Lattice instability at phase transitions near the Lifshitz point in proper monoclinic ferroelectrics

The temperature dependence of acoustic properties of the Sn(2)P(2)(Se(x)S(1-x))(6) uniaxial ferroelectric in the vicinity of the Lifshitz point (LP) was investigated by Brillouin spectroscopy and analysed in the Landau-Khalatnikov approximation. An anomalous decrease of the longitudinal hypersound velocity in the paraelectric phase caused by fluctuation effects and crystal structure defects has been found near the LP. Besides this, a small softening of the transverse acoustic phonons is observed, which is due to their linear interaction with the soft optic mode found for incommensurate phase transitions in proper ferroelectrics. The lattice instability analysis of Sn(2)P(2)S(6) and Sn(2)P(2)Se(6) crystals and their solid solutions in a polarizable ion model shows that a possible reason for the absence of a soft acoustic mode is nonorthogonality of the spontaneous polarization vector and modulation wavevector which both lie in the monoclinic symmetry plane.