Magnetic anisotropy in density-functional theory

Magnetic anisotropy is discussed in terms of relativistic density-functional theory. Spin-orbit coupling in the kinetic energy operator of the Dirac equation is responsible for a nonzero value of the orbital angular momentum in cubic systems. Additional spin-orbit coupling terms originate from the Breit interaction between the electrons. The Hartree approximation to the Breit energy yields a magnetic dipole-dipole interaction, which is the cause of the magnetic shape anisotropy. All these terms have to be included in a discussion of the magnetic anisotropy of cubic systems.