Numerical Calculation of the Hopf Index for 3D Magnetic Textures
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908300462784512 |
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| author | Knapman, Ross Azhar, Maria Pignedoli, Alessandro Gallard, Louis Hertel, Riccardo Leliaert, Jonathan Everschor-Sitte, Karin |
| author_facet | Knapman, Ross Azhar, Maria Pignedoli, Alessandro Gallard, Louis Hertel, Riccardo Leliaert, Jonathan Everschor-Sitte, Karin |
| contents | To gain deeper insight into the complex, stable, and robust configurations of magnetic textures, topological characterisation has proven essential. In particular, while the skyrmion number is a well-established topological invariant for 2D magnetic textures, the Hopf index serves as a key topological descriptor for 3D magnetic structures. In this work, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical Calculation of the Hopf Index for 3D Magnetic Textures Knapman, Ross Azhar, Maria Pignedoli, Alessandro Gallard, Louis Hertel, Riccardo Leliaert, Jonathan Everschor-Sitte, Karin Mesoscale and Nanoscale Physics To gain deeper insight into the complex, stable, and robust configurations of magnetic textures, topological characterisation has proven essential. In particular, while the skyrmion number is a well-established topological invariant for 2D magnetic textures, the Hopf index serves as a key topological descriptor for 3D magnetic structures. In this work, 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. |
| title | Numerical Calculation of the Hopf Index for 3D Magnetic Textures |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2410.22058 |