Microscopic theory of spin-orbit torques and skyrmion dynamics

TL;DR

This paper develops a microscopic theory for spin-orbit torques in ferromagnet/heavy-metal bilayers, linking local electron spin polarization to magnetization dynamics without relying on spin currents, and applies it to Skyrmion motion.

Contribution

It introduces a novel microscopic approach to spin-orbit torques that avoids the spin current concept and directly relates torques to local electron polarization, with symmetry analysis and application to Skyrmion dynamics.

Findings

Different symmetries for Rashba and Dresselhaus spin-orbit interactions.

Major cancellation of torques in spin-independent disorder models.

Application to Skyrmion dynamics under electric current.

Abstract

We formulate a general microscopic approach to spin-orbit torques in thin ferromagnet/heavy-metal bilayers in linear response to electric current or electric field. The microscopic theory we develop avoids the notion of spin currents and spin-Hall effect. Instead, the torques are directly related to a local spin polarization of conduction electrons, which is computed from generalized Kubo-St\v{r}eda formulas. A symmetry analysis provides a one-to-one correspondence between polarization susceptibility tensor components and different torque terms in the Landau-Lifshitz-Gilbert equation for magnetization dynamics. The spin-orbit torques arising from Rashba or Dresselhaus type of spin-orbit interaction are shown to have different symmetries. We analyze these spin-orbit torques microscopically for a generic electron model in the presence of an arbitrary smooth magnetic texture. For a model with spin-independent disorder we find a major cancelation of the torques. In this case the only remaining torque corresponds to the magnetization-independent Edelstein effect. Furthermore, our results are applied to analyze the dynamics of a Skyrmion under the action of electric current.