Propagation of acoustic and electromagnetic waves in piezoelectric, piezomagnetic, and magnetoelectric materials with tetragonal and hexagonal symmetry

The propagation of the acoustic and the electromagnetic signals is studied in materials with tetragonal and hexagonal symmetries that are piezoelectric, piezomagnetic, or magnetoelectric. Three magnetic spatial symmetries are considered: 622 for hexagonal crystals and 422 and 4(')22(') for tetragonal crystals. The equations for the five modes (three mainly acoustic and two mainly electromagnetic) are solved both in the general case and in specific cases in which the material is only piezoelectric, piezomagnetic, or magnetoelectric. It is found that the piezomagnetic and the magnetoelectric coefficients and the magnetic permeability renormalize the elastic constants, the piezoelectric coefficients, and the dielectric tensor. The acoustic frequencies depend on the angle theta that the component of the wave vector in the a-b plane forms with the a axis. The main contribution to the electromagnetic modes derives only from the dielectric tensor and the magnetoelectric coefficients and it is independent of theta and of the piezoelectric and the piezomagnetic coefficients. Starting from the general equations, a method has been devised to study separately the acoustic and the electromagnetic solutions. It is found that a number of relations must be verified in order to have stability of the electromagnetic and the acoustic modes.