Observation of a periodic array of flux-closure quadrants in strained ferroelectric PbTiO3 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 PbTiO3 films, mediated by tensile strain on a GdScO3 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 PbTiO3 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. Engineering strain at the nanoscale may facilitate the development of nanoscale ferroelectric devices.