Observation of a periodic array of flux-closure quadrants in strained ferroelectric PbTiO 3 films
Nanoscale ferroelectrics are expected to exhibit various exotic domain configurations, such as the full flux-closure pattern that is well known in ferromagnetic materials. Here we observe not only the atomic morphology of the flux-closure quadrant but also a periodic array of flux closures in ferroelectric PbTiO 3 films, mediated by tensile strain on a GdScO 3 substrate. Using aberration-corrected scanning transmission electron microscopy, we directly visualize an alternating array of clockwise and counterclockwise flux closures, whose periodicity depends on the PbTiO 3 film thickness. In the vicinity of the core, the strain is sufficient to rupture the lattice, with strain gradients up to 10 9 per meter. We found engineering strain at the nanoscale may facilitate the development of nanoscale ferroelectric devices.