Magnetic anisotropy

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Magnetic anisotropy is the direction dependence of a material's magnetic properties. A magnetically isotropic material has no preferential direction for its magnetic moment in zero field, while a magnetically anisotropic material will align its moment to an easy axis.

[edit] Sources of magnetic anisotropy

There are different sources of magnetic anisotropy^[1]:

Magnetocrystalline anisotropy: the atomic structure of a crystal introduces preferential directions for the magnetisation.
Shape anisotropy: when a particle is not perfectly spherical, the demagnetizing field will not be equal for all directions, creating one or more easy axes.
Stress anisotropy: tension may alter magnetic behaviour, leading to magnetic anisotropy.
Exchange anisotropy: a relatively new type that occurs when antiferromagnetic and ferromagnetic materials interact^[2].

[edit] Anisotropy energy

Consider a magnetic particle with one easy axis and a (forced) magnetisation. The anisotropy energy can be expressed as $E = K sin 2 (θ)$ , with $K$ the anisotropy constant, and $θ$ the angle between the easy axis and the particle's magnetisation. When shape anisotropy is explicitly considered, the symbol $\mathcal{N}$ is often used to indicate the anisotropy constant, instead of $K$ .

^ McCaig, Malcolm (1977). Permanent magnets in theory and practice. Pentech press. ISBN 0727316044.
^ Meiklejohn, W.H.; Bean, C.P. (1957-02-03). "New Magnetic Anisotropy". Physical Review 105 (3): 904–913. doi:10.1103/PhysRev.105.904.