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 ${\mathrm{EuAl}}_{12}{\mathrm{O}}_{19}$, 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 ${\mathrm{EuAl}}_{12}{\mathrm{O}}_{19}$ arises primarily from exchange striction and provide a framework for modeling similar transitions in other anisotropic ferromagnets.

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• Elastic modulus
• Frustrated magnetism
• Magnetism
• Magnetoelastic effect
• Ultrasound techniques