Phase transition and polar cluster behavior above Curie temperature in ferroelectric BaTi$_{0.8}$Zr$_{0.2}$O$_3$

We study the phase transition behavior of the ferroelectric BaTi$_{0.8}$Zr$_{0.2}$O$_3$ in the paraelectric region. The temperature dependencies of thermal, polar, elastic and dielectric properties indicate the presence of local structures above the paraelectric-ferroelectric transition temperature Tc = 292 K. The non-zero remnant polarization is measured up to a characteristic temperature T* ~350 K, which coincides with the temperature where the dielectric constant deviates from Curie-Weiss law. Resonant Piezoelectric Spectroscopy shows that DC field-cooling above Tc using fields smaller than the coercive field leads to an elastic response and remnant piezoelectricity below T*, which likely corresponds to the coherence temperature associated with polar nanostructures in ferroelectrics. The observed remnant effect is attributed to the reorientation of polar nanostructures above Tc.