Transverse acoustic phonon excitation of two-dimensional Heisenberg ferromagnetic system

A magnon-phonon inter-action model is developed on the basis of two-dimensional square Heisenberg ferromagnetic system. The transverse acoustic phonon excitation is studied through Matsubara Green function theory, and the transverse acoustic phonon dispersion curve is calculated at the main symmetric point and on the symmetric line in the first Brillouin zone. It's found that on the line Sigma in first Brillouin zone, there is hardening for the transverse acoustic phonon in the smaller wave vector zone (point Gamma near k(x)a < 0.2), but there is softening for the transverse acoustic phonon in the softening zone (0.25 < k(x)a < 0.7), there is hardening for the transverse acoustic phonon at point M near (0.75 < k(x)a). On the line Delta, there is no phonon softening and hardening for transverse acoustic phonon. On the line Z, there is softening for transverse acoustic phonon in smaller wave vector zone (point X near k(x)a < 0.65), but there is hardening for the transverse acoustic phonon at the point M nearby. The influences of different parameters on the transverse acoustic phonon excitation are also illustrated. It's found that the coupling of the magnon-phonon coupling and the spin wave stiffness are the main factors affecting the transverse acoustic phonon softening.