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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

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

Tools for controlling electrically the motion of magnetic skyrmions are important elements towards their use in spintronic devices. Here, we propose and demonstrate the transport of skyrmions via GHz and THz electric pulses. The method relies on using polarization textured pulses such that the skyrmion experiences (via its inherent magnetoelectricity) the out-of-plane and in-plane components of the pulse electric field. It is shown how the electric field drags efficiently the skyrmion. The control of the skyrmion motion depends solely on the amplitude of electric fields, frequency, polarization, or phase in case two pulses are applied. Micromagnetic calculations supported by analytic modeling and analysis indicate the experimental feasibility of the control scheme., Comment: 5 pages, 5 figures

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

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)

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.

The magnonic spin Seebeck effect is a key element of spin caloritronic, a field that exploits thermal effects for spintronic applications. Early studies were focused on investigating the steady-state nonequilibrium magnonic spin Seebeck current, and the underlying physics of the magnonic spin Seebeck effect is now relatively well established. However, the initial steps of the formation of the spin Seebeck current are in the scope of recent interest. To address this dynamical aspect theoretically we propose here a new approach to the time-resolved spin Seebeck effect. Our method exploits the supersymmetric theory of stochastics and Ito - Stratonovich integration scheme. We found that in the early step the spin Seebeck current has both nonzero transversal and longitudinal components. As the magnetization dynamics approaches the steady-state, the transversal components decay through dephasing over the dipole-dipole reservoir. The time scale for this process is typically in the sub-nanoseconds pointing thus to the potential of an ultrafast control of the dynamical spin Seebeck during its buildup., Comment: to appear in Phys. Rev. B

Strong magneto-electric coupling in two-dimensional helical materials leads to a peculiar type of topologically protected solutions -- skyrmions. Coupling between the net ferroelectric polarization and magnetization allows control of the magnetic texture with an external electric field. In this work we propose the model of optical tweezer -- a particular configuration of an external electric field and Gaussian laser beam that can trap or release the skyrmions in a highly controlled manner. Functionality of such a tweezer is visualized by micromagnetic simulations and model analysis.

In this article we consider the chiral Hall effect due to topologically protected kink states formed in topological insulators at boundaries between domains with differing topological invariants. Such systems include the surfaces of three dimensional topological insulators magnetically doped or in proximity with ferromagnets, as well as certain two dimensional topological insulators. We analyze the equilibrium charge current along the domain wall and show that it is equal to the sum of counter-propagating equilibrium currents flowing along external boundaries of the domains. In addition, we also calculate a dissipative current along the domain wall when an external voltage is applied perpendicularly to the wall., Comment: 6 pages, 4 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

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., Comment: to appear in Phys. Rev. B

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 analyze shot noise in a magnetic tunnel junction with a two-level quantum dot attached to the magnetic electrodes. The considerations are limited to the case when some transport channels are suppressed at low temperatures. Coupling of the two dot's levels to the electrodes are assumed to be generally different and also spin-dependent. To calculate the shot noise we apply the approach based on the full counting statistics. The approach is used to account for experimental data obtained in magnetic tunnel junctions with organic barriers. The experimentally observed Fano factors correspond to the super-Poissonian statistics, and also depend on relative orientation of the electrodes' magnetic moments. We have also calculated the corresponding spin shot noise, which is associated with fluctuations of spin current.

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

Thermally activated domain wall (DW) motion in magnetic insulators has been considered theoretically, with a particular focus on the role of Dzyaloshinskii-Moriya Interaction (DMI) and thermomagnonic torques. The thermally assisted DW motion is a consequence of the magnonic spin current due to the applied thermal bias. In addition to the exchange magnonic spin current and the exchange adiabatic and the entropic spin transfer torques, we also consider the DMI-induced magnonic spin current, thermomagnonic DMI field-like torque and the DMI entropic torque. Analytical estimations are supported by numerical calculations. We found that the DMI has a substantial influence on the size and the geometry of DWs, and that the DWs become oriented parallel to the long axis of the nanostrip. Increasing the temperature smoothes the DWs. Moreover, the thermallyinduced magnonic current generates a torque on the DWs, which is responsible for their motion. From our analysis it follows that for a large enough DMI the influence of DMI-induced field-like torque is much stronger than that of the DMI and the exchange entropic torques. By manipulating the strength of the DMI constant, one can control the speed of the DW motion, and the direction of the DW motion can be switched, as well. We also found that DMI not only contributes to the total magnonic current, but also it modifies the exchange magnonic spin current, and this modification depends on the orientation of the steady state magnetization. The observed phenomenon can be utilized in spin caloritronics devices, for example in the DMI based thermal diodes. By switching the magnetization direction, one can rectify the total magnonic spin current., Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev. B

We present a tight binding description of electronic properties of the interface between LaAlO$_3$ (LAO) and SrTiO$_3$ (STO). The description assumes LAO and STO perovskites as sets of atomic layers in the $x$-$y$ plane, which are weakly coupled by an interlayer hopping term along the $z$ axis. The interface is described by an additional potential, $U_0$, which simulates a planar defect. Physically, the interfacial potential can result from either a mechanical stress at the interface or other structural imperfections. We show that depending on the potential strength, charge carriers (electrons or holes) may form an energy band which is localized at the interface and is within the band gaps of the constituting materials (LAO and STO). Moreover, our description predicts a {\it valve effect} at a certain critical potential strength, $U_{0cr}$, when the interface potential works as a valve suppressing the interfacial conductivity. In other words, the interfacial electrons become dispersionless at $U_0= U_{0cr}$, and thus cannot propagate. This critical value separates the {\it quasielectron} ($U_0<$ $U_{0cr}$) and {\it quasihole} ($U_0>$ $U_{0cr}$) regimes of the interfacial conductivity., Comment: 8 pages, 4 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

The influence of an asymmetric in-plane magnetic anisotropy on the thermally activated spin current is studied theoretically for two different systems; (i) the system consisting of a ferromagnetic insulator in a direct contact with a nonmagnetic metal, and the sandwich structure consisting of a ferromagnetic insulating part sandwiched between two nonmagnetic metals. It is shown that when the difference between the temperatures of the two nonmagnetic metals in a structure is not large, the spin pumping currents from the magnetic part to the nonmagnetic ones are equal in amplitude and have opposite directions, so only the spin torque current contributes to the total spin current. The spin current flows then from the nonmagnetic metal with the higher temperature to the nonmagnetic metal having a lower temperature. Its amplitude varies linearly with the difference in temperatures. In addition, we have found that if the magnetic anisotropy is in the layer plane, then the spin current increases with the magnon temperature, while in the case of an out-of-plane magnetic anisotropy the spin current decreases when the magnon temperature enhances. Enlarging the difference between the temperatures of the nonmagnetic metals, the linear response becomes important, as confirmed by analytical expressions inferred from the Fokker-Planck approach and by the results obtained upon a full numerical integration of the stochastic Landau-Lifshitz-Gilbert equation., Comment: 11 pages, 9 figures

It has been shown recently [J. L. Lado et al., Phys. Rev. Lett. 113, 027203 (2014)] that edge magnetic moments in graphene-like nanoribbons are strongly influenced by the intrinsic spin-orbit interaction. Due to this interaction an anisotropy comes about which makes the in-plane arrangement of magnetic moments energetically more favorable than that corresponding to the out-of-plane configuration. In this paper we raise both the edge magnetism problem as well as differential conductance and shot noise Fano factor issues, in the context of finite-size flakes within the Coulomb blockade (CB) transport regime. Our findings elucidate the following problems: (i) modification of the CB diamonds by the appearance of the in-plane magnetic moments, (ii) modification of the CB diamonds by intrinsic spin-orbit interaction.

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

We consider theoretically a wide graphene ribbon, that on both ends is attached to electronic reservoirs which generally have different temperatures. The graphene ribbon is assumed to be deposited on a substrate, that leads to a spin-orbit coupling of Rashba type. We calculate the thermally induced charge current in the ballistic transport regime as well as the thermoelectric voltage (Seebeck effect). Apart from this, we also consider thermally induced spin current and spin polarization of the graphene ribbon. The spin currents are shown to have generally two components; one parallel to the temperature gradient and the other one perpendicular to this gradient. The latter corresponds to the spin current due to the spin Nernst effect. Additionally, we also consider the heat current between the reservoirs due to transfer of electrons.

We analyze theoretically optical generation of a spin-polarized charge current (photogalvanic effect) and spin polarization in graphene with Rashba spin-orbit coupling. An external magnetic field is applied in the graphene plane, which plays a crucial role in the mechanism of current generation. We predict a highly efficient resonant-like photogalvanic effect in a narrow frequency range which is determined by the magnetic field. A relatively less efficient photogalvanic effect appears in a broader frequency range, determined by the electron concentration and spin-orbit coupling strength.

Taking into account the available experimental results, we model the electronic properties and current-voltage characteristics of a ferromagnet-semiconductor junction. The Fe/GaAs interface is considered as a Fe/(i-GaAs)/n+-GaAs/n-GaAs multilayer structure with the Schottky barrier. We also calculate numerically the current-voltage characteristics of a double-Schottky-barrier structure Fe/GaAs/Fe, which are in agreement with available experimental data. For this structure, we have estimated the spin current in the GaAs layer, which characterizes spin injection from the ferromagnet to the semiconductor., Comment: 3 pages, 5 figures, presented on The European Conference Physics of Magnetism 2014 (PM'14), June 23-27, 2014 Pozna\'n, POLAND

Thermoelectric effects in graphene are considered theoretically with particular attention paid to the role of impurities. Using the T -matrix method we calculate the impurity resonant states and the momentum relaxation time due to scattering on impurities. The Boltzmann kinetic equation is used to determine the thermoelectric coefficients. It is shown that the resonant impurity states near the Fermi level give rise to a resonant enhancement of the Seebeck coefficient and of the figure of merit $ZT$ . The Wiedemann-Franz ratio deviates from that known for ordinary metals, where this ratio is constant and equal to the Lorentz number. This deviation appears for small chemical potentials and in the vicinity of the resonant states. In the limit of a constant relaxation time, this ratio has been calculated analytically for $\mu=0$.

We calculate the efficiency of infrared optical spin injection in single-layer graphene with Rashba spin-orbit coupling and for in-plane magnetic field. The injection rate in the photon frequency range corresponding to the Rashba splitting is shown to be proportional to the ratio of the Zeeman and Rashba splittings. As a result, large spin polarization can be controllably achieved for experimentally available values of the spin-orbit coupling and in magnetic fields below 10 Tesla., Comment: 5 pages, 3 figures

Using ab-initio methods we calculate thermoelectric and spin thermoelectric properties of silicene nanoribbons with bare, mono-hydrogenated and di-hydrogenated edges. Asymmetric structures, in which one edge is either bare or di-hydrogenated while the other edge is mono-hydrogenated (0H-1H and 2H-1H nanoribbons) have ferromagnetic ground state and display remarkable conventional and spin thermoelectric properties. Strong enhancement of the thermoelectric efficiency, both conventional and spin ones, results from a very specific band structure of such nanoribbons, where one spin channel is blocked due to an energy gap while the other spin channel is highly conducting. In turn, 0H-2H and 2H-2H nanoribbons (with one edge being either bare or di-hydrogenated and the other edge being di-hydrogenated) are antiferromagnetic in the ground state. Accordingly, the corresponding spin channels are equivalent, and only conventional thermoelectric effects can occur in these nanoribbons.

Electric and thermoelectric properties of silicene nanoribbons doped with Al and P impurity atoms are investigated theoretically for both antiparallel and parallel orientations of the edge magnetic moments. In the former case, appropriately arranged impurities can lead to a net magnetic moment and thus also to spin thermoelectric effects. In the latter case, in turn, spin thermoelectric effects also occur in the absence of impurities. Numerical results based on ab-initio calculations show that the spin thermopower can be considerably enhanced by the impurities.

Following the theoretical approach by Xiao et al [Phys. Rev. B 81, 214418 (2010)] to the spin Seebeck effect, we calculate the mean value of the total spin current flowing through a normalmetal/ ferromagnet interface. The spin current emitted from the ferromagnet to the normal metal is evaluated in the framework of the Fokker-Planck approach for the stochastic Landau-Lifshitz-Gilbert equation. We show that the total spin current depends not only on the temperature difference between the electron and the magnon baths, but also on the external magnetic field and magnetic anisotropy. Apart from this, the spin current is shown to saturate with increasing magnon temperature, and the saturation temperature increases with increasing magnetic field and/or magnetic anisotropy., Comment: 7 pages, 3 figures

Spin polarization induced by an external electric field in graphene is considered theoretically in the linear response regime. The graphene is assumed to be deposited on a substrate which leads to the spin-orbit interaction of Rashba type. The induced spin polarization is shown to be in the graphene plane and perpendicular to the electric field. However, the spin polarization changes sign when the Fermi level, whose position can be controlled by an external gate voltage, crosses the Dirac points., Comment: 4 pages, 4 figures

Intrinsic spin Hall effect in the AA-stacked bilayer graphene is studied theoretically. The low-energy electronic spectrum for states in the vicinity of the Dirac points is obtained from the corresponding $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian. The spin Hall conductivity in the linear response regime is determined within the Green function formalism. Conditions for the existence of spin Hall insulator phase are also analyzed, and it is shown that the spin Hall insulator phase can exist for a sufficiently large spin-orbit coupling, which opens a gap in the spectrum. The electric field perpendicular to the graphene plane leads then to reduction of the gap width and suppression of the spin Hall insulator phase. The low temperature spin Nernst effect is also calculated from the zero temperature spin Hall conductivity., Comment: 5 pages, 7 figures

Transport and thermoelectric coefficients (including also spin thermopower) of silicene nanoribbons with zigzag edges are investigated by {\it ab-initio} numerical methods. Local spin density of such nanoribbons reveals edge magnetism. Like in graphene, one finds antiferromagnetic and ferromagnetic ordering, with spin polarization at one edge antiparallel or parallel to that at the other edge, respectively. Thermoelectric properties, especially the Seebeck coefficient, significantly depend on the electronic band structure and are enhanced when the Fermi level is in the energy gap. However, these thermoelectric properties are significantly reduced when the phonon contribution to the heat conductance is included. This phonon contribution has been calculated numerically by two different methods. Transition from antiferromagnetic to ferromagnetic states leads to a large magnetoresistance as well as to a considerable magnetothermopower. Thermoelectric parameters in the antiparallel configuration, when spin polarization in the left part of the nanoribbon is opposite to that in the right part, are also analyzed., Comment: 12 pages, 11 figures

Spin polarization of a two-dimensional electron gas with Rashba spin-orbit interaction, induced by a thermo-current, is considered theoretically. It is shown that a temperature gradient gives rise to an in-plane spin polarization of the electron gas, which is normal to the temperature gradient. The low-temperature spin polarization changes sign when the Fermi level crosses bottom edge of the upper electronic subband. We also compare the results with spin polarization induced by an external electric field (current)., Comment: 5 pages, 3 figures

We study the spin-resolved transport through single-level quantum dots strongly coupled to ferromagnetic leads in the Kondo regime, with a focus on contact and material asymmetry-related effects. By using the numerical renormalization group method, we analyze the dependence of relevant spectral functions, linear conductance and tunnel magnetoresistance on the system asymmetry parameters. In the parallel magnetic configuration of the device the Kondo effect is generally suppressed due to the presence of exchange field, irrespective of system's asymmetry. In the antiparallel configuration, on the other hand, the Kondo effect can develop if the system is symmetric. We show that even relatively weak asymmetry may lead to the suppression of the Kondo resonance in the antiparallel configuration and thus give rise to nontrivial behavior of the tunnel magnetoresistance. In addition, by using the second-order perturbation theory we derive general formulas for the exchange field in both magnetic configurations of the system.

We predict two spin-dependent transport phenomena in two-dimensional electron systems, which are induced by spatially fluctuating Rashba spin-orbit interaction. When the electron gas is magnetized, the random Rashba interaction leads to the anomalous Hall effect. An example of such a system is a narrow-gap magnetic semiconductor-based symmetric quantum well. We show that the anomalous Hall conductivity reveals a strongly nonlinear dependence on the magnetization, decreasing exponentially at large spin density. We also show that electron scattering from a fluctuating Rashba field in a two-dimensional nonmagnetic electron system leads to a negative magnetoresistance arising solely due to spin-dependent effects., Comment: 5 pages, 3 figures

Intrinsic contribution to the spin Hall effect in a two-dimensional silicene is considered theoretically within the linear response theory and Green function formalism. When an external voltage normal to the silicene plane is applied, the spin Hall conductivity is shown to reveal a transition from the spin Hall insulator phase at low voltages to the conventional insulator phase at higher voltages. This transition resembles recently reported phase transition in a bilayer graphene. The spin-orbit interaction responsible for this transition in silicene is much stronger than in graphene, which should make the transition observable experimentally., Comment: 3 pages, 3 figures

Spin Hall effect due to random Rashba spin-orbit coupling in the two-dimensional honeycomb lattice of carbon atoms (graphene) is considered theoretically. Using the Green function method and diagrammatic technique we show that fluctuations of the Rashba interaction around zero average value give rise to nonzero spin Hall conductivity. Generally, the conductivity is not universal, but depends on the ratio of the total momentum and spin-flip relaxation rates., Comment: 4 pages, 3 figures

We demonstrate that shot noise in Fe/MgO/Fe/MgO/Fe double-barrier magnetic tunnel junctions is determined by the relative magnetic configuration of the junction and also by the asymmetry of the barriers. The proposed theoretical model, based on sequential tunneling through the system and including spin relaxation, successfully accounts for the experimental observations for bias voltages below 0.5V, where the influence of quantum well states is negligible. A weak enhancement of conductance and shot noise, observed at some voltages (especially above 0.5V), indicates the formation of quantum well states in the middle magnetic layer. The observed results open up new perspectives for a reliable magnetic control of the most fundamental noise in spintronic structures., Comment: 8 pages, 4 figures

We report on theoretical studies of transport through graphene quantum dots weakly coupled to external ferromagnetic leads. The calculations are performed by exact diagonalization of a tight-binding Hamiltonian with finite Coulomb correlations for graphene sheet and by using the real-time diagrammatic technique in the sequential and cotunneling regimes. The emphasis is put on the role of graphene flake shape and spontaneous edge magnetization in transport characteristics, such as the differential conductance, tunneling magnetoresistance (TMR) and the shot noise. It is shown that for certain shapes of the graphene dots a negative differential conductance and nontrivial behavior of the TMR effect can occur.