Field-induced magnetization structure in small isotropic spheres

Computations of cylindrically-symmetric magnetization distributions are reported for a perfect and isotropic ferromagnetic sphere. The total energy is minimized numerically for various applied fields, with no constraint other than imposing that symmetry. It is found that the curling configuration at zero field is maintained throughout the whole magnetization process, with only a tilt towards the field direction, which increases with increasing field. There is no hysteresis in such an ideally-soft sphere, and the theoretical initial susceptibility is infinite.