Magnon lifetime of two-dimensional insulating ferromagnet at T = 0 K

A magnon-phonon interaction model is developed for a two dimensional square insulating ferromagnet. By Matsubara-Green function method, the magnon damping under such on interaction is studied, with the magnon damping calculated on the main symmetric point/line in Brillouin zone for different parameters in the system. It is found that at the boundary of Brillouin zone the magnon damping is strong, while it is very weak in the zone of small wave vectors, and especially the magnon damping becomes maximal at T = 0 K. The influences of longitudinal phonon and transverse phonon on the magnon damping are compared, and the influences of all relevant parameters on magnon damping are also discussed. The expression - Im∑*(1) (k) = /(2τ) is available to take as a criterion for the magnon lifetime.