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Advanced vector imaging techniques provide us with 3D maps of magnetizationfields in which topological concepts can be directly applied to describereal-space experimental textures in non-ideal geometries. Here, the 3Dmagnetization of a low symmetry permalloy microstructure is obtained by X-rayvector magnetic tomography and analysed in detail in terms of topologicalcharges and emergent fields. A central asymmetric domain wall with a complex 3Dstructure is observed in which magnetization chirality transitions are mediatedby Bloch points arranged in several dipoles and a triplet. The ideal sphericalsymmetry of the emergent field of an isolated monopole is severely modified dueto shape effects of the permalloy microstructure. Emergent field linesaggregate into bundles that either connect adjacent Bloch points within atopological dipole or tend towards the surface. These bundles may presentdifferent textures such as helical vortices or half merons, depending onasymmetries and confinement, but are constrained by topological chargeconservation in a given sample volume. This precise description of thesingularities in realistic systems, enabled by the quantitative experimentalinformation on magnetization vector fields, can significantly improve ourunderstanding of topological constraints in 3D magnetic systems and provideadvancements in the design of magnetic devices.

Topological magnetic dipoles and emergent field bundles in a ferromagnetic microstructure by X-ray magnetic vector tomography