Mean-field magnetization relaxation in conducting ferromagnets

TL;DR

This paper models how magnetization in conducting ferromagnets relaxes through interactions with itinerant carriers, revealing different damping regimes influenced by spin-flip rates and spin-orbit coupling.

Contribution

It provides a linear-response calculation of magnetization relaxation considering carrier dynamics and identifies regimes analogous to known damping mechanisms.

Findings

Magnetization damping grows linearly with spin-flip rate at low rates.

Damping inversely proportional to spin-flip rate at high rates.

Strong spin-orbit interaction in semiconductors enhances relaxation efficiency.

Abstract

Collective ferromagnetic motion in a conducting medium is damped by the transfer of the magnetic moment and energy to the itinerant carriers. We present a calculation of the corresponding magnetization relaxation as a linear-response problem for the carrier dynamics in the effective exchange field of the ferromagnet. In electron systems with little intrinsic spin-orbit interaction, a uniform magnetization motion can be formally eliminated by going into the rotating frame of reference for the spin dynamics. The ferromagnetic damping in this case grows linearly with the spin-flip rate when the latter is smaller than the exchange field and is inversely proportional to the spin-flip rate in the opposite limit. These two regimes are analogous to the "spin-pumping" and the "breathing Fermi-surface" damping mechanisms, respectively. In diluted ferromagnetic semiconductors, the hole-mediated magnetization can be efficiently relaxed to the itinerant-carrier degrees of freedom due to the strong spin-orbit interaction in the valence bands.