Theory of birefringence of sound in easy-plane rhombohedral antiferromagnets with inclusion of hexagonal anisotropy and mechanical stresses

The constructed thermodynamic theory of magnetic birefringence of transverse sound in easyplane weak ferromagnets with an axial basal anisotropy induced by boundary conditions has been generalized to the case of additional inclusion of the hexagonal anisotropy enhanced by isotropic mechanical stresses. The magnetoelastic contribution $\Delta C_a$ to the effective elastic modulus $C_{44}^{\mathrm{eff}}=C_{44}+\Delta C_a$, which determines the phase velocity of the magnetic mode of the acoustic wave in a crystal, has been calculated. It has been shown that the induced anisotropy with the twofold and sixfold symmetry leads to the appearance of an additional anisotropic term of the fourfold symmetry in the contribution $\Delta C_a$. The developed theory has made it possible to satisfactorily describe the existing experiments.