GaAs substrate. The \nepitaxial relationship of \nMnGa(001)[100]||GaAs(001)[110] can be derived \nfrom the high-resolution TEM image, coinciding \nwith reflection high energy electron diffraction \n(RHEED) patterns. Figure 2(b) shows examples of \nsynchrotron x-ray diffraction θ-2θ patterns of Mn\nx\nGa \n(x=1.5) films grown at different temperature.\n[16] \nFor \nall the films grown at temperatures from 100 to 350 \no\nC, only sharp (001) superlattice peaks and (002) \nfundamental peaks of L1\n0\n-Mn\nx\nGa films can be \nobserved in the range from 20\no \nto 70\no\n besides the \npeaks of GaAs substrates, i ndicating that these are all \n(001)-textured single-crystalline films with c-axis \nalong the normal direction, in agreement with \ncross-sectional TEM images and in situ  RHEED \npatterns. \nFig.3. (a) Perpendicular \nand in-plane hysteresis \nloops of the 100 \no\nC-grown L1\n0\n-Mn\n1.5\nGa \nfilms measured by \nPPMS. (b) Perpendicular \nhysteresis loops of the \nL1\n0\n-Mn\n1.5\nGa films \ngrown at different \ntemperature ( T\ns\n) \nmeasured by SQUID. (c) \nM\nr\n/M\ns\n, (d) M\ns\n, (e) H\nc\n and \n(f) K\nu\n plotted as a \nfunction of T\ns\n. Reprinted \nwith permission from \n[16]. \nFigure 3(a) shows both perpendicular and \nin-plane hysteresis loops of a typical Mn\n1.5\nGa film \nmeasured at 300 K.\n[16]\n A nearly square loop with \nultrahigh coercivity ( H\nc\n) of 42.8 kOe and remnant \nmagnetization ( M\nr\n) of 27.3 emu/cc is observed from \nthe perpendicular M-H  curve. However, the in-plane \nM-H  curve exhibits almost anhysteretic loop, zero \nremnant magnetization and high saturation field \nexceeding 90 kOe. This observation offers a direct \nevidence for the giant perpendicular magnetic \nanisotropy. The same feature holds for all the films \ngrown at temperatures between 100 and 300\n o\nC. \nFigure 3(b) shows the perpendicular M-H  curves of \nMn\n1.5\nGa films grown at different temperature, \nrevealing a significant influence of growth \ntemperature ( T\ns\n) on the magnetic properties. Figures \n3(c)-3(f)  summarize the values of M\nr\n/M\ns\n, M\ns\n, H\nc\n and \nK\nu\n as a function of T\ns\n. As shown in Fig. 3(c), M\nr\n/M\ns \nkeeps a nearly invariant value large than 0.94 for all \nthe films, very different from those of L1\n0\n-Mn\n1.5\nGa \n[40-49 ] \nM\ns\nfilms grown on GaN, GaSb, Si and Al\n2\nO\n3\n.\nincreases monotonically from 27.3 to 270.5 emu/cc \nas T\ns\n increases, which is much smaller than the \ncalculated value of 2.51 μ\nВ\n/Mn (~845 emu/cc) for \nL1\n0\n-MnGa\n[16,21-23 ]\nstoichiometric due to both the overall strains and off-stoichiometry. As shown in \nFig. 3(e), H\nc \nhas a maximum of 42.8 kOe at 100\n o\nC, \nthen drops to 8.1 kOe at 250\n o\nC, and finally climbs \nup to 10.8 kOe at 300\n o\nC. The ultrahigh H\nc\n in these \nL1\n0\n-Mn\n1.5\nGa films was attributed to the combination \nof giant perpendicular magnetic anisotropy and \nimperfection including chemical disorder, lattice \ndefects and overall tensile strains.\n[16]\n Importantly, the \nimperfection contribution to H\nc\n seems to be the same \norder of magnitude as the contribution from the \nmagnetic anisotropy since H\nc \ncan be tailored so \nobviously over the large scale from 8.1 to 42.8 kOe. \nWith increasing T\ns\n, K\nu \ngoes up monotonically and \nreaches the maximum value at 250 \no\nC and then \ndecreases with further increasing T\ns\n. The maximum \nK\nu \nof 21.7 Merg/cc is roughly consistent with the \ntheoretical value of 26 Merg/cc for L1\n0\n-Mn\n50\nGa\n50\n,\n[21] \nwhile much larger than reported Mn\nx\nGa films grown \non other semiconductors\n[38-41 ]\n and MgO.\n[22] \nImportantly, such a giant K\nu\n of 21.7 Merg/cc in these \nL1\n0\n-Mn\n1.5\nGa films supports nanoscale spintronic \ndevices, such as spin-transfer-torque MRAMs bits, \ndown to 5 nm in size and high-density bit-patterned \nrecording with areal density up to 27 Tb/inch\n2\n and \n60-year thermal stability.\n[16] \n4 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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 \nFig. 4. Experimental magnetic energy products \n(BH)\nmax\n of L1\n0\n-Mn\n1.5\nGa films with comparison with \nideal value (2 πM\ns\n)\n2 \n. The inset shows the B-BH \ncurves. Reprinted with permission from [16]. \nMagnetic materials with large magnetic energy \nproduct and noble-metal-free composition are also \npromising in permanent magnets applications.\n[20]\n The \nmagnetic energy product ( BH)\nmax\n of L1\n0\n-Mn\nx\nGa \nfilms was further evaluated and compared with the \nideal value (2 πM\ns\n)\n2\n in Fig. 4. (BH)\nmax\n climbs up \nmonotonically from 0.02 to 2.60 MGOe as T\ns \nincreases and almost the same as ideal value (2 πM\ns\n)\n2 \nwhen T\ns\n<250\n o\nC because of the very high M\nr\n/M\ns\n. \n(BH)\nmax\n at T\ns\n = 300 \no\nC is slightly smaller than the \nideal value probably due to the rounding at corner of \nM-H  loops and the small difference between M\ns\n and \nM\nr\n (M\nr\n/M\ns \n= 0.94). The largest magnetic energy \nproduct up to 2.60 MGOe are observed in the film \ngrown at 300\n o\nC, which is larger than that previously \nreported in bulk polycrystalline D0\n22\n-Mn\n2~3\nGa alloys \n(<5.5 kJ/m\n3\n or 0.68 MGOe)\n[35]\n and steels magnets \n(~1 MGOe)\n[20]\n, and also comparable with hard ferrite \nmagnets (~3 MGOe).\n[20]\n Therefore, the \nrare-earth-free compositions,  high coercivity and \nlarge magnetic energy product together make this \nkind of L1\n0\n-Mn\nx\nGa films promising to be developed \nfor economical permanent magnets. \nBoth the structural and magnetic properties of \nMn\nx\nGa epitaxial films were observed to be very \nsensitive to the composition. Recently, Mizukami et \nal. and Zhu et al.  carried out symmetrical studies on \nthe synthesis and strongly x-dependent magnetic \nproperties of (001)-orientated Mn\nx\nGa epitaxial films \nwith x=1.2-3 grown on Cr-buffered MgO (001)\n[36] \nand films with x=0.76-2.6 grown on GaAs (001),\n[17] \nrespectively. Figure 5(a) shows examples of XRD \nθ-2θ patterns of 250 \no\nC-grown Mn\nx\nGa films with \ndifferent x grown on GaAs (001) by MBE.\n[17]\n For \n0.76≤ x ≤1.75, L1\n0\n-MnGa films shows both sharp \n(001)  superlattice peaks and (002) fundamental peaks \nin the range from 20\no \nto 70\no\n besides the peaks of \nGaAs substrates, indicating that these are all \n(001)-textured single -crystalline films. For film with \nx=0.74, three small peaks irrelative to L1\n0\n appear, which become dominating for film with x = 0.55. \nThe new phase could be best fitted by cubic MnGa\n4 \nwith enlarged c axis of 3.91 Å. For film with x = 2.60, \nonly the fundamental peak could be found due to the \nhigh disorder. As shown in Fig. 5(b), the x-ray \nreflection (XRR) curves with the strong oscillations \nsuggest sharp interfaces and good homogeneity of \nthese samples. \nFig. 5. (a) XRD patterns of MnGa films with \ndifferent composition ( x). (b) XRR curves of MnGa \nfilms with x = 0.76 and 2.6. Reprinted with \npermission from [ 17]. \nFig. 6. (a) Temperature dependence of remanent \nmagnetization ( M\nr\n); (b) Perpendicu lar and in-plane \nhysteresis loops of Mn\n1.4\nGa films grown at 250 \no\nC. \nReprinted with permission from [17]. \n5 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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 \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 Figure 6(a) shows a typical temperature \ndependence of remanent magnetization of Mn\nx\nGa \nfilms with Curie temperature of 630 K.\n[17]\n Figure 6(b) \nshow an example of hysteresis loops of L1\n0\n-Mn\n1.4\nGa \nfilms grown at 250 \no\nC.\n[17]\n The sample exhibites a \nfairly square perpendicular loop with high \nperpendicular coercivity of  11 kOe and anhysteretic \nin-plane loops with giant saturation fields exceeding \n14 T. These characteristics imply strong anisotropy \nexisting in this kind of films. \nFigures 7(a)-(c)  display the x-dependent \nmagnetic properties including M\nr\n/M\ns\n, M\ns\n and H\nc \ndetermined from the 300 K perpendicular M-H \ncurves of these 250 \no\nC-grown films. The Mn\nx\nGa \nfilms with x=0.97-1.75 exhibit high M\nr\n/M\ns\n exceeding \n0.90; but those with x deviated from this range show \ndramatically decreased  M\nr\n/M\ns\n. As shown in Fig.  7(b) , \nM\ns \ndecreases dramatically from 450 to 52 emu/cc \nwith x increases from 0.76 to 2.60, which should be \nattributed partly to the increase of antiferromagnetic \ncoupling between Mn atoms at different sites,\n[21] \npartly to the increase of strains induced by short c \naxis.\n[16,23 ] \nThe maximum M\ns\n of 445 emu/cc in \nMn\n0.76\nGa, is still below the calculated value of 845 \nemu/cc for stoichiometric L1\n0\n-MnGa\n[16,21 ]\n and \nexperimental value of 600 emu/cc in 400-450 \no\nC-annealed Mn\n1.17\nGa grown on MgO\n[36]\n probably \ndue to the low growth temperature. H\nc\n climbs up \nfrom 4.38 to 20.1 kOe as x increases from 0.76 to \n1.75, and then drops to 1.1 kOe at x=2.60. This \nchange tendency is consistent well with that of K\nu \nestimated in Fig. 7(d) following the method used in \nref. 16 . K\nu\n exhibits large values from 8.6 to 21.0 \nMerg/cc in L1\n0\n range, while quickly degrades to 0.02 \nMerg/cc in D0\n22\n-Mn\n2.6\nGa grown on GaAs because of \nincreased disorder. Noticeably, D0\n22\n-Mn\nx\nGa with \nhigh ordering and high quality may also demonstrate \nhigh K\nu\n values, such as those grown on MgO \nsubstrates at high temperatures.\n[36,45 ] \nAs ever \ndiscussed,\n[16,25 ]\n rare-earth-free and noble-metal-free \nMn\nx\nGa alloys are considerable for economical \npermanent magnet application. Since intrinsic \ncoercivity H\nc\n determined from M-H  curves, normal \ncoercivity H\ncB\n determined from B-H curves and \nmagnetic energy products ( BH)\nmax\n are three key \nfeatures of quality of permanent magnets, we further \ncalculated H\ncB\n and ( BH)\nmax\n in Figs. 7(e) and (f). With \nincreasing x in the phase-pure range, both H\ncB\n and \n(BH)\nmax\n decrease nearly  monotonically, \ncorresponding to the decrease of M\ns\n. The film with x \n= 1.07 shows the highest H\ncB\n and ( BH)\nmax\n of 3.6 kOe \nand 3.4 MGOe, respectively. The maximum of 3.4 \nMGOe is larger than that recent reported in Mn\n1.5\nGa \nfilm (2.6 MGOe)\n[16]\n and ferrite magnets (3 \nMGOe),\n[20]\n which makes L1\n0\n-Mn\nx\nGa alloys with low \nMn compositions still promising to be developed for cost-effective and high-performance permanent \nmagnets applications. Taking into consideration of all \nthe magnetic properties shown in Figs. 7(a)-7(f) , \nlow-Mn-composition L1\n0\n-Mn\nx\nGa films are more \nadvantageous than those D0\n22\n films to be developed \nfor applications in magnetic recording with areal \ndensity over 10 Tb/inch\n2\n, high-pe rformance \nnanoscale spintronic devices like MRAM bits with \nsize down to several nm and economical permanent \nmagnet applications, since they simultaneously \nexhibit high M\nr\n/M\ns\n, M\ns\n, K\nu\n, H\nc\n, H\ncB\n and ( BH)\nmax\n. \nFor further understanding of the \ncomposition-dependent magnetism, the structural \nand magnetic data for typical Mn\nx\nGa films grown on \nMgO (001) substrates are summarized in Table 2. \nThe magnetization of these films grown on MgO \nsubstrates degrades monotonically with increasing x, \nin consistence with on the case of Mn\nx\nGa films \ngrown on GaAs, which should be attributed partly to \nthe increase of antiferromagnetic coupling between \nMn atoms at different sites,\n[21]\n partly to the increase \nof strains induced by short c axis.\n[16,23 ]\n These films \nalso demonstrated giant perpendicular anisotropy K\nu \nof 10\n6\n-10\n7 \nerg/cc and huge coercivity H\nc\n varying \nfrom 1 to 18 kOe. Noticeably, the values of H\nc \nalways tend to be larger in films with higher \nMn-composition than films with lower \nMn-composition, while values of  K\nu\n s e e m  t o  h a v e \ncomplicated dependences on compositions, probably \ndue to the influence of different growth conditions or \nbuffers. \nIt is also worth mentioning that the magnetism \ncould be effectively tailored by post-growth \nannealing \n[17]\n and choosing different substrates. By \nusing different substrates like semiconductors (GaAs, \nGaSb, GaN, Si, ScN, etc), insulators (SiO\n2\n, Al\n2\nO\n3\n, \nMgO, etc) and metals (Cr, Pt, etc), Mn\nx\nGa films \nwould crystallized into diff erent structures, such as \ndifferent crystalline orientation,\n[42,43 ]\n different \n[35,47-49 ]\nmorphology and different strains,\n[16]\n and \nfurther have different magnetic anisotropy and other \nmagnetic properties. \nTherefore, Mn\nx\nGa films are observed to \nexhibit giant perpendicular magnetic anisotropy, \nflexible magnetization, huge coercivity, large energy \nproducts and high Curie temperature. Meanwhile, the \nmagnetism of Mn\nx\nGa films could be effectively \ntailored via several reliable ways, especially by \ncontrolling growth temperature, tuning compositions, \npost-growth annealing and selecting substrates. \nThese data provide a comprehensive diagram for \ntailoring and improving the structure and magnetism \nof Mn\nx\nGa films, which would be helpful for \nunderstanding this kind of material and approaching \nsuccessful applications in a variety of spintronic \ndevices, magnetic recording and permanent magnets \n6 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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  \nFig. 7. Composition x dependence \nof (a) M\nr\n/M\ns\n, (b) M\ns\n, (c) H\nc\n and (d) \nK\nu\n of Mn\nx\nGa films grown on \nGaAs (001) at 250 \no\nC. Reprinted \nwith permission from [ 17]. \nTable 2 Structural parameters and magnetic data of typical Mn\nx\nGa films grown on MgO (001). T represents \ngrowth or annealing temperature.\n Substrate T \n(\no\nC) a \n(Å) c \n(Å) M\ns\n (300 K) \n(emu/cc) K\nu\n(300 \nK) \n(Merg/cc) H\nc \n(300 \nK) \n(kOe) Reference \nMn\n3\nGa Pt-MgO 250 - 7.12 110 8.9 18 [35, 47 ] \nMn\n3\nGa MgO 350 - 7.07 140 19.1 18 [35, 47 ] \nMn\n3\nGa Cr-MgO 350 - 6.96 140 4 17 [35, 47 ] \nMn\n3\nGa Cr-MgO 400 - 7.10 200 - 15 [36] \nMn\n2.5\nGa Cr-MgO 400 3.91 7.11 250 12 6 [46] \nMn\n2.1\nGa MgO 450-500 3.92 7.11 305 15 - [22] \nMn\n2\nGa MgO 360 - 7.16 470 23.5 3.6 [35] \nMn\n1.2\nGa Cr-MgO 400-500 3.90 3.60 600 15 1 [36] \n2.3 Other spin-dependent properties of Mn\nx\nGa \nepitaxial films \n2.3.1  Spin polarization \nFor magnetic sensors, memories and \noscillators, it is advantageous to use materials with \nhigh spin polarization, which allows for high \nmagnetoresistance ratio and high signal to noise \nratio. As calculated by Sakuma and Winterlik et al. \nstoichiometric L1\n0\n-MnGa and D0\n22\n-Mn\n3\nGa should \nhave high spin polarization of 71% and 88% at the \nFermi level, respectively.\n[21,25 ]\n The spin polarization \nwas also predicted to decrease with Mn deficiency, \natomic disorder and strain.\n[25]\n Kurt et al.  performed \npoint contact Andreev reflection spectroscopy \nmeasurements and determined spin polarization of \n58% and 40% at 2.2 K in D0\n22\n-Mn\n3\nGa and Mn\n2\nGa \nfilms, respectively.\n[47]\n Higher spin polarization was \nexpected in perfectly ordered D0\n22\n-Mn\nx\nGa films \nalthough detailed investigations are still missing. To \nour best knowledge, there have also been no available reports about experimental measurements \nof spin polarization of L1\n0\n-Mn\nx\nGa alloys. Further \ninvestigations on spin polarization are needed. \n2.3.2  Magnetic damping \nSpin-transfer-torque (STT) is a phenomenon of \nmagnetization switching induced by spin current. \nFor STT-driven spintronic devices, a low critical \ncurrent for current-induced magnetization switching \nis preferred for low energy consumption and reliable \nswitching.\n[2,55]\n The critical switching current can be \nwritten as: \n\n \neI =\n \nK V \nC0 u \n\nB\ng(P,\n \n) \n(1) \nwhere α is magnetic damping constant; K\nu\n, \nperpendicular anisotropy; V, volume of magnets; γ, \ngyromagnetic ratio; μ\nB\n, Bohr magnetron; e, the \nelementary charge; g(P,θ), function of spin \n7 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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 \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 polarization ( P) of tunnel current and the angle ( θ) \nbetween the magnetization of the free and the \nreference layers. \nAs indicated in Eq. (1), perpendicular \nmagnetized materials with combination of high P, \nlow α and low K\nu\n are preferred for \nlow-switching-current STT device applications. \nGenerally, a high K\nu\n and a low critical switching \ncurrent I\nc0\n are in contrast, but high K\nu\n is absolutely \nessential for long time stability. However, a \ncombination of high P and K\nu\n with low enough α \ncould still provide a possibility for a low I\nc0\n and long \ntime thermal stability. Except for the high P and K\nu\n, \nthe noble-metal-free Mn\nx\nGa alloys also have much \nlower magnetic damping constants than those of all \nthe other perpendicular-anisotropy materials to our \nbest knowledge, due to the low density of states at \nthe Fermi level and the weak spin-orbit interaction \nin light 3 d elements Mn and Ga.\n[22]\n Time-resolved \nMOKE experiment revealed the damping constants \nof 0.008 (0.015) for Mn\n1.54\nGa (Mn\n2.12\nGa) films, \nwhich are one or two order smaller than that of \nknown materials with large perpendicular \nanisotropy.\n[2]\n First-principles calculations indicate \neven lower damping constant of 0.0003 (0.001) for \nL1\n0\n-MnGa ( D0\n22\n-Mn\n3\nGa) defect-free alloys.\n[22] \nTherefore, with respect to both high thermal stability \nand low critical switching current, Mn\nx\nGa alloys \nwith either L1\n0\n or D0\n22\n ordering are advantageous \nfor low-current-switching STT-memory and \noscillator applications. \n2.3.3 Magneto-optical Kerr effect \nPerpendicularly magnetized materials with \nlarge Kerr rotation angle and optical reflectivity are \nalso promising in high-density perpendicular \nmagneto-optical recording. Krishnan first studied the \nmagneto-optical properties of L1\n0\n-Mn\n1.5\nGa films \ngrown on GaAs (001) in 1992.\n[38]\n The film exhibited \na large Kerr rotation angle of ~0.1\no\n at 820 nm. \nFurthermore, reflectivity around 65%-70% were \nfound over a broad wavelength range from \nultraviolet to far infrared. From a technological point \nof view, the epitaxial growth on semiconductor and \nthe high-performance magneto-optical properties \nwould make the exciting possibility of the \nintegration of magneto-optic and semiconductor \ndevices a reality. \n2.3.4  Anomalous Hall effect \nAnomalous Hall effect (AHE), related to \nspin-orbit interaction in magnetic materials, has \npotential for sensor, memory and magnetic logic \napplications.\n[45]\n Large AHE has been observed in \nvarious PMA films including L1\n0\n-FePt, FePd, \netc.\n[56,57 ]\n Accordingly, study of AHE in Mn\nx\nGa films \nis of great importance not only for practical \napplications but also helpful for comprehending the \nwidely disputed mechanism of AHE. Tanaka  et al. measured the AHE hysteresis of L1\n0\n-Mn\n1.5\nGa films \non GaAs and found the AHE resistivity \n[39]\nsample-dependent, changing from 0.5-4 μΩ.cm.\nBedoya-Pinto revealed noticeably \ncomposition-dependent scaling behavior in \nL1\n0\n-Mn\nx\nGa (x=0.96, 1.38 and 2.03) films on GaN.\n[41] \nWu et al.  observed AHE resistivity up to 11.5 μΩ.cm \nin D0\n22\n-Mn\n2\nGa,\n[45]\n which is much larger than that of \nother perpendicular-anisotropy materials, such as \nL1\n0\n-FePt (1-6 μΩ cm).\n[56,57 ]\n Glas  et al. studied \nD0\n22\n-Mn\nx\nGa ( x=2.3, 2.6 and 2.9) films grown on \nMgO and SrTiO\n3\n, and discussed the determined \nskew scattering and side jump coefficients with \nregard to the film composition and compared to the \ncrystallographic and magnetic properties.\n[54]\n Zhu et \nal. reported AHE and the scaling behavior of \nL1\n0\n-Mn\n1.5\nGa films grown on GaAs (001) and found \nsignificant influence of disorder on the scaling \nbehaviors.\n[58]\n However, for furthe r understanding of \nthe underlying physics, more detailed studies will be \nneeded. \n2.4. Thermal and Chemical stability \nStructural stability of materials is of particular \nimportance for practical applications. L1\n0\n-ordered \nMn\nx\nGa have been widely believed to keep \nthermal-dynamically stable up to at least 800 K,\n[31,32 ] \nby contrast, Mn\nx\nGa with D0\n22\n-ordering are observed \nto be metastable and will transfer to \nantiferromagnetic hexagonal D0\n19\n phase at \nK.\n[25,33,34 ]\ntemperature over 770 Zhu et al. \ninvestigated the thermal stability of MnGa/GaAs \ninterface by performing systematical post-growth \nannealing experiments taking L1\n0\n-Mn\n0.76\nGa film as \nan example, which exhibits the largest M\ns\n among all \nthe as-grown films with different x (Fig. 7(b)). \nFigure 8(a) shows XRD patterns of as-grown and 10 \nmin-annealed Mn\n0.76\nGa films, from which we found \nthe Mn\n0.76\nGa film itself is thermal stable up to 450 \no\nC, and the interface could keep stable up to at least \n350 \no\nC. This result roughly agrees with previous \nreport that Mn\nx\nGa with  x<1.5 should keep stable on \no\nC.\n[59]\nGaAs below 400 Interestingly, very weak \nMn\n2\nAs (003) peak as a result of interfacial reaction \nis observable by high-sensitivity synchrotron XRD \nmeasurement, which may be undetectable by \ncommon XRD with Cu K α radiation.\n[59]\n Fortunately, \nthe stable temperature of at least 350\n o\nC could still \nsatisfy the demand of integration with \nmetal-oxide-semiconductor transistors. \nAs to the chemical stability in the ambient \nconditions, there have been disputations on the \nchemical stability of Mn\nx\nGa alloys. Roy et al.  found \nan oxide layer of less than 5 nm formed at the \nMn\nx\nGa surface,\n[60]\n but Wang et al.  found no signs of \noxidation of Mn\nx\nGa films in air atmosphere.\n[61]\n In \nfact, a capping layer is al ways used to prevent \npossible oxidation of Mn\nx\nGa film.\n[16,36,38 ]\n In order to \nmake clear the chemical stability in the ambient \n8 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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  \n \n \n  \n \n \n  \n \n \n \n  \n  conditions, we show in Fig. 8(b) x-ray photoelectron \nspectroscopy (XPS) of Mn and Ga on the surfaces of \nMn\nx\nGa films with and without capping layer which \nwere exposed in the air at room temperature for a \nweek.\n[24]\n Mn\nx\nGa films with Al capping layer showed \nasymmetric elemental peaks for both Mn 2 p and Ga \n3d spectrums. The asymmetry of these peaks should \nbe attributed to the significant shielding effect to the \ncore levels by the high-density at the Fermi level \ndue to the alloy nature of the film, which further \nreveals the good protection of a 2 nm Al layer from \noxidation. By contrast, Mn\nx\nGa films without Al \ncapping layer showed evident peak shifts and \nreduced asymmetry, indicating significant oxidation \noccurred. Therefore, it is necessary to protect Mn\nx\nGa \nfilms from oxidation by using suitable capping \nlayers. \nFig. 8 (a) XRD patterns of Mn\n0.76\nGa films annealed \nat 250, 300, 350, 400,450 \no\nC, respectively \n(Reprinted with permission from [17]); XPS patterns \nof Mn\n0.97\nGa films (b) with an d (c) without Al cap \nlayer after exposed in ai r atmosphere for a week \n(Reprinted with permission from [24]). \n2.5. Mn\nx\nGa-based spintronic devices \nMagnetic tunneling junctions (MTJ) and giant \nmagnetoresistance (GMR) devices based on \nperpendicularly magnetized materials are expected \nto ensure thermal stability of nanoscale spintronic \ndevices and to be developed as high-performance MR sensors, STT-MRAM and STT-oscillators. As \ndiscussed above, (001)-orientated Mn\nx\nGa alloys \nwith L1\n0\n or D0\n22 \nordering simultaneously show giant \nK\nu\n, high P, high T\nc\n, huge H\nc\n, moderate M\ns\n and low α, \nwhich make this kind of material an ideal \ncombination for high-fi eld sensors, Gbit \nSTT-MRAM and high-power STT-oscillators. \nRecently, a few groups have carried out theoretical \nand experimental work from this point of view. \nUsing first-principle calculations based on density \nfunctional theory and non-equilibrium Green’s \nfunction, Bai et al.  predicted large tunnel \nmagnetoresistance (TMR) effect of 1000% in \nMn\n2\nGa/MgO/Mn\n2\nGa magnetic tunnel junctions, \nwhereas no tunneling magnetoresistance effect in the \nMn\n3\nGa/MgO/Mn\n3\nGa MTJ stack due to the \nsymmetry selective spin filtering effect of MgO.\n[62] \nKubota et al. observed TMR ratios no more than 23% \nat 10 K and annealing endurance up to 375 \no\nC in a \nseries of Mn\nx\nGa/MgO/CoFe MTJ with different \ncompositions of Mn\nx\nGa electrode.\n[50]\n The small \nTMR ratios were attributed to the large misfit \nbetween MgO and Mn\nx\nGa, which may cause lattice \ndislocations and an unfavorable growth of the MgO \nbarrier. Kubota et al.  further made attempts to \nimprove TMR ratios by using Fe or Mg insertion \nlayers between Mn\nx\nGa and MgO interface,\n[51,52 ] \nhowever, the optimized TMR ratios still below 25% \nat 10 K. So far, the highest TMR ratio in \nMn\nx\nGa-based MTJs is 40% at room temperature \nobserved in Mn\n1.63\nGa/MgO/CoFeB MTJ with Co \n(1.5 nm)/Mg (0.4 nm) insertion between Mn\n1.63\nGa \nand MgO.\n[53]\n Noticeably, Zha et al.  also fabricated \n(112)-textured Mn\n2.3−2.4\nGa/Cu/CoFe cu rrent-in-plane \npseudo spin valve with GMR up to 3.88%.\n[63]\n Roy et \nal. studied the oscillatory dependence of the \ninterlayer exchange coupl ing strength on spacer \nlayer thickness in Mn\nx\nGa/GaAs (Mn\n2\nAs, \nMn\n2\nSb)/Mn\nx\nGa trilayers.\n[64] \nIn addition, Adelmann \net al.  demonstrated electrical spin-injection from \nMn\n1.38\nGa into (Al,Ga)As p-i-n  light-emitting diode \n(LED) at remanence.\n[12] \nIt is still an open issue to explore Mn\nx\nGa-based \nMTJ, spin valve devices and semiconductor \nspintronic devices with high performance for \npractical applications, and take advantage of the \namazing properties of this candidate material. \n3. L1\n0\n-Mn\nx\nAl epitaxial films on semiconductors \n3.1 Lattice structure and synthesis of Mn\nx\nAl \nbulks \nDespite the complex phase diagram (Fig. 9),\n[65] \nalloys of Mn and Al only have one ferromagnetic \nphase with a lattice unit similar to that of L1\n0\n-MnGa \n(i.e. τ-phase) shown in Fig. 1(b). The lattice \nconstants of L1\n0\n-MnAl bulk are a=3.92 Å and \nc=3.57 Å.\n[66]\n In 1960, Koch et al.  synthesized \nL1\n0\n-Mn\n1.25\nAl bulk by rapid cooling of nonmagnetic \nε-MnAl and observed T\nc\n of 653 K, M\ns\n of 490 emu/cc, \n9 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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 \n   \n K\nu\n of ~10 Merg/cc and ( BH)\nmax\n of 3.5 MGOe.\n[66]\n In \n1977, Ohtani et al.  synthesized MnAl bulk with \ngiant ( BH)\nmax\n over 7 MGOe by doping C element \ninto the alloys.\n[67]\n As  shown in Fig. 9, a \ncomposition range with x from 1 to 1.5 and \nannealing temperature between 500 to 900 \no\nC are \nneeded for synthesis of L1\n0\n-MnAl bulks. L1\n0\n-MnAl \nbulks are metastable phase and easily decompose \ninto β-Mn and nonmagnetic γ-MnAl. \nFig. 9 Binary phase diagram of MnAl alloys. \nReprinted with permission from [ 65]. \n3.2 Growth and magnetic properties of Mn\nx\nAl \nepitaxial films \nSince 1990s, the growth and magnetic \nproperties of L1\n0\n-MnAl thin films have been widely \n (001),\n[68,69,71-74 ]\nstudied on AlAs-buffered GaAs\nGaAs (001),\n[26,70 ] \nCr-buffered MgO (001)\n[75,76 ] \nand \nglass\n[77]\n by MBE, sputtering, e-beam evaporator and \npulse laser deposition. Despite of these progresses, \nonly a few L1\n0\n-MnAl epitaxial films grown on GaAs \n(001) and MgO (001) substrates exhibited \nperpendicular anisotropy.\n[68-76]\n We should point out \nthat many metal (e.g. Pt, Pd, Al and Cr, etc), \ninsulator (e.g. SrTiO\n3\n) and semiconductor (e.g. Si, \nGaAs, InAs and AlAs) buffers could allow for \nepitaxial growth of L1\n0\n-MnAl thin films in view of \nlattice mismatch (Table 1). However, there are no \navailable reports on the epitaxial growth of \nL1\n0\n-MnAl thin films on buffers or substrates other \nthan GaAs (with or without AlAs buffer) and \nCr-buffered MgO (001). \nThe magnetic properties of L1\n0\n-MnAl thin \nfilms are observed to be very sensitive to the \ncomposition and growth te mperature. As recently \ninvestigated systematically,\n[70]\n although L1\n0\n-ordered \nMn\nx\nAl films could been epitaxially grown on GaAs \n(001) in a wide composition range with x from 0.5 to \n1.2, films with x=1.1 exhibit the strongest XRD \nsatellite peaks, indicating the optimized composition \nand the nearly perfect L1\n0\n-ordered superlattice \nstructures. Mn\n1.1\nAl (or MnAl\n0.9\n) also shows the \nhighest M\nr\n/M\ns\n and M\ns\n.\n [70]\n For further optimizing and \ntailoring of the structure and magnetic properties the \nsystematical experiments were carried out on the \ngrowth temperature effects.\n[26]\n As shown in Fig. 10, the XRD patterns for Mn\n1.1\nAl films grown at \ndifferent Ts from 100 to 400 \no\nC, revealing that all \nthe Mn\n1.1\nAl films are single-crystalline with c-axis \nalong the normal direction. Moreover, Mn\n1.1\nAl film \nat 350\n o\nC exhibits the satellite peaks disclosing the \noptimized growth temperature range for the best \ncrystalline quality. However, Mn\n1.1\nAl films grown \nbeyond 250\n o\nC show a peak of nonmagnetic ε \n-phase. The sharp interface between Mn\n1.1\nAl and \nGaAs were confirmed by both the high-resolution \nTEM image and XRR curves. \nFig. 10. XRD patterns of L1\n0\n-Mn\n1.1\nAl films \ngrown at 100, 200, 250, 300, 350 and 400 \no\nC, \nrespectively. Reprinted with permission from [ 26]. \nFigure 11(a) shows typical perpendicular and \nin-plane hysteresis loops of L1\n0\n-Mn\n1.1\nAl sample \ngrown at 350\n o\nC. The almost squa re perpendicular \nhysteresis loop and anhysteretic in-plane hysteresis \nloop clearly demonstrate that the sample is more \neasily magnetized in out-of-plane direction. The \nperpendicular hysteresis loops of MnAl films grown \nat different T\ns\n are shown in Fig. 11(b) , and it can be \nfound that perpendicular M\nr\n/M\ns\n, M\ns\n, H\nc\n and  K\nu \nstrongly depend on T\ns\n, the details of which are \nsummarized in Figs. 11(c) and 11(d) . M\ns\n increases \nfrom 47.8 to 361.4 emu/cc as T\ns\n increases from 100 \nto 350 \no\nC, and then decreases to 316.4 emu/cc at 400 \no\nC. These changes are mainly linked to crystalline \nquality of the samples. H\nc\n has a minimum of 330 Oe \nat 100 \no\nC, then increases to 10.7 kOe at 250 \no\nC, and \nfinally drops to 8.1 kOe at 400 \no\nC. K\nu\n show a \nmaximum of 15 Merg/cc at 350\n o\nC. Moreover, MnAl \nfilms are another candidate for rare-earth-free \npermanent magnets. As shown in Fig. 11(a), (BH)\nmax \nfirst increases from 0.001 to 4.44 MGOe as T\ns \nincreases from 100 to 350 \no\nC, then decreases to 2.46 \nMGOe at 400 \no\nC. As compared in Fig. 11(b), the \nexperimental value of ( BH)\nmax \nis lower than the ideal \nvalue (2 πM\ns\n)\n2\n probably due to the differences \nbetween M\ns\n and M\nr\n and the rounding of M-H  loops. \nThe largest ( BH)\nmax\n up to 4.44 MGOe is larger than \nthat previously reported in MnAl alloys (3.5 \nMGOe),\n[66] \nMn\n1.5\nGa films (2.6 MGOe),\n16 \nand hard \nferrite magnets (3MGOe).\n[20] \n10 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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 \nFig. 11. (a) Perpendicular and in-plane hysteresis loops of the 350 \no\nC-grown L1\n0\n-Mn\n1.1\nAl films. (b) Perpendicular \nhysteresis loops of the L1\n0\n-Mn\n1.1\nAl films grown at different temperature ( T\ns\n). (c)  M\nr\n/M\ns\n, M\ns\n, (d) H\nc\n and K\nu\n plotted \nas a function of T\ns\n. Reprinted with permission from [ 26]. \nFig. 12 (a) T\ns\n dependence of the \nmagnetic energy products. (b) \nComparison of the experimental \n(BH)\nmax \nwith ideal value (2 πM\ns\n)\n2\n. \nReprinted with permission from \n[26]. \nfilms grown on Cr-MgO, which is probably related \nto the shorter c-axis and corresponding strains. \nNoticeably, despite the different buffers and growth \n(annealing) temperature, all these MnAl films \ndisplay a high K\nu\n exceeding 10 Merg/cc. \nTable 3 Structure parameters and magnetic data for representative Mn\nx\nAl films grown on different substrates. T\ns \n(T\na\n) represents growth (annealing) temperature.\nFor better understanding, the typical data of \nstructure and magnetic properties of MnAl films \ngrown on different buffers are compared in Table 3. \nMn\nx\nAl films grown on AlAs and GaAs buffers \nexhibited much lower magnetization than bulk and \nT\ns \n(T\na\n) \n(\no\nC) a \n(Å) c \n(Å) M\ns\n (300 \nK) \n(emu/cc K\nu \n(300 K\n) \n(Merg/cc) H\nc \n(300 K) \n(kOe) \n Substrate ) Reference \nMn\n1.50\nAl AlAs-Ga \nAs 200~270 \n(350) - 3.41 285 - ~4.0 [73] \nMn\n1.11\nGa GaAs 350 - 3.47 361 13.7 ~8.0 [26] \nMn\n1.32\nAl Cr-MgO 250 \n(250) - ~3.57 530 10 - [75] \nMn\n0.92\n Al Cr-MgO 200 \n(450) 3.92 3.57 600 10 - [76] \n11 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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  \n \n \n \n \n \n  \n \n  \n \n \n  \n  \n   \n \n   \n  \n \n  \n  \n    3.3 Other spin-dependent properties \n3.3.1  Magneto-optical Kerr effect \nCheeks et al.  investigated the polar \nmagneto-optical Kerr effect in 5 and 10 nm thick \nL1\n0\n-MnAl epitaxial films grown on AlAs-buffered \nGaAs (001) and found a large Kerr rotation of 0.11\no \nin a wide wave length range from 220 to 820 nm.\n[71] \nThe 0.11\n o\n value is modest compared to the 0.3-0.4\n o \nvalues reported for materials such as TbFeCo, \ncurrently used in the industry. Although thicker \nfilms are expected to give higher Kerr rotation, there \nis so far no further progress report available. \n3.3.2 Anomalous Hall effect \nThe anomalous Hall effect of L1\n0\n-MnAl films \nwere intensively studied in 1990s. Sands et al.\n[68] \nand Leadbeater et al.\n[69]\n prepared single-crystalline \nL1\n0\n-MnAl films on AlAs-GaAs (001) with a \nperpendicular c-axis and observed a large Hall \nhysteresis. Angadi and Thanigaimani reported the \nHall effect of MnAl films evaporated on glass \nsubstrates with different compositions and thickness \n(25-150 nm), and found that the ordinary Hall \ncoefficient R\n0 \nand anomalous Hall coefficient R\ns\n are \nof the same order over the entire thickness range.\n[77] \nBoth R\n0\n and R\ns\n are positive for lower thickness, and \nnegative for higher thickness. Boeck et al.  observed \nrectangular Hall hysteresis loops in Mn\n1.5\nAl grown \non AlAs-GaAs (001) and AHE resistivity in the \norder of 4-8 μΩ.cm,\n[72]\n depending on width of Hall \nbars. Despite of these progresses, detailed \nknowledge about the microscopic mechanism of \nAHE in this kind of material remains a shortage and \nneeds further exploration in the future. \n4. Conclusions and outlook \nNumerous studies have been carried out on the \nsynthesis and characterizations of Mn\nx\nGa and Mn\nx\nAl \nepitaxial films with perpendicular anisotropy. \nMn\nx\nGa alloys with both L1\n0\n and D0\n22\n ordering show \ngiant perpendicular anisotropy, high spin \npolarization, high Curie temp erature, huge coercivity, \nmoderate magnetization, large energy product, low \ndamping constant, giant Kerr rotation and large \nanomalous Hall resistivity and high thermal \ndynamical stability. L1\n0\n–ordered Mn\nx\nAl films grown \non GaAs and MgO also exhibit giant perpendicular \nanisotropy, high Curie temper ature, huge coercivity, \nmoderate magnetization, large energy product, giant \nKerr rotation and large anomalous Hall resistivity \n(2-8 μΩ.cm). Importantly, the magnetism of both \nMn\nx\nGa and Mn\nx\nAl films could be tailored \neffectively by several methods including controlling \ngrowth temperature, tuning composition, varying \nannealing conditions and selecting different \nsubstrates. These pronounced magnetic properties \nand effective controllability make these \nperpendicularly magnetized Mn-based binary alloy \nfilms much promising fo r high-performance novel \nspintronic devices, ultrahigh-density perpendicular \nmagnetic recording and economical permanent magnets, although there have rarely been progress \non high-performance spintronic devices, magnetic \nrecording practical permanent magnets \napplications.  Mor \noreover, the Mn\nx\nGa and Mn\nx\nAl \nferromagnetic films with both high K\nu\n and good \ncompatibility with semiconductor have great \napplications in not only semiconductor spintronics \nlike spin-LED, spin-FET, and lateral spin valves \nwith perpendicular spin injectors and detectors ，but \nalso in high-density integration of metallic \nspintronics functional devices like nonvolatile \nmagneto-resistive random access memory on \nsemiconductor photonic and electronic circuits. \nWe expect detailed exploration on \nfundamental issues as tomore \ndetailed knowledge on spin \npolarization, magnetic damping and AHE of Mn\nx\nGa \nand Mn\nx\nAl alloys, and possible practical \napplications like ultrahigh-density magnetic \nrecording, economical permanent magnets, \nnonvolatile memory, high-field magnetoresistive \nsensors and high-performance oscillators and \nsemiconductor spintronic devices with perpendicular \ninjectors and detectors taking advantage of the \namazing properties of this candidate material. It is \nalso admirable to explore new kinds of \nferromagnetic films with both high K\nu\n and good \ncompatibility with semiconductors. We are also \nlooking forward to new progress on high-density \nintegration of metallic spintronics functional devices \nwith semiconductor circuits taking advantage of \nsuch films. \nReferences \n[1] Chappert C, Fert A and Dau F N V, 2007 Nature \nMater. 6, 813 \n[2] Ikeda S, Miura K, Yamamoto H, Mizunuma K, \nGan H D, Endo M, Kanai S, Hayakawa J, Matsukura \nF and Ohno H, 2010 Nat. Mater. 9, 721 \n[3] Mangin S, Ravelosona D,  Katine J A, Carey M J, \nTerris B D and Fullerton E E, 2006 Nat. Mater. 5, \n210 \n[4] Houssameddine D, Ebels U, Delaët B, Rodmacq \nB, Firastrau I, Ponthenier F, Brunet M, Thirion C, \nMichel J -P, Prejbeanu-Buda L, Cyrille M C, Redon \nO and Dieny B, 2007 Nat. Mater. 6, 447 \n[5] Mancoff F B, Dunn J H, Clemens B M and \nWhite R L, 2000 Appl. Phys. Lett. 77, 1879 \n[6] Datta S and Das B, 1990, Appl. Phys. Lett . 56, \n665 \n[7] Koo H C, Kwon J H, Eom J, Chang J, Han S H \nand Johnson M 2009 Science 325, 1515 \n[8] Wunderlich J, Park B, Irvine A C, Zârbo L P, \nRozkotová E, Nemec P, Novák V, Sinova J and \nJungwirth T, 2010 Science 330, 1801 \n[9] Kohda M, Kita T, Ohno Y, Matsukura F and \nOhno H, 2006 Appl. Phys. Lett . 89, 012103 \n[10] Ohno Y, Young D K, Beschoten B, Matsukura \nF, Ohno H and Awschalom D D, 1999, Nature, 402, \n790 \n[11] Lou X, Adelmann C, Crooker S A, Garlid E S, \n12 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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  \n \n  \n \n  \n \n  \n   \n  \n \n   \n  \n \n \n  \n  \n \n   \n  \n  \n   \n  Zhang J J, Reddy K S M, Flexner S D, Palmstrøm C \nJ and Crowell P A, 2007 Nat. Mater. 3, 197 \n[12] Adelmann C, Hilton J L, Schultz B D, \nMcKernan S, Palmstrøm C J, Lou X, Chiang H S \nand Crowell P A, 2006 Appl. Phys. Lett. 89, 112511. \n[ 1 3 ]  L u  E ,  I n g r a m  D  C ,  S m i t h  A  R ,  K n e p p e r  J  W \nand Yang F Y , 2006 Phys. Rev. Lett . 97, 146101. \n[14] Tanaka M, Harbison J P, DeBoeck J, Sands T, \nPhilips B, Cheeks T L and Keramidas V G, 1993 \nAppl. Phys. Lett . 62, 1565. \n[15] Krishnan K M, 1992 Appl. Phys. Lett. 61, 2365 \n[16] Zhu L J, Nie S H, Meng K K, Pan D, Zhao J H \nand Zheng H Z, 2012 Adv. Mater . 24, 4547 \n[17] Zhu L J, Pan D, Nie S H, Lu J and Zhao J H, \n2013 Appl. Phys. Lett . 102, 132403 \n[18] Ohno H, 2010 Nat. Mater. 9, 952 \n[19] Challener W A, Peng C, Itagi A V, Karns D, \nPeng W, Peng Y G, Yang X M, Zhu X B, \nGokemeijer N J, Hsia Y T, Ju G, Rottmayer R E, \nSeigler M A and Gage E C, 2009 Nat. Photon 3, 220 \n[20] Gutfleisch O, Willard M A, Brück E, Chen C \nH, Sankar S G and Liu J P, 2011 Adv. Mater. 23, \n821 \n[21] Sakuma A, 1998 J. Magn. Magn. Mater. 187, \n105 \n[22] Mizukami S, Wu F, Sakuma A, Walowski J, \nWatanabe D, Kubota T, Zhang X, Naganuma H, \nOogane M, Ando Y and Miyazaki T, 2011 Phys. \nRev. Lett . 106, 117201 \n[23] Yang Z, Li J, Wang D, Zhang K and Xie X, J. \nMagn. Magn. Mater. 182, 369 \n[24] Zhu L J and Zhao J H, 2013 Appl. Phys. A \n111,379 \n[25] Winterlik J, Balke B, Fecher G H, Felser C, \nAlves M C M and Bernardi F, Morais J, 2008 Phys. \nRev. B 77, 054406 \n[26] Nie S H, Zhu L J, Lu J, Pan D, Wang H L, Yu X \nZ, Xiao J X and Zhao J H 2013 Appl. Phys. Lett 102, \n152405 \n[27] Sakuma A 1994  J. Phys. Soc. Jpn . 63, 1422 \n[28] Meissner HG and Schubert K, 1965 Z. \nMetallkd . 56,523 \n[29] Wu J S and Kuo K H, 1997  Metall. Mater. \nTrans. A 28A, 729 \n[30] Massalski T B, 1990 Binary Alloy Phase \nDiagrams , 2nd edn. (Ohio: Materials Information \nSoc., Materials Park) \n[31] Bither T A and Cloud W H, 1965  J. Appl. Phys. \n36, 1501 \n[32] Lu X, Liang J and Yang Z, 1979 Acta Phys. \nSin. 28, 54 (in Chinese) \n[33] Krén E and Kádár G, 1970 Solid State \nCommun . 8, 1653 \n[34] Niida H, Hori T, Onodera H, Yamaguchi Y and \nNakagawa Y, 1996 J. Appl. Phys. 79, 5946 \n[35] Kurt H, Rode K, Venkatesan M, Stamenov P \nand Coey J M D, 2011 Phys. Status. Solidi B 248, \n2338 \n[36] Mizukami S, Kubota T, Wu F, Zhang X, Miyazaki T, Naganuma H, Oogane M, Sakuma A \nand Ando Y, 2012 Phys. Rev., B 85, 014416 \n[37] Huh Y, Kharel P, Shah V R, Li X Z, Skomski R \nand Sellmyer D J, 2013 J. Appl. Phys. 114, 013906 \n[38] Krishnan K M, 1992 Appl. Phys. Lett. 61, 2365 \n[39] Tanaka M, Harbison J P, DeBoeck J, Sands T, \nPhilips B, Cheeks T L and Keramidas V G, 1993 \nAppl. Phys. Lett. 62, 1565 \n[40] Lu E, Ingram D C, Smith A R, Knepper J W \nand Yang F Y, 2006 Phys. Rev. Lett. 97, 146101 \n[41] Bedoya-Pinto A, Zube C, Malindretos J, Urban \nA and Rizzi A, 2011 Phys. Rev. B 84, 104424 \n[42] Wang K, Lu E, Knepper J W, Yang F and \nSmith A R, 2011 Appl. Phys. Lett. 98, 162507 \n[43]W.  Feng, D. V. Thiet, D. D. Dung, Y. Shin and \nS. Chob, 2010 J. Appl. Phys. 108, 113903 \n[44] Wang K, Chinchore A, Lin W, Ingram D C, \nSmith A R, Hauser A J and Yang F, 2009 J. Cry. \nGrowth 311, 2265 \n[45] Wu F, Sajitha E P, Mizukami S, Watanabe D, \nMiyazaki T, Naganuma H, Oogane M and Ando Y, \n2010 Appl. Phys. Lett. 96, 042505 \n[46] Wu F, Mizukami S, Watanable D, Naganuma \nH, Oogane M and Ando Y, 2009 Appl. Phys. Lett . \n94, 122503 \n[47] Kurt H, Rode K, Venkatesan M, Stamenov P \nand Coey J M D, 2011 Phys. Rev. B 83, 020405(R) \n[48] Nummy T J, Bennett S P, Cardinal T and \nHeiman D, 2011 Appl. Phys. Lett. 99, 252506 \n[49] Zha C L, Dumas R K, Lau J W, Mohseni S M, \nSani S R, Golosovsky I V, Monsen Å F, Nogués J \nand Åkerman J, 2011 J. Appl. Phys. 110, 093902 \n[50] Kubota T, Araidai M, Mizukami S, Zhang X, \nMa Q, Naganuma H, Oogane M, Ando Y, Tsukada \nM and Miyazaki T, 2011 Appl. Phys. Lett . 99, \n192509 \n[51] Kubota T, Mizukami S, Watanabe D, Wu F, \nZhang X, Naganuma H, Oogane M, Ando Y and \nMiyazaki T, 2011 J. Appl. Phys. 110, 013915 \n[52] Kubota T, Ma Q, Mizukami S, Zhang X, \nNaganuma H, Oogane M, Ando Y and Miyazaki T, \n2012 Appl. Phys. Express 5, 043003 \n[53] Ma Q L, Kubota T, Mizukami S, Zhang X M, \nNaganuma H, Oogane M, Ando Y and Miyazaki T, \n2012 Appl. Phys. Lett . 101, 032402 \n[54] Glas M, Imort I –M, Thomas P, Reiss G and \nEbke D, 2013 J. Magn. Magn. Mater. 333, 134 \n[55] Brataas A, Kent A D and Ohno H, 2012 Nat. \nMater. 11, 372 \n[56] Yu J, Ruediger U, Kent A D, Farrow R F C, \nMarks R F, Weller D, Folk s L and Parkin S S P, \n2000 J. Appl. Phys. 87, 6854 \n[57] He P, Ma L, Shi Z, Guo G Y, Zheng J G, Xin Y \nand Zhou S M, 2012 Phys. Rev. Lett. 109, 066402 \n[58] Zhu L J, Pan D and Zhao J H, “Proper scaling \nof anomalous Hall effect in disordered \nL1\n0\n-Mn\n1.5\nGa”, (submitted) \n[59] Hilton J L, Schultz B D, McKernan S and \nPalmstrøm C J, 2004 Appl. Phys. Lett. 84, 3145 \n13 \nL J Zhu et al. ArXiv:1309.0298 (2013) \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  [60] Roy W V, Akinaga H, Miyanishi S, Tanaka K \nand Kuo L H,1996 Appl. Phys. Lett. 69, 711 \n[61] K. Wang, A. Chinchore, W. Lin, A. Smith and \nK. Sun, 2009 MRS. Proceedings , 1118, \n1118-K06-06 \n[62] Z. Bai, Y. Cai, L. Shen, M. Yang, V. Ko, G. \nHan and Y. Feng, 2012 Appl. Phys. Lett. 100, \n022408 \n[63] C. L. Zha, R. K. Dumas, J. Persson, S. M. \nMohseni, J. Nogués and J. Åkerman, 2010 IEEE \nMag. Lett. 1, 2500104 \n[64] W. V. Roy, H. Akinaga and S. Miyanishi, 2001 \nPhys. Rev. B 63, 184417 \n[65] Jiménez-Villacorta F, Marion J L, Sepehrifar T, \nDaniil M, Willard M A and Lewis L H, 2012 Appl. \nPhys. Lett 100, 112408 \n[66] Koch A J J, Hokkeling P, Steeg M G and Vos K \nJ 1960 J. Appl. Phys.  31, 75S \n[67] Ohtani T, Kato N, Kojima K, Sakamoto Y, \nKonno I, Tsukahara M and Kubo T, 1997, IEEE \nTrans. Magn . 13,5 \n[68] Sands T, Harbison J P, Leadbeater M L, Allen \nS J, Hull G W, Ramesh R, Florez L T and \nKeramidas V. G 1990 Appl. Phys. Lett 57, 2609 \n[69] Leadbeater M L, Allen S J, DeRosa F, Harbison \nJ P, Sands T, Ramesh R, Florez L T and Keramidas \nV. G 1991 J. Appl. Phys. 69, 4689 \n[70] Nie S H, Zhu L J, Pan D, Lu J and Zhao J H \n2013 Acta Phys. Sin. (in Chinese) (to be published) \n[71] Cheeks T L, Brasil M J S P, Sands T, Harbison \nJ P, Aspnes D E, Keramidas V G and Allen S J, \n1992 Appl. Phys. Lett 60, 1393 \n[72] Boeck J D, Sands T, Harbison J P, Scherer A, \nGilchrist H, Cheeks T L, Tanaka M and Keramidas \nV G, 1993 Electronics Lett. 29, 421 \n[73] Roy W V, Boeck J D, Bender H, Bruynseraede \nC, Esch A V and Borghs G, 1995, J. Appl. Phys. 78, \n398 \n[74] Rosier T M, He Y W and El-Masry N A, 1996 \nMater. Lett . 26, 227 \n[75] Saruyama H, Ooga ne M, Kurimoto Y, \nNaganuma H and Ando Y, 2013 Jpn. J. Appl. \nPhys. 52, 063003 \n[76] Hosoda M, Oogane M, Kubota M, Kubota T, \nSaruyama H, Lihama S, Naganuma H and Ando Y, \n2012, J. Appl. Phys. 111, 07A324 \n[77] Angadi M A and Thanigaimani V, 1991, Thin \nSolid Films , 195,7 \n14 \nL J Zhu et al. ArXiv:1309.0298 (2013)"    },    {        "title": "1309.2066v2.Strain_induced_magnetism_in_MoS2_monolayer_with_defects.pdf",        "content": "arXiv:1309.2066v2  [cond-mat.mtrl-sci]  1 Mar 2014Strain-induced magnetism in MoS 2monolayer with defects\nPeng Tao,1Huaihong Guo,1Teng Yang,1,a)and Zhidong Zhang1\nShenyang National Laboratory for Materials Science, Insti tute of Metal Research and International\nCentre for Materials Physics, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016,\nPRC\n(Dated: 1 November 2018)\nThe strain-induced magnetism is observed in single-layer MoS 2with atomic single vacancies from density\nfunctional calculations. Calculated magnetic moment is no less than 2 µBper vacancy defect. The strain-\ninduced band gap closure is concurrent with the occurrence of the magnetism. Possible physical mechanism\nof the emergence of strain-induced magnetism is illustrated. We also demonstrate the possibility to test the\npredicted magnetism in experiment. Our study may provide an oppor tunity for the design of new type of\nmemory-switching or logic devices by using earth-rich nonmagnetic m aterials MoS 2.\nI. INTRODUCTION\nVacancy-induced magnetism in graphene1–4has at-\ntracted tremendous attention lately as a completely\nnew generation of materials for spintronics. The pos-\nsible physical mechanisms have also been intensively\nstudied2,5–8. Analogous to graphene, single-layer MoS 2\nhas been demonstrated to be powerful in nanoelectronic\napplications9–13. Meanwhile, atomic vacancy defects in\nsingle-layer MoS 214,15can be easily and even control-\nlably obtained by chemical vapor deposition(CVD)16,\nfield evaporation17,18and electron irradiation method19.\nHowever, reports have barely been found on magnetism\nappearing in MoS 2with single vacancy20,21.\nIn this work, we studied a possible emergence of mag-\nnetism in MoS 2monolayer with S 2or Mo single vacancy\nunder strain. The idea of applying strain arises from the\nfollowing considerations: first, the magnetism found in\nthe defected graphene may arise partly from an itinerant\norigin2,5,22in which conducting electrons play a role. In\nthis regard, the absence of magnetism in defected MoS 2\nis possibly due to the existence of a sizable band gap;\nsecondly, tensile strain has been proven to be efficient\nin reducing band gap of pristine single-layer MoS 2(P-\nMoS2)11,13and in improving carrier mobility as well9,12.\nFrom our calculation, indeed, tensile strain can not only\nhelp close the band gap of the defected MoS 2, but also\ngive rise to a vacancy-related magnetism. More impor-\ntantly, we found a concurrent appearance of the strain-\ninduced band gap closure and the magnetism. Our anal-\nysis shows that the emergence of magnetic moments does\nhave some relevance to the delocalized electronic proper-\nties in those defected structures.\nII. COMPUTATIONAL METHOD\nWe performed first-principles plane wave calcula-\ntions within density functional theory(DFT) using the\na)E-mail: yangteng@imr.ac.cnprojector augmented wave(PAW)23pseudopotential as\nimplemented within the Vienna Ab-initio Simulation\nPackage(VASP)24. The electronic exchange-correlation\npotential wastreated by the generalizedgradientapprox-\nimation(GGA) with the Perdew-Burke-Ernzerhof(PBE)\nflavor25. We used the DFT-D2 method of Grimme26to\ndescribe Van der Waals(VdW) interactions between va-\ncancies. A vacuum spacing of 20 ˚A was used to avoid\ninteraction between MoS 2layers. Electronic kinetic en-\nergy cutoff was set to be 450 eV. Self-consistency was\nreached once energy difference between two consecutive\nsteps was smaller than 10−5eV, and atomic Hellman-\nFeynman force was minimized less than 0.01 eV/ ˚A. In\nthe self-consistent total energy calculations the Brillouin\nzone was sampled by 7 ×7×1 k mesh. We employed the\nfixedspinmomentmethod27,28tosearchforthemoststa-\nblespinconfigurationandmeanwhiletocalculatethecor-\nresponding value of spin moment. Biaxial strain rather\nthan uniaxial strain was applied due to a practical con-\nsideration that strain arising from the coupling of mono-\nlayer MoS 2to substrate is usually isotropic. Our cal-\nculated lattice constant of P-MoS 2was 3.19 ˚A, which\nis slightly larger than experimental value of 3.16 ˚A. A\ndirect band gap of 1.67 eV, a little smaller than experi-\nmentalvalue29, wasobtained. Bothvaluesarereasonably\nacceptable since the GGA approximation usually under-\nestimates the band gap size and the binding strength.\nSeveral supercell sizes (3 ×3, 4×4 and etc.) were tested\nbut vacancystability remainsunchangedas supercell size\ngoesbiggerthan4 ×4. So4×4waschosenallthroughthis\nmanuscript.\nIII. RESULTS AND DISCUSSION\nRepresentative Mo or S 2single vacancy (V Moor VS2)\nwas created within a 4 ×4 supercell of MoS 2and marked\nin dashedcirclesasshownin Fig. 1(a). From ourcalcula-\ntion, the inter-S distance of 2.80 ˚A within V Mois smaller\nthan the 3.19 ˚A in P-MoS 2, while within V S2the Mo-\nMo distance is found to be 3.27 ˚A. To compare stability\nbetween V Moand V S2, we calculated vacancy formation\nenergy E formas a function of biaxial tensile strain, as2\nFIG. 1. Schematics of single-layer MoS 2with atomic vacancy.\n(a) The Mo or S 2vacancy V Moor VS2marked by a dashed\ncircle is within a 4 ×4 supercell. (b)Vacancy formation energy\nEformas a function of biaxial tensile strain.\nshown in Fig. 1(b). The E formis defined by N*E atom+\nEd-Ep, whereNand E atomrefertothe numberand total\nenergy of Mo or S atoms, E dand Epare the total energy\nof defective and P-MoS 2, respectively. Both E dand E p\nwere calculated under the same level of strain. We found\nthe formation energies without lattice strain are respec-\ntively 11.94 eV and 14.26 eV per S 2and Mo vacancy,\nagreeing with the trend obtained by others16. VS2is al-\nways obtainable more easily than V Mowithin our strain\nwindow. Encouragingly, biaxial tensile strain can lower\nthe formation energy, which helps increase the vacancy\nstability and vacancy creation by particle bombardment\nin experiment.\nBesides helping stabilize the vacancy, strain, more im-\nportantly, can give rise to magnetism in V Mo- and V S2-\nMoS2systems. Figure 2 shows energy gain (E-E 0) as\na function of constrained spin moment munder a se-\nries of tensile strains. The energy gain (E-E 0) is defined\nas the total energy difference between nonzero and zero\nspin moment mstates of defected MoS 2under the same\nstrain. Under a small value of strain ( <10% for V S2and\n<7% for V Mo), the energy gain has a global minimum\nat zero spin moment, showing the V Mo- and V S2-MoS2\nsystems are both nonmagnetic. However, as strain goes\nbeyond some critical value (10% for V S2, 7% for V Mo)30,\ntheenergygainachievesaglobalminimumatafinitespin\nmoment, suggesting a spontaneous magnetism appearing\nin both V S2and V Mosystems. This is in contrast to P-\nMoS2which remains nonmagnetic no matter how big the\nstrain is applied. From Fig.2(a,b), the magnitude of spin\nmoment is no less than 2 µB/vacancy and much bigger\nthan that obtained in defected graphene2,5. It’s worth\nnoting that absolute value of energy gain at equilibrium\nstate increases with strain, suggesting a strain-enhanced\nFIG. 2. The energy gain E-E 0(in eV) as a function of mag-\nnetic moment mper formula unit (in µB) of (a) V S2- and\n(b) VMo-MoS2systems obtained from the fixed spin moment\n(FSM) method under a series of biaxial tensile strains. E and\nE0are the total energies under the same strain with nonzero\nand zero m, respectively.\nstability of magnetism.\nTo get an insight into the strain-induced magnetism,\nwe studied the strain effect on electronic structures. Fig-\nure 3 shows the strain dependence of electronic and mag-\nneticpropertiesintheP-, V Mo-, andV S2-MoS2monolay-\ners. Allbandgapsdecreasewithincreasingbiaxialstrain,\nas depicted in Fig. 3(a). For the P-MoS 2, the band gap\ndrops almost linearly with the strain, till it vanishes at\n10%, which is consistent with previous calculations31,32.\nFor the V S2- and V Mo-MoS2, band gaps were found\nsmaller than that of P-MoS 2and close at 9% and 7%,\nrespectively. Interestingly, the critical value of strain\nfor band-gap closing agree quantitatively with that for\nmagnetism emergence in both V S2- and V Mo-MoS2, sug-\ngesting a close relationship between the magnetism and\nelectron conduction induced by strain.\nTo have a microscopic scenario, we first look into the\nband structures in Fig. 3(b). Comparing P-MoS 2with\neither V Mo- or V S2-MoS2under zero strain, we found\nsome nearly dispersionless bands in V Mo- or V S2-MoS2\ndistributing within the band gap of P-MoS 2. We con-\nsidered these almost flat bands as defect levels and high-\nlighted them in red. The defect levels are from the Mo\nand S atoms in the vicinity of vacancy. Along with in-\ncreasing strain, they gain a bigger bandwidth. Fig. 3(b)\nshows that once these defect levels start to interact with\nthe ”bulk” bands around the Fermi level as indicated by\nblue lines, the spin majority (in solid lines) and minority\nbands (in dashed lines) split and magnetism appears.\nComparing electronic density of states (DOS) at the\ncritical strain from both non spin-polarized and spin-\npolarized calculations may give us some idea on how the\nspin splitting occurs. The DOSs from non spin-polarized\ncalculations are shown by black line in the upper panel\nof Fig. 3(c) for each defected system. Fermi level E F\nis found to lie in a DOS peak – a signature of magnetic\ninstability, which therefore givesrise to a spin splitting in\nthe DOS from spin-polarized calculation, as shown in the\nlower panel of Fig. 3(c). Besides the peaks close to E F3\nE (eV) -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Biaxial tensile strain (  a/a 0)0.00 0.02 0.04 0.06 0.08 0.10 0.12 \nPristine \n(a) \n(b) \nVS2\nVMo \n(c) \nVS2: Non spin-polarized \nVS2: spin-polarized \nVMo : Non spin-polarized \nVMo : spin-polarized 0% 10% \n0% 7% \n10%  \n7%  0% Band gap (eV) 2.0 \n1.6 \n1.2 \n0.8 \n0.4 \n0.0 \n!MK!E-E F(eV) 2.0 \n1.5 \n1.0 \n0.5 \n-0.5 \n-1.0 0.0 \n!MK!2.0 \n1.5 \n1.0 \n0.5 \n-0.5 \n-1.0 0.0 2.0 \n1.5 \n1.0 \n0.5 \n-0.5 \n-1.0 0.0 \n!MK!DOS (states/eV) 100 \n50 \n0\n40 \n020 \nSpin up Spin down Pristine DOS (states/eV) 100 \n50 \n0\n40 \n020 10%  \n7%  \nFIG. 3. (Color online) Electronic structure of V Mo, VS2, and\npristine MoS 2. (a) Band gap as a function of biaxial tensile\nstrain (b) Band structures and (c) densities of states (DOSs )\nat the corresponding critical strain. Localized defect ban ds\nare highlighted in red or blue in (b). The DOS of P-MoS 2\nmarked in green is shifted down for a direct compare with the\nDOS of defected MoS 2systems, in which spin majority is in\nsolid red and minority in dashed blue line in (c).\ndue to the defect levels, the DOS of both V Mo- and V S2-\nMoS2remain a DOS background of P-MoS 2under the\ncorresponding strain. For example, as shown in the top\npanel of Fig. 3(c), a nearly constant DOS background of\nVS2-MoS2spanning an energy range of 1.5 eV was found\ntoagreewiththeDOSofP-MoS 2, displayinganextended\nelectronic state existing near E Fwhich is obviously due\nto E∼k2energy dispersion (qualitatively different from a\nlinear dispersion of Dirac Fermions in graphene33). The\nFIG. 4. (Color online) (a) The spin charge density ρspin(=\nρ↑−ρ↓) and (b) total charge density ρSTM(=ρ↑+ρ↓) in\nthe energy range from (E F-0.5eV) to E Fat the critical strain\nwhere the band gap closes. An extended distribution of ρspin\nandρSTMbeyond vacancy region is found, suggesting a pos-\nsible itinerant magnetism in defected systems.\nextended electronic state, coupled with the defect states,\nresults in a possible itinerant origin of magnetism or so-\ncalled Stoner ferromagnetism34. In our case, V Mohas a\nrelativelyhigherpeakvalueofDOSthanthatofV S2, and\nmay have a stronger ferromagnetism than V S2, which is\nactually consistent with the energy stability obtained in\nFig.2.\nTo uncover the origin behind the strain-induced mag-\nnetism, pictureinrealspaceiscomplementaryto(oreven\nmore straightforwardthan) that in reciprocal space. Fig.\n4 gives spin chargedensity ρspin(=ρ↑-ρ↓) and scanning\ntunneling microscopy (STM) charge density ρSTM(=ρ↑\n+ρ↓) under criticalstrainfor defected MoS 2. Both V Mo-\nand V S2-MoS2monolayer have strong strain-induced lo-\ncalized magnetic moments around the vacancies, as seen\nfrom the ρspinisosurface on the left side and the contour\nplot on the right side of Fig. 4(a). The spin magnetiza-\ntion is mainly from the Mo atoms in the vacancy vicin-\nity of V S2-MoS2and from both Mo and S atoms in the\nvacancy vicinity of V Mo-MoS2. This may give an im-\npression that magnetic moment arises mostly from the\ndangling bonds of edge atoms. But in the meantime,\nwe found in the contour plot of ρspinof Fig. 4(a) that\nthere exists a delocalized distribution of spin charge den-4\nFIG. 5. The curve of stress vs. biaxial tensile strain for\npristine, V Mo, and V S2MoS2single layer.\nsity over whole unit cell. This relatively small net spin\nmagnetization beyond the vacancy is substantially from\nall the Mo atomic sites. Actually, the STM charge den-\nsity integrated from 0.5 eV below E Fto Fermi level in\nFig. 4(b), which contributes to electrical conductivity,\nalso shows a feature of electronic delocalization mainly\namong Mo sites. Since almost the same amount of elec-\ntrons are responsible for both the electronic conduction\n(ρ↑+ρ↓) and the spin moments( ρ↑-ρ↓), we believe that\nthe strain-induced Stoner magnetism exist in the MoS 2\nmonolayer with atomic vacancies.\nFor the response of magnetism to the strain, we found\nsome difference existing between MoS 2monolayer and\ngraphene with single vacancies. Santos et al.22studied\ngraphene with single vacancy and found tensile-strain-\nenhanced spin moment. In contrast to graphene, V S2-\nand V Mo-MoS2have no magnetism found till strain in-\nduces a semiconductor-metal transition. Magnitude of\nthe spin moment seems not very much dependent on the\nstrain size. We believe that these differences arise mainly\nfrom the following aspects. (1) Bigger degree of free-\ndom for atomic relaxation in V S2- and V Mo-MoS2than\nin graphene. This may help eliminate dangling bonds\nin the vacancy vicinity of V S2- and V Mo-MoS2. Indeed,\nthe bond length of Mo-S in the vicinity of vacancies is\nabout 0.05 ˚A shorter than the ”bulk” one, suggesting\na stronger interaction between Mo and S atoms around\nvacancy than in the ”bulk” phase. So no local spin mo-\nment is anticipated under zero or small strain. (2) Role\nof conducting electrons for magnetism. In graphene with\nsingle vacancy, besides the delocalized p zelectrons, sp2\ndangling bonds1,3,4,22were also considered to contribute\nto the magnetism, even at zero strain. Tensile strain\nincreases the sp2dangling bonds to enhance the spin\nmoments, whereas compressive strain leads to hybridiza-\ntion between in-plane sp2and pzorbitals and therefore\nto the suppression of magnetism. For MoS 2monolayer,\nwe believe that conducting electrons play a more sub-\nstantial role in determining magnetism. Tensile strain\ntriggers a semiconductor-metal transition, and more im-portantly induces hybridization between orbitals in the\nvicinity of vacancies and delocalized Mo-d zorbitals32.\nThis hybridization gives rise to magnetic instability in\nthe Fermi level and to itinerant magnetism.\nStrain seems indispensable for the magnetism emerg-\ning in defected MoS 2monolayer, it is essential to make\nsure that this happens before structure breaks. We plot\na stress vs. biaxial tensile strain curve in Fig. 5. Fortu-\nnately, the critical biaxial strains above which material\nstarts to break ( ∼18% and ∼14% for V Mo- and V S2-\nMoS2, respectively, compared to 22% for P-MoS 2in Fig.\n5) are well beyond the strain for the emergence of mag-\nnetism. It is therefore very plausible to test the strain-\ninduced magnetism in MoS 2monolayer with atomic va-\ncancies in experiment.\nIV. CONCLUSION\nIn conclusion, we studied the magnetic, electronic and\nmechanical properties of single-layer MoS 2with S 2and\nMo vacancy under biaxial tensile strain, based on ab.\ninitio.density functional calculations. A spontaneous\nmagnetization appears as band gap closes under certain\nbiaxial tensile strain. We understand the strain-induced\nmagnetism for V Mo- and V S2-MoS2from the itinerant\norigin based on the analysis of electronic structures, den-\nsity of states and charge density at the critical strain.\nThedelocalizedelectronsofMoarebelievedtoberespon-\nsible for this unique itinerant magnetism in the defected\nMoS2. We also discussed the possibility to experimen-\ntally test our theoretical predictions. The strain-induced\nmagnetic moments may provide MoS 2an opportunity to\nthe design of magnetic-switching or logic devices.\nACKNOWLEDGMENTS\nThe work is supported by the National Basic Research\nProgram (No. 2012CB933103)of China, Ministry of Sci-\nence and Technology China and the NSFC under Grant\nNo. 11004201, 51331006. T.Y. acknowledges the IMR\nSYNL-Young Merit Scholars for support.\n1M. M. Ugeda, I. Brihuega, F. Guinea, and J. M. G´ omez-\nRodr´ ıguez, Phys. Rev. Lett. 104, 096804 (2010).\n2O. V. Yazyev, Rep. Prog. Phys. 73, 056501 (2010).\n3D. Monroe, Phys. Rev. Focus 25, 6 (2010).\n4R. R. Nair, M. Sepioni, I.-L. Tsai, O. Lehtinen, J. Keinonen,\nA. V. Krasheninnikov, T. Thomson, A. K. Geim, and I. V.\nGrigorieva, Nature Physics 8, 199 (2012).\n5O. V. Yazyev and L. Helm, Phys. Rev. B 75, 125408 (2007).\n6J. J. Palacios, J. Fern´ andez-Rossier, and L. Brey,\nPhys. Rev. B 77, 195428 (2008).\n7P. O. Lehtinen, A. S. Foster, Y. Ma, A. V. Krasheninnikov, and\nR. M. Nieminen, Phys. Rev. Lett. 93, 187202 (2004).\n8H. Kumazaki and D. S. Hirashima,\nJournal of the Physical Society of Japan 76, 064713 (2007).\n9B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, a nd\nA. Kis, Nat Nano 6, 147 (2011).5\n10Y. Yoon, K. Ganapathi, and S. Salahuddin, Nano Letters 11,\n3768 (2011).\n11E. Scalise, M. Houssa, G. Pourtois, V. Afanasev, and A. Stes-\nmans, Nano Research 5, 43 (2012).\n12W. S. Yun, S. W. Han, S. C. Hong, I. G. Kim, and J. D. Lee,\nPhys. Rev. B 85, 033305 (2012).\n13H. J. Conley, B. Wang, J. I. Ziegler, R. F. Haglund Jr., S. T.\nPantelides, and K. I. Bolotin, arXiv.\n14J. N. Coleman, M. Lotya, A. ONeill, S. D. Bergin, P. J. King,\nU. Khan, K. Young, A. Gaucher, S. De, R. J. Smith, I. V. Shvets,\nS. K. Arora, G. Stanton, H.-Y. Kim, K. Lee, G. T. Kim, G. S.\nDuesberg, T. Hallam, J. J. Boland, J. J. Wang, J. F. Donegan,\nJ. C. Grunlan, G. Moriarty, A. Shmeliov, R. J. Nicholls, J. M.\nPerkins, E. M. Grieveson, K. Theuwissen, D. W. McComb, P. D.\nNellist, and V. Nicolosi, Science 331, 568 (2011).\n15K. S.Novoselov, D.Jiang, F.Schedin, T.J. Booth, V. V.Khotk e-\nvich, S. V. Morozov, and A. K. Geim, Proc Natl Acad Sci U S\nA.102, 10451 (2005).\n16W. Zhou, X. Zou, S. Najmaei, Z. Liu, Y. Shi, J. Kong,\nJ. Lou, P. M. Ajayan, B. I. Yakobson, and J.-C. Idrobo,\nNano Letters 13, 2615 (2013).\n17S. Hosoki, S. Hosaka, and T. Hasegawa, Applied Surface Scien ce\n60-61, 643 (1992).\n18S. Hosaka, S. Hosoki, T. Hasegawa, H. Koyanagi, and T. Shin-\ntani, J. Vac. Sci. Technol. B 13, 2813 (1995).\n19H.-P. Komsa, J. Kotakoski, S. Kurasch, O. Lehtinen, U. Kaise r,\nand A. V. Krasheninnikov, Phys. Rev. Lett. 109, 035503 (2012).\n20Y. Zhou, P. Yang, H.Zu, F. Gao, and X. Zu, Phys. Chem. Chem.\nPhys.15, 10385 (2013).21C. Ataca and S. Ciraci, The Journal of Physical Chemistry C\n115, 13303 (2011).\n22E. J. G. Santos, S. Riikonen, D. S´ anchez-Portal, and A. Ayuela,\nThe Journal of Physical Chemistry C 116, 7602 (2012).\n23G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).\n24G. Kresse and J. Furthm¨ uller, Phys. Rev. B 54, 11169 (1996).\n25J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77,\n3865 (1996).\n26S.Grimme,Journal of Computational Chemistry 27, 1787 (2006).\n27A. R. Williams, V. Moruzzi, J. K¨ ubler, and K. Schwarz, Bull.\nAm. Phys. Soc. 29, 278 (1984).\n28K. Schwarz and P. Mohn, J. Phys. F: Met. Phys. 14, 1129 (1984).\n29K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Phys.\nRev. Lett. 105, 136805 (2010).\n30Here, V S2at 9% or V Moat 6% is not treated to be magnetic\nsince the global minimum state occurs at zero spin moment.\n31E. Scalise, M. Houssa, G. Pourtois, V. Afana´ sev, and A. Stes-\nmans, Nano. Res. 5, 43 (2012).\n32H. Guo, T. Yang, P. Tao, Y. Wang, and Z. Zhang, J. Appl. Phys.\n113, 013709 (2013).\n33K. Novoselov, A. Geim, S. Morozov, D. Jiang, M. I. Katsnel-\nson, I. Grigorieva, S. Dubonos, and A. Firsov, Nature 438, 197\n(2005).\n34P. Mohn, Magnetism in the Solid State (Springer-Verlag, Berlin,\n2003)."    },    {        "title": "1309.6427v1.Prediction_of_half_metallic_properties_in_Ti_raisebox___2ex___scriptsize_2_CoSi_Heusler_alloy_based_on_density_functional_theory.pdf",        "content": "arXiv:1309.6427v1  [cond-mat.mtrl-sci]  25 Sep 2013Prediction of half metallic properties in Ti2CoSi\nHeusler alloy based on density functional theory.\nA. Birsana, P. Paladea, V. Kuncsera\naNational Institute of Materials Physics, PO Box MG-07, Buch arest, Romania\nAbstract\nThe electronic and magnetic properties of Ti2CoSiHeusler compound are\ninvestigated using density functional calculations. The optimized lat tice con-\nstant is found to be 6.030 ˙A. The compound is a half-metallic ferromagnet\nwithanenergygapinminority spinchannel of 0.652eVat equilibrium latt ice\nconstant, which leads to a 100% spin-polarization. The obtained tot al mag-\nnetic moment from spin-polarized calculations is 3.0 µBfor values of lattice\nconstants higher than 5.941 ˙A. The half-metallicity is spoiled for a com-\npressed volume of 4%, suggesting a possible application as pressure sensitive\nmaterial.\nKeywords: electronic structure; magnetic properties; Ti2CoSi; Heusler\nalloys\n1. Introduction\nHeusler compounds areternaryintermetallics, known since 1903[1], when\nwas proved that Cu2MnAlcompound has magnetic properties, even though\nby itself, none of its constituents is ferromagnetic.\nFrom the structural of view, the large Heusler family are described by\nonly two variants: the so-called full-Heusler X2YZphases which typically\ncrystallize in Cu2MnAl(L21) -type structure and the half-Heusler XYZ\nvariants with C1bstructure; Xis a transition metal, Ymay be a transition\nmetal or a rare-metal and Zis a main group element. In full Heusler alloys, if\nthe atomic number of Yis higher than the one of X, making the Yelement\nmore electronegative than X, is observed the inverse Heusler structure of\nHg2CuTi-type with F¯43mspace group and Xatoms placed on the Wyckoff\npositions 4a(0,0,0) and 4c(1/4,1/4,1/4), YandZin 4b(1/2,1/2,1/2) and\n4d(3/4,3/4,3/4) respectively [2].\nPreprint submitted to Elsevier November 7, 2018The properties of Heusler compounds can be altered by substitutio n of el-\nements, however nosinglesetofpropertiescancharacterize the entireHeusler\nfamily. Due to all kind of magnetic behavior and multifunctional prope rties,\nHeusler alloys are expected to play an important role in the research field of\nspintronics [3], magneto-optical reading and recording devices [4], m agnetic\ntunnel junctions or tunneling magnetoresistance devices [5].\nThe half-metallic properties, discovered first by de Groot and his co llab-\norators in NiMnSb [6] characterize the large family of magneto-electrical\nHeusler compounds. Half-metallic materials being hybrids between me tals\nand semiconductors or isolators, can provide a fully spinpolarised cu rrent\ndue to metallic behavior for electrons of one spin orientation and the semi-\nconducting nature for electrons with opposite spin orientation [7]. Numerous\nstudiedofstructure-to-propertiesrelationsof Mn2[8],Fe2[9,10,11]and Co2\n[12, 13, 14, 15, 16]-based Heusler compounds provide an insight into this out-\nstanding class of materials. The Co2-based Heusler compounds, due to their\nCurie temperatures are used today in magnetic tunnel junctions [1 7, 18, 19]\nwhileMn2-based compounds might be incorporated in spin torque devices\nbecause of perpendicular magnetic anisotropy, achieved in thin films [20].\nRecently, scientific interest was stimulated by theoretical investig ations of\nmanyTi2based compounds, Ti2YZ(Y=V, Cr, Mn, Fe, Co, Ni, Cu, Zn and\nZ=B, Al, Ga, In, Si, Ge ) [21, 22, 23, 24, 25, 26, 27, 28, 29], which exhib it\nhalf metallic character. However, the electronic configuration of Ti2CoSi\ncompound has never been analyzed. In this article, the comprehen sive the-\noretical study, by means of the self-consistent full potential line arized aug-\nmented plane wave (FPLAPW) method is focused on the spin-polariza tion\nelectronic structure and magnetic properties of the new full Heus ler com-\npound,Ti2CoSi. Based on the analysis of these properties is predicted that\nTi2CoSisystem presents half metallic character being suitable in spintronics\nand pressure sensitive devices.\n2. Method of calculation\nSelf-consistent electronic-structure calculations were perform ed using the\nfull-potential linearized augmented plane wave (FPLAPW) method, im ple-\nmented in WIEN2K [30]. The Perdew Burke Ernzerhof [31] generalized gra-\ndient approximation GGA was employed for the exchange and correla tion\npotential; the muffin-tin model for the crystal assumes that the u nit cell is\ndivided in two regions, within and outside the muffin-tin spheres. The p lane\n2/s53/s46/s57/s53 /s54/s46/s48/s48 /s54/s46/s48/s53 /s54/s46/s49/s48 /s54/s46/s49/s53/s45/s54/s55/s56/s50/s46/s52/s48/s45/s54/s55/s56/s50/s46/s51/s56/s45/s54/s55/s56/s50/s46/s51/s54\n/s32/s78/s111/s110 /s45/s109/s97/s103/s110 /s101/s116/s105/s99\n/s32/s70/s101/s114/s114/s111/s109/s97/s103/s110 /s101/s116/s105/s99\n/s32/s32/s69/s110/s101/s114/s103/s121/s32/s40/s82/s121/s47/s102/s46/s117/s46/s41\n/s76/s97/s116/s116/s105/s99/s101/s32/s99/s111/s110 /s115 /s116/s97/s110 /s116/s32/s40/s65/s41/s54/s46/s48/s51\nFigure 1: Structural optimization for Ti2CoSi. - the calculated total energyvs. the lattice\nconstant.\nwave cut-off value KmaxRMT= 7 was used (where Kmaxis the maximum\nmodulus for the reciprocal lattice vector). The muffin-tin radius RMTwere\n2.21 atomic units (a.u.) for both Ti and Co and 2.35 a.u. for Si. The ener gy\neigenvalues andeigenvectors of a gridcontaining 2925kpoints was c onsidered\nfor integration over the irreducible part of the Brillouin zone (BZ), u sing the\nmodified tetrahedron method [32]. The self-consistency was attain ed when\nthe integrated charge difference between two successive iteratio ns was less\nthan 0.0001e/a.u.3 and the total energy deviation better than 0.01 mRy per\ncell.\n3. Results and Discussions\nToexplainthepropertiesof Ti2CoSi, thetotalenergyminimizationneeds\nto be considered, for estimation of equilibrium lattice constant. In o rder to\ndefine the unit cell of Ti2CoSisystem, for both magnetic and non-magnetic\nconfigurations, thetotalenergyiscalculatedasfunctionoflattic econstantfor\nHg2CuTistructure. This prototype structure is expected to occur beca use\nnumber of 3d electrons of Coatom exceed that of Ti2atom the Ti2CoSi\ncompound [2]. The ferromagnetic phase has lower energy than the n on-\nmagnetic phase as shown in Figure 1. The following calculations are all\nbased on the estimated equilibrium lattice constant, which is found to be\n6.030˙Afor ferromagnetic phase.\nThe spin-polarized calculations for Ti2CoSicompound performed using\nthe equilibrium lattice constant are displayed in Figure 2 and 4c, 4a, 4b and\n3/s45/s53/s48/s53\n/s45/s50/s48/s50\n/s45/s50/s48/s50\n/s45/s50/s48/s50\n/s45/s54 /s45/s53 /s45/s52 /s45/s51 /s45/s50 /s45/s49 /s48 /s49 /s50 /s51/s45/s48/s46/s53/s48/s46/s48/s48/s46/s53\n/s32/s32\n/s84/s111 /s116/s97 /s108/s32/s68/s79/s83\n/s48/s46/s54/s53/s51/s32/s101/s86 /s97/s32/s61/s32/s54/s46/s48/s51/s32/s65 /s32\n/s32/s32\n/s84/s105/s32/s40/s52/s99/s41\n/s32/s68 /s101/s110/s115/s105/s116/s121/s32/s111/s102/s32/s115/s116/s97/s116/s101/s115/s32/s40/s115/s116/s97/s116/s101/s115/s47/s101/s86 /s41/s84/s105/s32/s40/s52/s97 /s41\n/s32/s32\n/s67/s111 /s32/s40/s52/s98\n/s69/s110/s101 /s114/s103/s121 /s32/s69/s45/s69\n/s70/s32/s40/s101 /s86/s41\n/s32/s32\n/s83/s105/s32/s40/s52/s100/s41\nFigure 2: The spin projected total DOS and partial DOS calculated a t predicted equilib-\nrium lattice constant.\n4d represent the Wyckoff positions.\nThe compound exhibits half-metallic nature with a prominent energy g ap\nat the Fermi level in minority spin channel (spin-down band) and met allic\ncharacter in majority spin channel (spin-up band). The significant contri-\nbution to the energy between -3eV and -1eV comes from d electron s of Co\natoms, while between -6 eV and -3 eV from p electrons of Si.\nThe Fermi level for equilibrium lattice parameter is found nearly on th e\nedge of the conduction band. The highest occupied states of valen ce band\nare located at -0.613 eV below the EFand belong to triple degenerated\nstates Ti (4c) dt2g. The lowest unoccupied states of the conduction band,\n4/s45/s50/s48/s50\n/s97/s32/s61/s32/s54/s46/s48/s51/s32/s65 \n/s32/s32\n/s84/s105/s32/s40/s52/s99/s41\n/s45/s48/s46/s54/s49/s51/s32/s101/s86/s32\n/s45/s50/s48/s50/s84/s105/s32/s40/s52/s97/s41\n/s32/s32/s68/s101/s110/s115/s105/s116/s121/s32/s111/s102/s32/s115/s116/s97/s116/s101/s115/s32/s40/s115/s116/s97/s116/s101/s115/s47/s101/s86/s41\n/s45/s51 /s45/s50 /s45/s49 /s48 /s49 /s50 /s51/s45/s50/s48/s50\n/s48/s46/s48/s51/s57/s51/s32/s101/s86/s32/s67/s111/s32/s40/s52/s98/s41/s32\n/s69 /s110/s101/s114/s103/s121 /s32/s69 /s45/s69 \n/s70 /s32/s40/s101/s86 /s41\nFigure 3: The main partial densities of states at optimized lattice par ameter of Ti2CoSi,\nFermi level, deganddt2gbeing indicated by dotted, solid and dashed line, respectively\nwith a strong Co character, the double degenerated states degare situated\nat 0.0393 eV above the EF(Figure 3). As result, the energy gap from mi-\nnority spin channel is formed due to Ti(4c) - Co hybridization. Beside s\nthe Ti(4c)-Co bounding interactions, Ti(4c)-Ti(4a) couplings prov ide also a\nstrong hybridization around the Fermi level. However, because of the dis-\nsimilar next-nearest neighborhood, Ti(4c)-Ti(4a) is different than the typical\nX-X(X2YZ) couplings, which determine the band gap in full-Heusler com-\npounds, with L21structure [16].\nThecritical transitionpoint between themetallicandhalfmetallicbeha v-\nior of the system is found for a 4% compression of optimized volume wh ich\ncorresponds to the lattice parameter value of 5.941 ˙A. Figure 4 shows the\ntotal densities of states for the critical transition point, when EFis located\nat 0.012 eV distance from the lowest unoccupied states of conduct ion band.\nTherefore, if the lattice constant is reduced to a value lower than t he lattice\nconstant corresponding to critical transition point the Fermi leve l doesn’t lie\ninto the energy gap from minority spin channel and the Ti2CoSicompound\nloses its half-metallic nature.\nThe band structure of Ti2CoSicompound at equilibrium geometry is\nshown in Figure 5. In the left panel of the figure is plotted the metallic\n5/s45/s50 /s45/s49 /s48 /s49 /s50/s45/s56/s48/s56/s32/s68 /s101/s110/s115/s105/s116/s121/s32/s111/s102/s32/s115/s116/s97/s116/s101/s115/s32/s40/s115/s116/s97/s116/s101/s115/s47/s101/s86 /s41\n/s69/s110/s101/s114/s103/s121/s32/s40/s101/s86/s41/s97/s61/s53/s46/s57/s52/s49/s32/s65/s84/s111/s116/s97/s108/s32/s68/s79/s83\n/s48/s46/s48/s49/s50/s32/s101/s86\nFigure 4: Electronic structure of Ti2CoSiat 4% compression of optimized volume.\nintersectionofFermilevelfrommajorityspinchannel whileintherig htpanel,\nthe energy band gap from the minority spin channel. The band gap is a n\nindirect onewith awidth of0.652eV, calculatedbetween theenergy f romthe\nhighest occupied band at the G point (0.613 eV) and the lowest unocc upied\nband, at the L point (0.039eV), in the minority spin channel. In Ti2CoB\nsystem the width of the band gap predicted is 0.64 eV [23], in Ti2CoAl,\n0.49eV[24], Ti2CoGaalloyexhibitsagapof0.5eV[25],whileinthe Ti2CoGe\ncompound the energy gap is 0.6 eV. [26] or 0.61 eV [27]. It is larger tha n\nthe energy gap reported not only for other Ti2Cobased compounds but\nalsoTi2Ni[21, 28, 29] and Ti2Fe[22, 28, 29] -based Heusler alloys. The\ndependenceofthehalf-metallicbehavioronthelatticeparameteris plottedin\nFigure6. The Ti2CoSicompoundpresents 100%spinpolarizationabovethe\ncritical transition point and this starts decreasing while the half met allicity\nis spoiled.\nThe calculated values of the total spin magnetic moment Mcalc\ntot(µB/f.u.)\nand the spin magnetic moment of each atom Mcalc(µB/atom) as function\nof lattice parameters are plotted in Figure 7. The total magnetic mo ment is\nconstant at 3 µBfor lattice constant higher than 5.941 ˙A. The site-resolved\nmagnetic moments per atom resulted at the optimized lattice consta nt are\n0.705, 1.410, 0.395 and -0.028 µBfor Ti(4c), Ti(4a), Co and Si, respectively.\nSurprisingly, the highest spin magnetic moments come from Ti atoms which\nnativelydon’thavemagneticproperties. Inaddition,theinfluenceo fdifferent\nneighborhood determines Ti atoms to have dissimilar magnetic momen ts: Ti\natoms located in 4a - Wyckoff position and surrounded by Si atoms at a dis-\n6dt2g Ti(4c)\ndeg Co(4b)\nFigure 5: The band structure of Ti2CoSifor majority spin channel (spin-up) in the left\npanel and minority spin channel (spin-down) in the right panel for g eometrical optimized\nstructure\n/s54/s46/s48 /s54/s46/s52 /s54/s46/s56/s45/s48/s46/s53/s48/s46/s48/s48/s46/s53\n/s32/s32/s69/s110/s101/s114/s103/s121/s32/s40/s101/s86/s41\n/s76/s97/s116/s116/s105/s99/s101/s32/s112/s97/s114/s97/s109 /s101/s116/s101/s114/s32/s40/s65/s41/s32/s86/s97/s108/s101/s110 /s99/s101/s32/s66/s97/s110 /s100/s32/s109/s97/s120 /s105/s109/s117 /s109\n/s32/s67/s111/s110 /s100/s117 /s99/s116/s105/s111/s110 /s32/s66/s97/s110 /s100/s32/s109/s105/s110 /s105/s109/s117 /s109\n/s99/s114/s105/s116/s105/s99/s97/s108/s32/s116/s114/s97/s110 /s115 /s105/s116/s105/s111/s110 \n/s32/s112/s111/s105/s110 /s116/s32/s40/s53/s46/s57/s52/s49/s32/s65/s41\nFigure 6: The positions of highest occupied states from valence ban d (solid squares)and of\nlowest unoccupied states from the conduction band (solid circles) o f total DOSs (minority\nspin channel) for Ti2CoSias function of lattice parameter.\n7/s51/s46/s48/s48/s48/s51/s46/s48/s48/s51/s51/s46/s48/s48/s54\n/s48/s46/s54/s48/s46/s55/s48/s46/s56/s48/s46/s57/s49/s46/s48\n/s49/s46/s51/s53/s49/s46/s51/s56/s49/s46/s52/s49/s49/s46/s52/s52\n/s45/s48/s46/s52/s45/s48/s46/s50/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s48/s46/s56/s49/s46/s48\n/s54/s46/s48 /s54/s46/s51 /s54/s46/s54/s45/s48/s46/s48/s51/s48/s46/s48/s48/s48/s46/s48/s51\n/s32/s32\n/s32/s32/s84/s111 /s116/s97 /s108/s32\n/s32/s32\n/s32/s32/s84/s105/s32/s40/s52/s99/s41\n/s32/s32\n/s32/s77/s97/s103/s110/s101/s116/s105/s99/s32/s109/s111/s109/s101/s110/s116/s32/s40 /s41\n/s32/s84/s105/s32/s40/s52/s97 /s41\n/s32/s32\n/s32/s32/s67/s111 /s32/s40/s52/s98/s41\n/s32/s32\n/s32/s76/s97 /s116/s116/s105/s99/s101 /s32/s99/s111 /s110/s115/s116/s97 /s110/s116/s32/s40/s65/s41/s32/s83/s105/s32/s40/s52/s100/s41\n/s54/s46/s48/s51/s32/s65 \nFigure 7: Total and site-specific magnetic moments of Ti2CoSivs lattice parameter.\n8tance of 2.74 ˙A, present higher magnetic moments than those with Co atoms\nneighbors . Similar results were obtained for other Ti2Co-based Heusler al-\nloys [23, 24, 25, 26, 27]. The atom resolved magnetic moments of Ti ( 4a),\nCo and Si decrease with increasing of lattice constant, while for Ti ( 4c), it\nincreases.\n4. Conclusions\nIn summary, the density of states, energy bands, and magnetic m oments\nof the new full-Heusler compound, Ti2CoSi, based on the inverse Heusler\nstructure are studied within the framework of the density of stat es the-\nory with the Perdew Burke Ernzerhof generalized gradient approx imation\n(GGA). The energy gap present in the minority spin channel is 0.652 e V\nat the optimized lattice constant of 6.030 ˙A. The total magnetic moment re-\nsultedfromspinpolarizedcalculationsis3 µBandafullypolarizedcharacter,\nfor values of lattice constant higher than 5.941 ˙A. The main contribution to\nthemagneticmomentscomesfromTiatoms. Fromapplicationspoint ofview\nTi2CoSicompound is predicted to be suitable not only for spintronic devices\ndue to high spin polarization and the small energy separation betwee n the\nconduction band minimum and the Fermi level, but also as pressure se nsi-\ntive material, because of transition from half-metal to metal obta ined at 4%\ncompression of optimized volume.\n5. Acknowledgments\nThisworkwasfinancially supportedfromtheprojectsPNIIIDEI75 /2011\nand Core Program PN09-450103 of the Romanian Ministry of Educat ion\nResearch, Youth and Sport.\nReferences\n[1] F. Heusler, W. Starck, E. Haupt, Verh DPG 5 (1903) 220.\n[2] H.C. Kandpal, G.H. Fecher, C. Felser, Journal of Physics D: Applie d\nPhysics 40 (2007) 1507.\n[3] C. Felser, GH. Fecher, B. Balke, Angew Chem Int 46 (2007) 668.\n[4] P.G. van Engen, K.H.J. Bushow, R. Jongebreuer, M. Erman, Applie d\nPhysics Letters 42 (1983) 202.\n9[5] JS. Moodera, J. Nassar, G. Mathon, Annu Rev Mater 29 (1999) 381.\n[6] R.A.deGroot,F.M.Mueller, P.G.vanEngen, K.H.J.Buschow, Physic al\nReview Letters 50 (1983) 2024.\n[7] J. de Boeck, W. van Roy, J. Das, V. Motsnyi, Z. Liu, L. Lagae, H.\nBoeve, K. Dessein, G. Borghs, Semiconductor Science and Techno logy\n17 (2002) 342.\n[8] X-P. Wei, X-R. Hu, B. Liu, Y. Lei, H. Deng, M-K. Yang, J-B. Deng,\nJournal of Magnetism and Magnetic Materials 323 (2011) 1606.\n[9] H. Luo, G. Liu, F. Meng, J. Li, E. Liu, G. Wu, Journal of Magnetism\nand Magnetic Materials 324 (2012) 3295.\n[10] S.T. Li, Z.Ren, H.Z.Luo, X.H.Zhang, Y.Liu, Physica B 407 (2012) 1275 .\n[11] N. Kervan, S. Kervan, Intermetallics 24 (2012) 56.\n[12] S. Wurmehl, GH. Fecher, Hem C. Kandpal, V. Ksenofontov, C. F elser,\nH-J. Lin, J. Morais. Physical Review B 72 (2006) 184434.\n[13] HC. Kandpal, GH. Fecher, C. Felser. Journal of Magnetism and Mag-\nnetic Materials 310 (2007) 1626.\n[14] T. Marukame, T. Ishikawa, K-i. Matsuda, T. Uemura, M. Yamam oto.\nJournal of Applied Physics 99 (2006) 08A904.\n[15] N. Tezuka, N. Ikeda, S. Sugimoto, K. Inomata. Applied Physics Letters\n89 (2006) 252508.\n[16] I. Galanakis, P. H. Dederichs, N. Papanikolaou, Physical Review B 66\n(2002) 174429.\n[17] S. Wurmehl, GH. Fecher, HC. Kandpal, V. Ksenofontov, C. Fels er, H-J.\nLin. Applied Physics Letters 88 (2006) 032503.\n[18] W. Wang, E. Lui, M. Kodzuka, H. Sukegawa, M. Wojcik, E. Jedry ka.\nPhysical Review B 81 (2010) 140402.\n[19] M. Sargolzaei, M. Richter, K. Koepernik, I. Opahle, H. Eschrig, I. Chap-\nlygin, Physical Review B 74 (2006) 224410.\n10[20] F. Wu, S. Mizukami, D. Watanabe, H. Naganuma, M. Oogane, Y. A ndo.\nApplied Physics Letters 94 (2009) 122503.\n[21] Lei Feng, Chengchun Tang, Shuangjin Wang, Wenchen He Jour nal of\nAlloys and Compounds 509 (2011) 5187.\n[22] N. Kervan and S. Kervan, Journal of Physics and Chemistry of Solids\n72 (2011) 1358.\n[23] S. Kervan and N. Kervan, Solid State Communications 151 (2011 ) 1162.\n[24] E. Bayar, N. KervanandS. Kervan, JournalofMagnetismand Magnetic\nMaterials 323(2011) 2945.\n[25] N. Kervan, S. Kervan. Journal of Magnetism and Magnetic Mat erials\n324(2012) 645.\n[26] H.M. Huang, S.J. Luo, K.L. Yao. Journal of Magnetism and Magne tic\nMaterials 324(2012) 2560.\n[27] S. Kervan and N. Kervan, Journal of Electronic Materials 41 (2 012)\n1978.\n[28] Zheng N, Jin Y. Journal of Magnetism and Magnetic Materials 324\n(2012) 3099.\n[29] X-P. Wei, J-B. Deng, G-Y. Mao, S-B. Chu, X-R. Hu, Intermeta llics 29\n(2012) 86.\n[30] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, 2009\nWIEN2k, An Augmented Plane Wave Plus Local Orbitals Program for\nCalculating Crystal Properties (Wien: Technische Universit¨ at Wien )\nhttp://www.wien2k.at\n[31] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77 (1996)\n3865.\n[32] P.E. Bl¨ ochl, O. Jepsen, O.K. Andersen, Physical Review B 49 (19 94)\n16223.\n11"    },    {        "title": "1309.7399v1.Synthetic_Multiferroic_Interconnects_for_Magnetic_Logic_Circuits.pdf",        "content": "1 \n Synthetic Multiferroic Interconnects  for Magnetic Logic C ircuits  \nAlexander Khitun  \nElectrical Engineering Department, University of California Riverside, California 92521  \n \n \nAbstract  \nIn this work, we consider  the possibility of using synthetic multiferroics comprising piezoelectric and \nmagnetostrictive materials as an interconnect for nano -magnetic logic circuits.  The proposed \ninterconnect resembles a parallel plate capacitor filled with a piezoelectric, where  one of the  plates is \nmade of a magnetoelastic material.   The operation of the interconnect is based on the effect of stress -\nmediated anisotropy modulation , where an electric field applied across the piezoelectric material \nproduces stress, which, in turn,  affects the anisotropy field in the magnetostrictive material. We present \nthe results of numerical modeling illustrating signal prop agation through  the interconnect . The model \ncombines electric and magneti c parts , where the electric part describes the distribution of an electric \nfield through the piezoelectric  and the magnetic part describes the change of magnetization in the \nmagnetoelastic layer. The model is based on the Landau –Lifshitz –Gilbert equation with the electric field \ndependent anisotropy term inclu ded.  The utilization of the electro -magnetic coupling makes it possible \nto amplify magnetic signal during its propagation via energy conversion from the electric to magnetic \ndomains. Potentially, synthetic  multiferroic interconnects can be implemented in  a variety of spin -based \ndevices ensuring reliable and low -energy consuming data transmission. According to the estimates, the \ngroup velocity o f magnetic signals may be up to 105 m/s with energy dissipation less than 10-18 J per bit  \nper 100nm . The fundamen tal limits and practical shortcoming of the proposed approach are also \ndiscussed.        \n \n  2 \n  \nI. Introduction  \nThere is a gr owing interest in novel computational devices able to overcome the limits of the current \ncomplimentary -metal -oxide -semiconductor (CMOS) t echnology 1.  Magnetic logic circu its are among the \nmost promising approaches  offering a significant  reduction of consumed power by utilizing the inherent \nnon-volatility of magnetic elements. In magnetic logic circuitry,  a bit of information is  encoded into the \nmagnetization state of a nan o-magnet, which may  be kept for long time wit hout any  power \nconsumption , while the external energy is required only to perform computation  (i.e. switching between  \nthe magnetization states) . Though magnetic memory became a widely used commercial product  a long \ntime  ago, magnetic logic is pret ty much at its infancy stage . The development of energetically efficient \nand reliable m agnetic interconnects is one the main challenge s to be solved . Similar to electronic \ntransistor -based circuits, where one transistor drives the next stage transist ors by electric signals , \nmagnetic logic circuits requires one magnet to drive  the next stage magne ts by sending magnetic \nsignals . There are different possible ways to interconnect the input and the output magnets  (i.e. by \nmaki ng an array of nano -magnets sequentially switched in a domino fashion2, by sending a spin \npolarized current3, by sending a spin wave4, or by moving a domain wall 5). There is always a tradeoff \nbetween  the speed, the energy per bit and the reliability of magnetic signal  transmission . It takes either \na large amount of energy for error -prone signal tran smission  or the error probability increases with the \ndistance  due to the thermal noise, defects,  and signal  dispersion . The lack of amplification is one of the \nkey issues inherent to the  above mentioned approaches.  In this work, we consider synthetic \nmultiferroics for magnetic interconnects, which may provide magnetic signal amplification by \ntransferring energy between the electric and magnetic domains.  \nSynthetic multiferroics (or two-phase composite multiferroics ) comprise  piezoel ectric and \nmagnetoelastic  materials, where an electric field applied acro ss the piezoelectric produces stress, which, \nin turn, affects the magnetization of the magnetoelastic material. Although work in this area can be \ntraced back to the 1970s 6, synth etic multiferroics have been in a shadow of the single -phase \nmultiferroics (i.e. BiFeO 3 and its derivatives7) for a long time. The recent resurgence of interest in \ncomposite multiferroics is due to the technological flexibility  allowing for independent variation of  \npiezoelectric or magnetostrictive layers . More importantly, the strength of the electro -magnetic \ncouplin g in the two -phase systems can significantly exceed the limits of the single -phase counterparts 8.  \nDuring the past two  years, there have been several experimental works showing magnetization r otation \nin two -phase multiferroics as a function of the applied voltage9,10.  For instance,  a reversible and \npermanent magnetic anisotropy reorienta tion was reported in a magnetoelectric polycrystalline Ni thin \nfilm and (011) -oriented [Pb(Mg 1/3Nb 2/3)O3](1−x)–[PbTiO 3]x (PMN -PT) heterostructure 9. An important \nfeature of the magneto -electric coupling is that the changes in magnetization states are stable without \nthe application of an electric field and can be re versibly switched by an electric field near a critical value \n(i.e. 0.6 MV/m for Ni/PMN -PT).  Such a relatively weak electric field promises an ultra -low energy \nconsumption required for magnetizati on rotation11.  The idea of using stress -mediated mechanism for \nnano -magnet swi tching  is currently extensively studied 12 13. Here, we propose to extend this approach \nto magnetic interconnects and exploit the strain mediated electro -magnetic coupling for magnetic s ignal 3 \n amplification.  The rest of the paper is organized as follows. In Section II, we describe the material \nstructure and the principle of operation of the synthetic multiferroic interconnects. The results of \nnumerical modeling illustrating signal propaga tion are presented in Section III. The Discussion and \nConclusions are given in Sections IV and V, respectively.  \n \nII. Material Structure and Principle of Operation  \nThe schematics of the proposed interconnect  on top of a silicon wafer  are shown in Figure 1 (A). It \nconsists fro m the bottom to the top from a conducting layer (e.g. Pt), a layer of piezoelectric material \n(e.g. P MN-PT), and a  layer o f magnetoelastic  material (e.g. Ni) .  The whole structure represents a parallel \nplate capacitor filled with a piezoelectric , were one plane (the bottom) is made of a non -magnetic metal \nand the top plate is made of a magnetoelastic  metal. The top  layer is the media for magnetic signal \npropagation  between the nano -magnets to be placed on the top of the layer.  For simplicity, we  have \nshown just two nano -magnets marked as  A and B in Figure 1(A). The nano -magnet market A is the  input \nelement to send a magnetic signal to the receiver nano -magnet  B. The spins of the nano -magnets are \ncoupled t o the spins of the ferromagnetic magnetost ricitve  layer via the exchange interaction.  The \nnano -magnets are assumed t o be of a special shape to ensure the two thermally stable states of \nmagnetization. Hereaf ter, we assume the magnetoelastic  layer to be polarized along the X axis, and the \nnano -magn ets to have two sta tes of magnetization  along or opposite to the Y axis. Each of the nano -\nmagnets has an electric contact where a control voltage is applied. The bottom layer made of a \nnonmagnetic metal s erves as a common  ground plate .   \nThe principle of o peration is the following.   In order to send a signal from A to B, a  control voltage V is \napplied to the nano -magnet  A. The applying of voltage starts the charge diffusion through the \nconducting plates. The equivalent circuit is shown in Figure 1(B).   The charge diffu sion through the \ncapacitor plates  is well described by the RC model, where the resistance R and the capacitance C are \ndefined by the geometric size and the material properties of the conducting plates and the piezoelectric \nlayer .  An electric field appearing across the piezoelectric produces stress, wh ich affects the anisotropy  \nof the magnetostrictive material  by rotating its  easy -axis. It is assumed that the applying of voltage \nrotates the easy axis from X axis towards the Y axis. The change o f the anisotropy field caused by the \napplied voltage affects the magne tization of the magnetoelastic  layer. There are two possible \ntrajectories for the magnetization to follow: along or opposite to the Y axis. The particular trajectory is \ndefined by the ma gnetization state of the sender nano -magnet A .  (i.e. the magnetization of the \nferromagnetic layer copies the magnetization of the sender nano -magnet) .  \nIn Figure 1(C), we present the results of numerical modeling showing the snapshot of the distribution o f \nthe electric field E(x), and the magnetization component My(x) through the interconnect .  The details of \nnumerical modeling are presented in the next Section. Here, we want to illustrate the main idea of using \nsynthetic multiferroics as a magnetic inter connect:  magnetic signals (i.e. the local change of \nmagnetization) can be sent through large distances  without degradation as  the angle of magnetization \nrotation is controlled by the applied voltage.  The direction of signal propagation (e.g. from A to B, or  vice 4 \n \n eff eff Hm Hmdtmd \n \n21\ndttxdV\ndxtxVdCRss),( ),(\n22\n\nsMMm /\nmversa) is controlled by the applied voltage s as well. The charging of the  capacitor eventually leads to the \nuniform electric field distribution among the plates and static distribution of magnetization thro ugh the \nmagnetoelastic  layer. There are seve ral possible ways for the output nanomagnet B switching. For \nexample, it can be preset in a metastable state prior to computation (e.g. magnetization along the Z \naxis), so the magnetic signal sent by A triggers the relaxation towards the one of the thermal ly stable \nstates along or opposite to the Y axis. There may be also possible scenarios where the receiver nano -\nmagnet is connected to the two or more nano -magnets, so the final state is defined by the interplay of \nseveral incoming signals (e.g. MAJ operati on). In this work, we focus on  the mechanism of signal \ntransmission  only , though the utilization of synthetic multiferroic interconnects may further evolve the \ndesign of magnetic logic circuit s similar to ones presented in Refs. 3,4,14.   \n \nIII. Numerical Modeling  \nThe model for signal propagation in the synthetic multiferroic combines electric and magnetic parts. The \nelectric part is aimed to find the distribution of an elect ric field through the piezoelectric , and the \nmagneti c part describes  the change of magnetization  in the magnetoelastic layer .  The charg e \ndistribution is model ed via the following equation:  \n ,                                                                                                                   (1) \nwhere Rs and Cs are the resistance and c apasitance per unit length, V(x,t) is the voltage distribution over \nthe distance . The simulations start with V(0,0)=V in, and V(x,0)=0 everywhere else thorugh the plates.  \nThe pro cess of the magnetization rotation is modeled via  the Landau -Lifshitz equation:  \n,                                                                                               (2) \nvector,  Ms is the saturation magnetization,  where is the unit magnetization \nis the gyro -magnetic ratio, and η is the phenomenological Gilbert damping \ncoefficient. The effective magnetic field \neffH is the sum of the following:   \n                                                                                                                       (3) \n where Hd is the magnetostatic field,  Hex is the exchange field ,  Ha is the anisotropy field \nccm MK HS a \n) )(/2(  \n (K is the uniaxial anisotropy constant, and \nc  is the unit vector along the \nuniaxial direction), Hb is the external bias magnetic field.  The two parts are connected via the voltage -\ndependent anisotropy term as follows:   \ncx=cos ( ), cy=sin( ), cz=0                                                                                                                     (4) \n\n\n\n\nVxV)(\n2\n \nb a ex d eff H H H H H\n5 \n where Vπ is the voltage resulting  in a 90 degree easy axis rotation in the X -Y plane.   \nThe introduction of the vo ltage -dependent anisotropy field (Eq.4 ) significan tly simplifies simulations  as it \npresumes an immediate anisotropy response on the applied electric field without considering the stress -\nmediated mechanism of the electro -magnetic coupling. Such a model can be taken as a  first-order \napproximation . Nevertheless, this model is useful in capturing the genera l trends of signal propagation  \nand can provide estimates on the maximum speed of signal propagation and energy losses.  In our \nnumerical simulations,  we use  the following material parameters :  the dielectric constant ε of the \npiezoelectric is 2,000 ; the electrical resistivity  of the magnetoelastic  material  is 7.0×10-8 Ω·m, the gyro -\nmagnetic ratio   =2×107 rad/s , the saturation magnetization Ms=10kG/4 π; 2K/Ms=100 Oe, external \nmagnetic field H b=100Oe is along the X axis, and the Gilbert damping coefficient  η=0.1 for the \nmagnetostrictive material . For simplicity , we also assumed the same resistance for the  bottom and the \ntop conducting plates. The strength of the  electro -magnetic coupling (i.e. V π) is calculated based on the \navailable experimental data for PMN -PT/Ni (i.e. 0.6 MV/m for 90 degree rotation  9). \nThe results of num erical simulations shown in Figure 1 (C) are obtained fo r the interconnect comprisin g \n40nm of piezoelectric and 4 nm of magnetoelastic  materials. The two curves in Figure 1(C) depict the \ndistribution of the electric field E(x) and the projection of magnetization My(x) along the interconnect \nafter the voltage has been applied through the na no-magnet A.  The curves are plotted in the normalized \nunits E/E 0 and M y/M s, where E 0=Vπ/d, were  d is the thickness of the multiferroic layer  (40nm) .  The \ndistribution of the electric filed was found by solving Eq.(1). Then, the anisotropy field was found via Eq. \n(4), and, finally, magnetization change was simulated via Eqs. (2 -3). The results  in Fig.1(C) show a \nsnapshot taken  at 0.4ns after the vol tage  has been applied. In these simulations, we assumed the nano -\nmagnet A to be polarized along the Y axis, and the magnetization of the interconnect beyond the nano -\nmagnet M y(0)=0.1M s due to the exchange coupling with the spins of the nano -magnet. The spins o f the \nmagnetoelastic material are tend to rotate in the same direction as the spins of the sender nano -magnet \nA. Eventually, the Y -component of magnetization of the interconnect saturates along the constant value, \nwhich is defined by the interplay of the a nisotropy and the bias magnetic fields.  \nIn Fig ure 2, we show the resul ts of numerical modeling illustrating  the dynamics of magnetization \nrotation in the interconnect. The curves in Figure 2 depict the evolution of local magnetization in the \ninterconnect  located  1m, 2m and 3m away from the excitation point.  The insets in Fig.2 show the \ninitial state of magnetization of the sender nano -magnet A. In all cases, the magnetization trajectory in \nthe interconnect repeats the initial magnetization of the nano -magnet A (e.g. the magnetization \ncomponent My is positive if nano -magnet A is polarized along the Y axis, and the M y is negative if nano -\nmagnet A is polarized opposite to the Y axis). The absolute value of the final steady state is the same \n(about 0.5M s) for all six  curves. These results illistrate  the main i dea of implementing electric fi eld-driven \nmultiferroic interconnect allowing to maintain the amplitude of the magnetic signal constant regardless \nthe propagation distance.   \n \n 6 \n IV. Discussion  \nThe ability to pump energy int o the magnetic signal during its  propag ation is the most appealing \nproperty  of the described  interconnects . The pumping is via the magneto -electric coupling in the \nmultiferroic, where the some portion of the electric energy provided to the  capacit or is transferred to \nthe energy of the magnetic signal.  The amplitude of the magnetic signal (i.e. the angle of magnetization \nrotation) is controlled by the applied voltage and saturates to the certain value as the  electric field  \nacross the piezoelec tric reaches its steady state  distribution . This property is critically important for logic \ncircuit construction allowing us to minimize the effect of structure imperfections and to  make  logic \ncircuit  immune to the thermal n oise.  It should be also noted t hat the absolute value of magnetization \nchange in the interconnect may exceed the initial magnetization state of the  sender nano -magnet. For \ninstance, the  Y componen t of magnetization of the  nano -magnet A may be 0.1Ms, while the Y \nmagnetization of the magn etic signal in the interconnect may saturate around 0.5 Ms as illustrated by \nnumerical modeling in the previous Section . In other words, the proposed interconnects may serve as  an \namplifier for magnetic signals similar to the multiferroic spin wave amplifi er described in Ref.15.  Another \nimportant property of the proposed interconnect is the ability to control the direction  of signal \npropagation by the  applied voltage.  Similar to t he “All Spin Logic” approach 3, where the direction \nmagn etic signal is defined by the direction of spin polarized current flow, the change of magnetization in \nthe multiferroic interconnect follows the charge diffusion. This property  resolves the problem of input -\noutput isolation and provides an additional degre e of freedom for logic circuit construction.   \nEnergy dissipation in a two -phase magnetoelastic /piezoelectric multiferroic  has been studied in \nRefs.13,16,17.  According to the estimates, a single two -phase magnetoelastic/piezoelectric multiferroic \nsingle -domain shape -anisotropic nano -magnet can be switched consuming as low as 45kT for a delay of \n100ns at room temperature, where the main contribution to the dissi pated energy comes from the \nlosses during the charging /discharging ( CV2) 17.  The capacitance of a micrometer long multiferroic \ninterconnects comprising 40nm of PZT and 4nm of Ni with the width of 40nm is about 15fF, and  t he \ncontrol voltage requir ed for 90 degree anisotropy easy -axis change is 0.6MV/m40nm= 24mV . Thus, \nassuming all the electric energy dissipated during signal propagation one has 9aJ per signal per 1 m \ntransmitted.   It is important to note, that according to the theoretical estimate s 17, the energy \ndissipa tion increases sub -linearly with the switching speed. For example, in order to increase the \nswitching speed by a factor of 10, the dissipation needs to increase by a factor of 1.6.    \nThe propagation of magnetization signal involves several physical process es: charge diffusion, \nmechanical response of the piezoelectric to the applied electric field, change of the anisotropy field \ncaused by the stress, and magnetization relaxation. Thus, t he total  delay time τt is the sum of the \nfollowing:   \nτt = τe + τmech + τmag,                                                                                                                                                (5) \nwhere τe is the time delay due to the charge diffusion τe=RC;  τmech is the delay time of the mechanic al \nresponse τmech d/v a, where  d is the thickness of the piezoelectric layer,  va is the speed of sound in the \npiezoelectric, τmag  is the time required for the spins of magnetostrictive material to follow the changing 7 \n anisotropy field. In the theoretical mod el presented in the previous Section, we introduced a direct \ncoupling among the electric field and t he anisotropy field (i.e. Eq.4 ) presuming an immediate anisotropy \nfield response on the applied electric field. The latter may be valid for  the thin piezoel ectric layers (e.g. \ntaking d=40nm, va=1103m/s, τmech is about 40ps). We also introduced a high damping coefficient η, \nwhich minimizes the magnetic relaxation time  τmaa<50ps. In this approximation, the speed o f signal \npropagation is mainly  defined by the charge  diffusion rate . The smaller is RC is the faster is the charge \ndiffusion and the lower are the energy losses for interconnect charging/discharging.         \nIn Figure  3, we show the results of numerical modeling on the speed of signal propagation for different \nthicknes ses of piezoelectric layer. The four curves correspond to the signal propagation in the \ninterconnects with different PMN -PT thickness (e.g. 20nm, 40nm, 80nm, and 200nm) respectively. The  \nthickness of nickel layer is 4 nm fo r all cases. We also plotted a reference line corresponding to the \nmagnetostatic spin wave with typical group velocity of 3.1 104 m/s.   According to these estimates, one \nmay observe that the magnetic signal in the multiferroic interconnect may propagate  faster than the \nspin wave at short distances (<500nm) and slower than the spin wave at longer distances.  The latter \nleads to  an interesting question  whether or not it is possible  to transmit  magnetic signal s faster than the  \nspin wave i n the magnetoelasti c material.   Though magnetic coupling does not define the speed of \nsignal propagation, it sho uld determine the trajectory of  spin relaxation.  Exceeding the speed of spin \nwave in ferromagnetic material may lead to a chaotic magnetic  reorientation along the ferromagnetic \nlayer.   This is a one of many questions to be answered with  further  study.   \nFinal ly, we want to compare the main  characteristics of different magnetic interconnects and discuss \ntheir advantages and shortcomings. Moving a domain wall is a reli able and e xperimentally proven way \nfor ma gnetic signal transmission  18.  A domain wall propagate s through  a magnetic wire as long as an \nelectric current or an external magnetic field is applied , and remains at  a constant position if the driving \nforce is absent.  This property is extremely useful for building  magnetic memory (e.g. the “race track ” \nmemory 19).   T he speed of domain motion may exceed hundreds of meters per second  if the driving \nelectric current has a sufficiently large density  (e.g. 250m/s at 1.5 ×108 A/cm2  from Ref.19).  Slow \npropagation speed and high energy per bit are the main disadvantages of the logic circuits exploding \ndomain wall motion.   \nRelatively faster and less power consu ming are the interconnects made as the sequence of nano -\nmagnets , where the nearest neighbor nano -magnets are coupled via the dipole -dipole interaction  (so \ncalled the Nano -Mag netic Logic  (NML)  20). Experimentally realized wires formed from a line  of anti-\nferromagnetically ordered  nano -magnets sho w signal propagation speed up to  103m/s with an internal \n(without the losses in the magnetic field generating contours)  power dissipation  per bit about  tens of \natto Joules14.    There is a tradeoff between the speed of signal propagation and the dissipated energy. \nThe slow is the speed of propagat ion and lower is the energy  dissipated within the interconnect . The \nmain shortcoming of the nano -magnet interconnect is associated with reliability, as the t hermal noise \nand fabrication -related imperfections can cause errors in signal transmission and overall logic \nfunction ality of the  NML circuits 21.    8 \n Interconnects exploiting spin  waves  may provide signal propagation wit h the speed of 104m/s-105m/s . \nAt the same time, the amplitude of the spin wave signal is limited by the several degrees of \nmagnetization rotation in contrast to the complete magnetization reversal provided by the domain wall \nmotion or NML. The amplitude of the spin wave decreases during the propagation (e.g. the attenuation \ntime for magnetostatic surface spin waves in NiFe is 0.8ns at Room temperature 22). The unique \nadvantage of the spin wav e approach is that the  interc onnects themselves can be  used  passi ve logic \nelements  exploiting  spin wave interference.  The latter offers an additional degree of freedom for logic \ngate construction and makes it possible to minimize the number of nano -magnets per logic circuit 4.     \nThe All S pin Logic (ASL) proposal suggests the use of spin polarized current s for nano -magnet coupling 3. \nThis approach allows for much higher defect tolerance as the variations in the size and the position of \ninput/output nano -magnets are  of minor importance. It is also scalable since shorter distances between \nthe input/output cells would require less spin polarized currents for switching. According to the \ntheoretical estimates 23, ASL can potentially re duce the switching energy -delay product.  The major \nconstrain is associated with the need of the spin -coherent c hannel, where the length of the  \ninterconnects exploiting spin -polarized currents is limited by the spin diffusion length.  \nThe described magnetic  interconnects based on synthetic multiferroics combines  high transmission \nspeed  (as fast as the spin waves)  with the possibility of transmitting large  amplitude signal s (up to 90 \ndegrees of the magnetization rotation) .  As we stated above, the main appe aling property of the \nproposed interconnect is the ability to keep the constant amplitude of the magnetization signal. All \nthese advantages are the result  of using the electro -magnetic coupling in multiferroics allowing us to \npump energy from the electric to the magnetic domain. Based on the presented estimates, the energy \nper transmitted bit may be as low as several atto Joules  per 100nm transmitted distance . From the \npractical point of view, the implementation of synthetic multiferroic interconnects is feasible, as  it relies  \non the integration of th e well -known materials (e.g. PMN -PT and Ni)  and can be integrated on a silicon \nplatform . However, the dynamics of the electro -mechanical -magnetic coupling in synthetic multiferroics \nremains mainly unexplored. The expected challenges are associated with the  limited scalability, as the \nthickness of the piezoelectric should be sufficient to generate stress required for anisotropy change. In \nTable I, we have summarized the estimates on the main characteristics of d ifferent magnetic \ninterconnects and outlined their major advantages and shortcomings.  \n \nV. Conclusions  \nIn summary, we consider ed a novel type of magnetic interconnect exploiting electro -magnetic \ncoupling in two -phase synthetic multiferroics.  According to the  presented estimates, synthetic \nmulti ferroic interconnects combines the advantages of fast signal propagation (up to 105m/s) and \nlow power dissipation (less than 1aJ per 100nm).  The most appealing property of the multiferroic  \ninterconnects  is the ability to pump energy into the magnetic signal and amplify it during  \npropagation . Voltage -driven magnetic interconnect may be utilized in nano -magnetic logic circuitry  \nand provide an efficient tool for logic gate construction. The fundamental limits and practical  9 \n constrains inherent to two -phase multiferroics are associated with the efficiency of the stress -\nmediated coupling at high frequencies. There  are many questions related to the dynamic of the \nstress -mediated signal propagation, which will be clarified with further theoretical and experimental \nstudy.   \n \nAcknowledgments  \nThis work was supported in part by  the FAME Center, one of six centers of STARnet, a Semiconductor \nResearch Corporation program sponsored by MARCO and DARPA  and by the National Science \nFoundati on under the  NEB2020 Grant ECCS -1124714 . \n  10 \n  \nFigure Captions  \n \nFigure 1(A)  Schematics of the synthetic multiferroic interconnect compr ising a piezoelectric layer (PMN -\nPT) and a magnetostrictive layer (Ni). The struc ture resembles a parallel plate  capacitor. An applying of \nvoltage at point A results in the charge diffusion through the plates .  In turn, a n electric field applied \nacross the piezoelectric  produces stress, which  rotates the e asy axis of the magnetoelastic  material.  (B) \nThe equival ent electric circuit – RC line,  which is used in numerical simulations. (C) Results of numerical \nsimulations showing the distribution of the electric field and the magnetization along the interconnect. \nThe change of m agne tization in the magnetoelastic  layer fo llows the charge diffusion.  \n \nFigure 2. Results of numerical modeling showing the normalized magnetization M Y/M S as a function of \ntime. The two sets of  curves show  magnetization trajectorie s following the initial state of the sender \nnano -magnet  A (e.g. alo ng or opposite to axis Y). The black, the red, and the blue curves show \nmagnetization at 1.0µm, 2.0µm, and 3.0µm distance away from the starting point A.  \n \nFigure 3. Results of numerical modeling illustrating the speed of signal propagation in the syntheti c \nmultiferroic interconnect. There are shown several curves corresponding t o different thickness of the \nPMN-PT layer (20nm, 40nm, 80nm, and 200nm) . The blue line is the reference data for the \nMagnetostatic Surface Spin Wave ( MSSW) with group velocity of 3.0 ×104 m/s.  \n \n  11 \n   \nFigure  1  \n0 1 2 3 40.00.20.40.60.81.0\n  \nDistance [m]black curve:  electric field E(x) /E0\nred curve: magnetization MY(x)/MS\nA) \nB) \nC) 12 \n \n0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4-0.6-0.4-0.20.00.20.40.6\n  MY/MS\nTime [ns] \n 1.5 µm \n1.7 µm \n2.0 µm \nFigure  2 13 \n   \nFigure  3 \n14 \n Table I  \n* Signal propagation speed is determined by th e charge diffusion and decreases with the distance.   \n** The estimates for 103m/s propagation speed and include only for the energy dissipated inside the \nmagnetic interconnect (without considering the energy losses in the magnetic field generating contours)  \n \n   Domain Wall  MCA  Spin Wave  ASL Multiferroics  \nMechanism of \ncoupling  Domain wall \nmotion  Dipole -dipole \ncoupling  Spin waves  Spin polarized \ncurrent  Magnetization \nsignal  \nSpeed of \npropagation  102 m/s 103 m/s 104m/s-\n105m/s * 105m/s  * 105m/s  \nEnergy  \ndissipated per \nbit transmitted  >1000 aJ  **1aJ  0.1aJ  N/A 1aJ \nMain \nadvantage  Non -volatile , \ncan be stopped \nat any time and \npreserve its \nposition  Internal \ndissipated \nenergy \napproaches \nzero at the \nadiabatic \nswitching  Computation \nin wires – \nadditional  \nfunctionality \nvia wave \ninterference  Scalable, \ndefect \ntolerant  Fast signal \npropagation, \nsignal \namplification  \nMain \ndisadvantage  Slow and \nenergy \nconsuming  Effect of \nthermal noise \nincreases with \nthe \npropagation \ndistance  Propagation \ndistance is \nlimited due to \nthe spin wave \ndamping  Propagation \ndistance is \nlimited by the \nspin diffusion \nlength  Limited \nscalability  15 \n  \nReferences:  \n1 International Technology Roadmap Semiconductors, \"2011,\" http://www.itrs.net  Chapter PIDS . \n2 R. P. Cowburn and M. E. Welland, \"Room temperature magnetic quantum cellular automata,\" \nScience 287 (5457), 1466 -1468 ( 2000).  \n3 Behtash Behin -Aein, Deepanjan Datta, Sayeef Salahuddin, and Supriyo Datta, \"Proposal for an \nall-spin logic device with built -in memory,\" Nature Nanotechnology 5 (4), 266 -270 (2010).  \n4 A. Khitun and K.L. Wang, \"Non -Volatile Magnonic Logic Circuits Engineering,\" J. Appl. Phys.  110 \n(3), 034306 -034310 (2011).  \n5 Dmitri E. Nikonov, George I. Bourianoff, and Tahir Ghani, \"Proposal of a Spin Torque Majority \nGate Logic,\" IEEE Electron Device Letters 32 (8), 1128 -1130 (2011).  \n6 Amjg Vanrun, D. R. Terrell, a nd J. H. Scholing, \"INSITU GROWN EUTECTIC MAGNETOELECTRIC \nCOMPOSITE -MATERIAL .2. PHYSICAL -PROPERTIES,\" Journal of Materials Science 9 (10), 1710 -\n1714 (1974).  \n7 J. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V. Vaithyanatha n, \nD. G. Schlom, U. V. Waghmare, N. A. Spaldin, K. M. Rabe, M. Wuttig, and R. Ramesh, \"Epitaxial \nBiFeO3 multiferroic thin film heterostructures,\" Science 299 (5613), 1719 -1722 (2003).  \n8 W. Eerenstein, N. D. Mathur, and J. F. Scott, \"Multiferroic and magnet oelectric materials,\" \nNature 442 (17), 759 -765 (2006).  \n9 T. Wu, A. Bur, P. Zhao, K. P. Mohanchandra, K. Wong, K. L. Wang, C. S. Lynch, and G. P. Carman, \n\"Giant electric -field -induced reversible and permanent magnetization reorientation on \nmagnetoelectric N i/(011) *Pb(Mg1/3Nb2/3)O3+(1−x) –[PbTiO3]x heterostructure,\" Applied \nPhysics Letters 98 (1), 012504 -012507 (2011).  \n10 P. Shabadi, A. Khitun, K. Wong, P. Khalili Amiri, K.L.Wang, and C.A. Andras, \"Spin wave functions \nnanofabric update,\" Proceedings of the IE EE/ACM International Symposium on Nanoscale \nArchitectures (NANOARCH -11), pp.107 -113 (2011).  \n11 P. Shabadi, A. Khitun, P. Narayanan, Bao Mingqiang, I. Koren, K. L. Wang, and C. A. Moritz, \n\"Towards logic functions as the device,\" 2010 IEEE/ACM International Symposium on Nanoscale \nArchitectures (NANOARCH 2010) (2010).  \n12 Noel D'Souza, Jayasimha Atulasimha, and Supriyo Bandyopadhyay, \"An Ultrafast Image Recovery \nand Recognition System Implemented With Nanomagnets Possessing Biaxial Magnetocrystalline \nAnisotropy ,\" Ieee Transactions on Nanotechnology 11 (5), 896 -901 (2012);  Mohammad \nSalehi Fashami, Jayasimha Atulasimha, and Supriyo Bandyopadhyay, \"Magnetization dynamics, \nthroughput and energy dissipation in a universal multiferroic nanomagnetic logic gate with fa n-\nin and fan -out,\" Nanotechnology 23 (10) (2012).  \n13 Kuntal Roy, Supriyo Bandyopadhyay, and Jayasimha Atulasimha, \"Energy dissipation and \nswitching delay in stress -induced switching of multiferroic nanomagnets in the presence of \nthermal fluctuations,\" JOUR NAL OF APPLIED PHYSICS 112 (2) (2012).  \n14 M. T. Niemier, G. H. Bernstein, G. Csaba, A. Dingler, X. S. Hu, S. Kurtz, S. Liu, J. Nahas, W. Porod, \nM. Siddiq, and E. Varga, \"Nanomagnet logic: progress toward system -level integration,\" Journal \nof Physics -Conden sed Matter 23 (49) (2011).  \n15 Alexander Khitun, Dmitri E. Nikonov, and Kang L. Wang, \"Magnetoelectric spin wave amplifier \nfor spin wave logic circuits,\" JOURNAL OF APPLIED PHYSICS 106 (12) (2009).  \n16 Mohammad Salehi Fashami, Kuntal Roy, Jayasimha Atulasimh a, Supriyo Bandyopadhyay, and A. \nMarkwitz, \"Magnetization dynamics, Bennett clocking and associated energy dissipation in \nmultiferroic logic (vol 22, 155201, 2011),\" Nanotechnology 22 (30) (2011).  16 \n 17 Kuntal Roy, Supriyo Bandyopadhyay, and Jayasimha Atulasi mha, \"Hybrid spintronics and \nstraintronics: A magnetic technology for ultra low energy computing and signal processing,\" \nApplied Physics Letters 99 (6) (2011).  \n18 D. A. Allwood, G. Xiong, C. C. Faullkner, D. Atkinson, D. Petit, and R. P. Cowburn, \"Magnetic  \ndomain -wall logic,\" Science 309 (5741), 1688 -1692 (2005).  \n19 Stuart S. P. Parkin, Masamitsu Hayashi, and Luc Thomas, \"Magnetic domain -wall racetrack \nmemory,\" Science 320 (5873), 190 -194 (2008).  \n20 R. P. Cowburn and M. E. Welland, \"Room temperature magneti c quantum cellular automata,\" \nScience 287 (5457), 1466 -1468 (2000).  \n21 Federico M. Spedalieri, Ajey P. Jacob, Dmitri E. Nikonov, and Vwani P. Roychowdhury, \n\"Performance of Magnetic Quantum Cellular Automata and Limitations Due to Thermal Noise,\" \nIEEE Trans actions on Nanotechnology 10 (3), 537 -546 (2011).  \n22 M. Covington, T. M. Crawford, and G. J. Parker, \"Time -resolved measurement of propagating \nspin waves in ferromagnetic thin films,\" Physical Review Letters 89 (23), 237202 -237201 -237204 \n(2002).  \n23 Behtash  Behin -Aein, Angik Sarkar, Srikant Srinivasan, and Supriyo Datta, \"Switching energy -delay \nof all spin logic devices,\" Applied Physics Letters 98 (12) (2011).  \n \n "    },    {        "title": "1310.5803v1.Evidence_for_Multiferroic_Characteristics_in_NdCrTiO5.pdf",        "content": " \nEvidence for Multiferroic  Characteristics  in NdCrTiO 5 \nJ. Saha, G. Sharma  and S. Patnaik * \nSchool of Physical Sciences, Jawaharlal Nehru University, New Delhi -110067, India . \ne-mail: spatnaik@mail.jnu.ac.in   \nKeywords:  A. Multiferroics;  B. Polarization; D. Magneto -electric coupling ; D. Magnetostriction  \n \nAbstract:  \nWe report NdCrTiO 5 to be an unusual  multiferroic material with large  magnetic field \ndependent  electric polarization.  While magneto -electric coupling in this two magnetic sub -\nlattice oxide  is well established, the purpose of this study is to look for spontaneous \nsymmetry breaking at the magnetic transition.  The conclusions are  based on extensive \nmagnet ization , dielectric  and polarization measurements around its ant iferromagnetic \nordering temperature  of 18K. Room temperature X-ray diffraction pattern of NdCrTiO 5 \nreveal s that the sample is single phase  with an orthorhombic crystal structure  that allows \nlinear magneto -electric coupling . DC magnetization  measuremen t shows magnetization \ndownturn  at 11 K together with  a small kink corresponding to t he Co+3 sub-lattice ordering at \n~18K. An anomaly in dielectric constant is observed around the magnetic ordering \ntemperature that increases substantially with increasing magnetic field.  Through detailed \npyroelectric current measurement s at zero magnetic field, particularly as a function of \nthermal cycling , we establish that NdCrTiO 5 is a genuine multiferroic material that is \npossibly driven by collinear magneto -striction.  \n \n \n  Introduction:  \n Multiferroic materials exhibit co -existence of multipl y ordered ferroic states [1 -4]. \nThe consequent co -dependence of such orderings has been envisaged towards realization of \nnovel memory devices and in spintronics [ 5]. In the recent past, a  set of novel materials that \nhas attracted considerable attention relate s to magnetic multiferroics where the ferroelctricity \nis driven b y magnetic structure  (e.g. TbMnO 3) rather than  ab-initio non-centro -symmetric \ncrystal structure  (e.g. BaTiO 3). The ferroelectric phase in this case is enabled by spontaneous \nspatial inversion symmetry breaking at the magnetic ordering temperature.  In such cases, \ndielectric constant  is generally suppressed with external magnetic field.  In this regard a \ncontroversial example is NdCrTiO 5.  While the  magnetic structure and the possibility of large \nmagneto -electric (ME) coupling in NdCrTiO 5 were studied  in early 1970’s, the open question \nthat remains is whether this compound is a genuine mul tiferroic or simply a linear magneto -\nelectric  (ME)  material. In both cases, the strength of the polarization depends on the strength \nand orientation of the magnetic field.  Experimentally, t he distinction between the two can be \naccessed;  a multiferroic wou ld show induction of ferroelectricity even in the absence of \nexternal magnetic field where as electric polarizatio n due to magneto -electric coupling could \nbe achieved only in the presence of magnetic field.  This general requirement  is valid for \nmany of the recently claimed multiferroic systems where the low temperature saturation \npolarization is typically two orders of magnitude lower than other established multiferroics \nsuch as BiFeO 3.[6]         \nWhat is confirmed  in NdCrTiO 5 is the emergence of electric polarization around its \nanti-ferromagnetic  (AFM)  ordering temperature T N ~ 18 K.  However, unlike other spin \nfrustrated multiferroic systems , such as  YMnO3 [7], Ni 3V2O8 [8], or Y 2CoMnO 6 [9], the \nelectric  polarization  and anomaly in dielectric constant  in NdCrTiO 5 reportedly appears only  \nin the presence of external magnetic field .  This feature is reminiscent of linear magneto -\nelectric effect as evidenced in MnTiO 3 [11]. Two major factors co ntribute to large ME  effect . \nIn composite materials the ME effect is generated as a product property of magnetostriction \nand piezoelectricity . In such  materials the ME effect depends on the strength of coupling \nbetween the magnetic and electric ordering. On the other hand in intrinsic multiferroic  \nmaterials where the electric (magnetic)  field is  induced by magnetic (electric) ordering the \nME effect largely depends on the corresponding free energy  [12]. Two theoretical models \nappropriate for magnetism driven ferroelectricity have been suggested [ 10].  In most systems \nwith spiral spin structure e.g TbMnO 3 [13, 14 ], DyMnO 3 [15], Ni 3V3O8 [16-17] etc, the induced ferroelectricity is described by spin current model  [18, 19 ]. The inverse \nDzyaloshinkii -Moriya (DM) interaction in such cases drives  the onset of ferroelectricity by \ncomplex magnetic ordering [20, 21 ]. Here, t he symmetry breaking leads to induction of \npolarization P which can be described by , where  is unit vector joining \nthe spin moments  Si and Sj [18]. If NdCrTiO 5 is a multiferroic, then the  spin current model  is \napplicable if both  magnetic sublattices of Cr+3 and Nd+3 order ed separately leading to overall \nnon-collinear spin configuration .  On the other hand, a  modified  magneto -striction driven \nmechanism , as seen  for Y 2CoMnO 6, is suggested if only the collinearly ordered (along c -axis) \nCr+3 sublattice played the dominant role for ME coupling .  This would then indirectly conjure \nthe ab plane aligned moment s of Nd+ through exchange coupling.  Such collinear ordering, \nwhere DM term vanishes  yet the spatial inversion symmetry is broken , is achieved via the \nmagnetosriction phenomenon  [22].   In this communication  we report a detailed structural, \nmagnetic and dielectric property analysis in NdCrTiO 5 towards an un derstanding of the \nnature of multiferroicity, ME effect and its correlation with AFM  ordering . We establish that \nNdCrTiO 5 is a multiferroic material due to  collinear spin ordering.    \n \nExperimental:   \nPolycrystalline sample s of NdCrTiO 5 were prepared by standard solid state reaction \nmethod.  Stoichiometric amount of Nd 2O3, Cr 2O3, TiO 2 were used. The mixture was well \nground  for several hours in agate mortar -pestle . After grinding , the mixture was sintered for \n24 hours in air at 1000°C. After the first sintering , the mixture was again well ground for few \nhours and the n pressed in form of pellets  (Dia=10mm, thickness=1mm) . The se pellets w ere \nheated again in air at 13 00°C for another 24 hours.   Both heating and cooling rates were kept \nat a rate o f 5°C/min. Room temperature X-ray diffraction (XRD) pattern was recorded  by \nusing Cu Kα radiation with an X’pert Pro P anAlytical diffractometer. The DC magnetization \nmeasur ements were done in  Cryogenic  PPMS .  The dielectric measurements were done using \nan Agilent E4980A LCR meter. For dielectric and pyroel ectric current  measurements , \nelectrodes were prepared  on the sample  by painting silver paste on the  planar surfaces.  The \npyroelectric measurement  was performe d by using a Kiethley 6514 electrometer and  \npolarization was derived from the pyroelectric current by integrating over time.   The sample \nwas poled  each time from well above  ordering temperature  under various combination s of \nelectric  and magnetic  field.  The poling field was removed at lowest temperature and terminals were sorted for 15 minute s to avoid any role of electrostatic stray charges .  The \nwarming ramp rate was fixed at  5K per minute.  \nResults and Discussion:   \nFigure 1 shows the room temperature XRD  pattern of NdCrTiO 5 in range  of 2θ = 10° \nto 90°. The refinement done by Fullprof method  confirms that the sample has been \nsynthesized in near single phase.  It is found  that NdCrTiO 5 has an orthorhombic structure \nwith space group Pbam  and t he estimated lattice parameters  are a = 7.5661(4)  Å, b = \n8.6513(5) Å and  c = 5.800 3(3)Å. The goodness of fit indicators  are Rwp = 5.75, Rp = 7.21 and \nχ2 = 1.27 . The atomic coordinates, bond length and bond angles are also estimated from the \nroom temperature XRD and are summa rized  in Table 1. The compound is isomorphous with \nHoMn 2O5. The schematic cell for orthorhombic NdCrTiO 5 is shown in Figure 2.  The 8 Cr3+ \natom s (blue)  occupy the 4 faces and are stacked  along the c axis .  Each Cr3+\n ion is surrounded \nby oxygen octahedra l. Nd3+ ions (gray) lie along ab plane and the planes formed by Cr3+ ions \nare interspaced between a Nd3+ and a Ti4+ plane.  Ti4+ ions (cyan)  are surrounded  by edge \nsharing  oxygen tetragonal pyramid s and lie in ab plane between the two planes formed by \nCr3+ ions.  Oxygen pyramid s around Ti4+ share corner  with the oxygen octahedra  of Cr3+ ions.   \nAccording to the neutron study by G Buisson [23],  95% of Cr3+ ions and 5% of Ti4+ ions are \ndistributed at 4 f sites, while 5% of Cr3+ ions and 95% of Ti4+ ions are distributed over 4 h \nsites.  The Nd3+ ions are distributed at 4 g sites.  \nFigure 3 shows the magnetization curve taken at 0.1T.  A sharp downturn in \nmagnetization is observed at 11 K. This is the marker for AFM ordering in both Nd3+ and Cr3+ \nions [23]. On careful observation we observe a small bending at 1 8 K as well . This is the \nantiferromagnetic tr ansition temperature  corresponding to Cr+3 ions,  which has been \nconfirmed by heat capacity measurement s [10]. This feature is magnified in the inset  3(a). \nThe inverse susceptibility (χ-1 = (T-θ)/C) is plotted in inset  3(b).  This yields the Curie -Weiss \nconstant C = 4.102  emu Oe-1 mole-1 K-1 and the intercept θ = - 85.5K.  The effective magnetic \nmoment is found to b e 5.728  μB which is close to theoretical value corresponding to one Nd3+ \n(S = +3/2) and one Cr3+ ions (S = +3/2) per formula unit.  The M-H measurement at 2 K (inset \n3c) shows non-hysteretic behaviour (without saturation) , that reflects the non - canting nature \nof the aligned spins below the ordering temperature.   To ascertain the magneto -electric coupling, n ext we discuss the measured dielectric \nconstant  as a function of temperature in the presence of magnetic  field (Fig. 4) .  In the \nabsen ce of magnetic field, slight  bending in the curve around the transition temperature  TN = \n18 K is observed . As the magnetic field is applied , a clear peak appears at the transition \ntemperature. The height of the peak at the transition temperatur e increases  with magnetic \nfield increment . We tried to find out the effect on the dielectric constant, when the sample is \ncooled in the presence of magnetic field but no additional features were observed.   We also \nnote that for higher fields, the peak maxima shifts to lower temperature. This is because the \nNeel transition temperature of antiferromagnet s decrease with increasing field . Inset 4a  \namplifies  the magneto -capacitance nature of NdCrTiO 5. On increasing  magnetic field the \ncapacitance increase s. Th is change is most prominent around the AFM transition temperature \nand is substantially reduced  at temperatures above and  below TN.  We note that  magneto -\ncapacitance at 10K and 25K is negligible i n comparison to that at 16K .  \nNext we address the question whether the induction of electric polarization \nnecessarily requires the presence of magnetic field.  The results from J. Hwang et al. could \nnot conclude decisively on this because of the extremely low pyroelectric current magni tude \nin the absence of magnetic field.  Fig. 5(a) shows the measured pyroe lectric current  as a \nfunction of temperature  with ±200V/mm  poling electric  fields .  It shows a consistently \nobserved pyroelectric current of magnitude 0.2-0.3pA  even in the absence of magnetic field .  \nThis current reverses its direction when the electric field direction is reversed.  To establish \nthis unambiguously, w e have also measured pyroelectric current with temperature cycling .  \nAs shown in Fig. 5(b), we observe the direction c hange of the pyroelectric current during \nheating and cooling  cycles [ 24, 25]. The temperature cycle is varied from ~15K to ~17K in a \nperiodic manner and pyroelectric current changes sign follow ing the profile of temperature \nvariation .  Th is pyroelectric  current in the absence of magnetic field does not decay over \ntime, which proves that  it is associated with the movement of permanent dipole .  This occurs \ndue to preservation of polarized state below the transition temperature. When heat is supplied \nto pol arized dipoles , their arrangement tends towards the low ordered state and this is \nrecovered when specimen temperature  is lowered . Such reversible phenomenon leads to \ngeneration of opposite current in intrinsic ferroelectric material. This emergent phenomen a \nsquarely places NdCrTiO 5 into the group of genuine multiferroic  materials.    \nIn Fig. 6 we plot the calculated polarization at a fixed magnetic field of 4T with \nvarying poling electric fields. The corresponding pyroelectric currents are shown in inset 6a. For a negative electric field,  the pyroelectric current shows a peak in reverse direction with \nsame magnitude. Inset  (b) of Fig. 6 shows the polarization s at different magnetic fields. This \nconfirms robust magneto -electric coupling in NdCrTiO 5. The magnetoelectric coefficient αij \nfrom the first order linear relation  is found to be of the order of ~ 0.43 μC/m2T. \nThis is smaller than typical collinear multiferroic like Y 2CoMnO 6[9].  Though not shown \nhere, we also investigate d whether there is any spin capture  or kinetic arrest of different \nmagnetic phases  [26] in which a threshold field is needed to break the spin symmetry . We did \nnot observe such an effect.  \nConclusion :  \nIn conclusion , we find direct evidence for multiferroic  behaviour in NdCrTiO 5. This is \nover and above large  field dependence of electric polarization which is due to strong \nmagneto -electric coupling . Our results suggest that below T N ~ 18K, the Cr3+ ions become \nanti-ferromagnetically ordered that subsequently drives anti - ferromagnetism in Nd3+ ions \nalong ab plane through exchange coupling.  Effectively no spin canting is observed in low \ntemperature hyster esis measurements.  A model based on collinearly ordered Cr3+ions along \nc-axis giving rise to magneto -striction is proposed to explain  multiferroicity in NdCrTiO 5. \nSuch multiferroic compound s with large magnetic field dependence of electric polarization \nauger  well for potential applications.  \n \nAcknowledgement:   \nThe authors acknowledge Prof. A. K. Rastogi  for discussion on magnetic properties of \nthe sample. We thank AIRF JNU for X RD, SEM and magnetization measurements. JS thanks \nCSIR -Govt of India  and GS thanks UGC -Govt of India  for fellowship s. \n \n \n \n  References:  \n 1T. Kimura, T. Goto, H. Shintani , K. Ishizaka, T. Arima, and Y. Tokura, Nature 426,                            \n55 (2003)  \n2S.-W. Cheong and M. Mostovoy, Nature Mater. 6, 13 (2007)  \n3R. Ramesh and N. A. Spaldin, Nature Mater.  6, 21 (2007)  \n4Nicola A. Hill, J. Phys. Chem. B 104, 6694 (2000)  \n5R. Ramesh, Nature Mater. 9, 380 -381(2010)  \n6D. Lebeugle, D. Colson, A. Forget, M. Viret, P. Bonville, J. F. Marucco and S. Fusil, \nPhys. Rev. B 76, 024116 (2007)  \n7A. K. Singh, S. D. Kaushik, V. Siruguri and S. Patnaik, Phys. Rev. B 81, 184406 (2010)  \n8A. K. Singh, D. Jain, V. Ganeshan and S. Patnaik, Euro. Phys. Lett. 86, 57001 (2009)  \n9G. Sharma, J. Saha, S. D. Kaushik, V. Siruguri and S. Patanik; Appl. Phys. Lett. 103, \n012903 (2013)  \n10J. Hwang,  E. S. Choi,  H. D. Zhou,  J. Lu,  and P. Schlottmann , Phys. R ev. B. 85, 024415 \n(2012)  \n11N. Mufti, G. R. Blake, M. Mostovoy, S. Riyadi, A. A. Nugroho and T. T. M. Palstra, \nPhys. Rev. B 83, 104416(2011)  \n12M. Fiebig, J. Phys. D: Appl. Phys. 38 (2005) R123 -R152  \n13M. Kenzelmann, A. B. Harris, S. Jonas, C. Brohol m, J. Schefer, S. B. Kim, C. L. Zhang, \nS.-W. Cheong, O. P. Vajk, and J. W. Lynn, Phys. Rev. Lett. 95, 087206 (2005)  \n14T. Goto , T. Kimura , G. Lawes , A. P. Ramirez , and  Y. Tokura,  Phys. Rev. Lett. 92, \n257201 (2004)  \n15T. Arima, A. Tokunaga, T.Goto, H. Kimura,Y . Noda, andY. Tokura, Phys. Rev. Lett. \n96, 097202 (2006)  \n16I. Cabrera,  M. Kenzelmann,  G. Lawes, Y. Chen,  W. C. Chen,  R. Erwin,  T. R. \nGentile,  J. B. Leao,  J.W. Lynn,  N. Rogado,  R. J. Cava,  and C. Broholm, Phys. Rev. \nLett. 103, 087201(2009)  \n 17G. Lawes, A. B. Harris, T. Kimura, N. Rogado, R. J. Cava, A. Aharony, O. Entin -\nWohlman, T. Yildrim, M. Kenzelmann, C. Broholm, and A. P. Ramirez, Phys. Rev. \nLett. 95, 087205 (2005)   \n18H. Katsura, N. Nagaosa, and A. V. Balatsky, Phys. Rev. Lett. 95,057205 (2005) \n19I. A. Sergienko and E. Dagotto, Phys. Rev. B 73, 094434 (2006)  20I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958)  \n21T. Moriya, Phys. Rev. 120, 91 (1960)  \n22Y. Tokunaga, S. Iguchi, T. Arima, and Y. Tokura, Phys. Rev. Lett. 101, 097205 (2008)  \n23G. Buisson, J. Phys. Chem. Solids 31, 1171 (1970)  \n      24I. Lubomirsky and O. Stafsudd, Rev. Sci. Instru. 83, 051101(2012)  \n25L. Nougaret, P. Combette, R. Erinero, J. Podlecki, F. Pascla -Delannoy; Thin Solid \nFilms. 515, 3971 (2007)  \n26V. Siruguri, P.D. Babu , S.D. Kaushik, Aniruddha Biswas, S.K. Sarkar, K. Madangopal, \nP. Chaddah;  arXiv:1307.2486  (2013)  \n \n \n \n \n \n \n \n \n \n \n  Figure Captions:  \n  \nFig. 1. (Color online)  Room temperature XRD pattern of NdCrTiO 5 polycrystalline powder  \nsample with Reitvel d refinement . The observed data (red), calculated line (black) and \ndifference (blue) between the two are shown along with the Bragg positions (green).  \nOrthorhombic crystal structure in space group Pbam  is confirmed.  \n \nFig. 2. (Color online)  (a) Schematic of unit cell orthorhombic c rystal structure of NdCrTiO 5 \nas seen along the c axis.  Nd+3, Cr+3 and Ti+4 ions are shown  in dark yellow, blue and cyan \nrespectively.  (b) The unit cell as seen from the basal plane.  \n \nFig. 3.  Magnetization of NdCrTiO 5 measured in presence of 0.1T magnetic  field between  \ntemperatures  5K to 300K.  The inset (a) shows magnified low temperature data . Inset (b) \nshows the inverse susceptibility (χ-1) as a function of temperature  with the Curie -Weiss \nfitting.  Inset (c) shows the M -H hysteresis curve  at T = 2K . \n \nFig. 4 (Color online) Dielectric constant  is plotted  as a function of temperature. A large \nincrease is seen with increasing magnetic field.  Inset  shows the capacitance versus  magnetic \nfield at different temperatures 10K, 16K and 25K.  Large magneto -capacitance is observed \njust below the Neel Temperature.  \n \nFig. 5. (Color online) (a) Pyroelectric current as a function of temperature at H = 0T . The \ndirection of current rev ersal is also confir med for negative poling field (b) Pyroelectric  \ncurrent as a function of time with cyclic change o f temperatu re.  Such variation can only be \nobserved because of reversible ferroelectric domain condensation.   \n \nFig. 6. (color online)  Electric p olarization  is plotted as a function of temperature at ± 200  V \npoling field.  A constant magnetic field of 4  Tesla is applied while warming . Inset  (a) \nPyroelectric current as a function of temperature at ± 200 V poling field and H=  4T. Inset  (b) \nPolarization  as a function of temperature at various magnetic fields.   \n \n \n   \nTable 1. Structure parameters of NdCrTiO 5 \nAtom                                                     X Y Z \nNd                            0.14091  0.17045  0 \nCr 0.11730  -0.14443  1/2 \nTi 0 ½ 0.25319  \nO1 0.10715  -0.28281  0.26618  \nO2 0.16262  0.44428  0 \nO3 0.15288  0.43262  1/2 \nO4 \nBond  0 0 0.30046  \nLength(Å)  \nNd-O1   2.486  \nNd-O2   2.375  \nNd-O2   2.457  \nTi-O1   1.811  \nTi-O3   1.836  \nTi-O4   1.921  \n \nBond     \nAngle (Degree)  \nNd-O1-Ti   122.696  \nNd-O1-Cr   97.554  \nNd-O2-Cr   101.557  \nTi-O3-Cr   131.962  \nNd-O4-Ti   127.018  \n \n \n \n \n \n \n  \nFigure1.  \n \n \n \n \n \n  \nFigure2.  \n \n \n \n \n \n \n \n  \n \nFigure 3. \n \n \n \n \n \n  \n \nFigure 4. \n \n \n \n \n \n \n \n \n \n \n  \n \nFigure 5. \n \n \n \n  \nFigure 6. \n \n \n \n \n"    },    {        "title": "1310.6117v1.Magnetization_Characteristic_of_Ferromagnetic_Thin_Strip_by_Measuring_Anisotropic_Magnetoresistance_and_Ferromagnetic_Resonance.pdf",        "content": "\t\r \n1\t\r \t\r Magnetization Characteristic of Ferromagnetic Thin Strip by Measuring Anisotropic Magnetoresistance and Ferromagnetic Resonance Ziqian Wang, Guolin Yu, Xinzhi Liu, Bo Zhang, Xiaoshuang Chen and Wei Lu National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai, 200083, China  Abstract The magnetization characteristic in a permalloy thin strip is investigated by electrically measuring the anisotropic magnetoresistance and ferromagnetic resonance in in-plane and out-of-plane configurations. Our results indicate that the magnetization vector can rotate in the film plane as well as out of the film plane by changing the intensity of external magnetic field of certain direction. The magnetization characteristic can be explained by considering demagnetization and magnetic anisotropy. Our method can be used to obtain the demagnetization factor, saturated magnetic moment and the magnetic anisotropy.  Key words: A. Permalloy Thin Strips; D. Anisotropic Magnetoresistance; D. Demagnetization; D. Magnetic Anisotropy.  \t\r \n2\t\r \t\r   1. Introduction Anisotropic magnetoresistance (AMR) effect, which is resulted from the anisotropy of spin-orbit interaction in ferromagnetic materials [1,2], was first discovered by Thomson in 1857 [3]. The effect bears an essential role for both scientific perspectives and technological applications [4-8]. AMR is manifested in the dependence of the resistivity on the angle between current and magnetization direction [1,2], and is given by 20- sinAARR RRθ=+.     (1) Here R0 represents the resistance while the magnetization M is perpendicular to the induced current, RA is the decrement resistance, and θ is the angle of magnetization M with respect to current. In ferromagnetic devices of certain structures, M is parallel to the effective magnetic field Heff, including external field Hex, anisotropy built-in field Ha and demagnetization field Hd. Researchers can obtain these parameters through finding θ.   The purpose of this article is to obtain magnetization characteristic of a ferromagnetic thin strip through AMR measurement. Ferromagnetic resonance (FMR) detection is considered as an ancillary method to \t\r \n3\t\r \t\r determine the magnetization based on fitting the measured FMR dispersion curves via Kittel’s theory [9].   2. Material and Methods The present work is performed on a Ni80Fe20 (Permalloy, Py) thin film deposited on a 5×6 mm2 GaAs single crystal substrate. This polycrystalline structured Py film is patterned to a stripe shape by photolithography and lift off techniques. The dimensions of our sample is: length=2400µm, width=200µm and thickness=50nm.  The Py strip is fixed on a rotatable holder by an adjustable wedge. The external magnetic field, represented as (),,ex x y zHH H H=v, encloses an intersection angle α with the long-axis of the strip, and β represents the dip of the wedge. Accurate α and β are recorded by a readout on the holder and a goniometer. AMR is measured by detecting the resistance between two electrodes at each side of the strip’s length, as illustrated in Fig. 1(a). In FMR measurement, modulated microwaves are propagating to the holder normally through a rectangular waveguide of X band, while the modulation frequency is 5.37 kHz. The FMR signals are also electrically measured in field-swept mode by using a lock-in amplifier connecting those two electrodes via gold bonding wires and coaxial cables.  \t\r \n4\t\r \t\r The coordinate system we select in this article is demonstrated in Fig. 1(b).  The long axis of the thin strip is set as z-axis, the direction perpendicular to the strip’s plane is defined as y-axis, and the strip lies in the xz-plane. ΦH, ΦM are recorded as the misalignments of Hex and M with respect to xz-plane. The in-plane components of Hex and M encloses the angles ΘH, ΘM with z-axis, respectively. Hence ΘH, ΦH, α and β follows the relations as()1tan tan cosHαβ−Θ=and()1sin sin sinHαβ−Φ=.  In section 3.1, AMR and FMR measurements in weak Hex are illustrated, and both of Ha and Hd are taken into account. We will show how M rotates from parallel to Ha via only changing the magnitude of Hex generated by an electromagnet at room temperature. The detailed process of obtaining the demagnetization factors and magnetization through AMR and FMR experiments is also introduced in this subsection. For further investigating, AMR in out-of-plane configuration in stronger Hex is discussed in section 3.2. In this subsection, the Py thin strip is placed in Hex produced by a cryomagnet, which is carried out at liquid helium temperature.   3. Results and Discussion 3.1. Weak External Field Condition It is noted as “weak field condition” when the magnitude of Hex is \t\r \n5\t\r \t\r smaller than 2000 Oe. The measured AMR and FMR data of this Py thin strip in in-plane and out-of-plane configurations are shown in Fig. 2. Meanwhile, the demagnetization coefficient and M are obtained via fitting  these experimental results by selecting appropriate models. Fig. 2(a) shows the measured sheet resistance R versus Hex at different ΘH in in-plane magnetized configuration. It is illustrated that R reaches its maximum at Hex=0, hence M is parallel, or anti-parallel, to z-axis as a higher resistance state without external magnetic field. The increment of R achieved by decreasing the magnitude of Hex implies M’s rotation from parallel with Hex to z-axis, as demonstrated in Eq. (1). The direction of M at zero-field state is caused by Ha, the anisotropic built-in field. Ha is along with z-axis because of the lowest free energy for thin strip structure in this direction.   Here we assume Ha as a static filed, which is parallel to z-axis and is expressed as ()0, 0,aaHH=v. The effect of other important factor on the rotation of M is Hd, the demagnetization field. Hd depends on the direction and magnitude of M, it is written by(),,dx x x y y y z z zHN M N M N M=−v, where Nxx, Nyy, and Nzz are the demagnetization factors in x, y and z directions. The demagnetization factors satisfy the correlation of 1xx yy zzNNN++=for SI and 4xx yy zzNNNπ++=for CGS [11]. Accordingly, the yielded relations \t\r \n6\t\r \t\r between Μ and Ηex are: ,cos sin , sin , cos cos ,cos sin , sin , cos cosy yy yx xx x z axy zx ex H H x ex H z ex H HxM M y M zM MHN MHN M HHMM MHH HH HHMM MM MM−−+===Φ Θ = Φ =Φ Θ=Φ Θ = Φ =Φ Θvv vvv v    (2)  The demagnetization field along z-axis is neglected since Nzz is much smaller than Nxx and Nyy in thin strip structure, as shown in Fig. 1(b). It is difficult to provide analytical solutions for Eqs. (2), however getting numerical solutions is not a hard task. We use the numerical method to fit the experiment data. In in-plane configuration under weak field condition, ΦH=ΦM=0 and Hy=0, and Eqs. (2) are transformed as, sin sin cossin cosex H xx M ex H aMMHN MHHMMΘ− Θ Θ+=ΘΘvv vvv .        (3) Considering ΦH=ΦM=0, we have θ=ΘH. Taking the numerical results of Eq. (3) into Eq. (1), Ha and NxxMx are obtained. R0 and RA can be recorded directly through Fig. 1 as R0=87.7 Ω and Ra=1.5Ω. Other fitted results are Ha=1.95Oe and NxxMx=5.1Oe.  The demagnetization factor Nyy is significantly larger than Nxx according to the thin strip structure. If Hex consists of y-component, M should be misaligned away to Hex, which causes the surface magnetic charges in each side of xz-plane [10]. These surface magnetic charges generate a demagnetization field inside the sample with its direction \t\r \n7\t\r \t\r opposite to the y-component of Hex, and finally prohibit the misalignment of M. According to the shape of our sample, the demagnetization field generated by a very slight y-component of M can offset the y-component of Hex. Thus, only the xz-component of Hex is worth to be considered, the motion of M according to changing Hex is almost in-plane, and we have, cos sin sin cos cos,sin cos.ex H H xx M ex H H aMMMHN M HHMMθΦΘ − Θ ΦΘ +=ΘΘΘ≈vv vvv        (4)  The larger out-of-plane component of Hex can be provided by increasing the dip angle β of the wedge. Comparating to the in-plane Hex, larger out-of-plane Hex is needed for obtaining the same Heff and θ, as showing in Fig. 2(b).  The calculated magnitudes of M is obtained by fitting FMR experiment. The dispersion curves in different configurations are recorded in Fig. 2(c). For an in-plane M assisted with microwave in a magnetic field H, the resonant frequency fr for the rf signal is given by()()2ry y z z x x z zfH N N M H N N Mπγ⎡⎤=+ − + −⎡⎤⎣⎦⎣⎦[9].\t\r In our sample, we have eff ex d aHH H H H==+ +vv v and 0181 GHz/Tγµ= for Py, here µ0 is the permeability of vacuum. The Hex’s range is from 1000Oe to 1800Oe, such amplitudes are much smaller than ΝyyM, and consequently a very slight ΦH can generate large enough Hd to overcome the y-component of \t\r \n8\t\r \t\r Hex unless the in-plane component of Hex is significantly smaller than its y-component. For the schematic of β= 0, 45°and 70° in Fig. 2(c) for Hex larger than 1000Oe, NxxMx and Ha are ignorable, and the simplified expression of dispersion curve is given by: ()2c o s c o sre x H y y e x HfH N M Hπγ=Φ + Φ.                          (5)  In weak field condition, since Hex’s y-component is offseted by Hd, higher Hex is needed in order to achieve high enough resonant Heff for larger β while the assisted microwave’s frequency is fixed. Eq. (5) is used to fit the electrically detected FMR dispersion curves in Fig. 2(c) at different β.  The fitted magnetization is M=10750Oe, and the demagnetization factor along with x-axis is calculated as Nxx=0.00047.  3.2. Strong External Field Condition According to Eq. (2), larger Hex may provide y-component for Heff, and the direction of M can be tilted away from xz-plane. In terms of ΦM≠0 for this situation, Eq. (1) would be revised as, ()22 2 20-s i n c o s c o t c o sAA M M M MRR RR=+ Φ + Θ Θ Φ.                (6) Here ΦM and ΘM are deduced from Eqs. (2). The magnetization characteristic of Py thin strip under stronger Hex is investigated in liquid helium temperature around 4.2K. Although R0, RA and M vary at different temperatures, AMR feature of this Py thin strip in low \t\r \n9\t\r \t\r temperature and Hex up to 5 T evolves as the prediction of Eqs. (2), seeing in Fig. 3.  The movement of M from z-axis to Hex is separated by two steps, the in-plane magnetization as investigated in the former paragraphs, and the out-of-plane magnetization while is Hex high enough. The movement of M can be illustrated by an approximate picture. ΦM≈0 in the first step, M rotates rapidly from ΘM=0 to ΘM= ΘH. The process is displaced in the embedded picture of Fig. 3. In the second step, larger xz-component of Hex only keeps ΘM= ΘH. However, ΦM increases with stronger y-component of Hex, as shown in Fig. 3.   Meanwhile, we should indicate that the two-step magnetic movement does not exist in every applied out-of-plane Hex. Taking ΦH=90° as an instance, the movement of M only includes out-of-plane step in yz-plane because Hex contributes no x-component field to the effective field.   4. Conclusions In summary, we have demonstrated how the magnetization characteristic of a ferromagnetic thin strip changes in different external magnetic field based on the AMR and FMR measurements by considering demagnetization and magnetic anisotropy. It is shown that \t\r \n10\t\r \t\r the magnetization vector can rotate in the film plane as well as out of the film plane by sweeping the intensity of external magnetic field, while the direction of external field is fixed. The out-of-plane AMR’s low-temperature and high-field features are also well explained.  Our method can be used to obtain the demagnetization factor, saturated magnetic moment and the magnetic anisotropy.  Acknowledgement   The work is supported by the State Key Program for Basic Research of China (2013CB632705, 2011CB922004), the National Natural Science Foundation of China (10990104).            \t\r \n11\t\r \t\r References: [1] T. R. McGuire and R. I. Potter, IEEE Trans. Magn. 11, 1018 (1975). [2] R. C. O’Handley, Modern Magnetic Materials: Principles and Applications (Wiley, New York, 2000), p. 573. [3] W. Thomson, Proc. R. Soc. London 8, 546 (1857) [4] R. E. Camley, B. V. Mcgrath, Y. Khivintsev, and Z. Celinski, Phys. Rev. B, 78, 024425 (2008). [5] M. P. Kostylev, G. Gubbiotti, J.-G. Hu, G. Carlotti, T. Ono, and R. L. Stamps, Phys. Rev. B, 76, 054422 (2007). [6] A. V. Chumak, A. A. Serga, B. Hillebrands, G. A. Melkov, V. Tiberkevich, and A. N. Slavin, Phys. Rev. B, 79, 014405 (2009). [7] Pawel. Buczek, Arthur. ernst, and Leonid. M. Sandratskii, Phys. Rev. Lett, 105, 097205 (2010). [8] A. Taroni, A. Bergman, L. Bergqvist, J. Hellsvik, and O. Eriksson, Phys. Rev. Lett, 107, 037202 (2011). [9] C. Kittel, Phys. Rev. 78, 266 (1950) [10] Masanori. Kobayashi, and Yoshifumi. Ishikawa, IEEE Trans on Magn, Vol.28, pp1810 (1992). [11] C. Kittel, Introduction to Solid State Physics (John Wiley & Sons, Inc., New York, 1986) 6th edition.   \t\r \n12\t\r \t\r  \n Figure 1. (a) The schematic of our experiment and (b) the coordinate system used in this article. The rf signal and Lock-In amplifier are only applied in FMR measurement. The demagnetization field along x and y direction are also notified as -NxxMx and -NyyMy.    \n\t\r \n13\t\r \t\r  \n Figure 2. The experimental (colored dots) and fitted (solid lines) results for (a). in-plane magnetized AMR at different ΘH, (b). AMR of in-plane and out-of-plane magnetizations for ΘH=90° at different ΦH, and (c). the resonant frequency of FMR with respect to external field for both in-plane and out-of-plane configurations at different β, here α is fixed at 45°.  \n\t\r \n14\t\r \t\r  \n Figure 3. AMR measurement in stronger Hex at 4.2K. α and β are set as 45° and 30°, respectively. Inset: detailed sheet resistance of this thin strip at lower external field.  \n"    },    {        "title": "1311.4318v1.Fabrication__properties__and_applications_of_flexible_magnetic_films.pdf",        "content": "Chin. Phys. B Vol. 22, No. 12 (2013) 127502 \nTOPICAL REVIEW — Ma gnetism, magnetic materials,  and interdisciplinary research  \nFabrication, properties, and applicat ions of flexible magnetic films * \nLiu Yiwei ( 刘宜伟 ), Zhan Qingfeng ( 詹清峰 ) †, and Li Run-Wei ( 李润伟 )† \nKey Laboratory of Magnetic Materials and Devices, Ningbo Institute of Material Technology and \nEngineering (NIMTE), Chinese Academy of Sciences (CAS), Ningbo 315201, People’s Republic of China. \n \nAbstract: \nFlexible magnetic devices, i.e., magnetic devices fabricated on flexible substrates, are \nvery attractive in application of detecting magnetic field in arbitrary surface, non-contact \nactuators, and microwave devices due to the stretchable, biocom patible, light-weight, portable, \nand low cost properties. Flexible magnetic films are essential for the realization of various \nfunctionalities of flexible magnetic devices. To give a comprehensive understanding for \nflexible magnetic films and related devices, we have reviewed recent ad vances in the studies \nof flexible magnetic films including fabricatio n methods, magnetic and transport properties of \nflexible magnetic films, and their applications in magnetic sensors, actuators, and microwave devices. Three typical methods were introduce d to prepare the flexible magnetic films. \nStretching or bending the flexible magnetic films offers a good way to apply mechanical \nstrain on magnetic films, so that magnetic anisotropy, exchanged bias, coercivity, and \nmagnetoresistance can be effectively manipulate d. Finally, a series of examples were shown \nto demonstrate the great potential of flexib le magnetic films for future applications. \nKeywords: flexible, magnetic films, strain  \nPACS: 75.70.-i, 75.75.-c  \n \n                                                        \n*Project supported by the National Natural Foundation of China (11274321, 11174302, 11374312, \n11304326), the State Key Project of Fundamental Research of China (2012CB933004, 2009CB930803), the Chinese Academy of Sciences (CAS), and the Ningbo Science and Technology Innovation Team \n(2011B82004, 2009B21005),  and the Zhej iang and Ningbo Natural Science Foundations \n(2013A610083). \n†Corresponding author. E-mail: zhanqf@n imte.ac.cn and runweili@nimte.ac.cn \n 1. Introduction \nSilicon wafers have been widely used in manufacturing electronic devices [1]. However, \nmany natural things, such as human bodies, organi sms, clothes, etc., are elastic, soft, and \ncurved [2]. Therefore, the electronic devices based on rigid silicon wa fers are not suitable for \nthese new coming applications. Flexible electr onics is a technology of  assembling electronic \ncircuits and devices on flexible substrates, which are signifi cantly of lower cost, lighter, and \nmore compact, as compared to the conventional electronic devices [3]. By thinning single \ncrystal silicon wafer to 100 μm, the first flexible solar cell was made in 1960 [4,5], which \nstarted the development of flexible electroni cs. In 1997, polycrystallin e silicon thin film \ntransistor (TFT) made on plastic substrates was reported and received lots of attentions \nbecause of its poten tial applications in flexible display [6,7]. Since then, flexible electronics has \nbeen developed rapidly, and comm ercialized products have app eared in our daily life. Now, \nflexible electronic devices have  b e e n  w i d e l y  u s e d  i n  d i s p l a y, radio-frequency identification \n(RFID), solar cell, lighting, and sensors, among which flexible displays occupied more than \n80% of the market of flexible electronics [8,9,10]. With the development of various flexible \ndevices, display, logic, sensor, a nd memory are expected to be integrated in a multi-functional \nsystem and be fabricated on a flexible substrate [11].  \nIt is well known that magnetic materials are important for fabr ication of electronic \ndevices [1 2]. For example, soft magnetic material s are usually applied in inductors, \ntransformers, microwave devices, and screening of magnetic field [13,14]. Hard magnetic \nmaterials are widely used in loudspeak ers, generators, me mories, and sensors [1 5]. \nMagnetostrictive materials are used in actuators [16]. Permalloy can be used in anisotropic \nmagnetoresistance (AMR) sensors [1 7]. Giant magnetoresistance (GMR) or tunneling \nmagnetoresistance (TMR) multilayered structures can  be used in high-speed read/write heads \nin disk memory devices owning to their large magnetoresistance [18,19]. Recently, GMR or \nTMR sensors fabricated on flexible substrates , so called flexible magnetoelectronics, have \nattracted a lot of interests due to their potent ial applications in dete cting magnetic field in \nliving organisms [20,21]. Because of the extensive applications of the magnetic materials, it is \ninevitable to integrate flexible magnetic materials in flexible electronics. In this review, we first introduced the techni ques of fabricating fl exible magnetic films \nand devices. Then, we focused on the propertie s of flexible magnetic films and devices. \nFinally, the applications of flexible ma gnetic films and devices were discussed. \n2. Fabrication of flex ible magnetic films \n2.1 Magnetic films deposited on flexible substrates \nFabricating magnetic films directly on flexible substrates is a straig htforward way to get \nflexible magnetic films. The most used flexib le substrates are organic polymers including \npolyethylene terephthalate (PET), polyethylene naphthalate (PEN ), polyethersulphone (PES), \npolyimide (PI), and polydimethylsiloxane (PDMS) [22]. These organic polymers are highly \nflexible, inexpensive, and compatib le with the roll-to-roll processing [2 3]. Most of the \npolymers cannot suffer a high-temperature treatment [24], but they are still suitable for \nfabrication of most of magnetic films and de vices because of the near room temperature \ndeposition and low temperatur e (usually lower than 400 oC) post-annealing.  \nFor fabricating magnetic films on flexible substrates, a suitable buffer layer is often \nrequired to reduce the roughness of flexible substrates and ensure the continuity and \nfunctionality of magnetic films and multilayered structures , such as GMR and spin-valve \ndevices [25,26,27]. For example, the root-mean-square (R MS) roughness of a PET substrate is \nabout 2.16 nm, which is much larger than that of the thermally oxidized Si substrate. The \n150-nm-thick Fe 81Ga19 film directly grown on flexible  PET substrates exhibits a RMS \nroughness of 3.34 nm[28]. A 30-nm-thick Ta buffer layer can reduce the roughness of \nFe81Ga19/Ta/PET films to 2.04 nm [29]. By growing a Ta buffer layer,  flexible exchange biased \nTa(5 nm)/Fe 81Ga19(10 nm)/Ir 20Mn 80(20 nm)/Ta(30 nm)/PET heterostructures were \nsuccessfully fabricated , which could be used to stabilize the magnetization of magnetic layers \nin flexible spin-valve devices [3 0]. Chen et al. , have fabricated flexible Co/Cu GMR \nmultilayers on polyester substrates by dc magnetron sputtering [31]. The sample structure is \nschematically shown in Fig. 1( a). Figure 1(b) shows the photogr aphic image of circularly \nbended Co/Cu multilayer deposited on polyester substrates. Before deposition the Co/Cu multilayer, AR-P 3510 positive photoresist (Allr esist, Germany) buffer layer with the \nthickness of 2 μm has been spin-coated on flexible subs trates to reduce the surface roughness. Besides, Oh et al. , fabricated flexible spin-valve structur es of Ta (3 nm)/NiFe (10 nm)/Cu (1.2 \nnm)/NiFe (3 nm)/IrMn (10 nm)/Ta (3 nm) on PEN substrates using AZ 5214E photoresist as \nthe buffer layers [32]. Melzer et al. , provided another wa y to fabricate flexible spin-valve \nstructures, as shown in Fig. 2 [33]. First, PDMS was spin-coate d onto silicon wafers with \nsurface roughness < 0.5 nm. Then, the structure of Ta (2 nm)/IrMn (5 nm)/ [Permalloy (Py) (4 \nnm)/CoFe (1 nm)]/Cu (1.8 nm)/[CoFe (1 nm)/Py (4 nm)] with 5-nm-thick Ta buffer layer was \nfabricated by magnetron sputtering. After a lit hographic lift-off process, by means of the \nantistick layer, the PDMS film was peeled from  the rigid silicon wafer, forming a flexible \nmagnetic multilayered structure.  \nwith the development of magnetoelectric mate rials, multiferroic composites consisting of \nmagnetostrictive materials and organic ferroelectric materials, such as polyvinylidene fluoride  \n(PVDF) and polyvinylidene-fluoride–trifluoroethylene (PVDF-TrFE), have received much \nattention [34]. Sm–Fe/PVDF heterostruct ural films have been pr epared by depositing Sm–Fe \nnanoclusters onto flexible PVDF membranes us ing cluster beam deposition, which exhibits \nlarge magnetoelectric voltage output  of 210 μV at an external magnetic bias of 2.3 kOe[34]. \nBesides organic polymers, people  also seek for other types of flexible substrates to \nprepare magnetic films. Liang et al. , have successfully produced flexible graphene/Fe 3O4 \n \nFig. 1.  (a) Schematic illustration of (Co/Cu) N film s deposited on Si and flexible substrates. (b) A \nphotographic image of circularly bended (Co/Cu) 20 film deposited on polyester substrate.[31] \n \nFig. 2.  Fabrication process of stretchable spin-valve structure. [33] hybrid papers by using graphene as flex ible substrates, as shown in Fig. 3 [35]. During \nfabrication, a two-step process was used: (I)  mixing of graphene aqueous solution with \nwater-soluble Fe 3O4 nanoparticles  and (II) chemical reducti on of the suspension of \nwater-soluble Fe 3O4 nanoparticles and graphene sheets w ith hydrazine. In a broad sense, \ncantilevers with several micrometer in thickne ss, which have been applied as sensors in \nmicro-electro-mechanical systems (MEMS) [36], can be employed as flexible substrates. The \ncantilevers are usually made of ma terials including Si, polyimide, Si 3N4, etc [37]. Onuta et al. , \nhave fabricated a flexible multiferroic composite as an energy harvester consisting of a magnetostrictive Fe\n0.7Ga0.3 thin film and a Pb(Zr 0.52Ti0.48)O3 piezoelectric thin film on a \n3.8-μm-thick Si cantilever, as shown in Fig. 4 [38]. Magnetic polymers fabr icated by dispersing \nmagnetic components in polymer matrix, can be served as flexible functional cantilevers, \nwhich can respond to external magnetic fields  and mechanical vibra tions. If the magnetic \ncomponents are magnetostrictive materials and th e polymers are ferroelectric materials, three \nmain types of polymer-based multiferroic materials, nano-composites, laminated composites, and polymer as a binder composite can be achieve d, as shown in Figs. 5 (a), 5(b), and 5(c), \nrespectively\n[39]. The investigations on polymer-based multiferroic materials are challenging \nand innovative, which bridge the gap between f undamental research and applications in the \nnear future.  \n \n \n \nFig. 3. The flexible graphene/Fe 3O4 hybrid papers using graphene as the flexible substrates. [35]  \n2.2 Transfer and bonding approach \nIn transfer and bonding approach, magnetic films or structures are fabricated on \nconventional rigid substrates like Si wafer, glass, MgO, etc., by standard fabrication methods. \nThen, the magnetic films or structures can be transferred by removing the substrates through \nlaser annealing, chemical solution, or directly peeling off the films [40,41,42]. Finally, the \ntransferred films or structures can be bonded to flexible subs trates by glue or \n \nFig. 4.  A scanning electron micrograph (SEM) of a flexible multiferroic energy harvester.[38] \n \nFig. 5. Three main types of Polymer-based multiferroic materials. [39] \n \nFig. 6.  Schematic show of the t ransfer and bonding approach to get flexible magnetic films. [45] physical/chemical adsorption [40,41,42]. Generally , conventional rigid substrates are much more \nflat than flexible substrates. Therefore, the transfer and bonding approach can provide flexible \nmagnetic films and structures with high quality and high performance. However, it is difficult to prepare a large area flexible film by mean s of this method due to the random damage \nduring the transfer procedure. After the discov ery of graphene, a variety of transfer and \nbonding approaches have been developed to transfer graphene films onto flexible substrates\n \n[43]. However, these methods cannot be directly employed to prepare flexible magnetic films, \nbecause some chemicals used in the transfer procedure  may damage the magnetic films [44]. \nDonolato et al. , have developed another i nnovative, simple, and versat ile pathway to transfer \nmagnetic films and structures onto flexible polymer substrates, as shown in Fig. 6 [45]. At first, \na trilayered structure of Ti/Au/SiO 2, which acts as the donor substrate, was grown onto a \nconventional Si substrate usi ng a sputter deposition system. Th en, magnetic nanostructures \nmade of permalloy (Ni 80Fe20) were fabricated on the trilay er by means of an electron beam \nlithography process. After that, PDMS was spin coated on the magnetic nanostructure. Finally, \nthe transfer was accomplished by simple imme rsion of the chip in water and a gentle \nmechanical lifting of the polymer membrane off th e substrate. In this approach, the selection \nof Au and SiO 2 layers is the key aspect. Due to  the hydrophobic character of Au and \nhydrophilic behavior of SiO 2, the bond between them is rather weak, so the Au and SiO 2 \nlayers can be easily separated via th e water-assisted lift-off process. \n2.3 Release of sacrificial layers  \nThe general processes of releasing sacrificial layers for preparing flexible magnetic films \nare shown in Fig. 7. Magnetic films are first de posited on bulk substrates  or bulk substrates \nwith sacrificial layers. For the simple film/substrate structures, the substrates themselves can be treated as sacrificial layers. The substrates  or the sacrificial la yers can be removed by \naqueous solution of chemicals, chemical etch ing, or dry etching to achieve freestanding \nmagnetic films\n [46,47]. This method has the similar a dvantage as the above-mentioned transfer \nand bonding approach and can provide flex ible magnetic films with high quality. The most used sacrificial layers are NaCl  and photoresist. Heczko and Thomas have \nepitaxially grown Ni-Mn-Ga films on water-sol uble (001)-oriented NaCl single crystals and \nobtained high quality free-standing Ni-Mn-Ga  films by dissolving the NaCl substrates[48]. On \nthe other hand, Tillier et al. , have used photoresist  as sacrificial layers to fabricate flexible \nNi-Mn-Ga films [49]. Ni-Mn-Ga films were first depos ited on photoresist (Shipley S1818) \nlayers, which have been spin-coated on polycrystalline Al 2O3 substrates. After deposition, the \nsamples were placed in an acetone bath to remove the photoresist sacrificial layer and obtain the freestanding magnetic films. Other materials, such as Au, MgO, and Cr, can also be used as sacrificial layers due to th eir chemical soluble properties \n[50,51,52]. For example, Bechtold et \nal., have prepared 1.2- μm-thick Fe 70Pd30 films on Au(50 nm)/Cr(8 nm)/MgO substrates [50]. \nAfter deposition, the Fe 70Pd30 films were released from the substrate by wet chemical etching \nof the sacrificial Au layer in an aqueous solu tion of potassium iodide and iodine. Although \nremoving sacrificial layers is a good way to prepare high quality flexible magnetic films, this \nmethod still has some disadvantages. For example, the aqueous solution of chemicals may damage the magnetic films. Alternatively, flexible membranes of inert materials, such as Pt \nand Au, can be prepared by rem oving sacrificial layers. Then ma gnetic films can be deposited \non the thin metallic membranes. We have etched  platinized Si substrates (Pt(200 nm)/Ti(50 \nnm)/SiO\n2(500 nm)/Si) in 10 wt% HF solutions for 4 h[53]. Because Ti and SiO 2 layers reacted \nwith HF, producing soluble SiF 4 and TiF 3, respectively, the 200-nm-t hick Pt layers were \nreleased from Si substrates. The flexible Pt foils can be used as flexible substrate for \npreparing ferromagnetic or ferroelectric films at an elevated temperature. The detailed \nprocesses are schematically shown in Fig. 8. \n \nFig. 7. The general processes of releasing sacrificial layers for preparing flexible magnetic films.  \n \n3. Properties of flexible magnetic films \n3.1 Effect of buffer layer \nPrior to fabricating flexible magnetic films and devices, an appropriate buffer layer needs \nto be introduced to decrease the roughness of flexible  substrates, improve the crystal \norientation of magnetic films, and release the re sidual stress. Therefore, the buffer layers are \nextremely important in determining the properties of flexible magnetic films, such as Fig. 8. Method to obtain flexible functional thin-films using Pt foils. [53] \n \nFig. 9. Hysteresis loops for flexible Fe 81Ga19(50 nm)/Ta/PET films with a magnetic field applied \nalong (a) the easy ( ψ=0o) and (b) hard axes ( ψ=90o ), and the corresponding angular dependence of \n(c) squareness and (d) coercive field. Ta(0), Ta(10), and Ta(20) indicate Ta buffer layer with \nthickness of 0, 10, and 20 nm, respectively. [29] magnetic anisotropy, coercivity, magnetoresistance, etc. We have investigated the effect of a \nTa buffer layer on the magnetic pr operties of magnetostrictive Fe 81Ga19 films grown on \nflexible PET substrates [29]. As shown in Fig. 9, with increasing the thickness of Ta buffer \nlayer, both the uniaxial magnetic anisotropy and coercivity of Fe 81Ga19/Ta/PET films are \ndecreased. Obviously, the Ta buffe r layer could effectively release the residual stress in PET \nsubstrates, and therefore reduce the stre ngth of the uniaxia l anisotropy of Fe 81Ga19 layers. The \ndecrease of coercivity of Fe 81Ga19 films may result from both the decrease of uniaxial \nanisotropy and the flatness of the films. Chen  et al. , have shown that the GMR effect of \nCo/Cu multilayers (MLs) on a flexible organic substrate can be enhanced up to 200% by introducing a photoresist (PR) buffer laye r to flatten the plastic substrates\n [31]. They have \ncompared three Co/Cu multilayers grown on Si substrate, polyester substrate (P), and polyester substrate with 2 μm photoresist (PR) buffer layer (PR+P). As shown in Fig. 10(d), \nthe RMS roughness, Rq, of the P substrate is one order of magnitude larger than that of Si \nsubstrate, and Rq of the PR+P substrate has a similar value obtained for the Si substrate. As \nshown in Figs. 10(a), 10(b), and 10(c), GMR valu es significantly increa se after introducing a \nPR buffer layer and rise to even higher values than those achieved on Si substrates due to an \nincreased antiferromagnetic coupling fraction of the flexible PR buffered Co/Cu multilayers.  \n \nFig. 10.   (a) GMR curves of (Co/Cu) 10 MLs deposited on Si, P, and PR+R substrates. (b) GMR \ncomparison of (Co/Cu) N MLs on various substrates with different numbers of bilayers. (c) GMR ratio \nof (Co/Cu) N MLs deposited on Si, P, and PR+P substrat es. (d) RMS roughness, Rq, of Si, P, PR+P \nbare substrate and Co/Cu films on corresponding substrates. [31] 3.2 Strain dependence of magnetic properties \nControl of magnetic properties of flexible magnetic films via mechanical strains is an \ninteresting topic from the view point of both fundamental resear ches and potential applications \n[54]. Magnetic anisotropy is a key characteristic in  determining the dir ection of magnetization \nand affecting the performa nce of spintronic devices [55]. For flexible spintronic devices applied \nin curved surfaces or used to evaluate the mechanical strain, their magnetic anisotropy under \nvarious mechanical strains need to be known and well controlled. FeGa magnetostrictive \nalloys exhibiting moderate magne tostriction (~ 350 ppm for Ga  content of 19%) under very a \nlow magnetic field (~ 100 Oe) but good mechani cal properties is a poten tial material applied \nin strain controllable spintronic devices. We have fabricated magnetostrictive Fe 81Ga19 films \non flexible PET substrates [28]. Due to the residual stress of th e flexible substrates, a uniaxial \nmagnetic anisotropy is observed for the as-grown Fe 81Ga19 films. By inward or outward \nbending the PET substrates, the compressive and tensile strains can  be applied on Fe 81Ga19 \nfilms. The hysteresis loops for Fe 81Ga19/PET films under tensile and compressive strains are \nmeasured by bending the substrates along the easy or hard axes of Fe 81Ga19 films, as shown in \nFig. 11 [28]. For the magnetic field oriented along the easy axis, a tensile strain along the hard \naxis gives rise to a drastic d ecrease in Mr/Ms ratio, as shown in  Fig. 11(a). In contrast, under a \ncompressive strain, the Mr/Ms ratio is increas ed, as shown in Fig. 11(b). For the magnetic \nfield oriented along the hard axis, the Mr/Ms ra tio is decreased and increased under a tensile \nand compressive strain applied along the easy ax is, respectively, as shown in Figs. 11(c) and \n11(d). The results provide an alternative way to mechanically tune magnetic properties, which \nis particularly important for deve loping flexible magnetic devices.  \nIn addition, we have also studied the effect  of mechanical strain on magnetic properties \nof flexible exchange biased Fe 81Ga19/IrMn heterostructures grown on PET substrates [56]. \nFigure 12 shows the typical result s for the in-plane strain de pendence of normalized magnetic \nhysteresis loops of Fe 81Ga19(10 nm)/IrMn(20 nm) bilayers with  strain applied perpendicular \nor parallel to the pinning direction (PD). The exchange bias field achieves a maximum value \nof 69 Oe for magnetic field applied along the induced PD and vanishes for magnetic field \nperpendicular to the PD, as shown in Figs. 12(a)  and 12(b). The loop sq uareness is decreased \nwhen a tensile strain is applied perpendicular to the PD with magnetic field parallel to the PD or a tensile strain is applied parallel to the PD with magnetic field perpendicular to the PD. \nDifferent from the previously reported works on rigid exchange biased systems, a drastic \ndecrease in exchange bias field was observed u nder a compressive strain with magnetic field \nparallel to the PD, but only a slightly decrea se was shown under a tensile strain. Based on a \nmodified Stoner-Wohlfarth model calculation, we suggested that the di stributions of both \nferromagnetic and antiferromagnetic anisotropies be the key to induce the mechanically tunable exchange bias.  \n \nIn order to understand the effect of stra in on magnetic properties from the view of \nmicrocosmic, it is necessary to image the magne tic domain structures under different strains. \nChen et al. , have prepared 100 nm Co films on pol yester substrates. The magnetic domain \nstructures with and without plastic strains we re obtained by Kerr microscopy, as shown in Fig.  \n \nFig. 11.  Hysteresis loops for Fe 81Ga19/PET obtained under various ex ternal strains using different \nmeasuring configurations, (a) Magnetic field H parallel to the uniaxial anisotropy Ku and a tensile \nstrain ε (outward bending of PET substrates) applied perpendicular to Ku, (b) H parallel to Ku and a \ncompressive strain – ε (inward bending) perpendicular to Ku, (c) H perpendicular to Ku and ε parallel \nto Ku, and (d) H perpendicular to Ku and ε parallel to Ku. [28] 13 [57]. It is found that the size of magnetic domains become mu ch larger and ordered when \nthe magnetic field is aligned along the easy axis . A tensile strain applied along easy axis can \nfurther increase the size of the domains. When  the magnetic field is applied along the hard \naxis, the density of magnetic dom ains is increased after applyi ng a tensile strain along easy \naxis. \n3.3 Strain dependence of magnetoresistance  \nMagnetoresistance (MR), where the resistance  of the material changes with applied \nmagnetic field, has been extensively used as ma gnetic field sensors, r ead-write heads, and \n \nFig. 12. The strain dependence of magnetic hysteresis loops for Fe 81Ga19(10 nm)/IrMn(20 nm) bilayers with \nmagnetic field (a) parallel and (b) pe rpendicular to the PD. The compressive and tensile strains are applied \nperpendicular or parallel to the PD, as shown in the insets of (a) and (b), respectively. [56] \n \nFig. 13. Effect of strain on the magnetic domain structur es of 100 nm Co films on polyester substrates. \n(a)  Strain ε=0 and H along hard axis, (b) Tensile strain ε=0.75% along easy axis and H along hard axis, \n(c) Strain ε=0 and H along easy axis, (d) Tensile strain ε=0.75% along easy axis and H along easy axis. [57] magnetic random access memory [19]. As early as 1992, Parkin et al. , have prepared flexible \nGMR multilayers on Kapton substrates, which di splay 38% room-temperature GMR, almost \nas large as that found in similar structures prepared on silicon wa fers. Such flexible structures \nsuggest potential technological applic ations in light-weight read heads [58]. In 1996, Parkin \nalso demonstrated flexible exchange-biased magnetic sandwiches with lower saturation field \nand 3% room-temperature MR suggesting the po ssibility of manufacturi ng flexible MR read \nhead [30]. In 2010, Barraud, et al. , have successfully prepared flexible Co/Al 2O3 /Co TMR \nstructure on polyester based organic substr ates with 12.5% room-temperature TMR ratio[59]. \nSince the flexible substrates are easy to di stort, due to the magnetostriction effect, the \nmagnetic and transport properties of flexible  magnetic films and devices strongly depend on \nthe strain status of samples. How to make th e magnetic films and devi ces insensitive to the \nstrain is a challenging task. Melzer et al. , demonstrated an easy approach to fabricate highly \nelastic spin-valve sensors insensitive to the strain on flexible PDMS [33]. By means of a \npredetermined periodic fracturing mech anism and random wrinkling, meander-like \nself-patterning devices can be achieved, as seen in Fig. 2. Th is meander-like structure makes \nthe device insensitive to the stra in. The influence of strain on GMR and sample resistance is \nshown in Fig. 14 [33]. It is clearly seen that both GM R magnitude and sample resistance \nmaintain their values very stably under different strains, which are suitable as stretchable sensors to detect magnetic field.  \n \n \nFig. 14.  GMR magnitude (circles) and sample resistance (triangles) during a cyclic loading \nexperiment between 5% (filled symbols) and 10% (open symbols) strain. [33] On the other hand, if MR devices are designed to evaluate strain or  controlled by strain, \nthe MR of devices is required to be sensitive to  the strain. Such strain  tunable MR devices can \nbe used in novel stra intronic devices, which consume extremely low power. Generally, a \nGMR film consists of periods of two ferromagn etic layers separated by a conducting layer, \nand the MR depends on the relative magnetiza tion directions of the adjacent ferromagnetic \nlayers and the interlayer exchange coupling [60]. An in-plane tensile strain can reduce the \nthickness of the spacer layers in a GMR structure, resulting in the change of interlayer exchange coupling and the MR, as Chen et al., have reported\n [31]. Another approach for strain \ncontrol of MR is to tune the magnetic anisot ropy of ferromagnetic laye rs. As mentioned in \nsection 3.2, the magnetic anisotropy of magneto strictive materials ca n be manipulated by \nmechanical strain or stress. Since most ferro magnetic materials exhibit the magnetostriction \neffect, the mechanical strain control of MR can be realiz ed through the strain-induced \nmagnetic anisotropy [61,62]. Özkaya  et al ., have prepared Co(8 nm)/Cu(4.2 nm)/Ni(8 nm) \npseudo-spin-valve (PSV) structur es on flexible PI substrates [63].The low GMR magnitude for \n \nFig. 15. GMR magnitude for Co(8 nm)/Cu(4.2 nm)/Ni(8 nm) GMR structures in \n(a) as-prepared state, (b ) 0.25%, (c) 0.5% and (d ) 0.75% strained states. [63] the as-prepared sample at zero-field indicates that the magnetization directions of Co and Ni \nare parallel at the remanent  state, as shown in Fig. 15 [63]. Applying a uniaxial strain may lead \nto opposite rotation of the magnetization directions  in both magnetic layers to each other due \nto different signs of the magnetostriction coeffi cients of Co and Ni. Upon applying a strain \nperpendicular to the easy axis of Co and Ni , the zero-field GMR magn itude increases with \nincreasing strain, as shown in Figs. 15 (b), 15(c) and 15(d), which in dicates that the angle \nbetween the magnetizations of each layer in the remanent state increases. This result suggests \nthat both the magnetic field sensitivity an d the magnetic field ope rating range of GMR \ndevices can be optimized  via applying strain. \n4. Applications \n4.1 Flexible spintronic devices applied in biomedical  techniques \nMagnetic particles can be used to deliver dr ug or gene, and help to detect proteins, \nnucleic acids, or to enhance magnetic resonance imaging (MRI) contrast, all of which are very \nimportant for the modern biomedical techniques [64,65,66]. In a biomedical system, monitoring \nand analyzing the signals from ma gnetic particles are the essent ial issue, which increases the \ndemand for integration of magnetic field sensing devices into biomedical systems. In this \nrespect, spintronic devices, such as GMR and TMR sensors, provide an efficient solution for \ndetecting magnetic particles due to their high magnetic field sensitivity [67,68]. However, \nmagnetic particles usually flow in the micro-flui dic channels, so that integrating the magnetic \nsensors with the micro-fluidic channels can si gnificantly improve the sensitivity for detecting \nmagnetic particles. Mönch et al. , have successfully fabricated  a fully integrative rolled-up \nGMR sensor simultaneously acting as a fluidi c channel for in-flow detection of magnetic \nparticles, as shown in Fig. 16 [69]. This flexible and rolled-up GMR sensor  leads to better \nsignal-to-noise ratio and magnetic particles in a fluidic channel can be easily detected and \ncounted. A small disadvantage of this rolled-up GMR sensor is that it requires intensive \nlithography processing  and is therefore expensive and time consuming. Melzer et al. , provide \nanother way to prepare the low-cost flexib le GMR sensors used in detecting magnetic \nparticles. The preparation process is shown in Fig. 2 [33]. After preparation, the optimized \nGMR sensors are wrapped around the circumferen ce of a Teflon tube, as shown in Fig. 17(a) [70]. Figures 17(b) and 17(c) demonstrate the sens or's output, when the magnetic particles are \npassing through the flexible GMR sensors [70]. \n \nThe flexible electronic circuits used in the biomedical systems are generally prepared by \nmeans of a new-developed printing method, which could revolutionize large area and \nlow-cost electronics manufacturing [71]. However, the fabricati on of printable magnetic \nsensors remains challenging due  to lack of magnetic inks containing various components. \nKarnaushenko et al. , have for the first time develope d a kind of magnetic ink with GMR \nflakes which can be easily printed on various substrates, such as paper, polymer and ceramic \n \nFig. 16. Schematics revealing the main concept of rolled-up magnetic sensor for in-flow detection of \nmagnetic particles. [69] \n \nFig. 17.  Detection of magnetic particles in a fluidic channel: (a) Elastic GMR sensor wrapped around the \ncircumference of a Teflon tube. The magnetic particles are approaching the GMR sensor. (b) Signal of the \nelastic GMR sensor on a screen (background) as the magnetic cluster is passing the sensor (foreground). \n(c) Several consecutive detection events of particles passing the elastic GMR sensor. [70] [72]. In order to fabricate the magnetic ink, GMR sensors are first deposit ed on 3 inch silicon \nwafers with photosensitive polymer AR-P 3510 as the buffer layer. After preparation, the \nsamples are rinsed in acetone to release the deposited GMR se nsors from the substrates. The \nobtained GMR sensors show flake-like or rolled-up structures arising from the intrinsic strain \nof the deposited GMR films on rigid substrates, as shown in Fig. 18(a) [72]. To assure high \nelectrical conductivity of  as-prepared GMR flakes, a multilaye r stacked structure is prepared \nfrom the originally obtained material by a ball milling. The resulting powder is filtered \nthrough a grid that defines the maximum la teral size of a GMR flake to about 150 μm, as \nshown in Fig.18 (b). A GMR ink is prepared by mixing 500 mg of the GMR powder with 1 \nml of a binder solution that is an acrylic rubber based on poly (methyl  methacrylate) (PMMA) \ndissolved in a methyl isobutyl ketone. Finall y, using a brush the so lution is painted on \ndifferent surfaces, i.e. paper, polymers and ceramic. As show n in Fig.18 (c), the cross-section \nscanning electron microscopy (SEM) image of a large-area film shows continuous layer \nstacked structures, which signi ficantly facilitate the electron transpor t along the in-plane \ndirection to achieve a high GMR effect. This method uses standard sputter deposition, milling \nand mixing machines for high yi eld production, demonstrating the suitability of the printable \nmagnetoelectronic devices for la rge scale industrial production. \n  \n4.2 Flexible multiferroic structur e applied in energy harvesting \nEnergy harvesting is a process by which energy can be captured from external sources, \nsuch as solar power, thermal energy, vibrational energy, elec tromagnetic waves, etc, and \nconverted into electrical energy [73]. Energy harvesting technologies  can be a substitute for \nbatteries, minimizing the power consumption. Among various energy harvesting technologies, \nthere has been significant interest in the area of vibration energy base d on piezoelectric and \nmagnetic harvesters [74,75]. Figure 19 shows the magnetoelect ric energy harvesting mechanism \nof multiferroic composites made by combini ng magnetostrictive and piezoelectric phases \ntogether [39]. First, an external magnetic field leads to deformation the magnetostrictive phase \n  \nFig. 18.  SEM images of GMR powder on various stages  of ink preparation: (a) Initial GMR powder \ndirectly after delamination from Si substrates that consists of large metallic flakes (inset 1) and a \nvariety of tube like structures (inset 2) self-assembled by releasing of film intrinsic stress. (b) The \nmagnetic film is milled using ceramic beads in order to produce magnetic powder consisted of \nvariously shaped flakes. (c) SEM image of the cross-section through printed sensor shows the \ninternal structure of metallic flakes percolated inside polymer; (inset) schematic drawing \ndemonstrate the principle of flake percolation.[72] through the magnetostriction effect, and the deformation could be transmitted to the \npiezoelectric phase across the in terface between the two phases, which would generate the \nelectric charges due to the c onverse piezoelectric effect. With  the development of wearable \nelectronics, more and more electronics are incr easingly integrated into clothing, either for \nfunctional or fashion reasons. This requires th e next generation of energy harvesters moves \ninto wearable electronics, which needs the magnetic  and piezoelectric materials to be flexible \nand lightweight. Onuta et al. , have fabricated an electroma gnetic energy harvester consisting \nof a magnetostrictive Fe 0.7Ga0.3 thin film and a Pb(Zr 0.52Ti0.48)O3 piezoelectric thin film on a \n3.8-μm-thick Si cantilever, as shown in Fig. 4 [38]. The dependence of output voltage and \nharvested power on the AC magne tic field is shown in Fig. 20 [38]. The harvested peak power \nof 0.7 mW/cm3 at 1 Oe is about 6 times larger  than the value reported in the \nTerfenol-D/PZT/Terfenol-D laminate structures [76,77], which promotes the development of \nflexible energy harvesting materials. \n \n \n \n \nFig. 19.   Schematic show of harvesting mechanism for multiferroic materials. [39]  \n4.3 Flexible polymer based magnetic  composite applied in actuators \nPolymer-based magnetic composite are flexib le, lightweight, and eas ily processed, which \nare widely applied in MEMS [78]. The magnetically actuated micr o-devices can be controlled \nwithout wire as long as the act uation environment is magnetically  transparent, and therefore \ncan be operated in air, vacuum, water, etc [79]. The flexible, wireless c ontrol of micro-devices \nmakes polymer based magnetic composite attr active for many applications. However, the \n \nFig. 20.  Dependence of the output voltage and harvested power on the AC magnetic field of \nPb(Zr 0.52Ti0.48)O3/ Fe 0.7Ga0.3 cantilevers [38] \n \nFig. 21.  Schematic view with photograph of a fabricated NiFe thin film worm actuator and its \ndeflected motion. [80] actuation or precise control of the polyme ric components is a difficult issue. Lee et al. , have \nprepared an actuator cons isting of a body plate of 50 μm thickness and four legs using \nphotoresist SU-8 [80]. Three square sections  of NiFe films of 10 μm thickness are in turn \nelectroplated on the top and bottom side s of the SU-8 body, as  shown in Fig. 21 [80]. When the \nmagnetic field is applied to the actuat or along with longitudinal direction, the \nmagnetostriction of NiFe films make the actu ator curve and move along the field direction, \nwhich is useful in the micro-machine area su ch as magnetic field dr iven drug delivery. Kim et \nal., have presented a new magnetic polymeric mi cro-actuator, which allows the programming \nof heterogeneous magnetic anisotropy at the microscale [8 1]. As seen in Fig. 22, the \nmicro-actuator is composed of four magnetic bodies having different  magnetic easy axes, \nsuch that it has various configurations acco rding to the applied external magnetic field \ndirection. By freely programming the rotation al axis of each component, the polymeric \nmicro-actuators can undergo predesigned, comp lex two- and three-dimensional motions. \n \n \n \nFig. 22.  Movement of polymeric micro-actuators by magnetic field. [81] 4.4 Flexible soft magnetic films applied in microwave devices \nFlexible soft magnetic films exhibit high microwave permeability, which are of practical \nimportance for a number of appl ications, such as high freque ncy inductors, transformers, \nshielding, and electromagneti c interference (EMI) devices [82,83,84]. Additionally, the flexible \nfilms can be cut easily and be used on arbitrary surface. Due to  the magnetostriction effect, \nthe magnetic anisotropy of flexible soft magnetic  films can be tuned by changing the status of \nstrain in flexible films, which provides the pos sibility to overcome the Snoek’s limits and \ndesign the frequency tunable microwave devices [85,86]. Flexible thin films of magnetic alloys, \nsuch as FeCoB, FeCoBSi, FeTaN, FeZrN,  and CoAlO, and the polymer-nanoparticle \ncomposites have been prepared due to  their high frequency applications [87,88,89,90,91,92]. Zuo et \nal., have prepared [Fe–Co–Si ( d)/native oxide] 50 multilayer films with different metallic layer \nthicknesses ( d) on flexible Kapton substrat es by DC magnetron sputtering [93]. Figure 23 \ndepicts the permeability spectra for the multilayer films with various d. The films exhibit \nrelatively high values of complex permeability and ferromagnetic resonance frequency up to 7.9 GHz, indicating the great potential for appli cations in high-freque ncy electromagnetic \ndevices. Rasoanoavy, et al. , have prepared a flexible CoFeB/PVDF/CoFeB composite \nmaterial and observed a 30% variation in the microwave permeability under the application of \na 1.5 MV/m electric field, due to the m odified magnetic anisotropy caused by the \nstrain-mediated magnetoelectric effect \n[94].  \nEmploying the exchange bias effect is anot her way to promote the resonance frequency \nof the magnetic films and devices. Phuoc  et al. , have prepared Permalloy-FeMn multilayers \non flexible Kapton substrates [95]. A multiple-stage magnetization reversal and consequently \nplural ferromagnetic resonance absorption has b een observed, which is po ssibly interpreted in \nterms of the different exchange interfacial ener gy acting on each layers. Ba sed on these results, \nthey have demonstrated a wide-band microwave absorber by using flexible Permalloy-FeMn \nmultilayers. Figure 24 shows the frequency dependence of the reflection loss of flexible Permalloy-FeMn multilayers. The working ba ndwidth (the absorption width where the \nreflection loss is less than 10 dB) of the present film is rather broad ranging from 1 to 4 GHz, \nindicating that flexible exchange-biased multilayer systems are promising for future \nhigh-frequency applications.  \n5. Conclusions and perspectives \nInvestigations on flexible magnetic films a nd their applications are new-arising areas, \nwhich show potential importance for the developmen t of flexible electronics. In order to give \na comprehensive understanding of the flexible magnetic films and related applications, we \nhave reviewed recent advances in the stud y of flexible magnetic films including the \nfabrication methods, the physical properties, and the applicati ons of the flexible magnetic \n \nFig. 23.  Permeability spectr a of [Fe–Co–Si ( d)/native oxide] 50 multilayer films. [93] \n \nFig. 24.  Frequency dependence of the reflection loss of flexible Permalloy–FeMn multilayers.[95] films and devices. (a) By deposition of magnetic films on the flexible substrates, transfer and \nbonding approach, or removing sacrificial layers, one ca n prepare the desired flexible \nmagnetic films. Generally, all flexible magne tic films require fabricated on a supporting \nflexible substrate. Therefore, flexible su bstrates with good flat ness, high treatment \ntemperature, stable thermal stability, good mechanic al properties, etc, are very important for \nthe fabrication of high quality flexible magnetic films. (b) Due to the flexibility of flexible \nmagnetic films, the strain effect on the magnetic-related properties is very important both for the fundamental research and the practical ap plications. The magnetic anisotropy, exchanged \nbias, coercivity, and magnetoresistance of fl exible magnetic films and devices can be \neffectively manipulated by applying external st rains, which has a good potential application in \nthe straintronic devices. However, in order to realize the multifunctional straintronic devices, the further comprehensive studies on the physic al properties of flexible magnetic films are \nnecessary, especially under multi-field conditions,  like electric field, magnetic field, and strain \nfield, etc. (c) Flexible magnetic films can be  applied in the spintronic devices, energy \nharvester, actuators, and microwave devices, et c, due to the propertie s of bio-compatible, \nlow-cost, light-weigh t, and compact.   \n             \n References: \n                                                        \n1 Gosele U and Tong Q Y 1998 Annu. Rev. Mater. Sci.  28 215 \n2 Rogers J A, Someya T and Huang Y G 2010 Science  327 1603 \n3 Kim D H and Rogers J A 2008 Adv. Mater.  20 4887 \n4 Crabb R L and Treble F C 1967  Nature  213 1223  \n5 Ray K A 1967 IEEE Trans. Aerosp. Electron.  Syst.  AES-3(1)  107 \n6 Yang N D, Harkin G, Bunn R M, McCu lloch D J, Wilks RW and Knapp A G 1997  IEEE \nElectron . Device Lett. 1819 \n7 Smith P M, Carey P G and Sigmon T W 1997 Appl. Phys. Lett. 70 342 \n8 Someya T, Sekitani T, Iba S, Ka to Y, Kawaguchi H and Sakurai T 2004 Proc. Natl. Acad. \nSci. USA  101 9966 \n9 Forrest S R 2004 Nature  428 911 \n10 Rogers J A, Bao Z, Baldwin K, Dodabalapur A, Crone B, Raju V R,  Kuck V, Katz H, \nAmundson K, Ewing J and Drzaic P 2001 Proc. Natl. Acad. Sci. USA 98 4835 \n11 Kanti J, Klosner M, Zemel M and Raghunandan S 2005 Proceedings of the IEEE  93 1500 \n12 Dobrzański L A, Drak M and Zi ębowicz B 2006 J. Achievem. Mater. Manufact. Eng.  17 \n37 \n13 Osaka T, Takai M, Hayashi K, Ohashi K, Saito M A and Kazuhiko Yamada 1998 Nature  \n392, 796 \n14 McHenry M E, Willard M A and Lauglin D E 1999  Prog. Mater. Sci.  44 291 \n15 Fastenau H J and Loenen E J 1996  J. Magn. Magn. Mater. 1570158  1 \n16 OlabiA AG and Grunwald A 2008 Mater. Design 29 469 \n17 Thompson D A, R L T and Mayadas A 1975 IEEE Trans. Magn. 11 1039  \n18 Wolf S A, Awschalom D D, Buhrman R A, Daughton J M, von Molnar S, Roukes M L, \nChtchelkanova A Y and Treger D M 2001 Science  294 1488 \n19 Fert A 2008 Rev. Mod. Phys. 80 1517 \n20 Huang G S and Mei Y F 2012 Adv. Mater.  24 2517  \n21 Melzer M, Makarov D, Calvimontes A, Karn aushenko D, Baunack S, Kaltofen R, Mei Y . F \nand Schmidt O G 2011 Nano. Lett. 11, 2522 \n22 Choi M C, Kim Y K and Ha C S 2008 Prog. Polym. Sci. 33 581 \n23 Eder F, Klauk H, Halik M, Zschieschang U, Schmid G, and Dehm C 2004 Appl. Phys. Lett.                                                                                                                                                                               \n84 2673 \n24 Chang W Y, Fang T H and Lin Y C 2008 Appl. Phys. A  92 693 \n25 Bouziane K, Al Rawas A D, Maaz M and Mamor M 2006 J. Alloys Compounds 414 42 \n26 Breidbach M, Burgler D E and Grunberg P 2006 J. Magn. Magn. Mater. 307 L1 \n27 Tian Z C, Sakaue K and Terauchi H 1994 J. Appl. Phys. 76 3899  \n28 Dai G H, Zhan Q F, Liu Y W, Yang H L, Zhang X S, Chen B and Li R W 2012 Appl. Phys.  \nLett. 100 122407 \n29 Zhang X S, Zhan Q F, Dai G H, Liu Y W, Zuo Z H, Yang H L, Chen B and Li R W 2013 J. \nAppl. Phys. 113 17A901 \n30 Parkin S S P 1996 Appl. Phys. Lett.  69 3092 \n31 Chen Y F, Mei Y F, Kaltofen R, Monch J I, Schuhmann J, Freudenberger J, Klau β H J and \nSchmidt O G 2008 Adv. Mater.  20 3224 \n32 Oh S J, Jadhav M, Lim J, Reddy V , Kim C G 2013  Biosens. Bioelectron.  41 758 \n33 Melzer M, Lin G, Makarov D and Schmidt O G 2012 Adv. Mater.  24 6468 \n34 Zhao S F, Wan J G, Yao M L, Liu J M, Song F Q and Wang G H 2010 Appl. Phys. Lett. 97 \n212902  \n35 Liang J J, Xu Y F, Sui D, Zhang L, Huang Y , Ma Y F, Li F F and Chen Y S 2010 J. Phys. \nChem. C 114 17465 \n36 Bell D J, Lu T J, Fleck N A and Spearing S M 2005 J. Micromech. Microeng.  15 S153 \n37 Kim Y S, Jang S, Lee C S, Jin W Hg, Cho II J,  Ha M H, Nam H J, Bu J U, Chang S II and \nYoon E 2007 Sens. Actuators A  135 67 \n38 Onuta T D, Wang Y , Long C J and Takeuchi 2011 Appl. Phys. Lett. 99 203506 \n39 Martins P and Lanceros-Méndez S 2013 Adv. Funct. Mater. DOI:10.1002/adfm.201202780 \n40 Inoue S, Utsunomiya S, Saeki T and Shimoda T 2002 IEEE Trans. Electron. Devices  49 \n1353  \n41 Lee Y, Li H and Fonash S J 2003 IEEE Electron. Device Lett.  24 19 \n42 Reese C, Roberts M, Ling M M and Bao Z N 2004 Materials Today  ISSN:1369 7021 \n(Elsevier Ltd.)  \n43 Meitl M A, Zhu Z T, Kumar V, Lee K J, Feng X, Huang Y Y, Adesida I, Nuzzo R G and \nRogers J A 2006 Nat. Mater. 5 33 \n44 Lee Y, Bae S, Jang H, Jang S, Zhu S, Sim S H, Song Y I, Hong B H and Ahn J H 2010                                                                                                                                                                              \nNano Lett. 10 490 \n45 Donolato M, Tollan C, Porro J M, Berger A and Vavassori P 2013 Adv. Mater. 25 623 \n46 Linder V, Gates B D, Ryan D, Parviz B A and Whitesides G M 2005  small 1 730 \n47 Buhlery J, Steiner F P and Baltes H 1997 J. Micromech. Microeng. 7 R1 \n48 Heczko O,  Thomas M, Niemann R, Schultz L and Fähler S 2009 Appl. Phys. Lett. 94 \n152513 \n49 Tillier J, Bourgault D, Barbara B, Pairis S, Porcar L, Chometon P, Dufeu D, Caillault N \nand Carbone 2010 J Alloys Compd.  489 509 \n50 Bechtold C, Buschbeck J, Lotnyk A, Erka rtal B, Hamann S, Zamponi C, Schultz L, \nLudwig A, Kienle L, Fahler S and Quandt E 2010 Adv. Mater.  22 2668 \n51 Edler T and Mayr S G 2010 Adv. Mater.  22 4969 \n52 Backen A, Yeduru S R, Kohl M, Baunack S, Diestel A, Holzapfel B, Schultz L, Fahler S \n2010 Acta Mater. 58 3415 \n53 Zuo Z H, Chen B, Zhan Q F, Liu Y W, Yang H L, Li Z X, Xu G J and Li R W 2012 J. Phys. \nD: Appl. Phys.  45 185302  \n54 Shin J, Kim S H, Suwa Y , Hashi S and Ishiyama K 2012  J. Appl. Phys.  111, 07E511 \n55 Cullity B D 1972 Introduction to Magnetic Materi als (Addison-Wesley, Reading)  \n56 Zhang X S, Zhan Q F, Dai G H, Liu Y W, Zuo Z H, Yang H L, Chen B and Li R W 2012 \nAppl. Phys. Lett.  100 022412  \n57 Chen Y F,  McCord J, Freudenberger J, Kaltofen R and Schmidt O G 2009 J Appl. Phys. \n105, 07C302 \n58 Parkin S S P, Roche K P and Suzuki T 1992 Jpn. J. Appl. Phys.  31 L1246 \n59 Barraud C, Deranlot C, Seneor P, Mattana R,  Dlubak B, Fusil S, Bouzehouane K, Deneuve \nD, Petroff F and Fert A 2010 Appl. Phys. Lett.  96 072502 \n60 Baibich M N, Broto J M, Fert A, Nguyen F,  Dau V, Petroff F, Eitenne P, Creuzet G, \nFriederich A and Chazelas J 1988 Phys. Rev. Lett.  61 2472 \n61 Florez S H and Gomez R D 2003 IEEE Trans. Magn. 39 3411 \n62 Dokupil S, Bootsmann M T, Stein S, Lohndorf M and Quandt E 2005 J. Magn. Magn. \nMater.  291 795 \n63 Özkaya B, Saranu S R, Mohanan S and Herr U 2008  phys. stat. sol. (a) 205 1876 \n64 Salata O V 2004 J. Nanobiotechnol.  2 3                                                                                                                                                                              \n65 Yu J, Huang D Y, Muhammad Z Y,Hou Y and Gao S 2013 Chin. Phys. B  22 027506 \n66 Nam J M, Thaxton C C, Mirkin C A 2003 Science  301 1884 \n67 Parkin S S P 1995 Annu. Rev. Mater. Sci  25 257 \n68 Pannetier M, Fermon C, Goff G L, Simola J and Kerr E 2004 Science  304 1648  \n69 Monch I, Makarov D, Koseva R, Baraban L,  Karnaushenko D, Kaiser C, Arndt K F and \nSchmidt O G 2011  ACS Nano 5 7436 \n70 Melzer M, Karnaushenko D, Makarov D, Bara ban L, Calvimontes A, Monch I, Kaltofen R, \nMei Y F and Schmidt O G 2012 RSC Advances  2 2284 \n71 Ma Z Q 2011 Science  333 830 \n72 Karnaushenko D, Makarov D, Yan C L, Streubel R and Schmidt O G 2012 Adv. Mater. 24 \n4518 \n73 Chalasani S and Conrad J M 2008 Southeastcon IEEE 442-447 \n74 Stanton S C, McGehee, C C and Mann Brian P 2009 Appl. Phys. Lett.  95 174103 \n75 Qi Y and McAlpine M C 2010 Energy Environ. Sci.  3 1275 \n76 Zhang C L, Yang J S and Chen W Q 2009 Appl. Phys. Lett. 95 1  \n77 Li P, Wen Y, Liu P, Li X , Jia C 2010 Sens. Actuators A  157 100 \n78 Winey K I and Vaia R A 2007 MRS Bull. 32 314 \n79 Cugat O, Delamare J and Reyne G 2003 IEEE Trans. Magn.  39 3607 \n80 Lee H S, Cho C D,  Zehnder A T and Choi K W 2011 J Appl. Phys. 109, 07E501 \n81 Kim J Y, Chung S E, Choi S E, Lee H W, Kim J H and Kwon S H 2011 Nat. Mater. 10 \n747 \n82 Ha N D, Phan M H and Kim C O 2007 Nanotechnology 18 155705  \n83 Qiao L, Wen F, Wei J, Wang J and Li F 2008 J. Appl. Phys. 103 063903  \n84 Phuoc N N, Xu F and Ong C K 2009 Appl. Phys. Lett. 94 092505  \n85 Acher O and Dubourg S 2008 Phys. Rev. B 77 104440 \n86 Iakubov I T, Lagarkov A N, Maklakov S A,  Osipov A V, Rozanov K N, Ryzhikov I A  \nand Starostenko S N 2006 J. Magn. Magn. Mater.  300 74 \n87 Phuoc N N, Hung L T and Ong C K 2010  J. Phys. D: Appl. Phys. 43 255001 \n88 Lu H P,Yang J and Deng L J 2010 Piers Online  6 105 \n89 Liu Z W, Liu Y, Yan L,  Tan C Y and Ong C K 2006 J. Appl. Phys. 99 043903 \n90 Liu Z W, Zeng D C, Rama nujan R V and Ong C K 2010 J. Appl. Phys. 107 09A505                                                                                                                                                                              \n91 Ma Y G and Ong C K  2007  J. Phys. D: Appl. Phys.  40 3286 \n92 Stojak K, Pal S, Srikanth H, Morales C, Dewdney J, Weller T and Wang J 2011 \nNanotechnology  22 135602 \n93 Zuo H P, Ge S H, Wang Z K, Xiao Y H and Yao D S 2010 Scripta Mater.  62 766 \n94 Rasoanoavy F,  Laur V, Blasi S D, Lezaca J, Quéffélec P, Garello K and Viala B 2010 J. \nAppl. Phys. 107 09E313 \n95 Phuoc N N, Xu F, Ma Y G, Ong C K 2009 J. Magn. Magn. Mater.  321 2685 "    },    {        "title": "1311.6022v1.Universal_Scaling_Law_to_Predict_the_Efficiency_of_Magnetic_Nanoparticles_as_MRI_T2_Contrast_Agents.pdf",        "content": " Submitted to \n \n1 DOI: 10.1002/adhm.201200078 Article type: Full Paper   Universal Scaling Law to Predict the Efficiency of Magnetic Nanoparticles as MRI T2-Contrast Agents  By Quoc L. Vuong, Jean-François Berret, Jérôme Fresnais, Yves Gossuin* and Olivier Sandre*   Dr. Q. L. Vuong, Author-One,  Université de Mons, Biological Physics Department, 20 Place du Parc, 7000 Mons, Belgium  Dr. J.-F. Berret, Author-Two, Université Denis Diderot Paris-VII, CNRS UMR7057, Matière et Systèmes Complexes 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France  Dr. J. Fresnais, Author-Three, UPMC Univ Paris 06, CNRS UMR7195, Physicochimie, Colloïdes et Sciences Analytiques 4 place Jussieu, 75005 Paris, France [*] Dr. Y. Gossuin, Corresponding-Author,  Université de Mons, Biological Physics Department, 20 Place du Parc, 7000 Mons, Belgium E-mail: yves.gossuin@umons.ac.be [*] Dr. O. Sandre, Corresponding-Author,  Université de Bordeaux, CNRS UMR5629, Laboratoire de Chimie des Polymères Organiques ENSCBP, 16 Avenue Pey Berland, 33607 Pessac, France E-mail: olivier.sandre@ipb.fr   Keywords: Magnetic Resonance Imaging Contrast Agents; Transverse Relaxivity; Motional Averaging Regime; Static Dephasing Regime; Superparamagnetic Iron Oxide Nanoparticles   Abstract: Magnetic particles are very efficient Magnetic Resonance Imaging (MRI) contrast agents. In the recent years, chemists have unleashed their imagination to design multi-functional nanoprobes for biomedical applications including MRI contrast enhancement. This study is focused on the direct relationship between the size and magnetization of the particles and their nuclear magnetic resonance relaxation properties, which condition their efficiency. Experimental relaxation results with maghemite particles exhibiting a wide range of sizes and magnetizations are compared to previously published data and to well-established relaxation theories with a good agreement. This allows deriving the experimental master curve of the transverse relaxivity versus particle size and to predict the MRI contrast efficiency of any type of magnetic nanoparticles. This prediction only requires the knowledge of the size of the particles impermeable to water protons and the saturation magnetization of the corresponding volume. To predict the T2 relaxation efficiency of magnetic single crystals, the crystal size and magnetization – obtained through a single Langevin fit of a magnetization curve – is the only information needed. For contrast agents made of several magnetic cores assembled into various geometries (dilute fractal aggregates, dense spherical clusters, core-shell micelles, hollow vesicles…), one needs to know a third parameter, namely the intra-aggregate volume fraction occupied by the magnetic materials relatively to the whole (hydrodynamic) sphere. Finally a calculation of the maximum achievable relaxation effect – and the size needed to reach this maximum – is performed for different cases: maghemite single crystals and dense  Submitted to \n \n2 clusters, core-shell particles (oxide layer around a metallic core) and zinc-manganese ferrite crystals.  1. Introduction Magnetic Resonance Imaging contrast agents (MRI CAs) allow a high sensitivity for the early detection of different pathologies and the tracking of magnetically tagged cells in vivo through molecular and cellular imaging.[1] The efficiency for MRI CAs consists in lowering the longitudinal (T1) or transverse (T2) relaxation times of the nuclear spins of water protons in tissues at the lowest CA concentration, expressed in equivalent mM of magnetic ions. This acceleration of proton magnetization relaxations near a magnetic particle is usually ascribed to fluctuations of magnetic dipolar interactions between the nuclear and the electronic spins. Therefore the “relaxivity” defined as the slope of the relaxation rate in s-1 (either T1 or T2) versus the equivalent ion concentration in mM is a direct measurement of this efficiency. In the various magnetic nanoparticles or magnetic hybrids proposed so far, authors have interpreted their relaxivity results compared to literature and specifications of commercial products by referring to different notions such as the nature and the size of the Ultra-small Superparamagnetic Iron Oxide (USPIO) grains, the clustering effect (several USPIOs per contrast agent), the influences of a non magnetic shell, of a hydrophobic membrane, of water permeability… In this work, we propose a general treatment of new results and of literature data with a unified method using only two (for individual USPIOs) or three (for clusters or hybrids) parameters: diameter and magnetization of the whole particle, and volume fraction of magnetic materials inside.  2. Magnetic nanoparticles and clusters of various sizes and geometries  2.1. Samples prepared for this study Magnetic particles and clusters were prepared from USPIO nanoparticles made of maghemite (γ–Fe2O3) synthesized in water according to Massart’s procedure (see Experimental).[2] These nanoparticles were readily dispersed in water and formed a true “ionic ferrofluid”. The iron oxide surface bears positive charges due to adsorption of protons in acidic media, in that case a dilute HNO3 solution at pH between 1.2 and 1.7. Such ionic ferrofluids remain in a monophasic state under the application of a magnetic field of arbitrary value. On the microscopic scale, those crystals exhibit a Log-Normal distribution of diameters with parameters d0 =7 nm and σ = 0.38, as measured by vibrating sample magnetometry (VSM).[3] Maghemite nanoparticles with such a broad dispersity were treated with a size-sorting procedure based on fractionated phase-separation.[4] After the increase of ionic strength to induce demixtion and magnetic sedimentation on a strong ferrite magnet, a concentrate could be separated from the supernatant in few minutes. By repeating the phase-separation protocol on both the concentrate and the supernatant, we obtained four new fractions at second level of refined distribution of sizes, and so on after a third and fourth level. To take into account the residual polydispersity, we estimated a weight-averaged diameter characteristic of each sample by calculating the 4th and 3rd order moments of the Log-normal distributions deduced by VSM: dw = <d4>/<d3> = d0 exp(3.5σ2). This choice of the characteristic size enabled comparing samples of varying size distributions (even for a same median size d0). It also fairly compares to the mean diameter observed on the electron microscopy pictures and to twice the gyration radius that can be obtained by a common experiment (Guinier’s plot) from several scattering techniques (light, X-rays or neutrons). After the size-sorting process, the fractions of interest were coated either by coordination bonding of surface iron ions with tri-sodium citrate (Na3Cit) ligand[5] or by electrostatic complexation with sodium polyacrylate (PAA2k or PAA5k) using a precipitation-redispersion protocol.[6] Superparamagnetic Iron  Submitted to \n \n3 Oxide (SPIO) particles consisting in spherical clusters of a limited number of individual crystals were also prepared by a coacervation protocol with oppositely charged hydrophilic copolymers controlled by salinity.[7] Experimental details for the size sorting and coating procedures of the USPIOs and their controlled clustering into SPIO coacervates are described in section 4.  2.2. Samples from literature Among the huge literature published in the recent years on novel particles as potential MRI contrast agents, we focused our attention on articles reporting precisely the physical (structural, geometrical, magnetic…) properties of the systems. Thus we gathered a broad range of data for individually dispersed maghemite nanoparticles with only a thin permeable coating,[8–10] maghemite core-silica shell particles,[11,12] maghemite or magnetite nanoparticles clustered by hydrophilic[13–15] or amphiphilic[16–18] polymers, encapsulated in the aqueous lumen of liposomes[19] or embedded in the membrane of lipid[20] or polymer[21] vesicles. Other magnetic materials such as pristine iron–iron/manganese-ferrite core-shell nanoparticles[22] and manganese-ferrite nanoparticles clusters[23] were also used to complete our relaxation analysis. Except for Ultra Ultra-small Superparamagnetic Iron Oxide (UUSPIO) of diameter 4 nm only which can be used as positive contrast agents with T1-weighted sequences,[24] magnetic particles are only effective as T2 negative contrast agents since at the magnetic fields of most clinical and research MR imagers (1.5 T or above), their longitudinal relaxation rate R1 falls down due to the absence of the so-called “secular term” in the theoretical expression of R1.[25] Since R2/R1 becomes very high, any hyper-signal is lost because of spin-spin relaxation in the transverse plane where the detection antennas are sensitive. This was checked for our samples – by recording the evolution of R1 on a large range of magnetic fields – confirming the small effect of the particles on water longitudinal relaxation (Figure S5 in Supporting Information). On the opposite, water transverse relaxation rate R2 was strongly enhanced by the presence of the samples with no significant variation versus magnetic field values between 0.47 and 1.41 T (Figure S6).  2.3. Classical relaxation models revisited For magnetic particles of diameter d and saturation magnetization Mv (corresponding to the total magnetic moment divided by the particle volume and expressed in the SI unit, A⋅m-1), the value of R2 is given either by the motional averaging regime (MAR) – also called outer sphere theory (as opposite to inner sphere) – or by the static dephasing regime (SDR). But to compare the relaxation data with these models, one needs first to properly define the structure and geometry of the T2 contrast agent, as depicted by the different cases on Scheme 1. We recall here only the final equations of MAR and SDR models, but readers can refer to recent reviews to learn about the quantum mechanics treatment of magnetic dipolar interactions between nuclear and electronic spins which are founding them.[25]  2.3.1. Particles in the motional average regime (MAR): ΔωτD<1 In this case, the protons of freely diffusing water molecules surrounding the particle explore all the possible values of magnetic dipolar field created by the electronic magnetic moment and the transverse relaxation rate at high field is given by: ()2D2245161ωτΔ==fTR         (1) where f is the volume fraction occupied by the particles in the suspension, Δω = γµ0Mv/3 is the angular frequency shift experienced by a proton at the equator of the particle, γ = 2.67513×108 rad⋅s-1⋅T-1 the gyromagnetic factor of the proton, µ0 = 4π10-7 T⋅m⋅A-1 the  Submitted to \n \n4 magnetic permeability of vacuum and τD = d 2/4D the translational diffusion time of the protons in the magnetic field inhomogeneities created by the particles (D being the water translational diffusion constant and d the particle diameter).[25] To obtain the transverse relaxivity r2 – defined as the relaxation rate R2 normalized by the equivalent iron concentration [Fe] in mM – the volume fraction f should be expressed in terms of equivalent iron concentration. This concept of relaxivity is widely used in the literature to normalize the relaxation rates and compare the efficiencies of different contrast agents. The iron concentration is indeed more direct to measure (by UV-Vis absorption, atomic emission or inductively coupled plasma mass spectroscopy) than the volume fraction occupied by the particles in water. However, normalization by the volume fraction is more rigorous from a theoretical point of view as seen on Equation (1). The numerical factor between f and [Fe] depends on the type of magnetic material, through its molar volume vmat given by the ratio of the molar mass divided by the number of magnetic ions in the formula and by the mass density, both expressed in SI units to obtain the iron concentration in mol⋅m-3 equivalent to mmol⋅L-1.  For maghemite (Mγ–Fe2O3=0.1597 kg⋅mol-1 and ργ–Fe2O3=5100 kg⋅m-3), this writes: 1-35OFe-γOFe-γmatmolm1057.12Fe][3232⋅×===−ρMvf      (2a) and in the general case of an iron spinel MO⋅Fe2O3: {}1-35OFeMOOFeMOmatmolm105.13[M]Fe][3232⋅×≈==+−⋅⋅ρMvf     (2b) The nature of the divalent cation in the iron spinel structure (Fe2+, Co2+, Ni2+, Mn2+, Zn2+, |) varies this result only by ±5%. Then equation (1) writes: DdMvRr4054]Fe[22vmat20222µγ==        (3) which is valid only if the Redfield condition is fulfilled: 1D<Δωτ           (4) This is the case for small single nanoparticles of pure magnetic materials or with a thin fully hydrated shell,[8-10,13] and for hybrid entities with an overall magnetization (Mv) remaining small compared to the specific magnetization of the inorganic part (mS), for example dilute micelles[17] or vesicles[19,20] containing few iron oxide nanoparticles, or magnetic cores either single[11] or clustered[12] wrapped by a rather thick silica coating. In the latter case (porous SiO2), the permeability of the non magnetic mantle to water molecules can lead to an additional fast mode, but its contribution to the overall relaxation process remains small as long as the water protons diffusing in the “outer shell” represent a larger volume fraction than the internal protons linked to the porous network. For magnetic particles respecting Equation (4), the transverse relaxivity can be divided by Mv2 to point out the dependence on diameter. Replacing the different constants by their numerical values and using D = 3×10-9 m2⋅s-1 as the water diffusion constant at 37 °C leads to: 2122theo2v2109.5ddaMr−×==        (5) To test this relationship, the ratio r2/Mv2 was calculated for 9 sizes of single maghemite USPIOs. The values of saturation magnetization Mv (A⋅m-1) of all these samples were obtained from the fits of the magnetometry curves with a precise knowledge of the solid volume fraction f in the suspension from an independent titration of iron (also necessary to deduce the relaxivities r2 in s-1⋅mM-1). Data from literature corresponding to various types of ferrite nanoparticles and clusters in the MAR are also presented on Figure 1. For relaxivities  Submitted to \n \n5 measured at a temperature different from 37 °C, a correction factor corresponding to the tabulated variation of viscosity was applied, reflecting the change of diffusion constant of water molecules. The values of diameter of the individually dispersed USPIO nanoparticles plotted on the curve are the weight average diameter (dw) obtained by magnetometry (14 samples) or by TEM (4 samples) or from the simulated curve fitting a T1 NMRD profile (3 samples). Concerning the clusters, micelles, vesicles and single magnetic cores surrounded by an impermeable non magnetic coating (e.g. silica or polymer), the plotted diameter was either measured by electron microscopy (dTEM) or by dynamic light scattering (dH) depending on availability in the corresponding references. For clusters and hybrids, we introduce the intra-aggregate volume fraction of magnetic materials φintra to derive a corrected relaxivity r2’ = r2×φintra. This normalization for SPIO clusters enables to properly compare their relaxation data r2×φintra/Mv2 as if they were filling the same volume fraction of suspension as single USPIO nanoparticles at 1 mM iron concentration. Even though the relaxation efficiency is usually expressed in terms of relaxivity per equivalent mM of iron atoms, the normalization by Mv2 is theoretically justified for the same total volume fraction of particles f in the suspension, including both parts (iron oxide and impermeable coating). For example with clusters containing φintra = 10% in volume of magnetic nanoparticles, the volume fraction f of clusters in a 1 mM [Fe] suspension will be 10 times larger than for a 1 mM suspension of the dispersed USPIOs. The measured relaxivities should thus be divided by ten to compare the relaxation efficiencies at the same volume fraction of magnetic particles. Figure 1 shows r2×φintra/Mv2 versus d for samples following the MAR model (see Table 1), from this study and from literature. This figure presents the normalized relaxivity, obtained as described above, while Figure S7 (supporting information) directly presents the relaxivity in order to ease the comparison with measured values. Both figures show that samples respecting Equation (4) are indeed quantitatively following a quadratic dependence on diameter over almost two decades (4–300 nm): 2122exp2vintra2106.11ddaMr−×==×φ        (6) where aexp was obtained by a one-parameter quadratic fit of correlation factor R=0.93. The agreement between aexp and atheo values is fairly good, since the size distribution of the nanoparticles – although contained in the weight (dw) or intensity (dH) averaged diameter – is expected to influence relaxation and thus the actual value of prefactor a.[26] Moreover, the diffusion coefficient of bulk water was used to calculate prefactor atheo while water diffusion might be hampered in the vicinity of the particles, as shown in the case of especially hydrophilic polymer shells.[27] By using the scaling law expressed in Equation (6), it is now possible to predict the transverse relaxivity at magnetic fields above 1 T and at 37 °C of any sample of particles or clusters inducing relaxation in the MAR whose diameter (dw, dTEM or dH), magnetic content φintra and saturation magnetization Mv are known, prior to any NMR or MRI measurement. Figure 1 also presents the data for two samples whose ΔωτD values are slightly larger than 1 and thus appear below the master curve of MAR, as expected.[10,22] Among these cases, iron-iron oxide core-shell particles[22] locate slightly below the corresponding particles in the MAR with a similar size d ≈ 15 nm (see Table 1). This is logical since for this sample ΔωτD = 1.5, a value corresponding to the transition between MAR and SDR relaxation regimes. Even though r2/Mv2 is smaller than predicted, the experimental value r2=324 s-1 mM-1 is twice as large as for a pure iron oxide USPIO of same outer diameter. However, the comparison is somehow complicated by the different stoichiometry and density of both compounds (pristine iron in the core and iron oxide in the  Submitted to \n \n6 shell), implying different volume fractions f for iron oxide and core-shell particles with identical iron concentration: respectively f=1.57×10-5 for iron oxide and f=10-5 for Fe@Fe2O3 at 1 mM equivalent [Fe], so that the increase of specific magnetization (Mv=6.6×105 A⋅m-1 or 115 emu⋅g-1) is somehow counterbalanced by the decrease of molar volume vmat.   2.3.2. Particles out of the motional averaging regime: ΔωτD > 1 For particles with size d and magnetization Mv such that ΔωτD > 1, the Static Dephasing Regime (SDR) – implying that water protons explore only a small space compared to the hydrodynamic volume also called “outer shell” around the particle – should be used instead of MAR, yielding a relaxation rate of the form: 2*2*23321RfTR≈Δ==ωπ         (7) With the same transformation as above, one obtains: 2vmat0*2*2392]Fe[rMvRr≈==µγπ        (8) The SDR model does not take into account the effect of the refocusing pulses used in all T2 measurement sequences. Therefore Equation (7) and Equation (8) are only exact for R2* and r2* respectively, which determine the signal contrast in MR imaging conditions without spin echoes (e.g. with gradient echoes sequences). Nevertheless, the SDR formulas (7) and (8) give good approximations of R2 and r2 as long as 5 < ΔωτD < 20 and a provide good estimate of the maximum values reached in the middle of the SDR range, when ΔωτD ≈ 10.[26] Above an upper limit ΔωτD ≈ 20, R2 is no more approximated by the SDR, since the refocusing pulses used in the T2 measurement sequence become effective. In this third relaxation regime described by the Partial Refocusing Model (PRM), R2 is lower than R2* and exhibits a strong dependence on the echo time chosen for the measuring sequence.[28] For particles with characteristics corresponding to 1 < ΔωτD < 5, neither Equation (3) nor Equation (8) is valid and a transition between MAR and SDR relaxation is observed. As ΔωτD > 20, one observes a transition between SDR and PRM. Figure 2 represents the normalized relaxivities r2’ = r2×φintra for all the systems with ΔωτD > 1 (see Table 1). Only particles of approximately same Mv can be compared together. The figure also gives – for different Mv ranges – the predictions of the empirical function recently validated by computer simulations for particles outside the MAR.[26] The trend of these empirical curves is compatible with the experimental data. It should be stressed that the comparison between all the samples – and also with theory – is difficult since these systems are in a “theoretical no-man’s-land” and also because, for many samples, R2 surely depends on the echo-time of the measurement sequence. Nevertheless, most experimental data are located in the domains of Figure 2 corresponding to their size and magnetization, except those derived from the article by C. Paquet et al on magnetic hydrogels,[15] which show higher r2×φintra values than expected from the simulations (for particle sizes ~150 nm and 175 nm). The simulations shown here do not take into account the mechanism reported recently for highly hydrated particles.[27] In that case, the slowing down of proton diffusion near the magnetic particle surface – where the magnetic gradients are the strongest – induces fast proton dephasing, which significantly raises the relaxivity.[27] The present study holds for the two limit cases of either impermeable coatings or completely permeable shells. Therefore “smart” coatings modifying proton diffusion such as the magnetic hydrogels somehow deviate from the general behavior.  2.3.3. Maximal achievable transverse relaxivities As learned from computer simulations[26] and supported by the data presented in Figure 2, the relaxation enhancement effect of magnetic particles is expected to reach a maximum value for  Submitted to \n \n7 a particular size. This maximum occurs when the system is completely in the SDR. As previously stated, this is the case when ΔωτD≈10. It is thus possible to estimate, using Equation (8), the maximum efficiency of different types of magnetic particles as well as the optimal size at which this maximum should be reached. The results, obtained by using the expressions of Δω and τD, are presented in Table 2. The first important information obtained from Table 2 is that the maximum relaxivity is the same for maghemite nanoparticles and clusters of maghemite particles, only the optimal size of particles needed to reach the maximum is different (obtained through the condition ΔωτD≈10). In the case of individual magnetic cores, such a diameter of 55 nm falls above the classical limit size of 40 nm for USPIOs defined relatively to the sizes of biological barriers, but remains below the maximum size of magnetic (Weiss) monodomains.[25] Moreover, it will be a challenge to reach it experimentally in a proper dispersed (colloidal) state because of strong inter-particular attractions. In the literature, different clusters of γ–Fe2O3 or Fe3O4 cores[15-18] plotted on Figure 2 already exceeded a T2 relaxivity of 500 s-1⋅mM-1 but remained below the theoretical maximum of 750 s-1⋅mM-1 not yet reached experimentally, according to the authors’ knowledge. Other studies presenting dense magnetite clusters around 100 nm only show a moderate increase of r2 compared to the individual USPIOs,[29] presumably due to too high size dispersity. Secondly and as expected,[22,30] core-shell or special compositions of ferrite particles with a higher saturation magnetization than pure iron oxide led to higher relaxivities. It was recently proven that an appropriate composition of zinc and manganese ferrite enables reaching r2=860 s-1⋅mM-1 for a diameter d=15 nm.[30] According to Table 2, r2 should reach even larger values (up to 1200–1860 s-1⋅mM-1) by increasing the size both for Fe@Fe2O3 core-shells and (Zn0.4Mn0.6)Fe2O4 mixed ferrite nanoparticles. Increasing the specific magnetization of USPIOs by an appropriate choice of their metal composition is indeed an interesting option to optimize MRI contrast agents, as long as toxicity is not introduced by the non ferrous metals.  3. Conclusions Despite the broad variety of superparamagnetic MRI contrast agents differing by their size, geometry (filled micelles or hollow vesicles, dense or loose clusters…), type of coating (organic or inorganic, impermeable or porous, hydrophilic or hydrophobic…), no specific models need to be introduced. We have indeed evidenced in this article that the classical MAR and SDR models can correctly represent the experimental data once structural and magnetic parameters are known (external diameter, volume fraction and magnetization of the magnetic materials) and the relaxivity is appropriately normalized. More precisely, the MAR is verified by individual USPIOs or clusters which are either compact or diluted in a non magnetic material. In the latter case, the porosity (e.g. silica) or permeability to water (e.g. hydrogel) is not an issue: such internal protons relax much faster than external ones, but their contribution to the measured relaxation rate remains limited due to their low volume fraction compared to the water protons diffusing in the “outer shell” around the particle. The relaxivity at high magnetic field / Larmor frequency of particles in the MAR follows a universal scaling law varying with the square of diameter, square of magnetization and inverse of the internal volume fraction of magnetic material. The experimental prefactor of this power law is in good accordance with the physical constants of the models. For larger or more concentrated clusters, the SDR model correctly describes the plateau value that is observed experimentally. Moreover, the size and magnetization of the particle can be chosen to satisfy the condition ΔωτD≈10 in order to design contrast agents of maximum T2 relaxivity.[26] But it should be stressed that this optimum r2 will only be approached by particles presenting a rather narrow size distribution centered on the optimal size, since smaller (in motional averaging regime) and larger particles (following the Partial Refocusing Model) will present lower efficiencies  Submitted to \n \n8 and decrease the mean transverse relaxivity of the sample. This explains why some already reported SPIO clusters did not exhibit tremendous r2 despite mean values of magnetization, volume fraction and hydrodynamic diameter close to the optimal ones.[29] To conclude, by validating simple principles of the theory of proton relaxation on a wide range of experimental systems, this article proposes a unified method to predict the transverse relaxivity r2 of MRI contrast agents at clinical field based on materials (Mv) and geometrical (d, φintra) parameters. These results offer practical tools to the chemists who aim at optimizing the relaxation properties for MRI in the design of more elaborated particles than the commercially available T2 contrast agents, such as multi-modal probes or theranostic nanovectors.  4. Experimental Synthesis of Ultra-small Superparamagnetic Iron Oxide. USPIO nanoparticles made of maghemite (γ-Fe2O3) were synthesized in water according to Massart’s procedure.2 At first, magnetite Fe3O4 nanocrystals (also called ferrous ferrite FeO.Fe2O3) were prepared from an alkaline coprecipitation of a quasi-stoichiometric mixture of iron +II (0.9 mol) and iron +III (1.5 mol) chloride salts in HCl solution (3L, pH≈0.4). One liter of a concentrated ammonia solution (7 mol) was quickly added onto the acidic iron salts mixture, which produced a black solid suspension almost instantaneously. After 30 minutes of stirring at 800 rpm, the Fe3O4 nanoparticles were attracted by a strong ferrite magnet (152×101×25.4 mm3, Calamit Magneti, Milano-Barcelona-Paris). Then the supernatant (≈2.25 L) containing non magnetic ferrihydrites (reddish flakes) was discarded and the magnetic precipitate (black) was washed with 1 L water. After sedimentation on the ferrite magnet, the flocculate was acidified with 0.26 L of nitric acid (69%) and stirred 30 min after being completed up to 2 L with water. In order to be completely oxidized from magnetite into maghemite, the solid phase was separated from the supernatant (≈1.5 L, red) and immersed in a boiling solution of ferric nitrate (0.8 mol in 0.8 L). After 30 min under stirring at 90-100 °C, the suspension had turned into the red colour characteristic of maghemite γ-Fe2O3. After washing steps in acetone and diethyl-ether to remove the excess ions, the nanoparticles readily dispersed in water and formed a true “ionic ferrofluid” made of maghemite nanoparticles. The iron oxide surface bore positive charges due to adsorption of protons in acidic media, in that case a dilute HNO3 solution at pH between 1.2 and 1.7. Therefore such ferrofluid remains in a monophasic state under the application of a magnetic field of arbitrary value.[2–5] Size sorting. On the microscopic scale, those crystals exhibit a Log-Normal distribution of diameters of parameters d0 =7 nm and σ =0.38, as measured by magnetometry.[3] Maghemite nanoparticles with such a high size-dispersity can be treated with a size-sorting procedure based on fractionated phase-separation.[4] More precisely, the addition of an excess of HNO3 not only lowers the pH but also raises the ionic strength, thereby screening the electrostatic repulsions between the nanoparticles. Above a threshold electrolyte concentration, a liquid-liquid phase separation occurs between a concentrated “liquid-like” phase and a dilute “gas-like” phase. After magnetic sedimentation on a strong ferrite magnet (152×101×25.4 mm3, Calamit Magneti, Milano-Barcelona-Paris) to accelerate demixtion, a concentrate (denoted C1) could be readily separated from the supernatant (denoted S1). Once washed with acetone to remove the excess of ions, the two separated fractions were dispersed in water. The fit of their magnetization curve by VSM leads to their size distributions modelled by a Log-normal law with d0 as median diameter and σ as standard width of the logarithms of diameters: d0 = 8.7 nm (σ =0.35) for C1 and d0 = 7.1 nm (σ =0.29) for S1. The enrichment of the “liquid-like” phase by the larger size tail of the distribution compared to the dilute “gas-like” phase originates from the sensitivity of the inter-nanoparticle potential with the diameters (the larger nanoparticles exhibiting much higher Van der Waals interactions between them). By  Submitted to \n \n9 repeating the phase-separation protocol on both samples C1 and S1, we obtained four new fractions at second level of refined distribution of sizes, and so on after a third and fourth level as indicated on Sketch S1, among which several fractions were used in the following of the article either as they were in nitric acid conditions (C1S2, C1C2C3, C1C2S3, S1S2C3) or after coating with citrate or polyacrylate ligands (S1S2S3, S1S2C3, C1C2C3C4). Unlike the preceding steps for which fractions were divided into culots (C) and supernatants (S) by phase separation under increased HNO3 concentration, for the final step C1C2C3C4S5 another method was used. Namely S5 stands in that case for “sedimentation”: a strong magnetic gradient was used indeed to induce a vertical concentration gradient (but not a true separation into 2 phases as with the electrolyte). A colloidal suspension enriched in the largest magnetic nanoparticles was pipetted at the bottom of the cuvette.[31] After the size-sorting process, the fractions of interest (S1S2S3, S1S2C3, C1C2C3C4 and C1C2C3S4) were coated either with tri-sodium citrate[5] Na3Cit or sodium polyacrylate[6,32] (PAA2k or PAA5k) using a protocol based on electrostatic complexation and adsorption. Coating with citric acid. Briefly, the grafting was made by reacting 37.4 g of Na3Cit per mole of iron oxide (20% molar) around pH 8 for 30 min at 70 °C under vigorous stirring and subsequent removal of the supernatant by magnetic sedimentation. Then three washing cycles were performed with acetone to remove the excess ions and finally with diethyl ether to remove acetone. The obtained precipitate of citrate-coated USPIOs can be readily suspended in pure water by simple vortexing. To insure a perfect colloidal stability with low hydrodynamic diameters as probed by dynamic light scattering, the salinity caused by unbound citrate ions was decreased by dialysis for 24 hours against 8 mM Na3Cit. Coating with Poly(acrylic acid). Poly(sodium acrylate), the salt form of polyacrylic acid, with a molar mass Mn = 2000 g mol-1 (PAA2k) or Mn = 5000 g mol-1 (PAA5k) and a polydispersity index Mw/Mn=1.7 was purchased from Sigma Aldrich (references 81130 and 81132) and used without further purification. In order to adsorb polyelectrolytes onto the surface of the nanoparticles, we followed the “precipitation-redispersion” protocol.[6,32] The precipitation of the cationic iron oxide dispersion by PAA2k/5k was performed in acidic conditions (pH 2) at weight concentrations of 1 g⋅L-1 for both nanoparticles and polymer. The precipitate was separated from the solution by centrifugation, and its pH was increased by addition of ammonium hydroxide. The precipitate redispersed spontaneously at pH≈7–8, yielding a clear solution that now contained the polymer-coated particles. The hydrodynamic sizes of γ-Fe2O3 USPIOs coated by PAA2k were found to be 5 nm larger than the hydrodynamic diameter of the uncoated particles, indicating a corona thickness h = 2.5 nm.[32] In terms of coverage, the number of adsorbed chains per particle was estimated to be 1 nm-2 (assuming a 1:1 PAA2k-iron oxide weight ratio for an USPIO of molar mass ≈106 g⋅mol-1 and surface ≈500 nm2). As a final step, the dispersions were dialyzed against DI-water which pH was first adjusted to 8 (Spectra/Por 2 dialysis membrane with MWCO 12 kD). At this pH, 90 % of the carboxylate groups of the PAA coating were ionized. Electrophoretic mobilities were found at values µE = -3.76×10-4 and -3.52×10-4 cm2 V-1 for Cit–γ-Fe2O3 and PAA2k–γ-Fe2O3 respectively. As a final step of the procedures described above, the dispersions were dialyzed against DI-water which pH was first adjusted to 8 by addition of sodium hydroxide (Spectra Por 2 dialysis membrane with MWCO 12 kD). For the citrate-coated particles, DI-water was supplemented with 8 mM of free citrates. At this pH, 90 % of the carboxylate groups of the citrate and PAA2K coating were ionized. The suspension pH was adjusted with reagent-grade nitric acid (HNO3) and with sodium or ammonium hydroxides. For the assessment of the stability with respect to ionic strength (IS), sodium and ammonium chloride (NaCl and NH4Cl, Fluka) were used to control IS in the range 0 – 1 M.[32] Clustering. Different clusters were prepared with the S1S2C3 iron oxide cores. The principle consists in mixing negatively charged USPIOs coated with PAA and a double-hydrophilic  Submitted to \n \n10 diblock copolymer (DHBC) such as poly(trimethylammonium ethylacrylate methylsulfate)-b-polyacrylamide (PAM30k-b-PTEA11k) made of a neutral block (PAM) and a cationic block (PTEA) at a high salt concentration where the electrostatic interactions are totally screened. When the salinity is decreased at a controlled rate either by dilution or dialysis, below a threshold concentration ([NH4Cl]=0.4 mol/L) a microphase separation occurs by association between the oppositely charged species. The coacervates are perfectly spherical, with a magnetic core containing a limited number of USPIOs wrapped by a neutral polymer shell that prevents further aggregation. Different clusters of varying size and magnetization can be prepared by varying the salinity decrease rate.[32] For example, spherical SPIO particles containing approximately 70 iron oxide crystals with a hydrodynamic diameter of 127 nm (see also TEM picture on Figure S2) were obtained by mixing S1S2C3@PAA2k USPIOs (0.75 g⋅L-1) and PAM30k-b-PTEA11k (1.5 g⋅L-1) in 0.43 mol⋅L-1 NH4Cl and diluting 3 times with pure water (down to 0.143 mol⋅L-1 NH4Cl). Iron oxide represents 33 % w/w of these hybrid particles and thus an average volume fraction of 6 % v/v only. Vibrating sample magnetometry. A laboratory made VSM instrument was used, measuring the magnetization curve versus excitation M(H) at RT for a magnetic suspension of volume fraction f from the signal induced in detection coils when the sample is moved periodically in an applied magnetic field varied from 0 to 1 T (thanks to synchronous detection and with an appropriate calibration to convert the signal in mV into A⋅m-1). Dynamic light scattering. DLS measurements were performed on a Malvern NanoZS apparatus operating at a 173 ° scattering angle. The collective diffusion coefficient D was determined from the second-order autocorrelation function of the scattered light. From the value of the coefficient, the hydrodynamic diameter of the colloids was calculated according to the Stokes-Einstein relation, dH = kBT/3πηSD, where kB is the Boltzmann constant, T the temperature (T = 298 K) and ηS the solvent viscosity (ηS = 0.89×10-3 Pa s for water). The autocorrelation functions were interpreted using the 2nd order cumulants (Z-average diameter and Poly-Dispersity Index) and the multimodal fit provided by the instrument software. Relaxometry. Relaxation time measurements were performed at low fields on BRUKER (Germany) mq 20, mq 60 instruments and a Spintrack relaxometer operating at magnetic fields (B0) of 0.47, 1.41, 0.67 and 0.93 T respectively. BRUKER AVANCE-200 (4.7 T), BRUKER AMX 300 (7 T) and AMX 500 (11.7 T) spectrometers were used for the high-field T1 measurements. T1 relaxation profiles were recorded at 5 °C and 37 °C from 0.00023 to 0.23 T on a Spinmaster fast field cycling relaxometer (STELAR, Mede, Italy). In most of the graphs, the magnetic field is expressed in term of proton Larmor frequency: a field of 1 Tesla corresponds to a Larmor frequency of 42.6 MHz. The results are expressed as longitudinal and transverse relaxivities which are defined by the increase in the longitudinal and transverse relaxation rates due to an increase of 1 mM in the paramagnetic ion concentration. The relaxivity values were properly calculated by an accurate titration of the iron content in all samples as determined using Inductively Coupled Plasma Atomic Emission spectroscopy (Thermo, USA), after micro-wave mineralization of the suspensions with a mixture of nitric acid and hydrogen peroxide. Varying shapes of the T1 profiles reflect the differences in sizes, magnetizations and Néel relaxation times of the particles.[33] T2 was measured with a CPMG sequence using an inter-echo time of 1 ms. T2* was not measured for our samples. Indeed, different tests on the high resolution spectrometers showed that even for reference solutions (simply containing gadolinium ions, for example), the value of T2* evaluated with the line-width of the resonance peak was always significantly lower than the T2 value, while for such systems T2 and T2* should be identical. The influence of the shims seems to be critical when estimating T2* with this technique. For strongly magnetic compounds, the measurement of a “real” T2*, comparable to the value predicted by the different microscopic relaxation theories, could be very difficult.  Submitted to \n \n11 Numerical simulation. The empirical expression used to plot the solid curves on Figure 2 was validated by a previously described Monte Carlo simulation of T2 decay at high fields.[26] The methodology consists mainly in three steps. Firstly, static and impenetrable spherical magnetic particles are distributed in the simulation space. Secondly, the diffusion of each proton is simulated by a random walk. At each time step, the spin dephasing of each proton – proportional to local dipolar magnetic field produced by the particles – is computed. Finally, the MR signal decay is obtained by averaging all the protons spins and an exponential law can be fitted to the data to obtain the transverse relaxation rate r2.  Supporting Information Supporting Information is available online from the Wiley Online Library or from the author. S1. Synoptic scheme of the size sorting procedure. S2. Characterization of the nanoparticles: a) Magnetometry; b) Transmission Electron Microscopy; c) NMR Relaxometry.  Acknowledgements Author-One and Author-Four are grateful to Dr Alain Roch for helpful discussions and to Prof. Dr. Robert N Muller for the access to the 60 MHz relaxometer. Authors also thank Aude Michel and Delphine Talbot (PECSA) respectively for TEM and iron atomic emission spectroscopy. This research was supported in part (UMONS) by the Fonds de la Recherche Scientifique (IISN 4.4507.10), (MSC/PECSA/LCPO) by the Agence Nationale de la Recherche under the contracts BLAN07-3_206866 “ITC-nanoProbe”, and (MSC/PECSA) by the European Community through the project “NANO3T—Biofunctionalized Metal and Magnetic Nanoparticles for Targeted Tumor Therapy”, project number 214137 (FP7-NMP-2007-SMALL-1). Author-One is a research fellow from FRS-FNRS.  Annotations CA, contrast agents; CPMG, Carr-Purcell-Meiboom-Gill; DLS, dynamic light scattering; MAR, motional averaging regime; MRI, magnetic resonance imaging; NMRD, nuclear magnetic resonance dispersion; OS, outer sphere; SDR, static dephasing regime; SI, système international d’unités; SPION, superparamagnetic iron oxide nanoparticle; USPIO, ultra-small superparamagnetic iron oxide; VSM, vibrating sample magnetometry.  Received: ((will be filled in by the editorial staff)) Revised: ((will be filled in by the editorial staff)) Published online: ((will be filled in by the editorial staff))  [1] a) J. A. Frank, H. Zywicke, E. K.Jordan, J. Mitchell, B. K. Lewis, B. Miller, L. H. Jr Bryant, J. W. Bulte, Acad. Radiol. 2002, 9, S484; b) C. Billotey, C. Wilhelm, M. Devaud, J-C. Bacri, J. Bittoun, F. Gazeau, Magn. Res. Med. 2003, 49, 646; c) P. Smirnov, F. Gazeau, J-C. Beloeil, B. T. Doan, C. Wilhelm, B. Gillet, Contrast Med. Mol. Imaging 2006, 1, 165; d) H. B. Na, I. C. Song, T. Hyeon, Adv. Mater. 2009, 21, 2133; e) F. Xu, C. Cheng, F. Xu, C. Zhang, H. Xu, X. Xie, D. Yin, H. Gu, Nanotechnology 2009, 20, 405102. [2] R. Massart, IEEE Trans. Mag. 1981, 17, 1247. [3] R. W. Chantrell, J. Popplewell, S. W. Charles, IEEE Trans. Mag. 1978, 14, 975. [4] a) J-C. Bacri, R. Perzynski, D. Salin, V. Cabuil, R. Massart, J. Coll. Int. Sci. 1989, 132, 43; b) R. Massart, E. Dubois, V. Cabuil, E. Hasmonay, J. Magn. Magn. Mater. 1995, 149, 1. [5] J. A. Galicia, O. Sandre, F. Cousin, D. Guemghar, C. Ménager, V. Cabuil, J. Phys. Cond. Mat. 2003, 15, S1319. [6] A. Sehgal, Y. Lalatonne, J-F. Berret, M. Morvan, Langmuir 2005, 21, 9359.  Submitted to \n \n12 [7] J. Fresnais, J-F. Berret, B. Frka-Petesic, O. Sandre, R. Perzynski, Adv. Mater. 2008, 20, 3877. [8] D. Forge, Y. Gossuin, A. Roch, S. Laurent, L. Vander Elst, R. N. Muller, Contrast Med. Mol. Imaging 2010, 5, 126. [9] S. H. Koenig, K. E. Kellar, D. K. Fujii, W. H. H. Gunther, K. Briley-Saebø, M. Spiller, Acad. Radiol. 2002, 9, S5. [10] L. Lartigue, C. Innocenti, T. Kalaivani, A. Awwad, M. del Mar Sanchez Duque, Y. Guari, J. Larionova, C. Guérin, J-L. Georges Montero, V. Barragan-Montero, P. Arosio, A. Lascialfari, D. Gatteschi, C. Sangregorio, J. Am. Chem. Soc. 2011, 133, 10459. [11] S. L. Pinho, G. A. Pereira, P. Voisin, J. Kassem, V. Bouchaud, L. Etienne, J. A. Peters, L. Carlos, S. Mornet, C. F. Geraldes, J. Rocha, M.-H. Delville, ACS Nano 2010, 4, 5339. [12] E. Taboada, R. Solanas, E. Rodríguez, R. Weissleder, A. Roig, Adv. Funct. Mater. 2009, 19, 2319. [13] C. W. Jung, P. Jacobs, Magn. Reson. Imaging. 1995, 13, 661. [14] J-F. Berret, N. Schonbeck, F. Gazeau, D. El kharrat, O. Sandre, A. Vacher, M. Airiau, J. Am. Chem. Soc. 2006, 128, 1755. [15] C. Paquet, H. W. de Haan, D. M. Leek, H.-Y. Lin, B. Xiang, G. Tian, A. Kell, B. Simard, ACS Nano 2011, 5, 3104. [16] H. Ai, C. Flask, B. Weinberg, X. Shuai, M. D. Pagel, D.; Farrell, J. Duerk, J. Gao, Adv. Mater. 2005, 17, 1949. [17] Y. Wang, Y. W. Ng, Y. Chen, B. Shuter, J. Yi, J. Ding, S-C. Wang, S-S. Feng, Adv. Funct. Mater. 2008, 18, 308. [18] X. Xie, C. Zhang, J. Nanomaterials 2011, 152524. [19] M.-S. Martina, J-P. Fortin, C. Ménager, O. Clément, G. Barratt, C. Grabielle-Madelmont, F. Gazeau, V. Cabuil, S. Lesieur, J. Am. Chem. Soc. 2005, 127, 10676. [20] G. Beaune, M. Levy, S. Neveu, F. Gazeau, C. Wilhelm, C. Ménager, Soft Matter 2011, 7, 6248. [21] C. Sanson, O. Diou, J. Thévenot, E. Ibarboure, A. Soum, A. Brûlet, S. Miraux, E. Thiaudière, S. Tan, A. Brisson, V. Dupuis, O. Sandre, S. Lecommandoux, ACS Nano 2011, 5, 1122. [22] a) S. Cheong, P. Ferguson, K. W. Feindel, I. F. Hermans, P. T. Callaghan, C. Meyer, A. Slocombe, C-H. Su, F-Y. Cheng, C-S. Yeh, B. Ingham, M. F. Toney, R. D. Tilley, Angew. Chem. Int. Ed. 2011, 50, 4206; b) T-J. Yoon, H. Lee, H.; Shao, R. Weissleder, Angew. Chem. Int. Ed. 2011, 50, 4663. [23] a) J. Yang, C-H. Lee, H-J. Ko, J.-S. Suh, H-G. Yoon, K. Lee, Y-M. Huh, S. Haam, Angew. Chem. Int. Ed. 2007, 46, 8836; b) E-K. Lim, Y-M. Huh, J. Yang, K. Lee, J-S. Suh, S. Haam, Adv. Mater. 2011, 23, 2436. [24] U. I. Tromsdorf, O. T. Bruns, S. C. Salmen, U. Beisiegel, H. Weller, Nano Lett. 2009, 9, 4434. [25] a) P. Gillis, A. Roch, R. A. Brooks, J. Magn. Reson. 1999, 137, 402; b) S. Laurent, D. Forge, M. Port, A. Roch, C. Robic, L. Vander Elst, R. N. Muller, Chem. Rev. 2008, 108, 2064; c) Y. Gossuin, P. Gillis, A. Hocq, Q. L. Vuong, A. Roch, WIREs Nanomed. Nanobiotechnol. 2009, 1, 299; d) M. R. J. Carroll, R. C. Woodward, M. J. House, W. Y. Teoh, R. Amal, T. L. Hanley, T. G. St Pierre, Nanotechnology 2010, 21, 035103. [26] Q. L. Vuong, P. Gillis, Y. Gossuin, J. Magn. Reson. 2011, 212, 139. [27] H. W. de Haan, C. Paquet, Magn. Reson. Med. 2011, 66, 1759. [28] P. Gillis, F. Moiny, R. A. Brooks, Magn. Reson. Med. 2002, 47, 257. [29] B. A. Larsen, M. A. Haag, N. J. Serkova, K. R. Shroyer, C. R. Stoldt, Nanotechnology 2008, 19, 265102.  Submitted to \n \n13 [30] J. Jang, H. Nah, J-H. Lee, S. H. Moon, M. G. Kim, J. Cheon, Angew. Chem. Int. Ed. 2009, 48, 1234. [31] J-F. Berret, O. Sandre, A. Mauger, Langmuir 2007, 23, 2993. [32] B. Chanteau, J. Fresnais, J-F. Berret, Langmuir 2009, 25, 9064. [33] A. Roch, R. N. Muller, P. Gillis, J. Chem. Phys. 1999, 110, 5403.  Submitted to \n \n14 \n Scheme 1. In the commonly used relaxation models, d is defined as twice the minimum approach distance of a water molecule to the center of the contrast agent. For a single nanoparticle, d is equal to its diameter (case a). If there is a layer inaccessible to water molecules (case b), d must include this impermeable coating thickness (dark blue shell). If nanoparticles are clustered (case c), d corresponds to the whole hydrodynamic diameter, determined by dynamic light scattering. The MAR model can predict the relaxivities induced by such systems, assimilating the cluster to a single magnetic particle with adapted diameter d and magnetization Mv (case d). But in order to compare with MAR equations, the r2 relaxivity has to be multiplied by the intra-aggregate volume fraction φintra to get a corrected relaxivity r2’ induced by the aggregate (see text).  Submitted to \n \n15 Size (nm)1101001000r2 x intra / Mv2 (s-1mM-1m2A-2)\n1e-111e-101e-91e-81e-71e-61e-5This study (USPIOs)Jung et al. AMI227Koenig et al. MION46-LForge et al.Martina et al.Sanson et al.Cheong et al.Beaune et al. (REV)Pinho et al.Lartigue et al.Wang et al. RESOVISTWang et al.Tromsdorf et al.Taboada et al.MAR predictionLartigue Cheong et al.\n  Figure 1. Samples in the motional averaging regime (MAR), with ΔωτD<1. Influence of the size on transverse relaxivity at high field (≥1T) and at 37°C with the appropriate weighting by the intra-aggregate volume fraction φintra and normalization by the square of the magnetization enabling to compare USPIOs (single cores), maghemite core-silica shell particles, magnetic vesicles and SPIOs (clusters) on the same curve. The solid line is Equation (6).   Submitted to \n \n16 Size (nm)50100150200250300350r2 x intra (s-1mM-1)\n0.11101001000Simulations 2000<MV<10000Simulations 10000<MV<30000Simulations 30000<MV<100000Beaune et al. (ME)Tabaoda et al.Paquet et al.Paquet et al.Sanson et al.This study (clusters)Ai et al.Berret et al.Jung et al.Paquet et al.This study (clusters)Xie et al.Yang et al.2000<MV<1000010000<MV<3000030000<MV<100000  Figure 2. Samples out of the MAR, with ΔωτD>1. Influence of the size on transverse relaxivity at high field (≥1T) and at 37°C with the appropriate weighting by the intra-aggregate volume fraction φintra. The colored regions correspond to the relaxivities obtained by computer simulations, through the use of an empirical function which was recently validated.[26]  Submitted to \n \n17  Table 1 summarizes the parameters used for the samples presented in Figure 1 and Figure 2. Reference Sample code Magnetic materials Nature of  coating Size (nm) Method φintra Mv (A⋅m-1) r2 (s-1⋅mM-1) φintra⋅r2⋅Mv-2 (s-1⋅mM-1 A-2⋅m2) ΔωτD In motional averaging regime – ΔωτD<1 \nThis study S1S2S-PAA2k γ-Fe2O3 Hydrophilic Polymer (PAA2k or PAA5k) 7.8 VSM-dw 1 280000 70 8.9⋅10-10 0.16 C1C2-PAA2k 14.6 370000 211.46 1.54⋅10-9 0.74 S1S2C3-PAA2k 9.1 290000 86.5 1.03⋅10-9 0.22 C1C2C3C4S5-PAA5k 17.8 327000 292.6 2.74⋅10-9 0.97 S1-PAA2k 9 300000 69.8 7.8⋅1010 0.23 C1C2C3 adsorbed H+ only 15.1 342000 181.6 1.55⋅10-9 0.73 C1S2S3 14.8 333000 166 1.50⋅10-9 0.68 C1S2 13.2 328000 205 1.90⋅10-9 0.53 C1C2C3C4-cit Citrate 15.9 312000 133.3 1.37⋅10-9 0.73 Jung et al [13] AMI227 Ferumoxtran Sinerem (brand names) γ-Fe2O3 /Fe3O4 mixture Hydrophilic Polymer (Dextran) 6.2 TEM-dw 1 339000 53 4.6⋅10-10 0.13 Koenig et al [9] MION46L Clariscan (brand names) 8.05 VSM 1 274000 44 5.9⋅10-10 0.17 Forge et al [8] 250 Gauss γ-Fe2O3 aminoproyl-trimethoxy-silane 10.4 VSM 1 326000 133 1.24⋅10-9 0.33 1000 Gauss 9.6 332000 95.2 8.64⋅10-10 0.29 2000 Gauss 8.4 306000 54.7 5.84⋅10-10 0.20 Lartigue et al [10] Rha-4 γ-Fe2O3 rhamnose-phosphonate 4.6 NMRD 1 399000 42 2.64⋅10-10 0.08 Rha-10 10.3 363000 266 2.02⋅10-9 0.36 Rha-18 18.5 337000 292 2.57⋅10-9 1.1 Tromsdorf et al [24] 4nm-PEG1100 Fe3O4 PEG-phosphate 4 TEM 1 363000 17.5 1.3⋅10-10 0.05 6nm-PEG1100 6 42 3.2⋅10-10 0.12 Martina et al [19] Conventional MFL γ-Fe2O3 Citrate-coated Magnetic Fluid encapsulated in Liposomes 300 DLS 5⋅10-4 [a] 177 67 1.08⋅10-6 0.15 PEG-ylated MFL 202 2.6⋅10-3 [a] 896 124 4.06⋅10-7 0.34 195 3.3⋅10-3 [a] 1150 130 3.24⋅10-7 0.41 Sanson et al [21] WDi-20 γ-Fe2O3 Hydrophobic Membrane of Polymersome (PTMC-PGA) 100 DLS 2.3⋅10-2 [b] 6460 81 4.49⋅10-8 0.60 WDi-35 90 4.4⋅10-2 [b] 12200 134 3.93⋅10-8 0.92 Cheong et al [22] oxide γ-Fe2O3 Dimercapto-succinic acid (DMSA) 15 TEM 1 350000 145 1.2⋅10-9 0.74 Beaune et al [20] DDAB magnetic vesicles: REV γ-Fe2O3 Oleic acid (OA) 150 TEM 1.6 10-2 [c] 4200 177 1.6⋅10-7 0.87                                                 [a] From the iron/lipid molar ratio converted into a weight ratio inside the membrane. Assuming a lipid density of 1 and a membrane thickness of 3.5 nm, we deduced the volume of iron oxide inside the whole volume of the vesicle.  [b] From the feed weight ratios inside the membrane (20%, 35%, 50 % and 70%). Assuming a polymer density of 1 and a membrane thickness of 10 nm (SANS), we deduced the volume of iron oxide inside the whole volume of the vesicle. [c] Measured by magnetophoresis. REV stands for “reverse phase evaporation”, ME for “multiple emulsion”, DDAB for didodecyldimethyl ammonium bromide. The USPIOs have a dw=7.5 nm, Mv=2.6⋅105 A/m and r2=105 s-1m⋅M-1.   Submitted to \n \n18 Reference Sample code Magnetic materials Nature of  coating Size (nm) Method φintra Mv (A⋅m-1) r2 (s-1⋅mM-1) φintra⋅r2⋅Mv-2 (s-1⋅mM-1 A-2⋅m2) ΔωτD In motional averaging regime – ΔωτD<1 (continued) Pinho et al [11] FF (core) γ-Fe2O3 Porous SiO2 12.5 VSM [d] 1 282000 228 2.11⋅10-9 0.41 0A 14 TEM 0.71 201000 100 1.29⋅10-9 0.37 1A 27 0.1 27900 64 6.37⋅10-9 0.19 2A 40 3⋅10-2 8550 47 1.44⋅108 0.13 3A 50 1.5⋅10-2 4400 38 2.24⋅10-8 0.10 4A 66 6.8⋅10-3 1920 23 3.12⋅10-8 0.08 5A 114 1.3⋅10-3 370 15 1.05⋅10-7 0.04 6A 145 6.1⋅10-4 170 12 1.95⋅10-7 0.03 Wang et al. [17] IOs (Resovist) γ-Fe2O3 Hydrophilic Polymer (Dextran) 60 DLS 8.4⋅10-2 [e] 19500 282.4 3.5⋅10-8 0.65 IO-loaded PLGA-mPEG Amphiphilic Copolymer Micelle (PLGA-PEG) 233 4⋅10-3 [e] 1160 532.7 8.8⋅10-7 0.59 Taboada et al. [12] S1 γ-Fe2O3 Porous SiO2 (aerogel) 160 DLS 1.1⋅10-2 3180 148 1.6⋅10-7 0.76 S2 120 1.5⋅10-2 4590 164 1.16⋅10-7 0.62 Out of motional averaging regime – ΔωτD>1 Taboada et al. [12] S3 γ-Fe2O3 Porous SiO2 (aerogel) 313 DLS 1.2⋅10-2 3880 326 2.6⋅10-7 3.6 This study Clusters S1S2C γ-Fe2O3 cluster Double Hydrophilic Copolymer (PAM-PTEA) 127 DLS 9⋅10-2 26000 91 1.22⋅10-8 3.9 Beaune et al [20] DDAB magnetic vesicles: ME γ-Fe2O3 Oleic acid (OA) 300 TEM 8⋅10-3 [c] 2100 185 3.36⋅10-7 1.6 This study S2C14 γ-Fe2O3 cluster Double Hydrophilic Copolymer (PAM-PTEA) 132 DLS 8.3⋅10-2 24200 91 1.29⋅10-8 3.9 S2C12 260 0.15 44000 216 1.7⋅10-8 28 C1C2C3C4-PAA5k γ-Fe2O3 demixted droplet Hydrophilic Polymer (PAA) 114 0.286 89000 427 1.54⋅10-8 10.8 Berret et al [14] PTEA(5k) γ-Fe2O3 cluster Double Hydrophilic Block Copolymer (PAM-PTEA) 70 DLS 0.22 57200 74 4.98⋅10-9 2.2 PTEA(11k) 170 0.38 99000 162 6.28⋅10-9 25 Xie et al [18] Loosen SPION cluster (A) Fe3O4 cluster Oleic acid (OA) / Oleylamine in Amphiphilic Copolymer Micelle (PEG-PLA) 58 DLS 0.12 [f] 42000 117 8⋅10-9 1.3 Condense cluster B 73 0.20 [f] 70000 233 9.5⋅10-9 3.5 Condense cluster C 95 363 1.48⋅10-8 5.9 Condense cluster D 97 413 1.69⋅10-8 6 Condense cluster E 144 458 1.87⋅10-8 14 Condense cluster F 199 512 2.09⋅10-8 26                                                 [d] We are in debt to the authors of this reference to have provided us their ferrofluid to make this VSM measurement. Volume fractions were calculated from TEM images. Relaxivities at 25 °C were rescaled by a factor 0.686/0.895.  [e] Calculated from the iron weight ratio measured by inductively coupled plasma mass spectroscopy (ICP-MS). The volume fractions enable to get the volume magnetizations using given values of specific magnetizations (72.9 emu⋅g-1 for IOs and 83.5 emu⋅g-1 for IO-loaded PLGA-mPEG). [f] Measured by thermogravimetry analysis (TGA). The USPIOs have a dw=10.5 nm (TEM, N=1822) and Mv=3.3⋅10 5 A⋅m-1.  Submitted to \n \n19 Reference Sample code Magnetic materials Nature of  coating Size (nm) Method φintra Mv (A⋅m-1) r2 (s-1⋅mM-1) φintra⋅r2⋅Mv-2 (s-1⋅mM-1 A-2⋅m2) ΔωτD Out of motional averaging regime – ΔωτD>1 (continued) Ai et al [16] 8 nm SPIO PCL5k-b-PEG5k Fe3O4 cluster Amphiphilic Copolymer Micelle (PEG-PCL) 97 DLS 0.11 41900 318 1.94⋅10-8 3.7 16 nm SPIO PCL5k-b-PEG5k 110 0.19 79200 471 1.42⋅10-8 9 Cheong et al [22] core/shell Fe–γFe2O3 core- shell Dimercapto-succinic acid (DMSA) 15.4 TEM 1 660000 [g] 324 8.3⋅10-10 1.5 Paquet et al [15] Densely packed SPIONs γ-Fe2O3 /Fe3O4 mixture cluster Surfactant (SDS) 68 TEM 0.34 98600 270 9.3⋅10-9 6 SPION Cluster core inside a hydrogel shell γ-Fe2O3 /Fe3O4 mixture cluster Polymer (PNIPAM) Hydrophilic at T<32°C, Hydrophobic at T>32°C 88 0.157 45500 394 3⋅10-8 3.3 112 0.076 22100 420 6.6⋅10-8 2.6 130 0.049 14100 436 1.1⋅10-7 2.2 108 0.085 24600 467 6.5⋅10-8 2.7 152 0.03 8800 484 1.9⋅10-7 1.9 176 0.02 5700 505 3.1⋅10-7 1.6 Jung et al [13] AMI-25 Feridex Ferumoxide Endorem (brand names) γ-Fe2O3 /Fe3O4 mixture cluster Hydrophilic Polymer (Dextran) 80 DLS 0.23 [h] 77000 107 4.1⋅10-9 4.4 Yang et al [23] Fe3O4-MMPNs Fe3O4 cluster Amphiphilic Copolymer Micelle (PLGA-PEG) 73 TEM 0.118 [i] 45000 333 1.92⋅10-8 2.2 MnFe2O4-MMPNs MnFe2O4 cluster 70 0.125 [j] 51000 567 2.78⋅10-8 2.3 Sanson et al [21] WDi-50 γ-Fe2O3 Hydrophobic Membrane of Polymersome (PTMC-PGA) 94 DLS 5.8⋅10-2 [b] 16200 173 3.81⋅10-8 1.34 WDi-70 104 7.1⋅10-2 [b] 19800 182 3.27⋅10-8 2.0  \n                                                [g] Core diameter is 9 nm, representing 18% of the particle volume. Alpha-iron density being 7.874 g⋅cm-3, an average mass density of the core-shell of 5.5 g⋅cm-3 was used to derive Mv from the mass magnetization of 115 emu⋅g-1. [h] 63.8 wt% iron oxide from thermogravimetry analysis (TGA). The USPIOs have a dw=5.6 nm (TEM, N=694). [i] 40.9 wt% iron ferrite from TGA. The USPIOs have dw=9 nm (TEM), Mv=3.3 10 5 A/m (74 emu⋅g-1). [j] 41.7 wt% manganese ferrite from TGA. The USPIOs have dw=9 nm (TEM), Mv=4.0⋅105 A/m (80.8 emu⋅g-1).  Submitted to \n \n20  Table 2. Saturation magnetizations, optimal diameters and maximum relaxivities for different types of magnetic particles used as T2 MRI contrast agents. Materials Mv [A⋅m-1] [a] doptimal [nm] [b] r2max [s-1⋅mM-1] [c] Maghemite nanoparticles 3.5×105 55 750 Clusters of maghemite nanoparticles at a volume dilution of 5 (φintra=20% v/v maghemite fraction) 7×104 120 750 Iron-iron oxide core-shell nanoparticles 6.6×105 38 1200 (Zn0.4Mn0.6)Fe2O4 nanoparticles 8.75×105 35 1860 [a] saturation magnetization [b] optimal diameter [c] maximum transverse relaxivity   Submitted to \n \n21 Table of contents entry. This study evidences size, magnetization and magnetic volume fraction as the only control parameters of MRI T2 contrast agents. Experimental relaxation and magnetometry data on magnetic particles draw up a master curve, allowing the prediction of the efficiency of any nanoparticles or clusters. A calculation of the optimal size for T2 contrast agents of different natures is also performed.  Keyword list. Magnetic Resonance Imaging Contrast Agents; Transverse Relaxivity; Motional Averaging Regime; Static Dephasing Regime; Superparamagnetic Iron Oxide Nanoparticles  Quoc L. Vuong, Jean-François Berret, Jérôme Fresnais, Yves Gossuin* and Olivier Sandre*  Universal Scaling Law to Predict the Efficiency of Magnetic Nanoparticles as MRI T2-Contrast Agents  \n ToC figure   Submitted to \n \n22 Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2010.  Supporting Information   for Adv. Healthcare Mater., DOI: 10.1002/ adhm.201200078  Universal Scaling Law to Predict the Efficiency of Magnetic Nanoparticles as MRI T2-Contrast Agents  By Quoc L. Vuong, Jean-François Berret, Jérôme Fresnais, Yves Gossuin* and Olivier Sandre*   Dr. Q. L. Vuong, Author-One,  Université de Mons, Biological Physics Department, 20 Place du Parc, 7000 Mons, Belgium  Dr. J.-F. Berret, Author-Two, Université Denis Diderot Paris-VII, CNRS UMR7057, Matière et Systèmes Complexes 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France  Dr. J. Fresnais, Author-Three, UPMC Univ Paris 06, CNRS UMR7195, Physicochimie, Colloïdes et Sciences Analytiques 4 place Jussieu, 75005 Paris, France [*] Dr. Y. Gossuin, Corresponding-Author,  Université de Mons, Biological Physics Department, 20 Place du Parc, 7000 Mons, Belgium E-mail: yves.gossuin@umons.ac.be [*] Dr. O. Sandre, Corresponding-Author,  Université de Bordeaux, CNRS UMR5629, Laboratoire de Chimie des Polymères Organiques ENSCBP, 16 Avenue Pey Berland, 33607 Pessac, France E-mail: olivier.sandre@ipb.fr  Outline: S1. Synoptic scheme of the size sorting procedure S2. Characterization of the nanoparticles a. Magnetometry b. Transmission Electron Microscopy  c. NMR Relaxometry  Submitted to \n \n23 S1. Synoptic scheme of the size sorting procedure                      Sketch S1: Fractions of USPIOs obtained by successive phase separations in added electrolyte concentration (HNO3) to refine the sizes’ distribution as measured by VSM. The shadowed boxes correspond to the samples further characterized by TEM and relaxometry (either in their raw dispersed state in HNO3 or after coating or in a controlled clustered state). C1 d0=8.7 nm σ = 0.35 Mv = 3.7×105 A/m (74 emu/g)  S1 d0=7.1 nm σ = 0.29 Mv = 3.0×105 A/m (60 emu/g)  S1C2 d0=8.3 nm σ = 0.26 dw= 10.6 nm Mv = 3.5×105 A/m (70 emu/g)  C1S2 d0=9.0 nm σ = 0.33 dw= 13.2 nm Mv = 3.3×105 A/m (66 emu/g)  S1S2S3 d0=6.7 nm σ = 0.21 dw= 7.8 nm Mv = 2.8×105 A/m (56 emu/g) C1C2C3 d0=10.4 nm σ = 0.32 dw= 15.1 nm Mv = 3.4×105 A/m (68 emu/g)  S1S2C3 d0=7.7 nm σ = 0.22 dw= 9.1 nm Mv = 2.9×105 A/m (58 emu/g)  C1C2 d0=9.1 nm σ = 0.37 dw= 14.6 nm Mv = 3.7×105 A/m (74 emu/g)  S1S2 d0=6.3 nm σ = 0.28 dw= 8.3 nm Mv = 3.0×105 A/m (60 emu/g)  C1C2S3 d0=10 nm σ = 0.33 dw= 14.8 nm Mv = 3.3×105 A/m (66 emu/g)  Polydisperse USPIOs d0=7 nm σ = 0.38 Mv = 3.1×105 A/m (62 emu/g)  \nC1C2C3C4 d0=13 nm σ = 0.25 dw= 16.2 nm Mv = 3.5×105 A/m (70 emu/g)  C1C2C3S4 d0=10.4 nm σ = 0.29 dw= 13.9 nm Mv = 3.5×105 A/m (70 emu/g)  C1C2C3C4S5 d0=9.5 nm σ = 0.44 dw= 17.8 nm Mv = 3.27×105 A/m (65.4 emu/g)   Submitted to \n \n24 S2. Characterization of the nanoparticles S2.a Magnetometry We use two populations (S1S2S3 and S1C2) as a comparison. Figure S1 shows the typical evolution of the macroscopic magnetization M(H) normalized by its saturation value MS for the γ-Fe2O3 superparamagnetic NP. Here, MS = f mS, where mS is the specific magnetization of colloidal maghemite (approximately mS = 3.5×105 A m−1) which is lower than for bulk maghemite. It decreases when the diameter of the superparamagnetic NP decreases due to some disorder of the magnetic moments located near the surface. The solid curves on Figure S1 were obtained by Langevin fits convoluted with log-normal distribution laws of the particle sizes. The parameters of the distribution are the median diameter and the standard variations, respectively 0VSMd=6.7±0.1nm with VSMσ=0.21±0.03 for S1S2S3 and 0VSMd=8.3±0.1nm with VSMσ=0.21±0.02 for S1C2.  Figure S1: Magnetic field dependence of the macroscopic magnetization M(H) normalized by its saturation value MS for cationic maghemite dispersions. The solid curve was obtained using the Langevin function for superparamagnetism convoluted with a log-normal distribution function for the particle sizes, given with median diameters 0VSMd and width VSMσ. \n   S2.b Transmission Electron Microscopy (TEM)  \n Figure S2: Iron oxide superparamagnetic NPs. (a) S1S2S3 and (b) S1C2 as observed by TEM. The stability of the dispersion was ensured by electrostatic interactions mediated by the native cationic charges in diluted HNO3 (pH=1.2– 1.7).  S1C2 S1S2S3  Submitted to \n \n25 In fact, the median diameter 0VSMd obtained by VSM is related to the crystal structure inside the γ-Fe2O3 nanoparticle. We then compared these values with the physical diameters 0TEMdby using image analysis of transmission electron microscopy (TEM). Figure S2 displays images of the two batches of γ-Fe2O3 USPIOs chosen as examples (S1S2S3 and S1C2).   Figure S3 shows probability distribution functions of sizes for these NPs observed by TEM on a series of images similar to Figure S2. The data are fitted by a log-normal function with physical diameters 0TEMd= 6.8±0.2 nm and 0TEMd= 9.3±0.2 nm, with polydispersities TEMσ= 0.21±0.01 and TEMσ= 0.18±0.01.  2002ln ( / )1(, , ) e x p2( )2DDDddpdddσσπσ⎛⎞=−⎜⎟⎝⎠      (S1)  These values are in good agreement with the ones obtained from VSM, albeit with a minor difference between the median diameter 0VSMd and physical diameter 0TEMd, which could originate from defects located close to the particles’ surface not contributing to the magnetic properties. \n  Figure S3: Probability distributions function of sizes for two γ-Fe2O3 USPIOs: a) S1S2S3; b) S1C2. The continuous line was derived from best fit calculation using a Log-normal distribution. For these dispersions, the average diameters by TEM were 6.8 nm and 9.3 nm, and the polydispersity 0.21 and 0.18.  Using the Log-normal distributions deduced by VSM, we can estimate a weight-averaged diameter dw = <d4>/<d3> characteristic of each sample by calculating the 4th and 3th order moments of the Log-normal distributions: dw = d0×exp(3.5×σ2). This fairly compares to the average diameter dTEM obtained by the analysis of TEM pictures (Figure S3). From this comparison between TEM and VSM, we conclude that the weight average diameter dw calculated from the two fitting parameters d0 and σ of the VSM curve correctly reflects both the size distribution of the samples and their magnetic surface disorder and therefore can be used as a single characteristic size.  Submitted to \n \n26 \nC1C2C3 in HNO3 (pH 1.5)  \nC1C2C3C4 in HNO3 (pH 1.5)  \nS1S2-citrate (pH 7)  \nC1C2S3 in HNO3 (pH 1.5)  \nS1S2C3@PAA/PAM-b-PTEA clusters  \nS1S2S3@PAA/PAM-b-PTEA clusters  Figure S4: Typical TEM images of the synthesized particles. The images were acquired on a JEOL100 transmission electron microscope operating at 80 kV by Aude Michel, “Physicochimie des Electrolytes, Colloïdes et Sciences Analytiques” at UPMC Univ Paris 6.  Submitted to \n \n27 S2.c NMR Relaxometry  Figure S5 shows the longitudinal NMRD profiles for all the (U)SPIO samples prepared in this study. As expected, the r1 relaxivities at high fields are really low. \nMagnetic field (T)0.00010.0010.010.1110r1 (s-1mM-1)\n020406080100120140160C1C2C3C4-PAA5kC1C2C3C1C2S3C1S2C1C2-PAA2kC1C2C3C4S5-PAA5k S1S2S-PAA2kS1S2C-PAA2k S1-PAA-2ks2c12s2c14cluster-s1s2cpaa2k Figure S5: longitudinal relaxation of the samples at different magnetic fields.  The transverse relaxivity of all samples at different magnetic fields are shown on Figure S6. The relaxivity at 1.41 T was used in the article since it is close to classical clinical imaging fields. We also checked on some samples that the transverse relaxation was almost the same at 1.41 T and at very high fields (e.g. 9.4 T/400 MHz), as expected for maghemite particles. \nMagnetic field (T)0.40.60.81.01.21.4r2 (s-1mM-1)\n0100200300400500C1C2C3C4 -PAA5kC1C2C3 C1C2S3 C1S2 C1C2-PAA2kC1C2C3C4S5 -PAA5kS1S2S-PAA2k S1S2C -PAA2kS1-PAA2kclusters-s1s2cs2c12 s2c14  Figure S6: transverse relaxation of the samples at different magnetic fields.  Submitted to \n \n28 MV2 x d2 / φintra= mS2 x d2 x φintra1e+121e+131e+141e+15r2  (s-1mM-1)\n101001000This study (USPIOs)Jung et al. AMI227Koenig et al. MION46-LForge et al.Martina et al.Sanson et al.Cheong et al.Beaune et al. (REV)Pinho et al.Lartigue et al.Wang et al. RESOVISTWang et al.Tromsdorf et al.Taboada et al.Lartigue et al.Cheong et al.Regression\n Figure S7: Raw values of the transverse relaxivity at high field (≥1T) for samples in the MAR. r2 is appearing linear with the squares of the magnetization and of the diameter divided by the intra-aggregate volume fraction for individual USPIOs (for which φintra=100%) and clusters (either of low size or dilute) in the MAR i.e. satisfying Equation (4). We can also introduce the specific magnetization of the magnetic cores in the cluster mS and relate it to the whole body magnetization Mv=φintra×mS. Then the transverse relaxivity r2 becomes linear with mS2×d 2×φintra in the MAR. The other clusters corresponding to ΔωτD>1 exhibit a lower r2 than the power law and saturate below a plateau value given by Table 2.  "    },    {        "title": "1401.1871v1.Persistent_Optically_Induced_Magnetism_in_Oxygen_Deficient_Strontium_Titanate.pdf",        "content": "arXiv:1401.1871v1  [cond-mat.mes-hall]  9 Jan 2014Persistent Optically Induced Magnetism in Oxygen-Deficien t Strontium Titanate\nW. D. Rice,1P. Ambwani,2M. Bombeck,3J. D. Thompson,4C. Leighton,2and S. A. Crooker1\n1National High Magnetic Field Laboratory, Los Alamos Nation al Laboratory, Los Alamos, NM 87545, USA\n2Department of Chemical Engineering and Materials Science,\nUniversity of Minnesota, Minneapolis, MN 55455, USA\n3Experimentelle Physik 2, Technische Universit ¨at Dortmund, D-44221 Dortmund, Germany\n4Materials Physics and Applications, Los Alamos National La boratory, Los Alamos, NM 87545, USA\n(Dated: April 29, 2018)\nStrontium titanate (SrTiO 3) is a foundational\nmaterial in the emerging field of complex oxide\nelectronics [1–6]. While its electronic and optical\nproperties have been studied for decades [7–10],\nSrTiO 3has recently become a renewed materials\nresearch focus catalyzed in part by the discov-\nery of magnetism and superconductivity at inter-\nfaces between SrTiO 3and other oxides [6, 11–16].\nThe formation and distribution of oxygen vacan-\ncies may play an essential but as-yet-incompletely\nunderstood role in these effects [17–21]. More-\nover, recent signatures of magnetization in gated\nSrTiO 3[22, 23] have further galvanized interest\nin the emergent properties of this nominally non-\nmagnetic material. Here we observe an optically\ninduced andpersistent magnetization in oxygen-\ndeficient SrTiO 3−δusing magnetic circular dichro-\nism (MCD) spectroscopy and SQUID magnetom-\netry. This zero-field magnetization appears below\n∼18K, persists for hours below 10K, and is tun-\nable via the polarization and wavelength of sub-\nbandgap (400-500nm) light. These effects occur\nonly in oxygen-deficient samples, revealing the\ndetailed interplay between magnetism, lattice de-\nfects, and light in an archetypal oxide material.\nTo explore the relationship between oxygen vacancies\n(VO) and magnetism in SrTiO 3, we prepared a series of\nslightly oxygen-deficient SrTiO 3−δsingle crystal samples\nby annealing ( i.e., reducing) commercial SrTiO 3sub-\nstrates in ultra-high vacuum at varying temperatures.\nIsolated VOin SrTiO 3are shallow donors: if every VO\ndonates one to two electrons to the conduction band,\nthe total VOconcentration can be approximately in-\nferred by measuring the electron density n[24]. Here,\nnranged from ∼3×1012cm−3to 8×1017cm−3. To\nprobe magnetism in these samples we use MCD spec-\ntroscopy, whereinsmall differencesbetween the transmis-\nsion of right- and left-circularly polarized (RCP/LCP)\nprobe light are sensitively measured (Fig. 1a; see Meth-\nods). Non-zero MCD signals typically imply the pres-\nence of broken time-reversal symmetry ( e.g., magneti-\nzation) [25]. The samples could also be weakly illu-\nminated with a separate source of wavelength-tunable,\npolarization-controlled pump light.\nFigure 1b displays optical absorptionspectra from sev-eral SrTiO 3−δsingle crystals. As-received (unannealed\nand nominally undoped) substrates show only the sharp\nonset of band-edge absorption at 380 nm (3.26 eV);\nat longer wavelengths the absorption is small, with a\nweak sub-bandgap tail. In contrast, increasingly oxygen-\ndeficient SrTiO 3−δcrystals develop an additional sub-\nbandgap absorption peaked at ∼430 nm (380 meV be-\nlow the band-edge), with a weak shoulder at ∼400 nm.\nHowever, this absorption does not scale linearly with n,\nstrongly suggesting that only a fraction of the total VO\ndensity contributes to this absorption peak, for exam-\nple via specific VO-related complexes or clusters [17].\nEarly studies of bulk SrTiO 3revealed similar absorption\npeaks in this spectral range that were associated with Fe\ndopants and Fe- VOcomplexes [8–10]. Iron is only one\nof many metal impurities found in significant quantities\neven in nominally “pure” SrTiO 3crystals [26] and thus\nan unambiguous assignment is difficult [8].\nSurprisingly, Fig. 1c shows that these VO-related ab-\nsorption features are accompanied by the ability to in-\nduce – and control – a robust MCD signal at zero\nmagnetic field by illuminating with weak, circularly po-\nlarized pump light at sub-bandgap wavelengths (here,\nλpump=405 nm, which pumps the entire sample thick-\nness). The optically induced MCD signal oscillates with\nprobe wavelengthover the same spectral range where the\nVO-relatedabsorptionoccurs,exhibitingpeakamplitudes\nat∼400, 425, and 455 nm. Moreover, the MCD signal\nexactly inverts when the pump polarization is switched\nfrom RCP to LCP and disappears when the pump is lin-\nearly polarized. In contrast, unannealed SrTiO 3exhibits\nno optically induced MCD. Importantly, allSrTiO 3−δ\ncrystals showing a measurable sub-bandgap absorption\npeak(thosewith n/greaterorsimilar1014cm−3)demonstrateopticallyin-\nduced MCD with identical spectral shape, showing peaks\nand nodesat the sameλprobe. Thesedata point to an op-\ntically induced magnetization arising from localized VO-\nrelated complexes.\nThe temperature dependence of the optically induced\nmagnetization is shown in Fig. 1d. To probe magnetiza-\ntion continuously, we monitor the MCD signalat its peak\n(λprobe=425 nm). Under steady optical pumping, the\ninduced magnetization is approximately constant at low\ntemperatures T,but abruptlydisappearsfor T/greaterorsimilar18K.All\nof the SrTiO 3−δsamples display the same temperature2\n/s45\n/s48/s46/s50/s48/s46/s52/s48/s46/s54/s48/s46/s56/s49/s46/s48\n/s32/s110 /s32/s61/s32/s54/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s32/s49/s120/s49/s48/s49/s53\n/s32/s99/s109/s45/s51\n/s32/s50/s120/s49/s48/s49/s52\n/s32/s99/s109/s45/s51\n/s32/s85/s110/s97/s110/s110/s101/s97/s108/s101/s100\n/s32\n/s32/s32/s79/s112/s116/s105/s99/s97/s108/s32/s68/s101/s110/s115/s105/s116/s121\n/s84 /s32/s61/s32/s51/s46/s48/s32/s75\n/s45/s55/s48/s55\n/s84 /s32/s61/s32/s51/s46/s48/s32/s75/s85/s110/s97/s110/s110/s101/s97/s108/s101/s100/s76/s105/s110/s101/s97/s114/s32/s112/s117/s109/s112\n/s82/s67/s80/s32/s112/s117/s109/s112/s32\n/s32/s77/s67/s68/s32/s40/s120/s49/s48/s45/s51\n/s41/s76/s67/s80/s32/s112/s117/s109/s112\n/s110 /s32/s61/s32/s54/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s52/s48/s48 /s53/s48/s48 /s54/s48/s48 /s55/s48/s48/s45/s55/s48/s55\n/s32/s32\n/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s45/s50/s120/s49/s48/s45/s51/s48/s50/s120/s49/s48/s45/s51\n/s32/s76/s105/s110/s101/s97/s114/s32/s112/s117/s109/s112\n/s82/s67/s80/s32/s112/s117/s109/s112/s32/s77/s67/s68/s32/s40\n/s112/s114/s111/s98/s101/s32/s61/s32/s52/s50/s53/s32/s110/s109/s41\n/s110 /s32/s61/s32/s49/s120/s49/s48/s49/s55\n/s32/s99/s109 /s45/s51/s76/s67/s80/s32/s112/s117/s109/s112\n/s48 /s50/s48 /s52/s48/s45/s53/s120/s49/s48/s45/s55/s48/s53/s120/s49/s48/s45/s55\n/s76/s105/s110/s101/s97/s114/s32/s112/s117/s109/s112/s76/s67/s80/s32/s112/s117/s109/s112\n/s82/s67/s80/s32/s112/s117/s109/s112/s77/s97/s103/s110/s101/s116/s105/s99/s32/s77/s111/s109/s101/s110/s116/s32/s40/s101/s109/s117/s41\n/s84/s101/s109/s112/s101/s114/s97/s116/s117/s114/s101/s32/s40/s75/s41/s110 /s32/s61/s32/s54/s120/s49/s48/s49/s55\n/s32/s99/s109 /s45/s51/s52/s48/s48 /s53/s48/s48/s45/s49/s120 /s49/s48/s45/s51/s48/s49/s120 /s49/s48/s45/s51\n/s112/s114/s111/s98/s101/s32\n/s53/s32/s75\n/s52/s48/s48 /s53/s48/s48/s45/s49/s120 /s49/s48/s45/s51/s48/s49/s120 /s49/s48/s45/s51\n/s112/s114/s111/s98/s101/s51/s48/s32/s75/s32\n/s100\n/s99 /s101/s98/s97\n/s45/s45\nFIG. 1.Optically induced magnetization in oxygen-deficient SrTiO 3−δat zero applied magnetic field. a,\nSchematic of the magnetic circular dichroism (MCD) experiment used to detect magnetization in SrTiO 3−δsingle\ncrystals. Continuous-wave (CW) probe light is modulated between r ight- and left-circular polarization (RCP/LCP)\nby a linear polarizer (LP) and photoelastic modulator (PEM), then tr ansmitted through the samples and detected\nby an avalanche photodiode (APD). The polarization of the additiona l CW pump light is controlled with a quarter-\nwave plate (QWP). b,Optical absorption spectra of several SrTiO 3−δcrystals at low temperature (3 K) and at zero\nmagneticfield. The samplesaredenoted bytheirelectrondensity, n, fromwhich the VOconcentrationmaybe inferred.\nOptical density=-ln(T/T 0); these spectra have not been corrected for simple Fresnel refl ection.c,The corresponding\nMCD spectra from a SrTiO 3−δand an as-received (unannealed) SrTiO 3single crystal after being weakly illuminated\nwith 50µW of RCP, LCP, and linearly polarized pump light at 405 nm (black, red, a nd green curves, respectively).\nThe oscillatory MCD signals indicate a pump-induced magnetization, wh ich inverts sign upon switching between\nRCP and LCP illumination. d,The temperature dependence of the induced magnetization (as mo nitored by MCD\natλprobe=425 nm), while being pumped at 405 nm. Insets: MCD at 5 K and 30 K. e,The temperature dependence\nof the optically induced magnetization as measured by SQUID magnet ometry, showing similar behavior as in d.\ndependence regardless of n, which again suggests local-\nized independent complexes, rather than collective phe-\nnomena such as ferromagnetism. The 430 nm absorption\ndoes not significantly changeabove18 K (Supplementary\nFig. S1).\nConventional SQUID magnetometry was used to di-\nrectly confirm and quantify the induced magnetization\n(see Methods). Here, polarization-controlled 405 nm\npump light was coupled to the samples via optical\nfiber. Figure 1e shows an induced magnetic moment of\n∼5×10−7emu at zero applied field, following the same\ntemperature and polarization dependence as measured\nby MCD. A signal of this magnitude is expected in thissample if every VOinduces a moment of ∼0.01µB. More\nlikely, only asmallfractionofthe VOmayinduce a(much\nlarger) moment, a scenario consistent with only a subset\nof theVOdensity contributing to optically induced mag-\nnetization. As with the MCD data, no SQUID signal was\nobserved in unannealed samples (Fig. S2).\nRemarkably, the optically induced magnetization in\nSrTiO 3−δis extremely long-lived at low tempera-\ntures,i.e.the magnetizationpersistslong afterthe pump\nillumination is turned off. Figure 2a shows the induced\nmagnetization over ∼1 hour as the pump illumination is\nvaried. The magnetization is initially zero. At t=150 s,\nRCP pump light illuminates the sample, causing the3\n/s48 /s49/s48/s48/s48 /s50/s48/s48/s48 /s51/s48/s48/s48/s45/s49/s48/s49\n/s76/s105/s110/s101/s97/s114/s32/s112/s117/s109/s112\n/s76/s67/s80/s32/s112/s117/s109/s112/s76/s105/s110/s101/s97/s114/s32/s112/s117/s109/s112\n/s66/s108/s111/s99/s107/s101/s100/s66/s108/s111/s99/s107/s101/s100\n/s32/s77/s67/s68/s32/s40/s120/s49/s48/s45/s50\n/s59\n/s112/s114/s111/s98/s101/s61/s32/s52/s50/s53/s32/s110/s109/s41\n/s84/s105/s109/s101/s32/s40/s115/s101/s99/s41/s66/s108/s111/s99/s107/s101/s100/s82/s67/s80/s32/s112/s117/s109/s112\n/s110 /s32/s61/s32/s56/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51/s84 /s32/s61/s32/s51/s46/s48/s32/s75\n/s66 /s32/s61/s32/s32/s48/s32/s84\n/s49/s48/s48 /s50/s48/s48 /s51/s48/s48/s48/s49/s50\n/s84 /s32/s61/s32/s51/s46/s48/s32/s75\n/s66 /s32/s61/s32/s32/s48/s32/s84\n/s110 /s32/s61/s32/s49/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51/s32/s53/s48/s32 /s87 \n/s32/s50/s53/s32 /s87 \n/s32/s53/s32 /s87 \n/s32/s50/s46/s53/s32 /s87 /s32/s32/s32/s32/s32/s32\n/s32\n/s32/s32/s77/s67/s68/s32/s40/s120/s49/s48/s45/s51\n/s59\n/s112/s114/s111/s98/s101/s61/s32/s52/s50/s53/s32/s110/s109/s41\n/s45/s55/s46/s48/s45/s51/s46/s53/s48/s46/s48/s51/s46/s53/s55/s46/s48/s32/s32/s32/s32/s77/s67/s68/s32/s40/s120 /s49/s48/s45/s51\n/s59\n/s112/s114/s111 /s98/s101/s32/s61/s32/s52/s50/s53/s32/s110/s109/s41\n/s49/s48/s48/s32 /s109\n/s49/s48/s48/s32 /s109/s48 /s51/s48/s48/s48 /s54/s48/s48/s48 /s57/s48/s48/s48/s49/s48/s45/s50/s49/s48/s45/s49/s49/s48/s48\n/s32/s49/s49/s32/s75/s32/s32\n/s32/s49/s50/s32/s75/s32/s32\n/s32/s49/s51/s32/s75/s32/s32\n/s32/s49/s52/s32/s75\n/s32/s49/s53/s32/s75\n/s32/s49/s54/s32/s75\n/s32/s49/s55/s32/s75\n/s32/s77/s67/s68/s32/s40/s97/s114/s98/s46/s32/s117/s110/s105/s116/s115/s59\n/s112/s114/s111/s98/s101/s61/s32/s52/s50/s53/s32/s110/s109/s41\n/s84/s105/s109/s101/s32/s40/s115/s101/s99/s41/s110 /s32/s61/s32/s56/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51/s80/s117/s109/s112/s32/s111/s102/s102/s53/s48 /s55/s53 /s49/s48/s48 /s49/s50/s53 /s49/s53/s48/s49/s120 /s49/s48/s48/s49/s120 /s49/s48/s50/s49/s120 /s49/s48/s52/s49/s120 /s49/s48/s54\n/s110 /s32/s61/s32/s56/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s32/s32/s40/s115/s101/s99/s41\n/s49/s48/s48/s48/s47/s84/s101/s109/s112/s101/s114/s97/s116/s117/s114/s101/s32/s40/s75 /s32/s45/s49\n/s41/s69 /s32/s61/s32/s50/s52/s32/s109/s101/s86/s50/s48 /s49/s53 /s49/s48 /s56 /s55/s84/s101/s109/s112/s101/s114/s97/s116/s117/s114/s101/s32/s40/s75/s41\n/s100\n/s101\n/s99/s98/s97\nFIG. 2.Persistence of the optically induced magnetization in SrTi O3−δ. a,Temporal evolution of the mag-\nnetization (as monitored by MCD at λprobe=425 nm) for different polarizations of 405 nm pump light. The optically\ninduced magnetization persists even after the pump is blocked, and the pump polarization can control and invert the\nmagnetization. b,As the pump intensity increases, the induced magnetization satura tes more quickly. c,Measuring\nthe slow exponential decay of the optically induced magnetization at different temperatures. Relaxation at 11 K was\nprobed intermittently to limit any probe-induced relaxation. d,τincreases over four orders of magnitude as temper-\nature is reduced from 17 K to 7 K. An Arrenhius fit (black line) to the lin ear portion of the data gives an activation\nenergy ∆ E=24 meV. e,A demonstration that magnetic information can be optically written in to SrTiO 3−δ, stored,\nand then optically read out.\nmagnetization to build up and saturate within about one\nminute. Unexpectedly, this magnetization persistsafter\nthe pump light is blocked at t=450 s. Subsequent pump-\ning with linearlypolarized light causesthe magnetization\nto rapidly re-equilibrate back to zero. Using LCP pump\nlight, equivalent but oppositely oriented magnetization\ndynamics are produced. Similar temporal behavior is\nobserved using SQUID magnetometry (Fig. S2).\nFigure 2b shows that the induced magnetization grows\nmore rapidly with increasing pump intensity, but satu-\nrates at approximately the same value. Despite achiev-\ning saturation, the induced MCD signal is only ∼10−3,\nindicating that the total absorption at this wavelength\n(λprobe=425 nm) changes only minimally (see also Fig.S3).\nThe relaxation rate of the induced magnetization after\nthe pump light is blocked is strongly temperature depen-\ndent. The magnetization relaxation fits very well to a\nsingle-exponential decay with time constant τ(Fig. 2c).\nFig. 2d shows that at 17 K relaxation occurs within sec-\nonds; however, as the temperature drops, τincreases to\nseveralhours(see also Fig. S4). Data between 13 and\n17 K suggest an approximately activated (Arrhenius) be-\nhavior [τ=τ0exp(∆E/kBT)], from which an activation\nenergy ∆ E=24 meV is inferred. Below 13 K, τdeviates\nfrom activated behavior, but this may be due to small\namounts of unintended light on the samples.\nTo demonstrate the potential utility of this persistent4\n/s51/s57/s48 /s52/s50/s48 /s52/s53/s48 /s52/s56/s48/s51/s57/s48/s52/s50/s48/s52/s53/s48/s52/s56/s48\n/s32/s32\n/s80/s114/s111/s98/s101/s32/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s80/s117/s109/s112/s32/s87/s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41\n/s45/s49/s46/s56/s48/s46/s48/s49/s46/s56\n/s52/s48/s48 /s52/s53/s48 /s53/s48/s48 /s53/s53/s48/s45/s50/s48/s50/s52\n/s32/s82/s67/s80\n/s32/s76/s67/s80\n/s32/s32/s77/s67/s68/s32/s40/s120/s49/s48/s45/s50\n/s41\n/s80/s114/s111/s98/s101/s32/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s52/s55/s53/s32/s110/s109/s52/s50/s53/s32/s110/s109/s112/s117/s109 /s112/s61/s32/s52/s48/s48/s32/s110/s109\n/s51/s57/s48 /s52/s50/s48 /s52/s53/s48 /s52/s56/s48/s45/s50/s48/s50\n/s112/s114/s111/s98/s101/s61/s32/s52/s50/s54/s32/s110/s109\n/s32/s77/s67/s68/s32/s40/s120/s49/s48/s45/s50\n/s41\n/s80/s117/s109/s112/s32/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s77/s67/s68/s32/s40/s120/s49/s48/s45/s50\n/s41\n/s112/s114/s111/s98/s101/s61/s32/s52/s48/s48/s32/s110/s109\n/s48/s50/s46/s52/s50/s46/s54/s50/s46/s56/s51/s46/s48/s51/s46/s50\n/s77/s67/s68/s84/s114/s97/s110/s115/s105/s116/s105/s111/s110/s32/s69/s110/s101/s114/s103/s121/s32/s40/s101/s86/s41/s99\n/s98/s97\n/s100\nFIG. 3.Controlling the induced magnetization in SrTiO 3−δby the pump wavelength. a, MCD spectra from\nSrTiO 3−δ(n= 8×1017cm−3) after being optically pumped at λpump=400 nm, 425 nm, and 475 nm ( T=3 K,B=0).\nThe induced magnetization is inverted when λpump=425 nm. b,The induced MCD, detected at λprobe=400 nm and\n426 nm, as a function of λpump. The oscillatory behavior mimics that of the measured MCD spectra s hown in panel\na.c,A contour map of the MCD spectra ( x-axis) at different λpump(y-axis).d,A possible level diagram, showing\na manifold of (at least) three levels optically coupled to a polarizable gr ound state level |g/angbracketright(note these levels could\nalso lie below |g/angbracketright). Circularly polarized optical selection rules allow optical pumping and partial orientation of |g/angbracketright.\nIf|g/angbracketrightis oriented spin-down, the selection rules are reversed. A non-zer o MCD signal (right) is produced when these\nground states are preferentially polarized.\nmagnetization, Fig. 2e shows that detailed magnetic pat-\nterns can be optically written, stored, and optically read\nout in SrTiO 3−δ. The acronyms “LANL” and “UMN”\nwere written using 400 nm pump light, where the circu-\nlar polarization (and hence the magnetization direction)\nwas reversed between adjacent letters. Subsequently, the\nmagnetic patterns were read using raster-scanned MCD\nwithλprobe=425 nm.\nBoth the magnitude and sign of the optically induced\nmagnetization can also be controlled by the wavelength\nof the pump light, providing insight into the underly-\ning nature of the VO-related magnetization. Figure 3a\nshows MCD spectra acquired after illumination with\nλpump=400, 425, and 475 nm. The signals invert when\nλpump=425 nm, indicating an oppositely oriented mag-\nnetization. Fig. 3b shows the induced MCD versus\nλpump, measured at λprobe=400 and 426 nm. The in-\nduced magnetization oscillates with λpump, closely track-\ning the measured MCD spectrum itself (peaks at 400,\n430, and 475 nm, and nodes at 415 and 440 nm). Fig. 3c\ndisplays how the full MCD spectra evolve as λpumpisvaried. It is particularly noteworthy that MCD signals\nat shorter wavelengths are influenced by pump light at\nlongerwavelengths,suggestingamanifoldofopticaltran-\nsitions obeying circularly polarized selection rules, which\nare coupled to a common, optically polarizable ground\nstate as portrayed in Fig. 3d.\nTo confirm that oxygen vacancies play an essential\nrole in optically induced magnetism, we reduced an\nas-received (insulating) SrTiO 3substrate and then re-\noxygenated it, measuring the optical properties before\nand after each step (see Figs. 4a,b). Only when ap-\npreciable VOwere present, as determined by a measur-\nablen, did we observe sub-bandgap absorption at ∼430\nnm and optically induced MCD signals. Following re-\noxygenation, the absorption disappeared (as also seen\nin [8]), the crystal was again electrically insulating, and\nmost importantly the MCD signals vanished.\nWe also investigated the role of excess electrons and\nconcurrent changes in Fermi level by studying SrTiO 3\nsubstrates doped with 0.02% Nb (an electron donor).\nWhile SrTiO 3:Nb exhibits an absorption feature at5\n/s48/s46/s51/s48/s46/s52/s48/s46/s53/s48/s46/s54\n/s32/s85/s110/s97/s110/s110/s101/s97/s108/s101/s100\n/s32/s82/s101/s100/s117/s99/s101/s100/s32/s40/s49/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s41\n/s32/s82/s101/s45/s111/s120/s121/s103/s101/s110/s97/s116/s101/s100\n/s32/s32/s79/s112/s116/s105/s99/s97/s108/s32/s68/s101/s110/s115/s105/s116/s121\n/s84 /s32/s61/s32/s51/s46/s48/s32/s75\n/s66 /s32/s61/s32/s48/s32/s84\n/s52/s48/s48 /s53/s48/s48 /s54/s48/s48 /s55/s48/s48/s48/s52/s56/s49/s50/s32\n/s32/s82/s67/s80/s32/s80/s117/s109/s112\n/s32/s76/s67/s80/s32/s80/s117/s109/s112/s84 /s32/s61/s32/s51/s46/s48/s32/s75\n/s66 /s32/s61/s32/s48/s32/s84\n/s32/s77/s67/s68/s32/s40/s120/s49/s48/s45/s51\n/s41\n/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s85/s110/s97/s110/s110/s101/s97/s108/s101/s100\n/s82/s101/s100/s117/s99/s101/s100/s32/s40/s49/s120/s49/s48/s49/s55\n/s32/s99/s109 /s45/s51\n/s41\n/s82/s101/s45/s111/s120/s121/s103/s101/s110/s97/s116/s101/s100/s48/s46/s51/s48/s46/s54/s48/s46/s57/s49/s46/s50/s32\n/s32/s32/s78/s98/s45/s100/s111/s112/s101/s100/s32/s83/s114/s84/s105/s79\n/s51/s45\n/s32/s78/s98/s45/s100/s111/s112/s101/s100/s32/s83/s114/s84/s105/s79\n/s51\n/s84 /s32/s61/s32/s51/s46/s48/s32/s75\n/s66 /s32/s61/s32/s48/s32/s84\n/s32/s32\n/s52/s48/s48 /s53/s48/s48 /s54/s48/s48 /s55/s48/s48/s48/s53/s49/s48/s32/s84 /s32/s61/s32/s51/s46/s48/s32/s75\n/s66 /s32/s61/s32/s48/s32/s84\n/s78/s98/s45/s100/s111/s112/s101/s100/s32/s83/s114/s84/s105/s79\n/s51/s78/s98/s45/s100/s111/s112/s101/s100/s32/s83/s114/s84/s105/s79\n/s51/s45\n/s32/s32\n/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s97\n/s98/s100/s99\nFIG. 4.Magneto-optical properties of SrTiO 3and SrTiO 3:Nb single crystals after creating and removing\noxygen vacancies. a, The absorptionspectra from an as-received(unannealed) SrTiO 3crystal, againafter annealing\nin UHV to create VO, and again after re-oxygenation to remove VO.b,The corresponding MCD spectra (offset for\nclarity) after optically pumping with RCP (black) and LCP (red) light at 400 nm. Absorption and MCD features\ndisappear after re-oxygenation. c,The absorption of SrTiO 3:Nb before (grey) and after (purple) introducing VO.d,\nThe corresponding MCD spectra (offset for clarity).\n500 nm, optically induced MCD signals were not ob-\nserved, despite electron densities ( n∼8×1017cm−3)\ncomparable to our SrTiO 3−δsamples. However, after re-\nducingthissubstrate(adding VO), both a430nmabsorp-\ntion feature and optically induced MCD were observed\n(Figs. 4c,d). Thus, excess electron density appears to\nplay a minor role in these magneto-optical effects and\ndoes not significantly influence magnetization relaxation.\nThis view is further supported by the observation that\napplied currents (up to 2 mA) have no discernible influ-\nence onthe optically induced magnetization(not shown).\nSeparately, we checked for surface-related MCD artifacts\nby mechanically polishing away several microns of both\nsides of a SrTiO 3−δsample. The optically induced mag-\nnetization was unchanged.\nFinally, Fig. 5 shows MCD spectra at non-zero ap-\nplied magnetic fields, B. As-received SrTiO 3exhibits\nonly a simple, monotonically decaying MCD spectrum\nbelow the bandgap, likely arising from band splitting in\nthe absorption tail. This MCD inverts when Bis re-\nversed, as expected. In contrast, reduced SrTiO 3−δcrys-\ntals show not only this background, but also the same os-\ncillatory MCD signals that appear after optically pump-\ning atB=0 T. Applied magnetic fields therefore polarize\nthese localized complexes in the same manner as optical\npumping. Importantly, at fixed Bthese MCD signals donotdecay, again consistent with a stable ground state\nspin polarization.\nWhile these magneto-optical data cannot precisely\nidentify the localizedcomplex responsibleforthe induced\nmagnetization, some general inferences can be made. All\nSrTiO 3−δsamples – independent of total VOdensity –\nexhibit: i) an additional sub-bandgap optical absorption\ncentered at ∼430 nm (Fig. 1b), ii) an optically induced\nMCD having the same spectral shape (Fig. 1c), and iii)\nthe same temperature dependence of the induced MCD\n(Fig. 1d). These data point to the formation of polar-\nizableVO-related states exhibiting sub-bandgap absorp-\ntion, onecandidatebeingtheFe- VOcomplexespreviously\nstudied in Refs. [8, 10]. Moreover, the extremely long-\nlived nature of the induced magnetization, its activated\nrelaxation dynamics (Fig. 2), and the stability of MCD\nspectra in non-zero Bare consistent with a polarizable\nground state. Finally, the oscillatory MCD spectrum,\nanditsdependenceonpumpwavelength(Fig.3), support\na scenarioin which this ground state is coupled to a man-\nifold of (at least) three levels split by crystal field and/or\nJahn-Teller effects, and spin-orbit coupling. In this pic-\nture, circularlypolarizedopticalselectionrulesapplyand\nsome degree of optical orientation of the ground state\nspin is possible.\nAs noted above, the polarizable VO-related complex6\n/s52/s48/s48 /s53/s48/s48 /s54/s48/s48 /s55/s48/s48/s45/s50/s48/s50\n/s32/s32/s77/s67/s68/s32/s40/s120/s49/s48/s45/s50\n/s41\n/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s110 /s32/s61/s32/s51/s120/s49/s48/s49/s54\n/s32/s99/s109 /s45/s51\n/s84 /s32/s61/s32/s51/s46/s48/s32/s75/s45/s50/s48/s50\n/s32/s32/s48/s32/s84/s32/s32/s32 /s32/s50/s32/s84\n/s32/s32/s52/s32/s84/s32/s32/s32 /s32/s54/s32/s84\n/s32/s45/s54/s32/s84\n/s85/s110/s97/s110/s110/s101/s97/s108/s101/s100\n/s84 /s32/s61/s32/s51/s46/s48/s32/s75\n/s32\n/s32/s77/s67/s68/s32/s40/s120/s49/s48/s45/s50\n/s41\n/s98/s97\nFIG. 5.MCD spectra from SrTiO 3−δin an applied\nmagnetic field. a, As-received (unannealed) SrTiO 3\ncrystals show only a simple, monotonically decaying sub-\nbandgap MCD signal when a magnetic field, B, is ap-\nplied. This background MCD grows with Band inverts\nsign when Bis reversed, as expected. Bis applied along\nthe sample normal, parallel to the optical axis. b,Re-\nduced SrTiO 3−δsamples not only exhibit this back-\nground signal, but also show the oscillatory MCD struc-\nturethatwaspreviouslyobservedunderopticalpumping.\nmay involve other neighboring impurities. Even the\nhighest-quality SrTiO 3crystals currently available con-\ntain a variety of impurity atoms, typically with non-\nnegligible concentrations of tens of parts-per-million\n[8, 26]. Although electron spin resonance studies have\nestablished that Fe and other impurities in SrTiO 3can\nexist in a variety of oxidation states, we do not observe\nanypump-inducedchangesinthetotalopticalabsorption\nor any other such ‘photochromic’ behavior [9]. More-\nover, the magnetometry data and dependence on circu-\nlar pump polarization (Fig. 1) rule out effects due to the\nselective population of defect complexes along different\ncrystal axes (as demonstrated, e.g., for Fe-VOcomplexes\nbylinearlypolarized light [27]). Rather, our studies rep-\nresent a fundamentally different phenomenon: the con-\ntrolled generation of a net magnetic moment with cir-\ncularly polarized light – in zero magnetic field – analo-\ngous to optical pumping and orientation of electron and\nhole spins in classic semiconductor spintronic materials\nlike GaAs, but here with extremely long-lived relaxation\ntimes.\nA cartoon outlining a possible level scheme for this\ncomplex is shown in Fig. 3d. Note that the manifold of\nthree levels could also lie below the ground state. (This\nlatter situation would be analogous to strained n-typeGaAs, where the light-hole, heavy-hole, and split-off va-\nlence bands are split by spin-orbit coupling and crys-\ntal distortion, so that RCP light pumps electrons with\nSz= +1\n2,−1\n2,+1\n2, respectively.) Our SrTiO 3−δMCD\ndata suggest energy splittings of ∼200 meV between\nthese optical transitions, which exceeds the splitting re-\ncently observed in the 3 dconduction bands of SrTiO 3\nsurfaces [28], but may be commensurate with 2 pvalence\nband splitting [29]. Defect complexes can introduce large\nlocal energy scales, particularly if lattice distortions are\ninvolved. It is worth noting that local deformations can\nalsoplayanessentialrolein long-livedormetastablephe-\nnomena, for example persistent photoconductivity from\nDXcenters in III-V semiconductors [30].\nOur data point to exciting possibilities for exploiting\nmagneto-optical effects in perovskite oxides. The ability\nto optically read, write, and store magnetic information\nat technologically relevant wavelengths ( e.g., 405 nm) in\nSrTiO 3−δsuggests new opportunities for device applica-\ntions. This work may also shed new light on possible\nmechanisms for VO-related local moment formation and\nlong-range magnetism at complex oxide interfaces.\nMETHODS\nOxygen-deficient (reduced) SrTiO 3−δsamples . A\nseries of nine 500 µm thick undoped SrTiO 3(100) crystals\nfrom MTI Corp. were annealed in ultra-high vacuum (oxygen\npartial pressure <10−9Torr) at temperatures between\n650-750◦C to promote diffusion of oxygen out of the lat-\ntice [24]. Indium contacts were soldered to the corners of\neach sample in a van der Pauw geometry, and the electron\nconcentration nwas measured using longitudinal resistivity\nand/or Hall studies, from which the approximate VOdensity\nwas inferred. For this study, nranged from ∼3×1012cm−3\nto 8×1017cm−3. Sub-bandgap absorption and optically\ninduced magnetization were only observed when n>1014\ncm−3.\nMCD studies of SrTiO 3−δmagnetization. MCD spec-\ntroscopy was used to obtain a spectrally resolved measure of\nmagnetization in SrTiO 3−δ. MCD detects the normalized dif-\nference between the transmission of right- and left-circul arly\npolarized probe light ( TRandTL, respectively) through the\nsample: ( TR−TL)/(TR+TL). Non-zero MCD signals gener-\nally indicate the presence of time-reversal-symmetry-bre aking\nphenomena ( e.g., magnetization). MCD typically arises in\nzero magnetic field in materials possessing a remnant mag-\nnetization ( e.g., ferromagnets), or in applied magnetic fields\nfrom diamagnetic or paramagnetic materials. A benefit of\nMCD spectroscopy as compared toglobal magnetization tech-\nniques (such as SQUID magnetometry) is that MCD sig-\nnals typically occur in specific wavelength ranges, which ca n\nhelp identify the underlying nature of the magnetic species\nand its coupling to the optical constants of the material.\nMCD is directly related via Kramers-Kronig relations to the\nwell-knownmagneto-optical phenomenonofFaradayrotatio n,\nwhich measures magnetic circular birefringence.\nThe samples were mounted in the variable-temperature\n(1.5-300 K) insert of an 8 T superconducting magnet with di-\nrect optical access. Spectrally narrow, continuous-wave p robe\nlightoftunablewavelengthwas derivedfrom axenonarc lamp7\nand a 300 mm scanning spectrometer. The probe light was\nmechanically chopped, and its polarization was modulated\nbetween right- and left-circular by a photoelastic modulat or\n(PEM). Very low optical powers were used (1-100 nW) for the\nprobe. The probe light was weakly focused through the crys-\ntals (∼1 mm2spot area) and was detected by an avalanche\nphotodiode. TR−TLandTR+TLwere measured using lock-\nin amplifiers referenced to the PEM and the chopper, respec-\ntively. Magnetization was induced and controlled in the cry s-\ntals by a separate, defocused, and independently polarizab le\npump beam (see Fig. 1a). This light was derived from ei-\nther a 405 nm laser diode or from a frequency-doubled and\nwavelength-tunable Ti:sapphire laser. Low pump powers on\nthe order of 5-200 µW were typically used. The unfocused\npumplaser beamglobally illuminatedthesampleswithatypi -\ncalspotareaof13mm2forthe405nmlaser diodeand18mm2\nfor the doubled Ti:sapphire laser.\nSQUID studies of optically induced magnetization.\nA commercial (Quantum Design MPMS) SQUID magne-\ntometer was used to confirm and quantify the optically\ninduced magnetization. 405 nm light with controlled optica l\npolarization was coupled to the SrTiO 3−δsamples using a\nsingle-mode optical fiber. Sample sizes were approximately 3\nmm x 3 mm x 0.5 mm.\nAcknowledgements\nWe thank D.L. Smith, Q. Jia, P. Littlewood and A.V. Bal-\natsky for helpful discussions. This work was supported by\nthe Los Alamos LDRD program under the auspices of the US\nDOE, Office of Basic Energy Sciences, Division of Materials\nSciences and Engineering. Work at UMN supported in part\nby NSF under DMR-0804432 and in part by the MRSEC\nProgram of the NSF under DMR-0819885.\n[1] Ramesh, R. & Schlom, D. G. Whither oxide electronics?\nMRS Bulletin 33, 1006 (2008).\n[2] Cen, C., Thiel, S., Mannhart, J. & Levy, J. Oxide nano-\nelectronics on demand. Science323, 1026 (2009).\n[3] Mannhart, J. & Schlom, D. G. Oxide interfaces–an op-\nportunity for electronics. Science327, 1607 (2010).\n[4] Chambers, S. A. Epitaxial growth and properties of\ndoped transition metal and complex oxide films. Adv.\nMater.22, 219-248 (2010).\n[5] Zubko, P., Gariglio, S., Gabay, M., Ghosez, P. &\nTriscone, J.-M. Interface physics in complex oxides het-\nerostructures. Annu. Rev. Cond. Matter Phys. 2, 141\n(2011).\n[6] Hwang, H. Y. et al.Emergent phenomena at oxide inter-\nfaces.Nature Mater. 11, 103 (2012).\n[7] M¨ uller, K. A. & Burkard, H. SrTiO 3: An intrinsic quan-\ntum paraelectric below 4 K. Phys. Rev. B 19, 3593\n(1979).\n[8] Lee, C., Destry, J. & Brebner, J. L. Optical absorption\nand transport in semiconducting SrTiO 3.Phys. Rev. B\n11, 2299 (1975).\n[9] Faughnan, B. W. Photochromism in transition-metal-\ndoped SrTiO 3.Phys. Rev. B 4, 3623 (1971).\n[10] Wild, R. L., Rockar, E. M. & Smith, J. C. Ther-\nmochromism and electrical conductivity in doped\nSrTiO 3.Phys. Rev. B 8, 3828 (1973).[11] Brinkman, A. et al.Magnetic effects at the interface be-\ntween non-magnetic oxides. Nature Mater. 6, 493 (2007).\n[12] Dikin, D. A. et al.Coexistence of superconductivity and\nferromagnetism in two dimensions. Phys. Rev. Lett. 107,\n056802 (2011).\n[13] Li, L., Richter, C., Mannhart, J. & Ashoori, R. C. Coex-\nistence of magnetic order and two-dimensional supercon-\nductivity at LaAlO 3/SrTiO 3interfaces. Nature Phys. 7,\n762 (2011).\n[14] Bert, J. A. et al. Direct imagining of the coexis-\ntence of ferromagnetism and superconductivity at the\nLaAlO 3/SrTiO 3interface. Nature Phys. 7, 767 (2011).\n[15] Ariando et al. Electronic phase separation at the\nLaAlO 3/SrTiO 3interface. Nature Comm. 2, 188 (2011).\n[16] Moetakef, P. et al.Carrier-controlled ferromagnetism in\nSrTiO 3.Phys. Rev. X 2, 021014 (2012).\n[17] Muller, D. A., Nakagawa, N., Ohtomo, A., Grazul, J. L.\n& Hwang, H. Y. Atomic-scale imaging of nanoengineered\noxygen vacancy profiles in SrTiO 3.Nature430, 657\n(2004).\n[18] Eckstein, J. N. Watch out for the lack of oxygen. Nature\nMater.6, 473 (2007).\n[19] Kalabukhov, A. et al.Effect of oxygen vacancies in\nthe SrTiO 3substrate on the electrical properties of the\nLaAlO 3/SrTiO 3interface. Phys. Rev. B 75, 121404(R)\n(2007).\n[20] Shen, J., Lee, H., Valent´ ı, R. & Jeschke, H. O. Ab initio\nstudy of the two-dimensional metallic states at the sur-\nface of SrTiO 3: Importance of oxygen vacancies. Phys.\nRev. B86, 195119 (2012).\n[21] Pavlenko, N., Kopp, T., Tsymbal, E. Y., Sawatzky, G. A.\n& Mannhart, J. Magnetic and superconducting phases\nat the LaAlO 3/SrTiO 3interface: The role of interfacial\nTi 3delectrons. Phys. Rev. B 85, 020407(R) (2012).\n[22] Lee, M., Williams, J. R., Zhang, S., Frisbie, C. D.\n& Goldhaber-Gordon, D. Electrolyte gate-controlled\nKondo effect in SrTiO 3.Phys. Rev. Lett. 107, 256601\n(2011).\n[23] Lee, Y. et al.Phase diagram of electrostatically doped\nSrTiO 3.Phys. Rev. Lett. 106, 136809 (2011).\n[24] Spinelli, A., Torija, M. A., Liu, C., Jan, C. & Leighton,\nC. Electronic transport in doped SrTiO 3: Conduction\nmechanisms and potential applications. Phys. Rev. B\n81, 155110 (2010).\n[25] Stephens, P. J. Theory of magnetic circular dichroism.\nJ. Chem. Phys. 52, 3489 (1970).\n[26] Son, J. et al.Epitaxial SrTiO 3films with electron mobil-\nities exceeding 30,000 cm2V−1s−1.Nature Mater. 9, 482\n(2010).\n[27] Berney, R. L. & Cowan, D. L. Photochromism of three\nphotosensitive Fe centers in SrTiO 3.Phys. Rev. B 23, 37\n(1981).\n[28] Santander-Syro, A. F. et al.Two-dimensional electron\ngas with universal subbands at the surface of SrTiO 3.\nNature469, 189 (2011).\n[29] Blazey, K. W., Aguilar, M., Bednorz, J. G. & M¨ uller, K.\nA. Valence-band splitting of SrTiO 3.Phys. Rev. B 27,\n5836 (1983).\n[30] Mooney, P. M. Deep donor levels ( DXcenters) in III-V\nsemiconductors. J. Appl. Phys. 67, R1 (1990).8\nSUPPLEMENTAL INFORMATION\nTemperature Dependent Absorption\nAs discussed in the main text, optically induced magnetic\ncircular dichroism (MCD) in SrTiO 3−δdisappeared abruptly\nwhen the temperature was raised above ∼18 K. To deter-\nmine if this coincided with any change in the VO-related sub-\nbandgap optical absorption, we measured the optical densit y\nof both SrTiO 3−δand SrTiO 3samples over a broad temper-\nature range.\n/s98\n/s52/s48/s48 /s53/s48/s48 /s54/s48/s48 /s55/s48/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s32/s79/s112/s116/s105/s99/s97/s108/s32/s68/s101/s110/s115/s105/s116/s121\n/s32/s32\n/s32/s32/s32/s51/s32/s75/s32/s32/s32 /s32/s49/s48/s32/s75/s32/s32/s32\n/s32/s50/s48/s32/s75/s32/s32/s32 /s32/s51/s48/s32/s75/s32/s32/s32\n/s32/s54/s48/s32/s75/s110 /s32/s61/s32/s49/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s52/s48/s48 /s53/s48/s48 /s54/s48/s48 /s55/s48/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54\n/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s32\n/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s82/s101/s45/s111/s120/s121/s103/s101/s110/s97/s116/s101/s100\n/s83/s114/s84/s105/s79\n/s51/s97\nFIG. 6. Supplemental Fig. S1: Temperature depen-\ndent optical absorption for SrTiO 3−δand SrTiO 3.The\noptical density for a, oxygen-deficient SrTiO 3−δandb, re-\noxygenated SrTiO 3changes only minimally as the tempera-\nture is increased from 3 K to 60 K. In particular, the VO-\nrelated sub-bandgap absorption at ∼430 nm remains largely\nunchanged, despitethedisappearance ofmagneto-optical p he-\nnomena at temperatures exceeding 18 K.\nFigures 6a and 6b show the sub-bandgap absorption spec-\ntra for a SrTiO 3−δsample and for the same sample after it\nhas beenre-oxygenated. For bothsamples, theoptical densi ty\nis only minimally altered as the temperature is raised from 3\nto 60 K; the sub-bandgap absorption features that are relate d\nto oxygen vacancies do not vanish above 18 K.\nSQUID studies of optically induced magnetization\nOptically induced magnetization in SrTiO 3−δwas mea-\nsured using a commercial SQUID magnetometer (Quantum\nDesign MPMS) in zeromagnetic field. Polarization-controll ed\n405 nm pump light was coupled to the sample via single-mode\noptical fiber. The end of the fiber was positioned several cen-\ntimeters above the sample, so that the pump light globally\nilluminated the sample. The top panel of Fig. 7 demonstrates\nthe ability to manipulate the magnetization of the sample\nwithpolarized light, justas theMCD resultsshowedinFig. 2 a\nof the main text. As a control, we also tested an unannealed,\nas-received SrTiO 3sample. No optically induced magnetiza-\ntion was observed, in agreement with the MCD results pre-\nsented in Fig. 1c of the main text. The small magnetization\noffset in the data is attributed to the diamagnetic response o f\nSrTiO 3created by the small remnant field ( <10−4T) present\nin the superconducting magnet of the SQUID magnetometer./s48 /s50/s53 /s53/s48/s45/s53/s120/s49/s48/s45/s55/s48/s53/s120/s49/s48/s45/s55/s66/s108/s111/s99/s107/s101/s100\n/s82/s67/s80/s32/s112/s117/s109/s112\n/s32/s32/s77/s97/s103/s110/s101/s116/s105/s99/s32/s77/s111/s109/s101/s110/s116/s32/s40/s101/s109/s117/s41\n/s84/s105/s109/s101/s32/s40/s109/s105/s110/s46/s41/s76/s67/s80/s32/s112/s117/s109/s112/s66/s108/s111/s99/s107/s101/s100\n/s85/s110/s97/s110/s110/s101/s97/s108/s101/s100\n/s84 /s32/s61/s32/s53/s46/s48/s32/s75/s44/s32 /s66 /s32/s126/s32/s48/s32/s84/s45/s53/s120/s49/s48/s45/s55/s48/s53/s120/s49/s48/s45/s55/s48 /s52/s48 /s56/s48 /s49/s50/s48\n/s32/s66/s108/s111/s99/s107/s101/s100/s110 /s32/s61/s32/s54/s46/s54/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s84 /s32/s61/s32/s53/s46/s48/s32/s75/s44/s32 /s66 /s32/s126/s32/s48/s32/s84/s66/s108/s111/s99/s107/s101/s100/s76/s67/s80/s32/s112/s117/s109/s112\n/s82/s67/s80/s32/s112/s117/s109/s112\n/s32/s84/s105/s109/s101/s32/s40/s109/s105/s110/s46/s41/s32\nFIG. 7. Supplemental Fig. S2: SQUID mea-\nsurements of the optically induced magnetic mo-\nment in SrTiO 3−δand in as-received (unannealed)\nSrTiO 3.Pump polarization dependence of the magnetiza-\ntion of SrTiO 3−δ(upper panel) and SrTiO 3(lower panel)\nshows that only SrTiO 3−δexhibits optically induced mag-\nnetization. In a similar manner to the MCD results, the op-\ntically induced magnetization in SrTiO 3−δpersists long after\nthe pump illumination is blocked.\nPump Power Dependent Measurements\nFig. 2b of the main text shows that the equilibration rate of\noptically induced magnetization depends strongly on the in -\ntensity of the pump illumination, and that the induced mag-\nnetization saturates at approximately the same magnitude i n-\ndependentof pump intensity. This behavior is consistent wi th\na material containing a fixed density of ground state levels i n\nthe gap that are optically polarizable and that have extreme ly\nlong spin relaxation times. Fig. 8a shows that the MCD sig-\nnals saturate not just at one wavelength, but over the entire\nMCD spectrum, independent of pump intensity. These data\nfurther support the scenario described in the main text: a\nmanifold of (at least) three circularly polarized optical t ransi-\ntions are coupled to a common ground state, and the buildup\nof polarization in this ground state affects all three optica l\ntransitions simultaneously.\nAs discussed in the main text, even though the magneti-\nzation (MCD) is saturated, the MCD signals themselves are\nsmall: the differential change in transmission between RCP\nandLCPlightisonlyoforder10−3. Thereisverylittlechange\nin thetotaloptical absorption in the 400-500 nm range, as\nshown in Fig. 8b. This observation is consistent with the ab-\nsence of long-lived excitedstates, whose presence would likely\ncreate more significant changes in the overall optical densi ty.\nSlow Temporal Dynamics of Optically Induced\nMagnetism\nThe extremely slow relaxation of optically induced mag-\nnetism in SrTiO 3−δsuggests a potential for magneto-optical\ninformation storage at low temperatures. However, the abil -\nity to induce and control magnetization with polarized pump\nlight also means that optical probes of magnetization (such as\nMCD or Faraday rotation) can potentially perturb the mag-\nnetization. Thus, it is important to recognize and to min-9\n/s98\n/s52/s48/s48 /s52/s53/s48 /s53/s48/s48 /s53/s53/s48/s45/s49/s48/s49/s50\n/s32/s77/s67/s68/s32/s40/s120/s49/s48/s45/s51\n/s41\n/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s80\n/s112/s117/s109/s112/s58\n/s32/s53/s32 /s87 \n/s32/s50/s53/s32 /s87 \n/s32/s53/s48/s32 /s87 \n/s32/s53/s48/s48/s32 /s87 \n/s52/s48/s48 /s52/s53/s48 /s53/s48/s48 /s53/s53/s48/s48/s46/s52/s48/s46/s53/s48/s46/s54/s32/s110 /s32/s61/s32/s49/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s84 /s32/s61/s32/s51/s46/s48/s32/s75\n/s66 /s32/s61/s32/s48/s32/s84/s79/s112/s116/s105/s99/s97/s108/s32/s68/s101/s110/s115/s105/s116/s121\n/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s97\nFIG. 8. Supplemental Fig. S3: Saturation of MCD\nspectra at different pump intensities. a, MCD spectra\natB=0 T measured after optical pumping with 405 nm light\nof different power (5, 25, 50, and 500 µW). The spectra are\napproximately identical, indicating a saturation of the op ti-\ncally induced magnetization. (From each of these spectra th e\nsmall, but non-zero, MCD spectrum acquired without opti-\ncal pumping was subtracted.) b,The corresponding optical\nabsorption spectra.\nimize any influence of the probelight on the magnetization\nwhen measuring the relaxation dynamics of SrTiO 3−δ. One\nway to accomplish this is to use very low intensities of probe\nlight. As Fig. 9a shows, the act of continuously probing the\nMCD (here using λprobe=425 nm) causes an optically induced\nmagnetization to relax more quickly than if probed intermit -\ntently. Unsurprisingly, the relaxation rate is faster when us-\ning higher probe intensity, as the inset displays. Therefor e,\nin both Figs. 9a and b, we used a very weak ( Pprobe= 4 nW)\nprobe beam to measure the magnetization at discrete inter-\nvals. Each point shown in Figs. 9a-c is an average of data\ncollected over tens of seconds with the error bars denoting t he\nstandard deviation (error bars are not shown in Fig. 9b for\nclarity). We investigated temperatures from 20 to 3 K, with\n17.5 K being the fastest magnetization decay that we could\nreliably measure. From 3 to 14 K, probing was performed\nintermittently, while above those temperatures (as given i n\nFig. 2c in the main text) a continuous probe was employed.\nWhether continuously or intermittently probed, each data\ntrace was normalized to unity during the optically pumped\nportion of the curve (the first 100 seconds). A single exponen -\ntial decay, exp( −t/τ), fit every data trace quite well, allowing\nus to extract τas a function of temperature (these values of\nτare shown in Fig. 2d of the main text). τapproximately\nfollows an activated (Arrhenius) behavior for temperature s\nbetween 13 K and 17 K, but deviates significantly from ac-\ntivated behavior below ∼10 K. We note however that owing\nto the extremely long magnetization relaxation times in thi s\nlow-temperature regime, even very tiny amounts of inadver-\ntent light leaking on to the samples could account for this\nbehavior.\nIn a different set of experiments, a SrTiO 3−δsample ( n=\n1×1017cm−3) was magnetized in a 6 T magnetic field. The\nfield was then ramped to zero, and a MCD spectrum was then\nacquired using a 0.4 nW probe. Over the next ≈9 hours, the\nsample magnetization was intermittently probed by MCD (at\n425 nm) for tens of seconds at a time, after which another\nfull MCD spectrum was acquired. Figure 9c shows the aver-\naged results of the intermittent probing, in units of relati ve/s48 /s56/s48/s48/s48 /s49/s54/s48/s48/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48/s32/s73/s110/s116/s101/s114/s109/s105/s116/s116/s101/s110/s116/s32/s80/s114/s111/s98/s105/s110/s103\n/s32/s67/s111/s110/s116/s105/s110/s117/s111/s117/s115/s32/s80/s114/s111/s98/s105/s110/s103\n/s32/s32/s78/s111/s114/s109/s97/s108/s105/s122/s101/s100/s32/s77/s67/s68\n/s40\n/s112/s114/s111/s98/s101/s61/s52/s50/s53/s32/s110/s109/s41\n/s84/s105/s109/s101/s32/s40/s115/s101/s99/s41/s110 /s32/s61/s32/s56/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s80\n/s112/s114/s111/s98/s101/s32/s61/s32/s52/s32/s110/s87 \n/s84 /s32/s61/s32/s49/s48/s32/s75\n/s48 /s49/s48/s48/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48/s32/s52/s48/s32/s110/s87 \n/s52/s32/s110/s87 \n/s48 /s53 /s49/s48/s48/s46/s57/s52/s48/s46/s57/s54/s48/s46/s57/s56/s49/s46/s48/s48/s49/s46/s48/s50\n/s32/s32/s82/s101/s108/s97/s116/s105/s118/s101/s32/s77/s67/s68\n/s40\n/s112/s114/s111/s98/s101/s61/s52/s50/s53/s32/s110/s109/s41\n/s84/s105/s109/s101/s32/s40/s104/s114/s115/s41/s110 /s32/s61/s32/s49/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s84 /s32/s61/s32/s51/s46/s48/s32/s75/s48 /s54/s48/s48/s48 /s49/s50/s48/s48/s48 /s49/s56/s48/s48/s48/s48/s46/s48/s49/s48/s46/s49/s49\n/s32/s32 /s32/s84 /s32/s40/s75/s41/s58/s32 /s32/s32/s32/s32 /s32/s49/s50/s32/s75/s32/s32/s32/s32/s32/s32\n/s32/s53/s32/s75/s32/s32 /s32/s49/s50/s46/s53/s32/s75/s32/s32\n/s32/s55/s32/s75/s32/s32 /s32/s49/s51/s32/s75/s32/s32/s32/s32/s32\n/s32/s49/s48/s32/s75 /s32/s49/s51/s46/s53/s32/s75\n/s32/s49/s49/s32/s75 /s32/s49/s52/s32/s75\n/s32/s32/s78/s111/s114/s109/s97/s108/s105/s122/s101/s100/s32/s77/s67/s68\n/s40\n/s112/s114/s111/s98/s101/s61/s52/s50/s53/s32/s110/s109/s41\n/s84/s105/s109/s101/s32/s40/s115/s101/s99/s41/s110 /s32/s61/s32/s56/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s52/s48/s48 /s53/s48/s48 /s54/s48/s48/s45/s49/s48/s49\n/s110 /s32/s61/s32/s49/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s84 /s32/s61/s32/s51/s46/s48/s32/s75/s32/s116/s32/s61/s32/s48/s46/s48/s32/s104/s114/s115\n/s32/s116/s32/s61/s32/s57/s46/s50/s32/s104/s114/s115\n/s32/s32/s77/s67/s68/s32/s40/s120/s49/s48/s45/s50\n/s41\n/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s99/s97 /s98\n/s100\nFIG. 9. Supplemental Fig. S4: Temporal dynam-\nics of magnetization relaxation in SrTiO 3−δ. a,Con-\ntinuous probing (red trace) and intermittent probing (gree n\npoints) of the MCD signal after optical pumping with RCP\nlight (λpump=405 nm, λprobe=425 nm). The faster decay with\ncontinuous probing shows that the MCD measurement itself\ncan accelerate the relaxation of the optically induced mag-\nnetization. Inset: MCD signal as a function of time after\noptical pumping, using 40 nW and 4 nW of probe power.\nThe higher probe power clearly produces a faster decay of the\nmagnetization. b,Intermittent probing of the 425 nm MCD\nsignal after 405 nm optical excitation, for several tempera -\ntures. The black lines indicate single-exponential fits to t he\ndata.c,Measuring the relaxation of optically induced mag-\nnetization at 3 K over the course of ≈9 hours. Only a small\ndecay of approximately 4% is observed over that time span. A\nprobe power of 0.4 nW was used in order to minimize probe-\ninduced relaxation. d,The full MCD spectrum measured just\nafter magnetizing the sample (black line) and 9.2 hours late r\n(red dashed line) shows that the induced magnetization at 3\nK has barely changed. As with c, 0.4 nW of probe power was\nused to minimize probe-induced relaxation.\ndecay from a starting normalized value of 1. Remarkably,\nthe MCD decays by less than 4% over the course of 9 hours,\ndemonstrating the persistence of the induced magnetizatio n\natB= 0 T. A comparison of the full MCD spectra at t=\n0 and at t= 9.2 hours is given in Fig. 9d; the spectra are\nessentially identical. This ability to induce a long-lived mag-\nnetization using either circularly polarized light oramagnetic\nfield is consistent with a scenario in which magnetization in\nSrTiO 3−δoriginates from polarizable ground state levels with\nan extremely long relaxation time.\nPhotoluminescence Measurements\nPhotoluminescence (PL) was excited using either a He-Cd\nlaser (325 nm) or a frequency-doubled Ti:sapphire laser (tu n-\nable wavelengths from 360-490 nm). The latter permits ei-\nther above-bandgap or below-bandgap excitation. A series o f\noxygen-deficient SrTiO 3−δsamples and an unannealed (as-\nreceived) SrTiO 3sample was measured. For the case of 32510\nnm (above-gap) excitation, all samples showed a very broad\nand very similar PL band peaked well below the band-edge\n(see Fig. 10a), consistent with prior results and likely due to\nself-trapped excitons or defects. No significant difference s be-\ntween oxygen-deficient and as-received samples was observe d\nin the PL.\nFigure 10b shows the marked difference in PL between\nabove- and below-bandgap excitation, for both as-received\nSrTiO 3(top) andfor SrTiO 3−δ(bottom). Here, the PL inten-\nsities for each sample were scaled by the integration time an d\nthen normalized to the PL peak of the unannealed SrTiO 3\nsubstrate. For both samples, the below-bandgap PL is neg-\nligible when compared to above-bandgap excitation, and no\nsignificant differences between the samples are observed.\n/s50/s48/s48 /s52/s48/s48 /s54/s48/s48 /s56/s48/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48/s32/s80/s76/s32/s73/s110/s116/s101/s110/s115/s105/s116/s121/s32/s40/s97/s114/s98/s46/s32/s117/s110/s105/s116/s115/s41\n/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41/s32/s54/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51\n/s32/s51/s120/s49/s48/s49/s54\n/s32/s99/s109/s45/s51\n/s32/s49/s120/s49/s48/s49/s53\n/s32/s99/s109/s45/s51\n/s32/s85/s110/s97/s110/s110/s101/s97/s108/s101/s100/s112/s117/s109/s112/s61/s32/s51/s50/s53/s32/s110/s109\n/s32/s32/s32/s32/s84 /s32/s61/s32/s49/s48/s32/s75\n/s48/s46/s48/s48/s46/s53/s49/s46/s48\n/s32/s32/s32/s32/s32/s32 /s32\n/s112/s117/s109/s112/s58\n/s32/s51/s55/s52/s32/s110/s109\n/s32/s51/s57/s48/s32/s110/s109/s85/s110/s97/s110/s110/s101/s97/s108/s101/s100\n/s120/s49/s48/s51\n/s51/s48/s48 /s52/s53/s48 /s54/s48/s48 /s55/s53/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48\n/s120/s50\n/s120/s49/s48/s51\n/s32/s87 /s97/s118/s101/s108/s101/s110/s103/s116/s104/s32/s40/s110/s109/s41\n/s32/s32/s84 /s32/s61/s32/s51/s46/s48/s32/s75\n/s110 /s32/s61/s32/s54/s120/s49/s48/s49/s55\n/s32/s99/s109/s45/s51/s98 /s97FIG. 10. Supplemental Fig. S5: Photolumines-\ncence (PL) from SrTiO 3−δusing above- and below-\nbandgap excitation. a, Using weak above-bandgap excita-\ntion (325 nm), normalized PL spectra from substrates with\ndifferent VOdensities shows that the PL remains largely un-\naffected by oxygen removal from the lattice. b,Comparison\nof PL from an unannealed, as-received sample and an oxygen-\ndeficient sample, for weak excitation both above-bandgap\n(374 nm) and below-bandgap (390 nm). Below-bandgap exci-\ntation generates negligible PL relative to above-bandgap e x-\ncitation. Regardless of excitation wavelength, the PL from\nunannealed and from reduced SrTiO 3looks qualitatively sim-\nilar."    },    {        "title": "1402.0540v1.A_Physical_Model_of_a_Smart_Magneto_Composite_Material_and_the_Methodology_of_Research_of_the_Elastic_Properties_of_Nano_Magnetic_Composite_Materials.pdf",        "content": "A Physical Model of a Smart Magneto-Composite Material and  \nthe Methodology of Research of the Elastic Properties of Nano  \nMagnetic Composite Materials\nIgor DIMITROV      Ulaş DINÇ\nBAHÇEŞEHİR HIGH SCHOOL FOR SCIENCE and  \nTECHNOLOGY , ISTANBUL, TURKEY\nResearch Duration of the Project\nStarted: October 2011\nFinished: October 2012\n1A Physical Model of a Smart Magneto-Composite Material and  \nthe Methodology of Research of the Elastic Properties of Nano  \nMagnetic Composite Materials\nIgor DIMITROV         Ulaş DINC\nBAHÇEŞEHİR HIGH SCHOOL FOR SCIENCE and TECHNOLOGY , \nISTANBUL, TURKEY\n2A Physical Model of a Smart Magneto-Composite Material and the  \nMethodology of Research of the Elastic Properties of Nano Magnetic  \nComposite Materials\nList of Illustrations\nFig. 1. The ground state of a 200x200-dipole system ………………………………...….10\nFig. 2. The gound state of a 60x60 dipole system in a magnetic field…………………....11\nFig. 3. The gound state of a 40x40 dipole system …………………………………….....12\nFig. 4. The gound state of a 10x10 dipole system …………………………………….....13\nFig. 5. The gound state of a 2x2 dipole system ……………………………………….…14\nFig.6  The experimental set up for force measuring……………………………….……..17\nFig.7. The Sketch of the experimental set up for force measuring…………………….…17\nFig.8. The spring force as a function  of compression……………………………….…..18\nFig.9. The spring force and the spring plus magnetic force as a function  of \ncompression………………………………………………………………………………19\nFig.10. The schem of the experimental set up for magnetic force measuring……………20\nFig.11. The magnetic force as a function  of distance between magnets………………...20\nFig.12. The magnetic force constant   as a function  of distance between magnets…...…22\nFig. 13.The magnetic field of a magnetic dipole and a short cylindrical permanent\nmagnet………………………………………………………………………………….…24\n3 List of Symbols\nε: energy\nijε: the energy between i-th and j-th dipole\nRij, rij: the distance between i-th and j-th dipoles\nmi, mj, m: magnetic moment\nµ0: magnetic permitivity of the free space\nµΒ                    Bohr magneton\nB,b: magnetic field\nE,H,h: energy\nR0: the nearest neighbor distance\na: the nearest neighbor distance\nτ::  torque \n0/E Eα=\nF: force\n4a Eβ=\n3γ β=\nk: elastic constant\nkeff:effective elastic constant\nk(a):magnetic elastic constant\nks: elastic constant of a spring\ne: unit vector\n4Abstract\nIn this study, we show that any system consisting of magnetic dipoles forming ordered or  \ndisordered configurations can be simplified to a form mathematically equivalent to a  \nsystem consisting of two magnetic dipoles. It is shown that the energy of all kinds of  \nmagnetic dipole systems can be written as  3Eaβ=−, where a is the nearest distance  \nbetween the dipoles and β is a certain constant depending on the magnetic moments of  \ndipoles  and  configuration.  Using  this  fact  we  model  any  nano-magnetic  composite  \nmaterial  by  a  simple  two-magnetic  dipole  system.  Then  we  experimentaly  and  \ntheoreticaly show that under certain conditions the elastic properties of the composite  \nmaterial can be changed using exernal magnetic field which leads to creation of smart  \ncomposite materials.\n5Table of Contents \n1.Introduction.............................................................................................................................7\n2.The Model of a Magnetic Dipole System …………………………………………...…...…9\n3. Investigation of the Contribution of Magnetic Forces to Stiffness\n   of the Composite Nano-magnetic Material………………………………………..….........16\n3.1. The method of Investigation……………………………….……….….………...16\n            3.2 The experiment……………………………………………….……..……………17  \n4. Results and Discussions ……………………………………………………………………23\n5. Conclusion…………………………………………………………………………...…….25\nReferences……….………………………………………………..…………………………..26\n6A  Physical  Model  of  a  Smart  Magneto-Composite  Material  and  the  \nMethodology of Research of the Elastic Properties of Nano Magnetic  \nComposite Materials\n1. Introduction\nSince their synthesis in 1964 [1] suspensions of magnetic nanoparticles (diameters of the  \nmagnetic core ≈10–50 nm) in nonmagnetic carrier liquids have been called magnetic  \nfluids  (ferrofluids,  ferrocolloids),  and  their  investigation  has  become  an  independent  \nbranch of science. Particles in ferrofluids are made of Fe, Co, Ni, and their oxides. The  \nsize of the magnetic particle is smaller than the critical size of the monodomain state for  \nthe  latter  ferromagnetic  and  antiferromagnetic  materials.  Therefore,  each  particle  is  \nhomogeneously magnetized. Its magnetic moment is proportional to the particle volume  \nand the saturation magnetization of the bulk material. For nonelectrolyte carrier liquids, a  \nsteric coating of magnetic cores is used to prevent the coagulation, with an oleic acid  \n(commonly)  taken as a stabilizer  [2] . Strong response to an external  magnetic  field,  \nrepresented by ferrocolloids in combination with a liquid state, gives rise to numerous  \napplications of magnetic fluids in engineering and natural science. \nIn  general,  if  the  dimension  of  a  magnetic  particle  is  reduced  drastically,  to  a  few  \nnanometers, the domains in the particle merge into a single one, creating what is known as  \na single-domain particle and the total magnetic moment is the sum of all moments of the  \natomic particle. Therefore, the total magnetic moment of a single-domain nanoparticle can  \nbe about 10,000 times greater than the atomic moments of the constituent atoms. The  \nbehavior of such single-domain nanoparticles can be very complex because the magnetic  \nmoment of each particle disturbs the behavior of neighboring particles. In general, this  \ninteraction between particles serves to align the magnetic moments reducing the energy of  \nthe  system.  It  is  commonly  believed  that  the  magnetic  behavior  of  a  magnetic  \nnano-composite material is of super paramagnetic type.\nSimilar to ferrofluids, there has recently been renewed interest in the magnetic properties  \nof nano-composite materials that consist of very fine magnetic particles embedded in a  \n7metallic or dielectric nonmagnetic host [3-9] and in nano-composite materials that consist  \nof  multi-layers  with  very  thin  magnetic  layers  [10-11],  which  exhibit  certain  \nsuper-paramagnetic  properties,  too.  The  complexity  of  the  magnetic  properties  of  \nnano-composite  magnetic  materials  is  basically  due  to  the  dual  nature  of  magnetic  \ndipole-dipole  interactions:  if  the  dipoles  are  along  a  line  their  magnetic  moment  \norientation is along the line (ferromagnetic ordering), however, when two dipoles are  \nparallel then their magnetic moments are anti-parallel (anti-ferromagnetic ordering). The  \nsituation is much more complicated in a three dimensional ensemble of magnetic dipoles. \nThe  electromagnetic  properties  of  nano-composite  materials  can  be  very  unusual  \ncompared to common materials and have been explored in many different branches of  \nmaterials science engineering. At the same, it is commonly believed that the magnetic  \ninteraction is, not enough compared to the elastic forces of the host non-magnetic material  \nin  order  to  make  significant  contribution  to  mechanical  properties  of  the  composite  \nmaterial. In fact it depends on the nature of the host material, because starting with fluid  \nhost  materials  and  going  up  to  solid  host  ones,  the  magnetic  interactions  can  play  \nsignificant role in forming of the mechanical properties of the composite nano magnetic  \nmaterials. \nThe aim of the present study is to show that at certain conditions, namely in the case of  \nstrong magnetic dipole interactions between the nano particles, compared with the elastic  \nproperties of the host material, magnetic interactions can contribute considerably to the  \nelastic properties  of the compound material. Though a real nano-composite magnetic  \nmaterial is a very complicated system from point of view of dipole-dipole interactions,  \nany dipole system, being in its stable state, is equivalent to a single dipole system. This  \nmakes  it  possible  to  investigate  the  elastic  behavior  of  a  nano  composite  magnetic  \nmaterial by means of physical modeling of simple two magnetic dipole system formed by  \nsmall permanent magnets and a simple string. This investigation is a preliminary theory  \nfor more complicated smart nano composite materials. \n82. The Model of a Magnetic Dipole System \n In this section, we use results obtained by different authors (for example, [12-13]) about  \nthe structure of a magnetic dipole system. The interaction energy between two point  \ndipoles occupying lattice sites j, and i is written as:\n()()()033\n4ıj j ij i ij j i\nijrµε\nπ = − × × − × m e m e m m (1)\nThus, the energy of the system is \n()()()03, 1 11324N N\nj ij i ij j i ii j iijj iHrµ\nπ= =≠ = − × × − × − ∑ ∑m e m e m m B m (2)\nHere, mi,  ri, µ0, B is  the dipole moment, the position vector of the i-th lattice site and \npermeability of free space, and the external magnetic field, respectively;  ijijrrr−=, \nijijijrrre−=.  It is convenient to present Eq,(2) in a dimensionless form: if we assume  \niBinemµ=and ijijRrr0= with r0 the nearest neighbor distance we get hEH0= where \n()()() 3, 1 11 132N N\nj ij i ij j i ii j iijj ihR= =≠ = − × × − × − ∑ ∑e e e e e e b e, (3)\n2 220 003 30 04 4BmE n\nr rµ µ µ\nπ π= = ; 0EBbBµ= (4)\nE0 is the energy unit, n is an integer number and µ B is the Bohr magneton. The first term  \nin the above energy equation represents the sum of all pairs of dipole-dipole interaction  \nenergies. The second term is the energy of the aligned dipoles in the direction of the  \napplied magnetic field. At zero temperature, the equilibrium state of the system is the state  \nwith H being at minimum. At equilibrium the torque acting on any dipole,\n ()[]\n\n\n\n\n+−⋅×=∑\n≠=beeeeeτN\nijjjijijjijiiR1331(5)\nmust be equal to zero. It is possible to find out the minimum energy configuration of the  \nsystem, i.e. to find its ground state, by using numerical methods. According to Bolcal  \net.al.[12], the ground state of line of diploes is equal to\n 3112 2.404\njh N Nj∞\n== − = −∑ (6)\n9thus, the energy per dipole is -2.404  (in E0 units).  At the same time, these authors found  \nthat the energy of a simple square lattice model or simple cubic lattice model is almost the  \nsame :-2.550 and -2.679 per dipole, respectively. For an infinitive simple square lattice  \nmodel it was found that the ground state energy of the system per dipol is 2.549436ε= −. \nSome of these models are shown in the figures below. According to Fig.1, the magnetic  \nstructure of the system consists of anti-ferromagnetic domains with anti-ferromagnetic  \ndomain walls. \nFig.1 Projection of the dipole moments on the  x-y plane of a 200x200 dipoles at zero  \ntemperature and in a zero magnetic field. The unit distance along the x and y-axis is the \ndouble lattice parameter of the model.\nFig.2 demonstrates the behavior of the 60x60-dipole model in the presence of an external  \nmagnetic  field.  In  the  example  the  magnetic  field  is  along  the  x-direction  and  its \nmagnitude b=1. Fig.3 and 4 present a 40x40 and 10x10 dipole systems, respectively, in  \nmore detailed form. \n10Fig.2 Projection of the dipole moments on the x-y plane of a 60x60 dipoles model at zero  \ntemperature and with the magnitude of magnetic field b=1, applied along the x-axis. The  \nunit distance along the x and y-axis is the double lattice parameter of the model.\n11 \n0510152025303505101520253035\nXYThe ground State of the Square 40x40 Dipole Model: E=-2.5335\nFig. 3. The gound state of a 40x40 dipole system \n1201234567890123456789\nXYThe Ground State of the Square 10x10 Dipole system: E=-2.4379\nFigure 4. 10x10 magnetic dipole system at its ground state.\n \nHere we show that even a single pair of two magnetic dipoles can model the behavior of  \nthe large dipol system. Let us now first consider the two-dipoles model the first dipole to  \nbe at the origin of the coordinate system, and the other at point (0,1), i.e.\n1\n2 2\n12=\n=\n=m i\nm e\ne i. (7)\nAccording  to  Eq(7)  the  torque  acting  on  the  second  dipole,  is  2 2 2= ×τ e b,  where \n() () 2 1 12 12 1 1 13 3 2   = × − = × − =   b m e e m e i i e i  is the magnetic field at the position of  \nthe second dipole. Thus, the torque equals to 2 22= ×τ e i.  Therefore, the stable state of  \nthis system is when 2 22 0= × =τ e i, i.e., when2 1= =m m i, thus the configuration energy  \nof the system is \n()()() 2 2 1 2 1 23 2ε= − × = − × × − × = −  m b m i m i m m (8)\nNow, let us consider a 2x2-dipole system. The configuration of the model obtained by the  \nnumerical calculations by Bolcal et.al.[12] is shown in Fig.5.\n13-0.500.511.5-0.500.511.5Ground state of 2x2 square dipol sistem\nXY\nFig. 5. The ground state configuration of the 2x2-dipol system \n That this is the ground state of the model, we can show analytically in a straight way.  \nAccording to Fig.5: \n1 1\n2 2\n3 3\n4 41(1, 1); (0,0)\n2\n1(1,1); (1,0)\n2\n1( 1,1); (1,1)\n2\n1( 1, 1); (1,0)\n2= − =\n\n= =\n= − =\n\n= − − =m r\nm r\nm r\nm r(9)\nThen, the magnetic field at the position of the first dipole is \n() () ()\n() ()()2 2 2 3 3 3 4 4 4 3 2 4\n1 5 3 5 3 5 3\n2 2 3 3 4 4\n1 13 3 3\n1 1 6 2 1 6 22 2 2 ( )2 2 2 2 2r r r r r r     × × ×= − + − + − ⇒ ÷  ÷  ÷ ÷  ÷  ÷     \n   + += − + − + − = − =  ÷  ÷ ÷  ÷   m r r m r r m r r m m mb\nb i j i j i j i j m       \nConsequently, \n1 11 6 2\n2 2 += ÷ ÷ b m (10)\nFollowing the symmetry: \n141 1\n2 2\n3 3\n4 41 6 2\n2 2\n1 6 2\n2 2\n1 6 2\n2 2\n1 6 2\n2 2 += ÷ ÷ \n += ÷ ÷   += ÷ ÷ \n += ÷ ÷ b m\nb m\nb m\nb m(11)\nConsequently, any dipole of the system is along the magnetic field that is the system is at  \na stable equilibrium and its energy is equal to \n4\n.\n11 1 6 2 1 6 222 2 2 2i i\niE\n= + += − × = − = −  ÷ ÷ ∑m b (12)\nThen, the energy per dipole is \n1 6 21.67678\n4 2ε+= − ≈ − (13)\nBolcal et. al. [12], showed that if the model size is of order of 10 units and higher, the  \nenergy per dipole of the model is quite close to that of the infinitive, i.e. it is realistic to  \nextrapolate the properties of  a finite model to that of an infinitive one.  Therefore,  the \nmagnetic  energy  of  any  dipole  system,  per  a  dipole  can  be  presented  in  general  \ndimensional form as  \n0E\nEα= −, where  20034mEaµ\nπ=,  a is the nearest-neighbor distance  \nbetween  the  dipoles,  and  α is  a  dimensionless  parameter  which  depends  on  the  \ndimension, type, size and shape of the sample nano-magnetic composite material. It is  \nimportant to underline that α does not differ so much for different dipole configuration  \nand its value is nearby 2. Thus, the energy per dipole can be written as: \n203 34mEa aµβαπ= − = − ,   (14)\n15here20\n20\n2 20 0\n20\n202          - two dipoles4\n1.68     - four dipoles at the corner of a square4\n2.404   - infinitive line of dipoles4 4\n2.55     - infinitive square lattice of d ipoles4\n2.68     4m\nm\nm m\nm\nmµ\nπ\nµ\nπ\nµ µβ απ π\nµ\nπ\nµ\nπ= =\n- infinitive cubic lattice of  dipoles\n\n\n\n\n\n\n\n\n\n\n\n\n\n \ndepends on configuration of dipoles and their magnetic moments. Therefore, the elastic  \nproperties of a large magnetic dipole system can be modeled by a single pair of two  \ndipoles, which we use in our next step of the investigation. \n3. Methodology of Investigation of the Contribution of Magnetic Forces to Stiffness\nof the Composite Nano-magnetic Material\n3.1 The method of the investigation \nHere  we  assume  that  combination  of  the  nearest  distance  between  the  magnetic  \nnano-particles and their magnetic moment yields enough strong magnetic interaction to  \ncontribute to the mechanical properties of the compound material. As we proved in the  \nprevious section, the energy per dipole for all magnetic dipole systems can be presented in  \na form of Eq.(14). Therefore, we investigate the elastic properties of a simple physical  \nmodel, which consists of two permanent magnets and a spring as shown in the figure  \nbelow. Before going into experimental details, let us first shortly present the method of  \ncalculation of the elastic coefficient of a ‘magnetic dipole string’, made by two magnetic  \ndipoles. For simplicity, we make use of only repealing magnetic interactions. According  \nto Eq.(14) the magnitude of the force acting between two dipoles is\n4 43 3dE EFda aa aβ γ= = = =  (15)\nThus, the magnitude of the elastic coefficient corresponding to this ‘string’,\n2 202 5 54 3( )m dF d Ek adada a aµγ α\nπ= = = = , (16)\n16is a function of the distance  a  between the nearest neighbor dipoles in the composite  \nmaterial. At the same time, the effective elastic constant of the composite material will be  \nsuperposition of the elastic constants of the non-magnetic host material and that of the  \nmagnetic force. For our physical model, when the two permanent magnets repeal each  \nother, the effective elastic coefficient will be a sum of  the conventional elastic constant  \n(that of the host  material, here the string) and the magnetic one. Supposing that the  \nmagnetic interaction does not influence the elastic one, the effective elastic coefficient of  \nthe physical ‘dipole-string’ model well be \n2053( ) ( )eff s smk a k k a kaµα\nπ= ± = ± , (17)\nhere ks is the spring elastic constant. \n3.2 The experiment \nThe experiment is reduced to measuring a force: in one of the cases this is the spring  \nforce, in the other two cases, the force is magnetic or it is combination of spring and  \nmagnetic ones. The experimental set up used in all experiments is shown in Figure 6. The  \nmain part of the experimental set up is the electronic weight scale, which has a high  \naccuracy  strain-gauge  sensor,  providing  accuracy  measurement  of  the  force  within  \n310N−±. In order to observe the behavior of the physical model for short and long  \nseparetions of the magnets we investigated one short, 12 mm long, and enough stiff spring,  \nand  one 17mm long and more soft non-magnetic spring. \nFig.6 The experimental set up for force measuring\n17The  schematic  illustration  of  the  experimental  set  up  is  shown  in  Figure  7.  \nFig.7. The sketch of the experimental set up for force measuring. The numbers indicate  \nthe following: (1)Base; (2)Scale; (3)Transparent cylinder with a small cylindrical cavity  \n(5mm  diameter);  (4)Spring  or  neodymium  magnets  (In  the  figure  just  the  spring  is  \nshown); (5)Height adjuster; (6)Small rod used for pressing spring and magnets; (7)Upper  \nplatform with adjustable height.\n3.2.1 Measuring of Elastic Constant of Springs\nFirst, we determine the elastic constant of the spring in the following way. When turned  \n1800, the adjuster moves 1mm along the shaft.  This enables a precise control of how  \nmuch spring is compressed. When the spring is compressed, the scale reads corresponding  \nvalue in grams. When multiplied with gravitational acceleration we easily obtain the  \nforces on the spring. The initial length of the spring is 12 mm. The graph obtained from  \nthis experiment is shown in Fig.8. \n18Fig.8. The spring force F (in mN) as a function  of compression, X,  of the 12mm-long  \nspring (in mm)\nCalculating the average slope of of the experimental curve of the elastic force as function  \nof the stretch of the string, we found the elastic coefficient of the spring to be equal to  \n569.56( / )sk N m=. \nBy the same way we investigated the 17mm-long soft non-magnetic spring. The result is  \npresented in Fig.9. According to this experiment, the spring constant was calculated to be  \napproximately 367.4( / )sk N m=\n19Fig.9. The spring force  ( )F X and the total, spring plus magnetic, force  ( )mF Xas a \nfunction  of compression  X of the 17mm-long non-magnetic spring\n3.2.2 Measuring of Magnetic Interaction Force between the Magnets\nThe next step of our experiment  is to determine  the law of interaction  between the  \npermanent magnets used in the investigation. The magnetic  forces were measured with  \ntwo neodymium magnets, one larger in size and with stronger magnetic properties. The  \nexperimental system was set up as shown in  Fig.10. \nFig.10. The sketch of the experimental set up for magnetic force measuring\n20The methodology in data collection remained the same as for the spring force measuring.  \nThe graph obtained from this experiment is shown in Fig.11.  \n                                                                                                                                             F i\ng.11. The magnetic force F as a function  of distance between magnets, x\nAt large distances, these magnets behave like magnetic dipoles, however, the interaction  \nbetween them does not follow the exact law of  dipole-dipole interaction, Eq.(14), because  \nthese magnets are not exactly point-like dipoles, and as a result, the law of interaction will  \ndiffer from Eq.(15). If we take the data measured for both long and short distances, the  \nlaw of interaction differs from Eq.(15) in the power of the exponent: for a pure dipole it is  \n-4, while the experimental one the exponent is between -2 and -3. Therefore, we fit the  \nexperimental result according to the equation  \n0 0nF x\nF xγ− = ÷\n  (18)\nwhere n and β are dimensionless parameters of the model to be fitted to the experimental  \ncurve,  309.81 10F N−= ×,  01x mm=are  units  for  force  and  distance,  respectively.  \n21According to the experimental data the average values of these parameters are 218100γ= \nand 2.08n=. Thus, for the magnitude of the ‘magnetic’ elastic constant we get \n1\n100( )( )n\nn dF x F xk x k n n x ndx x xγ γ− −\n− − = = = = ÷\n , (19)\nhere 0001( / )Fk N mx= =is the unit for elastic constant, and the distance x is measured in \nmm. As it should be, this constant is a function of distance. Its graph is presented in  \nFig.12. Accuracy of the experimentally obtained parameters ( , ,  and )n kγis within 8%.\n \nFig.12. The magnetic force konstant  ( )( )dF F xk x ndx x= =  as a function  of distance  \nbetween magnets, x\n3.2.3 Measuring of Magnetic and Elastic Interaction Forces in the Compound \nSpring-Magnets Sysytem\nIn this  section, we investigate  the elastic  properties  of the compound string-magnets  \nsystem, which models the real nano-composite magnetic materials. In the model, the most  \n22important problem is whether the principle of superposition of elastic and magnetic forces  \nworks. The principle of adding the magnetic and elastic  forces in the experiment  is  \nobeyed much better for non-magnetic springs then for magnetic ones. This is so, because  \nthe  magnetic  springs,  due  to  their  magnetization,  contribute  to  some  extend  to  the  \ninteractions in the magnet-spring system. Therefore, we check the superposing of the  \nelastic  and  magnetic  forces  on  the  non-magnetic  spring.   For  this,  we  put  the  \nnon-magnetic spring between the magnets and measure the force acting on the weight  \nscale.  The  experiment  done  confirmed  the superposition  of the  elastic  and  magnetic  \nforces.  For  example,  when  the  separation  between  the  magnets  was  14 mm (i.e.  the \ncompression of the spring was 3 mm), the measured force was 1590( mN). For the same \ndistance, according to Fig.9, the elastic force is 990( mN), while, the calculated magnetic  \nforce is approximately 530(mN), i.e. quite good consistence is observed for the principle  \nof superposition  of  elastic  and  magnetic  forces. Similar  result  is  observed  for other  \ncompressions of the nonmagnetic spring. Unfortunately, with the available nonmagnetic  \nspring,  we  could  not  go  beyond  the  minimum  (12 mm)  separation  between  magnets  \nbecause this distance corresponded to the maximum compressing of the spring used in the  \nexperiment, as well as there was an upper limitation for the separation, which was equal  \nto the free length of the spring, equal to 17 mm. In this range for separation of magnets the  \nslope of the magnetic curve cannot be calculated with a good accuracy (the force varies  \nslowly  for  these  separations),  while  force  itself  is  measured  enough  accurate.  The  \nexperimental  curve  obtained  for  the  force  as  a  function  of  the  compression  of  the  \nspring-magnets system is shown in Fig.9. In this region of compression of the system the  \ncontribution of the magnetic forces to the effective elastic constant is considerable, about  \n35%.\n4. Results and Discussions\nWe have proposed a realistic physical model for investigation of the elastic properties of a  \ncomposite ferromagnetic material. The physical model consists of two magnetic dipoles  \nand a string. The physical model represents adequately the stiffness properties of a real  \nnano magnetic composite material because a system consisting of large number of dipoles  \nmathematically  is  equivalent  with  a  system  of  two  magnetic  dipoles  only.  In  our  \nexperiment,  instead  of  a  real  magnetic  dipole,  which  magnetic  field  is  presented  in  \n23Fig13.a, we have used a short cylindrical magnet, which magnetic field is shown in  \nFig.13.b.  The  reason  is  that  more  massive  is  the  magnet  the  grater  is  the  force  of  \ninteraction and the higher accuracy of the experiment. \n \n          \nFig. 13. The magnetic field of a magnetic dipole and a short cylindrical permanent magnet\nFrom  Fig.13,  it  becomes  evident  that  the  shapes  of  these  magnetic  systems  are  \nmathematically different, therefore the force of acting between the magnets used in our  \nexperiment does not follow the form of the magnetic force of dipole, Eq.(15). However,  \nwhen  the  distance  between  the  magnets  becomes  some  multiples  of the  size  of  the  \nmagnets, the law of magnetic interactions tends to that of Eq.(15), i.e. the power of the  \nexponents start tending towards 4. \nThe contribution of the magnetic interactions to the stiffness of the magneto-composite  \nmaterials expressed trough the effective stiffness coefficient, 54( ) ( )eff s sk a k k a k\naγ= + = +\n,  depends  basically  on  the  nearest  distance  between  the  dipoles  and  the  coefficient  \n2034mµγ απ=. This coefficient accounts for many factors, such as dimension, size, and  \nshape of the composite material, as well as the magnitude of the magnetic moments of  \ndiploes  constituting  the  compound  material.  If  the  magnetic  forces  were  forces  of  \nattraction then the effective elastic coefficient were 54( ) ( )eff s sk a k k a kaβ= − = − . Thus, \nvarying the above-mentioned factors it is possible to design a composite material of  \ndesired  stiffness.  Applying  of  external  magnetic  field  will  change  parameter  α \nresponsible for the magnetic configuration of the dipoles, which will change mechanical  \nproperties of the material. Indeed, the stiffness of the host material is very important, for  \n24example if the stiffness of the host material is much grater of the contribution of the  \nmagnetic force, as it is true for very hard solid materials, then controlling the mechanical  \nproperties of a composite material does not work. However, if the host material is soft  \ncomparing to magnetic  interaction,  as  it is valid  for ferrofluids, then controlling  the  \nmechanical properties via the magnetic field would become a powerful tool for creation of  \nsmart composite materials. In our physical model the combination of the used magnets  \nand the soft spring leads to the class of soft host materials in the compound, the increase  \nof the elastic constant was about 35%. \n5. Conclusion\nThe elastic properties of nano-magnetic composite materials can be modeled by a pair of  \ntwo magnetic dipoles separated by a string representing the elastic properties of the host  \nnon-magnetic  material.  Depending on the  elastic  properties  of the  host material,  the  \nmagnetic dipole-dipole interactions can significantly change the elastic properties of the  \ncompound materials especially when the host material is not stiff enough. For these types  \nof materials,  the  elastic  properties  of  the  compound  can  be  modified  by an applied  \nexternal magnetic field. The magnetic interactions  between the magnets, used in our  \nphysical model, changed the elastic constant of the spring used in the experiment about  \n35%. This contribution can be varied by using different magnets or springs.\nWhen  designing  a  smart  magneto-composite  material  we  should  first  calculate  the  \nstiffness constant of the magnetic dipole forces following the expression for the stiffness  \nof the magnetic dipole forces, Eq.(16):\n2 20 05 53( ) 2m mk aa aµ µα\nπ= ≈\nIf the combination between the magnetic moment of nano particles ( m) and the nearest \ndistance (a) between them gives stiffness comparable of that of the host material ( ks), then \nit is possible to design a smart material. Because, by applying magnetic field we can  \nchange the configuration of the dipole system, thus to change coefficient α in Eq.(16) and \ngetting desirable effective stiffness coefficient 2053( )eff smk a kaµα\nπ= ± for the compound \nmaterial. This coefficient can be done even zero, like for liquids. \n2526References\n[1] E. L. Resler and R. E. Rosensweig, AIAA J. 2, 1418 (1964).\n[2] E. Blum, M. M. Maiorov, and A. Cebers, Magnetic Fluids, Walter de Gruyter, Berlin,\n(1997.)\n[3] M.F. Hansen, S.M οrup, J. Magn. Magn. Mater. 184, 262 (1998).\n[4] J.L. Dormann, L. Bessais, D. Fiorani, J. Phys. C 21, 2015 (1988).\n[5] S. Morup, E. Tronc, Phys. Rev. Lett. 72, 3278 (1994).\n[6] J.L. Dormann, D. Fiorani, E. Tronc, Adv. Chem. Phys. 98, 283 (1997).\n[7]  J.L.  Dormann, D.  Fiorani,  E.  Tronc ,  J.  Magn.  Magn.  Mater.  202, \n251(1999).\n[8] F.C. Fonseca, G.F. Gya,R.F. Jardim, R. Muccillo, N.L.V. Carreno, E.  \nLongo, \nE.R. Leite, Phys. Rev. B 66, 104406 (2002).\n[9] A. Fnidiki, C. Dorien, F. Richomme, J. Teillet, D. Lemarchand, N.H.  \nDuc, \nJ. Ben Youssef, H. Le. Gall, J. Magn. Magn. Mater.  262, 368 (2003).\n[10] I.T.Iakubov, A.N.Lagarkov, S.A.Maklakov, A.V.Osipov, K.N.Rozanov,\n I.A.Ryzhikov, V.V. Samsonova, A.O.Sboychakov, J. Magn. Magn. Mater. 321, \n726 \n(2009).\n[11] V.V. Samsonova, A.O.Sboychakov, J. Magn. Magn. Mater. 321, 2707 (2009).\n[12] E.Bolcal, V.Dimitrov B.Aktaş, H.Aslan and A.Bozkurt, Acta Phys.Pol. Vol.121 \n(2012) 259.\n[13]  T.  A.  Prokopieva,  V.A.  Danilov,  S.S.  Kantorovich,  and  C.  Holm,  \nPhys.Rev E 80, \n031404  (2009)\n \n27"    },    {        "title": "1402.3565v2.Coupling_of__ferro_electricity_and_magnetism_through_Coulomb_blockade_in_Composite_Multiferroics.pdf",        "content": "Coupling of ferroelectricity and magnetism through Coulomb blockade in Composite\nMultiferroics\nO. G. Udalov,1, 2N. M. Chtchelkatchev,1, 3, 4and I. S. Beloborodov1\n1Department of Physics and Astronomy, California State University Northridge, Northridge, CA 91330, USA\n2Institute for Physics of Microstructures, Russian Academy of Science, Nizhny Novgorod, 603950, Russia\n3L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences,117940 Moscow, Russia\n4Department of Theoretical Physics, Moscow Institute of Physics and Technology, 141700 Moscow, Russia\n(Dated: October 1, 2018)\nComposite multiferroics are materials exhibiting the interplay of ferroelectricity, magnetism, and\nstrong electron correlations. Typical example | magnetic nano grains embedded in a ferroelectric\nmatrix. Coupling of ferroelectric and ferromagnetic degrees of freedom in these materials is due to\nthe in\ruence of ferroelectric matrix on the exchange coupling constant via screening of the intragrain\nand intergrain Coulomb interaction. Cooling typical magnetic materials the ordered state appears at\nlower temperatures than the disordered state. We show that in composite multiferroics the ordered\nmagnetic phase may appear at higher temperatures than the magnetically disordered phase. In\nnon-magnetic materials such a behavior is known as inverse phase transition.\nPACS numbers: 77.55.Nv, 75.25.-j, 75.30.Et, 71.70.Gm\nI. INTRODUCTION.\nCurrently composite materials with combined mag-\nnetic and electric degrees of freedom attract much of\nattention for their promise to produce new e\u000bects and\nfunctionalities1{3. The idea of using ferromagnetic and\nferroelectric properties in a single phase multiferroics was\ndeveloping since seventeenths4. However, in bulk homo-\ngeneous materials this coupling is weak due to relativistic\nparameterv=c, withvandcbeing the electron velocity\nand the speed of light, respectively. Only recently the\nnew classes of two-phase multiferroic materials such as\nsingle domain multiferroic nanoparticles5, laminates6,7,\nepitaxial multilayers8,9, and granular materials10{12were\ndiscovered giving a new lease of life to this \feld. So far,\nthe interface strain generated by the ferroelectric layer\nwas considered as the promising mechanism for strong\nenough magnetoelectric coupling in two-phase multifer-\nroic materials1,10,12{14. This strain modi\fes the magneti-\nzation in the magnetic layer and the magnetic anisotropy\nenergy.\nWe propose a di\u000berent mechanism for magnetoelec-\ntric coupling emerging at the edge of strong long-range\nelectron interaction, ferroelectricity, and magnetism. In\ncomposite multiferroics | materials consisting of metal-\nlic ferromagnetic grains embedded into ferroelectric (FE)\nmatrix, Fig. 1, the origin of this coupling is twofold: i)\nStrong in\ruence of FE matrix on the Coulomb gap de\fn-\ning the electron localization length and the overlap of\nelectron wave functions, and therefore controling the ex-\nchange forces. ii) Dependence of the long-range part of\nCoulomb interaction, and thus the exchange interaction,\non the dielectric permittivity of the FE matrix.\nGranular magnets consist of nanosized single domain\nferromagnetic particles. Each particle has uniform mag-\nnetization and its own non zero magnetic moment. Di-\nrection of a single particle magnetization and collective\ntemperature\npacking ratio, /\nd a\nexchange, Jtemperature\npacking ratioa)\nd)\nFM stateSPM state\nFMSPM\nSPM\nb)FM\nFMSPM\ntemperaturec)temperature\nTCFEmetalic\nmagnetic\ngrainsmagnetic\nmoments\nferroelectric (FE)FIG. 1. (Color online) a) Sketch of a granular multiferroic\n(GMF) consisting of ferromagnetic grains with magnetic mo-\nments embedded in a ferroelectric matrix. Cooling typical\nmagnetic materials the ordered phase appears at lower tem-\nperature than the disordered phase. In composite multifer-\nroics the ordered (FM) state may appear at higher temper-\nature (upper panel) than the disordered (SPM) state (lower\npanel). In non-magnetic materials such a behavior is known\nas inverse phase transition. Diagrams b) and c) show mag-\nnetic state of GMF in coordinates temperature, T vs. packing\nratio,d=a, withdandabeing the average intergrain distance\nand the grain size, respectively. The diagrams b) and c) cor-\nrespond to the limits of large and small intergrain distance\nd, respectively. Graph d) shows the intergrain exchange con-\nstantJvs. temperature Tand the packing ratio, d=a.\nbehavior of the particle ensemble depend on particle mag-\nnetic anisotropy and the interparticle interaction. For\nweak interparticle interaction and small anisotropy the\nmagnetic moment of a single particle is not \fxed and \ruc-\ntuates in time. Magnetic moments of di\u000berent particles\nare not correlated. This is so-called superparamagnetic\n(SPM) state.15Interparticle interactions (such as dipole-\ndipole,16,17and exchange,18,19) can lead to establishing ofarXiv:1402.3565v2  [cond-mat.mes-hall]  21 May 20152\nmagnetic order with correlated magnetic moments of dif-\nferent particles. Due to interactions the disordered SPM\nsystem can come to the ordered ferromagnetic (FM) or\nantiferromagnetic state with decreasing temperature. We\ndiscuss in this paper the in\ruence of ferroelectric matrix\non the interparticle exchange interaction.\nWe show that the e\u000bective ferromagnetic exchange con-\nstantJbetween the ferromagnetic grains strongly de-\npends on temperature near the ferroelectric Curie tem-\nperature TFE\nCin granular multiferroics due to the above\nmentioned mechanisms. The transition temperature be-\ntween ordered and disordered magnetic states can be\nfound approximately using the equation J(T) =T. FM\nstate corresponds to J(T)> T. If mechanism (i) is the\nstrongest, the FM state appears at higher temperatures\nthan the disordered SPM state, Fig. 1. Such a behavior\noriginates from the fast growth of the exchange coupling\nwith temperature,dJ\ndT\u001d1, in the vicinity of paraelectric-\nferroelectric phase transition. This is known as an inverse\nphase transition. It appears in various systems such as\nHe3and He4, metallic alloys, Rochelle salt ferroelectrics,\npolymers, and high- Tcsuperconductors20{24. Here we\npredict the inverse phase transition in magnetic materi-\nals and address the main question of why the interplay of\nCoulomb blockade, ferroelectricity, and ferromagnetism\nin granular multiferroics (GMF) leads to such a peculiar\ntemperature dependence of the exchange coupling J(T).\nII. QUANTUM NATURE OF COMPOSITE\nMULTIFERROICS.\nComposite multiferroics are characterized by two tem-\nperatures: i) the ferroelectric Curie temperature TFE\nC\ndescribing the paraelectric-ferroelectric transition of FE\nmatrix, and ii) the ferromagnetic grains Curie temper-\nature, TFM\nC. For temperatures T >TFM\nCthe grains are\nin the paramagnetic state with zero magnetic moments.\nFor temperatures T <TFM\nCeach grain is in the FM state\nwith \fnite spontaneous magnetic moment. The temper-\natureTFM\nCdepends on grain sizes. Here we assume that\nall grains have the same ordering Curie temperature TFM\nC\nwithTFM\nC\u001dTFE\nC.\nAlthough each grain is in the ferromagnetic state\nfor temperatures T <TFM\nCthe whole system has sev-\neral types of magnetic behavior depending on the ra-\ntio of temperature and several energy scales: 1) the\ngrain anisotropy energy Ea15, 2) the intergrain exchange\ncouplingJ18,19, and 3) the magneto-dipole interaction\nEd16,17. For temperatures T >max(Ea;J;Ed) the grain\nmagnetic moments are uncorrelated and \ructuate in\ntime. In this case the whole system is in the SPM state25.\nFor temperatures Tbelow than one of the above energy\nscales the system magnetic state changes. Depending on\nthe ratio of Ea,J, andEdthe di\u000berent states are possi-\nble19.\nThe grain anisotropy energy Eahas two contributions\ncoming from the grain bulk and grain surface. The\nFIG. 2. (Color online) Mechanism for magnetoelectric cou-\npling in composite multiferroics. Right panel shows the over-\nlap of the electron wave functions (blue and red curves) lo-\ncated in grains G 1and G 2embedded into ferroelectric (FE)\nmatrix. This overlap de\fnes the exchange coupling Jin\nEq. (1) and the strength of spin correlations (blue arrows).\nThe localization length \u0018(\u000f), with\u000fbeing the dielectric per-\nmittivity of FE matrix, shows the characteristic decay of elec-\ntron wave functions. Left panel shows \u000f(T) vs. temperature\nT. The dielectric permittivity \u000fis small for temperatures\nT=T1\u001cTFE\nC, withTFE\nCbeing the FE transition tempera-\nture, leading to small localization length \u0018(\u000f) and small over-\nlap of electron wave functions resulting in a small exchange\ncouplingJand uncorrelated spin state. Close to the FE tran-\nsition (T=T2) the dielectric permittivity \u000fis large leading to\nthe large overlap of electron wave functions and to the strong\nexchange coupling resulting in the ferromagnetic state.\nanisotropy axis varies from grain to grain due to the grain\nshape and disorder orientation. For large anisotropy en-\nergy,Ea>max(J;Ed) and temperatures T < Eathe\ngrain moments are frozen and not correlated. The tem-\nperature TB=Eais called the blocking temperature.\nIn this paper we consider the opposite case of large ex-\nchange energy, J > max(Ea;Ed), with negligible bulk\nand surface magnetic anisotropies, Eaand magneto-\ndipole interaction, Ed. This limit is realized for small\ngrains25{27. The magnetic phase transition occurs at\ntemperatures TM=Jin this case. The system moves\nfrom the SPM state with uncorrelated magnetic moments\nof grains to the FM state with co-directed spins of grains.\nThe temperature TM=Jis called the ordering temper-\nature. Below we study the in\ruence of FE matrix on\nintergrain exchange interaction and on the ordering tem-\nperature TMof GMF.\nConsider the exchange interaction of two metallic fer-\nromagnetic grains of equal sizes, a. Each grain is charac-\nterized by the Coulomb energy Ec=e2=(a\u000f) witheand\n\u000fbeing the electron charge and the average dielectric\npermittivity of the granular system, respectively. We as-\nsume that the Coulomb energy is large, Ec\u001dTand the\nsystem is in the insulating state with negligible electron\nhopping between the grains. In this case the exchange in-\nteraction has a \fnite value due to the overlap of electron\nwave functions located in di\u000berent grains.3\nWe describe the coupling of each pair of electrons as\n\u0000Jij(^si\u0001^sj) with ~^sbeing the spin operator with indexes\niandjnumbering electrons in the \frst and the second\ngrain, respectively, and the parameter Jijbeing the ex-\nchange interaction of two electrons. The total exchange\ninteraction of two grains can be written as a sum over all\nelectrons, Jtot=\u0000P\nijJij(^si\u0001^sj). Below for simplicity\nwe assume that Jij=Jdoes not depend on indexes iand\nj. Thus, the Hamiltonian has the form Jtot=\u0000J(^S1\u0001^S2),\nwhere ~^S1;2is the total spin of the \frst (second) grain.\nFor temperatures T <Jtot<TFM\nCeach grain is in the\nFM state with di\u000berent grains magnetic moments being\ncorrelated such that the whole system may experience\nthe FM phase transition.\nThe exchange coupling constant Jhas the form28,29\nJ/Z Z\n\t\u0003\n1(~ r2)\t\u0003\n2(~ r1)e2\n\u000fj~ r1\u0000~ r2j\t1(~ r1)\t2(~ r2)d3r1d3r2:\n(1)\nHere \t 1;2is the spatial part of the electron wave func-\ntion located in the \frst (second) grain; \u000fis the average\ndielectric permittivity. The in\ruence of FE matrix on\nthe exchange integral in Eq. (1) is twofold:\ni) The\u000f-dependent Coulomb interaction potential.\nThis interaction, and thus the exchange coupling J,\ndecreases with increasing \u000fin the vicinity of the\nparaelectric-ferroelectric transition temperature TFE\nC.\nii) The\u000f-dependent electron localization length \u0018,\nFig. 2. This length depends on the Coulomb energy Ec,\nand thus on the dielectric permittivity \u000f30\n\u0018=a=ln(E2\nc=T2gt); (2)\nwheregtis the average tunneling conductance. It in-\ncreases with increasing \u000fleading to larger overlap of the\nelectron wave functions, and thus to the increase of the\nexchange coupling J.\nTo summarize, there are two competing mechanisms\nin Eq. (1): with increasing the dielectric permittivity \u000f\nthe intergrain Coulomb interaction decreases, while the\nelectron wave function overlap increases.\nWe now estimate the exchange coupling Jin Eq. (1)\nusing the following form of the electron wave function\n\t1;2(~ r) =C(\ne\u0000a\n\u0018;j~ r\u0006~d=2j<a;\ne\u0000j~ r\u0006~d=2j\n\u0018;j~ r\u0006~d=2j>a:(3)\nHereC=\u0000R\nj\t1;2j2dV\u0001\u00001=2is the normalization con-\nstant anddis the distance between two grain centres.\nEquation (3) describes electrons uniformly smeared in-\nside a grain and decaying exponentially outside the grain.\nSubstituting Eq. (3) into Eq. (1) we \fnd the intergrain\nexchange coupling constant\nJ\u00181\n\u000f\u001a\ne\u00004d=\u0018; d\u001da\ne\u00004(d\u00002a)=\u0018; d\u00002a\u001ca:(4)\nIn general, the exchange coupling can be estimated as\nJ\u0018(1=\u000f)e\u0000\rd=\u0018, with numerical constant \r\u00144. Using\n/s32\n/s83/s80/s77\n/s32\n/s84/s70/s77\n/s84\n/s51/s83/s80/s77\n/s84\n/s49/s84\n/s84\n/s50/s70/s77/s83/s80/s77/s40/s98/s41\n/s67/s70/s69\n/s84/s101/s109/s112/s101/s114/s97/s116/s117/s114/s101 /s44/s32/s84/s32 /s91/s97/s46/s117/s46/s93/s74 /s40/s84 /s41/s32/s83/s80/s77\n/s69/s120/s99/s104/s97/s110/s103/s101/s32/s105/s110/s116/s101/s103/s114/s97/s108 /s44/s32/s74 /s32/s91/s97/s46/s117/s46/s93/s83/s80/s77\n/s84\n/s49\n/s32/s32/s69/s120/s99/s104/s97/s110/s103/s101/s32/s105/s110/s116/s101/s103/s114/s97/s108 /s44/s32/s74 /s32/s91/s97/s46/s117/s46/s93\n/s84/s74 /s40/s84 /s41\n/s84\n/s50/s70/s77/s40/s97/s41\n/s84\n/s67/s70/s69\n/s84/s101/s109/s112/s101/s114/s97/s116/s117/s114/s101 /s44/s32/s84/s32 /s91/s97/s46/s117/s46/s93FIG. 3. (Color online) Exchange coupling constant Jvs.\ntemperature T. The dotted line stands for temperature with\ntemperatures T1;2;3being the solutions of Eq. (6). (a) Limit of\nlarge intergrain distances, \rd>a in Eq. (5), with superpara-\nmagnetic (SPM) state existing for temperatures T < T 1or\nT >T 2and the ferromagnetic (FM) state appearing for tem-\nperaturesT1<T <T 2. (b) Limit of small intergrain distance,\n\rd<a in Eq. (5), with FM state appearing for temperatures\nT <T 1andT2<T <T 3and the SPM state being above the\ntemperature T3and in the temperature interval T1<T <T 2.\nEq. (2) we \fnd\nJ=J0\u000f\rd\na\u00001; (5)\nwhereJ0>0 is the exchange coupling for permittiv-\nity\u000f= 1.J0decays exponentially with increasing the\nintergrain distance dleading to the decrease of overall\nexchange coupling Jin Eq. (5) with increasing the dis-\ntanced. This can be seen using Eq. (4). The exponent\nin Eq. (5) has a clear physical meaning: the \frst term,\n\rd=a , is due to \u000f-dependent localization length \u0018, the\nsecond term (\u00001) is due to \u000f-dependent Coulomb inter-\naction. These mechanisms compete with each other.\nThe exchange coupling Jin Eq. (5) depends on the\nratio of grain sizes aand the intergrain distances d. For\nlarge intergrain distances, \rd > a , the exponent of di-\nelectric permittivity \u000fin Eq. (5) is positive leading to\nthe increase of exchange coupling Jdue to the delocal-\nization of electron wave functions. In the opposite case,\nof small intergrain distances, \rd<a , the exchange cou-\nplingJdecreases with increasing of \u000f.\nThe criterion of SPM - FM phase transition in com-\nposite multiferroics can be formulated as follows\nJ(\u000f(TM)) =TM: (6)\nHereJis the exchange coupling averaged over all pair\nof grains (it includes e\u000bective nearest neighbor number)\nandTMis the transition (or ordering) temperature.4\npacking ratio, \nd/a\n Temperature Temperatureb) a)\nJ, TJ, T\npacking ratio, \nd/aJ(T,d/a)\nJ(T,d/a)\nFIG. 4. (Color online) Graphs a) and b) show the dependence\nof the exchange coupling J(complicated surface) in the coor-\ndinates packing ratio, d=aand temperature T. Plots a) and\nb) correspond to the limits of large and small intergrain dis-\ntanced, respectively. Plane surface stands for temperature T.\nIntersection of exchange coupling Jand temperature Tcor-\nrespond to the magnetic phase transition. The regions with\ntemperature T > J correspond to the SPM state, while the\nregion with T <J corresponds to the FM state. Following a)\nand b) we obtain the phase diagrams b) and c) in Fig. 1.\nThe temperature dependence of the dielectric per-\nmittivity\u000f(T) of composite ferroelectrics | materials\nconsisting of metallic grains embedded into FE matrix\nwas discussed recently31,32. We assume that the metal\ndielectric constant is very large (in\fnite) at zero fre-\nquency. Therefore we can write for sample permittivity\n\u000f=\u000ffe(\n=\nfe), where\u000ffe= 1 + 4\u0019\u001fand \n, \n febeing the\nsample and FE matrix volume, respectively and \u001fis the\naverage susceptibility of FE matrix.\nTo estimate the dielectric permittivity of FE matrix we\nconsider the region between two particular neighbouring\ngrains as thin FE \flm with local polarization perpen-\ndicular to the \flm (grain) boundaries. The direction of\nlocal polarization varies from one pair to another pair\nof grains, and its sign is de\fned by the external and in-\nternal electric \felds. The origin of internal \feld is the\nelectrostatic disorder inevitably present in granular ma-\nterials. The behavior of local polarization is described by\nthe Landau-Ginzburg-Devonshire (LGD) theory33,34.\nIII. DISCUSSION.\nFigure 3 shows the average exchange coupling con-\nstantJvs. temperature. For large intergrain distances,\n\rd > a , the exchange coupling Jhas a maximum in\nthe vicinity of the ferroelectric Curie temperature TFE\nC,\nFig. 3(a). For small intergrain distances, \rd < a , the\nexchange constant Jhas a minimum, Fig. 3(b). In Fig. 3\nwe assume that the grain ferromagnetic Curie temper-\nature is large, TFM\nC>TFE\nC. The dotted line in Fig. 3\nstands for temperature and the intersections of this line\nwith exchange coupling curve Jcorrespond to the solu-\ntion of Eq. (6). The temperatures T1;2;3in Fig. 3 stand\nfor di\u000berent ordering temperatures of SPM - FM phase\ntransitions and correspond to the solution of Eq. (6).The most interesting region in Fig. 3 is the intersec-\ntion of temperature Tdotted line with exchange coupling\ncurve, J. For large intergrain distances, \rd > a the ex-\nchange coupling Jexceeds the thermal \ructuations for\ntemperatures T1< T < T 2near the ferroelectric Curie\ntemperature TFE\nCleading to the appearance of the global\nFM state, Fig. 3(a). For temperatures T <T 1orT >T 2\nthe system is in the SPM state. Interestingly, the FM\nstate appears with increasing the temperature, in con-\ntrast to the usual case where ordering appears with de-\ncreasing the temperature. This is related to the fact that\nwhile the magnetic system becomes ordered the FE ma-\ntrix becomes disordered with increasing the temperature.\nFor small intergrain distances, \rd < a , the exchange\ncoupling Jhas the opposite behavior, Fig. 3(b): The\nsystem is in the FM state for temperatures T < T 1and\nbecomes SPM for temperatures T1<T <T 2. Increasing\nthe temperature the system \frst experience the transition\nto the FM state for temperatures T2<T <T 3and then\ngoes to the SPM state for temperatures above T3.\nEquation (6) may not have a solution at any tempera-\ntures for small enough coupling constants J0in Eq. (5).\nIn this case the system will stay in the SPM state.\nFigure 4 shows the behavior of intergrain exchange\nconstant Jas a function of temperature Tand the pack-\ning ratio,d=a. The \rat surface represents the tempera-\ntureT. The regions with J> T correspond to the FM\nstate, while the regions with J< T to the SPM state.\nFigure 4 was used to obtain the phase diagrams in Fig. 1.\nTo summarize, we obtain the magnetic phase diagram\nof granular multiferroics with several phases appearing\ndue to the interplay of ferroelectricity, magnetism, and\nstrong electron correlations, Fig. 3.\nA. Requirements for experiment.\nFirst, we assumed an insulating state of composite\nmultiferroic due to strong Coulomb blockade, Ec\u001d\nmax(T;J). The last inequality is not valid in the close\nvicinity of the ferroelectric Curie temperature TFE\nC32\nsince the charging energy Ecis\u000f-dependent and is\nstrongly suppressed in the vicinity of TFE\nC. This sup-\npression may lead to the appearance of the metallic state\nwith di\u000berent criterion of SPM - FM transition where\nmagnetic coupling between grains occurring due to elec-\ntron hopping between the grains35,36. This e\u000bect was not\nconsidered here.\nAbove restriction is rather strong and reduces the num-\nber of possible FE materials. The Coulomb gap for 5 nm\ngrains isEc= 2000=\u000fK and thus Ec<200 K for di-\nelectric permittivity \u000f >10. In conventional bulk ferro-\nelectrics, such as BTO and PZT, the dielectric permittiv-\nity is large, \u000f>100. However, in granular materials the\nthin FE layers are con\fned by grains leading to a much\nsmaller dielectric constant37. Another way to reduce the\ndielectric constant is to use the relaxor FE matrix, such\nas P(VDF-TrFE)38{40.5\nThe origin of magneto-electric coupling in GMF is the\nlong-range Coulomb interaction. Thus, the magnetic and\nelectric subsystems can be separated in space with FM\n\flm placed above the FE substrate. This geometry al-\nlows using ferroelectrics with large dielectric permittivity.\nIncreasing the distance between the FE and the FM \flm\none can reduce the in\ruence of FE on the Coulomb gap.\nSecond, we assumed that all grains have equal sizes\nand all intergrain distances are the same. For broad dis-\ntribution of grain sizes and intergrain distances the in\ru-\nence of FE matrix on the exchange coupling constant is\nsmeared. This e\u000bect was not taken into account here.\nThird, we assumed that the intergrain exchange in-\nteraction is larger than the magneto-dipole interaction\nand magnetic anisotropy. This limit is realized in many\nmaterials including Ni-SiO 2granular system25, where\n5 nm Ni grains were embedded into SiO 2matrix with\nSPM - FM phase transition observed at temperature\nTM\u0019300K\u001dTB, where TBis the blocking temper-\nature. Such a high transition temperature can occur due\nto the intergrain exchange interaction only. The results\nof Ref.25were repeated for Co-SiO 227and Fe-SiO41sys-\ntems with ordering temperature TM\u0019300K.\nFinally, we mention that granular FM show an ac-\ntivation conductivity behavior supporting the fact that\nin these materials electrons are localized inside the\ngrains42,43. Thus, these materials can be used for ob-\nserving the e\u000bect discussed in this paper with the proper\nsubstitution of FE matrix instead of SiO 2matrix.\nB. Electric \feld control of GMF properties.\nThe dielectric permittivity of FE matrix can be con-\ntrolled by the external electric \feld in addition to temper-ature. This opens an opportunity to control the magnetic\nstate of GMF by the electric \feld. For example, the mag-\nnitude of dielectric permittivity of P(VDF/TrFE) ferro-\nelectric relaxor can be doubled by the electric \feld44.\nAccording to Eq. 5 this leads to four times change in the\nintergrain exchange interaction. This change can cause\nthe magnetic phase transition driven by electric \feld.\nIV. CONCLUSION.\nWe studied the phase diagram of composite multifer-\nroics, materials consisting of magnetic grains embedded\ninto FE matrix, in the regime of Coulomb blockade. We\nfound that the coupling of ferroelectric and ferromagnetic\ndegrees of freedom is due to the in\ruence of FE matrix on\nthe exchange coupling constant via screening of the in-\ntragrain and intergrain Coulomb interaction. We showed\nthat in these materials the ordered magnetic phase may\nappear at higher temperatures than the magnetically dis-\nordered phase.\nV. ACKNOWLEDGEMENTS.\nI. B. was supported by NSF under Cooperative Agree-\nment Award EEC-1160504 and NSF Award DMR-\n1158666.\n1W. Eerenstein, N. D. Mathur, and J. F. Scott, Nature\n442, 759 (2006).\n2R. Ramesh and N. A. Spaldin, Nature Mat. 6, 21 (2007).\n3M. Bibes and A. Barthelemy, Nature Mat. 7, 425 (2008).\n4A. M. J. G. van Run, D. R. Terrell, and J. H. Scholing, J.\nMater. Sci. 9, 1710 (1974).\n5N. Mathur, Nature 454, 591 (2008).\n6N. Cai, C.-W. Nan, J. Zhai, and Y. Lin, Appl. Phys. Lett.\n84, 3516 (2004).\n7G. Srinivasan, E. T. Rasmussen, B. J. Levin, and R. Hayes,\nPhys. Rev. B 65, 134402 (2002).\n8S. Mukherjee, A. Roy, S. Auluck, R. Prasad, R. Gupta,\nand A. Garg, Phys. Rev. Lett. 111, 087601 (2013).\n9I. C. Infante, S. Lisenkov, B. Dupe, M. Bibes, S. Fusil,\nE. Jacquet, G. Geneste, S. Petit, A. Courtial, J. Juraszek,\nL. Bellaiche, A. Barthelemy, and B. Dkhil, Phys. Rev.\nLett. 105, 057601 (2010).\n10X. L. Zhong, J. B. Wang, M. Liao, G. J. Huang, S. H. Xie,\nY. C. Zhou, Y. Qiao, and J. P. He, Appl. Phys. Lett. 90,\n152903 (2007).11H. Ryu, P. Murugavel, J. H. Lee, S. C. Chae, T. W. Noh,\nY. S. Oh, H. J. Kim, K. H. Kim, J. H. Jang, M. Kim,\nC. Bae, and J.-G. Park, Appl. Phys. Lett. 89, 102907\n(2006).\n12H. Zheng, J. Wang, S. E. Lo\rand, Z. Ma, L. Mohaddes-\nArdabili, T. Zhao, L. Salamanca-Riba, S. R. Shinde, S. B.\nOgale, F. Bai, D. Viehland, Y. Jia, D. G. Schlom, M. Wut-\ntig, A. Roytburd, and R. Ramesh, Science 303, 661 (2004).\n13J. Atulasimha and S. Bandyopadhyay, Appl. Phys. Lett.\n97, 173105 (2010).\n14K. Schroder, J. Appl. Phys. 53, 2759 (1982).\n15C. Bean and J. D. Livingston, J. Appl. Phys. 30, 120S\n(1959).\n16P. Allia, M. Coisson, M. Knobel, P. Tiberto, and F. Vinai,\nPhys. Rev. B 60, 12207 (1999).\n17D. Kechrakos and K. N. Trohidou, Phys. Rev. B 58, 12169\n(1998).\n18M. R. Scheinfein, K. E. Schmidt, K. R. Heim, and G. G.\nHembree, Phys. Rev. Lett. 76, 1541 (1996).\n19Z. Mao and X. Chen, J. Phys. D: Appl. Phys. 43, 425001\n(2010).6\n20E. R. Dobbs, Helium Three (Oxford University Press, Ox-\nford, U.K., 2002, 2002).\n21U. Schneider, P. Lunkenheimer, J. Hemberger, and\nA. Loidl, Ferroelectrics 242, 71 (2000).\n22S. Rastogi, G. W. H. Hohne, and A. Kelle, Macromolecules\n32, 8897 (1999).\n23F. H. Stillinger, P. Debenedetti, and T. M. Truskett, J.\nPhys. Chem. B 105, 11809 (2001).\n24C. Chevillard and M. A. V. Axelos, Colloid Polym. Sci.\n275, 537 (1997).\n25J. I. Gittleman, Y. Goldstein, and S. Bozowski, Phys. Rev.\nB5, 3609 (1972).\n26S. Bedanta, T. Eimuller, W. Kleemann, J. Rhensius,\nF. Stromberg, E. Amaladass, S. Cardoso, and P. P. Fre-\nitas, Phys. Rev. Lett. 98, 176601 (2007).\n27S. Barzilai, Y. Goldstein, I. Balberg, and J. S. Helman,\nPhys. Rev. B 23, 1809 (1981).\n28L. D. Landau and E. M. Lifshitz, Quantum Mechanics\nNonrelativistic Theory, Course of Theoretical Physics , 3rd\ned., Vol. 3 (Nauka, Moscow, 1976).\n29A. Auerbach, Interacting electrons and quantum mag-\nnetism (Springer, 1994).\n30I. S. Beloborodov, A. V. Lopatin, V. M. Vinokur, and\nK. B. Efetov, Rev. Mod. Phys. 79, 469 (2007).\n31O. G. Udalov, A. Glatz, and I. S. Beloborodov, Euro.\nPhys. Lett. 104, 47004 (2013).\n32O. G. Udalov, N. M. Chchelkatchev, A. Glatz, and I. S. Be-\nloborodov, Phys. Rev. B tbd, tbd (2014), arXiv:1401.5429[cond-mat].\n33B. A. Strukov and A. P. Levanyuk, Ferroelectric Phenom-\nena in Crystals (Springer, Geidelberg, 1998, 1998).\n34P. Chandra and P. B. Littlewood, in Physics of Ferro-\nelectrics (Springer, 2007) pp. 69{116.\n35M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys.\n70, 1039 (1998).\n36S. V. Vonsovskii, Magnetism (Wiley, New York, 1974) p.\n1034.\n37A. V. Bune, V. M. Fridkin, S. Ducharme, L. M. Blinov,\nS. P. Palto, A. V. Sorokin, S. G. Yudin, and A. Zlatkin,\nNature 391, 874 (1998).\n38A. E. Glazounov and A. K. Tagantsev, Appl. Phys. Lett.\n73, 856 (1998).\n39V. Bharti and Q. M. Zhang, Phys. Rev. B 63, 184103\n(2001).\n40V. Bobnar, A. Erste, X.-Z. Chen, C.-L. Jia, and Q.-D.\nShen, Phys. Rev. B 83, 132105 (2011).\n41B. P. Khrustalev, A. D. Balaev, and V. G. Pozdnyakov,\nThin solid \flms 130, 195 (1985).\n42A. Milner, A. Gerber, B. Groisman, M. Karpovsky, and\nA. Gladkikh, Phys. Rev. Lett. 76, 475 (1996).\n43S. L. Yuan, Z. C. Xia, L. Liu, W. Chen, L. F. Zhao, J. Tang,\nG. H. Zhang, L. J. Zhang, H. Cao, W. Feng, Y. Tian, L. Y.\nNiu, and S. Liu, Phys. Rev. B 68, 184423 (2003).\n44J. S. Lee, A. A. Prabu, K. J. Kim, and C. Park, Fibers\nand Polymers 8, 456 (2007)."    },    {        "title": "1403.0784v1.All_optical_control_of_ferromagnetic_thin_films_and_nanostructures.pdf",        "content": "All-optical control  of ferromagnetic thin films  and nanostructures  \nC-H. Lambert1,2, S. Mangin1,2, B. S. D. Ch. S. Varaprasad3, Y.K. Takahashi3, M. Hehn2, M. Cinchetti4, G. \nMalinowski2,, K. Ho no3, Y. Fainman5, M. Aeschlimann4, and E.E. Fullerton1,5 \n \n1) Center for Magnetic Recording Research, University of California San Diego, La Jolla, CA 92093 -\n0401, USA  \n2) Institut Jean Lamour, UMR CNRS 7198 –Université de Lorraine - BP 70239, F -54506 Vandoeuvre, \nFrance  \n3) Magnetic Materials Unit, National Institut e for Materials Science, Tsukuba 305 -0047, Japan  \n4) Department of Physics and Research Center OPTIMAS , University of Kaiserslautern, Erwin \nSchroedinger Str. 46, 67663 Kaiserslautern, Germany  \n5) Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA \n92093 -0401, USA  \nThe interplay of light and magnetism has been a topic of interest since the original observation s of \nFaraday and Kerr where magnetic material s affect the light polarization . While these  effects have \nhistorically been exploited to use light as a probe of magnetic materials there is increasing research on \nusing polarized light to alter or manipulate magnetism . For instance d eterministic magnetic switching  \nwithout any applied magnetic field s using laser pulses of  the circular polarized light has been observed for  \nspecific  ferrimagnetic materials . Here we demonstrate, for the first time,  optical control  of ferromagnetic \nmaterials ranging from magnetic thin films  to multilayers and  even granular films being explored for \nultra-high-density magnetic recording. Our finding show s that optical control of magnetic materials  is a \nmuch  more general phenomenon  than previously assumed . These results challenge the current theoretical \nunderstanding and will have a major impact on data m emory and storage industries via the integration of \noptical control of ferromagnetic bits. \n  The dynamic response of magnetic order to ultrafast external excitation is one of the more  fascinating \nissue s of modern magne tism [1, 2]. Optical probing at the femto -second time sc ale allows investigating \nultrafast magnetization dynamics including different fundamental  interactions between spins, electrons, \nand lattice degrees of freedom when materials are far from equilibrium  [1, 3-5]. It further has the \nopportunity to explore the potential for novel technologies such as heat -assisted magnetic recording \n(HAMR) [6, 7]. An interesting and important outcome from studies of ultra -fast dynamics of magnetic \nsystems is the demonstration that circularly polarized light  can directly switch magnetic domains witho ut \nany applied magnetic field. In the ir pioneering work the Rasing group in Nijmegen showed fully \ndeterministic magnetization switching in a ferrimagnetic GdFeCo alloy film using circularly polarized \nfemtosecond laser pulses [8]. This phenomenon is now referred to as All-Optical Helicity -Dependent \nSwitching (AO-HDS) .   \nSince th is initial experimental discovery , there have been extensive explorations of these  phenomena \nwith a particular attention  on the ferrimagnetic nature of the magnetic materials that , until now, have  been \nthe only materials to  show AO -HDS . While initial  studies were focused on rare-earth transition -metal \n(RE-TM) GdFeCo alloys there have b een recent examples of AO -HDS  in other RE-TM materials such as \nTbCo  [9], TbFe [10], DyCo and HoCo alloys, Tb/Co and Ho/Co multilayers as well as  Co/Ir/CoPtNiCo/Ir \nsynthetic ferrimagnets  [11]. In all these cases , AO-HDS was observed for ferrimagnetic systems with two \ndistinct sublattices  that are antiferromagnetically -coupled and exhibit a  compensation temperature near or \nabove room temperature. The initially discussed models for AO-HDS were based on t he existence of an \neffective field created by the circular polarized light via the inverse Faraday effect [12, 13] or directly by \nthe transfer of angular momentum from the light to the magnetic system [14]. More recent models are \nfocused  on the formation of a transient ferromagnetic state due to different demagnetization times for RE \nand TM sub -lattices  and the trans fer of angular momentum both between the different magnetic sub -\nlattices and the lattice . In these  latter model s the light ’s helicity plays a secondary role, via the helicity \ndependence of the absorption  (i.e. circular dichroism)  and no transfer of angular  momentum  and any \ncoherent effect s from the light to matter is require d [15-17]. These models  have been supported by recent \nmeasurements in GdFeCo alloys [18]. Further, t here is al so emerging evidence that laser -induced \nsuperdiffusive spin currents can flow in heterogeneous systems [17, 19-22]. It is suggested that  angular \nmomentum is removed during  demagnetization  by a flow of spin -polarized currents  leading to a transfer \nof angular momentum  between different lateral regions of the sample  potentially contributing to the AO -\nHDS process  [20]. \n Besides the still unclear microscopic explanation of AO -HDS  the most intriguing and important open \nquestion is whether AO -HDS  is specific to a subset of  ferrimagnetic materials o r is a fundamentally  \ngeneral process and  can be applied to much more widely used ferromagnetic materials . Further more can it \nbe also applied to reverse technologically important high-anisotropy granular  or patterned  materials that \nare anticipated for future h igh-density magnetic recording  [23]? In this paper we demonstrate  first that \nAO-HDS  occurs  for a range of ferromagnetic thin films  with perpendicular magnetic anisotropy  including \nPt/Co/Pt trilayers  and Co/Pt , Co/Pd , Co1-xNix/Pd and Co/Ni multilayers. In these cases we only observe \nAO-HDS for films where the magnetic film thickness  is less than ~3 nm  and this thickness appears  \nlimited by the demagnetization energies that drive domai n formation  during heating by the laser pulses . \nWe then  show a high degree of optical control of 15-nm thick granular FePt films currently being pursued \nfor HAMR media which exhibit  a room -temperature coercive field s exceeding  3.5 T  [24, 25]. The level of \ncontrol in the granular FePt case is determined  by thermal activation of the grains after the application of \nthe optical pulse.  To probe t he optical response of ferromagnetic sa mples we use  an optical/heat -assisted magnet ic \nswitching facility  with a 100-femtos econd pulsed laser  source (see Methods section and supplementary \ninformation  for details) . Shown in Fig s. 1a-c are Faraday microscope images of laser line scans for \n[Co(0.4 nm)/Pt(0.7)]N multilayers where N=8, 5 and 3 for 1a, 1b and 1c, respectively . The  laser is scanned \nacross the sample and final magnetic configuration  is subsequently imaged. For each figure the laser \nhelicity is either  right circular polarization (+), left circular polarization (-) or linear polarization  (L) as \nlabeled in the image . The samples have perpendicular magnetic anisotropy  so the magnetization easy axis \nis normal to the film surface and the contrast results from the two possible direction s of the \nmagnetization. For Figs. 1a -c, the left hand of the image is magnetized up while the right is magnetized \ndown with a domain wall that runs vertically in the middle of each image .   \nFor N=8 (Fig. 1a ) we observe domain formation  where t he region scanned by the laser is filled with \nstripe subdomains tha t minimizes the dipole energy  [26]. This process is independent of the light \npolarization and we describe  it as laser-induced thermal demagnetization (TD) . A rim is observed at the \nedge of the scanned area where the magnetic  orientation  is opposite to the back ground  and is stabilized by \nthe dipolar fields arising from the surrounding film that supports the opposite direction of magnetization . \nFor N=5 (Fig. 1b) , we again observe  the formation of subdomains  in the scanned region . However, the \naverage domain size is much larger than in Fig. 1a . This increase in domain size is expected for \ndecreasing number of layers since  the equilibrium domain size increases exponential with decreasing film \nthickness in the thin -film limit (see Ref. [26] and references within). More importantly we observe that \nthe resulting domain struct ure depend s on the light polarization. For + light we observe white isolated \nbubble -like domains in a dark background while for - we observe isolated dark domains in a white \nbackground.  For linear polarization we obser ve symmetric domain formation. We further see th at the \nmagnetization near the edges of the line scan again tends to favor the direction opposite of the \nsurrounding film similar to that observed for N=8.   \nFor N=3 (Fig. 1c) we observe something intrinsically different. We observe  fully deterministic \nmagnetization reversal of the material under the beam with no external magnetic field  for both left and \nright circular polarization . In th is case the orientation of the magnetization after the laser has passed \ndepends solely on the h elicity of the laser . This is the clear demonstration of  AO-HDS in a ferromagnetic \nmaterial . The process is reversible with reversing the helicity  of the light  and the  final magnetization  \norientation  can be related to the light helicity . Surprisingly the l ight absorption in the Co/Pt multilayer  \nsample s that show AO -HDS is lower when the light has the circular po larization needed for switching  \n(i.e. the magnetization switches into the high absorption state). This observation i s opposite to the \ndichroism -induced switching discussed in Ref [27]. Finally, t he domains created in the case of linear \npolarization  are much bigger for N=3 in accord with  the small dipolar energy gain by domain formation in \nthis case [26]. \nShown in Fig. 1d are images of domain patterns for the N=3 sample for various laser powers where \nthe film is saturated in one direction and the laser spot is fixed and not scanned on the surface . We see \nthat for low power (362 nW) a reversed domain is written for right circular polarization while there is no \nchange to the film for left circular polarization. A region of random domains is obs erved for linear \npolarization. With increasing laser power from right to left, regions of demagnetized random domains \ndevelop in the center of the laser spot for all three polarizations indicating that the pow er is such that the \ntemperature exceeds a critical temperature for which domains are formed. This can result from exceeding \nthe Curie temperature (T C) or from a critical temperature where there is a loss of perpendicular anisotropy or enhanced domain fluct uations . However for right circular polarized light there is a rim at the edge of \nthe demagnetized area that shows deterministic switching that is not present for left circular or linear \npolarized light . The rim is not visible for the left circular polariz ation as it is in the same direction as \nbackground film. If the magnetization is reversed the rim for left circular polarized light is observed. This \nrim is similar to what has been previously observed for ferrimagnetic films (Fig. 2 of Ref [8]) and \nindicates a window of laser power for AO -HDS as the laser power decreases moving  away from the \ncenter of the spot beam.  \nWe further explored the effective driving energy for AO-HDS and domain formation by adding \nexternal magnetic fields to the experiments shown in Fig s. 1a-c (see supplementary Figs. S1-S3).  While \nlinear polarization leads to domain formation in zero applied field the application of a magnetic  field can \nstabilize a uniform magnetization state. This field increas es from 3 -4 Oe for the N=3 sa mple to ~12 Oe \nfor N=5 and to ~40 Oe for N=8 demonstrat ing the increased demagnetization energy with thickness. In \nother word, for increasing magnetic thickness  larger  applied field s are needed to suppress domain \nformation  after heating with the laser . When an applied field is combined with circular polarization the \napplied field can either support o r oppose the circular polarization.  For N=3 a field of 7 Oe is need ed to \noppose the circular polarized light and yield a demagnetized film  while a field of ~12  Oe will saturate the \nfilm in the opposite direction as that expected for the helicity of the light  (Supplementary Fig. S3) . For \nN=5 the field to yield a demagnetized film is  ~12 Oe  while a field of ~ 25 Oe is need ed to saturate the \nfilm opposite to the light helicity  (Supplementary Fig. S2) .  However, when comparing the effects of \ncircular polarization of the light to the applied magnetic field in these experiments one has to remember \nthat the field is applied during  the entire thermal process while the role of the helicity of the pulse persist s \nonly for a few  picoseconds after the laser excitation [28]. \nWe have explored a range of thin  ferromagnetic film materials to determine how general the \nphenomena shown in Fig. 1 c is by studying  [Co(tCo)/Pt(tPt)]N, [Co( tCo)/Pd( tPt)]N, [Co xNi1-\nx(0.6nm)/Pt(0.7nm)] 3 and [Co/Ni] N multilayer structures where we have varied  several material \nparameters ( e.g. tCo, tPt, N and Ni concentration ). In short we observe AO -HDS in all these ferromagnetic \nmaterials classes including single Co layers sandwich between two Pt layers . Shown in Fig. 2 are selected \nresults for the threshold laser power needed to achieve either AO -HDS (solid symbols) or TD (open \nsymbols) . Figure 2a are results for [Co( tCo)/Pt(0.7nm)] N  where  the threshold laser power increases with \nboth N and tCo. These results show  AO-HDS for N=2 or 3 and tCo ≤ 0.6 nm ( i.e. the thinnest samples) and \nTD for thicker samples  (consistent with Fig. 1) . The trends of the threshold powers are independent of \nAO-HDS or TD processes and increasing linearly with either tCo or N.  This suggests that the two \nphenomena are linked by a common mechanism  or similar temperatures are needed for both processes .  \nFigure  2b are the results for [Co(0.4 nm)/Pt( tPt)]2 samples where we tune the Pt thickness for fixed N \nand tCo (we also measured [Co(0.4nm)/Pd( tPd)]2 samples as a function of Pd thickness and observed \nsimilar results). This increased the thickness of the film but leaves the total magnetic moment relatively  \nunaffected. This also dramatically changes the exchange coupling between the Co layers  since there is \ninduced ferromagnetic moments in the interfacial Pt atoms . As can be seen in Fig. 2b the threshold power \ndecreases slightly with increasing Pt thickness.  For tPt = 1.2 nm  (Fig. 2b) the two Co layer are only \nweakly coupled suggesting that sin gle Co layers may also switch. Shown in Fig. 2c are the results for N=1 \ntrilayer structures ( i.e. a Pt/Co( tCo)/Pt structures ) where we increase the Co layer thickness. We observed \nAO-HDS for samples 0.6 nm ≤ tCo ≤  1.5 nm. The upper limit is set by the thickness where the sample \nmaintains perp endicular magnetic anisotropy. The lower limit is set by the sensiti vity of the optica l detection. Again, the threshold power increases linearly and we observe AO -HDS f or a single \nferromagnetic film.  In fact the threshold values for a single Co layers are consistent with the extrapolation \nthe data in Fig. 2a to N=1.  Figure 2d shows the thr eshold power for [Co 1-xNix(0.6nm)/Pt(0.7nm)] N \nmultilayers as a function of both N and Ni concentration. We find the threshold power incre ases with N as \nseen in Fig. 2a and decreases with Ni concentration  and the trends are independent of TD or AO -HDS .  \nFinally we observe AO-HDS for these following Co/Ni structure \nTa(3nm)/Cu(10nm)/[Ni(0.5nm)/Co(0.1nm)] 2/Ni(0.5nm)/Cu(5nm) where perpendicular anisotropy arises \nprimarily from the Co -Ni interfaces .  \nThese results show  that AO -HDS is a ra ther general phenom ena for magnetic films but seem  to be \nlimited to the thin -film limit. Such structures are useful in a number of spintronic applications (e.g. \nmagnetic random access memory). However applications such as high -density magnetic recording  require  \nsmall magneti c grains or patterned bits for high signal -to-noise readback of the data and high anisotropy \nto remain thermally stable at the nanoscale [29]. The current challenge is that the magnetic fields required \nto write high -anisotropy grains is above what can be achieved b y electromagnetic write heads. HAMR  is \nthe leading technology to address the challenge where a laser spot heats the magnetic material close to T C \nwhere the anisotropy field is lowered sufficiently to allow the grains to be written with an external \nmagnetic field  [6, 7]. Further using the polarization of the light to directly write the bits or to supplement \nthe write field would greatly simplify the desi gn of the write elements.   \nTo explore this issue we have studied the role of AO -HDS on high -anisotropy granular FePt -based \nfilms being developed as a candidat e media for high -density HAMR  [24]. We studied both FePtAgC and \nFePtC granular media grown onto single -crystal MgO.  The preparation method leads to the formation of \nhigh-anisotropy FePt grain separated by C grain boundaries . The average FePt grain size is ~9.7 nm and \n~7.7 nm for the FePtAgC and FePtC granular medi a, respectively. T he room -temperature perpendicular \nmagnetic anisotropy and coercive fields are  7 T and 3.5 T, respectively, for both films. Plan-view electron \nmicroscope image s and m agnetization characterization are  shown in supple mentary Figs. S4 and S5. \nShown in Fig. 3 are results of optical studies for the FePt AgC granular film where we start with the film \nin a random magnetic state with equal up or down oriented magnetic grains  (similar results are obtained \nfor the FePtC film) . Because the grain size i s well below the resolution of the Faraday microscope the \nrandomly magnetized sample appears grey. As can be seen from Fig. 3 there is a clear net magnetization \nachieved that depends on the helicity of the circularly polarized light and no change is observ ed in the \nimage with linear polarization.  This clearly shows that a percentage of the films is being magnetized and \ncontrolled by the polarization of the light.  Shown in Fig. 3b are images of the laser spot without scanning \nthe laser beam similar to th ose in Fig. 1d. As shown there is a laser power to achieve AO -HDS which \nexists for a rela tively narrow range of powers. With increasing power above the threshold power (~420 \nnW) there i s a region of reversed grains. Above ~600 nW a ring forms where AO -HDS occurs at a \nparticular radius (and this radius grow s with increasing power).  The center of the ring where the laser \nintensity is the highest the films is demagnetized, presumably from exceeding T C.   \nWhile clear AO -HDS is observed the degree of ma gnetizati on is less than 100%. By comparing the \ncontrast to the saturated film we can estimate that the induced magnetization is ~10-20 % of saturation.   \nThe lack of saturation can arise from at least two effects  or the combination of these effects . The first is \nthat AO -HDS is only aff ecting a subset of the grains. The second is that the AO -HDS is efficient  and \nsaturates the sample,  but that the magnetic grains that make up the films sample are highly thermally \nactivated and between the time of AO -HDS and the sample cooling the grain assembly  partially demagnetize s due to thermal switching of the grains . When the sample is heated toward T C there is a \nstrong drop in the magnetic anisotropy (K U) near T C. This is the basis of HAMR where this lower s the \ncoercive field to a point where when a modest field is able to reverse the grains. However, at this point the \nenergy stored in the grain K UV where V is the volume of the grain becomes comparable to thermal energy \nkBT and therefore there is a high probability for thermal reversal of the g rains while the sample is cooling . \nThis effect is further driven by the dipolar fields from the neighboring grains that support a demagnetized \nground state.  This proces s is described in detail in the literature, see  for example  Ref. [30].   \nTo quantify the relative role of thermal activation we applied magnetic fields while the sample was \nillum inated by the polarized light. Shown in Fig. 4 are the result s of line scans with both right (+) and \nleft (-) circular polarization in increasing applied static magnetic field. The field direction  is chosen so it \nsupports the right circular polarized light and opposes the left circularly polarized light. We find that an \napplied field of ~700 Oe is sufficient to suppress  the effects of the helicity of the light  where  no contrast \nis observed for left circular polarization  in a 700 Oe field . For right circular polarization the contrast \nincreases with increasing field. Similar ly, we can excite th e films with linear polarized light and an \napplied field of ~600 Oe is needed to obtain a similar magnetization as the AO -HDS results  (see \nsupplemental materials  Fig. S6). The fact that these modest field s are sufficient  to counter the polarization \nof the light indicates we are heating near T C where the small 700-Oe field (a factor of 50 less than the \nroom temperature coercive field) can alter the magnetization orientation of the grains . Moreover the fact \nthat applied fiel ds up to 1100 Oe are not sufficient to fully saturate the film after the laser excitation \nindicates that the grains are highly thermally activated during optical excitation and we are o bserving \nstochastic processes. This is also consistent with measurement s of the saturated film where the \nmagnetization is decreased with any polarization, even for the circular polarization that supports the \nmagnetization . Further control or deterministic switching may require careful engineering of the laser \npulse shape and thermal response of the magnetic film and substrate through , for example,  the \nintroduction of heat sink  layers .  \nOur results show that a ferrimagnetic structure is not necessary  for AO -HDS to be observed and \ntherefore antiferromagnetic exchange coupling between two magnetic sublattices  is not required . \nHowever, these finding cannot rule out  the role of two magnetic sublattices  on the magnetic reversal since  \nall of our examples have two magnetic elements  that are ferroma gnetically coupled . While the data shown \nin Fig. 2c is for a single Co film sandwiched by Pt, the Pt atoms at the interface are polar ized by the Co \nand are magnetic and, t herefore , these systems sample ha ve two magnetic elements. This also applies for \nFePt films the Pt con tributes to the magnetization. Given that we observe AO -HDS switching on single \nCo films  as well as Co/Pt multilayers  it is unlikely that super -diffusive currents that couple different  \nmagnetic  regions in a heterogeneous sample is required . However, we cannot rule out that flow of \ncurrents into the Pt layer do es not play a role.  \nOur results do suggest that  we are  heating near the Curie point and that this is important for the AO -\nHDS  in ferromagnetic materials . The threshold intensities shown in Fig. 2 generally track with what is the \nexpected trends for T C for these systems (increasing tCo or N increases T C while increasing  tPt or Ni \nconcentration decreases T C). The final state is  most likely determined by angular momentum transfer of \nthe light to the magnetization or a resulting  effective field from the light acting on the magnetization. This \nis expected to be most effective when  approaching TC where even modest angular moment  transfer , \neffective field s or applied magnetic fields  can lead  to a symmetry breaking such that magnetizat ion is \ndeterministically switched. This  magnetization  state will be maintained unless the demagnetization and thermal energies  that favors domain formation  are too large and cause demagnetization during cooling . \nAO-HDS is then expected to be generally observed as long as the energy gain by domain formation is \nsufficiently small or controlled  to avoid demagnetization during cooling.  For perpendicular magnetized \nfilms there are strong  demagnetizing fields within the film that support  domain formation. The energy \ngain for domain formation is strongly suppressed in the ultrathin film limit yield ing increasing domain \nsizes  with reduced thickness and explain s the observation  of AO -HDS only in the thin -film limit. A \nsecondary way to avoid domain formation is usi ng low magnetization materials.  Note that such a \ndescription is consistent with previous measurements of ferr imagnetic alloys, multilayers and \nheterostructures where AO -HDS switching is generally observed when the compensation temperature ( i.e. \nthe temperature where the net ferr imagnetic moment  is zero) is near or above room temperature. Having a \ncompensation temperature between room temperature and TC will help suppress  domain formation ev en \nfor relatively thick films.  \nIn conclusion we demonstrated the  optical control of the magnetization of a variety of  ferromagnetic  \nmaterials  (thin film, multi layers and granular media). These results demonstrate  a new and \ntechnologically important class  of material s showing AO -HDS phenomenon. By challenging the current \ntheories in the field, this study offers significant progress toward a better understanding of the interaction \nbetween pulsed polarized light and magneti c materials. However it is clear that a number of questions still \nneed to be addressed to gain a fundamental understanding of all the mechanisms involved. The control of \nthe magnetic orientation of ferromagnetic thin film and granular media using light ope ns new application s \nin magnetic  memory,  data storage  and processing . Given the  current trends for silicon nanophotonics, \nminiaturization, and photonic -electronic integration, the ability to couple photonic, electronics, and \nmagnetic materials will signific antly extend the level of flexibility  in existing d evices and enabling \ncompletely new applications.    \nMethods:  \nWe use d optical pulses, having a central wavelength of 800 nm (1.55 eV), a pulse duration of about \n100 fs at the sample positi on and a repetition  rate of 0.1-1 kHz. A schematic of the optical test facilities \nwhere AO -HDS measurements were performed is shown in the Supplementary Fig. S 7.  The response of \nthe magnetic film was studied using a static Faraday microscope with 1 -m resolution that to image the \nmagnetic domains while  or after  the laser  illuminates  the sample. The helicity of the beam is controlled by \na zero -order quarter wave -plate, which transforms linear polarized light (L) into circularly left - (+) or \nright-polarized light ( -).The  present measurements were  performed at room temperature (RT) and the \nlaser beam was swept at a constant rate of ~3 -20 m/s with the typical laser spot size of ~80 m.  The \nlaser power was adjusted to achieve either TD or AO -HDS and varied from sample to s ample.  Typical \nlaser powers for 1 kHz repetition rates are 0. 05 - 2 W.  The threshold power scales with the repetition \nrate indicating it is the energy/pulse that determines the threshold power.  \nAll the thin-film samples (with the exception of the FePt samples) were grown by DC magnetron \nsputtering from elemental sources onto roo m-temperature glass substrates coa ted with a thin Ta seed \nlayer. Alloys were grown by co -sputtering where the source powers controlled the composition.  \nMultilayers and heterostr uctures were formed by sequential deposition of layers. The samples were then \ncovered with a thin Ta capping layer.  The FePt-C and FePtAg -C granular films were fabricated by DC \nmagnetron sputtering using Fe, Pt and C targets on MgO substrates [1]. The film  stack was MgO (001) \nsub./[FePt -C(0.25)/FePt(0.15)]25/C(15). The number in the parenthesis is the thickness of the each layer \nand the unit is nm. Multilayers of FePt -C/FePt were deposited at elevated temperatures of 550oC and C capping layer was deposited at RT. The volume fraction of C was about 28%. The composition ratio of Fe \nand Pt is 1:1. Silver contained samples also produced in similar procedure as mentioned above except ten \natomic percent is added during the depos ition. Due to high deposition rates of Ag, we added 10 seconds \nper minute. In this way, we controlled the atomic percentage. The film stack for silver containing  film \nwas MgO (001)/[FePtAg -C(0.3)/FePt(0.15)]22/C(15). The total thickness of FePtAg -C is abou t 10 nm. \nMagnetic moment and hysteresis measurements were performed using a vibrating sample magnetometry \nand magneto -optic Kerr effect measurements.  Sample structures were charac terized by x -ray reflectivity \nand transmission electron microscopy.  \n[1] B.S. D.Ch.S. Varaprasad, Y.K. Takahashi and K. Hono, Japanese patent application 2013 -189727.  \nAcknowledgements  \nWe would like to the Rob ert Tolley and Matthias Gottwald with help on sample fabrication and helpful \ndiscussions with Marco M enarini and Vitaliy Lomak in. This work was supported by the ANR, ANR -10-\nBLANC -1005 “Friends,” and work at UCSD was supported by the Office of Naval Research (ONR) \nMURI program and a grant from the Advanced Storage Technology Consortium. It was also supported by \nThe Partner Univers ity Fund “Novel Magnetic Materials for Spin Torque Physics” as well as the \nEuropean Project (OP2M FP7 -IOF-2011 -298060) and the Region Lorraine.   Work at the National \nInstitute for Materials Science  was supported by IDEMA -ASTC.  \nAuthor Contributions  SM, MA, YS, and EEF designed and coordinated the project; C.-H. L.  grew, \ncharacterized and optimized the thin films samples  while B. S. D. Ch. S. V ., Y. K. T., and K. H. \ndeveloped and grew the FePt -based granular media.  C.-H. L., S. M., Y. K. T.  operated the Kerr \nmicroscope and the pu mp laser experiment. S. M. and E. E. F.  coordinated work on the paper with \ncontributions from C.-H. L, M. H., M. C., and G. M.  with regular discussions with all authors.  \n \nReferences  \n1. B. Koopmans, G. Malinow ski, F.D. Longa, D. Steiauf, M. Faehnle, T. Roth, M. Cinchetti, and M. \nAeschlimann, Explaining the paradoxical diversity of ultrafast laser -induced demagnetization,  \nNature Materials 9(3), 259 -265 (2010).  \n2. A. Kirilyuk, A.V. Kimel, and T. Rasing, Laser -induced magnetization dynamics and reversal in \nferrimagnetic alloys,  Reports on Progress in Physics 76(2), 026501 (2013).  \n3. E. Beaurepaire, J.C. Merle, A. Daunois, and J.Y. Bigot, Ultrafast spin dynamics in ferromagnetic \nnickel,  Physical Review Letters 76(22), 4250 -4253 (1996).  \n4. S.O. Mariager, F. Pressacco, G. Ingold, A. Caviezel, E. Mohr -Vorobeva, P. Beaud, S.L. Johnson, \nC.J. Milne, E. Mancini, S. Moyerman, E.E. Fullerton, R. Feidenhans'l, C.H. Back, and C. \nQuitmann, Structural and Magnetic Dynamics of a Laser Induced Phase Transition in FeRh,  \nPhysical Review Letters 108(8), 087201 (2012).  \n5. A. Cavalleri, C. Toth, C.W. Siders, J.A. Squier, F. Raksi, P. Forget, and J.C. Kieffer, \nFemtosecond structural dynamics in VO2 during an ultrafast solid -solid phase  transition,  \nPhysical Review Letters 87(23), 237401 (2001).  \n6. M.H. Kryder, E.C. Gage, T.W. McDaniel, W.A. Challener, R.E. Rottmayer, G.P. Ju, Y.T. Hsia, \nand M.F. Erden, Heat Assisted Magnetic Recording,  Proceedings of the IEEE 96(11), 1810 -1835 \n(2008).  \n7. B.C. Stipe, T.C. Strand, C.C. Poon, H. Balamane, T.D. Boone, J.A. Katine, J.L. Li, V. Rawat, H. \nNemoto, A. Hirotsune, O. Hellwig, R. Ruiz, E. Dobisz, D.S. Kercher, N. Robertson, T.R. Albrecht, and B.D. Terris, Magnetic recording at 1.5 Pb m( -2) using an i ntegrated plasmonic \nantenna,  Nature Photonics 4(7), 484 -488 (2010).  \n8. C.D. Stanciu, F. Hansteen, A.V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, All-\noptical magnetic recording with circularly polarized light,  Physical Review Letters 99(4), \n047601 (2007).  \n9. S. Alebrand, M. Gottwald, M. Hehn, D. Steil, M. Cinchetti, D. Lacour, E.E. Fullerton, M. \nAeschlimann, and S. Mangin, Light -induced magnetization reversal of high -anisotropy TbCo \nalloy films,  Applied Physics Letters 101(16), 162408 (2012).  \n10. A. Hassdenteufel, B. Hebler, C. Schubert, A. Liebig, M. Teich, M. Helm, M. Aeschlimann, M. \nAlbrecht, and R. Bratschitsch, Thermally Assisted All -Optical Helicity Dependent Magnetic \nSwitching in Amorphous Fe100 -xTbx Alloy Films,  Advanced Materials 25(22), 3122 -3128 \n(2013).  \n11. S. Mangin, M. Gottwald, C. -H. Lambert, D. Steil, V. Uhlíř, L. Pang, M. Hehn, S. Alebrand, M. \nCinchetti, G. Malinowski, Y. Fainman, M. Aeschlimann, and E.E. Fullerton, Engineered \nmaterials for all -optical helicity -dependent magneti c switching,  Nature Materials, PUBLISHED \nONLINE: 16 FEBRUARY 2014 | DOI: 10.1038/NMAT3864 (2013).  \n12. J.P. van der Ziel, P.S. Pershan, and L.D. Malmstrom, Optically -induced magnetization resulting \nfrom inverse Faraday effect Physical Review Letters 15(5), 190-193 (1965).  \n13. A. Kirilyuk, A.V. Kimel, and T. Rasing, Ultrafast optical manipulation of magnetic order,  \nReviews of Modern Physics 82(3), 2731 -2784 (2010).  \n14. C.D. Stanciu, A.V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and T. Rasing, \nUltrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: The role of \nangular momentum compensation,  Physical Review B 73(22), 220402 (2006).  \n15. T.A. Ostler, J. Barker, R.F.L. Evans, R.W. Chantrell, U. Atxitia, O. Chubykalo -Fesenko, S. El  \nMoussaoui, L. Le Guyader, E. Mengotti, L.J. Heyderman, F. Nolting, A. Tsukamoto, A. Itoh, D. \nAfanasiev, B.A. Ivanov, A.M. Kalashnikova, K. Vahaplar, J. Mentink, A. Kirilyuk, T. Rasing, \nand A.V. Kimel, Ultrafast heating as a sufficient stimulus for magneti zation reversal in a \nferrimagnet,  Nature Communications 3, 666 (2012).  \n16. J.H. Mentink, J. Hellsvik, D.V. Afanasiev, B.A. Ivanov, A. Kirilyuk, A.V. Kimel, O. Eriksson, \nM.I. Katsnelson, and T. Rasing, Ultrafast Spin Dynamics in Multisublattice Magnets,  Physical \nReview Letters 108(5), 057202 (2012).  \n17. C.E. Graves, A.H. Reid, T. Wang, B. Wu, S. de Jong, K. Vahaplar, I. Radu, D.P. Bernstein, M. \nMesserschmidt, L. Muller, R. Coffee, M. Bionta, S.W. Epp, R. Hartmann, N. Kimmel, G. Hauser, \nA. Hartmann, P. Holl, H. Gorke, J.H. Mentink, A. Tsukamoto, A. Fognini, J.J. Turner, W.F. \nSchlotter, D. Rolles, H. Soltau, L. Struder, Y. Acremann, A.V. Kimel, A. Kirilyuk, T. Rasing, J. \nStohr, A.O. Scherz, and H.A. Durr, Nanoscale spin reversal by non -local angular momentum \ntransfer following ultrafast laser excitation in ferrimagnetic GdFeCo,  Nature Materials 12(4), \n293-298 (2013).  \n18. I. Radu, K. Vahaplar, C. Stamm, T. Kachel, N. Pontius, H.A. Durr, T.A. Ostler, J. Barker, R.F.L. \nEvans, R.W. Chantrell, A. Tsukamoto, A. Itoh, A. Kirilyuk, T. Rasing, and A.V. Kimel, \nTransient ferromagnetic -like state mediating ultrafast reversal of antiferromagnetically coupled \nspins,  Nature 472(7342), 205 -208 (2011).  \n19. E. Turgut, P. Grychtol, C. La -O-Vorakiat, D.E. Adams, H.C. Kapteyn, M.M. M urnane, S. \nMathias, M. Aeschlimann, C.M. Schneider, J.M. Shaw, H.T. Nembach, and T.J. Silva, Ultrafast \nDemagnetization Measurements Using Extreme Ultraviolet Light: Comparison of Electronic and \nMagnetic Contributions (vol 3, 038002, 2013),  Physical Review X 3(3), 039901 (2013).  \n20. E. Turgut, C. La -o-Vorakiat, J.M. Shaw, P. Grychtol, H.T. Nembach, D. Rudolf, R. Adam, M. \nAeschlimann, C.M. Schneider, T.J. Silva, M.M. Murnane, H.C. Kapteyn, and S. Mathias, \nControlling the Competition between Optically Induced Ultrafast Spin -Flip Scattering and Spin \nTransport in Magnetic Multilayers,  Physical Review Letters 110(19), 197201 (2013).  21. M. Battiato, K. Carva, and P.M. Oppeneer, Superdiffusive Spin Transport as a Mechanism of \nUltrafast Demagnetization,  Physical Rev iew Letters 105(2), 027203 (2010).  \n22. G. Malinowski, F.D. Longa, J.H.H. Rietjens, P.V. Paluskar, R. Huijink, H.J.M. Swagten, and B. \nKoopmans, Control of speed and efficiency of ultrafast demagnetization by direct transfer of spin \nangular momentum,  Nature Physics 4(11), 855 -858 (2008).  \n23. B. Varaprasad, M. Chen, Y.K. Takahashi, and K. Hono, L1(0) -Ordered FePt -Based \nPerpendicular Magnetic Recording Media for Heat -Assisted Magnetic Recording,  IEEE  \nTransactions on Magnetics 49(2), 718 -722 (2013).  \n24. L. Zhang , Y.K. Takahashi, K. Hono, B.C. Stipe, J.Y. Juang, and M. Grobis, L1(0) -ordered \nFePtAg -C granular thin film for thermally assisted magnetic recording media (invited),  Journal \nof Applied Physics 109(7), 07b703 (2011).  \n25. L. Zhang, Y.K. Takahashi, A. Peruma l, and K. Hono, L1(0) -ordered high coercivity (FePt)Ag -C \ngranular thin films for perpendicular recording,  Journal of Magnetism and Magnetic Materials \n322(18), 2658 -2664 (2010).  \n26. O. Hellwig, A. Berger, J.B. Kortright, and E.E. Fullerton, Domain structure  and magnetization \nreversal of antiferromagnetically coupled perpendicular anisotropy films,  Journal of Magnetism \nand Magnetic Materials 319(1-2), 13 -55 (2007).  \n27. A.R. Khorsand, M. Savoini, A. Kirilyuk, A.V. Kimel, A. Tsukamoto, A. Itoh, and T. Rasing, Role \nof Magnetic Circular Dichroism in All -Optical Magnetic Recording,  Physical Review Letters \n108(12), 127205 (2012).  \n28. S. Alebrand, A. Hassdenteufel, D. Steil, M. Cinchetti, and M. Aeschlimann, Interplay of heating \nand helicity in all -optical magnetiza tion switching,  Physical Review B 85(9) (2012).  \n29. A. Moser, K. Takano, D.T. Margulies, M. Albrecht, Y. Sonobe, Y. Ikeda, S.H. Sun, and E.E. \nFullerton, Magnetic recording: advancing into the future,  Journal of Physics D -Applied Physics \n35(19), R157 -R167 ( 2002).  \n30. H.J. Richter, A. Lyberatos, U. Nowak, R.F.L. Evans, and R.W. Chantrell, The thermodynamic \nlimits of magnetic recording,  Journal of Applied Physics 111(3), 033909 (2012).  \n  Figure s  \n \nFigure 1:   Magneto -photonic response of Co/Pt multilayers.  Magneto -photonic response in zero \napplied magnetic field of [Co(0.4nm )/Pt(0.7nm)] N multilayer sample s to various laser \npolarizations  where (a) N=8, (b) N=8 and (c) and (d) N=3.  For each image from  top to bo ttom \nthe laser polarization is right circularly polarized light ( +), left circularly polarized light ( -) or \nlinear polarized light (L).  For (a) -(c) the laser beam was  swept over the sample  with a magnetic \ndomains  and the magnetization pattern was subsequently imaged.   In (d) the laser was fixed at \nindividual spots where  the average laser intensity increased as shown in the image.  \nFigure 2:  Magneto -photonic response of multilayer thin-film samples  to circular polarization \nlight and varying powers.  Plotted  is the evolution of the threshold power to  achieve either \nthermal demagnetization (TD) or all -optical helicity -depenedent switching (AO -HDS)  of various \nsamples .  For each sample the threshold power is given either as a filled symbol for AO -HDS or \nopen symbols for TD.  (a) Threshold power vs. N for [Co( tCo)/Pt(0.7 nm)] N samples with tCo = \n0.4, 0.6 and 1.0 nm,  (b) threshold power vs. tPt for [Co(0.4nm )/Pt(tPt)]2 multilayer samples, (c) \nthreshold power vs. tCo for Pt/Co( tCo)/Pt trilayer samples and (d) threshold power vs. Ni \nconcentration for [Co 1-xNix(0.6nm)/Pd(0.7nm)] N with N=2, 3 or 4.   \n \nFigure 3:  Magneto -photonic response in z ero applied magnetic field of a 15 -nm FePtAgC \ngranular film sample  starting with an initially demagnetized sample .  (a) Line scans for  various \nlaser polarizations from top to bottom right circularly polarized light ( +), left circularly \npolarized light ( -) and linear polarized light (L).  The laser beam was  swept over the sample  and \nthe magnetizat ion p attern was subsequently imaged.  (b) Images of magnetic domains for right \ncircularly polarized light (left column) and left circularly polarized light (right column ) laser spot \nfor various laser powers shown next to the image.  \n \nFigure 4:   Magneto -photonic response in various applied magnetic field of a 15-nm FePtAg C \ngranular film sample  starting with an initially demagnetized sample .  Shown are line scans for \nright circularly polarized light ( +) in the left column and left circularly polar ized light ( -) in \nthe right column . The laser power was 677 nW.  The magnitude of the magnetic field is given in \nthe figures and the orientation of the field supports the right circular polarization and opposes the \nleft circular polarization.  \n \nSupplement ary Information  \n We further explored the effective driving energy for laser -induced AO -HDS and TD by applying \nan external magnetic fields during the experiments on the samples shown in Figs. 1a -c.  In Supplementary \nFig. S1 are the results obtained on the [Co(0.4 nm)/Pt(0.7nm)] 8 multilayer sample presented in Fig 1a of \nthe main manuscript.  At room temperature this sample exhibits a square hysteresis loop with a coercive \nfield of 368 Oe.  What is shown are line scans for different helicities (left and right  circular polarization \nand linear polarization) with increasing applied magnetic fields.  In zero applied field the sample shows \nTD as seen in Fig. 1a but with increasing applied field the contrast in the area where the laser is swept \nincreases. A field on  the order of 35 -40 Oe is needed to saturate the film.  When comparing left circular \npolarized light with linear polarized light that have same applied magnetic fields the results are very \nsimilar indicating the helicity of the light is not contributing to  the final state of the magnetization.   \n \nSupplementary Figure S1:  Magnetic response of a [Co(0.4 nm)/Pt(0.7nm)] 8 multilayer to the combined \neffect of optical excitation and an external magnetic field starting with two domains and a domain well in \nthe mid dle of each image.  The magnitude of the magnetic field is shown to the left of each line scan and \nthe average laser power was 682 nW .   \n In Supplementary Fig. S2 are the results for the [Co(0.4 nm)/Pt(0.7nm)] 5 multilayer sample \nshown in Fig 1b of the main  manuscript.  At room temperature this sample exhibits a square hysteresis \nloop with a coercive field of 297 Oe.  Line scans for different helicities (left and right circular polarization \nand linear polarization) with increasing magnetic fields are shown.  In the left image ( +) the helicity of \nthe light and the magnetic support the magnetization of the sample. Conversely for the middle images ( -\n) the applied field opposes the helicity of the light. The right images are for linear polarization. When the \nhelicity of the light supports the external magnetic field ( +)an external magnetic field of 7 Oe is needed \nto saturate the film. Conversely for same applied field and the opposite helicity ( -) requires an external \nfield of 21 -25 Oe to achieve saturation in dicating a clear helicity dependent response.  For linear light an \nexternal field of ~ 12 Oe is needed to achieve saturation.   \n \n \nSupplementary Figure S2:  Magnetic response of a [Co(0.4 nm)/Pt(0.7)] 5 multilayer to the combined \neffect of optical excitation  and an external magnetic field starting with two domains and a domain well in \nthe middle of each image.  The magnitude of the magnetic field is shown to the left of each line scan and \nthe average laser power was 720  nW. \n  \nIn Supplementary Fig. S3 are the results for the [Co(0.4 nm)/Pt(0.7nm)] 3 multilayer sample \nshown in Figs. 1c and 1d of the main manuscript. At room temperature this sample exhibits a square \nhysteresis loop with a coercive field of 204 Oe. Line scans for di fferent helicities (left and right circular \npolarization and linear polarization) are shown for increasing magnetic fields.  In the left image ( +) and \nthe middle image ( -) the applied field opposes the helicity of the light. When the helicity of the exte rnal \nmagnetic field opposes the helicity of the light an external magnetic field of 7 Oe is yields a demagnetized \nfilm while 11.5 Oe will saturate the film in the field direction and opposite to the AO -HDS direction. For \nlinear light an external field of ~  3 Oe is needed to achieve saturation.   \n \nSupplementary Figure S3:  Magnetic response of a [Co(0.4 nm)/Pt(0.7nm)] 3 multilayer to the combined \neffect of optical excitation and an external magnetic field starting with two domains and a domain well in \nthe mi ddle of each image.  The magnitude of the magnetic field is shown to the left of each line scan and \nthe average laser power was 523  nW.  \n  \nShown in Supplementary Figs. S4 and S5 are the electron microscopy and magnetometry results \nfor the FePt films studie d. \n \nSupplementary Figure S4:  Transmission electron microscopy (TEM) plan -view images (left) and \nanalysis (right) of the FePtAgC granular film (upper) and FePtC granular film (lower).  The right images \nshow the analysis of the grain diameter distribution d etermined from each TEM image.  For the FePtAgC \nfilm the mean grain diameter is 9.7 ± 2.1 nm and the average pitch distance is 15.5 ± 2.9 nm.  For the \nFePtC film the mean grain diameter is 7.7 ± 2.1 nm and the average pitch distance is 10.8 ± 1.8 nm.  \n \n \nSupplementary Figure S5:  Room -temperature magnetometry measurements for the FePtAgC (left) and \nFePtC (right) samples showing perpendicular magnetic anisotropy with coercive fields of ~3.5 T.  \n  \n \nSupp lementary Figure S6:  Magneto -optical response of the FePtAgC sample.  Shown are a line scan for \nright circular polarization in zero applied field (bottom) and line scans for linear polarization with \nincreasing applied magnetic field.  The magnitude of the field is shown in the right of the image.  \n  \n \n \nSupplementary Figure S7:  Schematic of magnetic measurements apparatus showing a 50fs laser exiting \nthe sample and the domain structure imaged using a Faraday microscope.  \n \n"    },    {        "title": "1403.2469v1.Piezo_Voltage_Manipulation_of_the_Magnetization_and_Magnetic_Reversal_in_Thin_Fe_Film.pdf",        "content": "Piezo-Voltage Manipulation of the Magnetization and Magnetic \nReversal in Thin Fe Film\nY. Y. Li, W. G. Luo, L. J. Zhu, J. H. Zhao, and K. Y. Wang1\nSKLSM, Institute of Semiconductors, CAS, P. O. Box 912, 100083 Beijing, People’s Republic of China\nAbstract\nWe carefully investigated the in-plane magnetic reversal and corresponding magnetic domain \nstructures in Fe/GaAs/piezo-transducer heterostructure using longitudinal magneto-optical Kerr \nmicroscopy. The coexistence of the <100> cubic magnetic anisotropy and ]01[1 uniaxial magnetic \nanisotropy was observed in our Fe thin film grown on GaAs. The induced deformation along [110] \norientation can effectively manipulate the magnetic reversal with magnetic field applied along \nmagnetic uniaxial hard [110] axes. The control of two-jump magnetization switching to one-jump \nmagnetization switching during the magnetic reversal was achieved by piezo-voltages with magnetic \nfield applied in [100] direction. The additional uniaxial anisotropy induced by piezo-voltages at ±75 V \nare ±1.4×103 J/m3.\n                                                            \n1Corresponding author’s E-mail: kywang@semi.ac.cnI. INTRODUCTION\nElectric field control of the ferromagnetic magnetization process has become increasingly \nimportant because it has great potential applications for the memory device, magnetic logic, \nmagneto-electric sensor and the integration of magnetic functionalities into electronic circuits [1,2]. \nThe approaches adopted to achieve this aim including the electric field gating to change the magnetic \nanisotropy of an ferromagnetic semiconductors or ultrathin ferromagnetic metals [3,4], electric current \ngenerating spin-orbit coupling field to assist the magnetization reversal [5-7] , ultrafast polarized optics\nto switch the magnetization [8], and strain to change the anisotropy and the magnetization reversal of \nmagnetic thin film [9,10]. Since the magneto crystalline anisotropy is originated from the spin-orbital \ncoupling of the materials, modification of lattice constant using piezo-voltage can thus directly \nmanipulate the magnetic anisotropy and the magnetization reversal. For decades, the interest of Fe \nfilms anisotropy research never diminishes because of its broad promising application [11]. The thin Fe \nfilm grown on GaAs substrate has the Curie temperature well above the room temperature and it also \nintegrates ferromagnetism and traditional semiconductor GaAs together [12,13]. Very rich magnetic \nanisotropy, coexistence of the in-pane cubic and uniaxial anisotropy, was observed in the epitaxial \ngrowth of thin Fe film on GaAs substrate [14,15]. Thus understanding the physics of piezo-voltage \ncontrol of the magnetic anisotropy and magnetic reversal of this system could be very important for \nrealization the future metallic-semiconducting spintronic applications [16,17].\nIn this paper, we firstly investigated the magnetic hysteresis and the corresponding magnetic \ndomain structures during the magnetic reversal in the virgin state of the Fe/GaAs/piezo-transducer \nheterostructure. We then compared the hysteresis loops of the Fe thin film with magnetic field applied \nin-plane different crystalline orientations under positive/negative piezo-voltages. The piezo-voltages \ncan effectively control the magnetization crossing the intermediate magnetic state during the magnetic \nreversal. Also the magnitude of the additional uniaxial anisotropy induced by piezo-voltages was \nobtained to be ±1.4×103 J/m3at ±75 V.\nII. EXPERIMENTS\nThe ultra-thin 5 nm Fe was grown on n-type GaAs/GaAs substrate using molecular-beam epitaxiy \n(MBE). The substrate of the sample was first polished to 120±10 μm to ensure that the deformation can \nbe transferred to the sample. Then the sample was bonded to the lead zirconate titanate (PZT) \npiezotransducer using two-component epoxy after thinning the substrate. The positive/negative voltage produces a uniaxial tensile/compressive strain in the direction of [110]. The induced strain/stress along \n[110] orientation was measured by strain gauge, which was found to be linearly changed with the \napplied voltage. The magnitude of the additional uniaxial strain/stress for a piezo-voltage of +/-75 V is \napproximately +/-3.5 10−4. Under zero and applied piezo-voltages, the magnetization vectors and the \ncorresponding magnetization domains of the thin Fe film during magnetization reversal along in-plane \ndifferent orientations were measured by using longitudinal magneto-optical Kerr microscopy \n(LMOKM). In the longitudinal setup, the Kerr rotation angle is proportional to the magnitude of the \nmagnetization component along the projection direction of the incident light in the plane. The \nmagnetization vectors thus can be used to determine the relative magnitude ( M/M S) (where Mis the \nmagnetization component along the magnetic field direction and MSis the saturation magnetization) \nand direction of the magnetization. Thus, the hysteresis loops with magnetic field along different \nin-plane orientations measured by the longitudinal Kerr effect can be used to investigate the in-plane \nmagnetic anisotropy. In this work, the experimental measurements were all performed at room \ntemperature, and the magnetic field is at a fixed frequency of 0.5 Hz.\nIII. RESULTS AND DISCUSSIONS\nA. Magnetic anisotropy in virgin state\nRotating the sample in the plane, the LMOKM was used to measure the hysteresis loops and the \ncorresponding magnetic domain structures with magnetic field applied in any direction in plane.\nFigs.1(a)-(c) show the Kerr rotation angle during the magnetization reversal with field applied close to \nthe in-plane major crystalline [110], ]01[1 and [100] orientations, respectively. Each curve was \nmeasured deviating 50from the main crystalline to make sure the magnetization procedure route \ntowards counterclockwise. \nAs shown in Figs. 1(a) and (b), although only one step magnetization switching was observed \nduring magnetization reversal with magnetic field applied in both [110] and ]01[1 directions.\nHowever, the inside physics of magnetic reversal in these two directions are very different. The \nremnant Kerr rotation angle is close to the saturation Kerr rotation angle (about 40 mdeg) with the \nmagnetic field applied in ]01[1 direction. Also the very square and sharp magnetic hysteresis loop was observed along the ]01[1 orientation, indicating the easiest magnetic anisotropy orientation. However, \nthe remnant Kerr rotation angle in [110] direction is only 20 mdeg and the magnetization reversal is \nmuch less abrupt, indicating the relative hard magnetic anisotropy orientation. With magnetic field \nsweeping from positive to negative in ]01[1 direction, the magnetization directly switches from the \ninitial ]01[1 orientation single domain state crossing the 180 degree energy barrier to the final ]101[\nmagnetic state, which is confirmed by the corresponding magnetic domain structures in Fig. 1(b). The \nsystem is only broken into magnetic domains mentioned as II and IV during magnetization switching in \nFig. 1(b). However, the magnetization along [110] orientation is different from that of the ]01[1\norientation during the magnetization reversal. Sweeping the magnetic field (the amplitude is larger than \nsaturated magnetization field) from positive to negative in [110] direction, the magnetization firstly \ncoherently rotates from the field direction to the easy axis direction, then the system breaks into \ndomains and prorogates through 1800domain walls at HC, after that the magnetization coherently \nrotates again from the easy axis to the external magnetic field direction. The strong asymmetry of \nmagnetic hysteresis between [110] and ]01[1 orientation suggests that there is a uniaxial magnetic \nanisotropy between these two directions, which originates from the surface reconstruction of Fe grown \non GaAs [13,14].\nAs shown in Fig. 1(c), a two-step-jump magnetic switching behavior was observed during \nmagnetic reversal with magnetic field applied along [100] orientation. Very similar behavior was also \nobserved in [010] orientation. This symmetry is attributed to the four fold in-plane magnetic anisotropy. \nWith magnetic field sweeping from positive to negative in [100] direction, the magnetization firstly \nswitched anticlockwise to the intermediate state rather than directly switched from the initial state \ncrossing a 180 degree barrier to the final state. The magnitude of the Kerr rotation angle of the \nintermediate state is about 22/to that of the initial state for the [100] direction hysteresis loop, \nwhich suggests that the intermediate state is along ]01[1 direction and about 450away from the initial \nstate. So when the external field along the [100] orientation sweeping from positive to negative through \nzero field, the free energy minima was along [100], ]101[ , 00]1[ orientation, respectively. The \ncorresponding domain states during the magnetization reversal were shown in the inserted images ofFig. 1(c). The scanning area of the magnetic domain images is 580 μm ×580 μm. The three plateaus\n(marked as I, III and V) from positive to negative represent the single domain state of magnetization \nalong [100], ]01[1 and 00]1[ , respectively. While the magnetization of film breaks into domains in \nthe two sharp transitions (II and IV) in Fig. 1(c), which is corresponding to the low and high two-step \nswitching coercive fields HC1and HC2, respectively. \nThe coexistence of the <100> cubic magnetic anisotropy and ]01[1 uniaxial magnetic \nanisotropy was found in our Fe thin film grown on GaAs substrate [13]. Similar magnetic anisotropy \nwas also observed in Fe grown on InAs substrate and GaMnAs grown on GaAs substrate [18,19]. \nConsidering the <100> cubic magnetic anisotropy and ]01[1 uniaxial magnetic anisotropy, the \nmagnetic free energy of our system under external magnetic field can be written down as: \n) cos(HM cosMH cosMHS S S        221281E22\n1                 (1)\nwhere 1His the cubic anisotropy anisotropic field, 2His the uniaxial anisotropy field, MSis the \nsaturated magnetization of Fe film which is about to 1700 A/m [20], is the angle between the \nmagnetization and hard axis [110] orientation and the is the angle between the applied field and \n[110] direction. According to the Stoner-Wohlfarth formula, at a given applied field, the magnetization \ncoherently follows the global free energy minimum: 0/E . This formula can well describe the \nmagnetization reversal in [110] direction with the magnitude of the magnetic field above 20 Oe, as \nshown in the insert of Fig. 2(a). With cosθ =M/M S, the relationship between the anisotropic fields (or \nanisotropy) and external magnetic field H applied in the [110] direction can be written down as: \n)M/M)(H H()M/M(H HS S 1 23\n12               (2).\nBy fitting the coherent rotation part of the magnetization reversal with magnetic field applied in [110] \norientation, the anisotropic fields thus can be calculated. The cubic anisotropic and uniaxial anisotropic\nfields are 356 Oe and 100 Oe in the virgin state. However, this formula can’t be used to describe the \nmagnetization reversal with magnetic field applied in both [110] and ]01[1 orientations. The \nmagnetization reversal was confirmed to not rotate coherently with sweeping the external magnetic \nfield along [110] and [100] orientations, proved by the domain images in Figs. 1(b) and (c). The \nmagnetization switching will happen if the gaining energy of magnetic domains is larger than the \nenergy barrier of the two neighbor local minimas. Cowburn et al. has developed a magnetization reversal model considering both the 900and 1800domain walls [21]. From the obtained magnetic \nanisotropy above by fitting the coherent rotation in [110] orientation, the two global energy minima \ndirections of this sample are ]01[1 and ]101[ directions. Considering the energy barrier between \nthese two global energy minimas, at coercive field this energy barrier of the 1800domain wall is equal \nto the pining field 0180 . The pinning energy can be written down as:   sin HMC,CS 2 20180 , where \nHCis the coercivity when the external field near the uniaxial easy axis. In order to obtain the pinning \nfield, the angular dependence of the coercive field was measured, which was plotted in Fig.2 (b). By \nfitting the angular dependence of coercive field HC2, the energy barrier 0180 = 560 J/cm3 through the \nhard axis [110]/ 0]11[ was obtained.\nB. Piezo-voltage induced magnetic anisotropy\nWith the piezo-voltage induced deformation along [110] direction, we carefully investigated the \nin-plane magnetic hysteresis under strained or stressed situation of the Fe/GaAs thin film. Figs. 3(a)-(c) \nshow the Kerr rotation angle during the magnetization reversal at strain/stress (+/-75 V) states with \nfield applied in [110], ]01[1 and [100] orientations with 50deviation, respectively. For reference, the \nmagnetic hysteresis without strain is shown in Fig. 3 as well. It is very interesting that we can \nefficiently manipulate the magnetization process with piezo-voltages. With magnetic field applied in \n[110] orientation, the magnetic hysteresis loops shows very clear difference close to HC, which is \nshown in Fig. 3(a). Compared with U = 0 V , the magnetic hysteresis becomes more square and the \ncoercive field increases with U = -75 V . However, the magnetic hysteresis becomes less square and the \ncoercivity decreases with U = 75 V. This is due to piezo-voltages induced additional uniaxial anisotropy, \nwhich widens the 1-jump region about the uniaxial easy direction and diminishes the l-jump region \nabout the uniaxial hard direction [20]. However, the magnetic hysteresis loops show no clear difference \nwith magnetic field along ]01[1 orientation. This could be the piezo-voltages induced energy which is \ninsignificant to the magnitude of the uniaxial anisotropy K2. As shown in Fig. 3(c), the magnitude of \nKerr rotation angle in the three plateaus was unvaried under piezo-voltages with magnetic field applied \nin [100] direction, while the most pronounced changes of the two sharp magnetization switches was \nobserved with applied piezo-voltages. The coercive fields of the two sharp changes HC1and HC2correspond to the magnetization crossing from [100] to ]01[1 (00]1[ to ]101[ ) and from ]01[1 to \n00]1[ ( ]101[ to [100]), respectively. The HC2increases with U = 75 V , while it decreases with U = -75 \nV . With sweeping magnetic field from positive to negative in [100] direction, the first switching of HC1\nwas happened much early at positive field with U = 75 V . However, the HC1increases dramatically and \nthe first step switching nearly matches with the second step switching with U= -75 V . The relative \nchange of the HC1and HC2depends not only on the exact direction of applied magnetic field and also \nthe magnitude of the strain/stress. Figs. 3(a) and (c) show that the most effectively manipulation by the \nstrain and stress is the magnetic switching from ]01[1 to ]101[ ( ]101[ to ]01[1 ) direction with field \napplied in [110] direction and the 180 degree switching from [100] to ]01[1 (00]1[ to ]101[ ) \ndirection with field applied in [100] orientation. This is attributed to contribution of an extra uniaxial \nanisotropy induced by the positive/negative piezo-voltages induced the strain/stress, which will \nenhance/decrease ]01[1 uniaxial magnetic anisotropy, corresponding to increase/decrease the energy \nbarrier along [110] orientation. \nWith magnetic field applied in [110] orientation, the magnetic hysteresis loops were measured \nwith applied different piezo-voltages, which is shown in Fig. 4(a). The magnetic hysteresis becomes \nmore and squarer and the coercive field increases with increasing the magnitude of the negative \npiezo-voltages (stress). However, the magnetic hysteresis becomes less and less abrupt and the \ncoercivity decreases with increasing the strain. With piezo-voltage increased from -75 to 75 V (stress to \nstrain), the corresponding coercive field decreases from 1.6 to 0.8 Oe. Compared the coercivity at U = \n+/-75 V to the virgin state, the strain/stress induced the change of the coercive fields along this\norientation is up to 30%. The coercivity was found to roughly decrease linearly with increasing the \npiezo-voltages from -75 to 75 V, which is shown in Fig. 4(b). This phenomenon is attributed to the \npiezo-voltages induced the extra uniaxial anisotropy.\nWhen there is a deformation along [110] orientation, the induced additional uniaxial anisotropic \nterm will be superimposed on the magnetic free energy. In this work the additional uniaxial term \ninduced by strain/stress has the same symmetry as2K. Then the magnetic free energy of Eq. (1) can be \nmodified as: ) cos(HM cosMH cosMH cosMH ES S a S S         2 2\n22\n121\n21281  (3)\nwhere aHis the additional uniaxial anisotropic field induced by the deformation along [110] orientation. Thus the relationship between the anisotropic fields and external magnetic field H applied\nin the [110] direction with the extra uniaxial anisotropic field can be written down as:\n)M/M)(H H H()M/M(H HS a S 1 23\n12                                  (4).\nUsing the virgin state fitted cubic and uniaxial anisotropy H1= 356 and H2= 100 Oe , then the \npiezo-voltages induced uniaxial anisotropy can be obtained by fitting the coherent rotation \nmagnetization with magnetic field applied in [110] direction using Eq. (4), which is shown in Fig. 5.\nThe additional uniaxial anisotropic fields under strain/stress are +/- 8 Oe with the piezo-voltage +/-75 \nV respectively, which is about 8% of the magnitude of H2. Thus the additional uniaxial anisotropy \ninduced by piezo-voltages at +/- 75 V are +/-1.4×103 J/m3. \nIV.CONCLUSION\nIn summary, the magnetic anisotropy and magnetic reversal of Fe/GaAs/PZT hetero-structure\nwith and without piezo-voltages were carefully investigated using longitudinal magneto-optical Kerr \nmicroscopy. The coexistence of cubic anisotropy and in-plane uniaxial anisotropy in [110] direction \nwas found in the virgin state. The system was found to break into domains only at sharp magnetization \nswitching regime, which was confirmed by the corresponding magnetic domain structures. With \npiezo-voltages induced deformation in [110] orientation, the strain/stress was found to effectively \nmanipulate the magnetization reversal. The coercivity during the magnetic reversal was found to \nroughly decrease linearly with increasing the piezo-voltages from -75 to 75 V with magnetic field \napplied in [110] direction. The two jump magnetization switching to one jump magnetization switching \nduring the magnetic reversal was achieved by piezo-voltages with magnetic field applied in [100] \ndirection. The additional uniaxial anisotropy induced by piezo-voltages at +/- 75V are +/-1.4×103 J/m3, \nwhich is large enough to control the magnetization reversal in our Fe/GaAs/PZT hetero-structure.\nACKNOWLEDGEMENTS\nWe thank X. Q. Ma for useful discussions. We also thank Shanghai Synchrotron Radiation \nFacility for characterizing FCC structure of the Fe film. This work was supported by “973 Program” \nNo. 2011CB922200, NSFC Grant Nos. 11174272 and 61225021. K.Y.W. acknowledges the support of \nChinese Academy of Sciences “100 talent program”. \nReferences[1] Arne Brataas, Andrew D. Kentand Hideo Ohno, Nat. mat. 11, 372 (2012).\n[2] D. A. Allwood, G. Xiong, C. C. Faulkner, D, Atkinson, D. Petit, P. R. Cowburn, Science, 309, \n1688 (2005). \n[3] D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura and H. Ohno, Nature, 455, 25 \n(2008). \n[4] T. Maruyama, Y. Shiota, T. Nozaki, K. Ohta, N. Toda, M. Mizuguchi1, A. A. Tulapurkar, T. \nShinjo, M. Shiraishi, S. Mizukami, Y. Ando and Y. Suzuki, Nat. Nano. 4, 158 (2009). \n[5] A. Chernyshov, M. Overby, X. Liu, J. K. Furdyna, Y. Lyanda-Geller, and L. P. Rokhinson, Nat. \nPhys. 5, 656 (2009).  \n[6] Yuanyuan Li, Y. F. Cao, G. N. Wei, Yanyong Li, Y. Ji, K. Y. Wang, K. W. Edmonds, R. P. \nCampion, A. W. Rushforth, C. T. Foxon, and B. L. Gallagher, App. Phys. Lett. 103, 022401 \n(2013).    \n[7] I. Miron, G. Gaudin, S. Auffret, B. Rodmacq, A. Schuhl, S. Pizzini, J.Vogel and P. Gambardella, \nNat. Mat. 9, 230 ( 2010 ).       \n[8] Th. Gerrits, H. A. M. van den Berg, J. Hohlfeld, L. Bär and Th. Rasing, Nat. 418, 509 (2002).\n[9] N. Lei, T. Devolder, G. Agnus, P. Aubert, L. Daniel, J.-V. Kim, W. Zhao, T. Trypiniotis, R. P. \nCowburn, C. Chappert, D. Ravelosona and P. Lecoeur, Nat. Comms. 4, 1378 (2013).\n[10] A. W. Rushforth, E. De Ranieri, J. Zemen, J. Wunderlich,K. W. Edmonds,C. S. King, E. Ahmad, \nR. P. Campion, C. T. Foxon, B. L. Gallagher, K. Výborný, J. Kučera, and T. Jungwirth, Phys. Rev. \nB, 78, 085314 (2008).\n[11] J. Ye, W. He, Q. Wu, H. L. Liu, X. Q. Zhang, Z. Y. Chen and Z. H. Cheng, Scientific Reports, 3, \n2148 (2013).          \n[12] G. A. Prinz and J. J. Krebs, Appl. Phys. Lett. 39, 397 (1981).   \n[13] K. K. Meng, J. Lu, S. L. Wang, H. J. Meng, J. H. Zhao, J. Misuraca, P. Xiong, and S. von Molnár, \nAppl. Phys. Lett. 97, 23250 (2010).           \n[14] E. M. Kneedler, B. T. Jonker, P. M. Thibado, R. J. Wagner, B. V. Shanabrook, and L. J. Whitman, \nPhys. Rev. B, 56, 8163 (1997).        \n[15] E. Gu, J. A. C. Bland, C. Daboo, M. Gester, and L. M. Brown, Phys. Rev. B, 51, 3596 (1995).  \n[16] G. Wastlbauer and J. A. C. Bland, Adv. Phys. 54, 137 (2005). \n[17] X.H. Lou, C. Adelmann, S. A. Crooker, E. S. Garlid, J.J. Zhang, K. S. M. Reddy, S. D. Flexner, C. \nJ. Palmstrøm And P. A. Crowell, Nature Physics, 3, 197 ( 2007). \n[18] Y. B. Xu, D. J. Freeland, M. Tselepi and J. A. C. Bland, Phys. Rev. B 62, 1167 (2000).\n[19] K.Y. Wang, M. Sawicki, K.W. Edmonds, R. P. Campion, S. Maat, C. T. Foxon, B. L. Gallagher, \nand T. Dietl, Phys. Rev. Lett. 95, 217204 (2005).  \n[20] Y. B. Xu, E. T. M. Kernohan, D. J. Freeland, A. Ercole, M. Tselepi, and J. A. C. Bland ɼPhys. Rev. \nB, 58, 890(1998). \n[21] R. P. Cowburn and S. J. Gray, J. Ferré, J. A. C. Bland, J. Miltat, J. Appl. Phys. 78, 7212, (1995).\nFigure Captions:FIG .1. Magnetic hysteresis loops in the virgin state with magnetic field applied along in-plane (a) [110] \norientation, (b) ]01[1 orientation, and (c) [100] orientation. The insert of (a) shows the magnetic \nhysteresis loop in a wide field range, the insert images of (b) and (c) corresponding to the magnetic \ndomain structures during the magnetic reversal in ]01[1 and [100] orientations, respectively. The \nscanning area of the magnetic domain images is 580 μm×580 μm. \nFIG .2 . (a) The experimental and the fitting of coherent magnetization with magnetic field in [110] \norientation; (b) Angular dependent of the coercive fields with magnetic field applied along different \nin-plane orientations in the virgin state , where θ=0 º, along [110] direction. The areas marked I is the \nareas with one-step hysteresis loop, and the areas marked II is the areas with two-step hysteresis loop. \nFIG .3. Magnetic hysteresis loops under piezo-voltages at 0 V (black curve), 75 V (red curve) and -75 V\n(blue curve) with magnetic field applied along (a) [110] direction, (b) ]01[1 direction, and (c) [100]\ndirection, respectively. \nFIG .4. (a) The magnetic hysteresis loops with sweeping magnetic field along [110] direction at \ndifferent piezo-voltages; (b) The coercivity dependence of the piezo-voltages with magnetic field \napplied in [110] direction, the line is guide to the eye.\nFIG .5. The experimental data with field applied in [110] direction in the coherent rotation with \npiezo-voltages at 75 V (open square) and -75 V (open triangle), respectively. The lines are fitting \ncurves. Figure 1 Y.Y. Li et al.\nFigure 2 Y.Y. Li et al.\nFigure 3 Y.Y. Li et al.\nFigure 4 Y.Y. Li et al.\nFigure 5 Y.Y. Li et al.\n"    },    {        "title": "1404.7389v1.The_AC_multi_harmonic_magnetic_susceptibility_measurement_setup_at_the_LNF_INFN.pdf",        "content": "Submitted\nto\n“\nApplied\nMechanics\nand\nMaterials\n”\nThe\nAC\nmulti-harmonic\nmagnetic\nsusceptibility\nmeasurement\nsetup\nat\nthe\nLNF-INFN\nShenghao\nWang\n1\n,a\n,\nAugusto\nMarcelli\n2\n,1\n,b\n*\n,\nDaniele\nDi\nGioacchino\n2\n,c\nand\nZiyu\nWu\n1\n,d\n*\n1\nNational\nSynchrotron\nRadiation\nLaboratory,\nUniversity\nof\nScience\nand\nTechnology\nof\nChina,\nHefei\n,\n230026,\nP.R.\nChina\n2\nIstituto\nNazionale\ndi\nFisica\nNucleare\n-\nLaboratori\nNazionali\ndi\nFrascati,\nP.O.Box\n13,\n00044\nFrascati\n(RM),\nItaly\na\nronaldo9@mail.ustc.edu.cn\n,\nb\nAugusto.Marcelli@lnf.infn.it\n,\nc\ndaniele.digioacchino@lnf.infn.it\n,\nd\nwuzy@ustc.edu.cn\nKeywords\n:\nAC\nmagnetic\nsusceptibility,\nmeasurement,\ninstrumental\ncontrol,\ndata\nacquisition,\nLabVIEW.\nAbstract\n.\nThe\nAC\nmagnetic\nsusceptibility\nis\na\nfundamental\nmethod\nin\nmaterials\nscience\n,\nwhich\nallows\nto\nprobe\nthe\ndynamic\nmagnetic\nresponse\nof\nmagnetic\nmaterials\nand\nsuperconductors.\nT\nhe\nLAMPS\nlaboratory\nat\nthe\nLaboratori\nNazionali\ndi\nFrascati\nof\nthe\nINFN\nhost\ns\nan\nAC\nmulti-harmonic\nmagnetometer\nthat\nallows\nperforming\nexperiments\nwith\nan\nAC\nmagnetic\nfield\nranging\nfrom\n0.1\nto\n20\nGauss\nand\nin\nthe\nfrequency\nrange\nfrom\n17\nto\n2070\nHz.\nA\nDC\nmagnetic\nfield\nfrom\n0\nto\n8\nT\nproduced\nby\na\nsuperconducting\nmagnet\ncan\nbe\napplied,\nwhile\ndata\nmay\nbe\ncollected\nin\nthe\ntemperature\nrange\n4.2-300\nK\nusing\na\nliquid\nHe\ncryostat\nunder\ndifferent\ntemperature\ncycles\nsetups.\nThe\nfirst\nseven\nAC\nmagnetic\nmulti-harmonic\nsusceptibility\ncomponents\ncan\nbe\nmeasured\nwith\na\nmagnetic\nsensitivity\nof\n1x10\n-6\nemu\nand\na\ntemperature\nprecision\nof\n0.01\nK.\nHere\nwe\nwill\ndescribe\nin\ndetail\nabout\nschematic\nof\nthe\nmagnetometer,\ns\npecial\nattention\nwill\nbe\ndedicated\nto\nthe\ninstruments\ncontrol\n,\ndata\nacquisition\nframework\nand\nthe\nuser-friendly\nLabVIEW-based\nsoftware\nplatform.\nIntroduction\nThe\nAC\nmagnetic\nsusceptibility\nmeasurement\nis\na\nunique\nmethod\nsuitable\nto\nprovide\na\nprecise\ncharacterization\nof\nmagnetic\nand\nsuperconducting\nmaterials\nin\na\nnon-destructive\nway,\nparticularly\nappropriate\nto\nstudy\nthe\ndynamic\nmagnetic\nresponse\nof\na\nmaterial\n[1]\n.\nIn\nan\nAC\nmagnetic\nsusceptibility\nmeasurement\nexperiment,\nthe\nmagnetization\nis\nperiodically\nchanged\nin\nresponse\nto\na\ntime-varying\nexciting\nm\nagnetic\nfield\nh(t)\n:\n0\n( ) cos( )\nh t h t\n\n\n.\n(1)\nwhose\nmagnetization\noscillations\ncan\nbe\ndescribed\nas\n:\n' ''\n0 0\n( ) cos( ) sin( )\nM t h t h t\n   \n \n.\n(2)\nwhere\nχ\n'\nand\nχ\n''\nrepresent\nrespectively\nthe\nin-phase\nand\nout-of-phase\ncomponents\nof\nthe\nmagnetic\nsusceptibility\nwith\nthe\napplied\nmagnetic\nfield.\nThe\nin-phase\ncomponent\nχ\n'\nis\nassociated\nto\nthe\ndispersive\nmagnetic\nresponse\nof\nthe\nsample,\nwhile\nthe\nimaginary\npart\nχ\n''\nis\nproportional\nto\nthe\nenergy\ndissipation.\nThe\nlatter\nis\nconverted\nin\nto\nheat\nduring\none\ncycle\nof\nthe\nAC\nfield\nor\nthe\nenergy\nabsorbed\nby\nthe\nmaterial\nfrom\nthe\napplied\nAC\nfield.\nUsing\na\ncomplex\nnotation,\nχ\n'\nand\nχ\n''\ncan\nbe\ncombined\nto\nform\nthe\ncomplex\nsusceptibility.\nIf\nthe\nsystem\nhas\na\nmagnetic\nlinear\nresponse\n,\nonly\nthe\nfundamental\nsinusoidal\nexciting\nfrequency\nwaveform\nis\npresent.\nHowever,\nwhen\nthe\nmagnetic\nresponse\nof\nthe\nsample\nis\nnon\nlinear\n(e.g.,\nfor\nmagnetic\nor\nsuperconductor\nsamples),\nthe\npure\nsinusoidal\nfield\ninduces\na\ndistorted\nwaveform\ncharacterized\nby\nnon-sinusoidal\noscillations\nof\nthe\nmagnetization\nof\nthematerial.\nThese\noscillations\nmay\nbe\ndescribed\nas\na\nsum\nof\nsinusoidal\ncomponents\nthat\noscillate\nat\nharmonics\nof\nthe\ndriving\nfrequency:\n' ''\n0 n n\n( ) [ cos( ) sin( )]\nM t h n t n t\n   \n \n\n.\n(3)\nwhere\nχ\n'\nn\nand\nχ\n''\nn\n(n\n=\n1,\n2,\n3\n…\n)\nare\nthe\nin-phase\nand\nout-of-phase\ncomponents\nof\nthe\nharmonic\nsusceptibilities.\nIn\nthe\ncomplex\nnotation,\nχ\n'\nn\nand\nχ\n''\nn\ncan\nbe\ncombined\nto\nform\nthe\ncomplex\nharmonic\nsusceptibilities.\n' ''\nn n n\ni\n  \n \n.\n(4)\nA\nreliable\ncharacterization\nof\nmaterials\nwith\na\nnon-linear\nmagnetic\nresponse\nrequires\nthe\nmeasurement\nof\nharmonic\nsusceptibilities\nbeyond\nthe\nfundamental\none.\nMoreover,\nthe\nAC\nmagnetic\nmulti-harmonic\nsusceptibility,\nby\nprobing\nthe\nreal\nand\nimaginary\nparts\nof\nthe\nfirst\nand\nthe\nhigher\nharmonic\nsusceptibility,\nmay\nseparate\nlinear\nand\nnon-linear\ntransport\nprocesses\noccurring\nin\na\nmaterial,\nallowing\nthe\ndetermination\nof\ndifferent\nmagnetic/superconducting\nphases\neventually\npresent\nin\nthe\nsample\nunder\nanalysis.\nA\nmulti-harmonic\nAC\nmagnetic\nsusceptibility\nmeasurement\nsetup\nis\noperational\nin\nthe\nLAMPS\nlaboratory\n(\nLAboratory\nfor\nMagnetism\nHigh\nPressure\nand\nSpectroscopy\n)\nof\nthe\nLaboratori\nNazionali\ndi\nFrascati\n(LNF)\nof\nthe\nIstituto\nNazionale\ndi\nFisica\nNucleare\n(INFN\n).\nIt\nwas\nbuilt\nfrom\ncommercial\navailable\ncomponents\nand\ncustom\nmade\ndevices,\nthese\nscientific\ninstruments\ncome\nfrom\ndifferent\nsoftware\nbackground\n.\nTo\nmeasure\nthe\nsusceptibility\n,\nusers\nneed\nto\nchange\nthe\ntemperature\nthousands\nof\ntimes\nduring\nan\nacquisition\nand\nit\nis\nalmost\nimpossible\nto\nrecord\ndata\nand\ndisplay\nthem\nusing\nthe\noriginal\ninstrumental\ninterfaces,\ncontrols\nand\ndata\nacquisition\npackages.\nIn\norder\nto\noptimize\nthe\nmanagement\nof\ninstruments,\nand\nto\nrealize\nautomatic\ndata\nacquisition,\ndisplay\nand\nrecording,\na\ndedicated\nsoftware\nplatform\nwas\nsupposed\nto\nget\ndeveloped.\nAs\na\ngraphical\nprogramming\nlanguage,\nLabVIEW\n(National\nInstrument's\nLaboratory\nVirtual\nInstrumentation\nEngineering\nWorkbench)\nis\nnow\na\nvery\npopular\ndevelopment\ntool\nwidely\nused\nin\nmany\nscientific\nand\nindustrial\nareas.\nThe\neasy\navailability\nof\nhardware\ndrivers\nfor\na\nvery\nlarge\nnumber\nof\nscientific\ninstruments,\nthe\neasy-to-use\nmultithreaded\nprogramming,\nthe\nconvenient\ngraphic\nuser\ninterface\n(GUI)\ndesign,\nthe\nhigh-efficiency\ndebugging\nfunctions\nand\nmany\nother\nremarkable\nfeatures\nmake\nLabVIEW\na\nflexible\ntool\noptimized\nfor\nan\ninstrument-oriented\nprogramming\nenvironment.\nActually,\nit\nhas\nbeen\nalready\nsuccessfully\nused\nin\nmany\nother\nsimilar\napplications\n[2-4]\n.\nHere\nwe\nwill\ndescribe\nschematically\nthe\ndiagram\nand\nthe\nworking\nprinciple\nof\nthe\nAC\nmagnetic\nsusceptibility\nmeasurement\nsetup\navailable\nat\nLAMPS.\nT\nhe\ncontrol\nof\nthe\ninstruments,\nthe\ndata\nacquisition\nframework\nand\nthe\nuser-friendly\nLabVIEW-based\nsoftware\nplatform\nwill\nalso\nbe\nintroduced\n.\nFinally,\nas\nan\nexample\n,\nexperimental\nresults\nperformed\non\na\nsuperconducting\npnictide\nsample\nusing\nthis\nmeasurement\nsetup\nwill\nbe\npresented\n.\nThe\nmeasurement\nsetup\nand\nthe\nworking\nprinciple\nIn\nthe\nAC\nmagnetic\nsusceptibility\nsetup\n,\nthe\nmagnetic\nmoment\nand\nthe\nsusceptibility\nof\nthe\nsample\nare\nmeasured\nby\nthe\ninduction\nin\ntwo\ncounter-wound\ncoils\nwhile\nthe\nAC-magnetic\nfield\nis\napplied.\nIndeed,\nthe\nvoltage\ninduction\nin\nthe\ncoils\nis\ndirectly\nrelated\nto\nthe\nmagnetic\nmoment\nin\nthe\nsample.\nFig.\n1\nillustrates\nthe\nlayout\nof\nthe\nAC\nmagnetometer.\nThe\nheart\nof\nthe\ninstrument\nis\na\ngradiometer\nbased\non\na\nbridge\nmade\nby\ntwo\npick-up\ncoils\nconnected\nin\nseries\nand\nwounded\nin\nthe\nopposite\nsense.\nIt\nis\nsurrounded\nby\na\ndriving\nexcitation\ncoil,\nwhich\nis\ncalled\nthe\nfirst\nderivative\nconfiguration\nof\nthe\ngradiometer\ncoil.\nThe\ndesign\nis\nused\nto\nreduce\nthe\nmagnetic\nfield\nfluctuations\nnoise\nin\nthe\ndetection\ncircuit\ndue\nto\nthe\napplied\nmagnetic\nfield.\nThe\nexcitation\ncoil\nreceives\nthe\nAC\nsignal\nfrom\na\nfunction\ngenerator,\nmagnified\nby\nan\namplifier\nthat\nyields\nto\nan\nalternating\ndriving\nmagnetic\nfield,\nwhose\nfrequency\nmay\nrange\nfrom\n17\nHz\nto\n1070\nHz\nwith\na\nvariable\namplitude\nfrom\n0\nto\n20\nGauss.Figure\n1\n.\nLayout\nof\nthe\nAC\nmagnetic\nsusceptibility\nsetup\n.\n1.double\nvessel\ncryostat,\n2.\nliquid\nN\n2\n,\n3.\ncarbon\nresistor\ninside\nthe\nchamber,\n4.\ncarbon\nresistor\nat\nthe\nVTI\nposition,\n5.\nliquid\nHe,\n6.\ncarbon\nresistor\non\ntop\nof\nthe\nmagnet,\n7.\nmagnet,\n8.\nexcitation\ncoil,\n9.\ncarbon\nresistor\nat\nthe\nbottom\nof\nthe\nmagnet,\n10.\npinhole,\n11.\npick-up\nbridge\n(balance)\ncoil,\n12.\npick-up\nbridge\n(sensing)\ncoil,\n13.\nPt\nthermometer,\n14.\ncarbon\nresistor\nthermometer,\n15.\ncarbon\nresistor\n(sample\nheater),\n16.\nsample.\nThe\nsample\nis\nmounted\non\na\nsapphire\nholder\nslab\nlocated\nat\nthe\ncentre\nof\none\nof\nthe\ntwo\npick-up\ncoils\n(the\n\"\nsensing\n\"\ncoil)\nof\nthe\nbridge\nwhile\nthe\nsecond\none\n(the\n\"\nbalance\n\"\ncoil)\nhas\nto\nremain\nempty.\nBeing\nnon-magnetic\nand\na\ngood\nthermal\nconductor,\nsapphire\nwas\nchosen\nas\nthe\n\"\nsubstrate\n\".\nAlso\nimportantly,\ncharacterized\nby\na\nlow\nelectric\nconductivity\n,\nsapphire\nguarantees\nlow\ncurrent\nlosses.\nA\nPt\nthermometer\nand\na\ncarbon\nresistor\nplaced\nnear\nthe\nsample\nare\nin\nthermal\ncontact\nwith\nthe\nsapphire\nholder.\nThe\nfirst\nreads\nthe\ntemperature\nof\nthe\nsample\nwhile\nthe\ncarbon\nresistor\nis\nused\nto\nheat\nthe\nsample\nin\norder\nto\nperform\nexperiments\nvs.\ntemperature\nin\na\nrange\ngoing\nfrom\n4.2\nto\n300\nK.The\nAC\nmagnetic\nfield\ngenerated\nby\nthe\ndriving\ncoil\ninduces\na\nvariable\nmagnetic\nmoment\non\nthe\nsample\nand\nconsequently\na\nflux\nvariation\nin\nthe\npick-up\ncoils,\nwhose\nvoltage\nsignal\nis\nmeasured\nby\na\nmulti-harmonic\nlock-in\namplifier.\nThe\nlatter\nacts\nas\na\ndiscriminating\nvoltmeter\n,\nit\nmeasures\nthe\namplitude\nand\nthe\nrelative\nphase\nof\nthe\nAC\nsignal,\nu\nsing\nthe\nsame\nfundamental\nfrequency\nof\nthe\nexcitation\nas\nthe\nreference\nsignal\nwhile\na\nfixed\nphase\nrelationship\nis\nprovided\nrespect\nto\nit.\nThe\nlock-in\namplifier\nis\na\nband\npass\nfilter\nwith\na\nvery\nlarge\nQ\nwith\nits\ncenter\nfrequency\nset\nat\nthe\nselected\nsignal\nfrequency.\nThe\noutput\nis\nan\namplified\nDC\nvoltage\nproportional\nto\nthe\nsynchronous\nAC\ninput\nsignal.\nThe\ntemperature\nof\nthe\nsample\nholder\nand\nthe\ncoils\nassembly\ncan\nbe\nvaried.\nThey\nare\nlocated\nin\na\ndouble\nvessel\ncryostat\nthermally\ncontrolled\nby\na\nHe\ngas-flow.\nThe\nouter\nvessel\nis\nfilled\nwith\nliquid\nnitrogen,\nwhile\nthe\nliquid\nHe\nfills\nthe\ninner\none,\nwhere\na\nsuperconducting\nmagnet\noperates\nin\nthe\nrange\nfrom\n0\nto\n8\nT\nin\npersistent\nor\nnon-persistent\nmodes.\nThe\nsample\nis\nmounted\nat\nthe\ncentre\nof\nthe\nsuperconducting\nmagnet\nand\nits\ntemperature\ncan\nbe\nchanged\nvia\nthe\ncold\nHe\ngas\nflow\nfrom\na\npinhole\nthat\nis\nmanually\ncontrolled\nvia\na\nthrottle\nand\na\nneedle\nvalve\non\nthe\ntop\nof\nthe\ncryostat.\nBefore\nany\nmeasurement\na\npurging\nof\nthe\nsample\ncompartment\nwith\nclean\nHe\ngas\nhas\nto\nbe\ndone.\nThe\nmagnetic\nmeasurements\ncan\nbe\nperformed\nboth\nin\nthe\nzero\nfield\ncooled\n(ZFC)\nand\nin\nthe\nfield\ncooled\n(FC)\nmodes.\nIn\nthe\nZFC\nmode\nthe\nsample\nis\nslowly\ncooled\nbelow\nthe\ntransition\ntemperature\nwithout\nthe\nDC\nmagnetic\nfield,\nthen\nthe\nmagnetic\nfield\nis\nturned\non,\nwhile\nin\nthe\nFC\nmode\nthe\nmagnetic\nfield\nis\nturned\non\nabove\nthe\ncrit\nical\ntemperature\nT\nc\nof\nthe\nsuperconducting\nor\nof\nthe\nmagnetic\nphase.\nThen\nthe\nsample\nis\ncooled\ndown\nbelow\nthe\ntransition\ntemperature\nand\nafter\nthat,\nthe\ntemperature\nis\nlet\nto\nincrease\nand\nthe\nmeasurement\nstarts.\nAC\nmagnetic\nmulti-harmonic\nsusceptibility\nexperiments\nwith\na\nmagnetic\nsensitivity\ndown\nto\n1x10\n-6\nemu\nand\na\ntemperature\nprecision\nof\n0.01\nK\ncan\nbe\nperformed\nwith\nthis\nsetup.\nHigher\ncomponents\nof\nthe\nmagnetic\nsusceptibility\ncan\nbe\ncollected\nup\nto\nthe\nseventh\nharmonic.\nAll\nthese\ncharacteristics\nmake\nthis\ninstrument\nparticularly\nsuitable\nto\nprobe\nweak\nmagnetic\nphases\npresent\nin\ndiluted\nmagnetic\nstructures\nsuch\nas\nantiferromagnet,\nsuper\nparamagnetic\nsystems,\nspin\nglass\nand\nthe\ntransport\nproperties\nof\nmany\ncomplex\nmaterials\nand\nin\nparticular,\nto\ninvestigate\nthe\nvortex\ndynamics\nof\nsuperconductor\nmaterials.\nInstrumental\ncontrol\nand\ndata\nacquisition\nFig.\n2\nshows\nthe\ninstrumental\ncontrol\nand\nthe\ndata\nacquisition\nscheme\nof\nthe\nmagnetic\nsusceptibility\nmeasurement\nsetup.\nWe\nutilize\nHP\n8116A\nfunction\ngenerator\nto\nproduce\na\nsinusoidal\nsignal,\nwhich\nis\nmagnified\nby\na\ncustom\nmade\namplifier.\nThe\nreleased\nsinusoidal\nsignal\nis\nmonitored\nby\nthe\nTektronix\nTDS\n1002\noscilloscope\n,\nand\nthen\nthe\nsignal\nis\ntransmit\nted\nto\nthe\nexcitation\ncoil.\nThe\nsignal\nrecovery\n7265\nmulti-harmonic\nlock-in\namplifier\nis\nused\nhere\nto\nmeasure\nthe\nvoltage\nsignal\ngenerated\nby\nthe\nflux\nvariation\nin\nthe\npick-up\ncoils.\nThe\ntemperature\nof\nthe\nsample\nunder\nanalysis\nis\ncollected\nby\nthe\nLake\nShore\n218\nthermometer\nand\nthe\nOxford\ntemperature\ncontroller\nITC503.\nThe\nDC\nsuperconducting\nmagnet\nis\ncontrolled\nby\nthe\nOxford\npower\nsupply\nIPS120-10.\nAn\nAgilent\n34970A\ndata\nacquisition\nswitch\nunit\nis\ndedicated\nto\nmeasur\ning\nthe\nresistance\nof\nthe\nfour\ncarbon\nresistors\nmounted\nat\nfour\nreference\npositions\nof\nthe\nliquid\nHe\ntank,\nby\nwhich\nwe\ncould\nevaluate\ncontinuously\nthe\nlevel\nof\nthe\nliquid\nHe\ninside\nthe\nreservoir.\nCommunications\nof\nall\ninstruments\nand\ntheir\nmanagement\nwith\na\npersonal\ncomputer\nwere\nrealized\nin\ndifferent\nways\nfollowing\ncorrelated\nprotocols\nschematically\nillustrated\nin\nFig.\n2\n.\nThis\nmultipurpose\nconfiguration\nincludes\ntwo\npersonal\ncomputers,\none\nlocated\nnear\nthe\ninstruments\nand\none\nin\nthe\ncontrol\nroom\n,\nb\noth\nshould\nbe\ncapable\nto\nrun\ndata\nacquisition\nand\nto\ncontrol\ninstruments.\nThe\nmission\nis\nfulfilled\nby\nmeans\nof\nspecial\nnetwork\ncommunication\ndevices\nand\nthe\nhelp\nof\na\nserial\nserver\nMoxaNport\n5410.\nMoreover,\nthe\noriginal\nRS-232\nserial\ncommunication\nmode\nof\nthe\nsuperconducting\nmagnet\npower\nsupply\nwas\ntransferred\nto\nthe\nEthernet-based\n(LAN)\nTCP/IP\nprotocol\nthat\nmakes\nthis\ninstrument\nalso\navailable\non\nthe\nnetwork\n.\nA\nhigh-performance\nEthernet-to-GPIB\ncontroller\n(NI\nGPIB-ENET/1000),\nwith\na\nmaximum\nGPIB\ntransfer\nrate\nof\n5.6\nMB/s\nsupports\nthe\naccess\nvia\nTCP/IP\nto\nall\naforementioned\ninstruments\n.\nFinally,\nthe\nAsus\nGX1008\nis\nthe\nswitchboard\nthat\nallows\nto\nshareall\ninstruments\namong\ntwo\nusers\non\nthe\nnetwork\nby\nhinging\ntogether\nthe\nserial\nserver,\nthe\nEthernet-to-GPIB\ncontroller\nand\nup\nto\ntwo\npersonal\ncomputers.\nFigure\n2\n.\nControl\nand\ndata\nacquisition\nlogic\nof\nthe\nmagnetic\nsusceptibility\nsetup\n.\n1.\nexcitation\ncoil,\n2.\nPt\nthermometer,\n3.\ncarbon\nresistors,\n4.\npick-up\nbridge\ncoil,\n5.\ncarbon\nresistor,\n6.\nmagnet.\nThe\nLabVIEW-based\nsoftware\nplatform\nFig.\n3\nis\nthe\nmain\nGUI\nof\nthe\nLabVIEW\nbased\nsoftware\nplatform.\nIn\nthe\nnext\nwe\nwill\ndescribe\nhow\na\ntypical\nexperiment\nrun.\nAfter\nstarting\nthe\nprogram,\nusers\nneed\nto\nlogin\nfrom\nthe\nmain\nmenu\n,\nh\nelp\nand\ncontacts\ninformation\nare\nalso\naccessible\nfrom\nthe\nsame\nmenu.\nIn\nthe\nsecond\nphase\nusers\nwould\nbe\nasked\nwhether\nto\nenable\nthe\nsuperconducting\nmagnet\nfield.\nThe\npositive\nanswer\nstarts\nthe\nmodule\nofsuperconducting\nmagnet\ncontrolling,\nwhile\nthe\nprogram\njumps\nto\nthe\nnext\nprocedure\nif\nyou\nlikely\nrun\nexperiments\nwith\nthe\nDC\nmagnet\nfield\nsets\nto\nzero.\nIn\nthe\nfollowing\nstep,\nusers\nare\nrequired\nto\nset\nexperimental\nparameters\nand\ninstruments:\nfile\nname\nof\nthe\nrecorded\ndata,\nmeasurement\ntime\ninterval\nand\na\nvalid\ntemperature\nrange\nfor\nthe\nsample.\nOn\nthe\nright\npart\nof\nthe\nGUI\nwe\nfound\nhow\nto\nset\neach\ninstrument.\nExperimental\nnotes\ncan\nbe\nwritten\ndown\nby\nusers\nin\nthe\nbottom\nof\nthe\nGUI.\nFigure\n3\n.\nMain\nGUI\nof\nthe\nAC\nsusceptibility\nmeasurement\nsoftware\nplatform.\nAfter\ncorrect\nsetting\nof\nthe\nrequired\nparameters,\nthe\n\"Start\nAcquisition\"\nbutton\ntriggers\ninitialization\nof\nall\nthe\ninvolved\ndevices\n.\nThen,\ndata\nwould\nbe\nacquired\nfrom\nthe\ntemperature\ncontroller,\nthermometer\nand\nsignal\nrecovery,\nat\nthe\nsame\ntime,\ngraph\nof\ntemperature\nvs.\ntime,\ntogether\nwith\nthe\n1\nst\nharmonic\nand\nthe\nother\nharmonics\nvs.\ntemperature\nwould\nbe\ndisplayed\nin\ndifferent\npages\nof\nthe\nTab\ncontrol.\nAnd\nmeasurement\nresults\nwill\nbe\nstored\n(with\na\nfeatured\nformat)\nas\na\ntext\nfile\nthat\nallow\nusers\nto\nconduct\noff-line\ndata\npost-\nprocessing.\nFrom\nmain\nGUI\nof\nthe\nsoftware\nplatform,\nmeasurement\nof\nthe\nlevel\nof\nthe\nliquid\nHe\nand\nmonitoring\nof\nthe\nexcitation\nsignal\nwaveform\nare\navailable\nvia\nthe\n\"He\ndetection\"\nand\n\"Oscilloscope\"\nmenu,\nrespectively.\nMore\ndetails\nabout\nthe\nsoftware\ndevelopment\nprocedure,\nthe\nflow\nchart\nand\nother\nfeatures\ncan\nbe\nfound\nin\nRef.\n[5].\nExperimental\nresults\nand\ndiscussion\nTo\ngive\na\nbetter\nfeeling\nof\nthe\ninstrument\n,\nwe\nwill\nshow\nAC\nmulti-harmonic\nsusceptibility\ndata\ncollected\non\nthe\nN\nd\nFeAsO\n1-0.14\nF\n0.14\ncompound\nusing\nthe\nabove\nexperimental\nsetup\nand\nsoftware\n.\nThe\nsample\nwas\nsynthesized\nin\nBeijing\nby\na\nhigh-pressure\nsynthesis\nmethod\nstarting\nfrom\nNd,\nAs,\nFe,\nFe\n2\nO\n3\n,\nFeF\n3\npowders.\nAdditional\ninformation\nof\nthis\nsample\nare\navailable\nin\nRef.\n[6]\n.\nIn\nthe\nexperiments,\nthe\nsample\nwas\ncooled\nwith\na\nzero\nfield\ncooling\n(ZFC)\nprocedure,\nthe\namplitude\nof\nthe\napplied\nAC\nmagnetic\nfield\nwas\nset\nto\n3.9\nG\nand\ndata\nwere\ncollected\nat\nthe\nfrequency\nof\n507\nHz.First\nand\nthird\nharmonics\nof\nthe\nAC\nmagnetic\nsusceptibility\nwere\nrecorded\nand\ndata\ns\nare\nshown\nin\nFig.\n4\n.\nFrom\nthe\nbehaviour\nof\nthe\nfirst\nand\nthird\nharmonics\nof\nthe\nAC\nmagnetic\nsusceptibility\nvs.\ntemperature\n,\nwe\nrecognized\na\nsuperconducting\ndiamagnetic\nphase\naround\nT\nc\n(47\nK)\nand\nan\nantiferromagnetic\nphase\naround\nT\nm\n(90\nK).\nSpectra\nare\nclearly\nseparated,\nin\nparticular\nin\nthe\nplot\nof\nthe\nreal\npart\nof\nthe\nfirst\nharmonic\nχ\n'\n1\n.\nMoreover,\nthe\nimaginary\npart\nof\nthe\nfirst\nharmonic\nχ\n''\n1\nshows\nan\nincrease\nof\nthe\narea\naround\nthe\nphase\ntransitions.\nBoth\nthe\nreal\nand\nthe\nimaginary\nparts\nof\nthe\nthird\nharmonic,\nnamed\nχ\n'\n3\nand\nχ\n''\n3\n,\nrespectively,\nconfirm\nthat\nboth\nphase\ntransitions\noccur.\nThe\nmeasurement\npoints\nout\nalso\nthat\nin\nthe\nN\nd\nFeAsO\n1-0.14\nF\n0.14\ncompound\nthe\nanti-ferromagnetic\nand\nthe\nsuperconducting\nphase\ncoexist,\na\nphenomenon\nunusual\nin\na\nsuperconductor\nmaterial.\nThis\nobservation\ncould\nbe\nexplained\nhere\nby\nthe\npresence\nof\nan\nexchange\nfield\nof\nlocal\nNd\n4f\nspins\n(AF\nphase)\nand\n3d\nFe\nelectron\npairs\nin\nthe\nFeAs\nlayer\n(superconducting\nphase)\nof\nthis\npnictide\n[7]\n.\nFigure\n4\n.\nAC\nmulti-harmonic\nsusceptibility\nof\nN\nd\nFeAsO\n1-0.14\nF\n0.14\n.\n(top):\nreal\n(\nχ\n'1)\nand\nimaginary\npart\n(\nχ\n''\n1\n)\nof\nthe\nfirst\nharmonic;\n(bottom):\nreal\n(\nχ\n'\n3\n)\nand\nimaginary\npart\n(\nχ\n''\n3\n)\nof\nthe\nthird\nharmonic.\nConclusion\nIn\nthis\nmanuscript\nwe\ndescribed\nthe\nAC\nmagnetic\nsusceptibility\nmeasurement\nsetup\navailable\nat\nthe\nLAMPS\nlaboratory\nof\nINFN-LNF,\nt\nh\nis\nsystem\nis\nrunning\nat\nFrascati\nsince\n1998\nand\nmany\nfruitful\nscientific\nachievements\nhave\nbeen\nobtained\n[8-14]\n.\nIn\nthis\ncontribution\na\nspecial\nattention\nhas\nbeen\ndevoted\nto\ndescribe\nits\ninstrument\ns\ncontrol\n,\ndata\nacquisition\nframework\nand\nthe\nLabVIEW-based\nuser-friendly\n,\nconvenient\nsoftware\nplatform\n.Acknowledgements\nThe\nauthors\nwould\ngreatly\nthank\nDr.\nXing\nChen\nfor\nfruitful\ndiscussion\nand\nsupport.\nThis\nwork\nwas\npartly\nsupported\nby\nthe\nNational\nBasic\nResearch\nProgram\nof\nChina\n(2012CB825800),\nthe\nScience\nFund\nfor\nCreative\nResearch\nGroups\n(11321503),\nthe\nKnowledge\nInnovation\nProgram\nof\nthe\nChinese\nAcademy\nof\nSciences\n(KJCX2-YW-N42),\nthe\nNational\nNatural\nScience\nFoundation\nof\nChina\n(NSFC\n11179004,\n10979055,\n11205189,\nand\n11205157)\nand\nthe\nFundamental\nResearch\nFunds\nfor\nthe\nCentral\nUniversities\n(WK2310000021).\nReferences\n[1]\nR.A.\nHein,\nT.L.\nFrancavilla\nand\nD.H.\nLiebenberg,\nMagnetic\nSusceptibility\nof\nSuperconductors\nand\nOther\nSpin\nSystems\n,\nSpringer,\n1991.\n[2]\nS.\nKohout,\nJ.\nRoos\nand\nH.\nKeller,\n\"Automated\noperation\nof\na\nhomemade\ntorque\nmagnetometer\nusing\nLabVIEW,\"\nMeasurement\nScience\nand\nTechnology,\n16\n(2005)\n2240\n-2246\n.\n[3]\nL.\nJoshi\nand\nS.\nKeshri,\n\"Magneto-transport\nproperties\nof\nFe-doped\nLSMO\nmanganites,\"\nMeasurement,\n44\n(2011)\n938-945.\n[4]\nD.\nP.\nSrinivasan,\n\"Automation\nof\nSquid\nBased\nVibrating\nSample\nMagnetometer\nusing\nLabview,\"\nProcedia\nEngineering,\n38\n(2012)\n130-137.\n[\n5\n]\nS.Wang,\nA.\nMarcelli,\nD.\nDi\nGioacchino\n,\nZ.\nWu,\n\"The\nAC\nmulti-harmonic\nmagnetic\nsusceptibility\nmeasurement\nsetup\nat\nthe\nLNF-INFN,\"\nLaboratori\nNazionali\ndi\nFrascati\n,\n(2013)\n,\nINFN-13-18\n.\n[\n6\n]\nK.\nMatano,\nZ.\nRen,\nX.\nDong,\nL.\nSun,\nZ.\nZhao,\nand\nG.\nZheng,\n\"Spin-singletsuperconductivity\nwith\nmultiple\ngaps\nin\nPrFeAsO\n0.89\nF\n0.11\n,\"\nEurophysics\nLetters,\n83\n(2008)\n57001.\n[\n7\n]\nA.\nPuri,\n\"Experiments\non\nstrongly\ncorrelated\nmaterials\nunder\nextreme\nconditions,\"\nGraduate\nSchool\n\"\nVito\nVolterra\"\n,\nDoctorate\nin\nMaterial\nScience\n-XXIV\nCycle\n,\nSapienza\nUniversity\nof\nRome\nAA\n2011/12,\npp.35-36\n.\n[\n8\n]\nD.\nDi\nGioacchino,\nP.\nTripodi,and\nJ.\nD.\nVinko,\n\"Glass-collective\npinning\nand\nflux\ncreep\ndynamics\nregimes\nin\nMgB\n2\nbulk,\"\nIEEE\nTransactions\non\nApplied\nSuperconductivity,\n15\n(2005)\n3304-3307.\n[\n9\n]\nD.\nDi\nGioacchino,\nP.\nTripodi,\nJ.D.\nVinko,\nV.\nMihalache\nand\nS.\nPopa,\n\"Flux\ndynamic\nchanges\nby\nneutron\nirradiation\nin\nBISCCO:\nHigh\nharmonics\nAC\nsusceptibility\nanalysis,\"\nIEEE\nTransactions\non\nApplied\nSuperconductivity,\n17\n(2007)\n3675-3678.\n[\n10\n]\nD.\nDi\nGioacchino,\nA.\nMarcelli,\nS.\nZhang,\nM.\nFratini,\nN.\nPoccia,\nA.\nRicci\n,\net\nal.\n,\n\"Flux\nDynamics\nin\nNdO\n1\n−\nx\nF\nx\nFeAs\nBulk\nSample,\"\nJournal\nof\nsuperconductivity\nand\nnovel\nmagnetism,\n22\n(2009)\n549-552.\n[1\n1\n]\nD.\nD.\nGioacchino,\nA.\nMarcelli,\nA.\nPuri\nand\nA.\nBianconi,\n\"The\nac\nsusceptibility\nthird\nharmonic\ncomponent\nof\nNdO\n1\n−\n0.14\nF\n0.14\nFeAs:\nA\nflux\ndynamic\nmagnetic\nanalysis,\"\nJournal\nof\nPhysics\nand\nChemistry\nof\nSolids,\n71\n(2010)\n1046-1052.\n[1\n2\n]\nD.\nDi\nGioacchino,\nA.\nMarcelli,\nA.\nPuri,\nA.\nIadecola,\nN.\nSaini\nand\nA.\nBianconi,\n\"Influence\nof\nthe\nExtra\nLayer\non\nthe\nTransport\nProperties\nof\nNdFeAsO\n1\n−\n0.14\nF\n0.\n14\nand\nFeSe\n0.\n88\nSuperconductors\nfrom\nMagneto\nDynamic\nAnalysis,\"\nJournal\nof\nsuperconductivity\nand\nnovel\nmagnetism,\n25\n(2012)\n1289-1292.\n[13]\nN.\nPoccia,\nA.\nRicci,\nG.\nCampi,\nM.\nFratini,\nA.\nPuri,\nD.\nDi\nGioacchino,\nA.\nMarcelli,\nM.\nReynolds,\nM.\nBurghammer,\nN.L.\nSaini,\nG.\nAeppli\nand\nA.\nBianconi\n,\n\"\nOptimum\ninhomogeneity\nof\nlocal\nlattice\ndistortions\nin\nLa\n2\nCuO\n4+y\n,\n\"\nPNAS\n,\n109\n(2012)\n15685\n.\n[14]\nD.\nDi\nGioacchino,\nA.\nPuri,\nA.\nMarcelli\nand\nN.\nSaini,\n\"Flux\ndynamics\nin\niron-based\nsuperconductors,\"\nIEEE\nT\nransactions\non\nA\npplied\nS\nuperconductivity,\n23\n(2013)\n7300505\n."    },    {        "title": "1405.5420v1.Magnetoresistance_peculiarities_and_magnetization_of_materials_with_two_kinds_of_superconducting_inclusions.pdf",        "content": "Magnetoresistance  peculiarities and magnetization of materials \nwith  two kinds of superconducting inclusions  \nО. N. Shevtsova  \n \nNational Technical University of Ukraine “Kiev Polytechnic Institute” , 37 Prospect Peremogy, Kyiv, 03056, \nUkraine  \n \nE-mail: oksana.shevtsova@kpi.ua  \n \nAbstract.  Low-temperature properties of a crystal containing superconducting inclusions of two different materials \nhave been studied. In the approximation that the inclusions ’ size is much smaller than the coherence length/penetration \ndepth of the magnetic field the theory for magnetoresistance of a crystal containing spherical superconducting \ninclusions of two different materials  has been developed , and ma gnetization  of crystals has been calculated . \n \nKeywords:  spherical superconducting inclusion, magnetoresistance, magneti zation , type I superconductors  \n \nPACS :  \n74.25.  fc  Electric and thermal conductivity,  \n74.70.     Superconducting materials , \n74.78 . Na Mesoscopic  and nanoscale systems , \n74.25. Ha  Magnetic properties , \n74.81. Bd Granular, melt -textured, amorphous, and composite superconductors  \n \n \n1. Introduction.  \nOne of the results of the rapid development of nanotechnology is creation of various types of composite \nmaterials or structurally heterogeneous systems, which consist of a matrix (host material) and disperse \ninclusions, and are characterized by the propert ies that are absent in the material components. Depending on \nthe shape and size of these inclusions such composite materials have different properties.  \nThe contact doping was initially proposed as an alternative method f or production of alloys from  non-\nmixing components , which is differ ent from traditional alloying or sintering technologies. The new \ntechnology is based on anomalously quick migration of components in the systems with monotectic \ntransformation  [1]. The p roposed solution has made it possible to remove  all limitations regarding  chemical \ncomposition, microstructure uniformity and volume  of the  final products - the limitations  which are inherent \nto sintering and alloying of composites , and thus allowed  one to create new composite materials, which \nproduction has been  considered impossible  before that .  \nThe contact doping technology allows  to get Al-Cu-Pb alloys , containing up to 20% of Cu and 30% of Pb \nwith uniform distribution of Pb  in the alloy volume in the form of spherical inclusions encapsulated into \nintermetallic shell, Cu -Pb-Bi and Cu -Pb-Sn alloys in which inclusions of heavy low -melt elements are \nuniformly spread in the Cu matrix [1]. The problem of micro -structural irregularities and uncontrolle d \ndispersion was solved by transmission of electric current pulses of definite duration, amplitude and shape \nthrough a sample.    \nModern technolog ies actively use also the method of dispersed fillers injection to modify material \nproperties, such as increased strength and service life, and to reduce the production cost of a new structural \nmaterial, just by changing the type of inclusions. Technology -controlled structures or ordered composites are \nof special interest. Examples of such structures are in dium -opal composites formed by the pressure -induced \ninjection of indium into periodically located submicron pores of opal dielectric matrix. The resulting \ncomposite with a lattice of indium granules is characterized by 2 -step run of temperature -resistance plot and \nthe size dependence of the critical temperature and critical magnetic field [ 2 - 8]. \nGrain sizes in the composite materials vary from a few nanometres  to several hundred nanometres , and \nthe materials themselves are characterized by rather specific  and unusual electric properties, such as electron \ntunnelling  and Josephson links between the grains in superconducting state [ 9]. \n The formation of structurally inhomogeneous systems is not only a technologically controlled process. In \nthe multi component  systems it is observed an effect of segregation and creation of microscale inclusions of \nother phases, such as precipitation of metal phase [ 10]. Nuclear irradiation or doping of complex compounds \nsuch as semiconductors leads to creation of a structurally  inhomogeneous material which is characterized by \nnew properties.  One of the methods to create a new phase is a method of ion implantation, and the phases created by it are \ncalled the \"ion beam synthesized phases\" [1 1]. Among the recent applications of thi s method is the synthesis of \nsuperconducting nanocrystals of MgB 2. The presence of ion -implanted nanostructures can completely change \nthe physical and chemical properties of a crystal. The latest achievement of the ion implantation technology is \nits role i n creation of surface superconductivity in single crystals of SrFe 2As2 [12]. Experiments with the \nmagnetization and resistance of single crystals irradiated by ions K+ and Ca2+ (at a certain dose of irradiation) \nshowed that there is a superconducting phase transition with the temperature slightly below 25 K. The surface \nsuperconductivity occurs in a layer, which is determined by the penetration depth of the ions.  \nAn important as pect of the composite systems study is the use of their known properties and \ncharacteristics to identify the structural composition of new structurally inhomogeneous material formed as a \nresult of irradiation or doping. Semiconductors of III - V groups, a typical representative of which is indium \narsenide, are also the complex structures in which precipitation, i.e. the loss of another phase was observed \n[13]. It is known that precipitation of such crystal phase may be caused by a variety of technological \nprocesses, such as the dissociation of solid solutions [1 4]. If the metallic phase is formed, then by cooling a \nsample to a certain temperature we can get a crystal with superconducting inclusions in it. Superconductivity \nunder high pressure in non -doped se miconductors GaSb, GaAs and GaP has been identified long time ago \n[15]. The phenomenon of superconductivity was discovered also in many chemical elements, alloys and in \ndoped semiconductors. The conductivity features, which can be interpreted as a phase tr ansition to the \nsuperconducting state, were found in the binary semiconductors PbTe [1 6 - 19]. The appearance of \nsuperconductivity in GaAs with deviation s from normal stoichiometric composition was also observed in \n[20]. \nThe search for new materials for sp intronics led to intensive research of doped semiconductors [2 1 - 23]. \nThe unexpected result of these studies was the discovery of superconducting gallium precipitates and \nchromium precipitates in the bulk samples of GaAs and GaP, alloyed with chromium. Ma gnetic measurements \nconfirmed that the critical parameters of gallium ( Tc ≈ 6,2 K і Hc ≈ 600 Е) is the characteristic ones for type I \nsuperconductors [2 4]. \nPresence of superconducting inclusions leads to a jump of the sample’s conductivity at low temperatures \nand to strong dependence of conductivity on the magnetic field (magnetoresistance). The occurrence of jump -\nlike behaviour  of magnetoresistance caused by  the phase transition of inclusions from superconducting to \nnormal state with increase of magnetic field was explained in the framework of the theory of magnetoresistance \nof crystals containing superconducting inclusions [2 5-27]. Specific features of magne toresistance observed in \nInAs, irradiated by \n -particles [2 9], also indicate the presence of a phase transition. Since in this case the \nenergy of the particles is very high (80 MeV), the indium -enriched metallic regions can be created in the crystal \nas the result of exposure, and at low temperatures they may become  superconducting. In the framework of the \nmagnetoresistance model of the crystal with randomly placed superconducting inclusions the calculations of the \nmagnetoresistance of irradiated crystals were performed for different values of temperature, and the calculation \nresults were compared with the available experimental data. Peculiarities of magnetoresistance observed in \nexperiments were qualitatively explained in the framework of the magnetoresistance theory [ 30-32]. \nIt should be noted that the calculatio n of magnetoresistance of complex materials is an important method \nto detect the presence of inclusions  in multi -component samples.  \nAn important method for detecting impurities in complex compounds is also plotting of dependencies of \nmagnetization on magne tic field because low -temperature features of magnetization detected in the \nexperiment under certain temperature indicate the presence of non -uniform inclusions . This method also \nallows  estimating the size of inclusions and calculating  their concentration.  \n \n2. The conductivity of the crystal with two types of  superconducting inclusions  \nLet’s calculate the conductivity of a system containing superconducting spherical inclusion that randomly \nlocated in the crystal. We believe that the total amount of inclusions or concentration of impurities is not \nsufficient for occurrence  of superconduct ivity in the whole sample, i.e., the system is below the percolation \nthreshold. Since the formation of the metallic phase is not technologically controlled, it would be logical to \nassume that the formed superconducting inclusion s are  characterized by dispe rsion of a certain size. In \ncalculating the conductivity it can be assumed that, depending on the temperature and magnetic field , an \ninclusion can exist in two states: in superconducting state with infinite conductivity or in normal state, \ncharacterized by  resistance, corresponding to the inclusion of material at a certain temperature . \nThe theory of magnetoresistance of a crystal with superconducting inclusions [24 - 27] is based on the \nassumption that the concentration of superconducting regions is low, th e amount of inclusions  in order of \nmagnitude coincides with the coherence length and the critical magnetic field of the I type superconducting  \ninclusions is described by the well -known Gin zburg formula [32] : \n \n20 /inc\nccHHR\n,           \n         (1) \nwhere \n( , )cTT  is the magnetic field penetration depth ; \ncH  is the critical field of a bulk superconductor;\nR\n is an inclusion radius.  That is, in the framework of this theory the structure of the superconducting \ninclusion is not taken into account , and is considered homogeneous. In the case when the size of the \nsuperconducting spherical inclusions  is larger than the coherence length / penetration depth of the magnetic \nfield, it is necessary to take into consider ation  the vortex structures which are to be born in such \nsuperconducting inclusion s. \nThe conductivity of the system depends on the volume of superconducting inclusions and matrix \nconductivity. To calculate the conductivity of the system the method of effective medium is used [33]. Let’s \ncalculate the conductivity of a crystal containing two types of spherical superconducting inclusions; such \ninclusions are generally characterized by different criti cal temperatures and varying dispersion. We’ll use the \nformula for the conductivity of multi  component systems [34, 35]  \n \n \n02) 1(2 2 2 22 1\n22\n2\n22\n2\n11\n1\n11\n1 \nhh\nnn\nn\nss\ns\nnn\nn\nss\ns PP P P P P\n\n\n\n\n     (2) \n \nwhere  \nis  is the conductivity of \ni -type of inclusions in the superconducting state , \nin is the  \nconductivity of \ni -type of inclusions in the normal state,  \nh is the conductivity of a matrix, \nisP and \ninP is the  \nrelative amount of inclusions in the superconducting and normal states, respectively, index  \ni=1,2 \ncorresponds to inclusions of type I and II, respectively  \n3\n3( , )\n ( ) \n0\n ( ) \n0i\nc\ni\nis i\niR T H\nR W R dR\nPP\nR W R dR\n\n\n,  \nin i isP P P ,   (3) \nwhere \niP is the relative volume of inclusions  of \ni-type \n12P P P is the  full relative amount of i nclusion s in \nthe sample , \n()iWR is the probability that in the unit interval with the radius R one can found  the inclusion of \ni\n-type. For numerical calculations we have used a normal distribution of inclusions by their radius with \ndispersion\nis and radius\niR0       \n2\n0\n2()( ) exp2i\ni\niRRW R Zs\n,                (4) \nwhere Z is determined from the normalization condition \n0( ) 1iW R dR\n . \nIt should be noted that the lower limit of integration in equation (3) is to be determined by some minimal \nradius of an inclusion, defined as the limit value, which allows one to use the G insburg -Landau \napproximation. And as the size distribution of the inclusions  is chosen in such a way that the amount of very \nsmall inclusions  (and t herefore their contribution to the conductivity) is negligibly low, so, conventionally, \nthe minimum radius can be considered as zero.  \nTo calculate the effective conductivity \n of the crystal containing two types of superconducting \ninclusions, which are generally characterized by two different critical temperatures \n1cT  and \n2cT , two \ndifferent values of Ginzburg -Landau parameters \n1 and \n2 , and by different dispersion, is necessary to solve \nequation (2). The effective conductivity of such a system is the value that is determined by many parameters: \nthe relative volume of inclusions , the average size of inclusions and material properties of sup erconducting \ninclusions. Key parameters of the system are the temperature and the external magnetic field, because by \nchanging them one can induce the phase transition of the system from superconducting to normal state and \nthus adjust the relative volume o f superconducting (normal) inclusions. Therefore we’ll consider the \ntemperature dependence of conductivity for different values of the magnetic field and specific features of the \nmagnetic resistance at fixed values of temperature.  \n 3. Temperature dependence of conductivity  \nLet consider the system containing two type s of inclusions. T he critical temperature of the inclusions of type I \nis lower than the critical temperature of inclusions of type II, i.e. \n12ccTT For the calculations a dielectric \nmatrix was considered which contains Sn and Pb inclusions with critical temperature s \n1Sn\ncT = 3.7 K, and \n2Pb\ncT = \n7.2 K, respectively. Then the dynamics of the phase transition of inc lusions caused by temperature changes, \nshould be considered for three cases: 1)\n0H ; 2)\n(1) (2)( , )cc H H H ; 3)\n(2)\nc HH , where \ni\ncH  is the  characteristic \nvalue of the critical field for inclusions of \ni -type. The results of the temperature dependence of conductivity for \nthe corresponding value of the magnetic field for inclusions  with different dispersion values are pr esented in \nfigure  1. Since the matrix contains two different types of superconducting inclusions, a double -jump of the \nconductivity is observed at low temperatures. In absence of an external field (\n0H ) the jumps are very sharp \n(see figure 1, curve 1), because in this model the critical temperature in absence of the magnetic field does not \ndepend on the radius, so the phase transition is realized simultaneously for all inclusions  with the same \ntemperature. In the applied magnetic field, the phase transition of superconducting inclusions depends on the \nradius of the inclusions , and therefore at a given temperature \nT only the inclusions with \n( , , )ci ci R R T H T  are \nin the superconducting state. Accordingly, at (\n(1) (2)( , )cc H H H ) a smeared 2 -step phase transition (see figure 1, \ncurves 2a, 2b, 3a, 3b) is observed in the system, and the temperature region, which is characterized by high \nconductivity, decr eases with the increase of magnetic field. The result of the further increase of the external \nfield (situation\n(2)\nc HH ) (see figure 1, curves 4a, and 4b) is the disappearance of superconductivity in the \ninclusions of type I, and the condu ctivity of the system is characterized by the smeared single -step dependence, \nwhich is caused by the phase transition of type II inclusions. It is clear that the degree of smearing of the phase \ntransition is determined by the dispersion value.  \nThe dynamics  of inclusions transition from the superconducting into normal state is illustrated in figure  2 \nfor a fixed dispersion value (\n0,01s ) and for different values of the magnetic field. The relative volume of \nthe inclusions  is 1% and 2 % for inclusions  of type I and II, respectively. It is seen that at the minimum value \nof the field (\n(2)/c HH  = 0.16) one can observe phase transitions for inclusions of I and II types and the phase \ntransition is sharp (curves 2a and 2b); with further increase of the magnetic field phase transitions occur \nearlier (curves 3a and 3b), and the phase transition begins to sm ear, and at subsequent increase of the \nexternal field values only very smeared phase transition of type II inclusions can be observed (curves 4a and \n4b). One can see that the relative amount of superconducting inclusions become lower with the increase of  \nthe magnetic field and, respectively, the relative volume of inclusions  that have turned into the normal state, \nis increased.  Computational paramet ers of the system:\n00/ 0,2r ; \n10,01P ; \n20,02P ; \n13,7cTK ;\n27,2cTK\n;\n10,13 ;\n20,23 ; \n1/6h ; \n2/3h . \n \n \nFigure 1. Temperature dependence of conductivity \nfor different values of the magnetic field : \n2()/c HH\n=: 1) 0; 2) 0.16; 3) 0.3; 4) 0.5;  \na)\n0,01s ; b)\n0,02s .  Figure 2. Dynamics of superconducting and normal \ninclusions at \n0,01s and the same values of the \nmagnetic field. Letters ‘a’ and ‘b’ indicate the \nsuperconducting and normal state of inclusions , \nrespectively.  \n \n4. Low Temperature Conductivity Peculiarities in Applied Magnet ic field    \nPeculiarities of conductivity versus applied magnetic field should also be considered for 3 temperature ranges:  \n1) \n1c TT - all inclusions of \n12( ( , ), ( , ))cc R R T H R T H are in the superconducting state,  2) (\n12ccT T T ) only \nthe type II inclusions remained in the superconducting  state, 3) (\n2c TT ) - all inclusions turned back into the  \nnormal state. The results of c omputation for conductivity as magnetic field function for inclusions with \ndifferent dispersion are shown in figure 3. One can see that at (\n1c TT ) there is a strong 2 -step conductivity \n(magnetoresistance) (curves 1a , and  1b), which decreases with  the increase of magnetic field. In the \ntemperature range (\n12ccT T T ) the high conductivity area decreases (curves 2a, and 2b), and at \n2c TT the \nphase transition is realized only for inclusions with a higher critical te mperature (curves 3a, 3b).  \nSuch peculiarity of magnetoresistance is caused by suppression of superconductivity first in the larger \ninclusions, and then, at increase of the magnetic field the smaller inclusions become  involved. This \nphenomenon is shown in figure  4, which presents the dependence of conductivity on the magnetic field for \ndifferent values of the average size of inclusions. The range of the magnetic field that is characterized by \nhigh conductivity, is the largest in the case of the smallest average size of inclusions (curve 1a), and with the \nincrease of the average size of the inclusions  (curves 1b, 1c) the areas with high conductivity become \nsmaller. Growth of temperature also significantly reduces the area of high conductivity ( 1a\n 2a), (1b\n\n2b), the range of magnetic fields in which magnetore sistance is decreased is determined by the average size \nof inclusions, and the area of such decrease is regulated by variance. Thus, the temperature and field \ndependencies of the conductivity are mainly determined by the size and variance of inclusions.  The next \ncomputational parameters of the system were used:\n00/ 0,2r ; \n10,01P ; \n20,02P ; \n13,7cTK ;\n27,2cTK\n;\n10,13 ;\n20,23 ; \n1/6h ; \n2/3h . \n \n  \nFigure 3. The conductivity of the system as a function \nof magnetic field at different values of temperature  \n1)\n1TK ; 2)\n3TK ; 3)\n6TK ; a)\n0,01s ;  \nb)\n0,02s ; \n00/ 0,2r ; \n10,01P ; \n20,05P .  Figure 4. The dependence of the conductivity on \nthe magnetic field for inclusions of different sizes: \na)\n00/ 0,1r ; b)\n00/ 0,2r ;\n0,02s ; 1 )\n1TK ; \n2) \n3TK ; 3) \n6TK .  \n10,05P ; \n20,05P . \n \n5. Magneti zation of a crystal with different kinds of superconducting inclusions  \nTo calculate the effective magnetization of the crystal containing spherical inclusions of different types, it is \nnecessary to determine the magnetization of an individual inclusion , and then perform the procedure of \naveraging the magnetization of individual inclusions , which take s into account the dispersion of inclusions \non the radius, conc entration of inclusions  and their distribution in the host crystal.  \nTo calculate the magnetization of a single superconducting inclusion is necessary to write  the self -\nconsistent system of GL equations with the relevant boundary conditions on the surface of the  inclusions . \nAnd since we restrict our consideration by the inclusions of small radii, the length of which is less than the \ncoherence length, than in thi s case an order parameter that characterizes the superconducting state can be \nconsidered constant, and only the second -order GL equation can be considered for the magnetic field, which \nin a spherical coordinate system with the beginning in the centre  of th e inclusion of radius \nR can be written \nas: \n2\n2\n2 2 2 21 1 1( ) (sin( ) )sin( )in\nin inAAA          \n,  at \nR ,                             (5)  \n2\n2\n2 2 211( ) (sin( ) ) 0sin( )out\noutAA         \n,  at \nR.                              (6) \nSolutions of equations (5) and (6) can be obtained by separation of variables  \n1/2 1/2\n1( (cos( ))//22n\nin n n n n\nndPA C I D Kd      \n    \n\n            \n,                          (7)  \n where \n1/2nI\n , \n1/2nK\n  are modified Bessel functions; \n(cos( ))nP  is Legendre polynomial. Since the \nsolution at zero must be finite, then \n0nD . Similarly, we can write the solution of equation (6) for the \nvector potential outside the sphere : \n \n1\n1( (cos( ))n nn\nout n n\nnb d PAad\n\n\n.          (8) \nThe radial and angular components of the magnetic field \nrH  and \nH  were found from the equation  \n \nH rotA\n.                               (9) \nFrom the condition of continuity of the radial and angular component of the magnetic field on the sphere \nsurface the expressions for the distribution of the magnetic field in a spherical superconductor can be \nobtained:  \n \n2\n1\n32 cosh sinh cos( )in\nrC r r rHr               \n,  (10) \n \n2\n2 1\n3cosh sinh sinh sin( )in C r r r r rHr                             \n,                         (11) \n \n1\n0 32(1 ) cos( )out\nrbHH    \n,                (12)\n   \n1\n0 3(1 ) sin( )out bHH    \n,                (13) \nwhere  \n0\n13\n2sinhHRCR\n\n, \n3 2 2\n1 0 0 0cosh( )1 3 3\n2 2 2sinhR\nb H R H R H RR\n  \n .             (14) \nThe value of the magnetization is calculated by the formula  \n \n0 4M H H  \n.                         (15) \nIf the size of the inclusion is small enough \n/0R , then one  can obtain  the classic expression for the \nmagnetic moment of a spherical superconducting inclusion [36]  \n2\n3\n01\n30 (T)Rm H R \n.                    (16) \nLet’s calculate magneti zation of the crystal containing superconducting inclusions of two types. In papers  \n[24] and [18] experimental measurements were fulfilled of magnetization as a function of the magnetic field \nfor doped semiconductors containing modified Ga -inclusions with (Tc=6.2K) and Pb -inclusions . \nPeculiarities of magnetoresistance were observed in the  experiment [28]  as well , and computation of the \nmagnetoresistance [29 -31] have shown that irradiation of a crystal creates radiation -induced spherical \ninclusions enriched with indium, which are characterized by a certain variance of sizes.   \nThe calculation of magnetization versus magnetic field was fulfilled for a crystal containing inclusion s of \nsmall sizes  (\nR ). In this case, the magnetization behavio ur is determined by the dynamics of the \ntransition of superconducting i nclusions of two different materials . For computation the Sn and Pb  inclusions \nwere considered, which are the type I superconductors, and are characterized by the following values of \ncritical parameters :\n13,7cTK ;\n27,2cTK ;\n10,13 ;\n20,23 . For simplification of our consideration  \nwe can assume that both types of inclusions are characterized by the same size and the same variance, but by \ndifferent values of part of inclusions . In this  case, the magnetization is characterized by two minima  of \ndifferent depth ; each of them is caused by a specific type of inclusions. It can be seen ( figure  5 and  figure  6) \nthat at temperature increas ing one of the minima caused by phase transitions of incl usions of the I type  \ndisappears, and with further increase of temperature the magnetization value is decreased. Thus, the obtained \ndependence characterizes the presence of inclusions of various materials that are in the superconducting \nstate, and the prese nce of two  minima  (or more in more complex samples) indicate s the presence of \nappropriate number of types of inclusions in the material. That is, if the experimental results of \nmagnetization of the material are characterized by such type of behavio ur, than it can be stated that \ninclusions of some other material are incorporated in the crystal. Moreover, changing the temperature of a \nsample in the course of  the experiment, we can determine rather accurately the exact type of material of the \ninclusions  in the sample , their size and variance.  \n \n \n  \nFigure 5. Magnetization versus magnetic field of the \nmaterial containing Sn and Pb inclusions at different \ntemperatures: 1)\n1TK ; 2)\n3TK ; 3)\n6TK . Parts \nof superconducting inclusions are equal to\n10,01P , \n20,05P\n. \n2()\ncH  is the critical field of a  \n Pb bulk sample.  Figure 6. Magnetization versus magnetic field of the \nmaterial containing Sn and Pb inclusions at different \ntemperatures: 1)\n1TK ; 2 \n3TK ; 3) \n6TK . \n0,01s\n; \n00/ 0,2r . Parts of superconducting \ninclusions are equal to\n10,05P ,\n20,01P . \nIn the third temperature range (\n1c TT ) the behavio ur of the magnetization or diamagnetic response, \ncaused by the presence of superconducting inclusions of one type in the crystal can be interpreted as a phase \ntransition of only Pb superconducting inclusions with the change of the field (for fixed values of \ntemperature) ( figures  5,6, curves 3). It is seen that the appropriate magnetization curve consists of a linear \nand non -linear part, and with growth of temperature the magnetization value is decreased  as well . \n \n6. Conclusions  \nThus, the presence of superconducting inclusions significantly changes physical  properties of a crystal. The \nconductivity at low temperatures is increasing and there is a strong dependence of conductivity on the \nmagnetic field, and the magnetic field range  in which high conductivity is realized, increases with decreasing \nof the size of inclusions. This dependence is caused by phase transitions of inclusions from the \nsuperconducting to the normal state with the increase of magnetic field. The obtained result s can be used for \ncorrect explanation of the conductivity at low temperatures in binary and more complex semiconductors, in \nwhich the precipitation of the superconducting phase is possible during the technological processing or under \nexternal impact. These  characteristics of electrical conductivity and magnetic properties were observed in \nPbTe, PbJ 2, InAs, GaAs, GaP, where the metal - enriched phase precipitation is possible (the lead in PbTe and \nPbJ 2, indium in InAs, GaAs and gallium in GaP) . \n The presence of inclusions  can be revealed at measurement of low -temperature magnetization, which is \ncharacterized by the characteristic minima caused by phase transitions of various types of superconducting \ninclusions in the magnetic field. Depths of these minima are determined by the volume and sizes of \ninclusions, and their variance . \n \nReferences  \n \n1. Avraamov Yu.S., Shlyapin A.D. 2004 Mechanical engineering  and engineering education. #1. 48 -50.  \n2. Graf M. J., Huber T. E.  and Huber C.A . 1992  Phys. Rev. B  45 3133 - 3136.  \n3. Charnaya E.V., Tien C., Lin K. J.  and Wur C. S.  1998  Phys. Rev. B.  58, No. 1. 467 - 472. \n4. Shamshur D.V., Chernyaev A.V., Fokin A.V.  and Romanov S.G. 2005  Physics of the Solid State  47 2005 - 2014.  \n5. Lungu A. , Bleiweiss M, Amirzadeh J. , Saygi S., Dimofte A., Yin M., Iqbal Z. And Datta T.  2001  \nPhysica C.  349 1 - 7. \n6. Michotte S., Piraux L., Dubois S. ,Pailloux F., Stenuit G. And Govaerts J. 2002 Physica C . 377 267 - 276. \n7. Aliev A.E., Lee S.B., Zakhidov A.A.  and Baughman R.H.  2007  Physica C.  453 15 - 23. \n8. Butler J.F., Hartman T.C.  J. Electrochem. 1969  Soc.: Sol. St. Sci.  -. 116 260 - 263.  \n9. Gadza M., Kuzz B., Murawskii L. , Stizza S. and Natali R.  2008  Optica Applicata  XXXYIII  153 - 161.  \n10.  Russel K.C.  1984  Prog. Mat. Sci.  28, No. 3. 229 - 434. \n11.  Kirkby K.J.  and Webb R.P.  2003  Ion Implanted Nanostructures // Encyclopedia of Nanoscience and \nNanotechnology / Ed.  by H.S. Nalwa  4. 1 - 11. \n12.  Chong S.V., Tallon J. L., Fang F. , Kennedy J., Kadowaki K. And Williams G.V.M.  2011  Europhys. Lett.  \n94 37009 p1 - 37009 - p6.  \n13. Buzea C.  and Robbie K.  2005  Supercond. Sci. Technol.  18 - R1 \n14.  Milvidskii М.G.  and Osvenskii V.B.  1984  Structural defects in monocrystals of semiconductors . \nМoscow : Metallurgy  256   \n15.  Berman I.V., Brandt N. B.  and Sidorov V. I.   1971  Pisma. Zh. Eksp. Teor. Fiz  14, No. 1. 11 - 12. \n16.  Dedekaev  T.T., Moshnikov  V.A., Chesnokova D .B. and Yaskov  D.A. 1980  Pisma. Zh.  Eksp. Teor. Fiz . 6 \n1030 - 1033.  \n17.  Darchuk  S.D., Ditl T., Korovina  L.A., Kolesnik S., Savitskii M. and Sizov F.F.  1998  Fizika I Technika \npolyprovodnikov . 32 786 - 789. \n18.  Darchuk L.A. , Darchuk S.D. , Sizov F.F.  and Golenkov  А.G. 2007  Fizika i Technika polyprovodnikov . 41 \n144 - 148. \n19.  Takaoka S., Sugita T.  and Murase R.  1987  JJAP. Supplement.  26. 1345 - 1346.  \n20.  Baranowski J.M., Liliental -Weber Z., Yau W. -F. and Weber E.R.  1991  Phys. Rev. Lett.  66, 3079 - 3082.  \n21.  Ohno H.  1999  J. Magn. Magn. Mater.  200 110 - 129. \n22.  Dietl T.  2002  Semicond. Sci. Technol . 17 377 - 392. \n23.  Pearton S. J. , Abernathy C. R., Overberg M. E. , Thaler G.T., Norton D.P., Theodoropoulou N., Hebard A.F., \nPark Y.D., Ren F., Kim J. and Boatner L.A.  2003  J. Appl. Phys  93 1. 1 - 13. \n24.  Gosk J.B., Puzniak R., Strzelecka G. , Materna A.,  Hruban A.,Wisniewski A., Szewczyk A, Kowalskii \nG., Korona K., Kaminska M. And Twardowskii A.  2008  Supercond. Sci. Technol.  21. 065019 - 065024.  \n25. Sugakov V.I.  and Shevtsova O.N. 2000  Supercond. Sci. Technol . 13 1409 - 1414.  \n26.  Sugakov V.I.  and Shevtsova O.N. , 2001  Low Temp. Phys.  27 88 - 92. \n27.  Sugakov V.I.  and Shevtsova O.N. , 2001  Proceedings of Institute for Nuclear Research  № 3(5). 100 - 104.  \n28.  Vikhlii  G.A., Ка rpenko  А.Ya. and Litovchenko P .G. 1998  Ukrainian Physical Journal . 43 103- 106. \n29.  Sugakov V.I., Shevtsova О.N., Каrpenko А.Ya. , Litovchenko P.G . and Vikhlii G.A.  2003  Low Temp. \nPhys.  29 551 - 555. \n30.  Mikhailovskii  V.V., Sugakov  V.I., Shevtsova О.N.  Каrpenko А.Ya.,  Litovchenko P.G . and Vikhlii G.A.  \n2007  VANT . Physics of radiation damages and radiation study of materials . 90 55 - 62. \n31.  Ginzburg  V.L. 1958  JETP  34 113 - 125. \n32.  Kirkpatrick S . 1973  Rev. Mod. Phys . 45 574 - 588. \n33.  Shklovskii B.I.  and Efross A.L.,  1975  Uspekhi  physicheskich nauk 117 401-435.  \n34.  Springett B.E . 1973  Phys. Rev. Lett.  31 1463 - 1465.  \n35.  Lifshits E.M.  and Pitaevskii L.P.,  1978  Statistical physics, part 2, M oscow:  Nauka – p.447  "    },    {        "title": "1405.5636v1.Magnetic_phases_of_erbium_orthochromite.pdf",        "content": "1\nMagnetic phases of erbi um orthochromite   \nBrajesh Tiwari#, M Krishna Surendra and M. S. Ramachandra Rao* \nNano Functional Materials Technology Centre, Materials Science Research Centre and \nDepartment of Physics, Indian Institut e of Technology Madras, Chennai-600036, India \n# Present address: Quantum Phenomenon a nd Application Division, National Physical \nLaboratory, New Delhi-110012, India. * Corresponding authors: msrrao@iitm.ac.in\n \nAbstract: \n Erbium orthochromite, ErCrO 3, is a distorted-perovskite  which has antiferromagnetic \nground state below 10 K while Cr3+ magnetic moments order at 133 K. The temperature \ndependence of magnetization is studied ac ross different magnetic phases for ErCrO 3 and \ndifferent magnetization isotherms are analyzed. In the presence of external magnetic field, \npolycrystalline ErCrO 3 develops weak ferromagnetism from  antiferromagnetic ground state. \nThese magnetic phase transitions are observed to be of first order which is justified by thermal \nhysteresis and Arrott-plots.  \nKeywords: Rare earth orthochromit e, antiferromagnetism, first order magnetic phase transitions.    \n1. Introduction: \n Rare earth orthochromites (RCrO 3) and orthoferrites (RFeO 3) which contain two \nmagnetic ions (3dn and 4fm) have attracted research interest from several decades due to complex \nmagnetic phases over temperature, pressure and magnetic field1-4. Recently these material \nsystems received considerable attention in co nnection with magnetoelectric and multiferroic \nproperties and their potential multifunctional applications3,5,6,7. The strong exchange interaction \nwithin the transition metal 3d, Cr3+(Fe3+)- Cr3+(Fe3+) subsystems, is predominantly \nantiferromagnetic and usually orders  at higher temperatures(several hundreds of Kelvin)than that \nof rare earth 4f,R3+-R3+subsystems,but are also less anisotropic compared to the rare earth ions. \nHence rare earth magnetic ions can control the orientation of transiti on metal magnetic moments \nand give rise to complex magnetic structures . Such re-orientation transitions have profound 2\neffects on their magnetic, optical and elastic  properties. It was shown by Hornreich et al.  that the \nmagnitude of rare earth- transition metal ion, R3+- Cr3+(Fe3+),coupling strength is large for \northochromites (RCrO 3) compared to orthoferrites (RFeO 3) because Cr3+ does not have fourfold \nanisotropic terms 1. This coupling plays a decisive role in determining the different magnetic \nphases in orthochromites due to spin reorie ntation transitions. These several important \ndifferences make orthochromites esp ecially erbium orthochromite, ErCrO 3, more suitable for the \nstudy of magnetic phases depending on temperatur e, pressure and applied magnetic fields. \nErCrO 3 belongs to the cr ystal space group D 2h16 –Pbnm which contains f our distorted perovskite \nunits in the crystallographic cell2,3. Since Er3+ ion has an electroni c configuration of 4f11, the \nquantum number of total angular momentum J = 15/2 is a half inte gral number. Therefore, each \nmultiplet can be split into J+1/2 Kram er’s doublet in low symmetric crystals6,8,9. Due to \ninteraction with Cr3+ spins, this Er3+ multiplet splitting reflects different effective fields in \ndifferent magnetic phases wh ich are given in table 1.  \nTable 1 Transformation properties of represen tation of space group Pbnm under generators m x, \nmy and m z (m x, m y and m z. for Pnma)2,3. Considering chemical and ma gnetic unit cells, identical \npossible magnetic point groups and their comp atibilities of Cr and Ln ions in LnCrO 3.  \nMagnetic Symmetry \nGroup Compatible Spin Configur ations (Magnetic Phases) \nPoint group: \nd2h(mmm)  Pbnm setting Pnma setting \nAtom  Cr Ln Cr Ln \nmmm (mmm: d 2h) Г1 ܣ௫ܩ௬ܥ௭ 0௫′0௬′ܥ௭′ ܩ௫ܥ௬ܣ௭ 0௫′ܥ௬′0௭′ \nmmm (2/m:c 2h) Г2 ܨ௫ܥ௬ܩ௭ ܨ௫′ܥ௬′0௭′ ܥ௫ܩ௬ܨ௭ ܥ௫′0௬′ܨ௭′ \n Г3 ܥ௫ܨ௬ܣ௭ ܥ௫′ܨ௬′0௭′ ܨ௫ܣ௬ܥ௭ ܨ௫′0௬′ܥ௭′ \n Г4 ܩ௫ܣ௬ܨ௭ 0௫′0௬′ܨ௭′ ܣ௫ܨ௬ܩ௭ 0௫′ܨ௬′0௭′ \nmmm  (222:d 2) Г5  ܩ௫′ܣ௬′0௭′  ܣ௫′0௬′ܩ௭′ \n mmm  (mm2:c 2v) Г6  0௫′0௬′ܣ௭′  ܣ௫′0௬′0௭′ \n Г7  0௫′0௬′ܩ௭′  ܩ௫′0௬′0௭′ \n Г8  ܣ௫′ܩ௬′0௭′  ܩ௫′0௬′ܣ௭′ 3\nGenerators of the group Pb nm two glide planes; m x: (x,y,z)(1/2−x,1/2+y,z) and  \nmy:(x,y,z)(1/2+x,1/2 −y,1/2+z), and the mirror m z: (x,y,z)(x,y,1/2−z). \nDifferent magnetic phases of ErCrO 3 have been studied usi ng different experimental \ntechniques such as  neutron diffraction 3, magnetization measurements 4,5 and extensively by \noptical studies 6,8-11.  Below T N the spin structure of Cr3+ ions in ErCrO 3 is G x and belongs to Γ4 \n(GxAyFz;F’z) in Bertaut notations 2. Spin reorientation transition T SR takes place abruptly at 10 K \nin absence of external magnetic field where Cr3+ spins reorient in G y and belongs to Γ1 \n(AxGyCz;C’ z). This spin reorientation transition from Γ4 (G xAyFz;F’z) to Γ1 (A xGyCz;C’ z), where \nthe weak ferromagnetic moment disappear is a first-order phase transi tion based as symmetry \narguments 12.It is therefore important to under stand the magnetic response of ErCrO 3 in its \ndifferent magnetic phases apart from phase transitions. The temperature dependence of magnetization was measured across di fferent magnetic phases for ErCrO\n3 and analyzed by \ndifferent magnetization isotherms. \n2. Experimental details:  \nThe samples were prepared by conventional solid state reaction rout with nominal \nchemical composition of ErCrO 3 from starting materials of Er 2O3 (99.9 % Alfa Aesar) and Cr 2O3 \n(99.9 % Alfa Aesar). Before the final heat treatment at 1300 oC for 24 h stoichimetric powder of \nEr2O3 and Cr 2O3 were mixed thoroughly in agate mortar and two intermediate calcinations were \ncarried out at 600 oC and 900 oC for 12 h. The resulting dark green powder samples were used \nfor structural and magnetic studies. The powder x-ray diffrac tion (XRD) data of the powder \nsamples were collected using a PANalytical X’Pert Pro x-ray diffractometer with Cu K α \nradiation under ambient conditions. Crystal struct ure refinements were carried out using General \nStructure Analysis System (GSAS) [10] for D 2h16: Pnma (#62) and structural parameter were \nobtained. Magnetic measurements of ErCrO 3 were performed using vibrating sample \nmagnetometer (VSM), an att achment in PPMS (Model 6000, Qu antum Design, USA) in the \ntemperature range of 5-300 K.  Temperature dependent magnetiz ation measurements were done \nas follows:  zero-field cooled (ZFC) data coll ected while warming, field-cooled cooling (FCC) \nand field-cooled warming (FCW) procedures at  an applied field. Magnetization (M) isotherms \nwere recorded at different temperatures up to an  applied magnetic field (H ) of 7 kOe in vicinity \nof magnetic transitions.  4\n3. Results and discussion:  \n3.1 Structural analysis: \nThe Rietveld refinement of ErCrO 3 X-ray powder diffraction data is shown in figure 1. \nThe refinement was carried out using GSAS softwa re for the orthorhombic crystal structure with \nspace group Pnma  (# 62)13. The difference-profile (Diff.) between the observed (Obs.) and \ncalculated (Calc.) diffraction patt erns is shown at the bottom of  the plot. A good fit was obtained \nwith R factors, w Rp = 7.52 %, Rp = 5.23 %, and χ2 = 1.53. The lattice constants and volume of \nthe unit cell are found to be a = 5.512(1) Å, b = 7.520(1) Å and c = 5.226(1) Å and V = \n216.58(1) Å3 respectively. \n \nFigure. 1. X-ray diffraction pattern of ErCrO 3 which is Reitveld refined for model structure \nPnma (Calc) with the observed pattern (Obs) to minimize the difference (Diff). The vertical bars \nrepresent the positions of Bragg refl ections. Inset shows unit cell of ErCrO 3. \nThe inset in figure 1 shows the chemical unit cell of ErCrO 3 which has a total of 20 atoms \n(4 Er, 4 Cr and 12 O) per unit cell.  Each chemical unit cell of ErCrO 3 has corner-linked \noctahedra CrO 6  with the centers occupied by centrosymme tric Cr ions (pink) with Wyckoff \n5\nposition 4b (0, 0, 1/2) while corner atoms of octahedra are oxygen ions (red) with two \ninequivalent positions, the ap ex oxygen (O1 ion) at 4c (- 0.025, 0.250, 0.597) and planar oxygen \n(O2 ion) at 8d (0.714, -0.032, 0.307). Erbium ions (green) occupy the space among the octahedra \nat 4c (0.064, 0.25, 0.015). The distortion from ideal  perovskite structure happens because of \ngeometric tolerance factor of 0.903 as well as anti phase tilt of adjacent octahedra which in turn \nlead to Cr-O1-Cr bond angle ~ 144o.  \n3.2 Magnetization study:  \nThe temperature dependence of magnetization was measured across different magnetic \nphases for ErCrO 3 and analyzed by different magneti zation isotherms. Figure 2 shows the \nmagnetization curves as a func tion of temperature for ErCrO 3 recorded using an applied \nmagnetic field of 100 Oe for different thermal cy cles to understand the magnetic interactions; \nfirst, in zero-field sample is cooled down to 5 K and data recorded while warming (ZFC), \nsecond , data is recorded along w ith cooling in presence of external field (FCC) and third , field-\ncooled and data is recoded while warming (FCW).  The temperature dependence of reciprocal of \nmagnetic susceptibility 1/ χ is fitted to Curie-Weiss equation (red line), presente d as right of y-\naxis. Inset of figure 2 shows magnified magnetizati on curves in the vicinity of antiferromagnetic \nordering of Cr3+ magnetic moments. Two distinct magnetic transitions can be observed; first at \n133 K corresponds to Cr3+ antiferromagnetic orderi ng and the second at 10 K related to the spin \nreorientation transition of ErCrO 3. \nAbove T N = 133 K in paramagnetic phase of ErCrO 3, 1/χ vs. T curve follows the Curie-\nWeiss law and fitted as shown in figure 2. The estimated effective magnetic moment is ߤൌ\n10.23ߤ for ErCrO 3which is close to the theoretical value ߤ௧ሺܱݎܥݎܧ ଷሻൌ 10.35ߤ calculated \nfrom the free ion values 9.59Bfor Er3+ and 3.87Bfor Cr3+ (spin only values) moments added \nassuming their total randomness in paramagnetic phase i.e. ߤ௧ሺܱݎܥݎܧ ଷሻൌටߤாయశଶߤయశଶߤ. \nBelow chromium ordering, it is also observed that magnetization gradually reaches a maximum \nat 19 K for ErCrO 3 showing paramagnetic ‘Er’ moments until ordering occurs at ~ 10 K. \nAsymptotically observed Weiss constant Θ = -29 K for ErCrO 3 is negative, indicating the \npredominance of antiferromagnetic interactions. The value of /NT for ErCrO 3 is 0.21 (<1) \nwhich differs from unity implying that the next -nearest neighbor coupli ngs have considerable 6\nstrength for the determination of gr ound state magnetic st ructure of ErCrO 3which is effectively \nantiferromagnetic.   \nFigure 2 Magnetization of ErCrO 3 recorded under 100 Oe applied magnetic field for different \nthermal cycle; first, zero-field cooled down to  5 K and data recorded while warming (ZFC), \nsecond,  field-cooled (100 Oe) a nd data is recorded along with cooling (FCC) and third, field-\ncooled (100 Oe) and data is recoded while warming (FCW). The temperature dependence of \nreciprocal of magnetic  susceptibility 1/ χ is fitted to Curie-Weiss e quation (red line), presented on \nthe right hand side of y-axis. Inset: Magnetization curves are magnified in the vicinity of \nantiferromagnetic ordering of Cr3+ magnetic moments.               \nMagnetization curves show a thermal hysteresis in the vicinity of antiferromagnetic \nordering of Cr3+ magnetic moments as shown as inse t of figure 2 (a magnified view of \nmagnetization curves). The magnetization onset for ZFC and FCW curves is 133.7 K while FCC \nshows at 131.6 K. A difference of 4.6 K is obse rved when magnetization is recorded during \ncooling \nwarmin g\nHoCrO 3 \nFigure 3 \nwith tw o\nThere is K. b) Sc\nh\nfree (V’)\nF\nmagneti c\nof 4.6 K\nconcludi n\nthermal possibili\nt\nthe mag n\nof ErCrO 3 \ng (FCW an d\nand YCrO 31\na) ZFC (bl a\no different a\na thermal h y\nhematic of t\n to the clam p\nigure 3 (a) \nc fields 100 \nK. In La do p\nng it to be f\nhysteresis \nty that the l a\nnetically or d\nin presenc e\nd ZFC) wh i\n4. \nack) FCC (r e\napplied mag n\nysteresis be t\nthermal hys t\nped (V 0) in p\nshows a cl e\nOe (lower p\nped GdCrO 3\nfirst order p h\nin magneti z\nattice is defo\ndered state16\ne of magne t\nich will be \ned) and FC W\nnetic fields \ntween FCC \nteresis in m a\npresence of m\near thermal \npanel) and 1\n3 a similar t\nhase transit i\nzation mea\nrmable and \n. Though t h\n7tic field (F C\nexplained l\nW (blue) m a\n100 Oe (lo\nand FCW w\nagnetization \nmagnetic fi e\nhysteresis i\n000 Oe (up p\nthermal hy s\nion between \nsurements c\na spontaneo u\nhere are sev e\nCC) compa r\nlatter whic h\nagnetization \nwer panel) \nwith a clear t\ndue to cha n\neld in its ma g\nin the mag n\nper panel) w\nsteresis was \ndifferent m\ncan be ex p\nus lattice de\neral other o r\nred to data \nh is signific a\nas a functi o\nand 1000 O\ntemperature \nnge in unit c\ngnetic state (\nnetization c u\nwith a temp e\nobserved b\nmagnetic ph a\nplained by \nformation o f\nrigins of thi s\nrecorded d\nant compar e\non of tempe r\nOe (upper p a\ndifference o\ncell volume \n(see the text )\nurves for a p\nerature diffe r\nby Sharma e\nases. This ty p\nconsiderin g\nf lattice occ u\ns type of th e\nduring \ned to \n \nrature \nanel). \nof 4.6 \nfrom \n).     \npplied \nrence \net.al15 \npe of \ng the \nurs in \nermal \n8\nhysteresis. For example in doped Lanthanum mang anites systems which show thermal hysteresis \ndue to first order ferromagnetic to antiferromagnetic in conjugation to metal to insulator transition in orbital and/or charge order systems.\n17 18 19 The exchange interac tion that gives rise \nto magnetically ordered state and also determine the transition temperature is a strong function of \ninteratomic spacing. Figure 3 (b) shows the sche matic to explain the phenomenon that leads to \nthermal hysteresis in magnetization. In the high temperature state and above Curie temperature \nthe lattice volume is V o and the transition temperature is T C, if the sample is cooled across the \ntransition temperature then the volume due to la ttice distortion is V’ and corresponding transition \ntemperature is T o. In the cooled state if the sample is warmed then the volume is V’ and the \ncorresponding transition temperature T o is seen. This can be underst ood based on the fact that the \nif the sample is cooled to the lowest temperatur e in the presence (or absence) of field which can \ndistort the lattice (or free system ) at the transition temperature (T C or T N) and if the sample is \nwarmed from its lowest temperature (in figur e 2 down to 5 K and figure 3 (a) down to 120 K) \nthen the free energy may be lowered in the direction of increasing transition temperature (T C or \nTN) as in the case when magnetization is record ed while warming, i.e. FCW (or ZFC). Now if \nmagnetization data while warming (FCW or ZFC)  is compared with the magnetization curve \nrecorded while cooling (FCC) the sample shows its intrinsic (or clamped system ) lattice volume \n(V0) and a lower magnetic ordering temperature (T 0).          Figure 4\ncurves a t\n70 kOe a\nnot sho w\napplied m\nmagneti z\nshow sh a\nF\nErCrO 3, \nshown i n\nfigure 4 (\nthe spin magneti\nc\nthe temp\n Magnetiza t\nt different t e\nand b) mag n\nwn for clarit y\nmagnetic fi e\nzation isoth e\narp maxima a\nurther to un\nmagnetizati\nn figure 4. M\n(a) indicate \nreorientatio n\nc fields (-2 k\nerature ran g\ntion measu r\nemperatures \nnified view o\ny). c) Magn e\nelds as deri v\nerms at 5, 1 0\nat different f\nderstand th e\non isother m\nMagnetizati o\na sign of m a\nn transition \nkOe to 2 kO e\nge 5 - 300 K\nrements of E\nin the rang e\nof magnetiz a\netic suscepti b\nved from m\n0, 15, 20 a n\nfields indic a\ne different m\nms over the t\non curves u p\nagnetization \nof 10 K do\ne) are show n\nK are shown \n9ErCrO 3 at d\ne 5 K to 30 0\nation curves \nbility (M/H )\nmagnetizatio n\nnd 25 K (fo r\nating a clear c\nmagnetic ph a\ntemperature \np to applied \nsaturation o\n not saturat e\nn in figure 4 (\nin log-log s\ndifferent te m\n0 K with an \nat low fiel d\n) as a functi o\nn curves. d )\nr clarity ot h\nchange in m\nases and nat u\nrange 5 K t\nmagnetic f i\nonly at 5 K w\ne. Magnetiz\n(b). Magnet i\nscale in fig u\nmperatures. a\napplied ma g\nds up to 2 k O\non of tempe r\n) First deri v\nher isotherm s\nmagnetizatio n\nure of magn e\nto 300 K w\nields of 70 k\nwhile others\nation curve s\nic susceptib i\nure 4 (c) wh\na) Magneti z\ngnetic field \nOe (all curv e\nrature at dif f\nvative of d M\ns are not s h\nn behavior. \netic transiti o\nere recorde d\nkOe as sho w\n isotherms a\ns for low a p\nilities (M/H )\nich was obt a\nzation \nup to \nes are \nferent \nM/dH \nhown) \nons of \nd and \nwn in \nabove \npplied \n) over \nained 10\nfrom magnetization isotherms from figure 4 (a).  At low magnetic fields (0.1 kOe and 1.0 kOe) \nspin reorientation transition (T SR = 10 K) can be observed which is similar to magnetization as a \nfunction of temperature (figure 2) , but for high applied magnetic fi elds, this spin reorientation \ntransition gets suppressed as can be seen from figure 4 (c) retaining weak ferromagnetic nature \nof ErCrO 3. The applied magnetic field which suppresses the spin reorientation transition can be \ndetermine by the first derivative (dM/dH) of magnetization isotherm s, as shown in figure 4 (d) \nfor temperatures close to T SR. For temperatures above sp in reorientation (T > T SR), dM/dH shows \ntwo sharp maxima one in the magnetic fields 5-12 kOe while second around 16 kOe, indicating \ntwo magnetic behavior/phases change whic h are weak ferromagnetic phases of ErCrO 3, \nΓଶሺܥ௫ܩ௬ܨ௭;ܥ௫′ܨ௭′ሻ and Γସሺܣ௫ܨ௬ܩ௭;ܨ௬′ሻ. Also it is important to  note that the magnetic \nsusceptibility dM/dH, at 5 K, shows minimum value in absence of external field in contrast to \nother higher temperatures which justifies the fact that ground state of ErCrO 3 is \nantiferromagnetic Γଵሺܩ௫ܥ௬ܣ௭;ܥ௬′ሻ. \nMagnetization curve at 5 K does not show any loop for low field opening indicating \nperfect antiferromagnetic phase Γଵሺܩ௫ܥ௬ܣ௭;ܥ௬′ሻ in the absence of strong magnetic fields for \nErCrO 3 in Bertaut notation which are given in tabl e 1. As the applied magnetic fields increase, \nthe magnetization starts increasi ng and tending towards saturati on which corresponds to weak \nferromagnetic phases Γଶሺܥ௫ܩ௬ܨ௭;ܥ௫′ܨ௭′ሻ when applied magnetic field is above 1 kOe along \ncrystallographic z-axis and Γସሺܣ௫ܨ௬ܩ௭;ܨ௬′ሻ and when the applied magnetic field is above 10 kOe \nalong crystallographic y-axis. These magnetic pha ses are well studied using optical absorption \nby Hasson et.al.  and Toyokawa et. al8,10. These field induced transi tions are first order phase \ntransition. Even in the absence of magnetic field along y-axis Cr3+ magnetic moments undergo a \nspin reorientation-type transition around 10 K from weak ferromagnetic Γସሺܣ௫ܨ௬ܩ௭;ܨ௬′ሻ phase to \nΓଵሺܩ௫ܥ௬ܣ௭;ܥ௬′ሻ in which the ferromagnetic moments vanish.  11\n \nFigure 5 Different magne tic phases of ErCrO 3 below Cr3+ magnetic ordering (133 K) and other \nmagnetic phases depending on temperature a nd direction of exte rnal magnetic field H (O atoms \nare not shown for clarity).   \nSince in the present st udy, polycrystalline ErCrO 3 is used, apart from 5 K magnetization \nisotherm at low magnetic field which is perfect antiferromagnetic with  Γଵሺܩ௫ܥ௬ܣ௭;ܥ௬′ሻ  a s  \nshown in figure 5, however magnetization isotherms between T SR and T N  show the magnetic \nphase ofΓସሺܣ௫ܨ௬ܩ௭;ܨ௬′ሻ even in absence of magnetic field. In Γଵሺܩ௫ܥ௬ܣ௭;ܥ௬′ሻ phase below T SR \n~ 10 K, if external magnetic field is applied parallel crystallographic z-axis above some critical \nvalue H c//z the spin of Cr3+ reorientation themselves from G x to G y and induces weak \nferromagnetism F z in z-direction which is represented as Γଶሺܥ௫ܩ௬ܨ௭;ܥ௫′ܨ௭′ሻ. Similarly either by \nincreasing temperature above T SR or by applying external magnetic field parallel to y-axis above \na critical value H c//y results in Γସሺܣ௫ܨ௬ܩ௭;ܨ௬′ሻ which have ferroma gnetic component  F y in y-\ndirection, see figure 5. These w eak ferromagnetic phases of ErCrO 3up on application of external \nfields Γଶሺܥ௫ܩ௬ܨ௭;ܥ௫′ܨ௭′ሻandΓସሺܣ௫ܨ௬ܩ௭;ܨ௬′ሻ along two different directions as observed as two \nmagnetization behavior in figure 5. Transiti ons between two magnetic phases of ErCrO 3 either \nby magnetic field or upon temperature are first orde r which can be justified by Arrot plots which \nis based on phenomenological Ginzberg-Landau theory  in vicinity to these magnetic transitions \n12,20,21.   \nG\nwhere  M\napplied m\nܪܯ,whe\nreduces t\nhigh ap p\nnegative \net al.20. I\nNeel te m\nhysteres i\nisotherm\nFigure 6\nArrot’s p\ntransitio n\nM\nfigure 6 \nover the figure 6 \nErCrO\n3. A\nGinzburg-La n\nM is experim e\nmagnetic fi e\nre α, β are t\nto  ܯܪൗൌߚ\nplied magn e\nfor first or d\nIn order to c\nmperature T N \nis (figure 2 )\ns in vicinity \n6 a) Magne t\nplots M2~H/M\nn is negativ e\nMagnetizatio n\nfor ErCrO 3. \nmagnetic ra\n(a). Below \nArrot plots a\nndau form u\nentally obs e\neld, the the r\ntemperature \nߚܯଶߙ .A\netic field 21.\nder magneti c\nconfir m the \n= 133 K an\n) are first o\nof these tra n\ntization isot h\nM at differe n\ne.    \nn isotherms \nA linear in\nnge (0-2 k O\nTN=133 K \nas presented \nulation whi c\nerved specif i\nrmodynami c\ndependent c\nrrott plot, is\n For secon d\nc phase tran s\ntwo magne t\nd spin reori e\norder magn e\nnsitions are r\nherms clos e\nnt temperat u\nat different \ncrease in th e\nOe) is clear s i\na nonlinea r\nin figure 6 (\n12ch includes \nic magnetiz a\nc potential i s\nconstants. I n\notherms of ܯ\nd order ph a\nsition accor d\ntic transitio n\nentation tra n\netic transiti o\nrecorded.   \ne t o  C r  o r d e\nures indicate s\ntemperatur e\ne magnetiz a\nignature pa r\nr behavior i n\n(b) show th e\nthe magne\nation as an o\ns given by \nn equilibriu m\nܯଶagainst ܪ\nase transitio\nding to the c\nns in ErCr O\nnsition at T SR\nons or not, f\nering tempe r\ns first order \nes between 1\nation above 1\nramagnetic p\nndicates th e\ne slopes of M\ntostatic fie l\norder param\nΦൌΦଵ\nଶ\nm ߲Φܯ߲ൗൌ\nܪܯൗshould b\nns, β shoul\ncriteria prop o\nO3, antiferro m\nR = 10 K wh i\nfirst quadra n\nrature and b\ntransition a s\n128 K to 13 8\n133 K (134 ,\nphase of ma t\ne antiferro m\n2M vs. HM\nld energy ( M\neter and H i\nଵܯߙଶଵ\nସߚܯ\n0 the expr e\nbe straight l i\nd positive w\nosed by Ba n\nmagnetic Cr \nich show th e\nnt magneti z\nb) correspo n\ns slope just b\n8 K are sho w\n, 136 and 1 3\nterial as sho w\nmagnetic ph a\nM curves ne g\nMH), \nis the \nܯସെ\nession \nine in \nwhile \nnerjee \nwith \nermal \nzation \n \nnding \nbelow \nwn in \n38 K) \nwn in \nase of \ngative \nbelow t h\n4.6 K) i n\nFigure 7 \ntemperat u\nErCrO 3. \nA\n(TSR= 10\nabsence genuinel\ny\nmagneti z\nplots are is linear \nmagneti\nc\nF\nantiferro m\nTN= 133 \nwith no n\nΓଵሺܩ௫ܥ௬ܣ\n(ferrima g\nof excha n\nhe T N (133 K\nn FCC and F C\na) First co o\nure and b) c\nAs it is obser v\n0 K) from h\nof external \ny show fi r\nzation isoth e\nshown in f i\nindicating t\nc fields indi c\nor ErCrO 3 \nmagnetic o r\nK while pr e\nn-zero net \nܣ௭;ܥ௬′ሻ  a\ngnetic). The s\nnge energy \nK) means n e\nCW magnet i\nordinate ma g\ncorrespondi n\nved from m a\nigh temper a\nmagnetic f\nrst order t r\nerms were r\ngure 7 (b). A\nthe transitio n\ncating this tr a\ntwo first \nr weak ferr o\nesence of se c\nmagnetic m\nappears at \nse transition\nas a strong \negative β wh\nization mea s\ngnetization i\nng Arrot’s p\nagnetizatio n\nature Γସሺܣ௫ܨ\nfields. Tran\nransition th\necorded as \nAt spin reor i\nn whereas a\nansition to b\norder m a\nomagnetic o r\ncond magn e\nmoment, re o\nTSR = 10 \ns proved to \nfunction of \n13hich support\nsurements a s\nisotherms i n\nplots which \nn measurem e\nܨ௬ܩ௭;ܨ௬′ሻ to \nsition betw e\nough not n\nshown in f i\nientation tra n\nt 5 K (< T S\nbe first order\nagnetic tra n\nrder of pha s\netic ion E r3+\norient the C\nwhich m a\nbe of first o\ninter-atomi c\ns the obser v\ns shown in fi\nn vicinity o f\nshow a cle a\nents there is a\nlow tempe r\neen these t w\nnecessary. T\nigure 7 (a) a\nnsition i.e. T\nSR) shows a \n.       \nnsitions ca n\nse Γସሺܣ௫ܨ௬ܩ\nwhich has a\nCr3+ such t h\nakes ErCrO\nrder whose \nc spacing a n\nved thermal \nfigure 2 and f\nf spin reorie n\nar negative \na spin reori e\nrature Γଵሺܩ௫\nwo magnet i\nTo confir m\nand the cor r\nTSR =10 K M\nclear negat i\nn be obse r\nܩ௭;ܨ௬′ሻof Cr\naspherical c h\nhat a new \n3 perfect a\norigin lies i n\nnd bond stre n\nhysteresis ( a\nfigure 3.   \nntation tran s\nslope at 5 K\nentation tran s\n௫ܥ௬ܣ௭;ܥ௬′ሻ i\nic phases s h\nm, first qu a\nresponding A\nM2 vs. H/M c\nive slope fo r\nrved. A c a\n3+ ions occ u\nharge distri b\nmagnetic p\nantiferroma g\nn the depen d\nngth. At ab s\nabout \n \nsition \nK for \nsition \nin the \nhould \nadrant \nArrot \ncurve \nr low \nanted \nurs at \nbution \nphase \ngnetic \ndence \nsolute \n14\nzero the distortion of lattice fa vors increasing transition temperature as we observed for \nErCrO 3in which the onset of magnetic ordering ha s been found to increase by ~4.6 K in FCW \ncompared to FCC measurement cycle. \nConclusion: \n Erbium orthochromite in its distorted-perovs kite structure is synthesized and magnetic \nproperties are studied. We observed a thermal hysteresis of 4.6 K in magnetization and is \nindependent of applied magnetic field strength ( upto 1000 Oe) which indicates transition type is \nfirst order. Below 10 K, the complex magnetic pha ses indicate the signifi cance of Er-Cr coupling \nin ErCrO 3. At 5 K, with external magnetic field the antiferro magnetic ground state \nΓଵሺܩ௫ܥ௬ܣ௭;ܥ௬′ሻ changes to weak ferromagnetic Γସሺܣ௫ܨ௬ܩ௭;ܨ௬′ሻ and Γଶሺܥ௫ܩ௬ܨ௭;ܥ௫′ܨ௭′ሻ phases. \nAcknowledgments: \nThe authors would acknowledge the Department of  Science and Technology (DST) of India for \nthe financial support (grant  No. SR/NM/NAT-02/2005).  \nReferences: \n1 R. M. Hornreich,  Journal of Magnetism and Magnetic Materials 7 (1–4), 280 (1978). \n2 EF Bertaut, GT Rado, and H Suhl,  Edite d by Rado GT, Suhl H. New York: Academic \n149 (1963). \n3 E. F. Bertaut and J. Marescha l,  Solid State Communications 5 (2), 93 (1967). \n4 L. Holmes, Eibschut.M, and Vanuite r.Lg,  Journal of Applied Physics 41 (3), 1184 \n(1970). \n5 Y. L. Su, J. C. Zhang, L. Li, Z. J. Feng, B. Z. Li, Y. Zhou, and S. X. Cao,  Ferroelectrics \n410 (1), 102 (2010);  M. Eibschut, L Holmes, J. P Maita, and Vanuiter.Lg,  Solid State \nCommunications 8 (22), 1815 (1970). \n6 M Kaneko, S Kurita, and K Tsushima,  Journal of Physics C: Solid State Physics 10 (11), \n1979 (1977). \n7 B. Tiwari, A. Dixit, R. Naik, G. Lawes, and M. S. R. Rao,  Applied Physics Letters 103 \n(15) (2013). 15\n8 A. Hasson, R. M. Hornreich, Y. Komet, B. M. Wanklyn, and I. Yaeger,  Physical Review \nB 12 (11), 5051 (1975). \n9 R. Courths and S. Hufner,  Zeitsc hrift Fur Physik B-Condensed Matter 22 (3), 245 \n(1975). \n10 K. Toyokawa, S. Kurita, and K. Tsushima,  Physical Review B 19 (1), 274 (1979). \n11 R. L. White,  Journal of Applied Physics 40 (3), 1061 (1969). \n12 K. Binder,  Reports on Progress in Physics 50 (7), 783 (1987). \n13 Allen C Larson and Robert B Von Dreele,   General Structure Analysis System. \nLANSCE, MS-H805, Los Alam os, New Mexico (1994). \n14 B. Tiwari, M. K. Surendra, and M. S. R.  Rao,  Journal of Physics-Condensed Matter 25 \n(21) (2013). \n15 Neha Sharma, Bipin K Srivastava, Anjali Krishnamurthy, and AK Nigam,  Journal of \nAlloys and Compounds 545, 50 (2012). \n16 DS Rodbell and CP Bean,  Journal of Applied Physics 33 (3), 1037 (2004). \n17 Joonghoe Dho, W. S. Kim, and N. H. Hur,  Physical Review Letters 87 (18), 187201 \n(2001). \n18 W Zhong, WP Ding, YM Zhou, W Chen, ZB G uo, YW Du, and QJ Yan,  Solid state \ncommunications 107 (2), 55 (1998). \n19 S Mollah, HL Huang, and HD Yang,  Materials Letters 61 (11), 2329 (2007). \n20 B. K. Banerjee,  Physics Letters 12 (1), 16 (1964). \n21 A Arrott,  Physical Review 108 (6), 1394 (1957). \n \n "    },    {        "title": "1406.3341v3.A_Simple_Apparatus_for_the_Direct_Measurement_of_Magnetic_Forces_and_Magnetic_Properties_of_Materials.pdf",        "content": "A Simple Apparatus for the Direct Measurement of Magnetic Forces and Magnetic\nProperties of Materials\nJan A. Makkinje and George O. Zimmerman\nBoston University\n(Dated: November 12, 2021)\nIn this paper, we describe a simple apparatus consisting of a scale, capable of a one milligram\nresolution, and a commonly obtainable magnet to measure magnetic forces. This simple apparatus\nis capable of measuring magnetic properties of materials in either a research or an instructional\nlaboratory. We illustrate the capability of this apparatus by the measurement of the force of iron\nsamples exerted on the magnet, the force of a paramagnetic sample, that by a current carrying wire,\nand the force of a high temperature superconductor.\nI. INTRODUCTION\nThe measurements of magnetic susceptibility (MS)\nand magnetic properties of materials have contributed\nsubstantially to the understanding of the quantum-\nmechanical nature of condensed matter. But, for most\npart, the methods for the quantitative measurement\nof MS have been complicated, cumbersome and costly.\nElectronic methods rely on the measurement of the\nchange of mutual inductance with some parameter (tem-\nperature or magnetic \feld), and are frequency dependent\ndue to magnetic relaxation times and electrical conduc-\ntivity [1], [2], [3]. Static measurements rely on the force\na magnetic material experiences in a magnetic \feld [4],\n[5], [6], [7]. With the availability of high powered and in-\nexpensive permanent magnets, one can easily construct\na device for the measurement of magnetic forces on a\nmagnet atop a scale. For many substances, the forces\nare of the order of milligrams, and since a ferromagnetic\nor paramagnetic material would attract the magnet, it\nwould lessen the weight, or force the magnet exerts on\nthe scale. Thus the scale needs to have the capability to\ndetect either decrease or an increase in the weight of the\nmagnet.\nII. APPARATUS\nWe have constructed an apparatus for the static mea-\nsurement of magnetic susceptibilities. The apparatus\nshown in Fig. 1 consists of a scale capable of one mil-\nligram resolution and a neodymium cylindrical magnet,\nbought in a toy store, 10mm diameter and 6mm high\nwith a magnetic \feld of 0.27T at its surface. It is advan-\ntageous if the scale comes with a computer interface so\nthat its readings can be recorded together with any other\nrelevant parameters. What one measures is the force on\nthe magnet when a magnetic material is placed at a \fdu-\ncial point. The force is due to the \feld which is sup-\nplied by the magnet at the location of the sample. Fig. 1\nshows the general setup with the scale, sample centered\nabove the magnet, and the magnet sitting on the scale.\nIt is prudent to make sure that the pan of the scale is\nnonmagnetic, since a magnetic pan can distort the \feld.Since the magnetic \feld changes drastically with the dis-\ntance, one also needs a means for the determination of\nthe distance between the sample and the magnet face. In\nour case this was done by projecting the ray of a laser\nlevel on a ruler so we could achieve a one-millimeter accu-\nracy. Another means of measurement could be to rigidly\nattach the sample to a micrometer drive.\n!!!\nMagnet!!Scale!!!Tube!to!hold!sample.!!!\nSample!!!\nFIG. 1. The apparatus set up for the measurement of the\nforce of a sample on a magnet on top of a scale with 1mg\nresolution. The scale, magnet and sample are indicated.\nIII. CALCULATION OF THE MAGNETIC\nFIELD\nThe magnetic \feld was calculated assuming a set of\n2000 positive and negative monopoles, separated by 6\nmillimeters, arrayed on opposite faces of the magnet in a\nrectangular con\fguration within a circle of 1 cm diame-\nter. Because the diameter of the magnet is of the same\norder of magnitude as the distance between the magnet\nand the sample, a dipolar approximation is not su\u000ecient.\nFig. 2 shows the calculated \feld Bz, at the center of the\nmagnet as a function of Z, the distance from the X\u0000Y\nplane. The origin is assumed to be at the center of the\nmagnet. The maximum distance in this calculation is\n8cm. That distance was chosen because the magnet con-\ntribution of the B-\feld at that distance is equivalent to\nthat of Earth's contribution. Fig. 3 shows the deviation\nof the calculated \feld from the1\nr3dipolar approximation\nlaw [8] with r, equal to ZatX=Y= 0, being the\ndistance from the magnet. The constant was determinedarXiv:1406.3341v3  [cond-mat.mtrl-sci]  30 Jul 20142\n0\"50\"100\"150\"200\"250\"300\"\n0\"1\"2\"3\"4\"5\"6\"7\"8\"9\"Bz(mT)\"Z(cm)\"\nFIG. 2. The calculated magnetic \feld of the magnet above\nthe center of the magnet as a function of the distance from\nthe mid plane of the magnet. The origin is assumed at the\ncenter of the magnet.\n0\"0.05\"0.1\"0.15\"0.2\"0.25\"0.3\"\n2\"2.2\"2.4\"2.6\"2.8\"3\"3.2\"3.4\"3.6\"3.8\"4\"R,3\"minus\"Bz,calculated(mT)\"Z(cm)\"\nFIG. 3. Di\u000berence between a dipole approximation to the Bz\n\feld at the center of the magnet and the calculated \feld. The\ndipole approximation overestimates the \feld. See text.\nfrom the best \ft at rgreater than 3cm. One can see\nthat at a distance smaller than 2cm, the1\nr3law deviates\nsigni\fcantly from that which is calculated.\nIV. IRON SAMPLE MEASUREMENT\nPure chemical reagent type iron wire was used as the\nas the sample. Fig. 4 shows the result of two samples\nweighing 1mg and 2mg respectively. Since the wire is\nferromagnetic, it will attract the magnet, thus making\nit to appear lighter than if the wire were absent. The\n\fgure shows that the negative change in the weight of\nthe magnet, as a function of the sample distance from the\nmagnet, is about twice as large for the 2mg sample as it is\nfor the 1mg sample. The deviation from the ratio of 2 is\ndue to the accuracy with which the samples were weighed\nsince the resolution of the scale was only 1mg. In each\ncase, the force seems to reproduce the magnitude of the\nmagnetic \feld as a function of distance from the center\nof the magnet. (A mirror image of the \feld re\rected in\ntheZ= 0 plane.)\nNext, a 3cm length of iron wire, 0.22mm in diameter\nwas placed vertically in the \feld and the force measured\nas a function of the distance of its lowest point from the\nupper face of the magnet. That measurement was re-peated with the wire in the horizontal position. Here we\nmeasure the di\u000berence of the force due to the demagne-\ntization factor [2], [3], [9]. For a long cylinder with the\n\feld parallel to the cylindrical axis, the demagnetization\nfactor is zero. If the \feld is perpendicular to the axis,\nthe demagnetization factor is1\n2. Fig. 5 shows the results.\nThe force is smaller with the axis of the wire parallel to\nthe \feld. The proportions seem of the right order of mag-\nnitude, with the di\u000berence likely due to the averaging of\ntheB\feld when the wire is in the horizontal position.\n!900$!800$!700$!600$!500$!400$!300$!200$!100$0$100$\n0$0.5$1$1.5$2$2.5$3$3.5$Force$(dynes)$Distance$(cm)$1mg$2mg$\nFIG. 4. Force on the magnet, attraction, of 1mg and 2mg iron\nsamples. Note that the force of the 2 mg sample is about twice\nthat of the 1mg sample. Of course, iron is ferromagnetic.\n!5000$!4500$!4000$!3500$!3000$!2500$!2000$!1500$!1000$!500$0$\n0$1$2$3$4$5$Force$(dynes)$Distance$(cm)$Ver:cal$Wire$Horizontal$Wire$\nFIG. 5. Force of an iron wire with its axis parallel, and per-\npendicular to the magnetic \feld, as a function of the perpen-\ndicular distance. The perpendicular con\fguration experiences\na greater force partly due to the demagnetization factor. The\nforce is attractive resulting in a magnet weight decrease.\nV. PARAMAGNETISM\nA cylindrical sample of Gd2O3, 3mm in diameter and\n15 mm long, equivalent to one cgs unit of susceptibility\nwas suspended from a string, and its force on the magnet\nmeasured as a function of its lower end from the magnet.\nAgain the force shows attraction as seen in Fig. 6. It also\nmimics the calculated \feld shape.\nIt also turns out that many of the items made out of\nplastic seem to be paramagnetic. As a sample we mea-\nsured a plastic commercial CD case, jewel case. That\nresult is shown in Fig. 7, again as a function of distance3\nfrom the magnet. Here the force seems to vary somewhat\nslower than in the case of the iron samples. The surface\nof the jewel case was in the X\u0000Yplane and was averaged\nover a much larger area.\n!400$!350$!300$!250$!200$!150$!100$!50$0$\n0$0.2$0.4$0.6$0.8$1$1.2$Force$(dynes)$Distance$from$Magnet$(cm)$\nFIG. 6. Measured force on the magnet by a cylindrical para-\nmagnetic sample of Gd2O3equivalent to a one cgs unit of\nmagnetic susceptibility. See text.\n!60$!50$!40$!30$!20$!10$0$\n0$2$4$6$8$10$12$14$Force$(dynes)$Distance$above$Magnet$(cm)$$\nFIG. 7. Force of a commercial CD Jewell Case. See text.\nVI. CURRENT-CARRYING WIRE\nFig. 8 shows the set up for the measurement of the force\nexerted on the magnet by a current carrying wire. The\nscale with the magnet sitting on top of it, are indicated.\nAs previously described, the magnet is again 6mm high\nand 10mm in diameter with a magnetic \feld of 0.27T\nas measured on its face. The dashed lines denote the\ncurrent carrying wire which is moved horizontally and\nwhich exerts a force on the magnet. One end of the wire is\n\fxed while the other is mechanically tied to the slider of a\nrheostat. The rheostat supplies a voltage which depends\non the position of the slider when a battery is placed\nacross the rheostat. In that way, a signal proportional to\nthe position of the wire, tied to the slider, can be recorded\nat the same time as the force on the scale.\nVII. LORENTZ FORCE\nAs can be found in any introductory physics book,\n([8], eq.(31.16)), the force exerted by a magnetic \feld\n!\n!\nFixed!Axis!for!wire!!\nMagnet!!Wire!as!it!scans!across!!!\nScale!!!Modified!Rheostat!!FIG. 8. Apparatus for the measurement of the force of a\ncurrent carrying wire, dashed lines, on the magnet. Shown are\nthe scale, the magnet, the wire and the rheostat which, with\nthe wire attached to the slider, gives a voltage proportional\nto the horizontal position of the wire.\non a current-carrying wire in the absence of electrostatic\ncharges is\n~F=l~I\u0002~B (1)\nwhere Fdenotes the force and IandBare the current\nand the magnetic \feld, respectively. We assume that the\n+Zdirection is along the magnetic moment at the center\nof the magnet, and the current is along the Y-axis. The\nforce on the magnet is measured as the wire changes its\nposition along the X-axis. Actually, there is a slight angle\nbetween the Ydirection and the wire, but because of the\ngeometry, the deviation from Yis minimal. As previously\nstated, one end of the wire is mechanically attached to\na vertical rod, while the other is mechanically attached\nto the slider of a rheostat. An upward force will give\na negative weight indication while downward force gives\na positive change. Because we are only measuring the\nvertical force Fzand assume the current to be Iy, only\nthe\u0000IyBxcomponent is measured. The force was then\nsummed along the length of the wire.\nAs before, the magnetic \feld was calculated assuming\na set of 2000 positive and negative monopoles, arrayed\non opposite faces of the magnet in a rectangular con\fg-\nuration within a circle of 1 cm diameter. Fig. 9 shows\ntheXandYcomponents of the \feld as seen by looking\ndown on the magnet. The positive, north-pole, is point-\ning up along the + Zdirection, while the viewer is looking\ndown, along the \u0000Zaxis. The length of the arrows indi-\ncates the X\u0000Yplane intensity of the B\feld, and the\narbitrary colors give a concept of the total \feld intensity.\nThe superimposed curve and blue points denote the Z-\ncomponent of the force due to the current on the magnet.\nThe current carrying wire is parallel to the Y-axis, up.\nFig. 10 gives the force due to a current carrying wire\nfor several elevations Z, of the wire, as a function of X,\nthe horizontal distance from the center of the magnet\nat a constant elevation, Z. Note that the force maxima\nand minima shift with the Zdistance. The units are\narbitrary.4\n!\nFIG. 9. Calculated X\u0000Ycomponents of the magnetic \feld\nas one looks down on the X\u0000Yplane. The circle denotes\nthe magnet, while the curve denotes the force of the wire on\nthe magnet.\n-6 -4 -2 0 2 4 6 X Fz  z=1 z=2  z=3  z=4 \nFIG. 10. Force of the wire on the magnet as a function of X,\nthe distance of the wire from the center of the magnet, for\nseveral elevations Zabove the magnet. The current is in the\nYdirection, up.\nVIII. MEASUREMENT OF CURRENT\nCARRYING WIRE\nFig. 11 shows the measurement of the force of a wire,\nwith a 4 ampere current, as a function of X, the distance\nfrom the center of the magnet, at an elevation of 2cm.\nOne can easily see the features shown in the calculations:\nthe zero force far away; an attraction which has a max-\nimum at about one centimeter; the force going to zero\nwhen the wire crosses the center of the magnet; and the\nreversal of the force and its maximum as Xincreases.\nIX. MEASUREMENT OF SUPERCONDUCTING\nMATERIAL DIAMAGNETISM\nA beaker with YBCO-123 material in the form of a\n3cm diameter disk of mass 13.766g was placed 1.27cm\nabove the magnet. YBCO-123 is a high transition tem-\nperature superconductor [10]. The sample was cooled to\nbelow its superconducting transition temperature, which\nwas 96K, by pouring liquid nitrogen into the beaker and\nthen letting it evaporate. The temperature was mea-\nsured by means of a thermocouple. Caution should be\ntaken that the placement of the thermocouple be such\n!250%!200%!150%!100%!50%0%50%100%150%200%250%\n0%5%10%15%20%25%30%35%Force%(dynes)%Wire%Distance%(cm)%FIG. 11. Measurement of the force of a current carrying wire\non the magnet at constant Z= 2cm, as a function of X.Yis\nthe direction of the current. One can see the essential features\nof the calculations reproduced in the measurements. See text.\nthat their interaction with the magnetic \feld is minimal,\nsince it itself exhibits magnetic properties as a function\nof temperature.\nFig. 12 shows the force exerted by the superconduct-\ning material as a function of time. Note, that unlike\nin the case of the ferromagnetic or paramagnetic mate-\nrials, the force is positive, showing a repulsion between\nthe material and the magnet. That is due to the fact\nthat a superconductor is highly diamagnetic, exhibiting\nthe Meissner E\u000bect [11]. Initially at room temperature,\nthe sample cools to 77K as liquid nitrogen is poured into\nthe beaker. The sample then becomes superconducting\nand, because of the Meissner E\u000bect, repels the magnet\nwhich results in an increase in the weight of the magnet.\nAs the liquid nitrogen evaporates, the sample warms and\nbecomes normal. That results in a steep decrease in the\nrepulsion. Subsequent force is that of the normal phase\nof YBCO as the sample warms.\n0\"100\"200\"300\"400\"500\"600\"\n0\"50\"100\"150\"200\"250\"300\"Force\"(dynes)\"Time\"(s)\"\nFIG. 12. The force of a Y B 2C3O7\u0000dhigh transition temper-\nature superconductor on the magnet as it cools while liquid\nnitrogen is poured into the sample beaker. One can see the\nsubsequent warming of the sample while the liquid nitrogen\nevaporates and the sample loses its superconductivity. The\nforce is repulsive. See text.5\nX. CONCLUSIONS\nWe have demonstrated a versatile, inexpensive appara-\ntus for the measurement of magnetic properties of mate-\nrials. We have illustrated its versatility by the measure-\nment of the magnetic properties of various samples offerromagnetic, paramagnetic and diamagnetic samples.\nXI. ACKNOWLEDGMENTS\nWe want to thank Mr. Erich Burton and the Boston\nUniversity Physics Department for help with aspects of\nthe research reported here.\n[1] E. Maxwell, Rev. Sci. Instruments. 36, 553 ,(1965).\n[2] White, G. K.m Experimental Techniques in Low Temper-\nature Physics . Oxford: Oxford University, 1959. Print.\n[3] Lounasmaa, O.V., Experimental Principles and Methods\nBelow 1K New York: Academic Press, 1974. Print.\n[4] Saunderson, A. (1968). A Permanent Magnet Gouy Bal-\nance. Physics Education 3 ( 5): 272{273.\n[5] Ernshaw, A. Introduction to Magnetochemistry . Aca-\ndemic Press,(1968), p.89;\n[6] O'Connor, C.J. (1982). Lippard, S.J., ed. Magnetic sus-\nceptibility measurements. Progress in Inorganic Chem-\nistry. Wiley. pp. 203.[7] Giggis, B.N., Lewis, J., The Magnetochemistry of Com-\nplex Compounds in J. Lewis and R.G. Wilkins Modern\nCoordination Chemistry, Wiley (1960), pp.415\n[8] Serway, R. A. Physics for Scientists and Engineers . New\nYork: Saunders, 1982. Print\n[9] Osborn, J. A. (1945). \"Demagnetizing Factors of the\nGeneral Ellipsoid\". Physical Review 67(351{357).\n[10] Sheahen, T. P., Introduction to High-Temperature Super-\nconductivity . New York: Plenum, 1994. Print.\n[11] London, Fritz. Macroscopic Theory of Superconductivity .\nNew York: Dover, 1960. Print."    },    {        "title": "1406.3688v1.Computer_Simulations_on_Barkhausen_effects_and_Magnetizations_in_Fe_Nano_Structure_Systems.pdf",        "content": "1\n*obata@mail.dendai.ac.jpComputer Simulations on Barkhausen effect sand Magnetization s\ninFe Nano -Structure Systems\nShuji Obata *\nSchool of Science & Engineering, Tokyo Denki University ,\nIshizaka, Hatoyama, Hiki,Saitama 350 -0394, Japan\n( )\nThe magnetization processes in Fenano -systems areinvestigated\nusing the numerical simulations based on classical magnetic dipole\nmoment interactions . The domain energies are calculated from\nmoment -moment interactions over whole systems using large scale\ncomputing resources .The results directly show most of basic\nmagnetization phenomena . The Barkhausen effects are represented\nwith jumps and terraces ofmagnetization steps induced from external\nfield changes of ΔH.\nKEYWORDS: magnetization curve ,Barkhausen effect, magnetic dipole\nmoment, domain energy, F e2\n1.Introduction\nIn recent studies, it has been cleared that characters of nano -scale magnetic materials show\ncompletely different from those inbulk systems , which are determined from theboundary\nconditions and thebody shapes .As for Fe, the nano -scale systems induce strong coercivit ies\nHcand high remanent magnetization sBras the hard magnetic materials, where the bulk\nsystems only induce the soft magnetic characteristics .The bulk systems constructed from\nthese nanostructured local compositions show the various particular characteristics. These\nscientific problems have been investigated as the BulkNano-Structured M aterials in recent\nyears .For clearing such phenomen a,in this paper, themagnetization curves in Fe nano -scale\nsystems areinvestigated based on long range classical magnetic dipole moment interactions\nas a theoretical study .Realistic magnetizations are cleared bythe use of the large scale\ncomputing resources , where exact results have not be en produced till inthese days.1-5)\nNevertheless , the correct theory already existed, the f irst stage studies of these in a century\nago could not correctly discuss the magnetizations because of very few computing resources .\nA simple cubic structure system of Fe hasno magnetic phe nomenon in one domain . It\nneed ssome type anti -magnetized walls to make ferromagnetic states. T hese results are\nobtained through large scale computing in large systems. Generally, m agnet ic characters in\nindustrial devices are distinguished to soft or hard magnetization, which phenomena are\ninduced from the magnetic domain structures in large scale systems. In arecentstudy by\nKoyama et al,3)the hysteresis curves of FePt are calculated using aPhase -Field method\nincluding the long range dipole moment inte ractions, where full interaction sin a whole\nsystem areconsidered , and time delay of magnetizations istaken into account . Precise B-H\ncurves could be theoretically calculated only using such long range interactions including the\ntime delay magnetizations .But,itmight be impossible to se ek out the reference explain ing\nclearly such two key words now.\nThe magnetizations and the Barkhausen ( B)noises are explained using th e domain energy\nsystems equated in§2.1, and the basic energy factors between two moments areformulated in\n§2.2.The nano -scale simulations using the classical magnetic dipole moment interactions are\nperformed in§3for representing the character differences in nao -systems caused by only\ndifferen ces of the body shapes .The structure sof nano -Fe systems are explained in §3.1.Four\nnumerical simulations areexecuted about a thin film structure in §3.2, a cubic structure in\n§3.3,ashort belt structure in§3.4andalong belt structure in§3.5respectively. The B effects\nare realized as transitions of domain structures along with changes of flow out fluxes , which\nare directly shown through thefield changes ΔHBofthe B noises in §3.2andthe domain\nbreak down aberrances in§3.5.The calculated ΔHBnicely fit with the experimental data.9)\nThese numerical simulations in §3clearly show thegeneral magnetization characteristics\nsuch as themagnetization curves, the B effects and the ΔHBdistributions , which also coincid e\nwith the experimental data in good agreements.9)-13)\n2.Magnetic Dipole Moment Interaction and Domain Energy3\n2.1Classical f ormulations\nThe B effects are investigated variously in various materials.14)-19)The domain structures\nare also investigated in various materials using various methods.20)-24)For these many results,\nmost of them are directly explained with the simulations using the domain energy calculations ,\nwhich are based on the atomic dipole moment interactions in the classical theory. In this paper,\nthe atomic dipole moment s in Fe systems are set to be nbμBcomposed of theBohr magnetons\nμBwith theeffective spin number nbin an atom determined with the experimental data.\nInclassical theories, B-Hcharacteristics are calculat ed with long range interactions\nbetween these magnetic dipole moments μiandμjlocalized at sites iandjrespectively. The\nBohr magneton :μB=eh/4πm=9.274×10-24[Am2]becomes the element of these magnetic\ndipole moments, where constants are e=1.602 ×1016[C], h=6.626 ×10-34[J.s] and m\n=9.109 ×10-31[kg]. The atomic m agnetic moment is replaced by a dipole moment of a\nmagnetic rod with small distance vector δ[m] and flux ΔφorΔψ as\n   δμμB B 00, i Bb inδμμ0[J.m/A] , (1)\nwhereμ0=4π×10-7[H/m]is the vacuum magnetic permeability . In the body center cubic lattice\n(Fe),the regular dipole moment directions are drawn as like A B C in Fig. 1.In these types,\nthe type A has the largest energy factor s.25)In high temperature circumstance s, these dipole\nmoment directions distribute variously in thermal fluctuations. Such conditions explain that\nthe domain structures do not depend on grain boundaries compos ed of various adjacent crystal\ndirections. Under the restriction to be the type A, the structures of the dipole moment\ninteractions in Fe are basically taken into two types ofparallel and cross directions as shown\nin Fig. 2.\nFig. 1.\nFig. 2\nSetting the distance vector dij=eijdijbetween the dipole moment satiandj, the moment\ninteraction energies are equated using the Taylor expansion of2/1) (d as\n)} )( (3) {(41\n3\n0ij j ij i j i\nijijdW eμeμμμ  . (2)\nCrystal Fe takes the BCC structure with thelattice constant a=2.86×10-10[m] up to 911 ℃\nand have 2 atoms in a lattice. This Fe metal has thedipole moments of 2nbμB0per a lattice.\nNow, the distance dijis represented using coefficient scijand the constant aas\nij ijac d . (3)\nAs for the parallel moment μiandμj, the interaction energy Wijbecomes\n) cos31(42\n32 2\n0 ij\nijB b\nijdnW   ijafE , d , (4)4\n32 2\n04anEB b\na )22.2 (Fe:J 10 812.124 \nbn , (5)\n3 2/) cos31(ij ij ij c f  , (6)\nwhereθijare the angle between the distance vector djiand the moment vector μi. The position\nfactors fijare expanded to 4 terms in the ijlattice point representation with 2 atoms in a cubic\nlattice. The total energy Wd[J] of the whole magnetic dipole moment interactions in a system\nbecome\n\niij j f f,\n\njiijf f, (7)\n\niij j W W,\n\njiij f W W, (8)\nwhere the count i<jmeans half of the count i,j. The atomic dipole moments μiin a cluster\nmake the magnetization field M[T] for the moment μjas like\n  \niij ij i i\nijjd}) (3 {41\n21\n3eeμμ M. (9)\nThus, in the external field H[A/m] by currents I[A], a system energy Wis equated as\n \njj j f HW W W )/ (0 M Hμ\n \nja j fE Hμ) (, (10)\nwhere the magnetization field Mis composed of the exact magnetic dipole moment arrays. It\nis the key point that the factor fdepends on the shape of the system. Themagnetization Mzfor\nthe field Hzisderived from thezcomponent of the total dipole moment summation as\n\njzj zM ) (μ. (11)\nInthesimulation processes, the external field His divided intoNpoints inlinear sweeps as\nNnNnH Hn   1:)12(0 ,\nNnNNnH Hn 2 :)23(0   . (12)\nInthese field alternations, the drastic domain structure changes are observed as the\nBarkhausen transitions constructing theterraces and the jumps in the magnetization curves .\n2.2Energy factors between two dipole moments\nEqs. (1) -(7) represent the interact ion energy system of the dipole moments caused by the\nBohr magneton . It is not proved that the dipole moment in Fe atoms has the same states of the\nBohr magnetons of electron spins, but the calculated results with this condition show the good\nagreement with the experimental data. The quantum theory such as the Heisenberg model and\nIsing modelscannot treat the long range interaction energies in (2) because of a large number\nofspins : 2N.Thus the exact calculations of thedomain e nergies using the long range\ninteractions areonly discussed by classical ways, and there are not so many theoretical works\nin this subject .1-5)Fortunately in Fe, the spin states affect as the magnetic dipole moments5\nliving in the quantum eigenstates of electrons .The magnetization energies are equated using\nsuch dipole moment interactions instead of the quantum spin interactions .In some magnetism,\nlocal spins interact through electrons in a conduction band, which do not be have as thedipole\nmoments. In such case, the magnetizations are investigated with various approaches such as\nband theories.26)\nHere, the stable energy states are estimated using equations (1)-(10)ina body center cubic\nlattice of Fe .Setting the unit vector eiof the magnetic moment μiat the lattice point i;\nkjiz y x i e e ee , (13)\nthe body center position vector is determined in each lattice point as\n)/2 ( kjiab .\nPutting a j-th lattice point on the origin O, the energy factors of beltshape domains forthej-th\nmoments at th isorigin are estimated in three dipole moment directions eA,eB, and eCof A, B\nand C type directions in Fig. 1:\nA: kie ,B: 2/) (kjie ,C: 3/) ( kjiie .(14)\nInthe parallel state, t hese directions counted by iandjareset to the same as\nei=ej, (15.a)\nand in cross moment states as\nA: ije ,B: ije ,C: 2/) ( jije (15.b)\nin a domain. According to Fig. 2 and eq. (2) and setting b=1/2,theposition vectors are\ndefined for two sites Aiandaiat lattice point i,and two sites Bjandbjat lattice point j\nrespectively ;\n) ( ),,( k ji ml ka mlkba BA r r ,\n2 2 2),,( mlk c mlkcba BA  , (16)\n}) () () {( ),,( k j i bm bl bka mlkBa  r ,\n2 2 2) () () ( ),,( bm bl bk mlkcBa  (17)\n}) () () {(),,( k j i bm bl bka mlkbA  r ,\n2 2 2) () () ( ),,( bm bl bk mlkcbA  . (18)\nThe angle relations between theabove 2 dipole moments become\n   r mlki/) (),,( cos er , (19.a)\n   r mlkj/) (),,( sin er . (19.b)\nThese4position factors between lattice points iandjin parallel direction are estimated as\n32\n32\n32\n, cos31 cos31 cos312\nbAbA\nBaBa\nBABA AFF\nklmc c cf    , (20.a)\nwhere the minus sign of the second and third terms indicates Anti-Ferro state. For the cross\ndirection dipole moments, the4position factors are estimated as\n)cos sin cos sin cos sin2(33 3 3,\nbAbA bA\nBaBa Ba\nBABA BA AFF\nklmc c cf   .(20.b)6\nUsing these formulas, full energy calculations between dipole moments are performed in\ntreated systems. The calculated results using (1 3)-(15) show that the most stable dipole\nmoment direction is the type A.\n3.Simulations innano -scale systems\n3.1System representation\nWe can simulate the Fe magnetization in nano -scale systems using the eqs. (9) -(21).\nCharacters of nano -scale magnetizations are observed directly in nano -scale systems as\nshown in Fig. 3.\nFig. 3.\nThe system size is set inthe number of lattice points asNx,NyandNz.Setting the values\n11e , 2/12e and 3/13e ,the26 dipole moment directions are represented using the\nmarks as‘>’: ( e1,0,0), ‘ +’:(0,e1,0), ‘ 1’:(0,0,e1), ‘-’:(-e1,0,0),‘•’:(0,-e1,0),‘W’:(0,0,-e1),‘g’:\n(e2,e2,0),‘h’:(0,e2,e2),‘^’:(e2,0,e2),‘j’:(-e2,e2,0),‘k’:(0,-e2,e2),‘`’:(-e2,0,e2),‘m’:(e2,-e2,0),\n‘n’:(0,e2,-e2),‘]’:(e2,0,-e2),‘p’:(-e2,-e2,0),‘q’:(0,-e2,-e2),‘(’:(-e2,0,-e2),‘s’:(e3,e3,e3),‘t’:\n(-e3,e3,e3),‘u’:(e3,-e3,e3),‘v’:(e3,e3,-e3),‘w’: ( -e3,-e3,e3), ‘x’: ( -e3,e3,-e3), ‘y’: ( e3,-e3,-e3), ‘z’:\n(-e3,-e3,-e3).The main marks are show n in Fig. 3 (C). These arrays in the sheets show the\ndomain patterns. The first domain sate is made of a down direction uniform array. Cooling are\nexecuted by X-Zplane traces of sites jfrom the front surface to the back surface wit h taking\nthe energy minimum state of Wjin (10) under full summations of the other sites i. The cooling\ntrace forajmoment isexecuted byctime iteration sunder the condition as\n4\n, , 1, 10 /) (\n  cj cj cj W W W or c<40. (21)\nThe steady states should represent low temperature states to be T<10 [K]. Such calculations\nrequire the large scale computing resources in recent years. Using thissimple orthorhombic\nlattice, many characteristics of the magnetizations are rep resented by changing the sizes,\nwhere near neighbor interactions become meaningless.\nAfter next section, the experimental data are related to the simulations using the unit\ntransformation as t he field intensity μ0H=10-4Tcorrespond ingtoH= 1Oe= 79.577 A/m.The\nscale of the magnetization Mis normalized to be the atomic magnetic moment value nb.The\nminimum energy states in (10) are determined after the annealing processes in (21).\n3.2 Nano -thin film system and the Barkhausen effects\nHere, aFe nano -film ofNxNyNz=30×4×30 lattice points is simulated for clearing the\nBarkhausen effects and the results nicely coincide with the experimental data. The\nmagnetization curve using the liner field change trace s in (12) with H0=2×105A/m andN=150\nsteps (ΔHk=3×103A/m) are represented in Fig. 4 . Thedetail trace with N=500 steps of\nΔHk=40A/m width is shown in Fig. 5 to clear the B effect scomposed of thejumps and the\nterraces .\nFig. 47\nFig. 5\nThe hysteresis structures of the magnetization curves are variously obtained in many\nreferences under various conditions. In these, the coercivities roughly become\nHc=3.5~4.5×104A/m =440~570Oe be ingμ0Hc=0.044~0.057Tingeneral nano -scale Fe\nmagnetization s.10)27)28)Inthissquare film, the coercivit yHc=3.83×104A/m =480 Oe (0.048 T)\nand the remanent magnetization Br/atom= 1.27 normalized to nbadapt edtheobserved value\nnb=2.22inbulk system s.Using the several layer systems of Fe nanoparticles on\nAl2O3/NiAl(100)11), the < nb>values are determined by the interactions between 3d and 4s\norbitals composing chemical and metallic bond states including thermal fluctuations at\ntemperature T. The value of <nb>=2.22 should be generally adapted to large scale systems as\ndiscussed in ref . 11).\nThe precise magnetization curve in Fig. 5 shows the terraces and jumps in the B effects ,\nwhere themajor width becomes μ0ΔHa=0.8×10-3T. As for the experimental data in ref. 29),\nthecoercivities becomes Hc=30 Oe at 10 K insomething large Fe -film systems of 20~500 μm\nspot and 90 nm thick . Inthese data, the distribution ρ(ΔH)(peak is normalized to 1) for the\nterrace widthΔHare observed as ρ=1.0, 0.5, 0.25 and 0.2 for ΔH=0.5, 1.0, 1.5 and 2.0 Oe\nrespectively. ThiswidthΔHpat the density peak has the relation asΔHp/Hc=0.5/30=1/60. To\nsay,this result is same order of ourresult in Fig. 5 as ΔHa/Hc=0.8×10-3/0.048=1/60.\nThe domain structures inX-Zplane ata,bandcin Fig. 4 are drawn schematically in Fig. 6\nand directly shown in Fig. 7 (a), (b) and (c) respectively. The figures (1) ~ (4) correspond to4\nsheets intheYcoordinate. The flux loop {right -down -left-up}construct ions areclearly drawn\nwith the continued marks such as { >> WW —11}.\nFig. 6\nFig. 7\nTheschematic drawings in Fig. 6 show the flux vectors in the domains .The domains of cross\nsquare structures generally appear in the field alternations of H. This nature depends on the\nlarge minus structure factors of cross direction moments in (20.b). The do wn vectors out of\nthe loops in (a) indicate the remanent magnetization flux ofBr. The fluxes constructing the\ntwo looped domains in (b) have no flow out flux. The up vector fluxes on the both side in (c)\nflow out from the system, where the double looped d omains are observed similarly to (a) and\n(b).The domain structures take more sharp structures in lager systems.9)It is clearly observed\nin these figures that t he B noises are caused by the break downs of the local lylooped dipole\nmoment constructions.\n3.3Nano-cube system\nThe magnetization in (11) under the alternate field withμ0H0=3×105[T] in (12) are\ncalculated inanano -cube system ofNxNyNz=13×13×13 lattice points, where Hc=3.6×104A/m\n(0.0452 T) and Br/atom= 0.34(nb=2.22) are obtained. The character of slow -saturated8\nhysteresis curves appears at low temperatures as shown in Fig. 8. This reason is considered as\nthat t he interaction energies of dipole moments in cubic systems become 0 in a uniform\ndirection and the energy minimum condition require santi-direction moment arrays in\nnano -scale subsystems . This condition produces the slow -saturate magnetization forthe\nexternal field sunder local strong anti -Ferro domain structures .The domain structures at a,b\nandcpoints in Fig. 8 are repres ented in Fig. 9 about the 5 sheets in Fig. 3 (b) .\nFig.8\nFig. 9\nThe slow -saturate curves are observed experimentally in nanowire magnetizations\nencapsulated in aligned carbon nanotubes being non -saturate at room temperature10)andinFe\nlayer systems individually composed of Fe nanoparticles saturated in 3kOe at 10 K27)28).\n3.3 Nano-beltsystem\nThemagnetization curves in a nano -belt system ofNxNyNz=16×4×32lattice points are\ncalculated as in Fig. 10 with Hc=3.6×104A/m andBr/atom= 1.88.These domain structures at\na,bandcpoints are represented in Fig. 11 about every X-Zsheet .\nFig.10\nFig. 11\nNanoparticle clusters joined with common fluxes show the strong Hcand the high Bratzero\ntemperature ,27)28)which magnetization curves should correspond to the data in Fig. 10. The\nmagnetization character schange in nanoparticle assemble system sasreported using Fe:\nAl2O3nano -composite films .12)In these large systems as > 250 ×250 nm2, the Hchas the\ntendency to be small according with the short joined distances and the massive particle\ndensities as like 1/10 values comparing with the nano -particle cluster systems27).\n3.4 Longnano -belt system and domain break down avalanches\nThestrong coercivity Hcand high and high remanent magnetization Brappears in the long\nnano -belt,-rod and -wire system s.For clearly representing the domain break downs , the long\nnano -belt system ofNxNyNz=16×4×64 lattice points isrepresented in this section ,where\nHc=4.14×104A/m (520 Oe) andBr/atom=2. 07(nb=2.22) are obtained .The hysteresis curve is\nclose to the square type structure. The dipole moments are going to uniformly array with\nlongitudinal directions in thelong body domains aslikethe marks of {WWW} and {111} in\nFig. 13.The magnetization sextend step by step according with theincreased field energy of\nΔHkin (10) as the Barkhause neffect , where the field densities are retarded from the\nself-consistent condition waiting for theincreas edfield. The domain break down avalanche s\narestrongly induced near the Hcinlong body systems as shown in Fig. 13 (a), (b) and (c),9\nwhere every step of the increased field is ΔHk=4×103A/m.\nFig.12\nFig.13\nThe domains structures are not stable and distorted broken patterns are observed .These\ndrastic transitions in the magnetizations are observed in various experiments11)-22).The\nobservation of negative Barkhausen jumps is reported in ref. 9) with permalloy thin -film\nmicrostructures as a violent case.\n4.Summa ry\nThe magnetization mechanisms in Fe are directly represented by the computer simulations\nbased on the domain energy calculations using the atomic magnetic dipole moment\ninteraction s under the classical theory. The results obtained by using large scale computing\nresources show thevarious nono -scale magnetization characteristics andnicely explain many\nexperimental data. The nano -belt structure materials covered with non -magnetic materials\ncould be easily created by spatter ing techniques with masks in plasma CVD. We can hope the\nappearance of the high ability magnets in these.\nAcknowledgements\nThis work is accomplished bythe use of thesuper computer system in I nstitute of Solid\nState Physics , University of Tokyo. The autho r greatly thanks for theISSP computer center .\nREFERENCS\n1)S.L.A. de Queiroz and M. Bahiana : Phys. Rev. E .64,(2001) 066127 -1-6.\n2)H.T. Savage, D -X. Chent, C. Go’mez -Polo,M. Va’zquez, and M. Wun -Fogle : J. Phys. D;\nAppl. Phys. 27(1994) 681-684.\n3)T.Koyama : Sci. Technol. Adv. Mater. 9(2008) 013006_1 -9.\n4)H. Kronmüller, H. -R. Hilzinger, P. Monachesi, and A. Seeger : Appl. Phys. 18(1979)\n183-193.\n5)S. Chikazumi: Physics of Ferromagnetism (2nd edn. Oxford: Oxford University Press ,\n1997) pp. 1 -10.\n6)B. Hille brands, and K. Ounadjela: Spin dynamics in confined magnetic structures I ,\n(Springer, 2002).\n7)S. Obata : IEEJ Trans. FM, 131(2011) 838-845.\n8)S. Obata : J. Magn. Soc. Jpn. ,36(2012) 161-168.\n9)Shuqiang Yang, G.S.D. Beach, and J.L. Erskine: J. Appl. Phys. 100(2006) 113914\n10)B.C. Satishkumar, A. Govindaraj, P.V. Vanitha, Arup K. Raychaudhuri, and C.N.R. Rao: Chem. Phys.\nLet.362(2002) 301 -306\n11)N.M. Dempsey, L. Ranno, D. Givord, J. Gonzalo, R. Sema, G.T. Fei, A.K. Petford -Long, R.C. Doole,\nand D.E. Hole: J. Appl . Phys, 90 (2001) 6268 -6274.10\n12)Wen-Chin Lin, C.B. Wu, P.J. Hsu, H.Y. Yen, Zheng Gai, Lan Gao, Jian Shen, and Minn -Tsong Lin: J.\nAppl. Phys., 108(2010) 034312.\n13)S. Zapperi, and G. Durin : Comp. Mater. Science ,20(2001) 436-442.\n14)S. Zapperi, P. Cizeau, G. Duri n, and E. Stanley : Phys. Rev. B ,58(1998) 6353 -6366 .\n15)F. Colaiori, and A. Moro : Advances in Physics, 57(2008) 287-359.\n16)S. Yang and J.L. Erskine : Phys. Rev. B, 72(2005) 064433 -1-13.\n17)K. Kova’cs, and Z. Ne’da : J. Opt. Elect. Adv. Mater ,8(2006) 1093 -7.\n18)D.A. Christian, K.S. Novoselov, and A.K. Geim : Phys. Rev. B ,74(2006) 06443_1 -6.\n19)G. Durin, and S. Zapperi : J. Stat. Mech. ,2006 (2006) P01002_1 -11.\n20)D.C. Jiles : Czech. J. Phys. ,50(2000) 893-988.\n21)O. Gutfleisch, K. -H. M ller, K. Khlopkov, M. Wolf, A. Yan, R. Sch a”fer, T. Gemming, and L. Schultz :\nActa Materialia, 54(2006) 997-1008.\n22)T. Eim u”ller, P. Fischer, G. Schu”tz, P. Guttmann, G. Schmahl, K. Pruegl, and G. Bayreuther : J. Alloys\nand Compounds, 286(1999) 20-25.\n23)P. Fischer, M. -Y. Im, T . Eim u”ller, G. Sch tz, and S. -C. Shin : J. Magn. Magn. Mater ,286 (2005)\n311-314.\n24)N.I. Vlasova, G.S. Kandaurova, and N.N. Shchegoleva : J. Magn. Magn. Mater, 222(2000) 138-158.\n25)S. Obata : IEEJ Trans. FM, 133No 9 (2013) 489-499.\n26)S.Wakoh, and J. Yamashita : J. Phys. Soc. Jpn. ,21(1966) 1712 -1726.\n27)M. Yoon, Y.M. Kim, Y. Kim, V. V olkov, H.J. Song, Y.J. Park, S.L. Vasilyak, and I. -W. Park: J. Magn.\nMagn. Mater. 265(2001) 357 -362.\n28)K.D. Sorge, J.R. Thompson, T.C. Schulthess, F.A. Mondin e, T.E. Haynes, S. Honda, A. Meldrum, J.D.\nBudai, C.W. White, and L.A. Boatner : IEEE Trans. Magn. 37(2001) 2197 -2199.\n29)E. Puppin and M. Zani : J. Phys.: Condens. Matter 16(2004) 1181 -1188.11\nθiδΔψ\n-ΔψδΔψ\n-Δψdi\ndidi- di+naμB0=δΔψ\nθiδ\nΔψ-Δψ\nδΔψ\n-Δψdi++\ndi-+di--di+-naμB0=δΔψ\nA BFIGURES\nFig. 1.\nFig. 1Ferro magnetic moments in a BCC lattice. The dipole moment directions are mainly\ndivided to 3 types of A, B and C. The domain energies have the largest value in the type A.\nFig.2\n(a) Parallel moment interaction\n(b) Cross moment interaction\nFig.2Two type i nteractions between magnetic moments.A B C12\nFig.3\nFig. 3. Nano -scale system size and divided planes in Yaxis and direction marks .(a)Nx,Ny\nandNzare the lattice point numbers ofX,YandZaxis in a orthorhombic system. (b) Domain\nstructures in a system are represented in cut sheets. (c) Direction marks in X-Z,X-YandY-Z\nplanes.(c)Directions and marks in X-Z,X-YandY-Zplanes .12345\n(a)System structure\nand lattice sizes.NzNy\nHNx\n(b) Cut sheet number\nWh\n+ .\nq nk1\nY-ZW^\n> -\n( ]”1\nX-Z X-Y•g\n> -\np mj+13\n0.2 0.1 0.1 0.2\n2112\nabc\nμ0H[T] AMFig. 4\nFig. 4 Magnetization curve ( nb=2.22) in a Fe nano -film composed of NxNyNz=30×4×30\nlattice points with the field H=2×105[A/m]. The area A is precisely traced in Fig. 5 for\nshowing the B jumps and the terraces . The domain structures at the points a,bandcare\ndrawn in Fig. 6.\nFig. 5\nFig. 5 The p recise magnetization curve at the area A in Fig. 4. The represent ative widths of\nterraces are ΔHa=Hc/60.0.010 0.015 0.020 0.025 0.0301.00.80.60.40.2\nM\nAΔHa\nExternal field μ0H[T]14\nFig. 6\nFig. 6 Schematic domain structures at point a,bandcin Fig. 5 correspond to real simulated\nresults (a), (b) and (c) in Fig. 7 respectively.(a) (b) (c)15\nFig. 7\nFig. 7 The X-Zdomain structures of 4 sheets in the Fe nano -film system of 30 ×4×30 lattice\npoints, which correspond to the point a,bandcin Fig. 4. The schematic figures are drawn in\nFig. 8\n(a) D omain structures at a point ain Fig. 4.(3) (4)(1) (2)\n(1) (2)\n(b) Domain structures at a point bin Fig. 4.(3) (4)\n(1) (2)\n(c) Domain structures at a point cin Fig. 4.(3) (4)\n16\n0.30.20.1 0.1 0.2 0.3\n2112\nac b\nμ0H[T]M\nFig.8 Magnetization curve in a Fe nano -cube system of 13 ×13×13 lattice points with the\nfield Hm=3×105[A/m]. The domain structures at the points a,bandcare drawn in Fig. 9.17\nFig. 9.\nFig. 9 The domain structures in the Fe nano -cube system of 13 ×13×13 lattice points, which\ncorrespond to the point a,bandcin Fig. 8. The numbers (1) -(5) represent the cut sheet 1, 4,\n7, 10 and 13 as in Fig. 3 (b).(1) (2) (3)\n(a) Domain structures at apoint ain(4) (5)\n(b) Domain structures at apoint bin(4) (5)(1) (2) (3)\n(1) (2) (3)\n(c) Domain structures at apoint ain(4) (5)\n18\n0.10 0.05 0.05 0.10\n2112\ndM\nabcμ0H[T]Fig. 10.\nFig. 10 Magnetization curve in a Fe nano -belt system of 16 ×4×32 lattice points with the\nfield Hm=1×105[A/m]. The domain structures at the points a,bandcare drawn in Fig. 11.\nThe typical patterns are observed.19\nFig. 11.\nFig. 11. The X-Zdomain structures of 4 sheets in the Fe nano -belt 16 ×4×32 system. (a), (b),\n(c) and (d) correspond to the a,b,canddpoints in Fig. 10 respectively.(a) D omain structures at a point ain Fig. 9.(1) (2) (3) (4)\n(b) D omain structures at a point bin Fig. 9.(1) (2) (3) (4)\n(c) D omain structures at a point cin Fig. 9.(1) (2) (3) (4)\n(d) D omain structures at a point din Fig. 9.(1) (2) (3) (4)\n20\n0.10 0.05 0.05 0.10\n2112\nM\nM\na\ndb\nbc\nμ0H[T]Fig. 12.\nFig. 12 Magnetization curve in a Fe nano -belt system of 16 ×4×64 lattice points with the\nfield Hm=1.0×105[A/m]. The domain structures at the points a,bandcare drawn in Fig. 13.\nThe point bis a large scale avalanche state which needs the cooling processes over 40 times in\nΔH=10-3[A/m] . The hysteresis curve becomes the square type structure.21\nFig. 13.\nFig. 13 The X-Zdomain structures of 4 sheets in the Fe nano -belt 16 ×4×64 system. (a), (b)\nand (c) correspond to the a,bandcpoints of the avalanche states in Fig. 12 respectively.(a)The d omain structures at thepoint ain Fig. 11.(1) (2) (3) (4)\n(b)The d omain structures at thepoint ain Fig. 11.(1) (2) (3) (4)\n(c)The d omain structures at thepoint ain Fig. 11.(1) (2) (3) (4)\n"    },    {        "title": "1406.3690v1.Numerical_Analysis_of_Magnetic_Domain_Energy_System_in_Nano_scale_Fe.pdf",        "content": "1Numerical Analysis of Magnetic Domain Energy S ystem in\nNano -scale Fe\nShuji O BATA\nSchool of Science & Engineering, Tokyo Denki University ,Hatoyama, Hiki, Saitama\n350-0394, Japan\n(Received )\nMagnetic materials generally construct magnetic domains in\nexternal field H. These domain structure sare changed with the field\nchanges ΔHaccompanying the Barkhausen effects. These\nphenomena are shown using Fedomain energy systems composed\nofclassical magnetic dipole mome nt interactions. Themagnetization\ncurves are created with terraces and jumps , where the flux structure\nchanges produce the Barkhausen noise. The terraces indicate the\ndelays of the magnetization processes forthefield H. The se\nnumerical simulations are performed in Fenano -scale regular lattice\nsystems of rods and belts , which directly show the evidences of\nthese basic phenomena.\nKEYWORDS: nano Fe magnetization, Barkhausen effect, magnetic dipole\nmoment, domain energy\n1.Introduction\nNano -scale magnets are variously proposed by a large number of processes using high\ntechnologies , which show various structures and properties.1)-5)The s trong coercivity Hcand\nthehigh remanent magnetization sBrareobserved in recent experiment sof nano -scale\nmagneti zations. These results indicate new magnetic states and domain systems different\nfrom the general concepts for bulk states. As for Fe metal of soft magnetic materials, the\nnanowires ofFe produce the coercivity ofHc=450~600 Oe=4.0~4.8 ×104A/m, which are\ncreated in carbon nanotubes.1)Non-saturate magnetization curves arealso observed at room\ntemperature in this system. Single domain Fe nanoparticle layers show the Hc=500 Oe :\nμ0Hc=0.05 T ,2)where the atomic magnetic moment is observed as nbμB:nb=2.1 (nbandμBare\nthe atomic spin number and t he Bohr magneton respectively). In the report of Fe: Al2O3\nnano -composite films, the value of magnetization per Fe atom is observed as a function of the\nFe concentration from nb=1.4to2.2in a field of 2 T at 10 K, where thecoercivity is shown as2Hc=500 Oe .3)The low values ofnb=1.4correspond to the slow saturation characteristics of\nnanoparticle magnetization s.\nAnalytical performances of acomputer simulation method based on the classical magnetic\ndipole moment interactions are already confirmed in Ref s.6)and 7) . The a bove experimental\ndata are quantitatively analyzed using this method in this paper .For the Fe nano -scale\nsystems, the almost same coercivit iesHc=450~510 are obtained in our simulations. The\nenergy minimum states calculated using whole moment interactions in the system directly\nshow the domain structures and Barkhausen effects in Fe nano -scale BCC lattices .The\nBarkhausen effects are produced inthe magnetization curves composed of terraces ΔHand\njumps ΔMin the external field change s. These terraces and jumps areprecisely obtained in\nthecomputer simulations, which clearly explain the experimental data. However, these\nsimulation shave not been correctly reported until now, because the calculations of the whole\nsystem interactions require the large scale computing resources in these days .8)-11)These\ncalculations are impossible till10 years ago in general circumstances , and finite temperature\nsimulations using aMonte Carlo method require the largest scale computer system in present .\nThe simulation processes and the detail s of the minimum domain energy states are\ndiscussed in §2 for explaining the domain constructions. The magnetization energ ies are\nequated in§2.1based on t heclassical magnetic dipole moment interactions. Themoment\nenerg iesof the parallel direction sand the cross direction sarecalculated to find the energy\nminimum state with shifting the positions around various length nano -rod domains in§2.2.In\n§3, numerical simulations are performed using anano -beltregular la ttice of Fe. Thedomain\nstructures and the energy systems are concretely represented in §3.1~ §3.3. The B effects are\nshown as the only domain structure transitions , which change flow out flux es.\n2.Magnetic Dipole Moment Interactions and Domain Energies\n2.1 Magnetic dipole moment interactions\nThe B effects12)-17)and the domain structures18)-22)are investigated variously in various\nmaterials. Most of these results could be explained by simulations ofthe domain energy\nsystem composed of the atomic dipole moment interactions in the classical theory. The B-H\ncharacteristics are calculat ed with long range interactions between these magnetic dipole\nmoments μiandμjlocalized at sites iandjrespectively. The Bohr magneton\n2410 274.94meh\nBμ [A.m2][J/T]\nbecomes the element of these magnetic moments, where constants are μ0=4π×10-7[N/A2],\ne=1.602 ×10-19[C], h=6.626 ×10-34[J.s] and m=9.109 ×10-31[kg]. The atomic magnetic\nmoment [J.m/A] [Wb.m] is replaced by the dipole moment with small distance vectorδ[m]\nand magnetic charges ΔφorΔψ[Wb] as\n  δμμB B 00, i Bb inδμμ0, (1)\nwhere nbis the effective number of spins in atoms. In a body center cubic lattice, dipole\nmoment directions distribute variously in thermal fluctuations, where these regular type3directions are drawn as A, B and C in Fig. 1.Arbitrary dipole moment interactions of these are\nshown in Fig. 2, where typical structures take parallel and cross moment directions in ground\nstates.\nFig. 1.\nFig. 2.\nSetting the distance vector dij=eijdijbetween the dipole moments at iandjsites, the moment\ninteraction energies are equated using the Taylor expansion of2/1) (d as\n)} )( (3) {(41\n3\n0, ij j ij i j i\nijijfdW eμeμμμ  . (2)\nRegular lattice Fe takes the BCC structure with the lattice constant a=2.86×10-10[m] at low\ntemperature below 911 ℃and have 2 atoms per a unit lattice. Now, the distance dijis\nrepresented using coefficients cijand the lattice constant aas\nij ijac d . (3)\nSetting uito the normal vector of the moment vector μiat site i, the interaction energy Wf,ijare\nrepresented between the moments μiandμjas like\nija ij j ij i j i\nijB B\nijf fEdnW   )} )( (3) {(432 2\n0 , eueu uu , (4)\n3/)} )( (3) {(ij ijj iji j i ij c f eueu uu  , (5)\n32 2\n04ISB B\naanE 22.2 :J 10 166.726 \nBn . (6)\nThe position factors fijinclude 4 terms for two BCC lattice points. The structure energy Wf,j[J]\nabout thej-thdipole moment in a system become s\n\niij j f f ,ja jf fE W,,\n\n\njiijf f ,\n\njiij a f f E W , (7)\nwhere the total count s take the summation si<jevaluating the half count of i,j. The diagonal\nparts indicate the terms in unit lattices. The field -moment energies are equated in the linear\nsuperposition theory as\nHμj jHW, ,\njj HW Hμ . (8)\nThe atomic dipole moments μiin a domain make the magnetization field M[T] for the\nmomentμjas like\n  \niij ij i i\nijB B\njdn}) (3 {430\neeu u M. (9)\nThus, in external field H[H/m] by current I[A], the total domain energy Wis equated as like\n\njj f H W W W W4fEa\njj j   HM M Hμ )/21(0 , (10)\nwhere the magnetization field Mis composed of the magnetic dipole moment arrays. Here, it\nbecomes the important key point that the factor fdepends on the shape of the system in\nnano -scale. The magnetization Mzin the field Hzis estimated as the zcomponent of the total\ndipole moments:\n\njzj zM ) (μ. (11)\nThe lowest energy state calculated in (10) constructs the domain scomposed of the same\ndipole moment clusters as in Fig. 3, where the domains make alooped flux structure in an\naria. In Fe systems, the domains in a common flux loop aria produce the square loop structure\nas the energy minimum state .These looped domains close the fluxes inside the magnet body.\nThe break down sof these or transitions to an other looped structures produce the flow out\nfluxesas the B effect with the external field change ΔH.These energy systems of the dipole\nmoment interactions are analyzed in following sections.\nFig. 3.\n2.2Energy factors between two lattice points\nAs for Fe, the atomic spin states exist as the classical magnetic dipole moments in the\nquantum eigen -states. This fact has not been proved, nevertheless the calculated results show\nthe good agreement with the experimental data.1)-5)Eqs. (1) -(11) represent the interaction\nenergy system caused by the Bohr magneton, and the magnetization energies are equated\nusing these classical dipole moment interactions. Although domain energies using the\nclassical theory have been discussed from ne arly 50 years ago, very fewconcrete works are\nreported under a few computational abilities.8)-10)In some magnetism, local spins interact\nthrough electrons in a conduction band, which do not behave as simple dipole moments. In\nsuch case, the magnetization s are investigated with different approaches such as the Stoner\nmodel ass-dcoupling orbitals states .24)\nHere, the stable energy states are estimated using eqs. (1) -(10) in a BCC lattice. The unit\nvector uiand the body center position vector siare set as\nkj iiz iy ix i u u uu , (12)\n)/2 ( kjiais . (13)\nAccording to eq. (2) and setting s=1/2, the position vectorsrare defined for 4 atoms Ai,ai\nandBj,bjas aA, and bB, atiandjlattice points ;\n) ( ),,( k ji ml ka mlkba BA r r , (14)\n}) () () {(),,( k j i sm sl ska mlkBa  r , (15)\n}) () () {(),,( k j i sm sl ska mlkbA  r . (16)5The atomic dipole moment takes energy state sforeach direction around some directed\ndomain structure. These energy calculations are very important to know themechanism ofthe\ndomain structure construction s. In this paper, two typical energy sta tes of parallel and cross\nmoment directions arecalculated to find the lowest energy states briefly .In Fig. 2, the\nrestricted relations between p arallel upand the c ross ucdipole moments are equated using the\nangle  i i i j )2/ (or as\n) (),,( cos   eup mlk , (17)\n) (),,( sin   euc mlk . (18)\nEnergy structure factors fjin (7) ofamagnetic dipole moment are calculated for nano -rod\ntype domains which center is set to the coordinate origin O .In these BCC lattice calculations,\nthe lowest energ yofdipole -domain interactions appear sinparallel orcross moment direction\naccording to thedomain position s.Theseenergy mechanisms areinvestigated using the\nstructure factors fjatvarious positions in next section , where only checks inX-position sare\nintroduced in Ref.6).Practical energy values about one moment are determined by several\nenvironment domains. These actual steady states are calculated in §3as domain structuring\nsimulations using the 26 directions.\n2.3Parallel and cross dipole moment energy factors\nGenerally, the thermal fluctuations destroy the dipole moment fields .Thus, the systems are\nassumed to be in low temperature in this section . The basic energy systems between the dipole\nmoments and the magnetic domains are calculated for clearing the do main structure\nconstructions. The energy factors fijin (7) are estimated between the moments at a lattice\npoint j(nk,nl,nm) and other points i(k,l,m) in rod type domains in Fig. 4and Fig. 5.\nFig.4.\nFig. 5.\nThe Ferro-stats are calculated on a X-coordinated direction asin Fig. 1-Aasaground state.\nThe factor fFis set to merely f. Now, we consider magnetizations innano -rodtype domains\ndirected to Zaxis with sizes\nN=(2nx+1)(2 ny+1)(2 nz+1), (19)\nwhere nx,nyandnzare half size of the domain rods .For estimating the energy factors, t hefull\nlattice points o fiinthese domain s are counted by k,landmforeach sampling momentμjat\nthe position nk,nlandnm:\nx k x n nk n  , y l y nnln  , z m z nnmn  .(20)\nIn Fig. 6, the parallel moment energy factor sf0//at the domain center arerepresented as the\ntypical st ructure . The parallel moment energy factors fj//traced on Xaxis and Zaxis in Fig. 4\nare represented inFig. 7Trace{I} and Trace {II} respectively. The cross moment energy\nfactorsjftraced on Xaxis and Yaxis onthe domain edge surface in Fig. 5are represented6inFig.8Trace {III} andTrace {IV} respectively.\nFig. 6.\nFig. 7.\nThe important results ofthe parallel moment energy factors fj//in rod type domains are\nclarified as follows. ○1The moments in short domains are quite unstable with large + values\nas like at nz=5fornx=ny> 6in Fig. 6.○2Themiddle part moments in long domains are stable\nas like at nz=20 for nx=ny< 11 in Fig. 6.○3The sign of near the side edges becomes –in long\ndomains, and this sign changes drastically to + at the edge points ( 1x xn n ) as shown in\nFig. 7(c) and (d). This means that the adjacent domains at sides become stable with\nanti-parallel moments. ○4The + sign appears near the cross section edges, and the sign\nchanges drastically to –at the edge points ( 1z zn n ) as in Fig. 7(g) and (h). Th ese results\nmean that the docking of small domains produces stable state andincreas escontinued long\ndomain s.\nFig. 8.\nThe important results of the cross moment energy factorsjfon the edge surface in Fig. 8\nare clarified as follows. ○5In Fig. 8Trace {III} ( l);nk=-(nx+1), the factors take the energy\nminimum values. This means that near the rod domain edges, adjacent domains become\nstable with the cross moment and should be going to make the looped flux structures. ○6All\nof the cross moment factors have the –sign to be stable, which make the looped stru cture\ndomains .\nIn the previous work inRef.6), it is clarified that the energy factors of fijbetween magnetic\ndipole moments fbandfcwith the directions in Fig. 1 B and C become all smaller than faofX,\nYandZaxis directions in Fig. 1 A. The energy factors of fbandfcwith parallel and cross\nmoment direction s produce the weaken values in oblique rod systems as like\n2/)(kjPe , iCea b f f 91.0 (21)\n3/) ( kjiPe , 2/) (j-iCe a c f f 82.0 . (22)\nThese decay factors in Fe are not so large compared with the energy factors of the domain\nconstructions .General domain structure sdepend on such easy magnetization axes, and show\nquite different configurations accordi ng to the se decay factors .Relations of the domain\nstructures and the easy axesarealsocomplex in polycrystalline including grain boundaries .25)\n3.Domain structure and the Barkhausen Effect\n3.1Magnetic dipole moment array7We can directly simulate the Fe magnetization sin nano -scale regular lattice systems using\ntheenergy equations in§2.1, where themagnetization characteristics nicely confirm with\nexperimental data in nano -scale materials .1)-5)Based on the energy constructions of the dipole\nmoments, the domain structures are analyzed precisely and visually in this section. The\nsimulations are performed in anano -beltsystem unde rthe26moment directions in Fig. 9.\nFig. 9.\nSetting the values 11e , 2/12e and 3/13e ,the 26 directions are represented\nusing the marks as ‘>’: ( e1,0,0), ‘+’: (0, e1,0), ‘1’: (0,0,e1), ‘-’:(-e1,0,0), ‘ •’:(0,-e1,0), ‘W’:\n(0,0,-e1), ‘g’: (e2,e2,0), ‘h’: (0,e2,e2), ‘^’: (e2,0,e2), ‘j’: ( -e2,e2,0), ‘k’: (0,-e2,e2), ‘`’: (-e2,0,e2),\n‘m’: (e2,-e2,0), ‘n’: (0,e2,-e2), ‘]’: (e2,0,-e2), ‘p’: ( -e2,-e2,0), ‘q’: (0,-e2,-e2), ‘(’: (-e2,0,-e2), ‘s’:\n(e3,e3,e3), ‘t’: (-e3,e3,e3), ‘u’: (e3,-e3,e3), ‘v’: ( e3,e3,-e3), ‘w’: ( -e3,-e3,e3), ‘x’: ( -e3,e3,-e3),‘y’:\n(e3,-e3,-e3), ‘z’: ( -e3,-e3,-e3).The main marks are shown in Fig. 9(b).The energy minimum\nstates are calculated by means of thesedirected dipole moment interaction sin a\nNxNyNz=20×4×40 lattice system with nb=2.22. The obtained moment directions are drawn\nusing these marks to show the domain structures. The first step random array and the\nannealed state inthe initial trace curve at H=5×104A/m are shown in Fig. 10 .\nFig. 10.\nThe simulations are performed using following 4processes. A:Random state start.At first,\nthe above 26 directions are randomly set for all sites.B:External field trace. In this paper, a\nlinear field trace is adapted using the values of integer k,Hm=1×105A/m and K=100 as\nKkH Hm k , Kk0 , K kK , KkK . (23)\nIn the precise calculation s, the division is set toK=1250 and the concerned data are picked up\nin the third trace. C:Cooling. Cooling is performed as almost 0 K using a direct energy cut off\nmethod instead of a usual Monte Carlo method. This process is executed in X-Zplane traces\nof sites jfrom the front surface to the back surface with taking the energy minimum state of\nWjin (10) under full summations of the other sites i. The energies are checked in 26 directions\nand the minimum energy state is selected at every site. This process is contentiously\nperformed with tracing the X,ZandYcoordinate step by step. The sum mation soffijin (7) are\ncounted over full system moments .These processes are executed through ntime iterations till\n(Wj,n-Wj,n+1)/Wj,n< 10-4, where the converg ing process is performed with almost n~5iterations\nunder n<40.D:Representation. The dipole moment directions are printed using the above 26\nmark sasthe energy minimum structures , where the looped domain structures are observed\nclearly. The dipole moment energies are represented using a density plot method with the\nintensity from black of the minimum value to white ofthemaximum value.\nIn the cooling processes, there are important comments as follows. I: The Monte Carlo8method based on the replacement with the Boltzmann factor probability is very slow f or this\ncooling. II: The temperature of the domain structures should be set based on averaged value\nof gained energies from the grand state. This determination could not be performed with usual\nmethod s, where the difficulty lurks in aberrance transitions o fdomain sdeviating from the\nthermal equilibrium states. III:There is an important question thatthesedomain transitions\nhow toinclude the quantum phenomena under absolutely quantized fluxes .\n3.2 Magnetization curve and Barkhausen effect\nThe a riacomposed of a same dipole moment direction is called the domain, and such\nmagnetic domains construct looped flux structures through long range interactions. The\nmagnetization curves are obtained in thenano -belt system under linear external field trace of\nHm=1.0×105A/m as in Fig. 11 . The maximum magnetization Bmpar atom is normalized to nb.\nThe magnetization curve sconfirm with the experimental data indicated in §1 asthe coercivity\nμ0Hc=0.0456T,theremanent magnetization par atom Br=2.0.\nFig. 11.\nTheterrace sΔHand the jump sΔMare observed in precise calculations of magnetization\ncurve s. The sample atan aria A in Fig. 11 is drawn to show the seB effects as in Fig. 12 . This\nprecise curve is different from the coarse onebecause of a short calculation using a different\nfield trace .The terraces indicate that t he domains do not break down at external field Htill\nsome amount of added field ΔH, where t he jump sofΔMmake the B noise s.These are\nobserved as flux changes of Δφflowed out from a magnet body and are transformed to\nvoltage mΔφ/Δtin amturn coil.\nFig. 12\n3.4System energy, d omain patterns and energy distribution s\nWecansimulate the Fe regular -lattice magnetization in the nano -scale syst ems using E q.\n(10)under nice confirmations with the many experimental data1)-5)introduced in§1.The\nsimulations are performed inthenano -belt system shown in Fig. 9, where the magnetization\ncurves include big transitions as in Fig. 11 .The B effects are certified with the precise\ncalculations of these curves including theterrace sΔHandthe jumps ΔMshown in Fig. 12 .\nThese jumps accompany the domain structure changes . In this paper , new treatments are\nintroduced for representing such domain changes using thedipolemoment distributions\ncompared with t he energy distributions.\nThedomain energy Wis composed of two components as the field term WH=-M•Hand the\nstructure term Wf=Eafin (10). These energy structures inthe 20 ×4×40 lattice point system are\ndrawn in Fig. 13 about (a) the field term, (b) the structure term and (c) the total energy. These\nenerg ieshave the following characters inthe field tracing .○1In decreasing field, these three\nenergies commonly change with linear lines .○2In increasing field, these energies change9variously accompanying jumps.○3The f ield term s are weaker (larger) than thestructure\ntermsabout 3.5 ×10-20J.○4In the field terms, the increasing trace arelarger than the\ndecreasing trace .○5Inthestructure term s,theincreasing trace issmaller than thedecreasing\ntrace .○6The f ield terms in increasing trace sometimes take plus energy values .○7Inthe\ntotal energy, twoincreasing trace sare cancelled each other without jumping arias. ○8In low\nfields, the total energy take large value s, where the moments store miss much energy stress es.\nFig. 13.\nThedomain structures and the moment energy distributions are drawn in Fig. 14 (a) (b) and\n(c), which are corresponded to figures atJa, JbandHcpoints in Fig. 12 and ○ marks in Fig. 13 \n(c)respectively. The upside figures show the domain structure susing the marks in Fig. 9 (b).\nFig.14\nThe downside figures show the energy distributions of Wjin (10), where the darkness from\ntheblacktothewhite show the values from -7.5× 10-24to-2.5× 10-24J.The domain structure\ntransitions are directly observed in the movement sof the white arias representing the domain\nwalls .The figures (a) and (b) represent the drastic domain transitions as an avalanche in the\nfield change ΔH=159 A/m (2 Oe) .\nAs for theexperiments, t heselocal domain structure changes are realistically observed in\npermalloy thin -film microstructures,23)which correspond to drastic jumps in the\nmagnetization curves producing the giant B noise . These phenomena are observed in many\nexperimental data invario usnano -scale magnets .\n4.Summary\nThe magnetization mechanisms in Fe are directly represented by the numerical simulations\nusing the atomic magnetic dipole moment interactions under the classical theory. The energy\nsystem in the magnetization processes is clearly shown using the magnetization curves, the\ndomain patterns, the energy curves of the dipole moments and these distribution patterns. The\nBarkhausen effects in the regular lattices areclarified with the precise calculations ofthe\nmagnetization curve sandwith thedomain break down structures .\nAcknowledgement\nThis work is accomplished by using the supercomputer system in Institute of Solid State\nPhysics, University of Tokyo. The author greatly than ks for ISSP computer center.101)B.C. Satishkumar, A. Govindaraj, P.V . Vanitha, Arup K. Raychaudhuri, and C.N.R. Rao:\nChem. Phys. Let. 362(2002) 301 .\n2)K.D. Sorge, J.R. Thompson, T.C. Schulthess, F.A. Modine, T.E. Haynes, S. Honda, A.\nMeldrum, J.D. Budai, C.W. White, and L.A. Boatner : IEEE Trans. Magn., 37(2001)\n2197.\n3)N.M. Dempsey, L. Ranno, D. Givord, J. Gonzalo, R. Sema, G.T. Fei, A.K. Petford -Long,\nR.C. Doole, and D.E. Hole: J. Appl. Phys, 90 (2001) 6268 -6274.\n4)M. Yoon, Y .M. Kim, Y . Kim, V . V olkov, H.J. Song, Y .J. Park, S.L. Vasilyak, and I. -W.\nPark: J. Magn. Magn. Mater. 265(2001) 357 -362.\n5)Wen-Chin Lin, C.B. Wu, P.J. Hsu, H.Y . Yen, Zheng Gai, Lan Gao , Jian Shen, and\nMinn -Tsong Lin: J. Appl. Phys., 108(2010) 034312.\n6)S. Obata: IEEJ Trans. FM, 133No 9 (2013) 489.\n7)T. Koyama : Sci. Technol. Adv. Mater. 9(2008) 013006_1 -9.\n8)S. Chikazumi: Physics of Ferromagnetism (2nd edn. Oxford: Oxford University Press,\n1997) pp. 1 -10.\n9)S.L.A. de Queiroz and M. Bahiana : Phys. Rev. E. 64, (2001) 066127 -1-6.\n10)H.T. Savage, D -X. Chent, C. Go’mez -Polo,M. Va’zquez, and M. Wun -Fogle : J. Phys. D;\nAppl. Phys. 27(1994) 681 -684.\n11)H. Kronmü ller, H. -R. Hilzinger, P. Monachesi, and A. Seeger : Appl. Phys. 18(1979)\n183-193.\n12)S. Zapperi, P. Cizeau, G. Durin, and E. Stanley : Phys. Rev. B, 58(1998) 6353 -6366.\n13)F. Colaiori, and A. Moro : Advances in Physics, 57(2008) 287 -359.\n14)S. Yang and J.L. Erskine : Phys. Rev. B, 72(2005) 064433 -1-13.\n15)K. Kova’cs, and Z. Ne’da : J. Opt. Elect. Adv. Mater, 8(2006) 1093 -7.\n16)D.A. Christian, K.S. Novoselov, and A.K. Geim : Phys. Rev. B, 74(2006) 06443_1 -6.\n17)G. Durin, and S. Zapperi : J. Stat. Me ch.,2006 (2006) P01002_1 -11.\n18)D.C. Jiles : Czech. J. Phys., 50(2000) 893 -988.\n19)O. Gutfleisch, K. -H. M üller, K. Khlopkov, M. Wolf, A. Yan, R. Schäfer, T. Gemming, and\nL. Schultz : Acta Materialia, 54(2006) 997 -1008.\n20)T. Eim üller, P. Fischer, G. Sch ütz, P. Guttmann, G. Schmahl, K. Pruegl, and G.\nBayreuther : J. Alloys and Compounds, 286(1999) 20 -25.\n21)P. Fischer, M. -Y . Im, T. Eim üller, G. Sch tz, and S. -C. Shin : J. Magn. Magn. Mater, 286\n(2005) 311 -314.\n22)N.I. Vlasova, G.S. Kandaurova, a nd N.N. Shchegoleva : J. Magn. Magn. Mater, 222\n(2000) 138 -158.\n23)S. Yang and J.L. Erskine : Phys. Rev. B, 72(2005) 064433 -1-13.\n24)S. Wakoh, and J. Yamashita : J. Phys. Soc. Jpn., 21(1966) 1712.\n25)K. Sato, Y . Murakami, D. Shindo, S. Hirosawa, and A. Yasuhara: Materials Transactions,\n51(2010) 333.11Figures\nFig. 1Ferro magnetic moments in a BCC lattice. The dipole moment directions are mainly\ndivided to 3 types of A, B and C. The domain energies have the largest value in the type A.\nFig. 2. Two magnetic moment interactions inarbitrary directions . The dipole moments are\nequated as i Bb inδμμ0.\nFig. 3 . Atomic dipole moments in a naria.Astable energy state ariamake sa looped flux\nstructure. These flux structures arethe bases of the domain constructions.A B C\nθiδjΔψj\n-ΔψjδiΔψi\n-Δψidij++\ndij--dij-+dij+-\nθj\nLooped\nflux\nμi\nμjμL12Fig.4.Dipole moment traces on the central axes .{I}:Xaxis, {II} :Zaxis.\nFig. 5. Dipole moment traces on axes .{III} :Xdirection at l=0 and m=-nz-1, {IV} :Y\ndirection at k=-nx-1and m=-nz-1.\nFig. 6. A moment energy factor of a jlattice point at the domain center. Main phenomena\nare included in this figure. It is directly shown that long rod domains are stable.rod domain\n{III}\n{IV}sampling\nmoment\njZ\nY\nX\nno\np\nqklm\n0 5 10 15 20 25 3020100102030Energyfactorf\nRod length nznx=ny\n=1611162126\n(a) At rod center nk=0.rod domain\n{I}\n{II}f\ng\nh\nie d c b aZ\nY\nX\nsampling\nmoment13Fig. 7. Energy factors of parallel dipole moments for domains tracing on X{I} and Z{II}\naxes in Fig. 4.0 5 10 15 20 25 3020100102030\n0 5 10 15 20 25 30201001020300 5 10 15 20 25 3020100102030\n611\n162126\n0 5 10 15 20 25 3030201001020\n0 5 10 15 20 25 303020100102061116\n2126\n6\n11 162126\n6\n1116\n2126Rod length nz\nRod length nz\nRod length nz\nRod length nznz=ny=1\nnz=ny=1nz=ny=1nz=ny=1\nTraces {I}. Traces {II}.(i)At far from edge nm=-(nz+6).Energyfactorf\n0 5 10 15 20 25 3020100102030\n0 5 10 15 20 25 3020100102030\n0 5 10 15 20 25 3020100102030Energyfactorf\n(b)At quarter point nk=-nx/2.6111621\nRod length nz26\nnx=ny\n=1Energyfactorf EnergyfactorfRod length nz\nRod length nz\nRod length nz(c) At side edge nk=-nx.\n(d)At adjacent edge nk=-(n.+1).\n(e) At far from edge nk=-(nx+6).nx=ny=1\nnx=ny=1\nnx=ny=161116 21\n2126\n611\n111626\n616 2126(h)At adjacent edge nm=-(nz+1).(g) Atsideedge nm=-nz.(f)At quarter point nm=-nz/2.14Fig.8. Energy factors of cross direction dipole moments for rod domains tracing on X{III}\n(l=0,m=-nz-1) and Y{IV} ( k=-nx-1,m=-nz-1) axes in Fig. 5.0 5 10 15 20 25 3040302010010\n16 2111266\nRod length nznz=ny=1Energyfactorf\n(j)At quarter point nk=-nx/2.\n(m)At far from edge nk=-(nx+6).0 5 10 15 20 25 3040302010010\n26 16 21\nRod length nz\nTraces {IV}.(q)At far from edge nl=-(ny+6).nz=ny=1\n611\n0 5 10 15 20 25 3040302010010\n212616Energyfactorf\nTraces {III} .Rod length nznz=ny=1\n6\n110 5 10 15 20 25 3040302010010\n6\n16 2111nz=ny=1\nRod length nz\n(p)At adjacent edge nl=-(ny+1).26\n0 5 10 15 20 25 3040302010010Energyfactorf\n(l)At adjacent edge nk=-(nx+1).116\nRod length nznz=ny=1\n26 21160 5 10 15 20 25 3040302010010Energyfactorf\n116\n26\nRod length nznz=ny=1\n(k)At side edge nk=-nx.1621\n0 5 10 15 20 25 3040302010010\n6\n26 16 2111nz=ny=1\nRod length nz\n(o)At side edge nl=-ny.0 5 10 15 20 25 3040302010010\nnz=ny=1\nRod length nz\n(n)At quarter point nl=-ny/2.6 21 26 11 1615Fig. 9. Nano -scale system size and moment direction marks .(a) T hesystem scale ofNx,Ny\nandNzlattice points and cut sheets in a orthorhombic system . (b) Main direction marks in\nX-Z,X-YandY-Zplanes.\nFig. 1 0.Nano -beltdipole moment arrays at y=2 in a NxNyNz=20×4×40lattice point system\nwith nb=2.22. (a ) The first random arrays. (b ) The annealed moment arrays in the initial trace\ncurve atH=5×104A/m and T<10 K.(a)System sizes and cut sheet number .NzNy\nH\nNx1234\n(b)Directions and marks in X-Z,X-YandY-Zplanes .Y-ZW^\n> -\n( ]”1\nX-Z X-Y•g\n> -\np mj+\nWh\n+ .\nq nk1\n(a) Random states (b)Annealed states\n16Fig. 11. Magnetization curve ( Bm=nb) in a NxNyNz =20×4×40 lattice point system. The aria\nA isprecisely calculated and drawn in Fig. 12 to show the B effects.\nFig. 12. The terraces ΔHand the jumps ΔMofthe B effects in theprecise magnetization\ncurve at the aria A in Fig. 11. The coercivity becomes μ0Hc=0.0456 T.0.100.05 0.05 0.10\n2112\nAM\nμ0H\n0.02 0.03 0.04 0.05\n2.01.51.00.50.0\nJaHcΔH\nΔMμ0H\nMAJb17Fig. 13. System magnetization energies. (a) The variations of the moment -field energy: WH.\n(b) The moment -structure energy: Wf. (c) The total energy: W. The energy curves are\ncorresponded to the magnetization curves in Fig. 11. The ○marks in (c) indicate the J a, Jband\nHcpoints in Fig. 12 respectively.0.150.100.05 0.00 0.05 0.10 0.151.51.00.50.00.5\n(a)\nExternal field μ0H [T]WH ×10-20[J]\n0.150.100.05 0.00 0.05 0.10 0.155.04.54.03.53.0\n(b)\nExternal field μ0H [T]Wf ×10-20[J]\n0.150.100.05 0.00 0.05 0.10 0.155.04.54.03.53.0\n(c)\nExternal field μ0H [T]×10-20[J] W18Fig.1 4. Domain structures (up side) and energy distributions of Wj(down side). The figures\nof (a), (b) and (c) are corresponded to theJa, JbandHcpoints in Fig. 12 and the ○marks in\nFig. 13 (c) respectively. The numbers of (1)~(4) indicate the sheet positions iny-axis.\n(a) Structures with μ0H=0.0183TattheJapoint.(1) (2) (3) (4)\n(1) (2) (3) (4)(1) (2) (3) (4)\n(b) Structures with μ0H=0.0185TattheJbpoint.\n(c) Structures with μ0H=0.0456TattheHcpoint."    },    {        "title": "1406.6412v1.Magnetomechanical_response_of_bilayered_magnetic_elastomers.pdf",        "content": "arXiv:1406.6412v1  [cond-mat.soft]  24 Jun 2014Magnetomechanical response of bilayered magnetic\nelastomers\nElshad Allahyarov\nInstitut f¨ ur Theoretische Physik II, Heinrich-Heine-Universit¨ a t D¨ usseldorf\nUniversit¨ atstrasse 1, 40225 D¨ usseldorf, Germany\nTheoretical Department, Joint Institute for High Temperatures , Russian Academy of\nSciences (IVTAN), 13/19 Izhorskaya street, Moscow 125412, R ussia\nDepartment of Macromolecular Science and Engineering, Case West ern Reserve\nUniversity, Cleveland, Ohio 44106-7202, United States\nAndreas M. Menzel\nInstitut f¨ ur Theoretische Physik II, Heinrich-Heine-Universit¨ a t D¨ usseldorf\nUniversit¨ atstrasse 1, 40225 D¨ usseldorf, Germany\nLei Zhu\nDepartment of Macromolecular Science and Engineering, Case West ern Reserve\nUniversity, Cleveland, Ohio 44106-7202, United States\nHartmut L¨ owen\nInstitut f¨ ur Theoretische Physik II, Heinrich-Heine-Universit¨ a t D¨ usseldorf\nUniversit¨ atstrasse 1, 40225 D¨ usseldorf, Germany\nE-mail:elshad.allakhyarov@case.edu\nAbstract.\nMagnetic elastomers are appealing materials from an application point of view:\nthey combine the mechanical softness and deformability of polymer ic substances with\nthe addressability by external magnetic fields. In this way, mechan ical deformations\ncan be reversibly induced and elastic moduli can be reversibly adjust ed from outside.\nSo far, mainly the behavior of single-component magnetic elastomer s and ferrogels\nhas been studied. Here, we go one step further and analyze the ma gnetoelastic\nresponse of a bilayered material composed of two different magnet ic elastomers. It\nturns out that, under appropriate conditions, the bilayered magn etic elastomer can\nshow a strongly amplified deformational response in comparison to a single-component\nmaterial. Furthermore, a qualitatively opposite response can be ob tained, i.e. a\ncontraction along the magnetic field direction (as opposed to an elon gation in the\nsingle-component case). We hope that our results will further stim ulate experimental\nandtheoreticalinvestigationsdirectlyonbilayeredmagneticelasto mers,or, inafurther\nhierarchical step, on bilayered units embedded in yet another polym eric matrix.Magnetomechanical response of bilayered magnetic elastom ers 2\n1. Introduction\nThe terms “magnetic hybrid materials” or “magnetic composite mate rials” are typically\nassociated with classical magnetic elastomers or ferrogels [1]. Thes e substances consist\nofamoreorlesschemically crosslinked andpossiblyswollen polymericma trixintowhich\nparamagnetic, superparamagnetic, orferromagnetic colloidal pa rticles areembedded. In\nthisway, theadvantageousfeaturesoftwodifferentclassesofm aterialsarecombinedinto\none: on the one hand, one obtains free-standing soft elastic solids of typical polymeric\nproperties [2,3]; on the other hand, the materials can be addresse d by external magnetic\nfields and in this way their properties can be tuned reversibly from ou tside as for\nconventional ferrofluids and magnetorheological fluids [4–14].\nA lot of work has been spent on investigating how such ferrogels mec hanically\nrespond to external magnetic fields. In particular, these analyse s focused on the nature\nof the induced shape changes [1,15–29]. It turned out that the sp atial distribution of\nthe magnetic particles within a sample can qualitatively influence its res ponse to the\nexternal field. This is because the magnetic interaction between th e magnetic particles\ndepends ontheir spatial arrangement. Forexample, when thepar ticles were arrangedon\nregularlatticestructures, thesystem showedeither anelongatio nalongtheexternal field\nor a contraction, depending on the particular lattice [19,24,29]. L ikewise, anisotropic\nparticle distributions and the presence of chain-like aggregates th at can for example\nresult fromcrosslinking thepolymer matrixinthepresence ofastro ngexternal magnetic\nfield [30–34] can change the mechanical properties in and the defor mational response\nto an external magnetic field [1,18,20,27,28,35,36]. Even the pr esence of randomly\ndistributed dimer-like arrangements instead of single isolated magne tic particles was\nshown to be able to switch the distortion of a ferrogel from contra ctile along the field\ndirection to extensile [22,26].\nThe coupling of mechanical and deformational behavior to externa l magnetic\nfields, often referred to as “magnetomechanical coupling”, open s the way to various\ndifferent types of application. Soft actuators [37] or magnetic se nsors [38,39] can\nbe constructed that react mechanically to external magnetic field s or field gradients.\nVibration absorbers [40] and damping devices [41] can be manufact ured, the properties\nof which can be reversibly tuned from outside by applying an externa l magnetic field.\nIn the search for an increased magnitude of magnetomechanical c oupling, a new class of\nferrogelswas synthesized [42,43]. Via surfacefunctionalizationof themagnetic particles,\nthe polymer chains could be directly chemically attached to the partic le surfaces. In this\nway, the magnetic particles became part of the embedding crosslink ed polymer network.\nFor such materials, a restoring mechanical torque acts on the par ticles when they rotate\nout of their initial orientations acquired during crosslinking [25], which constitutes a\nform of orientational memory [44].\nHere we analyze a further type of magnetomechanical coupling tha t arises when\nlayered materials of magnetic elastomers are considered. In our ca se, we investigate\nthe deformational response of a bilayered magnetic elastomer to a n external magneticMagnetomechanical response of bilayered magnetic elastom ers 3\nfield combining phenomenological magnetostatics with elasticity theo ry. This type of\ndeformation is related to the magnetic pressure on the material bo undaries, similar\nto the Maxwell pressure in dielectrics. The boundary-related magn etic pressure acts\nnot only on the outer surfaces of the sample, but also on the inner in terfaces in the\nconsidered composite materials containing two (or many) layers of m agnetic elastomers\nof different magnetic susceptibilities [45]. In conventional ferromag netic materials this\nsetup was for example suggested for sensor applications when two ferromagnetic prisms\nare separated by a piezolayer [46].\nIn this paper we theoretically analyze basic principles of the deforma tion in\ncomposite magnetic elastomers generated by the magnetic pressu re of external fields.\nWeconnect theultimate deformationofthecomposite material tot heeffective magnetic\npole distribution on the material boundaries and at the bilayer interf ace. The material\nproperties of the composite elastomer, such as its susceptibility an d demagnetization\ncoefficients, define a crucial parameter, called a geometrical func tionA, which plays\na major role in the material reaction to the applied field. It turns out that, under\nappropriate conditions, the bilayered magnetic elastomer can show a strongly amplified\ndeformational response in comparison to a single-component mate rial. Furthermore, a\nqualitatively opposite response can be obtained, i.e. a contraction a long the magnetic\nfield direction (as opposed to an elongation in the single-component c ase).\nThe rest of the paper is organized as follows. In the next section th e magnetic\npressure on the particle boundaries and the geometry function Aare explained. The\ndependence of thefunction Aonthedemagnetization coefficient αis discussed insection\n3. In section 4 we investigate the magnetization of the different laye rs in the bilayer.\nThe magnetic pole distribution and the expression for the elastic str ain are discussed in\nsection 5. Finally we conclude in section 6.Magnetomechanical response of bilayered magnetic elastom ers 4\n2. Magnetic energy density and magnetic driving pressure\nWhen a homogeneous material with a magnetic permittivity µis placed into a uniform\nexternal magnetic field /vectorH0, the driving pressure on the material boundary is associated\nwith the difference between the relative energy densities\n∆u=µH2\n2−µ0H2\n0\n2. (1)\nHereµ0isthesusceptibility ofvacuum, µ0= 1.26×10−6mkg\ns2A2, andHdenotestheinternal\nmagnetic field. Using the relation between the magnetization Mand the internal field\nHin an isotropic material,\nM=χH, (2)\nwhereχis the susceptibility of the material, and\nH=H0\n1+αχ(3)\nis the internal field in the material. Here, αis the demagnetization coefficient of the\nsample along the field direction /vector z. Assuming a rectangular prism geometry for the\nmaterial, the full energy difference can be rewritten as\n∆U=V∆u=µ0MH0\n2A(α,χ)V. (4)\nHereV=L2Lzis the volume of the material, with Lzthe edge length of the sample\nalong the field direction /vector z, andLthe edge lengths in the remaining lateral directions\nset equal for simplicity. The demagnetization coefficient αdepends on the dimensional\nlengths of the sample. In general, the factor α(l)hasl=x,y,zcomponents, which\nobey/summationtext\nlα(l)= 1. Whereas for simple geometrical shapes the coefficients α(l)are well\nknown, for example, for a sphere and a cube α(x)=α(y)=α(z)= 1/3, and for a slab\nwith infinite lateral ( xy) dimensions α(x)=α(y)= 0, and α(z)= 1, for the rectangular\nprisms considered in this work the coefficients α(l)are not known apriori. Their values,\nhowever, can be calculated using analytical expressions given in Ref . [47,48], or taken\nfrom the tabulated results available in Ref. [49]. In the following we will a dopt the\nnotionα=α(z).\nThe geometry factor A(α,χ) in Eq.(4) turns out to be\nA(α,χ) =1−2α−α2χ\n1+αχ(5)\nand obeys |A(α,χ)| ≤1. This function defines the type of the deformation: a positive\nA(α,χ) means a stretching, and a negative A(α,χ) means a compression of the material\nalong the applied field. A full description of this function is presented in section 3.\nUnder the driving pressure the material is deformed because of th e propagation of\nthe material boundary from the area with high susceptibility into the surrounding area\nwith low susceptibility. The deformational changes of the material, n amely the changes\nin its thickness Lzand area S=L2, lead to the magnetic energy difference in Eq.(4)\n∆U=∂U\n∂Lz∆Lz+∂U\n∂S∆S. (6)Magnetomechanical response of bilayered magnetic elastom ers 5\nAssuming that the density of the material does not change during t his type of\ndeformation, which is referred to as a constant volume condition, w ritten as\nSLz= (S+∆S)(Lz−∆Lz), (7)\nwe get the following relation between ∆ Sand ∆Lzwhen ∆Lz/Lz≪1\n∆S=S∆Lz\nLz(8)\nFrom Eq.(4), assuming that neither MnorHstrongly depend on the changes in\nthe material geometry, which is valid only for small shape deformatio ns, for the partial\nderivatives of the stored energy we find\n∂U\n∂Lz=1\n2µ0H0MSA(α,χ),\n∂U\n∂S=1\n2µ0H0MLzA(α,χ). (9)\nInserting Eq.(9) into Eq.(6) and using Eq.(8) we obtain\n∆U=µ0H0MS∆LzA(α,χ). (10)\nTaking into account the force-energy relation F= ∆U/∆Lz, we obtain the final\nexpression for the magnetic pressure,\np=|/vectorF|/S=µ0|/vectorH0|A(α,χ)(/vectorM·/vector n). (11)\nHere/vector nis a unit vector normal to the material surface pointing outward th e sample\nsurface. It should be noted that for specific cases when the cons tant volume condition\nEq.(7) does not apply, for example, in magnetic liquids which can leave t he field area\nwhen squeezed by magnetic forces, the second term containing ∆ Sin Eq.(6) can be\nzero. For such cases the magnetic pressure will be half the pressu re defined by Eq.(11).\nThe term /vectorM·/vector nin Eq.(11) defines the effective magnetic pole density [50]\nσM=/vectorM·/vector n (12)\nat the boundaries of the sample. The sign of these magnetic poles is p ositive on the\nupperboundary, andnegativeonthebottomboundaryofthesam pleifthefielddirection\nis from the bottom to the top.Magnetomechanical response of bilayered magnetic elastom ers 6\n3. Geometry-dependent deformation under an applied field\nIt is evident from Eq.(11) that the magnetic driving force /vectorFacts on the upper and\nbottom surfaces in opposite directions trying to stretch the prism ifA(α,χ) is positive.\nIn the opposite case, when A(α,χ) is negative, the driving force /vectorFpushes the upper\nand bottom boundaries towards each other.\nThe limiting boundaries of A(α,χ) are dictated by the dependence of the coefficient\nαon the geometry of the material. For an infinite slab with Lz/L→0 andα≈1 the\nfunction Areaches its bottom limit A(α,χ)≈ −1 from Eq.(5), which recovers the\nclassical relation u=−µ0MH0/2 for the magnetic energy density [51]. Putting α= 0\n(the case of an elongated cylinder along the z-axis) into Eq.(5) we get the upper limit\nforA(α,χ) = 1. The function A(α,χ) changes its sign at α=√1+χ−1, as shown in\nFigure 1. The zeros of Acorrespond to the particular dimensions of the prism at which\nno deformation of the material is observed.\nFigure 1. (Color in online) Geometrical factor A(α,χ) for four different values of\nthe magnetic susceptibility χ. Note that the zeros of Acorrespond to the particular\ndimensions of the prism at which no deformation of the material is obs erved.\nFor the case 0 < χ <10 considered in this paper, the function A(α,χ) is always\npositive for α <0.23, which corresponds roughly to the size ratio Lz/L >3.3. An\nopposite scenario, a shrinking of the prism for all 0 < χ <10 is predicted for α >0.5\nwhichroughlycorrespondstothesizeratio Lz/L <1.4. ThisisdemonstratedinFigure2\nwhere the magnetic pressure F/Sis plotted against the susceptibility χ.Magnetomechanical response of bilayered magnetic elastom ers 7\n0246810−1−0.500.511.52\n χ  F/(S µ0 H02) \n  \nα=1/10\nα=1/5\nα=0.23\nα=1/3\nα=1/2\nα=1\nFigure 2. (Color in online) Normalized pressure F/(Sµ0H2\n0) as a function of the\nmagnetic susceptibility χfor six different values of α. Note that the force becomes\ncompletely positive at α <0.23, and completely negative at α >0.5.F >0\ncorresponds to an elongation along the magnetic field direction, whe reasF <0 implies\na contraction.Magnetomechanical response of bilayered magnetic elastom ers 8\n4. Magnetization of a magnetic bilayer under external field\nWe now consider a composite bilayered magnetic elastomer of a recta ngular shape with\na 2-2 connectivity [52] as shown in Figure 3. The rectangular prism ha s dimensions\nLx,Ly,Lz, and for simplicity we assume that its lateral dimensions are the same ,\nLx=Ly=L. The bottom and upper parts of the prism, denoted as layers i=1\nandi=2, are made from different materials with magnetic susceptibilities µ1andµ2,\nand elastic moduli Y1andY2, and have thicknesses d1andd2=Lz−d1correspondingly.\nThere is no gap between the layers of the prism, d= 0, hence the stacking density of\nthe composite is ρ=Lz/(d+Lz) = 1.\nFigure 3. (Colorin online) Schematic illustration ofthe composite bilayeredmagn etic\nelastomer in the form of a prism with 2-2 connectivity under an exter nal magnetic field\nH0.\nWhen an external magnetic field /vectorB0=µ0/vectorH0is applied along the z-axis,/vectorH0/bardbl/vector z,\nthe field /vectorBiin the layer iis determined as\n/vectorBi=µ0(/vectorHi+χi/vectorHi) (13)\nwhere the magnetic field /vectorHiis defined as\n/vectorHi=/vectorH0+/vectorH(i)\nd+/vectorRi(/vectorHj). (14)\nHere/vectorH(i)\ndis a demagnetization field in the prism i[53]. This field originates from the\nexistence of magnetic poles at the boundaries of the prism iperpendicular to the field,\nin analogy to the polarization charges at the dielectric boundaries un der an external\nelectric field. In the linear response theory the field /vectorH(i)\ndreads\n/vectorH(i)\nd=−αi/vectorMi, (15)\nwhereαiis the demagnetization factor of the prism ialong the z-axis.\nThe last term on the right hand side of Eq.(14), /vectorRi(/vectorHj), represents the average\nvalue of the magnetic field /vectorHjgenerated by the magnetized layer jin the volume ofMagnetomechanical response of bilayered magnetic elastom ers 9\nlayeri, wherej/negationslash=i. The full distribution of this cross field can be calculated using\nnumerical methods, see Ref. [54]. The field /vectorR1(/vectorH2), schematically drawn in Figure 4, is\ninhomogeneous along the z-axis: it has a maximum value at the top of the layer 1and\nbecomes weaker towards the bottom edge of the layer 1. There are different approaches\nabout accepting the best approximation for Ri, see Ref. [55]. The so-called ’ballistic’\napproach defines /vectorRias the averaged /vectorRi(/vectorH2) in the xymid-plane of layer 1. Or, the\n’local’ approach defines /vectorRi(/vectorH2,z) along the central line zwithx=y= 0. Within\nthe ’side’ approach /vectorRiis measured as an averaged field over the surfaces of the layer i\nperpendicular to z. In our generalized approach we assume that the average field /vectorRiis\nhomogeneous across the layer iand is a fraction of the magnetization of layer j,\n/vectorRi=γi/vectorMj. (16)\nFigure 4. (Color in online) Schematic presentation of the cross term /vectorR1(/vectorH2), which\ncorresponds to the field lines generated by /vectorM2of layer2in the volume of layer 1.\nTheconnectivity coefficient γicanbeeasilydefinedfromtheboundaryconditionfor\nthe magnetic field /vectorBassuming that there is no external field, H0= 0, anda permanently\nmagnetized layer jis the only source that generates a magnetic field in the layer i. For\ni= 1 and j= 2, the case shown in Figure 4, the field inside layer 2is\n/vectorB2=µ0(/vectorH2+/vectorM2). (17)\nOutside layer 2, at its bottom boundary,\n/vectorBout=µ0/vectorHout, (18)Magnetomechanical response of bilayered magnetic elastom ers 10\nPutting\n/vectorH2=/vectorH0−α2/vectorM2=−α2/vectorM2 (19)\ninto Eq.(17), we get\n/vectorB2=µ0(1−α2)/vectorM2. (20)\nApplying the boundary condition for the continuity of the perpendic ular component of\n/vectorBat the bottom boundary of layer 2,/vectorBout=/vectorB2, we get from Eq.(18) and Eq.(20)\n/vectorHout= (1−α2)/vectorM2. (21)\nWithin the ”upper side” approach R1=Hout, and using Eq.(16) and Eq.(21) we\narrive at the preliminary connectivity coefficient\n/tildewiderγ1= 1−α2. (22)\nHowever, within our generalized approach R1< Hout, and thus using R1=β1Hout,\nwhereβ1<1 is a coefficient that, generally speaking, depends on the coefficient sα1and\nα2, we get for the connectivity coefficient\nγ1=β1(1−α2). (23)\nThe exact value of β1can be calculated only using numerical procedures. In our\nanalytical approach we can define the upper limit for β1, above which non-physical\neffects of negative magnetization might take place, see Appendix A f or more details.\nIn a similar manner we define the connectivity coefficient for the seco nd layer as\nγ2=β2(1−α1). It is worth to mention that, for an infinitely wide ( L≫Lz) prism\nαi= 1 (i=1,2), and the connectivity coefficients γi= 0 regardless of the values of βi,\nmeaning that Ri(Hj) = 0. In other words, the cross term Ri(Hj) is negligible for flat\ngeometries.\nFinally we arrive at the following relation for the field /vectorHiinside the layer iof the\nprism placed under the external field /vectorH0,\n/vectorH1=/vectorH0−α1/vectorM1+β1(1−α2)/vectorM2,\n/vectorH2=/vectorH0−α2/vectorM2+β2(1−α1)/vectorM1. (24)\nBelow, for simplicity, we will assume that β1=β2=βin order to proceed to\nanalytical results. Thus putting /vectorHi=/vectorMi/χi, whereχiis the susceptibility of the layer\niwe find\nM1=H0χ1(1+α2χ2)+βχ1χ2(1−α2)\n(1+χ1α1)(1+χ2α2)−β2(1−α1)(1−α2)χ1χ2,\nM2=H0χ2(1+α1χ1)+βχ1χ2(1−α1)\n(1+χ1α1)(1+χ2α2)−β2(1−α1)(1−α2)χ1χ2. (25)\nFor a single layer, i.e. when χ2= 0, from Eq.(25) we recover the magnetization M1of\nthe single layer\n/vectorM1=/vectorH0χ1\n1+α1χ1. (26)\nEq.(25) is the main result for the magnetization of the bilayer and will b e used to\ncalculate the magnetic pressure on the composite prism in the next s ection.Magnetomechanical response of bilayered magnetic elastom ers 11\n5. Magnetic pole distribution at the bilayer interface\nFigure 5. (Colorinonline)Distributionofthemagneticpolesattheprismbounda ries.\nThe sign of the poles is defined from σ(j)\ni=/parenleftBig\n/vectorMi·/vector n/parenrightBig\nj, wherejindicates the bottom\n(j= 1) and upper ( j= 2) boundaries of each layer i= 1,2./vector nis a unit vector pointing\noutward from the layer surface.\nFor the set-up presented in Figure 3 the distribution of the poles is s chematically\nshown in Figure 5. For the pole density on layer 1we haveσ(1)\n1=−M1for the bottom\nandσ(2)\n1= +M1for the top boundaries, and for layer 2the density of boundary poles\nareσ(1)\n2=−M2andσ(1)\n2= +M2correspondingly. As a result, the net magnetic pole\ndensity at the interface between layers 1and2is\n∆σ=σ(2)\n1+σ(1)\n2=M1−M2, (27)\nor, taking into account Eq.(25),\n∆σ=H0χ1−χ2+(α1−α2)(1−β)χ1χ2\n(1+χ1α1)(1+χ2α2)−β2(1−α1)(1−α2)χ1χ2. (28)\nFrom Eq.(11) for the driving pressure p=F\nS=F1−F2\nSacting on the interface 1-2\nwe have\np=µ0|/vectorH0|/bracketleftBig\nA(α1,χ1)/vectorM1−A(α2,χ2)/vectorM2/bracketrightBig\n·/vector n. (29)\nThis expression reduces to a simple form\np=µ0|/vectorH0|A(α)∆σ (30)Magnetomechanical response of bilayered magnetic elastom ers 12\nforα1=α2=α,χ1≪1, andχ2≪1, hence A(α) = (1−2α). A positive (negative)\npin Eq.(29) and Eq.(30) means that the layer 1will be stretched (squeezed) into the\nlayer2, whereas the layer 2will be squeezed (stretched).\nAs has been mentioned in section 2, both the thickness Lzand the area Sof the\nprism deform under the constant volume condition. The total chan ge ∆Lzof the bilayer\nthickness is a sum of the thickness changes in each layer,\n∆Lz=2/summationdisplay\ni=1∆di, (31)\nwhere ∆diis defined through Hooke’s relation for the boundary forces F1andF2,\nF+F1=SY1∆d1\nd1,\n−F+F2=SY2∆d2\nd2, (32)\nwhereFi,i= 1,2 is given by Eq.(11).\nPutting everything together we have for the strain Σ B= ∆Lz/Lz,\nΣB=d1\nLz/parenleftbiggF+F1\nSY1+F−F2\nSY2/parenrightbigg\n+F2−F\nSY2. (33)\nThis expression, together with the definitions for the forces Fi\nFi\nS=µ0|/vectorH0|A(αi,χi)(/vectorMi·/vector n) (34)\nand the magnetization Midefined by Eq.(25) constitute our main result for the reaction\nof the bilayered magnetic elastomer to the applied field H0. Note that whereas the pole\ndistribution term ( /vectorMi·/vector n) and the geometry factor A(αi,χi) in the magnetic pressure\nequationEq.(34)togetherdetermine themagneticforceonthelay eriduetotheexternal\nfield, the total deformation of the layer iis regulated by the forces given in Eq.(32)Magnetomechanical response of bilayered magnetic elastom ers 13\n6. Results\nThe strain Σ Bin Eq.(33) depends on the forces Fi, the conformation parameter\nx=d1/Lz, and the elasticity moduli Yi. The forces Fi, according to Eq.(25) and\nEq.(34), are also functions of the four parameters α1,α2andχ1,χ2:\nFi=Fi(α1,χ1,α2,χ2).\n(35)\nIn total, the strain Σ Bdepends on the six parameters making the analyses of the strain\nΣBa very complicated task. However, a consideration of the relative s train, defined as\nΣ = Σ B/ΣS, (36)\nwhere the single layer strain is\nΣS=F3\nSY2(37)\n(assuming that the single layer is made of material 2, has the same thickness Lzas\nthe composite prism, and F3/Sis the magnetic pressure acting on this single-layered\nreference sample under an identical external magnetic field), brin gs the number of\nindependent system parameters from six down to four.\n6.1. Relative strain of the bilayered composite\nThe relative strain Σ in Eq.(36) measures how effective the reaction o f the bilayered\nstructure to the applied field is, and can be rewritten in parametric f orm as\nΣ = (1−x)/parenleftBigg\n2θ−f\n2/parenrightBigg\n+(2f−θ)x\ny. (38)\nHere we have adopted f=F1\nF3,y=Y1\nY2,x=d1\nLz, andθ=F2/F3. The strain Σ now\ndepends on four variables instead of six variables for Σ B, which makes its analyses\nrelativelysimple. Wecanfix θandx, andexplorethedependence ofΣontheparameters\nyandf.\nThe most interesting cases are\n(i) Σ>1, the case of strong bilayer stretching (squeezing) relative to th e single layer\nstretching (squeezing), and\n(ii) Σ<0, the case of bilayer shrinking (stretching) while the single layer str etches\n(shrinks).\nThe case 0 <Σ<1 corresponds to a weak bilayer reaction and thus is not\ninteresting to us. The parameters fandθcan run between −∞and +∞, but for\nsimplicity we will restrict ourselves to considering f >1 andθ >1, which corresponds\neither to the case when F1> F3,F2> F3, as well as F3>0, or to the case F1< F3,\nF2< F3, as well as F3<0.\nFrom Eq.(38) for Σ >1 we have the following relation for y(f):\ny <x(2f−θ)\n1−(1−x)(2θ−f/2). (39)Magnetomechanical response of bilayered magnetic elastom ers 14\nSimilarly, the condition Σ <0 leads to the following relation\ny >x(2f−θ)\n(1−x)(f/2−2θ). (40)\nRepresentative pictures for both of these curves, Eq.(39) and E q.(40), and for θ= 1\nare shown in Figure 6. It is evident that as the composition factor xincreases, a\ntransition from strong stretching (Σ >1) to squeezing (Σ <0) appears at high yvalues.\nAlso, the area of the weak reaction, 0 <Σ<1, widens as the composition factor x\nincreases.\nThe 3D pictures for the relative strain, plotted in Figure 7, show tha t a mild\nstretching and a strong squeezing at low xis replaced by the strong stretching and the\nweak squeezing at large x.Magnetomechanical response of bilayered magnetic elastom ers 15\n20406080100123456\n  f=F1/F2  y=Y1/Y2 \n20406080100123456\n  f=F1/F2  y=Y1/Y2 \n20406080100123456\n  f=F1/F2  y=Y1/Y2 \n204060801002468101214161820\n  f=F1/F2  y=Y1/Y2 \nFigure 6. (Color in online) Logarithmic plot for relative strain curves correspo nding\nto Eq.(39) and Eq.(40) for the composition parameter x= 0.25 (a),x= 0.4 (b),\nx= 0.5 (c),x= 0.75 (d). Dashed line (red in color) corresponds to Σ = 0, solid line\n(blue in color) is for Σ = 1. Above the dashed line Σ <0, and below the solid line\nΣ>1. In the area between these two lines 0 <Σ<1.Magnetomechanical response of bilayered magnetic elastom ers 16\n20\n40\n60\n80\n100 20406080100−30−20−10010 \n  f=F1/F2  y=Y1/Y2    relative strain Σb/Σs \n−35−30−25−20−15−10−50510\n20\n40\n60\n80\n10020406080100−2002040 \n  f=F1/F2  y=Y1/Y2    relative strain Σb/Σs \n−20−1001020304050\n2040608010020406080100−200204060 \n  f=F1/F2  y=Y1/Y2    relative strain Σb/Σs \n−20−10010203040506070\n2040608010020406080100 020406080100120 \n  f=F1/F2  y=Y1/Y2    relative strain Σb/Σs \n020406080100120\nFigure 7. (Color in online) 3D pictures for the relative strain Σ as a function of t he\nparameters yandffrom Eq.(38) and for the composition parameter x= 0.25 (a),\nx= 0.4 (b),x= 0.5 (c),x= 0.75 (d). The color code from dark red to dark blue\ncorresponds to a decreasing strain strength.Magnetomechanical response of bilayered magnetic elastom ers 17\n6.2. Full strain of the bilayer composite\nFigure 8. (Color in online) Geometrical illustration for the 4 different setups fr om\nTable 1. Upper row: Setups 1, 2, and 3; bottom row: Setup 4.\nIn this section we analyze the full strain of the bilayer Σ Bgiven by Eq.(33). We\nconsider three representative cases for x, namely x= 0.25,0.5,0.75. Four different\nsetup configurations with the corresponding parameters αiandA(αi,χi) are shown in\nTable 1. These setups cover the cases when the coefficients A(αi,χi) are simultaneously\neither positive or negative, or have opposite signs. Corresponding setup configurations\nare graphically presented in Figure 8.\nTable 1. Geometry-defined demagnetization coefficients αiand the geometry\nfunctions A(αi,χi) for the three composition parameters xdescribing the four different\nsetups in Figure 8. χ1= 1 and χ2= 10−3were used to calculate A(αi,χi).\nSetup xα1α2A(α1,χ1)A(α2,χ2)\n10.252\n31\n10-0.47 0.8\n20.51\n31\n30.25 0.33\n30.751\n102\n30.72 -0.33\n40.52\n32\n3-0.47 -0.33\nThe bilayer strain for Setup 1 as a function of parameters χ=χ1/χ2andy=Y1/Y2\nis plotted in Figure 9a. For this case the bilayer has a completely positiv e deformation,\nmeaning that it always experiences a stretching. A relatively high def ormation at fixed\nyhappens at larger values of χ. If an imaginary line at fixed y= 104is followed fromMagnetomechanical response of bilayered magnetic elastom ers 18\nχ= 1 toχ= 106, the composite strain will increase gradually from zero to several\npercents achieving a value of about 10 % at χ >105.\nA completely different scenario is observed for Setup 2 with x= 0.5, see Figure 9b.\nIn this equivalent case when the layers have the same thicknesses d1=d2, the strain\nshows both negative and positive domains. The black line correspond s to ΣB= 0, a zero\ndeformation of the composite for ∆ Lz=0. This zero strain happens when the changes\nin the layer 1 and layer 2 thicknesses compensate each-other, ∆ L1=−∆L2. A negative\nstrain, or a shrinking of the bilayer along the z-axis, takes place at high χand low y\nvalues. Another negative strain region is visible for χ <103and at about y >2. Also,\nin addition to the strong stretching similar to the Setup 1, there is th e second, though\nvery mild, stretching in the very tiny strip at low χand theystripes around the bottom\nleft corner of the left plot in Figure 9b. If an imaginary line at fixed y= 104is followed\nfromχ= 1 toχ= 106, the composite deformation will be first positive, then negative,\nand then positive again. Thus the positive deformation of the compo site is reentrant as\na function of χ.\nInSetup3weagainobserve two positive andtwo negative deformat iondomains, see\nFigure 9c. However, the overall picture is totally different from the results for Setups\n1 and 2. First, the areas of strong stretching for previous setup s now show a small\nstretching less than a few percents. Second, the shrinking of the composite increases,\nreaching −15 %, wheres in Setup 2 it was around −6 %. Third, a visible negative well\ndevelops for 102< χ <105. And fourth, a strong stretching is visible at very small y\naroundχ≈104. If we again follow an imaginary line at fixed y= 104and from χ= 1 to\nχ= 106, the composite deformation will first be negative, then becomes mo re negative,\nand then positive.\nSetup 4has thesame compositionfactor x= 0.5 astheSetup 2. The onlydifference\nbetween these Setups is the fact that in the former case both geo metry functions are\nnegative, while in the latter case they are positive. As seen from Figu re 9d, here we\nonly have a single positive and a single negative strain domain. Basically t he strain\nmaximum and minimum values stay the same as for Setup 2, but now the lowχstripe\nat the left bottom corner of Figure 9d is negative. Again, if an imagina ry line at fixed\ny= 104is followed from χ= 1 toχ= 106, the composite deformation will first be\nnegative and then positive.Magnetomechanical response of bilayered magnetic elastom ers 19\nFigure 9. (Color in online) Logarithmic plot for the bilayer strain from the four\nSetups given in Table 1. From top to bottom, Setup 1 (a), Setup 2 (b ), Setup 3\n(c), and Setup 4 (d). The other system parameters are: L= 100µm,Lz= 200µm,\nχ2= 10−3,Y2= 105N\nm2,B0=µ0H0= 0.13 Tesla. The left picture corresponds to the\ntop view of the 3D surface that is shown on the right. Black lines indica te a zero strain\nof the composite, Σ B= 0. The color code from dark red to dark blue corresponds to\na decreasing strain strength.Magnetomechanical response of bilayered magnetic elastom ers 20\n7. Conclusions\nAs explained in the introduction, there are different sources of mag netomechanical\ncoupling in ferrogels and magnetic elastomers. The most obvious one is associated\nwith the magnetic interactions between embedded magnetic particle s, which can induce\nmechanical deformations [19–29]. Furthermore, the aligning magne tic torque onto\nembedded ferromagnetic particles can directly induce distortions w hen the particles\nare chemically crosslinked into the polymer mesh [25,42,43].\nIn this paper, we have analyzed a completely different source of mag netomechanical\ncoupling. It results from the structural arrangement of two mag netic elastomers into a\nbilayered composite material. More technically speaking, it follows fro m the interplay of\nthe magnetic pressures acting on the outer boundaries of the sam ple and on the internal\ninterfacial boundaries between the layers.\nUsing linear response theory for the magnetization and demagnetiz ation fields of a\ncomposite material of a rectangular prism geometry, we have defin ed the strain of the\nbilayer structure to the applied field. We have connected the ultimat e deformation of\nthe sample to the magnetic pole distribution on the outer boundaries and at the bilayer\ninterface. The material properties of the composite particle, suc h as its susceptibilities\nand demagnetization coefficients, define a crucial parameter, calle d the geometrical\nfunction A, which plays a major role in the reaction to the applied field. According\nto our results, the composite magnetic elastomer is able to respond more efficiently\nto the external field in comparison to a single-component material. T his response also\nstrongly depends on the composition factor of the sample. By chan ging the composition\nfactorx=d1/Lzof the bilayer, it is possible to shift from a mostly stretching composit e\nto a mostly squeezing one when all other material parameters are k ept fixed.\nOur results are important for the design of optimized bilayered comp osites of\nmagnetic elastomers and gels. We hope that our analysis will stimulate further research\nin this direction, both experimentally and theoretically. Nevertheles s, we are already\nthinking one step further in a structural hierarchy of magnetic ela stomers. Just like\nmagnetic particles embedded in a surrounding polymer matrix in magne tic elastomers\nor ferrogels, we intend to consider on an upper hierarchical level u nits of bilayered\nmagnetic elastomers embedded in yet another non-magnetic polyme ric matrix.\nObviously, when the bilayered units stretch along an external magn etic field, the\noverall hierarchical material will elongate along the applied field and g et squeezed\nperpendicular to it due to volume conservation. In the opposite cas e, when the bilayered\nunits squeeze along the field direction, the overall sample will extend perpendicularly\nto the field, and its shrinking will be along the field. The right manageme nt of\ndifferently shaped or differently composed bilayered units and the rig ht regulation of\ntheir embedding places in the overall sample can adjust its overall de formation to the\nneeded demand. For example, it is possible to heterogeneously tune the response of the\nsystem during synthesis, making it elongate in one part and at the sa me time shrink in\nanother part. All these effects are potentially interesting for the ir application in a newMagnetomechanical response of bilayered magnetic elastom ers 21\ngeneration of sensors and in creating new smart (intelligent) mater ials.\nAcknowledgments\nA.M.M. and H.L. thank the Deutsche Forschungsgemeinschaft for s upport of the work\nthrough the SPP 1681 on magnetic hybrid materials.Magnetomechanical response of bilayered magnetic elastom ers 22\nAppendix A. Field correction coefficient β\nThe meaning of the coefficient βis obvious from the relation between the magnetization\nMand the external field H0in magnetic gels: the magnetization should have the same\ndirection as the applied field. As shown in Figure A1, where the magnet izationM1of\nlayer1is plotted as a function of its susceptibility χ1for the different values of β, at\nsomeβa pole develops in Eq.(25). The pole causes a nonphysical flipping over of the\nmagnetization vector /vectorM1. Decreasing the value of βguarantees the “correct” behavior\nof/vectorM1. All the setup configurations used in the main text are free from su ch pole effect\nfor the values of β≤1. Physically, the factor βcontains the widening of the field lines\naway from the interfacial boundary of layer 2, see Figure 4.\n0246810−50−2502550\n χ1  M1/H0 \n  β=1.0\nβ=0.8\nβ=0.6\nβ=0.5\nFigure A1. (Color in online) The magnetization /vectorM1of layer 1depends on the\nparameter β. Other parameters: χ1=χ2,α1=α2= 1/3.Magnetomechanical response of bilayered magnetic elastom ers 23\n[1] G. Filipcsei, I. Csetneki, A. Szil´ agyi, and M. Zr´ ınyi. Magnetic field- responsive smart polymer\ncomposites. Adv. Polym. Sci. , 206:137–189, 2007.\n[2] M. Doi and S. F. Edwards. The Theory of Polymer Dynamics . Clarendon Press, Oxford, 1988.\n[3] G. Strobl. The Physics of Polymers . Springer, Berlin/Heidelberg, 2007.\n[4] R. E. Rosensweig. Ferrohydrodynamics . Cambridge University Press, Cambridge, 1985.\n[5] S. Odenbach. Ferrofluids–magnetically controlled suspensions. Colloid Surface A , 217(1–3):171–\n178, 2003.\n[6] S. Odenbach. Magnetoviscous effects in ferrofluids . Springer, Berlin/Heidelberg, 2003.\n[7] B. Huke and M. L¨ ucke. Magnetic properties of colloidal suspens ions of interacting magnetic\nparticles. Rep. Prog. Phys. , 67(10):1731–1768, 2004.\n[8] S. Odenbach. Recent progress in magnetic fluid research. J. Phys.: Condens. Matter , 16:R1135–\nR1150, 2004.\n[9] B. Fischer, B. Huke, M. L¨ ucke, and R. Hempelmann. Brownian re laxation of magnetic colloids.\nJ. Magn. Magn. Mater. , 289:74–77, 2005.\n[10] P. Ilg, M. Kr¨ oger, and S. Hess. Structure and rheology of mo del-ferrofluids under shear flow. J.\nMagn. Magn. Mater. , 289:325–327, 2005.\n[11] J. P. Embs, S. May, C. Wagner, A. V. Kityk, A. Leschhorn, and M. L¨ ucke. Measuring the\ntransverse magnetization of rotating ferrofluids. Phys. Rev. E , 73(3):036302, 2006.\n[12] P. Ilg, E. Coquelle, and S. Hess. Structure and rheology of fer rofluids: simulation results and\nkinetic models. J. Phys.: Condens. Matter , 18(38):S2757–S2770, 2006.\n[13] C. Gollwitzer, G. Matthies, R. Richter, I. Rehberg, and L. Tobis ka. The surface topography of\na magnetic fluid: a quantitative comparison between experiment and numerical simulation. J.\nFluid Mech. , 571:455–474, 2007.\n[14] J. de Vicente, D. J. Klingenberg, and R. Hidalgo-Alvarez. Magne torheological fluids: a review.\nSoft Matter , 7(8):3701–3710, 2011.\n[15] M. Zr´ ınyi, L. Barsi, and A. B¨ uki. Deformation of ferrogels indu ced by nonuniform magnetic fields.\nJ. Chem. Phys. , 104(21):8750–8756, 1996.\n[16] M. Zr´ ınyi, L. Barsi, D. Szab´ o, and H.-G. Kilian. Direct observat ion of abrupt shape transition in\nferrogels induced by nonuniform magnetic field. J. Chem. Phys. , 106(13):5685, 1997.\n[17] X. Guan, X. Dong, and J. Ou. Magnetostrictive effect of magne torheologicalelastomer. J. Magn.\nMagn. Mater. , 320(3–4):158–163, 2008.\n[18] G. Filipcsei and M. Zr´ ınyi. Magnetodeformation effects and the swelling of ferrogels in a uniform\nmagnetic field. J. Phys.: Condens. Matter , 22(27):276001, 2010.\n[19] D. Ivaneyko, V. P. Toshchevikov, M. Saphiannikova, and G. He inrich. Magneto-sensitive\nelastomers in a homogeneous magnetic field: a regular rectangular la ttice model. Macromol.\nTheor. Simul. , 20(6):411–424, 2011.\n[20] D. S. Wood and P. J. Camp. Modeling the properties of ferrogels in uniform magnetic fields.\nPhys. Rev. E , 83(1):011402, 2011.\n[21] P. J. Camp. The effects of magnetic fields on the properties of f errofluids and ferrogels.\nMagnetohydrodyn. , 47(2):123–128, 2011.\n[22] O. V. Stolbov, Y. L. Raikher, and M. Balasoiu. Modelling of magnet odipolar striction in soft\nmagnetic elastomers. Soft Matter , 7(18):8484–8487, 2011.\n[23] A. Y. Zubarev. On the theory of the magnetic deformation of f errogels. Soft Matter , 8(11):3174–\n3179, 2012.\n[24] D. Ivaneyko, V. Toshchevikov, M. Saphiannikova, and G. Heinr ich. Effects of particle distribution\non mechanical properties of magneto-sensitive elastomers in a hom ogeneous magnetic field.\nCondens. Matter Phys. , 15(3):33601, 2012.\n[25] R. Weeber, S. Kantorovich, and C. Holm. Deformation mechanis ms in 2d magnetic gels studied\nby computer simulations. Soft Matter , 8(38):9923–9932, 2012.\n[26] X. Gong, G. Liao, and S. Xuan. Full-field deformation of magneto rheological elastomer under\nuniform magnetic field. Appl. Phys. Lett. , 100(21):211909, 2012.Magnetomechanical response of bilayered magnetic elastom ers 24\n[27] A. Y. Zubarev. Effect of chain-like aggregates on ferrogel ma gnetodeformation. Soft Matter ,\n9(20):4985–4992, 2013.\n[28] A. Zubarev. Magnetodeformation of ferrogels and ferroelas tomers. Effect of microstructure of the\nparticles spatial disposition. Physica A , 392(20):4824–4836, 2013.\n[29] D. Ivaneyko, V. Toshchevikov, M. Saphiannikova, and G. Heinr ich. Mechanical properties\nof magneto-sensitive elastomers: unification of the continuum-me chanics and microscopic\ntheoretical approaches. Soft Matter , 10:2213–2225, 2014.\n[30] D. Collin, G. K. Auernhammer, O. Gavat, P. Martinoty, and H. R. Brand. Frozen-in magnetic\norder in uniaxial magnetic gels: preparation and physical propertie s.Macromol. Rapid\nCommun. , 24(12):737–741, 2003.\n[31] Z. Varga, J. Feh´ er, G. Filipcsei, and M. Zr´ ınyi. Smart nanocom posite polymer gels. Macromol.\nSymp., 200(1):93–100, 2003.\n[32] D. G¨ unther, D. Y. Borin, S. G¨ unther, and S. Odenbach. X-r aymicro-tomographiccharacterization\nof field-structured magnetorheological elastomers. Smart Mater. Struct. , 21(1):015005, 2012.\n[33] T. Borb´ ath, S. G¨ unther, D. Y. Borin, Th. Gundermann, and S. Odenbach. X µCT analysis\nof magnetic field-induced phase transitions in magnetorheological e lastomers. Smart Mater.\nStruct., 21(10):105018, 2012.\n[34] T. Gundermann, S. G¨ unther, D. Borin, and S. Odenbach. A co mparison between micro and\nmacro-structure of magnetoactive composites. J. Phys.: Conf. Ser. , 412(1):012027, 2013.\n[35] S. Bohlius, H. R. Brand, and H. Pleiner. Macroscopic dynamics of uniaxial magnetic gels. Phys.\nRev. E, 70(6):061411, 2004.\n[36] Y. Han, W. Hong, and L. E. Faidley. Field-stiffening effect of magn eto-rheological elastomers.\nInt. J. Solids Struct. , 50(14–15):2281–2288, 2013.\n[37] K. Zimmermann, V. A. Naletova, I. Zeidis, V. B¨ ohm, and E. Kolev . Modelling of locomotion\nsystemsusingdeformablemagnetizablemedia. J. Phys.: Condens. Matter , 18(38):S2973–S2983,\n2006.\n[38] D. Szab´ o, G. Szeghy, and M. Zr´ ınyi. Shape transition of magn etic field sensitive polymer gels.\nMacromolecules , 31(19):6541–6548, 1998.\n[39] R. V. Ramanujan and L. L. Lao. The mechanical behavior of sma rt magnet-hydrogel composites.\nSmart Mater. Struct. , 15(4):952–956, 2006.\n[40] H.-X. Deng, X.-L. Gong, and L.-H. Wang. Development of an adap tive tuned vibration absorber\nwith magnetorheological elastomer. Smart Mater. Struct. , 15(5):N111–N116, 2006.\n[41] T. L. Sun, X. L. Gong, W. Q. Jiang, J. F. Li, Z. B. Xu, and W.H. Li. S tudy on the damping\nproperties of magnetorheological elastomers based on cis-polybu tadiene rubber. Polym. Test. ,\n27(4):520–526, 2008.\n[42] N. Frickel, R. Messing, and A. M. Schmidt. Magneto-mechanical coupling in CoFe 2O4-linked\nPAAm ferrohydrogels. J. Mater. Chem. , 21(23):8466–8474, 2011.\n[43] R. Messing, N. Frickel, L. Belkoura, R. Strey, H. Rahn, S. Oden bach, and A. M. Schmidt. Cobalt\nferrite nanoparticles as multifunctional cross-linkers in PAAm ferr ohydrogels. Macromolecules ,\n44(8):2990–2999, 2011.\n[44] M. A. Annunziata, A. M. Menzel, and H. L¨ owen. Hardening tran sition in a one-dimensionalmodel\nfor ferrogels. J. Chem. Phys. , 138(20):204906, 2013.\n[45] W. W. Mullins. Magnetically induced grain-boundarymotion in bismut h.Acta Metall. , 4(4):421–\n432, 1956.\n[46] E. Liverts, A. Grosz, B. Zadov, M. I. Bichurin, Y. J. Pukinskiy, S. Priya, D. Viehland, and\nE. Paperno. Demagnetizing factors for two parallel ferromagnet ic plates and their applications\nto magnetoelectric laminated sensors. J. Appl. Phys. , 109(7):07D703, 2011.\n[47] A. Aharoni. Demagnetizing factors for rectangular ferromag netic prisms. J. Appl. Phys. ,\n83(6):3432–3434, 1998.\n[48] A. Aharoni, L. Pust, and M. Kief. Comparing theoretical demag netizing factors with the observed\nsaturation process in rectangular shields. J. Appl. Phys. , 87(9):6564–6566, 2000.Magnetomechanical response of bilayered magnetic elastom ers 25\n[49] D.-X. Chen, E. Pardo, and A. Sanchez. Demagnetizing factors for rectangular prisms. IEEE T.\nMagn., 41(6):2077–2088, 2005.\n[50] J. D. Jackson. Classical Electrodynamics . John Wiley and Sons, New York, 1998.\n[51] A. D. Sheikh-Ali, D. A. Molodov, and H. Garmestani. Boundarymig rationin Zn bicrystal induced\nby a high magnetic field. Appl. Phys. Lett. , 82(18):3005–3007, 2003.\n[52] C. R. Bowen and V. Y. Topolov. Piezoelectric sensitivity of PbTiO 3-based ceramic/polymer\ncomposites with 0 −3 and 3−3 connectivity. Acta Mater. , 51(17):4965–4976, 2003.\n[53] A. Smith, K. K. Nielsen, D. V. Christensen, C. R. H. Bahl, R. Bjør k, and J. Hattel. The\ndemagnetizing field of a nonuniform rectangular prism. J. Appl. Phys. , 107(10):103910, 2010.\n[54] D. V. Christensen, K. K. Nielsen, C. R. H. Bahl, and A. Smith. Dem agnetizing effects in stacked\nrectangular prisms. J. Phys. D: Appl. Phys. , 44(21):215004, 2011.\n[55] A. Aharoni. ”Local“ demagnetization in a rectangular ferromag netic prism. Phys. Status Solidi\nB, 229(3):1413–1416, 2002."    },    {        "title": "1407.2184v1.Competing_magnetic_phases_and_field_induced_dynamics_in_DyRuAsO.pdf",        "content": "arXiv:1407.2184v1  [cond-mat.str-el]  8 Jul 2014Competing magnetic phases and field-induced dynamics in DyR uAsO\nMichael A. McGuire, V. Ovidiu Garlea, Andrew F. May, and Brian C. Sale s\nOak Ridge National Laboratory, Oak Ridge, Tennessee 37831 U SA\n(Dated: August 12, 2021)\nAnalysis of neutron diffraction, dc magnetization, ac magne tic susceptibility, heat capacity, and\nelectrical resistivity for DyRuAsO in an applied magnetic fi eld are presented at temperatures near\nand below those at which the structural distortion ( TS= 25 K) and subsequent magnetic ordering\n(TN= 10.5 K) take place. Powder neutron diffraction is used to det ermine the antiferromagnetic\norder of Dy moments of magnitude 7.6(1) µBin the absence of a magnetic field, and demonstrate\nthe reorientation of the moments into a ferromagnetic config uration upon application of a magnetic\nfield. Dy magnetism is identified as the driving force for the s tructural distortion. The magnetic\nstructure of analogous TbRuAsO is also reported. Competiti on between the two magnetically\nordered states in DyRuAsO is found to produce unusual physic al properties in applied magnetic\nfields at low temperature. An additional phase transition ne arT∗= 3 K is observed in heat\ncapacity and other properties in fields /greaterorsimilar3 T. Magnetic fields of this magnitude also induce spin-\nglass-like behavior including thermal and magnetic hyster esis, divergence of zero-field-cooled and\nfield-cooled magnetization, frequency dependent anomalie s in ac magnetic susceptibility, and slow\nrelaxation of the magnetization. This is remarkable since D yRuAsO is a stoichiometric material\nwith no disorder detected by neutron diffraction, and sugges ts analogies with spin-ice compounds\nand related materials with strong geometric frustration.\nPACS numbers:\nI. INTRODUCTION\nThe common crystallographic feature of layered iron\nsuperconductorsistheFe Xlayer,composedofFebonded\ntoX, a pnictogen or chalcogen, in edge-sharing tetrahe-\ndral coordination. There are several related structural\nfamiliesofsuchcompounds, whicharedifferentiatedfrom\none another by what is found between the Fe Xlayers\n[1,2]. In manycases, isostructuralcompounds areknown\nwith other elements in place of Fe. Among 1111-type\nmaterials (ZrCuSiAs structure type) with compositions\nLnFeAsO (Ln= trivalent lanthanide) [3], Fe can be fully\nreplaced to form LnMAsO where M= Mn [4], Ru [3],\nCo [3], Rh [5], Ir [6], Ni [7], Zn [8], and Cd [9].\nThe physical properties of LnMAsO materials reflect\na wide range of behaviors and associated ground states.\nThese range from insulating to superconducting, and in-\nclude many types of magnetism. LnMnAsO compounds\nare semiconductors displaying giant magnetoresistance\nand antiferromagnetic (AFM) ordering of Mn moments\nat temperatures often exceeding room temperature, and\noften accompanied by spin reorientation transitions at\nlower temperatures [10–13]. The well known Fe com-\npoundsLnFeAsO exhibit spin-density-wave-like AFM\nwhich is at least partly itinerant, and is strongly coupled\nto the lattice distortion which occurs near the magnetic\nordering transition[2, 14–16]. Ferromagnetism (FM) as-\nsociated with itinerant magnetic moments on Co is ob-\nserved in LnCoAsO, and a transition to AFM order is\nobserved at lower temperatures due to effects of local-\nized 4fmoments on the magnetic lanthanides [17–20].\nStudies of the 4 dand 5dtransition metal analogues of\ntheCocompounds( LnRhAsOand LnIrAsO)reportonly\nrare-earth magnetic ordering and only in the case of Ln\n= Ce [5, 6]. Some LnNiAsO compounds are supercon-ducting at low temperatures ( Ln= La[7, 21], Pr [22]),\nwhile others are not. CeNiAsO shows two magnetic or-\ndering transitions associated with Ce moments, and is\ndescribed as a dense Kondo lattice metal [23]. With a\nfilled 3dshell,LnZnAsO compounds are semiconductors\nwith band gaps near 2 eV, and form as transparent crys-\ntals with colors varying from yellow-orange to red [24].\nClearly this structure type provides fertile grounds for\ninteresting physics accessible by simple chemical substi-\ntutions.\nAmong the many studied substitutions, Ru is unique\nin that it is isoelectronic with Fe. Partial replacement\nof Fe with Ru in the related 122 materials SrFe 2As2\nand BaFe 2As2produces superconductivity with transi-\ntion temperatures near 20 K [25, 26], while partial sub-\nstitution of Ru into 1111-type materials only suppresses\nthe magnetism without the appearance of superconduc-\ntivity [27, 28]. LnRuAsO compounds are metals, and\nshow magnetic ordering at low temperatures when mag-\nnetic lanthanides are included [29–31].\nOur previous study of Ru containing 1111 materials\nuncovered particularly interesting behaviors in DyRu-\nAsO [31]. This material undergoes a structural phase\ntransition from tetragonal to orthorhombic near TS= 25\nK, but adopts a different low temperature structure (Fig.\n1c)thanthatobservedin LnFeAsO.Thedistortionwhich\noccurs in DyRuAsO involves a stretching of the unit cell\nalong the a-axis, maintaining a single Ru −Ru distance\nwithin the Ru net, but Ru −Ru−Ru angles which devi-\nate from 90◦. This is unlike the distortion which occurs\nin the parent phases of the layered iron superconductors,\nwhich shears the unit cell and results in a rectangular\nnet of Fe atoms [14]. In addition, anomalies in heat ca-\npacityandmagnetizationofDyRuAsO indicatemagnetic\nordering below TN= 10.5 K.2\nThe temperature and magnetic field dependence of the\nphysical properties indicated complex physics related to\nmagnetism is at play in DyRuAsO, and indications of\nstrong magnetoelastic coupling were observed. A meta-\nmagnetictransition wasobservedbelow TN, and the heat\ncapacity anomaly at the structural transition responded\nstrongly to a magnetic field. The present work aims to\nimprove our understanding of the underlying physics re-\nlated to these phenomena by identifying the magnetic\nstructures, determining the possible role of Ru mag-\nnetism, and further examining the effects of the com-\npetition between ordered ground states on the thermal,\ntransport, and magnetic properties of this material.\nHere we report results of neutron powder diffraction\nexperiments which reveal the low temperature magnetic\norderings, and the nature of the field induced transition,\nwhich involves competing AFM and FM phases. Effects\nof the competition between these phases include thermal\nand magnetic hysteresis in the magnetization and electri-\ncal resistivity, divergence between zero field cooled and\nfield cooled magnetization data, frequency dependence\nof the dynamical (ac) susceptibility, and time dependent\nproperties over a range of magnetic fields and tempera-\ntures. These behaviors highlight the complexity of the\nmagnetic interaction in DyRuAsO, and are reminiscent\nof spin-glass physics under some conditions. Dy mag-\nnetism is identified as the driving force for the structural\nphase transition, with little or no influence from Ru. In\naddition, detailed heat capacity, electrical resistivity, and\nmagnetization measurements provide evidence of a third\nphase transition which appears to be related to the com-\npeting magnetic ground states. The transition occurs\nnearT∗= 3 K and is strongest at magnetic fields of 3 −4\nT, diminished at higher fields, and absent at fields of 0 −2\nT.\nII. EXPERIMENTAL DETAILS\nPolycrystalline samples were synthesized from Dy,\nDy2O3, and RuAs as described in Ref. 31. Rietveld\nrefinement of powder diffraction patterns (neutron and\nx-ray) of the samples used in this study show them to be\n/greaterorsimilar95% pure, with Dy 2O3as the main impurity. Neutron\ndiffraction experiments were conducted at the High Flux\nIsotope Reactor at Oak Ridge National Laboratoryusing\nthe Neutron Powder Diffractometer (beamline HB-2A).\nData were collected at multiple temperatures and mag-\nnetic fields and using two neutron wavelengths, 1.538 ˚A\nand 2.41 ˚A. A collection of rectangular bars (4 ×4×7\nmm3) were cut from a sintered polycrystalline pellet for\nthe neutron diffraction measurement to prevent rotation\nof the powder grains in the applied magnetic field. A\nvanadium can with inner diameter of 6 mm was used to\ncontain the sample, which was loaded into a 5 T vertical-\nfield cryomagnet. Thefield wasdirected perpendicularto\nthe scattering plane. Dy has a high thermal neutron ab-\nsorption cross section; however, this did not preclude thecollection of data of sufficient quality for Rietveld anal-\nysis, which was performed using FullProf [32]. Similar\nneutron powder diffraction measurements, with no ap-\nplied magnetic field, were also performed on TbRuAsO,\nalso prepared as described in Ref. 31.\nMeasurements of the temperature and magnetic field\ndependence of the electrical resistivity, ac and dc mag-\nnetization, and heat capacity were performed using a\nQuantum Design Physical Property Measurement Sys-\ntem. Electrical contacts were made using platinum wires\nand conducting silver paste.\nIII. RESULTS AND DISCUSSION\nA. Magnetic structure\nFigure1 showsneutron powderdiffraction (NPD) data\ncollected in the paramagnetic, tetragonal state at 40 K,\nin the paramagnetic, orthorhombic state at 15 K, and in\nthe magnetically ordered, orthorhombic state at 1.5 K.\nRietveld analysis(not shown)ofthe patterns at 40Kand\n15Kareconsistentwiththetetragonalandorthorhombic\nstructures [31], respectively, with no indication of mixed\nor partial occupancy of any of the atomic sites. No indi-\ncations of long range magnetic order accompanying the\nstructural transition is seen. Strong magnetic reflections\nare observed at 1.5 K. All of the magnetic scattering oc-\ncurs at the positions of nuclear Bragg reflections, indi-\ncating the magnetic and nuclear unit cells are identical\n[propagation vector k= (0 0 0)]. The temperature de-\npendence of the intensity of the 001 reflection is shown in\nthe inset of Figure 1. The onset of magnetic order occurs\nnear 10 K, consistent with magnetization measurements\nwhich identify TN= 10.5 K in Ref. 31 and below, with\nsaturation of the ordered moment occurring near 5 K.\nRepresentational analysis was used to determine the\nsymmetry-allowed magnetic structures that can result\nfrom a second-order magnetic phase transition, given the\ncrystal symmetry before the transition ( Pmmn) and the\npropagation vector of the magnetic ordering, k=( 0 0\n0) . These calculations were carried out using the pro-\ngram SARA h-Representational Analysis.[33] The decom-\nposition of the magnetic representation (i.e. irreducible\nrepresentations (IRs)) for the Dy site (0 .25,0.25, z) is\nΓMag= 1Γ2+1Γ3+1Γ4+1Γ5+1Γ6+1Γ7. The labeling\nof the propagation vector and the IRs follows the scheme\nused by Kovalev[34]. Each representation contains only\none basis vector meaning that the magnetic moments are\nconfined to one direction, while the two Dy atoms of the\nprimitive cell can carry parallel or antiparallel moments.\nStrong magnetic contributions to the 00 ℓreflections in-\ndicate moments with large components in the ab-plane.\nRietveld refinement results of the diffraction data col-\nlected below TNusing wavelength 1.538 ˚A are shown in\nFigure 1(b). The orthorhombic distortion ( a>b) allows\nthe distinction of the directions in the ab-plane, and the\nbest fits were obtained with the Dy moments along the3\n(c)10 20 30 40 50 60 70 80 90 0 10 20 30 0.6 0.8 1.0 1.2 1.4 \n1.5 K 15 K intensity (arbitrary units) \n2θ (deg) T = 40 K DyRuAsO \nλ = 1.538 Å\n001 \nI (10 3 cts.) \nT (K) 001 \n (a)\n20 40 60 80 100 -50 050 100 150 200 250 300 \n  DyRuAsO \nT = 1.5 K \nλ = 1.538 Å\n2θ (deg.) intensity (b)99.5 100.5 2θ (deg)  40K  15K 400-tet \nFIG. 1: (Color online) (a) Neutron powder diffraction pat-\nterns from DyRuAsO collected in the tetragonal state at 40\nK, the orthorhombic state at 15 K, and the magnetically or-\ndered state at 1.5 K. The insets in (a) show the splitting\nof the tetragonal 400 reflection resulting from the structur al\ntransition and the intensity of the 001 reflection (labeled i n\nthe main panel) as a function of temperature, illustrating t he\nonset of magnetic order below about 10 K. (b) Rietveld fits\nof the nuclear and magnetic structures of DyRuAsO at 1.5 K.\nThe lower ticks locate reflections from the Dy 2O3impurity.\nThe AFM arrangement of the Dy moments determined from\nthe diffraction analysis is shown in (c).b-axis, corresponding to the representation Γ 4(or Shub-\nnikov magnetic space group Pm′mn). In this model, the\nmoments on the two Dy atoms in the primitive cell are\naligned AFM. This produces FM layers of Dy in the ab-\nplane, with AFM alignment between neighboring Dy lay-\ners.The resulting magnetic structure is shown in Figure\n1(c). Because of the compression of the ODy 4tetrahe-\ndral units along the c-axis(Fig. 1c), the shortest Dy −Dy\ndistances (3.5 ˚A) are those between neighboring layers\nwithin the DyO slabs. The shortest distance between Dy\natoms within a single layer are considerably longer (4.0\n˚A).\nNeutron powder diffraction analysis of isostructural\nTbRuAsO was also performed, and the same magnetic\nstructure as DyRuAsO was determined for the Tb mo-\nments. In this case, however, no distinction between the\naandbdirections can be made, since TbRuAsO remains\ntetragonal within experimental resolution to at least 1.5\nK. Structural information and magnetic moments deter-\nmined from the refinements of both compounds at the\nlowest temperatures investigated are collected in Table\nI. No conclusive evidence for ordered magnetic moments\non Ru is seen in the data. Small, non-zero values ( /lessorsimilar0.5\nµB) are obtained when Ru moments are included in the\nrefinements at the lowest temperatures, but the quality\nof the fit is not improved by their addition. The refined\nvalues of the rare-earth moment at 1.5 K are 7.6(1) µB\nfor Dy in DyRuAsO and 5.76(8) µBfor Tb in TbRuAsO.\nThe refined ordered moments are reduced from their\nfree ion values of gJ, which are 9 µBfor Tb and 10 µB\nfor Dy, as commonly found in related Fe-based materi-\nals [35–38]. This is attributed to crystalline electric field\neffects, the details of which are not known at this time.\nIn these materials the rare earths are in somewhat irreg-\nular coordination environments. The nearest neighbors\nof the Dy and Tb sites form distorted square-antiprisms,\nwith the squares formed by As on one side and O on\nthe other (distorted squares in the case of orthorhombic\nDyRuAsO). At 1.5 K the site symmetry is mm2for Dy\n(Wyckoffposition2 a) and 4mmforTb(Wyckoffposition\n2c). It is likely that the temperature and magnetic field\ndependence of the relative positions of the crystal field\nlevels plays an important role in the unusual magnetic\nproperties described below.\nSince evidence for a metamagnetic transition and a\nstrongmagnetic field effect on the heat capacity has been\nobservedin DyRuAsO [31], NPD data werealsocollected\nin applied magnetic fields. Results of these experiments\nare shown in Figure 2. As seen in the difference curves in\nthe middle of Fig. 2a, application of a 2 T magnetic field\natT= 3 K has little effect on the diffracted intensities;\nhowever, significant changes are observed as the field is\nincreased to 5 T. It is important to note that many re-\nflections show little or no response to the magnetic field.\nThis shows that the texture of the pelletized sample is\nnot affected. The magnetic field dependence of the inten-\nsity of two diffraction peaks, measured upon decreasing\nthe magnetic field, is shown in Fig. 2b. These peaks4\nµ0H\nFIG. 2: (Color online) (a) Neutron powder diffraction pat-\nterns collected at 3 K with applied magnetic field of µ0H=\n0, 2, and 5 T. The difference between the data collected at\n2 T and zero field, and between the data collected at 5 T\nand 2 T are also shown. The lowest two patterns are simu-\nlations including only magnetic scattering for AFM and FM\nmoments on Dy. Patterns are offset vertically for clarity. (b )\nThe field dependence of the relative scattered intensity at t he\npeaks marked by the square and circle in (a), showing a di-\nvergence for fields above about 2 T. The data are labeled by\nMiller indices of the overlapping reflections which contrib ute\nmagnetic scattering intensity to the measured peaks. (c) Ri -\netveld refinement results for µ0H= 5 T and T = 3 K using\na predominately FM model (see text for details) with all Dy\nmoments along the b-axis.TABLE I: Results and agreement factors from Rietveld re-\nfinement of neutron ( λ= 1.538 ˚A) powder diffraction data\nfor DyRuAsO and TbRuAsO at 1.5 K with no applied mag-\nnetic field. Dy/Tb and As occupy sites at (1/4, 1/4, z), while\nRu and O occupy sites at (3/4, 1/4, z).\nDyRuAsO TbRuAsO\nspace group Pmmn P 4/nmm\na (˚A) 4.0222(1) 4.0215(1)\nb (˚A) 4.0070(1) = a\nc (˚A) 8.0092(3) 8.0558(3)\nzDy/Tb 0.1311(5) 0.1332(8)\nzRu 0.500(2) 1/2\nzAs 0.665(1) 0.664(1)\nzO 0.013(2) 0\nmDy/Tb(µB) 7.6(1) 5.76(8)\nχ21.03 3.56\nRmag 8.29 4.77\nare labeled by the Miller indices of the reflections which\ncontribute magneticscatteringintensity to them, and are\nidentified in Fig. 2a by the data markers used in Fig. 2b.\nThere is a clear change in the field dependence which\nonsets near 2 T, which is identified as a transition from\nAFM to FM order. At the bottom of Fig. 2a, simulated\ndiffraction patterns including only the magnetic contri-\nbution are shown for the AFM structure determined at\nzero applied field (Fig. 1c) and for the FM structure ob-\ntained by aligning all the Dy moments along the b-axis\n(corresponding to IR Γ 5and Shubnikov group Pm′mn′).\nComparing these simulations with the difference curve\nbetween the 5 T and 2 T data reveals that the peaks\nwhich are strongly suppressed at high fields are associ-\nated only with the AFM structure and those which are\nenhanced at high field are associated only with the FM\nstructure.\nResults from Rietveld refinement of data collected at\nµ0H= 5 T and T= 3 K are shown in Fig. 2c. The\nmajority of the magnetic scattering is accounted for us-\ning the FM model with Dy moments of 7.3(3) µBalong\nthe b-axis; however, the data indicates the presence of a\nsmall AFM component as well. The fit shown includes\nboth FM and AFM contributions, and the fraction of\nthe AFM phase is estimated to be about 13% at 5 T.\nThe refinement is relatively insensitive to the direction\nof the moment within ab-plane, and similar results are\nobtained when the FM moment is constrained along the\nb-axis,orallowedtohavecomponentsalongboth aandb.\nNo indication of a c-component is observed. The tran-\nsition between the AFM and FM structures involves a\nchange in the relative orientation of moments on nearest\nneighbor Dy atoms. In addition, the data is not consis-\ntent with a fully polarized powder, in which every grain,\nregardless of crystallographic orientation, would have a\nmoment directed perpendicular to the scattering plane.\nThese results arein agreementwith the magnetic proper-\nties discussed below, in which a preference for moments\nin theab-plane is inferred, and a field of 5 T is seen to be5\ninsufficient to fully polarize the polycrystalline material.\nSimilar fits (not shown) were performed for data col-\nlected at fields of 2 and 5 T and temperatures of 15 K\n(below the structural transition) and 40 K (above the\nstructural transition). Of these, only the pattern from 15\nK at 5 T indicated the presence of magnetic scattering,\nwhich was well modeled with FM ordering of 5.5(3) µB\nmoments on Dy aligned along the b-axis. This tempera-\nture is above TN, and no indication of an AFM compo-\nnent was observed at any field at this temperature. This\nshows that FM order emerges out of the orthorhombic,\nparamagnetic state ( TS> T > T N) when a large mag-\nnetic field is applied.\nIt is expected that the competing FM and AFM states\nmay strongly affect the physical properties of DyRuAsO,\nand consideration of this competition is required in un-\nderstanding the behavior of magnetic, transport, and\nthermal properties presented below.\nB. dc magnetization\nFigure 3a shows the results of dc magnetization mea-\nsurements as a function of applied field for a wide range\nof temperatures. Similar results restricted to lower fields\nand fewer temperatures were previously reported [31].\nAt temperatures below TN, a rapid increase in the mag-\nnetic moment ( m) is observed as the field is increased\nbeyond 2 −3 T. This is consistent with the analysis of\nthe neutron diffraction data presented above. At 2 K,\nthe magnetic moment approaches a saturation value of\n6.8µBper formula unit at 12 T similar to but less than\nthe ordered moment on Dy of 7.6(1) µBdetermined by\nneutron diffraction in zero applied field. An approach to\nsaturation near the same value can be inferred from the\ndata above TNin the paramagnetic state as well, as ex-\npected for large moments in high fields at relatively low\ntemperatures.\nIt is interesting to compare the measured magnetiza-\ntion with the results of the neutron diffraction measure-\nments. At 3 K, in a field of 5 T, the refined value of the\nFM moment on Dy is 7.3(3) µB, and the data suggest\nthe moments are constrained to lie in the ab-plane. The\nmeasuredmagneticmomentatthis temperatureandfield\nis 5.1µBper Dy. This is about 2/3 of the refined mo-\nment. Such a suppression of the measured moment rela-\ntive to the ordered moment is expected due to the mag-\nnetic anisotropy; some crystallites in the magnetization\nsample will have their c-axes along the field direction,\nand thus not contribute to the measured magnetization.\nResults of dc magnetization vs. temperature measure-\nments are summarized in Fig. 3b, which shows the tem-\nperature dependence of M/Hat low temperatures in ap-\nplied fields ranging from 1 to 6 T. Data were collected\nusing both zero field cooled (ZFC) and field cooled (FC)\nprocedures. At temperatures above about 50 K, similar\nbehavioris observedin all of the applied fields. The large\ndecreasein M/Hupon coolingthrough TNforµ0H <3T/s48 /s50 /s52 /s54 /s56 /s49/s48 /s49/s50/s48/s50/s52/s54/s56\n/s48 /s53 /s49/s48 /s49/s53 /s50/s48 /s50/s53 /s51/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s68/s121 /s82/s117/s65/s115/s79\n/s32/s32/s84/s32 /s61/s32/s50/s32/s75\n/s32/s53/s32/s75/s109 /s32/s40\n/s66 /s32/s47/s32/s70/s46/s85/s46/s41\n/s48/s72 /s32/s40/s84/s41/s84 /s32/s61/s32/s49/s48/s44/s32/s49/s53/s44\n/s50/s48/s32/s46/s46/s46/s32/s53/s48/s32/s75\n/s32\n/s48/s72 /s32/s61/s32/s49/s32/s84\n/s32/s50/s32/s84\n/s32/s51/s32/s84\n/s32/s52/s32/s84\n/s32/s53/s32/s84\n/s32/s54/s32/s84/s40/s98/s41/s40/s97/s41\n/s32/s77/s47/s72 /s32/s40/s99/s109/s51\n/s32/s47/s32/s109/s111/s108/s32/s70/s46/s85/s46/s41\n/s84 /s32/s40/s75/s41/s115/s111/s108/s105/s100/s32/s61/s32/s90/s70/s67\n/s111/s112/s101 /s110/s32/s61/s32/s70/s67\nFIG. 3: (Color online) (a) The field dependence of the mag-\nnetic moment per formula unit determined from dc magneti-\nzation measurements. (b) Low temperature behavior of M/H\nmeasured on warming after zero field cooling (ZFC) and field\ncooling (FC), showing a divergence which is strongest at in-\ntermediate fields.\nin Figure 3b is noteworthy. At the lowest applied fields,\nthe moment decreases by approximately two-thirds rel-\native to the value observed just above TN. In a typical\nAFM, the powder-averaged moment decreases by only\none third below TN[39]. This is indicative of anisotropic\nsusceptibility in the paramagnetic state, with a larger\nthan average value in the direction along which the mo-\nments order below TN, theb-axis in this case. Since\nthe orthorhombic distortion is small, it may be expected\nthatχa≈χb, which then would imply that χcis small\ncompared to the in-plane susceptibility. This suggests\nthat the Dy moments prefer to lie in the ab-plane above\nTN, as well as in the ordered state. Similar easy-plane\nanisotropy has been observed in the paramagnetic state\nof CeFeAsO [40], which has ordered Ce moments lying\nnearly in the ab-plane at low temperatures [41]. A di-\nvergence between the ZFC and FC data is observed in\nFigure 3b near 5 K for magnetic fields larger than 2 T,\nassociated with the emerging FM.\nAspreviouslynoted[31], ananomalyoccursin M/Hat6\n/s48 /s49/s48 /s50/s48 /s51/s48 /s52/s48 /s53/s48/s48/s49/s48/s50/s48/s51/s48\n/s50 /s51 /s52 /s53/s48/s49/s50\n/s48 /s49/s48 /s50/s48 /s51/s48 /s52/s48 /s53/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48/s49/s46/s53/s50/s50 /s50/s52 /s50/s54 /s50/s56/s49/s50/s49/s52/s49/s54\n/s40/s98/s41\n/s32/s32\n/s32\n/s48/s72 /s32/s61/s32/s48\n/s32/s49/s32/s84\n/s32/s50/s32/s84\n/s32/s51/s32/s84\n/s32/s52/s32/s84\n/s32/s53/s32/s84\n/s32/s54/s32/s84/s99\n/s80 /s40/s74/s32/s47/s32/s75/s32/s109/s111/s108/s32/s70/s46/s85/s46/s41\n/s84 /s32/s40/s75/s41/s68/s121 /s82/s117/s65/s115/s79/s40/s97/s41\n/s32/s32/s99\n/s80/s40/s74/s32/s47/s32/s75/s32/s109/s111/s108/s32/s70/s46/s85/s46/s41\n/s84 /s32/s40/s75 /s41\n/s84/s32/s42/s84\n/s78/s32/s32\n/s48 /s72 /s32/s61/s32/s48\n/s32/s32/s50/s32/s84\n/s32/s32/s52/s32/s84\n/s32/s32/s54/s32/s84/s32\n/s32/s32/s83 /s32/s40/s82/s41\n/s84 /s32/s40/s75/s41/s84\n/s83/s32\n/s99\n/s80/s40/s74/s32/s47/s32/s75/s32/s109/s111/s108/s32/s70/s46/s85/s46/s41/s32\n/s84 /s32/s40/s75 /s41\nFIG. 4: (Color online) (a) Heat capacity of DyRuAsO at\nthe indicated magnetic fields. The insets shows the behav-\niors near TS= 25KandT∗= 3K. (b) The entropy change\ndetermined by integration of cP/T, after subtracting a esti-\nmated background contribution determined by scaling data\nfrom LaRuAsO to match the data measured at zero field and\n50 K.\nTS, most easily seen at low fields. No long ranged mag-\nnetic order is seen in the diffraction data, so this could\nsignal a change in the crystal field levels of the Dy ion ac-\ncompanying the structural distortion. This could explain\nwhy the effective moment determined by the Curie-Weiss\nmodel in Ref. 31 agree well with the expectations for the\nfree Dy ion, while the ordered moment at low tempera-\ntures does not. The evolution of the crystal field levels\nwith temperature and magnetic field below this struc-\ntural phase transition is expected to be complex, but\nmay prove important in understanding this material.\nC. Heat capacity\nApplication of a 6 T magnetic field has been shown\nto affect strongly the heat capacity anomalies at TSand\nTN[31]. Heat capacity data collected at µ0H= 0−6 T\nin 1 T increments are shown in Fig. 4a. As the mag-netic field is increased, the peak at TNis gradually sup-\npressed and broadened toward lower temperatures, with\nonly a small anomaly remaining at 6 T. The insets show\nthe behaviors near TS(upper inset) and at low tempera-\ntures (lower inset). For fields up to 2 T, the heat capac-\nity anomaly at TSis nearly unchanged. When the field\nis increased to 3 T and above, the peak is suppressed\nand skewed toward higher temperatures. The suppres-\nsion and skewing increase with field for µ0H≥3T. This\nfield effect on the anomaly at TSindicates a magnetic\ncomponent to the phase transition occurring at this tem-\nperature, or at minimum supports strong magnetoelastic\ncoupling. The field dependence is similar to that ex-\npected for FM ordering, although no long range ordering\naboveTNis discernable in the neutron diffraction data\ndiscussed above. To gain some insight into the origin of\nthestructuraldistortion, samplesofthe transition-metal-\nfree analog DyZnAsO were synthesized and preliminary\nheat capacity and diffraction measurements were per-\nformed (see Supplemental Material). The tetragonal to\northorhombic distortion indeed occurs in DyZnAsO at a\ntemperaturenear 30K.This eliminates Ru magnetismor\norbital ordering as a source for the structural distortion,\nand implicates Dy magnetism.\nAt the lowest temperatures (Fig. 4a, lower inset), the\neffect of increasing the field from 0 to 2 T is an over-\nall increase in magnitude, caused at least in part by the\nbroadening of the anomaly at TN. However, a qualita-\ntive change in the low temperature heat capacity occurs\nasµ0His increased to 3 T, as also noted near TS. At\nthis field an additional peak appears below T∗= 3 K, in-\ndicating an additional phase transition in this material.\nThe strong field response suggests that this transition is\nmagnetic in nature, and appears to be related to several\nunusual behaviors of the magnetic and transport proper-\nties which will be discussed below.\nThe entropy change (∆ S) up to 50 K, estimated by in-\ntegration of cP/Tafter subtraction of a background cP,\nare shown in Fig. 4b. The background data were esti-\nmated by scaling the heat capacity of LaRuAsO [30] to\nmatch the measured heat capacity of DyRuAsO at zero\nfield and 50 K. Isostructural LaRuAsO is not known to\nundergo any magnetic or crystallographic phase transi-\ntions in this temperature range. For purposes of integra-\ntion, the background-subtracted cP/Tdata were linearly\ninterpolated from the lowest measurement temperature\nto the origin. In all of the studied magnetic fields, the\ntotal entropy change up to 50 K is similar. Although in-\ncreasingthe fieldfromzeroto2Tsignificantlysuppresses\nthe sharpness of the peak at TN, the total entropy asso-\nciated with it is not changed and is about 80% of Rln(2).\nIncreasing the field beyond 2 T results in a suppression\nof the entropy obtained upon integration up to TN. The\nchange in ∆ Sbetween TNand 50 K is similar in all the\nfields studied (0.8 −0.9R). This suggests the total en-\ntropy associated with the structural transition at TSnot\nstronglydependentontheappliedfield, thoughtheshape\nof the anomaly is significantly changed.7\nThe phasetransitions observedin DyRuAsO appear to\nbesecondorderinnature. Thisisindicatedbytheshapes\nof the heat capacity anomalies in Fig. 4a, the lack of any\nanomalous behavior in the raw heat capacity data [42],\nthe temperature dependence of the magnetic order pa-\nrameter (Fig. 1a) and the absence of thermal hysteresis\nin the physical properties measured at zero field.\nD. Magnetoresistance\nMagnetic field effects on the temperature dependence\nof the electrical resistivity ( ρ) of DyRuAsO are depicted\nin Fig. 5. An abrupt decrease in ρis observed upon cool-\ning through TNforµ0H/lessorsimilar2T. This feature is diminished\nsignificantly at higher fields. The effect of the structural\ntransitionisnotdirectlyapparentfromtheobservedtem-\nperature dependence; however, a slope change in dρ/dT\nis seen at TS(Fig. 5b). Though it is subtle, this anomaly\npersists up to 10 T, suggesting the structural transition\noccurs at all fields investigated here.\nEffects of the field induced transition at T∗are also\nobserved in the resistivity data. This is manifested as\nan abrupt upturn in ρoccurring below 3 K for µ0H≥\n3 T (Fig. 5a). This is clearly observed in the derivative\n(Fig. 5b). The upturn in ρis strongest for µ0H= 3 and\n4 T, the fields at which the heat capacity anomaly at\nT∗is also strongest. In the inset of Fig. 5a, ρdata are\nshown for cooling in the applied field followed immedi-\nately by warming in the applied field. In addition to the\nupturn upon cooling already noted, an apparent thermal\nhysteresis is observed below T∗forµ0H≥3 T, and is\nobserved most clearly at 3 T. In the following discussion,\nthis will be shown to be related to slow relaxation of the\nmagnetic state ofthe material upon movingthrough that\nparticular region of the H−Tphase diagram.\nE. Time and frequency dependent phenomena\nCompetition between the AFM state stable at low\nfields and the FM state stable at high fields leads to\nseveral unusual properties occurring near the associated\ncritical temperatures and magnetic fields. The ZFC-FC\ndivergence in dc magnetization below about 5 K (Fig.\n3b) and the apparent thermal hysteresis in the electrical\nresistivity (Fig. 5a) were noted above when the applied\nfield was ≥3 T. The dynamics in DyRuAsO were fur-\nther examined by measurement of the time dependence\nof the magnetization, with results shown in Fig. 6. The\nsample was cooled to 2 K in zero field, and then the field\nwas increased in 1 T increments up to 6 T. At each field,\nthe magnetic moment ( M) was measured every minute\nfor 60 minutes. The time required to ramp and stabi-\nlize the field was approximately 3 minutes. The data\nare shown in Fig. 6a, plotted as a percentage difference\nrelative to the value measured just after the magnetic\nfield stabilized ( t= 0). When the field is increased from/s48 /s49/s48 /s50/s48 /s51/s48 /s52/s48 /s53/s48/s54/s55/s56/s57/s49/s48\n/s48 /s53 /s49/s48/s53/s46/s56/s54/s46/s48/s54/s46/s50/s54/s46/s52\n/s48 /s49/s48 /s50/s48 /s51/s48 /s52/s48 /s53/s48/s48/s46/s48/s48/s46/s49/s48/s46/s50/s48/s46/s51/s48/s46/s52/s48/s46/s53/s68/s121 /s82/s117/s65/s115/s79\n/s32/s32\n/s32\n/s48/s72 /s32/s61/s32/s48\n/s32/s49/s32/s84\n/s32/s50/s32/s84\n/s32/s51/s32/s84\n/s32/s52/s32/s84\n/s32/s53/s32/s84\n/s32/s54/s32/s84\n/s32/s49/s48/s32/s84/s32/s40/s109 /s32/s99/s109/s41\n/s84/s32 /s40/s75/s41\n/s40/s98/s41/s54\n/s53\n/s52\n/s51\n/s49/s50\n/s32/s32\n/s99/s111/s111/s108/s105/s110/s103\n/s119/s97/s114/s109/s105/s110/s103/s32/s40/s109 /s32/s99/s109/s41\n/s84 /s32/s40/s75 /s41/s48 /s72 /s32/s40/s84/s41\n/s48/s40/s97/s41\n/s84/s32/s42/s84\n/s78/s49/s48/s32/s84\n/s54/s32/s84\n/s53/s32/s84\n/s52/s32/s84\n/s51/s32/s84\n/s50/s32/s84\n/s32/s32/s100 /s100 /s84 /s32/s40/s109 /s32/s99/s109/s32/s75/s45/s49\n/s41\n/s84 /s32/s40/s75/s41/s48/s72 /s32/s61/s32/s48/s49/s32/s84/s84\n/s83\nFIG. 5: (Color online) (a)Resistivity ( ρ) below 50 K in the\nmainpanel, withthebehaviornearandbelow TNshowninthe\ninset. Data were collected on cooling in the indicated appli ed\nfield (open markers), followed immediately by warming in the\nsame field (solid markers). (b) Temperature derivative of ρ\nwith phase transition temperatures marked on the plot. The\ncurves in (b) are offset vertically for clarity.\n0→1 T and 1 →2 T, no relaxation of the magnetization is\nobserved; the measured moment is independent of time.\nHowever, when the field is increased further, a time de-\npendent moment is observed. The time dependence is\nstrongest after increasing the field from 2 →3 T and 3 →4\nT. A small change with time occurs for higher fields as\nwell.\nThe time evolution of the moment was also examined\nat higher temperatures. The results after increasing the\nfield from 2 →3T at 2, 4, and 6 K are shown in Fig. 6b.8\nThe relaxation seen at 2 K is strongly suppressed, but\nstill observable, at 4 K and absent at 6 K. Similar behav-\nior is seen in the magnetoresistance (not shown). This\nis likely related to the ZFC-FC divergence in the mag-\nnetization (Fig. 3b) and the divergence of the resistivity\nmeasuredupon coolingandthen warming(Fig. 5a)when\nthe field is 3 T or higher.\nThe dynamics resulting from the competition between\nthe AFM andFM states isalsodemonstratedin the mag-\nnetic moment and magnetoresistance ( MR) measured at\nfixed temperature upon increasing and then decreasing\nthe field. Figure 6c shows the field dependence of the\nmoment (field sweep rate of 15 Oe ·s−1), which displays\na divergence which is strongest between about 2 and 4\nT at 2 K, but no detectable divergence at 4 K. Similar\nresults are seen for the magnetoresistance (field sweep\nrate of 25 Oe ·s−1) in Fig. 6d. The local maximum in\nMRupon decreasing the field at 2 K indicates a sig-\nnificant enhancement in charge carrier scattering under\nthese conditions.\nTheobservationofslowdynamicsatintermediatemag-\nneticfieldsfortemperaturesbelow T∗butnotabove(Fig.\n6), suggests that the dissipation is related to the changes\nin other physical properties near in this temperature and\nfield range. For comparison, thermal, transport, and\nmagnetic properties measured at 3 T near T∗are re-\nplotted together in Fig. 7. These anomalies suggest a\nphase transition occurs near this temperature for mag-\nnetic fields exceeding about 2 T, the field above which\nthe FM phase fraction appears to increase most rapidly\nat low temperatures. The heat capacity (Figs. 7a and 4)\nshows a small but relatively sharp anomaly at T∗for\nµ0H= 3−5 T. It is significantly suppressed at higher\nfields. Theelectricalresistivity(Figs. 7b and 5) increases\nsharply upon cooling through this transitions in fields\ngreater than 3 T. This behavior is still clearly observed\nat 6 T, but is suppressed at 10 T. In the dc magnetiza-\ntion (Fig. 3), the strong signal from Dy moments over-\nwhelm subtle features at low temperature, but a marked\nFC-ZFC divergence onsets just above T∗in this same\nrange of magnetic fields. In addition, a subtle downturn\nis observed in FC data at T∗forµ0H= 3 T (Fig. 7c).\nAnomalies near T∗are observed in both components of\nthe ac susceptibility at µ0H= 3 T (Fig. 7d), which is\npresented in more detail below.\nThe shape and relative sharpness of the heat capac-\nity anomaly at T∗and the observation of anomalies at\nthis temperature in other physical properties are indica-\ntive of a thermodynamic phase transition, and not, for\nexample, a Schottky anomaly. Better understanding of\nthis transitionmay come fromadditional neutron diffrac-\ntion studies to investigate how the crystal and magnetic\nstructures evolve with temperature near T∗at different\nmagnetic fields. From the present data, it can be con-\ncluded that magnetism is involved in the transition di-\nrectly or indirectly (through for example magnetoelastic\ncoupling). The observation of an increase in resistivity\nupon cooling through the transition suggests that either/s48 /s49/s48 /s50/s48 /s51/s48 /s52/s48 /s53/s48 /s54/s48/s48/s53/s49/s48/s49/s53\n/s48/s50/s52/s54\n/s48 /s50 /s52 /s54 /s56/s48/s50/s52/s54/s48 /s49/s48 /s50/s48 /s51/s48 /s52/s48 /s53/s48 /s54/s48/s48/s53/s49/s48/s49/s53\n/s48/s53/s49/s48\n/s48 /s50 /s52 /s54 /s56/s48/s53/s49/s48/s48/s72 /s32/s61/s32/s48/s32 /s32/s49/s32/s84/s32\n/s49/s32 /s32/s50/s32/s84/s32\n/s50/s32 /s32/s51/s32/s84/s32\n/s51/s32 /s32/s52/s32/s84\n/s52/s32 /s32/s53/s32/s84\n/s53/s32 /s32/s54/s32/s84\n/s32/s32/s77 /s32/s40/s37/s41\n/s116/s105/s109/s101/s32/s40/s109/s105/s110/s41/s68/s121 /s82/s117/s65/s115/s79\n/s84 /s32/s61/s32/s50/s32/s75\n/s32/s32\n/s32/s32\n/s84 /s32/s61/s32/s52/s32/s75/s40/s99/s41\n/s32/s32/s109 /s32/s40\n/s66 /s32/s47/s32/s70/s85/s41\n/s48/s72 /s32/s40/s84/s41/s84 /s32/s61/s32/s50/s32/s75/s48/s72 /s32/s61/s32/s50/s32 /s32/s51/s32/s84/s40/s98/s41\n/s32/s32\n/s32/s84 /s32/s61/s32/s50/s32/s75\n/s32/s52/s32/s75\n/s32/s54/s32/s75/s77 /s32/s40/s37/s41\n/s116/s105/s109/s101/s32/s40/s109/s105/s110/s41/s40/s97/s41\n/s40/s100/s41/s32/s77/s82 /s32/s40/s37/s41/s84 /s32/s61/s32/s52/s32/s75\n/s84 /s32/s61/s32/s50/s32/s75/s32\n/s48/s72 /s32/s40/s84/s41\nFIG. 6: (Color online) (a) Time dependence of the magnetic\nmoment of DyRuAsO after increasing the field as indicated\nin the legend at a temperature of 2 K. (b) Time dependence\nof the magnetic moment after increasing the field from 2 to 3\nT at T = 2, 4 and 6 K. (c) Field dependence of the magnetic\nmoment measured upon increasing then decreasing the field\nat T = 2 and 4 K. (d) Field dependence of the magnetore-\nsistance relative to the zero field resistivity values measu red\nupon increasing then decreasing the field at T = 2 and 4 K.\nthe electronic structure is altered, or the scattering rate\nis increased. The former could be due to a subtle struc-\ntural distortion or orbital ordering involving Ru, and the\nlatter could be related to magnetic domain walls which\nform in the mixed AFM/FM state.\nThe dynamics of the low temperature magnetism in\nDyRuAsO were also investigated using ac magnetic sus-\nceptibility measurements. The frequency, temperature,\nandfield dependence ofthe real( m′) andimaginary( m′′)9\n/s49/s46/s48/s49/s46/s53/s50/s46/s48\n/s48/s46/s51/s48/s48/s46/s51/s53/s48/s46/s52/s48/s48/s46/s52/s53/s48/s46/s53/s48/s54/s46/s48/s53/s54/s46/s49/s48/s54/s46/s49/s53/s54/s46/s50/s48\n/s50/s46/s48 /s50/s46/s53 /s51/s46/s48 /s51/s46/s53 /s52/s46/s48 /s52/s46/s53 /s53/s46/s48/s48/s46/s53/s49/s46/s48\n/s102/s32/s61/s32/s49/s48/s48/s32/s72/s122/s32/s99\n/s80 /s32/s40/s74/s32/s47/s32/s75/s32/s47/s32/s109/s111/s108/s41/s68/s121 /s82/s117/s65/s115/s79\n/s48/s72 /s32/s61/s32/s51/s32/s84\n/s84/s42/s32/s61/s32/s51/s46/s48/s32/s75/s40/s97/s41\n/s100/s40 /s77 /s47/s72 /s41/s47/s100 /s84/s77 /s47/s72/s40/s99/s41/s32/s77 /s47/s72 /s32/s40/s99/s109/s51\n/s32/s47/s32/s109/s111/s108/s41/s40/s98/s41/s32/s40/s109 /s32/s99/s109/s41\n/s109 /s39/s39/s40/s100/s41/s32\n/s84/s32 /s40/s75/s41/s109 /s39/s44/s32/s109 /s39/s39 /s32/s40/s49/s48/s45/s52\n/s32/s101/s109/s117/s41/s109 /s39\nFIG. 7: (Color online) (a) Heat capacity, (b) electrical res is-\ntivity, (c) dc “susceptibility” ( M/H), and (d) ac magnetiza-\ntion of DyRuAsO near T∗in an applied magnetic field of 3\nT. In (c) the temperature derivative of M/His also shown, in\narbitrary units.\nparts of the ac magnetization were studied near the mag-\nnetic orderingtemperatures. The results aresummarized\nin Fig. 8.\nIn zero applied dc field (Fig. 8a,b), the ac magne-\ntization resembles closely the low field dc magnetization\ndata (Fig. 3b), with a sharp drop just below TN. A weak\nfrequency dependence is seen for 4.5 < T <8.0 K, well\nbelowTN. A corresponding anomaly is seen in m′′at\nµ0H= 0 (Fig. 8b) and increases in both magnitude and\ntemperature as frequency increases. The temperatures\nspanned by the m′′peak position is similar to the tem-\nperature range over which m′is found to be frequency\ndependent.\nWhen the applied dc field is increased to 3 T, near the\nmeta-magnetic transition, the features noted in the zero-\nfield data are enhanced. A strong frequency dependence\nis observed in m′(Fig. 8c), and m′′is about one order\nof magnitude larger at 3 T (Fig. 8d) than in zero field\n(Fig. 8b). The temperature of the cusp in m′(Fig. 8c)\nincreases with frequency from 6.5 K at 10 Hz to 8.5 K at\n1 kHz, while the peak magnitude of m′decreases. The(e) (f)\n(g) (h)µ0H = 0 µ0H = 0\nµ0H = 3 T µ0H = 3 Tµ0H\nµ0H = 3 T\nµ0H = 3 TT T\nT T\nf Tfm’ m’’ \nm’ ’ m’ ’ m’ ’ m’ m’\nFIG. 8: (Color online) (a-d) Temperature dependence of the\nreal (m′) and imaginary ( m′′) parts of the ac magnetization\nmeasured at µ0H= 0 and 3 T using frequencies indicated\nin panel (a). (e,f) Contour plots of the real part ( m′) and\nimaginary part ( m′′) of the ac magnetization measured at\n100 Hz as functions of temperature and applied dc magnetic\nfield. (g) Arrhenius fit using the temperatures ( TP) at which\nm′peaks at different frequencies for H= 3 T. (h) Frequency\ndependenceof m′′atH=3Tandtheindicatedtemperatures.\nAll measurements were conductedusing asample of mass 27.1\nmg and an ac excitation field of 10 Oe.\ntemperature at which m′′peaks clearly increases with\nfrequency, while its magnitude shows a more subtle in-\ncrease. Contour plots of the real and imaginary parts of\nthe the ac susceptibility measured at 100 Hz are shown\nin Fig. 8e and 8f. The m′′data indicate that the dissipa-\ntion is strongest below TNand for magnetic fields near\n3 T, the region where AFM-FM competition is expected\nto be strongest.\nThe behaviors shown in Fig. 8c,d are precisely those\nexpected for a spin-glass near its freezing temperature\n[43, 44]. In fact, it is interesting to note the similarities10\nof many of the behaviors of DyRuAsO at low temper-\natures and fields near 3 T to those of a spin glass, in-\ncluding frequency dependent ac susceptibility, FC-ZFC\ndivergence in dc magnetization, and slow relaxation of\nthe magnetic moment when the applied field is changed.\nHowever, there is no chemical disorder detected by neu-\ntron diffraction in this material.\nGlass-likebehaviorwithout chemicaldisordercan arise\nfrom strong geometrical frustration, as realized, for ex-\nample, inDy-pyrochlorespin-icesystems[45,46]. Similar\nbehavior has been reported in the related Ising antiferro-\nmagnet Dy 2Ge2O7, which does not adopt the pyrochlore\nstructure, and in which the glass-like behavior is spec-\nulated to arise from collective relaxation of short-range\nspin correlations [47]. The magnetic structure adopted\nby DyRuAsO (Fig. 1c) does not suggest strong frustra-\ntion in this compound, due to the FM coupling within\neach Dy net in the ab-plane. For purely AFM inter-\nactions, however, the structure does support geometrical\nfrustration. Comparingthe ac susceptibility and heat ca-\npacity behavior of DyRuAsO and Dy 2Ge2O7[47], strong\nsimilarities are observed. An important exception is the\nZFC-FC divergence of dc magnetization seen in DyRu-\nAsO (Fig. 3b). This is absent in Dy 2Ge2O7, and its\nabsence is used to distinguish this material from a spin-\nglass. In this respect, DyRuAsO appears to behave more\nlike a spin-glass than does the pyrogermanate. The prox-\nimity ofthe glass-likebehaviorin DyRuAsO to the meta-\nmagnetic transition suggests that domain walls separat-\ning FM and AFM domains may also play a role in the\nobserved dynamics. Similarly, it has been suggested that\nAFM domain walls may contribute to the frequency de-\npendent phenomena observed in Dy 2Ge2O7[47].\nFurther analysisof the ac magnetization data collected\nin a dc field of 3 T are shown in Fig. 8g,h. The relation-\nship between the temperature at which m′peaks (TP)\nand the measurement frequency is seen to follow an Ar-\nrhenius law f=f0e−EA/kBT(Fig. 8g), as typically seen\nin spin-glasses [43, 44], but not spin-ices [48]. The acti-\nvation energy determined from the fit is EA/kB= 110\nK, and the attempt frequency is f0= 360 MHz. A simi-\nlar activation energy of 162 K is reported for Dy 2Ge2O7,\nwhich wasfound to correspondto the separationbetween\nthe ground and first excited crystal field states [47]. The\nfrequency dependence of m′′at temperatures from 4.0 to\n7.5 K is shown in Fig. 8h. Plotted in this way, a peak\ncorresponds to characteristic spin relaxation frequencies\n[45, 49]. The uniform shift in peak position with temper-\nature is consistent with classical thermal relaxation.\nIV. SUMMARY AND CONCLUSIONS\nNeutron diffraction has been used to identify the mag-\nnetic ordering of Dy moments in DyRuAsO at low tem-\nperature, and how the moments respond to application\nof magnetic fields. The results provide a framework nec-\nessary for understanding the peculiar physical propertiesof this material, which is structurally and electronically\nrelated to the 1111 Fe superconductor systems. In the\nabsence of an applied magnetic field, AFM ordering oc-\ncurs at 10.5 K. The magnetic unit cell is the same as\nthe orthorhombic crystallographic unit cell. Magnetic\nmoments on Dy of magnitude 7.6(1) µBlie long the b-\naxis. The moments are arranged FM within sheets in\nthe ab-plane, with AFM stacking along the c-axis. This\nsame magnetic structure describes the diffraction data\ncollected in a magnetic field of 2 T at T= 3 K. A re-\nlated FM structure was determined when the field was\nincreased to 5 T, with moments of magnitude 7.3(3)\nµBaligned in the ab-plane. The neutron diffraction re-\nsults distinguish the meta-magnetic transition occurring\nin DyRuAsO from the more commonly observed spin-\nflop.\nAt intermediate fields, the competition between the\nAFM and FM states is evident in the physical proper-\nties of DyRuAsO, and results in several unusual behav-\niors. Many of the field induced phenomena appear to\nbe related to a thermal anomaly identified at T∗= 3 K,\nwhich is evident in the heat capacity for magnetic fields\nnear 3 T. The resistivity increases upon cooling through\nT∗. The dc magnetization shows a subtle inflection near\nT∗, and develops a FC-ZFC divergence slightly above\nT∗. In addition, the transport and magnetic properties\ndevelop a time dependence below T∗for fields near 3\nT, producing apparent thermal and magnetic hysteresis\nin magnetization and magnetoresistance measurements.\nThe observed slow relaxation of magnetization, as well\nas frequency dependent ac magnetic susceptibility val-\nues, are reminiscent of behaviors associated with spin-\nglasses [43] and Dy-based spin-ice and related materials\n[45–47,49]. Thisissomewhatsurprising; nochemicaldis-\norder is detected in this material, and the geometry does\nnot indicate strong magnetic frustration [31]. Movement\nof magnetic domain walls related to the competing AFM\nandFMphasesprovideonepossiblesourceofdissipation.\nSince the magnetism in DyRuAsO is dominated by\nthe Dy atoms, crystalline electric field effects likely play\nan important role in determining the magnetic proper-\nties. Indeed, it has been noted that the energy barrier to\nspin-relaxation in Dy 2Ge2O7corresponds to the energy\nsplitting of the lowest crystal field levels [47].The cur-\nrent experimental data show a saturation moment near\n7µB(similar to the refined ordered moment from the\ndiffractionresults), whichissignificantlysmallerthanthe\nfree ion value of 10 µB, and the magnetic entropy deter-\nmined from the heat capacity is relatively small. The\nCurie Weiss behavior of the magnetization for tempera-\ntures just above TSis consistent with the free ion value\nof the effective moment. Detailed calculations and in-\nelastic scattering experiments (complicated by relatively\nstrong neutron absorption by Dy) would be desirable in\ndeveloping an understanding of these effects. Since this\nmaterial undergoes a structural phase transition and dis-\nplays meta-magnetic behavior, the dependence of the Dy\ncrystalfieldlevelsontemperature,field,andcoordination11\ndetails will be required to develop a complete picture.\nIron magnetism is closely linked to the structural dis-\ntortion that occurs in the isoelectronic Fe compounds\n[2, 15, 16]. In the present data, no conclusive evidence\nfor ordered magnetic moments on Ru atoms is seen, and\nno magnetic order is observed between TNandTSin the\nabsence of an applied magnetic field. The driving force\nfor the structural transition at TS, which also occurs in\nDyZnAsO, is identified as Dy magnetism. The distortion\nmustaltertheDycrystalfieldlevels,whichprovidessome\ndegree of magnetoelastic coupling. In addition, TbRu-\nAsOisisostructuralwithDyRuAsOatroomtemperature\nand was found here to have a low temperature magnetic\nstructure similar to DyRuAsO, but no structural distor-\ntion occurs in TbRuAsO at temperatures as low as 1.5\nK.\nZrCuAsSi-type oxyarsenides incorporating heavy\ntransition metal atoms have been relatively little studied\ncompared to the 3 dmetal analogues or the relatedThCr2Si2-type arsenides. The structure type shows a\nlarge degree of chemical flexibility. Many interesting\nmaterials and behaviors have already been identified;\nhowever, many compounds and phenomena likely remain\nundiscovered or understudied. The surprisingly complex\nand glass-like magnetic behavior of DyRuAsO suggest\nfurther study of such compounds will uncover other new\nand interesting cooperative phenomena, and motivates\nfurther study of dynamic effects in rare-earth magnetic\nmaterials.\nResearch sponsored by the US Department of Energy,\nOffice of Basic Energy Sciences, Materials Sciences and\nEngineering Division. Neutron scattering at the High\nFlux Isotope Reactor was supported by the Scientific\nUser Facilities Division, Basic Energy Sciences, US De-\npartment of Energy. The authors thank J.-Q. Yan for\nhelpful discussions.\n[1] D. Johrendt, H. Hosono, R.-D. Hoffmann, and\nR. P¨ ottgen, Z. Kristallogr. 226, 435 (2011).\n[2] M. A. McGuire, in Handbook of Magnetic Materials ,\nedited by K. H. J. Buschow (North-Holland, Amsterdam,\n2014), vol. 22.\n[3] P. Quebe, L. J. Terb¨ ue, and W. Jeitschko, J. Alloys\nCompd. 302, 70 (2000).\n[4] A. T. Nientiedt, W. Jeitschko, P. G. Pollmeier, and\nM. Brylak, Z. Naturforsch. 52b, 560 (1997).\n[5] S. Muir, A. W. Sleight, and M. A. Subramanian, Mater.\nRes. Bull. 45, 392 (2010).\n[6] S. Muir, A. W. Sleight, and M. A. Subramanian, J. Solid\nState Chem. 184, 1972 (2011).\n[7] T. Watanabe, H. Yanagi, Y. Kamihara, T. Kamiya,\nM. Hirano, and H. Hosono, J. Solid State Chem. 181,\n2117 (2008).\n[8] A. T. Nientiedt and W. Jeitschko, Inorg. Chem. 37, 386\n(1998).\n[9] D. O. Charkin, P. S. Berdonosov, V. A. Dolgikh, and\nP. Lightfoot, J. Alloys Compd. 292, 118 (1999).\n[10] A. Marcinkova, T. C. Hansen, C. Curfs, S. Margadonna,\nand J.-W. G. Bos, Phys. Rev. B 82, 174438 (2010).\n[11] N. Emery, E. J. Wildman, J. M. S. Skakle, G. Giriat,\nR. I. Smith, and A. C. Mclaughlin, Chem. Commun. 46,\n6777 (2010).\n[12] Y. Tsukamoto, Y. Okamoto, K. Matsuhira, M.-H.\nWhangbo, and Z. Hiroi, J. Phys. Soc. Jpn. 80, 094708\n(2011).\n[13] N. Emery, E. J. Wildman, J. M. S. Skakle, A. C.\nMclaughlin, R. I. Smith, and A. N. Fitch, Chem. Com-\nmun.46, 6777 (2010).\n[14] C. de la Cruz, Q. Huang, J. W. Lynn, J. Li, W. Ratcliff\nII, J. L. Zarestky, H. A. Mook, G. F. Chen, J. L. Luo,\nN. L. Wang, et al., Nature 453, 899 (2008).\n[15] D. C. Johnston, Advances in Physics 59, 803 (2010).\n[16] M. D. Lumsden and A. D. Christianson, J. Phys.: Con-\ndens. Matter 22, 203203 (2010).\n[17] H. Yanagi, R. Kawamura, T. Kamiya, Y. Kamihara,\nM. Hirano, T. Nakamura, H. Osawa, and H. Hosono,Phys. Rev. B 77, 224431 (2008).\n[18] H. Ohta and K. Yoshimura, Phys. Rev. B 80, 184409\n(2009).\n[19] M. A. McGuire, D. J. Gout, V. O. Garlea, A. S. Sefat,\nB. C. Sales, and D. Mandrus, Phys. Rev. B 81, 104405\n(2010).\n[20] A. Marcinkova, D. A. M. Grist, I. Margiolaki, T. C.\nHansen, S. Margadonna, and J.-W. G. Bos, Phys. Rev.\nB81, 064511 (2010).\n[21] Z. Li, G. Chen, J. Dong, G. Li, W. Hu, D. Wu, S. Su,\nP. Zheng, T. Xiang, N. Wang, et al., Phys. Rev. B 78,\n060504(R) (2008).\n[22] S. Matsuishi, A. Nakamura, Y. Muraba, and H. Hosono,\nSupercond. Sci. Technol. 25, 084017 (2012).\n[23] Y.Luo, H. Han, H. Tan, X. Lin, Y. Li, S. Jiang, C. Feng,\nJ. Dai, G. Cao, Z. Xu, et al., J. Phys.: Condens. Matter\n23, 175701 (2011).\n[24] H. Lincke, R. Glaum, V. Dittrich, M. H. M¨ oller, and\nR. P¨ ottgen, Z. Anorg. Allg. Chem. 635, 936 (2009).\n[25] W. Schnelle, A. Leithe-Jasper, R. Gumeniuk,\nU. Burkhardt, D. Kasinathan, and H. Rosner, Phys.\nRev. B79, 214516 (2009).\n[26] S. Sharma, A. Bharathi, S. Chandra, V. R. Reddy,\nS. Paulraj, A. T. Satya, V. S. Sastry, A. Gupta, and\nC. S. Sundar, Phys. Rev. B 81, 174512 (2010).\n[27] M. A. McGuire, D. J. Singh, A. S. Sefat, B. C. Sales, and\nD. Mandrus, J. Solid State Chem. 182, 2326 (2009).\n[28] I. Pallecchi, F. Bernardini, M. Tropeano, A. Palenzona ,\nA. Martinelli, C. Ferdeghini, M. Vignolo, S. Massidda,\nand M. Putti, Phys. Rev. B 84, 134524 (2011).\n[29] G.-F. Chen, Z. Li, D. Wu, J. Dong, G. Li, W.-Z. Hu,\nP. Zheng, J.-L. Luo, and N.-L. Wang, Chin. Phys. Lett.\n25, 2235 (2008).\n[30] M. A. McGuire, A. F. May, and B. C. Sales, J. Solid\nState Chem. 191, 71 (2012).\n[31] M. A. McGuire, A. F. May, andB. C. Sales, Inorg. Chem.\n51, 8502 (2012).\n[32] J. Rodriguez-Carvajal, Physica B 192, 55 (1993), pro-\ngram available at www.ill.fr/dif/Soft/fp/.12\n[33] A. Wills, Physica B 276, 680 (2000), program available\nfrom www.ccp14.ac.uk.\n[34] O. V. Kovalev, Representations of the Crystallographic\nSpace Groups (Gordon and Breach, Switzerland, 1993),\n2nd ed.\n[35] J. Zhao, Q. Huang, C. de la Cruz, S. Li, J. W. Lynn,\nY. Chen, M. A. Green, G. F. Chen, G. Li, Z. Li, et al.,\nNature Materials 7, 953 (2008).\n[36] J. Zhao, Q. Huang, C. de la Cruz, J. W. Lynn, M. D.\nLumsden, Z.A. Ren, J. Yang, X. Shen, X.Dong, Z. Zhao,\net al., Phys. Rev. B 78, 132504 (2008).\n[37] Y. Qiu, W. Bao, Q. Huang, T. Yildirim, J. M. Simmons,\nM. A.Green, J. W.Lynn, Y.C. Gasparovic, J. Li, T. Wu,\net al., Phys. Rev. Lett. 101, 257002 (2008).\n[38] Y. Xiao, M. Zbiri, R. A. Downie, J.-W. G. Bos,\nT. Br¨ uckel, and T. Chatterji, Phys. Rev. B 88, 214419\n(2013).\n[39] J. S. Smart, Effective Field Theories of Magnetism (W.\nB. Saunders Company, Philadelphia and London, 1966),\n1st ed.\n[40] A. Jesche, C. Krellner, M. de Souza, M. Lang, and\nC. Geibel, New J. Phys. 11, 103050 (2009).\n[41] J. Zhao, Q. Huang, C. de la Cruz, S. Li, J. W. Lynn,Y. Chen, M. A. Green, G. F. Chen, G. Li, Z. Li, et al.,\nNature Materials 7, 953 (2008).\n[42] J. C. Lashley, M. F. Hundley, A. Migliori, J. L. Sarrao,\nP. G. Paliuoso, T. W. Darling, M. Jaime, J. C. Coo-\nley, W. L. Hults, L. Morales, et al., Cryogenics 43, 369\n(2003).\n[43] J. A. Mydosh, Spin Glasses: An Experimental Introduc-\ntion(Taylor and Francis, London, 1993).\n[44] K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801\n(1986).\n[45] K. Matsuhira, Y. Hinatsu, and T. Sakakibara, J. Phys.:\nCondens. Matter 13, L737 (2001).\n[46] K. Matsuhira, Y. Hinatsu, K. Tenya, H. Amitsuka, and\nT. Sakakibara, J. Phys. Soc. Jpn. 71, 1576 (2002).\n[47] X. Ke, M. L. Dahlberg, E. Morosan, J. A. Fleitman, R. J.\nCava, and P. Schiffer, Phys. Rev. B 78, 104411 (2008).\n[48] J. Snyder, B. G. Ueland, J. S. Slusky, H. Karunadasa,\nR. J. Cava, and P. Schiffer, Phys. Rev. B 69, 064414\n(2004).\n[49] J. Snyder,J.S.Slusky,R.J.Cava, andP.Schiffer, Natur e\n413, 48 (2001)."    },    {        "title": "1408.0992v1.Tunable_asymmetric_magnetoimpedance_effect_in_ferromagnetic_NiFe_Cu_Co_films.pdf",        "content": "arXiv:1408.0992v1  [cond-mat.mtrl-sci]  5 Aug 2014Tunable asymmetric magnetoimpedance effect in ferromagnet ic NiFe/Cu/Co films\nE. F. Silva,1M. Gamino,2A. M. H. de Andrade,2M. A. Corrˆ ea,1M. V´ azquez,3and F. Bohn1,∗\n1Departamento de F´ ısica Te´ orica e Experimental,\nUniversidade Federal do Rio Grande do Norte, 59078-900 Nata l, RN, Brazil\n2Instituto de F´ ısica, Universidade Federal do Rio Grande de Sul, 91501-970 Porto Alegre, RS, Brazil\n3Instituto de Ciencia de Materiales de Madrid, CSIC, 28049 Ma drid, Spain\n(Dated: January 1, 2018)\nWe investigate the magnetization dynamics through the magn etoimpedance effect in ferromag-\nnetic NiFe/Cu/Co films. We observe that the magnetoimpedanc e response is dependent on the\nthickness of the non-magnetic Cu spacer material, a fact ass ociated to the kind of the magnetic\ninteraction between the ferromagnetic layers. Thus, we pre sent an experimental study on asym-\nmetric magnetoimpedance in ferromagnetic films with biphas e magnetic behavior and explore the\npossibility of tuning the linear region of the magnetoimped ance curves around zero magnetic field\nby varying the thickness of the non-magnetic spacer materia l, and probe current frequency. We\ndiscuss the experimental magnetoimpedance results in term s of the different mechanisms governing\nthe magnetization dynamics at distinct frequency ranges, q uasi-static magnetic properties, thickness\nof the non-magnetic spacer material, and the kind of the magn etic interaction between the ferro-\nmagnetic layers. The results place ferromagnetic films with biphase magnetic behavior exhibiting\nasymmetric magnetoimpedance effect as a very attractive can didate for application as probe element\nin the development of auto-biased linear magnetic field sens ors.\nPACS numbers: 75.40.Gb, 75.30.Gw, 75.60.-d\nKeywords: Magnetic systems, Magnetization dynamics, Magn etoimpedance effect, Ferromagnetic films\nThe magnetoimpedance effect (MI), known as the\nchange of the real and imaginary components of elec-\ntrical impedance of a ferromagnetic conductor caused by\nthe action of an external static magnetic field, is com-\nmonly employed as a tool to investigate ferromagnetic\nmaterials. For a general review on the effect, we sug-\ngest the Ref.1. In recent years, the interest for this phe-\nnomenon has grown considerably not only for its contri-\nbution to the understanding of fundamental physics as-\nsociated to magnetization dynamics2, but also due to the\npossibility of application of materials exhibiting magne-\ntoimpedance as probe element in sensor devices for low-\nfield detection3. In this sense, the sensitivity and linear-\nity as a function of the magnetic field are the most im-\nportantparametersinthepracticalapplicationofmagne-\ntoimpedance effect for magnetic sensors4. Experiments\nhave been carried out in numerous magnetic systems,\nincluding ribbons5–7, sheets8, wires9–13, and, magnetic\nfilms14–16,16,17,17–23. However, although soft magnetic\nmaterials are highly sensitive to small field variations at\nlow magnetic fields, due to magnetization process most\nof them essentially have nonlinear MI behavior around\nzero magnetic field, which prevents a simple straightfor-\nward derivation of an appropriate signal for sensor appli-\ncations23,24.\nThe shift ofthe sensoroperational regionand the lead-\ning of the linear MI behavior at around zero magnetic\nfield can be obtained primarily by applying a bias field or\nan electrical current to the ordinary MI element24. How-\never, this approach proved to be disadvantageous from\nthe practical and technological point of view, mainly due\nto energetic consumption. Recently, it has been shown\nthat materialsexhibiting asymmetricmagnetoimpedance\n(AMI) effect arise as promising alternative with poten-tial of application, opening possibilities for the use of this\nkind of materials for the development of auto-biased lin-\nearmagnetic field sensors. For thesematerials, the asym-\nmetric effects are obtained by inducing an asymmetric\nstatic magnetic configuration, usually done by magneto-\nstatic interactions13,24,25or exchange bias4,16,23,26,27.\nFor ferromagnetic films, the primary AMI results have\nbeen measured for exchange biased multilayers16,23,27.\nTheory and experiment agree well for MI curves shifted\nby the exchange bias field, following the main features\nof the magnetization curve, as well as it is verified that\nthe linear region of AMI curves can be tuned to around\nzero just by modifying the angle between applied mag-\nnetic field and exchange bias field, or changing the probe\ncurrent frequency. On the other hand, another promis-\ning possibility of AMI material resides in films presenting\nbiphase magnetic behavior, with hard and soft ferromag-\nnetic phases intermediated by a non-magnetic layer act-\ning together.\nIn this work, we investigate the magnetoimpedance ef-\nfectin ferromagneticNiFe/Cu/Cofilms. We observethat\nthe MI response is dependent on the thickness of the\nnon-magnetic Cu spacer material, a fact associated to\nthe kind of the magnetic interaction between the ferro-\nmagnetic layers. Here we show that the linear region\nof the asymmetric magnetoimpedance curves in these\nfilms is experimentally tunable by varying the thickness\nof the non-magnetic spacer material, and probe current\nfrequency. The results place ferromagnetic films with\nbiphase magnetic behavior exhibiting asymmetric mag-\nnetoimpedance effect as a very attractive candidate for\napplication as probe element in the development of auto-\nbiased linear magnetic field sensors.\nFor this study, we produce Ni 81Fe19(252\nnm)/Cu( tCu)/Co(50 nm) ferromagnetic films, with\ntCu= 0, 1.5, 3, 5, 7, and 10 nm. The films are\ndeposited by magnetron sputtering from targets of\nnominally identical compositions onto glass substrates,\nwith dimensions of 8 ×4 mm2. A buffer Ta layer is\ndeposited before the NiFe layer to reduce the roughness\nof the substrate, as well as a cap Ta layer is inserted\nafter the Co layer in order to avoid oxidation of the\nsample. The deposition is carried out with the following\nparameters: base vacuum of 10−8Torr, deposition\npressure of 2 .0 mTorr with a 99 .99% pure Ar at 32 sccm\nconstant flow, and DC source with power of 150 W for\nthe deposition of the NiFe and Co layers, while 100 W\nfor the Cu and Ta layers. During the deposition, the\nsubstrate rotates at constant speed to improve the film\nuniformity, and a constant magnetic field of 2 kOe is\napplied perpendicularly to the main axis of the substrate\nin order to induce a magnetic anisotropy and define\nan easy magnetization axis. X-ray diffraction results,\nnot shown here, calibrate the deposition rates and\nverify the Co(111) and NiFe(111) preferential growth\nof all films. Magnetization curves are obtained with a\nvibrating sample magnetometer, measured along and\nperpendicular to the main axis of the films, to verify the\nquasi-static magnetic behavior. Magnetization dynamics\nis investigated through MI measurements obtained using\na RF-impedance analyzer Agilent model E4991, with\nE4991Atest head connected to a microstrip in which\nthe sample is the central conductor. Longitudinal MI\nmeasurements are performed by acquiring the real R\nand imaginary Xparts of the impedance Zover a wide\nrange of frequencies, from 0 .1 GHz up to 3 .0 GHz, with\n0 dBm (1 mW) constant power applied to the sample,\ncharacterizing the linear regime of driving signal, and\nmagnetic field varying between ±300 Oe, applied along\nthe main axis of the sample. Detailed information\non the MI experiment is found in Refs.21,22. In order\nto quantify the sensitivity and MI performance as a\nfunction of the frequency, we calculate the magnitude\nof the impedance change at the low field range ±6 Oe\nusing the expression23\n|∆Z|\n|∆H|=|Z(H= 6Oe)−Z(H=−6Oe)|\n12.(1)\nHere, we consider the absolute value of ∆ Z, since the\nimpedance around zero field can present positive or neg-\native slopes, depending on the sample and measurement\nfrequency. In particular, it is verified that |∆Z|/|∆H|is\nroughly constant at least for a reasonable low field range.\nFigure 1 shows the quasi-static magnetization curves\nfor selected films, measured with the external in-plane\nmagnetic field applied along and perpendicular to the\nmain axis. When analyzed as a function of the the thick-\nness of the non-magnetic Cu spacer material, it is ob-\nserved an evolution of the shape of the magnetization\ncurves, indicating the existence of a critical thickness\nrange,∼3 nm, which splits the films in groups according\nthe magnetic behavior. For films with tCubelow 3 nm,the NiFe and Co layers are ferromagnetically coupled.\nThe angular dependence of the magnetization curves in-\ndicatesanuniaxialin-planemagneticanisotropy,induced\nby the magnetic field applied during the deposition pro-\ncess, and oriented perpendicularly to the main axis. De-\nspitethe similarmagneticbehavior, thefilm with 1 .5nm-\nthick Cu layer (not shown) has slightly higher coercive\nfield if compared to the one for the film without spacer\nmaterial, possibly associated to the increase of the whole\nsample disorder due to the non-formation of a regular\ncomplete Cu layer. The film with tCu= 3 nm, within\nthe critical Cu thickness range, presents an intermediate\nmagnetic behavior, with smaller magnetic permeability,\ncharacterized by the first evidences of a small plateau\nin the measurement perpendicular to the main axis, and\nthe appearance of magnetization regions associated to\ndistinct anisotropy constants of the NiFe and Co layers.\nFilms with tCuabove the critical thickness range exhibit\na biphase magnetic behavior. The two-stage magnetiza-\ntion process is characterized by the magnetization rever-\nsion of the soft NiFe layer at low magnetic field, followed\nbythereversionofthehardColayerathigherfield. None\nsubstantial difference between the magnetization curves\nmeasured for films with tCu>3 nm is verified. In prin-\nciple, the biphase magnetic behavior suggests that the\nferromagnetic layers are uncoupled. The easy magneti-\nzation axis remains perpendicular to the main axis of the\nsubstrate, as expected. The weaker anisotropy induction\nand increase of hysteretic losses are primarily related to\nthe roughness of the interfaces and lack of homogeneity\nof the Cu layer arisen as its thickness is raised18.\nIt is well-known that quasi-static magnetic proper-\nties play a fundamental role in the dynamic magnetic\nresponse and are reflected in the MI behavior23. The\nshape and amplitude of the magnetoimpedance curves\nare strongly dependent on the orientation of the applied\nmagnetic field and accurrent with respect to the mag-\nnetic anisotropies, magnitude of the external magnetic\nfield, and probe current frequency, as well as are di-\nrectly related to the main mechanisms responsible for\nthe transversemagnetic permeability changes: skin effect\nand ferromagnetic resonance (FMR) effect23,28,29. How-\never, magnetoimpedance effect can also provide a further\ninsights on the nature of the interactions governing the\nmagnetization dynamics and energy terms affecting the\ntransverse magnetic permeability.\nRegarding the MI results, Fig. 2 shows the MI curves,\nat the selected frequency of 0 .75 GHz, for the films with\ndifferent thicknesses tCuof the non-magnetic Cu spacer\nmaterial. All samples exhibit a double peak behavior for\nthe whole frequency range, a signature of the perpen-\ndicular alignment of the external magnetic field and ac\ncurrent with the easy magnetization axis. An interesting\nfeature related to the MI behavior of the NiFe/Cu/Co\nfilms resides in the amplitude and position of the peaks\nwith the thickness of the non-magnetic Cu spacer mate-\nrial, and the probe current frequency.\nFilms with tCu<3 nm present the well-known sym-3\n−100 −50 0 50 100\nH (Oe)−1.0−0.50.00.51.0M/Ms0 nm\n⟂\n∥\n−100 −50 0 50 100\nH (Oe)−1.0−0.50.00.51.0M/Ms3 nm\n−100 −50 0 50 100\nH (Oe)−1.0−0.50.00.51.0M/Ms7 nm\nFIG. 1: Representative normalized quasi-static magnetiza tion curves for selected NiFe/Cu/Co films with different thic knesses\nof the non-magnetic Cu spacer material, obtained with the in -plane magnetic field applied along ( /bardbl) and perpendicular ( ⊥) to\nthe main axis. Films with tCubelow 3 nm present behavior similar to that verified for the fil m withtCu= 1.5 nm, while the\nfilms with tCuabove the critical thickness range have behavior identical to the one observed for the film with tCu= 7 nm. The\nfilm with tCu= 3 nm is within the critical Cu thickness range and have an int ermediate behavior.\nmetric magnetoimpedance behavior for anisotropic sys-\ntems. The MI curves have the double peak behavior,\nsymmetrical at aroud H= 0, with peaks with roughly\nthe same amplitude. For frequencies up to ∼0.85 GHz,\nthe position of the peaks remains unchanged close to the\nanisotropyfield, indicatingthattheskineffectisthemain\nresponsibleby the changesoftransversemagnetic perme-\nability governing the magnetization dynamics. For fre-\nquencies above this value, not presented here, besides the\nskin effect, the FMR effect also becomes an important\nmechanism responsible for variations of the MI effect, a\nfact evidenced by the displacement of the peaks position\ntoward higher fields as the frequency is increased. The\ncontribution of the FMR effect to Zis also verified us-\ning the method described by Barandiar´ an et al.30, and\npreviously employed by our group17.\nOn the other hand, films with tCu≥3 nm present\nnoticeable asymmetric magnetoimpedance effect. The\nasymmetric behavior is assigned by two characteristic\nfeatures: shift of the MI curve in field, depicted by the\nasymmetric position of the peaks, and asymmetry in\nshape, evidenced by the difference of amplitude of the\npeaks. Figure 3 shows the evolution of the MI curves, at\nselected frequencies between 0 .5 GHz and 3 .0 GHz, for\nthe film with tCu= 7 nm, as an example of the exper-\nimental result obtained for the ferromagnetic films with\ntCuabove 3 nm. Here, it is important to notice that\nthe presented MI behavior is acquired when the field\ngoes from negative to positive values. However, the MI\ncurves are acquired over a complete magnetization loop\nand present hysteretic behavior. In particular, when the\nfield goes from positive to negative values, the MI behav-\nior is reversed.\nFrom Fig. 3, regarding the position of the peaks, since\nthe skin effect commands the dynamical behavior, the\npeaks remain invariable at the low frequency range. For\nthis film, the peak at negative field values is located at\n∼ −4 Oe, while the one at positive fields is at ∼+30\nOe. For the other films with tCu>3 nm and biphase\nmagnetic behavior, the peak at positive field is placed\nat similar value, although the location of the peak at−300 −150 0 150 300\nH (Oe)4.204.224.244.264.28Z (Ω)0 nm\n−300 −150 0 150 300\nH (Oe)4.294.314.334.35Z (Ω)1.5 nm\n−300 −150 0 150 300\nH (Oe)4.924.944.964.98Z (Ω)3 nm\n−300 −150 0 150 300\nH (Oe)5.035.065.095.125.15Z (Ω)5 nm\n−300 −150 0 150 300\nH (Oe)4.284.314.344.374.40Z (Ω)7 nm\n−300 −150 0 150 300\nH (Oe)5.325.355.385.415.44Z (Ω)10 nm\nFIG. 2: The MI curves at frequency of 0 .75 GHz measured\nfor the films with different thicknesses of the non-magnetic\nCu spacer material tCu. The MI curves are acquired over a\ncomplete magnetization loop and present hysteretic behavi or.\nHere, we show just part of the curve, when the field goes from\nnegative to positive values, to make easier the visualizati on\nof the whole MI behavior.\nnegative field present dependence with tCu, as will be\ndiscussed. With respect to the amplitude of the peaks\nat low frequencies, for all films with tCu>3 nm, the\nMI behavior exhibits an asymmetric two-peak behavior,\nwith the peak at negative field being with higher am-\nplitude than the peak at positive field. As a signature\nof the emergence of the FMR effect, the displacement of\nthe peak at negative field begins at ∼0.6 GHz, while the4\n−300 −150 0 150 300\nH (Oe)3.883.903.923.943.96Z (Ω)0.50 GHz\n−300 −150 0 150 300\nH (Oe)4.284.314.344.374.40Z (Ω)0.75 GHz\n−300 −150 0 150 300\nH (Oe)4.924.954.985.015.04Z (Ω)1.0 GHz\n−300 −150 0 150 300\nH (Oe)6.526.566.606.646.68Z (Ω)1.5 GHz\n−300 −150 0 150 300\nH (Oe)8.638.718.798.87Z (Ω)2.0 GHz\n−300 −150 0 150 300\nH (Oe)14.714.915.115.3Z (Ω)3.0 GHz\nFIG. 3: Evolution of the experimental MI curves for selected\nfrequencies for the ferromagnetic biphase fil with tCu= 7\nnm. Similar results are obtained for all the ferromagnetic\nfilms with tCuabove 3 nm and biphase magnetic behavior.\nWe show just part of the curve, when the field goes from\nnegative to positive values.\nposition of peak at positive field starts changing at ∼1.1\nGHz. Above ∼1.5 GHz, strong skin and FMR effects are\nresponsible by the MI variations. At this high frequency\nrange, the asymmetry still remains in the portion of the\nimpedance curve around the anisotropy fields. However,\nthe displacement of the peaks toward higher fields sup-\npress the impedance peak asymmetry, in position and\namplitude, resulting is symmetric peaks around H= 0\nwith same amplitude. For the film with tCu= 3 nm with\nintermediate magnetic behavior, similar features are ob-\nserved respectively at ∼0.75 GHz, ∼1.1 GHz, and ∼2.0\nGHz.\nThe most striking finding in the dynamic magnetic re-\nsponse resides in the asymmetry of the MI curves mea-\nsured for the films with biphase magnetic behavior. It\nis important to notice that the magnetoimpedance re-\nsponse is nearly linear for low magnetic field values, and\nthe shape of the Zcurves depends on the thickness of\nthe non-magnetic Cu spacer material and probe current\nfrequency. As a consequence, the best response can be\ntuned by playing with both parameters. Figure 4 shows\nthe frequency spectrum of impedance variations between\n±6 Oe, as defined by Eq. (1), for each film, indicating\nthe sensitivity around zero field.\nFrom the figure, we verify that the films split in dif-\nferent groups according the sensitivity around zero field.0.0 0.5 1.0 1.5 2.0 2.5 3.0\nf (GHz)0246810|∆Z|/|∆H| (mΩ/Oe) 10 nm\n 7 nm\n 5 nm\n 3 nm\n 1.5 nm\n 0 nm\nFIG. 4: Frequency spectrum of impedance variations between\n±6 Oe for the films with different thicknesses of the non-\nmagnetic Cu spacer material tCu, indicating the sensitivity\naround zero field. Notice the kind of saturation effect ob-\nserved as the tCuincreases above 3 nm, related to the ampli-\ntude and frequency at which the maximum impedance change\nis reached.\nIt is important to notice that each one is related to a\ngiven magnetic behavior, verified through the magneti-\nzation curves. Films with tCu<3 nm have the largest\nsensitivity valuesat ∼1.0GHz, the film with tCu= 3 nm\nat∼0.9 GHz, while the ones with tCu>3 nm at∼0.75\nGHz. For all of them, the sensitivity peak is found to\nbe at frequencies just after the FMR effect starts ap-\npearing, and while the MI peaks are still placed close to\nthe anisotropy fields. The highest sensitivity is observed\nfor the films with tCu>3 nm, reaching ∼8 mΩ/Oe,\nand seems to be insensitive to the thickness of the non-\nmagnetic spacer material. In this situation, the AMI\ncurves have nearly linear behavior at low magnetic field\nvalues, and the slope of the linear region at nearly zero\nfield is negative, due to the shape of the MI curve.\nOur results raise an interesting issue on the behav-\nior of the peaks in the magnetoimpedance effect and the\nenergy terms affecting the transverse magnetic perme-\nability. Generally, our films consist of two ferromagnetic\nlayers,withdistinctanisotropyfieldstrengths, intermedi-\nated by non-magnetic spacer material. We interpret our\nexperimental data as a result caused by the competition\nbetween two types of magnetic interactions between fer-\nromagnetic layers: exchange coupling between touching\nferromagnetic phases, and long-range dipolarlike or mag-\nnetostatic coupling31. In particular, they are strongly\ndependent on the thickness of the spacer material, and\nthe action of each one affect in different ways the MI\nbehavior.\nIf both ferromagneticlayersarequasi-saturated, where\nthere are no walls with wall stray fields, the coupling\nshould adjust the magnetizationofthe twoferromagnetic\nlayers parallel to each other. For tCu<3 nm, the strong\ncoupling is caused by the exchange interaction between5\ntouching ferromagnetic layers and through pinholes in\nthe non-magnetic spacer, and the whole sample behaves\nas a single ferromagnetic layer18. In this sense, we con-\nfirm the expected symmetric magnetoimpedance behav-\nior of single anisotropic systems.\nFortCu>3 nm, the Cu layer is completelly filled18,\nand the nature of the coupling is magnetostatic. If\nthe ferromagnetic layers were completely uncoupled, one\ncould expect multiple peak MI behavior, associated to\nthe anisotropy fields of each different layers, around ±30\nOe and±10 Oe. This behavior is not verified here, in-\ndicating that the AMI can not be explained assuming\nindependent reversal of the NiFe and Co layers. Thus,\nthe asymmetry arises as a result of the magnetostatic\ncoupling between the ferromagnetic layers. The origin\nof the magnetostatic coupling is ascribed to the hard Co\nmagnetic phasein terms ofan effective biasfield, induced\nby divergences of magnetization mainly due to roughness\nin the interfaces and limits of the sample24, that must be\ntaken into account as a contributorto the transverseper-\nmeability. The field penetrates the non-magnetic spacer\nlayer and results in a torque on the magnetization of\nthe opposite layer. It is important to point out that the\nanisotropyfieldofthe hardColayerisconsiderablelarger\nthan the soft NiFe layer, the reason why this asymmetric\nbehavior is not verified in traditional multilayers.\nInthissense, themainfeaturesoftheasymmetricmag-\nnetoimpedance verified in films with biphase magnetic\nbehavior can be explained through the effective interac-\ntion between the ferromagnetic layers. The influence on\nthe soft NiFe layer is dependent on the magnetic state of\nthe hard Co layer, as well as on the thickness of the Cu\nlayer spacer. The difference of amplitude of the peaks is\nunderstood from the magnetic saturated state in terms\nof the orientation of the two layers. The peak at nega-\ntive field is higher than that in positive field, since the\nmagnetization of the soft NiFe layer is parallel to the\nmagnetization of the hard Co layer and consequently to\nthe magnetostatic field, as well as to the external field.\nSince the magnetization of the NiFe layer is reverted as\nthe field is increased,the senseofthis magnetizationwith\nrespect to the magnetostatic field is modified, and this\nform closes the magnetic flux, resulting a lower peak24.\nSimilar dependance with the orientation of magnetiza-\ntions has alreadybeen verified in field-annealed Co-based\namorphous ribbons4. When the MI measurement is ana-\nlyzed for decreasingmagnetic field, the reverted behavior\nis observed, with the higher and smaller peaks at posi-\ntive and negative fields, respectively, since the sense of\nthe magnetization of the hard Co layer is the opposite.\nBy employing MI measurements, it is possible to es-\ntimate the effective coupling strenght between the NiFe\nand Co layers. This can be done by considering the lo-\ncation of the peaks in the MI curves at the low frequen-\ncies. Figure 5 shows the magnetic field values in which\nthe impedance peaksarelocated, for differentthicknesses\nof the non-magnetic Cu spacer material, at the low fre-\nquency range. The position of the impedance peak at0.0 2.5 5.0 7.5 10.0\nThickness (nm)010203040|Hpeak | (Oe)Peak at negative H\nPeak at positive H\nFIG. 5: Magnetic field values in which the impedance peaks\nare located, at0 .5 GHz, for thefilmswith differentthicknesses\nof the non-magnetic Cu spacer material tCu. Notice that the\nfilms with tCu≤1.5 nm present double peak behavior, sym-\nmetrical at aroud H= 0.\nnegative field presents a noticeable dependence with tCu.\nIn particular, it is verified a reduction of the field value\nwhere the peak is located as tCuis increased, corroborat-\ning the assumption of a magnetostatic origin of the cou-\npling between the ferromagnetic layers. In this sense, we\ninterpret the reduction as an indication of the decrease\nof the bias field intensity acting on the soft NiFe layer\nas the Cu thickness is increased. On the other hand, the\npeak atpositive field is located at ∼30Oe, except for the\nsample without the non-magnetic spacer material. The\nconstancy in the peak location, irrespective of tCuand\nfield value of the Co reversion for each sample, suggests\nthat this value corresponds to a intrinsic feature of the\nferromagnetic Co layer, since it presents similar thick-\nnesses for all samples. Thereby, we understand it as the\nmagnitude of the bias field inducedby the hard Co layer.\nIn conclusion, we have investigated the magne-\ntoimpedance effect in ferromagnetic NiFe/Cu/Co films\nand observed the dependence of the MI curves, in par-\nticular, amplitude and position of the peaks, with the\nthickness of the non-magnetic Cu spacer material. We\nhave verified that the MI response of these films can be\ntaylored by the kind of magnetic interaction between the\nferromagnetic layers. In this sense, the coupling between\nthe layers is usefull to develop materials with asymmet-\nric MI. From the results, we have observed the crossover\nbetween two distinct magnetic behavior, associated to\ndistict kind of the magnetic behavior between the ferro-\nmagnetic layers, exchange interaction and magnetostatic\ncoupling, as the Cu thickness is altered crossing through\ntCu= 3 nm. Thus, we have tuned the linear regionof the\nasymmetric magnetoimpedance curves around zero mag-\nnetic field by varying the thickness of the non-magnetic\nspacer material, and probe current frequency. The high-\nest sensitivity is observed for the films with tCu>3 nm,6\nreaching ∼8 mΩ/Oe, and seems to be insensitive to the\nthickness of the non-magnetic spacer material. These\nresults extend the possibilities for application of ferro-\nmagnetic films with asymmetric magnetoimpedance as\nprobe element for the development of auto-biased linear\nmagnetic field sensors, placing films with biphase mag-\nnetic behavior as promissing candidates to optimize the\nMI performance.\nAcknowledgments\nThe authors thank Vivian Montardo Escobar for the\nfruitful discussions. The research is supported by theBrazilian agencies CNPq (Grants No. 471302/2013-9,\nNo. 310761/2011-5, No. 555620/2010-7), CAPES, and\nFAPERN (Grant Pronem No. 03 /2012). M.A.C. and\nF.B. acknowledge financial support of the INCT of Space\nStudies.\n∗Electronic address: felipebohn@gmail.com\n1M. Knobel, M. V´ azquez, and L. Kraus, Handbook of Mag-\nnetic Materials (Elsevier Science B. V., Amsterdam, 2003),\n(ed. K. H. Buschow)Ch. 5, 1 – 69.\n2A. Yelon, D. Menard, M. Britel, and P. Ciureanu, Appl.\nPhys. Lett. 69, 3084 (1996).\n3H. Chiriac, M. Tibu, A.-E. Moga, and D. D. Herea, J.\nMagn. Magn. Mater. 293, 671 (2005).\n4C. G. Kim, K. J. Jang, D. Y. Kim, and S. S. Yoon, Appl.\nPhys. Lett. 75, 2114 (1999).\n5R. L. Sommer and C. L. Chien, Phys. Rev. B 53, R5982\n(1996).\n6K. R. Pirota, L. Kraus, M. Knobel, P. G. Pagliuso, and\nC. Rettori, Phys. Rev. B 60, 6685 (1999).\n7F. Amalou and M. A. M. Gijs, J. Appl. Phys. 95, 1364\n(2004).\n8M. Carara, A. Gundel, M. N. Baibich, and R. L. Sommer,\nJ. Appl. Phys 84, 3792 (1998).\n9R. S. Beach and A. E. Berkowitz, Appl. Phys. Lett. 64,\n3652 (1994).\n10J. Vel´ azquez, M. V´ azquez, D.-X. Chen, and A. Hernando,\nPhys. Rev. B 50, 16737 (1994).\n11D. P. Makhnovskiy, L. V. Panina, and D. J. Mapps, Appl.\nPhys. Lett. 77, 121 (2000).\n12M. V´ azquez, M. Knobel, M. L. Sanchez, R. Valenzuela,\nand A. P. Zhukov, Sens. Actuators A 59, 20 (1997).\n13G. V. Kurlyandskaya et al., J. Appl.Phys. 87, 4822 (2000).\n14R. L. Sommer and C. L. Chien, Appl. Phys. Lett. 67, 3346\n(1995).\n15A. D. C. Viegas et al., J. Appl. Phys. 101, 033908 (2007).16R. B. da Silva et al., Appl. Phys. Lett. 94, 042501 (2009).\n17M. A. Corrˆ ea et al., J. Phys. D: Appl. Phys. 43, 295004\n(2010).\n18M. S. Marques et al., Thin Solid Films 520, 2173 (2012).\n19G. Kurlyandskaya et al., J. Magn. Magn. Mater. 242-245 ,\n291 (2002).\n20G. V. Kurlyandskaya et al., J. Phys.: Cond. Mat. 16, 6561\n(2004).\n21M. A. Corrˆ ea et al., J. Phys. D: Appl. Phys. 41, 175003\n(2008).\n22A. M. H. de Andrade, M. A. Corra, A. D. C. Viegas,\nF. Bohn, and R. L. Sommer, J. Appl. Phys. 115, 103908\n(2014).\n23R. B. da Silva et al., Appl. Phys. Lett. 104, 102405 (2014).\n24J. Torrej´ on, M. V´ azquez, and L. V. Panina, J. Appl. Phys.\n105, 033911 (2009).\n25J. Sinnecker, A. de Araujo, R. Piccin, M. Knobel, and\nM. V´ azquez, J. Magn. Magn. Mater. 295, 121 (2005).\n26N. A. Buznikov, C. Kim, C.-O. Kim, and S.-S. Yoon, Appl.\nPhys. Lett. 85, 3507 (2004).\n27C. Garc´ ıa, J. M. Florez, P. Vargas, and C. A. Ross, Appl.\nPhys. Lett. 96, 232501 (2010).\n28R. L. Sommer and C. L. Chien, Appl. Phys. Lett. 67, 857\n(1995).\n29M. A. Corrˆ ea et al., J. Appl. Phys. 110, 093914 (2011).\n30J. M. Barandiaran, A. Garcia-Arribas, and D. de Cos, J.\nAppl. Phys. 99, 103904 (2006).\n31T. C. Schulthess and W. H. Butler, J. Appl. Phys. 87,\n5759 (2000)."    },    {        "title": "1408.1277v1.Permanent_magnet_with_MgB2_bulk_superconductor.pdf",        "content": " 1 Permanent magnet with MgB 2 bulk superconductor  \n \nAkiyasu Yamamoto *1, 3, Atsushi Ishihara2, Masaru Tomita2 & Kohji Kishio1  \n1The University of Tokyo, 7 -3-1 Hongo, Bunkyo, Tokyo 113 -8656, Japan   \n2Railway Technical Research Institute, 2 -8-38 Hikari, Kokubunji,  Tokyo 185 -8540, Japan  \n3 JST-PRESTO, 4 -1-8 Honcho, Kawaguchi, Saitama 332 -0012, Japan  \n \nAbstract:  \nSuperconduct ors with persistent zero -resistance current s serve as permanent magnet s for \nhigh-field applications requir ing a strong and stable  magnetic  field, such as magnetic resonance \nimaging (MRI) . The recent global helium shortage has quickened research into high-temperature \nsuperconductor s (HTS s)—materials that  can be used without conventional liquid -helium cooling to \n4.2 K. Herein, we demonstrate that 40 -K-class metallic HTS  magnesium diboride  (MgB 2) makes  an \nexcellent permanent bulk magnet, maintaining 3 T at 20 K for 1 week with an extremely high \nstability (<0.1 ppm/h ). The  magnetic  field trapped in  this magnet  is uniformly distributed, as for \nsingle -crystalline neodymium -iron-boron. Magnetic hysteresis loop of the MgB 2 permanent  bulk \nmagnet  was detrmined . Because  MgB 2 is a simple -binary -line compound that does not contain \nrare-earth  metals , polycrystalline bulk  material  can be industrially fabricated at low cost and with  \nhigh yield  to serve as strong magnet s that are compatible with  conventional compact cryocooler s, \nmaking MgB 2 bulks promising for the next  generation of Tesla -class permanent -magnet applications.  \n  2 Superconducting bulk magnet s are a direct m anifestation of quantum phenomen a on the \nmacroscopic scale. By magnetizing at below its transition temperature Tc, the entire bulk acts as a \ncompact Tesla -class magnet because of the presence of induced macroscopic circulating \nsupercurrent s [1-8]. If the magnetized  bulk is kept cold , it will act as a  permanent magnet. \nSuperconducting bulk magnet s are suitable for new compact -magnet applications such as desktop \nNMR, MRI , motors, and particle accelerators [9-11], which require very strong field s that cannot b e \nobtained by conventional permanent magnet s and flexible magnet -shape design. S tate-of-the-art \ntexturing  growth techniques  overcome the electromagnetic weak -link problem in  quasi -single -crystal  \nform s of HTS  rare-earth barium copper oxide  (HTS -REBCO) , and a record  high field of 17 T was \ntrapped in a 1-inch compact  bulk [2,8]. Although v arious potential applications of superconducting \nbulk magnets have emerged [12,13], insufficient  field uniformity and reproducibility  due to  anisotropic \nand unpredictable cry stal growth hinder the industrial use of HTS -REBCO bulks . Efforts to improve \ntheir properties, especially field uniformity [14-16] and productivity [17,18], are being performed.  \nMgB 2 is a metallic HTS discovered in 2001 [19]. Because of its high Tc (40 K) and recent \nprogress in high-performance cryocoolers, it is a strong contender for future cryocooled, \nliquid -helium -free applications  at 5–30 K.  In practice , the distinct advantage of MgB 2 is that its \nmetallic superconductivity (i.e., it’s simple and symme tric pairing mechanism, high carrier density , \nand long coherence length ) drives  a weak -link-free supercurrent flow across grain boundaries , and \nthis occurs even in untextured polycrystalline bulks  [20]. Moreover , the nanoscale grain boundaries \nstrong ly pin the flux quantum [21-24], and in superconducting bulk magnet s, this effect is  expected to \nyield strong, uniform, and stable magnetic  fields. We recently found that a MgB 2 bulk with a large \ntrapped magnetic field can be synthesized by simple sintering;  a technique that can lead  to the \nlow-cost, high -yield, and scalable production of superpowerful liquid -helium -free magnets .  \nBulk polycrystalline MgB 2 was synthesized by a conventional sintering  process with a  mixture \nof magnesium and boron  powders and by  using a modified powder -in-closed -tube technique  [25]. \nMagnesium (99.8% purity)  and boron (99.9% purity)  powders were weighed and then mixed at a \nmolar ratio of 1:2 in an agate mortar . Subsequently,  the resulting  powder was uniaxially pressed at  \n100 MPa  to fo rm a disk -shaped pellet (30 mm in diameter and 10 mm thick) . To prevent the \nmagnesium  from oxidiz ing, the pellet was  sealed in a stainless -steel tube  and heat  treated in a tube \nfurnace  at 850 °C for 3 h under an argon atmosphere.  \n The inset of Fig. 2 show s the photograph  of a disk-shape d bulk MgB 2. The surface structure is \nhomogeneous with no cracks or crystal domains to disrupt the uniform  super current flow. Analysis \nby powder X-ray diffraction confirms that the bulk  is nearly -single -phase MgB 2 with small  amount \nof MgO . Moreover,  our bulk MgB 2 has a  mass density of 1.3 g/cm3, which  is ~5.2 times lighter than \nREBCO  (6.7 g/cm3) and ~5.7 times lighter than neodymium –iron–boron (NIB: 7.4 g/cm3) bulks.  \nTo measure the magnetic flux density , two disk-shape d bulk MgB 2 (30 mm diameter and 10 mm  3 thick ) were  stacked vertically across a spacer  containing a transversal cryogenic Hall sensor s \n(HGCT -3020, Lake  Shore ). The disk pair was cooled by a Gifford –McMahon (GM) cryocooler  \n(CRT -HE05 -CSFM, Iwatani Gas) .  \nFor practic al application s of superconducting bulk  materials  as permanent magnet s, one must \ndetermine the  magnetic response and stability over time, including  the change  in the  applied external \nfield during the initial magnetization process  and the residual magnetiza tion as well as its \ncorresponding creep as a function of time after field removal. To this end , we measured the cyclic \nmagnetic hysteresis o f the pair of MgB 2 bulk disks . After cooling the sample to various  temperatures  \nin the absence of a  magnetic field, an external field was cyclically applied at a constant rate of ±1.8 \nT/h; the magnetization was recorded as the local magnetic flux density at the center of the sample . \nHysteresis loops were obtained at 10, 20 , and 30 K. In Fig. 1, Hp, Br, and −Hc represent  the most \nimportant parameters describing the loops. The penetration field  Hp is the external field when  the \npenetrating magnetic field front reaches the center of the sample disk. The quantity Br corresponds to \nthe remnant  local magnetization at the zero applied field of the descending step  and is commonly \nreferred to as  the trapped  remnant field . Similarly,  −Hc is the coercive field where the field in the \nmagnet reaches zero.  These practically important parameters in the macroscopic magnetization curve \nfor MgB 2 can be defined in a similar manner to those for a conventional, electron spin -based \npermanent ferr omagnets,  even though the microscopic origin of the magnetism is entirely  different \nfor the bulk MgB 2 superconductor.  \nFigure 2 shows the temperature dependence of the magnetic field trapped in the pair of bulk  \nMgB 2 disks . The sample was cooled to ~10 K  under an external field of 4.5 T, following which  the \nexternal field  was removed . After field -cooling magnetization , the magnetic flux density  trapped in \nthe disk pair was measured at two positions, including at  the center of the spacer (bulk center) and  at \nthe center of the bulk surface  (bulk surface)  as a function of temperature at a sweep rate of 0.1 K/min. \nA maximum trapped field of 4.02 T at 11 K was recorded, which is three times larger than  the \nremnant  magnetization Br of conventional  NIB materials . With increasing temperature, the field \ndecreased continuously due to  a decreasing critical current density in the bulk, until it vanished at 38 \nK (Tc for MgB 2). At 15, 20, 25 , and 30 K the trapped field was 3.6, 2.9, 2.1 , and 1.3 T, respectively. \nThe differe nce in trapped fields at the surface and the center is due to a geometrical factor, and the \nratio Bcenter/Bsurface  ~ 1.35 is considered reasonable if we compare with Biot -Savart calculation (~1.6) \nwhich assumes that the current density is constant in bulk.  These results suggest  that MgB 2 bulks \nhold promis e for applications requiring high-field magnets  that function without liquid -helium \ncooling , such as 200  MHz NMR (4.7 T) at ~10 K and 1.5 - to 3-T-class MRI at ~20 K.   \nFigure 3 show s the distribution of the local trapped field of a magnetized MgB 2 disk at 20 K. \nThe data was obtained by scanning  a Hall sensor 3 mm above the bulk surface.  As shown in  Fig. 3(a), \nthe spatial distribution of the trapped field is  conical , as expected for an ideal superconducting  4 magnetized disk with a uniform supercurrent J = 1/0 × ∂B/∂r [26]. The local field , as a function of \nposition , was consistent between different radial directions  (Fig. 3(b)), which suggests that the \nsupercurrent is circumferentially perfectly homogeneous . As a result , contour lines for the equivalent \nlocal field (Fig . 3(c)) are circular  (with a 99.4%  degree of circularity ), indicating  that the trapped \nfield is circumferentially  constant , similar to that of  a NIB disk. We attribute th e excellent  field \nuniformity to the metallic  superconductivity of polycrys talline MgB 2. More precisely, the field \nuniformity is due  to the weak -link-free uniform supercurrent flow and strong , uniform  flux pinning, \nwhich in turn are caused by the naturally distributed nanoscale grain boundaries.   \nTo assess  the stability of bulk -MgB2 magnets,  the magnet creep was measured for 7 days. Figure \n4(a) shows the time dependence of  the trapped field in the 30 -mm pair of bulk-MgB 2 disks . After \nmagnetization at 20 K and holding at 20 K, the trapped field undergoes continuous decay. The \ntrapp ed field after magnetization was 2.87 T  and decreased to 2.82 T after 3 days, which corresponds \nto a loss of 1.7%. After 1 hour,  the trapped field decreased linearly over time on a logarithmic scale \nand was well fit by B/B(t = 0) = 1.018 −  2.84 x 10−3 ln(t) for t > 104, where t is dimensionless time  \nstandardized by second . When the sample was magnetized and h eld at a higher temperature the \ndecay rate of the trapped field increased  and, at 30 K , was fit by B/B(t = 0) = 1.027 −  4.06 x 10−3 \nln(t). These results suggest that magnet  creep is due to  the motion of trapped flux quantum [27,28]. \nFlux quantum  in pinning potential U are depinned by the thermal activation process driven by the \nLorentz force  FL = 0 x J at the rate R = 0 exp(−U/kBT), where 0 is the flux quantum , 0 is the \nattempt  frequency of the flux, and kBT is the thermal energy.  \nThe thermal activation of flux can be suppressed by  operating at a temperature lower than that \nused to establish the critical state  [29,30]. To further  improve the magnet stability, the bulk pair  was \nmaintained  at 19 K , which is 1 K below the magnetizing temperature. By lowering the holding \ntemperature,  the stability of the trapped field improved  significantly , show ing a decay  of less than 1 \n× 10−4 T in 1 week (Fig . 4(b)). The decay rate  was fitted to  BT(t)/BT(0) = 1.000 −  4.79 x 10−6 ln(t), \nconfirm ing the  extremely slow average -magnet -creep rate  of <0.1 ppm/h . This creep rate is identical \nto that specifi ed for  MRI  scanners. Thus , the MgB 2 bulk ma gnet is a quasi -permanent  magnet that is  \nextremely  stable at operating temperatures. We attribute the improved magnet ic stability at 19 K to \nthe decreased motion of trapped flux quantum , which cause s the dissipation  of circulating \nsupercurrent . The flux is shifted upon transitioning from the  creep state to the frozen state due to a \ndecreas e in J/Jc at the operating temperature that increas es the activation energy U and suppresse s \nthermal activation .  \nThe trapped field as a function of  temperature, position,  time, and external field clearly show s \nthat bulk polycrystalline MgB 2 is a novel strong Tesla -class quasi -permanent magnet that can \nproduce a magnetic field greater than  4 T with excellent field uniformity , very high magnet stability , \nand a response to cy clic field s similar to that of spin-based  magnet s. The mechanism by which the   5 high, uniform , and stable field in bulk MgB 2 develops is unique  among HTS materials and is \nattributed to  grain boundaries  that act as homogeneous flux pinning sites rather than a s \ncurrent -blocking defects.  On the other hand, iron and/or rare -earth elements, which are considered \nessential for  spin-based permanent magnets, are not critical  for superconducting bulk magnets \nbecause  their high magnetic field s originate from macroscopic  electromagnetic induction due to  a \npersistently  circulating supercurrent . Therefore , bulk liquid -helium -free superconducting \nquasipermanent magnet s using MgB 2 or even new HTS materials are very interesting prospects in  \nthe ongoing search for strong magnet s that do not require rare-earth  metal s [31].  \nThus, our present  results  demonstrate that polycrystalline bulk superconducting MgB 2 is the \nstrongest reported rare-earth -metal –free permanent  magnet capable of operat ing with  existing  \ncryocooler s without conv entional liquid -helium cooling. Given that  the irreversibility field is greater \nthan 10 T at 20 K [32], we expect that it is possible to trap even higher field by increasing the \ndiameter of bulk MgB 2 and the current density, which can be done by tuning the  electronic - and \nmicro -structure [33,34] or by hybridizing with other HTSs . Because  MgB 2 is free of rare-earth  metals \nand is a  simple binary line -compound, magnet s made of  bulk polycrystalline MgB 2 for use with  \ncompact cryocooler s can be industrially fabri cated at low cost and with  high yield . These make  bulk \nMgB 2 extremely promising  for the next  generation of Tesla -class permanent -magnet applications , \nliquid -helium -free 3-T-class MRI, desktop NMR , and particle accelerators.  \n \nWe are very grateful to  T. Akas aka of RTRI and K. Iwase, J. Shimoyama of the University of \nTokyo for experimental assistance. We thank E. E. Hellstrom and D. C. Larbalestier of the Applied \nSuperconductivity Center, National High Magnetic Field Laboratory for their valuable suggestions  \non the manuscript and encouragement. This work was partially supported by a Grant -in-Aid for \nScientific Research from the Japan Society for the Promotion of Science  under grant Nos. 23246110  \nand 22860019  and by the Japan Science and Technology Agency, PREST O.  6 References  \n[1] G. Fuchs, G. Krabbes, P. Schätzle, S. Gruβ, P. Stoye, T. Staiger, K. -H. Müller, J. Fink, and L. \nSchultz , Appl. Phys. Lett.  76, 2107  (2000 ). \n[2] M. Tomita, and M. Murakami, Nature  421, 517 (2003).  \n[3] N. H. Babu, Y. Shi, K. Iida, and D. A. Cardwell, Nat. Mater.  4, 476 (2005).  \n[4] A. Yamamoto, H. Yumoto, J. Shimoyama, K. Kishio, A. Ishihara, and M. Tomita , 23th Intl . \nSymp . on Superconductivity, Tokyo (November, 2010).  \n[5] T. Naito, T. Sasaki, and H. Fujishiro, Supercond. Sci. Technol. 25, 095012 (2012).  \n[6] J. H. Durrell, C. E. J. Dancer, A. Dennis, Y. Shi, Z. Xu, A. M. Campbell, N. Hari Babu, R. I. \nTodd, C. R. M. Grovenor, and D. A. Cardwell , Supercond. Sci. Technol. 25, 112002 (2012).  \n[7] G. Fuchs, W. Haessler, K. Nenkov, J. Scheiter, O. Perner, A. Handstein, T. Kana i, L. Schultz, \nand B. Holzapfel , Supercond. Sci. Technol.  26, 122002 (2013).  \n[8] J. Durrell, A . Dennis, J . Jaroszynski, M . Ainslie, K . Palmer, Y . Shi, A . Campbell, J . Hull, M . \nStrasik, E . Hellstrom , and D . Cardwell , Supercond. Sci. Technol.  27, 082001  (2014). \n[9] Y. Iwasa, S . Y. Hahn, M . Tomita, H . Lee, and J . Bascuñán , IEEE Trans. Appl. Supercond. 15, \n2352 (2005).  \n[10] T. Nakamura, Y. Itoh, M. Yoshikawa, T. Oka, and J. Uzawa , Concept Magn. Reson.  B 31 , 65 \n(2007).  \n[11] T. Kii, R. Kinjo, N. Kimura, M. Shibata, M. A. Bakr, Y .  W. Choi, M. Omer, K. Yoshida, K. \nIshida, T. Komai, K. Shimahashi, T. Sonobe, H. Zen, K. Masuda, and H. Ohgaki , IEEE Trans. \nAppl. Supercond.  22, 4100904 (2012).  \n[12] D. A. Cardwell, and N. H. Babu, Physica C  445-448, 1 (2006).  \n[13] T. Oka, Physica C  463-465, 7 (2007 ). \n[14] M. Sekino, H. Yasuda, A. Miyazoe, and H. Ohsaki, IEEE Trans. Appl. Supercond. 21, 1588 \n(2011).  \n[15] S. Hahn, J. Voccio, D. K. Park, K. -M. Kim, M. Tomita, J. Bascuñán, and Y . Iwasa , IEEE Trans. \nAppl. Supercond. 22, 4302204 (2012).  \n[16] S. B. Kim, T. Kimoto, M. Ima i, Y. Yano, J. H. Joo, S. Hahn, Y. Iwasa, and M. Tomita , Physica C  \n471, 1454 (2011).  \n[17] M. Muralidhar , K. Suzuki, A. Ishihara, M. Jirsa, Y. Fukumoto, and M. Tomita,  Supercond. Sci. \nTechnol.  23, 124003  (2010). \n[18] Y. Shi, N. Hari Babu, K. Iida, W. K. Yeoh, A. R. D ennis, S. K. Pathak, and D. A. Cardwell , \nPhysica C  470, 685 (2010).  \n[19] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Nature  410, 63 (2001).  \n[20] D. C. Larbalestier, L. D. Cooley, M. O. Rikel, A. A. Polyanskii, J. Jiang, S. Patnaik, X. Y . Ca i, \nD. M. Feldmann, A. Gurevich, A. A. Squitieri, M. T. Naus, C. B. Eom, E. E. Hellstrom, R. J.  7 Cava, K. A. Regan, N. Rogado, M. A. Hayward, T. He, J. S. Slusky, P. Khalifah, K. Inumaru , \nand M. Haas , Nature  410, 186 (2001).  \n[21] P. C. Canfield, D. K. Finnemore, S. L. Bud'ko, J. E. Ostenson, G. Lapertot, C. E. Cunningham, \nand C. Petrovic , Phys. Rev. Lett. 86, 2423 (2001).  \n[22] G. Giunchi, G. Ripamonti, T. Cavallin, and E. Bassani, Cryogenics  46, 237 (2006).  \n[23] P. Mikheenko, E. Martínez, A. Bevan, J. S. Abell, and J. L. Ma cManus -Driscoll , Supercond. Sci. \nTechnol.  20, S264 (2007).  \n[24] T. Matsushita, M. Kiuchi, A. Yamamoto, J. Shimoyama, and K. Kishio , Supercond. Sci. Technol.  \n21, 015008 (2008).  \n[25] A. Yamamoto, J. Shimoyama, S. Ueda, Y. Katsura, S. Horii, and K. Kishio , Supercond. S ci. \nTechnol.  20, 658 (2007).  \n[26] C. P. Bean, Rev. Mod. Phys. 36, 31 (1964).  \n[27] P. W. Anderson, and Y . B. Kim, Rev. Mod. Phys. 36, 39 (1964).  \n[28] T. Matsushita, Flux Pinning in Superconductors  (Springer, German, 2006) . \n[29] M. R. Beasley, R. Labusch,  and W. W. Webb, Phys. Rev. 181, 682 (1969).  \n[30] G. Krabbes, G. Fuchs, W. R. Canders, H. May, and R. Palka,  High Temperature Superconductor \nBulk Materials , p.88 (Willey -VCH, German, 2006).  \n[31] N. Jones, Nature  472, 22 (2011).  \n[32] A. Gurevich, Nat. Mater.  10, 255 (2011).  \n[33] A. Yamamoto, J. Shim oyama, S. Ueda, Y . Katsura, I. Iwayama, S. Horii, and K. Kishio , Appl. \nPhys. Lett.  86, 212502 (2005).  \n[34] V. Braccini, A. Gurevich, J.E. Giencke, M.C. Jewell, C.B. Eom, D.C. Larbalestier, A. \nPogrebnyakov, Y. Cui, B. T. Liu, Y. F. Hu, J. M. Redwing, Q. Li, X. X . Xi, R. K. Singh, R. \nGandikota, J. Kim, B. Wilkens, N. Newman, J. Rowell, B. Moeckly, V. Ferrando, C. Tarantini, D. \nMarré, M. Putti, C. Ferd eghini, R. Vaglio, and E. Haanappel , Phys. Rev. B.  71, 012504 (2005).   8 Figure captions:  \n \nFig. 1. (Color online)  Magnetic hysteresis loops of bulk -MgB 2 magnet at 10, 20, and 30 K. The \nmagnetic field was measured at the center of the bulk -MgB 2 disk pair. Arrows indicate the \ncounterclockwise direction of the loop. Hp, Br, and − Hc represent the penetration field , the trapped \nremnant field, and the coercive field, respectively.  \n \nFig. 2. (Color online)  Trapped magnetic field measured as a function of continuously increasing \ntemperature at center and surface of magnetized b ulk-MgB 2 disk pair. The upper right inset shows \nschematic cross -sectional configuration of the bulk pair: two MgB 2 bulk disks and two Hall sensors. \nThe lower -left inset shows the photograph  of a bulk -MgB 2 disk.  \n \nFig. 3.  (Color online)  Distribution of tra pped magnetic field in MgB 2 bulk disk magnet at 20 K \nmeasured 3 mm above bulk surface. (a) A three -dimensional representation of the measured \nlocal -trapped -field distribution. (b) The local magnetic field as a function of relative position in \ndifferent rad ial directions, including  = 0, 0.25, 0.50, and 0.75 , as shown in panel (c). (c) Top \nview of magnetic field distribution. Dashed circles represent contour lines of equivalent local \nmagnetic fields.  \n \nFig. 4.  (Color online)  Time dependence of magnetic f ield trapped in bulk -MgB 2 magnet with \ndifferent magnetic -flux-stability conditions. (a) The field is normalized by the remnant trapped field \nB(t = 0) immediately after magnetization. The bulk -MgB 2 sample was magnetized at 20 K (orange \ncurve) and at 30 K (p ink curve) and isothermally maintained for 3 days (flux -creep state). The \nbulk-MgB 2 sample was magnetized at 20 K and maintained for 7 days at 19 K (purple curve; raw \ndata on a magnified absolute -field scale is shown in panel (b), which is 1 K less than th e \nmagnetizing temperature (flux -frozen state). (b) Stable trapped field of ~2.91 T at 19 K for 1 week \ngenerated by circulating supercurrent in persistent current mode. Dashed lines show decay rates (1 \nppm/h) of reference magnetic field.   9 Figure 1  \n \n \nFig. 1. (Color online)  Magnetic hysteresis loops of bulk -MgB 2 magnet at 10, 20, and 30 K. The \nmagnetic field was measured at the center of the bulk -MgB 2 disk pair. Arrows indicate the \ncounterclockwise direction of the loop. Hp, Br, and − Hc represent the penetration field , the trapped \nremnant field, and the coercive field, respectively.   10 Figure 2  \n \n \nFig. 2. (Color online)  Trapped magnetic field measured as a function of continuously increasing \ntemperature at center and surface of ma gnetized bulk -MgB 2 disk pair. The upper right inset shows \nschematic cross -sectional configuration of the bulk pair: two MgB 2 bulk disks and two Hall sensors. \nThe lower -left inset shows the photograph  of a bulk -MgB 2 disk.  \n  11 Figure 3  \n \n \nFig. 3.  (Color onlin e)  Distribution of trapped magnetic field in MgB 2 bulk disk magnet at 20 K \nmeasured 3 mm above bulk surface. (a) A three -dimensional representation of the measured \nlocal -trapped -field distribution. (b) The local magnetic field as a function of relative po sition in \ndifferent radial directions, including  = 0, 0.25, 0.50, and 0.75 , as shown in panel (c). (c) Top \nview of magnetic field distribution. Dashed circles represent contour lines of equivalent local \nmagnetic fields.  \n  12 Figure 4  \n \n \nFig. 4.  (Color on line)  Time dependence of magnetic field trapped in bulk -MgB 2 magnet with \ndifferent magnetic -flux-stability conditions. (a) The field is normalized by the remnant trapped field \nB(t = 0) immediately after magnetization. The bulk -MgB 2 sample was magnetized a t 20 K (orange \ncurve) and at 30 K (pink curve) and isothermally maintained for 3 days (flux -creep state). The \nbulk-MgB 2 sample was magnetized at 20 K and maintained for 7 days at 19 K (purple curve; raw \ndata on a magnified absolute -field scale is shown in panel (b), which is 1 K less than the \nmagnetizing temperature (flux -frozen state). (b) Stable trapped field of ~2.91 T at 19 K for 1 week \ngenerated by circulating supercurrent in persistent current mode. Dashed lines show decay rates (1 \nppm/h) of reference magnetic field.  \n "    },    {        "title": "1409.1712v1.Analysis_of_the_magnetic_field__force__and_torque_for_two_dimensional_Halbach_cylinders.pdf",        "content": "arXiv:1409.1712v1  [physics.class-ph]  5 Sep 2014Publishedin Journalof MagnetismandMagneticMaterials,V ol. 322(1),133–141,2014\nDOI:10.1016/j.jmmm.2009.08.044\nAnalysis of the magnetic field, force, and torque for\ntwo-dimensional Halbach cylinders\nR. Bjørk, C.R. H.Bahl, A. Smithand N.Pryds\nAbstract\nThe Halbach cylinder is a construction of permanent magnets used in applications such as nuclear magnetic\nresonance apparatus, accelerator magnets and magnetic coo ling devices. In this paper the analytical expres-\nsion for the magnetic vector potential, magnetic flux densit y and magnetic field for a two dimensional Halbach\ncylinder are derived. The remanent flux density of a Halbach m agnet is characterized by the integer p. For a\nnumber of applications the force and torque between two conc entric Halbach cylinders are important. These\nquantities are calculated and the forceis shown to be zero ex ceptfor the casewhere pfor the inner magnet is\none minus pfor the outer magnet. Also the force is shown never to be balan cing. The torque is shown to be\nzero unless the inner magnet pis equal to minus the outer magnet p. Thus there can never be a force and a\ntorque in thesamesystem.\nDepartmentofEnergy ConversionandStorage, TechnicalUni versityof Denmark-DTU,Frederiksborgvej399,DK-4000Ros kilde,Denmark\n*Correspondingauthor : rabj@dtu.dk\n1. Introduction\nThe Halbach cylinder ( 1;2) (also known as a hole cylinder\npermanent magnet array (HCPMA)) is a hollow permanent\nmagnet cylinder with a remanent flux density at any point\nthat variescontinuouslyas, inpolarcoordinates,\nBrem,r=Bremcos(pφ)\nBrem,φ=Bremsin(pφ), (1)\nwhereBremisthemagnitudeoftheremanentfluxdensityand\npis an integer. Subscript rdenotes the radial component of\nthe remanence and subscript φthe tangential component. A\npositive value of pproduces a field that is directed into the\ncylinder bore, called an internal field, and a negative value\nproduces a field that is directed outwards from the cylinder,\ncalledan externalfield.\nA remanence as given in Eq. ( 1) can, depending on the\nvalue ofp, produce a completely shielded multipole field in\nthe cylinder bore or a multipole field on the outside of the\ncylinder. InFig. 1Halbachcylinderswithdifferentvaluesof\npareshown.\nTheHalbachcylinderhaspreviouslybeenusedinanum-\nberofapplications( 3;4),suchasnuclearmagneticresonance\n(NMR) apparatus ( 5), accelerator magnets ( 6) and magnetic\ncoolingdevices( 7).\nIntheseapplicationsitisveryimportanttoaccuratelycal -\nculate the magnetic flux density generated by the Halbach\ncylinder. Thereexistseveralpaperswherethemagneticfiel d\nandfluxdensityforsomepartsofaHalbachcylinderarecal-\nculated (8;9;10;11), but a complete spatial calculation as\nwell as a detailed derivationof the magneticvectorpotenti al\nhaspreviouslynotbeenpublished.p = 1 p = 2 \np = −2 p = −3 ϕ\nFigure1. Theremanenceofa p=1,p=2,p=−2and\np=−3Halbachcylinder. Theangle φfromEq. ( 1)isalso\nshown.Analysisofthemagneticfield,force,andtorquefortwo-dim ensionalHalbachcylinders—2/ 11\nIn this paper we wish to calculate the magnetic vector\npotential and subsequently the magnetic flux density at any\npoint in a two dimensional space resulting from a Halbach\ncylinder.\nOncetheanalyticalsolutionforthemagneticfluxdensity\nhas been obtainedwe will proceedto calculate the forceand\ntorquebetweentwoconcentricHalbachcylinders.\nForp=1 and a relative permeabilityof 1 the morecom-\nplicated problem of computing the torque between two fi-\nnitelengthconcentricHalbachcylindershasbeenconsider ed\n(12), and it is shown that a torque arises due to end effects.\nHowever, neither the field nor the torque is evaluated explic -\nitly. Below we show that for special values of pa nonzero\nforceandtorquemayariseeveninthetwo dimensionalcase.\n2. Definingthemagnetostatic problem\nTheproblemoffindingthemagneticvectorpotentialandthe\nmagnetic flux density for a Halbach cylinder is defined in\nterms of the magnetic vector potential equation through the\nrelation between the magnetic flux density, B, and the mag-\nnetic vectorpotential, A,\nB=∇×A. (2)\nIf there are no currents present it is possible to express\nthe magneticvectorpotentialas\n−∇2A=∇×Brem. (3)\nFor the two dimensional case considered here the vector\npotentialonlyhasa z-component, Az,andtheaboveequation,\nusingEq. ( 1),isreducedto\n−∇2Az(r,φ)=Brem\nr(p+1)sin(pφ). (4)\nThis differentialequationconstitutesthemagneticvecto rpo-\ntential problem and must be solved. In the air region of the\nproblemtherighthandsidereducestozeroashere Brem=0.\nOnceAzhasbeen determinedEq. ( 2)can be used to find\nthe magnetic flux density. Afterwards the magnetic field, H,\ncanbe foundthroughtherelation\nB=µ0µrH+Brem, (5)\nwhereµris the relativepermeabilityassumedto beisotropic\nand independent of BandH. This is generally the case for\nhardpermanentmagneticmaterials.\n2.1 Geometryoftheproblem\nHavingfoundtheequationgoverningthemagnetostaticprob -\nlem oftheHalbachcylinderwe nowtakea closerlookat the\ngeometryoftheproblem. FollowingtheapproachofXiaetal.\n(11) we will start by solvingthe problemof a Halbachcylin-\nder enclosing a cylinder of an infinitely permeable soft mag-\nnetic material, while at the same time itself being enclosed\nby another such cylinder. This is the situation depicted in\nFig.2. This configuration is important for e.g. motor ap-\nplications. The Halbach cylinder has an inner radius of Riµ = \n8\nµ = \n8Magnet\nR\noRR\nRi\nc\ne\n                   Region III\nRegion I\nRegion II\nFigure2. A Halbachcylinderwithinnerradius Riandouter\nradiusRoenclosinganinfinitelypermeablecylinderwith\nradiusRcwhileitself beingenclosedbyanotherinfinitely\npermeablecylinderwithinnerradius Reandinfiniteouter\nradius. TheregionsmarkedIandIIIareairgaps.\nand an outer radius of Roand the inner infinitely permeable\ncylinderhasaradiusof Rcwhiletheouterenclosingcylinder\nhas a inner radius of Reand an infinite outer radius. Later\nin this paper we will solve the magnetostatic problem of the\nHalbach cylinder in air by letting Rc→0 andRe→∞. The\nuseofthesoftmagneticcylindersresultsinawelldefinedse t\nof boundaryequationsas will be shown later. Of course one\ncan also solve directly for the Halbach cylinder in air using\ntheboundaryconditionsspecific forthiscase.\nWhen solving the magnetostatic problem three different\nexpressions for the magnetic vector potential, field and flux\ndensity will be obtained, one for each of the three different\nregions shown in Fig. 2. The geometry of the problem re-\nsults in six boundaryconditions. The requirementis that th e\nradial component of Band the parallel component of Hare\ncontinuousacrossboundaries,i.e.\nHI\nφ=0|r=Rc\nBI\nr=BII\nr|r=Ri\nHI\nφ=HII\nφ|r=Ri\nBIII\nr=BII\nr|r=Ro\nHIII\nφ=HII\nφ|r=Ro\nHIII\nφ=0|r=Re. (6)\nThetwoequationsfor Hφ=0comefromthefactthatthesoft\nmagneticmaterialhasaninfinitepermeability.Analysisofthemagneticfield,force,andtorquefortwo-dim ensionalHalbachcylinders—3/ 11\n2.2 Solution forthevectorpotential\nThe solution to the vector potential equation, Eq. ( 4), is the\nsumofthesolutiontothehomogenousequationandapartic-\nularsolution. Thesolutionis\nAz(r,φ)=∞\n∑\nn=1(Anrn+Bnr−n)sin(nφ)+Bremr\np−1sin(pφ),\n(7)\nwhereAnandBnare constants that differ for each different\nregion and that are different for each n. Using the boundary\nconditionsforthegeometrydefinedaboveonecanshowthat\nthese areonlynonzerofor n=p.\nThusthesolutionforthedefinedgeometrybecomes\nAz(r,φ)=(Arp+Br−p)sin(pφ)+Bremr\np−1sin(pφ),(8)\nwhereAandBare constants that differ for each different\nregionandthataredeterminedbyboundaryconditions.\nThe solution is not valid for p=1. For this special case\nthe solutiontoEq. ( 4)isinstead\nAz(r,φ)=(Ar+Br−1)sin(φ)−Bremrln(r)sin(φ),(9)\nwhereAandBaredefinedlikeforEq. ( 8).\nNotethatfor p=0wehavethat Brem,r=BremandBrem,φ=\n0 in Eq. ( 1). This means that Az=0 and consequently Bis\nzero everywhere. The magnetic field, H, however, will be\nnonzero inside the magnetic material itself, i.e. in region II,\nbut will bezeroeverywhereelse.\nWe now derive the constants in Eq. ( 8) and (9) directly\nfromtheboundaryconditions.\n3. Derivingthevector potential constants\nTheconstantsofthevectorpotentialequationcanbederive d\nfrom the boundary conditions specified in Eq. ( 6). We first\nderivethe constantsforthecase of p/negationslash=1.\nFirst we note that the magneticflux density and the mag-\nnetic field can be calculated fromthe magnetic vector poten-\ntial\nBr=1\nr∂Az\n∂φ\nBφ=−∂Az\n∂r\nHr=1\nµ0µr(Br−Brem,r)\nHφ=1\nµ0µr(Bφ−Brem,φ). (10)Performingthedifferentiationgives\nBr=/bracketleftbigg\npArp−1+pBr−p−1+Bremp\np−1/bracketrightbigg\ncos(pφ)\nBφ=/bracketleftbigg\n−pArp−1+pBr−p−1−Brem1\np−1/bracketrightbigg\nsin(pφ)\nHr=/bracketleftbiggp\nµ0µr(Arp−1+Br−p−1)\n+Brem\nµrµ0/parenleftbiggp\np−1−1/parenrightbigg/bracketrightbigg\ncos(pφ)\nHφ=/bracketleftbiggp\nµ0µr(−Arp−1+Br−p−1)\n−Brem\nµrµ0/parenleftbigg1\np−1−1/parenrightbigg/bracketrightbigg\nsin(pφ). (11)\nUsing the radial component of the magnetic flux density\nandthe tangentialcomponentof the magneticfield in the set\nof boundary equations we get a set of six equations contain-\ningthesixunknownconstants,twoforeachregion. Thecon-\nstantsAandBwillbetermed AIandBIinregionI, AIIand\nBIIin regionII,and AIIIandBIIIinregionIII.\nIntroducingthefollowingnewconstants\na=R2p\ne−R2p\no\nR2p\ne+R2p\no\nb=−R2p\ni−R2p\nc\nR2p\ni+R2p\nc, (12)\ntheconstantsaredeterminedto be\nBII=−R1−p\no−R1−p\ni\nµra−1\nµra+1R−2p\no−µrb−1\nµrb+1R−2p\niBrem\np−1, (13)\nand\nAI=BII\nR2p\ni+R2p\nc/parenleftbigg\n1−µrb−1\nµrb+1/parenrightbigg\nBI=AIR2p\nc\nAII=−BIIµra−1\nµra+1R−2p\no−Brem\np−1R1−p\no\nAIII=BII\nR2p\no+R2p\ne/parenleftbigg\n1−µra−1\nµra+1/parenrightbigg\nBIII=AIIIR2p\ne. (14)\nUsingtheseconstantsinEq. ( 8)and(11)allowsonetocalcu-\nlate the magnetic vector potential, the magnetic flux densit y\nandthemagneticfieldrespectively.\nThe constants are not valid for p=1. The solution for\nthiscasewill bederivedina latersection.\n3.1 Halbach cylinder in air\nWe can find the solution for a Halbach cylinder in air if we\nlook at the solution for Re→∞andRc→0. Looking at theAnalysisofthemagneticfield,force,andtorquefortwo-dim ensionalHalbachcylinders—4/ 11\npreviousexpressionfortheconstants aandbwe see that\nforp>1 :a→1\nb→−1\nforp<0 :a→−1\nb→1(15)\nin thelimit definedabove.\nThismeansthat theconstant BIInowbecomes\nBII=\n\n−R1−p\no−R1−p\ni\nµr−1\nµr+1R−2p\no−µr+1\nµr−1R−2p\niBrem\np−1p>1\n−R1−p\no−R1−p\ni\nµr+1\nµr−1R−2p\no−µr−1\nµr+1R−2p\niBrem\np−1p<0(16)\nandtheremainingconstantsfor p>1become\n\nAI\nBI\nAII\nAIII\nBIII\n=\n\nBIIR−2p\ni/parenleftBig\n1−µr+1\nµr−1/parenrightBig\n0\n−BIIµr−1\nµr+1R−2p\no−Brem\np−1R1−p\no\n0\nBII/parenleftBig\n1−µr−1\nµr+1/parenrightBig(17)\nwhile for p<0 theybecome\n\nAI\nBI\nAII\nAIII\nBIII\n=\n\n0\nBII/parenleftBig\n1−µr−1\nµr+1/parenrightBig\n−BIIµr+1\nµr−1R−2p\no−Brem\np−1R1−p\no\nBIIR−2p\no/parenleftBig\n1−µr+1\nµr−1/parenrightBig\n0(18)\nThis is the solution for a Halbach cylinder in air. Note\nthat the solution is only valid for µr/negationslash=1. In the special case\nofµr=1the constantscanbereducedevenfurther.\n3.2 Halbach cylinderin air and µr=1\nWe now look at the special case of a Halbach cylinder in air\nwithµr=1. This is a relevant case as e.g. the highest en-\nergy density type of permanent magnet produced today, the\nso-called neodymium-iron-boron (NdFeB) magnets, have a\nrelativepermeabilityveryclose toone: µr=1.05(13).\nUsing the approximation of µr→1 for a Halbach cylin-\nderin airreducestheconstant BIIto\nBII=0. (19)\nTheremainingconstantsdependonwhethertheHalbach\ncylinderproducesan internalorexternalfield.\nFortheinternalfieldcase, p>1,theconstant AIIwillbe\ngivenby\nAII=−Brem\np−1R1−p\no. (20)\nThe constant AIdetermining the field in the inner air re-\ngionisequalto\nAI=Brem\np−1/parenleftBig\nR1−p\ni−R1−p\no/parenrightBig\n. (21)Theremainingconstants, BI,AIIIandBIIIarezero.\nUsing Eq. ( 11) the two componentsof the magneticflux\ndensityinboththecylinderbore,regionI,andinthemagnet ,\nregionII,canbe found.\nBI\nr=Bremp\np−1/parenleftBigg\n1−/parenleftbiggRi\nRo/parenrightbiggp−1/parenrightBigg\n×\n/parenleftbiggr\nRi/parenrightbiggp−1\ncos(pφ)\nBI\nφ=−Bremp\np−1/parenleftBigg\n1−/parenleftbiggRi\nRo/parenrightbiggp−1/parenrightBigg\n×\n/parenleftbiggr\nRi/parenrightbiggp−1\nsin(pφ)\nBII\nr=Bremp\np−1/parenleftBigg\n1−/parenleftbiggr\nRo/parenrightbiggp−1/parenrightBigg\ncos(pφ)\nBII\nφ=−Brem\np−1/parenleftBigg\n1−p/parenleftbiggr\nRo/parenrightbiggp−1/parenrightBigg\nsin(pφ).(22)\nConsidering now the external field case, p<0, the con-\nstantAIIisgivenby\nAII=−Brem\np−1R1−p\ni. (23)\nThe constant AIIIdetermining the field in the outer air\nregionisgivenby\nAIII=Brem\np−1/parenleftBig\nRp−1\no−Rp−1\ni/parenrightBig\n. (24)\nTheremainingconstants, AI,BIandBIIIarezero.\nAgain using Eq. ( 11) we find the two componentsof the\nmagneticfluxdensityinregionIIandIIItobe\nBIII\nr=Bremp\np−1/parenleftBigg\n1−/parenleftbiggRi\nRo/parenrightbigg−p+1/parenrightBigg\n×\n/parenleftbiggRo\nr/parenrightbigg−p+1\ncos(pφ)\nBIII\nφ=−Bremp\np−1/parenleftBigg\n1−/parenleftbiggRi\nRo/parenrightbigg−p+1/parenrightBigg\n×\n/parenleftbiggRo\nr/parenrightbigg−p+1\nsin(pφ)\nBII\nr=Bremp\np−1/parenleftBigg\n1−/parenleftbiggRi\nr/parenrightbigg−p+1/parenrightBigg\ncos(pφ)\nBII\nφ=−Brem\np−1/parenleftBigg\n1−p/parenleftbiggRi\nr/parenrightbigg−p+1/parenrightBigg\nsin(pφ).(25)\nTheequationsfor BIII\nrandBIII\nφareidenticaltotheexpressions\nforBI\nrandBI\nφin Eq. (22) except for a minus sign in both\nequations.Analysisofthemagneticfield,force,andtorquefortwo-dim ensionalHalbachcylinders—5/ 11\n3.3 Theconstantsfora p=1Halbach cylinder\nHaving determined the solution to the vector potential equa -\ntion and found the constants in the expression for the mag-\nneticfluxdensityandthemagneticvectorpotentialforaHal -\nbach cylinder both in air and enclosed by a soft magnetic\ncylinder for all cases except p=1 we now turn to this spe-\ncific case. This case is shown in Fig 1. We have already\nshown that the solution to the vector potential problem for\nthis case is given by Eq. ( 9). The boundary conditions are\nthe sameasprevious,i.e. theyaregivenbyEq. ( 6).\nInorderto findtheconstantsthe componentsofthemag-\nnetic field and the magnetic flux density must be calculated\nforp=1 as the boundary conditions relate to these fields.\nUsing Eq. ( 10)we obtain\nBr= [A+Br−2−Bremln(r)]cos(φ)\nBφ= [−A+Br−2+Brem(ln(r)+1)]sin(φ)\nHr=1\nµ0µr/bracketleftbig\nA+Br−2−Brem(ln(r)+1)/bracketrightbig\ncos(φ)\nHφ=1\nµ0µr/bracketleftbig\n−A+Br−2+Bremln(r)/bracketrightbig\nsin(φ).(26)\nUsingtheseexpressionsforthemagneticfluxdensityand\nthe magnetic field we can again write a set of six equations\nthrough which we can determine the six constants, two for\neachregion.\nReintroducingthetwoconstantsfromEq. ( 12)\na=R2\ne−R2\no\nR2e+R2o\nb=−R2\ni−R2\nc\nR2\ni+R2c, (27)\nthe followingequationsfortheconstantsareobtained:\nAI=BII\nR2\ni+R2c/parenleftbigg\n1−µrb−1\nµrb+1/parenrightbigg\nBI=AIR2\nc\nAII=−BIIµra−1\nµra+1R−2\no+Bremln(Ro)\nBII=−/parenleftbiggaµr−1\naµr+1R−2\no−µrb−1\nµrb+1R−2\ni/parenrightbigg−1\n×\nBremln/parenleftbiggRi\nRo/parenrightbigg\nAIII=BII\nR2e+R2o/parenleftbigg\n1−µra−1\nµra+1/parenrightbigg\nBIII=AIIIR2\ne. (28)\nWe see that the constants AI,BI,AIIIandBIIIare identical\nto theconstantsinEq. ( 14).\nThemagneticfluxdensityandthemagneticfieldcannow\nbe foundthroughtheuse ofEq. ( 26).3.4 Halbach cylinder in air, p=1\nWecanfindthesolutionfora p=1Halbachcylinderinairif\nwe look at the solution for Re→∞andRc→0. In this limit\nthepreviouslyintroducedconstantsarereducedto\na→1\nb→ −1. (29)\nTheexpressionsfortheconstantscanthenbe reducedto\nAI=BIIR−2\ni/parenleftbigg\n1−µr+1\nµr−1/parenrightbigg\nBI=0\nAII=−BIIµr−1\nµr+1R−2\no+Bremln(Ro)\nBII=−/parenleftbiggµr−1\nµr+1R−2\no−µr+1\nµr−1R−2\ni/parenrightbigg−1\n×\nBremln/parenleftbiggRi\nRo/parenrightbigg\nAIII=0\nBIII=BII/parenleftbigg\n1−µr−1\nµr+1/parenrightbigg\n. (30)\nAgain we see that the constants AI,BI,AIIIandBIIIare\nequal to the constants in Eq. ( 17). This solution is valid for\nallµrexceptµr=1.\nCombiningtheaboveconstantswithEq. ( 26)weseethat\nthe magnetic flux density in the cylinder bore is a constant,\nandthatitsmagnitudeisgivenby\n||BI||=/parenleftbiggµr−1\nµr+1R−2\no−µr+1\nµr−1R−2\ni/parenrightbigg−1\n×/parenleftbiggµr+1\nµr−1−1/parenrightbigg\nR−2\niBremln/parenleftbiggRi\nRo/parenrightbigg\n,(31)\nforµr/negationslash=1.\n3.5 Halbach cylinder in air, p=1andµr=1\nFor the special case of µr=1 for ap=1 Halbach cylinder\ninair theconstantscanbereducedfurtherto\nAI=Bremln/parenleftbiggRo\nRi/parenrightbigg\nAII=Bremln(Ro)\nBI,BII,AIII,BIII=0. (32)\nCombining the above constants with Eq. ( 26) one can\nfindthemagneticfluxdensityinthebore,regionI,andinthe\nmagnet,regionII,\nBI\nr=Bremln/parenleftbiggRo\nRi/parenrightbigg\ncos(φ)\nBI\nφ=−Bremln/parenleftbiggRo\nRi/parenrightbigg\nsin(φ)\nBII\nr=Bremln/parenleftbiggRo\nr/parenrightbigg\ncos(φ)\nBII\nφ=−Brem/parenleftbigg\nln/parenleftbiggRo\nr/parenrightbigg\n−1/parenrightbigg\nsin(φ). (33)Analysisofthemagneticfield,force,andtorquefortwo-dim ensionalHalbachcylinders—6/ 11\nAs for the case of µr/negationslash=1 the magnetic flux density in the\ncylinder bore is a constant. The magnitude of the magnetic\nfluxdensityinthe boreisgivenby\n||BI||=Bremln/parenleftbiggRo\nRi/parenrightbigg\n. (34)\nwhichwe recognizeasthewell knownHalbachformula( 2).\n3.6 Validity ofthesolutions\nTo show the validity of the analytical solutions we compare\nthesewithanumericalcalculationofthevectorpotentiala nd\nthe magneticfluxdensity.\nWe have chosen to show a comparison between the ex-\npressionsderivedinthispaperandnumericalcalculations for\ntwo selectedcases. Theseareshownin Fig. 3and4.\nIn Fig.3the magnitude of the magnetic flux density\nis shown for a enclosed Halbach cylinder. Also shown in\nFig.3is a numerical calculation done using the commer-\nciallyavailablefiniteelementmultiphysicsprogram, Comsol\nMultiphysics (14). The Comsol Multiphysics code has pre-\nviously been validated through a number of NAFEMS (Na-\ntional Agency for Finite Element Methods and Standards)\nbenchmark studies ( 15). As can be seen the analytical so-\nlutioncloselymatchesthenumericalsolution.\nIn Fig.4we show the magnetic vector potential, Az, as\ncalculatedusingEqs. ( 8)and(18)comparedwithanumerical\nComsol simulation. As can be seen the analytical solution\nagaincloselymatchesthe numericalsolution.\nWe havealsotestedtheexpressionsforthemagneticflux\ndensity given by Xia et. al.(2004)(11) and comparedthem\nwith those derived in this paper and with numerical calcula-\ntions. UnfortunatelytheequationsgivenbyXia et. al.(2004)\n(11)containerroneousexpressionsforthemagneticfluxden-\nsityofaHalbachcylinderinairwith µr=1aswellasforthe\nexpressionforaHalbachcylinderwithinternalfieldenclos ed\nbysoft magneticmaterial.\n4. Forcebetween twoconcentric Halbach\ncylinders\nHaving foundthe expressionsfor the magnetic vector poten-\ntial and the magnetic flux density for a Halbach cylinder we\nnowturntotheproblemofcalculatingtheforcebetweentwo\nconcentricHalbachcylinders,e.g. asituationasshowninF ig.\n5. In alater sectionwe will calculatethe torqueforthesame\nconfiguration. This configuration is interesting for e.g. mo -\ntor applications and drives as well as applications where th e\nmagneticfluxdensitymustbeturned“on”and“off”without\nthe magnetbeingdisplacedin space( 7).\nThe force between the two Halbach cylinderscan be cal-\nculated by using the Maxwell stress tensor,← →T, formulation.\nThe forceperunitlengthisgivenby\nF=1\nµ0/contintegraldisplay\nS← →T·dS. (35)Analytical solution \nx [mm] y [mm] \n−40 −20 0 20 40 −40 −20 020 40 \nNumerical solution \nx [mm] y [mm] \n−40 −20 0 20 40 −40 −20 020 40 \nFigure3. (Coloronline)Comparingtheanalyticalsolution\nasgivenbyEq. ( 11)and(14)witha numericalsolution\ncomputedusingComsol. Shownarecontoursof\n||B||=[0.3,0.5,0.7,0.9]T foraninternalfield p=2\nenclosedHalbachcylinderwith dimensions Rc=10mm,\nRi=20mm,Ro=30mm,Re=40mm,and Brem=1.4T,\nµr=1.05. Thesolutionsareseen tobeidentical. The\nshadedareasinthefigurescorrespondto thesimilarshaded\nareasin Fig. 2.Analysisofthemagneticfield,force,andtorquefortwo-dim ensionalHalbachcylinders—7/ 11\n0.006 0.006 \n0.008 0.008 \n−0.008 \n−0.008 −0.006 \n−0.006 0.002 0.002 \n0.004 0.004 \n0.006 0.006 −0.006 \n−0.006 −0.004 \n−0.004 −0.002 \n−0.002 Analytical solution in air \nx [mm]y [mm]\n−40 −20 020 40 −40 −20 020 40 \n0.006 0.006 \n0.008 0.008 \n−0.008 −0.006 \n−0.006 0.004 0.004 \n0.006 0.006 −0.006 \n−0.006 −0.004 \n−0.004 Numerical solution \nx [mm]y [mm]\n−40 −20 020 40 −40 −20 020 40 \nFigure4. (Coloronline)Comparingthe analyticalsolution\nasgivenbyEqs. ( 8)and(18)with anumericalsolution\ncomputedusingComsol. Shownare contoursof\nAz=±[0.002,0.004,0.006,0.008]Vsm−1foranexternal\nfieldp=−2Halbachcylinderinairwith dimensions\nRi=20mm,Ro=30mmand Brem=1.4T,µr=1.05. The\nredcontoursarepositivevaluesof Azwhiletheblueare\nnegativevalues. AswithFig. 3thesolutionsareseentobe\nidentical.φ\n0\nFigure5. Anexampleofa concentricHalbachcylinder\nconfigurationforwhichtheforceandtorqueiscalculated.\nTheoutermagnethas p=2 whiletheinnermagnetisa\np=−2. Theinnermagnethasalso beenrotatedanangleof\nφ0=45◦. Thedottedcircleindicatesa possibleintegration\npath.\nTheCartesian componentsoftheforcearegivenby\nFx=1\nµ0/contintegraldisplay\nS(Txxnx+Txyny)ds\nFy=1\nµ0/contintegraldisplay\nS(Tyyny+Tyxnx)ds, (36)\nwherenxandnyare the Cartesian components of the out-\nwards normal to the integration surface and where Txx,Tyy\nandTxyarethecomponentsoftheMaxwellstresstensorwhich\naregivenby\nTxx=B2\nx−1\n2(B2\nx+B2\ny)\nTyy=B2\ny−1\n2(B2\nx+B2\ny)\nTxy,Tyx=BxBy. (37)\nWhen using the above formulation to calculate the force\na closed integration surface in free space that surrounds th e\nobjectmustbechosen. Asthisisatwodimensionalproblem\nthe surface integral is reduced to a line integral along the a ir\ngapbetweenthemagnets. Ifacircleofradius ristakenasthe\nintegration path, the Cartesian components of the outwards\nnormalaregivenby\nnx=cos(φ)\nny=sin(φ). (38)\nExpressingtheCartesiancomponentsthroughthepolarcom-Analysisofthemagneticfield,force,andtorquefortwo-dim ensionalHalbachcylinders—8/ 11\nponentsas\nBx=Brcos(φ)−Bφsin(φ)\nBy=Brsin(φ)+Bφcos(φ), (39)\nthe relationforcomputingtheforceperunitlengthbecomes\nFx=r\nµ0/integraldisplay2π\n0/parenleftbigg1\n2(B2\nr−B2\nφ)cos(φ)−BrBφsin(φ)/parenrightbigg\ndφ\nFy=r\nµ0/integraldisplay2π\n0/parenleftbigg1\n2(B2\nr−B2\nφ)sin(φ)+BrBφcos(φ)/parenrightbigg\ndφ,\n(40)\nwhereris some radius in the air gap. The computed force\nwill turnouttobeindependentoftheradius rasexpected.\nWe consider the scenario where the outer magnet is kept\nfixed and the internal magnet is rotated by an angle φ0, as\nshowninFig. 5. Bothcylindersarecenteredonthesameaxis.\nBoth of the cylinders are considered to be in air and have a\nrelative permeability of one, µr=1, so that their magnetic\nflux density is given by Eqs. ( 22) and (25) forp/negationslash=1. For\np=1Eq. (33)appliesinstead.\nAsµr=1themagneticfluxdensityintheairgapbetween\nthe magnetswill be a sum oftwo terms, namelya term from\ntheoutermagnetandatermfromtheinnermagnet. Iftherel-\native permeabilitywere differentfromone the magneticflux\ndensity of one of the magnets would influence the magnetic\nfluxdensityoftheother,andwewouldhavetosolvethevec-\ntor potential equation for both magnets at the same time in\norderto findthemagneticfluxdensityintheairgap.\nAssuming the above requirementsthe flux density in the\nair gapisthusgivenby\nBr=BIII\nr,1+BI\nr,2\nBφ=BIII\nφ,1+BI\nφ,2, (41)\nwherethesecondsubscriptreferstoeitherofthetwomagnet s.\nTheinnermagnetistermed“1”andtheoutermagnettermed\n“2”, e.g. Ro,1is the inner magnets outer radius. The integer\np1thusreferstotheinnermagnetand p2totheoutermagnet.\nTherecanonlybe a forcebetweenthecylindersif the in-\nnercylinderproducesanexternalfieldandtheoutercylinde r\nproduces an internal field. Otherwise the flux density in the\ngap between the magnets will be produced solely by one of\nthe magnetsandtheforcewill bezero.\nPerforming the integrals in Eq. ( 40) one only obtains a\nnonzerosolutionfor p1=1−p2andp2>1. Inthiscase the\nsolutionis\nFx=2π\nµ0Kcos(p1φ0)\nFy=2π\nµ0Ksin(p1φ0), (42)\nwhereKisaconstantgivenby\nK=Brem,1Brem,2(Rp1\ni,2−Rp1\no,2)(Rp2\no,1−Rp2\ni,1).(43)0 60 120 180 240 300 360 −1 −0.8 −0.6 −0.4 −0.2 00.2 0.4 0.6 0.8 1x 10 5\nφ0 [degree]Fx and F y [N m −1 ]\n  \nFx,ana \nFy,ana \nFx,num \nFy,num \nFigure6. Thetwocartesiancomponentsoftheforceper\nunitlengthgivenbyEq. ( 42)comparedwitha Comsol\ncalculationforasystem wheretheoutermagnethas p2=2,\nRi,2=45mm,Ro,2=75mmand Brem,2=1.4Tandthe\ninnermagnethas p1=−1,Ri,1=15mm,Ro,1=35mmand\nBrem,1=1.4T.Theanalyticalexpressionisin excellent\nagreementwith thenumericaldata. Theforceisperunit\nlengthaswe consideratwo dimensionalsystem.\nNoticethatthe forceisindependentof r, asexpected.\nIn Fig.6we compare the above equation with a numer-\nical calculation of the force. The results are seen to be in\nexcellentagreement. Noticethattheforcesneverbalancet he\nmagnets,i.e. when Fxiszero,Fyisnonzeroandviceversa.\nIfp2=1themagneticfluxdensityproducedbytheouter\nmagnet is not given by Eq. ( 22) but is instead given by Eq.\n(33). However this equation has the same angular depen-\ndence as Eq. ( 22) and thus the force will also be zero for\nthiscase.\n5. Torquebetween twoconcentric nested\nHalbach cylinders\nHavingcalculatedtheforcebetweentwoconcentricHalbach\ncylinderswenowfocusoncalculatingthetorqueforthesame\nsystem.\nThe torque can also be calculated by using the Maxwell\nstress tensor,← →T, formulation. The torque per unit length is\ngivenby\nτ=1\nµ0/contintegraldisplay\nSr×← →T·dS\n=1\nµ0/contintegraldisplay\nSr/parenleftbigg\n(B·n)B−1\n2B2n/parenrightbigg\ndS, (44)\nwhere again the integration surface is a closed loop in free\nspace that surrounds the object. Again choosing a circle of\nradiusrastheintegrationpath,therelationforcomputingtheAnalysisofthemagneticfield,force,andtorquefortwo-dim ensionalHalbachcylinders—9/ 11\ntorqueperunitlengtharoundthecentralaxisbecomes\nτ=1\nµ0/integraldisplay2π\n0r2BrBφdφ, (45)\nwhereBrandBφarethe radialandtangentialcomponentsof\nthe magnetic flux density in the air gap and ris some radius\nintheairgap. Againthecomputedtorquewillbeshowntobe\nindependent of the radius rwhenrvaries between the inner\nandouterradiioftheair gap.\nWe consider the same case as with the force calculation,\ni.e. the outer magnet is kept fixed, both magnets have the\nsame axis, the internal magnet is rotated by an angle φ0and\nboth of the cylinders are considered to be in air and have\na relative permeability of one. Again there can only be a\ntorque between the cylinders if the inner cylinder produces\nan external field and the outer cylinder produces an internal\nfield.\nTofindthetorqueperunitlengthwe mustthusintegrate\nτ=1\nµ0/integraldisplay2π\n0r2(BIII\nr,1+BI\nr,2)(BIII\nφ,1+BI\nφ,2)dφ.(46)\nThisintegrationwill bezeroexceptwhen p1=−p2. For\nthisspecialcase theintegralgives\nτ=2π\nµ0p2\n2\n1−p2\n2K1K2sin(p2φ0), (47)\nwheretheconstants K1andK2are givenby\nK1=Brem,2/parenleftBig\nR1−p2\ni,2−R1−p2\no,2/parenrightBig\nK2=Brem,1/parenleftBig\nRp2+1\no,1−Rp2+1\ni,1/parenrightBig\n. (48)\nThe validity of this expression will be shown in the next\nsection. It isseenthatthereare p2periodsperrotation.\nForp2=1 the expression for the magnetic flux density\nproduced by the outer magnet is not given by Eq. ( 22) but\ninstead by Eq. ( 33),and so we must lookat this special case\nseparately.\n5.1 Thespecial caseof p2=1\nForthespecialcaseofa p2=1outermagnetthefluxdensity\nproduced by this magnet in the air gap will be given by Eq.\n(33). The externalfield producedbythe innermagnetis still\ngivenbyEq. ( 25).\nPerformingtheintegrationdefinedinEq. ( 46)againgives\nzero except when p2=1 andp1=−1. The expression for\nthe torquebecomes\nτ=−π\nµ0K2K3sin(φ0) (49)\nwherethetwo constants K2andK3aregivenby\nK2=Brem,1/parenleftbig\nR2\no,1−R2\ni,1/parenrightbig\n(50)\nK3=Brem,2ln/parenleftbiggRo,2\nRi,2/parenrightbigg\n.\nNote that K2is identical to the constant K2in Eq. (48) for\np2=1. We also see that Eq. ( 49) is in fact just τ=m×B\nfora dipoleina uniformfield timestheareaofthemagnet.Table1.Theparametersforthetwo casesshownin Fig. 7\nand8.\nMagnet RiRop Brem\n[mm] [mm] [T]\nCase 1:inner 5 15 -2 1.4\nouter 20 30 2 1.4\nCase 2:inner 10 35 -1 1.4\nouter 45 75 1 1.4\n5.2 Validating theexpressions forthetorque\nWe have shown that there is only a torque between two Hal-\nbachcylindersif p1=−p2forp2>0,withthetorquebeing\ngivenbyEq. ( 47)forp2/negationslash=1andEq. ( 49)forp2=1.\nTo verify the expressionsgiven in Eq. ( 47) and Eq. ( 49)\nwe have computed the torque as a function of the angle of\ndisplacement, φ0, for the two cases given in Table 1, and\ncomparedthis with a numericalcalculation performedusing\nComsol. Theresultscanbeseen inFig. 7and8.\n0 60 120 180 240 300 360 −800 −600 −400 −200 0200 400 600 800 \nφ0 [degree]τ [N]\n  \nAnalytical\nNumerical\nFigure7. A numericalcalculationofthetorqueperunit\nlengthbetweentwoconcentricHalbachcylinderscompared\nwiththe expressiongiveninEq. ( 47)forthephysical\npropertiesgivenforCase 1 inTable 1. Theanalytical\nexpressionisinexcellentagreementwiththenumericaldat a.\nτisperunitlengthaswe consideratwo dimensional\nsystem.\nAs can be seen from the figures the torque as given by\nEq. (47) and Eq. ( 49) are in excellent agreement with the\nnumericalresults.\n6. Forceand Torqueforfinitelength\ncylinders\nTheforceandtorqueforfinitelengthcylinderswillbediffe r-\nentthantheanalyticalexpressionsderivedabove,because of\nfluxleakagethroughtheendsofthecylinderbore.\nTo investigate the significance of this effect three dimen-\nsional numerical simulations of a finite length system corre -\nsponding to the system shown in Fig. 6has been performedAnalysisofthemagneticfield,force,andtorquefortwo-dim ensionalHalbachcylinders— 10/ 11\n0 60 120 180 240 300 360 −3000 −2000 −1000 01000 2000 3000 \nφ0 [degree]τ [N]\n  \nAnalytical\nNumerical\nFigure8. ThetorqueperunitlengthgivenbyEq. ( 49)\ncomparedwitha numericalcalculationforthephysical\npropertiesgivenforCase 2inTable 1. Aswiththecase for\np2/negationslash=1,i.e. Fig. 7,theanalyticalexpressionisin excellent\nagreementwiththe numericaldata. τisperunitlengthas\nwe considera twodimensionalsystem.\nusing Comsol. For this system the force has been calculated\nper unit length for differentlengths. The results of these c al-\nculations are shown in Fig. 9. From this figure it can be\nseen that as the length of the system is increased the force\nbecomesbetterapproximatedbytheanalyticalexpressiono f\nEq. (42). A short system produces a lower force due to the\nleakage of flux through the ends of the cylinder. However,\nevenforrelativelyshortsystemsthe two-dimensionalresu lts\ngive the right order of magnitudeand the correct angular de-\npendenceoftheforce.\nSimilarly, the torque for a three dimensional system has\nbeen considered. Here the system given as Case 1 in Ta-\nble1was considered. Numericalsimulationscalculating the\ntorquewereperformed,similarto theforcecalculations,a nd\nthe results are shown in Fig. 10. The results are seen to be\nsimilar to Fig. 9. The torque approaches the analytical ex-\npression as the length of the system is increased. As before\nthe twodimensionalresultsarestill qualitativelycorrec t.\nAbove we have considered cases where the two dimen-\nsional results predicta force( p1=1−p2) or a torque( p1=\n−p2). However,for finite length systems a force or a torque\ncan be present in other cases. One such case is given by\nMhiochainetal. ( 12)whoreporta maximumtorqueof ≈12\nNm for a system where both magnets have p=1, are seg-\nmented into 8 pieces and where the outer magnet has Ri,2=\n52.5 mm,Ro,2=110 mm, L2=100 mm and Brem,2=1.17\nT and the inner magnet has Ri,1=47.5 mm,Ro,1=26 mm,\nL1=100 mm and Brem,1=1.08 T. This torque is produced\nmainlybythe effectoffinite lengthandto a lesser degreeby\nsegmentation. The torque producedby this system is ≈120\nN per unit length, which is significant compared to the ex-\npected analytical value of zero. The torque for finite lengthL = 0.25*R o,2L = 0.5*R o,2\nL = 1*R o,2L = 2*R o,2\nL = 10*R o,2Fx,ana Fy,ana φ0 [degree] Fx and F y [N m −1 ]\n0 60 120 180 240 300 360 −1 −0.8 −0.6 −0.4 −0.2 00.2 0.4 0.6 0.8 1x 10 5\nFigure9. Thetwocartesiancomponentsoftheforceper\nunitlengthforathreedimensionalsystemwithdimensions\nasthosegiveninFig. 6. Theanalyticalexpressionsaswell\nastheresultsofathreedimensionalnumericalsimulation\nareshown.\nAnalytical \nL = 0.25*R o,2L = 0.5*R o,2\nL = 1*R o,2L = 2*R o,2\nL = 10*R o,2φ0 [degree] τ [N]\n0 60 120 180 240 300 360 −800 −600 −400 −200 0200 400 600 800 \nFigure10. Thetorqueperunitlengthfora three\ndimensionalsystemwithdimensionsasthosegivenasCase\n1inTable 1. Theanalyticalexpressionsaswellastheresults\nofathreedimensionalnumericalsimulationareshown.\nsystems with p1/negationslash=−p2is, as notedabove,a higherorderef-\nfect. This makes it significantly smaller per unit length tha n\nforthecorrespondingsystem with p1=−p2.\n10this system, which is designed to have a torque, pro-\nducea largertorqueeventhoughthe systemismuchsmaller.\nThe end effects due to a finite length of the system canAnalysisofthemagneticfield,force,andtorquefortwo-dim ensionalHalbachcylinders— 11/ 11\nberemediedbyseveraldifferenttechniques. Bycoveringth e\nends of the concentric cylinder with magnet blocks in the\nshape of an equipotential surface, all of the flux can be con-\nfined inside the Halbach cylinder ( 16). Unfortunately this\nalso blocksaccess to the cylinderbore. The homogeneityof\nthefluxdensitycanalsobeimprovedbyshimming,i.e. plac-\ning small magnets or soft magnetic material to improve the\nhomogeneity ( 17;18;19). Finally by sloping the cylinder\nboreorbyplacingstrategiccutsinthemagnetthehomogene-\nity can also be improved ( 20). However, especially the last\ntwo methods can lower the flux density in the bore signifi-\ncantly.\n7. Discussion and conclusion\nWe have derived expressions for the magnetic vector poten-\ntial,magneticfluxdensityandmagneticfieldforatwodimen-\nsional Halbach cylinder and compared these with numerical\nresults.\nTheforcebetweentwoconcentricHalbachcylinderswas\ncalculated and it was found that the result depends on the\nintegerpin theexpressionforthe remanence. If pforthe in-\nnerandoutermagnetis termed p1andp2respectivelyit was\nshown that unless p1=1−p2there is no force. The torque\nwas also calculated for a similar system and it was shown\nthat unless p1=−p2there is no torque. We compared the\nanalytical expressions for the force and torque to numerica l\ncalculations and found an excellent agreement. Note that ei -\nthertherecanbea forceora torque,butnotboth.\nThe derived expressions for the magnetic vector poten-\ntial, flux density and field can be used to do e.g. quick pa-\nrameter variation studies of Halbach cylinders, as they are\nmuchmoresimplethanthecorrespondingthreedimensional\nexpressions.\nAninterestinguseforthederivedexpressionsforthemag-\nneticfluxdensitywouldbetoderiveexpressionsfortheforc e\nbetween two concentricHalbachcylinders,whereone of the\ncylinders has been slightly displaced. One could also con-\nsider the effect of segmentationof the Halbach cylinder,an d\nof course the effect of a finite length in greater detail. Both\neffectswillingeneralresultinanonzeroforceandtorquef or\notherchoicesof p1andp2,butasshownthesewillingeneral\nbe smallerthanforthe p1=1−p2andp1=−p2cases.\nItisalsoworthconsideringcomputingtheforceandtorque\nfor Halbach cylinders with µr/negationslash=1. Here one would have to\nsolvethecompletemagnetostaticproblemofthetwoconcen-\ntricHalbachcylinderstofindthemagneticfluxdensityinthe\ngapbetweenthecylinders.\nAcknowledgements\nThe authors would like to acknowledge the support of the\nProgrammeCommissiononEnergyandEnvironment(EnMi)\n(Contract No. 2104-06-0032) which is part of the Danish\nCouncilforStrategicResearch.References\n[1]J. C. Mallinson,IEEETrans.Magn.9 (4)(1973),678.\n[2]K.Halbach,Nucl.Instrum.Methods169(1980).\n[3]Z.Q. Zhu and D. Howe, IEE Proc. Elec. Power. Appl.\n148(4)(2001),299.\n[4]J. M.D. Coey,J.Magn.Magn.Mater.248(2002),441.\n[5]S. Appelt, H. K¨ uhn, F. W H¨ asing, and B. Bl¨ umich, Nat.\nPhys.2(2006),105.\n[6]J.K. Lim, P. Frigola, G. Travish, J.B. Rosenzweig, S.G.\nAnderson, W. J. Brown, J. S. Jacob, C. L. Robbins, and\nA.M.Tremaine,Phys.Rev.ST - Accel.Beams8 (2005),\n072401.\n[7]A. Tura and A. Rowe, Proc. 2nd Int. Conf. on Magn.\nRefrig. at Room Temp., Portoroz, Solvenia, IIF/IIR:363\n(2007).\n[8]Z.Q. Zhu, D. Howe, E. Bolte, and B. Ackermann, IEEE\nTrans.Magn.29(12)(1993),124.\n[9]K. Atallah, D. Howe, and P.H. Mellor, Eighth Int. Conf.\non Elec. Mach. and Driv. (Conf. Publ. No.444) (1997),\n376.\n[10]Q. Peng,S. M.McMurry,andJ.M.D.Coey,IEEETrans.\nMagn.39(42)(2003),1983.\n[11]Z.P.Xia,Z.Q.Zhu,andD.Howe,IEEETrans.Magn.40\n(2004),1864.\n[12]T. R. Ni Mhiochain, D. Weaire, S. M. McMurry, and J.\nM.D. Coey,J. Appl.Phys.86(1999),6412.\n[13]Standard Specifications for Permanent Magnet Materi-\nals, Magn.Mater.Prod.Assoc., Chicago,USA (2000).\n[14]COMSOL AB, Tegn` ergatan 23, SE-111 40 Stockholm,\nSweden.\n[15]Comsol, Comsol Multiphysics Model Library, third ed.\nCOMSOL AB, ChalmersTeknikpark41288G (2005).\n[16]E. Potenziani, J. P. Clarke, and H. A. Leupold, J. Appl.\nPhys.61(1987),3466.\n[17]M.G.Abele,H.Rusinek,andW.Tsui,J.Appl.Phys.99\n(8)(2006),903\n[18]R.Bjørk,C.R.H.Bahl,A.Smith,andN.Pryds,J.Appl.\nPhys.,104(2008),13910\n[19]A. Rowe, and A. Tura, J. Magn. Magn. Mater. 320\n(2008),1357.\n[20]J.E.Hilton,andS.M.McMurry,IEEETrans.Magn.,43\n(5)(2007),1898"    },    {        "title": "1409.8046v1.Review_and_comparison_of_magnet_designs_for_magnetic_refrigeration.pdf",        "content": "Published in International Journal of Refrigeration, Vol. 33 (3), 437-448, 2010\nDOI: 10.1016/j.ijrefrig.2009.12.012\nReview and comparison of magnet designs for\nmagnetic refrigeration\nR. Bjørk, C. R. H. Bahl, A. Smith and N. Pryds\nAbstract\nOne of the key issues in magnetic refrigeration is generating the magnetic field that the magnetocaloric material\nmust be subjected to. The magnet constitutes a major part of the expense of a complete magnetic refrigeration\nsystem and a large effort should therefore be invested in improving the magnet design. A detailed analysis of\nthe efficiency of different published permanent magnet designs used in magnetic refrigeration applications is\npresented in this paper. Each design is analyzed based on the generated magnetic flux density, the volume of\nthe region where this flux is generated and the amount of magnet material used. This is done by characterizing\neach design by a figure of merit magnet design efficiency parameter, Lcool. The designs are then compared and\nthe best design found. Finally recommendations for designing the ideal magnet design are presented based on\nthe analysis of the reviewed designs.\nDepartment of Energy Conversion and Storage, Technical University of Denmark - DTU, Frederiksborgvej 399, DK-4000 Roskilde, Denmark\n*Corresponding author : rabj@dtu.dk\n1. Introduction\nMagnetic refrigeration is an evolving cooling technology that\nhas the potential of high energy efficiency using environmen-\ntally friendly refrigerants. Magnetic refrigeration utilizes\nthe magnetocaloric effect (MCE), which is the temperature\nchange that most magnetic materials exhibit when subjected to\na changing magnetic field. This temperature change is called\nthe adiabatic temperature change, DTad, and is a function of\ntemperature and magnetic field. The temperature change is\ngreatest near the Curie temperature, Tc, which is different for\ndifferent magnetocaloric materials [Pecharsky and Gschneid-\nner Jr, 2006]. Because the MCE in the best magnetocaloric\nmaterials currently available exhibit a temperature change of\nno more than 4 K in a magnetic field of 1 T, a magnetic refrig-\neration device must utilize a regenerative process to produce\na large enough temperature span to be useful for refrigeration\npurposes. The most utilized process for this is called active\nmagnetic regeneration (AMR).\nAt present, a great number of magnetic refrigeration test\ndevices have been built and examined in some detail, with\nfocus on the produced temperature span and cooling power of\nthe devices [Barclay, 1988; Yu et al., 2003; Gschneidner and\nPecharsky, 2008]. So far the magnet, a key component in the\nmagnetic refrigeration system, has been largely overlooked,\neven though it is often the single most expensive part of a\nmagnetic refrigerator. Also little effort has been made to\ncompare existing magnet designs in order to learn to design\nmore efficient magnetic structures.\nIn general a magnet design that generates a high magnetic\nflux density over as large a volume as possible while using\na minimum amount of magnet material is to be preferred.\nSince the magnet is expensive it is also important that themagnetic refrigerator itself is designed to continuously utilize\nthe magnetic flux density generated by the magnet.\n1.1 Magnetic refrigeration magnets\nAs previously stated a substantial number of magnetic refrig-\neration devices have been built. In all devices, one of three\ntypes of magnets has been used to generate the magnetic field.\nThe first magnetic refrigeration device used a superconducting\nelectromagnet [Brown, 1976], and other systems also using a\nsuperconducting electromagnet have since been built [Zimm\net al., 1998; Blumenfeld et al., 2002; Rowe and Barclay, 2002].\nDevices using a non superconducting electromagnet have also\nbeen constructed [Bahl et al., 2008; Coelho et al., 2009], but\nthe greater majority of devices built in recent years have used\npermanent magnets to generate the magnetic field [Bohigas\net al., 2000; Lee et al., 2002; Lu et al., 2005; Vasile and\nMuller, 2006; Okamura et al., 2007; Tura and Rowe, 2007;\nZimm et al., 2007; Zheng et al., 2009; Engelbrecht et al.,\n2009].\nThe reason permanent magnets are preferred is that they\ndo not require power to generate a magnetic field. This is\nnot the case for an electromagnet where a large amount of\npower is needed to generate e.g. a 1 T magnetic flux density\nin a reasonable volume. This can be seen from the relation\nbetween the current, I, and the generated flux density, B, for an\nelectromagnet in a single magnetic circuit consisting of a soft\nmagnetic material with relative permeability, mr, and where\nthe core has roughly the same cross sectional area throughout\nits length and the air gap is small compared with the cross\nsectional dimensions of the core,\nNI=B\u0012Lcore\nmrm0+Lgap\nm0\u0013\n; (1)arXiv:1409.8046v1  [physics.ins-det]  29 Sep 2014Review and comparison of magnet designs for magnetic refrigeration — 2/12\nwhere Nis the number of turns in the winding, Lcoreis the\nlength of the soft magnetic material, m0is the permeability\nof free space and Lgapis the length of the air gap. In order to\ngenerate a 1.0 T magnetic flux density over e.g. a 30 mm air\ngap, which is typical for a magnetic refrigeration device, an\niron cored solenoid with mr=4000 would need to have 24000\nampere windings. The length of the soft magnetic material\nis irrelevant as the expression is dominated by the second\nterm. Such an electromagnet with 24000 ampere windings\nwould need a massive power supply and an equally massive\ncooler to prevent the solenoid from overheating. Based on\nthis simple calculation, it can be seen why an electromagnet\nis not preferred in most magnetic refrigeration devices.\nA superconducting electromagnet is a better option than\nthe traditional electromagnet because it requires little power to\noperate once the electromagnet has become superconducting\nas no power is lost to ohmic resistance. Although a super-\nconducting electromagnet can create magnetic flux densities\nof the order of 10 T, continuous cooling is needed. This\ncan be an expensive process and the apparatus surrounding\nthe superconducting electromagnet can be of substantial size.\nHowever for large scale applications, e.g. large refrigerators\nfor warehouses etc., a superconducting electromagnet might\nbe a relevant solution. For common household refrigeration\nthe superconducting electromagnet is at present not an option.\nThe only suitable choice left for generating the magnetic\nfield is permanent magnets, which require no power to gener-\nate a flux density. The remainder of this paper will be concen-\ntrating on permanent magnet magnetic refrigerators, useable\nin common household refrigeration, as almost all research in\nmagnetic refrigeration is focussed on this area. However the\nconclusions from this article will be applicable to any device\nusing magnetocaloric materials, e.g. heat pumps, and not only\nmagnetic refrigeration devices.\n2. Characterizing a magnet design\nWhen reviewing different magnet designs it is of the utmost\nimportance that the different designs can be compared using a\nsimple figure of merit. A previous suggestion for a comparison\nparameter was defined using the masses of the magnet and that\nof the magnetocaloric material used in the device [Nikly and\nMuller, 2007]. This parameter is not useful for two reasons:\nit contains no information about the magnetic flux density\nproduced by the magnet design and using the same magnetic\nstructure with two different magnetocaloric materials with\ndifferent densities will yield different characterization results.\nA general figure of merit, M\u0003, used to characterize a mag-\nnet design is defined by Jensen and Abele [1996] as\nM\u0003=R\nVfieldB2dV\nR\nVmagB2remdV(2)\nwhere Vfieldis the volume of the region where the magnetic\nfield is created and Vmagis the volume of the magnets. It\ncan be shown that the maximum value of M\u0003is 0.25, and a\nstructure is considered reasonably efficient if it has M\u0003\u00150:1.The strength of the magnetic field that is generated can\nalso be quantified by a dimensionless number, K, which is the\nratio between the magnetic flux density and the remanence\nof the magnets [Coey and Ni Mhiochain , 2003]. For a two\ndimensional structure with completely uniform remanence\nand magnetic flux density the two numbers KandM\u0003are\nrelated by the expression\nM\u0003=K2Afield\nAmag: (3)\nwhere Afieldis the area of the high flux density region and\nAmagis the area of the magnet. The figure of merit, M\u0003, often\nshown as a function of K, is useable for characterizing magnet\ndesigns in general, but for magnet design used in magnetic\nrefrigeration the parameter does not take into account the flux\ndensity in the low field region of the magnet system where the\nmagnetocaloric material is placed when it is demagnetized.\nAlso, and more importantly, the scaling of the magnetocaloric\neffect itself with magnetic field is not taken into account. The\nimportance of this will be considered shortly.\nFinally a general performance metric for active magnetic\nrefrigerators has been suggested [Rowe, 2009a]. The cost\nand effectiveness of the magnet design is included in this\nmetric as a linear function of the volume of the magnet. The\ngenerated flux density is also included in the metric. However,\nthe metric does not make it possible to evaluate the efficiency\nof the magnet design alone.\nHere the Lcoolparameter proposed by Bjørk et al. [2008]\nwill be used to characterize a magnet design for use in mag-\nnetic refrigeration. This parameter is designed to favor magnet\ndesigns that generate a high magnetic flux density in a large\nvolume using a minimum of magnetic material. It also fa-\nvors system designs in which the amount of time where the\nmagnetic flux density is ”wasted” by not magnetizing a mag-\nnetocaloric material is minimized.\n2.1 The Lcoolparameter\nTheLcoolparameter is a figure of merit that depends on a num-\nber of different parameters related to the magnetic assembly\nbeing evaluated.\nTheLcoolparameter is defined as\nLcool\u0011\u0010\nhB2=3i\u0000hB2=3\nouti\u0011Vfield\nVmagPfield; (4)\nwhere Vmagis the volume of the magnet(s), Vfieldis the volume\nwhere a high flux density is generated, Pfieldis the fraction of\nan AMR cycle that magnetocaloric material is placed in the\nhigh flux density volume, hB2=3iis the volume average of the\nflux density in the high flux density volume to the power of\n2/3 andhB2=3\noutiis the volume average of the flux density to the\npower of 2/3 in the volume where the magnetocaloric mate-\nrial is placed when it is being demagnetized. Some of these\nvariables are illustrated for the case of a Halbach cylinder in\nFig. 1. Note that it is the magnetic flux density generated\nin an empty volume that is considered, and so B=m0H, andReview and comparison of magnet designs for magnetic refrigeration — 3/12\n<B2/3 >VV\nfield mag \n<Bout2/3 >MC plateMC plate\nFigure 1. An illustration of some of the different variables in\ntheLcoolparameter for the case of a Halbach cylinder. A\nplate of magnetocaloric (MC) material is shown in both the in\nand out of field position.\nthus it is equivalent to speak of the magnetic flux density or\nthe magnetic field.\nNotice that Lcooldepends on the flux density to the power\nof 2/3. The reason for this is that Lcoolis defined to be propor-\ntional to the temperature change of the magnetocaloric mate-\nrial, and not the magnetic flux density, as the former is what\nis used to generate the temperature span and cooling power\nof the refrigeration device. This temperature change does not\nscale linearly with the magnetic flux density. A large number\nof different materials have been suggested as the active com-\nponent of a magnetic refrigeration machine [Gschneidner Jr\net al., 2005]. The adiabatic temperature change at the Curie\ntemperature of a general second order magnetocaloric phase\ntransition material is predicted by mean field theory to scale\nwith the power of 2/3 of the magnetic field [Oesterreicher\nand Parker, 1984]. This is in good accordance with the ma-\nterial most often used, i.e. the “benchmark” magnetocaloric\nmaterial at room temperature, gadolinium, which has a mag-\nnetocaloric effect that scales with the magnetic field to the\npower of 0.7 at the Curie temperature [Pecharsky and Gschnei-\ndner Jr, 2006], as also shown in Fig. 2. This is why the Lcool\nparameter is proportional to the magnetic flux density to the\npower of 2/3. The scaling of the adiabatic temperature change\naway from Tcwill in general be different from 2/3, but as\nlong as the exponent is below 1 the conclusions of this article\nremain substantially unchanged. It should be noted that the\nentropy change of a number of magnetocaloric materials also\nscales as a power law with an exponent that in general is of\nthe order of 2/3 [Franco et al., 2007; Dong et al., 2008].\nIt is not only the flux density in the magnetization region\nthat is of importance to the magnetocaloric effect. The volume\nin which the magnetocaloric material is placed when it is\nµ0H [T] ∆Tad  [K] \n00.2 0.4 0.6 0.8 11.2 1.4 1.6 1.8 20123456∆Tad  = κ ( µ0H) γ\nκ = 3.82 ± 0.04 K \nγ = 0.71 ± 0.02 Figure 2. The scaling of the adiabatic temperature change of\nGadolinium as a function of magnetic field at Tc(293 :6 K).\nData are from Pecharsky and Gschneidner [2008] and are\ncorrected for demagnetization using Aharoni [1998].\ndemagnetized is equally important. In order to maximize the\nmagnetocaloric effect, the flux density in this volume must\nbe as low as possible. In a reciprocating device this can of\ncourse be accomplished by simply moving the magnetocaloric\nmaterial far away from the magnet, but this will increase the\nphysical size and cycle time of the magnetic refrigeration\nmachine. In a rotating device the high and low flux density\nregions will generally be adjacent and care must be taken to\nminimize the “leak” of flux into the low flux density region.\nTo take into account the amount of magnetocaloric mate-\nrial that can experience a temperature change, the Lcoolpa-\nrameter is proportional to the volume of the high flux density\nregion. Note that Lcoolis proportional to the whole volume of\nthe high flux density region and not only the volume occupied\nby the magnetocaloric material. Thus Lcooldoes not depend\non the porosity of the magnetocaloric material, nor on the\namount of e.g. plastic housing used to confine the magne-\ntocaloric material. Also Lcoolis inversely proportional to the\nvolume of magnet material used, as the more magnet material\nused the more expensive the design will be.\nFinally, the Lcoolparameter is proportional to the fraction\nof the AMR cycle in which magnetocaloric material is placed\nin the high flux density volume. The reason for this is that if,\ne.g., magnetocaloric material is only placed inside the high\nflux density volume half the time of a full AMR cycle, the\n(expensive) magnet is not utilized during the remaining half\nof the cycle and it is thus essentially being wasted during this\ntime. The fraction of time the magnetic flux generated by the\nmagnet is being used to generate a magnetocaloric effect must\nbe maximized.\nOne should note that the Lcoolparameter will favor a\ndesign with a small magnetic flux density and large volume\nof the high flux density region. This is because the magneticReview and comparison of magnet designs for magnetic refrigeration — 4/12\nflux generated by a magnet scales with a power less than 2/3\nwith the volume of the magnet. In an actual device, heat\ntransfer rates and thermal losses will set a lower limit on\nthe flux density needed to produce a given temperature span\nand cooling capacity. Therefore for practical applications\none would choose to optimize Lcoolunder the condition of a\ncertain minimum flux density in the high flux density region.\nThe remanence of the magnets is not explicitly consid-\nered in the Lcoolparameter. The reason for this is twofold.\nFirst this information is almost always not available for pub-\nlished magnet designs. Secondly the remanence of the NdFeB\nmagnets used in all magnetic refrigeration magnet assemblies\nvaries only between 1.2-1.4 T and so the exact value is not crit-\nical for comparison of different designs. Therefore, geometry\naccounts for almost all of the differences between different\ndesigns. Any soft magnetic material used in the magnet as-\nsembly is ignored, as the price of this material is in general\nmuch lower than that of the permanent magnets.\n3. Published magnet designs\nHaving introduced the Lcoolparameter, different published\nmagnet designs can now be compared. There exist a substan-\ntial number of published designs of magnetic refrigerators\nbut unfortunately many publications lack the necessary spec-\nifications to either reconstruct or directly calculate the Lcool\nparameter [Richard et al., 2004; Shir et al., 2005; Zimm et al.,\n2006; Buchelnikov et al., 2007; Chen et al., 2007; Vuarnoz\net al., 2007; Coelho et al., 2009; Dupuis et al., 2009; Sari et al.,\n2009]. The designs presented below are the ones that repre-\nsents the main magnets configurations and contain sufficient\ninformation to calculate Lcool. A short description of each\ndesign is given prior to the calculation.\nIt should be noted that many of the magnetic refrigerators\npresented here are test devices and should be evaluated as\nsuch. However, it is also in the test design phase that large im-\nprovements to the design should be suggested. Therefore the\nevaluation of the designs can potentially lead to improvements\nfor both current and future magnetic refrigerators.\nFor all designs an “ideal” device is considered when es-\ntimating the Pfieldparameter. In such a device the time for\nmoving either the magnet or a bed of magnetocaloric material\nis minimized. This has been done in order that the Lcoolpa-\nrameter will not depend on, e.g., the power of the motor in the\ndevice. An example is the rotating design by Okamura et al.\n[2007], shown in a later section. Using the actual rotation\nspeed of the magnet gives Pfield=0:66. However, we estimate\nthat using a more powerful motor would allow Pfield=0:9. In\nthe calculation of Lcoolfor the given design the latter value\nwill be used. The AMR cycle is assumed to be symmetric, i.e.\nthe magnetization and demagnetization steps are assumed to\ntake the same amount of time.\nThe designs reviewed here have been classified into three\ngroups, depending on the complexity of the design. After\nall designs have been presented the designs are compared in\nTable 1.\nFigure 3. The design by Zheng et al. [2009]. From Zheng\n[2009]. The arrow indicate the direction of magnetization of\nthe magnet. The blue structure consists of soft magnetic\nmaterial.\n3.1 Simple magnetic circuits\nThe designs presented in this subsection all have a simple geo-\nmetric structure and consist of rectangular blocks of magnets.\n3.1.1 Design by Zheng et al. [2009]\nThe general refrigerator design by Zheng et al. [2009] is a\nreciprocating design where the magnet is moving and two\npacked beds of magnetocaloric material are kept stationary.\nWhen one of the beds is in the magnetic field the other bed\nis out of the field. The flux density in the design is provided\nby a single rectangular magnet and the flux lines are guided\nby a soft magnetic material through a small air gap, as shown\nin Fig. 3. Based on Zheng [2009] the volume of the magnet\nis 0.5 L and the volume of the high flux density region is\n0.09 L. The mean magnetic flux density is 0.93 T. Based on\nthe cycle time, movement speed of the beds and the distance\nbetween these the actual Pfieldparameter is calculated to be\n0.60. However using a faster and more powerful motor to\nmove the magnet, as well as considering that the magnet has\nto be moved across a finite distance between the beds where\nno magnetocaloric material is present, the Pfieldparameter\ncould be as high as 0.90.\n3.1.2 Design by Vasile and Muller [2006]\nThe magnet design by Vasile and Muller [2006] is a “C”\nshaped magnet assembly of rectangular magnet blocks with\nsoft magnetic material inside and outside of the “C” as seen in\nFig. 4. In this design the magnets are rotating around a circle\nwith inserts filled with magnetocaloric material. The cross\nsectional area of the magnets is estimated to be 9.2 L/m andReview and comparison of magnet designs for magnetic refrigeration — 5/12\nFeCo \nFeCo Soft magnetic material \n1\n68\n7543\n2\nFigure 4. After Vasile and Muller [2006]. Reprinted with\npermission. ( c\r2006 Elsevier). The arrows indicate the\ndirection of magnetization of the magnets.\nthe high field gap cross sectional area to be 0.75 L/m. The\nmagnetic flux density is given as 1.9 T in the high field region,\nbut this is based on a two dimensional simulation so a real\nworld assembly would have a significantly lower value. As\nthe magnets are rotating continuously and the inserts for the\nmagnetocaloric material fill most of the circle along which\nthe magnet is rotating Pfieldis estimated to be 0.90.\n3.1.3 Design by Bohigas et al. [2000]\nThe design by Bohigas et al. [2000] is a rotating design in\nwhich the magnets are stationary and the magnetocaloric mate-\nrial is rotated in and out of the high flux density region. A total\nof eight rectangular magnets are used, four of them placed on\nthe inside of the rotating wheel and four placed outside the\nwheel. The design can be seen in Fig. 5. The dimension of\none of the inner blocks is given as 40 \u000240\u000220 mm3and one\nof the outside blocks has dimensions 50 \u000250\u000225 mm3. The\nsize of the air gap is given to be 7 mm and there are a total of\nfour air gaps. From these figures we estimate the dimensions\nof one air gap to be 40 \u00027\u000220 mm3. Thus the volume of\nthe magnets is 0.38 L and the volume of the high flux density\nregion is 0.02 L. The flux density is given as 0.9 T. This design\nhas magnetocaloric material continuously entering the high\nflux density region and thus the Pfieldparameter is 1.\n3.1.4 Design by Tagliafico et al. [2009]\nThe magnet design by Tagliafico et al. [2009] consists of ten\nmagnets in a rectangular structure which uses soft magnetic\nFigure 5. The design by Bohigas et al. [2000]. Reprinted\nwith permission. ( c\r2000 IEEE).\nFigure 6. The magnet design by Tagliafico et al. [2009]\n(c\r2009 IIR/IIF). The magnetocaloric material passes\nthrough the gap in the structure.\nmaterial to guide the flux lines round through the magnetic\ncircuit. The magnet has a slot 50\u00029:5\u0002100mm3in the\ncenter, through which the magnetocaloric material is moved,\nas seen in Fig. 6. The volume of the high flux density region\nis thus 0.07 L. The flux density in the center of the slot is 1.55\nT. A reported 5 kg of magnet is used, which corresponds to\nVmag=0:68L. As two regenerative beds are run in parallel,\nand as the beds can be moved fairly quickly in and out of the\nhigh flux density region, the ideal Pfieldparameter is estimated\nto be 0:95. The actual value for the Pfieldparameter, which\ncan be estimated based on the total cycle time, is very close\nto this figure.\n3.1.5 Design by Tu ˇsek et al. [2009]\nThe refrigeration system presented by Tu ˇsek et al. [2009]\nuses a rotating AMR and a stationary magnet system. The\nmagnet system consists of an inner and outer magnetic circuit\nwith the magnetocaloric material placed in between the two\nstructures. There are four high flux density regions and four\nlow flux density regions along the circumference between the\ninner and the outer structure. A drawing of the design can beReview and comparison of magnet designs for magnetic refrigeration — 6/12\nFigure 7. The design by Tu ˇsek et al. [2009]. The\nmagnetocaloric material is placed between the inner and\nouter magnetic structure. The direction of magnetization is\nshown as arrows on the magnet blocks. Adapted from Tu ˇsek\net al. [2009].\nseen in Fig. 7. The volume of the high flux density regions\nis four times 48\u000210\u000255mm3, or 0.11 L. The amount of\nmagnet material used is four times 90\u000230\u000290mm3, or 0.65\nL. The average mean flux density in the high field region\nis 0.97 T while it is 0.1 T in the low flux density region.\nThe remanence of the magnets is 1.27 T. As magnetocaloric\nmaterial is continuously rotated into the high field regions the\nmagnets are constantly being used and thus Pfield=1.\n3.2 Halbach type magnet assemblies\nThe magnetic structures presented in this subsection are all\nbased on the Halbach cylinder design [Halbach, 1980; Mallinson,\n1973].\n3.2.1 Design by Lee et al. [2002]\nThe magnet design by Lee et al. [2002] is suited to a recip-\nrocating design with a stationary magnet and a moving bed\nof magnetocaloric material, but no actual device has been\nbuilt. The magnet system is shaped like the letter “C”, with\na high homogenous flux density in the center. The design\nresembles an 8-segmented Halbach cylinder where one of the\nhorizontal segmented has been removed. The flux density in\nSM \nSM Figure 8. The design by Lee et al. [2002]. The blocks labeled\n“SM” consists of soft magnetic material. Reprinted with\npermission. ( c\r2002 American Institute of Physics).\nthe center is enhanced by blocks of soft magnetic material,\nplaced in the center of the “C”. An illustration of the design\ncan be seen in Fig. 8. The design is very similar to the design\nby Vasile and Muller [2006] shown in Fig. 4. However, this\ndesign is presented in this section because the shape of the\nmagnets are more complex than in the latter design. The cross\nsectional dimensions of the array are given as 114 \u0002128 mm2\ni.e. 14.6 L/m. The cross sectional area of the high flux region\nis estimated to be 25 \u000212.7 mm2, i.e. 0.32 L/m. The magnetic\nflux density is given to be 1.9 T in the high flux region but\nthis is based on a two dimensional simulation. Depending on\nthe length of an actual device this figure will be significantly\nlower. No actual device has been built so the Pfieldis simply\ntaken to be 0.90.\n3.2.2 Design by Engelbrecht et al. [2009]\nThe magnetic refrigeration test machine designed at Risø DTU\nis a reciprocating device in which plates of magnetocaloric\nmaterial are moved in and out of a stationary magnet [En-\ngelbrecht et al., 2009]. The magnet is a Halbach cylinder\nconsisting of 16 blocks of permanent magnets. The cylinder\nhas an inner radius of 21 mm, an outer radius of 60 mm and\na length of 50 mm. An illustration of the Halbach cylinder\nis shown in Fig. 9. The average magnetic flux density in the\ncylinder bore is 1.03 T. The volume of the magnet is 0.50\nL and the volume of the high flux density region, i.e. the\ncylinder bore, is 0.07 L. The remanence of the magnets used\nin the Halbach cylinder is 1.4 T. The Pfieldparameter for thisReview and comparison of magnet designs for magnetic refrigeration — 7/12\nFigure 9. The design by Engelbrecht et al. [2009]. The\nHalbach cylinder has an inner radius of 21 mm, an outer\nradius of 60 mm and a length of 50 mm.\nsystem design is 0.5. This is because for half the cycle time\nthe stack of plates is out of the high field region leaving this\nempty. The actual Pfieldis slightly less than 0.5 due to the\nfinite velocity of the moving regenerator.\n3.2.3 Design by Lu et al. [2005]\nThe magnetic refrigeration device designed by Lu et al. [2005]\nis a reciprocating device with two separate packed beds of\nmagnetocaloric material moving in and out of two station-\nary magnet assemblies to provide force compensation. Both\nmagnets are 16 segmented Halbach cylinders with an inner\nradius of 15 mm and an outer radius of 70 mm. An illustration\nof the design is not shown as this design is very similar to\nthe one shown in Fig. 9. The flux density produced is given\nas 1.4 T, and the length of the cylinder is 200 mm. Given\nthese numbers the volume of the magnet is 2.94 L and the\nvolume of the high flux density region is 0.14 L, for either\nof the magnets. For the same reasons as for the design by\nEngelbrecht et al. [2009] the Pfieldparameter for this device is\n0.5.\n3.2.4 Design by Kim and Jeong [2009]\nThe magnet design by Kim and Jeong [2009] is a 16 seg-\nmented Halbach cylinder. A single bed of magnetocaloric\nmaterial is reciprocated through the cylinder bore. The radius\nof the cylinder bore is 8 mm, the outer radius of the cylinder is\n38 mm and the length is 47 mm. An illustration of the design\nis not shown as this design is very similar to the one shown\nin Fig. 9. The volume of the high flux density region is 0.01\nL while the volume of the magnet is 0.20 L. The flux density\nis 1.58 T at the center of the bore and 1 T at the edge, with amean value of 1.4 T. As only a single magnetocaloric bed is\nused the high flux density region is only used half the time,\nand thus Pfieldis 0.5.\n3.2.5 Design by Tura and Rowe [2007]\nThe magnetic refrigerator presented by Tura and Rowe [2007]\nis a rotating system in which the magnetocaloric material is\nkept stationary and a magnet is rotated to alter the flux density.\nAn illustration of the design can be seen in Fig. 10. The\nmagnet design used in the device consists of two separate\nmagnets each of which consists of two concentric Halbach\ncylinders. The reason that two separate magnets are used is\nthat the system can be run such that the magnetic forces are\nbalanced. In the concentric Halbach cylinder design the flux\ndensity in the inner cylinder bore can be controlled by rotating\nthe inner or outer magnet. Tura and Rowe [2007] report that\nwhen the inner magnet is rotated the mean magnetic flux\nproduced can be changed continuously from 0.1 T to 1.4 T.\nThe total volume of the magnetic material is 1.03 L, while the\ntotal volume of the high flux density region is 0.05 L [Rowe,\n2009b]. These values are for one of the concentric Halbach\ncylinders. The remanence of the blocks in the inner cylinder\nis 1.15 T while for the outer magnet it is 1.25 T. The Pfield\nparameter for this system design is 0.5 as half of a cycle the\ninner magnet will be turned such that it cancels the magnetic\nflux generated by the outer magnet. In this configuration there\nis no high flux density region, and the magnets are not being\nused to generate cooling.\n3.3 Complex magnetic structures\nThe designs presented in this subsection have a complex struc-\nture and consists of irregularly shaped magnet blocks.\n3.3.1 Design by Zimm et al. [2007]\nThe magnetic refrigeration machine presented by Zimm et al.\n[2007] utilizes a rotating design in which the magnetocaloric\nmaterial is stationary and the magnet is rotating. The mag-\nnet design is quite complex, utilizing both magnets and soft\nmagnetic materials, but essentially consists of two Y-shaped\nmagnetic structures separated by an air gap. The design is\nshown in Fig. 11. The high flux density region spans an angle\nof 60 degrees on two opposite sides of the design. Based on\nChell [2009] the total volume of the magnet assembly is 4.70\nL, the volume of the high flux density region is 0.15 L and\nthe mean flux density is 1.5 T. The Pfieldparameter for this\ndesign is essentially given by the speed at which the magnet\nrotates from one bed of magnetocaloric material to the next.\nThese are separated by an angle of 30 degrees. If the magnet\nis rotated fast the Pfieldparameter could be as high as 0.90.\n3.3.2 Design by Okamura et al. [2007]\nThe design by Okamura et al. [2007] is a rotating device in\nwhich the magnet is rotated past ducts packed with magne-\ntocaloric material. The magnet design consists of a complex\narrangement of permanent magnets and soft magnetic materi-\nals which is assembled in the shape of an inner rotor consisting\nboth of magnets and soft magnetic material with an outer yokeReview and comparison of magnet designs for magnetic refrigeration — 8/12\nFigure 10. A sketch of the concentric Halbach magnet design\nby Tura and Rowe [2007], viewed from the front. The inner\nand outer radius of the inner cylinder is 12.5 mm and 27 mm\nrespectively while the corresponding figures for the outer\ncylinder is 30 mm and 60 mm respectively. The length of the\nactual concentric cylinder is 100 mm. The rotational\nconfiguration shown here is the high flux density\nconfiguration.\nFigure 11. The complex magnet design by Zimm et al.\n[2007] ( c\r2007 IIR/IIF). The magnetocaloric material passes\nthrough the gap between the upper and lower “Y” structures.\nThe dark grey blocks are individual magnets, while the light\ngrey structure is made of soft magnetic material. The\ndirection of magnetization of the individual blocks are taken\nfrom Chell and Zimm [2006].\nconsisting of only soft magnetic material. The magnetocaloric\nmaterial is placed in four ducts in the air gap between the\nFigure 12. The inner magnetic structure in the design by\nOkamura et al. [2007]. From Okamura [2009]. The outer\nmagnetic structure consists of a cylinder of soft magnetic\nmaterial (not shown). The arrows indicate the direction of\nmagnetization of the magnets, which are white in color.\ninner and outer structure. The inner rotor is designed such\nthat magnets with identical poles are facing each other and\nseparated by a soft magnetic material. This increases the flux\ndensity and ”pushes” the flux lines from the inner rotor to\nthe outer yoke. A photo of the design can be seen in Fig. 12.\nThe mean flux density is 1.0 T and the magnet design con-\ntains 3.38 L of magnet and 0.80 L of high flux density region\n[Okamura, 2009]. As with the design by Zimm et al. [2007]\nthePfieldparameter for this design is essentially given by the\nspeed at which the magnet rotates from one duct to the next.\nThe actual Pfieldparameter can be estimated using the total\ncycle time and the time to rotate between two ducts, separated\nby an angle of 40 degrees, and is found to be 0.66. However a\nfaster rotation might be possible and thus we estimate that the\nPfieldparameter can be as high as 0.90.\n4. Comparing the designs\nIn Table 1 the different magnet designs are presented. In the\ntable the Lcoolparameter has been calculated for each design,\nthus allowing a direct comparison of the designs.\nIn Fig. 13 the parameter Lcool=Pfield, which only takes\nthe magnet assembly into account and not the design of the\nrefrigeration device, as well as the actual Lcoolparameter are\nshown. From the figure it is seen that the magnet design\nby Okamura et al. [2007] outperforms the remaining magnet\ndesigns. Compared to Lu et al. [2005] the design by Okamura\net al. [2007] uses almost the same amount of magnets but\ncreates a high flux density region over three times larger. An\ninteresting thing to note is that although the design by Zimm\net al. [2007] creates a very high flux density the design has a\nrather low Lcoolvalue because the magnetocaloric temperature\nchange only scales with the magnetic field to the power of 2/3\nat the Curie temperature and this, as mentioned previously,\ndoes not favor high flux densities. However Lcoolshould\nbe optimized under the condition of a certain minimum fluxReview and comparison of magnet designs for magnetic refrigeration — 9/12\nTable 1. The specifications of different magnet designs used in magnetic refrigeration devices. In all cases is it assumed that\nhBi2=3=hB2=3i, which is only true if the flux density is completely homogenous.\u0003designates a quantity estimated by the\nauthors of this article.Hindicates that the value of the flux density is the highest possible attainable flux density in the center of\nthe design, and as such is not a representative average of the magnetic flux density for the whole of the high flux density region.\n2Dindicates that the flux density is based on a two dimensional simulation. These notoriously overestimate the flux density\nexcept for very long assemblies and so Lcoolwill be overestimated for these designs. Some of the two dimensional designs also\nhave their volumes given per meter.\nName Vmag VfieldhBi h BoutiPfield Magnet typeLcool\nPfieldLcool\n[L] [L] [T] [T]\nBohigas et al. [2000] 0.38 0.02 0.9H0\u00031 Rectangular magnets on round\nsurface0.05 0.05\nEngelbrecht et al. [2009] 0.5 0.07 1.03 0 0.5 Halbach cylinder 0.14 0.07\nKim and Jeong [2009] 0.20 0.01 1.4 0 0.5 Halbach cylinder 0.06 0.03\nLee et al. [2002] 14.6/m 0.32/m 1.9H;2D0\u00030.90\u0003“C” shaped Halbach cylinder 0.03 0.03\nLu et al. [2005] 2.94 0.14 1.4H0 0.5 Halbach cylinder 0.06 0.03\nOkamura et al. [2007] 3.38 0.80 1.0 0 0.90\u0003Inner magnet rotor, soft mag-\nnetic yoke0.24 0.21\nTagliafico et al. [2009] 0.68 0.07 1.55H0 0.95 Rectangular magnetic circuit\nwith slot0.14 0.13\nTura and Rowe [2007] 1.03 0.05 1.4 0.1 0.5 Concentric Halbach cylinders 0.05 0.03\nTuˇsek et al. [2009] 0.11 0.65 0.97 0.1 1 Stationary magnet, rotating MC\nmaterial0.13 0.13\nVasile and Muller [2006] 9.2/m 0.75/m 1.9H;2D0\u00030.90\u0003“C” shaped circuit 0.12 0.11\nZheng et al. [2009] 0.5 0.09 0.93 0\u00030.90\u0003Single magnet magnetic circuit 0.17 0.15\nZimm et al. [2007] 4.70 0.15 1.5 0.1\u00030.90\u0003“Y” shaped magnetic structure 0.04 0.03\ndensity in the high flux density region, e.g. the flux density\nrequired to obtain a given temperature span of the device.\nIt is also seen that many of the reciprocating designs only\nutilize the magnet in half of the AMR cycle, i.e. that the Pfield\nparameter is 0.5. This means that the expensive magnet is only\nutilized half the time, which is very inefficient. It is also seen\nthat the different Halbach cylinders do not perform equally\nwell. This is because the efficiency of a Halbach cylinder is\nstrongly dependent on the relative dimensions of the cylinder\n[Bjørk et al., 2008].\nNote that the actual magnetic refrigeration machines, when\nranked by their temperature span and cooling capacity, does\nnot necessarily follow the trend of Fig. 13 [Engelbrecht et al.,\n2007; Gschneidner and Pecharsky, 2008; Rowe, 2009a]. This\ncan be caused by different types of magnetocaloric material,\ndifferent regenerator designs and different operating parame-\nters.\nHaving evaluated existing magnet designs we now ana-\nlyze the advantages of these designs and focus on how to\ndesign the optimal magnet for a magnetic refrigerator. The\noptimal design is limited by the energy density in the magnets\nthemselves. Also for, e.g., very large Halbach cylinders the\ncoercivity of the magnet is a limiting factor because the mag-\nnetic field is opposite to the direction of magnetization around\nthe inner equator of the Halbach cylinder [Bloch et al., 1998;\nBjørk et al., 2008]. A standard grade NdFeB magnet with a\nremanence of 1.2 T has a intrinsic coercivity of m0HC=3:2\nT, so the reversal of the magnet will only be a problem abovethis flux density. One should note that for NdFeB magnets\nwith a higher energy density, e.g. 1.4 T, the intrinsic coercivity\ncan be significantly lower, e.g. around m0HC=1:4 T.\n4.1 Design of an optimal magnet assembly\nBased on the knowledge gained from the magnet assemblies\nreviewed certain key features that the magnet assembly must\naccomplish or provide can be stated. It must produce a region\nthat has a high flux density preferably with as high uniformity\nas possible. Also the magnet must be designed such that the\namount of leakage of flux or stray field is as low as possible.\nThis includes both leakage to the surroundings and leakage\nto low flux density regions in the magnet assembly. The\nrecommendations to maximize Lcoolfor a given flux density\ncan be summed up as\n\u000fUse minimum amount of magnets\n\u000fMake the volume for magnetocaloric material as large\nas possible\n\u000fUtilize the magnet at all times\n\u000fEnsure that the flux density in the low flux density\nregion is low\n\u000fMinimize leakage to surrounding by e.g. using soft\nmagnetic material as flux guides\n\u000fUse the lowest possible flux density necessary to obtain\nthe chosen temperature span and cooling capacityReview and comparison of magnet designs for magnetic refrigeration — 10/12\nOkamur a\n2007 Zheng 2009 \nEngelbrecht 2009 Tagliaficio 2009 Tusek 2009 Vasile 2006 Lu \n2005 Kim \n2009 Bohigas 2000 Tura \n2007 Zimm 2007 Lee \n2002 Λcool /Pfield  and Λcool  [T 2/3]\n0.02 0.06 0.1 0.14 0.18 0.22 \nFigure 13. The parameters Lcool=Pfield(hatched) and Lcool(full). The Lcool=Pfieldparameter only takes the magnet design into\naccount and not the fraction of a cycle the magnet is used. As Pfield\u00141 theLcoolparameter is always less than or equal\nLcool=Pfield. Completely filled bars have Pfield=1. Note that the best design is five times as good as the design with the lowest\nvalue of Lcool=Pfield.\nIf magnetic refrigeration is to become a viable alternative to\nconventional refrigeration technology these simple design\ncriteria must be followed.\n5. Conclusion\nDifferent ways of generating the magnetic field used in a\nmagnetic refrigeration device have been discussed and it has\nbeen shown that permanent magnets are the only viable\nsolution, at present, to common household magnetic\nrefrigeration devices. Twelve published magnet designs were\nreviewed in detail and were compared using the Lcool\nparameter. The best design was found to be five times better\nthan the worst design. Finally guidelines for designing an\noptimal magnet assembly was presented.\nAcknowledgements\nThe authors would like to acknowledge the support of the\nProgramme Commission on Energy and Environment (EnMi)\n(Contract No. 2104-06-0032) which is part of the Danish\nCouncil for Strategic Research. The authors also wish to\nthank T. Okamura, A. Rowe, C. Zimm, J. Chell, Z.G. Zheng\nand J. Tu ˇsek for useful discussions and for providing some of\nthe figures and values in this article.\nReferences\nAharoni, A., 1998. Demagnetizing factors for rectangular\nferromagnetic prisms. Journal of Applied Physics 83, 3432.\nBahl, C., Petersen, T., Pryds, N., Smith, A., Petersen, T.,\n2008. A versatile magnetic refrigeration test device.\nReview of Scientific Instruments 79 (9), 093906.Barclay, J. A., 1988. Magnetic refrigeration: a review of a\ndeveloping technology. Advances in Cryogenic\nEngineering 33, 719–731.\nBjørk, R., Bahl, C. R. H., Smith, A., Pryds, N., 2008.\nOptimization and improvement of Halbach cylinder design.\nJournal of Applied Physics 104 (1), 13910.\nBloch, F., Cugat, O., Meunier, G., Toussaint, J., 1998.\nInnovating approaches to the generation of intense\nmagnetic fields: Design and optimization of a 4 tesla\npermanent magnet flux source. IEEE Transactions on\nMagnetics 34 (5), 2465–2468.\nBlumenfeld, P. E., Prenger, F. C., Sternberg, A., Zimm, C.,\n2002. Magnetic refrigerators - high temperature\nsuperconducting magnetic refrigeration. Advances in\nCryogenic Engineering 47 (A), 1019.\nBohigas, X., Molins, E., Roig, A., Tejada, J., Zhang, X., 2000.\nRoom-temperature magnetic refrigerator using permanent\nmagnets. IEEE Transactions on Magnetics 36, 538–544.\nBrown, G., 1976. Magnetic heat pumping near room\ntemperature. Journal of Applied Physics 47 (8),\n3673–3680.\nBuchelnikov, V ., Taskaev, S., Bychkov, I., Chernets, I.,\nDenisovskiy, A., 2007. The prototype of effective device\nfor magnetic refrigeration. Proceedings of the 2nd\nInternational Conference of Magnetic Refrigeration at\nRoom Temperature, Portoroz, Slovenia, 371–376.\nChell, J., 2009. Private communication.Review and comparison of magnet designs for magnetic refrigeration — 11/12\nChell, J., Zimm, C. B., 2006. Permanent magnet assembly.\nUS Patent 7148777.\nChen, Y ., Tang, Y ., Wang, B., Xue, Q., Tu, M., 2007. A\npermanent magnet rotary magnetic refrigerator.\nProceedings of the 2ndInternational Conference of\nMagnetic Refrigeration at Room Temperature, Portoroz,\nSlovenia, 309–313.\nCoelho, A., Gama, S., Magnus, A., Carvalho, G., 2009.\nPrototype of a Gd-based rotating magnetic refrigerator for\nwork around room temperature. Proceedings of the 3rd\nInternational Conference on Magnetic Refrigeration at\nRoom Temperature, Des Moines, Iowa, USA, 381–386.\nCoey, J. M. D., Ni Mhiochain, T. R., 2003. Permanent\nmagnets. High Magnetic Fields, World Scientific, 25-47.\nDong, Q., Zhang, H., Sun, J., Shen, B., Franco, V ., 2008. A\nphenomenological fitting curve for the magnetocaloric\neffect of materials with a second-order phase transition.\nJournal of Applied Physics 103 (11), 116101–1–3.\nDupuis, C., Vialle, A. J., Legait, U., Kedous-Lebouc, A.,\nRonchetto, D., 2009. New investigations in magnetic\nrefrigeration device, AMR cycle and refrigerant bed\nperformance evaluation. Proceedings of the 3rd\nInternational Conference on Magnetic Refrigeration at\nRoom Temperature, Des Moines, Iowa, USA, 437–442.\nEngelbrecht, K., Jensen, J. B., Bahl, C. R. H., Pryds, N.,\n2009. Experiments on a modular magnetic refrigeration\ndevice. Proceedings of the 3rdInternational Conference on\nMagnetic Refrigeration at Room Temperature, Des Moines,\nIowa, USA, 431–436.\nEngelbrecht, K. L., Nellis, G. F., Klein, S. A., Zimm, C. B.,\n2007. Recent developments in room temperature active\nmagnetic regenerative refrigeration. HV AC and R Research\n13 (4), 525–542.\nFranco, V ., Conde, A., Pecharsky, V . K., Gschneidner, K. A.,\nj., 2007. Field dependence of the magnetocaloric effect in\nGd and (Er1-xDyx)Al2: Does a universal curve exist? EPL\n(Europhysics Letters) 79 (4), 47009.\nGschneidner, K.A., J., Pecharsky, V ., 2008. Thirty years of\nnear room temperature magnetic cooling: Where we are\ntoday and future prospects. International Journal of\nRefrigeration 31 (6), 945–961.\nGschneidner Jr, K. A., Pecharsky, V . K., Tsokol, A. O., 2005.\nRecent developments in magnetocaloric materials. Rep.\nProg. Phys 68, 1479–1539.\nHalbach, K., 1980. Design of permanent multipole magnets\nwith oriented rare earth cobalt material. Nuclear\ninstruments and methods 169.Jensen, J. H., Abele, M. G., 1996. Maximally efficient\npermanent magnet structures. Journal of Applied Physics,\n79 (2), 1157-1163\nKim, Y ., Jeong, S., 2009. Investigation on the room\ntemperatre active magnetic regenerative refrigerator with\npermanet magnet array. Proceedings of the 3rd\nInternational Conference on Magnetic Refrigeration at\nRoom Temperature, Des Moines, Iowa, USA, 393–400.\nLee, S. J., Kenkel, J. M., Pecharsky, V . K., Jiles, D. C., 2002.\nPermanent magnet array for the magnetic refrigerator.\nJournal of Applied Physics 91 (10), 8894–8896.\nLu, D. W., Xu, X. N., Wu, H. B., Jin, X., 2005. A permanent\nmagnet magneto-refrigerator study on using Gd/Gd-Si-Ge/\nGd-Si-Ge-Ga alloys. Proceedings of the 1stInternational\nConference on Magnetic Refrigeration at Room\nTemperature, Montreux, Switzerland, 1–6.\nMallinson, J. C., 1973. One-sided fluxes - a magnetic\ncuriosity? IEEE Transactions on Magnetics 9 (4), 678 –\n682.\nNikly, G., Muller, C., 2007. Technical and economical\ncriteria to design and realize a magneto-caloric heat pump.\nProceedings of the 2ndInternational Conference of\nMagnetic Refrigeration at Room Temperature, Portoroz,\nSlovenia, 59–70.\nOesterreicher, H., Parker, F., 1984. Magnetic cooling near\ncurie temperatures above 300k. Journal of Applied Physics\n55, 4334–4338.\nOkamura, T., 2009. Private communication.\nOkamura, T., Rachi, R., Hirano, N., Nagaya, S., 2007.\nImprovement of 100w class room temperature magnetic\nrefrigerator. Proceedings of the 2ndInternational\nConference of Magnetic Refrigeration at Room\nTemperature, Portoroz, Slovenia, 377–382.\nPecharsky, V . K., Gschneidner Jr, K. A., 2006. Advanced\nmagnetocaloric materials: What does the future hold?\nInternational Journal of Refrigeration 29 (8), 1239–1249.\nPecharsky V . K., Gschneidner, Jr. K. A., 2008. Private\ncommunication.\nRichard, M.-A., Rowe, A., Chahine, R., 2004. Magnetic\nrefrigeration: Single and multimaterial active magnetic\nregenerator experiments. Journal of Applied Physics 95 (4),\n2146–2150.\nRowe, A. and Barclay J. A., 2002. Design of an Active\nMagnetic Regenerator Test Apparatus. Advances in\nCryogenic Engineering 47, 325–333.Review and comparison of magnet designs for magnetic refrigeration — 12/12\nRowe, A., 2009a. Performance metrics for active magnetic\nrefrigerators. Proceedings of the 3rdInternational\nConference on Magnetic Refrigeration at Room\nTemperature, Des Moines, Iowa, USA, 195–206.\nRowe, A., 2009b. Private communication.\nSari, O., Balli, M., Trottet, G., Bonhote, P., Egolf, P., Muller,\nC., Heitzler, J., Bour, S., 2009. Initial results of a test-bed\nmagnetic refrigeration machine with practical running\nconditions. Proceedings of the 3rdInternational\nConference on Magnetic Refrigeration at Room\nTemperature, Des Moines, Iowa, USA, 371–380.\nShir, F., Bennett, L., Della Torre, E., Mavriplis, C., Shull, R.,\n2005. Transient response in magnetocaloric regeneration.\nIEEE Transactions on Magnetics 41 (6), 2129–2133.\nTagliafico, L., Scarpa, F., Tagliafico, G., Valsuani, F., Canepa,\nF., Cirafici, S., Napoletano, M., C., B., 2009. Design and\nassembly of a linear reciprocating magnetic refrigerator.\nProceedings of the 3rdInternational Conference on\nMagnetic Refrigeration at Room Temperature, Des Moines,\nIowa, USA, 425–430.\nTura, A., Rowe, A., 2007. Design and testing of a permanent\nmagnet magnetic refrigerator. Proceedings of the 2nd\nInternational Conference of Magnetic Refrigeration at\nRoom Temperature, Portoroz, Slovenia, 363–370.\nTuˇsek, J., Zupan, S., Sarlah, A., Prebil, I., A., P., 2009.\nDevelopment of a rotary magnetic refrigerator.\nProceedings of the 3rdInternational Conference on\nMagnetic Refrigeration at Room Temperature, Des Moines,\nIowa, USA, 409–414.\nVasile, C., Muller, C., 2006. Innovative design of a\nmagnetocaloric system. International Journal of\nRefrigeration 29 (8), 1318–1326.\nVuarnoz, D., Kitanovski, A., Diebold, M., Gendre, F., Egolf,\nP., 2007. A magnetic heat pump with porous magneto\ncaloric material. Physica Status Solidi (C) Current Topics\nin Solid State Physics 4 (12), 4552–4555.\nYu, B., Gao, Q., Zhang, B., Meng, X., Chen, Z., 2003.\nReview on research of room temperature magnetic\nrefrigeration. International Journal of Refrigeration 26 (6),\n622–636.\nZheng, Z., 2009. Private communication.\nZheng, Z., Yu, H., Zhong, X., Zeng, D., Liu, Z., 2009. Design\nand performance study of the active magnetic refrigerator\nfor room-temperature application. International Journal of\nRefrigeration 32, 78-86.\nZimm, C., Auringer, J., Boeder, A., Chell, J., Russek, S.,\nSternberg, A., 2007. Design and initial performance of a\nmagnetic refrigerator with a rotating permanent magnet.Proceedings of the 2ndInternational Conference of\nMagnetic Refrigeration at Room Temperature, Portoroz,\nSlovenia, 341–347.\nZimm, C., Boeder, A., Chell, J., Sternberg, A., Fujita, A.,\nFujieda, S., Fukamichi, K., 2006. Design and performance\nof a permanent-magnet rotary refrigerator. International\nJournal of Refrigeration 29 (8), 1302–1306.\nZimm, C., Jastrab, A., Pecharsky, A. S. V ., Gschneidner Jr,\nK., Osborne, M., Anderson, I., 1998. Cryocoolers:\nRegenerative - description and performance of a near-room\ntemperature magnetic refrigerator. Advances in Cryogenic\nEngineering 43 (B), 1759."    },    {        "title": "1410.1987v1.An_optimized_magnet_for_magnetic_refrigeration.pdf",        "content": "Published in Journal of Magnetism and Magnetic Materials, Vol. 322 (21), 3324-3328, 2010\nDOI: 10.1016/j.jmmm.2010.06.017\nAn optimized magnet for magnetic refrigeration\nR. Bjørk, C. R. H. Bahl, A. Smith, D. V. Christensen and N. Pryds\nAbstract\nA magnet designed for use in a magnetic refrigeration device is presented. The magnet is designed by applying\ntwo general schemes for improving a magnet design to a concentric Halbach cylinder magnet design and\ndimensioning and segmenting this design in an optimum way followed by the construction of the actual magnet.\nThe final design generates a peak value of 1.24 T, an average flux density of 0.9 T in a volume of 2 L using only\n7.3 L of magnet, and has an average low flux density of 0.08 T also in a 2 L volume. The working point of all\nthe permanent magnet blocks in the design is very close to the maximum energy density. The final design is\ncharacterized in terms of a performance parameter, and it is shown that it is one of the best performing magnet\ndesigns published for magnetic refrigeration.\nDepartment of Energy Conversion and Storage, Technical University of Denmark - DTU, Frederiksborgvej 399, DK-4000 Roskilde, Denmark\n*Corresponding author : rabj@dtu.dk\n1. Introduction\nMagnetic refrigeration is a potentially energy efficient and en-\nvironmentally friendly evolving cooling technology that uses\nthe magnetocaloric effect (MCE) to generate cooling through\na regenerative process called active magnetic regeneration\n(AMR).\nAt present, a great number of magnetic refrigeration test\ndevices have been built and examined in some detail, with\nfocus on the produced temperature span and cooling power of\nthe devices [ 1;2;3]. A substantial number of magnet designs\nhave also been published [ 4;5;6;7;8;9;10;11] (see Ref.\n[12] for a review), but for almost all magnet designs no argu-\nment is presented for the specific design and dimensioning of\nthe magnet.\nIn this paper we present the full design approach of a mag-\nnet used for magnetic refrigeration. The magnet is designed\nby applying two general ways or schemes for improving a\nmagnet design to a concentric Halbach cylinder design. The\nresulting design is dimensioned and segmented and is then\ncharacterized by comparing flux density measurements to a\nnumerical simulation. Finally, the magnet design is compared\nto other magnet designs used in magnetic refrigeration.\n2. Modeling the magnet design\nThe magnet is designed for a cylindrical rotating magnetic\nrefrigeration device under construction at Risø DTU, in which\nplates of magnetocaloric material rotate in an air gap between\nan outer and inner cylindrical magnetic structure. The dimen-\nsions of the design, which have been chosen based on the\ndesired temperature span and cooling capacity of the device,\nare such that the volume between the inner and outer magnet\nis 4 L. The magnetic refrigeration device is designed such that\nthe magnet must provide four high flux density regions and\nfour low flux density regions in the air gap between the twomagnets.\nA similar magnetic refrigerator, i.e. with a stationary\nmagnet and a rotating magnetocaloric material, was also con-\nsidered in Ref. [ 11], where a magnet design that generates\na magnetic field between 0.1 T and 1 T in four low and four\nhigh field regions is presented. Rotary magnetic refrigerators\nwhere the magnet rotates and the magnetocaloric material is\nkept stationary are considered in, e.g., Refs. [ 13], [14] and\n[15]. One of these designs uses rectangular magnets while\nthe other two use highly irregularly shaped magnets. The\ngenerated magnetic field is between 1.0 and 1.9 T, although\nthe latter value is based on a two dimensional numerical sim-\nulation which is known to overestimate the magnitude of the\nmagnetic field except for very long assemblies.\nBased on numerical modeling of the AMR process using\nthe model of Ref. [ 16] the length of the Risø DTU device was\nchosen to be 250 mm [ 17]. Based on practical engineering\nrequirements, as well as to allow ample room for the inner\nmagnet, an external radius of the inner magnet of 70 mm and\nan internal radius of the outer magnet of 100 mm was chosen.\nThe regenerator itself can consist of either plates or a\npacked bed of magnetocaloric material. The dimensions,\nshape and stacking of the plates or the dimensions and shape\nof the packed bed can vary, and the performance of the re-\nfrigeration device will of course depend on these parameters.\nThe magnetocaloric material is contained in a plastic structure\nwith low heat conduction, so the heat transfer between the\nmagnet and the magnetocaloric material is kept low. As the\nmagnetocaloric material is rotated in the magnetic field there\nwill be an eddy current induced in the magnetocaloric mate-\nrial. The heating due to this eddy current is negligible because\nthe magnetization is small and the rotation rate is only on the\norder of 1 Hz.\nA magnet design that fulfils the requirement of generat-\ning four high and low flux density regions is the concentricarXiv:1410.1987v1  [physics.ins-det]  8 Oct 2014An optimized magnet for magnetic refrigeration — 2/6\nAir Inner magnet\nR\nout, int RR\nRinn, ext \ninn, int \nout, ext                    Air gapOuter magnet\nFigure 1. The concentric Halbach cylinder design. The\ndirection of magnetization is shown as arrows. The different\nradii have been indicated.\nHalbach cylinder design [ 18]. Here each cylinder is magne-\ntized such that the remanent flux density at any point varies\ncontinuously as, in polar coordinates,\nBrem;r=Bremcos(pf)\nBrem;f=Bremsin(pf); (1)\nwhere Bremis the magnitude of the remanent flux density\nandpis an integer [ 19;20]. Subscript rdenotes the radial\ncomponent of the remanence and subscript fthe tangential\ncomponent. A magnet with four high and four low flux density\nregions, as described above, can be created by having a p=2\nouter Halbach cylinder and a p=\u00002inner Halbach cylinder.\nThe concentric Halbach cylinder design is shown in Fig. 1.\nThis magnet design is the starting design for the optimized\nmagnet design presented here. The design is improved by\napplying an algorithm to increase the difference in flux density\nbetween a high and low flux density region in an air gap in a\nmagnetic structure, as described in Ref. [ 21]. The algorithm\nlowers the flux density in a given area by replacing magnet\nmaterial enclosed by an equipotential line of the magnetic\nvector potential, Az, with a soft magnetic material or vacuum.\nFurthermore, the design is improved by replacing mag-\nnet material with a high permeability soft magnetic material\nwhere the component of the magnetic field along the rema-\nnence is not large and negative, i.e. where m0H\u0001ˆBrem>\u0000g,\nwith an appropriately chosen positive g, as here a high perme-\nability soft magnetic material will produce a similar value of\njBjas the magnet produces [22; 23; 21].\nThese two improvements are applied to the design us-\ning a numerical two dimensional model implemented in thecommercially available finite element multiphysics program\nComsol Multiphysics [24] and using magnets with a rema-\nnence of 1.44 T and a relative permeability of 1.05, which are\nthe properties of standard neodymium-iron-boron (NdFeB)\nmagnets [ 25]. A two dimensional model is used as the magnet\ndesign is symmetric along the length of the design and the\nratio of the gap to the length of the assembly is much smaller\nthan 1, making end effects relatively unimportant.\nFor the algorithm the equipotential line of Azis chosen\nto be the line that goes through the point (r=100 mm ;f=\n22:5\u000e), i.e. the point on the internal radius of the outer magnet,\nhalf way between the center of the high and low flux density\nregions, as this equipotential line encircles the low flux density\nregion. Iron is used as the soft magnetic material as it has\na very high permeability as well as being easily workable\nand reasonable priced. A value of g=0:125T is used for\nreplacing magnet material with iron where the component\nof the magnetic field along the remanence is not large and\nnegative.\n2.1 Dimensioning of the design\nThe remaining dimensions of the magnet design, i.e. the\nexternal radius of the outer magnet, Rout;ext, and the internal\nradius of the inner magnet, Rinn;int, are chosen based on a\nparameter variation of the concentric Halbach design where\nthe two improvements discussed above have been applied.\nThe external radius of the outer magnet was varied from 110\nmm to 155 mm in steps of 5 mm and the internal radius of\nthe inner magnet was varied from 10 mm to 50 mm in seven\nequidistant steps. The optimization parameter is taken as\nthe difference in flux density between the high and low flux\ndensity regions to the power of 0.7 as a function of the cross-\nsectional area of the magnet; this is shown in Fig. 2. Here\nhB0:7\nhighidenotes the average of the flux density to the power\nof 0.7 in the high field region and similarly hB0:7\nlowifor the\nlow flux density region. For this design the high and low flux\ndensity regions are defined to be of the same size and span an\nangle of 45 degree each making them adjacent.\nThe reason the power of 0.7 is chosen is that the adiabatic\ntemperature change of a second order magnetocaloric material\nscales with the magnetic field to the power of 0:7at the Curie\ntemperature [ 12;26]. Thus it is this value that is important to\nthe performance of a magnet used in magnetic refrigeration.\nTo limit the cost of the magnet, a cross-section of Amag\n= 0.025 m2was chosen. Based on this value and Fig. 2 the\noptimal design was chosen. This design has an external radius\nof the outer magnet of 135 mm and an internal radius of the\ninner magnet of 10 mm.\nThe original concentric Halbach cylinder design and the\ndesign after the application of the different improvements are\nshown in Fig. 3 for the dimensions found above.\n3. The physical magnetAn optimized magnet for magnetic refrigeration — 3/6\n(a) Original design\n (b) Design with applied improvements\nFigure 3. (Color online) Fig (a) shows a quadrant of the a concentric Halbach cylinder with pouter =2 and pinner =\u00002. The\nremaining quadrants can be obtained by mirroring along the coordinate axes. The magnetization is shown as black arrows on\nthe magnets, which are light grey. Iron is dark grey. The flux density in the air gap between the cylinders is shown as a color\nmap. Fig (b) shows the same design after the two improvement schemes have been applied. The line in the iron region in the\nouter magnet separates the iron regions generated by the two improvement schemes, and it is only shown for reference.\nAmag[m2]\n/angbracketleftB0.7\nhigh/angbracketright − /angbracketleftB0.7\nlow/angbracketright[T0.7]0.4 0.5 0.6 0.7 0.80.010.0150.020.0250.030.035\nFigure 2. (Color online) The difference in flux between the\nhigh and low flux density regions to the power of 0.7 as a\nfunction of the cross-sectional area of the magnet, Amag, for a\nrange of different external radii of the outer magnet, Rout;ext,\nand internal radii of the inner magnet, Rinn;int. The area is\nused as the model is two-dimensional. The chosen set of\ndimensions have been encircled.\n3.1 Segmentation of the final design\nTo allow construction of the magnet, the design shown in\nFig. 3(b) must be segmented. The number of segments is\nan important parameter as the more segments used the moreexpensive the manufacturing process becomes. Generally\nit is the total number of segments that determines the cost\ntogether with the overall magnet volume, due to the handling\nof the individual segments. However, segments with different\ngeometric shapes introduce an additional cost as these must be\nseparately manufactured. If different segments have the same\ngeometrical shape but different directions of magnetization\nthese introduce little additional cost as the same molds and\nfixation tools can be used [27].\nThe segmentation of the optimized design is done man-\nually. The size of the iron regions is decreased a bit in or-\nder to generate a higher flux density in the high flux den-\nsity region. In order to find the optimal direction of mag-\nnetization of the individual segments an optimization pro-\ncedure has been applied. The optimization routine used is\na modified version of the Matlab function FMINSEARCH\n[28], called FMINSEARCHBND , which finds the minimum\nof an unconstrained multivariable function with boundaries\nusing a derivative-free method [ 29]. A Comsol model with\na predefined geometry is used as input, with the direction of\nmagnetization as variables. The optimization criteria is that\nthe difference between hB0:7\nhighiandhB0:7\nlowibe maximized. The\nsegmentation of the magnet design and the resulting directions\nof magnetization are shown in Fig. 4.\nThe effectiveness of the magnet design can be judged from\nthe working point of the magnets, i.e. the size of the magnetic\nfield times the size of the flux density, both measured in the\ndirection of the remanence: jB\u0001ˆBremjjH\u0001ˆBremj. In Fig. 5 the\nworking point is shown as calculated from a model of theAn optimized magnet for magnetic refrigeration — 4/6\n355 o\n315 o275 o\n  55 o120 o150 o\n215 o\nFigure 4. (Color online) The segmentation of the final design.\nThe direction of magnetization has been found by\nmaximizinghB0:7\nhighi\u0000hB0:7\nlowi. The direction of magnetization\nis indicated on each segment. The small white areas in the air\ngap have a flux density higher than the maximum value on\nthe color bar.\nmagnet design. For magnets with a remanence of 1.44 T, as\nis used here, the maximum energy density, i.e. the optimal\nworking point (jB\u0001ˆBremjjH\u0001ˆBremj)max, is 400 kJ m\u00003[30].\nAs can be seen from the figure most parts of the magnets\nare close to the maximum energy density thus illustrating the\nefficiency of the design.\n3.2 The final design realized\nThe magnet design shown in Fig. 4 has been constructed and\na photo of the magnet is shown in Fig. 6. The magnet has a\nlength of 250 mm.\nAll spatial components of the flux density in the air gap\nhave been measured using a Hall probe (AlphaLab Inc, Model:\nDCM) as a function of angle, radius and length of the device.\nA three dimensional simulation of the design has also been per-\nformed. The measured flux density was found to be periodic\nwith a period of 90\u000e, as expected. The measured flux density\nfor the first 90\u000eand the results of the simulation are shown\nin Fig. 7. An excellent agreement between the simulated and\nmeasured flux density is seen.\nIn the four high field regions the peak flux density is\naround 1.24 T while it is very close to 0 T in the four low field\nregions. The gradient between the high and low field regions\nis quite sharp, but it is clear that the field is not homogeneous\nin the high field region. However, as the magnetocaloric\neffect scales with the magnetic field to the power of 0.7 it is\npreferable to have a zero flux density in the low field region\nrather than to have part of the flux density gradient in the\nlow field region. Therefore the gradient is concentrated in the\nhigh field region. The field is also seen to drop off only at\nthe very ends of the device, i.e. jzj>100mm. Finally the\nFigure 5. (Color online) The working point,\njB\u0001ˆBremjjH\u0001ˆBremj, of the magnets. The maximum working\npoint for a 1.44 T remanence magnet, as is used here, is 400\nkJ m\u00003.\nfield is seen to be slightly larger radially near the inner and\nouter magnet compared to the center of the air gap, but the\ndifference is small and is not expected to have an impact on\nthe performance of the AMR.\n3.3 Performance of the magnet\nThe performance of the magnet with regards to magnetic\nrefrigeration can be evaluated using the Lcoolparameter [ 31],\nwhich is defined as\nLcool\u0011\u0010\nhB0:7\nhighi\u0000hB0:7\nlowi\u0011Vfield\nVmagPfield; (2)\nwhere Vmagis the volume of the magnet(s), Vfieldis the volume\nwhere a high flux density is generated and Pfieldis the fraction\nof an AMR cycle that magnetocaloric material is placed in\nthe high flux density volume. Note that Vmagis the volume of\npermanent magnet material used, excluding any soft magnetic\nmaterial as the price of this material is in general significantly\nlower than permanent magnet material. Also, the magnet\ndesign presented above has not been optimized with respect\nto the total weight of the design. More soft magnetic material\nthan needed is present, as the saturation magnetization of the\nsoft magnetic material is not reached. This was done for ease\nof construction.\nOther published magnet designs for magnetic refrigera-\ntion devices have a Lcoolparameter between 0.03 to 0.21 [ 12].\nThe magnet designed here has Vmag=7:3L,Vfield=2:0L,\nhB0:7\nhighi=0:91T andhB0:7\nlowi=0:15T. Assuming Pfield=1, as\nis the aim of the device, the design achieves Lcool=0:21, thus\nequaling the best performing magnet published to date. The\nrotary magnetic refrigeration devices mentioned earlier, Refs.\n[11], [13], [14] and [ 15] haveLcool=0:13;0:11;0:21 and 0 :03\nrespectively.An optimized magnet for magnetic refrigeration — 5/6\nzrϕ\nFigure 6. (Color online) A photo of the actual constructed\nmagnet (in red) including a stand and an outer stainless steel\ncasing. The coordinate system used for the measurements of\nthe flux density is also shown.\nFor this particular design the choice of the high and low\nflux density regions is rather arbitrary and so they could have\nbeen chosen to span less than 45 degree. This would lead\nto a higher value for hB0:7\nhighiand a lower value of hB0:7\nlowi, but\nalso to a lower value of Vfield. It has been verified that Lcool\nattains the highest value for this design when the high and\nlow flux density regions combined span the entire air gap\ncircumference, i.e. as done here.\n4. Conclusion\nThe complete process of designing a magnet for use in a mag-\nnetic refrigeration device has been described. Two different\nways for improving the performance of a magnet design were\napplied to a concentric Halbach magnet design which was\ndimensioned and subsequently segmented once the optimal\ndimensions had been found. The direction of magnetization\nwas also optimized for each of the individual segments. The\nfinal design generates a peak value of 1.24 T, an average flux\ndensity of 0.9 T in a volume of 2 L using 7.3 L of magnet,\nand has an average low flux density of 0.08 T. The difference\nin flux to the power of 0.7 is 0.76 T0:7. The working point of\nthe magnets is close the maximum energy density possible.\nFinally the flux density of the design has been measured and\ncompared with a three dimensional numerical simulation of\nthe design, and an excellent agreement was seen. A magnetic\nrefrigeration device utilizing the magnet is under construction\nat Risø DTU.\nAcknowledgements\nThe authors would like to acknowledge the support of the\nProgramme Commission on Energy and Environment (EnMi)\n(Contract No. 2104-06-0032) which is part of the Danish\nCouncil for Strategic Research. The authors also wish to\nthank F. B. Bendixen and P. Kjeldsteen for useful discussions.\nφ [degree]|B| [T]\n  \n010203040506070809000.20.40.60.811.2 z = −125 mm\nz = −62.5 mm\nz = 0 mm\nz = 62.5 mm\nz = 125 mm\nSimulation data(a)jBjas function of fin the middle of the air gap, r=85 mm.\nz [mm]|B| [T]\n  \n−150−100−5005010015000.20.40.60.811.2\nφ = 0 degree\nφ = 22.5 degree\nφ = 45 degree\nSimulation data\n(b)jBjas function of zin the middle of the air gap, r=85 mm.\nr [mm]|B| [T]\n  \n70758085909510000.511.52φ = 0, z = 0 mm\nφ = 0, z = −125 mm\nφ = 45, z = 0 mm\nSimulation data\n(c)jBjas function of r\nFigure 7. Measurements of the flux density as a function of\nangle f, length z, and radius r, in the middle of the air gap of\nthe magnet compared with numerical simulations. The\ndashed vertical lines on Fig. (a) separate the high and low\nflux density regions.An optimized magnet for magnetic refrigeration — 6/6\nReferences\n[1]J. A. Barclay, Adv. Cryog. Eng. 33 (1988), 719.\n[2]B. Yu, Q. Gao, B. Zhang, X. Meng and Z. Chen, Int. J.\nRefrig. 26 (6) (2003), 622.\n[3]K. A Gschneidner Jr and V . K. Pecharsky, Int. J. Refrig.\n31 (6), (2008), 945.\n[4]A. Coelho, S. Gama, A. Magnus and G. Carvalho, Proc.\n3th Int. Conf. on Magn. Refrig. at Room Temp., Des\nMoines, Iowa, USA (2009), 381.\n[5]C, Dupuis, A. J. Vialle, U. Legait, A. Kedous-Lebouc and\nD. Ronchetto, Proc. 3th Int. Conf. on Magn. Refrig. at\nRoom Temp., Des Moines, Iowa, USA (2009), 437.\n[6]K. Engelbrecht, J. B. Jensen, C. R. H. Bahl and N. Pryds,\nProc. 3th Int. Conf. on Magn. Refrig. at Room Temp.,\nDes Moines, Iowa, USA (2009), 431.\n[7]Y . Kim and S. Jeong, Proc. 3th Int. Conf. on Magn. Refrig.\nat Room Temp., Des Moines, Iowa, USA (2009), 393.\n[8]O. Sari, M. Balli, G. Trottet, P. Bonhote, P. Egolf, C.\nMuller, J. Heitzler and S. Bour, Proc. 3th Int. Conf. on\nMagn. Refrig. at Room Temp., Des Moines, Iowa, USA\n(2009), 371.\n[9]L. Tagliafico, F. Scarpa, G. Tagliafico, F. Valsuani, F.\nCanepa, S. Cirafici, M. Napoletano and C. Belfortini,\nProc. 3th Int. Conf. on Magn. Refrig. at Room Temp.,\nDes Moines, Iowa, USA (2009), 425.\n[10]Z. Zheng, H. Yu, X. Zhong, D. Zeng and Z. Liu, Int. J.\nRefrig. 32 (2009), 78.\n[11]J. Tu ˇsek, S. Zupan, A. Sarlah, I. Prebil and A. Poredos,\nInt. J. Refrig. 33 (2) (2010), 294\n[12]R. Bjørk, C. R. H. Bahl, A. Smith and N. Pryds, Int. J.\nRefrig. 33 (2010), 437\n[13]C. Vasile and C. Muller, Int. J. Refrig. 29 (8) (2006), 1318\n[14]T. Okamura, R. Rachi, N. Hirano and S. Nagaya, Proc.\n2nd Int. Conf. on Magn. Refrig. at Room Temp., Portoroz,\nSlovenia (2007), 377.\n[15]C. Zimm, J. Auringer, A. Boeder, J Chell, S. Russek and\nA. Sternberg, Proc. 2nd Int. Conf. on Magn. Refrig. at\nRoom Temp., Portoroz, Slovenia (2007), 341.\n[16]K. K. Nielsen, C. R. H. Bahl, A. Smith, R. Bjørk, N.\nPryds and J. Hattel, Int. J. Refrig. 32 (6), (2009), 1478.\n[17]K. K. Nielsen, K. Engelbrecht, C. R. H. Bahl, A. Smith\nand J. Geyti. Unpublished (2009).\n[18]R. Bjørk, C. R. H. Bahl and A. Smith, J. Mag. Mag. Mater.\n322 (2010), 133.[19]J. C. Mallinson, IEEE Trans. Magn. 9 (4) (1973), 678.\n[20]K. Halbach, Nucl. Instrum. Methods 169 (1980).\n[21]R. Bjørk, C. R. H. Bahl, A. Smith and N. Pryds, IEEE\nTrans. Magn. 47 (6), 1687 (2011).\n[22]F. Bloch, O. Cugat, G. Meunier and J. C. Toussaint, IEEE\nTrans. Magn. 34 (5), 2465 (1998).\n[23]J. M. D. Coey and T. R. Ni Mhiochain, High Magnetic\nFields (Permanent magnets), Edt: F. Herlach and N.\nMiura, World Scientific, 25 (2003).\n[24]COMSOL AB, Tegn ´ergatan 23, SE-111 40 Stockholm,\nSweden.\n[25]Standard Specifications for Permanent Magnet Materials,\nMagn. Mater. Prod. Assoc., Chicago, USA. www.intl-\nmagnetics.org. (2000)\n[26]V . K. Pecharsky and K. A. Gschneidner Jr, Int. J. Refrig.\n29 (8) (2006) 1239.\n[27]F. B. Bendixen, 2009. Private communication.\n[28]Matlab, version 7.7.0.471 (R2008b) (2008).\n[29]J. D’Errico. http://www.mathworks.com/matlabcentral/\nfileexchange/8277, Release: 4 (7/23/06) (2006).\n[30]Vacuumschmelze GMBH & Co, KG. Pd 002 - Va-\ncodym/Vacomax (2007).\n[31]R. Bjørk, C. R. H. Bahl, A. Smith and N. Pryds, J. Appl.\nPhys. 104 (1) (2008), 13910."    },    {        "title": "1410.2679v1.Improving_magnet_designs_with_high_and_low_field_regions.pdf",        "content": "Published in IEEE Transactions on Magnetics, Vol. 47 (6), 1687-1692, 2011\nDOI: 10.1109/TMAG.2011.2114360\nImproving magnet designs with high and low field\nregions\nR. Bjørk, C. R. H. Bahl, A. Smith and N. Pryds\nAbstract\nA general scheme for increasing the difference in magnetic flux density between a high and a low magnetic field\nregion by removing unnecessary magnet material is presented. This is important in, e.g., magnetic refrigeration\nwhere magnet arrays has to deliver high field regions in close proximity to low field regions. Also, a general way\nto replace magnet material with a high permeability soft magnetic material where appropriate is discussed. As\nan example these schemes are applied to a two dimensional concentric Halbach cylinder design resulting in a\nreduction of the amount of magnet material used by 42% while increasing the difference in flux density between\na high and a low field region by 45%.\nDepartment of Energy Conversion and Storage, Technical University of Denmark - DTU, Frederiksborgvej 399, DK-4000 Roskilde, Denmark\n*Corresponding author : rabj@dtu.dk\n1. Introduction\nDesigning a permanent magnet structure that contains regions\nof both high and low magnetic field and ensuring a high flux\ndifference between these can be challenging. Such magnets\ncan be used for a number of purposes but here we will consider\nmagnetic refrigeration as an example. Magnetic refrigeration\nis a potentially highly energy efficient and environmentally\nfriendly cooling technology, based on the magnetocaloric ef-\nfect. This effect manifests itself as a temperature change that\nso-called magnetocaloric materials exhibit when subjected to\na changing magnetic field. In magnetic refrigeration a magne-\ntocaloric material is moved in and out of a magnetic field, in\norder to generate cooling. The magnetic field is usually gen-\nerated by permanent magnets [ 1;2]. In such magnet designs\nused in magnetic refrigeration it is very important to obtain a\nlarge difference in flux density between the high and the low\nflux density regions, between which the magnetocaloric mate-\nrial is moved in order to generate the magnetocaloric effect.\nThis is because the magnetocaloric effect scales with the mag-\nnetic field to the power of 0.7 near the Curie temperature for\nmost magnetocaloric materials of interest, and in particular for\nthe benchmark magnetocaloric material Gd [ 3;4]. Because\nof this scaling it is very important that the magnetic field in\na low field region is very close to zero. This is especially a\nproblem in rotary magnetic refrigerators [ 2;5;6;7] where\nthe high and low magnetic field regions are constrained to be\nclose together. Here it is crucial to ensure that flux does not\nleak from the high field region into the low field region.\nThe permanent magnet structure can be designed from the\nground up to accommodate this criterion, e.g., by designing\nthe structure through Monte Carlo optimization [ 8], or by\noptimizing the direction of magnetization of the individual\nmagnets in the design [ 9;10]. However, the resulting design\nmay be unsuitable for construction. Here we present a schemethat applied to a given magnet design will lower the flux\ndensity in the low flux density region, thus increasing the\ndifference in flux density, and lower the amount of magnet\nmaterial used at the same time. No general way to improve\nthe flux density difference for a magnet design has previously\nbeen presented.\n2. Physics of the scheme\nThe properties of field lines of the magnetic flux density can be\nexploited to minimize the magnetic flux in a given region. A\nfield line is a curve whose tangent at every point is parallel to\nthe vector field at that point. These lines can be constructed for\nany vector field. The magnitude of the magnetic flux density,\nB, is proportional to the density of field lines. For a two\ndimensional problem, as will be considered here, with a static\nmagnetic field, lines of constant magnetic vector potential,\nAz, are identical to field lines of Bif the Lorenz gauge, i.e.\nÑ\u0001A=0, is chosen [ 11]. We begin by calculating a field line\nof the magnetic flux density, B, i.e. an equipotential line of\nconstant Az, that encloses the area in which the flux density\nis to be minimized. All field lines enclosed by the calculated\nfield line are confined to the enclosed area as field lines do not\ncross. These enclosed field lines are creating the flux density\ninside the calculated area. This procedure will only work for\na two dimensional case, as in three dimensions a field line\nwill not enclose a volume. Here a surface of field lines that\nenclose the volume must be used instead.\nIf we remove all magnet material enclosed within the\nchosen field line, it might be thought that no field lines should\nbe present inside the area and the flux density should be zero.\nHowever, this is not precisely the case as by removing some\nmagnet material the magnetostatic problem is no longer the\nsame, and a new solution, with new field lines of B, mustarXiv:1410.2679v1  [physics.ins-det]  10 Oct 2014Improving magnet designs with high and low field regions — 2/7\nbe calculated. Thus a new field line that confines the area in\nwhich we wish to minimize the flux density can be found and\nthe procedure can be iteratively repeated.\nIt must be made clear that the magnet material inside the\ncalculated field line, i.e. the material that is removed, does\ncontribute a non-zero flux density to areas outside the enclos-\ning field line. This can be seen by considering each little piece\nof a magnet as a dipole, which will generate a flux density at\nany point in space. Thus by removing the enclosed magnet\nmaterial the flux density will also be lowered in the high flux\ndensity region. However, this is more than compensated by\nthe lowering ofjjBjjin the low flux density region, due to\nthe fact that the high flux density region is farther away from\nthe removed material. This makes it possible to increase the\ndifference between the high and low flux density regions.\nField lines that do not pass through the high flux density\nregion do not contribute to the flux density there. The scheme\ncan also be used to remove the magnet material enclosed by\nthese field lines.\nThe scheme must be run until a stopping criterion has\nbeen reached. This can be, e.g., that the flux density in the low\nflux density region has dropped below a certain value or that\nthe volume of magnetic material has been reduced by a certain\nfraction. This is to ensure that the flux density in the high\nflux density region is not significantly reduced. In some cases\nsuccessive applications of the scheme might result in removal\nof all magnet material. If, for example, one tried to remove\nthe flux density on one side of an ordinary bar magnet by\napplying the scheme, one would simply remove slices of the\nbar magnet, until the magnet would be removed completely.\nThis does result in zero flux density, but does not leave any\nregion with flux at all.\nAs an additional improvement, the removed magnet ma-\nterial can be replaced by a high permeability soft magnetic\nmaterial, to shield the low flux density area from field lines\nfrom the new magnet configuration. This will lower the flux\ndensity in the low flux density region further. If the magnet\nmaterial is replaced by air the scheme is henceforth referred\nto as improvement scheme (Air), while if magnet material\nis replaced by soft magnetic material the reference term is\nimprovement scheme (Iron). The difference between these\ntwo cases is illustrated in the next section.\nDue to the high permeability of the soft magnetic material\none would not necessarily have to replace all the enclosed\nmagnet material with a soft magnetic material. Removing the\nmagnet material and using only a small layer of soft magnetic\nmaterial along the edge of the remaining magnet to shield\nthe low flux density region will in general result in the same\nmagnetic field as replacing all the magnet material with soft\nmagnetic material. This will be an attractive option if the\nweight of the final assembly is an issue. However, the only\ndifference between these two solutions is the amount of soft\nmagnetic material used, and this option will not be considered\nfurther here.\nIn practice the scheme is implemented numerically and\nModel two- \n   dimensional \n      magnet design Find equipotential \nline of A  enclosing \nlow flux density region \nReplace magnet \nmaterial confined \nby equipotential \nline by ... z\nRecalculate field \nIs stop criteria \nreached? no \nProceed to \nfurther \noptimization yes Soft magnetic \nmaterial Air Figure 1. The flow diagram for the improvement scheme.\napplied to a numerical simulation of a magnet design. The\nscheme is presented as a flow diagram in Fig. 1.\n3. Applying the scheme\nThe improvement scheme is best illustrated through an exam-\nple. Here we consider the concentric Halbach cylinder design,\nwhich is a cylindrical magnet with an air gap in between an\nouter and inner cylindrical magnet structure [ 12]. Each cylin-\nder is magnetized such that the remanent flux density at any\npoint varies continuously as, in polar coordinates,\nBrem;r=Bremcos(pf)\nBrem;f=Bremsin(pf); (1)\nwhere Bremis the magnitude of the remanent flux density\nandpis an integer [ 13;14]. The subscript rdenotes the\nradial component of the remanence and the subscript fthe\ntangential component. A positive value of pproduces a field\nthat is directed into the cylinder bore, and a negative value\nproduces a field that is directed outwards from the cylinder.\nAs an example we consider a magnet with four high and\nfour low flux density regions which can be created by having\nap=2outer Halbach cylinder and a p=\u00002inner HalbachImproving magnet designs with high and low field regions — 3/7\ncylinder and with dimensions Rinn;int=10mm, Rinn;ext=120\nmm, Rout;int=150mm and Rout;ext=220mm, which are\nindicated in Fig. 2. The scheme could be equally well applied\nto any magnetic circuit with adjacent high and low flux density\nregions where the aim is to increase the difference between\nthese regions.\nIn the example setup magnets with a remanence of Brem=\n1:4T and a relative permeability of mr=1:05which are the\nproperties of standard neodymium-iron-boron (NdFeB) mag-\nnets [ 15] are used. We define the high and low flux density\nregions to be of the same size and to span an angle of 45\ndegree each.\nThe improvement scheme will be applied to this design\nusing a numerical two dimensional model implemented in the\ncommercially available finite element multiphysics program\nComsol Multiphysics [16].\nAs an equipotential line of Azthat encircles the low flux\ndensity region is chosen the equipotential line of Azthat goes\nthrough the point r=135 mm ;f=22:5\u000e, i.e. the point in the\nmiddle of the air gap, half way between the centers of the high\nand low flux density regions. This equipotential line is shown\nin Fig. 2(b).\nThe improvement scheme in which the magnet material\nis replaced by air is shown in Fig. 3, while the same scheme\nwhere the magnet material is replaced by iron is shown in Fig.\n4. Iron was chosen as the soft magnetic material because it\nhas a very high permeability as well as being easily workable\nand reasonably priced.\nIt is seen that applying the improvement scheme does\nreduce the flux density in the low flux density region, but the\nflux density in the high flux density region also decreases as\nmore and more magnet material is removed.\nThe effects of applying the two versions of the improve-\nment scheme are shown in Fig. 5, which shows the magnetic\nflux density in the middle of the air gap as a function of the\nangle, f.\nIt is seen from the figure that some flux is lost in the high\nflux density region, but the flux density in the low flux density\nregion is also almost completely removed. Substituting with a\nsoft magnetic material lowers the flux density in the low field\nregion more than by substituting with air, because the soft\nmagnetic materials shields the low field region.\nThe effect of applying the scheme is shown in Fig. 6\nwhere the difference in flux density as a function of the cross-\nsectional area of the magnet is plotted. Both improvement\nschemes (Air) and (Iron) are shown. The data shown in Fig.\n5, but integrated over the complete high and low field regions\nare thus shown in this figure. As can clearly be seen applying\nthe optimization schemes at first reduces the cross-sectional\narea of the magnet, Amag, while at the same time improving\nthe difference in flux density between the high and the low\nflux density regions. The largest difference in flux density is\nobtained after only one iteration for both the improvement\nscheme (Air) and improvement scheme (Iron). In the latter\ncase, which is also the best case, the amount of magnet mate-\nAir Inner magnet\nR\nout, int RR\nRinn, ext \ninn, int \nout, ext                    Air gapOuter magnet\nϕ(a) The full concentric Halbach cylinder.\n(b) A quadrant of the concentric Halbach cylinder design.\nFigure 2. The full concentric Halbach cylinder (a) and a\nquadrant of the design (b). The magnetization is shown as\nblack arrows on the magnets, which are grey. The flux\ndensity in the air gap between the cylinders is shown as a\ncolor map. In (b) the equipotential line of Azwhich encloses\nthe low flux density region is shown as a thick black line,\nwhereas other contours of Azare shown as thin black lines. It\nis magnet material inside the thick black line that is removed.\nrial used is reduced by 15% and the difference in flux density\nis increased by 41%.Improving magnet designs with high and low field regions — 4/7\n(a) Iteration 1.\n (b) Iteration 6.\nFigure 3. The improvement scheme (Air) applied to a quadrant of the magnet design. The first iteration step (a) and the sixth\nstep (b) are shown. The first iteration step corresponds to Fig. 2(b) where the magnet material enclosed by the thick black line\nhas been removed.\n(a) Iteration 1.\n (b) Iteration 3.\nFigure 4. The improvement scheme (Iron) applied to a quadrant of the magnet design. The first iteration step (a) and the third\nstep (b) are shown. The first iteration is identical to the first iteration in Fig. 3, expect that iron has been substituted instead of\nair. Areas of iron are indicated by dark grey.Improving magnet designs with high and low field regions — 5/7\nφ [degree]|B|[T]\n  \n0 22.5 45 67.5 9000.20.40.60.811.21.41.61.8\nOriginal design\n1st ite. imp. scheme (Air)\n6th ite. imp. scheme (Air)\n1st ite. imp. scheme (Iron)\n3rd ite. imp. scheme (Iron)\nFigure 5. The flux density as a function of angle in the\nmiddle of the air gap for the models shown in Figs. 3 and 4.\nThe vertical lines separate the high and low flux density\nregions.\nAmag [m2]/angbracketleftBhigh/angbracketright − /angbracketleftBlow/angbracketright[T]\n  \n0.04 0.06 0.08 0.1 0.12 0.140.40.50.60.70.80.911.1\nOriginal design\nImp. scheme (Air)\nImp. scheme (Iron)\nµ0H·ˆBrem>−0.075 T\nFigure 6. The difference in flux density as a function of the\ncross-sectional area of the magnet for the improvement\nscheme. Decreasing values of Amagindicates further iteration\nsteps. Also shown is the difference in flux gained by\nreplacing magnet material with a high permeability soft\nmagnetic material where the applied magnetic field is parallel\nor almost parallel to the magnetization, i.e. where\nm0H\u0001ˆBrem>\u0000g. This has been done on the model with a\nsingle application of the improvement scheme (Iron), i.e. the\nmodel with the highest flux difference.\n4. Further design considerations\nThe magnetic design produced by applying the improvement\nscheme might not be easily manufacturable, as is the case\nfor the example considered above. Also, for this examplethe direction of magnetization varies continuously which is\nalso unsuitable for manufacturing purposes. To overcome\nthese problems the design must be segmented into regular\npieces of permanent magnets, each with a constant direction of\nmagnetization, and pieces of high permeability soft magnetic\nmaterial. This segmentation can be accomplished in numerous\nways, and is in itself a process that must be optimized. It must\nalso be considered whether the added manufacturing cost\nof the magnet design is worth the increased difference in\nflux density and the lowered material cost. However, before\nsegmenting a design an additional way of lowering the amount\nof permanent magnet material used in a given magnet design\nshould also be considered.\nAs also stated in Ref. [ 17] and [ 18] it is advantageous to re-\nplace magnet material with a high permeability soft magnetic\nmaterial if the applied magnetic field is parallel to the rema-\nnence. In an ideal hard magnet the anisotropy field is infinite\nwhich mean that components of the magnetic field, H, and B\nthat are perpendicular to the direction of the remanence, ˆBrem,\nhave no effect on the magnet. Here ˆBrem=Brem=jjBremjj,\ni.e. the unit vector in the direction of Brem. Here we also\npropose to replace magnet material that has a small negative\ncomponent ofjjH\u0001ˆBremjj, as this has a poor working point far\nfrom the maximum energy density of the magnet. This will\nof course affect the flux density generated in the air gap, so\ncare must be taken not to remove to much magnetic material.\nWe thus propose to replace magnet material where\nm0H\u0001ˆBrem>\u0000g; (2)\nwhere gis a positive number. The value for gcan be changed\ndepending on the demagnetization curve for the magnet mate-\nrial being used, however in general gmust be chosen small,\ni.e. on the order of at most 0.1 T.\nHaving replaced magnet material by soft magnetic mate-\nrial according to Eq. (2) and resolved the magnetic system,\nthe magnet design must be investigated if there are now new\nregions where Eq. (2) holds and magnet material can be\nreplaced. The result of performing this replacement with a\nvalue of g=0:075T to the model produced by a single ap-\nplication of the improvement scheme (Iron) is shown in Fig.\n7. This value of 0.075 T has been chosen such that magnet\nmaterial is replaced in both the inner and outer magnet. For\na lower value of gonly material in the outer magnet is re-\nplaced. The optimal value of gwould have to be analyzed for\neach individual magnet design. For this model the magnet\nmaterial is replaced three successive times until the change\nin magnet volume from one iteration to the next is less than\n5%, at which point replacing the small remaining areas does\nnot change the flux density significantly. The result of the\nreplacement is also shown in Fig. 6. By replacing magnet\nmaterial with high permeability soft magnetic material the\namount of magnet material is reduced by an additional 27%\ncompared to the original design while the difference in flux\ndensity was increased slightly by 4%, again compared to the\noriginal design.Improving magnet designs with high and low field regions — 6/7\nFigure 7. Replacing magnet material with a high\npermeability soft magnetic material where the applied\nmagnetic field is parallel or almost parallel to the remanence\non the model shown in Fig. 4 (a) three successive times\nresults in the magnet design shown. The line in the iron\nregion in the outer magnet separates the iron regions\ngenerated by the improvement scheme and the parallel\nreplacement method and it is only shown for reference.\nWhen replacing magnet material by soft magnetic mate-\nrial it is important to ensure that the shapes of the replaced\nsegments are not such that the demagnetization of the seg-\nments are high as this can reduce the internal field in the soft\nmagnetic material. However, as a high permeability material\nis used, even a very small field will cause the material to sat-\nurate, and thus this problem can be ignored except for cases\nwith extremely high demagnetization.\nAs can be seen from Figs. 6 and 7 replacing magnet\nmaterial with soft magnetic material can also reduce the man-\nufacturability of the magnet design, and thus the same con-\nsideration as with the improvement scheme applies. Here we\nwill not consider segmenting the concentric Halbach cylinder\ndesign, as the design is only meant to serve as an example and\nalso because no clear optimum segmentation procedure can\nbe suggested. In Ref. [ 19] we apply the present improvement\nschemes to a magnet design which is then segmented and\nconstructed. The resulting magnet show high performance for\nmagnetic refrigeration.\nWhen using a magnet design in an application a mag-\nnetic material will usually be placed within the air gap in\nthe high and low field regions. This might alter the mag-\nnetic field in the high field region, which will alter the field\nlines and thus might lead to a different magnet design if the\nimprovement scheme is applied with the material present in\nthe air gap. However, unless high permeability materials are\nused, the magnetic field will change little. As an example\nconsider magnetic refrigeration where Gd is commonly used\nx [mm]y [mm]\n  \n406080100120140160406080100120140160 Air\nGd\nPlatesFigure 8. The equipotential line of Azthat goes through the\npoint r=135 mm ;f=22:5\u000efor a system with an empty air\ngap, i.e. Fig. 2b, and for a system where the air gap is\ncompletely filled with Gd or with 500 plates of Gd with a\nthickness of 0.9 mm. The permeability of Gd at 273 K has\nbeen used.\nas the magnetocaloric material that is placed in the air gap.\nThis material has a relative permeability in the range of 2-10,\ndepending on temperature and magnetic field. Using the per-\nmeability of Gd at 273 K as a function of magnetic field, as\nobtained from Ref. [ 4], we have calculated the equipotential\nline of Azfor a case where the air gap was completely filled\nwith Gd at a temperature of 273 K. For the first iteration this\nleads to a similar shaped equipotential line of Az, but which\nencloses an area that is 6.9% larger than for the case without\nGd. It is especially in the outer magnet that the equipotential\nline for the Gd case is larger than for the case with an empty\nair gap. For a packed sphere bed the porosity is usually around\n0.36, which will lower the impact of placing Gd in the air gap.\nWe have also calculated the equipotential line of Azfor a case\nwhere the air gap is filled with 500 plates of Gd. These plates\nhave a thickness of 0.9 mm and a spacing in the center of the\nair gap of 0.8 mm. Using these plates the change in area of\nthe equipotential line is only 2.9% and the contours are almost\nidentical. The equipotential line for both cases are shown in\nFig. 8. Thus placing a low permeability magnetic material\nin the air gap does not significantly change the equipotential\nline.\n5. Conclusion\nAn algorithm for improving the difference in flux density be-\ntween a high and a low flux density region in an air gap in\na magnetic structure has been presented and as an example\napplied to a two dimensional concentric Halbach magnet de-\nsign. For the design considered, applying the scheme reduces\nthe amount of magnet material used by 15% and increases the\ndifference in flux density by 41%. For the design consideredImproving magnet designs with high and low field regions — 7/7\nhere it was also shown that by replacing magnet material with\na high permeability soft magnetic material where the applied\nmagnetic field is parallel or almost parallel to the remanence\nthe amount of magnet material used can be reduced by an\nadditional 27% compared to the original design while the\ndifference in flux density was increased slightly by 4%, again\ncompared to the original design.\nAcknowledgements\nThe authors would like to acknowledge the support of the\nProgramme Commission on Energy and Environment (EnMi)\n(Contract No. 2104-06-0032) which is part of the Danish\nCouncil for Strategic Research.\nReferences\n[1]K. A. Gschneidner Jr and V . K. Pecharsky, Int. J. Refrig.\n31 (6), 945 (2008).\n[2]R. Bjørk, C. R. H. Bahl, A. Smith, and N. Pryds, Int. J.\nRefrig. 33, 437 (2010).\n[3]V . K. Pecharsky and K. A. Gschneidner Jr, Int. J. Refrig.\n29 (8), 1239 (2006)\n[4]R. Bjørk, C. R. H. Bahl and M. Katter, J. Magn. Magn.\nMater. 322, 3882 (2010).\n[5]T. Okamura, R. Rachi, N. Hirano, and S. Nagaya, Proc. 2nd\nInt. Conf. on Magn. Refrig. at Room Temp. 377 (2007).\n[6]C. Zimm, J. Auringer, A. Boeder, J. Chell, S. Russek, and\nA. Sternberg, Proc. 2ndInt. Conf. on Magn. Refrig. at\nRoom Temp., 341 (2007).\n[7]J. Tu ˇsek, S. Zupan, A. Sarlah, I. Prebil, and A. Poredos,\nProc. 3rdInt. Conf. on Magn. Refrig. at Room Temp., 409\n(2009).\n[8]W. Ouyang, D. Zarko, T. A. Lipo, Conference Record\nof the 2006 IEEE Industr. Appl. Conf. Forty-First IAS\nAnnual Meeting 4, 1905 (2006).\n[9]A. E. Marble, IEEE. Trans. Mag. 44 (5), 576 (2008).\n[10]J. Choi and J. Yoo, IEEE. Trans. Mag. 44 (10) (2008).\n[11]Z. Haznadar, and Z. Stih. Electromagnetic Fields, Waves\nand numerical methods. IOS Press (2000).\n[12]R. Bjørk, A. Smith, and C. R. H. Bahl, J. Magn. Magn.\nMater. 322, 133 (2010).\n[13]J. C. Mallinson, IEEE Trans. Magn. 9 (4), 678 (1973).\n[14]K. Halbach, Nucl. Instrum. Methods 169 (1980).\n[15]Standard specifications for permanent magnet materials,\nInt. Mag. Assoc., Chicago, USA, (2000).[16]COMSOL AB, Tegnergatan 23, SE-111 40 Stockholm,\nSweden.\n[17]F. Bloch, O. Cugat, G. Meunier, and J. C. Toussaint, IEEE\nTrans. Magn. 34 (5), 2465 (1998).\n[18]J. M. D. Coey and T. R. Ni Mhiochain, Permanent mag-\nnets. In: High Magnetic Fields, Edt: F. Herlach and N.\nMiura, World Scientific Publishing, 25 (2003).\n[19]R. Bjørk, C. R. H. Bahl, A. Smith, D. V . Christensen and\nN. Pryds. J. Magn. Magn. Mater. 322, 3324 (2010)."    },    {        "title": "1410.2681v1.Comparison_of_adjustable_permanent_magnetic_field_sources.pdf",        "content": "Published in Journal of Magnetism and Magnetic Materials, Vol. 322 (22), 3664-3671, 2010\nDOI: 10.1016/j.jmmm.2010.07.022\nComparison of adjustable permanent magnetic field\nsources\nR. Bjørk, C. R. H. Bahl, A. Smith and N. Pryds\nAbstract\nA permanent magnet assembly in which the flux density can be altered by a mechanical operation is often\nsignificantly smaller than comparable electromagnets and also requires no electrical power to operate. In this\npaper five permanent magnet designs in which the magnetic flux density can be altered are analyzed using\nnumerical simulations, and compared based on the generated magnetic flux density in a sample volume and\nthe amount of magnet material used. The designs are the concentric Halbach cylinder, the two half Halbach\ncylinders, the two linear Halbach arrays and the four and six rod mangle. The concentric Halbach cylinder design\nis found to be the best performing design, i.e. the design that provides the most magnetic flux density using the\nleast amount of magnet material. A concentric Halbach cylinder has been constructed and the magnetic flux\ndensity, the homogeneity and the direction of the magnetic field are measured and compared with numerical\nsimulation and a good agreement is found.\nDepartment of Energy Conversion and Storage, Technical University of Denmark - DTU, Frederiksborgvej 399, DK-4000 Roskilde, Denmark\n*Corresponding author : rabj@dtu.dk\n1. Introduction\nA homogeneous magnetic field for which the flux density\ncan be controlled is typically produced by an electromagnet.\nTo generate a magnetic flux density of 1.0 T over a reason-\nably sized gap an electromagnet requires a large amount of\npower, typically more than a thousand watts, and additionally\na chiller is needed to keep the electromagnet from overheating.\nThis makes any application using such an electromagnet very\npower consuming.\nInstead of using an electromagnet a permanent magnet\nconfiguration for which the flux density can be controlled by a\nmechanical operation can be used. A number of such variable\npermanent magnetic flux sources have previously been inves-\ntigated separately [ 1;2], and presented in a brief overview [ 3]\nbut no detailed investigations determining the relative efficien-\ncies of the different designs have been published. Here five\nsuch designs are compared and the best performing design\nis found. The efficiency of some of the magnet designs dis-\ncussed in this paper have also been analyzed elsewhere [ 4;5].\nHowever, there only the efficiency of designs of infinite length\nis characterized. In this paper we consider designs of finite\nlength, which is important as the flux density generated by a\nfinite length magnet assembly is significantly reduced com-\npared to designs of infinite length. Also we parameterize the\noptimal designs, allowing other researchers to build efficient\nmagnet assemblies.\nExamples of applications where an adjustable permanent\nmagnet assembly can be used are nuclear magnetic resonance\n(NMR) apparatus [ 6], magnetic cooling devices [ 7] and parti-\ncle accelerators [ 8]. The flux density source designed in this\npaper is dimensioned for a new differential scanning calorime-ter (DSC) operating under magnetic field designed and built at\nRisø DTU [ 9], but the general results apply for any application\nin which a variable magnetic field source is needed.\n2. Variable magnetic field sources\n2.1 Design requirements\nIn the analysis of a variable magnetic field source some de-\nsign constrains must be imposed, such as the minimum and\nmaximum producible flux density. In this analysis the maxi-\nmum flux density is chosen to be 1.5 T which is a useful flux\ndensity for a range of experiments. The minimum flux density\nis required to be less than 0.1 T both to allow measurements\nat low values of the magnetic flux density, as well as to allow\nplacement of a sample with only small interaction with the\nmagnetic field. Also a flux density of less than 0.1 T is more\neasily realizable in actual magnet assemblies than if exactly 0\nT had been required. Ideally the flux density must be homo-\ngeneous across the sample at any value between the high and\nlow values. The mechanical force needed to adjust the flux\ndensity is also considered.\nThe magnet assembly must be able to contain a sample\nthat can be exposed to the magnetic field, and the sample\nmust of course be able to be moved in and out of the magnet\nassembly. The size of a sample can be chosen arbitrarily, and\nfor this investigation a sample volume shaped as a cylinder\nwith a radius of 10 mm and a length of 10 mm was chosen.\nTo allow the sample to be moved we require that the clearance\nbetween the magnet and the sample must be at least 2.5 mm,\nin effect increasing the gap radius to 12.5 mm. The sample\nvolume is sufficiently large to allow the magnet designs to bearXiv:1410.2681v1  [physics.ins-det]  10 Oct 2014Comparison of adjustable permanent magnetic field sources — 2/9\nused in the DSC device discussed above.\n2.2 Numerical analysis\nGiven the above design requirements five different permanent\nmagnet designs have been selected for detailed investigation.\nIn each of the designs it is possible to adjust the generated flux\ndensity by a mechanical operation. Numerical simulations of\neach design for a range of parameters were performed and\nthe designs are evaluated based on the mean flux density in\nthe sample volume. Each design was always centered on the\nsample cylinder.\nAll numerical work in this paper was done in three di-\nmensions using the commercially available finite element\nmultiphysics program, Comsol Multiphysics [10]. The equa-\ntion solved in the simulations is the magnetic scalar potential\nequation,\n\u0000Ñ\u0001(m0mrÑVm\u0000Brem) =0; (1)\nwhere Vmis the magnetic scalar potential, Bremis the remanent\nflux density, m0is the permeability of free space and mris\nthe relative permeability, defined as¶B\n¶Hto account for the\nremanence of the permanent magnets, and assumed to be\nisotropic.\nOnce the magnetic scalar potential has been found, the\nmagnetic field, H, can be found as\nH=\u0000ÑVm; (2)\nand subsequently the magnetic flux density, B, can be deter-\nmined.\nThe permanent magnets are modeled by the relation B=\nm0mrH+Brem, which is justified because the intrinsic coer-\ncivity of a NdFeB magnet, which is used as a permanent\nmagnet in present calculations, can be as high as 3 T [ 11].\nThe transverse susceptibility of the magnets is ignored, as\nthe anisotropy field has a value of 8 T[ 12]. The remanence\nof the permanent magnets in all designs considered here is\nBrem=1:2T and the relative permeability is mr=1:05, in\naccordance with values for a standard NdFeB magnet [11].\nAn important issue to note is that the magnetostatic prob-\nlem is scale invariant, i.e. if all dimensions are scaled by the\nsame factor the magnetic field in a given point will be the\nsame if this point is scaled as well. This means that quantities\nsuch as the average value and the homogeneity of the mag-\nnetic field in a scaled volume of space will be the same. Thus\nthe conclusions of this paper apply equally to any sample\nvolume that has the same relative dimensions as the sample\nvolume used here, as long as the magnet designs are scaled\nappropriately.\nIn the following subsections the five designs are intro-\nduced and analyzed.\n2.3 Concentric Halbach cylinders\nThe concentric Halbach cylinder consists of two Halbach\ncylinders, which are cylindrical permanent magnet assembliesthat have a direction of magnetization that changes continu-\nously as, in polar coordinates,\nBrem;r=Bremcos(f)\nBrem;f=Bremsin(f); (3)\nwhere Bremis the magnitude of the remanent flux density\n[13; 14].\nFor practical applications the Halbach cylinder is con-\nstructed from segments, each with a constant direction of\nmagnetization. A Halbach cylinder with eight segments pro-\nduces 90% of the flux density of a perfect Halbach cylinder\nwhile a configuration with 16 segments obtains 95% of the\nflux density [15].\nIf two Halbach cylinders are placed concentrically inside\neach other, the flux density in the inner cylinder bore can\nbe adjusted by rotating one of the cylinders relative to the\nother. If the permanent magnets used to construct the Halbach\ncylinders have a permeability close to one, as is the case\nfor NdFeB magnets, the total flux density of the concentric\nHalbach cylinder is approximately the vector sum of the flux\ndensities produced by the individual cylinders. An illustration\nof the concentric Halbach cylinder design is shown in Fig. 1.\nThe concentric Halbach cylinder system is characterized\nby eight parameters, namely the internal radius, rin, external\nradius, rex, and the length, L, of each of the two cylinders, and\nthe number of segments of each cylinder. The segments of the\ntwo cylinders were always aligned in the high field position,\nas shown in Fig. 1.\nThe advantages of the concentric Halbach cylinder design\nis that adjusting the flux density by rotating either of the\ncylinders does not change the geometry of the device. Also,\nin the infinite length case with no segmentation, there is no\ntorque when rotating one of the cylinders [ 16]. However,\na small torque is present in real-world assemblies, due to\nsegmentation and flux leakage through the cylinder bore [ 2].\nThe disadvantage of the concentric Halbach cylinders is that\neven though the cylinders are designed to have exactly the\nsame flux density in the center of the cylinder bore, so that the\nflux density will be zero when they are offset by 180degree,\nthis will not completely cancel the magnetic field away from\nthe center of the bore. This is because the cylinders have\ndifferent internal radii which means that the flux loss through\nthe ends of each cylinder will not be the same and the flux\ndensity will not cancel all the way out of the cylinder bore.\nThis can be important when placing samples in the magnet,\nas they will respond to the gradient of the magnetic field as\nthey are moved in and out of the cylinder bore.\nThe parameters varied for the modeling of this design are\npresented in Table 1. The internal radius of the outer Halbach\ncylinder was kept fixed at the external radius of the inner Hal-\nbach cylinder plus 2 mm to allow room for the inner cylinder\nto rotate. Both the inner and outer Halbach cylinder were\nmodeled from eight segments to make the design economi-\ncally affordable. Many of the above configurations do not\nproduce a sufficiently low magnetic flux density ( <0:1T) inComparison of adjustable permanent magnetic field sources — 3/9\nFigure 1. A two dimensional illustration of the concentric\nHalbach cylinder. Each Halbach cylinder is segmented into\neight parts. Shown as arrows is the direction of\nmagnetization. The sample volume is shown as a dashed\ncircle. In the configuration shown the total field in the sample\nvolume is maximized.\nthe bore when the cylinders are oppositely aligned. These are\nnot suitable designs and were not considered further.\nThe field in the exact center of a finite length Halbach\ncylinder can be calculated analytically by the expression[17]\nB(r=0;z=0) =Brem0\n@ln\u0012rex\nrin\u0013\n+z0\n2q\nz2\n0+r2\nin\n\u0000z0\n2q\nz2\n0+r2ex\u0000ln0\n@z0+q\nz2\n0+r2ex\nz0+q\nz2\n0+r2\nin1\nA1\nA(4)\nwhere z0=L=2. The calculated flux density must be corrected\nfor segmentation of the Halbach cylinder. Using this expres-\nsion the parameters that do not produce a concentric Halbach\ncylinder for which the field in the center is zero, could also\nhave been found and disregarded. This expression is later\ncompared with the results of the numerical simulations.\n2.4 Two half Halbach cylinders\nAs previously mentioned it is not possible to adjust the flux\ndensity of a single particular Halbach cylinder. However,\nif the Halbach cylinder is split into two parts that can be\nmoved away from each other the flux density between the\nhalf-cylinders can be controlled in this way. An illustration\nof this idea is shown in Fig. 2. This design is termed the two\nhalf Halbach cylinders. The design can be characterized by\nfour parameters, namely the internal and external radii and\nthe length of the identical half-cylinders as well as the number\nof segments. Notice that an additional gap has been included\nby removing some of the magnet from the top and bottom\nx xFigure 2. A two dimensional illustration of the two half\nHalbach cylinders. In total 10 segments are used, of which\nseveral are identical. The direction of magnetization is shown\nas arrows. The sample volume is shown as a dashed circle.\nNotice the top and bottom gaps between the half-cylinders.\nThis allows room for handling and securing the magnets. The\nhalf-cylinders are moved along the x-direction to control the\nflux density.\nbetween the half-cylinders. This has been done to allow room\nfor handling and securing the magnets.\nThe advantage of this design is that only a simple linear\ndisplacement is needed to control the flux density between\nthe cylinders. However, the disadvantage is that there must\nbe enough room to move the half-cylinders away from each\nother to lower the flux density, and when the half-cylinders are\napart the flux density they each generate will influence nearby\nmagnetic objects. Also, a substantial force will in some cases\nbe needed to keep the two half Halbach cylinders close to\neach other to generate a high flux density.\nThe parameters varied for this design can again be seen in\nTable 1. The number of segments was fixed at ten, again to\nmake the design economically affordable.\n2.5 Two linear Halbach arrays\nThe linear Halbach array is a magnetic assembly that uses the\nsame principle as the Halbach cylinder to generate a one-sided\nflux [ 13]. The linear Halbach array is characterized by the\nwidth, height and length of the identical blocks as well as the\nnumber of blocks used in the array. For the array considered\nhere three blocks are used, as this is the minimum number of\nblocks needed to create a one-sided array. An adjustable flux\ndensity configuration can be made by placing two mirrored\nlinear Halbach arrays opposite each other, as with the two half\nHalbach cylinders. By moving the arrays closer or further\napart the flux density between them can be controlled. An\nillustration of the two linear Halbach array design is shown in\nFig. 3.Comparison of adjustable permanent magnetic field sources — 4/9\nTable 1. The parameters varied of each design. The number in parentheses denotes the step size. A asterisk denotes\nnon-equidistant steps and no parentheses indicates a fixed value. For the two linear Halbach arrayadenotes the width andb\ndenotes the height of a magnet block.\nConcentric Two half Two linear Four Six\nHalbach Halbach Halbach rod rod\ninner magnet outer magnet cylinders array mangle mangle\nInner radius [mm] 12.5 21-37 (*) + 2 12.5 25-150a(5) - -\nOuter radius [mm] 21-37 (*) 37-115 (*) 30-150 (10) 25-150b(5) 10-100 (2.5) 1-70 (1)\nLength [mm] 35-95 (10) 35-95 (10) 30-300 (10) 25-150 (5) 10-250 (5) 10-600 (5)\nSegments/rods 8 8 10 3 4 6\nHeight\nLength Width \nSample \nvolume xx\nFigure 3. A three dimensional illustration of two three block\nlinear Halbach arrays. The high flux density region is created\nin between the two arrays, where the sample volume is\nplaced. The arrays are moved along the x-direction to control\nthe flux density.\nThe sample volume can, because of its short length, be\nrotated, so that the arrays can be placed closer to each other.\nThis configuration has also been considered, although it might\nrequire an alternative method for mounting the sample than\nfor the other designs considered here.\nThe advantage of the linear Halbach array is that it is easy\nto construct, as it can be made using simple rectangular mag-\nnet blocks. However, the design has the same disadvantages\nas the two half Halbach cylinders in that a large force will, in\nsome cases, be needed to keep the arrays close together and a\nhigh flux density will still be generated when the arrays are\nmoved apart, which could influence nearby magnetic objects.\nFor the sample position as shown in Fig. 3 the two linear\nHalbach arrays were separated by a distance of 25 mm, so\nthat the sample volume fitted in between the arrays. For the\nalternative sample orientations the arrays were separated by a\ndistance of 15 mm, so that the rotated sample fitted betweenthe arrays. For either of the sample positions the height, width\nand length of a rectangular permanent magnet block were\nindependently varied as given in Table 1. Each array consists\nof three identical blocks.\nOne can envision designs that have a geometrical form\n“between” the two linear Halbach arrays and the two half Hal-\nbach cylinders. The performance of these will be comparable\nto the performance of either of the two linear Halbach arrays\nor the two half Halbach cylinders.\n2.6 The mangle\nThe mangle is made up of identical transversely magnetized\npermanent magnet rods that can be rotated to alter the flux\ndensity at the center of the assembly [ 1] . The rods must be\nrotated alternately clockwise and counterclockwise to con-\ntinuously alter the flux density in a homogeneous way. The\ndesign can be characterized by three parameters, namely the\nradius and the length of a rod as well as the number of rods\nused. An illustration of a mangle design with four cylinders\nin the orientation that generates a high flux density is shown\nin Fig. 4 A. The conventional low flux density orientation for\nthe four rod mangle, shown in Fig. 4 B, does not produce a\nvery low flux density, typically around 0.1-0.3 T across the\nsample volume (if magnet rods with a remanence of 1.2 T are\nused). An alternative orientation of the rods, shown in Fig. 4\nC, produces a much lower flux density, typically less than 0.05\nT across the sample volume. Unfortunately there is no way to\nadjust the flux density from the configuration shown in Fig. 4\nA to that shown in Fig. 4 C while maintaining homogeneity in\nthe sample volume. Thus in the four rod mangle considered\nhere we envision a design where the rods are rotated from the\nconfiguration shown in Fig. 4 A to that in Fig. 4 B and finally\nto that in Fig. 4 C.\nA six rod mangle design is also considered. The high\nflux density orientation of the rods is shown in Fig. 5 A,\nwhile the low flux density configuration is shown in Fig. 5\nB. Notice that the rods have simply been turned 90 degrees\nalternately. The low flux density orientation produce a flux\ndensity typically less than 0.1 T across the sample volume, so\nno alternate orientations need be considered.\nThe advantage of this design is economical as transversely\nmagnetized rods are readily available. The design is also\ncompact and produces a low stray flux density. The disad-Comparison of adjustable permanent magnetic field sources — 5/9\nA B C\nFigure 4. A schematic drawing of the four rod mangle\ndesign. (A) shows the high flux density position of the four\nrod mangle design. The high flux density is created across the\nsample volume. (B) shows the low flux density configuration,\nas suggested by [1]. This position is reached by a 90 degree\nalternate rotation of the rods shown in (A). (C) shows an\nalternate position of the rods that generate a much lower flux\ndensity in the sample volume than the position shown in Fig.\nB.\nA B\nFigure 5. A schematic drawing of the six rod mangle design.\nThe high flux density position of the six rod mangle is shown\nin Fig. A, while the low flux density position of the six rod\nmangle in shown in Fig. B. In the latter figure the rods have\nbeen alternately rotated 90 degree from the position shown in\nFig. A.\nvantage is that the volume between the rods scales with the\nradius of the rods. Therefore the flux density can only be\nincreased to a maximum value for a given sample volume,\nwithout increasing the size of the volume between the rods.\nThe parameters varied for both the four and six rod man-\ngles are given in Table 1. The rods are always placed as\nclosely as possible to each other or to the sample, depending\non the mangle parameters.\n3. Comparing the different designs\nTo find the best parameters for each design parameter variation\nsimulations were conducted for each of the different designs\nwith the parameters previously stated.\nTo allow the designs to be more easily compared, the best\nperforming of each of the five different designs are selected.\nThis is done by selecting the parameters that produce a high\naverage flux density in the sample volume and at the same\ntime has a low volume of magnet material. This approach has\npreviously been used to optimize the Halbach cylinder design\n[15], but other optimization methods exist such as the figure ofmerit, M\u0003, which is almost identical to the optimization used\nhere except that it also include the remanence of the magnets\n[5]. Also an optimization parameter for permanent magnet\nassemblies used in magnetic refrigeration devices exists [ 18].\nIn Fig. 6 both these optimally dimensioned designs, as well\nas the other parameter variations tried, are shown for the two\nhalf Halbach cylinder design. Some of the optimal designs\nhave been indicated in the figure, and it is clearly seen that\nthese produce a given flux density using the lowest amount of\nmagnet material. The same analysis has been performed for\nthe four other designs.\nIt is worth noting that the designs referred to here as\n“optimal” are not necessarily the global optimal designs. They\nare the optimal designs of the conducted parameter survey,\nand as such designs might exist outside the parameter space, or\nat resolutions smaller than the varied parameters that perform\nbetter than the designs referred to as optimal here. However,\nbased on the detail of the parameter survey the potential for\nimprovement will be small.\n3.1 The best parameters for each design\nThe parametrization of the optimal designs of each individual\ndesign type have been found by analyzing the dimensions of\nthe optimal designs for each flux density. For the concentric\nHalbach cylinder the optimal designs fulfil\n0:8<rinner ;ex=rinner ;in\nrouter ;ex=router ;in<1 and 0 :8<Linner\nLouter<1;(5)\nwhere the first subscript denotes the inner or outer magnet and\nthe second denotes the internal or external radius. However,\nthis criteria is not enough, as some designs that fulfil these\nrequirements produce a flux density in the low flux density\nconfiguration that is higher than 0.1 T. Thus the analytical\nexpression for the flux density in the center of the system, Eq.\n(4), must be calculated to ensure that this will be less than 0.1\nT.\nThe optimal mangle designs are those where the radius, r,\nof the individual mangle rods is sufficiently small that the rods\ncan be placed close to the sample without touching each other.\nFor the four rod mangle, the relation r\u001432:5mm applies for\nthe optimal designs. Also, the ratio of the radius to the length\nmust be in the range of 0:2<radius =length <0:5. Increasing\nthe length of the rods increases the flux density in the sample\nvolume.\nFor the six rod mangle only the designs that have r\u001410\nmm are optimal. Also, the ratio of the radius to the length\nmust obey 0:05<radius =length <0:5, where the lower bond\nis necessary to obtain a high flux density.\nFor the linear Halbach array with the sample volume as\nshown in Fig. 3 the optimal designs are parameterized by\nheight'0:22\u0001width +0:02[mm]\nlength'1:0\u0001width +0:05[mm] ; (6)\nwhere the length, width and height are as shown in Fig. 3.Comparison of adjustable permanent magnetic field sources — 6/9\n0.5 0.6 0.7 0.8 0.9 11.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 00.5 11.5 22.5 33.5 4\n<B> [T] Vmag  [L] \n  \nParameterized models \nOptimal models \nFigure 6. The volume of the magnets as a function of the\naverage flux density in the sample volume for the two half\nHalbach cylinders design. Some of the optimal designs are\nmarked by circles.\nFor the linear Halbach array with the rotated sample vol-\nume the optimal designs are parameterized by\nheight'0:08\u0001width +0:02[mm]\nlength'1:3\u0001width +0:02[mm] ; (7)\nwhere the dimensions are again as shown in Fig. 3. Because\nthe sample volume has been rotated a much smaller height\nand a longer length is now favored.\nFor the two half Halbach cylinders the optimal parame-\nterized designs are characterized by the relation: radius'\n0:95\u0001length . This relation is in agreement with the optimal\ndimensions for a Halbach cylinder[15].\nThese parameterizations are obviously only valid for the\nsample volume with the relative dimensions as chosen here.\nIf a different sample volume were chosen the relations would\nbe different. However, if the sample volume is simply scaled\nby a factor then, owing to the linearity of the magnetostatic\nproblem, the magnet dimensions need simply be scaled by\nthe same factor to produce the same flux density, and thus in\nthis situation the parameterizations found above remain valid\nappropriately scaled.\nThe optimal designs for the different design types are\nshown in Fig. 7. The magnetic flux density produced by a\ngiven optimal design, i.e. a design whose dimensions follow\nthe above parameterizations, can be found from Fig. 7 by\ncalculating the volume of the magnet in the design.\nIt is seen that the concentric Halbach cylinder design is the\noptimal design as it produces a given magnetic flux density\nusing the lowest amount of magnet material. An interesting\nobservation is that the mangle designs are not able to produce\na high flux density. This is because, as already stated, as the\nradius of the rods in the mangle increases the rods must be\nmoved further away from each other, so as not to touch, and\nthus the volume in between them increases. The two half\n<B> [T] Vmag  [L] \n  \n0.5 0.6 0.7 0.8 0.9 11.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 012345\nTwo half Halbach cylinders \nTwo linear Halbach arrays \nTwo linear Halbach arrays − Rotated sample \nMangle, 4 rods \nMangle, 6 rods \nConcentric Halbach cylinder Figure 7. (Color online) The volume of the magnets as a\nfunction of the average flux density in the sample volume for\nthe best individual designs for the six designs considered.\nHalbach cylinders and the concentric Halbach cylinder do not\nperform identically due to the top and bottom gaps between\nthe half-cylinders and due to the gap between the concentric\ncylinders.\nIt is also interesting to consider the homogeneity of the\nflux density in the sample volume. To characterizes the homo-\ngeneity, the best parameter set for each design that produces\n1\u00060:01T in the high flux density position have been found.\nThe six rod mangle is not able to produce this flux density\nand so it is not present in the figure. The flux density for\nthese designs have then been varied either by rotation (man-\ngle and concentric Halbach cylinder) or translation (two half\nHalbach cylinder and two linear Halbach array). Fig. 8 shows\nthe standard deviation of the flux density,p\nhB2i\u0000hBi2, as\na function of the average flux density, hBi, for these optimal\n1 T designs. All the design types produce a quite homoge-\nneous flux density across the sample volume, but again the\nbest design is the concentric Halbach cylinder design.\nThe high homogeneity of the concentric Halbach cylinder\nmeans that the difference between the flux density calculated\nusing Eq. (4) and the numerically calculated mean flux density\nin the sample volume is less than 0.05 T in all considered\ncases.\nIn Fig. 9 the maximum force as a function of flux density\nfor the two half Halbach cylinder and the linear Halbach array\ndesigns are shown. The force shown in the figure is the force\non the optimal designs that is needed to keep the two halfs of\neach design as close together as the sample volume allows.\nAs can be seen a substantial force is needed for the designs\nthat generate a high flux density.\n4. A constructed variable field source\nAn adjustable permanent magnet has been built based on\nthe concentric Halbach cylinder design, as this is the bestComparison of adjustable permanent magnetic field sources — 7/9\n<B> [T] <B 2>−<B> 2 [T] \n  \n0 0.2 0.4 0.6 0.8 100.02 0.04 0.06 0.08 0.1 0.12 \nTwo half Halbach cylinders \nTwo linear Halbach arrays \nTwo linear Halbach arrays − Rotated sample \nMangle, 4 rods \nConcentric Halbach cylinder \nFigure 8. (Color online) The homogeneity, characterized by\nthe standard deviationp\nhB2i\u0000hBi2, for the optimal\ndifferent types of designs that produce 1 T as a function of\nthe average flux density. The mangle was turned from the\nposition shown in Fig. 4 A to that shown in Fig. 4 B.\n<B> [T] Force [N] \n  \n0.5 0.6 0.7 0.8 0.9 11.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 01000 2000 3000 4000 5000 6000 \nTwo half Halbach cylinders \nTwo linear Halbach arrays \nTwo linear Halbach arrays − Rotated sample \nFigure 9. (Color online) The maximum force needed to keep\nthe design at the maximum flux density.\nTable 2. The dimensions of the constructed concentric\nHalbach cylinder magnet.\nInner Outer\nmagnet magnet\nInternal radius [mm] 12.5 29.5\nExternal radius [mm] 27.5 80\nLength [mm] 55 65\nperforming and most practical magnet design. A maximum\nflux density of 1.5 T was chosen as the desired value in the\nsample volume. The dimensions of the magnet are given in\nTable 2.\nThe magnet was constructed and using a Hall probe (Al-\nDistance from center [mm] B [T] \n−20 −10 0 10 20 30 40 00.2 0.4 0.6 0.8 11.2 1.4 Figure 10. The measured magnetic flux density as a function\nof distance from the center of the concentric Halbach cylinder.\nBetween each measurement series the cylinders were rotated\nrelative to each other by 22.5 degree. Due to of the design of\nthe magnet it was only possible to measure down to \u000025mm.\nphaLab Inc, Model: DCM) the flux density produced by the\ndesign was measured. Both components of the magnetic flux\ndensity in the plane perpendicular to the cylinder axis, as well\nas the component parallel to the axis, were measured at 5 mm\nintervals in the center of the cylinder for nine relative rotation\npositions of the two cylinders, each separated by 22.5 degrees.\nThe initial angle was chosen to be a close to a flux density\nof zero as possible. The norm of the vector sum of the three\ncomponents of the magnetic flux density is shown in Fig. 10.\nThe uncertainty on the position of the Hall probe is esti-\nmated to be\u00061mm. There is also an uncertainty in the 90\ndegree rotation of the Hall probe necessary to measure the two\ncomponents of the flux density that are perpendicular to the\ncylinder axis. It is estimated that these uncertainties result in\na total uncertainty of \u00065%for the magnetic flux density. The\ninstrumental uncertainty of the Hall probe is \u00060:2%, which is\nmuch less than the uncertainty due to the positioning of the\nHall probe. No errorbars are shown in Fig. 10 in order to\nmaintain clarity in the plot.\nThe axial component of the magnetic flux density is in-\ncluded in the flux density shown in Fig. 10, but is quite small.\nAt no point in the cylinder bore does the axial component\nexceed 0.15 T for any rotation angle, and in the center it is\nalways less than 0.05 T for any rotation angle.\nThe measured values of the magnetic flux density have\nbeen interpolated to find the value at the center of the concen-\ntric cylinder. These values are shown in Fig. 11 as a function\nof the displacement angle, f, between the two cylinders. A\nsine function of the form B=asin(0:5(f+b)), where a\nandbare constants, has been fitted to the data as this is how\nthe field should theoretically vary. This is so because the\nmagnetic flux density produced by the inner and outer magnet\nis identical in the center and thus the combined flux densityComparison of adjustable permanent magnetic field sources — 8/9\nφ [degree] B [T] \n  \n0 30 60 90 120 150 180 00.2 0.4 0.6 0.8 11.2 1.4 1.6 \nB in center \nB( φ) = 1.47*sin(0.5* φ)\n95% confidence interval \nSimulation data \nFigure 11. The center value of the flux density as a function\nof rotation angle, f. A sine function has been fitted to the\ndata. Also shown are the results from numerical simulations.\ncan be found based on law of cosine for an isosceles triangle.\nThe fit is shown in Fig. 11 as well as the 95% confidence\ninterval of the fit for a new measurement. The constants were\ndetermined to be a=1:47\u00060:04 T and b=0\u00063 degree.\nThe magnet design has also been simulated numerically\nand the resulting flux densities are also shown in Fig. 11.\nA reasonable agreement between the measured flux density\nand the value predicted by simulation is seen. It is seen that\nthe flux density can easily be adjusted by rotating the inner\ncylinder relative to the outer cylinder.\nThe homogeneity of the flux density has been investigated\nby measuring the flux density at four off-center positions.\nThese are located 5.5 mm from the center along an angle cor-\nresponding to respectively 0, 90, 180 and 270 degrees. The\nresults for three different displacement angles, f=0;90;180\ndegrees respectively, are shown in Fig. 12. The standard\ndeviation,p\nhB2i\u0000hBi2, can be calculated for the sample\nvolume based on the data in Fig. 12. Using the four cen-\ntral data points to represent the sample volume one obtainsp\nhB2i\u0000hBi2=0:61\u000110\u00002;2:18\u000110\u00002and 2 :17\u000110\u00002for\nf=0;90 and 180 degree respectively. Thus the flux density\ndistribution is quite homogeneous.\nThe direction of the flux density changes as the cylinders\nare rotated with respect to each other. Fig. 13 shows the\ndirection as a function of the rotation angle, f, for the mea-\nsured flux density as well as simulation data for the coordinate\nsystem as shown in the figure. A good agreement between\nthese is seen.\nThe agreement between the measured magnetic flux den-\nsity and the simulation results is limited by several factors. A\nperfect agreement is not expected as the transverse susceptibil-\nity for the magnets is ignored. However, the major source of\nerror is estimated to be the positioning and rotation of the Hall\nprobe in the conducted measurements, as described earlier.\nFor all the five designs it is important to consider the coer-\nDistance from center [mm] B [T] \n  \n−10 0 10 20 30 40 00.2 0.4 0.6 0.8 11.2 1.4 1.6 \nCenter \nUp \nRight \nDown \nLeft \nφ = 0 degree \nφ = 90 degree \nφ = 180 degree Up \nDown Left Right \nCenter Figure 12. The homogeneity of the measured magnetic flux\ndensity as a function of distance from the center of the\nconcentric Halbach cylinder. The positions labeled Up,Right ,\nDown andLeftare located 5.5 mm from the center along the\ndirection corresponding to, respectively, 0, 90, 180 and 270\ndegrees.\nφ [degree] tan −1 (B y/B x) [degree] \n  \n0 30 60 90 120 150 180 −180 −165 −150 −135 −120 −105 −90 \ntan −1 (B y/B x) in center \nSimulation data xϕ\ny\nFigure 13. The direction of the field as a function of rotation\nangle, fin the coordinate system shown in the figure. The\nfield changes direction by 180 degree when f=0is crossed,\nat which point B=0.\ncivity of the permanent magnets used. For, e.g. the concentric\nHalbach cylinder design when the cylinders are offset by 180\ndegree the flux density produced by the outer cylinder will be\nparallel and opposite to the remanence of parts of the inner\ncylinder, and if this flux density is higher than the coercivity\nof the magnets the direction of magnetization will be reversed,\nwhich will render the device useless [ 15;19]. For the simu-\nlated permanent magnets a remanence of 1.2 T was used. A\ntypical industry NdFeB magnet with such a remanence has a\nhigh coercivity, m0Hc=3:2T, which is sufficiently strong to\nkeep the direction of magnetization constant.Comparison of adjustable permanent magnetic field sources — 9/9\n5. Conclusion\nFive different variable permanent magnet designs, the concen-\ntric Halbach cylinder, the two half Halbach cylinders, the two\nlinear Halbach arrays and the four and six rod mangles, were\ninvestigated and evaluated based on the generated magnetic\nflux density in a sample volume and the amount of magnet\nmaterial used. As the dipole field is scale invariant the con-\nclusion holds for all sample volumes with the same relative\ndimensions as used here. The best performing design, i.e.\nthe design that provides the highest magnetic flux density\nusing the least amount of magnet material, was the concentric\nHalbach cylinder design. Based on this result a concentric\nHalbach cylinder was constructed and the magnetic flux den-\nsity, the homogeneity and the direction of the magnetic flux\ndensity were measured. These were compared with numerical\nsimulation and a good agrement was found.\nAcknowledgements\nThe authors would like to thank J. Geyti for his technical\nassistance. Also, the authors would like to acknowledge the\nsupport of the Programme Commission on Energy and Envi-\nronment (EnMi) (Contract No. 2104-06-0032) which is part\nof the Danish Council for Strategic Research.\nReferences\n[1]O. Cugat, P. Hansson, and J. M. D. Coey. , IEEE Trans.\nMagn. 30, 4602 (1994).\n[2]T. R. Ni Mhiochain, D. Weaire, S. M. McMurry, and J.\nM. D. Coey, J. Appl. Phys. 86, 6412 (1999).\n[3]J. M. D. Coey, J. Magn. Magn. Mater. 248, 441 (2002).\n[4]M. G. Abele, Structures of permanent magnets, Wiley\n(1993).\n[5]J. M. D. Coey and T. R. Ni Mhiochain, in “High Magnetic\nFields, Science and Technology”, 1, World Scientific\n(2003).\n[6]S. Appelt, H. K ¨uhn, F. W H ¨asing, and B. Bl ¨umich, Nature\nPhysics 2, 105 (2006).\n[7]A. Tura, and A. Rowe. Proc. 2nd Int. Conf. on Magn.\nRefrig. at Room Temp., Portoroz, Solvenia, IIF/IIR:363\n(2007).\n[8]M. Sullivan, G. Bowden, S. Ecklund, D. Jensen, M.\nNordby, A. Ringwall, and Z. Wolf, IEEE 3, 3330 (1998).\n[9]S. Jeppesen, S. Linderoth, N. Pryds, L. T. Kuhn, and J. B.\nJensen, Rev. Sci. Instrum., 79 (8) , 083901 (2008).\n[10]COMSOL AB, Tegnergatan 23, SE-111 40 Stockholm,\nSweden.[11]Standard Specifications for Permanent Magnet Materi-\nals, Magnetic Materials Producers Association, 8 South\nMichigan Avenue, Suite 1000, Chicago, Illinois 60603,\n(2000).\n[12]G. Zimmermann, J. Appl. Phys. 73, 8436 (1993).\n[13]J. C. Mallinson, IEEE Trans. Magn. 9 (4) , 678 (1973).\n[14]K. Halbach, Nucl. Instrum. Methods 169(1980).\n[15]R. Bjørk, C. R. H. Bahl, A. Smith, and N. Pryds, J. Appl.\nPhys. 104, 13910 (2008).\n[16]R. Bjørk, C. R. H. Bahl, and A. Smith, J. Magn. Magn.\nMater. 322, 133 (2010).\n[17]H. Zijlstra,Phillips J. Res., 40, 259 (1985).\n[18]R. Bjørk, C. R. H. Bahl, A. Smith and N. Pryds, Int. J.\nRefrig. 33, 437 (2010).\n[19]F. Bloch, O. Cugat, G. Meunier, and J. C. Toussaint, IEEE\nTrans. Magn. 34, 5 (1998)."    },    {        "title": "1410.6248v1.Determining_the_minimum_mass_and_cost_of_a_magnetic_refrigerator.pdf",        "content": "Published in International Journal of Refrigeration, Vol. 34 (8), 1805-1816, 2011\nDOI: 10.1016/j.ijrefrig.2011.05.021\nDetermining the minimum mass and cost of a\nmagnetic refrigerator\nR. Bjørk, A. Smith, C. R. H. Bahl and N. Pryds\nAbstract\nAn expression is determined for the mass of the magnet and magnetocaloric material needed for a magnetic\nrefrigerator and these are determined using numerical modeling for both parallel plate and packed sphere bed\nregenerators as function of temperature span and cooling power. As magnetocaloric material Gd or a model\nmaterial with a constant adiabatic temperature change, representing a infinitely linearly graded refrigeration\ndevice, is used. For the magnet a maximum figure of merit magnet or a Halbach cylinder is used. For a cost of\n$40 and $20 per kg for the magnet and magnetocaloric material, respectively, the cheapest 100 W parallel plate\nrefrigerator with a temperature span of 20 K using Gd and a Halbach magnet has 0.8 kg of magnet, 0.3 kg of Gd\nand a cost of $35. Using the constant material reduces this cost to $25. A packed sphere bed refrigerator with\nthe constant material costs $7. It is also shown that increasing the operation frequency reduces the cost. Finally,\nthe lowest cost is also found as a function of the cost of the magnet and magnetocaloric material.\nDepartment of Energy Conversion and Storage, Technical University of Denmark - DTU, Frederiksborgvej 399, DK-4000 Roskilde, Denmark\n*Corresponding author : rabj@dtu.dk\n1. Introduction\nMagnetic refrigeration is a new environmentally friendly cool-\ning technology with a potential for high energy efficiency.\nThe technology is based on the magnetocaloric effect (MCE),\nwhich is the temperature change that most magnetic materials\nexhibit when subjected to a changing magnetic field. For the\nbenchmark magnetocaloric material (MCM) used in magnetic\nrefrigeration, gadolinium, the adiabatic temperature change is\nno more than 4 K in a magnetic field of 1 T [Dan’kov et al.,\n1998; Bjørk et al., 2010a], and therefore a magnetic refrigera-\ntion device has to utilize a regenerative process to produce a\nlarge enough temperature span to be useful for refrigeration\npurposes. The most utilized process for this is called active\nmagnetic regeneration (AMR) [Barclay, 1982].\nAn AMR consists of a porous matrix of a solid mag-\nnetocaloric material and a heat transfer fluid that can flow\nthrough the matrix and reject or absorb heat. The solid matrix\nis termed the regenerator. The heat is then transferred to a\ncold and hot heat exchanger at either end of the AMR. Using\nthis system a temperature gradient can be built up that can be\nmuch larger than the adiabatic temperature change produced\nby the magnetocaloric material. Typically the porous matrix\nis either a packed sphere bed [Okamura et al., 2005; Tura and\nRowe, 2009] or consists of parallel plates [Zimm et al., 2007;\nBahl et al., 2008]. A review of different magnetic refrigeration\ndevices is given in Yu et al. [2010].\nThe temperature span and cooling power generated by an\nAMR device depends on the process parameters specific to\neach AMR system. These are the shape and packing of the\nmagnetocaloric material, the temperature of the surroundings\nand the properties of the MCM used, as well as the propertiesof the heat transfer fluid, flow system, magnetic field, geome-\ntry of the AMR etc. In operation, two performance parameters\nare of key importance, the temperature span, Tspan, which is\nthe difference between the temperature of the hot and the cold\nreservoir at either end of the AMR, ThotandTcold, respectively,\nand the cooling power, ˙Q, generated by the AMR. For given\nprocess parameters, Tspanand ˙Qtrace out a curve called the\ncooling curve. In a ( Tspan,˙Q) diagram the cooling curve is in\nmany cases of interest approximated by a straight line going\nfrom (0;˙Qmax)to(Tspan ;max;0)with a negative slope. As the\nmaximum cooling power and the maximum temperature span\ncannot be realized at the same time, the operation point will\nlie on the cooling curve somewhere in between the two ex-\ntrema. Neither extremity of the curve is of interest for actual\noperation.\nDetermining the cost of an AMR is of general interest in\norder to evaluate the cost-performance of the technology. An\nassessment of the costs for a residential air conditioner based\non magnetic cooling presented in Russek and Zimm [2006]\nconcluded that the cost of the magnet is of great importance\nand furthermore found that the cost of the magnet and mag-\nnetocaloric material for such a magnetic air conditioner can\nbe competitive with conventional air conditioners. It has also\nbeen investigated [Egolf et al., 2007] whether magnetic heat\npumps can compete with conventional heat pumps. Based on\nsimple theoretical calculations it is estimated that magnetic\nheat pumps are only 30% more expensive than conventional\nheat pumps. However, the price of the magnet is never con-\nsidered in this analysis. The total cost of a AMR magnetic\nrefrigeration device has recently been considered in Rowe\n[2009] and Rowe [2011] who defined a general performancearXiv:1410.6248v1  [physics.ins-det]  23 Oct 2014Determining the minimum mass and cost of a magnetic refrigerator — 2/12\nmetric for active magnetic regenerators. The cost and effec-\ntiveness of the magnet design is included in this metric as a\nlinear function of the volume of the magnet, and the gener-\nated field and the amount of magnetocaloric material used\nis also included in the metric. However, the metric has to\nbe calculated for a specific refrigeration system and can not\nbe used to predict the general performance per dollar of the\nmagnetic refrigeration technology. A figure of merit used to\nevaluate the efficiency of a magnet design used in magnetic\nrefrigeration has been introduced in Bjørk et al. [2008] but\nthis does not take the performance of the actual AMR system\ninto account.\nHere, we are interested in determining the lowest com-\nbined cost of magnet and magnetocaloric material needed for\na magnetic refrigerator as a function of a desired temperature\nspan and cooling power. Determining the lowest combined\ncost of magnet and magnetocaloric material allows for the\ndetermination of the major source of cost of a magnetic refrig-\neration device and thus allows the technology to be compared\nto competing refrigeration technologies. Note that we wish\nto determine the lowest combined cost, i.e. the cost of the\nmaterials for the cheapest magnetic refrigerator. Thus when-\never a cost is given in this article it is the cost of the materials\nneeded to construct the device that is meant. It is important to\nstate that the cheapest system might not be the most efficient\ndevice possible, i.e. the device that has the highest coefficient\nof performance (COP). However, such a device would use\nmore magnet and magnetocaloric material than the lowest cost\ndevice. The overall lifetime cost of a magnetic refrigeration\ndevice include both capital cost and operating cost but this is\nnot considered in the present analysis.\n2. Determining the mass of the magnet\nA magnetic refrigerator in which the magnetic field is pro-\nvided by a permanent magnet assembly, as is the case for\nalmost all magnetic refrigeration devices [Bjørk et al., 2010b],\nis considered. A measure of the efficiency of a magnet used\nin magnetic refrigeration is given by the Lcoolparameter, as\ndefined in Bjørk et al. [2008]. The Lcoolparameter is defined\nas\nLcool\u0011\u0010\nhB2=3i\u0000hB2=3\nouti\u0011Vfield\nVmagPfield; (1)\nwhere Vmagis the volume of the magnet(s), Vfieldis the volume\nwhere a high flux density is generated, Pfieldis the fraction of\nan AMR cycle that magnetocaloric material is placed in the\nhigh flux density volume, hB2=3iis the volume average of the\nflux density in the high flux density volume to the power of\n2/3 andhB2=3\noutiis the volume average of the flux density to the\npower of 2/3 in the volume where the magnetocaloric material\nis placed when it is being demagnetized. Note that it is the\nmagnetic flux density generated in an empty volume that is\nconsidered, i.e. B=m0H, and thus it is equivalent to speak of\nthe magnetic flux density or the magnetic field.A high Lcoolgenerally favors small magnetic fields. How-\never, this decreases the rate of heat transfer between the mag-\nnetocaloric material and the heat transfer fluid, ultimately\ndecreasing the performance of the device. The optimum mag-\nnet configuration will reflect a trade-off between high magnet\nefficiency and high rates of heat transfer. This, in turn, will de-\npend on the detailed configuration of the device. A number of\nmagnet arrays for magnetic refrigeration have been compared\nin Bjørk et al. [2010b].\nAn alternative way to classify permanent magnet arrays is\nto consider the so-called figure of merit, M\u0003, which is defined\nas [Jensen and Abele, 1996]\nM\u0003=R\nVfieldjjm0Hjj2dV\nR\nVmagjjBremjj2dV(2)\nwhere Vfieldis the volume of the air gap where the desired\nmagnetic field, m0H, is created and Vmagis the volume of\nthe magnets which have a remanence Brem. For isotropic\nmaterials with linear demagnetization characteristics this is a\nmeasure of the magnetic field energy in the air gap, divided\nby the maximum amount of magnetic energy available in\nthe magnet material. Although magnet arrays with a high\nvalue of M\u0003are not necessarily good magnets for magnetic\nrefrigeration, M\u0003offers a succinct way of characterizing the\nfield strength attained in the high field region. It has the added\nadvantage that an upper bound is known: It can be shown that\nthe maximum value of M\u0003is0:25. Here such a magnet will\nbe termed the M25magnet. For the remainder of this paper we\nwill characterize the magnet array using the figure of merit.\nFor specific permanent assemblies it is possible to calcu-\nlateM\u0003analytically; this will be considered later. Further-\nmore, if we limit ourselves to three-dimensional structures\nwith a constant magnitude of the remanence (whose direction\nis allowed to vary) which generate a constant magnetic field\nin the gap, Eq. (2) can be rewritten as\nM\u0003=\u0012m0H\nBrem\u00132Vfield\nVmag: (3)\nRearranging this equation by substituting the volume of\nthe high field region for the mass of magnetocaloric material,\nmmcm ;field, divided by the mass density of the MCM, rmcm,\ntimes one minus the porosity of the regenerator (including\nsupport structure), (1\u0000e), and substituting the volume of\nthe magnet by the mass, mmag, divided by the density, rmag,\nyields\nmmag=\u0012m0H\nBrem\u00132mmcm ;fieldrmag\n(1\u0000e)rmcmM\u0003: (4)\nAll terms that are a function of the magnetic field are on one\nside of the equation and thus from this equation we can calcu-\nlate the mass of the magnet needed for a magnetic refrigerator,\nif we know the mass of magnetocaloric material as a func-\ntion of m0Hrequired to provide the desired temperature span,\nTspan, and cooling power, ˙Q. Also, M\u0003as a function of m0H\nmust of course also be known.Determining the minimum mass and cost of a magnetic refrigerator — 3/12\nNote that the masses that are related in Eq. (4) are the\nmass of the magnet and the mass of magnetocaloric material\nthat is placed inside the magnet during an AMR cycle. If an\nsymmetric AMR cycle and only a single regenerator is used\nthe magnet will only be in use half of the cycle time, which is\nvery inefficient. However, if one uses two regenerators, run\ncompletely out of phase and using the same magnet, double\nthe amount of cooling power will be produced, of course using\ndouble the amount of magnetocaloric material but using the\nsame amount of magnet. This system, in which the magnet is\nutilized at all times, is the most efficient system possible, and\nthus allows for a modification of Eq. (4) such that\nmmag=1\n2\u0012m0H\nBrem\u00132mmcmrmag\n(1\u0000e)rmcmM\u0003: (5)\nwhere mmcmis now the total amount of magnetocaloric ma-\nterial, and it is assumed that the magnet is in use, i.e. filled\nwith magnetocaloric material with a mass of mmcm=2, at all\ntimes. AMR devices in which the magnet is in use almost\ncontinuously have previously been demonstrated [Tu ˇsek et al.,\n2010; Bjørk et al., 2010c]. Such an AMR which uses the\nmagnet at all times is what is considered in the following.\nAs an example assume that the densities of the magne-\ntocaloric material and the magnet are identical and that the\nsystem has a porosity of 0.5. Also, consider a magnetic field\nwith the value of the remanence. For the magnet with the\nlargest possible figure of merit, M\u0003=0:25, i.e. the M25mag-\nnet, we obtain from Eq. (5) that the mass of the magnet must\nbe four times the mass of magnetocaloric material used if\nthe magnet is used at all times. If only a single regenerator\nwas used then the mass of the magnet would be eight times\nthat of the magnetocaloric material. However, for specific\nregenerator geometries and magnetocaloric material the mass\nof the magnet can be calculated more precisely.\n3. Determining the minimum mass of\nmagnetocaloric material\nIn order to use Eq. (5) to calculate the cost of a magnetic refrig-\neration system we need to know the mass of magnetocaloric\nmaterial as function of m0Hrequired to provide the desired\ntemperature span, Tspan, and cooling power, ˙Q. In order to de-\ntermine this a parameter survey has been conducted where the\ncooling power has been computed using a numerical model for\ntwo different magnetic refrigeration devices, both using Gd\nmodeled using the mean field theory (MFT) [Morrish, 1965].\nThe model used is a publicly available one-dimensional nu-\nmerical model [Engelbrecht et al., 2006]. By varying the\nNusselt-Reynolds correlations the model is capable of model-\ning both packed bed and parallel plate regenerators. For both\nregenerator geometries the model has previously been com-\npared with both experimental data and other numerical models\n[Engelbrecht, 2008; Petersen et al., 2008a; Bahl et al., 2008].\nIn the numerical model, the temperature span is an input pa-\nrameter and the cooling power is calculated for the specifiedTable 1. The packed sphere parameters varied.\nParameter Values Unit\nDx 70, 90, 110, 135, 150, 180, 215 [%]\nf 1, 2, 4, 10 [Hz]\ntrel 0.1, 0.25, 0.5 [-]\ndp 0.1, 0.25, 0.5 [mm]\nm0H 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6 [T]\nTcold 268, 272, 276, 278, 280, 284\n288, 292, 296, 298 [K]\nprocess parameters. The governing equations of the model for\nthe packed sphere bed and the parallel plate cases are given\nin Engelbrecht et al. [2006] and Petersen et al. [2008a]. The\nGd material has a Curie temperature of Tc=293:6K and\nproperties as given in Petersen et al. [2008b].\nAs previously mentioned the performance of the AMR\ndepends on a number of process parameters, which are differ-\nent for a parallel plate and a packed sphere bed regenerator.\nHere we consider a variety of process parameters, all of which\nhave been chosen to span realistic values. A number of com-\nmon process parameters which are shared between the parallel\nplate and the packed bed models have been fixed during the\nnumerical experiments considered here. These are the length\nof the modeled regenerator which is taken to be 50 mm and\nthe heat transfer fluid which is taken to be water with constant\nproperties as given in Petersen et al. [2008a]. Also, the tem-\nperature of the hot end of the AMR is kept fixed at Thot=298\nK and only a symmetric AMR cycle is considered. Other\ncommon process parameters include the cycle frequency, f,\nthe relative cycle time, trel, which is the ratio between the time\nused for magnetization or demagnetization of the AMR and\nthe time used for fluid displacement, the fluid stroke length,\nDx, which describes the fraction of fluid that is displaced, the\ntemperature of the cold end, Tcoldand the maximum magnetic\nfield, m0H. However, these parameters have been varied inde-\npendently for the parallel plates and the packed bed cases. For\nboth regenerator types a magnetic field with a temporal width\nof 55% of a flow cycle and a temporal width of maximum field\ntime of 45% of the cycle time is used [Bjørk and Engelbrecht,\n2011a]. Thus the time it takes to ramp the magnetic field\nfrom 0 to the maximum value is 5% of the cycle time. The\nmagnetic field is ramped up at the start of the AMR cycle.\nFor the packed sphere bed regenerator the process pa-\nrameters are the particle size, dp, and the porosity, e. For a\nrandomly packed sphere bed regenerator used in magnetic\nrefrigeration the latter for a number of recently published sys-\ntems is near 0.36 [Okamura et al., 2005; Jacobs, 2009; Tura\nand Rowe, 2009] and therefore this parameter is fixed. The\ndifferent process parameters are listed in Table 1. The values\nfor the particle size, dp, have been chosen based on reported\nexperimental values [Okamura et al., 2005; Engelbrecht et al.,\n2007; Tura and Rowe, 2009]. The total number of parameter\nsets considered is 15876.\nFor the parallel plate regenerator two process parametersDetermining the minimum mass and cost of a magnetic refrigerator — 4/12\nTable 2. The parallel plate parameters varied.\nParameter Values Unit\nDx 40, 50, 60, 70, 80, 90 [%]\nf 0.167, 0.33, 1, 2, 4 [Hz]\ntrel 0.25, 0.50 [-]\nhfluid 0.1, 0.25, 0.5 [mm]\nhplate 0.1, 0.25, 0.5 [mm]\nm0H 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6 [T]\nTcold 268, 273, 278, 283, 288, 293, 298 [K]\nmust be specified. These are the height of the fluid channel,\nhfluid, and the height of the plate, hplate. These have been\nchosen based on realistic experimental values [Bahl et al.,\n2008; Engelbrecht et al., 2010]. The different process pa-\nrameters considered for the parallel plate case are listed in\nTable 2. However, for the parallel plate regenerator model\na comparison with a two-dimensional AMR model leads to\nthe requirement that a “1D correctness” parameter, G, must\nbe much greater than one for the one-dimensional model to\nproduce comparable results to a two-dimensional model [Pe-\ntersen et al., 2008a]. Here all process parameters with G<3\nwill not be considered further. These are process parameters\nwith large values of hfluidand large values of f. Therefore the\ntotal number of parameter sets considered is 14994.\nFor each of the set of process parameters the cooling\npower is calculated. Using this data, the mass of magne-\ntocaloric material can be directly determined as a function\nofm0Hfor a desired ˙QandTspanby only assuming that the\ncooling power is directly proportional to the mass of magne-\ntocaloric material. For each temperature span and magnetic\nfield the combined cost of the magnet and the MCM is simply\ncalculated using Eq. (5) for all process parameters and the\nlowest cost selected. In the following we take the cost of the\nmagnet material to be $40 per kg and the cost for the magne-\ntocaloric material to be $20 per kg, similarly to Rowe [2011].\nThe cost of assembly of the magnet and the regenerator is\nnot included; although these costs may be substantial for the\ninitial market entry devices, for a mass-produced product they\nare expected to be relatively minor. Differing cost estimates\nfor the materials will be discussed subsequently. Using these\nnumbers the total cost is calculated by adding the cost of\nthe magnet and magnetocaloric material and minimizing this\nvalue for all process parameters. Note that, as argued previ-\nously, substantially more magnet compared to magnetocaloric\nmaterial must be used. Therefore the calculation of the total\ncost is not very sensitive to the cost of the magnetocaloric\nmaterial, but will scale roughly linearly with the cost of the\nmagnet material.\n4. Cost of a Gd AMR\nIn order to determine the lowest combined cost of magnet and\nmagnetocaloric material needed to produce a given desired\ntemperature span and cooling power certain parameters must\nµ0H/BremM*\n0.5 1 1.5 2 2.500.050.10.150.21.6 2.7 4.5 7.4 12.2ro/riFigure 1. The figure of merit, M\u0003, as a function of magnetic\nfield in units of the remanence for a Halbach cylinder of\ninfinite length.\nbe specified. Here, we consider magnets with a remanence of\n1.2 T, which is a common value for NdFeB magnets, which\nare the most powerful magnets commercially available today.\nThese have a density of rmag=7400 kg/m3. The density of Gd\nisrmcm =7900 kg/m3. For the parallel plate regenerators the\nporosity of the regenerator is calculated as e=hfluid=(hfluid+\nhplate), while for the packed sphere bed the porosity is constant\nate=0:36. Note that none of these values for the porosity\nincludes any support or housing structure for the regenerator.\nAs previously mentioned for an M25magnet the figure of\nmerit is M\u0003=0:25for all values of m0H. However, we will\nalso consider the Halbach cylinder [Mallinson, 1973; Halbach,\n1980] which is a magnet design that has previously been used\nextensively in magnetic refrigeration devices [Lu et al., 2005;\nTura and Rowe, 2007; Engelbrecht et al., 2009; Kim and\nJeong, 2009]. For this magnet design the efficiency parameter\ncan be found analytically for a cylinder of infinite length,\nthrough the relation for the field in the cylinder bore, m0H=\nBremln\u0010\nro\nri\u0011\n, where riandroare the inner and outer radius\nof the Halbach cylinder, respectively. Using this relation one\ngets [Coey and Ni Mhiochain, 2003]\nM\u0003=ln\u0010\nro\nri\u00112\n\u0010\nro\nri\u00112\n\u00001=\u0010\nm0H\nBrem\u00112\ne2m0H\nBrem\u00001: (6)\nThis function is shown in Fig. 1 and has an optimal value of\nM\u0003\u00190:162for a value of m0H=Brem\u00190:80. For a Halbach\nof finite length the efficiency is lowered, depending on the\nlength and inner radius of the device [Bjørk, 2011b]. Here,\nfor simplicity, we will only consider a Halbach cylinder of\ninfinite length.Determining the minimum mass and cost of a magnetic refrigerator — 5/12\n(a) a\n(b) b\nFigure 2. The minimum cost in $ of a parallel plate magnetic\nrefrigeration system of Gd as a function of temperature span\nand cooling power for (a) a M25permanent magnet assembly\nand (b) a Halbach cylinder of infinite length.\n4.1 A parallel plate regenerator of Gd\nWe begin by analyzing the cost of a parallel plate regenerator\nof Gd, as this is the benchmark system in magnetic refrigera-\ntion. Using the approach described above the total minimum\ncombined cost of a parallel plate Gd regenerator with an M25\nmagnet as a function of desired temperature span and cooling\npower of the AMR is shown in Fig. 2a while for a Halbach\nmagnet the minimum cost is shown in Fig. 2b for the process\nparameters considered here. The corresponding amount of\nmagnet material, magnetocaloric material and magnetic field\nfor the minimum cost device using a Halbach magnet are\nshown in Fig. 3. Here we are only interested in determining\nthe minimum cost of a magnetic refrigeration device, and thus\nthe process parameters for the lowest cost device will not be\nanalyzed.From Fig. 2 we see that the cost of a refrigeration system\nincreases with both temperature span and cooling power and\nthat a device using a Halbach cylinder is \u001825\u000050% more\nexpensive than when an M25magnet is used. For example\na system that produces 100 W of continuous cooling at a\ntemperature span of 20 K using a Halbach magnet will have a\nminimum cost of $35.\nIn Fig. 3 we see that increasing the desired cooling power\nand temperature span increases the amount of magnet that\nmust be used, as expected. It is also seen that the magnetic\nfield is constant as a function of cooling power while it in-\ncreases monotonically with temperature span. The reason for\nthis behavior is that the only way to increase the temperature\nspan is to increase the magnetic field as Tspandoes not depend\nonmmcm. Also, note that even for very low temperature spans\na magnetic field above 0.6 T is favored. This is because the\nM\u0003parameter for a Halbach cylinder drops off significantly\nat low magnetic fields as shown in Fig. 1. This is not the case\nfor the M25magnet, where low magnetic fields are favored.\nFrom the figure we also see that the amount of magnetocaloric\nmaterial increases with cooling power, especially for a high\nvalue of the temperature span. This can be explained based\non Eq. (6) which shows that it is too expensive to generate\na strong magnetic field and thus it is more favorable to use\nmore magnet material to generate a large cooling power. Fi-\nnally, note that about two to three times more magnet than\nmagnetocaloric material is used. Therefore the total cost will\nbe roughly proportional to the cost of the magnet.\n4.2 A packed sphere bed regenerator of Gd\nHaving considered the cost of the parallel plate regenerator\nwe now consider the packed sphere bed regenerator. In Fig.\n4 the minimum combined cost of a packed sphere bed regen-\nerator of Gd and using either an M25or a Halbach magnet is\nshown. From this figure we see that the total minimum cost of\na packed sphere bed regenerator is several times less than that\nof a parallel plate regenerator. As for the parallel plate case\nchanging from an M25magnet to a Halbach cylinder increases\nthe cost by up to\u001850%. Note that we do not consider the\nCOP, i.e. the cost of operating the magnetic refrigerators, but\nonly the cost of the materials for the devices. So although\npacked sphere beds are better than the parallel plates the en-\nergy needed for operation may be higher due to the increased\npressure loss.\nIn Fig. 5 the corresponding amount of magnetocaloric\nmaterial, magnetic field and magnet material for the minimum\ncombined cost packed sphere bed AMR with Gd and using\na Halbach magnet, i.e. the cost shown in Fig. 4b, is plot-\nted. Compared to the parallel plate case (see Fig. 3) we see\nthat both the amount of magnet and magnetocaloric material\nneeded has been greatly reduced, which explains the signif-\nicant reduction in the overall cost of the system. Otherwise,\nthe amount of magnetocaloric material and the value of the\nmagnetic field follow the same trends as seen for the parallel\nplate case.Determining the minimum mass and cost of a magnetic refrigerator — 6/12\n(a) a\n(b) b\n(c) c\nFigure 3. (a) The amount of magnet material, (b) the\ncorresponding amount of magnetocaloric material and (c) the\ncorresponding magnetic field for the parallel plate magnetic\nrefrigeration system using Gd with the lowest combined cost\nof the magnet and magnetocaloric material for a Halbach\ncylinder of infinite length, i.e. with M\u0003given by Eq. (6).\n(a) a\n(b) b\nFigure 4. The minimum cost in $ of a packed sphere bed\nmagnetic refrigeration system of Gd as a function of\ntemperature span and cooling power of an AMR for (a) a M25\npermanent magnet assembly and (b) a Halbach cylinder of\ninfinite length.Determining the minimum mass and cost of a magnetic refrigerator — 7/12\n5. A graded magnetocaloric material\nIt has previously been shown that a gain in cooling power can\nbe obtained by using several magnetocaloric materials with\ndifferent Curie temperatures in a so called multimaterial AMR\nsystem [Rowe and Tura, 2006; Jacobs, 2009; Nielsen et al.,\n2010; Hirano et al., 2010; Russek et al., 2010]. Therefore the\ncost of a multimaterial AMR will also be considered.\nHere we consider a material with a constant DTadprofile\nas function of temperature. Such a material can be thought\nof as representing an infinitely linearly graded AMR for a\ngiven temperature span in a AMR operating at steady state.\nThe adiabatic temperature change is chosen to be equal to\nthe peak adiabatic temperature change for commercial grade\nGd as reported in Bjørk et al. [2010a], which is DTad=3:3\nK. The specific heat capacity as a function of temperature\nin zero applied magnetic field is taken to be constant with a\nvalue of cp=270:36J kg\u00001K\u00001, which is the average of the\nmeasured value of cpfor commercial grade Gd in the tem-\nperature interval from 220 K to 340 K as reported in Bjørk\net al. [2010a]. Then the remaining magnetocaloric proper-\nties for this material, e.g. the specific heat capacity as a\nfunction of magnetic field, are constructed in a thermodynam-\nically consistent way as described in Engelbrecht and Bahl\n[2010]. Finally the adiabatic temperature change is chosen\nto scale as a power law with an exponent of 2/3 for all tem-\nperatures, i.e. DTad(m0H) =DTad(1 T)(m0H)2=3. This is the\ntheoretical scaling of a second order material calculated us-\ning mean field theory at the Curie temperature [Oesterreicher\nand Parker, 1984] and it has been observed for both Gd and\nLaFe 13\u0000x\u0000yCoxSiymaterials [Pecharsky and Gschneidner Jr,\n2006; Bjørk et al., 2010a]. As the material with the constant\nadiabatic temperature change is always operating at the Curie\ntemperature the 2/3 power law scaling is assumed to be true\nfor all temperatures. The remaining material properties are\ntaken to be identical to Gd.\nThe cooling power has been computed for all process\nparameters given in Table 1 and 2, as for Gd. Shown in Fig. 6\nis the minimum combined cost for a magnetic refrigeration\nsystem using the constant DTadmaterial, for both an M25and\na Halbach magnet. Compared to the device using Gd (see\nFig. 2) it is seen that using a material with constant DTad\ncan optimally reduce the cost of the refrigeration device by\n50%. The same conclusions apply to Fig. 7 which shows the\nminimum combined cost for the packed bed system using a\nconstant DTadmaterial.\nShown in Fig. 8 is the corresponding amount of magne-\ntocaloric material, magnetic field and magnet material for the\nminimum combined cost parallel plate AMR with a constant\nDTadmaterial and using a Halbach magnet, cf. Fig. 6b. Com-\npared to Fig. 3 the amount of magnet material needed has\nbeen halved, which is also the reason for the overall reduc-\ntion in cost. Even though the cooling power of the constant\nDTadmaterial for most temperatures is higher than for Gd it\nis seen that the same amount of magnetocaloric material is\nused in the AMR. However, the value of the magnetic field\n(a) a\n(b) b\n(c) c\nFigure 5. (a) The amount of magnet material, (b) the\ncorresponding amount of magnetocaloric material and (c) the\ncorresponding magnetic field for the magnetic refrigeration\nsystem with the lowest combined cost of the magnet and\nmagnetocaloric material for a packed bed AMR with Gd and\na Halbach cylinder permanent magnet assembly.Determining the minimum mass and cost of a magnetic refrigerator — 8/12\n(a) a\n (b) b\nFigure 6. The minimum combined cost in $ of a parallel plate magnetic refrigeration system with a magnetocaloric material\nwith constant DTadas a function of temperature span and cooling power for (a) a M25permanent magnet assembly and (b) a\nHalbach cylinder of infinite length.\n(a) a\n (b) b\nFigure 7. The minimum combined cost in $ of a packed sphere bed magnetic refrigeration system with a constant DTad\nmagnetocaloric material as a function of temperature span and cooling power for (a) a M25permanent magnet assembly and (b)\na Halbach cylinder of infinite length.\nhas been reduced by up to \u00180:3T compared to Fig. 3. The\nreason for this is that much more magnet material is used than\nmagnetocaloric material and as the magnet material is twice\nas expensive as the magnetocaloric material it is much more\nadvantageous to reduce the amount of magnet material that is\nused, thereby lowering the value of the magnetic field.6. Discussion\nThe cost determined above is only the cost of the permanent\nmagnet material and the magnetocaloric material that go into\nthe magnetic refrigeration system. Additional costs such as\nmotors, pump etc. needed for the refrigeration system have not\nbeen included in the analysis. Especially for the packed sphere\nbed regenerator the pressure drop across the AMR may be\nhigh and this will introduce a significant energy consumptionDetermining the minimum mass and cost of a magnetic refrigerator — 9/12\n(a) a\n(b) b\n(c) c\nFigure 8. (a) The amount of magnet material, (b) the\ncorresponding amount of magnetocaloric material and (c) the\ncorresponding magnetic field for the magnetic refrigeration\nsystem with the lowest combined cost of the magnet and\nmagnetocaloric material for a parallel plate constant DTad\nAMR with a Halbach cylinder permanent magnet assembly.and thus operating cost. This aspect has not been included\nin the analysis presented here, but could easily be included if\nthe “price per pressure drop” is known or the true operating\ncost could be estimated. Also, as previously mentioned, the\nprocess parameters that produce the lowest combined cost do\nnot necessarily represent the process parameters with highest\nCOP. This implies that the device with highest COP will be\nmore expensive to produce then the minimum cost found here.\nFinally, the cooling power is computed using a numerical\nmodel which have been shown to produce higher cooling\ncapacities than seen experimentally [Engelbrecht, 2008], due\nto experimental heat losses. Also, demagnetization effects\nhave not been taken into account, which will lower the internal\nmagnetic field in the magnetocaloric material. Therefore a\nlarger magnetic field or more magnetocaloric material might\nbe needed than found above, which will increase the total cost\nof the system.\nThe material with constant adiabatic temperature change,\nused here to represent an infinitely linearly graded AMR,\nmight also not represent the optimal grading of an AMR. The\nideal grading will depend on the magnetocaloric materials\nused, and thus a more efficient grading and thereby a lower\ncost device might be possible. Also, using magnetocaloric\nmaterials with a higher adiabatic temperature change will\nlower the cost of the device, as more cooling power can be\nproduced per mass of magnetocaloric material. Note that the\ncalculations of the cost assume that the magnet is utilized,\ni.e. filled with magnetocaloric material, at all times. If this is\nnot the case, the system will become more expensive. Nev-\nertheless, although this analysis as mentioned above contain\nseveral assumptions, the estimation of the cost based on the\nprediction of the model is still valid for a large number of\nprocess parameters and as a reasonable minimum cost of a\nmagnetic refrigeration system.\nIt is of interest to consider the reduction in cost that is pos-\nsible by increasing the operating frequency, f, of the system.\nShown in Fig. 9 is the minimum combined cost of a magnetic\nrefrigerator with a Halbach magnet and with a temperature\nspan of 20 K and a cooling power of 100 W as a function\nof frequency. These numbers represent reasonable operating\nparameters of a magnetic refrigerator.\nIt can clearly be seen that increasing the frequency sig-\nnificantly reduces the cost of the refrigerator. No optimum\nin frequency is seen, but this might be caused by the limited\nchoice of process parameters studied. However, note that the\noperating cost will also depend on the frequency. Besides\nincreasing the frequency the cost found in the above analysis\ncan also be lowered by examining other process parameters\nthan those considered here or by considering alternative regen-\nerator geometries where the thermal contact between the heat\ntransfer fluid and the regenerator is higher but the pressure\ndrop is not excessive.\nIn the present study the cost of permanent magnet (PM)\nmaterial was assumed to be $40 per kg and for the magne-\ntocaloric material (MCM) the cost was $20 per kg. However,Determining the minimum mass and cost of a magnetic refrigerator — 10/12\nf [Hz]Cost [$]\n  \n100101101102103\nParallel plate − Gd\nParallel plate − Constant ∆Tad\nPacked sphere bed − Gd\nPacked sphere bed − Constant ∆Tad\nFigure 9. The minimum combined cost as a function of\nfrequency for a magnetic refrigeration device using a\nHalbach magnet and with a temperature span of 20 K and a\ncooling power of 100 W. The lines are only meant to serve as\nguides to the eye.\nit is of interest to investigate the total cost of the AMR for\ndifferent costs of the magnet and magnetocaloric material.\nShown in Fig. 10 is the minimum total cost of several dif-\nferent types of AMR with a temperature span of 20 K and a\ncooling power of 100 W as a function of the ratio of the cost\nof the magnet and magnetocaloric material. As can be seen\nfrom the figure the minimum total cost for all AMRs behave\nin much the same way. For a small ratio of Cost MCM / Cost\nPM the total cost scales linearly with the cost of the magnet\nas the price of the magnetocaloric material is small compared\nto the price of magnet and thus can be ignored. It is also seen\nthat it is always better to use an M25magnet compared to a\nHalbach magnet, as expected. Using this figure the minimum\ncost of a given AMR can be calculated for any cost of the\nmagnet and magnetocaloric materials.\n7. Conclusion\nIn this paper an expression is proposed for the total mass and\nthus cost of the magnet material and magnetocaloric material\nneeded to construct a magnetic refrigerator. It is shown that\nfor equal densities of the magnet and magnetocaloric material\nand a magnetic field equal to the remanence and a system\nwith a porosity of 0.5 that the magnet with the largest possible\nfigure of merit, termed the M25magnet, must have a mass at\nleast four times the mass of magnetocaloric material used, if\nthe magnet is used at all times. For a Halbach cylinder the\nmass of the magnet is even larger.\nThe total minimum mass and cost of both a parallel plate\nand packed sphere bed regenerator consisting of the mag-\nnetocaloric material Gd or a material with a constant adia-\nbatic temperature change profile was also studied. Using the\nCost MCM [$]/ Cost PM [$]Total cost [$]/ Cost PM [$]\n  \n10−210−110010110210−210−1100101102Packed bed − M25 Magnet\nPacked bed − Halbach cylinder\nParallel plates − M25 Magnet\nParallel plates − Halbach cylinder(a) a\nCost MCM [$]/ Cost PM [$]Total cost [$]/ Cost PM [$]\n  \n10−210−110010110210−210−1100101102Packed bed − M25 Magnet\nPacked bed − Halbach cylinder\nParallel plates − M25 Magnet\nParallel plates − Halbach cylinder\n(b) b\nFigure 10. The ratio of the minimum total cost and the cost\nof the permanent magnet (PM) material as a function of the\nratio between the cost of the magnetocaloric material (MCM),\nand the permanent magnet material for different AMRs but\nall with a temperature span of 20 K and a cooling power of\n100 W. The magnetocaloric material in (a) is taken to be Gd\nwhile in (b) it is the constant DTadmaterial.\ncooling power computed from a numerical model for 15876\npacked sphere bed process parameters and for 14994 parallel\nplate process parameters, all realistically chosen, the mini-\nmum cost of such regenerators was estimated. This was done\nfor both an M25magnet and for a Halbach cylinder of infi-\nnite length. The cost, amount of magnet and magnetocaloric\nmaterial as well as the magnetic field was determined as func-\ntions of desired temperature span and cooling power for the\ncheapest overall design. Assuming a cost of magnet material\nof $40 per kg and of magnetocaloric material of $20 per kg\nthe cheapest parallel plate refrigerator with Gd that produces\n100 W of continuous cooling at a temperature span of 20 K\nusing a Halbach magnet will use around 0.8 kg of magnet, 0.3Determining the minimum mass and cost of a magnetic refrigerator — 11/12\nkg of Gd, have a magnetic field of 0.8 T and have a minimum\ncost of $35. The cost is dominated by the cost of the magnet.\nUsing a magnetocaloric material with a constant adiabatic\ntemperature profile reduces this cost to $25 while using a\npacked sphere bed, also of a constant magnetocaloric material,\nbrings the cost down to $7. It was also shown that the cost can\nbe reduced by increasing the frequency of the AMR. Finally,\nthe lowest cost was also found as a general function of the\ncost of the magnet and magnetocaloric material.\nAcknowledgments\nThe authors would like to acknowledge the support of the\nProgramme Commission on Energy and Environment (EnMi)\n(Contract No. 2104-06-0032) which is part of the Danish\nCouncil for Strategic Research.\nReferences\nBahl, C. R. H., Petersen, T. F., Pryds, N., Smith, A., Petersen,\nT. F., 2008. A versatile magnetic refrigeration test device.\nReview of Scientific Instruments 79 (9), 093906.\nBarclay, J. A., 1982. The theory of an active magnetic regen-\nerativ refrigerator. NASA STI/Recon Technical Report N\n83, 34087.\nBjørk, R., (2011b). The ideal dimensions of a halbach cylinder\nof finite length. Journal of Applied Physics 109, 013915.\nBjørk, R., Bahl, C. R. H., Katter, M., 2010a. Magnetocaloric\nproperties of LaFe 13\u0000x\u0000yCoxSiyand commercial grade Gd.\nJournal of Magnetism and Magnetic Materials 322, 3882–\n3888.\nBjørk, R., Bahl, C. R. H., Smith, A., Pryds, N., 2008. Op-\ntimization and improvement of halbach cylinder design.\nJournal of Applied Physics 104 (1), 13910.\nBjørk, R., Bahl, C. R. H., Smith, A., Pryds, N., 2010b. Review\nand comparison of magnet designs for magnetic refrigera-\ntion. International Journal of Refrigeration 33, 437–448.\nBjørk, R., Bahl, C. R. H., Smith, A., Christensen, D. V ., Pryds,\nN., 2010c. An optimized magnet for magnetic refrigeration.\nJournal of Magnetism and Magnetic Materials 322, 3324–\n3328.\nBjørk, R., Engelbrecht, K., 2011a. The influence of the mag-\nnetic field on the performance of an active magnetic regen-\nerator (AMR). International Journal of Refrigeration 34,\n192–203.\nCoey, J. M. D., Ni Mhiochain, T. R., 2003. High Magnetic\nFields (Permanent magnets). World Scientific, Ch. 2, pp.\n25–47.Dan’kov, S. Y ., Tishin, A. M., Pecharsky, V . K., Gschneidner\nJr, K. A., 1998. Magnetic phase transitions and the mag-\nnetothermal properties of gadolinium. Physical Review B\n(Condensed Matter) 57 (6), 3478–3490.\nEgolf, P. W., Gendre, F., Kitanovski, A., 2007. Magnetic heat\npumps - an approximate energy efficiency and cost study:\npart II. Proceedings of the 2ndInternational Conference of\nMagnetic Refrigeration at Room Temperature, Portoroz,\nSlovenia, 399–408.\nEngelbrecht, K., 2008. A numerical model of an active mag-\nnetic regenerator refrigerator with experimental validation.\nPh.D. thesis, University of Wisconsin - Madison.\nEngelbrecht, K., Bahl, C. R. H., 2010. Evaluating the effect\nof magnetocaloric properties on magnetic refrigeration per-\nformance. Journal of Applied Physics 108, 123918.\nEngelbrecht, K., Jensen, J. B., Bahl, C. R. H., Pryds, N.,\n2009. Experiments on a modular magnetic refrigeration\ndevice. Proceedings of the 3rdInternational Conference on\nMagnetic Refrigeration at Room Temperature, Des Moines,\nIowa, USA, 431–436.\nEngelbrecht, K., Nellis, G., Klein, S., 2006. Predicting the\nperformance of an active magnetic regenerator refrigerator\nused for space cooling and refrigeration. HV AC and R\nResearch 12 (4), 1077–1095.\nEngelbrecht, K., Nellis, G., Klein, S., Zimm, C., 2007. Re-\ncent developments in room temperature active magnetic\nregenerative refrigeration. HV AC and R Research 13 (4),\n525–542.\nEngelbrecht, K., Nielsen, K. K., Pryds, N., 2010. An ex-\nperimental study of passive regenerator geometries. Pro-\nceedings of the 4rdInternational Conference on Magnetic\nRefrigeration at Room Temperature, Baotou, China, 305–\n312.\nHalbach, K., 1980. Design of permanent multipole magnets\nwith oriented rare earth cobalt material. Nuclear instru-\nments and methods 169.\nHirano, N., Nagaya, S., Okamura, T., Kawanami, T., Wada,\nH., 2010. Development of room temperature magnetic re-\nfrigerator in japan. Proceedings of the 4rdInternational\nConference on Magnetic Refrigeration at Room Tempera-\nture, Baotou, China, 37–48.\nJacobs, S., 2009. Modeling and optimal design of a multilayer\nactive magnetic refrigeration system. Proceedings of the\n3rdInternational Conference on Magnetic Refrigeration at\nRoom Temperature, Des Moines, Iowa, USA, 267–274.\nJensen, J. H., Abele, M. G., 1996. Maximally efficient perma-\nnent magnet structures. Journal of Applied Physics 79 (2),\n1157–1163.Determining the minimum mass and cost of a magnetic refrigerator — 12/12\nKim, Y ., Jeong, S., 2009. Investigation on the room tempera-\ntre active magnetic regenerative refrigerator with permanet\nmagnet array. Proceedings of the 3rdInternational Confer-\nence on Magnetic Refrigeration at Room Temperature, Des\nMoines, Iowa, USA, 393–400.\nLu, D. W., Xu, X. N., Wu, H. B., Jin, X., 2005. A permanent\nmagnet magneto-refrigerator study on using Gd/Gd-Si-Ge/\nGd-Si-Ge-Ga alloys. Proceedings of the 1stInternational\nConference on Magnetic Refrigeration at Room Tempera-\nture, Montreux, Switzerland, 1–6.\nMallinson, J. C., 1973. One-sided fluxes - a magnetic curios-\nity? IEEE Transactions on magnetics 9 (4), 678 – 682.\nMorrish, A. H., 1965. The Physical Priciples of Magnetism.\nJohn Wiley & Sons, Inc.\nNielsen, K. K., Bahl, C. R. H., Engelbrecht, K., Smith, A.,\nPryds, N., Hattel, J., 2010. Numerical modeling of graded\nactive magnetic regenerators. Proceedings of the 4rdInter-\nnational Conference on Magnetic Refrigeration at Room\nTemperature, Baotou, China, 437–446.\nOesterreicher, H., Parker, F. T., 1984. Magnetic cooling near\ncurie temperatures above 300k. Journal of Applied Physics\n55, 4334–4338.\nOkamura, T., Yamada, K., Hirano, N., S., N., 2005. Per-\nformance of a room-temperature rotary magnetic refriger-\nator. Proceedings of the 1stInternational Conference on\nMagnetic Refrigeration at Room Temperature, Montreux,\nSwitzerland, 319–324.\nPecharsky, V . K., Gschneidner Jr, K. A., 2006. Advanced\nmagnetocaloric materials: What does the future hold? In-\nternational Journal of Refrigeration 29 (8), 1239–1249.\nPetersen, T. F., Engelbrecht, K., Bahl, C. R. H., Pryds, N.,\nSmith, A., Elmegaard, B., 2008a. Comparison between a\n1d and a 2d numerical model of an active magnetic regen-\nerative refrigerator. Journal of Physics D: Applied Physics\n41 (10), 105002.\nPetersen, T. F., Pryds, N., Smith, A., Hattel, J., Schmidt, H.,\nHøgaard-Knudsen, H. J., 2008b. Two-dimensional mathe-\nmatical model of a reciprocating room-temperature active\nmagnetic regenerator. International Journal of Refrigeration\n31 (3), 432–443.\nRowe, A., 2009. Performance metrics for active magnetic\nrefrigerators. Proceedings of the 3rdInternational Confer-\nence on Magnetic Refrigeration at Room Temperature, Des\nMoines, Iowa, USA, 195–206.\nRowe, A., 2011. Configuration and performance analysis of\nmagnetic refrigerators. International Journal of Refrigera-\ntion, 34 (1), 168–177.Rowe, A., Tura, A., 2006. Experimental investigation of a\nthree-material layered active magnetic regenerator. Interna-\ntional Journal of Refrigeration 29 (8), 1286–1293.\nRussek, S. L. and Zimm, C., 2006. Potential for cost effec-\ntive magnetocaloric air conditioning systems. International\nJournal of Refrigeration 29 (8), 1366–1373.\nRussek, S., Auringer, J., Boeder, A., Chell, J., Jacobs, S.,\nZimm, C., 2010. The performance of a rotary magnet mag-\nnetic refrigerator with layered beds. Proceedings of the\n4rdInternational Conference on Magnetic Refrigeration at\nRoom Temperature, Baotou, China, 339–350.\nTura, A., Rowe, A., 2007. Design and testing of a permanent\nmagnet magnetic refrigerator. Proceedings of the 2ndInter-\nnational Conference of Magnetic Refrigeration at Room\nTemperature, Portoroz, Slovenia, 363–370.\nTura, A., Rowe, A., 2009. Progress in the characterization\nand optimization of a permanent magnet magnetic refrig-\nerator. Proceedings of the 3rdInternational Conference on\nMagnetic Refrigeration at Room Temperature, Des Moines,\nIowa, USA, 387–392.\nTuˇsek, J. and Zupan, S. and Sarlah, A. and Prebil, I. and Pore-\ndos A., 2010. Development of a rotary magnetic refrigerator.\nInternational Journal of Refrigeration 33 (2), 294–300.\nYu, B., Liu, M., Egolf, P. W., Kitanovski, A., 2010. A review\nof magnetic refrigerator and heat pump prototypes built\nbefore the year 2010. International Journal of Refrigeration\n33 (6), 1029–1060.\nZimm, C., Auringer, J., Boeder, A., Chell, J., Russek, S.,\nSternberg, A., 2007. Design and initial performance of a\nmagnetic refrigerator with a rotating permanent magnet.\nProceedings of the 2ndInternational Conference of Mag-\nnetic Refrigeration at Room Temperature, Portoroz, Slove-\nnia, 341–347."    },    {        "title": "1411.4147v2.Orbital_selective_behavior_in_Y5Mo2O12_and__Cd_Zn_V2O4.pdf",        "content": "arXiv:1411.4147v2  [cond-mat.mtrl-sci]  26 Dec 2014Orbital-selective behavior in Y 5Mo2O12and\n(Cd,Zn)V 2O4\nSergey V. Streltsov\nInstitute of Metal Physics, S.Kovalevskoy St. 18, 620990 Ek aterinburg, Russia\nUral Federal University, Mira St. 19, 620002 Ekaterinburg, Russia\nAbstract\nWe present two examples of the real materials, which show orbital-s elective\nbehavior. Inbothcompoundsapartoftheelectronsislocalizedont hemolecular\norbitals, which lead to a significant reduction of the magnetic moment on the\ntransition metal ion.\nKeywords: Orbital degrees of freedom, dimers\n1. Introduction\nIt was recently shown that there may exist so called orbital-selectiv e state\nin the dimerized systems with orbital degrees of freedom [1]. This is th e state\nin which different orbitals behave in different manners. All electrons ( orbitals)\nin the orbital-selective state are split on two qualitatively different gr oups. One 5\npart of the electrons occupy molecular orbitals and form spin singlet s being\nmagnetically inactive, while other electrons are effectively decoupled from them\nand have local magnetic moments (which can be ordered, i.e. lead to f ormation\nof ferro- or antiferromagnetic states, or disordered, i.e. param agnetic). As\na result one of the main features of the orbital-selective state is su bstantially 10\nreduced magnetic moment. Because of the formation of molecular o rbitals this\nmoment turns out to be much smaller, than expected basing on the p urely ionic\nmodel consideration.\nIn the present paper we show that the orbital-selective state is re alized in\ntwo real materials: Y 5Mo2O12and ZnV 2O4(and also in CdV 2O4, which is 15\nPreprint submitted to Journal of Magnetism and Magnetic Mat erials January 31, 2020iso-electronic and iso-structural to ZnV 2O4).\n2. Calculation details\nWe used the density functional theory within the generalized gradie nt ap-\nproximation (GGA) [2] to study electronic properties of Y 5Mo2O12. We used\nfull-potential WIEN2k code [3]. The radii of atomic spheres were set as follow- 20\ningRY= 2.19 a.u.,RMo= 1.88 a.u., and RO= 1.70 a.u. The Brillouin-zone\n(BZ) integration in the course of the self-consistency was perfor med overa mesh\nof 200k-points. The parameter of the plane wave expansion was chosen to be\nRMTKmax= 7, where RMTis the smallest atomic sphere radii and Kmax-\nplane wave cut-off.25\n3. Y5Mo2O12\nThe crystal structure of Y 5Mo2O12is formed by the edge sharing MoO 6\nchains,whicharedimerized. ThesechainsareseparatedbytheYion s,seeFig.1.\nThe electronic configuration of Mo having formal valence 4.5+ is 4 d1.5. Hence\none may expect that the local magnetic moment would be µloc= 1.5µB/Mo, 30\nwhile effective magnetic moment in the Curie-Weiss theory will be µeff=\n2.29µB/Mo orµeff= 1.15µB/dimer. Experimentally, however, effective mo-\nment equals µeff= 1.7µB/Mo [4]. We attribute this feature to the fact that\nthis compound is actually in the orbital-selective state.\nThe total density of states obtained in the nonmagnetic GGA calcula tion 35\nis shown in Fig. 2. In the edge-shared geometry there are two type s of thet2g\norbitals: σ-bonded xyorbitals (which look directly to each other) and π-bonded\nyzandzxorbitals on different Mo centers (it is assumed that the local zaxis is\nperpendicular to the plane defined by the Mo-Mo bond and common ed ge for\ntwo MoO 6octahedra). Direct overlap between the xyorbitals on two Mo sites 40\nleads to huge bonding-antibonding splitting ∼2.7 eV. Therefore one may gain\nenergy occupying bonding orbital with two electrons (total numbe r of electron\nis 3 per dimer). Remaining electron will provide net magnetic moment of the\n2dimer, giving S= 1/2 per dimer. This yields µeff= 1.74µB/Mo, which agrees\nwith experimental data [4]. Resulting state is orbital-selective and is r ealized 45\ndue to rather uncommon set of the parameters: one of the hoppin g parameter\ntxy/xy∼1.35 eV is much larger both than intra-atomic Hund’s rule exchange\n(which is estimated for early 4 dtransition metals to be ∼0.7 eV [5, 6]) and\nhopping integrals between other orbitals ( txz/xz,tyz/yz)≪txy,xy.\n4. CdV 2O4and ZnV 2O4 50\nThe electronic and magnetic properties of the V spinels are thoroug hly in-\nvestigated last years. [7, 8] E.g. it was found that CdV 2O4is multiferroic below\nTN=33 K [7]. The mechanism of the multiferroicity is the magnetostriction :\nunconventional ↑↑↓↓↑↑magnetic order results in the dimerization of the V ions\nhaving the same spin projection (i.e. ↑↑). This in turn leads to the shift of the 55\noxygen ions away from the high symmetry positions and onset of the sponta-\nneous electric polarization [7]. The missing element in this microscopic mo del\nis why the spins of V ions forming dimers show ferromagnetic order. W e know\nfrom the basics of the quantum mechanics that the spin singlet (i.e. a ntiferro\nFigure 1: Left: the unit cell of Y 5Mo2O12; Mo ions are shown in violet, O −in blue, and Y\n−in grayish green. Right: main structural element of Y 5Mo2O12−dimerized Mo chain.\n3-2 -1.5 -1 -0.5 0 0.5 1 1.5\nEnergy (eV)0123456789101112DOS (states/[eV u.c.])Bonding-antibonding splitting        ~2.9 eVY5Mo2O12, GGA\nFigure 2: Total density of states of the Y 5Mo2O12, obtained in the nonmagnetic GGA calcu-\nlation.\nordering of the spins, as e.g. in the hydrogen molecule) is more typica l for 60\ndimers.\nWe argue that it can be related with the orbital-selective physics. Th e\nsituation here is rather similar to Y 5Mo2O12, since neighboring VO 6octahedra\nalso share their edges. There is again strong overlap between the xyorbitals.\nSince V3+has 3d2electronic configuration, there are four delectrons per dimer. 65\nTwo electrons may occupy molecular orbital of the xysymmetry, while other\ntwo stay on the yzandzxlocal orbitals and provide S= 1 per V dimer, or\nS= 1/2 per V. Corresponding exchange constant (added in the revised v ersion\nofthe manuscript) in this shortV-Vpair in CdV 2O4isferromagneticand equals\nJ= 56 K as calculated in the LSDA+U method for U−JH=0.7 eV using the 70\nGreen’s function formalism [9, 10].\nThe distortionsof the crystalstructure and type of the magnet ic structure in\nZnV2O4are the same as in CdV 2O4[8], but there is an additional information\nabout magnetic properties of ZnV 2O4. The local magnetic moment on V was\nfound to be 0.66 µBin ZnV 2O4[11]. This qualitatively agrees with the model 75\ntreatment presented above. In the ionic model this corresponds to the local spin\nmoment µ=gS= 1µB, but this value is further reduced due to hybridization\n4Figure 3: Left: the pair of the xyorbitals in V dimer, which have the largest hopping param-\neters in the system. Right: sketch illustrating energy leve ls splitting in (Cd,Zn)V 2O4.\neffects, which are always exist in real materials.\n5. Conclusions\nIn the present paper we show two examples of the orbital-selective behavior, 80\nwhich results in the suppression of the magnetic moment in (Cd,Zn)V 2O4and\nY5Mo2O12.\n6. Acknowledgments\nAuthorisgratefultoD.Khomskiiwithwhomthe investigationofthe orbital-\nselective state was performed. The calculation of exchange const ants is sup- 85\nported by the Russian Science Foundation via RNF 14-22-00004.\nReferences\nReferences\n[1] S. V. Streltsov, D. I. Khomskii, Orbital-dependent singlet dimers and\norbital-selective Peierls transitions in transition-metal compounds , Phys. 90\nRev. B 89 (2014) 161112.\n[2] J. P. Perdew, K. Burke, M. Ernzerhof,\nGeneralized Gradient Approximation Made Simple., Phys. Rev. Lett.\n577 (18) (1996) 3865.\nURLhttp://www.ncbi.nlm.nih.gov/pubmed/10062328 95\n[3] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, WIEN2 k, An\nAugmented Plane Wave + Local Orbitals Program for Calculating Crys tal\nProperties, Techn. Universit¨ at Wien, Wien, 2001.\n[4] C. C. Torardi, C. Fecketter, W. H. McCarroll, F. J. DiSalvo, Stru cture and\nProperties of Y$ 5$Mo$2$0${12}$ and Gd$ 5$M0$2$0${12}$ : Mixed 100\nValence Oxides with Structurally Equivalent Molybdenum Atoms, Jour nal\nof Solid State Chemistry 60 (1985) 332–342.\n[5] S. Lee, J.-G. Park, D. Adroja, D. Khomskii, S. Streltsov, K. A. M cEwen,\nH. Sakai, K. Yoshimura, V. I. Anisimov, D. Mori, R. Kanno, R. Ibbers on,\nSpin gap in Tl$ 2$Ru$2$O$7$ and the possible formation of Haldane chains in three-dimensional crystals., 105\nNature materials 5 (6) (2006) 471. doi:10.1038/nmat1605 .\nURLhttp://www.ncbi.nlm.nih.gov/pubmed/16699512\n[6] S.V.Streltsov,D.I.Khomskii,Unconventional magnetism as a c onsequence of the charge disproportionation and the molecular or bital formation in Ba$ 4$Ru$3$O${10}$,\nPhysical Review B 86 (6) (2012) 064429.\ndoi:10.1103/PhysRevB.86.064429 . 110\nURLhttp://link.aps.org/doi/10.1103/PhysRevB.86.064429\n[7] G. Giovannetti, A. Stroppa, S. Picozzi, D. Baldomir, V. Pardo,\nS. Blanco-Canosa, F. Rivadulla, S. Jodlauk, D. Niermann,\nJ. Rohrkamp, T. Lorenz, S. Streltsov, D. I. Khomskii, J. Hemberg er,\nDielectric properties and magnetostriction of the collinear multiferr oic spinel CdV$ 2$O$4$, 115\nPhysical Review B 83 (6) (2011) 060402.\ndoi:10.1103/PhysRevB.83.060402 .\nURLhttp://link.aps.org/doi/10.1103/PhysRevB.83.060402\n[8] V. Pardo, S. Blanco-Canosa, F. Rivadulla,\nD. Khomskii, D. Baldomir, H. Wu, J. Rivas, 120\nHomopolar Bond Formation in ZnV$ 2$O$4$ Close to a Metal-Insulator Transition,\n6Physical Review Letters 101 (25) (2008) 256403.\ndoi:10.1103/PhysRevLett.101.256403 .\nURLhttp://link.aps.org/doi/10.1103/PhysRevLett.101.256 403\n[9] D. M. Korotin, V. V. Mazurenko, V. I. Anisimov, S. V. Streltsov, 125\nCalculation of the exchange constants of the Heisenberg model in\nthe plane-wave based methods using the Green s function ap-\nproacharXiv:arXiv:1411.4169 .\n[10] A. Liechtenstein, V. Gubanov, M.Katsnelson, V. Anisimov, Mag netictran-\nsition state approach to ferromagnetism of metals: Ni, Journal of Mag- 130\nnetism and Magnetic Materials 36 (1983) 125.\n[11] M. Reehuis, A. Krimmel, N. Bottgen, A. Loidl, A. Prokofiev,\nCrystallographic and magnetic structure of ZnV$ 2$O$4$, The Euro-\npean Physical Journal B - Condensed Matter 35 (3) (2003) 311–3 16.\ndoi:10.1140/epjb/e2003-00282-4 . 135\nURLhttp://www.springerlink.com/openurl.asp?genre=artic le&id=doi:10.1140/epjb/e2003-00282-4\n7"    },    {        "title": "1411.6960v1.Computing_with_spins_and_magnets.pdf",        "content": "Page 1 of 18 \n \nComputing with Spins and Magnets  \nBehtash Behin -Aein1, Jian -Ping Wang2, Roland Wiesendanger3 \n1GLOBALFOUNDRIES Inc. , Santa Clara, USA , 2University of Minnesota,  Minneapolis, USA  \n 3University of Hamburg, Hamburg, Germany  \n \n \nKey Words:  Magnetic Memory, Gain, Directionality , Non -Volatile Logic, Reconfigurable Logic, \nLogic -in-Memory, Memory -in-Logic, Spintronics, Magnetic Tunnel Junction, Spin Transfer Torque, \nMagneto -Resistance, Perpendicular Magnetic Anisotropy, Hysteresis, Spin -Polarized Scanning Tunneling \nMicroscopy, RKKY Interaction .  \n \nAbstract:  The possible use of spin and magnets in place of charge and capacitors to store \nand proc ess information is well known. Magnetic tunnel junctions are being widely investigated  \nand developed for magnetic rando m access memories. The se are two terminal devices that \nchange their resistance based on switchable magnetization of magnetic materials. T hey utilize \nthe interaction between electron spin and magnets to read information from the magnets and \nwrite onto them. Such advances in memory devices could also translate into a new class of logic \ndevices that offer the advantage of nonvolatile and recon figurable information processing over \ntransistors. Logic devices having a transistor -like gain and directionality could be used to build \nintegrated  circuits without the need  for transistor -based  amplifiers and clocks at every stage.  We \nreview d evice charac teristics and basic  logic gates that comput e with spins and magnets from the \nmesoscopic to the atomic  scale , as well as materials, integration , and fabrication challenges and \nmethods.  \n \n \n \n \n \n Page 2 of 18 \n \nI. Introduction  \n \nRecent experimental advances in spintronics and magnetics ha ve merged the two fields \nand made possible the use of a single device , namely the magnetic tunnel junction (MTJ),  to both \nread ( R) information from magnets and to write ( W) information onto magnets.1 Such devices \nare being widely researched and developed in industry and academia for spin -based memories. It \nseems natural to ask whether these advances in memory devices could also translate into a new \nclass of logic de vices based on nanoscale magnets or even single spins. What makes logic \ndevices different from memory is the need for such devices to have gain and directionality . \nMemory bits  act as isolated  cells for information storage and read out . Logic devices m ust \ncommunicate with each other requiring some bits as inputs and some as outputs.   It is essential \nfor inputs to write on to outputs and not the other way around necessitating  directionality.  \nMoreover, s ince logic circuits require multiple cascaded  logic bits  for computing , information  \nwill be lost if not regenerated with gain.   Such  properties will subsequently enable building of \ncomplex circuits  for Boolean logic, neural networks, etc .   Complementary metal oxide \nsemiconductor ( CMOS ) devices , which are the current workhorse of transistor -based logic \ntechnology , incorporate  such characteristics. From this perspective , two catego ries for spin -based \nlogic exist. In  one category , logic is performed in conjunction with transistors and/or clocks2–8 to \nprovide  gain a nd/or directionality. I n the other case , such effects are built into spin devices .9–16 \nWhile covering both categories , our goal here is to present an overview of advancements in \ncomputing with spins and magnets from the macroscopic scale to  the atomic scal e.16–25 \n \nII. Magnetic Tunnel Junction  \n \nBefore we discuss spin -based logic, a brief point about MTJs is in order. MTJs currently \nact as the most important elemental building block  for spin -based memories. As an example, a \nsimplified schemati c of an MTJ is shown i n Figure 1 a. It mainly consists of two magnetic layers  \n(one in dark blue and one in light blue)  separated from each other by a thin tunnel barrier  made \nof MgO . The two magnetic layers have different switching thresholds , where one of the layers is \nutilized  as the fixed (reference) layer and the other one as the free (storage) layer. Role of the \nthird magnetic layer (below Ru) is to cancel the stray field of the reference layer on the storage \nlayer. Depending on the parallel ( P) or anti -parallel ( AP) orienta tion of the magnetization of the Page 3 of 18 \n \nfree and fixed layers, the resistance26,27 (Figure 1a) of the MTJ can change by more than 100%.27 \nIn addition, the free layer in the MTJ can be electrically switched in a sub-200 ps time scal e.28 \nThe switching energy of the  MTJ can be reduced , utilizing different mechanisms such as using a \ncomposite structure that preserves the thermal stability while reducing the switching energy.29 \nSince  magnets hold non -volatile information, the MTJ preserves its state over an electrical power \nshutdown. All of these properties make the MTJ a promising candidate for logic and memory \napplications . \nIII. Computing  with spins and magnets using  transistors or clocks  \nThere have been several proposals for utilizing MTJs in computational circuits either  as \nthe main core of the computation2–4 or as a temporary storage element that can hold information , \nwhich is called memory -in-logic.5–7 Figure 2 a shows a n example of a computational circuit that \nutilizes an MTJ for its operation and fan out.6 Here MTJ fun ction as the basic building block for \nthe logic operation and memory unit. Fan out means to transfer the information from one MTJ to \nanother. Once  all three input MTJs are in the low resistance (parallel magnetization) state, the \ncurrent is large enough to  switch the magne tization of the output MTJ. Figure 2 b demonstrates \nanother computational circuit that works using MTJs.7 This circuit implements an arithmetic and \nlogic unit.  MTJs are connected through a thin and narrow magnetic stripe (or named as \nnanowi re). Magnetic domain walls can be generated and transferred within this magnetic \nnanowire.  The information transfers between MTJs using magnetic domain wall displacement. \nAn actual processor that utilizes MTJs in a logic-in-memor y configuration is shown i n Figure \n2c.4,5 It is based on 90  nm MTJ/MOS hybrid technology and contains about 0.5 million \ntransistors and 13 ,400 MTJ cells. In contrast to the conventional electronic, spin information can \nbe transferred over a long distance using dipolar coupling with out direct contact of the cells.30 \nThere have been some proposals for  using this dipolar interaction in conjunction with MTJs for \ncomputational circuit s called magnetic quantum cellular automata (MQCA).31,32 Figure 2 d shows \na MTJ -based MQCA that was design ed for computation  and transfer of information . \n \nIV. Computing  with spins and magnets without transistors or clocks  \nThe approaches discussed thus far involve transistors and/or special clocks33,36,40 to \nprovide gain and directionality in order to propagate inf ormation. We now discuss another \napproach where such characteristics are inherently built into spin devices .9,10,13 Figure 3 a Page 4 of 18 \n \nillustrates a spin switch  in which the magnetic free layer,  ̂, acts as the logic data bit and can \norient into the page or out of the page,  representing binary 0 or 1. The read process occurs \nthrough a double MTJ structure labeled R in the upper dashed box with two fixed magnetic \nlayers   ̂ and – ̂. Depending on the magnetic orientation of the free layer  ̂, one MTJ will be \nin a low resistance (parallel) state , and one will be in a high resistance (anti -parallel) state. This \ndual MTJ read unit converts positive or negative magnetization (data bits 0 or 1) int o a bipolar \n(that is, positive or negative) output voltage , resulting in a bipolar output current exiting the \nmetal interconnect. Based on the equivalent circuit shown in  Figure 3b, the output current can be \nexpressed as :9,10 \n \n          \n       ̂  ̂,  (1) \nwhere V is the applied voltage which is also the energy supply  to the device, G is the sum of the \nconductances of the two MTJs and    is their difference.  RL is the load resistance that could be \nthe next spin switch  or fan -out in an in tegrated  circuit. This describes the output characteristics \n(read process) based on the state of the output magnetic data bit  ̂. The write (W) process occurs \nin the lower dashed box of Figure 3a  which is separated  from the read (R) section by an \ninsulat or,  role of which is to provide electrical  input-output isolation.  \nWe know from equation (1) that the state of  ̂ determines the output. In turn, t he \nswitching of this layer is dictated by the free layer  ̂  in the (W) section through magnetic \ncouplin g. Every time  ̂  switches,  ̂ switches accordingly in order to lower the interaction \nenergy between the two layers that favor the anti-ferromagnetic order to make  ̂ and  ̂  anti-\nparallel (  ̂    ̂ ). The switching of  ̂  itself is governed b y the giant spin Hall effect \n(GSHE) .34,35 Passing a charge current through a material with high spin –orbit coupling such as \nTa drives a spin current into  ̂  that can switch its magnetization depending on the polarity of the \ncurrent.34,35 The spin Hall e ffect provides a natural gain .9,10, 36 Without such gain, the output \ncurren t, instead of the input current , could determine  the state of the output , hence eliminating \nthe input -output asymmetry.  The e quivalent circuit of Figure 3c  can be used to calculate gain:9,10 \n Page 5 of 18 \n \n          \n        \n      \n     , (2) \n \nwhere Isc is the critical spin current needed to switch  ̂ . Spin current refers to the flow of \nelectron spins that may (spin polarized charge current  in MTJs ) or may not (pure spin current  for \nGSHE34,35) be accompanied by a net  non-zero charge  current . The symbol   is the ratio of the \nspin current entering  magnet   ̂  and the input charge current . For GSHE, a s each electron ic \ncharge  traverses through a material with high spin–orbit coupling , depending on its length, it \ncould  emit multiple electron spins to the adjacent  magnet. A s such,   can be larger than  one,9,10 \nthus providing gain in the spin switch . However,  mechanisms other than GSHE could also prove \nuseful.12,13,37–39\n \nThe input-output  characteristic s of the spin  switch based on detailed simulations9,10 is \npresented in Figure 3b . Hysteresis is present because the magnetic free layer  ̂ has non -volatile \nmemory. This figure clearly illustrates the presence of gain and input -output asymm etry causing \ndirectionality: for  a small change in input , ther e is a large change in output at the transition \npoints , analogous to CMOS devices.  One of the simplest circuits where such in -built gain and \ndirectionality clearly manifest themselves is tha t of a ring oscillator. Figure 3d  shows an odd \nnumber of spin switch es connected together. The R unit from each device is connected to the W \nunit of the next. Since each spin switch is essentially an inverter and there are an odd number of \nswitches , there is n o satisfactory steady state  that result s in an oscillatory output as obtained from \ndetailed simulation s9,10 with no loss of signal strength or compounding errors. The spin switches \nact autonomously with no need for external transistors or clocks for provid ing gain and /or \ndirectionality in order to propagate information.  \nVarious interconnections of such devices can  lead to integrated circuits . Universal \nBoolean logic gates such as NAND or NOR can be obtained by using spin -based majority \nlogic,12,15,40 where the output of one device is determined by the majority of the inputs coming \nfrom other devices. More interestingly, there are other possibilities beyond standard Boolean \nlogic such as reconfigurable non -volatile circuits9,10 and neural networks11 that are enabled with \ndevices that satisfy the essential characteristics discussed previously . \n \n Page 6 of 18 \n \nV. Materials for computing with spins and magnets   \nIn magnetic nanoscale devices,  magnetization can be either in the thin -film plane and \nhave in -plane anisotropy (IPA) or nor mal to the film plane and have perpendicular magnetic \nanisotropy (PMA). The magnetic thermal stability is usually indicated by the thermal stability \nfactor  \nΔ (= Kef fΩ/kBT),       (3) \nwhere Kef f is the effective magnetic anisotropy, Ωis the volume of the magnetic logic/memory \ncell, kB is the Boltzmann constant, and T is the temperature. For 10 -year data retention, Δ should \nexceed 60 at room temperature. Since the magnetic IPA is usually defined by the geometrical \naspect ratio of the magnetic nanostructure, m agnetic structures with IPA face major thermal \nstability issue s in sub -100 nm dimension s.41–43 In addition, an IPA-based MTJ requires a large \nthreshold current for spin transfer torque -induced magnetization switching due to the large \ndemagnetization field .44,45 Here sp   tr  sfer torque (STT) refers to the “tr  sferred” torque th t \nis exerted on a nanomagnet by a polarized spin current that passes through the nanomagnet. For a \nMTJ case, magnetic free layer is the nanomagnet and the polarized spin current is  generated by \nthe magnetic fixed layer.  In PMA materials, the magnetic anisotropy originates from volume \n(bulk anisotropy) and interfaces (surface anisotropy). The effective anisotropy energy \n            obeys the relation :46            \n   where           is the volume anisotropy and \n          is the interfacial anisotropy. PMA that is induced by i nterfacial magnetic anisotropy \n(IPMA) requires a very thin magnetic layer.  \nThere are two classes of IPMA , including bilayer  and trilayer structures. Bilayer IPMA \nhas the form of [X|{Co,Fe,CoFe}] n , where X is either a heavy transition metal (TM) such as  Au, \nPd, and Pt , or it is a thin magnetic layer such as  Ni. These structures show PMA for certain \nthickness es of the magnetic and TM layers .47–49 This bilayer stack structure needs to  be deposited \nfor several periods to provide a strong PMA.50 This multilayer structure is just like the basic \nstructure of a superlattice of one magnetic layer (e.g. Co) and one non -magnetic layer (e .g. Pd). \nFurthermore, the PMA can be tuned using the repetition period. There are major drawbacks for \nthis class of bilayer IPMA. The p resence of heavy metals lifts their damping constant up to \n0.5.51,52 In addition, the crystalline structure of these mate rials usually does not match  the MgO \ncrystalline struct ure, and they have a low spin polarization all together , result ing in a low TMR Page 7 of 18 \n \nratio.53 There have been some proposed remedies such as by insertion of a thin magnetic layer \nbetween the IPMA and the tu nnel barrier.54  \nThe second class of IPMA is a trilayer structure  in the form of X|[Co,Fe,CoFeB]|OX , \nwhere X is a heavy element such as  Au, Pd, Pt, and Ta, while OX could be any oxide material , \nsuch as  MgO, GdO x, and Al 2O3.27,55,56 Among the trilayer struc tures, Ta|CoFeB|MgO is the most \nstudied structure where a high TMR ratio above 120%44,57,58 and a decent damping of about \n0.015 can be achieved. The      of the trilayer structure is 1–2×106 erg/cc , which fails for the \nthermal stability of sub -20 nm MTJ.44 The bulk perpendicular magnetic  anisotropy (BPMA) \noriginates  from the strong lattice anisotropy field. BPMA materials have a strong      that can be \nas high as 7×107 erg/cc in FePt films .59 These alloys incorporat e a heavy element , and thus they \nhave a large damping constant on the order of 0.5.60 BPMA materials usually have a low spin \npolarization on the order of 50% or less.61 One solution to  the problem  of a large damping \nconstant  in some promising BPMA materials is to have a composite free layer that consists of a \nlow-damping and high spin polarization magnetic layer exchan ged coupled to a BPMA layer .29 \n \nVI. Computing with spins and magnets  at the atomic scale  \nThe benefits of scaling electronic circuits are widely known. Higher  density reduces cost \nand improves computational throughput. As such scalability is always an imperative topic for \nany potential technology. Computing with spins and magne ts is not an exception either.  An \nultimate goal of spintronic research is realizing such concepts at the atomic scale. In fact, it is \nnow possible to characterize materials and their magnetic interactions at these  scale s. Spin-\npolarized scanning tunneling microscopy (SP-STM)17 is a unique enabling tool for transforming  \nspin logic concepts into reality thanks to the unique combination of spin sensitivity ,18 atomic -\nscale spatial resolution ,19,20 and atom manipulation capability .21 \nAs an initial step, a bottom -up approach for fabricating artificial nanomagnets with full \ncontrol over each constituent atom and their mutual spin -dependent couplings has been \ndeveloped. The distance dependency of the indirect magnetic exchange ( Ruderman -Kittel -\nKasuya -Yosida or RKKY)  interaction in pairs of magnetic Fe adatoms on Cu(111) was deduced \nby measuring magnetization curves22 of each atom in the pairs.23 The observed oscillatory type of \nmagnetic coupling on the level of individual atoms allowed the tailoring of nanomagnets by  \ncontrolling the type of pairwise magnetic interactions (either ferro - or antiferromagnetic). A Page 8 of 18 \n \nplethora of different nanomagnets ranging from even and odd numbered chains to building \nblocks of lattices with different symmetries have been realized using ti p-induced atom \nmanipulation and simultaneous spin -sensitive imaging (Figure  4). The magnetic ground states of \nthese nanomagnets have then been studied in real space as a function of an external magnetic \nfield by means of single -atom magnetometry using SP -STM.24 The building blocks of the spin -\nfrustrated lattices show stepwise lifting of multiple degenerate ground states. To reproduce small \ntrends in the magnetization curves of the chains, the correct next -nearest neighbor interactions \nfrom an ab initio  calculation of the full nanomagnet, which slightly differ s from the \ncorresponding pairwise interactions, had to be taken into account.  \nBased on the unique combination of bottom -up atomic fabrication and spin -resolved \nSTM imaging , a prototype system for logical  operations has been realized16 that uses atomic \nspins of adatoms adsorbed on to a non -magnetic metallic surface and their indirect magnetic \nexchange interaction in order to transmit and process information (Figure  5). The adatoms have \ntwo different states,  0 or 1, depending on the orientation of their magnetization (down or up, \nrespectively). They are constructed to form antiferromagnetically RKKY -coupled chains  (as in \nFigure  4c) that transmit information on the state of small ferromagnetic islands ( “input islands”) \nto the gate region. The gate region, which comprises two “input atoms ” from each chain and an \n“output atom ,” forms the core where the logic operation is performed. The states of the inputs \nand the resultant state of the output atom are read out b y the magnetic tip of the SP -STM (i.e., in \nthe local tunneling magnetoresistance device geometry ).18 Although the STM is used to construct \nand characterize the device, it is not required to perform the given logic operation. The states of \nthe inputs can be  switched independently by external magnetic field pulses. Based on an all -spin \nconcept, this model device is principally non -volatile and functions without the flow of electrons, \npromising an inherently large energy efficiency.16 Compared to nanoelectroni c devices based on \ncharge transport, contact resistance problems do not occur. Moreover, all -spin atomic -scale \ndevices,  such as the one shown in Figure  5 ultimately promise high-speed operation  since the \ntime scale for a Fe -adatom spin to flip is only on t he order of 200 f s.25 \n \n \n \n Page 9 of 18 \n \nVII. Summary  \n \nComputing with spins and magnets offers several  advantages  if implemented. The \ninformation would be non -volatile preventing the logic circuitry from los ing information if \npowered off. This can reduce power  dissipation due to l eakage for non -active circuitry. Magneti c \ndevices have operating voltages well below 1V14,62-64 enabling  interconnects to operate at lower \nvoltages.  This could significantly reduce power consumption in the wiring on the wafer (back \nend of line) which is a  substantial portion of overall power consumption. Computing with spins \nand m agnets can  employ  majority  logic.9,15 This enable s more compact functional  gates65 \nresulting in increased  density.  Some logic bits in majority logic  can be toggled to reconfigure \ncomputational gates  making them electrically programmable.   Moreover, t here have also been \nproposals for novel computing schemes11,66 using spins and magnets that could  augment current \nBoolean logic based comp uting model .  \nOur objective was  to present an o verview of how spins and magnets can be used for \ncomputing ,  a necessary step  towards implement ation of logic  circuits  that can exploit the \nadvantages mentioned previously . Various state -of-the-art proposals and experiments for spin -\nbased logic ap plication s along with material and fabrication challenges  and method s were \ndiscussed . The choices of read and write mechanisms presented here are not unique and might \nchange in the future. However, we believe the general topics  and concepts  we discussed can \nguide the way for capable s pintronic -based logic devices that could enhance computing beyond \nwhat is feasible with current technology .  \n \nAcknowledgements  \nB. Behin -Aein is indebted to S. Datta for his invaluable advice  and consultation. We woul d also \nlike to thank M. Jamali,  B. Chilian, A.A. Khajetoorians, F. Meier, J. Wiebe, A. Klemm,  and L. \nZhou for their contributi ons. Financial support from the  National Science Foundati on (NSF) \nNanoelectronics Beyond  2020 (NEB) and the E RC Advanced Grant FURORE and by  the \nDeutsche Forschungs gemeinschaft via the SFB 668 is  gratefully acknowledged.  \n \n \n Page 10 of 18 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nRAP\nAP\nto P\nP to APRP(b) Resistance versus current \ncharacteristics of MTJ\n(m A )I    (a) Example MTJ structure \nBottom Electrode Seed Layer Pinning \nLayerRuMgOCapping Layer  Top Electrode\n1\n2     \n3 (b) Example Resistance \nversus current characteristic \nof MTJ \nReferenceStorage Figure 1. (a) A simplified schematic of a magnetic tunnel junction (MTJ).  It is mainly consisted of a storage layer and \nreference layer separated by an MgO layer. Role of the third magnetic layer below Ru is to cancel out the magnetic \nstray field of the reference layer on the storage layer. (b) Two distinct resistance levels based on the relative orientation \nof the reference layer and the storage layer are shown when current  (I) is passed through the structure. Reprinted with \npermission from Reference 26. © 2008  Macmillan Publishers .  Note: AP, antiparallel; P, parallel; RAP, resistance in \nthe AP state ; RP, resistance in the P state . Page 11 of 18 \n \n \n \n \n(a) (b)\n(c) (d)\nFigure 2.  (a) A computation circuit fully based on magnetic tunnel junctions (MTJs). 2 The bottom red arrows present \nthe fi xed layer of  MTJs, while the top arrows show the free layer of MTJs. Reproduced with permission from \nReference 2. © 2010 AI P Publishing LLC.  (b) An arithmetic logic unit that utilizes 20 MTJ cells for operation. 7 The \nmain MTJ cells in each logic unit are: R1, R2 , R3 , R4 , R5 , and R6 .The status of each main MTJ cell is controlled by the \ninput MTJ cells in each logi c unit throug h a nanomagnetic channel (NMC).  These input MTJ cells are  R'1, R'2 , R'3 , R'4 , \nR'5 , and R'6, which are controlled by one or more current inputs: A , B , and C . R L and R H are reference cells, which \nhave a fi xed low and high resistance, respectively. Each NMC is co ntrolled by one or more control  signals: M1– M'1 , \nM2– M'2, M3– M'3 , M4– M'4 , and M5– M'5 . With permission from Reference 7 . © 2012 IEEE. (c) A microgr aph of a \nnonvolatile logic -in-memory array processor in 90 nm MTJ/MOS technology4 , 5. The inset table l ists elements of the \nprocessor,  including 474,019 MOS transistors and 13,400 MT Js. The sum of absolute differences (SAD) and \nprocessing element (PE) correspond  to the SAD and PE circuits. Reprinted with permission from Reference 5. © 2013 \nIEEE. (d) MTJ -based magnetic quantum cellular  automata that utilize the magnetic dipolar interac tion for \ntransferring information and for computation. 32 The left part represents  the timing of the clock ( H clk ) and the \ninput signal ( I input ) as well as the way the spin signal propaga tes through the magnetic dipole  coupling, while the \nright one sh ows a scanning electron micrograph (SEM) of the actual fabricate d device. The SEM is taken at a  7.5 kV \nacceleration voltage for a working distance (WD) of 2.8 mm.  Page 12 of 18 \n \n \n \n(c) Input -output characteristics\nV=4Is,c\nbDG\n,4 /in\nscI\nI\n0 V\n1Lout\nVGG\nRI\n\n(a) Spin Switch (b) Input -output Characteristics \n(c) Equivalent Circuit(d) Ring Oscillator\n0 100 200 300 400 500-101\n0 100 200 300 400 500-101\n0 100 200 300 400 500-101Time\n(Normalized Units) 1\n23  V\nV V\nR\nW\nR\nWR\nW\nR\nW\nR\nWIN  Supply  \nSymbolOUT   \nRL\n RL\n1 /GIin+\n-\nMmGGV ˆˆ\nin s I I'Iout\nTime\n(Normalized Units)\nMgO\nMetal Interconnect  \nMetal \nInterconnect  Giant Spin Hall \nMaterial \nyˆx\nyˆFree Layer\nFree LayerInsulator \nMˆx+V -V \nMagnetic \nCoupling\nmˆ\nmˆ\nMˆ\nIin\nRL\n'\nsI\nGIVcs\n,4\ncs inI I,4\nGRGVI\nLout\n\n1Figure 3. (a) A suggested structure  for the spin switch  compo sed of read (R) and write (W) units  along with a symbol \ndepicting input, output , and energy supply . The y   d y’ d rect o s  re out of the p ge   d   to the p ge respectively . \n(b) Input -output characteristics of the spin switch derived from (c) the equivalent circuit of spin switch . Directionality \nand gain are evident because small changes in input result in large changes in output  at the edges  of the hysteresis . \nThe input signal  is amplified  with gain as defined in equation (2).  These are necessary attributes to make large scale \ncircuits. (d) A simple circuit . An odd number of spin  switch  devices  can be connected to form a ring oscillator similar \nto complementary metal oxide semiconductor  ring oscillators with no loss of signal strength or compounding errors  \nbecause  these devices have gain and directionality . The information is transferred from  switch  1 to 2 to 3 and then \nback to 1  and each switch oscillates . The spin switches act autonomously wi thout the need for external transistors or \nclocks to propagate information .9,10 This enables complex and large -scale circuits9–11 for computation . V is the applied \nvoltage which is the energy supply.   ̂ is the magnetization of the two fixed layers that point into and out of the plane. \n ̂ is the magnetization of the free layer acting as the storage layer.   ̂ is the magnetization of the free layer whose \norientation controls the orientation of the storage layer.   ̂ and  ̂ are opposite directions into and out of the page and \nrefer to the an ti-ferromagnetic orientation of the two free layers.  Iin is the input current. I’\nS is the spin current entering \nthe bottom free layer. IS,C is the critical spin current needed for switching.  Iout is the outgoing current through R L which \nis the load resist   ce. (Th s lo d c   be   other sp   sw tch or c rcu try.)    s the r t o (   m g  tude) betwee  I’\nS and \nIin. G  s the sum of the co duct  ces of the two MTJs   d Δ G is the difference.  Page 13 of 18 \n \n                                                                                                                                         \n \nFigure 4. (a) Spin-polarized scanning tunneling \nmicroscopy (SP-STM ) image (25 nm x 20 nm) of \nfabricated nanomagnets consisting of indirect \nexchange  -coupled Fe atoms on Cu(111). (b –c) \nMagnetization states from an Ising model (left, \npartly degenerate) and spin-polarized scanning \ntunneling spectroscopy  () images (right) of chains of \nantiferromagnetically coupled Fe atoms with a \nlength of six (b) and seven (c) atoms. The distance \nbetween individual Fe atoms is 1 nm. (d–f): \nDegenerate magnetization states from an Ising \nmodel for an  array of 12 antiferromagnetically \ncoupled atoms at magnetic fields  (B), as indicated \nby the arrows in ( 1,m). (g–k): Five SP-STM images \nof a kagomé lattice unit of Fe atoms recorded at B -\nfields  of -2 T, -1 T, 0 T, +1 T, +2 T , respectively,  as \nindicated by the dashed lines in ( 1,m). The distance \nbetween individual Fe atoms is 1 nm.  (1,m): \nMagnetization curves measured on the kagomé \natoms ( corresponding to the red circles  for (l) and \nthe blue circles for (m)  in the inset of (l) ). Thick \ncolored lines in the magnetization plots show \nmagnetization curves as calculated from an Ising \nmodel.24  Note: I: spin -resolved tunneling current  ; \nV: applied sample bias voltage  . Page 14 of 18 \n \n \nFigure 5. (a) Device  concept  for all -spin atomic -scale logic: Two chains of antiferromagnetically coupled \nmagnetic atoms (yellow spheres) on a nonmagnetic metallic substrate are exchange -coupled to two \n“input islands ” (1, 2) of different size, consisting of patches  of ferromagnetic layers. The “input atom ” (1, \n2) of each spin lead and the final “output atom ” form a magnetically frustrated triplet with an \nantiferromagnetic coupling , which constitutes the logic gate. The field pulse Bpulse is used to switch the \ninputs. The magnetic tip of a  scanning tunneling microscop e () is used to construct and characterize the \ndevice. (b –e) Side -view of 3D topographs colored with simultaneously measured spin-polarized scanning \ntunneling spe ctroscopy  image s of the constructed OR -gate for all four possible input permutations. By \napplying out -of-plane magnetic field pulses of different strength and direction, each input island can be \ncontrollably switched , and the two spin leads transmit the information to their end atoms. The spin state \nof the output atom in the gate triplet responds accordingly, thereby reflecting the logic operation OR .16 Page 15 of 18 \n \nReferences  \n1. A. Brataas, A.D. Kent, H. Ohno, Nat. Mater . 11, 372 (2012).  \n2. A. Lyle , J. Harms, S. Patil, X. Yao, D. J. Lilja, J.-P. Wang, , Appl. Phys. Lett.  97 (15), 152504  (2010).  \n3. H. Meng,  J. Wang, J. -P. Wang,  IEEE Electron Device Lett.  26 (6), 360 (2005).  \n4. S. Matsunaga , J. Hayakawa, S. Ikeda, K. Miura, H. H asegawa, T. Endoh, H. Ohno, T. Hanyu,  Appl. \nPhys. Express  1 (9), 091301 (2008).  \n5. M. Natsui , D. Suzuki, N. Sakimura, R. Nebashi, Y. Tsuji, A. Morioka, T. Sugibayashi, S. Miura, H. \nHonjo, K. Kinoshita, S. Ikeda, T. Endoh, H. Ohno, T. Hanyu,  in 2013 IEEE International Solid -State \nCircuits Conference Digest of Technical Papers  94, 194 (2013).  \n6. Y. Jiang, J. Harms , J.-P. Wang, IEEE Trans . Electron Devices  59, 2917 (2012).  \n7. X. Yao , J. Harms, A. Lyle, F. Ebrahimi, Y. Zhang, and J. -P. Wang,  IEEE Trans. Nanotechnol.  11 (1), \n120 (2012).  \n8. S.H. Kang , K. Lee,  Acta Mater.  61 (3), 952 (2013).  \n9. S. Datta, S. Salahuddin, B. Behin -Aein,  Appl. Phys. Lett.  101 (25), 252411 (2012).  \n10. S. Datta, V.Q. Diep, B. Behin -Aein, in Ed. Emerging Nanoelectronic Devices , A. Chen, J. Hutchby, \nV. Zhirnov, G. Bourianoff , Eds. (Wiley, New York, 2014) , chap. 2, in press  (available at \nhttp://arxiv.org/abs/1404.2254 ). \n11. V.Q.  Diep, B. Sutton, B. Behin -Aein, S. Datta,   Appl. Phys. Lett . 104, 222405  (2014) .  \n12. B. Behin -Aein, D. Datta, S. Salahuddin, S. Datta, Nature Nanotech.  5 (4), 266 (2010).  \n13. S. Srinivasan, A. Sarka r, B. Behin -Aein, S. Datta,  IEEE Trans. Magn.  47 (10), 4026 (2011).  \n14. B. Behin -Aein, A. Sarkar, S. Srinivasan, S. Datta,  Appl. Phys. Lett.  98 (12), 123510 (2011).  \n15. A. Sarkar, S. Srinivasan, B. Behin -Aein, S. Datta. IEEE Int. Electron Devices Meeting ( IEDM) \nTechnical Digest 11.1 (2011).  \n16. A.A. Khajetoorians, J. Wiebe, B. Chilian, R. Wiesendanger, Science  332, 1062 (2011).  \n17. R. Wiesendanger, Rev. Mod. Phys.  81, 1495 (2009).  \n18. R. Wiesendanger, H. -J. Güntherodt, G. Güntherodt, R.J. Gambino, R. Ruf,  Phys. Rev. Lett.  65, 247 \n(1990).  \n19. R. Wiesendanger ,I.V. Shvets, D. Bürgler, G. Tarrach, H. -J. Güntherodt, J.M.D. Coey, S. Gräser,   \nScience  255, 583 (1992).  \n20. S. Heinze ., M. Bode, A. Kubetzka, O. Pietzsch, X. Nie, S. Blügel, R. Wiesendanger,   Science  288, \n1805 (2000).  Page 16 of 18 \n \n21. D. Serrate ., P. Ferriani, Y. Yoshida, S. -W. Hla, M. Menzel, K. von Bergmann, S. Heinze, A. \nKubetzka, R. Wiesendanger, Nature Nanotech. 5, 350 (2010).  \n \n22. F. Meier, L. Zhou, J. Wiebe, R. Wiesendanger, Science  320, 82 (2008).  \n \n23. L. Zhou ., J. Wiebe, S. Lounis, E. Vedmedenko, F. Meier, S. Blügel, P. H. Dederichs, and R. \nWiesendanger,   Nature Phys.  6, 187 (2010).  \n \n24. A.A. Khajetoorians , J. Wiebe, S. Lounis, E. Vedmedenko, F. Meier, S. Blügel, P. H. Dederichs, R. \nWiesendanger,  Nature Phys.  8, 497 (2012).  \n25. A.A. Khajetoorians , S. Lounis, B. Chilian, A. T. Costa, L. Zhou, D. L. Mills, J. Wiebe,  R. \nWiesendanger,  Phys. Rev. Lett.  106, 037205 (2011).  \n26. H. Kubota , A. Fukushima, K. Yakushiji, T. Nagahama, S. Yuasa, K. Ando, H. Maehara, Y. \nNagamine , K. Tsunekawa, D. D.  Djayaprawira, N. Watanabe, Y. Suzuki, Nature Phys.  4 (1), 37 (2007).  \n27. M. Nakayama ., T. Kai, N. Shimomura, M. Amano, E. Kitagawa, T. Nagase, M. Yosh ikawa, T. Kishi, \nS. Ikegawa,  H. Yoda,  J. Appl. Phys. , 103 (7), 07A710 (2008).  \n28. H. Zhao ., B. Glass, P. K. Amiri, A. Lyle, Y. Zhang, Y. -J. Chen, G. Rowlands, P. Upadhyaya, Z. Zeng, \nJ. a Katine, J. Langer, K. Galatsis, H. Jiang, K . L. Wang, I. N. Krivorotov,  J.-P. Wang,  J. Phys. D: Appl. \nPhys. , 45 (2), 25001 (2012).  \n29. H. Meng, J. -P. Wa ng, Appl. Phys. Lett.  89 (15), 152509 (2006).  \n30. R.P. Cowburn ,M.E. Welland,  Science  287 (5457 ), 1466 (2000).  \n31. A. Lyle et al.,  J. Harms, T. Klein, A. Len tsch, D. Martens, A. Klemm, J.-P. Wang,  Appl. Phys. Lett.  \n100 (1), 012402 (2012).  \n32. A. Lyle  J. Ha rms, T. Klein, A. Lentsc h, A. Klemm, D. Martens,  J.-P. Wang, AIP Adv. ,, 1  (4), 042177 \n(2011).  \n33. B. Behin -Aein, S. Salahuddin, S. Datta. IEEE Tran s. Nanotech nol. 8 (4), 505 (2009).  \n34. L.Q. Liu , L. Liu, Y. Li, H. W. Tseng, D. C. Ralph, and R. A. Buhrman,   Science  336 (6081 ), 555 \n(2012).  \n35. L. Liu, O.J. Lee, T.J. Gudmundsen, D.C. Ralph, R.A. Buhrman, Phys . Rev. Lett.  109, 096602 (2012).  \n36. D. Bhowmik , L. You , S. Salahuddin , Nat. Nanotech nol. 9, 59 (2014).  \n37. J.T. Heron , M. Trassin, K. Ashraf, M. Gajek, Q. He, S. Y. Yang, D. E. Nikonov, Y. -H. Chu, S. \nSalahuddin, and R. Ramesh,  Phys. Rev. Lett.  107 (21), 217202 (2011).  \n38. P. Khalili, K.L. Wang, SPIN  2 (3), 1240002 (2012).  \n39. J. Zhu , , J. A. Katine, G. E. R owlands, Y. -J. Chen, Z. Duan, J. G. Alzate, P. Upadhyaya, J. Langer, P. \nK. Amiri, K. L. Wang, and I. N. Krivorotov, Phys. Rev. Lett.  108 (19), 197203 (2012).  \n40. A. Imre , G. Csaba, L.J. Orlov, G.H. Bernstein, W. Porod, Science  311 (5758 ), 205 (2006).  Page 17 of 18 \n \n41. J. Wang, W. Shen, J. Bai,  IEEE TRANSACTIONS ON MAGNETICS, 41, 3138 (2005),  41 (10), \n3181 (2005).  \n42. S. Mangin ., D. Ravelosona, J. A. Katine, M. J. Carey, B. D. T erris, and E. E. Fullerton,  Nature Mater.  \n5 (3), 210 (2006).  \n43. H. Meng, J. -P. Wang, Appl. Phys. Lett.  88 (17), 172506 (2006).  \n44. S. Ikeda , K. Miura, H. Yamamoto, K. Mizunuma, H. D. Gan, M. Endo, S. Kanai, J. Hayakawa, \nNature Mater.  9 (9), 721 (2010).  \n45. P. Khalili , Z. M. Zeng, J. Langer, H. Zhao, G. Rowlands, Y. -J. Chen, I. N. Krivorotov,  Appl. Phys. \nLett. 98 (11), 112507 (2011).  \n46. M.T. Johnson, P.J.H. Bloemen, F.J.A. den Broeder, J.J. de Vries, Rep. Prog. Phys.  59 (11), 1409 \n(1996).  \n47. F.J.A. den Br oeder, H.C. Donkersloot, H.J.G. Draaisma, W.J.M. de Jonge, J. Appl. Phys.  61 (8), 4317 \n(1987).  \n48. P.F. Carcia, A.D. Meinhaldt, A. Suna,  Appl. Phys. Lett.  47 (2), 178 (1985).  \n49. G. Daalderop, P. Kelly, F. den Broeder, Phys. Rev. Lett . 68 (5), 682 (1992).  \n50. S. Mohanan, U. Herr,  J. Appl. Phys.  102 (9), 93903 (2007).  \n51. J. Dou, M.J. Pechan, E. Shipton, N. Eibagi, E.E. Fullerton,  J. Appl. Phys.  113 (17), 17C115  (2013).  \n52. S. Pal, B. Rana, O. Hellwig, T. Thomson, A. Barman, Appl. Phys. Lett.  98 (8), 082501 (2011).  \n53. Z. Kugler ,V. Drewello, M. Schäfers , J. Schmalhorst, G. Reiss, A. Thomas,  J. Magn. Magn. Mater.  \n323 (2), 198 (2011).  \n54. K. Mizunuma ,Shoji Ikeda, Hiroyuki Yamamoto, Hua Dong Gan, Katsuya Miura, Haruhiro Hasegawa, \nJun Hayakawa, Kenc hi Ito, Fumih iro Matsukura,  Hideo Ohno,  Jpn. J. Appl. Phys.  49 (4S), 04DM04 \n(2010).  \n55. D.C. Worledge , G. Hu, D. W. Abraham , J. Z. Sun, P. L. Trouilloud1,J. Nowak1, S. Brown1, M. C. \nGaidis1, E. J. O’Sull v  1 and R. P. Robertazzi  Appl. Phys. Lett.  98 (2), 22501 (2011).  \n56. R. Lavrijsen, Appl. Phys. Let t. 98 (13), 132502 (2011).  \n57. T. Devolder , , P.-H. Ducrot, J. -P. Adam, I. Barisic, N. Ve rnier, J. -V. Kim, B. Ockert,  D. Ravelosona,  \nAppl. Phys. Lett.  102 (2), 022407 (2013).  \n58. M. Jamali, A. Klemm, J. -P. Wang,  Appl. Phys. Lett.  103 (25), 252409 (2013).  \n59. J.-U. Thiele, L. Folks, M.F. Toney, D.K. Weller, J. Appl. Phys.  84 (10), 5686 (1998).  \n60. S. Mizukami , D. Watanabe, M. Oogane, Y. Ando, Y. Miura, M. Shirai, and T. Miyazaki,  Appl. Phys. \nLett. 98 (5), 052501 (2011).  Page 18 of 18 \n \n61. B. Dai, T. Kato, S. Iwata, S. Tsu nashima, IEEE Trans. Magn.  48 (11), 3223 (2012).  \n62. A. Sarkar, D. E. Nikonov, I. A. Young,  B. Behin -Aein, Supriyo Datta,  IEEE Trans. Nanotech.  13 \n(1), 143 (2014).  \n63. J. Z. Sun,  S. L. Brown,  W. Chen,  E. A. Delenia,  M. C. Gaidis,  J. Harms,  G. Hu, Xin Jia ng, R. Kilaru,  \nW. Kula,  G. Lauer,  L. Q. Liu,  S. Murthy,  J. Nowak,  E. J. O’Sull v  ,  S. S. P. Parkin,  R. P. Robertazzi,  P. \nM. Rice,  G. Sandhu,  T. Topuria, D. C. Worledge , Phys. Rev. B. , 88, 104426 (2013).   \n \n64. J. Z. Sun, R. P. Robertazzi, J. Nowak, P. L. T rouilloud, G. Hu, D. W. Abraham, M. C. Gaidis, S. L. \nBrown, E. J. O ’Sull v  , W. J.   ll gher, D. C. Worledge , Phys. Rev. B  84, 064413  (2011).  \n \n65. C. Augustine, G. Panagopoulos, B. Behin -Aein,  S. Srinivasan , A. Sarkar , K. Roy,  IEEE NANOARCH \nProceedings , 129 (2011).  \n \n66. B. Behin -Aein, United States Patent , US 8558571 B2.  \n "    },    {        "title": "1412.1059v1.Third_order_effect_in_magnetic_small_angle_neutron_scattering_by_a_spatially_inhomogeneous_medium.pdf",        "content": "arXiv:1412.1059v1  [cond-mat.mtrl-sci]  2 Dec 2014Third-order effect in magnetic small-angle neutron scatter ing by a spatially\ninhomogeneous medium\nKonstantin L. Metlov\nDonetsk Institute for Physics and Technology NAS, Donetsk, Ukraine 83114∗\nAndreas Michels\nPhysics and Material Science Research Unit, University of L uxembourg,\n162A Avenue de la Fa¨ ıencerie, L-1511 Luxembourg, Grand Duc hy of Luxembourg\n(Dated: May 27, 2021)\nMagnetic small-angle neutron scattering (SANS) is a powerf ul tool for investigating nonuniform\nmagnetization structures inside magnetic materials. Here , considering a ferromagnetic medium with\nweakly inhomogeneous uniaxial magnetic anisotropy, satur ation magnetization, and exchange stiff-\nness, we derive the second-order (in the amplitude of the inh omogeneities) micromagnetic solutions\nfor the equilibrium magnetization textures and compute the corresponding magnetic SANS cross\nsections up to the next, third order. We find that in the case of perpendicular scattering (the inci-\ndent neutron beam is perpendicular to the applied magnetic fi eld) if twice the cross section along\nthe direction orthogonal to both the field and the neutron bea m is subtracted from the cross section\nalong the field direction, the result has only a third-order c ontribution (the lower-order terms are\ncanceled). This difference does not depend on the amplitude o f the exchange inhomogeneities and\nprovides a separate gateway for a deeper analysis of the samp le’s magnetic structure. We derive\nand analyze analytical expressions for the dependence of th is combination on the scattering-vector\nmagnitude for the case of spherical Gaussian inhomogeneiti es.\nPACS numbers: 61.05.fg, 75.60.-d, 75.25.-j\nKeywords: micromagnetics, neutron scattering, magnetic s mall-angle neutron scattering\nI. INTRODUCTION\nMagnetic small-angle neutron scattering (SANS) is an\nimportant tool for the analysis of magnetic structures\non the nanoscale.1Traditional scalar magnetometry, for\nexample, only measures the sample’s total magnetic mo-\nment and has no spatial resolution. Magnetic force mi-\ncroscopy is sensitive to the spatial features of the magne-\ntization only in the near-vicinity of the sample’s surface\nand is also prone to disturbing the magnetic structure\nduringthemeasurement. Opticalmagnetometryiseither\nalsoonlysurface-sensitive(suchasinKerrmicroscopy)or\nis applicable only to optically transparent magnets (such\nasinFaradaymicroscopy). MagneticSANScomplements\nthese techniques by permitting analysis of the sample’s\nmagnetic structure throughout the volume, even in non-\ntransparent materials, while also being sensitive to the\nspatial arrangement of the magnetization.\nThe analysis of magnetic SANS cross sections is\nclosely interwoven2with the continuum theory of\nmicromagnetics.3This is because, unlike nonmagnetic\nnuclear SANS (which is sensitive to nanoscale density\nand compositional fluctuations), magnetic SANS cross\nsection images are formed by the distribution of the\nmagnetic moments within the sample. These magnetic\nmoments are influenced by magnetic material inhomo-\ngeneities, but, due to their mutual interaction, do not\nfollow the inhomogeneities exactly. Thus, in order to un-\nderstand magnetic SANS cross sections, one must also\nunderstand the process of magnetic-structure formation\nand its dependence on the external magnetic field, whichis the subject of micromagnetic theory.\nCurrently, the interpretation of magnetic SANS cross\nsections of heterogeneous multiphase magnets with small\ninhomogeneities of the saturation magnetization and the\nmagnetic anisotropy is based on a second-order (in the\ninhomogeneities amplitude) theory,4which has its origin\nin the theory of the approach to magnetic saturation.5\nThe latter stems from the works of Schl¨ omann,6which,\nin turn, is a follow up on the work by N´ eel.7\nThe motivation for the present study is to probe the\nlimits of the second-order magnetic SANS theory4by\nlooking for prominent third-order effects. Specifically,\nthose, which are not masked by the second-order ones.\nOne such effect—a central result of this work—is pin-\npointedattheendofthepaper(Sec.VI).Anattemptwas\nmade to include all the interactions which are common\nin micromagnetics. In particular, our solution for the\nmicromagnetic problem of weakly inhomogeneous mag-\nnetsincludes inhomogeneousexchangeinteraction, which\nis irrelevant for the problem of the approach to mag-\nnetic saturation and for the second-order SANS theory.\nAlso, the present theory explicitly includes a weak, fluc-\ntuating random-axis uniaxial anisotropy and full three-\ndimensional anisotropy-direction averaging.\nThe paper is organized as follows. Sec. II introduces\nthe magnetic SANS cross sections, Sec. III details the so-\nlution of the micromagnetic problem in Fourier space,\nSec. IV provides a discussion of the defect distribu-\ntion and averaging procedures, the second and higher-\norder SANS cross sections are, respectively, discussed in\nSecs.VandVI,andSec. VIIsummarizesthe mainresults2\nof this study.\nII. MAGNETIC SANS CROSS SECTIONS\nThe current theoretical and experimental understand-\ning of magnetic SANS of bulk ferromagnets has recently\nbeen summarized.1The quantity of interest—the differ-\nential SANS cross sectiondΣ\ndΩ—is related to the Fourier\ntransform of the Cartesian components of the magneti-\nzation vector field /tildewiderM={/tildewiderMX,/tildewiderMY,/tildewiderMZ}. In particular,\nthe total unpolarized nuclear and magnetic SANS cross\nsection is8\ndΣ⊥\ndΩ= 8π3Vb2\nH/bracketleftBigg\n|/tildewideN|2\nb2\nH+|/tildewiderMX|2+|/tildewiderMY|2cos2α+\n|/tildewiderMZ|2sin2α−2Re(/tildewiderMY/tildewiderMZ)sinαcosα/bracketrightBig\n,(1)\ndΣ/bardbl\ndΩ= 8π3Vb2\nH/bracketleftBigg\n|/tildewideN|2\nb2\nH+|/tildewiderMX|2sin2β+|/tildewiderMY|2cos2β+\n|/tildewiderMZ|2−2Re(/tildewiderMY/tildewiderMX)sinβcosβ/bracketrightBig\n, (2)\nwhere the first expression refers to the perpendicular\nscattering geometry, for which q⊥=q{0,sinα,cosα},\nand the second equation relates to the parallel geometry,\nwithq/bardbl=q{cosβ,sinβ,0};Vis the scattering volume,\nbH= 2.9×108A−1m−1,/tildewideN(q) is the nuclear scattering\namplitude, Re stands for taking the real part of a com-\nplex number and over-barfor its complex conjugate. The\ncross section is generally measured in units of cm−1sr−1.\nFourier transforms (distinguished by tildes above the\nsymbol) are defined for a representative cube of the ma-\nterial with dimensions L×L×L. Most of the time we\nshall work with discrete transforms (the continuous ones\ncorrespond to the limit L→ ∞):\n/tildewideX(q) =1\nV/integraldisplay/integraldisplay/integraldisplay\nVX(r)e−ıqrd3r, (3)\nX(r) =/summationdisplay\nq/tildewideX(q)eıqr, (4)\nwhereı=√−1,V=L3is the representative cube vol-\nume and Xis a quantity which is defined inside the vol-\nume. The components of q={qX,qY,qZ}take on all val-\nues which areinteger multiples of 2 π/L. Note that unlike\nRef. 8ourdefinitionoftheforwardFouriertransformcar-\nries a prefactor of 1 /V, so that the Fourier transform has\nthe same dimension as the transformed quantity. This,\nhowever, renders the prefactor in the expressions for the\ncross sections, Eqs. (1) and (2), also slightly different.\nIn order to get rid of the nuclear scattering |/tildewideN|2, the\ncross sections are typically split into the residual and the\nmagnetic parts, Σ = Σ res+ΣM, where the residual part\ncorresponds to the magnet in the fully saturated state.\nAssuming that a large saturating external magnetic fieldis directed along the Z-axis,\ndΣ⊥\nres\ndΩ= 8π3Vb2\nH/bracketleftBigg\n|/tildewideN|2\nb2\nH+|/tildewiderMS|2sin2α/bracketrightBigg\n,(5)\ndΣ/bardbl\nres\ndΩ= 8π3Vb2\nH/bracketleftBigg\n|/tildewideN|2\nb2\nH+|/tildewiderMS|2/bracketrightBigg\n, (6)\nwhere/tildewiderMSis the Fourier transform of the inhomogeneous\nsaturation magnetization of the magnet, which is defined\nin the next section. The residual part can then be mea-\nsured independently and subtracted from the measured\ntotal cross section at a lower field to yield the magnetic\npart:\ndΣ⊥\nM\ndΩ= 8π3Vb2\nH/bracketleftBig\n|/tildewiderMX|2+|/tildewiderMY|2cos2α+\n(|/tildewiderMZ|2−|/tildewiderMS|2)sin2α−\n2Re(/tildewiderMY/tildewiderMZ)sinαcosα/bracketrightBig\n, (7)\ndΣ/bardbl\nM\ndΩ= 8π3Vb2\nH/bracketleftBig\n|/tildewiderMX|2sin2β+|/tildewiderMY|2cos2β+\n(|/tildewiderMZ|2−|/tildewiderMS|2)−2Re(/tildewiderMY/tildewiderMX)sinβcosβ/bracketrightBig\n.\n(8)\nThus, in order to compute the magnetic SANS cross\nsection one needs to know the Fourier components of\nthe magnetization vector field inside the material. Their\nderivation is the main subject of the two following sec-\ntions.\nIII. MAGNETIZATION DISTRIBUTION IN A\nWEAKLY INHOMOGENEOUS MAGNET\nConsider an infinite magnet, whose saturation magne-\ntization depends explicitly on the position vector r,\nMS(r) =M0[1+Im(r)], (9)\nwhere the magnitude of Im(r) is a small quantity. We\nalso assume that the spatial average /an}b∇acketle{tIm(r)/an}b∇acket∇i}ht= 0, so that\nM0=/an}b∇acketle{tMS(r)/an}b∇acket∇i}htis the average saturation magnetization\nof the magnet.\nIf the representative volume contains a magnetic ma-\nterial, the equilibrium distribution of the magnetization\nvectorM(r)isthesolutionofBrown’sequations9ateach\npointrin the volume,\n[Heff,M] = 0, (10)\nwhere the square brackets denote the vectorial cross\nproduct. The effective field Heff(r) is defined as the\nfunctional derivative of the ferromagnet’s energy-density\nfunctional eover the magnetization vector field,\nHeff(r) =−1\nµ0δe\nδM=−1\nµ0/parenleftBigg\n∂e\n∂M−∂\n∂r∂e\n∂M\n∂r/parenrightBigg\n.(11)3\nFrom the magnetic-units standpoint, following\nAharoni,10we use the defining relation for the magnetic\ninduction\nB=µ0(H+γBM), (12)\nwhich can be made valid in all systems of magnetic units\nby appropriately choosing the constants µ0andγB. For\nexample, in the SI system µ0is the permeability of vac-\nuum and γB= 1, inthe CGSsystem µ0= 1andγB= 4π.\nThe energy density erepresents our knowledge of the\ninteractions in the magnetic material. Here, we include\nthe effectsofexchange, randomuniaxialanisotropy,mag-\nnetostatic interaction, and the influence of the uniform\nexternal magnetic field, so that the total energy density\nof the magnet can be written as a sum,\ne=eEX+eA+eMS+eZ. (13)\nDifferent interactions enter both the energy density and\nthe effective field additively, so that\nHeff=HEX+HA+HMS+HZ,(14)\nwhereHZis simply the external field.\nThe exchange interaction is deemed inessential in the\ntheory of the approach to magnetic saturation,6,7but\nSANS is sensitive to small spatial variations of the mag-\nnetization vector field, despite their negligible contribu-\ntion to the total magnetization of the sample. That is\nwhy we have included the exchange interaction into con-\nsideration. Its energy density in a material with varying\nsaturation magnetization is conventionally defined as\neEX=C(r)\n2/summationdisplay\ni=X,Y,Z/parenleftbigg\n∇/bracketleftbiggMi(r)\nMS(r)/bracketrightbigg/parenrightbigg2\n,(15)\nwhereC(r) is the exchange stiffness; X,Y,Zare the\nlabels of the Cartesian coordinate-system axes; ∇=\n{∂/∂X,∂/∂Y,∂/∂Z }is the gradient operator. Using\nvector-calculus identities, it can be transformed into\neEX=µ0γBL2\nEX(r)\n2\n−[∇MS(r)]2+/summationdisplay\ni=X,Y,Z[∇Mi(r)]2\n,\n(16)\nwith the exchange length\nLEX(r) =/radicalbig\nC(r)/[µ0γBMS(r)].(17)\nThe first term in Eq. (16) vanishes under the variation of\nMand gives no contribution to the effective field. This\nis a manifestation of the fact that the exchange energy\ndepends only on relative angles of the magnetization vec-\ntors and not on their magnitude. Thus,\nHEX=γBL2\nEX(r)∆M(r)+γB∇L2\nEX(r)∇M(r),(18)\nwhere ∆ is the Laplaceoperatorand ∇M(r) is a matrix,\nwhose rows are the gradients of the components of thevectorM(r). Similarly to Eq. (9) we will now assume\nthat the squared exchange length is weakly inhomoge-\nneous\nL2\nEX(r) =L2\n0[1+Ie(r)], (19)\nwhereIeis a small position-dependent quantity of\nthe same order as ImandL0is an average position-\nindependent exchange length. In real materials, since\nthe values of both CandMSare determined by the\nsame quantum exchange interaction (and both grow as\nexchange becomes stronger), the value of L0displays lit-\ntle variation across a wide range of magnetic materials\nand is of the order of 5 −10 nm for most of them. Nev-\nertheless, we shall keep track of the weak spatial depen-\ndence of LEXin this calculation.\nThe presence of uniaxial anisotropy creates the follow-\ning energy density\neA=−kU(r)[d(r)·M(r)]2\nM2\nS(r), (20)\nwherekU(r) is the spatially inhomogeneous anisotropy\nconstant, and d(r) is a unit vector along the local direc-\ntion of the anisotropy axis. The corresponding effective\nfield is\nHA=γBQ(r)[d(r)·M(r)]d(r),(21)\nwhere the dimensionless quality factor\nQ(r) = 2kU(r)/[µ0γBM2\nS(r)] =Ik(r) (22)\nis assumed to be small and of the same order as Im.\nThe magnetostatic energy density is\neMS=−1\n2µ0(HD·M), (23)\nwhereHDis the magnetostatic (or demagnetizing) field.\nThe expression for the latter in the static case with no\nmacroscopic currents is simplest in Fourier representa-\ntion. It follows11from the expression of the magnetic\ninduction (12) with the internal field H=HZ+/tildewiderHD\nand Maxwell’s equations ∇×HD= 0 and∇·B= 0 that\n/tildewiderHD=−γBq(q·/tildewiderM)\nq2forq/ne}ationslash= 0. (24)\nTheaveragedemagnetizing field /tildewiderHD(0) is anti-parallelto\nthe external field HZ. Thus, we can add these fields as\nscalarsH=HZ−|/tildewiderHD(0)|. All the following results will\nbe computed as functions of this internal field H(which,\nin particular, contains the information about the shape\nof the sample) and not directly of the external field HZ.\nHavingasimple expressionforthe demagnetizingfield,\nEq. (24), suggests trying to solve Brown’s equations,\nEqs. (10), directly in Fourier space. There is, however,\na complication, since products of functions in real space\nbecome their convolutions in Fourier space. Thus, to4\nsimplify the expressions, let us introduce a shorthand\nnotation for convolutions:\nX⊗Y(q) =/summationdisplay\nq′X(q′)Y(q−q′),(25)\nwhere the argument qon the left hand side (which some-\ntimes will be omitted in the following text) is the argu-\nment of the whole convolution (not just of Y) and sum-\nmation is carried out over all the values of q′. The alge-\nbra of convolutions is commutative ( X⊗Y=Y⊗X),\ndistributive ( X⊗(Y+Z) =X⊗Y+X⊗Z), and as-\nsociative with respect to multiplication of a constant,\na(X⊗Y) = (aX)⊗Y=X⊗(aY), where ais a constant.\nIt also has an identity element (a product of Kronecker\ndeltasinthediscretecaseorDirac’sdeltafunctionsinthe\ncontinuous case), which we will denote as δ(q), so that\nδ⊗X=X. We will also sometimes specify functions in-\nline by underlining them, so that qZ⊗Yis convolution\nof the function X(q) =qZ(q) with the function Y(q).\nUsing this notation, we can now express Fourier rep-\nresentations of the effective-field terms:\n/tildewiderHEX=−γB/tildewidestL2\nEX⊗q2/tildewiderM\n−γBq/tildewidestL2\nEX⊗q×/tildewiderM, (26)\n/tildewiderHA=γB/tildewideQ⊗/parenleftBig\n/tildewidedX⊗/tildewiderMX+/tildewidedY⊗/tildewiderMY+\n/tildewidedZ⊗/tildewiderMZ/parenrightBig\n⊗/tildewided, (27)\n/tildewiderHMS+/tildewiderHZ=Hδ−γBq[q·(/tildewiderM−δ/tildewiderM)]\nq2,(28)\nwhere the cross ( ×) denotes a direct product of two vec-\ntors (forming a matrix, having the products of the left\nvector by each element of the right vector in the rows)\nand convolution of a vector with a matrix is like their\nnormal product but with convolutions instead of multi-\nplications. The final subtraction, together with the con-\ndition that/tildewiderM−δ/tildewiderM→0 asq→0 is a mathematical\ntrick, allowing not to pay further attention to the fact\nthat the expression for the demagnetizing field, Eq. (24),\nis valid only for q/ne}ationslash= 0. This limiting condition is fulfilled,\nif/an}b∇acketle{tIm(r)/an}b∇acket∇i}ht=/tildewideIm(0) = 0, which is assumed from the start\nof this computation.\nIn completely homogeneous infinite isotropic magnets,\nthe magnetization will alwaysbe uniform, saturated, and\naligned parallel to the external (and the internal) field\n(however small it is). In our weakly-inhomogeneous and\nweakly anisotropic case, there will be a small deviation\nfrom uniformity. Let us choose the coordinate system in\nsuch a way that the direction of the external field coin-\ncides with Z-axis, so that H={0,0,H}and, using the\nmagnitude of Imas a small parameter, represent this\nweakly inhomogeneous magnetization via Taylor-series\nexpansion\n/tildewiderM={0,0,M0}δ+/tildewiderM(1)+/tildewiderM(2)+...,(29)\nwhereM(i)contains the terms of the order iinIm.Due to the constraint M2(r) =M2\nS(r) there are only\ntwo independent components of M. Considering MX=\nM(1)\nX+M(2)\nXandMY=M(1)\nY+M(2)\nYindependent and\nsmall, the expansion of the constraint up to the second\norder allows us to express the remaining component of\nMin real space as\nMZ=M0+M0Im−(M(1)\nX)2+(M(1)\nY)2\n2M0.(30)\nRendering products as convolutions in Fourier space and\nintroducing the dimensionless magnetization vector m=\nM/M0we get\n/tildewidemZ=δ+/tildewideIm−FZ, (31)\nwhere\nFZ=/tildewidem(1)\nX⊗/tildewidem(1)\nX+/tildewidem(1)\nY⊗/tildewidem(1)\nY\n2. (32)\nBrown’sequations(ofwhich onlytwoareindependent)\nin Fourier space also contain convolutions. For example,\nthe first one of them reads\n/tildewideHeff\nZ⊗/tildewiderMY=/tildewideHeff\nY⊗/tildewiderMZ, (33)\nwhile the second independent one can be obtained by\nreplacing the subscript Y by X everywhere. After substi-\ntuting the expressionforthe effective field and the Taylor\nexpansion of the magnetization components in powers of\nIm, Brown’s equations become Taylor series themselves.\nBy collecting the terms of the same order in Im, we get\na chain of coupled equations for Taylor-expansion coeffi-\ncientsm(1)\nX/Y,m(2)\nX/Y, etc. For example, the equations in\nthe first order read\n(h+L2\n0q2+y2\nq)/tildewidem(1)\nY+xqyq/tildewidem(1)\nX=/tildewideAY−yqzq/tildewideIm,\n(h+L2\n0q2+x2\nq)/tildewidem(1)\nX+xqyq/tildewidem(1)\nY=/tildewideAX−xqzq/tildewideIm,\nwhereh=H/(γBM0) is the dimensionless field, /tildewideAX=\n/tildewidedX⊗/tildewidedZ⊗/tildewideIk,/tildewideAY=/tildewidedY⊗/tildewidedZ⊗/tildewideIk, and the dimensionless\ncomponents of the qdirection vector are {xq,yq,zq}=\nq/q. Quantities L0andqare still carrying dimensions,\nbut their product is dimensionless. These linear equa-\ntions are solved by\n/tildewidem(1)\nX=/tildewideAX(hq+y2\nq)−xq(/tildewideAYyq+hqzq/tildewideIm)\nhq(hq+x2q+y2q),(34)\n/tildewidem(1)\nY=/tildewideAY(hq+x2\nq)−yq(/tildewideAXxq+hqzq/tildewideIm)\nhq(hq+x2q+y2q),(35)\nwherehq=h+L2\n0q2. When both the exchange interac-\ntion and the anisotropy are neglected ( /tildewideAX= 0,/tildewideAY= 0,\nhq=h), these expressions coincide with the first-order\nsolution by Schl¨ omann.6Otherwise they coincide with\nthe first order solution,4which is extensively used at\npresent as a basis for magnetic SANS, except that now5\nwe have an explicit expression for /tildewideAXand/tildewideAYvia the\nmagnitude and the direction fields of the local uniaxial\nanisotropy.\nInthesecondorder(aswellashigherorders),theequa-\ntions are also linear and differ from the first-order ones\nonly by their right hand side, which now contains sums\nover the lower-order solutions:\n(h+L2\n0q2+y2\nq)/tildewidem(2)\nY+xqyq/tildewidem(2)\nX=FY+yqzqFZ,\n(h+L2\n0q2+x2\nq)/tildewidem(2)\nX+xqyq/tildewidem(2)\nY=FX+xqzqFZ.\nTheir solutions are also similar,\n/tildewidem(2)\nX=FX(hq+y2\nq)−xq(FYyq−hqzqFZ)\nhq(hq+x2q+y2q),(36)\n/tildewidem(2)\nY=FY(hq+x2\nq)−yq(FXxq−hqzqFZ)\nhq(hq+x2q+y2q).(37)\nThe special functions are\nFX=/tildewidedX⊗/tildewideIk⊗(2/tildewidedZ⊗/tildewideIm+/tildewidedX⊗/tildewidem(1)\nX+/tildewidedY⊗/tildewidem(1)\nY)−\nqL0xq/tildewideIe⊗qL0xq/tildewidem(1)\nX−qL0yq/tildewideIe⊗qL0yq/tildewidem(1)\nX−\nqL0zq/tildewideIe⊗qL0zq/tildewidem(1)\nX−/tildewidedZ⊗/tildewidedZ⊗/tildewideIk⊗/tildewidem(1)\nX−\n/tildewideIe⊗L2\n0q2/tildewidem(1)\nX−\n/tildewideIm⊗L2\n0q2/tildewidem(1)\nX+xq(zq/tildewideIm+xq/tildewidem(1)\nX+yq/tildewidem(1)\nY)+\n/tildewidem(1)\nX⊗L2\n0q2/tildewideIm+zq(zq/tildewideIm+xq/tildewidem(1)\nX+yq/tildewidem(1)\nY),\nand a similar expression is obtained for FYwith the X\nandYsubscripts as well as the functions xqandyqinter-\nchanged. Thefunction FZ=−/tildewidem(2)\nZisdefinedbyEq.(32).\nJust to give a simpler example: if the effects of in-\nhomogeneous anisotropy and exchange are neglected (by\nputting/tildewideIk= 0 and/tildewideIe= 0) and the expressions for /tildewidem(1)\nX\nand/tildewidem(1)\nYare substituted, the special functions are\nFX/Y/Z(q) =/summationdisplay\nq′/tildewideI(q′)/tildewideI(q−q′)\nuquq−q′fX/Y/Z(q′,q−q′)\nwith\nfX=−hxq′zq′uq−q′−\n(z2\nq′(h+L2\n0q′2)+uq′L2\n0q′2)xq−q′zq−q′,\nfY=−hyq′zq′uq−q′−\n(z2\nq′(h+L2\n0q′2)+uq′L2\n0q′2)yq−q′zq−q′,\nfZ=1\n2zq′zq−q′(xq′xq−q′+yq′yq−q′), (38)\nwhereuq=hq+x2\nq+y2\nq. Expression (38) for fZis\nvalid even if inhomogeneous exchange and anisotropyare\npresent. If we further neglect the effects of exchange (by\nputtingL0= 0), the solutions for /tildewiderm(2)coincide exactly\nwith those obtained by Schl¨ omann.6\nThese analytical calculations complete the second-\norder solution of the micromagnetic problem of a weaklyinhomogeneous magnetic material under the influence of\nan externally applied magnetic field. Let us now proceed\nwith the evaluation of the ensuing magnetic SANS cross\nsections.\nIV. MODEL FOR DEFECTS AND THEIR\nAVERAGING\nThe theory of magnetic SANS relates to experiment in\na similar way as the theory of the approach to magnetic\nsaturation, being a microscopic theory for a macroscopic\nmeasurement. The micromagnetic analysis of the previ-\noussectionallowsustoexpressthemagnetizationFourier\nimage at a specified magnetic field via those of the in-\nhomogeneous saturation magnetization, anisotropy, and\nexchange. The latter, however, are usually unknown for\na specific piece of magnetic material. In fact, it is realis-\ntic to assume that the inhomogeneity functions ( /tildewideIm,/tildewideIk,\nand/tildewideIe) arerandom processes, havingspecific realizations\nin each representative volume into which a macroscopic\nmagnet is subdivided. Then, the magnetic SANS cross\nsection,resultingfromthescatteringoftheneutronbeam\noff the macroscopic magnet comprising many representa-\ntive volumes, can be expressed as an average (both over\nthe random process realization and over the orientation,\nsince the defect realizationsin representativevolumesare\nalso randomly oriented).\nAlso, the inhomogeneities of different material param-\neters are usually not independent. The underlying phys-\nical reasons behind their formation (such as nanocrys-\ntallization) imply that the material consists of two or\nmore phases, each having a specific set of magnetic pa-\nrameters, separated by transition regions (such as grain\nboundaries). That is why later on we will assume that\nthe inhomogeneity functions are proportional to a uni-\nversal inhomogeneity function /tildewideI, describing the material\nmicrostructure: /tildewideIm=/tildewideI,/tildewideIk=κ/tildewideI,/tildewideIe=ǫ/tildewideI, whereκ,ǫ/lessorsimilar1.\nFor performing the averaging procedure, it is easiest\nto start with a specific model for the inhomogeneities.\nHere, we will consider inhomogeneities which are ran-\ndomly placed,\nI(r) =/summationdisplay\nnfn(r−pn), (39)\nwherepnare uniformly-distributed random vectors and\nthe summation is carriedout overall the inhomogeneities\nin the representative volume. The Fourier transform of\nthis function is\n/tildewideI(q) =/summationdisplay\nne−ıqpn/tildewidefn(q), (40)\nwhere/tildewidefn(q) is the Fourier transform of fn(r).\nWe further assume that the inhomogeneities have a\nGaussian profile,\nfn(r) =ane−1\n2r⊺Ar, (41)6\nwhereandenotes their (random) amplitude, the sub-\nscript⊺indicatestransposition,andtheboldcapitalsym-\nbol denotes a square matrix. Moreover, the matrix A\nis assumed to be positive definite and its elements have\nunits of inverse squared length (so that the argument\nof the exponential is dimensionless). Assuming that the\ninhomogeneities are much smaller than the representa-\ntive volume, we can extend the integration limits in the\nFourier transform up to infinity to get a simple represen-\ntation for/tildewidefn(q),\n/tildewidefn(q) =anv\nVe−1\n2q⊺A−1q, (42)\nwherev= (2π)3/2/√\nDis the volume of a single inhomo-\ngeneity,D= detAis the determinant of A, andA−1is\nits inverse.\nSince we are going to perform the directional averag-\ning over all the possible inhomogeneity orientations, it is\nsufficient, without loss of generality, to specify the pos-\nitive definite matrix Ain diagonal form. Specifically,\nto consider spheroidal inhomogeneities, we can write the\nmatrixAas\nA=\nτ/s20 0\n0τ/s20\n0 0 1 /(τs)2\n, (43)\nwheresis a real number with units of length specifying\nthe defect size, and τis a dimensionless quantity, speci-\nfying their shape. The case τ= 1 corresponds to spher-\nical inhomogeneities, τ≪1 to planar and τ→ ∞to\nneedle-like elongateddefects. The aboveparametrization\nis chosen in such a way that the volume v= (2π)3/2s3of\na single inhomogeneity is independent of τ.\nNow we can explicitly include a rotation matrix Ointo\nthe description of the inhomogeneities. For example, we\ncan use a matrix which is parametrized via the spherical\nanglesϕR∈[0,2π] andθR∈[0,π]:\nO=\nc2\nϕcθ+s2\nϕcϕsϕ(cθ−1)cϕsθ\ncϕsϕ(cθ−1)c2\nϕ+s2\nϕcθsϕsθ\n−cϕsθ −sϕsθcθ\n,(44)\nwherecϕ= cosϕR,sϕ= sinϕR,cθ= cosθR, andsθ=\nsinθR; it rotates the direction vector {0,0,1}towards\nthe unit-vector v={cϕsθ,sϕsθ,sθ}and, consequently,\nhas the property O−1v={0,0,1}.\nThequadratic-formmatrix Aintherotatedcoordinate\nsystem can be represented as OAO−1=OAO⊺, since for\nthe rotation matrix O−1=O⊺. Similarly, ( OAO⊺)−1=\nOA−1O⊺andq⊺pnintherotatedcoordinatesystemshould\nbe replaced by q⊺Opn. Thus, for the Fourier image of the\nrotated inhomogeneity function we have\n/tildewideI(q) =v\nV/tildewideJ(q)e−1\n2q⊺OA−1O⊺q, (45)\n/tildewideJ(q) =/summationdisplay\nnane−ıq⊺Opn. (46)\nBesides the averaging over the full range of the rotation\nanglesϕRandθR, the expressions containing /tildewideI(q) willneed to be averagedover the random defect positions pn.\nThe function /tildewideIdepends on these positions only via the\nfactorJ. In orderto learn how to compute the configura-\ntional averageof this function, consider its mean-squared\nvalue:\n/angbracketleftBig\n|/tildewideJ(q)|2/angbracketrightBig\n=/angbracketleftBigg/summationdisplay\nn/summationdisplay\nn′anan′eıq′⊺O(pn−pn′)/angbracketrightBigg\n=N/an}b∇acketle{ta2\nn/an}b∇acket∇i}ht,\nwhereNis the number of defects in the representative\nvolume. This is because the averagingof the exponent in\nthe last expression yields a Kronecker delta. The sum-\nmation can then be easily performed. Similarly, it is pos-\nsible to show that the various m-products of/tildewideJ, such as\nthe triple product |/tildewideJ(q)|2ReJ(q) or the quadruple prod-\nuct|/tildewideJ(q)|4, average over various defect configurations to\nN/an}b∇acketle{tam\nn/an}b∇acket∇i}ht, which is independent of q.\nFinally, we will assume that the direction of the local\nanisotropyaxisisindependent ofthe particleshape. This\nmeans that all the expressions for the SANS cross sec-\ntionswillneedtobeaveragedovertherandomanisotropy\ndirection as well.\nV. SECOND-ORDER MAGNETIC SANS CROSS\nSECTIONS\nAs we have seen in Sec. II, the magnetic SANS cross\nsections depend on the squared magnetization Fourier\ncomponents. Since the magnetization components start\nwith the first order in /tildewideI, the lowest order terms in the\ncross sections will be of second order. Let us compute\nthese terms.\nFor simplicity, we assume that the magnitude of the\nanisotropyinhomogeneitiesis relatedtothe magnitudeof\nthe saturation-magnetization inhomogeneities by a fac-\ntor/tildewideIk=κ/tildewideI, and also that the anisotropy direction is\nconstant inside each inclusion (but randomly oriented\nin different ones), so that /tildewidedX=δcosϕAsinθA,/tildewidedY=\nδsinϕAsinθA, and/tildewidedZ=δcosθA. Then, substituting the\nmagnetization components, Eqs. (34) and (35), into the\nexpressions for the parallel [Eq. (8)] and perpendicular\n[Eq. (7)] magnetic SANS cross sections, and averaging\nover the anisotropy directions,\n/an}b∇acketle{tF/an}b∇acket∇i}htA=1\n4π/integraldisplay2π\n0/integraldisplayπ\n0FsinθAdϕAdθA,(47)\nwe get\ndΣ/bardbl\nM\ndΩ= 8π3Vb2\nHM2\n0/an}b∇acketle{t/tildewideI2/an}b∇acket∇i}htκ2\n15h2q, (48)\ndΣ⊥\nM\ndΩ= 8π3Vb2\nHM2\n0/an}b∇acketle{t/tildewideI2/an}b∇acket∇i}ht/bracketleftbiggκ2cos2α\n15(hq+sin2α)2+κ2\n15h2q+\n(3+4hq−cos2α)sin22α\n8(hq+sin2α)2/bracketrightbigg\n, (49)7\n0 0.2 0.4 0.6 0.8 1\nτ/(1+τ)00.20.40.60.81Υ(µ,δ)µ=0\nµ=0.1\nµ=0.2\nµ=0.3\nFIG.1. Dependenceofthemean-squaredinhomogeneityfunc-\ntion/angbracketleft/tildewideI2/angbracketright=N/angbracketlefta2\nn/angbracketright(v/V)2Υ(qs,τ) on the inclusion shape τfor\ndifferent values of µ=qsin the range from 0 to 2 in equal\nsteps of 0 .1./angbracketleft/tildewideI2/angbracketrighthas an extremum at τ= 1, corresponding\nto spherical defects. The left side of the plot corresponds t o\nplanar defects, while the right side to needle-like ones.\nwhere we have introduced an angle in the plane of\nthe detector ( qX= 0) for the perpendicular cross sec-\ntionqZ=qcosα,qY=qsinαand angular brackets\nstand for the directional averaging over the representa-\ntive volume orientations ( ϕR,θR). For Gaussian defects,\nEqs. (41) −(43), this averaging can be performed analyt-\nically, yielding /an}b∇acketle{t/tildewideI2/an}b∇acket∇i}ht=N/an}b∇acketle{ta2\nn/an}b∇acket∇i}ht(v/V)2Υ(qs,τ) with\nΥ(µ,τ) =\n\ne−µ2\nτ√π\n2µ/radicalBig\nτ\n1−τ3Erfi(µ/radicalBig\n1−τ3\nτ)τ <1\ne−µ2τ= 1\ne−µ2\nτ√π\n2µ/radicalBig\nτ\nτ3−1Erf(µ/radicalBig\nτ3−1\nτ)τ >1,\n(50)\nwhere Erf( z) = (2/√π)/integraltextz\n0e−t2dtdenotes the error func-\ntion, andErfi( z) = Erf(ız)/ıisitsimaginarycounterpart.\nDependence of Υ( µ,τ) on particle shape at different val-\nues ofµ=qsis plotted in Fig. 1.\nThe parallelcrosssection in the secondorder, Eq. (48),\nis fully isotropic in the detector plane ( qZ= 0), while the\nperpendicular one, Eq. (49), besides the isotropic term\nκ2\n15h2q, contains two terms, which depend on α. One of\nthese terms is due to the effect of magnetic anisotropy,\nwhile the other is of purely magnetostatic origin. They\nare plotted in Fig. 2.\nRemember that hq=h+L2\n0q2, which means that hq\ntakes on values starting with the external field h >0\nand up to some larger limiting value, dictated by the pa-\nrameters of the SANS detector. There are two distinct\nregimes, when hqis small (small hand small qwith re-\nspect to the inverse exchange length squared 1 /L0) and\nwhenhqis large (either when his large, or when qis\nlarge for small h). In the former regime, the angular00.511.5cos2(α)/(hq+ sin2(α))2hq= 0\nhq= 0.1\nhq=2hq= 0.2a)\n0 0.5 1 1.5 2\nα/π00.511.5(3 + 4hq- cos(2α)sin2(2α)/(8(hq+ sin2(α))2)hq=0\nhq=0.1\nhq=0.2\nhq=2b)\nFIG. 2. Angular dependence of the anisotropic terms in the\nperpendicular magnetic SANScross section at different valu es\nofhq. (a) displays the first and (b) the third term in Eq. (49).\ndependence of both anisotropic terms displays a similar\ntwo-fold angular dependence with sharp maxima along\nα= 0,π. Together with the isotropic halo, described by\nthe second term in Eq. (49), this gives rise to the recently\nobserved12UFO-like shape of the SANS image,13shown\nin Fig. 3.\nAt large hq, the angular dependence of the first and\nthe third term in Eq. (49) is different. The former\nis two-fold, while the latter tends asymptotically to\n(1−cos4α)/(4hq), which has fourfold symmetry. This\nopens the possibility of separating the anisotropy and\nthe magnetostatic contributions by performing a Fourier\nanalysis of the cross sections at large hq(either at mod-\nerately large hor at the outskirts of the cross section,\nmeasured at small h).\nRegarding the asymptotic q-dependence, it is readily\nverifiedthat both magneticSANS crosssections vary(for\nsphericalinclusionswith τ= 1) as∼e−s2q2(sq)−4, where\nsdenotes the defect size. Other assumptions about the\nprofileoftheinclusions, e.g., asharpinterface, mayresult\nin different asymptotic dependencies.\nVI. HIGH-ORDER TERMS IN MAGNETIC\nSANS CROSS SECTIONS\nThe structure of the second-order solutions for the\nmagnetization components, Eqs. (36) and (37), is similar\nto that of the first-order ones, but now magnetostatic ef-8\n-0.3-0.2-0.1 0 0.1 0.2 0.3\n-0.3 -0.2 -0.1  0  0.1  0.2  0.3qY\nqZ\nFIG. 3. UFO-like magnetic SANScross section shape at small\nh= 0.01 andqin a sample with spherical ( τ= 1) Gaussian\ninclusions. The other parameters for this plot are: κ= 1,\ns= 1,L0= 1. The outer contour corresponds to a value of\n15, which increases inwards in steps of 100. There is a very\nsharp maximum at the center.\nfects also contribute to FXandFY. These functions play\nthe same role in the second-order solutions as the func-\ntionsAXandAYdo in the first-order ones, except that\nthey have an additional dependence on the magnitude\nand the direction of the q-vector.\nThemainproblemwiththis(andanyother)high-order\ncontribution to physical properties is that it is usually\nvery small and, if lower-order effects are present at the\nsame time, is completely masked by them. On the other\nhand, analysis of the higher-order effects allows one to\nextract independently additional information about the\nsystem, which the lower-order effects do not provide.\nTherefore, it is desirable to establish the experimental\nconditions when the lower-order effects are canceled out\nand only the higher-order terms contribute, thus, en-\nabling their analysis.\nIn the present problem this can be achieved by con-\nsidering the following combination of SANS cross-section\nvalues:\n∆Σ⊥\nM=dΣ⊥\nM\ndΩ/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nα=0−2dΣ⊥\nM\ndΩ/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nα=π/2.(51)\nAs can be readily checked from Eq. (49), this combina-\ntion is exactly zero in second order. This is true both\nin the presence of anisotropy inhomogeneities κ >0\nandexchange-constantinhomogeneitieswithanarbitrary\n(not only Gaussian) spatial profile, since /an}b∇acketle{t/tildewideI2/an}b∇acket∇i}htalways\ndepends only on the magnitude of qdue to the direc-\ntional averaging. It is also independent of the assump-\ntion that the anisotropy inhomogeneities are related to\nthe saturation-magnetization inhomogeneities by a fac-\ntor of/tildewideIk=κ/tildewideI. In other words, the cancellation of the\nsecond-orderterms in ∆Σ⊥\nMis a universal property of the00.010.020.030.040.050.060.070.080.09gAh=0.1\nh=0.2\nh=0.3λ=0.7\n0 0.5 1 1.5 2 2.5 3\nµ00.010.020.030.040.050.060.07gAh=0.4λ=0.2\nλ=0.4\nλ=0.6\nλ=0.8\nFIG. 4. The functions gA(µ,h,λ) (solid lines) and their ap-\nproximation by decaying exponentials (dotted lines) for di f-\nferent values of hat fixed λ(upper plot) and for different\nvalues of λat fixedh(lower plot).\nSANS cross sections, which is independent of the specific\nmodel.\nIn next significant order (which is the third one), the\ncontributions of FXandFYare also canceled and ∆Σ⊥\nM\ntakes on an especially simple form,\n∆Σ⊥\nM= 32π3V b2\nHM2\n0/an}b∇acketle{tFZ/tildewideI/an}b∇acket∇i}ht/vextendsingle/vextendsingle/vextendsingle\nqZ=0,(52)\nwhereq=qY,FZis defined by Eq. (32), and the angular\nbracketsdenote a triple (configurational, directional, and\nanisotropy direction) average.\nTo make the following expressions simpler, let us as-\nsume a spherical particle shape ( τ= 1), which obvi-\nates the directional averaging, and, again, assume that\n/tildewideIk=κ/tildewideI. Then, averaging is easy to perform,\n∆Σ⊥\nM= 32π3b2\nHM2\n0ρv2/an}b∇acketle{ta3\nn/an}b∇acket∇i}ht[κ2gA(qs)+gMS(qs)],(53)\nwhereρ=N/Vis the defect density. The dimensionless\nfunctions gA(µ) andgMS(µ), which also depend on hand\nλ=L0/s, are described in the Appendix and plotted in\nFigs. 4 and 5. The remaining integrals in these functions\nare due to the convolution embedded in the definition of\nthe function FZ.\nThe dependence of the third-order perpendicular mag-\nnetic difference SANS cross section, Eq. (53), on µfor\nthe considered spherical Gaussian defect model is mostly9\n00.0050.010.0150.02gMSh=0.1\nh=0.2\nh=0.3λ=0.7\n0 0.5 1 1.5 2 2.5 3\nµ00.0050.010.0150.020.025gMSh=0.4λ=0.2\nλ=0.4\nλ=0.6\nλ=0.8\nFIG. 5. The functions gMS(µ,h,λ). The curves correspond to\nthe same values of parameters as those in Fig. 4.\na featureless decaying exponential. Only for small val-\nues of the externally applied magnetic field hdoes this\ndependence become sharper at small values of µ. In the\ncase of a very small amplitude of the anisotropy inhomo-\ngeneities κ, such that the cross section is dominated by\nthe function gMS, it is possible to have negative values of\n∆Σ⊥\nMforµ∼=1.5. This does not, of course, imply that\nthe total cross section is negative.\nVII. SUMMARY AND CONCLUSIONS\nWe have presented an analytical solution of the micro-\nmagnetic problem of a weakly inhomogeneous magnetic\nmaterial in an applied magnetic field up to the second or-\nder in the amplitude of inhomogeneities. On the basis of\nthis solution, we have computed the second-order mag-\nnetic SANS cross sections, which, at sufficiently small\nvalues of the applied magnetic field h, inevitably display\na prominent UFO-like shape. It is shown that under very\ngeneral assumptions in a magnet with arbitrary small\ninhomogeneities of exchange, anisotropy, and saturation\nmagnetization, a specific combination of the perpendicu-\nlar SANS cross-section values, Eq. (51), is exactly zero in\nthe second order. The next significant third-order con-\ntribution to this combination is also computed here and\nis non-zero. Detection and analysis of its q-dependenceshould provide a deeper insight into the magnet’s mi-\ncrostructure. So far there is no experimental confirma-\ntion of this newly predicted effect.\nACKNOWLEDGMENTS\nFinancial support by the National Research Fund of\nLuxembourg(Project No. FNR/A09/01)is gratefully ac-\nknowledged.\nAppendix A: The functions gAandgMS\nThe functions gAandgMSappear as the result of com-\nputing the average /an}b∇acketle{tFZ/tildewideI/an}b∇acket∇i}htover random defect positions,\nanisotropy direction, and the orientation of the repre-\nsentative volume (if the inclusions are not of spherical\nshape) with FZdefined by Eq. (32) and /tildewideIby Eq. (40).\nFZ, however, contains convolutions of the first-order so-\nlutions for the magnetization vector field, Eqs. (34) and\n(35), which, in turn, are proportional to /tildewideI. For comput-\ning these convolutions, it is easiest to approximate the\ntriple summation by a triple integration, according to\n/summationdisplay\nq...=V\n(2π)3/integraldisplay/integraldisplay/integraldisplay\n...d3q, (A1)\nand integrate over the whole qspace in a spherical co-\nordinate system. Nevertheless, even in the simplest case\nof spherical defects (which obviates the directional aver-\nages)the full expressionsaretoo complex tobe presented\nhere; they are given in the attached Mathematica file14\nand plotted in Figs. 4 and 5 (solid lines).\nA relatively simple formula can be written for the val-\nues ofgAandgMSatµ= 0, which reads\ng|µ=0=∞/integraldisplay\n√1+he−(p2−1−h)/λ2u(p)/radicalbig\np2−1−h\n2√\n2πλ3dp,(A2)\nwhere the functions u(p) are given by\nuA=p(3p2−1)\n(p2−1)2+coth−1p\n15p2, (A3)\nuMS=−3p+(3p2−1)coth−1p. (A4)\nAlso, a simple closed-form asymptotic expression for gA\nat largehcan be obtained,\ngA(h≫1) =e−3µ2/4\n30√\n2h2. (A5)10\n∗metlov@fti.dn.ua\n1A. Michels, Journal of Physics: Condensed Matter 26,\n383201 (2014)\n2H. Kronm¨ uller, A. Seeger, and M. Wilkens,\nZeitschrift f¨ ur Physik 171, 291 (1963), ISSN 0044-3328,\nhttp://dx.doi.org/10.1007/BF01379357\n3W. Brown, Micromagnetics , Interscience tracts on\nphysics and astronomy (Interscience Publishers, 1963)\nhttp://books.google.com.ua/books?id=v9rvAAAAMAAJ\n4D. Honecker and A. Michels, Phys. Rev. B 87, 224426\n(2013)\n5H. Kronm¨ uller and M. F¨ ahnle, Micromagnetism\nand the Microstructure of Ferromagnetic Solids ,\nCambridge studies in magnetism (Cambridge\nUniversity Press, 2003) ISBN 9780521331357,\nhttp://books.google.com.ua/books?id=h6nKtwcYyNEC\n6E. Schl¨ omann, J. Appl. Phys. 42, 5798 (Dec. 1971)\n7L. N´ eel, Compt. Rend. 220, 738 (1945)8A. Michels and J. Weissm¨ uller, Reports\non Progress in Physics 71, 066501 (2008),\nhttp://stacks.iop.org/0034-4885/71/i=6/a=066501\n9J. W. F. Brown, Micromagnetics (New York: Wiley, 1963)\n10A. Aharoni, Introduction to the theory of ferromagnetism\n(Oxford University Press, Oxford, 1996) ISBN 0198517912\n11C. Herring and C. Kittel, Phys. Rev. 81, 869 (1951)\n12´E. P´ erigo, E. P. Gilbert, G. C. Hadjipanayis, K. L. Metlov,\nand A. Michels, “Experimental observation of magnetic\npoles inside the bulk magnets via q/negationslash= 0 Fourier modes\nof magnetostatic field,” (2014), accepted to New Journal\nof Physics\n13J. Weissm¨ uller, R. McMichael, A. Michels, and R. Shull,\nJ. Research NIST 104, 261 (1999)\n14See supplementary Mathematica file at [URL will be in-\nserted by APS]."    },    {        "title": "1501.00732v1.Effect_of_the_double_counting_functional_on_the_electronic_and_magnetic_properties_of_half_metallic_magnets_using_the_GGA_U_method.pdf",        "content": "arXiv:1501.00732v1  [cond-mat.mtrl-sci]  4 Jan 2015submitted to Physical Review B\nEffect of the double-counting functional on the electronic a nd magnetic properties of\nhalf-metallic magnets using the GGA+U method\nChristos Tsirogiannis and Iosif Galanakis∗\nDepartment of Materials Science, School of Natural Science s, University of Paras, GR-26504 Patra, Greece\n(Dated: April 12, 2018)\nMethods based on the combination of the usual density functi onal theory (DFT) codes with\nthe Hubbard models are widely used to investigate the proper ties of strongly correlated materi-\nals. Using first-principle calculations we study the electr onic and magnetic properties of 20 half-\nmetallic magnets performing self-consistent GGA+U calcul ations using both the atomic-limit (AL)\nand around-mean-field (AMF) functionals for the double coun ting term, used to subtract the corre-\nlation part from the DFT total energy, and compare these resu lts to the usual generalized-gradient-\napproximation (GGA) calculations. Overall the use of AMF pr oduces results similar to the GGA\ncalculations. On the other hand the effect of AL is diversified depending on the studied material. In\ngeneral the AL functional produces a stronger tendency towa rds magnetism leading in some cases\nto unphysical electronic and magnetic properties. Thus the choice of the adequate double-counting\nfunctional is crucial for the results obtained using the GGA +U method.\nPACS numbers: 75.50.Cc, 71.20.Lp, 71.15.Mb\nI. INTRODUCTION\nThe rapid expansion of the field of spintronics and\nmagneto-electronics brought magnetic materials at the\nnanoscale to the center of attention of modern electron-\nics. The spin ofthe electron offersan additionaldegreeof\nfreedominelectronicdeviceswithrespecttoconventional\nelectronicsbasedonsemiconductors.1Thedesignofmag-\nneticnanomaterialswithnovelpropertiesoffersnewfunc-\ntionalities to future devices, and to this respect ab-initio\n(also known as first-principles) studies of the electronic\nstructure within density functional theory (DFT) play\na crucial role allowing the modelling of the properties\nof several materials prior to their experimental growth.\nAmong the most studied magnetic materials are the\nso-called half-metallic (HM) magnets,2,3which present\nmetallic behavior for the majority-spin electronic band\nstructure and semiconducting for the minority-spin elec-\ntronic band structure. The ferromagnetic semi-Heusler\ncompound NiMnSb was the first material for which the\nHM character was predicted and described,4and since\nthen several HM compounds have been discovered.5–7\nThe implementation of half-metallic magnets in devices\nis an active field of research (see Ref. 8 for a review of\nthe literature).\nDFT-based ab-initio electronic structure calcula-\ntions using either the local-spin-density approxima-\ntion (LSDA)9or the generalized-gradient-approximation\n(GGA)10for the exchange-correlation functional are\nquite successful for magnetic materials from weak to in-\ntermediate electronic correlations, but fail for systems\nwith strong electronic correlations. There are two com-\nmon ways to include correlations in first-principles elec-\ntronic structure calculations. The first one is the so-\ncalled LDA+ Uscheme, in which the local–(spin)-density\napproximation (L(S)DA) of DFT is augmented by an\non-site Coulomb repulsion term and an exchange term\nwith the Hubbard Uand Hund exchange Jparame-ters, respectively.11,12Such a scheme has been applied\nfor example to Co 2FeSi, showing that correlations re-\nstore the HM character of the compound,13and to\nNiMnSb.14When the GGA functional is used instead\nof the L(S)DA the method is usually referred to as\nGGA+U scheme. A more elaborate modern computa-\ntional scheme, which combines many-body model Hamil-\ntonian methods with DFT, is the so-called LDA+DMFT\nmethod, where DMFT stands for Dynamical Mean-Field\nTheory.15,16LDA+DMFT has been applied to several\nHM magnetic systems like Co 2MnSi,17NiMnSb,18–20\nFeMnSb,21Mn2VAl,22VAs23and CrAs.24,25\nIn the case of both LSDA+U (GGA+U) and\nLDA+DMFT schemes, the addition of the Hubbard U\ninteraction introduces the need for a double-counting\ncorrection term in the energy functional to account for\nthe fact that the Coulomb energy between the corre-\nlated states is already included in the LSDA (GGA)\nfunctional. Several double-counting schemes have been\nproposed in literature,26–28and in all proposed schemes\nan averaged energy for the occupation of a selected ref-\nerence state is subtracted. Among the proposed func-\ntionals for the double-counting term, two are most com-\nmonly used: the so-called around-mean-field (AMF)\nfunctional and the atomic-limit (AL) functional; the lat-\nter is also referred to in literature as the fully local-\nized limit (FLL) functional. The performance of these\ntwo functionals has attracted little attention in litera-\nture. In 2009 Ylvisaker and collaborators presented an\nextensive study on the effect of the two functionals when\nperforming self-consistent LSDA+U calculations for sev-\neral magnetic materials.29They have shown that the use\nof the LSDA+U interaction term usually enhances spin\nmagnetic moments, but the AMF double-counting term\ngivesmagneticstatesasignificantlylargerenergypenalty\nthan does the AL(FLL) functional and thus AL gives a\nstronger tendency to magnetism than AMF.292\nII. MOTIVATION AND COMPUTATIONAL\nMETHOD\nAs mentioned above, ab-initio electronic structure\ncalculations based on the mixed LSDA+U/GGA+U\nschemesas wellas LDA+DMFT arewidely used to study\nthe influence of electronic correlations on the electronic\nand magnetic properties of half-metallic magnets. Thus\nthe study of the influence of the double-counting term on\nthe calculated properties for these materials is extremely\nimportant with respect to their potential use in realistic\ndevices. The aim of the present study is to explore the\neffect of both AL and AMF functionals when perform-\ning GGA+U calculations with respect to usual electronic\nband structure calculations using the GGA functional\nfor a wide range of half-metallic magnets (the reader is\nreferred to Ref. 29 for an extended discussion on the\nexact formulation of the two functionals). To achieve\nour goal we have employed the full-potential nonorthog-\nonal local-orbital minimum-basis band structure scheme\n(FPLO).30For the GGA calculations we have used the\nPerdew-Burke-Ernzerhof parametrization.10In the case\nof the GGA+U calculations the on-site Coulomb inter-\nactions for the correlated dorporbitals are introduced\nviatheF0,F2,F4andF6Slaterparameters.31Forallcal-\nculations a dense 20 ×20×20 grid in the reciprocal space\nhas been used to carry out the integrals and both the\ncharge density (up to 10−6in arbitrary units) and the\ntotal energy (up to 10−8Hartree) have been converged\nin each case.\nIn order to cover a wide range of half-metallic mag-\nnets in a coherent way, we have used in our calculations\nthe ab-initio determined Coulomb effective interaction\nparameters (Hubbard Uand Hund exchange Jbetween\nlocalized dorpelectrons) calculated in Ref. 32 using the\nconstrained Random Phase Approximation (cRPA)33–36\nfor 20 half-metallic magnets. We should note that (i)\nthe determination of these parameters from experimen-\ntal data is a difficult task, and (ii) the constrained local-\ndensity approximation (cLDA), although is the most\npopulartheoreticalapproach,37–40itiswellknowntogive\nunreasonably large Hubbard Uvalues for the late tran-\nsition metal atoms due to difficulties in compensating\nfor the self-screening error of the localized electrons,34\nand thus cRPA which does not suffer from these dif-\nficulties, although numerically much more demanding\nthan cLDA, offers an efficient way to calculate the effec-\ntive Coulomb interaction parameters in solids.33,36We\npresent results for all 20 half-metallic magnets studied\nin Ref. 32 which include representatives of the (i) semi-\nHeusler compounds like NiMnSb, (ii) ferrimagnetic full-\nHeuslercompoundslikeMn 2VAl, (iii)inversefull-Heusler\ncompounds like Cr 2CoGa, (iv) usual L2 1-type ferromag-\nnetic full-Heusler compounds, (v) transition-metal pnic-\ntides like CrAs, and finally (vi) sp-electron (also called\nd0) ferromagnets like CaN. We have used the lattice pa-\nrameters presented in Table 1 of Ref. 32. The Slater\nparameters entering the FPLO method are connected tothe Hubbard parameter ULDA+Uand to the Hund ex-\nchangeJpresented in Table II of Ref. 32 for the corre-\nlatedp-states though the relations\nF0=ULDA+U, F2= 5×J, F4=F6= 0,(1)\nand for the correlated d-states\nF0=ULDA+U,F2+F4\n14=J,F4\nF2= 0.625, F6= 0.(2)\nWe should note here that ULDA+Uis an effective param-\neter depending both on the on-site intra-orbitalCoulomb\nrepulsion between electrons occupying the same orbital\nandon-siteinter-orbitalCoulombrepulsionbetween elec-\ntrons occupying orbitals of the same ℓcharacter but dif-\nferentmℓvalue. Thus, our study covers a wide range\nof half-metallic magnets allowing for a deeper under-\nstanding of the behavior of the AL and AMF double-\ncountingfunctionals inthe GGA+Ucalculatedelectronic\nand magnetic properties of different HM magnetic sys-\ntems.\nIII. RESULTS AND DISCUSSION\nA. Binary Compounds\nWe will start the presentation of our results from\nthe binary compounds. There are two families of half-\nmetallic binary compounds. The first includes the\nso-called sp-electron ferromagnets (also known as d0-\nferromagnets).41,42These compounds adopt the rocksalt\ncubic structure and have no transition-metal atoms in\ntheir chemical formula. We consider the nitrides and the\ncarbides (CaN, SrN, SrC, and BaC) since they have the\nlargest calculated Curie temperatures among the stud-\niedsp-electron ferromagnets.43–49Their total spin mag-\nnetic moment in units of µBequals 8 −Zt, where Z tis\nthe total number of valence electrons in the unit cell;\nthis behavior is known as Slater-Pauling (SP).50,51A de-\ntailed discussion on the origin of this rule and its con-\nnection to the half-metallicity can be found in Ref. 42.\nThe usual GGA calculations produced for all four stud-\nied compounds a half-metallic state with total spin mag-\nnetic moments of 1 µBfor the nitrides and 2 µBfor the\ncarbides. The results are gathered in Table I. The spin\nmomentiscarriedmainlybytheNandCatoms. Ourcal-\nculated GGA results aresimilar to the GGA ones derived\nwith the full-potential linearized augmented plane-wave\n(FLAPW) method as implemented in the FLEUR52code\nin Ref. 32. The use of the AMF within the GGA+U\nscheme leaves intact both the calculated spin magnetic\nmoments and density of states (DOS) with respect to\nGGA calculations (we do not present the DOS since they\nare similar to the ones presented in literature). On the\ncontrary the use of the AL functional has a tremendous\neffect on the calculated results. It produces an unreason-\nable and unphysical charge transfer from the Ca(Sr,Ba)3\nTABLE I: Atom-resolved and total spin magnetic moment\nper formula unit for the XY binary compounds. Results have\nbeen obtained within the FPLO method30using the GGA\nfunctional for the exchange interaction potential10and the\nGGA+U scheme employing both the atomic-limit (AL - also\nknown as fully-localized-limit FLL) and the around-mean-\nfield (AMF) functionals for the double counting term. Val-\nues for the on-site Coulomb and exchange parameters are the\nab-initio determined ones within the constrained Random-\nPhase-Approximation (cRPA) in Ref. 32. Lattice constants\nare the ones presented in Table 1 in the later reference. Note\nthat for the compounds which do not contain transition metal\natoms (known as d0-ferromagnets) GGA+U within the AL\nfunctional gives unrealistic results.\nComp. Functional mXmYmtotal\nCaN GGA -0.065 1.065 1.000\nGGA+U (AL) 11.836 -4.836 7.000\nGGA+U (AMF) -0.065 1.065 1.000\nSrN GGA -0.072 1.072 0.999\nGGA+U (AL) 16.363 -9.362 7.000\nGGA+U (AMF) -0.072 1.072 0.999\nSrC GGA -0.004 2.004 1.999\nGGA+U (AL) 15.578 -9.578 6.001\nGGA+U (AMF) -0.004 2.004 1.999\nBaC GGA 0.057 1.943 2.000\nGGA+U (AL) 3.261 0.378 3.999\nGGA+U (AMF) 0.057 1.943 2.000\nVAs GGA 2.427 -0.427 2.000\nGGA+U (AL) 2.415 -0.415 2.000\nGGA+U (AMF) 2.151 -0.151 2.000\nCrAs GGA 3.614 -0.614 3.000\nGGA+U (AL) 3.880 -0.880 3.000\nGGA+U (AMF) 3.541 -0.541 3.000\nMnAs GGA 4.173 -0.311 3.862\nGGA+U (AL) 4.476 -0.476 3.999\nGGA+U (AMF) 3.979 -0.326 3.652\natoms to the N(C) atoms resulting to huge values of the\natom-resolved spin moments. This state is obviously an\nartifact of the method. We cannot explain the origin of\nthis behavior but starting form various configurations all\ncalculationsinvolving the AL functional convergedto the\nsame results and thus the breakdown of the AL should\nbe attributed to its characteristics.\nThe second family of binary compounds under study\nare the binary VAs, CrAs, and MnAs transition metal\npnictides. The first observation of such a compounds\nbeing half-metal was made in 2000 when Akinaga\nand his collaborators managed to grow multilayers of\nCrAs/GaAs.53CrAs was found to adopt the zincblende\nstructure of GaAs and was predicted to be a half-metal\nwith a total spin magnetic moment of 3 µBin agreement\nwith experiments.53Several studies followed this initial\ndiscovery, and electronic structure calculations have con-\nfirmed that also similar binary XY compounds, where X\nis an early transition-metal atom and Y an spelement,\nshould be half-metals and the total spin magnetic mo-\nment follows a SP rule similar to d0-ferromagnets being-4,5 -3 -1,5 0 1,5 3\nEnergy-EF (eV)-10-50510DOS (states/eV/spin)GGA\nGGA+U (AMF)-10-50510\nGGA\nGGA+U (AL)\nCrAs\nFIG. 1: (color online) Total density of states (DOS) as a\nfunction of the energy for the CrAs compound within the\nGGA+U method using both the atomic-limit (AL) and the\naround-mean-field (AMF) functionals for the double-counti ng\nterm. GGA+U results are compared to the GGA calculated\nDOS. The zero in the energy axis has been set to the Fermi\nlevel. Positive(negative) values of the DOS correspond to t he\nmajority(minority)-spin electrons.\nnow equal to Zt−8.54,55\nIn Table I we gathered all the calculated spin mag-\nnetic moments. GGA gives a half-metallic state for VAs\nand CrAs, while for MnAs the Fermi level is slightly\nabove the minority-spin energy gap and the total spin\nmagnetic moment slightly smaller than the ideal value\nof 4µBfor half-metallicity to occur. These results have\nbeen largely discussed in literature.54,55For both VAs\nand CrAs, GGA+U self-consistent calculations yield a\nhalf-metallic state within both AL and AMF function-\nals with the same total spin magnetic moment but with\nsubstantial variations of the atom-resolvedspin magnetic\nmoments. For MnAs the use of AL functional leads to a\nhalf-metallic state contrary to AMF for which the Fermi\nlevel is above the minority-spin gap. Overall AL leads to\nlarger absolute values of the atomic spin moments with\nrespect to GGA while AMF leads to smaller values. This\nbehavior of the atomic spin magnetic moments confirms\nthe conclusion in Ref. 29 that AMF gives the magnetic\nstate a large energy penalty with respect to AL.\nSince DOS present similar trends between the three\ntransition metal binary compounds, we present in Fig. 1\nthe calculated DOS per formula unit for CrAs. In the\nupper panel we compare the GGA+U calculated DOS\nwithin the AL functional to the usual GGA calculated\nDOS, and in the lower panel we present a similar graph\nfor the AMF case. In the presented energy Cr DOS dom-4\ninates. GGA produces a large minority-spin gap with a\nlarge exchange splitting between the occupied majority-\nspin bands and the unoccupied minority-spin bands and\nthus strong tendency to magnetism manifested also by\nthe large ( ∼3.6µB) Cr spin moment. The use of the AL\ndouble-counting functional in the GGA+U calculations\nlead to an almost rigid shift of the minority spin DOS\ntowards higher energies, while in the majority-spin DOS\nonly the double-degenerate egstates at about -1.5 eV\nmove lower in energy (see Ref. 54 for a discussion of the\ncharacterofthebands). InthecaseofAMFthemajority-\nspinbandstructureshowsasimilarbehaviorwith respect\nto the GGA results as the AL case. But in the minority-\nspin band structure the tendency is the opposite now.\nSince AMF does not favor magnetism as strongly as AL,\nthe minority-spin band structure now presents an almost\nrigid shift towards lower energy values. These finding\nalso explain the behavior of the MnAs compound. In\nthe case of AL the minority-spin band structure moves\ntowards higher energy values and the Fermi level now\nmoves within the gap and half-metallicity appears.\nB. Heusler compounds\nHeusler compounds are a huge family of intermetallic\ncompounds presenting various types of electronic and\nmagnetic behaviors.56,57Several among them are half-\nmetallic ferromagnets/ferrimagnets/antiferromagnets\nand are of particular interest due to their very high\nCurie temperatures, which usually exceed 1000 K, mak-\ning them ideal for applications.8There are four main\nfamilies of Heusler compounds: (i) the semi-Heuslers\nalso known as half-Heuslers like NiMnSb which have the\nchemical type XYZ with X and Y being transition metal\natoms, (ii) the usual full Heuslers like Co 2MnSi with the\nchemical type X 2YZ wherethe valence ofXis largerthan\nthe valence of Y and the two X atoms are equivalent,\n(iii) the quaternary Heuslers like (CoFe)MnSi which\npresent similar properties with the full-Heuslers, and\nfinally (iv) the so-called inverse-Heuslers, like Cr 2CoGa\nwhich have also the chemical type X 2YZ but now the\nvalence of X is smaller than the valence of Y and due to\nthe change of the sequence of atoms in the unit cell the\ntwo X atoms are no more equivalent.56,57We present\nresults for all families of compounds with the exception\nof quaternary-Heuslers which present similar behavior to\nthe full-Heuslers and for which no Hubbard parameters\nhave been derived in Ref. 32.\n1. Semi-Heuslers\nThe first family of Heusler compounds for which we\nwill present results are the semi-Heuslers. The first com-\npound that was predicted to be a half-metal was actu-\nally a semi-Heusler, NiMnSb.4Their total spin magnetic\nmoment follows also a SP rule being Zt-18 (for an ex--6-3 0 3\nEnergy-EF (eV)-4-2024DOS (states/eV/spin)-4-2024\nGGA\nGGA+U (AL)\n-6-3 0 3GGA\nGGA+U (AMF)NiMnSbNi Ni\nMn Mn\nFIG. 2: (color online) Ni and Mn atom-resolved DOS in\nNiMnSb. Details as in Fig. 1.\ntended discussion see Ref. 58). In Table II we have gath-\nered our calculated spin magnetic for all studied cases\nandforthreecompoundsFeMnSb, CoMnSbandNiMnSb\n(note that for FeMnSb we were not able to converge the\nGGA+U calculations using the AMF functional). As we\nmove from one compound to the other, the total num-\nber of valence electrons increases by one and so does the\nGGA calculated total spin magnetic moment. Mn atoms\nin all case posses a large value of spin magnetic moment\nwhich starts from ∼3.4µBin FeMnSb and exceeds 4 µB\nin NiMnSb. As we increase the total number of valence\nelectrons the spin magnetic of the X atoms also increases\nbeing∼-1.3µBfor Fe, -0.34 µBfor Co and 0.14 µBfor\nNi in the corresponding compounds. The GGA calcu-\nlated DOS, presented in Fig. 2 for NiMnSb, has been\nstudied in detail in literature and it is mainly character-\nized by the largeexchangesplitting between the occupied\nmajority-spin and the unoccupied minority-spin d-states\nat the Mn site which together with the very small weight\nof the occupied minority-spin states are responsible for\nthe large Mn spin magnetic moments. This feature is\ncommon for all three studied compounds and has been\nalready observed in literature.58–60\nThe self-consistent GGA+U calculations using the\nAMF functional for the CoMnSb and NiMnSb com-\npounds produced a similar picture to the GGA calcu-\nlations. The total spin magnetic moment, as shown in\nTableII remainsidenticaltotheGGAcaseandtheatom-\nresolved spin magnetic moments only scarcely changed.\nThis is also reflected on the Ni and Mn resolved DOS for\nNiMnSb in Fig. 2 where the GGA+U within AMF cal-\nculated DOS is almost identical to the GGA calculated\nDOS. The effect of the use of the AL functional is more5\nTABLE II: Similar to Table I for the semi-Heusler compounds\ncrystallizing in the C1 blattice structure having the XYZ\nchemical formula.\nComp. Functional mXmYmZmtotal\nFeMnSb GGA -1.279 3.374 -0.095 2.000\nGGA+U(AL) -2.274 4.559 0.042 2.327\nCoMnSb GGA -0.340 3.568 -0.227 3.000\nGGA+U (AL) -1.264 4.520 -0.186 3.068\nGGA+U (AMF) -0.358 3.535 -0.177 3.000\nNiMnSb GGA 0.143 4.031 -0.174 3.999\nGGA+U (AL) -0.087 4.553 -0.301 4.164\nGGA+U (AMF) 0.144 4.026 -0.171 3.999\ndrastic. As shown in Fig. 2 GGA+U within the AL\nfunctional compared to usual GGA leads to large mod-\nifications of the DOS of the transition metal atoms. In\nthe case of Mn, the exchange splitting between the oc-\ncupied majority-spin and the unoccupied minority-spin\nstates increase considerably. In the majority-spin band\nstructure of Mn, the occupied states move lower in en-\nergy and as a result they are no more in the same en-\nergy with the Ni majority-spin states. This leads to a\nweaker hybridization between the dstates of Ni and Mn\natomsandintheNiDOSthewidthofthemajoritybands\nbecomes smaller as a result of the weaker hybridization\neffects. Almost all the weight of the occupied minority-\nspin band structure is located at the Ni atoms while al-\nmost all unoccupied minority-spin states are located at\nthe Mn atom. Thus there is almost no hybridization be-\ntween the minority-spin d-states of Ni and Mn and the\nformer are not affected by the shift of the later to larger\nenergy values being identical to the GGA case. These\nchanges in DOS are also reflected on the spin magnetic\nmoments in Table II. The larger tendency to magnetism\nwithin AL compared to AMF leads to slightly larger to-\ntal spin magnetic moments which deviate from the ideal\ninteger values of the SP rule and the Fermi level is lo-\ncated slightly below the minority-spin energy gap. In the\ncase of FeMnSb and CoMnSb, both the absolute values\nof the Fe(Co) and Mn spin magnetic moments increase\nby about 1 µBalmost cancelling each other. In the case\nof NiMnSb the variations in the atomic spin magnetic\nmoments are considerably smaller since almost all Ni d-\nstates are occupied in all studied cases. But even for\nNiMnSb the Mn spin moment increases by ∼0.5µBand\nthe Ni spin moment decrease by about 0.3 µB. The Sb\natoms in all cases also present changes in their atomic\nspin magnetic moments between the various calculations\nalthough these variations are considerably smaller than\nfor the transition metal atoms.\n2. Full-Heuslers\nThe second family of Heusler compounds which may\npresent half-metallicity are the so-called usual full-\nHeuslers crystallizing in the cubic L2 1structures. Half-TABLE III: Similar to Table I for the full-Heusler compounds\ncrystallizing in the L2 1lattice structure having the X 2YZ\nchemical formula.\nComp. Functional mXmYmZmtotal\nMn2VAl GGA -1.670 1.227 0.113 -1.999\nGGA+U (AL) -4.102 3.169 0.483 -4.551\nGGA+U (AMF) -1.798 1.527 0.079 -1.990\nMn2VSi GGA -0.801 0.557 0.060 -0.985\nGGA+U (AL) -2.248 2.759 0.376 –1.362\nCo2CrAl GGA 0.737 1.684 -0.160 2.999\nGGA+U (AMF) 0.965 1.222 -0.153 3.000\nCo2CrSi GGA 0.934 2.242 -0.111 4.000\nGGA+U (AL) 0.871 2.525 -0.267 4.000\nGGA+U (AMF) 0.890 2.187 0.031 4.000\nCo2MnAl GGA 0.673 2.910 -0.231 4.025\nGGA+U (AL) 1.381 4.176 -0.501 6.438\nGGA+U (AMF) 1.048 1.998 -0.096 3.999\nCo2MnSi GGA 0.972 3.195 -0.140 4.999\nGGA+U (AL) 0.732 3.954 -0.338 5.080\nGGA+U (AMF) 0.987 3.020 -0.004 5.000\nCo2FeAl GGA 1.163 2.870 -0.203 4.999\nGGA+U (AL) 1.188 3.326 -0.520 5.177\nGGA+U (AMF) 1.216 2.673 -0.105 4.999\nCo2FeSi GGA 1.327 2.926 -0.042 5.539\nGGA+U (AL) 1.375 3.450 -0.201 5.999\nmetallicity can be combined either with the appearance\nof ferrimagnetism, when the X atoms in the X 2YZ is the\nMn one, or with ferromagnetism when X is Co. In all\ncases the total spin magnetic moment in µBfollows a\nSP rule being Zt-24.61In Table III we have gathered the\ncalculated spin magnetic moments for all studied com-\npounds with both GGA and GGA+U methods using\nboth the AL and AMF double-counting functional in the\nlater case. When one case is missing in the table, this is\ndue to the fact that we were not able to get convergence\nirrespectively of the starting input which we have used.\nFirst, we will discuss our results on the half-metallic\nferrimagnetic Mn 2VAl and Mn 2VSI compounds where\nthe total spin magnetic moments is negative since the\ntotal number of valence electrons is less than 24. More-\nover the Mn spin magnetic moments are antiferromag-\nnetically coupled to the V spin moments due to their\nsmall distance.61In the case of Mn 2VAl, GGA+U cal-\nculations within AMF produced similar spin moments\nand DOS to the GGA case; we were not able to con-\nverge GGA+U within AMF for the Mn 2VSi compound.\nForboth compounds the use ofAL double-countingfunc-\ntional produced unphysical results similar to the case of\nd0-ferromagnets in Sec. IIIB. The use of AL tripled,\nwith respect to the GGA case, the absolute values of the\nspin magnetic moments of the transition metal atoms in\nMn2VA; in thecaseofVinMn 2VSi the increaseisalmost\n600% . Thus the use of AL for the half-metallic ferrimag-\nnetic Heusler compounds obviously is inadequate.\nIn the case of ferromagnetic full-Heuslers containing\nCo the effect of using both AMF and AL on the calcu-\nlated electronic and magnetic properties is more complex6\n-6-3 0 3\nEnergy-EF (eV)-4-2024DOS (states/eV/spin)-4-2024\nGGA\nGGA+U (AL)\n-6-3 0 3GGA\nGGA+U (AMF)Co2MnSiCo Co\nMn Mn\nFIG. 3: (color online) Co and Mn atom-resolved DOS in\nCo2MnSi. Details as in Fig. 1.\nthan in all the previously studied cases. When Y is Cr\n(Co2CrAlandCo 2CrSi)bothALandAMFyieldedaper-\nfect half-metallic state with the total spin magnetic mo-\nment being equal to the ideal values predicted by the SP\nrule as shown in Table III. When Y is Mn (Co 2MnAl and\nCo2MnSi) AMF produced a half-metallic states and both\natom-resolved and total spin magnetic moments where\nclose to the GGA case, but AL led to a considerable\nincrease of the Mn spin moment similarly to the semi-\nHeuslers. The increase of the Mn spin moment within\nAL led to an increase also of the total spin magnetic mo-\nment which is only 0.80 µBfor Co 2MnSi but reaches\nthe∼1.4µBfor Co 2MnAl. When Y is Fe (Co 2FeAl\nand Co 2FeSi) the behavior of the spin moments with re-\nspect to the GGA results is similar within both AL and\nAMF to the case where Y is Mn. Moreover in the case\nof Co2FeSi which is not half-metallic within GGA, the\nuse of GGA+U combined with AL leads to a total spin\nmagnetic moment of 6 µBand to a half-metallic state\nas shown also in Ref. 13. Although the GW scheme62\nproduced similar results to the GGA+ calculations, cor-\nrelations in this materials are still an open issue since\nrecent results by Meinert and collaborators show that a\nself-consistent calculation fixing the total spin magnetic\nmoment to 6 µBreproduces more accurately the posi-\ntion of the band with respect to available experimental\ndata.63\nTo understand the behavior of the spin moments we\nhave to examine in detail the behavior of the DOS. Since\nthe trends when either AMF or AL is employed are simi-\nlar for all six ferromagnetic Co-based full-Heuslers under\nstudy, we will use Co 2MnSi as an example and in Fig.\n3 we present the Co and Mn resolved DOS. When the-6-3 0 3\nEnergy-EF (eV)-8-4048DOS (states/eV/spin)-8-4048\nGGA\nGGA+U (AL)\n-6-3 0 3GGA\nGGA+U (AMF)Co2MnSi\nCo2MnAl\nFIG. 4: (color online) Total DOS per formula unit for the\nCo2MnSi and Co 2MnAl compounds. Details as in Fig. 1.\nGGA+Ucombined with AMF is used (left panel) there is\na significantchangein the DOS unlikely all other families\nof half-metallic compounds discussed above. AMF en-\nhances the tendency to magnetism with respect to GGA.\nFor the Mn atom the occupied majority spin states shift\nlower in energy but the minority-spin energy gap in the\nMn DOS remains unchanged. Through hybridization\nalso the Co majority-spin DOS shifts lower in energy\nandsodoalsothe occupiedCominority-spinstates. This\nleads to an increaseof the energy gap in the Co minority-\nspin band structure. Since as explained in Ref. 61 Co\natoms present in usual GGA calculations a much smaller\ngap than the Mn atoms and thus determine the energy\ngap in the total DOS, the opening of the former further\nstabilizes the half-metallic state.\nThe GGA+U method combined with AL even fur-\nther enhances the tendency to magnetism with respect to\nAMF as concluded in Ref. 29. In the case of Mn atoms\nthe exchange splitting between the occupied majority-\nspin and unoccupied minority-spin states is greatly en-\nhanced as for Mn in NiMnSb and thus the energy gap\nbecomes much larger. As a side-effect some weight in\nthe minority-spin band structure appears just below the\nFermi level. Thus although with respect to the GGA\ncase, AL opens the gap the Fermi level is located close to\nthe left edge of the gap instead of the middle in the GGA\ncase. CoDOS followsthroughhybridizationthe behavior\nof the Mn d-states and the gap is now also much larger\nbut the occupied minority-spin states move closer to the\nFermi level which now just crosses the states just below\nthe low-energy edge of the gap and the total spin mag-\nnetic moment within AL is slightly larger than the ideal\nvalue of 5 µB.7\nTABLE IV: Similar to Table I for the full-Heusler compounds\ncrystallizing in the inverse XAlattice structure having the\nCr2YZchemical formula, where thetwoCr atoms occupysites\nof different symmetry (see text).\nComp. Functional mCrAmCrBmYmZmtotal\nCr2FeGe GGA -1.454 1.753 -0.313 0.027 0.012\nGGA+U(AL) -4.162 4.672 -1.054 0.551 0.006\nCr2CoGa GGA -2.680 1.973 0.379 -0.014 0.069\nGGA+U (AL) -4.860 4.137 1.160 -0.082 0.520\nIn the case of Co 2MnAl the change in the spin mag-\nnetic moments is larger within both AL and AMF func-\ntionals. As shown in Fig. 4, although we just change\nAl for Si in Co 2MnSi, the AMF DOS shows a different\ntendency with respect to the energy gap. The exchange\nsplitting between occupied majority and unoccupied mi-\nnority spin states is smaller, and within AMF the gap\nis smaller than within GGA showing the contrary ten-\ndency to Co 2MnSi where AMF produced a larger gap\nwith respect to GGA. For Co 2MnAl within usual GGA\nthe Fermi level is close to the left edge of the gap while\nfor Co 2MnSi it is located at the middle of the gap. Thus\nin the case of AL based calculations the shift of the Co\noccupied minority spin states towards higher energies for\nCo2MnAl, discussed just above also for Co 2MnSi, leads\ntothelossofthehalf-metallicitysincenowtheFermilevel\ncrosses the occupied minority-spin states. The other Al-\nbased Heuslers (Co 2CrAl and Co 2FeAl) exhibit within\nGGA a DOS around the minority-spin energy gap simi-\nlar to Co 2MnSi and not Co 2MnAl and thus the increase\nin their total spin magnetic moment within AL is much\nsmaller than for Co 2MnAl.\n3. Inverse-Heuslers\nThe last family of potential half-metallic Heusler com-\npounds ar the so-called inverse Heusler compounds.64\nAmong these half-metals the most interesting are the\nso-called fully-compensated ferrimagnets (also known\nas half-metallic antiferromagnets) like Cr 2FeGe and\nCr2CoGa. These materials are of special inter-\nest since they combine half-metallicity to a zero to-\ntal net magnetization and thus are ideal for spin-\ntronic/magnetoelectronic devices due to the vanishing\nexternal stray fields created by them.65We should note\nthat films of Cr 2CoGa have been grown experimentally66\nand this compounds has been predicted to exhibit ex-\ntremely large Curie temperature.67As shown in Table IV\nGGA yields for both Cr 2FeGe and Cr 2CoGa compounds\na total spin magnetic moment close to zero (for an ex-\ntended discussion on the half-metallic inverse Heuslerssee Ref. 64). Note that we have two inequivalent Cr\natoms in these compounds denoted by the superscripts\nAandBin Table IV. We were not able to converge\nthe GGA+U self-consistent calculations using the AMF\ndouble-counting functional. For the AL functional al-\nthough the total spin magnetic moment stays close to\nzero, the absolute values of the Cr spin magnetic mo-\nments are about doubled leading to an unphysical sit-\nuations. Thus for these materials the use of GGA+U\ncombined with AL is not able to produce a reasonable\ndescriptionoftheelectronicstructureaswasalsothecase\nfor the semi-Heuslers and the ferrimagnetic full-Heuslers.\nIV. CONCLUSIONS\nWe have studied the electronic and magnetic proper-\ntiesof20half-metallicmagnetsperformingself-consistent\nGGA+U calculations using both the atomic-limit (AL)\nand around-mean-field (AMF) functionals for the dou-\nble counting term and compared them to the usual GGA\ncalculations. Overall the use of AMF produced results\nsimilar to the usual GGA calculations. The effect of AL\nwas diversified depending on the studied material. In\nthe case of d0-ferromagnets, semi-Heuslers, ferrimagnetic\nfull-Heuslers and inverse Heuslers the use of AL leads to\nunrealisticelectronicandmagneticpropertiesofthestud-\nied compounds and thus its use is not justified. On the\nother hand in the case of transition-metal binary com-\npounds and usual ferromagnetic full-Heusler compounds\nthe use of AL enhanced the tendency towards magnetism\nwith respect to both GGA and GGA+U combined with\nAMF. Depending onthe positionoftheFermi level, there\nwerecaseslikeMnAsandCo 2FeSiforwhichALproduced\na half-metallic state contraryto GGA and GGA+U com-\nbined with AMF, cases like VAs, CrAs and Co 2CrSi\nwhere all three methods produced a half-metallic state,\nand cases like Co 2MnAl, Co 2MnSi and Co 2FeAl where\nthe use of AL led to the loss of half-metallicity.\nMethodsbasedonthe combinationoftheusualdensity\nfunctionaltheory(DFT)-based codesandoftheHubbard\nU- Hund’s exchange Jare widely used to investigate the\nproperties of strongly correlated materials. Our results\nsuggest that especially in the case of half-metallic mag-\nnets the choice for the double counting functional used\nto subtract the part from the DFT total energy, which\nis associated to the Coulomb repulsion between the cor-\nrelated orbitals, plays a decisive role on the obtained re-\nsults. Thusthestudyofcorrelationsinhalf-metallicmag-\nnets is still an open issue and further studies are needed\nto establish the predictive power of methods based on\ntheUandJparameters like GGA+U or LDA+DMFT\nmethods.\n∗Electronic address: galanakis@upatras.gr1I.ˇZuti´ c, J. Fabian, and S. Das Sarma, Rev. Mod. Phys.8\n76, 323 (2004).\n2M. I. Katsnelson, V. Yu. Irkhin, L. Chioncel, A. I. Lichten-\nstein, and R.A. de Groot, Rev. Mod. Phys. 80, 315 (2008).\n3K. Sato, L. Bergqvist, J. Kudrnovsk´ y, P. H. Dederichs, O.\nEriksson, I. Turek, B. Sanyal, G. Bouzerar, H. Katayama-\nYoshida, V. A. Dinh, T. Fukushima, H. Kizaki, and R.\nZeller, Rev. Mod. Phys. 82, 1633 (2010).\n4R. A. de Groot, F. M. Mueller, P. G. van Engen, and K.\nH. J. Buschow, Phys. Rev. Lett. 50, 2024 (1983).\n5W. E. Pickett and H. Eschrig, J. Phys.: Condens. Matter\n19, 315203 (2007).\n6C. Felser, G. H. Fecher, and B. Balke, Angew. Chem. Int.\nEd.46, 668 (2007).\n7T. Graf, C. Felser, and S. S. P. Parkin , Progress in Solid\nState Chemistry 39, 1 (2011).\n8A. Hirohata and K. Takanashi, J. Phys. D: Appl. Phys.\n47, 193001 (2014).\n9J.P. Perdew and Y. Wang, Phys. Rev. B 45 (1992) 13244.\n10J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.\nLett.77, 3865 (1996).\n11K. Karlsson, F. Aryasetiawan, and O. Jepsen, Phys. Rev.\nB81, 245113 (2010).\n12I. V. Solovyev, J. Phys.: Condens. Matter 20, 293201\n(2008).\n13H. M. Kandpal, G. H. Fecher, C. Felser, and G.\nSch¨ onhense, Phys. Rev. B 73, 094422 (2006).\n14A. Yamasaki, L. Chioncel, A. I. Lichtenstein, and O. K.\nAndersen, Phys. Rev. B 74, 024419 (2006).\n15J. Min´ ar, J. Phys.: Condens. Matter 23, 253201 (2011).\n16F. Lechermann, A. Georges, A. Poteryaev, S. Biermann,\nM. Posternak, A. Yamasaki, and O. K. Andersen, Phys.\nRev. B74, 125120 (2006).\n17L. Chioncel, Y. Sakuraba, E. Arrigoni, M. I. Katsnelson,\nM. Oogane, Y. Ando, T. Miyazaki, E. Burzo, and A. I.\nLichtenstein Phys. Rev. Lett 100, 086402 (2008).\n18L. Chioncel, M. I. Katsnelson, R. A. de Groot, and A. I.\nLichtenstein, Phys. Rev. B 68, 144425 (2003).\n19S. Chadov, J. Min´ ar, H. Ebert, A. Perlov, L. Chioncel, M.\nI. Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 74,\n140411(R) (2006).\n20H. Allmaier, L. Chioncel, E. Arrigoni, M. I. Katsnelson,\nand A. I. Lichtenstein, Phys. Rev. B 81, 054422 (2010).\n21L. Chioncel, E. Arrigoni, M. I. Katsnelson, and A. I. Licht-\nenstein, Phys. Rev. Lett 96, 137203 (2006).\n22L. Chioncel, E. Arrigoni, M. I. Katsnelson, and A. I. Licht-\nenstein Phys. Rev. B 79, 125123 (2009).\n23L. Chioncel, Ph. Mavropoulos, M. Leˇ zai´ c, S. Bl¨ ugel, E.\nArrigoni, M. I. Katsnelson, and A. I. Lichtenstein, Phys.\nRev. Lett. 96, 197203 (2006).\n24L. Chioncel, M. I. Katsnelson, G. A. de Wijs, R. A. de\nGroot, and A. I. Lichtenstein, Phys. Rev. B 71, 085111\n(2005).\n25L. Chioncel, I. Leonov, H. Allmaier, F. Beiuseanu, E. Ar-\nrigoni, T. Jurcut, and W. Ptz, Phys. Rev. B 83, 035307\n(2011).\n26V. I. Anisimov, J. Zaanen, and O. K. Andersen, Phys. Rev.\nB44, 943 (1991).\n27V. I. Anisimov, I. V. Solovyev, M. A. Korotin, M. T.\nCzy´ zyk, and G. A. Sawatzky, Phys. Rev. B 48, 16929\n(1993).\n28M. T. Czy´ zyk and G. A. Sawatzky, Phys. Rev. B 49, 14211\n(1994).\n29E. R. Ylvisaker, W. E. Pickett, and K. Koepernik, Phys.\nRev. B79, 035103 (2009).30K. Koepernik and H. Eschrig, Phys. Rev. B 59, 1743\n(1999).\n31K. Kopernik, Full Potential Local Orbital Min-\nimum Basis Bandstructure Scheme Users Manual\n(http://www.fplo.de/download/ doc.pdf).\n32E. S ¸a¸ sıo˘ glu, I.Galanakis, C. Friedrich, andS. Bl¨ ugel, Phys.\nRev. B88, 134402 (2013).\n33F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S.\nBiermann, and A. I. Lichtenstein, Phys. Rev. B 70, 195104\n(2004).\n34F. Aryasetiawan, K. Karlsson, O. Jepsen, and U.\nSch¨ onberger, Phys. Rev. B 74, 125106 (2006).\n35T. Miyake and F. Aryasetiawan, Phys. Rev. B 77, 085122\n(2008); T. Miyake, F. Aryasetiawan, and M. Imada Phys.\nRev. B80, 155134 (2009).\n36E. S ¸a¸ sıo˘ glu, C. Friedrich, and S. Bl¨ ugel, Phys. Rev. B 83,\n121101(R) (2011).\n37P. H. Dederichs, S. Bl¨ ugel, R. Zeller, and H. Akai, Phys.\nRev. Lett. 53, 2512 (1984).\n38V. I. Anisimov and O. Gunnarsson, Phys. Rev. B 43, 7570\n(1991).\n39M. Cococcioni and S. de Gironcoli, Phys. Rev. B 71,\n035105 (2005).\n40K. Nakamura,R. Arita, Y. Yoshimoto, and S. Tsuneyuki,\nPhys. Rev. B 74, 235113 (2006).\n41K. Kusakabe, M. Geshi, H. Tsukamoto, and N. Suzuki, J.\nPhys.:Condens. Matter 16, S5639 (2004).\n42A. Laref, E. S ¸a¸ sıo˘ glu, and I. Galanakis, J. Phys.:Conden s.\nMatter23, 296001 (2011).\n43G. Y. Gao, K. L. Yao, and N. Li, J. Phys.:Condens. Matter\n23, 075501 (2011).\n44M. Sieberer, J. Redinger, S. Khmelevskyi, and P. Mohn,\nPhys. Rev. B 73, 024404 (2006).\n45M. Geshi, K. Kusakabe, H. Nagara, and N. Suzuki, Phys.\nRev. B76, 054433 (2007).\n46K.¨Ozdo˘ gan, E. S ¸a¸ sıo˘ glu, and I. Galanakis, J. Appl. Phys.\n111, 113918 (2012).\n47G. Y. Gao and K. L. Yao, Appl. Phys. Lett. 91, 082512\n(2007).\n48G. Y. Gao, K. L. Yao, E. S ¸a¸ sıo˘ glu, L. M. Sandratskii, Z.\nL. Liu, and J. L. Jiang, Phys. Rev. B 75, 174442 (2007).\n49S. Dong and H. Zhao, Appl. Phys. Lett. 98, 182501 (2011).\n50J. C. Slater, Phys. Rev. 49, 931 (1936).\n51L. Pauling, Phys. Rev. 54, 899 (1938).\n52http://www.flapw.de\n53H. Akinaga, T. Manago, andM. Shirai, Jpn.J. Appl.Phys.\n39, L1118 (2000).\n54I. Galanakis and P. Mavropoulos, Phys. Rev. B 67, 104417\n(2003).\n55Ph. Mavropoulos andI. Galanakis, J. Phys. Condens. Mat-\nter19, 315221 (2007).\n56P. J. Webster and K. R. A. Ziebeck, in Alloys and Com-\npounds of d-Elements with Main Group Elements. Part 2. ,\nedited by H. R. J. Wijn, Landolt-B¨ ornstein, New Series,\nGroup III, Vol. 19,Pt.c (Springer-Verlag, Berlin 1988), pp .\n75-184.\n57K. R. A. Ziebeck and K.-U. Neumann, in Magnetic Prop-\nerties of Metals, Edited H. R. J. Wijn, Landolt-B¨ ornstein,\nNew Series, Group III, Springer, Berlin (2001), Vol. 32/c,\npp. 64-414.\n58I. Galanakis, P. H. Dederichs, and N. Papanikolaou, Phys.\nRev. B66, 134428 (2002).\n59R. A. De Groot, A. M. van der Kraan, K. H. J. Buschow,9\nJ. Magn. Magn. Mater. 61, 330 (1986).\n60H. M. Huang, S. J. Luo, K. L. Yao, Physica B 406, 1368\n(2011).\n61I. Galanakis, P. H. Dederichs, and N. Papanikolaou, Phys.\nRev. B66, 174429 (2002).\n62M. Meinert, C. Friedrich, G. Reiss, and S. Bl¨ ugel, Phys.\nRev. B86, 245115 (2012).\n63M. Meinert, J.-M. Schmalhorst, M. Glas, G. Reiss, E.\nArenholz, T. B¨ ohnert, and K. Nielsch, Phys. Rev. B 86,\n054420 (2012); M. Meinert, Phys. Rev. B 87, 045103(2013).\n64S. Skaftouros, K. ¨Ozdo˘ gan, E. S ¸a¸ sıo˘ glu, and I. Galanakis,\nPhys. Rev. B 87, 024420 (2013).\n65H. van Leuken and R. A. de Groot, Phys. Rev. Lett. 74,\n1171 (1995).\n66T. Graf, F. Casper, J. Winterlik, B. Balke, G.H. Fecher,\nand C. Felser, Z. Anorg. Allg. Chem. 635, 976 (2009).\n67I. Galanakis and E. S ¸a¸ sıo˘ glu, Appl. Phys. Lett. 99, 052509\n(2011)."    },    {        "title": "1501.07312v1.Experimental_Characterization_of_Magnetic_Materials_for_the_Magnetic_Shielding_of_Cryomodules_in_Particle_Accelerators.pdf",        "content": "1 \n Experimental Characterization of Magnetic \nMaterials for the Magnetic Shielding of \nCryomodules in Particle Accelerators \nSanjay SAH1, Ganapati MYNENI2, Jayasimha \nATULASIMHA1 \n1 Virginia Commonwealth University, Dept. of \nMechanical and Nuclear Engineering, \n401 W. Main Street, Richmond, VA 23284-3015 \n2Thomas Jefferson National Accelerator Facility \n12000 Jefferson Avenue, Newport News, VA 23606 \nABSTRACT  \nThe magnetic properties of two important passive \nmagnetic shielding materials (A4K and Amumetal) for accelerator applicatio ns, subjected to various \nprocessing and heat treatment conditions are studied \ncomprehensively over a wide range of temperatures: from Cryogenic to room temperature. We analyze the \neffect of processing on the extent of degradation of \nthe magnetic properties of both materials and investigate the possibility of restoring these \nproperties by re-annealing.   \n \nI. INTRODUCTION \nMagnetic shielding is extremely vital for the \nenhanced performance of cryomodules (CMs) of particle accelerators. This can be understood in terms \nof the effect of stray magnetic fields on the quality \nfactor (Q\no) of the CM that is given by [1] \nܳൌீ\nோೞ,                                          (1) \nHere, G is the geometric factor of the accelerating \ncavity and R s is the cavity surface resistance. The \ncavity surface resistance (R s) can be divided into \ncontributions from the surface magnetic field (R H) \nand other components (R other). The R H can be \nestimated using the equation (2) as follows [1] \nܴுൌுೣ\nଶுమܴൎ9 . 4 9ൈ1 0ିଵଶܪ௫௧ඥ݂,(        2) \nHext is the external field that in this case is the earth's \nmagnetic field (~500 mG), f is the fundamental frequency of the Niobium cavity, H\nc2 is the type-II superconductor (Niobium) magnetic quench field and \nRn is the normal conducting resistance of niobium. \nThus, it is clear that a high stray magnetic field \nincreases the cavity surfa ce resistance, thereby \ndegrading the cavity’s quality factor. Furthermore, \nduring quenching, of the cryomodule cavities, the Nb \nis not in its superconducting state and therefore \nmagnetic flux can penetrate the cavity.  \nThese issues can be effectively addressed by the \nappropriate use of magnetic shields [2] that reduce \nthe magnetic field in a prescribed region. The \nmagnetic shielding can be provided by an active shield [3] that uses a magnetic field produced by \nutilizing a superconducting coil to cancel an external \nmagnetic field or a passive shield [4] that works by \ndrawing the field onto itself, providing a path for the \nfield lines around the shielding volume and minimizing the magnetic field inside the cryomodule.  \nHere we study magnetic properties of materials used \nin passive shields that mitigate the effect of the \nEarth's axial and transverse magnetic field \ncomponents on cryomodules. Specifically, we focus \non understanding of the manner in which magnetic permeability varies with temperature, applied \ndeformation during manufacturing and heat \ntreatment. While some prior work exists on \ncharacterizing the magnetic [2], [4-6], [8] properties, \na comprehensive study of the effect of deformation during the manufacturing process and annealing on \nthe magnetic permeability of shielding materials over \na broad range of temperatures (cryogenic to room \ntemperature) is not available. This paper bridges this \ngap in knowledge by performing such experimental studies on these magnetic materials. \nThe current materials of interest for magnetic \nshielding are Amumetal an d A4K and therefore these \nmaterials are studied in this paper. Both materials are \nhigh nickel content alloys. A4K is composed of 81% \nnickel, 4.5% molybdenum and rest iron by weight. \nAmumetal is composed of 80% nickel, 4.5% \nmolybdenum and rest iron by weight. The samples studies were obtained from Amuneal Manufacturing \nCorporation [5]. \n \n 2 \n II. EXPERIMENTAL METHODS  \ni. Sample Preparation \nTwo mill-annealed samples of A4K and Amumetal \nwere obtained from Amuneal Manufacturing \nCorporation with planar dimensions 3’x3’ and 1 mm in thickness (Fig 1 a). The samples were cut into 2 \nmm x 2 mm pieces of thickness 1mm (Fig 1 b) using \nWire Electrical Discharge Machine (Wire-EDM) at \nthe Jefferson Lab. The Wire-EDM was used so that \nthe external stress induced in the samples during cutting is minimized. The magnetic properties of both \nun-annealed samples and those that were hydrogen \nannealed (pure hydrogen and dry atmosphere) at \nAmuneal Manufacturing Corporation at 1150\noC for \nfour hours were studied. We  note that after the anneal \nprocess, the cooling rates for Amumetal and A4K \nwere 200oC/h and 50oC/h respectively.   \n(a.) \n (b.) \n \n \n(c.) \n \nFIG. 1. (a.) Amumetal and A4K samples (b.) \nAmumetal or A4K sample after EDM cutting, and \n(c.) Schematic of Amumetal or A4K Sample with dimension. \nTwo samples of each metal were then deformed by \napplying bending stress, which is equivalent to a \nmaximum tensile/compressive stress of 3.18 MPa. \nThe deformation process is designed to produce the \ntypical stress induced in samples by the manufacturing processes while fabricating the \nshields. The magnetic properties of the deformed \nsamples were studied to understand the effect of this \nmanufacturing process on permeability. \nFinally, these deformed samples were annealed again \nand tested to determine if the magnetic properties that \nwere degraded during the deformation process could be restored by approp riate heat treatment. \nii. Magnetic Testing \nThe magnetic characterization on the different \nsamples (unannealed, annealed and deformed) at 50K, 100K, 150K, 200K, 250K and 300K was \nperformed using a Quantum Design Versalab \nVibrating Sample Magnetometer (VSM) at the \nNanomaterial Core Characterization (NCC) Facility \nof the Virginia Commonwealth University (VCU). The magnetic characterization of samples annealed \nafter deformation were tested only at 300K as \nexplained later. \nMagnetic moment as a function of field applied in the \nZ-direction (axes shown in Fi g. 1 c) was collected for \neach sample at the differen t temperatures mentioned \nabove. A SQUID (Quantum Design Magnetic \nProperty Measurement System-3) magnetometer at \nthe University of Maryland was used to obtain \nmagnetic moment vs. applied field at temperature of \n5K.  \niii. Demagnetizing Factor A demagnetizing field is generated when samples are \nmagnetized.  This needs to be correctly accounted for \nwhile reporting the magnetic moment at a given applied field. The effectiv e field inside the sample \nthat produces the moment is given as [7], [9-10], \n                      (3) \nWhere, H\nin is the effective magnetic field inside the \nsample, H app is the applied magnetic field, N is \ndemagnetizing factor that is influenced by the geometry of the sample and M is the magnetic \nmoment. \n N is approximately determined from the \nexperimental data using N ≈ H\napp/M from the linear \nregion of M-H curve where χ is very large. (Details \n3 \n of the derivation and when this approximation holds \ncan be found in Appendix -1 of this paper).  \nIII. RESULTS AND ANALYSIS \nRegular, annealed and deformed samples of \nAmumetal and A4K were tested at the temperatures of 5K, 50K, 100K, 150K, 200K, 250K and 300K. \nThe plots Fig. 2-4 respectively show the M-H curves \nof AMU metal without annealing, after annealing and \nafter deformation, while Fig. 5-7 respectively show \nthe M-H curves of A4K for the same conditions.  \nIn both materials, irrespective of the processing \ncondition, we note that saturation magnetization (the \nplots we show are zoomed and M\ns is not exactly \nresearched at the highest field shown on the plot ~ \n2×104 A/m, but the trends still stay the same) \ndecreases with the increase in temperature as expected in any second order system. Also, as \nexpected, deformed samples have the lowest \npermeability and need high fields to drive them to \nsaturation due to the large number of defects that act \nas pinning sites and impede the magnetization rotation or movement of magnetic domains walls. \nThe undeformed but unannealed samples show \nhigher permeability, likely due to lesser defect \ndensity while the annealed samples show the best \npermeability as the annealing process greatly reduces the defects/pinning sites[11-13].   \nThe comparative value of the low field permeability \n(differential permeability at 0.5 Oe, approximate \nmagnitude of the Earth’s magnetic field) and the \nintermediate field permeability (differential \npermeability at ~250 Oe and ~500 Oe) for two materials (Amumetal and A4K) are tabled at two \ntemperatures: 5K and 300K (in Table.1 and Table. \n2.). These temperatures are of relevance to the inner \nmagnetic shield at cryogenic temperature and the \nouter magnetic field at room temperature respectively. In addition to confirming that \npermeability at both temperatures is highest for \nannealed samples and lowest for deformed samples at \nlow fields, it also shows that the low field \npermeability of annealed Amumetal and A4K are comparable at 300 K while that of annealed A4K is \nsignificantly better than that  of annealed Amumetal at \nCryogenic temperature (5K). This suggests that A4K is better suited for shielding Earth’s magnetic field at \nlow temperatures and should be the preferred \nmaterial for design of inner shields. \nTable. 1.  Permeability at 5K \nMaterial Permeability (µ r) at 5K \nµr=∆B/∆H \nat 0.5Oe \n(~40 A/m) µr=B/H \nat ~250 \nOe \n(~2×104 \nA/m) µr=∆B/∆H \nat ~250 \nOe \n(~2×104 \nA/m) µr=∆B/∆H \nat ~500 \nOe \n(~4×104 \nA/m) \nAmumetal-\nRegular 8670.28 433.1 32.67 21.7 \nAmumetal-\nAnnealed 12640.10 452.92 31.48 20.8 \nAmumetal-\nStressed  3723.10 374.61 80.42 32.9 \nA4K-\nRegular 16688.68 429.44 30.84 21.4 \nA4K-\nAnnealed 51904.52 422.83 28.552 20.7 \nA4K-\nStressed 10080.62 402.91 61.97 28 \n \nTable. 2.  Permeability at 300K \nMaterial Permeability (µ r) at 300K \nµr=∆B/∆H \nat 0.5 Oe  \n(~40 A/m) µr=B/H \nat ~250 \nOe \n(~2×104 \nA/m) µr=∆B/∆H \nat ~250 \nOe \n(~2×104 \nA/m) µr=∆B/∆H \nat ~500 \nOe \n(~4×104 \nA/m) \nAmumetal-\nRegular 10296.49 356.00 27.50 19.5 \nAmumetal-\nAnnealed 11662.11 356.10 27.50 19.2 \nAmumetal-\nStressed  8473.87 329.24 59.20 26.2 \nA4K-\nRegular 4102.02 357.19 27.90 20.0 \nA4K-\nAnnealed 11676.87 359.41 27.50 19.3 \nA4K-\nStressed 2839.67 345.32 40.30 22.4 \n \nAt intermediate fields (~250 Oe) the differential \npermeability of the stressed samples is better than \nthat of either the annealed  or the regular samples. \nThis is because the annealed (and regular) samples \ntend to almost reach sa turation at low fields, \nthereafter the increase in magnetization with \nincreasing field is small. In contrast, the stressed  \n 4 \n  \nFIG. 2.  M-H curves for regular amumetal sample at \nvarious temperatures.  \n \nFIG. 3.  M-H curves for annealed amumetal sample at \nvarious temperatures. \n \nFIG. 4.  M-H curves for stressed amumetal sample at \nvarious temperatures.  \nFIG. 5.   M-H curves for regular A4K sample at \nvarious temperatures. \n \nFIG. 6.  M-H curves for annealed A4K sample at \nvarious temperatures. \n \nFIG. 7.    M-H curves for stressed A4K sample at \nvarious temperatures. \n \n5 \n  \nFIG. 8.  M-H curves for all samples at High field and \n300K. \n \nFIG. 9.  M-H curves for all samples at High field and \n5K. \n \nFIG. 10.  M-H curves for all samples at low field and \n300K.  \nFIG. 11.  M-H curves for all samples at low field and \n5K. \n \nFIG. 12.  M-H curves for an AMU sample at 300K.   \n \nFIG. 13.  M-H curves for an A4K sample at 300K.   \n \n6 \n samples need a larger field to drive close to saturation \nand hence they show a higher differential \npermeability compared to the annealed (and regular) \nsamples at intermediate fields. This trend is less \npronounced at higher field ~500 Oe and it is expected \nthat they would be roughly comparable (µ r ~ 1) at \nvery higher fields as the magnetization in all samples \nwould reach saturation.  However, even at \nintermediate fields (~250 Oe) if one looks at the \nabsolute permeability (B/H) instead of the differential \npermeability, at either 0 K or 300K the annealed samples are highest followed by regular and the \nstressed samples have the least permeability (least B \nor M for a given H). \nWe also note that there is some anomalous behavior \nat the intermediate temperatures 50K-250K in \nFigures 2-7. Specifically, it appears that is some cases (see for example, Fig 2) the 200K and 250 K \nappears to have lower permeability at low fields \ncompared to 300K followed by a crossover point as \nthey take higher fields for the M-H fields to nearly \n“flatten out” compared to  the 300 K M-H curves. \nThese trends were found to be repeatable across \ndifferent samples.   \nNext, the M-H curves at room temperature (300 K) \nand cryogenic temperature (5K) are plotted for high \nfields (Fig 8 and 9) and low fields (Fig. 10 and 11) \nfor both Amumetal and A4K samples. This again shows the permeability decreases greatly due to \ndeformation. This effect is particularly large at 5 K as \nthe thermal energy avoided to overcome pinning \ndefects introduced due to the deformation is very \nsmall.  \nIV. CONCLUSIONS \nAn extensive and detailed magnetic characterization \nof Amumetal and A4K was performed. The results \nshow, deformation due to the manufacturing process has a significant effect on permeability and can be \ndetrimental to magnetic shielding. For the magnetic \nshielding at room temper ature, either annealed \nAmumetal or annealed A4K can be used as both have \nrelatively comparable permeability. However, annealed A4K has relatively higher permeability at \nlow-field (~0.5 Oe) and low temperature (~5K) and will be more efficient for shielding at these \ntemperatures compared to annealed Amumetal.  \nCompared to deformed samples, annealed samples of \nboth A4K and Amumetal show a significant \nimprovement in permeability at low fields (~0.5G) at \nlow temperature (5K) compared to its effect at higher \ntemperature (300K). This is possibly due to the fact that at low temperature there is minimal thermal \nnoise to overcome pining defects (abundant in \ndeformed samples) which makes it harder to align the \nmagnetization with a small field compared to \nannealed samples (fewer pinning sites).  \nFurthermore, the permeability is more or less restored \nafter the stressed samples are annealed again as \nshown in figure 12 and figure 13. Since, we found on room temperature magnetic ch aracterization, that the \nmagnetic properties of stressed samples were restored \nupon annealing, we did not repeat the low temperature magnetic characterization on the stressed \nsamples that were re-annealed as we expect to find \nthat the low temperature magnetic properties will be \nrecovered as well.   \nV. ACKNOWLEDGEMENTS \nWe acknowledge a collaboration between Virginia \nCommonwealth University (VCU) and Jefferson Lab \n(U.S. DOE Contract No. DE-AC05-06OR23177) that \npartly supports Sanjay Sah. We acknowledge Dr. Sama Bilbao Y Leon at VCU Mechanical and \nNuclear Engineering for tr avel support to attend \nmagnetic shielding workshop at FRIB, Dr. Brian \nHinderliter at Univ. of Minnesota, Duluth for earlier \ndiscussion on Sanjay Sah’ s PhD research topic, Mr. \nMichael Adolf at Amuneal Corp. for Amumetal and \nA4K samples, NCC at VCU for use of the VSM and \nProf. Greene and Dr. S. Saha at University of \nMaryland for use of SQUID Magnetometer. \nVI. REFERENCES \n[1] G. Cheng, E. F. Daly, and W. R. Hicks, C100 \nCryomodule Magnetic Shielding Finite Element \nAnalysis (Jefferson Lab, 2008), JLAB-TN-08-015. \n[2] M. Masuzawa, N. Ohuchi, A. Terashima, and K. \nTsuchiya, Applied Superconductivity, IEEE 7 \n Transactions Volume:20 , Issue: 3, 1773 - 1776 \n(2010). \n[3] T. Rikitake, Magnetic and Electromagnetic \nShielding (Springer, 1987). \n[4] R. E. Laxdal, Review of Magnetic Shielding \nDesigns of Low-beta Cryomodules,  in SRF2013, \nParis, France, (2013). \n[5] Material data sets of amumetal and A4K, \nAmuneal Manufacturing Corporation (private \ncommunication). \n[6.] R. C. O'Handley, Modern Magnetic Materials \nPrinciples and Applications (John Wiley & Sons, Inc., 1999). \n[7.] F. Fiorillo, Characterization and Measurement of \nMagnetic Materials (Elsevier 2004). \n[8]\n O. L. Boothby and R. M. Bozorth, Journal of \nApplied Physics Volume:18 , Issue: 2 (1947). [9] A. Zieba and S. Foner, Review of Scientific \nInstruments Volume:53 , Issue: 9 (1982). \n[10] A. Aharoni, Journal of Applied Physics Volume \n83, Issue 6, pp. 3432-3434 (1998). \n[11] S. Tumanski, Handbook of Magnetic \nMeasurements (CRC Press, 2011), p. 390. \n[12] J. Vargasa, C. Ramosa , R. D. Zyslera, and H. \nRomerob, Physica B: Condensed Matter Volume \n320, Issues 1–4 (2002). \n[13] K. Suzuki, N. Kataoka, A. Inoue, A. Makino, \nand T. Masumoto, Materials Transactions, JIM \nVol.31 No.8 (1990). \n   \n \n \n      \n \n      \n \n      \n \n     8 \n VIII. APPENDIX \n1. Demagnetizing Factors \nThe effective field inside the sample that induces \nmagnetization in the sample is given as: [7] \nܪൌܪ െ,ܯܰ (                                   3) \n \nThe demagnetizing factor (N) in equation 3 can be \nwritten as:   ܰ ൌுೌ\nெെு\nெ,                             (4) \nHin/M is the magnetic susceptibility of the material.   \nܰൌுೌ\nெെଵ\nఞ ,                              (5) \n1\n߯ ൎ 0     \nSince, the magnetic susceptibility is very high \n(χ~10,000) for the ferromagnetic material it can be \nneglected as a first approximation. Hence, the \ndemagnetizing demagnetizing factor (N) can be \ndirectly estimated from experimental data as:  \nܰൌுೌ\nெ ,                              (6) \nThe “N” thus determined was used to correctly \nestimate the H in using equation 3. All M-H curves \nplotted in this paper employ this correction to plot M \nvs. the H in, from the measured M vs. H app data. \n \n \n  \n \n \n"    },    {        "title": "1504.04547v1.Model_for_the_FC_and_ZFC_Ferrimagnetic_Spinel.pdf",        "content": "arXiv:1504.04547v1  [cond-mat.str-el]  17 Apr 2015Model for the FC and ZFC Ferrimagnetic Spinel\nN. Karchev\nDepartment of Physics, Sofia University, James Bourchier 5 b lvd., 1164 Sofia, Bulgaria\n(Dated: October 20, 2021)\nThere are two methods of preparation of ferrimagnetic spine l. If, during the preparation, an\nexternal magnetic field as high as 300 O¨ e is applied upon cool ing the material is named field-cooled\n(FC).Iftheappliedfieldisabout1O¨ ethematerial iszero-fi eldcooled (ZFC).Toexplorethemagnetic\nand thermodynamic properties of these materials we conside r two-sublattice spin system, defined\non the bcc lattice, with spin- sAoperators SA\niat the sublattice Asite and spin- sBoperators SB\niat\nthe sublattice Bsite, where sA> sB. The subtle point is the exchange between sublattice A and\nB spins, which is antiferromanetic. Applying magnetic field along the sublattice A magnetization,\nduring preparation of the material, one compensates the Zee man splitting, due to the exchange, of\nsublattice B electrons. This effectively leads to a decrease of thesBspin. We consider a model with\nsBvarying parameter which accounts for the applied, during th e preparation, magnetic field.\nIt is shown that the model agrees well with the observed magne tization-temperature curves of\nzero field cooled (ZFC) and non-zero field cooled (FC) spinel f errimagnetic spinel and explains the\nanomalous temperature dependence of the specific heat.\nPACS numbers: 75.50.Gg,71.70.Ej,75.10.Dg,75.10.Lp\nI. INTRODUCTION\nThe magnetization-temperature and magnetic suscep-\ntibility curves for zero field cooled (ZFC) and non-zero\nfield cooled (FC) ferrimagnetic spinel display a notable\ndifference below N´ eel TNtemperature [1–13]. The (ZFC)\ncurve exhibits a maximum and then a monotonic de-\ncrease upon cooling from TN, while the (FC) curve in-\ncreases steeply, shows a dip near the temperature at\nwhich the (ZFC) curve has a maximum and finally in-\ncreases monotonically. There is also difference between\nso-called field-cooled-cooling and field-cooled-warming\nprocedures [14].\nThe specific heat curves for spinel ferrimagnetics show\nsharp peak at N´ eel temperature, which indicates fer-\nrimagnetic to paramagnetic transition, and tiny peak\nat temperature below N´ eel’s where the magnetization-\ntemperature curve has a maximum [3, 6, 9].\nAlthough the FC and ZFC spinel ferrimagnetics have\nintensively been studied, their magnetic and thermody-\nnamic properties have not been understood. There is\nnot an effective model which in unified way to explain\nthe experimental results.\nIn the present paper we consider two-sublattice spin\nsystem, defined on the bcc lattice, with spin- sAopera-\ntorsSA\niat the sublattice Asite and spin- sBoperators\nSB\niat the sublattice Bsite, where sA> sB. The subtle\npoint is the exchange between sublattice A and B spins,\nwhich is antiferromanetic. Applying magnetic field along\nthesublatticeAmagnetization, duringpreparationofthe\nmaterial, one compensates the Zeeman splitting of sub-\nlattice B electrons due to the exchange. This effectively\nleads to decrease of the sBspin. One can obtain an intu-\nition for this from spin-fermion model of spinel ferrimag-\nnetic with spin-1 /2itinerantelectronsat the sublattice B\nsite and spin- slocalizedelectronsat the sublattice Asite.\nAn applied, alongthe magnetizationof the localized elec-trons, external magnetic field compensates the Zeeman\nsplitting due to the spin-fermion exchange. Integrating\nout the fermions we obtain an effective spin model with\neffective spin sBwhich depends on the external magnetic\nfield (see Appendix A).\nWe consider a model with sBvarying parameter which\naccounts for the applied, during the preparation, mag-\nnetic field. First we present the method of calcula-\ntion exploring ZFC spinel with sA= 1.5 andsB= 1.\nWe obtained that the system has two phases. At low\ntemperature (0 ,T∗) the magnetic orders of the Aand\nBspins contribute to the magnetization of the sys-\ntem, while at the high temperature ( T∗,TN), the mag-\nnetic order of the sublattice B with smaller spin sBand\nwith a weaker intra-sublattice exchange is suppressed by\nmagnon fluctuations. Only the sublattice A spins, with\nstronger intra-sublattice exchange, have non-zero spon-\ntaneous magnetization. There is no additional symmetry\nbreaking, and the Goldstone boson has a ferromagnetic\ndispersion in both phases, but partial-order transition\ndemonstrates itself through tiny peak of specific heat as\na function of temperature.\nPartial order is well known phenomenon and has been\nsubject to extensive studies. Frustrated antiferromag-\nnetic systems has been studied by means of Green func-\ntion formalism. Partial order and anomalous temper-\nature dependence of specific heat have been predicted\n[15]. Experimentally the partial order has been observed\ninGd2Ti2O7[16]. Monte Carlo method has been uti-\nlized to study the nature of partial order in Ising model\nonkagom´elattice [17]. There are exact results for the\npartially ordered systems which precede the above stud-\nies [17–19]. The advantage of the present method of cal-\nculation is that it permits to consider the sublattice B\nspin as a varying parameter sB<1. We calculate the\nmagnetization-temperature curves and the specific heat\nas a function of temperature for sB= 0.7,sB= 0.4,2\nsB= 0.2 and fixed sA= 1.5, thus accounting for the in-\ncreasing of the applied, during preparation of FC spinel,\nmagnetic field.\nII. METHOD OF CALCULATION\nThe Hamiltonian of the ZFC ferrimagnetic spinel is\nH=−JA/summationdisplay\n≪ij≫ASA\ni·SA\nj−JB/summationdisplay\n≪ij≫BSB\ni·SB\nj\n+J/summationdisplay\n/angbracketleftij/angbracketrightSA\ni·SB\nj (1)\nwhere the sums are over all sites of a body-centered cu-\nbic (bcc) lattice: ∝angbracketlefti,j∝angbracketrightdenotes the sum over the nearest\nneighbors, ≪i,j≫Adenotes the sum over the sites of\nthe A sublattice, ≪i,j≫Bdenotes the sum over the\nsites of the B sublattice. The first two terms describe\nthe ferromagnetic Heisenberg intra-sublattice exchange\nJA>0,JB>0, while the third term describes the inter-\nsublattice exchange which is antiferromagnetic J >0.\nTo study a theory with the Hamiltonian Eq.(1) it\nis convenient to introduce Holstein-Primakoff represen-\ntation for the spin operators SA\ni(a+,a) andSB\ni(b+,b).\nRewriting the effective Hamiltonian in terms of the Bose\noperators ( a+,a,b+,b) we keep only the quadratic and\nquartic terms. The next step is to represent the Hamil-\ntonian in the Hartree-Fock approximation:\nH≈HHF=Hcl+Hq (2)\nwith\nHcl= 6NJA(sA)2(uA−1)2+6NJB(sB)2(uB−1)2\n+ 8NJsAsB(u−1)2, (3)\nand\nHq=/summationdisplay\nk∈Br/bracketleftbig\nεa\nka+\nkak+εb\nkb+\nkbk−γk/parenleftbig\na+\nkb+\nk+bkak/parenrightbig/bracketrightbig\n,\n(4)\nwhereN=NA=NBis the number of sites on a sublat-\ntice. The two equivalent sublattices A and B of the bcc\nlattice are simple cubic lattices. The wave vector kruns\nover the reduced first Brillouin zone Brof a bcc lattice\nwhich is the first Brillouin zone of a simple cubic lattice.\nThe dispersions are given by equalities\nεa\nk= 4sAJAuA(3−coskx−cosky−coskz) + 8sBJu\nεb\nk= 4sBJBuB(3−coskx−cosky−coskz) + 8sAJu\nγk= 8J u√\nsAsBcoskx\n2cosky\n2coskz\n2(5)\nThe equations (5) show that Hartree-Fock parameters\n(uA,uB,u) renormalize the intra and inter-sublattice ex-\nchange constants ( JA,JB,J) respectively.To diagonalize the Hamiltonian one introduces new\nBose fields αk, α+\nk, βk, β+\nkby means of the transforma-\ntion\nak=ukαk+vkβ+\nka+\nk=ukα+\nk+vkβk\n(6)\nbk=ukβk+vkα+\nkb+\nk=ukβ+\nk+vkαk,\nwherethe coefficients ofthe transformation ukandvkare\nrealfunctionsofthewavevector k(B7). Thetransformed\nHamiltonian adopts the form\nHq=/summationdisplay\nk∈Br/parenleftBig\nEα\nkα+\nkαk+Eβ\nkβ+\nkβk+E0\nk/parenrightBig\n,(7)\nwith new dispersions\nEα\nk=1\n2/bracketleftbigg/radicalBig\n(εa\nk+εb\nk)2−4γ2\nk−εb\nk+εa\nk/bracketrightbigg\n(8)\nEβ\nk=1\n2/bracketleftbigg/radicalBig\n(εa\nk+εb\nk)2−4γ2\nk+εb\nk−εa\nk/bracketrightbigg\nand vacuum energy\nE0\nk=1\n2/bracketleftbigg/radicalBig\n(εa\nk+εb\nk)2−4γ2\nk−εb\nk−εa\nk/bracketrightbigg\n(9)\nFor positive values of the Hartree-Fock parameters and\nall values of k∈Br, the dispersions are nonnegative\nEα\nk≥0, Eβ\nk≥0. When sA> sBtheαkboson is\nthe long-range (magnon) excitation in the system with\nEα\nk∝ρk2, near the zero wavevector, while the βkbo-\nson is a gapped excitation, with gap proportional to the\ninter-sublattice exchange constant Eβ\n0= 8Ju(sA−sB) .\nThe free energy of a system with Hamiltonian HHF\nequations (2), (3) and (4) is\nF= 6NJA(sA)2(uA−1)2+6NJB(sB)2(uB−1)2\n+ 8NJsAsB(u−1)2+1\nN/summationdisplay\nk∈BrE0\nk (10)\n+1\nβN/summationdisplay\nk∈Br/bracketleftBig\nln/parenleftBig\n1−e−βEα\nk/parenrightBig\n+ ln/parenleftBig\n1−e−βEβ\nk/parenrightBig/bracketrightBig\n,\nwhereβ= 1/Tis the inverse temperature. Then, the\nsystem of equations for the Hartree-Fock parameters is\n∂F/∂uA= 0, ∂F/∂uB= 0, ∂F/∂u= 0.(11)\nThe Hartree-Fock parameters are positive functions\nofT/J, solution of the system of equations (11) (see\nEqs.(B8)). Utilizing these functions, one can calculate\nthe spontaneous magnetization on the two sublattices\nMA=< S3\n1j> j is from sublattice A\n(12)\nMB=< S3\n2j> j is from sublattice B3\nandM=MA+MB, the spontaneous magnetization of\nthe system. In terms of the Bose functions of the αand\nβexcitations they adopt the form\nMA=sA−1\nN/summationdisplay\nk∈Br/bracketleftBig\nu2\nknα\nk+v2\nknβ\nk+v2\nk/bracketrightBig\n(13)\nMB=−sB+1\nN/summationdisplay\nk∈Br/bracketleftBig\nv2\nknα\nk+u2\nknβ\nk+v2\nk/bracketrightBig\n,\nwhereukandvkare functions of the wavevector k, coef-\nficients in the transformation (6).\nThemagnonexcitation- αkisacomplicatedmixtureof\nthe transversal fluctuations of the AandBspins (6). As\na result the magnons’ fluctuations suppress in a different\nwaythemagnetizationonsublattices AandB. Quantita-\ntivelythis dependsonthe coefficients ukandvk. At char-\nacteristic temperature T∗spontaneous magnetization on\nsublattice Bbecomes equal to zero, while spontaneous\nmagnetization on sublattice Ais still nonzero (see Fig.1).\nTo study the magnetic properties of the system above\nT∗we first consider the paramagnetic phase. To this end\nwe make use of the Takahashi modified spin-wave theory\n[20] and introduce two parameters λAandλBto enforce\nthe magnetization on the two sublattices to be equal to\nzero. The new Hamiltonian is obtained from the old one\nequation (1) by adding two new terms:\nˆH=H−/summationdisplay\ni∈AλASA3\ni+/summationdisplay\ni∈BλBSB3\ni (14)\nIn momentum space the new Hamiltonian ˆHadopts the\nform Eq.(4) with new dispersions\nˆεa\nk=εa\nk+λA,ˆεb\nk=εb\nk+λB.(15)\nUtilizing the same transformation (6) one obtains the\nHamiltonian ˆHin diagonal form (7) with dispersions ˆEα\nandˆEβobtained from Eqs.(8) replacing εa\nkandεb\nkwith\nˆεa\nkand ˆεb\nkrespectively. It is convenient to represent the\nparameters λAandλBin the form\nλA= 6JusB(µA−1), λB= 6JusA(µB−1).(16)\nThe dispersions ˆ εa\nkand ˆεb\nkarepositivefor all valuesofthe\nwavevector k, if the parameters µAandµBare positive.\nThe dispersions ˆEα\nkandˆEβ\nkare well defined if\nµAµB≥1. (17)\nTheβkexcitation is gapped ( ˆEβ\nk>0) for all values of\nparameters µAandµBwhich satisfy equation (17). The\nαexcitation is gapped if µAµB>1, but in the particular\ncase\nµAµB= 1 (18)\nˆEα\n0= 0, and near the zero wavevector ˆEα\nk≈ˆρk2. There-\nfor, in the particular case Eq. (18) αkboson is the long-\nrange excitation (magnon) in the system./s48 /s53 /s49/s48 /s49/s53 /s50/s48 /s50/s53 /s51/s48\n/s45/s49/s44/s48/s45/s48/s44/s53/s48/s44/s48/s48/s44/s53/s49/s44/s48/s49/s44/s53/s83/s80/s79/s78/s84/s65/s78/s69/s79/s85/s83/s32/s32/s77/s65/s71/s78/s69/s84/s73/s90/s65/s84/s73/s79/s78/s84/s47/s74/s77/s65 \n/s77/s65 \n/s43/s77/s66\n/s77/s66/s115/s65 \n/s61/s49/s46/s53\n/s115/s66\n/s61/s49\nFIG. 1: (Color online) Spontaneous magnetization MA,MB\nandMA+MBas a function of the temperature in units of\nexchange constant T/Jfor ferrimagnetic spinel on bcc lattice\nwithsA= 1.5,sB= 1,JA/J= 2 and JB/J= 0.002. The\npartial order transition temperature T∗is the temperature\nabove which MB= 0.\nAboveN´ eeltemperature we introduced the parameters\nµAandµB(λA,λB) to enforce the sublattice AandB\nspontaneous magnetizations to be equal to zero. We find\nout these and Hartree-Fock parameters, as functions of\ntemperature, solving the system of five equations, equa-\ntions (11) and the equations MA=MB= 0, where the\nspontaneous magnetization has the same representation\nasequations(13)butwithcoefficients ˆ uk,ˆvk, anddisper-\nsionsˆEα\nk,ˆEβ\nkin the expressions for the Bose functions.\nThe numerical calculations show that above N´ eel tem-\nperature µAµB>1. When the temperature decreases\nthe product µAµBdecreases, remaining larger than one.\nThe temperature at which the product becomes equal to\none (µAµB= 1) is the N´ eel temperature Fig.(6).\nBelowTN, the spectrum contains long-range(magnon)\nexcitations. Thereupon, µAµB= 1 and one can use the\nrepresentation µB= 1/µA. Then,µAand Hartree-Fock\nparameters are solution of a system of four equations,\nequations (11) and the equation MB= 0.\nWe utilize the obtained functions µA(T),µB(T)uA(T),\nuB(T),u(T) (see Appendix C) to calculate the sponta-\nneous magnetization as a function of the temperature.\nFor a system with sA= 1.5,sB= 1,JA/J= 2 and\nJB/J= 0.002 the functions MA(T/J),MB(T/J) and\nMA(T/J) +MB(T/J) are depicted in figure (1). The\npartial order transition temperature T∗is the tempera-\nture above which MB= 0.\nThe customary formula for the entropy of a Bose sys-\ntem with Hamiltonian (7) is\nS=1\nN/summationdisplay\nk,δ/bracketleftbig\n(1+nδ\nk)ln(1+nδ\nk)−nδ\nklnnδ\nk/bracketrightbig\n,(19)\nwhereδstays for αandβ. The dispersions Eα\nkandEβ\nk\n(8) areused to define the Bosefunctions nα\nkandnβ\nkbelow\nT∗, dispersions ˆEα\nkandˆEβ\nkwithµB= 1/µAare used for4\n/s48 /s50 /s52 /s54 /s56 /s49/s48 /s49/s50 /s49/s52 /s49/s54 /s49/s56 /s50/s48 /s50/s50 /s50/s52 /s50/s54 /s50/s56 /s51/s48 /s51/s50/s48/s50/s52/s54/s56/s49/s48/s49/s50/s49/s52/s67\n/s84/s47/s74/s115/s65\n/s61/s49/s46/s53\n/s115/s66\n/s61/s49\nFIG. 2: (Color online) Specific heat Cvs temperature, in\nunits of the exchange constant T/J, forJA/J= 2,JB/J=\n0.002,sA= 1.5 andsB= 1. The high temperature (green)\nvertical line marks N´ eel TNtemperature, while the low tem-\nperature (red) line marks partial order transition tempera ture\nT∗.\npartial order phase T∗< T < T N, and with µAµB>1\nfor paramagnetic phase above N´ eel temperature. With\nentropy, as a function of temperature in mind, one can\ncalculatethecontributionofmagnonstothespecificheat:\nC=TdS\ndT(20)\nThe resultant curve C(T/J), for a system with the same\nparameters, as above, is depicted in figure (4).\nThefigures(1)and(2)showthatthepresentmethodof\ncalculation describes correctlythe features of the system,\npartial order transition and anomalous behavior of the\nspecific heat at the temperature of this transition T∗.\nIII. FC SPINEL FERRIMAGNETICS\nFC spinel ferrimagnetics are prepared applying mag-\nnetic field along the sublattice A magnetization upon\ncoolingthematerial. ThiscompensatestheZeemansplit-\nting of sublattice B electrons which effectively leads to\ndecrease of the sBspin. The Hamiltonian of the FC\nspinel ferrimagnet is given by Eq.(1) with sBa varying\nparameter. The advantage of the method of calculation,\npresented above, is that we can use the same systems of\nequations for the three phases, 0 < T < T∗,T∗< T <\nTN,T > T N, and different values of the parameter sB.\nWe calculate the magnetization-temperature curves and\nthespecificheatasafunctionoftemperaturefor sA= 1.5\nand three different values of sB(sB= 0.7,sB= 0.4 and\nsB= 0.2), thus accounting for the increasing of the ap-\nplied, during preparation of FC spinel, magnetic field.\nThe resultant magnetization-temperature curves are\ndepicted in figure (3). The curve ”a” corresponds to\nZFC spinel (see figure (1)). The increasing of the ap-\nplied, during the preparation, magnetic field is mod-\neled by decreasing of sB. The curves ”b”, ”c” and ”d”/s48 /s53 /s49/s48 /s49/s53 /s50/s48 /s50/s53 /s51/s48/s48/s44/s48/s48/s44/s50/s48/s44/s52/s48/s44/s54/s48/s44/s56/s49/s44/s48/s49/s44/s50/s49/s44/s52/s83/s80/s79/s78/s84/s65/s78/s69/s79/s85/s83/s32/s32/s77 /s65/s71/s78/s69/s84/s73/s90/s65/s84/s73/s79/s78\n/s84/s47/s74/s97/s98/s99/s100\nFIG. 3: Color online) Spontaneous magnetization MA+MB\nas a function of the temperature in units of the exchange\nconstant T/Jfor ferrimagnetic spinel on bcc lattice with\nJA/J= 2,JB= 0.002,sA= 1.5 and :a)(black) sB= 1,\nb)(red)sB= 0.7, c)(blue) sB= 0.4 and d)(green) sB= 0.2.\nThe dash (magenta) line shows the spontaneous magnetiza-\ntionMAof sublattice AforsA= 1.5 andsB= 0.2.\n/s48 /s53 /s49/s48 /s49/s53 /s50/s48 /s50/s53 /s51/s48/s48/s50/s52/s54/s56/s49/s48/s49/s50/s49/s52/s67/s32/s115/s66\n/s61/s49\n/s32/s115/s66\n/s61/s48/s46/s55\n/s32/s115/s66\n/s61/s48/s46/s50/s115/s65\n/s61/s49/s46/s53\n/s84/s47/s74\nFIG. 4: (Color online) Specific heat Cvs temperature, in\nunits of the exchange constant T/J, forsA= 1.5 and different\nvalues of the effective spin sB: black curve sB= 1, red curve\nsB= 0.7 and blue curve sB= 0.2 .\nare magnetization-temperature curves for FC spinel fer-\nrimagnetics with sB= 0.7,sB= 0.4 andsB= 0.2. The\ncurve ”c” agrees well with the observed magnetization-\ntemperature curve of FC spinel MnV2O4with an exter-\nnal magnetic field as high as 300 O¨ e applied upon cool-\ning the material [4, 5]. The dash line shows the spon-\ntaneous magnetization MAof sublattice AforsA= 1.5\nandsB= 0.2. Comparing with line ”d”, which shows\nthe spontaneous magnetization MA+MBof the same\nsystem one can conclude that contribution of the sublat-\ntice B magnetization is small and Zeeman splitting, of\nsublattice B electrons, is approximately compensated.\nThe dependence of specific heat on temperature for\ndifferent values of sBis shown in figure (4). The curve\nwith higher maximumcorrespondsto ZFC spinel (see fig-\nure (2)) With increasing the applied, during the prepara-\ntion, magnetic field (with decreasing sB) the anomalous\ntemperature behavior of specific heat, at temperature of\npartialordertransition, remainswell defined but the pick5\ndecreases. The anomalous pick is well observed experi-\nmentally [3, 6, 9], and one can use it to determine the T∗\ntemperature of the partial order transition.\nIV. SUMMARY\nIn this paper is pointed out that a model which agrees\nwell with the observed magnetic and thermodynamic\nproperties of ZFC and FC spinel ferrimagnets is a two-\nsublattice Heisenberg model with spin- sAoperators at\nthe sublattice Asite, spin- sBoperators at the sublat-\nticeBsite, ferromagnetic intra-sublattice exchange and\nantiferromagnetic inter-sublattice exchange. The ap-\nplied magnetic field, along the sublattice A magnetiza-\ntion upon cooling the material, is accounted for varying\nonly one parameter sB.\nThe subtle point is that MnV2O4spinel hasan obvious\nanomalousmagnetic behavior,but the appearanceofthis\nanomaly is attributed to the strong orbital-spin coupling\n[4] which is not discussed in the model (1). The spinel\nMnV2O4is a two-sublattice ferrimagnet, with site Aoc-\ncupied by the Mn2+ion, which is in the 3 d5high-spin\nconfiguration with quenched orbital angular momentum,\nwhich can be regarded as a s= 5/2 spin. The B site is\noccupied by the V3+ion, which takes the 3 d2high-spin\nconfiguration in the triply degenerate t2gorbital and has\norbital degrees of freedom. Because of the strong spin-\norbitalinteractionit isconvenientto consider jjcoupling\nwithJA=SAandJB=LB+SB. The sublattice A\ntotal angular momentum is jA=sA= 5/2, while the\nsublattice Btotal angular momentum is jB=lB+sB,\nwithlB= 3, and sB= 1 [1]. Then the g-factor for\nthe sublattice AisgA= 2, and for the sublattice B\ngB=5\n4. The sublattice Amagnetic order is antiparallel\nto the sublattice Bone and the saturated magnetization\nisσ= 25\n2−5\n44 = 0, in agreement with the experimen-\ntal finding for ZFC spinel that the magnetization goes to\nzero when the temperature approaches zero. The Hamil-\ntonian of the system is\nH=−κA/summationdisplay\n≪ij≫AJA\ni·JA\nj−κB/summationdisplay\n≪ij≫BJB\ni·JB\nj\n+κ/summationdisplay\n/angbracketleftij/angbracketrightJA\ni·JB\nj (21)\nThe first two terms describe the ferromagnetic Heisen-\nberg intra-sublattice exchange κA>0,κB>0, while the\nthird term describes the inter-sublattice exchange which\nisantiferromagnetic κ >0. Theoperators JA\njandJB\njsat-\nisfy theSU(2) algebra, therefor we can use the Holstein-\nPrimakoff representation of the total angular momen-\ntum vectors JA\nj(a+\nj,aj)andJB\nj(b+\nj, bj), wherea+\nj, ajand\nb+\nj, bjare Bose fields. Farther on, we repeat the calcula-\ntions from sections II and III. The only difference is the\nexpression for the magnetization gAMA+gBMB. The\njjmodel shows that the anomalous magnetic and ther-\nmodynamic behavior of MnV2O4is a consequence of theferrimagnetic nature of the system.\nAppendix A: Spin-fermion model of spinel\nferrimagnet\nThe Hamiltonian of the spin-fermion model of ferri-\nmagnetic spinel defined on a body centered cubic lattice\nis\nH=−t/summationdisplay\n≪ij≫B/parenleftbig\nc+\niσcjσ+h.c./parenrightbig\n−µ/summationdisplay\ni∈Bni\n−JB1/summationdisplay\n≪ij≫BSB\ni·SB\nj+J/summationdisplay\n/angbracketleftij/angbracketrightSA\ni·SB\nj(A1)\n−JA/summationdisplay\n≪ij≫ASA\ni·SA\nj−H/summationdisplay\ni∈ASzA\ni−H/summationdisplay\ni∈BSzB\ni,\nwhereSνB\ni=1\n2/summationtext\nσσ′c+\niστν\nσσ′ciσ′, with the Pauli matrices\n(τx,τy,τz), is the spin of the itinerant electrons at the\nsublattice Bsite ,SA\niis the spin ofthe localizedelectrons\nat the sublattice Asite,µis the chemical potential, and\nni=c+\niσciσ. The sums are over all sites of a body cen-\nteredcubic lattice, ∝angbracketlefti,j∝angbracketrightdenotesthe sum overthe nearest\nneighbors, while ≪ij≫Aand≪ij≫Bare sums over\nall sites of sublattice AandBrespectively. The Heisen-\nberg term ( JA>0) describes ferromagnetic Heisenberg\nexchangebetweenlocalizedelectronsand J >0is the an-\ntiferromagnetic exchange constant between localized and\nitinerant electrons. H >0 is the Zeeman splitting en-\nergy due to the external magnetic field (magnetic field\nin units of energy). We represent the Fermi operators,\nthe spin of the itinerant electrons and the density oper-\natorsniσin terms of the Schwinger bosons ( ϕi,σ,ϕ+\ni,σ)\nand slave fermions ( hi,h+\ni,di,d+\ni). The Bose fields are\ndoublets ( σ= 1,2) without charge, while fermions are\nspinless with charges 1 ( di) and -1 ( hi):\nci↑=h+\niϕi1+ϕ+\ni2di, c i↓=h+\niϕi2−ϕ+\ni1di,\nni= 1−h+\nihi+d+\nidi, sν\ni=1\n2/summationdisplay\nσσ′ϕ+\niστν\nσσ′ϕiσ′,\nc+\ni↑ci↑c+\ni↓ci↓=d+\nidi (A2)\nϕ+\ni1ϕi1+ϕ+\ni2ϕi2+d+\nidi+h+\nihi= 1 (A3)\nTo solve the constraint (Eq.A3), one makes a change of\nvariables, introducing Bose doublets ζiσandζ+\niσ[21]\nζiσ=ϕiσ/parenleftbig\n1−h+\nihi−d+\nidi/parenrightbig−1\n2,\nζ+\niσ=ϕ+\niσ/parenleftbig\n1−h+\nihi−d+\nidi/parenrightbig−1\n2,(A4)\nwhere the new fields satisfy the constraint ζ+\niσζiσ= 1. In\nterms of the new fields the spin vectors of the itinerant\nelectrons have the form\nSνB\ni=1\n2/summationdisplay\nσσ′ζ+\niστν\nσσ′ζiσ′/bracketleftbig\n1−h+\nihi−d+\nidi/bracketrightbig\n(A5)6\nWhen, in the ground state, the lattice site is empty, the\noperator identity h+\nihi= 1 is true. When the lattice\nsite is doubly occupied, d+\nidi= 1. Hence, when the lat-\ntice site is empty or doubly occupied the spin on this\nsite is zero. When the lattice site is neither empty nor\ndoubly occupied ( h+\nihi=d+\nidi= 0), the spin equals\nsi= 1/2ni,where the unit vector\nnν\ni=/summationdisplay\nσσ′ζ+\niστν\nσσ′ζiσ′(n2\ni= 1) (A6)\nidentifies the local orientation of the spin of the itinerant\nelectron.\nThe part of Hamiltonian Eq.(A1) with itinerant\nfermions can be rewritten in terms of Bose fields Eq.(A4)\nand slave fermions\nHB=−t/summationdisplay\n≪ij≫B/bracketleftbig/parenleftbig\nd+\njdi−h+\njhi/parenrightbig\nζ+\niσζjσ\n+/parenleftbig\nd+\njh+\ni−d+\nih+\nj/parenrightbig\n(ζi1ζj2−ζi2ζj1)+h.c./bracketrightbig\n×/parenleftbig\n1−h+\nihi−d+\nidi/parenrightbig1\n2/parenleftbig\n1−h+\njhj−d+\njdj/parenrightbig1\n2\n−JB1/summationdisplay\n≪ij≫Bmimjni·nj\n+U/summationdisplay\ni∈Bd+\nidi−µ/summationdisplay\ni∈B/parenleftbig\n1−h+\nihi+d+\nidi/parenrightbig\n(A7)\n−H/summationdisplay\ni∈B1\n2nz\ni[1−h+\nihi−d+\nidi].\nwhere\nmi=1\n2[1−h+\nihi−d+\nidi]. (A8)\nThe mixed, spin-fermion term, adopts the form\nHAB=J/summationdisplay\n/angbracketleftij/angbracketrightSA\ni·njmj (A9)\nThe Hamiltonian (A1) can be rewritten in the form\nH=HA+HB+HAB(A10)\nwhereHAis the contribution of sublattice A spins SA\ni.\nAn important advantage of working with Schwinger\nbosons and slave fermions is the fact that Hubbard term\nis in a diagonal form. The fermion-fermion and fermion-\nboson interactions are included in the hopping term.\nOne treats them as a perturbation. To proceed we ap-\nproximate the hopping term of the Hamiltonian Eq.(A7)\nsetting/parenleftbig\n1−h+\nihi−d+\nidi/parenrightbig1\n2∼1 and keeping only the\nquadratic, with respect to fermions, terms. This means\nthat the averagingin the subspace of the fermions is per-\nformed in one fermion-loop approximation. Further, we\nrepresenttheresulting hBandhABHamiltonianasasum\nof two terms\nHf=Hf\n0+Hfb\nint, (A11)where\nHf\n0=−t/summationdisplay\n≪ij≫B/parenleftbig\nd+\njdi−h+\njhi+h.c./parenrightbig\n+U/summationdisplay\ni∈Bd+\nidi\n−µ/summationdisplay\ni∈B/parenleftbig\n1−h+\nihi+d+\nidi/parenrightbig\n(A12)\n+4sJ−H\n2/summationdisplay\ni∈B/parenleftbig\nh+\nihi+d+\nidi/parenrightbig\n,\nis the Hamiltonian of the free dandhfermions, and\nHfb\nint=−t/summationdisplay\n≪ij≫B/bracketleftbig/parenleftbig\nd+\njdi−h+\njhi/parenrightbig/parenleftbig\nζ+\niσζjσ−1/parenrightbig\n(A13)\n+/parenleftbig\nd+\njh+\ni−d+\nih+\nj/parenrightbig\n(ζi1ζj2−ζi2ζj1)+h.c./bracketrightbig\n−JB1/summationdisplay\n≪ij≫Bmimjni·nj\nis the Hamiltonian of boson-fermion interaction.\nThegroundstateofthe system, without accountingfor\nthe spin fluctuations, is determined by the free-fermion\nHamiltonian h0and is labeled by the density of electrons\nn= 1−< h+\nihi>+< d+\nidi> (A14)\n(see equation (A2)) and the ”effective spin” of the sub-\nlattice B electron\nsB=1\n2/parenleftbig\n1−< h+\nihi>−< d+\nidi>/parenrightbig\n.(A15)\nAt half-filling\n< h+\nihi>=< d+\nidi> . (A16)\nTo solve this equation one sets the chemical potential\nµ=U/2. Utilizing this representation of µwe calculate\nthe effective spin sBas a function of applied magnetic\nfieldhfor parameters 4 t/U= 2.2 and 4sAJ/U= 4. The\nresult is depicted in figure (5).\nLet us introduce the vector,\nMν\ni=sB/summationdisplay\nσσ′ζ+\niστν\nσσ′ζiσ′M2\ni= (sB)2.(A17)\nThen, the spin-vector of itinerant electrons Eq.(A5) can\nbe written in the form\nSB\ni=1\n2mMi/parenleftbig\n1−h+\nihi−d+\nidi/parenrightbig\n,(A18)\nwhere the vector Miidentifies the localorientationof the\nspin of the sublattice B itinerant electrons.\nThe Hamiltonian is quadratic with respect to the\nfermions di,d+\niandhi,h+\ni, and one can average in the\nsubspace of these fermions (to integrate them out in the\npath integral approach). As a result, accounting for the\ndefinition of sB(see Eq.A15), one obtains SBi=Miand\nan effective model for spin vectors SBiwith Hamiltonian\nHeff=−JB2/summationdisplay\n≪ij≫BSB\ni·SB\nj,(A19)7\n/s48/s44/s48 /s48/s44/s50 /s48/s44/s52 /s48/s44/s54 /s48/s44/s56 /s49/s44/s48/s48/s44/s49/s48/s44/s50/s48/s44/s51/s48/s44/s52/s48/s44/s53\n/s52/s116/s47/s85/s61/s50/s46/s50\n/s52/s115/s65\n/s74/s47/s85/s61/s52/s115/s66\n/s104\nFIG. 5: (Color online) Sublattice B effective spin sBas a\nfunctionofapplied magnetic field hfor parameters 4 t/U= 2.2\nand 4sAJ/U= 4.\nwhere the effective exchange constant JB2is calculated\nin the one loop approximation. The term with JB1ex-\nchange constant in equation (A7) and the mixed, spin-\nfermion term (A9), adopt the form\n−JB1/summationdisplay\n≪ij≫BSBi·SBj (A20)\nand\nJ/summationdisplay\n/angbracketleftij/angbracketrightSA\ni·SB\nj (A21)\nrespectively. Collecting all terms one obtains the Hamil-\ntonian of the FC ferrimagnetic spinel\nH=−JA/summationdisplay\n≪ij≫ASA\ni·SA\nj−JB/summationdisplay\n≪ij≫BSB\ni·SB\nj\n+J/summationdisplay\n/angbracketleftij/angbracketrightSA\ni·SB\nj,\nwhereJB=JB1+JB2andsBdepending on the field\napplied during preparation Fig.(5). After the process of\npreparation the external magnetic field is set equal to\nzero. For systems with sB= 1, discussed in the pa-\nper, one has to consider two-band model for sublattice\nB fermions. The result remains the same even for this\nmore complicate system: the effective spin sBdecreases\nwhen the applied, under the preparation, magnetic field\nincreases.\nAppendix B: Hartree-Fock approximation\nLet us consider a theory with Hamiltonian (1). We\nintroduce Holstein-Primakoff representation for the spinoperators\nSA+\nj=SA1\nj+iSA2\nj=/radicalBig\n2sA−a+\njajaj\nSA−\nj=SA1\nj−iSA2\nj=a+\nj/radicalBig\n2sA−a+\njaj(B1)\nSA3\nj=sA−a+\njaj\nwhen the sites jare from sublattice Aand\nSB+\nj=SB1\nj+iSB2\nj=−b+\nj/radicalBig\n2sB−b+\njbj\nSB−\nj=SB1\nj−iSB2\nj=−/radicalBig\n2sB−b+\njbjbj(B2)\nSB3\nj=−sB+b+\njbj\nwhen the sites jare from sublattice B. The operators\na+\nj, ajandb+\nj, bjsatisfythe Bosecommutationrelations.\nIn terms of the Bose operators and keeping only the\nquadratic and quartic terms, the effective Hamiltonian\nEq.(1) adopts the form\nH=H2+H4 (B3)\nwhere\nH2=sAJA/summationdisplay\n≪ij≫A/parenleftbig\na+\niai+a+\njaj−a+\njai−a+\niaj/parenrightbig\n+sBJB/summationdisplay\n≪ij≫B/parenleftbig\nb+\nibi+b+\njbj−b+\njbi−b+\nibj/parenrightbig\n(B4)\n+J/summationdisplay\n/angbracketleftij/angbracketright/bracketleftBig\nsAb+\njbj+sBa+\niai−√\nsAsB/parenleftbig\na+\nib+\nj+aibj/parenrightbig/bracketrightBig\nH4=1\n4JA/summationdisplay\n≪ij≫A/bracketleftbig\na+\nia+\nj(ai−aj)2+(a+\ni−a+\nj)2aiaj/bracketrightbig\n+1\n4JB/summationdisplay\n≪ij≫B/bracketleftbig\nb+\nib+\nj(bi−bj)2+(b+\ni−b+\nj)2bibj/bracketrightbig\n+1\n4J/summationdisplay\n/angbracketleftij/angbracketright/bracketleftBigg/radicalbigg\nsA\nsB/parenleftbig\naib+\njbjbj+a+\nib+\njb+\njbj/parenrightbig\n(B5)\n+/radicalbigg\nsB\nsA/parenleftbig\na+\niaiaibj+a+\nia+\niaib+\nj/parenrightbig\n−4a+\niaib+\njbj/bracketrightBigg\nThe next step is to represent the Hamiltonian in the\nHartree-Fock approximation (2,3) and\nHq=sAJAuA/summationdisplay\n≪ij≫A/parenleftbig\na+\niai+a+\njaj−a+\njai−a+\niaj/parenrightbig\n+sBJBuB/summationdisplay\n≪ij≫B/parenleftbig\nb+\nibi+b+\njbj−b+\njbi−b+\nibj/parenrightbig\n(B6)\n+Ju/summationdisplay\n/angbracketleftij/angbracketright/bracketleftBig\nsAb+\njbj+sBa+\niai−√\nsAsB/parenleftbig\na+\nib+\nj+aibj/parenrightbig/bracketrightBig\nIt is convenient to rewrite the Hamiltonian in momen-\ntum space representation Eq.(4) The two equivalent sub-\nlattices A and B of the bcc lattice are simple cubic lat-\ntices. The wave vector kruns over the reduced first Bril-\nlouin zone Brof a bcc lattice which is the first Brillouin8\nzone of a simple cubic lattice. The dispersions are given\nby equalities Eqs. (5)\nTo diagonalize the Hamiltonian one introduces new\nBose fields αk, α+\nk, βk, β+\nkby means of the transforma-\ntion (6) where the coefficients of the transformation uk\nandvkare real function of the wave vector k\nuk=/radicaltp/radicalvertex/radicalvertex/radicalvertex/radicalbt1\n2\nεa\nk+εb\nk/radicalBig\n(εa\nk+εb\nk)2−4γ2\nk+ 1\n\n(B7)\nvk=sign(γk)/radicaltp/radicalvertex/radicalvertex/radicalvertex/radicalbt1\n2\nεa\nk+εb\nk/radicalBig\n(εa\nk+εb\nk)2−4γ2\nk−1\n.\nThe transformed Hamiltonian adopts the form Eqs.(7)\nwith dispersionsEqs.(8) The free energy ofa system with\nHamiltonian HHF(7,8) is Eq.(10) The system of equa-\ntions for the Hartree-Fock parameters Eqs.(11), in terms\nof the Bose functions of the αandβexcitations, adopt\nthe form\nuA= 1−1\n3sA1\nN/summationdisplay\nk∈Brεk/bracketleftBig\nu2\nknα\nk+v2\nknβ\nk+v2\nk/bracketrightBig\nuB= 1−1\n3sB1\nN/summationdisplay\nk∈Brεk/bracketleftBig\nv2\nknα\nk+u2\nknβ\nk+v2\nk/bracketrightBig\nu= 1−1\nN/summationdisplay\nk∈Br/bracketleftbigg1\n2sA/parenleftBig\nu2\nknα\nk+v2\nknβ\nk+v2\nk/parenrightBig\n(B8)\n+1\n2sB/parenleftBig\nv2\nknα\nk+u2\nknβ\nk+v2\nk/parenrightBig\n−8Ju/parenleftBig\n1+nα\nk+nβ\nk/parenrightBig/parenleftBig\ncoskx\n2cosky\n2coskz\n2/parenrightBig2\n/radicalBig\n(εa\nk+εb\nk)2−4γ2\nk\n\nwherenα\nkandnβ\nkare the Bose functions of αandβex-\ncitations.\nAppendix C: Takahashi modified spin-wave theory\n[20]\nTo study the paramagnetic phase of the system we\nmakeuseofthe Takahashimodified spin-wavetheory[20]\nand introduce two parameters λAandλBto enforce the\nmagnetization on the two sublattices to be equal to zero.\nIt is convenientto representthe parameters λAandλBin\nthe form Eqs.(16). We find out these and Hartree-Fock\nparameters, as functions of temperature, solving the sys-\ntem of five equations, equations (B8) and the equations\nMA=MB= 0. The numerical calculations show thatabove N´ eel temperature µAµB>1 (blue line in Fig.(6)).\nWhen the temperature decreases the product µAµBde-\ncreases, remaining larger than one. The temperature at\nwhich the product becomes equal to one ( µAµB= 1) is\n/s48 /s53 /s49/s48 /s49/s53 /s50/s48 /s50/s53 /s51/s48 /s51/s53/s49/s50/s51/s52/s53/s54\n/s84/s47/s74/s32\n/s32\n/s32\nFIG. 6: (Color online) Parameters µA,µBandµAµBas a\nfunction of the temperature, in units of the exchange con-\nstantT/J, for ferrimagnet with sublattice A spin sA= 1.5\nand sublattice B spin sB= 1. The high temperature vertical\n(cyan) line corresponds to the N´ eel temperature of ferrima g-\nnet to paramagnet transition. The low temperature vertical\n(green) line corresponds to partial order transition tempe ra-\nture.\nthe N´ eel temperature, marked by vertical cyan line in\nFig.(6).\nAt low temperature µA= 1 and µB= 1 (λA=λB=\n0). The Hartree-Fock parameters are positive functions\nofT/J, solution of the system of equations (B8). Uti-\nlizing these functions, one can calculate the spontaneous\nmagnetizationon the twosublattices at low temperature.\nAt characteristic temperature T∗spontaneous magneti-\nzationon sublattice Bbecomes equalto zero, while spon-\ntaneous magnetization on sublattice Ais still nonzero\n(see Fig.1 in the paper).\nAboveT∗the spectrum contains long-range (magnon)\nexcitations. Thereupon, µAµB= 1 and one can use the\nrepresentation µB= 1/µA. Then,µAand Hartree-Fock\nparameters are solution of a system of four equations,\nequations (B8) and the equation MB= 0.\nThe functions µA(T/J),µB(T/J) and\nµA(T/J)µB(T/J) are depicted in figure (6) for a\nsystem with sA= 1.5,sB= 1,JA/J= 2 and\nJB/J= 0.002.\nFor the same system the Hartree-Fock parameters\nuA(T/J),uB(T/J)u(T/J) are depicted in figure (7).\n[1] K. Adachi, T. Suzuki, K. Kato, K. Osaka, M. Takata and\nT. Katsufuji, Phys. Rev. Lett. 95, 197202 (2005).[2] Zhaorong Yang, Shun Tan, Zhiwen Chen, and Yuheng9\n/s48 /s53 /s49/s48 /s49/s53 /s50/s48 /s50/s53 /s51/s48 /s51/s53/s48/s44/s48/s48/s44/s50/s48/s44/s52/s48/s44/s54/s48/s44/s56/s49/s44/s48/s49/s44/s50/s49/s44/s52/s49/s44/s54/s49/s44/s56/s50/s44/s48/s50/s44/s50\n/s84/s47/s74/s117\n/s117/s65\n/s117/s66/s72/s65/s82/s84/s82/s69/s69/s45/s70/s79/s67/s75/s32/s80/s65/s82/s65/s77 /s69/s84/s69/s82/s83\nFIG. 7: (Color online) Hartree-Fock parameters as a functio n\nof the temperature, in units of the exchange constant T/J, for\nferrimagnet with sublattice A spin sA= 1.5 and sublattice\nB spinsB= 1. The high temperature vertical (cyan) line\nmarks the N´ eel temperature of ferrimagnet to paramagnet\ntransition. The low temperature vertical (blue) line marks\nthe partial order transition temperature.\nZhang, Phys. Rev. B 62, 13872 (2000).\n[3] H. D. Zhou, J. Lu, and C. R. Wiebe, Phys. Rev. B 76,\n174403 (2007).\n[4] V. O. Garlea, R. Jin, D. Mandrus, B. Roessli, Q. Huang,\nM. Miller, A. J. Schultz, and S. E. Nagler, Phys. Rev.\nLett.100, 066404 (2008).\n[5] S-H. Baek, K-Y. Choi, A. P. Reyes, P. L. Kuhns, N.\nJ. Curro, V. Ramanchandran, N. S. Dalal, H. D. Zhou,\nand C. R. Wiebe, J. Phys.: Condens. Matter 20, 135218\n(2008).[6] Kim Myung-Whun, J. S. Kim, T. Katsufuji, and R. K.\nKremer, Phys. Rev. B 83, 024403 (20011).\n[7] A. Kiswandhi, J. S. Brooks, J. Lu, J. Whalen, T. Siegrist,\nand H. D. Zhou, Phys. Rev. B 84, 205138 (2011).\n[8] A. Kismarahardja, J. S. Brooks, A. Kiswandhi, K. Mat-\nsubayashi, R. Yamanaka, Y. Uwatoko, J. Whalen, T.\nSiegrist, and H. D. Zhou, Phys. Rev. Lett. 106, 056602\n(2011).\n[9] Q. Zhang, K. Singh, F. Guillou, C. Simon, Y. Breard,\nV. Caignaert, and V. Hardy, Phys. Rev. B 85, 054405\n(2012).\n[10] Y. Nii, H. Sagayama, T. Arima, S. Aoyagi, R. Sakai, S.\nMaki, E. Nishibori, H. Sawa, K. Sugimoto, H. Ohsumi,\nand M. Takata, Phys. Rev. B 86, 125142 (2012).\n[11] Z. H. Huang, X. Luo, S. Lin, Y. N. Huang, L. Hu, L.\nZhang, Y. P.Sun, Solid State Communications 159, 88\n(2013).\n[12] Z. H. Huang, X. Luo, L. Hu, S. G. Tan, Y. Liu, B. Yuan,\nJ. Chen, W. H. Song, and Y. P. Sun, Journal of Applied\nPhysics115, 034903 (2014).\n[13] Dina Tobia, Juli´ an Milano, Maria Teresa Causa and\nElin L. Winkler, J. Phys.: Condens. Matter 27, 016003\n(2015).\n[14] Vincent Hardy, Yohann Br´ eard, and Christine Martin,\nPhys. Rev. B 78, 024406 (2008).\n[15] R. Quartuand H. T. Diep, Phys.Rev. B 55, 2975 (1997).\n[16] J. R. Stewart, G. Ehlers, A. S. Wills, S. T. Bramwell,\nand J. S. Gardner, J. Phys.: Condens. Matter 16, L321\n(2004).\n[17] P. Azaria, H. T. Diep, and H. Giacomini, Phys. Rev.\nLett.59, 1629 (1987).\n[18] V. G. Vaks, A. I. Larkin, and Y. N. Ovchinnikov, JETP\nLetters. 22, 820 (1966).\n[19] H. T. Diep, Ed., Frustrated Spin Systems , World Scien-\ntific (2004)\n[20] M. Takahashi, Phys. Rev. Lett. 58, 168 (1987).\n[21] D. Schmeltzer, Phys. Rev. B 43, 8650 (1991).\n[*] Electronic address: naoum@phys.uni-sofia.bg"    },    {        "title": "1504.04958v1.Recent_Progress_in_the_thermodynamics_of_ferrotoroidic_materials.pdf",        "content": "Recent progress in the thermodynamics of ferrotoroidic materials\nAntoni Planes1, Teresa Cast\u0013 an1, Avadh Saxena2\n1Departament d'Estructura i Constituents de la Mat\u0012 eria, Facultat de F \u0013 \u0010sica, Universitat de Barcelona,\nDiagonal 647, 08028 Barcelona, Catalonia\n2Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA\nAbstract. Recent theoretical and experimental progress on the study of ferrotoroidic materials\nis reviewed. The basic \feld equations are \frst described and then the expressions for magnetic\ntoroidal moment and toroidization are derived. Relevant materials and experimental observation\nof magnetic toroidal moment and toroidal domains are summarized next. The thermodynamics\nof such magnetic materials is discussed in detail with examples of ferrorotoidic phase transition\nstudied using Landau modelling. Speci\fcally, an example of application of Landau modelling to\nthe study of toroidocaloric e\u000bect is also provided. Recent results of polar nanostructures with\nelectrical toroidal moment are \fnally reviewed.\n1. Introduction\nAccording to the common point of view, ferroelastic, ferroelectric and ferromagnetic materials\nconstitute the family of ferroic materials [1]. More recently ferrotoroidic materials have also\nbeen included in this family [2, 3]. Ferrotoroidics describe materials where toroidal moments\nshow cooperative long range order. Ferrotoroidic materials intrinsically belong to the class of\nmultiferroic materials [4]. Ferrotoroidicity spontaneously emerges at a phase transition from a\nparatoroidic to a ferrotoroidic phase in which both time and spatial inversion symmetries are\nsimultaneously broken [2, 3, 4, 5]. The order parameter for this transition is toroidization. Note\nthat in ferroelectrics only the spatial inversion symmetry is broken whereas in ferromagnets\nonly the time reversal symmetry is broken. In ferroelastics neither symmetry is broken; only\nthe rotational symmetry is broken [5].\nFerrotoroidal order can be understood in terms of an ordering of magnetic-vortex like struc-\ntures characterized by a toroidal (dipolar) moment. This order is also related to (asymmetric)\nmagnetoelectricity, i.e. \u000bij6=\u000bji[3]. In the present article we are mainly concerned with mag-\nnetic toroidal moments [2, 6, 7, 8, 9] as observed for instance, in LiCo(PO 4)3[10]. Electrical\ntoroidal moments can also exist in nanostructures such as polar dots [11, 12, 13] but not as a\nlong range ordered state in bulk materials as no symmetry is broken. In Section 7 we will sum-\nmarize recent results on nanoscale ferroelectric materials which exhibit electric toroidization as\na consequence of dipolar vortex formation.\nFigure 1 shows the symmetry properties of the four ferroic vector order parameters. Po-\nlarization is a polar vector, magnetization is an axial vector (it contains a sense of time), and\ntoroidization is an axio-polar vector. Note that strain is a (second rank polar) tensor order\nparameter. In addition, there are physical properties described by a second rank axial ten-\nsor such as magnetogyration [14, 15] likely present in the spin-half antiferromagnet potassium\nhyperoxide, KO 2, as well as in CdS, (Ga xIn1\u0000x)2Se3, Pb 5Ge3O11and Bi 12GeO 20.\nTherefore, the table can be conceivably generalized to include tensor ferroics . The two\nentries in the left column would be strain (second rank polar tensor) and magnetogyrationarXiv:1504.04958v1  [cond-mat.mtrl-sci]  20 Apr 2015(second rank axial tensor) but at present the tensor analogs of polarization and toroidization\nthat would complete the table have not been properly identi\fed. Note that in principle this\nidea could be generalized further to third (and higher) rank tensor ferroic properties. We intend\nto present these results elsewhere in the near future.\nAny ferroic order is usually accompanied by domain walls [1]. Indeed, ferrotoroidic domain\nwalls have been observed in LiCo(PO 4)3using nonlinear optics, i.e. second harmonic generation.\nLitvin has provided a symmetry based classi\fcation of such domains [16] as well as ferrotoroidal\ncrystals [17, 18]. Another material, BCG (Ba 2CoGe 2O7), also exhibits spontaneous toroidal mo-\nments [19]. Similarly MnTiO 3thin \flms show ferrotoroidic ordering [20]. Multiple ferrotoroidic\nphase transitions have been studied in Ni-Br and Ni-I boracites [9, 21]. Interestingly, some\nquasi-one dimensional materials such as pyroxenes [22] also exhibit ferrotoroidic behaviour.\nFig. 1: Symmetry properties of the four vectorial ferroic orders.\n2. Basic \feld equations\nWe will introduce here the toroidic moment and toroidization following ideas published by\nDubovik et al. in Ref. [8]. Assume distributions of charges \u001a(r) and currents j(r) localized\nin a given region of space. These distributions create electric and magnetic \felds that satify\nMaxwell equations. In the presence of matter, within the continuum dipolar approximation,\nthese equations are usually expressed as [23]:\nr\u0002H\u0000@D\n@t=j; (1)\nr\u0001D=\u001a; (2)\nr\u0002E+@B\n@t= 0; (3)\nr\u0001B= 0: (4)\nThe electric displacement, D, and the magnetic \feld, H, are de\fned as:\nD=\"0E+P; (5)\nH=1\n\u00160B\u0000M; (6)where PandMare the electric and magnetic polarizations of the medium, and \"0and\u00160\nthe electric permittivity and the magnetic permeability of free space. Electric polarization (or\nsimply polarization) and magnetic polarization (or magnetization) are introduced as volume\ndensities of the electric and magnetic moments which are de\fned from a multipole expansion\nfar from charge and current distribution of the electric scalar potential, ', and the magnetic\nvector potential, A, at dipolar order respectively [24]. These potentials are de\fned from eqs.\n(1) and (4) as:\nE=\u0000r'\u0000_A; (7)\nB=r\u0002A: (8)\nWe will see that the dipolar approximation is not su\u000ecient for some peculiar (electric and\nmagnetic) moment con\fgurations. In this case, higher order terms in the expansion must be\ntaken into account.\nNow let us assume a situation where the con\fguration of magnetic or electric moments is\nspiral-like. This is illustrated in Fig. 2. For this con\fguration, the magnetization (or polariza-\ntion) is along the z-axis, while the projection on the xy-plane, which has a circle-like con\fgura-\ntion, is zero. This circle-like con\fguration can be understood as being originated by a toroidal\ncon\fguration of loop-currents or electric dipoles in the magnetic and electric cases respectively.\nFor this kind of con\fgurations MorPalone do not provide enough information about the\nordering of magnetic/electric moments. Irene A. Beardsley [25] noticed that in this case an\narbitrary amount of a divergence-free magnetization/polarization distribution can be added\ntoMorPwithout a\u000becting the external \feld created by the distribution of magnetic/electric\nmoments. This divergence-free term can be written as the curl of some vector that characterizes\nthe circle-like con\fguration of magnetic/electric moments in the xy-plane. In the magnetic case,\nthis vector is the magnetic toroidization, r\u0002TM, while in the electric case it is the electric\ntoroidization,r\u0002TE. Note that the existence of magnetic toroidization implies that both,\ntime-reversal and spatial-inversion symmetries are broken. Therefore, magnetic toroidization\nis represented by an axiopolar (or time-odd polar) vector. In contrast, no broken symmetry is\nassociated with electric toroidization. As we will discuss later in Section 7, these toroidizations\nare related to the moment of the distributions of magnetic and electric moments respectively.\nIn practice, this means that the magnetization Mmust be replaced by M+r\u0002TM, while in\nthe electric case, the electric polarization Pmust be replaced by P+r\u0002TE.\nWhen electric and magnetic toroidizations are taken into account, the new macroscopic\nMaxwell equations take the same formal expressions as the standard ones after the following\nrede\fnition of the \felds.\nD!bD=\"0E+P+r\u0002TE=\"0E+bP; (9)\nH!bH=1\n\u00160B\u0000M\u0000r\u0002 TM=1\n\u00160B\u0000cM: (10)\nTherefore, the new macroscopic Maxwell equations read:\nr\u0002bH\u0000@bD\n@t=j; (11)\nr\u0001bD=\u001a; (12)\nr\u0002E+@B\n@t= 0; (13)\nr\u0001B= 0: (14)Fig. 2: Spiral-like con\fguration of moments along the surface of a cylinder.\nThe energy density accounting for the interaction of the generalized polarization and mag-\nnetization with external \felds are given by E\u0001bPandB\u0001cMrespectively. Hence, the cou-\npling energies of the \feld with electric and magnetic toroidizations areR\nE\u0001[r\u0002TE]d3randR\nB\u0001[r\u0002TM]d3rrespectively. These terms can be written in the form:\nZ\nE\u0001[r\u0002TE]d3r=Z\nr\u0001(TE\u0002E)d3r+Z\n(r\u0002E)\u0001TEd3r; (15)\nZ\nB\u0001[r\u0002TM]d3r=Z\nr\u0001(TM\u0002B)d3r+Z\n(r\u0002B)\u0001TMd3r; (16)\nwhere the \frst terms on the right-hand sides of both eq. (15) and eq. (16) are zero taking into\naccount the Gauss theorem. In the electric case, r\u0002E= 0, and thus this energy vanishes. In\nthe magnetic case, it is given byR\n(r\u0002B)\u0001TMd3r. Therefore, this shows that the conjugate\n\feld of the magnetic toroidization is r\u0002B.\nWe can now generalize the ideas discussed above and assume systems with spiral-like con\fg-\nurations of toroidal moments (either electric or magnetic) arising from toroidal con\fgurations\nof electric or magnetic moments. This kind of double-vortex con\fguration should be character-\nized by divergence-free vectors expressed as the curl of higher order toroidal moments. These\nmoments are denoted as hypertoroidal moments [26]. In the case of magnetism, for instance,\nthis means that in the macroscopic Maxwell equations the toroidization TM, should be replaced\nby:\nTM!TM+r\u0002TM\n(2); (17)\nwhere TM=TM\n(1)is the magnetic \frst-order toroidization and TM\n(2)is the magnetic second-order\ntoroidization (or hypertoroidization). Hence, magnetization should be replaced by:\nM!cM(2)=M+r\u0002TM\n(1)+r\u0002 (r\u0002TM\n(2)): (18)\nOf course this idea can be formally generalized to any order by de\fning higher order hyper-\ntoroidal moments (see Fig. 3). At order nwe will have:\ncM(n)=M+r\u0002TM\n(1)+r\u0002r\u0002 TM\n(2)+:::+r\u0002::::\u0002r\u0002 TM\n(n): (19)Indeed, one can proceed similarly in the electric case. Therefore, Maxwell equations at the nth\norder, similar to equations (11-14), can be established by de\fning the following \felds:\nbD(n)=\"0E+bP(n); (20)\nbH(n)=1\n\u00160B\u0000cM(n): (21)\nWith similar arguments as those given above, it is easy to show that the \feld conjugated\nto thenth order magnetic hypertoroidization is, r\u0002::::\u0002r\u0002 B.\nFig. 3: Magnetic moment, toroidal moment and the generation of successive hypertoroidal\nmoments.\n3. The magnetic toroidal moment and toroidization\nSimilar to polarization and magnetization, electric and magnetic toroidizations are de\fned in\nthe continuum approximation as volume densities of electric and magnetic toroidal moments\nrespectively. Since the symmetries associated with electric toroidization are trivial (no change\nof sign is expected either under spatial inversion or under time reversal) no phase transition\nto an electric toroidal phase should be envisaged. Actually, this is consistent with the fact\nthat toroidal moment associated with electric moment vorticity is not expected to occur in the\nthermodynamic limit [27]. From the discussion in the preceding section, it seems intuitively\nreasonable to foresee that the toroidal moment should be related to the moment of the dis-\ntribution of magnetic moments. This is what we will discuss in the rest of this section where\nwe will introduce the toroidal moment based on the multipolar expansion beyond the dipolar\napproximation. We will also introduce a second de\fnition based on symmetry considerations\nwhich is of interest from a more macroscopic thermodynamic point of view.In the former case we consider a \fnite distribution of steady currents J(r). The vector\npotential of this distribution is given by\nA(R) =\u00160\n4\u0019Z\nVJ(r)\njR\u0000rjdv; (22)\nwhere Ris the vector position of a point P,rthe vector position of the volume element dvand\nVthe volume of the distribution, and the Coulomb gauge ( r\u0001A= 0) has been assumed. The\nmultipole expansion of A(R) (about r= 0) takes the form [24],\nA(R) =\u00160\n4\u00191X\nn=0(\u00001)n\nn!Z\nVJ(r)[r\u0001r]n\u00121\nR\u0013\ndv: (23)\nIt is easy to see that the zeroth-order term vanishes for a steady current distribution for\nwhich the continuity equation yields r\u0001J= 0. The \frst order term in the expansion is the\ndipolar term that can be expressed as,\nA(1)=\u0000m\u0002r1\nR=m\u0002R\nR3; (24)\nwhere mis the magnetic dipolar moment de\fned as,\nm=1\n2Z\nV(r\u0002J)dv: (25)\nThe next term can be expressed as the sum of magnetic quadrupolar and toroidal contributions.\nThe quadrupolar part is given by,\n(Aquad)(2)\ni=\u0000\"ijkqklrirl1\nR(26)\nwhere\"ijkis the Levi-Civita symbol and qklis the magnetic quadrupolar moment given by,\nqij=2\n3Z\nV(r\u0002J)irjdv; (27)\nwhich is a traceless symmetric tensor. The toroidal term is given by,\nA(2)\ntor=r(t\u0001r)1\nR+t\u000e(R); (28)\nwhere tis the toroidal moment that can be expressed as\nt=1\n4Z\nvr\u0002[r\u0002J(r)]dv: (29)\nThis pseudovector represents the dual antisymmetric part of the complete tensor which appears\nin the second order term of the multipole expansion. De\fning m(r) =1\n2[r\u0002J(r)] as the\ndistribution of magnetic moments, the toroidal moment can be written as,\nt=1\n2Z\nv[r\u0002m(r)]dv; (30)which indicates that the toroidal moment can be understood as the moment of the distribution\nof magnetic moments (see Fig. 3b).\nFor a discrete distribution of Npoint charges q\u000bof massm\u000blocalized at positions r\u000bwith\nvelocities u\u000b, the current density can be written as\nJ(r) =NX\n\u000b=1q\u000bu\u000b\u000e(r\u0000r\u000b): (31)\nThe magnetic moment then takes the form:\nm=1\n2NX\n\u000b=1q\u000br\u000b\u0002u\u000b;=NX\n\u000b=1m\u000b (32)\nwhere m\u000bis the magnetic moment of charge \u000b. Similarly, the toroidal moment of interest here\ncan be written as,\nt=1\n4NX\n\u000b=1q\u000b(r\u000b\u0002[r\u000b\u0002u\u000b]) =1\n2NX\n\u000b=1[r\u000b\u0002m\u000b]: (33)\nFor a system consisting of a distribution of Nspins s\u000blocalized at positions r\u000b,m\u000b=g\u00160s\u000b,\nwheregis the gyromagnetic ratio and \u0016Bthe Bohr magneton. Therefore, the corresponding\ntoroidal moment is given by\nt\u000b=1\n2g\u00160NX\n\u000b=1(r\u000b\u0002s\u000b): (34)\nIt is worth noting that treatment similar to the one discussed above can be developed from\nthe multipolar expansion of the electric scalar potential \u001e. In particular, from the \frst order\nterm the electric dipolar moment can be de\fned as\np=Z\nVr\u001a(r)dv: (35)\nOnce the toroidal moment is introduced, magnetic toroidization, hereafter simply denoted\nas toroidization, T, is de\fned as the volume density of toroidal moments. That is T=dt=dv.\nWe have already seen that its corresponding conjugated \feld is r\u0002Band hence, the energy\ndensity of a distribution of toroidal moments characterized by a toroidization Tis given by\nE=\u0000T\u0001(r\u0002B). Therefore, a net toroidization might be induced by means of a current\ndensity J=r\u0002B. Schmid [2] noticed that reversing toroidal dipoles by means of such a\n\feld in order to modify toroidization appears unfeasible since this would require the action of\ncoherent circular currents of very small size (comparable to the unit cell of the crystal).\nThe observation of toroidization in the absence of applied \felds indicates the existence of\nlong range order associated with toroidal moments. This long range order is usually denoted as\nferrotoroidic order and should be related to some kind of coupling between toroidal moments.\nTaking into account the basic symmetries of the toroidal moment, the occurrence of ferrotoroidic\norder supposes the simultaneous breaking of spatial inversion and time reversal symmetries.\nMaterials with toroidal moments are expected to intrinsically display magnetoelectric cou-\npling. In these systems, an applied magnetic \feld breaks inversion symmetry and thus induces\npolarization. On its turn, an applied electric \feld breaks time reversal symmetry and inducesmagnetization. Therefore, we expect that these materials respond to applied electric and mag-\nnetic \felds according to the following equations,\nP=\u001feE+\u000bTB; (36)\nM=\u000bTE+\u001fmB; (37)\nwhere\u001feand\u001fmare respectively, electric and magnetic susceptibility tensors, and \u000bTis the\nmagnetoelectric tensor (all are rank-2 tensors). From a thermodynamic point of view, if the\nfree energy of the system is F, these polarizations and magnetizations should be expressed as\n\u0000@F=@Eand\u0000@F=@B, respectively. Therefore, we expect that the free energy of a magne-\ntoelectric term is of the type Fm\u0000e=\u0000E\u000bTB(or\u0000\u000bT\nijEiBj, in coordinate notation). The\ndecomposition of this magnetoelectric term into pseudoscalar, vector, and symmetric traceless\nterms enables one to express Fm\u0000ein the form (see Ref. [3]),\nFm\u0000e\u0018\u0000E\u0001B\u0000T0\u0001[E\u0002B]\u0000Qij[EiBj+EjBi]; (38)\nwhere T0is a vector with the same symmetry properties as toroidal moment and toroidization.\nIdentifying this vector with toroidization Tsupposes that its conjugated \feld is G=E\u0002B. This\nassumption is in agreement with recent experiments that showed that toroiodal moments can\nbe controlled by this \feld [28]. Therefore, polarization, Pt, and magnetization, Mt, intrinsically\nassociated with the energy term \u0000G\u0001T, induced, respectively, under application of electric and\nmagnetic \felds, can be expressed as\nPt=\u0000@T\u0001[E\u0002B]\n@E=B\u0002T; (39)\nMt=\u0000@T\u0001[E\u0002B]\n@B=T\u0002E; (40)\nwhere we have taken into account that T\u0001[E\u0002B] =B\u0001[T\u0002E] =E\u0001[B\u0002T].\nIn the far-\feld approximation, from multipolar expansions of electric (scalar) and vector\npotentials, the toroidal \feld Gcan be expressed as,\nG=E\u0002B=A(p\u0002m) +B(p\u0002r) +C(r\u0002m); (41)\nwhere, pandmare electric and magnetic dipole moments, and the coe\u000ecients A,B, andC\nare coe\u000ecients that decay with distance rasr\u00006,r\u00007andr\u00007respectively. Taking into account\neq. (41), it is worth pointing out that if pandmare parallel, then G= 0 as expected. On the\nother hand, Ghas maximum strength when pandmare perpendicular.\nTaking Gas the \feld conjugated to toroidization, suggests the following alternative de\fni-\ntion of the toroidal moment:\nt=\u00160\n4\u0019(p\u0002m): (42)\nThis de\fnition neglects residual terms in eq. (41) associated with the magnetic and electric\nmoments. The choice is supported by the fact that these terms decay (with distance) faster\nthan the magneto-toroidal one.\nIt is worth noticing that this de\fnition of the toroidal moment is not strictly equivalent to\nthe de\fnition in eq. (29) resulting from the second order term in the multipole expansion of the\nvector potential. Nevertheless, it is, in fact, expected to provide a good measure of the toroidal\nmoment in systems which are simultaneously ferroelectric and ferromagnetic [29]. In thesesystems the coupling of t(or the toroidization obtained as the volume density of this toroidal\nmoment) to Gleads to a magnetoelectric response similar to that of magnetic ferrotoroidics [3].\nIn general, however, a non-zero toroidal moment should be possible even in antiferroelectric and\nantiferromagnetic systems. Indeed, resonant x-ray di\u000braction observations of orbital currents\nin CuO provide direct evidence of antiferrotoroidic ordering [30]. Actually, these situations can\nonly be considered when the standard de\fnition (arising from the multipole expansion) of the\ntoroidal moment is taken into account. Note that a multipole expansion including the toroidal\nmoment has been considered in [31].\n4. Materials and relevant experimental results\nAt present direct measurements of toroidization or toroidal moment seem very di\u000ecult. Present\nexperimental techniques can only detect magnetization and magnetic moment, for instance from\npolarized neutron scattering or Lorentz microscopy. In principle, these techniques should be able\nto detect speci\fc arrangements of magnetic moments characterized by toroidal moments that\nmight order to yield net toroidization and thus, ferrotoroidal order. In practice, this appears to\nbe unfeasible.\nIndirectly ferrotoroidal order can be inferred from an asymmetric magnetoelectric response.\nTherefore, this needs measurement and analysis of the appropiate magnetoelectric tensor com-\nponents. Sannikov [32] has argued that observation of \u000bij6=\u000bjiis an indication of possible\nferrotoroidic order. It is however important to take into account that this condition is not suf-\n\fcient to justify the occurrence of toroidization. Asymmetric behaviour of the magnetoelectric\ntensor has been reported for some boracites (G 2phase of Co-I and Ni-Cl boracites). It has been\nreported also for some oxides such as Ga 2\u0000xFexO3and Cr 2O3[33, 34].\nVisualization of ferrotoroidal order requires an experimental technique that is sensitive\nto both space inversion and time reversal broken symmetries which is the inherent feature\nassociated with ferrotoroidal order. As shown by Van Aken and co-authors [10] non-linear\noptics o\u000bers this possibility. These authors used optical second harmonic generation (SHG) to\nresolve ferrotoroidal domains in LiCoPO 4. Similar experiments were already carried out some\nyears before [35, 36] but were much less conclusive in relation to the existence of ferrotoroidal\ndomains. In this technique, electromagnetic light \feld E(!) of given frequency is incident on\na crystal and induces a polarization at double the frequency which acts as a wave source.\nThe symmetry a\u000bects the corresponding susceptibility. This means that the second harmonic\ngeneration light from domains with opposite order should have a phase shift of 180\u000e.\nLiCoPO 4crystallizes in the orthorhombic Pnma olivine structure [37, 38]. It displays unique\nproperties including large linear magnetoelectric e\u000bect and large Li-ionic conductivity. Co2+\nions belonging to (100) Co-O layers carry the magnetic moments that are strongly coupled by\nsuperexchange Co-O-Co interactions. Layers, however, are only weakly coupled by higher order\ninteractions. Thus, the system behaves as a magnetic 2- dsystem to a very good approximation.\nAntiferromagnetic order in the material occurs below a N\u0013 eel temperature TN= 21.4 K. Due\nto large magnetocrystalline anisotropy the magnetic moments are con\fned to directions lying\nwithinb-cplanes, approximately 4.6\u000eaway from the baxis. Actually, the Co magnetic moments\nare not completely compensated, and the system shows a small net magnetic moment which, in\nfact, is not consistent with the orthorhombic symmetry and can only be understood assuming\na small monoclinic distortion. Interestingly, the monoclinic symmetry allows for a non-zero\ndielectric polarization and a non-zero toroidal moment (along the pseudo-orthorhombic a-axis)\nto occur.Van Aken et al. SHG experiments [10] detected four di\u000berent domain states. It was shown\nlater from symmetry considerations [39] that the four domains are equivalent with di\u000berent\norientations of the net magnetic moment. Thus they carry toroidal moments with signs and\ndirections mutually coupled. The fact that the SHG signal intensity is observed to disappear\nprecisely at the N\u0013 eel temperature, corroborates the coupling between magnetic and toroidal\norder parameters.\nIn addition to Ba 2CoGe 2O7[19] and MnTiO 3thin \flms [20] toroidal moments have been\nconsidered in BiFeO 3and related multiferroics [40, 41, 42]. Another candidate material is the\nmagnetoelectric MnPS 3as indicated by neutron polarimetry [43]. Based on an initio calculations\nthe olivine Li 4MnFeCoNiP 4O16is possibly a ferrotoroidic material [44]. Note that apart from\nquasi-one dimensional materials called pyroxenes [22] the toroidal moment in the molecular\ncontext is also of interest, e.g. in dysprosium triangle based systems [45]. In a related context\na physical realization of toroidal order is an interacting system of disks with a triangle of spins\non each disk [46].\nIt is worth noting that the existence of a true long range ordered ferrotoroidic phase has only\nbeen established in a su\u000eciently reliable way in very few cases and, perhaps the clearer evidence\nhas been provided by Van Aken et al. SHG results [10]. In other cases, only indirect results\nsuggest the existence of such a phase. The fact that interaction between toroidal moments is very\nweak as indicated by the short range dipolar interaction (see eq. (41)), suggests that any small\namount of disorder in the material is enough to yield a toroidal glassy state, which represents\na frozen state with local order only [47]. The existence of toroidal glass in Ni 0:4Mn 0:6TiO 3\nhas been foreseen from the behaviour of the magnetoelectric response which was observed to\nstrongly depend on cooling history [48]. This is indeed a very interesting result suggesting that\nmaterials which are candidates to display ferrotoroidal order should also be analysed within\nthis point of view. In fact, possible observation of toroidal glass completes the quartet of ferroic\nglasses, namely spin glass, relaxor ferroelectrics and strain glass [49].\n5. Thermodynamics\nWe consider a macroscopic body where the vector ferroic properties, namely polarization, P,\nmagnetization, M, and toroidization, T, coexist. Only part of the polarization and magnetiza-\ntion will be assumed to be intrinsic, thus originating from preexisting electric and magnetic mo-\nments. The remaining part will arise from the toroidization originating from magnetic toroidal\nmomemts in the presence of external magnetic and electric \felds respectively. That is,\nP=Pi+Pt; (43)\nM=Mi+Mt: (44)\nFor this kind of closed systems, the fundamental thermodynamic equation reads\ndU=\u001cdS+E\u0001dP+B\u0001dM; (45)\nwhereUis the internal energy density, Sthe entropy density and \u001cthe temperature.\nTaking into account eq. (39), the term E\u0001dPcan be expressed as,\nE\u0001dP=E\u0001dPi+E\u0001dPt=E\u0001dPi+G\u0001dT+T\u0001[E\u0002dB]: (46)\nSimilarly, using eq. (40), the term B\u0001dMcan be expressed as,\nB\u0001dM=B\u0001dMi+B\u0001dMt=B\u0001dMi+G\u0001dT+T\u0001[dE\u0002B]: (47)Therefore,\ndU=\u001cdS+E\u0001dPi+B\u0001dMi+G\u0001dT+d(G\u0001T): (48)\nHelmholtz,F, and Gibbs,G, free energies are de\fned as follows,\nF=U\u0000\u001cS (49)\nG=F\u0000E\u0001P\u0000B\u0001M=F\u0000E\u0001Pi\u0000B\u0001Mi\u00002G\u0001T: (50)\nTheir di\u000berential expressions are,\ndF=\u0000Sd\u001c+E\u0001dP+B\u0001dM; (51)\ndG=\u0000Sd\u001c\u0000P\u0001dE\u0000M\u0001dB; (52)\nwhich can be alternatively expressed as,\ndF=\u0000Sd\u001c+E\u0001dPi+B\u0001dMi+G\u0001dT+d(G\u0001T); (53)\ndG=\u0000Sd\u001c\u0000Pi\u0001dE\u0000Mi\u0001dB\u0000T\u0001dG: (54)\nNote that this expression suggests that we can assume that the three ferroic properties, po-\nlarization, magnetization, and toroidization can be assumed as independent (vector) quantities\nthermodynamically conjugated to the electric, magnetic and toroidal \felds, respectively.\nThe response of the system to applied electric and magnetic \felds is given by the generalized\nsusceptibility,\n\u0018=\u0012@2G\n@E2@2G\n@B@E\n@2G\n@E@B@2G\n@B2\u0013\n=\u0000\u0012@P\n@E@P\n@B@M\n@E@M\n@B\u0013\n=\u0000\u0012\u001fe\u000b\n\u000bT\u001fm\u0013\n: (55)\nDiagonal terms, \u001feand\u001fm, de\fne electric and magnetic susceptibilities. These susceptibilities\nhave two contributions. The intrinsic contribution, given by \u001fei=@Pi=@E(=\u0000@2G=@E2),\nand\u001fmi=@Mi=@B(=\u0000@2G=@B2), and the toroidal contributions arising from toroidization.\nThese last contributions are given by,\n\u001fet=@Pt\n@E=@B\u0002T\n@E=B\u0002@T\n@E; (56)\n\u001fmt=@Mt\n@B=@T\u0002E\n@B=@T\n@B\u0002E: (57)\nA toroidal susceptibility can also be de\fned as,\n\u001fT=@T=@G=\u0000@2G=@G2: (58)\nNeglecting the intrinsic contributions to the polarization and magnetization, this toroidal sus-\nceptibility can be expressed as,\n\u001fT=\"\nE\u00021\n@T\n@B\u0002E\u00001\n@T\n@E\u0002B\u0002B#\u00001\n=\u0014\nE\u00021\n\u001fmt+1\n\u001fet\u0002B\u0015\u00001\n; (59)\nwhich shows that it is related to \u001fetand\u001fmt.\nCross terms de\fne the magnetoelectric coe\u000ecients. Maxwell relations require that second\nderivatives ofGare independent of the order in which they are performed. Therefore, this yields\n\u000bT=\u000b: (60)Assuming that the whole magnetoelectric interplay arises from the existence of toroidization,\nthe magnetoelectric coe\u000ecient is given by,\n\u000b=@Pt\n@B=@T\u0002B\n@B=@T\n@B\u0002B+T\u0002I; (61)\nand\n\u000bT=@Mt\n@E=@E\u0002T\n@E=E\u0002@T\n@E+I\u0002T; (62)\nwhere Iis the identity tensor. Notice that thermodynamic stability requires that \u0018is positive-\nde\fnite. This implies that both \u001feand\u001fmmust be positive-de\fnite and, \u001fe\u001fm\u0015\u000bT\u000b.\nThermal response is determined by the second order derivatives of Ginvolving temperature.\nOn the one hand, the heat capacity Cis given by\n@2G\n@\u001c2=C\n\u001c: (63)\nTaking into account Maxwell relations, the derivatives involving temperature and \felds satisfy,\n@2G\n@\u001c@E=@2G\n@E@\u001c)@S\n@E=@P\n@\u001c; (64)\nand\n@2G\n@\u001c@B=@2G\n@B@\u001c)@S\n@B=@M\n@\u001c: (65)\nIt can also be obtained that\n@2G\n@\u001c@G=@2G\n@G@\u001c)@S\n@G=@T\n@\u001c: (66)\nThese expressions determine the cross-response to electric or magnetic \feld and temperature.\nThey are adequate for the study of thermal response of the materials to applied external \felds\nwhich are commonly denoted as caloric e\u000bects. These e\u000bects are quanti\fed by the entropy\nchange that occurs by isothermally applying or removing a given \feld, and the temperature\nchange that results when the same \feld is applied or removed adiabatically. From a practical\npoint of view, materials displaying large caloric e\u000bects are nowadays of great interest thanks\nto their potential use in energy harvesting, and particularly, in refrigeration applications [50].\nIn general in ferroic and multiferroic materials, large caloric e\u000bects are expected in the vicinity\nof phase transitions to ferroic and multiferroic phases due to the expected strong temperature\ndependence of thermodynamic properties [51]. In the case of toroidal materials, caloric e\u000bects\nhave been analyzed from a theoretical perspective in Ref. [52]. The entropy change induced\nby application of an electric \feld, (0 !E), which quanti\fes the electrocaloric e\u000bect, can be\nobtained from integration of eq. (64) as,\n\u0001S(\u001c;0!E) =EZ\n0@P\n@\u001c\u0001dE: (67)\nSimilarly the entropy change induced by application of a magnetic \feld, (0 !B), which\nquanti\fes the magnetocaloric e\u000bect, can be obtained from integration of eq. (65) as,\n\u0001S(\u001c;0!B) =BZ\n0@M\n@\u001c\u0001dB: (68)Taking into account eqs. (43) and (44), the preceding entropy changes characterizing elec-\ntrocaloric and magnetocaloric e\u000bects, can be, respectively, decomposed into two terms asso-\nciated with intrinsic contributions and contributions arising from the toroidal moment. The\nintrinsic electro- and magnetocaloric terms are respectively,\n\u0001Si(\u001c;0!E) =EZ\n0@Pi\n@\u001c\u0001dE; (69)\n\u0001Si(\u001c;0!B) =BZ\n0@Mi\n@\u001c\u0001dB: (70)\nThe contributions arising from the toroidal moment can be written in the form,\n\u0001St(\u001c;0!E) =EZ\n0@Pt\n@\u001c\u0001dE=EZ\n0\u0012\nB\u0002@T\n@\u001c\u0013\n\u0001dE; (71)\n\u0001St(\u001c;0!B) =BZ\n0@Mt\n@\u001c\u0001dB=BZ\n0\u0012@T\n@\u001c\u0002E\u0013\n\u0001dB: (72)\nA change of entropy can be isothermally induced by application of a toroidal \feld G=E\u0002B.\nThis entropy change characterizes the toroidocaloric e\u000bect, and when taken into account with\neq. (66), it can simply be expressed as,\n\u0001S(\u001c;0!G) =GZ\n0@T\n@\u001c\u0001dG=EZ\n0\u0012\nB\u0002@T\n@\u001c\u0013\n\u0001dE+BZ\n0\u0012@T\n@\u001c\u0002E\u0013\n\u0001dB\n= \u0001St(\u001c;0!E) + \u0001St(\u001c;0!B); (73)\nwhich shows that the toroidocaloric entropy change is simply the sum of the electrocaloric and\nmagnetocaloric contributions associated with the toroidal moment as expected.\nSimilar expressions can be written for electrically and magnetically induced adiabatic tem-\nperature changes. The corresponding total change can be obtained by taking into account that\nfrom eqs. (63), (64) and (65), the constant entropy condition (adiabaticity in thermodynamic\nequilibrium) can be expressed as,\nC\n\u001cd\u001c+@P\n@\u001c\u0001dE+@M\n@\u001c\u0001dB= 0: (74)\nTherefore, the adiabatic temperature change induced by application of an electric \feld is given\nas,\n\u0001\u001c(S;0!E) =EZ\n0\u001c\nC@P\n@\u001c\u0001dE; (75)\nand the adiabatic temperature change induced by application of a magnetic \feld as,\n\u0001\u001c(S;0!B) =BZ\n0\u001c\nC@M\n@\u001c\u0001dB: (76)On its turn, the adiabatic temperature change induced by application of a toroidal \feld is given\nby,\n\u0001\u001c(S;0!G) =GZ\n0\u001c\nC@T\n@\u001c\u0001dT=EZ\n0\u001c\nC\u0012\nB\u0002@T\n@\u001c\u0013\n\u0001dE+BZ\n0\u001c\nC\u0012@T\n@\u001c\u0002E\u0013\n\u0001dB; (77)\nwhere the last two terms in the right-hand side correspond to the sum of electrocaloric and\nmagnetocaloric contributions associated with the toroidal moment. That is,\n\u0001\u001c(S;0!G) = \u0001\u001ct(S;0!E) + \u0001\u001ct(S;0!B): (78)\nIt is worth noting that both \u0001 S(\u001c;0!G) and \u0001\u001c(S;0!G) vanish if either EorBis\nzero or if they are parallel. For the sake of simplicity let us consider that E= (E;0;0) and\nB= (0;B;0). In this case, G= (0;0;EB) and assuming electric and magnetic isotropy,\nP= (P;0;0),M= (0;M;0) and T= (0;0;T), and eqs. (73) and (77) are simply expressed as\n\u0001S(\u001c;0!EB) =EBZ\n0@T\n@\u001cd(EB) =BEZ\n0@T\n@\u001cdE+EBZ\n0@T\n@\u001cdB; (79)\nand\n\u0001\u001c(S;0!EB) =EBZ\n0\u001c\nC@T\n@\u001cd(EB) =BEZ\n0\u001c\nC@T\n@\u001cdE+EBZ\n0\u001c\nC@T\n@\u001cdB; (80)\nrespectively.\n6. Landau and Ginzburg-Landau modelling and domains\nPhase transitons in ferroic and multiferroic materials are associated, as we have discussed\nabove, with some symmetry change. This change is captured by an order parameter which\nis zero at temperatures above the transition and non-zero below it. Landau and Ginzburg-\nLandau theories provide reliable expressions of the free energy of the materials in the region\nof the transition in homogeneous and non-homogeneous cases, respectively. The approach is\nphenomenological in nature and its combination with the thermodynamics formalism provides\na powerful method to study macroscopic and mesoscopic behaviour of ferroic and multiferroic\nmaterials. This approach enables one to relate measurable quantities to the input parameters of\nthe theories that can be determined either from experiments or from \frst-principle calculations.\nIn Landau theory the free energy is expressed as a series expansion of the order parameter. As\nthis free energy must be invariant under the symmetry operations of the system, only those\nterms allowed by symmetry are included in the series expansion.\nIn ferrotoroidic materials toroidization is the primary order parameter but magnetization\nand polarization must also be included in the free energy. So far, few Landau models have\nbeen proposed to account for ferrotoroidal transition in speci\fc materials. Sannikov [21] al-\nready proposed a model to account for the anomalous behaviour of the component \u000b32of the\nmagnetoelectric tensor near the cubic (43 m10) to the orthorrombic ( m0m20) phase transition in\nboracites.\nBased on a group theoretic analysis Sannikov has provided a free energy for ferrotoroidic\nphase transitions in boracites [21, 32]. It consists of a usual double well F(T) =aT2+bT4in thetoroidization Tand harmonic terms cP2anddM2in polarization and magnetization. In addi-\ntion, it has symmetry allowed coupling terms between various components of the three dipolar\nvectors, namely of the form PiT2\nj,MiT3\njand the trilinear coupling PiMjTk. The free energy is\nthen analysed to obtain a phase diagram in terms of the free energy coe\u000ecients indicating the\nvarious ferrotoroidic phase transitions. Note that Litvin has extended the symmetry analysis\nfor ferroics to ferrotoroidic materials including the possible toroidic domains and domain walls\n[16, 17, 18]. This analysis is very helpful in obtaining the free energy for ferrotoroidic phase\ntransitions for any crystal symmetry.\nEderer and Spaldin, taking into account that the symmetries which allow for a macroscopic\ntoroidal moment are the same that give rise to an antisymmetric component of the linear\nmagnetoelectric e\u000bect tensor, proposed the simplest possible Landau free energy that describes\na phase transition between a paratoroidic and a ferrotoroidic phase that includes the energies\nassociated with the e\u000bect of electric and magnetic \feld on polarization and magnetization, and\ntheir coupling to toroidization [53]. It has the following form,\nF(T;T;P;M) =1\n2A0(\u001c\u0000\u001c0\nc)T2+1\n4CT4+1\n2\u001f\u00001\npP2+1\n2\u001f\u00001\nmM2\n\u0000B\u0001M\u0000E\u0001P+\u0014T\u0001(P\u0002M); (81)\nwhere\u001fpand\u001fmare electric and magnetic susceptibilities respectively, A0is the toroidic\nsti\u000bness , andC > 0 is the nonlinear toroidic coe\u000ecient. \u0014measures the strength of the mag-\nnetoelectric coupling. The last term in the previous free energy represents the lowest possible\norder coupling term between the three order parameters consistent with the required space and\ntime reversal symmetries.\nMinimization of the free energy (81) with respect to polarization and magnetization provides\nthe equilibrium values of polarization and magnetization. They are given by the following\nequations,\nP=\u001fpE\u0000\u001fp\u0014(M\u0002T); (82)\nand\nM=\u001fmB\u0000\u001fm\u0014(T\u0002P): (83)\nWe can now solve these two equations assuming (for simplicity) that E= (E;0;0) and B=\n(0;B;0) and, assuming isotropy, P= (P;0;0),M= (0;M;0) and T= (0;0;T). We obtain:\nP=\u001fpE\u0000\u0014\u001fp\u001fmBT+O(T2)'\u001fpE\u0000\u000bB (84)\nand\nM=\u001fmH\u0000\u0014\u001fp\u001fmET+O(T2)'\u001fmB\u0000\u000bE; (85)\nwhere we have neglected the nonlinear magnetoelectric e\u000bects in the above two equations. The\nmagnetoelectric coe\u000ecient \u000b=\u0014\u001fp\u001fmTis a quadrilinear product of electric susceptibility,\nmagnetic susceptibility, the coupling constant \u0014and the toroidization. Thus, either for \u0014= 0\nor\u001c= 0 there is no magnetoelectric e\u000bect.\nSubstitution of P(84) andM(85) in the free energy (81) gives the following general type\nof e\u000bective free energy:\nFe=F0(E;H ) +1\n2A0(\u001c\u0000\u001cc)T2+1\n3\fT3+1\n4CT4+\u0015T; (86)where,\nF0=\u00001\n2\u0000\n\u001fpE2+\u001fmB2\u0001\n; (87)\n\u001cc=\u001c0\nc+\u00142\nA0\u001fp\u001fm[\u001fmB2+\u001fpE2]; (88)\n\f= 3\u00143\u001f2\nm\u001f2\npEB= 3\u00142\u001fm\u001fp\u0015; (89)\n\u0015=\u0014\u001fm\u001fpEB: (90)\nThe e\u000bective free energy (86) corresponds to the free energy of a toroidal system subjected to\nan e\u000bective applied toroidal \feld \u0015(proportional to G). Interestingly, the coe\u000ecient of the third\norder term, \f, depends also on \u0015(and thus, on G). WhenG= 0,\f= 0 then (86) describes a\nparatoroidal-to-ferrotoroidal second-order phase transition. Under the application of a toroidal\n\feldG6= 0 (and\f6= 0), the transition becomes \frst-order for j\u0015j>j\fj3C2=27. It is worth\npointing out that the addition of nonlinear terms in eqs. (84) and (85) would lead to higher\norder terms in the expansion (86) that go beyond the minimal model. However, within the\nspirit of the Landau Theory, it is expected that such terms are not essential.\nFig. 4: Toroidal order parameter as a function of temperature (in arbitrary units) for three\ndi\u000berent values of the coupling parameter \u0014= 0:90,\u0014= 1 and\u0014= 1:05 and selected values of\nthe applied toroidal \feld G. The arrow in the lower panel indicates the occurrence of the \frst\norder transition. Taken from [52].\nIt is worth noting that the free energy (86) does not include a term directly coupling G\nandT, which is in agreement with the thermodynamic formulation developed in section 5. In\nRef. [53], however, P,MandTwere assumed to be independent order parameters and a term\u0000G\u0001Twas included in the free energy. The same e\u000bective free energy (86) is obtained, but in\nthis case the parameter \u0015is given by, ( \u0014\u001fm\u001fp\u00001)EB. Similar results are obtained with this\nmodel which leads to a richer physics due to the fact that the \u0015and\fterms can have di\u000berent\nsign. The model has been used in [52] in order to study toroidocaloric e\u000bects in ferrotoroidic\nmaterials. The entropy of the system can be obtained as,\nS(\u001c;T;G ) =\u0000@Fe\n@\u001c=\u00001\n2A0T2(\u001c;G); (91)\nwhereT(\u001c;G) is the equilibrium value of the toroidal order parameter which is a solution of\n@Fe=@T = 0. Then, the change of entropy isothermally induced by application of a toroidal\n\feld is obtained as,\nS(T;G =EH)\u0000S(T;G = 0) =\u00001\n2A0[T2(T;G =EH)\u0000T2(T;G = 0)]: (92)\nIt is easy to show (see [51]) that this expression coincides with the general thermodynamic\nexpression (73). The variation of toroidization as a function of temperature for three di\u000berent\nvalues of the coupling parameter ( \u0014) is shown in Figure 4. The corresponding isothermal entropy\nchange (\u0001S) or the toroidocaloric e\u000bect is depicted in Figure 5.\nFig. 5: Toroidocaloric e\u000bect, i.e. the isothermal change in entropy, as a function of transition\ntemperature (in arbitrary units) and selected values of the applied toroidal \feld Gfor three\ndi\u000berent values of the coupling parameter \u0014= 0:90,\u0014= 1 and\u0014= 1:05. Taken from [52].\nThe present Landau approach to ferrotoroidic materials can be generalized by including\nsymmetry allowed gradient term ( rT)2[9], i.e. the Ginzburg term. This should allow one to\nstudy domains and domain walls in ferrotoroidic materials as observed in LiCo(PO 4)3usingoptical second harmonic generation techniques [10]. With doping induced disorder in such\nmaterials we expect that novel phases such as toroidic tweed and toroidic glass should also\nexist and remain to be observed experimentally with certainty [48]. With symmetry allowed\ncoupling of strain to toroidization, if we apply stress to such a crystal we expect toroidoelastic\ne\u000bects, i.e. a change in toroidization with hydrostatic pressure or shear. We expect that these\nimportant topics will be explored in near future.\n7. Electric ferrotoroidics at the nanoscale\nWe have already discussed in Section 3 that no broken symmetry is associated with electric\ntoroidization which is consistent with the fact the formation of electric moment vortex is forbid-\nden in the thermodynamic limit. However, the situation can drastically change when the scale\nof the material decreases towards the nanoscale. It has been predicted that vortex structures\ncan be stabilized below a certain critical temperature in both ferroelectric and ferromagnetic\nnanodots [54, 55]. These zero-dimensional structures have been studied in detail from ab initio\nsimulations of an e\u000bective hamiltonian under appropriate boundary conditions [11]. They nu-\nmerically simulated Pb(Zr,Ti)O 3ferroelectric nanodisks and nanorods under open circuit-like\nelectric boundary conditions and found vortex states comprising electric dipoles that form a\nclosed structure yielding spontaneous electric toroidal moment. Indeed, in recent years electro-\ntoroidic behavior has been found experimentally [56, 57, 58, 59, 60]. Atomistic simulations of\nKTaO 3seem to indicate an incipient ferrotoroidic response wherein quantum vibrations sup-\npress the formation of polar vortices [61]. In addition, electrogyration or electric \feld induced\noptical rotation has been predicted in materials exhibiting electrotoroidic behavior [13]. They\nsuggest that these nanostructures are potentially interesting for data storage applications. Note\nthat the e\u000bect of long-range elastic interactions on the electric toroidization in a ferroelectric\nnanoparticle has been considered in [62].\nFrom a practical point of view, using these nanostructures based on electric toroidal moment\nas writing memory nanodevices is not straightforward since, in principle, these moments cannot\nbe switched by standard methods as they are una\u000bected by applied electric \felds. However,\nseveral solutions have been envisaged. In [63] it has been shown that vortices, both electric\nand magnetic, can be manipulated by inhomogeneous static \felds. The coupling with elasticity\nenables controlling vortices by mechanical load, which gives rise to a rich temperature-stress\nphase diagram [64]. Another possibility, considers nanodots with the shape of nanorings with an\no\u000b-central hole. The interest in these objects relies on the fact that they are characterized by a\ntransverse hypertoroidal moment, which is a polar vector and thus sensitive to an homogeneous\napplied electric \feld [65]. Following similar ideas, it has been recently proposed [66] and numer-\nically predicted that ferroelectric nanotori can possess an homogeneous hypertoroidal moment\nas well as exhibit the coexistence of axial toroidal moment and hypertoroidal moment phases.\nIn these nanoscale objects the hypertoroidal moment could be manipulated by an homogeneous\napplied electric \feld. Note that as a di\u000berent application, metamaterials based on the electric\ntoroidal moment have been proposed [67].\n8. Conclusions\nWith the recent emergence of magnetoelectric and multiferoic materials the fourth primary\nferroic property, namely ferrotoroidicity, has gained special attention. In the present article we\nhave developed a general thermodynamic framework for the study of phase transitions, domainwalls and caloric e\u000bects within the context of Landau theory in ferrotoroidic materials such as\nLiCo(PO 4)3. Both magnetic and electric toroidal moments were considered although the latter\ncan only exist in polar nanostructures. The generalization to hypertoroidal moments was also\npresented. We discussed a variety of materials where toroidic order has been observed. In the\npresence of su\u000ecient disorder the other three primary ferroics exhibit glassy behaviour, namely\nas spin glass, relaxor ferroelectrics and strain glass [49]. Similarly, toroidal glass has been poten-\ntially observed as well in the study of dynamics of a linear magnetoelectric Ni 0:4Mn 0:6TiO 3[48].\nPresence of toroidal moments is also an indicator of magnetoelectric coupling in the material\n[68]. Similarly, toroidal magnon excitations in multiferroics relate to magneto-optical e\u000bects\n[69]. In this article we did not consider the \felds and radiation from moving toroidal dipoles\nwhich is also an important area of research [70, 71]. Clearly, exploration of toroidal phenomena\nis a fertile area of research with a great potential for both fundamental science and device\napplications. Indeed, toroidal metamaterials have been proposed, studied and experimentally\nrealized [72, 73, 74] including in double-ring [75] and double-disk [76] structures.\nAcknowledgments\nThis work received \fnancial support from CICyT (Spain), Project No. MAT2013-40590-P and\nwas partially supported by the U.S. Department of Energy.\nReferences\n[1] V. K. Wadhawan, Introduction to Ferroic Materials , Gordon and Breach, 2000.\n[2] H. Schmid, On ferrotoroidics and electrotoroidics, magnetotoroidics and piezotoroidics e\u000bects ,\nFerroelectrics 252, 41-50 (2001).\n[3] N. A. Spaldin, M. Fiebig, and M. Mostovoy, The toroidal moment in condensed-matter physics\nand its relation to the magnetoelectric e\u000bect , J. Phys. Condens. Matter 20, 434203 (2008).\n[4] D. Khomskii, Classifying multiferroics: Mechanisms and e\u000bects , Physics 2, 20 (2009).\n[5] A. Saxena and T. Lookman, Magnetic symmetry of low-dimensional multiferroics and ferroelas-\ntics, Phase Trans. 84, 421 (2011).\n[6] V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, Axial toroidal moments in electrodynamics\nand solid-state physics , Zh. Eksp. Teor. Fiz. 90, 590 (1986) [Sov. Phys. JETP 63, 344 (1986)].\n[7] V. M. Dubovik and V. V. Tugushev, Toroid moments in electrodynamics and solid-state physics ,\nPhys. Rep. 187, 145 (1990).\n[8] V. M. Dubovik, M. A. Martsenyuk, and B. Saha, Materials equations for electromagnetism with\ntoroidal polarization , Phys. Rev. E 61, 7087 (2000).\n[9] Yu. V. Kopaev, Toroidal ordering in crystals , Phys. Uspekhi 52, 1111-1125 (2009).\n[10] B. B. Van Aken, J. P. Rivera, H. Schmid, and M. Fiebig, Observation of ferrotoroidic domains ,\nNature 449, 702 (2007).\n[11] I. I. Naumov, L. Bellaiche, and H. Fu, Unusual phase transitions in ferroelectric nanodisks and\nnanorods Nature 432, 737-740 (2004).[12] S. Prosandeev, I. Ponomareva, I. Naumov, I. Komev, and L. Bellaiche, Original properties of\ndipole vortices in zero-dimensional ferroelectrics , J. Phys.: Condens. Mat. 20, 193201 (2008).\n[13] S. Prosandeev, A. Malashevich, Z. Gui, L. Louis, R. Walter, I. Souza, and L. Bellaiche, Natural\noptical activity and its control by electric \feld in electrotoroidic systems , Phys. Rev. B 87, 195111\n(2013).\n[14] M. E. Lines and M. A. B osch, Magnetogyration , Phys. Rev. B 23, 263 (1981).\n[15] I. S. Zheludev, O. G. Vlokh, and V. A. Sergatyuk, Magnetogyration and other phenomena de-\nscribed by second-rank axial tensors , Ferroelectrics 63, 97 (1985).\n[16] D. B. Litvin, Property tensors and ferrotoroidic domains , Ferroelectrics 376, 354 (2008).\n[17] D. B. Litvin, Ferroic classi\fcations extended to ferrotoroidic crystals , Acta Cryst. A 64, 316\n(2008).\n[18] D. B. Litvin, On the symmetry analysis of surface induced e\u000bects , Ferroelectrics 460, 173 (2014).\n[19] P. Toledano, D. D. Khalyavin, and L. C. Chapon. Spontaneous toroidal moment and \feld-induced\nmagnetotoroidic e\u000bects in Ba 2CoGe 2O7, Phys. Rev. B 84, 094421 (2011).\n[20] H. Toyosaki, M. Kawasaki, and Y. Tokura, Atomically smooth and single crystalline MnTiO 3thin\n\flms with a ferrotoroidic structure , Appl. Phys. Lett. 93, 072507 (2008).\n[21] D. G. Sannikov, Phenomenological theory of the magnetoelectric e\u000bect in some boracites , JETP\n84, 293-299 (1998).\n[22] B. Mettout, P. Toledano, and M. Fiebig, Symmetry replication and toroidic e\u000bects in the multi-\nferroic pyroxene NaFeSi 2O7, Phys. Rev. B 81, 214417 (2010).\n[23] J. D. Jackson, Classical electrodynamics , Wiley, New York 1974.\n[24] R. E. Raab and O. L. de Lange, Multipole Theory in Electromagnetism , Oxford Univ. Press, 2004.\n[25] I. A. Beardsley, Reconstruction of the magnetization in a thin \flm by a combination of Lorentz\nmicroscopy and external \feld measurements , IEEE Trans. Mag. 25, 671-677 (1989).\n[26] S. Prosandeev and L. Bellaiche, Hypertoroidal moment in complex dipolar structures , J. Mater.\nSci., 44, 5235-5248 (2009).\n[27] Vortices of electric moments may occur due to con\fnement e\u000bects at the nanoscale. See, for in-\nstance, S. Prosandeev, I. Ponomareva, I. Naumov, I. Kornev, and L. Bellaiche, Original properties\nof dipole vortices in zero-dimensional ferroelectrics , J. Phys.: Condens. Matter 20, 193201 (2008).\n[28] M. Baum, K. Schmalzl, P. Ste\u000bens, A. Hiess, L. P. Regnault, M. Meven, P. Becker, L. Bohat\u0013 y,\nand M. Braden, Controlling toroidal moments by crossed electric and magnetic \feld , Phys. Rev.\nB88, 024414 (2013).\n[29] K. Sawada and N. Nagaosa, Optical magnetoelectric e\u000bect in multiferroic materials: Evidence for\nLorentz force acting on a ray of light , Phys. Rev. Lett 95, 237402 (2005).\n[30] V. Scagnoli, U. Staub, Y. Bodenthin, R. A. de Souza, M. Garcia-Fernandez, M. Garganourakis,\nA. T. Boothroyd, D. Prabhakaran, and S. W. Lovesey, Observation of Orbital Currents in CuO ,\nScience 332, 696 (2011).[31] A. Gongora T. and E. Ley-Koo, Complete electromagnetic multipole expansion including toroidal\nmoments , Rev. Mex. Fis. 52, 188 (2006).\n[32] D. G. Sannikov, Ferrotoroics , Ferroelectric 354, 39-43 (2007).\n[33] Yu. F. Popov, A. M. Kadomtseva, G. P. Vorob'ev, V. A. Tomofeeva, D. M. Ustinin, A. K. Zvezdin,\nand M. M. Tegeranchi, Magnetoelectric e\u000bect and toroidal ordering in Ga 2\u0000xFexO3, JEPT 87,\n146-151 (1998).\n[34] Yu. F. Popov, A. M. Kadomtseva, D. V. Belov, G. P. Vorob'ev, and A. K. Zvezdin, Magnetic-\feld\ninduced toroidal moment in the magnetoelectric Cr 2O3, JEPT Lett. 69, 300-335 (1999).\n[35] M. Fiebig, D. Fr ohlich, B. B. Krichevtsov, and R. V. Pisarev, Second Harmonic Generation and\nMagnetic-Dipole-Electric-Dipole Interference in Antiferromagnetic Cr 2O3, Phys Rev. Lett. 73,\n2127 (1994).\n[36] M. Fiebig, D. Fr ohlich, G. Sluyterman V. L. and R. V. Pisarev, Domain topography of antiferro-\nmagnetic Cr 2O3by second harmonic generation , Appl. Phys. Lett. 66, 2906 (1995).\n[37] J. Molenda, Lithium ion batteries - state of art. novel phospho-olivine cathode materials , Mater.\nSci.-Poland 24, 61 (2006).\n[38] A. Szewczyk, M. U. Gutowska, J. Wieckowski, A. Wisniewski, R. Diduszko, Yu. Kharchenko, M.\nF. Kharchenko, and H. Schmid, Phase transitions in single-crystalline magnetoelectric LiCoPO 4,\nPhys. Rev. B 84, 104419 (2011).\n[39] H. Schmid, Some symmetry aspects of ferroics and single phase multiferroics , J. Phys. Cond.\nMatter 20, 434201 (2008).\n[40] A. A. Gorbatsevich and Y. V. Kopaev, Toroidal order in crystals , Ferroelectrics 161, 321 (1994).\n[41] Yu. F. Popov, A. M. Kadomtseva, S. S. Krotov, D. V. Belov, G. P.Vorob'ev, P. N. Makhov, and\nA. K. Zvezdin, Features of the magnetoelectric properties of BiFeO 3in high magnetic \felds , Low\nTemp. Phys. 27, 478 (2001).\n[42] Y. Tokura, Multiferroics{toward strong coupling between magnetization and polarization in a\nsolid, J. Magn. Magn. Mater. 310, 1145 (2007).\n[43] E. Ressouche, M. Loire, V. Simonet, R. Ballou, A. Stunault, and A. Wildes, Magnetoelectric\nMnPS 3as a candidate for ferrotoroidicity , Phys. Rev. B 82, 100408 (2010).\n[44] H.-J. Feng and F.-M. Liu, Ab initio prediction on ferrotoroidic and electronic properties of olivine\nLi4MnFeCoNiP 4O16, Chinese Phys. B 18, 2481 (2009).\n[45] S.-Y. Lin, W. Wernsdorfer, L. Ungur, A. K. Powell, Y.-N. Guo, J. Tang, L. Zhao, L. F. Chibotaru,\nand H.-J. Zhang, Coupling Dy3 triangles to maximize the toroidal moment , Angewndte Chemie\n124, 12939 (2012).\n[46] A. B. Harris, A system exhibiting toroidal order , Phys. Rev. B 82, 184401 (2010).\n[47] T. Cast\u0013 an, A. Planes, and A. Saxena, Thermodynamics of multiferroic materials , in Mesoscopic\nPhenomena in Multifunctional Materials, ed. by A. Saxena and A. Planes, Springer Series in\nMaterials Science, Vol. 198, pp. 73-108, Springer-Verlag, Berlin, 2014.\n[48] Y. Yamaguchi and T. Kimura, Magnetoelectric control of frozen state in a toroidal glass , Nature\nCommun. 4, 2063 (2013).[49] X. Ren, Y. Wang, K. Otsuka, P. Lloveras, T. Castan, M. Porta, A. Planes, and A. Saxena,\nFerroelastic nanostructures and nanoscale transitions: Ferroics with point defects , MRS Bull. 34,\n838 (2009).\n[50] O. Gut\reisch, M. A. Williard, E. Br uck, C. H. Chen, S. G. Sankar, and J. P. Lin, Magnetic\nmaterials and devices for the 21st century: stronger, lighter and more energy e\u000ecient , Adv. Mater.\n27, 821-842 (2011).\n[51] A. Planes, T. Cast\u0013 an, and A. Saxena, Thermodynamics of multicaloric e\u000bects in multiferroics ,\nPhilos. Mag. 94, 1893-1908 (2014).\n[52] T. Cast\u0013 an, A. Planes, and A. Saxena, Thermodynamics of ferrotoroidic materials: Toroidocaloric\ne\u000bect , Phys. Rev. B 85, 144429 (2012).\n[53] C. Ederer and N. Spaldin, Towards a microscopic theory of toroidal moments in bulk periodic\ncrystals , Phys. Rev. B 76, 214404 (2007).\n[54] M. Dawber, I. Szafraniak, M. Alexe, and J. F. Scott, Self-patterning of arrays of ferroelectric\ncapacitors: description by theory of substrate mediated strain interactions , J. Phys. Condens.\nMatter 15, L667-L671 (2003).\n[55] S. D. Bader, Opportunities in nanomagnetism , Rev. Mod. Phys. 78, 1-15 (2006).\n[56] A. Gruverman, D. Fu, H.-J. Fan, I. Vrejoiu, M. Alexe, R. J. Harrison, and J. F. Scott, Vortex\nferroelectric domains ,20, 342201 (2008).\n[57] R. G. P. McQuaid, L. J. McGilly, P. Sharma, A. Gruverman, and A. Gregg, Mesoscale \rux-closure\ndomain formation in single-crystal BaTiO 3, Nature Commun. 2, 404 (2011).\n[58] R. K. Vasudevan, Y. C. Chen, H. H. Tai, N. Balke, P. Wu, S. Bhattacharya, L. Q. Chen, Y. H.\nChu, I. N. Lin, S. V. Kalinin, and V. Nagarajan, Exploring topological defects in epitaxial BiFeO 3\nthin \flms , ACS Nano 5, 879 (2011).\n[59] C. T. Nelson, B. Winchester, Y. Zhang, S. J. Kim, A. Melville, C. Adamo, C. M. Folkman, S.\nH. Baek, C. B. Eom, D. G. Schlom, L. Q. Chen, and X. Pan, Spontaneous vortex nanodomain\narrays at ferroelectric heterointerfaces , Nano Lett. 11, 828 (2011).\n[60] N. Balke, B. Winchester, W. Ren, Y. H. Chu, A. N. Morozovska, E. A. Eliseev, M. Huijben, R.\nK. Vasudevan, P. Maksymovych, J. Britson, S. Jesse, I. Kornev, R. Ramesh, L. Bellaiche, L. Q.\nChen, and S. V. Kalinin, Enhanced electrical conductivity at ferroelectric vortex cores in BiFeO 3,\nNature Phys. 8, 81 (2012).\n[61] S. Prosandeev, A. R. Akbarzadeh, and L. Bellaiche, Discovery of incipient ferrotoroidics from\natomistic simulations , Phys. Rev. Lett. 102, 257601 (2009).\n[62] J. Wang and T.-Y. Zhang, E\u000bect of long-range elastic interactions on the toroidal moment of\npolarization in a ferroelectric nanoparticle , Appl. Phys. Lett. 88, 182904 (2006).\n[63] S. Prosandeev, I. Ponomareva, I. Kornev, I. Naumov, and L. Bellaiche, Controlling toroidal mo-\nment by means of an inhomogeneous static \feld: An Ab Initio study , Phys. Rev. Lett. 96, 237601\n(2006).\n[64] W. J. Chen, Y. Zheng, and B. Wang, Vortex domain structures in ferroelectric nanoplatelets and\ncontrol of its transformation by mechanical load , Sci. Reports 2, 1-8 (2012).[65] S. Prosandeev, I. Ponomareva, I. Kornev, and l. Bellaiche, Control of vortices by homogeneous\n\felds in asymmetric ferroelectric and ferromagnetic rings , Phys. Rev. Lett. 100, 047201 (2008).\n[66] G. Thorner, J. M. Kiat, C. Bogicevic, and I. Kornev, Axial hypertoroidal moment in a ferroelectric\nnanotorus: A way to switch local polarization , Phys. Rev. B, 89, 220103R (2014).\n[67] L. Y. Guo, M. H. Li, Q. W. Ye, B. X. Xiao, and H. L. Yang, Electrical toroidal dipole response\nin split-ring resonator metamaterials , Eur. Phys. J. B 85, 208 (2012).\n[68] C. Ederer, Toroidal moments as indicator for magneto-electric coupling: the case of BiFeO 3versus\nFeTiO 3, Eur. Phys. J. B 71, 349 (2009).\n[69] S. Miyahara and N. Furukawa, Theory of magneto-optical e\u000bects in helical multiferroic materials\nvia toroidal magnon excitation , Phys. Rev. B 89, 195145 (2014).\n[70] V. L. Ginzburg and V. N. Tsytovich, Fields and radiation of toroidal dipole moments moving\nuniformly in a medium , Zh. Eksp. Teor. Fiz. 88, 84 (1985) [Sov. Phys. JETP 61, 48 (1985)].\n[71] J. A. Heras, Electric and magnetic \felds of a toroidal dipole in arbitrary motion , Phys. Lett. A\n249, 1 (1998).\n[72] K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, Toroidal metamaterials , New J.\nPhys. 9, 324 (2007).\n[73] T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, Toroidal dipolar\nresponse in a metamaterial , Science 330, 1510 (2010).\n[74] Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, Low-loss and high-Q planar metamaterial\nwith toroidal moment , Phys. Rev. B 87, 115417 (2013).\n[75] Z.-G. Dong, P. Ni, J. Zhu, X. Yin, and X. Zhang, Toroidal dipole response in a multifold double-\nring metamaterial , Opt. Exp. 20, 13065 (2012).\n[76] J. Li, J. Shao, J.-Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, Optical responses of magnetic-\nvortex resonance in double-disk metamaterial variations , Phys. Lett. A 378, 1871 (2014)."    },    {        "title": "1504.07824v3.The_formation_of_regular_interarm_magnetic_fields_in_spiral_galaxies.pdf",        "content": "arXiv:1504.07824v3  [astro-ph.GA]  18 May 2015Astronomy& Astrophysics manuscriptno.arms7˙corra c/ci∇clecopy∇tESO 2021\nJune16,2021\nThe formation of regular interarmmagnetic fields inspiral\ngalaxies\nD.Moss1,⋆,R.Stepanov2,M.Krause3, R.Beck3,and D.Sokoloff4\n1School of Mathematics, Universityof Manchester, OxfordRo ad, Manchester, M13 9PL,UK\n2Institute of Continuous Media Mechanics, Koroleva, 1,6140 13, Perm, Russia\n3MPI f¨ ur Radioastronomie, Aufdem H¨ ugel 69, 53121 Bonn, Ger many\n4Department of Physics,Moscow StateUniversity, 119991, Mo scow, Russia\nReceived .....;accepted .....\nABSTRACT\nContext.Observationsofregularmagneticfieldsinseveralnearbyga laxiesrevealmagneticarmssituatedbetweenthemateriala rms.Thenature\nof these magnetic arms is a topic of active debate. Previousl y, we found a hint that taking into account the e ffects of injections of small-scale\nmagnetic fields(e.g. generated byturbulent dynamo action) intothe large-scale galacticdynamo canresult inmagnetic arm formation.\nAims.We now investigate the joint roles of an arm /interarm turbulent di ffusivity contrast and injections of small-scale magnetic fie ld on the\nformationof large-scale magnetic field(”magnetic arms”) i nthe interarm region.\nMethods. We use the relatively simple ”no- z” model for the galactic dynamo. This involves projection on to the galactic equatorial plane of\nthe azimuthal and radial magnetic field components; the field component orthogonal to the galactic plane is estimated fro m the solenoidality\ncondition.\nResults. We find that the addition of di ffusivity gradients to the e ffects of magnetic field injections makes the magnetic arms muc h more\npronounced. Inparticular, the regular magnetic fieldcompo nent becomes largerinthe interarm space thanthat withinth e material arms.\nConclusions. The joint action of the turbulent di ffusivity contrast and small-scale magnetic field injections (with the possible participation of\nother effects previously suggested) appears tobe a plausible explan ation for the phenomenon of magnetic arms.\nKey words. Galaxies: spiral –Galaxies: magnetic field–Dynamo –Magnet ic fields –Galaxy: disc –ISM:magnetic fields\n1. Introduction\nDynamo modelling of galactic magnetic fields has a long his-\ntory, being particularly intensive over the last 30 years. W e do\nnotintendtogiveacomprehensivereviewhere,butRuzmaiki n\netal.(1988)canbementionedasaseminalwork,andcompre-\nhensivereviewsweregivenbyBecketal.(1996),Brandenbur g\n(2015); see also Beck et al. (2015) for more recent devel-\nopments. Substantial progress has been made towards under-\nstanding the basic mechanisms of dynamo excitation, includ -\ning both detailed direct numerical simulations in ”boxes”, and\nalsosomemoredetailedmodelsforglobalfieldstructure.\nAconspicuousfeatureofsome”granddesign”spiralgalax-\nies (e.g. M81, NGC6946)is the presence in the regular (large -\nscale) magnetic field of prominent magnetic arms, situated i n\nthe interarm regions between the material arms, as delineat ed\nby regions of active star formation. Such arms are not always\nwellpronouncedorcomplete,andmayincludeanumberoffil-\naments,asinIC342(Beck2015).Theoriginofmagneticarms\nhas attracted significant attention, but so far there is no co m-\nSend offprint requests to : D.Moss\n⋆Corresponding author, e-mail: moss@ma.man.ac.ukpletelysatisfactoryexplanationoftheirorigin.Earlyst udiesin-\ncludeMoss (1998)and Shukurov(1998)whoin the contextof\nsimplemeanfielddynamomodelsappealedtovariationsinthe\nalpha coefficient and turbulent resistivity ( η) that were modu-\nlatedbythelocationofthematerialarms;specifically,itc anbe\nexpected thatηwill be enhanced by the additional turbulence\nassociatedwith starformingregions(SFRs).\nLaterrelevantstudiesincludeChamandyetal.(2013,2014,\n2015) who use a sophisticated mean field dynamo model and\nargue that enhanced vertical outflows within the arms region s\nwill preferentiallyremovelarge-scalefieldsfromthere.S mall-\nscale helicity is also removedby the vertical flows, prevent ing\ncatastrophicquenching.Additionally,theyincludemodul ations\nof the alpha term. These models do produce some of the ob-\nserved properties,but possibly are not completely satisfa ctory.\nFor example, these models require dynamo numbers that are\nclosetomarginaltogeneratemagneticarmse fficiently,andthe\noutflows cannot be too strong. Gradients of turbulent di ffusiv-\nity are ignored and pitch angles of the fields are rather small\ncomparedto thoseoftypicalgalaxies.\nMoss et al. (2013) took a somewhat di fferent approach,\nmodellingthe effectsof SFRs in the material arms by stochas-2 Moss etal.:Regular interarm magnetic fields\nticinjectionofsmall-scalemagneticfieldwithinthearms, sup-\nposedly the result of small-scale dynamo action in the SFRs.\nTheirmodelproduces(maybeunsurprisingly)asatisfactor yen-\nhancement of small-scale fields in the arms, but no significan t\nenhancementofinterarmregular(large-scale)fields.\nA significant omission from the last paper, for perceived\ntechnical reasons, was an enhanced turbulent di ffusivity in the\narmsassociatedwiththeassumedturbulencedrivenbythest ar\nformation. The authors speculated that this might be a signi f-\nicant omission. The presence of such variations in the turbu -\nlent diffusivity cannot be verified directly by observations,but\ngivenour understandingof the physicalprocessesoperatin g,it\nappears a plausible assumption. Accordingly, we here prese nt\nsimilarmodelstothoseinMossetal.(2013),butnowincludi ng\nthe terms associated with inhomogeneitiesin ηin the dynamo\nequations (including the diamagnetic terms), and we demon-\nstrate that regularmagnetic arms located between the mater ial\narmsare indeedproduced.We note in passingthat contrastsi n\ndiffusivitybetweendiscandhaloregionshavebeenincludedin\ndynamo models for at least 25 years (see e.g. Brandenburg et\nal.1992).\n2. Themodel\n2.1. Thedynamo setup\nThedynamoequationis\n∂B\n∂t=∇×/parenleftBigg\nΩr×B+αB−1\n2∇η×B/parenrightBigg\n−∇×(η∇×B) (1)\nin the standardnotation.Note the presenceof gradientsof d if-\nfusivity, both in the diamagnetic term and the di ffusion term.\nThe model is basically the thin disc model (”no- z” approxi-\nmation) described in Moss et al. (2012, 2013). In these earli er\npapersit hadnotbeenpossible to includetermscorrespondi ng\nto gradients ofη. The relevant part of the algorithm was reor-\nganized slightly, and a typo in the code corrected, after whi ch\nthe code ran smoothly with gradients of ηincluded. (The typo\ndid not affect the part of the code used in earlier papers.) The\nnovel feature of the models of Moss et al. (2012, 2013) is the\ncontinualstochasticinjectionofsmall-scalefieldatdisc retelo-\ncations,to simulatethe e ffectsof star formingregionsinintro-\nducing small-scale field into the ISM. In short, random fields\nBinj=Binj0f(r,t) are added at approx nspot=75 randomly\nchosen discrete locations in the material arms (defined belo w)\nwith re-randomization (i.e. changing the location of the in jec-\ntion sites and the distribution of field strengths over them b y\nchoosing a new independent set of random numbers) at inter-\nvalsdtinj≈10 Myr.nspotandBinj0are free parameters in the\nmodel, which are regarded as a proxies for unmodelled pro-\ncesses in the SFRs. Another key point is that the seed field at\ntime zero is random,in discrete patches,and of approximate ly\nequilibrium strength. This is envisaged as being the result of\nsmall-scale dynamo action within very early SFRs. (Note tha t\nthe no-zapproximation implicitly preserves the solenoidality\ncondition∇·B=0 for both the dynamo generated and in-\njected fields.) Full details are in Moss et al. (2012). The dis ccan be flared or flat, noting that there is currently some un-\ncertainty as to whether galactic discs are substantially fla t or\nflared (cf. Lazio & Cordes 1998); further investigation of th is\npointisneeded,buttheresultsarenotsensitivetothisass ump-\ntion. The HI disc of the MilkyWay does flare, but it is unclear\nwhethertheionizedgasdiscdoesso,andtheobservationald ata\nforexternalgalaxiesareinconclusive.Thisissueappears unim-\nportant for our modelling – see Sect. 3.1 and also Moss et al.\n(2012).\nNon-dimensionaltime τismeasuredinunitsof h2/η.When\nη=1026cm2s−1andh=500 pc, this is approximately 0 .78\nGyr. Radius ris measured in units of the galactic radius R,\ntakenas10kpc.\nThecode was implementedon a Cartesian gridwith 537 ×\n537points,equallyspaced,extendedtobeyondthegalactic ra-\ndiustoabout1.17R,i.e.over−1.17R<∼R<∼1.17R.Inthisouter\nregionbeyond r=R,thereisnoalpha-e ffectandthediffusivity\nretains its global background value. This enables satisfac tory\ntreatment of the boundaryconditions– see Moss et al. (2012) .\nThetimestepisfixedat approximately0 .04Myr.\n2.2. Thearm generationalgorithm\nWe definea function\np=cos(0.5(2φ−blog(r/ra)−2φ0)),\nwherera,bare arbitraryvalues and φ0=ωpτ, whereωpis the\ndimensionlesspatternspeed.\nThenwe put\ng=exp(−(p\na)2)η1(r),\nwhereη1=1,r>0.4, and goes smoothly to zero as r→0.\nThen\nη=1+η10gm,\nwheremis an arbitrary number. The di ffusivity contrast is de-\nfinedas∆ηa=1+η10.\nThis algorithm is rather arbitrary,but gives satisfactory re-\nsults with the values ra=1,a=π/4,b=4 (as in Moss et\nal. (2012)). In the illustrative computations described be low\nm=4.\nThe arms rotate rigidly with pattern speed ωp, chosen to\ngivecorotationradii0 .5R<∼rcorr<∼0.7R–see Table1.\n3. Results\n3.1. Maincomputations\nA number of models were computed, with both flat and flared\ndiscs. The essential features of the results were the same fo r\neach class of model, and so only results for flat discs are pre-\nsented here. Salient parameters are shown in Table 1. The un-\nderlying models are in general similar to Model 75 of Moss\net al. (2013), for example, but here with a flat disc. We take\nh0=500 pc and a slightly larger value Rα=5 is taken to\ncompensate for the increased value of the di ffusivityηin the\narms. Plots of field vectors at dimensionless times τ=3 andMoss etal.:Regular interarm magnetic fields 3\n−1 0 1−1.175−1011.175\nxy\n−1 0 1−1.175−1011.175\nxy\nFig.1.Fieldvectorsatdimensionlesstimes t≈3.0and17.0(2.3and13.3Gyr),forModel2withthedi ffusivitycontrastparameter\nηa=4. (Here, and in subsequent similar Figures, the vectors giv e the magnetic field direction, with lengths proportional to the\nmagneticfieldstrengths,andthe contoursdelineatethearm s.Thecorotationradiusisapproximately0 .7R.\n17 are shown in Fig. 1, with the di ffusivity contrast parame-\nter∆ηa=4. The strong visual impression is that the large-\nscalefield isreducedinthearms,andthattherearepronounced\nlarge-scalemagneticstructures(correspondingtoregula rfield)\nbetweenthe material arms. Moreover,these e ffects are seen at\nveryearlytimes. This impressionis reinforced(in a somewh at\ndifferentrepresentation)byFig.2, showingmapsofthe large-\nscale field at dimensionless times between τ=3 and 17 ap-\nproximately 2.3 and 13.3 Gyr. This figure can be compared to\nFig. 4 of Moss et al. (2013). Additionally, Fig. 3 shows the\nglobal amplitudes of large-and small-scale fields in the arm s\nand interarm regions.This figure can be comparedto Fig. 8 of\nMoss et al. (2013), and clearly demonstrates the e ffects of the\nassumedη-gradients, in that in the interarm region the large-\nscale(regular)fieldisnowtwoorthreetimeslargerthanint he\narms.\nModel 2 has corotation radius at approximately 0 .7R. We\ncomputedmodelswithdi fferentcorotationradii,anditappears\nthattheresultsarequiteinsensitivetosuchchanges.Fore xam-\nple, Fig. 5 shows field vector plots at τ=17 for a model with\ncorotationatapproximately0 .5R.(Theanomalouslylargevec-\ntorsinFig.5(and9cbelow)areattributabletoafieldinject ion\nsoonbeforeplotting.)\nThe value taken for the di ffusivity contrast parameter ∆ηa\nis rather arbitrary,so the computationof Model 2 (Fig. 1) wa s\nrepeatedwith∆ηa=6,seeFig.6.Themagneticarmsaremore\nmarkedandtheinterarmmagneticstructuresaresomewhatna r-\nrower.Furtherincreasein ∆ηacangivemorefilamentarymag-\nnetic’arms’.arms, large\narms, small\ninterarm, large\ninterarm, small\n4 6 8 10 120.30.40.50.60.70.8\ntime,Gyramplitude\nFig.3.Model2,showingglobalamplitudesoflarge-andsmall-\nscale field in the arms (respectivelythick and thin red dashe d)\nandlarge-andsmall-scalefieldintheinterarmregions(res pec-\ntivelythickandthinbluecurves).\n3.2. Fieldreversals\nLarge-scale field reversals are a common feature of the mod-\nels and were also present in the models of Moss et al. (2012,\n2013) see also Poezd et al. (1993). Moss & Sokolo ff(2013)\nshowedthat whenthe seed field isinhomogeneousand ofnear\nequipartitionstrength,whetherornotreversalsappeared inthe\nstatistically steadyfield (andindeedthe detailsofthisco nfigu-\nration more generally) dependsquite sensitively on the det ails\noftheinitialfielddistribution.Severalmodelswererunwi ththe\nsame parameters as Model 2, but using di fferent sequences of\nthe(pseudo-)randomnumbersthatdefinetheinitialfielddis tri-\nbutionandsubsequentfieldinjections.Thefieldconfigurati ons\nat the endof therunsweregenericallysimilar, severalwith re-4 Moss etal.:Regular interarm magnetic fields\nt/Equal2.34Gyr\n/Minus1.0/Minus0.5 0.0 0.5 1.0/Minus1.0/Minus0.50.00.51.0 t/Equal3.9 Gyr\n/Minus1.0/Minus0.5 0.0 0.5 1.0/Minus1.0/Minus0.50.00.51.0 t/Equal7.8 Gyr\n/Minus1.0/Minus0.5 0.0 0.5 1.0/Minus1.0/Minus0.50.00.51.0\nt/Equal11.7Gyr\n/Minus1.0/Minus0.5 0.0 0.5 1.0/Minus1.0/Minus0.50.00.51.0 t/Equal12.48Gyr\n/Minus1.0/Minus0.5 0.0 0.5 1.0/Minus1.0/Minus0.50.00.51.0 t/Equal13.26 Gyr\n/Minus1.0/Minus0.5 0.0 0.5 1.0/Minus1.0/Minus0.50.00.51.0\nFig.2.Model 2. Intensity of the large-scale magnetic field at times 2.34, 3.9, 7.8, 11.7, 12.48 and 13.26 Gyrs (left to right, top\nto bottom).Contoursshowsisolines of large-scalefield int ensity (darkercorrespondsto a largervalue).The first and l ast panels\ncanbecomparedwith thepanelsofFig.1.\n−1 0 1−1.175−1011.175\nxy\nFig.4.Model7.Computationstartingfromarandomseedfield\n(as Model 2), but with no ongoingsmall-scale field injection s.\n∆ηa=4.−1 0 1−1.175−1011.175\nxy\nFig.5.Fieldvectorsatdimensionlesstime τ=17.0(13.3Gyr),\nfor model 3 with di ffusivity contrast parameter ηa=4. The\ncorotationradiusisapproximately0 .5R.\nversals but one (Fig. 7) with only a very weak feature near the\nouterradius.Moss etal.:Regular interarm magnetic fields 5\n−1 0 1−1.175−1011.175\nxy\nFig.6.Fieldvectorsatdimensionlesstime τ=17.0(13.3Gyr),\nfor Model 8 with the largerdi ffusivity contrast parameter ηa=\n6.Thecorotationradiusisapproximately0 .7R.\n−1 0 1−1.175−1011.175\nxy\nFig.7.Fieldvectorsatdimensionlesstime τ=17.0(13.3Gyr),\nfor Model 9 with parameters as Model 2, but a di fferent se-\nquenceofrandomnumbersdefiningthe initialfield andsubse-\nquentinjections.\nWe also made an experiment in which the seed field was\nweakandsmooth,andthemodelwasallowedtoevolvewithout\ninjections until the dynamo was saturated, with a ”standard ”\nlooking smooth spiral structure. At τ=8 the injections were\nturned on and evolution proceeded as in the other cases. The−1 0 1−1.175−1011.175\nxy\nFig.8.Fieldvectorsatdimensionlesstime τ=17.0(13.3Gyr),\nfor Model 19. Here the seed field was weak and smooth, and\nthere were no random injections until τ=8. The corotation\nradiusisapproximately0 .7R.\nfield atτ=17is shownin Fig. 8. Nowthereare nolarge-scale\nreversals, but other features of the field are similar to thos e in\nother models. Thisclearly demonstratesthat the occurrenc eof\nlarge-scale reversals is a consequence of the form of the see d\nfield andtheinjectionhistory.\nThemodelspresentedaboveall havea moreor less homo-\ngeneousinnerringoffield,withareversalbetweentheringa nd\ntheouterarms.A fieldreversalhasbeenobservedintheMilky\nWay, but it is unclear whether it is a global or local feature.\nReversals have not (so far) been detected in external galaxi es.\nIn some ways the presence of the ring is a consequence of the\nwaythemodelisset up,asthearmsareonlydistinctlydefined\noutsideofthecentralregions(see Mossetal. 2013).\n3.3. Additionalcomputations\nSimulationsstronglysuggestthatspiralarmsarenotperma nent\nstructures,butdissolveandreformovercomparativelysho rtin-\ntervals (see the review by Dobbs& Baba 2014).It is also pos-\nsible that armsmay disappear altogetherfor intervalsand t hen\nreappear.We also conductedtwo experimentsto test howsuch\nchanges in the structure of the material arms might influence\nour results. In the first (Model 10), the position of the spira l\narms jumps randomly at time intervals [ t]≈5×108yr. In the\nsecond (Model 6 – see Fig. 9), the spiral arms are removed\naltogetherfortwointervalsofabout1 .6×109Gyrbeforereap-\npearing. The conclusion from these computations is that the\nmagneticinterarmstructuresarepresentsoonafterthemat erial\narmsreappear.Model6hasthesameparametersasModel2de-\nscribedabove,butthearms(andassociateddi ffusivityinhomo-\ngeneities)areremovedfor8 .5≤τ≤10.5and13.0≤τ≤15.0.\nFig. 9 shows field vectors at times τ=8.4 (i.e. just before the6 Moss etal.:Regular interarm magnetic fields\nTable 1.Summaryofmodels\nModel∆ηarcorrcomment\n2 4 0.7 basic model\n3 4 0.5\n7 4 0.7 no ongoing fieldinjections\n6 4 0.7 as Model 2, noinjections between τ=8.5and10.5\n8 6 0.7\n9 4 0.7 as Model 7, di fferent sequence of random numbers\n10 4 0.7 as Model 2, arms jumpinpositionrandomly\n19 4 0.7 small smooth seedfield,random injections turnedon a tτ=8\narms are ”turned o ff”),τ=9.9, andτ=10.6 (i.e. soon after\nrestoringthe arms). At τ=8.4 field structuresare as in Fig. 1.\nThesedisappearalmostimmediatelythearmsareremoved,an d\na near-circular field is present (Fig. 9b at τ=9.9). When the\narms are turned back ”on” structures similar to those seen in\nFig.1rapidlyreappear–see fieldplotsat τ=10.6inFig.9c.\nAdditionally, when the arms jump randomly (Model 10),\nsimilar structures quickly adjust to the new positions of th e\narms.Fieldvectorsarenotshownforthiscase.Theseideali zed\nexperimentssuggest that magneticfield structuresare notv ery\ndependentontheevolutionaryhistoryofthematerialarms.\n3.4. Rolesofsmall-scale field injections anddiffusivity\ngradients\nIn order to separate the role of di ffusivity gradients alone in\nproducing the magnetic structures discussed above, Model 7\nshowstheresultofacomputationwithparametersasModel2,\nexcept that there are no ongoing field injections. The field\nrapidly(byτ<∼3)becomessteady.Fig.4showsthefieldstruc-\nture (nominally at 13.26 Gyr, i.e, τ=17). Enhanced interarm\nfields(magneticarms) are clearlyvisible (we note that ther eis\nonly ”regular” field in this computation). In Fig. 10 the con-\ntrast between the global amplitudes of the regular field in th e\narmandinterarmregionsis clearlyvisible.\nThis suggests strongly (and consistently with the sugges-\ntion of Moss et al. (2012) – and even Moss (1998)) – that\nthe diffusivity gradients postulated can be largely responsible\nfor the formation of (regular field) magnetic arms. The small -\nscale field injectionsprovide(unsurprisingly)the observ eden-\nhancedsmall-scalefield withinthematerialarms.These inj ec-\ntionsformaconsistentpartofthemodelinthattheyareadir ect\nconsequence of the strong star formation in the arms, that in\nturn drives the turbulence that is responsible for the incre ased\ndiffusivitythere.\n4. Discussionand conclusions\nWe have presented a mechanism for magnetic arm formation\nbased on the joint action of turbulent di ffusivity contrasts and\nsmall-scale magneticfield injectionsfromsmall-scale dyn amo\naction, plausibly associated with supernovae complexes an d\nHII regions, although we cannot use this energy input to the\nISM directly to calibrate our parameter Binj0. This mechanismarms, large\narms, small\ninterarm,large\ninterarm,small\n0246810120.10.20.30.40.50.60.7\ntime,Gyramplitude\nFig.10.Model 7, showing global amplitudes of large- and\nsmall-scale field in the arms (respectively thick and thin re d\ndashed)andlarge-andsmall-scalefieldintheinterarmregi ons\n(respectivelythickandthinbluecurves).\nproducesquitemarkedlarge-scalemagneticstructuressit uated\nmainly between the material arms (see, e.g., Fig. 1). Howeve r,\nfrom time to time a magnetic arm can intersect somewhere a\nmaterial arm, e.g. Figs. 1 (right hand panel) and 6. The mag-\nnetic arms obtained are quite robust structures and do not re -\nquirefinetuningofthedynamogoverningparameters.\nIn general, the effect of introducingthe di ffusivity contrast\nis to increase the global mean di ffusivity and to reduce the\nglobal mean large-scale field. However the increased locali za-\ntionofthelarge-scalefield couldresultin localenhanceme nts,\nbut in practice this e ffect seems smaller. The much increased\nlocal diffusivity in the arms results in a more rapid decay of\ntheinjectedsmall-scalefield,andsoagreatercontrastbet ween\nlarge-andsmall-scalefields,assuggestedbytheFigures.A test\ncase omittingthe term indicatesthat the turbulentdiamagn etic\nvelocity−1\n2∇ηappearinginEqn.(1)playsonlyaminorrole.\nOurmodelreproducesthemainfeatureofthee ffect,butno\nattempthasbeenmadetoreproducealldetailsofmagneticar m\nformation. In particular, small-scale dynamo action is rep re-\nsentedonlybymagneticfieldinjections.Thestatisticalpr oper-\ntiesofinjectionsareobviouslysimplified,e.g.injection soccur\natregularprescribedinstantsratherthanbeingdistribut edmore\nor less homogeneouslyin time. Presumably, this statistica l in-\nhomogeneityisresponsibleforasharppeakinevolutionoft he\nsmall-scale field in arms shown in Fig. 3. Development of theMoss etal.:Regular interarm magnetic fields 7\na)−1 0 1−1.175−1011.175\nxy\nb)−1 0 1−1.175−1011.175\nxy\nc)−1 0 1−1.175−1011.175\nxy\nFig.9.Field vectors at dimensionless times a) t≈8.4, b) 9.9 and c) 10.6, for Model 6 with the di ffusivity contrast parameter\nηa=4. The arms are removed between τ=8.5 and 10.5, and panel c) shows that the interarm regular fields appear a lmost\nimmediatelyafterthearmsreappear.Theanomalouslylongv ectorsarethe resultofafield injectionjust before τ=10.6.\nmodel in order to obtain a more realistic description of smal l-\nscale dynamoactionseemsto beanimportantundertaking.\nThepitchanglesofthefieldstructuresaregenerallysmalle r\nthan those of the spiral arms (similarly to those of Chamandy\net al. 2013, obtained using a quite di fferent mechanism), but\nlocally have more realistic values, especially in the model\n(Fig. 6) with larger di ffusivity contrast. Additionally, their B-\nstructures are not aligned along the structures, again di ffering\nfrom most observations – small deviations are possibly oc-\ncasionally present. In some cases the interarm structures a re\nrather broad compared to those observed, but M 81, for ex-\nample, does have broad interarm structures (e.g. Krause et a l.\n1989).Largerdiffusivitycontraststhanillustratedcangivenar-\nrower and more filamentary arms. Our model assumes a link\nbetween star formation and magnetic arms. Indeed, stronger\nstar formation gives larger di ffusivity contrast which in turn\ngives more pronounced magnetic arms – compare Figs. 1 and\n6. Isolation of a correlation between star formation and mag -\nnetic arms as well as verification of other possible conse-\nquences of the model requires a richer observational basis f or\ninvestigationofthemagneticarms.Atthemomentitisnotve ry\nclear how much can be deduced from observations of several\nnearby galaxies (NGC 6946 appears likely to yield initial re -\nsults). Although our models are restricted to the no- zapproxi-\nmation, this does seem to be quite robust when applied to disc\ngalaxies(e.g.Chamandyet al.2014).\nWe recognize that our assumed di ffusivity gradients are a\ntheoretical (but plausible) assumption and are not based di -\nrectly on observational evidence, and that there are severa l\nother mechanisms that can contribute to formation of mag-\nnetic arms. In particular, modulation of the alpha e ffect and\ntimedelaybetweenthedistributionsofdynamodriversandd y-\nnamosuppression,thetreatmentofhelicityfluxesincludin gen-\nhanced outflow in the interarm regions, etc, can all play a rol e\n(e.g. Chamandy et al. 2013, 2014, 2015). We believe however\nthatthemechanismdescribedhere,basedonjointactionoft he\nturbulentdiffusivitycontrastandsmall-scalemagneticfieldin-\njections, gives a natural basis for explaining the phenomen on\nwithinclassical mean-fielddynamotheory.Acknowledgements. RS and DS are grateful to MPIfR for financial\nsupportandhospitalityduringvisitstoBonn.DSacknowled ges finan-\ncial support from RFBR under grant 15-02-01407. RB acknowle dges\nsupport byDFG ResearchUnit FOR1254.\nReferences\nBrandenburg, A.2015, eprint arXiv:1402.0212\nBeck, R.2015, toappear inA&A,eprint arXiv:1502.05439\nBeck, R.,Bomans, D.,Colafrancesco, S., Dettmar,R.-J.,Fe rri´ ere, K.,\nFletcher,A.,Heald,G.,Heesen,V.,Horellou,C.,Krause,M .,Lou,\nY.-Q.,Mao, S.A.,Paladino, R.,Schinnerer, E.,Sokolo ff, D.,Stil,\nJ.,Tabatabaei, F.,2015, eprint arXiv:1501.00385\nBeck, R., Brandenburg, A., Moss, D., Shukurov, A., Sokolo ff, D.,\n1996, Ann. Rev. Astron.Astrophys., 34, 155\nBrandenburg, A.,Donner, K.-J.,Moss, D.,Shukurov, A.,Sok oloff,D.\nD.,Tuominen, I.1992, A&A,259, 453\nChamandy, L., Shukurov, A., Subramanian, K. 2013, MNRAS, 42 8,\n3569\nChamandy, L., Shukurov, A., Subramanian, K., Stoker, K. 201 4,\nMNRAS,443, 1867\nChamandy, L., Shukurov, A., Subramanian, K. 2015, MNRAS, 44 6,\nL6\nDobbs, C.& Baba, J.D.2014, PASA,31, 35\nKrause, M., Beck, R.,& Hummel, E.1989, A&A,217, 17\nLazio, T.J.W., Cordes, J.M. 1998, in: Radio Emission from Ga lactic\nand Extragalactic Compact Sources, IAU Colloquium 164, eds .\nJ.A.Zensus, G.B.Taylor,&J.M. Wrobel,p. 329\nMoss, D. 1998, MNRAS,297, 860-866\nMoss, D., Stepanov, R., Arshakian, T.G., Beck, R., Krause, M .,\nSokoloff, D.2012, A&A,537, A68\nMoss, D.,Sokoloff, D.2013, GAFD,107, 497\nMoss,D.,Beck,R.,Sokolo ff,D.,Stepanov,R.,Krause,M.,Arshakian,\nT.G.2013, A&A, 556, A147\nPoezd, A.,Shukurov, A.,Sokolo ff, D. 1993, MNRAS,264, 285\nRuzmaikin, A., Shukurov, A., Sokolo ff, D. 1988, Magnetic Fields of\nGalaxies,Kluwer, Dordrecht\nShukurov, A.1998, MNRAS,299, L21"    },    {        "title": "1505.03216v1.Optical_detection_of_magnetic_orders_in_HgCr__2_O__4__frustrated_spin_magnet_under_pulsed_high_magnetic_fields.pdf",        "content": "arXiv:1505.03216v1  [cond-mat.mtrl-sci]  13 May 2015Typeset with jpsj3.cls <ver.1.1> Full Paper\nOptical detection of magnetic orders in HgCr 2O4frustrated spin magnet\nunder pulsed high magnetic fields\nDaisuke NAKAMURA, Atsuhiko MIYATA∗, Hiroaki UEDA†, Shojiro TAKEYAMA‡\nInstitute for Solid State Physics, University of Tokyo, 5-1 -5, Kashiwanoha, Kashiwa, Chiba,\n277-8581, Japan\nA magneto-optical survey was conducted for HgCr 2O4powder samples under pulsed high\nmagnetic fields of up to 55 T. Intensity changes in magnetic fields obs erved for the exciton-\nmagnon-phonon optical transition spectra coincide well with those of magnetization, lattice\ndistortion from X-ray diffraction, and electron-magnetic resonan ces. The last-ordered phase\nwas detected prior to the fully polarized magnetic phase, similarly to t he other chromium\nspinel oxide, ZnCr 2O4and CdCr 2O4.\nKEYWORDS: Magnetization, pulsed high magnetic field, geome trically frustrated magnet,\nmagneto-optical spectra\n1. Introduction\nHgCr2O4isoneofthechromiumspineloxides ACr2O4(A=Mg, Zn,Cd,Hg),comprisinga\nthree-dimensional pyrochlore antiferromagnet with corne r-sharing tetrahedra, and shows typ-\nical characteristics of geometrical spin frustration, rep resented by the large difference between\nthe N´ eel and Weiss temperatures. It is well known that stron g underlying spin-lattice cou-\npling plays an important role in the magnetic properties of t his magnetic-frustration system.\nWhen subjected to strong external magnetic fields, successi ve magnetic phase transitions take\nplace accompanied by discontinuous lattice distortions.1)The remarkable half-magnetization\nplateau phase2)and other antiferromagnetic phases realized in magnetic fie lds have been\nunderstood using a bilinear-biquadratic model that takes i nto account the spin-lattice inter-\nactions, as described in the theory developed by Penc et al.3)\nOndecreasing atomic size going from Hgto Zn or Mg at the Acation site in thepyrochlore\nlattice, much stronger magnetic fields are required to revea l all of the rich magnetic phases up\nto fully saturated magnetization, owing to the increased ne arest-neighbor antiferromagnetic\nexchange interaction. Strong magnetic fields above 100 T, wh ich could be used for solid-state\n∗Present address: Laboratoire National des Champs Magnetiq ues Intenses-Toulouse, 143, av. de Rangueil\n31400 Toulouse, France\n†Present address: Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502,\nJapan.\n‡E-mail: takeyama@issp.u-tokyo.ac.jp\n1/8J. Phys. Soc. Jpn. Full Paper\nphysics measurements, have only been generated by magnet-c oil destructive methods in an\nextreme environment, such as the single-turn coil and the el ectro-magnetic flux compression\ntechniques, and are associated with relatively large instr uments with their operation limited\nto microsecond time duration. Our group has explored an opti cal detection technique to\nstudy magnetic phases in extremely high magnetic fields and t he methods have been applied\nto CdCr 2O4,4,5)ZnCr2O4,6–8)and MgCr 2O4.9)The optical method was found to be a new\nand useful tool for detecting a magnetic phase that is hidden in conventional magnetization\ndata and has revealed a new magnetic phase (described as the l ast ordered phase, LOP)\nprior to the fully polarized moment state.5)The novel phase was concluded to be a phase\ncorrespondingto amagnetic ‘superfluidstate’, inferredfr om an analogy to symmetry breaking\nof the quantum phases in4He as proposed by Matsuda and Tsuneto10)and Liu and Fisher.11)\nThe magnetic superfluid state is a state in which magnetic ord ering takes place in the plane\nperpendicular to the magnetic field. Details of the spin stru cture of the novel phase could only\nbe determined with comprehensive study based on other probe s and measurements. However,\nthemagnetic-field strengths ( B) at which theLOPis realized areextremely large andmethods\nof measurement probes are quite restricted.\nWe address two questions. One is whether the LOP observed in o ther chromium oxides\nalso exists in HgCr 2O4. The second is how the optically detected signals relate to t he other\nmeasurements, such as X-ray diffraction and electron magneti c resonance (EMR). This pa-\nper focuses on magneto-absorption spectra appeared as an ex citon-magnon-phonon (EMP)\ntransition in HgCr 2O4in magnetic fields of up to 55 T. The results are discussed base d on a\ncomparison with those obtained from magnetization,12)X-ray diffraction,1)and EMR.13)\n2. Experiments\nPolycrystalline powder of HgCr 2O4, which was synthesized using thermal decomposi-\ntion,12)was dispersed in Stycast 1266B (liquid) catalyst with a weig ht ratio of the powder to\nthe resign of 1:4. First, the B catalyst with dispersed powde r was blended into the Stycast\n1266A resin after confirmation of complete and uniform mixtu re of the powder with an assist\nof an ultrasonic disperser. The blended components were the n dropped on a quartz disk (4\nmm diameter and 0.4 mm thickness) and were dried one day in the air. The solidified mixture\nwas then polished to a disk form with its thickness of approxi mately 50 µm as shown in Fig.1\n(a). Pulsed magnetic fields were generated from a nondestruc tive-type pulsed magnet which\nis capable of generating a magnetic field of up to 55 T with a hal f-period of 35 ms. A Xe-flash\nlamp was used as a light source. Optical fibers were used to gui de the light in and out from\n2/8J. Phys. Soc. Jpn. Full Paper\nFig. 1. (Color online)(a) Polycrystallinepowder HgCr 2O4and a disk with the powder embedded in a\nStycast resin synthesized in a manner described in the text. (b) Ab sorption spectra obtained at 1.8\nK in a region of wavelengths where4A2−4T2and EMP transitions are observed in polycrystalline\npowder HgCr 2O4embedded in Stycast resin.\nthe sample situated at the center of the magnet, and also to th e polychromator equipped with\nan ICCD (image-intensified-charge-coupled device). The IC CD optical gate was open for 5\nms at the peak of the magnetic field so that the transmission li ght was recorded on the CCD\narrays at each value of the magnetic field. The error in the mag netic field during the optical\nexposure time was approximately 2 T at the peak of 55 T. The sam ple temperature was kept\nat 1.8 K in a liquid helium cryogenic container.\n3. Results\nFigure 1(b) displays the absorption spectra of a disk sample prepared in the manner\ndescribed above. From the analogy of the spectra measured fo r CdCr 2O45)and ZnCr 2O4,8)a\nbroad but intense absorption peak at 590 nm is assigned as ari sing from the4A2−4T2intra-d-\nband transitions (also see ref. 14). The small peaks that app ear around 675 nm are attributed\nto the EMP transitions. The intra-d-band absorption peak (4A2−4T2) is much broader than\n3/8J. Phys. Soc. Jpn. Full Paper\nthose observed in CdCr 2O4and ZnCr 2O4, probably because of the polycrystalline powder\ncharacteristics having associated stress and surface diso rders. The EMP absorption spectra\nshow decreasing peak intensity with increasing magnetic fie ld, as seen in Fig. 2 (a), where the\nintegrated intensity of the peak is plotted against magneti c field. As noted from this plot, the\nrate of intensity decrease is not constant. There are severa l ranges of magnetic-field strength\nfor which the rate of decrease changes. The intensity is almo st constant up to 13 T, and then\ndecreases until 27 T, where the rate of decrease slows down. T here are kinks at 35 T, 45 T,\nand 48 T indicative of the changes of the decreasing rate. The magnetic-field strengths at\nwhich the rate changes exhibit very good correspondence wit h magnetization steps. Figure\n2(b) is a plot of a magnetization Mand its derivative d M/dBin magnetic fields measured\nat a temperature of 1.8 K,12)where the successive field-induced phase transitions have b een\nreported up to a full saturation of the moment. Starting from the antiferromagnetic phase, M\nincreases linearly up to 10 T ( Bc1), then exhibits a sudden jump associated with hysteresis\nbefore entering into the half-magnetization plateau phase (a collinear three-up, one-down\nspin configuration) above 13 T. This plateau continues up to 2 7 T (Bc2), above which M\nincreases linearly again up to 35 T ( Bc3), where it exhibits a canted 3:1 phase. Finally, M\nshows a sudden increase with a small hysteresis jump prior to a gradual saturation of the\nmagnetization moment of 3 µB/Cr3+in magnetic fields between 37 T and 45 T.\n4. Discussion\nAs seen in Fig. 2(b), the transition points observed in Mare associated with a finite\nwidth in magnetic fields, which are well recognized using the peak width in dM/dB, and\nare illustrated by a hatching zone. Note that the width at the Bc1transition is very wide in\ncomparison to the other chromium spinels, as has already bee n pointed out in ref. 12. They\nspeculated that this is due to the effect of disorder in the nonm agnetic cation site (the Hg\nsite) in the polycrystalline samples. It is readily evident from Fig. 2(a) and (b) that the kinks\nobserved in the intensity of the EMP transition spectra alwa ys occur in these hatching zones\nup toBc3, i.e., there is always a good correspondence between the mag netic field at which the\nkink takes place and those in the transition field in M.\nDetails about successive distortions of the pyrochlore lat tice with an application of mag-\nnetic fields in HgCr 2O4were revealed using synchrotron X-ray diffraction with a spec ially\ndesigned pulse magnet in magnetic-field strengths up to 38 T.1)Figure 2(c) is a plot of a\nchange in the lattice parameter, ∆ a(B) =a(B)−a(B= 0) in magnetic fields, which is repro-\nduced from ref. 1. We note the following two major results. Th e lattice constant changes up\n4/8J. Phys. Soc. Jpn. Full Paper\ntoBc1, whereas the EMP intensity stays constant. In the plateau ma gnetic phase, the lattice\nconstant stays constant, while the EMP intensity shows a lin ear decrease. These contrasting\nbehaviors of the EMP intensity are evidence that the EMP inte nsity predominantly reflects\nthe state of the magnons (the magnon density of states) but is less influenced by the changes\nin the lattice, in spite of the tight involvement of both phon ons and magnons for the EMP\noptical transition.\nAccording to the discussion of Tanaka et al.,1)all the bond lengths elongate equally in\nthe pyrochlore lattice in the fully polarized phase in magne tic fields above Bc3. Hence, the\nlattice constant should be constant above Bc3, andMis regarded as showing full saturation\naccompanied by gradual increases due to an effect of finite temp erature. However, the EMP\nintensity shows a kink at Bc3and continues to decrease followed by another kink at 45 T\n(Bc4). The anomaly observed in the EMP transition intensity betw eenBc3andBc4suggests\nthe existence of a novel phase in the region that is believed t o be a fully polarized phase. A\nsimilar phase has already been reported by our group, inferr ed from anomalies in the optical\nabsorption spectra of ZnCr 2O47,8)and CdCr 2O4.5)\nLet us note here the discussion by Kimura et al. who have condu cted EMR together with\nmagnetization measurements in strong pulsed magnetic field s.13)Firstly, they observed in\ndM/dB an evident but weak peak around 39 T beside the main sharp peak at 35 T ( Bc3),\nwhich was attributed to a possible new phase between the cant ed (3:1) ferromagnetic phase\nand the fully polarized phase. A similar but rather broad pea k around 82 T in dM/dBwas\nalso observed by our group for CdCr 2O4measured using a single-turn coil.5)We ascribed this\nanomaly to a transition to a novel phase, i.e., the LOP, in whi ch a magnetic ‘superfluid’ state\nin a boson picture (such as either an umbrella-like spin stru cture or a spin-nematic state)\nis realized. Second, rapid disappearance of the EMR wumode at 36 T, corresponding to a\nsharp transition peak in dM/dB, is indicative of the last field-induced lattice transition to a\nhigh-symmetry cubic structure. This scenario is also consi stent with those in the discussion\nabove by Tanaka et al. Therefore, the LOP transition from the 3:1 canted phase is first-order\nand accompanied by the lattice distortion transformed into a higher symmetry.\nAccording to a finite-temperature Monte-Carlo simulation o f carried out by Motome et\nal. for a magnetization in a classical pyrochlore lattice wi th incorporation of the bilinear and\nthe biquadratic interactions,15)there appears in susceptibility a broad shoulder at the high\nmagnetic field side of the sharp peak of the transition into th e final fully polarized phase. This\nshoulder-like structure arises from the temperature-depe ndent broadening of the last first-\norder transition and never exhibits a peak structure as is ob served in real experiments. There-\n5/8J. Phys. Soc. Jpn. Full Paper\nfore, the small peak in dM/dB magnetization data around 39 T that appears for HgCr 2O4\nis similarly associated with a phase transition to the LOP pr ior to the full-saturation phase,\nas has been observed in CdCr 2O4and ZnCr 2O4. A sudden decrease of the EMP intensity is\nobserved above Bc4, where magnetization showed almost complete saturation. T his sudden\ndecrease suggests the existence of a finite gap for magnon exc itation from the fully polarized\nstate, which is regarded as the ground state in a magnon pictu re.\n5. Summary\nOptical absorption arising from an EMP transition observed in powdered HgCr 2O4was\nmeasured in magnetic fields up to 55 T. The EMP absorption, refl ecting a magnon density\nof states, showed intensity changes corresponding to phase transitions consistent with mag-\nnetization, lattice distortions, and EMR successive anoma lies reported previously. This study\nhas revealed that a fourth phase, termed LOP, also exists in H gCr2O4and is related to the\nmagnetic superfluid state that has also been observed in CdCr 2O4and ZnCr 2O4between the\ncanted (3:1) phase and the full-saturation phase.\nAcknowledgments\nThe authors are obliged to Prof. K. Kindofor providing us wit h a non-destructive magnet.\nA.M. thanks to a support of the Grant-in-Aid for JSPS Fellows .\n6/8J. Phys. Soc. Jpn. Full Paper\nFig. 2. (Color online) (a) Changes in an integratedintensity of the EM P absorption peak in magnetic\nfields. (b) Magnetization Mand its derivative dM/dBas a function of magnetic field, measured\nat 1.8 K, (ref.12) and (c) Change of the lattice parameter ∆ aplotted against a magnetic field.\nThe data (circle) are reproduced from Fig.2 in ref. 1.\n7/8J. Phys. Soc. Jpn. Full Paper\nReferences\n1) Y. Tanaka , Y. Narumi , N. Terada , K. Katsumata, H. Ueda, Urs Staub, K. Kindo, T. Fukui, T.\nYamamoto, R. Kammuri ,M. Hagiwara, A. Kikkawa, Y. Ueda, H. Toyoz awa , T. Ishikawa , and H.\nKitamura: J. of Phys. Soc. Jpn., 76(2007) 043708.\n2) H. Ueda, H. Aruga Katori, H. Mitamura, T. Goto, and H. Takagi: P hys. Rev. Lett. 94(2005)\n047202.\n3) K. Penc, N. Shannon, and H. Shiba, Phys. Rev. Lett. 93(2004) 197203.\n4) E. Kojima, A. Miyata, S. Miyabe, S. Takeyama, H. Ueda, and Y. Ue da; Phys. Rev. B 77(2008)\n212408 .\n5) A. Miyata, S. Takeyama, and H. Ueda: Phys. Rev. B 87(2013) 214424.\n6) A. Miyata, H. Ueda, Y. Motome, N. Shannon, K. Penc, and S. Tak eyama: J. Phys. Soc. Jpn. 80\n(2011) 074709.\n7) A. Miyata, H. Ueda, Y. Ueda, H. Sawabe, and S. Takeyama: Phys . Rev. Lett. 107(2011) 207203.\n8) A. Miyata, H. Ueda, Y. Ueda, Y. Motome, N. Shannon, K. Penc, a nd S. Takeyama: J. Phys. Soc.\nJpn.81(2012) 114701.\n9) A. Miyata, H. Ueda, and S. Takeyama; J. of Phys. Soc. Jpn. 83(2014) 063702.\n10) H. Matsuda and T. Tsuneto: Prog. Theor. Phys. Suppl. 46(1970) 411.\n11) K. S. Liu and M. E. Fisher: J. Low Temp. Phys. 10(1973) 655.\n12) H.Ueda, H. Mitamura, T. Goto, and Y. Ueda: Phys. Rev. B 73(2006) 094415.\n13) S. Kimura, M. Hagiwara, T. Takeuchi, H. Yamaguchi, H. Ueda, Y. Ueda, and K. Kindo: Phys.\nRev. B83(2011) 214401.\n14) M. Schmidt, Zhe Wang, Ch. Kant, F. Mayr, S. Toth, A. T. M. N. I slam, B. Lake, V. Tsurkan, A.\nLoidle, and J. Deisenhofer: Phys. Rev. B 87(2013) 224424.\n15) Y. Motome, K. Penc, and N. Shannon: J. Magn. Magn. Mater. 300(2006) 57.\n8/8"    },    {        "title": "1506.01805v3.On_the_magnetization_process_of_ferromagnetic_materials.pdf",        "content": "On the magnetization process in ferromagnetic materials\nRuben Khachaturyan\u0003and Vahram Mekhitariany\nInstitute for Physical Research, NAS of Armenia, Ashtarak, Armenia\n(Dated: June 18, 2021)\nThe present article concludes that a ferromagnetic sample could be considered as a paramagnetic\nsystem where roles of magnetic moments play magnetic domains. Based on this conclusion and\ntaking into account presence of an anisotropy \feld the formula which describes magnetization de-\npendence on the external magnetic \feld is derived. Expressions for a remanent magnetization and a\ncoercive force are presented. The new parameter to characterize a magnetic sti\u000bness of a material is\nintroduced. A physical expression for a dynamic magnetic susceptibility as a function of materials\ncharacteristics, external magnetic \feld, and temperature is given.\nI. INTRODUCTION\nA physical theory permits correctly involve all inter-\nactions in a magnetization process and to reveal rela-\ntionship between structure and physical properties of a\nmagnetic material.\nApplicable mathematical model could be derived from\nsuch a theory. This model will give a possibility to inves-\ntigate real physical and structural properties of magnetic\nmaterials from experimental data. It is essential for syn-\nthesis of new materials with desired properties.\nNowadays there are several models for describing mag-\nnetization of ferromagnetic materials. More detailed de-\nscription and analyzes of advantages and disadvantages\nof these models one can \fnd in works [1]-[4].\nIn the present paper, there suggests a new theory of\nmagnetization and an attempt to derive an applicable\ngeneral mathematical model to describe magnetization\ncurve for soft and sti\u000b magnetic materials. Such generic\nspecial points in magnetization curve are also elicited\nfrom the model.\nA formula for dynamic magnetic susceptibility is de-\nrived from a magnetization \feld dependence.\nA new parameter which can numerically characterizes\nthe magnetic sti\u000bness of a material is introduced and its\nphysical interpretation is given.\nII. MAIN IDEA\nTwo competing interactions could be distinguished in\nferromagnetic materials: an exchange interaction ( exch)\nwhich tends to orient magnetic moments in the same di-\nrection and by this magnetizes the system and dipole-\ndipole interaction ( dip-dip ) which tends to orient mag-\nnetic moments antiparallel to each other and by this\ndemagnetize the system. A relevant di\u000berence between\nthese interactions is that exch acts between nearest atoms\nand its energy is independent of a magnetic moment of\n\u0003rubenftf@gmail.com\nyvahram.mekhitarian@gmail.coma system. On the contrary, dip-dip energy rises as mag-\nnetic moment increases. Increasing a material size a dip-\ndipenergy can overcome exch energy. In this case, two\nand more domains structures become more favorable. It\nis schematically shown in \fgure 1.\nAsexch energy is much bigger than dip-dip energy be-\ntween nearest atoms magnetic moments inside a domain\nare \frmly connected in the same direction. The magnetic\nshell where dip-dip energy becomes equal to exch energy\ncould be accepted as a border of the domain and by this\nde\fning a size of a domain [5]. So, after a domain was\ncompleted the next shell of magnetic moments will recline\nin the opposite direction, \fgure 1. It should be mentioned\nthat magnetic moments inside a domain are not strictly\ndirected in the same direction. They recline under an\nangle to each other from shell to shell until the domain\nwould not be \fnished. The transition layers behaviour\nis detailed described in the work of Landau-Lifshitz [6].\nBecause of it, a magnetic moment of a domain is less\nthan a sum of magnetic moments of atoms inside it.\n() dipdip E V−exchE const=E\nsize\nFIG. 1. Diagram representation how exch energy and dip-dip\nenergy behave with increasing of size.\nOn the assumption of foregoing we could consider do-\nmains like solitary magnetic particles. The separated\nquasiparticles we would call supermagneton ( sm) analog-\nically to R.Harrison [7]-[9] where domains are also sup-\nposed to be a unit magnetic moments in the magnetiza-\ntion processes.\nWe know that exch is compensated by dip-dip between\nsms. It means that sms magnetic moments are exempt\nfrom exch. So, the problem of ferromagnetic materials isarXiv:1506.01805v3  [cond-mat.mtrl-sci]  15 Jul 20162\nbrought to a problem of paramagnetic materials where\nsms play the role of magnetic moments.\nSeeing that there are axes of easiest magnetization in\nferromagnetic materials [10] sms are distributed in a \feld\nof anisotropy according to the Boltzmann distribution.\nFor simplicity, we would consider a case of uniaxial\nanisotropy. Sms with a positive projection on any se-\nlected direction along the anisotropy axis separated from\nsms with negative projection by anisotropy barrier, \fg-\nure 2.\nθaEθ\nθπ+aEE\nπ\n20π\nFIG. 2. Sms separated by anisotropy barrier.\nIII. III. MAGNETIZATION PROCESS\nBy applying magnetic \feld Hto a ferromagnetic ma-\nterial a magnetic \feld Bis induced inside. Sms with\npositive projection on the magnetic \feld direction obtain\nenergy - m+B, and sms with negative projection obtain\nenergy m\u0000B, where m+andm\u0000are magnetic moments\nofsms with positive and negative projection respectively.\nTaking into account that m++m\u0000= 2m,mis mag-\nnetic moment of sms in zero \feld, we can conclude that\nm\u0000B+m+B= 2mB. It means that domains could be\ne\u000bectively replaced by sms magnetic moment of which\nremains unchanged and equal to a magnetic moment of\ndomain in nonmagnetized state.\nSo, potential wells shift on a value 2 mB, as shown on\n\fgure 3.\nFIG. 3. Shift of potential wells in the induced \feld B.As a result of the energetic shift magnetization of the\nsample is appeared.\nTo estimate the magnetization one needs to calculate a\ndi\u000berence between magnetic moments with positive and\nnegative projections. Here and in further positive and\nnegative directions would be considered relative to the\ndirection in which external magnetic \feld is applied.\nTaking into account that at any \feld value distribution\nofsms is obey to the Boltzmann statistics we can calcu-\nlate a di\u000berence between amount of smswith negatie and\npositive projections:\nN1\u0000N2=\nZ\ng(E+Ea)e\u0000E\nkBTdE\u0000\n\u0000Z\ng(E\u0000Ea\u00002mB)e\u0000E\nkBTdE=\n=e\u0000Ea\nkBT\u0000e\u00002mB\u0000Ea\nkBT(1)\nN1+ N 2=e\u0000Ea\nkBT\u0010\n1 +e\u00002mB\u00002Ea\nkBT\u0011\n(2)\nBy the same way we get:\nN1+ N 2=e\u0000Ea\nkBT\u0010\n1 +e\u00002mB\u00002Ea\nkBT\u0011\n(3)\nDividing 2 on 3 we get:\nN1-N2=1\u0000e\u00002(mB+Ea)\nkBT\n1 +e\u00002(mB+Ea)\nkBT=\n= (N 1+N2) tanh\u00142 (mB\u0000Ea)\nkBT\u0015(4)\nMultiplying 4 on mand taking into account that by de\u000b-\ninition:\n\u001a\nMS=m(N1+ N 2)\nM=m(N1- N2)(5)\n\fnally we obtain:\nM=MStanh\u00142 (mB\u0000Ea)\nkBT\u0015\n(6)\nwhere MSis saturation magnetization and Mis magne-\ntization in \feld B.\nTo explore magnetization process more thoroughly it is\nnecessary to understand \feld distribution inside a mate-\nrial during magnetization. As direction of external \feld\nis given we will concentrate on distribution of dipolar\n\feld.\nThe magnetic \feld which is induced by magnetic mo-\nment in any point could be calculated in \frst approxima-\ntion as [12]:\n~H=3^n(~ m\u0001^n)\u0000~ m\nr3(7)3\nFIG. 4. Dipolar \feld distribution around the magnetic mo-\nment. aand bare lines where magnetic \feld change their\nprojection sing on magnetization direction.  is an angle\nbetween magnetization direction and lines aandb. 1, 3 are\nspace regions where dipolar \feld has positive projection on\nmagnetic moment direction and 2, 4 are space regions where\ndipolar \feld has negative projection on magnetic moment di-\nrection.\nwhere~ nis a unit vector in the direction to the point, and\nris distance between magnetic moment and the point\nwhere the \feld is calculated.\nIt is seen from 7 that Hhas negative or positive pro-\njection on the direction of magnetic moment in di\u000berent\npoints. It is not di\u000ecult to found points where Hchanges\nits projection sign on direction of the magnetization from\n7.\n3_n\u0010\n~M\u0001_n\u0011\n\u0000~M= 0 (8)\n8\n<\n:3\u0010\n~M_n\u00112\n\u0000~M_n= 0\n~M_n=Mcos ( )(9)\ncos ( ) =p\n3\n3(10)\n \u001955\u000e(11)\nThese points belong to the lines aandbwhich decline\nunder angles  to magnetization direction as shown on\n\fgure 4. Lines aandbdemarcate space around magnetic\nmoment on four regions: 1, 2, 3, 4.\nSo,Hhas positive projection in any point which be-\nlongs to regions 1 and 3 with biggest value when or and\nhas negative projection in any pint of region 2 and 4 with\nbiggest value ~H=2~ m\nr3when = 0\u000eor 180\u000e.\nBy this, dipolar \feld plays both magnetize (positive)\nand demagnetize (negative) roles. Due to positive in-\n\ruence of depolar \feld it is possible to magnetize bulk\nsamples.\nThus magnetic \feld inside a sample could be repre-\nsented as:\nB=H\u0000\u0011M\na3(12)where\u0011M\na3is a dipolar term, ais a distance between near-\nest domains domains (linear size of a sm),\u0011is a coe\u000ecient\nwhich represents di\u000berence between positive and negative\ndipolar in\ruences.\nAs an example, we will consider two-domain rod as\nshown on \fgure 5. Lets compare processes of magneti-\nzation of such a rod when the external magnetic \feld is\ndirected along longitude (x axis) and when the external\nmagnetic \feld is directed along width (y or z axes).\nz\nyx\nFIG. 5. Two domain rod.\nWhen the rod is magnetized along x axis the dipolar\n\feld of one domain will magnetize the second domain be-\ncause it belongs to the region of the space where dipolar\n\feld has positive projection on magnetization direction.\nThe diagram of the process is shown in \fgure 6. By this\ndipolar \feld will help to magnetize the system. In this\ncase s-shaped hysteresis loop would be observed [7]-[8].\nWhen the rod is magnetized along z axis one domain will\n \nx\nH\nFIG. 6. The rod is magnetized along longitude.\ndirect the second domain in the opposite direction be-\ncause it belongs to the region of the space where dipolar\n\feld has negative projection on magnetization direction\nas shown in \fgure 8. In this case \u0011= 1. Because of\nall written above, the magnetic energy term in 6 should\nbe replaced by \u0011mMa, where\u0011is a parameter which\ndepend on di\u000berence between demagnetizing and magne-\ntizing parts of dip-dip in\ruences, by this \u0011depends on\nshould depend on surface and surface volume ratio. At\neach certain values of external magnetic \feld the certain\ndistribution of \feld inside a material exists. This \feld\ndistribution changes with external \feld, and by this \u0011\nchange with external \feld as well.\nM=MStanh\u0014mH\u0000\u0011m\na3M+Ea(\r)\nkBT\u0015\n(13)4\n \nz\nH\nFIG. 7. The rod is magnetized along width.\nAs equation 13 is trancendent it could be rewritten in\nmore convenient form as done in [7]-[9]:\nH=\u0011\na3M+kBT\n2mln\u0012MS\u0000M\nMS+M\u0013\n+Ea(\r)\nm(14)\nIt should be noticed that the last term in 14 is indepen-\ndent on the value of magnetic moment as both magnetic\nmoment of the domains and anisotropy energy term are\nboth volume dependant.\nIV. REMANENT MAGNETIZATION AND\nCOERCIVE FORCE\nAfter the external magnetic \feld was abolished a dip-\ndiptends to demagnetize the sample. Because of this\nsms would turn from positive projection to negative\nthrough anisotropy barrier. But not all sms can over-\ncome anisotropy barrier and the part of them would re-\nmain with positive projection. So, after the external\nmagnetic \feld was abolished ferromagnetic sample would\nsteel remain in magnetize condition. This magnetization\nis called remanent magnetization. It is represented in\n\fgure 9. In order to get expression for remanent magne-\ntization it is necessary to put H=0 into 13:\nMR=MStanh\u0014\u0000\u0011m\na3MR+Ea(\r)\nkBT\u0015\n(15)\nwhere MRis remanent magnetization.\nAs is known a coercive force is a magnetic \feld which\nshould be applied to the sample to demagnetize it. So to\nget an expression of coercive force one need to put M=0\ninto 14:\nHC(T) =\u0000Ea(\r)\nm(16)\nIt is seen that coercive force depends on the \feld di-\nrection (angle between \feld and anisotropy axis).\nV. MAGNETIC STIFFNESS\nThe next parameter can characterize magnetic sti\u000bness\nof ferromagnetic materials:\nk=e\u00002\u0011mMRa\u0000Ea(\r)\nkBT (17)\n \nSRMM\naE\nEFIG. 8. sms overcome anisotropy barrier when sample change\nits state from saturated magnetization to remanent magneti-\nzation.\nDividing 2 on 3 it is possible to show that k=N2\nN1and\nrepresents the ratio of the amount of sms which overcame\nanisotropy barrier to the amount of sms which remain\nwith positive projection after the external magnetic \feld\nwas abolished, \fgure ??.\nValues of kcould change in the range from 0 to 1. The\nbigger the value of kthe softer magnetic material is and\nvice verse. For example, in case of strong anisotropy no\nofsms are able to overcome anisotropy barrier, it means\nthat there are no sms with negative projection ( k= 0)\nandMR=MSrectangular-like hysteresis loop, \fgure\n12 a). In the case when all sms were able to overcome\nanisotropy barrier, the amount of sms with negative pro-\njection is equal to the amount of positive projection ( k\n= 1 ) and consequently MR= 0, \fgure 12 c).\n \n)a\n)b\nFIG. 9. Three possible case of sms distribution in a state of\nremanent magnetization: a) k= 0; b)k= 1;; Cases a) and\nb) corresponds to a magneto sti\u000b material and magneto soft\nmaterials correspondingly.\nVI. DYNAMIC MAGNETIC SUSCEPTIBILITY\nA low which describes magnetization dependence on\nexternal magnetic \feld gives possibility to \fnd out a law\nfor magnetic susceptibility:\n\u001f=dM\ndH=MSd\ndHtanh\u0014m(H\u0000\u0011Ma) +Ea(\r)\nkBT\u0015\n=\n=MSm\u0001\u0010\n1\u0000d\u0011\ndHMa\u00004\u0019\u0011\na3\u001f\u0011\n+MSdEa(\r)/dH\nkBT\u0001ch2h\nm(H\u0000\u0011Ma)+Ea(\r)\nkBTi\n(18)5\n\u001f=MSh\nm\u0010\n1\u0000d\u0011\ndHMa\u0011\n+dEa(\r)/dHi\nkBTch2h\nm(H\u0000\u0011Ma)+Ea(\r)\nkBTi\n+\u0011\na3mMS(19)\nIt should be noted that \u0011decreases with increasing of\nHthusd\u0011/dHM < 0.\nThis term is one of factors which are responsible for\nhigh value of magnetic susceptibility of ferromagnetic\nmaterials.\nIt is seen that a magnetic susceptibility depends on\nthe external magnetic \feld, the dipolar interaction, the\ntemperature of the sample and the anisotropy energy, as\nit was expected.\nIn case of high temperature or small external magnetic\n\feld (tanh ( x)!x;\u0011!1) from 19 one can get:\n\u001f=MS\u0010\nm+dEa(\r)/dH\u0011\nkBT+mMS\u000e\na3(20)\nVII. CONCLUSION\nThere was shown that a magnetic sample could be con-\nsidered as a set of magnetic particles, called superpara-\nmagnetons ( sms). Magnetic moment of smis equal to\na magnetic moment of domain plus magnetic moment\nof the domain wall, before external magnetic \feld was\napplied. The stark di\u000berence of the smis that it's mag-\nnetic moment doesn't change during magnetisation pre-cess and sms are free from exchange interaction what\ngives a possibility to apply the Boltzmann statistics for\nthem as it done for paramagnetic samples.\nBased on this assumption there was derived the analyt-\nical excretion to describe a dependence of magnetization\nof a ferromagnetic material on an internal 6.\nConsidering dipolar \feld distribution inside a material\nan analytical expression of magnetization dependence on\nan external magnetic \feld 13 is also deduced.\nIt is important that all energies that take place in\nthe process of magnetization are included additively. It\nmeans that additional energies like energies on domain\nwalls pinning could be easily added in the formula in 13.\nThere were derived expressions for a remanent mag-\nnetization 15 and a coercive force 16 as special points\nonM(H) curve. It is seen that temperature dependence\nof remanent magnetization bears exponential character\nand depend on dip-dip in a sample and on an anisotropy\nbarrier. It is also seen how coercive force depend on\nanisotropy barrier and a magnetic moment of a domain.\nA new parameter which characterizes a magnetic sti\u000b-\nness of a material and its temperature dependence is in-\ntroduced 17.\nFrom M(H) function there was derived an expression\nfor a magnetic susceptibility 19. It is shown that in ex-\ntremal cases, like high temperature or low \feld, magne-\ntization depends on \feld linearly, and magnetic suscepti-\nbility is \feld independent like in the paramagnetic case.\nIt is essential to note that expressions 19 20 are appli-\ncable at all temperature regions.\n[1] D.C Jiles, X. Fang, W. Zhang, Handbook of Advanced\nMagnetic Materials , (2006).\n[2] F.Liorzou, B. Phelps, and D.L. Atherton, Macroscopic\nmodels of magnetization ,IEEE transactions on magnet-\nics, vol.36, No.2., (2000).\n[3] Sergey E. Zirka, Yuriy L. Moroz, Robert G. Harrison, and\nKrzysztof Chwastek, On the physical aspects of the Jiles-\nAtherton hysteresis models , J. Appl. Phys. 112, (2012).\n[4] D.C. Jiles and D.L. Atherton, \"Theory of ferromagnetic\nhysteresis\", J. Magn. Magn. Mater. 61, 48, (1986).\n[5] J. Frankel and J. Dorfman; \"Spontaneous and Induced\nMagnetisation in Ferromagnetic Bodies\", (1930).\n[6] L. Landau, E. Lifshits, \"On the theory of the dispersion of\nmagnetic permeabillity in ferromagnetic bodies\", Phys.\nZeitsch. der Sow. 8, pp. 153-169, (1935).\n[7] R.G. Harrison, \"Physical model of spin ferromagnetism\",\n(2003).[8] R.G. Harrison, \"Variable-Domain-Size theory of spin fer-\nromagnetism\", (2004).\n[9] R.G. Harrison, \"Physical theory of ferromagnetic \frst-\norder return curves\", IEEE TRANSITION ON MAG-\nNETICS, Vol. 45 NO, 4, (2009).\n[10] L. D. Landau and E. M. Lifshitz, Course of Theoretical\nPhysics, Vol. 8, (2005).\n[11] C. Kittel, \"Theory of the structure of ferromagnetic do-\nmains in \flms and small particles\", Phys.Rev. vol.70,\nNO. 11 and 12, (1946).\n[12] L. D. Landau and E. M. Lifshitz, Course of Theoretical\nPhysics, Vol. 2: The Classical Theory of Fields (Nauka,\nMoscow, 1988; Pergamon, Oxford, 1975).\n[13] Alberto P. Gimaraes, Principles of Nanomagnetism,\nSpringer, 2009."    },    {        "title": "1506.02346v1.Approximate_solution_of_wave_propagation_in_transverse_magnetic_mode_through_a_graded_interface_positive_negative_using_asymptotic_iteration_method.pdf",        "content": "arXiv:1506.02346v1  [cond-mat.mtrl-sci]  8 Jun 2015Approximate solution of wave propagation in transverse mag netic mode through a\ngraded interface positive-negative using asymptotic iter ation method∗\nAndri S. Husein,1,†C. Cari,1A. Suparmi,1and Miftachul Hadi2,3,4,5\n1Department of Physics, University of Sebelas Maret\nJalan Ir. Sutami 36 A, Surakarta 57126, Indonesia\n2Department of Mathematics, Universiti Brunei Darussalam\nJalan Tungku Link BE1410, Gadong, Negara Brunei Darussalam\n3Physics Research Centre, Indonesian Insitute of Sciences ( LIPI)\nKompleks Puspiptek, Serpong, Tangerang 15314, Indonesia\n4Department of Physics, School of Natural Sciences\nUlsan National Institute of Science and Technology (UNIST)\n50, UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan, South Korea\n5Institute of Modern Physics, Chinese Academy of Sciences\n509 Nanchang Rd., Lanzhou 730000, China\n(Dated: March 18, 2021)\nWe investigate the propagation of electromagnetic waves in transverse magnetic (TM) mode\nthrough the structure of materials interface that have perm ittivity or permeability profile graded\npositive-negativeusingasymptoticiterationmethod(AIM ).Astheopticalcharacterofmaterials, the\npermittivity and the permeability profiles have been design ed from constant or hyperbolic functions.\nIn this work we show the approximate solution of magnetic fiel d distribution and the eight models\nof wave vector of materials or interface positive-negative gradation.\nI. INTRODUCTION\nA new class of artificial composite material is negative refractive ind ex metamaterials (NRM), which is also called\nleft-handed metamaterials(LHM), has attracted the interest of manyscientists for more than a decade. Veselago1who\nfirst published a review of theoretical NRM for more than four deca des ago. Then Pendry translate these concepts\ninto practical applications3–5which then attracted great attention on this topic. Experimental confirmation is given\nby Smith et al6and Shelby et al17.\nThe concept of NRM is quite simple. The function of the material is mor e likely to be determined by the structure\nrather than by chemical composition. This is a new class of materials t hat goes beyond conventionalmaterials because\nit has the effect of which has never been observed before14.\nNRM has structure in the order of subwavelengths and is able to pro vide negative refractive index in a certain\nwavelengthrange. The artificialstructurecontainsnegativeper meabilityobtainedfrom the double split-ringresonator\nand negativepermittivity obtained from nano-wires6. The initial ideaofVeselagoderivedfrom the dispersion equation\nwhich expresses the interaction of electromagnetic waves with a die lectric. Dielectric response to the presence of\nan electromagnetic wave is expressed by the basic characteristics of the two quantities, i.e. permittivity, ε, and\npermeability, µ. That is because only these two quantities that appear in the disper sion equation1.\nUsing a diagram of ε−µ, the material properties can be grouped into four classes i.e.1: (i) Ordinary materials\n(ε >0, µ >0); (ii) Materials with negative permittivity and positive permeability ( ε <0, µ >0); (iii) NRM\n(ε<0, µ<0) and (iv) Materials with positive permittivity and negative permeabilit y (ε>0, µ<0).\nAnalysis of the wave propagation through the NRM structures mos t commonly done with modeling and numerical\nsimulation, in particular using the finite difference time domain method ( FDTD). FDTD method has been widely\naccepted as one of the popular numerical methods in computationa l electromagnetic2. At present, the method used\nto design and to obtain insight into the physical characteristics of e lectromagnetic NRM13. NRM structures with\ngraded refractive index interface negative-positive has been solv ed analytically by M. Dalarsson for the special case\nin which its index profile is a linear or exponential function15.\nActually, the realstructureofanymaterialcontainspositive and negativerefractiveindex and at the sametime tend\nto have a gradation profile10. NRM gradation index has been widely studied. Ramakrishna describe s an NRM lenses\ncomposed of media with a gradient index9. Calculation of the transmittance at an exponential gradation str ucture\nNRM has been given by N. Dalarsson10. Analytical solutions obtained from hypergeometry differential eq uations\ncompared with the numerical solution using the transfer matrix met hod (TMM) seem to have a good pattern match.\n∗Presented at the ICTAP Bali, Indonesia, Oct 20142\nElectromagnetic wave equation for inhomogeneous medium can be co nverted into a second order homogeneous\nordinary differential equation which is linear in one dimensional case. T hus, the analytical solution of Maxwell’s\nequations can be solved in this domain. Homogeneous second order o rdinary differential equations appeared widely in\nthe literature and there are several ways to obtain an exact solut ion such as using methods of hypergeometry, super-\nsymmetry quantum mechanics7, Nikiforov-Uvarov(NU)18, Romanovski polynomials19–21and which has recently been\nused is asymptotic iteration method (AIM) to solve the eigenvalue pr oblem8and electromagnetic wave propagation\nin inhomogeneous ordinary material12.\nExact solution of field distribution (eigenfunction) and energy (eige nvalue) can be obtained using the AIM if the\nHamiltonian of the system is shaped like a harmonic oscillator8. In this paper we try to apply the AIM in the case\nof inhomogeneous materials where permittivity or permeability has a p ositive-negative gradation profile. Here we\nrestrict the calculation just on the approximate solution.\nII. METHOD\nIn this section we present mathematical background to manage ca lculations of light propagation in the interface of\nNRM with positive-negative gradation. We will discuss this study in thr ee subsections: (i) we manipulate Maxwell’s\nequations to construct the wave equation in inhomogeneous mater ials; (ii) we apply AIM approach to obtain solutions\nof second order homogeneous differential equation; (iii) we apply AI M to obtain approximate solution to the eight\nmodels of wave vector of materials.\nA. Field Equation\nTo simplify the calculations, we set the xz-plane as the plane of ray incident, so ∂/∂y= 0. In addition, the optical\ncharacteristics of ε(x) andµ(x) are considered as functions of material thickness, x. Using Maxwell’s equations and\nconsidering the geometry of the material, we obtain a second order differential equation of electromagnetic waves\nin inhomogeneous materials on mode Transverse Magnetic (TM). Act ually, in two-dimensional study, there are two\nindependentmodesi.e. TMmode, thegroupoffields: {Ex, Ey, Hz},{Ey, Ez, Hx},{Ez, Ex, Hy}andTransverse\nElectric (TE) mode, the group of fields: {Hx, Hy, Ez},{Hy, Hz, Ex},{Hz, Hx, Ey}.\nIn principle, these two modes (TM and TE) are similar to each other, s o we only need to do one calculation, e.g.\nthe TM mode. Now, let’s start by defining the form of plane waves whic h is a special solution of the wave equation\nH=H(x)ei(ωt−kz)(1)\nand from Maxwell’s equations is known that\niωµ(x)H=−∇×E;iωε(x)E=∇×H (2)\nConsider the group of fields in the TM mode which we use i.e. {Ez, Ex, Hy}. From eq.(1) and eq.(2) we obtain\n∂2H(x)\n∂x2−ε′(x)\nε(x)∂H(x)\n∂x+[ω2µ(x)ε(x)−k2]H(x) = 0 (3)\nwhere in eq.(3) above, the prime symbol (′) indicates the operation of differentiation with respect to x. This second\norder differential equation does not always have the exact solution to a number of functions ε(x) andµ(x) . In the\nnext subsection, we will introduce the approach that is needed to a chieve that goal.\nB. Asymptotic Iteration Method\nAsymptotic iteration method aims to obtain the exact solution of a se cond order differential equation which has\nthe following form\nY′′(x)−λ0(x)Y′(x)−s0(x)Y(x) = 0 (4)\nwhereλ0(x)/ne}ationslash= 0 ands0(x) is the differential equation coefficients and they are so well-defined functions which are\ndifferentiable. To find the general solution, eq.(4) needs to be differ entiable in ( m+1) times and ( m+2) times, where\nm= 1,2,3,..is the number of iterations. Then one can obtain\nY(m+1)(x)−λm−1(x)Y′(x)−sm−1(x)Y(x) = 0 (5)3\nY(m+2)(x)−λm(x)Y′(x)−sm(x)Y(x) = 0 (6)\nwhere\nλm(x) =λ′\nm−1(x)+λm−1(x)λ0(x)+sm−1(x) (7)\nsm(x) =s′\nm−1(x)+s0(x)λm−1(x) (8)\nwhich are also called recursive relations of eq.(4). The calculation of t he ratio of derivatives of ( m+2) and (m+1)\ngives\nd\ndxln/bracketleftBig\nY(m+1)(x)/bracketrightBig\n=Y(m+2)(x)\nY(m+1)(x)\n=λm[Y′(x)+(sm/λm)Y(x)]\nλm−1[Y′(x)+(sm−1/λm−1)Y(x)](9)\nFurthermore, with the introduction of the asymptotic aspects of this iteration method, i.e. by assuming that the value\nofmis large enough, we obtain\nsm(x)\nλm(x)−sm−1(x)\nλm−1(x)≡α(x) (10)\nSo eq.(9) can be written as\nd\ndxln[Y(m+1)(x)] =λm(x)\nλm−1(x)(11)\nSubstitute eq.(7) into eq.(11) and using eq.(10), we obtain\nY(m+1)(x) =C0λm−1(x) exp/braceleftbigg/integraldisplay\n[α(x)+λ0(x)]dx/bracerightbigg\n(12)\nwhereC0is the constant of integration. Substitute eq.(12) into eq.(5) and s olve forY(x), then we obtain the general\nsolution eq.(4) as\nY(x) = exp/bracketleftbigg\n−/integraldisplay\nα(x)dx/bracketrightbigg\n×/parenleftbigg\nC1+C0/integraldisplay\nexp/braceleftbigg/integraldisplay\n[2α(x)+λ0(x)]dx/bracerightbigg\ndx/parenrightbigg\n(13)\nwhereC1is the constant of integration.\nEigenvalue of energy is obtained from the combination of termination conditions, eq.(10) and eqs.(7)-(8).\nλm(x)sm−1(x)−λm−1(x)sm(x) = 0;m= 1,2,3 (14)\nIn general, if the problem expressed by eq.(4) has λ0(x) ands0(x) which are forming a constant function, then the\ngeneral solution of eq.(4) can directly follow to eq.(13). The most fr equent case is that λ0(x) ors0(x) is not a constant\nfunction. In such cases, the exact solution eq.(4) requires a spec ial technique that can be found in811,1216.\nHere, we will apply the AIM to the case where the electromagnetic op tical character changed gradually. Our\nmain attention is the solution domain where the positive-negative inte rface occurs and how to develop appropriate\napproaches. As an overview of approaches that we use here, let u s look at the following example.\nExample:\nOptical characteristics of vacuum space is defined as follows\nε(x) =ε0;µ(x) =µ0 (15)\nwithε0(x) andµ0are respectively the permittivity and permeability constants of vac uum space, and µ0ε0= 1/c2.\nSubstitute eq.(15) into eq.(3), we obtain\nd2H(x)\ndx2+(ω2/c2−k2)H(x) = 0 (16)4\nFurthermore, if we let\nH(x) =e−x2/2ψ(x) (17)\nwhereψ(x) needs to be determined using an iterative procedure. Substitute eq.(17) into eq.(16) gives\nd2ψ(x)\ndx2−λ0(x)dψ(x)\ndx+s0(x)ψ(x) = 0 (18)\nwith\nλ0(x) = 2x;s0(x) = (ω2/c2−k2)−1+x2(19)\nIn the solution domain close to zero, eq.(19) can be approximated by MacLaurin series. The approach is carried by\ntaking the first two terms of the MacLaurin series, giving\nλ0(x) =λ0(0)+λ′\n0(0)x+λ′′\n0(0)\n2!x2+λ′′′\n0(0)\n3!x3+...\n= 0+2x+0+...\n= 2x\ns0(x) =s0(0)+s′\n0(0)x+s′′\n0(0)\n2!x2+s′′′\n0(0)\n3!x3+...\n= (ω2/c2−k2)−1+0×x+2\n2!x2+0+...\n= (ω2/c2−k2)−1 (20)\nSubstitute eq.(20) into eq.(18), we obtain\nd2ψ(x)\ndx2−2xdψ(x)\ndx+[(ω2/c2−k2)−1]ψ(x) = 0 (21)\nat−δ≤x≤δ, withδ= 1. Furthermore, using eq.(14), it can be obtained\nλmsm−1−λm−1sm= Πm\nn=0[(ω2/c2−k2−1)−2n];m= 1,2,3,4,... (22)\nAccording to these conditions, the eigenvalues of energy can be ob tained as follows\nω2\nc2−k2−1 = 2n→kn=/radicalbigg\nω2\nc2−(2n+1);n= 0,1,2,3,... (23)\nUsing eq.(23), eq.(21) can be written as\nd2ψ(x)\ndx2−2xdψ(x)\ndx2nψ(x) = 0;n= 0,1,2,3,... (24)\nEq.(24) known as Hermite differential equation which has a solution in a polynomial of order n. The approximate\nsolution of eq.(16) is\nHn(x) =e−x2/2(−1)nex2d\ndxn(e−x2);n= 0,1,2,3,.. (25)\nat−δ≤x≤δ, withδ= 1. Using similar techniques, we develop a method to solve the eight mo dels of interface\npositive-negative gradation as follows.\n1. 1st Model\nDefine the character of the optical interface gradation as follows\nε(x) =ε0[csch(ρx)−coth(ρx)]5\nµ(x) =−µ0[csch(ρx)+coth(ρx)] (26)\nwithρis the gradation parameters. If we let u=ρx, substitute eq.(26) into eq.(3) gives\nd2H\ndu2−csch(u)\nρdH\ndu+1\nρ2/parenleftbiggω2\nc2−k2/parenrightbigg\nH= 0 (27)\nIn the solution domain close to zero, using the MacLaurin series for t he first three terms, then we obtain\ncsch(u) =1\nu(28)\nHowever, eq.(28) is not defined at u= 0, so we need an assumption. If σis the value of uthat close to zero then using\neq.(28) it can be obtained csch(σ) = 1/σ, andcsch(−σ) =−1/σ. Furthermore, at intervals of −σ≤u≤σ, eq.(28)\nis considered to have a linear function form which connects the point s (−σ,−1/σ) and (σ,1/σ), i.e.\nf(u) =1\nσ2u (29)\nUsing (29) and letting z=u//radicalbig\n2ρσ2, eq.(27) can be written as\nd2H\ndz2−2zdH\ndz+/parenleftbigg2σ2ω2\nρc2−2σ2\nρk2/parenrightbigg\nH= 0 (30)\nat−σ≤u≤σ, withσ= 1. Furthermore, using the eq.(14), it can be obtained\nλmsm−1−λm−1sm= Πm\nn=0/bracketleftbigg/parenleftbigg2σ2ω2\nρc2−2σ2\nρk2/parenrightbigg\n−2n/bracketrightbigg\n(31)\nAccording to these conditions, the eigenvalues of energy can be ob tained as follows\n/parenleftbigg2σ2ω2\nρc2−2σ2\nρk2/parenrightbigg\n= 2n→kn=/radicalbigg\nω2\nc2−ρn\nσ2(32)\nUsing eq.(32), eq.(30) can be rewritten as\nd2H\ndz2−2zdH\ndz+2nH= 0;n= 0,1,2,3,... (33)\nEq.(33) is known as Hermite differential equation. The approximate s olution of eq.(27) is\nHn(z) = (−1)nez2dn\ndzn(e−z2);n= 0,1,2,3,... (34)\n2. 2nd Model\nDefine the character of the optical interface gradation as follows\nε(x) =−ε0[csch(ρx)+coth(ρx)]\nµ(x) =µ0[csch(ρx)−coth(ρx)] (35)\nIf we letu=ρx, substitute eq.(35) into eq.(3) gives\nd2H\ndu2+csch(u)\nρdH\ndu+1\nρ2/parenleftbiggω2\nc2−k2/parenrightbigg\nH= 0 (36)\nCompare to eq.(30), eq.(36) differs only the sign in the middle term of e q.(30). So, in the same way we can obtain\nd2H\ndz2+2zdH\ndz+/parenleftbigg2σ2ω2\nρc2−2σ2\nρk2/parenrightbigg\nH= 0 (37)6\nat−σ≤u≤σ, withσ= 1. Furthermore, using eq.(14), we obtain\nλmsm−1−λm−1sm= Πm\nn=0/bracketleftbigg/parenleftbigg2σ2ω2\nρc2−2σ2\nρk2/parenrightbigg\n+2n/bracketrightbigg\n(38)\nAccording to these conditions, the eigenvalues of energy can be ob tained as follows\n/parenleftbigg2σ2ω2\nρc2−2σ2\nρk2/parenrightbigg\n=−2n→kn=/radicalbigg\nω2\nc2+ρn\nσ2(39)\nUsing eq.(39), eq.(37) can be written as\nd2H\ndz2+2zdH\ndz−2nH= 0;n= 0,1,2,3,.. (40)\nEq.(40) is known as Differential Equations of Complementary Error F unction. The approximate solution of eq.(36) is\nHn(z) =A erf c n(z)+B erf c n(−z);n= 0,1,2,3,.. (41)\nwithAandBare constant.\nerf cn(z) =/integraldisplay∞\nz.../integraldisplay∞\nzerf(z)dz\n= 2−ne−z2/bracketleftbigg\n1F1[1/2(n+1);1/2;z2]\nΓ[1+(1/2)n]−2z1F1[1+(1/2)n;3/2;z2]\nΓ[1/2(n+1)]/bracketrightbigg\n(42)\nis an integral ntimes the Complementary Error Function, and\n1F1(a;b;z) = 1+a\nbz+a(a+1)\nb(b+1)z2\n2!+a(a+1)(a+2)\nb(b+1)(b+2)z3\n3!+...\n= Σ∞\nk=0(a)kzk\n(b)kk!(43)\nis the confluent hypergeometric function of first kind, whereas Γ( z) is the gamma function.\n3. 3rd Model\nDefine the character of the optical interface gradation as follows\nε(x) =ε0;µ(x) =µ0[csch(ρx)−coth(ρx)] (44)\nIf we letz=1\n2ρx, substitute eq.(44) into eq.(3) we obtain\nd2H\ndz2−4\nρ2/parenleftbiggω2\nc2tanh(z)+k2/parenrightbigg\nH= 0 (45)\nIn the solution domain close to zero, it can be approached, tanh( z) =z, in order to obtain\nd2H\ndz2−/parenleftbigg4ω2\nρ2c2+4\nρ2k2/parenrightbigg\nH= 0 (46)\nat−δ≤z≤δwithδ= 1. If we let s=/parenleftbig\n4ω2/ρ2c2/parenrightbig1/3z, and\nH(s) =es3\n6−s2\n2ψ(s) (47)\nwithψ(s)ψ(x) needs to be determined using an iterative procedure, we obtain\nd2ψ\nds2−λ0(s)dψ\nds−s0(s)ψ= 0 (48)7\nwith\nλ0(s) = 2s−s2(49)\nand\ns0(s) = 1+4\nρ2/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\nk2−s2+s3−1\n4s4(50)\nUsing the MacLaurin series for the first two terms, eq.(49) and eq.( 50) can be respectively reduced to\nλ0(s) = 2s (51)\nand\ns0(s) = 1+4\nρ2/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\nk2(52)\nSubstitute eq.(51) and eq.(52) into eq.(48), we obtain\nd2ψ\nds2−2sdψ\nds−/bracketleftBigg\n1+4\nρ2/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\nk2/bracketrightBigg\nψ= 0 (53)\nFurthermore, using eq.(14), it can be obtained\nλmsm−1−λm−1sm= Πm\nn=0/braceleftBigg/bracketleftBigg\n1+4\nρ2/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\nk2/bracketrightBigg\n+2n/bracerightBigg\n;m= 1,2,3,4,.. (54)\nAccording to these conditions, the eigenvalues of energy can be ob tained as follows\n1+4\nρ2/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\nk2=−2n→kn=iρ\n2/parenleftbigg2ω\nρc/parenrightbigg2/3√\n2n+1 (55)\nUsing eq.(55), eq.(53) can be rewritten as\nd2ψ\nds2−2sdψ\nds+2nψ= 0;n= 0,1,2,3,... (56)\nEq.(56) is known as Hermite differential equation. The approximate s olution of eq.(45) is\nHn(s) =es3\n6−s2\n2(−1)nes2dn\ndsn/parenleftBig\ne−s2/parenrightBig\n;n= 0,1,2,3,... (57)\n4. 4th Model\nDefine the character of the optical interface gradation as follows\nε(x) =ε0[csch(ρx)−coth(ρx)];µ(x) =µ0 (58)\nIf we letz=1\n2ρxand substitute eq.(58) into eq.(3) we obtain\nd2H\ndz2−csch(z)sech(z)\nρdH\ndz−4\nρ2/parenleftbiggω2\nc2tanh(z)+k2/parenrightbigg\nH= 0 (59)\nIn the solution domain close to zero, using the MacLaurin series for t he first three terms, we obtain\ntanh(z) =z (60)\ncsch(z)sech(z) =1\nz(61)8\nHowever, eq.(61) is not defined at z= 0, so it needs an assumption. If σis the value of zthat close to zero then\nusing eq.(61) it can be obtained csch(σ)sech(σ) = 1/σandcsch(−σ)sech(−σ) =−1/σ. Furthermore, at intervals\nof−σ≤z≤σ, eq.(61) is considered to have a linear function form which is connect ing the points ( −σ,−1/σ) and\n(σ,1/σ), i.e.\nf(u) =1\nσ2z (62)\nUsing eq.(60) and eq.(62), eq.(59) can be rewritten as\nd2H\ndz2−z\nσ2ρdH\ndz−4\nρ2/parenleftbiggω2\nc2z+k2/parenrightbigg\nH= 0 (63)\nat−σ≤z≤σwithσ= 1. If we let s= (4ω2/ρ2c2)1/3z, and\nH(s) =es3/6ψ(s) (64)\nwithψ(s) needs to be determined using an iterative procedure, then subst itute eq.(64) into eq.(63) we obtain\nd2ψ\nds2−λ0(s)dψ\nds−s0(s)ψ= 0 (65)\nwith\nλ0(s) =1\nσ2ρ/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\ns−s2(66)\nand\ns0(s) =4\nρ2/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\nk2+1\n2σ2ρ/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\ns3−1\n4s4. (67)\nUsing the MacLaurin series for the first two terms, eq.(66) and eq.( 67) respectively can be reduced to\nλ0(s) =1\nσ2ρ/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\ns (68)\nand\ns0(s) =4\nρ2/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\nk2(69)\nSubstitute eq.(68) and eq.(69) into eq.(65), we obtain\nd2ψ\nds2−1\nσ2ρ/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\nsdψ\nds−4\nρ2/parenleftbiggρ2c2\n4ω2/parenrightbigg2/3\nk2ψ= 0 (70)\nFurthermore, we let r=/parenleftbig\nρ2c2/4ω2/parenrightbig1/3s//radicalbig\n2σ2ρ, eq.(70) can be written as\nd2ψ\ndr2−2rdψ\ndr−8σ2\nρk2ψ= 0 (71)\nThen, using eq.(14), we obtain\nλmsm−1−λm−1sm= Πm\nn=0/parenleftbigg8σ2\nρk2+2n/parenrightbigg\n;m= 1,2,3,4,.. (72)\nAccording to these conditions, the eigenvalues of energy can be ob tained as follows\n8σ2\nρk2=−2n→kn=i\n2σ√ρn;n= 0,1,2,3,.. (73)\nUsing eq.(73), then eq.(71) can be written as\nd2ψ\ndr2−2rdψ\ndr+2nψ= 0;n= 0,1,2,3,... (74)\nEq.(74) known as Hermite differential equation. The approximate so lution of eq.(59) is\nHn(r) =e4√\n2σω2\n3√\nρc2r3\n(−1)ner2dn\ndrn(e−r2);n= 0,1,2,3,... (75)9\n5. 5th Model\nDefine the character of the optical interface gradation as follows\nε(x) =ε0;µ(x) =−µ0[csch(ρx)+coth(ρx)] (76)\nIf we letu=ρx, and substitute eq.(76) into eq.(3), we obtain\nd2H\ndu2−1\nρ2/braceleftbiggω2\nc2[csch(u)+coth(u)]+k2/bracerightbigg\nH= 0 (77)\nIn the solution domain close to zero, using the MacLaurin series for t he first three terms, it gives\ncsch(u) coth(u) =2\nu+u\n2(78)\nHowever, eq.(78) is not defined at u= 0, so it needs an assumption. If σis the value of uthat close to zero then\nusing eq.(78) we obtain csch(σ) +coth(σ) = (σ2+4)/2σandcsch(−σ) +coth( −σ) =−(σ2+4)/2σ. Furthermore,\nat intervals of −σ≤u≤σ, eq.(78) is considered to have a linear function form which is connect ing the points\n[−σ,−(σ2+4)/2σ] and [σ,(σ2+4)/2σ], i.e.\nf(u) =σ2+4\n2σ2u (79)\nUsing eq.(79), then eq.(77) can be written as\nd2H\ndu2−1\nρ2/parenleftbiggω2\nc2σ2+4\n2σu+k2/parenrightbigg\nH= 0 (80)\nat−σ≤u≤σwithσ= 1. If we let β=ω2(σ2+4)/2c2ρ2σ2,z=β1/3uand\nH(z) =ez3\n6−z2\n2ψ(z) (81)\nwithψ(z) needs to be determined using an iterative procedure, then subst itute eq.(81) into eq.(80) we obtain\nd2ψ\ndz2−λ0(z)dψ\ndz−s0(z)ψ= 0 (82)\nwith\nλ0(z) = 2z−z2(83)\nand\ns0(z) = 1+k2\nβ2/3ρ2−z2+z3−1\n4z4(84)\nUsing the MacLaurin series for the first two terms, eq.(83) and eq.( 84) respectively can be reduced to\nλ0(z) = 2z (85)\nand\ns0(z) = 1+k2\nβ2/3ρ2(86)\nSubstitute eq.(85) and eq.(86) into eq.(82), we obtain\nd2ψ\ndz2−2zdψ\ndz−/parenleftbigg\n1+k2\nβ2/3ρ2/parenrightbigg\nψ= 0 (87)10\nThen, using eq.(14), we obtain\nλmsm−1−λm−1sm= Πm\nn=0/parenleftbigg\n1+k2\nβ2/3ρ2+2n/parenrightbigg\n;m= 1,2,3,4,.. (88)\nAccording to these conditions, the eigenvalues of energy can be ob tained as follows\n1+k2\nβ2/3ρ2=−2n→kn=iβ2/3ρ√\n2n+1;n= 0,1,2,3,.. (89)\nUsing eq.(89), then eq.(87) can be written as\nd2ψ\ndz2−2zdψ\ndz+2nψ= 0;n= 0,1,2,3,.. (90)\nEq.(90) known as Hermite differential equation. The approximate so lution of eq.(77) is\nHn(z) =ez3\n6−z2\n2(−1)nez2dn\ndzn/parenleftBig\ne−z2/parenrightBig\n;n= 0,1,2,3,... (91)\n6. 6th Model\nDefine the character of the optical interface gradation as follows\nε(x) =−ε0[csch(ρx)+coth(ρx)];µ(x) =µ0 (92)\nIf we letu=ρxand substitute eq.(92) into eq.(3) gives\nd2H\ndu2+csch(u)\nρdH\ndu−1\nρ2/braceleftbiggω2\nc2[csch(u)+coth(u)]+k2/bracerightbigg\nH (93)\nIn the solution domain close to zero, using the MacLaurin series for t he first three terms, functions of csch(u) and\ncsch(u)+coth(u) can be approximated by the MacLaurin series as eq.(28) and eq.(78 ), so that eq.(93) can be reduced\nto\nd2H\ndu2+u\nσ2ρdH\ndu−1\nρ2/bracketleftbiggω2\nc2/parenleftbiggσ2+4\n2σ2/parenrightbigg\nu+k2/bracketrightbigg\nH= 0 (94)\nat−σ≤u≤σwithσ= 1. Furthermore, if we let β=ω2(σ2+4)/2c2ρ2σ2,z=β1/3u\nH(z) =ez3/6ψ(z) (95)\nwithψ(z) needs to be determined using an iterative procedure, then subst itute eq.(95) into eq.(94), we obtain\nd2ψ\ndz2+λ0(z)dψ\ndz−s0(z)ψ= 0 (96)\nwith\nλ0(z) =z\nσ2β2/3ρ+z2(97)\nand\ns0(z) =k2\nβ2/3ρ2−z3\n2σ2β2/3ρ−1\n4z4(98)\nUsing the MacLaurin series for the first two terms, eq.(97) and eq.( 98) respectively can be reduced to\nλ0(z) =z\nσ2β2/3ρ(99)11\nand\ns0(z) =k2\nβ2/3ρ2(100)\nSubstitute eq.(99) and eq.(100) into eq.(96), we obtain\nd2ψ\ndz2+z\nσ2β2/3ρdψ\ndz−k2\nβ2/3ρ2ψ= 0 (101)\nIf we lets=z//radicalbig\n2σ2β2/3ρ, eq.(101) can be written as\nd2ψ\nds2+2sdψ\nds−2σ2\nρk2ψ= 0 (102)\nThen, using eq.(14), it can be obtained\nλmsm−1−λm−1sm= Πm\nn=0/parenleftbigg2σ2\nρk2−2n/parenrightbigg\n;m= 1,2,3,4,... (103)\nAccording to these conditions, the eigenvalues of energy can be ob tained as follows\n2σ2\nρk2= 2n→kn=√ρn\nσ;n= 0,1,2,3,.. (104)\nUsing eq.(104), then eq.(102) can be written as\nd2ψ\nds2+2sdψ\nds−2nψ= 0;n= 0,1,2,3,.. (105)\nEq.(105) is known as the Complementary Error Function Differential Equations. The approximate solution of eq.(93)\nis thus\nHn(s) =eω2σ(σ2+4)\n3c2√2ρs3\n[A erf c n(s)+B erf c n(−s)];n= 0,1,2,3,... (106)\nwitherf cn(s) refers to eq.(42).\n7. 7th Model\nDefine the character of the optical interface gradation as follows\nε(x) =ε0[csch(ρx)−coth(ρx)]\nµ(x) =µ0[csch(ρx)−coth(ρx)] (107)\nIf we letz=1\n2ρx, and substitute eq.(107) into eq.(3), we obtain\nd2H\ndz2−csch(z)sech(z)\nρdH\ndz+4\nρ2/bracketleftbiggω2\nc2tanh2(z)−k2/bracketrightbigg\nH= 0 (108)\nIn the solution domain is close to zero, the functions of tanh( z) andcsch(z)sech(z) can be approximated by a\nMacLaurin series in the first three terms, and follow the same way of eq.(60)-eq.(62), then eq.(108) can be reduced to\nd2H\ndz2−z\nσ2ρdH\ndz+4\nρ2/parenleftbiggω2\nc2z2−k2/parenrightbigg\nH= 0 (109)\nat−σ≤z≤σwithσ= 1. If we let s= (4ω2/ρ2c2)1/4, eq.(109) can be written as\nd2H\nds2−λ0(s)dH\nds−s0(s)H= 0 (110)12\nwith\nλ0(s) =c\n2ωσ2s (111)\nand\ns0(s) =2c\nρωk2−s2(112)\nEq.(111) and eq.(112) can be reduced using the MacLaurin series fo r the first two trems, so that eq.(110) can be\nwritten as\nd2H\nds2−c\n2ωσ2sdH\nds−2c\nρωk2H= 0 (113)\nFurthermore, if we let r=s/radicalbig\nc/4ωσ2, eq.(113) can be written as\nd2H\ndr2−2rdH\ndr−8σ2\nρk2H= 0 (114)\nNext, using the eq.(14), we obtain\nλmsm−1−λm−1sm= Πm\nn=0/parenleftbigg8σ2\nρk2+2n/parenrightbigg\n;m= 1,2,3,4,.. (115)\nAccording to these conditions, the eigenvalues of energy can be ob tained as follows\n8σ2\nρk2=−2n→kn=i\n2σ√ρn;n= 0,1,2,3,... (116)\nUsing eq.(130), eq.(114) can be written as\nd2H\ndr2−2rdH\ndr+2nH= 0;n= 0,1,2,3,... (117)\nEq.(117) is known as Hermite differential equation. The approximate solution of eq.(108) is\nHn(r) = (−1)ner2dn\ndrn/parenleftBig\ne−r2/parenrightBig\n;n= 0,1,2,3,... (118)\n8. 8th Model\nDefine the character of the optical interface gradation as follows\nε(x) =−ε0[csch(ρx)+coth(ρx)]\nµ(x) =−µ0[csch(ρx)+coth(ρx)] (119)\nIf we letu=ρx, and substitute eq.(119) into eq.(3) we obtain\nd2H\ndu2+csch(u)\nρdH\ndu+1\nρ2/braceleftbiggω2\nc2[csch(u)+coth(u)]2−k2/bracerightbigg\nH= 0 (120)\nIn the solution domain is close to zero, the functions of csch(u) andcsch(u)+coth(u) are reduced in the same way\nas in eq.(28) and eq.(78), so that eq.(120) can be written as\nd2H\ndu2+u\nσ2ρdH\ndu+1\nρ2/bracketleftBigg\nω2\nc2/parenleftbiggσ2+4\n2σ2/parenrightbigg2\nu2−k2/bracketrightBigg\nH= 0 (121)13\nat−σ≤u≤σwithσ= 1. If we let γ=ω2(σ2+4)2/ρ2c2(2σ2)2, andz=γ1/4u, then eq.(121) can be written as\nd2H\ndz2+λ0(z)dH\ndz−s0(z)H= 0 (122)\nwith\nλ0(z) =z\nσ2γ1/2ρ(123)\nand\ns0(z) =k2\nρ2γ1/2−z2(124)\nEq.(123) and eq.(124) can be reduced using the MacLaurin series fo r the first two terms, so that eq.(122) can be\nwritten as\nd2H\ndz2+z\nσ2γ1/2ρdH\ndz−k2\nρ2γ1/2H= 0 (125)\nNext if we let s=z//radicalbig\n2σ2γ1/2ρ, then eq.(125) can be written into\nd2H\nds2+2sdH\nds−2σ2\nρk2H= 0 (126)\nNext, using eq.(14), it can be obtained\nλmsm−1−λm−1sm= Πm\nn=0/parenleftbigg2σ2\nρk2−2n/parenrightbigg\n;m= 1,2,3,4,... (127)\nAccording to these conditions, the eigenvalues of energy can be ob tained as follows\n2σ2\nρk2= 2n→kn=√ρn\n2σ;n= 0,1,2,3,.. (128)\nUsing eq.(128), eq.(126) can be written as\nd2H\nds2+2sdH\nds−2nH= 0;n= 0,1,2,3,.. (129)\nEq.(129) is knownas the Complementary ErrorFunction Differential Equations. The approximatesolution ofeq.(120)\nis thus\nHn(s) =A erf c n(s)+B erf c n(−s);n= 0,1,2,3,... (130)\nwitherf cn(s) refers to eq.(42).\nIII. RESULTS AND DISCUSSION\nIt has been shown through the eight models that AIM can be used to find approximate solution of electromagnetic\nwavepropagationinthepositive-negativegradationofNRM.Somem aterialsthataremathematicallycanbedescribed\nas a function which has a singular point has been approached by a linea r function in the domain such that pretty\nclose to the singular point.\nIV. CONCLUTION\nThis paper has developed an approach for analyzing the distribution of the magnetic field and electromagnetic\nwave-vector in the positive-negative gradation NRM constructed based on the AIM. As a test of this method, has\nbeen used as an example of vacuum-space calculation. Differential e quation approach results from the eight NRM\nmodels can be solved by Hermite polynomials and the Complementary Er ror Function.14\nV. ACKNOWLEDGMENTS\nASH grateful to beloved mother, Siti Ruchanah, for her great su pport. Thanks to Dr Miftachul Hadi for nice\ndiscussions and good motivation. Thanks to Professor Muhaimin for very helpful advice. Thanks to Mrs. Yayuk, Dr\nImron and Dr Yuni for their kindness. Thanks to Mr. Sjaifuddin Ach mad for his inspiring discussion.\n†Electronic address: decepticon1022@gmail.com\n1V. G. Veselago, The Electrodynamics of Substance with Simultaneously Nega tive, Soviet Physics Uspekhi, Volume 10, Number\n4, January-February, 1968.\n2KurtL.ShrlagerandJohnB. Sclineider, A Selective Survey of the Finite-Difference Time-Domain Lite rature, IEEEAntennas\nand Propagation Magazine, Vol. 37, No. 4, August 1995.\n3J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart, Low frequency plasmons in thin-wire structures , Journal of\nPhysics: Condensed Matter Volume 10Number 22, p. 4785-4809, 1998.\n4J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, Magnetism from Conductors and Enhanced Nonlinear\nPhenomena , IEEE Transaction on Microwave Theory and Techniques, Vol. 47, No. 11, November 1999.\n5J. B. Pendry, Negative Refraction Makes a Perfect Lens , Physical Review Letters, Vol. 85, No. 18, 30 October 2000.\n6D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser , and S. Schultz, Composite Medium with Simultaneously\nNegative Permeability and Permittivity , Physical Review Letters, Vol. 84, No. 18, 1 May 2000.\n7Suparmi, Mekanika Kuantum II , Surakarta: FMIPA UNS, ISBN 978-602-99344-2-7, 2001.\n8Hakan Ciftci, Richard L Hall and Nasser Saad, Asymptotic Iteration Method for Eigenvalue Problems , J. Phys. A: Math.\nGen.36(2003) 1180711816, 2003.\n9S. Anantha Ramakrishna, Physics of negative refractive index materials , Department of Physics, Indian Institute of Tech-\nnology, Kanpur 208 016, India, stacks.iop.org/RoPP/68/44 9, doi:10.1088/0034-4885/68/2/R06, 2005.\n10Nils Dalarsson, Zoran Jaksic and Milan Maksimovic, Ab Initio Analytical Approach to Spectral Behavior of Grade d Interfaces\nIncorporating Negative-Index Nanocomposites , IWON 2005 Belgrade, Serbia and Montenegro, November 2005.\n11M. Aygun, O. Bayrak and I. Boztosun, Solution of the Radial Schrodinger Equation for the Potenti al Family V(r) =\nA\nr2−B\nr+Crkusing the Asymptotic Iteration Method , arXiv:math-ph/0703040v1, 2007\n12A. Rostami and H. Motovali, Asymtotic Iteration Method: A Powerful Approach for Analys is of Inhomogeneus Dielectric\nSlab Waveguide , Progress In Electromagnetics Research B, Vol 4, 171 - 182, 2008.\n13Yang Hao and Raj Mittra, FDTD Modeling of Metamaterials: Theory and Applications , Artech House, Inc. ISBN-13:\n978-1-59693- 160-2. 2009.\n14John Pendry, Metamaterials In the Faculty of Natural Sciences , Flyer of Imperial College London, September 2009.\n15M. Dalarsson, Z. Jaksic, P. Tassin, Exact analytical solution oblique incidence on a graded ind ex interface between a\nrighthanded and a left-handed material , Journal of Optoelectronics and Biomedical Materials, Vol .1, Issue 4, p. 345-352,\nDecember 2009.\n16O. Ozer, G. LeVai, Asymtotic Iteration Method Applied to Bound-State Problem with Unbroken Supersymmetry , Rom. Journ.\nPhys., Vol. 57, Nos. 3-4, P, 582 - 593, Bucharest, 2011\n17R. A. Shelby, D. R. Smith, S. Schultz, Experimental Verification of a Negative Index of Refraction , www.sciencemag.org on\nDecember 19, 2012.\n18Suparmi, Cari, Jeffry Hendhika, Solusi Persamaan Schrodinger untuk Potensial Coulombic Ri ngshaped Non-Central meng-\ngunakan Metode Nikiforov-Uvarov , Seminar Nasional Fisika 2012.\n19C. Yanuarief, Suparmi, Cari, Analisis Energi dan Fungsi Gelombang Non Sentral Coulombic Rosen Morse menggunakan\nPolinomial Romanovski , Seminar Nasional Fisika 2012.\n20Cari and Suparmi, Approximate Solution of Schrodinger Equation for Hulthen P otential plus Eckart Potential with Centrifu-\ngal Term in terms of Finite Romanovski Polynomials , International Journal of Applied Physics and Mathematics , Vol.2,\nNo. 3, May 2012.\n21A. Suparmi, C. Cari, and J. Handhika, Approximate Solution of Schrodinger Equation for Eckart Po tential Combined with\nTrigonormetric Poschl-Teller Non-Central Potential usin g Romanovski Polynomials , Journal of Physics: C"    },    {        "title": "1506.07864v1.Dynamical_systems_study_in_single_phase_multiferroic_materials.pdf",        "content": "arXiv:1506.07864v1  [cond-mat.mes-hall]  18 Jun 2015epl draft\nDynamical systems study in single-phase multiferroic mate rials\nKuntal Roy(a)\nSchool of Applied and Engineering Physics, Cornell Univers ity, Ithaca, New York 14853, USA(b)\nPACS75.85.+t – Multiferroics\nPACS75.60.Jk – Magnetization reversal\nPACS75.78.-n – Magnetization dynamics\nPACS84.30.Ng – Magnetization oscillation\nAbstract – Electric field induced magnetization switching in single- phase multiferroic materials is\nintriguing for both fundamental studies and potential tech nological applications. Here we develop\na framework to study the switching dynamics of coupled polar ization and magnetization in such\nmultiferroic materials. With the coupling term between the polarization and magnetization as\nan invariant dictated by the Dzyaloshinsky-Moriya vector, the dynamical systems study reveals\nswitching failures and oscillatory mode of magnetization i f the polarization and magnetization\nrelax slowly during switching.\nIntroduction. – Multiferroics usually represent ma-\nterialsthatarebothferroelectricandferromagnetic[1–12].\nSuch materials in single-phase were usually thought to be\nrare [13], and hence multiferroic composites in 2-phase,\ni.e., a ferroelectric layer strain-coupled to a ferromagnet,\nare usually deemed to be the replacement [5,14–20]. How-\never, there have been recent resurgence of interests [21,22]\nandsomemechanismsofcouplingpolarizationandmagne-\ntizationinsingle-phasematerialsarecomingalong[23–25].\nThis can lead to possible technological applications [26] of\nswitching a bit of information (stored in the magnetiza-\ntion direction) by an electric field [27]. This eliminates\nthe need to switch magnetization by a cumbersome mag-\nneticfieldorspin-polarizedcurrent[14], althoughnewcon-\ncepts are being investigated e.g., utilizing giant spin-Hall\neffect [28]. The electric field switches the polarization and\nthe intrinsic coupling between the polarization and mag-\nnetization switches the magnetization between its 180◦\nsymmetry equivalent states. One way to couple polar-\nization and magnetization that has taken attention is due\nto Dzyaloshinsky-Moriya (DM) interaction [29,30], which\narises due to spin-orbit correction to Anderson’s superex-\nchange [31]. This is called ferroelectrically induced weak\nFerromagnetism (wFM), in which two magnetic sublat-\ntices of an antiferromagnet cant in a way to produce a\nresidual magnetization [23,32–35].\n(a)E-mail:royk@purdue.edu\n(b)Present Address: School of Electrical and Computer Enginee r-\ning, Purdue University, West Lafayette, Indiana 47907, USAWhile first-principles calculationsand experiments have\nbeen underway on the search of strongly-coupled multifer-\nroic magnetoelectric materials possibly working at room-\ntemperature, little have been studied on the dynamical\nnature of switching. The study of switching dynamics of\nmagnetization in multiferroic composites, i.e., a piezoelec-\ntric layer strain-coupled to a magnetostrictive nanomag-\nnet, have been very successful to understand the perfor-\nmance metrics, e.g., switching delay, energy dissipation,\nand switching failures [14,15,17]. Here, the switching dy-\nnamics of polarization is studied by forming a Hamilto-\nnian system with Landau-Ginzburg functional [36], while\nthe magnetization dynamics is studied by the Landau-\nLifshitz-Gilbert (LLG) equation of motion [37,38]. We\nfocus on magnetization switching due to electric field in-\nduced polarization switching, i.e., converse magnetoelec-\ntric (ME) effect for technological applications rather than\nthe switching dynamics due to direct ME effect. We par-\nticularly consider the dynamics in single-domains with an\neyetoachievehigh-densityofdevicesratherthanconsider-\ning domain walls in higher dimensions, for which we need\nto consider the competition between the exchange interac-\ntion and dipole coupling among the spins [39]. Note that\nswitching dynamics in BiFeO 3has been studied using a\nfirst-principles-based effective Hamiltonian within molec-\nulardynamicssimulations[40,41]. Hereweperforma com-\nprehensive analysis in emergingstrongly-coupledmultifer-\nroics (ferroelectrically-inducedwFM by design dictated by\nDM interaction [23]) by varying different parameters in\np-1Kuntal Roy\nFig. 1: (a) Energy of the two spins in a predominantly antifer romagnetic configuration with respect to canting angle θc. The\ncanting happens due to Dzyaloshinsky-Moriya (DM) interact ion. The DM vector is proportional to polarization, i.e., D∝P\nand acts in the z-direction. When θcis positive, the net magnetization Mpoints up (+ y-axis), and if θcis negative, the\nnet magnetization Mpoints down ( −y-axis). Without any canting, the net magnetization is zero a s in the case of a perfect\nantiferromagnet. (b) Magnetization initially points alon g the−y-xis. To respect the invariant dictated by the DM interactio n\n[∝P·(L×M)], with the reversal of polarization P, either the magnetization M(case 1) or the AFM vector L(case 2) may\nflip.\nthe LLG dynamics. The analysis of switching dynamics\nreveals very significant motion of magnetization when po-\nlarization is switched by an electric field. It is shown that\nmagnetization may fail to switch or even can go into an\noscillatory state of motion. The phenomenological damp-\ning parameter for both polarization and magnetization\nplays a crucial role in shaping the dynamics of the coupled\npolarization-magnetizationin these multiferroicmaterials.\nModel. – We consider two spins, one representative\ntoeachmagneticsublatticeofanantiferromagnet,tobuild\nup the present model. The dynamics of the two spins S1\nandS2can be described by the Landau-Lifshitz-Gilbert\n(LLG) equation [37,38] as follows:\ndS1\ndt=−|γ′|S1×HS1−α|γ′|\nSS1×(S1×HS1) (1)\ndS2\ndt=−|γ′|S2×HS2−α|γ′|\nSS2×(S2×HS2),(2)\nwhereHS1andHS2are the effective fields on the spins S1\nandS2, respectively, defined as HS1=−(∂H/∂S1) and\nHS2=−(∂H/∂S2),His the potential energy of the two\nspin system, expressed as\nH=−JS1·S2−D·(S1×S2)−KS2\n1,z−KS2\n2,z,(3)\nJdenotes the exchange coupling between the spins, Dis\nthe Dzyaloshinsky-Moriya (DM) vector [29,30] (here, we\nwill consider the case when the vector Dpoints along per-\npendicular to the plane ( x-yplane) on which the spins\nreside, i.e., along the z-direction and proportional to po-\nlarization P, whichisalsointhe z-direction[23])expressed\nasD=D(t)ˆ ezmaking\nD(t)∝P(t), (4)Kis the single-ion anisotropy constant, γ′=γ/(1+α2),γ\nisthegyromagneticratioofelectrons, αisthephenomeno-\nlogical Gilbert damping constant [38], and S=|S1|=\n|S2|. As required, it is possible to include the long-range\ninteraction too in the energy term [42]. The net magneti-\nzationMand the antiferromagnetic (AFM) vector Lfor\nthe two spin system are M=S1+S2andL=S1−S2,\nrespectively. Note that the following two identities hold:\nM·L= 0 and M2+L2= 4S2.\nThe polarization dynamics is based on the Landau-\nGinzburg functional [36]\nG=/bracketleftBig\n−a1\n2P2+a2\n4P4/bracketrightBig\n−E.P, (5)\nwherea1anda2are the ferroelectric coefficients (both are\ngreaterthanzero)and E=Eˆ ezistheappliedelectricfield\nthat switches the polarization Pin thez-direction. We as-\nsume single-domain case [43] and follow the prescription\nin Ref. [36] to trace the trajectory of polarization. Note\nthat polarization is switched by moving ions, which cou-\nples to the magnetization dynamics via the DM term D\n[see Eq. (3)]. On the other hand, rotation of spins does\nnot quite move the heavy ions affecting the polarization.\nFigure 1a depicts how the asymmetric Dzyaloshinsky-\nMoriya (DM) interaction can lead to two anti-parallel\nmagnetization directions, i.e., 180◦symmetry equivalent\nstates. Depending on the sign of the canting angle θcof\nthe spins, the direction of the DM vector changes and\nthe energy expression as in the Equation (3) gives rise to\ntwo magnetization states in opposite directions. The DM\nvectorDis proportional to polarization Pand hence, if\nwe switch the polarization, two cases can happen to re-\nspect the invariant due to DM interaction P·(L×M)\np-2Dynamical systems study in single-phase multiferroic materials\nFig. 2: (a) The potential landscape ofpolarization with ele ctric fieldas aparameter [Equation(5)]. Notethat itrequir es acritical\nelectric field to topple the barrier between polarization’s two 180◦symmetry equivalent states. (b) Switching of polarization\nwith the application of an electric field. Initially, the pol arization was pointing towards −z-axis. With the application of electric\nfield, the polarization does not reach instantly towards the +z-axis, how fast the polarization relaxes to the minimum ener gy\nposition depends on the polarization damping. Note that aft er the withdrawal of electric field, the polarization direct ion is\nmaintained, i.e., the switching is non-volatile. The sligh t increase of polarization over Psis due to the application of electric\nfield [see the potential landscapes in part (a)], which can be followed from the Equation (5) too.\n[∝D·(S1×S2) term in Equation (3)]: (1) The magneti-\nzationMcan change the direction (i.e., switches success-\nfully), and (2) The AFM vector Lmay change the direc-\ntion (i.e., Mfails to switch). The two cases are depicted\nin the Fig. 1b.\nResults and Discussions. – We consider a per-\novskite system NiTiO 3[23,44] in R3c space group [45] as\na prototype to analyzethe switching dynamics. Although,\nNiTiO 3in R3c space group is not yet experimentally re-\nalized, the concept of polarization-magnetization coupling\npredicted from group theory is promising. The parame-\nters are chosen as follows: saturation polarization Ps=\n110µC/cm2, ferroelectric coefficients a1= 1.568×1010\nVm/C, a2= 1.296×1010Vm/C, polarization damp-\ningβ= 0.286 VmSec/C (that switches the polarization\nin realistic time 100 ps [46], see Fig. 2), S= 1.6µB,\nM= 0.25µB,J=−2.2 meV,Ds= 0.35 meV [corre-\nsponding to Ps, i.e.,D(t) = (Ds/Ps)P(t)],K=−0.03\nmeV [23]. We will consider that the electric field switches\nthe polarization from −Psto +Psin thez-direction.\nThe magnetization damping, through which magne-\ntization relaxes to the minimum energy position, can\nhave a wide range of values (10−4– 0.8) by modifying\nthe spin-orbit strength, doping etc. and it can be de-\ntermined by ferromagnetic resonance (FMR), magneto-\noptical Kerr effect, x-ray absorption spectroscopy, and\nspin-current driven rotation with the addition of a spin-\ntorque term [47–49]. Hence, we focus on investigating the\nmagnetization dynamics for a wide range of phenomeno-\nlogical damping parameter.\nWe will initially assume the single-ion anisotropy K=\n0 and we will see later the consequence of considering\nit. Figure 3 shows the dynamics of magnetization when\ndamping parameter is on the higher side, e.g., 0.1. Wesee that magnetization has switched successfully in the\nend (see Fig. 3d), while the AFM vector did not switch\n(see Fig. 3c). Note that the spins S1andS2are deflected\nfrom the x-yplane, in the z-direction due to rotational\nmotion of magnetization. Also, note that magnetization’s\nx- andz-component and AFM vector’s y-component have\nnot changed at all due to the complimentary dynamics of\nthe spins S1andS2. This corresponds to the case (1) in\nFig. 1b.\nFigure 4 plots the dynamics when magnetization damp-\ningα= 0.01. We see that magnetization has failed to\nswitch(seeFig.4d), while theAFMvectorisswitchedsuc-\ncessfully (see Fig. 4c). Magnetization was on the way to\nchange its direction, but eventually, magnetization came\nback to its initial state. This corresponds to the case (2)\nin Fig. 1b. Due to low damping, we notice ringing in all\nthe plots in the Fig. 4.\nFor the lower damping of α= 0.01, from the simulation\nresults as shown in the Fig. 4, the positions of the two\nspins have just got interchanged, which is depicted as the\ncase (2) in Fig. 1b. Since the canting angle ofthe spins are\nsmall (θc≃5◦), one can say that the spins have rotated\nmuch more than that of the case for the higher damping\nofα= 0.1 [case (1) in Fig. 1b and the simulation results\nas shown in the Fig. 3]. While both the cases as shown in\nthe Fig. 1b respect the DM invariant at steady-state , the\ndynamics of magnetization dictates the final state that is\nreached. With a lower damping, the spins get deflected\nout-of-plane more (see the z-components of the spins S1\nandS2intheFigs.3and4)andthisout-of-planeexcursion\neventuallycanleadthe spins tointerchangetheir positions\nas can be noticed from the Fig. 4. The interchange of the\nspinsS1andS2indeed respects the DM invariant [case\n(2) of Fig. 1b], but the magnetization Mfailsto switch in\nthis case, while the AFM vector Lgets switched.\np-3Kuntal Roy\nFig. 3: Dynamics of magnetization for damping parameter α=\n0.1. Magnetization does switch successfully. (a) Dynamics of\nS1, (b) Dynamics of S2, (c) Dynamics of AFM vector L, and\n(d) Dynamics of magnetization M.\nTo understand the magnetizationdynamics further that\nhow switching may be successful even at magnetization\ndamping α= 0.01, we first investigate its dependence on\nthe polarization dynamics. Simulation results show that\nmagnetization switches successfully if we make the polar-\nization damping 200 times faster [see Fig. 5a]. Basically,\ndue to the coupling between the polarization and mag-\nnetization, if polarization is switched faster, magnetiza-\ntion is also switched faster, which makes the switching\nsuccessful. We further investigate the effect of single-ion\nanisotropy parameter Kon magnetization dynamics. The\nion-anisotropy basically adds an extra field that tries to\nkeep the magnetization in-plane (i.e., x-yplane) and the\nsimulation results show that magnetization switches suc-\ncessfully if we take the single-ion-anisotropy into account\nand the ringing in the magnetization dynamics does not\nFig. 4: Dynamics of magnetization for damping parameter α=\n0.01. Magnetization fails to switch successfully. (a) Dynami cs\nofS1, (b) Dynamics of S2, (c) Dynamics of AFM vector L,\nand (d) Dynamics of magnetization M.\nshow up in this case [see Fig. 5b]. However, if the single-\nion-anisotropy is reduced to a value of K=−0.003µeV,\nit is noticed that the magnetization fails to switch success-\nfully.\nWe further study the effect of varying the DM interac-\ntion strength Dson the switching dynamics. It is found\nquiteobviouslythat as Dsdecreasesforafixedcantingan-\ngleθc, i.e., polarization-magnetization coupling weakens,\nthe AFM vector Ldeflects more, which can be interpreted\nas that the magnetization Mis more prone to switching\nfailures. For α= 0.1, ifDsis reduced 10 times, the mag-\nnetization Mstill switches successfully.\nAn interesting investigation would be to see whether\nmagnetization, being a rotational body, oscillates for a\ncertain range of damping parameter. For example, a spin-\npolarized current can spawn oscillatory states in a nano-\np-4Dynamical systems study in single-phase multiferroic materials\nFig. 5: Magnetization switches successfully at damping par ameterα= 0.01. (a) Polarization is switched 200 times faster by\nchanging the polarization damping. The magnetization swit ches successfully. (b) The single-ion anisotropy constant Kis taken\ninto account. In this case, magnetization switches success fully too.\nmagnet [50]. Figure 6a shows the magnetization dynam-\nics when damping parameter α= 0.001. The single-ion-\nanisotropy is included here and magnetization was able\nto get past towards the + y-direction, however, could not\nsettle there and oscillates with a time period of 3.3 ps.\nWith further lowering of the damping parameter, magne-\ntizationstilloscillates, howeverwith alowerfrequency[see\nFig. 6b].\nThe oscillatory mode of magnetization too can be ex-\nplained from the out-of-plane excursion ofthe spins due to\nlow damping. The spins get deflected out-of-plane (i.e., z-\ndirection) and when they go completely out-of-plane, they\ncontinue rotating and reach the out-of-plane in the oppo-\nsite directions than the previous ones. Therefore the spins\nsustaina self-oscillation . The DM interactionensuresthat\nthex- andz-component of the spins are canceled out and\nthey-components are added due to symmetry, as can be\nnoticed in the Fig. 6. Note that such self-oscillation oc-\ncursandsustainsevenintheabsenceofanexternalelectric\nfield, making the system unstable. Such spontaneous self-\noscillation is not uncommon in electronic systems having\nnegative damping due to positive feedback leading to in-\nstabilities. The oscillationtime-period increasesat a lower\ndamping (see Fig. 6b) since it takes more time for magne-\ntization to traverse for a lower damping parameter.\nThe research on single-phase multiferroic materials is\nstill emerging, and the search for a room-temperature sys-\ntem that requires a low enough electric field for switch-\ning the polarization is still underway. It will be interest-\ning to incorporate the thermal fluctuations in the model\nto understand the consequence on magnetization dynam-\nics [14,51]. Also for a shape-anisotropic single-domain\nnanomagnet, the corresponding anisotropy needs to be in-\ncluded for detailed simulation [39].\nConclusions. – We have investigated the electric\nfield induced magnetization switching dynamics in single-\nphase multiferroic materials. The dynamical system anal-\nysis, contrary to steady-state analysis, revealed important\nintriguing phenomena of switching failures and oscillatorymode of magnetization. The key parameters that can\nshape the dynamics of magnetization are identified. The\nphenomenological magnetization damping turns out to be\na key parameter that can prevent successful switching of\nmagnetization. Hence, the present analysis puts forward\nanimportantstep towardanalyzingmagnetizationswitch-\ning dynamics between 180◦symmetry equivalent states in\nthe emerging multiferroic materials. Moreover, the anal-\nysis identifies the oscillatory mode of magnetization that\ncan act as a source of microwave signals. The present\nanalysis can facilitate designing multiferroic materials for\nrelevant technological purposes.\nREFERENCES\n[1]Schmid H. ,Ferroelectrics ,162(1994) 317.\n[2]Eerenstein W., Mathur N. D. andScott J. F. ,Na-\nture,442(2006) 759.\n[3]Scott J. F. ,Nature Mater. ,6(2007) 256.\n[4]Daraktchiev M., Catalan G. andScott J. F. ,Phys.\nRev. B,81(2010) 224118.\n[5]Spaldin N. A. andFiebig M. ,Science,309(2005) 391.\n[6]Fiebig M. ,J. Phys. D: Appl. Phys. ,38(2005) R123.\n[7]Ramesh R. andSpaldin N. A. ,Nature Mater. ,6(2007)\n21.\n[8]Fiebig M., Lottermoser T., Fr ¨ohlich D., Goltsev\nA. V.andPisarev R. V. ,Nature,419(2002) 818.\n[9]Pyatakov A. P. andZvezdin A. K. ,Eur. Phys. J. B ,\n71(2009) 419.\n[10]Pyatakov A. P. andZvezdin A. K. ,Physics-Uspekhi ,\n55(2012) 557.\n[11]Glinchuk M. D., Eliseev E. A., Morozovska A. N.\nandBlinc R. ,Phys. Rev. B ,77(2008) 024106.\n[12]Glinchuk M. D., Morozovska A. N., Eliseev E. A.\nandBlinc R. ,J. Appl. Phys. ,105(2009) 084108.\n[13]Hill N. A. ,Annu. Rev. Mater. Res. ,32(2002) 1.\n[14]Roy K.,SPIN,3(2013) 1330003.\n[15]Roy K.,Appl. Phys. Lett. ,103(2013) 173110.\n[16]Roy K.,Appl. Phys. Lett. ,104(2014) 013103.\n[17]Roy K.,J. Phys. D: Appl. Phys. ,47(2014) 252002.\n[18]Roy K.,J. Phys.: Condens. Matter ,26(2014) 492203.\np-5Kuntal Roy\nFig. 6: Magnetization oscillation for low damping paramete rs. The electric field is withdrawn at 0.5 ns. (a) Damping para meter\nα= 0.001. Magnetization has got past from −y-axis to + y-axis but could not settle there rather oscillates around th at position\nwith a time period of 3.3 ps. (b) Damping parameter α= 10−4. Magnetization got past from −y-direction to + y-direction but\ncould not settle there rather oscillates around that positi on with a time period of 5.3 ps. With the removal of electric fie ld, the\nmagnetization traverses toward −y-direction and oscillates around there. The three-dimensi onal dynamics of the spins S1and\nS2are shown at the lower part of the figure for both the cases (a) a nd (b).\n[19]Roy K., Bandyopadhyay S. andAtulasimha J. ,Appl.\nPhys. Lett. ,99(2011) 063108.\n[20]Roy K., Bandyopadhyay S. andAtulasimha J. ,Sci.\nRep.,3(2013) 3038.\n[21]Khomskii D. I. ,J. Magn. Magn. Mater. ,306(2006) 1.\n[22]Tokura Y. ,J. Magn. Magn. Mater. ,310(2007) 1145.\n[23]Fennie C. J. ,Phys. Rev. Lett. ,100(2008) 167203.\n[24]Birol T., Benedek N. A., Das H., Wysocki A. L.,\nMulder A. T., Abbett B. M., Smith E. H., Ghosh S.\nandFennie C. J. ,Curr. Opin. Sol. St. Mater. Sci. ,165\n(2012) 227.\n[25]Rondinelli J. M., May S. J. andFreeland J. W. ,\nMRS Bulletin ,37(2012) 261.\n[26]Chappert C., Fert A. andDau F. N. V. ,Nature\nMater.,6(2007) 813.\n[27]Lottermoser T., Lonkai T., Amann U., Hohlwein\nD., Ihringer J. andFiebig M. ,Nature,430(2004) 541.\n[28]Roy K.,J. Phys. D: Appl. Phys. ,47(2014) 422001.\n[29]Dzyaloshinsky I. ,J. Phys. Chem. Sol. ,4(1958) 241.\n[30]Moriya T. ,Phys. Rev. ,120(1960) 91.\n[31]Anderson P. W. ,Phys. Rev. ,115(1959) 2.\n[32]Fox D. L. andScott J. F. ,J. Phys. C: Solid St. Phys. ,\n10(1977) L329.\n[33]Ederer C. andSpaldin N. A. ,Phys. Rev. B ,74(2006)\n020401(R).\n[34]Ederer C. andSpaldin N. A. ,Phys. Rev. B ,71(2005)\n060401(R).\n[35]Ederer C. andFennieC. J. ,J. Phys.: Condens. Matter ,\n20(2008) 434219.\n[36]Bandyopadhyay A. K., Ray P. C. andGopalan V. ,\nJ. Appl. Phys. ,100(2006) 114106.\n[37]Landau L. andLifshitz E. ,Phys. Z. Sowjet. ,8(1935)\n153.[38]Gilbert T. L. ,IEEE Trans. Magn. ,40(2004) 3443.\n[39]Chikazumi S. ,Physics of Ferromagnetism (Oxford Uni-\nversity Press, USA) 1997.\n[40]Bhattacharjee S., Rahmedov D., Wang D., niguez\nJ. I.andBellaiche L. ,Phys. Rev. Lett. ,112(2014)\n147601.\n[41]Rahmedov D., Wang D., niguez J. I. andBellaiche\nL.,Phys. Rev. Lett. ,109(2012) 037207.\n[42]Mochizuki M. andNagaosa N. ,Phys. Rev. Lett. ,105\n(2010) 147202.\n[43]Kalinin S. V., Rodriguez B. J., Jesse S., Chu Y. H.,\nZhao T., Ramesh R., Choudhury S., Chen L. Q.,\nEliseev E. A. andMorozovska A. N. ,Proc. Natl.\nAcad. Sci. U.S.A. ,104(2007) 20204.\n[44]Varga T., Droubay T. C., Bowden M. E.,\nNachimuthu P., Shutthanandan V., Bolin T. B.,\nShelton W. A. andChambers S. A. ,Thin Sol. Films ,\n520(2012) 5534.\n[45]Stokes H. T., Kisi E. H., Hatch D. M. andHoward\nC. J.,Acta Crystallogr. Sect. B ,58(2002) 934.\n[46]Li J., Nagaraj B., Liang H., Cao W., Lee C. and\nRamesh R. ,Appl. Phys. Lett. ,84(2004) 1174.\n[47]Gilmore K., Idzerda Y. U. andStiles M. D. ,Phys.\nRev. Lett. ,99(2007) 027204.\n[48]Bailey W., Kabos P., Mancoff F. andRussek S. ,\nIEEE Trans. Magn. ,37(2001) 1749.\n[49]Kajiwara Y., Harii K., Takahashi S., Ohe J.,\nUchida K., Mizuguchi M., Umezawa H., Kawai H.,\nAndo K. andTakanashi K. ,Nature,464(2010) 262.\n[50]Zeng Z., Finocchio G. andJiang H. ,Nanoscale ,5\n(2013) 2219.\n[51]Brown W. F. ,Phys. Rev. ,130(1963) 1677.\np-6"    },    {        "title": "1507.04560v1.Coherent_radiation_by_magnets_with_exchange_interactions.pdf",        "content": "arXiv:1507.04560v1  [cond-mat.mes-hall]  16 Jul 2015Coherent radiation by magnets with exchange\ninteractions\nV.I. Yukalov1,∗and E.P. Yukalova2\n1Bogolubov Laboratory of Theoretical Physics,\nJoint Institute for Nuclear Research, Dubna 141980, Russia\n2Laboratory of Information Technologies,\nJoint Institute for Nuclear Research, Dubna 141980, Russia\nAbstract\nA wide class of materials acquires magnetic properties due t o particle interactions\nthrough exchange forces. These can be atoms and molecules co mposing the system\nitself, as in the case of numerous magnetic substances. Or th ese could be different\ndefects, as in the case of graphene, graphite, carbon nanotu bes, and related materials.\nThe theory is suggested describing fast magnetization reve rsal in magnetic systems,\nwhose magnetism is caused by exchange interactions. The effec t is based on the cou-\npling of a magnetic sample with an electric circuit producin g a feedback magnetic field.\nThis method can find various applications in spintronics. Th e magnetization reversal\ncan be self-organized, producing spin superradiance. A par t of radiation is absorbed\nby a resonator magnetic coil. But an essential part of radiat ion can also be emitted\nthrough the coil sides.\nKeywords : Magnetic materials, Exchange interactions, Magnetic graphene, Spintronics,\nSpin superradiance, Maser radiation\nPACS numbers : 84.40.Dc; 84.40.Ik; 84.90+a; 85.75.Hh; 85.75.Ff\n∗Corresponding author: V.I. Yukalov\nE-mail: yukalov@theor.jinr.ru\n11 Introduction\nMagnetic materials, whose magnetism is caused by exchange interac tions, form a very wide\nclass of magnets of different sizes, including the samples of nanosize s, which find a variety\nof applications [1]. A novel class of exchange-interaction magnetic m aterials is the graphene\nfamily with defects, including graphene flakes and ribbons, graphite , and carbon nanotubes\n[2–4]. Magnetic materials find numerous applications in quantum electr onics, for example,\nin spintronics, information processing etc.\nIn the present paper, we concentrate on two interconnected fe atures of magnetic mate-\nrials: (i) First, we study the way of fast magnetization reversal in t hese materials that is\na property crucially important for spintronics and information proc essing. We show that\nby coupling a magnetic sample to a resonant electric circuit it is possible to achieve fast\nmagnetization reversal. The details of the reversal can be easily re gulated by varying the\nsystem parameters. (ii) Second, fast magnetization reversal sh ould produce magneto-dipole\nspinradiationinradio-frequency ormicrowave region. However, a la rgepart of thisradiation\nwould be absorbed by the coil of the coupled electric circuit. We aim at studying whether\nsome part of the maser radiation could be emitted through the coil s ides. The possibility of\nthis effect would essentially widen the region of applicability of such mag netic materials.\nThe fact that coupling a resonant electric circuit to a spin system co uld essentially in-\nfluence spin dynamics is the essence of the Purcell effect [5]. A detaile d theory of spin\ndynamics, employing the Purcell effect, has been developed for nuc lear spins [6–10], mag-\nnetic nanomolecules [11–13], and magnetic nanoclusters [14–17] (se e also the review arti-\ncle [18]). The characteristic feature of all these materials is that th eir particle interactions\nare described by dipolar forces. Also, only the total radiation inten sity has been consid-\nered. However, in the typical setup, the magnetic sample is inserte d into a coil of a resonant\nmagnetic circuit, so that an essential part of radiation is absorbed by this coil. In order to\nunderstand whether some part of magneto-dipole radiation could b e emitted through the\ncoil sides, it is necessary to study the spatial distribution of the ra diation.\nThe main novelty of the present paper is twofold: (i) We consider the class of magnetic\nmaterials with exchange interactions. This class is widespread and imp ortant, including a\nnumber of known magnetic materials as well as new nanomaterials, su ch as graphene with\ndefects. (ii) We study the spatial distribution of radiation in order t o conclude whether a\nsample inside a coil could serve as an emitter of radiation passing thro ugh the coil sides.\n2 Magnets with exchange interactions\nThe Hamiltonian of a system of Nparticles is the sum\nˆH=ˆHex−µ0N/summationdisplay\nj=1B·Sj. (1)\nThe first term is the Hamiltonian of an anisotropic Heisenberg model,\nˆHex=−1\n2/summationdisplay\ni/negationslash=j/bracketleftbig\nJij/parenleftbig\nSx\niSx\nj+Sy\niSy\nj/parenrightbig\n+IijSz\niSz\nj/bracketrightbig\n, (2)\n2describing particles with exchange interactions. The second is a Zee man term, with µ0being\nmagnetic moment, and with the total magnetic field\nB=B0ez+Hex (3)\nconsisting of an external magnetic field B0along thezaxis and a feedback field H, along\nthexaxis, caused by the magnetic coil of an electric circuit. The sample is in serted into the\ncoil, with its axis along the xaxis. The feedback field is defined by the Kirchhoff equation\nthat can be written [8,9,18] as\ndH\ndt+2γH+ω2/integraldisplayt\n0H(t′)dt′=−4πdmx\ndt. (4)\nHereγis the circuit attenuation, ωis the circuit natural frequency, and the effective elec-\ntromotive force is due to the moving magnetization of the sample,\nmx=µ0\nVcN/summationdisplay\nj=1/an}bracketle{tSx\nj/an}bracketri}ht, (5)\nwhereVcis the coil volume and angle brackets imply statistical averaging.\nThezaxis is assumed to be the axis of the easy magnetization, so that Iijshould be\nlarger than Jij. If exchange interactions are due to electrons, then µ0<0. Therefore, if\nB0>0, then the equilibrium spin value S0of a particle is negative, S0<0. In this case, the\nZeeman frequency is positive,\nω0≡ −µ0B0>0. (6)\nThe effective particle spin Scan be arbitrary. The ladder spin operators\nS±\nj≡Sx\nj±iSy\nj\nsatisfy the commutation relations\n/bracketleftbig\nS+\ni, S−\nj/bracketrightbig\n= 2δijSz\nj,/bracketleftbig\nS−\ni, Sz\nj/bracketrightbig\n= 2δijS−\nj.\nIn terms of the ladder spin operators, the exchange Hamiltonian (2 ) is\nˆHex=−1\n2/summationdisplay\ni/negationslash=j/parenleftbig\nJijS+\niS−\nj+IijSz\niSz\nj/parenrightbig\n. (7)\nWriting down the Heisenberg equations of motion, we compliment them by the atten-\nuationγ1, caused by spin-lattice interactions and γ2, due to other spin interactions, e.g.,\ndipole interactions that usually are smaller than the exchange intera ctions. I that way, the\nequations of motion read as\nidS±\nj\ndt=/bracketleftBig\nS±\nj,ˆH/bracketrightBig\n−iγ2S±\nj, idSz\nj\ndt=/bracketleftBig\nSz\nj,ˆH/bracketrightBig\n−iγ1/parenleftbig\nSz\nj−S0/parenrightbig\n. (8)\nAccomplishing the related commutations, we get the equations for t he transverse spin,\ndS−\ni\ndt=i/summationdisplay\nj(/negationslash=i)/parenleftbig\nIijS−\niSz\nj−JijSz\niS−\nj/parenrightbig\n−iω0S−\ni−iµ0HSz\ni−γ2S−\ni, (9)\nand for the longitudinal spin\ndSz\ni\ndt=i\n2/summationdisplay\nj(/negationslash=i)Jij/parenleftbig\nS+\niS−\nj−S−\niS+\nj/parenrightbig\n+i\n2µ0H/parenleftbig\nS+\ni−S−\ni/parenrightbig\n−γ1(Sz\ni−S0).(10)\n33 Stochastic mean-field approximation\nWeshallbeinterestedintheevolutionoftheaveragedquantitiesch aracterizing the transition\nfunction\nu≡1\nNSN/summationdisplay\nj=1/an}bracketle{tS−\nj/an}bracketri}ht, (11)\nthecoherence intensity\nw≡1\nN(N−1)S2N/summationdisplay\ni/negationslash=j/an}bracketle{tS+\niS−\nj/an}bracketri}ht, (12)\nand thespin polarization\nz≡1\nNSN/summationdisplay\nj=1/an}bracketle{tSz\nj/an}bracketri}ht. (13)\nAveraging equations (9) and (10), we invoke stochastic mean-field approximation [19],\nreplacing spin pair correlators as\n/an}bracketle{tSα\niSβ\nj/an}bracketri}ht → /an}bracketle{tSα\ni/an}bracketri}ht/an}bracketle{tSβ\nj/an}bracketri}ht+/an}bracketle{tSα\ni/an}bracketri}htδSβ\nj+/an}bracketle{tSβ\nj/an}bracketri}htδSα\ni, (14)\nwherei/ne}ationslash=jandδSα\njis treated as a stochastic variable, such that its stochastic avera ge be\nzero:\n/an}bracketle{t/an}bracketle{tδSα\nj/an}bracketri}ht/an}bracketri}ht= 0. (15)\nThen the averages /an}bracketle{tSα\nj/an}bracketri}htbecome functions of the stochastic variables.\nAlso, we introduce the composite stochastic variables\nξ0≡/summationdisplay\nj(/negationslash=i)/parenleftbig\nJijδSz\ni−IijδSz\nj/parenrightbig\n, ξ≡/summationdisplay\nj(/negationslash=i)/parenleftbig\nIijδS−\ni−JijδS−\nj/parenrightbig\n,\nϕ≡/summationdisplay\nj(/negationslash=i)Jij/parenleftbig\nδS−\ni−δS−\nj/parenrightbig\n. (16)\nAnd we define the effective anisotropy\n∆J≡1\nN/summationdisplay\ni/negationslash=j(Iij−Jij). (17)\nWe assume that /an}bracketle{tSα\nj/an}bracketri}htdoes not depend on the index enumerating spins and that the variab les\n(16) also are not index-dependent.\nIn this way, from equation (9), we obtain the equation for the tran sition function,\ndu\ndt=−i(ω0+ξ0−S∆Jz−iγ2)u−i(µ0H−ξ)z , (18)\nand for the coherence intensity,\ndw\ndt=−2γ2w+i(µ0H−ξ∗)zu−i(µ0H−ξ)zu∗. (19)\n4While equation (10) yields the equation for the spin polarization,\ndz\ndt=i\n2u∗(µ0H−ϕ)−i\n2u(µ0H−ϕ∗)−γ1(z−ζ), (20)\nwhereζ≡S0/S. The initial conditions\nu0=u(0), w 0=w(0), z 0=z(0),\ncompliment the above equations.\n4 Resonator feedback field\nThe Kirchhoff equation (4) can be represented [8,13] as the integr al equation\nH=−4π/integraldisplayt\n0G(t−t′) ˙mx(t′)dt′, (21)\nwith the transfer function\nG(t) =/bracketleftBig\ncos(ωt)−γ\nωsin(ωt)/bracketrightBig\ne−γt,ω≡/radicalbig\nω2−γ2,\nand where\n˙mx=µ0NS\n2Vcd\ndt(u∗+u). (22)\nThe longitudinal and transverse attenuations are assumed to be s mall, as compared to the\nZeeman frequency,γ1\nω0≪1,γ2\nω0≪1. (23)\nThe coupling of the magnet with the resonant electric circuit leads to the appearance of the\ncoupling attenuation\nγc≡πµ2\n0SN\nVc. (24)\nThe latter, together with the circuit attenuation, are small, as com pared to the resonator\nnatural frequency,γ\nω≪1,γc\nω≪1. (25)\nThe stochastic variables (16), because of condition (15), can also be treated as effectively\nsmall.\nTo be efficient, the resonator has to be tuned to the Zeeman frequ ency, so that the\nresonance condition\n|∆|\nω≪1 (∆ ≡ω−ω0) (26)\nbe valid. Also, the magnetic anisotropy has to be small, with the anisot ropy parameter\nA≡S∆J\nω0<1. (27)\nOtherwise the sample magnetization would be frozen.\n5In this way, the feedback equation (21) can be solved iteratively, t aking for the initial\napproximation u≈u0exp(−iωSt), with\nωS≡ω0−S∆Jz=ω0(1−Az). (28)\nThen in the first iteration, we get\nµ0H=i(uψ−u∗ψ∗), (29)\nwith the coupling function\nψ=γcωS/bracketleftbigg1−exp{−i(ω−ωS)t−γt}\nγ+i(ω−ωS)+1−exp{−i(ω+ωS)t−γt}\nγ−i(ω+ωS)/bracketrightbigg\n.(30)\nIn view of the above conditions, the first, resonant, term of the c oupling function prevails,\nso that\nψ∼=γcωS1−exp{−i∆St−γt}\nγ+i∆S, (31)\nwith the effective dynamic detuning\n∆S≡ω−ωS= ∆+ω0Az . (32)\nDefining the dimensionless coupling parameter\ng≡γcω0\nγγ2, (33)\nthe real and imaginary parts of the coupling function can be written as\nReψ=gγ2γ2\nγ2+∆2\nS(1−Az)/braceleftbigg\n1−/bracketleftbigg\ncos(∆ St)−∆S\nγsin(∆St)/bracketrightbigg\ne−γt/bracerightbigg\n(34)\nand, respectively,\nImψ=−gγγ2∆S\nγ2+∆2\nS(1−Az)/braceleftbigg\n1−/bracketleftbigg\ncos(∆St)+γ\n∆Ssin(∆St)/bracketrightbigg\ne−γt/bracerightbigg\n.(35)\nNote that in the case of resonance, when ∆ = 0, and under weak anis otropyA≪1,\nwe have ∆ S→0. Then the imaginary part (35) is close to zero, and the real part c an be\nsimplified to\nReψ≈gγ2(1−Az)/parenleftbig\n1−e−γt/parenrightbig\n.\nThe latter form can be employed only when the anisotropy is not stro ng, so that A≪1.\n5 Scale separation approach\nSubstituting equality (28) into the evolution equations (18), (19), and (20), we have the\nequations for the transverse function,\ndu\ndt=−i(ωS+ξ0)u−(γ2−zψ)u−zψ∗u∗+iξz , (36)\n6the coherence intensity,\ndw\ndt=−2(γ2−αz)w+i(u∗ξ−ξ∗u)z−z/bracketleftbig\nψu2+ψ∗(u∗)2/bracketrightbig\n, (37)\nand for the spin polarization,\ndz\ndt=−αw−i\n2(u∗ϕ−ϕ∗u)+1\n2/bracketleftbig\nψu2+ψ∗(u∗)2/bracketrightbig\n−γ1(z−ζ). (38)\nHere the notation\nα≡1\n2(ψ∗+ψ) = Reψ (39)\nis introduced.\nWe solve the system of equations (36), (37), and (38) by resortin g to the scale separation\napproach [6,8,9,13,18,19]. The function uis classified as fast, while wandz, as slow. First,\nwe solve equation (36) for the fast variable, keeping the slow variab les as quasi-integrals of\nmotion and taking account of the resonance condition (26). This giv es\nu=u0exp/braceleftbigg\n−(iωS+γ2−zψ)t−i/integraldisplayt\n0ξ0(t′)dt′/bracerightbigg\n+\n+iz/integraldisplayt\n0ξ(t′)exp/braceleftbigg\n−(iωS+γ2−zψ)(t−t′)−i/integraldisplayt\nt′ξ(t′′)dt′′/bracerightbigg\ndt′. (40)\nStochastic variables, in view of condition (15), are zero-centered ,\n/an}bracketle{t/an}bracketle{tξ0(t)/an}bracketri}ht/an}bracketri}ht=/an}bracketle{t/an}bracketle{tξ(t)/an}bracketri}ht/an}bracketri}ht=/an}bracketle{t/an}bracketle{tϕ(t)/an}bracketri}ht/an}bracketri}ht= 0. (41)\nThe stochastic variable ξ0is real, while ξandφare complex-valued. Therefore\n/an}bracketle{t/an}bracketle{tξ0(t)ξ(t′)/an}bracketri}ht/an}bracketri}ht=/an}bracketle{t/an}bracketle{tξ0(t)ϕ(t′)/an}bracketri}ht/an}bracketri}ht=/an}bracketle{t/an}bracketle{tξ(t)ϕ(t′)/an}bracketri}ht/an}bracketri}ht= 0. (42)\nFor the non-zero pair stochastic correlators, we set\n/an}bracketle{t/an}bracketle{tξ∗(t)ξ(t′)/an}bracketri}ht/an}bracketri}ht= 2γ3δ(t−t′),/an}bracketle{t/an}bracketle{tξ∗(t)ϕ(t′)/an}bracketri}ht/an}bracketri}ht= 2γ3δ(t−t′), (43)\nwithγ3playing the role of an attenuation caused by stochastic fluctuation s.\nSubstituting expression (40) into equations (37) and (38) and ave raging the latter over\nfast temporal oscillations and stochastic variables, we come to the equations for the guiding\ncenters, describing the coherence intensity,\ndw\ndt=−2(γ2−αz)w+2γ3z2(44)\nand the spin polarization,\ndz\ndt=−αw−γ3z−γ1(z−ζ). (45)\nRecall that αis given by equations (34) and (39).\n76 Triggering spin waves\nStochastic variables are the fluctuations that trigger spin motion. To clarify the nature\nof stochastic variables, let us show that these correspond to spin waves describing spin\nfluctuations around the average local spin polarization z=z(t). It is worth recalling that\nspin waves can be well defined for nonequilibrium systems [20,21].\nSpin fluctuations are defined as small oscillations around the averag e spin, which can be\nrepresented as\nSα\nj=/an}bracketle{tSα\nj/an}bracketri}ht+δSα\nj. (46)\nSubstituting this into the equations of motion (9) and (10), we omit, for simplicity, the\nattenuations, keeping in mind the initial stage of the process, when time is yet much shorter\nthan the relaxation times. Separating the zero-order equations, we get\nd\ndt/an}bracketle{tS−\nj/an}bracketri}ht=−iωS/an}bracketle{tS−\nj/an}bracketri}ht,d\ndt/an}bracketle{tSz\nj/an}bracketri}ht= 0. (47)\nAnd to first order, we have\nd\ndtδS−\nj=−i/parenleftbig\nω0δS−\nj+/an}bracketle{tS−\nj/an}bracketri}htξ0−/an}bracketle{tSz\nj/an}bracketri}htξ/parenrightbig\n,\nd\ndtδSz\nj=i\n2/parenleftbig\n/an}bracketle{tS−\nj/an}bracketri}htϕ∗−/an}bracketle{tS+\nj/an}bracketri}htϕ/parenrightbig\n. (48)\nKeeping in mind that zis a slow variable, from equations (47), we find\n/an}bracketle{tS−\nj/an}bracketri}ht=u0Se−iωSt,/an}bracketle{tSz\nj/an}bracketri}ht=zS . (49)\nIn order to stress the role of fluctuations, let us set u0= 0. Then\nδS−\nj=S−\nj, δSz\nj= 0 (u0= 0), (50)\nwhere we take into account condition (15). The first of equations ( 48) yields\nd\ndtS−\nj=−iω0S−\nj+izSξ . (51)\nLet us employ the Fourier transformation for the ladder spin opera tors,\nS−\nj=/summationdisplay\nkS−\nkeik·rj, S−\nk=1\nN/summationdisplay\njS−\nje−ik·rj,\nand for the exchange interactions,\nJij=1\nN/summationdisplay\nkJkeik·rij, J k=/summationdisplay\nj(/negationslash=i)Jije−ik·rij,(rij≡ri−rj)\nwith the similar transformation for Iij. For the stochastic variable ξ, we get\nξ=/summationdisplay\nk(I0−Jk)S−\nkeik·rj.\n8Then equation (51) reduces to\nd\ndtS−\nk=−iωkS−\nk, (52)\nwith the spin-wave spectrum\nωk=ω0+zS(Jk−I0). (53)\nFor long waves, when k→0, we obtain\nωk≃ωS−zS\n2/summationdisplay\nj(/negationslash=i)Jij(k·rij)2. (54)\nThis demonstrates that stochastic fluctuations are nothing but s pin waves.\nFor what follows, it is useful to keep in mind the restriction\nw+z2=/vextendsingle/vextendsingle/vextendsingle/vextendsingle/vextendsingle1\nNSN/summationdisplay\nj=1/an}bracketle{tSj/an}bracketri}ht/vextendsingle/vextendsingle/vextendsingle/vextendsingle/vextendsingle2\n≤1, (55)\nwhich is necessary to take into account when setting initial condition s for equations (44) and\n(45).\n7 Qualitative classification of regimes\nSuppose that the initial state of the magnet is nonequilibrium, such t hat the external mag-\nnetic field is directed along the z-axis, together with spins. Spin waves trigger spin motion,\nforcing spins to move, which generates the resonator feedback fi eld acting back on spins and\ncollectivizing their motion. The spins tend to reach an equilibrium state , reversing from\npositive to negative values. The overall dynamics can be classified on to several qualitatively\ndifferent stages. Below, we give this qualitative classification, settin g for simplicity zero\ndetuning ∆ = 0 and considering the limit of negligibly weak anisotropy A→0. Thus, we\nset\n∆→0, A→0,∆S→0. (56)\nThen the coupling function (39) reduces to the simple form\nα→gγ2/parenleftbig\n1−e−γt/parenrightbig\n. (57)\n7.1 Chaotic stage\nAt the beginning, before coherence in spin motion sets up at time tcoh, the process is yet\nchaotic. At short times in the interval\n0<t<t coh, (58)\nthe coupling function is yet very small, such that\nα≪γ2, α≪γ3. (59)\nThen the linear in time solutions of equations (44) and (45) are\nw≃w0+2/parenleftbig\nγ3z2\n0−γ2w0/parenrightbig\nt, z ≃z0−[(z0−ζ)γ1+γ3z0]t. (60)\n9This regime lasts till the time, when the coupling function grows, so th at\nαz=γ2(t=tcoh), (61)\nwhich defines the coherence time\ntcoh=1\nγlngz0\ngz0−1. (62)\nAt large coupling parameter, this gives\ntcoh=γ2\nγcω0z0(gz0≫1). (63)\n7.2 Coherent stage\nAfter the coherence time, spins become well correlated by means o f the resonator feedback\nfield. In the time interval\ntcoh<t<T 2, (64)\nwhereT2≡1/γ2, the coupling function is large,\nα≫γ1, α≫γ3, (65)\nreaching the value\nα≃gγ2(γ2<γ). (66)\nThe spin-lattice attenuation is usually small, such that γ1≪γ2andγ1≪γ3. Then\nequations (44) and (45) read as\ndw\ndt=−2γ2(1−gz)w,dz\ndt=−gγ2w. (67)\nThe exact solutions of these equations give the coherence intensit y\nw=/parenleftbiggγp\ngγ2/parenrightbigg2\nsech2/parenleftbiggt−t0\nτp/parenrightbigg\n(68)\nand the spin polarization\nz=−γp\ngγ2tanh/parenleftbiggt−t0\nτp/parenrightbigg\n+1\ng. (69)\nHeret0andτpare the integration constants that are defined by the values w(tcoh)≡wcoh\nandz(tcoh)≡zcoh. This gives the delay time\nt0=tcoh+τp\n2ln/vextendsingle/vextendsingle/vextendsingle/vextendsingleγp+γg\nγp−γg/vextendsingle/vextendsingle/vextendsingle/vextendsingle(70)\nand thepulse time\nτp=1\nγp, (71)\nwhere\n2γ2\np=γ2\ng\n1+/radicalBigg\n1+4/parenleftbigggγ2\nγg/parenrightbigg2\nwcoh\n, γ p=γ2(gzcoh−1). (72)\n10Under a large coupling parameter and small coherence intensity, at the coherence time tcoh,\nwe get\nγg≃gγ2zcoh(gzcoh≫1),\nγp≃gγ2/radicalBig\nz2\ncoh+wcoh(wcoh≪zcoh). (73)\nThe maximum of the coherence intensity occurs at the time t0, being\nw(t0) =wcoh+/parenleftbigg\nzcoh−1\ng/parenrightbigg2\n. (74)\nAt this moment of time, the spin polarization is\nz(t0) =1\ng. (75)\n7.3 Relaxation stage\nAfter the transverse decoherence time T2, there is the relaxation stage in the interval\nT2<t<T 1, (76)\nwhereT1≡1/γ1. Fort≫t0, the coherence intensity relaxes as\nw≃4w(t0)exp/parenleftbigg\n−2t\nτp/parenrightbigg\n, (77)\nand the spin polarization tends to\nz≃ −zcoh+2\ng+2/parenleftbigg\nzcoh−1\ng/parenrightbigg\nexp/parenleftbigg\n−2t\nτp/parenrightbigg\n. (78)\n7.4 Quasi-stationary stage\nIn the limit of very long times, when\nT1<t<∞, (79)\nthe solutions exhibit small oscillations around the fixed points w∗andz∗given by the equa-\ntions\nγ2(1−gz∗)w∗−γ3(z∗)2= 0, gγ 2w∗+γ3z∗+γ1(z∗−ζ) = 0. (80)\n7.5 Punctuated superradiance\nThe coherent stage of radiation corresponds to the regime of sup erradiance, which can be\npure, ifw0= 0, or triggered, if w0>0. It is also possible to realize the regime of punctuated\nsuperradiance [18], when in the process of spin dynamics either the e xternal magnetic field\nis reversed or the magnetic sample is rotated, so that to reproduc e the initial nonequilibrium\nconditions. In this case, radiation exhibits a series of coherent puls es, with the temporal\nintervals that can be regulated.\n118 Numerical investigation of dynamics\nWesolveequations (44)and(45)numerically, withthecoupling funct iondefined inequations\n(34) and (39). The case of exact resonance is assumed, with ω=ω0. Then ∆ = 0 and\n∆S=ωAz. The chosen initial conditions correspond to a purely self-organize d process, in\nthe absence of imposed initial coherence, so that w0= 0, and when the initial polarization\nz0= 1 defines a strongly nonequilibrium state, since the equilibrium polariz ation of a single\nspin, under the given setup, corresponds to ζ=−1.\nIn the presence of a resonator feedback field, spin reversal hap pens much faster than\nthe homogeneous transverse relaxation time T2≡1/γ2. We measure all attenuations and\nfrequencies in units of γ2. The spin-lattice attenuation γ1is usually much smaller than γ2.\nTaking this into account, we set γ1= 0.001. The dynamic attenuation γ3is assumed to be\nof order ofγ2, which, in units of the latter, implies γ3= 1. Time is measured in units of T2.\nFirst, we consider the more general form corresponding to expre ssion (34), which reads\nas\nα=gγ2γ2(1−Az)\nγ2+(ωAz)2/braceleftbigg\n1−/bracketleftbigg\ncos(ωAzt)−ω\nγAzsin(ωAzt)/bracketrightbigg\ne−γt/bracerightbigg\n.\nThe temporal behaviour of the coherence intensity and spin polariz ation, for different system\nparameters, is shown in Figures 1 to 8.\nFigures 1 and 2 show the role of magnetic anisotropy for different re sonator frequencies.\nIncreasing the anisotropy, generally, shifts the delay time, widens the coherence pulse, and\ndecreases the coherence peak maximum, and the reversed spin po larization.\nFigures 3 and 4 demonstrate the role of the resonator attenuatio n. The larger γ, the\nhigher the coherence peak maximum and the shorter the delay time. Spin reversal is better\npronounced for larger attenuations.\nFigures 5 and 6 illustrate the role of the coupling strength between t he magnet and\nresonator. The larger coupling parameter leads to a shorter delay time and higher coherence\nmaximum. The value of ωdoes not influence much the behavior, when the anisotropy is\nweak,A≪1. Stronger coupling leads to a better spin reversal.\nFigures 7 and 8 show the role of anisotropy for a large value of the co upling parame-\nter. The stronger anisotropy increases the delay time and diminishe s the coherence peak\nmaximum. Spin reversal is more effective for a weaker anisotropy.\nThe general form of the above coupling function looks a bit cumbers ome, because of\nwhich we also check its approximate form, discussed in Section 4, whic h is given by the\nexpression\nα≈gγ2(1−Az)/parenleftbig\n1−e−γt/parenrightbig\n.\nIt turns out that this approximate form is applicable under weak anis otropy, with the\nanisotropy parameters A≪1, but becomes invalid for larger anisotropies.\n9 Spatial distribution of radiation\nThe spatial distribution ofradiationfor atomicsystems can befoun din references [22,23]. In\nthe case of spin systems, the calculational procedure is similar, with the difference that the\nradiation is produced by moving magnetic moments. The other slight d ifference is connected\nwiththechosen geometry. Foratomicsystems, oneusuallyconside rs acylindric sample, with\nthe axis along the zaxis. In the setup, related to a magnetic system, as we study here , the\n12magnetic sample is inserted into a coil, with the axis along the xaxis, while an external\nmagnetic field defines the zaxis, so that the sample axis is orthogonal to the zaxis.\nThe operator of magnetic moment, related to a j-th spin, can be written in the form\nµ0Sj=/vector µS+\nj+/vector µ∗S−\nj+/vector µ0Sz\nj, (81)\nwhere\n/vector µ=µ0\n2(ex−iey), /vector µ=µ0ez. (82)\nThe radiation intensity in the direction of the vector\nn≡r\n|r|=r\nr(83)\ncan be represented [19] as\nI(n,t) = 2ω0γ0/summationdisplay\nijϕij(n)/an}bracketle{tS+\ni(t)S−\nj(t)/an}bracketri}ht, (84)\nwhereγ0is a natural width,\nγ0≡2\n3|/vector µ|2k3\n0=1\n3µ2\n0k3\n0/parenleftBig\nk0≡ω0\nc/parenrightBig\n, (85)\nand the system form-factor is\nϕij(n) =3\n8π|n×eµ|2exp(ik0n·rij). (86)\nHere we introduce the unit vector\neµ≡/vector µ\n|/vector µ|=1√\n2(ex−iey) (87)\nand take into account that\n|/vector µ|=µ2\n0\n2,|/vector µ0|2=µ2\n0.\nDenoting by ϑthe angle between nandez, we have\n|n×eµ|2= 1−1\n2sin2ϑ=1\n2/parenleftbig\n1+cos2ϑ/parenrightbig\n.\nThe form factor (86) becomes\nϕij(n) =3\n16π/parenleftbig\n1+cos2ϑ/parenrightbig\nexp(ik0n·rij). (88)\nThe radiation intensity (84) can be separated into two terms,\nI(n,t) =Iinc(n,t)+Icoh(n,t), (89)\nthe incoherent radiation intensity\nIinc(n,t) = 2ω0γ0/summationdisplay\njϕ(n)/an}bracketle{tS+\nj(t)S−\nj(t)/an}bracketri}ht, (90)\n13and the coherent radiation intensity\nIcoh(n,t) = 2ω0γ0/summationdisplay\ni/negationslash=jϕij(n)/an}bracketle{tS+\ni(t)S−\nj(t)/an}bracketri}ht, (91)\nwhere\nϕ(n)≡ϕjj(n) =3\n16π/parenleftbig\n1+cos2ϑ/parenrightbig\n. (92)\nTaking into account the identity\nS+\njS−\nj=S(S+1)−/parenleftbig\nSz\nj/parenrightbig2+Sz\nj\nand the approximate equality\n/an}bracketle{t/parenleftbig\nSz\nj/parenrightbig2/an}bracketri}ht ≈S2,\nwhich is exact for spin S= 1/2, as well as for large S→ ∞, makes it possible to rewrite the\nincoherent radiation intensity as\nIinc(n,t) = 2ω0γ0/summationdisplay\njϕ(n)/parenleftbig\nS+/an}bracketle{tSz\nj/an}bracketri}ht/parenrightbig\n. (93)\nIntroducing the local functions\nuj(t)≡1\nS/an}bracketle{tS−\nj(t)/an}bracketri}ht, w j(t)≡1\nS2| /an}bracketle{tS−\nj(t)/an}bracketri}ht |2,\nzj(t)≡1\nS/an}bracketle{tSz\nj(t)/an}bracketri}ht, (94)\nand using the semiclassical approximation, we come to the incoheren t radiation intensity\nIinc(n,t) = 2ω0γ0S/summationdisplay\njϕij(n)[1+zj(t)], (95)\nand the coherent radiation intensity\nIcoh(n,t) = 2ω0γ0S2/summationdisplay\ni/negationslash=jϕij(n)u∗\ni(t)uj(t). (96)\nAssuming that the radiation wave length is comparable or larger than the linear sample\nsizes, we can resort to the uniform approximation, passing to func tions (11), (12), and (13).\nIn this procedure, we consider the sum\n/summationdisplay\ni/negationslash=jϕij(n) =ϕ(n)N2/bracketleftbigg\nF(k0n)−1\nN2/bracketrightbigg\n, (97)\nin which\nF(k0n)≡/vextendsingle/vextendsingle/vextendsingle/vextendsingle/vextendsingle1\nNN/summationdisplay\nj=1eik0n·rj/vextendsingle/vextendsingle/vextendsingle/vextendsingle/vextendsingle2\n. (98)\nThen we find the incoherent radiation intensity\nIinc(n,t) = 2ω0γ0NSϕ(n)[1+z(t)] (99)\n14and the coherent radiation intensity\nIcoh(n,t) = 2ω0γ0N2S2ϕ(n)F(k0n)w(t). (100)\nThe total radiation intensity, integrated over the spherical angle s, is\nI(t)≡/integraldisplay\nI(n,t)dΩ(n) =Iinc(t)+Icoh(t), (101)\ncontaining the incoherent part\nIinc(t) = 2ω0γ0SN[1+z(t)] (102)\nand the coherent part\nIcoh(t) = 2ω0γ0S2N2ϕ0w(t), (103)\nwith the shape factor\nϕ0≡/integraldisplay\nϕ(n)F(k0n)dΩ(n). (104)\nWhen spins are uniformly distributed in the sample, function (98) can be represented as\nan integral over the sample volume:\nF(k0n) =/vextendsingle/vextendsingle/vextendsingle/vextendsingle1\nV/integraldisplay\nVeik0n·rdr/vextendsingle/vextendsingle/vextendsingle/vextendsingle2\n. (105)\nThe direction vector, in terms of spherical coordinates, is\nn={sinϑcosϕ,sinϑsinϕ,cosϑ}. (106)\nIntegrating over the sample, we meet the integral\n/integraldisplaya\n0sin/parenleftBig\nc√\na2−x2/parenrightBig\ncos(bx)dx=πac\n2√\nb2+c2J1/parenleftBig\na√\nb2+c2/parenrightBig\nexpressed through the Bessel function J1of the first kind. Finally, we obtain\nF(k0n) =16sin2/parenleftbigk0L\n2sinϑcosϕ/parenrightbig\nk2\n0L2sin2ϑcos2ϕJ2\n1(k0R/radicalbig\nsin2ϑsin2ϕ+cos2ϑ)\nk2\n0R2(sin2ϑsin2ϕ+cos2ϑ).(107)\nRecall that k0≡ω0/c= 2π/λ.\nSince the magnetic sample is inserted into a coil aligned along the axis x, the radiation\nin thezdirection is absorbed by the coil. Radiation can be emitted only in the xdirection,\nwhen\nF(k0n) =4\nk2\n0L2sin2/parenleftbiggk0L\n2/parenrightbigg/parenleftBig\nϑ=π\n2, ϕ= 0/parenrightBig\n. (108)\nThenϕ(n) = 3/(16π), which is only twice smaller than its value in the zdirection.\nIf the sample is a very narrow cylinder, or represents a linear chain o f spins aligned along\nthe axisx, then expression (107) leads to\nF(k0n) =4sin2/parenleftbigk0L\n2sinϑcosϕ/parenrightbig\nk2\n0L2sin2ϑcos2ϕ(R→0). (109)\n15Magnetic dipole radiation usually corresponds to long waves, such th at the wavelength\nλis longer that the sample linear sizes. To consider this limit, we notice th at the Bessel\nfunctionJν(x), at smallx≪1, has the asymptotic property\nJν(x)≃1\nΓ(ν+1)/parenleftBigx\n2/parenrightBigν\n−1\nΓ(ν+2)/parenleftBigx\n2/parenrightBigν+2\n,\nbecause of which\nJ1(x)≃x\n2(x→0).\nHence, in the long-wave limit,\nF(k0n)≃1/parenleftbigg2πR\nλ≪1,πL\nλ≪1/parenrightbigg\n. (110)\nIn this way, although a part of radiation is absorbed by the coil, neve rtheless, an essential\npart of radiation can be emitted through the sides of the sample alon g the coil axis x.\n10 Discussion\nWe have considered a large class of magnetic materials, composed of particles interacting\nthroughexchange interactions. Such materials arewell represen ted by ananisotropic Heisen-\nberg Hamiltonian. By coupling a magnetic sample to a resonant electric circuit it is possible\nto efficiently regulate spin dynamics. The present investigation comp lements the earlier\nstudies of spin dynamics in different materials, accomplished for polar ized nuclei, magnetic\nnanomolecules, and magnetic nanoclusters. The systems compose d of these particles pos-\nsess several common properties. Such systems, except polarize d nuclei, exhibit magnetic\nanisotropy. For example, the spins of magnetic nanomolecules are f rozen below the block-\ning temperature TB∼1−10 K, with the frozen magnetization protected by an anisotropy\nbarrier of energy EA∼10−100 K. For magnetic nanoclusters, the blocking temperature\nisTB∼10−100 K. Polarized nuclei can be represented by polarized protons in h ydro-\ngenated materials, such as propanediol, butanol, and ammonia. Alth ough these materials\ndo not enjoy magnetic anisotropy, however their spins, at low temp erature, can remain po-\nlarized for extremely long time. The common feature of all above mat erials is that their spin\ninteractions are described by dipolar forces.\nHowever, there exists a very wide class of materials made of particle s with magnetic\nexchange interactions. Also, recently there have appeared a new type of magnetic nanoma-\nterials characterized by exchange interactions, such as magnetic graphene, where magnetic\nproperties are induced by defects [2–4].\nGraphene is a two-dimensional carbon material intermediate betwe en an insulator and a\nmetal [24,25]. Carbon-carbon spacing is a≈1.42˚A, and its surface density is ρ≈3.9×1015\ncm−2.\nMagnetic graphene can be well described by an anisotropic Heisenbe rg model [2–4]. For\ndefects on a zigzag edge, one has an exchange interaction potent ialJ∼0.1 eV, orJ∼10−13\nerg. Thisgives J//planckover2pi1∼1014s−1andJ/kB∼103K.Dipolarinteractionsaremuchweaker, with\nµ2\nB/a3∼10−17erg, orµ2\nB/(/planckover2pi1a3)∼1010s−1. In temperature units, this gives µ2\nB/(kBa3)∼\n0.1 K. Magnetic anisotropy is not strong, with ∆ J/J∼10−4, hence, ∆J//planckover2pi1∼1010s−1.\nThus,γ2∼µ2\nB/(/planckover2pi1a3)∼1010s−1. Ifγ3∼∆J//planckover2pi1, thenγ3∼1010s−1, that is, of the same\n16order asγ2. In the case of an external magnetic field B0= 1 T, the Zeeman frequency is\nω0=|µBB0|//planckover2pi1∼1011s−1. Therefore the radiation wavelength is λ∼10 cm. Since there\nare many ways of generating defects in graphene, the system par ameters can be varied.\nIt is important to stress that a self-organized spin dynamics, when there is no initial\ncoherence imposed onto the sample, cannot be correctly describe d by phenomenological\nequations, like Landau-Lifshitz, Gilbert, or Bloch equations. This is w hy, we use a micro-\nscopic approach with a realistic Hamiltonian. Such an approach makes it possible to take\ninto account quantum fluctuations, crucially important at the begin ning of spin relaxation.\nAlso, the use of a microscopic model has an advantage of containing well defined parameters\nassociated with the considered Hamiltonian.\nWhen the system is prepared in a nonequilibrium state, and no initial co herence is im-\nposed onto the sample, spin wave fluctuations serve as a triggering mechanism starting spin\nmotion. It is possible to show that spin wave fluctuations is the sole tr iggering mechanism,\nwhile thermal Nyquist noise of the coil cannot play the role of a trigge r.\nIn the process of motion, spins are collectivized by means of the res onator feedback\nfield. Superradiance in spin systems cannot be caused by photon ex change. That is, spin\nsuperradiance is due to the Purcell effect and is impossible without a r esonator. This is\ncontrary to atomic systems, where superradiance develops as a D icke effect.\nThe microscopic equations of motion are investigated by employing st ochastic mean-\nfield approximation and scale separation approach. The equations f or guiding centers are\nsolved numerically. Depending on initial conditions and system parame ters, there can exist\ndifferent regimes of spin dynamics, slow free relaxation during the tim eT1, free induction in\ntimeT2, weak superradiance intimeslightly shorter tan T2, puresuperradiance andtriggered\nsuperradiance, whenthereversal timeofmagnetizationcanbema demuchshorterthan T2, of\norder 10−11s or 10−12s. The regime of punctuated superradiance can be realized, produ cing\na sequence of coherent pulses.\nWe have analyzed the spatial distribution of radiation produced by m oving magnetic\nmoments. Although a part of radiation is absorbed by the coil surro unding the sample,\nanyway, radiation can be emitted through the sides of the sample, w here there is no coil.\nThe studied effects can be used in a variety of problems in spintronics and in quantum\ninformation processing.\nAcknowledgement . Financial support from RFBR (grant # 14-02-00723) is appreci-\nated.\n17References\n[1] Evans RFL, Fan WJ, Chureemart P, Ostler TA, Ellis MOA and Chantr ell RW 2014 J.\nPhys. Condens. Matter 26103202\n[2] Yaziev OV 2010 Rep Prog Phys 73056501\n[3] Katsnelson MI 2012 Graphene: Carbon in Two Dimensions (Cambridge: Cambridge\nUniversity Press)\n[4] Enoki T and Ando T 2013 Physics and Chemistry of Graphene (Singapore: Pan Stan-\nford)\n[5] Purcell EM 1946 Phys. Rev. 69681\n[6] Yukalov VI 1995 Phys. Rev. Lett. 753000\n[7] Yukalov VI 1995 Laser Phys. 5526\n[8] Yukalov VI 1995 Laser Phys. 5970\n[9] Yukalov VI 1996 Phys. Rev. B 539232\n[10] Yukalov VI, Yukalova EP 1998 Laser Phys. 81029\n[11] Yukalov VI 2002 Laser Phys. 121089\n[12] Yukalov VI, Yukalova EP 2005 Eur. Phys. Lett. 70306\n[13] Yukalov VI 2005 Phys. Rev. B 71184432\n[14] Yukalov VI, Henner VK, Kharebov PV, Yukalova EP 2008 Laser Phys. Lett. 5887\n[15] Yukalov VI, Yukalova EP 2011 Laser Phys. Lett. 8804\n[16] Yukalov VI, Yukalova EP 2012 J. Appl. Phys. 111023911\n[17] Kharebov PV, Henner VK, Yukalov VI 2013 J. Appl. Phys. 113043902\n[18] Yukalov VI, Yukalova EP 2004 Phys. Part. Nucl. 35348\n[19] Yukalov VI 2014 Laser Phys. 24094015\n[20] R¨ uckriegel A, Kreisel A, Kopietz P 2012 Phys. Rev. B 85054422\n[21] Birman JL, Nazmitdinov RG, Yukalov VI 2013 Phys. Rep 5261\n[22] Rehler NE, Eberly JH 1971 Phys. Rev. A 31735\n[23] Allen L, Eberly JH 1975 Optical Resonance and Two-Level Atoms (New York: Wiley)\n[24] Goerbig MO 2011 Rev. Mod. Phys. 831193\n[25] Wehling TO, Black-Schaffer AM, Balatsky AV 2014 Adv. Phys. 631\n18Figure Captions\nFigure 1 . Role of magnetic anisotropy in spin dynamics for the parameters γ= 1,\ng= 10, andω= 10, under different anisotropy parameters, A= 0.1 (solid line), A= 0.5\n(dashedline), and A= 1(dashed-dottedline): (a)Coherenceintensity; (b)Spinpolariz ation.\nFigure 2 . Role of magnetic anisotropy in spin dynamics for the parameters γ= 1,\ng= 10, butω= 100, under different anisotropy parameters, A= 0.1 (solid line), A= 0.5\n(dashedline), and A= 1(dashed-dottedline): (a)Coherenceintensity; (b)Spinpolariz ation.\nFigure 3 . Roleof resonator attenuation for the parameters g= 10,A= 0.1, andω= 10,\nunder different attenuation parameters, γ= 1 (solid line), γ= 10 (dashed line), and γ= 100\n(dashed-dotted line): (a) Coherence intensity; (b) Spin polarizat ion.\nFigure 4 . Role of resonator attenuation for the parameters g= 10,A= 0.1, but\nω= 100, under different attenuation parameters, γ= 1 (solid line), γ= 10 (dashed line),\nandγ= 100 (dashed-dotted line): (a) Coherence intensity; (b) Spin pola rization.\nFigure 5 . Role of magnet-resonator coupling for the parameters γ= 10,A= 0.1, and\nω= 10, under different coupling parameters g= 10 (solid line) and g= 100 (dashed line):\n(a) Coherence intensity; (b) Spin polarization.\nFigure 6 . Role of magnet-resonator coupling for the parameters γ= 10,A= 0.1, but\nω= 100, under different coupling parameters, g= 10 (solid line) and g= 100 (dashed line):\n(a) Coherence intensity; (b) Spin polarization.\nFigure 7 . Role of magnetic anisotropy for the parameters γ= 10,g= 100, and ω= 10,\nunder different anisotropy parameters, A= 0 (solid line), A= 0.1 (dashed line), A= 0.5\n(dashed-dotted line), and A= 1 (dashed line with dots): (a) Coherence intensity; (b) Spin\npolarization.\nFigure 8 . Role of magnetic anisotropy for the parameters γ= 10,g= 100, but ω= 100,\nunder different anisotropy parameters, A= 0 (solid line), A= 0.1 ( dashed line), A= 0.5\n(dashed-dottedline), and A= 1(dottedline): (a)Coherence intensity; (b)Spinpolarization.\n190 0.5 1 1.5 200.20.40.60.81\nw\nt(a)\nA = 0.5A = 0.1\nA = 1\n0 0.5 1 1.5 2−0.5−0.2500.250.50.751\ntz (b)\nA = 1A = 0.5\nA = 0.1\nFigure 1: Role of magnetic anisotropy in spin dynamics for the parame tersγ= 1,g= 10,\nandω= 10, under different anisotropy parameters, A= 0.1 (solid line), A= 0.5 (dashed\nline), andA= 1 (dashed-dotted line): (a) Coherence intensity; (b) Spin polariz ation.\n0 0.5 1 1.5 200.20.40.60.81\ntw(a)\nA = 1A = 0.1 A = 0.5\n0 0.5 1 1.5 2−0.5−0.2500.250.50.751\ntz (b)\nA = 1\nA = 0.1A = 0.5\nFigure 2: Role of magnetic anisotropy in spin dynamics for the parame tersγ= 1,g= 10,\nbutω= 100, under different anisotropy parameters, A= 0.1 (solid line), A= 0.5 (dashed\nline), andA= 1 (dashed-dotted line): (a) Coherence intensity; (b) Spin polariz ation.\n200 0.25 0.5 0.75 1 1.25 1.500.20.40.60.81\ntw\nγ = 1γ = 100\nγ = 10(a)\n0 0.25 0.5 0.75 1 1.25 1.5−0.8−0.6−0.4−0.200.20.40.60.81\ntz\nγ = 1\nγ = 10γ = 100(b)\nFigure 3: Role of resonator attenuation for the parameters g= 10,A= 0.1, andω= 10,\nunder different attenuation parameters, γ= 1 (solid line), γ= 10 (dashed line), and γ= 100\n(dashed-dotted line): (a) Coherence intensity; (b) Spin polarizat ion.\n0 0.25 0.5 0.75 1 1.25 1.500.20.40.60.81\ntw (a)\nγ = 1γ = 10γ = 100\n0 0.25 0.5 0.75 1 1.25 1.5−0.8−0.6−0.4−0.200.20.40.60.81\ntz(b)\nγ = 1\nγ = 10γ = 100\nFigure 4: Role of resonator attenuation for the parameters g= 10,A= 0.1, butω= 100,\nunder different attenuation parameters, γ= 1 (solid line), γ= 10 (dashed line), and γ= 100\n(dashed-dotted line): (a) Coherence intensity; (b) Spin polarizat ion.\n210 0.2 0.4 0.6 0.8 100.20.40.60.81\ntw\ng = 10g = 100(a)\n0 0.2 0.4 0.6 0.8 1−1−0.500.51\ntz\ng = 10\ng = 100(b)\nFigure 5: Role of magnet-resonator coupling for the parameters γ= 10,A= 0.1, and\nω= 10, under different coupling parameters g= 10 (solid line) and g= 100 (dashed line):\n(a) Coherence intensity; (b) Spin polarization.\n0 0.2 0.4 0.6 0.8 100.20.40.60.81\ntw\ng = 10g = 100(a)\n0 0.2 0.4 0.6 0.8 1−1−0.500.51\ntz\ng = 10\ng = 100(b)\nFigure 6: Role of magnet-resonator coupling for the parameters γ= 10,A= 0.1, but\nω= 100, under different coupling parameters, g= 10 (solid line) and g= 100 (dashed line):\n(a) Coherence intensity; (b) Spin polarization.\n220 0.05 0.1 0.15 0.200.20.40.60.81\ntw\nA = 0A = 0.1\nA = 0.5\nA = 1(a)\n0 0.05 0.1 0.15 0.2−1−0.75−0.5−0.2500.250.50.751\ntz\nA = 0A = 0.1A = 0.5\nA = 1(b)\nFigure 7: Role of magnetic anisotropy for the parameters γ= 10,g= 100, and ω= 10,\nunder different anisotropy parameters, A= 0 (solid line), A= 0.1 (dashed line), A= 0.5\n(dashed-dotted line), and A= 1 (dashed line with dots): (a) Coherence intensity; (b) Spin\npolarization.\n0 0.2 0.4 0.6 0.8 100.20.40.60.81\ntw (a)A = 0\nA = 0.1A = 0.5\nA = 1\n0 0.2 0.4 0.6 0.8 1−1−0.75−0.5−0.2500.250.50.751\ntz(b)\nA = 0\nA = 0.1A = 0.5A = 1\nFigure 8: Role of magnetic anisotropy for the parameters γ= 10,g= 100, but ω= 100,\nunder different anisotropy parameters, A= 0 (solid line), A= 0.1 ( dashed line), A= 0.5\n(dashed-dottedline), and A= 1(dottedline): (a)Coherence intensity; (b)Spinpolarization.\n23"    },    {        "title": "1508.02486v2.Transport_between_metals_and_magnetic_insulators.pdf",        "content": "Transport between metals and magnetic insulators\nJiang Xiao ( '_)1, 2and Gerrit E. W. Bauer3, 4\n1Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China\n2Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai, 200433, China\n3Institute for Materials Research and WPI-AIMR, Tohoku University, Sendai, Japan\n4Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands\n(Dated: June 25, 2021)\nWe derive the Onsager response matrix of fluctuation-mediated spin-collinear transport through a ferromag-\nnetic insulator and normal metal interface driven by a temperature difference, spin accumulation, or magnetic\nfield. We predict magnon-squeezing spin currents, magnetic field-induced cooling (magnon Peltier effect), tem-\nperature induced magnetization (thermal magnetic field) as well as universal spin Seebeck/Peltier coefficients.\nFinite temperature effects on the transport properties of\nmagnetic nanostructures [1] attracts considerable attention\nsince the discovery of the spin Seebeck effect [2–4] that\nthwarts conventional thermoelectrics. Of special interest are\nheterostructures of magnetic insulators such as yttrium iron\ngarnets (YIG) with heavy normal metals such as Pt, where the\nlatter, via the inverse spin Hall effect, function as spin cur-\nrent detectors. Here we report a linear response approach to\nthermal transport through interfaces between ferro- or ferri-\nmagnetic insulators (FI) and normal metals (N) that extends\nour treatment of the spin Seebeck effect [5] to the spin Peltier\neffect and leads to the prediction of, e.g., a magnon Peltier\neffect and its Onsager reciprocal, a thermal effective field.\nThe Landau-Lifshitz-Gilbert equation for the dynamics of\na magnetization in an effective magnetic field B0\n_m=\u0000\rm\u0002(B0+b) +\u000bm\u0002_m (1)\nis based on the assumption that the modulus of the spa-\ntiotemporal magnetization texture M(r;t)is constant, i.e.\nM(r;t) =Msm(r;t)andjmj= 1, which is valid at tem-\nperatures sufficiently below that of the magnetic phase tran-\nsition. The LLG predicts a temperature-induced reduction of\nthe time-averaged equilibrium magnetization by considering a\nstochastic magnetic field b(r;t)that induces thermal fluctua-\ntions of maround the equilibrium direction. Thermal noise\nis characterized by the spatiotemporal correlation function\nhbi(r;t)bj(r0;t0)ithat by the Fluctuation-Dissipation Theo-\nrem (FDT) can be expressed in terms of an integral over the\nBose-Einstein distribution function of the magnon excitations\nand proportional to the Gilbert damping constant \u000b[6]. Mi-\ncroscopically, the magnetization noise in insulating ferromag-\nnets is caused by the magnetoelastic interaction that couples\nand equilibrates the magnetic and elastic order parameters. At\ninterfaces to metals, spin pumping induces an additional en-\nergy and angular momentum dissipation that increases the ef-\nfective damping and the magnetic fluctuations [7–9].\nSpin accumulations in the normal metal at interfaces to\nferromagnets with transverse spin polarization generate spin-\ntransfer torques [10, 11], while the longitudinal ones have at\nzero temperature no effect on the magnetization. One might\ntherefore, naively, expect that the magnetization of the insula-\ntor in FIjN bilayers is inert without outside spin injection ornon-collinear magnetic fields. However, spin collinear trans-\nport phenomena in FI jN systems exist at finite temperatures\nby the magnetic thermal fluctuations that allow a longitudi-\nnal spin accumulation in N to act on instantaneous transverse\nmagnetization components. The ensemble/time average of the\nthus induced spin currents is polarized along the equilibrium\nmagnetization direction.\nPerturbation on a system at thermal equilibrium generates a\nresponse or “current” that is proportional to the “force” when\nthe latter is sufficiently weak (Ohm’s Law). In the presence\nof multiple forces and currents cross-correlations exist, ther-\nmoelectrics being a prominent example. The linear response\nof such a system is then described by a “conductance” matrix\nthat relates forces and currents, which possesses a fundamen-\ntal symmetry referred to as Onsager reciprocity [12] that is\nvery useful in spintronics [13]. Here we establish the Onsager\nmatrix for transport through a normal metal and a ferromag-\nnetic insulator contact (N jFI) that is actuated by a spin accu-\nmulation in N, temperature difference over the interface, and\n(pulsed) external magnetic field. Each matrix element rep-\nresents a different physical phenomenon, of which the spin\nSeebeck effect is just one [5, 14, 15]. The extended Onsager\nmatrix discussed in the following has already been implic-\nitly used (without details and with reference to the present\nwork) in the analysis of the spin Peltier effect [16] and in\nmodelling spin Seebeck generators [17]. The N jFI system\nhas recently been analyzed by Bender et al. [18] using a\n“Golden Rule” treatment of the interface exchange interaction\nincluding angle-dependent spin transfer torques and quantum\neffects. However, this study does not take into account the\nmagnetic field component parallel to the magnetization that is\ncentral to the present work. We focus on symmetry conserv-\ning perturbations, thereby disregarding deterministic trans-\nverse spin accumulations and spin-transfer torques, which is\nallowed as long as the systems is far from the threshold of\ncharge current-induced magnetic self-oscillations or magneti-\nzation reversal. All elements of the response matrix are then\nscalars. Recently, Nakata et al. [19] derived the Onsager ma-\ntrix for a bilayer of magnetic insulators actuated by inhomo-\ngeneous magnetic fields and temperature differences.\nFig. 1 sketchs the ferromagnetic insulator (FI) with nor-\nmal metal (N) contact. The equilibrium FI magnetizationarXiv:1508.02486v2  [cond-mat.mtrl-sci]  13 Aug 20152\nBappTFTN\nFI NIflIspm\nxz\ny⊗\n0\nFIG. 1: (Color online) Spin and energy current driven by the thermal\nbias ( \u0001T=TF\u0000TN), spin chemical potential Vs, and an external\nmagnetic field Bappat an FIjN interface.\nis parallel to the uniaxial anisotropy field B0=B0^z=\n(!0=\r)^zkhmi. We adopt the “three reservoir model” by as-\nsuming that thermalization of spin waves in FI and electrons\nin N is sufficiently efficient. The steady state in the pres-\nence of a temperature gradient is then characterized by the\ntemperatures of phonon (FI and N), magnon (FI), and elec-\ntron (N) systems, thereby disregarding spin dependent elec-\ntron temperatures in N [22]. Transport is generated by the\ndifferences in the thermodynamic variables on both sides of\nthe interface. This situation is amenable to magnetoelectronic\nscattering theory of transport parameterized by the interface\nscattering matrix. This picture has a wider applicability in cir-\ncuit theories, in which the interfaces generate boundary condi-\ntions between “bulk regions” that may be described by quasi-\nequilibrium distribution functions [23]. For comparison with\nexperiments, the present analysis is a (crucial) building block\nin simulating entire devices [16, 24].\nFor simplicity, we consider here the limit of small phonon\n(Kapitza) heat conductances, which allows us to discard the\nphonons altogether [17]. The thermodynamic state of the in-\nsulating ferromagnet is then characterized by the temperature\nTFonly. The normal metal is at electron and phonon temper-\natureTN. We include the option of having long-lived spin ac-\ncumulation, i.e., a chemical potential difference between the\nspin up and spin down electrons in the frame of the FI equi-\nlibrium magnetization with quantization axis along ^z. The\nthermodynamic forces are then the external magnetic field\nBapp=Bapp^z= (!app=\r)^z, longitudinal spin accumulation\nVs=Vs^ z= (~!s=2e)^ z(in units of volt) in N, and temper-\nature difference \u0001T=TF\u0000TNacross the interface. With\nT= (TF+TN)=2, the rate of change of the free energy reads\n_F=_SVs+_Q\u0001T\nT\u0000_MzBapp; (2)\nwhere S(t) =R\nNs(r;t)dV=S^zis the total spin (in units\nof electric charge jej) in N with spin density s(r;t),_Qis\nthe heat current entering N, Mz(t) =MsR\nFImz(r;t)dVis\nthe total magnetization in FI with local magnetization com-\nponentMsmz(r;t). The volume of the FI is V=Adwith\ninterface area Aand thickness d._Fincludes contributions\nfrom the electrons (first two terms) and the magnetization (last\nterm). Since Onsager symmetry holds when the entropy gen-\neration rate _S=_F=T equals the sum of the product of cur-rents and forces, we identify in Eq. (2) Vs;\u0000\u0001T=T;\u0000Bapp\nas thermodynamic driving forces with spin current density\njs= (~=2e)_S=A, energy current density jQ=_Q=A , and\nmagnetization dynamics _Mz=\rA, as the conjugated flows, re-\nspectively. The linear response coefficient matrix in\n0\n@_Mz\n\rA\njs\njQ1\nA=0\n@LmmLmsLmQ\nLsmLssLsQ\nLQmLQsLQQ1\nA0\n@!app\n!s\n\u0001T\nT1\nA (3)\nmust then satisfy the Onsager reciprocal relations [12], which\ndemand that our response matrix is symmetric. The matrix\nelementLsQparametrizes the spin Seebeck effect [5, 14, 15].\nOther elements represent various physical effects; Lssis the\nlongitudinal spin conductance, LQsgoverns the spin Peltier\neffect ,LQQis the heat conductance, while the signficance of\nthe new matrix elements LQmandLmQis discussed below.\nMacrospin model - We first treat the macrospin limit in\nwhich m=M=MwithM=MsVconstant in space and\ndescribed by the Landau-Lifshitz-Gilbert equation including\ninterface torques:\n_m=\u0000\rm\u0002Be\u000b+\u000bm\u0002_m\u0000\u000b0!sm\u0002(m\u0002^z):(4)\nwhere Be\u000b=B0+Bapp+bincludes the internal field\nB0k^zand the applied field Bappk^z. The last term is the in-\nstantaneous spin-transfer torque acting on the magnetization\nby the longitudinal spin accumulation in N [10, 11]. The\nGilbert damping parameter \u000bis the sum of the intrinsic \u000b0\nand\u000b0=\r~gr=(4\u0019Msd), the interface damping [25], where\ngris the real part of the spin mixing conductance per unit area\nof the FIjN interface [23]. Thermal effects are modeled by the\nstochastic fields b=b0+b0, which by the FDT, is associ-\nated with the damping \u000b=\u000b0+\u000b0[6, 26]. Sufficiently far\nfrom the Curie temperature, only the transverse xandycom-\nponents of m;b, andb0matter. To lowest order, the Fourier\ncomponents of mx;ysatisfy ~m!\ni=P\nj\u001f!\nij\r~b!\nj(i;j=x;y),\nintroducing the magnetic susceptibility\n\u001f!=\u0000(1 +\u000b2)\u00001\n(!\u0000!+\n0)(!\u0000!\u0000\n0)\u0012!0\u0000i\u000b!\u0000i!\ni! ! 0\u0000i\u000b!\u0013\n(5)\nwith!\u0006\n0=\u0006!0=(1\u0006i\u000b). According to the FDT [27], the\nmagnetic fluctuations for kBT\u001d~!0satisfy\nh~m!\ni~m!0\nji=\r~kBTF\nM\u0000\n\u001f\u0000\u001fy\u0001\nij\ni~!\u000e(!\u0000!0): (6)\nwhereh\u0001\u0001\u0001i denotes the thermal ensemble average. The cor-\nresponding random fields are white:\nhbi(t)bj(t0)i=2\u000bkBTF\n\rM\u000eij\u000e(t\u0000t0): (7)\nThe auto-correlation for the interface-induced random field b0\nhas the form Eq. (7) but with \u000b!\u000b0andTF!TN.\nWe are interested in the DC (ensemble or time averaged)\nspin and energy currents across the FI jN interface. The trans-\nverse components average to zero, while the z-component in3\nEq. (4) has a bulk contribution driven by Bappand interfacial\ncontribution jz\nsdriven by (Bapp;Vs;\u0001T):\n_Mz\n\rA=\u0000M\n\rA\u000b0!apphm\u0002(m\u0002^z)iz+jz\ns; (8)\nwhereh\u0001\u0001\u0001izis the thermal average of the z-component,\njz\ns=M\n\rAh\u000b0m\u0002_m\u0000\rm\u0002b0\n\u0000\u000b0(!s+!app)m\u0002(m\u0002^z)iz(9)\nwith _m\u0019\u0000\rm\u0002B0. The associated energy current equation\njQ=M\n\rAh\u000b0_m\u0001_m\u0000\r_m\u0001b0\n\u0000\u000b0(!s+!app)^z\u0001(m\u0002_m)i (10)\nfollows from the interface contribution (terms proportional to\n\u000b0andb0) of the energy change rate: dE=dt = (d=dt)h\u0000B0\u0001\nMi. At zero temperature, m=^zandb0=_m= 0 ,\nand bothjz\nsandjQvanish, as expected. At finite temper-\natures, and in spite of hmik^z,jz\nsandjQare finite because\nmandb0are correlated. The relevant equal-time correlators\nhmimji;hmib0\nji;hmi_mji, andh_mib0\njican be derived from:\nhmi(t)mj(0)i=\rkBTF\nMZd!\n2\u0019e\u0000i!t\ni!\u0000\n\u001f\u0000\u001fy\u0001\nij;(11a)\nhmi(t)\rb0\nj(0)i=2\u000b0\rkBTN\nMZd!\n2\u0019e\u0000i!t\u001fij: (11b)\nPlugging these into Eqs. (9, 10), we arrive at the linear re-\nsponse relation\n0\n@_Mz\n\rA\njz\ns\njQ1\nA=2\u000b0\nAkBT\n!00\n@\u000b\n\u000b01!0\n1 1!0\n!0!0!2\n01\nA0\n@!app\n!s\n\u0001T\nT1\nA: (12)\nMagnon model - The macrospin model above holds only in\nthe presence of strong applied magnetic fields or nanomagnets\nsmaller than the exchange length. Otherwise the thermal spin\nwave excitations and magnetization texture m(r;t)(~mk;!\niin\nFourier space) may not be disregarded. The internal magnetic\nfield should then be augmented by the exchange interaction\nB0!B0+ (D=\r~)r2mwhereDis the spin wave stiff-\nness. The stochastic fields b0(r;t)andb0(r;t)then depend\non position and b0(r;t) = \u0016b0(y;z;t )\u000e(x)acts at the inter-\nface. After linearizing and Fourier transforming Eq. (4) into\nfrequency and momentum space, ~mk;!\ni=\u001fk;!\nij\r~bk;!\nj, where\nthe magnetic susceptibility \u001fk;!takes the form Eq. (5) with\n!0!!0+ (D=~)k2. According to the FDT, the equilibrium\nmagnetization fluctuations satisfy [27]:\nhmk;!\nimk0;!0\nji=\r~\nMsi\u0000\n\u001fy\u0000\u001f\u0001\nij\ne~!=kBTF\u00001\u000ekk0\n!!0; (13)\nwhere\u000ekk0\n!!0\u0011\u000e(!\u0000!0)\u000e(k\u0000k0). The correlations for b0\nandb0(or\u0016b0) can be inferred from Eq. (13). The Planck dis-\ntribution regulates the frequency integral over the continuumof magnon density of states. We note that the magnetic field\ndependence of the spin Seebeck effect at room temperature\nindicates a magnon cut-off lower than kBTF=~. [28–30].\nThe spin and energy currents across the FI jN interface are\nstill given by Eqs. (9, 10) when substituting \u000b0!\u0016\u000b0=\u000b0d,\nb0!\u0016b0, andM!M=d =MsA. Using Eq. (13), all equal-\ntime-positon correlators in Eqs. (9, 10) can be infered from:\nhmi(0;0)mj(0;0)i=nFJ0(x0)\u000eij; (14a)\nhmi(0;0)\r\u0016b0\nj(0)i=\u0000\u0016\u000b0TN\nTFh_mi(0;0)mj(0;0)i;(14b)\nwherenF=\r~=Ms\u00153is the total number of spins in the\nvolume\u00153= (4\u0019D=kBT)3=2and\u0015is the de Broglie ther-\nmal wave length for magnons. Jl(x0) =R1\n02p\nx=\u0019(x0+\nx)l=(ex0+x\u00001)dxwithx0=~!0=kBTF. The expressions\nhold to leading order in \u000b. In the classical limit x0\u001c1,\nJl!Zl+3=2withZnthe Zeta function. Using these correla-\ntors in Eqs. (9, 10) leads to the central result of this paper:\n0\n@_Mz\n\rA\njz\ns\njQ1\nA=2\u0016\u000b0~\n\u001530\nB@\u000b\n\u000b0Z3\n2Z3\n23\n2\f~Z5\n2\nZ3\n2Z3\n23\n2\f~Z5\n23\n2\f~Z5\n23\n2\f~Z5\n215\n4\f2~2Z7\n21\nCA0\n@!app\n!s\n\u0001T\nT1\nA\n(15)\nwith\f\u00001=kBTF. The response matrix is symmetric as\nrequired by Onsager reciprocity and invertible, i.e.the forces\nare linear-independent as long as \u000b06= 0.\nDiscussion - The spin Seebeck effect represented by LsQ:\njz\ns= 3Z5\n2\u0016\u000b0\n\u00153kB\u0001T'\u0001T\n0:1 K0:14\u0016J\nm2; (16)\nspecifies the longitudinal spin current induced by the temper-\nature difference \u0001T[5, 14, 15]. The numerical estimates here\nand in the following are for the Pt jYIG system at T= 300\nK with parameters given in Table I. The inverse of the spin\nSeebeck effect is the spin Peltier effect given by LQs:\njQ= 3Z5\n2\u0016\u000b0\n\u00153kBT2e\n~Vs'Vs\n0:1\u0016V1:3\u0002105J\nm2\u0001s: (17)\nVsdrives an energy current that cools/heats the magnons [16].\nThe spin current driven by spin accumulations and external\nmagnetic field\njz\ns=Lsm!app+Lss!s= 2Z3\n2\u0016\u000b0\n\u00153~\u0012\n\rBapp+2e\n~Vs\u0013\n(18)\nvanishes with temperature since we disregarded quantum fluc-\ntuations and the magnon chemical potential in the ferromag-\nnet [18].Lsmin Eq. (18) quantifies the spin current induced\nby shifting the spin wave gap or “squeezing” the magnon dis-\ntribution function. The spin conductance Lssin Eq. (18) de-\nscribes the spin current injection by a collinear spin accumu-\nlationVsas observed recently by Cornelissen et al. [33]. The\nmagnon accumulation rate induced by this spin injection is\ndescribed by Lms.4\nParameter Value Unit Reference\nMs 1:4\u0002105A/m [34]\nD 8:5\u000210\u000040J\u0001m2[35, 36]\n\u000b0 10\u00004\ngr 10191/m2[37]\n\u0015 1:6 nm\n\u0016\u000b00:1 nm\nTABLE I: Parameters for YIG and YIG jPt interface.\nThe energy current driven by the external field via LQm\njQ= 3Z5\n2\u0016\u000b0\n\u00153kBT\rB app'Bapp\n1 T7:4\u0002107J\nm2\u0001s: (19)\nreflects what we call a magnon Peltier effect . It can be ob-\nserved by a temperature change of the ferromagnet generated\nby the applied magnetic field, analogous to the spin Peltier ef-\nfect caused by a spin accumulation [16]. The reciprocal to the\nmagnon Peltier effect is the magnetization dynamics induced\nby a temperature gradient via LmQ\n_Mz\n\rA= 3Z5\n2\u0016\u000b0\n\u00153kB\u0001T; (20)\nsimilar to applying a magnetic field. The magnitude of this\nthermal effective magnetic field can be estimated by setting\n_Mz= 0:\nB\u0001T=\u0000\u000b0\n\u000b3Z5=2\n2Z3=2kB\u0001T\n\r~=\u0016\u000b0\n\u0016\u000b0+\u000b0d\u0001T\n0:1 K60 mT;(21)\nwhere the prefactor is of the order of unity as long as d\u001c\n\u0016\u000b0=\u000b0(\u00181\u0016m for YIG).\nThe conventional Seebeck coefficient refers to the open cir-\ncuit thermopower voltage induced by a temperature differ-\nence. We may analogously define a spin Seebeck coefficient\nSSin terms of the spin thermopower, i.e.the spin accumula-\ntion generated by a temperature bias \u0001Tin a spin-open cir-\ncuit:SS= (Vs=\u0001T)jzs=0. This coefficient is not very rele-\nvant for metals that act as spin sinks such as Pt, but it charac-\nterizes the efficiency for weakly spin-dissipating metals such\nas Cu [17]. The thermally induced spin accumulation at zero\nspin current reads:\nVs=\u00003Z5=2\n4Z3=2kB\ne\u0001T=)SS=\u0000zkB\ne; (22)\nwithz= 3Z5=2=4Z3=2'0:385. For single (or multiple)\nparabolic magnon bands SS'33\u0016V/K is a universal con-\nstant that does not depend on the spin wave stiffness, uniaxial\nanisotropy, and (in the considered regime) temperature.\nThe spin-magnonic interfacial thermal conductance \u0014m=\n(jQ=\u0001T)jz\ns=0= (LQQ\u0000LsQLQsL\u00001\nss)=T:\n\u0014m=z0\u0016\u000b0\n\u00153k2\nBTF\n~'0:76\u0002108W\nm2\u0001Kwithz0= (15Z7=2\u00009Z2\n5=2=Z3=2)=2, is of the same order of\nmagnitude as the electron-phononic thermal conductance for\nAljAl2O3interface of\u00182\u0002108W=(m2\u0001K)[38].\nWe can estimate the time scale of the transient response to\na suddenly switched-on magnetic field. According to the first\nmatrix element in Eq. (15) with !app=\rBapp\nh_mzi=2\r~\nMs\u00153Z3\n2\u000b0!app= 2nFZ3\n2\u000b0!app: (23)\nOn the other hand, the value of mzat thermal equilibrium\ndepends on the spin wave gap ~!0:\nhmz(!0)i=q\n1\u0000hm2xi\u0000hm2yi'1\u0000nFJ0(x0);(24)\nthat is shifted by !app, therefore\n\u000emz=dhmz(!0)i\nd!0!app=nFLi1\n2(x0)~!app\nkBT; (25)\nwhere Li is the PolyLog function. The magnon relaxation\ntime to the new equilibrium is therefore\n\u001c'\u000emz\nh_mzi=~\n\u000bkBTLi1\n2(x0)\n2Z3\n2\u0019~\n\u000bpkBT~!0p\u0019\n2Z3\n2;(26)\nwhere the approximate expression is valid for x0=\n~!0=kBT\u001c1. For YIG with f=!0=2\u0019= 10 GHz at\nroom temperature, \u001c'2ns. Judging from the experimen-\ntal magnetic field dependence of the spin Hall effect at room\ntemperature, kBTshould be replaced by a magnon spectrum\ncut-off of 30K [28–30], leading to the estimate \u001c\u00187ns. At\neven lower temperatures, kBTin Eq. (26) should be replaced\nby~!0, leading to an upper estimate of 50ns.\nThe non-equilibrium magnetization Ms\u000emzin Eq. (25) can\nbe interpreted as a non-equilibrium magnon accumulation and\nthe magnetic field as its driving force. This interpretation pro-\nvides the link to theories of the electrically or thermally in-\njected magnon Bose condensate in which the self-organized\nmagnon chemical potential plays a crucial role [20, 21]. The\nweak magnon-phonon interaction reported recently by Cor-\nnelissen et al. . [33] is encouraging that a long lived magnon\nchemical potential and condensate can be electrically gener-\nated. The pulsed magnetic field experiments suggested here\ndo not require such a chemical potential and should yield use-\nful insights into the magnon distribution function.\nIn conclusion, we studied the magnetization dynamics cou-\npled to spin and energy currents through FI jN interfaces at\nfinite temperature as driven by collinear magnetic fields, spin\naccumulations, and/or a temperature bias. The response in this\nconfiguration vanishes with thermal fluctuations of the mag-\nnetization. We establish the Onsager reciprocal relations for\nthese response functions. The elements in the Onsager matrix\nare identified as the spin Seebeck effect, the spin Peltier effect,\nand previously overlooked ones such as the magnon Peltier ef-\nfect, effective thermal field, and magnon squeezing that have\nstill to be observed experimentally. We identified a (nearly)\nuniversal spin Seebeck thermopower of 33\u0016V/K.5\nG.B. is grateful for the the hospitality of Rembert Duine\nat Utrecht University and his helpful explanations of the con-\ncept of the magnon chemical potential. J.X. thanks Yaroslav\nTserkovnyak for the helpful discussion on the magnon re-\nlaxation time. Bart van Wees importantly helped us to un-\nderstand the experiments by Cornelissen et al. [33]. This\nwork was supported by the National Natural Science Foun-\ndation of China (11474065), National Basic Research Pro-\ngram of China (2014CB921600), the Foundation for Funda-\nmental Research on Matter (FOM), DFG Priority Programme\n1538 \"Spin-Caloric Transport\", JSPS Grant-in-Aid for Scien-\ntific Research (Nos. 25247056, 25220910, 26103006), and\nEU-FET Grant InSpin 612759.\n[1] F. Pulizzi, Nature Materials 11, 367 (2012).\n[2] K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae,\nK. Ando, S. Maekawa, and E. Saitoh, Nature 455, 778 (2008).\n[3] K. Uchida, J. Xiao, H. Adachi, J. Ohe, S. Takahashi, J. Ieda,\nT. Ota, Y . Kajiwara, H. Umezawa, H. Kawai, et al., Nature Ma-\nterials 9, 894 (2010).\n[4] C. M. Jaworski, J. Yang, S. Mack, D. D. Awschalom, J. P. Here-\nmans, and R. C. Myers, Nature Materials 9, 898 (2010).\n[5] J. Xiao, G. E. W. Bauer, K.-c. Uchida, E. Saitoh, and\nS. Maekawa, Phys. Rev. B 81, 214418 (2010); ibid82, 099904\n(2010).\n[6] W. F. Brown, Phys. Rev. 130, 1677 (1963).\n[7] J. Foros, A. Brataas, Y . Tserkovnyak, and G. E. W. Bauer, Phys.\nRev. Lett. 95, 016601 (2005).\n[8] J. Foros, A. Brataas, G. E. W. Bauer, and Y . Tserkovnyak, Phys.\nRev. B 75, 092405 (2007).\n[9] J. Xiao, G. E. W. Bauer, S. Maekawa, and A. Brataas, Phys.\nRev. B 79, 174415 (2009).\n[10] J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996).\n[11] L. Berger, Phys. Rev. B 54, 9353 (1996).\n[12] L. Onsager, Phys. Rev. 37, 405 (1931); ibid38, 2265 (1931).\n[13] M. Johnson and R. H. Silsbee, Phys. Rev. B 35, 4959 (1987).\n[14] H. Adachi, J.-i. Ohe, S. Takahashi, and S. Maekawa, Phys. Rev.\nB83, 094410 (2011).\n[15] S. Hoffman, K. Sato, and Y . Tserkovnyak, Phys. Rev. B 88,\n064408 (2013).\n[16] J. Flipse, F. Dejene, D. Wagenaar, G. Bauer, J. B. Youssef, and\nB. van Wees, Phys. Rev. Lett. 113, 027601 (2014).\n[17] A. B. Cahaya, O. A. Tretiakov, and G. E. W. Bauer, Appl. Phys.Lett.104, 042402 (2014).\n[18] S. A. Bender and Y . Tserkovnyak, Phys. Rev. B 91, 140402\n(2015).\n[19] K. Nakata, P. Simon, and D. Loss, arXiv:1507.03807 (2015).\n[20] S. A. Bender, R. A. Duine, and Y . Tserkovnyak, Phys. Rev. Lett.\n108, 246601 (2012).\n[21] R. A. Duine, A. Brataas, S. A. Bender, and Y . Tserkovnyak,\narXiv:1505.01329 (2015).\n[22] F. K. Dejene, J. Flipse, G. E. W. Bauer, and B. J. van Wees,\nNature Physics 9, 636 (2013).\n[23] A. Brataas, G. E. Bauer, and P. J. Kelly, Physics Reports 427,\n157 (2006).\n[24] M. Schreier, A. Kamra, M. Weiler, J. Xiao, G. E. W. Bauer,\nR. Gross, and S. T. B. Goennenwein, Phys. Rev. B 88, 094410\n(2013).\n[25] Y . Tserkovnyak, A. Brataas, and G. E. W. Bauer, Phys. Rev.\nLett.88, 117601 (2002).\n[26] J. Foros, A. Brataas, G. E. W. Bauer, and Y . Tserkovnyak, Phys.\nRev. B 79, 214407 (2009).\n[27] L. D. Landau, E. M. Lifsic, L. P. Pitaevskii, J. Sykes, and M. J.\nKearsley, Statistical physics Vol. 9 (Butterworth-Heinemann,\nOffice, 1980).\n[28] S. R. Boona and J. P. Heremans, Phys. Rev. B 90, 064421\n(2014).\n[29] T. Kikkawa, K.-i. Uchida, S. Daimon, Z. Qiu, Y . Shiomi, and\nE. Saitoh, arXiv:1503.05764 (2015).\n[30] U. Ritzmann, D. Hinzke, A. Kehlberger, E.-J. Guo, M. Kläui,\nand U. Nowak, arXiv:1506.05290 (2015).\n[31] Y .-T. Chen, S. Takahashi, H. Nakayama, M. Althammer,\nS. T. B. Goennenwein, E. Saitoh, and G. E. W. Bauer, Phys.\nRev. B 87, 144411 (2013).\n[32] Y . Zhou, H. Jiao, Y .-t. Chen, G. E. W. Bauer, and J. Xiao, Phys.\nRev. B 88, 184403 (2013).\n[33] L. J. Cornelissen, J. Liu, R. A. Duine, J. B. Youssef, and B. J.\nVan Wees, arXiv:1505.06325 (2015).\n[34] P. C. Dorsey, S. E. Bushnell, R. G. Seed, and C. Vittoria, J.\nAppl. Phys. 74, 1242 (1993).\n[35] V . Cherepanov, I. Kolokolov, and V . L’vov, Physics Reports\n229, 81 (1993).\n[36] C. M. Srivastava and R. Aiyar, Journal of Physics C: Solid State\nPhysics 20, 1119 (1987).\n[37] M. Weiler, M. Althammer, M. Schreier, J. Lotze, M. Pernpeint-\nner, S. Meyer, H. Huebl, R. Gross, A. Kamra, J. Xiao, et al.,\nPhys. Rev. Lett. 111, 176601 (2013).\n[38] D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Ma-\njumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys.\n93, 793 (2003)."    },    {        "title": "1509.00744v2.Elastic_scattering_of_electron_vortex_beams_in_magnetic_matter.pdf",        "content": "Elastic scattering of electron vortex beams in magnetic matter\nAlexander Edström,1Axel Lubk,2and Ján Rusz1\n1Department of Physics and Astronomy, Uppsala University, Box 516, 75121 Uppsala, Sweden\n2Triebenberg Laboratory, Technische Universität Dresden, Germany\n(Dated: October 15, 2018)\nElastic scattering of electron vortex beams on magnetic materials leads to a weak magnetic con-\ntrast due to Zeeman interaction of orbital angular momentum of the beam with magnetic fields\nin the sample. The magnetic signal manifests itself as a redistribution of intensity in diffraction\npatterns due to a change of sign of the orbital angular moment. While in the atomic resolution\nregime the magnetic signal is most likely under the detection limits of present transmission electron\nmicroscopes, for electron probes with high orbital angular momenta, and correspondingly larger\nspatial extent, its detection is predicted to be feasible.\nRapid developments in nanoengineering call for char-\nacterizationmethodscapabletoreachhighspatialresolu-\ntion. In this domain, the scanning transmission electron\nmicroscope (STEM) provides a broad scale of measure-\nment techniques ranging from Z-contrast [1] or electron\nenergy-loss elemental mapping [2], differential phase con-\ntrast(DPC)[3,4], vialocalelectronicstructurestudiesof\nsingle atoms [5] to counting individual atoms in nanopar-\nticles [6]. As a specific case of high-spatial resolution\nelectron energy loss spectroscopy, an electron magnetic\ncircular dichroism (EMCD) method has been introduced\n[7] as an analogue to x-ray magnetic circular dichroism,\nwhich is a well established quantitative method of mea-\nsuring spin and orbital magnetic moments in an element-\nselective manner [8, 9].\nRecenly, the introduction of electron vortex beams\n(EVB) [10–12], i.e., beams with nonzero orbital angular\nmomentum, aimed at probing EMCD at atomic spatial\nresolution. It was shown theoretically that EVBs need\nto be of atomic size in order to be efficient for magnetic\nstudies [13–15]. Several methods of generating atomic\nsize electron vortex beams have been proposed [16–19],\nyet an experimental demonstration of atomic resolution\nEMCD has not been presented in the literature.\nAn alternative route to utilizing EVBs for magnetic\nmeasurements is based on Zeeman interaction between\ntheir angular momentum and the magnetic field in the\nsample. The Pauli equation for an electron with energy\nEin an electrostatic potential V(r)and a constant mag-\nnetic field Bcreads\n/bracketleftbiggˆp2\n2m+e\nm(ˆL+ 2ˆS)·Bc−eV(r)/bracketrightbigg\nΨ(r) =EΨ(r),(1)\nwhere−eis the electron charge, mis the electron mass,\nˆp=−i~∇isthemomentumoperator, ˆLandˆSaretheor-\nbital and spin angular momentum operators, and Ψ(r)is\na two-component spinor wavefunction. The second term\non the left hand side of Eq. 1 manifests a coupling be-tween the magnetic field and the orbital and spin angu-\nlar momenta of the electron beam. A previous study has\nindicated that the effect of spin on elastic scattering is\nvery weak [20]. Moreover, generating intense spin polar-\nizedelectronbeamsremainsatechnologicalchallenge[21]\nand so far magnetic field mapping with spin-polarized\nelectrons in the TEM could not be demonstrated. While\nthe spin angular momentum of electrons in the propaga-\ntion direction is at most~\n2, EVBs can be generated with\nvery high orbital angular momenta (OAM) [12, 22, 23],\nwhich permits an increase of the Zeeman interaction by\nmore than two orders of magnitude.\nIn this Letter, we show that there is a magnetic con-\ntrast in elastic scattering of EVBs originating from the\nenhanced Zeeman interaction of the beam OAM with\nmagnetic fields in the sample. The described effect is\nsensitive to magnetic fields parallel to beam-direction,\nwhich would complement holographic or DPC methods\nmeasuring the in-plane components of the magnetic field.\nFor a realistic description of magnetism in a solid, tak-\ningintoaccountmerelyaconstantmagneticfieldisinsuf-\nficient. Hence, we consider a stationary Pauli equation\nwith a non-uniform magnetic field [24] B(r) =∇×A(r)\nand corresponding vector potential A(r)in Coulomb\ngauge,∇·A(r) = 0. Due to large acceleration voltages\ncommonly applied in TEM, a relativistically corrected\nelectron mass m=γm0is used. Subsequently, as in the\nderivation of the conventional multislice method [25], we\nintroduce a paraxial approximation [26] via the substitu-\ntion\nΨ(r) = eikz/parenleftbiggψ↑(r)\nψ↓(r)/parenrightbigg\n, (2)\nand neglect the second derivatives of the envelope func-\ntionsψ↑,↓(r)with respect to the beam propagation direc-\ntionk= (0,0,k). The resulting two-component paraxial\nPauli equation reads [27]arXiv:1509.00744v2  [cond-mat.mtrl-sci]  28 Jan 20162\n∂\n∂z/parenleftbiggψ↑(r)\nψ↓(r)/parenrightbigg\n=im\n~(~k+eAz)−1/braceleftbigg~2\n2m∇2\nxy+ie~\nmAxy·∇xy−~keAz\nm−e\nmˆS·B+eV/bracerightbigg/parenleftbiggψ↑(r)\nψ↓(r)/parenrightbigg\n≡ˆH/parenleftbiggψ↑(r)\nψ↓(r)/parenrightbigg\n,(3)\nwhich upon setting A=B= 0reduces to the parax-\nial Schrödinger equation [26] for each of the spin com-\nponentsψ↑,↓separately. Eq. 3, however, represents a\nsystem of two differential equations coupled via an inter-\naction of the spin of the probe with the magnetic field in\nthe sample. It can be integrated slice-by-slice according\nto [25, 28]\nψ(x,y,z + ∆z) =ˆZ{e/integraltextz+∆z\nzˆH(x,y,z/prime)dz/prime\n}ψ(r)≈\n≈∞/summationdisplay\nn=1∆zn\nn!ˆHn(r)ψ(r),(4)\nwhere ˆZis Dyson’s z-ordering operator. Similar com-\nputational methods were recently discussed for the fully\nrelativistic case of the Dirac equation [20] and in the con-\ntext of spin polarization devices [29].\nIn the following numerical simulations we constructed\nthe electrostatic potential from tabulated values of in-\ndependent atoms [26], whereas the magnetic vector po-\ntential and the corresponding magnetic field are obtained\nfrom density function theory (DFT) in the following way.\nIn a crystal, Bconsists of a constant part due to the\nsaturationmagnetization Bc=µ0Msandaperiodicpart\nBpthat averages to zero. The constant part originates\nfromanon-periodiccomponentofvectorpotential Anp=\n1\n2µ0Ms×r, while the periodic part of the magnetic field\noriginates from Apcomputed as a periodic solution of\n∆Ap(r) =−µ0j(r), where j(r)isthespincurrentdensity.\nBy using a Gordon decomposition and neglecting orbital\ncurrents, the spin current density is [20] j(r) =∇×m(r),\nwhere the spin magnetization density m(r)is computed\nfrom electronic structure spin DFT calculations.\nWe expect that the microscopic variations of the mag-\nnetic field, Bp, will only play a role in atomic resolution\nregime. For larger probes, such as EVBs with high OAM,\neffects of these variations average to zero and only the\nconstant part of the magnetic field Bcwill influence the\nscattering on top of the Coulomb potential. The situa-\ntion can then essentially be understood in terms of Eq. 1.\nResults of the procedure described above, applied to\nbcc Fe, are illustrated in Fig. 1. In the case of collinear\nmagnetism, m(r)is parallel to the z-direction, whereby\nj(r), and in the gauge chosen here also A(r), have non-\nzerox- andy-components only. The spin magnetiza-\ntion density as obtained via a collinearly spin-polarized\nfull-potential linearized augmented plane wave [30] cal-\nculation in the generalized gradient approximation [31]\nis shown on an xy-cross section containing the central Fe\natom of the bcc unit cell, Fig. 1a. The z-component of\ntheB-field, Fig.1b, andthe x-componentofthe Ap-field,\nFig. 1c, are plotted within the same plane. Note that the\nxy\nelectrons /Å3\n012345a)\nxy\nBz(T)\n0102030405060 b)\nxy\nAx(ÅT)\n-6-4-20246c)\nx (Å)2 1 01y (Å)200.511.522.5 z (Å)d)Figure 1. a) Spin magnetization density, b) z-component of\ntheB-field, c)x-component of the Ap-field and d) the B-field\nin a unit cell of bcc Fe as obtained from DFT calculations.\nz-component of Bpreaches values in the order of 60 T—\nsignificantly larger than µ0Ms= 2.2T in bcc Fe. Ay(not\nshown) is identical to Axrotated by 90◦about thez-axis\nandAz= 0everywhere. Finally, the microscopic Bp-\nfield (to which a Bc= 2.2T in thez-direction should be\nadded) is plotted as a vector field in one unit cell, Fig. 1d.\nAlthough the shape of the spin density is very similar to\nthat ofBz, they are not identical, and, even though only\ncollinear spin density along the z-direction is considered,\ntheBp-field has non-zero x- andy-components.\nDue to persisting limitations in the creation of EVBs,\nelectron beams with large OAMs ( /greatermuch1~) cannot be fo-\ncussed on an atomic scale. We thus concentrate first on\na situation, where we do not aim for atomic resolution,\nbut rather enhance the Zeeman interaction by a large ini-\ntial OAM ( =l~) of the beam. Using Eq. 4 we propagate\nelectron beams with an initial OAM of 20~,30~and40~,\nthrough a bcc Fe crystal of thickness up to 400 unit cells\n(115 nm). The radial shape of the beams is described by\nψl(k⊥,φ)∼eilφΘ(αk−k⊥), (5)\nwherek⊥andφarecylindricalcoordinatesin k-spaceand\nαis the convergence semi-angle. The lateral supercell\ndimension was 48×48unit cells and each unit cell was\ndiscretized on a 64×64×64pixel grid. The acceleration\nvoltage was 200kV andα= 10mrad, corresponding to\nouter full-widths at half-maximum of 2.2,3.1, and 3.9nm\nforl= 20, 30, and 40, respectively. Beams were centered\nonanatomiccolumn,butwehaveverifiedthattheresults\ndo not depend on the exact beam position, as is expected3\nforbeamswithspatialextentsignificantlylargerthanthe\ncrystal unit cell.\nθ (mrad)0 50 100 150signal (arb. u.)\n-4-3-2-101234\nSum of l= ± 20 \n(106/20) × difference of l= ± 20\n(106/30) × difference of l= ± 30\n(106/40) × difference of l= ± 40\n106 × difference of sz=± 1/2 for l=-20\n106 × difference of sz=± 1/2 for l=30a)\nt (u.c.)0 100 200 300 400Relative signal × 103\n-1-0.500.51\nθ ≤ 2 mrad\nθ ≤ 4 mrad\nθ ≤ 6 mrad\nθ ≤ 8 mradb)\nFigure 2. a) Magnetic signal (difference of intensities) as a\nfunction of collection angle. Differences are shown for unpo-\nlarized beams with l=±20,±30and±40, as well as beams\nwithlfixed to −20or30, but with difference taken over oppo-\nsite spin channels. For l=±20the total signal (sum of inten-\nsities for opposite OAM) is also shown. Sample thickness was\nset tot= 42unit cells (12 nm). b) Thickness dependence of\nthe relative magnetic signal for a circular collection aperture\nwith collection angle indicated ( l=±30).\nA non-spin-polarized beam is in a mixed state, with\n50% of electrons with spin-up and 50% spin-down, re-\nspectively. Therefore each simulation consists of two\nruns, one for each spin orientation, and the resulting\ndiffraction patterns were averaged over the two spin ori-\nentations. It is worth mentioning that the proportion of\nspin-up electrons scattering into spin-down states or vice\nversa is negligible (of the order 10−14), although it has\nbeen suggested that for magnetization in the xy-plane\nthe spin-flip scattering can be more significant [32].\nThe Zeeman interaction leads to a redistribution of\nintensity in the diffraction pattern. Total intensity of\nscattered electrons is of course the same for positive or\nnegative OAM, but the intensity of electrons scattered\nto smaller or larger angles varies depending on the OAM\n(see Fig. 2a). For large collection angles the intensity of\nscattered electrons saturates at a value of one, as dic-\ntated by normalization of the initial probe wavefunction.\nThe intensity difference for, e.g., l=±20shows a peak\naround a collection angle of 10 mrad, after which its am-plitude decreases eventually reaching zero. Computing\nsuch differences in a simulation with zero magnetic fields\nmerelyyieldsanumericalnoisearoundtenordersofmag-\nnitude smaller. The kink observed close to θ= 130mrad\nappears near a higher order Laue zone [33].\nNotice, how the magnetic signal is approximately pro-\nportional to the initial OAM of the EVB. This suggests\nthat the strength of this signal can be further scaled up\nfor beams with larger OAM. Consistently with Eq. 1, the\nmagnetic signal obtained as an intensity difference from\nopposite spin channels, but for a fixed initial OAM, is 1)\nindependent of OAM, and 2) of the same order of magni-\ntude as the intensity difference due to changing the sign\nof OAM, when normalized per unit of OAM.\nIn Fig. 2b) the magnetic signals, for a disc shaped re-\ngion with collection angles indicated in the legend, are\nshown for the l=±30case as a function of sample thick-\nness. Accordingly, the magnetic signal can become sig-\nnificantly stronger for thicker samples. After 100 u.c.\nsignificant values of the relative magnetic signal in the\nrange of 10−3are observed. Considering that the sig-\nnal is proportional to OAM and OAMs of size several\nhundreds have been reported [23], signal strengths of few\npercent can be reached. While the intensity differences\nsensitively depend on the shape of the probe, magnetism\nshouldbemeasurableinanexperimentalsetupwithsym-\nmetrical +land−lOAM probes — such as those gen-\nerated by holographic zone plates [11, 12]. Relative sig-\nnals of several percent are well within the the detection\nlimits of current bright field EVB STEM experiments,\nwhich easily integrate order of 106electrons (for typi-\ncal probe currents, dwell times, collection angles) with a\ncorresponding shot noise order of 103, i.e., 1‰.\nNow we turn our attention to the atomic resolution\nregime. As was mentioned above, to focus EVB with\nlarge OAM onto atomic scales requires very large con-\nvergence angles in the range of hundreds of milliradi-\nans, which is outside of present instrumental possibili-\nties. Therefore, we restrict ourselves to EVBs of small\ninitial OAM, thereby reducing the magnitude of the Zee-\nman term. However, we remind that the strength of local\nmicroscopic magnetic fields can reach substantial values\nof several tens of Teslas (see Fig. 1b), which could po-\ntentially lead to significant magnetic signals even in the\natomic resolution regime. To assess the effect, we have\nperformed simulations using beams with l=±1and a\nrather large convergence angle of 40mrad at an accel-\neration voltage of 300 kV. The supercell dimension was\n24×24×100unit cells of bcc Fe (28.7 nm thick), each\ncell discretized on a 112×112×112grid. The collection\nangle was set to 5 mrad.\nFig. 3 summarizes atomic resolution simulations. The\nSTEM image (Fig. 3a) should be compared to the\nmagnetic signal computed from the l=±1difference\n(Fig. 3b) and spin-difference at l= 1(Fig. 3c). Note\nthat a mirror image of vortex beam with OAM equal to4\n(a)\n0.1\n0.01\n(b)\n10-73\n-12 10-7\n(c)\n10-74\n-2 10-7xx x\nx\nFigure 3. Simulated STEM image for a collection angle\n5 mrad, as obtained from a) the spin averaged beam for\nl= +1, b) magnetic signal obtained as difference signal due\nto OAMl=±1, c) difference between spin-up and spin-down\nbeams forl= +1.\nl~is a vortex beam with OAM equal to −l~[34]. For this\nreason the magnetic signal is obtained as a difference of\nintensity of l= +1beam at position (x,y)andl=−1\nbeam at (y,x).\nBoth spin and OAM differences are of the same order\nof magnitude, which is about 10−5of the total signal. In\nthe following we explore some routes to enhance the mag-\nnetic signal. An increase in its relative strength can be\nachieved by a further optimization of sample thickness,\nconvergence angle, acceleration voltage, initial OAM and\ncollection angle. To find the global maximum of this\nmultidimensional optimization problem is a formidable\ntask, which will furthermore depend on the material to\nbe investigated. Therefore, we focus on a few parame-\nters only and assess the increase in magnetic signal in an\napproximative manner.\nTo investigate the effect of larger OAM on the mag-\nnetic signal strength, a few beam positions were recalcu-\nlated with with l=±2as well asl=±4, see Fig. 4a)-f).\nAccordingly, theproportionalitybetweenmagneticsignal\nandlis lost in the atomic resolution regime. This is most\nlikely due to a different form of the magnetic interaction\n∝A·p, which is not anymore directly proportional to\nthe OAM and depends on details of spatial distribution\nof the magnetic field and the probe wavefunction. Note\nfor example the radial intensity profiles for beams with\nl= 1,2,4. The differences are mostly due to strong pin-\nning of beams with low OAM to atomic columns [35],\nless pronounced for OAM= 2~and4~, respectively. Nev-\nertheless, magnetic signals are still somewhat stronger\nfor beams with larger OAM.\nAn alternative route to enhancing the magnetic signal\nconsists of reducing the acceleration voltage. Upon in-\nspection of Eq. 3 we note an additional prefactor γ−1in\nfront of the magnetic coupling compared to the electric\none resulting in a relative increase of the magnetic signal\nat lower acceleration voltages. Fig. 4g)-i) compares re-\nsultsobtainedwithvoltages100kVand300kVforbeams\nwith initial OAM of ±~and other parameters kept fixed.\nAn increase of magnetic signal by a factor of ∼3or 4\ncan be observed for the lower acceleration voltage.\n00.511.52\na)\n00.511.52\nb)\n00.511.52\nl=1\nl=2\nl=4c)signal (arb. u.)×10-6\n-10-8-6-4-2024\nd)×10-6\n-6-5-4-3-2-1012\ne)×10-6\n-6-4-202468\nl=1\nl=2\nl=4f)\n0 50 100 150×10-5\n-3-2-101\ng)\nθ(mrad)0 50 100 150×10-6\n-15-10-505\nh)\n0 50 100 150×10-5\n-1012\n300 keV\n100 keVi)Figure 4. Sum in a)-c) and difference in d)-f) of signal inte-\ngrated over collection angles from 0toθfor+land−lbeams\nwithl= 1,2and 4at beam positions (0,0)in a), d), g),\n(1,1)a\n14in b), e), h) and (1,0)a\n2in c), f), i). g)-h) show\nthe difference between acceleration voltage of 100 keV or 300\nkeV with other parameters kept same for the three respective\nbeam positions.\nCombining all the effects a further optimization of all\nparameters is suited to increase the relative magnetic sig-\nnal strength by one order of magnitude to 10−4. Yet,\nthe relative magnetic signal strength of 10−4means that\nit will be extremely sensitive to scan noise, drifts and\nchanges of sample orientation during data acquisition,\nwhich renders atomic resolution measurements of a mag-\nnetic signal based on the Zeeman interaction of OAM\nwith magnetic fields in the sample extremely challeng-\ning, most likely beyond the possibilities of present in-\nstruments.\nIn conclusion, we have demonstrated computationally\nthat the elastic scattering of electron vortex beams on\nmagneticsamplesintheTEMdependsontherelativeori-\nentation of the initial OAM and the magnetization in the\nsample. In principle, this effect opens a new way for mea-\nsurement of magnetic properties. For beams with OAM\nof few hundreds of ~, the predicted relative strength of\nmagnetic signal should reach up to a few percent, call-\ning for an experimental verification. If successful, this5\npermits a new way of characterization of magnetic prop-\nerties at about 10 nm spatial resolution. In the atomic\nresolution regime, the calculated relative magnetic signal\nstrength reaches only up to 10−4, making it unlikely to\nbe detected with present-date instruments, particularly\ndue to scan noise and unavoidable sample drifts.\nAE and JR acknowledge Swedish Research Council\nand Göran Gustafsson’s Foundation for financial sup-\nport. AL acknowledges financial support from the Euro-\npean Union under the Seventh Framework Program un-\nder a contract for an Integrated Infrastructure Initiative\n(Reference 312483 - ESTEEM2). Valuable discussions\nwith Nobuo Tanaka, Jo Verbeeck and Vincenzo Grillo\nare gratefully acknowledged.\n[1] O. L. Krivanek, M. F. Chisholm, V. Nicolosi, T. J. Pen-\nnycook, G. J. Corbin, N. Dellby, M. F. Murfitt, C. S.\nOwn, Z. S. Szilagyi, M. P. Oxley, et al., Nature 464, 571\n(2010).\n[2] S. J. Pennycook, M. Varela, A. R. Lupini, M. P. Oxley,\nand M. F. Chisholm, Journal of Electron Microscopy 58,\n87 (2009).\n[3] N. Shibata, S. D. Findlay, Y. Kohno, H. Sawada,\nY. Kondo, and Y. Ikuhara, Nature Physics 8, 611 (2012).\n[4] K. Müller, F. F. Krause, A. Béché, M. Schowal-\nter, V. Galioit, S. Löffler, J. Verbeeck, J. Zweck,\nP. Schattschneider, and A. Rosenauer, Nature commu-\nnications 5, 5653 (2014).\n[5] Q. M. Ramasse, C. R. Seabourne, D.-M. Kepaptsoglou,\nR. Zan, U. Bangert, and A. J. Scott, Nano Letters 13,\n4989 (2013).\n[6] S. V. Aert, K. J. Batenburg, M. D. Rossell, R. Erni, and\nG. V. Tendeloo, Nature 470, 374 (2011).\n[7] P. Schattschneider, S. Rubino, C. Hábert, J. Rusz,\nJ. Kuneš, P. Novák, M. F. E. Carlino, G. Panaccione,\nand G. Rossi, Nature 441, 486 (2006).\n[8] B. T. Thole, P. Carra, F. Sette, and G. van der Laan,\nPhys. Rev. Lett. 68, 1943 (1992).\n[9] P. Carra, B. T. Thole, M. Altarelli, and X. Wang, Phys.\nRev. Lett. 70, 694 (1993).\n[10] M. Uchida and A. Tonomura, Nature 464, 737 (2010).\n[11] J. Verbeeck, H. Tian, and P. Schattschneider, Nature\n467, 301 (2010).\n[12] B. J. McMorran, A. Agrawal, I. M. Anderson, A. a. Herz-\ning, H.J.Lezec, J.J.McClelland, andJ.Unguris, Science\n(New York, N.Y.) 331, 192 (2011).[13] J. Rusz and S. Bhowmick, Physical Review Letters 111,\n105504 (2013).\n[14] P. Schattschneider, S. Löffler, M. Stöger-Pollach, and\nJ. Verbeeck, Ultramicroscopy 136, 81 (2014).\n[15] J. Rusz, J.-C. Idrobo, and S. Bhowmick, Phys. Rev. Lett.\n113, 145501 (2014).\n[16] A. Blackburn and J. Loudon, Ultramicroscopy 136, 127\n(2014).\n[17] G. V. T. Armand Béché, Ruben Van Boxem and J. Ver-\nbeeck, Nature Physics 10, 26 (2014).\n[18] O. L. Krivanek, J. Rusz, J.-C. Idrobo, T. J. Lovejoy, and\nN. Dellby, Microscopy and Microanalysis 20, 832 (2014).\n[19] D. Pohl, S. Schneider, J. Rusz, and B. Rellinghaus, Ul-\ntramicroscopy 150, 16 (2015).\n[20] A. Rother and K. Scheerschmidt, Ultramicroscopy 109,\n154 (2009).\n[21] M. Kuwahara, F. Ichihashi, S. Kusunoki, Y. Takeda,\nK. Saitoh, T. Ujihara, H. Asano, T. Nakanishi, and\nN. Tanaka, Journal of Physics: Conference Series 371,\n012004 (2012).\n[22] K. Saitoh, Y. Hasegawa, N. Tanaka, and M. Uchida,\nJournal of electron microscopy 61, 171 (2012).\n[23] V. Grillo, G. C. Gazzadi, E. Mafakheri, S. Frabboni,\nE. Karimi, and R. W. Boyd, Physical Review Letters\n114, 034801 (2015).\n[24] P. Strange, Relativistic Quantum Mechanics (Cambride\nUniversity Press, 1998), ISBN 978-0-521-56583-7.\n[25] J. M. Cowley and a. F. Moodie, Acta Crystallographica\n10, 609 (1957).\n[26] E. J. Kirkland, Advanced Computing in Electron Mi-\ncroscopy (Springer, 2009), 2nd ed., ISBN 978-1-4419-\n6532-5.\n[27] A term proportional to A2is neglected as a higher order\nrelativistic correction.\n[28] C. Y. Cai, S. J. Zeng, H. R. Liu, and Q. B. Yang, Micron\n40, 313 (2009).\n[29] V.Grillo, L.Marrucci, E.Karimi, R.Zanella, andE.San-\ntamato, New Journal of Physics 15, 093026 (2013).\n[30] P. Blaha, G. Madsen, K. Schwarz, D. Kvasnicka, and\nJ. Luitz, WIEN2k, An Augmented Plane Wave + Lo-\ncal Orbitals Program for Calculating Crystal Properties\n(2001).\n[31] J. P. Perdew, K. Burke, and M. Ernzerhof, Physical Re-\nview Letters 77, 3865 (1996).\n[32] V. Grillo and E. Karimi, Private communication (2015).\n[33] R. Juchtmans, A. Béché, A. Abakumov, M. Batuk, and\nJ. Verbeeck, Physical Review B 91, 094112 (2015).\n[34] J. Rusz, S. Bhowmick, M. Eriksson, and N. Karlsson,\nPhysical Review B 89, 134428 (2014).\n[35] A. Lubk, L. Clark, G. Guzzinati, and J. Verbeeck, Phys-\nical Review A 87, 033834 (2013)."    },    {        "title": "1509.03981v3.Torsional_chiral_magnetic_effect_in_Weyl_semimetal_with_topological_defect.pdf",        "content": "arXiv:1509.03981v3  [cond-mat.mes-hall]  31 Mar 2016Torsional chiral magnetic effect in Weyl semimetal with topo logical defect\nHiroaki Sumiyoshi1and Satoshi Fujimoto2\n1Department of Physics, Kyoto University, Kyoto 606-8502, J apan and\n2Department of Materials Engineering Science, Osaka Univer sity, Toyonaka 560-8531, Japan\n(Dated: April 1, 2016)\nWe propose a torsional response raised by lattice dislocati on in Weyl semimetals akin to chiral\nmagnetic effect; i.e. a fictitious magnetic field arising from screw or edge dislocation induces charge\ncurrent. We demonstrate that, in sharp contrast to the usual chiral magnetic effect which vanishes\nin real solid state materials, the torsional chiral magneti c effect exists even for realistic lattice\nmodels, which implies the experimental detection of the effe ct via SQUID or nonlocal resistivity\nmeasurements in Weyl semimetal materials.\nPACS numbers: 72.80.-r, 72.15.-v, 11.30.Rd, 11.15.Yc\nRecently, manycandidatematerialsforDiracsemimet-\nalsandWeylsemimetals(WSMs)[1–4],havebeendiscov-\nered [5–23]. These topological semimetals are intriguing\nbecause of exotic transport phenomena associated with\nthe chiral anomaly in quantum field theory [24], such\nas the anomalous Hall effect [25, 26], chiral magnetic ef-\nfect (CME) [27], negativelongitudinal magnetoresistance\n[5, 12, 19–21, 28, 29], and chiral gauge field [30].\nAmong them, the CME has been discussed in broad\nareas of quantum many-body physics, including nuclear\nand nonequilibrium physics as well as condensed matter\nphysics. It is the generation of charge current parallel to\nan applied magnetic field even in the absence of electric\nfields. In nuclear physics, together with the chiral vor-\ntical effect [31], it is expected to play an important role\nin heavy ion collisions experiments [32, 33]. The CME\nalso caused a stir in nonequilibrium statistical physics,\nsince it leads to the existence of the ground state which,\nrecently, attracts a renewed interest in connection with\nthe realizationofquantum time crystal[34], and then the\nCME has been studied from this point of view [35, 36].\nHowever, unfortunately, their results are negative for its\nrealization: the macroscopic ground state current in re-\nalistic WSMs is always absent.\nIn this letter, we propose a chiral response in WSMs,\nnamed “torsional chiral magnetic effect (TCME)”, in\nwhich the ground state charge current is caused by the\neffective magnetic field induced by lattice dislocation as\nshown in FIG.1. By using the Cartan formalism of the\ndifferential geometry, we can describe the lattice strain\nand dislocation in terms of vielbein and torsion [37].\nFromthe viewpointofthe quantumfield theoryincurved\nspace-time, the TCME is raised by the mixed action of\nelectromagnetic and torsional fields that is prohibited in\nfour-dimensional spacetime with the Lorentz symmetry,\nbut made possible in non-relativistic band electrons in\nsolid state systems. Furthermore, we demonstrate that\nthe TCME is possible in realistic lattice models by carry-\ning out numerical calculations. Our results imply the ex-\nistence of experimentally observable current induced by\nthe TCME in real WSM materials. We also resolve therelation between our results and the no-go theorem that\nthe CME is absent in equilibrium states [35, 36]. First of\nall, we clarify the notations. The indices i,j,···=x,y,z\nanda,b,···= ¯x,¯y,¯zrepresent the coordinates in the lab-\noratoryand local orthogonal (or Lorentz) frames, respec-\ntively. In the following, we use the Einstein summation\nconvention.\nLinear response theory for torsional response— Here,\nwe briefly introduce the Cartan formalism, which can\nbe applied to description of crystal systems with lattice\nstrain as follows. It is an approach to curved space and\nbasedonthelocalorthonormalframeform ea=ea\ni(r)dri,\nwhere the coefficient fields ea\ni(r) are referred to as the\nvielbein [38]. We introduce the coordinate measured by\nan observer on the deformed lattice Raand the labora-\ntory coordinate ri, and identify its exterior derivative\nas the local orthonormal frame ea=dRa. Then, to\nthe first order in the displacement field /vector u, the vielbein\nis written as ea\ni=δa\ni−∂ua/∂ri. For this observer,\nthe lattice is not deformed, and then the Hamiltonian\nof the system is given by H(−i∂R¯x,−i∂R¯y,−i∂R¯z) =\nH(−iei\n¯x∂ri,−iei\n¯y∂ri,−iei\n¯z∂ri), whereH(px,py,pz) is the\nHamiltonian without lattice deformation and eµ\nαis the\ninverse ofeα\nµ. In this way, the emergent vielbein appears,\nand therefore we can describe the elastic response by us-\ning the Cartan formalism. The coupling between the\nvielbein and electrons is similar to the minimal coupling\nof theU(1) gauge field, pi→pi−eAi. Then, we can de-\nfine the analog of the field strength by Ta\nij=∂iea\nj−∂jea\ni,\nwhich is referred to as the torsion, or “torsional mag-\nnetic field” (TMF) [39–41], where the spin connection is\ndropped for simplicity. Using the displacement vector,\nthe torsion is rewritten as Ta\nij= (∂j∂i−∂i∂j)ua. The\npoint is that, if ua(r) is a well-defined function, the tor-\nsion is always zero, and the multivaluedness of ua(r) is\nnecessary for nonzero torsion. Indeed, the edge dislo-\ncation along z-axis with Burgers vector bgˆycauses the\nTMF,Ty\nxy=−bgδ(2)(x,y), and the screw one with bgˆz,\nTz\nxy=−bgδ(2)(x,y), as shown in FIG.1. For more details\nabout the lattice strain and differential geometry, see, for\nexample, Refs. [42–44].2\nNow, using the linear response theory with the Car-\ntan formalism, we investigate the TCME of WSMs due\nto dislocation. We calculate the current density in the\npresence of TMF and magnetic field up to the linear or-\nder. We use the model of a pair of Weyl fermions with\nthe opposite chirality, whose Weyl points are at k=λL\nandλRin the momentum space, and Fermi energies are\ngiven byE=vFλL\n0andvFλR\n0, respectively. Therefore\nthe 4×4 Hamiltonian is given by\nH(k) :=/parenleftbigg\nHL(k) 0\n0HR(k)/parenrightbigg\n(1)\nwithHs(k) :=vF[χs(k−λs)·σ−λs\n0], wheres=\nLorRis the index of the chirality and χL(R)= +1(−1),\nandσiis the Pauli matrix. Well, we calculate the cur-\nrent density in the presence of the external fields. The\ncalculation is performed by the variation of the effective\naction,Seff[Ai,ea\ni], with respect to the gauge field, as\nja(r) :=−(ea\ni(r)/|e(r)|)(δSeff/δAi(r)). The effective ac-\ntion is defined as\ne−Seff[Ai,ea\ni]:=/integraldisplay\nDψDψ†exp/parenleftbig\n−S[ψ,ψ†,Ai,ea\ni]/parenrightbig\n,\nS[ψ,ψ†,Ai,ea\ni] :=1\n2/integraldisplay\ndτd3r/bracketleftBig\nψ†(τ,r)ˆLψ(τ,r)+c.c./bracketrightBig\n,\nˆL:=|e(r)|[∂/∂τ−H(−i∇a)], (2)\nwhereψis the fermionic field, τandrdenote the imag-\ninary time and spatial coordinate, respectively, and Ai\nis the vector potential. Here c.c.represents the complex\nconjugate combined with the change of the sign of the\nderivative operator ∂/∂τ. Also, in Eq.(2), the Jacobian\nis given by|e(r)|:= detea\ni(r), and the covariant deriva-\ntive is−i∇a:=ej\na(r)(−i∂j−eAj(r)) witha=¯i. Using\nEq.(2), we obtain that the current density up to the first\norder of the magnetic field and the TMF is given by\nj(r) =/bracketleftbigge2vF(λR\n0−λL\n0)\n4π2B+evF(λR\na−λL\na)Λ\n4π2Ta/bracketrightbigg\n,\n(3)\nat zero temperature and up to the linear order in λL(R)\nµ,\nwhere the details of the calculations are described in\nRef.[45]. Here, The vector representation of the TMF,\nTa, is defined by ( Ta)i:= (1/2)εijkTa\njk. For the deriva-\ntion of Eq.(3), we introduced a momentum cutoff scheme\n|k−λs|<Λ for the Weyl node of the chirality s. Phys-\nically, Λ corresponds to the momentum range from the\nWeyl points in which the cone structures of the band of\nthe lattice system is approved.\nThe first term represents the CME in the presence of\nthe chiral chemical potential (i.e. λL\n0∝ne}ationslash=λR\n0), and then\nreproduces the previous result for the CME [46]. On the\notherhand, thesecondtermin Eq.(3)isanewone, which\nraises the TCME; i.e. the current is generated by the\nTMF for the pair of Weyl points which are shifted in the\nFIG. 1. (Color Online) Ground state current jinduced by\n(a) edge and (b) screw dislocation with the Burgers vector b.\nmomentum space due to broken time-reversal symmetry\n(TRS). This point is in sharp contrast to the usual CME,\nwhich requires breaking inversion symmetry.\nWe comment on the relation between the TCME and\nthe chiral anomaly. One may expect that when, λR\nµ=\n−λL\nµ, the TCME is described by the topological θ-term,\nwhich is the consequence of the chiral anomaly like the\nCME and anomalous Hall effect. However, there is no\nmixed chiral anomaly term of U(1) field strength and\ntorsioninfour-dimensionalspacetime[40,47]. Thispoint\nisresolvedbytheobservationthattheLorentzsymmetry,\nwhichispostulatedinthecalculationschemeinRefs. [40,\n47], is broken in the cutoff scheme used for the derivation\nofthesecondtermofEq.(3), whichiscorrectlyapplicable\nto realistic condensed matter systems.\nNow we discuss the consequencesand physicalpictures\nof the TCME. The TCME is realized in two types of\nlattice dislocations. (a) case of edge dislocation :jx∝\n∆λzTz\nx, and (b) case of screw dislocation :jz∝∆λzTz\nz,\nwith∆λa:=λL\na−λR\na. Theirschematicpicturesareshown\nin FIG.1. These responses can be understood with the\nfollowing semiclassical picture: Case(a): Edge disloca-\ntion is regarded as the (0,1,0)-“surface” of the extra lat-\ntice plane made up of the blue and green atoms in FIG.1-\n(a), which harbors a chiral Fermi arc, when two Weyl\npoints are shifted in the kz-direction. The electrons in\nthe Fermi arc state are the very origin of the current in-\nduced bythe edgedislocation. Case(b): Thereis achiral\nFermi arc mode on the dislocation line. The electrons in\nthe mode rotate around the screw dislocation line, and\ndue to the screw dislocation the rotating motion causes\nthe current along the Burgers vector.\nThe situation is similar to that of the three-\ndimensional integer quantum Hall state (3DIQHS) [48]\nwith dislocation which is the staking of quantum Hall\nstate layers characterized by the vector Gc= (2πnc/a)ˆn,\nwherenc,a, and ˆnare the first Chern number, the lat-\ntice constant, and the unit vectoralongthe stakingdirec-\ntion. In the 3DIQHS, there are one dimensional nchiral\nmodes along the dislocation line, when the topological\nnumber,n=bg·Gc/2π, is nonzero [49]. This condition\nfor the chiral modes is similar to that for the TCME,\nbg·(λL−λR)∝ne}ationslash= 0.3\nHowever, there arethe followingsignificant differences.\nThe chiral modes of the 3DIQHS are exponentially lo-\ncalized at the dislocation, and separated from the bulk\nhigher-energy states, while, as will be shown below, the\nchiral modes of the WSMs exhibit power-law decay. We\ncall them quasi-localized modes. Moreover their spec-\ntrum is not isolated from the bulk spectrum but appears\nas its envelope as shown in FIG.2a, and therefore they\ncan be easily mixed with the bulk modes.\nSpectral asymmetry and ground state current— We\nconfirm the TCME due to dislocation by using an al-\nternative approach other than the linear response the-\nory based on (3). Our approach here is to calculate\nexplicitly the spectrum and the eigenstates of the Weyl\nHamiltonian with dislocation and the ground state cur-\nrent. We also show that the quasi-localized modes along\nthe envelope of the bulk spectrum contribute to the ef-\nfect. For simplicity, we set vF=e= 1 and assume\nλL\n0=λR\n0= 0, and the Weyl points lie symmetrically on\nthekz-axis,λL=−λR=λˆz. In the presence of the\nscrew dislocation at x=y= 0 along z-axis, of which\nBurgers vector is bg=−bgˆz, the vielbeins are given by\nez\n¯x=−bgy/2πρ2, ez\n¯y=bgx/2πρ2, andeµ\na=δµ\nafor others,\nwithρ=/radicalbig\nx2+y2[42]. Evenwiththedislocation, kzre-\nmains a good quantum number. Then, when kzis fixed,\nthe Hamiltonian is equivalent to that of two dimensional\nmassive Dirac model in the presence of the magnetic flux\nat the origin, whose amplitude is Φ kz=kzbg,\nHscrew\ns,kz=χs/bracketleftbig\nH⊥\nkz+ms\nkzσz/bracketrightbig\n,\nH⊥\nkz=/parenleftbigg\n−i∂x−Φkzy\n2πρ2/parenrightbigg\nσx+/parenleftbigg\n−i∂y+Φkzx\n2πρ2/parenrightbigg\nσy,(4)\nwiththemass ms\nkz=kz−χsλ. Theequivalenceofascrew\ndislocation and momentum-dependent magnetic field has\nalso been pointed out in Refs. [40, 50].\nThe spectrum of Hscrew\ns,kzconsists of two types of eigen-\nstates: one with the eigenenergies satisfying |E|>|ms\nkz|\nand the other one with E=±ms\nkz. The former does\nnot contribute to the ground state current owing to the\none-to-one correspondence between E+>|ms\nkz|and\nE−<−|ms\nkz|modes asE+=−E−, and between the\nstates of Weyl nodes with the opposite chiralities [45].\nOn the other hand, the latter does contribute owing to\nasymmetry, i.e. the absence of one-to-one correspon-\ndence between E=ms\nkzandE=−ms\nkzmodes. This\nasymmetry is called the parity anomaly [51, 52]. The\nasymmetric spectrum consists of discrete modes whose\nwavefunctions exhibit power-law decay, and continuum\nscattering modes which spread over the whole system\n[45, 53, 54]. The schematic picture of the density-of-\nstate of the full spectrum is shown in FIG.2a. Moreover,\nthe ground state current calculated from the asymmetric\nspectrum is Jz=−LzbgΛλ/2π2, which coincides with\nthe expression obtained directly from the linear response\ntheory (3) [45].\nFIG. 2. (Color Online) (a) Schematic picture of the spectrum\nof the WSM with the screw dislocation. The black (white)\nbands along E=±ms\nkzrepresent the relatively higher (lower)\ndensity-of-state compared with that of the opposite energy\nE=∓ms\nkz. (b) Lattice with a pair of screw dislocations with\nopposite Burgers vectors. (c) Numerical result for the spec -\ntrum of the WSMs with a pair of screw dislocations. The blue\ncurves are the envelope of the bulk spectrum. The opacity of\nthe dots represents the expectation value of |ρ−ldis|2/LxLy\n(see the gray scale bar). In the figures (c1-3), the modes with\nthis value smaller than 0 .1, 0.15, and 0 .2 are plotted. (d)\nCurrent density along z-direction, jz(x,y).\nNumerical calculation — We confirm the spectrum\nasymmetry and the TCME for realistic lattice models by\nnumerical calculations. We use the tight-binding model\nof WSMs [35] generalized to the case with dislocation,\nH=/summationdisplay\nr\nit/summationdisplay\ni=x,y,zc†\nr+ˆi+δi,zbgΘ(r)Γicr+r\n3c†\nrΓ4cr\n−/summationdisplay\ni=x,y,zc†\nr+ˆi+δi,zbgΘ(r)Γ4cr\n+d\n2c†\nrΓ12cr\n+h.c.,(5)\nwhere the 4×4-matrices, Γi, satisfy the SO(5) Clif-\nford algebra{Γi,Γj}= 2δij[55], Γij:= [Γi,Γj]/2i,\nr= (x,y,z) andˆidenote the position of the atoms and\nthexi-direction unit vector, respectively, and t,r, and\ndare the real parameters, and we suppose the lattice\nconstant as 1 and lattice size Lx×Ly×Lz. We intro-\nduced a pair of screw dislocations along z-direction with\nopposite Burgers vector at ±ldis=±(ldis\nx,0) as shown\nin FIG.2-b, by sliding the hopping directions in the first\nand third terms of Eq. (5) as Θ( r) =−1 for the re-4\ngionx= 0,−ldis\nx< y < ldis\nx, while Θ( r) = 0 for other\nregions. We numerically diagonalized this model and ob-\ntained the spectrums and current. Here the material pa-\nrameters are set as t=r= 1 andd= 3.6. The lattice\nconstant is 1 and the amplitudes ofthe Burgersvectors is\nset asbg= 1. For the calculation, we imposed the open\nboundary condition along the x−andy−directions and\nperiodic boundary condition along the z−direction, and\nsetLx=Ly= 4ldis\nx= 38 andLz= 100.\nAs shown in FIG.2c1-3, we obtained the asymmet-\nric spectrum in agreement with the analytic calculation.\nThe asymmetric modes are localized at the dislocation\nline. The quasi-localized chiral modes are not isolated\nfrom the bulk but easily mixed with the bulk modes\n(FIG.2c1-3). The current density at zero temperature\nis shown in FIG.2d. We obtained the upward current\nalong the screw dislocation and downward current along\nthe anti-screw dislocation due to the TCME. The to-\ntal current per the unit length toward z-direction due\nto one dislocation line is Jz/Lz= 0.087, which is cal-\nculated by the summation of the current density in the\nx >0 half-plane, and this value is in the same order\nas that estimated from the linear response theory (3),\nJz/Lz∼0.1. For the estimation, we set the cutoff as\nΛ∼1/(lattice constant) = 1.\nNo-go theorem of CME — The existence of the TCME\nintherealisticlatticesystemmayseemtocontradictwith\nthe no-go theorems of the ground state current [35, 36].\nHowever, they prohibit the total current, but not the\nlocal current density. Therefore, the current along the\ndislocation line can exist, as we found[45].\nExperimental implication — Here we present two ex-\nperimental setups to observe the TCME in TRS-broken\nWSMs, for which Eu 2Ir2O7[22] and YbMnBi 2[23] are\ncandidate materials. The first one is a scanning SQUID\nmeasurement, which can detect weak inhomogeneous\nmagnetic fields [56, 57]. If there is a pair of disloca-\ntion, the circulating current occurs. The magnitudes of\nthe current and the induced magnetic field are estimated\nasI∼10−5A andB∼10−7T, respectively, for both\nEu2Ir2O7and YbMnBi 2. Here we used Eq.(3) and the\nmaterial parameters, vF∼105m/sanda∼10˚A and set\nbg=aandλ∼Λ∼1/a, whereais the lattice con-\nstant. Also, for the estimation of the magnitude of the\nmagnetic field, we used a typical value of inter-distance\nbetween dislocations, 105˚A [58]. It is feasible to detect\nB∼10−7T via the scanning SQUID.\nThe second one is a nonlocal transport phenomenon,\nwhich was observed in quantum Hall materials [59, 60].\nThe experimental setup is shown in FIG.3. If the bulk\ncontributions are completely negligible and there are\nonly the chiral modes at the dislocation lines, V34:=\nV3−V4= 0 despite I12∝ne}ationslash= 0, then, the nonlocal resistiv-\nityR12,34:=V34/I12is equal to zero [59]. On the other\nhand, if the nonlocal transport is negligible, V34> V3′4′\nholds forL1L3< L1L3′whenI12∝ne}ationslash= 0. Therefore, if\nFIG. 3. (Color Online) Experimental setup for the nonlo-\ncal transport due to the TCME. The thick red solid (blue\ndashed) line represents the (anti-)dislocation line. The l eads\nare attached at the black points, Li(i= 1,2,3,4,3′,4′). The\nlineL1L2,L3L4, andL3′L4′are parallel and have the same\nlength. Here we suppose L1L3< L1L3′.Viis the voltage at\nLi, andI12is the current.\nR12,34< R12,3′4′is observed, it is the fingerprint of\nthe chiral current due to the TCME. The effect can be\ndiscriminated from any previously reported conventional\ntransport induced by dislocation[58, 61–69].\nWe also comment on effects of impurities and disori-\nentation of the dislocation. First, the current due to the\nTCME is expected to be robust against weak disorder.\nIt is because that Eq.(3) is independent of the scatter-\ning time, like the intrinsic contribution to the anomalous\nHall effect [70]. More precisely, the current is due to the\nedgemodesin the Fermi arcon the surfaceofWSMs, and\nthese modes are supported by the Weyl points, which are\nprotectedbythe Chernnumber, andhence, robustagaint\nweak disorder.\nNext, in real experimental setups, it is difficult to align\nthe dislocation line orthogonal (parallel) to the line con-\nnecting the Weyl nodes exactly in the case (a) (case (b)).\nEven when they are not orthogonal (parallel), as long as\nthey are not parallel (orthogonal), the current parallel to\nthe dislocation line still exists. Supposing that the dislo-\ncation line is parallel to the z-axis, the current is given\nbyJz=evFLzΛ(λR−λL)·bg/4π2in the both cases (a)\nand (b).\nSummary — In this letter, we have discussed the\nTCME in WSMs caused by dislocation. We have con-\nfirmed that it is possible to occur and experimentally\nobservable in realistic materials, and argued that the\nLorentz symmetry breaking is important for it.\nAcknowledgement — We thank H. Fujita, Y. Kikuchi,\nT. Kimura, K. Ohmori, D. Schmeltzer, K. Shiozaki, and\nA. Shitade for fruitful discussions. We also thank one\nof the referees for suggesting scanning SQUID measure-\nments. This work is supported by the Grant-in-Aids\nfor Scientific Research from MEXT of Japan [Grant No.\n23540406, No. 25220711, and No. 25103714 (KAKENHI\nonInnovativeAreasTopologicalQuantumPhenomena”),\nNo. 15H05852 (KAKENHI on Innovative Areas Topo-\nlogical Materials Science”)]. HS is supported by a JSPS5\nFellowship for Young Scientists (14J00647).\nSupplemental Material\nDerivation of Eq.(3)\nIn this section, we derive the expression for the current\nin the presence of the magnetic and torsional magnetic\nresponses of the current density, Eq.(3). The derivation\nconsists of two steps: first we derive the expression for\nthe Green function in the presence of the gauge field and\nvielbein using the gradient expansion Eq.(S-4), and next\nwe calculate the current density by using Eq.(S-4) and\nobtain Eq.(S-18), which is equivalent to Eq.(3).\nFirst, we calculate the single-electron Green function.\nThe Green function in the presence of the gaugefield and\nvielbein which is defined by\nG(τ1,r1,τ2,r2)\n:=/integraltext\nDψDψ†ψ(τ1,r1)ψ†(τ2,r2)exp/parenleftbig\n−S[ψ,ψ†,Ai,ea\ni]/parenrightbig\n/integraltextDψDψ†exp(−S[ψ,ψ†,Ai,ea\ni]).\n(S-1)\nThen, the following differential equation holds :\n1\n2/bracketleftBig\nˆL(εN,r1,−i∂r1)G(εN,r1,r2)\n+G(εN,r1,r2)← −ˆL∗(−εN,r2,−i∂r2)/bracketrightbigg\n=δ(3)(r1−r2),\n(S-2)\nwithˆL(εN,r,−i∂r) :=|e(r)|[iεN−H(−i∇a)]−eA0],\nand|e(r)|:= detea\ni(r) HereεN= (2N+ 1)πTis the\nFermionic Matsubara frequency with the temperature\nT, andG(εN,r1,r2) :=/integraltextβ\n0G(τ,r1,0,r2)e−iεNτdτis the\nFourier component of the Green function. Now, using\nthe spatial Wigner transformation defined as ˜f(R,p) :=/integraltext\nd3re−ir·pf(R+r/2,R−r/2), Eq. (S-2) is rewritten\ninto\n1\n2/bracketleftBig\nˆL(εN,R,p)ei\n2(←−∂R− →∂p−← −∂p−→∂R)˜G(εN,R,p)\n+˜G(εN,R,p)ei\n2(←−∂R− →∂p−← −∂p−→∂R)ˆL(εN,R,p)/bracketrightBig\n= 1.(S-3)\nIn the gradient expansion up to the first order in ∂iAjor\n∂iea\nj, the Green function becomes\n˜G(εN,R,p) =˜G(0)(εN,R,p)+˜G(1)(εN,R,p)+···,\n˜G(0)(εN,R,p) =1\n|e(R)|[L0(εN,π)]−1\nπa=ei\na(R)(pi−eAi(R)),\n˜G(1)(εN,R,p)\n=i\n2|e(R)|L−1\n0(εN,π)∂L0(εN,π)\n∂πaL−1\n0(εN,π)∂L0(εN,π)\n∂πb\n·L−1\n0(εN,π)[eFab(R)+Tc\nab(R)πc]/vextendsingle/vextendsingle\nπa=eia(R)(pi−eAi(R)).\n(S-4)Hereπa:=ei\na(R)(pi−eAi(R)) is the gauge-invariant\nmechanical momentum, while piis the canonical momen-\ntum, and the field strength and the torsion with the in-\ndices of the local orthogonal coordinate are, respectively,\ndefined asFab:=ei\naej\nbFijandTc\nab:=ei\naej\nbTc\nij. The free\nLagrangian is defined as L0(εN,π) := iεN−H(π).\nNext, using Eq. (S-4), we calculate the current density\nand derive Eq.(2). The current density are defined by\nja(r) :=−(ea\ni(r))/|e(r))|)(δSeff/δAi(r)). Therefore\nj¯1(R)\n=e¯1\ni\n|e(R)|/integraltext\nDψDψ†ψ†(τ,r1)1\n2δˆL\nδAiψ(τ,r2)e−S\n/integraltext\nDψDψ†e−S/vextendsingle/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nr1,r2→R,+c.c.\n=eT\n2/summationdisplay\nNTr\n∂L0(ǫN,π)\n∂π¯1/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nπa=eia(r2)(−i∂ri\n2−eAi(r2))\nG(εN,r2,r1)]|r1,r2→R+c.c.\n=eT\n2/summationdisplay\nN/integraldisplayd3p\n(2π)3Tr/bracketleftbigg∂L0(ǫN,π)\n∂π¯1/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nπa=ei\na(R)(pi−eAi(R))\nei\n2(←−∂R− →∂p−← −∂p−→∂R)˜G(εN,R,p)/bracketrightBig\n+c.c. (S-5)\nHere Tr means the trace over the band indices, we used\nthatδˆL/δAi=e|e(r)|ei\na(r)∂L0/∂πaand the second line\ndoes not depend on τdue to imaginary time-translation\nsymmetry. Note that πof the third line is the operator\nthough that of the fourth one is the c-number. Using\nEq.(S-4), up to the first order in ∂iAjor∂iea\nj, the ex-\npression of the current density becomes\nj¯1(R) =j¯1(0)(R)+j¯1(1)(R), (S-6)\nwith the zeroth-order terms,\nj¯1(0)(R)\n=eT\n2/summationdisplay\nN/integraldisplayd3p\n(2π)3Tr/bracketleftBigg\n∂L0(ǫN,π)\n∂π¯1/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nπa=eia(R)(pi−eAi(R))\n˜G(0)(εN,R,p)/bracketrightBig\n+c.c. (S-7)\nand the first-order terms,\nj¯1(1)(R)\n=eT\n2/summationdisplay\nN/integraldisplayd3p\n(2π)3Tr/bracketleftBigg\n∂L0(ǫN,π)\n∂π¯1/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nπa=eia(R)(pi−eAi(R))\n˜G(1)(εN,R,p)/bracketrightBig\n+ieT\n4/summationdisplay\nNTr/bracketleftBigg\n∂L0(ǫN,π)\n∂π¯1/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nπa=ei\na(R)(pi−eAi(R))\n(← −∂R− →∂p−← −∂p− →∂R)˜G(0)(εN,R,p)/bracketrightBig\n+c.c.. (S-8)\nThe zeroth-order terms (S-7) can be rewritten as\nj¯1(0)(R) =e/summationdisplay\nn/integraldisplayd3π\n(2π)3vn,¯1(π)nF(εn,π).(S-9)6\nFor the derivation, we inserted the iden-\ntity, 1 π=/summationtext\nn|un\nπ∝an}⌊∇a⌋ket∇i}ht∝an}⌊∇a⌋ketle{tun\nπ|, between ∂L0/∂π¯1\nand˜G(0)in Eq.(S-7), and used the formula,/summationtext∞\nN=−∞[1/(iεN−t)+1/(−iεN−t)] = (1−2nF(t))/T,\nfor the summation over the Matsubara frequency,\nand/integraltext\nd3p=|e(R)|/integraltext\nd3π. Here,nis the band index, εn,π\nis the energy, vn,a(π) :=∂εn,π/∂πais the group velocity,\nnF(ε) := 1/(eε/T+1) is the Fermi distribution function,\nand|un\nπ∝an}⌊∇a⌋ket∇i}htis the Bloch state. This term corresponds to\nthe summation of all contributions to the current from\nthe electrons in the occupied states in the absence of\nmagnetic and torsional magnetic field.\nNow, we move on the calculation of Eq.(S-8). The\nsum of the second term of Eq.(S-8) and its complex con-\njugate is zero, since [ ···]∗= [···]|εN→−εN. Then, by\nusing Eq.(S-4), we obtain\nj¯1(1)(R)\n=ieT\n4/summationdisplay\nN/integraldisplayd3π\n(2π)3Tr/bracketleftbigg∂L0(εN,π)\n∂π¯1L−1\n0(εN,π)∂L0(εN,π)\n∂πa\nL−1\n0(εN,π)∂L0(εN,π)\n∂πbL−1\n0(εN,π)/bracketrightbigg\n[eFab(R)+Tc\nab(R)πc]\n+c.c.. (S-10)\nMoreover,inserting the identities, 1 π=/summationtext\nn|un\nπ∝an}⌊∇a⌋ket∇i}ht∝an}⌊∇a⌋ketle{tun\nπ|, we\nobtain\nj¯1(1)(R)\n=−ieT\n4/summationdisplay\nN,n,m,l/integraldisplayd3π\n(2π)3/angbracketleftbigg\nn/vextendsingle/vextendsingle/vextendsingle/vextendsingle∂H\n∂π¯1/vextendsingle/vextendsingle/vextendsingle/vextendsinglem/angbracketrightbigg/angbracketleftbigg\nm/vextendsingle/vextendsingle/vextendsingle/vextendsingle∂H\n∂πa/vextendsingle/vextendsingle/vextendsingle/vextendsinglel/angbracketrightbigg\n×/angbracketleftbigg\nl/vextendsingle/vextendsingle/vextendsingle/vextendsingle∂H\n∂πb/vextendsingle/vextendsingle/vextendsingle/vextendsinglen/angbracketrightbigg1\n(iεN−εn)(iεN−εm)(iεN−εl)\n×[eFab(R)+Tc\nab(R)πc]+c.c., (S-11)\nwhere the indices πare omitted like εn:=εn,πand\n|n∝an}⌊∇a⌋ket∇i}ht:=|un\nπ∝an}⌊∇a⌋ket∇i}ht. There are three types of contributions to\nthe summation over the band indices n,m,l: (a) all the\nthree are the same, (b) two of them are the same and\nthe other is different, and (c) each one is different respec-\ntively. However the contribution (a) is found to be zero\nbecause of the antisymmetry of [ eFab(R)+Tc\nab(R)πc]\nundera↔b. Moreover, the contribution (c) is also zero,\nsince our model of the WSM, Eq.(1), consists of two two-\nband Hamiltonians independent of each other, and then\nthe overlap of three or more bands is zero. Therefore,\nwe have only to consider the contribution (b), and then\nobtain\nj¯1(1)(R)\n=−ie\n4/summationdisplay\nn/integraldisplayd3π\n(2π)3[eFab+Tc\nabπc](M¯1ab+Mab¯1+Mb¯1a)\n+c.c., (S-12)with\nMabc:=vn\nan′\nF(εn)∝an}⌊∇a⌋ketle{tn,b|(εn−H)|n,c∝an}⌊∇a⌋ket∇i}ht\n+vn\na∝an}⌊∇a⌋ketle{tn,b|nF(H)|n,c∝an}⌊∇a⌋ket∇i}ht−vn\nanF(εn)∝an}⌊∇a⌋ketle{tn,b|n,c∝an}⌊∇a⌋ket∇i}ht,\n(S-13)\nwhere we used the abridged notation, |n,a∝an}⌊∇a⌋ket∇i}ht:=/vextendsingle/vextendsingle/vextendsingle∂un\nπ\n∂πa/angbracketrightBig\n.\nFor the derivation of Eqs.(S-12,S-13) we used the formu-\nlae/summationtext∞\nN=−∞1\n(iεN−t)2(iεN−s)=tn′\nF(s)−sn′\nF(t)+nF(s)−nF(t)\nT(t−s)2 ,\n∝an}⌊∇a⌋ketle{tn|∂H/∂π a|m∝an}⌊∇a⌋ket∇i}ht= (εm−εn)∝an}⌊∇a⌋ketle{tn|m,a∝an}⌊∇a⌋ket∇i}htforn∝ne}ationslash=m, and/summationtext\nmf(εm)∝an}⌊∇a⌋ketle{tn,b|n,c∝an}⌊∇a⌋ket∇i}ht=∝an}⌊∇a⌋ketle{tn,b|f(H)|n,c∝an}⌊∇a⌋ket∇i}htfor any func-\ntionf. Moreover,usingthe relationship( Mabc)∗=Macb,\nwe obtain\nj¯1(1)(R)\n=−ieT\n2/summationdisplay\nn/integraldisplayd3π\n(2π)3/bracketleftbig\neF¯2¯3+Td\n¯2¯3πd/bracketrightbig\nεabcMabc,(S-14)\nwhereεabcis the antisymmetric symbol. Furthermore,\nsincevn\nan′\nF(εn) =∂nF(εn)/∂πaand only antisymmetric\nparts ofMabccontribute, using integration by parts, we\nfind\nj¯1(1)(R)\n= ie/summationdisplay\nn/integraldisplayd3π\n(2π)3/bracketleftbig\neF¯2¯3+Td\n¯2¯3πd/bracketrightbig\nεabcvn\nanF(εn)∝an}⌊∇a⌋ketle{tn,b|n,c∝an}⌊∇a⌋ket∇i}ht\n+ie\n2/summationdisplay\nn/integraldisplayd3π\n(2π)3Ta\n¯2¯3εabcεnnF(εn)∝an}⌊∇a⌋ketle{tn,b|n,c∝an}⌊∇a⌋ket∇i}ht.(S-15)\nUsing the Berry curvature is defined by Ωn\na:=\n−iεabc∝an}⌊∇a⌋ketle{tn,b|n,c∝an}⌊∇a⌋ket∇i}ht, and the vector representation of the\nTMF,Ta, is defined by Ta\ni:= (1/2)εijkTa\njk, it can be\nrewritten as\nj¯1(1)(R)\n=−e/summationdisplay\nn/integraldisplayd3π\n(2π)3(vn·Ωn)(eB¯1+Ta\n¯1πa)nF(εn)\n−e\n2/summationdisplay\nn/integraldisplayd3π\n(2π)3Ωn\naTa\n¯1εnnF(εn). (S-16)\nIt is noted that the term containing B¯1is equal to\nthe expression for the CME derived by Son and Ya-\nmamoto [46], and the others are new terms that rep-\nresent the current induced by the torsion. Neglecting\nthe last term, which is, as we will discuss later, less im-\nportant than the others in the case of WSMs, Eq.(S-\n16) can also shortly derived from the substitution of\nthe magnetic field or the field strength in the absence\nof the vielbein,−i[(−i∂2−eA2),(−i∂3−eA3)] =eB1\nwith the field strength in the presence of the vielbein,\n−i[−i∇¯2,−i∇¯3] =eB¯1+Ta\n¯1(−i∇a), where [U,V] :=\nUV−VUis the commutator. This justifies the anal-\nogy between the TMF and the magnetic field.7\nFinally, we substitute the energy, group velocity, and\nBerry curvature of the model of the WSM, (1), into\nEq.(S-16) and derive Eq.(3). We characterize the four\nbands of the Hamiltonian (1) as n= (s,±), withs=\nLorR, wheresis the index of the chirality and +( −)\nmeans the higher (lower) band of the Weyl cone. Then,\ntheir energy, group velocity, and Berry curvature are\ngiven by\nεs,±(k) =vF[±|k−λs|−λs\n0]\nvs,±(k) =±vF(k−λs)\n|k−λs|\nΩs,±(k) =±χsk−λs\n2|k−λs|3. (S-17)\nUsing Eqs.(S-16, S-17), we obtain\nj¯1(1)(R)\n=/bracketleftbigge2vF(λR\n0−λL\n0)\n4π2B¯1(R)+evF(λR\na−λL\na)Λ\n4π2Ta\n¯1(R)/bracketrightbigg\n,\n(S-18)\nat zero temperature and up to the linear order in λL(R)\nµ.\nFor the derivation of Eq.(S-18), we introduced a momen-\ntum cutoff scheme |k−λs|<Λ for the Weyl node of\nthe chirality s. Physically, Λ corresponds to the momen-\ntum range from the Weyl points in which the cone struc-\ntures of the band of the lattice system is approved. Note\nthat the last term of Eq.(S-16) yields second(or more)-\norder contributions in λL(R)\nµ, and then less important as\nmentioned before. Eq.(S-18) is the correction of current\ndue to the TMF and magnetic field and is equivalent to\nEq.(3), then the derivation ofEq.(3) has been completed.\nGround state current in the presence of screw\ndislocation: analytical calculation\nIn this section, we calculate the ground state current\nraised by the TCME in the case of screw dislocation, by\ncalculating directly the eigenstates of the Hamiltonian\nwith the torsion. This is an alternative approach for the\nderivation of the TCME, which does not rely on Eq. (3).\nFor this purpose, we, first, analyze the spectrum of the\nHamiltonian (Eq.(4) in the main text),\nHscrew\ns,kz=χs/bracketleftbig\nH⊥\nkz+ms\nkzσz/bracketrightbig\n,\nH⊥\nkz=/parenleftbigg\n−i∂x−Φkzy\n2πρ2/parenrightbigg\nσx+/parenleftbigg\n−i∂y+Φkzx\n2πρ2/parenrightbigg\nσy.\n(S-19)\nwherems\nkz=kz−χsλ, Φkz=kzbg,ρ=/radicalbig\nx2+y2,\nχL(R)= +1(−1), andσiis the Pauli matrix.\nFor the calculation of the spectrum, it is useful to clar-\nify the symmetry of the eigenstates of H⊥\nkz. Suppose|κ∝an}⌊∇a⌋ket∇i}htkzthe eigenstate of H⊥\nkzwith eigenvalue κ. Since\n{H⊥\nkz,σz}= 0, where{U,V}:=UV+VUis the an-\nticommutator,the state σz|κ∝an}⌊∇a⌋ket∇i}htkzis also the eigenstate\nwith eigenvalue−κ. Therefore, we can choose the eigen-\nfunctions to preserve the doublet structure, |−κ∝an}⌊∇a⌋ket∇i}htkz=\nσz|κ∝an}⌊∇a⌋ket∇i}htkz, forκ∝ne}ationslash= 0. On the other hand, there is no double\nstructure in the zero eigenstates. Since the hermitian op-\neratorσzmapszeroeigenstatesof H⊥\nkztozeroeigenstates\nofH⊥\nkz, then we can choose the zero eigenstates also as\neigenstates of σz, denoted by|0i,σi∝an}⌊∇a⌋ket∇i}htkzwithσz|0i,σi∝an}⌊∇a⌋ket∇i}htkz=\nσi|0i,σi∝an}⌊∇a⌋ket∇i}htkzandσi=±1. There is another symmetrical\nproperty between the eigenstates of H⊥\nkzwith different\nkz. Since the transformation kz→−kzcorresponds to\nthe flip of the direction of the effective magnetic field,\nΘH⊥\nkzΘ−1=H⊥\n−kzholds, where Θ = i σyKis the time-\nreversaloperatorfor spin-1 /2fermions and Kis the com-\nplex conjugation operator [71]. Therefore we can impose\n|κ∝an}⌊∇a⌋ket∇i}ht−kz= Θ|κ∝an}⌊∇a⌋ket∇i}htkzand|0i,−σi∝an}⌊∇a⌋ket∇i}ht−kz= Θ|0i,σi∝an}⌊∇a⌋ket∇i}htkz, because\nof{σz,Θ}= 0.\nThe eigenstates of Hscrew\ns,kzcan be constructed\nfrom|κ∝an}⌊∇a⌋ket∇i}htkzand|0σi∝an}⌊∇a⌋ket∇i}htkz. Indeed,|ψL,±\nkz(κ)∝an}⌊∇a⌋ket∇i}ht:=\ncL,±\nkz,1(κ)|κ∝an}⌊∇a⌋ket∇i}htkz+cL,±\nkz,2(κ)|−κ∝an}⌊∇a⌋ket∇i}htkz, withκ >0, and\n|0σi∝an}⌊∇a⌋ket∇i}htkzare the full spectrum of Hscrew\nL,kz, with eigen-\nvalues±/radicalBig\nκ2+(mL\nkz)2andσimL\nkz, respectively. Here\nthe coefficients are given by ( cL,±\nkz,1(κ),cL,±\nkz,2(κ)) =\n(4(κ2+ (mL\nkz)2))−1/4(±sgn(mL\nkz)((κ2+ (mL\nkz)2)1/2±\nκ)1/2,((κ2+(mL\nkz)2)1/2∓κ)1/2)). Moreover,|ψR,±\nkz(κ)∝an}⌊∇a⌋ket∇i}ht:=\nΘ|ψL,∓\n−kz(κ)∝an}⌊∇a⌋ket∇i}htand|0σi∝an}⌊∇a⌋ket∇i}htkzare the eigenstates of Hscrew\nR,kz,\nwith eigenvalues ±/radicalBig\nκ2+(mR\nkz)2and−σimR\nkz, respec-\ntively.\nNow, we calculate the ground state currentin the pres-\nence of the screw dislocation. As yet, we have not distin-\nguished discrete and continuum states. From now on, we\nuseκitoexpressthe discreteeigenvaluesof H⊥\nkzand(κ,l)\nto label the continuum states, where κis the continuum\nenergy eigenvalue, and lis a discrete quantum number,\ne.g., the angular momentum. The current operator is\ndefined by ∂Hscrew\ns,kz/∂kz=χsσz+χs{−(bgy/2πρ2)σx+\n(bgx/2πρ2)σy}. At least up to the first order in bg, the\ncorrection to the current operator due to the dislocation,\ni.e. the second and third term above, does not contribute\nto the expectation value because these terms are odd un-\nder the transformation x→−xory→−y. Therefore,\nthe current is the sum of the expectation values of χsσz\nfor the occupied states which consist of discrete nonzero,8\ndiscrete zero, and continuum states, and then we obtain,\nJz=/summationdisplay\ns=L,R/integraldisplay\n|ms\nkz|<ΛLzdkz\n2π/bracketleftBigg/summationdisplay\nκi>0∝an}⌊∇a⌋ketle{tψs,−\nkz(κi)|χsσz|ψs,−\nkz(κi)∝an}⌊∇a⌋ket∇i}ht\n+/summationdisplay\ni:σiχsms\nkz<0∝an}⌊∇a⌋ketle{t0i,σi|χsσz|0i,σi∝an}⌊∇a⌋ket∇i}htkz\n+/integraldisplay∞\n0dκ/summationdisplay\nl∝an}⌊∇a⌋ketle{tψs,−\nkz(κ,l)|χsσz|ψs,−\nkz(κ,l)∝an}⌊∇a⌋ket∇i}ht/bracketrightBigg\n=/integraldisplay\n|mL\nkz|<ΛLzdkz\n2π\n/summationdisplay\nκi/negationslash=0∝an}⌊∇a⌋ketle{tκi|σz|κi∝an}⌊∇a⌋ket∇i}htkz\n+/summationdisplay\ni∝an}⌊∇a⌋ketle{t0i,σi|σz|0i,σi∝an}⌊∇a⌋ket∇i}htkz+/integraldisplay∞\n−∞dκ/summationdisplay\nl∝an}⌊∇a⌋ketle{tκ,l|σz|κ,l∝an}⌊∇a⌋ket∇i}htkz/bracketrightBigg\n,\n(S-20)\nwhereLzis the size of the system. Here we introduce the\nmomentum cutoff scheme, |ms\nkz|<Λ, i.e. the domain of\nthe integrationis the same as that used in the calculation\nof Eq.(4). The first term in the square braket is equal\nto zero, since σz|κi∝an}⌊∇a⌋ket∇i}htkz=|−κi∝an}⌊∇a⌋ket∇i}htkzis orthogonal to|κi∝an}⌊∇a⌋ket∇i}htkz.\nThe second term is the index of the Dirac operator, H⊥\nkz,\nwhich is an integer and the difference in the number of\nits normalizable zero modes with σ3= +1 and σ3=\n−1. The index is given by Nkz:=−sgn(Φkz)⌊|Φkz|/2π⌋\n[53, 54]. The normalizable zero modes exhibit power-law\ndecay for large distance from the dislocation; i.e. they\nbehavelike|0i,−1∝an}⌊∇a⌋ket∇i}ht∝(0,ρ−Φkz/2π(x−iy)i−1) forΦ kz>0,\nand|0i,+1∝an}⌊∇a⌋ket∇i}ht∝(ρΦkz/2π(x+iy)i−1,0) for Φ kz<0, where\ni= 1,2,···,|Nkz|[53, 54]. Now, we move on to the\nthird term of Eq.(S-20). One may expect that it is equal\nto zero, since σz|κ,l∝an}⌊∇a⌋ket∇i}ht=|−κ,l∝an}⌊∇a⌋ket∇i}ht, is orthogonal to |κ,l∝an}⌊∇a⌋ket∇i}htfor\nalmostallvaluesof κ. However,thescatteringstatesnear\nκ= 0 (their amplitudes ∝cos(κρ+δl)/√ρwithδlthe\nphase shift) cause a delta function peak of ∝an}⌊∇a⌋ketle{tκ,l|σz|κ,l∝an}⌊∇a⌋ket∇i}htkz\natκ= 0. Indeed, from an explicit calculation [53], it\nhas been shown that/summationtext\nl∝an}⌊∇a⌋ketle{tκ,l|σz|κ,l∝an}⌊∇a⌋ket∇i}htkz=ckZδ(κ), with\nckz= Φkz/2π−Nkz, and then the third term is equal to\nckz. Substituting them into Eq.(S-20), we obtain\nJz=/integraldisplayΛ−λ\n−Λ−λLzdkz\n2πΦkz\n2π=−LzbgΛλ\n2π2,(S-21)\nwhich is coincident with the expression obtained directly\nfrom Eq.(3) by the following reason. In the presence\nof the screw dislocation with the Burgers vector −bgˆz\nthe torsion is given by Tz\nz=Tz\nxy=bgδ(2)(x,y). There-\nfore, the total current derived from Eq.(3) is Jz=\n−LzevF(λR\nz−λL\nz)Λbg/4π2. In this section we have set\nλL\nz=−λR\nz=λande=vF= 1, and therefore we obtain\nJz=−LzλΛbg/2π2, which reproduces Eq.(S-21).Absence of total current and possibility of local\ncurrent\nIn this section, we show that, if the system is periodic\nin a certain direction, the totalcurrent is always zero,\neven in the presence of a magnetic field or lattice stain\nand dislocations, while the localcurrent is not. The argu-\nment is the extension of that presented in Ref. [35]. We\nstart with the general Hamiltonian of electrons in solids\n(sete= 1 in this section):\nH=/integraldisplay\nd3r1\n2m(−i∇i−Ai(ρ,z))2+V(ρ,z),(S-22)\nwhereVis the potential term, in which the effect of the\ndislocation is included. Here i=x,y,z,r= (ρ,z),\nandρ= (x,y), and we impose the periodicity in the\nz-direction:\nAi(ρ,z) =Ai(ρ,z+a),V(ρ,z) =V(ρ,z+a).(S-23)\nSupposeψis one eigenfunction of the Hamiltonian\nand define the Bloch wave function ψn,kz(ρ,z) =\neikzzun,kz(ρ,z), whose energy is εn,kz. The total current\nalong thez-direction is given by\nJz=/summationdisplay\nn/integraldisplay\nBZdkz\n2π/integraldisplay\nd3rψ∗\nn,kz(ρ,z)δH\nδAzψn,kz(ρ,z)nF(εn.kz)\n=−/summationdisplay\nn/integraldisplay\nBZdkz\n2π/integraldisplay\nd3ru∗\nn,kz(ρ,z)∂Hkz\n∂kzun,kz(ρ,z)nF(εn.kz),\n(S-24)\nwhereHkz=e−ikzzHeikzzandnFis the Fermi distribu-\ntion function. Here we use the identity :\n/integraldisplay\nd3ru∗\nn,kz(ρ,z)∂Hkz\n∂kzun,kz(ρ,z)\n=∂\n∂kz/integraldisplay\nd3ru∗\nn,kz(ρ,z)Hkzun,kz(ρ,z)\n=∂εn,kz\n∂kz, (S-25)\nwhich follows from\n∂\n∂kz/bracketleftbigg/integraldisplay\nd3r u∗\nn,kz(ρ,z)un,kz(ρ,z)/bracketrightbigg\n=∂\n∂kz1 = 0,(S-26)\nand then we can rewrite Eq. (S-24) into\nJz=−/summationdisplay\nn/integraldisplay\nBZdkz\n2π∂εn,kz\n∂kznF(εn.kz)\n=−1\n2π/summationdisplay\nn/summationdisplay\ni=1,...,i(n)/integraldisplayε\nn,k(n)\ni\nε\nn,k(n)\ni−1dε nF(ε) (S-27)\nHere for each region k∈(k(n)\ni−1,k(n)\ni),εn,kmonotonically\nincreasesordecreases,and k(n)\n0= 0andk(n)\ni(n)= 2π/a. We9\nfind that Eq.(S-27) is always equal to zero owing to the\nperiodicity of the dispersion in the wave number space,\nεn,k=0=εn,k=2π/a. Therefore, we found that the to-\ntalcurrent along the z-direction is zero. In the above\nderivation, it is essential that the integrand with respect\ntokzcan be rewritten into the total derivative with re-\nspect tokz, and this key factor follows from the fact that\nthe integral over the real space of |un,kz(ρ,z)|2is equal\nto 1, which results in Eq. (S-26). Instead, without the\nintegration over the real space,\n∂\n∂kz/bracketleftbig\nu∗\nn,kz(ρ,z)un,kz(ρ,z)/bracketrightbig\n∝ne}ationslash= 0. (S-28)\nThen, in the case of localcurrent, the above argument in\nthe case of the totalcurrent does not hold. Hence, the\nlocal current is not always zero, unlike the total current.\n[1] X. Wan, A. M. Turner, A. Vishwanath, and S. Y.\nSavrasov, Phys. Rev. B 83, 205101 (2011).\n[2] A. A. Burkov and L. Balents, Phys. Rev. Lett. 107,\n127205 (2011).\n[3] G. B. Hal´ asz and L. Balents, Phys. Rev. B 85, 035103\n(2012).\n[4] S. Murakami, New Journal of Physics 9, 356 (2007).\n[5] H.-J. Kim, K.-S. Kim, J.-F. Wang, M. Sasaki, N. Satoh,\nA. Ohnishi, M. Kitaura, M. Yang, and L. Li, Phys. Rev.\nLett.111, 246603 (2013).\n[6] Z. Wang, Y. Sun, X.-Q. Chen, C. Franchini, G. Xu,\nH. Weng, X. Dai, and Z. Fang, Phys. Rev. B 85, 195320\n(2012).\n[7] Z. Wang, H. Weng, Q. Wu, X. Dai, and Z. Fang, Phys.\nRev. B88, 125427 (2013).\n[8] Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng,\nD. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai,\net al., Science 343, 864 (2014).\n[9] M. Neupane, S.-Y. Xu, R. Sankar, N. Alidoust, G. Bian,\nC. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, H. Lin,\net al., Nat Commun 5(2014).\n[10] S. Borisenko, Q. Gibson, D. Evtushinsky, V. Zabolotnyy ,\nB.B¨ uchner, andR.J.Cava, Phys.Rev.Lett. 113, 027603\n(2014).\n[11] Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M.\nWeng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin,\net al., Nat Mater 13, 677 (2014).\n[12] Q. Li, D. E. Kharzeev, C. Zhang, Y. Huang, a. V. Fe-\ndorov, R. D. Zhong, J. a. Schneeloch, G. D. Gu, and\nT. Valla (2014), 1412.6543v1.\n[13] H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai,\nPhys. Rev. X 5, 011029 (2015).\n[14] S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee,\nG. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane,\nC. Zhang, et al., Nat. Commun 6(2015).\n[15] S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane,\nR. Sankar, S.-M. Huang, C.-C. Lee, B. Wang, G. Bian,\nH. Zheng, et al. (2015), 1502.03807v1.\n[16] C. Zhang, Z. Yuan, S. Xu, Z. Lin, B. Tong, M. Z.\nHasan, J. Wang, C. Zhang, andS.Jia, 1502.00251 (2015),\n1502.00251v1.[17] B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao,\nJ. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen,\net al., Phys. Rev. X 5, 031013 (2015).\n[18] C. Shekhar, A. K. Nayak, Y. Sun, M. Schmidt, M. Nick-\nlas, I. Leermakers, U. Zeitler, Y. Skourski, J. Wosnitza,\nZ. Liu, et al., Nat Phys (2015).\n[19] X. Huang, L. Zhao, Y. Long, P. Wang, D. Chen, Z. Yang,\nH. Liang, M. Xue, H. Weng, Z. Fang, et al., Phys. Rev.\nX5, 031023 (2015).\n[20] X. Yang, Y. Li, Z. Wang, Y. Zheng, and Z.-A. Xu (2015),\n1506.03190v1.\n[21] C. Shekhar, F. Arnold, S.-C. Wu, Y. Sun, M. Schmidt,\nand N. Kumar, pp. 1–26 (2015), 1506.06577v1.\n[22] A. Sushkov, B. J. Hofmann, G. S. Jenkins, J. Ishikawa,\nS. Nakatsuji, S. D. Sarma, and H. D. Drew (2015),\n1507.01038.\n[23] S. Borisenko, D. Evtushinsky, Q. Gibson, A. Yaresko,\nT. Kim, M. N. Ali, B. B¨ uchner, M. Hoesch, and R. J.\nCava (2015), 1507.04847.\n[24] K. Fujikawa and H. Suzuki, Path Integrals and Quantum\nAnomalies (Oxford University Press, 2004).\n[25] A. A. Zyuzin and A. A. Burkov, Phys. Rev. B 86, 115133\n(2012).\n[26] P. Goswami and S. Tewari, Phys. Rev. B 88, 245107\n(2013).\n[27] P. Hosur and X. Qi, Comptes Rendus Physique 14, 857\n(2013).\n[28] H. Nielsen and M. Ninomiya, Physics Letters B 130, 389\n(1983).\n[29] P. Goswami, J. H. Pixley, and S. D. Sarma (2015),\n1503.02069v1.\n[30] C.-X. Liu, P. Ye, and X.-L. Qi, Phys. Rev. B 87, 235306\n(2013).\n[31] D. E. Kharzeev, Annals of Physics 325, 205 (2010).\n[32] D. E. Kharzeev, Progress in Particle and Nuclear Physic s\n75, 133 (2014).\n[33] K. Fukushima, D. E. Kharzeev, and H. J. Warringa,\nPhys. Rev. D 78, 074033 (2008).\n[34] F. Wilczek, Phys. Rev. Lett. 109, 160401 (2012).\n[35] M. M. Vazifeh and M. Franz, Phys. Rev. Lett. 111,\n027201 (2013).\n[36] N. Yamamoto, Phys. Rev. D 92, 085011 (2015).\n[37] Effects of dislocation in topological materials have be en\nextensively studied so far in different contexts [72–81].\n[38] M. Nakahara, Geometry, topology, and physics (Institute\nof Physics Publishing, Bristol, Philadelphia, 2003).\n[39] A. Shitade, Progress of Theoretical and Experimental\nPhysics2014, 123I01 (2014).\n[40] O. Parrikar, T. L. Hughes, and R. G. Leigh, Phys. Rev.\nD90, 105004 (2014).\n[41] In this letter, Tα\nijis called the TMF and Tα\ni0the tor-\nsional electric field, following the terminology in Ref.[39 ].\nAmong the latter, the temporal ( α= 0) component\ncorresponds, for example, to the temperature gradient\n[39, 82, 83], and the spatial ( α=a) one the mechanical\nrotation [84] .\n[42] D. Edelen and D. Lagoudas, Gauge theory and defects in\nsolids(North Holland, 1988).\n[43] T. L. Hughes, R. G. Leigh, and O. Parrikar, Phys. Rev.\nD88, 025040 (2013).\n[44] H. Kleinert, Multivalued Fields: In Condensed Mat-\nter, Electromagnetism, and Gravitation (World Scien-\ntific, 2008).\n[45]Supplemental material .10\n[46] D. T. Son and N. Yamamoto, Phys. Rev. Lett. 109,\n181602 (2012).\n[47] S. D. R. Mu˜ noz and J. Gamboa, Master’s thesis, Pontif-\nicia Universidad Cat´ olica de Chile (2010).\n[48] M. Kohmoto, B. I. Halperin, and Y.-S. Wu, Phys. Rev.\nB45, 13488 (1992).\n[49] J. C. Y. Teo and C. L. Kane, Phys. Rev. B 82, 115120\n(2010).\n[50] K.-I. Imura and Y. Takane, Phys. Rev. B 84, 245415\n(2011).\n[51] R. Jackiw, Phys. Rev. D 29, 2375 (1984).\n[52] F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).\n[53] J. Kiskis, Phys. Rev. D 15, 2329 (1977).\n[54] Y. Aharonov and A. Casher, Phys. Rev. A 19, 2461\n(1979).\n[55] S. Murakami, N. Nagaosa, and S.-C. Zhang, Phys. Rev.\nB69, 235206 (2004).\n[56] D. Vasyukov, Y. Anahory, L. Embon, D. Halbertal,\nJ. Cuppens, L. Neeman, A. Finkler, Y. Segev, Y. Mya-\nsoedov, M. L. Rappaport, et al., Nat Nano 8, 639 (2013),\nISSN 1748-3387.\n[57] Y. H. Wang, J. R. Kirtley, F. Katmis, P. Jarillo-Herrero ,\nJ. S. Moodera, and K. A. Moler, Science 349, 948 (2015),\nISSN 0036-8075.\n[58] Z. S. Basinski and J. S. Dugdale, Phys. Rev. B 32, 2149\n(1985).\n[59] P.L.McEuen, A.Szafer, C.A.Richter, B. W.Alphenaar,\nJ. K. Jain, A. D. Stone, R. G. Wheeler, and R. N. Sacks,\nPhys. Rev. Lett. 64, 2062 (1990).\n[60] J. K. Wang and V. J. Goldman, Phys. Rev. Lett. 67, 749\n(1991).\n[61] J. Bardeen and W. Shockley, Phys. Rev. 80, 72 (1950).\n[62] S. C. Hunter and F. R. N. Nabarro, Proc. Roy. Soc. Lon-\ndon A220, 542 (1953).\n[63] Z. S. Basinski, J. S. Dugdale, and A. Howie, Phil. Mag.\n8, 1989 (1963).\n[64] B. R. Watts, in Basic Problems and Applications, volume\n8 of Dislocations in Solids, edited by F. R. N. Nabarro\n(North-Holland, 1989).\n[65] B. R. Watts, J. Phys. F: Met. Phys. 18, 1183 (1988).[66] A. Bergmann, M. Kaveh, and N. Wiser, Phys. Rev. B\n24, 6807 (1981).\n[67] A. U. Kasumov, C. H. V. Kopetskii, L. S. Kokhanchik,\nandV.N.Matveev, Sov.Phys.SolidState 23, 151(1981).\n[68] A. S. Karolik and A. A. Luhvich, J. Phys.: Condensed\nMatter6, 873 (1994).\n[69] K. Viswanathan and S. Chandrasekar, J. Appied Phys.\n116, 245103 (2014).\n[70] N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and\nN. P. Ong, Rev. Mod. Phys. 82, 1539 (2010), URL http:\n//link.aps.org/doi/10.1103/RevModPhys.82.1539 .\n[71] J. J. Sakurai and J. J. Napolitano, Modern Quantum\nMechanics (Addison-Wesley, 2010), 2nd ed.\n[72] G. Sundaramand Q.Niu, Phys.Rev. B 59, 14915 (1999).\n[73] M. Lazar, J. of Phys. A: Math. and General 35, 1983\n(2002).\n[74] Y. Ran, Y. Zhang, and A. Vishwanath, Nature Phys. 5,\n298 (2009).\n[75] A. Mesaros, D. Sadri, and J. Zaanen, Phys. Rev. B 82,\n073405 (2010).\n[76] F. de Juan, A. Cortijo, and M. A. H. Vozmediano, Nucl.\nPhys. B 828, 625 (2010).\n[77] Z. Wang and S. C. Zhang, Phys. Rev. B 87, 161107(R)\n(2013).\n[78] J. Zhou, H. Jiang, Q. Niu, and J. Shi, Chin. Phys. Lett.\n30, 027101 (2013).\n[79] R.-J. Slager, A.Mesaros, V.Juriˇ ci´ c, andJ. Zaanen, P hys.\nRev. B90, 241403 (2014).\n[80] V. Juriˇ ci´ c, A.Mesaros, R.-J.Slager, andJ. Zaanen, P hys.\nRev. Lett. 108, 106403 (2012).\n[81] R.-J. Slager, A. Mesaros, V. Juricic, and J. Zaanen, Nat\nPhys9, 98 (2013), ISSN 1745-2473.\n[82] A. GromovandA. Abanov, Physical ReviewLetters 114,\n016802 (2014).\n[83] B. Bradlyn and N. Read, Physical Review B 91, 125303\n(2015).\n[84] A. Shitade and T. Kimura, Phys. Rev. B 90, 134510\n(2014)."    },    {        "title": "1509.08997v1.Roadmap_for_Emerging_Materials_for_Spintronic_Device_Applications.pdf",        "content": " \n 1 Roadmap for Emerging Materials  for Spintronic Device Applications  Atsufumi Hirohata,1 Senior Member, IEEE, Hiroaki Sukegawa,2 Hideto Yanagihara,3 Igor Žutić,4 Takeshi Seki,5  Shigemi Mizukami 6 and Raja Swaminathan 7  1 Department of Electronics, University of York, York YO10 5DD, UK 2 Magnetic Materials Unit, National Institute for Materials Science, Tsukuba 305-0047, Japan 3 Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8577, Japan 4 Department of Physics, University at Buffalo, State University of New York, Buffalo, NY 14260, USA 5 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan 6 WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan 7 Intel Corporation, Chandler, AZ 85226, USA  The Technical Committee of the IEEE Magnetics Society has selected 7 research topics to develop their roadmaps, where major developments should be listed alongside expected timelines; (i) hard disk drives, (ii) magnetic random access memories, (iii) domain-wall devices, (iv) permanent magnets, (v) sensors and actuators, (vi) magnetic materials and (vii) organic devices. Among them, magnetic materials for spintronic devices have been surveyed as the first exercise. In this roadmap exercise, we have targeted magnetic tunnel and spin-valve junctions as spintronic devices. These can be used for example as a cell for a magnetic random access memory and spin-torque oscillator in their vertical form as well as a spin transistor and a spin Hall device in their lateral form. In these devices, the critical role of magnetic materials is to inject spin-polarised electrons efficiently into a non-magnet. We have accordingly identified 2 key properties to be achieved by developing new magnetic materials for future spintronic devices: (1) Half-metallicity at room temperature (RT); (2) Perpendicular anisotropy in nano-scale devices at RT. For the first property, 5 major magnetic materials are selected for their evaluation for future magnetic/spintronic device applications: Heusler alloys, ferrites, rutiles, perovskites and dilute magnetic semiconductors. These alloys have been reported or predicted to be half-metallic ferromagnets at RT. They possess a bandgap at the Fermi level EF only for its minority spins, achieving 100% spin polarisation at EF. We have also evaluated L10-alloys and D022-Mn-alloys for the development of a perpendicularly anisotropic!ferromagnet with large spin polarisation. We have listed several key milestones for each material on their functionality improvements, property achievements, device implementations and interdisciplinary applications within 35 years time scale. The individual analyses and projections are discussed in the following sections.  Index Terms—Magnetic materials, half-metallic ferromagnets, Magnetic anisotropy, Spintronics.  I.!HEUSLER ALLOYS EUSLER alloys are ternary alloys originally discovered by Heusler [1]. He demonstrated ferromagnetic behaviour in an alloy consisting of non-magnetic atoms, Cu2MnSn. Since then, these alloys have been investigated due to their properties of shape-memory and thermal conductance. In 1983, de Groot et al. reported half-metallic ferromagnetism in one of the Heusler alloys, half-Heusler NiMnSb alloy [2]. A great deal of effort has been accordingly devoted to achieve the half-metallicity at RT using a Heusler alloy. In particular, Block et al. measured a large tunnelling magnetoresistance (TMR) in bulk full-Heusler Co2(Cr,Fe)Si alloy [3], followed by a similar measurement in a thin-film form [4]. Among these Heusler alloys, Co-based full-Heusler alloys are the most promising candidates to achieve the RT half-metallicity due to their high Curie temperature (TC >> RT), good lattice matching with major substrates, large minority-spin bandgap (≥ 0.4 eV, see Fig. 1), and large magnetic moments in general [≥ 4 µB per formula unit (f.u.)] [5],[6]. The main obstacle to achieving the half-metallicity in the Heusler-alloy films is the vulnerability against the crystalline disorder, such as the atomic displacement, misfit dislocation and symmetry break in the vicinity of the surface of the films. For the full-Heusler alloys forming X2YZ, where the X and Y atoms are transition metals, while Z is either a semiconductor or a non-magnetic metal, the unit cell of the ideal crystalline structure (L21 phase, see Fig. 2.1) consists of four face-centered cubic (fcc) sublattices. When the Y and Z atoms exchange their sites (Y-Z disorder) and eventually occupy their sites at random, the alloy transforms into the B2 phase. In addition, X-Y and X-Z disorder finally leads to the formation of the A2 phase. By increasing the disorder, the magnetic properties depart further from the half-metallicity. Towards the RT half-metallicity, two milestones have been identified as listed below: (m1.1) Demonstration of >100% giant magnetoresistance (GMR) ratio at RT; (m1.2) Demonstration of >1,000% tunnelling magnetoresistance (TMR) ratio at RT. Here, we have regarded these criteria using the MR as indicator of the half-metallicity at RT  H \nCorresponding author: A. Hirohata (e-mail: atsufumi.hirohata@york.ac.uk). All the authors contributed equally.  \n 2 \n Fig. 1.  Minority-spin bandgap [7] and L21 phase [6] of the full-Heusler alloys.  Regarding (m1.1), in 2011, 74.8% GMR ratio was reported by Sato et al. [8] using a junction consisting of Co2Fe0.4Mn0.6Si/Ag/Co2Fe0.4Mn0.6Si. This is a significant improvement from 41.7% reported by Takahashi et al. about 5 months earlier. By using such a GMR junction as a read head, he GMR ratio of approximately 75% with the resistance area product (RA) of almost 0.17 Ω⋅µm2 satisfies the requirement for 2-Tbit/in2 areal density in a hard disk drive (HDD). Figure 2 shows the requirement and recent major efforts towards the Tbit/in2 areal density. It is clear that the Heusler-alloy GMR junctions are the only candidates satisfying the requirement to date. By reflecting on the development over the last 5 years, one can expect the Heusler-alloy GMR junctions can achieve 100% GMR ratios within 3 years. This will satisfy (m1.1) and will lead to device applications as HDD read heads.  \n Fig. 2.  Requirement for Tbit/in2 HDD read head and recent major results [9].  For (m1.2), Figure 3 shows the development of the TMR ratios using amorphous and MgO barriers with both conventional ferromagnets and Heusler alloys as electrodes. As shown here the largest TMR reported to date is 604% at RT using a magnetic tunnel junction (MTJ) of CoFeB/MgO/CoFeB [10]. In 2005, an MTJ with an epitaxial L21 Co2MnSi film has been reported to show very high TMR ratios of 70% at RT [11]. These are the largest TMR ratio obtained in an MTJ with a Heusler alloy film and an Al-O barrier. The TMR is purely induced by the intrinsic spin polarisation of the Heusler electrodes which is different from an MTJ with an oriented MgO barrier, where a TMR ratio of 386% has been achieved at RT (832% at 9 K) for Co2FeAl0.5Si0.5 [12]. The TMR ratio reported here is the highest ever in an MTJ with a Heusler alloy film but with the assistance of coherent tunnelling through an oriented MgO barrier. By taking a moderate extrapolation, one can estimate that 1,000% TMR ratios (m1.2) can be achieved within 10 years time period, i.e., the RT half-metallicity by 2024.  \n Fig. 3.  Recent developments in the TMR ratios.  The other device application expected is to fabricate all Heusler junctions consisting of antiferromagnetic/ ferromagnetic/non-magnetic/ferromagnetic Heusler-alloy layers. Such junctions can offer a template to avoid any crystalline disorder at the interfaces as the lattice matching and symmetry can be precisely controlled by atom substitution in these alloy layers. As a first step, Nayak et al. reported an antiferromagnetic Heusler alloy of Mn2PtGa for the first time but at low temperature (below 160K) [13]. One can anticipate RT antiferromagnetism can be demonstrated within 5 years, leading to the all Heusler-alloy junctions in 20 years.  \n Fig. 4.  Roadmap on the Heusler-alloy films.  By summarising the above consideration, one can anticipate a roadmap on the Heusler-alloy films as shown in Fig. 4. The Heusler-alloy films are expected to be used in GMR read heads and sensors within 3 years. These films are also to be combined with antiferromagnetic and/or non-magnetic Heusler-alloy films to form all Heusler junctions. Such junctions may be used in a magnetic random access memory  \n 3 subject to their perpendicular magnetic anisotropy, which is still in the infant stage in research. II.!OXIDES Ferromagnetic oxide thin films have been intensively studied for more than last two decades due to their a large variety and tunability of physical properties such as ferro-, ferri-, anti-ferromagnetism, ferroelectricity, superconductivity, optical properties, and colossal magnetoresistance effect [14], [15]. In particular, some of ferromagnetic oxides are predicted as promising candidates of a half-metal and a spin-filter, which directly lead to a large magnetoresistance (MR) as discussed in the previous section. In addition, due to a high compatibility with other oxides and organic materials, establishment of high quality all oxide heterostructure beyond CMOS device are highly expected. In this section, milestones and their associated roadmaps for 3 half-metallic oxide ferromagnets, spinel ferrites (2.1), rutiles (2.2) and perovskites (2.3), are discussed. A.!Spinel Ferrites The most commonly studied oxides of Fe is Fe3O4, which has an inverse spinel structure and a magnetic moment of 4.1 µB/f.u. [16]. Among the various spinel-type ferrites, Fe3O4 is a major conductive oxide at room temperature. The Curie temperature TC is ~850 K and the characteristic metal-insulator transition point (Verwey temperature) is 123 K. According to a band calculation, half-metallicity has been predicted [18],[19] and spin-resolved photoemission experiments show that Fe3O4 exhibits spin polarisation of up to −80% [20]. Very high spin polarisation has also been suggested by the measurement of an MR ratio of over 500% through a nano-contact [21]. Epitaxial Fe3O4 films have been grown by various techniques, including molecular beam epitaxy (MBE) under an oxygen atmosphere, magnetron sputtering and laser ablation [20]. By replacing one of the Fe ions with a divalent metal ion, e.g., Mn, Co, Ni etc., a ferrite can be formed [20]. Pénicaud has predicted half-metallicity in Mn, Co and Ni ferrites [22] although the bulk materials are insulators except Fe3O4. In particular, NiFe2O4 shows a bandgap in the majority band, indicating that this compound can become an insulator or semi-metallic half-metal. The discrepancy of the bandgap structure between ab initio calculation results and experimental results suggests that the treatment of electron correlation is significant. Some ferrites are expected as a good candidate of a spin-filter because of their ferromagnetic insulator properties and high TC. The spin-filtering device consists of a ferromagnetic insulator layer sandwiched between a non-magnetic metallic (NMM) layer and a ferromagnetic metallic (FMM) layer (or a superconductive layer). Due to the exchange splitting of the energy levels in the conduction band of the ferromagnetic insulator, the effective barrier height for the up-spin electron differs from that for the down-spin one, leading to a large difference in the tunnelling probabilities between the two spin orientations. Therefore, ideally, an almost perfectly spin-polarized current is generated and this results in an infinite MR if a ferromagnetic insulator with a large exchange splitting is used. Here, MR ratio is defined as 2PSFP/(1 − PSFP), where PSF is the spin filtering efficiency [= (Iup − Idown)/( Iup + Idown), Iup(down) ∝ exp(−d⋅φ up(down)1/2), where I is the tunnelling current, d is the thickness of the spin-filter, and φ is the effective barrier height] and P is the spin polarisation of the FMM layer. RT spin-filtering effect has been demonstrated using CoFe2O4-based spin-filter devices [23],[24]. However |PSF| at RT is below 5%. Related to Section 4, perpendicular magnetization behaviour with a high uniaxial magnetic anisotropy of Ku = 1.47 × 106 J/m3 in CoFe2O4 ferrite [25] has been reported. In addition to the ferromagnetic spinel ferrites, nonmagnetic spinel, MgAl2O4 has also attracted much attention as a new spintronics material because an ultrathin MgAl2O4 layer shows coherent tunnelling properties (symmetry selective tunnelling) and high MR ratios like an MgO tunnel barrier. Using an epitaxial CoFe/MgAl2O4 (with cation-site disordered)/CoFe structure, an MR ratio of more than 300% at room temperature was reported [26]. Towards the magnetic ferrites as a spintronic material, the following milestones have been recognised: (m2.1.1) Half-metallic behaviour and high MR by improving microstructure and control of interface states; (m2.1.2) High spin-filtering effects at RT by reducing structural and chemical defects; (m2.1.3) Tuning of perpendicular magnetic anisotropy; (m2.1.4) Development of new non-magnetic spinel-based materials to tune the transport properties and the coherent tunnelling effect. Regarding (m2.1.1) and (m2.1.2), ferrite films with a very high quality crystalline structure, i.e., without any crystal imperfections such as anti-phase boundaries (APBs), atomic site disorder and dislocations, are necessary to obtain high saturation magnetisation, high squareness of the hysteresis loops and high TC. The presence of APBs within a ferrite film, for instance, significantly degrades the saturation magnetisation under a high magnetic field and the remanence. It also increases the resistivity of the film since the APBs induce the electron scattering centre. Consequently, high quality films are indispensable to achievement of stable half-metallic characteristics and a spin-filtering effect at RT. In addition, realisation of a perfect and an abrupt ferrite/non-magnetic interface is required to preserve high effective spin polarisation at the interface states. Therefore, establishment of the growth method and procedures for high quality ferrite films, as well as a high quality interface with ferro- and non-magnetic metallic layers are strongly desired. The development of an advanced growth process will lead to RT half-metallicity using ferrite family materials such as Fe3O4, γ-Fe2O3, CoFe2O4, NiFe2O4, MnFe2O4, and ZnFe2O4. The milestone of (m2.1.3) is important to ensure the high thermal stability for nano-scale structures using CoFe2O4-based ferrites for future spin-filtering devices and other spintronics use at RT. Especially, strong perpendicular magnetic anisotropy in a very thin region (below several nm)  \n 4 is desirable to control the tunnelling resistance for device applications. For (m2.1.4), providing the new non-magnetic tunnel barrier is now considered as an important issue to establish novel spintronic hetero-structures since only a limited tunnel barrier material (Al2O3 and MgO) are currently available to obtain high RT MR ratios. Especially, the ability to tune physical properties is required to achieve higher performance, multi-functionality and better compatibility to ferromagnetic electrodes. For instance, MR enhancement by crystalline barrier (coherent tunnelling), a perfect lattice matching (lattice constant tuning), a low tunnelling resistance (barrier height tuning), and applicability of high electric fields to a ferromagnetic layer facing the barrier (dielectric constant tuning) are presumably possible in spinel-based nonmagnetic barrier with tailored compositions. In summary, one can propose a roadmap on spinel ferrite films as shown in Fig. 5. Using spinel ferrite based MTJs consisting of ferrite/non-magnetic (NM) barrier/ferrite (or FMM) structure, >100% RT TMR (corresponding |P| is ~0.7 according to the Julliere model) is expected within 10 years through development of high quality spinel ferrite thin films and selection of a proper NM barrier. Further improvement of an MTJ structure and suppression of a rapid TMR reduction with increasing temperature will lead to giant TMR over 1000% (corresponding |P| is ~0.9) within 25 years.  \n Fig. 5.  Roadmap on the ferrite films.  To construct spin-filtering devices, one can use the techniques for the MTJ fabrication; a typical stacking structure is NMM/ferrite spin-filter/NM barrier/FMM, where the NM barrier is used to weaken the exchange coupling between the ferrite and FMM layers. Recently a higher P of \u00008% at RT (MR ~ 6%) has been demonstrated using an epitaxial Pt/CoFe2O4/Al2O3/Co nano-contact junction [27]. Thus, improvement of the junction structure as well as the ferrite film quality can enhance MR ratio. >100% RT MR ratio due to the spin-filtering effect is expected within 10 years by reducing structural and chemical defects in spin-filter junctions. Using new NM barriers, one can highly expect a giant TMR ratio exceeding 500% at RT within 5 years. Furthermore, the tuning of physical properties will be achieved by searching for new candidate barrier materials within 10 years. B.!Rutiles Using Andreev reflection, CrO2 has been proven to show a half-metallic nature at low temperature as suggested by ab initio calculations [16],[17]. High spin polarisation of 90% has been confirmed at low temperature using point-contact Andreev reflection method [18],[19] and high powder magnetoresistance has been reported [20]. However, RT half-metallicity has not been demonstrated yet. CrO2 has a tetragonal unit cell with a magnetic moment of 2.03 µB/f.u. at 0 K [21]. The ferromagnetism of CrO2 appears below 391 K [22]. Above this temperature another phase of Cr2O3 is known to show antiferromagnetism, which is the major cause of the reduction of the half-metallicity. Highly-ordered CrO2 films are predominantly grown by chemical vapour deposition [23]. However, obtaining the CrO2 single phase as a thin film is not easy, and thus MR properties steeply decrease below RT. In order to utilise the rutiles in a spintronic device, the following milestones have been identified: (m2.2.1) Development of a high quality CrO2 thin film with a single rutile phase and achievement of a clean interface structure with tunnel junctions;  \n Fig. 6.  Roadmap on the rutile films.   (m2.2.2) Search for new rutile-based materials with higher TC and robust half-metallicity by tailoring their composition. Regarding (m2.2.1), the undesirable reduction in MR ratio below TC could be suppressed by the improvement of the crystal structure and the interface state. Optimisation of an epitaxial growth process for a single rutile phase and use of a suitable non-magnetic barrier which does not invade the interface of CrO2 will be effective. In addition, the elimination of the nonmagnetic Cr2O3 phase, which generally forms on the surface of the CrO2 film, using sophisticated deposition and treatment processes will enhance the magnetic and half-metallic properties. For (m2.2.2), to obtain a more stable half-metallic phase with high TC, doping of other elements to CrO2 or searching  \n 5 ternary or quaternary rutile-based ferromagnetic materials would be necessary. Such a new composition and a new material will lead to stable half-metallic properties and higher MR at RT. In summary, one can anticipate a roadmap on the half-metallic rutile films as shown in Fig. 6. Obtaining epitaxial thin films with a single CrO2 phase will lead to observation of RT TMR ratios within 10 years. To demonstrate high TMR ratios (>100%) at RT is still challenging. Searching new rutile type ferromagnetic oxides and a sophisticated MTJ structure might yield a technological breakthrough toward a higher TMR ratio in the future. C.!Perovskites Perovskites, such as (La,Sr)MnO3, exhibit both strong ferromagnetism and metallic conductivity with partial substitution of La+3 ions with 2+ ions such as Ca, Ba, Sr, Pb and Cd [28],[29]. Since only one spin band exists at EF in these films, 100% spin polarisation can be achieved. Using these materials instead of a conventional ferromagnet, a very high MR of ~150% at RT has been observed [30]. This is known as colossal magnetoresistance (CMR). Using Mn-perovskite thin films and SrTiO3 oxide tunnel barrier, a TMR ratio of up to 1850% has been reported but only below TC [31]. CMR can be induced either by breaking the insulating symmetry of Mn3+ and Mn4+ alternating chains or by suppressing spin fluctuation near TC. Even so, it is unlikely to achieve the RT half-metallicity in the conceivable future. Much effort has been spent to search for new high TC perovskites for a RT half-metallicity. The family of double perovskites with a chemical composition of A2BB’O6 (A is an alkaline earth or rare earth ion, B and B’ are transition metal ions), has been focused for more than 15 years since some of the double perovskites exhibit high TC above RT and half-metallic band structures [32]. Sr2FeMoO6 (SFMO) has high TC of 420 K and has been predicted to be a half-metal [33], indicating the double perovskites are a promising oxide family for high MR at RT. At low temperature, high P ~ \u000080% in a SFMO film has been demonstrated using a Co/SrTiO3/SFMO MTJ. Much higher TC of 635 K is reported in Sr2CrReO6 [34]. Recently 2-dimensional electron gas (2DEG) at the interface of a nonmagnetic perovskite hetero-structure consisting of LaAlO3/SrTiO3 has been investigated intensively due to a high mobility in the 2DEG. Highly efficient spin transport in the 2DEG could be usable to establish the new type spin transistors in the future. The following milestones have been established towards the perovskites as a spintronic material: (m2.3.1) Search for new perovskite-based materials with TC > RT; (m2.3.2) Development of a high MR at RT. Regarding (m2.3.1), the double perovskites with A2FeMoO6 or A2FeReO6 series are promising due to their high TC. However, high MR using an MTJ structure has not been achieved since there are some considerable obstacles against (m2.3.2); (1) site disorder of magnetic ions deteriorates the magnetic properties and the spin polarisation, and (2) their high reactivity to water, which restricts use of common microfabrication techniques. In order to overcome these obstacles, improvement of film quality and preparation of a clean interface are necessary to achieve high MR ratios at RT. Especially, specific microfabrication method should be newly developed to reduce the damage during the processes. In addition, a new barrier material that matches with the perovskites will be needed to compose a high quality perovskite-based MTJ. In summary, one can expect a roadmap on the perovskite films as shown in Fig. 7. RT TMR ratios will be obtained using MTJs with a high TC perovskite layer within 5 years. >100% TMR at RT will be expected in the future after demonstration of high TMR ratios at low temperatures.! \n Fig. 7.  Roadmap on the perovskite films. III.!DILUTE MAGNETIC SEMICONDUCTORS Unlike metals, semiconductors have relatively low carrier density that can be drastically changed by doping, electrical gates, or photo-excitations, to control their transport and optical properties. This versatility makes them the materials of choice for information processing and charge-based electronics. In magnetically-doped semiconductors, such as (Cd,Mn)Te, (In,Mn)As, or (Ga,Mn)As, these changes of carrier density also enable novel opportunities to control magnetic properties and lead to applications that are not available or ineffective with ferromagnetic metals [35]. For example, a carrier-mediated magnetism in semiconductors offers tunable control of the exchange interaction between carriers and magnetic impurities. The onset of ferromagnetism and the corresponding change in the TC can be achieved by increasing the carrier density using an applied electric field, photo-excitations, or even heating. Two milestones for the research on novel magnetic semiconductors are identified: (m3.1) search for tunable ferromagnetism in semiconductors with TC > RT. (m3.2) demonstrating RT devices that are not limited to magnetoresistive effects. Considering (m3.1), despite numerous reports for TC > 300 K in many semiconductors, a reliable RT ferromagnetic  \n 6 semiconductor remains elusive [36],[37]. However, even the existing low-TC magnetic semiconductors have provided demonstrations of novel magnetic effects and ideas that have subsequently been also transferred to ferromagnetic metals, for example, electric-field modulation of coercivity and magnetocrystalline anisotropy at RT [37]. An early work on ferromagnetic semiconductors dates back to CrB3 in 1960 [38]. Typically studied were concentrated magnetic semiconductors, having a large fraction of magnetic elements that form a periodic array in the crystal structure. Important examples are Eu-based materials in which the solid-state spin-filtering effect was demonstrated for the first time [39]. However, complicated growth and modest TC (up to ~150 K) limited these materials to fundamental research. Starting with mid-1970s, the dilute magnetic semiconductors (DMS), alloys of nonmagnetic semiconductor and magnetic elements (typically, Mn) [40], became intensely explored first in II-IV, and later in III-V nonmagnetic hosts. In II-VIs Mn2+ is isovalent with group II providing only spin doping, but not carriers and thus making robust ferromagnetism elusive. In III-Vs Mn yields both spin and carrier doping, but low-Mn solubility limit complicates their growth and can lead to an extrinsic magnetic response due to nanoscale clustering of metallic inclusions. This complex dual role of Mn doping in III-Vs possess both: (i) challenges to establish universal behavior among different nonmagnetic III-V hosts. (Ga,Mn)N predicted to have TC > 300 K [41], but shown to only have TC ~ 10 K [42], (ii) makes the ab initio studies less reliable, requiring careful considerations of secondary phases and magnetic nano-clustering – a source of many reports for an apparent high-TC in DMS.  \n Fig. 8.  (a) Theoretical predictions for TC in DMS [41], adapted from Ref. [45]. (b) Reliable highest experimental TC reported for Mn-doped DMS, adapted from Ref. [36].  An important breakthrough came with the growth of III-V DMS: (In,Mn)As in 1989 and (Ga,Mn)As in 1996 [43],[44] , responsible for demonstrating tunable TC, coercivity, magnetocrystalline anisotropy, as well as the discovery of tunnelling anisotropic magnetoresistance [37]. However, even if the low-Mn solubility is overcome (maximum ~ 10%), the upper TC limit is given MnAs with TC ~ 330 K. This suggests that (Ga,Mn)As, with the current record TC ~ 190 K [41], is not a viable candidate for RT ferromagnetism in DMS. Influential mean-field calculations [39] for DMS with 5% Mn in Fig. 8(a) show a strong correlation with an inverse unit cell volume [45]. However, ab initio studies reveal a more complex, material-dependent situation [46]. Instead of III-V compounds, more promising are recently discovered II-II-V DMS [47]. They are isostructural to both 122 class of high-temperature Fe-based superconductors and antiferromagnetic BaMn2As2, offering intriguing possibilities to study their multilayers with different types of ordering. In (Ba,K)(Zn,Mn)2As2 with an independent carrier (K replacing Ba) and spin doping (Mn replacing Zn), some of the previous limitations are overcome: the absence of carriers in II-VIs and the low-Mn solubility in III-Vs. With 30 % K and 15 % Mn doping, their TC ~ 230 K [48] exceeds the value in (Ga,Mn)As. Selected highest reliable experimental TC reported for Mn-doped DMS are shown in Fig. 8(b). Circles are given for GaN which has about 30 times smaller TC, than predicted in panel (a), and (Ba,K)Zn2As2, a current record for DMS. Ab initio studies predict a further increase in TC [49]. We expect that tunable RT carrier-mediated ferromagnetism will be realized in II-II-V DMS within 5 years. (m3.2) While DMS are often viewed as the materials for multifunctional devices to seamlessly integrate nonvolatile memory and logic [35], other device opportunities could be more viable. In fact, DMS-based optical isolators [50],[51] were already commercialized by Tokin Corporation [52]. Such devices, relying on large magneto-optical effects (Faraday and Kerr) that are proportional to the giant Zeeman splitting in DMS, are used to prevent feedback into laser cavities and provide one-way transmission of light. Even without demonstrating TC > RT, enhancing RT Zeeman splitting is important for DMS (exceeding a large g-factor ~ 50 for InSb).  \n Fig. 9.  Roadmap on dilute magnetic semiconductors.  Spin-lasers [53],[54] are another example of devices not limited to MR effects. They can outperform [55],[56] conventional lasers with injected spin-unpolarized carriers. For spin-lasers electrical spin injection is desirable, currently limited up to ~ 230 K [57]. TC > RT in DMS would be beneficial for such spin-lasers, both as an efficient spin injector and possibly a tunable active region that could alter the laser operation through tunable exchange interaction. To remove the need for an applied B-field, perpendicular anisotropy of the spin injector is suitable. We expect RT electrical spin injection in spin-lasers by 2020. It is important to critically assess if extrinsic TC > RT in DMS, from  \n 7 magnetic metallic nano-inclusions and secondary phases [having GaAs+MnAs, rather than (Ga,Mn)As, a true DMS] is a viable path for RT spintronic devices. RT magnetoamplification was demonstrated in (In,Mn)As-based magnetic bipolar transistor, operating above the TC < 100 K of a single-phase (In,Mn)As [58]. Another test for useful extrinsic (multiphase) DMS is a robust RT electrical spin injection. A road map for DMS is given in Fig. 9. IV.!PERPENDICULARLY ANISOTROPIC FERROMAGNETS A perpendicularly magnetised system is currently an important building block in spintronic devices since it enables us to shrink the size of memory bits and to reduce the electric current density required for spin-transfer switching. There are several ways to obtain perpendicular magnetic anisotropy in a thin film. To use an ordered alloy showing high magnetocrystalline anisotropy is one possible way. If its easy magnetisation axis is aligned along the normal direction to the film plane and the magnetocrystalline anisotropy field overcomes the demagnetisation field, the film shows the perpendicular magnetisation. Another way is to use the interface magnetic anisotropy between a ferromagnetic layer and a non-magnetic layer. In addition, multilayered structures are useful to obtain perpendicular magnetisation. Towards the perpendicularly anisotropic ferromagnet as a spintronic material, the following milestones have been established: (m4.1) High thermal stability of perpendicular magnetisation; (m4.2) Structural stability against the thermal process; (m4.3) Demonstration of high spin-polarisation; (m4.4) Reduction of the magnetic damping constant. (m4.1) means the stability of magnetisation at a nanometer scale overcoming the magnetisation fluctuation due to the thermal energy. Considering several thermal treatments in device fabrication processes, (m4.2) should be satisfied. (m4.3) is a key determining the performance of MTJ and GMR devices. In terms of spin-transfer torque (STT) magnetisation switching, as indicated in (m4.4), the magnetic damping should be small to reduce the electric current density for switching. An L10-ordered structure exists in the thermodynamically stable phase and is composed of the alternative stacking of two kinds of atomic planes along the c-axis. Thus, L10-ordered alloys, such as FePt, FePd, CoPt, MnAl and MnGa, exhibit uniaxial magnetic anisotropy along the c-axis direction. When one aligns the c-axis of L10-ordered structure in the normal direction to the film plane, a perpendicular magnetic anisotropy is obtained. Since the L10-ordered structure is thermally stable, L10-ordered alloys have an advantage from the viewpoint of (m4.2). Among the L10-ordered alloys, L10-FePt shows the largest uniaxial anisotropy (Ku) of 7 × 106 J/m3 [59], which leads to the excellent thermal stability of magnetisation at a reduced dimension, e.g., 4 nm diameter in L10-FePt nano-particles. This property satisfies (m4.1). Thanks to its perpendicular magnetisation for FePt (001) films, L10-FePt has been regarded as an ideal material for perpendicular recording media in a HDD. In addition, the spin polarisation of FePt is theoretically predicted to be approximately 70% [60], which is a good characteristic for a spintronic material. L10-ordered FePt films have already been implemented in both MTJ [61] and GMR [60] junctions. In the case of GMR nano-pillars consisting of two FePt layers separated by nonmagnetic Au, the STT phenomena have been examined systematically by tuning the crystalline order of the FePt layer [60]. However, the observed TMR and GMR ratios are still low for L10-FePt. Another important issue is that the major L10-ordered alloys contain the heavy transition metals such as Pt. The Pt atom shows strong spin-orbit coupling, which leads to the significant enhancement of magnetisation damping. This feature is an opposite trend to (m4.4). L10-FePd exhibits a large Ku and rather smaller damping constant compared with that of L10-FePt, probably because Pd is lighter element than Pt [62]. However, the usage of such noble metals as Pt and Pd is not suitable from the viewpoint of element strategic trend. Considering these recent demands, a new kind of L10-alloy is eagerly desired, which possesses a large Ku and a small damping constant. One of the candidates is L10-FeNi. Since a paper reported that an L10-FeNi bulk alloy exhibited high uniaxial magnetic anisotropy of Ku = 1.3 × 106 J/m3 [63], L10-FeNi is a future material having a possibility to substitute high Ku materials containing the noble metals and rare earths. Kojima et al. reported the preparation of L10-FeNi thin films with relatively high Ku of 0.7 × 1 06 J/m3 [64], and also the small damping constant has been reported in L10-FeNi [65]. Another candidate material showing perpendicular magnetisation is a Mn-based alloy system, such as L10-MnAl. Recently, epitaxial Mn-Ga films including L10 and D022 ordered phases have also been found to exhibit strong perpendicular magnetic anisotropy (Ku = 1.2-1.5×106 J/m3) with small saturation magnetisation (MS = 250-500 emu/cm3) and small magnetic damping (α = 0.0075-0.015) at RT [66],[67]. Moreover, it has been found that D022-Mn3Ge epitaxial films exhibited Ku of 0.91 × 106 J/m3 [68] and 1.18 × 106 J/m3 [69]. These Mn-based alloy systems can also be used as a perpendicular magnetised layer for STT-application because the ab-initio calculations predicted the high spin polarisation of 88% for Mn3Ga [70] and a half-metallic band dispersion for Mn3Ge that leads a high TMR like Fe/MgO-MTJs [71],[72]. However, the observed TMR ratios are also still low for L10-and D022-Mn-Ga [73]. Experimental realisation of high spin polarisation is essential for all the ordered alloys to achieve (m4.3). Multilayered structures, such as Co/Pt, Co/Pd, Co/Ni and so on, also show perpendicular magnetisation. The main origins for perpendicular magnetic anisotropy in the multilayered structures are as follows: (i) breaking the crystal symmetry at the interface, which leads to the interface magnetocrystalline anisotropy, (ii) the effect of magnetostriction due to the interface between different atomic planes, or (iii) interface alloying. Although the multilayered films show high magnetic anisotropy, we need to consider the stability of the layered  \n 8 structure against a thermal process. In some cases, the high temperature annealing degrades the layered structure and its magnetic properties, which should be improved for (m4.2). Mangin et al. [74], and Meng and Wang [75] also demonstrated the STT switching in CPP-GMR nano-pillars with perpendicularly magnetised Co/Ni and Co/Pt multilayers, respectively. As in the case of the ordered alloys, however, increasing MR effect and lowering magnetization damping are inevitable issues for the multilayered structures to achieve (m4.3) and (m4.4). To explore the adequate materials combination is one of the ways for the multilayered structure to solve the current problems. One of the new types of multilayering films is an artificial superlattice grown by using nearly mono-atomic-layer alternation of Co and Pt or Pd. Such ultrathin superlattice films had an annealing stability higher than that of conventional multilayering films [76].  \n Fig. 10.  Roadmap on the perpendicularly anisotropic films.  It has also been reported that the CoFeB/MgO junction shows perpendicular magnetic anisotropy [77]. The perpendicular magnetisation components of the CoFeB are induced at the MgO interface, which originates from the interface magnetic anisotropy. The perpendicularly magnetised CoFeB/MgO layers have a significant advantage because MgO-based tunnel junctions show high TMR ratio. Actually, it has also been demonstrated that a CoFeB/MgO/CoFeB stack with perpendicular magnetisation shows the TMR ratio over 120% and the low STT switching current of 49 µA at a 40-nm-diameter junction. This is a promising candidate as a building block for the MRAM cell. However, because the interfacial magnetic anisotropy constant is not large enough and a thin ferromagnetic layer is required to exploit the interface effect, the small volume of the magnetic layer may give rise to the thermal instability of magnetisation in a deeper sub-nanometer region. (m4.1) is an important step for the perpendicular anisotropic ferromagnets using the interface magnetic anisotropy. Also, perpendicularly magnetised Heusler alloy layers, where interface magnetic anisotropy is used, are attracting attention as an alternative perpendicularly magnetised system, which may lead to high spin polarisation (m4.3) and a low damping constant (m4.4). Recently, perpendicular magnetization and the TMR ratio of 132% at room temperature have been demonstrated using an ultra-thin Co2FeAl Heusler alloy/MgO/CoFeB MTJ [78]. V.!OVERVIEW In this roadmap, we have identified two key properties to develop new (and/or improved) spintronic devices. The first one is the half-metallicity at room temperature (RT), which can be achieved by clearing milestones to realise large MR and resulting large spin polarisation. The second one is the perpendicular anisotropy in nano-scale devices at RT. This is based on milestones, including large perpendicular magnetic anisotropy and small damping constant. Such development is expected to be achieved not only by the development of these alloys but also by the fundamental understanding on these properties using a well-studied test system, i.e., zincbelendes. As summarised in Fig. 11, we anticipate these materials investigated here to realise all Heusler and all oxides junctions. These can be implemented in next-generation MRAM and high-frequency devices within 35 years.  \n Fig. 11.  Roadmap for magnetic materials. ACKNOWLEDGMENT The authors wish to thank the Technical Committee of the IEEE Magnetics Society, who initiated this roadmap as the first exercise of this kind. AH and TS appreciate financial support by PRESTO-JST. AH also appreciates the financial support by EPSRC (EP/K03278X/1 and EP/M02458X/1) and EU-FP7 (NMP3-SL-2013-604398). SM thanks to a NEDO Development of an Infrastructure for Normally-off Computing Technology project and ASPIMATT (JST). IZ was supported by US ONR N000141310754, NSF ECCS-1508873, NSF ECCS-1102092 and NSF DMR-1124601. REFERENCES [1]!F. Heusler, “Über magnetische Manganlegierungen,” Verh. d. deut. Phys, Gesel. 5, 219 (1903). [2]!R. A. de Groot, F. M. Mueller, P. G. van Engen and K. H. J. Buschow, “New class of materials: half-metallic ferromagnets,” Phys. Rev. Lett. 50, 2024 (1983). [3]!T. Block, C. Felser, G. Jakob, J. Ensling, B. Mühling, P. Gütlich and R. J. Cava, “Large negative magnetoresistance effects in Co2Cr0.6Fe0.4Al,”! \n 9 J. Solid State Chem. 176, 646 (2003). [4]!K. Inomata, S. Okamura, R. Goto and N. Tezuka, “Large tunneling magnetoresistance at room temperature using a Heusler alloy with the B2 structure,” Jpn. J. Appl. Phys. 42, L419 (2003). [5]!I. Galanakis and P. H. Dederichs (Eds.), Half-Metallic Alloys (Springer, Berlin, 2005). [6]!A. Hirohata, M. Kikuchi, N. Tezuka, K. Inomata, J. S. Claydon, Y. B. Xu and G. van der Laan, “Heusler alloy/semiconductor hybrid structures,” Curr. Opin. Solid State Mater. Sci. 10, 93 (2006). [7]!I. Galanakis and P. H. Dederichs, “Slater-Pauling behavior and origin of the half-metallicity of the full-Heusler alloys,” Phys. Rev. B 66, 174429 (2002). [8]!J. Sato, M. Oogane, H. Naganuma and Y. Ando, “Large magnetoresistance effect in epitaxial Co2Fe0.4Mn0.6Si/Ag/Co2Fe0.4Mn0.6Si devices,” Appl. Phys. Express 4, 113005 (2011). [9]!A. Hirohata, J. Sagar, L. Lari, L. R. Fleet and V. K. Lazarov, “Heusler-alloy films for spintronic devices,” Appl. Phys. A 111, 423 (2013). [10]!S. Ikeda, J. Hayakawa, Y. Ashizawa, Y. M. Lee, K. Miura, H. Hasegawa, M. Tsunoda, F. Matsukura and H. Ohno, “Tunnel magnetoresistance of 604% at 300K by suppression of Ta diffusion in CoFeB/MgO/CoFeB pseudo-spin-valves annealed at high temperature,\"Appl. Phys. Lett. 93, 082508 (2008). [11]!Y. Sakuraba, J. Nakata, M. Oogane, H. Kubota, Y. Ando, A. Sakuma and T. Miyazaki, “Huge spin-polarization of L21-ordered Co2MnSi epitaxial Heusler alloy film,” Jpn. J. Appl. Phys. 44, L1100 (2005). [12]!N. Tezuka, N. Ikeda, F. Mitsuhashi and S. Sugimoto, “Improved tunnel magnetoresistance of magnetic tunnel junctions with Heusler Co2FeAl0.5Si0.5 electrodes fabricated by molecular beam epitaxy,” Appl. Phys. Lett. 94, 162504 (2009). [13]!A. K. Nayak, M. Nicklas, C. Shekhar and C. Felser, “Large zero-field cooled exchange-bias in bulk Mn2PtGa,” Phys. Rev. Lett. 110, 127204 (2013). [14]!M. Bibes and A. Barthelemy, “Oxide spintronics,” IEEE Trans. Elec. Dev. 54, 1003 (2007). [15]!J.-B. Moussy, “From epitaxial growth of ferrite thin films to spin-polarized tunnelling,” J. Phys. D: Appl. Phys. 46, 143001 (2013). [16]!L. J. Swartzendruber, “Properties, units and constants in magnetism,” J. Magn. Magn. Mater. 100, 573 (1991). [17]!S. P. Lewis, P. B. Allen and T. Sasaki, “Band structure and transport properties of CrO2,” Phys. Rev. B 55, 10253 (1997). [18]!R. J. Soulen Jr., J. M. Byers, M. S. Osofsky, B. Nadgorny, T. Ambrose, S. F. Cheng, P. R. Broussard, C. T. Tanaka, J. Nowak, J. S. Moodera, A. Barry, J. M. D. Coey, “Measuring the spin polarization of a metal with a superconducting point contact,” Science 282, 85 (1989). [19]!Y. Ji, G. J. Strijkers, F. Y. Yang, C. L. Chien, J. M. Byers, A. Anguelouch, G. Xiao and A. Gupta, “Determination of the spin polarization of half-metallic CrO2 by point contact Andreev reflection,” Phys. Rev. Lett. 86, 5585 (2001). [20]!J. M. D. Coey, A. E. Berkowitz, L. Balcells, F. F. Putris and A. Barry, “Magnetoresistance of Chromium dioxide powder compacts,” Phys. Rev. Lett. 80, 3815 (1998). [21]!A. Yanase and K. Siratori, “Band structure in the high temperature phase of Fe3O4,” J. Phys. Soc. Jpn. 53, 312 (1984). [22]!K. Siratori and S. Iida, “Magnetic property of MnxCr1−xO2,” J. Phys. Soc. Jpn. 15, 210 (1960). [23]!R. B. Flippen, “Applications of miniature coil, pulsed-field techniques to studies of magnetic phase transitions,” J. Appl. Phys. 34, 2026 (1963). [24]!C. A. F. Vaz, “Magnetization reversal in epitaxial FePt thin layers by spin-polarized current,” in Epitaxial Ferromagnetic Films and Spintronic Applications, A. Hirohata and Y. Otani (Eds.) (Research Signpost, Kerala, 2009) p. 145. [25]!A. V. Ramos, M.-J. Guittet, J.-B. Moussy, R. Mattana, C. Deranlot, F. Petroff, and C. Gatel, “Room temperature spin filtering in epitaxial cobalt-ferrite tunnel barriers,” Appl. Phys. Lett. 91, 122107 (2007). [26]!Y. K. Takahashi, S. Kasai, T. Furubayashi, S. Mitani, K. Inomata and K. Hono, “High spin-filter efficiency in a Co ferrite fabricated by a thermal oxidation,” Appl. Phys. Lett. 96, 072512 (2010). [27]!T. Niizeki, Y. Utsumi, R. Aoyama, H. Yanagihara, J. Inoue, Y. Yamasaki, H. Nakao, K. Koike and E. Kita, “Extraordinarily large perpendicular magnetic anisotropy in epitaxially strained cobalt-ferrite CoxFe3−xO4(001) (x=0.75, 1.0) thin films,” Appl. Phys. Lett. 103, 162407 (2013). [28]!H. Sukegawa, Y. Miura, S. Muramoto, S. Mitani, T. Niizeki, T. Ohkubo, K. Abe, M. Shirai, K. Inomata and K. Hono, “Enhanced tunnel magnetoresistance in a spinel oxide barrier with cation-site disorder,” Phys. Rev. B 86, 184401 (2012). [29]!S. Matzen, J.-B. Moussy, R. Mattana, K. Bouzehouane, C. Deranlot F. Petroff, “Nanomagnetism of Cobalt ferrite-based spin filters probed by spin-polarized tunneling,” Appl. Phys. Lett. 101, 042409 (2012). [30]!J. M. D. Coey, M. Viret and S. von Molnr, “Mixed-valence manganites,” Adv. Phys. 48, 167 (1999). [31]!Y. Tokura and Y. Tomioka, “Colossal magnetoresistive manganites,” J. Magn. Magn. Mater. 200, 1 (1999). [32]!R. von Hemlolt, J. Wecker, B. Holzapfel, L. Schults and K. Samwer, “Giant negative magnetoresistance in perovskitelike La2/3Ba1/3MnOx ferromagnetic films,” Phys. Rev. Lett. 71, 2331 (1993). [33]!M. Bowen, M. Bibes, A. Bartélémy, J.-P. Contour, A. Anane, Y. Lemaître and A. Fert, “Nearly total spin polarization in La2/3Sr1/3MnO3 from tunneling experiments,” Appl. Phys. Lett. 82, 233 (2003). [34]!D. Serrate, J. M. D. Teresa and M. R. Ibarra, “Double perovskites with ferromagnetism above room temperature,” J. Phys.: Condens. Matter. 19, 023201 (2007). [35]!I. Žutić, J. Fabian and S. D. Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys. 76, 323 (2004). [36]!T. Dietl, “A ten-year perspective on dilute magnetic semiconductors and oxides,” Nature Mater. 9, 965 (2010). [37]!H. Ohno, “A window on the future of spintronics,” Nature Mater. 9, 952 (2010). [38]!E. L. Nagaev, Physics of Magnetic Semiconductors (Mir, Moscow, 1983). [39]!L. Esaki, P. Stiles and S. von Molnar, “Magnetointernal field emission in junctions of magnetic insulators,” Phys. Rev. Lett. 19, 852 (1967). [40]!J. K. Furdyna, “Diluted magnetic semiconductors,” J. Appl. Phys. 64, R29 (1988). [41]!T. Dietl, H. Ohno, F. Matsukura, J. Cibert and D. Ferrand, “Zener model description of ferromagnetism in Zinc-blende magnetic semiconductors,” Science 287, 1019 (2000). [42]!M. Sawicki, T. Devillers, S. Galeski, C. Simserides, S. Dobkowska, B. Faina, A. Grois, A. Navarro-Quezada, K. N. Trohidou, J. A. Majewski, T. Dietl and A. Bonanni, “Origin of low-temperature magnetic ordering in Ga1-xMnxN,” Phys. Rev. B 85, 205204 (2012). [43]!H. Munekata, H. Ohno, S. von Molnar, A. Segmüller, L. L. Chang and L. Esaki, “Diluted magnetic III-V semiconductors,” Phys. Rev. Lett. 63, 1849 (1989). [44]!H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. End, S. Katsumoto and Y. Iye, “(Ga,Mn)As: A new diluted magnetic semiconductor based on GaAs,” Appl. Phys. Lett. 69, 363 (1996). [45]!I. Žutić, J. Fabian and S. C. Erwin, “Bipolar spintronics: Fundamentals and applications,” IBM J. Res. Dev. 50, 121 (2006). [46]!S. C. Erwin and I. Žutić, “Tailoring ferromagnetic chalcopyrites,” Nature Mater. 3, 410 (2004). [47]!K. Zhao, Z. Deng, X. C. Wang, W. Han, J. L. Zhu, X. Li, Q. Q. Liu, R. C. Yu, T. Goko, B. Frandsen, L. Liu, F. Ning, Y. J. Uemura, H. Dabkowska, G. M. Luke, H. Luetkens, E. Morenzoni, S. R. Dunsiger, A. Senyshyn, P. Böni and C. Q. Jin, “New diluted ferromagnetic semiconductor with Curie temperature up to 180K and isostructural to the ‘122’ iron-based superconductors,” Nature Commun. 4, 1442 (2013). [48]!K. Zhao, B. Chen, G. Q. Zhao, X. Li, Z. Yuan, Z. Deng, Q. Q. Liu and C. Q. Jin, “Ferromagnetism at 230K in (Ba0.7K0.3)(Zn0.85Mn0.15)2As2 diluted magnetic semiconductor,” Chin. Sci. Bull. 59, 2524 (2014). [49]!J. K. Glanbrenner, I. Žutić and I. I. Mazin, “Theory of Mn-doped II-II-V semiconductors,” Phys. Rev. B 90, 140403(R) (2014). [50]!K. Onodera, T. Masumoto and M. Kimura, “980 nm compact optical isolators using Cd1−x−yMnxHgyTe single crystals for high power pumping laser diodes,” Electron. Lett. 30, 1954 (1994). [51]!V. Zayets, M. C. Debnath and K. Ando, “Complete magneto-optical waveguide mode conversion in Cd1−xMnxTe waveguide on GaAs substrate,” Appl. Phys. Lett. 84, 565 (2004). [52]!Tokin Corporation, U.S. Patent No. 5, 757538 (26 May 1998). [53]!J. Rudolph, S. Döhrmann, D. Hagele, M. Oestreich and W. Stolz, “Room-temperature threshold reduction in vertical-cavity surface- emitting lasers by injection of spin-polarized electrons,” Appl. Phys. Lett. 87, 241117 (2005). [54]!M. Holub, J. Shin, D. Saha and P. Bhattacharya, “Electrical spin injection and threshold reduction in a semiconductor laser,” Phys. Rev. Lett. 98, 146603 (2007). [55]!J. Lee, R. Oszwałdowski, C. Gøthgen and I. Žutić, “Mapping between quantum dot and quantum well lasers: From conventional to spin lasers,” Phys. Rev. B 85, 045314 (2012).  \n 10 [56]!H. Höpfner, M. Lindemann, N. C. Gerhardt and M. R. Hofmann, “Controlled switching of ultrafast circular polarization oscillations in spin-polarized vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 104, 022409 (2014). [57]!D. Saha, D. Basu, and P. Bhattacharya, “High-frequency dynamics of spin-polarized carriers and photons in a laser,” Phys. Rev. B 82, 205309 (2010). [58]!N. Rangaraju, J. A. Peters and B.W. Wessels, “Magnetoamplification in a bipolar magnetic junction transistor,” Phys. Rev. Lett. 105, 117202 (2010). [59]!O. A. Ivanov, L. V. Solina, V. A. Demshina and L. M. Magat, “Determination of the anisotropy constant and saturation magnetization, and magnetic properties of powders of an iron-platinum alloy,” Phys. Met. Metallogr. 35, 81 (1973). [60]!T. Seki, S. Mitani and K. Takanashi, “Magnetization reversal in epitaxial FePt thin layers by spin-polarized current,” in Epitaxial Ferromagnetic Films and Spintronic Applications, A. Hirohata and Y. Otani (Eds.) (Research Signpost, Kerala, 2009) p. 255. [61]!S. Mitani, K. Tsukamoto, T. Seki, T. Shima and K. Takanashi, “Fabrication and characterization of L10-ordered FePt/AlO/FeCo magnetic tunnel junctions,” IEEE Trans. Magn. 41, 2606 (2005). [62]!S. Iihama, A. Sakuma, H. Naganuma, M. Oogane, T. Miyazaki, S. Mizukami and Y. Ando, “Low precessional damping observed for L10-ordered FePd epitaxial thin films with large perpendicular magnetic anisotropy,” Appl. Phys. Lett. 105, 142403 (2014). [63]!J. Paulevé, A. Chamberod, K. Krebs and A. Bourret, “Magnetization curves of Fe–Ni (50–50) single crystals ordered by neutron irradiation with an applied magnetic field,” J. Appl. Phys. 39, 989 (1968). [64]!T. Kojima, M. Mizuguchi, T. Koganezawa, K. Osaka, M. Kotsugi and K. Takanashi, “Magnetic anisotropy and chemical order of artificially synthesized L10-ordered FeNi Films on Au–Cu–Ni buffer layers,” Jpn. J. Appl. Phys. 51, 010204 (2012). [65]!M. Ogiwara, S. Iihama, T. Seki, T. Kojima, S. Mizukami, M. Mizuguchi and K. Takanashi, “Magnetization damping of an L10-FeNi thin film with perpendicular magnetic anisotropy,” Appl. Phys. Lett. 103, 242409 (2013). [66]!F. Wu, S. Mizukami, D. Watanabe, H. Naganuma, M. Oogane, Y. Ando and T. Miyazaki, “Epitaxial Mn2.5Ga thin films with giant perpendiculat magnetic anisotropy for spintronic devices,” Appl. Phys. Lett. 94, 122503 (2009). [67]!S. Mizukami, F. Wu, A. Sakuma, J. Walowski, D. Watanabe, T. Kubota, X. Zhang, H. Naganuma, M. Oogane, Y. Ando and T. Miyazaki, “Long-lived ultrafast spin precession in Manganese alloys films with a large perpendicular magnetic anisotropy,” Phys. Rev. Lett. 106, 117201 (2011). [68]!H. Kurt, N. Baadji, K. Rode, M. Venkatesan, P. Stamenov, S. Sanvito and J. M. D. Coey, “Magnetic and electronic properties of D022-Mn3Ge (001) films,” Appl. Phys. Lett. 101, 132410 (2012). [69]!A. Sugihara, S. Mizukami, Y. Yamada, K. Koike and T. Miyazaki, “High perpendicular magnetic anisotropy in D022-Mn3+xGe tetragonal Heusler alloy films,” Appl. Phys. Lett. 104, 132404 (2014). [70]!B. Balke, G. H. Fecher, J. Winterlik, and C. Felser, “Mn3Ga a compensated ferrimagnet with high Curie temperature and low magnetic moment for spin torque transfer applications,” Appl. Phys. Lett. 90, 152504 (2007). [71]!S. Mizukami, A. Sakuma, A. Sugihara, T. Kubota, Y. Kondo, H. Tsuchiura and T. Miyazaki, “Tetragonal D022 Mn3+xGe epitaxial films grown on MgO(100) with a large perpendicular magnetic anisotropy,” Appl. Phys. Express 6, 123002 (2013). [72]!Y. Miura and M. Shirai, “Theoretical study on tunneling magnetoresistance of magnetic tunnel junctions with D022-Mn3Z (Z=Ga, Ge),” IEEE Trans. Magn. 50, 1400504 (2014). [73]!T. Kubota, M. Araidai, S. Mizukami, X. Zhang, Q. Ma, H. Naganuma, M. Oogane, Y. Ando, M. Tsukada and T. Miyazaki, “Spin-dependent tunneling spectroscopy for interface characterization of epitaxial Fe/MgO/Fe magnetic tunnel junctions,” Appl. Phys. Lett. 99, 192509 (2011). [74]!S. Mangin, D. Ravelosona, J. A. Katine, M. J. Carey, B. D. Terris and E.E. Fullerton, “Current-induced magnetization reversal in nanopillars with perpendicular anisotropy,” Nature Mater. 5, 210 (2006). [75]!H. Meng and J. P. Wang, “Spin transfer in nanomagnetic devices with perpendicular anisotropy,” Appl. Phys. Lett. 88, 172506 (2006). [76]!K. Yakushiji, T. Saruya, H. Kubota, A. Fukushima, T. Nagahama, S. Yuasa and K. Ando, “Ultrathin Co/Pt and Co/Pd superlattice films for MgO-based perpendicular magnetic tunnel junctions,” Appl. Phys. Lett. 97, 232508 (2010). [77]!S. Ikeda, K. Miura, H. Yamamoto, K. Mizunuma, H. D. Gan, M. Endo, S. Kanai, J. Hayakawa, F. Matsukura and H. Ohno, “A perpendicular-anisotropy CoFeB–MgO magnetic tunnel junction,” Nature Mater. 9, 721 (2010). [78]!Z. C. Wen, H. Sukegawa, T. Furubayashi, J. Koo, K. Inomata, S. Mitani, J. P. Hadorn, T. Ohkubo and K. Hono, “A 4-fold-symmetry hexagonal Ruthenium for magnetic heterostructures exhibiting enhanced perpendicular magnetic anisotropy and tunnel magnetoresistance, Adv. Mater. 26, 6483 (2014).  Atsufumi Hirohata (M’01–SM’10) was born in Tokyo in 1971. He received his BSc and MSc in Physics from Keio University in Japan in 1995 and 1997, respectively. He then received his PhD in Physics from the University of Cambridge in the U.K. His major fields of study are spintronic devices and magnetic materials. Hirohata was a Post-Doctoral Research Associate at the University of Cambridge and the Massachusetts Institute of Technology. He then served as a Researcher at Tohoku University and RIKEN in Japan. He became a Lecturer at the University of York in the U.K. in 2007 and was promoted to be a Reader in 2011, followed by a Personal Chair appointment since 2014. He has edited Epitaxial Ferromagnetic Films and Spintronic Applications (Karela, Research Signpost, 2009) and Heusler Alloys (Berlin, Springer, 2015). Current research interests are spin injection in ferromagnet/semiconductor hybrid structures, lateral spin-valve devices, magnetic tunnel junctions and Heusler alloys. Prof. Hirohata is a member of the American Physical Society, Materials Research Society, Institute of Physics, Magnetics Society of Japan, Physical Society of Japan and Japan Society of Applied Physics. In the IEEE Magnetics Society, he served as a member of the Administrative Committee between 2012 and 2014, and is a member of the Technical Committee since 2010. Hiroaki Sukegawa received his MEng degree in materials science from Tohoku University, Sendai, Japan in 2004, and his PhD degree in Materials Science from Tohoku University, in 2007. He became a researcher at National Institute for Materials Science in 2007. He is currently a senior researcher of Magnetic Materials Unit, National Institute for Materials Science. His research interests include magnetic thin films and spintronics devices. Hideto Yanagihara received his BSc and MSc in Materials Science from Keio University in Japan in 1993 and 1995, respectively. He then received his PhD in Applied Physics from the University of Tsukuba in Japan. Yanagihara was a Post-Doctoral Research Associate at the University of Tsukuba and the University of Illinois at Urbana-Champaign. Current research interests are magnetic thin films and oxides. Prof. Yanagihara is a member of the American Physical Society, Japan Society of Applied Physics, Magnetics Society of Japan and Physical Society of Japan. Igor Žutić was born in Zagreb, Croatia in 1967. He received his BSc and PhD in Physics from the University of Zagreb, Croatia in 1992 and the University of Minnesota in 1998, respectively. He was a postdoc at the University of Maryland and at the Naval Research Lab. In 2005, he joined the University at Buffalo, The State University of New York, as an assistant professor and was promoted to an associate professor in 2009 and a full professor in 2013. Following the success of Spintronics 2001: International Conference on Novel Aspects of Spin-Polarized Transport and Spin Dynamics, at Washington, DC, which he proposed and chaired, he was invited to write a comprehensive review, Spintronics: Fundamentals and Applications, for the Reviews of Modern Physics. The review written with Jaroslav Fabian and Sankar Das Sarma is currently among the most cited articles on spintronics and magnetism. With Evgeny Tsymbal he co-edited Handbook of Spin Transport and Magnetism (Chapman and Hall/CRC Press, New York, 2011). His research interests include superconductivity, magnetism, and spintronic devices. Dr Žutić is a member of the American Physical Society and since 2013 of the Technical Committee in the IEEE Magnetics Society. He is a recipient of the 2006 National Science Foundation CAREER Award, 2005 National Research Council/American Society for Engineering Education Postdoctoral Research Award, and the National Research Council Fellowship (2003–2005). Takeshi Seki was born in Shizuoka, Japan in 1980. He received his BEng, MEng and PhD in Materials Science from Tohoku University in Japan in 2002, 2003 and 2006, respectively. His major field of study is the materials development for spintronic devices. Seki was a Post-Doctoral Researcher at Tohoku University and Osaka University in Japan. He then became an assistant professor at Tohoku University in 2010. Current research interests are spin transfer phenomena,  \n 11 magnetization dynamics in a nanosized region, and magnetization reversal mechanism. Shigemi Mizukami was born in Sendai, Japan in 1973. He received his BSc and MSc in Applied Physics from Tohoku University in Japan in 1996 and 1998, respectively. He then received his Ph. D in Applied Physics from the Tohoku University. His major fields of study are spintronic devices, high frequency magnetism, and magnetic materials. Mizukami was a Research Associate at the Nihon University and promoted to be a Lecturer in 2005. He then became an Assistant Professor at the Tohoku University in Japan in 2008, and then promoted to be an Associate Professor in 2011, and also to be a Professor in 2014. He was one of guest editors of special issues: Advancement in Heusler compounds and other spintronics material designs and applications (J. Phys. D: Appl. Phys., 2015). Current research interests are ultra-high frequency magnetization dynamics, low damping Heusler materials, perpendicular magnetic tunnel junctions based on Mn-based tetragonal Heusler-like alloys. Prof. Mizukami is a member of Magnetics Society of Japan, Physical Society of Japan, Japan Society of Applied Physics, and the Japan Institute of Metals and Materials. Dr. Raja Swaminathan is an IEEE senior member and is a package architect at Intel for next generation server, client and SOC products. His primary expertise is on delivering integrated HVM friendly package architectures with optimized electrical, mechanical, thermal solutions. He is also an expert in magnetic materials synthesis, structure, property characterizations and has seminal papers in this field. He is an ITRS author and iNEMI technical WG chair on packaging and design. He has also served on IEEE micro-electronics and magnetics technical committees. He has 13 patents and 18 peer reviewed publications and holds a Ph.D in Materials Science and Engineering from Carnegie Mellon University.  "    },    {        "title": "1510.00746v3.Magnetic_and_gaseous_spiral_arms_in_M83.pdf",        "content": "arXiv:1510.00746v3  [astro-ph.GA]  19 Nov 2015Astronomy& Astrophysics manuscriptno.M83˙2015.revised.3.arXiv c/circlecopyrtESO 2021\nApril2,2021\nMagnetic andgaseous spiralarms inM83\nP.Frick1,R.Stepanov1,R.Beck2⋆,D.Sokoloff3,A.Shukurov4,M. Ehle5, and A.Lundgren6\n1Institute of Continuous Media Mechanics, Korolyov str.1, 6 14061 Perm,Russia\n2MPI f¨ ur Radioastronomie, Aufdem H¨ ugel 69, 53121 Bonn, Ger many\n3Department of Physics,Moscow StateUniversity, Moscow, 11 7588, Russia\n4School of Mathematics and Statistics,Newcastle Universit y, Newcastle upon Tyne NE17RU, U.K.\n5XMM-Newton Science Operations Centre,ESAC,ESA,POBox 78, 28691 Villa nueva de laCa˜ nada, Madrid, Spain\n6Joint ALMA Observatory, Alonso de Cordova 3107, Santiago,C hile\nPreprintonline version: April 2,2021\nABSTRACT\nContext. The magnetic field configurations in several nearby spiral ga laxies contain magnetic arms that are sometimes located be-\ntweenthematerialarms.ThenearbybarredgalaxyM83provid esanoutstanding exampleofaspiralpatternseenintracers ofgasand\nmagnetic field.\nAims.Weanalyse the spatial distributionof magnetic fields inM83 and their relationtothe material spiral arms.\nMethods. Isotropicandanisotropic wavelettransforms areusedtode compose the imagesof M83invarious tracerstoquantifystru c-\ntures in a range of scales from 0.2 to10kpc. We used radio pola rization observations at λ6.2cm andλ13cm obtained withthe VLA,\nEffelsberg and ATCA telescopes and APEX sub-mm observations at 870µm, which are first published here, together with maps of\nthe emissionof warm dust, ionized gas,molecular gas, andat omic gas.\nResults.The spatial power spectra are similar for the tracers of dust , gas, and total magnetic field, while the spectra of the order ed\nmagnetic fieldare significantly di fferent. As a consequence, the wavelet cross-correlation bet ween all material tracers and total mag-\nnetic field is high, while the structures of the ordered magne tic field are poorly correlated with those of other tracers. T he magnetic\nfield configuration in M83 contains pronounced magnetic arms . Some of them are displaced from the corresponding material arms,\nwhileothers overlapwiththe materialarms.Thepitchangle s ofthe magnetic andmaterialspiralstructures are general lysimilar.The\nmagnetic field vectors at λ6.2cm are aligned with the outer material arms, while significa nt deviations occur in the inner arms and,\nin particular, in the bar region, possibly due to non-axisym metric gas flows. Outside the bar region, the typical pitch an gles of the\nmaterial and magnetic spiral arms are very close to each othe r at about 10◦. The typical pitch angle of the magnetic field vectors is\nabout 20◦larger thanthat of the materialspiral arms.\nConclusions. OneofthemainmagneticarmsinM83isdisplacedfromthegase ousarmssimilarlytothegalaxyNGC6946,whilethe\nothermainarmoverlaps agaseous arm,similartowhatisobse rvedinM51. Wepropose thataregular spiralmagnetic fieldge nerated\nbyamean-fielddynamo iscompressed inmaterialarmsandpart lyalignedwiththem.Theinteractionofgalacticdynamo act ionwith\na transient spiralpattern isa promising mechanism for prod ucing such complicated spiral patterns as inM83.\nKey words. magnetic fields –MHD –galaxies: ISM–galaxies: individual: M83 –galaxies:magnetic fields –galaxies: spiral\n1. Introduction\nM83 (NGC 5236) is the nearest barred galaxy and is well stud-\nied at all wavelengths, including polarized and unpolarize d ra-\ndio continuum emission that traces the interstellar magnet ic\nfield.EarlypolarizationobservationsofM83wereperforme dby\nSukumaret al. (1987) at the wavelengths λ92cm,λ20cm,and\nλ6.3cmataresolutionof33′′×55′′,whichcorrespondstoabout\n1.4×2.4kpc at the assumed distance to the galaxy of 8.9Mpc\n(Sandage&Tammann 1974)1, so that 1′≈2.6kpc. Significant\npolarizedemission has beendetected, indicatingthat the g alaxy\nhosts an ordered magnetic field approximately aligned with t he\nspiral arms. Sukumar&Allen (1989a,b) observed the galaxy\nwith the VLA at λ20cmat a resolution of 30′′×70′′and found\nthattheregionswherepolarizedemissionisstrongestarel ocated\noutside the prominent optical spiral arms. However, the res olu-\ntion of these observations was too low and Faraday depolariz a-\n⋆Corresponding author: e-mail: rbeck@mpifr-bonn.mpg.de\n1The distance toM83isnot wellknown; distance estimateslis tedin\ntheNASA/IPACExtragalacticDatabase(NED)rangebetween4.5Mpc\nand 14.6Mpc .tion at this wavelengthwas too strongto reach firm conclusio ns\nabout the spatial distribution of the ordered magnetic field and\nits relation to the material spiral pattern. Neiningeret al . (1991)\nobservedM83at λ2.8cmandfoundorderedfieldsalongthecen-\ntral bar and betweenthe innerspiral arms. The Faradayrotat ion\nmeasures between these wavelengths indicated a bisymmetri c\nfieldstructurepossiblydrivenbythebar(Neiningeret al.1 993).\nMorerecentobservationsat λ12.8cmwiththeATCAdatashow\nthe radio continuum emission from the bar and spiral arms in\ndetail(Figs.1 and2).\nOur aim is to determine the parameters of the spiral arms\nin M83, as seen in di fferent tracers, and to study their morpho-\nlogical relations. We are particularly interested in the re lative\npositions of gaseous and magnetic arms, especially those of the\nlarge-scale magnetic field. Beck &Hoernes (1996) discovere d\nthat the ordered magnetic field in the galaxy NGC6946, traced\nby polarized radio continuum emission, concentrates in wel l-\ndefined magnetic arms, which are interlaced with the gaseous\narms. The comparative morphology of the spiral patterns vis i-\nble in different tracers was discussed by Fricket al. (2000) who\nconfirmed the conclusions of Beck& Hoernes (1996) and de-\n1P.Fricket al.:Magnetic andgaseous arms inM83\nFig.1.Polarizedradiocontinuumintensity(contours)and Bvec-\ntors of M83 at λ6.17cm, obtained by combining data from the\nVLA and Effelsberg telescopes, overlayed on an optical image\nfromtheAnglo-AustralianObservatorybyDaveMalin.Thean -\ngularresolutionis22′′.Faradayrotationofthe Bvectorshasnot\nbeencorrected,butissmallbecauseoftheshortwavelength and\nthelowinclinationofthegalaxy.\ntermined such parameters as the pitch angle, width, and arm–\ninterarmcontrastforthemagneticarmsandthoseseeninopt ical\nredlight.AremarkablefeatureofthespiralpatterninNGC6 946\nis that the phase shift between the magnetic and stellar /gaseous\narmsismoreorlessconstantwithradius.Inotherwords,the two\nspiralarmsystemshavesimilarpitchanglesanddonotinter sect\ninthepartofthegalaxyexplored.\nThe phenomenonof magneticarmsmaybe commonamong\nspiral galaxies. It was first observed in the spiral galaxy IC 342\nby Krauseet al. (1989) (see also Krause 1993). However, the\nrelation between magnetic and gaseous arms in IC342 (Beck\n2015) and other galaxies is not as simple and clear-cut as in\nNGC6946. Another example is providedby M51 where the or-\ndered magnetic field is maximum at the spiral arms traced by\ndust lanes in some regions and displaced from them at other\nlocations (Fletcheret al. 2011). When applying a wavelet an al-\nysis with anisotropic wavelets, the pitch angle of the spira l\narms in M51 was found to vary with the galacto-centric radius\n(Patrikeevetal. 2006). Systematic shifts betweenthe spir al arm\nridges in gas, dust, and magnetic field indicate a time sequen ce\nthat isconsistent with thegaseousspiral armscausingcomp res-\nsionthatresultsina strongermagneticfield.\nTo assess theorigin,role,andsignificanceofmagneticarms\nandtheirrelationtomaterialarms,oneneedsasampleofgal ax-\nies with different spiral patterns. This paper adds one remark-\nable galaxy to this sample. We performed a systematic analys is\nofthespiralpatternsinM83usingancillarydataandnewobs er-\nvationsandisotropicandanisotropicwaveletanalysissim ilar to\nFig.2.Polarizedradiocontinuumintensity(contours)and Bvec-\ntors of M83 at λ12.8cm, observed with the ATCA telescope\nand overlayedonto an optical image fromthe Anglo-Australi an\nObservatory by Dave Malin. The angular resolution is 22′′.\nComparison with Fig. 1 shows that the Faraday rotation of the\nBvectorsissignificantatthiswavelength.\nthat of Frick etal. (2001) and Patrikeevetal. (2006). Our qu an-\ntitative methodsare free of restrictive ad hoc assumptions , such\nas logarithmicspirals with a fixed numberof arms and constan t\npitchangles.Tomakeouranalysismorecomprehensive,weus ed\npolarized radio continuum observations at λ6cm (Fig. 1) and\nλ13cm(Fig.2), whicharefirst publishedhere.\nThe main message from the analysis performed here is that\ntheconfigurationofmagneticandmaterialarmsinM83ispart ly\nsimilar to M51. In both galaxies, the magnetic arms overlapt he\nmaterial pattern in large areas but not everywhere. Of cours e,\nthe numbers of arms, their pitch angle, and other quantitati ve\nparametersarespecificforeachgalaxy.\n2. Thedata\n2.1. ATCAradiocontinuumobservations at λ13cm\nWe performed radio continuum observations of M83 with the\nAustraliaTelescopeCompactArray(ATCA)2,consistingofsix\nparabolicdishes,eachof22mindiameter,forminganeast-w est\nradiointerferometer.\nWe observed M83 with di fferent baseline configurations\n(Table 1), each observation session lasting 12hours to achi eve\nmaximum uvcoverage.The array was used in its five-telescope\ncompactconfigurationignoringthe longestbaselines(i.e. , com-\n2The Australia Telescope Compact Array is part of the Austral ia\nTelescope National Facility, which is funded by the Commonw ealth of\nAustralia foroperation as a National Facilitymanaged by CS IRO.\n2P.Fricket al.:Magnetic andgaseous arms inM83\nM83   RM(6cm/13cm) + Total Intensity (6cm)   HPBW=30\"\nLevs = 1 mJy/beam * (1, 2, 3, 4, 6, 8, 12, 16, 32, 64, 128)Declination (J2000)\nRight Ascension (J2000)13 37 15 00 36 45-29 46\n48\n50\n52\n54\n56\n58-40 -20 0 20 rad/m**2 40\nFig.3.Faraday rotation measures between λ6.17cm and\nλ12.8cm (colours) and total radio continuum intensity at\nλ6.17cm(contours).Theangularresolutionis 30′′.\nbinations with the Antenna 6) that are most prone to phase in-\nstabilities. The names of the configurations used in the tabl e\ngive approximately the largest baseline (750m) used for thi s\nproject. The full width at half maximum (FWHM) of the pri-\nmary beam at λ13cm is 22′, large enough to map the radio\nemission of M83 with an angular size of about 15′atλ20cm\n(Neiningeret al. 1993). Also, the sampling of the shortest b ase-\nlinesishighenoughto maptheextendedradioemission.\nEach antenna receiver was used in the 128MHz bandwidth\ncontinuum polarization mode. This bandwidth consists of 32\nseparately sampled channels. Linear polarization was meas ured\nusing the orthogonal XandYfeeds on each antenna. Two fre-\nquencies (IFs) and the two polarization channels at each fre -\nquencywererecordedsimultaneouslywith15stime resoluti on.\nFor all observations the phase centre was set at RA =\n13h37m00.s3,Dec=−29◦53′04′′(J2000), which included an\noffset of 1′south of the galaxy’s center, so as to place the ob-\nservational phase center away from the bright nuclear emiss ion\nof M83. This was done to check for systematic phase errors in\nthesynthesisarraythatwouldbevisiblearoundthephasece ntre.\nTo calibrate the observations of M83, the phase calibra-\ntor QSO J1313−333 (unresolved at our baselines) was ob-\nserved every half hour for about 5min. The primary calibrato r\nPKS 1934−638,observedfora shorttimeduringeachsynthesis\nrun, was used as an absolute flux density calibratorto which a ll\nothermeasurementswerescaled.\nData processing was done with the AIPS software pack-\nage. The data of linearly polarized intensity were calibrat ed\nwithintheMIRIAD(MultichannelImageReconstructionImag e\nAnalysisand Display) package.The calibratedvisibility d ata of\nM83 were converted into maps of the Stokes parameters I,Q,\nandU. The self-calibrationhasimprovedthe total-powerimage\nof Fig. 4 (Panel 8). The QandUmaps were combined into aTable 1.ATCA configurations used to obtain the λ13cm radio\ncontinuumdataofM83\nFrequency λConfiguration Dateof\n[MHz] [cm] observation\n2368 12.7 750A 28 /01/93\n2368 12.7 750B 08 /06/93\n2240 13.4 750B 08 /06/93\n2368 12.7 750C 08 /09/93\n2378 12.6 750C 08 /09/93\nmapofpolarizedintensity P=(Q2+U2)1/2(Fig.2andPanel10\nofFig.4).Thepositivebiasduetormsnoisehasbeencorrect ed\nfor the inner parts of the galaxy where the noise is smallest a nd\nalmostconstant.\nThe polarized emission at λ13cm is strongest in the outer\nregionsofthegalaxy.Thetypicaldegreesofpolarizationa re2%\nin the central region and 30% in the outer galaxy.In contrast to\nλ13cm, the polarized emission at λ6.2cm (Fig. 1) is strongest\nin the central region, confirming that Faraday depolarizati on is\nstrongest in this region (Neiningeret al. 1993). In both map s,\nthe rmsnoise increases with increasingdistance fromthe ma p’s\ncentre.\nComparisonofthepositionangles χoftheBvectorsbetween\nFigs. 1 and 2 reveals a generally clockwise rotation at λ13cm.\nWe computed classical Faraday rotation measures, defined as\nRM=∆χ/(λ2\n2−λ2\n1) (Fig. 3). Classical RMs are not reliable in\ntheinnerpartofthegalaxy( <3′radius)whereFaradaydepolar-\nizationisstrongat λ13cm.Intheouterdisk,RMs varybetween\nabout−60radm−2and+60radm−2.NosystematicvariationRM\nwith azimuthal angle, a signature of a large-scale regular m ag-\nnetic field in the disk, as in M51 (Fletcheret al. 2011) and in\nIC342 (Beck 2015), and no traces of spiral arms are found,\nwhichisnotsurprisingin viewofthesmall magneticfield com -\nponent of the disk field along the line of sight in a weakly in-\nclined galaxy like M83. Furthermore, the strong depolariza tion\natλ13cmintheinnerregionleadstodeviationsofFaradayrota-\ntion angle∆χfrom theλ2law, so that classical RMs are not re-\nliable and wide-band spectro-polarimetric data and applic ation\nof RM Synthesis (Brentjens&de Bruyn 2005) are required to\nmeasurethe large-scalefields.\nStill, the average rotation measure of ≃−11±18radm−2is\nusefulasameasureoftherotationintheforegroundofourMi lky\nWay. The correspondingrotation angle is ≃−2◦atλ6.2cm and\n≃−10◦atλ13cm. According to Oppermannet al. (2012), the\nforegroundRM fgaroundthepositionofM83is −34±10radm−2.\nSincethisvalueisanaverageoveramuchlargerarea,thedi ffer-\nence could be due, for example, to Faraday rotation in the hal o\nofM83orto localvariationsinRM fgoftheMilkyWay.\n2.2. APEXsub-mmobservations ofcold dust\nThe870µmdatawereobtainedwiththeLargeAPEXBolometer\nCamera (LABOCA) (Siringoet al. 2009), a 295-pixel bolome-\nter array for continuum observations, operated at the Ataca ma\nPathfinder Experiment 12m-diameter telescope (APEX)3\n(G¨ ustenetal. 2006) at Chanjantor, Chile. We observed M83 i n\nJune, August, and September 2008 in excellent weather condi -\n3APEX is a collaboration between the Max-Planck-Institut f¨ ur\nRadioastronomie, the European Southern Observatory, and t he Onsala\nSpace Observatory.\n3P.Fricket al.:Magnetic andgaseous arms inM83\nFig.4.Maps of various tracers in M83: material tracers (H II, HI, CO, total neutral gas, warm dust, and cold dust) and tracers of\nthetotal magneticfield (mainlyits small-scalepart)(I6an dI13)anditsorderedcomponent(P6, P13,andP6 +P13),asindicatedin\nthe upperright cornerof each frame.The coordinatesare giv enin kpc, the intensity unitsare arbitraryunits (H II), 1020cm−2(HI),\nK km/s(CO), 1020cm−2(gas), MJy/sterad (warm dust), Jy /beam (cold dust), µJy/beam (radio I6, I13, P6, P13, P6 +P13). The axis\nscalesareinkpc.\n4P.Fricket al.:Magnetic andgaseous arms inM83\ntions(theprecipitablewatervapourcontentrangedfrom0. 1mm\nto0.4mm).\nM83wasmappedinthespiralrastermode(inthefive-of-the-\ndicepattern),providingafullysampledmapofthesize25′×25′\n(compared to the LABOCA field of view of 11′×11′) in each\nscan.Thetotalon-sourceintegrationtimewasabout11.5ho urs.\nThedatawerecalibratedbyobservingMarsandUranustogeth er\nwith the secondarycalibrator J1246-258,and the flux scale w as\nfound to be accurate within 15%. The data were reduced us-\ningtheBOA(BOlometerarrayAnalysis)software(Siringoet al.\n2009;Schulleretal.2009).Afterflaggingoutbadandnoisyp ix-\nels, the data were de-spiked, and correlated noise was remov ed\nfor each scan. Then the 280 scans were combined(weightedby\nthe squared rms noise) to produce the final map shown in the\ncolddustpanelofFig. 4.\n2.3. Otherdata\nIn this paper the following data were used, referred to in Fig . 4\nasindicatedbelow:\n–Hii(Hα), ionized hydrogen: 3.9m telescope of the Anglo-\nAustralian Observatory (AAO) with the TAURUS II focal\nreducer,observedon20May1990(S.Ryder,priv.comm.);\n–Hi, neutralhydrogen:VLA (Tilanus& Allen1993);\n–CO, molecular hydrogen (traced by CO): SEST\n(Lundgrenetal. 2004);\n–Gas, totalneutralgas(H I+CO)(Lundgrenet al. 2004);\n–Warmdust ,infraredemissionofwarmdustat12–18 µm:ISO\n(Vogleretal. 2005);\n–Cold dust , sub-mm emission of cold dust at 870 µm\n(Section2.2);\n–I6, total radio continuumintensity at λ6cm, combinedfrom\nVLAandEffelsbergmapsintotalintensity(seeVogleret al.\n2005,fordetails);\n–P6andP13, linearly polarized radio continuum intensity at\nλ6cmandλ13cm(Figs.1and2).\nThe infrared (warm dust) and H IImaps provide a proxy to\nthestar-formationrateinthestarburstregions(mainlyin thebar\nregion) and elsewhere. Total radio continuum intensity has two\ncomponents,a nonthermal(synchrotron)component,a trace rof\nthecomponentsofthetotal(turbulent +ordered)magneticfields\nin the sky plane, and a thermal component, contributing abou t\n12%inM83at λ6cm(Neiningeret al.1991),whichisneglected\ninthispaper.\nLinearly polarized radio continuum intensity has a purely\nsynchrotronorigin.Itisatraceroforderedmagneticfields witha\npreferredorientationwithinthetelescopebeamifFaraday depo-\nlarization is small, which is generally the case in M83 at λ6cm\nandalsointhe outerdisksofM83at λ13cm.\nThe orientationsofpolarization“vectors”are ambiguousb y\nmultiplesof180◦.Asaconsequence,theorderedmagneticfields\nas traced by linearly polarized emission can be either “regu lar”\nfields,preservingtheirdirectiononlargescales,“anisot ropictur-\nbulent”, or “anisotropic tangled” fields with multiple field re-\nversalswithin the telescope beam.To distinguishbetween t hese\nfundamentallydifferenttypesofmagneticfieldsobservationally,\nadditional Faraday rotation data is needed. Faraday rotati on is\nonly sensitive to the component of the regular field along the\nline of sight. Owing to the irregular distribution of Farada y ro-\ntation measuresin M83(Fig. 3), we cannot distinguishbetwe en\nthecomponentsoforderedfields.\nThe maps of total emission at λ6cm andλ13cm (I6 and\nI13), representing the total magnetic field, are very simila r, sothat theλ13cm map was not used for our analysis. The ther-\nmal contributionto the total radio emission of spiral galax iesat\nthese wavelengths is generally less than 20% (Tabatabaeiet al.\n2007).ThedegreeofpolarizationinM83islargelybelow20% at\nλ6cm(Neiningeretal.1993)andevenlowerat λ13cm(Fig.2).\nThe total radio emission at both wavelengths is thus dominat ed\nby unpolarized synchrotron emission from turbulent magnet ic\nfields.\nOn the other hand, the maps of polarized emission at λ6cm\nandλ13cm (P6 and P13), representing the ordered magnetic\nfield, are different. The signal-to-noise ratio is higher at λ13cm\nbecause of the steep synchrotron spectrum, but Faraday depo -\nlarization is also stronger at this wavelength. As a result, the\npolarized emission at λ13cm (Fig. 2) emerges mostly from the\nouter regionsof the galaxy, while the lower sensitivity at λ6cm\n(Fig. 1) restrictsthe detected polarizedemission to the in nerre-\ngions. The sum 1 .91P6+P13 (P6+P13 in the following, see\nFig. 4), where P6 is scaled by a factor of 1.91 to account for\nthe average synchrotronspectral index of −0.9 (Neiningeret al.\n1993),isusedtorepresentthepolarizedemissionfromthew hole\ndiskofM83.Thisproceduregiveshigherweightstotheregio ns\nat intermediate distances from the centre that are seen in bo th\npolarizationimages,butthisisnotrelevanttothepurpose ofthis\npaper.\nAllthemapsweresmoothedtoacommonresolutionof12′′,\ncorresponding to 0 .52kpc at the assumed distance to M83, ex-\ncept for the CO map that has a resolution of 23′′. As a conse-\nquence,themapoftotalneutralgasalsohasaresolutionof2 3′′.\nAll maps and their wavelet transformspresented here are in t he\nsky plane: the galaxy is oriented nearly face-on, making a ne g-\nligible correction for its inclination to the line of sight ( 24◦–\nTilanus&Allen1993).\n3. Themethod\nIn image analysis, wavelet-based methods are used to decom-\npose a map into a hierarchy of structures on di fferent scales.\nWavelets are a tool for data analysis based on self-similar b asis\nfunctions that are localized well in both the physical and wa ve-\nnumber domains. The localization of the basis functions in t he\nphysicalspacedistinguishesthewavelettransformfromth eoth-\nerwiseconceptuallysimilarFouriertransform.One-dimen sional\nandisotropicmulti-dimensionalwavelettransformsareba sedon\nthe space-scale decomposition of the data. (In other words, the\nfamilyofwaveletshastwoparameters,thelocationandthes cale\nof the basis function.) Using the continuous isotropic wave let\ntransform,a2Dimageisdecomposedintoa3Dcubeofwavelet\ncoefficients(obtainedfromthecontinuouswavelettransformby\nsampling it at a discrete set of scales) with the scale as the a d-\nditional, third dimension. Cross-sections of the cube are s lices\nthat contain the image details on a fixed scale. As a result, th e\nwavelettransformpreservesthelocalpropertiesoftheima geon\nallscales.Ifrequired,theoriginalimagecanbesynthesiz edfrom\nthe cube by summing over all scales. (This procedure is calle d\ntheinversewavelettransformation.)\nAnanisotropic wavelet transform is the convolution of the\nimage with a set of wavelets having di fferent locations, sizes,\nandorientations . Such a family of basic functions is generated\nby the translations, dilations, and rotationsof the basic w avelet.\nApplying the two-dimensional anisotropic wavelet transfo rm\nto an image generates a four-dimensional data set that repre -\nsents a space-scale-orientation decomposition.Fixing th e space\nand scale parameters – based on some objective criteria – en-\nables one to track the orientation of an elongated structure .\n5P.Fricket al.:Magnetic andgaseous arms inM83\nAn extended description of the continuum wavelet transform\ncan be found in various books, for example, in Holschneider\n(1995). In extragalactic radio astronomy, galactic images have\nbeen analysed using isotropic wavelets by Fricket al. (2001 );\nTabatabaeiet al. (2007, 2013a) and anisotropic wavelets by\nPatrikeevet al.(2006).\nBoth isotropic and anisotropic 2D wavelets can be con-\nstructed from a popular real-valued wavelet, the Mexican Ha t\n(MH). In 1D, the MH is given by ψ(x)=(1−x2)exp(−x2/2).\nThe MH can be generalizedto 2D, leading to an isotropic basis\nfunction,\nψ(r)=(2−r2)exp/parenleftBig\n−r2/2/parenrightBig\n, (1)\nwherer=(x2+y2)1/2. Another possibility is an anisotropic\nwaveletobtainedbysupplementingthe1DMHinonedimension\nwitha Gaussian-shapedwindowalongthe otheraxis.Theresu lt\nis an anisotropic wavelet introduced by Patrikeevet al. (20 06),\ncalledtheTexanHat (TH):\nψ(x,y)=(1−y2)exp/parenleftBigg\n−x2+y2\n2/parenrightBigg\n. (2)\nThis wavelet is sensitive to the structures elongated along the\nlocalx-axis.Rotationin the( x,y)-plane,x→(xcosϕ+ysinϕ),\nandy→(ycosϕ−xsinϕ) in Eq. (2), introduces the angle ϕ\ncountedfromthe x-axisinthecounterclockwisedirectionasthe\nwavelet parameter. Finally, a set of basis functions of di fferent\nsizes and orientations is obtained by applying both dilatio n and\nrotation to the basic wavelet. Since the TH is a symmetric wit h\nrespecttorotationby180◦,ψϕ(x,y)=ψϕ+π(x,y),itissensitiveto\ntheorientation of an elongatedstructure but not to its direction,\nwhich could be defined for structures in vector fields, such as\nmagnetic field or velocity. The anisotropy of the TH makes it\nespecially convenient in analyses of galactic spiral patte rns. A\ndetailed description of the technique and the illustration of how\nit works with test images and the spiral structure maps of the\ngalaxyM51weregivenbyPatrikeevet al.(2006).\nThe continuous wavelet transform of a 2D map f(x),x=\n(x,y),is definedby\nW(a,ϕ,x)=1\naκ/iintegdisplay\nRf(x′)ψϕ/parenleftBiggx′−x\na/parenrightBigg\nd2x′, (3)\nwhere the integration is extended over the image area R, and\nthe normalization factor a−κallows one to fine-tune the inter-\npretation of the wavelet transform: κ=3/2 is for direct com-\nparison of the wavelet spectra to the Fourier spectra, where as\nκ=2, used here, ensuresthat a power-lawapproximationto the\nwavelet spectrum has the same exponent as obtained from the\nsecond-order structure function (Fricket al. 2001). In the case\nofanisotropicwavelet, ϕshouldbe omittedinEq.(3).\nThemaximumvalueofthewavelettransform W(a,ϕ,x)over\nall positionangles ϕfora givenscale a,\nWm(a,x)=max\n0≤ϕ≤πW(a,ϕ,x), (4)\ncan be used to quantify the anisotropic fraction of structur es\nidentifiableintheimage.Theorientationoftheanisotropi cstruc-\ntureis thengivenby thecorrespondingvalueof the position an-\ngle,ϕm,suchthat Wm=W(a,ϕm,x).\nThe distribution of the energy content of the signal, f2, on\nthe scales and at the orientations can be characterized by th e\nwavelet power spectrum , defined as the energy density of thewavelettransformonscale aandatorientation ϕintegratedover\ntheimage,\nM(a,ϕ)=/iintegdisplay\nR|W(a,ϕ,x)|2d2x. (5)\nTheisotropicwaveletspectrumis obtainedas\nM(a)=/iintegdisplay\nR|W(a,x)|2d2x, (6)\nwhere the wavelet coe fficientsW(a,x) are obtained using the\nisotropicwavelet (1).\n4. Results\nWe applied the MH and TH wavelet transforms to the maps of\nM83presentedinSection2withtheaimofidentifyingstruct ures\n(and their orientation,if appropriate)revealedin variou stracers\nwithparticularemphasisonthespiralstructure.\n4.1. Isotropicwavelets: spectra andcorrelations\nWe start our analysis with the wavelet spectra M(a) calculated\nfor each tracer using the isotropic MH, Eq. (1). Our aim here i s\ntocomparethedominantspatialscalesofthedi fferentmaps,i.e.,\nthe scales at which the wavelet powerspectra havea maximum.\nThemagnitudesofthemaximaarenotinformativebecausethe y\ndepend on the signal intensities measured in di fferent units in\nsomemaps.Topresenttheresultsinoneplot,wemultipliede ach\nspectrum by a factor chosen to avoid excessive overlapping o f\nthecurves.TheisotropicMHpowerspectraareshowninFig.5 .\nThe spectra reveal that the distribution of the ISM seen in\nvarioustracersischaracterizedbycertaindominantscale s.4The\nmaximum at the largest scales corresponds to the size of the\ngalaxy as a whole, 2 a≈10′in both polarized emission (either\nλ6cm orλ13cm) and H I. The images of I6, dust, total neutral\ngas, and H IIare more compact, and the corresponding spectral\nmaximum appears on smaller scales, 2 a≈5′–7′. The decrease\nin the spectra on the largest scales occurs due to the large vo id\nareasin thesignalmaps.\nMaxima on smaller scales are producedby structuresinside\nthegalacticimage,bar,andspiralarms.Amaximumonthesca le\n2a≈0.7′is prominent in I6, dust, CO, and total neutral gas.\nThe spectrum of H IIalso has a local maximum on this scale,\nbut it is much broader and extends down to 2 a≈0.4′. The sec-\nondmaximumofthe polarizedintensityspectrumat λ6cm(P6)\nis at 2a=0.4′, probably reflecting sharp features in the bar.\nRemarkably,the spectrumof the othermagnetic field tracer, the\npolarized emission at λ13cm (P13), is quite di fferent when it\ngrows with areaching a weak maximum at 2 a≈3′. The P13\nmap contains large structures that are absent in the other ma ps.\nThisscale canbe related to the outer,broadspiral arms. The HI\nspectrum is nearly flat on small scales with a weak, broad max-\nimum at 0.2′<2a<1′. The values of the peak scales should\nbe considered with an uncertainty of about 20% because of the\nlimitedscale resolutionofthe wavelet.\nThewaveletcross-correlationbetweentwomaps(1and2)is\ndefinedas(seeFricket al. 2001)\nrw(a)=/iintegtext\nRW1(a,x)W2(a,x)d2x\n[M1(a)M2(a)]1/2, (7)\n4Thescaleofastructureusedhere,2 a,representsthediameterrather\nthanthe radius of the structure.\n6P.Fricket al.:Magnetic andgaseous arms inM83\nFig.5.Wavelet powerspectraoftheM83images,obtainedwith\nthe isotropic 2D Mexican Hat from bottom to top: H II, HI, CO,\ntotal neutral gas, warm dust, cold dust, total synchrotron i nten-\nsity atλ6cm, polarizedintensityat λ6cm, polarizedintensityat\nλ13cm,andaweightedsumofthepolarizedintensitiesat λ6cm\nandλ13cm defined in Section 2.3. All the spectra have been\nmultiplied by various factors chosen to avoid overcrowding of\nthecurves:whatmattersistherelativedistributionofthe wavelet\nspectral power between scales in a given image rather than th e\nrelativepowerindi fferentimages.Errorbarsareevaluatedfrom\nthevarianceofthesamplemean.\nwheretheintegrationiscarriedoverthemaparea.Thisquan tity,\ndesigned to characterize scale-by-scale correlations in M aps 1\nand2,issensitivetostructuresinthetwomapsthathavesim ilar\nscales and a similar position, but may not overlapas do, for e x-\nample,spiral arm segmentswith a relativeshift in position .The\nstandard cross-correlation function fails to detect such s ubtle\ncorrelations, whereas examples presented by Fricket al. (2 001)\ndemonstratetheefficiencyofthe waveletcross-correlation.\nThe wavelet correlations have been calculated for all pairs\noftracersin the wholescale rangeavailable.Figure6shows the\ncross-correlationsofthe total neutralgasandall othertr acersin\nthe upper panel, whereas the lower panel is for the scale-wis e0.2 0.5 1.0 2.0 5.0 10.0/Minus0.20.00.20.40.60.81.0\nGas\nPI6I6\nHIHIICO\nDust\nPI6/PlusPI13\nPI13\n0.2 0.5 1.0 2.0 5.0 10.0/Minus0.20.00.20.40.60.81.0\nPI6/PlusPI13\nPI6\nI6HI\nHIIGasCO\nDustPI13\nFig.6.Wavelet cross-correlations between the M83 maps as a\nfunctionofscale(inarcmin).Correlationsbetweenthetot alneu-\ntral gas and other tracers (H II, HI, warm dust, I6, P6 +P13) are\nshownintheupperpanelandcorrelationsofthepolarizedem is-\nsionwithothertracersinthelowerpanel.\nI \nII c \nc \nb b \na \na \nFig.7.Schematicrepresentationofthespiralarmsandbar(thick\nsolid line) in M83. Each of the two arms (labelled I and II) is\nseparated into three sections, labelled as a, b, and c and sho wn\nas solid, dotted, and solid lines, respectively. The backgr ound\nimage represents the cold dust distribution. The axis scale is in\nkpc,assumingthedistancetoM83of8.9Mpc.\ncross-correlation between the polarized emission P6 +P13 and\nall othertracers.\nThe tracers of matter (gas and dust) are more or less well\ncorrelated with each other. Not surprisingly, since they ar e not\nindependent, this is true at all scales for the CO and the tota l\nneutral gas. Dust, H IIand H Ihave maximum correlation with\n7P.Fricket al.:Magnetic andgaseous arms inM83\nGas\n/Minus15/Minus10/Minus5 0 5 10 15/Minus15\n/Minus10\n/Minus5\n0\n5\n10\n15\n1. 2.5 4. 5.5 7.\n/Multiply102\nGas\n/Minus15/Minus10/Minus5 0 5 10 15/Minus15\n/Minus10\n/Minus5\n0\n5\n10\n15\n0.6 1.3 2. 2.7\n/Multiply102\nFig.8.Anisotropicwavelettransformsofthetotalneutralgason\nthe scales 2 a=0.7′(top) and 1.4′(bottom).The wavelet orien-\ntation angles are shown by bars whose lengths are proportion al\nto the magnitudesof the wavelet transform. The axis scale is in\nkpc.\nthe total neutral gas near the scale 0 .7–0.9′(1.8–2.3kpc). The\ncorrelation coefficient for dust and gas is about 0 .7,while the\ncorrelation coefficient of H Iand the total gas is below 0 .4). In\na striking contrast,the orderedmagnetic field tracers are a lmost\nuncorrelatedwiththetotalneutralgasanddustonscalesup to2′\nandevenexhibitsomeanticorrelation(e.g.gasversusP13o nthe\nscale of about 2′and P6+P13 versus H IIon the scale of about\n1.5′).\nThe correlations between particular tracers can be summa-\nrized as follows. (We do not show all the plots.) The correla-\ntion between the total radio continuum (I6) and infrared (wa rm\ndust) intensities is high on all scales, similar to the situa tion\nin NGC6946 (Fricketal. 2001; Tabatabaeietal. 2013b) and\nM33 (Tabatabaeiet al. 2013a); this can be explained by the\ncontributions of thermal radio emission and synchrotron em is-\nsion from magnetic fields that are closely related to molecu-\nlar gas (Niklas&Beck 1997). The correlation between the ra-\ndio synchrotron and infrared intensities is known to be wors e\non small scales due to the propagation of cosmic-ray electro ns\n(Tabatabaeiet al.2013a),sothatthecorrelationcoe fficientisex-\npected to be below 0.5 on scales that are smaller than the cos-\nP6\n/Minus15/Minus10/Minus5 0 5 10 15/Minus15\n/Minus10\n/Minus5\n0\n5\n10\n15\n0.6 1.3 2. 2.7 3.4\n/Multiply102\nP6\n/Minus15/Minus10/Minus5 0 5 10 15/Minus15\n/Minus10\n/Minus5\n0\n5\n10\n15\n0.2 0.6 1. 1.4 1.8\n/Multiply102\nFig.9.As in Fig. 8 but for P6, the polarized radio emission at\nλ6cm.\nmic ray diffusion scale along the large-scale magnetic field of\nabout0.2′or0.5kpc.Theratiooftheorderedandturbulentfield\nstrengths q≈0.5followsfromtheaveragedegreeofsynchrotron\npolarization of p≈20% in the M83 disk at λ6cm using the re-\nlation between pandqfor a uniform cosmic-ray distribution\n(Eq.(2)inBeck2007)(underperfectequipartitionbetween cos-\nmicraysandmagneticfield, q≈0.43).Withtheformervalueof\nq, M83 fits the relation between the parallel di ffusion scale and\nthe degree of field orderingfoundby Tabatabaeietal. (2013a )).\nAmoredetailedanalysiswouldneedaseparationofsynchrot ron\nand thermal radio emission, which is beyond the scope of this\npaper.\nThecorrelationbetweenH IIandinfrared(warmdust)inten-\nsities is also high on all scales, except for a minimum around\n2′, probably because of the bar that is bright in the infrared bu t\nweakinH II.\nTheI6,dust,andH IImapsdisplayhighcorrelationsonsmall\nscales (rw>0.5 for 0.2′<2a<1′), where correlations of the\nother tracers are weak. The maps of polarized intensity P6 an d\nP13 display quite di fferent properties. The P6 map shows lit-\ntle correlationwith most tracers on all scales, except the l argest\nones, and an anticorrelationwith H Ion the scale 2 a≈2.5′. All\ncorrelations with P13 show an absence of correlation on smal l\nscales and have a deep minimum (anticorrelation) on the scal e\n8P.Fricket al.:Magnetic andgaseous arms inM83\nofabout3′withH II,dust,CO,andI6(butnotwithH I).Wenote\nthatP13andH Iarethetwomapswithemissiondistributedover\nthe largest areas, but just this pair of maps gives the minimu m\ncorrelationoverthewholerange0 .2′<2a<4′(neithercorrela-\ntion nor anticorrelation).The highest anticorrelation( rw≈−0.4\nis found between H IIand P13 at 2 a≈3′. The H IIand P6 have\na weaker anticorrelation, r≈−0.2 at 2a≈1.7′. The anticor-\nrelation with H IIaround this scale indicates a general shift be-\ntween the optical and magnetic spiral arms, similar to the sh ift\ninNGC6946(Fricket al.2001).\nOn scales of≤0.7′, corresponding to the maximum in the\nspectrumofP6, the emission emergesfromthe innerpartof th e\ngalaxy.InP13,however,theemissionfromthecentralparto fthe\ngalaxyisstronglysuppressedbyFaradaydepolarization,a ndthe\nlargerscales attributedto the outerpartsof the galaxydom inate\nin the wavelet spectrum. Thus the anticorrelation with P13 i s\nprobablytheeffectofdepolarization.\n4.2. Materialversus magneticpatterns\nA more detailed comparison of the spatial patterns in the int er-\nstellar matter and magnetic fields is facilitated by the use o f the\nanisotropic wavelet introduced in Section 3. It is convenie nt to\nintroduce a simple reference pattern of the dominant materi al\nstructuresshowninFig.7thatincludestwospiralarms,lab elled\nArmsIandII,emergingfromtheoppositeendsofthebarshown\nby a thick straight line in the figure. Each arm is divided into\nthreesegments,a,b,andc,becausesomeofthemarenotvisib le\ninall thetracersconsideredhere.\nAn anisotropic wavelet transform is useful on those scales\nwhere the spatial structures are clearly elongated, i.e., o n the\nscalescomparableto andexceedingtheirthickness,0 .5′<2a<\n2′in the case of M83. Figure 8 shows the anisotropic wavelet\ntransform of the total neutral gas distribution obtained wi th the\nTH wavelet. A similar map for the polarized intensity P6 is\nshowninFig.9.Weselectedtworepresentativescalestosho win\nthesefigures,2 a≈0.7′and1.4′assuggestedbythepowerspec-\ntra of Fig. 5. The maximum value Wmof the wavelet transform\nover all position angles ϕon a given scale is shown as colour-\ncoded, whereas the correspondingwavelet orientation angl eϕm\nisindicatedwith abar.\nFigures 8 and 9 demonstrate clearly that the distribution of\npolarizedradioemissionismorestructuredthanthatofthe tem-\nplatepattern(Fig.7).Onthesmallerscale,0 .7′,thebarispromi-\nnentinthetotalneutralgas,whereasthepolarizedstructu resare\noffset from the bar axis and are hardly aligned with it. Their\noverallpattern is similar to the barredgalaxyNGC1097, whe re\nit suggests the amplification of magnetic fields by compressi on\nand shearing gas flow in the dust lanes displaced from the bar\naxis(Becket al. 2005).\nOnthelargerscale,1 .4′,mostfeaturesvisibleonthesmaller\nscale remain, although some smaller structures of the upper\npanel have merged on this larger scale. The P6 map has a well-\npronounced long arm extended from west to north in the outer\npart of the image (Part c of Arm I) apparently merging with\nArm II in the east, but this appearsto be an artefact of strong er,\npositively biased noise in polarized emission at large dist ances\nfromthemapcentrethata ffectsthe wavelettransform.\nThe patternsisolated with the anisotropicTH wavelet in the\nmaterialtracersarecomparedwiththoseintheorderedmagn etic\nfieldinFig.10wherethetotalneutralgasdensityischosena sthe\nreferencevariable.Inallthepanels,thesolidlinecorres pondsto20% of the maximum intensity in the arm region.5Arm II is\nvery visible in all three segments (IIa, IIb, and IIc) in the g as\ndistribution. The CO distribution on this scale is very simi lar to\nthat of the total neutral gas (unsurprisingly, because mole cular\ngas dominates over H Iin the inner part of the galaxy) and is\nnot shown here. The only di fference of the CO map is that the\nsegments IIa, IIb, IIc are separated from each other by small\ngaps. The warm and cold dust have the same pattern as the gas,\nwith the exception of the segment IIc. The H IIimage contains\nonlytheinnerpartofArmII,whileH Iclearlydisplaysthewhole\nofArmII.ConcerningArmI,onlythefirst segmentIaisvisibl e\ningas,CO,andwarmandcolddust.ItsouterpartIcispromine nt\nintheH Iimagebutnotintheothermaterialtracers.Toconclude,\ntherearenodiscernibledi fferencesintheappearance,invarious\nmaterial tracers, of the bar as well as of Arms Ia, IIa, and IIb ,\nwhereasArmsIb,IcandIIcappeardi fferentindifferentmaterial\ntracers.\nThe tracers of the total magnetic field, I6 and I13, are pre-\nsumablydominatedbysmall-scale,randommagneticfields.T he\nstructures in I6 and I13 are very similar to those in H IIand the\nwarm and cold dust, with the bar and Arms Ia and IIa being\nprominent. The spiral segments Ib and Ic are absent in I6 and\nI13.\nThe patterns in P13 and the combined P6 +P13 are similar\nto each otheronthis scale with prominentouter spiral segme nts\nIc and IIc, as well as Arm Ib. As we quantify below, the ridges\ninradiopolarizationare noticeablydi fferentfromthegasridges\nin the bar, often being shifted with respect to each other. Ar m\nIIbisnotvisibleinpolarizedradioemission,whereasArmI Iais\nshifted with respect to IIa of the total neutral gas. The segm ent\nIboccursinP6+P13,thusdelineatingthewholeArmI.ArmIIc\nlargely overlapsthe correspondinggas arm in both P6 and P13 .\nRemarkably,thepolarizedArmIIaisdisplacedtowardstheo uter\ngalaxy with respect to the corresponding gas arms by 2–3kpc,\nwhereas Arm Ia is shifted inwards by a comparable magnitude.\nThemutualdisplacementsofthegaseousandpolarizedarmsa re,\non the one hand, systematic and coherent over several kilopa r-\nsecs along the arms, but on the other hand, they take di fferent\ndirections in different arms even in the same range of galacto-\ncentric radii. Arm IIa (south-east of the galaxy, the ”Gas” a nd\n”P6+P13” panels) shows the clearest picture of a polarizedarm\nbeingparalleltothegaseousarmalongabout8kpc.Ontheoth er\nhand, in Arm IIc (the next outer arm in the south-east) a polar -\nizedarmoverlapsthegaseousarmnearlyperfectlyatleasta long\n12kpc,andonlyitsenddeviatesoutwardsfromthegaseousar m.\nThisimpliesthatthemechanismsproducingsuchadisplacem ent\nare more complex than just advection of a large-scale magnet ic\nfield fromthe gaseousarms by the rotationalvelocityor the e n-\nhanced tangling of a large-scale magnetic field within the ga s\narms. Furthermore, Arms Ib and Ic appear mainly in the radio\npolarization data but not in the total radio intensity (domi nated\nby small-scale magnetic fields) and are visible in only one ma -\nterial tracer, H I. The physical nature of the magnetic Arms IIc,\nIb, and Ic is likely to be di fferent from Arms I, IIa, and IIb (see\nSect. 5). A more detailed comparison of the gaseous and mag-\nneticspiralarmsandtheirsegmentsarmsispresentedinthe next\nsection.\n5We do not use the absolute maximum because it is located in the\nbright core that dominates the gas map.\n9P.Fricket al.:Magnetic andgaseous arms inM83\nFig.10.Anisotropic (TH) wavelet transforms of various tracer dist ributions at 2 a=1′are shown (dotted contour at 20% of the\nmaximum intensity), together with the similar wavelet tran sform of the total neutral gas distribution (solid contour a t 20% of the\nmaximumintensity).Theaxisscale isinkpc.\n4.2.1. The orientationsofthe orderedmagneticfield andthe\nspiralarms\nThe wavelet representation allows us to investigate anisot ropic\nstructures on any given scale. Figure 11 helps for appreciat ing\nthe complicated relation between the orientation of magnet ic\nvectorsandtheorientationofstructuresinthedistributi onofthe\nvarioustracersofspiral arms.Thewaveletcoe fficientsshowthe\nintensity of the signal that is smoothed over a domain of scal e\na. Thus,gapsin the originalmapsseen onsmaller scalescan be\nfilledonlargerscales.\nThe magnetic vectors (uncorrected for Faraday rotation)\nin the magnetic arms, shown in the lower left-hand panel ofFigure 11, are well (and yet imperfectly) aligned with the ar ms\nof polarized emission, while the magnetic vectors in the bar re-\ngion are noticeably inclined to its axis, especially near th e ends\nofthebar.\nThe near-alignment of magnetic field with the spiral struc-\ntures requires quantifying. For this purpose, we compared t he\norientations of the magnetic field vectors ( polarization angles )\nwiththeorientationsoftheanisotropic(elongated)struc tureson\nany given scale. Figure 12 shows the normalizedangularpowe r\nspectraM(a,ϕm) of the pitch angles ϕmof the structures on a\nfixedscale 2 a=1′in thedistributionsof polarizedintensityP6,\nlabelled as ”P6 pos.a”, and of the interstellar gas, i.e. the total\nneutral gas, ”Gas pos.a”, and molecular gas, ”CO pos.a”. Her e,\n10P.Fricket al.:Magnetic andgaseous arms inM83\nFig.11.Elongated structures on the scale 2 a=1′of the anisotropic wavelet transform in the tracer indicate d in the upper right\ncornerofeachframeareshownwiththesolidcontourdrawnat 20%ofthemaximumintensityinthattracerinthearmregion. Red\ndashes, representingthe Bvectors of the polarizedradio emission at λ6cm, with length proportionalto the polarized intensity, a re\nshownin thesameregions.\nϕmis measured from the tangent to the local circumference in\nthe plane of the sky.6The spectra of Fig. 12 characterize the\norientation of the ridges in the distributions of interstel lar gas\nand polarizedradio intensity on averageover the correspon ding\nregion, the whole galaxy in the upper panel, and the spiral ar m\nregioninthelowerpanel.\nFigure 12 also presents the angular spectrum M(ϕp) of the\nmagneticpitch angles ϕpderivedfromthe polarizedintensityat\nλ6cm. This spectrum is defined as the integral of polarized in-\ntensitiesoverallpositionswherethepitchangleofthemag netic\nfieldvectorsat λ6cm,χ,isequaltoa given ϕp:\nM(ϕp)=/iintegdisplay\npitch(χ)=ϕpP6(x)dx. (8)\nTheangleϕpisalsomeasuredfromthelocalcircumference,thus\nrepresenting the magnetic pitch angle (uncorrected for Far aday\nrotation, which is small at λ6cm, and for the inclination of the\ngalaxytothelineofsight,whichisonlymodest).\nThe most pronounceddi fference between the spectra shown\nin the two panels of Fig. 12 is in the position angles of the\nanisotropic CO structures dominated by the bar that provide s\na strong maximum at pitch angles ϕmof about 70◦−80◦(90◦\nwould correspond to a structure aligned along the radial dir ec-\ntion). When the bar is excluded, this peak becomestwice lowe r\nthan the other CO maximum centred at about 13◦, with a half-\n6We neglect the small di fference in the pitch angle measured in the\nplane of the galaxy because the inclination of M83 to the line of sight\nisonly 24◦(Tilanus & Allen1993).widthat half-maximum(HWHM)of9◦thatarisesfromthespi-\nralarms.Thesharppeakinthespectrumforthetotalgasdens ity\nis due to the gaseous spiral arms with a well-defined pitch an-\ngleϕmof about 8◦with a HWHM of 6◦. We note that the pitch\nanglesofthespiralarmsinthetotalgasdistributionshows ome-\nwhatlessscatter(narrowerspectralmaximum)thanthosein CO.\nThe difference between the positions of the maxima in CO and\nthe total gasis dueto smaller pitchanglesof spiral structu resin\nthe outergalaxy,which are traced byHI, while CO tracesspir al\nfeatureswith larger pitch angles in the inner galaxy.A decr ease\nin spiral pitch angles with increasing radius has been obser ved\ninmanygalaxies(e.g.Beck2007, 2015; VanEcketal. 2015).\nThelowerpanelofFig.12showsclearlythatthedistributio n\nof thepitch angles of the structures ϕmprominent in polarized\nintensity (magnetic arms) is almost identical to the distri bution\noftheCO structures:MostoftheCOemissionandpolarizedin -\ntensity are localized in regions with ϕ <30◦. The pitch angles\nof the polarization structures are only slightly larger (th e peak\npitch anglesat ϕ≈14◦) than those of the total gas. It is notable\nthatthepitchanglesofthemagneticfieldvectors ϕpareconcen-\ntratedatsignificantlydi fferentvalues,20◦–35◦withamaximum\natϕ≈26◦and the HWHM of 15◦. This difference cannot be\nexplained by Faraday rotation in the foreground of the Milky\nWay, whichis onlyabout −2◦atλ6cm, as estimatedfromthe B\nvectorsatλ6cmandλ13cm(see Sect.2.1).\nTo summarize,the peak pitch angles ϕmof the total gas and\nmagnetic spiral arms are very close to each other at about 10◦,\nwhereasthemagneticfieldvectorshaveadi fferentpeakpitchan-\ngleϕpofabout26◦±15◦,wheretherangesrepresenttheHWHM\n11P.Fricket al.:Magnetic andgaseous arms inM83\nFig.12.Angularwaveletpowerspectraofpitchangles ϕonthe\nscale 2a=1′normalized to unit maximum: the pitch angles\nϕmof the structuresofthe polarizedintensity P6 (blackdotte d),\nneutral gas (green), and CO (blue dashed). The spectrum of th e\npitchangles ϕpofthemagneticfieldvectorsdefinedinEq.(8)is\nshownwiththe reddot-dashedcurve.The pitchanglesaremea -\nsured clockwise from the tangent to the local circumference on\nthe sky plane. The upper panel shows the spectra for the whole\ngalaxy,whilethelowerpanelshowsthemfortheregionofspi ral\narms(i.e.withthe barregionexcluded).\nof the spectral maxima. The local di fferences between the pitch\nanglesof the magneticfield vectorsand the spiral armscan st ill\nbequitelarge(asisobviousfromFig. 14).\nToconfirmtheidentificationoftheregionsthatcontributet o\nthemaximaintheangularspectraofFig.12,weshowinFig.13\nthe polarization vectors of the ordered magnetic field posit ion\nangles of the gas structures in the regions that contribute t o the\nmaximaintheirangularspectra.Theupperpanelshowsthear m\nfragments where the orientation of the ordered magnetic fiel d\ndiffersby18◦±15◦fromthelocalaxisofamaterialarm,which\nisthecase inmostpartsofArmsIandII.\nThe lower panel demonstratesthat the two angles di ffer sig-\nnificantly and systematically in the bar, apart from localiz ed re-\ngions elsewhere in the galaxy. Such deviations occur where t he\nposition angleof the gasarm turns sharply(arm sectionsIb a nd\nIIb). This is a hint that di fferent mechanisms can be responsi-\nble for the magnetic field alignment along the material arms i n\ndifferentpartsofthegalaxy.\nTheanalysisoftherelativeorientationsofmagneticpitch an-\nglesandthose ofspiral arm segmentsiscomplicatedbythe fa ct\nthat the magnetic and material arms often do not overlap, eve n\nif parallel to each other. In order to improvethe comparison we\ntakeadvantageofthefact,quantifiedabove,thatthepitcha ngles\nof the spiral arms in CO and P6 are very similar to each other,\nand present in Fig. 14 the polarization and position angles o b-\ntainedfromthemagnetictracerP6,whichisthepolarizedin ten-\nsity atλ6cm. Now the area where the comparisonis possible isFig.13.Position angles of the elongated structures of the total\nneutral gas (blue bars), obtained from the anisotropic wave let\ntransformonthescale2 a=1′,andmagneticpolarizationangles\n(red bars); the isocontourof the total gas intensity at 20% o f its\nmaximuminthearmsisshownasadashedline.Theupperpanel\nshows the data points where the di fference between two angles\nisbetween3◦and33◦withapositivevaluemeaningaclockwise\nrotation with respect to the gas structure), as suggested by the\nrelative shift of the corresponding peaks in the angular spe ctra\n(Fig.12),whilethelowerpanelshowstheremainingdatapoi nts.\nTheaxisscalesarein kpc.\nsubstantially larger than in the previous figure, confirming that\nthe ordered magnetic field is well aligned with the spiral arm s\nalong most sections of the Arms I and II (as discussed above,\nthe two orientations di ffer systematically by an angle of about\n10◦which is difficult to discern visually), while there is little or\nnoalignmentinthebarregion.\nThereason for the misalignmentin the bar regionin Fig. 14\n(bottom) is a structure in P6 that appears on large scales due to\nmergingofsmallerstructures(Fig.9bottom).Theexistenc eofa\nsmaller structure becomesclear fromcomparingP6 fromFig. 4\nwith P6 from Fig. 9. In the unfiltered map (Fig. 4), P6 is con-\ncentrated in two narrow features with a position angle of abo ut\n50◦, running roughly parallel to the bar visible in I6, gas, and\ndust, with the polarization angles (Fig. 1) roughly aligned with\nthem. At both ends of the bar, the position angles of the struc -\ntures, as well as the polarization angles, jump by about 70◦, to\nbecomeorientedroughlyinthenorth-southorientation.Mo stof\n12P.Fricket al.:Magnetic andgaseous arms inM83\nFig.14.As in Fig. 13, but with blue bars showing the position\nanglesofthestructuresofthepolarizedintensityP6,thei socon-\ntour of P6 at 20% of its maximum intensity shown as dashed.\nTheupperandlowerpanelsshowdatapointswiththedi fference\nbetweentheanglesintherange −1◦to29◦andoutofthisrange,\nrespectively.\nthese features are lost in Fig. 9 because the wavelet transfo rm\naverages over small structures. In Fig. 9 bottom, the strong est\nwavelet structure near the centre is a combination of many na r-\nrow features in the original image and no longer resembles th e\nbar. Not surprisingly, the structure position angles are be tween\n80◦and130◦,socompletelydifferentfromthoseofthepolariza-\ntionangles.\nHIand the combination of polarized emission at λ6cm and\nλ13cm cover the largest part of the galaxy and thus reveal the\nmost extended spatial distributions. Only these two maps al low\nusto identifybotharmsalongtheirwholelengths.Othertra cers\ncontain lacunae and often exhibit only short segments of arm s,\nespeciallyintheinnergalaxy(e.g.intheH IImap).Thewavelet-\nfilteredimageofH Iandanisocontourofcombinedpolarizedra-\ndioemission,P6+P13,areshowninFig.15onthescale2 a=1′.\nThe spiral arms are very visible in both tracers. In H I, there are\ntwo bridges with large pitch angles (but not radial), which a re\nseen in both tracers (Fig. 4). The figure supportsthe conclus ion\nthat all tracersshow Arm II at the same positions, while the p o-\nsitionsofArmIdisplayasystematic relativeshift: themag netic\narm is shifted with respect to the H Iarm, inwards in the inner\nP6/PlusP13\nHI\n/Minus15/Minus10/Minus5 0 5 10 15/Minus15\n/Minus10\n/Minus5\n0\n5\n10\n15\n5. 10. 15. 20. 25.\nFig.15.Locationsof the elongatedstructures,on the scale 2 a=\n1′, of the combined polarized radio emission (P6 +P13) (black\nisocontour at 20% maximum intensity) and in the distributio ns\nof HI(top panel) and warm dust (bottom panel), respectively,\nshown in colour and as dotted contoursat 20% of its maximum\nintensity.Theaxisscaleisgiveninkiloparsecsassumingt hedis-\ntance to M83 of 8 .9Mpc. The dashed ellipse shows the corota-\ntionradius.\ngalaxy (arm segment Ia) and outwards in the outer galaxy (Ib\nandIc).\n5. Discussion\nA traditional approach to quantifying galactic spiral stru ctures\nand estimating their pitch angles is based on the Fourier tra ns-\nform of the light (or any other suitable variable) distribut ion in\nazimuth (Puerari&Dottori 1992, and references therein). S uch\na spectral analysis involves a fit to an average pitch angle fo r a\nwholegalaxyassumingthelogarithmic-spiralshapeofthea rms.\nGiventhecomplexstructureofthespiralpatternswithnume rous\nbranches and strong spatial variations of the pitch angle, e tc.,\neven in galaxies with grand-design patterns such as M51, the\nglobal approach to quantifying the spiral structure is rath er re-\nstrictive. Puerariet al. (2014) attempted to improve the me thod\nin this respect by applying it to relatively narrow annuli ra ther\nthan to a galaxy as a whole. However, a better way to resolve\n13P.Fricket al.:Magnetic andgaseous arms inM83\nthese problems would be to employ wavelet transforms, as we\ndo here (see also Fricketal. 2000, 2001; Patrikeevetal. 200 6).\nThe wavelet-based approach is free of any model assumptions\nabout the shape of the spiral arms, and their segments (such a s\naperfectm-armedpatternoralogarithmicspiral)allowsfordif-\nferent widths of arms and inter-arm regions and works equall y\nwell foranystructures,whetherspiral,azimuthal,orradi al.\n5.1. Magneticarms\nM83 has well-defined magnetic arms where the ordered mag-\nnetic field is concentrated, which is visible as structures i n po-\nlarizedradioemissionofabout1′inwidth.Similartothegalaxy\nNGC6946, the polarized arms appear to be more or less inde-\npendentofthespiralpatternsseeninothertracers,sincet heyare\ndisplaced from the latter in large areas by about 20◦along the\nazimuthonaveragein the meanshortest distance.This doesn ot\nexclude a physical relation between them, which is suggeste d\nby their close spatial proximity and the fact that their axes are\nwellalignedwitheachother.Themutuallocationofthegase ous\nand magnetic arms is diverse, with magnetic Arms Ib, Ic, and\nIIa extended along the inner edge of the correspondinggaseo us\narms, but magnetic Arm IIb and the inner part of Arm IIc su-\nperimposed on the correspondinggaseous arms (Figs. 8, 9, an d\n15).\nThisdiversitysuggeststhatavarietyofphysicalmechanis ms\nareresponsiblefortheformationofthemagneticarms,poss ibly\nacting simultaneously. A remarkable feature of the large-s cale\ngalactic magnetic field that manifests itself as magnetic ar ms\ndisplaced from the gaseous arms is that its strength is great er\nwhere the gas density is lower. This may imply that the large-\nscale galactic magnetic fields are not frozen into the inters tellar\ngas and thus need to be continuously replenished, presumabl y\nbythegalacticmean-fielddynamoaction(Shukurov2007).Th e\nonly apparent alternative is that magnetic arms represent s low\nMHD density waves (Lou& Fan 1998, 2003; Lou&Bai 2006,\nandreferencestherein).However,mean-fielddynamoequati ons\nin a thin disk, either linear or nonlinear, do not admit wave-\nlike solutions under realistic conditions even when genera lized\nto include the second time derivative of the magnetic field (t he\ntelegraph equation) (Chamandyet al. 2013, 2014). It cannot be\nexcluded that more advanced nonlinear dynamo models, espe-\nciallythosewiththedirectcouplingoftheinductionandNa vier–\nStokes equations, will reveal a new class of dynamo solution s\nreminiscentoftheslow MHDwaves.\nThere are several physical processes that can contribute to\nthe formation of magnetic arms displaced from the gaseous\narms:\n1. The mean-field dynamo action can be suppressed within\nthe gaseous arms by either a presumably enhanced fluctu-\nation dynamo driven by stronger star formation (Mosset al.\n2013) or a stronger galactic outflow driven by stronger star\nformation (Suret al. 2007; Chamandyetal. 2015) (see also\nShukurov1998).\nA generic problemof such mechanismsis that they produce\nthe desired displacement only within a few kiloparsecs of\nthe corotation radius of the spiral pattern (Shukurov 1998;\nChamandyet al. 2013, 2014), because the residence time of\navolumeelementwithinagaseousspiralarmisshorterthan\nthe dynamo time scale of order 5 ×108yr at large distances\nfrom the corotation. A few mechanisms, briefly discussed\nbelow, have been suggested to produce magnetic arms dis-placed from the gaseous ones far away from the corotation\nradius.\n2. ThemodelbyMosset al.(2013,2015)assumesthatalarge-\nscaleregularfieldisgeneratedeverywhereinthedisk,whil e\nasmall-scale dynamoinjectsturbulentfieldsonlyin thespi -\nral arms. This gives polarization arms between the gaseous\narms at all radii, but with pitch angles of the polarization\nstructures and pitch angles of the polarization vectors tha t\nare significantly smaller than those of the gaseous arms, in\ncontrasttothe observationsdiscussedinthispaper.\n3. Afinitemean-fielddynamorelaxationtime(atemporalnon-\nlocality of the mean electromotive force) does produce, un-\nderrealisticparametervalues,adisplacementofupto30◦in\nazimuthatthecorotationradius,withmagneticarmslaggin g\nbehind the gaseous ones (Shukurov 1998; Chamandyet al.\n2013). The ridges of magnetic arms thus produced have a\nsystematically smaller pitch angle than do the gaseous spi-\nralsbecauseoftheactionofdi fferentialrotationonthelarge-\nscalemagneticfield.Thepitchangleoftheorderedmagnetic\nfield in M83 is, on average, larger than that of the material\narms, contrary to this model (which, however, has not been\nspecificallydevelopedforM83).\n4. A different approach to the problem of displaced magnetic\nandgaseousspiralpatternsemergesif thematerialpattern is\nnot a solidly rotating structure, as suggested by the densit y\nwave theory, but rather a transient and evolving system of\nspiral arm segments producedby a bar, galactic encounters,\nlocal instabilities, etc., and wound up by the galactic di ffer-\nential rotation. As shown by Chamandyet al. (2013, 2014,\n2015),themechanismsmentionedabovearerelievedoftheir\nproblems in this case, producing diverse interlaced or inte r-\nsecting magnetic and gaseous spiral patterns depending on\ntherelativecontributionofeachmechanism.\n5. Compression of the both the large-scale and turbulent mag -\nnetic fields in the gaseous arms enhances polarized syn-\nchrotron emission within them, also by amplifying the\nanisotropy of the random magnetic field (see Section 8 of\nBecket al. 2005; Patrikeevetal. 2006; Fletcheret al. 2011) .\nThe resulting ridges of enhancedpolarized emission are ex-\npected to be located at the inner edge of the material arms\ninsidethecorotationradiusandatthe outeredgeoutsideth e\ncorotation. Offsets between the spiral arm ridges in various\ntracers, of a few 100pc, are predicted by the density wave\ntheory (Roberts 1969) and were detected in a wavelet anal-\nysis of M51 data (Patrikeevetal. 2006). Compression of a\nturbulentfieldalignsthemagneticarmalongtheshockfront ,\nwhile compressionof an ordered field changesthe pitch an-\ngleofthepolarizationangletobecomemoresimilar(butnot\nidentical)tothepitchangleofthematerialarm.\nMostofthesemechanisms(exceptthoseofMosset al.2013,\n2015) are sensitive to the location of the corotation radius\nsinceadvectionofmagneticfieldsfromthegaseousarmswoul d\nunavoidably affect the relative positions of the magnetic and\ngaseousarms.Ithasbeensuggestedthatthecorotationradi usin\nM83isabout2 .3′–2.4′(Kenney&Lord1991;Randet al.1999;\nHirotaet al.2014),about6kpcatadistanceof8.9Mpc.Asusu al\ninbarredgalaxies,thisradiusisonlyslightlylargerthan thema-\njoraxisofthebar.Thisdoesnotallowustoclarifytheroleo fthe\ncorotation radius in the formation of magnetic arms using M8 3\nasanexample.\nThe magnetic Arm IIb–IIc coincides with the correspond-\ning material arm (Fig. 15). This may still be consistent with the\nmechanisms (3) or (4). The similarity of the magnetic pitch a n-\n14P.Fricket al.:Magnetic andgaseous arms inM83\ngles as compared to the pitch angles of the gas arms (Figs. 12\nand13)donotlendsupporttothemechanism(2).Aregularfiel d\nwithaspiralpatterngeneratedbya mean-fielddynamoisposs i-\nbly compressed and partly aligned in density waves interact ing\nwith the magnetic field. Another possibility may be associat ed\nwitha couplingbetweenmagneticfieldsanddensitywaves.\nSeveralnarrowspiralarmsegmentsareprominentinthedust\nemissionintheinnergalaxy(Fig.4),whichisindicativeof com-\npression. These features are visible in the anisotropic wav elet\ntransformmapsonthescale0 .7′(Figs.8and9,toppanels).The\nfeaturesin total neutral gasand orderedmagnetic field coin cide\nwith them in the west and north of the galaxy. Density wave\nmodels predict an o ffset of a few 100pc between such features,\ncorrespondingto0 .1′,whichcannotberesolvedwiththepresent\nobservations. However, Patrikeevetal. (2006) find evidenc e of\nsuchoffsetsin thegalaxyM51.\nThemagneticArmIa–Ibisdisplacedfromthecorresponding\nmaterialarm(Fig.15).Itspropertiescouldbeconsistentw iththe\nmechanism(4)ifthecorotationradiusofM83islocatedatab out\n7kpcat theassumeddistance(Lundgrenet al.2004),andthis is\napparently the case. However, the displacement is too large to\nbe consistent with density-wave compression.Alternative ly,the\nwholeofArmImaybegeneratedbythemean-fielddynamovia\nthe mechanisms (1)–(3). A rather good alignment of the polar -\nization angles with the position angle is seen in the magneti c\nArm I (Fig. 14, top panel). Such an alignment is facilitated b y\nthemechanism(4).\nAn additional aspect of the magnetic field configuration in\nM83 is related to the presence of the bar. Although the bar of\nM83 is shorter (about 7kpc) than that of NGC1097 (of about\n16kpc), the ordered magnetic fields are inclined with respec t\nto the bar in both galaxies (Fig. 13). The behaviour of polar-\nization angles in the bar of M83 looks similar to the behaviou r\nin NGC1097 and NGC1365, which are other barred galaxies\n(Becket al. 2005), and indicates a non-axisymmetric gas flow\nin the bar region. Indeed, Fig. 1 shows that the magnetic field\nis inclined to the bar axis in the regions SE and NW of the bar\n(atx≈−2′,y≈0′andx≈+3′,−2′<y<+2′), seen also in\nthebottomleftofFig.11, thoughlesswell owingtothewavel et\nsmearing. Furthermore, the ordered magnetic field near the b ar\nis concentrated in two narrow regions where the magnetic fiel d\nvectorsarealignedalongthebaronthedownstream(outer)s ides\nof the bar (at x≈0′,y≈+2′andy≈−1′). This is most visi-\nble in Fig. 1, but hardlyin Fig. 11. Thiswhole patternis simi lar\nto what is observed in NGC1097 and NGC1365, though on a\nsmaller scale. The inner region of IC342 also shows magnetic\nfieldsstronglyinclinedtothebar(Beck2015).\n5.2. Magneticfield alignmentwith spiralarms\nTheapplicationofanisotropicwavelettransformprovides anex-\ncellent opportunity to estimate the pitch angles of various spi-\nralstructureswithoutanymodelassumptionsandtoobtaint heir\nquantitativecharacteristicsin a controlledmanner.In pa rticular,\nthe estimates of the pitch angles from the angular spectra pr e-\nsentedinSection4.2.1areperhapsthemostreliableamongs tthe\nexistingestimatesofthiskind.Onaverage,thepitchangle ofthe\nmagnetic field vectorsat λ6.2cm (presumably,mostly the regu-\nlar field contaminated by an anisotropic random part) is larg er\nthanthatofthematerialspiral armsbyabout20◦: Themagnetic\nfieldlinesformslightlymoreopenspiralsthanthematerial arms.\nVanEcketal.(2015)presentacompilationofthemeasuremen ts\nof magnetic and spiral-arm pitch angles in a sample of nearby\ngalaxies(theirFig.11andtheaccompanyingtext)andconcl udethattheyarecloselycorrelatedandyetgivesatypicaldi fference\nin their data of about 5◦−10◦, with the magnetic lines being\nmoreopenthanthespiral arms.M83generallyfitsthisrelati on.\n6. Conclusions\nMagnetic structures and their inter-relations with the mat erial\nstructures are more complicated in M83 than in NGC6946 and\nM51, where they were previously investigated in some detail .\nThe polarization angles in the vicinity of the barof M83 are\nstrongly inclined with respect to the orientation of the bar , pos-\nsiblyindicatingnon-axisymmetricgasflows,asalsoobserv edin\notherbarredgalaxies.Therelativeintensitiesof spiralstructures\nat various scales, quantified by the wavelet power spectra, a re\nsimilar for the dust, gas, and total magnetic field. The patte rn\nof the total radio continuum emission, mainly associated wi th\nsmall-scale (turbulent)magneticfields, looksmore or less simi-\nlar to the material pattern. On the other hand, ordered magne tic\nfields(tracedbypolarizedradioemission)aredistributed differ-\nently,showingweakcorrelationwithothertracers.\nWe have identified two main material spiral arms that start\nat the endsofthe bar. M83also haswell-definedmagneticarms\nwhere the orderedmagnetic field is concentrated.The magnet ic\narms are partially displaced from the corresponding materi al\narms (as in NGC6946), while they partially coincide with the\nmaterialarmsinotherregionssimilartoM51).\nThe magnetic Arm IIb–IIc (see Fig. 7 for the notation) co-\nincides with the material arm, so behaves similarly to the ou ter\nsouth-western arms of M51 (Patrikeevet al. 2006). The polar -\nization angles are mostly aligned with the orientations of t he\nmain material Arm II, but generally have pitch angles larger\nby about 20◦. This could be a signature of a spiral field gener-\natedbythemean-fielddynamothatisalignedbyastillunknow n\nmechanism, possibly interacting with density waves. Major de-\nviations occur in two regions where the gas arms have a sharp\nbend(north-eastandsouth-westofthebar),whichthemagne tic\nfield does not follow. Figure 1 shows that the pattern of mag-\nnetic vectors at the bar ends in the north-east and south-wes t is\nsmootherthanthestructureofgasanddust,whichisnotane ffect\noflimitedresolution.\nThemostprominentmagneticarmisdisplacedinwardswith\nrespect to the material Arm I in the south (Ia), located in the\ninter-armspacebetweenthecorrespondingmaterialarmand the\nbar (Fig. 15), resembling the magnetic arms in NGC6946. The\nmagnetic arm continues to the west and north, displaced out-\nwards with respect to the material Arm Ic. The approximate\nalignment of the polarization angles with the magnetic arms\n(Fig.14)wasalso foundforthemagneticarmsin NGC6946.\nThe two types of magnetic arms may be di fferent in their\ngeneration.Adisplacementcanindicategenerationbythem ean-\nfield dynamo, while coincidence could be due to shear or com-\npressionbydensitywaves.A regularfieldgeneratedbya mean -\nfield dynamo can be compressed in material arms and thus be\npartly aligned with them. Interaction with nearby dwarf gal ax-\nies in the M83 galaxy group (Karachentsevet al. 2007) may\nalsoaffectthe gaskinematicsandthemagneticfield pattern;the\ndwarf galaxy NGC 5253 is possibly causing the warp in the H I\ndisk (Rogstadet al. 1974). The coexistence of di fferent genera-\ntion mechanisms could be the result of the di fferent timescales\ninvolved: While the dynamo operates on timescales of severa l\nrotation periods, density waves or disturbances by interac tion\nact on shorter timescales. Dynamo models have indicated tha t\ngas streaming due to an encounter can enhance total and polar -\n15P.Fricket al.:Magnetic andgaseous arms inM83\nized emission withoutanyincreasein theregularmagneticfi eld\nstrength(Mosset al. 2014).\nIn summary, the modulation of the galactic dynamo by a\ntransient spiral pattern is a promisingmechanism for produ cing\nsuchcomplicatedspiral patternsasin M83.\nA better understanding of the structure and origin of the\nmagnetic arms observed in M83 needs a high-resolution map\nof Faradayrotationto allow one to distinguishregularmagn etic\nfieldsfromtheanisotropicmagneticfieldsproducedbycompr es-\nsionandshearinthebarandspiralarmregions.Theradiopol ar-\nization data presented in this paper are insu fficient to provide\nreliable rotation measures because Faraday depolarizatio n is\nstrongintheinnergalaxyat λ13cm.Spectro-polarimetricobser-\nvationsandapplicationofRMSynthesis(Brentjens& deBruy n\n2005)aredesirable,e.g.withVLAdataintheLband(1–2GHz)\nand S band (2–4GHz) giving a resolution in Faraday depth of\n≃40radm−2. M83 is also proposed as a prime target for the\nSquareKilometreArray(SKA)(Becket al.2015).\nAcknowledgements. We thank Stuart Ryder for providing the H αimages of\nM83. We thank Sui Ann Mao and the anonymous referee for useful sugges-\ntions that helped to improve the paper. RB acknowledges supp ort from the DFG\nResearch Unit FOR1254. AS is grateful to STFC (grant ST /L005549/1) and the\nLeverhulmeTrust(grantRPG-2014-427)fortheirsupport.P F,RS,andDSthank\nProf. Michael Kramer for supporting several visits to the MP IfR.\nReferences\nBeck, R.2007, A&A,470, 539\nBeck, R.2015, A&A,578, A93\nBeck, R., Bomans, D., Colafrancesco, S., et al. 2015, Advanc ing Astrophysics\nwith theSquare Kilometre Array (AASKA14),94\nBeck, R.,Fletcher, A.,Shukurov, A.,etal. 2005, A&A,444, 7 39\nBeck, R.&Hoernes, P.1996, Nature, 379, 47\nBrentjens, M.A.&de Bruyn, A.G.2005, A&A,441, 1217\nChamandy, L.,Shukurov, A.,&Subramanian, K.2015, MNRAS,4 46, L6\nChamandy, L.,Subramanian, K.,&Quillen, A.2014, MNRAS,43 7, 562\nChamandy, L.,Subramanian, K.,&Shukurov, A.2013, MNRAS,4 28, 3569\nFletcher, A., Beck, R., Shukurov, A., Berkhuijsen, E. M., & H orellou, C. 2011,\nMNRAS,412, 2396\nFrick, P., Beck, R., Berkhuijsen, E. M., & Patrickeyev, I. 20 01, MNRAS, 327,\n1145\nFrick, P.,Beck, R., Shukurov, A.,etal. 2000, MNRAS,318, 92 5\nG¨ usten, R.,Nyman, L.Å.,Schilke, P.,etal. 2006, A&A,454, L13\nHirota, A.,Kuno,N.,Baba, J.,etal. 2014, PASJ,66, 46\nHolschneider, M. 1995, Wavelets: Tool of Analysis (Oxford, Oxford University\nPress),423\nKarachentsev, I.D.,Tully, R. B.,Dolphin, A.,et al. 2007, A J,133, 504\nKenney, J.D.P.&Lord, S.D.1991, ApJ,381, 118\nKrause, M. 1993, in IAU Symposium, Vol. 157, The Cosmic Dynam o, ed.\nF.Krause, K.H.R¨ adler, &G.R¨ udiger, 305\nKrause, M.,Hummel, E.,&Beck, R. 1989, A&A,217, 4\nLou,Y.-Q.& Bai, X.-N.2006, MNRAS,372, 81\nLou,Y.-Q.& Fan, Z.1998, ApJ, 493,102\nLou,Y.-Q.& Fan, Z.2003, MNRAS, 341, 909\nLundgren, A. A., Wiklind, T., Olofsson, H., & Rydbeck, G. 200 4, A&A, 413,\n505\nMoss,D.,Beck, R.,Sokolo ff, D.,et al. 2013, A&A,556,A147\nMoss,D.,Sokoloff, D.,Beck, R.,&Krause, M.2014, A&A,566, A40\nMoss, D.,Stepanov, R., Krause, M.,Beck, R., & Sokolo ff, D. 2015, A&A,578,\nA94\nNeininger, N.,Beck, R.,Sukumar, S.,&Allen, R. J.1993, A&A ,274,687\nNeininger, N.,Klein, U.,Beck, R.,&Wielebinski, R.1991, N ature, 352, 781\nNiklas, S.&Beck, R.1997, A&A,320, 54\nOppermann, N.,Junklewitz, H.,Robbers, G.,etal. 2012, A&A ,542, A93\nPatrikeev, I.,Fletcher, A.,Stepanov, R.,etal. 2006, A&A, 458, 441\nPuerari, I.& Dottori, H.A.1992, A&AS,93,469\nPuerari, I.,Elmegreen, B.G.,&Block, D.L.2014, AJ,148, 13 3\nRand, R. J.,Lord,S.D.,&Higdon, J. L.1999, ApJ, 513,720\nRoberts, W.W.1969, ApJ, 158,123\nRogstad, D.H.,Lockhart, I.A.,&Wright, M.C.H.1974, ApJ, 1 93, 309\nSandage, A.& Tammann,G.A.1974, ApJ,194, 559\nSchuller, F.,Menten, K.M.,Contreras, Y.,etal. 2009, A&A, 504, 415Shukurov, A. 1998, MNRAS,299, L21\nShukurov,A.2007,inMathematical AspectsofNaturalDynam os,ed.E.Dormy\n&A.M. Soward (Chapman &Hall /CRC), 313–359\nSiringo, G.,Kreysa, E.,Kov´ acs, A.,et al. 2009, A&A,497,9 45\nSukumar, S.&Allen, R. J.1989a, Nature, 340, 537\nSukumar, S.&Allen, R. J.1989b, ApJ,341, 883\nSukumar, S.,Klein, U.,& Gr¨ ave, R. 1987, A&A,184, 71\nSur,S.,Shukurov, A.,& Subramanian, K. 2007, MNRAS,377, 87 4\nTabatabaei, F.S.,Beck, R.,Krause, M.,etal. 2007, A&A,466 , 509\nTabatabaei,F.S.,Berkhuijsen,E.M.,Frick,P.,Beck,R.,& Schinnerer,E.2013a,\nA&A,557, A129\nTabatabaei, F.S.,Schinnerer, E.,Murphy, E.J.,et al. 2013 b, A&A,552, A19\nTilanus, R. P.J.& Allen, R. J.1993, A&A,274, 707\nVan Eck,C. L.,Brown, J.C.,Shukurov, A.,&Fletcher, A.2015 , ApJ, 799,35\nVogler, A.,Madden, S.C.,Beck, R.,etal. 2005, A&A,441, 491\n16"    },    {        "title": "1601.00592v1.Mechanically_Stimulated_Domain_Re_arrangement_in_Cryogenic_Magnetic_Shielding_Materials.pdf",        "content": " \n  \nAbstract—Room temperature properties  and behavior of \nseveral types of cryogenic magnetic shielding materials  are \nmeasured and  reported  here .   Large changes in the effective  \nrelative permeability are observed when the materials are \nperturbed with a relatively small mechanical stimulation.  The \nchange in per meability is a reversible effect.  \nI. INTRODUCTION  \nHE importance of cryogenic magnetic shielding material \nhas increased significantly since the introduction of “High -\nQ” nitrogen doped niobium as a practical surface for \nsuperconducting RF (SRF) cavities inten ded for particle \naccelerator and storage ring use.  The RF surface resistance of \n“N-doped” cavities is more sensitive to trapped magnetic flux \nthan the surface of pure niobium cavities  [1], and requires  \nextremely  effective ambient field attenuation from magnetic \nshielding.  \nThis report summarizes  measurements made on sample \ncylinders of shielding material at room temperature  with the \naim of characterizing their ability to attenuate low ( ~50 µTesla ) \nsteady state  magnetic field.   \nII. SHIELDING MATERIAL  \nMaterial s from three suppliers  take part  in this study.  They \nare listed in Table 1.  All are heat treated to increase their \npermeability at  cryogenic temperatures . \n \n   Cryogenic shielding material in a cavity cryomodule can be \nat temperatures usually in the range 1.8K≤T≤80K.  T908he \npermeability of commercially available cryogeni c magnetic \nshielding material has been  found to decrease by as much as a \nfactor of two when cooled from 300K to 4K.   \n \nSubmitted 12 -31-2015.  Fermilab is o perated by Fermi Research Alliance, \nLLC under Contract No. De -AC02 -07CH11359 with the United States \nDepartment of Energy.   A. Material Composition  \nThe chemical composition of the materials was analyzed  \nusing a Bruker S1 TurboSD spectrometer . Results are shown in \nTable II.   Components that measured les s than 0.4 % are not  \nincluded in the table . \n \nIt is notable that both the 1115 material and A4K are  \nchemically similar to Permalloy80 , invented at Bell Telephone \nLaboratories in 1914 .  The antiquity of Permalloy80 is such that \nAlexander Graham Bell would still live for six years after its \nintroduction!  \nB. Material Heat Treatment  \nAll samples were heat treated by Ad -Vance after being \nformed and welded into the shape of tubes . A generic heat \ntreatment for cryogenic magnetic shields is described in  \nreference [2]:  “2-4 h at 1,100C in vacuum; 2 h cooling to 500C \nand then with helium  or argon gas to room temperature ;  \nannealing under vacuum for 0.5 h at 570C; slow cooling to \n470C  and annealing th ere for 2 h; fast He or AR gas cooling to \nroom temperature.”  \nIII. ATTENUATION MEASUREMENTS  \nThe method used for this report  is to measure the attenuation \nof applied magnetic field in the axial direction of open \ncylinders . Obtaining adequate a xial attenuation, or as it is \nsometimes  called,  longitudinal attenuation, is the most difficult \ntask facing the SRF cryomodule magnetic shield de signer. This \nis because the attenuation of a cylinder along its axis decreases \nas the square of the ratio of di ameter to length , and m ost SRF \ncavity  shields are long, narrow  cylinders. The intention of the \npresent study is  to be practical , with a goal of making \nAnthony C. Crawford  is a physicist  with the Fermilab/Technical \nDivision/S uperconducting RF Dept.  (e-mail: acc52@fnal.gov ).  \n Anthony C. Crawford,  Fermilab  Mechanically  Stimulated Domain Re -\narrangement  in Cryogenic Magnetic Shielding \nMaterials  \nT \nTABLE  I \nSHIELDING MATERIALS  \nSUPPLIER  MATERIAL  \n \nAd-Vance  Magnetics   \nCP-EXP -1115  \nCP-EXP -1184  \nAmuneal  Mfg. Corp  A4K  \nSekels, GMBH  Cryoperm10  \n  \n \n \n TABLE  II \nSHIELDING MATERIAL % COMPOSITION  \nELEMENT  1115  1184  A4K  CRYOPERM 10 \nCr - 2.3 - - \nMn 0.4 0.5 0.5 0.5 \nFe 15.3 16.8 15.0 15.8 \nNi 78.6 75.2 79.7 76.3 \nCu - 5.1 - 5.0 \nMo 5.1 - 4.4 2.4 \n     \n \n \n  \n measurements  that lead to useful  design parameters for \nmagnetic shields, rather than those that are more relevant for \ninvestigation of the underlying physics.  \nA. Test Geometry  \n   The axis of the sample cylinder was oriented in the vertical \ndirection.  All magnetic field in the direction transvers e to the \ncylinder axis was cancelled with a large set of external \nHelmholtz  coils . Cancellation was done when the sample \ncylinder and all magnetic material (except for the ma gnetic \nsensor) was not present within the active volume of the \nHelmholtz coils. The field in the vertical direction was adjusted \nwith external coils to be 50.0 µTesla  when there was no \nmagnetic sample material present.   A Bartington  single axis \nfluxgate magnetometer  was located at the geometric center  of \nthe tube.  The orientation of the sensor axis was in the vertical \ndirection.  The Bartington sensor  was a model suited for \ncryogenic use . The  accuracy of the fluxgate  with its readout \nelectronics is ±1 percent of the measured field, dominated by \nuncertainty in the scaling coefficient . \nB. Measured Attenuation  \nAttenuated field  values (Baxial) are listed in Table III, where \nlength and diameter measurements are listed in millimeters and  \nattenuated field is in µTesla .  The axial a ttenuation factor is \ncalculated by dividing the ambient axial field ( 50.0 µTesla ) by \nthe attenuat ed field value at the geometric center of  each \nsample.   All measurements were taken at room temperature \n(~20C).   Remanent field in the samples w as adjusted to zero \nbefore measurements were taken.  The thickness of all tested \nmaterials was 1 millimeter.  \n \n \nIV. ESTIMATED RELATIVE PERMEABILITY  \nA two dimensional finite element magnetic modeling \nprogram was used to obtain a value for relative permeability \nthat best predict s the measured value for attenuation i n Table \nIII [3]. Permeability is forced to have a  constant value  over the \nrange of magnetic field inside the shielding material . The range  \nof field inside the metal of the shield  is approximately 1000 \nµTesla  to 8000 µTesla .  Field values this small justify the use \nof a linear B -H curve segment for the model. Table IV lists the \ncalculated  relative permeability . The model featured the \nspecific geometry of each test cylinder  immersed in an applied  \naxial field of  50.0 µTesla . \n \n  \nV. MEASUREMENTS WITH MECHANICAL STIMULATION  \n   In the course of taking measurements, it was observed that \nsmall mechanical perturbations in the form of applied \nmechanical shock would change the value of attenuated field. \nThe trend was that larger perturbations resulted in larger \nchanges in the fie ld and that attenuation always increased with \nthe application of shock . In order  to quantify this effect, each \nsample was tapped  with a plastic hammer weighing 3.3 grams  \nwhile the sample was immersed in a 50.0 µTesla  axial applied \nfield. The estimated maximum kinetic energy of the hammer  \nwas 1x10-4 joule.   The mass of each sample was approximately \n90 grams. Since less than the full kinetic energy of the hammer \nwas transferred to the sample, the added energy to the sample \nwas less than 1 millijoule p er kilogram per hammer strike. It \nshould be noted that the hammer strikes were executed by hand, \nand not by a machine with precise control and repeatability. The \nimpact energy per strike was approximately 1x10-4 joule +0 \njoule –0.5x10-4 joule . \n   With each su ccessive strike of the hammer, the attenuated \nfield would decrease until a c onstant value was reached.  \nApproximately 100 strikes were required to achieve the \nminimum. The value would  not change with additional hammer \nstrikes .  The change of attenuated fie ld as a function of the \nnumber of hammer strikes is shown for the Cryoperm10 sample \nin Figure 1.  \n \nFig 1. Hammer strike sequence for the Cryoperm10 sample.  \n    \n \nTABLE  III \nATTENUATED FIELD MEASUREMENTS  \nSAMPLE  INNER \nDIAMETER   \nLENGTH  \n BAXIAL  \n(µTESLA ) ATTENUATION  \nFACTOR  \n \n1115   \n25.1  \n127.0   \n0.081   \n617 \n1184  22.8 127.0  0.168  298 \nA4K  25.3 127.0  0.090  556 \nCryoperm10  25.4 127.0  0.178  281 \n     \n \n \n TABLE  IV \nCALCULATED CONSTANT RELATIVE PERMEABILITY  \nSAMPLE  RELATIVE PERMEABILITY  \n \n1115   \n98,500  \n1184  47,500  \nA4K  88,500  \nCryoperm10  44,000 \n  \n \n  \n    Average values for measured attenuated field and calculated \nrelative permeability (µ r) for the ca ses of before and after \nmechanical perturbation are listed in Table V.   The applied axial \nfield is  50.0 µTesla . \n \n   The change to  attenuated field due to mechanical stimulation \nwas found to be a reversible effect. Sequential measurements \nmade on al l samples are shown in Figures 2 through 5 . The  \nsequence for each sample is:  1.  Measureme nt with rema nent \nfield in sample adjusted to zero,  2. Stimulate , 3. Reverse axial \norientation of sample , 4. Stimulate , 5. Reverse , 6. Stimulate , 7. \nReverse , 8. Stim ulate , 9. Reverse , 10. Stimulate , 11. Reverse . \nThe even numbers are measu rements where the sample has \nbeen stimulated within the applied field in which the \nmeasurement was made.  For odd numbers  greater than one , the \naxial orientation  of the sample within the constant applied field \nhas been reversed from the time of the mechanical stimulation .  \n \nFig 2 . Sequence of measurements  on the 1115  sample .  \nFig 3 . Sequence of measurements  on the 1184  sample . \n \n \nFig 4 . Sequence of measurements  on the A4K  sample . \n \nFig 5 . Sequence of  measurements  on the Cryoperm10  sample . \n \n   When hammer strikes with a larger amount of kinetic energy \nwere applied, the attenuated field would decrease to a new, \nsmaller equilibrium  value  with higher effective permeability . It \nis anticipated that with increasing energy level the effects will  \ncease to be reversible at some point. Within the reversible \nlimits, we have, in effect, a mechanically stimulated hysteresis \nfunction for a given applied magnetic field.  \n \nTABLE  V \nEFFECT OF STIMULATION  ON ATTENUATION  \nSAMPLE  BAXIAL  before  \n(µTESLA ) BAXIAL  after \n(µTESLA ) µr before µr after \n \n1115   \n0.081   \n0.069   \n98,500   \n116,000  \n1184  0.168  0.110  47,500  75,500  \nA4K  0.090  0.062  88,500  128,000  \nCryoperm10  0.178  0.101  44,000 77,500  \n     \n \n \n  \n VI. DISCUSSION  \nWhen  magnetic shiel ding material is removed from the  \nannealing furnace it possesses two different forms of internal \nstructure that are dependent on the thermal treatment \nconditions : crystalline grains and magnetic domains. It is likely \nthat the samples in this study have not been subjecte d to forces \nsufficient to cause re -ordering of grain boundaries or to \nintroduce significant permanent in ternal stress. We are \nobserving magnetic domain re -arrangement resulting from  \nmechanical stimula tion and  applied ambient magnetic field.  \nThe small amou nt of mechanical stimulation given to the \nsamples is enough to allow the magnetic domain walls to move \nin a way that allows lessening of the total Gibbs free energy of \nthe system in the applied magnetic field  [4]. This translates to a \nlarger integrated  magnetization within the sample  in alignment \nwith the applied field. This type of metastable equilibrium is \ncommon in nature. A ball on a perfectly level table will remain \nstationary under normal conditions.  If someone hits the table \nwith a hammer, there is a chance that the ball will roll off the \ntable.  If someone hits the table with a hammer one hundred \ntimes, there is a larger probability  that the ball will roll off the \ntable.  When the ball falls from the table, the free energy of the \nsystem is lowered.  \nThe amount of energy imparted to the samples in this study \nis small , an amount that  can be transmitted to magnetic shields \neven after they are installed in cryomodul es. If cryomodule \nshields behave like the samples, then v ibrational energy from \nhandling an d transportation can cause the effect seen in this test.   \nMagnetic domain walls would  be arranged according to the \nmagnetic and mechanical history of the cryomodule’s journey \nto its final location.  The result is not likely to be the optimum \narrangement fo r permeability of the shield in -situ. \nDo cryomodule shields behave like the samples? By the time \nthat cryomodule shields are installed they have usually been \nsubjected to enough force to modify the grain structure and to \ncause permanent inter nal stress.  Previous m easurements \nindicate that the room temperature relative permeabilit y of \nCryoperm10 shields for Fermilab  International Linear Collider \n(ILC) cryomodules is not higher than 24,000 [5]. Measurements \non Cr yoperm10 shields for t he Linac Coherent Light Source -II \n(LCLS -II) prototype cryomodule indicate a relative \npermeability of 10,000. These values are significantly lower \nthan for any  samp le of this study.  \nCould in -situ mechanical stimulation be used to increase the \nrelative permeab ility of cryomodule shields? So far, the  answer \nseems to be, no. Sections of ILC and LCLS -II magnetic shields \nhave been tested in a similar manner to the samples in this \nstudy. No change was observed in effective permeability with  \napplied  mechanical stimulation , even with energy reaching 1.5 \njoules per Kilogram . Speculation is that this is due to grain \ndamage and stress c oncentration in the  ILC shields.  The \nprofound effect of stress on permeability of cryogenic magnetic \nshiel ding materials is demonstrated in reference [6].  \nWhere does this leave the SRF magnetic shield designer? \nHow does one answer the question “What is the permeability?” \nwhen designing shields? The answer is that the pe rmeability is \nunknown unless attenuat ion is measured in -situ under the exact circumstances that the shield will be used. The conservative \ndesigner will use a reasonable approximation of the worst case \npermeability for the material  that he is using , and include \nsuitable cryogenic magnetometr y in the cryomodule to measure \nthe field at the cavities for verification.  An assumed relative \npermeability of 10,000 appears to be a reasonable choice  to use \nfor mode ling until suitable techniques can be developed to \npreserve the fur nace treated permeability of  shielding  material . \n \nVII. CONCLUSION  \nSpecimens of magnetic shielding materials prepared for \ncryogenic use show large changes in their relative permeability \nwhen subjected to small mechanical shock. The effe ct is \nreversible, causing no permanent change to the magnetic \nproperties.  Limited m echanical shock increases the effective \npermeability  and therefore the ability of the material to \nattenuate applied field.  \nThe results of this study apply to carefully prep ared and \nhandled samples only. They do not represent practically \nrealizable permeability for real world magnetic shields.  Real \nworld performance is likely to be significantly worse than the \nattenuation factors measured here . \nVIII. FUTURE WORK  \nThe samples of thi s study will be tested at 77K and 4.2K . Work \nwill continue toward better understanding of the best realizable \npermeability for cryomodule magnetic shields, with special \nattention applied to identifying where the loss of permeability \noccurs from the anneali ng furnace to the cryomodule.  \nACKNOWLEDGMENT  \nThe author thanks Derrick Vanc e of Ad -Vance magnetics for \nproviding very interesting sample specimens  and for their \npreparation .  Thanks to Sam Posen for thoughtful  and helpful \ncomments on this report . \n  \nREFERENCES  \n[1] D. Gonnella, J. Kaufman, and M. Liepe, 2015, Nov 25, “Sensitivity of \nNiobium Superconducting Cavities to Trapped Magnetic Flux \nDissipation ,” Cornell Univ. , http://arxiv.org/pdf/1509.04127.pdf  \n[2] F. Pobell , “Matter and Methods at Low Temperatures,” Springer, 2007, p. \n367. \n[3] D. Meeker, Finite Element Method Magnetics, Version 4.2 (15Nov2013 \nBuild), http://www.femm.info  \n[4] A. Crawford, “Observation of Magnetic Superviscosity in Metglas \n2605SA1,”  http://arxiv.org/ftp/arxiv/papers/1511/1511.05127.pdf  \n[5] A. Crawford, “Modeling of Mechanical Overlap Joints in Ma gnetic \nShields,” http://arxiv.org/ftp/arxiv/papers/1510/1510.03846.pdf  \n[6] M. Masuzawa, K. Tsuchiya, A. Terashima, A. Dael, O.  Napoly, and J. \nPlouin, “Magnetic Shielding: Our Experience with  Various  Shielding \nMaterials, ”SRF2013  \nhttp://accelconf.web.cern.ch/AccelConf/SRF2013/papers/weiod02.pdf  \n \n  \n APPENDIX  \nMagnetic viscosity effects were observed in all the samples  of \nthis study.  This was especially evident when the sample \ncylinders were reversed in the 50 µTesla field.  The time \nconstant for decay of the attenuated field was approximately 10 \nseconds.  All measured values in this report are taken after the \nattenuated  field has approached its asymptotic limit (6 time \nconstants).  The materials of this study do not exhibit magnetic \nsuperviscosity effects as does  the Metglass of reference [4].  "    },    {        "title": "1601.01805v1.Extreme_Sensitivity_of_Magnetic_Properties_on_the_Synthesis_Routes_in_La___0_7__Sr___0_3__MnO__3_.pdf",        "content": "arXiv:1601.01805v1  [cond-mat.mtrl-sci]  8 Jan 2016preprint - thermoelectric group, iitp/iitb\nExtreme Sensitivity of Magnetic Properties on the Synthesi s\nRoutes in La 0.7Sr0.3MnO3\nAshutosh Kumar1, Himanshu Sharma2, C. V. Tomy2, Ajay D. Thakur1,3\n1Department of Physics, Indian Institute of Technology Patn a, Patna 801118, India\n2Department of Physics, Indian Institute of Technology Bomb ay, Mumbai 400076, India\n3Center for Energy and Environment,\nIndian Institute of Technology Patna, Patna 801118, India\n(Dated: January 11, 2016)\nAbstract\nLa0.7Sr0.3MnO3polycrystalline samples have been prepared using different s ynthesis routes. X-\nray Diffraction (XRD) confirms that the samples are of single ph ase with R ¯3c space group. The\nsurface morphology and particle size has been measured usin g Field Emission Scanning Electron\nMicroscopy (FESEM). Magnetic measurement shows that the ma gnetization in the materials are\naffected by low crystallite size which destroys the spin order ing due to strain at grain boundaries\nandinturnalsoleadtoreductioninmagnetization aswell as anenhancedcoercivity inthematerial.\nPACS numbers:\n1I. INTRODUCTION\nMagnetic measurements of divalent element substituted rare eart h manganites,\nR1−xAxMnO3where R= rare earth element (La, Pr, Sm etc.), A= divalent alkaline element\n(Sr, Ca, Ba, etc.), having perovskite structure have been widely in vestigated [1]. The inter-\nesting physical properties in these materials like colossal magnetor esistance, metal-insulator\ntransition, etc., where interplay of spin, charge and orbital couplin g leads to massive interest\ndue to many application in spintronics devices. However, The very dis covery of phenomenon\nlike double exchange, Jahn-Teller distortion have been successful to explain the physics be-\nhind the magnetic properties of these materials, where charge and spin ordering leads to\nconductivity and ferromagnetism at certain substitution at A-site by alkaline elements (fol-\nlowing Hunds rule). It has been widely investigated[1] that when La sit e in LaMnO 3is\npartially replaced by Sr, it becomes conducting and ferromagnetic i.e . La0.7Sr0.3MnO3. The\nmagnetic properties in La 0.7Sr0.3MnO3are affected by geometrical factors like shape, size,\nand structure. Since ferromagnetic materials consist of domains w hich are spontaneously\nmagnetized separated by domain walls, but formation of domains and domain walls depends\non different kinds of energy and also these domains and domains wall c an be affected due\nto size of the crystallite present in the material. In this report, we h ave investigated the\ncrystallite size affect on magnetic properties of La 0.7Sr0.3MnO3.\nII. EXPERIMENTAL DETAILS\nLa0.7Sr0.3MnO3(LSMO) samples were prepared by sol gel (SG) route, standard s olid\nstate route (SSR) and ball milling (BM) method. In standard SSR, St oichiometric amount\nof La2O3, SrCO 3and Mn 2O3were mixed and ground for 10 hours then heated at 1200oC for\n20 hours. Planetary ball milling was used for nanostructuring the pr epared material from\nSSR. For sol gel route, La(NO 3)3.6H2O, Sr(CH 3COO) 2and Mn(CH 3COO) 2were dissolved\nin deionized water in stoichiometric amount. All the individual water so lutions were mixed\nand required amount of citric acid (C 6H8O7) was added. The mixed solution was then\nheated at 120oC till gel formation and then at 150oC until the entire solution turns into\nblack powder. The powder were then ground for 30 minutes and hea ted at 900oC for 2\nhours. All the prepared samples were characterized for phase pu rity by X-ray Diffraction\n2(XRD)usingCu-K alpharadiation( λ= 1.5406˚A). Particlesizedistributionswerecalculated\nby using Scherers formula. The surface morphology of all the samp les was observed by Field\nEffect Scanning Electron Microscope (FESEM). The magnetic measu rement of samples was\ncompletedusingVibrationSampleMagnetometer(VSM)atroomtemp eratureinamagnetic\nfield of 2T.\nIII. RESULTS AND DISCUSSION\nLSMO samples prepared by different routesareof single phase, sho w rhombohedral struc-\nture with space group R −3c as shown in figure 1(a). It has been observed that the full width\nat half maximum (FWHM) of peak increases as we go from SSR to sol ge l to Ball milling\nroute. The FWHM is inversely proportional to the crystallite size of t he sample, according\nto Scherers formula, which is given by\nd=Kλ\nβcosθ(1)\nHereK0.9 (constant) and λ= wavelength of X-ray. Figure. 2. shows the FESEM\nimages of LSMO samples. The reduction in crystallite size has been con firmed by FESEM\nimagesFigure.3. shows thechangeincoercive field(H C)andsaturationmagnetization(M S)\nas a function of FWHM ( β). It has been observed that the M sand remnant magnetization\n(Mr) is maximum and H cis minimum for samples having large crystallite size (i.e. for SSR)\nwhile as the crystallite size decreases, H cincreases and M rand M sdecreases.\nThe magnetization in the materials are affected by domain walls, forma tion of which\ndepends on balance of several energies [2] like exchange energy wh ich is been used to align\nthe magnetic moment of the atoms in the material in the same directio n while orientation\nof magnetic moments in a particular direction is due to magneto cryst alline anisotropy and\nelimination of magnetization of the material is due to magneto static e nergy. When the\nsample consists of large crystallite size, they consist of multi domain structures in which\nthe magnetization regions are separated by domain walls. These dom ain walls result due to\nbalance of the external magneto static energy and domain wall ene rgy. The former increases\nas the volume of the particle increases and latter is due to materials h aving large interfacial\narea between the domains. As the size of the crystallite decreases , the volume reaches a\ncritical value called critical volume, below which the more energy is req uired to create a\n3domain wall than to balance the external magneto static energy.\nThevaluesofM s, MrandH cfordifferent synthesis routeareshownintable.1. Ithasbeen\nobserved that the reduced particle size also leads to a higher coerc ivity. When the particle\nsize are reduced enough to have only single domain particle and all the spins in the domain\nare aligned in the same direction and since there is no domain wall there fore when we apply\na magnetic field in opposite direction to demagnetize the sample, samp le gets demagnetized\nvia spin rotation rather than domain wall motion [3]. This leads to high c oercivity of the\nlow crystallite size materials. Also the decrease in magnetization is att ributed to the fact\nthat as the particle size of the material decreases, spins which are aligned in a particular\ndirection gets disordered due to strain created at the grain bound ary due to small crystallite\nsize of the material and therefore the saturation magnetization o f the material reduces.\nIV. CONCLUSION\nWe have successfully synthesized the LSMO samples through differe nt synthesis route.\nCrystallite size peak broadening effect has been confirmed by FESEM . The magnetic prop-\nerties of the samples suggest that as the crystallite size is reduced to a critical value, the\ndisordered spins in the materials at the grain boundary leads to low ma gnetization as well\nas spin rotation demagnetization leads to high coercive field in the sam ples.\n[1] M.B. Salamon, M. Jaime, Review of Modern Physics, 73, 200 1, 583-628.\n[2] C. Kittel, Introduction to solid state physics, (John Wi ley and sons, Inc, 2005).\n[3] S. Blundell, Magnetism in Condensed Matter, (Oxford Uni versity Press, 2001).\n4TABLE I: Magnetic parameters as a function of synthesis rout e\nSynthesis Route Saturation Magnetization (emu/g) Remnant Magnetization (emu/g) Coercive Field (Oe)\nSolid State Route 60.77 55.30 20\nSol Gel Route 40.60 31.60 859\nBall Milling 33.06 23.84 1283\n/s50/s48 /s51/s48 /s52/s48 /s53/s48 /s54/s48 /s55/s48 /s56/s48/s40/s49/s49/s51/s41\n/s40/s49/s51/s52/s41/s40/s51/s49/s50/s41/s40/s50/s48/s56/s41/s40/s50/s50/s48/s41/s40/s51/s48/s48/s41\n/s40/s48/s49/s56/s41/s40/s49/s49/s54/s41/s40/s49/s50/s50/s41/s40/s48/s50/s52/s41/s40/s48/s48/s54/s41/s40/s50/s48/s50/s41/s40/s49/s48/s52/s41/s40/s49/s49/s48/s41\n/s73 /s73 /s73 /s73 /s73 /s73 /s73 /s73 /s73 /s73 /s73 /s73 /s73 /s73 /s73\n/s32/s32/s73/s110/s116/s101/s110/s115/s105/s116/s121/s32/s40/s97/s46/s117/s46/s41\n/s50 /s32/s40/s100/s101/s103/s114/s101/s101/s41/s73\n/s40/s48/s49/s50/s41\n/s73/s67/s68/s68/s32/s70/s105/s108/s101/s32/s78/s111/s46/s45/s32/s48/s49/s45/s48/s56/s57/s45/s56/s48/s57/s54\nFIG. 1: (Color online) (a) XRD pattern of La 0.7Sr0.3MnO3samples prepared by (i) Solid State\nRoute (ii) Sol Gel route (iii) Ball Milling. (b) XRD peak broa dening of La 0.7Sr0.3MnO3samples\nfor (i) Solid State Route (ii) Sol Gel route (iii) Ball Millin g.\n5FIG. 2: (Color online) FESEM images of LSMOsamples prepared by (a) Solid State Route (b)\nSol Gel route (c) Ball Milling.\n/s51/s50/s46/s53 /s51/s51/s46/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s48/s46/s56/s49/s46/s48\n/s45/s48/s46/s52 /s45/s48/s46/s50 /s48/s46/s48 /s48/s46/s50 /s48/s46/s52/s45/s51/s48/s45/s50/s48/s45/s49/s48/s48/s49/s48/s50/s48/s51/s48/s32/s32/s73/s110 /s116/s101/s110 /s115/s105/s116/s121/s32/s40/s32/s97/s46/s117 /s46/s32/s41\n/s50 /s32/s40/s32/s100/s101/s103/s114/s101/s101/s32/s41\n/s32/s32/s77 /s32/s40/s32/s101/s109 /s117 /s47/s103/s32/s41\n/s77/s97/s103/s110 /s101/s116/s105/s99/s32/s102/s105/s101/s108/s100/s32/s40/s32/s84/s32/s41/s72\n/s67/s77\n/s83/s77\n/s114 \n/s48/s46/s49/s48 /s48/s46/s49/s53 /s48/s46/s50/s48 /s48/s46/s50/s53 /s48/s46/s51/s48 /s48/s46/s51/s53 /s48/s46/s52/s48 /s48/s46/s52/s53 /s48/s46/s53/s48 /s48/s46/s53/s53/s48/s50/s48/s48/s52/s48/s48/s54/s48/s48/s56/s48/s48/s49/s48/s48/s48/s49/s50/s48/s48/s49/s52/s48/s48\n/s40/s66/s77/s41/s40/s66/s77/s41\n/s40/s83/s71/s41/s40/s83/s71/s41\n/s40/s83/s83/s82/s41/s32\n/s70/s87/s72/s77/s44/s32 /s32/s40/s32/s100/s101/s103/s114/s101/s101/s32/s41/s72\n/s67/s32/s40/s32/s79/s101/s32/s41/s40/s83/s83/s82/s41\n/s51/s48/s51/s53/s52/s48/s52/s53/s53/s48/s53/s53/s54/s48/s54/s53/s77\n/s83/s40/s32/s101/s109/s117/s47/s103/s32/s41\nFIG. 3: (Color online) Variation of coercive field (H C) and saturation magnetization (M S) as a\nfunction of FWHM (for SSR- 0.15o, for SG- 0.40oand for BM- 0.50o). Left inset shows the FWHM\nfound by fitting the XRD data. Right inset is the M-H curve of LSMOsamples prepared by BM\nroute, showing the M S, Mrand HC.\n6"    },    {        "title": "1602.00262v2.Topological_Excitations_in_Magnetic_Materials.pdf",        "content": "Topological Excitations in Magnetic Materials\nD. Bazeia1\u0003, M.M. Doria2;3and E.I.B. Rodrigues1\n1Departamento de F\u0013 \u0010sica, Universidade Federal da Para\u0013 \u0010ba, 58051-970 Jo~ ao Pessoa, PB, Brazil\n2Instituto de F\u0013 \u0010sica, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil and\n3Dipartimento di Fisica, Universit\u0012 a di Camerino, I-62032 Camerino, Italy\n(Dated: September 25, 2018)\nIn this work we propose a new route to describe topological excitations in magnetic systems\nthrough a single real scalar \feld. We show here that spherically symmetric structures in two spatial\ndimensions, which map helical excitations in magnetic materials, admit this formulation and can be\nused to model skyrmion-like structures in magnetic materials.\nPACS numbers: 75.70.Kw, 75.50.-y, 11.27.+d\nI. INTRODUCTION\nMagnetic materials [1] are rich enough to support complex localized topological structures known as skyrmions\n[2, 3]. Indeed, depending of the type of material, the localized excitations may appear as isolated structures or as\nspatially organized arrays or lattices; see, e.g, Refs. [4{11], for theoretical investigations, and Refs. [12{15] for the\nexperimental observations of skyrmions and lattices of skyrmions. See also [16{21] and references therein, for other\ninteresting investigations on the subject.\nWe go back in time to the 1960's and note that, soon after the proposal of skyrmions, Hobard [22] and Derrick\n[23] stablished with simple scaling arguments that localized particle-like structures are not stable when described by\nscalar \felds in dimension greater then one. To circumvent the scaling obstruction, the authors of [24] have suggested\nmodi\fcation of the scalar \feld kinematics. More recently, in [25] one proposes a di\u000berent route, relying on taking\nthe scalar \feld with standard kinematics, but changing the way the self-interactions enter the game, with explicit\ndependence on the spatial coordinates. With the proposal of [25], it was possible to suggest the presence of stable,\nspherically symmetric structures in arbitrary spatial dimension, constructed from a single real scalar \feld.\nIn the current work we follow [25] to study the case of planar solutions which are skyrmion-like structures and can\nbe used to model magnetic excitations in planar magnetic metals such as the ones studied in [6{8, 11, 26]. Here we\nfocus on the presence of analytical solutions, paying attention to the case of excitations with the magnetization having\nconstant modulus, and we postpone to a future work other possibilities, in particular the case where the modulus of\nthe magnetization may vary.\nWe organize the work such that in Sec. II we describe some basic facts about skyrmions, and adjust the degrees of\nfreedom needed to model the planar skyrmion-like excitations which we suppose are present in the magnetic material.\nIn Sec. III we deal with models that describe the scalar \feld in two spatial dimensions, as suggested in [25]. There, we\nintroduce two distinct models and \fnd analytical results for the corresponding \feld con\fgurations and energy density.\nWe also study stability of the solutions and show an interesting way to describe the magnetization in the case where\nit is a vector of constant modulus, capable of mapping the presence of helical excitations in magnetic materials. The\ntwo models have di\u000berent solutions, and map magnetic excitations that connect distinct ground states, engendering\ndistinct properties, which appear associated with the corresponding skyrmion numbers. We also illustrate how the\nhelical pro\fle appears in each case. We end the work in Sec. IV, where we include our comments and conclusions.\nII. GENERALITIES\nLet us follow [7, 8, 11, 26] and comment on the planar model of interest in this work. In general, in models where the\nmagnetization vector is homogeneous along the z direction, the cylindrically symmetric magnetization is described\nby the two main degrees of freedom, one being the local amplitude of the magnetic moments and the other, the\ndirection in the plane, both as function r, the distance to the cylinder axis in cylindrical coordinates. The standard\nprocedure then relies on writing a free energy density, usually based on Dzyaloshinsky-Moriya interactions [27, 28]\nto obtain the equations of motion for the main degrees of freedom. This is a line of investigation, and that leads to\ntwo coupled second-order nonlinear di\u000berential equations. The speci\fc form of the equations depend on the model\n\u0003Corresponding author. Email: bazeia@\fsica.ufpb.brarXiv:1602.00262v2  [cond-mat.mes-hall]  31 Mar 20162\nunder consideration, and usually require numerical investigations. The models engenders several parameters, which\nare in general used to control the sti\u000bness, strength and other physical properties of the magnetic interactions in the\nmagnetic material.\nIn the current work we want to o\u000ber an alternative description to the numerical investigation, focusing mainly\non the construction of analytical results. As usual, we consider that the magnetization is homogeneous along the ^ z\ndirection, but we also suppose that it has constant modulus. Thus, the normalized magnetization vector has the form\nM=M1^x+M2^y+M3^z, and should obey the constraint M2\n1(x;y) +M2\n2(x;y) +M2\n3(x;y) = 1, which reduces the\nproblem to two degrees of freedom.\nWe will further reduce the problem to a single degree of freedom, supposing that the magnetization Mis a unit\nvector ortogonal to the radial direction ^ r, such that the model now engenders helical pro\fle, which is known to\nbe present in systems with D2dsymmetry, with the behavior reminding us of the magnetization vector for Bloch\nwalls in a diversity of ferromagnetic materials [1, 7]. The helical pro\fle which we investigate in the current work is\ninspired from [7], where it is well illustrated. This type of structure appears, for instance, in magnetic metals such as\nMnSi; see, e.g., [8, 26]. In cylindrical coordinates, the model is then described by M=M1(r;\u0012)^z+M2(r;\u0012)^\u0012, with\nM2\n1(r;\u0012) +M2\n2(r;\u0012) = 1.\nHowever, instead of describing the problem with two degrees of freedom and a constraint, we will model it via the\ndynamical scalar \feld that appears in [25], in the case of two spatial dimensions. Since we are dealing with helical\nexcitations, we have to consider the magnetization Mas a unit vector orthogonal to the radial direction. We use\ncylindrical coordinates to model this situation with the magnetization given by\nM= ^zsin\u0010\u0019\n2\u001e+\u000e\u0011\n+^\u0012cos\u0010\u0019\n2\u001e+\u000e\u0011\n; (1)\nwhere\u001eis a scalar \feld that may vary in the ( r;\u0012) plane, and \u000eis a constant. If \u001eis a uniform solution \u001e=constant ,\nwe have the magnetization vector pointing in a \fxed direction throughout the magnetic material, and this represents\na ground state. The constant phase \u000ecan be used to adequately describe the ground state of the system. Thus,\nwe have to search for \feld con\fgurations that vary in space, leading to the construction of magnetic solutions, that\nconnect distinct ground states and have non vanishing energy density and positive energy, when compared to the\nenergy of the ground states.\nMoreover, since we are searching for skyrmions, we follow the usual route, and we introduce the skyrmion number,\nthe topological quantity that usually appears in the investigation. It is given by\nQ=1\n8\u0019Z\nd2xM\u0001@iM\u0002@jM\"ij; (2)\nwherei;j= 1;2, and@istands for the derivative with respect to xi, with\u000fijbeing the completely antisymmetric\ntensor such that \u000f12= 1. This topological quantity will guide us to the search of skyrmions in the models that we\ninvestigate below.\nBefore investigating the \feld con\fguration, however, let us comment a little further on the behavior of the magnetic\nsolutions that we are going to study below. We see from Eqs. (1) and (2) that the scalar \feld determines both the\nmagnetization and the skyrmion number. Moreover, the energy associated to the \feld con\fguration depends on the\nspeci\fc model and the basic symmetries which we use to describe it. We then focus on this, and we model the\nmagnetization with the scalar \feld investigated in [25], as we explain in details in the next Section.\nIII. THE MODELS\nLet us now pay attention to the scalar \feld \u001ewhich we introduced in Eq. (1). We suppose that it is described by\nthe planar model of Ref. [25]. Thus, the Lagrange density Lhas the form\nL=1\n2_\u001e2\u00001\n2r\u001e\u0001r\u001e\u0000U(\u001e); (3)\nwhere dot stands for time derivative, and rrepresents the gradient in the ( x;y) or (r;\u0012) plane. In the case of time\nindependent and spherically symmetric con\fguration, \u001e=\u001e(r), it is supposed to obey the equation of motion\n1\nrd\ndr\u0012\nrd\u001e\ndr\u0013\n=dU\nd\u001e; (4)\nwhereU=U(r;\u001e) is given by\nU(r;\u001e) =1\n2r2P(\u001e); (5)3\nwithP(\u001e) an even polynomial which contains nongradient terms in \u001e. The energy for solution \u001e=\u001e(r) is given by\nE= 2\u0019Z1\n0rdr\u001a (r); (6)\nwith\u001a(r) being the energy density, such that\n\u001a(r) =1\n2\u0012d\u001e\ndr\u00132\n+1\n2r2P(\u001e): (7)\nThis is the framework we use to describe the scalar \feld \u001ethat controls the magnetization which we proposed in (1).\nWe go on and get inspiration from the Landau theory to expand the nongradient contributions that appears from\nP(\u001e) to consider two di\u000berent possibilities, which lead to two distinct models, described by\nP4(\u001e) =1\n(1\u0000s)2(\u0016s2\u0000\u001e2)2; (8)\nand\nP6(\u001e) =1\n(1\u0000s)2\u001e2(\u0016s2\u0000\u001e2)2; (9)\nwhere the dimensionless parameters s2[0;1) and \u0016s >0 are introduced to control the strength of the interactions,\nwhich is important to make contact with realistic models. The two models engender spontaneous symmetry breaking,\nas it is required for the presence of topological structures: the \frst model presents interactions modulated by the\nfourth-order power in the \feld, and support two asymmetric ground states, \u0016\u001e\u0006=\u0006\u0016s. We will use these two ground\nstates and the magnetization (1) to guide us to describe magnetic excitations in this model in Sec. III B. The second\nmodel is di\u000berent, and presents interactions modulated by the fourth- and sixth-order power, supporting a symmetric\nground state, \u0016\u001e0= 0, and two asymmetric ones, \u0016\u001e\u0006=\u0006\u0016s. Also, we will use these ground states and the magnetization\n(1) to guide us to describe magnetic excitations in this model, in Sec. III B. For simplicity, we will take \u0016 s= 1 from\nnow on.\nWe follow Ref. [25] and consider that the \feld, coordinates and parameters are all dimensionless, so we shall need\nto introduce a quantity to measure distance. This is an important issue, which we further deal with below. The\nmodels (8) and (9) are known to support kinklike solutions in one spatial dimension, and here we will show that they\nsupport stable radial con\fgurations having energy density localized around a given radial position, depending on the\nvalue ofs. We then associate swith the characteristic size of the structure. We do this denoting the size \u0016 ras the\nmean matter radius of the \feld con\fguration, de\fned as the radial distance rweighted by the energy density of the\nstatic scalar \feld which we will use below to describe the skyrmion con\fguration. This mean matter radius is given\nby\n\u0016r=R1\n0\u001a(r)r2drR1\n0\u001a(r)rdr: (10)\nThis de\fnition is very natural, since we are working with static \feld and so the energy corresponds to the mass of\nthe con\fguration. We can use it to describe the size of the skyrmion; see, e.g., Refs. [18, 19], for other investigations\nconcerning this issue.\nWe can also attain to the structure, a topological property. Since the \feld con\fguration at the origin \u001e(0) should\nrepresent a ground state, and since it should connect another ground state asymptotically, we must have \u001e(0)6=\u001e(1).\nWe can describe the correct pro\fle using speci\fc boundary conditions, which will be of good use to de\fne the skyrmion\nnumber associated to the magnetization vector, as we further investigate below. To explore this route, let us \frst deal\nwith the model (8); we can write its equation of motion as\nr2d2\u001e\ndr2+rd\u001e\ndr+2\u001e(1\u0000\u001e2)\n(1\u0000s)2= 0: (11)\nWe see that if \u001eis a solution, so is \u0000\u001e. We shall then concentrate on one of them. We consider the boundary\nconditions such that \u001e(0) = 1 and \u001e(1) =\u00001, which are compatible with the form of the polynomial interactions\nthat the model engender, as we see from (8), and from the equation of motion (11) as well. We have been able to\nsolve (11) analytically for sarbitrary, and the solution can be expressed in the form\n\u001es(r) =1\u0000r2=(1\u0000s)\n1 +r2=(1\u0000s): (12)4\nr\n/Minus11Φ/LParen1r/RParen1\nrΡ/LParen1r/RParen1\nFIG. 1: (Color online) The solution (left panel) and the energy density (right panel) for the model (8), depicted for s= 0 with\nblack, dotted line, for s= 0:4 with blue, dashed line, and for s= 0:8 with red, solid line.\nAs we commented before, there is another solution, with the minus sign, which behaves similarly. We depict the\nsolution (12) in Fig. 1, for some values of s.\nThe corresponding energy density \u001a(r) is given by (7), associated to the \feld theory model (3). It has the form\n\u001as(r) =16r2(1+s)=(1\u0000s)\n(1\u0000s)2(1 +r2=(1\u0000s))4: (13)\nWe also depict the energy density in Fig. 1. We see that it becomes sharper and sharper, as sincreases in the interval\n[0;1). The total energy is given by\nE=8\u0019\n3(1\u0000s): (14)\nIt increases as sincreases in the interval [0 ;1), and we note that the sharper the solution is, the higher the energy\nbecomes. Also, we follow (10) and introduce the size of the solution. It is \u0016 rs, and it is given by\n\u0016rs=\u0019(3\u0000s)(1\u0000s2)\n8 cos\u0000\u0019\n2s\u0001: (15)\nFor the second model (9), the equation of motion is\nr2d2\u001e\ndr2+rd\u001e\ndr\u0000\u001e(1\u0000\u001e2)2\n(1\u0000s)2+2\u001e3(1\u0000\u001e2)\n(1\u0000s)2= 0: (16)\nThe situation here is di\u000berent, since the model (9) has three minima, one at zero, and two at \u00061. They are uniform\nsolutions, which correspond to distinct ground state possibilities. Also, we note that if \u001eis solution, so is\u0000\u001e. Thus,\nwe now search for solution that obey the boundary conditions \u001e(0) = 0 and \u001e(1) = 1. Such solution corresponds to\na \feld con\fguration that connects the two ground states \u001e= 0 and\u001e= 1. We have been able to solve the equation\nof motion exactly, and we could write the solution in the form\n\u001es(r) =r1=(1\u0000s)\np\n1 +r2=(1\u0000s): (17)\nWe depict this solution in Fig. 2, for some speci\fc values of s.\nThe energy density is this case has the form\n\u001as(r) =r2=(1\u0000s)\n(1\u0000s)2(1 +r2=(1\u0000s))3; (18)\nwhich is also depicted in Fig. 2. The total energy is given by\nE=\u00192s\n2 sin(\u0019s): (19)5\n0r1Φ/LParen1r/RParen1\nrΡ/LParen1r/RParen1\nFIG. 2: (Color online) The solution (left panel) and the energy density (right panel) for the model (9), depicted for s= 0 with\nblack, dotted line, for s= 0:4 with blue, dashed line, and for s= 0:8 with red, solid line.\nWe see that it increases as sincreases in the interval [0 ;1), and we note that the sharper the solution is, the higher\nthe energy becomes; see Fig. 2. The behavior is similar to the case observed in the previous model. In this case, the\nmean matter radius has the form\n\u0016rs=3(1\u00003s) sin(\u0019s)\n4scos\u00003\u0019\n2s\u0001: (20)\nA. Stability\nAs we have just shown, the solutions (12) and (17) are obtained under speci\fc boundary conditions, which suggest\nthat they are stable. In spite of this, we now study stability of the solutions against spherically symmetric deformations.\nWe study stability using that \u001e=\u001es(r) +\u000f\u0011s(r), with\u000fbeing very small real and constant parameter. We then\nexpand the total energy in the form\nE\u000f=E0+\u000fE1+\u000f2E2+\u0001\u0001\u0001 (21)\nwhereEn;n= 1;2;:::is the contribution to the energy at order nin\u000f. For the model (8), Engoes up to n= 4, and\nfor the model (9), Engoes up ton= 6. Of course, E0is the energy of the solution \u001es(r), and we can use the equation\nof motion to show that E1= 0. We have that the energy of the solution is\nE0= 2\u0019Z1\n0rdr \n1\n2\u0012d\u001es\ndr\u00132\n+1\n2r2P(\u001es)!\n: (22)\nFor the model (8) it gets to the form\nE0=8\u0019\n3(1\u0000s): (23)\nIt reproduces the previous result (14), as expected. Also, from E1= 0 we get that the zero mode is given by\n\u0011s(r) =Asr2=(1\u0000s)\n(1 +r2=(1\u0000s))2: (24)\nHere,Asis a normalization constant, which depends on s. We can then show that E2= 0,E3= 0, andE4has the\nform\nE4=3\u0019\n35(1\u0000s): (25)\nWe see that it is positive, E4>0, and this shows that the energy E0is a minimum of E\u000ffor the model (8), so the\nsolution\u001es(r) which we obtained in (12) is stable against spherically symmetric \ructuations. We follow the same\nsteps for the model (9). We have that\nE0=\u00192s\n2 sin(\u0019s); (26)6\n(a)\n(b)\n(c)\nFIG. 3: (Color online) The magnetization Mfor the model (8), depicted in (a), (b) and (c) for s= 0;0:4 and 0 :8, respectively.\nas expected from (19). Also, from E1= 0 we get that the zero mode is now given by\n\u0011s(r) =Asr2=(1\u0000s)\n(1 +r2=(1\u0000s))3=2: (27)\nWe can show that E2= 0 and\nE3=15\u00192\n64(1\u0000s): (28)\nWe see that it is positive, E3>0, and this shows that the spherically symmetric solution (17) is stable against\nspherically symmetric \ructuations.\nThe spherically symmetric solutions that we have found may also be disturbed by non spherically symmetric\n\ructuations. This would appear from the presence of defects and/or impurities in the magnetic material, and also\nfrom external \felds. Such perturbations would break the spherical symmetry which we consider to be present in\nthe system, so we do not study them here. We emphasize that we are supposing that the magnetic material is\nhomogeneous along the zdirection, to make it a planar system, and that it behaves along the planar directions, in a\nway such that the spherical symmetry is e\u000bective in the plane.\nB. The planar solutions\nWith the assumptions discussed in the previous sections, we can now concentrate in the planar system, and search\nfor an appropriate way to represent the magnetization. As we have stated in Sec. II, we are dealing with helical\nexcitations, with the magnetization Mbeing a unit vector orthogonal to the radial direction. In the case of the model\ndescribed by the polynomial (8), we have two distinct ground states, one with the magnetization vector pointing along\nthe positive zaxis, and the other, along the negative zaxis. We can represent this situation with the magnetization\n(1) with\u000e= 0, which gives\nM= ^zsin\u0010\u0019\n2\u001e(r)\u0011\n+^\u0012cos\u0010\u0019\n2\u001e(r)\u0011\n: (29)\nThis shows that if \u001eis the uniform solution \u001e=\u00001, we have the magnetization vector pointing downward in the\n^zdirection in the magnetic material. If the uniform solution is \u001e= 1, we have the magnetization vector pointing7\nFIG. 4: (Color online) The magnetization Mfor the model (9), depicted in (a), (b) and (c) for s= 0;0:4 and 0 :8, respectively.\nupward in the ^ zdirection in the magnetic material. These are the two possible ground states. However, if the \feld \u001e\nis represented by the solution (12), we have another state, with energy given by (14). If we take the magnetization\nvector as in (29), with \u001e(r) given by (12), we then have an array of vectors in the plane, which represents the helical\nmagnetic excitation which is depicted in Fig. 3 for three distinct values of s. The magnetization vectors that we depict\nin Fig. 3 describe magnetic excitations supported by \frst model, investigated above.\nWe now concentrate on the second model (9). For \u001ebeing uniform \feld con\fguration, the model has three distinct\nground states, one with \u001e= 0, and two with \u001e=\u00061. Here we take the two ground states \u001e=\u00061 represented by\nvectors pointing in the positive or negative sense, along the ^\u0012direction. Also, we consider the uniform ground state\n\u001e= 0 represented by the magnetization vector along the ^ zdirection. With this in mind, we describe the magnetization\n(1) with\u000e=\u0019=2, in the form\nM= ^zcos\u0010\u0019\n2\u001e(r)\u0011\n+^\u0012sin\u0010\u0019\n2\u001e(r)\u0011\n: (30)\nWe then use the result in Eq. (12) to show that the magnetization (30) describes an array of vectors in the plane,\nwhich represents the helical magnetic excitations that we depict in Fig. 4 for some values of s.\nC. Skyrmion number\nLet us now concentrate on the skyrmion features of the solutions found above. The fact that we have found stable\nsolutions with speci\fc boundary conditions encourages us to investigate how to attain skyrmion number to them.\nWe introduced the skyrmion number in Eq. (2), which we now use to make it explicit. Since M=M(r), we change\nvariables from ( x;y) to (r;\u0012) in Eq. (2) and use Eq. (1) to get the result\nQ=\u00001\n2sin\u0010\u0019\n2\u001e(1)+\u000e\u0011\n+1\n2sin\u0010\u0019\n2\u001e(0)+\u000e\u0011\n: (31)\nThis is the expression we have to use to associate skyrmion number to the magnetic solutions that we found above.\nAs expected, it only depends on the asymptotic behavior os the scalar \feld. Thus, since the asymptotic behavior of\nthe scalar \feld is associated to the boundary conditions we used to solve the equation of motion, and since they are\nused to describe stable ground state solutions of the model under investigation, it appears that the above skyrmion\nnumber is a very natural choice in the current investigation.\nTo make the skyrmion number explicit, we now focus attention on the two models studied above. We consider the\n\frst model, where \u001e(0) = 1,\u001e(1) =\u00001, and\u000e= 0, to get Q= 1. Thus, the magnetic excitation described in Fig. 5\nhas skyrmion number Q= 1; the other magnetic excitation, with \u001e!\u0000\u001ehas skyrmion number Q=\u00001. For the\nsecond model, we have \u001e(0) = 0,\u001e(1) = 1, and\u000e=\u0019=2, and so we get Q= 1=2; the other magnetic excitation, with\n\u001e!\u0000\u001ehas skyrmion number Q=\u00001=2. These solutions are then skyrmions, but they are di\u000berent from each other.8\nThe solutions with Q=\u00061=2 are vortices [29, 30], and we see here that vortices ( Q=\u00061=2) and skyrmions\n(Q=\u00061) appear under similar dynamical assumptions, controlled by the scalar \feld model (3), but requiring distinct\npolynomial contributions, as noted from the two models (8) and (9). This approach considers the dynamics of\nvortices and skyrmions qualitatively similar, described under the same framework, and is in accordance with the\ncurrent understanding; see, e.g., Ref. [31].\nIn order to highlight the di\u000berence between the two solutions, we note that we can associate a number of the chiral\ntype to the localized excitations that we found in the second model, depicted in Fig. 4. We see from the solutions\nthere depicted, that they have a chiral-like number (+); the excitations obtained with the sign change \u001e!\u0000\u001ewould\nthen have chiral-like number ( \u0000). This is an interesting feature, which is not present in the \frst model, depicted in\nFig. 3. Thus, they may have di\u000berent collective behavior, as we \fnd if we want to construct a lattice of excitations, for\ninstance. We can use the magnetic excitations of the \frst model to construct both the triangular and square lattices,\nbut with the excitations of the second model, we will end up with frustration, if we want to construct the triangular\nlattice. This behavior is similar to the e\u000bect that appears in a triangular lattice of spins with antiferromagnetic\ninteractions.\nBefore ending the work, it seems of interest to further highlight the helical pro\fle of the magnetic excitations\ndepicted in Figs. 3 and 4. We illustrate this in Fig. 5, where we show how the magnetization rotates in the plane\northogonal to the radial direction, as a function of r. We depict the magnetization vector Mwith similar colors and\nthe same values of rthat we have used to draw both Figs. 3 and 4. As it is clear, the magnetization has constant\nmodulus, but it rotates in the (^ z;^\u0012) plane asrincreases to higher and higher values.\nFIG. 5: (Color online) Illustration of the magnetization vector Mfor the two models, depicted with s= 0 for the model (8) in\nthe bottom panel, and with s= 0:8 for the second model (9) in the top panel.\nIV. ENDING COMMENTS\nIn this work we studied the presence of localized structures of the skyrmion type in planar magnetic materials. We\ndescribed the magnetization vector Min terms of a single degree of freedom, in the case of helical excitations, in\nwhich the magnetization has constant modulus but is allowed to rotate in the (^ z;^\u0012) plane, orthogonal to the radial\ndirection. The topological excitations that we found are skyrmions, and we could associate a skyrmion number to\nthem.\nWe used the scalar \feld \u001e, which is described by the model of Ref. [25] in the case of two spatial dimensions, to\ncontrol the magnetization M, in the plane orthogonal to the radial direction. The assumption that the magnetization\nis orthogonal to the radial direction is appropriate to describe helical excitations in magnetic metals, as suggested\nbefore in [7, 8] and identi\fed experimentally for instance in [12].\nAll the results obtained in the current work are constructed analytically, and they seem to map magnetic excitations\nvery appropriately. For the second model, de\fned from (9), we have identi\fed magnetic excitations that present a\nchiral feature, being di\u000berent from the magnetic excitations that appear in the \frst model, de\fned from (8). The study\nencourages us to go further and investigate other models, described with di\u000berent polynomials P(\u001e), contributing to\ngenerate magnetic excitations with distinct pro\fle. Also, we can study models described by two or more real scalar\n\felds, leading to a richer distribution of minima, which could be of good use to describe more general scenarios; see,\ne.g., Ref. [32, 33] for some studies of kinks with two real scalar \felds in one spatial dimension, that can be seen as\nbackground for the investigation in two spatial dimensions.\nWe can also consider the case where the size of the magnetization vector is allowed to vary along the radial direction.\nAnother issue of current interest concerns the formation of lattices of magnetic solitons. As we have commented at the9\nend of the previous section, an interesting situation occurs if we think of constructing a triangular lattice of excitations\nwhich appear in the second model, since the triangular con\fguration would con\rict with the boundary conditions\nrequired to support each excitation in the lattice. These and other related issues are presently under consideration,\nand will be reported elsewhere.\nThis work is partially supported by the Brazilian agency CNPq. DB thanks support from grants CNPq:455931/2014-\n3 and CNPq:06614/2014-6, and MMD and EIBR acknowledge support from grants CNPq:23079.014992/2015-39 and\nCNPq:160019/2013-3, respectively.\n[1] A. Hubert and R. Sch afer, Magnetic Domains. The Analysis of Magnetic Microstructures (Springer-Verlag, 1998).\n[2] T.H. Skyrme, Proc. R. Soc. Lond. Ser. A 260, 127 (1961).\n[3] N.S. Manton and P.M. Sutcli\u000be, Topological Solitons (Cambridge, 2004)\n[4] A.N. Bogdanov and D. A. Yablonskii, Sov. Phys. JETP 68, 101 (1989).\n[5] A. Bogdanov and A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994).\n[6] A. Bogdanov and A. Hubert, J. Magn. Magn. Mater. 195, 182 (1999).\n[7] A.N. Bogdanov, U.K. R ossler, M. Wolf, and K.-H. M uller, Phys. Rev. B 66, 214410 (2002).\n[8] U.K. R ossler, A.N. Bogdanov, and C. P\reiderer, Nature 442, 797 (2006).\n[9] B. Binz, A. Vishwanath, and V. Aji, Phys. Rev. Lett. 96, 207202 (2006).\n[10] S. Tewari, D. Belitz, and T.R. Kirkpatrick, Phys. Rev. Lett. 96, 047207 (2006).\n[11] A.B. Butenko, A.A. Leonov, A.N. Bogdanov, and U.K. R oler, Phys. Rev. B 80, 134410 (2009).\n[12] S. M uhlbauer et al. Science 323, 915 (2009).\n[13] X.Z. Yu et al. Nature 465, 901 (2010).\n[14] C. P\reiderer, Nature Phys. 7, 673 (2011).\n[15] S. Heinze, Nature Phys. 7, 713 (2011).\n[16] A. Fert, V. Cros, and J. Sampaio, Nature Nanotech. 8, 152 (2013).\n[17] N. Nagaosa and Y. Tokura, Nature Nanotech. 8, 899 (2013).\n[18] K. von Bergmann, A. Kubetzka, O. Pietzsch, and R. Wiesendanger, J. Phys. Condens. Matter 26, 394002 (2014).\n[19] N. Romming et al. Phys. Rev. Lett. 114, 177203 (2015).\n[20] N. Romming, A. Kubetzka, and C. Hanneken, Phys. Rev. Lett. 114, 177203 (2015).\n[21] W. Jiang et al. Science 349, 283 (2015).\n[22] R. Hobart, Proc. Phys. Soc. Lond. 82, 201 (1963).\n[23] G.H. Derrick, J. Math. Phys. 5, 1252 (1964).\n[24] H. Aratyn, L.A. Ferreira, and A.H. Zimerman, Phys. Rev. Lett. 83, 1723 (1999).\n[25] D. Bazeia. J. Menezes, and R. Menezes, Phys. Rev. Lett. 91, 241601 (2003).\n[26] P. Bak and M.H. Jensen, J. Phys. C 13, L881 (1980).\n[27] I. Dzyaloshinsky, J. Phys. Chem. Solids, 4, 241 (1958).\n[28] T. Moriya, Phys. Rev. 120, 91 (1960).\n[29] M. Schneider et al. Appl. Phys. Lett. 77, 2909 (2000).\n[30] A. Wachowiak et al. Science 298, 577 (2002).\n[31] J.-V. Kim, Phys. Rev. B 92, 014418 (2015).\n[32] D. Bazeia and F.A. Brito, Phys. Rev. D 61, 105019 (2000).\n[33] P.P. Avelino, D. Bazeia, R. Menezes, and J.C.R.E. Oliveira, Phys. Rev. D 79, 085007 (2009)."    },    {        "title": "1602.01134v1.Magnetic_Field_Tunable_Capacitive_Dielectric_Ionic_liquid_Sandwich_Composites.pdf",        "content": "1\n \n \nMagnetic Field Tunable Capacitive Dielectric:Ionic\n-\nliquid \nSandwich Composites\n \nYe Wu\n \nT\nhe University of Texas at San \nAntonio,\n \nDepartment of Electrical and Computer Engineering, One UTSA \nCircle, San Antonio, TX 78249.\n       \n \nAbstract\n: \nWe examine\nd\n \nthe \ntunability\n \nof the capacitance for GaFeO\n3\n-\nionic liqui\nd\n-\nGaFeO\n3\n \ncomposite material \nby external\n \nmagnetic \nand electric \nfield. Up to \n1.6\n \nfolds\n \nof capacitance\n \ntunability could be achieved \nat 957kHz \nwith \nvoltage\n \n4\nv\n \nand magnetic field\n \n0.02T\n \napplied\n. We show that the \ncapacitance\n \nenhancement is due to the \npolarization coupling between dielectric layer and ionic liquid layer.\n \nPACS codes:81\n \nKeywords\n: \nmagnetocapacitance,ionic liquid\n, capacitance enhancement\n \n1.\nINTRODUCTION\n \nThere could be two effective strategies for \nstrengthening the\n \nelectro\n-\nmagnetic coupling\n \nin material\ns\n. \nOne \nstrategy\n \nis\n \nthe introduction of magnetic ion dopant to make nonmagnetic\n \nelectric \nmaterials\n \nmagnetic. This is shown in \nthe\n \nsynthesis of\n \nroom temperature ferromagnetic or antiferromagnetic \nsemiconductor\ns\n,\n[1]\n-\n[\n5\n]\n \nwh\nich \nis made by dopping magnetic \nparticles\n \ninto III\n-\nV semiconductors.\n \nDue \nto the low solubility of magnetic particles in the semiconductor composites, the \nelectro\n-\nmagnetic \neffects\n \nis relatively small.\n[\n1\n]\n \n  \nAnother strategy is to\n \nreconstruct\n \nelectric counterparts of conventional magnetic compound. This \ninvolves the reconstruction of the \ncharge density\n \nand\n \nthus\n \nthe electrical\n \nmodification of\n \nthe\n \nelectric \npolarization in the\n \nmagnetic material \nsystem.\n \nOne approach could be integrating guest material which \ncontains high carriers concentration.  \nOne candidate for this approach \ncould be the\n \nionic liquid, a 2\n \n \nconductive fluid which has been\n \nintensively used \nfor \ncarriers \nengineering of \nstrongly correlated \nelectron system. \nFor example, it has been used for introducing novel superconducting states,\n \nachieving\n \nelectroresistance tunability.\n \n[6]\n-\n[14]\n. \nIn this letter\n, we\n \nsandwiched the ionic li\nquid between \ntwo GaFeO\n3\n \nlayers, a we\nll known \nmultiferroic\n \nmaterials.\n[15]\n-\n[21]\n \nWe\n \nperform\ned\n \nthe study of dielectric response of the GaFeO\n3\n-\nionic liquid\n-\nGaFeO\n3\n \ncomposite \nmaterial\n \nunder external magnetic field and bias voltage\n. \nWe expect th\nis\n \ncomposite material could hold \nthe \nelectro\n-\nmagneto\n-\ndielectric properties. The motivation for this strategy is to find out the\n \nhighly\n \ntunable\n \ndielectric response \nof\n \ncomposite material\n \nwith respect\n \nto the external field\n, which is crucial \nfor possible \nfuture applications in tunable microwave devices.\n \n2.Experiments.\n \nThe \nGaFeO\n3\n \nthick film \nsamples\n(110nm)\n \nused in the study were produced by polymer assis\nted \ndeposition\n \nmethod\n.[\n22\n] \nThe \nGaFeO\n3\n \nphases were\n \nconfirmed by x\n-\nray powder diffraction.\n \nThe phases \nwas confirmed by XRD (Fig\nure \n1(\na\n)). The structure of \nGaFeO\n3\n \nwas refined and drawn by GSAS \nsoftware package. [\n23\n][\n24\n] Then the refined unit cell is drawn by DRAWxtl.[\n25\n]\n \nO\nne drop of\n \nionic \nliquid \n1\n-\nn\n-\nButyl\n-\n3\n-\nmethylimidazo\n-\nli\n-\numh\nexafluorophosphate\n \n(Alfa Aesar) \nwas placed between two \nslides of GaFeO\n3\n \nand\n \nmechani\ncally\n \npressed to have a thickness around 100\nm\n\n. \nThis gave us \nthe \nGaFeO\n3\n-\nionic liquid\n-\nGaFeO\n3\n \nsandwich structure.\n \nThe electric resistivity was measured by a standard \n4 probes measurement setup equipped with an oven. \nThe temperature hadn’t\n \nbeen\n \nincrease\nd\n \nto higher \nthan \n398\nK for sample damage concern.\n \nThe magnetic field strength up to 21A/m was generated by a \nDC magnet. A dc power source( Agilent E3648A) was used for applying external bias voltage. \nWe \nmeasured the capacitance\n \nusing a LCR met\ner (Hp HEWLETT PACKARD 4284A).\nIn order to \neliminate possible leakage current from power source, the sample was placed between two 3\n \n \ncommercial capacitors \nwhich\n \nprovide isolation. \nThe measurement unit was \nfurther \nelectrically \nshielded and guarded in order to \nprevent leakage current.\n \nThe magnetic field direction is \nperpendicular to the sample surface.\n \nT\nhe capacitance \nof the GaFeO\n3\n-\nionic liquid\n-\nGaFeO\n3\n \nsandwich \nstructure \nwas measured \nwith respect to the external magnetic field and \nunder \ndc voltage\ns\n.\n \n3.\nTheory\n.\n \nFor the following, \nit would be important to explore\n \nthe nature of magento\n-\nelectro\n-\ndielectric coupling \nin this composite material. Since it contains the bulky ionic liquid layer and the magnetic layer, we \nmay suppose the total electric polarization is the s\nuperposition of the two kinds of polarization \ngenerated from these two distinct layers. This assumption is based on our dielectric measurement of \nionic liquid and GaFeO\n3\n \nmaterial. The dielectric response of either GaFeO\n3\n \nor ionic liquid doesn’t \nshow any di\nstinct characterization when electric field or magnetic field is applied. \n \nWe suppose there are three major kinds of electric polarization in this composite material. The first is \nthe polarization P\n1 \nthat is generated from the dielectric layer of GaFeO\n3\n. T\nhe second is P\n2\n \nfrom the \nionic liquid layer and the third is from the interface polarization between the GaFeO\n3\n \nand ionic liquid \nlayer, which could be represented by\n2\n0\n2\n1\n0\n1\n12\nE\nCP\nE\nCP\nP\n\n\n\n\n\n\n.\n                      \n(3.1)\n \n  \nHere C represents the coupling factor[\n2\n6\n] between the GaFeO\n3\n \nand ionic liquid layer. E\n1\n \nand E\n2\n \nare \nthe local electric field which could be fitted from the experimental data. The total polarization is \n3\n2\n2\n1\n1\n\n\n\n\n\n\nP\nP\nP\n,    \n                                                      \n  \n(3.2)\n \nwhere \nλ\n1\n,\nλ\n2\n \nand \nλ\n3\n \nare the constants which could be fitted from the experimental data.P\n12\n \nis not shown \nin this expression, since it could be also represented by P\n1\n \nor P\n2\n \nin Eq.(3.1) . \n \nP\n1\n \ncould be calculated using classical method,[2\n7\n]\n0\n1\n)\n(\n4\n\n\n\n\n\n\n\n\n\nH\nC\nC\nE\n      \n  \n       \n(3.3)\n \nwhere \nC\nω\n \nis the parameter which depends on the electric signal frequency. \nC\nβ\n \nis the constant that is 4\n \n \nassociated with\n \nΣ\nH\nβ\n. E is the electric field across the sample.\n \nIn the following, we will calculate P\n2\n. \nTh\nis\n \ncalculation of the second kind of polarization could be \nstarted from the analysis of ions dynamic \nwith respect\n \nto the magnetic field. \n \n  \nThe ionic liquid would involve with the process of the exchange of two ions, which is actually the \nreplacement of an anion by a cation. \n[28]\n[\n29]\nWe consider an anion in position A is replaced by a \ncation in position B. For simplicity, the velocity of cation\n \nfrom A to B is supposed to be the same with \nthat of anion from B to A. The charge\nQ\nwould undergo a magnetic force\nQHv\n \nand travel with a \ncertain distance of\nx\n.\n \n  \nThe work required in this exchange is \n \nQHvx\nQ\nx\nQHv\nQ\nQ\nW\nA\nB\nAB\nAB\nA\nB\nB\nA\n2\n)\n(\n2\n2\n)\n(\n)\n)(\n(\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n,\n               \n(\n3.4\n)\n \nWhere\nQHvx\n2\n \nis the work attributed to the magnetic force.\n \n  \nUsing Boltzmann’s law, the equilibrium ionic concentrations at the two spots are in the ratio of \n \n]\n2\n)\n(\n2\nexp[\n)\nexp(\nkT\nQHvx\nQ\nkT\nW\nc\nc\nB\nA\nA\nB\n\n\n\n\n\n\n\n          \n                           \n(\n3.5\n)\n \n  \nWe assume the total ionic concentration is constant, which is\nc\nc\nc\nA\nB\n\n\n.\n                \n(\n3.6\n)\n \n  \nUsing Eq.(3.5) and Eq.(3.6\n), we can derive \n)\nexp(\n1\nt\nc\nc\nA\n\n\n, (\n3\n.\n7\n) \n)\nexp(\n1\n)\nexp(\nt\nt\nc\nc\nB\n\n\n,(\n3\n.\n8\n)where \nkT\nQHvx\nx\nQ\nkT\nQHvx\nQ\nt\nB\nA\n2\n)\n(\n2\n2\n)\n(\n2\n\n\n\n\n\n\n\n\n. (\n3\n.\n9\n)\n \nThe Poission’s law indicates \n\n\n\n)\n(\n)\n(\n2\n2\nx\ndx\nx\nd\n\n\n.       \n                             \n(\n3.10\n)\n \nHere the charge density could be expressed as\n)\nexp(\n1\n)\n1\n)\n(exp(\n)\n(\n)\n(\nt\nc\nt\nF\nc\nc\nF\nx\nA\nB\n\n\n\n\n\n\n.     \n \n \n \n(\n3\n.\n11\n)     \n \nF\n \nis the Faraday constant.\n \nPlugging Eq.(\n3\n.\n9\n) and Eq.(\n3\n.\n11\n) into Eq.(\n3.10\n), we can generate  \n1\n)\nexp(\n1\n)\nexp(\n2\n2\n\n\n\n\nt\nt\nFc\ndx\nt\nd\n\n,   \n(\n3.12\n)  \n 5\n \n \nwhich could be solved as \n)]\n1\nln(\n2\n[\n2\nt\ne\nt\nFc\ndx\ndt\n\n\n\n\n \n.    \n                          \n \n(\n3\n.\n13\n)\n \nWe suppose the charge on the dielectric \nsurface is q, then the charge in the diffuse layer would be \n-\nq \nwhen the electroneutrality is concerned.\n \nIt should be noted that \n \n\n\n\n\nx\ndl\nl\nq\n)\n(\n\n.    \n                                     \n                    \n  \n(\n3\n.1\n4\n) \n \nCombining Eq.(\n3\n.1\n1\n) and Eq.(\n3\n.1\n4\n)\n \n, we can get \n)]\n1\nln(\n2\n[\n2\nt\ne\nt\nFc\nq\n\n\n\n\n   \n      \n    \n \n(\n3\n.1\n5\n)\n \nUsing Eq.(3.13),we can have \n \n\n\n2\n)]\n1\nln(\n2\n[\n2\nq\ne\nt\nFc\ndx\ndt\nt\n\n\n\n\n    \n                                            \n \n(\n3\n.1\n6\n)\n \nThe\nn the\n \npolarization could be calculated as \n \n\n\n\n\n\n\n\n\n\n\n\n\n\nt\nt\nq\nq\nP\n2\n)\n1\n(\n)\n1\n(\n2\n)\n1\n(\n)\n1\nln(\n2\n)\n1\n(\n2\nt\nt\nt\nt\nt\ne\nt\nkT\ne\nQ\nFc\ne\ne\nt\nkT\ne\nQ\nFc\n\n\n\n\n\n\n\n\n\n\n\n.               \n \n(\n3\n.1\n7\n)\n \nwhere\nA\ndE\n/\n0\n\n\nis the constant that associated with sample dimension\nd\n, sample area \nA\nand \nlocalized field\n0\nE\n.\n \nCombining Eq.(3.3) and Eq.(3.17),t\nhe total capacitance \nof dielectric: ionic structure \nis \ncalculated\n \nas   \n \n)\n1\n(\n)\n1\n(\n2\n)\n(\n4\n/\n2\n0\n1\nt\nt\ntot\ne\nt\nkT\ne\nQ\nFc\nH\nC\nC\nE\nP\nC\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n.\n                      \n     \n(3.\n19\n)\n \n4. \nResults and analysis.\n \nFig.\nA\n1\n(a)\n \n(listed in Appendix A)\nshows the XRD result of GaFeO\n3\n \nfilm.\n \nWe used GSAS package to \nrefine \nthe structure.\nThe \nlattice length\n \nwas refined as,\n \na=8.7\n51\nÅ\n, b=9.\n398\nÅ\n, c=5.\n079\nÅ\n. The\n \nlattice \nangle\ns are\n \nα=β=\nγ=90\n°\n.\n \nT\nhe \nspace group\n \nis\n \nPc21n\n. As shown in Fig.\nA\n1(b)\n(Appendix A)\n, \nevery \ngal\nl\nium atom\n \nis located\n \nat the center of octahedron formed by six ozone atoms.\n \nWe measure the \nresistance dependence on temperature.\nWhen 295K<T<388K, this \nGaFeO\n3\n:ionic liquid sandwich \nstructure show\ns quasi\n-\nsemiconductor transport\n \n(Fig.\nA\n1(c)).\n \n 6\n \n \nIt should be noted that the \nelectrochemical window of the ionic liquid is in the\n \nrange \nnot higher than\n \nthan \n6v. For this reason\n, \nthe external voltage applied \nwas only 4v,5v and \n6v, respectively, which could \nmake physical and chemical properties of the ionic liquid stable.\n \nIn order to\n \ninvestigate the electro\n-\nmagneto\n-\ndielectric properties of this composite material, we \ninvestigated the capacitance tunabilities corresponding to\n \nvaried\n \nelectric frequencies\n,\n \nvoltages\n \nand \nmagnetic\n \nfield\n \n(Fig.A2\n). The cap\nacitance tunabilities in Fig.A\n2 are \ndefined as\n \nΔ\nC/C\n0\n, where \nC\n0\n  \nis \nthe origin capacitance with magnetic field H=0.0069T.\nΔ\nC is the variation of \ncapacitance \ncorresponding to\n \nC\n0\n \n.\n \nIt shows \nthat \nthe capacitance tunability \nwith\n \nvoltage \n4v is relatively higher than \nthose\n \nwith \nvoltage \n0v,\n \n5v and \n6v\n.\n \nThis result \nindicates\n \nthe 4v may be the optimized bias voltage.\n \n160%\n \ncapacitance tunability could be achieved at the frequency \n957kHz \nwith \nthe \nvoltage \n4\nv and \nthe \nmagnetic \nfield\n \n0.02T.\n \n       \n \nFigure \n1\n \nComparing the experimental and simulated data of magnetocapacitance for the \n957\nk Hz and \nwith \nvaried voltage and magnetic field\n \napplied.\n( \nThe dash lines represent the experimental results \nwhile t\nhe solid lines represent the simulated results)\n          \n    \n  \n  \n \nFigure \n1\n \ncompares\n \nthe exp\nerimental and simulated data of\n \nthe capacitance\n \nwith \nfixed\n \nvoltage\n \nof 4v\n,5v \nand 6v\n \nand \nwith \nvaried \nmagnetic field\n. \nThe order of the capacitance dependence on the magnetic field \nβ\n(Eq.(3.19))\nwas fitted as 7, which suggested a \nvery strong coupling between the magnetic field and \npolarization.\n \n7\n \n \nIt should be noted that\n \nthe \nexperimental \ndata corresponding to 957Hz in fig.\n1\n \nwas \nactually picked up \nfrom one of the data points in fig.\nA\n2(b). It would be cumbersome if we have to show all t\nhe simulated \ndata corresponding to different frequency. For this reason we only choose the presentation of the \nexperimental and simulated d\nata corresponding to \none specific\n \nfrequency of 957Hz. The other results \nwith other frequency are similar, which all s\nhow\n \nnonlinear dependence of the capacitance on the \nmagnetic field. \nIn closing, we do show\n \na very \nprecise quantitative analysis of our data in terms of \ntheoretical calculations capturing all the details of the composite material investigated \nin\n \nthe\n \npres\nent \nscope;\n \nwe \nalso\n \nshow the\n \ntrend of\n \ntransition and predict the trend of the capacitance dependence on the \nexternal magnetic field and voltage. This simple model\n \nsimulates the important characteristics of \ncapacitance \nwith varied \nmagnetic\n \nfield and electric fie\nld \nin this composite material.  \n \n4\n.CONCLUSION\n.\n \n  \nGaFeO\n3\n-\nionic liquid\n-\nGaFeO\n3\n \ncomposite material \nshows quasi\n-\nsemiconductor transport\n \nw\nhen\n295K<T<388K\n.\nWe examined the electro\n-\nmagneto\n-\ndielectric effect on th\nis structure\n. We find that \nup to \n1.6\n \nfolds capacitance tunability could be achieved \nat 975kHz \nwith the interaction of the \nmagnetic field\n \n0.02T\n \nand\n \nbias\n \nvoltage\n \n4v\n. We present a mechanism which takes account of the \ncoupling between the ionic liquid layer and the\n \nsolid\n \ndielectric layer.\n \nThe ef\nfect shows a possible route \nto use\n \nthe\n \nionic liquid \nintegrated\n \nwith the dielectric material and suggests a simple way to \nintroduce \ntunable dielectric permittivity.\n \n  \n \nACKNOWLEDGMENTS\n \n  \nThe authors thank Prof.Robert Whetten in UTSA Physics Department for \nmany useful discussions.\n \nThis work was supported by \nthe National Science Foundation under the Grants ECCS #1002380 and \nDMR #0844081. \n 8\n \n \nAppendix A\n:\n \nFigure \nA\n1.(a)XRD profile of GaFeO\ncharacterization of the GaFeO\n3\n: ionic liquid sandwich structure.\n  \nFigure\n \nA\n \n2 \n. 2D\n \ncapacitance tunability\n(c)\n5v\n(d)\n6v\n.\n \nReferences\n:\n \n(b)\n \n1.(a)XRD profile of GaFeO\n3\n.(b)the unit cell of GaFeO\n3\n.(c)Resistance vs. temperature \n: ionic liquid sandwich structure.\n \n                \ncapacitance tunability\n \nmapping\n \ncorresponding to \ndifferent\n \nbias voltage \n \n.(c)Resistance vs. temperature \n                              \n      \n \nbias voltage \n(a)\n0v\n \n(b) \n4v\n \n9\n \n \n[1]\n \nOhno\n \nH:\n \nMaking nonmagnetic semiconductors ferromagnetic\n.\n \nScience\n.1998;\n \n281\n:\n \n951\n.\n \n[2]\n \nMatsumoto\n \nY\n \net al.\n \n:\n \nRoom\n-\ntemperature ferromagnetism in transparent transition metal\n-\ndoped \ntitanium dioxide.\n \nScience\n \n.2001;\n291\n \n:\n \n854\n.\n \n \n[3]\n \nNguyen\n \nHH\n,\n \nSakai\n \nJ\n,\n \nPoirot\n \nN\n \nand\n \nBrize\n \nV\n:\n \nRoom\n-\ntemperature ferromagnetism observed in \nundoped semiconducting and insulating oxide thin films\nPhys. Rev\n.\n \nB\n. 2006;\n \n73\n:\n \n132404\n.\n \n \n[4]\n \nPan\n \nH\n \net al.\n \n:\n \nRoom\n-\nTemperature Ferromagnetism in Carbon\n-\nDoped ZnO\n. \nP\nhys.\nR\nev.\nL\nett.\n \n2007;\n99\n \n:\n \n127201.\n \n[\n5\n] \nMarti\n \nX\n \net al.\n \n:\n \nRoom\n-\ntemperature antiferromagnetic memory resistor\n.\nNature Materials\n \n2014\n; \n13:\n367.\n \n[\n6\n]\nZhang\n \nY\n, Jianting\n \nY\n,\n \nYusuke\n \nM\n, and Yoshihiro\n \nI: \nAmbipolar MoS2 Thin Flake Transistors\n.\nNano \nLett. \n2012;\n12\n:\n \n1136\n.\n \n \n[\n7\n]\n \nUeno\n \nK\n \net al.\n:\n \nDiscovery of \nsuperconductivity in KTaO\n3\n \nby electrostatic carrier doping\n.\n \nNature Nanotechnology\n.2011;\n \n6\n:\n408\n.\n \n[8] Hiroyasu \nN \net al.\n \n:\nElectroresistance Effect in Gold Thin Film Induced by Ionic\n-\nLiquid\n-\nGated \nElectric Double Layer\n. \nA\nppl\n.\nPhys\n.Exp\n. \n2012;\n5\n:\n \n023002.\n \n[9] \nKasahara\n \nY\n \net al.\n:\n \nElectric\n-\nField\n-\nInduced Superconductivity Detected by Magnetization\n \nMeasurements of an Electric\n-\nDouble\n-\nLayer Capacitor\n.\nJ\n.\n \nPhys\n.\n \nSoc\n.\n \nof Jpn\n.\n \n2012;\n80\n:\n \n0\n2\n3708.\n \n[10]\nYe\n \nJ\n \net al.\n:\n \nAccessing the transport properties of graphene and its \nmultilayers at high carrier density\n \n.\nProc\n.\n \nof\n \nNat\n.\n \nAca\n.\n \nSci\n.\n \n2011;\n108\n \n:\n \n13002.\n \n[11]\nYe\n \nJ\n \net al.\n:\nLiquid\n-\ngated interface superconductivity on an atomically flat film\n. \nNature \nmaterials\n.2010;\n \n9\n:\n125.\n \n[12]\nYe\n \nJ \net al.\n \n:\n \nSuperconducting Dome in a Gate\n-\nTuned Band \nInsulator\n. \nScience\n.2012;\n \n338\n:\n1193.\n 10\n \n \n[13]Yuan\n \nH \net al.\n \n:\n \nElectrostatic and Electrochemical Nature of Liquid\n-\nGated Electric\n-\nDouble\n-\nLayer \nTransistors Based on Oxide Semiconductors\n.\nJ\n. of Am.\n \nChem\n.\n \nSoc\n.\n \n2010;\n132\n:\n18402.\n \n[14]\n \nUeno\n \nK\n \net al.\n,\n \nField\n-\nInduced \nSuperconductivity in Electric Double Layer Transistors\n.\nJ. Phys. Soc. \nJpn.\n \n2014;\n83\n:\n \n032001\n.\n \n[15]Remeika\n \nJP:\n \nGaFeO3: A Ferromagnetic\n-\nPiezoelectric Compound\n.\n \nJ. Appl. Phys.\n1960;\n \n31\n:\n \nS263.\n \n[16]M.B.\nMohamed\n \net al.\n:\nDielectric relaxation and magnetic properties of\n \nCr doped GaFeO3\n.\n \nJ. Phys. \nD: Appl. Phys.\n \n2010;\n43\n:\n \n455409.\n \n[1\n7\n]\nSaha\n \nR\n \net al.\n \n:\nPhase Transitions of AlFeO\n3 \nand GaFeO\n3 \nfrom the Chiral Orthorhombic \n(\nPna\n21\n) \nStructure to the Rhombohedral \n(\nR\n3̅\nc) Structure\n.\nInorg. Chem.\n \n2011;\n50\n:\n9527\n.\n \n[1\n8\n]\nSaha\n \nR\n \net al.\n:\n \nMultiferroic and magnetoelectric nature of GaFeO\n3\n, AlFeO\n3\n \nand \nrelated oxides\n.\n \nSolid State Comm\n.\n \n2012;\n152\n:\n1964.\n \n[1\n9\n]\nMukhopadhyay\n \nK\n \net al.\n:\n \nEnhanced Magnetic Behavior of Chemically Prepared Multiferroic \nNanoparticles of GaFeO3 in (GaFeO3)0.50 \n(Ni0.4Zn0.4Cu0.2 Fe2O4)0.5 Nanocomposite\n.\nJ. Phys. \nChem. C\n \n2012;\n116\n:\n4948\n.\n \n[20]\nBahoosh\n \nSG\n \nand \nWesselinowa\n \nJM:\nOrigin of the different multiferroism in BiFeO\n3\n \nand \nGaFeO\n3\n.\nJ\n.\nof Appl\n.\n \nPhys\n.\n \n2013;\n113\n:\n \n063905\n.\n \n \n[21]\nMukherjee\n \nS\n \net al.\n:\n \nRoom Temperature Nanoscale \nFerroelectricity in Magnetoelectric GaFeO\n3\n \nEpitaxial Thin Films\n.\n \nPhys. Rev. Lett.\n \n2013;\n111\n:\n \n087601\n.\n \n[22]\nJia\n \nQX\n \net al.\n \n:\nPolymer\n-\nassisted deposition of metal\n-\noxide films\n.\n \nNature Materials\n \n2004;\n \n3\n:\n \n529.\n \n[23]\nLarson \nAC\nand \nVon Dreele\n \nRB: \nGENERAL STRUCTURE ANALYSIS SYSTEM \n.\nLos Alamos \nNational Laboratory Report LAUR \n.1994;\n \n86\n-\n748.\n \n[24]\nToby\n \nBH:\n \nEXPGUI, a graphical user interface for GSAS\n.\nJ. Appl. Cryst. \n2001;\n34\n:\n210\n-\n213.\n 11\n \n \n[25]\nFinger\n \nLW \net al.\n:\n \nDRAWxtl, an open\n-\nsource computer program to produce\n \ncrystal\n \nstructure drawings\n.\n \nJ. Applied Crystallography\n.2007;\n40\n:\n188\n-\n192\n.\n \n[26]\nOkatan\n \nMB\n \net al.\n:\n \nPolarization coupling in ferroelectric multilayers\n.\n \nPhys.Rev.B\n \n2009;\n79\n:\n \n174113.\n \n[27]\nWu\n \nY\n,\n \nGuo\n \nR\n, Bhalla\n \nA: \nMagneto\n-\nresistance and \n-\ncapacitance dual tunability of\n \nSmFeO\n3\n.\n \n( in \npreparation)\n \n[28]\nKornyshev\n \nAA :\n \nDouble\n-\nLayer in Ionic Liquids: Paradigm Change?\nJ. Phys. Chem. B\n.2007;\n \n111\n:\n \n5545.\n \n[2\n9\n]\nOldham\n \nKB\n \n:\nA Gouy\n–\nChapman\n–\nStern model of the double layer\n \nat a (metal)/(ionic liquid) \ninterface\n.\n \nJ. \nof Electroanalytical \nChem\n. \n2008;\n613\n:\n131.\n \n "    },    {        "title": "1603.08730v1.Generic_aspects_of_skyrmion_lattices_in_chiral_magnets.pdf",        "content": "Generic aspects of skyrmion lattices in chiral magnets\nAndreas Bauer\u0003and Christian P\reiderer\nPhysik-Department, Technische Universit at M unchen,\nJames-Franck-Stra\u0019e, D-85748 Garching, Germany\nAbstract\nMagnetic skyrmions are topologically non-trivial spin whirls that may not be transformed con-\ntinuously into topologically trivial states such as ferromagnetic spin alignment. In recent years\nlattice structures composed of skyrmions have been discovered in certain bulk chiral magnets with\nnon-centrosymmetric crystal structures. The magnetic phase diagrams of these materials share\nremarkable similarities despite great variations of the characteristic temperature, \feld, and length\nscales and regardless whether the underlying electronic state is that of a metal, semiconductor, or\ninsulator.\n1arXiv:1603.08730v1  [cond-mat.str-el]  29 Mar 2016I. INTRODUCTION AND OUTLINE\nIn 1961 British nuclear physicist Tony Skyrme proposed a theoretical model in which\nneutrons and protons arise as topological solitons of pion \felds, i.e., fermions are derived\nfrom bosonic \felds1{3. Representing the, perhaps, \frst example of what is now broadly\nreferred to as fractionalization, the implications of Skyrme's model only began to be fully\nappreciated two decades later, when Witten and Adkins demonstrated its relevance for real\nexperiments4. Since the days of this early work many di\u000berent variants of Skyrme's original\nnotion have been worked out in entirely di\u000berent \felds of physics. These states and exci-\ntations are now rather generously called skyrmions . Examples include areas as diverse as\nparticle physics4{8, the quantum Hall state at half-\flling9{11, Bose-Einstein condensates12{14,\nand liquid crystals15. However, in recent years skyrmions are probably most actively inves-\ntigated in the area of solid state magnetism, where certain spin textures are referred to as\nskyrmions. These magnetic textures display a non-trivial real-space topology, i.e., it is not\npossible to continuously transform them into conventional (topologically trivial) forms of\nspin order such as ferromagnetism or antiferromagnetism.\nWhile skyrmions were theoretically predicted to exist in non-centrosymmetric magnetic\nmaterials with uniaxial anisotropy as early as 198916,17, it was despite concerted e\u000borts\nrather unexpected, when skyrmions in magnetic materials were identi\fed experimentally\nfor the \frst time in the cubic transition metal compounds MnSi18and Fe 1\u0000xCoxSi19in\nthe form of a lattice structure. Since then similar topologically non-trivial spin textures\nhave been reported to exist for a rapidly growing number of rather di\u000berent bulk and thin\n\flm systems. The interest driving this search for further materials stabilizing skyrmions\nis quite diverse, ranging from fundamental questions on the possible break down of Fermi\nliquid theory20{22all the way to new forms of spintronics applications23. From a practical\npoint of view the most important implication of the non-trivial topology is their emergent\nelectrodynamics leading to an exceptionally e\u000ecient coupling between the spin textures and\nspin currents24,25. Further, the very detailed understanding of the spin excitations achieved\nto date suggests strongly that tailored microwave devices may be designed through the\ncombination of di\u000berent materials26{30.\nA precondition for further advances is a detailed understanding of the magnetic phase\ndiagrams of these compounds. In turn, this chapter provides a review of the most extensively\n200 .51 .000.51.0H / Hc2T\n / Tcp\naramagnetich\nelicalskyrmionl\natticeconical \nfield-polarizeds\ningle skyrmion\nH\nH\n = 0〈\n100〉\nH〈111〉s kyrmion lattice\nFIG. 1. Spin structures the cubic chiral magnets. Typical magnetic phase diagram (center) and\nschematic spin structures of the helical, the conical, the paramagnetic, and the \feld-polarized\nstate. In a phase pocket (red) in \fnite \felds just below the helimagnetic ordering temperature,\nTc, a regular arrangement of topologically non-trivial spin whirls is observed, a so-called skyrmion\nlattice. Schematic depictions by Markus Garst and from Ref.31.\nstudied class of skyrmion materials to date, namely cubic chiral magnets crystallizing in the\nspace group P213. We begin in Sec. II with a brief introduction to the basic properties of\nthis class of compounds focusing on the salient properties of the skyrmion lattice state. This\nis followed by an introduction to the Ginzburg-Landau model of these materials in Sec. III.\nThe main part of this chapter in Sec. IV is dedicated to an account of the determination\nof magnetic phase diagrams based on measurements of thermodynamic bulk properties.\nDespite great variations of the characteristic temperature, \feld, and length scales between\nthe di\u000berent materials of interest, the magnetic phase diagrams observed are remarkably\nsimilar. This brings us to a summary of the main consequences that arise from the non-trivial\ntopological winding of skyrmions in Sec. V, in particular their emergent electrodynamics.\nThe chapter closes in Sec. VI with a brief account of topologically non-trivial spin structures\nas recently discovered in other materials.\nII. SKYRMION LATTICE IN CUBIC CHIRAL MAGNETS\nThe helimagnetism of the materials reviewed in this chapter is homochiral with a modula-\ntion wavelength that is large as compared to typical lattice constants. The latter represents\nan important precondition for the description of the magnetic properties in a continuum\n3model and the characterization of the topological properties. Well-known representatives\nare the (pseudo-)binary B20 transition metal monosilicides and monogermanides MnSi,\nMn1\u0000xFexSi, Mn 1\u0000xCoxSi, Fe 1\u0000xCoxSi, FeGe, MnGe, and mixtures thereof, as well as the\ninsulator Cu 2OSeO 3. All of these compounds crystallize in the space group P213, which\nlacks inversion symmetry such that two crystalline enantiomers stabilize.\nThe long-wavelength helimagnetic order observed in these compounds originates in a well-\nunderstood set of hierarchical energy scales, as already pointed out in Landau-Lifshitz, Vol.\nVIII, Sec. 52,32. On the strongest scale exchange interactions favor parallel spin alignment.\nOn intermediate scales isotropic Dzyaloshinskii-Moriya spin-orbit interactions arise due to\nthe lack of inversion symmetry of the crystal structure favoring perpendicular spin align-\nment33{35. In competition with the stronger exchange a helical modulation is stabilized36,37.\nThe chirality of the Dzyaloshinskii-Moriya interaction and thus of the helical modulation is\n\fxed by the enantiomer of the crystal structure38,39. Finally, on the weakest energy scale\nhigher-order spin-orbit coupling terms, also referred to as crystal electric \feld e\u000bects or cubic\nanisotropies, determine the propagation direction of the helical modulations40.\nThe hierarchy of energy scales is directly re\rected in a rather universal magnetic phase\ndiagram, as schematically depicted in Fig. 1. As summarized below, the same phase diagram\nis observed regardless whether the materials are metals, semiconductors, and insulators\n(MnGe is perhaps the only exception as discussed in Sec. VI). In particular, the phase\ndiagram appears to be insensitive to the quantitative values of the transition temperatures,\ntransition \felds, and helix wavelengths, which vary by roughly two orders of magnitude\nbetween di\u000berent compounds.\nAt su\u000eciently high temperatures the magnetic properties are characteristic of exchange-\nenhanced paramagnetism with large \ructuating moments41. At low temperatures and zero\nmagnetic \feld multi-domain helical order is observed with equal domain populations, where\nthe helical propagation vector is determined by weak cubic magnetic anisotropies, fourth-\norder in spin-orbit coupling. Under small applied magnetic \felds the domain population\nchanges, until the helical state undergoes a spin-\rop transition at a transition \feld Hc142.\nThe spin-\rop phase is broadly referred to as conical state, with a single-domain state of spin\nspirals propagating along the magnetic \feld direction. The expression conical phase alludes\nto the notion, that the spins tilt towards the \feld direction while twisting helically along\nto the \feld direction. When increasing the magnetic \feld further this conical angle closes\n4and a transition takes place to a \feld-polarized state above Hc243. We will return to a more\ndetailed discussion of the transitions at Hc1andHc2below.\nIn recent years the perhaps largest scienti\fc interest has been attracted by a small phase\npocket at intermediate \felds just below the helimagnetic transition temperature, Tc. Histor-\nically this phase pocket has been referred to as A-phase. The existence of the A-phase, \frst\ndiscovered in MnSi, had already been reported in the 1970s44,45. However, the detailed mi-\ncroscopic spin structure was only identi\fed in 2008 (publication in 2009), when small-angle\nneutron scattering established the \frst realization of a skyrmion lattice in a bulk solid state\nsystem18.\nThe skyrmion lattice consists of a regular hexagonal arrangement of spin whirls, that\nmay essentially be described by the phase-locked superposition of three helices under 120\u000e\nin a plane perpendicular to the applied magnetic \feld in combination with a ferromagnetic\ncomponent along the \feld. Of particular interest is the non-trivial topology of this spin\ntexture, meaning, it cannot be continuously transformed into a topologically trivial state\nsuch as a paramagnet, ferromagnet, or helimagnet. The associated winding number of the\nstructure, \b, is an integer and the integrated value of the skyrmion density, \u001ei, per magnetic\nunit cell, given by\n\u001ei=1\n8\u0019\u000fijk^ \u0001@j^ \u0002@k^ (1)\nwhere,\u000fijkis the antisymmetric unit tensor and ^ =M(r)=M(r) is the orientation of\nthe local magnetization. Along the \feld direction the quasi two-dimensional spin structure\nrepeats itself, forming skyrmion lines as depicted in the right panel of Fig. 1. Perhaps\nmost intriguing, the interaction of each skyrmion with an electron spin corresponds to one\nquantum of emergent \rux and an emergent electrodynamics presented in Sec. V.\nExperimentally, the existence of skyrmions was \frst recognized in the form of the\nskyrmion lattice as observed in reciprocal space using small-angle neutron scattering (SANS)\nin bulk samples18,19,48{50. Further detailed SANS studies on MnSi revealed the presence of\nweak higher-order scattering, indicating a weak particle-like character of the skyrmions.\nThe evolution of this higher-order scattering as a function of temperature and \feld proved\nthe long-range crystalline nature of the skyrmion lattice and, in particular, the phase-locked\nmulti-Qnature of the modulation at heart of the non-trivial topological winding46. These\nmeasurements were soon followed-up by real-space imaging studies using Lorentz force\ntransmission electron microscopy (LF-TEM). This method is sensitive to in-plane com-\n5〈/s49/s49/s48〉\n〈/s49/s49/s48〉\n/s50\n/s56/s46/s53/s32/s75〈/s49/s49/s48〉〈\n/s49/s49/s48〉\n/s49/s48/s48/s32/s110/s109/s53 /s48/s48/s32/s110/s109/s48 /s46/s50/s32/s110/s109/s45/s49H/s32/s61/s32/s48\n/s40/s99/s41/s40 /s97/s41/s40 /s98/s41/s76/s70/s45/s84/s69/s77/s32/s8211/s32/s67/s117/s50/s79/s83/s101/s79/s51/s77/s70/s77/s32/s8211/s32/s70/s101/s49/s45/s120/s67/s111/s120/s83/s105/s32/s40x/s32/s61/s32/s48/s46/s53/s41helical state〈\n/s49/s49/s48〉〈/s49/s48/s48〉/s51\n/s50 /s48/s49 /s57 \n/s83/s65/s78/s83/s32/s8211/s32/s77/s110/s83/s105〈\n/s49/s48/s48〉〈/s49/s49/s48〉〈 /s50/s49/s49〉Hskyrmion lattice state/s40/s101/s41/s40 /s102/s41/s40 /s100/s41〈/s49/s48/s48〉〈\n/s49/s49/s49〉/s54\n/s48/s176/s50\n/s56/s46/s53/s32/s75/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s50/s48/s48/s32/s109/s84/s53/s32/s75/s53\n/s32/s75/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s56/s48/s32/s109/s84/s49/s48/s32/s75/s49\n/s48/s32/s75/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s32/s50/s48/s32/s109/s84FIG. 2. Helical and skyrmion lattice state as observed in reciprocal and real space. (a){(c) Helical\nstate in zero magnetic \feld. (d){(f) Skyrmion lattice state in \fnite \feld. Data from small angle\nneutron scattering (SANS)18,46, magnetic force microscopy (MFM)31, and Lorentz force transmis-\nsion electron microscopy (LF-TEM)26,47are shown. The color-coded in-plane orientation in the\nLF-TEM data was obtained by a transport-of-intensity (TIE) analysis.\nponents of the magnetic moments. However, it may only be used to study thinned bulk\nsamples26,47,51,52, whereas magnetic force microscopy (MFM) allowed the detection of the\nstray magnetic \feld above the surface of bulk samples31. As the most recent achievement of\nreal-space imaging, the spin arrangement in the skyrmion lattice could even be reconstructed\nin three dimensions by means of electron holography53.\nTypical data from SANS, MFM, and LF-TEM recorded on di\u000berent chiral magnets are\nshown for the helical and the skyrmion lattice state in Fig. 2. In the helical state at zero\nmagnetic \feld SANS experiments show intensity maxima along the easy axes of the helical\npropagation vector q, typically either h100iorh111i36,40. Real-space images reveal stripy\npatterns with qperpendicular to the stripes54. The skyrmion lattice state in \fnite \felds\n6in SANS experiments, see Fig. 2(d), is characterized by a sixfold scattering pattern in a\nplane perpendicular to the applied magnetic \feld that is only fully revealed if the magnetic\n\feld is applied parallel to the neutron beam. In earlier experiments the magnetic \feld\nand the neutron beam had been applied perpendicular to each other leading to erroneous\ninterpretations42,55{57. Note that the wave vector in the skyrmion lattice has the same\nabsolute value as in the helical state, q= 2\u0019=\u0015h. Thus, due to the hexagonal packing of\nthe skyrmions in real space, the distance between neighboring skyrmion cores is a factor of\n2=p\n3\u00191:15 larger than the helix wavelength. In real-space images, see Figs. 2(e) and 2(f),\na trigonal lattice of objects is observed. The magnetic moments in their cores are aligned\nantiparallel to the applied \feld, cf. blue color in Fig. 2(e), i.e., the spin structure in the cubic\nchiral magnets in fact consists of anti-skyrmions.\nInterestingly, when the size of bulk samples along the \feld direction becomes comparable\nto the helical modulation length, the skyrmion lattice extents over increasingly larger parts\nof the magnetic phase diagram as demonstrated in LF-TEM studies51. In contrast, the\nmagnetic properties of epitaxially grown thin \flms of the same chiral magnets, forming\nequal crystalline domain populations with both chiralities in the same \flm, are still debated\ncontroversially58{61. Here, in addition to the e\u000bects resulting from the heterochirality and\nthe reduced dimensionality, strain arising from the lattice mismatch with the substrate needs\nto be taken into account.\nIII. THEORETICAL DESCRIPTION\nThe thermodynamic properties of the cubic chiral magnets may be described extremely\nwell in the framework of a Ginzburg-Landau model of the free energy density, see also chapter\nby Markus Garst. It is convenient to distinguish two contributions, f=f0+fcub, where\nthe \frst term accounts for isotropic contributions and the second term accounts for the\ne\u000bects of magnetic anisotropies. More speci\fcally, f0includes ferromagnetic exchange, the\nDzyaloshinskii-Moriya interaction as the highest-order (isotropic) spin-orbit coupling term,\nand the Zeeman term as the response on an external magnetic \feld. It may be written as:\nf0=1\n2 (r\u0000Jr2) +D (r\u0002 ) +u\n4!( 2)2\u0000\u00160\u0016 H (2)\n7We choose the three component order parameter \feld,  , with dimensionless units yielding a\nmagnetization density M=\u0016 with\u0016=\u0016B=f:u:, i.e., a single Bohr magneton per formula\nunit (\u0016B>0). The parameter rtunes the distance to the phase transition, Jis the exchange\nsti\u000bness and uthe lowest order mode-coupling parameter. The second term, D (r\u0002 ),\ncorresponds to the Dzyaloshinskii-Moriya interaction with the coupling constant D. This\nterm is justi\fed by the lack of inversion symmetry of the crystal structure. The last term\ndescribes the Zeeman coupling to an applied magnetic \feld H. An ansatz for a single conical\nhelix is:\n (r) = 0^ 0+\thel^e\u0000eiQr+\t\u0003\nhel^e+e\u0000iQr(3)\nHere, 0is the amplitude of the homogeneous magnetization and \thelis the complex am-\nplitude of the helical order characterized by the pitch vector Q. The vectors ^e1\u0002^e2=^e3\nform a normalized dreibein where ^e\u0006= (^e1\u0006i^e2)=p\n2 andQ=Q^e3.\nThis brings us to the second term of the free energy density, fcub, which contains spin-\norbit coupling of second or higher order breaking the rotation symmetry of f0already in\nzero \feld.\nfcub=Jcub\n2\u0002\n(@x x)2+ (@y y)2+ (@z z)2\u0003\n+::: (4)\nThis leading-order term of the cubic anisotropies, where Jcub\u001cJ, implies that the easy axis\nof the helical propagation vector is either a h100ior ah111idirection as explored by Bak and\nJensen40. As the \feld is increased the Zeeman term gains importance and \fnally overcomes\nthe cubic anisotropies, stabilizing the conical state with the propagation vector parallel to\nthe magnetic \feld, in analogy to the spin-\rop transition of a conventional antiferromagnet.\nIn order to account for more subtle e\u000bects, further cubic anisotropies need to be considered\nconsistent with the non-centrosymmetric space group P213.\nWhile the contributions in f0andfcubare su\u000ecient to describe the helical, the conical,\nthe \feld-polarized, and the paramagnetic ground states, speci\fc issues require consideration\nof the higher-order spin-orbit coupling terms mentioned above and other contributions. For\ninstance, for an universal account of the collective spin excitations it is necessary to in-\nclude dipolar interactions29. Moreover, just above the paramagnetic-to-helimagnetic phase\ntransition at Tcnon-analytic corrections to the free energy functional arise from strong\ninteractions between isotropic chiral \ructuations. These interactions suppress the correla-\ntion length and the second-order mean-\feld transition resulting in a \ructuation-disordered\n8-6-5-4-3-2-100123(a)c\nonicalparamagnetH / H0t\nskyrmionl\nattice0\n0.20.40.60.81.000.10.20.3c\nonical(b)s\nkyrmionl\natticeh\nelicalH / JT\n / J00.20.40.6-0.0100.010.02f\nluctuations  \nΔG (a.u.) \nH\n / Hc2mean fieldFIG. 3. Stabilization of the skyrmion lattice. (a) Theoretical magnetic phase diagram as obtained\nfrom a Ginzburg-Landau ansatz. The inset shows that thermal \ructuations already in Gaussian or-\nder stabilize the skyrmion lattice at intermediate \felds18. (b) Magnetic phase diagram as obtained\nfrom Monte-Carlo simulations67.\nregime just above Tcand a \ructuation-induced \frst-order transition. The scenario relevant\nfor cubic chiral magnets was originally predicted by Brazovskii62and recently demonstrated\nin MnSi by a study combining neutron scattering, susceptibility, and speci\fc heat measure-\nments63. Depending on the strength of the interaction between the \ructuations, for other\nchiral magnets an extended Bak-Jensen or a Wilson-Fischer scenario may be relevant64{66.\nAs a hidden agenda the \ructuation-induced \frst-order transition underscores that the\nskyrmion lattice state is stabilized by thermal \ructuations, as depicted in Fig. 3(a). The\nleading-order correction arise from Gaussian \ructuations around the mean-\feld spin con-\n\fgurations of the conical and the skyrmion lattice state, respectively. Interestingly, both\nshort-range and long-range \ructuations favor the skyrmion lattice for intermediate magnetic\n\felds18. Consistently, the skyrmion lattice forms rather independently from the orientation\nof the underlying crystalline lattice, where the cubic anisotropies only lead to a slightly\nanisotropic temperature and \feld range of the skyrmion lattice phase pocket68,69and deter-\nmine the precise orientation of the skyrmion lattice18,49.\nBoth the Brazovskii scenario and the stabilization of the skyrmion lattice by thermal\n\ructuations have recently been corroborated by classical Monte Carlo simulations67. Here,\na fully non-perturbative study of a three-dimensional lattice spin model, i.e., going beyond\nGaussian order, reproduced the thermodynamic signatures associated with a Brazovskii-type\n\ructuation-induced \frst-order phase transition and, as shown in Fig. 3(b), the experimental\n9magnetic phase diagram.\nAll of these recent advances compare and contrast with the seminal studies of Bogdanov\nand coworkers, who anticipated the existence of skyrmions in non-centrosymmetric materials\nwith a uniaxial anisotropy and in the presence of a magnetic \feld16,17. In particular, based\non mean-\feld calculations ignoring the importance of thermal \ructuations, they concluded\nfor cubic compounds that the skyrmion lattice would be metastable. Moreover, recently they\npredicted more complex magnetic phase diagrams comprising, besides the phases discussed\nso far, of meron textures and skyrmion liquids70,71. Putative evidence for such complex\nphase diagrams has been reported in FeGe based on susceptibility72,73, speci\fc heat74, and\nSANS data50. However, as illustrated in Sec. IV, all data reported to date for all cubic\nchiral magnets are qualitatively extremely similar. Thus, when consistently inferring the\ntransition \felds and temperatures by virtue of the very same conditions, the magnetic phase\ndiagrams of all compounds including FeGe are highly reminiscent of each other supporting\nstrongly a rather universal scenario as described in the following without evidence of these\ncomplexities..\nIV. MAGNETIC PHASE DIAGRAMS\nIn the following we focus on the determination of the magnetic phase diagrams of cubic\nchiral magnets based on magnetization, ac susceptibility, and speci\fc heat data, where the\nconditions for determining the transition \felds are con\frmed by microscopic probes, notably\nextensive neutron scattering. In the \frst part of this section we present typical data, explain\nhow transition \felds or temperatures are de\fned, and illustrate that demagnetization e\u000bects\nmay lead to signi\fcant corrections. This is followed in the second part by the presentation of\nmagnetic phase diagrams of the most-extensively studied stoichiometric compounds MnSi,\nFeGe, and Cu 2OSeO 3as well as the magnetic and compositional phase diagrams of the most\nextensively studied doped compounds, namely Mn 1\u0000xFexSi and Fe 1\u0000xCoxSi.\nA. Phase transitions in the susceptibility and speci\fc heat\nThe di\u000berent magnetic states in the cubic chiral magnets and the phase transitions be-\ntween them give rise to distinct signatures in various physical properties. Experimentally,\n1026283032060120180240300T\n2TcTA2(f)T\nA1/s61549\n0H (mT)1004003\n002\n202\n001\n801\n601\n40 \n   0Cel / T (mJ mol-1K-2) \nT\n (K)500Tc0\n0.10.20.30.400.020.04(e)Im /s61539ac \n \n/s61549\n0H (T)00.10.2c\nonS\nF\nPhelc\non( c)M (µB / f.u.)MnSi − H || 〈100〉 T\n = 28 K0\n0.10.20.30.4H\nA2HA1Hc1(d)dM / dH, Re /s61539ac dM / dH \nRe /s61539ac-++H\nc2-0\n0.10.20.30.40.5T\nCPS\nF\nDh\nelicalconicalP\nMRe /s61539ac/s615490H (T)0 .200.250.30F\nP(a)0\n0.10.20.30.4 /s61549\n0Hint (T)2\n72829303100.10.20.30.40.5 \nC \ndM / dH    \nRe /s61539ac/s615490H (T)T\n (K)0.000.010.020.03I m /s61539ac( b)0\n0.10.20.30.4 /s61549\n0Hint (T)FIG. 4. Typical magnetization, ac susceptibility, and speci\fc heat data of MnSi. (a) Color map\nof the real part of the ac susceptibility. We distinguish the following regimes; helical, conical,\nskyrmion lattice (S), \ructuation-disordered (FD), paramagnetic (PM), and \feld-polarized (FP).\nA \feld-induced tricritical point (TCP) is located at the high-\feld boundary of the FD regime.\n(b) Color map of the imaginary part revealing considerable dissipation only between the conical and\nthe skyrmion lattice state. (c){(e) Typical data of the magnetization, the susceptibility calculated\nfrom the magnetization, d M=dH, as well as the real and imaginary part of the ac susceptibility as\na function of \feld. Note the de\fnitions of the various transition \felds. (f) Electronic contribution\nto the speci\fc heat as a function of temperature for several applied magnetic \felds. Data has been\no\u000bset for clarity.\nthe magnetic ac susceptibility and speci\fc heat are easily accessible for most compounds\nand allow the determination of a very detailed magnetic phase diagram, based on feature-\ntracking. This provides the starting point for further studies and motivated us to concentrate\non these quantities in the following. As an overview, we start with colormaps of the real\nand imaginary part of the ac susceptibility, Re \u001facand Im\u001fac, in Figs. 4(a) and 4(b), where\nblue shading corresponds to low and red shading to high values. As an example we show\ndata for a cube-shaped single crystal of MnSi measured at an excitation frequency of 120 Hz\n11and an excitation amplitude of 0.5 mT. The \feld was applied after zero-\feld cooling along\nanh100iaxis, i.e., along the hard direction for the helical propagation vector.\nIn Re\u001facthe conical state is characterized by a plateau of high and rather constant sus-\nceptibility (orange to red shading). The reduced value at low \felds is associated with the\nhelical state. Just below the helimagnetic ordering temperature, Tc, a plateau of reduced\nsusceptibility in \fnite \felds is characteristic for a single pocket of skyrmion lattice state (light\nblue shading). Just above Tcan area of relatively large susceptibility (green shading) is as-\nsociated with the \ructuation-disordered (FD) regime that emerges as a consequence of the\nBrazovskii-type phase transition from paramagnetism to helimagnetism. At high temper-\natures or high \felds, respectively, the system is in a paramagnetic (PM) or \feld-polarized\n(FP) state with low susceptibility (blue). A broad maximum observed in temperatures\nsweeps of Re \u001fac(not shown) marks the crossover between these two regimes75. Im\u001faconly\nshows contributions at the phase transitions and, in particular, between the skyrmion lattice\nand conical state. Here, the \fnite dissipation suggests a regime of phase coexistence where\nthe nucleation process of topologically non-trivial skyrmions within the conical phase and\nvice versa eventually triggers a \frst-order transition31,68,76. In contrast, at the \ructuation-\ninduced \frst-order transition between the skyrmion lattice and the \ructuation-disordered\nregime as a function of temperature no signi\fcant contribution to Im \u001facis observed.\nIn order to de\fne the di\u000berent transition \felds and temperatures, it is instructive to\nconsider the typical \feld dependence of the magnetization, M, the susceptibility calculated\nfrom the measured magnetization, d M=dH, and the measured ac susceptibility for a tem-\nperature just below Tcas shown in Figs. 4(c) through 4(e). Starting at H= 0, i.e., in the\nhelical state, with increasing \feld the material undergoes transitions to the conical and the\nskyrmion lattice state before returning to the conical state and \fnally reaching the \feld-\npolarized state above Hc2. BelowHc2the magnetization increases almost linearly as shown\nin Fig. 4(c), where the changes of slope at the di\u000berent phase transitions are best resolved\nin the derivative d M=dHdepicted as open symbols in Fig. 4(d). Here, we compare the\nmeasured ac susceptibility, Re \u001fac, with dM=dHwhich may be viewed as zero-frequency\nlimit of Re \u001fac.\nAt the transition between the helical and conical state and in the regimes between the\nconical and the skyrmion lattice state d M=dHshows pronounced maxima that are not\ntracked by Re \u001fac. In the former case this discrepancy may be attributed to the slow,\n12complex, but well-understood reorientation of macroscopic helical domains. In the latter\ncase the discrepancy is accompanied by strong dissipation, which may be inferred from\nIm\u001facin Fig. 4(e) and attributed to regimes of phase coexistence between the conical and\nthe skyrmion lattice state as expected for \frst-order phase transitions. In these regimes\nboth Re\u001facand Im\u001facshow a pronounced dependence on the excitation frequency with a\ncharacteristic frequency that increases with temperature68,77.\nWe de\fne the helical-to-conical transition at Hc1as the maximum of d M=dHthat typi-\ncally coincides with a point of in\rection in Re \u001fac. The low-\feld and high-\feld boundary of\nthe skyrmion lattice state, HA1andHA2, may be \fxed by maxima in d M=dH. The regimes\nof phase coexistence between the conical and the skyrmion lattice state are characterized\nby dM=dH6= Re\u001facand Im\u001fac\u001d0, where the corresponding boarders are labeled H\u0006\nA1\nandH\u0006\nA2, respectively. For H <H\u0000\nA1andH >H+\nA2the constant susceptibility of the conical\nphase is observed, while in the skyrmion lattice state for H+\nA1< H < H\u0000\nA2the system dis-\nplays a plateau of lower susceptibility. The second-order transition from the conical to the\n\feld-polarized state belonging to the XY universality class is \fnally indicated by a point\nof in\rection in both d M=dHand Re\u001fac. Similar criteria may be used to extract transition\ntemperatures from data recorded as a function of temperature (not shown)68.\nImportant related information on the nature of the phase transitions may be extracted\nfrom measurements of the speci\fc heat. Using a quasi-adiabatic large heat pulse technique\nallows to determine transition temperatures with high precision49,76. Fig. 4(f) shows the\nelectronic contribution to the speci\fc heat, i.e., after subtraction of the phononic contribu-\ntion, divided by temperature, Cel=T, as a function of temperature for di\u000berent applied \feld\nvalues. In zero \feld a sharp symmetric peak marks the onset of helimagnetic order at the\n\ructuation-induced \frst-order transition at Tc. The peak resides on top of a broad shoulder\nthat displays for small \felds a so-called Vollhardt invariance78atT2, i.e., an invariant cross-\ning point of the speci\fc heat, @C=@HjT2= 0, that coincides with a point of in\rection in the\nmagnetic susceptibility, T@2M=@T2jT2\u0019TH@2\u001f=@T2jT2= 075. At intermediate \felds two\nsymmetric peaks, labeled TA1andTA2, track the phase boundaries of the skyrmion lattice\nstate indicating two \frst-order transitions. In larger \felds again one anomaly, labeled Tc,\nis observed. Increasing the \feld further causes a change of the shape of the anomaly from\nthat of a slightly broadened symmetric delta peak to the asymmetric lambda anomaly of a\nsecond-order transition at a \feld-induced tricritical point (TCP). This \feld-induced change\n13/s48/s48/s46/s49/s48/s46/s50/s48/s46/s51/s48/s46/s52/s48/s48/s46/s49/s48/s46/s50/s48/s46/s51/s48/s46/s52T/s32/s61/s32/s50/s56/s46/s53/s32/s75/s40 /s97/s41/s100\nM/s32/s47/s32/s100H/s32\n〈/s49/s48/s48〉/s32\n〈/s49/s49/s48〉/s32\n〈/s50/s49/s49〉/s32\n〈/s49/s49/s49〉/s77/s110/s83/s105/s100M/s32/s47/s32/s100H/s44/s32/s61539/s97/s99/s32\n/s61549\n/s48H/s32/s40/s84/s41/s82/s101/s32/s61539/s97/s99/s50\n/s32/s215/s32/s73/s109/s32/s61539/s97/s99/s48\n/s50/s53/s53/s48/s48/s48/s46/s52/s48/s46/s56/s49/s46/s50/s49/s46/s54T/s32/s61/s32/s53/s55/s46/s50/s32/s75/s50\n/s32/s215/s32/s73/s109/s32/s61539/s97/s99/s67/s117/s50/s79/s83/s101/s79/s51/s100M/s32/s47/s32/s100H/s44/s32/s61539/s97/s99/s32\n/s61549\n/s48H/s32/s40/s109/s84/s41H/s32/s124/s124/s32〈/s49/s49/s49〉/s40/s101/s41/s32/s32/s32/s32/s32/s48\n/s53/s48/s49/s48/s48/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s40/s100/s41/s32/s32/s32/s32/s32H\n/s32/s124/s124/s32〈/s49/s49/s48〉/s100M/s32/s47/s32/s100H/s44/s32/s61539/s97/s99/s32\n/s61549\n/s48H/s32/s40/s109/s84/s41/s70/s101/s49/s45x/s67/s111x/s83/s105T\n/s32/s61/s32/s50/s54/s46/s48/s32/s75x\n/s32/s61/s32/s48/s46/s50/s48/s50\n/s32/s215/s32/s73/s109/s32/s61539/s97/s99/s48\n/s51/s48/s54/s48/s48/s48/s46/s54/s49/s46/s50/s49/s46/s56/s50/s46/s52/s40/s99/s41/s32/s32/s32/s32/s32H\n/s32/s124/s124/s32〈/s49/s48/s48〉/s70/s101/s71/s101/s100M/s32/s47/s32/s100H/s44/s32/s61539/s97/s99/s32\n/s61549\n/s48H/s32/s40/s109/s84/s41T/s32/s61/s32/s50/s55/s55/s46/s53/s32/s75/s50\n/s32/s215/s32/s73/s109/s32/s61539/s97/s99/s48\n/s48/s46/s50/s48/s46/s52/s48/s48/s46/s49/s48/s46/s50/s48/s46/s51H\n/s32/s124/s124/s32〈/s49/s48/s48〉/s77/s110/s49/s45x/s70/s101x/s83/s105/s100M/s32/s47/s32/s100H/s44/s32/s61539/s97/s99/s32\n/s61549\n/s48H/s32/s40/s84/s41T/s32/s61/s32/s49/s52/s46/s48/s32/s75x\n/s32/s61/s32/s48/s46/s48/s52/s50\n/s32/s215/s32/s73/s109/s32/s61539/s97/s99/s40/s98/s41/s32/s32/s32/s32/s32FIG. 5. Typical \feld dependence of the susceptibility for a temperature crossing the skyrmion lat-\ntice state. (a) Real and imaginary part of the ac susceptibility as well as susceptibility calculated\nfrom the magnetization, d M=dH, for MnSi and \felds along major crystallographic directions. Be-\nsides well-understood anisotropies of the helical-to-conical transition and the extent of the skyrmion\nlattice phase pocket, the magnetic properties of MnSi are essentially isotropic. (b){(e) Susceptibil-\nity for Mn 1\u0000xFexSi (x= 0:04), FeGe, Fe 1\u0000xCoxSi (x= 0:20), and Cu 2OSeO 3. Qualitatively very\nsimilar behavior is observed. Data in panel (c) taken from Ref.73.\nfrom \frst to second order is expected in the Brazovskii scenario, as the interactions between\nthe chiral paramagnons become quenched under increasing magnetic \felds.\nIn the magnetic phase diagram, see Figs. 4(a) and 4(b), the crossovers between the\n\ructuation-disordered and the paramagnetic regime as well as between the paramagnetic and\nthe \feld-polarized regime as observed in temperature sweeps of the susceptibility emanate\nfrom this TCP. An analysis of the entropy released at the phase transitions (not shown) also\ncorroborates the position of the TCP. It suggests that the skyrmion lattice state possesses an\nentropy that is larger than the surrounding conical state, consistent with a stabilization by\nthermal \ructuations76. The latter is supported by the detailed shape of the phase boundary\nbetween the \ructuation-disordered and the long-range ordered states, where the skyrmion\nlattice extents to higher temperatures as compared to the conical state.\nFollowing the detailed description of data recorded in MnSi with the magnetic \feld applied\nalongh100i, we now turn to Fig. 5 illustrating typical susceptibility data as a function\nof \feld for di\u000berent \feld directions and materials. Fig. 5(a) shows data of MnSi for \feld\napplied along the major crystallographic axes after zero-\feld cooling measured on two cubes,\n14i.e., with unchanged demagnetization e\u000bects. In general, the magnetic behavior is very\nisotropic. Changing the \feld direction only in\ruences the weakest energy scale in the system,\nthe cubic anisotropies, and has two well-understood consequences for the magnetic phase\ndiagram. First, the helical-to-conical transition \feld is smallest for the easy axis of the helical\npropagation vector h111iand largest for the hard axis h100i. In addition, the transition is\nonly second-order if it is symmetry-breaking and otherwise represents a crossover. Second,\nthe extent of the skyrmion lattice in both temperature and \feld decreases as the conical\nstate is favored by the cubic anisotropies, i.e., in MnSi it is largest for \feld along h100i\nand smallest forh111i. It is important to note, that even for \feld along the easy axis of the\nhelix the skyrmion lattice is observed for all chiral magnets questioning a stabilization of the\nskyrmion lattice by cubic anisotropies only. In fact, for doped compounds such as Fe 1\u0000xCoxSi\nor Mn 1\u0000xFexSi the anisotropies are usually less pronounced or even completely suppressed,\npresumably due to the large amount of chemical disorder present in the system19,75, and yet\nthe skyrmion lattice state represents nonetheless a well-de\fned stable phase.\nFigs. 5(b) through 5(e) show typical susceptibility data for Mn 1\u0000xFexSi (x= 0:04), FeGe,\nFe1\u0000xCoxSi (x= 0:20), and Cu 2OSeO 3highlighting the universal aspects of di\u000berent cubic\nchiral magnets. Despite the di\u000berent temperature, \feld, length, and moment scales the\nsusceptibilities of the di\u000berent materials are qualitatively highly reminiscent. Omitting\nquantitative information on temperature, \feld, and susceptibility, even an expert would\nstruggle to distinguish data between the di\u000berent materials.\nIt is \fnally essential to account for demagnetization e\u000bects, for instance when data\nrecorded on samples with di\u000berent sample shapes are combined in a single magnetic phase\ndiagram. In general, the internal magnetic \feld, Hint, is calculated as Hint=Hext\u0000\nNM(Hext) with the externally applied magnetic \feld Hextand the 3\u00023 demagnetization\nmatrix Nthat obeys trfNg= 1 in SI units. While a proper treatment of the dipolar in-\nteractions in the cubic chiral magnets requires to take several matrix entries into account29,\nin most cases consideration of the scalar equation Hint=Hext\u0000NM(Hext) is su\u000ecient, in\nwhich for \feld along the z-direction the matrix entry Nzzis referred to as N. Note that for\nthe measured ac susceptibility, \u001fext\nac, not only the \feld scale but also the absolute value of\nthe susceptibility depends on demagnetization e\u000bects via the applied excitation \feld Hext\nac.\nFrom a practical point of view many samples are essentially rectangular prisms for which\ne\u000bective demagnetization factors for \felds applied along the edges may be calculated follow-\n15ing Ref.79. In addition, in the cubic chiral magnets the susceptibility assumes essentially a\nconstant value in the conical phase. Using the measured value, \u001fext\ncon, as a \frst approximation\nfor the entire helimagnetically ordered part of the magnetic phase diagram, i.e., for T <T c\nandH < H c2, the magnetization may be expressed as M(Hext) =\u001fext\nconHext=\u001fint\nconHint.\nHence, the internal and the externally applied magnetic \felds are related by:\nHint=Hext\u0000\n1\u0000N\u001fext\ncon\u0001\n=Hext\n1 +N\u001fint\ncon(5)\nWe note that the internal value of the constant susceptibility of the conical state, \u001fint\ncon, is\nan important dimensionless measure for the e\u000bective strength of dipolar interactions in the\nchiral magnets29. If the magnetic properties and a second quantity, e.g., electrical resistivity,\nare determined on samples with di\u000bering demagnetization factors, N1andN2, the formula\nto calculate the internal \feld of the second sample may be written as:\nHint;2=Hext;2\u0012\n1\u0000N2\u001fext\ncon;1\n1\u0000\u001fext\ncon;1(N1\u0000N2)\u0013\n(6)\nIn the \feld-polarized state above Hc2one may, again in \frst approximation, assume the\nmagnetization as saturated and thus M(Hext) =\u001fext\nconHext\nc2=\u001fint\nconHint\nc2leading to a constant\no\u000bset,Hint=Hext\u0000N\u001fext\nconHext\nc2.\nDespite the crude nature of the approximation given above, this treatment proves to be\nsu\u000ecient to account for the most prominent e\u000bects of demagnetizing \felds in the chiral mag-\nnets such as the shift of transition \felds. Additionally, a smearing of phase transitions and\nvery broad regimes of phase coexistence between the conical and the skyrmion lattice state\nmay be observed in samples with large and, in particular, inhomogeneous demagnetization\ne\u000bects68. Such unfavorable sample shapes are, for instance, thin platelets with their short\nedge along the \feld or irregular shapes in general. Materials with a large absolute value of\nthe susceptibility intensify the issue.\nB. Magnetic phase diagrams for di\u000berent materials\nUsing the de\fnitions for the transition \felds and temperature given in the previous sub-\nsection on susceptibility and speci\fc heat data we have compiled magnetic and compositional\nphase diagrams of various cubic chiral magnets as shown in Fig. 6. Data extracted from\nmeasurements of the derivative of the magnetization, the ac susceptibility, and the speci\fc\n16/s48/s50/s48/s52/s48/s54/s48/s40/s102/s41/s32 /s77/s252/s110/s122/s101/s114/s32\n/s71/s114/s105/s103/s111/s114/s105/s101/s118/s32\n/s79/s110/s111/s115/s101/s32\n/s77/s97/s110/s121/s97/s108/s97/s32\n/s67/s104/s101/s114/s110/s105/s107/s111/s118/s32\n/s73/s115/s104/s105/s109/s111/s116/s111/s32\n/s66/s101/s105/s108/s108/s101T/s32/s40/s75/s41T/s50T\n/s99/s72/s77/s80/s77/s70/s101/s49/s45x/s67/s111x/s83/s105/s53\n/s52/s53/s54/s53/s56/s54/s48/s48/s49/s48/s50/s48/s51/s48/s52/s48H/s32/s124/s124/s32〈/s49/s49/s49〉/s40/s104/s41/s80\n/s77/s67/s117/s50/s79/s83/s101/s79/s51/s61549/s48H/s105/s110/s116/s32/s40/s109/s84/s41T\n/s32/s40/s75/s41/s70/s68/s115/s107/s121/s114/s109/s105/s111/s110/s108\n/s97/s116/s116/s105/s99/s101/s70/s80/s99\n/s111/s110/s105/s99/s97/s108/s104\n/s101/s108/s105/s99/s97/s108/s50/s55/s50/s56/s50/s57/s51/s48/s51/s49/s48/s48/s46/s49/s48/s46/s50/s48/s46/s51/s48/s46/s52H/s32/s124/s124/s32〈/s49/s48/s48〉/s40/s97/s41/s77/s110/s83/s105/s61549/s48H/s105/s110/s116/s32/s40/s84/s41T\n/s32/s40/s75/s41/s115/s107/s121/s114/s109/s105/s111/s110/s108\n/s97/s116/s116/s105/s99/s101/s104\n/s101/s108/s105/s99/s97/s108/s99/s111/s110/s105/s99/s97/s108/s70 /s80/s80\n/s77/s70\n/s68/s48\n/s49/s48/s50/s48/s51/s48/s40/s98/s41/s72\n/s77T/s50T/s32/s40/s75/s41/s70\n/s68/s77/s110/s49/s45x/s70/s101x/s83/s105/s80\n/s77T\n/s99/s50\n/s55/s50/s50/s55/s54/s50/s56/s48/s50/s56/s52/s48/s49/s48/s50/s48/s51/s48/s52/s48H /s32/s124/s124/s32〈/s49/s48/s48〉/s40/s100/s41/s61549 /s48H/s105/s110/s116/s32/s40/s109/s84/s41T\n/s32/s40/s75/s41/s115/s107/s121/s114/s109/s105/s111/s110/s108\n/s97/s116/s116/s105/s99/s101/s99\n/s111/s110/s105/s99/s97/s108/s70/s80/s70\n/s68/s104/s101/s108/s105/s99/s97/s108/s80/s77/s70/s101/s71/s101/s48/s49/s48/s50/s48/s51/s48/s48/s52/s48/s56/s48/s49/s50/s48H/s32/s124/s124/s32〈/s49/s48/s48〉/s40/s101/s41/s70/s101/s48/s46/s56/s67/s111/s48/s46/s50/s83/s105/s61549/s48H/s105/s110/s116/s32/s40/s109/s84/s41T\n/s32/s40/s75/s41/s80/s77/s70/s80/s70\n/s68/s104 /s101/s108/s105/s99/s97/s108/s32/s40/s122/s102/s99/s41/s99/s111/s110/s105/s99/s97/s108/s115\n/s107/s121/s114/s109/s105/s111/s110/s108\n/s97/s116/s116/s105/s99/s101/s48\n/s48 /s46/s49/s48 /s46/s50/s48/s48/s46/s51/s48/s46/s54H /s32/s124/s124/s32〈/s49/s48/s48〉/s40/s99/s41/s61549 /s48H/s105/s110/s116/s32/s40/s84/s41/s32\nx\nH/s99/s50H\n/s99/s49/s48/s49/s48/s50/s48/s32\n/s70\n/s101/s83/s105/s32/s77\n/s110/s83/s105/s61548/s104/s61548\n/s104/s32/s40/s110/s109/s41/s48\n/s49/s48/s48/s50/s48/s48/s51/s48/s48/s48/s52/s48/s56/s48/s49/s50/s48/s32/s32\nk/s104/s32/s124/s124/s32〈/s49/s49/s49〉k\n/s104/s32/s124/s124/s32〈/s49/s48/s48〉/s61549/s48H/s105/s110/s116/s32/s40/s109/s84/s41/s32\nT\n/s32/s40/s75/s41/s48/s49/s48/s50/s48/s51/s48/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s32\n/s32/s61549/s48H/s105/s110/s116/s32/s40/s84/s41/s32\nT\n/s32/s40/s75/s41/s115\n/s107/s121/s114/s109/s105/s111/s110/s108\n/s97/s116/s116/s105/s99/s101/s48\n/s49/s48/s50/s48/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s32\n/s32/s61549/s48H/s105/s110/s116/s32/s40/s84/s41/s32\nT\n/s32/s40/s75/s41x/s32/s61/s32/s48/s46/s48/s52/s104\n/s101/s108/s105/s99/s97/s108/s32/s40/s122/s102/s99/s41/s48\n/s50/s48/s52/s48/s54/s48/s48/s50/s53/s53/s48/s55/s53/s32\n/s32/s61549/s48H/s105/s110/s116/s32/s40/s109/s84/s41/s32\nT\n/s32/s40/s75/s41/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s48/s46/s56/s49/s48/s48/s46/s49/s48/s46/s50/s32\n/s70\n/s101/s83/s105/s61549/s48H/s105/s110/s116/s32/s40/s84/s41/s32\nx\n/s32/s67\n/s111/s83/s105/s48/s49/s48/s48/s50/s48/s48H /s32/s124/s124/s32〈/s49/s48/s48〉/s40/s103/s41/s61548\n/s104/s32/s40/s110/s109/s41H\n/s99/s49H/s99/s50/s61548\n/s104FIG. 6. Magnetic phase diagrams of selected cubic chiral magnets. (a) MnSi. (b),(c) Mn 1\u0000xFexSi.\nSubstitutional doping of MnSi with Fe leads to a suppression of the ordering temperature and\na decrease of the helix wavelength, \u0015h. The magnetic phase diagram, as shown in the inset for\nx= 0:04, stays qualitatively similar for x\u00140:10. (d) FeGe. Susceptibility data from Refs.72,73,\nspeci\fc heat data from Ref.74, and further information from Refs.42,80,81were analyzed in the same\nmanner as for all other compounds. (e) Fe 0:8Co0:2Si. (f),(g) Fe 1\u0000xCoxSi. As a function of cobalt\ncontentxthe characteristic temperature, \feld, and length scales may be varied over a large range.\nValues are taken from Refs.19,82{87. (h) Cu 2OSeO 3. In contrast to the other materials, this local-\nmoment insulator displays substantial magnetoelectric coupling. Still, the magnetic phase diagram\nis unchanged.17heat are shown as circles, squares, and diamonds, respectively. Light and dark colors rep-\nresent data from temperature and \feld sweeps, respectively. Magnetic \felds were applied\nafter zero-\feld cooling. All \feld values are given on internal \feld scales, i.e., after correcting\nfor demagnetization e\u000bects. In general the magnetic phase diagrams of the cubic chiral mag-\nnets are qualitatively extremely similar. We distinguish the following six regimes; helical,\nconical, skyrmion lattice (S), \ructuation-disordered (FD), paramagnetic (PM), and \feld-\npolarized (FP). In addition, we mark the regime of phase coexistence between the conical\nand the skyrmion lattice state by a faint red shading. Solid and dashed lines indicate phase\ntransitions and crossovers, respectively, while dotted lines represent guides to the eye.\nFig. 6(a) reproduces the magnetic phase diagram of MnSi for \feld along h100i, i.e., the\nhard axis for the helical propagation vector, as discussed in the previous subsection. The\ninset shows the phase diagram across the entire parameter range of long-range helimagnetic\norder. We note that the helix wavelength, \u0015h, in MnSi increases from \u0018165\u0017A atTcto\n\u0018180\u0017A at lowest temperatures36,57,63.\nSubstitutional doping of iron at the manganese sites of MnSi results in a reduction of\nthe helimagnetic ordering temperature while the critical \feld values in the zero-temperature\nlimit change only weakly, cf. Figs. 6(b) and 6(c). The magnetic phase diagram is qualitatively\nvery similar to pure MnSi for x\u00140:10 as shown in the inset of Fig. 6(b) for Mn 1\u0000xFexSi\nwithx= 0:04. The most notable di\u000berence concerns the helical state, which forms in\nMn1\u0000xFexSi only properly after zero-\feld cooling. In addition, Hc1becomes essentially\nisotropic and increases with decreasing temperature. These e\u000bects, however, may be related\nto the increased amount of disorder present in the system. The helix wavelength and hence\nalso the skyrmion lattice constant decreases by up to a factor of roughly 2 resulting in an\nincrease of the skyrmion density by a factor of 448,88.\nThe complex quantum critical behavior that emerges at high iron concentrations, where\nstatic magnetic order is fully suppressed, is the topic of ongoing research65,75. Doping with\niron, cobalt, and nickel leads to an essentially identical modi\fcation of the magnetic behavior\nif scaled by the number valance electrons per formula unit75,89. Doping with chromium, i.e.,\nreducing the number of valance electrons, leads to a suppression of Tccomparable to iron\ndoping90. This behavior is consistent with the notion that the main e\u000bects of chemical\ndoping are due to a rigid shift the Fermi level, as recently inferred from a combined study\nof ab initio calculations and the electric transport properties in Mn 1\u0000xFexSi??.\n18We now turn to FeGe which is rather similar to MnSi, however, with a transition tem-\nperature near room temperature and \u0015h= 700 \u0017A. Around 230 K the easy direction of the\nhelical pitch changes from h100iat high temperatures to h111iat low temperatures, where a\nlarge thermal hysteresis of \u001835 K is observed81. Recent publications50,72{74claimed putative\nexperimental evidence for the formation of a very complex magnetic phase diagram with\nmultiple pockets and precursor phenomena around the skyrmion lattice state. The authors\nconcluded that these \fndings prove that the skyrmion lattice is in fact not stabilized by\nthermal \ructuations but by a combination of uniaxial anisotropies and a softened modulus\nof the magnetization.\nIn stark contrast, applying accurately the same de\fnitions given in the previous sub-\nsection to the data published in Refs.72{74provides the phase diagram shown in Fig. 6(d).\nThis phase diagram strongly resembles that of the other cubic chiral magnets. The broad\nregimes of phase coexistence may be attributed to large demagnetization e\u000bects as a conse-\nquence of the relatively large absolute value of the susceptibility in FeGe and the shape of\nthe samples used in these studies; we extract \u001fext\ncon= 1:6 andN\u00190:33 from Ref.73yield-\ning\u001fint\ncon= 3:4. Most importantly, however, we observe no signatures of additional phase\npockets or mesophases. We \fnally note that a temperature discrepancy of the maximum in\nthe speci\fc heat in Refs.73,74indicates that care has to be taken when combining data from\ndi\u000berent samples or measurement setups.\nFigs. 6(e) through 6(g) are dedicated to Fe 1\u0000xCoxSi, a pseudo-binary B20 system that\ndisplays helimagnetism in a large composition range, 0 :05.x.0:882,85,91, albeit the\nparent compounds FeSi and CoSi are a paramagnetic insulator92and a diamagnetic metal93,\nrespectively. Starting from the strongly correlated insulator FeSi94, an insulator-to-metal\ntransition takes place around x\u00190:0284. However, due to the comparatively high absolute\nvalue of the electrical resistivity and an upturn at low temperatures helimagnetic Fe 1\u0000xCoxSi\nis typically referred to as a strongly doped semiconductor82,86,95.\nCompared to the stoichiometric helimagnets, Fe 1\u0000xCoxSi o\u000bers the opportunity to vary\nthe characteristic parameters of the helimagnetism over a wide range by compositional tuning\nwhile the magnetic phase diagrams stays that of a typical cubic chiral magnet, cf. Fig. 6(e).\nAs summarized in Figs. 6(f) and 6(g), the helimagnetic transition temperature reaches up\nto\u001850 K, the critical \felds assume values up to \u0018150 mT, and the helix wavelength ranges\nfrom about 300 \u0017A to more than 2000 \u0017A. As for doped MnSi, a proper helical state is observed\n19only after zero-\feld cooling. Fe 1\u0000xCoxSi displays easyh100iaxes that, especially for larger\ncobalt contents, are less pronounced than for other cubic chiral helimagnets87. Forx= 0:20\na helical pitch along h110iwas identi\fed in Ref.19. The latter study also revealed the\nexistence of a skyrmion lattice in Fe 1\u0000xCoxSi that is sensitive to the \feld and temperature\nhistory. While the reversible pocket of skyrmion lattice state is comparable to other systems,\n\feld cooling may result in a metastable extension down to lowest temperatures allowing for\nconceptionally new types of experiments31. A similar behavior was later also discovered\nin low-quality MnSi samples under applied pressure96. Moreover, depending on the \feld\ndirection, two Skyrmion lattice domains with di\u000berent in-plane orientations were observed\nleading to a twelvefold small-angle scattering pattern97.\nFig. 6(h) \fnally shows the magnetic phase diagram of copper-oxo-selenite, Cu 2OSeO 3.\nThe crystalline structure of this compound is more complex than that of the B20 transition\nmetal systems, but also belongs to space group P21398. Magnetically, on the strongest\nscale Cu 2OSeO 3shows local-moment ferrimagnetic order of the spin-1\n2Cu2+ions. Here,\nthe ferromagnetically aligned moments on the CuIsites couple antiferromagnetically to the\nions on the CuIIsites leading to a 3:1 ratio99with exchange constants JFM=\u000050 K and\nJAFM = 65 K100. No breaking of the ferrimagnetic coupling is observed up to 55 T101.\nThe ferrimagnetism is superimposed by a long-wavelength helical modulation based on the\nDzyaloshinskii-Moriya interaction with \u0015h= 620 \u0017A26. The resulting magnetic phase diagram\nis highly reminiscent of the helimagnetic B20 compounds with an easy h100ifor the helical\npropagation vector and a delicate pinning within the skyrmion lattice state49,102. A study\nusing resonant soft x-ray di\u000braction further suggested that the CuIand CuIIsites may form\nindividual but coupled skyrmion lattices that are rotated by a few degree with respect to\neach other giving rise to a moir\u0013 e pattern103. More recent work reveals, however, that this\nconjecture may be wrong.\nCu2OSeO 3, albeit being a non-polar insulator, possesses a magnetically induced electri-\ncal polarization in \fnite \felds and, in particular, within the skyrmion lattice state69. The\npolarization resulting from this magnetoelectric coupling may be described in a d-phy-\nbridization model104, where the covalency between copper dand oxygen porbitals is mod-\nulated according to the local magnetization direction via the spin-orbit interaction leading\nto a local electric dipole along the bond direction69. Hence, though Cu 2OSeO 3is actually\na (heli-)ferrimagnetic magnetoelectric, it is often erroneously referred to as a multiferroic.\n2000.20.4-30-20-10010(c)       /s61555 Ax\ny (103 \nΩ-1m-1) \nm\ns,0 (/s61549B / f.u.) TheoryE\nxperiment: \nMnSi \nMn1-xFexSi0\n0.20.4-20246(d)       E\nxperiment: \nMnSi \nMn1-xFexSi \nMn1-xCoxSi,\n T → 0 TheoryRtopy\nx (nΩ cm T-1) \nm\ns,0 (/s61549B / f.u.)0\n2 4 6 02468M\nnSiH || 〈100〉 \n I || 〈110〉(e)/s615490Hint = 200 mT \n  T (K) \n26.2 \n28.2vd|| / vpinj\n / jcjc+0.20\n5 1 01 50204060(b)temp. sweep (T = 2 K) f\nield sweepΔ/s61554topx\ny (nΩ cm)p\n (kbar)dmred / dpM\nnSi0.100.150.200.25091827(a)2\n8.828.9Δ/s61554topx\ny (nΩ cm)/s61549\n0Hint (T)28.7T (K)M nSiH || 〈110〉, I || 〈100〉2\n8.428.528.62\n8.028.128.228.30\n51015200102030 \n P\nMN\nFLT (K) \np\n (kbar)FLh\nelicalFIG. 7. Examples of the e\u000ecient coupling of spin currents to the skyrmion lattice. (a) Topological\nHall contribution, \u0001 \u001atop\nxy, in MnSi as a function of \feld109. (b) Topological Hall contribution,\n\u0001\u001atop\nxy, as a function of hydrostatic pressure in MnSi96. The intrinsic size (open symbols) may only\nbe observed after \feld-cooling down to the lowest temperatures. The inset shows the pressure-\ntemperature phase diagram of MnSi highlighting the extended regime of non-Fermi liquid (NFL)\nbehavior22,110. (c),(d) Anomalous Hall conductivity, \u001bA\nxy, and topological Hall constant, Rtop\nyx,\nas a function of the magnetic moment as varied, e.g., by iron or cobalt doping. First-principle\ncalculations and experimental data are in excellent agreement88. (e) Drift velocity of the skyrmion\nlattice,vdk, as a function of current density, j. Ultra-low current densities in the order of jc\u0018\n106A=m2unpin the skyrmion lattice24,111.\nThe origin of this notion may be seen in the hitherto unique opportunity to manipulate\na topologically non-trivial entity of magnetoelectric nature using various external control\nparameters, see for example Refs.28,105{108.\n21V. EMERGENT ELECTRODYNAMICS\nA particularly exciting consequence of the non-trivial topology of the skyrmions concerns\ntheir coupling to spin currents. In the following we focus on the consequences in metallic\ncompounds and we refer to the chapter by Markus Garst for a more detailed account. The\nspin structure of the skyrmion, as seen from the point of view of an electron traversing it,\ngives rise to real-space Berry phases which may be expressed as emergent magnetic and\nelectric \felds, Be\ni=~\n2\u000fijk^ \u0001@j^ \u0002@k^ andEe\ni=~^ \u0001@i^ \u0002@t^ , respectively, with @i=@=@r i\nand@t=@=@t111. As a consequence an additional topological contribution to the Hall e\u000bect\nmay be observed in the skyrmion lattice state as illustrated in Fig. 7(a)109.\nUsing the charge carrier spin polarization Pand assuming the absence of spin-\rip scatter-\ning, while non-spin-\rip scattering is captured by the normal Hall constant R0, the topological\nHall contribution may be estimated as \u0001 \u001atop\nxy=PR 0Be\u000b. The e\u000bective emergent \feld, Be\u000b,\nis topologically quantized in the sense that it is given by the product of the emergent \rux\nquantum that each skyrmion supports, \u001e0=h=e, and the skyrmion density \u001e. Thus, the sign\nof the topological Hall contribution allows to distinguish, in principle, between skyrmions\n(\b= +1) and anti-skyrmions ( \b=\u00001), such as in MnSi, provided the normal Hall constant\nR0is su\u000ecient to express the details of the band structure109.\nIn real materials the electronic structure at the Fermi surface may contribute in di\u000berent\nways and the spin polarization as well as the skyrmion lattice constant may change as a\nfunction of temperature or \feld. In addition, processes such as spin-\rip scattering may\ncause a reduction compared to the intrinsic value of \u0001 \u001atop\nxy. For instance, in MnSi the\ntopological Hall contribution in the skyrmion lattice is of the order of 4 n\n cm whereas an\nintrinsic topological Hall signal of the order of 50 n\n cm is expected for its emergent \feld\nofBe\u000b=\u000013 T96. Field-cooling the skyrmion lattice down to low temperatures allows to\nreduce the \fnite temperature e\u000bects, as it is for instance possible in high-pressure studies\nof MnSi. Here, as shown in Fig. 7(b), the intrinsic value of \u0001 \u001atop\nxycould be inferred which\nin turn scales with the charge carrier spin polarization that follows the reduced magnetic\nmomentmred=m(p)=m(p= 0).\nAt higher pressures where static helimagnetic order in MnSi is fully suppressed at pc=\n14:6 kbar more complex behavior has been observed, cf. inset of Fig. 7(b)110,112,113. In par-\nticular, in a large pressure and \feld range the standard description of the metallic state,\n22namely the Fermi liquid (FL) theory, breaks down20,114. In addition, neutron scattering\nreveals so-called partial magnetic order in a pocket above pc21. In combination with the lack\nof observable relaxation in muon data115, it has been concluded that the spin correlations\nof the partial order are dynamic on a timescale between 10\u000010s and 10\u000011s. Finally, a clear\nconnection between the topological Hall e\u000bect in the skyrmion lattice at ambient pressure\nand a large topological Hall signal that coincides with the non-Fermi liquid (NFL) regime\nabovepcempirically suggests that spin correlations with non-trivial topological character\ndrive the breakdown of Fermi liquid theory22.\nCalculations based on density functional theory allow to determine the sign and the\nmagnitude of the anomalous and the topological Hall e\u000bect and, in particular, how they\nevolve when the spin polarization changes. Experimentally, the latter may be realized by\nsubstitutional doping of Fe or Co into MnSi, where excellent agreement between theory\nand experiment has been observed as shown in Figs. 7(c) and 7(d)88. These results provide\nthe quantitative microscopic underpinning that, while the anomalous Hall e\u000bect is due to\nthe reciprocal-space Berry curvature116, the topological Hall e\u000bect originates in real-space\nBerry phases. As a theoretical prediction that awaits further con\frmation even contributions\narising from mixed phase-space Berry phases have been proposed96,117.\nThe e\u000ecient coupling of spin currents to the magnetic structure, together with the ex-\nceptional long-range order of the skyrmion lattice46and the resulting very weak collective\npinning to defects, causes a sizeable response of the magnetic textures at ultra-low current\ndensities. Above an exceptionally low threshold current density of the order of jc\u0018106A/m2\nthe skyrmion lattice unpins and begins to drift24,118. Numerical simulations revealed that\nthe skyrmion motion exhibits a universal current-velocity relation that is (on the scale of the\nstudy) una\u000bected by impurities and non-adiabatic e\u000bects119. Flexible shape-deformations of\nindividual skyrmions and the skyrmion lattice permit to avoid pinning centers.\nTheoretically, the spin transfer torques in the cubic chiral magnets may be accounted\nfor in the framework of a Landau-Lifshitz-Gilbert equation using the Thiele approach120,121.\nHere, a Magnus force perpendicular to the current direction and a dissipative drag force\nalong it are balanced by pinning forces, e.g., due to defects. The Magnus force represents\nthe e\u000bective Lorentz force arising from the emergent magnetic \feld Beand leads to a certain\nangle between the current direction and the drift direction of the skyrmion lattice. According\nto Faraday's law of induction, a moving skyrmion, which supports exactly one quantum of\n232.4 T〈100〉\n3\n45 K/s48\n/s53/s48/s49/s48/s48/s49/s53/s48/s48/s52/s56/s49/s50/s32\n/s61554xy/s32\n/s61554xx/s32\nM/s61549/s48H/s32/s40/s84/s41T\n/s32/s40/s75/s41/s115/s105/s109/s112/s108/s101/s32/s99/s117/s98/s105/s99/s115\n/s107/s121/s114/s109/s105/s111/s110/s32/s108/s97/s116/s116/s105/s99/s101/s77/s110/s71/s101/s48\n/s50/s52/s54/s40/s100/s41/s32\n/s83/s104/s105/s111/s109/s105/s32\n/s75/s97/s110/s97/s122/s97/s119/s97/s61548\n/s104/s32/s40/s110/s109/s41/s61548/s104200 nm〈110〉\n6\n5 mT/s48\n/s53/s49/s48/s49/s53/s52/s48/s53/s48/s48/s51/s48/s54/s48/s57/s48/s40/s99/s41/s114 /s104/s111/s109/s98/s111/s104/s101/s100/s114/s97/s108/s99/s117/s98/s105/s99/s80\n/s77/s70\n/s69/s49/s78/s233/s101/s108/s45/s116/s121/s112/s101/s115\n/s107/s121/s114/s109/s105/s111/s110/s32/s108/s97/s116/s116/s105/s99/s101/s70\n/s69/s52/s80/s77/s80\n/s69/s99\n/s121/s99/s108/s111/s105/s100/s97/s108/s70\n/s69/s51/s70/s77/s70\n/s69/s50H/s32/s124/s124/s32〈/s49/s49/s49〉/s32C/s32\nΔP/s32\n/s61539/s97/s99/s61549/s48H/s32/s40/s109/s84/s41T\n/s32/s40/s75/s41/s71/s97/s86/s52/s83/s56/s48/s49/s50/s51/s48/s49/s48/s48/s50/s48/s48/s51/s48/s48/s52/s48/s48/s40/s97/s41/s32/s32/s32/s32/s32/s32/s32/s80\n/s77/s32/s32\nx\nT/s99/s32/s40/s75/s41/s32\n/s67\n/s111/s49/s48/s45x/s90/s110/s49/s48/s45x/s77/s110/s50x/s61548\n/s104/s72\n/s77/s48\n/s54/s48/s49/s50/s48/s49/s56/s48/s32/s61548\n/s104/s32/s40/s110/s109/s41/s61549\n0H (mT)302\n01\n0 \n 040F\nPc\nonicals\nkyrmionl\nattice3\n05T\n (K)290\nCo8Zn9Mn33\n20helical\n(b)C\no8Zn10Mn2HM nGe3\n5 K0.30.6dM / dH0\nHFIG. 8. Topologically non-trivial spin structures in further bulk materials. (a) Part of the com-\npositional phase diagram of the system Co 10\u0000xZn10\u0000yMnx+y. Long-wavelength helimagnetic order\nwith transition temperatures exceeding room temperature has been reported123. (b) Colormap of\nthe susceptibility of Co 8Zn9Mn3revealing a skyrmion lattice state and corresponding real-space\nspin structure in Co 8Zn10Mn2as obtained by LF-TEM123. The behavior is highly reminiscent of\nthe cubic chiral magnets. (c) Magnetic phase diagram of GaV 4S8exhibiting a N\u0013 eel-type skyrmion\nlattice and various types of ferroelectric order30,124. (d) Magnetic phase diagram of MnGe125{127\ngiving rise to a simple cubic lattice of spin whirls as recently observed by LF-TEM128.\nemergent magnetic \rux, may then induce an emergent electric \feld Eethat inherits the\ntopological quantization122. These electric \felds have been observed directly111. A scaling\nplot as depicted in Fig. 7(e) reveals a universal relation between the current density, j, and\nthe drift velocity of the skyrmion lattice, vdk, where typical pinning velocities are of the\norder of 0.1 mm/s, i.e., the drift velocity of conduction electrons.\n24VI. CONCLUSIONS AND OUTLOOK\nTaken together, cubic chiral magnets with non-centrosymmetric space group P213 rep-\nresent a class of materials that share a universal magnetic phase diagram. The skyrmion\nlattice state occupies a single phase pocket and the entire magnetic phase diagram is well\naccounted for by a Ginzburg-Landau approach including the e\u000bects of thermal \ructuations.\nDepending on the speci\fc material, key parameters such as the transition temperatures,\ncritical \felds, or the helix wavelength may be varied by two orders of magnitude. With\ncompounds ranging from pure metals to magnetoelectric insulators, this material class pro-\nvides well-understood model systems for experiments, theory, and simulations. In recent\nstudies, for instance, aspects were addressed such as the topological unwinding at the tran-\nsition to conventional helimagnetic order31or the collective excitations of the di\u000berent spin\nstructures27,129{131.\nCurrent research activities on topologically non-trivial spin states, however, are not re-\nstricted to cubic chiral magnets. In thin \flms or monolayers, where the inversion symmetry\nis broken by the surface, skyrmions may be stabilized by the Dzyaloshinskii-Moriya in-\nteraction as combined with four-spin exchange interactions132,133. Another route towards\nskyrmionic textures may be long-range magnetodipolar interactions134. In such systems, it\nwas already demonstrated that skyrmions may be created and annihilated individually using\nspin-polarized currents of a scanning tunneling microscope133or laser pulses135. The cre-\nation, manipulation, and the dynamics of skyrmions in thin \flms, nanowires, and patterned\nnanostructures o\u000ber great potential for future applications, see for instance Refs.23,136{143.\nThe e\u000ecient gyromagnetic coupling, the topological stability, and the small size of the\nskyrmions promise devices for ultra-dense information storage and spintronics25, while their\nunique collective excitations may be exploited for the design of conceptually new microwave\ndevices28,29,144.\nIn parallel, topologically non-trivial spin states have been identi\fed in a rapidly growing\nnumber of bulk compounds suggesting that these complex magnetic structures may be in fact\nrather common. In Fig. 8 we summarize three recent examples. The \frst material, CoZn,\ncrystallizes in the cubic space group P4132 orP4332, depending on the handedness, and\norders magnetically well above room temperature145. Doping manganese into the system, see\nFig. 8(a), reduces the transition temperature. Fig. 8(b) shows the magnetic phase diagram\n25of Co 8Zn9Mn3extracted from the magnetic susceptibility. It is highly reminiscent to that\nof the cubic chiral magnets including a pocket of skyrmion lattice state as identi\fed by LF-\nTEM and SANS measurements123. Hence, the material system Co 10\u0000xZn10\u0000yMnx+yis not\nonly the \frst bulk compound with a space group other than P213 that exhibits a skyrmion\nlattice state, but also the \frst compound stabilizing skyrmions above room temperature.\nAnother important example is shown in Fig. 8(c), which depicts the magnetic phase dia-\ngram of the lacunar spinel GaV 4S8. This system crystallizes in the cubic space group F\u001643m\nat room temperature. At TJT= 44 K GaV 4S8shows a structural phase transition146into\nthe rhombohedral space group R3mdriven by Jahn-Teller orbital order and accompanied\nby an onset of ferroelectricity (FE). The structural transition creates a multi-domain state\nwith submicron-thick sheets of the four di\u000berent rhombohedral domains30. BelowTC= 13 K\nmagnetic order sets in147and as a function of temperature and \feld a rich magnetic phase\ndiagram unfolds with various magnetically ordered states of multiferroic nature124. This\nphase diagram hosts a pocket of ferroelectric spin vortices forming a hexagonal skyrmion\nlattice as identi\fed by means of force microscopy and SANS30. However, in contrast to\nthe cubic chiral magnets or Co 10\u0000xZn10\u0000yMnx+ywhere Bloch-type chiral skyrmions are de-\nscribed in terms of spin helices, in GaV 4S8N\u0013 eel-type non-chiral skyrmions are addressed in\nform of a superposition of spin cycloids. Moreover, while in the cubic chiral magnets the\nskyrmion lines are always essentially parallel to the applied magnetic \feld, in GaV 4S8the\nvortex cores are con\fned along an h111iaxis. In combination with the multiferroic nature\nof this polar magnetic semiconductor new ways of controlling and manipulating skyrmions\nmay be possible.\nLast but not least, we return to MnGe which is isostructural to the cubic chiral magnets\nwith a magnetic phase diagram that di\u000bers from the ones described so far. In this compound,\nmeasurements of the topological Hall e\u000bect125and the topological Nernst e\u000bect127as well\nas data from SANS126and LF-TEM128consistently suggest the formation of a simple cubic\nlattice of spin whirls in zero and \fnite \feld. The magnetic lattice vectors are oriented along\ntheh100iaxes of the crystal lattice. The resulting magnetic phase diagram is depicted in\nFig. 8(c), where the inset schematically shows the spin structure and the upper panel shows\nthe in-plane distribution of magnetic moments as obtained from LF-TEM. Compared to the\ncubic chiral magnets the corresponding lattice period is relatively small and exhibits a strong\nincrease from 3 nm at low temperatures to 6 nm close to Tc= 170 K. To what extent this\n26marks the starting point of a new generic understanding of complex spin textures remains\nto be seen.\nWe are deeply indebted to our co-workers, in particular: T. Adams, R. Bamler, G. Benka,\nH. Berger, S. Bl ugel, P. B oni, G. Brandl, S. Buhrandt, A. Chacon, C. Duvinage, H.-\nM. Eiter, L. M. Eng, K. Everschor, C. Franz, F. Freimuth, M. Gangl, M. Garst, R. Georgii,\nD. Grundler, R. Hackl, M. Halder, F. Haslbeck, W. H au\u0019ler, T. Hesjedal, J. P. Hinton,\nC. Hugenschmidt, M. Janoschek, F. Jarzembeck, P. Jaschke, F. Jonietz, J. Kindervater,\nD. K ohler, J. D. Koralek, P. Krautscheid, M. Kugler, A. Kusmartseva, P. Lemmens, N. Mar-\ntin, S. Mayr, D. Meier, M. Meven, P. Milde, Y. Mokrousov, S. M uhlbauer, J. Orenstein,\nS. A. Parameswaran, B. Pedersen, R. Ramesh, T. Reimann, M. Reiner, R. Ritz, A. Rosch,\nF. Rucker, S. S aubert, C. Schnarr, R. W. Schoenlein, T. Schr oder, S. Schulte, T. Schulz,\nC. Sch utte, T. Schwarze, K. Seemann, J. Seidel, A. Senyshyn, I. Stasinopoulos, A. Vish-\nwanath, M. Wagner, J. Waizner, T. Weber, S. Weichselbaumer, B. Wiedemann, S. Zhang,\nand the team of FRM II. Financial support through DFG FOR960, DFG TRR80, and ERC\nadvanced grant 291079 (TOPFIT) is gratefully acknowledged.\nThe \fnal publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-\n25301-5 1.\n\u0003andreas.bauer@frm2.tum.de\n1T. H. R. Skyrme, \\A Non-Linear Field Theory,\" Proc. R. Soc. Lond. A 260, 127 (1961).\n2T. H. R. Skyrme, \\Particle States of a Quantized Meson Field,\" Proc. R. Soc. Lond. A 262,\n237 (1961).\n3T. H. R. Skyrme, \\A uni\fed \feld theory of mesons and baryons,\" Nucl. Phys. 31, 556 (1962).\n4G. S. Adkins, C. R. Nappi, and E. Witten, \\Static properties of nucleons in the Skyrme\nmodel,\" Nucl. Phys. B 228, 552 (1983).\n5I. Zahed and G. E. Brown, \\The Skyrme model,\" Phys. Rep. 142, 1 (1986).\n6D. Diakonov, V. Petrov, and M. Polyakov, \\Exotic anti-decuplet of baryons: prediction from\nchiral solitons,\" Z. Phys. A 359, 305 (1997).\n7E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schae\u000ber, \\A Skyrme parametrization\nfrom subnuclear to neutron star densitie,\" Nucl. Phys. A 627, 710 (1997).\n278E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schae\u000ber, \\A Skyrme parametrization\nfrom subnuclear to neutron star densities Part II. Nuclei far from stabilities,\" Nucl. Phys. A\n635, 231 (1998).\n9S. L. Sondhi, A. Karlhede, S. A. Kivelson, and E. H. Rezayi, \\Skyrmions and the crossover\nfrom the integer to fractional quantum Hall e\u000bect at small Zeeman energies,\" Phys. Rev. B\n47, 16419 (1993).\n10A. Schmeller, J. P. Eisenstein, L. N. Pfei\u000ber, and K. W. West, \\Evidence for Skyrmions and\nSingle Spin Flips in the Integer Quantized Hall E\u000bect,\" Phys. Rev. Lett. 75, 4290 (1995).\n11K. Yang, S. Das Sarma, and A. H. MacDonald, \\Collective modes and skyrmion excitations\nin graphene SU(4) quantum Hall ferromagnets,\" Phys. Rev. B 74, 075423 (2006).\n12T.-L. Ho, \\Spinor Bose Condensates in Optical Traps,\" Phys. Rev. Lett. 181, 742 (1998).\n13U. A. Khawaja and H. Stoof, \\Skyrmions in a ferromagnetic Bose-Einstein condensate,\" Nature\n(London) 411, 918 (2001).\n14L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, \\Creation and\nDetection of Skyrmions in a Bose-Einstein Condensate,\" Phys. Rev. Lett. 103, 250401 (2009).\n15J. Fukuda and S. \u0014Zumer, \\Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid\ncrystal,\" Nat. Commun. 2, 246 (2011).\n16A. N. Bogdanov and D. A. Yablonskii, \\Thermodynamically stable \"vortices\" in magnetically\nordered crystals. The mixed state of magnets,\" Sov. Phys. JETP 95, 178 (1989).\n17A. Bogdanov and A. Hubert, \\Thermodynamically stable magnetic vortex states in magnetic\ncrystals,\" J. Magn. Magn. Mater. 138, 255 (1994).\n18S. M uhlbauer, B. Binz, F. Jonietz, C. P\reiderer, A. Rosch, A. Neubauer, R. Georgii, and\nP. B oni, \\Skyrmion Lattice in a Chiral Magnet,\" Science 323, 915 (2009).\n19W. M unzer, A. Neubauer, T. Adams, S. M uhlbauer, C. Franz, F. Jonietz, R. Georgii, P. B oni,\nB. Pedersen, M. Schmidt, A. Rosch, and C. P\reiderer, \\Skyrmion lattice in the doped semi-\nconductor Fe 1\u0000xCoxSi,\" Phys. Rev. B 81, 041203 (R) (2010).\n20C. P\reiderer, S. R. Julian, and G. G. Lonzarich, \\Non-Fermi-liquid nature of the normal state\nof itinerant-electron ferromagnets,\" Nature (London) 414, 427 (2001).\n21C. P\reiderer, D. Reznik, L. Pintschovius, H. v. L ohneysen, M. Garst, and A. Rosch, \\Partial\norder in the non-Fermi-liquid phase of MnSi,\" Nature (London) 427, 227 (2004).\n22R. Ritz, M. Halder, M. Wagner, C. Franz, A. Bauer, and C. P\reiderer, \\Formation of a\n28topological non-Fermi liquid in MnSi,\" Nature (London) 497, 231 (2013).\n23N. Nagaosa and Y. Tokura, \\Topological properties and dynamics of magnetic skyrmions,\"\nNature Nano. 8, 899 (2013).\n24F. Jonietz, S. M uhlbauer, C. P\reiderer, A. Neubauer, W. M unzer, A. Bauer, T. Adams,\nR. Georgii, P. B oni, R. A. Duine, K. Everschor, M. Garst, and A. Rosch, \\Spin Transfer\nTorques in MnSi at Ultralow Current Densities,\" Science 330, 1648 (2010).\n25A. Fert, V. Cros, and J. Sampaio, \\Skyrmions on the track,\" Nature Nano. 8, 152 (2013).\n26S. Seki, X. Z. Yu, S. Ishiwata, and Y. Tokura, \\Observation of Skyrmions in a Multiferroic\nMaterial,\" Science 336, 198 (2012).\n27M. Mochizuki, \\Spin-Wave Modes and Their Intense Excitation E\u000bects in Skyrmion Crystals,\"\nPhys. Rev. Lett. 108, 017601 (2012).\n28Y. Okamura, F. Kagawa, M. Mochizuki, M. Kubota, S. Seki, S. Ishiwata, M. Kawasaki,\nY. Onose, and Y. Tokura, \\Microwave magnetoelectric e\u000bect via skyrmion resonance modes\nin a helimagnetic multiferroic,\" Nat. Commun. 4, 2391 (2013).\n29T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, A. Rosch, C. P\rei-\nderer, and D. Grundler, \\Universal helimagnon and skyrmion excitations in metallic, semi-\nconducting and insulating chiral magnets,\" Nature Mater. 14, 478 (2015).\n30I. K\u0013 ezsm\u0013 arki, S. Bord\u0013 acs, P. Milde, E. Neuber, L. M. Eng, J. S. White, H. M. R\u001cnnow, C. D.\nDewhurst, M. Mochizuki, K. Yanai, H. Nakamura, D. Ehlers, V. Tsurkan, and A. Loidl,\n\\N\u0013 eel-type Skyrmion Lattice with Con\fned Orientation in the Polar Magnetic Semiconductor\nGaV 4S8,\" arXiv:1502.08049 (2015).\n31P. Milde, D. K ohler, J. Seidel, L. M. Eng, A. Bauer, A. Chacon, J. Kindervater, S. M uhlbauer,\nC. P\reiderer, S. Buhrandt, C. Sch utte, and A. Rosch, \\Unwinding of a Skyrmion Lattice by\nMagnetic Monopoles,\" Science 340, 1076 (2013).\n32L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics (Pergamon Press, New York,\n1980).\n33I. E. Dzyaloshinsky, \\Thermodynamic theory of weak ferromagnetism in antiferromagnetic\nsubstances,\" Sov. Phys. JETP 5, 1259 (1957).\n34T. Moriya, \\Anisotropic Superexchange Interaction and Weak Ferromagnetism,\" Phys. Rev.\n120, 91 (1960).\n35I. E. Dzyaloshinsky, \\Theory of helicoidal structures in antiferromagnets,\" Sov. Phys. JETP\n2919, 960 (1964).\n36Y. Ishikawa, K. Tajima, D. Bloch, and M. Roth, \\Helical spin structure in manganese silicide\nMnSi,\" Solid State Commun. 19, 525 (1976).\n37K. Motoya, H. Yasuoka, Y. Nakamura, and J.H. Wernick, \\Helical spin structure in MnSi-NMR\nstudies,\" Solid State Commun. 19, 529 (1976).\n38G. Shirane, R. Cowley, C. Majkrzak, J. B. Sokolo\u000b, B. Pagonis, C. H. Perry, and Y. Ishikawa,\n\\Spiral magnetic correlation in cubic MnSi,\" Phys. Rev. B 28, 6251 (1983).\n39M. Ishida, Y. Endoh, S. Mitsuda, Y. Ishikawa, and M. Tanaka, \\Crystal Chirality and Helicity\nof the Helical Spin Density Wave in MnSi. II. Polarized Neutron Di\u000braction,\" J. Phys. Soc.\nJpn.54, 2975 (1985).\n40P. Bak and M. H. Jensen, \\Theory of helical magnetic structures and phase transitions in MnSi\nand FeGe,\" J. Phys. C: Solid State 13, L881 (1980).\n41Y. Ishikawa, Y. Noda, Y. J. Uemura, C. F. Majkrzak, and G. Shirane, \\Paramagnetic spin\n\ructuations in the weak itinerant-electron ferromagnet MnSi,\" Phys. Rev. B 31, 5884 (1985).\n42B. Lebech, Recent Advances in Magnetism of Transition Metal Compounds (World Scienti\fc,\nSingapore, 1993) p. 167.\n43D. Bloch, J. Voiron, V. Jaccarino, and J. H. Wernick, \\The high \feld-high pressure magnetic\nproperties of MnSi,\" Phys. Lett. A 51, 259 (1975).\n44E. Fawcett, J. P. Maita, and J. H. Wernick, \\Magnetoelastic and thermal properties of MnSi,\"\nInt. J. Magn. 1, 29 (1970).\n45S. Kusaka, K. Yamamoto, T. Komatsubara, and Y. Ishikawa, \\Ultrasonic study of magnetic\nphase diagram of MnSi,\" Solid State Commun. 20, 925 (1976).\n46T. Adams, S. M uhlbauer, C. P\reiderer, F. Jonietz, A. Bauer, A. Neubauer, R. Georgii, P. B oni,\nU. Keiderling, K. Everschor, M. Garst, and A. Rosch, \\Long-Range Crystalline Nature of the\nSkyrmion Lattice in MnSi,\" Phys. Rev. Lett. 107, 217206 (2011).\n47X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa, and\nY. Tokura, \\Real-space observation of a two-dimensional skyrmion crystal,\" Nature (London)\n465, 901 (2010).\n48C. P\reiderer, T. Adams, A. Bauer, W. Biberacher, B. Binz, F. Birkelbach, P. B oni, C. Franz,\nR. Georgii, M. Janoschek, F. Jonietz, T. Keller, R. Ritz, S. M uhlbauer, W. M unzer,\nA. Neubauer, B. Pedersen, and A. Rosch, \\Skyrmion lattices in metallic and semiconducting\n30B20 transition metal compounds,\" J. Phys.: Condens. Matter 22, 164207 (2010).\n49T. Adams, A. Chacon, M. Wagner, A. Bauer, G. Brandl, B. Pedersen, H. Berger, P. Lem-\nmens, and C. P\reiderer, \\Long-Wavelength Helimagnetic Order and Skyrmion Lattice Phase\nin Cu 2OSeO 3,\" Phys. Rev. Lett. 108, 237204 (2012).\n50E. Moskvin, S. Grigoriev, V. Dyadkin, H. Eckerlebe, M. Baenitz, M. Schmidt, and H. Wilhelm,\n\\Complex Chiral Modulations in FeGe Close to Magnetic Ordering,\" Phys. Rev. Lett. 110,\n077207 (2013).\n51X. Z. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W. Z. Zhang, S. Ishiwata, Y. Matsui, and\nY. Tokura, \\Near room-temperature formation of a skyrmion crystal in thin-\flms of the heli-\nmagnet FeGe,\" Nature Mater. 10, 106 (2011).\n52A. Tonomura, X. Yu, K. Yanagisawa, T. Matsuda, Y. Onose, N. Kanazawa, H. S. Park, and\nY. Tokura, \\Real-Space Observation of Skyrmion Lattice in Helimagnet MnSi Thin Samples,\"\nNano Lett. 12, 1673 (2012).\n53H. S. Park, X. Yu, S. Aizawa, T. Tanigaki, T. Akashi, Y. Takahashi, T. Matsuda, N. Kanazawa,\nY. Onose, D. Shindo, A. Tonomura, and Y. Tokura, \\Observation of the magnetic \rux and\nthree-dimensional structure of skyrmion lattices by electron holography,\" Nature Nano. 9, 337\n(2014).\n54M. Uchida, Y. Onose, Y. Matsui, and Y. Tokura, \\Real-Space Observation of Helical Spin\nOrder,\" Science 311, 359 (2006).\n55Y. Ishikawa and M. Arai, \\Magnetic Phase Diagram of MnSi near Critical Temperature Studied\nby Neutron Small Angle Scattering,\" J. Phys. Soc. Jpn. 53, 2726 (1984).\n56B. Lebech, P. Harris, J. S. Pedersen, K. Mortensen, C. I. Gregory, N. R. Bernhoeft, M. Jermy,\nand S. A. Brown, \\Magnetic phase diagram of MnSi,\" J. Magn. Magn. Mater. 140{144 , 119\n(1995).\n57S. V. Grigoriev, S. V. Maleyev, A. I. Okorokov, Yu. O. Chetverikov, and H. Eckerlebe, \\Field-\ninduced reorientation of the spin helix in MnSi near Tc,\" Phys. Rev. B 73, 224440 (2006).\n58S. X. Huang and C. L. Chien, \\Extended Skyrmion Phase in Epitaxial FeGe(111) Thin Films,\"\nPhys. Rev. Lett. 108, 267201 (2012).\n59Y. Li, N. Kanazawa, X. Z. Yu, A. Tsukazaki, M. Kawasaki, M. Ichikawa, X. F. Jin, F. Kagawa,\nand Y. Tokura, \\Robust Formation of Skyrmions and Topological Hall E\u000bect Anomaly in\nEpitaxial Thin Films of MnSi,\" Phys. Rev. Lett. 110, 117202 (2013).\n3160P. Sinha, N. A. Porter, and C. H. Marrows, \\Strain-induced e\u000bects on the magnetic and\nelectronic properties of epitaxial Fe 1\u0000xCoxSi thin \flms,\" Phys. Rev. B 89, 134426 (2014).\n61M. N. Wilson, A. B. Butenko, A. N. Bogdanov, and T. L. Monchesky, \\Chiral skyrmions in\ncubic helimagnet \flms: The role of uniaxial anisotropy,\" Phys. Rev. B 89, 094411 (2014).\n62S. A. Brazovskii, \\Phase transition of an isotropic system to a nonuniform state,\" Sov. Phys.\nJETP 41, 85 (1975).\n63M. Janoschek, M. Garst, A. Bauer, P. Krautscheid, R. Georgii, P. B oni, and C. P\reiderer,\n\\Fluctuation-induced \frst-order phase transition in Dzyaloshinskii-Moriya helimagnets,\" Phys.\nRev. B 87, 134407 (2013).\n64S. V. Grigoriev, S. V. Maleyev, E. V. Moskvin, V. A. Dyadkin, P. Fouquet, and H. Eckerlebe,\n\\Crossover behavior of critical helix \ructuations in MnSi,\" Phys. Rev. B 81, 144413 (2010).\n65S. V. Grigoriev, E. V. Moskvin, V. A. Dyadkin, D. Lamago, T. Wolf, H. Eckerlebe, and S. V.\nMaleyev, \\Chiral criticality in the doped helimagnets Mn 1\u0000yFeySi,\" Phys. Rev. B 83, 224411\n(2011).\n66I.\u0014Zivkovi\u0013 c, J. S. White, H. M. R\u001cnnow, K. Pr\u0014 sa, and H. Berger, \\Critical scaling in the cubic\nhelimagnet Cu 2OSeO 3,\" Phys. Rev. B 89, 060401 (2014).\n67S. Buhrandt and L. Fritz, \\Skyrmion lattice phase in three-dimensional chiral magnets from\nMonte Carlo simulations,\" Phys. Rev. B 88, 195137 (2013).\n68A. Bauer and C. P\reiderer, \\Magnetic phase diagram of MnSi inferred from magnetization\nand ac susceptibility,\" Phys. Rev. B 85, 214418 (2012).\n69S. Seki, S. Ishiwata, and Y. Tokura, \\Magnetoelectric nature of skyrmions in a chiral magnetic\ninsulator Cu 2OSeO 3,\" Phys. Rev. B 86, 060403 (2012).\n70U. K. R o\u0019ler, A. N. Bogdanov, and C. P\reiderer, \\Spontaneous skyrmion ground states in\nmagnetic metals,\" Nature (London) 442, 797 (2006).\n71A. B. Butenko, A. A. Leonov, U. K. R o\u0019ler, and A. N. Bogdanov, \\Stabilization of skyrmion\ntextures by uniaxial distortions in noncentrosymmetric cubic helimagnets,\" Phys. Rev. B 82,\n052403 (2010).\n72H. Wilhelm, M. Baenitz, M. Schmidt, U. K. R o\u0019ler, A. A. Leonov, and A. N. Bogdanov,\n\\Precursor Phenomena at the Magnetic Ordering of the Cubic Helimagnet FeGe,\" Phys. Rev.\nLett. 107, 127203 (2011).\n73H. Wilhelm, M. Baenitz, M. Schmidt, C. Naylor, R. Lortz, U. K. R o\u0019ler, A. A. Leonov, and\n32A. N. Bogdanov, \\Con\fnement of chiral magnetic modulations in the precursor region of FeGe,\"\nJ. Phys.: Condens. Matter 24, 294204 (2012).\n74L. Cevey, H. Wilhelm, M. Schmidt, and R. Lortz, \\Thermodynamic investigations in the\nprecursor region of FeGe,\" Phys. Status Solidi B 250, 650 (2013).\n75A. Bauer, A. Neubauer, C. Franz, W. M unzer, M. Garst, and C. P\reiderer, \\Quantum phase\ntransitions in single-crystal Mn 1\u0000xFexSi and Mn 1\u0000xCoxSi: Crystal growth, magnetization, ac\nsusceptibility, and speci\fc heat,\" Phys. Rev. B 82, 064404 (2010).\n76A. Bauer, M. Garst, and C. P\reiderer, \\Speci\fc Heat of the Skyrmion Lattice Phase and\nField-Induced Tricritical Point in MnSi,\" Phys. Rev. Lett. 110, 177207 (2013).\n77I. Levati\u0013 c, V. \u0014Surija, H. Berger, and I. \u0014Zivkovi\u0013 c, \\Dissipation processes in the insulating\nskyrmion compound Cu 2OSeO 3,\" Phys. Rev. B 90, 224412 (2014).\n78D. Vollhardt, \\Characteristic Crossing Points in Speci\fc Heat Curves of Correlated Systems,\"\nPhys. Rev. Lett. 78, 1307 (1997).\n79A. Aharoni, \\Demagnetizing factors for rectangular ferromagnetic prisms,\" J. Appl. Phys. 83,\n3432 (1998).\n80L. Ludgren, O. Beckman, V. Attia, S. P. Bhattacheriee, and M. Richardson, \\Helical Spin\nArrangement in Cubic FeGe,\" Phys. Scr. 1, 69 (1970).\n81B. Lebech, J. Bernhard, and T. Freltoft, \\Magnetic structures of cubic FeGe studied by\nsmall-angle neutron scattering,\" J. Phys.: Condens. Matter 1, 6105 (1989).\n82J. Beille, J. Voiron, and M. Roth, \\Long period helimagnetism in the cubic B20 Fe xCo1\u0000xSi\nand Co xMn1\u0000xSi alloys,\" Solid State Commun. 47, 399 (1983).\n83K. Ishimoto, Y. Yamaguchi, J. Suzuki, M. Arai, M. Furusaka, and Y. Endoh, \\Small-angle\nneutron di\u000braction from the helical magnet Fe 0:8Co0:2Si,\" Physica B 213{214 , 381 (1995).\n84M. A. Chernikov, L. Degiorgi, E. Felder, S. Paschen, A. D. Bianchi, H. R. Ott, J. L. Sarrao,\nZ. Fisk, and D. Mandrus, \\Low-temperature transport, optical, magnetic and thermodynamic\nproperties of Fe 1\u0000xCoxSi,\" Phys. Rev. B 56, 1366 (1997).\n85N. Manyala, Y. Sidis, J. F. DiTusa, G. Aeppli, D. P. Young, and Z. Fisk, \\Magnetoresistance\nfrom quantum interference e\u000bects in ferromagnets,\" Nature (London) 404, 581 (2000).\n86Y. Onose, N. Takeshita, C. Terakura, H. Takagi, and Y. Tokura, \\Doping dependence of\ntransport properties in Fe 1\u0000xCoxSi,\" Phys. Rev. B 72, 224431 (2005).\n87S. V. Grigoriev, V. A. Dyadkin, D. Menzel, J. Schoenes, Yu. O. Chetverikov, A. I. Okorokov,\n33H. Eckerlebe, and S. V. Maleyev, \\Magnetic structure of Fe 1\u0000xCoxSi in a magnetic \feld\nstudied via small-angle polarized neutron di\u000braction,\" Phys. Rev. B 76, 224424 (2007).\n88C. Franz, F. Freimuth, A. Bauer, R. Ritz, C. Schnarr, C. Duvinage, T. Adams, S. Bl ugel,\nA. Rosch, Y. Mokrousov, and C. P\reiderer, \\Real-Space and Reciprocal-Space Berry Phases\nin the Hall E\u000bect of Mn 1\u0000xFexSi,\" Phys. Rev. Lett. 112, 186601 (2014).\n89J. Teyssier, E. Giannini, V. Guritanu, R. Viennois, D. van der Marel, A. Amato, and S. N.\nGvasaliya, \\Spin-glass ground state in Mn 1\u0000xCoxSi,\" Phys. Rev. B 82, 064417 (2010).\n90E. W. Achu, H. J. Al-Kanani, J. G. Booth, M. M. R. Costa, and B. Lebech, \\Studies of the\nincommensurate structures of B20 alloys,\" J. Magn. Magn. Mater. 177{181 , 779 (1998).\n91M. Motokawa, S. Kawarazaki, H. Nojiri, and T. Inoue, \\Magnetization measurements of\nFe1\u0000xCoxSi,\" J. Magn. Magn. Mater. 70, 245 (1987).\n92V. Jaccarino, G. K. Wertheim, J. H. Wernick, L. R. Walker, and Sigurds Arajs, \\Paramagnetic\nExcited State of FeSi,\" Phys. Rev. 160, 476 (1967).\n93D. Shinoda and S. Asanabe, \\Magnetic Properties of Silicides of Iron Group Transition Ele-\nments,\" J. Phys. Soc. Jpn. 21, 555 (1966).\n94M. Arita, K. Shimada, Y. Takeda, M. Nakatake, H. Namatame, M. Taniguchi, H. Negishi,\nT. Oguchi, T. Saitoh, A. Fujimori, and T. Kanomata, \\Angle-resolved photoemission study\nof the strongly correlated semiconductor FeSi,\" Phys. Rev. B 77, 205117 (2008).\n95N. Manyala, Y. Sidis, J. F. DiTusa, G. Aeppli, D. P. Young, and Z. Fisk, \\Large anomalous\nHall e\u000bect in a silicon-based magnetic semiconductor,\" Nature Mater. 3, 255 (2004).\n96R. Ritz, M. Halder, C. Franz, A. Bauer, M. Wagner, R. Bamler, A. Rosch, and C. P\reiderer,\n\\Giant generic topological Hall resistivity of MnSi under pressure,\" Phys. Rev. B 87, 134424\n(2013).\n97T. Adams, S. M uhlbauer, A. Neubauer, W. M unzer, F. Jonietz, R. Georgii, B. Pedersen,\nP. B oni, A. Rosch, and C. P\reiderer, \\Skyrmion Lattice Domains in Fe 1\u0000xCoxSi,\" J. Phys.:\nConf. Ser. 200, 032001 (2010).\n98G. Meunier and M. Bertaud, \\Constantes cristallographiques de CuSe 2O5, CuSeO 3et\nCu2SeO 4,\" J. Appl. Cryst. 9, 364 (1976).\n99K. Kohn, \\A New Ferrimagnet Cu 2SeO 4,\" J. Phys. Soc. Jpn 42, 2065 (1977).\n100M. Belesi, I. Rousochatzakis, H. C. Wu, H. Berger, I. V. Shvets, F. Mila, and J. P Ansermet,\n\\Ferrimagnetism of the magnetoelectric compound Cu 2OSeO 3probed by77Se NMR,\" Phys.\n34Rev. B 82, 094422 (2010).\n101C. L. Huang, K. F. Tseng, C. C. Chou, S. Mukherjee, J. L. Her, Y. H. Matsuda, K. Kindo,\nH. Berger, and H. D. Yang, \\Observation of a second metastable spin-ordered state in ferri-\nmagnet Cu 2OSeO 3,\" Phys. Rev. B 83, 052402 (2011).\n102S. Seki, J.-H. Kim, D. S. Inosov, R. Georgii, B. Keimer, S. Ishiwata, and Y. Tokura, \\Formation\nand rotation of skyrmion crystal in the chiral-lattice insulator Cu 2OSeO 3,\" Phys. Rev. B 85,\n220406 (R) (2012).\n103M. C. Langner, S. Roy, S. K. Mishra, J. C. T. Lee, X. W. Shi, M. A. Hossain, Y.-D. Chuang,\nS. Seki, Y. Tokura, S. D. Kevan, and R. W. Schoenlein, \\Coupled Skyrmion Sublattices in\nCu2OSeO 3,\" Phys. Rev. Lett. 112, 167202 (2014).\n104C. Jia, S. Onoda, N. Nagaosa, and J. H. Han, \\Bond electronic polarization induced by spin,\"\nPhys. Rev. B 74, 224444 (2006).\n105J. S. White, I. Levati\u0013 c, A. A. Omrani, N. Egetenmeyer, K. Pr\u0014 sa, I. \u0014Zivkovi\u0013 c, J. L. Gavilano,\nJ. Kohlbrecher, M. Bartkowiak, H. Berger, and H. M. R\u001cnnow, \\Electric \feld control of the\nskyrmion lattice in Cu 2OSeO 3,\" J. Phys.: Condens. Matter 24, 432201 (2012).\n106M. Mochizuki and S. Seki, \\Magnetoelectric resonances and predicted microwave diode e\u000bect of\nthe skyrmion crystal in a multiferroic chiral-lattice magnet,\" Phys. Rev. B 87, 134403 (2013).\n107M. Mochizuki, X. Z. Yu, S. Seki, N. Kanazawa, W. Koshibae, J. Zang, M. Mostovoy, Y. Tokura,\nand N. Nagaosa, \\Thermally driven ratchet motion of a skyrmion microcrystal and topological\nmagnon Hall e\u000bect,\" Nature Mater. 13, 241 (2014).\n108Y. Okamura, F. Kagawa, S. Seki, M. Kubota, M. Kawasaki, and Y. Tokura, \\Microwave\nMagnetochiral Dichroism in the Chiral-Lattice Magnet Cu 2OSeO 3,\" Phys. Rev. Lett 114,\n197202 (2015).\n109A. Neubauer, C. P\reiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P. B oni, \\Topo-\nlogical Hall E\u000bect in the APhase of MnSi,\" Phys. Rev. Lett. 102, 186602 (2009).\n110C. P\reiderer, P. B oni, T. Keller, U. K. R o\u0019ler, and A. Rosch, \\Non-Fermi Liquid Metal\nWithout Quantum Criticality,\" Science 316, 1871 (2007).\n111T. Schulz, R. Ritz, A. Bauer, M. Halder, M. Wagner, C. Franz, C. P\reiderer, K. Everschor,\nM. Garst, and A. Rosch, \\Emergent electrodynamics of skyrmions in a chiral magnet,\" Nature\nPhys. 8, 301 (2012).\n112C. P\reiderer, G. J. McMullan, S. R. Julian, and G. G. Lonzarich, \\Magnetic quantum phase\n35transition in MnSi under hydrostatic pressure,\" Phys. Rev. B 55, 8330 (1997).\n113C. Thessieu, C. P\reiderer, A. N. Stepanov, and J. Flouquet, \\Field dependence of the magnetic\nquantum phase transition in MnSi,\" J. Phys.: Condens. Matter 9, 6677 (1997).\n114N. Doiron-Leyraud, I. R. Walker, L. Taillefer, M. J. Steiner, S. R. Julian, and G. G. Lonzarich,\n\\Fermi-liquid breakdown in the paramagnetic phase of a pure metal,\" Nature (London) 425,\n595 (2003).\n115Y. J. Uemura, T. Goko, I. M. Gat-Malureanu, J. P. Carlo, P. L. Russo, A. T. Savici, A. Aczel,\nG. J. MacDougall, J. A. Rodriguez, G. M. Luke, S. R. Dunsiger, A. McCollam, J. Arai,\nCh. P\reiderer, P. B oni, K. Yoshimura, E. Baggio-Saitovitch, M. B. Fontes, J. Larrea, Y. V.\nSushko, and J. Sereni, \\Phase separation and suppression of critical dynamics at quantum\nphase transitions of MnSi and (Sr 1\u0000xCax)RuO 3,\" Nature Phys. 3, 29 (2007).\n116N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, \\Anomalous Hall e\u000bect,\"\nRev. Mod. Phys. 82, 1539 (2010).\n117F. Freimuth, R. Bamler, Y. Mokrousov, and A. Rosch, \\Phase-space Berry phases in chiral\nmagnets: Dzyaloshinskii-Moriya interaction and the charge of skyrmions,\" Phys. Rev. B 88,\n214409 (2013).\n118X. Z. Yu, N. Kanazawa, W. Z. Zhang, T. Nagai, T. Hara, K. Kimoto, Y. Matsui, Y. Onose,\nand Y. Tokura, \\Skyrmion \row near room temperature in an ultralow current density,\" Nat.\nCommun. 3, 988 (2012).\n119J. Iwasaki, M. Mochizuki, and N. Nagaosa, \\Universal current-velocity relation of skyrmion\nmotion in chiral magnets,\" Nat. Commun. 4, 1463 (2013).\n120A. A. Thiele, \\Steady-State Motion of Magnetic Domains,\" Phys. Rev. Lett. 30, 230 (1973).\n121K. Everschor, M. Garst, R. A. Duine, and A. Rosch, \\Current-induced rotational torques in\nthe skyrmion lattice phase of chiral magnets,\" Phys. Rev. B 84, 064401 (2011).\n122J. Zang, M. Mostovoy, J. H. Han, and N. Nagaosa, \\Dynamics of Skyrmion Crystals in Metallic\nThin Films,\" Phys. Rev. Lett. 107, 136804 (2011).\n123Y. Tokunaga, X. Z. Yu, J. S. White, H. M. R\u001cnnow, D. Morikawa, Y. Taguchi, and Y. Tokura,\n\\A new class of chiral materials hosting magnetic skyrmions beyond room temperature,\"\narXiv:1503.05651 (2015).\n124E. Ru\u000b, S. Widmann, P. Lunkenheimer, V. Tsurkan, S. Bord\u0013 acs, I. K\u0013 ezsm\u0013 arki, and A. Loidl,\n\\Ferroelectric Skyrmions and a Zoo of Multiferroic Phases in GaV 4S8,\" arXiv:1504.00309\n36(2015).\n125N. Kanazawa, Y. Onose, T. Arima, D. Okuyama, K. Ohoyama, S. Wakimoto, K. Kakurai,\nS. Ishiwata, and Y. Tokura, \\Large Topological Hall E\u000bect in a Short-Period Helimagnet\nMnGe,\" Phys. Rev. Lett. 106, 156603 (2011).\n126N. Kanazawa, J.-H. Kim, D. S. Inosov, J. S. White, N. Egetenmeyer, J. L. Gavilano, S. Ishiwata,\nY. Onose, T. Arima, B. Keimer, and Y. Tokura, \\Possible skyrmion-lattice ground state in\ntheB20 chiral-lattice magnet MnGe as seen via small-angle neutron scattering,\" Phys. Rev. B\n86, 134425 (2012).\n127Y. Shiomi, N. Kanazawa, K. Shibata, Y. Onose, and Y. Tokura, \\Topological Nernst e\u000bect in\na three-dimensional skyrmion-lattice phase,\" Phys. Rev. B 88, 064409 (2013).\n128T. Tanigaki, K. Shibata, N. Kanazawa, X. Z. Yu, S. Aizawa, Y. Onose, H. S. Park, D. Shindo,\nand Y. Tokura, \\Real-space observation of short-period cubic lattice of skyrmions in MnGe,\"\narXiv:1503.03945 (2015).\n129M. Janoschek, F. Bernlochner, S. Dunsiger, C. P\reiderer, P. B oni, B. Roessli, P. Link, and\nA. Rosch, \\Helimagnon bands as universal excitations of chiral magnets,\" Phys. Rev. B 81,\n214436 (2010).\n130J. D. Koralek, D. Meier, J. P. Hinton, A. Bauer, S. A. Parameswaran, A. Vishwanath,\nR. Ramesh, R. W. Schoenlein, C. P\reiderer, and J. Orenstein, \\Observation of Coherent\nHelimagnons and Gilbert Damping in an Itinerant Magnet,\" Phys. Rev. Lett. 109, 247204\n(2012).\n131Y. Onose, Y. Okamura, S. Seki, S. Ishiwata, and Y. Tokura, \\Observation of Magnetic Ex-\ncitations of Skyrmion Crystal in a Helimagnetic Insulator Cu 2OSeO 3,\" Phys. Rev. Lett. 109,\n037603 (2012).\n132S. Heinze, K. v. Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer,\nand S. Bl ugel, \\Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions,\" Nature\nPhys. 7, 713 (2011).\n133N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. v. Bergmann, A. Kubetzka,\nand R. Wiesendanger, \\Writing and Deleting Single Magnetic Skyrmions,\" Science 341, 636\n(2013).\n134X. Yu, M. Mostovoy, Y. Tokunaga, W. Zhang, K. Kimoto, Y. Matsui, Y. Kaneko, N. Nagaosa,\nand Y. Tokura, \\Magnetic stripes and skyrmions with helicity reversals,\" P. Natl. Acad. Sci.\n37USA109, 8856 (2012).\n135M. Finazzi, M. Savoini, A. R. Khorsand, A. Tsukamoto, A. Itoh, L. Du\u0012 o, A. Kirilyuk, Th.\nRasing, and M. Ezawa, \\Laser-Induced Magnetic Nanostructures with Tunable Topological\nProperties,\" Phys. Rev. Lett. 110, 177205 (2013).\n136J. Sampaio, V. Cros, S. Rohart, A. Thiaville, and A. Fert, \\Nucleation, stability and current-\ninduced motion of isolated magnetic skyrmions in nanostructures,\" Nature Nano. 8, 839 (2013).\n137X. Yu, J. P. DeGrave, Y. Hara, T. Hara, S. Jin, and Y. Tokura, \\Observation of the Magnetic\nSkyrmion Lattice in a MnSi Nanowire by Lorentz TEM,\" Nano Lett. 13, 3755 (2013).\n138J. Iwasaki, M. Mochizuki, and N. Nagaosa, \\Current-induced skyrmion dynamics in constricted\ngeometries,\" Nature Nano. 8, 742 (2013).\n139S.-Z. Lin, C. Reichhardt, C. D. Batista, and A. Saxena, \\Driven Skyrmions and Dynamical\nTransitions in Chiral Magnets,\" Phys. Rev. Lett. 110, 207202 (2013).\n140J. Iwasaki, W. Koshibae, and N. Nagaosa, \\Colossal Spin Transfer Torque E\u000bect on Skyrmion\nalong the Edge,\" Nano Lett. 14, 4432 (2014).\n141S.-Z. Lin, C. D. Batista, C. Reichhardt, and A. Saxena, \\ac Current Generation in Chiral\nMagnetic Insulators and Skyrmion Motion induced by the Spin Seebeck E\u000bect,\" Phys. Rev.\nLett. 112, 187203 (2014).\n142J. M uller and A. Rosch, \\Capturing of a magnetic skyrmion with a hole,\" Phys. Rev. B 91,\n054410 (2015).\n143X. Zhang, G. P. Zhao, H. Fangohr, J. P. Liu, W. X. Xia, J. Xia, and F. J. Morvan, \\Skyrmion-\nskyrmion and skyrmion-edge repulsions in skyrmion-based racetrack memory,\" Sci. Rep. 5,\n7643 (2015).\n144N. Ogawa, S. Seki, and Y. Tokura, \\Ultrafast optical excitation of magnetic skyrmions,\" Sci.\nRep.5, 9552 (2015).\n145W. Xie, S. Thimmaiah, J. Lamsal, J. Liu, T. W. Heitmann, D. Quirinale, A. I. Goldman,\nV. Pecharsky, and G. J. Miller, \\ \f-Mn-Type Co 8+xZn12xas a Defect Cubic Laves Phase: Site\nPreferences, Magnetism, and Electronic Structure,\" Inorg. Chem. 52, 9399 (2013).\n146R. Pocha, D. Johrendt, and R. P ottgen, \\Electronic and Structural Instabilities in GaV 4S8\nand GaMo 4S8,\" Chem. Mater. 12, 2882 (2010).\n147C. S. Yadav, A. K. Nigam, and A. K. Rastogi, \\Thermodynamic properties of ferromagnetic\nMott-insulator GaV 4S8,\" Physica B 403, 1474 (2008).\n38"    },    {        "title": "1604.03488v1.Accumulative_magnetic_switching_of_ultra_high_density_recording_media_by_circularly_polarized_light.pdf",        "content": "1 \n Accumulative magnetic switching of ultra-high-density recording media by circularly \npolarized light  \n \n1Y.K. Takahashi *, 2R. M edapalli, 1S. Kasai, 1J. Wang, 1K. Ishioka,  3S.H. Wee, 3O. Hellwig,  1K. Hono \nand 2E.E. Fullerton  \n \n1 Magnetic Materials Unit, National Institute for Materials Science , 1-2-1 Sengen, Tsukuba 305 -0047, \nJapan  \n2 Center for  Memory and Recording Research, U niversity of California San Diego , 9500 Gilman \nDrive, La Jolla, C A 92093 -0401, USA  \n3 San Jose Research Center, H GST a Western Digital company, 3403 Yerba Buena Road, San Jose, \nCA 95135, USA  \n \nCorresponding author,  \nY.K. Takahashi  \nMagnetic Materials Unit, National Institute for Materials Science , 1-2-1 Sengen, Tsukuba 305-0047, \nJapan  \ne-mail: t akahashi.yukiko@nims.go.jp  \n  2 \n Manipulation of the m agnetization by external energ ies other than magnetic field, such as \nspin-polarized  current1-4, electric voltage5,6 and circularly polarized light7-11 gives a paradigm \nshift in magnetic nanodevices . Magnetization control  of ferromagnetic materials only by \ncircularly  polarized light  has received increasing  attention  both as a fundamental probe of the \ninteractions of light and magnetism but also for future  high -density magnetic recording \ntechnolog ies. Here we show  that for granular FePt films , designed for ultrahigh -density \nrecording, the optical magnetic switching by circularly polarized light is an accumulat ive effect \nfrom multiple optical pulses. We further show that deterministic  switching of high anisotrop y \nmaterials by the combination of circularly polarized light and modest  external magnetic  fields, \nthus revealing a pathway towards technological implementation.  \nDeterministic control of m agnetization by light , often referred to as all -optical switching \n(AOS), is an attractive recording method for magnetic nanotechnologies  because magnetization \ncontrol becomes possible without the need of an  external magnetic f ield7-11 and therefore \nincorporates the  potential for ultra-fast magnetization switching  up to  1000 times faster than that by \nmagnetic fields while using low er energies12. The first demonstration of the magnetization switching \nby light  was in ferrimangnetic GdFeCo film which is a magneto -optical material7 where the  Gd and \nFeCo  spin sub -lattices are antiferromagnetically exchange  coupled . While  several mechanisms  for \nthe ultrafast magnetization switching of GdFeCo have been explored14-16, the current understanding \nfor AOS in GdFeCo  is that the ultrafast laser excitation demagnetizes the two sublattices at different \ntime-scales12 resulting  in a transient ferromagnetic state whe re the Gd and FeCo sublattices are \nparallel. At later times as the Gd moment reemerges in the antiparallel o rientation due to the \nexchange interaction  the sublattice  moment s end up  in the opposite dir ection as compared to  the \ninitial state. The deterministic  helicity dependent switching observed in the experiments result s from \nhelicity dependent absorption  (dichroism)  which favor s one magnetic configuration over the other \nfor a narrow range of fluence17. 3 \n It was believed that AOS  occur s only in ferrimagnetic materials including synthetic \nstructure s7-10 since the mechanism determined for GdFeCo f ilms required antiparallel exchange of \ntwo sublattice systems. However , recently  Lambert et al . reported that the optical control of the \nmagnetization occurs in ferromagnet s including Co-based multilayer thin films  and FePtAg -C \ngranular thin film materials11. Therefore  the potential mechanisms for AOS in ferromagnetic \nmaterials must be reexamined. In addition the observation of AOS in granular FePt-based films being \ndeveloped for heat -assisted magnetic recording  (HAMR)18,19 directly impact s the magnetic recording \ncommunity , since it provides a  potential solution to the so-called “trilemma problem” in high -density \nhard disk drive s (HDD s) beyond 1 Tbit/in2, 20,21. Here, to probe both the mechanism s of optical \nreversal and its potential for novel technologies , we report the observation of accumulative magnetic \nswitching from multiple circularly  polarized light pulses o n FePt -C granular HAMR media.   \nFigure 1 (a) shows t he magnetic image of a demagnetized  FePt-C granular film after \nscanning it with both right circularly polarized (RCP ) or left circularly polarized  (LCP) light pulses . \nAs was reported in Ref. 11 t he optical pulses induce a net magnetization in the FePt granular media \nand the sign of the magnetization is determined by the  helicity of the light. To quantify the  \noptically -induced magnetization change s we patterned the granular magnetic film into a Hall cross  \n(see the m ethods section and Fig. S 2). The Hall resistance corresponds to the average out -of-plane \ncomponent in the magnetization of the FePt grains  within the Hall -cross area . Hall resistance \nchange s are normalized by the field dependent  hysteresis loop , which reveals  ~ 2.75  change in \nHall resistance  between negative and positive saturation  in Fig. 1( b). We first swe ep the laser over \nthe Hall cross in a similar way as shown in Fig. 1 (a) and measure a n induced magnetization of \nroughly 66% of the saturation magnetization as shown in Fig. 1 (b). We then fixed the laser over the \nHall cross region to measure the evolution of t he magnetization to a  series of ultrafast laser pulses . \nWe initially used 40 optical pulses for the first two exposure  steps,  and then,  increase d to 80 pulses \nfor the next six  exposure  steps  (see methods and Fig. S2) . The Hall resistance was measured after 4 \n each sequence. T he initial state is remanence after applying saturating magnetic field s of -7 T (Fig. \n1(c)) and 7 T (Fig. 1 (d)). Figure 1(c) shows  the normalized Hall resistance change after the exposure \nto RCP, linear ly polarized  and LCP . For RCP light , the normalized magnetization gradually decreases \nto zero, then reverses and saturate s at about -0.5. This indicates that ~3/4 of the FePt grains switch to \nthe opposite  direction. On the other hand, the exposure to  left circularly polarized (LCP) light \ndecreases the  magnetization to about half of the initial value , corresponding to the switching of ~1/4 \nthe FePt grains . For exposure  to linearly polarized light, the normalized Hall resistance gradually \napproaches  zero. In the case of the opposite initial state  (negative saturation)  shown  in Fig. 1(d) , RCP, \nLCP and linearly polarized light exposures  result in the same final normalized magnetization of -0.5, \n0.5 and zero, respectively . Thus, t he magnetization state after exposure  to polarized light only \ndepends on the helicity of the light  and i s independent on the initial magnetization state.  More \nimportantly, the results show that the final state is only achieved after ~500 pulses  are applied for this \nspecific laser power . The behavior shown in Fig. 1 (c) and (d)  is generally seen also for other  pulse \nsequences and laser powers ( Fig. S 3). Independent of laser conditions , the m aximum optical induced \nmagnetization switching  using a fix ed layer beam  is roughly half the saturation magnetization  and is \nan accumulative effect using multiple optical pulses .  \nTo probe  the microstructural  effect on the magnetization switching, we compare the Hall \nresistance change in the granular FePt-C film  to a continuous 10-nm-thick FePt films  (see methods \nand Fig. S1) . While the continuous film has strong perpendicular anisotropy  the perpendicular H c is \nonly 0.17 T  due to the small number of pinning site for magnetic domain wall motion  in the epitaxial \ncontinuous film . Fig ure 2 shows the normalized Hall resistance change as a function of the RCP \noptical pulses in the FePt -C granular and FePt continuous films. The normalized Hall resistance \ndecreases in both of the samples. However, in c ontrast to the granular  FePt film , the continuous film \nsimply  demagnetiz es with further increase of the RCP light  pulse power (and this result is \nindependent of laser helicity) , which is consistent with the thermal demagnetization and the 5 \n formation of domains as seen in thick Co/Pt multilayer films11 driven by strong dipolar energies . In \nthe granular film, the dipole energy is much smaller than that of the continuous film  and the \nmagnetization reversal cannot progress by domain wall motion because of the break in magnetic \nexchange between the magnetic grains. We have further shown a continuous transition al behavior  \nbetween these two extreme behaviors in  intermediate exchange  composite granular/c ontinuous films \nas shown in Fig. S4.  \nThe data shown in Fig. 1(c) and ( d) were fitted by  a simple  accumulative switching model  \nwhere we treat the  FePt grains as having  two magnetic states, spin -up and spin -down  state, because \nof its high magnetic anisotropy and small grain size. The total number of FePt grains N is expressed \nby the summation  of spin -up grains N  and spin -down grains N  and the normalized magnetization is \ngiven by ( N - N)/(N + N). We assum e that with each optical pulse there is a switching probability \nfrom the spin-up to spin -down state given by  P1 and from spin -down to spin -up by P2. The number of \nFePt grains with spin -up and spin -down state s after the n pulses  can be expressed by the following : \n  𝑁𝑛=𝑁𝑛−1(1−𝑃1)+𝑁𝑛−1𝑃2  and 𝑁𝑛=𝑁−𝑁𝑛     (1) \nThe fitted line s to Eq. (1) are shown in the Fig. 1(c) and (d)  using the same switching probabilities \nfor RCP, LCP and linearly polarized light exposure : (P1, P2) = (0.0048, 0.0 016), (0.0016, 0.0 048) and \n(0.003 2, 0.003 2), respectively.  The fits suggest that the switching probability by a single pulse is \nvery small , less than 1% . However,  accumulating the small switching  probabilit ies results  in a \ncontinuous change in the magnetization until the  final equilibrium state where NP1 = NP2 (a final \nstate normalized magnetization of (P 2-P1)/(P 2+P1) ) is reach ed. This final state is independent of the \ninitial state of the magnetization as seen experimentally.  \nWhat is the origin for different switching probability of P 1 and P 2 for circular ly polarized \nlight pulses? The fact that linear light leads to demagnetization of the sample suggest that h eating  of \nthe FePt grains by the femto -second laser exposure  is sufficient to cause thermal activat ed reversal. \nThe circularly polarized light then breaks the symmetry of the system favoring one magnetic state 6 \n over the other and leading to an imbalance in the P 1 and P 2. This symmetry breaking could result \nfrom a direct interaction between the light and the magnetic systems such as the inverse Faraday \nfield that prefer s one direction over the other22. The difference in P 1 and P 2 could also arise from \ndifferential absorption  for RCP and LCP (i.e.  magnetic circular dichroism ) that will result in  a slight \ndifferen ce in temperature for one set of grain s compared to the other .17 We have roughly estimated \nthe difference in temperature needed during the optical excitation to explain the difference in \nswitching probability  using a  simple Arrhenius -Néel model  for single domain particles  (see \nsupplementary section for details). A temperature difference of 1 -2 K would be sufficient to explain \nthe difference in P 1 and P 2 observed in Fig. 1 , which is consist ent with typical dichroism differences \nin magnetic metals.17 \nHowever, independent of the mechanism we find that magnetic switching for granular FePt \nfilms is statistical in nature in contrast to the reports on GdFeCo films. Because of this we don’t \nachieve  full deterministic switching , which would be needed for magnetic recording applications. To \nachieve full switching , we additionally applied a small external magnetic field, while applying 80 \noptical pulses at the laser power of 1 .00 mW for each sequence.  Figure 3(a) shows the normalized \nHall resistance change after exposure to the  linear polarized laser under an external magnetic field of \n0.051 T . Regardless of the polarity of the external magnetic field, the magnetization of the FePt -C \ngranular film remains close to the demagnetized  state. When the external magnetic field is increased \nto ~0.2 T  as shown in Fig. 3(b), the magnetization change s depending on the external magnetic field \npolarity , but only about half of the total magnetization can be switch ed by a 0.2-T field. However , by \nthe combination of the circularly polarized light and an external magnetic field of 0.2 T , a \nmagnetization reversal  >90 % of the saturation magnetization  can be achieved  as shown in Fig. 3(c).  \nThe results described here show that the AOS observed in FePt granular media can be \ndescribed by a statistical model w ith a small probability of switching magnetic grains for each light \npulse and these probabilities depend on the helicity of the light. This is qualita tively different from 7 \n the original reports for GdFeCo , but closer to the behavior reported for Pt/Co/Pt structures23. We \nshow that nearly deterministic switching can be achieved by the combination of circularly  polarized \nlight and small external field s suggesting that the control  of the light helicity can aid the writing in a \nHAMR like recording process. This study s hows that the fully deterministic switching in using only \nAOS for high -anisotropy nanostructures will require more complex structures.   \n.   8 \n Methods  \nFilm and device fabrication:   \nThe FePt -30vol%C (hereafter, FePt -C) granular film was deposited by co -sputtering of FePt \nand C targets on a MgO(001) single crystal substrate by DC magnetron sputtering under 0.48 Pa Ar \npressure at 600 C. After the deposition of FePt -C, the sample was cooled down to RT and \n10-nm-thick C  was deposited as a capping layer . In this work, we used a compositionally graded \nsputtering method to obtain the columnar FePt grains24. In this process, the C composition gradually \nchanged during the deposition , which gives nice FePt grain isolation as shown in Fig. S1(a) . The \nFePt continuous  film was deposited by the sputtering from an FePt alloy target under 0.48 Pa Ar \npressure at 400C. A 10-nm-thick C capping was deposited on the FePt continuous  film at RT. The \ndetailed description of the film processing conditions and their magnetic characteristics were \nreported elsewhere25. Hall cross es were used for the measurement of the magnetization change by \nthe light exposure  and the applied magnetic fields . They were fabricated directly from the films by \nphoto -lithography using a lift -off process and a  subsequent  Ar ion -milling  step. The width of the Hall \ncross is about 15 m. \n \nOptical setup  and m icrostructural , magnetic measurements :  \nFigure S2 shows the optical setup for this experiment. A 590 nm wavelength LED was used \nfor the observation of the magnetic domain of the sample. To excite the magnetization state, we use \nfemtosecond laser exposures with cent er wavelength of 800 nm, the pulse duration of 150 fs and the \nrepetition rate of 1 kHz.  Femto -second laser  pulses was focused onto a spot on the sample  whose  \ndiameter is 20-50 m, which covers the whole region of the Hall cross. To estimate the \nmagnetization change by the  light illumination, Hall cross devices were set at the foc al point of the \nlight. After exposing the sample to several optical  pulses, the Hall voltage was measured. The \nnumber of pulses exposed on the sample was controlled by the shutter.  9 \n The sample microstruc ture and magnetic properties were measured by transmission electron \nmicroscopy (TEM ) and vibrating sample magnetometer ( VSM ), respectively . \n \nAcknowledgment  \nThis work was supported in part by Grand -in-Aid for Scientific Research (B) Grant Number \n26289232  and the work at UCSD was supported by the Office of Naval Research (ONR) MURI \nprogram . \n \nAuthor contributions  Y.K.T and E.E.F designed and coordinated the projects; J.W, S.H.W., O.H. \nand K.H. grew and characterized the thin film samples. Y .K.T, R.M., S.K. and K.I performed the \nlaser experiment. Y .K.T and E.E.F. coordinated  work on the paper with contributions  from  R.M., \nS.K., J.W., K.I., S.H.W, O.H. K.H. with regular  discussions with all authors.  \n \nCompeting financial interests   The authors declare no competing financial interests.  \n \n  10 \n References  \n[1] Slonczewski, J. C. Current -driven excitation of magnetic multilayer s. J. Magn.Magn. Mater .  159, \nL1–L7 (1996).  \n[2] Mangin,S., Ravelosona, D., Katine1,J. A., Carey, M. J., Terris, B. D., &  Fullerton, E.E.,  \nCurrent -induced magnetization reversal in nanopillars with perpendicular anisotropy . Nat.  \nMater . 5, 210 -215 (2006).  \n[3] Berger, L. Emission of spin waves by a magnetic multilayer traversed by a current. Phys. Rev. B  \n54, 9353 –9358 (1996).  \n[4] Myers, E. B., Ralph, D. C., Katine, J. A., Louie, R. N. & Buhrman, R. A. , Current induced \nswitching of domains in magnetic multil ayer devices. Science  285,867–870 (1999).  \n[5] Maruyama , T., Shiota , Y., Nozaki,  T., Ohta , K., Toda,  N., Mizuguchi,  M., Tulapurkar,  A.A.,  \nShinjo, T., Shiraishi, M., Mizukami,  S., Ando , Y ., & Suzuki , Y., Large voltage -induced magnetic \nanisotropy change in a few atomic layers of iron . Nature Nanotech  4, 158 -161 (2009)  \n[6]Wang , W-G.,, Li, M., , Hageman , S., & Chien , C.L., Electric -field-assisted switching in magnetic \ntunnel junctions . Nature Mat.  11, 64-68 (2012)  \n[7] Stanciu,  C.D.,  Hansteen, F., Kimel,  A.V., Kirilyuk, A., Tsukamoto, A., Itoh, A., & Rasing , Th.,  \nAll-Optical Magnetic Recording with Circularly Polarized Light . Phys. Rev. Lett.  99, 047601 , \n(2007 ). \n[8] Hassdenteufel , A., Hebler,  B., Schubert,  C., Liebig,  A., Teich,  M., Helm, M., Aeschlimann,  M., \nAlbrecht,  M., & Bratschitsch,  R., Thermally assisted all -optical helicity dependent magnetic \nswitching in amorphous Fe 100-xTbx alloy films. Adv. Mater .  25, 3122 –3128 (2013).  \n[9] Alebrand, S., Gottwald, M., Hehn, M., Steil, D., Cinchetti, M., Lacour,  S., Fullerton,  E.E., \nAeschlimann,  M., & Mangin , S.,, Light -induced magnetization reversal of high -anisotropy TbCo \nalloy  films. Appl. Phys. Lett.  101, 162408 (2012).  \n[10] Mangin,  S., Gottwald, M., Lambert,  C-H., Steil,  D., Uhlíř,  V., Pang,  L., Hehn,  M., Alebr and, 11 \n S., Cinchetti,  M., Malinowski,  G., Fainman,  Y., Aeschlimann , M., & Fullerton , E.E., Engineered \nmaterials for all -optical helicity -dependent magnetic switching . Nature Mat . 13, 287 -293 (2014 ). \n[11] Lambert , C-H., Mangin,  S., Varaprasad,  B.S.D.Ch.S.,  Takahashi,  Y.K., Hehn,  M., Cinchetti,  M., \nMalinowski,  G., Hono,  K., Fainman,  Y., Aeschlimann,  M., & Fullerton , E.E. , All-optical control of \nferromagnetic thin films and nanostructures . Science  345, 1337 -1340 (2014 ). \n[12] Radu,  I., Vahaplar,  K., Stamm,  C., Kachel,  T., Pontius, N., Dürr,  H.A.,  Ostler, T.A., Barker, J., \nEvans, R.F.L., Chantrell, R.W., Tsukamoto, A , Itoh, A., Kirilyuk, A., Rasing, T., & Kimel,  A.V.,  \nTransient ferromagnetic -like state mediating ultrafast reversal of antiferromagnetically  coupled spins. \nNature  472, 205 –208 (2011).  \n[13] Ziel, J.P., Pershan, P.S., & Malmstrom, L.D., Optically -induced magnetization resulting from \ninverse Faraday effect. Phys. Rev. Lett.  15, 190 –193 (1965).  \n[14] Kirilyuk, A., Kimel,  A.V., & Rasing, T., Ultraf ast optical manipulation of magnetic order. Rev. \nMod. Phys.  82, 2731 –2784 (2010).  \n[15] Zhang  G.P., & Hubner, W., Laser -Induced ultrafast demagnetization in ferromagnetic metals . \nPhys. Rev. Lett.  85, 3025 -3028  (2000) . \n[16] Graves,  C. E. , Reid, A.H., Wang,  T., Wu, B., Jong,  S., Vahaplar, K., Radu, I., Bernstein,  D.P.,  \nMesserschmidt, M., Müller, L., Coffee, R., Bionta,  M., Epp, S.W., Hartmann, R., Kimmel,  N., \nHauser, G., Hartmann, A., Holl,  P., Gorke, H., Mentink,  J.H., Tsukamoto, A., Fognini, A., Turner, J.J.,  \nSchlotter,  W.F., Rolles, D., Soltau, H., Strüder, L., Acremann,  Y., Kimel,  A.V.,  Kirilyuk, A., Rasing,  \nT., Stöhr,  J., Scherz, A.O., & Dürr, H.A., Nanoscale spin reversal by non -local angular momentum \ntransfer following ultrafast laser excitation in ferrimagnetic GdFeCo. Nat. Mater .  12, 293 –298 \n(2013).  \n[17] Khorsand, A.R., Savoini, M., Kirilyuk, A., Kimel, A.V., Tsukamoto, A., Itoh, A.,. & Rasing, T h., \nRole of magnetic circular dichroism in all -optical magnetic recording. Phys. Rev. Lett.  108, 127205 \n(2012).  12 \n [18] Kryder, M.H., Gage, E.C., McDaniel, T.W., Challener,  W.A.,  Rottmayer,  R.E.,  Ju, G.P .,  Hsia, \nY.T., & Erden, M.F., Heat assisted magnetic recording. Proc. IEEE  96, 1810 –1835 (2008).  \n[19] Stipe, B.C., Strand, T.C., Poon, C.C. Balamane, H., Boone, T.D., Katine, J.A., Li, J.-l., Rawat, \nV., Nemoto, H., Hirotsune, A., Hellwig, O., Ruiz, R., Dobisz,  E., Kercher, D.S., Rober tson, N., \nAlbrecht, T.R., & Terris, B.D., Magnetic recording at 1.5 Pb m –2 using an integrated plasmonic \nantenna. Nat. Photonics  4, 484 –488 (2010).  \n[20] Suess, D., Schrefl, T., Faehler, S., Kirschner, M., Hrkac, G., Dorfbauer, F., Fidler, J., Exchange \nspring media for perpendicular recording. Appl. Phys. Lett. 87, 012504 (2005).  \n[21] Victora, R.H., Shen, X., Composite media for perpendicular magnetic recording. IEEE Trans. \nMagn .41, 537 -542 (2005).  \n[22] Nieves, P ., Chubykalo -Fesenko, O ., Modeling of ultrahast heat - and field -assisted magnetization \ndynamics in FePt, Phys. Rev. Appl . 5, 014006 (2016).  \n[23] Two types of all -optical magnetization switching mechanisms using femtosecond laser pulses . \nEl Hadri,  M.S. , Pirro, P. , Lambert, C. -H., Petit-Watelot,  S., Quessab,  Y., Hehn,  M., Montaigne,  F., \nMalinowski, G. , and S. Mangin, arXiv:1602.08525 . \n[24] Varaprasad , B.S.D.Ch.S., Wang , J., Shiroyama. T., Takahashi. Y.K., Hono. & K, Columnar \nstructure in FePt -C granular media for heat -assisted magnetic recording.  IEEE Trans. Magn  51, \n3200904, (2015 ).  \n[25] Wang, J., Sepehri -Amin, H., Takahashi, Y.K., Okamoto, S., Kasai, S., Kim, J.Y.,, Schrefl, T., \nHono, K., Acta Materialia, (2016) in press.  \n \n \n  13 \n Fig. 1 Magnetization change  observed from a FePt -C granular film  by exposure to  circular  \npolarized light.  (a) Magnetic image after exposure to  right and left circular  polarized light  at the \nlaser power of 0.70 mW. The initial state was demagnetized. We show  a subtracted  image obtained \nfrom  before and after applying the laser exposure . (b) Anomalous Hall Effect curve for the FePt-C \ngranular film.  The additional data points  at zero field correspond to the amount of magnetization \nswitch ed by exposure to right and left circular  polarized light  in the Hall cross  as indicated . (c) \nNormalized  Hall resistance after applying  circular  and linear  polarized light as a function of the \nintegrated  number of pulse s. Red, blue and black dots correspond to the normalized Hall resistance \nafter applying  the RCP, LCP and linear  polarized light. The initial state is the spin -up state in all FePt \ngrains.  The dotted lines show the fitting results using the accumulative magnetic switching  model  \ndescribed in the main text . The laser power was 1.28 mW.  (d) Normalized Hall resistance a fter \nillumination with RCP, LCP and linear  polarized light. The initial  state is the spin -down state in all \nFePt grains.  14 \n  \n  \n15 \n Fig. 2 Normalized Hall resistance  for FePt continuous (red) and FePt -C granular (blue) films  \nversus light  power. The initial state was spin -up in FePt grains. The number of pulse s was 80 for \nboth samples.  RCP light was used.  \n \n  \n16 \n Fig. 3 Deterministic switching by combination of circularly  polarized light  illumination  with \napplying  small magnetic field.  Normalized Hall resistances after the exposure to  linear  polarized  \nlight with (a) 0.051 T  and (b) 0.2 T. The pulse number is 80 and the light  power  is 1.35 mW. (c) \nNormalized Hall resistance after the illumination with  left and right  circular  polarized lig ht and \nmagnetic field of 0.2 T. \n \n \n1 \n Supplementary information  \n \nAccumulative magnetic switching of ultra-high-density recording media  \nby circularly polarized light  \n \nY .K. Takahashi, R. M edapalli, S. Kasai, J. Wang, K. Ishioka,  \nS.H. Wee, O. Hellwig, K. Hono and E.E. Fullerton  \n  2 \n Microstructure  and magnetic properties of FePt -C and FePt films  \nFigure S1(a) shows the transmission electron microscopy ( TEM ) bright field image  of the \nFePt-C films along with the  corresponding nanobeam  diffraction ( ND) pattern and histogram of the \ngrain size s. The dark  contrast areas are the  FePt grains  and the bright contrast area is the carbon \nsegregant . The average grain size is ~11.9 nm and these grains  are distributed within an  amorphous C \nmatrix. The ND pattern indicates  that all of the FePt grains have strong (001) texture because of the \nepitaxial growth on the MgO(001) single -crystal substrate. Figure S1(b) shows a cross sectional \nTEM image of the FePt -C granular film. The aspect ratio of the FePt grains is roughly  1. Figure \nS1(c) shows the magnetization curves of FePt -C granular film. Red and blue symbols  correspond to \nthe magnetization with the applied  magnetic field  perpendicular and parallel to  the film  surface , \nrespectively. The film shows strong perpendicular magnetic anisotropy with a saturation field of 7 T \nand high coercivity  field (0Hc) of 4 T due to the strong (001) texture  and highly L1 0 ordered FePt \ngrains . Figure S1(d) shows the corresponding TEM image and ND pattern of the FePt continuous  \nfilm. The film shows a continuous  microstructure and epitaxial  growth on the MgO(001) substrate. \nIn contrast to  the magnetic properties of the granular film shown in Fig. S1( c), the 0Hc of the FePt \ncontinuous  film is only 0.17 T due to the small number of pinning site s for the domain wall motion. \nAlthough the 0Hc is small, the anisotropy  field is about 4 T. The small er anisotropy field in FePt \ncontinuous  films is due to the low degree of order (S=0.51) originated from lower deposition \ntemperature of 400 C. \n \n Magnetization change as a function of laser  power and number of pulses  \nFigure S3 shows the change of the normalized Hall resistance of FePt -C film measured with \nincreasing  pulse number for various  laser power s. The initial state s is spin-up for all FePt grains  and \nthe sample was exposed to RCP light . At the lower power  of 1.00 mW show n in Fig ure S3(a) , \nexposing the sample to a series of 20 optical pulses does not significantly perturb the system . By 3 \n increasing the number of pulses  between measurements of the Hall voltage , the magnetization \ndecreases. However, we do not observe a net switching into the opposite  direction. This indicates that \nthe small light power  does not provide  enough instantaneous heat for a significant  magnetization \nswitching  to occur,  but that only  accumulated heat from many optical pulses at1 kHz rep rate can \nslowly thermally demagnetize the sample . At higher power  of 1.35 mW shown in Fig. S3(b) , the Hall \nresistance decreases much faster after the first laser exposure . In sets of 20 and 40 pulses, the Hall \nresistance decreases  significantly by illumination of  RCP light,  however, the overall magnetization \ndirection  of the film still remains positive, just  as for the initial state. When using sets of  60 and 80 \npulses, the normalized Hall resistance also changes sign to -0.5. However, for sets of  160 pulses  at a \ntime, the normalized Hall resistance decreases  only to -0.4, which may  be due to excess  accumulated \nheat in the sample  from the longer sequence of pulses . Further increase of the pulse number such as \n1000 pulses results in  an irreversible changes to sample  and the  Hall cross  response . \n \nEstimation of the temperature during the laser exposure  \nThe difference in P 1 and P 2 discussed in the main text could result from d ifferential \nabsorption  resulting from the circular dichroism . This difference in absorption could lead to a slight \ndifferen ce in temperature for one set of grain s compared to the other . To roughly estimate the \ntemperature difference needed to explain the difference in switching probability, we use a simple \nArrheniu s-Néel model for single domain particles where the time -dependence of magnetization of an \nensemble of particles versus time (t) is given by:  \n𝑀(𝑡)=𝑀(𝑡=0)exp (−𝑡\n𝜏)        (2) \nwhere  is the characteristic time for thermal switching.  In zero external field ,  is given by:  \n 𝜏=𝜏0exp (𝐾𝑈𝑉\n𝑘𝐵𝑇)               (3) \nwhere K uV is the magnetic energy of the particle that is the product of the magnetic anisotropy K u \nand the particle volume V and 0 is the attempt time for thermal activation (typically 0.1 ns for 4 \n high-anisotropy magnetic systems). Assuming that M(t)/M(t=0) equals 1 -P1 for RCP light and 1 -P2 \nfor LCP , then one can estimate LCP/RCP assuming the time  t is the same for RCP and LCP excitation \nby:  \n 𝜏𝐿𝐶𝑃\n𝜏𝑅𝐶𝑃=ln (1−𝑃1)\nln (1−𝑃2).        (4) \nCombing Eq. (2) and Eq. (3) , we can estimate the differen ce in K uV/k BT between RCP and LCP \nexcitation s, which  is given by  \n(𝐾𝑈𝑉\n𝑘𝐵𝑇)\n𝐿𝐶𝑃− (𝐾𝑈𝑉\n𝑘𝐵𝑇)\n𝑅𝐶𝑃=ln(𝜏𝐿𝐶𝑃\n𝜏𝑅𝐶𝑃)   .     (5) \nFor P 1= 0.0048 and P 2=0.0016 , then Eq. (4) gives LCP/RCP = 3.005 and the corresponding difference \nin K uV/k BT between LCP and RCP excitations from Eq. (5) is 1.1.   \nFrom the properties of FePt grains , we estimate the temperature difference to result in a \nchange in K uV/k BT of 1.1. For a magnetic grain with 12 nm diameter, 10 nm height, and a magnetic \nanisotropy of Ku=4.3x107 ergs/cm3, we can estimate room temperature K uV/k BT is ~ 1200.  Since \nKuV/k BT goes to zero at T C ~ 700 K , we can roughly estimate that K uV/k BT decreases on the order of \n3 per K temperature change  suggest ing a small difference in temperature of 0.3 K due to excitation \nof RCP and RCP is consistent with the observed P 1 and P 2 values.   However , these estimates ignore \nany interactions between particles, any distributions in particle size or the s pecific dependence of \ntemperature on time after excitation.  \nWe can further estimate how close to T C we would have to heat the sample to see the \nstatistical switching observed.  Using Eqs. (1) and (2) and assuming the sample is exposed  for 1 ns , \nKuV/k BT would need to be 7.6 to have a switching probably of P 1=0.0048 and 8.7 for the switching \nprobability of P 2=0.0016 , suggestin g we are heating close to T C. \n In the case of the FePt continuous  film, t he absorbed  heat from the  light can be dispersed \nquickly. T herefore, the film is not  irreversibly  damage even at 2 mW. However, for the granular film, \nFePt grains are heated more effectively by the  light exposure  because of the thermal isolation of \nadjacent grains by the amorphous C arbon segregant  whose thermal conductivity is more than ten 5 \n times lower than that of Fe Pt. For laser exposure  higher than 1.5 mW , it results in  irreversible  \ndamage  of the FePt -C granular film . \n \nAOS  in exchange -coupled composite (ECC) media  \nExchange -coupled composite ( ECC ) media was proposed in order to solve the so-called \n“trilemma  problem” 1,2. By putting the magnetically soft layer on top of the CoCrPt or FePt granular \nlayer , the switching field can be effectively  reduced while maintaining the energy barrier for the \nmagnetization rotation1-4. Wang et al. reported the significant reduction of switching field in FePt -C \ngranular media by adding  a continuous  FePt layer  to the high anisotropy granular layer5, which we \nuse for the AOS experiment here . Figure S4 shows the schematic view of the film stack , \nmagnetization curves and microstructure s of the ECC media with various FePt layer thickness es. The \nFePt layer was deposited at 400 C. Therefore, the degree of L10 order ing is lower than that of the \nFePt-C granu lar layer . The FePt -C granular layer  consist s of well-isolated FePt grains with uniform \nmicrostructure and average grain size of 10  nm. The morphology of the capping layer changed from \npartially granular to continuous  when increas ing the FePt cap layer  thickness. With increasing the \nthickness of the FePt layer from 0 to 15nm, the perpendicular H c reduces from 4.9 T  to 1.4 T . Figure \nS5 shows the change of the normalized Hall resistance  of the films  after exposure to  RCP light across \nthe Hall cross  with a  power of 0.48 mW . The initial magnetization state was demagnetized. The \nmagnetization switching ratio decreases with  increas ing thickness of the  FePt layer. The inset shows \nthe magnetization changes by circular  polarized light in FePt -C/FePt(15nm) ECC media. The \nmagnetization  switches depending on the helicity of the light and shows zero when linearly polarized \nlight was used. The resistance change by the light illumination  is reproducible. However, the \nmagnetiz ation switching ratio is very small , only 0.3 %.  These results also support  that the lack of \ntemperature and the large dipole energy only allow for a small magnetization switching in the \ncontinuous  film.  6 \n Fig. S1 Microstructure and magnetic properties of FePt -C and FePt films.  (a) plan-view TEM \nbright field image, corresponding nanobeam  diffraction pattern and histogram of FePt grain size, (b) \na cross sectional  TEM image and (c) magnetization curves of FePt -C granular film . (d), (e) and (f) is \nthe same data for the corresponding  FePt continuous film.  \n \n  \n7 \n Fig. S2 schematic view of the  optical setup.  In the experiments  for estimat ing the magnetization \nswitching ratio, several pulses are illuminated right after each other  on the Hall cross. The number of \nthe pulses w as controlled by the shutter. When we scan the laser on the sample, the sample was \nmanually moved.  \n \n  \n8 \n Fig. S3 Magnetization change for FePt -C film at  various condition s of right circular polarized \nlight. The number of optical pulses between Hall voltage measurements was varied from 20 to 160. \nThe power of  the light in (a) and (b) is 1.00 mW and 1.35 mW, respectively .  \n \n  \n9 \n Fig. S4 FePt -C ECC media.  Schematic view of the film stacks, magnetization curves and \nmicrostructures of FePt -C ECC media with various thickness es of the semi -hard FePt layer5. \n \n  \n10 \n Fig. S5 Magnetization switching in FePt -C ECC media.  The change of the magnetization \nswitching ratio  as a function of the film thickness of semi -hard FePt layer.  The inset shows the \nmagnetization change by the  light illumination  in FePt -C/FePt(15) ECC media.  \n \n  \n11 \n Reference  \n [1] Suess, D., Schrefl, T., Faehler, S., Kirschner, M., Hrkac, G., Dorfbauer, F., Fidler, J., Exchange \nspring media for perpendicular recording. Appl. Phys. Lett.87, 012504 (2005).  \n[2] Victora, R.H., Shen, X., Composite media for perpendicular magnetic recording. IEEE Trans. \nMagn.41, 537 -542 (2005).  \n[3] Sonobe, S., Tham, K.K., Umezawa, T., Takasu, T., Dumaya, J.A., Leo, P.Y., Effect of continuous \nlayer in CGC perpendicular recording media. J. Magn. Magn. Mater303, 292 -295 (2006).  \n[4] Suess, D., Schrefl, T., Dittrich, R., Kirschner, M., Dorfbauer, F., Hrkac, G., Fidler, J., Exchange \nsprin g recording media for areal densities up to 10 Tbit/in2. J. Magn. Magn. Mater290 -291, 551 -554 \n(2005)  \n[5] Wang, J., Sepehri -Amin, H., Takahashi, Y.K., Okamoto, S., Kasai, S., Kim, J.Y.,, Schrefl, T., \nHono, K., Acta Materialia ( Accepted ). "    },    {        "title": "1604.06546v1.Theoretical_methods_for_understanding_advanced_magnetic_materials__the_case_of_frustrated_thin_films.pdf",        "content": "arXiv:1604.06546v1  [cond-mat.stat-mech]  22 Apr 2016Theoretical methods for understanding advanced magnetic m aterials: the case of\nfrustrated thin films\nH. T. Diep∗\nLaboratoire de Physique Th´ eorique et Mod´ elisation,\nUniversit´ e de Cergy-Pontoise, CNRS, UMR 8089\n2, Avenue Adolphe Chauvin,\n95302 Cergy-Pontoise Cedex, France.\nMaterials science has been intensively developed during th e last 30 years. This is due, on the\none hand, to an increasing demand of new materials for new app lications and, on the other hand,\nto technological progress which allows for the synthesis of materials of desired characteristics and\nto investigate their properties with sophisticated experi mental apparatus. Among these advanced\nmaterials, magnetic materials at nanometric scale such as u ltra thin films or ultra fine aggregates\nare no doubt among the most important for electronic devices .\nIn this review, we show advanced theoretical methods and sol ved examples that help understand\nmicroscopic mechanisms leading to experimental observati ons in magnetic thin films. Attention is\npaid to the case of magnetically frustrated systems in which two or more magnetic interactions\nare present and competing. The interplay between spin frust ration and surface effects is the origin\nof spectacular phenomena which often occur at boundaries of phases with different symmetries:\nreentrance, disorder lines, coexistence of order and disor der at equilibrium. These phenomena are\nshownand explainedusingofsome exactmethods, theGreen’s function andMonte Carlo simulation.\nWe show in particular how to calculate surface spin-wave mod es, surface magnetization, surface\nreorientation transition and spin transport.\nPACS numbers: 05.10.-a , 05.50.+q , 64.60.Cn , 75.10.-b , 75. 10.Jm , 75.10.Hk , 75.70.-i\nI. INTRODUCTION\nMaterial science has made a rapid and spectacular progress during the last 30 years, thanks to the advance of ex-\nperimental investigation methods and a strong desire of scientific c ommunity to search for new and high-performance\nmaterials for new applications. In parallel to this intensive developme nt, many efforts have been devoted to under-\nstanding theoretically microscopic mechanisms at the origin of the pr operties of new materials. Each kind of material\nneeds specific theoretical methods in spite of the fact that there is a large number of common basic principles that\ngovern main properties of each material family.\nIn this paper, we confine our attention to the case of magnetic thin films. We would like to show basic physical\nprinciples that help us understand their general properties. The m ain purpose of the paper is not to present technical\ndetails of each of them, but rather to show what can be understoo d using each of them. For technical details of\na particular method, the reader is referred to numerous referen ces given in the paper. For demonstration purpose,\nwe shall use magnetically frustrated thin films throughout the pape r. These systems combine two difficult subjects:\nfrustrated spin systems and surface physics. Frustrated spin s ystems have been subject of intensive studies during\nthe last 30 years [1]. Thanks to these efforts many points have been well understood in spite of the fact that there\nremains a large number of issues which are in debate. As seen below, f rustrated spin systems contain many exotic\nproperties such as high ground-state degeneracy, new symmetr ies, successive phase transitions, reentrant phase and\ndisorder lines. Frustrated spin systems serve as ideal testing gro unds for theories and approximations. On the other\nhand, during the same period surface physics has also been widely inv estigated both experimentally and theoretically.\nThanksto technologicalprogress,films and surfaceswith desired propertiescould be fabricated and characterizedwith\nprecision. As a consequence, one has seen over the years numero us technological applications of thin films, coupled\nthin films and super-lattices, in various domains such as magnetic sen sors, magnetic recording and data storage. One\nof the spectacular effects is the colossal magnetoresistance [2, 3] which yields very interesting transport properties.\nThe search for new effects with new mechanisms in other kinds of mat erials continues intensively nowadays as never\nbefore.\n∗diep@u-cergy.fr2\nSection II is devoted to the presentation of the main theoretical b ackground and concepts to understand frustrated\nspin systems and surface effects in magnetic materials. Needless to say, one cannot cover all recent developments\nin magnetic materials but an effort is made to outline the most importan t ones in our point of view. Section III\nis devoted to a few examples to illustrate striking effects due to the f rustration and to the presence of a surface.\nConcluding remarks are given in Section IV.\nII. BACKGROUND\nA. Theory of Phase Transition\nMany materials exhibit a phase transition. There are several kinds o f transition, each transition is driven by the\nchange of a physical parameter such as pressure, applied field, te mperature ( T), ... The most popular and most\nstudied transition is no doubt the one corresponding to the passag e from a disordered phase to an ordered phase at\nthe so-called magnetic ordering temperature or Curie temperatur eTc. The transition is accompanied by a symmetry\nbreaking. In general when the symmetry of one phase is a subgrou p of the other phase the transition is continuous,\nnamely the first derivatives of the free energy such as internal en ergy and magnetization are continuous functions of\nT. The second derivatives such as specific heat and susceptibility, on the other hand, diverge at Tc. The correlation\nlength is infinite at Tc. When the symmetry of one phase is not a symmetry subgroup of th e other, the transition is in\ngeneral of first order: the first derivatives of the free energy a re discontinuous at Tc. At the transition, the correlation\nlength is finite and often there is a coexistence of the two phases. F or continuous transitions, also called second-order\ntransition, the nature of the transition is characterized by a set o f critical exponents which defines its ”universality\nclass”. Transitions in different systems may belong to the same unive rsality class.\nWhy is the study of a phase transition interesting? As the theory sh ows it, the characteristics of a transition are\nintimately connected to microscopic interactions between particles in the system.\nThe theory of phase transitions and critical phenomena has been in tensively developed by Landau and co-workers\nsince the 50’s in the framework of the mean-field theory. Microscop ic concepts have been introduced only in the early\n70’s with the renormalization group [4–6]. We have since then a clear pic ture of the transition mechanism and a clear\nidentification of principal ingredients which determine the nature of the phase transition. In fact, there is a small\nnumber of them such as the space dimension, the nature of interac tion and the symmetry of the order parameter.\nB. Frustrated Spin Systems\nA spin is said ”frustrated” when it cannot fully satisfy all the interac tions with its neighbors. Let us take a triangle\nwith an antiferromagnetic interaction J(<0) between two sites: we see that we cannot arrange three Ising s pins\n(±1) to satisfy all three bonds. Among them, one spin satisfies one ne ighbor but not the other. It is frustrated.\nNote that any of the three spins can be in this situation. There are t hus three equivalent configurations and three\nreverse configurations, making 6 the number of ”degenerate sta tes”. If we put XY spins on such a triangle, the\nconfiguration with a minimum energy is the so-called ”120-degree str ucture” where the two neighboring spins make a\n1200angle. In this case, each interaction bond has an energy equal to |J|cos(2π/3) =−|J|/2, namely half of the full\ninteraction: the frustration is equally shared by three spins, unlike the Ising case. Note that if we go from one spin\nto the neighboring spin in the trigonometric sense we can choose cos (2π/3) or−cos(2π/3) for the turn angle: there\nis thus a two-fold degeneracy in the XY spin case. The left and right t urn angles are called left and right chiralities.\nIn an antiferromagnetic triangular lattice, one can construct the spin configuration from triangle to triangle. The\nfrustration in lattices with triangular plaquettes as unit such as in fa ce-centered cubic and hexagonal-close-packed\nlattices is called ”geometry frustration”. Another category of fr ustration is when there is a competition between\ndifferent kinds of incompatible interactions which results in a situation where no interaction is fully satisfied. We\ntake for example a square with three ferromagnetic bonds J(>0) and one antiferromagnetic bond - J, we see that we\ncannot ”fully” satisfy all bonds with Ising or XY spins put on the corn ers.\nFrustrated spin systems are therefore very unstable systems w ith often very high ground-state degeneracy. In\naddition, novel symmetries can be induced such as the two-fold chir ality seen above. Breaking this symmetry results\nin an Ising-like transition in a system of XY spins [7, 8]. As will be seen in so me examples below, the frustration\nis the origin of many spectacular effects such as non collinear ground -state configurations, coexistence of order and\ndisorder, reentrance, disorder lines, multiple phase transitions, e tc.3\nC. Surface Magnetism\nIn thin films the lateral sizes are supposed to be infinite while the thick ness is composed of a few dozens of atomic\nlayers. Spins at the two surfaces of a film lack a number of neighbors and as a consequence surfaces have physical\nproperties different from the bulk. Of course, the difference is mor e pronounced if, in addition to the lack of neighbors,\nthere are deviations of bulk parameters such as exchange interac tion, spin-orbit coupling and magnetic anisotropy,\nand the presence of surface defects and impurities. Such change s at the surface can lead to surface phase transition\nseparated from the bulk transition, and surface reconstruction , namely change in lattice structure, lattice constant\n[9], magnetic ordering, ... at the surface [10–12].\nThin films of different materials, different geometries, different lattic e structures, different thicknesses ... when\ncoupled give surprising results such as colossal magnetoresistanc e [2, 3]. Microscopic mechanisms leading to these\nstriking effects are multiple. Investigations on new artificial archite ctures for new applications are more and more\nintensive today. In the following section, we will give some basic micros copic mechanisms based on elementary\nexcitations due to the film surface which allows for understanding ma croscopic behaviors of physical quantities such\nas surface magnetization, surface phase transition and transitio n temperature.\nD. Methods\nTo study properties of materials one uses various theories in conde nsed matter physics constructed from quantum\nmechanicsandstatisticalphysics[13,14]. Dependingonthepurpos eoftheinvestigation,wecanchoosemanystandard\nmethods at hand (see details in Refs. [15, 16]):\n(i) For a quick obtention of a phase diagram in the space of physical p arameters such as temperature, interaction\nstrengths, ... one can use a mean-field theory if the system is simple w ith no frustration, no disorder, ... Results are\nreasonable in three dimensions, though critical properties cannot be correctly obtained\n(ii) For the nature of phase transitions and their criticality, the ren ormalization group [4–6] is no doubt the best\ntool. However for complicated systems such as frustrated syste ms, films and dots, this method is not easy to use\n(iii) For low-dimensional systems with discrete spin models, exact met hods can be used\n(iv) For elementary excitations such as spin waves, one can use the classical or quantum spin-wave theory to get\nthe spin-wave spectrum. The advantage of the spin-wave theory is that one can keep track of the microscopic effect\nof a given parameter on macroscopic properties of a magnetic syst em at low temperatures with a correct precision\n(v) For quantum magnetic systems, the Green’s function method a llows one to calculate at ease the spin-wave spec-\ntrum, quantum fluctuations and thermodynamic properties up to r ather high temperatures in magnetically ordered\nmaterials. This method can be used for collinear spin states and non c ollinear (or canted) spin configurations as seen\nbelow\n(vi) For all systems, in particularfor complicated systems where an alytical methods cannot be easily applied, Monte\nCarlo simulations can be used to calculate numerous physical proper ties, specially in the domain of phase transitions\nand critical phenomena as well as in the spin transport as seen below .\nIn the next section, we will show some of these methods and how the y are practically applied to study various\nproperties of thin films.\nIII. FRUSTRATED THIN FILMS\nA. Exactly Solved Two-dimensional Models\nWhy are exactly solved models interesting? There are several reas ons to study such models:\n•Many hidden properties of a model cannot be revealed without exac t mathematical demonstration\n•We do not know of any real material which corresponds to an exact ly solved model, but we know that real\nmaterials should bear physical features which are not far from pro perties described in some exactly solved\nmodels if similar interactions are thought to exist in these materials.\n•Macroscopic effects observed in experiments cannot always allow us to find their origins if we do not already\nhave some theoretical pictures provided by exact solutions in mind.\nTo date, only systems of discrete spins in one and two dimensions (2D ) with short-range interactions can be exactly\nsolved. Discrete spin models include Ising spin, q-state Potts models and some Potts clock-models. The reader is4\nreferred to the book by Baxter [17] for principal exactly solved m odels. In general, one-dimensional (1D) models with\nshort-range interaction do not have a phase transition at a finite t emperature. If infinite-range interactions are taken\ninto account, then they have, though not exactlysolved, a trans ition ofsecond or first orderdepending on the decaying\npower of the interaction [18–21]. In 2D, most systems of discrete s pins have a transition at a finite temperature. The\nmost famous model is the 2D Ising model with the Onsager’s solution [ 22].\nIn this paper, we arealsointerested in frustrated2Dsystems bec ausethin films in asense arequasitwo-dimensional.\nWe have exactly solved a number of frustrated Ising models such as the Kagom´ e lattice [23], the generalized Kagom´ e\nlattice [24], the generalized honeycomb lattice [25] and various dilute c entered square lattices [26–28].\nFor illustration, let us show the case of a Kagom´ e lattice with neares t-neighbor (NN) and next-nearest neighbor\n(NNN) interactions. As seen below this Kagom´ e model possesses a ll interesting properties of the other frustrated\nmodels mentioned above.\nIn general, 2D Ising models without crossing interactions can be map ped onto the 16-vertex model or the 32-vertex\nmodel which satisfy the free-fermioncondition automaticallyas sho wnbelow with an Isingmodel defined on a Kagom´ e\nlattice with interactions between NN and between NNN, J1andJ2, respectively, as shown in Fig. 1.\n14 3\n25J2J1\nFIG. 1: Kagom´ e lattice. Interactions between nearest neig hbors and between next-nearest neighbors, J1andJ2, are shown by\nsingle and double bonds, respectively. The lattice sites in a cell are numbered for decimation demonstration.\nWe consider the following Hamiltonian\nH=−J1/summationdisplay\n(ij)σiσj−J2/summationdisplay\n(ij)σiσj (1)\nwhereσi=±1andthefirstandsecondsumsrunoverthespinpairsconnectedb ysingleanddoublebonds, respectively.\nNote that the Kagom´ e original model, with antiferromagnetic J1and without J2interaction, has been exactly solved\na long time ago showing no phase transition at finite temperatures [29 ].\nThe ground state (GS) of this model can be easily determined by an e nergy minimization. It is shown in Fig. 2\nwhere one sees that only in zone I the GS is ferromagnetic. In other zones the central spin is undetermined because\nit has two up and two down neighbors, making its interaction energy z ero: it is therefore free to flip. The GS spin\nconfigurations in these zones are thus ”partially disordered”. Aro und the line J2/J1=−1 separating zone I and zone\nIV we will show below that many interesting effects occur when Tincreases from zero.\nThe partition function is written as\nZ=/summationdisplay\nσ/productdisplay\ncexp[K1(σ1σ5+σ2σ5+σ3σ5+σ4σ5+σ1σ2+σ3σ4)+K2(σ1σ4+σ3σ2)] (2)\nwhereK1,2=J1,2/kBTand where the sum is performed over all spin configurations and the product is taken over all\nelementary cells of the lattice. To solve this model, we first decimate t he central spin of each elementary cell of the\nlattice and obtain a checkerboard Ising model with multi-spin interac tions (see Fig. 3).\nThe Boltzmann weight of each shaded square is given by\nW(σ1,σ2,σ3,σ4) = 2cosh( K1(σ1+σ2+σ3+σ4))exp[K2(σ1σ4+σ2σ3)\n+K1(σ1σ2+σ3σ4)] (3)5\nFIG. 2: Ground state of the Kagom´ e lattice in the space ( J1,J2). The spin configuration is indicated in each of the four zone s\nI, II, III and IV: + for up spins, −for down spins, x for undetermined spins (free spins). The di agonal line separating zones I\nand IV is given by J2/J1=−1.\nσ1σ2σ3 σ4/0/0/0/0\n/1/1/1/1\n/0/0/0/0/0/0\n/1/1/1/1/1/1\n/0/0/0/0\n/1/1/1/1\n/0/0/0/0/0/0\n/1/1/1/1/1/1\n/0/0/0/0/0/0/0/0/0\n/1/1/1/1/1/1/1/1/1\nFIG. 3: Checkerboard lattice. Each shaded square is associa ted with the Boltzmann weight W(σ1,σ2,σ3,σ4), given in the text.\nThe partition function of this checkerboard Ising model is thus\nZ=/summationdisplay\nσ/productdisplay\nW(σ1,σ2,σ3,σ4) (4)\nwhere the sum is performed over all spin configurations and the pro duct is taken over all the shaded squares of the\nlattice.\nTo map this model onto the 16-vertex model, we need to introduce a nother square lattice where each site is placed\nat the center of each shaded square of the checkerboard lattice , as shown in Fig. 4. At each bond of this lattice we\nassociate an arrow pointing out of the site if the Ising spin that is tra versed by this bond is equal to +1, and pointing\ninto the site if the Ising spin is equal to -1, as it is shown in Fig. 5. In this way, we have a 16-vertex model on the\nassociated square lattice [17]. The Boltzmann weights of this vertex model are expressed in terms of the Boltzmann6\n/0/0/0/0\n/1/1/1/1\n/0/0/0/0\n/1/1/1/1\n/0/0/0/0/0/0/0/0/0\n/1/1/1/1/1/1/1/1/1\n/0/0/0/0/0/0\n/1/1/1/1/1/1\n/0/0/0/0/0/0\n/1/1/1/1/1/1\nFIG. 4: The checkerboard lattice and the associated square l attice with their bonds indicated by dashed lines.\nweights of the checkerboard Ising model, as follows\nω1=W(−,−,+,+) ω5=W(−,+,−,+)\nω2=W(+,+,−,−) ω6=W(+,−,+,−)\nω3=W(−,+,+,−) ω7=W(+,+,+,+)\nω4=W(+,−,−,+) ω8=W(−,−,−,−)\nω9=W(−,+,+,+) ω13=W(+,−,+,+)\nω10=W(+,−,−,−) ω14=W(−,+,−,−)\nω11=W(+,+,−,+) ω15=W(+,+,+,−)\nω12=W(−,−,+,−) ω16=W(−,−,−,+)\n(5)\nTaking Eq. (3) into account, we obtain\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− −−\nFIG. 5: The relation between spin configurations and arrow co nfigurations of the associated vertex model.\nω1=ω2= 2e−2K2+2K1\nω3=ω4= 2e2K2−2K1\nω5=ω6= 2e−2K2−2K1\nω7=ω8= 2e2K2+2K1cosh(4K1)\nω9=ω10=ω11=ω12=ω13=ω14=ω15=ω16= 2cosh(2 K1) (6)\nGenerally, a vertex model is soluble if the vertex weights satisfy the free-fermion conditions so that the partition\nfunction is reducible tothe Smatrix ofa many-fermionsystem [30]. In the presentproblem the fr ee-fermionconditions7\nare the following\nω1=ω2, ω3=ω4\nω5=ω6, ω7=ω8\nω9=ω10=ω11=ω12\nω13=ω14=ω15=ω16\nω1ω3+ω5ω7−ω9ω11−ω13ω15= 0 (7)\nAs can be easily verified, Eqs. (7) are identically satisfied by the Boltz mann weights Eqs. (6), for arbitrary values of\nK1andK2. Using Eqs. (6) for the 16-vertex model and calculating the free e nergy of the model [17, 23] we obtain\nthe critical condition for this system\n1\n2[exp(2K1+2K2)cosh(4K1)+exp(−2K1−2K2)] +\ncosh(2K1−2K2)+2cosh(2 K1) = 2max {1\n2[exp(2K1+ 2K2)cosh(4K1)+\nexp(−2K1−2K2)]; cosh(2 K2−2K1) ; cosh(2 K1)} (8)\nThis equation has up to four critical lines depending on the values of J1andJ2. For the whole phase diagram, the\nreader is referred to Ref. [23]. We show in Fig. 6 only the small region o fJ2/J1in the phase diagram which has two\nstriking phenomena: the reentrant paramagnetic phase and a diso rder line.\nThe reentrant phase is defined as a paramagnetic phase which is loca ted between two ordered phases on the\ntemperature axis as seen in the region −1< J2/J1<−0.91: if we take for instance J2/J1=−0.94 and we go up\non the temperature axis, we will pass through the ferromagnetic p hase F, enter the ”reentrant” paramagnetic phase,\ncross the disorder line, enter the partial disordered phase X wher e the central spins are free, and finally enter the\nparamagnetic phase P [23]. The reentrant paramagnetic phase tak es place thus between a low- Tferromagnetic phase\nand a partially disordered phase.\nFXPT\nT\n− 0.6 − 0.8 − 1.002\n1\nα0 − 11\n2\nα\nFIG. 6: Phase diagram of the Kagom´ e lattice with NNN interac tion in the region J1>0 of the space ( α=J2/J1,T).Tis\nmeasured in the unit of J1/kB. Solid lines are critical lines, dashed line is the disorder line. P, F and X stand for paramagnetic,\nferromagnetic and partially disordered phases, respectiv ely. The inset shows schematically enlarged region of the en dpoint.\nNote that in phase X, all central spins denoted by the number 5 in Fig . 1 are free to flip at all Twhile other\nspins are ordered up to the transition at Tc. This result shows an example where order and disorder coexists in a n\nequilibrium state.\nIt is important to note that though we get the exact solution for th e critical surface, namely the exact location of\nthe phase transition temperature in the space of parameters as s hown in Fig. 6, we do not have the exact expression\nof the magnetization as a function of temperature. To verify the c oexistence of order and disorder mentioned above\nwe have to recourse to Monte Carlo simulations. This is easily done and the results for the order parameters and\nthe susceptibility of one of them are shown in Fig. 7 for phases F and X atJ2/J1=−0.94. As seen, the F phase\ndisappears at T1≃0.47 and phase IV (defined in Fig. 2) sets in at T2≃0.50 and disappears for T >1.14.Tis\nmeasured in the unit of J1/kB. The paramagnetic region between T1andT2is the reentrant phase. Note that the\ndisorder line discussed below cannot be seen by Monte Carlo simulation s.8\nFIG. 7: Left: Magnetization of the sublattice 1 composed of c ornered spins of ferromagnetic phase I (blue void squares) a nd\nthe staggered magnetization defined for the phase IV of Fig. 2 (red filled squares) are shown in the reentrant region with\nα=J2/J1=−0.94. See text for comments. Right: Susceptibility of sublatt ice 1 versus T.\nLet us now give the equation of the disorder line shown in Fig. 6:\ne4K2=2(e4K1+1)\ne8K1+3(9)\nUsually, one defines each point on the disorder line as the temperatu re where there is an effective reduction of\ndimensionality in such a way that physical quantities become simplified s pectacularly. Along the disorder line, the\npartition function is zero-dimensional and the correlation function s behave as in one dimension (dimension reduction).\nThe disorder line is veryimportant in understanding the reentrance phenomenon. This type of line is necessaryfor the\nchange of ordering from the high- Tordered phase to the low- Tone. In the narrowreentrant paramagnetic region, pre-\norderingfluctuations with different symmetries exist near each crit ical line. Thereforethe correlationfunctions change\ntheir behavior when crossing the ”dividing line” as the temperature is varied in the reentrant paramagnetic region.\nOn this dividing line, or disorder line, the system ”forgets” one dimens ion in order to adjust itself to the symmetry\nof the other side. As a consequence of the change of symmetries t here exist spins for which the two-point correlation\nfunction (between NN spins) has different signs, near the two critic al lines , in the reentrant paramagnetic region.\nHence it is reasonable to expect that it has to vanish at a disorder te mperature TD. This point can be considered as\na non-critical transition point which separates two different param agnetic phases. The two-point correlation function\ndefined above may be thought of as a non-local ”disorder paramet er”. This particular point is just the one which has\nbeen called a disorder point by Stephenson [31] in analyzing the beha vior of correlation functions for systems with\ncompeting interactions. Other models we solved have several disor der lines with dimension reduction [25, 26] except\nthe case of the centered square lattice where there is a disorder lin e without dimension reduction [27].\nWe believe that results of the exactly solved model in 2D shown above should also exist in three dimensions (3D),\nthough we cannot exactly solve 3D models. To see this, we have stud ied a 3D version of the 2D Kagom´ e lattice\nwhich is a kind of body-centered lattice where the central spin in the lattice cell is free if the corner spins are in\nan antiferromagnetic order: the central spin has four up and fou r down neighbors making its energy zero as in the\nKagom´ e lattice. We have shown that the partial disorder exists [32 , 33] and the reentrant zone between phase F and\nphase X in Fig. 6 closes up giving rise to a line of first-order transition [3 4].\nTo close this paragraph, we note that for other exactly solved fru strated models, the reader is referred to the review\nby Diep and Giacomini [35].\nB. Elementary Excitations: Surface Magnons\nWe consider a thin film of NTlayers with the Heisenberg quantum spin model. The Hamiltonian is writt en as\nH=−2/summationdisplay\n<i,j>Jij/vectorSi·/vectorSj−2/summationdisplay\n<i,j>DijSz\niSz\nj\n=−2/summationdisplay\n/angbracketlefti,j/angbracketrightJij/parenleftbigg\nSz\niSz\nj+1\n2(S+\niS−\nj+S−\niS+\nj)/parenrightbigg\n−2/summationdisplay\n<i,j>DijSz\niSz\nj\n(10)9\nwhereJijis positive (ferromagnetic) and Dij>0 denotes an exchange anisotropy. When Dijis very large with\nrespect to Jij, the spins have an Ising-like behavior.\nFor simplicity, let us suppose for the moment that all surface param eters are the same as the bulk ones with no\ndefects and impurities. One of the microscopic mechanisms which gov ern thermodynamic properties of magnetic\nmaterials at low temperatures is the spin waves. The presence of a s urface often causes spin-wave modes localized\nat and near the surface. These modes cause in turn a diminution of t he surface magnetization and the magnetic\ntransition temperature. The methods to calculate the spin-wave s pectrum from simple to more complicated are (see\nexamples given in Ref. [15]):\n(i) the equation of motion written for spin operators S±\niof spinSioccupying the lattice site iof a given layer.\nThese operators are coupled to those of neighboring layers. Writin g an equation of motion for each layer, one obtains\na system of coupled equations. Performing the Fourier transform in thexyplane, one obtains the solution for the\nspin-wave spectrum.\n(ii) the spin-wave theory using for example the Holstein-Primakoff sp in operators for an expansion of the Hamilto-\nnian. This is the second-quantization method. The harmonic spin-wa ve spectrum and nonlinear corrections can be\nobtained by diagonalizing the matrix written for operators of all laye rs.\n(iii) the Green’s function method using a correlation function betwee n two spin operators. From this function one\ncan deduce various thermodynamic quantities such as layer magnet izations and susceptibilities. The advantage of\nthis method is one can calculate properties up to rather high temper atures. However, with increasing temperature\none looses the precision.\nWe summarize briefly here the principle of the Green’s function metho d for illustration (see details in Ref. [36, 37]).\nWe define one Green’s function for each layer, numbering the surfa ce as the first layer. We write next the equation of\nmotion for each of the Green’s functions. We obtain a system of cou pled equations. We linearize these equations to\nreduce higher-order Green’s functions by using the Tyablikov deco upling scheme [38]. We are then ready to make the\nFourier transforms for all Green’s functions in the xyplanes. We obtain a system of equations in the space ( /vectorkxy,ω)\nwhere/vectorkxyis the wave vector parallel to the xyplane and ωis the spin-wave frequency (pulsation). Solving this\nsystem we obtain the Green’s functions and ωas functions of /vectorkxy. Using the spectral theorem, we calculate the layer\nmagnetization. Concretely, we define the following Green’s function for two spins /vectorSiand/vectorSjas\nGi,j(t,t′) =/an}bracketle{t/an}bracketle{tS+\ni(t);S−\nj(t′)/an}bracketri}ht/an}bracketri}ht (11)\nThe equation of motion of Gi,j(t,t′) is written as\ni/planckover2pi1dGi,j(t,t′)\ndt= (2π)−1/an}bracketle{t[S+\ni(t),S−\nj(t′)]/an}bracketri}ht+/an}bracketle{t/an}bracketle{t[S+\ni;H](t);S−\nj(t′)/an}bracketri}ht/an}bracketri}ht (12)\nwhere [...] is the boson commutator and /an}bracketle{t.../an}bracketri}htthe thermal average in the canonical ensemble defined as\n/an}bracketle{tF/an}bracketri}ht= Tre−βHF/Tre−βH(13)\nwithβ= 1/kBT. The commutator of the right-hand side of Eq. (12) generates fu nctions of higher orders. In a first\napproximation, we can reduce these functions with the help of the T yablikov decoupling [38] as follows\n/an}bracketle{t/an}bracketle{tSz\nmS+\ni;S−\nj/an}bracketri}ht/an}bracketri}ht ≃ /an}bracketle{tSz\nm/an}bracketri}ht/an}bracketle{t/an}bracketle{tS+\ni;S−\nj/an}bracketri}ht/an}bracketri}ht, (14)\nWe obtain then the same kind of Green’s function defined in Eq. (11). As the system is translation invariant in the\nxyplane, we use the following Fourier transforms\nGi,j(t,t′) =1\n∆/integraldisplay /integraldisplay\nd/vectorkxy1\n2π/integraldisplay+∞\n−∞dωe−iω(t−t′)gn,n′(ω,/vectorkxy)ei/vectorkxy.(/vectorRi−/vectorRj)(15)\nwhereωis the magnon pulsation (frequency), /vectorkxythe wave vector parallel to the surface, /vectorRithe position of the spin\nat the site i,nandn′are respectively the indices of the planes to which iandjbelong (n= 1 is the index of the\nsurface). The integration on /vectorkxyis performed within the first Brillouin zone in the xyplane. Let ∆ be the surface of\nthat zone. Equation (12) becomes10\n(/planckover2pi1ω−An)gn,n′+Bn(1−δn,1)gn−1,n′+Cn(1−δn,NT)gn+1,n′= 2δn,n′< Sz\nn> (16)\nwhere the factors (1 −δn,1) and (1 −δn,NT) are added to ensure that there are no CnandBnterms for the first\nand the last layer. The coefficients An,BnandCndepend on the crystalline lattice of the film. We give here some\nexamples:\n•Film of simple cubic lattice\nAn=−2Jn< Sz\nn> Cγk+2C(Jn+Dn)< Sz\nn>\n+2(Jn,n+1+Dn,n+1)< Sz\nn+1>\n+2(Jn,n−1+Dn,n−1)< Sz\nn−1> (17)\nBn= 2Jn,n−1< Sz\nn> (18)\nCn= 2Jn,n+1< Sz\nn> (19)\nwhereC= 4 and γk=1\n2[cos(kxa)+cos(kya)].\n•Film of body-centered cubic lattice\nAn= 8(Jn,n+1+Dn,n+1)< Sz\nn+1>\n+8(Jn,n−1+Dn,n−1)< Sz\nn−1> (20)\nBn= 8Jn,n−1< Sz\nn> γk (21)\nCn= 8Jn,n+1< Sz\nn> γk (22)\nwhereγk= cos(kxa/2)cos(kya/2)\nWriting Eq. (16) for n= 1,2,...,NT, we obtain a system of NTequations which can be put in a matrix form\nM(ω)g=u (23)\nwhereuis a column matrix whose n-th element is 2 δn,n′< Sz\nn>.\nFor a given /vectorkxythe magnon dispersion relation /planckover2pi1ω(/vectorkxy) can be obtained by solving the secular equation det|M|= 0.\nThere are NTeigenvalues /planckover2pi1ωi(i= 1,...,NT) for each /vectorkxy. It is obvious that ωidepends on all /an}bracketle{tSz\nn/an}bracketri}htcontained in the\ncoefficients An,BnandCn.\nTo calculate the thermal average of the magnetization of the layer nin the case where S=1\n2, we use the following\nrelation (see chapter 6 of Ref. [15]):\n/an}bracketle{tSz\nn/an}bracketri}ht=1\n2−/an}bracketle{tS−\nnS+\nn/an}bracketri}ht (24)\nwhere/an}bracketle{tS−\nnS+\nn/an}bracketri}htis given by the following spectral theorem\n/an}bracketle{tS−\niS+\nj/an}bracketri}ht= lim\nǫ→01\n∆/integraldisplay /integraldisplay\nd/vectorkxy+∞/integraldisplay\n−∞i\n2π[gn,n′(ω+iǫ)−gn,n′(ω−iǫ)]\n×dω\neβω−1ei/vectorkxy.(/vectorRi−/vectorRj). (25)\nǫbeing an infinitesimal positive constant. Equation (24) becomes\n/an}bracketle{tSz\nn/an}bracketri}ht=1\n2−lim\nǫ→01\n∆/integraldisplay /integraldisplay\nd/vectorkxy+∞/integraldisplay\n−∞i\n2π[gn,n(ω+iǫ)−gn,n(ω−iǫ)]dω\neβ/planckover2pi1ω−1(26)\nwhere the Green’s function gn,nis obtained by the solution of Eq. (23)11\ngn,n=|M|n\n|M|(27)\n|M|nis the determinant obtained by replacing the n-th column of |M|byu.\nTo simplify the notations we put /planckover2pi1ωi=Eiand/planckover2pi1ω=Ein the following. By expressing\n|M|=/productdisplay\ni(E−Ei) (28)\nwe see that Ei(i= 1,...,NT) are the poles of the Green’s function. We can therefore rewrite gn,nas\ngn,n=/summationdisplay\nifn(Ei)\nE−Ei(29)\nwherefn(Ei) is given by\nfn(Ei) =|M|n(Ei)/producttext\nj/negationslash=i(Ei−Ej)(30)\nReplacing Eq. (29) in Eq. (26) and making use of the following identity\n1\nx−iη−1\nx+iη= 2πiδ(x) (31)\nwe obtain\n/an}bracketle{tSz\nn/an}bracketri}ht=1\n2−1\n∆/integraldisplay /integraldisplay\ndkxdkyNT/summationdisplay\ni=1fn(Ei)\neβEi−1(32)\nwheren= 1,...,NT.\nAs< Sz\nn>depends on the magnetizations of the neighboring layers via Ei(i= 1,...,NT), we should solve by\niteration the equations (32) written for all layers, namely for n= 1,...,NT, to obtain the layer magnetizations at a\ngiven temperature T.\nThe critical temperature Tccan be calculated in a self-consistent manner by iteration, letting all < Sz\nn>tend to\nzero.\nLet us show in Fig. 8 two examples of spin-wave spectrum, one withou t surface modes as in a simple cubic film\nand the other with surface localized modes as in body-centered cub ic ferromagnetic case.\nIt is very important to note that acoustic surface localized spin wav es lie below the bulk frequencies so that these\nlow-lying energies will give larger integrands to the integral on the rig ht-hand side of Eq. (32), making < Sz\nn>to be\nsmaller. The same effect explains the diminution of Tcin thin films whenever low-lying surface spin waves exist in\nthe spectrum.\nFigure 9 shows the results of the layer magnetizations for the first two layers in the films considered above with\nNT= 4.\nCalculations for antiferromagnetic thin films with collinear spin configu rations can be performed using Green’s\nfunctions [36]. The physics is similar with strong effects of localized sur face spin waves and a non-uniform spin\ncontractions near the surface at zero temperature due to quan tum fluctuations [37].\nC. Frustrated Films\nWe showed above for a pedagogical purpose a detailed technique fo r using the Green’s function method. In the case\nof frustrated thin films, the ground-state spin configurations ar e not only non collinear but also non uniform from the\nsurface to the interior layers. In a class of helimagnets, the angle b etween neighboring spins is due to the competition\nbetween the NN and the NNN interactions. Bulk spin configurations o f such helimagnets were discovered more than\n50 years ago by Yoshimori [39] and Villain [40]. Some works have been d one to investigate the low-temperature\nspin-wave behaviors [41–43] and the phase transition [44] in the bulk crystals.12\nπ\nak = k  x= ky12\nE\n6\n0E\nπ0y10\n5\nMS\n= kxk=ka\nFIG. 8: Left: Magnon spectrum E=/planckover2pi1ωof a ferromagnetic film with a simple cubic lattice versus k≡kx=kyforNT= 8\nandD/J= 0.01. No surface mode is observed for this case. Right: Magnon s pectrum E=/planckover2pi1ωof a ferromagnetic film with a\nbody-centered cubic lattice versus k≡kx=kyforNT= 8 and D/J= 0.01. The branches of surface modes are indicated by\nMS.\nTM\nTM\n0 0TcTc\nFIG. 9: Ferromagnetic films of simple cubic lattice (left) an d body-centered cubic lattice (right): magnetizations of t he surface\nlayer (lower curve) and the second layer (upper curve), with NT= 4,D= 0.01J,J= 1.\nFor surface effects in frustrated films, a number of our works hav e been recently done among which we can mention\nthe case of a frustrated surface on a ferromagnetic substrate film [45], the fully frustrated antiferromagnetic face-\ncentered cubic film [46], and very recently the helimagnetic thin films in z ero field [47, 48] and under an applied field\n[49].\nThe Green’s function method for non collinear magnets has been dev eloped for the bulk crystal [50]. We have\nextended this to the case of non collinear thin films in the works just m entioned. Since two spins SiandSjform an\nangle cos θijone can express the Hamiltonian in the local coordinates as follows [4 7]:\nH=−/summationdisplay\n<i,j>Ji,j/braceleftBigg\n1\n4(cosθij−1)/parenleftbig\nS+\niS+\nj+S−\niS−\nj/parenrightbig\n+1\n4(cosθij+1)/parenleftbig\nS+\niS−\nj+S−\niS+\nj/parenrightbig\n+1\n2sinθij/parenleftbig\nS+\ni+S−\ni/parenrightbig\nSz\nj−1\n2sinθijSz\ni/parenleftbig\nS+\nj+S−\nj/parenrightbig\n+ cosθijSz\niSz\nj/bracerightBigg\n−/summationdisplay\n<i,j>Ii,jSz\niSz\njcosθij (33)\nThe last term is an anisotropy added to facilitate a numerical conver gence for ultra thin films at long-wave lengths\nsince it is known that in 2D there is no ordering for isotropic Heisenber g spins at finite temperatures [51].\nThe determination of the angles in the ground state can be done eith er by minimizing the interaction energy with13\nJ2/J1cosθ1,2 cosθ2,3 cosθ3,4 cosθ4,5α(bulk)\n-1.20.985(9.79◦)0.908(24.73◦)0.855(31.15◦)0.843(32.54◦)33.56◦\n-1.40.955(17.07◦)0.767(39.92◦)0.716(44.28◦)0.714(44.41◦)44.42◦\n-1.60.924(22.52◦)0.633(50.73◦)0.624(51.38◦)0.625(51.30◦)51.32◦\n-1.80.894(26.66◦)0.514(59.04◦)0.564(55.66◦)0.552(56.48◦)56.25◦\n-2.00.867(29.84◦)0.411(65.76◦)0.525(58.31◦)0.487(60.85◦)60◦\nTABLE I: Values of cos θn,n+1=αnbetween two adjacent layers are shown for various values of J2/J1. Only angles of the\nfirst half of the 8-layer film are shown: other angles are, by sy mmetry, cos θ7,8=cosθ1,2, cosθ6,7=cosθ2,3, cosθ5,6=cosθ3,4. The\nvalues in parentheses are angles in degrees. The last column shows the value of the angle in the bulk case (infinite thickne ss).\nFor presentation, angles are shown with two digits.\nrespect to interaction parameters or by the so-called steepest d escent method which has been proved to be very\nefficient [45, 46]. Using their values, one can follow the different steps presented above for the collinear magnetic\nfilms, one then obtains a matrix which can be numerically diagonalized to get the spin-wave spectrum which is used\nin turn to calculate physical properties in the same manner as for th e collinear case presented above.\nLet us show the case of a helimagnetic film. In the bulk, the turn angle in one direction is determined by the ratio\nbetween the antiferromagnetic NNN interaction J2(<0) and the NN interaction J1. For the body-centered cubic\nlattice, one has cos θ=−J1/J2. The helimagnetic phase is stable for |J2|/J1>1. Consider a film with the caxis\nperpendicular to the film surface. For simplicity, one supposes the t urn angle along the caxis is due to J2. Because\nof the lack of neighbors, the spins on the surface and on the secon d layer have the turn angles strongly deviated from\nthe bulk value [47]. The results calculated for various J2/J1are shown in Fig. 10 (right) for a film of Nz= 8 layers.\nThe values obtained are shown in Table I where one sees that the ang les near the surface (2nd and 3rd columns) are\nvery different from that of the bulk (last column).\ncaxis\nFIG. 10: Left: Bulk helical structure along the c-axis, in the case α= 2π/3, namely J2/J1=−2. Right: (color online) Cosinus\nofα1=θ1−θ2, ...,α7=θ7−θ8across the film for J2/J1=−1.2,−1.4,−1.6,−1.8,−2 (from top) with Nz= 8:αistands for\nθi−θi+1andXindicates the film layer iwhere the angle αiwith the layer ( i+1) is shown. The values of the angles are given\nin Table 1: a strong rearrangement of spins near the surface i s observed.\nThe spectrum at two temperatures is shown in Fig. 11 where the sur face spin waves are indicated. The spin lengths\natT= 0 of the different layers are shown in Fig. 12 as functions of J2/J1. WhenJ2tends to -1, the spin configuration\nbecomes ferromagnetic, the spin has the full length 1/2.\nThe layer magnetizations are shown in Fig. 13 where one notices the c rossoversbetween them at low T. This is due\nto the competition between quantum fluctuations, which depends o n the strength of antiferromagnetic interaction,\nand the thermal fluctuations which depends on the local coordinat ions.14\nFIG. 11: Spectrum E=/planckover2pi1ωversusk≡kx=kyforJ2/J1=−1.4 atT= 0.1 (left) and T= 1.02 (right) for Nz= 8 and\nd=I/J1= 0.1. The surface branches are indicated by s.\nFIG. 12: (Color online) Spin lengths of the first four layers a tT= 0 for several values of p=J2/J1withd= 0.1,Nz= 8.\nBlack circles, void circles, black squares and void squares are for first, second, third and fourth layers, respectively . See text\nfor comments.\nD. Surface Disordering and Surface Criticality: Monte Carl o Simulations\nAs said earlier, Monte Carlo methods can be used in complicated syste ms where analytical methods cannot be\nefficiently used. Depending on the difficulty of the investigation, we sh ould choose a suitable Monte Carlo technique.\nFor a simple investigation to have a rough idea about physical proper ties of a given system, the standard Metropolis\nalgorithmis sufficient [52, 53]. It consists in calculatingthe energy E1ofa spin, then changingits state and calculating\nits new energy E2. IfE2< E1then the new state is accepted. If E2> E1the new state is accepted with a probability\nFIG. 13: (Color online) Layer magnetizations as functions o fTforJ2/J1=−1.4 withd= 0.1,Nz= 8 (left). Zoom of the\nregion at low Tto show crossover (right). Black circles, blue void squares , magenta squares and red void circles are for first,\nsecond, third and fourth layers, respectively. See text.15\nproportional to exp[ −(E2−E1)/(kBT)]. One has to consider all spins of the system, and repeat the ”upd ate” over\nand over again with a large number of times to get thermal equilibrium b efore calculating statistical thermal averages\nof physical quantities such as energy, specific heat, magnetizatio n, susceptibility, ...\nWe need however more sophisticated methods if we wish to calculate c ritical exponents or to detect a first-order\nphase transition. For calculation of critical exponents, histogram techniques [54, 55] are very precise: comparison\nwith exact results shows an agreement often up to 3rd or 4th digit. To detect very weak first-order transitions, the\nWang-Landau technique [56] combined with the finite-size scaling the ory [57] is very efficient. We have used this\ntechnique to put an end to a 20-year-old controversy on the natu re of the phase transition in Heisenberg and XY\nfrustrated stacked triangular antiferromagnets [58, 59].\nTo illustrate the efficiency of Monte Carlo simulations, let us show in Fig. 14 the layer magnetizations of the\nclassical counterpart of the body-centered cubic helimagnetic film shown in section IIIC (figure taken from Ref. [47]).\nThough the surface magnetization is smaller than the magnetization s of interior layers, there is only a single phase\ntransition.\n00.20.40.60.81\n0 0.4 0.8 1.2 1.6M\nT00.20.40.60.81\n0 0.4 0.8 1.2 1.6M\nT\nFIG. 14: (Color online) Monte Carlo results: Layer magnetiz ations as functions of Tfor the surface interaction Js\n1/J1= 1\n(left) and 0.3 (right) with J2/J1=−2 andNz= 16. Black circles, blue void squares, cyan squares and red v oid circles are for\nfirst, second, third and fourth layers, respectively.\nTo see a surface transition, let us take the case of a frustrated s urface of antiferromagnetic triangular lattice coated\non a ferromagnetic film of the same lattice structure [45]. The in-plan e surface interaction is Js<0 and interior\ninteraction is J >0. This film has been shown to have a surface spin reconstruction as displayed in Fig. 15.\nS\nS\nSS\nS12\n33\n12\n'\n'β\nS\n'1\n2\nFIG. 15: Non collinear surface spin configuration. Angles be tween spins on layer 1 are all equal (noted by α), while angles\nbetween vertical spins are β.\nWe show an example where Js=−0.5Jin Fig. 16. The left figure is from the Green’s function method. As\nseen, the surface-layer magnetization is much smaller than the sec ond-layer one. In addition there is a strong spin\ncontraction at T= 0 for the surface layer. This is due to quantum fluctuations of the in-plane antiferromagnetic\nsurface interaction Js. One sees that the surface becomes disordered at a temperatur eT1≃0.2557 while the second\nlayer remains ordered up to T2≃1.522. Therefore, the system is partially disordered for temperatu res between T1\nandT2. This result is very interesting because it confirms again the existen ce of the partial disorder in quantum spin\nsystems observed earlier in the bulk [32, 33]. Note that between T1andT2, the ordering of the second layer acts\nas an external field on the first layer, inducing therefore a small va lue of its magnetization. Results of Monte Carlo\nsimulations of the classical model are shown on the right of Fig. 16 wh ich have the same features as the quantum\ncase.16\nTM\n00.050.10.150.20.250.30.350.40.450.5\n0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 TM\n00.10.20.30.40.50.60.70.80.91\n0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2\nFIG. 16: Left: First twolayer-magnetizations obtained byt heGreen’s functiontechniquevs. TforJs=−0.5Jwithanisotropies\nI=−Is= 0.1J. The surface-layer magnetization (lower curve) is much sma ller than the second-layer one. Right: Magnetiza-\ntions of layer 1 (circles) and layer 2 (diamonds) versus temp eratureTin unit of J/kB. See text for comments.\nTo close this paragraph we mention that the question of surface cr iticality has been a long-standing debate. On\nthe one hand, pure theories would tell us that as long as the thickne ss is finite the correlation in this direction can be\nrenormalized so that the nature of a phase transition in a thin film sho uld be that of the corresponding 2D model.\nOn the other hand, experimental observations and numerical simu lations show deviations of critical exponents from\n2D universality classes. The reader is referred to Refs. [60, 61] f or discussions on this subject.\nE. Surface Reorientation\nIn this paragraph, we would like to show the case ofthin films where a t ransition from an in-plane spin configuration\nto a perpendicular spin configuration is possible at a finite temperatu re. Such a reorientation occurs when there is\na competition between a dipolar interaction which tends to align the sp ins in the film surface and a perpendicular\nanisotropy which is known to exist when the film thickness is very small [10, 11]. Experimentally, it has been observed\nin a thin Fe film deposited on a Cu(100) substrate that the perpendic ular spin configuration at low temperatures\nundergoes a transition to a planar spin configuration as the temper ature (T) is increased [62–65]. Theoretically, this\nproblem has been studied by many people [66–70]. Let us consider a 2D surface for simplicity. The case of a film\nwith a small thickness has very similar results [70]. The Hamiltonian includ es three parts: a 6-state Potts model Hp,\na dipolar interaction Hdand a perpendicular anisotropy Ha:\nHp=−/summationdisplay\n(i,j)Jijδ(σi,σj) (34)\nwhereσiis a variable associated to the lattice site i.σiis equal to 1, 2, 3, 4, 5 and 6 if the spin at that site lies along\nthe±x,±yand±zaxes, respectively. Jijis the exchange interaction between NN at iandj. We will assume that\n(i)Jij=Jsifiandjare on the same film surface (ii) Jij=Jotherwise. For the dipolar interaction, we write\nHd=D/summationdisplay\n(i,j){S(σi)·S(σj)\nr3\ni,j−3[S(σi)·ri,j][S(σj)·ri,j]\nr5\ni,j} (35)\nwhereri,jis the vector of modulus ri,jconnecting the site ito the site j. One has ri,j≡rj−ri.S(σi) is a vector of\nmodulus 1 pointing in the xdirection if σi= 1, in the −xdirection if σi= 2, etc.\nThe perpendicular anisotropy is\nHa=−A/summationdisplay\nisz(i)2(36)\nwhereAis a constant.\nUsing Monte Carlo simulations, we have established the phase diagram shown in Fig. 17 for two dipolar cutoff\ndistances. Several remarks are in order: (i) in a small region above D= 0.1 (left figure) there is a transition from the\nin-plane to the perpendicular configuration when Tincreases from 0, (ii) this reorientation is a very strong first-orde r\ntransition: the energy and magnetization are discontinuous (not s hown) at the transition. Comparing to the Kagom´ e\nIsing case shown in Fig. 6, we do not have a reentrant paramagnetic phase between phases I and II. Instead, we have17\n0.920.9611.041.081.121.16\n0.070.080.090.10.110.120.13(I) (II)Tc\nD(P)\n0.920.9611.041.081.121.161.2\n0.060.070.080.090.10.110.12Tc\nD(II) (I)\nFIG. 17: (Color online) Phase diagram in 2D. Transition temp eratureTCversusD, withA= 0.5,J= 1, cutoff distance\nrc=√\n6 (left) and rc= 4 (right). Phase (I) is the perpendicular spin configuratio n, phase (II) the in-plane spin configuration\nand phase (P) the paramagnetic phase. See text for comments.\na first-order transition as also observed near phase frontiers in o ther systems such as in a frustrated body-centered\ncubic lattice [34].\nTo conclude this subsection, we mention that competing interaction s determine frontiers between phases of different\nsymmetries. Near these frontiers, we have seen many interesting phenomena such as reentrance, disorder lines,\nreorientation transition, ... when the temperature increases.\nF. Spin Transport in Thin Films\nThe total resistivity stem from different kinds of diffusion processe s in a crystal. Each contribution has in general a\ndifferent temperature dependence. Let us summarize the most imp ortant contributions to the total resistivity ρt(T)\nat low temperatures in the following expression\nρt(T) =ρ0+A1T2+A2T5+A3lnµ\nT(37)\nwhereA1,A2andA3are constants. The first term is T-independent, the second term proportional to T2represents\nthe scattering of itinerant spins at low Tby lattice spin-waves. Note that the resistivity caused by a Fermi liq uid is\nalso proportional to T2. TheT5term corresponds to a low- Tresistivity in metals. This is due to the scattering of\nitinerant electrons by phonons. At high T, metals however show a linear- Tdependence. The logarithm term is the\nresistivity due to the quantum Kondo effect caused by a magnetic imp urity at very low T.\nWe are interested here in the spin resistivity ρof magnetic materials. We have developed an algorithm which allows\nus to calculate the spin resistivity in various magnetically ordered sys tems [71–76, 76, 77, 77], in particular in thin\nfilms. Unlike the charge conductivity, studies of spin transport hav e been regular but not intensive until recently.\nThe situation changes when the electron spin begins to play a centra l role in spin electronics, in particular with the\ndiscovery of the colossal magnetoresistance [2, 3].\nThe main mechanism which governs the spin transport is the interact ion between itinerant electron spins and\nlocalized spins of the lattice ions ( s−dmodel). The spin-spin correlation has been shown to be responsible f or the\nbehavior of the spin resistivity [80–82]. Calculations were mostly done by mean-field approximation (see references\nin [83]). Our works mentioned above were the first to use intensive Mo nte Carlo simulations for investigating the\nspin transport. We also used a combination of the Boltzmann equatio n [15, 84] and numerical data obtained by\nsimulations [73, 74]. The Hamiltonian includes three main terms: interac tion between lattice spins Hl, interaction\nbetween itinerant spins and lattice spins Hr, and interaction between itinerant spins Hm. We suppose\nHl=−/summationdisplay\n(i,j)Ji,jSi·Sj (38)\nwhereSiis the spin localized at lattice site iof Ising, XY or Heisenberg model, Ji,jthe exchange integral between\nthe spin pair SiandSjwhich is not limited to the interaction between nearest-neighbors (N N). ForHrwe write\nHr=−/summationdisplay\ni,jIi,jσi·Sj (39)18\nwhereσiis the spin of the i-th itinerant electron and Ii,jdenotes the interaction which depends on the distance\nbetween electron iand spin Sjat lattice site j. For simplicity, we suppose the following interaction expression\nIi,j=I0e−αrij(40)\nwhererij=|/vector ri−/vector rj|,I0andαare constants. We use a cut-off distance D1for the above interaction. Finally, for Hm,\nwe use\nHm=−/summationdisplay\ni,jKi,jσi·σj (41)\nwhereKi,j=K0e−βrij(42)\nwithKi,jbeing the interaction between electrons iandj. The system is under an electrical field /vector ǫwhich creates an\nelectron current in one direction. In addition we include also a chemica l potential which keeps electrons uniformly\ndistributed in the system. Simulations have been carried out with the above Hamiltonian. The reader is referred\nto the original papers mentioned above for technical details. As ex pected, the spin resistivity reflects the spin-spin\ncorrelationofthe system: ρhas the formof the magnetic susceptibility, namely it showsa peak at the phase transition.\nIt is noted however that unlike the susceptibility which diverges at th e transition, the spin resistivity is finite at Tc\ndue to the fact that only short-range correlations can affect the resistivity (see arguments given in [81]). Moreover, it\nis known that near the phase transition the system is in the critical-s lowing-down regime. Therefore, care should be\ntaken while simulating in the transition region. This point has been cons idered in our simulations by introducing the\nrelaxation time [78].\nTo illustrate the efficiency of Monte Carlo simulations, we show in Fig. 18 the excellent agreement of our simulation\n[79] and experiments performed on MnTe [85]. The interactions and t he crystalline parameters were taken from Ref.\n[86].\n4000.40.60.81.01.21.4\n100 200 3000ρ(Ω.cm)\nT\t(K)\nFIG. 18: Left: Structure of MnTe of NiAs type. Antiparallel s pins are shown by black and white circles. NN interaction\nis marked by J1, NNN interaction by J2, and third NN one by J3. Right: ρversusT. Black circles are from Monte Carlo\nsimulation, white circles are experimental data taken from He et al.[85]. The parameters used in the simulation are take n from\n[86]:J1 =−21.5K,J2= 2.55 K,J3=−9 K,Da= 0.12 K (anisotropy), D1=a= 4.148˚A, andI0= 2 K,ǫ= 2∗105V/m.\nWhen a film has a surface phase transition at a low temperature in add ition to the transition of the bulk at a higher\ntemperature, one observes two peaks in the spin resistivity as sho wn in Ref. [73].\nIV. CONCLUSION\nTo conclude this review let us discuss on the relation between theorie s and experiments, in particular on the\ndifficulties encountered when one is confronted, on the one hand, w ith simplified theoretical pictures and hypotheses\nand, on the other hand, with insufficient experimental knowledge of what is really inside the material. We would\nlike to emphasize on the importance of a sufficient theoretical backg round to understand experimental data measured\non systems which are more complicated, less perfect than models us ed to describe them. Real systems have always\nimpurities, defects, disorder, domains, ... However, as long as thes e imperfections are at extremely small amounts,\nthey will not affect observed macroscopic quantities: theory tells u s that each observable is a result from a statistical\naverage over all microscopic states and over the space occupied b y the material. Such an averaging will erase away\nrare events leaving only common characteristics of the system. Es sential aspects can be thus understood from simple\nmodels if one includes correct ingredients based on physical argume nts while constructing the model.\nOne ofthe strikingpoints shown aboveis the fact that without soph isticatedcalculations, we cannot discoverhidden\nsecrets of the nature such as the existence of disorder lines with a nd without dimension reduction, the extremely19\nnarrow reentrant region between two ordered phases, the coex istence of order and disorder of a system at equilibrium\netc. These effects are from the competition between various inter actions which are unavoidable in real materials.\nThese interactions determine the boundaries between various pha ses of different symmetries in the space of physical\nparameters. Crossing a boundary the system will change its symme try. Theory tells us that if the symmetry of\none phase is not a subgroup of the other then the transition should be of first order or the two phases should be\nseparated by a narrow reentrant phase. Without such a knowledg e, we may overlook such fine effects while examining\nexperimental data.\nWe have used frustrated thin films to illustrate various effects due t o a combination of frustration and surface\nmagnetism. We have seen that to understand when and why surfac e magnetization is small with respect to the bulk\none we have to go through a microscopic mechanism to recognize tha t low-lying localized surface spin-wave modes\nwhen integrated in the calculation of the magnetization will indeed mat hematically lower its value. Common effects\nobserved in thin films such as surface reconstruction and surface disordering can be theoretically explained.\nWe should emphasize on the importance of a combination of Monte Car lo simulation and theory. We have seen for\nexample that we can determine the exact transition temperature in the Kagom´ e model but the nature of the ordering\nis understood only with Monte Carlo simulation. This is not the only exam ple: as theorists we need also hints and\nchecks while constructing a theory, and as a simulator we need to un derstand what comes out from the computer\nsince we often loose the track between inputs and outputs in a simula tion. In this respect, a combination of numerical\nand theoretical methods is unavoidable.\nI am grateful to my numerous former and present doctorate stu dents with whom I shared uncountable wonderful\nmoments of scientific discussions and from whom I draw my source of energy and joy.\n[1] H. T. Diep (Ed.), Frustrated Spin Systems, second ed., Wo rld Scientific, Singapore, 2013.\n[2] M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Pe troff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas ,\nPhys. Rev. Lett. 61(1988)2472.\n[3] P. Grunberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. S owers, Phys. Rev. Lett. 57(1986)2442; G. Binasch, P.\nGrunberg, F. Saurenbach, and W. Zinn, Phys. Rev. B 39(1989)4 828.\n[4] K. G. Wilson, Renormalization Group and Critical Phenom ena. I. Renormalization Group and the Kadanoff Scaling\nPicture, Phys. Rev. B 4(1971)3174.\n[5] D. J. Amit, Field Theory, Renormalization Group and Crit ical Phenomena, World Scientific, Singapore, 1984.\n[6] J. Zinn-Justin, Quantum Field Theory and Critical Pheno mena, Oxford Unversity Press, London, 2002.\n[7] B. Berge, H. T. Diep, A. Ghazali, P. Lallemand, Phase tran sitions in two-dimensional uniformly frustrated XY spin\nsystems, Phys. Rev. B 34(1986)3177.\n[8] E. H. Boubcheur, H. T. Diep, Critical Behavior of the Two- dimensional Fully Frustrated XY Model Phys. Rev. B\n58(1998)5163.\n[9] Virgile Bocchetti and H. T. Diep, Monte Carlo Simulation of Melting and Lattice Relaxation of the (111) Surface of Sil ver,\nSurface Science 614(2013)46.\n[10] J.A.C. Bland and B. Heinrich (Eds.), Ultrathin Magneti c Structures, vol. I and II, Springer-Verlag, Berlin, 1994.\n[11] A. Zangwill, Physics at Surfaces, Cambridge Universit y Press, London, 1988.\n[12] K. Binder, Critical Hehaviour at Surfaces, in: C. Domb a nd J. L. Lebowitz (Eds.), Phase Transitions and Critical Phe -\nnomena, Vol. 8, Academic Press, London, 1983.\n[13] N. W. Ashcroft et N. D. Mermin, Solid State Physics, Saun ders College, Philadelphia, 1976.\n[14] P. M. Chaikin and T. C. Lubensky, Principles of Condense d Matter Physics, Cambridge University Press, 1995.\n[15] H. T. Diep, Theory of Magnetism - Application to Surface Physics: Lectures, Problems and Solutions, World Scientifi c,\nSingapore, 2014.\n[16] H. T. Diep, Statistical Physics: Fundamentals and Appl ication to Condensed Matter, Lectures, Problems and Soluti ons,\nWorld Scientific, Singapore, 2015.\n[17] R. J. Baxter, Exactly Solved Models in Statistical Mech anics, Academic Press, New York, 1982.\n[18] E. Bayong, H. T. Diep, Effect of long-range interaction o n the critical behavior of the continuous Ising model, Phys. Rev\nB 59(1999)11919.\n[19] E. Bayong, H. T. Diep, V. Dotsenko, Potts model with long -range interaction in one dimension Phys. Rev. Lett. 83(199 9)14;\nPhys. Rev. Lett. 85(2000)5256.\n[20] S. Reynal, H. T. Diep, Reexamination of the long-ranged Potts model: a multicanonical approach, Phys. Rev. E\n69(2004)026169.\n[21] S. Reynal, H. T. Diep, Q-state Potts model with power-la w decaying interactions: along the tricritical line, J. App l. Phys.\n95(2004)6968.\n[22] L. Onsager, Phys. Rev. 65(1944)117.20\n[23] P. Azaria, H. T. Diep and H. Giacomini, Coexistence of or der and disorder and reentrance in an exactly solvable model ,\nPhys. Rev. Lett. 59(1987)1629.\n[24] M. Debauche, H. T. Diep, H. Giacomini and P. Azaria, Exac t Phase Diagram in a generalized Kagom Ising lattice:\nReentrance and Disorder Lines, Phys. Rev. B 44(1991)2369.\n[25] H. T. Diep, M. Debauche, H. Giacomini, Exact solution of an anisotropic centered honeycomb Ising lattice: Reentran ce\nand Partial Disorder, Phys. Rev. B (rapid communication) 43 (1991)8759.\n[26] M. Debauche and H. T. Diep, Successive Reentrances and P hase Transitions in exactly solved dilute centered square I sing\nlattices, Phys. Rev. B 46(1992)8214.\n[27] P. Azaria, H. T. Diep and H. Giacomini, Ordering in the ce ntered-square lattice Ising model, Phys. Rev. B 39(1989)74 0.\n[28] H. T. Diep, M. Debauche and H. Giacomini, Reentrance and Disorder Solutions in Exactly Solvable Ising Models, J. Mag .\nMag. Mater. 104-107(1992)184.\n[29] K. Kano and S. Naya, Prog. Theor. Phys. 10(1953)158.\n[30] A. Gaff and J. Hijmann, Physica A 80(1975)149.\n[31] J. Stephenson, J. Math. Phys. 11(1970)420; Can. J. Phys . 48(1970)2118; Phys. Rev. B 1(1970)4405.\n[32] R. Quartu and H. T. Diep, Partial Order in Frustrated Qua ntum Spin Systems, Phys. Rev. B 55(1997)2975.\n[33] C. Santamaria and H. T. Diep, Evidence of a Partial Disor der in a Frustrated Heisenberg System, J. Appl. Phys.\n81(1997)5276.\n[34] P. Azaria, H.T. Diep and H. Giacomini, First order trans ition, multicriticality and reentrance in a BCC lattice wit h Ising\nspins, Europhys. Lett. 9(1989)755.\n[35] H. T. Diep and Giacomini, Exactly Solved Frustrated Mod els, in: H. T. Diep (Ed.), Frustrated Spin Systems, second ed .,\nWorld Scientific, Singapore, 2013, pp. 1-58.\n[36] Diep-The-Hung, J. C. S. Levy and O. Nagai, Effect of surfa ce spin-waves and surface anisotropy in magnetic thin films a t\nfinite temperatures, Phys. Stat. Solidi (b) 93(1979)351.\n[37] H. T. Diep, Quantum effects in antiferromagnetic thin fil ms, Phys. Rev. B 43(1991)8509.\n[38] N. N. Bogolyubov and S. V. Tyablikov, Doklady Akad. Nauk S.S.S.R. 126(1959)53 [translation: Soviet Phys.-Doklady\n4(1959)604].\n[39] A. Yoshimori, J. Phys. Soc. Jpn 14(1959)807.\n[40] J. Villain, Phys. Chem. Solids 11(1959)303.\n[41] I. Harada and K. Motizuki, J. Phys. Soc. Jpn 32(1972)927 .\n[42] E. Rastelli, L. Reatto and A. Tassi, Quantum fluctuation s in helimagnets, J. Phys. C 18(1985)353.\n[43] H. T. Diep, Low-temperature properties of quantum Heis enberg helimagnets, Phys. Rev. B 40(1989)741.\n[44] H. T. Diep, Magnetic transitions in helimagnets, Phys. Rev. B 39(1989)397.\n[45] V. Thanh Ngo and H. T. Diep, Effects of frustrated surface in Heisenberg thin films, Phys. Rev. B 75(2007)035412, Selec ted\nfor the Vir. J. Nan. Sci. Tech. 15(2007)126.\n[46] V. Thanh Ngo and H. T. Diep, Frustration effects in antife rrormagnetic face-centered cubic Heisenberg films, J. Phys :\nCondens. Matter. 19(2007)386202.\n[47] H. T. Diep, Quantum Theory of Helimagnetic Thin Films, P hys. Rev. B 91(2015)014436.\n[48] Sahbi El Hog and H. T. Diep, Helimagnetic Thin Films: Sur face Reconstruction, Surface Spin-Waves, Magnetization, J.\nMagn. and Magn. Mater. 400(2016)276-281.\n[49] Sahbi El Hog and H. T. Diep, submitted for publication in Phys. Rev. B (March 2016).\n[50] R. Quartu and H. T. Diep, Phase diagram of body-centered tetragonal Helimagnets, J. Magn. Magn. Mater. 182(1998)38 .\n[51] N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17(1966)113 3.\n[52] N. Metropolis, A. W. Rosenbluth, M, N, Rosenbluth, and A . H. Teller, J. Chem. Phys. 21(1953)1087.\n[53] K. Binder and D. W. Heermann, Monte Carlo Simulation in S tatistical Physics, Springer-Verlag, Berlin, 1992.\n[54] A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Let. 61(1 988)2635; Phys. Rev. Let. 63(1989)1195.\n[55] A. M. Ferrenberg and D. P. Landau, Phys. Rev. B 44(1991)5 081.\n[56] F. Wang and D. P. Landau, Phys. Rev. Lett. 86(2001)2050; Phys. Rev. E 64(2001)056101.\n[57] M. N. Barber, Finite-Size Scaling, in: C. Domb and J. L. L ebowitz (Eds.), Phase Transitions and Critical Phenomena,\nVol. 8, Academic Press, 1983, pp. 146-268.\n[58] V. T. Ngo and H. T. Diep, Phase Transition in Heisenberg S tacked Triangular Antiferromagnets: End of a Controversy,\nPhys. Rev. E 78(2008)031119.\n[59] V. T. Ngo and H. T. Diep, Stacked Triangular XY Antiferro magnets: End of a Controversial Issue on the Phase Transitio n,\nJ. Appl. Phys. 103(2008)07C712.\n[60] X. T. Pham Phu, V. Thanh Ngo and H. T. Diep, Critical Behav ior of Magnetic Thin Films, Surface Science 603(2009)109-\n116 and references cited therein.\n[61] X. T. Pham Phu, V. Thanh Ngo and H. T. Diep, Cross-Over fro m First to Second Order Transition in Frustrated Ising\nAntiferromagnetic Films, Phys. Rev. E 79(2009)061106.\n[62] D. P. Pappas, K. P. Kamper and H. Hopster, Phys. Rev. Lett . 64(1990)3179-3182.\n[63] R. Allenspach and A. Bischof, Phys. Rev. Lett. 69(1992) 3385.\n[64] C. Won, Y. Z. Wu, J. Choi, W. Kim, A. Scholl, A. Doran, T. Ow ens, J. Wu, X. F. Jin, H. W. Zhao and Z. Q. Qiu, Phys.\nRev. B 71(2005)224429.\n[65] A. Vaterlaus, C. Stamm, U. Maier, M. G. Pini, P. Politi an d D. Pescia, Phys. Rev. Lett. 84(2000)2247.\n[66] A. Hucht, A. Moschel and K. D. Usadel, J. Magn. Magn. Mate r. 148(1995)32.21\n[67] A. Hucht and K. D. Usadel, Phys. Rev. B 55(1997)12309.\n[68] D. Pescia and V. L. Pokrovsky, Phys. Rev. Lett. 65(1990) 2599-2601.\n[69] C. Santamaria and H. T. Diep, J. Magn. Magn. Mater. 212(2 000)23.\n[70] Danh-Tai Hoang, Maciej Kasperski, H. Puszkarski, and H . T. Diep, J. Phys.: Condens. Matter 25(2013)056006.\n[71] K. Akabli, H. T. Diep and S. Reynal, Spin Transport in Mag netic Multilayers, J. Phys.: Condens. Matter 19(2007)3562 04.\n[72] K. Akabli and H. T. Diep, Effects of Ferromagnetic Orderi ng and Phase Transition on the Resistivity of Spin Current, J .\nAppl. Phys. 103(2008)07F307.\n[73] K. Akabli and H. T. Diep, Temperature Dependence of Spin Resistivity in Ferromagnetic Thin Films, Phys. Rev. B\n77(2008)165433.\n[74] K. Akabli, Y. Magnin, M. Oko, I. Harada and H. T. Diep, The ory and Monte Carlo Simulation of Spin Transport in\nAntiferromagnetic Films: Application to MnTe, Phys. Rev. B 84(2011)024428.\n[75] Danh-Tai Hoang, Y. Magnin and H. T. Diep, Spin Resistivi ty in the Frustrated J1-J2 Model, Mod. Phys. Lett. B\n25(2011)937.\n[76] Y. Magnin, K. Akabli, H. T. Diep and I. Harada, Monte Carl o Study of the Spin Transport in Magnetic Materials,\nComputational Materials Science 49(2010)S204-S209.\n[77] Y. Magnin, K. Akabli and H. T. Diep, Spin Resistivity in F rustrated Antiferromagnets, Phys. Rev. B 83(2011)144406.\n[78] Y. Magnin, Danh-Tai Hoang and H. T. Diep, Spin Transport in Magnetically Ordered Systems: Effect of the Lattice\nRelaxation Time, Mod. Phys. Lett. B 25(2011)1029.\n[79] Y. Magnin and H. T. Diep, Monte Carlo Study of the Spin Res istivity in Semiconducting MnTe, Phys. Rev. B\n85(2012)184413.\n[80] P.-G. de Gennes and J. Friedel, J. Phys. Chem. Solids 4(1 958)71.\n[81] M. E. Fisher and J.S. Langer, Phys. Rev. Lett. 20(1968)6 65.\n[82] T. Kasuya, Prog. Theor. Phys. 16(1956)58.\n[83] M. Kataoka, Phys. Rev. B 63(2001)134435.\n[84] C. Cercignani, The Boltzmann Equation and Its Applicat ions, Springer-Verlag, New York, 1988.\n[85] X. He, Y.Q. Zhang and Z.D. Zhang, J. Mater. Sci. Technol. 27(2011)64.\n[86] W. Szuszkiewicz, E. Dynowska, B. Witkowska and B. Henni on, Phys. Rev. B 73(2006)104403."    },    {        "title": "1604.07804v2.Compensation_temperatures_and_exchange_bias_in_La1_5Ca0_5CoIrO6.pdf",        "content": "arXiv:1604.07804v2  [cond-mat.mtrl-sci]  18 May 2016Compensation temperatures and exchange bias in La 1.5Ca0.5CoIrO 6\nL. T. Coutrim,1E. M. Bittar,2F. Stavale,2F. Garcia,2E. Baggio-Saitovitch,2M. Abbate,3\nR. J. O. Mossanek,3H. P. Martins,3D. Tobia,4P. G. Pagliuso,4and L. Bufai¸ cal1,∗\n1Instituto de F´ ısica, Universidade Federal de Goi´ as, 7400 1-970, Goiˆ ania, GO, Brazil\n2Centro Brasileiro de Pesquisas F´ ısicas, 22290-180, Rio de Janeiro, RJ, Brazil\n3Universidade Federal do Paran´ a, 19044, 81531-990 Curitib a, PR, Brazil\n4Instituto de F´ ısica “Gleb Wataghin”, UNICAMP, 13083-859, Campinas, SP, Brazil\n(Dated: October 21, 2021)\nWe report on the study of magnetic properties of the La 1.5Ca0.5CoIrO 6double perovskite. Via\nac magnetic susceptibility we have observed evidence of wea k ferromagnetism and reentrant spin\nglass behavior on an antiferromagnetic matrix. Regarding t he magnetic behavior as a function of\ntemperature, we have found that the material displays up to t hree inversions of its magnetization,\ndepending on the appropriate choice of the applied magnetic field. At low temperature the material\nexhibit exchange bias effect when it is cooled in the presence of a magnetic field. Also, our results\nindicate that this effect may be observed even when the system is cooled at zero field. Supported by\nother measurements and also by electronic structure calcul ations, we discuss the magnetic reversals\nandspontaneous exchangebias effectin termsof magnetic pha se separation andmagnetic frustration\nof Ir4+ions located between the antiferromagnetically coupled Co ions.\nI. INTRODUCTION\nMagnetic frustration emerges from competing mag-\nnetic interactions and degenerate multivalley ground\nstates1. An example of such systems are the spin glasses\n(SG), in which the interactions between magnetic mo-\nments are in conflict with each other due to the presence\nof frozen-in structural disorder. The intriguing physi-\ncal phenomena underlying the SG behavior have led to\ngreat interest in these materials since the 1970’s. The\ndevelopment of theories to model the SG found its ap-\nplicability in a wide variety of research fields, from real\nglassestoneuralnetworksandproteinfolding2,3. Despite\nthe great scientific interest and intense research over the\nlast decades, the underlying physics that govern the SG\nphenomena is far from being well understood.\nThe canonical example of a SG type material is an in-\ntermetallic alloy in which a few percent of magnetic ions\naredispersedarbitrarilyinanon-magneticmatrix. These\nmagnetic atomsaretherefore separatedby incidental dis-\ntances, and thus the RKKY (Ruderman-Kittel-Kasuya-\nYosida) interaction allows the coupling energy to have\nrandom sign. This class of systems corresponds to the\nhistorical discovery of SG, which traces back to the stud-\nies of strongly diluted magnetic alloys and the Kondo\neffect3.\nLater on, SG have been identified within other sys-\ntems, such as insulating intermetallics, layered thin films\nand magnetic oxides. For the later class of materi-\nals, is important to mention the geometric frustrated\npyrochlores4,5and the extensively studied Co/Mn-based\nperovskites6–8. For these A(Co,Mn)O 3materials, the\nSG-like behavior is usually ascribed to the phase seg-\nregation and inhomogeneity of the compounds, and the\ndynamical process of magnetic relaxation being related\nto the growth and interactions of magnetic clusters2,9.\nMany of these cobaltites and manganites exhibit the in-\nteresting exchange-bias (EB) effect, for which there isa shift of the magnetization as a function of the ap-\nplied magnetic field [ M(H)] curve in respect to its cen-\nter. This phenomena is usually attributed to the induced\nexchange anisotropy at the interface between antiferro-\nmagnetic (AFM) and ferromagnetic (FM)/ferrimagnetic\n(FIM) phases in heterogeneoussystems10, and it has also\nbeen observed at FM/FIM/AFM-SG interfaces11,12. It\nis commonly observed in multilayered systems, although\nalso found in bulk materials with competing magnetic\ninteractions with undefined magnetic interfaces between\nregions with AFM or FIM interactions10.\nWerecentlyreportedthestructuralandmagneticchar-\nacterization of the La 2−xCaxCoIrO 6double perovskite\nseries13. For La 2CoIrO 6the transition-metal ions va-\nlences are reported to be Co2+and Ir4+14. Our re-\nsults show that La3+to Ca2+substitution leads to Co\nvalence changes, and La 1.5Ca0.5CoIrO 6presents both\nCo2+and Co3+in high spin configuration. Moreover,\nit presents the two key ingredients to achieve a SG state,\nwhich are different competing magnetic interactions and\ndisorder2,3,13.\nIn the course of studying the magnetic properties of\nLa1.5Ca0.5CoIrO 6, we have observed a reentrant spin\nglass (RSG)-like state, i.e., there is a conventional mag-\nnetic ordering and, at lower temperature ( T), the system\nachieves the SG state concomitantly to other magnetic\nphases. This behavior is ascribed to the Ir magnetic\nfrustration due to Co AFM coupling and to the mag-\nnetic phase separation induced by the anti-site disorder\n(ASD) at the transition-metal sites.\nThis RSG state is intrinsically related to the EB ef-\nfect observed for La 1.5Ca0.5CoIrO 6. Another important\nfeature observed is that, for an appropriate choice of the\napplieddcmagneticfield( Hdc)thecompoundcanreverse\nits magnetization up to three times in the T-dependent\nmagnetization measurements.\nInthisworkwereporttheinvestigationofthemagnetic\nbehaviorofLa 1.5Ca0.5CoIrO 6. Usingacmagneticsuscep-2\ntibility measurements we have observed that the system\nexhibit conventionalmagnetic orderingsat T∼90 K and\na spin glass transition at T≃27 K, confirming its RSG\nstate at low- T. The dc magnetization measurements re-\nvealed that the high- Tanomaly is in fact associated with\ntwo conventionalmagnetic transitions, the AFM and FM\nphasesofCoions. Thecompensationtemperaturesinthe\nT-dependent magnetization measurements and the spon-\ntaneous EB effect in the isothermal magnetization mea-\nsurements were investigated in detail. Studies of x-ray\nabsorptionnearedgestructure(XANES), x-raymagnetic\ncircular dichroism (XMCD), x-ray photoelectron spec-\ntroscopy(XPS)andbandstructurecalculationswerealso\ncarried out. These data corroborates our argument that\nthe magnetization reversals and zero field cooled (ZFC)\nexchange bias effect observed for La 1.5Ca0.5CoIrO 6can\nbe both understood in terms of the same underlying\nmechanism, i.e., are due to the competing interactions\nof Co ions that leads to magnetic phase segregation and\nfrustration of the Ir magnetic moments.\nII. EXPERIMENTAL DETAILS\nPolycrystalline samples of La 1.5Ca0.5CoIrO 6were pre-\npared by the solid state reaction in a conventional tubu-\nlar furnace and air atmosphere. Stoichiometric amounts\nof La2O3, CaO, Co 3O4and metallic Ir were mixed and\nheated at 650◦C for 24 hours. Later the samples were\nre-grinded before a second step of 48 hours at 800◦C. Fi-\nnally the materials were grinded, pressed into pellets and\nheated at 975◦C for two weeks. X-ray powder diffrac-\ntion pattern revealed a single phase double perovskite\nstructure with monoclinic P21/nsymmetry, with 9% of\nASD at Co/Ir sites13. Magnetic data were collected on\na commercial Physical Property Measurement System.\nAC magnetic susceptibility was measured with driving\nfieldHac= 10 Oe, at the frequency range of 10-10000\nHz. DC magnetization was measured at ZFC and field\ncooled (FC) modes. XPS experiments were performed\nusing an ultra-high vacuum (UHV) chamber equipped\nwith a SPECS analyzer PHOIBOS 150. XMCD and\nXANES measurements were performed in the dispersive\nx-rayabsorption(DXAS) beam line at the BrazilianSyn-\nchrotronLight Laboratory(LNLS)15. The edge step nor-\nmalization of the data was performed after a linear pre-\nedge subtraction and the regression of a quadratic poly-\nnomial beyond the edge, using the software ATHENA16.\nThe band structure calculations were performed using\nthe WIEN2k software package17.\nIII. RESULTS AND DISCUSSION\nA. X-ray Photoelectron Spectroscopy (XPS)\nFig. 1 shows the XPS spectra for La 1.5Ca0.5CoIrO 6.\nAll the results presented correspond to the use ofmonochromatic Al Kαx-ray radiation ( hν= 1486.6\neV) using spectrometer pass energy ( Epass) of 15 eV.\nThe spectrometer was previously calibrated using the\nAu 4f7/2(84.0 eV) which results on a full-width-half-\nmaximum of 0.7 eV, for a sputtered metallic gold foil.\nThe samples were referenced by setting the adventitious\ncarbon C 1 speak to 284.6 eV. Prior to mounting in\nUHV, samples were slightly polished and ultra-sonicated\nsequentially in isopropyl alcohol and water. The photo-\nemission spectra were sequentially acquired after succes-\nsive cycles of gentle Ar+sputtering (5 ×10−7mbar Ar,1\nkV, 1µA/cm2, 10-15seconds intervals) for hydrocarbons\nremoval. All spectra shown correspond to 45 s Ar+sput-\ntering at the ideally found conditions to avoid surface\nspecies reduction.\nIn Fig. 1(a) all elements found are indicated. We ob-\nserve that residual carbon persist on the samples surface\nsince the in-situ sputtering has been employed at the op-\ntimal conditions to avoid chemical reduction. Particu-\nlarly important is the careful analysis of the cobalt 2 p\nregion which serves as a tool to assign Co cations sites\nand electronic configuration in several compounds18–20.\nNoteworthy, although XPS is most related to the sur-\nface chemical composition based on the limited photo-\nelectrons inelastic mean free path in solids, because of\nthe large mean free path of the cobalt photoelectrons\n(forEKin∼700 eV, about 1.5 nm) the spectra presented\ncan certainly reveal additional information from buried\nlayers. As reported extensively in the literature, the ex-\npected binding energies for Co3+and Co2+are 779.5and\n780.5 eV, respectively21. Importantly, depending on the\ncation symmetry one may observe satellite features re-\nlated to charge-transfermechanisms which appear signif-\nicantly stronger for Co2+in octahedral sites, in contrast\nto Co3+in octahedral or Co2+in tetrahedral sites. The\ndifferences has been discussed in the literature and arises\nfrom an enhanced screening of Co3+due to a larger Co\n3d-O 2phopping strength and a smaller charge-transfer\nenergy compared to those in the Co2+charge state22. In\nFig. 1, the Co 2 pXPS spectra show prominent peaks\nat 779.6 and 795.3 eV related to the Co 2 p3/2and 2p1/2,\nrespectively, in addition to the satellite feature located at\n785.3eV.TheintensesatelliteisaclearsignatureofCo2+\nin octahedral sites, most probably at a high-spin Co2+\nconfiguration as observed for the cobalt monoxide23.\nThe detailed analysis of the Co 2 pregion is however\nfar from trivial, and the main peaks are known to be\ncomposed by multiplet splitting as described by Gupta\nand Sen24, and extensively discussed in several recently\nstudies25,26. Nevertheless, we have considered that the\nintensityofeachspin-orbitcomponentcanbefitted using\ntwo curves related to the different Co cations and respec-\ntive satellites since Co2+and Co3+are known to display\nwelldistinguishbindingenergiesatabout780.1and779.6\neV26. The spectral analysis for La 1.5Ca0.5CoIrO 6com-\npound employing two fitting components results on the\nassignment of Co2+and Co3+species located at bind-\ning energies and full-width-half-maximum of 780.1 (3.03)3\nFIG. 1: (a) XPS survey spectra for La 1.5Ca0.5CoIrO 6. All\nelements observed in the sample are indicated. (b) High res-\nolution Co 2 pregion for several Ca doping levels and the\ncorresponding peak components fitting using a Shirley back-\nground and two Lorentzian-Gaussian peaks for Co2+and\nCo3+cations component. (c)The correspondingvalence band\nphotoemission features and themain peaks indicated byline 1\nand line 2, related to the high-spin state of the Co3+cations.\nand 779.3 (1.89) eV, respectively. In order to compare\nthe results obtained, the same procedure has been em-\nployed for La 2CoIrO 6and La 1.2Ca0.8CoIrO 6, as depicted\nin Fig. 1(b). The results indicate a Co2+/Co3+ratio of\n2.33 for La 2CoIrO 6, 2.44 for La 1.5Ca0.5CoIrO 6and 3.03\nfor La 1.2Ca0.8CoIrO 6. The increase of Co2+/Co3+ratio\nas a function of the Ca incorporation is expected and has\nserved to test our fitting procedure. Certainly, the ab-\nsolute amount can be hardly determined. However, the\ntrend observed can fairly indicate the relative amount of\nCo3+species in the compounds.\nFurthermore, the photoemission spectra close to the\nvalence band [Fig. 1(c)] is particularly helpful to dis-\ntinguish the spin state of the Co cations since it dis-\nplay noticeable multiplet structure. The spectral fea-\ntures observed have been discussed by several authors\nin great detail for CoO, Co 3O4and more recently for\nLaCoO 323,27,28. The most important structure are those\nclose to 1-8 eV range, indicated by line 1, which is ex-\npected for Co3+in octahedral sites, and the one indi-\ncated by line 2, related to strong multiplet effects in the\nfinal state of Co3+cations. Previous calculations and\nphotoemission studies have shown that Co3+in a purely,low-spin state is characterized by an intense peak close\nto 1 eV but broad features at energies ranging up to 8\neV27. In contrast, the La 1.5Ca0.5CoIrO 6compound dis-\nplays two features peaking at line 1 and line 2, which\nsuggest a Co3+high spin state.\nThe approximate 70%/30% proportion of Co2+/Co3+\nestimated from the XPS spectra is consistent to the ef-\nfective magnetic moment, µeff= 5.8µB/f.u., obtained\nfrom the Hdc= 500 Oe M(T) curve at the paramag-\nnetic state (see below). Applying the usual equation for\nsystems with two or more different magnetic ions29\nµ=/radicalbig\nµ12+µ22+µ32+... (1)\nand using the standard magnetic moments of Ir4+(1.73\nµB), HS Co2+(5.2µB) and HS Co3+(5.48µB), yields\nµ=/radicalbig\n0.7(5.2)2+0.3(5.48)2+(1.73)2= 5.6µB/f.u..\n(2)\nThe difference to the experimental value may be re-\nlated to spin-orbit coupling (SOC) on Co ions, as already\nreported for similar compounds14,27.\nB. ac and dc magnetization vs. T\nFig. 2(a) presents the ZFC-FC magnetization curves\nforHdc= 500 Oe, were two peaks can be clearly ob-\nserved. The inset shows a magnified view of a stretch of\nthe curve, where are evidenced two anomalies at T≃97\nandT≃86 K, associated to the magnetic ordering of the\nAFM and FM phases of Co ions, respectively, as it will\nbe addressed later. The lower- Tcusp at≃27 K is due to\na SG-like behavior, indicating a RSG phenomena. Since\neach peak is associated to a distinct mechanism, if an ap-\npropriate Hdcis applied in the opposite direction of the\nmaterial’s spontaneous magnetization ( Msp), the curve\ncan be shifted down and display up to three reversals of\nits magnetic moment.\nThis scenario can be understood in terms of the AFM\ncouplingofthe Coionsthat arelocatedat theirpredicted\nsite, resulting in the frustration of Ir4+magnetic mo-\nment, and the development of a FM component caused\nby the ASD. Studies of XANES on Co K- and IrL2-,L3-\nedges indicate a Co mixed valence on La 1.5Ca0.5CoIrO 6\n(See Supplemental Material30). Also, the XPS measure-\nment discussed above suggests a proportion ∼70%/30%\nof high spin Co2+/Co3+. Ir maintains 4+ valence by\nLa3+to Ca2+substitution. Reports of neutron pow-\nder diffraction studies on La 2−xSrxCoIrO 614and sev-\neral closely related compounds ( e.g.La2−xSrxCoRuO 638\nand LaBaCoIrO 639) revealed AFM coupling of Co\nions on these double perovskites, as predicted by the\nGoodenough-Kanamori-Anderson (GKA) rules40. More-\nover,ourelectronicstructurecalculationresults(seeSup-\nplemental Material30) indicate the AFM ordering as the\nmost stable structure for La 1.5Ca0.5CoIrO 6. Therefore,\nthis spin orientation can be assumed for the majority of\nCo ions. Consequently, the Ir4+located in between the4\n/s45/s48/s46/s48/s50/s48/s46/s48/s48/s48/s46/s48/s50\n/s51/s48 /s54/s48 /s57/s48 /s49/s50/s48 /s49/s53/s48 /s49/s56/s48 /s50/s49/s48/s45/s48/s46/s48/s50/s48/s46/s48/s48/s48/s46/s48/s50/s48/s46/s48/s52/s54/s48 /s55/s53 /s57/s48 /s49/s48/s53 /s49/s50/s48 /s49/s51/s53/s48/s46/s48/s48/s48/s48/s46/s48/s48/s51\n/s48 /s50/s48 /s52/s48 /s54/s48/s48/s46/s48/s54/s48/s46/s48/s57/s48/s46/s49/s50/s40/s97/s41\n/s84\n/s51/s84\n/s50\n/s32/s32/s32 /s77/s32\n/s66/s47/s102/s46/s117/s46 /s41\n/s32/s90/s70/s67\n/s32/s70/s67/s84\n/s49\n/s32/s72\n/s100/s99/s32/s61/s32/s53/s48/s48/s32/s79/s101\n/s32/s32/s32\n/s77/s32\n/s66/s47/s102/s46/s117/s46 /s41\n/s32/s90/s70/s67/s58/s32/s72\n/s100/s99/s32/s61/s32/s50/s48/s48/s32/s79/s101\n/s32/s90/s70/s67/s58/s32/s72\n/s100/s99/s32/s61/s32/s53/s48/s48/s32/s79/s101\n/s32/s90/s70/s67/s58/s32/s72\n/s100/s99/s32/s61/s32/s49/s48/s48/s48/s32/s79/s101\n/s84/s32/s40/s75/s41/s40/s98/s41\n/s32/s32/s32/s77/s32\n/s66/s47/s102/s46/s117/s46 /s41\n/s84/s32/s40/s75/s41\n/s32/s72\n/s100/s99/s32/s61/s32/s53/s48/s48/s32/s79/s101/s77 \n/s66/s47/s102/s46/s117/s46/s41\n/s32/s32\n/s32/s32\n/s84/s32/s40/s75/s41/s70/s67\nFIG. 2: (a) ZFC and FC magnetization as a function of T\nfor La 1.5Ca0.5CoIrO 6atHdc= 500 Oe. The inset shows the\nmagnified view of the AFM and FM transitions of Co ion.\n(b) ZFC magnetization as a function of TatHdc= 200 Oe\n(solid circle), Hdc= 500 Oe (solid square), and Hdc= 1000\nOe (solid line). The inset shows the Hdc= 500 Oe FC curve\nat low-T.\nAFM coupled Co2+ions might be frustrated. However,\nthe system exhibit 9% of ASD, which together with the\n30% of Co3+leads to other nearest neighbor interactions\nsuch as Co2+–O–Co3+, Co3+–O–Co3+and Ir4+–O–Ir4+.\nThe latter two couplings are AFM, as predicted by the\nGKA rules40–42, but Co2+–O–Co3+coupling is expected\nto be a short range FM interaction via double-exchange\nmechanism27,43,44.\nThe resulting magnetic moment of La 1.5Ca0.5CoIrO 6\ncan be estimated by the following argument. The main\nphase consists of AFM coupled Co2+and frustrated Ir\nions. Hence there is no contribution from the main phase\ntotheresultingmagnetization,aswellastheAFMCo3+–\nO–Co3+and Ir4+–O–Ir4+couplings. To calculate the\nmagnetization per formula unit, it must be taken into\naccount that from the 30% of the Co3+present in the\nsystem, in 9% it will permute to Ir site, giving rise to the\nFM Co2+–O–Co3+interaction, which is the only from\nthe interactions discussed above that is expected to con-\ntribute to the net magnetization. Using the standard\nmagnetic moments of HS Co2+and Co3+, the FM con-\ntribution totheresultingmagnetizationcanbeestimatedto be\nM= 0.3×0.09(0.5MCo3++0.5MCo2+)\n= 0.027(0.5×5.48+0.5×5.2)\n= 0.14µB/f.u..(3)\nThis result is very close to the low- Tvalue of the\nFC magnetization observed on inset of Fig. 2(b), 0.12\nµB/f.u., and to the remanent magnetization of M(H)\ncurve at 2 K ( MR= 0.13µB/f.u., see Fig. 6). It is also\nclose to the total magnetic moment obtained from band\nstructure calculation, M= 0.15µB/f.u. (see Supple-\nmental Material30). Surely, the above calculation is only\nan estimate, since it is not possible to establish the ex-\nact individual contribution of Co2+and Co3+magnetic\nmoments. Also, the Co2+/Co3+proportion may vary a\nbit from that obtained from XPS, leading to the discrep-\nancy between the observed and calculated values. The\nslightly larger experimental values may be also related\nto the contribution of the frozen SG ions, which were not\ntaken into account in the calculation. The above approx-\nimation only takes into account the linear exchange of\nIsing moments. In a 3D system, other exchange path-\nways may play a role, resulting in a more complex pic-\nture, but also with competing FM and AFM interactions\nand perhaps even canted spins5,40. Hence, also for a 3D\nmagneticmodel, onewouldexpectIr4+frustration. Frus-\ntration, alongwith the magneticsegregationdue toASD,\nfit very well the material’s magnetic behavior.\nThe magnetic interactions discussed above can explain\nthe curve of Fig. 2(a) as the following. After ZFC, at\nlow-T, there is only the Msprelated to the Co interac-\ntions, since the Ir moments are frustrated. The system’s\nMspis here always chosen as opposite (negative) to Hdc\ndirection (positive). Thus, applying Hdcin the opposite\ndirection of Msp, and ascending to higher- Tthere is the\nfirst compensation temperature at T1≃18 K, due to the\nSG-spins alignment to Hdcdirection. By increasing T\nthere is the decrease of the SG correlation length, result-\ning in the second magnetization reversal at T2≃42 K.\nWith the further enhancement of the thermal energy the\nCo-FM phase can achieve positive magnetization, and\nthere is the third compensation temperature at T3≃78\nK. Finally, there are the transitions of the Co2+-AFM\nand Co2+/Co3+-FM phases to the paramagnetic state.\nThis behavior is closely related to the dynamics of the\nspin clusters, which are strongly dependent on Hdcand\nmeasurement time. For different times of measurement\nthe compensation temperatures can vary. For a larger\nHdc, the system achieves positive magnetization values\nalready at low- T, and there is no magnetic reversal, as\ncan be observed on Fig. 2(b) for the curve measured\nunderHdc= 1000 Oe. On the other hand, for small\nHdcthe SG peak is not large enough to achieve the posi-\ntive magnetization and the system undergoes only to one\ncompensation temperature, T3. ForHdc= 200 Oe, one\nhaveT3= 92 K, as shown in Fig. 2(b). Another im-\nportant result obtained from Fig. 2(b) is that the low\nTpeak maxima shifts to lower- TasHdcincreases. For5\n/s48/s46/s48/s48/s48/s46/s48/s57/s48/s46/s49/s56/s48/s46/s50/s55/s48/s46/s51/s54\n/s48 /s50/s53 /s53/s48 /s55/s53 /s49/s48/s48 /s49/s50/s53 /s49/s53/s48 /s49/s55/s53/s48/s46/s48/s48/s48/s46/s48/s57/s48/s46/s49/s56/s48/s46/s50/s55/s49 /s50 /s51 /s52 /s53 /s54/s50/s52/s50/s53/s50/s55/s46/s48/s50/s55/s46/s53\n/s48 /s49/s53/s48 /s51/s48/s48 /s52/s53/s48/s50/s52/s50/s53/s50/s54/s50/s55/s50/s56\n/s32/s72\n/s100/s99/s32/s61/s32/s48/s72\n/s97/s99/s32/s61/s32/s49/s48/s32/s79/s101\n/s32/s32\n/s39/s39/s32/s53/s48/s32/s72/s122\n/s32/s49/s48/s48/s48/s32/s72/s122\n/s32/s49/s48/s48/s48/s48/s32/s72/s122/s97/s99/s32/s40/s101/s109/s117/s47/s109/s111/s108/s41/s39/s40/s97/s41\n/s32/s32\n/s97/s99/s32/s40/s101/s109/s117/s47/s109/s111/s108/s41\n/s84/s32/s40/s75/s41/s40/s98/s41\n/s39/s39/s39\n/s32/s32\n/s102/s32/s61/s32/s49/s48/s48/s48/s32/s72/s122/s72\n/s97/s99/s32/s61/s32/s49/s48/s32/s79/s101\n/s32/s72\n/s100/s99/s61/s32/s48\n/s32/s72\n/s100/s99/s61/s49/s48/s48/s32/s79/s101\n/s32/s72\n/s100/s99/s61/s49/s48/s48/s48/s32/s79/s101/s72\n/s100/s99/s61/s32/s53/s48/s48/s32/s79/s101\n/s102/s32/s49/s47/s122\n/s32/s32/s32\n/s84\n/s102/s32/s40/s75/s41/s72\n/s100/s99/s32/s61/s32/s48\n/s32/s84\n/s102/s32/s32/s101/s120/s112/s101/s114/s105/s109/s101/s110/s116/s97/s108\n/s32/s32/s102/s105/s116/s32/s119/s105/s116/s104 /s32/s72/s50/s47/s51\n/s32/s108/s97/s119\n/s72/s50/s47/s51/s84\n/s102/s32/s40/s75/s41\n/s32/s32\nFIG. 3: (a) χ’acandχ”acas a function of Tat various fre-\nquencies. The inset shows Tfas a function of frequency for\nHdc=0 and Hdc=500 Oe, obtained from χ’ac. The lines are\nbest fits to the power law Tf=Tsg[1+(τ0f)1/zν)]. (b)χ’acand\nχ”acvs.Tatf=1000 Hz for various Hdc. Inset shows Tffor\ndifferent applied Hdc.\nHdc= 200,500and1000Oethepeakmaximaarelocated\nat 27.8, 25.4 and 23.9 K respectively. This is an expected\nfeature of a SG-like material, as will be discussed next.\nThe ac magnetic susceptibility ( χac) was measured as\na function of Tfor seven frequencies in the range 10-104\nHz. Fig. 3(a) shows the real ( χ’ac) and imaginary ( χ”ac)\nparts of susceptibility for some selected frequencies. For\nχ’acit was observed for the low- Tpeak (Tf) a system-\natic shift of Tfto higher- Twith the increase of driving\nfrequency, where Tfshift from 27 K at 10 Hz to 27.84 K\nat 104Hz. It was also observed a decrease of the peak\namplitude with increasing frequency. Both results are\ncharacteristic of SG-like materials. On the other hand,\nfor theT≃90 K only a small amplitude decrease was\nobserved at higher frequencies, but no measurable shift,\nwhich characterizes ordinary magnetic transitions.\nThe frequency-dependent data turn out to be well de-\nscribed by the conventional critical slowing down model\nof the dynamic scaling theory3,46,47, which predicts apower law\nτ\nτ0=/bracketleftbigg(Tf−Tsg)\nTsg/bracketrightbigg−zν\n(4)\nwhereτis the relaxation time corresponding to the mea-\nsured frequency, τ0is the characteristic relaxation time\nof spin flip, Tsgis the SG transition temperature (as fre-\nquency tends to zero), zis the dynamical critical ex-\nponent and νis the critical exponent of the correlation\nlength. The solid line in the inset of Fig. 3(a) repre-\nsents the best fit to the power law divergence, that yields\nTsg= 26.6 K,τ0= 1.5×10−13s andzν= 6.5. These\nresults are in the realm of conventional SG phases.\nA criterion that is often used to comparethe frequency\ndependence of Tfin different SG systems is to compare\nthe relative shift in Tfper decade of frequency\nδTf=△Tf\nTf△(logf). (5)\nFor La 1.5Ca0.5CoIrO 6we found δTf≃0.008, which\nis within the range usually found for conventional\nSG (δTf/lessorsimilar0.01). For superparamagnets the usual\nvalue is δTf/greaterorsimilar0.1, while for cluster glasses (CG)\nit has intermediate values between canonical SG and\nsuperparamagnets3,45,46,48.\nThe SG cusps on Fig. 3(a) are broader than usually\nobserved for canonical SG. Since La 1.5Ca0.5CoIrO 6is a\nRSG material, this may be due to the internal molecular\nfield resulting from Co moments. In order to verify the\nfieldeffectonthemagnetizationitwasmeasured χacwith\nHdc= 500Oe. InsetofFig. 3(a)showsthat, forthis Hdc,\nTfalso shifts to higher- Twith increasing frequency. The\ndashed line is the fit to the power law, yielding T500Oe\nsg=\n23.7 K,zν= 5,f0= 1010Hz. With Hdc= 500 Oe, the\nrelative shift in Tf(Eq. 5) increases to δTf≃0.01. All\nthese results are compatible to those usually reported\nfor CG materials. Hence, Hdcinduces the increase of\nthe correlation length of the spin clusters, i.e., there is a\ntransition from SG to CG in the system.\nFig. 3(b) shows χ’acandχ”acmeasurements for fixed\nf= 1000 Hz and Hac= 10 Oe, but different Hdc. As ex-\npected, the SG peak is smeared out and shifts to lower- T\nwith increasing Hdc3. The inset shows that Tf(H) rea-\nsonably followsthe H2/3Almeida-Thouless relation49for\nHdc≤100 Oe, and the curve’s slope changes for higher\nfields. Since La 1.5Ca0.5CoIrO 6is a RSG compound, Hdc\nhave its effect on the underlying Co ions, inducing the\ntransition from conventional SG to CG. This result may\nbring important insights about the effect of strong Hdc\non the frozen spins and also on the limit of validity of\ntheH2/3relation for a RSG. Hdcseems to remove the\ncriticality of the transition, yet it does not fully prevent\nthe formation of the frozen state3.\nIn contrast to χ’ac, forχ”acthere was a small non-\nmonotonic variation of the peak position and ampli-\ntude. This is an unconventional behavior for a SG-\nlike material, and it was not found a reasonable sim-\nple explanation for it. It was already reported for the6\nFIG. 4: Temperature-field phase diagram showing the\nN´ eel (TN), critical ( TC) and freezing ( Tf) temperatures of\nLa1.5Ca0.5CoIrO 6. The lines are guides for the eye.\nternary intermetallic CeRhSn 3a shift toward lower- T\nwith increasing frequency45,50. But differently than for\nLa1.5Ca0.5CoIrO 6, the shift was on χ’, whileχ” goes to\nhigher-Twith increasing frequency. Here is important\nto stress that, despite the fact our measurements were\ncarefully taken, the overall smaller and more noisy χ”ac\nmakes it more difficult to precisely determine the Tfpo-\nsition, specially for lower frequencies.\nThe complex magnetic behavior of La 1.5Ca0.5CoIrO 6\ncan be summarized in a rich phase diagram, showing its\nconventionaland SG-like states. Fig. 4 displaysthe field-\ntemperaturephase diagramforthe compound, wherecan\nbe observed its N´ eel temperature ( TN) atTN≃97 K, its\ncritical temperature ( TC) atTC≃86 K, and its freezing\ntemperature ( Tf) atTf≃26.6 K. An important result\nobservedisthat, dependingon Hdc, atlow-Tthematerial\ncan behave as a conventional spin glass or as a cluster\nglass.\nC. Exchange bias\nM(H) curves for ordinary FM and FIM materials usu-\nally exhibit hysteretic behavior with coercive field due\nto the blocking of the domain wall motion. In SG-\nlike materials irreversibility can also be observed aris-\ning out of anisotropy3,51,52. Hence, in a RSG system\na large anisotropic coercivity can be expected due to\nthe combined action of FM, AFM and SG phases. The\nZFCM(H) measurements were performed for several\nTusing a systematic protocol detailed on Supplemental\nMaterial30, and two representative curves are displayed\nin Fig. 5(a), where one can see a small increase in the\nmagnetization from 5 to 15 K. The increase of thermal\nenergy results in an enhancement of the SG alignment\nto the field direction, yielding in a larger magnetization.\nHowever, due to thermal energy, these spins can flip to\nthe field direction, leading to the observed decrease of\ncoercivity. It is also important to note that the system\nexhibit a non-negligible Mspat zero field [inset of Fig./s45/s52/s48 /s45/s50/s48 /s48 /s50/s48 /s52/s48/s45/s48/s46/s54/s45/s48/s46/s52/s45/s48/s46/s50/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54\n/s48/s46/s48 /s48/s46/s49 /s48/s46/s50/s48/s46/s48/s48/s48/s48/s46/s48/s48/s55\n/s45/s49/s50 /s45/s49/s49 /s45/s49/s48 /s49/s48 /s49/s49 /s49/s50/s45/s56/s45/s52/s48/s52/s56\n/s45/s52/s48 /s45/s50/s48 /s48 /s50/s48 /s52/s48/s45/s48/s46/s50/s48/s46/s48/s48/s46/s50\n/s45/s48/s46/s54/s45/s48/s46/s51/s48/s46/s48/s48/s46/s51/s45/s52/s48 /s45/s50/s48 /s48 /s50/s48 /s52/s48\n/s32/s32/s32\n/s32/s72 /s32/s40/s107/s79/s101/s41/s77 /s32/s40\n/s66/s47/s102/s46/s117/s46 /s41/s40/s97/s41\n/s32/s32/s53/s32/s75\n/s32/s32/s49/s53/s32/s75\n/s32/s32/s52/s53/s32/s75\n/s32/s32/s54/s53/s32/s75\n/s32/s32\n/s32\n/s40/s98/s41/s77 /s32/s40\n/s66/s47/s102/s46/s117/s46 /s41\n/s32/s32/s48/s32/s45/s45/s62/s32/s43/s52/s32/s84\n/s32/s48/s32/s45/s45/s62/s32/s32/s45/s52/s32/s84\n/s32/s124/s72\n/s69/s66/s124/s61/s50/s57/s48/s32/s79/s101\n/s72 /s32/s40/s107/s79/s101/s41/s124/s72\n/s69/s66/s124/s61/s49/s51/s53/s32/s79/s101\n/s53/s32/s75/s40/s99/s41\n/s32/s32/s32\n/s32/s72 /s32/s40/s107/s79/s101/s41/s77 /s32/s40\n/s66/s47/s102/s46/s117/s46 /s41\n/s72 /s32/s40/s107/s79/s101/s41\n/s32/s32/s32\n/s32/s77/s32 /s40\n/s66/s47/s102/s46/s117/s46 /s41\nFIG. 5: (a) ZFC M(H) loops at 5 and15 K. The inset shows a\nmagnifiedviewoftheinitial magnetization valuesatzerofie ld.\n(b)ZFC M(H)loops at 2Kperformed as 0 →4T→ −4T→4\nT and 0 → −4 T→4 T→ −4 T. (c) FM + SG contributions\nto theM(H) loop at T= 5 K. The doted lines are guides\nfor the eye. The inset shows the original curve and the linear\nAFM contribution (see text).\n5(a)]. This Mspshows a systematic evolution with T,\nand plays an important role on the process of pinning\nthe spins, as it will be discussed next.\nHere we define the EB field as HEB=|H++H−|/2,\nwhereH+andH−represent the right and left field\nvalues of the M(H) loop at the M= 0 axis, respec-\ntively. The effective coercive field is HC=|H+−H−|/2.\nUsually, the EB effect is achieved when the system is7\ncooled in the presence of non-zero Hdc. Interestingly, for\nLa1.5Ca0.5CoIrO 6a non-negligible shift of the hysteresis\nloop is observed even when the system is cooled in zero\nfield. This spontaneous EB effect, also called zero field\ncooled EB (ZEB), was recently reported for distinct sys-\ntems such as Mn 2PtGa53and Ni-Mn-In54alloys, and the\nnanocomposite BiFeO 3-Bi2Fe4O455. But here we have\nfound, to the best of our knowledge, the first example\nof a material to have this phenomenon clearly related to\nthree distinct magnetic phases, namely FM, AFM and\nSG. At 2 K La 1.5Ca0.5CoIrO 6exhibit a negative shift\nHZEB≃290 Oe. In order to verify this effect we have\nmeasured M(H) with the initial Hdcin the opposite di-\nrection. As can be observed on Fig. 5(b), the curve\nexhibits a positive shift HZEB≃135 Oe. The shift in\nthe opposite direction is an expected behavior of a EB\nsystem, hence a clear evidence that this result is intrinsic\nof the material. The fact that HZEBis different depend-\ning on the direction of the initial magnetization process\nis an indicative that the internal Mspplays an important\nrole in the pinning of the spins.\nLa1.5Ca0.5CoIrO 6presentsFMandSGphasesincorpo-\nrated to an AFM matrix. Due to its predominant AFM\nphase, it does not saturate even at a large field of 9 T.\nAs will be discussed next, the ZEB effect here observed\nresultsfromthe a delicateexchangeinteractiononthe in-\nterfaces of the AFM/SG phases to the minor FM phase.\nHence, for large enough applied fields the pinned spins at\nthe interface may flip to the field direction, reducing the\neffect. This is actually what is observed for fields larger\nthan4T.Forinstance, foramaximumappliedfield( Hm)\nof 9 T the EB effect is reduced to HZEB=40Oe. In order\ntoevidence the FM contributionto the M(H)curves, the\nAFM contribution was subtracted from the loops. The\nlinear curve representing the AFM phase was obtained\nfrom the fit of the loops at high fields, which was ex-\ntrapolated to the whole field range and then subtracted\nfrom the loop. The resulting curve obtained for T= 5\nK is displayed in Fig. 5(c). It is almost symmetric in re-\nspect to the Maxis and displays the same HZEBas that\nobtained from the original curve. It must be mentioned\nthat the resulting curves contemplate both the contribu-\ntions of the FM and SG phases, i.e., it is not possible to\nseparate these phases on the curves.\nDespite theZEBbeinganeffectonlyrecentlyreported,\nthe conventional exchange-bias (CEB) is a well known\nphenomenon encountered in systems containing inter-\nfaces between distinct magnetic phases, being most likely\nfound in FM-AFM systems. But a shift of the magne-\ntization hysteresis loops along the field axis can be also\nobserved in situations not related to EB effect. In a con-\nventional FM material, if a minor M(H) loop is mea-\nsured,i.e., anM(H) with the maximum applied field\nnot large enough to the system achieve the magnetic sat-\nuration, it can exhibit a shift along the field axis similar\ntothat observedin EBsystems. Thisisin generalrelated\nto the incomplete magnetic reversion of the system56,57.\nHowever,differentlythanobservedinEBmaterials,these/s48 /s53 /s49/s48 /s49/s53 /s50/s48 /s50/s53/s48/s53/s48/s49/s48/s48/s49/s53/s48/s50/s48/s48/s50/s53/s48/s51/s48/s48\n/s48/s51/s54/s57/s49/s50\n/s48 /s50/s48 /s52/s48 /s54/s48 /s56/s48 /s49/s48/s48/s48/s46/s48/s48/s48/s46/s48/s51/s48/s46/s48/s54/s48/s46/s48/s57/s48/s46/s49/s50/s48/s46/s49/s53/s50 /s51 /s52 /s53/s57/s46/s54/s49/s48/s46/s52/s49/s49/s46/s50/s32\n/s32/s72\n/s69/s66/s72\n/s69/s66/s32/s40/s79/s101/s41\n/s84/s32/s40/s75/s41\n/s72\n/s67/s32/s40/s49/s48/s51\n/s32/s79/s101/s41\n/s32/s72\n/s67/s77\n/s82/s32/s40\n/s66/s47/s102/s46/s117/s46 /s41\n/s32/s32\n/s32/s32\n/s84/s32/s40/s75/s41/s84/s32/s40/s75/s41/s72\n/s67/s32/s40/s107/s79/s101/s41\n/s32/s32\nFIG. 6: (a) HZEBandHCevolution with T. The inset shows\na magnified view of the low- Tanomaly on HC.The lines are\nguides for the eye. (b) MRdependency with T.\nminorloopsalsoexhibitalargeshiftalongthemagnetiza-\ntion axis, and in general the loops are not closed at large\nfields58,59. As Fig. 5 shows, M(H) of La 1.5Ca0.5CoIrO 6\nis a closed loop with a very small shift along the ver-\ntical axis due to the pinned spins, as expected. It is a\nindicative that ZEB reported here is not due to a minor\nloop hysteresis. In order to reinforce the difference be-\ntween the curves here observed from those obtained from\nminor loops, we compare in the Supplemental Material\nthe results here described with that obtained from true\nminor loops30.\nThe evolution of HZEBandHCwithTare displayed\non Fig. 6(a). One can observe that the ZEB effect can\nonlybeachievedbelow Tf. Moreover,itrapidlydecreases\nwith the enhancement of the thermal energy. Usually, a\ndecrease in the magnetic unidirectional anisotropy (UA)\nis associated with an increase of the coercivity10. Hence,\nthe low-Tanomaly observed for HCon inset of Fig. 6(a)\nis another expected feature of EB systems.\nDifferent mechanisms are invoked to explain the ZEB\nfor distinct materials. For instance, for Ni-Mn-In it is\nproposed that the UA is formed at the interface between\ndifferent magnetic phases during the initial magnetiza-\ntion process of M(H) curves54. On the other hand,\nfor BiFeO 3-Bi2Fe4O4it is proposed that glassy moment\nat the interface between FM-AFM phases causes the\nEB effect55. Despite the distinct mechanisms claimed8\nto be the responsible for the ZEB effect on each com-\npound, they all have in common the RSG behavior.\nHere we conjecture that the internal molecular field\nplays an important role on the ZEB effect. We pro-\npose the following mechanism to explain the ZEB effect\non La1.5Ca0.5CoIrO 6. The internal field due to the FM\nphase have its impact on AFM and SG phases. It af-\nfects the correlation length of the SG clusters, favoring\nthe freezing of the glassy spins in the same direction, re-\nsulting in a spontaneous UA. The ZEB is enhanced by\nHdcduringtheinitialmagnetizationprocessofthe M(H)\nloop. The field induces the increase of the internal inter-\naction of FM domains, leading to the growth of the spin\nclusters. After the removal of Hdc, the spins at the grain\ninterfacesarepinned, resultinginastablemagneticphase\nwith UA at low- T. AsTincreases the pinned spins can\neasier flip to the field direction due to the enhanced ther-\nmal energy. This leads to the reduction of HZEBand the\ncorrelated increase of HCobserved on Fig. 6(a).\nThe same scenario can explain the system’s remanent\nmagnetization, MR=|M+\nR−M−\nR|/2, where M+\nRandM−\nR\nare the positive and negative values of the magnetization\nat zero field. Fig. 6(b) displays the MRevolution with\nT. On going from low to high- T, first there is an increase\nofMRdue to the thermally activated movement of the\nspins to the field direction. Then going to higher- Tthere\nis the continuous decrease of MRuntil it vanishes at the\nparamagnetic sate. It is important to observe that de-\nspite the fact the FM phase orders at ∼90 K, the ZEB\neffect only occurs below Tf. This, together with the fact\nthat at low- T MRandHCinitially increase while HEB\ndecreases on increasing T, are other evidences that the\nZEB observed is strongly related to the RSG state and is\nnot due to some minor hysteresis loop of the FM phase.\nAs addressed above, a significant evidence that the ob-\nservedZEBeffectonLa 1.5Ca0.5CoIrO 6isnotduetosome\nexperimental artifact is the fact that the M(H) loops\nshift to opposite directions depending on the initial ap-\nplied field be positive or negative. If there were remanent\ncurrentonthemagnetduetoantrappedfluxoranyother\nreason, both shifts should be expected to be in the same\ndirection. This inversionof HEBdepending on the initial\nfield value is also observed when the CEB effect is mea-\nsured,i.e., when the isothermal M(H) curve is measured\nafter the system being field cooled. Fig. 7(a) displaysthe\nM(H)loopwith Hm= 7T,afterthesamplebeingcooled\nin the presence of HFC= 3 T. The AFM contribution\nis also displayed, and the inset shows the deconvoluted\ncurve,i.e., the resulting curve when the AFM one is sub-\ntracted. On Fig. 7(b) is shown a magnified view of the\n2 K loops after the sample being cooled with HFC=±3\nT. Differently than for the ZEB curves, for CEB the two\ncurves are nearly symmetrically displaced with respect\nto the magnetization axis. Here the ±3 T cooling field\nis strong enough to flip the spontaneous magnetization,\nand the effect of the internal field becomes negligible.\nFig. 7(c) shows the temperature dependence of HCEB\nandHC. The CEB evolutionis similar to ZEB.Above Tf/s45/s54 /s45/s51 /s48 /s51 /s54/s45/s48/s46/s56/s45/s48/s46/s52/s48/s46/s48/s48/s46/s52/s48/s46/s56\n/s45/s50/s48 /s45/s49/s53 /s49/s53 /s50/s48/s45/s48/s46/s48/s50/s48/s46/s48/s48/s48/s46/s48/s50\n/s48 /s53 /s49/s48 /s49/s53 /s50/s48 /s50/s53 /s51/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s48/s46/s56/s49/s46/s48\n/s48/s46/s48/s48/s46/s51/s48/s46/s54/s48/s46/s57/s49/s46/s50/s49/s46/s53/s72 /s32/s40/s107/s79/s101/s41/s53/s32/s75/s40/s97/s41/s32\n/s32/s77/s32 /s40\n/s66/s47/s102/s46/s117/s46 /s41/s32\n/s40/s98/s41\n/s72 /s32/s40/s107/s79/s101/s41/s77/s32 /s40\n/s66/s47/s102/s46/s117/s46 /s41\n/s124/s72\n/s69/s66/s124/s61/s49/s48/s53/s48/s32/s79/s101/s124/s72\n/s69/s66/s124/s61/s49/s48/s55/s48/s32/s79/s101\n/s32/s32\n/s40/s99/s41\n/s32/s32/s32\n/s84/s32/s40/s75/s41/s72\n/s67/s69/s66/s32/s40/s107/s79/s101/s41\n/s72\n/s67/s32/s40/s84/s41\n/s32/s45/s48/s46/s50/s48/s46/s48/s48/s46/s50/s45/s54 /s45/s51 /s48 /s51 /s54/s72 /s32/s40/s84/s41\n/s32/s77 /s32 /s40\n/s66 /s47/s102/s46/s117/s46 /s41\n/s32/s32\nFIG. 7: (a) M(H) loop at 5 K after cooling the system with\nHFC= 3 T. The inset shows the deconvolute curve (see text).\n(b) Magnified view of the curves measured at 2 K after the\nsample being field cooled with HFC±3 T. (c)HCEBandHC\nevolution with T.\ntheHCEBbecomes negligible. It shows the importance\noftheSGphasetotheEBobservedonLa 1.5Ca0.5CoIrO 6.\nIt can be also observed that the EB effect is greatly en-\nhanced when the system is field cooled. At 2 K one have\nHCEB≃1070 Oe. On the FC procedure, the pinning of\nthe SG spins is favored already from above Tfdown to\nlow-T, and these spins get freezed on the field direction.\nIn EB systems, repeating the M(H) loop may lead to\nrelaxation of uncompensated spin configuration at the\ninterface. Consequently, HEBdepends on the number of\nconsecutive hysteresis loops measured. This property is9\n/s45/s49/s46/s54/s52 /s45/s49/s46/s54/s48 /s45/s49/s46/s53/s54/s45/s48/s46/s57/s48/s46/s48/s48/s46/s57\n/s49 /s50 /s51 /s52 /s53 /s54 /s55/s48/s46/s55/s48/s46/s56/s48/s46/s57/s49/s46/s48/s49/s46/s49/s110/s32/s61/s32/s55\n/s32/s32\n/s32/s32\n/s72 /s32/s40/s84/s41/s77 /s32/s40/s49/s48/s45/s51\n/s66/s47/s102/s46/s117/s46 /s41/s110/s32/s61/s32/s49\n/s32/s72\n/s67/s69/s66\n/s32/s102/s105/s116/s32/s98/s121/s32/s69/s113/s46/s54\n/s72/s121/s115/s116/s101/s114/s101/s115/s105/s115/s32/s110/s117/s109/s98/s101/s114/s32/s40/s110/s41\n/s32/s32/s32/s72\n/s67/s69/s66/s32/s40/s107/s79/s101/s41\nFIG. 8: Training effect of CEB at 2 K. The inset shows HCEB\nas a function of the hystereis number (n). The solid line\nrepresents the fitting of the experimental data to Eq. 6.\ncalledtrainingeffect. ForLa 1.5Ca0.5CoIrO 6thisbehavior\nwas investigated in both ZEB and CEB cases. For CEB,\n7 consecutive loops were measured at 2 K, after cooling\nthe sample in the presence of HFC= 3 T. Fig. 8 shows\na detailed view of the 7 loops close to the M= 0 axis.\nThe arrow indicates a systematic evolution of the curves.\nThe dependence of HCEBon the number of repeating\ncycles (n) is shown on inset. As can be observed, HCEB\ndecreasesmonotonicallywiththeincreasein n, indicating\nspinrearrangementattheinterface. The ndependenceof\nHCEBcan be fit to a model considering the contribution\nofboththefrozenspinsandtheuncompensatedrotatable\nspins at the interface55,60\nHn\nCEB=H∞\nCEB+Afe(−n/Pf)+Are(−n/Pr),(6)\nwherefandrdenote the frozen and rotatable spin com-\nponents respectively. Eq. 6 fits the data very well, for\nH∞\nCEB= 708 Oe, Af= 4627 Oe, Pf= 0.3,Ar= 282 Oe,\nP3= 3.1. The fact Af>Arindicates the importance of\nthe SG phase to the EB effect, and Pr>Pfsuggests that\nthe rotatable spins rearrange faster than the frozen ones.\nFor the ZEB mode, it was observed only a very small de-\ncrease of HZEBfrom first to second loop, thereafter thesystem exhibits only negligible variation. This indicates\nthat after the first cycle, the frozen and uncompensated\nspins became quite stable at the interfaces.\nIV. CONCLUSIONS AND OUTLOOK\nIn conclusion, we haveshown that La 1.5Ca0.5CoIrO 6is\na RSG-like material, in which there are two magnetic or-\nderingsoftheAFM andFMphasesofCoionsat TN= 97\nK andTC= 86 K, respectively, and a SG-like transition\natTsg= 26.6 K. The frequency dependence of Tfob-\ntained from χ’acfollows the power law of the dynamical\nscaling theory. Regarding the χacmeasurements with\nappliedHdcfields, the system transits from conventional\nspin glass to cluster glass with increasing Hdc. The coex-\nistence of conventional and glassy magnetic states leads\nto an exotic magnetic behaviorin the ZFC T-dependence\nof magnetization curve, in which the system can undergo\nthree magnetic reversals. Magnetization as a function of\nHdcsuggest a ZEB effect at low- T, related to the FM-\nAFM-SG interfaces. When the sample is cooled in the\npresence of an applied magnetic field, the EB effect is\nenhanced. XPS, XANES, XMCD and electronic struc-\nture calculations results corroborate our argument that\nthe magnetization reversals and the EB effect can be\nboth understood in terms of the same underlying mech-\nanism,i.e., are consequences of the Ir magnetic frustra-\ntion caused by the competing interactions with its neigh-\nboring Co ions. To verify these and other conjectures\ndiscussed in the text, other techniques such as neutron\nscattering, torque magnetometry and electronic spin res-\nonance are necessary.\nAcknowledgments\nThis work was supported by CNPq, FAPERJ,\nFAPESP and CAPES (Brazil). We thank E. Granado\nfor the helpful discussions. F. Stavale thanks the Sur-\nface and NanostructuresMultiuser Lab at CBPF and the\nMPG partnergroup programm. LNLS is acknowledged\nfor concession of beam time.\n∗Electronic address: lbufaical@ufg.br\n1J. Knolle, G.-W. Chern, D. L. Kovrizhin, R. Moessner, and\nN. B. Perkins, Phys. Rev. Lett. 113, 187201 (2014).\n2K.BinderandA.P.Young,Rev.Mod.Phys. 58, 801(1986).\n3J. A. Mydosh, Spin Glasses: An Experimental Introduction\n(Taylor & Francis, London, 1993).\n4D. K. Singh and Y. S. Lee, Phys. Rev. Lett. 109, 247201\n(2012).\n5J. E. Greedan, J. Mater. Chem. 11, 37 (2001).\n6J. M. De Teresa et al., Phys. Rev. Lett. 76, 18 (1996).7A. K. Kundu, P. Nordblad, and C. N. R. Rao, Phys. Rev.\nB72, 144423 (2005).\n8Q. Xuet al., Nature Sci. Rep 5, 9093 (2015).\n9D. Niebieskikwiat and M. B. Salamon, Phys. Rev. B 72,\n174422 (2005).\n10J. Nogu´ es and I. K. Schuller, J. Magn. Magn. Mater. 192,\n203 (1999).\n11M. Ali, P. Adie, C. H. Marrows, D. Greig, B. Hickey, and\nR. L. Stamps, Nature Mater. 6, 70 (2007).\n12M. Gruyters, Phys. Rev. Lett. 95, 077204 (2005).10\n13L. T. Coutrim et al., J. Solid State Chem. 221, 373 (2015).\n14A. Kolchinskaya et al., Phys. Rev. B 85, 224422 (2012).\n15J. C. Cezar et al., J. Synchrotron Radiat. 17, 93 (2010).\n16B. Ravel and M. Newville, J. Synchrotron Radiat. 12, 537\n(2005).\n17P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka,\nand J. Luitz, WIEN2k, An Augmented Plane Wave + Local\nOrbitals Program for Calculating Crystal Properties (Karl -\nheinz Schwarz, Techn. Universitat Wien, Austria), 2001.\n18S. C. Petitto, E. M. Marsh, G. A. Carson, and M. A. Lan-\ngell, J. Mol. Catal. A: Chem. 281, 49 (2008).\n19J. van Elp et al., Phys. Rev. B 44, 6090 (1991).\n20V. M. Jimenez, A. Fernandez, J. P. Espinos, and A. R.\nGonzalez-Elipe, J. Electron. Spectrosc. Relat. Phenom. 71,\n61 (1995).\n21M. Hassel and H.-J. Freund, Surf. Sci. Spectra 4, 273\n(1996).\n22C. A. F. Vaz, D. Prabhakaran, E. I. Altman, and V. E.\nHenrich, Phys. Rev. B 80, 155457 (2009).\n23C. R. Brundle, T. J. Chuang, and D. W. Rice, Surface Sci.\n60, 286 (1976).\n24R. P. Gupta and S. K. Sen, Phys. Rev. B 12, 1 (1975).\n25T. Ivanova, A. Naumkin, A. Sidorov, I. Eremenko and M.\nKiskin, J. Electron. Spectrosc. Relat. Phenom. 156-158 ,\n200 (2007).\n26M. C. Biesinger et al., Appl. Surface Sci. 257, 2717 (2011).\n27B. Raveau and Md. Motin Seikh, Cobalt Oxides: From\nCrystal Chemistry to Physics (Wiley-VCH, Weinheim,\n2012).\n28T. C. Koethe, Ph.D. thesis, Universit¨ at zu K¨ oln, 2007.\n29D. Niebieskikwiat et al., Phys. Rev. B 62, 5 (2000).\n30See Supplemental Material below for details of the magne-\ntometry results, x-ray near edge structure (XANES), x-ray\nmagnetic circular dichroism (XMCD) and electronic struc-\nture calculations, which includes Refs. [31-37].\n31T. Deyet al., Phys. Rev. B 93, 014434 (2016).\n32J. St¨ ohr and H. K¨ onig, Phys. Rev. Lett. 75, 3748 (1995).\n33B. T. Thole, P. Carra, F. Sette, andG. vanderLaan, Phys.\nRev. Lett. 68, 1943 (1992).\n34P. Carra, B. T. Thole, M. Altarelli, and X. Wang, Phys.\nRev. Lett. 70, 694 (1993).\n35C. T. Chen et al., Phys. Rev. Lett. 75, 152 (1995).\n36J. P. Perdew et al., Phys. Rev. Lett. 100, 136406 (2008).\n37I. D. Seymour, A. Chroneos, J. A. Kilner, and R. W.\nGrimes, Phys. Chem. Chem. Phys. 13, 15305 (2011).\n38M. Dlouh´ a et al., J. Magn. Magn. Mater. 322, 1189 (2010).\n39P. D.Battle, J. G. Gore, R.C. Hollyman, andA.V.Powell,\nJ. Alloys and Comp. 218, 110 (1995).\n40J. B. Goodenough, Magnetism and Chemical Bond (Inter-\nscience, New York, 1963).\n41Housung Seo, Agham Posadas and Alexander A. Demkov,\nPhys. Rev. B 86, 014430 (2012).\n42Sun-Woo Kim et al., Phys. Rev. Lett. 115, 096401 (2015).\n43Md. Motin Seikh et al., Chem. Mater. 20, 231 (2008).\n44H. Singh, H. Ghosh, T. V. Chandrasekhar Rao, A. K.\nSinha, and P. Rajput, J. Appl. Phys. 116, 214106 (2014).\n45V. K. Anand, D. T. Adroja, and A. D. Hillier, Phys. Rev.\nB85, 014418 (2012).\n46J. Souletie and J.L. Tholence, Phys. Rev. B 32, 516(R)\n(1985).\n47P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49,\n3 (1977).\n48A. Malinowski et al., Phys. Rev. B 84, 024409 (2011).\n49J. R. L. Almeida and D. J. Thouless, J. Phys. A 11, 983(1978).\n50V. K. Anand, D. T. Adroja, A. D. Hillier, W. Kockelmann,\nA. Fraile, and A. M. Strydom, J. Phys.: Cond. Matter 23,\n276001 (2011).\n51S. Mukherjee, R. Ranganathan, P. S. Anilkumar, and P.\nA. Joy, Phys. Rev. B 54, 9267 (1996).\n52K. De, M. Patra, S. Majumdar, and S. Giri, J. Phys.:\nCond. Matter 40, 7614 (2007).\n53A. K. Nayak et al., Phys. Rev. Lett. 110, 127204 (2013).\n54B. M. Wang et al., Phys. Rev. Lett. 106, 077203 (2011).\n55T. Maity, S. Goswami, D. Bhattacharya, and S. Roy, Phys.\nRev. Lett. 110, 107201 (2013).\n56J. J. Becker, IEEE Trans. Mag. MAG-12 , 6 (1976).\n57O. Benda, J. Bydzovisk´ y, P. Krivos´ ık, and E. Us´ ak, J.\nMagn. Magn. Mater. 215, 644 (2000).\n58L. Pi, S. Zhang, S. Tan, and Y. Zhanga, App. Phys. Lett.\n88, 102502 (2006).\n59L. Klein, App. Phys. Lett. 89, 036101 (2006).\n60S. K. Mishra, F. Radu, H. A. Durr, and W. Eberhardt,\nPhys. Rev. Lett. 102, 177208 (2009).11\n/s55/s55/s48/s48 /s55/s55/s50/s48 /s55/s55/s52/s48 /s55/s55/s54/s48 /s55/s55/s56/s48 /s55/s56/s48/s48 /s55/s56/s50/s48 /s55/s56/s52/s48/s48/s46/s48/s48/s46/s50/s48/s46/s52/s48/s46/s54/s48/s46/s56/s49/s46/s48/s49/s46/s50/s49/s46/s52/s49/s46/s54\n/s32\n/s32/s76/s97\n/s50/s67/s111/s73/s114/s79\n/s54\n/s32/s76/s97\n/s49/s46/s53/s67/s97\n/s48/s46/s53/s67/s111/s73/s114/s79\n/s54\n/s32/s76/s97/s67/s111/s79\n/s51/s32/s91/s67/s111/s51/s43\n/s93\n/s32/s67/s111/s79/s32/s91/s67/s111/s50/s43\n/s93/s40/s69 /s41\n/s69/s32/s40/s101/s86/s41/s67/s111/s32 /s75 /s32/s101/s100/s103/s101\nSupplementalFIG. 1: Normalized Co Kedge XANESspectra\nof La2CoIrO 6and La 1.5Ca0.5CoIrO 6at room temperature.\nThe references LaCoO 3and CoO XANES spectrum is also\nshown for comparison.\nSupplementary Material: “Compensation\ntemperatures and exchange bias in\nLa1.5Ca0.5CoIrO 6”\nX-ray near edge structure (XANES)\nRoom temperature x-ray near edge structure\n(XANES) measurements were performed in the dis-\npersive x-ray absorption (DXAS) beam line at the\nBrazilian Synchrotron Light Laboratory (LNLS)1. The\nedge step normalization of the data was performed\nafter a linear pre-edge subtraction and the regression\nof a quadratic polynomial beyond the edge, using the\nsoftware ATHENA2.\nThe normalized Co K-edge XANES spectrum µ(E) of\nLa2CoIrO 6and La 1.5Ca0.5CoIrO 6are given in Fig. 1.\nThe references LaCoO 3and CoO XANES spectrum are\nalso shown for comparison. Interestingly, our results in-\ndicate the presence of Co3+already at the parent com-\npound, which was also observed on the XPS. The small\nshift to higher energies obseved for La 1.5Ca0.5CoIrO 6\nsuggests an increase in the proportion of Co3+due to\nCa2+substitution on La3+site.\nThe normalized Ir L3-edge XANES spectrum µ(E)\nof La2CoIrO 6and La 1.5Ca0.5CoIrO 6are given in Fig.\n2. Our XANES measurements indicate no appreciable\nchange in the Ir valence by calcium doping. This is\nin agreement with the magnetometry results and to the\nXPS spectra at Ir 4 fregion (not shown). However, it\ncan be observed a small variation on the wavelength in-\ntensity from La 2CoIrO 6to La1.5Ca0.5CoIrO 6. Although\nour results indicate a majority of Ir4+, the possible va-\nlence mixing in Ir sublattice can not be discarded. Es-\npecially if we assume the oxygen content to be nearly\nstoichiometric, it should be expected a few percentage\nof Ir5+ions. Recent reports indicate long-range mag-\nnetic order in Ir5+-based double-perovskites3, hence it\ncould contribute to the magnetic behavior observed for\nLa1.5Ca0.5CoIrO 6./s49/s49/s49/s56/s48 /s49/s49/s50/s48/s48 /s49/s49/s50/s50/s48 /s49/s49/s50/s52/s48 /s49/s49/s50/s54/s48 /s49/s49/s50/s56/s48 /s49/s49/s51/s48/s48 /s49/s49/s51/s50/s48 /s49/s49/s51/s52/s48/s48/s46/s48/s48/s48/s46/s50/s53/s48/s46/s53/s48/s48/s46/s55/s53/s49/s46/s48/s48/s49/s46/s50/s53/s49/s46/s53/s48/s49/s46/s55/s53/s50/s46/s48/s48/s50/s46/s50/s53\n/s32/s76/s97\n/s50/s67/s111/s73/s114/s79\n/s54\n/s32/s76/s97\n/s49/s46/s53/s67/s97\n/s48/s46/s53/s67/s111/s73/s114/s79\n/s54/s40/s69 /s41\n/s69/s32/s40/s101/s86/s41/s73/s114/s32 /s76\n/s51/s32/s101/s100/s103/s101\nSupplemental FIG. 2: Normalized Ir L3edge XANES spectra\nof La2CoIrO 6and La 1.5Ca0.5CoIrO 6at room temperature.\n/s49/s49/s49/s54/s48 /s49/s49/s49/s56/s48 /s49/s49/s50/s48/s48 /s49/s49/s50/s50/s48 /s49/s49/s50/s52/s48 /s49/s49/s50/s54/s48 /s49/s49/s50/s56/s48 /s49/s49/s51/s48/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48/s49/s46/s53/s50/s46/s48/s50/s46/s53/s40/s69/s41\n/s69/s32/s40/s101/s86/s41/s45/s48/s46/s48/s49/s48/s46/s48/s48/s48/s46/s48/s49/s48/s46/s48/s50/s48/s46/s48/s51/s48/s46/s48/s52/s48/s46/s48/s53\n/s32/s88/s65/s78/s69/s83/s32/s115/s105/s103/s110/s97/s108\n/s32/s88/s77/s67/s68/s32/s115/s105/s103/s110/s97/s108/s32/s32/s88/s77 /s67/s68/s76/s97\n/s50/s67/s111/s73/s114/s79\n/s54\n/s73/s114/s32 /s76\n/s51/s32/s101/s100/s103/s101\nSupplemental FIG. 3: XANES and XMCD spectrum at the\nIrL3edge in La 2CoIrO 6.\nX-ray magnetic circular dichroism (XMCD)\nX-ray magnetic circular dichroism (XMCD) measure-\nments at the Ir L2,3edges were performed in the DXAS\nbeam line at LNLS1, with a calculated degree of circular\npolarizationof ∼75%. A rotative permanent magnet ap-\nplied 0.9 T at the sample, both parallel and antiparallel\nto the x-ray beam direction.\nIn Figs. 3 and 4 we present the XANES and XMCD\nspectra of La 2CoIrO 6at the Ir L3andL2edges, re-\nspectively, at 60 K. By applying the well known sum\nrules which relates the integrated XAS and XMCD sig-\nnals to polycrystalline samples (neglecting the magnetic\ndipole contribution4) we could extract the spin and or-\nbital moments5.\nFor La 2CoIrO 6we obtain for the Ir moments an or-\nbital magnetic moment µorb=−0.14(1)µBand a spin\nmagnetic moment µspin=−0.15(1)µB, thus resulting\nin a total magnetic moment µtotal=−0.29(1)µBper Ir\nandµorb/µspin= 0.93. These values are very close to the\nderived by Kolchinskaya et al.6.12\n/s49/s50/s55/s56/s48 /s49/s50/s56/s48/s48 /s49/s50/s56/s50/s48 /s49/s50/s56/s52/s48 /s49/s50/s56/s54/s48 /s49/s50/s56/s56/s48 /s49/s50/s57/s48/s48/s48/s46/s48/s48/s48/s46/s50/s53/s48/s46/s53/s48/s48/s46/s55/s53/s49/s46/s48/s48/s49/s46/s50/s53/s49/s46/s53/s48\n/s73/s114/s32 /s76\n/s50/s32/s101/s100/s103/s101/s32/s88/s65/s78/s69/s83/s32/s115/s105/s103/s110/s97/s108\n/s32/s88/s77/s67/s68/s32/s115/s105/s103/s110/s97/s108/s76/s97\n/s50/s67/s111/s73/s114/s79\n/s54/s40/s69/s41\n/s69/s32/s40/s101/s86/s41/s45/s48/s46/s48/s48/s52/s48/s46/s48/s48/s48/s48/s46/s48/s48/s52/s48/s46/s48/s48/s56/s48/s46/s48/s49/s50/s32/s88/s77 /s67/s68\nSupplemental FIG. 4: XANES and XMCD spectrum at the\nIrL2edge in La 2CoIrO 6.\n/s49/s49/s49/s54/s48 /s49/s49/s49/s56/s48 /s49/s49/s50/s48/s48 /s49/s49/s50/s50/s48 /s49/s49/s50/s52/s48 /s49/s49/s50/s54/s48 /s49/s49/s50/s56/s48 /s49/s49/s51/s48/s48/s48/s46/s48/s48/s46/s53/s49/s46/s48/s49/s46/s53/s50/s46/s48\n/s73/s114/s32 /s76\n/s51/s32/s101/s100/s103/s101/s32/s88/s65/s78/s69/s83/s32/s115/s105/s103/s110/s97/s108\n/s32/s88/s77/s67/s68/s32/s115/s105/s103/s110/s97/s108/s76/s97\n/s49/s46/s53/s67/s97\n/s48/s46/s53/s67/s111/s73/s114/s79\n/s54/s40/s69/s41\n/s69/s32/s40/s101/s86/s41/s45/s48/s46/s48/s48/s48/s53/s48/s46/s48/s48/s48/s48/s48/s46/s48/s48/s48/s53/s48/s46/s48/s48/s49/s48/s48/s46/s48/s48/s49/s53/s88/s77 /s67/s68\nSupplemental FIG. 5: XANES and XMCD spectrum at the\nIrL3edge in La 1.5Ca0.5CoIrO 6.\nFig. 5 shows the XANES and XMCD spectra of\nLa1.5Ca0.5CoIrO 6at the Ir L3edge at 60 K. No XMCD\nsignal was observed for L2edge, thus it was consid-\nered to be zero. Following the same procedure done\nfor La 2CoIrO 6, we obtain for the Ir moments µorb=\n−0.009(1)µBandµspin=−0.013(1)µB, thusµtotal=\n−0.022(1)µBper Ir and µorb/µspin= 0.69. This very\nsmall value in respect to the expected moment for a\nS= 1/2 confirms that the Ir4+ions are frustrated due\nto the AFM coupling of its Co2+neighbors.\nMagnetometry\nAs discussed in the main text, a shift in the magneti-\nzation as a function of applied field can be observed inconventional FM/FIM materials if a minor M(H) loop\nis measured, i.e., anM(H) curve with the maximum ap-\nplied field ( Hm) not large enough to the system achieve\nthe magnetic saturation. These minor loops are usually\nhighly asymmetric along both the field and magnetiza-\ntion axis. In order to further evidence that the EB ob-\nserved for La 1.5Ca0.5CoIrO 6is not related to a minor\nloop effect, we measuredminor loopswith Hm= 0.5T at\nseveral temperatures. Fig. 6(a) shows the minor M(H)\nloop measured at 5 K. As can be observed, the curve\nis highly asymmetric, exhibiting a large shift along the\nMaxis. This is completely different from the curve for\nHm= 4 T, which shows no appreciable asymmetry along\nthemagnetizationaxis. Fig6(b)showsthe T-dependence\nofHEB=|H++H−|/2 for both the loops with Hm= 0.5\nT andHm= 4 T, for comparison. For the 4 T loops the\nHEBvanishes below Tfwhile for the 0.5T loops the shift\npersists above Tfand only goes to zero on the paramag-\nnetic state. If the HEBobserved for the Hm= 4 T loops\nwere due to a minor loop effect, it should be expected to\npersist up to ∼85 K, in resemblance to the Hm= 0.5\nT curve. This remarkable difference between the curves\nindicate that the HEBobserved for the Hm= 4 T loop\nis an exchange biased phenomena which is intrinsically\nrelated to the RSG state.\nHere is important to discuss the concept of zero mag-\nnetic field for the experimental apparatus used. In order\nto minimize the remanent magnetization on the magnet,\nthe sample was always taken to the paramagnetic state\nfromone measurementtoanother, andthe magneticfield\nwas sent to zero on the oscillating mode. But this does\nnot warrant a precise zero field. To further confirm the\nresults here described we have also heated up to room- T\nand shut down the magnet, in order to ensure that there\nwas no trapped flux on the magnet, and then performed\nZFC measurements. For the checking M(H) loops the\nsample exhibit the same EB effect, indicating that the\nunidirectional anisotropy and ZEB here described are in-\ntrinsic of the material and not due to some experimental\nartifact.\nElectronic structure calculations\nThe band structure calculations were performed using\nthe WIEN2k softwarepackage7. The FM and AFM cases\nwere calculated with and without spin-orbit coupling on\nthe Ir 5dlevels. The spin-orbit effect on 3 dlevels is less\nimportant and was not included for the Co atoms. The\nexchange and correlation potential used was the PBEsol\nimplementation of the GGA8. The wave function of the\nvalence electrons was expanded using more than 193000\nplane waves. The self consistent potential was obtained\nsampling 343 points in the Brillouin zone. The conver-\ngence criteria were set to 10−5eV on the total energy\nand 10−3e−on the electronic charges.\nTableIgivestheenergiesandmagneticmomentsofthe\nLa1.5Ca0.5CoIrO 6compound in the PM, FM and AFM13\n/s45/s52/s48/s48/s48 /s45/s50/s48/s48/s48 /s48 /s50/s48/s48/s48 /s52/s48/s48/s48/s45/s48/s46/s48/s53/s45/s48/s46/s48/s50/s48/s46/s48/s49/s48/s46/s48/s52/s48/s46/s48/s55\n/s48 /s50/s48 /s52/s48 /s54/s48 /s56/s48 /s49/s48/s48/s45/s49/s48/s48/s48/s49/s48/s48/s50/s48/s48/s51/s48/s48/s57/s48/s48/s49/s48/s53/s48\n/s32/s32\n/s32/s32\n/s72/s32/s40/s79/s101/s41/s77 /s32/s40\n/s66/s47/s102/s46/s117/s46 /s41/s40/s97/s41\n/s40/s98/s41\n/s84/s32/s40/s75/s41/s72\n/s69/s66/s32/s40/s79/s101/s41\n/s32/s72\n/s109/s32/s61/s32/s48/s46/s53/s32/s84\n/s32/s72\n/s109/s32/s61/s32/s52/s32/s84\nSupplemental FIG. 6: (a) Zero field cooled (ZFC) M(H) loop\nforHm= 0.5T atT= 5 K. (b) Hebevolution with tempera-\nture for the ZFC magnetization as a function of applied field\nfor theHm= 0.5T andHm= 4TM(H) loops.\nSupplemental TABLE I: Relative energies and magnetic mo-\nments of La 1.5Ca0.5CoIrO 6obtained from band structure cal-\nculations for different magnetic structures. The energies a re\nrelative to the paramagnetic case.\n∆E (eV) µCo(µB)µIr(µB)µ(µB/f.u.)\nParamagnetic 0 0 0 0\nFM -0.86 2.5 0.6 4.30\nFM+SOC -6.46 2.4 0.3 3.48\nAFM -0.93 2.4 0.6 0.07\nAFM+SOC -6.48 2.4 0.3 0.06\nphases. The FM and AFM structures present lower total\nenergies than the paramagnetic case. This shows that\nthe magnetic interactions are very important in this ma-\nterial. Further, the FM and AFM energiesdecreasewhen\nspin-orbit coupling is included. Moreover, the magnetic\nmoment of the Ir 5 delectrons shrink to half by the spin-\norbit interaction. The AFM ordering is the most sta-\nble structure, although the FM arrangement is relatively\nclose in energy. This indicates that the magnetic inter-\nactions present a large degree of frustration, and helpsSupplemental FIG. 7: Calculated total and partial density o f\nstates (DOS) for La 1.5Ca0.5CoIrO 6at AFM configuration.\nto explain the observed spin glass behavior in this ma-\nterial. Considering the ∼70%/30% of Co2+/Co3+and\nthe 9% of ASD experimentally observed, and assuming\nthe magnetic moments of the AFM and FM phases of\nTable I, the system’s magnetization can be calculated\nasM=MAFM+MFM= [(0.7 + 0.3×0.91)mAFM] +\n[(0.3×0.09)mFM] = 0.15µB/f.u, which is very close to\nthe low-Texperimental values, ∼0.13µB/f.u..\nFigure 7 presents the total and partial densities of\nstates for AFM La 1.5Ca0.5CoIrO 6. All contributions are\nsplit into the majority and minority spin states and the\nzeroenergycorrespondstothe Fermilevel. Only the con-\ntributions of the spin up transition-metal ion and their\nligands are shown (the spin down contribution are just\ncomplementary and do not add much to the discussion).\nThe La 4 fstates are extremely intense and were clipped\nto better visualize the other contributions. The Co 3 d\nand Ir 5dstates are split by the approximately Ohcrys-\ntal field into the t2gandegstructures. The O 2 pband\nappears strongly mixed with the metal states throughout\nthe valence band, revealing a large covalent contribution14\nto the bonding in this compound. This is especially true\nfor the Ir 5 dstates which show an even larger mixing due\nto the larger spatial extent of 5 dlevels. The majority Co\n3dand Ir 5dstates present a minimum at the Fermi level,\nwhich resemble that observed in half-metallic magnetic\nmaterials. Finally, the La 4 f, La 5dand Ca 3 dstates ap-\npear at much higher energies, exhibiting a mostly ionic\ncontribution to the electronic structure.The anti-site formation was also calculated, with a su-\npercell with 80 inequivalent atomic sites. This gives an\nanti-site concentration of about 12%, in line with the es-\ntimated 9% concentration. The difference in total energy\nbetween the disordered and perfect lattice was about 1.1\neV. This is similar to the 0.94 eV result obtained for\nanti-site formation in the related LnBaCoO 5.5double-\nperovskite9.\n∗Electronic address: lbufaical@ufg.br\n1J. C. Cezar et al., J. Synchrotron Radiat. 17, 93 (2010).\n2B. Ravel and M. Newville, J. Synchrotron Radiat. 12, 537\n(2005).\n3T. Deyet al., Phys. Rev. B 93, 014434 (2016).\n4J. St¨ ohr and H. K¨ onig, Phys. Rev. Lett. 75, 3748 (1995).\n5B. T. Thole, P. Carra, F. Sette, and G. van der Laan, Phys.\nRev. Lett. 68, 1943 (1992); P. Carra, B. T. Thole, M.\nAltarelli, and X. Wang, Phys. Rev. Lett. 70, 694 (1993);\nC. T. Chen et al., Phys. Rev. Lett. 75, 152 (1995).\n6A. Kolchinskaya, P. Komissinskiy, M. B. Yazdi, M. Vafaee,\nD. Mikhailova, N. Narayanan, H. Ehrenberg, F. Wilhelm,A. Rogalev, and L. Alff, Phys. Rev. B 85, 224422 (2012).\n7P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and\nJ. Luitz, WIEN2k, An Augmented Plane Wave + Local\nOrbitals Program for Calculating Crystal Properties (Karl -\nheinz Schwarz, Techn. Universitat Wien, Austria), 2001.\n8J. 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).\n9I. D. Seymour, A. Chroneos, J. A. Kilner, and R. W.\nGrimes, Phys. Chem. Chem. Phys. 13, 15305 (2011)."    },    {        "title": "1604.08780v2.Ferroelectrics_Manipulate_Magnetic_Bloch_Skyrmions_in_a_Composite_Bilayer.pdf",        "content": "Ferroelectrics Manipulate Magnetic Bloch Skyrmions in a Composite Bilayer\nZidong Wang\u0003and Malcolm J. Grimsony\nDepartment of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand\n(Dated: March 7, 2022)\nTheoretical investigation demonstrates that the composite bilayer (i.e., chiral-\nmagnetic/ferroelectric bilayer) o\u000bers the possibility of electric-induced magnetic Skyrmions\n[Phys. Rev. B 94, 014311 (2016)]. In this Article, we propose a micromagnetic model to\nphysically manipulate magnetic Bloch Skyrmions propagating in a chiral-magnetic thin \flm\nwith a polarized ferroelectric essential to drive the system through the converse magnetoelectric\ne\u000bect. E\u000bects caused by di\u000berent velocities of the propagation, sizes of the thin \flm, and strength\nof the magnetoelectric couplings strongly impact on quality and quantity of the magnetic Skyrmions.\nE-print: http://arxiv.org/abs/1604.08780\nI. INTRODUCTION\nMagnetic Bloch Skyrmions behave as stable particle-\nlike spin textures in the chiral-magnetic crystals [1],\nsuch as B20 compound metallic MnSi [2], FeGe [3],\nFe1\u0000xCoxSi [4], MnGe and Mn 1\u0000xFexGe [5], and mul-\ntiferroic Cu 2OSeO 3[6]. These materials have no inver-\nsion symmetry that can allow the emergence of mag-\nnetic Bloch Skyrmions, due to their non-centrosymmetric\nlattice structures [7]. In micromagnetics, this phe-\nnomenon is caused by two components: the nearest-\nneighbor (symmetric exchange) interaction and the in-\nherent Dzyaloshinskii-Moriya (asymmetric exchange) in-\nteraction [8]. The competition between them stabilizes\nthe helicity of magnetic Skyrmions [9]. Mathematically,\nthe Dzyaloshinskii-Moriya interaction Hdmiis the contri-\nbution of a non-linear exchange interaction between two\nneighboring magnetic spins, S1andS2[10, 11], written\nas\nHdmi=D\u0001[S1\u0002S2]; (1)\nwhereDis an oriented vector, which indicates the con-\nstrained helicity to the symmetric state. The nearest-\nneighbor interaction Hintcommonly exists in ferromag-\nnets as a linear exchange interaction,\nHint=J[S1\u0001S2]; (2)\nwhereJis the termed exchange coupling. Magnetic\nSkyrmion holds great potential for applications in spin-\ntronic memory devices, due to their self-protection be-\nhavior.\nSo far, magnetic Bloch Skyrmions have been observed\nin insulating multiferroics, i.e., Cu 2OSeO 3[6]. This mul-\ntiferroism o\u000bers an opportunity to generate magnetic\nSkyrmions by electric polarization [12]. It is due to the\nconverse magnetoelectric e\u000bect, which is the phenomenon\n\u0003Zidong.Wang@auckland.ac.nz\nym.grimson@auckland.ac.nzof inducing magnetization by applying an external elec-\ntric \feld [13]. Unfortunately, the multiferroic insulators\nrequire a low transition temperature, and have a limited\nmagnetic response, which is adverse for applications [14].\nBut composite multiferroics, which are an arti\fcially syn-\nthesized heterostructure of ferromagnetic and ferroelec-\ntric order, have a remarkable magnetoelectric coupling\ndue to the microscopic mechanism of the strain-stress ef-\nfect [15]. This coupling describes the in\ruence of electric\npolarization on the magnetization at interface [16].\nA previous investigation has discussed the magnetic\nBloch Skyrmions induced by an electric driving \feld in\na composite chiral-magnetic (CM) and ferroelectric (FE)\nbilayer [17]. In this Article, we demonstrate a micromag-\nnetic model in Sec. II, for generating and manipulating\nthe magnetic Bloch Skyrmions in a CM thin \flm, which\nis driven by a piece of mobile and polarized FE thin \flm.\nBoth of \flms are glued by a strong magnetoelectric cou-\npling. The dynamical behaviors in the CM layer and the\ndynamics of the FE layer are described in Sec. III. Results\nin Sec. IV show the creation and propagation of magnetic\nBloch Skyrmions, including e\u000bects of the propagation ve-\nlocity in Sec. IV A, the size of thin \flm in Sec IV B, and\nthe strength of magnetoelectric coupling in Sec. IV C.\nThe paper concludes with a discussion in Sec. V.\nII. MODEL\nFigure 1 illustrates the model of a composite bilayer,\nwhich consists a CM thin \flm at top, and a mobile FE\nthin \flm attached at bottom. The CM \flm can hold the\nmagnetic Bloch Skyrmions. The FE \flm has a smaller\nsize, and can be physically driven by the technology of\nmicroelectromechanical systems under the CM \flm. The\ncombination between them induces the converse magne-\ntoelectric e\u000bect. The animation of this dynamics is shown\ninMovie 1 in the Supplemental Material [18].\nThe magnetic component of the system is described\nby the classical Heisenberg model in a two-dimensional\nrectangular lattice. The magnetic spin is represented by\nSi;j= (Sx\ni;j;Sy\ni;j;Sz\ni;j), which is a normalized vector, i.e.,\nkSi;jk= 1, andi;j2[1;2;3;:::;N ] characterizes the lo-arXiv:1604.08780v2  [cond-mat.mes-hall]  26 Aug 20162\nFIG. 1. Schematic of the CM/FE heterostructure\nbilayer. The top layer represents the CM thin \flm, which\ncan construct magnetic Bloch Skyrmions, as shown in the red\ncircles; The smaller FE thin \flm is movable and coupled with\nthe CM thin \flm. See Movie 1 in the Supplemental Material\n[18].\ncation of each spin in the \flm. The Hamiltonian His\nde\fned by\nH=\u0000JX\ni;j[Si;j\u0001(Si+1;j+Si;j+1)]\n\u0000DX\ni;j[Si;j\u0002Si+1;j\u0001^x+Si;j\u0002Si;j+1\u0001^y]\n\u0000KzX\ni;j(Sz\ni;j)2\n\u0000gX\n~i;~j(Sz\n~i;~jP): (3)\nThe \frst term represents the nearest-neighbor exchange\ninteraction, and J\u0003=J=kBTis the dimensionless ex-\nchange coupling coe\u000ecient. The second term repre-\nsents the two-dimensional Dzyaloshinskii-Moriya inter-\naction [8] , and D\u0003=D=k BTis the dimensionless\nDzyaloshinskii-Moriya coe\u000ecient, and ^ xand ^yare the\nunit vectors of the x- and y-axes, respectively. The\nthird term represents the magnetic anisotropy, and K\u0003=\nK=k BTrepresents the dimensionless uniaxial anisotropic\ncoe\u000ecient in the z-direction. The last term repre-\nsents the magnetoelectric coupling, which is generally\ndescribed as a linear spin-dipole interaction [19], where\ng\u0003=g=kBTis the dimensionless strength of the magne-\ntoelectric coupling. The analytic expression of the mag-\nnetoelectric coupling can be linear or non-linear, particu-\nlarly with respect to the thermal e\u000bect [20]. A non-linear\nexpression has not been studied here, for simplicity and\ndue to their minor e\u000bects in the micromagnetic modeling.\nNote that, the magnetoelectric coupling was discussed by\nSpaldin et al. [21]. The strength of coupling is, however,\nunknown. Hence, we only use the low-energy excitations\nbetween the CM and FE layers. So we restrict ourselves\nto the linear expression of the magnetoelectric interac-\ntion. The coupling sites of magnetic spins, ~i;~j, to the FE\nlayer are variable. This is a result of a polarization pulse\npropagating through the CM layer. Beach et al. have\nphysically built a similar model in metallic ferromagnets\nwith electric current-driven dynamics [22].III. METHOD\nThe dynamics of magnetic spins in the CM layer has\nbeen studied by the Landau-Lifshitz equation [23], which\nnumerically solves the rotation of a magnetic spin in re-\nsponse to its torques [24],\n@Si;j\n@t=\u0000\r[Si;j\u0002He\u000b\ni;j]\u0000\u0015[Si;j\u0002(Si;j\u0002He\u000b\ni;j)];(4)\nwhere\ris the gyromagnetic ratio which relates the spin\nto its angular momentum, and \u0015is the phenomenological\ndamping term. He\u000b\ni;jis the e\u000bective \feld acting on each\nmagnetic spin, which is the functional derivative of the\nsystem Hamiltonian [Eq. (3)] with respect to the mag-\nnitudes of the magnetic spin in each direction [25], as\nHe\u000b\ni;j=\u0000\u000eH\n\u000eSi;j. This Landau-Lifshitz equation is solved\nby a fourth-order Range-Kutta method with a dimension-\nless time increment \u0001 t\u0003= 0:0001 of in all simulations.\nThe CM layer is large and stationary, the polarized\nFE layer is under the CM layer has a much smaller size.\nThus FE layer is transversely traveling along the CM\nlayer with a certain velocity. This technology refers to\nthe microelectromechanical systems. In simulations, the\nelectric dipoles in the FE layer are coupled locally with\nmagnetic spins in the CM layer. So the FE layer moves\nat a certain rate which characterizes the propagation ve-\nlocity of Skyrmions in the CM layer. Movie 1 shows the\nanimation of this dynamics in the Supplemental Material\n[18].\nIV. RESULTS\nTo investigate the dynamical manipulation of magnetic\nBloch Skyrmions, we implement a dimensionless param-\neter set:J\u0003= 1,D\u0003= 1,K\u0003= 0:1,g\u0003= 0:5,\r\u0003= 1,\nand\u0015\u0003= 0:1. Note that \\\u0003\" characterizes dimensionless\nquantity. The CM layer with NCM= 20\u0002100 magnetic\nspins, andNFE= 20\u000220 electric dipoles in the FE layer\nare used. Free boundary conditions and a random initial\nstate are applied. The propagation step-time is measured\nas the non-dimensional time period stopped on each po-\nsition, like an intermittent pulse, with a magnitude of\nT\u0003= 20=step.\nFigure 2 summarizes a time evolution that generates\na magnetic Bloch Skyrmion and manipulates it propagat-\ning along the CM layer. The CM layer is contacted with\na polarized FE thin \flm, which starts from the left, then\nmoves to right as shown in Fig. 1 . Initially, the mag-\nnetic domain walls are randomly located without any\nexternal energy addition on the system in Fig. 2(a) .\nFigures 2(b)!(c)!(d)!(e)show the generation of\na Skyrmion from natural alignment. Subsequently, this\nSkyrmion propagates though the CM layer, as shown in\nFigs. 2(e)!(f)!(g)!(h). Eventually, this Skyrmion\nstops at the right-hand side of thin \flm [ Fig. 2(h) ]. The3\nFIG. 2. Generation and propagation of a mag-\nnetic Bloch Skyrmion in the CM layer. (a) An ran-\ndomly helimagnetic state at start. (b)!(c)!(d)!(e)im-\nages show details of a Skyrmion generation in the CM \flm.\n(e)!(f)!(g)!(h) images show details of the Skyrmion\npropagating through the CM \flm. The color scale represents\nthe magnitude of the local z-componential magnetization. See\nMovie 2 in the Supplemental Material [18].\nfully dynamical process is shown in Movie 2 in the Sup-\nplemental Material [18].\nAs seen in Figs. 2(d)!(e)!(f)!(g), another par-\ntial Skyrmion at the edge been devoured, due to the free\nboundary condition. This can be avoided by using peri-\nodic boundary conditions. This will be studied later in\nSec. IV B: Sizes of Thin Film . Additionally, passage of\nthe FE \flm leaves a spin spiral alignment in the CM layer.\nThis is due to the existence of a \fnite Dzyaloshinskii-\nMoriya interaction in equilibrium.\nA. Velocity of Propagation\nWe next discuss the e\u000bects due to the propagation ve-\nlocity to the Skyrmions. Since the transverse travel of\nFE thin \flm can be manually controlled, Skyrmions are\ntracking this FE layer with the velocity with a short re-\nlaxation time. In this case, a large propagation velocity\nrepresents short time period of the FE layer to stay in\none position (or one step), i.e., small traveling step-time.\nFigure 3(a) shows two schematics demonstrating the\ngeneral issues of traveling (left) and \fnishing (right) in\nthe following results. In Fig. 3(b) , a slow propaga-\ntion velocity with the traveling step-time T\u0003= 30=step.\nThree Skyrmions have been generated and propagated.\nAs we drop the step-time to T\u0003= 20=step in Fig. 3(c) ,\nthe number of Skyrmions reduces to two, but they are\nhave similar size as in Fig. 3(b) . Subsequently, only one\nFIG. 3. Propagating Skyrmions with di\u000berent trav-\neling step-time, T\u0003. (a) Schematic of two issues: traveling\nand \fnishing. (b)T\u0003= 30=step, (c)T\u0003= 20=step, (d)\nT\u0003= 10=step, and (e)T\u0003= 5=step. The color scale repre-\nsents the magnitude of the local z-componential magnetiza-\ntion. See Movie 3 in the Supplemental Material [18].\nSkyrmion survived in Fig. 3(d) withT\u0003= 10=step. If a\nstep-time shorter than this value is used, it is too fast to\ncreate and propagate Skyrmions in the CM layer. This\nhas been shown in Fig. 3(e) withT\u0003= 5=step. The\ndynamical processes and the velocities comparison are\nshown in Movie 3 in the Supplemental Material [18].\nB. Size of Thin Film\nLarger size of the thin \flm o\u000bers more space to allow\nmore Skyrmions. Figure 4 exempli\fes four cases for\ndi\u000berent sizes of the composite bilayer. Figure 4(a)\nshows the CM layer contains NCM= 10\u0002100 magnetic\nspins, which generates one Skyrmion. Subsequently, a\nlarger layer with NCM= 20\u0002100 magnetic spins shows\nthree Skyrmions in Fig. 4(b) .Figure 4(c) shows \fve\nSkyrmions with a layer size of NCM= 30\u0002100 magnetic\nspins, and Fig. 4(d) shows seven Skyrmions with a layer\nsize ofNCM= 40\u0002100 magnetic spins. Consequently, the\nquantity of Skyrmions increased as the \flm size increases,\nbut the quality of Skyrmions is the same. Movie 4 in\nthe Supplemental Material animates these cases [18].\nInterestingly, Skyrmions are found to collect together\nnear the top of thin \flm in Figs. 4(b) ,(c)and(d).\nThis occurs due to the helimagnetically ordered struc-\nture which points to the upper-right corner, and gener-\nates Skyrmions in this direction. Remember that the left\nhand side in each image is the structure after FE \flm has\npassed. This behavior is also observed in Figs. 3(c) and\n(d).4\nFIG. 4. E\u000bects by di\u000berent sizes of the CM thin \flm,\nNCM. (a) NCM= 10\u0002100,(b)NCM= 20\u0002100,(c)NCM=\n30\u0002100, and (d)NCM= 40\u0002100. Each subplot shows two\nissues as shown in Fig. 3(a) . The color scale represents the\nmagnitude of the local z-componential magnetization. See\nMovie 4 in the Supplemental Material [18].\nIn another simulation, we replace the free boundaries\nby a periodic boundary condition, which linked the spins\nat the top and the bottom. Now the dynamics shows\nSkyrmions on a race track moving longitudinally. Dif-\nferent to the behavior shown from the system with free\nboundary condition. See Movie 6 in the Supplemental\nMaterial [18].\nC. Strength of Magnetoelectric Coupling\nThe electric-induced magnetic Bloch Skyrmions result\nfrom the magnetoelectric coupling between the electric\ndipoles to the magnetic spins. It is noteworthy that the\nstrength of magnetoelectric coupling plays an important\nrole in mediating the energy transfer to sustain the mag-\nnetic Skyrmions [17]. Therefore, we examined di\u000berent\nmagnetoelectric coupling strength in Fig. 5 . Such as,\ng\u0003= 0:25 in Fig. 5(a) ,g\u0003= 0:5 inFig. 5(b) ,g\u0003= 0:75\ninFig. 5(c) andg\u0003= 1 in Fig. 5(d) . Firstly, Fig. 5(a)\nshows an insu\u000ecient strength of the magnetoelectric cou-\npling to generate Skyrmions. The magnetic domain\nshows a spin spiral alignment. With increased strength\nof the magnetoelectric coupling in Figs. 5(b) and(c),\nboth of them generate and propagate two Skyrmions in\nthe CM layer. Figure. 5(b) has larger size of Skyrmions\nthan in Fig. 5(c) , since the magnetoelectric interaction\nin the former is weak compared to its Dzyaloshinskii-\nMoriya interaction. In Fig. 5(d) , the ample strength\nof magnetoelectric coupling dominates the response in a\nsaturated FM state. Movie 5 in the Supplemental Ma-\nterial animates these cases [18].\nTo determine the size of a Skyrmion, we use the\nspin-plot, and count the number of magnetic spins in\nFIG. 5. E\u000bects by di\u000berent strength of the magne-\ntoelectric couplings, g\u0003. (a) g\u0003= 0:25,(b)g\u0003= 0:5,(c)\ng\u0003= 0:75 and (d)g\u0003= 1. Each subplot shows two issues as\nshown in Fig. 3(a) . See Movie 5 in the Supplemental Mate-\nrial [18]. (e)A spin-plot image shows the Skyrmion part from\nright image in (c). The color scale represents the magnitude\nof the local z-componential magnetization. (f)The total size\nof Skyrmions versus the strength of magnetoelectric coupling,\ndetermined from the \fnishing image of each dynamics. The\ncurve through the points is a guide to the eye. See Fig. 1 in\nthe Supplemental Material [18].\na Skyrmion. An example of spin-plot is shown in\nFig. 5(e) , which involves two Skyrmions. The num-\nber of magnetic spins contributing to these Skyrmions\ncan be counted, which is the size of a Skyrmion. There-\nfore, a phase diagram parameterized by the total size of\nSkyrmions versus the strength of magnetoelectric cou-\nplingg\u0003is presented in Fig. 5(f) . In this \fgure, four\nkinds of regime are apparent. (1) For smaller g\u0003, the size\nof Skyrmions is zero due to the magnetoelectric energy\nbeing insu\u000ecient to generate Skyrmions, but the lattice\nforms spin spiral structure. (2) Slightly larger g\u0003gives a\nmixed regime of spin spirals and Skyrmions co-existing\nin the lattice. (3) Certain larger magnitudes of g\u0003gen-\nerate stable Skyrmions. This region shows a non-linear\ndecrease of the size of a Skyrmion with the increased\nmagnetoelectric coupling. (4) For larger g\u0003, the uniform\nmagnetization appears in this stage, due to the magne-\ntoelectric energy dominating energy contribution in the\nFM system. More details are shown in the Supplemental\nMaterial Fig. 1 [18].5\nV. CONCLUSION\nThis Article has shown that by using the converse\nmagnetoelectric e\u000bect in a composite CM/FE bilayer,\nmagnetic Bloch Skyrmions can be induced and manipu-\nlated by attaching a mobile polarized FE thin \flm. The\nquantity and quality of these Skyrmions correspond to\nthe conditions: (1) Propagation velocity. High speed of\nthe polarized FE layer restricts the number of Skyrmion\nformations. (2) Thin \flm size. Larger space requires\nmore Skyrmions to minimize the local energy contribu-\ntion; (3) Magnetoelectric coupling strength. The compe-\ntition between the magnetoelectric interaction and the\nDzyaloshinskii-Moriya interaction may occur di\u000berent\nstates in chiral-magnets. Excessive strength favors in the\ncentrosymmetric structure, like in ferromagnetism; insuf-\n\fcient strength shows a spin spiral state. Only a delicatebalance of the magnetoelectric coupling can o\u000ber the ex-\nistence of magnetic Skyrmions.\nSingle-phase multiferroics have persistent coupling be-\ntween the magnetic moments and the electric moments,\ndue to their solid crystallographic structures. But,\nthe coupling in the composite multiferroics can be eas-\nily varied by di\u000berent material combinations, external\nstress or heat. Therefore, it opens a novel approach on\nmagnetoelectric-induced Skyrmions in the composite bi-\nlayer. From an application viewpoint, our proposal has\nthe potential lead to a unique technology for the future\nSkyrmion based memory devices.\nACKNOWLEDGMENTS\nThe authors thank X.C. Zhang and F. Xu for discus-\nsions. Z.W. gratefully acknowledges Wang Yuhua, Zhao\nBingjin, Zhao Wenxia and Wang Feng for support.\n[1] U. R o\u0019ler, A. Bogdanov, and C. P\reiderer, Nature 442,\n797 (2006).\n[2] S. M uhlbauer, B. Binz, F. Jonietz, C. P\reiderer,\nA. Rosch, A. Neubauer, R. Georgii, and P. B oni, Sci-\nence323, 915 (2009).\n[3] X. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W. Zhang,\nS. Ishiwata, Y. Matsui, and Y. Tokura, Nat. Mater. 10,\n106 (2011).\n[4] X. Yu, Y. Onose, N. Kanazawa, J. Park, J. Han, Y. Mat-\nsui, N. Nagaosa, and Y. Tokura, Nature 465, 901 (2010).\n[5] K. Shibata, X. Yu, T. Hara, D. Morikawa, N. Kanazawa,\nK. Kimoto, S. Ishiwata, Y. Matsui, and Y. Tokura, Nat.\nNanotech. 8, 723 (2013).\n[6] S. Seki, X. Yu, S. Ishiwata, and Y. Tokura, Science 336,\n198 (2012).\n[7] X. Zhang, M. Ezawa, D. Xiao, G. P. Zhao, Y. Liu, and\nY. Zhou, Nanotech. 26, 225701 (2015).\n[8] N. Nagaosa and Y. Tokura, Nat. Nanotech. 8, 899 (2013).\n[9] S. Buhrandt and L. Fritz, Phys. Rev. B 88, 195137\n(2013).\n[10] I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958).\n[11] T. Moriya, Phys. Rev. 120, 91 (1960).\n[12] J. S. White, K. Pr\u0014 sa, P. Huang, A. A. Omrani,\nI.\u0014Zivkovi\u0013 c, M. Bartkowiak, H. Berger, A. Magrez, J. L.\nGavilano, G. Nagy, J. Zang, and H. M. R\u001cnnow, Phys.\nRev. Lett. 113, 107203 (2014).\n[13] Y.-H. Liu, Y.-Q. Li, and J. H. Han, Phys. Rev. B 87,\n100402 (2013).[14] J.-W. G. Bos, C. V. Colin, and T. T. M. Palstra, Phys.\nRev. B 78, 094416 (2008).\n[15] C.-W. Nan, Phys. Rev. B 50, 6082 (1994).\n[16] F. Xue, J. Hu, S. X. Wang, and J. He, Appl. Phys. Lett.\n106, 262902 (2015).\n[17] Z. D. Wang and M. J. Grimson, Phys. Rev. B 94, 014311\n(2016).\n[18] See Supplemental Material at\n10.13140/RG.2.1.2015.8326/1, for animations about\nthe dynamical results.\n[19] C.-L. Jia, T.-L. Wei, C.-J. Jiang, D.-S. Xue, A. Sukhov,\nand J. Berakdar, Phys. Rev. B 90, 054423 (2014).\n[20] L. Chotorlishvili, S. R. Etesami, J. Berakdar, R. Khome-\nriki, and J. Ren, Phys. Rev. B 92, 134424 (2015).\n[21] F. Th ole, M. Fechner, and N. A. Spaldin, Phys. Rev. B\n93, 195167 (2016).\n[22] S. Woo, K. Litzius, B. Kruger, M.-Y. Im, L. Caretta,\nK. Richter, M. Mann, A. Krone, R. M. Reeve,\nM. Weigand, P. Agrawal, I. Lemesh, M.-A. Mawass,\nP. Fischer, M. Klaui, and G. S. D. Beach, Nat. Mater.\n15, 501 (2016).\n[23] Y. Li, K. Xu, S. Hu, J. Suter, D. K. Schreiber, P. Ra-\nmuhalli, B. R. Johnson, and J. McCloy, J. Phys. D Appl.\nPhys. 48, 305001 (2015).\n[24] Z. D. Wang and M. J. Grimson, J. Appl. Phys. 118,\n124109 (2015).\n[25] Z. D. Wang and M. J. Grimson, J. Appl. Phys. 119,\n124105 (2016)."    },    {        "title": "1604.08833v1.Viewpoint__Opportunities_and_challenges_of_two_dimensional_magnetic_van_der_Waals_materials__magnetic_graphene_.pdf",        "content": "1 \n Viewpoint: Opportunities and challenges of two-dimensional  magnetic van \nder Waals materials: magnetic graphene?  \nJe-Geun Park1,2* \n1 Center for Correlated Electron Systems, I nstitute for Basic Science, S eoul 08826 , Korea  \n2 Department of Physics and Astronomy, Seoul National University , Seoul 08826, Korea  \n* Email: jgpark10@snu.ac.kr  \n \nAbstract : There has been a huge increase of interests in two -dimensional van der Waals materials \nover the pa st ten years or so with the conspicuous absence of one particular class of materials: \nmagnetic van der Waals systems. In this Viewpoint, we point it out and illustrate how we might be \nable to benefit from exploring these so -far neglected materials.  \n \nA new  material matters in condensed matter physics : so much so that if one looks at the history  of \nthe condensed matter physics over the last  half-a century one immediately realizes that there have \nbeen star materials  almost every decade. These then new classes of materials  shaped  and ha ve \nbeen continuously shaping the big questions of the time s. For example, there were spin glass, heavy \nfermion, high-temperature superconductors, manganites, and multiferroic  materials , to name only a \nfew.  \nThe recent entry of gra phene is no different from its predecessors, if not more revolutionary  \n[1, 2]. One particularly amazing aspect of the graphene physics is  how so much of the new physics \nwas, at least initially, observed in graphene produced by such a simple mechanical exfo liation  \nmethod using Scotch tape. This simpl e elegance of doing physics with Scotch tape  in graphene  \nimpressed  the community  so much that  it has ever since remain ed a method of first choice when \nit comes to producing monolayer van der Waals ( vdW) materials . With the enormous recent \ndevelopment s, several new vdW materials  have been discovered, or rediscovered to put it more \ncorrectly, and the list of the vdW materials is growing very fast  [3].  \nHowever, there is one particular class of systems : magnetic vdW  materials,  conspicuously \nmissing in the list  known to date . In Figure 1, we show the numbers of annual publications on the \nsubject of ‘van der Waals ’ as compared with those on the subject of ‘magnetic , exfoliation ’ for the \npast 15 years.  Looking at the st atistics, i t is striking that although there were over 600 papers \npublished in 2015  alone under the keyword of van der Waals materials there are less than 10 2 \n publications under the name of magnetic exfoliation. This statistics just amply illustrates how  much \nthe field of  the magnetic van der Waals materials has been underexplored . As we argue in the \nremainder of this paper, however , we are in  a very sorry stat e given the potential that would be \nmade possible  by this new class of materials. This paper, we ho pe, serves as a timely wake-up call \nfor this situation.  \n \nTraditionally, vdW or layered magnetic materials have been considered as useful candidates for the \nstudy of low -dimensional magnetic systems  [4]. Transition metal phosphorus trisuflide  (or \nthiophosphate ), TMPS 3, is one such example and its bulk properties  have been extensively studied \nby using various techniques  [5-11]. It is a very attractive aspect  from a material ’s point of view  that \nTMPS 3 can ho st several transition metal elements at the TM sites  with correspondingly diverse \nphysical properties : TM = Mn, Fe, Co, Ni, Zn, and Cd. One can also replace S by Se while keeping \nthe same crystal structure , adding more flexibility to a  choice of materials . This diversity in the \nmaterials with diffe rent physical properties will turn out to be a huge advantage  when it comes to  \nactual  applications.  \nInterestingly enough, all three principal spin Hamiltonians are reported in these materials: two-\ndimensional ( 2D) Ising system (FePS 3), 2D Heisenberg system (MnPS 3), and 2D XY system (NiPS 3, \nCoPS 3) [8, 9]. From a study of the critical behavior, however MnPS 3 was claimed to be closer to an \nXY-like system [10] . More recently, it was  theoretically proposed that a rare spin -valley coupling \nmight  be realized in one of these materials, MnPS 3 [12]. Another interesting theoretical finding is \nthat upon ca rrier doping in the range of 1014/cm2 the magnetic ground state can be tuned  from \nthe antiferromagnetic to ferromagnetic ground states [13]. Then MnPS 3 was reported to have a  \nlinear magnetoelectric (ME) coupling  induced by the magnetic ordering and claimed to be a pure \nferrotoroidic  compound [14]. Adding further motivation to this class of materials , TMPS 3 has a band \ngap of 1 .5 – 3.5 eV [15], nicely  matching  with the energy  range of visible lights.  \nTMPS 3 has a weak  van der Waals interaction between the layers and so can be easily cleavable. \nWith hindsight, it is rather su rprising to see why it has taken so long  to produce a monolayer of \nthese compounds . At least, now there are two independent reports for the realization of mono and \na few layers of these systems [16-18]. It is interesting to note that the magnetic elements form a \nhoneycomb lattice just like graphene so one can call it ‘ magnetic graphene ’.  \nBoth groups have used the S cotch-tape method to achieve their goals and characterized their \nsamples using the  AFM and Raman techniques. As in graphene  before , Raman spectroscopy  is 3 \n found to be  a very useful tool in determin ing the thickness  of TMPS 3: both E g and A 1g Raman peaks \nshow a clear thickness dependence  [16]. The other noticeable  exfoliated magnetic material is Bi-\nbased high -temperature superconductor  [3, 19]. With this successful mechanical exfoliation of TMPS 3, \nthe door is now widely  open to exploring  the physical properties on the scale of  few atomic layers \nand, more importantly, to exploit ing its  potentials  for novel devices . We note that with these huge \nopportunities it is a welcome sign to see other magnetic vdW materials joinin g this rare group: for \nexample, there have been reports on CrSiTe 3 [20]. \n \nOne can think of several applications for t he successful ly exfoliat ed magnetic  TMPS 3 monolayer . \nOne of the most obvious cases is to  use it for the  study of fundamental 2 D magnetism  with reducing \nthickness as illustrated in Fig. 2 . It sounds very strange , but to our best knowledge no experimental \ntest has been  done using a real magnetic material of the Onsager solution for 2 D Ising magnets \n[21]. The only experimental test which we are  aware  of was carried out  using sub -monolayer CH 4 \nabsorbed on graphite, an odd coincidence  [22]. It is not that we ever have any doubt about  the \nanswer that Onsager came up  some 70 years ago, nevertheless it would be fantastic  to see the \nresults  obtained  from a real magnetic material confirming this historic achievement . \nMoreover, with the variation of the magnetic atoms of TMPS 3 it will also be possible to extend \nthis test  of fundamental magnetism  to other spin Hamiltonian s and to demonstrate the Merin -\nWagner-Hohenberg  theorem  [23, 24] . Another advantage of having the magnetic vdW monolayer \nof TMPS 3 is that Mott physics  with strong correlation  might be naturally  realized in the  2D materials . \nIf found correct, it  will then open another window of fascinating  opportunities to explore correlated \nphysics on naturally occurring 2D systems. Furthermore, it will generally  be an interesting question \nhow other control parameters only available with the 2D magnetic systems: substrate and the width \nof the monolayer, af fect the transition temperature . More specific to TMPS 3, it will also be intriguing \nto examine  the strain effects on the magnetism as  a recent theor y suggested [ 25]. At the same time, \nwith the band gap of T MPS 3 nicely overlapping with the energy range of visible light s, it will be \ninteresting to investigate how the band gap varies as one reduces the thickness and /or the samples \nare put under  external  strain.  The other potentially more far -reaching applications will be found in \nits use in conjunction wit h other vdW mater ials such as graphene and many other vdW materials  \nas part of heterostructures. Over the past few years, we have witnessed an explosive growth of this  \nfield of v dW materials -based  heterostructures with numerous novel discoveries  ensuing therefrom  \n[26, 27]. One is left only to guess how the already fast -growing field will change with the introduction \nof this new functionality of magnetism to the arsenal of vdW materials.  4 \n Despite the high notes, we have to admit that challenges lie ahead, in particular  how to prepare \nthe sample in a controller manner, e.g. with an accurate thickness control. The other problem that \nmight hinder the progress is a lack of handy characterization tools. As most conventional techniques \nused for bulk magnetic mate rials have only limited usage for atomically thin magnetic vdW materials, \nwe are in a desperate need of new techniques. However, with  our own experience we can be sure \nthat the following  techniques will be found helpful  for the field  in future : Raman, AFM,  PEEM, MFM, \nand MOKE.  \n \nAll in all, w e have no illusion as to how difficult and challenging the roads ahead will be even  to \nachiev e any one  of the goals. However, failure or success will be another science-in -making in a \ntrue sense. Given the opportunities, it will certainly be worth taking.  \n \nWe acknowledge Cheol -Hwan Park for his critical reading  of the manuscript and suggestions. The \nwork at the IBS CCES was supported by the research program of Institute for Basic Science (IBS -\nR009-G1)  \n \nReferences  \n[1] Novoselov  K S, et al. 2004 Science  306 666 \n[2] Zhang  Y, Tan Y W, Stormer  H L, and Kim P 2005 Nature  438 7065 \n[3] Novoselov  K S, et al. 2005 Proc. Natl. Acad. Sci. U.S.A.  102 10451 \n[4] L. J. De Jong, Magnetic properties of layered transition metal compounds (Kluwer Academic \nPublishers, Amsterdam, 1990)  \n[5] Clement  R, Girerd  J J, and Morgenstern -Badarau  I 1980 Inorg. Chem.  19 2852 \n[6] Ouvrard  G, Brec R, and Rouxel  J 1985 Mater. Res. Bulletin  20 1181 \n[7] Brec R 1986 Solid State Ionics  22 3 \n[8] Joy P A and Vasudevan  S 1992 Phys. Rev. B 46 5425 \n[9] Wildes  A R, et al. 2015 Phys. Rev. B  92 224408 \n[10] Wildes  A R, et al. 2007 J. Magn. Magn. Mater.  310 1221 \n[11] Kurosawa  K, Saito  S, and Yamaguchi  Y, 1983 J. Phys. Soc. Jpn  52 3919 \n[12] Li X, et al. 2013 Proc. Natl. Acad. Sci. U.S.A.  110 3738 \n[13] Li X, et al. 2014 J. Am. Chem. Soc. 136 11065  \n[14] Ressouche  E, et al. 2010 Phys. Rev. B  82 100408(R)  5 \n [15] Brec R, et al. 1979 Inorg. Chem. 18 1814 \n[16] Kuo Ch-T, et al. 2016 Scientific Reports  6 20904  \n[17] Du K, et al. 2016 ACS Nano  10 1738. \n[18] Kuo Ch-T, et al. 2016 Current Appl. Phys.  16 404 \n[19] Sandilands  L J, et al. 2010 Phys. Rev. B  82 064503 \n[20] Lin M-W, et al. 2016 J. Mat. Chem C  4 315 \n[21] Onsager L 1944 Phys. Rev.  65 117 \n[22] Kim H K and Chan H H W 1984 Phys. Rev. Lett.  53 170 \n[23] Mermin N  D and Wagner H 1966 Phys. Rev. Lett.  17 1133 \n[24] Hohenberg P  C 1967 Phys. Rev.  158 383 \n[25] Sivadas  N, et al. 2015 Phys. Rev. B 91 235425 \n[26] Geim  A K and  Grigorieva  I V 2013 Nature  499 419 \n[27] Wang L, et al. 2013 Science  342 614 \n \n200120022003200420052006200720082009201020112012201320142015100200300400500600700Numbers of VdW papers0246810Numbers of Mag. VdW papers\n \nFigure 1 Number  of annual publications over the past 15 years with the key words of (left axis  & \nblue colour) ‘ van der Waals ( vdW)’ and (right axis  & red colour) ‘magnetic exfoliation  (magnetic \nvdW)’. We used the Google scholar search engine to collect the statistics . 6 \n  \nFigure 2 Schematic  of how one can study the thickness dependence of the fundamental magnetic \nproperties  using the magnetic v dW materials  such as the transition temperatures and the ground \nstates.  \n"    },    {        "title": "1605.02524v1.The_lifetime_cost_of_a_magnetic_refrigerator.pdf",        "content": "Published in International Journal of Refrigeration, Vol. 63 , 48-62, 2016\nDOI: 10.1016/j.ijrefrig.2015.08.022\nThe lifetime cost of a magnetic refrigerator\nR. Bjørk, C.R.H. Bahl and K. K. Nielsen\nAbstract\nThe total cost of a 25 W average load magnetic refrigerator using commercial grade Gd is calculated using a\nnumerical model. The price of magnetocaloric material, magnet material and cost of operation are considered,\nand all influence the total cost. The lowest combined total cost with a device lifetime of 15 years is found to\nbe in the range $150-$400 depending on the price of the magnetocaloric and magnet material. The cost of\nthe magnet is largest, followed closely by the cost of operation, while the cost of the magnetocaloric material\nis almost negligible. For the lowest cost device, the optimal magnetic field is about 1.4 T, the particle size is\n0.23 mm, the length of the regenerator is 40-50 mm and the utilization is about 0.2, for all device lifetimes and\nmaterial and magnet prices, while the operating frequency vary as function of device lifetime. The considered\nperformance characteristics are based on the performance of a conventional A+++refrigeration unit. In a rough\nlife time cost comparison between the magnetic refrigeration device and such a unit we find similar costs, the\nformer being slightly cheaper, assuming the cost of the magnet can be recuperated at end of life.\nDepartment of Energy Conversion and Storage, Technical University of Denmark - DTU, Frederiksborgvej 399, DK-4000 Roskilde, Denmark\n*Corresponding author : rabj@dtu.dk\n1. Introduction\nMagnetic refrigeration is a promising efficient and environ-\nmentally friendly technology based on the magnetocaloric\neffect. A substantial number of scientific magnetic refrigera-\ntion devices have been published [Yu et al., 2010; Kitanovski\net al., 2015], but so far the technology has yet to be com-\nmercialized. The main challenge for this is the relatively\nsmall magnetocaloric effect present in currently used magne-\ntocaloric materials; the benchmark magnetocaloric material,\nGd, has an adiabatic temperature change of less than 4 K in\na magnetic field of 1 T [Dan’kov et al., 1998; Bjørk et al.,\n2010a], depending on purity. Therefore a regenerative pro-\ncess, called active magnetic regeneration (AMR), is used to\nproduce the desired temperature span [Barclay, 1982].\nAn important aspect in the commercialization of magnetic\nrefrigeration is proving the often mentioned (potentially) high\nefficiency of magnetic refrigeration devices. Furthermore, it\nis crucial to show that these devices will have a lower life-\ntime cost than vapour compression based devices. Magnetic\nrefrigeration devices will have a larger construction cost than\nvapour compression devices, due to the permanent magnet\nmaterial needed to provide the magnetic field in the device.\nHowever, if the operating cost is significantly lower than com-\npression based devices, then magnetic refrigeration devices\nmay be overall cheaper. Determining the operation and con-\nstruction cost of a magnetic refrigeration device is the purpose\nof this paper.\nThe total construction cost of a magnetic refrigeration unit\nhas previously been considered by a number of authors. Rowe\n[2011] defined a general performance metric for active mag-\nnetic regenerators, which included the cost and effectiveness\nof the magnet design as a linear function of the volume ofthe magnet and the generated field. A figure of merit used to\nevaluate the efficiency of the magnet design was introduced\nin Bjørk et al. [2008] not taking the performance of the actual\nAMR system into account. The optimal AMR system design,\ni.e. ignoring the magnet, has been considered by Tusek et al.\n[2013b].\nThe building cost of a magnetic refrigeration device was\nconsidered by Bjørk et al. [2011], for a device with a given\ntemperature span and cooling power calculated using a numer-\nical model. Both a Halbach cylinder and a “perfect” magnet\nwere considered, as well as both parallel plates and packed\nsphere regenerators. Assuming a cost of the magnet material\nof $40 per kg and of the magnetocaloric material of $20 per\nkg the cheapest packed sphere bed refrigerator with Gd that\nproduces 50 W of continuous cooling at a temperature span of\n30 K using a Halbach magnet was found to use around 0.15\nkg of magnet, 0.04 kg of Gd, having a magnetic field of 1.05\nT and a minimum cost of $6. The cost is dominated by the\ncost of the magnet. However, this calculation assumed mag-\nnetocaloric properties as predicted by the mean field theory,\nwhich is known to overestimate magnetocaloric properties\ncompared to commercial grade Gd [Bahl et al., 2012]. Also,\nthe operating cost of the device was not considered.\nThe model presented by Tura and Rowe [2014] determined\nthe total cost and optimal geometry and operating conditions\nfor a dual-regenerator concentric Halbach configuration using\na simple analytical model of an AMR. The magnetocaloric\nmaterial was taken to be ideally graded, i.e. the adiabatic\ntemperature change was defined as a linear function of tem-\nperature throughout the AMR and with a constant specific\nheat equal to that of Gd at the Curie temperature. Further-\nmore, a single particle size of 0.3 mm was considered. BotharXiv:1605.02524v1  [physics.ins-det]  9 May 2016The lifetime cost of a magnetic refrigerator — 2/17\nthe manufacturing and the operating costs were considered\nand the lowest cost device was found as a function of the de-\nsired cooling power and effectiveness of the magnetocaloric\nmaterial for a fixed temperature span of 50 K. For a cooling\npower of 50 W the system with the lowest cost had a magnetic\nfield of 1 T, a frequency around 4.5 Hz, a utilization of 0.35\nand a COP of 2. The capital costs are around $100 and $40\nfor the magnet and the magnetocaloric material, respectively,\nwhile the cost of operation is $0.004 h\u00001.\nIn this paper we will consider not only the construction\ncost of the magnetic refrigeration device, but also the operat-\ning cost. Based on these, we will calculate the overall lowest\ncost of the magnetic refrigeration device based on the price of\nthe magnet material, the price of the magnetocaloric material\nand the expected lifetime of the device.\n2. Required device performance\nIn order to get relevant cooling performance values we chose\nas a benchmark for this study a refrigerator appliance in the\nenergy class A+++(EU-label system), specifically a well\ninsulated appliance with a 350 L inner volume. As vapor\ncompression devices operate differently from magnetocaloric\ndevices it can be hard to find a fair way of making a direct com-\nparison between the two. Thus, the intention of this paper is\nto identify a magnetocaloric unit with an output performance\nresembling that experienced from the vapor compression unit.\nAccording to the calculation scheme of EU-directive 1060/2010,\nthe average electrical power consumption must not exceed\n8.6 W [Mrzyglod and Holzer, 2014]. At a coefficient of per-\nformance of about 3.2, which is the operating COP for an\nA+++appliance [Mrzyglod and Holzer, 2014], this is equiv-\nalent to an average cooling power of about 24 W, assuming\nan ambient temperature of 25\u000eC. However, door openings,\nloading and periods of increased ambient temperature will\nresult in an increase in the cooling power demand. In general\nthe compressor in the device will be dimensioned for loads\nwell above the average, and be operated in an on/off manner\nat times of lower cooling power demand.\nTaking the values from Mrzyglod and Holzer [2014], the\nmagnetocaloric device considered in the following will be\ndimensioned to deliver a maximum cooling power of Qhigh=\n50 W for 10% of the time and Qlow= 22 W for the remaining\n90% of the time. This gives an average cooling power of Qav=\n24.8 W, close to that of the considered A+++appliance. Thus,\nthe AMR must be large enough to deliver 50 W, but operate\nmost of the time at a much lower load. This will be compared\nto a device continuously operating at a cooling power of 24.8\nW, using a volume of cold storage to increase the cooling\npower at times of higher demand. Throughout we apply a tem-\nperature span in the AMRs of DT=30K. We are well aware\nthat the span in vapor compression appliances is significantly\nlarger than this, allowing for a significant temperature span\nin each of the heat exchangers of about 10 K. However, an\nAMR based appliance will operate differently compared to a\ntraditional appliance. One of the fundamental requirements ofa fully magnetocaloric system is a low span of about 2 K in\neach heat exchanger. Thus, these will have to be redesigned\nfor such a device. This can be done through increasing the\nareas and heat transfer, e.g. by forced convection. So with a\nreduction of a few degrees at each end the chosen span will\nresemble that experienced in a household refrigerator.\n3. Determining the performance of an\nAMR device\nThe regenerator in a magnetic refrigeration device consists of\na porous matrix of a solid magnetocaloric material and a heat\ntransfer fluid that can flow through the matrix while rejecting\nor absorbing heat. The excess heat is transferred to a hot-side\nheat exchanger connected to the ambient while a cooling load\nis absorbed at the cold end of the AMR. Typically, the porous\nmatrix is either a packed sphere bed [Okamura et al., 2005;\nTura and Rowe, 2009] or consists of parallel plates [Zimm\net al., 2007; Bahl et al., 2008]. It has been shown, at low oper-\nating frequency, that parallel plate regenerators can produce\nrelevant temperature spans [Bahl et al., 2012; Tusek et al.,\n2013a]. But for the study conducted here a packed sphere bed\nregenerator is considered since this is experimentally found to\nhave superior performance compared to parallel plate regener-\nators [Tura and Rowe, 2011; Tura et al., 2012]. The reason for\nthis is likely more of a practical nature rather than theoretical\nsince it has proven very difficult to manufacture parallel plate\nregenerators with sufficient accuracy to meet the performance\nof packed spheres [Nielsen et al., 2013b].\nWe therefore consider a regenerator consisting of ran-\ndomly packed spheres made of commercial grade Gd. The\ndensity of Gd is rs=7900 kg m\u00003and the porosity of the\nregenerator is assumed constant at e=0:36and the sphere\nsize is homogeneous throughout a given regenerator. Finally,\nedge or boundary effects such as channeling are ignored. The\nmagnetocaloric properties are plotted in Fig. 1. The adiabatic\ntemperature change is notably smaller than often reported in\nliterature [Dan’kov et al., 1998] as the sample was of commer-\ncial grade Gd with unknown purity.\nIn order to calculate the cost of a magnetic refrigeration\ndevice, the performance of the device needs to be known.\nHere, we use a numerical model to calculate the cooling power\nfor a fixed temperature span of DT=30K and a hot side\ntemperature of 300 K for a regenerator with cylindrical cross\nsection. The calculated cooling power is a function of several\nparameters in the AMR model, i.e. magnetic field, m0H,\nparticle size, dpar, length of the regenerator, L, cross sectional\narea, Ac, frequency of operation, f, and thermal utilization:\nj\u0011˙m0cf\n2f LA c(1\u0000e)rscs: (1)\nThe average mass flow rate during one of the blow periods\nis denoted ˙m0and the specific heat is cwith subscript f for\nfluid and s for the solid regenerator material. The parameters\nwere varied as given in Table 1, resulting in a set of 38,880\nsimulations.The lifetime cost of a magnetic refrigerator — 3/17\nTable 1. The parameters varied in the AMR model.\nParameter Minimum Maximum Step size Unit\nMagnetic field, m0H 0.8 1.5 0.1 T\nParticle size, dpar 0.1 0.5 0.05 mm\nLength of regenerator, L 10 100 10 mm\nCross sectional area Ac 1e-5/L mm2\nFrequency of operation [1 2 4 6 8 10] Hz\nUtilization 0.2 1.0 0.1 -\n260 280 300 320∆ Tad [K]\n0.511.522.53\n∆ Tad\n|∆ S|\nTemperature [K]260 280 300 320\n|∆ S| [J kg-1 K-1]\n0.511.522.53\nFigure 1. The adiabatic temperature change (solid line) and\nthe isothermal entropy change (dashed line) as a function of\ntemperature with a change in internal magnetic field from 0\nto 1.0 T. The data used in the model span the temperature\nrange given in the figure and ranges from 0 to 1.4 T internal\nfield. Even though the calculations done in this paper assume\napplied fields up to 1.5 T, the internal field in the AMR is\nnever above the limits of the dataset due to demagnetization\neffects in the regenerator.\nThe numerical AMR model solves the coupled partial\ndifferential equations describing heat transfer in the fluid and\nsolid, respectively. These are given by:\ncfrfe\u0012¶Tf\n¶t+u¶Tf\n¶x\u0013\n=¶\n¶x\u0012\nkdisp¶Tf\n¶x\u0013\n\u0000has(Tf\u0000Ts)\n+\f\f\f\fDp˙m\nrfLAc\f\f\f\f(2)\ncsrs(1\u0000e)¶Ts\n¶t=¶\n¶x\u0012\nkstat¶Ts\n¶x\u0013\n+has(Tf\u0000Ts)\n\u0000rsTs¶s\n¶H¶H\n¶t: (3)\nThe fluid flow is along the x\u0000direction. The pressure drop\nand mass flow rate to a given time tare denoted Dpand ˙m,\nrespectively. The specific surface area of the packed spheres\nisas=61\u0000e\ndparwhile the convective heat transfer coefficient\ndescribing heat transfer from the surface of the spheres to the\nfluid is denoted h. The thermal conductivity in the fluid isdescribed by an effective value including the effect of disper-\nsion ( kdisp) while the conductivity of the spheres is assumed\nequivalent to the static conduction of the regenerator ( kstat).\nThe correlations for these parameters as well as for the con-\nvective heat transfer coefficient and the pressure drop as a\nfunction of mass flow rate and regenerator aspect ratio are\nprovided alongside the numerical implementation details in\nNielsen et al. [2013a]. A detailed discussion of the derivation\nof the active magnetic regenerator equations can be found\nin Engelbrecht [2008]. The boundary conditions at the hot\nand cold end are constant temperatures ( ThotandTcold, respec-\ntively). The rest of the regenerator is assumed adiabatic with\nrespect to the ambient, i.e. parasitic losses are neglected. The\nregenerator equations (2–3) are discretized in space using a\n2ndorder finite difference approach and solved in time using\nthe fully implicity scheme. The details are provided in Nielsen\net al. [2013a]. The magnetic field profile and the flow profile\nare assumed trapezoidal in time with zero no-flow time. The\nramp between the hot and cold blow periods is 5 % of the\ntotal blow time.\nThe magnetocaloric effect is included as a source term in\nthe equations above. At each time step the derivative of the\nabsolute entropy with respect to magnetic field,¶s\n¶H, is found\nas a function of temperature and local magnetic field. This\nmagnitude of the field is found through solving the follow-\ning equation iteratively in each timestep and at each spatial\nlocation:\nH=Happ\u0000NM(T;H); (4)\nwhere Happis the applied magnetic field and M(T;H)is the\nmagnetization of the regenerator material. The average de-\nmagnetization factor, N, is found by combining the overall\nshape of the regenerator (which is cylindrical) and the ap-\nproximation for a porous medium [Bleaney & Hull , 1941]:\nN=1\n3+ (1\u0000e)(Ncyl\u00001\n3): (5)\nThe demagnetization factor for a cylindrical shape, Ncyl, is a\nfunction of the diameter and length of the cylinder and may\nbe found in Joseph [1966].The lifetime cost of a magnetic refrigerator — 4/17\nAll simulations considered a cylindrical regenerator with a\nvolume of 10 mL. This means that the aspect ratio of the regen-\nerator is decreased as the length of the regenerator increases.\nAs the effect of geometrical demagnetization is included in\nthe AMR model, the considered system cannot be “scaled”\nto produce an arbitrary cooling load. In general scaling a\nsystem involves keeping the regenerator length constant and\nincreasing the radius of the regenerator. This would change\nthe demagnetization factor of the regenerator thus leading to\na different performance of the AMR. Thus only regenerators\nwith aspect ratios as given by the regenerator length in Ta-\nble 1 and the volume of 10 mL are considered here. Such\nregenerators have an MCM mass of 47 g. In order to reach\na higher cooling capacity than these 47 g can provide, one\nwould explicitly have to build several systems, each with 47 g\n(i.e. a regenerator volume of 10 mL). However, in the follow-\ning we do assume a smooth scaling of the cooling power for a\ngiven device. This inevitably leads to optimized devices with\nmasses that are non-integer multiples of the base regenerator\nmodeled. The optimization should then be continued with\nthe found optimal regenerator volume (or mass) as the base\nregenerator. This must be, however, a second order effect in\nterms of the resulting cost and we have therefore chosen not\nto take this further step in the analysis.\n4. Total cost of an AMR\nThe cost of an AMR refrigeration device will be composed\nof the cost of the building blocks and the cost for operating\nthe device. Both factors are included in the analysis presented\nhere. Actual manufacturing, transportation and maintenance\nand auxillary systems are ignored.\nThe cost of the building blocks is assumed to consist of\nthe price of the magnetocaloric material and the price of the\npermanent magnet material, as the remaining parts will in\ngeneral be relatively cheap. In the following analysis we only\nconsider devices where the magnetic field is supplied by a\npermanent magnet, as these are both the most common and\nthe most cost-effective devices [Bjørk et al., 2010b]. The\ncost of operating the device is given by the power consumed\nby the device multiplied by the electricity cost and by the\nlifetime of the device. In order to select the device with the\nlowest overall cost, the building cost and the operating cost\nmust be optimized simultaneously. Before considering how\nto minimize the total cost, we first consider how to determine\nthe building cost and the cost of operation for a magnetic\nrefrigeration device.\n4.1 Operating cost\nThe running cost of the magnetic refrigerator is calculated\non the basis that the magnetic refrigerator is running continu-\nously, albeit in different modes depending on the cooling load.\nThis is in contrast to the operation of a compression-based re-\nfrigeration unit, which usually runs infrequently but provides\na high temperature span and cooling power when it does run.\nWe consider a system that will have to provide a high coolingload, Qhigh, for a given percentage of the operating time and\nsubsequently a lower cooling power, Qlow, for the remainder\nof the operating time, comparing this to one with a constant\naverage load of Qav.\nAs stated above the cost of operating the device is given\nby the power consumed by the device multiplied by the cost\nof electricity and by the lifetime of the device. The price of\nelectricity varies a lot from country to country and depending\non the pattern of usage. Here the cost of electricity is taken to\nbe 0.1 $ kWh\u00001, relevant for, e.g., the United States [Hankey,\n2015], China and India, while many European countries have\nhigher prices. The power needed to operate the device is\ngiven by the COP of the device once the cooling load is\nknown. Traditionally, one would select an AMR that operates\nat the highest possible COP thus reducing the operating cost.\nHowever, doing this will disregard the size of the AMR and the\nsize of the applied magnetic field. As these two factors have\na significant influence on the building cost of the magnetic\nrefrigeration device, the approach of minimizing the operation\ncost alone is invalid.\nInstead, the operating cost has to be calculated for every\nsingle device and for every single operating condition consid-\nered. It should then be combined with the building cost in\norder to find the lowest overall price. However, only some\nof the AMR parameters will influence the building cost of\na device. Of the parameters given in Table 1, the magnetic\nfield, particle size and length of the regenerator are inherent\nphysical parameters of the regenerator that cannot be changed\nonce it has been built. An AMR with a given set of values\nof these three parameters is here coined a “device”. The two\nremaining AMR parameters, the frequency and the utilization,\ncan be adjusted for an AMR in operation and do not affect\nthe building cost. These are the operating parameters that will\nbe adjusted to switch between the different cooling powers\nrequired for the device.\nWhen adjusting the operating parameters, one can either\nadjust the frequency and utilization such that the produced\ncooling power is exactly as required. Another alternative is to\nadjust the frequency and utilization to a slightly higher cooling\npower, but with a possibly higher COP, and then compensate\nthe too high cooling power with an electric heater. This will\nof course lower the total COP, by an amount as given in Eq.\n(6), but it cannot be ruled out a priori that this is not a viable\nalternative.\nCOP With heater =Qdesired\nQc\nCOP+Qc\u0000Qdesired(6)\nHere, the COP of the AMR, when the heater is added, is a\nfunction of the cooling power, Qc, and COP of the device\nwithout a heater, and the desired new cooling power Qdesired .\nThe COP of the device without a heater is simply given by\nCOP =Qc=W, where Wis the work consumed. However, for\nall considered AMR parameters here, using a heater results in\na lower performing device than merely adjusting the frequency\nand utilization, so this is not a viable approach.The lifetime cost of a magnetic refrigerator — 5/17\nAs mentioned, a total of 38,880 systems were modelled.\nThis corresponds to 720 devices, i.e. an AMR with fixed mag-\nnetic field, particle size and length. The minimum operating\ncost for each of these 720 devices must be determined. This\nis done using the following scheme given for each device\nand each possible set of operation parameters (frequency and\nutilization) for that device:\n\u000fChoose a device\n\u000fChoose a set of operating conditions (frequency and\nutilization)\nThe mass of MCM needed for the chosen device\nto reach Qhighis determined through linear scaling and\nthe COP is determined.\nDetermine the subset of operating conditions (fre-\nquency and utilization) where this scaled device delivers\nQlow.\nFind the highest COPs on this subset.\nThe power consumption is then found from the\nCOPs at QhighandQlow, weighted by the fraction of\noperation time.\n\u000fRepeat above for all values of frequency and utilization\nfor the given device.\n\u000fRepeat above for all devices\nIt is noted that the subset of operating conditions will have at\nleast one element with f>0 Hz andj>0since the cooling\npower of an AMR device is a continuous function of both\nthese variables and that it must be zero when f=j=0. A\nset,(f1;j1)that fulfills Q(f=0;j=0) =0<Qlow(f1;j1)<\nQhighmust therefore exist.\nConsider a cooling load of 50 W for 10 % of the time and\n22 W for the remaining 90 % of the time. First a device with a\ngiven magnetic field, particle size and length is selected. Then\nthe mass of the device needed to obtain Qhighis determined\nfor all values of the frequency and utilization. As an example,\nconsider a frequency and utilization of 3 Hz and 0.6, respec-\ntively. For these values the simulated device with a volume\nof 10 mL produces 20 W. This means that in order for the\ndevice to be able to produce the desired 50 W, it needs to be\na factor of 2.5 larger. Having determined this, the possible\nvalues of frequency and utilizations that allow this scaled de-\nvice to produce Qlow, here 22 W, are found, as also shown in\nFig. 2. Of these the operating condition with the highest COP\nis selected and this combined with the COP at the 50 W is\nused to calculate the operating cost, for that given frequency\nand utilization, here 3 Hz and 0.6, respectively. This is then\nrepeated for all values of frequency and utilization, until the\nlowest operating cost and the mass of every device is known\nas a function of frequency and utilization.\nFigure 2. The cooling power as a function of utilization and\nfrequency for an AMR with m0H=1:4T,dpar=0:2mm and\nL=60 mm. A given point, here a utilization of 0.6 and a\nfrequency of 3 Hz, has been selected. The mass of the AMR\nis scaled to produce a cooling power of 50 W in this point.\nThe contour of Qlow, here 22 W, is also shown. The point\nwith lowest COP on this contour is chosen for the operating\ncondition of Qlow.\n4.2 Building cost\nThe building cost of a magnetic refrigeration unit is deter-\nmined primarily by the amount of magnetocaloric material\nand magnet material. How to determine the amount of mag-\nnetocaloric material needed for producing the desired cooling\npower for a given device and operating parameters is described\nabove. An increase in cost is expected for decreasing particle\nsize and increasing homogeneity of the production of spheri-\ncal particles. These additions to the cost are not considered\nfurther as the production of Gd spheres is very limited and\nthus assessing the price in a future production is associated\nwith considerable uncertainty. Thus the remaining factor to\ndetermine is the cost of the magnet material.\nAs described in Bjørk et al. [2011] the amount of magnet\nmaterial needed to produce a given magnetic field can be\ncalculated from the mass of the magnetocaloric material alone,\nby knowing the remanence and density of the permanent\nmagnets, and the figure of merit, M\u0003, for the magnet system.\nAs the latter is known to vary from 0 to 0.25, the price can\nideally be determined as a function of the effectiveness of the\nmagnet system. However, this approach does not consider that\nthe regenerator cannot be completely enclosed in an assembly\nof permanent magnets, in order to reduce flux leakage, but\nthat the ends of the regenerator must usually be left open to\nallow fluid flow to enter and exit the regenerator.\nTherefore, we consider instead the well known Halbach\ncylinder design [Mallinson, 1973; Halbach, 1980] with a finite\nlength as the basis for the permanent magnet system. Close\nto 40,000 simulations of the Halbach design were conducted\nin order to determine the minimum amount of permanentThe lifetime cost of a magnetic refrigerator — 6/17\nRegenerator volume 10 mL\n<B> [T]0.8 1 1.2 1.4 1.6mMagnet [kg]\n02468101214\nL = 100 [mm]\nL = 90 [mm]\nL = 80 [mm]\nL = 70 [mm]\nL = 60 [mm]\nL = 50 [mm]\nL = 40 [mm]\nL = 30 [mm]\nL = 20 [mm]\nL = 10 [mm]\nHalbach without losses\nFigure 3. The mass of the magnet needed to provide a given\nmean magnetic field in a volume of 10 mL, with varying\nlength of the regenerator, i.e. varying cross-sectional area.\nThe theoretical case without any losses through the ends of\nthe cylinder is also shown.\nmagnet required to generate the desired average magnetic\nfield inside the volume of the regenerator, for the considered\ncross-sectional areas. The homogeneity of the magnetic field\nover the regenerator is not considered in this approach. We\nconsider magnets with a remanence of 1.2 T, which is a com-\nmon value for NdFeB magnets – the most powerful type of\nmagnet commercially available today. These have a density of\nrmag=7400 kg m\u00003. The choice of a remanence of 1.2 T is\nto ensure that the magnets are reasonably priced, as well as to\ndisregard possible demagnetization issues, as the coercivity of\nmagnets decreases strongly with increasing remanence. The\nfound magnet mass as a function of field is shown in Fig. 3 for\nthe different cross sectional areas considered. As can be seen\nfrom the figure, the larger the cross sectional area, the larger\nthe losses through the ends of the magnet, and thus the more\nmagnet material is needed to create the desired field. This\nwill subsequently be weighted against the increase in pressure\ndrop, and thus pumping power, for the longer regenerators.\n5. Minimizing the life-time cost of a\nmagnetocaloric refrigerator\nThe total cost of a magnetic refrigerator is given as the sum\nof the cost of the magnet material, the magnetocaloric mate-\nrial and the operating cost. This can also be put in terms of\nthe price of magnet material, $=kgMagnet , the price of magne-\ntocaloric material, $=kgMagnetocaloric , the price of electricity,\n$ kWh\u00001, and the mass of the magnet, mMagnet , the magne-\ntocaloric material, mMCM, the power used by the device, Pand finally the lifetime of the device, tLife, i.e.\nCost Total =Cost Magnet +Cost MCM +Cost Operation\n=$=kgMagnet mMagnet +$=kgMCMmMCM\n+$=kWh P tLife (7)\nThese are the major factors contributing to the cost of the\nmagnetic refrigerator. The cost of various standard compo-\nnents such as a motor as well as various materials for con-\nstruction are assumed to be small compared to the factors\nmentioned above. Furthermore, the price of these standard\ncomponents does not change the optimization, as their price\nremains constant. We consider the total cost of the refrigerator\nover its lifetime as a function of the price of magnet and mag-\nnetocaloric material. These values influence all factors in the\nequation, as e.g. a more expensive magnet price might lead to\na slightly smaller regenerator but with an increased operating\ncost. We do not consider that any of the cost from building\nthe AMR can be recovered, i.e. the price of the magnet and\nthe MCM are assumed to be lost once the device has been\nbuilt. This is a very conservative assumption representing a\nworst case scenario. In reality various recycling schemes will\nbe able to recover at least some parts of the magnet and MCM\ncosts [Habib and Wenzel, 2014].\nThe total minimum cost of the magnetic refrigerator with\nan expected lifetime of 15 years, as a function of the price of\nthe magnet material and the magnetocaloric material is shown\nin Fig. 4 for the two systems described above. An expected\nlifetime of 15 years was chosen in accordance with Kelso\n[2011]. The total cost over the entire lifetime of the device\nis seen to range from $150 to $400, depending on the price\nof the magnet material and the magnetocaloric material. For\nall material prices, the refrigerator running at constant load is\nseen to be cheaper by 15-25%, a value increasing as a function\nof the price of the magnet material.\nComparing the cost of two technologies should always\nbe done with some care, especially if the two are not at the\nsame stage of development. But if we were to consider the\nlifetime cost of the vapor compression appliance in a similar\napproach, we could make a very rough comparison. An A+++\ncompression based unit will use $113 of power during 15\nyears at 8.6 W and 0.1 $ kWh\u00001. The base price of the\ncompressor varies, but assuming a reasonable cost of about\n$30 (see, e.g. Vincent and Heun [2006]) this makes the total\ncost of the AMR based refrigeration unit only slightly more\nexpensive than the compressor based one. Assuming that the\ncost of the magnet AMR system can be recuperated at end of\nlife, the AMR device will actually end up being cheaper than\nthe compressor in this rough comparison.\nAs mentioned above the total cost is the sum of the cost\nof the magnet material, the magnetocaloric material and the\noperating cost. These individual components of the total cost\nare illustrated in Figs. 5, 6 and 7, respectively, for the two\nsystems. For both systems, the magnet is seen to be the largest\nfactor in determining the total cost, followed closely by the\ncost of operation. The cost of the magnetocaloric material isThe lifetime cost of a magnetic refrigerator — 7/17\n(a) 24.8 W\n (b) 50 W - 22 W\nFigure 4. The total cost as a function of the price of the magnet material and the magnetocaloric material for (a) a 24.8 W\nrefrigerator and (b) a 50 W - 22 W refrigerator\nseen to be almost negligible for both types of system. Interest-\ningly, the cost of operation is in some cases lower for the 50\nW - 22 W system than for the 24.8 W system. This is because\na much larger magnet, with a slightly higher magnetic field\nand with room for a larger regenerator, is preferred for this\nsystem. This is prioritized in order to reach the specified 50\nW. This also makes the magnet much more expensive for the\n50 W - 22 W, which results in the increase in total cost seen\nfor this system.\n5.1 Operating parameters\nThe operating parameters and other device specific param-\neters, such as the mass of the magnet and the mass of the\nmagnetocaloric material are shown in A for the two systems,\nrespectively. From these figures it is seen that a larger magnet\nis prioritized for the 50 W - 22 W system. The magnetic field\nis seen to be slightly larger, \u00180:05T, the regenerator is longer,\n\u00185mm, and the system is scaled so that the mass of magne-\ntocaloric material is larger by about 0.08 kg. The particle size\nremains the same for the two systems, 0.225-0.245 mm. The\nCOP for the 24.8 W system is very close to the average COP\nof the 50 W - 22 W system. Interestingly, a very high COP is\nprioritized for the 50 W - 22 W system operating at the lower\ncooling power, while the system has a low COP at the high\ncooling power. This is due to the 90 % - 10 % operating times\nof the system. The utilizations of the two systems are seen\nto be similar at 0.2-0.23. The frequency is, however, seen to\nbe quite different between the two systems. The 50 W - 22\nW system operates at a frequency of 7-9 Hz at high cooling\nload, 50 W, and at 2.5-3 Hz at low cooling load, 22 W. This\nis in contrast to the 24.8 W system which operates at 4.5-6\nHz continuously. Again, this is caused by the fact that the\n50 W - 22 W system needs to be able to provide 50 W, and\nthen adjust the frequency of the machine to reduce the cooling\npower to the 22 W cooling load operation.5.2 Cost as a function of expected lifetime\nThe total lifetime cost, the cost per year, and the different\ncomponents of the cost, can also be examined as a function of\nthe expected lifetime of the device. This is shown in Fig. 8 for\nthe case of a price of the magnet material of $40 per kg and\nthe price of the MCM of $20 per kg. As can be seen from the\nfigure, the total cost increases with the years in operation of\nthe device. This is expected, as the cost of operation continues\nto increase as the device is operating. Interestingly, the price\nof the magnet is also seen to increase as a function of the\nyears of operation. This is because the longer the device\nis in operation, the better it is to invest in a larger magnet\nwith a larger bore, allowing a larger cooling power, which in\nturn lowers the cost of operating the device. The cost of the\nMCM remains an insignificant contributor to the total cost. If\nexamined as the cost per year, all costs decrease substantially\nas a function of time, and the cost of operation approaches a\nconstant value.\n5.3 The optimal design and operation parameters\nThe operational and device parameters for the two systems,\ni.e. the particle size, magnetic field, length of the regenera-\ntor, frequency and utilization must also be considered as a\nfunction of the lifetime. As shown in A, most of the oper-\nation parameters for the magnetic refrigerator vary little as\na function of the price of the magnet material and the mag-\nnetocaloric material. This turns out also to be the case as a\nfunction of the expected lifetime of the device. This is the\ncase for the value of the magnetic field, utilization, particle\nsize and length of the regenerator. The mean values for these\nparameters for the lowest cost device, for expected lifetimes\nfrom 0 to 20 years and magnet material and magnetocaloric\nmaterial prices of 10-100 $ kg\u00001is given in Table 2. The\nremaining parameters, i.e. the amount of magnet material and\nmagnetocaloric material, as well as the COP, are functions ofThe lifetime cost of a magnetic refrigerator — 8/17\n(a) 24.8 W\n (b) 50 W - 22 W\nFigure 5. The cost of operating the refrigerator as a function of the price of the magnet material and the magnetocaloric\nmaterial for (a) a 24.8 W refrigerator and (b) a 50 W - 22 W refrigerator\n(a) 24.8 W\n (b) 50 W - 22 W\nFigure 6. The cost of the magnet as a function of the price of the magnet material and the magnetocaloric material for (a) a\n24.8 W refrigerator and (b) a 50 W - 22 W refrigerator\n(a) 24.8 W\n (b) 50 W - 22 W\nFigure 7. The cost of the regenerator as a function of the price of the magnet material and the magnetocaloric material for (a) a\n24.8 W refrigerator and (b) a 50 W - 22 W refrigeratorThe lifetime cost of a magnetic refrigerator — 9/17\nExpected lifetime [years]0 5 10 15 20Cost [$]\n050100150200250300350\nTotal cost\n$ Operation\n$ Magnet\n$ MCM\n50 W - 22 W\n24.8 W\n(a)\nExpected lifetime [years]0 5 10 15 20Cost per year [$ yr-1]\n10-1100101102103 (b)\nFigure 8. The (a) total cost and (b) the cost per year as a function of the expected lifetime of the AMR device for the different\ncomponents. The price of the magnet material is taken to be $40 per kg and the price of the MCM to be $20 per kg.\nthe material cost and the expected lifetime, and their optimal\nvalues must be determined based on these parameters.\nThe operating frequency of the optimal device is a strong\nfunction of the expected lifetime of the device, and only a\nweak function of the price of either the magnet material or\nthe magnetocaloric material. This is shown in Fig. 9, which\ngives the operating frequency as a function of the expected\nlifetime, for prices of the magnet material and the price of the\nmagnetocaloric material ranging from $10 to $100 per kg. As\ncan be seen from the error bars, the frequency is only a weak\nfunction of the price of either material. It can also be seen that\nfor the 50 W - 22 W device, a high frequency is prioritized for\nthe high cooling load, and a low frequency for the low cooling\nload. Thus the device regulates the cooling load by adjusting\nthe frequency at which it is operating. The desired operating\nfrequency is also seen to decrease as the expected lifetime of\nthe device increases.\n6. Comparison with previous results and\ndiscussion\nAs discussed in the introduction two previous studies of the\nbuilding costs of magnetic refrigerators have been reported\n[Bjørk et al., 2011; Tura and Rowe, 2014]. There is a very\ngood agreement between the values found by Tura and Rowe\n[2014] and those reported in this work. The utilization, fre-\nquency and mass of the magnet are all in agreement. However,\nthe COP and magnetic field found by Tura and Rowe [2014]\nare lower than those reported in this work. The lower value of\nthe COP is due to the larger temperature span, while the lower\nvalue of the magnetic field is due to the “poorer” commercial\ngrade Gd used in this study. If a better MCM can be found\nand applied an increase in the performance of the AMR would\nbe expected. The discrepancy between the values reportedby Bjørk et al. [2011] and those reported here is due to three\nreasons, each of which can be evaluated individually. The first\nis the use in Bjørk et al. [2011] of an infinite Halbach cylinder,\nas compared to the optimal cylinder of finite length used in\nthis study. From Fig. 3 this is seen to increase the mass of the\nmagnet by a factor between 1.5 and 2 for the optimal length\nof the regenerator of around 50 mm. The second effect is\nthe inclusion of demagnetization in the AMR model. For the\noptimal geometry considered here, the demagnetization factor\nis 0.44. Finally, the last factor is that of the material data. In\nthe previous study mean field Gd data were used. The material\ndata used in the present study are experimentally measured\nExpected lifetime [years]0 5 10 15 20Frequency [Hz]\n2468101250 W - 22 W at Qhigh\n50 W - 22 W at Qlow\n24.8 W\nFigure 9. The frequency as a function of the function of the\nexpected lifetime of the AMR device. The error bars are\ngiven by the value of frequency as a function of the price of\nthe magnet material and the price of the magnetocaloric\nmaterial, both ranging from $10 to $100 per kg.The lifetime cost of a magnetic refrigerator — 10/17\nTable 2. The optimal values for the AMR parameters. The standard deviation is given by the price of the magnet material and\nthe price of the magnetocaloric material, both ranging from $10 to $100 per kg, and the expected lifetime of the device from 0\nto 20 years.\nParameter 50 W - 22 W device 24.8 W device Unit\nMagnetic field, m0H 1.43\u00060.05 1.41 \u00060.05 T\nParticle size, dpar 0.23\u00060.01 0.23 \u00060.01 mm\nLength of regenerator, L 48\u00062 44 \u00064 mm\nUtilization at Qhigh 0.23\u00060.020.21\u00060.01-\nUtilization at Qlow 0.200\u00060.001 -\nproperties of commercial grade Gd. The difference between\nthe mean field Gd data and that of the data used in the present\nstudy is 1.3 K in a 1 T magnetic field.\nIt is also of interest to compare the AMR parameters\nfound in this study to those reported for actual operating\nAMR prototype devices. Thus, we can directly compare the\ncase of only a single Qloadwith previous results published\nin literature. However, as all of these devices are prototype\ndevices uniquely designed and constructed, the cost of them\nwill be very high and any comparison to the numbers in this\nstudy, optimized for mass production, will be meaningless.\nIn Tusek et al. [2013b] for an optimal COP configuration,\nthe optimal AMR, disregarding magnet, is reported to have a\nlength of 40 mm and 20 mm for 0.5 Hz and 3 Hz, respectively,\nand a particle size of 0.17 mm in both cases. These values are\nin good agreement with the values found here, even though\nthe magnet is not considered at all in the study by Tusek et al.\n[2013b]. The study by Tusek et al. [2013b] uses mean field\nGd for the MCM properties, which explains the difference in\nreported frequencies compared to those found here.\n7. Conclusion\nThe total cost of a magnetic refrigerator was calculated, using\na numerical model. The magnetocaloric material was assumed\nto be commercial grade Gd. Using a set of 38,880 simulations,\nthe cost of operating and the cost of building a magnetic re-\nfrigeration unit capable of operating at 50W for 10% of the\ntime and 22W at 90% of the time was determined. This was\ncompared with a device running 24.8 W continuously. Based\non these the lowest combined cost of the device was deter-\nmined, as a function of the price of magnetocaloric material\nand magnet material. The total cost, with a device lifetime of\n15 years, was found to be in the range $150-$400, with the\ncost being lowest for the 24.8 W operating device. The cost\nof the magnet is the dominant cost factor, followed closely\nby the cost of operation, while the cost of the magnetocaloric\nmaterial is almost negligible.\nThe optimal device and operating parameters of the mag-\nnetic refrigeration device were also determined. The optimal\nmagnetic field was about 1.4 T, the particle size was 0.23 mm,\nthe length of the regenerator was 40-50 mm and the utilization\nwas about 0.2, for all device lifetimes and all considered prices\nof the magnetocaloric and magnet materials. The operatingfrequency was found to vary as a function of device lifetime.\nFor the 50 W - 22 W system the frequency changed from 7-9\nHz at high cooling load to 2.5-3 Hz at low cooling load, in\ncontrast to the 24.8 W system which operated at 4.5-6 Hz\ncontinuously, for a device with a lifetime of 15 years.\nIn a rough life time cost comparison between the AMR\ndevice and a conventional A+++refrigeration unit we find\nsimilar costs, the AMR being slightly cheaper, assuming the\ncost of the magnet can be recuperated at end of life.\nAcknowledgments\nThis work was in part financed by the ENOVHEAT project\nwhich is funded by Innovation Fund Denmark (contract no 12-\n132673). The authors acknowledge Mr. Kai Nitschmann and\nDr. Carsten Weiß from BSH Hausger ¨ate GmbH for valuable\ndiscussions.The lifetime cost of a magnetic refrigerator — 11/17\n1. Operation parameters for a 24.8 W and a 50 W - 22 W system\nIn the figures below are given the operation parameters for a refrigerator cooling 24.8 W at all times and for a system cooling\n50 W for 10 % of the time and 22 W for the remaining 90 % of the time. Both have an expected lifetime of 15 years and the\noperating parameters are shown as a function of the price of the magnet material and the magnetocaloric material. The figures\nshow the mass of the regenerator (Fig. 10), the mass of the magnet (Fig. 11), the magnetic field (Fig. 12), the length of the\nregenerator (Fig. 13), the particle size (Fig. 14), the frequency (Fig. 15), the utilization (Fig. 16) and the COP (Fig. 17).\n(a) 24.8 W\n (b) 50 W - 22 W\nFigure 10. The mass of the regenerator.\n(a) 24.8 W\n (b) 50 W - 22 W\nFigure 11. The mass of the magnet.The lifetime cost of a magnetic refrigerator — 12/17\n(a) 24.8 W\n (b) 50 W - 22 W\nFigure 12. The magnetic field.\n(a) 24.8 W\n (b) 50 W - 22 W\nFigure 13. The length of the regenerator.The lifetime cost of a magnetic refrigerator — 13/17\n(a) 24.8 W\n (b) 50 W - 22 W\nFigure 14. The particle size.\n(a) 24.8 W\n (b) 50 W - 22 W @ 50 W\n(c) 50 W - 22 W @ 22 W\nFigure 15. The frequency.The lifetime cost of a magnetic refrigerator — 14/17\n(a) 24.8 W\n (b) 50 W - 22 W @ 50 W\n(c) 50 W - 22 W @ 22 W\nFigure 16. The utilization.The lifetime cost of a magnetic refrigerator — 15/17\n(a) 24.8 W\n (b) 50 W - 22 W Average\n(c) 50 W - 22 W @ 50 W\n (d) 50 W - 22 W @ 22 W\nFigure 17. The COP.The lifetime cost of a magnetic refrigerator — 16/17\nReferences\nBahl, C. R. H., Bjørk, R., Smith, A., Nielsen, K. K., 2012.\nProperties of magnetocaloric materials with a distribution\nof curie temperatures. Journal of Magnetism and Magnetic\nMaterials 324 (4), 564–568.\nBahl, C. R. H., Petersen, T. F., Pryds, N., Smith, A., Petersen,\nT. F., 2008. A versatile magnetic refrigeration test device.\nReview of Scientific Instruments 79 (9), 093906.\nBarclay, J. A., 1982. The theory of an active magnetic regen-\nerativ refrigerator. NASA STI/Recon Technical Report N\n83, 34087.\nBjørk, R., Bahl, C. R. H., Katter, M., 2010a. Magnetocaloric\nproperties of LaFe 13\u0000x\u0000yCoxSiyand commercial grade Gd.\nJournal of Magnetism and Magnetic Materials 322, 3882–\n3888.\nBjørk, R., Bahl, C. R. H., Smith, A., Pryds, N., 2008. Op-\ntimization and improvement of halbach cylinder design.\nJournal of Applied Physics 104 (1), 13910.\nBjørk, R., Bahl, C. R. H., Smith, A., Pryds, N., 2010b. Review\nand comparison of magnet designs for magnetic refrigera-\ntion. International Journal of Refrigeration 33, 437–448.\nBjørk, R., Smith, A., Bahl, C. R. H., Pryds, N., 2011. De-\ntermining the minimum mass and cost of a magnetic re-\nfrigerator. International Journal of Refrigeration 34 (8),\n1805–1816.\nB. Bleaney, R.A. Hull, 1941. The effective susceptibility of\na paramagnetic powder. Proceedings of the Royal Society\nof London series A, Mathematical and Physical Sciences,\n178 (972), 86–92.\nDan’kov, S. Y ., Tishin, A. M., Pecharsky, V . K., Gschneidner\nJr, K. A., 1998. Magnetic phase transitions and the mag-\nnetothermal properties of gadolinium. Physical Review B\n(Condensed Matter) 57 (6), 3478–3490.\nK. Engelbrecht, 2008. A Numerical Model of an Active Mag-\nnetic Regenerator Refrigerator with Experimental Valida-\ntion, PhD thesis, University of Wisconsin - Madison.\nHabib, K., Wenzel, H., 2014. Exploring rare earths supply\nconstraints for the emerging clean energy technologies and\nthe role of recycling. Journal of Cleaner Production 84,\n348–359.\nHalbach, K., 1980. Design of permanent multipole magnets\nwith oriented rare earth cobalt material. Nuclear instru-\nments and methods 169.\nHankey, R., April 2015. U.S. Energy Information Administra-\ntion: Electrical power monthly with data for february 2015.\nURLwww.eia.govJoseph, R. I., 1966. Ballistic demagnetizing factor in uni-\nformly magnetized cylinders. J. Appl. Phys. 37 (13), 4639–\n4643.\nKelso, J., 2011. Department of energy, energy efficiency and\nrenewable energy, buildings energy data book.\nURL buildingsdatabook.eren.doe.gov\nKitanovski, A., Tusek, J.and Tomc, U., Plaznik, U., Ozbolt,\nM., Poredos, A., 2015. Magnetocaloric Energy Conver-\nsion: From Theory to Applications. Springer International\nPublishing.\nMallinson, J. C., 1973. One-sided fluxes - a magnetic curios-\nity? IEEE Transactions on magnetics 9 (4), 678 – 682.\nMrzyglod, M., Holzer, S., 2014. Aspects of household cooling\ntechnology. International Refrigeration and Air Condition-\ning Conference, Paper 1390.\nNielsen, K., Nellis, G., Klein, S., 2013a. Numerical modeling\nof the impact of regenerator housing on the determination\nof nusselt numbers. Int. J. Heat Mass Transfer 65, 552–560.\nNielsen, K. K., Bahl, C. R. H., Engelbrecht, K., 2013b. The\ninfluence of flow maldistribution on the performance of in-\nhomogeneous parallel plate heat exchangers. International\nJournal of Heat and Mass Transfer 60, 432–439.\nOkamura, T., Yamada, K., Hirano, N., S., N., 2005. Per-\nformance of a room-temperature rotary magnetic refriger-\nator. Proceedings of the 1stInternational Conference on\nMagnetic Refrigeration at Room Temperature, Montreux,\nSwitzerland, 319–324.\nRowe, A., 2011. Configuration and performance analysis of\nmagnetic refrigerators. Int. J. Refrigeration. 34 (1), 168–\n177.\nTura, A., Nielsen, K., Rowe, A., 2012. Experimental and\nmodeling results of a parallel plate-based active magnetic\nregenerator. Int. J. Refrig. 35 (6), 1518–1527.\nTura, A., Rowe, A., 2009. Progress in the characterization\nand optimization of a permanent magnet magnetic refrig-\nerator. Proceedings of the 3rdInternational Conference on\nMagnetic Refrigeration at Room Temperature, Des Moines,\nIowa, USA, 387–392.\nTura, A., Rowe, A., 2011. Permanent magnet magnetic re-\nfrigerator design and experimental characterization. Int. J.\nRefrig. 34, 628–639.\nTura, A., Rowe, A., 2014. Concentric halbach cylinder mag-\nnetic refrigerator cost optimization. International Journal\nof Refrigeration 37, 106–116.\nTusek, J., Kitanovski, A., Zupan, S., Prebil, I., Poredos, A.,\n2013. A comprehensive experimental analysis of gadolin-\nium active magnetic regenerators. Appl. Therm. Eng. 53 (1),\n57–66.The lifetime cost of a magnetic refrigerator — 17/17\nTusek, J., Kitanovski, A., Poredos, A., 2013. Geometrical op-\ntimization of packed-bed and parallel-plate active magnetic\nregenerators. Int. J. Refrig. 36, 1456–1464.\nVincent, C. E., Heun, M. K., 2006. Thermoeconomic Analysis\n& Design of Domestic Refrigeration Systems. Proceedings\nof Domestic Use of Energy Conference 2006, Cape Town,\nSouth Africa.\nYu, B., Liu, M., Egolf, P. W., Kitanovski, A., 2010. A review\nof magnetic refrigerator and heat pump prototypes built\nbefore the year 2010. International Journal of Refrigeration\n33 (6), 1029–1060.\nZimm, C., Auringer, J., Boeder, A., Chell, J., Russek, S.,\nSternberg, A., 2007. Design and initial performance of a\nmagnetic refrigerator with a rotating permanent magnet.\nProceedings of the 2ndInternational Conference of Mag-\nnetic Refrigeration at Room Temperature, Portoroz, Slove-\nnia, 341–347."    },    {        "title": "1608.03582v1.Chiral_magnetic_excitations_in_FeGe_films.pdf",        "content": " 1 Chiral magnetic excitation s in FeGe films  \nEmrah  Turgut1, Albert  Park1, Kayla Nguyen1, Austin Moehle1, David A. Muller1,2, and Gregory \nD. Fuchs1,2 \n1. School  of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853 , USA \n2. Kavli  Institute at Cornell for Nanoscale Science, Ithaca, NY 14853, USA  \n \n \nAbstract:  \n \nAlthough chiral magnetic materials have emerged as a potential ingredient in future \nspintronic memory devices, there are few comprehensive studies of magnetic properties in \nscalably -grown thin  films. We present growth, systematic physical and magnetic \ncharacterization, and microwave absorption spectroscopy of B20 FeGe thin films.  We also \nperform micromagnetic simulations and analytical theory to understand the dynamical magneti c \nbehavior of this material. We find magnetic resonance features in both the helical and field -\npolarized magnetic states that are well explained by micromagnetic simulations and analytical \ncalculations. In particular, we show the resonant enhancement of sp in waves along the FeGe film \nthickness that has a wave vector matching the helical vector. Using our analytic model, we also \ndescribe the resonance frequency of a helical magnetic state , which depends solely on its \nuntwisting field. Our results pave the wa y for understanding and manipulating high frequency \nspin waves in thin -film chiral -magnet FeGe near room temperature.  \n \n \n1. Introduction  \n \nUnderstanding the static and dynamic magnetic properties of materials is a key to their \nincorporation in active spintronic devices. In the light of the recent  proposals  for power -efficient \nspintronic memory devices based in chiral magnetism  [1,2] , it is increasingly important to \ncharacterize chiral magnetic materials in scalably grown thin -film form. Although the resonant \nspin dynamics in chiral magnetic films are more complex than conventional ferromagnetic  2 resonance in uniformly -magnetized ferromagne tic films, understanding and measuring chiral \nmagnetic excitations enables physical insight into the magnetic states of these materials and it \noffers quantitative characterization of dynamical properties that  are relevant to future magnetic \ntechnologies.  \n \nThe n oncollinear spin texture  that appears  in chiral magnets is a consequence of  the \nDzyaloshinskii -Moriya  interaction (DMI) , which  presents  at interfaces and in the volume of \nnoncentrosymmetric materials with broken inversion symmetry  [3–6]. One class in these \nmaterials  is cu bic B 20 crystalline monosilicides and monogermanides of tran sition magnetic \nelements , e.g. MnSi, FeCoSi, and FeGe  [7]. Althou gh they are in the same symmetry group, these \nsilicides  and germanides have surprising  and distinctive electronic and magnetic properties \ndepending on  pressure, temperature, electric and magnetic fields  [8–11]. \n  \nAmong B20 compounds, FeGe has the highest critical temperature , 278 K , for ordered  \nchiral spin textures  [7,12] . FeGe also has -0.6% lattice mismatch with  the Si [111] surface, \nenabling scalable thin film growth  [13,14] , particularly in comparison with the mismatch of  -3% \nand -6% for MnSi and FeCoSi , respectively  [15,16] . Furthermore, in recent computational \nstudies  [17,18] , thin film and  nanoscale  confinement  of FeGe  has been  shown to stabilize  the \ncreation of a magnetic skyrmion , a two-dimensional chiral spin texture with non-trivial \ntopological order . These properties make also FeGe thin films attractive for emerging spintronic \napplications with chiral magnets.  \n \nAlthough B20 FeGe thin films have  been the subject of intense theoretical and \ncomputational studies, experimental studies have been  limited to reports of the topological Hall \neffect and polarized neutron scattering measurements  [13,14,19 –23]. Furthermore , recent \nLorentz transmission electron microscopy and transport  studies of FeGe and MnSi thin films have \nbrought into question the common interpretation of the  topological Hall effect  as arising solely \nfrom a skyrmion lattice phase  [13,19,24,25] . These studies point out  that transport \nmeasurements of B20 films are hard to interpret unambiguously because electron skew   3 scattering by complex helical spin structures  also contributes a Hall effect signal  [13,26] . These \ndifficulties motivate the application of alternative characterization methods to help identify \nchiral magnetic states and quantify  magnetic behavior in thin film materials.  \n \nMicrowave absorption spectroscopy (MAS) is a powerful tool  to probe magnetization in \nboth conventional ferromagnet ic and complex materials  [27–30]. In MAS, resonant absorption \nof a  micro wave magnetic field depends  on the magnetic properties and configuration. For \nexample,  ferromagnetic resonance has been used to characterize  effective  magnetization, the \ndamping parameter, and even magnetic anisotropies  [31,32] . Moreove r, MAS has been used to \nshow  universality of helimagnon and skyrmion excitation s in bulk B20s regardless of being a \nconductor or an insulator  [33]. Microwave fields are useful  not only for understanding chiral \nmagnets, but they can also  create a giant spin -motive force  in chiral magnet s [34,35] . \n \nHere  we report  an experimental, theoretical, and micromagnetic study of chiral magnetic \nexcitations in FeGe thin films by waveguide MAS . First, we describe the growth of B20 crystalline \nthin FeGe films via magnetron sputtering , and systematic characterization  of their physical and \nmagnetic  properties by X -ray diffraction, electron backscattering diffraction, and magnetometry. \nThen, using parameters extracted directly from magnetic characterization,  we study  spin wave  \nand resonant excitation s in the helical and field -polarized states  using  micromagnetic \nsimulation s. With this framework to  understand resonance frequencies and spin-wave modes , \nwe experimental ly perform  tempera ture and magnetic field dependent MAS . We find that \nalthough the field -polarized magnetic resonance can be described by Kitt el’s formula, the helical \nstate magnetic dynamics are more complex. In particular,  an important mode occurs when spin \nwaves are exci ted along the film thickness with a wavelength that matches the helical period . In \naddition, we theoretically calculate the resonant frequencies of the helicoids and find that it \ndepends strongly  on the value of the critical magnetic field that unwraps hel icoid into the field -\npolarized spin state.  \n  4  This paper is organized as follows: In Sec. 2,  we describe the growth and characterizati on \nof the FeGe film. W e report magnetometry studies  in Sec. 3, and present m icromagnetic \nsimulations  in Sec. 4. Then, we discuss  experimen tal measurements of microwave a bsorption \nspectroscopy in Sec. 5. We analytically calculate resonance dynamics in helical magnet in Sec. 6. \nFinally, we conclude in Sec. 7.  \n \n2. Film growth and  characterization  \n \nFeGe thin films are co-sputter ed from Fe and Ge targets on to the surface of  undoped Si \n[111] wafers and annealed post -growth  at 350 ˚C for 30 minutes to create  the B20 crystalline \nphase . The f ilms are then  characterize d by X-ray diffraction  and electron back -scatteri ng \ndiffraction  (EBSD) . In Fig. 1a, w e show  an X-ray 𝜃−2𝜃 scan and large area detector  \nmeasurements of a 176-nm-thick FeGe film, which was determined by cross section al imaging \nwith a scanning electron microscope [see SM]. The narrow and point -like diffraction  peak at \n=33.1 ° indicates a high degree of  alignment of FeGe unit cells with respect to  the Si [111] \nsubstrate.   \n \nFrom the X -ray diffraction data in Fig. 1a, the lattice constant s of FeGe and Si along the \nnormal axis of the film are found 4.680(2) Å and 5.441 (2) Å, respe ctively. The reported lattice \nconstant of FeGe at 290 K is  4.701  Å [36]. Then , we calculate the volume of a FeGe unit cell \nadjacent to the Si substrate  is 103.91 Å3, slightly larger than the bulk value of 103.86 Å3. To \nquantify the tension on the FeGe lattice  for a thin film , we use the bulk modules of 130 GPa and \nits derivative of 4.7, and Murnaghan formula from Ref.  [36,37] . We find the pressure  is -62 MPa. \nThe recent studies o f single crystal bulk MnSi reported  a change in the uniaxial anisotropy and \nsignificant modification of the skyrmion  phase diagram  by applying positive pressure on the scale \nof several tens of MPa , particularly in comparison with the robust helical phase  [38,39] . This \nagrees with Barla et al.’s study of bulk FeGe in which a several GPa pressure is needed to modify \nthe chiral spin ground state  [40]. Although a complete understanding of the magnetic phase \ndiagram of thin film FeGe unde r stress requires more comprehensive experimental and  5 theoretical stud y, to the best of our knowledge, our X -ray diffraction analysis ensures to form  the \nhelical and field -polarized magnetic states in our films .  \n \nNext  we characterize the FeGe grains using  plane -view  transmission electron microscopy \nand EBSD.  The transmission electron micrograph shown in Fig. 1b was  taken using a Tecnai -F20 \nat 200 kV electron  energy . It shows that our  films have both ordered  and disordered grains . We \nfurther  investigate the nanoscale crystal configuration of the grains with EBSD (Figs. 1c-1f). The \ntop image in Fig. 1c shows the scanning electron micrograph of  an 8 μm by 4 μm region of the \nsample. The s econd EBSD micrograph  (Fig. 1d) shows a crystalline phase map  of the same region , \nconfirming that 99% of the grains have the B20 phase. EBSD map ping  also reveals  grains and \nholes due to  the lattice mismatch . The -0.23 % la ttice mismatch between unit cells  at the growth \ntemperature  suggest s a 204 nm of average grain size  [see SM] . From Fig. 1d, we see wide range \nof grain sizes, but they are mainly  between 200 nm and 400 nm, which is close to our estimate .  \n \nIn addition, we show  the crystalline orientation  map with grains aligned to  the Si [111] \ndirection in  yellow  (Fig. 1e) , which also agre es with the  X-ray diffraction data . More than 95% of \nthe FeGe  film is aligned with respect  to Si substrate. Our in-plane orientation analysis of grains \n(Fig. 1f) shows  twinning of  the FeGe grains , which  are rotate d either +30 or -30 degrees in the \nplane with respect Si [111] unit cell . These  high -quality polycrystalline films with grain sizes larger \nthan the helical lattice constant of FeGe  (70 nm ) [41] allow us to study chiral magnetism in B20 \nthin film materials . \n \n3. Magnetic properties  \n \nIn this section , we characterize the  magnetic properties of  our FeGe thi n films.  First, we \nmeasure the magnetic moment of our film as a function of an external magnetic field and \ntemperature using a  vibrating sample magnetometer ( VSM ). Our films have  an easy -plane  \nmagnetic  anisotropy evidenced by  an out-of-plane magnetic saturation field that is four times \nlarger than the one for in  the plane , as shown in Fig . 2a. Additionally,  we find that  as the  6 temperature decreases , the magnetic moment and  the saturation magnetic field  increases . We \nnote that w hile the out-of-plane mag netic moment curves do not indicate an obvious magnetic  \nphase change,  the in-plane magnetization curves have a feature  at 400 Oe  that does not appear \nin the magnetic hysteresis of a conventional ferromagnetic material . To reveal the feature s \nbetter , in Fig. 2b, we plot the derivative of the in -plane magnetization with respect to the applied \nmagnetic field .  The emergence of a peak in the susceptibility below the critical temperature 273 \nK indicates a magnetic phase transition . Such magnetic phase changes  are evidence of  a \ntransformation from  an out-of-plane q -axis helical phase into a field -polarized phase by \nunwinding of the in-plane moment  in accordance with the data in the following  sections  and \nprevious polarized neutron scattering studies  in FeGe and MnSi thin films  [19,21] .  \n \n4. Micromagnetic simulations  \n \nIn this section , to identify the spin dynamics in FeGe thin films , we perform micromagnetic \nsimulation s using  the Mumax3 software  [42]. We identify  the magnetic  properties of the f ilm as \nsimulation parameter inputs using magnetometry measurements in Fig. 2 and the following \nrelations: 𝐻𝑘=𝜋2\n16𝐻𝑑, where 𝐻𝑘=450  𝑂𝑒 is the untwisting field and 𝐻𝑑=730  𝑂𝑒 is the \nsaturation field. The saturation field  in chiral magnets is descr ibed by 𝐻𝑑=𝐷2\n2𝐴𝑀𝑠=8𝜋2𝐴\n𝐿𝐷2𝑀𝑠, where \nthe saturation magnetization 𝑀𝑠=150 kA/m and the helical period 𝐿𝐷=70 𝑛𝑚 [21,24,34,43] . \nWe find  𝐴=6.8 ×10−13J/m. We also assume that  the helical period 𝐿𝐷=70 𝑛𝑚 does not \ndepend on the saturation magn etization or temperature  [21]. In the simulation , the sample \ndimension is 3.2x3.2x176 nm3 in the x, y, and z directions, and the unit cell is a 0.8x0.8x0.8 nm3 \ncube. We apply 16 repetitive periodic boundary conditions in the x and y directions to mimic the \nuniform film [see SM for a sample input code] . Furthermore, we study chiral dynamics at 0 K, so \nwe did not implement a fluctuating thermal field , which is necessary to quantitatively capture \nphase transitions between the helix and the field -polarized states. Thus, we supply this \ninformation to the simulation by initializing  the magnetic states based on experimental \nmagnetometry results .  \n  7 In micromagnetic simulation s, we use  the ringdown method  to obtain dynamic properties \nof spins. In the ri ngdown method , we first initialize the system in the helical state between -500 \nOe and 500 Oe, and the field -polarized state for the rest of the magnetic fields. Then, for each \nfield, we relax the system to its equilibrium state , where all torques vanish . For example, we show \nthese equilibrium spin configurations at 1750  Oe, 250  Oe, and 0 Oe in -plane fields in Figs.  3b-d. \nNext, we appl y a magnetic pulse  with a Gaussian profile , and  record the  x, y, and z components \nof the local magnetic moment s at 25 ps tim e steps for a 2 0 ns duration  [see SM for details] .  The \nGilbert damping parameter is set to an artificially small value ( =0.002) to capture enough \nperiods of the natural oscillations so that we can identify the modes that are sustained by \nmicrowave drivin g [44,45] . To be consistent with the coordinate system we use for theoretical \ncalculation s in Sec. 6 , we also perform a coordinate transformation of the  magnetization \ncomponents from  Cartesian coordinates into spherical  coordinates . The z component of \nmagnetization simply becomes θ, whereas the azimuthal angle ϕ is calcu lated from the x and y \ncomponents  in the plane.  \n \nTo calculate  the natural modes and frequencies , we compute  the discrete Fourier \ntransform of the local magnetic deviation from equilibrium  for each magnetic field . Because the \ndeviation in both θ and ϕ angle s result s in the same resonance frequencies and modes, we plot \nonly θ in Fig.  3. Next , we compute spatially -averaged Fourier coefficients of all spins to obtain the \npower spectral  density (PSD)  [45]. Fig. 3a shows the PSD for frequencies between 0.5 and 7 GHz, \nand in-plane magnetic fields between  -2000  Oe and 2000 Oe. We identify three magnetic fields \n(H=1750  Oe, 250  Oe, and 0 Oe ) to explore the resonance behavior and modes. We also define \nwrapping number , which is (𝜑𝑁−𝜑1)/2𝜋  total wrapping of spins at the equilibrium \nconfiguration. To reveal  the modes, we plot the Fourier coefficients as a function of the frequency \nand thickness ( z direction) in Figs.  3b-d, with the spin configurations along the thickness shown \nabove each plot.   \n \nThe f irst region is at H=1 750 Oe, where we observe a Kitt el-type  uniform resonance of the \nfield -polarized state at 5 GHz  (Fig. 3d .) There are also edge modes which are inversely  8 proportional to the magnetic field at 3 GHz. The s econd region is at H=250 Oe, where the spins \nwrap  = 2.46 times. The resonance frequencies are l ocated at 4.5  GHz, 2.6  GHz, and 0.5 GHz, and \nthe corresponding number of nodes are 4, 2, and 0,  with  only even numbers because 2  = 4.9 < \n5. On the other hand, in the third region at H=0 Oe, the system is driven into  = 2.65 times \nwrapping, which  is slightly larger than the expected 2.51 (176 nm /70 nm) because of the \ndemagnetizing field of the film. The resonance frequencies then increase to  5.5 GHz, 3.0  GHz, \nand 0.8 GHz, and the number of nodes becomes  odd–5, 3, and 1, respectively, because 2  = 5.3 \n>5. These results show sensitivity of spin waves in the spin configuration –helical wrapping in \nchiral magnet.  \n \n5. Experiment: Microwave absorption spectroscopy  \n \nAfter we account for spin  waves in the helical and field -polarized states , we \nexperimentally  perform magnetic resonance measurements by placing FeGe film on a broadband \nmetallic coplanar waveguide (CPW). More details about the design and characteristic of CPW can \nbe found in Ref  [46]. We apply  RF field with  a signal generator and monitor  the transmitted power \nwith  a RF diode as a function of magnetic field and temperature. To remove any non -magnetic \nsignal s, we lock-in to the transmitted RF power referenced a magnetic field modulation that we  \nintroduce using  an ac field  coil. Thus, we measure the derivati ve of the transmitted power, \n𝛥𝑃/𝐻𝑎𝑐, as shown in Fig. 4.  For each temperature, we fix the sample temperature and vary the \nmicrowave  frequency from 0.5  GHz to 7 GHz  with  a 0.25 GHz step size , and the  magnetic  field \nfrom 3000 Oe to -3000 Oe  with  a 30 Oe  step size . The temperature of the sample is controlled by \na Peltier element that allows a convenient  temperature control between 300  K and 255 K.  \n \nIn Fig. 4a and b, we plot the microwave absorption spectra at 285 K and 258 K, respectively \n(data for  the full temperature range can be found in SM). At 285 K, the film is in a paramagnetic \nstate, whereas it can be in either the helical or field -polarized state at 258 K. While, the \nparamagnetic state shows hardly any absorption, w e find two important resonances  in FeGe films  \nfrom Fig. 4 b. The first is a uniform , field -polar ized magnetic resonance that is well-described by   9 Kittel’s formula . We  extract  the resonance field s, frequenc ies f, and the linewidth s 𝛥𝐻 [see S M]. \nBy fitting linewidth to  𝛥𝐻 =𝛥𝐻0+4𝜋𝛼𝑓\n𝛾𝑒, where 𝛾𝑒 is the electron’s gyromagnetic ratio  (2.8 \nMHz/Oe)  [47], we find  the damping c onstant α is 0.038 ± 0.005 at 258 K. This α is substantially \nlower than the recently reported value of 0.28 in thinner FeGe  films in an  out-of-plane magnetic \nfield applied along the [111] orientation and at unreported temperature  [45].  \n \nThe second resonance  is the helical  resonance , also  known as the helimagnon.  As we \npoint out by a vertical arrow in Fig. 4b, the helical resonance has a narrow field range (45 0-500 \nOe) but a wide  frequency range (4 -5 GHz), in contrast to  the field -polarized phase. We attribute \nthis experimental observation to the helica l resonances that we described in the second region \nof the micromagnetic simulation that appeared  at 4.5 GHz  (Fig. 3c) . The wavelength of the 4.5 \nGHz spin wave matches to the helical period of the FeGe film, which shows  how spin waves are \nexplicitly filter ed by the helical spin texture in B20 thin films. In other words, two constraints : the \nthickness and the helical vector, impose a specific discretization of the spin  wave  spectrum  in our \nfilms .  \n \nWe also plot MAS  as a function of magnetic field and temperature at a constant frequency \nof 4.5 GHz (Fig. 4c.) It is interesting  to note that the field -polarized resonance  extends up to 280 \nK, whereas the helical resonance disappears at temperature above 265  K, which is close to the \ncritical temperature of F eGe. This finding  agrees with our magnetometry measurements that \nshow  some magnetic moment persists above the critical temperature 273 K. This precurs or \nmagnetic region between 273 and 280 K was also observed by Wilhelm et al . in the magnetic \nsusceptibilit y measurements of the bulk FeGe  [12]. However, Wilhelm et al.  found a relatively \nsmall precursor region only between 278 K and 280 K. From the magnetic susceptibility \nmeasurements [see SM], we find a  critical temperature 273 K for the helical order , which is lower \nthan the bulk crystal value of 278.2 K. Furthermore, Wilhelm et al.  observed a skyrmion phase \nonly between 273 K and 278 K  [12], which lies above the helical order ing temperature  in our \nfilms . Therefore, i t is an open  question as to whether  the skyrmion phase would shift to lower \ntemperatures or totally disappear  in thin films .   10 To better understand the helical resonance , we locate  the peak of  the resonance in field  \nand frequency  and track it  as a function of temperature. I n Fig . 4d, w e observe  a monoton ic \ndecrease of the resonance field and frequency as the temperature increases . This is consistent \nwith our magnetometry measurements (Fig. 2) that show both the magnetic moment of the film  \nand the unwrapping critical magnetic field decrease  with increasing temperature . Such a \ndecrease in the helical -phase  resonance frequenc y and in crease in the field -polarized phase \nresonance frequenc y for increasing temperature was also observed by Schwarze et al.  in bulk B20 \nmaterials  [33].  \n \nIn contrast to observations i n bulk crystal  [33] and micromagnetic simulations (Fig. 3),  our \nexperiment does not show any clear microwave absorption at 0 field . This difference  may arise  \nfrom the grain format ion in our films, which are not accounted for  in micromagnetic simulation s. \nAt H=0 Oe, we think, oscillations in twinned grains are irregular  and do not show strong \nabsorption, whereas a nonzero field helps unify the collective motion of spins perpendicular to \nthe field , enabling a strong helical state resonance absorption befor e untwisting into the field -\npolarized state.  \n \n6. Theoretical calculations  \n \nBy comparing the micromagnetic simulatio ns and experimental measurement s of MAS , \nwe identified th e resonance  frequencies and spin-wave modes  in the helical and field -polarized \nstates . In this section, we also  analytic ally model  excited chiral heli magnet s to account for  spin \nwave excitations .   \n \nWe describe the one dimensional Hamiltonian density of a chiral helimagnet by  \nℋ=𝐴(𝜕𝑧𝒎)2−𝑫.𝒎×𝜕𝑧𝒎−𝑩.𝒎+𝐾𝑢(𝒎.𝒏̂)𝟐−1\n2𝑯𝒎.𝒎 ,   (1) \nwhere A is the exchange stiffness constant, D is the DM interaction constant, B is the external \nmagnetic field, Ku is the anisotropy constant and Hm is the demagnetizing field due to shape of  \nthe sample. We use the normalized magnetization 𝑚= 11 [sin𝜃(𝑧,𝑡)cos𝜙(𝑧,𝑡),sin𝜃(𝑧,𝑡)sin𝜙(𝑧,𝑡),cos𝜃(𝑧,𝑡)] in the spherical coordinate  as in the \nprevious section  [21,34,48] . The external magnetic field B includes the dc field Bx and the ac \nmicrowave field By, and it is written as  𝑩=[𝐵𝑥,𝐵𝑦sin𝜔𝑡,0]. Next, we write down the \nLagrangian density  ℒ, \nℒ=−ℏ 𝑀𝑠\n𝑔𝑒𝜇𝐵(cos𝜃−1)𝜕𝑡𝜙−ℋ,     (2) \nwhere  Ms is the saturation magnetization, 𝜇𝐵 is the Bohr magnetron,  and ge is the electron g -\nfactor. The equation s of motion are constructed by expressing Eq. 1 and 2 in terms  of 𝜃(𝑧,𝑡) and \n𝜙(𝑧,𝑡) coordinates  [see SM].  \nFor the equilibrium  helical state  at B=0, the solutions are simply  𝜃=𝜋\n2 and 𝜙=𝑄𝑧, where \n𝑄=𝐷\n2𝐴 is the helix wave number. Application of an external magnetic field  creates a deviation  \nfrom equilibrium  by  𝜃1 and 𝜙1 as \n \n𝜙(𝑧,𝑡)=𝑄𝑧+𝜙1(𝑧)sin𝜔𝑡,     (3) \n𝜃(𝑧,𝑡)=𝜋\n2+𝜃1(𝑧)cos𝜔𝑡.      (4) \n \nThe distorted helix has been described by cosine expansions of the angles as in \n𝜙1(𝑧)[𝜃1(𝑧)]=𝐴1[𝐵1]+𝐴2[𝐵2]cos𝑄𝑧+𝐴3[𝐵3]cos2𝑄𝑧, where A1-3 and B1-3 are coefficients  \nfor 𝜙1 and 𝜃1, respectively  [34]. As the la st step, we substitute Eq.  3 and 4 into the equation s of \nmotion  using the small angle approximation  [see S M]. We also use the same material parameters \nobtained in the micromagnetic simulation section. Finally, we solve the eigenvalue problem for \nthe resonance frequencies and modes.   \n \nIn Fig. 5a, we plot the real part  of the three resonance frequencies f1, f2, and f3 as function s \nof in -plane field  Bx. If we define a critical field Hc=830 Oe, where the solutions to f1 and f2 become  \ndegenerate  (Fig. 5a) : 𝐼𝑚[𝑓1]=𝐼𝑚[𝑓2]=0 and 𝐼𝑚[𝑓3]≠0, for 𝐻<𝐻𝑐: whereas 𝐼𝑚[𝑓1]≠\n𝐼𝑚[𝑓2]≠0 and 𝐼𝑚[𝑓3]=0, for 𝐻>𝐻𝑐 [see S M]. Therefore , the  solutions to f1 and f2 above Hc \ndoes not support natural oscillation s. Additionally , the small angle approximation and series  12 expansion are only valid at the low field (in the pink -filled region of Fig . 5a), because the phase \nchange from the helical into the field -polarized state happens at Hd =730 Oe (Fig. 2. )  \n \nResonance modes in 𝜃1 at f1 and f2 are shown in Fig. 5b and 5d, and the ones in 𝜙1at f1 \nand f2 are shown in Fig. 5d and 5e, respectively. At f1, there are five nodes  that match the helical \nperiod, whereas the number of nodes double for f2. This doubling of nodes is because  of \nexpa nsion of 𝜃1 and 𝜙1 up to the second order ( cos2kz.) When we increase in -plane Bx field , the \noscillation amplitude s for f1 decrease  (Fig. 5b and 5d)  and the amplitudes for f2 increase  (Fig. 5c \nand 5e .) This suggests that an in-plane field drives the symmetric helimagnon into the distorted \nhelimagnon by decreasing the cos kz term and increasing  the cos2kz term . The static distortion of \nhelimagnets by an in -plane field was previously observed using  a polarized neutron scattering \nexperiment , which is in agreement with our findings  from  oscillation amplitudes  [19].  \n \nOur analytic calculation does not take into account the thickness of the film , therefore  we \ndo not observe additional modes along  the film thickness as we did in micromagnetic simulation. \nHowever, we confirm the increase of the resonance frequency by application of a larger magnetic \nfield, in agreement  with micromagnetic simulation (Fig. 3a). On the other hand, Schwarze et al.  \nobserved the o pposite in the bulk B20, i.e. the larger the field, the smaller the frequency. An \nimportant difference , however,  is that in our films , the magnetic field untwists the helix, while in \ntheir  bulk crystal  the magnetic field introduces a conic al angle to the h elical phase. Therefore, an \nopposite dependence to the magnetic field is consistent with our theoretical understanding . \nNevertheless, our calculation predicts two  resonance frequencies at Bx=0 regardless of the \ngeometry.  At Bx=0, t he resonance frequencies  become  𝑓1=𝑔𝑒𝐻𝑑𝜇𝑏\n2𝜋ℏ and 𝑓2=√10𝑔𝑒𝐻𝑑𝜇𝑏\n2𝜋ℏ. For \nexample, Schwarze  et al.  found resonance frequencies in the range of 14 –17 GHz, 3–4 GHz, and \n1.5–2 GHz for bulk MnSi, FeCoSi, and Cu 2OSeO 3, respectively  [33]. The critical fields were also \nrepor ted as 0.5, 0.1, and 0.04 T . From 𝑓1=𝑔𝑒𝐻𝑑𝜇𝑏\n2𝜋ℏ formula, we estimate f1= 14 GHz, 2.8  GHz, and  \n1.1 GHz for each materials, respectively, in close agreement with  observation s. Therefore,  our \ntheoretical approach  provides  a straightforward estimate  of helimagnon  frequencies .  \n  13 This relation to the critical field coincides with the recently developed microscopic theory \nof spin waves in cubic magnet s with DMI by Maleyev  [49]. He found that t he spin-wave stiffness \n𝐷𝑠𝑤=𝑔𝑒𝜇𝐵𝐻𝑑\n𝑄2, which  is 0.105 eV Å2 for our FeGe  thin film . This value is in precise  agreement with \nthe recent  neutron scattering experiment on bulk FeGe  at 250K  [50]. One can define the  spin-\nwave  resonance frequency in a chiral magnet by 𝑓=𝑓ℎ𝑒𝑙𝑖+𝐷𝑠𝑤\nℎ(𝜋𝑛\n𝐿)2\n, where h is Planck ’s \nconstant, L is the thickness, n is the mode number,  and 𝑓ℎ𝑒𝑙𝑖 is natural helical frequency which is \nfound 2 .0 GHz in our FeGe films using f1 (Fig. 5a.) Therefore , the frequency  becomes 𝑓=2.0+\n𝑛20.081 GHz. For n=3 and n=5, we find spin wave frequencies at 2.7 GHz and 4.0 GHz. These \nfrequencies are close to the one s we observed in the micromagnetic simulations in Fig. 3b. Small \ndifferences may be originated  from variations in the material parameters, because they are \nhighly  sensitive to the temperature around the critical temperature  Tc. Our analytic approach is \na direct  and simple method to identify the  resonance frequencies in chiral thin film magn ets. F ull \nunderstanding of spin -waves in confined chiral magnets will require  further theo retical and \nexperimental study .  \n \n \n7. Conclusion  \n \nIn conclusion, we present a comprehensive experimental and theoretical study of the \nmicrowave resonance dynamics in a chiral magnetic FeGe thin film. We grew FeGe films by \nmagnetron sputtering and systematically characterized their physical and magnetic prope rties. \nOur films are polycrystalline but have high -quality B20 crystal phase, confirmed by the electron \nbackscattering diffraction. Below the critical temperature, static magnetometry measurements \nshow that the film has a helical to field -polarized magneti c phase transition at 450 Oe under an \nin-plane magnetic field. Our microwave absorption measurements also show resonance features \nfor the helical and field -polarized states. By comparing our experimental measurements with \nmicromagnetic simulations and anal ytic calculations, we demonstrate that the helical state has \nresonant microwave dynamics that are highly sensitive to the twisting spin texture. Our analytical \ncalculations also show that the resonance frequencies can be described by the untwisting critica l  14 magnetic field, which is in agreement with micromagnetics and experimental observations. Our \nresults pave the way toward understanding spin wave dynamics in chiral and topological spin \ntextures, grown as thin films without any limitation to scalability, thus promising  for an \nintegration of chiral spintronics.  \n \n \n \n \nAcknowledgement  \n \nThis work was supported by the DOE Office of Science (Grant # DE -SC0012245).   We also \nacknowledge use of facilities of the Cornell Center for Materials Research  (CCMR) , an NSF MR SEC \n(DMR -1120296) , and CCMR research support for K.N. and D.M., who collaborated on \ntransmission electron microscopy measurements.  We further acknowledge facility use at the \nCornell Nanoscale Science and Technology Facility (Gran t # ECCS -1542081), a node of the NSF -\nsupported National Nanotechnology Coordinated Infrastructure.  We thank Robert M. Hovden \nand Lena F. Kourkoutis for valuable discussions and on -going help with electron microscopy, and \nF. Guo for reviewing the manuscript.   \n \n \n \n \n \n \n \n  15  \nFIG 1 X-ray and electron diffraction char acterizations and transmission electron micrograph of \nFeGe thin film. a) shows -2 scan of X -ray diffraction with an additional  angle profile in the \ninset. Having sharp peaks instead of rings suggests good  alignment of FeGe film. b)  is transmission \nelectron micrograph of plain -view of the film  (scale bar is 100nm). c) is scanning electron \nmicrograph, d) is the crystalline phase ma p of the same region indicating >99% B20 phase. e) is \nthe out -of-plane alignment and f) is the in -plane alignment of the grain. The scale bar is 2 m \nthrough (c) –(f). \n \n \n \n \n 16  \nFIG 2  Magnetometry measurements  of our thin film FeGe. (a) shows M -H curves  for both the in-\nplane and out -of-plane fields , and (b) shows the derivative of  the in-plane  magnetization with \nrespect to the applied magnetic field to better reveal  unwinding of the helical phase .   \n \n \n \n \n 17  \nFIG 3 Power spectr al density (PSD) and natural oscillation modes of spin waves. a) shows the PSD \nof spatially summed Fourier coefficients as a function of in -plane magnetic field. The helical spin \nconfiguration present s between -500 Oe and 500 Oe, and the field -polarized state presents  for \nthe rest. b)  at Bx = 1750 Oe field , the f ield-polarized state has a Kitt el-type uniform mode. c) at Bx \n= 250 Oe field, the wrapping number  𝜁 is 2.46, which allows only even nodes (0, 2, and 4.) d) at \nBx = 0 Oe field, the wrapping number  𝜁 is 2.65, which allows only odd nodes (1, 3, and 5.)  \n \n 18  \nFIG 4 Experimental me asurements of microwave absorption spectroscopy (MAS) of FeGe film at \ndifferent temperature, in-plane magnetic field, and microwave frequency. a) shows  the MAS \nabove the critical  temperature  with no clear absorption feature. b) shows the MAS below the \ncritical temperature,  which has the helical (arrow) and field -polarized s tate resonances . c) the \nMAS at 4.5 GHz as the field and the temperature vary.  (d) shows trend  of the frequenc y, field,  \nand amplitude of the helical resonance for each  temperature.  \n \n \n \n \n \n 19  \nFIG 5 Analytical calculation of the resonance frequencies and oscillation modes. a) the real parts \nof the eigenvalues of the equation s of motion result in three resonance frequencies f1, f2, and f3. \nThe inset shows the coordinate system and angle  variables  of spins. Because  of non -zero \nimaginary parts of the eigenvalues, only the pink -filled region represents correct resonance \nfeature. b) and c) show the  oscillation modes of  (out-of-plane) for f1 and f2, respectively. d) and \ne) show the  oscillation modes of  (in-plane) for f1 and f2 frequencies, respectively.   \n \n \n \n \n \n \n \n \n \n 20 References  \n[1]  A. Fert, V. Cros, and J. Sampaio, Nat. Nanotechnol. 8, 152 (2013).  \n[2]  S. Emori, U. Bauer, S. Ahn, E. Martinez, and G. S. D. Beach, Nat. Mater. 12, 611 (2013).  \n[3]  I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958).  \n[4]  M. L. Plumer and M. B. Walker , J. Phys. C Solid State Phys. 14, 4689 (1981).  \n[5]  A. Fert, Mater. Sci. Forum 59-60, 439 (1991).  \n[6]  U. K. Rössler,  a N. Bogdanov, and C. Pfleiderer, Nature 442, 797 (2006).  \n[7]  N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013).  \n[8]  G. A. Valkovskiy, E. V Altynbaev, M. D. Kuchugura, E. G. Yashina, V. A. Dyadkin, A. V \nTsvyashchenko, V. A. Sidorov, L. N. Fomicheva, M. Bykov, E. Bykova, L. Dubrovinsky, and \nS. V Grigoriev, J. Phys. Condens. Matter 28, 375401 (2016).  \n[9]  A. E. Petrova, V . N. Krasnorussky, A. A. Shikov, W. M. Yuhasz, T. A. Lograsso, J. C. Lashley, \nand S. M. Stishov, Phys. Rev. B - Condens. Matter Mater. Phys. 82, 155124 (2010).  \n[10]  S. M. Stishov, A. E. Petrova, S. Khasanov, G. K. Panova, A. A. Shikov, J. C. Lashley, D. W u, \nand T. A. Lograsso, J. Exp. Theor. Phys. 106, 888 (2008).  \n[11]  K. Shibata, X. Z. Yu, T. Hara, D. Morikawa, N. Kanazawa, K. Kimoto, S. Ishiwata, Y. Matsui, \nand Y. Tokura, Nat. Nanotechnol. 8, 723 (2013).  \n[12]  H. Wilhelm, M. Baenitz, M. Schmidt, U. K. R ößler, A. A. Leonov, and A. N. Bogdanov, \nPhys. Rev. Lett. 107, 127203 (2011).  \n[13]  N. A. Porter, J. C. Gartside, and C. H. Marrows, Phys. Rev. B 90, 024403 (2014).  \n[14]  S. X. Huang and C. L. Chien, Phys. Rev. Lett. 108, 267201 (2012).  \n[15]  M. N. Wilson,  E. A. Karhu, A. S. Quigley, U. K. Rößler, A. B. Butenko, A. N. Bogdanov, M. \nD. Robertson, and T. L. Monchesky, Phys. Rev. B 86, 144420 (2012).  \n[16]  P. Sinha, N. A. Porter, and C. H. Marrows, Phys. Rev. B 89, 134426 (2014).  \n[17]  M. Beg, R. Carey, W. Wang, D. Cortés -Ortuño, M. Vousden, M. -A. Bisotti, M. Albert, D. \nChernyshenko, O. Hovorka, R. L. Stamps, and H. Fangohr, Sci. Rep. 5, 17137 (2015).  \n[18]  M. Vousden, M. Albert, M. Beg, M. -A. Bisotti, R. Carey, D. Chernyshenko, D. Cort és-\nOrtuño, W. Wang, O. Hovorka, C. H. Marrows, and H. Fangohr, Appl. Phys. Lett. 108, \n132406 (2016).   21 [19]  N. A. Porter, C. S. Spencer, R. C. Temple, C. J. Kinane, T. R. Charlton, S. Langridge, and C. \nH. Marrows, Phys. Rev. B 92, 144402 (2015).  \n[20]  N. Ka nazawa, M. Kubota, A. Tsukazaki, Y. Kozuka, K. S. Takahashi, M. Kawasaki, M. \nIchikawa, F. Kagawa, and Y. Tokura, Phys. Rev. B 91, 041122(R) (2015).  \n[21]  M. N. Wilson, E. A. Karhu, D. P. Lake, A. S. Quigley, S. Meynell, A. N. Bogdanov, H. \nFritzsche, U. K. Rößler, and T. L. Monchesky, Phys. Rev. B 88, 214420 (2013).  \n[22]  M. Kugler, G. Brandl, J. Waizner, M. Janoschek, R. Georgii, A. Bauer, K. Seemann, A. \nRosch, C. Pfleiderer, P. Boni, and M. Garst, Phys. Rev. Lett. 115, 097203 (2015).  \n[23]  J. C. Gallagher,  K. Y. Meng, J. T. Brangham, H. L. Wang, B. D. Esser, D. W. McComb, and F. \nY. Yang, arXiv:1604.06684 1 (2016).  \n[24]  M. N. Wilson, A. B. Butenko, A. N. Bogdanov, and T. L. Monchesky, Phys. Rev. B 89, \n094411 (2014).  \n[25]  T. L. Monchesky, J. C. Loudon, M. D . Robertson, and A. N. Bogdanov, Phys. Rev. Lett. 112, \n059701 (2014).  \n[26]  S. A. Meynell, M. N. Wilson, J. C. Loudon, A. Spitzig, F. N. Rybakov, M. B. Johnson, and T. \nL. Monchesky, Phys. Rev. B 90, 224419 (2014).  \n[27]  C. Kittel, Phys. Rev. 73, 155 (1948) . \n[28]  C. Herring and C. Kittel, Phys. Rev. 81, 869 (1951).  \n[29]  E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and  R. A. Buhrman, Science  285, 867 \n(1999).  \n[30]  A. Brataas, A. D. Kent, and H. Ohno, Nat. Mater. 11, 372 (2012).  \n[31]  H. T. Nembach, J. M. Shaw, C. T. Boone, and T. J. Silva, Phys. Rev. Lett. 110, 117201 \n(2013).  \n[32]  A. A. Tulapurkar, Y. Suzuki, A. A, H. Kubota, H. Maehara, K. Tsunekawa, D. D. \nDjayaprawira, N. Watanabe, and S. Yuasa, Nature 438, 339 (2005).  \n[33]  T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer, and \nD. Grundler, Nat. Mater. 14, 478 (2015).  \n[34]  J. I. Kishine, I. G. Bostrem, A. S. Ovchinnikov, and V. E. Sinitsyn, Phys. Rev. B 86, 214426 \n(2012).   22 [35]  J. I. Kishine, I. Proskurin, I. G. Bostrem, A. S. Ovchinnikov, and V. E. Sinitsyn, Phys. Rev. B \n93, 054403 (2016).  \n[36]  P. Pedrazzini, H. Wilhelm, D. Jaccard, T. Jarlborg, M. Schmidt, M. Hanfland, L. Akselrud, \nH. Q. Yuan, U. Schwarz, Y. Grin, and F. Steg lich, Phys. Rev. Lett. 98, 047204 (2007).  \n[37]  F. D. Murnaghan, Proc. Natl. Acad. Sci. 30, 244 (1944).  \n[38]  Y. Nii, T. Nakajima, A. Kikkawa, Y. Yamasaki, K. Ohishi, J. Suzuki, Y. Taguchi, T. Arima, Y. \nTokura, and Y. Iwasa, Nat. Commun. 6, 8539 (2015).  \n[39]  A. Chacon, A. Bauer, T. Adams, F. Rucker, G. Brandl, R. Georgii, M. Garst, and C. \nPfleiderer, Phys. Rev. Lett. 115, 267202 (2015).  \n[40]  A. Barla, H. Wilhelm, M. K. Forthaus, C. Strohm, R. Rüffer, M. Schmidt, K. Koepernik, U. K. \nRößler, and M. M. Abd -Elmeguid, Phys. Rev. Lett. 114, 016803 (2015).  \n[41]  X. Z. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W. Z. Zhang, S. Ishiwata, Y. Matsui, and Y. \nTokura, Nat. Mater. 10, 106 (2011).  \n[42]  A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia -Sanchez, a nd B. Van \nWaeyenberge, AIP Adv. 4, 107133 (2014).  \n[43]  D. Wei, Maxwell Equations and Landau -Lifshitz Equations, Micromagnetics and \nRecording Materials  (Springer, 2012).  \n[44]  R. D. McMichael and M. D. Stiles, J. Appl. Phys. 97, (2005).  \n[45]  M. Beg, M. Al bert, M. -A. Bisotti, D. Cortés -Ortuño, W. Wang, R. Carey, M. Vousden, O. \nHovorka, C. Ciccarelli, C. S. Spencer, C. H. Marrows, and H. Fangohr, arXiv:1604.08347v1 \n(2016).  \n[46]  Y. Wiemann, J. Simmendinger, C. Clauss, L. Bogani, D. Bothner, D. Koelle, R. Kle iner, M. \nDressel, and M. Scheffler, Appl. Phys. Lett. 106, 193505 (2015).  \n[47]  S. S. Kalarickal, P. Krivosik, M. Wu, C. E. Patton, M. L. Schneider, P. Kabos, T. J. Silva, and \nJ. P. Nibarger, J. Appl. Phys. 99, 093909 (2006).  \n[48]  M. Janoschek, M. Garst, A. Bauer, P. Krautscheid, R. Georgii, P. Boni, and C. Pfleiderer, \nPhys. Rev. B 87, 134407 (2013).  \n[49]  S. V. Maleyev, Phys. Rev. B 73, 174402 (2006).  \n[50]  S. Siegfried, Gatchina: IV Polarized Neutron School (2015).   23   1 Supplemental Material: Chiral magnetic excitation s in \nFeGe films  \nEmrah  Turgut1, Albert  Park1, Kayla Nguyen1, Austin Moehle1, David A. Muller1,2, and Gregory \nD. Fuchs1,2 \n1. School  of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853 , USA \n2. Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY 14853, USA  \n \nThis Supplemental  Material (SM) provides additional information about the sample \ncharacterization, microwave absorption spectroscopy measurements , computational and \nanalytic  calculati ons.  \n \nS1. Cross section scanning electron micrograph of the FeGe film  \n \nTo simulate micromagnetics  accurately , we precisely measure the thickness of our film . This \nis essential  because standing spin wave modes and frequencies strongly depend on the film \nthickn ess. We use d a focus ed ion beam to make a cross section cut of the film and sca nning \nelectron microscopy  to measure the thickness . In Fig. S1, we show  the cross section images of \nthe film and measurement of the thickness as 176 nm.  \n \nS2. X-ray diffraction and lattice parameters  \n \nFrom the X-ray diffraction measurements  in Fig. 1a, we found d111 2.702 (1) Å for FeGe and \n3.141(1) Å for Si from the corresponding peak s. The vertical lattice constants are then found  to \nbe 4.680 Å for FeGe and 5.441 Å for the Si substr ate. The reported lattice constant for the bulk \nFeGe is 4.701 Å at 290 K  [1]. The lattice mismatch becomes  \n4.701 −5.441 cos30\n4.701=−0.23 %.  2 This lattice mismatch would be re leased at every ( 23/1000 0≈1/435) 435 lattice site s that equals \nto 204 nm. Indeed, our electron backscattering diffraction micrograph indicates an average 300 \nnm grain size.  \n \nTo find the stress on the FeGe film, we use Murnaghan formula  [2], which is  \n𝑉0\n𝑉=(1+𝑘𝑃)1/𝑐𝑘 \nwhere V0 is the equilibrium and V is the final volume, P is the pressure, c is the bulk modulus , i.e. \n𝑐=−𝑉𝑑𝑝\n𝑑𝑉, ck is the derivative, i.e. 𝑐𝑘=−𝑑\n𝑑𝑝(𝑉𝑑𝑝\n𝑑𝑉) . Solving using these formulas  numerically , \nwe find the pressure -62 MPa.  \n \nTo understand crystallization process in FeGe by post -growth  annealing, we calculate \nthermal expansion in FeGe and Si lattices. Thermal expansion coefficients in FeGe and Si were \nreported 1.7x10-5 and 3.6x10-6 C-1 respectively  [3,4] . At tempe rature 192 °C, the lattice constants \ntheoretically match, and at higher temperatures Fe and Ge atoms form into the B20 crystal \nconfiguration. In our FeGe films, we use relatively high temperature (350 °C) to form B20. Indeed, \nlower temperature annealing pr oduces weaker FeGe [111] peak in the x -ray diffraction. The \nrecent study on FeGe thin films also reported 290 °C is the optimum annealing temperature  [5].  \n \n  3  \nFIG S1. SEM cross section i mages of the film. The f ocus ed ion beam is used to make a cross \nsection  and the scanning electron micro scopy  reveals the thickness of 176 nm.  \n \nS3. AC Magnetic susceptibility  \n \nIn this section, we show the measurements of the critical temperature of FeGe film  \ndetermined  with AC magnetic susceptibility using  a Quantum Design Physical Property \nMeasurement System (Fig. S2 ).   \n 4  \nFIG S2. AC magnetic susceptibility measurements of FeGe film with  a 20 Oe constant field and \na 10 Oe ac excitation field at 25 Hz. The critical temperature is obtained 273 K, which is slightly \nlower than the bulk value of 278 K.  \n \n \nS4. Parameters used in the micromagnetic simulations  \n \nHere we show an example input file for the Mumax3 micromagnetic simulation. One can find \nused material parameters in the “Material parameter” section.  \nNx :=4 \nNy :=4 \nNz :=220  // number of cells in x, y, and z directions  \nc := 8e-10 // cell size in nm  \nSetMesh(Nx, Ny, Nz, 8e -10, 8e-10, 8e-10, 16, 16, 0) // Setting \nmesh with 16 periodic boundary conditions in x and y  \nlmd := 70e -9  // helix period in nm  \nmask := newVectorMask(Nx, Ny, Nz)  \n \nfor i:=0; i<Nx; i++{  \n for j:=0; j<Ny; j++{  \n  for k:=0; k<Nz; k++{  \n  xdir := cos(2*pi*k*c/lmd)  \n  ydir := sin(2*pi*k*c/lmd)  \n  zdir := 0  \n220 240 260 280 3000.02.0x10-74.0x10-7\nTemperature (K)TN=273 Kac(emu/Oe)AC magnetic susceptibility  5   mask.setVector(i, j, k, vector(xdir, ydir, zdir))  \n  } \n } \n} \nm.SetArray(mask)  \nsave(m) \n// Material parameters  \nKu1 = -3500 // uniaxial anisotropy  \nMsat = 150e3 // Saturation magnetization  \nexccons := 6.8e-13 // Exchange constant  \nAex = exccons  \nDD := 4*pi*exccons/lmd // Bulk DMI constant  \nDbulk = DD  \nKc1 = 0 // crystalline anisotrpy  \nanisc1 = vector(1,1,1)  \nanisU = vector(0, 0, 1) // vestors for anisotropies  \nB := -0.05 // Magnitude of the external magnetic field in Tesla  \nalpha = 0.002 //the damping constant  \nB_ext = vector(B, 0, 0) // External magnetic field vector  \nrelax() // Finding the equilimbrium  \nsave(m) \nTableAdd(B_ext)  \ntableAdd(E_total)  \ntableautosave(5e -13) \nautosave(m, 2.5e -11) // saving magnetization at  every 25 ps.  \nt0 :=2e-9 // ‘ringdown’ magnetic excitation time zero  \nfwhm := 1e -10 // full width at half maximum  \nA := 0.0005 // amplitude of the excitation in T esla \n \nB_ext = vector(B, A*exp( -(t-t0)*(t-t0)/pow(fwhm,2)), 0) // \nexternal field during excitatio n \nrun(20e-9) // 20 ns run time.  \nsave(m) \n \n \n \nS5. Additional m icrowave absorption spectrum  \n \nIn the main text, we show the microwave absorption spectrum on ly at 283 and 258 K , and at \n4.5 GHz frequency. Here in Fig. S3 and S4 , we show the rest of spectrum at other temperatures \nand microwave frequencies.  \n  6 S6. Kittle’s fit  and linewidth analysis of microwave absorption spectrum  \n \nWe describe o ur microwave absorption spectrum  lineshaps with a Lorentzian shape. Because \nwe measure the derivative of the spe ctrum, we fit the lineshapes  with  \n \n𝑓(𝐻)=𝑎+𝑏 (𝐻−𝐻0)\n[(𝛥𝐻)2+(𝐻−𝐻0)2]2+𝑐 𝐻 ,     (S3.1) \nwhere a, b, and c are arbitrary coefficients, H0 is the resonance  field, and 𝛥𝐻 is the linewidth. In \nFig. S 5, we show dependence of the linewidths on frequency at 258 and 263 K. Because the field -\npolarized states can be described by Kittel’s formula, H depends on Gilbert damping  by \n𝛥𝐻=𝛥𝐻0+4𝜋𝛼𝑓\n𝛾𝑒 ,      (S3.2) \nwhere 𝛥𝐻0 is frequency independent broadening component, and 𝛾𝑒 is the electron’s \ngyromagnetic ratio. After we fit linewidths  with Eq. S2, we find Gilbert damping 𝛼=0.038 ±\n0.005. This is significantly lower than recently reported 0.28 damping constant with an out -of-\nplane magnetic field along [111] direction  [6].   7  \nFig S3 . Microwave absorption spectrum of FeGe film at different temperatures.  \n \n 8  \n \n \nFIG S4 . Microwave absorption spectrum of FeGe film at different microwave frequencies.  \n \n 9  \nFIG S 5. Dependence of the linewidth to the microwave frequency at 258 K and 263 K \ntemperatures . We find Gilbert’s damping constant 0.038  and 0.021 at these temperatures. The \nfirst couple of data points have a contribution from helical resonance, we take data points \nbetween 5.25  GHz and 7 GHz  into account .  \n \nS7. Details of analytic calculation  \nWe describe the one dimensional Hamiltonian density  of a chiral helimagnet by  \nℋ=𝐴(𝜕𝑧𝒎)2−𝑫.𝒎×𝜕𝑧𝒎−𝑩.𝒎+𝐾𝑢(𝒎.𝒏̂)𝟐−1\n2𝑯𝒎.𝒎 ,   (S5.1) \nwhere A is the exchange stiffness constant, D is the DM interaction constant, B is the external \nmagnetic field, Ku is the anisotropy constant and Hm is the demagnetizing field due to shape of \nthe sample. We define the normalized magnetization 𝑚=\n[sin𝜃(𝑧,𝑡)cos𝜙(𝑧,𝑡),sin𝜃(𝑧,𝑡)sin𝜙(𝑧,𝑡),cos𝜃(𝑧,𝑡)] in spherical coordinate s, where 𝜃(𝑧,𝑡) \nand 𝜙(𝑧,𝑡) are the polar angles and 𝑧 is the normal axis of the film . The external magnetic field \nB includes dc field Bx and ac microwave field By, and is written as 𝑩=[𝐵𝑥,𝐵𝑦sin𝜔𝑡,0]. Next, we \nwrite down the Lagrangian density ℒ, \nℒ=−ℏ 𝑀𝑠\n𝑔𝑒𝜇𝐵(cos𝜃−1)𝜕𝑡𝜙−ℋ,     (S5.2) \nand the Rayleigh dissipation ℜ=𝛼\n2(𝜕𝑡𝒎)2, where 𝛼 is the Gilbert damping parameter , M s is the \nmagnetization, 𝜇𝐵 is the Bohr magnetron, g e is the electron g -factor. Next, the equation s of \nmotion are constructed from Eq. S5.2 in terms  of 𝜃(𝑧,𝑡) and 𝜙(𝑧,𝑡) using  \n 10 𝑑\n𝑑𝑡 𝛿ℒ\n𝛿(𝜕𝑡𝜃)−𝛿ℒ\n𝛿𝜃+𝛿ℜ\n𝛿(𝜕𝑡𝜃)=0,      (S5.3) \n𝑑\n𝑑𝑡 𝛿ℒ\n𝛿(𝜕𝑡𝜙)−𝛿ℒ\n𝛿𝜙+𝛿ℜ\n𝛿(𝜕𝑡𝜙)=0,      (S5.4) \n𝐿𝑚sin𝜃𝜕𝑡𝜙=sin2𝜃𝜕𝑧𝜙(−𝐷+𝐴𝜕𝑧𝜙)−cos𝜃(𝐵𝑥cos𝜙+𝐵𝑦sin𝜙sin𝜔𝑡)−2𝐴𝜕𝑧2𝜃,  (S5.5) \n2 𝐿𝑚𝜕𝑡𝜃=𝐵𝑦sin𝜔𝑡cos𝜙−𝐵𝑥sin𝜙+2cos𝜃𝜕𝑧𝜃(−𝐷+2𝐴𝜕𝑧𝜙)+2𝐴sin𝜃𝜕𝑧2𝜙.  (S5.6) \nwhere 𝐿𝑚=ℏ 𝑀𝑠\n𝑔𝑒𝜇𝐵 .  \nThen , we substitute following approximation for 𝜙1 and 𝜃1 by using small angle \napproximation:  \n𝜙(𝑧,𝑡)=𝑄𝑧+𝜙1(𝑧)sin𝜔𝑡,     (S5.7) \n𝜃(𝑧,𝑡)=𝜋\n2+𝜃1(𝑧)cos𝜔𝑡,      (S5.8) \n𝜙1(𝑧)=𝐴1+𝐴2cos𝑄𝑧+𝐴3cos2𝑄𝑧    (S5.9) \n 𝜃1(𝑧)=𝐵1+𝐵2cos𝑄𝑧+𝐵3cos2𝑄𝑧   (S5.10) \n \nHere , we use two methods : (1) With By=0, we  find t he natural frequencies by  solving the  \neigen value problem , and (2) we use a non -zero B y and solve ‘driven harmonic oscillator’ problem.  \nFor the first method  \n𝑰 𝜔2− 𝓜=0,     (S5.11) \nwhere I is the identity  matrix and M is  \n1\n2𝐿𝑚2(0 4 𝐵𝑥𝐴 𝑄240 𝐴2𝑄4\n−4 𝐴 𝐵𝑥𝑄2−8 𝐴2𝑄416 𝐴 𝐵𝑥𝑄2\n−𝐵𝑥2−12 𝐴 𝐵𝑥𝑄2−80 𝐴2𝑄4).   (S5.12) \n \nFor the second method, A and B coefficients have common  denominator  \n \n40𝐴4𝐵𝑥2𝑄8−8𝐴2𝐵𝑥4𝑄4+(62𝐵𝑥2𝑄4+160 𝐴2𝑄8)𝐿𝑚2𝐴2𝜔2−44𝐴2𝑄4𝐿𝑚4𝜔4+𝐿𝑚6𝜔6.    (S5.13) \n \nEq. S 5.13 must be zero for the resonance phenomena to give large oscillation amplitude. This \nalso gi ves the same frequencies as in Fig . 5 in the main text.  \n  11 Mor eover , we show the imaginary parts of the resonance frequencies  (Fig. S5)  to clarify  \nwhy the pink -filled region in the Fig. 5 is the correct descr iption for resonance. In Fig. S5, we show \nthe imaginary parts of the eigen values at f1 and f2, which have zero  imaginary parts below 830 \nOe magnetic field and non -zero above it. Thus, the solutions for hig her fields are not valid.  \n \n \nFIG S 6. The imaginary parts of the eigenvalues of f1 and f2 frequency solutions. Because of non -\nzero imaginary par ts above 83 0 Oe, only the low field solutions are valid. This also confirms the \nsmall angle approximation made in the analytic model.  \n \n[1]  P. Pedrazzini, H. Wilhelm, D. Jaccard, T. Jarlborg, M. Schmidt, M. Hanfland, L. A kselrud, \nH. Q. Yuan, U. Schwarz, Y. Grin, and F. Steglich, Phys. Rev. Lett. 98, 047204 (2007).  \n[2]  F. D. Murnaghan, Proc. Natl. Acad. Sci. 30, 244 (1944).  \n[3]  W. M. Yim and R. J. Paff, J. Appl. Phys. 45, 1456 (1974).  \n[4]  G. A. Valkovskiy, E. V Altynbaev , M. D. Kuchugura, E. G. Yashina, V. A. Dyadkin, A. V \nTsvyashchenko, V. A. Sidorov, L. N. Fomicheva, M. Bykov, E. Bykova, L. Dubrovinsky, and \n 12 S. V Grigoriev, J. Phys. Condens. Matter 28, 375401 (2016).  \n[5]  J. C. Gallagher, K. Y. Meng, J. T. Brangham, H. L . Wang, B. D. Esser, D. W. McComb, and F. \nY. Yang, arXiv:1604.06684 1 (2016).  \n[6]  M. Beg, M. Albert, M. -A. Bisotti, D. Cortés -Ortuño, W. Wang, R. Carey, M. Vousden, O. \nHovorka, C. Ciccarelli, C. S. Spencer, C. H. Marrows, and H. Fangohr, arXiv:1604.08347v 1 \n(2016).  \n "    },    {        "title": "1608.07429v1.Optimization_of_nanocomposite_materials_for_permanent_magnets_by_micromagnetic_simulations__effect_of_the_intergrain_exchange_and_the_hard_grains_shape.pdf",        "content": "arXiv:1608.07429v1  [cond-mat.mtrl-sci]  26 Aug 2016Optimization of nanocomposite materials for permanent mag nets by\nmicromagnetic simulations: effect of the intergrain exchan ge and the hard\ngrains shape\nSergey Erokhin and Dmitry Berkov\nGeneral Numerics Research Lab, Moritz-von-Rohr-Strasse 1 A, D-07749 Jena, Germany\nIn this paper we perform the detailed numerical analysis of r emagnetization processes in nanocom-\nposite magnetic materials consisting of magnetically hard grains (i.e. grains made of a material with\na high magnetocrystalline anisotropy) embedded into a magn etically soft phase. Such materials are\nwidely used for the production of permanent magnets, becaus e they combine the high remanence\nwith the large coercivity. We perform simulations of nanoco mposites with Sr-ferrite as the hard\nphase and Fe or Ni as the soft phase, concentrating our efforts on analyzing the effects of ( i) the\nimperfect intergrain exchange and ( ii) the non-spherical shape of hard grains. We demonstrate tha t\n- in contrast to the common belief - the maximal energy produc t is achieved not for systems with\nthe perfect intergrain exchange, but for materials where th is exchange is substantially weakened.\nWe also show that the main parameters of the hysteresis loop - remanence, coercivity and the en-\nergy product - exhibit non-trivial dependencies on the shap e of hard grains, and provide detailed\nexplanations for our results. Simulation predictions obta ined in this work open new ways for the\noptimization of materials for permanent magnets.\nPACS numbers: 75.40.Mg, 75.50.Ww, 75.50.Tt, 75.60.-d\nI. INTRODUCTION\nMagnetic materials which can be used for the\nmanufacturing of permanent magnets belong to\nthe key materials in many high-technology applica-\ntions today1. Modern electromotors, actuators and\nmagnetic-field-basedsensors(to name only a few ap-\nplications) require high-performance magnets. The\neffectivenessofthesemagnetsisusuallyestimatedby\nthe value of the maximal energy product ( BH)max\nachieved in the second quadrant of their B−Hhys-\nteresis loop. One of the most promising ways to\nobtain large values of this parameter is the usage\nof magnetic nanocomposites, i.e.materials which\ncombine a high coercivity of a magnetically hard\nphase (the phase made of a material possessing a\nlarge magnetocrystalline anisotropy) with the high\nsaturationmagnetizationoftheanother(soft)phase.\nAt present, best performance magnets are pro-\nduced basing on rare-earth metals (NdFeB, SmCo)\nand employing the precise fabrication control (see,\ne.g.2). Unfortunately, these magnets are relatively\nexpensive and subject to the availability and price\nfluctuations due to the high volatility of the rare\nearth elements market.\nAnother very important class of materials for per-\nmanent magnets is represented by nanocomposites\ncontaining ferrites as the hard phase. The energy\nproduct of Co-, Ba- and Sr-ferrite-based magnets is\nsufficient for many applications of permanent mag-\nnets, e.g. in microwave devices, telecommunication,recording media, and electronic industry. Another\nimportant advantage of these materials have a much\nbetter temperature and corrosion resistance than\nNdFeB-based magnets (see, e.g. Ch. 12.2 in3). In\naddition, situation with the production of ferrite-\nbased magnets is more stable, and costs are much\nlowerdue to the wideravailabilityofthe correspond-\ning raw materials.\nThe specified performance of a nanocomposite\nmaterial can in principle be achieved by tailoring\nvarious parameters of a nanocomposite, such as rel-\native fractions of the soft and hard phases, size\nand shape of hard grains, mutual arrangement of\ngrains belonging to different phases, and the qual-\nity of the intergrain boundaries. The development\nof new magnets of any type requires the thorough\nunderstanding of the relationship between their mi-\ncrostructure and magnetic properties4. Advanced\nstructural experimental techniques can provide a\nvery important information; well known examples\nare, e.g. the electron Bragg scattering diffraction\nstudies of the grain alignment in sintered NdFeB5or\nthe X-ray diffraction along with the high-resolution\ntransmission electron microscopy applied for the\nmeasurements of the grain size distribution in soft\nmagnetic alloys6.\nRecent publications of different scientific collabo-\nrations have shown that in order to study the ques-\ntion ofthe microstructure-magnetismrelationshipin\ndetails, it is absolutely necessary to employ numeri-\ncal modeling - in particular, micromagnetic simula-tions, combining it with other experimental meth-\nods like 3D atome probe7, energy-dispersive X-ray\nspectroscopy8or magnetic neutron scattering9,10.\nThe usage of micromagnetic modeling in the de-\nvelopment process allows the a priori performance\noptimization of permanent magnets, by predicting\nmagnetic characteristics of a nanocomposite mate-\nrial before its actual manufacturing.\nIn general, micromagnetic simulations are per-\nfectly suited for modeling of magnetic compos-\nites, because the typical micromagnetic character-\nistic length - a few nanometers - allows to resolve\nvery well the magnetization distribution inside the\nnanocomposite grains with sizes of several tens of\nnanometers. However,correspondingsimulationsre-\nquire an enormous computational effort due to two\nmain reasons. First, a very fine mesh of finite el-\nements is required for the adequate approximation\nof each single grain as a geometrical object with a\ncomplicated shape. Second, a large number of soft\nand (especially) hard grains should be present in the\nsimulated volume, in order to study the magneti-\nzation reversal as a collective phenomenon and to\nobtain a sufficiently accurate statistics for these dis-\nordered systems (see a detailed discussion of these\nissues in11–13).\nIn recent years, major simulation effort was de-\nvoted to the understanding of rare-earth-based ma-\nterials, with the strategic goal ”to push the border”\nof the conventional (non-superconducting) mag-\nnets. In the first line, a large amount of nu-\nmerical research was carried out for composites\nbased on NdFeB7,8,14–16and PrFeB17–19; some re-\nsults have been published also for SmCo and similar\ncompounds20.\nFor NdFeB-based materials, the question of the\ninternal magnetization structure (mainly vortex) in\na single grain have been studied14. The influence of\nthe soft phase concentration (Fe or FeB), the hard\ngrain size15and (very recently) magnetic behaviour\nof hard grains for several different shapes16was in-\nvestigated. Special attention was paid to Nd-rich\ncompositions, where it has been shown that the en-\nrichment with Nd leads to the coercivity enhance-\nment due to the concentration of the additional Nd\non intergrain boundaries7,8.\nStudies of composites based on PrFeB and con-\ntaining Fe as the soft phase have been devoted to\nthe increasingroleofthe magnetodipolarinteraction\nwith the growingsoft phase fraction17, correlationof\nthe magnetization reversal of soft and hard grains18\nand the effect of the hard grains alignment19. For\nSmCo-like materials different mechanisms of the\nmagnetization reversal when changing the angle be-tween the anisotropy axis and the applied field were\nidentified20.\nSomewhat apart from the main road lie the sim-\nulations of a highly interesting yet not really ap-\nplicable class of MnBi-based materials. Here the\ninfluence of the soft phase concentration (Co and\nFeCo) and the orientation degree of the hard grain\nanisotropy axes was studied numerically in21.\nIn contrast to the rare-earth-based composites,\nmaterials based on various ferrites as the hard phase\nhavenot been studied - up to ourknowledge - by mi-\ncromagnetic simulations, although this class of ma-\nterials becomes increasingly important for reasons\nlisted above. In the present paper we address this\nchallenge, starting with detailed studies of the effect\noftheintergrainexchangecouplingandthe influence\nof the hard grain shape on the material properties in\nnanocomposites SrFe 12O19/Fe and SrFe 12O19/Ni.\nOur polyhedron-based micromagnetic algorithm\nprovides a high statistical accuracy of simulated re-\nsults, because we are able to handle systems con-\ntaining a few thousand grains, including the ability\nto resolve a possibly non-trivial magnetization dis-\ntribution in every grain. Due to the flexibility of our\nmesh generation method, a nearly arbitrary grain\nshape can be adequately approximated, so that a\nsimulated sample may include the grains of different\nshapes and sizes.\nThe paper is organized as follows: in Sec. II we\nexplain the mesh generation method which we use\nto create a polyhedron mesh for a system containing\nnon-spherical hard grains embedded into a magnet-\nically soft matrix. Evaluation of micromagnetic en-\nergy contributions in our methodology is also briefly\npresented. Sec. III contains simulation results.\nHere, subsection IIIA is devoted to the analysis of\nthe influence of the intergrain exchange weakening\non the magnetization reversal, whereas subsection\nIIIB deals with the effect of non-spherical shapes of\nthe hard grains. Both subsections contain a detailed\nphysical discussion of results obtained. We conclude\nwith the summary of our findings and possible per-\nspectives for the improvement of ferrite-based com-\nposites in Sec. IV.\nII. OUR MICROMAGNETIC\nMETHODOLOGY FOR SIMULATION OF\nNANOCOMPOSITES\nTo overcome the difficulties in modeling mag-\nnetic nanocomposites using standard micromagnetic\nmethods (finite difference and tetrahedral finite ele-\nments), we have developed13a novel micromagnetic\n2methodology based on a discretization of magnetic\nmaterials using polyhedrons of a special type. This\nmethodology combines the flexibility of general fi-\nnite element schemes for the geometrical description\nof a nanocomposite structure with the possibility to\nuse Fast Fourier Transformation for the calculation\nofthe most time consumingcontribution tothe total\nenergy - magnetodipolar interaction.\nA. Mesh generation for grains of a general\nshape\nOne of the main questions discussed in this pa-\nper is the influence of the non-spherical (spheroidal)\nshape of hard grains on the magnetic behavior\nof nanocomposites. For such a system, we had\nto introduce two additional steps into the mesh\ngeneration procedure described in our previous\npublications11–13. Namely, in the present work the\nmesh for hard grains is generated separately from\nthe soft phase mesh (Fig.1) (additional step 1), and\nthen both systems are merged (Fig. 2) (additional\nstep 2).\nFIG. 1. (color online) Examples of the spatial distribu-\ntion of hard crystallites (soft crystallites not shown) in\nsimulated samples for different aspect ratio a/bof corre-\nsponding ellipsoids of revolution (see text for details).\nAsinourstandardmethodology,westartfromthe\ngeneration of mesh consisting of small nearly spheri-\ncal polyhedrons with the sizes less the characteristic\nmicromagnetic length. These polyhedrons will be\nused in micromagnetic simulations as corresponding\nfinite elements (see11–13for details).\nNext, we generate a system of non-overlapping el-\nlipsoidal particles (additional step 1) with sizes and\nshapes corresponding to the hard grains of our com-\nposite. We point out that the generation of an en-\nsemble of non-overlappingellipsoids is computation-\nally challenging: the evaluation of an overlapping\nFIG. 2. (color online) Example ofa microstructure (hard\nandsoftphases)usedinourmodelingofnanocomposites.\nof two ellipsoids and the introduction of the suitable\noverlappingcriterionrequire a development ofa spe-\ncial numerical scheme. We use a method described\nby Donev et al.22, which is based on the Perram-\nWertheim overlap potential and provides a suitable\nparameter describing the overlapping degree of two\nellipsoids. This parameter is then used in the model\nof interacting particles with a short-range repulsive\npotential, where initially ellipsoids are placed ran-\ndomly, but due to the nature of this potential the\nnumber of overlaps is continuously decreasing.\nAt the second additional step, these ellipsoids are\nmapped on the system of (much smaller) polyhe-\ndrons used as mesh elements in our micromagnetic\nsimulation. By this mapping all mesh elements with\ncenters inside ellipsoids, are assigned to the hard\nphase and the rest of elements - to the soft phase.\nAll mesh elements belonging to the same hard grain\nhave the same direction of the anisotropy axes; this\ndirection coincides with the rotational symmetry\naxis of the ellipsoid. Note, that the discretization\nof crystallites of the soft and hard phases is based\non mesh elements of the same size.\nB. Energy contributions and minimization\nprocedure\nIn our simulations we take into account all four\nstandard contributions to the total magnetic free\nenergy: energy in the external field, magnetocrys-\ntalline anisotropy energy, exchange stiffness and\nmagnetodipolar interaction energies11–13.\nThe local energy parts - energy in the external\nfield and the magnetocrystalline anisotropy energy -\narecomputedinastandardway,multiplyingthecor-\nresponding energy densities by the volume of finite\n3elements (polyhedrons in our case) and summing\nover all these elements. The magnetodipolar field\nand energy are computed using the optimized ver-\nsion of the lattice Ewald method for disordered sys-\ntems. In this algorithm, the mapping of the initial\n(disordered) system of mesh elements on the trans-\nlationally invariant regular lattice allows to keep the\nhigh speed of the lattice method (fast Fourier trans-\nformation), at the same time making the mapping\nerrors negligibly small.\nIn this work, we concentrate ourselves in particu-\nlar on the effect of the intergrain exchange. Hence\nwe remind that the exchange energy in our method-\nology is computed in the nearest neighbouring ap-\nproximation as\nEexch=−1\n2N/summationdisplay\ni=1/summationdisplay\nj⊂n.n.(i)2AijVij\n∆r2\nij(mimj),(1)\nwhereVij= (Vi+Vj)/2, ∆rijis the distance be-\ntween the centers of i-th and j-th finite elements\nwith volumes ViandVj. The exchange constant\nAijfor the homogeneous bulk material is equal\nto the corresponding exchange stiffness constant\nA, but is obviously site-dependent in composite\nmaterials12,13.\nFor the minimization of the total magnetic en-\nergy, obtained as the sum of all four contributions\ndescribed above, we use the simplified version of a\ngradient method employing the dissipation part of\nthe Landau-Lifshitz equationof motion for magnetic\nmoments23,24. The minimization is considered as\nconverged, when the condition for the local torque\nmax{i}|[mi×heff\ni]|< εis fulfilled (here miis a nor-\nmalized magnetic moment of the i-th mesh element\nandheff\niisthecorrespondingeffectivefield; thevalue\nε= 10−3was found to be small enough for our qua-\nsistatic minimization procedure).\nFurther details of our method can be found in13.\nIII. RESULTS AND DISCUSSION\nDue to the high performance of our methodology,\nwe are able to simulate bulk nanocomposites with\nhard grains of any prescribed shape, whereby the\nsimulated system may contain up to 600 hard grains\nwith an average discretization of 300 mesh elements\npro grain. Employing this algorithm, we could ob-\ntain systematic results with the high statistical ac-\ncuracy for two model systems: SrFe 12O19/Fe and\nSrFe12O19/Ni.For simulations of these nanocomposites we have\nused standard magnetic parameters of correspond-\ning materials (see, e.g.3, Chap. 5.3 and 11.6) which\nare summarized in the table below:\nSrFe12O19Fe Ni\nMs(G) 400 1700 490\nAnis. kind uniaxial cubic cubic\nK(erg/cm3)4.0·1065.0·105−4.5·104\nA(erg/cm) 0.6·10−62.0·10−60.8·10−6\nThe average grain volume for all phases was cho-\nsen to be equal to the volume of a spherical grain\nwith the diameter D= 25nm. The volume concen-\ntrationofthe hardphasein allpresentedsimulations\nwaschard= 40%.\nA. Effect of the exchange weakening in\nSrFe12O19/Fe\nOne of the central questions for permanent mag-\nnets made of nanocomposite materials is the depen-\ndence of magnetic properties on the exchange weak-\nening between different grains. This weakening is\nunavoidable in real systems, because it is nearly\nimpossible to obtain perfect intergrain boundaries.\nThe quality of these boundaries strongly depends\non the concrete method used for the manufactur-\ning of a nanocomposite and substantial efforts has\nbeen devoted to obtaining materials with more per-\nfect intergrain boundaries (and especially bound-\naries between grains belonging to different phases)\nin order to achieve better exchange coupling. How-\never, recently25is was demonstrated both experi-\nmentally and theoretically that the perfect inter-\ngrain exchange may strongly decrease the perfor-\nmance of a magnetic nanocomposite material, so\nthat this question requires a detailed theoretical\nstudy.\nThe exchange weakening in our methodology is\ndefined bymultiplying the exchangeenergyofneigh-\nboring mesh elements belonging to different crystal-\nlitesbyafactor0 ≤κ≤1. Thisexchangeweakening\ncoefficient is introduced into the expression (1) for\nthe exchange energy as\nEexch=−1\n2N/summationdisplay\ni=1/summationdisplay\nj⊂n.n.(i)κ2AijVij\n∆r2\nij(mimj),(2)\nif neighboring magnetic moments iandjare located\nin different grains (crystallites). From (2) it can be\n4seen that κ= 1 correspondsto the perfect intergrain\nexchange (equal to the exchange within a bulk ma-\nterial) and κ= 0 means no exchange interaction at\nall between different grains.\nDependence of magnetic properties on this ex-\nchange weakening was studied for the composite\nSrFe12O19/Fe with approximately spherical hard\ngrains (obtained from the random placement of\nspheres with D= 25nm, see Sec. IIA).\nFIG. 3. (color online). Simulated hysteresis curves of the\nnanocomposite SrFe 12O19/Fe with spherical hard grains\nfor different exchange weakening constant.\nThe overall trend is shown in Fig. 3, where the\nevolution of hysteresis curves by increasing the ex-\nchange coupling ( κ= 0.0→0.5) between grains is\ndemonstrated. Systems without ( κ= 0.0) or with a\nstrongly reduced ( κ= 0.05) exchange coupling be-\ntween grains exhibit the two-steps magnetization re-\nversal. The first step - large jump on the hystere-\nsis loop in small negative fields (see the panel for\nκ= 0.05 in Fig. 3) - represents the magnetization\nreversal of the soft phase, which volume fraction is\nrelatively high. The second step - reversal of hard\ngrains in much higher fields - leads to the closure\nof the loop. Reversal of the hard phase occurs in\nfields∼Hhard\nK, where the anisotropy field is defined\nasHK= 2K/Ms=βMs(β= 2K/M2\nsdenotes the\nreduced anisotropy constant). The large magnitude\nof the magnetization jump during the first reversal\nstep is due to the dominating contribution of thesoft phase to the system magnetization: msoft=\ncsoft·Msoft/(chard·Mhard+csoft·Msoft)≈0.86.\nFor the detailed analysis of the magnetization re-\nversal in a magnetic composite it is very useful to\nplot hysteresis loops for the soft and hard phase sep-\narately. Such loops can be easily obtained from sim-\nulated magnetization configurations by summing up\ncontributions from finite elements belonging to ei-\nther soft or hard phase and calculating correspond-\ning total magnetizations of these phases.\nWe begin our consideration from systems with\nan absent or very low intergrain exchange coupling,\nwhere the dominant interaction is the magnetodipo-\nlar one. To clarify the effect of this interaction, the\nabove mentioned magnetization reversal curves of\nhard and soft phases are plotted in Fig. 4 for the\ncomposite without any intergrain exchange coupling\n(κ= 0).\nIn order to understand the hysteretic behavior of\nboth phases, it is useful to calculate the reduced\nanisotropy constant β= 2K/M2\ns, which magnitude\ngives (roughly speaking) the relation of the magne-\ntocrystalline anisotropy field to the magnetodipo-\nlar field from the nearest neighbor in the system\nof spherical particles. Substitution of magnetic pa-\nrameters of our materials (see the table above) re-\nsults in the values βh= 50(≫1) for the hard phase\n(SrFe12O19) andβs= 0.34(∼1) for the soft phase\n(Fe). We note that the much higher value of βfor\nthe hard phase is due not only to its largeanisotropy\nconstant K(which is ’only’ 8 times larger than by\nFe), but mainly due to the much higher value of the\nsoftphasemagnetization MFe/MSrFeO= 4.25,which\ngives an additional factor of ≈18.\nConsidering the magnetization reversal of the soft\nphase first, we note that this phase would exhibit\nin the absence of the magnetodipolar interaction\nthe ’ideal’ hysteresis loop for a system of non-\ninteracting particles with the cubic anisotropy con-\nstantKcub>0 (as it is the case for Fe). Such a loop\nhas the remanence j(0)\nR≈0.83 and the coercivity\nH(0)\nc≈0.33HK= 0.33βMs≈195Oe (see, e.g.26).\nThe relatively low value of the reduced anisotropy\nforoursoftphase βs(Fe) = 0.34meansthat themag-\nnetodipolar interaction can considerably modify the\ncorresponding’ideal’ hysteresis. This influence man-\nifests itself primarily in the smoothing of the ’ideal’\nloop26, as it can be seen in Fig. 4, where the loop\nfor the soft phase of our system is shown in red. The\nremanence jR≈0.836is nearly the same and the co-\nercivityHc≈260Oe increased by ≈30% compared\nto the non-interacting case.\nUnfortunately, we are not awareof any systematic\n5theoreticalstudiesofthe magnetodipolarinteraction\neffects in systems of ’cubic’ particles, except for the\npaper27, whereonlysimulationresultsfortheHenkel\nplots are shown; any quantitative comparison with a\ndetailed study of these effects for ’uniaxial’ particles\npresented in28is meaningless due to very different\nenergy landscapes for these two anisotropy types.\nFor this reason, we can only suggest that the nearly\nunchanged remanence (compared to the ’ideal’ sys-\ntem) is due to the interplay of the magnetodipolar\ninteractions within the soft phase and between the\nsoft and hard phases. The increase of Hcis most\nprobably due to the ’supporting’ action of the mag-\nnetodipolar field from the hard phase onto the soft\ngrains. Magnetization of the hard phase in our sys-\ntem is rather low, so that the corresponding effect is\nrelatively small.\nFIG. 4. (color online). Simulated hysteresis loops for\nSrFe12O19/Fe (with spherical hard grains) without the\nintergrain exchange ( κ= 0) presented for hard (solid\nblue line) and soft (solid red line) phases separately.\nDashed line represents the unsheared loop of the SW\nmodel with particle parameters as for SrFe 12O19, solid\ngreen line - the SW loop sheared according the aver-\naged internal field (see text for details). External field\nis normalized by the anisotropy field of the hard phase\nHK=βhMh= 20kOe.\nThe non-interacting hardphase consisting of\ngrains with the uniaxial anisotropy (as for\nSrFe12O19) would reverse according to the ideal\nStoner-Wohlfarth (SW) loop29withjR= 0.5 and\nHc≈0.48HK≈10kOe shown in Fig. 4 with the\nthin dashed green line. The very large value of the\nreduced single-grain anisotropy βh(SrFeO) = 50 for\nthis phase means that intergraincorrelationsof hard\nphase magnetic moments are negligible. However,\nin our composite material hard grains are ’embed-ded’ into the soft phase. Hence, in order to prop-\nerly compare (at least in the mean-field approxi-\nmation) the simulated hard phase loop - blue solid\nline in Fig. 4 - with the SW model, we have to\ntake into account the average magnetodipolar field\n/angbracketleftHmd,z/angbracketright= (4π/3)/angbracketleftMsoft\nz/angbracketrightacting on a spherical par-\nticle inside a continuous medium with the average\nmagnetization of the soft phase /angbracketleftMsoft\nz/angbracketright.\nCorrection of the SW loop using this internal field\n(which depends on the external field via the corre-\nsponding dependence /angbracketleftMz(Hz)/angbracketright) leads to the loop\nshown with the thick solid green line in Fig. 4.\nIt can be seen that this corrected SW loop is in\na good agreement with the simulated hard phase\nloop. Remainingdiscrepanciesaredue to localinter-\nnal field fluctuations (always present in disordered\nmagnetic systems) which are especially pronounced\nin our composite due to the high difference between\nthe magnetizations of soft and hard phases.\nThis analysis reveals that the first jump on the\nhard phase loop in small negative fields is due to\nthe abrupt change in the internal averaged dipolar\nfield due to the magnetization reversal of the soft\nphase. The second jump - for Hz/Hk≈ −0.3 -\nis the manifestation of the singular behavior of the\nSW loop of the hard phase itself, which occurs for\nthe unsheared loop at Hcr=−Hk/2 (near this field\nMz∼/radicalbig\n−(Hz−Hcr) forHz< Hcr30).\nIn summary, despite a relatively high saturation\nmagnetization Ms= 1180G, the corresponding\ncomposite without any intergrain exchange coupling\nwould have only a relatively small maximal energy\nproduct of ≈15kJ/m3(see Fig. 5b). The reason is\nits very small coercivity Hc≈250Oe, which is de-\ntermined entirely by the magnetization reversal of\nthe soft phase in small negative fields.\nBefore we proceed with the analysis of the effect\nof the intergrainexchange coupling on the hysteretic\nproperties of a nanocomposite, an important me-\nthodical issue should be clarified. Namely, we have\ntodetermine the maximalvalue ofthe exchangecou-\npling(maximalvalueof κ), forwhichoursimulations\ncan produce meaningful results.\nThe problem is that with increasing the cou-\npling strength, the interaction between the grains\nincreases, so that grains are starting to form clus-\nters, inside which magnetic moments of constituting\ngrains reverse nearly coherently. The average size of\nsuch a cluster /angbracketleftdcl/angbracketrightobviously growths with increas-\ningκ. In order to obtain statistically significant re-\nsults, we have to assure that /angbracketleftdcl/angbracketrightis significantly less\n(ideally much less) than the maximal system size ac-\ncessible for simulations. Otherwise we might end up\n6with the case where we are simulating the magne-\ntization reversal of a system consisting of a single\n(or very few) cluster(s), so that corresponding re-\nsults will be non-representative for the analysis of\nreal experiments.\nThe best quantitative method to determine /angbracketleftdcl/angbracketright\nis the calculation of the spatial correlation function\nof magnetization components perpendicular to the\napplied field (in our case MxandMy): the average\nvalue of these components should be zero, and the\ndecay length of their correlation functions Cx(r) =\n/angbracketleftMx(0)Mx(r)/angbracketright(the same for My) would provide a\nmost reliable estimation of /angbracketleftdcl/angbracketright.\nHowever, taking into account a complex 3D char-\nacter of Cx,y(r), we have adopted another crite-\nrion to determine the approximate number of in-\ndependent clusters contained in our simulated sys-\ntem. Namely, as the figure of merit we have em-\nployed the maximal value of the perpendicular com-\nponent of the total system magnetization m⊥=/radicalBig\nM2x+M2y/Msduring the magnetization reversal.\nIf the system contains only one (or very few) clus-\nter(s), than for some field during the reversal pro-\ncess this component should be large (close to 1), be-\ncause one cluster reverses nearly in the same fashion\nas a single particle, i.e., its magnetization rotates\nas a whole without significantly changing its magni-\ntude. Hence at some reversal stage m⊥would un-\navoidably become relatively large. In the opposite\ncase, where a system contains many nearly indepen-\ndent clusters ( Ncl≫1), their components Mx,iand\nMy,i(i= 1,...,N), being independent variableswith\nzero mean, would averagethemselves out, leading to\nsmall values of m⊥.\nA simple statistical analysis based on the assump-\ntion of the independence of different clusters shows\nthat the number of such clusters can be estimated\nasNcl≥1/m2\n⊥. This means that up to m⊥≈0.3\nwe produce statistically significant results, because\nin this case Ncl≥10. Corresponding analysis shows\nthat for our systems (containing about ∼5·105fi-\nnite elements) this is the case up to κ≈0.5, so\nbelow we show results only in this range of exchange\ncouplings.\nSimulation results showing basic characteristics\nof the hysteresis loop - remanence jR, coercivity\nHcand energy product Emax= (BH)max- for\nthe SrFe 12O19/Fe composite as functions of the ex-\nchange weakening κare presented in Fig. 5. We\nremind that for these simulations approximately\nspherical hard grains were used.\nFrom Fig. 5 it can be clearly seen that the rema-\nnencejRof this material depends on the intergrain(a)\n(b)\n(c)\nFIG. 5. (color online). (a)Remanence, (b)coerciv-\nity and(c)energy product of simulated nanocomposite\nSrFe12O19/Fe with spherical hard grains as a functions\nof exchange weakening on the grain boundaries. Inset\nin (a) represents the maximal value of perpendicular (to\nthe directions of applied field) component of magnetiza-\ntion during the remagnetization process. Dashed lines\nare paths for the eye.\nexchange coupling relatively weak. The reason is\nthatjRis very high already for the fully exchange\ndecoupled composite ( jR(κ= 0)≈0.8). Such a high\nvalue, in turn, is due to the fact that the remanence\nis governed by the soft phase consisting of cubical\ngrains. The remanenceofthe non-interacting(ideal)\nensemble of such grains is j(0)\nR≈0.83. This high re-\nmanence can not be significantly increased by the\nexchange interaction within the soft phase (as it is\nthecaseforthesystemof uniaxialparticleswithran-\ndomly distributed anisotropy axes, where j(0)\nR= 0.5;\nsee also31for the analysis of a corresponding 2D\n7system). Neither can this remanence be substan-\ntially decreased by the exchange coupling with hard\ngrains, because their magnetizationat Hz= 0is still\nnearly aligned along the initial field direction due\nthe strong magnetizing field from the Fe soft phase,\n(with its high magnetization MFe= 1700 G).\nIn contrastto jR, the coercivity Hcexhibits a pro-\nnounced maximum as the function of the exchange\ncoupling κ, resulting in the corresponding maximum\nof theκ-dependence of the maximal energy product\n(BH)max(κ). We will explain the reasons for the\nappearance of this maximum below, analyzing the\nhysteretic behavior of our nanocomposite for vari-\nousκ.\nFor the smallest non-zero κstudied here the mag-\nnetization reversal process is visualized in Fig. 6,\nwhere hysteresis loops for soft and hard phases are\nshown separately and the magnetization configura-\ntion is displayed for several characteristic external\nfields. First, it can be clearly seen that the mag-\nnetizations of soft and hard phases reverse sepa-\nrately. The inspection of magnetization configura-\ntions shows that the reversal of magnetic moments\nstarts within the soft phase (see panel (a)) around\nthe hard grains which anisotropy axis are directed\n’favorably’(i.e. deviatestronglyfromtheinitialfield\ndirection). Then the reversed area expands, occupy-\ning even larger regions of the soft phase (panel (b))\nuntil nearly the entire soft phase is reversed (panel\n(c)). Note that in the negative field corresponding\nto this nearly complete reversal of the soft phase,\nthe majority of the hard phase is still magnetized\napproximately along the initial direction. Only in\nmuchlargernegativefields(rightdrawingofhystere-\nsis loops) the hard phase magnetization also starts\nto reverse (see panel (d)).\nWe emphasize here two important circumstances:\nalthoughtheexchangecouplingbetweenthesoftand\nhard phases is very weak ( κ= 0.05) and the concen-\ntration of the hard phase is moderate (40%), the\n’supporting’ action of the hard phase is enough to\nnearly double the coercivity of the soft phase and\nhence - of the whole system, when compared to the\ncase ofκ= 0 - see Fig. 5. At the same time, due\nto this low exchange coupling, hard grains reverse\nseparately from the soft phase and nearly separately\nfrom each other (see panel (c)), leading to a high\ncoercivity of the hard phase (right drawing of hys-\nteresis loops).\nFor the larger exchange coupling κ= 0.1 (see Fig.\n7) the ’supporting’ effect of the hard phase increases\nthe coercivity of the soft phase even further (com-\npared to κ= 0.05). At the same time, this larger\ncoupling also leads to the much earlier reversal of\nFIG. 6. (color online). Magnetization reversal process\nfor the composite with exchange weakening κ= 0.05.\nFrom top to bottom: microstructure of the system\n(warm colors - soft, cold colors - hard grains); hystere-\nsis shown as separate curves for the soft (red) and hard\n(blue line) phases (note different scales of the H-axis);\nmagnetization configurations shown as mz-maps for field\nvalues indicated on the hysteresis plots shown above.\nthe hard phase, significantly decreasing its coerciv-\nity - see hysteresis plots in Fig. 7. Magnetization\nreversal for this coupling starts in those system re-\n8FIG. 7. (color online). Magnetization reversal for the\ncomposite with the exchange weakening κ= 0.10 pre-\nsented in the same manner as in Fig. 6.\ngions where the hard phase is nearly absent (due to\nlocal structural fluctuations) - see panel (b) in Fig.\n7 - and is much more cooperative compared to the\ncase ofκ= 0.05.\nThe resulting coercivity of the entire system is at\nits maximum, because the interphase coupling is,\non the one hand, large enough to prevent the soft\nphase from the reversal in small fields, but on an-other hand, small enough to enable to the reverse of\nthe hard phase in much higher negative fields than\nthe soft phase.\nFIG. 8. (color online). Magnetization reversal for the\ncomposite with the exchange weakening κ= 0.20 pre-\nsented in the same way as in Fig. 6. Simultaneous re-\nversal of the hard and the soft phases is clearly visible.\nWhen the intergrain exchange coupling is in-\ncreased further, magnetization reversal of the sys-\ntem becomes fully cooperative, so that the soft and\nhardphasesreversesimultaneously(inthesameneg-\native fields) - see hysteresis loops shown in Fig. 8\nforκ= 0.2. Spatial correlations between the mi-\ncrostructure and the nucleation regions for the mag-\nnetization reversal become weak, as it can be seen\nfrom microstructural and magnetic maps presented\nin this figure. It is also apparent that the correlation\ndistance of the magnetization configuration strongly\nincreases, as it was noted in the discussion above.\nThe overallresult is the decreaseof the system co-\n9ercivity, because the soft phase causes the much ear-\nlierreversalofthehardphase,sothatthesupporting\neffect of the high anisotropy of the hard phase be-\ncomes smaller. However, for this relatively low value\nofκ= 0.2 this ’supporting’ effect is still present:\nHc(κ= 0.2) is nearly twice as large as Hc(κ= 0).\nWhen the exchange coupling increases even fur-\nther, the magnetizationreversalbecomes completely\ndominated by the soft phase due to its larger mag-\nnetization and volume fraction. In particular, for\nκ= 0.5 both the coercivity and the energy product\nare nearly the same as for κ= 0. We note that hys-\nteresis loops for these two cases ( κ= 0 and κ= 0.5)\nlook qualitatively different, but this physically im-\nportant difference (two-step vs one-step magnetiza-\ntion reversal) does not matter for the performance\nof the nanocomposite from the point of view of a\nmaterial for permanent magnets.\nThe non-monotonous dependence of the max-\nimal energy product on the exchange coupling\n(BH)max(κ) can be easily deduced from the depen-\ndenciesjR(κ) andHc(κ). When κincreases from 0\nto≈0.1, bothremanenceandcoercivityincrease,re-\nsultingintherapidgrowthof( BH)max. Forκ >0.1,\nthe small increase of the remanence (up to κ≈0.2)\ncan not compensate the large drop of coercivity, re-\nsulting in the overall decrease of the energy prod-\nuct. We point out here that such a behavior occurs\nonly when the dependence of the coercivity on the\ncorresponding parameter (in our case the exchange\nweakening κ) is really strong. The case when the co-\nercivity depends relatively weak on the parameter of\ninterest, is analyzed in detail in the next subsection.\nSummarizing this part, we have shown that, in\ncontrast to the common belief, there exist an op-\ntimalvalue of the interphase exchange coupling in\na soft-hard nanocomposite which provides the max-\nimal energy product. This optimal value obviously\ndepends on the fractionsof the soft and hard phases,\nbut it is very likely that the optimal coupling should\nbesignificantlylessthantheperfectcoupling( κ= 1)\nfor all reasonable compositions in this class of mate-\nrials.\nThis important insight opens a new route for the\noptimization of the permanent magnet materials.\nB. Effect of the grain shape of the hard phase\ninSrFe12O19/FeandSrFe12O19/Nicomposites\nOne of the intensively discussed questions when\noptimizing the nanocomposite materials for perma-\nnent magnets is whether the materials containing\nthe hard grains with the non-spherical shape couldprovide an improvement of the energy product for\ncorresponding composites (see corresponding refer-\nences in the Introduction).\nThe standard argument in favor of the possi-\nble improvement of Emaxis the additional shape\nanisotropy of non-spherical particles. For an elon-\ngated(prolate)ellipsoidofrevolutionthisanisotropy\ncould increase the already present magnetocrys-\ntalline anisotropy (mc-anisotropy), thus enhancing\nthe coercivity of the hard phase and hence - the en-\nergy product. Below we will demonstrate that this\nline of arguments is not really conclusive and that\nthe grainshape effect may be even the opposite - the\nenergy product can be larger for a material contain-\ningoblatehard grains.\nBefore proceeding with the analysis of our results,\nwe emphasize, that the relativecontribution of the\nshape anisotropy can be approximately the same for\nrare-earth and ferrite-based materials. The former\nmaterials have a much larger mc-anisotropy Kcr, so\nthat on the first glance shape effects for rare-earth\n’hard’ grains should be much smaller. But the the\nrelation between the shape anisotropy and the mc-\nanisotropy contributions is determined not only by\nthe value of Kcr, but by the reduced anisotropy con-\nstantβ= 2Kcr/M2\ns, which gives, roughly speaking,\nthe relation between the mc-anisotropy energy and\nthe self-demagnetizing energy of a particle.\nThe presence of the material magnetization in the\ndenominator of the expression for βmakes this con-\nstants for both material classes very similar. For ex-\nample, the mc-anisotropy Kcr≈4.6×107erg/cm3\nfor Nd 2Fe14B is more than one order of magnitude\nlarger than its counterpart Kcr≈4×106erg/cm3\nfor SrFe 12O19. However, the much lower magne-\ntization Ms≈400G of SrFe 12O19compared to\nMs≈1300G of Nd 2Fe14B makes the difference be-\ntween reduced anisotropies of these materials quite\nsmall:βNdFeB≈60, whereas βSrFeO≈50.\nIn the language of the anisotropy field we have to\ncompare the values of the mc-anisotropy field HK=\nβMs= 2Kcr/Mswith the values of the magnetiz-\ningmagnetodipolar field, which attains its maximal\nvalueHmax\ndip= 2πMsfor a needle-like particle. Cor-\nresponding relation Hmax\ndip/HK=πM2\ns/Kcr= 2π/β\nis≈10.5 for Nd 2Fe14B and≈12.5 for SrFe 12O19.\nThis means that in the best case the effect of\nthe shape anisotropy for both material classes can\nachieve≈20%, what would be a non-negligible im-\nprovement on a highly competing market of modern\npermanent magnet materials.\nUnfortunately, severalcircumstancesare expected\nto strongly diminish the shape anisotropy contribu-\n10tion. First, the estimate above holds for a strongly\nelongated particle; for ellipsoidal particles with a re-\nalistic aspect ratio a/b∼2−3 (ais the length of\nthe axis of revolution) the shape anisotropy field is\nonly about half its maximal value. Second, this es-\ntimation holds for a single-domain particle, whereas\nstrongly elongated or nearly flat particles acquire a\nmulti-domain state much easier than the spherical\nones, because the domain wall energy for strongly\nnon-spherical particles is much smaller, than for a\nsphere. Finally, the relation derived above is true\nonly for an isolated particle, and hard grains in\nnanocomposites are always embedded into a soft\nphase or are in a close contact with another hard\ngrains.\nFor these reasons we have performed a detailed\nnumerical study of the dependence of hysteresis\nproperties on the hard grain shape for nanocom-\nposite SrFe 12O19/Fe and - for comparison - for\nSrFe12O19/Ni . For this purpose we have simulated\nmagnetization reversal in these composites with the\nhard grains having the shape of ellipsoids of rev-\nolution (spheroids) with the aspect ratio a/b=\n0.33,0.5,1.0,2.0,3.0; aspect ratios a/b >1 corre-\nspond, as usual, to prolate spheroids. For all aspects\nratios the volume of a single hard grain was kept\nthe same (and equal to the volume of the approxi-\nmately spherical grains with D= 25 nm). Volume\nconcentration of the hard phase chard= 40% was\nthe same, as for simulations reported in the previ-\nous Sec. IIIA. The exchange weakening parameter\nκ= 0.1 was chosen close to the optimal value for\nspherical hard grains obtained above.\n1. Grain shape effect for SrFe12O19/Fe\nFirst we discuss simulation results obtained for\nthe composite SrFe 12O19/Fe - see Figs. 9, 10 and\n11. In Fig.9, magnetization reversal curves for dif-\nferentaspectratios a/bareshown; both theloopsfor\nthe entire system and for the soft and hard phases\nseparately are presented. The most interesting ob-\nservation here is the pronounced difference between\nthe reversal curves of ’soft’ and ’hard’ phases for\na/b= 1 and nearly synchronous magnetization re-\nversalofboth phasesforotheraspectratiosshownin\nthe figure. This is a key feature for the understand-\ning of the system behavior and will be discussed in\ndetail below.\nOverall dependencies of basic hysteresis parame-\ntersjR,Hcand (BH)maxon the aspect ratio a/bis\npresented in Fig. 5. Both main parameters of the\nhysteresis - remanence jRand coercivity Hcexhibita/b = 0.33 a/b = 1.0\na/b = 2.0 a/b = 3.0\nH (kOe) H (kOe)Mz/Ms Mz/Ms\nFIG. 9. (color online). Simulatedhysteresis curvesof the\nnanocomposite SrFe 12O19/Fe for the exchange weaken-\ningκ= 0.1 and differentaspect ratios of hardcrystallites\nas indicated on the panels. Black loops -hysteresis of the\ntotal system, blue curves - upper part of the hysteresis\nloop for the hard phase, red curve - the same for the soft\nphase.\na highly non-trivial dependence on this aspect ratio,\nwhich should be carefully analyzed.\nThe dependence jR(a/b) shown in Fig. 10\nis clearly counter-intuitive, because normally one\nwould expect a higherremanence for a system con-\ntaining elongated particles - in our case for a/b >1\n- due to the positive shape anisotropy constant for\nsuch particles. The simulated dependence shows\nthe opposite trend - the remanence increases with\ndecreasing the aspect ration a/b, i.e.,jRbecomes\nlarger for a composite with oblatehard grains.\nThis behavior can be explained taking into ac-\ncount that hard ellipsoidal grains are mostly embed-\ndedintothesoftmagneticmatrix(softphase), which\nmagnetization is larger than that of the hard phase:\nMFe> MSrFe12O19. This means that hard grains\nrepresent magnetic ’holes’ inside a soft matrix, what\nmeans, in turn, that the total magnetodipolar field\nacting on the magnetization of the hard grain, is\ndirected (on average) towards the initially applied\nfield. With another words, this field acts as a mag-\nnetizing field, i.e. it increases the remanence of the\nhard phase.\nThe magnitude ofthis magnetizingfield is propor-\ntional to the difference between magnetizations of\n11(a)\n(b)\n(c)\noblateprolate\nFIG. 10. (color online). (a)Simulated reduced re-\nmanence, (b)coercivity and (c)energy product of\nnanocomposites SrFe 12O19/Fe with different aspect ra-\ntios (a/b) of hard grains. Inset in (a) shows the demag-\nnetizing factor in dependence on a/b. Dashed lines are\nguides for an eye.\nthe soft and hard phases and is of the order Hmag\ndip∼\nNdem·(MFe−MSrFe12O19) =Ndem·∆M. Foroursys-\ntem parameters ∆ M= 1300G, so that, taking into\naccount that Ndem∼π, we obtain Hmag\ndip∼4kOe.\nThis value is comparable to the mc-anisotropy field\nof the hard grain itself ( HK(SrFe12O19) = 20kOe),\nso the effect of this magnetodipolar field can be sig-\nnificant.\nTo explain the trend jR(a/b) seen in Fig. 11, it\nremains only to note that this magnetizing field is\nlarger for oblatespheroids, for which it can achieve\nthe magnitude of 4 π∆Ms- the limiting case for a\nthin disk with the revolution axes along the mag-\nnetizing direction of the system. In contrast, for\nthe prolate spheroid Hmag\ndipbecomes weaker when\na/bincreases (spheroid becomes more prolate), be-cause the main contribution to this field comes from\nthe soft phase regions near the ends of this prolate\nspheroid.\nThe result of this complicated interplay is the\nbetter alignment of magnetic moments of the hard\nphase consisting of oblate particles. This leads to\nthe higher remanence of the whole system for two\nreasons: ( i) the remanence of the hard phase itself\nis larger and ( ii) the ’supporting’ action of the hard\nphase on the soft phase - due to the interphase ex-\nchange coupling - is more significant.\nThe explanation of the non-trivial dependence of\nthe coercivity on the aspect ration Hc(a/b) - with\nthe maximum between a/b= 0.5 anda/b= 1.0 -\nrequires a detailed understanding of the magnetiza-\ntion reversal mechanism in composites with partial\ninterphase exchange coupling.\nNamely, magnetizationreversalofthese nanocom-\nposites always occurs according to the following sce-\nnario: the soft phase switches first, and then exhibit\na torque on the hard grains due to the interphase\nexchange interaction. For non-negligible interphase\nexchange this torque is the main interaction mech-\nanism between the phases and leads (together with\nthe applied field) to the magnetization reversal of\nthe hard phase in larger negative external fields.\nIn order to understand, why the coercivity has\nits maximum for particles with a weak shape\nanisotropy, we have to recall that the interphase ex-\nchange interaction is a surface effect and as such is\nproportional to the interphase surface area. In our\ncase this is the surface area of hard grains, which are\nmostly surrounded by the soft phase. This means,\nthat exchange torque which the soft phase exhibits\non the hard grains, is proportional to the surface\narea of these grains. Hence, this torque should be\nminimalforthehardgrainswiththesphericalshape,\nbecause the surface area of an ellipsoid of revolu-\ntion with the given volume is minimal for a/b= 1\n(sphere).\nFor this reason hard phase with grains having the\nshape close to spherical will have the maximal coer-\ncivity, i.e. reverse in the largest negative field. Such\ngrains will be also able to ’support’ soft phase up to\nnegative fields larger than non-spherical hard grains\nwould do, leading to the largest coercivity of the\nwhole sample.\nTo provide further proof of this hypothesis, we\nhave plotted in Fig. 11 the coercivities of the hard\nand soft phases separately (see curves for Hhard\ncand\nHsoft\ncon the panel (a)) and the difference between\nthem∆Hconthepanel(b)asfunctionsoftheaspect\nratioa/b. The excellent qualitative agreement be-\ntween ∆Hc(a/b) and the inverse of the surface area\n12hard phasehard phase\nsoft phase(a)\n(b)\nFIG. 11. (color online) (a)Coercivities of the hard (blue\ncircles)Hhard\ncand soft (red circles) Hsoft\ncphases and (b)\ndifference ∆ Hcbetween these coercivities as functions of\nthe aspect ratio a/b; inset in (b) - inverse of the surface\narea of an ellipsoid of revolution in dependence on a/b\n. Dashed lines are guides for an eye. See text for the\ndetailed explanation.\nof an ellipsoid of revolution 1 /Sell(a/b) (see inset to\nthis panel) as the functions of a/bclearly shows that\nthe observed effect is due to the surface-mediated\ninteraction, what in our case clearly means the in-\nterphase exchange interaction.\nWe finish this subsection with the explanation\nwhy the dependence of the maximal energy prod-\nuct on the aspect ratio Emax(a/b) (panel (c) in\nFig.10)foroursystemcloselyfollowsthecorrespond-\ning trend of the remanence jR(a/b) (see panel (a)),\nbut is not influenced by the dependence Hc(a/b)\n(panel (b)).\nTo understand this phenomenon, we recall that\ntheenergyproductisdefinedasthemaximalvalueof\nthe product ( BH) within the second quadrant ofthe\nhysteresis loop, i.e. for external fields −Hc< H <0\n(here and below we omit for simplicity the index z\nbyH,BandM):\nEmax= max\n−Hc<H<0[B(H)·H] = max[( H+4πM(H))·H],\n(3)\nwhere it is important, that the energy product de-\npends on Hboth explicitly and implicitly - via the\ndependence M(H).Let us now assume that for some reference pa-\nrameter value (e.g. in our case for a/b= 1) with\nthe magnetization vs. field dependence given by the\nfunction Mref(H) the product (3) reaches its maxi-\nmumE(0)\nmaxfor the field value H0. This means that\nthe corresponding derivative of the energy product\ndE/dHvanishes at this point, leading to the condi-\ntion\nd\ndH[(H+4πMref(H))·H]|H=H0=\n=H0+2π/bracketleftBigg\nMref(H0)+H0dMref\ndH/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nH=H0/bracketrightBigg\n= 0(4)\nIf the parameter in question changes (i.e. we take\nanother value of a/b), then the hysteresis loop also\nchanges, becoming Mnew(H) =Mref(H)+∆Mand\nthe maximum of the energy product is achieved at\nanother field Hnew=H0+∆H. The new maximal\nenergy product then is\nEnew\nmax= (Hnew+4πMnew(Hnew))·Hnew].(5)\nAssuming that ∆ Mand ∆Hare small, we can\nexpand the functions Mref(H) and ∆M(H) in the\nvicinity of the point H0. Starting from Eq.5 and re-\ntaining only terms linear in ∆ Mand ∆H, we obtain\nforEnew\nmaxthe expression\nEnew\nmax=E(0)\nmax+4πH0∆M(H0)+\n+2∆H/braceleftBigg\nH0+2π/bracketleftBigg\nMref(H0)+H0dMref\ndH/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nH=H0/bracketrightBigg/bracerightBigg\n(6)\nThe coefficient in braces after ∆ His exactly the\nexpression (4) at the point where the reference en-\nergy product reaches its maximum and as such is\nequal to zero. Hence we are left with the expression\nof the new maximal energy product as\nEnew\nmax=E(0)\nmax+4πH0∆M(H0) (7)\nThis expression shows that the change of the en-\nergy product due to the variation of some exter-\nnal system parameter is controlled mainly by the\nchange of the magnetization curve (upper part of\ntheM−Hhysteresis loop) at the external field\nH0where the reference energy product reached its\nmaximum. Obviously, this magnetization change\nis roughly proportional to the remanence change,\n13which explains the semiquantitative correspondence\nbetween the dependencies jR(a/b) andEmax(a/b).\nWe point out once more that this statement is true\nonlyifthe coercivityshift due tothe variationofthis\nparameter is relatively small. If this is not the case,\nthen the position of the vertical side of the rectangle\n(in the ( B−H) plane) used for the determination\nof (BH)maxcan strongly depend on the coercivity\nvalue, making the derivation of Eq. (6) invalid.\n2. Grain shape effect for SrFe12O19/Ni\nThe second composite which we have used to\nstudy the grain shape effect - SrFe 12O19/Ni - is\nqualitatively different from the previous material\n(SrFe12O19/Fe) due to the much lower magnetiza-\ntion of the soft phase: Ms(Ni)≈490G. The idea\nbehind the usage of a soft phase with such a low\nmagnetization is that the coercivity of the resulting\nmaterial should be much higher due to the weaker\nresponse of the soft phase with a smaller magneti-\nzation to the external field. This higher coercivity\nmight compensate the decrease of the net magneti-\nzation, resulting in a competitive energy product.\na/b = 0.33 a/b = 1.0\na/b = 3.0 a/b = 2.0\nFIG. 12. (color online).Simulated hysteresis curves of\nthe composite SrFe 12O19/Ni forκ= 0.1 and different as-\npect ratios of hardcrystallites as indicated on thepanels.\nBlack loops - total hysteresis, blue curves - upper part\nof the hysteresis loop for the hard phase, red curve - for\nthe soft phase.(a)\n(b)\n(c)\nFIG. 13. (color online). (a)Remanence, (b)coer-\ncivity and (c)energy product of the nanocomposite\nSrFe12O19/Ni in dependence on the aspect ratio a/bof\nhard grains. Dashed lines are guides for an eye.\nSimulation results for SrFe 12O19/Ni with various\ngrain shapes are presented in Fig. 12 (hysteresis\nloops) and Fig. 13 (basic characteristics of the hys-\nteresis). As it can be clearly seen, the Ni-containing\ncomposite behaves itself qualitatively different com-\npared to Fe-containing material.\nThe main new feature is - as expected - the higher\ncoercivity of both soft and hard phases. The consid-\nerably larger coercivity of the Ni phase ( Hc(Ni)≈\n1000Oe - see Fig. 12, red loops) compared to the\ncoercivity of the Fe phase in the previously stud-\nied composite ( Hc(Fe)≈600Oe - see Fig. 11a) is\nmainlyduetothelowermagnetizationofNi, asmen-\ntioned above.\nThe much larger coercivity of the hard phase (we\nremind that this phase is the same for both stud-\nied materials) for SrFe 12O19/Ni can be most prob-\nably explained by three reasons. First, due to the\n14lowerMs(Ni) the reversal of the soft phase starts\nfor the Ni-containing composite in higher negative\nfields, what should by itself lead to larger Hhard\nc\nfor the hard phase also. However, this reason alone\ncould not be responsible for the more than fourfold\nincrease of Hhard\nc(Hhard\nc(SrFe12O19/Ni)≈4000Oe\nvsHhard\nc(SrFe12O19/Fe)<1000Oe).\nThesecondreasonisthatthemagnetodipolarfield\nof the soft phase acting on hard grains is much\nsmaller for Ni- than for Fe-containing composites\n(due to the same much lower magnetization of Ni).\nAfter the reversal of the soft phase this magne-\ntodipolar field is directed opposite to the initial ma-\nterial saturationand thus assiststhe reversalof hard\ngrains. Much smaller magnitude of this field thus\nleads to much higher external field required to re-\nverse the hard phase.\nFinally, the considerably smaller exchange con-\nstant of Ni compared to Fe (see Table 1) results in\nthe lower exchange torque acting on hard grains af-\nter the reversal of the soft phase, also decreasing the\ntotal torque acting on the hard phase and increasing\nits coercivity.\nThis qualitatively new situation - the non-\ncorrelated magnetization reversals of the soft and\nhard phases - leads to the another type of the co-\nercivity dependence on the aspect ratio a/bof hard\ngrains: coercivity Hc(a/b) decreases when this ratio\nincreases (see Fig. 13b), behaving itself in a very\nsimilar way as the remanence jR(a/b) (Fig. 13a).\nThe most likely explanation of this behavior is\nthe following: the degree of the magnetization align-\nment ofhardgrainsfortheir differentaspectratiosis\nnearly the same for various values of a/b. Hence the\nmain effect on the soft phase reversal is due to the\ndifference in the magnetodipolar field distributions\ncaused by hard grains having various shapes. Pro-\nlate ellipsoids of revolution produce a non-uniform\nmagnetodipolar field which maximal value is higher\nthan for oblate ellipsoids. However, the field of\nprolate particles is strongly concentrated near their\n’sharp’ ends, whereas the dipolar field of oblate el-\nlipsoids (magnetized on average along their axes of\nrevolution) occupies a much larger region near their\n’flat’ surfaces. For this reason the dipolar field of\noblate hardgrainssupportsthe magnetizationofthe\nsoft phasein largerspaceregions,thus leadingto the\nincrease of the soft phase (and total) coercivity with\ndecreasing a/b, i.e. when hard grains become more\noblate.\nAs the result of the decrease of both jRandHc,\nthe energy product also decreases with increasing\na/b, as shown in Fig. 13c. We point out that al-\nthough the resulting behavior is qualitatively some-what similar to the case of the Fe-containing ma-\nterial (compare to Fig. 10) - the energy product\ndecreases with increasing aspect ratio - the physical\nreasonsfor this behavior are fundamentally different\nfor these two composites.\nIt also interesting to note that despite the larger\ncoercivity of Ni-containing composite, its energy\nproduct remains smaller than for the Fe-containing\nmaterial due to its much lower net magnetization.\nThis relation can change for materials with different\nfractions of soft and hard phases.\nIV. CONCLUSION\nIn this paper we have presented a detailed numer-\nical study for the dependence of magnetic proper-\nties of Sr-ferrite-based nanocomposites on two very\nimportant material parameters: ( i) exchange cou-\npling between various crystallites (what includes the\ncoupling between soft and hard grains) and ( ii) the\nshape of the hard grains.\nFirst, we have demonstrated - in contrast to the\ncommon paradigm - that the maximal energy prod-\nuctEmax= (BH)maxis a non-monotonous func-\ntion of the intergrain exchange coupling κand that\nthe optimal κ-value (for which the energy product\nreachesitshighestvalue)isfarbelowtheperfectcou-\npling. This non-monotonous character of the func-\ntionEmax(κ)isduetothecorrespondingdependence\nof the coercivity on the exchange coupling Hc(κ).\nSecond, we have studied the dependence of the\nhysteresis properties and the maximal energy prod-\nuct on the shape ofhard grainsfor twovery different\nnanocomposite materials - SrFe 12O19/Fe (Ms(Fe)≈\n1700G) and SrFe 12O19/Ni (Ms(Ni)≈490G). Hard\ngrains have been assumed to have (approximately)\na shape of ellipsoids of revolution, which aspect ra-\ntio was varied in the range 1 /3≤a/b≤3 (a/b >1\ncorresponds to a prolate ellipsoid). We have shown,\nthat for both materials the aspect ratio dependence\nofthemaximalenergyproduct Emax(a/b)essentially\nfollows the corresponding dependence of the hys-\nteresis loop remanence jR(a/b) and have supported\nthis observation by analytical considerations. For\nboth materials, the maximal value of jR(a/b) - and\nhenceofEmax(a/b)-wasobtainedforthe oblatehard\ngrains with the smallest aspect ration a/b= 1/3\n(also in contrast with common expectations). Phys-\nical reasons for this behavior are revealed.\nFinally, we have also analyzed the dependence\nof the coercivity on the shape of hard grains\nHc(a/b) and have shown that this dependence for\n15the two composites under study is qualitatively dif-\nferent. For SrFe 12O19/Fe the function Hc(a/b) has\na pronounced maximum for approximately spher-\nical grains, whereas for SrFe 12O19/Ni coercivity\nmonotonously decreases with increasing a/b. This\ndifference is explained by analyzing the dominating\ninteraction mechanisms between the hard and soft\nphases in these materials.V. ACKNOWLEDGMENT\nFinancialsupport ofthe DFG projectBE2464/10-\n3 and the EU-FP7project ”NANOPYME”(310516)\n[www.nanopyme-project.eu] is greatly acknowl-\nedged. Also we would like to thank Dr. Alberto\nBollero, Dr. Adri´ an Quesada and Dr. Cesar de Ju-\nlian Fernandez for fruitful discussions and Dr. An-\ndreas Michels for critical reading of the manuscript.\n1R. L. Stamps, S. Breitkreutz, J. ˚Akerman, A. V.\nChumak, Y. Otani, G. E. W. Bauer, J.-U. Thiele,\nM. Bowen, S. A. Majetich, M. Kl¨ aui, I. L. Prejbeanu,\nB. Dieny, N. M. Dempsey, and B. Hillebrands,\nJournal of Physics D: Applied Physics 47, 333001 (2014),\narXiv:1410.6404.\n2O.Gutfleisch,Journal of Physics D: Applied Physics 33, R157 (2000).\n3J. M. Coey, Magnetism and magnetic materials\n(Cambridge University Press, 2010).\n4R. Skomski, P. Manchanda, P. K. Kumar, B. Bala-\nmurugan, A. Kashyap, and D. J. Sellmyer (2013) pp.\n3215–3220.\n5Y. Matsuura, J. Hoshijima, and R. Ishii,\nJournal of Magnetism and Magnetic Materials 336, 88 (2013).\n6R. Gr¨ ossinger, G. Badurek, J. Fidler,\nM. Zehetbauer, and C. D. Dewhurst,\nJournal of Magnetism and Magnetic Materials 294, 152 (2005).\n7J. Liu, H. Sepehri-Amin, T. Ohkubo, K. Hioki,\nA. Hattori, T. Schrefl, and K. Hono,\nActa Materialia 61, 5387 (2013).\n8H. Sepehri-Amin, T. Ohkubo, S. Nagashima,\nM. Yano, T. Shoji, A. Kato, T. Schrefl, and K. Hono,\nActa Materialia 61, 6622 (2013).\n9J. F. L¨ offler, H. B. Braun, W. Wag-\nner, G. Kostorz, and A. Wiedenmann,\nPhysical Review B - Condensed Matter and Materials Physics 71, 1 (2005).\n10F. Y. Ogrin, S. L. Lee, M. Wismayer, T. Thom-\nson, C. D. Dewhurst, R. Cubitt, and S. M. Weekes,\nJournal of Applied Physics 99, 2006 (2006).\n11S. Erokhin, D. Berkov, N. Gorn, and A. Michels,\nPhys. Rev. B 85, 024410 (2012).\n12S. Erokhin, D. Berkov, N. Gorn, and A. Michels,\nPhys. Rev. B 85, 134418 (2012).\n13A. Michels, S. Erokhin, D. Berkov, and N. Gorn,\nJournal of Magnetism and Magnetic Materials 350,\n55 (2014).\n14Y. Gao, D. Shindo, and A. K. Petford-Long,\nJournal of Applied Physics 93, 8119 (2003).\n15N. M. Saiden, T. Schrefl, H. A. Davies, and G. Hrkac,\nJournal of Magnetism and Magnetic Materials 365, 45 (2014).\n16M. Yi, O. Gutfleisch, and B.-X. Xu,\nJournal of Applied Physics 120, 033903 (2016).17C. B. Rong, H. W. Zhang, R. J.\nChen, S. L. He, and B. G. Shen,\nJournal of Magnetism and Magnetic Materials 302, 126 (2006).\n18B. Zheng, H. W. Zhang, S. F. Zhao, J. L. Chen, and\nG. H. Wu, Applied Physics Letters 93, 9 (2008).\n19S.-l. He, H.-w. Zhang, C.-b. Rong,\nJ. Chen, J.-r. Sun, and B.-g. Shen,\nJournal of Magnetism and Magnetic Materials 324, 3853 (2012).\n20R.-J. Chen, H. W. Zhang, C.-B.\nRong, J.-R. Sun, and B. G. Shen,\nJournal of Applied Physics 100, 43901 (2006).\n21Y. Li, M. Yue, T. Wang,\nQ. Wu, D. Zhang, and Y. Gao,\nJournal of Magnetism and Magnetic Materials 393, 484 (2015).\n22A. Donev, S. Torquato, and F. H. Stillinger,\nJournal of Computational Physics 202, 765 (2005),\narXiv:0405089 [physics].\n23L. Landau and E. Lifshitz, Phys. Z. Sowjetunion 8,\n153 (1935).\n24H. Kronm¨ uller and S. Parkin, Handbook of Mag-\nnetism and Advanced Magnetic Materials , Vol. 2, Mi-\ncromagnetism (Wiley, Chichester, 2007) edited by H.\nKronm¨ uller and S. Parkin.\n25A. Quesada, C. Granados-Miralles, A. L´ opez-Ortega,\nS. Erokhin, E. Lottini, J. Pedrosa, A. Bollero,\nA. M. Arag´ on, F. Rubio-Marcos, M. Stingaciu,\nG. Bertoni, C. de Juli´ an Fern´ andez, C. Sangregorio,\nJ. F. Fern´ andez, D. Berkov, and M. Christensen,\nAdvanced Electronic Materials 2, 1500365 (2016).\n26N. Usov and S. Peschany,\nJournal of Magnetism and Magnetic Materials 174, 247 (1997).\n27J. Garca-Otero, M. Porto, and J. Rivas,\nJournal of Applied Physics 87, 7376 (2000).\n28D.Berkov,Journal of Magnetism and Magnetic Materials 161, 337 (1996).\n29E. C. Stoner and E. P. Wohlfarth,\nPhilosophical Transactions of the Royal Society A: Mathema tical, Physical and Engineering Sciences 240, 599 (1948).\n30D. V. Berkov and S. V. Meshkov, Sov. Phys. JETP\n67, 2255 (1988).\n31D. V. Berkov and N. L. Gorn,\nPhysical Review B 57, 14332 (1998).\n16"    },    {        "title": "1609.08548v1.The_magnetic_properties_of_the_hollow_cylindrical_ideal_remanence_magnet.pdf",        "content": "Published in Journal of Magnetism and Magnetic Materials, Vol. 416, 321–324,, 2016\nDOI: dx.doi.org/10.1016/j.jmmm.2016.05.034\nThe magnetic properties of the hollow cylindrical\nideal remanence magnet\nR. Bjørk\nAbstract\nWe consider the magnetic properties of the hollow cylindrical ideal remanence magnet. This magnet is the\ncylindrical permanent magnet that generates a uniform field in the cylinder bore, using the least amount of\nmagnetic energy to do so. The remanence distribution of this magnet is derived and the generated field is\ncompared to that of a Halbach cylinder of equal dimensions. The ideal remanence magnet is shown in most\ncases to generate a significantly lower field than the equivalent Halbach cylinder, although the field is generated\nwith higher efficiency. The most efficient Halbach cylinder is shown to generate a field exactly twice as large as\nthe equivalent ideal remanence magnet.\nDepartment of Energy Conversion and Storage, Technical University of Denmark - DTU, Frederiksborgvej 399, DK-4000 Roskilde, Denmark\n*Corresponding author : rabj@dtu.dk\n1. Introduction\nGenerating a large uniform magnetic field in the most effi-\ncient way possible is of key interest, both for scientific and\ncommercial applications. A strong uniform magnetic field\nis required in a large number of applications, among these\nnuclear magnetic resonance (NMR) equipment, accelerator\nmagnets and magnetic refrigeration devices. Typically, the\nmagnetic field must be generated inside a cylindrical bore, and\nthe surrounding magnet is in this case usually also cylindrical.\nPrevious investigations of such a cylindrical system have\nfocussed on generating as large as field as possible in the\ncylinder bore ( 1;2;3), with little regard to the efficiency of\nthe magnet design. In an efficient magnet design the magnetic\nenergy in the magnets is utilized fully to create the desired\nmagnetic field. The efficiency of a permanent magnet design,\nM, can be defined as (4)\nM=R\nVfieldjjBjj2dV\nR\nVmagjjBremjj2dV; (1)\nwhere Vfieldis the volume of the region where the magnetic\nfield is created, Vmagis the volume of the magnets, Bis the\nmagnetic field and Bremis the remanence of the magnets used.\nThe maximum value of Mis 0.25 (4).\nInterestingly, the remanence distribution of the ideal cylin-\ndrical magnet that generates a uniform field in the cylinder\nbore, i.e. the design with the highest possible M, has been\nderived by Jensen & Abele (1996) ( 4), but the field generated\nby this ideal remanence magnet have not been considered in\ndetail. Little is known about this magnet design, even though\nit has been proven to be the most efficient design possible. It\nhas never been realized physically, nor has it been investigated\nnumerically or analytically in detail. Furthermore, only the\nmagnetic efficiency, and not the magnetic field itself generatedby this ideal remanence magnet, has been compared with the\ndesign most commonly used to generate a uniform field in a\ncylinder bore, namely the Halbach cylinder design. In this\nwork we calculate the magnetic field generated by the ideal\nremanence magnet, and compare it to the Halbach cylinder, in\norder to determine the most optimal way to generate a desired\nfield using the least amount of magnet energy.\nSome of the magnetic structures that are considered in the\nfollowing have a varying remanence through the magnetic\nstructure. While these may not be easy to realize in a practical\nsense, they nevertheless generate the desired magnetic field\nusing the least magnetic energy possible, and are therefore\ninteresting to investigate scientifically.\n2. The ideal remanence cylindrical\nmagnet\nAny ideal remanence magnet must have an irrotational and\nsolenoidal remanence distribution, Ñ\u0002Brem=0andÑ\u0001Brem=\n0, and have no net magnetic charge on the surface of the mag-\nnet (4). Utilizing these requirement Jensen & Abele (1996)\n(4) were able to calculate the most efficient cylindrical magnet\ndesign, that generates a uniform field in the cylinder bore\nin two dimensions. We will only consider two dimensional\nstructures in the following, i.e. flux leakage through the ends\nof the cylinder are ignored. This is a valid approximation as\nlong as the cylinder is much longer than the diameter of the\ncylinder bore.\n2.1 Non-yoked design\nFor the case where the cylindrical magnet is not surrounded by\nan iron yoke, the remanence potential for the ideal cylindricalarXiv:1609.08548v1  [physics.ins-det]  27 Sep 2016The magnetic properties of the hollow cylindrical ideal remanence magnet — 2/5\nHalbach cylinder\nr\noriBore Non-yoked ideal magnetYoked ideal magnetYoke of high µr\nFigure 1. The remanence distribution of an ideal non-yoked and yoked magnet, as well as for a Halbach cylinder. The three\nmagnets have the same maximum norm of the remanence.\nmagnet is given as (4)\nF\u0003\nJ=B0r2\ni\nr2o\u0000r2\ni\u0012\n(mr+1)r2\no\nr\u0000(mr\u00001)r\u0013\ncos(f) (2)\nwhere B0is the norm of the generated flux density in the\ncylinder bore, riandroare the inner and outer radii of the\nmagnet, respectively, mris the relative permeability of the\npermanent magnet and randfare polar coordinates. The\nremanence is given by\nBrem=\u0000ÑF\u0003\nJ (3)\nCalculating the gradient in Eq. (3), one get\nBrem;r=A(r)cos(f)ˆr\nBrem;f=B(r)sin(f)ˆf (4)\nwhere\nA(r) =\u0000B0r2\ni\nr2o\u0000r2\ni\u0010\n(mr+1)r2o\nr2+(mr\u00001)\u0011\nB(r) =\u0000B0r2\ni\nr2o\u0000r2\ni\u0010\n(mr+1)r2o\nr2\u0000(mr\u00001)\u0011\n(5)\nFor the case of mr=1, the components A(r)andB(r)are\nidentical. The remanence is seen to be a function of both r\nandf. The remanence distribution is illustrated in Fig. 1.\nThe norm of the remanence is given as\njjBremjj=q\nA(r)2cos2(f)+B(r)2sin2(f) (6)\nwhich simply reduces to jA(r)jfor the case of mr=1.\nPermanent magnets are limited in the maximum rema-\nnence that can be obtained. Therefore, it is of interest to\ndetermine the field that can be generated in the cylinder bore\nas function of the maximum remanence of the permanent\nmagnet. As mris always larger than or equal to 1 it can be\nseen from Eq. (5) that A(r)\u0015B(r). This means that the\nmaximum norm of the remanence will occur at r=riand\nf= [0;p]. At these points, the norm is simply jA(ri)j. Theminimum norm of the remanence will always occur at r=ro\nandf= [p=2;3p=2]. Here, the norm is simply jB(ro)j.\nUsing that the maximum norm of the remanence is given\nbyjA(ri)jand Eq. (5), we get\njjBrem;maxjj=Brem;max=B0r2\ni\nr2o\u0000r2\ni\u0012\n(mr+1)r2\no\nr2\ni+(mr\u00001)\u0013\n(7)\nThis is easily inverted in terms of B0as\nB0=Brem;max1\u0000r2\ni\nr2o\nmr+1+r2\ni\nr2o(mr\u00001)(8)\nThis is the magnitude of the uniform flux density generated\nby an ideal remanence magnet with a maximum remanence\nofBrem;max.\nFor the case of mr=1, this reduces to\nB0=Brem;max1\u0000r2\ni\nr2o\n2(9)\nwhile for an infinitely big magnet, ri=ro!0, so\nB0=Brem;max1\nmr+1(10)\nwhich for the case of mr=1means that B0=Brem;max=2. This\nis the maximum norm of the flux density that the ideal rema-\nnence magnet can generate for a given maximum remanence.\nThe factor of 1/2 between the maximum remanence and the\ngenerated flux density is the maximum factor for a maximally\nefficient magnet (4).\n2.2 Yoked design\nThe ideal distribution of remanence is different in the case\nthat the cylindrical magnet is surrounded on the outside by a\nyoke of high permeability material. In this yoked case, the\nremanence potential given by (4)\nF\u0003\nJ=B0r2\ni\u0012mr\nr2o\u0000r2\ni+1\nr2o+r2\ni\u0013\u0012r2\no\nr\u0000r\u0013\ncos(f)(11)The magnetic properties of the hollow cylindrical ideal remanence magnet — 3/5\nCalculating the remanence is similar to the non-yoked\ncase, and the result is\nBrem;r=A(r)cos(f)ˆr\nBrem;f=B(r)sin(f)ˆf (12)\nwhere\nA(r) =\u0000B0r2\ni\u0010\nmr\nr2o\u0000r2\ni+1\nr2\ni+r2o\u0011\u0010\nr2o\nr2+1\u0011\nB(r) =\u0000B0r2\ni\u0010\nmr\nr2o\u0000r2\ni+1\nr2\ni+r2o\u0011\u0010\nr2o\nr2\u00001\u0011\n(13)\nThe remanence distribution is illustrated in Fig. 1. Again, the\nnorm of the remanence will be largest at r=riandf= [0;p],\nwhere it will bejA(ri)j. However, unlike the case for the\nnon-yoked magnet, the components A(r)andB(r)are not\nidentical for mr=1.\nThe equation for the maximum remanence becomes\nBrem;max=\u0000B0\u0012mr\nr2o\u0000r2\ni+1\nr2\ni+r2o\u0013\u0000\nr2\no+r2\ni\u0001\n(14)\nwhich can be inverted in terms of B0as\nB0=Brem;max1\u0000r2\ni\nr2o\nmr+1+r2\ni\nr2o(mr\u00001)(15)\nThis is exactly the same as the equation for the non-yoked case,\ni.e. Eq. (8). Thus the non-yoked and the yoked cylindrical\nmagnets generate the same magnetic field for the same choice\nof maximum remanence and the same size of the magnet.\nHowever, the magnetic energy in the permanent magnets is\nsmaller in the yoked case, i.e. the yoked design have a higher\nefficiency.\n3. Comparing to the Halbach cylinder\nThe Halbach cylinder is the most common way to generate\na uniform magnetic field in a cylinder bore ( 5;6). For this\ndesign, the remanence is given by\nBrem;r=Bremcos(f)ˆr\nBrem;f=Bremsin(f)ˆf; (16)\nAs can be seen, the norm of the remanence is uniform through-\nout the magnet, unlike the case of the ideal remanence mag-\nnets discussed above. The Halbach design has been used in a\nlarge number of applications including nuclear magnetic reso-\nnance (NMR) equipment ( 7;8), accelerator magnets ( 9;10),\nmagnetic refrigeration devices ( 11;12) and medical applica-\ntions (13).\nFor the Halbach cylinder, the magnetic flux density gener-\nated in the cylinder bore is given as (6)\nB0=Bremln\u0012ro\nri\u0013\n(17)\nFigure 2. The ratio between the field generated by a Halbach\ncylinder and that generated by an ideal remanence magnet, as\nfunction of the size of the magnet and the relative\npermeability of the magnet material. The maximum\nremanence of the ideal remanence magnet is equal to the\nremanence throughout the Halbach magnet.\nThe efficiency of the Halbach cylinder, as defined by M, is\nwell known ( 14), and the maximum value of the efficiency is\nM\u00190:162for a ratio of the radii of ro=ri\u00192:2185 (15;16).\nThe efficiency of the ideal remanence magnets have previously\nbeen compared to that of the Halbach cylinder ( 4). Here it\nwas shown that the ideal remanence magnets are always more\nefficient then the Halbach cylinder. However, the efficiency of\nthe magnet design is of little interest if a magnetic field of the\ndesired field strength cannot be generated in the cylinder bore.\nTherefore it is of critical importance to compare the actual\nmagnitude of the magnet field generated in the cylinder bore\nin the different designs. Shown in Fig. 2 is the ratio between\nthe field generated by a Halbach cylinder and that generated\nby an ideal remanence magnet (both yoked and non-yoked\nas these generate the same field), for the case of the same\nmaximum remanence and same size of the magnets. The ratio\nof the generated fields is shown as a function of the ratio of\nthe inner and outer radius of the magnet as well as the relative\npermeability of the permanent magnet.\nAs can be seen from the figure, the Halbach cylinder\ngenerates a field that is always larger then that generated by the\nideal remanence magnet. For this reason alone, the Halbach\ncylinder is preferential to the ideal remanence magnet, even\nthough the latter has a higher efficiency, if the desired goal is\nto generate as high a field as possible.\nIt is of special interest to compare the two magnet design\nfor the case of mr=1, as this is very close to the remanence\nof standard neodymium-iron-boron (NdFeB) magnets, where\nmris in general taken to be 1.05 ( 17). Comparing the Halbach\nand ideal remanence magnets for mr=1and assuming the\nmaximum remanence of the ideal remanence magnet equal toThe magnetic properties of the hollow cylindrical ideal remanence magnet — 4/5\nro/ri [-]1 2 3 4 5B0/Brem [-]\n00.511.52\nB0,Halbach/B0,Ideal\nB0,Halbach/Brem\nB0,Ideal/Brem,max\n1 2 3 4 5\nBHalbach/BIdeal [-]\n12345\nFigure 3. The ratio between the field generated by a Halbach\ncylinder and that generated by an ideal remanence magnet, as\nfunction of the size of the magnet for mr=1. The fields\ngenerated, normalized by the remanence, are also shown. The\nmaximum remanence of the ideal remanence magnet is equal\nto the remanence throughout the Halbach magnet.\nthe remanence throughout the Halbach magnet, we get\nB0;Ideal\nB0;Halbach=1\u0000r2\ni\nr2o\n2ln\u0010\nro\nri\u0011 (18)\nThis equation, along with Eq. (8) and Eq. (17), for the\nideal remanence magnet and the Halbach cylinder, respec-\ntively, are shown in Fig. 3 for mr=1. As can be seen from the\nfigure, the Halbach cylinder always generate a substantially\nlarger field then the ideal remanence magnet.\nThe ideal remanence magnet and the Halbach magnet can\nbe compared in more detail for the size of the magnet where\nthe Halbach cylinder is the most efficient. As per Bjørk et al.\n(2015) ( 14), the optimal ratio of the radii for the most efficient\nHalbach is given as (ri=ro)opt=e\u0000W(\u00002e\u00002)=2\u00001\u00190:4508 ,\nwhere Wis the Lambert W-function. Using this expression in\nEq. (8) for the ideal remanence magnet, one can show that\n\u0012B0;Ideal\nBrem;max\u0013\nh\nro\nrii\nopt=1\n2 \n1+W\u0000\n\u00002e\u00002\u0001\n2!\n(19)\nFor the case of the Halbach cylinder, Eq. (17), we get\n\u0012B0;Halbach\nBrem\u0013\nh\nro\nrii\nopt=1+W\u0000\n\u00002e\u00002\u0001\n2(20)\nComparing Eqs. (19) and (20), one get\n\u0012B0;Ideal\nB0;Halbach\u0013\nh\nro\nrii\nopt=1\n2(21)This shows that at the optimal radius of the Halbach cylinder,\ni.e. the radius where it is the most efficient magnetically,\nthe Halbach cylinder generates exactly twice the flux density\ngenerated by the ideal remanence magnet of the same size. Of\ncourse at this radius, the efficiency of the two designs are not\nidentical. The efficiency of the Halbach is M\u00190:162, while\nit isM\u00190:199for the non-yoked ideal remanence magnet\nandM\u00190:240 for the yoked ideal remanence magnet.\n4. Discussion and conclusion\nWe have clearly shown that while the ideal remanence mag-\nnets are more magnetically efficient compared to the Halbach\ncylinder, they will always generate a lower field when com-\npared with the equivalently sized Halbach cylinder. Thus the\nwidespread use of the Halbach cylinder is justified, as the\nusual requirement in a application is to generate the largest\nfield possible, and not use the magnetically most optimal de-\nsign possible. Halbach cylinder are of course also easier to\nrealize, as it has a constant remanence throughout the struc-\nture, making it more suitable for practical applications.\nThe inherent problem of the ideal remanence magnets is\nthe low value of the generated field. By combining the ideal\nremanence magnet with a flux concentrating device, which is\nable to concentrate the field lines in a cylinder bore ( 18;19),\nthe field generated by the ideal remanence magnet can be\nenhanced as desired. The flux concentrating device cannot\nchange the efficiency of a given magnet design ( 20), but will\nenhance the field generated by the permanent magnetic struc-\nture by a factor of ro;con=ri;con, where these are the outer and\ninner radii of the flux concentrator. Since the ideal remanence\nmagnets can be made maximally efficiency (albeit only at\ninfinite ro), the desired field in the cylinder bore can be gener-\nated with maximum efficiency by fitting a flux concentrator\nof desired size in the cylinder bore of the magnet.\nWe have shown that the ideal remanence magnet that gen-\nerates a uniform field in a cylinder bore will only generate a\nfield substantially weaker than the maximum value of its re-\nmanence. Comparing with the Halbach cylinder, the optimum\nHalbach cylinder was shown to generate a field twice as large\nas the ideal remanence magnet of the same size.\nReferences\n[1]F. Bloch, O. Cugat, G. Meunier and J. C. Toussaint, IEEE\nTrans. Magn. 34(1998), 5.\n[2]M. Kumada, T. Fujisawa and Y . Hirao, Proc. Second\nAsian Part. Accel. Conf. (2001), 840.\n[3]R. Bjørk, J. Appl. Phys. 109(2011), 013915.\n[4]J. H. Jensen and M. G. Abele, J. Appl. Phys., 79(1996),\n1157.\n[5]J. C. Mallinson, IEEE Trans. Magn. 9 (4) (1973), 678.\n[6]K. Halbach, Nucl. Instrum. Methods, 169(1980).The magnetic properties of the hollow cylindrical ideal remanence magnet — 5/5\n[7]G. Moresi and R. Magin, Concepts in Magn. Reson. Part\nB (Magn. Reson. Eng.), 19B (2003), 35.\n[8]S. Appelt, H. K ¨uhn, F. W H ¨asing, and B. Bl ¨umich, Nat.\nPhys. 2(2006), 105.\n[9]M. Sullivan, G. Bowden, S. Ecklund, D. Jensen, M.\nNordby, A. Ringwall, and Z. Wolf, IEEE 3(1998), 3330.\n[10]J. K. Lim, P. Frigola, G. Travish, J. B. Rosenzweig, S. G.\nAnderson, W. J. Brown, J. S. Jacob, C. L. Robbins, and\nA. M. Tremaine, Phys. Rev. Spec. Top. - Accel. Beams, 8\n(2005), 072401.\n[11]A. Tura and A. Rowe, Proc. 2ndInt. Conf. on Magn.\nRefrig. at Room Temp. (2007), 363.\n[12]R. Bjørk, C. R. H. Bahl, A. Smith, and N. Pryds, Int. J.\nRefrig. 33(2010), 437.\n[13]A. Sarwar, A. Nemirovski, and B. Shapiro, J. Magn.\nMagn. Mater. 324 (5) (2012), 742-754.\n[14]R. Bjørk, A. Smith and C. R. H. Bahl, J. Magn. Magn.\nMater. 384(2015), 128-132.\n[15]M. G. Abele and H. Rusinek, J. Appl. Phys., 67(1990),\n4644.\n[16]J. M. D. Coey and T. R. Ni Mhiochain, High Magnetic\nFields (Permanent magnets), Chap. 2, p. 25, World Scien-\ntific (2003).\n[17]Standard specifications for permanent magnet materials,\nInt. Mag. Assoc., Chicago, USA, (2000).\n[18]C. Navau, J. Prat-Camps, and A. Sanchez, Phys. Rev. Lett.\n109 (26) (2012), 263903.\n[19]J. Prat-Camps, C. Navau, and A. Sanchez, Appl. Phys.\nLett. 105 (23) (2014), 234101.\n[20]R. Bjørk, A. Smith, C. R. H. Bahl, J. Appl. Phys. 114 (5)\n(2013), 053912."    },    {        "title": "1610.00498v1.Synthesis__structure_and_magnetism_of_the_new__S__frac_1__2___kagome_magnet_NH__4_Cu___2_5__V__2_O__7__OH___2__H__2_O.pdf",        "content": "Synthesis, structure and magnetism of the new\nS=1\n2kagome magnet NH 4Cu 2:5V2O7(OH) 2.H2O\nE Connolly1, P Reeves1;2, D Boldrin3and A S Wills1\n1Department of Chemistry, University College London, 20 Gordon St, London\nWC1H 0AJ\n2Present address: Department of Material Science and Metallurgy, University of\nCambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, UK\n3Department of Physics, Imperial College, Prince Consort Road, London SW7 2BZ,\nUK\nE-mail: a.s.wills@ucl.ac.uk\nAbstract. The study of quantum spin-liquid states (QSL) with lattice dimension\n>1 has proven an enduring problem in solid state physics. Key candidate materials\nare theS=1\n2kagome magnets due to their ability to host quantum \ructuations within\nthe high degeneracy of their frustrated geometries. Studies of an increasing library of\nknownS=1\n2kagome magnetic materials has challenged our understanding of the\npossible QSL states, for example, the recent discovery of a chiral spin-liquid ground\nstate in kapellasite showed that even magnets with ferromagnetic nearest-neighbour\nexchange are not necessarily trivial and that QSL states beyond the superposition of\nsimple singlet are possible.\nHere, we outline the synthesis, structure and preliminary magnetic characterisation\nof a candidate QSL material, the S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O.\nThe crystal structure of NH 4Cu2:5V2O7(OH) 2.H2O has the 3-fold symmetry of a\ngeometrically `perfect' kagome lattice while the magnetism shows a competition\nbetween ferromagnetic and antiferromagnetic characters reminiscent of kapellasite.\nSubmitted to: J. Phys.: Condens. Matter\n1. Introduction\nThe quest to discover what ground states occur when quantum \ructuations destabilize\nconventional magnetic order has become one of the backbones of modern condensed\nmatter physics. Much of this work has focused on S=1\n2kagome magnets, where\nthe moment-bearing ions make up a 2-dimensional network of vertex-sharing triangles.\nUnlike the ground states of square and triangular S=1\n2Heisenberg magnets, the S=1\n2\nkagome Heisenberg antiferromagnet was shown theoretically not to order into a N\u0013 eel\nstate, even at T= 0 K[1, 2, 3]. Research into these quantum frustrated magnets has\nlargely followed the picture of the ground states being dynamic superposition states of\ndegenerate local- or long-range entangled singlet pairs (Figure 1), quantum spin liquidsarXiv:1610.00498v1  [cond-mat.mtrl-sci]  3 Oct 2016Synthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O2\n(QSLs). QSLs di\u000ber fundamentally from conventional magnetic order in that they do\nnot break translational or rotational symmetry, but are instead de\fned by topological\norder parameters [4].\nRecent experimental and theoretical investigations into S=1\n2kagome magnets\nhave revealed that new types of QSL states are able to form when nearest-\nneighbour ferromagnetic exchange is frustrated by antiferromagnetic further-neighbour\ninteractions[5, 6], thereby expanding the \feld from one that was thought to be\nonly relevant for nearest-neighbour antiferromagnets to those with competing signs\nof exchange. This work, focused on kapellasite ( \u000b\u0000ZnCu 3(OH) 6Cl2) - which has a\n12-sublattice chiral spin-liquid (cuboc2) ground state [5] - and its isostructural and\nisomagnetic analogue haydeeite ( \u000b\u0000MgCu 3(OH) 6Cl2) helped formulate a new phase\ndiagram for the QSL ground state involving a diagonal exchange integral. Changes in\nits value caused by di\u000berences in the bonding around their diamagnetic ions (Mg2+and\nZn2+), is able to drive the conventional ferromagnetic ordering seen in haydeeite into\nthe 12-sublattice chiral spin-liquid (cuboc2) ground state[5, 6, 7, 8, 9].\nAt present, much of the research into experimental S=1\n2kagome magnets is\nbased on two main families of crystal structures: the atacamites (herbertsmithite\n\r\u0000ZnCu 3(OH) 6Cl2, kapellasite \u000b\u0000ZnCu 3(OH) 6Cl2and their isomagnetic relatives\n`Mg-herbertsmithite' \r\u0000MgCu 3(OH) 6Cl2, and haydeeite \u000b\u0000MgCu 3(OH) 6Cl2) and the\ncopper vanadates (volborthite \u000b\u0000Cu3V2O7(OH):2H2O, vesignieite BaCu 3V2O8(OH) 2\nand `Sr-vesignieite' SrCu 3V2O8(OH) 2). The di\u000berences between these magnets has been\nrevealing. The atacamites all have 3-fold symmetry, a quality that brings them close\nto the theoretical models. In the well studied herbertsmithite, the QSL state survives\nDzyaloshinskii-Moriya (DM) anisotropy as the anisotropic exchange is largely axial and\nits strength is below a quantum critical point, DC\nz=J'0:1. In contrast, the DM\ncomponent in vesignieite is dominated by the in-plane component, Dp[10, 11], despite\nDz=Jbeing similar to herbertsmithite, and this induces partial ferromagnetic order[11].\nEven closely related materials can show wildly di\u000berent behaviours, such as the QSL\nof dynamic singlets of herbertsmithite and of cuboc2 spin correlations in its polymorph\nkapellasite. At the root of this richness of properties are often subtleties in the crystal\nstructure, such as variation in bond angles related to site disorder or di\u000berences in orbital\nordering patterns and consequent superexchange pathways, as seen in volborthite[12],\nvesignieite[13, 14] and `Sr-vesignieite'[6].\nHere, we present the synthesis, structure and preliminary magnetic measurements of\na newS=1\n2kagome material NH 4Cu2:5V2O7(OH) 2.H2O based on the copper vanadates,\nand introduce its magnetic properties.\n2. Synthesis\nSyntheses using a scaled down version (to 30 % of the literature quantities) of that\npreviously given in a paper by Palacio[15] at T= 170\u000eC, produced a product\ncontaminated by an amorphous impurity phase and crystalline NH 4VO3. The latterSynthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O3\nFigure 1. Schematic of a kagome structure hosting a QSL state. The short and long\nrange entangled spins are highlighted in red. The entangled singlet states are in a\ndisordered arrangement over the kagome lattice. The degeneracy of the ground state\nallows for zero-point energy \ructuations to other disordered arrangements.\ncould be identi\fed by a peak in the di\u000braction data at 2 \u0012= 24\u000ethat is also visible in\n[15].\nFurther studies showed that the impurities form at T\u001480\u000eC andT\u0015130\u000eC. A\nphase pure sample was obtained as follows: NH 4OH (0.62 ml, 32 % wt, Sigma-Aldrich)\nwas diluted with distilled water (3.88 ml). To this solution, V 2O5(166 mg, 99.6 %,\nAldrich) was added and the suspension was stirred for 1 hour, whereupon it turned\nyellow. Finally, CuCl 2:2H2O (311 mg, 99.8 %, Aldrich) dissolved in distilled water (3.0\nml), was added to the yellow suspension. This was then stirred for 1 hour to homogenize,\nproducing a turquoise gel. The gel was loaded into a Pyrex pressure tube (15 ml, Ace\nGlass Inc.) and then suspended in a silicon oil bath at 115\u000eC for 24 hours. The product\nwas washed 3 times in water viacentrifugation (4 :5\u0002103rpm, 2 mins) and dried at 60\u000eC\nfor 5 hours. A yellow powder of NH 4Cu2:5V2O7(OH) 2.H2O was produced in a yield of\n\u001844 %.\nThe ratios of the \fnal reagent used are 1 V 2O5: 2 CuCl 2.2H 2O : 6 NH 4OH :\n422 H 2O. Powder XRD indicated that the product of the \frst reaction is NH 4VO3.\nThe pH of the second reaction was 9.6 before and after the synthesis. We propose the\nfollowing reaction mechanism for the formation of NH 4Cu2:5V2O7(OH) 2.H2O:\nV2O5(s)+ 2NH 4OH (aq)!2NH 4VO3(s)+ H 2O(l)\n2NH 4VO3(s)+5\n2CuCl 2:2H2O(aq)+ 4NH 4OH (aq)!NH4Cu2:5V2O7(OH) 2:H2O(s)Synthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O4\nFigure 2. Rietveld re\fnement of XRD data measured on a powdered sample of\nNH4Cu2:5V2O7(OH) 2:H2O at a wavelength of \u0015= 1:5406 \u0017A. The red, blue and grey\nlines, and blue markers represent the \ft, data, di\u000berence plot and re\rection positions,\nrespectively. The \fnal goodness-of-\ft parameter was \u001f2= 2:35 with 56 variables.\n+5NH 4Cl(aq)+ 3H 2O(l)+3\n2O2(g)\nThe hypothesized reaction scheme has a calculated reagent ratio for 1 M of\nNH4Cu2:5V2O7(OH) 2.H2O of 1 V 2O5: 2.5 CuCl 2.2H 2O : 6 NH 4OH, indicating that our\nsynthetic conditions correspond to a slight de\fcit of CuCl 2.2H 2O. The outlined synthetic\nprocedure can be used to understand how variation to concentrations or reagent types\nwill e\u000bect the product.\n3. Crystal structure determination\nThe powder XRD data was recorded on a STOE Stadi-P di\u000bractometer using Cu-\nK\u000b1radiation ( \u0015= 1:5406 \u0017A) with a rotating capillary sample holder. As no\ncrystal structure is known for NH 4Cu2:5V2O7(OH) 2.H2O, the starting lattice parameters,\nspace group and atomic positions for the crystal structure model were based on the\nengelhauptite (KCu 3V2O7(OH) 2Cl) structure in the P63=mmc space group[16]. The\nRietveld re\fnement was carried out using the TOPAS software package[17]. The data,\n\fnal calculated and di\u000berence plots are shown in Figure 2. The crystal structure data\nobtained from the re\fnement is displayed in Table 1; details of the data collection\nprocedure and re\fnement are given in the supplementary information. All crystal\nstructure \fgures were produced using VESTA [18].Synthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O5\nAtom Wycko\u000b site x y z Biso(\u0017A2) Occ.\nCu 6 g1\n21\n20 4.1(11) 0.7294(68)\nV 4 e 0 0 0.37355(19) 2.5(11) 1\nO(1) 12 k 0.15623(87) 0.3125(17) 0.59043(31) 3.4(11) 1\nO(2) 2 b 0 01\n45.0(11) 1\nO(H) 4 f1\n32\n30.06520(61) 2.1(10) 1\nO(w) 6 h 0.74537 0.3707(98)3\n45.8(75) 0.242(25)\nN 4 f1\n32\n30.2551(19) 2.1(20) 0.417(21)\nH(1) 4 f1\n32\n30.61500 5.7 [19] 1\nH(2) 24 l 0.64126 0.44028 0.76082 5.7 [19] =Owocc\n2\nH(3) 12 k 0.18614 0.59307 0.74228 5.7 [19] = N occ\nH(4) 4 f1\n32\n30.81662 5.7 [19] =Nocc\n2\nTable 1: The crystal structure data for NH 4Cu2:5V2O7(OH) 2:H2O displaying the atom,\nWycko\u000b site, atomic coordinates, thermal parameter and occupancies.\n3.1. Structural characterization\nNH+\n4and H 2O were assigned respectively to the framework cavities occupied by K+and\nCl\u0000in the similarly structured engelhauptite [16]. Structural re\fnements indicated that\nthese sites feature signi\fcant disorder which was modeled by lowering the symmetry of\nthe N site from 2 dto 4fand the O(w) site from 2 cto 6h. To help reveal how hydrogen\nbonding could stabilise the positions of these species, rigid bodies were de\fned with the\nbond lengths and angles set as the following for NH+\n4: N{H(3,4) = 0 :974\u0017A,\\H(3,4)-\n{N{H(3,4) = 109.5\u000e[20], and for H 2O and the OH\u0000group: O(w){H(2) = 1 :019\u0017A,\nO(H){H(1) = 1 :008\u0017A and \\H(3){O(w){H(3) = 109.5\u000e[19]\nDuring the re\fnement, the site occupancy of the divanadate and hy-\ndroxide groups were \fxed to be unity while the occupancies of the Cu2+,\nNH+\n4and H 2O groups were freely re\fned. The re\fned structural formula is\n(NH 4)0:834Cu2:188V2O7(OH) 2.0.726(H 2O), indicating that some loss of Cu2+occurs that\nis presumed to be charge compensated by protonation of the water molecules to form\nhydronium ions. (The latter cannot be distinguished from these data.)\n3.2. Structural analysis\nSelected bond distances and angles which are pertinent to the description and discussion\nof the structure of NH 4Cu2:5V2O7(OH) 2.H2O are displayed in Table 2 and the re\fned\nstructure viewed along the a- andc\u0000axes is displayed in Fig 3. The magnetic\nmoments reside on brucite-type Cu-octahedra sheets that are separated by pyrovanadate\npillars and interstitial pores, the latter contain NH+\n4and H 2O. The interlayer Cu{Cu\nseparation of 7.22 \u0017A is very similar to that of volborthite [19] (7.21 \u0017A) suggesting that\nthe superexchange between layers will be very weak and the magnetic Hamiltonian willSynthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O6\nInteratomic distances ( \u0017A) Angles (\u000e)\nCu-O(H) 1.9373(44) Cu-O(H)-Cu 99.54(29)\nCu-O(1) 2.1881(43) Cu-O(1)-Cu 85.05(21)\nO(1)-Cu-O(1) 91.63(38)\nO(H)-Cu-O(1) 92.48(20)\nV-O(2) 1.7867(25) V-O(2)-V 180.00\nV-O(1) 1.6881(78) O(2)-V-O(1) 108.19(19)\nO(1)-V-O(1) 110.72(17)\nN-H(4)\u0001\u0001\u0001O(1) 2.182(73)\nN-H(3)\u0001\u0001\u0001O(w) 2.060(69)\nO(H)-H(1)\u0001\u0001\u0001O(w) 1.749(21)\nTable 2: Selected bond distances and angles from the structure of\nNH4Cu2:5V2O7(OH) 2.H2O\nbe highly 2-dimensional. The stacking of the kagome layers di\u000bers for the 2 materials -\nin volborthite they are in phase while those of NH 4Cu2:5V2O7(OH) 2.H2O are staggered.\nThe Cu2+ions lie on a 2 =mpoint symmetry site to form an isotropic kagome lattice,\nmade up of identical equilateral triangular units (Cu{Cu=2.958 \u0017A). The isotropic\nkagome lattice has a ground state Hamiltonian with few exchange terms which better\nsimulates the simple model of theory.\nThe Cu on the 6 gsite was freely re\fned to an occupancy of \u001873%, a notable\ndeviation from the idealised level that would reduce the number of resonant states\navailable to a QSL state[21]. Despite this, the occupancy is still higher than the bond\npercolation threshold for a kagome ( pbond\nc=52%) [22]. Further, this situation does not\nnecessarily exclude the possibility of a QSL state as further neighbour entanglement\nmay still cause su\u000ecient degeneracies to allow one to occur. We note the that similar\nlevels of site disorder are seen in some kapellasite samples where they do not to destroy\nits QSL ground state [5].\nThe Cu{Cu nearest-neighbour superexchange interactions in NH 4Cu2:5V2O7(OH) 2.H2O\nare mediated by a O(H) group which sits on a 3-fold axis with a mirror plane, and O(1)\nwhich also lies on a mirror plane. The bridging angles of \\Cu{O(H){Cu = 99.54(29)\u000e\nand\\Cu{O(1){Cu = 85.05(21)\u000eare expected to mediate antiferromagnetic and ferro-\nmagnetic exchange, respectively, based on the Goodenough-Kanamori-Anderson rules\n[23, 24]. Weak exchange interactions can be expected through both of these pathways\nas they are close to the cross-over angle at 90\u000ethat is a minimum in both ferromagnetic\nand antiferromagnetic exchange. Such a situation increases the importance of other\nlow-energy exchange terms to the magnetic ground state, illustrated by Dzyaloshinskii-\nMoriya exchange's role in forming vesignieite's unique frozen and dynamic spin ground\nstate [11]. The Cu{O bond distances in NH 4Cu2:5V2O7(OH) 2.H2O and and the angles\ninvolved in superexchange across the kagome lattice are strikingly similar to those of\nvesignieite, Table 3. As both materials are then expected to display similar magnetic\nproperties, the Dzyaloshinskii-Moriya exchange is also likely to be important here.Synthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O7\nFigure 3. a. The structure of NH 4Cu2:5V2O7(OH) 2:H2O observed down the a-\naxis. The Cu-octahedra sheets and bivanadate layers are illustrated in blue and red,\nrespectively. The oxygen of the H 2O and the nitrogen of the NH+\n4are shown in the\ninterstitial sites. b.The kagome plane viewed down the c-axis. The Cu2+ions (black)\nsit on a 6gsite of the P63=mmc space group which has 3-fold rotational symmetry\nand so the Cu2+ions form a `perfect' kagome. The Cu2+ions ferromagnetic and\nantiferromagnetic superexchange pathways viathe O(2) (red) and O(H) (pink) species,\nrespectively, are shown.\nNH4Cu2:5V2O7(OH) 2.H2O BaCu 3V2O8(OH) 2BaCu 3V2O8(OH) 2\nP63=mmc C 2=m P 3121\nCu{O(H) 1.93691(63) \u0017A 1.913(2) \u0017A 1.91051(74)\nCu{O 2.18777(84) \u0017A 2.183(2) \u0017A 2.07250(28) / 2.14803(75)\n\\Cu{O(H){Cu 99.54(29)\u000e101.7(4)\u000e103.15(66)\n\\Cu{O{Cu 85.05(21)\u000e85.6(9)\u000e92.94(34) / 83.47(54)\nTable 3: Cu{O bond distances and angles for NH 4Cu2:5V2O7(OH) 2.H2O and two\nstructures of vesignieite which mediate superexchange are listed for comparison: the\ncrystal structure of vesignieite is disputed so comparisons were drawn with both the\nmonoclinic C2=m[25] and trigonal P3121 [26] structures; equivalent bond distances\nand bond angles from each structure have been compared. Some oxygens in the P3121\nstructure exhibit disorder over multiple sites; two values have been stated for bond\nlengths and angles formed with these oxygens.\nAn important structural feature that is seen in several of the Cu-vanadate\nkagome magnets [27, 28, 29] is an unusual axial compression [2+4] Jahn-Teller\ndistortion[29], formed of 2 short axial bonds and 4 longer equatorial bonds: Cu-\n{O(H)=1.9373(44) \u0017A and Cu{O(1)= 2.1881(43) \u0017A, respectively. At \frst sight, this\ncon\fguration could taken to indicate localisation of the unpaired electron in the dx2\u0000y2\norbital of Cu2+, but it has been argued that this type of distortion in powder di\u000braction isSynthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O8\nFigure 4. a The interstitial NH+\n4and H 2O molecules are displayed sitting on the\ndisordered sites between the Cu-octahedra sheets that make up the kagome layers.\nNH+\n4has two equivalent energy orientations that are mirror images in the ab-plane.\nN-H(4) lies along the c-axis and forms three equivalent hydrogen bonds with O(1). The\nN-H(3) bonds lie on the planes of the 3-fold axis and H(3) forms a hydrogen bond with\nO(w); O(w) lies o\u000b the 3-fold axis and also hydrogen bonds to H(1). bA single H 2O\nrigid body is displayed with the hydrogens canted out of the ab-plane as observed in\nvolborthite [12]: the lone pairs of O(w) are now pointing at H(1) for hydrogen bonding.\ncommonly an artifact of averaging when the half-occupied d z2orbital \ructuates between\ntwo degenerate orientations[30]. We therefore conclude that the Jahn-Teller e\u000bect of the\nCu2+ions in NH 4Cu2:5V2O7(OH) 2.H2O is dynamic at room temperature and that the\nCu2+orbitals \ructuate.\nOur re\fnements also show that the NH+\n4unit is displaced from the high symmetry\n2dsite along the c-axis; this displacement is likely stabilized by the formation of 3\nequivalent N{H(4) \u0001\u0001\u0001O(1) = 2.182 \u0017A hydrogen bonds and a linear N{H(3) \u0001\u0001\u0001O(w) =\n2.060 \u0017A (Figure 4). In turn, displacement of the H 2O from the 2 csite is such that the\nhydrogens point below the ab-plane of the O(w) site, as is also observed in volborthite\n[12], which would allow the lone pair orbitals of O(w) to point towards H(1), forming\nO(H){H(1)\u0001\u0001\u0001O(w) = 1.987 \u0017A. The orientations of these extra-framework molecules\ncould be con\frmed through neutron di\u000braction on a deuterated sample.\n4. Magnetic characterisation\nZero-\feld cooled magnetisation data were collected from NH 4Cu2:5V2O7(OH) 2.H2O\n(65.3 mg) using the vibrating sample magnetometer of a Quantum Design PPMS-Synthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O9\nFigure 5. All magnetization data was collected on a zero-\feld cooled sample\nof NH 4Cu2:5V2O7(OH) 2.H2Oa.The\u001f\u00001\nmvs T plot shows a deviation from the\nlinear Curie-Weiss law at T\u0014170 K due to a build up of local spin correlations.\nExtrapolation from the linear slope yields a Weiss temperature of \u0012W' \u0000 30 K\nindicating antiferromagnetic exchange, the absence of an antiferromagnetic transition\natT= 30 K indicates a frustration of magnetic ordering characteristic of quantum\nkagome magnets. b.A plot of\u001fmvsT shows a ferromagnetic transition at TC\u001817 K\nc.M vs: H at 2 K hysteresis loop with steps, con\frming ferromagnetic ordering and\nindicating a build up of magnetic domains.Synthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O10\n9T in a \feld of 1000 Oe and with heating rate of 2 K/min. Inspection of \u001fvs.T\nindicates that there is a ferromagnetic-like transition at TC\u001817 K that leads to a\nbroad maximum, while the temperature-dependence of the inverse susceptibility shows\na linear Curie-Weiss regime over the range 170 \u0014T\u0014400 K from which a Weiss\ntemperature of \u0012W'\u000030 K can be extrapolated. The deviation from linear behaviour\non cooling below 170 K indicates that while spin correlations are building up, ordering\nis suppressed to a temperature below T=j\u0012Wj: a well known characteristic of S=1\n2\nfrustrated magnets[31, 7, 9]. The juxtaposition of a ferromagnetic-like transition and\na negative Weiss temperature indicates there is a competition within the magnetism\nof NH 4Cu2:5V2O7(OH) 2.H2O. The dominant character of the mean \feld appears to be\nantiferromagnetic and the transition only occurs when a ferromagnetic energy scale\nbecomes relevant. The room temperature value of the e\u000bective moment, \u0016e\u000b= 2:06\u0016B,\nis higher than the spin-only value of \u0016e\u000b= 1:73\u0016Bindicating that the Land\u0013 e g-factor\nfor Cu2+exceeds 2 and that there is an orbital contribution to the magnetism[10].\nHysteresis in the magnetic \feld-dependence of the magnetisation data at 2 K shown\nin Figure 5c con\frms a coherent ferromagnetic component in the low temperature state\nand an unsaturated paramagnetic signal up to 5 T. The coexistence of ferromagnetic\nand paramagnetic signals has been observed for some other S=1\n2kagome magnets,\nnamely vesignieite, haydeeite, and `Mg-herbertsmthite' [32, 9, 33]. The contribution of\nthe ferromagnetic and paramagnetic signals to the hysteresis were previously isolated for\nhaydeeite using a paramagnetic Brillouin function with a constant term that accounts for\nthe ferromagnetic response [26]. In order to extract the ferromagnetic contribution and\nobtain a value of the spontaneous magnetisation independent of a paramagnetic signal\nthe following equation was used to \ft the hysteresis data for NH 4Cu2:5V2O7(OH) 2.H2O:\nM(H)=Msat= (1\u0000f)BJ;PM(H) +f (1)\nwhere M satis the saturated magnetisation, fis the ferromagnetic response constant and\nBJ;PMis the paramagnetic Brillouin function per molecule,\nBJ;PM(H) =tanh(g\u0016BJH=k BT) (2)\nTaking Cu2+to be spin only, J=S=1\n2,gandfwere re\fned to \ft the high-\feld curve\nand yielded values of g= 2:36 andf= 0:41. This latter value indicates that \u001841%\nof spins are frozen. A plot of the extracted ferromagnetic contribution to the hysteresis\nis shown in Figure 6a, and steps in the hysteresis are clearly illustrated in Figure 6b.\nMagni\fcation of one step, shown in \fgure 6c, illustrates the sensitivity of the measured\nmoment to small changes of \feld over the range -50 Oe .H.50 Oe. This behaviour\nmakes it di\u000ecult to determine the spontaneous moment as zero \feld coincides with the\napproximate center of the step, but an upper limit of \u00140:075\u0016BCu\u00001is estimated. The\nsteps in the hysteresis are unusual and are not observed for any other S=1\n2kagomeSynthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O11\nmagnets, indicating that the magnetic ground state is indeed exotic and warrants further\ninvestigation.\nAs discussed in section 3.2, NH 4Cu2:5V2O7(OH) 2.H2O and vesignieite have very\nsimilar superexchange pathways and are expected to display similar magnetic properties.\nIndeed, both feature antiferromagnetic Weiss temperatures, of \u0012W' \u0000 85(5) K and\n\u0012W'\u000030 K [14], respectively, and have magnetic transitions involving a ferromagnetic\ncomponent [32] to a state with a similar proportion of frozen spins at T\u00142 K [14]. V51\nNMR and\u0016SR studies of vesignieite have indicated that the spin ordering of only partial\n(\u001840 %) below TN= 9 K and that a dynamic component remains down to 1 K [14, 34].\nESR analysis of vesignieite revealed that the ordered spin structure was induced by an\nin-plane Dyaloshinsky-Moriya and is canted out of the kagome plane [11].\nA clear di\u000berence between the materials is the observed step structure in\nthe hysteresis of NH 4Cu2:5V2O7(OH) 2.H2O. This may be characteristic of a spin\nreorientation transition, of the type seen in the metallic kagome ferromagnetic Fe 3Sn2\n[35], though here it is unclear whether it would be continuous or involve a 1storder\ntransition and changes in domain occupation.\n5. Conclusion\nA hydrothermal synthesis and reaction mechanism for the production of pure crystalline\nsamples of the new kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O has been outlined. Its\ncrystal structure consists of `perfect' Cu2+kagome-planes that are separated by V 2O4\u0000\n7\npyrochlore pillars, with ammonium and water groups residing in the interstitial sites;\nthe orientation of the interstitial molecule has been speculated upon.\nPreliminary magnetization measurements indicate a suppression of magnetic\nordering and superparamagnetic correlations that are characteristic of S=1\n2kagome\nantiferromagnets, and a ferromagnetic transition at TC'17 K. Remarkably, steps are\nseen in the hysteresis data at low \feld which indicate that the ground state has a unusual\nand marked sensitivity to an applied magnetic \feld.\nStructural and magnetic similarities between NH 4Cu2:5V2O7(OH) 2.H2O and\nvesignieite suggest that an in-plane component to the Dyaloshinsky-Moriya exchange\nplays an important role in spin-ordering. We speculate that this may also involve\nan orbital freezing transition of the spin-bearing Cu2+ion. Further studies by \u0016SR\nand inelastic neutron scattering studies would help determine the ground state of this\nunusual kagome magnet and its location in the phase diagram of possible QSLs.\n6. Acknowledgments\nWe would like to thank Jeremy Cockcroft for informative discussions, Martin Vickers\nfor experimental assistance, and UCL for the provision of the studentship.Synthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O12\nFigure 6. a The extracted ferromagnetic contribution (red circles) to the hysteresis\nis shown along with the M vsH data taken at 2 K (black circles) bThe ferromagnetic\nhysteresis loop shows a step near zero-\feld. cA close up of region of the step shows it\nto occur between \u000050 Oe.H.50 Oe.Synthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O13\n7. References\n[1] Rokhsar D S and Kivelson S A 1988 Phys. Rev. Lett. 612376{2379\n[2] Sachdev S 1992 Phys. Rev. B 4512377\n[3] Lecheminant P, Bernu B, Lhuillier C, Pierre L and Sindzingre P 1997 Phys. Rev. B 562521\n[4] Balents L 2010 Nature 464199\n[5] F\u0017 ak B, Kermarrec E, Messio L, Bernu B, Lhuillier C, Bert F, Mendels P, Koteswararao B, Bouquet\nF, Ollivier J, Hillier A D, Amato A, Colman R H and Wills A S 2012 Phys. Rev. Lett. 109037208\n[6] Boldrin D, Fak B, Enderle M, Bieri S, Ollivier J, Rols S, Manuel P and Wills A S 2015 Phys. Rev.\nB92\n[7] Colman R H, Ritter C and Wills A S 2008 Chem. Mat. 202005\n[8] Janson O, Richter J and Rosner H 2008 Phys. Rev. Lett. 101106403\n[9] Colman R, Sinclair A and Wills A S 2010 Chem. Mat. 225774\n[10] Zorko A, Nellutla S, van Tol J, Brunel L C, Bert F, Duc F, Trombe J C, de Vries M A, Harrison\nA and Mendels P 2008 Phys. Rev. Lett. 101026405\n[11] Zorko A, Bert F, Ozarowski A, van Tol J, Boldrin D, Wills A S and Mendels P 2013 Phys. Rev.\nB88144419\n[12] Hiroi Z, Hanawa M, Kobayashi N, Nohara M, Takagi H, Kato Y and Takigawa M 2001 J. Phys.\nSoc. Jpn. 703377\n[13] Okamoto Y, Yoshida H and Hiroi Z 2009 J. Phys. Soc. Jap. 783\n[14] Colman R H, Bert F, Boldrin D, Hillier A D, Manuel P, Mendels P and Wills A S 2011 Phys. Rev.\nB83180416 ISSN 1098-0121\n[15] Palacio L A, Silva E R, Catal~ ao R, Silva J M, Hoyos D A, Ribeiro F R and Ribeiro M F 2008 J.\nHaz. Mat. 153628\n[16] Pekov I V, Siidra O I, Chukanov N V, Yapaskurt V O, Britvin S N, Krivovichev S V, Sch uller W\nand Ternes B 2015 Min. Petro. 3\n[17] Bruxer AXS 2008 Topas v4: General pro\fle and structure analysis software for powder di\u000braction\ndata\n[18] Momma K and Izumi F 2011 Vesta 3 for three-dimensional visualization of crystal, volumetric and\nmorphology data\n[19] Lafontaine M A, Le Bail A and Ferey G 1990 J. Sol. St. Chem. 85220\n[20] Hawthorne F C 1977 J. Sol. St. Chem. 170157{ 170\n[21] Lacroix C, Mendels P and Mila F (eds) 2011 Introduction to Frustrated Magnetism (New York,\nUSA: Springer)\n[22] Feng X, Deng Y and Bl ote H W J 2008 Phys. Rev. E 781{6\n[23] Goodenough J B 1955 Phys. Rev. 100564.\n[24] Kanamori J 1959 J. Phys. Chem. Sol. 1087\n[25] Zhesheng M 1991 Acta Geo. Sin. 42\n[26] Boldrin D 2015 Synthesis and Study of Quantum Kagome Magnets Ph.D Thesis UCL\n[27] Yoshida H, Yamaura J I, Isobe M, Okamoto Y, Nilsen G J and Hiroi Z 2012 Nat. Commun. 3860\n[28] Okamoto Y, Yoshida H and Hiroi Z 2009 J. Phys. Soc. Jap. 78033701\n[29] Boldrin D and Wills A S 2015 J. Mater. Chem. C 34308\n[30] Burns P and Hawthorne F 1996 Can. Mineral. 341089\n[31] Hiroi Z, Yoshida H, Okamoto Y and Takigawa M 2009 J. Phys. Conf. Ser. 145012002\n[32] Yoshida H, Michiue Y, Takayama-Muromachi E and Isobe M 2012 J. Mat. Chem. 2218793\n[33] Colman R H, Sinclair A and Wills A S 2011 Chem. Mat. 231811{1817\n[34] Quilliam J A, Bert F, Colman R H, Boldrin D, Wills A S and Mendels P 2011 Phys. Rev. B 84\n180401\n[35] Fenner L A, Dee A A and Wills A S 2009 J Phys. Condens. Matter 21452202\n[36] Stephens P W 1999 J. App. Crys. 32281\n[37] Roe R J and Krigbaum W R 1964 J. Chem. Phys. 402608Synthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O14\n[38] Young R A 2001 The Rietveld Method (New York, USA: Oxford University Press)Synthesis, structure and magnetism of the new S=1\n2kagome magnet NH 4Cu2:5V2O7(OH) 2.H2O15\nAppendix A. Supplementary information\nCrystallographic data\nChemical formula NH 4Cu2:5V2O7(OH) 2.H2O\nCrystal system Hexagonal\nSpace group P63=mmc (194)\na(\u0017A) 5.9159(2)\nc(\u0017A) 14.4430(6)\nVolume ( \u0017A3) 437.76(2)\nFormula units ( Z) 2\nData collection\nRadiation, \u0015(\u0017A) CuK \u000b1, 1.54\n2\u0012-step size increments (\u000e) 0.05\n2\u0012range (\u000e) 9 - 70\nGeometry Debye-Scherrer geometry\nTemperature (K) 293\nZero error (\u000e) 0.04809(5)\n\u0016R 1.6(4)\nNumber of observed re\rections 53\nRe\fnement\nInstrumental, unit cell and pro\fle parameters 36\nPeak area parameters 20\nPro\fle function Stephens' anisotropic broadening [36]\nSpherical harmonics [37]\nRexp[38] 1.43\nRwp[38] 3.34\n\u001f2[38] 2.35\nTable A1: Details of the data collection procedure and Rietveld re\fnement of\nNH4Cu2:5V2O7(OH) 2:H2O are displayed along with crystallographic data"    },    {        "title": "1610.04011v1.Electronic_control_of_magnonic_and_spintronic_devices.pdf",        "content": "Electronic control of magnonic and spintronic devices\nC. Tannous\nLaboratoire de Magn\u0013 etisme de Bretagne, UBO CNRS-FRE 3117,\n6 Avenue le Gorgeu C.S.93837, 29238 Brest Cedex 3, FRANCE.\nJ. Gieraltowski\nLaboratoire des Domaines Oc\u0013 eaniques, IUEM CNRS-UMR 6538,\nTechnop^ ole Brest Iroise, 29280 Plouzan\u0013 e, FRANCE.\nNanometric magnonic and spintronic devices need magnetic \feld control in addition to conven-\ntional electronic control. In this work we review ways to replace magnetic \feld control by an\nelectronic one in order to circumvent appearance of stray magnetic \felds or the di\u000eculty of creating\nlarge magnetic \felds over nanometric distances. Voltage control is compared to current control and\ncorresponding devices are compared from their energetic e\u000eciency point of view.\nPACS numbers: 85.75.-d, 85.75.-d, 75.76.+j, 75.30.Ds\nKeywords: Magnetoelectronics, Spintronics, Spin transport e\u000bects, Spin waves\nVersion: April 20, 2022\n1. INTRODUCTION\nMinimal feature in microelectronics CMOS planar\ntechnology progressed from 22 nm in 2012 to its present\nvalue of 14 nm and is slated to reach 10 nm in 2016.\nProgressing toward nanoelectronics with a minimal\nfeature approaching steadily the nanometer limit leads\nto at least \fve major consequences:\n1. Joule e\u000bect increase.2. Interconnection delay increase.\n3. Circuit size decrease with respect to some reference\nelectromagnetic (EM) wavelength.\n4. Enhancement of quantum e\u000bects.\n5. Emergence of spin degrees of freedom.\nJoule e\u000bect enhancement is due to resistor Rscaling\nby a factor s>1 increasing the resistance to sRwhereas\nwire (interconnection) delay increase is due to rise of com-\nmunicating wire length with number of components (see\nTable 1).\nMicroprocessor (year) Feature Size Transistors Frequency Pins Power consumption Wire Delay\n(nm) (MHz) (Watts) (clock cycle/cm)\nIntel 4004 (1971) 10,000 2,300 0.750 16 1 1/1,000\nPentium IV-670 (2005) 90 169 million 3,800 775 115 4\n(2005)/(1971) Ratio (1/111) 73,478 5,066 48 115 4,000\nTABLE 1: Comparison of two CPU characteristics dating from 1971 and 2005 and the evolution of their intrinsic properties\nwith feature size decrease. The 4004 is the \frst commercial 4-bit CPU whereas the Pentium IV-670 is a single-core 64-bit\nCPU. As number of transistors, frequency, number of pins all increase as expected, wire delay and power consumption increase\nagainst all expectations. Wire delay is extracted from the speed of an electronic signal which is about 20 cm per nanosecond\n(ns) within the wire. Hence one gets 0.5 ns for a 10 cm propagation length and in the case of a 1 GHz CPU, the delay represents\nhalf-a-clock cycle.\nWhile Joule e\u000bect and interconnection delay have been\nsomehow virtually solved in microprocessors by intro-\nducing multi-core architecture (see Table 1), the latter\nconcept appears as an intermediate solution awaiting a\nbetter technology to address, in a deeper way, power con-\nsumption and wire delays in devices.\nPower consumption issue is tackled in magnonic andspintronic devices that are based respectively on spin-\nwave and spin current manipulation. Extremely low\npower dissipation is reached in both cases (except with\nspin-transfer torque (STT) currents where critical den-\nsity required for switching is very large as described in\nnext section) since no Joule e\u000bect is expected when no\ncharges are moving in order to carry information. Un-arXiv:1610.04011v1  [cond-mat.mtrl-sci]  13 Oct 20162\ndulation of spin moments is the carrier of information\ntransport.\nMagnonics belong to a class of devices based on spin\nwaves to carry and process information on the nanoscale.\nThey are the magnetic counterpart of plasmons that\nare used in nanophotonics since the wavelength \u0015of\nmagnons is orders of magnitude shorter than that of EM\nwaves (photons) of the same frequency. Thus magnonic\ndevices represent a serious step toward the fabrication of\nnanometer-scale microwave devices.\nIn nanophotonics surface plasmons are used to me-\ndiate EM propagation in order to beat the \"di\u000braction\nlimit [1]\" requiring the photon wavelength \u0015 < a where\nais the optical \fber diameter. If \u0015is on the order of\na micron and aon the order of a nanometer, no propa-\ngation is possible. The situation is worse in nano-scale\nmicrowave circuits since frequencies are in the GHz ( \u0015\nabout 30 cm) and aon the order of a nanometer.\nThis work is concentrated on electrical means to con-\ntrol magnonic and spintronic devices exploiting spin-\nwaves and spin-currents for signal processing, logic, mem-\nories and telecommunication.\nDealing with such magnetic devices implies the require-\nment of controlling adequately magnetic \felds given the\nfact that in the microelectronics industry, electric voltage\n(or \feld) and not electric current control prevails.\nThus, fabrication of practical devices aims at the goal\nof replacing magnetic \feld control by an electrical one\n(whenever possible) since stray magnetic \felds might in-\nterfere with device operation besides, technically it is dif-\n\fcult presently to produce large magnetic \felds over a\nnanometer length.\nThis work is organised as follows. In section 2 elec-\ntronic control is discussed from the general viewpoint of\neither replacing magnetic control altogether or combin-\ning electricity and magnetism by either coupling or in-\nterconverting electrical and magnetic degrees of freedom\nusing speci\fc mechanisms with special types of materials\nsuch as composites, metamaterials or single-phase multi-\nferroics. Section 3 is concerned with electronic control of\nmagnonic devices whereas section 4 deals with electronic\ncontrol of spintronic devices. Conclusions and outlook\nare presented in section 5.\n2. COMBINING ELECTRICITY AND\nMAGNETISM\n1. Coupling electrical and magnetic degrees of\nfreedom\nElectric and magnetic degrees of freedom when cou-\npled can be described with the following free energy ex-\npansion [2]:\n\u0000F(E;H) = +1\n2\u000f0\u000fijEiEj+1\n2\u00160\u0016ijHiHj\n+\u000bijEiHj+1\n2\fijkEiHjHk+1\n2\rijkHiEjEk::: (1)\u000bijis \frst order (in E;Hcomponents) coupling con-\nstant whereas \fijkis \frst order in Esecond order in\nHwhereas\rijkis a \frst order in Hsecond order in E\ncomponents.\n\u000f0and\u00160are respectively permittivity and permeabil-\nity of free space whereas \u000fijand\u0016ijare respectively rel-\native permittivity and permeability.\nFmust satisfy symmetry [2] considerations such as\nspace-inversion symmetry (satis\fed in ferromagnets) and\ntime-inversion symmetry (satis\fed in ferroelectrics) im-\nposing constraints on the expansion coupling constants.\nIf a multiferroic is both ferroelectric and ferromagnetic,\nboth symmetries are not required [2].\nFerroelectric polarization Pand magnetization Mre-\nsponses are obtained by di\u000berentiating Fsuch as:\nPi=\u0014@F(E;H)\n@Ei\u0015\nEi=0=\u000bijHj+1\n2\fijkHjHk+:::\n\u00160Mi=\u0014@F(E;H)\n@Hi\u0015\nHi=0=\u000bjiEj+1\n2\rijkEjEk+:::\n(2)\nshowing how electric degrees of freedom a\u000bect mag-\nnetic ones and vice versa.\nRecall that electric polarization can also be in-\nduced in non-uniformly magnetized materials such that\nP/[(M\u0001r)M\u0000M(r\u0001M)].\nMaterials containing coupling terms of that nature are\nmagneto-electric (ME) materials whereas a more general\nclass of materials embodying additional coupling with\nelastic terms are called multiferroic which might be com-\nposite or single phase.\nIn composite materials, coupling between magnetic\nand electrical degrees of freedom e\u000bect or ME coupling\nis mediated through elastic interaction such as between a\nmagnetostrictive and an electrostrictive (or piezoelectric)\nsubstance.\nComposite materials made from ferroelectric (or piezo-\nelectric) elements containing lower dimensional magnetic\nelements such as thin \flms or multilayers (laminar cou-\npling), wires (\fber or rod coupling) and beads (spherical\ninclusions) [3] interacting with each other, may be the\nsimplest structures to couple electrical and magnetic de-\ngrees of freedom.\nIn addition to ME composites and multiferroic materi-\nals, dilute magnetic semiconductors (DMS [4]) respond to\nmagnetic \felds through dispersed magnetic elements that\nsense the perturbing magnetic \feld. Magnetic superlat-\ntices (also called metamaterials), the magnetic analog\nof semiconducting superlattices or photonic structures\n(with spatially variable dielectric constant) contain spa-\ntially modulated magnetization, anisotropy or magnetic\nphase (ferro, antiferro, ferri...) that can alter magnon\nproperties such as dispersion relations (gap and group\nvelocity) allowing spatially dependent adaptive control.3\n2. Interconverting electrical and magnetic degrees\nof freedom\nA magnetic insulator such as YIG (Ferrimagnetic Yt-\ntrium Iron Garnet Y 3Fe5O12[5, 6]) covered with a noble\nmetal such as Pt can interconvert electrical and magnetic\ndegrees of freedom. A spin current in YIG can be gener-\nated (see next section) and detected electrically by using\nspin and charge current interaction [7]. The signal can\ntravel over a long distance [5, 6] in YIG since it is an\ninsulator devoid of free charges that can act as scatter-\ning sources, moreover it has a very low intrinsic magnetic\ndamping coe\u000ecient (see Table 2) allowing a spin-wave to\ntravel freely without any loss.\nGenerally, spin currents belong to three types [8]:\n1. SPC (spin-polarized current) made of free (s-type)\nspin-polarized carriers,\n2. SWC (spin-wave current) carried by undulating lo-\ncalized spins (d-type),\n3. STT (spin-transfer torque) current stemming from\ns-d (double) exchange between free and localized\ncarriers [9].\nCurrent densities ought to be very large (in STT they\nare about 106-107A/cm2) in order to produce magneticswitching, this is why the ultimate goal is to rather aim\nfor a small voltage [10] (electric \feld control [11]) in or-\nder to generate a magnetic \feld or to produce a magnetic\ne\u000bect since it is the conventional control used in tradi-\ntional microelectronics and because it is spatially local-\nized in contrast with current control that might lead to\nuncontrolled stray \felds.\nMagnetic-Electric interconversion between YIG and Pt\nis based on transfer of spin-angular momentum from\n(localized) magnetization-precession motion (in YIG) to\n(free) conduction-electron spins (in Pt) and spin transfer\ntorque (STT). The latter is the reverse process i.e. the\ntransfer of angular momentum from conduction-electron\nspin (free) back to (localized) magnetization. Many inter-\nconversion aspects are allowed by the special properties\nof YIG displayed in Table 2.\nProgress in electronic control of magnetic devices sum-\nmarized in Table 3 shows that many magnetic properties\ncan be tightly controlled with an electric \feld leading\nto control of spin-waves and spin-currents as described\nbelow.\n3. ELECTRONIC CONTROL OF SPIN-WAVES\nIN THIN FILM DEVICES\nSpin waves can be generally divided into three cate-\ngories [18]:\na- Magnetostatic spin waves (MSW) originating from\nlong-range dipolar interactions between elements whose\ntypical size is the micron. Damon-Eshbach [19] MSW\nmodes are transverse (the wavevector kis perpendicular\nto local magnetization M).\nMagnetostatic Surface Spin-Waves (MSSW), the mag-\nnetic counterpart of Surface Acoustic Waves (SAW) can\nalso be excited in thin \flms or stripes made of YIG and\ntheir energy is on the order of a few GHz [18].b- Exchange spin-waves (ESW) originating from short-\nrange Heisenberg exchange interactions between elements\nwhose typical size is the nanometer. Their energy is on\nthe order of a tenth of a GHz (or a \u0016eV) reaching the\nTHz [18] in antiferromagnets.\nc- Dipolar-Exchange Spin Waves (DESW) in the case of\ndevices of mixed length type [18], such as Magnetic Quan-\ntum Dots (MQD) laid out periodically as planar arrays,\nwith a typical in-plane length (MQD diameter) on the\norder of a micron and a perpendicular-to-plane length\n(MQD height) on the order of a nanometer.\nIn the latter case, spin-waves with both types of contri-\nbutions occur as predicted for the \frst time by Herring-\nKittel [20] for in\fnite media and by Clogston et al. [21]\nfor \fnite media such as ellipsoids.\n1. Spin-wave generation energetics\nHeisenberg model for localized spins in a ferromagnet\ngives an interaction energy for a pair of neighbouring\nspins Si;Si+1as\u00002JexSi\u0001Si+1whereJexis the ex-\nchange integral. The Curie temperature is obtained from\nkBTc=2\n3JexzS(S+ 1) where zis the coordination num-\nber andSthe spin value. Jexleads also to spin-waveenergy dispersion: \u0016 h!k= 4JexS(1\u0000coska) wherekis\nthe wave vector. Considering a 1D array with lattice\nparameter a, reversing a single spin costs the spin-\rip\nenergy 4JexS2.\nFor a set of nspins, the total energy is 4 nJexS2meaning\nthat propagating a spin-\rip across a distance narequires\nsuch energy. By comparison, spin-wave propagation can\nbe performed with a wavelength chosen to match the4\nParameter Value\nLattice constant 12.376 \u00060.004 \u0017A\nDensity 5.17 g/cm3\nBand gap 2.85 eV\nSaturation induction 4 \u0019MS 1750 G\nCubic anisotropy constant K1 -610 J/m3\nAnisotropy \feld 2 K1=MS 88 Oe\nCubic anisotropy constant K2 -26 J/m3\nCurie temperature TC 563 K\nThermal expansion coe\u000ecient 8.3 x 10\u00006/K\nRelative dielectric constant (at 10 GHz) 14.7\nDielectric loss tangent (at 10 GHz) 0.0002\nFMR linewidth \u0001 H(at 10 GHz) 0.1 Oe\nIntrinsic LLG damping constant \u000b 3 x 10\u00005\nLand\u0013 e factor g 2.00\nTABLE 2: Structural, electric, magnetic, thermal and mi-\ncrowave properties of ferrimagnetic Yittrium Iron Garnet [5,\n6] at room temperature in practical units. YIG possesses\nthe narrowest FMR (ferromagnetic resonance) linewidth of all\nmaterials with smallest losses and almost zero LLG (Landau-\nLifshitz-Gilbert) damping.\nsame distance \u0015=na. The corresponding energy can\nbe evaluated for the wavevector k= 2\u0019=na substituted\nin 4JexS(1\u0000coska). This gives the energy 2 JexSk2a2\nequal to 8JexS\u00192=n2in the limit ka= 2\u0019=n<< 1.\nAs an application, we consider a Ni ribbon as part of\na Ni/Permalloy (Ni 81Fe19) bilayer considered as a spin-\nwave bus (see next subsection) to propagate spin-waves.\nDespite the fact, Ni is an itinerant magnet where the\nHeisenberg picture does not strictly apply, we infer that\nJex= 1:45\u000210\u000021Joules or 9 meV (in comparison,\nStoner exchange integral is 1.01 eV [26]) from the above\nCurie temperature formula with S=1\n2,Tc= 629K and\ncoordination number z= 12 (from Ni FCC structure).\nAs an example, the spin-\rip propagation energy for 1000\nspins is 1:45\u000210\u000021Joules whereas the corresponding\nspin-wave energy (with Ni lattice parameter a=3.52 \u0017A)\nis 5:71\u000210\u000026Joules which is about \fve orders of mag-\nnitude smaller.\nThe spin-wave to spin-\rip energy propagation ratio is in-\ndependent of the value of Jexand strongly decreases with\nthe number nof spins as2\u00192\nSn3suggesting that spin-wave\npropagation is de\fnitely lower in terms of energy cost.\n2. Voltage-induced spin wave generation with\nhybrid cells\nSingle-phase multiferroics have in general small ME\ncoupling. Instead of using large consumption devices\nsuch as inductive antennas or STT currents in order\nto generate spin-waves, Cherepov et al. [11] used hy-\nbrid (multiferroic ME) cells consisting of a magnetostric-\ntive Ni layer and a piezoelectric substrate PMN-PT i.e.[Pb(Mg 1=3Nb2=3)O3](1\u0000x)- [PbTiO 3]x.\nPMN-PT (lead magnesium niobate-lead titanate) is a fer-\nroelectric relaxor [10] with a large relative dielectric con-\nstant\u000fr. For 0< x < 0:35, the electromechanical cou-\npling and piezoelectric coe\u000ecients of PMN-PT are very\nlarge making it a sensitive material for ME control.\nApplying an AC voltage to (PMN-PT) induces an al-\nternating strain in the piezoelectric material. The strain\ntransmitted to the magnetostrictive Ni layer produces\nlocal anisotropy variation resulting in easy axis reori-\nentation that pulls on the magnetization. Magnetiza-\ntion oscillations propagate in the form of spin waves in a\nNi/Permalloy bilayer lithographically shaped in the form\nof a stripe that is called a spin-wave bus. While the Ni\nlayer provides the desired magnetostriction, NiFe being\na soft magnetic material is favorable to spin-wave prop-\nagation because of its low LLG damping constant \u000b.\nIn order to describe spin-wave generation electroni-\ncally, we need a process that entails tilting a single spin\nbelonging to an ordered spin array. This entails appli-\ncation of a localized magnetic induction \feld Bexfor a\nshort time.\nThe value of Bexrequired to tilt a spin in the ferromag-\nnetic stripe should be on the order of Bex=Bdemtan\u0012\nwith\u0012the tilt angle and Bdemthe demagnetization \feld\northogonal to Bex. This originates from the fact the in-\nternal \feld sensed by any spin Mis the sum of the ex-\nternal \feld Bexand the demagnetization \feld Bdemwith\nBdem=\u00004\u0019NM .Nis the demagnetization coe\u000ecient\nandMthe local magnetization.\nIf we approximate the ferromagnetic stripe by a satu-\nrated thin \flm, the demagnetization coe\u000ecient N= 1\nandM=Ms. Thus we infer that the required excitation\n\feld isBex= 4\u0019Mstan\u0012.\nThis \feld can be generated by an antenna [11] deliv-\nering a current pulse or an ME capacitive cell providing\nvoltage pulse whose duration is determined by the oper-\nating frequency fLOof the device local oscillator.\nAt a distance r, Amp\u0012 ere law provides the expression\nHex=I\n2\u0019rrelating the required current intensity Ito\nthe required magnetic \feld Hex=Bex=\u00160. Thus the\nrequired energy isRI2\nfLOwhereRis the resistance of the\nantenna traversed by I.\nAs an example, we take \u0012= 1\u000e,Ms=485 emu/cm3\n(Ni saturation magnetization) and fLO=5 GHz. At a\nnominal distance rabout 10 times the minimal feature\n(14 nm), we get the required current I=7.48 mA.\nTaking antenna typical dimensions such as length,\nheight and width `;a;b all around 10 times the minimal\nfeature value and a standard metallic resistivity of \u001a=1\n\u0016\n.cm, we get antenna resistance R=\u001a`\nab\u00190:07\n and\ndissipation energyRI2\nfLO\u00198\u000210\u000016Joule.\nMoving on to the ME capacitive cell made with a\nmaterial whose ME coe\u000ecient \f=\u000eH\n\u000eEis not small, we\nmay substitute e\u000eciently an electric \feld to a magnetic5\nElectrically controlled quantity Comments Reference\nExchange interaction Proposal for electric \feld modi\fcation\nof local exchange between neighbouring\nmagnetsGorelik et al. [12] (2003).\nNature of magnetic phase Ferromagnetic ordering in hexagonal\nHoMnO 3is reversibly controlled by an\nelectric \feldLottermoser et al. [13] (2004).\nCoercivity Electric control of coercivity in\nCoFeB/MgO/CoFeB magnetic tun-\nnel junctionWang et al. [14] (2005).\nExchange bias Electric-\feld control of exchange bias in\nmultiferroic epitaxial heterostructuresLaukhin et al. [15] (2006).\nSensors, transducers and microwave de-\nvicesME control in composites made with\nmagnetostrictive and piezoelectric ele-\nmentsNan et al. [3] (2008).\nMagnetic domain wall motion and mag-\nnetization directionWriting/Erasure of ferromagnetic do-\nmains and electric control of domain wall\nmotionLahtinen et al. [16] (2012).\nAnisotropy Electrically induced large mag-\nnetization reversal in multiferroic\nBa0:5Sr1:5Zn2(Fe0:92Al0:08)12O22Chai et al. [17] (2014).\nTABLE 3: Selected progress milestones in electronic control of magnetic devices.\nElectrical control type Comments Reference\nSpin-Wave logic gates Current-controlled Mach-Zender type\ninterferometer based on MSSW propa-\ngation in YIG thin \flmsKostylev et al. [22] (2005).\nSpin-Wave phase and wavelength Current control of phase and wavelength\nof Damon-Eshbach MSW propagating in\nPermalloy (Ni 81Fe19) ribbons deposited\nover Cu stripesDemidov et al. [23] (2009).\nSpin-Wave frequency control Electric-\feld tuning of ESW frequency\nat room temperature using multiferroic\nBiFeO 3Rovillain et al. [24] (2010).\nAmpli\fcation of spin-waves Electric-\feld ampli\fcation of ESW in\nYIG/Pt bilayers using Interfacial Spin\nScatteringWang et al. [25] (2011).\nGeneration of spin-waves Electric-\feld-induced ESW generation\nusing multiferroic ME cellsCherepov et al. [11] (2014).\nTABLE 4: Selected progress milestones in electronic control of magnonic devices with several types of spin-waves.\ninduction \feld via Eex=Bex\n\u00160\f.\nThus the voltage required for tilting a spin is Vex=Eex`\nwhere`is the inter-plate distance of a cell whose\ncapacitance C=\u000fr\u000f0ab=` with energy1\n2CV2.\nA material such as Fe 3O4/PMN-PT has an ME coe\u000e-\ncient\f= 67 Oe.cm/kV (see Liu et al. [10]) and a relative\ndielectric constant around several 1000.\nTaking all dimensions such as length, height and width\n`;a;b about 10 times the minimal feature value, we get a\ncapacitance C=\u000fr\u000f0ab\n`=1.23\u000210\u000015F, a voltage of 22.2\nmV and a tilting energy of1\n2CV2=3\u000210\u000015Joule which\nis three orders of magnitude below the antenna case.\nThe capacitive over resistive (antenna) energy ratio\u0011=1\n2CV2=RI2\nfLOcan be expressed in a scaling form as\n\u0011=\u000f0\u000fr`2fLO\n8\u00192\u001a\f2where`replaces all lengths in the device\nimplying that as minimal feature continues to decrease\n\u0011\u0018`2will decrease.\nMoreover\u0011\u0018\u000fr\n\f2implying that we need multiferroic ma-\nterials with a smaller \u000frand a larger ME coe\u000ecient \fin\norder to keep \u0011decreasing, in contrast to materials such\nas PMN-PT with both ( \u000fr,\f) large.\nOnce the spin is tilted, its time variation follows space-\ndependent LLG equation:6\n@M(r;t)\n@t=\u0000\rM(r;t)\u0002H\u0000\u000b\r\njMjM(r;t)\u0002[M(r;t)\u0002H]\n(3)\nwhere\ris the gyromagnetic ratio, Mthe magnetiza-\ntion vector, Hthe e\u000bective \feld obtained from total en-\nergy and\u000bthe intrinsic damping parameter (see Table 2).\nLLG equation describes a propagating Bloch equation for\na moment precessing around magnetic \feld Hdirection\nand damped by the \u000bterm that forces the moment to\nprecess closer to the magnetic \feld direction thus reduc-\ning the initial tilt angle \u0012. Choosing materials such as Ni,\nNi/NiFe bilayers as well as YIG that possess small \u000b, al-\nlows long-distance signal propagation since \u0012diminishes\nvery weakly in the course of time.\n4. ELECTRONIC CONTROL OF SPINTRONIC\nDEVICES\n1. Issues in electric-\feld controlled spintronic\ndevices\nSubstituting magnetic \feld control by an electrical one\nis possible in semiconductors via spin-orbit interaction\nsince it allows generation and manipulation of carrier\nspins by an electric \feld [27].\nSpin-orbit interaction has also been shown to allow\nelectric control of spin-waves in single-crystal YIG waveg-\nuides which paves the way to develop electrically tunable\nmagnonic devices [28, 29].\nAnother alternative is a tunable spin current that al-\nlows to generate a magnetic \feld or produce a mag-\nnetic e\u000bect (such as reversal or alteration of magnetiza-\ntion) since a spin current targets interconversion between\ncharge and spin degrees of freedom [8, 30].\nIn analogy with ordinary electronics, spintronics is\nbased on several operations such as spin injection, \fl-\ntering, accumulation, detection and pumping [27].\nThe notion of spin coherence underlies all these opera-\ntions, that is preservation of a given spin state over long\ndistances despite the presence of impurities, dislocations,\nnoise, stray magnetic \felds, Earth magnetic \feld etc...\nSpin injection might be done optically in complete\nanalogy with Haynes-Shockley experiment. It may also\nbe done with carbon nanotubes since they do not alter\nthe spin state over large distances (see Dietl et al. [30]).\nSpin \fltering is essentially the separation of spin-\npolarised carriers which is required for avoiding spin-\rips\nthat alter carrier spin states akin to geminate recom-\nbination between photo-generated electron-hole pairs.\nThin ferromagnetic layers as in spin valves (see Dietlet al. [30]) and chiral materials such as monolayers of\ndouble-stranded DNA molecules can be used [31].\nSpin accumulation is concerned with increase of con-\ncentration of spin polarized carriers without destroy-\ning their coherence or inducing spin-\rips among them\nwhereas spin detection relates to non-destructive deter-\nmination of spin value.\nSpin pumping [32] occurs in Ferromagnetic-Normal bi-\nlayers, when the precessing magnetization in the Ferro-\nmagnet (F) injects a spin-current into a normal metal\n(N) through the F-N interface (as in the YIG/Pt case\ndescribed previously).\nElectrodeV+PR\nElectrodeV−PR\nFIG. 1: (Color on-line) MeRAM cell showing the electric \feld\ncontrol and the di\u000berent materials composing the memory\ncell. A spin-valve made from two blue layers (ferromagnets)\nseparated by a metallic spacer (in magenta) has its resis-\ntance Rmonitored. The upper blue layer made from a hard\nmagnetic material is free and the lower blue layer is made\nfrom a soft magnetic material in close contact with a (green\nlayer) material made from a ferroelectric antiferromagnet, a\nsingle-phase multiferroic. Top \fgure shows positive voltage\nVapplied to electrode (gold yellow) with blue layer magne-\ntizations (black arrows) antiparallel resulting in a high re-\nsistance R. Bottom \fgure shows negative voltage Vapplied\nwhile blue layers have parallel magnetizations yielding a very\nlow resistance R. Magnetization (black arrow) in each lower\nblue layer follows green material magnetization represented\nby small white arrows. In a multiferroic, polarization Pand\nmagnetization are coupled [33]. Thus when Pis up ( Vpos-\nitive), magnetization (represented by small white arrows) is\noriented to the left and when Pis down ( Vnegative), mag-\nnetization is oriented to the right. Adapted from Bibes et\nal.[34]\nMany of the spin manipulation processes described\nabove intervene in the progress milestones for electric-\n\feld control of spintronic devices displayed in Table 5.\n2. Electric-\feld controlled magneto-electric RAM\ndevices\nMagnetic Random-Access Memories (MRAM) abolish\nthe distinction between volatile storage (used duringprocessing) and permanent massive storage. A RAM7\nElectrical control type Comments Reference\nDriving of microwave oscillation GHz oscillator excited by STT current Kiselev et al. [35] (2003).\nMagnetic Random-Access Memories\n(MRAM)Electric control of CoFeB/MgO/CoFeB\ntunnel magnetoresistance switchingWang et al. [14] (2005).\nSpin transport in nanotubes Electric-\feld control of magnetoresis-\ntance in carbon nanotubes connected by\nferromagnetic leadsSahoo et al. [36] (2005).\nSpin transport in Silicon Ballistic spin-dependent hot-electron \fl-\ntering through ferromagnetic thin \flmsAppelbaum et al. [37] (2007).\nMemory Read-Write operations Information processing in MRAM cell\nmade with a DMS: (Ga,Mn)AsMark et al. [38] (2011).\nSpintronic logic gates Voltage-controlled spin selection and\ntuning in graphene nanoribbons for logicZhang [39] (2014).\nTABLE 5: Selected progress milestones in electronic control of spintronic devices\nis used by a CPU or a DSP (Digital Signal Processor)\nduring processing, for loading an operating system (OS)\nor enabling application programs (AP). The implication\nthat the OS and the AP are permanently loaded in\nMRAM brings a paradigm shift in computing that has\nfar reaching consequences in terms of computing speed\nand e\u000eciency. The initial attempts to design MRAM\ncells were based on domain wall motion control with a\nstrong electric current (racetrack-type memories [30]).\nMeRAM memory is a new type of voltage controlled\nRAM based on ME multiferroic interacting with a\nferromagnet. The multiferroic is a ferroelectric antifer-\nromagnet whose electric polarization induces an internal\nmagnetization (see \fg. 1) that controls the neighbouring\nferromagnet magnetization at the interface. An example\nferroelectric antiferromagnet is BiFeO 3(BFO) that\ndisplays both ferroelectricity and antiferromagnetic\norder at room temperature [40].\nBFO has a rhombohedral perovskite crystallographic\nstructure. It is a high-temperature ferroelectric (with\nCurie temperature Tc\u00191100 K) possessing a large fer-\nroelectric dipole moment \u0019100\u0016C/cm2. At room tem-\nperature, bulk crystalline BFO is antiferromagnetic [40]\nwith N\u0013 eel temperature T Nof 640 K. Voltage control of\nBFO magnetic state has been shown both in bulk and in\nthin \flm case making it an excellent candidate for ME\napplications.\nThe ferroelectric polarization and the antiferromag-\nnetic vector in BFO are coupled [33] in a way such that\nby reversing the polarization, the antiferromagnetic spins\nrotate. Nevertheless the antiferromagnetic structure of\nBFO is complicated [40] making the work of Chu et\nal.[41] more appealing.\nThe latter [41] have shown that micrometre-size ferro-magnetic CoFe dots deposited on a BFO \flm are con-\nsistently coupled, in a reversible manner, with the BFO\nantiferromagnetic spins. This implies that when an in-\nplane electric \feld is applied, CoFe dot magnetization\nrotates by 90\u000eand when voltage polarity is reversed the\noriginal CoFe magnetic state is retrieved.\n5. CONCLUSIONS AND OUTLOOK\nElectric control of magnonic and spintronic devices is\nsteadily progressing [10], o\u000bering lower energy consump-\ntion devices and paving the way to potentially solve the\nnagging interconnection delay problem.\nSimultaneously, femtosecond optical control is also\nprogressing in antiferromagnets that represent the largest\nclass of spin ordered materials in Nature with spin-wave\nexcitations occurring typically at frequencies as high as\na THz. Eventually, this will lead to extremely fast con-\ntrol [42] of magnetic devices to reach the THz regime\nunlocking the frequency stalling problem around a few\nGHz in present CMOS devices.\nKampfrath et al. [42] used optical femtosecond pulses\nto control spin-waves in antiferromagnetic NiO and more\nrecently Shuvaev et al. [43] demonstrated electrical con-\ntrol of a dynamic ME e\u000bect in DyMnO 3, a single-phase\nmultiferroic material. ME coupling with spin-waves leads\nto rotation of polarization plane of light propagating\nacross a sample and a static voltage allows to control\nlight amplitude and polarization plane rotation.\nThe THz barrier is the last one to overcome among\nfour making the pillars of Digital Technology that is con-\ntinuously thriving toward THz operation speed, Tera\rop\nprocessing, Terabyte storage and \fnally Terabit/sec com-\nmunication.\n[1] D K. Gramotnev and S. I Bozhevolnyi, \"Plasmonics\nbeyond the di\u000braction limit\", Nature Photonics, 4, 83(2010).\n[2] W. Eerenstein, N. D. Mathur and J.F. Scott, \"Multifer-8\nroic and magneto-electric materials\", Nature 442, 759\n(2006).\n[3] C-W Nan, M. I. Bichurin, S.X. Dong, D. Viehland and\nG. Srinivasan, J. Appl. Phys. Applied Physics Reviews,\n103, 031101 (2008).\n[4] C. Liu, F. Yun, and H. Morko\u0018 c: \"Ferromagnetism of ZnO\nand GaN: A Review\", J. Mater. Sci. : Mater. Electron.\n16, 555 (2005).\n[5]U.Ozg ur, Y. Alivov and H. Morko\u0018 c \"Microwave Ferrites,\nPart 1: Fundamentals and self biasing\", J. Mater. Sci :\nMater. Electron. 20, 789 (2009).\n[6]U.Ozg ur, Y. Alivov and H. Morko\u0018 c \"Microwave Ferrites,\nPart 2: : Passive components and electrical tuning\", J.\nMater. Sci. : Mater. Electron. 20, 911 (2009).\n[7] Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida,\nM. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K.\nTakanashi, S. Maekawa, E. Saitoh, Nature 464, 262\n(2010).\n[8] M.Z. Wu and A. Ho\u000bmann, Solid State Physics Volume\n64,Recent Advances in Magnetic Insulators - From Spin-\ntronics to Microwave Applications , Academic Press and\nElsevier, New-York (2013).\n[9] J. C. Slonczewski, J. Magn. Magn. Mat. 195, L261\n(1999).\n[10] M. Liu, N. X. Sun, \"Voltage control of magnetism in mul-\ntiferroic heterostructures\", Phil. Trans. R. Soc. A 372,\n20120439 (2014).\n[11] S. Cherepov, P. K. Amiri, J. G. Alzate, K. Wong, M.\nLewis, P. Upadhyaya, J. Nath, M. Bao, A. Bur, T. Wu,\nG. P. Carman, A. Khitun and K. L. Wang \"Electric-\feld-\ninduced spin wave generation using multiferroic magneto-\nelectric cells\" Appl. Phys. Lett. 104, 082403 (2014).\n[12] L. Y. Gorelik, R. I. Shekhter, V. M. Vinokur, D. E. Feld-\nman, V. I. Kozub and M. Jonson, Phys. Rev. Lett. 91,\n088301 (2003).\n[13] T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J.\nIhringer and M. Fiebig, \"Magnetic phase control by an\nelectric \feld\", Nature 430, 541 (2004).\n[14] W-G Wang, M. G. Li, S. Hageman and C. L. Chien,\n\"Electric-\feld-assisted switching in magnetic tunnel\njunctions\", Nature Mater. 11, 64 (2012).\n[15] V. Laukhin, V. Skumryev, X. Marti, D. Hrabovsky, F.\nSanchez, M.V. Garcia-Cuenca, C. Ferrater, M. Varela,\nU. L uders, J.F. Bobo and J. Fontcuberta, Phys. Rev.\nLett. 97, 227201 (2006).\n[16] T. H. E. Lahtinen, K. J. A. Franke and S. van Di-\njken, \"Electric-\feld control of magnetic domain wall mo-\ntion and local magnetization reversal\", Sci. Rep. 2258;\ndoi:10.1038/srep00258 (2012).\n[17] Y. S. Chai, S. Kwon, S. H. Chun, I. Kim, B-G Jeon, K.\nH. Kim and S. Lee, \"Electrical control of large magneti-\nzation reversal in a helimagnet\", Nat. Commun. 5:4208\ndoi: 10.1038/ncomms5208 (2014). See also S. E. Barnes,\nJ. Ieda and S. Maekawa, \"Rashba Spin-Orbit Anisotropy\nand the Electric Field Control of Magnetism\", Sci. Rep.\n4, 4105; doi:10.1038/srep04105 (2014) who did a theo-\nretical analysis for electrical anisotropy control in thin\nmagnetic \flms.\n[18] B. Lenk, H. Ulrichs, F. Garbs, M. M unzenberg, \"The\nbuilding blocks of magnonics\" Physics Reports 507 107\n(2011).\n[19] R.W. Damon, J.R. Eshbach, J. Phys. Chem. Solids 19\n308 (1961).[20] C. Herring and C. Kittel, Phys. Rev. 81, 869 (1951).\n[21] A. M. Clogston, H. Suhl, L. R. Walker and P.W. Ander-\nson , J. Phys. Chem. Solids 1, 129 (1956).\n[22] M. P. Kostylev, A. A. Serga, T. Schneider, B. Leven, and\nB. Hillebrands, Appl. Phys. Lett. 87, 153501 (2005).\n[23] V. E. Demidov, S. Urazhdin and S. O. Demokritov, Appl.\nPhys. Lett. 95, 262509 (2009).\n[24] P. Rovillain, R. de Sousa, Y. Gallais, A. Sacuto, M. A.\nM\u0013 easson, D. Colson, A. Forget, M. Bibes, A. Barth\u0013 el\u0013 emy\nand M. Cazayous, \"Electric-\feld control of spin waves\nat room temperature in multiferroic BiFeO 3\", Nature\nMater., 9, 975 (2010).\n[25] Z. Wang, Y. Sun, M; Wu, V. Tiberkevich and A. Slavin,\nPhys. Rev. Lett. 107, 146602 (2011).\n[26] J.M.D. Coey, \"Magnetism and Magnetic Materials\",\nCambridge University Press, New-York (2009).\n[27] D. Awschalom and N. Samarth, \"Spintronics without\nmagnetism\" APS Physics 2, 50 (2009).\n[28] T. Liu and G. Vignale, Phys. Rev. Lett. 106, 247203\n(2011).\n[29] X. Zhang, T. Liu, M. E. Flatt\u0013 e and H. X. Tang, Phys.\nRev. Lett. 113, 037202 (2014).\n[30] T. Dietl, D. D. Awschalom, M. Kaminska and H. Ohno,\n\"Spintronics\" in \"Semiconductors and Semimetals: A\ntreatise\", Volume 82, edited by E. R. Weber, Academic\nPress and Elsevier (2008).\n[31] B.Gohler, V. Hamelbeck, T.Z. Markus, M. Kettner, G.F.\nHanne, Z. Vager, R. Naa-man, H. Zacharias , Science 331\n894 (2011).\n[32] Y Tserkovnyak, A. Brataas and G. E. W. Bauer, Phys.\nRev. Lett. 88, 117601 (2002).\n[33] T. Zhao, A. Scholl, F. Zavaliche, K. Lee, M. Barry, A.\nDoran, M. P. Cruz, Y. H. Chu, C. Ederer, N. A. Spaldin,\nR. R. Das, D. M. Kim, S. H. Baek, C. B. Eom and R.\nRamesh \"Electrical control of antiferromagnetic domains\nin multiferroic BiFeO 3\flms at room temperature\", Na-\nture Mater., 5, 823 (2006).\n[34] M. Bibes and A. Barth\u0013 el\u0013 emy, \"Towards a magneto-\nelectric memory\", Nature Mater., 7, 425 (2008).\n[35] S. I. Kiselev, J. C. Sankey, I. N. Krivorotov, N. C. Em-\nley, R. J. Schoelkopf, R. A. Buhrman and D. C. Ralph,\nNature 425, 380 (2003)\n[36] S. Sahoo, T. Kontos, J. Furer, C. Ho\u000bmann, M. Gr aber,\nA. Cottet and C. Sch onenberger, \"Electric \feld control\nof spin transport\" Nature Physics 1, 99 (2005).\n[37] I. Appelbaum, B. Huang and D. J. Monsma, \"Electronic\nmeasurement and control of spin transport in silicon\",\nNature Mater., 447, 295 (2007).\n[38] S. Mark, P. Durrenfeld, K. Pappert, L. Ebel, K. Brunner,\nC. Gould and L. W. Molenkamp Phys. Rev. Lett. 106,\n057204 (2011).\n[39] W. X. Zhang, \"Voltage-driven spintronic logic\ngates in graphene nanoribbons\", Sci. Rep. 4, 6320,\ndoi:10.1038/srep06320 (2014).\n[40] D. Talbayev, S. A. Trugman, S. Lee, H T Yi, S.-W.\nCheong and A. J. Taylor, Phys. Rev. B 83 , 094403\n(2011).\n[41] Y.H. Chu, L.W. Martin, M.B. Holcomb, M. Gajek, S-\nJ Han , Q. He, N. Balke, C.H Yang, D. Lee, W. Hu,\nQ. Zhan, P-L Yang, A. Fraile-Rodriguez, R. Scholl, S.X.\nWang and R. Ramesh \"Electric-\feld control of local fer-\nromagnetism using a magneto-electric multiferroic\", Na-\nture Mater., 7, 478 (2008).\n[42] T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mahrlein,9\nT. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer and R.\nHuber, \"Coherent Terahertz control of antiferromagnetic\nspin waves\", Nature Photonics, 5, 31 (2011).\n[43] A. Shuvaev, V. Dziom, A. Pimenov, M. Schiebl, A. A.Mukhin, A. C. Komarek, T. Finger, M. Braden, and A.\nPimenov, Phys. Rev. Lett. 111, 227201 (2013)."    },    {        "title": "1611.08548v1.Magnetism_in_the_KBaRE_BO3_2__RE_Sm__Eu__Gd__Tb__Dy__Ho__Er__Tm__Yb__Lu__series__materials_with_a_triangular_rare_earth_lattice.pdf",        "content": "Magnetism in the KBaRE(BO3)2 (RE=Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) series: materials with a triangular rare earth lattice   M. B. Sanders, F. A. Cevallos, R. J. Cava Department of Chemistry, Princeton University, Princeton, New Jersey 08544 *Corresponding authors: marisas@princeton.edu (M.B. Sanders), rcava@princeton.edu (R.J. Cava) Abstract  We report the magnetic properties of compounds in the KBaRE(BO3)2 family (RE= Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb), materials with a planar triangular lattice composed of rare earth ions. The samples were analyzed by x-ray diffraction and crystallize in the space group R-3m. Physical property measurements indicate the compounds display predominantly antiferromagnetic interactions between spins without any signs of magnetic ordering above 1.8 K. The ideal 2D rare earth triangular layers in this structure type make it a potential model system for investigating magnetic frustration in rare-earth-based materials.            Introduction   Geometrically frustrated magnetic materials are a fertile area of study in condensed matter physics. Competing interactions can lead to highly degenerate low temperature states and unconventional quantum phenomena, providing models for investigating exotic quasi-particle excitations and statistical mechanics. Built from corner-sharing magnetic tetrahedra, the 3D pyrochlore is a prime example of geometric frustration. These materials can exhibit a variety of magnetic properties, such as spin ice (Dy2Ti2O7, Ho2Sn2O7, Ho2Ti2O7),1,2 spin liquid (Tb2Ti2O7),3 long range ordered (Gd2Ti2O7, GdSn2O7, Er2Ti2O7),4 and spin glass (Tb2Mo2O7) behavior.5  Two-dimensional frustrated lattices are also of significant interest. In two dimensions, the simplest geometrically frustrated structure consists of a triangular lattice with a single magnetic ion per unit cell. This is the original system for which a 2D quantum spin liquid state was proposed over forty years ago.6 Since then, extensive theoretical and experimental research has been dedicated to the search for novel 2D frustrated magnetic materials. Two new series of compounds containing ideal rare earth kagome planes have recently been reported, RE3Sb3Mg2O14 and RE3Sb3Zn2O14.7,8 These materials display interesting magnetic ground states, including scalar chiral spin 1/2 order, kagome spin ice, dipolar spin order, and the KT transition.9,10 Moreover, recent studies on YbMgGaO4, which contains two-dimensional triangular layers of Yb3+, suggest that the material is a potential spin liquid candidate.11 The subtle interplay of the rare earth ion dependent crystal field anisotropy and frustrated lattice in these 2D materials can produce a variety of interesting magnetic phenomena. Realizing more rare earth-based 2D frustrated systems may lead to even more exotic physical properties.   Here we present the elementary magnetic properties and lattice parameters of KBaRE(BO3)2 (RE=Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu), a series of materials with a 2D triangular lattice of rare earth ions. This structure type has previously been reported for RE= Tb, Y, Lu, Gd12,13,14,15 The materials reported here are isostructural and crystallize with the Buetschliite [K2Ca(CO3)2] mineral structure type in the space group R-3m. The distinct triangular layers constructed by RE3+ in KBaRE(BO3)2 make this structure type a model system for exploring magnetic frustration on an ideal triangular lattice.   Experimental Samples were synthesized by solid state reaction using the rare earth oxides, BaCO3, K2CO3, and H3BO3 as starting materials. The rare earth oxides (Sm2O3, Eu2O3, Gd2O3, Tb4O7, Dy2O3, Ho2O3, Er2O3, Tm2O3, Yb2O3, and Lu2O3) were dried at 800 °C overnight prior to use. The carbonates were dried at 120°C for several days. Stoichiometric mixtures (with 5% excess H3BO3 and 3% excess K2CO3 and BaCO3) were ground thoroughly in an agate mortar and pestle, placed in alumina crucibles, and pre-reacted in air at 500 °C for 15 hours. Following this, the samples were reground, reacted in air at 900 °C for 20 hours, and then furnace-cooled to room temperature. KBaTb(BO3)2 was heated under flowing argon at 900 °C  for an additional 10 hours. The X-ray powder diffraction data were collected at room temperature using a Bruker D8 Advance Eco diffractometer with Cu Kα radiation (λ=1.5418 Å) and a Lynxeye detector. Le Bail fits on KBaRE(BO3)2 were performed with the program Fullprof. The magnetic susceptibilities for the KBaRE(BO3)2 materials were measured between 1.8 and 300 K in a Quantum Design Physical Properties Measurement System (PPMS) Dynacool in an applied field of 5000 Oe. The magnetizations were linearly proportional to the magnetic field for all temperatures above 1.8 K to up to fields of approximately 15,000 Oe in all materials. The magnetic susceptibility was therefore defined as M/H at the field of H=5000 Oe. Results and Discussion Crystal Structure of KBaRE(BO3)2  The crystal structure of KBaRE(BO3)2 has been previously reported and is shown in Figures 1 and 2.16,13,12,15 The materials reported here are all isostructural and crystallize in the space group R-3m. Several Le Bail profile fits to powder diffraction data from our samples are shown in Figures 3 and 4, while the lattice parameters are provided in Table 1. In the structure of KBaRE(BO3)2 (Figure 1), layers of flat BO3 triangular units extend orthogonal to the crystallographic c axis. Interlinked between these layers are double sheets of Ba/K atoms and single sheets of rare earth atoms. The rare earth layers are fully structurally ordered. Each 3+ rare earth ion is octahedrally coordinated to oxygen, while the Ba2+ and K+ ions are mixed on the same site in a 9-coordinated Ba/K-O polyhedron. As emphasized in Figure 2, the rare earth ions make up discrete triangular layers in the structure. The lattice parameters of the title compounds agree well with those previously reported.13,14,12,15 As expected, the unit cell parameters decrease with decreasing ionic radius of the rare earth, as shown in Figure 5.17   Magnetic Properties The magnetic data for KBaRE(BO3)2 was fit to the Curie-Weiss law χ=!!!!!\" where χ is the magnetic susceptibility, C is the Curie Constant, and 𝜃!\" is the Weiss temperature. The effective moments were then obtained using the following relationship: 𝜇!\"\"∝2.83𝐶. The parameters for the fits are presented in Table 2, along with comparisons to the expected moments for each RE3+ ion.18 At high temperatures, crystal field effects may influence magnetic correlations and thereby impact susceptibility measurements; therefore, data was fit to the Curie-Weiss law at both low and high temperatures for comparison. Figures 6-14 feature Curie-Weiss fits of the samples reported here, along with field-dependent magnetization curves for the compounds at 2 K.  KBaSm(BO3)2  The high temperature susceptibility of KBaSm(BO3)2 in Figure 6 reveals a large temperature independent Van Vleck paramagnetism contribution. This is characteristic of many Sm-containing compounds and arises from the first excited J=7/2 multiplet of Sm3+.19 Therefore, the Curie-Weiss law was fit at the low temperature regime between 1.8 and 10 K, yielding a moment of 0.44 µB/Sm and a Weiss temperature of -1.35 K. The negative Weiss temperature indicates the presence of antiferromagnetic nearest neighbor spin–spin interactions. While the µeff is somewhat smaller than the expected free ion value of 0.83 µB/Sm, it is similar to that of other reported Sm3+-containing oxides, such as Sm3Sb3Mg2O14 (0.53 µB/Sm) and Sm2Zr2O7 (0.50 µB/Sm).8,20 An effective moment as low as 0.15 µB has been reported for Sm2Ti2O7.20 The low moments observed for these compounds are likely related to samarium’s large crystal field splitting of its lowest J=5/2 multiplet. The field-dependent magnetization M(H) at 2 K in the left panel of Figure 6 shows slight curvature but no indication of saturation up to an applied field of µ0H= 9 T.  KBaEu(BO3)2  For Eu3+-containing compounds, typically µeff = 0. This arises because µeff = gJ[J(J + 1)], where for Eu3+, L = 3 and S = 3 and so J = 0. It is expected, therefore, that the ground state for Eu3+ may be non-magnetic, 7F0. At low temperatures (up to roughly ~100 K), KBaEu(BO3)2’s susceptibility displays Van Vleck paramagnetism (Figure 7). This is characteristic of Eu3+ compounds, and is a result of sole population of the non-magnetic ground state. As the temperature rises, crystal field states originating from the first excited multiplet,7F1, are populated. This ultimately leads to a temperature-dependent contribution to KBaEu(BO3)2’s magnetic susceptibility. Although this effect may appear Curie-Weiss-like, a fit of the data does not accurately reflect the exchange interactions, and so we do not apply the Curie-Weiss law to KBaEu(BO3)2. The field-dependent magnetization for KBaEu(BO3)2 at 2 K is shown in the right panel of Figure 7. The M(H) plot is linear and reversible with the field increasing and decreasing.   KBaGd(BO3)2  The temperature dependent magnetic susceptibility of KBaGd(BO3)2 is shown in Figure 8. As can be seen by both the susceptibility plot and the tabulated data in Table 2, this material maintains strict Curie-Weiss law behavior to the lowest temperatures studied, with Weiss temperatures relatively small, on the order of 1 K. Indeed, fitting the high temperature data (150-300 K) yields a magnetic moment of 7.70 µB/Gd and a Weiss temperature of 1.64 K. A low temperature fit (1.8-25 K) provides the same effective moment, but a negative Weiss temperature of -0.78 K. The moment calculated here is close to the expected value of 7.94 µB/Gd for the free ion 8 S7/2 ground state of Gd3+. Similar moments with Weiss temperatures of a comparable magnitude were observed for the rare earth double perovskites Ba2GdSbO6 (µeff=7.72; Θw=-1.22 K) and Sr2GdSbO6 (µeff=7.64; Θw=-0.14 K).21 The M(H) plot at 2 K in the right panel of Figure 8 reveals a nonlinear relationship between the magnetization and applied field and saturation at roughly 7.00 µB/Gd, slightly less than the moment calculated through the Curie-Weiss law and representative of all the Gd spins aligning in the powder sample in the direction of the applied field by roughly µ0H= 5 T.  KBaTb(BO3)2  The 𝜒(𝑇) plot of KBaTb(BO3)2 is shown in Figure 9. A high temperature fit of the data (150-300 K) gives an effective moment of 9.65 µB/Tb and a Weiss temperature of -15.06 K. A similar µeff of 9.69 and Θw of -11.09 were extrapolated from the low temperature regime. The moments calculated here are close to the expected free ion value of 9.72 µB/Tb. The antiferromagnetic Curie-Weiss temperature obtained from the high temperature fit is close to that observed for the pyrochlore Tb2Ti2O7 (Θw= ~17 K).22 The 2 K field dependent magnetization plot of KBaTb(BO3)2 displayed in the right panel of Figure 9 reveals a nonlinear response with some curvature but no signs of saturation up to an applied field of µ0H= 9 T.  KBaDy(BO3)2  Shown in Figure 10 is the magnetic susceptibility and inverse susceptibility of KBaDy(BO3)2. A high temperature (150-300 K) Curie-Weiss fit of the data yields a moment of 10.63 µB/Dy and a Weiss temperature of -16.12 K, in agreement with the free ion moment of 10.63 µB expected for Dy3+. The susceptibilities deviate toward smaller values at the lowest temperatures measured, suggesting increasing antiferromagnetic correlations and perhaps emergent long-range order.21 Indeed, fitting at low temperatures provide µeff= 10.07 µB/Dy and Θw=-5.42. This low temperature moment is close to the value of µeff= 10.00 µB, for a ground state mJ = ±15/2 doublet, with gJ = 4/3 and corresponds well with that of Dy2Ti2O7.23 The negative Weiss temperatures indicate antiferromagnetic interactions between spins. The field dependent magnetization at 2 K (Figure 10, right panel) reveals nonlinear variation of the magnetization as a function of applied field and the onset of saturation at roughly 5 µB/Dy, about half the expected maximum of the effective moment. Saturation at about half the value of the effective moment is typically due to powder averaging of Ising spins.   KBaHo(BO3)2  Displayed in Figure 11 is the 𝜒(𝑇) plot of KBaHo(BO3)2. The susceptibility behavior of the Dy analog is similar to that of KBaHo(BO3)2. A high temperature (150-300 K) fit of the inverse susceptibility results in a magnetic moment of 10.50 µB/Ho and a Weiss temperature of -15.05 K. Applying the Curie-Weiss law to the low temperature regime yields the following parameters:  µeff= 10.09µB/Ho and Θw=-3.10 K. The effective moments correspond well with the expected free ion value of 10.60 µB/Ho and the value expected for an mJ = ±8 doublet ground state, µeff = 10.00 µB.23 The field dependent magnetization M(H) plot at 2 K in the right panel of Figure 11 shows curvature with the onset of saturation at about 5.5 µB/Ho.   KBaEr(BO3)2  The magnetic susceptibility of KBaEr(BO3)2 is plotted in Figure 12. Fitting the data from 150 to 300 K presents an effective moment of 9.57 µB/Er and a Weiss temperature of -12.67 K, consistent with the free ion moment of µeff= 9.59 µB for Er3+ (4I15/2). A low temperature fit of the data yields µeff=8.86 µB and Θw=-3.09 K, in agreement with that of µeff = 9.0 µB for an mJ = ±15/2 doublet with gJ = 1.2.23 The field dependent magnetization at 2 K in the right panel of Figure 12 shows a nonlinear response, approaching saturation at roughly 5.5 µB/Er, a bit more than half the free ion value.   KBaTm(BO3)2  Exhibited in Figure 13 is the magnetic susceptibility for KBaTm(BO3)2. Data were fit to the Curie-Weiss law in the temperature range 200-300 K, yielding an effective moment of 7.58 µB and Θw of -29.37 K. Fitting the data to a lower temperature range (65-85 K) provides µeff= 7.80 µB and Θw= -34.61. The moments correspond well with that expected for Tm3+ (7.57 µB) and the negative Weiss temperatures are suggestive of antiferromagnetic interactions between spins.   Due to crystal-field level splitting, Tm3+ (4f12) often takes on a singlet ground state. In a low symmetry site like that of Tm3+ in KBaTm(BO3)2, -3m, the 3H6 free ion state splits into a collection of single-ion crystal-field ground states where the strength and symmetry of the crystal field influence the energy separations.24 As a result, the susceptibility features both a zero first order Zeeman contribution at low temperatures and a Van Vleck contribution due to the excited states. The anomaly in the 𝜒𝑇 plot for KBaTm(BO3)2 at around 15 K may therefore be interpreted as a Van Vleck component to the magnetic susceptibility. This anomaly was observed in all preparations of the Tm variant.   The M(H) plot at 2 K in Figure 13 of KBaTm(BO3)2 reveals slight curvature without any  signs of saturation up to an applied field of µ0H= 9 T.  KBaYb(BO3)2  Plotted in Figure 14 is the magnetic susceptibility of KBaYb(BO3)2. A high temperature fit of the data from 125-275 K gives an effective moment of 4.76 µB/Yb and a Weiss temperature of -110.60 K. Fitting the data to the Curie-Weiss law in the lower 1.8-25 K temperature regime yields µeff= 2.67 µB and Θw= -0.84 K. Similar temperature dependent behavior has been observed for Yb2Ti2O7.23,25  This trend is consistent with the free ion moment µeff= 4.54 µB of Yb+3 at room temperature and the movement of the ions into a Kramers doublet ground state at low temperature, with reduced moment. This behavior at low temperature is indicative of planar spin anisotropy. The field-dependent magnetization at 2 K in Figure 14 sheds more light on this anisotropy and reveals a nonlinear magnetization response with the appearance of saturation at about 1.5 µB/Yb.  Conclusion  We have synthesized and characterized several compounds in the KBaRE(BO3)2 family (RE= Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu). Le Bail profile fits were performed on the powder X-ray diffraction data from the compounds, from which the lattice parameters were extracted. They agree well with parameters previously reported in this structure type and show good evidence for the lanthanide contraction. Elementary magnetic property measurements show no signs of magnetic ordering above 1.8 K. Further low temperature characterization of these triangular rare earth materials, especially in single crystal form, is of significant interest; because many of these materials have been grown as single crystals12-15, such studies are expected to be reasonably performed.  Acknowledgments This research was performed under the auspices of the Institute for Quantum Matter, fully supported by the US DOE BES grant DE-FG02-08ER46544.       Works Cited  1 G. Ehlers, A. Huq, S. O. Diallo, C. Adriano, K. C. Rule, A. L. Cornelius, P. Fouquet, P. G. Pagliuso and J. S. Gardner, J. Phys. Condens. Matter Inst. Phys. J., 2012, 24, 076005. 2 J. E. Greedan, J. Alloys Compd., 2006, 408–412, 444–455. 3 A. Yaouanc, P. Dalmas de Réotier, Y. Chapuis, C. Marin, S. Vanishri, D. Aoki, B. Fåk, L.-P. Regnault, C. Buisson, A. Amato, C. Baines and A. D. Hillier, Phys. Rev. B, 2011, 84, 184403. 4 N. P. Raju, M. Dion, M. J. P. Gingras, T. E. Mason and J. E. Greedan, Phys. Rev. B, 1999, 59, 14489–14498. 5 J. S. Gardner, M. J. P. Gingras and J. E. Greedan, Rev. Mod. Phys., 2010, 82, 53–107. 6 P. W. Anderson, Mater. Res. Bull., 1973, 8, 153–160. 7 M. B. Sanders, J. W. Krizan and R. J. Cava, J. Mater. Chem. C, 2016, 4, 541–550. 8 M. B. Sanders, K. M. Baroudi, J. W. Krizan, O. A. Mukadam and R. J. Cava, Phys. Status Solidi B, 2016, 253, 2056–2065. 9 A. Scheie, M. Sanders, J. Krizan, Y. Qiu, R. J. Cava and C. Broholm, Phys. Rev. B, 2016, 93, 180407. 10 Z. L. Dun, J. Trinh, K. Li, M. Lee, K. W. Chen, R. Baumbach, Y. F. Hu, Y. X. Wang, E. S. Choi, B. S. Shastry, A. P. Ramirez and H. D. Zhou, Phys. Rev. Lett., 2016, 116, 157201. 11 Y. Li, G. Chen, W. Tong, L. Pi, J. Liu, Z. Yang, X. Wang and Q. Zhang, Phys. Rev. Lett., 2015, 115, 167203. 12 S. J. Camardello, J. H. Her, P. J. Toscano and A. M. Srivastava, Opt. Mater., 2015, 49, 297–303. 13 J. Gao, L. Song, X. Hu and D. Zhang, Solid State Sci., 2011, 13, 115–119. 14 Z. Lian, J. Sun, Z. Ma, L. Zhang, D. Shen, G. Shen, X. Wang and Q. Yan, J. Cryst. Growth, 2014, 401, 334–337. 15 N. Kononova, A. Kokh, V. Shevchenko, A. Bolatov, B. Uralbekov and M. Burkitbayev, in 10th International Conference of Polish Society for Crystal Growth, Zakopane, Poland, 2016. 16 S. J. Camardello, J. H. Her, P. J. Toscano and A. M. Srivastava, Opt. Mater., 2015, 49, 297–303. 17 R. D. Shannon, Acta Crystallogr. Sect. A, 1976, 32, 751–767. 18 S. Blundell, Magnetism in Condensed Matter, OUP Oxford, 2001. 19 S. K. Malik and R. Vijayaraghavan, Pramana, 1974, 3, 122–132. 20 S. Singh, S. Saha, S. K. Dhar, R. Suryanarayanan, A. K. Sood and A. Revcolevschi, Phys. Rev. B, 2008, 77, 054408. 21 H. Karunadasa, Q. Huang, B. G. Ueland, P. Schiffer and R. J. Cava, Proc. Natl. Acad. Sci., 2003, 100, 8097–8102. 22 G. Luo, S. T. Hess and L. R. Corruccini, Phys. Lett. A, 2001, 291, 306–310. 23 S. T. Bramwell, M. N. Field, M. J. Harris and I. P. Parkin, J. Phys. Condens. Matter, 2000, 12, 483. 24 M. P. Zinkin, M. J. Harris, Z. Tun, R. A. Cowley and B. M. Wanklyn, J. Phys. Condens. Matter, 1996, 8, 193. 25 K. A. Ross, T. Proffen, H. A. Dabkowska, J. A. Quilliam, L. R. Yaraskavitch, J. B. Kycia and B. D. Gaulin, Phys. Rev. B, 2012, 86, 174424.     Tables   Table 1. Lattice Parameters of KBaRE(BO3)2 determined from fits to room temperature powder X-ray diffraction data  RE RE Ionic Radius (Å) a (Å) c (Å) Sm 0.958 5.49112(4) 18.1138(7) Eu 0.947 5.48299(9) 18.0410(4) Gd 0.938 5.47536(4) 17.9790(3) Tb 0.923 5.46342(6) 17.8893(3) Dy 0.912 5.45536(2) 17.8340(8) Ho 0.901 5.44827(3) 17.7647(2) Er 0.890 5.43635(6) 17.7018(4) Tm 0.880 5.42881(2) 17.6358(8) Yb 0.868 5.41952(5) 17.6029(4) Lu 0.861 5.41331(5) 17.5726(3)           Table 2. Effective moments (p), Weiss temperatures (θw), and goodness of fit (R2) determined by least-squares fitting of the Curie-Weiss law to the magnetic susceptibility data in figures 6-14   RE High T Fit p  (High T) Θw (High T) R2 of fit Low T Fit p  (Low T) Θw (Low T) R2 of fit p exp Sm - - - - 1.8-10 K 0.43(9) -1.35(3) 0.99175 0.85 Eu - - - - - - - - 0.0 Gd 150-300 7.70(1) 1.64(7) 0.99994 1.8-25 K 7.70(1) -0.78(4) 0.99994 7.94 Tb 150-300 9.65(1) -15.06(2) 0.99977 10-25 K 9.68(9) -11.09(7) 0.99887 9.72 Dy 150-300  10.62(5) -16.11(5) 0.99971 15-30 K 10.07(4) -5.41(7) 0.99881 10.63 Ho 150-300 10.50(1) -15.05(7) 0.99981 10-25 K 10.09(1) -3.09(9) 0.99983 10.60 Er 150-300 9.57(2) -12.66(7) 0.99975 8-23 K 8.86(5) -3.09(3) 0.99963 9.59 Tm 200-300 7.58(3) -29.37(1) 0.99915 65-85 K 7.80(5) -34.61(2) 0.99939 7.57 Yb 125-275 4.76(4) -110.59(9) 0.99999 1.8-25 K 2.67(5) -0.83(7) 0.99817 4.53 Lu - - - - - - - -  0.0   Figure Captions  Figure 1. The crystal structure of KBaRE(BO3)2, showing the coordination polyhedra of the rare earth ions and boron. The magenta polyhedra represent REO6, while the triangular BO3 units are indicated in orange. Oxygens are excluded for clarity, but are found at the vertices of the coordination polyhedra.  Figure 2. Schematic of KBaRE(BO3)2 structure displaying the positions of the metal ions in the unit cell. To the right of the schematic is an extended lattice showing the discrete RE3+ triangular planes in the structure.   Figure 3. Le Bail profile fits for KBaEu(BO3)2 (left) and KBaDy(BO3)2 (right). The experimental pattern is in red, the calculated pattern in black, and the difference plot in blue. The green marks indicate Bragg reflections.  Figure 4. Le Bail profile fits for KBaHo(BO3)2 (left) and KBaTm(BO3)2 (right). The experimental pattern is in red, the calculated pattern in black, and the difference plot in blue. The green marks indicate Bragg reflections.  Figure 5. The a and c lattice parameters for KBaRE(BO3)2 as a function of rare earth ionic radius. The pink and black points represent the a and c parameters, respectively. The standard deviations are smaller than the plotted points and so error bars are excluded from the figure.   Figure 6. Left Panel: Magnetic susceptibility and inverse susceptibility of KBaSm(BO3)2 measured in an applied field of 5000 Oe. The Curie-Weiss fit is shown in black. The inset is a magnified view of the low temperature inverse susceptibility. The right panel displays the field-dependent magnetization at 2 K.   Figure 7. In the left panel is the temperature-dependent magnetic susceptibility of KBaEu(BO3)2 in an applied field of 5000 Oe. The inset displays the low temperature inverse susceptibility. The right panel exhibits the M(H) of the compound at 2 K.   Figure 8. The DC magnetic susceptibility and reciprocal susceptibility of KBaGd(BO3)2  measured in an applied field of 5000 Oe (left panel). The Curie–Weiss fits are shown in yellow. The plot in the right panel shows the field-dependent magnetization at 2 K. The inset reveals a magnified view of the compound’s low temperature inverse susceptibility.   Figure 9. Temperature-dependent magnetic susceptibility of KBaTb(BO3)2 measured in an applied field of 5000 Oe (left panel). The Curie–Weiss fits are shown in black. The right panel displays the field-dependent magnetization at 2 K. The inset shows the low temperature inverse susceptibility.   Figure 10. The DC magnetic susceptibility and inverse susceptibility of KBaDy(BO3)2 measured in an applied field of 5000 Oe. The Curie–Weiss fits are shown in yellow. The plot to the right of the M(T) displays the magnetization as a function of applied field M(H) at 2 K. The inset reveals the low temperature reciprocal susceptibility.  Figure 11. Right panel: the magnetic susceptibility and inverse susceptibility of KBaHo(BO3)2 in an applied field of 5000 Oe. The Curie-Weiss fits are shown in black. Left panel: the field-dependent magnetization at 2 K. The inset shows a magnified view of the low temperature reciprocal susceptibility.   Figure 12. Temperature-dependent magnetic susceptibility of KBaEr(BO3)2 in an applied field of 5000 Oe (left panel). The Curie–Weiss fits are shown in black. To the right of the susceptibility is the field-dependent magnetization at 2 K. The inset displays the low temperature inverse susceptibility.   Figure 13. The DC magnetic susceptibility and inverse susceptibility of KBaTm(BO3)2 in an applied field of 5000 Oe (left panel). The Curie–Weiss fits are shown in green. Right panel: the field-dependent magnetization at 2 K. The inset reveals a magnified view of the low temperature reciprocal susceptibility.  Figure 14. Right panel: the magnetic susceptibility and reciprocal susceptibility of KBaYb(BO3)2 in an applied field of 5000 Oe. The Curie-Weiss fits are shown in black. Displayed in the left panel is the field-dependent magnetization at 2 K. The inset reveals the low temperature inverse susceptibility.          Figure 1 \n                     \nFigure 2 \n                      \nFigure 3  \n  Figure 4 \n              \nFigure 5 \n                             \nFigure 6 \n  Figure 7 \n                \nFigure 8 \n  Figure 9 \n               \nFigure 10 \n  Figure 11 \n                \nFigure 12 \n  Figure 13 \n               \nFigure 14 \n \n"    }]