Temperature dependence of the magnon-phonon energy relaxation time in a ferromagnetic insulator

Abstract

We have used the Boltzmann kinetic equation for the phonon distribution function to analyze the relaxation kinetics of the spin system of a ferromagnetic insulator (F) lying on a massive dielectric substrate with high thermal conductivity. Under periodic heating of the spin system, the relaxation depends on the thickness of the F layer and on the frequency of the thermal source $\ensuremath{\omega}$. When the thickness of the F layer is much greater than the phonon-magnon scattering length, the magnon temperature dependence on the frequency has two features related to specific characteristic times of the system. One of them determines the dependence in the low-frequency regime and is related to the average phonon escape time from the F layer to the substrate ${\ensuremath{\tau}}_{\mathrm{es}}$. In turn, the high-frequency behavior is determined by the magnon-phonon collisions time ${\ensuremath{\tau}}_{mp}$. From the latter, the time of phonon-magnon collisions ${\ensuremath{\tau}}_{pm}$ can be found. In contrast, the response of effectively thin F layers is characterized by just one feature, which is determined by the time ${\ensuremath{\tau}}_{mp}$. Thus, based on the obtained theoretical results, the times ${\ensuremath{\tau}}_{\mathrm{es}},{\ensuremath{\tau}}_{mp}$, and ${\ensuremath{\tau}}_{pm}$ can be deduced from experiments on the parametric excitation of spin waves by electromagnetic radiation modulated at frequency $\ensuremath{\omega}$.