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.

中文翻译：

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氧化物多层中的大规模二维通量-封闭域阵列及其受控生长

铁电通量封闭器在高密度存储和其他纳米级电子设备中非常有前途。为了使数据位可寻址，要求纳米级通量闭合通过可控的增长是周期性的。尽管在应变铁电PbTiO ₃薄膜中观察到了垂直于界面（V形封闭）的具有180°畴壁的磁通封闭象限阵列，但其中的磁通封闭象限相当不对称。在这项工作中，我们不仅报告了对称的磁通封闭象限的周期性阵列，该对称磁通封闭象限具有与界面平行的180°畴壁（H封闭），而且还报告了PbTiO中V和H封闭阵列的大规模替代堆叠₃ /锶TiO ₃多层。在结合像差校正的扫描透射电子显微镜成像和相场建模的基础上，我们建立了逐层二维阵列中的相图与相邻PbTiO ₃膜的厚度比的关系，其中能量竞争发挥主导作用。这些通量闭合件的操纵可以刺激具有奇特性能的新型纳米级铁电器件的设计和开发。