This paper presents a physical model of the properties of polycrystalline ferrites below magnetic saturation, a common condition in many applications of ferrites in microwave devices. The properties are mainly characterized through the elements of the effective permeability tensor as functions of magnetization state, anisotropy field, and frequency. Partially magnetized states are characterized by a suitable distribution of magnetic domains over orientations. The magnetic domain shapes studied were cylinders and spheres. Homogeneity of the medium is obtained in the effective medium approximation, which allows us to treat heterogeneous magnetic materials as a function of the volume fraction of nonmagnetic matter present in the material. The model gives all the components of the permeability tensor in a single calculation phase. The paper presents results for different partially magnetized states at remanence (with no external field applied) and compares them with empirical formulations of permeability tensor components, in their domain of validity.

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This paper describes a mathematical model enabling the calculation of the effective permeability tensor of heterogeneous magnetic materials set in various magnetization states. The theoretical approach we propose permits to predict the microwave behavior of unsaturated magnetic loaded composites as well as those of unsaturated polycrystalline ferrites. The model gives all the complex components of the permeability tensor in a single calculation phase whatever the magnetization state of the material is. This is useful for the computer-aided design of microwave magnetic devices. The calculation of the effective permeability tensor is carried out from a limited number of parameters: saturation magnetization, anisotropy field, damping factor, external dc field strength, concentration, and shape of the magnetic particles or domains. The model is predictive in the way that the magnetization state of the material is determined from the strength of the external dc magnetic field applied on the material.