Magnetization and incremental susceptibilities of ferromagnets with angularly distributed uniaxial anisotropy above remanence

We calculate magnetization and incremental longitudinal and perpendicular susceptibilities for ferromagnets above remanence as functions of longitudinally applied field, assuming a local uniaxial anisotropy to have certain angular distributions. We give analytical formulas, together with computation results, under a wide range of conditions. For anisotropy uniformly oriented in all directions, the classical derivation of the law of approach to saturation is improved by adding a third term, but the resulting formula is inaccurate for most other conditions even if values of the coefficients of the second and third terms are changed. If the longitudinal field is high, the perpendicular incremental susceptibility at uniformly oriented anisotropy can be well approximated by the ratio of spontaneous magnetization to this field, which is the ideal result obtained for zero anisotropy, but a huge departure from this value can be encountered at low fields under certain conditions. Thus, the measurements of perpendicular incremental susceptibility as a function of longitudinal field can be a sensitive probe to the anisotropy and its distribution in ferromagnetic wires.