Sound propagation in magnets and its application to a planar ferromagnetic chain

The velocity shift and the attenuation of ultrasonic waves in magnetic insulators are studied theoretically. By the treatment of the volume and single-ion magnetostrictive interactions on an equal footing, interesting interference effects between these two spin-phonon coupling mechanisms are possible. The results are applied to a planar ferromagnetic chain at low temperatures. The attenuation coefficient is found to depend linearly on the temperature and quadratically on the frequency. The velocity shift is also linear in the temperature but does not depend on the frequency.