Magnon contribution to the ultrasonic attenuation in planar ferromagnets

The propagation of acoustic waves in magnetic insulators is studied theoretically, first from a general point of view and then in the weak coupling limit. Both the modulation of the exchange integral and the single-ion magnetostriction are considered as coupling mechanisms between the spin and the phonon systems. At low temperatures, where the spin system can be described by non-interacting magnons, the attenuation coefficient is calculated for a planar ferromagnet. For the 1-D material CsNiF₃ explicit expressions for the ultrasonic attenuation coefficient α_ph are computed in both zero and finite external field. α_ph is found to be linear in the temperature and quadratic in the phonon frequency for H=0. However, in a finite field the frequency dependence becomes linear and the temperature and field dependences are rather complicated.