3D calculation of hysteresis loops, magnetic orientations and reversal processes for exchange-spring bilayers with perpendicular anisotropy

Hysteresis loops and magnetic reversal processes have been determined by a three dimensional (3D) micromagnetic model for exchange-coupled Nd2Fe14B/α-Fe bilayers and carefully compared with a popular one-dimensional (1D) micromagnetic model. It is found that the calculated hysteresis loops, the critical fields and the magnetic phase diagrams agree well with the results given by the 1D model. However, the calculated nucleation mode is a quasi-curling one where the magnetic moment exhibits a curling in the film plane and varies in the thickness direction, in contrast with the reported quasi-coherent mode. The calculated spatial distribution of the magnetization orientation in the thickness direction at various applied fields signifies a three-step magnetic reversal process, which includes nucleation, growth and displacement of the domain wall as well as the rotation and the reversal of magnetization in the hard phase. The magnetic reversal of the hard phase is much slower than that given by the 1D model, leading to a more slant hysteresis loop near the coercivity point.