A coherent model for the complex permeability in polycrystalline ferrites

It is demonstrated that a grain size dependence exists for the rotational permeability of a series of MnZn polycrystalline ferrites, analogous to that predicted by the Globus model for wall permeability. To account for this behavior, a model has been developed which considers crystalline ferrite grains with intrinsic complex permeability, μ_i, surrounded by thin, nonmagnetic grain boundaries. The effectively measured permeability of the polycrystal (μ_e) is related in the model to the intrinsic permeability, the grain size ( D), and the grain boundary thickness (δ) according to the equation μ_e=μ_iD/μ_iδ+D. The almost linear dependence of permeability with grain size for fine-grained polycrystals emerges if one considers the limit where D is so small that D≪μ_iδ, and consequently μ_e=D/δ (providing δ remains constant). For large grains, where D≫μ_iδ, it is found that the model predicts a constant rotational permeability equivalent to that in a single crystal of the same material. In the situation where the intrinsic permeability of the ferrite displays a relaxational behavior and follows the Snoeks relationship, it is found that both the low-frequency permeability and the resonance frequency of the polycrystal are modified, but in a manner whereby the Snoeks relationship remains valid