Extension of the effective medium approximation for determination of the permeability tensor of unsaturated polycrystalline ferrites

Abstract

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.

High-frequency behavior of magnetic composites

“…For inhomogeneous materials, the magnetic loss peak is typically spread, with its form distorted relatively to the Lorentzian dispersion law to the extent that several isolated loss peaks may appear. A number of theoretical approaches have been developed to predict the frequency dependence of permeability in case of magnetically inhomogeneous structure, from pioneering papers by Polder and Smith [19] and Schloemann [20] to more recent studies [21,22]. Another important reason for distorted magnetic dispersion curves may be the effect of eddy currents in ferromagnetic metals, as discussed in Section 6.…”

Effective-medium approach to the magnetic susceptibility of composites with ferromagnetic inclusions

“…20,21 The permeability tensor of such particle again depends greatly on the domain configuration, and there are only some expressions for uniaxial particles. However, the permeability tensor of such particles has the familiar nondiagonal form and the calculation is essentially the same as in the case of fully magnetized particles.…”

“…[19][20][21] The susceptibility ͑permeability͒ tensor is intrinsically diagonal because of the averaging over domains inside the particle and in many cases it is scalar. 19 Similar conclusions also hold for cubic crystals.…”

Computation of Complex Eigenmodes for Resonators Filled With Gyrotropic Materials

“…Consequently, for an accurate computation of the eigenfrequencies also for low bias field strengths, modified expressions for the partially magnetized state are required. In this regime ferrites can by described by an effective permeability tensor, which depends on local properties [17] and which is discussed in the following subsections beginning with the fully demagnetized state.…”

“…However, it suffers from the inaccuracy of the main diagonal terms. Based on measurements on yttrium iron garnets and magnesium-manganese (zinc) ferrites, Green and Sandy formulated empirical expressions for ↔ µ [17,23]. According to this, the real part of the main diagonal elements can be described well by…”