Size dependence of microwave permeability of spherical ferromagnetic particles

Spherical, monodispersed, ferromagnetic, metallic particles of different compositions were obtained by the polyol process with a mean radius ranging from 30 nm to 1 μm. The microwave permeability of metallic particles-dielectric matrix composites were studied in the range of 0.1–18 GHz. In the wide particle size range investigated, a size dependence of the dynamic permeability was observed. Whereas the permeability of micrometer-sized particles shows a single resonance band, the permeability of submicrometer-sized particles exhibits several narrow resonance bands which are shifted to high frequencies with decreasing particle size. This latter behavior was found to be in qualitative agreement with the exchange resonance modes calculated by Aharoni. That theory, however, gives an R−2 dependence on particle radius for the resonance frequency instead of the R−0.66 dependence observed experimentally.