Pressure and Temperature Dependence of the Dielectric Properties and Phase Transitions of the Antiferroelectric Perovskites: PbZr${\mathrm{O}}_3$ and PbHf${\mathrm{O}}_3$

Hydrostatic-pressure measurements have shown that in PbZr${\mathrm{O}}_3$ the antiferroelectric (AFE)-paraelectric (PE) transition temperature $T_a$ increases ($\frac{d{T}_a}{\mathrm{dP}}=4.5\mathrm{}\pm 0.3°\mathrm{K}/\mathrm{kbar}$) whereas the extrapolated Curie-Weiss temperature $T_0$ decreases $\frac{d{T}_0}{\mathrm{dP}}=-16.0\mathrm{}\pm 0.5°\mathrm{K}/\mathrm{kbar}$ with increasing pressure. Interpreted in terms of the lattice dynamics, the results give the first experimental evidence that there are two independent low-frequency temperature-dependent lattice vibrational modes in PbZr${\mathrm{O}}_3$: a ferroelectric (FE) mode which determines the large polarizability and the Curie-Weiss behavior of the static dielectric constant in the paraelectric phase, and an AFE mode (probably a coupled mode) which causes the AFE transition. On cooling, the crystal becomes unstable against the AFE mode at $T_a$ just before the instability due to the FE mode is reached at $T_0$. Pressure increases the frequency of the FE mode but decreases ("softens") that of the AFE mode, and consequently, the static-dielectric-constant anomaly at the transition decreases sharply. The behavior of PbHf${\mathrm{O}}_3$ is qualitatively similar to that of PbZr${\mathrm{O}}_3$, but is complicated by the presence of two AFE phases at 1 bar. A third AFE phase becomes stable at high pressure. All the AFE transition temperatures increase with pressure, corresponding to the softening of their respective AFE modes. A brief discussion of the nature of the AFE mode in PbZr${\mathrm{O}}_3$ is given.