Ab initio Determination of Total-Energy Surfaces for Distortions of Ferroelectric Perovskite Oxides

Abstract

We established a new ab initio structure optimization technique of determining the valley line on a total-energy surface accurately for the zone-center distortions of ferroelectric perovskite oxides, and applied this technique to the analysis of barium titanate (BaTiO3), lead titanate (PbTiO3), and lead zirconate (PbZrO3). The proposed technique is an improvement over King-Smith and Vanderbilt's scheme [Phys. Rev. B 49 (1994) 5828] of evaluating total energy as a function of the amplitude of atomic displacements. The results of numerical calculations show that total energy can be expressed as a fourth-order function of the amplitude of atomic displacements in BaTiO3 but not in PbTiO3 and PbZrO3. These results will provide some hints about the reason Pb(ZrxTi1-x)O3(PZT) has a large piezoelectric response. These results are due to the fact that our structure optimization technique automatically takes account of the higher-order coupling between atomic displacements and strains, and not only the atomic displacements of the Γ15 soft mode but also that of the hard modes.