Shape Anisotropy:

The magnetostatic energy of a ferromagnetic ellipsoid, as shown in Fig.4.1, with magnetization M_S is given as

(4.1)

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Figure 4.1: Magnetization of a prolate ellipsoid of revolution with c > a , and no magnetocrystalline anisotropy. c -axis is the easy direction of magnetization.

The anisotropy energy is related to the difference in energy ΔE when the ellipsoid is magnetized along its hard and easy directions. N is the demagnetization factor for the easy direction. N ' =(1/2)(1-N) is the demagnetization factor for the hard directions. Hence,

→

(4.2)

The shape anisotropy is zero for a sphere, as N = 1/3. Shape anisotropy is only fully effective in samples which are so small that they do not break up into domains.