First-principles-inspired thermodynamic framework linking the condensed ground state to displacive ferroelectric phase transitions

TL;DR

This work develops a first-principles–inspired, self-consistent quantum-statistical framework for displacive ferroelectrics that treats the condensed soft phonon as a bosonic, vectorial polar mode. By renormalizing ground-state parameters through zero-point and thermal fluctuations of a collective vector mode, it predicts finite-temperature dielectric and ferroelectric properties, including transition temperatures and critical behavior, using only ground-state information. The approach quantitatively matches experimental data for PbTiO3, SrTiO3, KTaO3, and strain-engineered SrTiO3 without finite-temperature parameter fitting, and it provides a unified description of both classical and quantum paraelectric regimes. It also establishes a pathway to compute broader thermo-mechanical and dynamical properties, linking microscopic phonon physics to device-scale performance and extending to other bosonic phase transitions.

Abstract

Quantitative description of finite-temperature properties of displacive ferroelectrics, and in particular the critical behavior, is of fundamental importance to both theory and device design, going beyond the Landau-Ginzburg approach, which requires known knowledge of critical behaviors and temperature-dependent parameter fitting. Here within quantum statistic description of quasiparticles, we develop a self-consistent, microscopically based phase-transition framework, by treating the bosonic condensation of the unstable phonons and the emerging collective vectorial polar mode. It enables one to use only the ground-state properties to predict the finite-temperature properties and in particular, the criticality of phase transitions of various displacive ferroelectrics. Its applications to the classical ferroelectric PbTiO$_3$, quantum paraelectrics SrTiO$_3$ and KTaO$_3$, and recently fabricated ferroelectric strained SrTiO$_3$, demonstrate remarkable quantitative agreements with the experimentally measured dielectric/ferroelectric properties throughout the entire temperature ranges of the phases, including the critical behaviors of phase transitions. The framework offers a tractable and parameter-free quantitative basis for understanding and predicting phase transitions in a broad range of ferroelectric systems under diverse thermodynamic and external conditions, bridging microscopic modeling and device-level design.

Figures (5)

• Figure 1: Schematic of the renormalization in thermodynamic theory.
• Figure 2: Temperature dependence of the dielectric properties in ferroelectric PbTiO$_3$. a, inverse dielectric function; b, dielectric function; c, spontaneous polarization (order parameter); d, free-energy parameters $\alpha(T)$ and $\beta(T)$; e, normalized change of unit cell volume (tetragonality); f, difference between the calculated specific heat $c_p$ and the Dulong-Petit specific heat $c_0=3nR$ for bulk PbTiO$_3$ with $n=5$PhysRevB.111.094113. Experimental data in a and b are from Ref. remeika1970growth (squares) and Ref. ikegami1971electromechanical (circles). Insets of a and b zoom the corresponding temperature ranges. Inset of c shows the results of $d{P}/dT$, and the experimental data are from Ref. remeika1970growth. Inset in d shows the fluctuation $\langle\delta{P^2_{\rm th}}(T)\rangle$ and order parameter $P^2$. Experimental data in e and f are from Ref. Shirane1951 and Ref. Yoshida1960, respectively. In f, for comparison, we also addressed the numerical results from deep potential molecular dynamics (DPMD, with $T_c\approx821~$K) trained on DFT-based data PhysRevB.111.094113. The specific model parameters $a_{i}$, $a_{ij}$ and $a_{ijk}$ used in our simulation, and their determination using several independent measurements of the spontaneous polarization and dielectric function at long-temperature limit are discussed in Supplemental Materials.
• Figure 3: Temperature dependence of inverse dielectric function in quantum paraelectric a, SrTiO$_3$ and b, KTaO$_3$. The solid curves are predicted values from the present theory, and the dots come from the experimental measurement in Ref. rowley2014ferroelectric. The insets show the results at low-temperature limit. The used specific zero-temperature parameters, and their determination using several independent measurements are addressed in Supplemental Materials.
• Figure 4: Dielectric function and inverse dielectric function versus temperature in quantum paraelectric KTaO$_3$. In the figure, the solid curve are predicted values from the present theory, and the experimental results (circles) in a, b, c and d come from Refs. wemple1965some, abel1971effect, ang2001dielectric and aktas2014polar. The specific zero-temperature parameters, and their determination are addressed in Supplemental Materials.
• Figure 5: (a) Ferroelectric transition temperature as a function of externally applied strain. The solid curve represent calculated results from the present renormalization theory, whereas the data points are experimental measurements from Ref. li2025classical. The chain curve denotes an empirical power-law relation $T_c \propto (s-s_{\rm cp})^{0.606}$ proposed by experiments in Ref. li2025classical, and the dashed curve comes from the prediction by using Landau theory li2025classical, which predicts a scaling $T_c \propto (s-s_{\rm cp})^{0.5}$ when assuming $\alpha(T)\sim{T^2}$ (as suggested by experiment rowley2014ferroelectric). The inset shows the same data, but plotted with a linear vertical axis instead of a logarithmic one. (b) Calculated polarization as a function of strain at fixed low temperature from our theory and Density functional theory. DFT results are taken from Ref. xu2020strain.