Phenomenological theory of ferromagnets without anisotropy

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Abstract
For a ferromagnet without anisotropy, which may be a spin-(1/2 lattice or an amorphous substance, the distribution of magnetization depends on the shape of the sample. The phenomenological equations of micromagnetics which contain the exchange energy and the magnetic energy are generalized to allow for a change in the magnitude of the magnetization. This permits the treatment of line singularities in the field-free configurations with circular concentric magnetization lines. For an ellipsoid with a rotation axis the free energy of such an arrangement is compared with that of the homogeneously magnetized sample, which is the stable form for a sufficiently small sample (roughly with a radius ≤20 lattice constants).

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