Observationof Kibble-Zurek behavior near the Lifshitz point in ferroelectrics withincommensurate phase

Abstract

We have investigated non-equilibrium properties of proper uniaxial Sn2P2(SexS1−x)6 ferroelectrics with the Type II incommensurate phase above Lifshitz point xLP ∼ 0.28. We measured dielectric susceptibility with cooling and heating rate ranging 0.002-0.1 K/min, and high-resolution ultrasound experiments and hypersound Brillouin scattering. For samples with x > 0.28 clear anomalies were observed at incommensurate second order transition (Ti) and at first order lock-in transition (Tc) 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 Tc. 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.