Interpretation of Kronmüller Formula using Ginzburg-Landau Theory

• Published in: Journal of the Magnetics Society of Japan Vol. 46; no. 5
• Main Authors: Mitsumata, C, Kotsugi, M
• Format: Journal Article
• Language: English; Japanese
• Published: Tokyo Japan Science and Technology Agency 01.09.2022
• Subjects: Absolute zero; Coercivity; Entropy; Free energy; Magnetic anisotropy; Magnetic materials; Magnetism; Magnetization; Order parameters; Permanent magnets; Reduction
• ISSN: 1882-2924; 1882-2932
• DOI: 10.3379/msjmag.2209R001

The Kronmüller formula is used to qualitatively explain the coercivity of permanent magnets. Such simple expressions are useful for understanding the elements that influence the coercivity. This study attempts to derive Kronmüller formula within the framework of the Ginzburg-Landau theory. The results revealed that the coercivity of the magnetic material was defined by the slope of the free energy landscape. The reduction parameter α for the magnetic anisotropy field Hk in the Kronmüller formula depends on the functional form representing the free energy landscape that changes with the magnetization process of the material, and it is shown that α < 1 under the condition of absolute zero temperature T = 0. Furthermore, it was revealed that α depends on the entropy of the system and that it may show a larger reduction rate at a finite temperature T ≠ 0. Thus, it is important to acquire the free energy landscape and clarify the order parameter dependence of entropy in the magnetization process of the magnetic material.