Spherical random-bond–random-field model of relaxor ferroelectrics

Abstract

A model of relaxor ferroelectrics based on the interacting polar clusters picture has been formulated. The electric dipole moment of a nanosized polar domain is allowed a large number of discrete orientations and its length is assumed to fluctuate in a broad interval. Introducing a set of quasicontinuous order parameter fields and imposing a global spherical constraint, the spherical random-bond--random-field (SRBRF) model is written down and its static properties are investigated. It is found that for weak random fields the scaled third-order nonlinear susceptibility ${a}_{3}={\ensuremath{\chi}}_{3}/{\ensuremath{\chi}}_{1}^{4}$ shows a nearly divergent behavior in the spherical glass phase, but there is no such anomaly in a random-field frustrated ferroelectric state. The probability distribution of local cluster polarization is calculated and its relation to the quadrupole perturbed NMR line shape of ${}^{93}\mathrm{Nb}$ in PMN is discussed. The fact that the observed line shape is Gaussian at all temperatures provides strong support to the SRBRF model.