Splitting of spin-wave modes in thin films with Arrays of periodic perturbations: theory and experiment

We present an analytical theory focused on the description of the ferromagnetic resonance (FMR) response of thin lms in the case that periodic surface perturbations are introduced. These perturbations can be any kind of one- or two-dimensional rectangular arrays of defects patterned onto one surface of the magnetic lm. Our theory allows us to describe their influence in such a way that the periodic defect structure can have any given shape. We calculate the response functions that are the components of the dynamic susceptibility tensor of the lm exposed to the FMR microwave excitation. These allow us to obtain the resonant response of the system, trough relevant quantities as the microwave absorption, the FMR linewidth, and resonance eld. We show examples where the periodic defects have the shape of stripes, dots, and rectangles. In our framework the perturbations may be considered either as bumps or pits. Finally, we compare our results with recent experimental FMR results, which manifest a very good agreement with the theory.