Three- and two-dimensional calculations for the interface anisotropy dependence of magnetic properties of exchange-spring Nd2Fe14B/α-Fe multilayers with out-of-plane easy axes*

Abstract

Hysteresis loops, energy products and magnetic moment distributions of perpendicularly oriented Nd2Fe14B/α-Fe exchange-spring multilayers are studied systematically based on both three-dimensional (3D) and one-dimensional (1D) micromagnetic methods, focused on the influence of the interface anisotropy. The calculated results are carefully compared with each other. The interface anisotropy effect is very palpable on the nucleation, pinning and coercive fields when the soft layer is very thin. However, as the soft layer thickness increases, the pinning and coercive fields are almost unchanged with the increment of interface anisotropy though the nucleation field still monotonically rises. Negative interface anisotropy decreases the maximum energy products and increases slightly the angles between the magnetization and applied field. The magnetic moment distributions in the thickness direction at various applied fields demonstrate a progress of three-step magnetic reversal, i.e., nucleation, evolution and irreversible motion of the domain wall. The above results calculated by two models are in good agreement with each other. Moreover, the in-plane magnetic moment orientations based on two models are different. The 3D calculation shows a progress of generation and disappearance of vortex state, however, the magnetization orientations within the film plane calculated by the 1D model are coherent. Simulation results suggest that negative interface anisotropy is necessarily avoided experimentally.