Diffusive spin dynamics in ferromagnetic thin films with a Rashba interaction

TL;DR

This paper develops a theoretical framework for understanding spin dynamics in ferromagnetic thin films with Rashba interaction, revealing how diffusion influences spin torque components and explaining experimental magnetization switching.

Contribution

It introduces coupled charge and spin diffusion equations incorporating Rashba spin-orbit interaction and magnetism, providing new insights into spin torque mechanisms in ferromagnetic thin films.

Findings

Rashba spin torque has both in-plane and out-of-plane components.

Diffusion significantly enhances the ratio of torque components in thin wires.

The theory explains recent experimental observations of magnetization switching.

Abstract

In a ferromagnetic metal layer, the coupled charge and spin diffusion equations are obtained in the presence of both Rashba spin-orbit interaction and magnetism. The mis-alignment between the magnetization and the non-equilibrium spin density induced by the Rashba field gives rise to Rashba spin torque acting on the ferromagnetic order parameter. In a general form, we find that the Rashba torque consists of both in-plane and out-of-plane components, ie $\bm{T}=T_{\bot}\hat{\bm{y}}\times{\hat{\bm m}}+T_{\parallel}{\hat{\bm m}}\times({\hat{\bm y}}\times{\hat{\bm m}})$. Numerical simulations on a two dimensional nano-wire discuss the impact of diffusion on the Rashba torque, which reveals a large enhancement to the ratio $T_{\parallel}/T_{\bot}$ for thin wires. Our theory provides an explanation to the mechanism that drives the magnetization switching in a single ferromagnet as observed in the recent experiments.