Magnetization curling in superparamagnetic spheres

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Abstract
The change of magnetization distribution by thermal agitation, at zero applied field, is studied for a particular functional form, both for a uniaxial anisotropy, and for a cubic one. It is found that if the anisotropy is relatively small, there is always a certain region of particle size at which the energy barrier for magnetization reversal decreases with increasing size; and this anomaly is not restricted to cubic anisotropy only, as concluded by certain previous theories. The relaxation time for magnetization reversal does not always follow completely these changes in the barrier. In particular, no decrease is found for Ni-Fe alloy, with 37-at.% Ni, although the anomaly might come in if the assumed physical constants of this alloy are somewhat modified. The experiment on Fe particles is qualitatively accounted for by this theory, but the region of anomaly is shifted by an amount which seems larger than the experimental error. A similar anomaly is predicted for uniaxial anisotropy, which should be observed if the experiment is carried out for materials with low-enough anisotropy constant (which is rather rare among uniaxial materials).