Abstract
The inelastic light scattering spectrum of $\text{Pb}[{({\text{Mg}}_{1/3}{\text{Nb}}_{2/3})}_{1\ensuremath{-}x}{\text{Ti}}_{x}]{\text{O}}_{3}$ $(\text{PMN-}x\text{PT})$ 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 $\ensuremath{\sim}750\text{ }\text{K}$. 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 $x$.
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