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Based on the spinor Boltzmann equation, we obtain a temperature dependentthermal spin-orbit torque in terms of the local equilibrium distributionfunction 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 thethermal spin orbit torque under local equilibrium assumption. This temperaturedependent thermal spin-orbit torque originates from the temperature gradientapplied to the system. it is also sensitive to temperature due to the localequilibrium distribution function therein. In the spin diffusion equation, wecan 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 anexample of spin-polarized transport through a ferromagnet with Dresselhausspin-orbit coupling driven by temperature gradient, those torques includingthermal spin-orbit torque are demonstrated numerically.

Thermal Spin Orbit Torque with Dresselhaus Spin Orbit Coupling