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 theoretical description of magneto-optical effects in metallic transition metal systems on the basis of an itinerant description for the underlying electronic structure is presented and applications to the magneto-optical Kerr effect and the circular dichroism in x-ray absorption are discussed. Simple arguments based on symmetry considerations as well as electronic excitation schemes are given to show that magneto-optical effects are caused by the interplay of magnetic ordering and spin-orbit coupling. The various band structure techniques developed to deal with this situation are reviewed with an emphasize on fully relativistic methods based on the Dirac equation. The theoretical framework to calculate magneto-optical spectra on the basis of the underlying band structure is outlined in some detail. In addition, a number of sum rules derived by various authors are presented that allow one to estimate spin and orbital magnetic moments of an absorbing atom from the magnetic x-ray dichroism spectra. For the magneto-optical Kerr effect, as well as the magnetic xray dichroism, application of the theoretical formalism is presented for a great variety of systems, i.e. pure elements, compounds, alloys and multilayer systems. For both kinds of spectroscopies it is demonstrated that model calculations which allow one to manipulate the exchange splitting and the spin-orbit coupling strength give valuable information for a better understanding of the rather complex spectra. Concerning the sum rules, this technique together with the direct calculation of the dichroism spectra allow for a stringent test of the various assumptions on which these rules are based.

The notion of non-trivial topological winding in condensed matter systems represents a major area of present-day theoretical and experimental research. Magnetic materials offer a versatile platform that is particularly amenable for the exploration of topological spin solitons in real space such as skyrmions. First identified in non-centrosymmetric bulk materials, the rapidly growing zoology of materials systems hosting skyrmions and related topological spin solitons includes bulk compounds, surfaces, thin films, heterostructures, nano-wires and nano-dots. This underscores an exceptional potential for major breakthroughs ranging from fundamental questions to applications as driven by an interdisciplinary exchange of ideas between areas in magnetism which traditionally have been pursued rather independently. The skyrmionics roadmap provides a review of the present state of the art and the wide range of research directions and strategies currently under way. These are, for instance, motivated by the identification of the fundamental structural properties of skyrmions and related textures, processes of nucleation and annihilation in the presence of non-trivial topological winding, an exceptionally efficient coupling to spin currents generating spin transfer torques at tiny current densities, as well as the capability to purposedesign broad-band spin dynamic and logic devices. arXiv:2001.00026v3 [cond-mat.str-el]

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.

Ferromagnetic thin films of Heusler compounds are highly relevant for spintronic applications owing to their predicted half-metallicity, that is, 100% spin polarization at the Fermi energy. However, experimental evidence for this property is scarce. Here we investigate epitaxial thin films of the compound Co2MnSi in situ by ultraviolet-photoemission spectroscopy, taking advantage of a novel multi-channel spin filter. By this surface sensitive method, an exceptionally large spin polarization of () % at room temperature is observed directly. As a more bulk sensitive method, additional ex situ spin-integrated high energy X-ray photoemission spectroscopy experiments are performed. All experimental results are compared with advanced band structure and photoemission calculations which include surface effects. Excellent agreement is obtained with calculations, which show a highly spin polarized bulk-like surface resonance ingrained in a half metallic bulk band structure.