Coulomb interaction and ferroelectric instability of BaTiO

Using first-principles calculations, the phonon frequencies at the ${\mit \Gamma}$-point and the dielectric tensor are determined and analysed for the cubic and rhombohedral phases of $\rm BaTiO_3$. The dipole-dipole interaction is then separated à la Cochran from the remaining short-range forces, in order to investigate their respective influence on lattice dynamics. This analysis highlights the delicate balance of forces leading to an unstable phonon in the cubic phase and demonstrates its extreme sensitivity to effective charge changes. Within our decomposition, the stabilization of the unstable mode in the rhombohedral phase or under isotropic pressure has a different origin