Magnetostatic energy

Shape anisotropy is related to the magnetostatic energy of a magnet. A needle-shaped sample tends to line the atomic moments along the needle axis and a disk-shaped sample tends to line these moments parallel to the disk surface. 

For a single-domain ferromagnet, any nonspherical particle shape gives rise to shape anisotropy due to the internal magnetostatic energy. The magnetostatic energy, for an ellipsoid of revolution, is equal to... 

With decreasing particle size, the magnetic contributions from the surface will eventually become more important than those from the bulk of the particle, and hence surface anisotropy energy will dominate over the magnetocrystalline anisotropy and magnetostatic energies. A uniaxial anisotropy energy proportional to the particle surface S... 

Under the size reduction of small magnetic particle a critical volume exists when the energy to produce a domain wall becomes higher than the external magnetostatic energy for the single-domain state. This critical size depends on type of magnetic material and is about few tens nanometers. For a spherical particle, this critical diameter could be estimated as [1] ... 

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