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First-principles Investigations on Polytypes of BaTiO3: Hybrid Calculations and Pressure Dependences

We report our first-principles investigations on three polytypes of BaTiO3 (BTO): a paraelectric phase with cubic Pm-3m structure and two ferroelectric (FE) phases with tetragonal P4mm and rhombohedral R3m structures. We compared the structural and the electrical properties of BTO obtained by using various approaches: e.g., the Hartree-Fock (HF) theory, the density functional theory (DFT) with the local density approximation (LDA) or with the two generalized gradient approximations (two GGAs: PWGGA and PBE), and three hybrid functionals of the HF and the DFT (B3LYP, B3PW, and PBE0). For the P4mm structure, the two GGAs and the hybrid functionals reproduced the cell volumes, but slightly overestimated the c/a ratio. The hybrid functionals provided accurate predictions for the experimental energy gaps, but slightly underestimated the experimental dielectric constants. The calculated dielectric constants were inversely proportional to the c/a ratios for the P4mm structure (or the cH/aH ratio for the R3m structure), irrespective of the functional choice. Also, the over-estimated polarization could be ascribed to a super-tetragonality in the GGA/hybrid functionals. The pressure dependences for the cell parameters, fractional atomic displacements, energy gaps, dielectric constants, and FE polarizations were calculated by using the B3PW hybrid functional. As pressure was increased, the polarization decreased monotonically until it reached zero at a critical pressure of ~ 20 GPa for both the P4mm and the R3m structures. Anomalous behaviors were also observed in the atomic movements and the polarizations for the P4mm structure: (Omitted due to length..) Such behaviors of the polarizations, together with super-tetragonality/super-trigonality, are discussed.