Rotational invariance and dipolar magnetoelastic effects: Application to TmSb.

Abstract

In a magnetic material, the conservation of the total angular momentum is known to give rise to interactions between the magnetic moments and the phonons. The most spectacular effect is the lifting of the degeneracy between transverse sound waves when the directions of propagation and the polarization vectors are interchanged. Here the theory of rotational invariance is reconsidered. It is found that long-wavelength effects appear only in the presence of an external magnetic field. The second-order strain interactions, considered previously in conjunction with the rotational interactions, are found to be eliminated by the equilibrium conditions. The contributions due to finite deformations of the crystal, however, are significant. The magnetic dipole coupling changes rapidly at long wavelengths and it affects the field dependence of the transverse-sound velocities, in a way similar to the rotational interaction terms. The present theory, in which this dipolar contribution is included, gives a much improved account of the ultrasonic experiments performed by Wang and L\"uthi on TmSb.