Central peaks, acoustic modes, and the dynamics of polar nanoregions inPb[(Zn1∕3Nb2∕3)xTi1−x]O3single crystals studied by Brillouin spectroscopy

Abstract

Temperature dependence of acoustic behaviors and quasielastic central peaks (CPs) of $\mathrm{Pb}[{({\mathrm{Zn}}_{1∕3}{\mathrm{Nb}}_{2∕3})}_{x}{\mathrm{Ti}}_{1\ensuremath{-}x}]{\mathrm{O}}_{3}$ $(\mathrm{PZN}\text{\ensuremath{-}}x\mathrm{PT})$ single crystals with $x=4.5%$ and 9% have been investigated in a temperature range of $300\char21{}900\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ 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 $({T}_{B})$ of about $730\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ 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 $({T}_{d})$ located in $500\char21{}550\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, 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 $\mathrm{PZN}\text{\ensuremath{-}}x\mathrm{PT}$ 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, $\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}){\mathrm{O}}_{3}$ and $\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Ta}}_{2∕3}){\mathrm{O}}_{3}$, 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.