Magnetic anisotropy arises due to a combination of crystal structure and spin-orbit interaction. It can be generally written as:
where F, the anisotropy energy density, is a function of the orientation of the magnetization. Minimum-energy directions for F are called easy axes.
Time-reversal symmetry ensures that F is an even function of m. The simplest such function is
where K is called the anisotropy constant. In this approximation, called uniaxial anisotropy, the easy axis is the z direction.
The anisotropy energy favors magnetic configurations where the magnetization is everywhere aligned along an easy axis.