Spin waves in terbium. II. Magnon-phonon interaction

The selection rules for the linear couplings between magnons and phonons propagating in the $c$ direction of a simple basal-plane hcp ferromagnet are determined by general symmetry considerations. The acoustic-optical magnon-phonon interactions observed in the heavy-rare-earth metals have been explained by Liu as originating from the mixing of the spin states of the conduction electrons due to the spin-orbit coupling. We find that this coupling mechanism introduces interactions which violate the selection rules for a simple ferromagnet. The interactions between the magnons and phonons propagating in the $c$ direction of Tb have been studied experimentally by means of inelastic neutron scattering. The magnons are coupled to both the acoustic- and optical-transverse phonons. By studying the behavior of the acoustic-optical coupling, we conclude that it is a spin-mixed-induced coupling as proposed by Liu. The coupled magnon—transverse-phonon system for the $c$ direction of Tb is analyzed in detail, and the strengths of the couplings are deduced as a function of wave vector by combining the experimental studies with the theory.