Magnetoelastic coupling at the field-induced transition in EuAl$_{12}$O$_{19}$

TL;DR

This work investigates magnetoelastic coupling during a field-induced FM→PM transition in EuAl$_{12}$O$_{19}$ by measuring the shear-elastic response, specifically the velocity change of the $C_{44}$ mode, under a transverse magnetic field. The authors combine ultrasonic, magnetization, and specific-heat measurements on high-quality single crystals, and interpret the data with a strain-exchange MEC model using magnetization data. They observe dramatic softening of $C_{44}$ at the transition, with a clear dip in $rac{\nabla v}{v}$ indicative of a second-order transition, which is qualitatively reproduced by the model, implying exchange striction as the key MEC mechanism and enabling a framework for similar systems. The findings provide a quantitative approach to evaluate MEC strength in anisotropic ferromagnets and highlight ultrasound as a sensitive probe of magnetic critical fluctuations and phase boundaries in low-dimensional magnetic systems.

Abstract

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.

Figures (4)

• Figure 1: Temperature dependence of $\Delta v$/$v$ of $C_{44}$ mode in EuAl$_{12}$O$_{19}$ in a magnetic field of 0 and 0.3 T, respectively, applied along the $a^*$-axis.
• Figure 2: a) magnetization, b) heat capacity, and c) $\Delta v$/$v$ of $C_{44}$ mode dependencies on the magnetic field applied along the $a^*$-axis. The arrows point to $H_{c}$.
• Figure 3: $H-T$ phase diagram of EuAl$_{12}$O$_{19}$ in the magnetic field applied along the $a^*$-axis. The transition data points derived from our ultrasound - full squares, specific heat - full circles, and magnetization data - full triangles, and complementary specific heat - open circles and magnetization data - open triangles published by Bastien et al.BastienPRB.
• Figure 4: $\Delta v$/$v$ related to $C_{44}$ mode in EuAl$_{12}$O$_{19}$ at selected temperatures as function of the external magnetic field $H$ directed along the $a^*$-axis a) calculated within the strain-exchange model using the magnetization data from Ref. BastienPRB, b) determined by our ultrasound experiment.