Thermal spin–orbit torque in spintronics

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