Heat capacity and high-resolution Brillouin scattering studies of phase transitions inK2MgWO2(PO4)2: Observation of the coupled soft optic and acoustic mode

Abstract

High-resolution micro-Brillouin scattering and heat capacity studies of phase transitions in ferroelectric ${\mathrm{K}}_{2}\mathrm{Mg}\mathrm{W}{\mathrm{O}}_{2}{(\mathrm{P}{\mathrm{O}}_{4})}_{2}$ were performed in the temperature range $300\char21{}810\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Strong anomalies in Brillouin shift and attenuation were observed near 633, 519, and $434\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ upon cooling for the sound waves corresponding to the ${c}_{11}$ and ${c}_{33}$ elastic constants. The analysis of these anomalies and heat capacity results revealed that they correspond to second-order, typical first-order, and nearly second-order phase transitions, respectively. The highest temperature phase transition was shown to have mainly an order-disorder nature whereas the two remaining transitions may have both order-disorder and displacive nature. The obtained results revealed also very strong coupling between the ${c}_{44}$ acoustic mode and the soft optic mode of $E$ symmetry. The coupled mode model was employed to fit the experimental data. It was shown that the relaxation time of the order parameter exhibits slowing down indicating that the phase transition at $519\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is induced by instability of the $E$-symmetry soft mode. The possible microscopic origin of the soft mode is proposed.