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Understanding the effects of polar nanoregions (PNRs) dynamics on dielectric properties is a complex question of essential importance for both fundamental studies of relaxor ferroelectrics and their applications to electro-optic devices. The frequency dependence of dielectric response to the bias electric field opens a brand new window for the study of this problem. A novel model from mesoscopic to macroscopic, revealing the relationship between the dielectric permittivity to the applied electric field, temperature, and PNRs, was established based on mean field approximation and the theory of continuum percolation, and not only validates the field-induced percolation and the relaxation time divergency at the freezing temperature, but also predicts the frequency dependence of dielectric response. Unexpectedly, the model reveals the field-enhanced correlation length results in the nonmonotonic behavior of dielectric response, and implies that the increased orientation consistency of dipolar clusters and coercive fields originated from inherent inhomogeneity slow down the relaxation time of PNR reorientation. Considering the multi-scale heterogeneity of PNRs in relaxor, we found that the increased heterogeneity degree reduces the dielectric permittivity, but changes the slope of dielectric response to the bias electric field.

Explaining the Frequency Dependence of the DC-Biased Dielectric Response of Polar Nanoregions by Field-Enhanced Correlation Length