Generalization of Snoek’s limit for modeling initial permeability of magnetic materials

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Abstract
Permeability relates the magnetic field intensity in a magnetic material to the resulting flux density. The initial part of the permeability extending from dc fields to the radio‐frequency fields of a few hundred megahertz is due to domain wall displacement. A spin resonance occurs due to the presence of an anisotropy field, with the result that the permeability drops rapidly at frequencies above this resonance. It has been observed experimentally that the variation of the ratio of the magnetic oxides in a given ferrite crystal structure changes the initial permeability and the resonance frequency. The product of the resonance frequency and the initial permeability is approximately constant, i.e., Snoek’s limit. Thus, if the resonance frequency increases, the initial permeability decreases in inverse proportion. Experimental results in the literature confirm the variation of the initial permeability with composition. A modification of the equations for Snoek’s limit suggest that a variable quasistatic magnetic field would have the same effect on initial permeability as a variation in composition. This effect has been verified experimentally for magnesium‐zinc ferrite samples in a brass coaxial transmission line with an applied dc magnetic field of 0–500 Oe. The initial permeability of many magnetic materials can thus be modified in the VHF range by the application of an externally applied magnetic field.

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