Dynamics of magnetization coupled to a thermal bath of elastic modes

TL;DR

This paper models the magnetization dynamics in ferromagnetic thin films considering coupling with elastic modes, deriving equations for fluctuations and resonance behavior with potential experimental implications.

Contribution

It provides a realistic theoretical framework for magnetization dynamics coupled to elastic modes, including explicit expressions for fluctuation spectra and resonance line-width scaling.

Findings

Fluctuation correlation time scales with film thickness and sound speed.

Resonance line-width scales with magnetoelastic coupling squared and film thickness.

Derived equations applicable to insulating ferromagnetic thin films.

Abstract

We study the dynamics of magnetization coupled to a thermal bath of elastic modes using a system plus reservoir approach with realistic magnetoelastic coupling. After integrating out the elastic modes we obtain a self-contained equation for the dynamics of the magnetization. We find explicit expressions for the memory friction kernel and hence, {\em via} the Fluctuation-Dissipation Theorem, for the spectral density of the magnetization thermal fluctuations. For magnetic samples in which the single domain approximation is valid, we derive an equation for the dynamics of the uniform mode. Finally we apply this equation to study the dynamics of the uniform magnetization mode in insulating ferromagnetic thin films. As experimental consequences we find that the fluctuation correlation time is of the order of the ratio between the film thickness, $h$, and the speed of sound in the magnet and that the line-width of the ferromagnetic resonance peak should scale as $B_1^2h$ where $B_1$ is the magnetoelastic coupling constant.