  Magnetic skyrmions are chiral spin textures which have attracted intense
research for their fundamentally novel physics and potential applications as
spintronic information carriers. The stability which makes them so potentially
useful is a result of their underlying non-trivial topology. While skyrmions
were originally predicted and observed in crystalline materials lacking
inversion symmetry, some of the most promising host systems for skyrmions are
multilayer thin films, where skyrmions have been stabilized at ambient
conditions, which is critical for their use in real world devices. The
skyrmions found in multilayer thin films have additional three-dimensional
structure, with their domain wall helicities twisting through the thickness of
the film to create a hybrid skyrmion composed of a Bloch-type core with
N\'eel-type caps of opposite chiralities at the surfaces. In this work, we show
that this three-dimensional variation creates additional knotted topological
structure, providing an explanation for their exceptional stability in ambient
conditions. We show that hybrid skyrmions can be described as half-integer
Hopfions, and that their field lines have the knotted structure of the Hopf
fibration. Furthermore, we show that the topological charge of partially
twisted hybrid skyrmions can be related to the domain wall helicity at the
surfaces, providing a straightforward way to connect experimental measurements
to underlying topology.
