Calculation of the permeability of polycrystalline ferrites

Abstract

One of the main properties characterizing the behavior of magnetic materials in variable magnetic fields is the magnetic permeability m , which is a complex quantity: m5m8 2im9. The frequency dependence of the permeability is influenced mainly by two processes: motion of the domain boundaries, and rotation of the magnetization vector. There are numerous models that are used to describe and explain the behavior of the permeability as the frequency is varied. However, the calculations based on these models generally provide adequate descriptions of the frequency dependence of the permeability only in a narrow frequency range. This may be because most of the models considered do not take into account the rotation of the magnetization vector. At high frequencies ~for example, frequencies above 10 Hz for yttrium iron garnet! the influence of the rotation of the magnetization vector becomes comparable to the influence of the motion of the domain boundaries and even exceeds it, and at low frequencies the maximum contribution of the rotation of the magnetization vector is specified by the quantity x'M S /HA ~where M S is the saturation magnetization and HA is the anisotropy field! and can amount to only 20% of the contribution of the motion of the domain boundaries. In other models only the rotation of the magnetization vector is considered, and consequently these models describe the experimental data at high frequencies. This paper proposes a model for calculating the permeability with consideration of the contributions of both the motion of the domain boundaries and the rotation of the magnetization vector over a broad frequency range for polycrystalline ferrites. The permeability is calculated as the sum of two contributions: m5mdom1m rot , where mdom is the permeability due to the motion of the domain boundaries and m rot is the permeability due to the rotation of the magnetization vector. The calculations are performed under the assumption that the external magnetic field H0 is equal to zero and the anisotropy field HA is greater than 4pM S , as is typical of the independent-grain model. The applicability of the model is demonstrated in the example of yttrium iron garnet with an aluminum impurity, for which the independent-grain condition holds. Each domain boundary is characterized by its own resonance frequency f 0. With consideration of the independentgrain model, we assume that the spatial orientation of the grain boundaries is random in a polycrystalline medium. Then, with allowance for the eigenfrequency distribution function w( f 0) of the domain boundaries, the mean perme-