The modern version of the KKR (Korringa-Kohn-Rostoker) method represents the electronic structure of a system directly and efficiently in terms of its single-particle Green's function (GF). This is in contrast to its original version and many other traditional wave-function-based all-electron band structure methods dealing with periodically ordered solids. Direct access to the GF results in several appealing features. In addition, a wide applicability of the method is achieved by employing multiple scattering theory. The basic ideas behind the resulting KKR-GF method are outlined and the different techniques to deal with the underlying multiple scattering problem are reviewed. Furthermore, various applications of the KKR-GF method are reviewed in some detail to demonstrate the remarkable flexibility of the approach. Special attention is devoted to the numerous developments of the KKR-GF method, that have been contributed in recent years by a number of work groups, in particular in the following fields: embedding schemes for atoms, clusters and surfaces, magnetic response functions and anisotropy, electronic and spin-dependent transport, dynamical mean field theory, various kinds of spectroscopies, as well as first-principles determination of model parameters.

A Kubo-Greenwood-like equation for the Gilbert damping parameter α is presented that is based on the linear response formalism. Its implementation using the fully relativistic Korringa-KohnRostoker (KKR) band structure method in combination with Coherent Potential Approximation (CPA) alloy theory allows it to be applied to a wide range of situations. This is demonstrated with results obtained for the bcc alloy system FexCo1−x as well as for a series of alloys of permalloy with 5d transition metals. To account for the thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. The corresponding calculations for Ni correctly describe the rapid change of α when small amounts of substitutional Cu are introduced.

A method for the calculations of the Gilbert damping parameter α is presented, which based on the linear response formalism, has been implemented within the fully relativistic Korringa-KohnRostoker band structure method in combination with the coherent potential approximation alloy theory. To account for thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. This allows the determination of α for various types of materials, such as elemental magnetic systems and ordered magnetic compounds at finite temperature, as well as for disordered magnetic alloys at T = 0 K and above. The effects of spin-orbit coupling, chemical and temperature induced structural disorder are analyzed. Calculations have been performed for the 3d transition-metals bcc Fe, hcp Co, and fcc Ni, their binary alloys bcc Fe1−xCox, fcc Ni1−xFex, fcc Ni1−xCox and bcc Fe1−xVx, and for 5d impurities in transition-metal alloys. All results are in satisfying agreement with experiment.

A scheme suggested in the literature to determine the symmetry-imposed shape of linear response tensors is revised and extended to allow for the treatment of more complex situations. The extended scheme is applied to discuss the shape of the spin conductivity tensor for all magnetic space groups. This allows in particular investigating the character of longitudinal as well as transverse spin transport for arbitrary crystal structure and magnetic order that give rise e.g. to the spin Hall, Nernst and the spin-dependent Seebeck effects. In addition we draw attention to a new longitudinal spin transport phenomenon occurring in certain nonmagnetic solids.

We apply the self-interaction corrected local spin density approximation to study the electronic structure and magnetic properties of the spinel ferrites MnFe2O4, Fe3O4, CoFe2O4, and NiFe2O4. We concentrate on establishing the nominal valence of the transition metal elements and the ground state structure, based on the study of various valence scenarios for both the inverse and normal spinel structures for all the systems. For both structures we find all the studied compounds to be insulating, but with smaller gaps in the normal spinel scenario. On the contrary, the calculated spin magnetic moments and the exchange splitting of the conduction bands are seen to increase dramatically when moving from the inverse spinel structure to the normal spinel kind. We find substantial orbital moments for NiFe2O4 and CoFe2O4.