Broadband Permeability Spectra of Flake-Shaped Ferromagnetic Particle Composites

Broadband permeability spectra of aligned ferromagnetic flakes embedded in a nonmagnetic polymer matrix have been measured using an APC-7 coaxial line within the frequency range 10 MHz-18 GHz. These spectra reveal two well-defined resonance lines. The low-frequency one (sub-GHz range) has previously been attributed to the fundamental vortex translation mode in a multidomain magnetic structure, whereas the high-frequency resonance (beyond 1 GHz) is assigned to the natural spin resonance. A two-level analytical model combining a spin dynamics description including these two contributions at the flake scale and a Maxwell-Garnett mixing rule at the composite scale has been developed and reproduces very satisfactorily the experimental spectra in terms of resonance frequencies, resonance linewidths, and resonance mode amplitudes.