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Barium zirconate (BaZrO$_3$) is one of the very few perovskites that is claimed to retain an average cubic structure down to \SI{0}{\K}, while being energetically very close to an antiferrodistortive phase obtained by condensation of a soft phonon mode at the R point of the Brillouin zone boundary. In this work, we report a combined experimental and theoretical study of the temperature dependence of this soft phonon mode. Inelastic neutron and x-ray scattering measurements on single crystals show that it softens substantially from \SI{9.4}{\meV} at room temperature to \SI{5.6}{\meV} at \SI{2}{\K}. In contrast, the acoustic mode at the same R point is nearly temperature independent. The effect of the anharmonicity on the lattice dynamics is investigated non-perturbatively using direct dynamic simulations as well as a first-principles based self-consistent phonon theory, including quantum fluctuations of the atomic motion. By adding cubic and quartic anharmonic force constants, quantitative agreement with the neutron data for the temperature dependence of the antiferrodistortive mode is obtained. The quantum fluctuations of the atomic motion are found to be important to obtain the proper temperature dependence at low temperatures. The mean squared displacements of the different atoms are determined as function of temperature and are shown to be consistent with available experimental data. Adding anharmonicity to the computed fluctuations of the Ba-O distances also improves the comparison with available EXAFS data at \SI{300}{\K}.

The most characteristic functional property of antiferroelectric materials is the possibility to induce a phase transition from a non-polar to a polar phase by an electric field. Here, we investigate the effect of this field-induced phase transition on the birefringence change of $PbZr_{0.95}Ti_{0.05}O_{3}$. We use a transparent polycrystalline $PbZr_{0.95}Ti_{0.05}O_{3}$ film grown on $PbTiO_{3}/HfO_{2}/SiO_{2}$ with interdigitated electrodes to directly investigate changes in birefringence in a simple transmission geometry. In spite of the polycrystalline nature of the film and its moderate thickness, the field-induced transition produces a sizeable effect observable under a polarized microscope. The film in its polar phase is found to behave like a homogeneous birefringent medium. The time evolution of this field-induced birefringence provides information about irreversibilities in the antiferroelectric switching process and its slow dynamics. The change in birefringence has two main contributions, one that responds briskly (~ 0.5 s), and a slower one that rises and saturates over a period of as long as 30 minutes. Possible origins for this long saturation and relaxation times are discussed., 15 pages, 5 figures

Model materials are precious test cases for elementary theories and provide building blocks for the understanding of more complex cases. Here, we describe the lattice dynamics of the structural phase transition in francisite Cu3Bi(SeO3)2O2Cl at 115 K and show that it provides a rare archetype of a transition driven by a soft antipolar phonon mode. In the high-symmetry phase at hightemperatures, the soft mode is found at (0,0,0.5) at the Brillouin zone boundary and is measured by inelastic X-ray scattering and thermal diffuse scattering. In the low-symmetry phase, this softmode is folded back onto the center of the Brillouin zone as a result of the doubling of the unit cell, and appears as a fully symmetric mode that can be tracked by Raman spectroscopy. On both sides of the transition, the mode energy squared follows a linear behaviour over a large temperature range. First-principles calculations reveal that, surprisingly, the flat phonon band calculated for the high-symmetry phase seems incompatible with the displacive character found experimentally. We discuss this unusual behavior in the context of an ideal Kittel model of an antiferroelectric transition., Comment: 6 pages, 5 Figures, supplemental material included