Thermal Spin-Orbit Torque in Spintronics

TL;DR

This paper derives a temperature-dependent thermal spin-orbit torque using the spinor Boltzmann equation formalism, highlighting its origin from temperature gradients and demonstrating its effects in spin-polarized transport with Rashba coupling.

Contribution

It introduces a new derivation of thermal spin-orbit torque based on local equilibrium assumptions within the spinor Boltzmann framework, providing explicit and straightforward insights.

Findings

Thermal spin-orbit torque originates from temperature gradients.

The derived torque can be quantitatively analyzed in ferromagnets with Rashba coupling.

The approach simplifies understanding of thermal effects in spin transport.

Abstract

Within the spinor Boltzmann equation (SBE) formalism, we derived a temperature dependent thermal spin-orbit torque based on local equilibrium assumption in a system with Rashba spin-orbit interaction. If we expand the distribution function of spinor Boltzmann equation around local equilibrium distribution, we can obtain the spin diffusion equation from SBE, then the spin transfer torque, spin orbit torque as well as thermal spin-orbit torque we seek to can be read out from this equation. It exhibits 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.