Magnetoelastic coupling within a Landau model of phase transitions: Application to the frustrated triangular antiferromagnet CsNiCl3

Abstract

A model Landau free energy is proposed in order to describe elastic coupling to spin degrees of freedom in systems exhibiting phase transitions which involve long-range magnetic order. Using rigourous symmetry arguments, various interaction terms are derived for magnetic materials with a hexagonal crystal structure. The model is applied to the frustrated triangular antiferromagnet CsNiCl${}_{3}$ and used to analyze and correlate a wide variety of experimental results such as the magnetic phase diagram, magnetization, strains, and elastic constant measurements at low temperatures. Good agreement between the model and the data is obtained for the temperature and magnetic field dependence of ${C}_{33}$ and ${C}_{66}$ in the vicinity of phase transitions. In particular, the analysis shows that the anomaly observed in the field dependence of ${C}_{33}$, close to the spin-flop phase boundary (${H}_{\mathit{SF}}\ensuremath{\simeq}2$ T), is dominated by the field dependence of the magnetic susceptibility. It is also found that higher order magnetoelastic coupling terms are required to reproduce the qualitative behavior of the elastic constants in the vicinity of the phase transitions. Our results demonstrate that a straightforward mean-field model which incorporates the correct system symmetries provides a powerful tool for relating complex spin configurations to the elastic and other response functions. The present work also serves to complement and expand our earlier results [G. Quirion et al., Phys. Rev. Lett. 97, 077202 (2006)].