Nonlinear electrostriction in the mixed ferroelectric ${\mathrm{KTa}}_{1-x}{\mathrm{Nb}}_x{\mathrm{O}}_3$

The dielectric resonance previously reported in the paraelectric phase of the mixed ferroelectric ${\mathrm{KTa}}_{1-x}{\mathrm{Nb}}_x{\mathrm{O}}_3$ is studied quantitatively. A theoretical model is developed that incorporates a field-induced electrostrictive coupling mediated by polar nanoregions appearing above the transition, and their orientational relaxation. Theoretical expressions for the dielectric dispersion and absorption are calculated, fitted to the experimental data, and values are obtained for the electrostriction coefficient and the relaxation time of the polar regions. Starting approximately 5 K above the transition, and upon repetitive excitation, a remarkable growth in the resonance is observed, ending in a singular behavior where the resonance splits into two very sharp spikes. This observation is described in the framework of the model as a nonlinear electrostrictive effect.