Abstract
Ultrasonic velocity measurements are used to examine the elastic properties of the magnetoelectric compound $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_{2}$ in the vicinity of the magnetic and structural phase transitions near $14\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Strong softening of modes related to ${C}_{66}$ occurs at the transition from the high-temperature rhombohedral $R\overline{3}m$ to lower-temperature monoclinic $C2∕m$ symmetry. A Landau free energy is proposed and analyzed in order to understand the elastic properties of $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_{2}$. The principal features of sound velocity modes vs temperature are reproduced by the model. Our analysis suggests that the transition at $14\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is primary pseudoproper ferroelastic, with the spin acting as a secondary order parameter.
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