Polarization induced by oxygen octahedral rotations in strained sodium niobate thin films directly imaged by electron ptychography*

Due to its extremely complicated phase diagram, bulk sodium niobate (NaNbO₃) has often been dubbed as the most complex perovskite system. Unlike prototypical ferroelectric perovskites where the B-site displacement is the primary order parameter, the structure and electrical properties of NaNbO₃ are primarily governed by the oxygen octahedral rotations. For strained epitaxial thin films of sodium niobate, this makes it all the more important that the oxygen positions are determined precisely for an accurate determination of the structure and polarization. Reliable atomic scale characterization of light elements has always been a challenging problem in transmission electron microscopy, with traditional methods having well documented artefacts arising from mistilts, thickness variations and residual aberrations. By using the recently developed multislice electron ptychography method, we are able to overcome these artefacts, enabling a precise measurement of oxygen displacements that show ferroelectric textures in strained thin films of NaNbO₃.