The analytical investigation of the magnetic orientation and hysteresis loop in exchange-spring magnetic multilayers

Using the interface coupling constant J(1) and the soft layer thickness L-8 as the main variables, the changes of the magnetic moments with the applied field and the hysteresis loops of Nd2Fe14 B/alpha-Fe trilayers, whose easy axes of all layers lie in the film plane, have been investigated. Analysis shows that J(1) has significant influence on the magnetic orientation, the pinning field H-p and the coercivity mechanism. When L-8: is small, H-p equals to H-N where the coercivity mechanism transforms from nucleation to pinning as J(1) decreases, whereas for large L-s this trend is reversed. The critical thickness, at which the nucleation field and pinning field detaches, decreases as J(1) decreases. When the reduced exchange coupling is considered, the rigid composite magnet appears only when L-8 is very small. The reduced exchange coupling leads to a sudden change of angle of magnetization at the interface, which results in the change of the behavior of the trilayers from the single-phase one to the two-phase one and in the decrease of H-N whereas H-p increases when L-8 is larger.