三维磁性结构Hopf指数的数值计算

IF 3.7 2区物理与天体物理 Q1 Physics and Astronomy

Physical Review B Pub Date : 2025-04-04 DOI:10.1103/physrevb.111.134408

R. Knapman, M. Azhar, A. Pignedoli, L. Gallard, R. Hertel, J. Leliaert, K. Everschor-Sitte

{"title":"三维磁性结构Hopf指数的数值计算","authors":"R. Knapman, M. Azhar, A. Pignedoli, L. Gallard, R. Hertel, J. Leliaert, K. Everschor-Sitte","doi":"10.1103/physrevb.111.134408","DOIUrl":null,"url":null,"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. Published by the American Physical Society 2025 ","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"73 1","pages":""},"PeriodicalIF":3.7000,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Numerical calculation of the Hopf index for three-dimensional magnetic textures\",\"authors\":\"R. Knapman, M. Azhar, A. Pignedoli, L. Gallard, R. Hertel, J. Leliaert, K. Everschor-Sitte\",\"doi\":\"10.1103/physrevb.111.134408\",\"DOIUrl\":null,\"url\":null,\"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. Published by the American Physical Society 2025 \",\"PeriodicalId\":20082,\"journal\":{\"name\":\"Physical Review B\",\"volume\":\"73 1\",\"pages\":\"\"},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2025-04-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevb.111.134408\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.111.134408","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}

引用次数: 0

摘要

为了更深入地了解复杂、稳定和坚固的磁纹理构型，拓扑特征描述已被证明是必不可少的。特别是，天磁数是二维磁纹理的公认拓扑不变量，而霍普夫指数则是三维磁结构的关键拓扑描述符。在本文中，我们介绍并比较了各种数值计算霍普夫指数的方法，提供了实现方法，并对其准确性和计算效率进行了详细分析。此外，我们还发现并解决了与霍普夫指数数值计算相关的常见陷阱和挑战，为提高这些技术的稳健性提供了启示。美国物理学会出版 2025

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Numerical calculation of the Hopf index for three-dimensional magnetic textures

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.

Published by the American Physical Society

2025

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Physical Review B 物理-物理：凝聚态物理

CiteScore

6.70

自引率

32.40%

发文量

审稿时长

3.0 months

期刊介绍： Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide. PRB covers the full range of condensed matter, materials physics, and related subfields, including: -Structure and phase transitions -Ferroelectrics and multiferroics -Disordered systems and alloys -Magnetism -Superconductivity -Electronic structure, photonics, and metamaterials -Semiconductors and mesoscopic systems -Surfaces, nanoscience, and two-dimensional materials -Topological states of matter