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Although the exchange interaction keeps spins aligned, it does not align them in a particular direction.
Without magnetic anisotropy, the spins in a magnet randomly change direction in response to thermal fluctuations and the magnet is superparamagnetic.
There are several kinds of magnetic anisotropy, the most common of which is magnetocrystalline anisotropy.
This is a dependence of the energy on the direction of magnetization relative to the crystallographic lattice.
Another common source of anisotropy, inverse magnetostriction, is induced by internal strains.
Single-domain magnets also can have a shape anisotropy due to the magnetostatic effects of the particle shape.
As the temperature of a magnet increases, the anisotropy tends to decrease, and there is often a blocking temperature at which a transition to superparamagnetism occurs.

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