Size of Bloch Wall and Parameters of the Magnetic Susceptibility in Ferrimagnetic Spinels and Garnets

In this paper we investigate the influence of the granular structure on the curve of magnetic susceptibility as a function of an alternating field, for different compositions of spinel and garnet materials. An ideal curve is defined which presents when H increases first a flat part below H = Her, then a part showing an almost linear increase of (a' 1), and finally a peak of (mu -1)(c),. Five characteristic parameters of the curve are set : initial susceptibility, maximum susceptibility, critical field her, field H-m corresponding to the maximum value of (mu' - 1)(c), slope of the curve beyond h(er). It is shown, for a given composition and measurement temperature, that all these parameters are related to the mean grain diameter of the sample. The differences between experimental and ideal curves are explained by means of a loss of the quality of the elementary crystallites. The role of the porosity is particularly investigated: the grain porosity acts strongly only on the initial susceptibility and becomes inoperative beyond h(er). The total porosity has no determining influence on the curves. The results are explained by extending a model we have already published, which assumes a wall in a spherical shaped grain. The surface of the wall is defined by its intersection with the grain boundary. For H < h(er), the wall is deformed by curvature being fixed along a great circle to the grain boundary. For H > h(er),, the wall moves about inside the grain and reaches a smaller diameter d, determined by an equilibrium between the magnetic strength (proportional to d(2)) and the catching strength (proportional to d).