Neutron-Scattering Study of Soft Modes in Cubic BaTiO3

Abstract

The soft optic phonons in the cubic phase of BaTi${\mathrm{O}}_3$ have been reinvestigated by the neutron-scattering technique. Measurements were carried out on major symmetry directions for a temperature range between 150 to 450 °C. It is shown that, as in the case of the tetragonal phase, the lowest transverse-optic branches along the [111] direction and one of the branches along [110] rise rapidly with increasing wave vector $\overrightarrow{\mathrm{q}}$. Phonons are well defined except for those at very small $\overrightarrow{\mathrm{q}}$. On the other hand, in one of the branches along [110] and in the degenerate branches along [100] the phonons are overdamped as previously shown by Yamada et al. for small $\overrightarrow{\mathrm{q}}$ values. The present study extends the measurement to the entire zone and corrects the erroneous picture previously given. The most important result of the present study concerns the interaction between the soft optic modes and acoustic modes. Unusual scattering cross sections for both optic and acoustic modes are explained by interference effects in a coupled phonon model with a highly damped optic component. The interference permits, for the first time, a determination of the phase as well as the amplitude of the dynamical structure factors of the phonons involved. The energy of the optically inactive ${\Gamma }_{25}$ mode at the Brillouin zone center was found to be (39 ± 2) meV.