Orange peel coupling in multilayers with perpendicular magnetic anisotropy: Application to (Co/Pt)-based exchange-biased spin-valves

eel's theory of magnetostatic coupling between two magnetic layers with in-plane magnetization separated by a non-magnetic spacer has been extended to the case of multilayers with perpendicular anisotropy. It is shown that the presence of a correlated roughness between the successive interfaces induces an interlayer coupling through the spacer analogous to the well-known orange peel coupling. However, depending on the parameters describing the interfacial roughness, the magnetic anisotropy and the exchange stiffness constant, this coupling can favor either parallel or an antiparallel alignment of the magnetization in the two ferromagnetic layers. This model was used to quantitatively interpret the variation of interlayer coupling vs. thickness of Pt spacer layer in out-of-plane magnetized exchange-biased spin-valves comprising (Pt/Co) multilayers as free and pinned layers. It is shown that the net coupling can be interpreted by the coexistence of perpendicular orange peel and oscillatory RKKY couplings. Interestingly, since these two couplings have different thickness dependence, in certain range of Pt thickness, the coupling changes sign during growth, being antiferromagnetic at the early stage of the growth of the top (Co/Pt) multilayer but ferromagnetic once the growth is completed.