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

The phonon dispersion curves of cubic BaTiO3 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 KNbO3 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.