The Evidence of Giant Surface Flexoelectric Field in (111) Oriented BiFeO₃ Thin Film

In this work, the surface structure of a single-domain epitaxial BiFeO₃ film with (111) orientation was investigated by in situ grazing incidence X-ray diffraction and X-ray reflectivity. We found that a large strain gradient exists in the surface region (2-3 nm) of the BiFeO₃ film. The strain gradient is approximately 10⁷ m^-1, which is 2 or 3 orders of magnitude larger than the value inside the film. Moreover, we found that a surface layer with a lower electron density compared with the underlying BiFeO₃ layer exists on the surface of BiFeO₃ film, and this layer exhibits an irreversible surface structure transition occurs at 500 K, which should be associated with the surface flexoelectric field. We considered that this large strain gradient is originated from the surface depolarization field of ferroelectrics. Our results suggest a coupling between the surface structure and the flexoelectricity and imply that the surface layer and properties would be controlled by the strain gradient in ferroelectric films.