Angular dependence of longitudinal and perpendicular exchange biases in FeMn/(FeNi/FeMn)n multilayers

Perpendicular exchange bias can be established in ferromagnetic/antiferromagnetic multilayers with intrinsic in-plane shape anisotropy through out-of-plane field cooling. The induced anisotropy along the hard axis possesses the same interfacial nature as that after the conventional in-plane field cooling. While the in-plane angular dependence of longitudinal exchange bias can be well described by the uniaxial coherent rotation model, out-of-plane measurements show totally different angular dependent hysteretic behaviors for both longitudinal and perpendicular exchange biases. After taking into account the competitive field cooling induced anisotropy, the thin film shape anisotropy, the three-dimensional coherent rotation model alone can quantitatively explain the observed out-of-plane angular dependent magnetization reversal for both field cooling geometries. Magnetization reversal is found to be accomplished by coherent rotation out of the plane determined by anisotropic axis and applied field. The model is also applicable in predicting the more general thin-film magnetization reversal with out-of-plane applied fields.