AB initio phonon dispersion curves and interatomic force constants of barium titanate

The phonon dispersion curves of cubic BaTiO 3 have been computed within a first-principles approach and the results compared to the experimental data. The curves obtained are very similar to those reported for KNbO 3 by Yu and Krakauer (Phys. Rev. Lett., 74, 4067 (1995)). They reveal that correlated atomic displacements along (100) chains are at the origin of the ferroelectric instability. A simplified model illustrates that spontaneous collective displacements will occur when a dozen of aligned atoms are coupled. The longitudinal interatomic force constant between nearest neighbour Ti and O atoms is relatively weak in comparison to that between Ti atoms in adjacent cells. The small coupling between Ti and O displacements seems however necessary to reproduce a linear ferroelectric instability.