Magnetic anisotropy

Magnetic anisotropy is the directional dependence of a material's magnetic properties. The magnetic moment of magnetically anisotropic materials will tend to align with an "easy axis", which is an energetically favorable direction of spontaneous magnetization. The two opposite directions along an easy axis are usually equivalent, and the actual direction of magnetization can be along either of them (see spontaneous symmetry breaking).

In contrast, a magnetically isotropic material has no preferential direction for its magnetic moment unless there is an applied magnetic field.

Magnetic anisotropy is a prerequisite for hysteresis in ferromagnets: without it, a ferromagnet is superparamagnetic.

There are several sources of magnetic anisotropy:

Suppose that a ferromagnet is single-domain in the strictest sense: the magnetization is uniform and rotates in unison. If the magnetic moment is ${\displaystyle \scriptstyle {\boldsymbol {\mu }}}$ and the volume of the particle is ${\displaystyle \scriptstyle V}$, the magnetization is ${\displaystyle \scriptstyle \mathbf {M} ={\boldsymbol {\mu }}/V=M_{s}\left(\alpha ,\beta ,\gamma \right)}$, where ${\displaystyle \scriptstyle M_{s}}$ is the saturation magnetization and ${\displaystyle \scriptstyle \alpha ,\beta ,\gamma }$ are direction cosines (components of a unit vector) so ${\displaystyle \scriptstyle \alpha ^{2}+\beta ^{2}+\gamma ^{2}=1}$. The energy associated with magnetic anisotropy can depend on the direction cosines in various ways, the most common of which are discussed below.

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