Magnetoelastic coupling at the field-induced transition in EuAl$_{12}$O$_{19}$
Magnetoelastic coupling plays a crucial role in magnetic-field-induced transitions in anisotropic ferromagnets. Ultrasonic methods are suitable for experimental investigations of these phenomena. We investigate elastic constants in EuAl$_{12}$O$_{19}$, a quasi-two-dimensional anisotropic ferromagnet, by measuring sound velocity in magnetic fields perpendicular to spontaneous magnetization. The shear modulus $C_{44}$ exhibits dramatic softening at the field-induced transition from the ferromagnetic to a paramagnetic phase with magnetic moments forced to polarize along the applied transverse field. The softening is attributed to strong magnetic fluctuations near a second-order phase transition. Theoretical calculations based on magnetization data qualitatively reproduced the observed behavior within a strain-exchange mechanism. These results demonstrate that magnetoelastic coupling in EuAl$_{12}$O$_{19}$ arises primarily from exchange striction and provide a framework for modeling similar transitions in other anisotropic ferromagnets.