Structural phases and thermodynamics of BaTiO3 from an integrated machine learning model

Modeling the ferroelectric transition of any given material requires three key ingredients: (1) a model of the potential energy surface, that describes the energetic response to a structural distortion; (2) the free energy surface sampled at the relevant, finite-temperature conditions; and; (3) the polarization of individual configurations that determines, through averaging over samples, the observed polarization and the phase transitions. To this aim, we introduce an integrated machine-learning framework, based on a combination of an interatomic potential and a vector model for microscopic polarization, which we use to run Molecular Dynamics simulations of ferroelectrics with the same level of accuracy of the underlying DFT method, on time and length scales that are not accessible to direct ab-initio modeling. This allows us to uncover the microscopic nature of the ferroelectric transition in barium titanate (BaTiO3). The presence of an order-disorder transition is the main driver of ferroelectricity, while the coupling between symmetry breaking and cell distortions determines the presence of partly-ordered (tetragonal and orthorhombic) phases. The framework also allows us to reconstruct the temperature-dependent BaTiO3 phase diagram, with first-of-its-kind accuracy.