Coulomb interaction and ferroelectric instability of BaTiO3

Using first-principles calculations, the phonon frequencies at the $\Gamma$ point and the dielectric tensor are determined and analysed for the cubic and rhombohedral phases of BaTiO$_{3}$. The dipole-dipole interaction is then separated \`a 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 the extreme sensitivity of this close compensation to minute effective charge changes. Within our decomposition, the stabilization of the unstable mode in the rhombohedral phase or under isotropic pressure has a different origin.Comment: 9 pages, 4 tables, 1 figur

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 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 ferroelectric instability.Comment: 12 pages, 4 figure

Applications of the generalized gradient approximation to ferroelectric perovskites

The Perdew-Burke-Ernzerhof generalized gradient approximation to the density functional theory is tested with respect to sensitivity to the choice of the value of the parameter $\kappa$, which is associated to the degree of localization of the exchange-correlation hole. A study of structural and dynamical properties of four selected ferroelectric perovskites is presented. The originally proposed value of $\kappa$=0.804 %(best suited for atoms and molecules) works well for some solids, whereas for the ABO$_3$ perovskites it must be decreased in order to predict equilibrium lattice parameters in good agreement with experiments. The effects on the structural instabilities and zone center phonon modes are examined. The need of varying $\kappa$ from one system to another reflects the fact that the localization of the exchange-correlation hole is system dependent, and the sensitivity of the structural properties to its actual value illustrates the necessity of finding a universal function for $\kappa$.Comment: 15 pages, 2 figures, PRB in pres

Effet Brillouin du molybdate de gadolinium au voisinage du point de transition

The velocities of longitudinal acoustic phonons propagating perpendicularly to the fourfold axis of the high temperature phase, show discontinuities at 159°C. The broadening of the Brillouin lines is attributed to an anharmonic coupling with soft modes whose frequencies vanish at 155 and 161°C.Les vitesses des phonons acoustiques longitudinaux qui se propagent perpendiculairement à l'axe quaternaire de la phase haute température subissent des discontinuités à 159°C. L'élargissement des raies Brillouin est attribué à un couplage anharmonique avec des modes mous dont les fréquences s'annulent à 155 et 161°C