Precursor dynamics in the ferroelectric phase transition of barium titanate single crystals studied by Brillouin light scattering

Abstract

The acoustic anomalies and precursor dynamics of high-quality barium titanate single crystals were investigated by Brillouin light scattering and the birefringence measurements in the paraelectric phase above the cubic-to-tetragonal ferroelectric phase transition temperature (${T}_{c}$). Two elastic stiffness coefficients ${C}_{11}$ and ${C}_{44}$, the related sound velocities, and their absorption coefficients were determined from ${T}_{c}$ to 400${\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}$C for the first time. The longitudinal acoustic (LA) mode showed a substantial softening over a wide temperature range above ${T}_{c}$ which was accompanied by a remarkable increase in the acoustic damping as well as growth of central peaks. The broad central peak (CP) exhibited a two-mode and one-mode behavior in the paraelectric and ferroelectric phase, respectively, which was consistent with recent far-infrared reflectivity measurements and first-principle-based calculations [Ponomareva et al., Phys. Rev. B 77, 012102 (2008)]. The acoustic anomalies and CP behavior were correlated with the anomalous birefringence, piezoelectric effect, and the deviation of the Curie-Weiss law observed from the same crystal. This strongly indicates similarity between the dynamics of polar clusters in typical ferroelectrics and the dynamics of polar nanoregions in relaxors, consistent with recent acoustic emission measurements [Dul'kin et al., Appl. Phys. Lett. 97, 032903 (2010)]. The relaxation times estimated from the central peak and the LA mode anomalies exhibited similar temperature dependences with comparable orders of magnitude, indicating that the polarization fluctuations due to the precursor polar clusters couples to the LA mode through density fluctuations. All these anomalies share common microscopic origin, correlated Ti off-centered motions forming polar clusters having local symmetry breaking in the paraelectric phase. The existence of the polar clusters were directly evidenced by the temperature evolution of the precise birefringence map. The narrow central peak within $\ifmmode\pm\else\textpm\fi{}$5 GHz proposed before was not confirmed to exist in the present study.