On the Remanence of Ferromagnetic Powders

The angular dependence of the maximum remanence parallel to the applied field, $I_p$ , and perpendicular to it, $I_t$ , when the specimen is rotated through an angle $\beta$ about an axis perpendicular to the field direction, is considered theoretically. For a rather wide range of materials the relation $I_t{\mathrm{\hspace{0.17em}=\hspace{0.17em}(dI}}_p\mathrm{/d\beta )}$ should hold. For an assembly of noninteracting uniaxial single domains, it is shown that the distribution of the easy axes can be calculated from $I_p\mathrm{(\beta )}$ or $I_t\mathrm{(\beta )}$ and that ${\text{2∫}}_0^{\text{π/2}}{\mathrm{\hspace{0.17em}I}}_p\hspace{0.17em}\sin {\mathrm{\beta d\beta \hspace{0.17em}=\hspace{0.17em}I}}_s$ , where $I_s$ is the saturation magnetization. The above method yields a Legendre series for the distribution; it is deficient in that the high terms are quite sensitive to small changes in the remanences. Measurements of $I_p$ and $I_t$ with a vibrating-sample magnetometer were carried out on commercially oriented Ferroxdure, on magnetically oriented Ferroxdure powder, on oriented elongated single-domain iron particles and on anisotropic Alnico. For the first three materials $I_t$ was a few percent lower, for the last up to 20% higher, than the value theoretically expected from the relation between $I_p$ and $I_t$ . For Ferroxdure this small discrepancy is attributed to the reduction of $I_t$ by splitting into domains; for the elongated single-domain sample it is attributed to particle agglomeration. In order to furnish further magnetic evidence for the agglomeration of particles in magnetic powders, remanence curves are considered. Relations between remanences obtained by different methods are derived for the interacting-pair model. These relations differ from Wohlfarth's relations, which hold for an assembly of noninteracting single-domain particles. Comparison with experiment favors the pair model.