Domain wall motion and precursor dynamics inPbZrO3

Single crystals of ${\mathrm{PbZrO}}₃$ have been studied by dynamic mechanical analysis measurements in the low-frequency range $f=0.02$--50 Hz. The complex Young's modulus exhibits a quite rich behavior and depends strongly on the direction of the applied dynamic force. In pseudocubic ${[100]}_c$ direction, we found intrinsic elastic behavior as expected from the Landau theory; at the antiferroelectric transition ${T}_c\ensuremath{\approx}510$ K, a downwards cusp anomaly in ${Y}^{\ensuremath{'}}$ accompanied by a peak in ${Y}^{\ensuremath{'}\ensuremath{'}}$ points to a quadratic/linear order parameter/strain coupling in the Landau free energy. Both anomalies are increasing with decreasing frequency showing that the measurements are performed in the limit $\ensuremath{\omega}{\ensuremath{\tau}}_{\mathrm{th}}>1$. Frequency scans around ${T}_c$ show energy dissipation, which could result from interphase boundary motion and/or heat diffusion. Above ${T}_c$, we observe a pronounced precursor softening, quite similar as it was found in other perovskites, which can be perfectly fitted including isotropic order parameter fluctuations. The low-frequency elastic response in ${[110]}_c$ direction is different. Below ${T}_c$, we find in addition to the intrinsic anomaly a strong contribution from ferroelastic domains, which leads to an additional softening in ${Y}^{\ensuremath{'}}$. With decreasing temperatures this superelastic softening gradually disappears, due to an increasing relaxation time ${\ensuremath{\tau}}_{\mathrm{DW}}$ for domain wall motion, indicating glassy behavior of domain freezing in ${\mathrm{PbZrO}}₃$. In contrast to the ${[100]}_c$ direction, for forces along ${[110]}_c$, we found a pronounced precursor hardening, starting at about 60 K above ${T}_c$. Since this anomaly is of dynamic nature, starting at the same temperature as the observed birefringence and piezoelectric anomalies [Ko et al. Phys. Rev. B 87, 184110 (2013)], we conclude that it originates from slow dynamic polar clusters, which freeze at ${T}^*\ensuremath{\approx}550\phantom{\rule{4.pt}{0ex}}\text{K}>{T}_c$.