Numerical Calculation of the Hopf Index for 3D Magnetic Textures

Fuente: arXiv
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Main Authors: Knapman, Ross, Azhar, Maria, Pignedoli, Alessandro, Gallard, Louis, Hertel, Riccardo, Leliaert, Jonathan, Everschor-Sitte, Karin
Format: Preprint
Published: 2024
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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