Universal relaxor polarization inPb(Mg1/3Nb2/3)O3and related materials

Abstract

The dielectric permittivity \ensuremath{\varepsilon} at frequencies from ${(10}^{\ensuremath{-}1}--{10}^{\ensuremath{-}5})\mathrm{Hz}$ to ${10}^{5}\mathrm{Hz}$ is studied in perovskite $(1\ensuremath{-}x)\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}\ensuremath{-}x{\mathrm{PbTiO}}_{3}$ relaxor ferroelectric ceramics of different compositions $x=0.35,$ 0.25, and 0, which exhibit, below the temperature of the diffuse $\ensuremath{\varepsilon}(T)$ maximum ${T}_{m},$ a tetragonal ferroelectric, a rhombohedral ferroelectric, and a nonergodic relaxor phase, respectively. The universal relaxor dispersion previously observed at temperatures near and above ${T}_{m}$ in the ceramics of $x=0.25$ is also found to exist in other compositions. This dispersion is described by the fractional power dependence of the real and imaginary parts of susceptibility on frequency, ${\ensuremath{\chi}}_{U}^{\ensuremath{'}}(f)\ensuremath{\propto}{\ensuremath{\chi}}_{U}^{\ensuremath{''}}(f)\ensuremath{\propto}{f}^{n\ensuremath{-}1}.$ The real part of the universal relaxor susceptibility ${\ensuremath{\chi}}_{U}^{\ensuremath{'}}$ is only a comparatively small fraction of the total permittivity ${\ensuremath{\varepsilon}}^{\ensuremath{'}},$ but ${\ensuremath{\chi}}_{U}^{\ensuremath{''}}$ is the dominant contribution to the losses in a wide frequency-temperature range above ${T}_{m}.$ In the high-temperature phase a divergent temperature behavior is observed, ${\ensuremath{\chi}}_{U}^{\ensuremath{'}}(T)\ensuremath{\propto}(T\ensuremath{-}{T}_{0}{)}^{\ensuremath{-}\ensuremath{\gamma}}$ and ${\ensuremath{\chi}}_{U}^{\ensuremath{''}}(T)\ensuremath{\propto}(T\ensuremath{-}{T}_{0}{)}^{\ensuremath{-}\ensuremath{\gamma}},$ with ${T}_{0}<{T}_{m}$ and $\ensuremath{\gamma}\ensuremath{\cong}2,$ for all the three compositions studied. The universal relaxor susceptibility is attributed to the polarization of polar nanoregions, which are inherent in the relaxor ferroelectrics. A microscopic model of this polarization is proposed, according to which the dipole moments of some ``free'' unit cells inside the polar nanoregion can freely choose several different directions, while the direction of the total moment of the nanoregion remains the same. The ensemble of interacting polar nanoregions is described in terms of a standard spherical model, which predicts the quadratic divergence of susceptibility above the critical temperature, in agreement with the experimental results.