publicationDate,title,abstract,id 2019-11-27,How spin-orbital entanglement depends on the spin-orbit coupling in a Mott insulator,"The concept of the entanglement between spin and orbital degrees of freedom plays a crucial role in understanding various phases and exotic ground states in a broad class of materials, including orbitally ordered materials and spin liquids. We investigate how the spin-orbital entanglement in a Mott insulator depends on the value of the spin-orbit coupling of the relativistic origin. To this end, we numerically diagonalize a 1D spin-orbital model with the 'Kugel-Khomskii' exchange interactions between spins and orbitals on different sites supplemented by the on-site spin-orbit coupling. In the regime of small spin-orbit coupling w.r.t. the spin-orbital exchange, the ground state to a large extent resembles the one obtained in the limit of vanishing spin-orbit coupling. On the other hand, for large spin-orbit coupling the ground state can, depending on the model parameters, either still show negligible spin-orbital entanglement, or can evolve to a highly spin-orbitally entangled phase with completely distinct properties that are described by an effective XXZ model. The presented results suggest that: (i) the spin-orbital entanglement may be induced by large on-site spin-orbit coupling, as found in the 5d transition metal oxides, such as the iridates; (ii) for Mott insulators with weak spin-orbit coupling of Ising-type, such as e.g. the alkali hyperoxides, the effects of the spin-orbit coupling on the ground state can, in the first order of perturbation theory, be neglected.",1911.12180v2 2016-09-11,Spin-Orbit Coupling Induced Spin Squeezing in Three-Component Bose Gases,"We observe spin squeezing in three-component Bose gases where all three hyperfine states are coupled by synthetic spin-orbit coupling. This phenomenon is a direct consequence of spin-orbit coupling, as can be seen clearly from an effective spin Hamiltonian. By solving this effective model analytically with the aid of a Holstein-Primakoff transformation for spin-1 system in the low excitation limit, we conclude that the spin-nematic squeezing, a novel category of spin squeezing existing exclusively in large spin systems, is enhanced with increasing spin-orbit intensity and effective Zeeman field, which correspond to Rabi frequency and two-photon detuning within the Raman scheme for synthetic spin-orbit coupling, respectively. These trends of dependence are in clear contrast to spin-orbit coupling induced spin squeezing in spin-1/2 systems. We also analyze the effects of harmonic trap and interaction with realistic experimental parameters numerically, and find that a strong harmonic trap favors spin-nematic squeezing. We further show spin-nematic squeezing can be interpreted as two-mode entanglement or two-spin squeezing at low excitation. Our findings can be observed in ^{87}Rb gases with existing techniques of synthetic spin-orbit coupling and spin-selectively imaging.",1609.03141v1 2020-09-24,Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling,"Several realistic spin-orbital models for transition metal oxides go beyond the classical expectations and could be understood only by employing the quantum entanglement. Experiments on these materials confirm that spin-orbital entanglement has measurable consequences. Here, we capture the essential features of spin-orbital entanglement in complex quantum matter utilizing 1D spin-orbital model which accommodates SU(2)xSU(2) symmetric Kugel-Khomskii superexchange as well as the Ising on-site spin-orbit coupling. Building on the results obtained for full and effective models in the regime of strong spin-orbit coupling, we address the question whether the entanglement found on superexchange bonds always increases when the Ising spin-orbit coupling is added. We show that (i) quantum entanglement is amplified by strong spin-orbit coupling and, surprisingly, (ii) almost classical disentangled states are possible. We complete the latter case by analyzing how the entanglement existing for intermediate values of spin-orbit coupling can disappear for higher values of this coupling.",2009.11773v1 2011-08-31,Curvature-induced spin-orbit coupling and spin relaxation in a chemically clean single-layer graphene,"The study of spin-related phenomena in materials requires knowledge on the precise form of effective spin-orbit coupling of conducting carriers in the solid-states systems. We demonstrate theoretically that curvature induced by corrugations or periodic ripples in single-layer graphenes generates two types of effective spin-orbit coupling. In addition to the spin-orbit coupling reported previously that couples with sublattice pseudospin and corresponds to the Rashba-type spin-orbit coupling in a corrugated single-layer graphene, there is an additional spin-orbit coupling that does not couple with the pseudospin, which can not be obtained from the extension of the curvature-induced spin-orbit coupling of carbon nanotubes. Via numerical calculation we show that both types of the curvature-induced spin-orbit coupling make the same order of contribution to spin relaxation in chemically clean single-layer graphene with nanoscale corrugation. The spin relaxation dependence on the corrugation roughness is also studied.",1108.6128v3 2007-01-31,Coupled spin-charge drift-diffusion approach for a two-dimensional electron gas with Rashba spin-orbit coupling,"Based on kinetic equations for the density matrix, drift-diffusion equations are derived for a two-dimensional electron gas with Rashba spin-orbit coupling. Universal results are obtained for the weak coupling case. Most interesting is the observation that with increasing spin-orbit coupling strengths there is a sharp transition between spin diffusion and ballistic spin transport. For strong spin-orbit coupling, when the elastic scattering time is much larger than the spin relaxation time, undamped spin-coherent waves are identified. The existence of these long-lived spin-coherent states is confirmed by exact analytical results obtained from microscopic kinetic equations valid in the ballistic regime.",0701782v1 2015-05-28,Intrinsic spin Hall effect in systems with striped spin-orbit coupling,"The Rashba spin-orbit coupling arising from structure inversion asymmetry couples spin and momentum degrees of freedom providing a suitable (and very intensively investigated) environment for spintronic effects and devices. Here we show that in the presence of strong disorder, non-homogeneity in the spin-orbit coupling gives rise to a finite spin Hall conductivity in contrast with the corresponding case of a homogeneous linear spin-orbit coupling. In particular, we examine the inhomogeneity arising from a striped structure for a two-dimensional electron gas, affecting both density and Rashba spin-orbit coupling. We suggest that this situation can be realized at oxide interfaces with periodic top gating.",1505.07667v1 2018-05-25,Generation of Spin Current from Lattice Distortion Dynamics: Spin-Orbit Routes,"Generation of spin current from lattice distortion dynamics in metals is studied with special attention on the effect of spin-orbit coupling. Treating the lattice distortion by local coordinate transformation, we calculate spin current and spin accumulation with the linear response theory. It is found that there are two routes to the spin-current generation, one via the spin Hall effect and the other via the spin accumulation. The present effect due to spin-orbit coupling can be comparable to, or even larger than, the one based on the spin-vorticity coupling in systems with strong spin-orbit coupling.",1805.10328v2 2009-10-16,Current-induced spin polarization for a general two-dimensional electron system,"In this paper, current-induced spin polarization for two-dimensional electron gas with a general spin-orbit interaction is investigated. For isotropic energy spectrum, the in-plane current-induced spin polarization is found to be dependent on the electron density for non-linear spin-orbit interaction and increases with the increment of sheet density, in contrast to the case for $\bm k$-linear spin-orbit coupling model. The numerical evaluation is performed for InAs/InSb heterojunction with spin-orbit coupling of both linear and cubic spin-orbit coupling types. For $\delta$-type short-range electron-impurity scattering, it is found that the current-induced spin polarization increases with increasing the density when cubic spin-orbit couplings are considered. However, for remote disorders, a rapid enhancement of current-induced spin polarization is always observed at high electron density, even in the case without cubic spin-orbit coupling. This result demonstrates the collision-related feature of current-induced spin polarization. The effects of different high order spin-orbit couplings on spin polarization can be comparable.",0910.3050v1 2018-10-08,Zeeman spin-orbit coupling in antiferromagnetic conductors,"This article is a brief review of Zeeman spin-orbit coupling, arising in a low-carrier commensurate N\'eel antiferromagnet subject to magnetic field. The field tends to lift the degeneracy of the electron spectrum. However, a hidden symmetry protects double degeneracy of Bloch eigenstates at special momenta in the Brillouin zone. The effective transverse $g$-factor vanishes at such points, thus acquiring a substantial momentum dependence, which turns a textbook Zeeman term into a spin-orbit coupling. After describing the symmetry underpinnings of the Zeeman spin-orbit coupling, I compare it with its intrinsic counterparts such as Rashba coupling, and then show how Zeeman spin-orbit coupling may survive in the presence of intrinsic spin-orbit coupling. Finally, I outline some of the likely experimental manifestations of Zeeman spin-orbit coupling, and compare it with similar phenomena in other settings such as semiconducting quantum wells.",1810.03720v1 2021-01-27,Spin-memory loss induced by bulk spin-orbit coupling at ferromagnet/heavy-metal interfaces,"A spin current through a ferromagnet/heavy-metal interface may shrink due to the spin-flip at the interface, resulting in the spin-memory loss. Here we propose a mechanism of the spin-memory loss. In contrast to other mechanisms based on interfacial spin-orbit coupling, our mechanism is based on the bulk spin-orbit coupling in a heavy-metal. We demonstrate that the bulk spin-orbit coupling induces the entanglement between the spin and orbital degrees of freedom and this spin-orbital entanglement can give rise to sizable spin-flip at the interface even when the interfacial spin-orbit coupling is weak. Our mechanism emphasizes crucial roles of the atomic orbital degree of freedom and induces the strong spin-memory loss near band crossing points between bands of different orbital characters.",2101.11438v1 2023-10-07,"Orbital diffusion, polarization and swapping in centrosymmetric metals","We propose a general theory of charge, spin and orbital diffusion based on Keldysh formalism. Our findings indicate that the diffusivity of orbital angular momentum in metals is much lower than that of spin or charge due to the strong orbital intermixing in crystals. Furthermore, our theory introduces the concept of spin-orbit polarization by which a pure orbital (spin) current induces a longitudinal spin (orbital) current, a process as efficient as spin polarization in ferromagnets. Finally, we find that orbital currents undergo momentum swapping, even in the absence of spin-orbit coupling. This theory establishes several key parameters for orbital transport of direct importance to experiments.",2310.04763v1 2018-04-28,Spin-1 Bosons in the Presence of Spin-orbit Coupling,"In this paper, I'm going to talk about the theoretical and experimental progress in studying spin-orbit coupled spin-1 bosons. Realization of spin-orbit coupled quantum gases opens a new avenue in cold atom physics. In particular, the interplay between spin-orbit coupling and inter-atomic interaction leads to many intriguing phenomena. Moreover, the non-zero momentum of ground states can be controlled by external fields, which allows for good quantum control.",1805.00001v1 2021-03-10,Magnetic phases for two $t_{2g}$ holes with spin-orbit coupling and crystal field,"We investigate two holes in the the $t_{2g}$ levels of a square-lattice Mott insulator with strong spin-orbit coupling. Exact diagonalization of a spin-orbital model valid at strong onsite interactions, but arbitrary spin-orbit coupling and crystal field is complemented by an effective triplon model (valid for strong spin-orbit coupling) and by a semiclassical variant of the model. We provide the magnetic phase diagram depending on crystal field and spin-orbit coupling, which largely agrees for the semiclassical and quantum models, as well as excitation spectra characterizing the various phases.",2103.06033v1 2007-10-28,Some symmetry properties of spin currents and spin polarizations in multi-terminal mesoscopic spin-orbit coupled systems,"We study theoretically some symmetry properties of spin currents and spin polarizations in multi-terminal mesoscopic spin-orbit coupled systems. Based on a scattering wave function approach, we show rigorously that in the equilibrium state no finite spin polarizations can exist in a multi-terminal mesoscopic spin-orbit coupled system (both in the leads and in the spin-orbit coupled region) and also no finite equilibrium terminal spin currents can exist. By use of a typical two-terminal mesoscopic spin-orbit coupled system as the example, we show explicitly that the nonequilibrium terminal spin currents in a multi-terminal mesoscopic spin-orbit coupled system are non-conservative in general. This non-conservation of terminal spin currents is not caused by the use of an improper definition of spin current but is intrinsic to spin-dependent transports in mesoscopic spin-orbit coupled systems. We also show that the nonequilibrium lateral edge spin accumulation induced by a longitudinal charge current in a thin strip of \textit{finite} length of a two-dimensional electronic system with intrinsic spin-orbit coupling may be non-antisymmetric in general, which implies that some cautions may need to be taken when attributing the occurrence of nonequilibrium lateral edge spin accumulation induced by a longitudinal charge current in such a system to an intrinsic spin Hall effect.",0710.5316v1 2023-11-18,Thermal Spin Orbit Torque with Dresselhaus Spin Orbit Coupling,"Based on the spinor Boltzmann equation, we obtain a temperature dependent thermal spin-orbit torque in terms of the local equilibrium distribution function in a two dimensional ferromagnet with Dresselhaus spin-orbit coupling. We also derive the continuity equation of spin accumulation and spin current, the spin diffusion equation in Dresselhaus ferromagnet, which contains the thermal spin orbit torque under local equilibrium assumption. This temperature dependent thermal spin-orbit torque originates from the temperature gradient applied to the system. it is also sensitive to temperature due to the local equilibrium distribution function therein. In the spin diffusion equation, we can single out the usual spin-orbit torque as well as the spin transfer torque, which is conceded to our previous results. Finally, we illustrate them by an example of spin-polarized transport through a ferromagnet with Dresselhaus spin-orbit coupling driven by temperature gradient, those torques including thermal spin-orbit torque are demonstrated numerically.",2311.14719v1 2017-12-15,Large spin relaxation anisotropy and valley-Zeeman spin-orbit coupling in WSe2/Gr/hBN heterostructures,"Large spin-orbital proximity effects have been predicted in graphene interfaced with a transition metal dichalcogenide layer. Whereas clear evidence for an enhanced spin-orbit coupling has been found at large carrier densities, the type of spin-orbit coupling and its relaxation mechanism remained unknown. We show for the first time an increased spin-orbit coupling close to the charge neutrality point in graphene, where topological states are expected to appear. Single layer graphene encapsulated between the transition metal dichalcogenide WSe$_2$ and hBN is found to exhibit exceptional quality with mobilities as high as 100000 cm^2/V/s. At the same time clear weak anti-localization indicates strong spin-orbit coupling and a large spin relaxation anisotropy due to the presence of a dominating symmetric spin-orbit coupling is found. Doping dependent measurements show that the spin relaxation of the in-plane spins is largely dominated by a valley-Zeeman spin-orbit coupling and that the intrinsic spin-orbit coupling plays a minor role in spin relaxation. The strong spin-valley coupling opens new possibilities in exploring spin and valley degree of freedom in graphene with the realization of new concepts in spin manipulation.",1712.05678v2 2007-01-05,Deformation of SU(4) singlet spin-orbital state due to Hund's rule coupling,"We investigate the ground-state property and the excitation gap of a one-dimensional spin-orbital model with isotropic spin and anisotropic orbital exchange interactions, which represents the strong-coupling limit of a two-orbital Hubbard model including the Hund's rule coupling ($J$) at quarter filling, by using a density-matrix renormalization group method. At J=0, spin and orbital correlations coincide with each other with a peak at $q=\pi/2$, corresponding to the SU(4) singlet state. On the other hand, spin and orbital states change in a different way due to the Hund's rule coupling. With increasing $J$, the peak position of orbital correlation changes to $q=\pi$, while that of spin correlation remains at $q=\pi/2$. In addition, orbital dimer correlation becomes robust in comparison with spin dimer correlation, suggesting that quantum orbital fluctuation is enhanced by the Hund's rule coupling. Accordingly, a relatively large orbital gap opens in comparison with a spin gap, and the system is described by an effective spin system on the background of the orbital dimer state.",0701092v1 2010-04-08,Coupling of bonding and antibonding electron orbitals in double quantum dots by spin-orbit interaction,"We perform a systematic exact diagonalization study of spin-orbit coupling effects for stationary few-electron states confined in quasi two-dimensional double quantum dots. We describe the spin-orbit-interaction induced coupling between bonding and antibonding orbitals and its consequences for magneto-optical absorption spectrum. The spin-orbit coupling for odd electron numbers (one, three) %only weakly perturbs the ground-state wave functions. %Nevertheless, %the spin-orbit interaction opens avoided crossings between low energy excited levels of opposite spin orientation and opposite spatial parity. For two-electrons the spin-orbit coupling allows for low-energy optical transitions that are otherwise forbidden by spin and parity selection rules. We demonstrate that the energies of optical transitions can be significantly increased by an in-plane electric field but only for odd electron numbers. Occupation of single-electron orbitals and effects of spin-orbit coupling on electron distribution between the dots are also discussed.",1004.1250v1 2021-11-22,Particle and spin transports of spin-orbit coupled Fermi gas through a Quantum Point Contact,"The particle and spin transport through a quantum point contact between two Fermi gases with Raman-induced spin-orbit coupling are investigated. We show that the particle and spin conductances both demonstrate the structure of plateau due to the mesoscopic scale of the quantum point contact. Compared with the normal Fermi gases the particle conductance can be significantly enhanced by the spin-orbit coupling effect. Furthermore, the conversion of the particle and spin currents can take place in the spin-orbit coupled system, and we find that it is controlled by the parameter of two-photon detuning. When the parameter of two-photon detuning vanishes the particle and spin currents decouple.",2111.11054v1 2017-01-25,Direct Mapping of Spin and Orbital Entangled Wavefunction under Interband Spin-Orbit coupling of Rashba Spin-Split Surface States,"We use spin- and angle-resolved photoemission spectroscopy (SARPES) combined with polarization-variable laser and investigate the spin-orbit coupling effect under interband hybridization of Rashba spin-split states for the surface alloys Bi/Ag(111) and Bi/Cu(111). In addition to the conventional band mapping of photoemission for Rashba spin-splitting, the different orbital and spin parts of the surface wavefucntion are directly imaged into energy-momentum space. It is unambiguously revealed that the interband spin-orbit coupling modifies the spin and orbital character of the Rashba surface states leading to the enriched spin-orbital entanglement and the pronounced momentum dependence of the spin-polarization. The hybridization thus strongly deviates the spin and orbital characters from the standard Rashba model. The complex spin texture under interband spin-orbit hybridyzation proposed by first-principles calculation is experimentally unraveled by SARPES with a combination of p- and s-polarized light.",1701.07269v1 2002-11-05,"SU(4) Spin-Orbital Two-Leg Ladder, Square and Triangle Lattices","Based on the generalized valence bond picture, a Schwinger boson mean field theory is applied to the symmetric SU(4) spin-orbital systems. For a two-leg SU(4) ladder, the ground state is a spin-orbital liquid with a finite energy gap, in good agreement with recent numerical calculations. In two-dimensional square and triangle lattices, the SU(4) Schwinger bosons condense at (\pi/2,\pi/2) and (\pi/3,\pi/3), respectively. Spin, orbital, and coupled spin-orbital static susceptibilities become singular at the wave vectors, twice of which the bose condensation arises at. It is also demonstrated that there are spin, orbital, and coupled spin-orbital long-range orderings in the ground state.",0211074v1 2013-08-29,Spin-orbit coupling and spin Hall effect for neutral atoms without spin-flips,"We propose a scheme which realizes spin-orbit coupling and the spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hamiltonian can be created by all-optical means using a period- tripling, spin-dependent superlattice.",1308.6349v1 2003-01-28,Spin-orbital gapped phase with least symmetry breaking in the one-dimensional symmetrically coupled spin-orbital model,"To describe the spin-orbital energy gap formation in the one-dimensional symmetrically coupled spin-orbital model, we propose a simple mean field theory based on an SU(4) constraint fermion representation of spins and orbitals. A spin-orbital gapped phase is formed due to a marginally relevant spin-orbital valence bond pairing interaction. The energy gap of the spin and orbital excitations grows extremely slowly from the SU(4) symmetric point up to a maximum value and then decreases rapidly. By calculating the spin, orbital, and spin-orbital tensor static susceptibilities at zero temperature, we find a crossover from coherent to incoherent magnetic excitations as the spin-orbital coupling decreasing from large to small values.",0301533v2 2013-12-11,Spin-orbit coupling in quantum gases,"Spin-orbit coupling links a particle's velocity to its quantum mechanical spin, and is essential in numerous condensed matter phenomena, including topological insulators and Majorana fermions. In solid-state materials, spin-orbit coupling originates from the movement of electrons in a crystal's intrinsic electric field, which is uniquely prescribed. In contrast, for ultracold atomic systems, the engineered ""material parameters"" are tuneable: a variety of synthetic spin-orbit couplings can be engineered on demand using laser fields. Here we outline the current experimental and theoretical status of spin-orbit coupling in ultracold atomic systems, discussing unique features that enable physics impossible in any other known setting.",1312.3292v1 2012-08-28,Spin-orbit coupled particle in a spin bath,"We consider a spin-orbit coupled particle confined in a quantum dot in a bath of impurity spins. We investigate the consequences of spin-orbit coupling on the interactions that the particle mediates in the spin bath. We show that in the presence of spin-orbit coupling, the impurity-impurity interactions are no longer spin-conserving. We quantify the degree of this symmetry breaking and show how it relates to the spin-orbit coupling strength. We identify several ways how the impurity ensemble can in this way relax its spin by coupling to phonons. A typical resulting relaxation rate for a self-assembled Mn-doped ZnTe quantum dot populated by a hole is 1 $\mu$s. We also show that decoherence arising from nuclear spins in lateral quantum dots is still removable by a spin echo protocol, even if the confined electron is spin-orbit coupled.",1208.5606v1 2023-10-08,Vortex Lattice Formation in Spin-Orbit-Coupled Spin-2 Bose-Einstein Condensate Under Rotation,"We investigate the vortex lattice configuration in a rotating spin orbit-coupled spin-2 Bose-Einstein condensate confined in a quasi-two-dimensional harmonic trap. By considering the interplay between rotation frequency, spin-orbit couplings, and inter atomic interactions, we explore a variety of vortex lattice structures emerging as a ground state solution. Our study focuses on the combined effects of spin-orbit coupling and rotation, analyzed by using the variational method for the single-particle Hamiltonian. We observe that the interplay between rotation and Rashba spin-orbit coupling gives rise to different effective potentials for the bosons. Specifically, at higher rotation frequencies, isotropic spin-orbit coupling leads to an effective toroidal potential, while fully anisotropic spin-orbit coupling results in a symmetric double-well potential. To obtain these findings, we solve the five coupled Gross-Pitaevskii equations for the spin-2 BEC with spin-orbit coupling under rotation. Notably, we find that the antiferromagnetic, cyclic, and ferromagnetic phases exhibit similar behavior at higher rotation.",2310.05160v1 2007-09-21,Weak and strong coupling limits of the two-dimensional Fröhlich polaron with spin-orbit Rashba interaction,"The continuous progress in fabricating low-dimensional systems with large spin-orbit couplings has reached a point in which nowadays materials may display spin-orbit splitting energies ranging from a few to hundreds of meV. This situation calls for a better understanding of the interplay between the spin-orbit coupling and other interactions ubiquitously present in solids, in particular when the spin-orbit splitting is comparable in magnitude with characteristic energy scales such as the Fermi energy and the phonon frequency. In this article, the two-dimensional Fr\""ohlich electron-phonon problem is reformulated by introducing the coupling to a spin-orbit Rashba potential, allowing for a description of the spin-orbit effects on the electron-phonon interaction. The ground state of the resulting Fr\""ohlich-Rashba polaron is studied in the weak and strong coupling limits of the electron-phonon interaction for arbitrary values of the spin-orbit splitting. The weak coupling case is studied within the Rayleigh-Schr\""odinger perturbation theory, while the strong-coupling electron-phonon regime is investigated by means of variational polaron wave functions in the adiabatic limit. It is found that, for both weak and strong coupling polarons, the ground state energy is systematically lowered by the spin-orbit interaction, indicating that the polaronic character is strengthened by the Rashba coupling. It is also shown that, consistently with the lowering of the ground state, the polaron effective mass is enhanced compared to the zero spin-orbit limit. Finally, it is argued that the crossover between weakly and strongly coupled polarons can be shifted by the spin-orbit interaction.",0709.3429v2 2021-02-02,"Coupled spin-orbital fluctuations in a three orbital model for $4d$ and $5d$ oxides with electron fillings $n=3,4,5$ -- Application to $\rm NaOsO_3$, $\rm Ca_2RuO_4$, and $\rm Sr_2IrO_4$","A unified approach is presented for investigating coupled spin-orbital fluctuations within a realistic three-orbital model for strongly spin-orbit coupled systems with electron fillings $n=3,4,5$ in the $t_{2g}$ sector of $d_{yz},d_{xz},d_{xy}$ orbitals. A generalized fluctuation propagator is constructed which is consistent with the generalized self-consistent Hartree-Fock approximation where all Coulomb interaction contributions involving orbital diagonal and off-diagonal spin and charge condensates are included. Besides the low-energy magnon, intermediate-energy orbiton and spin-orbiton, and high-energy spin-orbit exciton modes, the generalized spectral function also shows other high-energy excitations such as the Hund's coupling induced gapped magnon modes. We relate the characteristic features of the coupled spin-orbital excitations to the complex magnetic behavior resulting from the interplay between electronic bands, spin-orbit coupling, Coulomb interactions, and structural distortion effects, as realized in the compounds $\rm NaOsO_3$, $\rm Ca_2RuO_4$, and $\rm Sr_2IrO_4$.",2102.01400v2 2023-07-27,Spin-orbit torque emerging from orbital textures in centrosymmetric materials,"We unveil a hitherto concealed spin-orbit torque mechanism driven by orbital degrees of freedom in centrosymmetric two-dimensional transition metal dichalcogenides (focusing on PtSe${}_2$ ). Using first-principles simulations, tight-binding models and large-scale quantum transport calculations, we show that such a mechanism fundamentally stems from a spatial localization of orbital textures at opposite sides of the material, which imprints their symmetries onto spin-orbit coupling effects, further producing efficient and tunable spin-orbit torque. Our study suggests that orbital-spin entanglement at play in centrosymmetric materials can be harnessed as a resource for outperforming conventional spin-orbit torques generated by the Rashba-type effects.",2307.14673v1 2001-08-01,The Rashba Effect within the Coherent Scattering Formalism,"The influence of spin-orbit coupling in two-dimensional systems is investigated within the framework of the Landauer-Buettiker coherent scattering formalism. This formalism usually deals with spin-independent stationary states and, therefore, it does not include a spin-orbit contribution to the current. In this article, we will rederive the coherent scattering formalism, accounting for the changes brought about by the spin-orbit coupling. After a short review of the features of spin-orbit coupling in two-dimensional electron gases, we define the creation/annihilaton operators in the stationary states of the spin-orbit coupling Hamiltonian and use them to calculate the current operator within the Landauer-Buettiker formalism. The current is expressed as it is in the standard spin-independent case, but with the spin label replaced by a new label which we call the spin-orbit coupling label. The spin-orbit coupling effects can then be represented in a scattering matrix which relates the spin-orbit coupling stationary states in different leads. This scattering matrix is calculated in the case of a four-port beamsplitter, and it is shown to mix states with different spin-orbit coupling labels in a manner that depends on the angle between the leads. The formalism is then used to calculate the effect of spin-orbit coupling on the current and noise in two examples of electron collision.",0108021v1 2006-06-22,"Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps","A continuum model for the effective spin orbit interaction in graphene is derived from a tight-binding model which includes the $\pi$ and $\sigma$ bands. We analyze the combined effects of the intra-atomic spin-orbit coupling, curvature, and applied electric field, using perturbation theory. We recover the effective spin-orbit Hamiltonian derived recently from group theoretical arguments by Kane and Mele. We find, for flat graphene, that the intrinsic spin-orbit coupling $\Hi \propto \Delta^ 2$ and the Rashba coupling due to a perpendicular electric field ${\cal E}$, $\Delta_{\cal E} \propto \Delta$, where $\Delta$ is the intra-atomic spin-orbit coupling constant for carbon. Moreover we show that local curvature of the graphene sheet induces an extra spin-orbit coupling term $\Delta_{\rm curv} \propto \Delta$. For the values of $\cal E$ and curvature profile reported in actual samples of graphene, we find that $\Hi < \Delta_{\cal E} \lesssim \Delta_{\rm curv}$. The effect of spin-orbit coupling on derived materials of graphene, like fullerenes, nanotubes, and nanotube caps, is also studied. For fullerenes, only $\Hi$ is important. Both for nanotubes and nanotube caps $\Delta_{\rm curv}$ is in the order of a few Kelvins. We reproduce the known appearance of a gap and spin-splitting in the energy spectrum of nanotubes due to the spin-orbit coupling. For nanotube caps, spin-orbit coupling causes spin-splitting of the localized states at the cap, which could allow spin-dependent field-effect emission.",0606580v3 2014-01-18,Position and Spin Control by Dynamical Ultrastrong Spin-Orbit Coupling,"Focusing on the efficient probe and manipulation of single-particle spin states, we investigate the coupled spin and orbital dynamics of a spin 1/2 particle in a harmonic potential subject to ultrastrong spin-orbit interaction and external magnetic field. The advantage of these systems is the clear visualization of the strong spin-orbit coupling in the orbital dynamics. We also investigate the effect of a time-dependent coupling: Its nonadiabatic change causes an interesting interplay of spin and orbital motion which is related to the direction and magnitude of the applied magnetic field. This result suggests that orbital state manipulation can be realized through ultrastrong spin-orbit interactions, becoming a useful tool for handling entangled spin and orbital degrees of freedom to produce, for example, spin desirable polarizations in time interesting for spintronics implementations.",1401.4554v1 2005-10-03,Spin relaxation in quantum dots with random spin-orbit coupling,"We investigate the longitudinal spin relaxation arising due to spin-flip transitions accompanied by phonon emission in quantum dots where the strength of the Rashba spin-orbit coupling is a random function of the lateral (in-plane) coordinate on the spatial nanoscale. In this case the Rashba contribution to the spin-orbit coupling cannot be completely removed by applying a uniform external bias across the quantum dot plane. Due to the remnant random contribution, the spin relaxation rate cannot be decreased by more than two orders of magnitude even when the external bias fully compensates the regular part of the spin-orbit coupling.",0510050v1 2009-05-05,Transport through a band insulator with Rashba spin-orbit coupling: metal-insulator transition and spin-filtering effects,"We calculate the current-voltage characteristic of a one-dimensional band insulator with magnetic field and Rashba spin-orbit coupling which is connected to nonmagnetic leads. Without spin-orbit coupling we find a complete spin-filtering effect, meaning that the electric transport occurs in one spin channel only. For a large magnetic field which closes the band gap, we show that spin-orbit coupling leads to a transition from metallic to insulating behavior. The oscillations of the different spin-components of the current with the length of the transport channel are studied as well.",0905.0611v1 2013-04-11,Large spin-orbit coupling in carbon nanotubes,"It has recently been recognized that the strong spin-orbit interaction present in solids can lead to new phenomena, such as materials with non-trivial topological order. Although the atomic spin-orbit coupling in carbon is weak, the spin-orbit coupling in carbon nanotubes can be significant due to their curved surface. Previous works have reported spin-orbit couplings in reasonable agreement with theory, and this coupling strength has formed the basis of a large number of theoretical proposals. Here we report a spin-orbit coupling in three carbon nanotube devices that is an order of magnitude larger than measured before. We find a zero-field spin splitting of up to 3.4 meV, corresponding to a built-in effective magnetic field of 29 T aligned along the nanotube axis. While the origin of the large spin-orbit coupling is not explained by existing theories, its strength is promising for applications of the spin-orbit interaction in carbon nanotubes devices.",1304.3234v1 2020-02-18,Majorana-like localized spin density without bound states in topologically trivial spin-orbit coupled nanowires,"In the topological phase of spin-orbit coupled nanowires Majorana bound states are known to localize at the nanowire edges and to exhibit a spin density orthogonal to both the magnetic field and the spin-orbit field. By investigating a nanowire exposed to a uniform magnetic field with an interface between regions with different spin-orbit couplings, we find that the orthogonal spin density is pinned at the interface even when both interface sides are in the topologically trivial phase, and even when no bound state is present at all. A trivial bound state may additionally appear at the interface, especially if the spin-orbit coupling takes opposite signs across the interface. However, it can be destroyed by a smoothening of the spin-orbit profile or by a magnetic field component parallel to the spin-orbit field. In contrast, the orthogonal spin density persists in various and realistic parameter ranges. We also show that, while the measurement of bulk equilibrium spin currents has been elusive so far, such robust orthogonal spin density peak may provide a way to detect spin current variations across interfaces.",2002.07779v2 2014-11-12,Fermi Gases with Synthetic Spin-Orbit Coupling,"We briefly review recent progress on ultracold atomic Fermi gases with different types of synthetic spin-orbit coupling, including the one-dimensional (1D) equal weight Rashba-Dresselhaus and two-dimensional (2D) Rasbha spin-orbit couplings. Theoretically, we show how the single-body, two-body and many-body properties of Fermi gases are dramatically changed by spin-orbit coupling. In particular, the interplay between spin-orbit coupling and interatomic interaction may lead to several long-sought exotic superfluid phases at low temperatures, such as anisotropic superfluid, topological superfluid and inhomogeneous superfluid. Experimentally, only the first type - equal weight combination of Rasbha and Dresselhaus spin-orbit couplings - has been realized very recently using a two-photon Raman process. We show how to characterize a normal spin-orbit coupled atomic Fermi gas in both non-interacting and strongly-interacting limits, using particularly momentum-resolved radio-frequency spectroscopy. The experimental demonstration of a strongly-interacting spin-orbit coupled Fermi gas opens a promising way to observe various exotic superfluid phases in the near future.",1411.3043v1 2024-01-19,Extremely strong spin-orbit coupling effect in light element altermagnetic materials,"Spin-orbit coupling is a key to realize many novel physical effects in condensed matter physics, but the mechanism to achieve strong spin-orbit coupling effect in light element antiferromagnetic compounds has not been explored. In this work, based on symmetry analysis and the first-principles electronic structure calculations, we demonstrate that strong spin-orbit coupling effect can be realized in light element altermagnetic materials, and propose a mechanism for realizing the corresponding effective spin-orbit coupling. This mechanism reveals the cooperative effect of crystal symmetry, electron occupation, electronegativity, electron correlation, and intrinsic spin-orbit coupling. Our work not only promotes the understanding of light element compounds with strong spin-orbit coupling effect, but also provides an alternative for realizing light element compounds with an effective strong spin-orbit coupling.",2401.11065v1 2012-11-09,Spin-orbit Coupled Bose-Einstein Condensates in Spin-dependent Optical Lattices,"We investigate the ground-state properties of spin-orbit coupled Bose-Einstein condensates in spin-dependent optical lattices. The competition between the spin-orbit coupling strength and the depth of the optical lattice leads to a rich phase diagram. Without spin-orbit coupling, the spin-dependent optical lattices separate the condensates into alternating spin domains with opposite magnetization directions. With relatively weak spin-orbit coupling, the spin domain wall is dramatically changed from N\'{e}el wall to Bloch wall. For sufficiently strong spin-orbit coupling, vortex chains and antivortex chains are excited in the spin-up and spin-down domains respectively, corresponding to the formation of a lattice composed of meron-pairs and antimeron-pairs in the pseudospin representation. We also discuss how to observe these phenomena in real experiments.",1211.2097v3 2015-04-11,Collapse of spin-orbit coupled Bose-Einstein condensates,"A finite-size quasi two-dimensional Bose-Einstein condensate collapses if the attraction between atoms is sufficiently strong. Here we present a theory of collapse for condensates with the interatomic attraction and spin-orbit coupling. We consider two realizations of spin-orbit coupling: the axial Rashba coupling and balanced, effectively one-dimensional, Rashba-Dresselhaus one. In both cases spin-dependent ""anomalous"" velocity, proportional to the spin-orbit coupling strength, plays a crucial role. For the Rashba coupling, this velocity forms a centrifugal component in the density flux opposite to that arising due to the attraction between particles and prevents the collapse at a sufficiently strong coupling. For the balanced Rashba-Dresselhaus coupling, the spin-dependent velocity can spatially split the initial state in one dimension and form spin-projected wavepackets, reducing the total condensate density. Depending on the spin-orbit coupling strength, interatomic attraction, and the initial state, this splitting either prevents the collapse or modifies the collapse process. These results show that the collapse can be controlled by a spin-orbit coupling, thus, extending the domain of existence of condensates of attracting atoms.",1504.02860v1 2015-05-16,Dynamics of a macroscopic spin qubit in spin-orbit coupled Bose-Einstein condensates,"We consider a macroscopic spin qubit based on spin-orbit coupled Bose-Einstein condensates, where, in addition to the spin-orbit coupling, spin dynamics strongly depends on the interaction between particles. The evolution of the spin for freely expanding, trapped, and externally driven condensates is investigated. For condensates oscillating at the frequency corresponding to the Zeeman splitting in the synthetic magnetic field, the spin Rabi frequency does not depend on the interaction between the atoms since it produces only internal forces and does not change the total momentum. However, interactions and spin-orbit coupling bring the system into a mixed spin state, where the total spin is inside rather than on the Bloch sphere. This greatly extends the available spin space making it three-dimensional, but imposes limitations on the reliable spin manipulation of such a macroscopic qubit. The spin dynamics can be modified by introducing suitable spin-dependent initial phases, determined by the spin-orbit coupling, in the spinor wave function.",1505.04301v1 2005-07-01,Spin-orbit coupling and spin transport,"Recent achievements in semiconductor spintronics are discussed. Special attention is paid to spin-orbit interaction, coupling of electron spins to external electric fields, and spin transport in media with spin-orbit coupling, including the mechanisms of spin-Hall effect. Importance of spin-transport parameters at spin-precession wave vector $k_{\rm so}$ is emphasized, and existence of an universal relation between spin currents and spin accumulation at the spatial scale of $\ell_{\rm so}\approx k_{\rm so}^{-1}$ is conjectured.",0507007v2 2015-05-14,Spatiotemporal spin fluctuations caused by spin-orbit-coupled Brownian motion,"We develop a theory of thermal fluctuations of spin density emerging in a two-dimensional electron gas. The spin fluctuations probed at spatially separated spots of the sample are correlated due to Brownian motion of electrons and spin-obit coupling. We calculate the spatiotemporal correlation functions of the spin density for both ballistic and diffusive transport of electrons and analyze them for different types of spin-orbit interaction including the isotropic Rashba model and persistent spin helix regime. The measurement of spatial spin fluctuations provides direct access to the parameters of spin-orbit coupling and spin transport in conditions close to the thermal equilibrium.",1505.03826v1 2022-07-13,Jahn-Teller states mixed by spin-orbit coupling in an electromagnetic field,"Spin-orbit coupling plays a pivotal role in condensed matter physics. For instance, spin-orbit interactions affect the magnetization and transport dynamics in solids, while spins and momenta are locked in topological matter. Alternatively, spin-orbit entanglement may play an important role in exotic phenomena, like quantum spin liquids in 4d and 5d systems. An interesting question is how electronic states mixed by spin orbit coupling interact with electromagnetic fields, which may hold potential to tune their properties and reveal interesting physics. Motivated by our recent discovery of large gyrotropic signals in some Jahn-Teller manganites, here we explore the interaction of light with spin-mixed states in a d4 transition metal. We show that spin-orbit mixing enables electronic transitions that are sensitive to circularly polarized light, giving rise to a gyrotropic response that increases with spin-orbit coupling. Interestingly, photoexcited transitions that involve spin reversal are behind such gyrotropic resonances. Additionally, we find that the interaction with the electromagnetic field depends strongly on the relative orientation of the propagation of light with respect to Jahn-Teller distortions and spin quantization. We suggest that such interactions offer the opportunity to use electromagnetic waves at optical wavelengths to entangle orbital and spin degrees of freedom. Our approach, which includes a group-theoretical treatment of spin-orbit coupling, has wide applicability and provides a versatile tool to explore the interaction of electromagnetic fields with electronic states in transition metals with arbitrary spin-orbit coupling strength and pointgroup symmetries.",2207.06501v1 2016-06-27,Nonreciprocal Transverse Photonic Spin and Magnetization-Induced Electromagnetic Spin-Orbit Coupling,"A study of nonreciprocal transverse-spin angular-momentum-density shifts for evanescent waves in magneto-optic waveguide media is presented. Their functional relation to electromagnetic spin- and orbital-momenta is presented and analyzed. It is shown that the magneto-optic gyrotropy can be re-interpreted as the nonreciprocal electromagnetic spin-density shift per unit energy flux, thus providing an interesting alternative physical picture for the magneto-optic gyrotropy. The transverse spin-density shift is found to be thickness-dependent in slab optical waveguides. This dependence is traceable to the admixture of minority helicity components in the transverse spin angular momentum. It is also shown that the transverse spin is magnetically tunable. A formulation of electromagnetic spin-orbit coupling in magneto-optic media is presented, and an alternative source of spin-orbit coupling to non-paraxial optics vortices is proposed. It is shown that magnetization-induced electromagnetic spin-orbit coupling is possible, and that it leads to spin to orbital angular momentum conversion in magneto-optic media evanescent waves.",1606.08334v2 2022-06-10,Quantum heat engine based on a spin-orbit and Zeeman-coupled Bose-Einstein condensate,"We explore the potential of a spin-orbit coupled Bose-Einstein condensate for thermodynamic cycles. For this purpose we propose a quantum heat engine based on a condensate with spin-orbit and Zeeman coupling as a working medium. The cooling and heating are simulated by contacts of the condensate with an external magnetized media and demagnetized media. We examine the condensate ground state energy and its dependence on the strength of the synthetic spin-orbit and Zeeman couplings and interatomic interaction. Then we study the efficiency of the proposed engine. The cycle has a critical value of spin-orbit coupling related to the engine maximum efficiency.",2206.05041v1 2005-06-23,Spin properties of single electron states in coupled quantum dots,"Spin properties of single electron states in laterally coupled quantum dots in the presence of a perpendicular magnetic field are studied by exact numerical diagonalization. Dresselhaus (linear and cubic) and Bychkov-Rashba spin-orbit couplings are included in a realistic model of confined dots based on GaAs. Group theoretical classification of quantum states with and without spin orbit coupling is provided. Spin-orbit effects on the g-factor are rather weak. It is shown that the frequency of coherent oscillations (tunneling amplitude) in coupled dots is largely unaffected by spin-orbit effects due to symmetry requirements. The leading contributions to the frequency involves the cubic term of the Dresselhaus coupling. Spin-orbit coupling in the presence of magnetic field leads to a spin-dependent tunneling amplitude, and thus to the possibility of spin to charge conversion, namely spatial separation of spin by coherent oscillations in a uniform magnetic field. It is also shown that spin hot spots exist in coupled GaAs dots already at moderate magnetic fields, and that spin hot spots at zero magnetic field are due to the cubic Dresselhaus term only.",0506610v1 2012-11-05,Spin-orbital Texture in Topological Insulators,"Relativistic spin-orbit coupling plays an essential role in the field of topological insulators and quantum spintronics. It gives rise to the topological non-trivial band structure and enables electric manipulation of the spin degree of freedom. Because of the spin-orbit coupling, rich spin-orbital coupled textures can exist both in momentum and in real space. For three dimensional topological insulators in the Bi$_2$Se$_3$ family, topological surface states with p$_z$ orbitals have a left-handed spin texture for the upper Dirac cone and a right-handed spin texture for the lower Dirac cone. In this work, we predict a new form of the spin-orbital texture associated with the p$_x$ and p$_y$ orbitals. For the upper Dirac cone, a left-handed (right-handed) spin texture is coupled to the ""radial"" (""tangential"") orbital texture, whereas for the lower Dirac cone, the coupling of spin and orbital textures is the exact opposite. The ""tangential"" (""radial"") orbital texture is dominant for the upper (lower) Dirac cone, leading to the right-handed spin texture for the in-plane orbitals of both the upper and lower Dirac cones. A spin-resovled and photon polarized angle-resolved photoemission spectroscopy experiment is proposed to observe this novel spin-orbital texture.",1211.0762v1 2012-06-14,Magnetic ordering phenomena of interacting quantum spin Hall models,"The two-dimensional Hubbard model defined for topological band structures exhibiting a quantum spin Hall effect poses fundamental challenges in terms of phenomenological characterization and microscopic classification. In the limit of infinite coupling U at half filling, the spin model Hamiltonians resulting from a strong coupling expansion show various forms of magnetic ordering phenomena depending on the underlying spin-orbit coupling terms. We investigate the infinite U limit of the Kane-Mele Hubbard model with z-axis intrinsic spin-orbit coupling as well as its generalization to a generically multi-directional spin orbit term which has been claimed to account for the physical scenario in monolayer Na2IrO3. We find that the axial spin symmetry which is kept in the former but broken in the latter has a fundamental impact on the magnetic phase diagram as we vary the spin orbit coupling strength. While the Kane-Mele spin model shows a continuous evolution from conventional honeycomb Neel to XY antiferromagnetism which avoids the frustration imposed by the increased spin-orbit coupling, the multi-directional spin-orbit term induces a commensurate to incommensurate transition at intermediate coupling strength, and yields a complex spiral state with a 72 site unit cell in the limit of infinite spin-orbit coupling. From our findings, we conjecture that in the case of broken axial spin symmetry there is a large propensity for an additional phase at sufficiently large spin-orbit coupling and intermediate U.",1206.3103v2 2010-12-27,The multi-state CASPT2 spin-orbit method,"We propose the multi-state complete-active-space second-order perturbation theory spin-orbit method (MS-CASPT2-SO) for electronic structure calculations. It is a two-step spin-orbit coupling method that does not make use of energy shifts and that intrinsically guarantees the correct characters of the small space wave functions that are used to calculate the spin-orbit couplings, in contrast with previous two-step methods.",1012.5572v1 2011-06-21,Effective one body Hamiltonian of two spinning black-holes with next-to-next-to-leading order spin-orbit coupling,"Building on the recently computed next-to-next-to-leading order (NNLO) post-Newtonian (PN) spin-orbit Hamiltonian for spinning binaries \cite{Hartung:2011te} we extend the effective-one-body (EOB) description of the dynamics of two spinning black-holes to NNLO in the spin-orbit interaction. The calculation that is presented extends to NNLO the next-to-leading order (NLO) spin-orbit Hamiltonian computed in Ref. \cite{Damour:2008qf}. The present EOB Hamiltonian reproduces the spin-orbit coupling through NNLO in the test-particle limit case. In addition, in the case of spins parallel or antiparallel to the orbital angular momentum, when circular orbits exist, we find that the inclusion of NNLO spin-orbit terms moderates the effect of the NLO spin-orbit coupling.",1106.4349v3 2014-07-13,Orbital angular momentum driven intrinsic spin Hall effect,"We propose a mechanism of intrinsic spin Hall effect (SHE). In this mechanism, local orbital angular momentum (OAM) induces electron position shift and couples with the bias electric field to generate orbital Hall effect (OHE). SHE then emerges as a concomitant effect of OHE through the atomic spin-orbit coupling. Spin Hall conductivity due to this mechanism is estimated to be comparable to experimental values for heavy metals. This mechanism predicts the sign change of the spin Hall conductivity as the spin-orbit polarization changes its sign, and also correlation between the spin Hall conductivity and the splitting of the Rashba-type spin splitting at surfaces.",1407.3446v1 2010-04-08,Spin-charge and spin-orbital coupling effects on spin dynamics in ferromagnetic manganites,"Correlation-induced spin-charge and spin-orbital coupling effects on spin dynamics in ferromagnetic manganites are calculated with realistic parameters in order to provide a quantitative comparison with experimental results for spin stiffness, magnon dispersion, magnon damping, anomalous zone-boundary magnon softening, and Curie temperature. The role of orbital degeneracy, orbital ordering, and orbital correlations on spin dynamics in different doping regimes is highlighted.",1004.1352v2 2016-07-29,Twisted spin vortices in a spinor-dipolar Bose-Einstein condensate with Rashba spin-orbit coupling,"We consider a spin-1 Bose-Einstein condensate with Rashba spin-orbit coupling and dipole-dipole interaction confined in a cigar-shaped trap. Due to the combined effects of spin-orbit coupling, dipole-dipole interaction, and trap geometry, the system exhibits a rich variety of ground-state spin structures, including twisted spin vortices. The ground-state phase diagram is determined with respect to the strengths of the spin-orbit coupling and dipole-dipole interaction.",1607.08724v1 2021-06-09,Chiral control of quantum states in non-Hermitian spin-orbit-coupled fermions,"Spin-orbit coupling is an essential mechanism underlying quantum phenomena such as the spin Hall effect and topological insulators. It has been widely studied in well-isolated Hermitian systems, but much less is known about the role dissipation plays in spin-orbit-coupled systems. Here, we implement dissipative spin-orbit-coupled bands filled with ultracold fermions, and observe parity-time symmetry breaking as a result of the competition between the spin-orbit coupling and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables us to tune the energy gap and close it at the critical dissipation value, the so-called exceptional point. In the vicinity of the critical point, the state evolution exhibits a chiral response, which enables us to tune the spin-orbit coupling and dissipation dynamically, revealing topologically robust chiral spin transfer when the quantum state encircles the exceptional point. This demonstrates that we can explore non-Hermitian topological states with spin-orbit coupling.",2106.04874v2 2013-10-15,Vanishing of interband light absorption in a persistent spin helix state,"Spin-orbit coupling plays an important role in various properties of very different materials. Moreover efforts are underway to control the degree and quality of spin-orbit coupling in materials with a concomitant control of transport properties. We calculate the frequency dependent optical conductivity in systems with both Rashba and Dresselhaus spin-orbit coupling. We find that when the linear Dresselhaus spin-orbit coupling is tuned to be equal to the Rashba spin-orbit coupling, the interband optical conductivity disappears. This is taken to be the signature of the recovery of SU(2) symmetry. The presence of the cubic Dresselhaus spin-orbit coupling modifies the dispersion relation of the charge carriers and the velocity operator. Thus the conductivity is modified, but the interband contribution remains suppressed at most but not all photon energies for a cubic coupling of reasonable magnitude. Hence, such a measurement can serve as a diagnostic probe of engineered spin-orbit coupling.",1310.3916v1 2010-07-28,Current-induced torques in the presence of spin-orbit coupling,"In systems with strong spin-orbit coupling, the relationship between spin-transfer torque and the divergence of the spin current is generalized to a relation between spin transfer torques, total angular momentum current, and mechanical torques. In ferromagnetic semiconductors, where the spin-orbit coupling is large, these considerations modify the behavior of the spin transfer torques. One example is a persistent spin transfer torque in a spin valve: the spin transfer torque does not decay away from the interface, but approaches a constant value. A second example is a mechanical torque at single ferromagnetic-nonmagnetic interface.",1007.5037v1 2021-02-10,Suppression of effective spin-orbit coupling by thermal fluctuations in spin-orbit coupled antiferromagnets,"We apply the finite-temperature variational cluster approach to a strongly correlated and spin-orbit coupled model for four electrons (i.e. two holes) in the $t_{2g}$ subshell. We focus on parameters suitable for antiferromagnetic Mott insulators, in particular Ca$_2$RuO$_4$, and identify a crossover from the low-temperature regime, where spin-orbit coupling is essential, to the high-temperature regime where it leaves few signatures. The crossover is seen in one-particle spectra, where $xz$ and $yz$ spectra are almost one dimensional (as expected for weak spin-orbit coupling) at high temperature. At lower temperature, where spin-orbit coupling mixes all three orbitals, they become more two dimensional. However, stronger effects are seen in two-particle observables like the weight in states with definite onsite angular momentum. We thus identify the enigmatic intermediate-temperature 'orbital-order phase transition', which has been reported in various X-ray diffraction and absorption experiments at $T\approx 260\;K$, as the signature of the onset of spin-orbital correlations.",2102.05489v1 2016-04-20,Second post-Newtonian Lagrangian dynamics of spinning compact binaries,"The leading-order spin-orbit coupling is included in a post-Newtonian Lagrangian formulation of spinning compact binaries, which consists of the Newtonian term, first post-Newtonian (1PN) and 2PN non-spin terms and 2PN spin-spin coupling. This makes a 3PN spin-spin coupling occur in the derived Hamiltonian. The spin-spin couplings are mainly responsible for chaos in the Hamiltonians. However, the 3PN spin-spin Hamiltonian is small and has different signs, compared with the 2PN spin-spin Hamiltonian equivalent to the 2PN spin-spin Lagrangian. As a result, the probability of the occurrence of chaos in the Lagrangian formulation without the spin-orbit coupling is larger than that in the Lagrangian formulation with the spin-orbit coupling. Numerical evidences support the claim.",1604.05810v2 2001-09-13,Formation of energy gap in higher dimensional spin-orbital liquids,"A Schwinger boson mean field theory is developed for spin liquids in a symmetric spin-orbital model in higher dimensions. Spin, orbital and coupled spin-orbital operators are treated equally. We evaluate the dynamic correlation functions and collective excitations spectra. As the collective excitations have a finite energy gap, we conclude that the ground state is a spin-orbital liquid with a two-fold degeneracy, which breaks the discrete spin-orbital symmetry. Possible relevence of this spin liquid state to several realistic systems, such as CaV$_4$V$_9$ and Na$_2$Sb$_2$Ti$_2$O, are discussed.",0109234v1 2018-09-20,Multiple-$Q$ magnetic orders in Rashba-Dresselhaus metals,"We study magnetic textures realized in noncentrosymmetric Kondo lattice models, in which localized magnetic moments weakly interact with itinerant electrons subject to Rashba and Dresselhaus spin-orbit couplings. By virtue of state-of-the-art numerical simulations as well as variational calculations, we uncover versatile multiple-$Q$ orderings under zero magnetic field, which are found to originate in the instabilities of the Fermi surface whose spin degeneracy is lifted by the spin-orbit couplings. In the case with equally-strong Rashba and Dresselhaus spin-orbit couplings, which is known to realize a persistent spin helix in semiconductor quantum wells, we discover a sextuple-$Q$ magnetic ordering with a checkerboard-like spatial pattern of the spin scalar chirality. In the presence of either Rashba or Dresselhaus spin-orbit coupling, we find out another multiple-$Q$ ordering, which is distinct from Skyrmion crystals discussed under the same symmetry. Our results indicate that the cooperation of the spin-charge and spin-orbit couplings brings about richer magnetic textures than those studied within effective spin models. The situations would be experimentally realized, e.g., in noncentrosymmetric heavy-fermion compounds and heterostructures of spin-orbit coupled metals and magnetic insulators.",1809.07582v1 2007-01-11,Some exact identities connecting one- and two-particle Green's functions in spin-orbit coupling systems,"Some exact identities connecting the one- and two-particle Green's functions in the presence of spin-orbit coupling have been derived. These identities is similar to the usual Ward identity in the particle or charge transport theory and a satisfying spin transport theory in spin-orbit coupling system should also preserve these identities.",0701227v1 2015-07-25,Quantum entanglement in the one-dimensional spin-orbital SU(2)$\otimes XXZ$ model,"We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)$\otimes XXZ$ model with SU(2) spin exchange and anisotropic $XXZ$ orbital exchange interactions and negative exchange coupling. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic SU(2)$\otimes$SU(2) limit. Surprisingly, for finite transverse orbital coupling the long-range spin singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size.",1507.07103v1 2015-11-16,Drude weight and optical conductivity of a two-dimensional heavy-hole gas with $k$-cubic spin-orbit interactions,"We present detailed theoretical study on zero-frequency Drude weight and optical conductivity of a two-dimensional heavy-hole gas(2DHG) with $k$-cubic Rashba and Dresselhaus spin-orbit interactions. The presence of $k$-cubic spin-orbit couplings strongly modifies the Drude weight in comparison to the electron gas with $k$-linear spin-orbit couplings. For large hole density and strong $k$-cubic spin-orbit couplings, the density dependence of Drude weight deviates from the linear behavior. We establish a relation between optical conductivity and the Berry connection. Unlike two-dimensional electron gas with $k$-linear spin-orbit couplings, we explicitly show that the optical conductivity does not vanish even for equal strength of the two spin-orbit couplings. We attribute this fact to the non-zero Berry phase for equal strength of $k$-cubic spin-orbit couplings. The least photon energy needed to set in the optical transition in hole gas is one order of magnitude smaller than that of electron gas. Types of two van Hove singularities appear in the optical spectrum are also discussed.",1511.04917v3 2017-04-03,Inverse spin galvanic effect in the presence of impurity spin-orbit scattering: a diagrammatic approach,"Spin-charge interconversion is currently the focus of intensive experimental and theoretical research both for its intrinsic interest and for its potential exploitation in the realization of new spintronic functionalities. Spin-orbit coupling is one of the key microscopic mechanisms to couple charge currents and spin polarizations. The Rashba spin-orbit coupling in a two-dimensional electron gas has been shown to give rise to the inverse spin galvanic effect, i.e. the generation of a non-equilibrium spin polarization by a charge current. Whereas the Rashba model may be applied to the interpretation of experimental results in many cases, in general in a given real physical system spin-orbit coupling also occurs due other mechanisms such as Dresselhaus bulk inversion asymmetry and scattering from impurities. In this work we consider the inverse spin galvanic effect in the presence of Rashba, Dresselhaus and impurity spin-orbit scattering. We find that the size and form of the inverse spin galvanic effect is greatly modified by the presence of the various sources of spin-orbit coupling. Indeed, spin-orbit coupling affects the spin relaxation time by adding the Elliott-Yafet mechanism to the Dyakonov-Perel and, furthermore, it changes the non-equilibrium value of the current-induced spin polarization by introducing a new spin generation torque. We use a diagrammatic Kubo formula approach to evaluate the spin polarization-charge current response function. We finally comment about the relevance of our results for the interpretation of experimental results.",1704.00532v1 2010-03-08,Spin-orbit coupling in a graphene bilayer and in graphite,"The intrinsic spin-orbit interactions in bilayer graphene and in graphite are studied, using a tight binding model, and an intraatomic LS coupling. The spin-orbit interactions in bilayer graphene and graphite are larger, by about one order of magnitude, than the interactions in single layer graphene, due to the mixing of pi and sigma bands by interlayer hopping. Their value is in the range 0.1 - 1K. The spin-orbit coupling opens a gap in bilayer graphene, and it also gives rise to two edge modes. The spin-orbit couplings are largest, 1-4K, in orthorhombic graphite, which does not have a center of inversion.",1003.1618v1 2022-02-28,Observation of long-range orbital transport and giant orbital torque,"Modern spintronics relies on the generation of spin currents through spin-orbit coupling. The spin-current generation has been believed to be triggered by current-induced orbital dynamics, which governs the angular momentum transfer from the lattice to the electrons in solids. The fundamental role of the orbital response in the angular momentum dynamics suggests the importance of the orbital counterpart of spin currents: orbital currents. However, evidence for its existence has been elusive. Here, we demonstrate the generation of giant orbital currents and uncover fundamental features of the orbital response. We experimentally and theoretically show that orbital currents propagate over longer distances than spin currents by more than an order of magnitude in a ferromagnet and nonmagnets. Furthermore, we find that the orbital current enables electric manipulation of magnetization with efficiencies significantly higher than the spin counterpart. These findings open the door to orbitronics that exploits orbital transport and spin-orbital coupled dynamics in solid-state devices.",2202.13896v2 2005-01-09,Electron Spin Dynamics in Impure Quantum Wells for Arbitrary Spin-Orbit Coupling,"Strong interest has arisen recently on low-dimensional systems with strong spin-orbit interaction due to their peculiar properties of interest for some spintronic applications. Here, the time evolution of the electron spin polarization of a disordered two-dimensional electron gas is calculated exactly within the Boltzmann formalism for arbitrary couplings to a Rashba spin-orbit field. The classical Dyakonov-Perel mechanism of spin relaxation is shown to fail for sufficiently strong Rashba fields, in which case new regimes of spin decay are identified. These results suggest that spin manipulation can be greatly improved in strong spin-orbit interaction materials.",0501174v3 2007-09-21,Spin-orbit mediated anisotropic spin interaction in interacting electron systems,"We investigate interactions between spins of strongly correlated electrons subject to the spin-orbit interaction. Our main finding is that of a novel, spin-orbit mediated anisotropic spin-spin coupling of the van der Waals type. Unlike the standard exchange, this interaction does not require the wave functions to overlap. We argue that this ferromagnetic interaction is important in the Wigner crystal state where the exchange processes are severely suppressed. We also comment on the anisotropy of the exchange between spins mediated by the spin-orbital coupling.",0709.3521v2 2012-03-06,Short-range correlations in dilute atomic Fermi gases with spin-orbit coupling,"We study the short-range correlation strength of three dimensional spin half dilute atomic Fermi gases with spin-orbit coupling. The interatomic interaction is modeled by the contact pseudopotential. In the high temperature limit, we derive the expression for the second order virial expansion of the thermodynamic potential via the ladder diagrams. We further evaluate the second order virial expansion in the limit that the spin-orbit coupling constants are small, and find that the correlation strength between the fermions increases as the forth power of the spin-orbit coupling constants. At zero temperature, we consider the cases in which there are symmetric spin-orbit couplings in two or three directions. In such cases, there is always a two-body bound state of zero net momentum. In the limit that the average interparticle distance is much larger than the dimension of the two-body bound state, the system primarily consists of condensed bosonic molecules that fermions pair to form; we find that the correlation strength also becomes bigger compared to that in the absence of spin-orbit coupling. Our results indicate that generic spin-orbit coupling enhances the short-range correlations of the Fermi gases. Measurement of such enhancement by photoassociation experiment is also discussed.",1203.1159v1 2018-02-01,Spin Seebeck effect and thermal spin galvanic effect in Ni80Fe20/p-Si bilayers,"The development of spintronics and spin-caloritronics devices need efficient generation, detection and manipulation of spin current. The thermal spin current from spin-Seebeck effect has been reported to be more energy efficient than the electrical spin injection methods. But, spin detection has been the one of the bottlenecks since metals with large spin-orbit coupling is an essential requirement. In this work, we report an efficient thermal generation and interfacial detection of spin current. We measured a spin-Seebeck effect in Ni80Fe20 (25 nm)/p-Si (50 nm) (polycrystalline) bilayers without heavy metal spin detector. The p-Si, having the centosymmetric crystal structure, has insignificant intrinsic spin-orbit coupling leading to negligible spin-charge conversion. We report a giant inverse spin-Hall effect, essential for detection of spin-Seebeck effect, in the Ni80Fe20/p-Si bilayer structure, which originates from Rashba spin orbit coupling due to structure inversion asymmetry at the interface. In addition, the thermal spin pumping in p-Si leads to spin current from p-Si to Ni80Fe20 layer due to thermal spin galvanic effect and spin-Hall effect causing spin-orbit torques. The thermal spin-orbit torques leads to collapse of magnetic hysteresis of 25 nm thick Ni80Fe20 layer. The thermal spin-orbit torques can be used for efficient magnetic switching for memory applications. These scientific breakthroughs may give impetus to the silicon spintronics and spin-caloritronics devices.",1802.00132v1 2017-03-18,Spin-orbit scattering visualized in quasiparticle interference,"In the presence of spin-orbit coupling, electron scattering off impurities depends on both spin and orbital angular momentum of electrons -- spin-orbit scattering. Although some transport properties are subject to spin-orbit scattering, experimental techniques directly accessible to this effect are limited. Here we show that a signature of spin-orbit scattering manifests itself in quasiparticle interference (QPI) imaged by spectroscopic-imaging scanning tunneling microscopy. The experimental data of a polar semiconductor BiTeI are well reproduced by numerical simulations with the $T$-matrix formalism that include not only scalar scattering normally adopted but also spin-orbit scattering stronger than scalar scattering. To accelerate the simulations, we extend the standard efficient method of QPI calculation for momentum-independent scattering to be applicable even for spin-orbit scattering. We further identify a selection rule that makes spin-orbit scattering visible in the QPI pattern. These results demonstrate that spin-orbit scattering can exert predominant influence on QPI patterns and thus suggest that QPI measurement is available to detect spin-orbit scattering.",1703.06234v1 2011-11-17,Intrinsic Spin Swapping,"Here, we study diffusive spin transport in two dimensions and demonstrate that an intrinsic analog to a previously predicted extrinsic spin swapping effect, where the spin polarization and the direction of flow are interchanged due to spin-orbit coupling at extrinsic impurities, can be induced by intrinsic (Rashba) spin-orbit coupling. The resulting accumulation of intrinsically spin-swapped polarizations is shown to be much larger than for the extrinsic effect. Intrinsic spin swapping is particularly strong when the system dimensions exceed the spin-orbit precession length and the generated transverse spin currents are of the order of the injected primary spin currents. In contrast, spin accumulations and spin currents caused by extrinsic spin swapping are proportional to the spin-orbit coupling. We present numerical and analytical results for the secondary spin currents and accumulations generated by intrinsic spin swapping, and we derive analytic expressions for the induced spin accumulation at the edges of a narrow strip, where a long-range propagation of spin polarizations takes place.",1111.4072v2 2017-10-09,Tunable superconducting critical temperature in ballistic hybrid structures with strong spin-orbit coupling,"We present a theoretical description and numerical simulations of the superconducting transition in hybrid structures including strong spin-orbit interactions. The spin-orbit coupling is taken to be of Rashba type for concreteness, and we allow for an arbitrary magnitude of the spin-orbit strength as well as an arbitrary thickness of the spin-orbit coupled layer. This allows us to make contact with the experimentally relevant case of enhanced interfacial spin-orbit coupling via atomically thin heavy metal layers. We consider both interfacial spin-orbit coupling induced by inversion asymmetry in an S/F-junction, as well as in-plane spin-orbit coupling in the ferromagnetic region of an S/F/S- and an S/F-structure. Both the pair amplitudes, local density of states and critical temperature show dependency on the Rashba strength and, importantly, the orientation of the exchange field. In general, spin-orbit coupling increases the critical temperature of a proximity system where a magnetic field is present, and enhances the superconducting gap in the density of states. We perform a theoretical derivation which explains these results by the appearance of long-ranged singlet correlations. Our results suggest that $T_c$ in ballistic spin-orbit coupled superconducting structures may be tuned by using only a single ferromagnetic layer.",1710.03228v2 2021-04-14,Spin-orbit gaps in the s and p orbital bands of an artificial honeycomb lattice,"Muffin-tin methods have been instrumental in the design of honeycomb lattices that show, in contrast to graphene, separated s and in-plane p bands, a p orbital Dirac cone, and a p orbital flat band. Recently, such lattices have been experimentally realized using the 2D electron gas on Cu(111). A possible next avenue is the introduction of spin-orbit coupling to these systems. Intrinsic spin-orbit coupling is believed to open topological gaps, and create a topological flat band. Although Rashba coupling is straightforwardly incorporated in the muffin-tin approximation, intrinsic spin-orbit coupling has only been included either for a very specific periodic system, or only close to the Dirac point. Here, we introduce general intrinsic and Rashba spin-orbit terms in the Hamiltonian for both periodic and finite-size systems. We observe a strong band opening over the entire Brillouin zone between the p orbital flat band and Dirac cone hosting a pronounced edge state, robust against the effects of Rashba spin-orbit coupling.",2104.06912v1 2007-10-15,Intersubband spin-orbit coupling and spin splitting in symmetric quantum wells,"In semiconductors with inversion asymmetry, spin-orbit coupling gives rise to the well-known Dresselhaus and Rashba effects. If one considers quantum wells with two or more conduction subbands, an additional, intersubband-induced spin-orbit term appears whose strength is comparable to the Rashba coupling, and which remains finite for symmetric structures. We show that the conduction band spin splitting due to this intersubband spin-orbit coupling term is negligible for typical III-V quantum wells.",0710.2866v1 2009-02-19,Impurity induced spin-orbit coupling in graphene,"We study the effect of impurities in inducing spin-orbit coupling in graphene. We show that the sp3 distortion induced by an impurity can lead to a large increase in the spin-orbit coupling with a value comparable to the one found in diamond and other zinc-blende semiconductors. The spin-flip scattering produced by the impurity leads to spin scattering lengths of the order found in recent experiments. Our results indicate that the spin-orbit coupling can be controlled via the impurity coverage.",0902.3244v1 2011-10-04,Spin-orbit-coupled dipolar Bose-Einstein condensates,"We propose an experimental scheme to create spin-orbit coupling in spin-3 Cr atoms using Raman processes. Employing linear Zeeman effect and optical Stark shift, two spin states within the ground electronic manifold are selected, which results in a pseudo-spin-1/2 model. We further study the ground state structures of a spin-orbit-coupled Cr condensate. We show that, in addition to the stripe structures induced by the spin-orbit coupling, the magnetic dipole-dipole interaction gives rise to the vortex phase, in which spontaneous spin vortex is formed.",1110.0558v3 2016-01-26,Double-Quantum Spin Vortices in SU(3) Spin-Orbit Coupled Bose Gases,"We show that double-quantum spin vortices, which are characterized by doubly quantized circulating spin currents and unmagnetized filled cores, can exist in the ground states of SU(3) spin-orbit coupled Bose gases. It is found that the SU(3) spin-orbit coupling and spin-exchange interaction play important roles in determining the ground-state phase diagram. In the case of effective ferromagnetic spin interaction, the SU(3) spin-orbit coupling induces a three-fold degeneracy to the magnetized ground state, while in the antiferromagnetic spin interaction case, the SU(3) spin-orbit coupling breaks the ordinary phase rule of spinor Bose gases, and allows the spontaneous emergence of double-quantum spin vortices. This exotic topological defect is in stark contrast to the singly quantized spin vortices observed in existing experiments, and can be readily observed by the current magnetization-sensitive phase-contrast imaging technique.",1601.06935v2 2021-10-14,Thermalization in a Spin-Orbit coupled Bose gas by enhanced spin Coulomb drag,"An important component of the structure of the atom, the effects of spin-orbit coupling are present in many sub-fields of physics. Most of these effects are present continuously. We present a detailed study of the dynamics of changing the spin-orbit coupling in an ultra-cold Bose gas, coupling the motion of the atoms to their spin. We find that the spin-orbit coupling greatly increases the damping towards equilibrium. We interpret this damping as spin drag, which is enhanced by spin-orbit coupling rate, scaled by a remarkable factor of $8.9(6)$~s. We also find that spin-orbit coupling lowers the final temperature of the Bose gas after thermalization.",2110.07094v3 2012-04-10,Spin-current absorption by inhomogeneous spin-orbit coupling,"We investigate the spin-current absorption induced by an inhomogeneous spin-orbit coupling due to impurities in metals. We consider the system with spin currents driven by the electric field or the spin accumulation. The resulting diffusive spin currents, including the gradient of the spin-orbit coupling strength, indicate the spin-current absorption at the interface, which is exemplified with experimentally relevant setups.",1204.2189v2 2014-03-19,Spin-orbit coupling effects on spin-dependent inelastic electronic lifetimes in ferromagnets,"For the 3d ferromagnets iron, cobalt and nickel we compute the spin-dependent inelastic electronic lifetimes due to carrier-carrier Coulomb interaction including spin-orbit coupling. We find that the spin-dependent density-of-states at the Fermi energy does not, in general, determine the spin dependence of the lifetimes because of the effective spin-flip transitions allowed by the spin mixing. The majority and minority electron lifetimes computed including spin-orbit coupling for these three 3-d ferromagnets do not differ by more than a factor of 2, and agree with experimental results.",1403.4728v1 2013-06-27,Meron Ground State of Rashba Spin-Orbit-Coupled Dipolar Bosons,"We study the effects of dipolar interactions on a Bose-Einstein condensate with synthetically generated Rashba spin-orbit coupling. The dipolar interaction we consider includes terms that couple spin and orbital angular momentum in a way perfectly congruent with the single-particle Rashba coupling. We show that this internal spin-orbit coupling plays a crucial role in the rich ground-state phase diagram of the trapped condensate. In particular, we predict the emergence of a thermodynamically stable ground state with a meron spin configuration.",1306.6610v2 2007-01-25,Spin-Hall effect and spin-coherent excitations in a strongly confined two-dimensional hole gas,"Based on a rigorous quantum-kinetic approach, spin-charge coupled drift-diffusion equations are derived for a strongly confined two-dimensional hole gas. An electric field leads to a coupling between the spin and charge degrees of freedom. For weak spin-orbit interaction, this coupling gives rise to the intrinsic spin-Hall effect. There exists a threshold value of the spin-orbit coupling constant that separates spin diffusion from ballistic spin transport. In the latter regime, undamped spin-coherent oscillations are observed. This result is confirmed by an exact microscopic approach valid in the ballistic regime.",0701612v1 2020-06-05,Intrinsic and extrinsic spin-orbit coupling and spin relaxation in monolayer PtSe$_2$,"Monolayer PtSe$_2$ is a semiconducting transition metal dichalcogenide characterized by an indirect band gap, space inversion symmetry, and high carrier mobility. Strong intrinsic spin-orbit coupling and the possibility to induce extrinsic spin-orbit fields by gating make PtSe$_2$ attractive for fundamental spin transport studies as well as for potential spintronics applications. We perform a systematic theoretical study of the spin-orbit coupling and spin relaxation in this material. Specifically, we employ first principles methods to obtain the basic orbital and spin-orbital properties of PtSe$_2$, also in the presence of an external transverse electric field. We calculate the spin mixing parameters $b^2$ and the spin-orbit fields $\Omega$ for the Bloch states of electrons and holes. This information allows us to predict the spin lifetimes due to the Elliott-Yafet and D'yakonov-Perel mechanisms. We find that $b^2$ is rather large, on the order of $10^{-2}$ and $10^{-1}$, while $\Omega$ varies strongly with doping, being about $10^{3} - 10^{4}$\,ns$^{-1}$ for %typical Fermi levels in the interval $(10-100)$ meV, carrier density in the interval $10^{13}-10^{14}$\,cm$^{-2}$ at the electric field of 1 V/nm. We estimate the spin lifetimes to be on the picosecond level.",2006.03384v1 2016-11-06,Effective magnetic interactions in spin-orbit coupled $d^4$ Mott insulators,"Transition metal compounds with the $(t_{2g})^4$ electronic configuration are expected to be nonmagnetic atomic singlets both in the weakly interacting regime due to spin-orbit coupling, as well as in the Coulomb dominated regime with oppositely aligned $L=1$ and $S=1$ angular momenta. However, starting with the full multi-orbital electronic Hamiltonian, we show the low energy effective magnetic Hamiltonian contains isotropic superexchange spin interactions but anisotropic orbital interactions. By tuning the ratio of superexchange to spin-orbit coupling $J_\mathrm{SE}/\lambda$, we obtain a phase transition from nonmagnetic atomic singlets to novel magnetic phases depending on the strength of Hund's coupling, the crystal structure and the number of active orbitals. Spin-orbit coupling plays a non-trivial role in generating a triplon condensate of weakly interacting excitations at antiferromagnetic ordering vector $\vec k=\vec \pi$, regardless of whether the local spin interactions are ferromagnetic or antiferromagnetic. In the large $J_\mathrm{SE} / \lambda$ regime, the localized spin and orbital moments produce anisotropic orbital interactions that are frustrated or constrained even in the absence of geometric frustration. Orbital frustration leads to frustration in the spin channel opening up the possibility of spin-orbital liquids with both spin and orbital entanglement.",1611.01840v1 2021-06-04,Efficient conversion of orbital Hall current to spin current for spin-orbit torque switching,"Spin Hall effect, an electric generation of spin current, allows for efficient control of magnetization. Recent theory revealed that orbital Hall effect creates orbital current, which can be much larger than spin Hall-induced spin current. However, orbital current cannot directly exert a torque on a ferromagnet, requiring a conversion process from orbital current to spin current. Here, we report two effective methods of the conversion through spin-orbit coupling engineering, which allows us to unambiguously demonstrate orbital-current-induced spin torque, or orbital Hall torque. We find that orbital Hall torque is greatly enhanced by introducing either a rare-earth ferromagnet Gd or a Pt interfacial layer with strong spin-orbit coupling in Cr/ferromagnet structures, indicating that the orbital current generated in Cr is efficiently converted into spin current in the Gd or Pt layer. Furthermore, we show that the orbital Hall torque can facilitate the reduction of switching current of perpendicular magnetization in spin-orbit-torque-based spintronic devices.",2106.02286v2 2014-12-17,Energy spectra of two interacting fermions with spin-orbit coupling in a harmonic trap,"We explore the two-body spectra of spin-$1/2$ fermions in isotropic harmonic traps with external spin-orbit potentials and short range two-body interactions. Using a truncated basis of total angular momentum eigenstates, non-perturbative results are presented for experimentally realistic forms of the spin-orbit coupling: a pure Rashba coupling, Rashba and Dresselhaus couplings in equal parts, and a Weyl-type coupling. The technique is easily adapted to bosonic systems and other forms of spin-orbit coupling.",1412.5634v2 2017-09-20,Superfluid transition temperature of spin-orbit and Rabi coupled fermions with tunable interactions,"We obtain the superfluid transition temperature of equal Rashba-Dresselhaus spin-orbit and Rabi coupled Fermi superfluids, from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) regimes in three dimensions. Spin-orbit coupling enhances the critical temperature in the BEC limit, and can convert a first order phase transition in the presence of Rabi coupling into second order, as a function of the Rabi coupling for fixed interactions. We derive the Ginzburg-Landau equation to sixth power in the superfluid order parameter to describe both first and second order transitions as a function of spin-orbit and Rabi couplings.",1709.07042v1 2012-12-03,Normal state properties of spin-orbit coupled Fermi gases in the upper branch of energy spectrum,"We investigate normal state properties of spin-orbit coupled Fermi gases with repulsive s-wave interaction, in the absence of molecule formation, i.e., in the so-called ""upper branch"". Within the framework of random phase approximation, we derive analytical expressions for the quasi-particle lifetime $\tau_s$, the effective mass $m_s^*$, and the Green's function renormalization factor $Z_s$ in the presence of Rashba spin-orbit coupling. In contrast to spin-orbit coupled electron gas with Coulomb interaction, we show that the modifications are dependent on the Rashba band index s, and occur in the first order of the spin-orbit coupling strength. We also calculate experimental observable such as spectral weight, density of state and specific heat, which exhibit significant differences from their counterparts without spin-orbit coupling. We expect our microscopic calculations of these Fermi liquid parameters would have the immediate applications to the spin-orbit coupled Fermi gases in the upper branch of the energy spectrum.",1212.0420v5 2016-10-07,The Role of Interaction in the Pairing of Two Spin-orbit Coupled Fermions,"We investigate the role of a repulsive s-wave interaction in the two-body problem in the presence of spin orbit couplings, motivated by current interests in exploring exotic superfluid phases in spin-orbit coupled Fermi gases. For weak spin orbit coupling where the density of states is not significantly altered, we analytically show that the high-energy states become more important in determining the binding energy when the interaction strength decreases. Consequently, tuning the interaction gives rise to a rich ground state behavior, including a zigzag of the ground state momentum or inducing transitions among the meta-stable states. By exactly solving the two-body problem for a spin-orbit coupled Fermi mixture, we demonstrate that our analysis can also apply to the case when the density of states is significantly modified by the spin-orbit coupling. Our findings pave the way for understanding and controlling the paring of fermions in the presence of spin orbit couplings.",1610.02927v2 2018-07-17,Effects of spin-orbit coupling on the optical response of a material,"We investigate the effects of spin-orbit coupling on the optical response of materials. In particular, we study the effects of the commutator between the spin-orbit coupling part of the potential and the position operator on the optical matrix elements. Using a formalism that separates a fullyrelativistic Kleinman-Bylander pseudopotential into the scalar-relativistic and spin-orbit-coupling parts, we calculate the contribution of the commutator arising from spin-orbit coupling to the squared optical matrix elements of isolated atoms, monolayer transition metal dichalcogenides, and topological insulators. In the case of isolated atoms from H ($Z = 1$) to Bi ($Z = 83$), the contribution of spin-orbit coupling to the squared matrix elements can be as large as 14 %. On the other hand, in the cases of monolayer transition metal dichalcogenides and topological insulators, we find that this contribution is less than 1 % and that it is sufficient to calculate the optical matrix elements and subsequent physical quantities without considering the commutator arising from spin-orbit coupling.",1807.06669v1 2011-10-31,Spin-Orbit Coupled Quantum Gases,"In this review we will discuss the experimental and theoretical progresses in studying spin-orbit coupled degenerate atomic gases during the last two years. We shall first review a series of pioneering experiments in generating synthetic gauge potentials and spin-orbit coupling in atomic gases by engineering atom-light interaction. Realization of spin-orbit coupled quantum gases opens a new avenue in cold atom physics, and also brings out a lot of new physical problems. In particular, the interplay between spin-orbit coupling and inter-atomic interaction leads to many intriguing phenomena. Here, by reviewing recent theoretical studies of both interacting bosons and fermions with isotropic Rashba spin-orbit coupling, the key message delivered here is that spin-orbit coupling can enhance the interaction effects, and make the interaction effects much more dramatic even in the weakly interacting regime.",1110.6798v1 2010-02-02,Spin-resolved scattering through spin-orbit nanostructures in graphene,"We address the problem of spin-resolved scattering through spin-orbit nanostructures in graphene, i.e., regions of inhomogeneous spin-orbit coupling on the nanometer scale. We discuss the phenomenon of spin-double refraction and its consequences on the spin polarization. Specifically, we study the transmission properties of a single and a double interface between a normal region and a region with finite spin-orbit coupling, and analyze the polarization properties of these systems. Moreover, for the case of a single interface, we determine the spectrum of edge states localized at the boundary between the two regions and study their properties.",1002.0441v2 2014-09-19,Angular dependence of spin-orbit spin transfer torques,"In ferromagnet/heavy metal bilayers, an in-plane current gives rise to spin-orbit spin transfer torque which is usually decomposed into field-like and damping-like torques. For two-dimensional free-electron and tight-binding models with Rashba spin-orbit coupling, the field-like torque acquires nontrivial dependence on the magnetization direction when the Rashba spin-orbit coupling becomes comparable to the exchange interaction. This nontrivial angular dependence of the field-like torque is related to the Fermi surface distortion, determined by the ratio of the Rashba spin-orbit coupling to the exchange interaction. On the other hand, the damping-like torque acquires nontrivial angular dependence when the Rashba spin-orbit coupling is comparable to or stronger than the exchange interaction. It is related to the combined effects of the Fermi surface distortion and the Fermi sea contribution. The angular dependence is consistent with experimental observations and can be important to understand magnetization dynamics induced by spin-orbit spin transfer torques",1409.5600v1 2006-08-18,Electric Dipole Spin Resonance for Heavy Holes in Quantum Dots,"We propose and analyze a new method for manipulation of a heavy hole spin in a quantum dot. Due to spin-orbit coupling between states with different orbital momenta and opposite spin orientations, an applied rf electric field induces transitions between spin-up and spin-down states. This scheme can be used for detection of heavy-hole spin resonance signals, for the control of the spin dynamics in two-dimensional systems, and for determining important parameters of heavy-holes such as the effective $g$-factor, mass, spin-orbit coupling constants, spin relaxation and decoherence times.",0608410v1 2007-05-25,Interplay of the Rashba and Dresselhaus spin-orbit coupling in the optical spin susceptibility of 2D electron systems,"We present calculations of the frequency-dependent spin susceptibility tensor of a two-dimensional electron gas with competing Rashba and Dresselhaus spin-orbit interaction. It is shown that the interplay between both types of spin-orbit coupling gives rise to an anisotropic spectral behavior of the spin density response function which is significantly different from that of vanishing Rashba or Dresselhaus case. Strong resonances are developed in the spin susceptibility as a consequence of the angular anisotropy of the energy spin-splitting. This characteristic optical modulable response may be useful to experimentally probe spin accumulation and spin density currents in such systems.",0705.3849v1 2008-07-23,Dynamics of coupled spins in quantum dots with strong spin-orbit interaction,"We investigated the time dependence of two-electron spin states in a double quantum dot fabricated in an InAs nanowire. In this system, spin-orbit interaction has substantial influence on the spin states of confined electrons. Pumping single electrons through a Pauli spin-blockade configuration allowed to probe the dynamics of the two coupled spins via their influence on the pumped current. We observed spin-relaxation with a magnetic field dependence different from GaAs dots, which can be explained by spin-orbit interaction. Oscillations were detected for times shorter than the relaxation time, which we attribute to coherent evolution of the spin states.",0807.3654v1 2010-12-21,Spin dephasing and pumping in graphene due to random spin-orbit interaction,"We consider spin effects related to the random spin-orbit interaction in graphene. Such a random interaction can result from the presence of ripples and/or other inhomogeneities at the graphene surface. We show that the random spin-orbit interaction generally reduces the spin dephasing (relaxation) time, even if the interaction vanishes on average. Moreover, the random spin-orbit coupling also allows for spin manipulation with an external electric field. Due to the spin-flip interband as well as intraband optical transitions, the spin density can be effectively generated by periodic electric field in a relatively broad range of frequencies.",1012.4757v1 2015-05-11,Current-induced spin polarization and spin-orbit torque in graphene,"Using the Green function formalism we calculate a current-induced spin polarization of weakly magnetized graphene with Rashba spin-orbit interaction. In a general case, all components of the current-induced spin polarization are nonzero, contrary to the nonmagnetic limit, where the only nonvanishing component of spin polarization is that in the graphene plane and normal to electric field. When the induced spin polarization is exchange-coupled to the magnetization, it exerts a spin-orbit torque on the latter. Using the Green function method we have derived some analytical formulas for the spin polarization and also determined the corresponding spin-orbit torque components.",1505.02530v2 2012-04-25,Spin freezing by Anderson localization in one-dimensional semiconductors,"One-dimensional quantum wires are considered as prospective elements for spin transport and manipulation in spintronics. We study spin dynamics in semiconductor GaAs-like nanowires with disorder and spin-orbit interaction by using a rotation in the spin subspace gauging away the spin-orbit field. If the disorder is sufficiently strong, the spin density after a relatively short relaxation time reaches a plateau. This effect is a manifestation of the Anderson localization and depends in a universal way on the disorder and the spin-orbit coupling strength. As a result, at a given disorder, semiconductor nanowires can permit a long-term spin polarization tunable with the spin-orbit interactions.",1204.5597v1 2024-01-17,Spin Orbit Torque on a Curved Surface,"We provide a general formulation of the spin-orbit coupling on a 2D curved surface. Considering the wide applicability of spin-orbit effect in spinor-based condensed matter physics, a general spin-orbit formulation could aid the study of spintronics, Dirac graphene, topological systems, and quantum information on curved surfaces. Particular attention is then devoted to the development of an important spin-orbit quantity known as the spin-orbit torque. As devices trend smaller in dimension, the physics of local geometries on spin-orbit torque, hence spin and magnetic dynamics shall not be neglected. We derived the general expression of a spin-orbit anisotropy field for the curved surfaces and provided explicit solutions in the special contexts of the spherical, cylindrical and flat coordinates. Our expressions allow spin-orbit anisotropy fields and hence spin-orbit torque to be computed over the entire surfaces of devices of any geometry.",2401.08966v1 2014-06-10,"Weak Localization, Spin Relaxation, and Spin-Diffusion: The Crossover Between Weak and Strong Rashba Coupling Limits","Disorder scattering and spin-orbit coupling are together responsible for the diffusion and relaxation of spin-density in time-reversal invariant systems. We study spin-relaxation and diffusion in a two-dimensional electron gas with Rashba spin-orbit coupling and spin-independent disorder, focusing on the role of Rashba spin-orbit coupling in transport. Spin-orbit coupling contributes to spin relaxation, transforming the quantum interference contribution to conductivity from a negative weak localization (WL) correction to a positive weak anti-localization (WAL) correction. The importance of spin channel mixing in transport is largest in the regime where the Bloch state energy uncertainty $\hbar/\tau$ and the Rashba spin-orbit splitting $\Delta_\mathrm{SO}$ are comparable. We find that as a consequence of this spin channel mixing, the WL-WAL crossover is non-monotonic in this intermediate regime, and use our results to address recent experimental studies of transport at two-dimensional oxide interfaces.",1406.2715v2 2011-04-04,Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field,"We consider the combined effects of large spin-orbit couplings and a perpendicular magnetic field in a 2D honeycomb fermionic lattice. This system provides an elegant setup to generate versatile spin textures propagating along the edge of a sample. The spin-orbit coupling is shown to induce topological phase transitions between a helical quantum spin Hall phase and a chiral spin-imbalanced quantum Hall state. Besides, we find that the spin orientation of a single topological edge state can be tuned by a Rashba spin-orbit coupling, opening an interesting route towards quantum spin manipulation. We discuss the possible realization of our results using cold atoms trapped in optical lattices, where large synthetic magnetic fields and spin-orbit couplings can be engineered and finely tuned. In particular, this system would lead to the observation of a time-reversal-symmetry-broken quantum spin Hall phase.",1104.0643v2 2005-02-14,Orbitronics: the Intrinsic Orbital Hall Effect in p-Doped Silicon,"The spin Hall effect depends crucially on the intrinsic spin-orbit coupling of the energy band. Because of the smaller spin-orbit coupling in silicon, the spin Hall effect is expected to be much reduced. We show that the electric field in p-doped silicon can induce a dissipationless orbital current in a fashion reminiscent of the spin Hall effect. The vertex correction due to impurity scattering vanishes and the effect is therefore robust against disorder. The orbital Hall effect can lead to the accumulation of local orbital momentum at the edge of the sample, and can be detected by the Kerr effect.",0502345v1 2018-03-09,Spin-vorticity coupling in viscous electron fluids,"We consider spin-vorticity coupling - the generation of spin polarization by vorticity - in viscous two-dimensional electron systems with spin-orbit coupling. We first derive hydrodynamic equations for spin and momentum densities in which their mutual coupling is determined by the rotational viscosity. We then calculate the rotational viscosity microscopically in the limits of weak and strong spin-orbit coupling. We provide estimates that show that the spin-orbit coupling achieved in recent experiments is strong enough for the spin-vorticity coupling to be observed. On the one hand, this coupling provides a way to image viscous electron flows by imaging spin densities. On the other hand, we show that the spin polarization generated by spin-vorticity coupling in the hydrodynamic regime can, in principle, be much larger than that generated, e.g. by the spin Hall effect, in the diffusive regime.",1803.03549v1 2013-10-29,Self-Quenching of Nuclear Spin Dynamics in Central Spin Problem,"We consider, in the framework of the central spin $s=1/2$ model, driven dynamics of two electrons in a double quantum dot subject to hyperfine interaction with nuclear spins and spin-orbit coupling. The nuclear subsystem dynamically evolves in response to Landau-Zener singlet-triplet transitions of the electronic subsystem controlled by external gate voltages. Without noise and spin-orbit coupling, subsequent Landau-Zener transitions die out after about $10^4$ sweeps, the system self-quenches, and nuclear spins reach one of the numerous glassy dark states. We present an analytical model that captures this phenomenon. We also account for the multi-nuclear-specie content of the dots and numerically determine the evolution of around $10^7$ nuclear spins in up to $2\times10^5$ Landau-Zener transitions. Without spin-orbit coupling, self-quenching is robust and sets in for arbitrary ratios of the nuclear spin precession times and the waiting time between Landau-Zener sweeps as well as under moderate noise. In presence of spin-orbit coupling of a moderate magnitude, and when the waiting time is in resonance with the precession time of one of the nuclear species, the dynamical evolution of nuclear polarization results in stroboscopic screening of spin-orbit coupling. However, small deviations from the resonance or strong spin-orbit coupling destroy this screening. We suggest that the success of the feedback loop technique for building nuclear gradients is based on the effect of spin-orbit coupling.",1310.7847v1 2015-11-11,Spin Swapping Transport and Torques in Ultrathin Magnetic Bilayers,"Planar spin transport in disordered ultrathin magnetic bilayers comprising a ferromagnet and a normal metal (typically used for spin pumping, spin Seebeck and spin-orbit torque experiments) is investigated theoretically. Using a tight-binding model that treats extrinsic spin Hall effect, spin swapping and spin relaxation on equal footing, we show that the nature of spin-orbit coupled transport dramatically depends on ratio between the layers thickness $d$ and the mean free path $\lambda$. While spin Hall effect dominates in the diffusive limit ($d\gg\lambda$), spin swapping dominates in Knudsen regime ($d\lesssim\lambda$). A remarkable consequence is that the symmetry of the spin-orbit torque exerted on the ferromagnet is entirely different in these two regimes.",1511.03454v1 2007-08-20,Manipulating the spin texture in spin-orbit superlattice by terahertz radiation,"The spin texture in a gate-controlled superlattice with Rashba spin-orbit coupling is studied in the presence of external terahertz radiation causing the superlattice miniband transitions. It is shown that the local distribution of spin density can be flipped by tuning the radiation intensity, allowing the controlled coupling of spins and photons with different polarizations.",0708.2595v2 2012-01-20,Josephson dynamics of a spin-orbit coupled Bose-Einstein condensate in a double well potential,"We investigate the quantum dynamics of an experimentally realized spin-orbit coupled Bose-Einstein condensate in a double well potential. The spin-orbit coupling can significantly enhance the atomic inter-well tunneling. We find the coexistence of internal and external Josephson effects in the system, which are moreover inherently coupled in a complicated form even in the absence of interatomic interactions. Moreover, we show that the spin-dependent tunneling between two wells can induce a net atomic spin current referred as spin Josephson effects. Such novel spin Josephson effects can be observable for realistically experimental conditions.",1201.4306v1 2014-08-27,Spin-orbit Coupling and Multiple Phases in Spin-triplet Superconductor Sr$_2$RuO$_4$,"We study the spin-orbit coupling in spin-triplet Cooper pairs and clarify multiple superconducting (SC) phases in Sr$_2$RuO$_4$. Based on the analysis of the three-orbital Hubbard model with atomic LS coupling, we show some selection rules of the spin-orbit coupling in Cooper pairs. The spin-orbit coupling is small when the two-dimensional $\gamma$-band is the main cause of the superconductivity, although the LS coupling is much larger than the SC gap. Considering this case, we investigate multiple SC transitions in the magnetic fields for both H // [001] and H // [100] using the Ginzburg-Landau theory and the quasi-classical theory. Rich phase diagrams are obtained because the spin degree of freedom in Cooper pairs is not quenched by the spin-orbit coupling. Experimental indications for the multiple phases in Sr$_2$RuO$_4$ are discussed.",1408.6353v1 2009-08-20,Theory of anisotropic exchange in laterally coupled quantum dots,"The effects of spin-orbit coupling on the two-electron spectra in lateral coupled quantum dots are investigated analytically and numerically. It is demonstrated that in the absence of magnetic field the exchange interaction is practically unaffected by spin-orbit coupling, for any interdot coupling, boosting prospects for spin-based quantum computing. The anisotropic exchange appears at finite magnetic fields. A numerically accurate effective spin Hamiltonian for modeling spin-orbit-induced two-electron spin dynamics in the presence of magnetic field is proposed.",0908.2961v2 2013-10-30,Spin-orbital state induced by strong spin-orbit coupling,"To clarify a crucial role of a spin-orbit coupling in the emergence of novel spin-orbital states in $5d$-electron compounds such as Sr$_{2}$IrO$_{4}$, we investigate ground state properties of a $t_{\rm 2g}$-orbital Hubbard model on a square lattice by Lanczos diagonalization. In the absence of the spin-orbit coupling, the ground state is spin singlet. When the spin-orbit coupling is strong enough, the ground state turns into a weak ferromagnetic state. The weak ferromagnetic state is a singlet state in terms of an effective total angular momentum. Regarding the orbital state, we find the so-called complex orbital state, in which real $xy$, $yz$, and $zx$ orbital states are mixed with complex coefficients.",1310.8016v1 2015-12-05,Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling: II. RPA response functions and collective modes,"The spin and density response functions in the random phase approximation (RPA) are derived by linearizing the kinetic equation including a magnetic field, the spin-orbit coupling, and mean fields with respect to an external electric field. Different polarization functions appear describing various precession motions showing Rabi satellites due to an effective Zeeman field. The latter turns out to consist of the mean-field magnetization, the magnetic field, and the spin-orbit vector. The collective modes for charged and neutral systems are derived and a threefold splitting of the spin waves dependent on the polarization and spin-orbit coupling is shown. The dielectric function including spin-orbit coupling, polarization and magnetic fields is presented analytically for long wave lengths and in the static limit. The dynamical screening length as well as the long-wavelength dielectric function shows an instability in charge modes, which are interpreted as spin segregation and domain formation. The spin response describes a crossover from damped oscillatory behavior to exponentially damped behavior dependent on the polarization and collision frequency. The magnetic field causes ellipsoidal trajectories of the spin response to an external electric field and the spin-orbit coupling causes a rotation of the spin axes. The spin-dephasing times are extracted and discussed in dependence on the polarization, magnetic field, spin-orbit coupling and single-particle relaxation times.",1512.01661v1 2013-07-09,Multi-Orbital Superconductivity in SrTiO3 /LaAlO3 Interface and SrTiO3 Surface,"We investigate the superconductivity in two-dimensional electron systems formed in SrTiO3 nanostructures. Our the- oretical analysis is based on the three-orbital model, which takes into account t2g orbitals of Ti ions. Because of the interfacial breaking of mirror symmetry, a Rashba-type antisymmetric spin-orbit coupling arises from the cooperation of intersite and interorbital hybridyzation and atomic LS coupling. This model shows a characteristic spin texture and carrier density dependence of Rashba spin-orbit coupling through the orbital degree of freedom. Superconductivity is mainly caused by heavy quasiparticles consisting of dyz and dzx orbitals at high carrier densities. We find that the Rashba spin-orbit coupling stabilizes a quasi-one-dimensional superconducting phase caused by one of the dyz or dzx orbitals at high magnetic fields along interfaces. This quasi-one-dimensional superconducting phase is protected against para- magnetic depairing effects by the Rashba spin-orbit coupling and realizes a large upper critical field Hc2 beyond the Pauli-Clogston-Chandrasekhar limit. This finding is consistent with an extraordinarily large upper critical field observed in SrTiO3 /LaAlO3 interfaces and its carrier density dependence. The possible coexistence of superconductivity and fer- romagnetism in SrTiO3 /LaAlO3 interfaces may also be attributed to this quasi-one-dimensional superconducting phase.",1307.2363v1 2020-09-15,Spin-orbital polarization of Majorana edge states in oxides nanowires,"We investigate a paradigmatic case of topological superconductivity in a one-dimensional nanowire with $d-$orbitals and a strong interplay of spin-orbital degrees of freedom due to the competition of orbital Rashba interaction, atomic spin-orbit coupling, and structural distortions. We demonstrate that the resulting electronic structure exhibits an orbital dependent magnetic anisotropy which affects the topological phase diagram and the character of the Majorana bound states (MBSs). The inspection of the electronic component of the MBSs reveals that the spin-orbital polarization generally occurs along the direction of the applied Zeeeman magnetic field, and transverse to the magnetic and orbital Rashba fields. The competition of symmetric and antisymmetric spin-orbit coupling remarkably leads to a misalignment of the spin and orbital moments transverse to the orbital Rashba fields, whose manifestation is essentially orbital dependent. The behavior of the spin-orbital polarization along the applied Zeeman field reflects the presence of multiple Fermi points with inequivalent orbital character in the normal state. Additionally, the response to variation of the electronic parameters related with the degree of spin-orbital entanglement leads to distinctive evolution of the spin-orbital polarization of the MBSs. These findings unveil novel paths to single-out hallmarks relevant for the experimental detection of MBSs.",2009.06956v1 2021-03-30,Numerical analysis of the spin-orbit coupling parameters in III-V quantum wells using 8-band Kane model and finite-difference method,"By means the envelope function approximation, 8-band Kane model and a finite-difference scheme with the coordinate space discretization, we numerically performed calculations of the spin-orbit coupling parameters for 2D electron gas confined in both symmetric and asymmetric [0 0 1] quantum wells based on zinc-blende III-V semiconductors. Influence of the quantum well band parameters and width as well as the magnitude of the external electric field applied along the growth direction on the Dresselhaus and Rashba spin-orbit coupling parameters is investigated. It has been found that in the symmetric InGaAs/GaAs quantum wells linear-in-momentum spin-orbit coupling disappears for the third electron subband at certain values of well width and the indium content. It is also shown that in asymmetric InGaAs/GaAs structures the spin-orbit coupling parameters can be equal at a certain electric field that is the condition for the realization of the SU(2) spin symmetry and formation of persistent spin helices. Besides, we calculated the spin-orbit coupling in the persistent spin helix regime as a function of the well width, indium content and external field. The proposed approach for the calculation of the spin-orbit coupling parameters can be applied to other 2D structures with the spin-orbit coupling.",2103.16721v1 2011-02-11,Chiral spin states in polarized kagome spin systems with spin-orbit coupling,"We study quantum spin systems with a proper combination of geometric frustration, spin-orbit coupling and ferromagnetism. We argue that such a system is likely to be in a chiral spin state, a fractional quantum Hall (FQH) state for bosonic spin degrees of freedom. The energy scale of the bosonic FQH state is of the same order as the spin-orbit coupling and ferromagnetism --- overall much higher than the energy scale of FQH states in semiconductors.",1102.2406v1 2013-04-30,Can electrostatic field lift spin degeneracy?,"There are two well known mechanisms which lead to lifting of energy spin degeneracy of single electron systems - magnetic field and spin-orbit coupling. We investigate the possibility for existence of a third mechanism in which electrostatic field can lead to lifting of spin-degeneracy directly without the mediation of spin-orbit coupling. A novel argument is provided for the need of spin-orbit coupling different from the usual relativistic considerations. It is shown that due to preserved translational invariance spin splitting purely by electrostatic field is not possible for Bloch states. A possible lifting of spin degeneracy by electrostatic field characterized by broken inversion and translational invariance is considered.",1304.7968v2 2011-09-22,Intrinsic coupling of orbital excitations to spin fluctuations in Mott insulators,"We show how the general and basic asymmetry between two fundamental degrees of freedom present in strongly correlated oxides, spin and orbital, has very profound repercussions on the elementary spin and orbital excitations. Whereas the magnons remain largely unaffected, orbitons become inherently coupled with spin fluctuations in spin-orbital models with antiferromagnetic and ferroorbital ordered ground states. The composite orbiton-magnon modes that emerge fractionalize again in one dimension, giving rise to spin-orbital separation in the peculiar regime where spinons are faster than orbitons.",1109.4745v1 2012-11-05,Tailoring spin-orbit torque in diluted magnetic semiconductors,"We study the spin orbit torque arising from an intrinsic linear Dresselhaus spin-orbit coupling in a single layer III-V diluted magnetic semiconductor. We investigate the transport properties and spin torque using the linear response theory and we report here : (1) a strong correlation exists between the angular dependence of the torque and the anisotropy of the Fermi surface; (2) the spin orbit torque depends nonlinearly on the exchange coupling. Our findings suggest the possibility to tailor the spin orbit torque magnitude and angular dependence by structural design.",1211.0867v2 2015-06-02,Spin-orbit coupling rule in bound fermions systems,"Spin-orbit coupling characterizes quantum systems such as atoms, nuclei, hypernuclei, quarkonia, etc., and is essential for understanding their spectroscopic properties. Depending on the system, the effect of spin-orbit coupling on shell structure is large in nuclei, small in quarkonia, perturbative in atoms. In the standard non-relativistic reduction of the single-particle Dirac equation, we derive a universal rule for the relative magnitude of the spin-orbit effect that applies to very different quantum systems, regardless of whether the spin-orbit coupling originates from the strong or electromagnetic interaction. It is shown that in nuclei the near equality of the mass of the nucleon and the difference between the large repulsive and attractive potentials explains the fact that spin-orbit splittings are comparable to the energy spacing between major shells. For a specific ratio between the particle mass and the effective potential whose gradient determines the spin-orbit force, we predict the occurrence of giant spin-orbit energy splittings that dominate the single-particle excitation spectrum.",1506.00911v2 2006-06-07,An Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System,"Spin-orbit coupled systems generally break the spin rotation symmetry. However, for a model with equal Rashba and Dresselhauss coupling constant (the ReD model), and for the $[110]$ Dresselhauss model, a new type of SU(2) spin rotation symmetry is discovered. This symmetry is robust against spin-independent disorder and interactions, and is generated by operators whose wavevector depends on the coupling strength. It renders the spin lifetime infinite at this wavevector, giving rise to a Persistent Spin Helix (PSH). We obtain the spin fluctuation dynamics at, and away, from the symmetry point, and suggest experiments to observe the PSH.",0606196v1 2010-08-09,Gate-dependent spin-orbit coupling in multi-electron carbon nanotubes,"Understanding how the orbital motion of electrons is coupled to the spin degree of freedom in nanoscale systems is central for applications in spin-based electronics and quantum computation. We demonstrate this coupling of spin and orbit in a carbon nanotube quantum dot in the general multi-electron regime in presence of finite disorder. Further, we find a strong systematic dependence of the spin-orbit coupling on the electron occupation of the quantum dot. This dependence, which even includes a sign change is not demonstrated in any other system and follows from the curvature-induced spin-orbit split Dirac-spectrum of the underlying graphene lattice. Our findings unambiguously show that the spin-orbit coupling is a general property of nanotube quantum dots which provide a unique platform for the study of spin-orbit effects and their applications.",1008.1600v2 2006-03-23,Intense terahertz laser fields on a quantum dot with Rashba spin-orbit coupling,"We investigate the effects of the intense terahertz laser field and the spin-orbit coupling on single electron spin in a quantum dot. The laser field and the spin-orbit coupling can strongly affect the electron density of states and can excite a magnetic moment. The direction of the magnetic moment depends on the symmetries of the system, and its amplitude can be tuned by the strength and frequency of the laser field as well as the spin-orbit coupling.",0603614v2 2008-10-30,Berry Phase in a Single Quantum Dot with Spin-Orbit Interaction,"Berry phase in a single quantum dot with Rashba spin-orbit coupling is investigated theoretically. Berry phases as functions of magnetic field strength, dot size, spin-orbit coupling and photon-spin coupling constants are evaluated. It is shown that the Berry phase will alter dramatically from 0 to $2\pi$ as the magnetic field strength increases. The threshold of magnetic field depends on the dot size and the spin-orbit coupling constant.",0810.5405v1 2011-06-28,Phase separation in a polarized Fermi gas with spin-orbit coupling,"We study the phase separation of a spin polarized Fermi gas with spin-orbit coupling near a wide Feshbach resonance. As a result of the competition between spin-orbit coupling and population imbalance, the phase diagram for a uniform gas develops a rich structure of phase separation involving gapless superfluid states which are topologically non-trivial. We find that these novel gapless phases can be stabilized by intermediate spin-orbit coupling strengths. We then demonstrate the phase separation induced by an external trapping potential and discuss the optimal parameter region for the experimental observation of the gapless superfluid phases.",1106.5667v2 2013-12-09,The Pairing of Spin-orbit Coupled Fermi Gas in Optical Lattice,"We investigate Rashba spin-orbit coupled Fermi gases in square optical lattice by using the determinant quantum Monte Carlo (DQMC) simulations which is free of the sign-problem. We show that the Berezinskii-Kosterlitz-Thoules phase transition temperature is firstly enhanced and then suppressed by spin-orbit coupling in the strong attraction region. In the intermediate attraction region, spin-orbit coupling always suppresses the transition temperature. We also show that the spin susceptibility becomes anisotropic and retains finite values at zero temperature.",1312.2292v1 2020-12-27,Microwave spectroscopy of spin-orbit coupled states: energy detuning versus interdot coupling modulation,"We study the AC field induced current peaks of a spin blockaded double quantum dot with spin-orbit interaction. The AC field modulates either the interdot tunnel coupling or the energy detuning, and we choose the AC field frequency range to induce two singlet-triplet transitions giving rise to two current peaks. We show that for a large detuning the two current peaks can be significantly stronger when the AC field modulates the tunnel coupling, thus making the detection of the spin-orbit gap more efficient. We also demonstrate the importance of the time dependence of the spin-orbit interaction.",2012.13914v1 2020-10-05,Detection of the Orbital Hall Effect by the Orbital-Spin Conversion,"The intrinsic orbital Hall effect (OHE), the orbital counterpart of the spin Hall effect, was predicted and studied theoretically for more than one decade, yet to be observed in experiments. Here we propose a strategy to convert the orbital current in OHE to the spin current via the spin-orbit coupling from the contact. Furthermore, we find that OHE can induce large nonreciprocal magnetoresistance when employing magnetic contact. Both the generated spin current and the orbital Hall magnetoresistance can be applied to probe the OHE in experiments and design orbitronic devices.",2010.01970v1 2018-12-19,Manifestations of spin-orbit coupling in a cuprate superconductor,"Exciting new work on Bi2212 shows the presence of non-trivial spin-orbit coupling effects as seen in spin resolved ARPES data [Gotlieb et al., Science, 362, 1271-1275 (2018)]. Motivated by these observations we consider how the picture of spin-orbit coupling through local inversion symmetry breaking might be observed in cuprate superconductors. Furthermore, we examine two spin-orbit driven effects, the spin-Hall effect and the Edelstein effect, focusing on the details of their realizations within both the normal and superconducting states.",1812.07949v2 2014-08-08,Spin-Orbital Order Modified by Orbital Dilution in Transition Metal Oxides: From Spin Defects to Frustrated Spins Polarizing Host Orbitals,"We study the $3d$ substitution in $4d$ transition metal oxides in the cases of $3d^3$ doping at either $3d^2$ or $4d^4$ sites which realize orbital dilution. We derive the effective $3d-4d$ (or $3d-3d$) superexchange in a Mott insulator with different ionic valencies, underlining the emerging structure of the spin-orbital coupling between the impurity and the host sites and demonstrate that it is qualitatively different from that encountered in the host itself. This derivation shows that the interaction between the host and the impurity depends in a crucial way on the type of doubly occupied $t_{2g}$ orbital. One finds that in some cases, due to the quench of the orbital degree of freedom at the $3d$ impurity, the spin and orbital order within the host is drastically modified by doping. The impurity acts either as a spin defect accompanied by an orbital vacancy in the spin-orbital structure when the host-impurity coupling is weak, or it favors doubly occupied active orbitals (orbital polarons) along the $3d-4d$ bond leading to antiferromagnetic or ferromagnetic spin coupling. This competition between different magnetic couplings leads to quite different ground states. We find that magnetic frustration and spin degeneracy can be lifted by the quantum orbital flips of the host but they are robust in special regions of the incommensurate phase diagram. The spin-orbit coupling can lead to anisotropic spin and orbital patterns along the symmetry directions and cause a radical modification of the order imposed by the spin-orbital superexchange. Our findings are expected to be of importance for future theoretical understanding of experimental results for doped $4d$ transition metal oxides doped with $3d^3$ ions. We suggest how the local or global changes of the spin-orbital order induced by such impurities could be detected experimentally.",1408.1838v3 2014-04-21,Graphene with wedge disclination in the presence of intrinsic and Rashba spin orbit couplings,"In this article, the modified Kane-Mele Hamiltonian is derived for graphene with wedge disclination and spin orbit couplings (intrinsic and Rashba). The wedge disclination changes the flat lattice into the conical lattice and hence modifies the spin orbit couplings. The Hamiltonian is exactly solved for the intrinsic spin orbit interaction and perturbatively for the Rashba spin orbit interaction. It is shown that there exists the Kramer's degenerate midgap localized spin separated fluxon states around the defect. These zero energy spin separated states occur at the external magnetic flux value $\Phi\pm\Delta\Phi$. The external magnetic flux $\Phi$ is introduced to make the wave-function periodic when the electron circulates around the defect. It is found that this separation occurs due to the effect of the conical curvature on the spin orbit coupling. Further, we find these results are robust to the addition of the Rashba spin orbit interaction which is important for the application to spintronics and nanoelectronics.",1404.5150v2 2004-08-18,Hole dynamics in spin and orbital ordered vanadium perovskites,"Hole dynamics in spin and orbital ordered vanadates with perovskite structure is investigated. A mobile hole coupled to the spin excitation (magnon) in the spin G-type and orbital C-type (SG/OC) ordered phase, and that to the orbital excitation (orbiton) in the spin C-type and orbital G-type (SC/OG) one are formulated on an equal footing. The observed fragile character of the (SG/OC) order is attributed to the orbiton softening caused by a reduction of the taggered magnetic order parameter. It is proposed that the qualitatively different hole dynamics in the two spin-orbital ordered phases in vanadates can be probed by the optical spectra.",0408395v1 2020-02-05,Correlated motion of particle-hole excitations across the renormalized spin-orbit gap in $\rm Sr_2 Ir O_4$,"The high-energy collective modes of particle-hole excitations across the spin-orbit gap in $\rm Sr_2IrO_4$ are investigated using the transformed Coulomb interaction terms in the pseudo-spin-orbital basis constituted by the $J=1/2$ and $3/2$ states arising from spin-orbit coupling. With appropriate interaction strengths and renormalized spin-orbit gap, these collective modes yield two well-defined propagating spin-orbit exciton modes, with energy scale and dispersion in excellent agreement with resonant inelastic X-ray scattering (RIXS) measurements.",2002.02415v1 2006-11-06,Spin relaxation in a generic two-dimensional spin-orbit coupled system,"We study the relaxation of a spin density injected into a two-dimensional electron system with generic spin-orbit interactions. Our model includes the Rashba as well as linear and cubic Dresselhaus terms. We explicitly derive a general spin-charge coupled diffusion equation. Spin diffusion is characterized by just two independent dimensionless parameters which control the interplay between different spin-orbit couplings. The real-time representation of the diffuson matrix (Green's function of the diffusion equation) is evaluated analytically. The diffuson describes space-time dynamics of the injected spin distribution. We explicitly study two regimes: The first regime corresponds to negligible spin-charge coupling and is characterized by standard charge diffusion decoupled from the spin dynamics. It is shown that there exist several qualitatively different dynamic behaviors of the spin density, which correspond to various domains in the spin-orbit coupling parameter space. We discuss in detail a few interesting phenomena such as an enhancement of the spin relaxation times, real space oscillatory dynamics, and anisotropic transport. In the second regime, we include the effects of spin-charge coupling. It is shown that the spin-charge coupling leads to an enhancement of the effective charge diffusion coefficient. We also find that in the case of strong spin-charge coupling, the relaxation rates formally become complex and the spin/charge dynamics is characterized by real time oscillations. These effects are qualitatively similar to those observed in spin-grating experiments [Weber et al., Nature 437, 1330 (2005)].",0611165v1 2011-10-06,Spin and pseudospin symmetry along with orbital dependency of the Dirac-Hulthen problem,"The role of the Hulthen potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the Dirac equation with attractive scalar S(r) and repulsive vector V(r) potentials. The spin and pseudospin symmetry along with orbital dependency (pseudospin-orbit and spin-orbit dependent couplings) of the Dirac equation are included to the solution by introducing the Hulthen-square approximation. This effective approach is based on forming the spin and pseudo-centrifugal kinetic energy term from the square of the Hulthen potential. The analytical solutions of the Dirac equation for the Hulthen potential with the spin-orbit and pseudospin-orbit-dependent couplings are obtained by using the Nikiforov-Uvarov (NU) method. The energy eigenvalue equations and wave functions for various degenerate states are presented for several spin-orbital, pseudospin-orbital and radial quantum numbers under the condition of the spin and pseudospin symmetry. Keywords: Spin and pseudospin symmetry; orbital dependency; Dirac equation; Hulthen potential; Nikiforov-Uvarov Method.",1110.1225v1 2013-11-07,Spin-Orbit Torques and Anisotropic Magnetization Damping in Skyrmion Crystals,"The length scale of the magnetization gradients in chiral magnets is determined by the relativistic Dzyaloshinskii-Moriya interaction. Thus, even conventional spin-transfer torques are controlled by the relativistic spin-orbit coupling in these systems, and additional relativistic corrections to the current-induced torques and magnetization damping become important for a complete understanding of the current-driven magnetization dynamics. We theoretically study the effects of reactive and dissipative homogeneous spin-orbit torques and anisotropic damping on the current-driven skyrmion dynamics in cubic chiral magnets. Our results demonstrate that spin-orbit torques play a significant role in the current-induced skyrmion velocity. The dissipative spin-orbit torque generates a relativistic Magnus force on the skyrmions, whereas the reactive spin-orbit torque yields a correction to both the drift velocity along the current direction and the transverse velocity associated with the Magnus force. The spin-orbit torque corrections to the velocity scale linearly with the skyrmion size, which is inversely proportional to the spin-orbit coupling. Consequently, the reactive spin-orbit torque correction can be the same order of magnitude as the non-relativistic contribution. More importantly, the dissipative spin-orbit torque can be the dominant force that causes a deflected motion of the skyrmions if the torque exhibits a linear or quadratic relationship with the spin-orbit coupling. In addition, we demonstrate that the skyrmion velocity is determined by anisotropic magnetization damping parameters governed by the skyrmion size.",1311.1778v1 2016-02-15,Effects of Dephasing on Spin Lifetime in Ballistic Spin-Orbit Materials,"We theoretically investigate spin dynamics in spin-orbit-coupled materials. In the ballistic limit, the spin lifetime is dictated by dephasing that arises from energy broadening plus a non-uniform spin precession. For the case of clean graphene, we find a strong anisotropy with spin lifetimes that can be short even for modest energy scales, on the order of a few ns. These results offer deeper insight into the nature of spin dynamics in graphene, and are also applicable to the investigation of other systems where spin-orbit coupling plays an important role.",1602.04611v1 2018-12-20,Non-local Spin-charge Conversion via Rashba Spin-Orbit Interaction,"We show theoretically that conversion between spin and charge by spin-orbit interaction in metals occurs even in a non-local setup where magnetization and spin-orbit interaction are spatially separated if electron diffusion is taken into account. Calculation is carried out for the Rashba spin-orbit interaction treating the coupling with a ferromagnet perturbatively. The results indicate the validity of the concept of effective spin gauge field (spin motive force) in the non-local configuration. The inverse Rashba-Edelstein effect observed for a trilayer of a ferromagnet, a normal metal and a heavy metal can be explained in terms of the non-local effective spin gauge field.",1812.08884v1 2003-09-24,Orbital Wave and its Observation in Orbital Ordered Titanates and Vanadates,"We present a theory of the collective orbital excitation termed orbital wave in perovskite titanates and vanadates with the triply degenerate $t_{2g}$ orbitals. The dispersion relations of the orbital waves for the orbital ordered LaVO$_3$, YVO$_3$ and YTiO$_3$ are examined in the effective spin-orbital coupled Hamiltonians associated with the Jahn-Teller type couplings. We propose possible scattering processes for the Raman and inelastic neutron scatterings from the orbital wave and calculate the scattering spectra for titanates and vanadates. It is found that both the excitation spectra and the observation methods of the orbital wave are distinct qualitatively from those for the $e_g$ orbital ordered systems.",0309538v2 2013-12-31,Anisotropic exchange coupling in a nanowire double quantum dot with strong spin-orbit coupling,"A spin-orbit qubit is a hybrid qubit that contains both orbital and spin degrees of freedom of an electron in a quantum dot. Here we study the exchange coupling between two spin-orbit qubits in a nanowire double quantum dot (DQD) with strong spin-orbit coupling (SOC). We find that while the total tunneling in the DQD is irrelevant to the SOC, both the spin-conserved and spin-flipped tunnelings are SOC dependent and can compete with each other in the strong SOC regime. Moreover, the Coulomb repulsion between electrons can combine with the SOC-dependent tunnelings to yield an anisotropic exchange coupling between the two spin-orbit qubits. Also, we give an explicit physical mechanism for this anisotropic exchange coupling.",1401.0101v2 2023-11-15,Chirality-induced emergent spin-orbit coupling in topological atomic lattices,"Spin-orbit coupled dynamics are of fundamental interest in both quantum optical and condensed matter systems alike. In this work, we show that photonic excitations in pseudospin-1/2 atomic lattices exhibit an emergent spin-orbit coupling when the geometry is chiral. This spin-orbit coupling arises naturally from the electric dipole interaction between the lattice sites and leads to spin polarized excitation transport. Using a general quantum optical model, we determine analytically the conditions that give rise to spin-orbit coupling and characterize the behavior under various symmetry transformations. We show that chirality-induced spin textures are associated with a topologically nontrivial Zak phase that characterizes the chiral setup. Our results demonstrate that chiral atom arrays are a robust platform for realizing spin-orbit coupled topological states of matter.",2311.09303v1 2012-05-15,Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas,"The coupling of the spin of electrons to their motional state lies at the heart of recently discovered topological phases of matter. Here we create and detect spin-orbit coupling in an atomic Fermi gas, a highly controllable form of quantum degenerate matter. We reveal the spin-orbit gap via spin-injection spectroscopy, which characterizes the energy-momentum dispersion and spin composition of the quantum states. For energies within the spin-orbit gap, the system acts as a spin diode. To fully inhibit transport, we open an additional spin gap, thereby creating a spin-orbit coupled lattice whose spinful band structure we probe. In the presence of s-wave interactions, such systems should display induced p-wave pairing, topological superfluidity, and Majorana edge states.",1205.3483v1 1998-12-02,Theory of Orbital Excitation and Resonant Inelastic X-ray Scattering in Manganites,"We study theoretically the collective orbital excitation named orbital wave in the orbital ordered manganites.The dispersion relation of the orbital wave is affected by the static spin structure through the coupling between spin and orbital degrees of freedom. As a probe to detect the dispersion relation, we propose two possible methods by utilizing resonant inelastic x-ray scattering. The transition probability of the orbital wave scattering is formulated, and the momentum and polarization dependences of the structure factor are calculated in several types of the orbital and spin structures. The elastic x-ray scattering in the L-edge case to observe the orbital ordering is also discussed.",9812028v1 2016-04-29,Tunable spin-charge conversion through topological phase transitions in zigzag nanoribbons,"We study spin-orbit torques and charge pumping in magnetic quasi-one dimensional zigzag nanoribbons with hexagonal lattice, in the presence of large intrinsic spin-orbit coupling. Such a system experiences topological phase transition from a trivial band insulator to a quantum spin Hall insulator either by tuning the magnetization direction or the intrinsic spin-orbit coupling. We find that spin-charge conversion efficiency (i.e. spin-orbit torque and charge pumping) is dramatically enhanced at the topological transition, displaying a substantial angular anisotropy.",1604.08782v1 2014-02-24,Low-Energy Effective Hamiltonian for Giant-Gap Quantum Spin Hall Insulators in Honeycomb X-Hydride/Halide (X=N-Bi) Monolayers,"Using the tight-binding method in combination with first-principles calculations, we systematically derive a low-energy effective Hilbert subspace and Hamiltonian with spin-orbit coupling for two-dimensional hydrogenated and halogenated group-V monolayers. These materials are proposed to be giant-gap quantum spin Hall insulators with record huge bulk band gaps opened by the spin-orbit coupling at the Dirac points, e.g., from 0.74 to 1.08 eV in Bi\textit{X} (\textit{X} = H, F, Cl, and Br) monolayers. We find that the low-energy Hilbert subspace mainly consists of $p_{x}$ and $p_{y}$ orbitals from the group-V elements, and the giant first-order effective intrinsic spin-orbit coupling is from the on-site spin-orbit interaction. These features are quite distinct from those of group-IV monolayers such as graphene and silicene. There, the relevant orbital is $p_z$ and the effective intrinsic spin-orbit coupling is from the next-nearest-neighbor spin-orbit interaction processes. These systems represent the first real 2D honeycomb lattice materials in which the low-energy physics is associated with $p_{x}$ and $p_{y}$ orbitals. A spinful lattice Hamiltonian with an on-site spin-orbit coupling term is also derived, which could facilitate further investigations of these intriguing topological materials.",1402.5817v2 2002-08-27,Conductance of a quantum point contact in the presence of spin-orbit interaction,"A recursive Green's function technique is developed to calculate the spin-dependent conductance in mesoscopic structures. Using this technique, we study the spin-dependent electronic transport of quantum point contacts in the presence of the Rashba spin-orbit interaction. We observed that some oscillations in the `quantized' conductance are induced by the spin-orbit interaction, and indicated that the oscillations may stem from the spin-orbit coupling associated multiple reflections. It is also indicated that the 0.7 structure of the conductance observed in mesoscopic experiments would not stem from the spin-orbit interaction.",0208506v1 2022-01-27,Superfluid transition temperature and fluctuation theory of spin-orbit and Rabi-coupled fermions with tunable interactions,"We obtain the superfluid transition temperature of equal Rashba-Dresselhaus spin-orbit and Rabi-coupled Fermi superfluids, from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) regimes in three dimensions for tunable $s$-wave interactions. In the presence of Rabi coupling, we find that spin-orbit coupling enhances (reduces) the critical temperature in the BEC (BCS) limit. For fixed interactions, we show that spin-orbit coupling can convert a first-order (discontinuous) phase transition into a second-order (continuous) phase transition, as a function of Rabi coupling. We derive the Ginzburg-Landau free energy to sixth power in the superfluid order parameter to describe both continuous and discontinuous phase transitions as a function of spin-orbit and Rabi couplings. Lastly, we develop a time-dependent Ginzburg-Landau fluctuation theory for an arbitrary mixture of Rashba and Dresselhaus spin-orbit couplings at any interaction strength.",2201.11823v2 2009-05-12,Pauli Spin Blockade in the Presence of Strong Spin-Orbit Coupling,"We study electron transport in a double quantum dot in the Pauli spin blockade regime, in the presence of strong spin-orbit coupling. The effect of spin-orbit coupling is incorporated into a modified interdot tunnel coupling. We elucidate the role of the external magnetic field, the nuclear fields in the dots, and spin relaxation. We find qualitative agreement with experimental observations, and we propose a way to extend the range of magnetic fields in which blockade can be observed.",0905.1818v1 2012-09-21,Adiabatic pumping through an interacting quantum dot with spin-orbit coupling,"We study adiabatic pumping through a two-level quantum dot with spin-orbit coupling. Using a diagrammatic real-time approach, we calculate both the pumped charge and spin for a periodic variation of the dot's energy levels in the limit of weak tunnel coupling. Thereby, we compare the two limits of vanishing and infinitely large charging energy on the quantum dot. We discuss the dependence of the pumped charge and pumped spin on gate voltages, the symmetry in the tunnel-matrix elements and spin-orbit coupling strength. We identify the possibility to generate pure spin currents in the absence of charge currents.",1209.4770v2 2017-07-14,Insights into the orbital magnetism of noncollinear magnetic systems,"The orbital magnetic moment is usually associated with the relativistic spin-orbit interaction, but recently it has been shown that noncollinear magnetic structures can also be its driving force. This is important not only for magnetic skyrmions, but also for other noncollinear structures, either bulk-like or at the nanoscale, with consequences regarding their experimental detection. In this work we present a minimal model that contains the effects of both the relativistic spin-orbit interaction and of magnetic noncollinearity on the orbital magnetism. A hierarchy of models is discussed in a step-by-step fashion, highlighting the role of time-reversal symmetry breaking for translational and spin and orbital angular motions. Couplings of spin-orbit and orbit-orbit type are identified as arising from the magnetic noncollinearity. We recover the atomic contribution to the orbital magnetic moment, and a nonlocal one due to the presence of circulating bound currents, exploring different balances between the kinetic energy, the spin exchange interaction, and the relativistic spin-orbit interaction. The connection to the scalar spin chirality is examined. The orbital magnetism driven by magnetic noncollinearity is mostly unexplored, and the presented model contributes to laying its groundwork.",1707.04518v1 2023-11-22,Effects of magnetic fields and orbital angular momentum on excitonic condensation in two-orbital Hubbard model,"We investigate the magnetic-field effects on a two-orbital Hubbard model that describes multiple spin states. Cobalt oxides have been investigated as materials possessing spin-state degrees of freedom due to the interplay between the Hund coupling interaction and crystalline field effect. In the competing region, quantum hybridizations between distinct spin states are expected to emerge, corresponding to excitonic condensation. Applied magnetic fields could also induce such a competition. To understand magnetic-field effects on excitonic condensation in multi-orbital systems, it is crucial to account for contributions from both spin and orbital degrees of freedom to magnetic properties. Here, we study field-induced phenomena in the two-orbital Hubbard model by focusing on the role of the orbital angular momentum. We comprehensively analyze this model on a square lattice employing the Hartree-Fock approximation. Omitting contributions from the orbital moment, we find that an applied magnetic field gives rise to two excitonic phases, besides the spin-state ordered phase, between the nonmagnetic low-spin and spin-polarized high-spin phases. One of these excitonic phases manifests a staggered-type spin-state order, interpreted as an excitonic supersolid state. Conversely, the other phase is not accompanied by it and exhibits only a spin polarization due to the applied magnetic field. When spin-orbit coupling is present, this phase displays a ferrimagnetic spin alignment attributed to spin anisotropy. Our analysis also reveals that incorporating the contribution of the orbital magnetic moment to the Zeeman term significantly alters the overall structure of the phase diagram. Notably, the orbital magnetization destabilizes the excitonic phase in contrast to scenarios without this contribution. We also discuss the relevance of our findings to real materials, such as cobalt oxides.",2311.13191v1 2016-06-27,Supercurrent-Induced Spin-Orbit Torques,"We theoretically investigate the supercurrent-induced magnetization dynamics of a two-dimensional lattice of ferromagnetically ordered spins placed on a conventional superconductor with broken spatial inversion symmetry and strong spin-orbit coupling. We develop a phenomenological description of the coupled dynamics of the superconducting condensate and the spin system, and demonstrate that supercurrents produce a reactive spin-orbit torque on the magnetization. By performing a microscopic self-consistent calculation, we show that the spin-orbit torque originates from a spin-polarization of the Cooper pairs due to current-induced spin-triplet correlations. Interestingly, we find that there exists an intrinsic limitation for the maximum achievable spin-orbit torque, which is determined by the coupling strength between the condensate and the spin system. In proximitized hole-doped semiconductors, the maximum achievable spin-orbit torque field is estimated to be on the order of $0.16$ mT, which is comparable to the critical field for current-induced magnetization switching in ferromagnetic semiconductors.",1606.08470v1 2005-08-02,Spin Accumulation in the Extrinsic Spin Hall Effect,"The drift-diffusion formalism for spin-polarized carrier transport in semiconductors is generalized to include spin-orbit coupling. The theory is applied to treat the extrinsic spin Hall effect using realistic boundary conditions. It is shown that carrier and spin diffusion lengths are modified by the presence of spin-orbit coupling and that spin accumulation due to the extrinsic spin Hall effect is strongly and qualitatively influenced by boundary conditions. Analytical formulas for the spin-dependent carrier recombination rates and inhomogeneous spin densities and currents are presented.",0508076v1 2021-08-13,Coupling the Higgs mode and ferromagnetic resonance in spin-split superconductors with Rashba spin-orbit coupling,"We consider the Higgs mode at nonzero momentum in superconductors and demonstrate that in the presence of Rashba spin-orbit coupling, it couples linearly with an external exchange field. The Higgs-spin coupling dramatically modifies the spin susceptibility near the superconducting critical temperature and consequently enhances the spin pumping effect in a ferromagnetic insulator/superconductor bilayer system. We show that this effect can be detected by measuring the magnon-induced voltage generated by the inverse spin Hall effect.",2108.06202v2 2020-06-03,"Magnetic reorientation transition in a three orbital model for $\rm Ca_2 Ru O_4$ -- Interplay of spin-orbit coupling, tetragonal distortion, and Coulomb interactions","Including the orbital off-diagonal spin and charge condensates in the self consistent determination of magnetic order within a realistic three-orbital model for the $4d^4$ compound $\rm Ca_2 Ru O_4$, reveals a host of novel features including strong and anisotropic spin-orbit coupling (SOC) renormalization, coupling of strong orbital magnetic moments to orbital fields, and a magnetic reorientation transition. Highlighting the rich interplay between orbital geometry and overlap, spin-orbit coupling, Coulomb interactions, tetragonal distortion, and staggered octahedral tilting and rotation, our investigation yields a planar antiferromagnetic (AFM) order for moderate tetragonal distortion, with easy $a-b$ plane and easy $b$ axis anisotropies, along with small canting of the dominantly $yz,xz$ orbital moments. With decreasing tetragonal distortion, we find a magnetic reorientation transition from the dominantly planar AFM order to a dominantly $c$ axis ferromagnetic (FM) order with significant $xy$ orbital moment.",2006.02114v2 2019-12-11,Selective tuning of spin-orbital Kondo contributions in parallel-coupled quantum dots,"We use co-tunneling spectroscopy to investigate spin-, orbital-, and spin-orbital Kondo transport in a strongly confined system of InAs double quantum dots (QDs) parallel-coupled to source and drain. In the one-electron transport regime, the higher symmetry spin-orbital Kondo effect manifests at orbital degeneracy and no external magnetic field. We then proceed to show that the individual Kondo contributions can be isolated and studied separately; either by orbital detuning in the case of spin-Kondo transport, or by spin splitting in the case of orbital Kondo transport. By varying the inter-dot tunnel coupling, we show that lifting of the spin degeneracy is key to confirming the presence of an orbital degeneracy, and to detecting a small orbital hybridization gap. Finally, in the two-electron regime, we show that the presence of a spin-triplet ground state results in spin-Kondo transport at zero magnetic field.",1912.05181v2 2018-01-25,Spin-relaxation anisotropy in a nanowire quantum dot with strong spin-orbit coupling,"We study the impacts of the magnetic field direction on the spin-manipulation and the spin-relaxation in a one-dimensional quantum dot with strong spin-orbit coupling. The energy spectrum and the corresponding eigenfunctions in the quantum dot are obtained exactly. We find that no matter how large the spin-orbit coupling is, the electric-dipole spin transition rate as a function of the magnetic field direction always has a $\pi$ periodicity. However, the phonon-induced spin relaxation rate as a function of the magnetic field direction has a $\pi$ periodicity only in the weak spin-orbit coupling regime, and the periodicity is prolonged to $2\pi$ in the strong spin-orbit coupling regime.",1801.08349v2 2012-05-10,"3D quaternionic condensations, Hopf invariants, and skyrmion lattices with synthetic spin-orbit coupling","We study the topological configurations of the two-component condensates of bosons with the $3$D $\vec{\sigma}\cdot \vec{p}$ Weyl-type spin-orbit coupling subject to a harmonic trapping potential. The topology of the condensate wavefunctions manifests in the quaternionic representation. In comparison to the $U(1)$ complex phase, the quaternionic phase manifold is $S^3$ and the spin orientations form the $S^2$ Bloch sphere through the 1st Hopf mapping. The spatial distributions of the quaternionic phases exhibit the 3D skyrmion configurations, and the spin distributions possess non-trivial Hopf invariants. Spin textures evolve from the concentric distributions at the weak spin-orbit coupling regime to the rotation symmetry breaking patterns at the intermediate spin-orbit coupling regime. In the strong spin-orbit coupling regime, the single-particle spectra exhibit the Landau-level type quantization. In this regime, the three-dimensional skyrmion lattice structures are formed when interactions are below the energy scale of Landau level mixings. Sufficiently strong interactions can change condensates into spin-polarized plane-wave states, or, superpositions of two plane-waves exhibiting helical spin spirals.",1205.2162v3 2013-01-21,Spin-orbit-induced bound state and molecular signature of the degenerate Fermi gas in a narrow Feshbach resonance,"In this paper we explore the spin-orbit-induced bound state and molecular signature of the degenerate Fermi gas in a narrow Feshbach resonance based on a generalized two-channel model. Without the atom-atom interactions, only one bound state can be found even if spin-orbit coupling exists. Moreover, the corresponding bound-state energy depends strongly on the strength of spin-orbit coupling, but is influenced slightly by its type. In addition, we find that when increasing the strength of spin-orbit coupling, the critical point at which the molecular fraction vanishes shifts from zero to the negative detuning. In the weak spin-orbit coupling, this shifting is proportional to the square of its strength. Finally, we also show that the molecular fraction can be well controlled by spin-orbit coupling.",1301.4718v2 2015-12-08,Multi-orbital quantum antiferromagnetism in iron pnictides --- effective spin couplings and quantum corrections to sublattice magnetization,"Towards understanding the multi-orbital quantum antiferromagnetism in iron pnictides, effective spin couplings and spin fluctuation induced quantum corrections to sublattice magnetization are obtained in the $(\pi,0)$ AF state of a realistic three band interacting electron model involving $xz$, $yz$, and $xy$ Fe 3d orbitals. The $xy$ orbital is found to be mainly responsible for the generation of strong ferromagnetic spin coupling in the $b$ direction, which is critically important to fully account for the spin wave dispersion as measured in inelastic neutron scattering experiments. The ferromagnetic spin coupling is strongly suppressed as the $xy$ band approaches half filling, and is ascribed to particle-hole exchange in the partially filled $xy$ band. The strongest AF spin coupling in the $a$ direction is found to be in the orbital off diagonal sector involving the $xz$ and $xy$ orbitals. First order quantum corrections to sublattice magnetization are evaluated for the three orbitals, and yield a significant $37\%$ average reduction from the Hartree-Fock value.",1512.02398v1 2003-10-01,Rashba coupling in quantum dots: exact solution,"We present an analytic solution to the problem of the Rashba spin-orbit coupling in semiconductor quantum dots. We calculate the exact energy spectrum, wave-functions, and spin--flip relaxation times. We discuss various effects inaccessible via perturbation theory. In particular, we find that the effective gyromagnetic ratio is strongly suppressed by the spin-orbit coupling. The spin-flip relaxation rate has a maximum as a function of the spin-orbit coupling and is therefore suppressed in both the weak- and strong coupling limits.",0310024v2 2003-05-30,Mesoscopic effects in adiabatic spin pumping,"We show that temporal shape modulations (pumping) of a quantum dot in the presence of spin-orbital coupling lead to a finite dc spin current. Depending on the strength of the spin-orbit coupling, the spin current is polarized perpendicular to the plane of the two-dimensional electron gas, or has an arbitrary direction subject to mesoscopic fluctuations. We analyze the statistics of the spin and charge currents in the adiabatic limit for the full cross-over from weak to strong spin-orbit coupling.",0306001v2 2003-10-06,Spin Current in Spin-Orbit Coupling Systems,"We present a simple and pedagogical derivation of the spin current as the linear response to an external electric field for both Rashba and Luttinger spin-orbital coupling Hamiltonians. Except for the adiabatic approximation, our derivation is exact to the linear order of the electric field for both models. The spin current is a direct result of the difference in occupation levels between different bands. Moreover, we show a general topological spin current can be defined for a broad class of spin-orbit coupling systems.",0310093v2 2006-04-21,Dissipationless spin-current between Heisenberg ferromagnets with spin-orbit coupling,"A system exhibiting multiple simultaneously broken symmetries offers the opportunity to influence physical phenomena such as tunneling currents by means of external control parameters. Time-reversal symmetry and inversion symmetry are both absent in ferromagnetic metals with substantial spin-orbit coupling. We here study transport of spin in a system consisting of two ferromagnets with spin-orbit coupling separated by an insulating tunneling junction. A persistent spin-current across the junction is found, which can be controlled in a well-defined manner by external magnetic and electric fields. The behavior of the spin-current for important geometries and limits is studied.",0604510v1 2007-08-27,Diffusive-Ballistic Crossover and the Persistent Spin Helix,"Conventional transport theory focuses on either the diffusive or ballistic regimes and neglects the crossover region between the two. In the presence of spin-orbit coupling, the transport equations are known only in the diffusive regime, where the spin precession angle is small. In this paper, we develop a semiclassical theory of transport valid throughout the diffusive - ballistic crossover of a special SU(2) symmetric spin-orbit coupled system. The theory is also valid in the physically interesting regime where the spin precession angle is large. We obtain exact expressions for the density and spin structure factors in both 2 and 3 dimensional samples with spin-orbit coupling.",0708.3618v1 2014-03-17,Single-parameter spin-pumping in driven metallic rings with spin-orbit coupling,"We consider the generation of a pure spin-current at zero bias voltage with a single time-dependent potential. To such end we study a device made of a mesoscopic ring connected to electrodes and clarify the interplay between a magnetic flux, spin-orbit coupling and non-adiabatic driving in the production of a spin and electrical current. By using Floquet theory, we show that the generated spin to charge current ratio can be controlled by tuning the spin-orbit coupling.",1403.4265v1 2005-03-07,Topological Orbital Angular Momentum Hall Current,"We show that there is a fundamental difference between spin Hall current and orbital angular momentum Hall current in Rashba- Dresselhaus spin orbit coupling systems. The orbital angular momentum Hall current has a pure topological contribution which is originated from the existence of magnetic flux in momentum space while there is no such topological nature for the spin Hall current. Moreover, we show that the orbital Hall conductance is always larger than the spin Hall conductance in the presence of both couplings. The topological part is expected to be free from the effect of disorder due to the topological nature. Therefore, the orbital angular momentum Hall current should be the major effect in real experiments.",0503149v2 2016-07-19,Emergent spin-valley-orbital physics by spontaneous parity breaking,"The spin-orbit coupling in the absence of spatial inversion symmetry plays an important role in realizing intriguing electronic states in solids, such as topological insulators and unconventional superconductivity. Usually, the inversion symmetry breaking is inherent in the lattice structures, and hence, it is not easy to control these interesting properties by external parameters. We here theoretically investigate the possibility of generating the spin-orbital entanglement by spontaneous electronic ordering caused by electron correlations. In particular, we focus on the centrosymmetric lattices with local asymmetry at the lattice sites, e.g., zig-zag, honeycomb, and diamond structures. In such systems, conventional staggered orders, such as charge order and antiferromagnetic order, break the inversion symmetry and activate the antisymmetric spin-orbit coupling, which is hidden in a sublattice-dependent form in the paramagnetic state. Considering a minimal two-orbital model on a honeycomb lattice, we scrutinize the explicit form of the antisymmetric spin-orbit coupling for all the possible staggered charge, spin, orbital, and spin-orbital orders. We show that the complete table is useful for understanding of spin-valley-orbital physics, such as spin and valley splitting in the electronic band structure and generalized magnetoelectric responses in not only spin but also orbital and spin-orbital channels, reflecting in peculiar magnetic, elastic, and optical properties in solids.",1607.05782v1 2022-07-21,"Spin-orbit transitions in the N$^+$($^3P_{J_A}$) + H$_2$ $\rightarrow$ NH$^+$($X^2Π$, $^4Σ^-$)+ H($^2S$) reaction, using adiabatic and mixed quantum-adiabatic statistical approaches","The cross section and rate constants for the title reaction are calculated for all the spin-orbit states of N$^+$($^3P_{J_A}$) using two statistical approaches, one purely adiabatic and the other one mixing quantum capture for the entrance channel and adiabatic treatment for the products channel. This is made by using a symmetry adapted basis set combining electronic (spin and orbital) and nuclear angular momenta in the reactants channel. To this aim, accurate {\it ab initio} calculations are performed separately for reactants and products. In the reactants channel, the three lowest electronic states (without spin-orbit couplings) have been diabatized, and the spin-orbit couplings have been introduced through a model localizing the spin-orbit interactions in the N$^+$ atom, which yields accurate results as compared to {\it ab initio} calculations including spin-orbit couplings. For the products, eleven purely adiabatic spin-orbit states have been determined with {\it ab initio} calculations. The reactive rate constants thus obtained are in very good agreement with the available experimental data for several ortho-H$_2$ fractions, assuming a thermal initial distribution of spin-orbit states. The rate constants for selected spin-orbit $J_A$ states are obtained, to provide a proper validation of the spin-orbit effects to obtain the experimental rate constants.",2207.10360v1 2016-01-28,Interfacial spin-orbit torque without bulk spin-orbit coupling,"An electric current in the presence of spin-orbit coupling can generate a spin accumulation that exerts torques on a nearby magnetization. We demonstrate that, even in the absence of materials with strong bulk spin-orbit coupling, a torque can arise solely due to interfacial spin-orbit coupling, namely Rashba-Eldestein effects at metal/insulator interfaces. In magnetically soft NiFe sandwiched between a weak spin-orbit metal (Ti) and insulator (Al$_2$O$_3$), this torque appears as an effective field, which is significantly larger than the Oersted field and sensitive to insertion of an additional layer between NiFe and Al$_2$O$_3$. Our findings point to new routes for tuning spin-orbit torques by engineering interfacial electric dipoles.",1601.07687v2 2023-06-05,Accurate and efficient treatment of spin-orbit coupling via second variation employing local orbitals,"A new method is presented that allows for efficient evaluation of spin-orbit coupling (SOC) in density-functional theory calculations. In the so-called second-variational scheme, where Kohn-Sham functions obtained in a scalar-relativistic calculation are employed as a new basis for the spin-orbit-coupled problem, we introduce a rich set of local orbitals as additional basis functions. Also relativistic local orbitals can be used. The method is implemented in the all-electron full-potential code \exciting. We show that, for materials with strong SOC effects, this approach can reduce the overall basis-set size and thus computational costs tremendously.",2306.02965v1 2011-06-26,Intrinsic spin-orbit coupling in superconducting δ-doped SrTiO3 heterostructures,"We report the violation of the Pauli limit due to intrinsic spin-orbit coupling in SrTiO3 heterostructures. Via selective doping down to a few nanometers, a two-dimensional superconductor is formed, geometrically suppressing orbital pair-breaking. The spin-orbit scattering is exposed by the robust in-plane superconducting upper critical field, exceeding the Pauli limit by a factor of 4. Transport scattering times several orders of magnitude higher than for conventional thin film superconductors enables a new regime to be entered, where spin-orbit coupling effects arise non-perturbatively.",1106.5193v1 2020-01-23,Bright solitons in a spin-tensor-momentum-coupled Bose-Einstein condensate,"Synthetic spin-tensor-momentum coupling has recently been proposed to realize in atomic Bose-Einstein condensates. Here we study bright solitons in Bose-Einstein condensates with spin-tensor-momentum coupling and spin-orbit coupling. The properties and dynamics of spin-tensor-momentum-coupled and spin-orbit-coupled bright solitons are identified to be different. We contribute the difference to the different symmetries.",2001.08794v1 2022-01-17,Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing,"An unconventional superconductor is distinguished with two types of gap functions: unitary and non-unitary. This core subject has been concentrated on purely spin-triplet or singlet-triplet mixed superconductors. However, the generalization to a purely spin-singlet superconductor has remained primarily of theoretical interest, which requires at least a multi-orbital correlated electronic systems. In this work, we present a possible establishment of both unitary and non-unitary pairings for spin-singlet superconductors with two atomic orbitals. Then we investigate the effects of atomic spin-orbit coupling and find a new spin-orbit-coupled non-unitary superconductor that supports exotic phenomena. Remarkably, there are mainly three features. Firstly, the atomic spin-orbit coupling locks the electron spins to be out-of-plane, which could give birth to the Type II Ising superconductivity with a large in-plane upper critical field compared to the Pauli limit. Secondly, topological chiral or helical Majorana edge state could be realized even in the absence of external magnetic fields or Zeeman fields. In addition, a spin-polarized superconducting state could even be generated by spin-singlet non-unitary pairings with spontaneous time-reversal breaking, which severs as a smoking gun to detect this exotic state by measuring the spin-resolved density of states. Therefore, our work might pave a new avenue to spin-orbit-coupled superconductors with spin-singlet non-unitary pairing symmetries.",2201.06265v2 2017-12-08,Spin-orbit coupling induced valley Hall effects in transition-metal dichalcogenides,"In transition-metal dichalcogenides, electrons in the K-valleys can experience both Ising and Rashba spin-orbit couplings. In this work, we show that the coexistence of Ising and Rashba spin-orbit couplings leads to a special type of valley Hall effect, which we call spin-orbit coupling induced valley Hall effect. Importantly, near the conduction band edge, the valley-dependent Berry curvatures generated by spin-orbit couplings are highly tunable by external gates and dominate over the intrinsic Berry curvatures originating from orbital degrees of freedom under accessible experimental conditions. We show that the spin-orbit coupling induced valley Hall effect is manifested in the gate dependence of the valley Hall conductivity, which can be detected by Kerr effect experiments.",1712.02942v2 2003-06-27,Orbital moment in CoO and in NiO,"The total, orbital and spin moment of the Co2+ ion in CoO has been calculated within the quasi-atomic approach with taking into account strong correlations, crystal-field interactions and the intra-atomic spin-orbit coupling. The orbital moment of 1.39 \mu B amounts at 0 K, in the magnetically-ordered state, to more than 34% of the total moment (4.01 \mu B). The same calculations yield for NiO the orbital and total moment of 0.46 \mu B and 2.45 \mu B, respectively. PACS No: 71.70.E; 75.10.D Keywords: 3d magnetism, crystal field, spin-orbit coupling, orbital moment, CoO, NiO",0306695v2 2008-02-10,Coupling of Spin and Orbital Motion of Electrons in Carbon Nanotubes,"Electrons in atoms possess both spin and orbital degrees of freedom. In non-relativistic quantum mechanics, these are independent, resulting in large degeneracies in atomic spectra. However, relativistic effects couple the spin and orbital motion leading to the well-known fine structure in their spectra. The electronic states in defect-free carbon nanotubes (NTs) are widely believed to be four-fold degenerate, due to independent spin and orbital symmetries, and to also possess electron-hole symmetry. Here we report measurements demonstrating that in clean NTs the spin and orbital motion of electrons are coupled, thereby breaking all of these symmetries. This spin-orbit coupling is directly observed as a splitting of the four-fold degeneracy of a single electron in ultra-clean quantum dots. The coupling favours parallel alignment of the orbital and spin magnetic moments for electrons and anti-parallel alignment for holes. Our measurements are consistent with recent theories that predict the existence of spin-orbit coupling in curved graphene and describe it as a spin-dependent topological phase in NTs. Our findings have important implications for spin-based applications in carbon-based systems, entailing new design principles for the realization of qubits in NTs and providing a mechanism for all-electrical control of spins in NTs.",0802.1351v1 2013-09-16,Spin Hot Spots in Single-Electron GaAs-based Quantum Dots,"Spin relaxation of a single electron in a weakly coupled double quantum dot is calculated numerically. The phonon assisted spin flip is allowed by the presence of the linear and cubic spin-orbit couplings and nuclear spins. The rate is calculated as a function of the interdot coupling, the magnetic field strength and orientation, and the dot bias. In an in-plane magnetic field, the rate is strongly anisotropic with respect to the magnetic field orientation, due to the anisotropy of the spin-orbit interactions. The nuclear spin influence is negligible. In an out-of-plane field, the nuclear spins play a more important role due selection rules imposed on the spin-orbit couplings. Our theory shows a very good agreement with data measured in [Srinivasa, et al., PRL 110, 196803 (2013)], allowing us to extract information on the linear spin-orbit interactions strengths in that experiment. We estimate that they correspond to spin-orbit lengths of about 5-15 $\mu$m.",1309.3852v1 2015-02-18,Quenching of dynamic nuclear polarization by spin-orbit coupling in GaAs quantum dots,"The central-spin problem, in which an electron spin interacts with a nuclear spin bath, is a widely studied model of quantum decoherence. Dynamic nuclear polarization (DNP) occurs in central spin systems when electronic angular momentum is transferred to nuclear spins and is exploited in spin-based quantum information processing for coherent electron and nuclear spin control. However, the mechanisms limiting DNP remain only partially understood. Here, we show that spin-orbit coupling quenches DNP in a GaAs double quantum dot, even though spin-orbit coupling in GaAs is weak. Using Landau-Zener sweeps, we measure the dependence of the electron spin-flip probability on the strength and direction of in-plane magnetic field, allowing us to distinguish effects of the spin-orbit and hyperfine interactions. To confirm our interpretation, we measure high-bandwidth correlations in the electron spin-flip probability and attain results consistent with a significant spin-orbit contribution. We observe that DNP is quenched when the spin-orbit component exceeds the hyperfine, in agreement with a theoretical model. Our results shed new light on the surprising competition between the spin-orbit and hyperfine interactions in central-spin systems.",1502.05400v1 2003-10-08,Efficient electron spin manipulation in a quantum well by an in-plane electric field,"Electron spins in a semiconductor quantum well couple to an electric field {\it via} spin-orbit interaction. We show that the standard spin-orbit coupling mechanisms can provide extraordinary efficient electron spin manipulation by an in-plane ac electric field.",0310192v1 2007-07-26,Quasiclassical approach and spin-orbit coupling,"We discuss the quasiclassical Green function method for a two-dimensional electron gas in the presence of spin-orbit coupling, with emphasis on the meaning of the $\xi$-integration procedure. As an application of our approach, we demonstrate how the spin-Hall conductivity, in the presence of spin-flip scattering, can be easily obtained from the spin-density continuity equation.",0707.3908v1 2007-06-04,Kinetic investigation on extrinsic spin Hall effect induced by skew scattering,"The kinetics of the extrinsic spin Hall conductivity induced by the skew scattering is performed from the fully microscopic kinetic spin Bloch equation approach in $(001)$ GaAs symmetric quantum well. In the steady state, the extrinsic spin Hall current/conductivity vanishes for the linear-$\mathbf k$ dependent spin-orbit coupling and is very small for the cubic-$\mathbf k$ dependent spin-orbit coupling. The spin precession induced by the Dresselhaus/Rashba spin-orbit coupling plays a very important role in the vanishment of the extrinsic spin Hall conductivity in the steady state. An in-plane spin polarization is induced by the skew scattering, with the help of the spin-orbit coupling. This spin polarization is very different from the current-induced spin polarization.",0706.0370v2 2013-02-05,Inertial effect on spin orbit coupling and spin transport,"We theoretically study the renormalization of inertial effects on the spin dependent transport of conduction electrons in a semiconductor by taking into account the interband mixing on the basis of k.p perturbation theory. In our analysis, for the generation of spin current we have used the extended Drude model where the spin orbit coupling plays an important role. We predict enhancement of the spin current resulting from the rerormalized spin orbit coupling effective in our model in cubic and non cubic crystal. Attention has been paid to clarify the importance of gauge fields in the spin transport of this inertial system. A theoretical proposition of a perfect spin filter has been done through the Aharanov Casher like phase corresponding to this inertial system. For a time dependent acceleration, effect of $\vec{k} . \vec{p}$ perturbation on the spin current and spin polarization has also been addressed. Furthermore, achievement of a tunable source of polarized spin current through the non uniformity of the inertial spin orbit coupling strength has also been discussed.",1302.1063v3 2020-02-04,Isotropic All-electric Spin analyzer based on a quantum ring with spin-orbit coupling,"Here we propose an isotropic all electrical spin analyzer in a quantum ring with spin-orbit coupling by analytically and numerically modeling how the charge transmission rates depend on the polarization of the incident spin. The formalism of spin transmission and polarization rates in an arbitrary direction is also developed by analyzing the Aharonov-Bohm and the Aharonov-Casher effects. The topological spin texture induced by the spin-orbit couplings essentially contributes to the dynamic phase and plays an important role in spin transport. The spin transport features derived analytically has been confirmed numerically. This interesting two-dimensional electron system can be designed as a spin filter, spin polarizer and general analyzer by simply tuning the spin-orbit couplings, which paves the way for realizing the tunable and integrable spintronics device.",2002.01151v1 2006-02-23,Spin-orbit interaction in quantum dots in the presence of exchange correlations,"We discuss the problem of spin-orbit interaction in a 2D chaotic or diffusive quantum dot in the presence of exchange correlations. Spin-orbit scattering breaks spin rotation invariance, and in the crossover regime between different symmetries of the spin-orbit coupling, the problem has no closed solution. A conventional choice of a many-particle basis in a numerical diagonalization is the set of Slater determinants built from the single-particle eigenstates of the one-body Hamiltonian (including the spin-orbit terms). We develop a different approach based on the use of a good-spin many-particle basis that is composed of the eigenstates of the universal Hamiltonian in the absence of spin-orbit scattering. We introduce a complete labelling of this good-spin basis and use angular momentum algebra to calculate in closed form the matrix elements of the spin-orbit interaction in this basis. Spin properties, such as the ground-state spin distribution and the spin excitation function, are easily calculated in this basis.",0602552v1 2011-10-30,Quasiparticle velocities in 2D electron/hole liquids with spin-orbit coupling,"We study the influence of spin-orbit interactions on quasiparticle dispersions in two-dimensional electron and heavy-hole liquids in III-V semiconductors. To obtain closed-form analytical results, we restrict ourselves to spin-orbit interactions with isotropic spectrum and work within the screened Hartree-Fock approximation, valid in the high-density limit. For electrons having a linear-in-momentum Rashba (or, equivalently, Dresselhaus) spin-orbit interaction, we show that the screened Hartree-Fock approximation recovers known results based on the random-phase approximation and we extend those results to higher order in the spin-orbit coupling. While the well-studied case of electrons leads only to a weak modification of quasiparticle properties in the presence of the linear-in-momentum spin-orbit interaction, we find two important distinctions for hole systems (with a leading nonlinear-in-momentum spin-orbit interaction). First, the group velocities associated with the two hole-spin branches acquire a significant difference in the presence of spin-orbit interactions, allowing for the creation of spin-polarized wavepackets in zero magnetic field. Second, we find that the interplay of Coulomb and spin-orbit interactions is significantly more important for holes than for electrons and can be probed through the quasiparticle group velocities. These effects should be directly observable in magnetotransport, Raman scattering, and femtosecond-resolved Faraday rotation measurements. Our results are in agreement with a general argument on the velocities, which we formulate for an arbitrary choice of the spin-orbit coupling.",1110.6661v2 2003-11-04,Twisted exchange interaction between localized spins embedded in a one- or two-dimensional electron gas with Rashba spin-orbit coupling,"We study theoretically the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in one- and two-dimensions in presence of a Rashba spin-orbit (SO) coupling. We show that rotation of the spin of conduction electrons due to SO coupling causes a twisted RKKY interaction between localized spins which consists of three different terms: Heisenberg, Dzyaloshinsky-Moriya, and Ising interactions. We also show that the effective spin Hamiltonian reduces to the usual RKKY interaction Hamiltonian in the twisted spin space where the spin quantization axis of one localized spin is rotated.",0311054v1 2005-07-13,Role of spin-orbit coupling on the spin triplet pairing in Na_{x}CoO_{2}yH_{2}O I: d-vector under zero magnetic field,"The d-vector in possibile spin triplet superconductor Na_{x}CoO_{2}yH_{2}O is microscopically investigated on the basis of the multi-orbital Hubbard model including the atomic spin-orbit coupling. As a result of the perturbation theory, we obtain the stable spin triplet superconductivity where the p-wave and f-wave states can be stabilized. If we neglect the spin-orbit coupling, superconducting state has 6-fold (3-fold) degeneracy in the p-wave (f-wave) state. This degeneracy is lifted by the spin-orbit coupling. We determine the d-vector within the linearlized Dyson-Gorkov equation. It is shown that the d-vector is always along the plane when the pairing symmetry is p-wave, while it depends on the parameters in case of the f-wave state. The lifting of degeneracy is significant in the p-wave state while it is very small in the f-wave state. This is because the first order term with respect to the spin-orbit coupling is effective in the former case, while it is ineffective in the latter case. The consistency of these results with NMR and \muSR measurements are discussed.",0507305v1 2015-03-02,The Kondo Temperature of a Two-dimensional Electron Gas with Rashba Spin-orbit Coupling,"We use the Hirsch-Fye quantum Monte Carlo method to study the single magnetic impurity problem in a two-dimensional electron gas with Rashba spin-orbit coupling. We calculate the spin susceptibility for various values of spin-orbit coupling, Hubbard interaction, and chemical potential. The Kondo temperatures for different parameters are estimated by fitting the universal curves of spin susceptibility. We find that the Kondo temperature is almost a linear function of Rashba spin-orbit energy when the chemical potential is close to the edge of the conduction band. When the chemical potential is far away from the band edge, the Kondo temperature is independent of the spin-orbit coupling. These results demonstrate that, for single impurity problem in this system, the most important reason to change the Kondo temperature is the divergence of density of states near the band edge, and the divergence is induced by the Rashba spin-orbit coupling.",1503.00449v2 2013-09-05,Current-induced torques and interfacial spin-orbit coupling,"In bilayer systems consisting of an ultrathin ferromagnetic layer adjacent to a metal with strong spin-orbit coupling, an applied in-plane current induces torques on the magnetization. The torques that arise from spin-orbit coupling are of particular interest. Here, we calculate the current-induced torque in a Pt-Co bilayer to help determine the underlying mechanism using first principles methods. We focus exclusively on the analogue to the Rashba torque, and do not consider the spin Hall effect. The details of the torque depend strongly on the layer thicknesses and the interface structure, providing an explanation for the wide variation in results found by different groups. The torque depends on the magnetization direction in a way similar to that found for a simple Rashba model. Artificially turning off the exchange spin splitting and separately the spin-orbit coupling potential in the Pt shows that the primary source of the ""field-like"" torque is a proximate spin-orbit effect on the Co layer induced by the strong spin-orbit coupling in the Pt.",1309.1356v1 2022-04-25,Harmonic generation in bent graphene with artificially-enhanced spin-orbit coupling,"We theoretically investigate the nonlinear response of bent graphene, in the presence of artificially-enhanced spin-orbit coupling, which can occur either via adatom deposition, or by placing the sheet of bent graphene in contact with a spin-orbit active substrate. We discuss the interplay between the spin-orbit coupling and the artificial magnetic field generated by the bending, for both the cases of Rashba and intrinsic spin-orbit coupling. For the latter, we introduce a spin-field interaction Hamiltonian addressing directly the electron spin as a degree of freedom. Our findings reveal that in this case, by controlling the amount of spin-orbit coupling, it is possible to significantly tune the spectrum of the nonlinear signal, achieving, in principle, efficient conversion of light from THz to UV region.",2204.11664v3 2009-04-07,Curvature-enhanced spin-orbit coupling in a carbon nanotube,"Structure of the spin-orbit coupling varies from material to material and thus finding the correct spin-orbit coupling structure is an important step towards advanced spintronic applications. We show theoretically that the curvature in a carbon nanotube generates two types of the spin-orbit coupling, one of which was not recognized before. In addition to the topological phase-related contribution of the spin-orbit coupling, which appears in the off-diagonal part of the effective Dirac Hamiltonian of carbon nanotubes, there is another contribution that appears in the diagonal part. The existence of the diagonal term can modify spin-orbit coupling effects qualitatively, an example of which is the electron-hole asymmetric spin splitting observed recently, and generate four qualitatively different behavior of energy level dependence on parallel magnetic field. It is demonstrated that the diagonal term applies to a curved graphene as well. This result should be valuable for spintronic applications of graphitic materials.",0904.1185v2 2020-03-23,Spin-orbit-coupling-assisted roton softening and superstripes in a Rydberg-dressed Bose-Einstein Condensate,"Rotons can exist in ultracold atomic gases either with long-range interactions or with spin-orbitcoupled dispersions. We find that two different kinds of rotons coexist in a joint system combining long-range interactions and spin-orbit coupling. One roton originates from spin-orbit coupling and two others come from long-range interactions. Their softening can be controlled separately. The interesting new phenomenon which we find is that spin-orbit-coupled roton can push down the energy of one long-range-interaction roton. The spin-orbit coupling accelerates the softening of this roton. The post phase of spin-orbit-coupling-assisted roton softening and instability is identified as a superstripe.",2003.10090v2 2022-04-14,Double version of the Rashba and Dresselhaus spin-orbit coupling,"The Rashba and Dresselhaus types of spin-orbit coupling are two typical linear coupling forms. We establish the fundamental physics of a model which can be viewed as the double version of the Rashba and Dresselhaus spin-orbit coupling. This model describes the low energy physics of a class of massless Dirac fermions in spin-orbit systems. The physical properties of the massless Dirac fermions are determined by the mathematical relations of spin-orbit coefficients. For equal Rashba and Dresselhauss coupling constants, k-independent eigenspinors and a persistent spin helix combined with massless birefringent Dirac fermions emerge in this model. The spin-orbit coupled systems described by this model have potential technological applications from spintronics to quantum computation.",2204.06680v1 2019-04-01,Spin-charge coupled transport in van der Waals systems with random tunneling,"We study the electron and spin transport in a van der Waals system formed by one layer with strong spin-orbit coupling and a second layer without spin-orbit coupling, in the regime when the interlayer tunneling is random. We find that in the layer without intrinsic spin-orbit coupling spin-charge coupled transport can be induced by two distinct mechanisms. First, the gapless diffusion modes of the two isolated layers hybridize in the presence of tunneling, which constitutes a source of spin-charge coupled transport in the second layer. Second, the random tunneling introduces spin-orbit coupling in the effective disorder-averaged single-particle Hamiltonian of the second layer. This results in non-trivial spin transport and, for sufficiently strong tunneling, in spin-charge coupling. As an example, we consider a van der Waals system formed by a two-dimensional electron gas (2DEG)--such as graphene--and the surface of a topological insulator (TI) and show that the proximity of the TI induces a coupling of the spin and charge transport in the 2DEG. In addition, we show that such coupling can be tuned by varying the doping of the TI's surface. We then obtain, for a simple geometry, the current-induced non-equilibrium spin accumulation (Edelstein effect) caused in the 2DEG by the coupling of charge and spin transport.",1904.01015v1 2014-11-14,Spin-orbit coupling and chaotic rotation for eccentric coorbital bodies,"The presence of a co-orbital companion induces the splitting of the well known Keplerian spin-orbit resonances. It leads to chaotic rotation when those resonances overlap.",1411.3950v1 2017-01-03,Universal Absence of Walker Breakdown and Linear Current-Velocity Relation via Spin-Orbit Torques in Coupled and Single Domain Wall Motion,"We consider theoretically domain wall motion driven by spin-orbit and spin Hall torques. We find that it is possible to achieve universal absence of Walker breakdown for all spin-orbit torques using experimentally relevant spin-orbit coupling strengths. For spin-orbit torques other than the pure Rashba spin-orbit torque, this gives a linear current-velocity relation instead of a saturation of the velocity at high current densities. The effect is very robust and is found in both soft and hard magnetic materials, as well as in the presence of the Dzyaloshinskii-Moriya interaction and in coupled domain walls in synthetic antiferromagnets, where it leads to very high domain wall velocities. Moreover, recent experiments have demonstrated that the switching of a synthetic antiferromagnet does not obey the usual spin Hall angle-dependence, but that domain expansion and contraction can be selectively controlled toggling only the applied in-plane magnetic field magnitude and not its sign. We show for the first time that the combination of spin Hall torques and interlayer exchange coupling produces the necessary relative velocities for this switching to occur.",1701.00786v2 2024-04-09,Hydrostatic pressure control of the spin-orbit proximity effect and spin relaxation in a phosphorene-WSe$_2$ heterostructure,"Effective control of interlayer interactions is a key element in modifying the properties of van der Waals heterostructures and the next step toward their practical applications. Focusing on the phosphorene-WSe$_2$ heterostructure, we demonstrate, using first-principles calculations, how the spin-orbit coupling can be transferred from WSe$_2$, a strong spin-orbit coupling material, to phosphorene and further amplified by applying vertical pressure. We simulate external pressure by changing the interlayer distance between bilayer constituents and show that it is possible to tune the spin-orbit field of phosphorene holes in a controllable way. By fitting effective electronic states of the proposed Hamiltonian to the first principles data, we reveal that the spin-orbit coupling in phosphorene hole bands is enhanced more than two times for experimentally accessible pressures up to 17 kbar. Finally, we find that the pressure-enhanced spin-orbit coupling boosts the Dyakonov-Perel spin relaxation mechanism, reducing the spin lifetime of phosphorene holes by factor 4.",2404.06097v1 2019-03-08,Intra- and inter-orbital correlated electron spin dynamics in $\rm Sr_2 Ir O_4$: spin-wave gap and spin-orbit exciton,"Transformation of Coulomb interaction terms to the pseudo-orbital basis constituted by $J=1/2$ and $3/2$ states arising from spin-orbit coupling provides a versatile tool. This formalism is applied to investigate magnetic anisotropy effects on low-energy spin-wave excitations as well as high-energy spin-orbit exciton modes in $\rm Sr_2 Ir O_4$. The Hund's coupling term explictly yields easy-plane anisotropy, resulting in gapless (in-plane) and gapped (out-of-plane) modes, in agreement with recent resonant inelastic x-ray scattering (RIXS) measurements. The collective mode of inter-orbital, spin-flip, particle-hole excitations with appropriate interaction strengths and renormalized spin-orbit gap yields two well-defined propagating spin-orbit exciton modes, with energy scale and dispersion in good agreement with RIXS studies.",1903.03360v1 2005-11-22,Entanglement production in chaotic quantum dots subject to spin-orbit coupling,"We study numerically the production of orbital and spin entangled states in chaotic quantum dots for non-interacting electrons. The introduction of spin-orbit coupling permit us to identify signatures of time-reversal symmetry correlations in the entanglement production previously unnoticed, resembling weak-(anti)localization quantum corrections to the conductance. We find the entanglement to be strongly dependent on spin-orbit coupling, showing universal features for broken time-reversal and spin-rotation symmetries.",0511555v3 2007-07-30,Temperature Dependence of Rashba Spin-orbit Coupling in Quantum Wells,"We perform an all-optical spin-dynamic measurement of the Rashba spin-orbit interaction in (110)-oriented GaAs/AlGaAs quantum wells. The crystallographic direction of quantum confinement allows us to disentangle the contributions to spin-orbit coupling from the structural inversion asymmetry (Rashba term) and the bulk inversion asymmetry. We observe an unexpected temperature dependence of the Rashba spin-orbit interaction strength that signifies the importance of the usually neglected higher-order terms of the Rashba coupling.",0707.4493v1 2007-08-19,Coupling of electron rotation with spin in semiconductors,"Account of an intrinsic spin-orbit coupling in the valence bands of common semiconductors yields the scalar spin-orbit-rotation term in the effective-mass Hamiltonian of the conduction-band electron. This result is obtained within the multiband envelope function approximation. Fundamentally, the spin-orbit-rotation coupling can be described in purely geometric terms as a consequence of the difference in the Berry phase acquired by the components of the spin-orbitally mixed Kramers-doublet during its cyclic evolution in the reciprocal momentum space.",0708.2565v2 2019-09-01,Switchable Josephson current in junctions with spin-orbit coupling,"We study the Josephson current in two types of lateral junctions with spin-orbit coupling and an exchange field. The first system (type 1 junction) consists of superconductors with heavy metal interlayers linked by a ferromagnetic bridge, such that the spin-orbit coupling is finite only at the superconductor/heavy metal interface. In the second type (type 2) of system we assume that the spin orbit coupling is finite in the bridge region. The length of both junctions is larger than the magnetic decay length such that the Josephson current is carried uniquely by the long-range triplet component of the condensate. The latter is generated by the spin-orbit coupling via two mechanisms, spin precession and inhomogeneous spin-relaxation. We show that the current can be controlled by rotating the magnetization of the bridge or by tuning the strength of the spin-orbit coupling in type 2 junctions., and also discuss how the ground-state of the junction can be tuned from a $0$ to a $\pi$ phase difference between the superconducting electrodes. In leading order in the spin-orbit coupling, the spin precession dominates the behavior of the triplet component and both junctions behave similarly. However, when spin relaxation effects are included junction of type 2 offers a wider parameter range in which $0$-$\pi$ transitions take place.",1909.00401v1 2004-06-29,Spin current and polarization in impure 2D electron systems with spin-orbit coupling,"We derive the transport equations for two-dimensional electron systems with spin-orbit interaction and short-range spin-independent disorder. In the limit of slow spatial variations of the electron distribution we obtain coupled diffusion equations for the electron density and spin. Using these equations we calculate electric-field induced spin accumulation in a finite-size sample for arbitrary ratio between spin-orbit energy splitting and elastic scattering rate. We demonstrate that the spin-Hall conductivity vanishes in an infinite system independent of this ratio.",0406730v2 2011-11-23,Rashba spin torque in an ultrathin ferromagnetic metal layer,"In a two-dimensional ferromagnetic metal layer lacking inversion symmetry, the itinerant electrons mediate the interaction between the Rashba spin-orbit interaction and the ferromagnetic order parameter, leading to a Rashba spin torque exerted on the magnetization. Using Keldysh technique, in the presence of both magnetism and a spin-orbit coupling, we derive a spin diffusion equation that provides a coherent description to the diffusive spin dynamics. The characteristics of the spin torque and its implication on magnetization dynamics are discussed in the limits of large and weak spin-orbit coupling.",1111.5466v1 2016-08-07,Spin-orbit coupling in Fe-based superconductors,"We study the spin resonance peak in recently discovered iron-based superconductors. The resonance peak observed in inelastic neutron scattering experiments agrees well with predicted results for the extended $s$-wave ($s_\pm$) gap symmetry. Recent neutron scattering measurements show that there is a disparity between longitudinal and transverse components of the dynamical spin susceptibility. Such breaking of the spin-rotational invariance in the spin-liquid phase can occur due to spin-orbit coupling. We study the role of the spin-orbit interaction in the multiorbital model for Fe-pnictides and show how it affects the spin resonance feature.",1608.02230v1 1995-11-26,Spin-flip scattering in the quantum Hall regime,"We present a microscopic theory of spin-orbit coupling in the integer quantum Hall regime. The spin-orbit scattering length is evaluated in the limit of long-range random potential. The spin-flip rate is shown to be determined by rare fluctuations of anomalously high electric field. A mechanism of strong spin-orbit scattering associated with exchange-induced spontaneous spin-polarization is suggested. Scaling of the spin-splitting of the delocalization transition with the strength of spin-orbit and exchange interactions is also discussed.",9511123v2 2013-04-09,Spin-orbital liquids in non-Kramers magnet on Kagome lattice,"Localized magnetic moments with crystal-field doublet or pseudo-spin 1/2 may arise in correlated insulators with even number of electrons and strong spin-orbit coupling. Such a non-Kramers pseudo-spin 1/2 is the consequence of crystalline symmetries as opposed to the Kramers doublet arising from time-reversal invariance, and is necessarily a composite of spin and orbital degrees of freedom. We investigate possible spin-orbital liquids with fermionic spinons for such non-Kramers pseudo-spin 1/2 systems on the Kagome lattice. Using the projective symmetry group analysis, we find {\it ten} new phases that are not allowed in the corresponding Kramers systems. These new phases are allowed due to unusual action of the time reversal operation on non-Kramers pseudo-spins. We compute the spin-spin dynamic structure factor that shows characteristic features of these non-Kramers spin-orbital liquids arising from their unusual coupling to neutrons, which is therefore relevant for neutron scattering experiments. We also point out possible anomalous broadening of Raman scattering intensity that may serve as a signature experimental feature for gapless non-Kramers spin-orbital liquids.",1304.2766v1 2019-06-11,Spin imbalance of charge carriers induced by an electric current,"We analyze the contribution of the inhomogeneous magnetic field induced by an electrical current to the spin Hall effect in metals. The Zeeman coupling between the field and the electron spin leads to a spin dependent force, and to spin accumulation at the edges. We compare the effect of this relativistic correction to the electron dynamics to the features induced by the spin-orbit interaction. The effect of current induced magnetic fields on the spin Hall effect can be comparable to the extrinsic contribution from the spin-orbit interaction, although it does not require the presence of heavy elements with a strong spin-orbit interaction. The induced spins are oriented normal to the metal slab.",1906.04851v1 2011-10-24,Manipulation of single electron spin in a GaAs quantum dot through the application of geometric phases: The Feynman disentangling technique,"The spin of a single electron in an electrically defined quantum dot in a 2DEG can be manipulated by moving the quantum dot adiabatically in a closed loop in the 2D plane under the influence of applied gate potentials. In this paper we present analytical expressions and numerical simulations for the spin-flip probabilities during the adiabatic evolution in the presence of the Rashba and Dresselhaus linear spin-orbit interactions. We use the Feynman disentanglement technique to determine the non-Abelian Berry phase and we find exact analytical expressions for three special cases: (i) the pure Rashba spin-orbit coupling, (ii) the pure Dresselhause linear spin-orbit coupling, and (iii) the mixture of the Rashba and Dresselhaus spin-orbit couplings with equal strength. For a mixture of the Rashba and Dresselhaus spin-orbit couplings with unequal strengths, we obtain simulation results by solving numerically the Riccati equation originating from the disentangling procedure. We find that the spin-flip probability in the presence of the mixed spin-orbit couplings is generally larger than those for the pure Rashba case and for the pure Dresselhaus case, and that the complete spin-flip takes place only when the Rashba and Dresselhaus spin-orbit couplings are mixed symmetrically.",1110.5366v1 2022-02-10,Local breaking of the spin degeneracy in the vortex states of Ising superconductors: Induced antiphase ferromagnetic order,"Ising spin-orbital coupling is usually easy to identify in the Ising superconductors via an in-plane critical field enhancement, but we show that the Ising spin-orbital coupling also manifests in the vortex physics for perpendicular magnetic fields. By self-consistently solving the Bogoliubov-de Gennes equations of a model Hamiltonian built on the honeycomb lattice with the Ising spin-orbital coupling pertinent to the transition metal dichalcogenides, we numerically investigate the local breaking of the spin and sublattice degeneracies in the presence of a perpendicular magnetic field. It is revealed that the ferromagnetic orders are induced inside the vortex core region by the Ising spin-orbital coupling. The induced magnetic orders are antiphase in terms of their opposite polarizations inside the two nearest-neighbor vortices with one of the two polarizations coming dominantly from one sublattice sites, implying the local breaking of the spin and sublattice degeneracies. The finite-energy peaks of the local-density-of-states for spin-up and spin-down in-gap states are split and shifted oppositely by the Ising spin-orbital coupling, and the relative shifts of them on sublattices $A$ and $B$ are also of opposite algebraic sign. The calculated results and the proposed scenario may not only serve as experimental signatures for identifying the Ising spin-orbital coupling in the Ising superconductors, but also be prospective in manipulation of electron spins in motion through the orbital effect in the superconducting vortex states.",2202.04797v1 2011-01-27,Magnetic excitations in one-dimensional spin-orbital models,"We study the dynamics and thermodynamics of one-dimensional spin-orbital models relevant for transition metal oxides. We show that collective spin, orbital, and combined spin-orbital excitations with infinite lifetime can exist, if the ground state of both sectors is ferromagnetic. Our main focus is the case of effectively ferromagnetic (antiferromagnetic) exchange for the spin (orbital) sector, respectively, and we investigate the renormalization of spin excitations via spin-orbital fluctuations using a boson-fermion representation. We contrast a mean-field decoupling approach with results obtained by treating the spin-orbital coupling perturbatively. Within the latter self-consistent approach we find a significant increase of the linewidth and additional structures in the dynamical spin structure factor as well as Kohn anomalies in the spin-wave dispersion caused by the scattering of spin excitations from orbital fluctuations. Finally, we analyze the specific heat c(T) by comparing a numerical solution of the model obtained by the density-matrix renormalization group with perturbative results. At low temperatures T we find numerically c(T) T pointing to a low-energy effective theory with dynamical critical exponent z=1.",1101.5301v1 2016-10-05,Exotic orbits due to spin-spin coupling around Kerr black holes,"We report exotic orbital phenomena of spinning test particles orbiting around a Kerr black hole, i.e., some orbits of spinning particles are asymmetrical about the equatorial plane. When a nonspinning test particle orbits around a Kerr black hole in a strong field region, due to relativistic orbital precessions, the pattern of trajectories is symmetrical about the equatorial plane of the Kerr black hole. However, the patterns of the spinning particles' orbit are no longer symmetrical about the equatorial plane for some orbital configurations and large spins. We argue that these asymmetrical patterns come from the spin-spin interactions between spinning particles and Kerr black holes, because the directions of spin-spin forces can be arbitrary, and distribute asymmetrically about the equatorial plane.",1610.01534v3 2023-11-01,Theory of Orbital Pumping,"We develop a theory of orbital pumping, which corresponds to the emission of orbital currents from orbital dynamics. This phenomenon exhibits two distinct characteristics compared to spin pumping. Firstly, while spin pumping generates solely spin (angular momentum) currents, orbital pumping yields both orbital angular momentum currents and orbital angular position currents. Secondly, lattice vibrations induce orbital dynamics and associated orbital pumping as the orbital angular position is directly coupled to the lattice. These pumped orbital currents can be detected as transverse electric voltages via the inverse orbital(-torsion) Hall effect, stemming from orbital textures. Our work proposes a new avenue for generating orbital currents and provides a broader understanding of angular momentum dynamics encompassing spin, orbital, and phonon.",2311.00362v1 2016-06-18,Spin Transport at Interfaces with Spin-Orbit Coupling: Formalism,"We generalize magnetoelectronic circuit theory to account for spin transfer to and from the atomic lattice via interfacial spin-orbit coupling. This enables a proper treatment of spin transport at interfaces between a ferromagnet and a heavy-metal non-magnet. This generalized approach describes spin transport in terms of drops in spin and charge accumulations across the interface (as in the standard approach), but additionally includes the responses from in-plane electric fields and offsets in spin accumulations. A key finding is that in-plane electric fields give rise to spin accumulations and spin currents that can be polarized in any direction, generalizing the Rashba-Edelstein and spin Hall effects. The spin accumulations exert torques on the magnetization at the interface when they are misaligned from the magnetization. The additional out-of-plane spin currents exert torques via the spin-transfer mechanism on the ferromagnetic layer. To account for these phenomena we also describe spin torques within the generalized circuit theory. The additional effects included in this generalized circuit theory suggest modifications in the interpretations of experiments involving spin orbit torques, spin pumping, spin memory loss, the Rashba-Edelstein effect, and the spin Hall magnetoresistance.",1606.05758v1 2020-03-27,Generalized magnetoelectronic circuit theory and spin relaxation at interfaces in magnetic multilayers,"Spin transport at metallic interfaces is an essential ingredient of various spintronic device concepts, such as giant magnetoresistance, spin-transfer torque, and spin pumping. Spin-orbit coupling plays an important role in many such devices. In particular, spin current is partially absorbed at the interface due to spin-orbit coupling. We develop a general magnetoelectronic circuit theory and generalize the concept of the spin mixing conductance, accounting for various mechanisms responsible for spin-flip scattering. For the special case when exchange interactions dominate, we give a simple expression for the spin mixing conductance in terms of the contributions responsible for spin relaxation (i.e., spin memory loss), spin torque, and spin precession. The spin-memory loss parameter $\delta$ is related to spin-flip transmission and reflection probabilities. There is no straightforward relation between spin torque and spin memory loss. We calculate the spin-flip scattering rates for N|N, F|N, F|F interfaces using the Landauer-B\""uttiker method within the linear muffin-tin orbital method and determine the values of $\delta$ using circuit theory.",2003.12221v1 2015-11-03,Spin-Orbit Coupling Induced Back-action Cooling in Cavity-Optomechanics with a Bose-Einstein Condensate,"We report a spin-orbit coupling induced back-action cooling in an optomechanical system, composed of a spin-orbit coupled Bose-Einstein condensate trapped in an optical cavity with one movable end mirror, by suppressing heating effects of quantum noises. The collective density excitations of the spin-orbit coupling mediated hyperfine states - serving as atomic oscillators equally coupled to the cavity field - trigger strongly driven atomic back-action. We find that the back-action not only revamps low-temperature dynamics of its own but also provides an opportunity to cool the mechanical mirror to its quantum mechanical ground state. Further, we demonstrate that the strength of spin-orbit coupling also superintends dynamic structure factor and squeezes nonlinear quantum noises, like thermo-mechanical and photon shot noise, which enhances optomechanical features of hybrid cavity beyond the previous investigations. Our findings are testable in a realistic setup and enhance the functionality of cavity-optomechanics with spin-orbit coupled hyperfine states in the field of quantum optics and quantum computation.",1511.01109v2 2008-06-03,Spin-Orbit Coupling in an f-electron Tight-Binding Model,"We extend a tight-binding method to include the effects of spin-orbit coupling, and apply it to the study of the electronic properties of the actinide elements Th, U, and Pu. These tight-binding parameters are determined for the fcc crystal structure using the equivalent equilibrium volumes. In terms of the single particle energies and the electronic density of states, the overall quality of the tight-binding representation is excellent and of the same quality as without spin-orbit coupling. The values of the optimized tight-binding spin-orbit coupling parameters are comparable to those determined from purely atomic calculations.",0806.0420v1 2011-07-04,Anomalous Hall conductivity from the dipole mode of spin-orbit-coupled cold-atom systems,"Motivated by recent experiments [Lin {\it et al.}, Nature {\bf 417}, 83 (2011)] that engineered spin-orbit coupling in ultra-cold mixtures of bosonic atoms, we study the dipole oscillation of trapped spin-orbit-coupled non-condensed Bose and Fermi gases. We find that different directions of oscillation are coupled by the spin-orbit interactions. The phase difference between oscillatory motion in orthogonal directions and the trapping frequencies of the modes are shown to be related to the anomalous Hall conductivity. Our results can be used to experimentally determine the anomalous Hall conductivity for cold-atom systems.",1107.0578v1 2011-08-10,"Erratum: Engineering a p+ip Superconductor: Comparison of Topological Insulator and Rashba Spin-Orbit Coupled Materials [Phys. Rev. B 83, 184520 (2011)]","In this erratum, we revisit the issue of bulk-disorder on proposals to realize an effective p+ip superconductor from spin-orbit coupled materials. Contrary to the claim in [Phys. Rev. B 83, 184520 (2011)], we show that the pair breaking effects of bulk-disorder are negligible, and that bulk disorder does not suppress the induced superconductivity. This argument does not apply to our conclusions regarding impurities residing in the spin-orbit coupled material or disorder at the interface to the bulk superconductor, both of which tend to suppress superconductivity unless spin-orbit coupling is large.",1108.2260v1 2013-01-16,Vortex lattice solutions to the Gross-Pitaevskii equation with spin-orbit coupling in optical lattices,"Effective spin-orbit coupling can be created in cold atom systems using atom-light interaction. We study the BECs in an optical lattice using the Gross-Pitaevskii equation with spin-orbit coupling. Bloch states for the linear equation are numerically obtained, and compared with stationary solutions to the Gross-Pitaevskii equation with nonlinear terms. Various vortex lattice states are found when the spin-orbit coupling is strong.",1301.3565v1 2018-11-22,Enhanced Rashba spin-orbit coupling in core-shell nanowires by the interfacial effect,"We report on $\vec{k}\cdot\vec{p}$ calculations of Rashba spin-orbit coupling controlled by external gates in InAs/InAsP core-shell nanowires. We show that charge spilling in the barrier material allows for a stronger symmetry breaking than in homoegenous nano-materials, inducing a specific interface-related contribution to spin-orbit coupling. Our results qualitatively agree with recent experiments [S. Futhemeier \textit{et al.}, Nat. Commun. \textbf{7}, 12413 (2016)] and suggest additional wavefunction engineering strategies to enhance and control spin-orbit coupling.",1811.09088v1 2017-01-17,Vortex pairs in a spin-orbit coupled Bose-Einstein condensate,"Static and dynamic properties of vortices in a two-component Bose-Einstein condensate with Rashba spin-orbit coupling are investigated. The mass current around a vortex core in the plane-wave phase is found to be deformed by the spin-orbit coupling, and this makes the dynamics of the vortex pairs quite different from those in a scalar Bose-Einstein condensate. The velocity of a vortex-antivortex pair is much smaller than that without spin-orbit coupling, and there exist stationary states. Two vortices with the same circulation move away from each other or unite to form a stationary state.",1701.04591v1 2023-07-22,Spin-orbit-coupling-induced phase separation in trapped Bose gases,"In a trapped spin-1/2 Bose-Einstein condensate with miscible interactions, a two-dimensional spin-orbit coupling can introduce an unconventional spatial separation between the two components. We reveal the physical mechanism of such a spin-orbit-coupling-induced phase separation. Detailed features of the phase separation are identified in a trapped Bose-Einstein condensate. We further analyze differences of phase separation in Rashba and anisotropic spin-orbit-coupled Bose gases. An adiabatic splitting dynamics is proposed as an application of the phase separation.",2307.12177v2 2000-06-30,On a q-analogue of the spin-orbit coupling,"Based on the tensor method, a q-analoque of the spin-orbit coupling is introduced in a q-deformed Schroedinger equation, previously derived for a central potential. Analytic expressions for the matrix elemnets of the representation j=l\pm 1/2 are derived. The spectra of the harmonic oscillator and the Coulomb potential are calculated numerically as a function of the deformation parameter, without and with the spin-orbit coupling. The harmonic oscillator spectrum presents strong analogies with the bound spectrum of an Woods-Saxon potential customarily used in nuclear physics. The Coulomb spectrum simulates relativistic effects. The addition of the spin-orbit coupling reinforces this picture.",0006081v1 2011-10-28,Artificial spin-orbit coupling in ultra-cold Fermi superfluids,"We develop a theory for interacting fermions in the presence of spin-orbit coupling and Zeeman fields, and show that many new superfluids phases, which are topological in nature, emerge. Depending on values of spin-orbit coupling, Zeeman fields, and interactions, initially gapped s-wave superfluids acquire p-wave, d-wave, f-wave and higher angular momentum components, which produce zeros in the excitation spectrum, rendering the superfluid gapless. Several multi-critical points, which separate topological superfluid phases from normal or non-uniform, are accessible depending on spin-orbit coupling, Zeeman fields or interactions, setting the stage for the study of tunable topological superfluids.",1110.6364v1 2014-01-03,Spin-Orbit Coupled Bose Gases at Finite Temperatures,"Spin-orbit coupling is predicted to have dramatic effects on thermal properties of a two-component atomic Bose gas. We show that in three spatial dimensions it lowers the critical temperature of condensation and enhances thermal depletion of the condensate fraction. In two dimensions we show that spin-orbit coupling destroys superfluidity at any finite temperature, modifying dramatically the cerebrated Berezinskii-Kosterlitz-Thouless scenario. We explain this by the increase of the number of low energy states induced by spin-orbit coupling, enhancing the role of quantum fluctuations.",1401.0575v1 2021-09-07,Creating moving gap solitons in spin-orbit-coupled Bose-Einstein condensates,"A simple and efficient method to create gap solitons is proposed in a spin-orbit-coupled spin-1 Bose-Einstein condensate. We find that a free expansion along the spin-orbit coupling dimension can generate two moving gap solitons, which are identified from a generalized massive Thirring model. The dynamics of gap solitons can be controlled by adjusting spin-orbit coupling parameters.",2109.02871v1 2023-02-10,Patterning by dynamically unstable spin-orbit-coupled Bose-Einstein condensates,"In a two-dimensional atomic Bose-Einstein condensate, we demonstrate Rashba spin-orbit coupling can always introduce dynamical instability into specific zero-quasimomentum states in all parameter regimes. During the evolution of the zero-quasimomentum states, such spin-orbit-coupling-induced instability can fragment the states and lead to a dynamically patterning process. The features of formed patterns are identified from the symmetries of the Bogoliubov-de Gennes Hamiltonian. We show that spin-orbit-coupled Bose-Einstein condensates provide an interesting platform for the investigation of pattern formations.",2302.05101v2 2017-05-12,Analytical slave-spin mean-field approach to orbital selective Mott insulators,"We use the slave-spin mean-field approach to study particle-hole symmetric one- and two-band Hubbard models in presence of Hund's coupling interaction. By analytical analysis of Hamiltonian, we show that the locking of the two orbitals vs.\,orbital-selective Mott transition can be formulated within a Landau-Ginzburg framework. By applying the slave-spin mean-field to impurity problem, we are able to make a correspondence between impurity and lattice. We also consider the stability of the orbital selective Mott phase to the hybridization between the orbitals and study the limitations of the slave-spin method for treating inter-orbital tunnellings in the case of multi-orbital Bethe lattices with particle-hole symmetry.",1705.04427v1 2014-11-11,Striped Ferronematic ground states in a spin-orbit coupled $S=1$ Bose gas,"We theoretically establish the mean-field phase diagram of a homogeneous spin-$1$, spin-orbit coupled Bose gas as a function of the spin-dependent interaction parameter, the Raman coupling strength and the quadratic Zeeman shift. We find that the interplay between spin-orbit coupling and spin-dependent interactions leads to the occurrence of ferromagnetic or ferronematic phases which also break translational symmetry. For weak Raman coupling, increasing attractive spin-dependent interactions (as in $^{87}$Rb or $^7$Li) induces a transition from a uniform to a stripe XY ferromagnet (with no nematic order). For repulsive spin-dependent interactions however (as in $^{23}$Na), we find a transition from an $XY$ spin spiral phase ($= 0$ and uniform total density) with uniaxial nematic order, to a biaxial ferronematic, where the total density, spin vector and nematic director oscillate in real space. We investigate the stability of these phases against the quadratic Zeeman effect, which generally tends to favor uniform phases with either ferromagnetic or nematic order but not both. We discuss the relevance of our results to ongoing experiments on spin-orbit coupled, spinor Bose gases.",1411.2990v1 2018-12-21,Influence of spin-orbit and spin-Hall effects on the spin Seebeck current beyond linear response,"We study the spin transport theoretically in heterostructures consisting of a ferromagnetic metallic thin film sandwiched between heavy-metal and oxide layers. The spin current in the heavy metal layer is generated via the spin Hall effect, while the oxide layer induces at the interface with the ferromagnetic layer a spin-orbital coupling of the Rashba type. Impact of the spin Hall effect and Rashba spin-orbit coupling on the spin Seebeck current is explored with a particular emphasis on nonlinear effects. Technically, we employ the Fokker-Planck approach and contrast the analytical expressions with full numerical micromagnetic simulations. We show that when an external magnetic field is aligned parallel (antiparallel) to the Rashba field, the spin-orbit coupling enhances (reduces) the spin pumping current. In turn, the spin Hall effect and the Dzyaloshinskii-Moriya interaction are shown to increase the spin pumping current.",1812.09270v1 1998-12-16,Elementary excitations of magnetically ordered systems with orbital degeneracy,"The Holstein-Primakoff transformation is generalized to develop a quantum flavor wave theory for spin systems with orbital degeneracy. Elementary excitations consist of spin, orbital, and spin-orbital waves. Spin and spin-orbital waves couple each other due to orbital anisotropy and Hund's rule, resulting in new modes observable by inelastic neutron scattering. In the SU(4) limit, flavor waves are dispersionless along one or more directions, and give rise to quantum fluctuations of reduced dimensionality.",9812289v1 2011-10-01,Spin-orbital phase synchronization in the magnetic field-driven electron dynamics in a double quantum dot,"We study the dynamics of an electron confined in a one-dimensional double quantum dot in the presence of driving external magnetic fields. The orbital motion of the electron is coupled to the spin dynamics by spin orbit interaction of the Dresselhaus type. We derive an effective time-dependent Hamiltonian model for the orbital motion of the electron and obtain a synchronization condition between the orbital and the spin dynamics. From this model we deduce an analytical expression for the Arnold tongue and propose an experimental scheme for realizing the synchronization of the orbital and spin dynamics.",1110.0114v1 2013-01-16,Mechanical generation of spin current by spin-rotation coupling,"Spin-rotation coupling, which is responsible for angular momentum conversion between the electron spin and rotational deformations of elastic media, is exploited for generating spin current. This method requires neither magnetic moments nor spin-orbit interaction. The spin current generated in nonmagnets is calculated in presence of surface acoustic waves. We solve the spin diffusion equation, extended to include spin-rotation coupling, and find that larger spin currents can be obtained in materials with longer spin lifetimes. Spin accumulation induced on the surface is predicted to be detectable by time-resolved Kerr spectroscopy.",1301.3596v1 2009-10-30,Gravitational waveforms from unequal-mass binaries with arbitrary spins under leading order spin-orbit coupling,"The paper generalizes the structure of gravitational waves from orbiting spinning binaries under leading order spin-orbit coupling, as given in the work by K\""onigsd\""orffer and Gopakumar [PRD 71, 024039 (2005)] for single-spin and equal-mass binaries, to unequal-mass binaries and arbitrary spin configurations. The orbital motion is taken to be quasi-circular and the fractional mass difference is assumed to be small against one. The emitted gravitational waveforms are given in analytic form.",0910.5931v2 2022-04-15,Quantum phases of spin-orbital-angular-momentum coupled bosonic gases in optical lattices,"Spin-orbit coupling plays an important role in understanding exotic quantum phases. In this work, we present a scheme to combine spin-orbital-angular-momentum (SOAM) coupling and strong correlations in ultracold atomic gases. Essential ingredients of this setting is the interplay of SOAM coupling and Raman-induced spin-flip hopping, engineered by lasers that couples different hyperfine spin states. In the presence of SOAM coupling only, we find rich quantum phases in the Mott-insulating regime, which support different types of spin defects such as spin vortex and composite vortex with antiferromagnetic core surrounded by the outer spin vortex. Based on an effective exchange model, we find that these competing spin textures are a result of the interplay of Dzyaloshinskii-Moriya and Heisenberg exchange interactions. In the presence of both SOAM coupling and Raman-induced spin-flip hopping, more many-body phases appear, including canted-antiferromagnetic and stripe phases. Our prediction suggests that SOAM coupling could induce rich exotic many-body phases in the strongly interacting regime.",2204.07323v2 2017-08-24,Strong influence of spin-orbit coupling on magnetotransport in two-dimensional hole systems,"With a view to electrical spin manipulation and quantum computing applications, recent significant attention has been devoted to semiconductor hole systems, which have very strong spin-orbit interactions. However, experimentally measuring, identifying, and quantifying spin-orbit coupling effects in transport, such as electrically-induced spin polarizations and spin-Hall currents, are challenging. Here we show that the magnetotransport properties of two dimensional (2D) hole systems display strong signatures of the spin-orbit interaction. Specifically, the low-magnetic field Hall coefficient and longitudinal conductivity contain a contribution that is second order in the spin-orbit interaction coefficient and is non-linear in the carrier number density. We propose an appropriate experimental setup to probe these spin-orbit dependent magnetotransport properties, which will permit one to extract the spin-orbit coefficient directly from the magnetotransport.",1708.07247v2 2018-07-13,Spin-orbit coupling and correlations in three-orbital systems,"We investigate the influence of spin-orbit coupling $\lambda$ in strongly-correlated multiorbital systems that we describe by a three-orbital Hubbard-Kanamori model on a Bethe lattice. We solve the problem at all integer fillings $N$ with the dynamical mean-field theory using the continuous-time hybridization expansion Monte Carlo solver. We investigate how the quasiparticle renormalization $Z$ varies with the strength of spin-orbit coupling. The behavior can be understood for all fillings except $N=2$ in terms of the atomic Hamiltonian (the atomic charge gap) and the polarization in the $j$-basis due to spin-orbit induced changes of orbital degeneracies and the associated kinetic energy. At $N=2$, $\lambda$ increases $Z$ at small $U$ but suppresses it at large $U$, thus eliminating the characteristic Hund's metal tail in $Z(U)$. We also compare the effects of the spin-orbit coupling to the effects of a tetragonal crystal field. Although this crystal field also lifts the orbital degeneracy, its effects are different, which can be understood in terms of the different form of the interaction Hamiltonian expressed in the respective diagonal single-particle basis.",1807.05106v2 2013-06-28,"The role of orbital order in the stabilization of the $(π,0)$ ordered magnetic state in a minimal two-band model for iron pnictides","Spin wave excitations and stability of the ($\pi,0$) ordered magnetic state are investigated in a minimal two-band itinerant-electron model for iron pnictides. Presence of hopping anisotropy generates a strong ferro-orbital order in the $d_{xz}$ and $d_{yz}$ Fe orbitals. The orbital order sign is as observed in experiments. The induced ferro-orbital order strongly enhances the spin wave energy scale and stabilizes the magnetic state by optimizing the strength of the emergent AF and F spin couplings through optimal band fillings in the two orbitals. The calculated spin-wave dispersion is in quantitative agreement with neutron scattering measurements. Finite inter-orbital Hund's coupling is shown to further enhance the spin wave energies state by coupling the two magnetic sub-systems. A more realistic two-band model with less hopping anisotropy is also considered which yields not only the circular hole pockets, also correct ferro-orbital order and emergent F spin coupling.",1306.6727v2 2024-02-02,Photonic Spin-Orbit Coupling Induced by Deep-Subwavelength Structured Light,"We demonstrate both theoretically and experimentally beam-dependent photonic spin-orbit coupling in a two-wave mixing process described by an equivalent of the Pauli equation in quantum mechanics. The considered structured light in the system is comprising a superposition of two orthogonal spin-orbit-coupled states defined as spin up and spin down equivalents. The spin-orbit coupling is manifested by prominent pseudo spin precession as well as spin-transport-induced orbital angular momentum generation in a photonic crystal film of wavelength thickness. The coupling effect is significantly enhanced by using a deep-subwavelength carrier envelope, different from previous studies which depend on materials. The beam-dependent coupling effect can find intriguing applications; for instance, it is used in precisely measuring variation of light with spatial resolution up to 15 nm.",2402.01080v1 2018-01-09,Inverse engineering for fast transport and spin control of spin-orbit-coupled Bose-Einstein condensates in moving harmonic traps,"We investigate fast transport and spin manipulation of tunable spin-orbit-coupled Bose-Einstein condensates in a moving harmonic trap. Motivated by the concept of ""shortcuts to adiabaticity"", we design inversely the time-dependent trap position and spin-orbit coupling strength. By choosing appropriate boundary conditions we obtain fast transport and spin flip simultaneously. The non-adiabatic transport and relevant spin dynamics are illustrated with numerical examples, and compared with the adiabatic transport with constant spin-orbit-coupling strength and velocity. Moreover, the influence of nonlinearity induced by interatomic interaction is discussed in terms of the Gross-Pitaevskii approach, showing the robustness of the proposed protocols. With the state-of-the-art experiments, such inverse engineering technique paves the way for coherent control of spin-orbit-coupled Bose-Einstein condensates in harmonic traps.",1801.02887v1 2019-08-03,Experimental evidence for Zeeman spin-orbit coupling in layered antiferromagnetic conductors,"Most of solid-state spin physics arising from spin-orbit coupling, from fundamental phenomena to industrial applications, relies on symmetry-protected degeneracies. So does the Zeeman spin-orbit coupling, expected to manifest itself in a wide range of antiferromagnetic conductors. Yet, experimental proof of this phenomenon has been lacking. Here, we demonstrate that the N\'eel state of the layered organic superconductor $\kappa$-(BETS)$_2$FeBr$_4$ shows no spin modulation of the Shubnikov-de Haas oscillations, contrary to its paramagnetic state. This is unambiguous evidence for the spin degeneracy of Landau levels, a direct manifestation of the Zeeman spin-orbit coupling. Likewise, we show that spin modulation is absent in electron-doped Nd$_{1.85}$Ce$_{0.15}$CuO$_4$, which evidences the presence of N\'eel order in this cuprate superconductor even at optimal doping. Obtained on two very different materials, our results demonstrate the generic character of the Zeeman spin-orbit coupling.",1908.01236v2 2018-03-14,Inter-orbital topological superconductivity in spin-orbit coupled superconductors with inversion symmetry breaking,"We study the superconducting state of multi-orbital spin-orbit coupled systems in the presence of an orbitally driven inversion asymmetry assuming that the inter-orbital attraction is the dominant pairing channel. Although the inversion symmetry is absent, we show that superconducting states that avoid mixing of spin-triplet and spin-singlet configurations are allowed, and remarkably, spin-triplet states that are topologically nontrivial can be stabilized in a large portion of the phase diagram. The orbital-dependent spin-triplet pairing generally leads to topological superconductivity with point nodes that are protected by a nonvanishing winding number. We demonstrate that the disclosed topological phase can exhibit Lifshitz-type transitions upon different driving mechanisms and interactions, e.g., by tuning the strength of the atomic spin-orbit and inversion asymmetry couplings or by varying the doping and the amplitude of order parameter. Such distinctive signatures of the nodal phase manifest through an extraordinary reconstruction of the low-energy excitation spectra both in the bulk and at the edge of the superconductor.",1803.05158v2 2011-12-02,The contribution of spin torque to spin Hall coefficient and spin motive force in spin-orbit coupling system,"We derive rigorously the relativistic angular momentum conservation equation by means of quantum electrodynamics. The novel nonrelativistic spin current and torque in the spin-orbit coupling system, up to the order of $1/c^{4}$, are exactly investigated by using Foldy-Wouthuysen transformation. We find a perfect spin Hall coefficient including the contribution of spin torque dipole. A novel spin motive force, analogue to the Lorentz force, is also obtained for understanding of the spin Hall effect.",1112.0394v1 2005-09-23,Physical Limits of the ballistic and non-ballistic Spin-Field-Effect Transistor: Spin Dynamics in Remote Doped Structures,"We investigate the spin dynamics and relaxation in remotely-doped two dimensional electron systems where the dopants lead to random fluctuations of the Rashba spin-orbit coupling. Due to the resulting random spin precession, the spin relaxation time is limited by the strength and spatial scale of the random contribution to the spin-orbit coupling. We concentrate on the role of the randomness for two systems where the direction of the spin-orbit field does not depend on the electron momentum: the spin field-effect transistor with balanced Rashba and Dresselhaus couplings and the (011) quantum well. Both of these systems are considered as promising for the spintronics applications because of the suppression of the Dyakonov-Perel' mechanism there makes the realization of a spin field effect transistor in the diffusive regime possible. We demonstrate that the spin relaxation through the randomness of spin-orbit coupling imposes important physical limitations on the operational properties of these devices.",0509611v1 2016-08-23,The effect of spin-orbit coupling on the effective-spin correlation in YbMgGaO4,"Motivated by the recent experiments on the triangular lattice spin liquid YbMgGaO$_4$, we explore the effect of spin-orbit coupling on the effective-spin correlation of the Yb local moments. We point out the anisotropic interaction between the effective-spins on the nearest neighbor bonds is sufficient to reproduce the spin-wave dispersion of the fully polarized state in the presence of strong magnetic field normal to the triangular plane. We further evaluate the effective-spin correlation within the mean-field spherical approximation. We explicitly demonstrate that, the nearest-neighbor anisotropic effective-spin interaction, originating from the strong spin-orbit coupling, enhances the effective-spin correlation at the M points in the Brillouin zone. We identify these results as the strong evidence for the anisotropic interaction and the strong spin-orbit coupling in YbMgGaO$_4$.",1608.06445v2 2024-01-27,Interplay of altermagnetism and weak ferromagnetism in two-dimensional RuF$_4$,"Gaining growing attention in spintronics is a class of magnets displaying zero net magnetization and spin-split electronic bands called altermagnets. Here, by combining density functional theory and symmetry analysis, we show that RuF$_4$ monolayer is a two-dimensional $d$-wave altermagnet. Spin-orbit coupling leads to pronounced spin splitting of the electronic bands at the $\Gamma$ point by $\sim 100$ meV and turns the RuF$_4$ into a weak ferromagnet due to non trivial spin-momentum locking that cants the Ru magnetic moments. The net magnetic moment scales linearly with the spin-orbit coupling strength. Using group theory we derive an effective spin Hamiltonian capturing the spin-splitting and spin-momentum locking of the electronic bands. Disentanglement of the altermagnetic and spin-orbit coupling induced spin splitting uncovers to which extent the altermagnetic properties are affected by the spin-orbit coupling. Our results move the spotlight to the non trivial spin-momentum locking and weak ferromagnetism in the two-dimensional altermagnets relevant for novel venues in this emerging field of material science research.",2401.15424v1 2012-11-09,Interaction induced staggered spin-orbit order in two-dimensional electron gas,"We propose and formulate an interaction induced staggered spin-orbit order as a new emergent phase of two-dimensional Fermi gases. We show that when some form of inherent spin-splitting via Rashba-type spin-orbit coupling renders two helical Fermi surfaces to become significantly `nested', a Fermi surface instability arises. To lift this degeneracy, a spontaneous symmetry breaking spin-orbit density wave develops, causing a surprisingly large quasiparticle gapping with chiral electronic states. Since the staggered spin-orbit order is associated with a condensation energy, quantified by the gap value, destroying such spin-orbit interaction costs sufficiently large perturbation field or temperature or de-phasing time. BiAg$_2$ surface state is shown to be a representative system for realizing such novel spin-orbit interaction with tunable and large strength, and the spin-splitting is decoupled from charge excitations. These functional properties are relevant for spin-electronics, spin-caloritronics, and spin-Hall effect applications.",1211.2018v1 2011-07-13,BCS-BEC crossover in spin-orbit coupled two-dimensional Fermi gases,"The recent experimental realization of spin-orbit coupling for ultra-cold atoms has generated much interest in the physics of spin-orbit coupled degenerate Fermi gases. Although recently the BCS-BEC crossover in three-dimensional (3D) spin-orbit coupled Fermi gases has been intensively studied, the corresponding two-dimensional (2D) crossover physics has remained unexplored. In this paper, we investigate, both numerically and analytically, the BCS-BEC crossover physics in 2D degenerate Fermi gases in the presence of a Rashba type of spin-orbit coupling. We derive the mean field gap and atom number equations suitable for the 2D spin-orbit coupled Fermi gases and solve them numerically and self-consistently, from which the dependence of the ground state properties (chemical potential, superfluid pairing gap, ground state energy per atom) on the system parameters (e.g., binding energy, spin-orbit coupling strength) is obtained. Furthermore, we derive analytic expressions for these ground state quantities, which agree well with our numerical results within a broad parameter region. Such analytic expressions also agree qualitatively with previous numerical results for the 3D spin-orbit coupled Fermi gases, where analytic results are lacked. We show that with an increasing SOC strength, the chemical potential is shifted by a constant determined by the SOC strength. The superfluid pairing gap is enhanced significantly in the BCS limit for strong SOC, but only increases slightly in the BEC limit.",1107.2627v3 2018-07-19,Three-boson spectrum in the presence of 1D spin-orbit coupling: Efimov's generalized radial scaling law,"Spin-orbit coupled cold atom systems, governed by Hamiltonians that contain quadratic kinetic energy terms typical for a particle's motion in the usual Schr\""odinger equation and linear kinetic energy terms typical for a particle's motion in the usual Dirac equation, have attracted a great deal of attention recently since they provide an alternative route for realizing fractional quantum Hall physics, topological insulators, and spintronics physics. The present work focuses on the three-boson system in the presence of 1D spin-orbit coupling, which is most relevant to ongoing cold atom experiments. In the absence of spin-orbit coupling terms, the three-boson system exibits the Efimov effect: the entire energy spectrum is uniquely determined by the $s$-wave scattering length and a single three-body parameter, i.e., using one of the energy levels as input, the other energy levels can be obtained via Efimov's radial scaling law, which is intimately tied to a discrete scaling symmetry. It is demonstrated that the discrete scaling symmetry persists in the presence of 1D spin-orbit coupling, implying the validity of a generalized radial scaling law in five-dimensional space. The dependence of the energy levels on the scattering length, spin-orbit coupling parameters, and center-of-mass momentum is discussed. It is conjectured that three-body systems with other types of spin-orbit coupling terms are also governed by generalized radial scaling laws, provided the system exhibits the Efimov effect in the absence of spin-orbit coupling.",1807.07653v1 2020-10-05,Terrestrial Orbit-Spin Coupling Torque Episodes in Late 2020,"Orbit-spin coupling torques on the Earth in November 2020 are larger than at any other time between 2000 and 2050. This affords an opportunity to observe the terrestrial atmospheric response to the putative torque in near real time.",2010.02289v1 2006-01-30,Electric Dipole Induced Spin Resonance in Quantum Dots,"An alternating electric field, applied to a quantum dot, couples to the electron spin via the spin-orbit interaction. We analyze different types of spin-orbit coupling known in the literature and find two efficient mechanisms of spin control in quantum dots. The linear in momentum Dresselhaus and Rashba spin-orbit couplings give rise to a fully transverse effective magnetic field in the presence of a Zeeman splitting at lowest order in the spin-orbit interaction. The cubic in momentum Dresselhaus terms are efficient in a quantum dot with non-harmonic confining potential and give rise to a spin-electric coupling proportional to the orbital magnetic field. We derive an effective spin Hamiltonian, which can be used to implement spin manipulation on a timescale of $10 {\rm ns}$ with the current experimental setups.",0601674v2 2001-11-22,Theory for high spin systems with orbital degeneracy,"High-spin systems with orbital degeneracy are studied in the large spin limit. In the absence of Hund's coupling, the classical spin model is mapped onto disconnected orbital systems with spins up and down, respectively. The ground state of the isotropic model is an orbital valence bond state where each bond is an orbital singlet with parallel spins, and neighbouring bonds interact antiferromagnetically. The possible relevance to the transition metal oxides are discussed.",0111426v1 2015-03-23,Spin-Orbit Torques in Two-Dimensional Rashba Ferromagnets,"Magnetization dynamics in single-domain ferromagnets can be triggered by charge current if spin-orbit coupling is sufficiently strong. We apply functional Keldysh theory to investigate Rashba spin-orbit torques in metallic two-dimensional ferromagnets. A reactive, anti-damping-like spin-orbit torque as well as a dissipative, field-like torque are calculated microscopically, to the leading order in the spin-orbit interaction strength. By calculating the first vertex correction we show that the intrinsic anti-damping-like torque vanishes unless the scattering rates are spin-dependent.",1503.06872v2 2024-03-11,Spin-orbit coupling in symmetric and mixed spin-symmetry,"Synthetically spin-orbit coupling in cold atoms couples the pseudo-spin and spatial degrees of freedom, and therefore the inherent spin symmetry of the system plays an important role. In systems of two pseudo-spin degrees, two particles configure symmetric states and anti-symmetric states, but the spin symmetry can be mixed for more particles. We study the role of mixed spin symmetry in the presence of spin-orbit coupling and consider the system of three bosons with two hyper-fine states trapped in a harmonic potential. We investigate the ground state and the energy spectrum by implementing exact diagonalization. It is found that the interplay between spin-orbit coupling and repulsive interactions between anti-aligned pseudo-spins increases the population of the unaligned spin components in the ground state. The emergence of the mixed spin symmetric states compensates for the rise of the interaction energy. With the aligned interaction on, the avoided crossing between the ground state and the first excited state is observed only for small interaction, and this causes shape changes in the spin populations. Furthermore, we find that the pair correlation of the ground state shows similarly to that of Tonks-Girardeau gas even for relatively small contact interactions and such strong interaction feature is enhanced by the spin-orbit coupling.",2403.07188v1 2012-06-04,Von Neumann Entropy Spectra and Entangled Excitations in Spin-Orbital Models,"We consider the low-energy excitations of one-dimensional spin-orbital models which consist of spin waves, orbital waves, and joint spin-orbital excitations. Among the latter we identify strongly entangled spin-orbital bound states which appear as peaks in the von Neumann entropy (vNE) spectral function introduced in this work. The strong entanglement of bound states is manifested by a universal logarithmic scaling of the vNE with system size, while the vNE of other spin-orbital excitations saturates. We suggest that spin-orbital entanglement can be experimentally explored by the measurement of the dynamical spin-orbital correlations using resonant inelastic x-ray scattering, where strong spin-orbit coupling associated with the core hole plays a role.",1206.1062v1 2004-07-16,Influences of spin accumulation on the intrinsic spin Hall effect in two dimensional electron gases with Rashba spin-orbit coupling,"In a two dimensional electron gas with Rashba spin-orbit coupling, the external electric field may cause a spin Hall current in the direction perpendicular to the electric field. This effect was called the intrinsic spin Hall effect. In this paper, we investigate the influences of spin accumulation on this intrinsic spin Hall effect. We show that due to the existence of boundaries in a real sample, the spin Hall current generated by the intrinsic spin Hall effect will cause spin accumulation near the edges of the sample, and in the presence of spin accumulation, the spin Hall conductivity will not have a universal value. The influences of spin accumulation on the intrinsic spin Hall effect in narrow strips of two dimensional electron gases with Rashba spin-orbit coupling are investigated in detail.",0407419v1 2020-08-03,Interfacial spin-orbit torques,"Spin-orbit torques offer a promising mechanism for electrically controlling magnetization dynamics in nanoscale heterostructures. While spin-orbit torques occur predominately at interfaces, the physical mechanisms underlying these torques can originate in both the bulk layers and at interfaces. Classifying spin-orbit torques based on the region that they originate in provides clues as to how to optimize the effect. While most bulk spin-orbit torque contributions are well studied, many of the interfacial contributions allowed by symmetry have yet to be fully explored theoretically and experimentally. To facilitate progress, we review interfacial spin-orbit torques from a semiclassical viewpoint and relate these contributions to recent experimental results. Within the same model, we show the relationship between different interface transport parameters. For charges and spins flowing perpendicular to the interface, interfacial spin-orbit coupling both modifies the mixing conductance of magnetoelectronic circuit theory and gives rise to spin memory loss. For in-plane electric fields, interfacial spin-orbit coupling gives rise to torques described by spin-orbit filtering, spin swapping and precession. In addition, these same interfacial processes generate spin currents that flow into the non-magnetic layer. For in-plane electric fields in trilayer structures, the spin currents generated at the interface between one ferromagnetic layer and the non-magnetic spacer layer can propagate through the non-magnetic layer to produce novel torques on the other ferromagnetic layer.",2008.01182v1 2019-08-02,Two-dimensional orbital Hall insulators,"The orbital-Hall effect (OHE), similarly to the spin-Hall effect (SHE), refers to the creation of a transverse flow of orbital angular momentum that is induced by a longitudinally applied electric field. For systems in which the spin-orbit coupling (SOC) is sizeable, the orbital and spin angular momentum degrees of freedom are coupled, and an interrelationship between charge, spin and orbital angular momentum excitations is naturally established. The OHE has been explored mostly in metallic systems, where it can be quite strong. However, several of its features remain unexplored in two-dimensional (2D) materials. Here, we investigate the role of orbital textures for the OHE displayed by multi-orbital 2D materials. We predict the appearance of a rather large orbital Hall effect in these systems both in their metallic and insulating phases. In some cases, the orbital Hall currents are larger than the spin Hall ones, and their use as information carriers widens the development possibilities of novel spin-orbitronic devices.",1908.00927v2 2023-05-10,Inverse orbital Hall effect and orbitronic terahertz emission observed in the materials with weak spin-orbit coupling,"The Orbital Hall effect, which originates from materials with weak spin-orbit coupling, has attracted considerable interest for spin-orbitronic applications. Here, we demonstrate the inverse effect of the orbital Hall effect and observe orbitronic terahertz emission in the Ti and Mn materials. Through spin-orbit transition in the ferromagnetic layer, the generated orbital current can be converted to charge current in the Ti and Mn layers via the inverse orbital Hall effect. Furthermore, the inserted W layer provides an additional conversion of the orbital-charge current in the Ti and Mn layers, significantly enhancing the orbitronic terahertz emission. Moreover, the orbitronic terahertz emission can be manipulated by cooperating with the inverse orbital Hall effect and the inverse spin Hall effect in the different sample configurations. Our results not only discover the physical mechanism of condensed matter physics but also pave the way for designing promising spin-orbitronic devices and terahertz emitters.",2305.05830v1 2024-01-11,Orbital Hanle Magnetoresistance in a 3d Transition Metal,"The Hanle magnetoresistance is a telltale signature of spin precession in nonmagnetic conductors, in which strong spin-orbit coupling generates edge spin accumulation via the spin Hall effect. Here, we report the existence of a large Hanle magnetoresistance in single layers of Mn with weak spin-orbit coupling, which we attribute to the orbital Hall effect. The simultaneous observation of a sizable Hanle magnetoresistance and vanishing small spin Hall magnetoresistance in BiYIG/Mn bilayers corroborates the orbital origin of both effects. We estimate an orbital Hall angle of 0.016, an orbital relaxation time of 2 ps and diffusion length of the order of 2 nm in disordered Mn. Our findings indicate that current-induced orbital moments are responsible for magnetoresistance effects comparable to or even larger than those determined by spin moments, and provide a tool to investigate nonequilibrium orbital transport phenomena.",2401.05703v1 2020-03-01,Spin-orbit interaction and spin selectivity for tunneling electron transfer in DNA,"Electron transfer (ET) in biological molecules such as peptides and proteins consists of electrons moving between well defined localized states (donors to acceptors) through a tunneling process. Here we present an analytical model for ET by tunneling in DNA, in the presence of Spin-Orbit (SO) interaction, to produce a strong spin asymmetry with the intrinsic atomic SO strength in meV range. We obtain a Hamiltonian consistent with charge transport through $\pi$ orbitals on the DNA bases and derive the behavior of ET as a function of the injection state momentum, the spin-orbit coupling and barrier length and strength. A highly consistent scenario arises where two concomitant mechanisms for spin selection arises; spin interference and differential spin amplitude decay. High spin filtering can take place at the cost of reduced amplitude transmission assuming realistic values for the spin-orbit coupling. The spin filtering scenario is completed by addressing the spin dependent torque under the barrier, with a consistent conserved definition for the spin current.",2003.00582v2 2013-05-16,Interplay between spin-orbit interactions and a time-dependent electromagnetic field in monolayer graphene,"We apply a circularly and linearly polarized terahertz field on a monolayer of graphene taking into account spin-orbit interactions of the intrinsic and Rashba type. It turns out that the field can not only be used to induce a gap in the energy spectrum, but also to close an existing gap due to the different reaction of the spin components on circularly polarized light. Signatures of spin-orbit coupling on the density of states of the driven system can be observed even for energies where the static density of states is independent of spin-orbit interactions. Furthermore it is shown that the time evolution of the spin polarization and the orbital dynamics of an initial wave packet can be modulated by varying the ratio of the spin-orbit coupling parameters. Assuming that the system acquires a quasi stationary state, the optical conductivity of the irradiated sample is calculated. Our results confirm the multi step nature of the conductivity obtained recently, where the number of intermediate steps can be changed by adjusting the spin-orbit coupling parameters and the orientation of the field.",1305.3810v2 2024-03-14,Spin-Orbit Coupled Insulators and Metals on the Verge of Kitaev Spin Liquids in Ilmenite Heterostructures,"Competition and cooperation between electron correlation and relativistic spin-orbit coupling give rise to diverse exotic quantum phenomena in solids. An illustrative example is spin-orbit entangled quantum liquids, which exhibit remarkable features such as topological orders and fractional excitations. The Kitaev honeycomb model realizes such interesting states, called the Kitaev spin liquids, but its experimental feasibility is still challenging. Here we theoretically investigate hexagonal heterostructures including a candidate for the Kitaev magnets, MgIrO$_3$, to actively manipulate the electronic and magnetic properties toward realizing the Kitaev spin liquids. For three different structure types of ilmenite bilayers MgIrO$_3$/$A$TiO$_3$ with $A$ = Mn, Fe, Co, and Ni, we obtain the optimized lattice structures, the electronic band structures, the stable magnetic orders, and the effective magnetic couplings. We find that the spin-orbital coupled bands characterized by the pseudospin $j_{\rm eff}=$ 1/2 are retained in the MgIrO$_3$ layer for all the heterostructures, but the magnetic state and the band gap depend on the types of heterostructures as well as the $A$ atoms. In particular, one type becomes metallic irrespective of $A$, while the other two are mostly insulating. We show that the insulating cases provide spin-orbit coupled Mott insulating states with dominant Kitaev-type interactions, accompanied by different combinations of subdominant interactions depending on the heterostructural type and $A$, while the metallic cases realize spin-orbit coupled metals with various doping rates. Our results indicate that these hexagonal heterostructures are a good platform for engineering electronic and magnetic properties of the spin-orbital coupled correlated materials, including the possibility of Majorana Fermi surfaces and topological superconductivity.",2403.09112v1 2013-08-15,Spintronics and Pseudospintronics in Graphene and Topological Insulators,"The two-dimensional electron systems in graphene and in topological insulators are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites in terms of spin-orbit coupling strength. We briefly review the status of efforts to achieve long spin relaxation times in graphene with its weak spin-orbit coupling, and to achieve large current-induced spin polarizations in topological-insulator surface states that have strong spin-orbit coupling. We also comment on differences between the magnetic responses and dilute-moment coupling properties of the two systems, and on the pseudospin analog of giant magnetoresistance in bilayer graphene.",1308.3428v1 2012-06-05,Spin-Orbit Coupling in LaAlO$_3$/SrTiO$_3$ interfaces: Magnetism and Orbital Ordering,"The combination of Rashba spin-orbit coupling and electron correlations can induce unusual phenomena in the metallic interface between SrTiO$_3$ and LaAlO$_3$. We consider effects of Rashba spin-orbit coupling at this interface in the context of the recent observation of anisotropic magnetism. Firstly, we show how Rashba spin-orbit coupling in a system near a band-edge can account for the observed magnetic anisotropy. Secondly, we investigate the coupling between in-plane magnetic-moment anisotropy and nematicity in the form of an orbital imbalance between d$_{xz}$ / d$_{yz}$ orbitals. We estimate this coupling to be substantial in the low electron density regime. Such an orbital ordering can affect magneto transport.",1206.1060v2 2016-06-24,Low-energy physics of three-orbital impurity model with Kanamori interaction,"We discuss the low-energy physics of the three-orbital Anderson impurity model with the Coulomb interaction term of the Kanamori form which has orbital SO(3) and spin SU(2) symmetry and describes systems with partially occupied $t_{2g}$ shells. We focus on the case with two electrons in the impurity that is relevant to Hund's metals. Using the Schrieffer-Wolff transformation we derive an effective Kondo model with couplings between the bulk and impurity electrons expressed in terms of spin, orbital, and orbital quadrupole operators. The bare spin-spin Kondo interaction is much smaller than the orbit-orbit and spin-orbital couplings or is even ferromagnetic. Furthermore, the perturbative scaling equations indicate faster renormalization of the couplings related to orbital degrees of freedom compared to spin degrees of freedom. Both mechanisms lead to a slow screening of the local spin moment. The model thus behaves similarly to the related quantum impurity problem with a larger SU(3) orbital symmetry (Dworin-Narath interaction) where this was first observed. We find that the two problems actually describe the same low-energy physics since the SU(3) symmetry is dynamically established through the renormalization of the splittings of coupling constants to zero. The perturbative renormalization group results are corroborated with the numerical-renormalization group (NRG) calculations. The dependence of spin Kondo temperatures and orbital Kondo temperatures as a function of interaction parameters, the hybridization, and the impurity occupancy is calculated and discussed.",1606.07654v1 2016-05-16,Characteristics of persistent spin current components in a quasi-periodic Fibonacci ring with spin-orbit interactions: Prediction of spin-orbit coupling and on-site energy,"In the present work we investigate the behavior of all three components of persistent spin current in a quasi-periodic Fibonacci ring subjected to Rashba and Dresselhaus spin-orbit interactions. Analogous to persistent charge current in a conducting ring where electrons gain a Berry phase in presence of magnetic flux, spin Berry phase is associated during the motion of electrons in presence of a spin-orbit field which is responsible for the generation of spin current. The interplay between two spin-orbit fields along with quasi-periodic Fibonacci sequence on persistent spin current is described elaborately, and from our analysis, we can estimate the strength of any one of two spin-orbit couplings together with on-site energy, provided the other is known.",1605.04716v2 2013-01-27,Kondo Effect in the Presence of Spin-Orbit Coupling,"Recently, a series of noncentrosymmetric superconductors has been a subject of considerable interest since the discovery of superconductivity in CePt_3Si. In noncentrosymmetric materials, the degeneracy of bands is lifted in the presence of spin-orbit coupling. This will bring about new effects in the Kondo effect since the band degeneracy plays an important role in the scattering of electrons by localized spins. We investigate the single-impurity Kondo problem in the presence of spin-orbit coupling. We examine the effect of spin-orbit coupling on the scattering of conduction electrons, by using the Green's function method, for the s-d Hamiltonian, with employing a decoupling procedure. As a result, we obtain a closed system of equations of Green's functions, from which we can calculate physical quantities. The Kondo temperature T_K is estimated from a singularity of Green's functions. We show that T_K is reduced as the spin-orbit coupling constant \alpha is increased. When 2\alpha k_F is comparable to or greater than k_BT_K(\alpha=0), T_K shows an abrupt decrease as a result of the band splitting. This suggests a Kondo collapse accompanied with a sharp decrease of T_K. The log T-dependence of the resistivity will be concealed by the spin-orbit interaction.",1301.6355v1 2002-06-20,Spin switching in semiconductor quantum dots through spin-orbit coupling,"The spin-orbit coupling influences the total spin of semiconductor quantum dots. We analyze the theoretical prediction for the combined effects of spin-orbit coupling, weak vertical magnetic fields and deformation of the dot. Our results allow the characterization of the quantum dots as spin switches, controllable with electric gates.",0206387v2 2002-08-22,Electronic spin precession in semiconductor quantum dots with spin-orbit coupling,"The electronic spin precession in semiconductor dots is strongly affected by the spin-orbit coupling. We present a theory of the electronic spin resonance at low magnetic fields that predicts a strong dependence on the dot occupation, the magnetic field and the spin-orbit coupling strength. Coulomb interaction effects are also taken into account in a numerical approach.",0208425v1 2005-02-16,Vanishing of the Dissipationless Spin Hall Effect in a Diffusive Two-Dimensional Electron Gas with Spin-Orbit Coupling,"We propose a nonequilibrium Green's function approach to study the spin-Hall effect in a two-dimensional electron system with both the Rashba and Dresselhaus spin-orbit couplings. By taking into account the long-range electron-impurity scattering, the derived kinetic equations are solved numerically. It is found the vanishing of the total zero-temperature dissipationless spin-Hall effect, contributing from the intrinsic and disorder-mediated processes. This result has been examined in the wide ranges of spin-orbit coupling constants and electron density.",0502392v1 2012-03-29,Soliton Magnetization Dynamics in Spin-Orbit Coupled Bose-Einstein Condensates,"Ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support localized dark soliton excitations that show periodic density dynamics in real space. In addition to the density feature, solitons also carry a localized pseudo-spin magnetization that exhibits a rich and tunable dynamics. Analytic results for Rashba-type spin-orbit coupling and spin-invariant interactions predict a conserved magnitude and precessional motion for the soliton magnetization that allows for the simulation of spin-related geometric phases recently seen in electronic transport measurements.",1203.6684v1 2012-03-19,Spin-orbit couplings between distant electrons trapped individually on liquid helium,"We propose an approach to entangle spins of electrons floating on liquid helium by coherently manipulating their spin-orbit interactions. The configuration consists of single electrons, confined individually on liquid helium by the microelectrodes, moving along the surface as the harmonic oscillators. It has been known that the spin of an electron could be coupled to its orbit (i.e., the vibrational motion) by properly applying a magnetic field. Based on this single electron spin-orbit coupling, here we show that a Jaynes-Cummings (JC) type interaction between the spin of an electron and the orbit of another electron at a distance could be realized via the strong Coulomb interaction between the electrons. Consequently, the proposed JC interaction could be utilized to realize a strong orbit-mediated spin-spin coupling and implement the desirable quantum information processing between the distant electrons trapped individually on liquid helium.",1203.4079v2 2012-01-08,Spin-orbit coupled Fermi liquid theory of ultra-cold magnetic dipolar fermions,"We investigate Fermi liquid states of the ultra-cold magnetic dipolar Fermi gases in the simplest two-component case including both thermodynamic instabilities and collective excitations. The magnetic dipolar interaction is invariant under the simultaneous spin-orbit rotation, but not under either the spin or the orbit one. Therefore, the corresponding Fermi liquid theory is intrinsically spin-orbit coupled. This is a fundamental feature of magnetic dipolar Fermi gases different from electric dipolar ones. The Landau interaction matrix is calculated and is diagonalized in terms of the spin-orbit coupled partial-wave channels of the total angular momentum J. The leading thermodynamic instabilities lie in the channels of ferromagnetism hybridized with the ferronematic order with J = 1+ and the spin-current mode with J = 1-, where + and - represent even and odd parities, respectively. An exotic propagating collective mode is identified as spin-orbit coupled Fermi surface oscillations in which spin distribution on the Fermi surface exhibits a topologically nontrivial hedgehog configuration.",1201.1607v3 2023-11-27,Gilbert damping in two-dimensional metallic anti-ferromagnets,"A finite spin life-time of conduction electrons may dominate Gilbert damping of two-dimensional metallic anti-ferromagnets or anti-ferromagnet/metal heterostructures. We investigate the Gilbert damping tensor for a typical low-energy model of a metallic anti-ferromagnet system with honeycomb magnetic lattice and Rashba spin-orbit coupling for conduction electrons. We distinguish three regimes of spin relaxation: exchange-dominated relaxation for weak spin-orbit coupling strength, Elliot-Yafet relaxation for moderate spin-orbit coupling, and Dyakonov-Perel relaxation for strong spin-orbit coupling. We show, however, that the latter regime takes place only for the in-plane Gilbert damping component. We also show that anisotropy of Gilbert damping persists for any finite spin-orbit interaction strength provided we consider no spatial variation of the N\'eel vector. Isotropic Gilbert damping is restored only if the electron spin-orbit length is larger than the magnon wavelength. Our theory applies to MnPS3 monolayer on Pt or to similar systems.",2311.16268v2 2018-09-28,Spin-orbit crossed susceptibility in topological Dirac semimetals,"We theoretically study the spin-orbit crossed susceptibility of topological Dirac semimetals. Because of strong spin-orbit coupling, the orbital motion of electrons is modulated by Zeeman coupling, which contributes to orbital magnetization. We find that the spin-orbit crossed susceptibility is proportional to the separation of the Dirac points and it is highly anisotropic. The orbital magnetization is induced only along the rotational symmetry axis. We also study the conventional spin susceptibility. The spin susceptibility exhibits anisotropy and the spin magnetization is induced only along the perpendicular to the rotational symmetry axis in contrast to the spin-orbit crossed susceptibility. We quantitatively compare the two susceptibilities and find that they can be comparable.",1809.10852v2 2019-03-29,Spin-Orbital Hallmarks of Unconventional Superconductors Without Inversion Symmetry,"The spin-orbital polarization of superconducting excitations in momentum space is shown to provide distinctive marks of unconventional pairing in the presence of inversion symmetry breaking.Taking the prototypical example of an electronic system with atomic spin-orbit and orbital-Rashba couplings, we provide a general description of the spin-orbital textures and their most striking changeover moving from the normal to the superconducting state. We find that the variation of the spin-texture is strongly imprinted by the combination of the misalignment of spin-triplet d-vector with the inversion asymmetry g-vector coupling and the occurrence of superconducting nodal excitations. Remarkably, the multi-orbital character of the superconducting state allows to unveil a unique type of topological transition for the spin-winding around the nodal points. This finding indicates the fundamental topological relation between chiral and spin-winding in nodal superconductors. By analogy between spin- and orbital-triplet pairing we point out how orbital polarization patterns can be also employed to assess the character of the superconducting state.",1903.12379v2 2024-03-21,Spin-orbit interaction with large spin in the semi-classical regime,"We consider the time dependent Schr\""odinger equation with a coupling spin-orbit in the semi-classical regime $\hbar\searrow 0$ and large spin number $\spin\rightarrow +\infty$ such that $\hbar^\delta\spin=c$ where $c>0$ and $\delta>0$ are constant. The initial state $\Psi(0)$ is a product of an orbital coherent state in $L^2(\R^d)$ and a spin coherent state in a spin irreducible representation space ${\mathcal H}_{2\spin +1}$. For $\delta <1$, at the leading order in $\hbar$, the time evolution $\Psi(t)$ of $ \Psi(0)$ is well approximated by the product of an orbital and a spin coherent state. Nevertheless for $1/2<\delta<1$ the quantum orbital leaves the classical orbital. For $\delta=1$ we prove that this last claim is no more true when the interaction depends on the orbital variables. For the Dicke model, we prove that the orbital partial trace of the projector on $\Psi(t)$ is a mixed state in $L^2(\R)$ for small $t>0$.",2403.14408v1 2011-12-19,Counterflow of spontaneous mass currents in trapped spin-orbit coupled Fermi gases,"We use the Bogoliubov-de Gennes formalism and study the ground-state phases of trapped spin-orbit coupled Fermi gases in two dimensions. Our main finding is that the presence of a symmetric (Rashba type) spin-orbit coupling spontaneously induces counterflowing mass currents in the vicinity of the trap edge, i.e. $\uparrow$ and $\downarrow$ particles circulate in opposite directions with equal speed. These currents flow even in noninteracting systems, but their strength decreases toward the molecular BEC limit, which can be achieved either by increasing the spin-orbit coupling or the interaction strength. These currents are also quite robust against the effects of asymmetric spin-orbit couplings in $x$ and $y$ directions, gradually reducing to zero as the spin-orbit coupling becomes one dimensional. We compare our results with those of chiral p-wave superfluids/superconductors.",1112.4468v2 2012-03-13,Impact of Dresselhaus vs. Rashba spin-orbit coupling on the Holstein polaron,"We utilize an exact variational numerical procedure to calculate the ground state properties of a polaron in the presence of Rashba and linear Dresselhaus spin-orbit coupling. We find that when the linear Dresselhaus spin-orbit coupling approaches the Rashba spin-orbit coupling, the Van-Hove singularity in the density of states will be shifted away from the bottom of the band and finally disappear when the two spin-orbit couplings are tuned to be equal. The effective mass will be suppressed; the trend will become more significant for low phonon frequency. The presence of two dominant spin-orbit couplings will make it possible to tune the effective mass with more varied observables.",1203.2795v1 2012-11-09,Metal-insulator transition in three-band Hubbard model with strong spin-orbit interaction,"Recent investigations suggest that both spin-orbit coupling and electron correlation play very crucial roles in the $5d$ transition metal oxides. By using the generalized Gutzwiller variational method and dynamical mean-field theory with the hybridization expansion continuous time quantum Monte Carlo as impurity solver, the three-band Hubbard model with full Hund's rule coupling and spin-orbit interaction terms, which contains the essential physics of partially filled $t_{2g}$ sub-shell of $5d$ materials, is studied systematically. The calculated phase diagram of this model exhibits three distinct phase regions, including metal, band insulator and Mott insulator respectively. We find that the spin-orbit coupling term intends to greatly enhance the tendency of the Mott insulator phase. Furthermore, the influence of the electron-electron interaction on the effective strength of spin-orbit coupling in the metallic phase is studied in detail. We conclude that the electron correlation effect on the effective spin-orbit coupling is far beyond the mean-field treatment even in the intermediate coupling region.",1211.2055v1 2013-07-05,Spin-orbit coupled fermions in ladder-like optical lattices at half-filling,"We study the ground-state phase diagram of two-component fermions loaded in a ladder-like lattice at half filling in the presence of spin-orbit coupling. For repulsive fermions with unidirectional spin-orbit coupling along the legs we identify a N\'{e}el state which is separated from rung-singlet and ferromagnetic states by Ising phase transition lines. These lines cross for maximal spin-orbit coupling and a direct Gaussian phase transition between rung-singlet and ferro phases is realized. For the case of Rashba-like spin-orbit coupling, besides the rung singlet phases two distinct striped ferromagnetic phases are formed. In case of attractive fermions with spin-orbit coupling at half-filling for decoupled chains we identify a dimerized state that separates a singlet superconductor and a ferromagnetic states.",1307.1607v1 2015-04-19,Hydrodynamics of Normal Atomic Gases with Spin-orbit Coupling,"Successful realization of spin-orbit coupling in atomic gases by the NIST scheme opens the prospect of studying the effects of spin-orbit coupling on many-body physics in an unprecedentedly controllable way. Here we derive the linearized hydrodynamic equations for the normal atomic gases of the spin-orbit coupling by the NIST scheme with zero detuning. We show that the hydrodynamics of the system crucially depends on the momentum susceptibilities which can be modified by the spin-orbit coupling. We reveal the effects of the spin-orbit coupling on the sound velocities and the dipole mode frequency of the gases by applying our formalism to the ideal Fermi gas. We also discuss the generalization of our results to other situations.",1504.04786v2 2017-10-29,Contact theory for spin-orbit-coupled Fermi gases,"We develop the contact theory for spin-orbit-coupled Fermi gases. By using a perturbation method, we derive analytically the universal two-body behavior at short distance, which does not depend on the short-range details of interatomic potentials. We find that two new scattering parameters need to be introduced because of spin-orbit coupling, besides the traditional $s$- and $p$-wave scattering length (volume) and effective ranges. This is a general and unique feature for spin-orbit-coupled systems. Consequently, two new adiabatic energy relations with respect to the new scattering parameters are obtained, in which a new contact is involved because of spin-orbit coupling. In addition, we derive the asymptotic behavior of the large-momentum distribution, and find that the subleading tail is corrected by the new contact. This work paves the way for exploring the profound properties of spin-orbit-coupled many-body systems, according to two-body solutions.",1710.10579v2 2018-10-16,Induced spin-orbit coupling in silicon thin films by bismuth doping,"We demonstrate an enhancement of the spin-orbit coupling in silicon (Si) thin films by doping with bismuth (Bi), a heavy metal, using ion implantation. Quantum corrections to conductance at low temperature in phosphorous-doped Si before and after Bi implantation is measured to probe the increase of the spin-orbit coupling, and a clear modification of magnetoconductance signals is observed: Bi doping changes magnetoconductance from weak localization to the crossover between weak localization and weak antilocalization. The elastic diffusion length, phase coherence length and spin-orbit coupling length in Si with and without Bi implantation are estimated, and the spin-orbit coupling length after the Bi doping becomes the same order of magnitude (Lso = 54 nm) with the phase coherence length (L{\phi} = 35 nm) at 2 K. This is an experimental proof that the spin-orbit coupling strength in Si thin film is tunable by doping with heavy metals.",1810.06878v1 2011-01-06,Quantum phase transitions in a strongly entangled spin-orbital chain: A field-theoretical approach,"Motivated by recent experiments on quasi-1D vanadium oxides, we study quantum phase transitions in a one-dimensional spin-orbital model describing a Haldane chain and a classical Ising chain locally coupled by the relativistic spin-orbit interaction. By employing a field-theoretical approach, we analyze the topology of the ground-state phase diagram and identify the nature of the phase transitions. In the strong coupling limit, a long-range N\'eel order of entangled spin and orbital angular momentum appears in the ground state. We find that, depending on the relative scales of the spin and orbital gaps, the linear chain follows two distinct routes to reach the N\'eel state. First, when the orbital exchange is the dominating energy scale, a two-stage ordering takes place in which the magnetic transition is followed by melting of the orbital Ising order; both transitions belong to the two-dimensional Ising universality class. In the opposite limit, the low-energy orbital modes undergo a continuous reordering transition which represents a line of Gaussian critical points. On this line the orbital degrees of freedom form a Tomonaga-Luttinger liquid. We argue that the emergence of the Gaussian criticality results from merging of the two Ising transitions in the strong hybridization region where the characteristic spin and orbital energy scales become comparable. Finally, we show that, due to the spin-orbit coupling, an external magnetic field acting on the spins can induce an orbital Ising transition.",1101.1268v3 2015-03-23,Critical Temperature and Tunneling Spectroscopy of Superconductor-Ferromagnet Hybrids with Intrinsic Rashba-Dresselhaus Spin-Orbit Coupling,"We investigate theoretically how the proximity effect in superconductor/ferromagnet hybrid structures with intrinsic spin-orbit coupling manifests in the density of states and critical temperature. To describe a general scenario, we allow for both Rashba and Dresselhaus type spin-orbit coupling. Our results are obtained via the quasiclassical theory of superconductivity, extended to include spin-orbit coupling in the Usadel equation and Kupriyanov--Lukichev boundary conditions. Unlike previous works, we have derived a Riccati parametrization of the Usadel equation with spin-orbit coupling which allows us to address the full proximity regime. First, we consider the density of states in both SF bilayers and SFS trilayers, where the spectroscopic features in the latter case are sensitive to the phase difference between the two superconductors. We find that the presence of spin-orbit coupling leaves clear spectroscopic fingerprints in the density of states due to its role in creating spin-triplet Cooper pairs. Unlike SF and SFS structures without spin-orbit coupling, the density of states in the present case depends strongly on the direction of magnetization. We show that the spin-orbit coupling can stabilize singlet superconductivity even in the presence of a strong exchange field $h \gg \Delta$. This leads to the possibility of a magnetically tunable minigap: changing the direction of the exchange field opens and closes the minigap. We also determine how the critical temperature $T_c$ of an SF bilayer is affected by spin-orbit coupling and demonstrate that one can achieve a spin-valve effect with a single ferromagnet. We find that $T_c$ displays highly non-monotonic behavior both as a function of the magnetization direction and the type and direction of the spin-orbit coupling, offering a new way to exert control over the superconductivity of proximity structures.",1503.06835v2 2019-03-17,Sensing Kondo correlations in a suspended carbon nanotube mechanical resonator with spin-orbit coupling,"We study electron mechanical coupling in a suspended carbon nanotube (CNT) quantum dot device. Electron spin couples to the flexural vibration mode due to spin-orbit coupling in the electron tunneling processes. In the weak coupling limit, i.e. electron-vibration coupling is much smaller than the electron energy scale, the damping and resonant frequency shift of the CNT resonator can be obtained by calculating the dynamical spin susceptibility. We find that strong spin-flip scattering processes in Kondo regime significantly affect the mechanical motion of the carbon nanotube: Kondo effect induces strong damping and frequency shift of the CNT resonator.",1903.07049v1 2017-11-19,SU($N$) spin-wave theory: Application to spin-orbital Mott insulators,"We present the application of the SU($N$) ($N>2$) spin-wave theory to spin-orbital Mott insulators whose ground states exhibit magnetic orders. When taking both the spin and orbital degrees of freedom into account rather than projecting onto the Kramers doublet, the lowest spin-orbital locking energy levels, due to the inevitable spin-orbital multipole exchange interactions, the SU($N$) spin-wave theory should take the place of the SU($2$) one. To implement the application, we introduce an efficient general local mean field approach which involves all the local fluctuations into the SU($N$) linear spin-wave theory. Our approach is tested firstly by calculating the multipolar spin-wave spectra of the SU($4$) antiferromagnetic model. Then we apply it to spin-orbital Mott insulators. It is revealed that the Hund's coupling would influence the effectiveness of the isospin-$1/2$ representation when the spin orbital coupling is not large enough. Besides, we also calculate the spin-wave spectra based on the first principle calculations for two concrete materials, $\alpha$-RuCl$_3$ and Sr$_2$IrO$_4$. The SU($N$) spin-wave theory appropriately depicts the low-energy magnons and the spin-orbital excitations qualitatively.",1711.07041v1 2020-06-24,Landau levels in spin-orbit coupling proximitized graphene: bulk states,"We study the magnetic-field dependence of Landau levels in graphene proximitized by large spin-orbit coupling materials, such as transition-metal dichalcogenides or topological insulators. In addition to the Rashba coupling, two types of intrinsic spin-orbit interactions, uniform (Kane-Mele type) and staggered (valley Zeeman type), are included, to resolve their interplay with magnetic orbital effects. Employing a continuum model approach, we derive analytic expressions for low-energy Landau levels, which can be used to extract local orbital and spin-orbit coupling parameters from scanning probe spectroscopy experiments. We compare different parameter regimes to identify fingerprints of relative and absolute magnitudes of intrinsic spin-orbit coupling in the spectra. The inverted band structure of graphene proximitized by WSe$_2$ leads to an interesting crossing of Landau states across the bulk gap at a crossover field, providing insights into the size of Rashba spin-orbit coupling. Landau level spectroscopy can help to resolve the type and signs of the intrinsic spin-orbit coupling by analyzing the symmetry in energy and number of crossings in the Landau fan chart. Finally, our results suggest that the strong response to the magnetic field of Dirac electrons in proximitized graphene can be associated with extremely large self-rotating magnetic moments.",2006.13651v1 2023-03-21,Intrinsic Magnon Orbital Hall Effect in Honeycomb Antiferromagnets,"We theoretically investigate the transport of magnon orbitals in a honeycomb antiferromagnet. We find that the magnon orbital Berry curvature is finite even without spin-orbit coupling and thus the resultant magnon orbital Hall effect is an intrinsic property of the honeycomb antiferromagnet rooted only in the exchange interaction and the lattice structure. Due to the intrinsic nature of the magnon orbital Hall effect, the magnon orbital Nernst conductivity is estimated to be orders of magnitude larger than the predicted values of the magnon spin Nernst conductivity that requires finite spin-orbit coupling. For the experimental detection of the predicted magnon orbital Hall effect, we invoke the magnetoelectric effect that couples the magnon orbital and the electric polarization, which allows us to detect the magnon orbital accumulation through the local voltage measurement. Our results pave a way for a deeper understanding of the topological transport of the magnon orbitals and also its utilization for low-power magnon-based orbitronics, namely magnon orbitronics.",2303.11687v1 2010-03-13,Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin-orbit and leading order in spin(1)-spin(2) and spin-squared couplings,"A quasi-Keplerian parameterisation for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin-spin and next-to-leading order spin-orbit interactions. Rotational deformation of the compact objects is incorporated. For arbitrary mass ratios the spin orientations are taken to be parallel or anti-parallel to the orbital angular momentum vector. The emitted gravitational wave forms are given in analytic form up to 2PN point particle, 1.5PN spin orbit and 1PN spin-spin contributions, where the spins are counted of 0PN order.",1003.2735v4 2010-04-18,Spin Orbit Coupling and Spin Waves in Ultrathin Ferromagnets: The Spin Wave Rashba Effect,"We present theoretical studies of the influence of spin orbit coupling on the spin wave excitations of the Fe monolayer and bilayer on the W(110) surface. The Dzyaloshinskii-Moriya interaction is active in such films, by virtue of the absence of reflection symmetry in the plane of the film. When the magnetization is in plane, this leads to a linear term in the spin wave dispersion relation for propagation across the magnetization. The dispersion relation thus assumes a form similar to that of an energy band of an electron trapped on a semiconductor surfaces with Rashba coupling active. We also show SPEELS response functions that illustrate the role of spin orbit coupling in such measurements. In addition to the modifications of the dispersion relations for spin waves, the presence of spin orbit coupling in the W substrate leads to a substantial increase in the linewidth of the spin wave modes. The formalism we have developed applies to a wide range of systems, and the particular system explored in the numerical calculations provides us with an illustration of phenomena which will be present in other ultrathin ferromagnet/substrate combinations.",1004.3066v1 2019-06-27,Extrinsic Spin-Orbit Coupling and Spin Relaxation in Phosphorene,"An effective Hamiltonian is derived to describe the conduction band of monolayer black phosphorus (phosphorene) in the presence of spin-orbit coupling and external electric field. Envelope function approximation along with symmetry arguments and Lowdin partitioning are utilized to derive extrinsic spin-orbit coupling. The resulting spin splitting appears in fourth order perturbation terms and is shown to be linear in both the magnitude of the external electric field and the strength of the atomic spin-orbit coupling, similar to the Bychkov-Rashba expression but with an in-plane anisotropy. The anisotropy depends on the coupling between conduction band and other bands both close and distant in energy. The spin relaxation of conduction electrons is then calculated within the Dyakonov-Perel mechanism where momentum scattering randomizes the polarization of a spin ensemble. We show how the anisotropic Fermi contour and the anisotropic extrinsic spin splitting contribute to the anisotropy of spin-relaxation time. Scattering centers in the substrate are considered to be charged impurities with screened Coulomb potential.",1906.11939v2 2017-07-31,Spin-orbit torques from interfacial spin-orbit coupling for various interfaces,"We use a perturbative approach to study the effects of interfacial spin-orbit coupling in magnetic multilayers by treating the two-dimensional Rashba model in a fully three-dimensional description of electron transport near an interface. This formalism provides a compact analytic expression for current-induced spin-orbit torques in terms of unperturbed scattering coefficients, allowing computation of spin-orbit torques for various contexts, by simply substituting scattering coefficients into the formulas. It applies to calculations of spin-orbit torques for magnetic bilayers with bulk magnetism, those with interface magnetism, a normal metal/ferromagnetic insulator junction, and a topological insulator/ferromagnet junction. It predicts a dampinglike component of spin-orbit torque that is distinct from any intrinsic contribution or those that arise from particular spin relaxation mechanisms. We discuss the effects of proximity-induced magnetism and insertion of an additional layer and provide formulas for in-plane current, which is induced by a perpendicular bias, anisotropic magnetoresistance, and spin memory loss in the same formalism.",1707.09847v1 2015-12-20,Magnetic and nematic phases in a Weyl type spin-orbit-coupled spin-1 Bose gas,"We present a variational study of the spin-1 Bose gases in a harmonic trap with three-dimensional spin-orbit coupling of Weyl type. For weak spin-orbit coupling, we treat the single-particle ground states as the form of perturbational harmonic oscillator states in the lowest total angular momentum manifold with $j=1, m_j=1,0,-1$. When the two-body interaction is considered, we set the trail order parameter as the superposition of three degenerate single-particle ground-states and the weight coefficients are determined by minimizing the energy functional. Two ground state phases, namely the magnetic and the nematic phases, are identified depending on the spin-independent and the spin-dependent interactions. Unlike the non-spin-orbit-coupled spin-1 Bose-Einstein condensate for which the phase boundary between the magnetic and the nematic phase lies exactly at zero spin-dependent interaction, the boundary is modified by the spin-orbit-coupling. We find the magnetic phase is featured with phase-separated density distributions, 3D skyrmion-like spin textures and competing magnetic and biaxial nematic orders, while the nematic phase is featured with miscible density distributions, zero magnetization and spatially modulated uniaxial nematic order. The emergence of higher spin order creates new opportunities for exploring spin-tensor-related physics in spin-orbit coupled superfluid.",1512.06394v1 2002-11-29,Spin-Orbit induced semiconductor spin guides,"The tunability of the Rashba spin-orbit coupling allows to build semiconductor heterostructures with space modulated coupling intensities. We show that a wire-shaped spin-orbit modulation in a quantum well can support propagating electronic states inside the wire only for a certain spin orientation and, therefore, it acts as an effective spin transmission guide for this particular spin orientation.",0211694v1 2003-07-27,Universal Intrinsic Spin-Hall Effect,"We describe a new effect in semiconductor spintronics that leads to dissipationless spin-currents in paramagnetic spin-orbit coupled systems. We argue that in a high mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin-current that flows perpendicular to the charge current is intrinsic. In the usual case where both spin-orbit split bands are occupied, the spin-Hall conductivity has a universal value.",0307663v2 2004-12-22,Spin-orbit induced interference in polygon-structures,"We investigate the spin-orbit induced spin-interference pattern of ballistic electrons travelling along any regular polygon. It is found that the spin-interference depends strongly on the Rashba and Dresselhaus spin-orbit constants as well as on the sidelength and alignment of the polygon. We derive the analytical formulae for the limiting cases of either zero Dresselhaus or zero Rashba spin-orbit coupling, including the result obtained for a circle. We calculate the nonzero Dresselhaus and Rashba case numerically for the square, triangle, hexagon, and circle and discuss the observability of the spin-interference which can potentially be used to measure the Rashba and Dresselhaus coefficients.",0412609v1 2018-08-24,"Residual spin susceptibility in the spin-triplet, orbital-singlet model","Nuclear magnetic resonance (NMR) and Knight shift measurements are critical tools in the identification of spin-triplet superconductors. We discuss the effects of spin orbit coupling on the Knight shift and susceptibilities for a variety of spin triplet multi-orbital gap functions with orbital-singlet character and compare their responses to ""traditional"" single band spin-triplet ($p_x+ip_y$) superconductors. We observe a non-negligible residual spin-susceptibility at low temperature.",1808.08029v1 2006-03-14,Spin entanglement induced by spin-orbit interactions in coupled quantum dots,"We theoretically explore the possibility of creating spin quantum entanglement in a system of two electrons confined respectively in two vertically coupled quantum dots in the presence of Rashba type spin-orbit coupling. We find that the system can be described by a generalized Jaynes - Cummings model of two modes bosons interacting with two spins. The lower excitation states of this model are calculated to reveal the underlying physics of the far infrared absorption spectra. The analytic perturbation approach shows that an effective transverse coupling of spins can be obtained by eliminating the orbital degrees of freedom in the large detuning limit. Here, the orbital degrees of freedom of the two electrons, which are described by two modes of bosons, serve as a quantized data bus to exchange the quantum information between two electrons. Then a nontrivial two-qubit logic gate is realized and spin entanglement between the two electrons is created by virtue of spin-orbit coupling.",0603363v2 2006-04-27,Orbital and spin relaxation in single and coupled quantum dots,"Phonon-induced orbital and spin relaxation rates of single electron states in lateral single and double quantum dots are obtained numerically for realistic materials parameters. The rates are calculated as a function of magnetic field and interdot coupling, at various field and quantum dot orientations. It is found that orbital relaxation is due to deformation potential phonons at low magnetic fields, while piezoelectric phonons dominate the relaxation at high fields. Spin relaxation, which is dominated by piezoelectric phonons, in single quantum dots is highly anisotropic due to the interplay of the Bychkov-Rashba and Dresselhaus spin-orbit couplings. Orbital relaxation in double dots varies strongly with the interdot coupling due to the cyclotron effects on the tunneling energy. Spin relaxation in double dots has an additional anisotropy due to anisotropic spin hot spots which otherwise cause giant enhancement of the rate at useful magnetic fields and interdot couplings. Conditions for the absence of the spin hot spots in in-plane magnetic fields (easy passages) and perpendicular magnetic fields (weak passages) are formulated analytically for different growth directions of the underlying heterostructure. It is shown that easy passages disappear (spin hot spots reappear) if the double dot system loses symmetry by an xy-like perturbation.",0604633v1 2017-12-21,Cooper Pairing in A Doped 2D Antiferromagnet with Spin-Orbit Coupling,"We study the two-dimensional Hubbard model with the Rashba type spin-orbit coupling within and beyond the mean-field theory. The antiferromagnetic ground state for the model at half-filling and the Cooper pairing induced by antiferromagnetic spin fluctuations near half-filling are examined based on the random-phase approximation. We show that the antiferromagnetic order is suppressed and the magnetic susceptibility turns out to be anisotropic in the presence of the spin-orbit coupling. Energy spectrums of transverse spin fluctuations are obtained and the effective interactions between holes mediated by antiferromagnetic spin fluctuations are deduced in the case of low hole doping. It seems that the spin-orbit coupling tends to form s+p-wave Cooper pairs, while the s+d-wave pairing is dominant when the spin-orbit coupling is absent.",1712.07908v1 2011-05-21,Quantum states and linear response in dc and electromagnetic fields for charge current and spin polarization of electrons at Bi/Si interface with giant spin-orbit coupling,"An expansion of the nearly free-electron model constructed by Frantzeskakis, Pons and Grioni [Phys. Rev. B {\bf 82}, 085440 (2010)] describing quantum states at Bi/Si(111) interface with giant spin-orbit coupling is developed and applied for the band structure and spin polarization calculation, as well as for the linear response analysis for charge current and induced spin caused by dc field and by electromagnetic radiation. It is found that the large spin-orbit coupling in this system may allow resolving the spin-dependent properties even at room temperature and at realistic collision rate. The geometry of the atomic lattice combined with spin-orbit coupling leads to an anisotropic response both for current and spin components related to the orientation of the external field. The in-plane dc electric field produces only the in-plane components of spin in the sample while both the in-plane and out-of-plane spin components can be excited by normally propagating electromagnetic wave with different polarizations.",1105.4215v1 2021-06-21,Spin structure factors of doped monolayer Germanene in the presence of spin-orbit coupling,"In this paper, we present a Kane-Mele model in the presence of magnetic field and next nearest neighbors hopping amplitudes for investigations of the spin susceptibilities of Germanene layer. Green's function approach has been implemented to find the behavior of dynamical spin susceptibilities of Germanene layer within linear response theoryand in the presence of magnetic field and spin-orbit coupling at finite temperature. Our results show the magnetic excitation mode for both longitudinal and transverse components of spin tends to higher frequencies with spin-orbit coupling strength. Moreover the frequency positions of sharp peaks in longitudinal dynamical spin susceptibility are not affected by variation of magnetic field while the peaks in transverse dynamical susceptibility moves to lower frequencies with magnetic field. The effects of electron doping on frequency behaviors of spin susceptibilities have been addressed in details. Finally the temperature dependence of static spin structure factors due to the effects of spin-orbit coupling, magnetic field and chemical potential has been studied.",2106.11377v1 2015-11-28,Spin-orbit torque engineering via oxygen manipulation,"Spin transfer torques allow the electrical manipulation of the magnetization at room temperature, which is desirable in spintronic devices such as spin transfer torque memories. When combined with spin-orbit coupling, they give rise to spin-orbit torques which are a more powerful tool for magnetization control and can enrich device functionalities. The engineering of spin-orbit torques, based mostly on the spin Hall effect, is being intensely pursued. Here we report that the oxidation of spin-orbit torque devices triggers a new mechanism of spin-orbit torque, which is about two times stronger than that based on the spin Hall effect. We thus introduce a way to engineer spin-orbit torques via oxygen manipulation. Combined with electrical gating of the oxygen level, our findings may also pave the way towards reconfigurable logic devices.",1511.08868v1 2002-11-29,The orbital moment in CoO,"The orbital and spin moment of the Co2+ ion in CoO has been calculated within the quasi-atomic approach with taking into account the intra-atomic spin-orbit coupling. The orbital moment of 1.38 \mu_{B} amounts at 0 K, in the magnetically-ordered state, to more than 34% of the total moment (4.02 \mu_{B}) and yields the L/S ratio of 1.04, close to the experimental value. PACS No: 71.70.E; 75.10.D Keywords: 3d magnetism, crystal field, spin-orbit coupling, orbital moment, CoO",0211705v1 2011-06-24,Spin-orbit coupling induced Mott transition in Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ (0