Sound behavior near the Lifshitz point in proper ferroelectrics

Abstract

The interaction between soft optic and acoustic phonons was investigated for ${\text{Sn}}_{2}{\text{P}}_{2}{({\text{Se}}_{0.28}{\text{S}}_{0.72})}_{6}$ proper uniaxial ferroelectrics by Brillouin-scattering and ultrasonic pulse-echo techniques. The elastic softening of hypersound velocity of transverse-acoustic phonons and for both longitudinal and transverse ultrasound waves which propagate near direction of the modulation wave vector (in the incommensurate phase at $x>{x}_{\text{LP}}$) was found at cooling to the Lifshitz point in the paraelectric phase. The strong increase in the ultrasound attenuation has also been observed. Such phenomena are related to the linear interaction of the soft optic and acoustic branches in the region of relatively short-range hypersound waves and to the strongly developed long-range order-parameter fluctuations in the ultrasound frequency range. The hypersound velocity temperature dependence was described within the Landau-Khalatnikov approximation for the ferroelectric phase.