-
磁性斯格明子是一种非平庸的拓扑磁结构, 它能够在具有Dzyaloshinskii-Moriya (DM)相互作用的手性磁体中稳定存在, 其静态以及动态特性与其结构特征息息相关. 然而, 一般情况下斯格明子结构解析式并不存在. 因此, 许多研究者给出了近似解析式. 本文介绍了使用符号回归算法探索磁性斯格明子结构解析式的新方法, 在考虑DM相互作用和外部磁场对磁性斯格明子结构的影响下, 使用符号回归算法得到了两个较为合适的近似解析式, 其适用范围与占主导地位的相互作用有关. 研究结果验证了符号回归算法在探索磁性斯格明子结构解析式的强大能力, 为磁结构的解析式探索提供了新思路.
-
关键词:
- 磁性斯格明子 /
- 符号回归 /
- 磁性斯格明子结构 /
- Dzyaloshinskii-Moriya相互作用
Magnetic skyrmion is a kind of nontrivial topological magnetic structure, which can exist stably in chiral magnet with Dzyaloshinskii-Moriya (DM) interaction, and its static and dynamic properties are closely related to its structural characteristics. However, there are no general analytical expressions for skyrmion profiles. Therefore, many researchers have provided approximate solutions. In this paper, a new approach to exploring magnetic skyrmion structures is introduced by using a symbolic regression approach. Considering the influence of DM interaction and external magnetic field on magnetic skyrmion structure, two suitable approximate expressions are obtained through symbolic regression algorithms. The applicability of these expressions depends on the dominant interaction. The research results in this work validate the powerful capability of symbolic regression algorithms in exploring the magnetic skyrmion profiles. So, the present study provides a new method for finding the analytical expressions for magnetic structure.-
Keywords:
- magnetic skyrmions /
- symbolic regression /
- structures of magnetic skyrmions /
- Dzyaloshinskii-Moriya interaction
[1] Abanov Ar, Pokrovsky V L 1998 Phys. Rev. B 58 R8889Google Scholar
[2] Rößler U K, Bogdanov A N, Pfleiderer C 2006 Nature 442 797Google Scholar
[3] Heinze S, von Bergmann K, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Bluegel S 2011 Nat. Phys. 7 713Google Scholar
[4] Wei W S, He Z D, Qu Z, Du H F 2021 Rare Met. 40 3076Google Scholar
[5] Ye C, Li L L, Shu Y, Li Q R, Xia J, Hou Z P, Zhou Y, Liu X X, Yang Y Y, Zhao G P 2022 Rare Met. 41 2200Google Scholar
[6] Braun H 1994 Phys. Rev. B 50 16485Google Scholar
[7] Romming N, Kubetzka A, Hanneken C, von Bergmann K, Wiesendanger R 2015 Phys. Rev. Lett. 114 177203Google Scholar
[8] Rohart S, Thiaville A 2013 Phys. Rev. B 88 184422Google Scholar
[9] Zhou Y, Iacocca E, Awad A A, Dumas R K, Zhang F C, Braun H B, Akerman J 2015 Nat. Commun. 6 8193Google Scholar
[10] Buttner F, Lemesh I, Beach G S D 2018 Sci. Rep. 8 4464Google Scholar
[11] Komineas S, Melcher C, Venakides S 2020 Nonlinearity 33 3395Google Scholar
[12] Komineas S, Melcher C, Venakides S 2021 Physica D 418 132842Google Scholar
[13] Komineas S, Melcher C, Venakides S 2023 New J. Phys. 25 023013Google Scholar
[14] Udrescu S M, Tegmark M 2020 Sci. Adv. 6 eaay2631Google Scholar
[15] Kim S, Lu P Y, Mukherjee S, Gilbert M, Jing L, Ceperic V, Soljacic M 2021 IEEE Trans. Neural Networks Learn. Syst. 32 4166Google Scholar
[16] Raissi M, Perdikaris P, Karniadakis G E 2019 J. Comput. Phys. 378 686Google Scholar
[17] Sun S, Ouyang R, Zhang B, Zhang T Y 2019 MRS Bull. 44 559Google Scholar
[18] Koksbang S M 2023 Phys. Rev. D 107 103522Google Scholar
[19] Hernandez A, Balasubramanian A, Yuan F, Mason S A M, Mueller T 2019 NPJ Comput. Mater. 5 112Google Scholar
[20] Baldi P, Sadowski P, Whiteson D 2014 Nat. Commun. 5 4308Google Scholar
[21] Carleo G, Troyer M 2017 Science 355 602Google Scholar
[22] Zhao G P, Zhao L, Shen L C, Zou J, Qiu L 2019 Chin. Phys. B 28 77505Google Scholar
[23] Jones A 1993 Nature 363 222Google Scholar
[24] Cranmer M 2023 arXiv: 10.48550/arXiv.2305.01582 [astro-ph.IM
[25] Wu H, Hu X, Jing K, Wang X R 2021 Commun. Phys. UK 4 1Google Scholar
-
图 4 不同A与K值下, (8)式拟合结果与一维单磁畴壁结构模拟数据比较图 (a) A = 1×10–12 J/m, K = 1×103 J/m3; (b) A = 5×10–12 J/m, K = 2×103 J/m3; (c) A = 13×10–12 J/m, K = 3×103 J/m3
Fig. 4. Comparison between the fitting results of Eq. (8) and simulation data of one-dimensional magnetic domain wall under various values of A and K: (a) A = 1×10–12 J/m, K = 1×103 J/m3; (b) A = 5×10–12 J/m, K = 2×103 J/m3; (c) A = 13×10–12 J/m, K = 3×103 J/m3.
图 6 不同$ {\lambda }^{2}/h $大小下(10a)式与 (10b)式的拟合情况 (a) 0.01; (b) 0.16; (c) 0.167; (d) 0.9. (e) 不同$ {\lambda }^{2}/h $大小下, 更高适应度解析式统计图(1代表(10a)式, 2代表(10b)式)
Fig. 6. Fitting results of equations (10a) and (10b) under various $ {\lambda }^{2}/h $ values: (a) 0.01; (b) 0.16; (c) 0.167; (d) 0.9$ . $ (e) Statistical chart of equations with higher fitness under various $ {\lambda }^{2}/h $ values (1 represents equation (10a), 2 represents equation (10b)).
-
[1] Abanov Ar, Pokrovsky V L 1998 Phys. Rev. B 58 R8889Google Scholar
[2] Rößler U K, Bogdanov A N, Pfleiderer C 2006 Nature 442 797Google Scholar
[3] Heinze S, von Bergmann K, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Bluegel S 2011 Nat. Phys. 7 713Google Scholar
[4] Wei W S, He Z D, Qu Z, Du H F 2021 Rare Met. 40 3076Google Scholar
[5] Ye C, Li L L, Shu Y, Li Q R, Xia J, Hou Z P, Zhou Y, Liu X X, Yang Y Y, Zhao G P 2022 Rare Met. 41 2200Google Scholar
[6] Braun H 1994 Phys. Rev. B 50 16485Google Scholar
[7] Romming N, Kubetzka A, Hanneken C, von Bergmann K, Wiesendanger R 2015 Phys. Rev. Lett. 114 177203Google Scholar
[8] Rohart S, Thiaville A 2013 Phys. Rev. B 88 184422Google Scholar
[9] Zhou Y, Iacocca E, Awad A A, Dumas R K, Zhang F C, Braun H B, Akerman J 2015 Nat. Commun. 6 8193Google Scholar
[10] Buttner F, Lemesh I, Beach G S D 2018 Sci. Rep. 8 4464Google Scholar
[11] Komineas S, Melcher C, Venakides S 2020 Nonlinearity 33 3395Google Scholar
[12] Komineas S, Melcher C, Venakides S 2021 Physica D 418 132842Google Scholar
[13] Komineas S, Melcher C, Venakides S 2023 New J. Phys. 25 023013Google Scholar
[14] Udrescu S M, Tegmark M 2020 Sci. Adv. 6 eaay2631Google Scholar
[15] Kim S, Lu P Y, Mukherjee S, Gilbert M, Jing L, Ceperic V, Soljacic M 2021 IEEE Trans. Neural Networks Learn. Syst. 32 4166Google Scholar
[16] Raissi M, Perdikaris P, Karniadakis G E 2019 J. Comput. Phys. 378 686Google Scholar
[17] Sun S, Ouyang R, Zhang B, Zhang T Y 2019 MRS Bull. 44 559Google Scholar
[18] Koksbang S M 2023 Phys. Rev. D 107 103522Google Scholar
[19] Hernandez A, Balasubramanian A, Yuan F, Mason S A M, Mueller T 2019 NPJ Comput. Mater. 5 112Google Scholar
[20] Baldi P, Sadowski P, Whiteson D 2014 Nat. Commun. 5 4308Google Scholar
[21] Carleo G, Troyer M 2017 Science 355 602Google Scholar
[22] Zhao G P, Zhao L, Shen L C, Zou J, Qiu L 2019 Chin. Phys. B 28 77505Google Scholar
[23] Jones A 1993 Nature 363 222Google Scholar
[24] Cranmer M 2023 arXiv: 10.48550/arXiv.2305.01582 [astro-ph.IM
[25] Wu H, Hu X, Jing K, Wang X R 2021 Commun. Phys. UK 4 1Google Scholar
计量
- 文章访问数: 2496
- PDF下载量: 112
- 被引次数: 0