Development of nanoscale polarization fluctuations in relaxor-based (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3ferroelectrics studied by Brillouin scattering

Abstract

The precursor dynamics of ferroelectric phase transitions in relaxor-based ferroelectric ($1\ensuremath{-}x$)Pb(Zn${}_{1/3}$Nb${}_{2/3}$)O${}_{3}$-$x$PbTiO${}_{3}$ single crystals, with $x=0.07$, 0.10, and 0.12, were investigated using inelastic light scattering from a longitudinal acoustic phonon. An acoustic anomaly in a broad temperature range, which is characteristic of relaxor ferroelectrics, was observed. We describe the anomalies in the paraelectric phase by assuming local piezoelectric coupling inside polar nanoregions, which are surrounded by a nonpolar matrix. On the basis of local piezoelectric coupling, a relaxation time $\ensuremath{\tau}$ and a dynamic characteristic length $L$ of the order-parameter (polarization) fluctuations were determined to be in the order of 10${}^{\ensuremath{-}13}$ s and 10${}^{\ensuremath{-}9}$ m, respectively. The $\ensuremath{\tau}$ and $L$ values increase sharply upon cooling from high temperatures but more gradually below the intermediate temperature ${T}^{*}$ ($=493\ensuremath{-}510\phantom{\rule{0.28em}{0ex}}\mathrm{K}$). This result implies that the local polarization fluctuations grow rapidly upon cooling down to above ${T}^{*}$ and the growth rate decreases below ${T}^{*}$. The inflexion point of this growth process in the paraelectric phase is related to the characteristic properties of relaxor-based solid solutions.