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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 a temperature gradient, those torques including thermal spin–orbit torque are demonstrated numerically. We study the thermal spin–orbit torque (TSOT) in a system with Dresselhaus Spin–Orbit Coupling. [ABSTRACT FROM AUTHOR]

Based on the spinor Boltzmann equation (SBE) formalism, we present a theory of temperature-dependent thermal spin–orbit torque for a system in the presence of Rashba spin–orbit interaction. Under the local equilibrium assumption, we can expand the distribution function of spinor Boltzmann equation around local equilibrium distribution; then, the spin diffusion equation can be derived from SBE, where the spin transfer torque, spin orbit torque as well as thermal spin–orbit torque can be naturally obtained. It is shown that this thermal spin–orbit torque originates from the temperature gradient of local equilibrium distribution function, which is explicit and straightforward than previous works. Finally, we illustrate them by an example of spin-polarized transport through a ferromagnet with Rashba spin–orbit coupling, in which those torques driven whatever by temperature gradient or bias are manifested quantitatively. We proposed a new expression for the thermal spin–orbit torque, which can be unified with the usual spin orbit torque as a generalized spin orbit torque. [ABSTRACT FROM AUTHOR]

Together with the spinor Boltzmann equation (SBE) satisfied by conduction electrons, we solve the Landau–Lifshitz–Gilbert–Slonczewski (LLGS) equation to study the domain wall (DW) motion driven by the spin-polarized current. The SBE and LLGS equation are coupled together by the spin transfer torque (STT) induced by the s–d exchange interaction between the conduction electrons and the local magnet of DW. Based on the spin diffusion equation derived from SBE, we obtain a generalized STT originated from the inhomogeneity of spin current density, which can be divided into adiabatic and nonadiabatic parts but with somewhat different terms from the previous works. We illustrate this by an example of DW motion in a ferromagnet metal under an external electric field, the spin accumulation, and spin current density of conduction electrons and the DW dynamics are presented. We find that the nonadiabatic STT has a comparable contribution to the total STT within the spin-flip relaxation time, which can play an important role in the nonequilibrium DW dynamics. We also estimate the velocity of DW ∼ 100 m/s when an 10 6 V/m electric field is applied. [ABSTRACT FROM AUTHOR]

We study the magnetization reversal of single-molecular magnets by a spin-polarized current in the framework of the spinor Boltzmann equation. Because of the spin–orbit coupling, the spin-polarized current will impose a non-zero spin transfer torque on the single-molecular magnets, which will induce the magnetization switching of the latter. Via the s–d exchange interaction between the conducting electrons and single-molecular magnets, we can investigate the magnetization dynamics of single-molecular magnets. We demonstrate the dynamics of the magnetization based on the spin diffusion equation and the Heisenberg-like equation. The results show that when the current is large enough, the magnetization of the single-molecular magnets can be reversed. We also calculate the critical current density required for the magnetization reversal under different anisotropy and external magnetic fields, which is helpful for the corresponding experimental design. [ABSTRACT FROM AUTHOR]

Based on Spinor Boltzmann equation beyond gradient approximation, we establish the continuity equations satisfied by the charge current and spin current, a generalized spin transfer torque is given when the potential in the system change rapidly. The numerical results for charge density, charge current, spin accumulation, spin current and spin transfer torque are illustrated by a system with periodic potential, they are obviously influenced by the rapid potential, whatever external electric field applied on the system or magnetization therein, where the gradient approximation fails. [ABSTRACT FROM AUTHOR]

There exist two kinds of spin transfer torque in spintronics: the electric spin transfer torque (STT) caused by spin-polarized current and the thermal spin torque (TSTT) caused by thermal spin current. In this manuscript, we will derive a unified torque which contain both of them. Based on spinor Boltzmann equation, we investigate the torques in a magnetoelectric device applied by voltage bias and temperature gradient, and find that the unified STT are contributed by two sources: the spin-polarized current induced by bias and the thermal spin current induced by the temperature gradient, moreover the TSTT can be further divided as local equilibrium TSTT and nonequilibrium TSTT. In addition to the usual electric STT and TSTT, a new term also appear in our expression, which can be interpreted by the inhomogeneity of magnetization. We illustrate them by an example of electric and thermal transport through a ferromagnet subject to some device, in which those torques originate from different sources are manifested quantitatively. [ABSTRACT FROM AUTHOR]