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 ω. 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 τes. In turn, the high-frequency behavior is determined by the magnon-phonon collisions time τmp. From the latter, the time of phonon-magnon collisions τpm can be found. In contrast, the response of effectively thin F layers is characterized by just one feature, which is determined by the time τmp. Thus, based on the obtained theoretical results, the times τes,τmp, and τpm can be deduced from experiments on the parametric excitation of spin waves by electromagnetic radiation modulated at frequency ω.