Thermal relaxation of magnons and phonons near resonance points in magnetic insulators

We theoretically investigate the energy relaxation rate of magnons and phonons near the resonance points to clarify the underlying mechanism of heat transport in ferromagnetic materials. We find that the simple two-temperature model is valid for the one-phonon/one-magnon process, as the rate of energy exchange between magnons and phonons is proportional to the temperature difference between them, and it is independent of temperature in the high temperature limit. We found that the magnon-phonon relaxation time due to the one-phonon/one-magnon interaction could be reduced to 1.48 $\mu s$ at the resonance point by applying an external magnetic field. It means that the resonance effect plays a significant role in enhancing the total magnon-phonon energy exchange rate, apart from the higher order interaction processes.