Theory of central peak and acoustic anomaly in cubic BaTiO3 close to ferroelectric transition

TL;DR

This paper develops a Ginzburg-Landau theoretical framework to explain the central peak and acoustic anomalies observed near the ferroelectric transition in cubic BaTiO3, emphasizing the role of electrostrictive coupling.

Contribution

It introduces a novel theoretical model linking electrostrictive coupling to central peaks and acoustic anomalies in ferroelectrics near transition points.

Findings

Central peak in displacement correlation function grows near transition

Frequency-dependent elastic moduli exhibit singular behavior due to ES coupling

Sound velocity and attenuation show characteristic anomalies close to transition

Abstract

We present a Ginzburg-Landau theory on statics and dynamics of BaTiO$_3$-type ferroelectrics in the paraelectric phase with the cubic structure, where the order parameter is the polarization $\bi p$. Unique effects are caused by the electrostrictive (ES) coupling between ${\bi p}$ and the elastic displacement $\bi u$. We show that the ES coupling gives rise to a central peak in the Fourier-Laplace transform of the displacement time-correlation function at small wave numbers. It emerges and grows with a narrow width as the transition is approached. Such central peaks have long been observed in a number of scattering experiments in various ferroelectrics, but their origin has not been well understood. From the acoustic part of the displacement dynamic correlation we obtain the frequency-dependent elastic moduli $C_{11}^*(\omega)$, $C_{12}^*(\omega)$, and $C_{44}^*(\omega)$, whose singular parts arise from the ES coupling, We then calculate the singular sound velocity and attenuation. In the central peak and the elastic moduli, the frequency $\omega$ appears in the scaled form $\omega\tau_D$, where $\tau_D$ is the Debye relaxation time in the frequency-dependent dielectric constant. {Keywords}: ferroelectric transition, central peak, acoustic anomaly, electrostrictive coupling