Polarization dynamics and formation of polar nanoregions in relaxor ferroelectrics

Polarization dynamics and formation of polar nanoregions (PNR) in relaxor ferroelectrics is considered within a model of interacting short range polar clusters formed by off-center ions in highly polarizable materials. The model is applicable on the mesoscopic level and takes explicitly into account the distribution of cluster relaxation times and the existence of quenched random fields which control the size of PNR. Using self-consistent random field theory and continuous time random walk approximation, a relationship is established between the average polarization dynamics contributing to the low frequency dielectric response, and the local polarization dynamics determining NMR spin lattice relaxation time [Blinc et al., Phys. Rev. B 63, 024104 (2001); Cordero et al., ibid. 71, 094112 (2005)]. The lengthscale of PNR estimated from the obtained universal relationship between the parameters of the soft mode dispersion curve and the static dielectric permittivity is in agreement with the experiment [Vakhrushev et al., Physica B 156-157, 90 (1989)]. The predicted proportionality, between the intensity of diffuse neutron scattering from dynamic PNR and square of PNR correlation length, which has been recently a subject of controversy, is also in agreement with experiment by Vakhrushev et al. Therefore, we conclude that the model captures essential features of the static and dynamic behavior of relaxor ferroelectrics, and could be used for the characterization of new relaxor materials.