3D and 1D calculation of hysteresis loops and energy products for anisotropic nanocomposite films with perpendicular anisotropy

In this paper, the magnetic reversal process, hysteresis loops and energy products for exchange-coupled Nd2Fe14B/α-Fe bilayers are studied systematically by a three-dimensional (3D) model. The 3D calculations are numerically solved using the finite difference method, where the results are carefully compared with those calculated by one-dimensional (1D) model. It is found that the calculated hysteresis loops and energy products based on the two methods are consistent with each other. Both nucleation fields and coercivities decrease monotonically as the soft layer thickness Ls increases. In addition, the calculated spatial distributions of magnetization orientations in the thickness direction at various applied fields based on both methods signify a three-step magnetic reversal process, which are nucleation, growth and displacement of the domain wall. The calculated magnetic orientations within the film plane, however, are totally different according to the two methods. The 3D calculation exhibits a process of vortex formation and annihilation. On the other hand, the 1D calculation gives a quasi-coherent one, where magnetization orientation is coherent in the film plane and varies in the thickness direction. This new reversal mechanism displayed in the film plane has a systematic influence on the nucleation fields, coercivity and energy products.