Abstract
Extended defects of vacancies in ferroelectrics (FE), where vacancies spread over an extended space, are of critical importance in terms of understanding the long-standing problems such as polarization fatigue and aging. However, extended defects in FEs are poorly understood. Here we investigate the extended planar oxygen vacancies in ferroelectric [Formula: see text] using density functional theory and the modern theory of polarization. Oxygen vacancies of different charge states, namely [Formula: see text], [Formula: see text], and [Formula: see text], are studied. We obtain interesting results such as: (i) The formation energy of planar [Formula: see text] vacancies can be very small (merely 0.54 eV) even under the oxygen-rich condition, which is considerably smaller than the formation energy (4.0 eV) of planar [Formula: see text] vacancies; (ii) Planar [Formula: see text] vacancies drastically reduce the ferroelectric polarization in [Formula: see text] by more than one order of magnitude, which provides a pivotal (theoretical) evidence that the planar oxygen vacancies could be the origin of polarization fatigue and imprinting. The polarization dead layer caused by planar oxygen vacancies is shown to be around 72 Å. Microscopic origin and insight, based on the local Ti-O relative displacements, are provided to understand these interesting phenomena.