Polarization dynamics in the mixed ferroelectric ${\mathrm{KTa}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Nb}}_{\mathrm{x}}$ ${\mathrm{O}}_3$s

Mixed ferroelectrics exhibit unusual precursor effects. In ${\mathrm{KTa}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Nb}}_{\mathrm{x}}$ ${\mathrm{O}}_3$ , polar nanoregions have been shown to condense approximately 20 K above the transition for all Nb concentrations, 1.2%<x<50%, as a result of medium-range collective interactions between Nb off-center ions. These interactions are also responsible for the observation of hysteresis loops in the polarization and dielectric nonlinearities far above the transition. In the present study we have identified three distinct polarization regimes: (1) dynamic and (2) quasistatic, both above the transition, and (3) static, below the transition. The first two regimes can be distinguished by the shape of the hysteresis loops, changing from oval to s shape, and by their frequency dependence. We have analyzed the harmonic content of the polarization response and show that the condensation of polar nanoregions coincide with the appearance of odd harmonics which are indicative of a nonlinear response. This is further supported by the observation of a nonlinear dielectric response that becomes progressively stronger with decreasing temperature below the condensation. We also show that there exists a direct relationship between dielectric and polarization response and that one can be calculated from the other. Finally, the low-frequency dynamics exhibited in the quasistatic range can be qualitatively explained by the strong interaction between neighboring off-center Nb ions within polar nanoregions and random interactions between these regions.