Spin orbit precession damping in transition metal ferromagnets

TL;DR

This paper presents a simplified model for spin-orbit precession damping in transition metal ferromagnets, incorporating state population changes and analyzing material-specific damping rates.

Contribution

It introduces a perturbative approach that includes state population variations, providing a more comprehensive understanding of damping mechanisms in ferromagnets.

Findings

Damping rate correlates strongly with density of states.

Intraband damping depends on the cube of the spin-orbit parameter.

Interband damping is proportional to the square of the spin-orbit parameter.

Abstract

We provide a simple explanation, based on an effective field, for the precession damping rate due to the spin-orbit interaction. Previous effective field treatments of spin-orbit damping include only variations of the state energies with respect to the magnetization direction, an effect referred to as the breathing Fermi surface. Treating the interaction of the rotating spins with the orbits as a perturbation, we include also changes in the state populations in the effective field. In order to investigate the quantitative differences between the damping rates of iron, cobalt, and nickel, we compute the dependence of the damping rate on the density of states and the spin-orbit parameter. There is a strong correlation between the density of states and the damping rate. The intraband terms of the damping rate depend on the spin-orbit parameter cubed while the interband terms are proportional to the spin-orbit parameter squared. However, the spectrum of band gaps is also an important quantity and does not appear to depend in a simple way on material parameters.