Noncollinear magnetism in itinerant-electron systems: theory and applications

The article attempts to review the present stage of the density functional theory for noncollinear magnetic states and its application to particular physical problems. The discussion starts with basic theorems of the theory and derivation of the Kohn-Sham equation for a noncollinear magnet. Special features of solving this equation are illustrated using the augmented-spherical-wave method generalized to the noncollinear magnetic structures as an example. Particular attention is devoted to the symmetry of the problem. It is shown that a traditional approach of the space group theory fails in the case of a noncollinear magnetic state. A generalized approach based on the notion of the spin space groups is presented which allows a consequent treatment of the symmetry properties of both nonrelativistic and relativistic problems. This approach allows the development of an exact procedure for a first-principles calculation of an incommensurate spiral structure and gives a sound basis for the calculation and physical interpretation of the noncollinear magnetic structures caused by the effects of relativity. Application of the theory to the first-principles determination of the complex noncollinear magnetic structures of various systems are discussed. Applications include the spiral structure of fee Fe, the uncompensated magnetic structure in U3X4 and compensated magnetic structure in U2P2Sn, and two different types of weak ferromagnetism in Fe2O3 and Mn3Sn. It is shown how the calculation technique can be applied to studies of unenhanced and enhanced non-uniform magnetic susceptibilities as well as susceptibilities in fields noncollinear to the atomic moments. Illustrating results of the calculation of the susceptibility of various systems are presented. The last part of the review is devoted to applications of the theory of noncollinear magnetism to studies of temperature effects in the electronic properties of itinerant magnets.