One dimensional Cherenkov processes in ferromagnetic isolators are studied with perturbation theory under the constraint condition of conservation of energy and momentum. It is shown that the magnon-phonon interaction channels are limited and wave number dependent, which result in respectively 1/k2 and 1/k4 dependence of the lifetime and the relaxation time of long wavelength magnons. The reciprocal of relaxation time between magnons and phonons, 1/τmp, is found to be a linearly increasing function of the temperature as T> 70 K. Based on the Sanders-Walton model, we further show that when a thermal (phonon) gradient is applied along the system, the temperature difference between the phonon bath and the magnons with wave-vector k becomes more pronounced as k decreasing.
@article{arxiv.1710.06155,
title = {One dimensional Cherenkov processes in ferromagnetic insulator},
author = {Tongli Wei and YaoJin Li and DeCheng Ma and ChengLong Jia},
journal= {arXiv preprint arXiv:1710.06155},
year = {2017}
}