Magnon–phonon coupling in two-dimensional Heisenberg ferromagnetic system

A magnon–phonon interaction model is set up for a two-dimensional insulating ferromagnetic system. By using Matsubara function theory, we have studied the magnon spectrum and calculated the magnon dispersion curve on the main symmetric point and line in the Brillouin zone for various parameters of the system. The results show that at the boundary of Brillouin zone, there is a strong magnon softening. The contributions of longitudinal and transverse phonons on the magnon softening are compared and the influences of various parameters are also discussed.