First-principles study of oxygen-vacancy pinning of domain walls in PbTiO 3

We have investigated the interaction of oxygen vacancies and $180\ifmmode^\circ\else\textdegree\fi{}$ domain walls in tetragonal ${\mathrm{PbTiO}}_{3}$ using density-functional theory. Our calculations indicate that the vacancies do have a lower formation energy in the domain wall than in the bulk, thereby confirming the tendency of these defects to migrate to, and pin, the domain walls. The pinning energies are reported for each of the three possible orientations of the original Ti-O-Ti bonds, and attempts to model the results with simple continuum models are discussed.