Dynamical behavior of coupled magnetic bilayers

We obtain the magnetic susceptibility of systems constituted of two coupled magnetic layers. We consider that the coupling of the films is well described by a Heisenberg like interaction to write the equation of motion for the magnetization of each part of the system. The dynamical response of each constituent material is calculated taking into account the presence of an interacting magnetic media (a magnetic layer) in its border. The susceptibility obtained incorporates the effects of a different magnetic film in the neighborhood (via the interfilm interaction), as well as the properties of the interface. We use a procedure similar to the effective medium approach developed for superlattices to obtain an effective magnetic permeability for the whole system. We show that the knowledge of this property allows one to have information on the interface of the magnetic bilayer through the analysis of its optical properties. We illustrate this point by calculating the dispersion relation of magnetic polaritons propagating in a system consisting of an antiferromagnetic (MnF2) layer grown in direct contact with a ferromagnetic film (Fe). We also simulate numerically an optical experiment where ATR (Attenuated Total Reflection) spectra are obtained.