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We consider longitudinal electronic transport in a graphene monolayer with an external in-plane magnetic field and with extrinsic spin-orbit Rashba interaction. Our main interest is in the in-plane magnetoresistance, observed experimentally. We show, that scattering on Rashba spin-orbit fluctuations leads to a negative magnetoresistance, in agreement with experimental observations. To calculate transport properties we assume an effective model valid for low energy states around the Dirac points, and use the Green function method to derive the electron scattering rate and longitudinal conductivity., Comment: 10 pages, 7 figures

We analyze magnetic properties of monolayers and bilayers of chromium trihalides, CrI$_3$, in two different stacking configurations: AA and rhombohedral ones. Our main focus is on the corresponding Curie temperatures, hysteresis curves, equilibrium spin structures, and spin wave excitations. To obtain all these magnetic characteristic, we employ the atomistic spin dynamics and Monte Carlo simulation techniques. The model Hamiltonian includes isotropic exchange coupling, magnetic anisotropy, and Dzyaloshinskii-Moriya interaction. Though the latter is relatively weak in CrI$_3$, we consider a more general case assuming also an enhancement of Dzyaloshinskii-Moriya interaction in the corresponding Janus structures and by external electric fields. An important issue of the analysis is the correlation between hysteresis curves and spin configurations in the system, as well as formation of the skyrmion textures., Comment: 15 pages, 11 figures

We consider the anomalous, spin, valley, and valley spin Hall effects in a pristine ex-so-tic graphene-based van-der-Waals (vdW) heterostructure consisting of a bilayer graphene (BLG) between semiconducting van-der-Waals material with strong SOC (e.g., WS$_2$) and ferromagnetic and insulating vdW material (e.g. Cr$_2$Ge$_2$Te$_6$). Reducing the effective Hamiltonian derived by Zollner et al [Phys. Rev. Lett. 125(19), 196402 (2020)] to low-energy states, and using the Green function formalism, we derived analytical results for the Hall conductivities as a function of the Fermi level and gate voltage. Depending on these parameters, we found quantized valley conductivity., Comment: 16 pages, 8 figures

In this paper we analyze spin waves in bilayers of two-dimensional van der Waals materials, like Vanadium based dichalcogenides, VX$_2$ (X=S, Se, Te) and other materials of similar symmetry. We assume that the materials exhibit Dzialoshinskii- Moriya interaction and in-plane easy-axis magnetic anisotropy due to symmetry breaking induced externally (eg, by strain, gate voltage, proximity effects to an appropriate substrate/oberlayer, etc). The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong in-plane magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Hollstein-Primakoff-Bogolubov transformation., Comment: 7 pages, 7 figures

The linear and nonlinear Hall effects in 2D systems are considered theoretically within the isotropic k-cubed Rashba model. We show that the presence of an out-of-plane external magnetic field or net magnetization is a necessary condition to induce a nonzero Berry curvature in the system, whereas an in-plane magnetic field tunes the Berry curvature leading to the Berry curvature dipole. Interestingly, in the linear response regime, the conductivity is dominated by the intrinsic component (Berry curvature component), whereas the second-order correction to the Hall current (i.e., the conductivity proportional to the external electric field) is dominated by the component independent of the Berry curvature dipole., Comment: 7 pages, 3 figures

Bilinear magnetoresistance has been studied theoretically in 2D systems with isotropic cubic form of Rashba spin-orbit interaction. We have derived the effective spin-orbital field due to current-induced spin polarization and discussed its contribution to the unidirectional system response. The analysed model can be applied to the semiconductor quantum wells as well as 2DEG at the surfaces and interfaces of perovskite oxides., Comment: 8 pages, 2 figures, as accepted to JMMM

The topological charge-Hall effect (TCHE) and the topological spin-Hall effect (TSHE), arising from ferromagnetic (FM) and antiferromagnetic (AFM) skyrmions, respectively; can be elucidated through the emergence of spin-dependent Berry gauge fields that affect the adiabatic flow of electrons within the skyrmion texture. TCHE is absent in systems with parity-time (PT) symmetry, such as collinear AFM systems. In this paper, we theoretically study TCHE and TSHE in a canted antiferromagnetic within the diffusive transport regime. Spin canting or weak ferromagnetism in canted AFMs, which break the PT symmetry, may arise, e.g., from strong homogeneous Dzyaloshinskii-Moriya interactions. Using a semiclassical Boltzmann approach, we obtain diffusion equations for the spin and charge accumulations in the presence of finite spin-flip and spin-dependent momentum relaxation times. We show that the weak ferromagnetic moment stemming from spin canting and the subsequent breaking of parity-time symmetry results in the emergence of both finite TCHE and TSHE in AFM systems., Comment: 15 pages, 9 figures; version as accepted to PRB

Atomically-thin van der Waals magnetic materials offer exceptional opportunities to mechanically and electrically manipulate magnetic states and spin textures. The possibility of efficient spin transport in these materials makes them promising for the development of novel nanospintronics technology. Using atomistic spin dynamics simulations, we investigate magnetic ground state, magnon dispersion, critical temperature, and magnon spin transport in CrCl$_3$ bilayers in the absence and presence of compressive and tensile strains. We show that in the presence of mechanical strain, the magnon band gap at the $\Gamma$ point and the critical temperature of the bilayer are increased. Furthermore, our simulations show that the magnon diffusion length is reduced in the presence of strain. Moreover, by exciting magnons through the spin Seebeck effect and spin Hall-induced torque, we illustrate distinctions between magnon spin transport in the antiferromagnetic state, under compressive strains, and ferromagnetic states, under tensile strains or in the unstrained case.

Using the Density Functional Theory (DFT) calculations, we determined the electronic and magnetic properties of a T-phase VS$_2$ bilayer as a function of tensile and compressive strain. First, we determine the ground state structural parameters and then the band structure, magnetic anisotropy, exchange parameters, and Curie temperature. Variation of these parameters with the strain is carefully analyzed and described. The easy-plane anisotropy, which is rather small in the absence of strain, becomes remarkably enhanced by tensile strain and reduced almost to zero by compressive strain. We also show that the exchange parameters and the Curie temperature are remarkably reduced for the compressive strains below roughly -4$\%$., Comment: 9 Pages, 7 figures, 3 Tables

We consider a thin film of a topological insulator (TI) sandwiched between two ferromagnetic (FM) layers. The system is additionally under an external gate voltage. The surface electron states of TI are magnetized due to the magnetic proximity effect to the ferromagnetic layers. The magnetization of ferromagnetic layers can be changed by applying an external magnetic field or by varying thickness of the topological insulator (owing to the interlayer exchange coupling). The change in the magnetic configuration of the system affects the transport properties of the surface electronic states. Using the Green function formalism, we calculate spin polarization, anomalous Hall effect, and magnetoresistance of the system. We show, among others, that by tuning the gate voltage and magnetizations of the top and bottom FM layers, one can observe the topological transition to the anomalous quantum Hall state.

We investigate topological Hall effects in a metallic antiferromagnetic (AFM) thin film and/or at the interface of an AFM insulator-normal metal bilayer with a single skyrmion in the diffusive regime. To determine the spin and charge Hall currents, we employed a Boltzmann kinetic equation with both spin-dependent and spin-flip scatterings. The interaction between conduction electrons and static skyrmions is included in the Boltzmann equation via the corresponding emergent magnetic field arising from the skyrmion texture. We compute intrinsic and extrinsic contributions to the topological spin Hall effect and spin accumulation, induced by an AFM skyrmion. We show that although the spin Hall current vanishes rapidly outside the skyrmion, the spin accumulation can be finite at the edges far from the skyrmion, provided the spin diffusion length is longer than the skyrmion radius. In addition, We show that in the presence of a spin-dependent relaxation time, the topological charge Hall effect is finite and we determine the corresponding Hall voltage. Our results may help to explore antiferromagnetic skyrmions by electrical means in real materials., Comment: 6 pages, 3 figures

Van der Waals magnetic materials are currently of great interest as materials for applications in future ultrathin nanoelectronics and nanospintronics. Due to weak coupling between individual monolayers, these materials can be easily obtained in the monolayer and bilayer forms. The latter are of specific interest as they may be considered as natural two-dimensional spin valves. In this paper, we study theoretically spin waves in bilayers of transition metal dichalcogenides. The considerations are carried within the general spin wave theory based on effective spin Hamiltonian and Hollstein-Primakoff-Bogolubov transformation. The spin Hamiltonian includes intra-layer as well as inter-layer nearest-neighbour exchange interactions, easy-plane anisotropy, and additionally a weak in-plane easy-axis anisotropy. The bilayer systems consist of two ferromagnetic (in-plane magnetization) monolayers that are coupled either ferromagnetically or antiferromagnetically. In the latter case, we analyse the spin wave spectra in all magnetic phases, i.e. in the antiferromagnetic, spin-flop, and ferromagnetic ones., Comment: 13 pages, 6 figures

We propose a mechanism for magnon-plasmon coupling and hybridization in ferromagnetic (FM) and antiferromagnetic (AFM) systems. The electric field associated with plasmon oscillations creates a non-equilibrium spin density via the inverse spin galvanic effect. This plasmon-induced spin density couples to magnons by an exchange interaction. The strength of magnon-plasmon coupling depends on the magneto-electric susceptibility of the system and the wavevector at which the level repulsion is happened. This wavevector may be tuned by an applied magnetic field. In AFM systems, the degeneracy of two chiral magnons is broken in the presence of a magnetic field, and we find two separate hybrid modes for left-handed and right-handed AFM magnons. Furthermore, we show that magnon-plasmon coupling in AFM systems is enhanced because of strong intra-sublattice spin dynamics. We argue that the recently discovered two-dimensional magnetic systems are ideal platforms to investigate proposed magnon-plasmon hybrid modes., Comment: 5 pages, 1 figure

We study the effect of spin-momentum locking inhomogeneity on the planar Hall effect in topological insulators (TIs). Using the minimal model describing surface states of 3D TIs and semiclassical Boltzmann formalism, we have derived the planar Hall conductivity within the generalized relaxation time approximation. We have found that the total planar Hall conductivity is a sum of linear and nonlinear to the external electric field components. The linear term is a conventional planar Hall conductivity which scales quadratically with an external magnetic field, whereas the nonlinear term reveals bilinear behaviour, i.e., changes its sign when either charge current density or in-plane magnetic field orientation is reversed. We have shown that the emergent nonlinear planar Hall effect is a consequence of spin-momentum locking inhomogeneity in the TIs with isotropic energy dispersion and dominates under the conventional planar Hall effect., Comment: 5 pages, 1 figure

We consider helical rotation of skyrmions confined in the potentials formed by nano-disks. Based on numerical and analytical calculations we propose the skyrmion echo phenomenon. The physical mechanism of the skyrmion echo formation is also proposed. Due to the distortion of the lattice, impurities, or pinning effect, confined skyrmions experience slightly different local fields, which leads to dephasing of the initial signal. The interaction between skyrmions also can contribute to the dephasing process. However, switching the magnetization direction in the nanodiscs (e.g. by spin transfer torque) also switches the helical rotation of the skyrmions from clockwise to anticlockwise (or vice-versa), and this restores the initial signal (which is the essence of skyrmion echo)., Comment: 9 pages, 11 figures, accepted in Phys. Rev. Lett

Thin ferromagnetic films can possess unconventional magnetic properties, opening a new road for using them in spintronic technologies. In the present work exploiting three different methods, we comprehensively analyze phason excitations of a skyrmion lattice in synthetic antiferromagnets. To analyze phason excitations of the skyrmion lattice, we have constructed an analytical model based on three coupled helices and found a linear gapless mode. Micromagnetic simulations also support this result. Moreover, a similar result has been achieved within the rigid skyrmion lattice model based on the coupled Thiele's equations, when the coupling between skyrmions in different layers of the synthetic antiferromagnetic is comparable to or larger than the intralayer coupling. In addition, we also consider the orbital angular momentum and spin pumping current associated with phason excitations. Due to the gapless excitations in the case of skyrmion lattice, the pumping current is nonzero for the arbitrary frequency of pumping microwaves. In the case of individual skyrmions, no current is pumped when microwave frequency is inside the gap of the spectrum of individual skyrmions., Comment: 12 pages, 8 figures, accepted in Phys. Rev. B

Using ab initio density functional theory (DFT), we demonstrated the possibility of controlling the magnetic ground-state properties of bilayer CrCl$_{3}$ by means of mechanical strains and electric fields. In principle, we investigated the influence of these two fields on parameters describing the spin Hamiltonian of the system. The obtained results show that biaxial strains change the magnetic ground state between ferromagnetic (FM) and antiferromagnetic (AFM) phases. The mechanical strain also affects the direction and amplitude of the uniaxial magnetic anisotropy (MAE). Importantly, the direction and amplitude of the Dzyaloshinskii-Moriya vectors are also highly tunable under external strain and electric fields. The competition between nearest neighbor interaction, MAE, and Dzyaloshinskii-Moriya interactions can lead to the stabilization of various exotic spin textures and novel magnetic excitations. The high tunability of magnetic properties by external fields makes bilayer CrCl$_{3}$ a promising candidate for application in the emerging field of two-dimensional quantum spintronics and magnonics., Comment: 14 pages, 10 figures

In the absence of an external magnetic field and a spin-polarized charge current, an antiferromagnetic system supports two degenerate magnon modes. An applied thermal bias activates the magnetic dynamics, leading to a magnon flow from the hot to the cold edge (magnonic spin Seebeck current). Both degenerate bands contribute to the magnon current but the orientations of the magnetic moments underlying the magnons are opposite in different bands. Therefore, while the magnon current is nonzero, the net spin current is zero., Comment: Phys. Rev. B 106, 014417 (2022)

Mechanical control of electronic and magnetic properties of 2D Van-der-Waals heterostructures gives new possibilities for further development of spintronics and information-related technologies. Using the density functional theory, we investigate the structural, electronic, and magnetic properties of silicene monolayer with substituted Chromium atoms and under a small biaxial strain ($-6\%< \epsilon < 8\%$). Our results indicate that the Cr-doped silicene nanosheets without strain have magnetic metallic, half-metallic or semiconducting properties depending on the type of substitution. We also show that the magnetic moments associated with the monomer and vertical dimer substitutions change very weakly with strain. However, the magnetic moment associated with the horizontal dimer substitution decreases when either compressive or tensile strain is applied to the system. Additionally, we show that the largest semiconductor band-gap is approximately 0.13 eV under zero strain for the vertical Cr-doped silicene. Finally, biaxial compressive strain leads to irregular changes in the magnetic moment for Cr vertical dimer substitution., Comment: This paper is including 11 pages as well as 7 figures

Bilinear magnetoresistance is a nonlinear transport phenomenon that scales linearly with the electric and magnetic fields, and appears in nonmagnetic systems with strong spin-orbit coupling, such as topological insulators (TIs). Using the semiclassical Boltzmann theory and generalized relaxation time approximation, we consider in detail the bilinear magnetoresistance in an effective model describing surface states of three-dimensional topological insulators. We show that the presence of magnetic impurities remarkably modifies the BMR signal. In general, scattering on magnetic impurities reduces magnitude of BMR. Apart from this, an additional modulation of the angular dependence of BMR appears when the spin-dependent component of the impurity potential dominates the scalar one., Comment: Accepted to JMMM

Vanadium based dichalcogenides, VSe$_2$, are two-dimensional materials in which magnetic Vanadium atoms are arranged in a hexagonal lattice and are coupled ferromagnetically within the plane. However, adjacent atomic planes are coupled antiferromagnetically. This provides new and interesting opportunities for application in spintronics and data storage and processing technologies. A spin valve magnetoresistance may be achieved when magnetic moments of both atomic planes are driven to parallel alignment by an external magnetic field. The resistance change associated with the transition from antiparallel to the parallel configuration is qualitatively similar to that observed in artificially layered metallic magnetic structures. Detailed electronic structure of VSe$_2$ was obtained from DFT calculations. Then, the ballistic spin-valve magnetoresistance was determined within the Landauer formalism. In addition, we also analyze thermal and thermoelectric properties. Both phases of VSe$_2$, denoted as H and T, are considered., Comment: This paper is including 8 pages as well as 4 figures

Electron states localized at a magnetic domain wall in a graphene caplayer with Rashba spin-orbit interaction and coupled to a magnetic overlayer are studied theoretically. It is shown that two one-dimensional bands of edge modes propagating along the domain wall emerge in the energy gap for each Dirac point, and the modes associated with different Dirac points K and K' are the same. The coefficients describing decay of the corresponding wavefunctions with distance from the domain wall contain generally real and imaginary terms. Numerical results on the local spin density and on the total spin expected in the edge states characterized by the wavenumber $k_y$ are presented and discussed. The Chern number for a single magnetic domain on graphene indicates that the system is in the quantum anomalous Hall phase, with two chiral modes at the edges. In turn, the number of modes localized at the domain wall is determined by the difference in Chern numbers on both sides of the wall. These numbers are equal to 2 and -2, respectively, so there are four modes localized at the domain wall.

Two-dimensional (2D) Rashba systems have been intensively studied in the last decade due to their unconventional physics, tunability capabilities, and potential for spin-charge interconversion when compared to conventional heavy metals. With the advent of a new generation of spin-based logic and memory devices, the search for Rashba systems with more robust and larger conversion efficiencies is expanding. Conventionally, demanding techniques such as angle- and spin-resolved photoemission spectroscopy are required to determine the Rashba parameter $\alpha_{R}$ that characterizes these systems. Here, we introduce a simple method that allows a quantitative extraction of $\alpha_{R}$, through the analysis of the bilinear response of angle-dependent magnetotransport experiments. This method is based on the modulation of the Rashba-split bands under a rotating in-plane magnetic field. We show that our method is able to correctly yield the value of $\alpha_{R}$ for a wide range of Fermi energies in the 2D electron gas at the LaAlO$_{3}$/SrTiO$_{3}$ interface. By applying a gate voltage, we observe a maximum $\alpha_{R}$ in the region of the band structure where interband effects maximize the Rashba effect, consistently with theoretical predictions.

We investigate spin-charge conversion phenomena in hybrid structures of topological insulator (TI) thin films and magnetic insulators. We find an anisotropic inverse spin-galvanic effect (ISGE) that yields a highly tunable spin-orbit torque (SOT). Concentrating on the quasiballistic limit, we also predict a giant anisotropic magnetoresistance (AMR) at low dopings. These effects, which have no counterparts in thick TIs, depend on the simultaneous presence of the hybridization between the surface states and the in-plane magnetization. Both the ISGE and AMR exhibit a strong dependence on the magnetization and the Fermi level position and can be utilized for spintronics and SOT-based applications at the nanoscale., Comment: 6+5 pages, 4+1 figures

A new mechanism of bi-linear magnetoresistance (BMR) is studied theoretically within the minimal model describing surface electronic states in topological insulators (TIs). The BMR appears as a consequence of the second-order response to electric field, and depends linearly on both electric field (current) and magnetic field. The mechanism is based on the interplay of current-induced spin polarization and scattering processes due to peculiar spin-orbit defects. The proposed mechanism is compared to that based on a Fermi surface warping, and is shown to be dominant at lower Fermi energies. We provide a consistent theoretical approach based on the Green function formalism and show that the magnetic field dependent relaxation processes in the presence of non-equilibrium current-induced spin polarization give rise to the BMR.

Using the Green functions method we study transport properties of surface electrons in topological insulators in the presence of a correlated random exchange field. Such an exchange field may be due to random magnetization with correlated fluctuations. We determine the relaxation time due to scattering from the magnetization fluctuations and from other structural defects. Then we calculate the longitudinal charge conductivity taking into account the contribution due to vertex correction., Comment: 6 pages, 2 figures

The anomalous Hall and Nernst effects are considered theoretically within Matsubara-Green's function formalism. The effective Hamiltonian of a magnetized two-dimensional electron gas with cubic Rashba spin-orbit interaction may describe transport properties of electronic states at the interfaces or surfaces of perovskite oxides or another type of heterostructures that, due to symmetry, may be described by the same effective model. In the quasi-ballistic limit, both effects are determined by the topological (Fermi sea) contribution whereas the states at the Fermi level gives a negligibly small response. For a wide range of parameters describing the considered system, the anomalous Nernst conductivity reveals a change of the sign before the magnetic phase transition., Comment: version as submitted to JMMM

We calculate the transport relaxation time $\tau _{\rm tr}$ and spin transport relaxation time $\tau _{s,{\rm tr}}$ for a two-dimensional electron gas with spatially fluctuating Rashba spin-orbit interaction. These relaxation times determine the electrical and spin conductivity of the two-dimensional system, respectively. It is shown that the transport relaxation time $\tau _{\rm tr}$ is a nonmonotonic function of electron energy $\varepsilon $, whereas the spin transport relaxation time $\tau _{s,{\rm tr}}$ decreases with increasing $\varepsilon $, similarly to the conventional electron relaxation time $\tau$ that characterizes the decay of an electron state corresponding to certain values of the momentum and spin. Such a behavior of the relaxation times leads to unusual temperature dependence of the electrical and spin conductivity., Comment: 7 pages, 4 figures

Using the Matsubara Green's function formalism we calculate the temperature dependence of the nonequilibrium spin polarization induced by an external electric field in the presence of spin-orbit coupling. The model Hamiltonian includes an isotropic k-cubed form of the Rashba spin-orbit interaction. Such a Hamiltonian captures the electronic and spin properties of two-dimensional electron (hole) gas at the surfaces or interfaces of transition metal oxides or in p-doped semiconductor heterostructures. The induced spin polarization is calculated for the nonmagnetic as well as magnetic electron/hole gas. Relation of the spin polarization to the Berry curvature is also discussed., Comment: 10 pages, 6 figures

Spin polarization induced by a temperature gradient (heat-current) in a magnetized two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction is considered theoretically within the linear response theory. Using the Matsubara Green function formalism we calculate the temperature dependence of the spin polarization for arbitrary orientation of the exchange field. The limit of a nonmagnetic 2DEG (zero exchange field) is also considered. The physical mechanisms of the spin polarization within our scheme are discussed., Comment: 9 pages, 3 figures

Spin, anomalous, and valley Hall effects in graphene-based hybrid structures are studied theoretically within the Green function formalism and linear response theory. Two different types of hybrid systems are considered in detail: (i) graphene/boron nitride/cobalt(nickel), and (ii) graphene/YIG. The main interest is focused on the proximity-induced exchange interaction between graphene and magnetic substrate and on the proximity-enhanced spin-orbit coupling. The proximity effects are shown to have a significant influence on the electronic and spin transport properties of graphene. To find the spin, anomalous and valley Hall conductivities we employ certain effective Hamiltonians which have been proposed recently for the hybrid systems under considerations. Both anomalous and valley Hall conductivities have universal values when the Fermi level is inside the energy gap in the electronic spectrum., Comment: 11 pages, 7 figures

Current-induced spin polarization in a two-dimensional electron gas with Rashba spin-orbit interaction is considered theoretically in terms of the Matsubara Green functions. This formalism allows to describe temperature dependence of the induced spin polarization. The electron gas is assumed to be coupled to a magnetic substrate via exchange interaction. Analytical and numerical results on the temperature dependence of spin polarization have been obtained in the linear response regime. The spin polarization has been presented as a sum of two terms - one proportional to the relaxation time and the other related to the Berry phase corresponding to the electronic bands of the magnetized Rashba gas. The spin-orbit torque due to Rashba interaction is also discussed. Such a torque appears as a result of the exchange coupling between the non-equilibrium spin polarization and magnetic moment of the underlayer., Comment: 13 pages, 6 figures

We calculate orbital spin-dependent magnetization in a two-dimensional electron gas with spin-orbit interaction of Rashba type. Such an orbital magnetization is admitted by the time-reversal symmetry of the system, and gives rise to spin currents when the system is not in thermal equilibrium. The theoretical approach is based on the linear response theory and the Matsubara Green's function formalism. To account for the spin-resolved orbital magnetization a spin-dependent vector potential has been introduced. The spin currents which appear in thermal nonequilibrium due to the spin-resolved orbital magnetization play an important role in the spin Nernst effect, and have to be included in order to correctly describe the low-temperature spin Nernst conductivity., Comment: 9 pages, 2 figures

Using the Matsubara Green function formalism we calculate the temperature dependence of spin Hall and spin Nernst conductivities of a two-dimensional electron gas with Rashba spin-orbit interaction in the linear response regime. In the case of spin Nernst effect we also include the contribution from spin-resolved orbital magnetization, which assures correct behavior of the spin Nernst conductivity in the zero-temperature limit. Analytical formulas for the spin Hall and spin Nernst conductivities are derived in some specific situations. Using the Ioffe-Regel localization criterion, we have also estimated the range of parameters where the calculated results for the spin Hall and spin Nernst conductivities are applicable. Analytical results show that the vertex correction totally suppresses the spin Hall conductivity at arbitrary temperature. The spin Nernst conductivity, in turn, vanishes at $T=0$ when the orbital contribution is taken into account, but generally is nonzero at finite temperatures., Comment: 15 pages, 4 figures

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., Comment: 9 pages, 3 figures, version as published