Magnetization dynamics and damping due to electron-phonon scattering in a ferrimagnetic exchange model

TL;DR

This paper models magnetization damping in a simplified ferrimagnetic system, analyzing how electron-phonon interactions and spin-orbit coupling influence spin dynamics and relaxation times.

Contribution

It introduces a microscopic approach to calculate magnetization damping considering electron-phonon scattering and spin-orbit effects in an antiferromagnetic exchange model.

Findings

Derived Boltzmann scattering integrals for spin distributions.

Extracted dephasing and relaxation times T_1 and T_2.

Compared microscopic results with phenomenological damping models.

Abstract

We present a microscopic calculation of magnetization damping for a magnetic "toy model." The magnetic system consists of itinerant carriers coupled antiferromagnetically to a dispersionless band of localized spins, and the magnetization damping is due to coupling of the itinerant carriers to a phonon bath in the presence of spin-orbit coupling. Using a mean-field approximation for the kinetic exchange model and assuming the spin-orbit coupling to be of the Rashba form, we derive Boltzmann scattering integrals for the distributions and spin coherences in the case of an antiferromagnetic exchange splitting, including a careful analysis of the connection between lifetime broadening and the magnetic gap. For the Elliott-Yafet type itinerant spin dynamics we extract dephasing and magnetization times T_1 and T_2 from initial conditions corresponding to a tilt of the magnetization vector, and draw a comparison to phenomenological equations such as the Landau-Lifshitz or the Gilbert damping. We also analyze magnetization precession and damping for this system including an anisotropy field and find a carrier mediated dephasing of the localized spin via the mean-field coupling.