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MA: Fachverband Magnetismus

MA 33: Non-Skyrmonic Magnetic Textures I

MA 33.2: Vortrag

Donnerstag, 20. März 2025, 09:45–10:00, H16

Characterising 3D Topological Magnetic Textures using the Hopf index: Hopfions, Fractional Hopfions and Screw Dislocations — •Maria Azhar, Sandra Chulliparambil Shaju, Ross Knapman, Alessandro Pignedoli, and Karin Everschor-Sitte — Faculty of Physics and CENIDE, University of Duisburg-Essen.

In magnetic systems, twisted, knotted, linked, and braided vortex tubes manifest as Skyrmions, Hopfions, Fractional hopfions, or screw dislocations [1]. These complex textures are characterized by topologically non-trivial quantities, such as a Skyrmion number, a Hopf index H, a Burgers vector (quantified by an integer), and linking numbers.

We address the common challenges and pitfalls associated with numerically calculating H using the traditional Whitehead integral [2]. We present an alternative analytical method for determining H, introducing a new discrete geometric formulation [3]. This approach separates H into contributions from the self-linking and inter-linking of flux tubes of the emergent magnetic field.

Our analysis reveals the natural emergence of fractional Hopfions or textures with non-integer H, which we interpret as “mixed topology” states. These states can smoothly transform into one of several possible topological sectors with integer H. We establish a robust physical foundation for the Hopf index to assume integer, non-integer, or specific fractional values, depending on the system’s underlying topology. [1] M. Azhar, et al., PRL 128, 157204 (2022)
[2] R. Knapman, M. Azhar, et al., arxiv:2410.22058
[3] M. Azhar, et al., arXiv:2411.06929

Keywords: Hopfions; Topological spin textures; Hopf index; Screw dislocations; Fractional Hopfions