Magnetoelastic coupling in hexagonal multiferroic Y Mn O 3 using ultrasound measurements

We report an ultrasonic investigation of the elastic moduli on a single crystal of hexagonal $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_{3}$ as a function of temperature. Stiffening anomalies in the antiferromagnetic N\'eel state below ${T}_{N}=72.4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ are observed on all the four elastic moduli ${C}_{ii}$. The anomalies are the most important on ${C}_{11}$ and ${C}_{66}$ for in-plane elastic deformations; this is consistent with a strong coupling of the lattice with the in-plane exchange interactions. We use a Landau free energy model to account for these elastic anomalies. We derive an expression which relates the temperature profile of the anomaly to the order parameter; the critical exponent associated with this parameter $\ensuremath{\beta}=0.42$ is not consistent with a chiral $XY$ or three-dimensional Heisenberg universality class, but more in agreement with a conventional antiferromagnetic long-range order. A tiny softening anomaly on ${C}_{11}$ for which hysteresis effects are observed could be indicative of an interaction between ferroelectric and magnetic domains at ${T}_{N}$. Moreover, magnetic fluctuation effects both above and below ${T}_{N}$ are identified through abnormal temperature and magnetic field effects.