Spin polarization and magnetism

Magnetism can come from localized electrons (e.g. from the 4f electron in rare earth elements) or from delocalized electrons. In the latter case the itinerant electrons can be well described by band theory. Without spin–orbit coupling the magnetism originates from the spin polarization, whereas the orbital moment is often quenched. For example, Fe, Co, Ni are ferromagnets (FM) which fall in this category. In this case DFT is generalized to allow for a spin polarization, in which the spin-up and spin-down electrons move in spin-dependent potentials, which can be deduced from the corresponding spin densities, for example using the local spin density approximation. Another case are antiferromagnets (AFM) (e.g. bcc Cr) in which neighboring atoms have the opposite spin alignment but the magnitude of the moment at each site is the same. The net bulk magnetization vanishes for AFM. When the magnitude differs we have ferrimagnetism and a net magnetization. All these cases belong to collinear magnets. The orientation of the magnetic moment with respect to the crystal axis is only defined when spin–orbit coupling is included. There are more complicated magnetic structures such as canted magnetic moments or spin spirals. In such cases the direction of the magnetization varies with position and this is called non-collinear magnetism.