Non-linear dielectric response of relaxor ferroelectrics within ginzburg-landau-devonshire approximation

The third-order dielectric susceptibility chi(3) of a ferroelectric is described within classic Ginzburg-Landau-Devonshire theory. It turns out that a correction term proportional to the square of the polarization, P-2, becomes relevant in relaxor ferroelectrics close to, but above the Curie temperature. It is due to the quasi-static polarization of polar nanoregions (PNRs), which are stabilized by fluctuations of quenched random electric fields. In contrast to normal ferroelectrics with continuous phase transitions, where chi(3) is negative at T > T-c, the contribution due to PNRs drives chi(3) positive in relaxors like strontium barium niobate (SBN). It becomes negative at enhanced driving field amplitudes when activating the flipping dynamics of the polar nanoregions.