Large Scale Two-Dimensional Flux-Closure Domain Arrays in Oxide Multilayers and Their Controlled Growth

Ferroelectric flux-closures are very promising in high-density storage and other nanoscale electronic devices. To make the data bits addressable, the nanoscale flux-closures are required to be periodic via a controlled growth. Although flux-closure quadrant arrays with 180° domain walls perpendicular to the interfaces (V-closure) have been observed in strained ferroelectric PbTiO₃ films, the flux-closure quadrants therein are rather asymmetric. In this work, we report not only a periodic array of the symmetric flux-closure quadrants with 180° domain walls parallel to the interfaces (H-closure) but also a large scale alternative stacking of the V- and H-closure arrays in PbTiO₃/SrTiO₃ multilayers. On the basis of a combination of aberration-corrected scanning transmission electron microscopic imaging and phase field modeling, we establish the phase diagram in the layer-by-layer two-dimensional arrays versus the thickness ratio of adjacent PbTiO₃ films, in which energy competitions play dominant roles. The manipulation of these flux-closures may stimulate the design and development of novel nanoscale ferroelectric devices with exotic properties.