The magnetic properties of ferromagnets (antiferromagnets and ferrimagnets, as well) depend on the crystallographic direction in which they are measured. This directional dependence, or anisotropy, has origins in the spin–orbit-lattice coupling. Thus, the internal energy of the magnetic material depends on the direction of spontaneous magnetization, and the coefficients, called magnetocrystalline anisotropy constants, that determine the phenomenological expressions for the energy are unique to each material. The dimensions of a macroscopic ferromagnet change when subjected to an external field; the resultant strain is called magnetostriction or magnetoelastic anisotropy. Further, the energy density of a magnetic material is affected by the application of an external stress. The resulting magnetoelastic energy is uniaxial in character and is given by the product of the magnetostriction and the applied stress. Other sources of anisotropy are shape, also known as magnetostatic energy, discussed in §1, and annealing and exchange effects. Annealing may cause atomic pair ordering that leads to a preference in magnetization direction and exchange effects are discussed later in §10. If a number of anisotropies are operative in a materials system, the effective anisotropy can be determined by a graphical method in double-angle vectors space. Anisotropy can also be observed in amorphous magnets. Finally, the phenomenon of anisotropy is of major practical interest because anisotropy is central to the formation of domains (§7) and its control is critical in the design of magnetic materials for technological applications.
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