Coupling between small polarons and ferroelectricity in BaTiO3

In this study, we investigate the formation of electron and hole small polarons in the prototypical ferroelectric material BaTiO3, with a focus on their interaction with ferroelectric distortive fields. To accurately describe the ferroelectric phase in electronically correlated BaTiO3, we employ the HSE06 hybrid density functional, which addresses the limitations of conventional density-functional theory (DFT) and Hubbard-corrected DFT + U models, providing a more precise depiction of both ferroelectric and polaronic behaviors. Our analysis spans three structural phases of BaTiO3: cubic, tetragonal, and rhombohedral. We uncover a unique phase-dependent trend in electron-polaron stability, which progressively increases across the structural phases, peaking in the rhombohedral phase due to the constructive coupling between the polaron and ferroelectric phonon fields. In contrast, hole polarons exhibit a stability pattern largely unaffected by the phase transitions. Furthermore, we observe that polaron self-trapping significantly alters the local ferroelectric distortive pattern, which propagates to neighboring sites but has a minimal effect on the long-range macroscopic spontaneous polarization. Charge trapping is also associated with localized spin formation, opening new possibilities for enhanced functionalities in multiferroic materials.