Year: 2025
Type: article
Abstract: To gain deeper insight into the complex, stable, and robust configurations of magnetic textures, topological characterization has proven essential. In particular, while the skyrmion number is a well-established topological invariant for two-dimensional magnetic textures, the Hopf index serves as a key topological descriptor for three-dimensional magnetic structures. In this paper, we present and compare various methods for numerically calculating the Hopf index, provide implementations, and offer a detailed analysis of their accuracy and computational efficiency. Additionally, we identify and address common pitfalls and challenges associated with the numerical computation of the Hopf index, offering insights for improving the robustness of these techniques.
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Awards: Topologische Ringe: Struktur, Dynamik und Kontrolle von Hopfionen, G1648955853, G3285732985, Kontrollierte Erzeugung und Dynamik von topologischen magnetischen Texturen in Ferro und Antiferromagneten, SFB 1242: Nichtgleichgewichtsdynamik kondensierter Materie in der Zeitdomäne, G3614653396, Exploiting the internal dynamics of inhomogeneous magnetization states for technological and biomedical applications., TRR 270: HystereseDesign magnetischer Materialien für effiziente Energieumwandlung, G571279759, TWIST Topologische Wirbel In SpinTronik, Topological Rings: Hopfion structure, Dynamics and Control, G933099165
OpenAlex ID: W4409163471