Microscopic Calculation of Spin Torques and Forces

TL;DR

This paper provides a microscopic calculation of spin torques and forces in magnetic systems, focusing on the eta-term and Gilbert damping with electron spin-relaxation effects modeled by impurities.

Contribution

It introduces a detailed microscopic framework for calculating spin torques and forces, emphasizing the roles of eta-term and Gilbert damping with impurity-induced spin relaxation.

Findings

Identification of two types of forces exerted by electric/spin currents on magnetization.

Explicit calculation of spin torques considering spin-relaxation processes.

Analysis of the eta-term and Gilbert damping effects in the presence of impurities.

Abstract

Spin torques, that is, effects of conduction electrons on magnetization dynamics, are calculated microscopically in the first order in spatial gradient and time derivative of magnetization. Special attention is paid to the so-called \beta-term and the Gilbert damping, \alpha, in the presence of electrons' spin-relaxation processes, which are modeled by quenched magnetic impurities. Two types of forces that the electric/spin current exerts on magnetization are identified based on a general formula relating the force to the torque.