Singular points in the magnetization curve of a polycrystalline ferromagnet

Abstract

The reversible magnetization curve M(H) of a polycrystalline ferromagnet has been investigated with the objective of examining the properties of the singularities located at H = −HA , the anisotropy field, along the hard direction. Using a simple model that approximates the system as a continuous assembly of noninteracting particles, we show that the singular point becomes apparent in the successive derivatives dnM/dHn plotted as functions of H. Indeed, differentiation accentuates more and more the singularity hidden in the magnetization curve, and the minimum order n* at which it can be detected is the order for which the function dn*M/dHn* has a discontinuity in the slope at the singular point. The general formula for the dependence of n* on the symmetry properties of the hard direction is given together with the analytical expression for the shape and amplitude of the singularity in the most important cases. The same sort of phenomenon is shown to be present in the reversible transverse susceptibility, and the general expression for n t * is also given. For all the symmetry cases, n t * turns out to be lower than n*. Experimental tests of the theory have been carried out for binary axes of both uniaxial and cubic materials—namely, BaFe12O19, Fe, and CoFe2O4. The singularity appears in d 2 M/dH 2, as expected, and position and amplitude are in good agreement with the values predicted by theory. The suggestion is made that singular point detection (SPD) could be used as a new technique for measuring the anisotropy in polycrystalline samples.