Effect of magnetic field on macroscopic hysteresis and microscopic magnetic domains for different ferromagnetic materials

The macroscopic hysteresis of ferromagnetic materials is influenced by their microscopic magnetic domains, establishing a correspondence between the two that enables a fundamental understanding of the magnetization process of ferromagnetic materials. Based on this, this study employs the phase field method to investigate the macroscopic hysteresis and microscopic magnetic domain evolution of soft, hard, and rectangular ferromagnetic materials. The hysteresis loops of the three materials present narrow, wide and rectangular characteristics respectively, which are quantitatively consistent with the experimental data. Subsequently, the influence of the magnetic field on the macroscopic hysteresis is analyzed. The results show that the hysteresis loop area increases when the magnetic field amplitude increases. Furthermore, the proportion of each type of energy under different magnetic fields is discussed, the dominant energy terms are generally consistent for the same category of ferromagnetic materials. Additionally, the corresponding magnetic domain evolution under different magnetic field is displayed, with soft magnetic materials exhibiting no vortex structures, hard ferromagnetic materials presenting a 45° vortex structure, and rectangular magnetic material showcasing a 90° vortex structure. Finally, the asymmetric characteristics of the major hysteresis loop and minor hysteresis loops are discussed. The change of the magnetic field path leads to the corresponding change of the major and minor hysteresis loops. At the same magnetic field, distinctions in magnetic domain configurations between the major and minor hysteresis loops are evident.