From picometre displacements to a three-dimensional lattice gas of polar skyrmions

Abstract

Polar skyrmions, the electric analogues of magnetic skyrmions, form arrays in PbTiO3/SrTiO3 superlattices that are known to be only short-range ordered, but how this disordered ensemble is organized in three dimensions, and how its microscopic structure underlies this organization, have remained largely inaccessible. Here, using three-dimensional difference pair distribution function (3D-ΔPDF) analysis of X-ray diffuse scattering, we show that the polar skyrmion bubbles form a three-dimensional lattice gas: they occupy discrete sites, but their order extends over only a few neighbours and is two to three times stronger across the SrTiO3 spacers than within a layer. This interlayer coupling is consistent with the polarization of the bubbles extending into the spacers. Within each bubble, the polarization rotates in a predominantly Néel-type manner, and Pb and Ti rotate together with comparable picometre displacements, demonstrating that both A- and B-site cations take part in the polar distortion.