Antiskyrmions in Ferroelectric Barium Titanate.

Typical magnetic skyrmion is a string of inverted magnetization within a ferromagnet, protected by a sleeve of a vortexlike spin texture, such that its cross-section carries an integer topological charge. Some magnets form antiskyrmions, the antiparticle strings which carry an opposite topological charge. Here we demonstrate that topologically equivalent but purely electric antiskyrmion can exist in a ferroelectric material as well. In particular, our computer experiments reveal that the archetype ferroelectric, barium titanate, can host antiskyrmions at zero field. The polarization pattern around their cores reminds ring windings of decorative knots rather than the typical magnetic antiskyrmion texture. We show that the antiskyrmion of barium titanate has just 2-3 nm in diameter, a hexagonal cross section, and an exotic topological charge with doubled magnitude and opposite sign when compared to the standard skyrmion string.

Structural Chirality of Polar Skyrmions Probed by Resonant Elastic X-Ray Scattering.

An escalating challenge in condensed-matter research is the characterization of emergent order-parameter nanostructures such as ferroelectric and ferromagnetic skyrmions. Their small length scales coupled with complex, three-dimensional polarization or spin structures makes them demanding to trace out fully. Resonant elastic x-ray scattering (REXS) has emerged as a technique to study chirality in spin textures such as skyrmions and domain walls. It has, however, been used to a considerably lesser extent to study analogous features in ferroelectrics. Here, we present a framework for modeling REXS from an arbitrary arrangement of charge quadrupole moments, which can be applied to nanostructures in materials such as ferroelectrics. With this, we demonstrate how extended reciprocal space scans using REXS with circularly polarized x rays can probe the three-dimensional structure and chirality of polar skyrmions. Measurements, bolstered by quantitative scattering calculations, show that polar skyrmions of mixed chirality coexist, and that REXS allows valuation of relative fractions of right- and left-handed skyrmions. Our quantitative analysis of the structure and chirality of polar skyrmions highlights the capability of REXS for establishing complex topological structures toward future application exploits.

Chiral structures of electric polarization vectors quantified by X-ray resonant scattering.

Resonant elastic X-ray scattering (REXS) offers a unique tool to investigate solid-state systems providing spatial knowledge from diffraction combined with electronic information through the enhanced absorption process, allowing the probing of magnetic, charge, spin, and orbital degrees of spatial order together with electronic structure. A new promising application of REXS is to elucidate the chiral structure of electrical polarization emergent in a ferroelectric oxide superlattice in which the polarization vectors in the REXS amplitude are implicitly described through an anisotropic tensor corresponding to the quadrupole moment. Here, we present a detailed theoretical framework and analysis to quantitatively analyze the experimental results of Ti L-edge REXS of a polar vortex array formed in a PbTiO3/SrTiO3 superlattice. Based on this theoretical framework, REXS for polar chiral structures can become a useful tool similar to x-ray resonant magnetic scattering (XRMS), enabling a comprehensive study of both electric and magnetic REXS on the chiral structures.