# Semiclassical theory of spin-orbit torques in disordered multiband electron systems

## TL;DR

This paper develops a semiclassical Boltzmann framework to analyze spin-orbit torques in disordered multiband electron systems, revealing the impact of disorder spin structure on torque behavior.

## Contribution

It introduces a semiclassical approach equivalent to the Kubo method, accounting for interband coherence effects and analyzing disorder influence on spin-orbit torques.

## Key findings

- Disorder-induced interband coherence significantly affects SOT.
- Spin-dependent disorder can reverse the sign of antidamping-like SOT.
- Cancellation of intrinsic and disorder-induced SOT occurs only with spin-independent short-range disorder.

## Abstract

We study spin-orbit torques (SOT) in non-degenerate multiband electron systems in the weak disorder limit. In order to have better physical transparency a semiclassical Boltzmann approach equivalent to the Kubo diagrammatic approach in the non-crossing approximation is formulated. This semiclassical framework accounts for the interband- coherence effects induced by both the electric field and static impurity scattering. Using the two-dimensional Rashba ferromagnet as a model system, we show that the antidamping-like SOT arising from disorder-induced interband-coherence effects is very sensitive to the spin structure of disorder and may have the same sign as the intrinsic SOT in the presence of spin-dependent disorder. While the cancellation of this SOT and the intrinsic one occurs only in the case of spin-independent short-range disorder.