Quantitative evaluation of nuclear quantum effects on the phase transitions in BaTiO₃ using large-scale molecular dynamics simulations based on machine learning potentials

The machine learning potential (MLP) based molecular dynamics (MD) method (MLPMD) was applied for constructing the pressure-temperature phase diagram in the barium titanate (BaTiO₃) crystals. The nuclear quantum effects (NQEs) on the phase transitions were quantitatively evaluated from the difference in the phase transition pressures between the NQEs-incorporated and classical simulations. In this study, the quantum thermal bath (QTB) method was used for incorporating the NQEs. The constructed phase diagrams verified that the NQEs lower the phase transition temperatures and pressures. The NQEs are more significant at lower temperatures but cannot be ignored even at room temperature. The phase diagram in the QTB-based MLPMD is in good agreement with those of the previous studies based on dielectric measurements and path-integral based simulations. The displacement distributions of Ti and O ions in the QTB-MLPMD suggest that the pressure-induced tetragonal-cubic phase transition is the displacive type, in contrast to the order-disorder type reported in the literature. Possible reasons for the discrepancy in the microscopic behavior are the differences in the simulation cell size and restriction for lattice dynamics. In contrast to the relatively small simulation cell (12 × 12 × 12 supercell or smaller) with some restriction to the degrees of freedom (DOFs) for lattice dynamics in the previous studies, the large cell (20 × 20 × 20 supercell) without any DOF restriction was employed in the present study.