5 papers
Topological Classification of Non-Normalizable Vector Fields
Philipp Gessler, Alessandro Pignedoli, Alexander Neuhaus +3
Topological classification of physical vector fields conventionally relies on field normalization and homotopy-based invariants. However, when field amplitudes vanish, normalizatio…
The 2026 Skyrmionics Roadmap
Sabri Koraltan, Claas Abert, Manfred Albrecht +64
Magnetic skyrmions and related topological spin textures have emerged as a central topic in condensed-matter physics, combining fundamental significance with potential for transfor…
Hopfions in screw chiral magnets
Sandra C Shaju, Maria Azhar, Karin Everschor-Sitte
Three-dimensional topological spin textures have attracted growing interest due to their rich geometry and potential for functional magnetic phenomena. In this work, we propose the…
3D Magnetic Textures with Mixed Topology: Unlocking the Tunable Hopf Index
Maria Azhar, Sandra C. Shaju, Ross Knapman +2
Knots and links play a crucial role in understanding topology and discreteness in nature. In magnetic systems, twisted, knotted and braided vortex tubes manifest as Skyrmions, Hopf…
Numerical Calculation of the Hopf Index for 3D Magnetic Textures
Ross Knapman, Maria Azhar, Alessandro Pignedoli +4
To gain deeper insight into the complex, stable, and robust configurations of magnetic textures, topological characterisation has proven essential. In particular, while the skyrmio…