Ferroelectricity in (Pb$_y$Sn$_{1-y}$)$_2$P$_2$S$_6$ mixed crystals and random field BEG model

For Sn$_2$P$_2$S$_6$ ferroelectrics the second order phase transitions line is observed until reaching the tricritical point at transition temperature lowering to 250 K by compression. Observed temperature-pressure phase diagram agrees with simulateddiagram by MC calculations based on early founded by DFT study local potential for Sn$_2$P$_2$S$_6$ crystals. In addition to the tricritical point, the possibility of disordered and quadrupolar phases occurrence was shown. For mixed crystals with tin by lead substitution, the investigated ultrasound, hypersound and low frequency dielectric properties also reveal appearance of heterophase peculiarities at decreasing of ferroelectric transition temperature below so named temperature waterline near 250~K. The tricriticality at similar temperature level also appears in mixed crystals at sulfur by selenium substitution. Such behavior agree with Blume-Emery-Griffiths (BEG) model, that is appropriated for investigated ferroelectric system with three-well local potential for the order parameter (spontaneous polarization) fluctuations.

Observation of Kibble-Zurek behavior near the Lifshitz point in ferroelectrics with incommensurate phase

We have investigated non-equilibrium properties of proper uniaxial Sn$_2$P$_2$(Se$_x$S$_{1-x}$)$_6$ ferroelectrics with the Type II incommensurate phase above Lifshitz point $x_{rm LP} sim 0.28$. We measured dielectric susceptibility with cooling andheating rate ranging 0.002-0.1~K/min, and high-resolution ultrasound experiments and hypersound Brillouin scattering. For samples with $x geqslant 0.28$ clear anomalies were observed at incommensurate second order transition ($T_i$) and at first order lock-in transition ($T_c$) in the regime of very slow cooling rate, whereas the intermediate IC phase is not observed when the rate is faster then 0.1~K/min. In general, increasing the cooling rate leads to smearing the anomaly at $T_c$. We explain this effect in terms of Kibble-Zurek model for non-equilibrium second order phase transitions. In the ferroelectrics with strongly nonlinear local potential cooling rate defines concentration of domain walls and their size: domain width decreases when cooling rate increases. At certain conditions the size of domain is comparable to the incommensurate phase modulation period, which lies in micrometer scale in the vicinity of Lifshitz point and leads to pinning of the modulation period by domain wall.