Spherical random-bond-random-field model of relaxer ferroelectrics

A model of relaxer 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) = chi(3)/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 Nb-93 in PMN is discussed. The fact that the observed line shape is Gaussian at all temperatures provides strong support to the SRBRF model. [S0163-1829(99)06943-X].