  Magnetic topological defects are energetically stable spin configurations
characterized by symmetry breaking. Vortices and skyrmions are two well-known
examples of 2D spin textures that have been actively studied for both
fundamental interest and practical applications. However, experimental evidence
of the 3D spin textures has been largely indirect or qualitative to date, due
to the difficulty of quantitively characterizing them within nanoscale volumes.
Here, we develop soft x-ray vector ptychography to quantitatively image the 3D
magnetization vector field in a frustrated superlattice with 10 nm spatial
resolution. By applying homotopy theory to the experimental data, we quantify
the topological charge of hedgehogs and anti-hedgehogs as emergent magnetic
monopoles and probe their interactions inside the frustrated superlattice. We
also directly observe virtual hedgehogs and anti-hedgehogs created by
magnetically inert voids. We expect that this new quantitative imaging method
will open the door to study 3D topological spin textures in a broad class of
magnetic materials. Our work also demonstrates that magnetically frustrated
superlattices could be used as a new platform to investigate hedgehog
interactions and dynamics and to exploit optimized geometries for information
storage and transport applications.
