大学物理 ›› 2026, Vol. 45 ›› Issue (2): 7-.doi: 10.16854 /j.cnki.1000-0712. 250304

• 教学讨论 • 上一篇    下一篇

Stoner Wohlfarth模型的解析解

薛德胜,刘钊辰,胡阳   

  1. 兰州大学 物理科学与技术学院,甘肃 兰州730000
  • 收稿日期:2025-06-23 修回日期:2025-07-04 出版日期:2026-05-15 发布日期:2026-05-21
  • 作者简介:薛德胜(1965—) ,男,山东安丘人,兰州大学物理学院教授,博士,主要从事普通物理、固体物理和磁性理论的教学及磁学与磁性材料研究工作
  • 基金资助:
    国家重点研发计划 (No: 2021YFB3501300), 国家自然科学基金委 (Grant Nos.91963201 and 12174163), 111计划 No. B20063

Analytical solution of the Stoner Wohlfarth model

XUE Desheng, LIU Zhaochen, HU Yang   

  1. Lanzhou University The School of Physical Science and Technology,Lanzhou, Gansu 730000, China
  • Received:2025-06-23 Revised:2025-07-04 Online:2026-05-15 Published:2026-05-21

摘要: Stoner-Wohlfarth模型是磁学的基本模型,然而传统求解方案只能获得三个特殊角度的解析解. 本文利用反函数的思路,得到了一般情况下该模型的简单解析解. 利用这一解析解,获得了描述静态磁性的磁滞回线,以及描述动态磁性的磁化强度运动轨迹. 解析解的获得,为定量化描述磁化强度一致转动的稳定方向和绕该方向的进动图像提供了简单、直观、准确的方案. 

关键词: Stoner-Wohlfarth模型, 磁化强度, 解析解, 磁滞回线, 进动轨迹

Abstract: The StonerWohlfarth model is a fundamental model in magnetism. However, the traditional solution methods can only provide analytical solutions for three specific angles. In this paper, by using the idea of inverse functions, a simple analytical solution for this model under general conditions is obtained. Using this analytical solution, the hysteresis loop describing static magnetism and the trajectory of magnetization intensity movement describing dynamic magnetism are obtained. The acquisition of this analytical solution provides a simple, intuitive and accurate scheme for quantitatively describing the stable direction of the uniform rotation of magnetization intensity and the precession image around that direction.