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Topologically nontrivial textures hold great promise as information units for future data manipulation and storage devices, as well as for unconventional computing paradigms such as reservoir computing.

In two dimensions, a key example of such a texture is the magnetic skyrmion. During my PhD, I investigated the creation and dynamics of skyrmions driven by electrical currents in the cycloidal state of a magnet. In this state, skyrmions typically appear as H-shaped (see figure) and their motion is confined to 1D [Knapman, et al., J. Phys. D: Appl. Phys. 54, 404003 (2021)].

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A schematic of a H-shaped skyrmion in a cycloidal background.
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A three-dimensional topologically non-trivial magnetic texture of significant interest is the magnetic hopfion (see figure). We provide and compare different numerical tools for calculating the corresponding topological index – the Hopf [Knapman, R. et al., arXiv:2410.22058]. Furthermore, we predicted and explored magnetic hopfions in (2+1)D spacetime.  [Knapman, R. et al., Commun. Phys. 7, 151 (2024)]

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Magnetic hopfion texture created from a tube of skyrmions, showing various preimages of the equatorial points on the unit sphere of magnetisation.
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