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 (Tc). Two elastic stiffness coefficients C11 and C44, the related sound velocities, and their absorption coefficients were determined from Tc to 400$\circ${}C for the first time. The longitudinal acoustic (LA) mode showed a substantial softening over a wide temperature range above Tc 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.

A strong relaxation mode was observed in the paraelectric phase of barium titanate $\left(\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\right)$ single crystals by Brillouin scattering study and was found to correlate with the softening of the longitudinal acoustic mode and the increase in the hypersonic damping. These observations support the existence of polar percursors and their electrostrictive coupling with the strain caused by the acoustic waves, consistent with former studies evidencing off-centered Ti ions in the high-symmetry cubic phase. A critical slowing down has been clearly observed in the vicinity of the cubic-tetragonal phase transition, indicating order-disorder component contributes to the phase transition of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ .

Temperature dependence of acoustic behaviors and quasielastic central peaks (CPs) of $\mathrm{Pb}\left[{\left({\mathrm{Zn}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right)}_x{\mathrm{Ti}}_{1-x}\right]{\mathrm{O}}_3$ $\left(\mathrm{PZN}\text{−}x\mathrm{PT}\right)$ single crystals with $x=4.5\%$ and 9% have been investigated in a temperature range of $300–900\mathrm{K}$ by using the Brillouin light scattering. The temperature dependence of the $C_{11}$ elastic constant of both crystals showed a deviation from normal lattice anharmonicity at the Burns temperature $\left(T_B\right)$ of about $730\mathrm{K}$ upon cooling, indicating the onset of the electrostrictive coupling between the polar nanoregions (PNRs) and the longitudinal acoustic (LA) waves. Upon further cooling, depolarized CP began to appear at a certain temperature $\left(T_d\right)$ located in $500–550\mathrm{K}$, which was accompanied by substantial softening of the $C_{44}$ elastic constant below this temperature suggesting anisotropic electrostrictive coupling between PNRs and the two acoustic waves. In addition, the onset of significant increase in the acoustic damping of both acoustic waves at $T_d$ could be seen from the temperature dependence of the linewidth of Brillouin doublets. These results suggested that electrostrictive coupling of the strain to the square of the local polarization of PNRs and the resultant order-parameter fluctuations are enhanced not at $T_B$ but at a much lower temperature of $T_d$, which may be ascribed to a local structural transformation occurring in PNRs at $T_d$. This suggestion is consistent with recent studies on $\mathrm{PZN}\text{−}x\mathrm{PT}$ single crystals reporting the appearance of strong acoustic emission signals [M. Roth et al., Phys. Rev. Lett. 98, 265701 (2007)] and substantial changes in the Raman spectrum [O. Svitelskiy, Phys. Rev. B 72, 172106 (2005)] at almost the same temperature. From the comparison of the present results to those of two typical relaxors, $\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3$ and $\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Ta}}_{2∕3}\right){\mathrm{O}}_3$, it was suggested that the existence of an intermediate characteristic temperature $T_d$ below $T_B$ may be considered as a more common characteristic in the temperature evolution of PNRs of relaxor ferroelectrics.

The inelastic light scattering spectrum of $\text{Pb}\left[{\left({\text{Mg}}_{1/3}{\text{Nb}}_{2/3}\right)}_{1-x}{\text{Ti}}_x\right]{\text{O}}_3$ $\left(\text{PMN-}x\text{PT}\right)$ single crystals with $x=0–0.55$ due to longitudinal-acoustic (LA) waves was investigated in a wide temperature range by using a Brillouin scattering technique. The acoustic frequency of LA modes of all $\text{PMN-}x\text{PT}$ crystals showed a significant softening upon cooling in the high-temperature range where the deviation from the high-temperature linearity starts from $\sim 750\text{K}$. In addition, hypersonic damping exhibited a remarkable increase upon cooling toward the freezing or ferroelectric phase-transition temperature. These acoustic anomalies were attributed to the polarization fluctuations due to the displacive polarization component arising from the condensation of transverse-optic mode, flipping of polar nanoregions, and, for $\text{PMN-}x\text{PT}$ with large $x$, correlated polar nanometer-sized regions (PNRs) as ordering units. The application of the modified superparaelectric model to the measured acoustic properties revealed that the activation energy for the flipping of PNRs displayed a sharp increase upon crossing the composition of morphotropic phase boundary (MPB) of $\text{PMN-}x\text{PT}$. This change was attributed to the appearance of order-disorder polarization component, i.e., polar clusters in $\text{PMN-}x\text{PT}$ with large $x$ beyond MPB, which indicated PNRs are correlated and oriented along the same direction. These results may suggest a crossover in the mechanism of phase transition with increasing $x$: disordered glass state with random directions of PNRs in PMN, comparatively abrupt growth of PNRs at the ferroelectric phase transition without changing the directions of their dipole moments at small $x$, and order-disorder type ferroelectric transition through alignment of PNRs into single direction via order-disorder mechanism at large $x$. These results are consistent with broadband dielectric and quasielastic scattering data that show critical slowing down for $\text{PMN-}x\text{PT}$ with large $x$.

The dynamic polar nanoregions (PNRs) which form below the Burns temperature and determine the unique properties of relaxor ferroelectrics were predicted [Tinte et al., Phys. Rev. Lett. 97, 137601 (2006)] to be pinned to the quenched chemically ordered regions (CORs) usually observed in lead-containing relaxors. In $\mathrm{Pb}\left[{\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right)}_{0.45}{\mathrm{Ti}}_{0.55}\right]{\mathrm{O}}_3$ crystal where CORs are known to be absent, we have found the phenomena typically related to the relaxation of dynamic PNRs, namely, the significant Brillouin quasielastic scattering, the softening of the longitudinal acoustic mode, and the deviation from the Curie-Weiss law above the Curie point. This implies that PNRs may appear in crystals without CORs.

Two PbZr_1−xTi_xO₃ (PZT) single crystals with $x\approx$ 0.45 and 0.42 near the morphotropic phase boundary were studied by Brillouin light scattering, giving rise to the first single-crystal elastic data which were discussed in terms of the correlation between the acoustic anomalies and the phase transition sequence. The ferroelectric phase transition of PZT with $x\approx$ 0.45 was second order (or very close to the second order) which accompanied very large polarization fluctuations resulting in the formation of strong central peaks. A revised phase diagram of PZT was suggested including refinement of the tilt phase boundary and a possible existence of tricritical point.