Magnon-phonon relaxation in yttrium iron garnet from first principles

We combine the theoretical method of calculating spin wave excitation with the finite-temperature modeling of lattice vibration and calculate the magnon-phonon relaxation time in the technologically important material yttrium iron garnet (YIG) from first principles. The finite lifetime of magnon excitation is found to arise from the fluctuation of the exchange interaction of magnetic atoms in YIG. At room temperature, the magnon spectra have significant broadening that is used to extract the magnon-phonon relaxation time quantitatively. The latter is a phenomenological parameter of great importance in YIG-based spintronics research. We find that the magnon-phonon relaxation time for the optical magnon is a constant, while that for the acoustic magnon is proportional to $1/{k}^{2}$ in the long-wavelength regime.