Self-Similar Nested Flux Closure Structures in a Tetragonal Ferroelectric

Abstract

In specific solid-state materials, under the right conditions, collections of magnetic dipoles are known to spontaneously form into a variety of rather complex geometrical patterns, exemplified by vortex and skyrmion structures. While theoretically, similar patterns should be expected to form from electrical dipoles, they have not been clearly observed to date: the need for continued experimental exploration is therefore clear. In this Letter we report the discovery of a rather complex domain arrangement that has spontaneously formed along the edges of a thin single crystal ferroelectric sheet, due to surface-related depolarizing fields. Polarization patterns are such that nanoscale "flux-closure" loops are nested within a larger mesoscale flux closure object. Despite the orders of magnitude differences in size, the geometric forms of the dual-scale flux closure entities are rather similar.