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Nucleation fields, hysteresis loops, magnetic phase diagrams and critical thickness in hard/soft multilayers

Magnetization distribution and hysteresis loops have been systematically investigated for various hard/soft multilayers in this paper, with the formulae for the nucleation fields and the critical thickness (where the nucleation and pinning fields detached) analytically derived. It is found that the nucleation fields equal to the pinning ones when the soft layer thickness L s is small, accompanied by the square hysteresis loops and corresponding to the rigid magnets. As L s increases, the pinning field detaches from the nucleation one and the hysteresis loops in the second quadrant are slant, corresponding to the exchange spring magnets. Further increase of L s will lead to independent reversal of the magnetizations in the soft and hard layers, signifying the decoupled magnets. The critical thickness is inversely proportional to the crystalline anisotropy of the hard phase according to our analytical derivation, which is consistent with the approximate formula by Kneller. Finally, the critical thicknesses have been calculated for various hard/soft multilayers and compared with Kneller’s formula as well as the experimental results, with the possible reason for the differences discussed.