Microwave Permeability of CO₂ Z Composites

The microwave permittivity and permeability of Co2Z barium ferrite composite samples are measured as functions of frequency and volume fraction of the ferrite. Magnetostatic properties of the bulk ferrite are determined. This allows Snoek\u27s law [J. L. Snoek, Physica 14, 204 (1948)] to be verified by comparing the microwave and magnetostatic Snoek\u27s constants. The modification of Snoek\u27s law for hexagonal ferrites suggested recently by Acher et al. [Phys. Rev. B 62, 11324 (2000)] is also verified. Acher\u27s constant is found from microwave measurements to agree with the value calculated from the magnetostatic properties of bulk ferrite, but microwave and magnetostatic Snoek\u27s constant do not agree. This may be attributed to the effect due to demagnetizing factors of ferrite inclusions that are not considered in the derivation of Snoek\u27s and Acher\u27s laws. The measured frequency-dependent permeability of composites satisfies the Lorentzian dispersion law and is consistent with the Maxwell Garnett approximation [J. C. Maxwell Garnett, Philos. Trans. R. Soc. London 203, 385 (1904)]. According to the theoretical analysis based on the Lorentzian dispersion law and the Maxwell Garnet mixing rule, both Snoek\u27s and Acher\u27s constants must be linear functions of the volume fraction, independent of whether microwave values of the constants are in agreement with the magnetostatic values. In contrast, the experimental measurements reveal a steady decrease of both constants with the volume fraction. The disagreement is discussed in terms of the influence of effective medium in composite on the inherent permeability of ferrite particles