Phase diagram of ferroelectrics with tricritical and Lifshitz points at coupling between polar and antipolar fluctuations
V. Liubachko, A. Oleaga, A. Salazar, R. Yevych, A. Kohutych, Yu. M. Vysochanskiǐ
Abstract
Available experimental data about static and dynamic critical behaviors of ${\text{Sn}}_{2}{\text{P}}_{2}{\text{S}}_{6}$-type ferroelectrics and $({\mathrm{Pb}}_{y}{\mathrm{Sn}}_{1\ensuremath{-}y}{)}_{2}{\mathrm{P}}_{2}{({\mathrm{Se}}_{x}{\mathrm{S}}_{1\ensuremath{-}x})}_{6}$ mixed crystals with a line of tricritical points and a line of Lifshitz points on the $T\ensuremath{-}x\ensuremath{-}y$ phase diagram, which meet at the tricritical Lifshitz point, are described in a combined Blume-Capel anisotropic next-nearest-neighbor Ising model. Such spin-1 Ising models with anisotropic competing first- and second-neighbor interactions is applied for the considered ferroelectrics with mixed displacive versus order/disorder character of phase transitions within the framework of a microscopic model with three-well total energy surface for ferroelectric distortion that was earlier built in an ab initio effective Hamiltonian approach. It was found that below the temperature of the tricritical Lifshitz point, the ``chaotic'' state accompanied by the coexistence of ferroelectric, metastable paraelectric, and modulated phases is expected. In addition to the frustration of polar fluctuations near the Brillouin zone center, in ${\mathrm{Sn}}_{2}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ crystals the antipolar fluctuations also strongly develop in the paraelectric phase on cooling to the continuous phase-transition temperature ${T}_{0}$. Here, the critical behavior can be described as a crossover between Ising and XY universality classes, which is expected near bicritical points with coupled polar and antipolar order parameters and competing instabilities in $q$ space.