Ab initio determination of total-energy surfaces for distortions of ferroelectric perovskite oxides

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 PbZrO ₃. These results will provide some hints about the reason Pb(Zr _xTi_1-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 ΓO₁₅ soft mode but also that of the hard modes.