中国物理B ›› 2022, Vol. 31 ›› Issue (4): 40202-040202.doi: 10.1088/1674-1056/ac401e

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Anti-function solution of uniaxial anisotropic Stoner-Wohlfarth model

Kun Zheng(郑坤)1, Yu Miao(缪宇)1, Tong Li(李通)1, Shuang-Long Yang(杨双龙)1, Li Xi(席力)1, Yang Yang(杨洋)1, Dun Zhao(赵敦)2,†, and De-Sheng Xue(薛德胜)1,‡   

  1. 1 Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China;
    2 School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
  • 收稿日期:2021-07-29 修回日期:2021-11-16 接受日期:2021-12-05 出版日期:2022-03-16 发布日期:2022-03-25
  • 通讯作者: Dun Zhao, De-Sheng Xue E-mail:zhaod@lzu.edu.cn;xueds@lzu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 91963201, 12174163, and 12075102), PCSIRT (Grant No. IRT-16R35), and the 111 Project (Grant No. B20063).

Anti-function solution of uniaxial anisotropic Stoner-Wohlfarth model

Kun Zheng(郑坤)1, Yu Miao(缪宇)1, Tong Li(李通)1, Shuang-Long Yang(杨双龙)1, Li Xi(席力)1, Yang Yang(杨洋)1, Dun Zhao(赵敦)2,†, and De-Sheng Xue(薛德胜)1,‡   

  1. 1 Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China;
    2 School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
  • Received:2021-07-29 Revised:2021-11-16 Accepted:2021-12-05 Online:2022-03-16 Published:2022-03-25
  • Contact: Dun Zhao, De-Sheng Xue E-mail:zhaod@lzu.edu.cn;xueds@lzu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 91963201, 12174163, and 12075102), PCSIRT (Grant No. IRT-16R35), and the 111 Project (Grant No. B20063).

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摘要： The anti-trigonometric function is used to strictly solve the uniaxial anisotropic Stoner-Wohlfarth (SW) model, which can obtain the relation of the angle α (θ) between the magnetization (the anisotropy field) and the applied magnetic field. Using this analytic solution, the hysteresis loops of uniaxial anisotropic SW particles magnetized in typical directions could be numerically calculated. Then, the hysteresis loops are obtained in randomly distributed SW particle ensembles while ignoring the dipole interaction among them with the analytic solution. Finally, the correctness of the analytic solution is verified by the exact solutions of remanence, switching field, and coercivity from the SW model. The analytic solution provides an important reference for understanding the magnetizing and magnetization reversal processes of magnetic materials.

关键词: Stoner-Wohlfarth model, anti-trigonometric function, hysteresis loop

Abstract: The anti-trigonometric function is used to strictly solve the uniaxial anisotropic Stoner-Wohlfarth (SW) model, which can obtain the relation of the angle α (θ) between the magnetization (the anisotropy field) and the applied magnetic field. Using this analytic solution, the hysteresis loops of uniaxial anisotropic SW particles magnetized in typical directions could be numerically calculated. Then, the hysteresis loops are obtained in randomly distributed SW particle ensembles while ignoring the dipole interaction among them with the analytic solution. Finally, the correctness of the analytic solution is verified by the exact solutions of remanence, switching field, and coercivity from the SW model. The analytic solution provides an important reference for understanding the magnetizing and magnetization reversal processes of magnetic materials.

Key words: Stoner-Wohlfarth model, anti-trigonometric function, hysteresis loop

中图分类号:  (Numerical simulation; solution of equations)

  • 02.60.Cb
75.30.Gw (Magnetic anisotropy) 75.40.Cx (Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)) 75.60.Ej (Magnetization curves, hysteresis, Barkhausen and related effects)