Retarded modes of lateral ferromagnetic/ferromagnetic superlattice

In this paper, we calculated the retarded modes of semi-infinite lateral ferromagnetic/ferromagnetic superlattice with the effective-medium theory. We took the Co/Ni system surface modes and bulk modes as the examples for the superlattice and found some interesting properties different from that of the lateral ferromagnetic/nonmagnetic superlattice. Lateral magnetic/magnetic superlattice have some complex retarded modes which are very common in the systems. Changing the ratio of the thicknesses of the ferromagnetic layers, the two branches of surface mode frequency and bulk mode frequency band can be adjusted consequently. This tailoring effect is related to the two ferromagnetic layers' saturation magnetization values, and it is quite pronounced when the two saturation magnetization values are quite different from each other. If the difference between the tow values is large, the tailoring effect of f1 is more obvious. When the saturation magnetization value of the second ferromangtic medium approaches to zero, this system will become the magnetic/nonmagnetic superlattice. If in Maxwell equation ε = 0, the retarded modes will transit to the ferromangtic/ferromangnetic superlattice magnetostatic modes.