Nonlinear relaxation between spin waves (magnons) and the crystal lattice (phonons) in an insulating ferromagnet is investigated theoretically. Magnons and phonons are described by equilibrium Bose-Einstein distributions with different temperatures, $T_s>T_l$. The magnon temperature is assumed to be much lower than the Debye temperature $T_s\ll {\mathrm{\Theta }}_D$, which is justified at low temperatures. The nonlinear heat current from magnons to phonons is calculated microscopically in terms of the Cherenkov radiation of phonons by magnons. The results are discussed in comparison with the well-known theoretical results on nonlinear electron-phonon relaxation in metals [M. Kaganov, I. M. Lifshitz, and I. V. Tanatarov, J. Exp. Theor. Phys. 31, 232 (1956)]. The elaborated theoretical description is relevant for spin-pumping experiments and thermoelectric devices in which the magnon temperature is essentially higher than the phonon one. The derived expression for the heat current can be used for calculation of the nonlinear heat boundary resistance in spin-caloritronic heterostructures.

• Received 14 June 2018
• Revised 23 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.104405