Modeling exchange-spring layered systems with perpendicular anisotropy using ferromagnetic resonance measurements

We have experimentally studied the FePt/Fe<sub>3</sub>Pt bilayer system using ferromagnetic resonance at room temperature. Measurements were taken as a function of the direction of the applied external magnetic field with respect to the sample plane. Results show that the effect of exchange coupling is manifest by the induction of a strong perpendicular anisotropy into the soft layer (Fe<sub>3</sub>Pt) from the hard layer (FePt). We have used the angular variation of the resonance field to allow us to assess the anisotropy constants for three different thicknesses of the soft layer (2, 3.5 and 5 nm). We observe a decrease of the overall perpendicular anisotropy as the soft layer thickness increases. We note that the hard layer does not contribute to the spectra under the experimental conditions used (9.3 GHz, magnetic fields up to 1 T). We have modeled the bilayer system using the free energy of the system, which includes the effective anisotropies of the layers. In order to fully appreciate the effects of exchange coupling, we have used previously published data of the spin orientation in the soft layer to assess the most appropriate values of the anisotropy constants for the FePt/Fe system. The results indicate that the best way to model these hard-soft coupled ferromagnetic layers is by using a variable effective anisotropy constant in the soft layer, from which almost exact solutions can be obtained. Averaging the anisotropy over the entire layer gives a good measure of the effective anisotropy and the thickness dependence of the effective anisotropy agrees very well with that found experimentally using ferromagnetic resonance