Finite-frequency effects for elastic waves in rare-earth compounds

Abstract

In rare-earth compounds, the deformation caused by an elastic wave interacts with the crystalline-electric-field- (CEF-) split energy levels of the incomplete $4f$ shell of the rare-earth ions. This magnetoelastic interaction is temperature dependent due to the different thermal population of the CEF levels at different temperatures and leads to a number of interesting effects. One type of effect is found in the zero-frequency limit of the elastic waves. Here we deal with effects that occur only at finite frequencies. We find interesting results in the presence of a magnetic field. In particular, for some geometries we find (1) nonreciprocal Rayleigh-wave propagation, i.e., $\omega \left(\overrightarrow{k}\right)\ne \omega (-\overrightarrow{k})$, where $\omega$ and $\overrightarrow{k}$ are the frequency and wave vector of the Rayleigh wave, (2) a mixing of bulk-longitudinal and bulk-transverse waves, and (3) the existence of a pure shear polarized surface wave.