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We have investigated the composition and frequency dependence of the permeability tensor in heterostructures composed of metal oxides nanoparticulate powders. Samples consist of grains of the magnetic phase (␥-Fe 2 O 3 ) homogeneously dispersed in a nonmagnetic insulating background ͑ZnO͒. A measurement capability has been used to investigate the permeability tensor components of the ferrimagnetic samples under an externaly magnetic field, as a function of composition. The samples exhibit a previously unobserved fielddependent anisotropic contribution to the permeability tensor. The gyromagnetic resonance frequency decreases with Fe 2 O 3 content and increases with applied magnetic field. The frequency-dependent response in the microwave frequency range can be fit reasonably well using a single parameter whose value is consistent with the determination from a ferromagnetic resonance experiment and can be rationalized by means of a recently developed coarse-grained multiscale model. The model is based on multiscale averaging techniques and takes into account magnetostatic intergranular interactions via a mean-field approximation. These observations are aimed at developing a more realistic description of magnetic nanophases that takes into account details of the microstructure and provide salient input to micromagnetic simulations.

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