The purpose of static micromagnetics is to solve for the spatial distribution of the magnetization M at equilibrium. In most cases, as the temperature is much lower than the Curie temperature of the material considered, the modulus |M| of the magnetization is assumed to be everywhere equal to the saturation magnetization M. The problem then consists in finding the spatial orientation of the magnetization, which is given by the magnetization direction vector m = M/M, also called reduced magnetization.
The static equilibria are found by minimizing the magnetic energy,
subject to the constraint |M|=M or |m|=1.
The contributions to this energy are the following: