Basic concepts for high permeability in soft ferrites

Abstract
The main concepts used to obtain high values of initial magnetic permeability in ferrimagnetic toroidal samples, arc presented. Generally the main contribution to the permeability is due to the mechanism of domain wall bulging which is proportional to (M_s² / K) x D, where Ms is the saturation magnetization, K the magnetic anisotropy constant and D the domain wall size (length) fixed either by the mean grain size, or by the mean distance between two wall pinning centers. Then, three concepts can be applied to increase the permeability. The first is based on the cancellation of anisotropy K, by using the phenomenon of compensation of the negative anisotropy of Fe³⁺ ions by ions with positive anisotropy, as for example for MnZn ferrite or TbSc(YIG). The second concept is to use the relative variation of magnetization M_s²(T) and anisotropy K(T) : for some specific temperatures, M_s²(T) /K(T) can have a maximum as for example near the Curie temperature "the Hopkinson peak" for all ferrites. The third concept is to increase the distance D, for example by increasing the mean grain size during the synthesis of polycrystalline samples of good crystalline quality. A striking linear law between permeability and grain size is observed in many materials : spinels, garnets, hexaferrites and even metals. So, the appropriate choice of adjustable parameters related, either to the ionic structure or to the granular structure, allows to obtain high permeability values.