  When electrons are driven through unconventional magnetic structures, such as
skyrmions, they experience emergent electromagnetic fields that originate
several Hall effects. Independently, ground state emergent magnetic fields can
also lead to orbital magnetism, even without the spin-orbit interaction. The
close parallel between the geometric theories of the Hall effects and of the
orbital magnetization raises the question: does a skyrmion display topological
orbital magnetism? Here we first address the smallest systems with nonvanishing
emergent magnetic field, trimers, characterizing the orbital magnetic
properties from first-principles. Armed with this understanding, we study the
orbital magnetism of skyrmions, and demonstrate that the contribution driven by
the emergent magnetic field is topological. This means that the topological
contribution to the orbital moment does not change under continous deformations
of the magnetic structure. Furthermore, we use it to propose a new experimental
protocol for the identification of topological magnetic structures, by soft
x-ray spectroscopy.
