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Soft mode theory of ferroelectric phase transitions in the low-temperature phase
Journal of Physics: Condensed Matter ( IF 2.7 ) Pub Date : 2021-03-16 , DOI: 10.1088/1361-648x/abdb68
Luigi Casella 1 , Alessio Zaccone 1, 2
Affiliation  

Historically, the soft mode theory of ferroelectric phase transitions has been developed for the high-temperature (paraelectric) phase, where the phonon mode softens upon decreasing the temperature. In the low-temperature ferroelectric phase, a similar phonon softening occurs, also leading to a bosonic condensation of the frozen-in mode at the transition, but in this case the phonon softening occurs upon increasing the temperature. Here we present a soft mode theory of ferroelectric and displacive phase transitions by describing what happens in the low-temperature phase in terms of phonon softening and instability. A new derivation of the generalized Lyddane–Sachs–Teller (LST) relation for materials with strong anharmonic phonon damping is also presented which leads to the expression ɛ 0/ɛ = |ω LO|2/|ω TO|2. The theory provides a microscopic expression for T c as a function of physical parameters, including the mode specific Grneisen parameter. The theory also shows that ${\omega }_{\mathrm{T}\mathrm{O}}\sim {\left({T}_{\mathrm{c}}-T\right)}^{1/2}$, and again specifies the prefactors in terms of Grneisen parameter and fundamental physical constants. Using the generalized LST relation, the softening of the TO mode leads to the divergence of ϵ 0 and to a polarization catastrophe at T c. A quantitative microscopic form of the Curie–Weiss law is derived with prefactors that depend on microscopic physical parameters.



中文翻译:

低温相中铁电相变的软模式理论

从历史上看,铁电相变的软模式理论已被开发用于高温(顺电)相,其中声子模式在降低温度时软化。在低温铁电相中,会发生类似的声子软化,也导致过渡时冻结模式的玻色子凝聚,但在这种情况下,声子软化会在温度升高时发生。在这里,我们通过描述低温阶段在声子软化和不稳定性方面发生的情况,提出了铁电和位移相变的软模式理论。还提出了具有强非谐声子阻尼材料的广义 Lyddane-Sachs-Teller (LST) 关系的新推导,其导致表达式ɛ 0 /ɛ = | ω | 2 /| ω | 2 . 该理论提供了作为物理参数函数的T c的微观表达式,包括模式特定的 Grneisen 参数。该理论还表明${\omega }_{\mathrm{T}\mathrm{O}}\sim {\left({T}_{\mathrm{c}}-T\right)}^{1/2}$, 并再次根据 Grneisen 参数和基本物理常数指定了前因数。使用广义 LST 关系,TO 模式的软化导致ϵ 0的发散和在T c处的极化灾难。居里-魏斯定律的定量微观形式是用取决于微观物理参数的前因数推导出来的。

更新日期:2021-03-16
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