Spin Hall Current and Spin-transfer Torque in Ferromagnetic Metal

TL;DR

This paper theoretically investigates how spin-orbit interaction influences spin-transfer torque in ferromagnetic metals, revealing a new contribution linked to the spin Hall current and inverse spin Hall effect.

Contribution

It introduces a novel term in the spin-transfer torque formula arising from spin-orbit interaction and spin Hall current, expanding understanding of spin dynamics in ferromagnets.

Findings

Identifies a new contribution to spin-transfer torque proportional to spin Hall current.

Connects the spin Hall effect with spin-transfer torque via spin motive force.

Provides theoretical basis for spin-orbit effects in ferromagnetic spintronics.

Abstract

We theoretically examine the spin-transfer torque in the presence of spin-orbit interaction (SOI) at impurities in a ferromagnetic metal on the basis of linear response theory. We obtained, in addition to the usual spin-transfer torque, a new contributioin $\sim {\bm j}_{\rm SH}^{\phantom{\dagger}} \cdot \nabla {\bm n}$ in the first order in SOI, where ${\bm j}_{\rm SH}^{\phantom{\dagger}}$ is the spin Hall current driven by an external electric field. This is a reaction to inverse spin Hall effect driven by spin motive force in a ferromagnet.