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Observation of Kibble-Zurek behavior near the Lifshitz point in ferroelectrics with incommensurate phase
Materials Science · Submitted 22 Sep 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We explain this effect in terms of Kibble-Zurek model for non-equilibrium second order phase transitions.
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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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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 $x_{\rm LP} \sim 0.28$. | contribution 0.98 | 0.94 | 0.04 | asserted 0.98 |
| s1 | 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. | method 1.00 | 0.97 | 0.02 | asserted 1.00 |
| s2 | 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. | result 1.00 | 0.95 | 0.25 | asserted 1.00 |
| s3 | In general, increasing the cooling rate leads to smearing the anomaly at $T_c$. | result 1.00 | 0.89 | 0.14 | asserted 0.97 |
| s4 | We explain this effect in terms of Kibble-Zurek model for non-equilibrium second order phase transitions. | interpretation 0.98 | 0.61 | 0.31 | asserted 0.99 |
| s5 | 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. | interpretation 0.86 | 0.70 | 0.26 | asserted 1.00 |
| s6 | 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. | interpretation 0.89 | 0.73 | 0.19 | asserted 0.94 |
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Original 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.
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Here we use a transformation of the local three-well potential $V(x_i)$ (Fig. [ref]) as function of pressure according to the results of [ref] .
Valence fluctuations in Sn(Pb)$_2$P$_2$S$_6$ ferroelectrics · Anharmonic quantum oscillators model · 0.92
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