B. Shearer | Searcharxiv

arXiv2026

3D Imaging of Complex Skyrmion and Hopf Topologies in an Extended Sample

Spin textures are key for emergent magnetic phenomena such as topological protection and underpin novel spintronic device paradigms based on racetrack memory, logic gates, and neuromorphic computing. Using a coherent diffractive imaging technique called vector ptycho-tomography, in combination with algorithms that are robust to noise, we image the 3D magnetic texture of skyrmion and Hopf topologies with no prior assumptions about the sample. This directly reveals experimentally for the first time an extended 3D skyrmion lattice, including the domain wall shape, topological charge, helicity, and Hopf index. Our findings demonstrate experimentally that dipole stabilized skyrmions in Fe/Gd multilayers exhibit barrel-shaped skyrmion tubes with a twisted helicity, transitioning from N$\'e$el-type winding at the surfaces to both clockwise and counterclockwise Bloch-type winding in the bulk, that can also be described as fractional hopfions. We image a lattice of 24 skyrmions with topological charge 1, average depth-dependent domain wall width of 23 to 40 nm, depth-dependent twisted helicity from $\pm$155$\deg$ to $\pm$30$\deg$, and fractional Hopf index of $\pm$0.3. Over 10 TB of data were analyzed to yield a fully-resolved 3D reconstruction over a >0.4 $\mu$m$^3$ volume, with high fidelity down to the Nyquist limit of 8 nm. This method fills a key gap in the current landscape of magnetic imaging by enabling high-resolution, element-specific 3D reconstructions of full-field extended spin textures - offering a new route for exploring the topological complexity of magnetic materials in three dimensions.

cond-mat.mtrl-sci↗

arXiv2023

Weighted Radon transforms of vector fields, with applications to magnetoacoustoelectric tomography

Currently, theory of ray transforms of vector and tensor fields is well developed, but the Radon transforms of such fields have not been fully analyzed. We thus consider linearly weighted and unweighted longitudinal and transversal Radon transforms of vector fields. As usual, we use the standard Helmholtz decomposition of smooth and fast decreasing vector fields over the whole space. We show that such a decomposition produces potential and solenoidal components decreasing at infinity fast enough to guarantee the existence of the unweighted longitudinal and transversal Radon transforms of these components. It is known that reconstruction of an arbitrary vector field from only longitudinal or only transversal transforms is impossible. However, for the cases when both linearly weighted and unweighted transforms of either one of the types are known, we derive explicit inversion formulas for the full reconstruction of the field. Our interest in the inversion of such transforms stems from a certain inverse problem arising in magnetoacoustoelectric tomography (MAET). The connection between the weighted Radon transforms and MAET is exhibited in the paper. Finally, we demonstrate performance and noise sensitivity of the new inversion formulas in numerical simulations.

math.AP↗