Modern theory of orbital magnetic moment in solids

The magnetic moment in a solid is usually associated with the electron spins but there is an additional contribution due to the orbital motion of the electrons. For a finite system such as an atom or molecule the orbital moment can be readily calculated. However, for a periodic system the formula used for finite systems becomes ill-defined due to the presence of the position operator. In the last decade a modern theory of orbital magnetization that allows for a rigorous calculation of the magnetic moment of periodic crystals has been developed. This article provides a survey of the theoretical development of this new topic as well as recent, albeit a few, applications of the new formula to real materials. Although the original theory was worked out for non-interacting systems, there has been recent progress in the theory of orbital magnetic moment of interacting electrons in solids. To include the effects of electron-electron interactions two approaches have been proposed, one based on current spin density functional theory and another on the many-body Green's function method. The two approaches are very different but both methods provide convenient yet rigorous means of including the effects of exchange and correlations beyond the commonly used local density approximation of density functional theory.