Soft phonon in BaTiO₃

Bandvs.polaron: vibrational motion and chemical expansion of hydride ions as signatures for the electronic character in oxyhydride barium titanate

“…When compared with experimental data 35 we notice that PBE and PBE + U underestimate the vibrational frequencies while HSE gives excellent results (see Table 1). The PBE error is partly due to the overestimated lattice constant but the improved performance of HSE also depends on the inclusion of exact exchange, which produces a more accurate electron density that leads to stiffening of the bonds.…”

Low-temperature phase of BaTiO3: Piezoelectric, dielectric, elastic, and photoelastic properties fromab initiosimulations

“…20 For the tetragonal phase, calculated optical phonon frequencies are in good agreement with the rich set of experimental values measured by Nakamura. 32 The only significant deviation refers to a TO phonon mode belonging to the totally-symmetric A irrep, for which the calculated value is 373 cm −1 and the measured one 275 cm −1 .…”

Soft Mode Behavior in Cubic and Tetragonal BaTiO3Crystals and Ceramics: Review on the Results of Dielectric Spectroscopy

“…Reliable MW dielectric data (at 24 GHz) on a single-domain sample, existing presumably only for the a-response [1,4], agree perfectly with the RT value ∼2000 given by the phonon contribution (even if at that time the clamped value was assumed much smaller). The problem of the low-frequency E-symmetry mode in tetragonal BTO was carefully studied by polariton Raman technique reviewed by Nakamura [54] who strongly supported its displacive (oscillatory) picture even though it is strongly overdamped in the limit of short polariton wavelengths. The low-frequency modes of both symmetries were also carefully studied by Dougherty et al [55] using impulsive stimulated Raman scattering.…”