Dynamical effects of the nanometer-sized polarized domains in Pb(Zn1/3Nb2/3)O3

Abstract

Results from an extensive single-crystal neutron-scattering study of the relaxor ferroelectric $\mathrm{Pb}\left({\mathrm{Zn}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3$ (PZN) in the cubic phase reveal an anomalous ridge of inelastic scattering that extends vertically from the transverse acoustic (TA) branch near 4 meV to the transverse optic (TO) branch near 9 meV at $q\sim 0.2\hspace{0.5em}{\mathrm{\AA }}^{-1}.$ No zone center optic mode was found. Similar results were recently reported in a sample of PZN doped with $8\%$ ${\mathrm{PbTiO}}_3.$ We are able to describe the dynamics of this unusual feature using a simple coupled-mode model that assumes the optic mode linewidth ${\Gamma }_1\mathrm{}\left(q\right)\mathrm{}$ increases sharply near $q=0.2\mathrm{}\hspace{0.5em}{\AA }^{-1}$ as $\overrightarrow{q}0.$ The dramatic increase in ${\Gamma }_1\mathrm{}\left(q\right)\mathrm{}$ is believed to occur when the wavelength of the optic mode becomes comparable to the size of small polarized nanoregions (PNR) that develop in the cubic phase of PZN, far above $T_c=410\mathrm{}\hspace{0.5em}\mathrm{K}.$ The consequence is that long-wavelength optic modes cannot propagate and become overdamped. Hence the q at which the anomalous scattering is peaked provides an important measure of the size of the PNR. Below $T_c,$ the intensity of this scattering diminishes. At lowest temperatures $\left(\sim 30\hspace{0.5em}\mathrm{K}\right)$ the feature is absent, and we observe the recovery of a zone center transverse optic mode near 10.5 meV.