Polarons: Energetics and their structural and electronic effects in ATiO3 perovskite systems

Understanding the formation of a polaron near vacancies in oxides is of vital importance for controlling defect properties and related functionalities. We examine the energetics and local structure of polarons in the vicinity of oxygen vacancies using density functional theory with the Hubbard on-site Coulombic correction. We systematically consider several $\mathrm{ATi}{\mathrm{O}}_{3}$ perovskite systems: cubic $\mathrm{SrTi}{\mathrm{O}}_{3}$ (c-STO), cubic $\mathrm{BaTi}{\mathrm{O}}_{3}$ (c-BTO), cubic $\mathrm{PbTi}{\mathrm{O}}_{3}$ (c-PTO), tetragonal $\mathrm{BaTi}{\mathrm{O}}_{3}$ (t-BTO), and tetragonal $\mathrm{PbTi}{\mathrm{O}}_{3}$ (t-PTO). The polaron formation energies vary by several orders of magnitude across the systems, where PTO systems have large polaron formation energies $(\ensuremath{\sim}\ensuremath{-}1.688\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$, c-BTO is intermediate (\ensuremath{-}0.234 eV), and c-STO and t-BTO have considerably smaller formation energies $(<\ensuremath{-}0.01\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$. The formation of a polaron is found to influence the charge density, atomic displacement, and electronic structure, with higher polaron energies corresponding to larger charge density changes and greater displacements of the ions surrounding the oxygen vacancy, especially the displacement of the first nearest neighbor A-site. Finally, a comparison of the projected band structures shows fictitious in-gap states present in the delocalized picture of the system moving to the conduction and valence bands in the polaron solution of the system, indicating an incompleteness of the description of a vacancy without considering charge localization as in the polaron picture. In this paper, we provide fundamental properties of polarons near vacancies, which can be used to control and tune defect, charge transport, magnetoelectric, and multiferroic properties of perovskite oxides.