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

TL;DR

This study explores non-equilibrium phase transition dynamics in ferroelectrics near the Lifshitz point, demonstrating how cooling rate influences domain formation and phase anomalies, consistent with the Kibble-Zurek model.

Contribution

It provides experimental evidence of Kibble-Zurek behavior in ferroelectrics near the Lifshitz point, linking cooling rate to domain wall density and phase transition anomalies.

Findings

Anomalies at phase transitions depend on cooling rate.

Faster cooling smears phase transition anomalies.

Domain size correlates with cooling rate and phase modulation.

Abstract

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 and heating 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.