Gilbert damping and spin Coulomb drag in a magnetized electron liquid with spin-orbit interaction

TL;DR

This paper provides a microscopic calculation of Gilbert damping in a spin-polarized 2D electron liquid with spin-orbit interaction, highlighting the role of spin Coulomb drag and various energy scales.

Contribution

It introduces a method to relate Gilbert damping to spin-orbit torque auto-correlation and explores its dependence on physical regimes and electron-electron interactions.

Findings

Gilbert damping expressed via spin-orbit torque auto-correlation

Relation between Gilbert constant and spin-channel conductivity in Rashba model

Impact of electron-electron interactions on damping through spin Coulomb drag

Abstract

We present a microscopic calculation of the Gilbert damping constant for the magnetization of a two-dimensional spin-polarized electron liquid in the presence of intrinsic spin-orbit interaction. First we show that the Gilbert constant can be expressed in terms of the auto-correlation function of the spin-orbit induced torque. Then we specialize to the case of the Rashba spin-orbit interaction and we show that the Gilbert constant in this model is related to the spin-channel conductivity. This allows us to study the Gilbert damping constant in different physical regimes, characterized by different orderings of the relevant energy scales -- spin-orbit coupling, Zeeman coupling, momentum relaxation rate, spin-momentum relaxation rate, spin precession frequency -- and to discuss its behavior in various limits. Particular attention is paid to electron-electron interaction effects,which enter the spin conductivity and hence the Gilbert damping constant via the spin Coulomb drag coefficient.