Theoretical guidelines to create and tune electric skyrmion bubbles.

Researchers have long wondered whether ferroelectrics may present topological textures akin to magnetic skyrmions and chiral bubbles, the results being modest thus far. An electric equivalent of a typical magnetic skyrmion would rely on a counterpart of the Dzyaloshinskii-Moriya interaction and seems all but impossible; further, the exotic ferroelectric orders reported to date rely on specific composites and superlattices, limiting their generality and properties. Here, we propose an original approach to write topological textures in simple ferroelectrics in a customary manner. Our second-principles simulations of columnar nanodomains, in prototype material PbTiO, show we can harness the Bloch-type structure of the domain wall to create objects with the usual skyrmion-defining features as well as unusual ones-including isotopological and topological transitions driven by external fields and temperature-and potentially very small sizes. Our results suggest countless possibilities for creating and manipulating such electric textures, effectively inaugurating the field of topological ferroelectrics.