Rotational invariance and magnetoelastic phenomena in paramagnets

Abstract

We measured sound-velocity changes for various geometries in the model paramagnet TmSb and in high magnetic fields. By measuring the $c_{44}$ mode with propagation direction $\overrightarrow{\mathrm{k}}$ parallel and perpendicular to the magnetic field one finds a field-dependent splitting between the two modes, which should be absent in noninvariant magnetoelastic theory. This is evidence for the presence of rotationally invariant magnetoelastic interactions. A recently developed theory by Dohm and Fulde is used to quantitatively account for this effect. All relevant material parameters are known for TmSb and we can therefore make for the first time a test for this theory without adjustable parameters. The result is a surprisingly good agreement between experiment and theory. The inclusion of other higher-order magnetoelastic terms is discussed. A similar effect is observed for the $c_{11}-c_{12}$ mode, where we can account for the mode splitting with opposite sign to the $c_{44}$ case and where we can account for the order of magnitude of the effect with a simplified calculation. We also present analogous experimental results for paramagnetic ${\mathrm{Pr}}_3$ ${\mathrm{Te}}_4$ in smaller fields, which we do not interpret quantitatively due to lack of knowledge of crystal electric field parameters for ${\mathrm{Pr}}^{3+}$.