Microscopic Calculation of Spin Torques in Disordered Ferromagnets

TL;DR

This paper provides a microscopic calculation of spin torques in disordered ferromagnets, focusing on the $eta$-term and Gilbert damping, considering electron spin-relaxation effects, applicable to both localized and itinerant ferromagnets.

Contribution

It introduces a microscopic approach to compute spin torques, including the $eta$-term and damping, accounting for impurity-induced spin relaxation in disordered ferromagnets.

Findings

The Gilbert damping $oldsymbol{ extalpha}$ differs from the $oldsymbol{eta}$-term.

Results apply to both localized and itinerant ferromagnetic systems.

Electron spin-relaxation influences the magnitude of spin torques.

Abstract

Effects of conduction electrons on magnetization dynamics, represented by spin torques, 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 (and spin-orbit) impurities. The obtained results such as $\alpha \ne \beta$ hold for localized as well as itinerant ferromagnetism.