  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.
