Effect of magnon–phonon interaction on transverse acoustic phonon excitation at finite temperature

A magnon–phonon interaction model is developed on the basis of two-dimensional square Heisenberg ferromagnetic system. By using Matsubara Green function theory transverse acoustic phonon excitation is studied and transverse acoustic phonon excitation dispersion curves is calculated on the main symmetric point and line in the first Brillouin zone. On line Σ it is found that there is hardening for transverse acoustic phonon on small wave vector zone (nearby point Γ), there is softening for transverse acoustic phonon on the softening zone and there is hardening for transverse acoustic phonon near point M. On line Δ it is found there is no softening and hardening for transverse acoustic phonon. On line Z it is found that there is softening for transverse acoustic phonon on small wave vector zone (nearby point X) and there is hardening for transverse acoustic phonon nearby point M. The influences of various parameters on transverse acoustic phonon excitation are also explored and it is found that the coupling of the magnon–phonon and the spin wave stiffness constant play an important role for the softening of transverse acoustic phonon.