We have investigated the magnetoelastic coupling in HoMnO${}_3$ by measuring the temperature and magnetic field dependence of two elastic moduli $C_{11}$ and $C_{33}$ with an ultrasonic velocity technique. In comparison with similar data in YMnO${}_3$, we have identified an enhanced elastic softening, predominantly on $C_{11}$, that scales with the spin susceptibility over a wide temperature range. Spin fluctuations induced by Ho-Mn interactions are responsible for this softening: when the softening is quenched by an in-plane magnetic field with a concomitant stabilization of the Mn order, it is rather enhanced for a field oriented along the $c$ axis. The H-T phase diagrams deduced from elastic anomalies appearing at the different phase transitions are consistent with previous microwave data. The origin of the Ho-Mn coupling is discussed in terms of a fourth-order trigonal anisotropy term in the spin Hamiltonian.

• Received 1 December 2010

DOI:https://doi.org/10.1103/PhysRevB.83.054418