无公度相铁电体中Lifshitz点附近Kibble-Zurek行为的观察
Observation of Kibble-Zurek behavior near the Lifshitz point in ferroelectrics with incommensurate phase
摘要：
本文研究了在Lifshitz点$x_{\rm LP} \sim 0.28$以上具有Ⅱ型无公度相的单轴Sn $_2$ P $_2$（Se $_x$ S $_{1-x}$）$_6$铁电体的非平衡性质。我们测量了冷却和加热速率范围为0.002-0.1~K/min的介电磁化率，以及高分辨率超声实验和超声布里渊散射。对于具有$x \geqslant 0.28$的样品，在很慢的冷却速率下，在无公度的二级相变（$T_i$）和一级锁定相变（$T_c$）处观察到明显的反常，而当冷却速率大于0.1~K/min时，没有观察到中间IC相。我们用Kibble-Zurek非平衡二级相变模型解释了这种效应。在具有强非线性局域势的铁电体中，冷却速率决定了畴壁的浓度和尺寸：畴宽随冷却速率的增大而减小。在一定条件下，畴壁的尺寸与无公度的相位调制周期相当，它位于Lifshitz点附近的微米尺度上，导致调制周期被畴壁钉扎。
英文摘要：
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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