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Magnetic topological defects are energetically stable spin configurationscharacterized by symmetry breaking. Vortices and skyrmions are two well-knownexamples of 2D spin textures that have been actively studied for bothfundamental interest and practical applications. However, experimental evidenceof the 3D spin textures has been largely indirect or qualitative to date, dueto the difficulty of quantitively characterizing them within nanoscale volumes.Here, we develop soft x-ray vector ptychography to quantitatively image the 3Dmagnetization vector field in a frustrated superlattice with 10 nm spatialresolution. By applying homotopy theory to the experimental data, we quantifythe topological charge of hedgehogs and anti-hedgehogs as emergent magneticmonopoles and probe their interactions inside the frustrated superlattice. Wealso directly observe virtual hedgehogs and anti-hedgehogs created bymagnetically inert voids. We expect that this new quantitative imaging methodwill open the door to study 3D topological spin textures in a broad class ofmagnetic materials. Our work also demonstrates that magnetically frustratedsuperlattices could be used as a new platform to investigate hedgehoginteractions and dynamics and to exploit optimized geometries for informationstorage and transport applications.

Direct observation of 3D topological spin textures and their interactions using soft x-ray vector ptychography