Microwave Behavior of Partially Magnetized Ferrites

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Abstract
The high frequency permeability of partially magnetized ferrites is calculated for some simple domain configurations, comprising only ``up'' and ``down'' domains. The method used is based upon the magnetostatic approximation and neglects exchange effects, but is otherwise substantially rigorous. The components of the effective permeability tensor (ratio of average induction to average magnetic field) in general depend upon details of the domain configuration in addition to the net dc magnetization. When the dc magnetization is cycled between the two states of complete magnetization the high frequency permeability, considered as a function of the dc magnetization, in general shows hysteresis. Detailed calculations of the high frequency permeability have been carried out for the case in which the domain configuration is cylindrically symmetric, i.e., invariant under rotation around the direction of magnetization. For any such domain configuration the two relevant components μeff and κeff of the effective permeability tensor obey the relation μeff2−κeff2=const, regardless of the number of domains and their relative size. This general theorem allows a simple derivation of the (isotropic) permeability in the completely demagnetized state, giving μeff=23{[(ω/γ)2−(Ha+4πM0)2]⧸[(ω/γ)2−Ha2]}1/2+13,where ω is the frequency, Ha the anisotropy field, and M0 the saturation magnetization.