Sound Propagation Near the Phase Transition to a Magnetically Ordered Phase in Media with Tetragonal Structure

The propagation of longitudinal elastic waves is investigated near the paramagnetic-to-incommensurate phase transition in layered systems with tetragonal structure. On the basis of [22], a conclusion is made that a second-order phase transition is possible if there are no shear deformations in the crystal and the renormalization of the interaction parameters does not change the sign of these parameters in the action terms containing the fourth powers of the order parameter components. For longitudinal sound waves propagating along the [100] direction, a power-law temperature variation of the sound velocity in the critical region and a shift of the minimum frequency point (and hence the velocity) of these waves with respect to the phase transition point are found by the renormalization group (RG) approach. The reasons are explained why the velocities of longitudinal sound waves propagating in the [100], [110], and [001] directions exhibit different variation patterns.