Angular Dependence of the Pinning Fields for Hard/Soft Multilayers

The influence of the deviation of the easy axis β on the magnetic reversal of a hard/soft multilayer is investigated within a rigorous micromagnetic method when the thickness of the hard layer th is finite. It is found that the pinning fields exhibit an angular symmetry where the minimum occurs at β = 45°, similar to that according to the well-known Stoner-Wohlfarth model. For intermediate soft layer thickness, the Kondorsly-like pinning is observed, where the pinning fields increase monotonically with β. On the other hand, the pinning field H_P goes up monotonically with th for all values of β when the hard layer thickness is less than roughly three times of its domain wall width.