Magnetic permeability for exchange-spring magnets: Application to Fe/Sm-Co

We investigate the properties of the dynamic permeability for a layered structure composed of a ferromagnet with low anisotropy coupled to a ferromagnet with high anisotropy. The permeability of a structure with a small number of layers (200) can be directly calculated numerically with few approximations in the long-wavelength limit. For larger structures we obtain analytic forms for the permeability which are appropriate in the weak-coupling limit. Our results give the resonance frequency as a function of the thickness of the two materials, the interface and bulk exchange fields, and the anisotropy in each material. We find that significant shifts in the resonance frequency, on the order of 40 GHz, can be obtained with only a small reduction in the strength of the resonance. This can be important for high-frequency signal-processing devices, and we calculate the properties of a filter based on a Fe/Sm-Co material.