Rotational invariance and the coupling of acoustic waves to zero frequency pseudospin modes in paramagnets

Non‐resonant changes in acoustic velocities due to pseudospin‐phonon interactions in anisotropic paramagnets are investigated with particular emphasis on the additional contributions to the interaction which arise from the requirement of rotational invariance and the coupling of the acoustic waves to the pseudospin normal modes. In general one does not know the pseudospin rotational properties and thus the pseudospin‐phonon interaction can only be written in the crystal coordinate system rather than the laboratory system. On the other hand, since the crystal coordinate system is a rotating reference frame, one cannot write equations of motion for the pseudospins. These restrictions limit acoustic velocity change calculations to the thermodynamic limit of ωτ≪1 where τ is a typical pseudospin relaxation time and ω is the frequency of an acoustic wave. However, we show that equations for the ’’zero frequency’’ pseudospin modes (like the pseudomagnetization) can be derived in either the crystal or laboratory ...