Angular Dependence of the Pinning Fields for Hard/Soft Multilayers

The influence of the deviation of the easy axis beta on the magnetic reversal of a hard/soft multilayer is investigated within a rigorous micromagnetic method when the thickness of the hard layer t(h) is finite. It is found that the pinning fields exhibit an angular symmetry where the minimum occurs at beta = 45 degrees, 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 beta. On the other hand, the pinning field HP goes up monotonically with t(h) for all values of beta when the hard layer thickness is less than roughly three times of its domain wall width.