The fully relativistic spin-polarized multiple-scattering theory is developed for inhomogeneous superconductors, including superconducting/normal-metal/ferromagnet heterostructures. The method allows the solution of the first-principles Dirac-Bogoliubov-de Gennes equations combined with a semiphenomenological parametrization of the exchange-correlation functional. Simple conditions are derived for the case when the right-hand-side and left-hand-side solutions must be treated separately when setting up the corresponding Green's function. As an application of the theory, we calculate the order parameters of Nb/Fe and Nb/Au/Fe systems. We find Fulde-Ferrell-Larkin-Ovchinnikov-like oscillations in the iron layers, but more interestingly an oscillatory behavior is observed in the gold layers as well. The band-structure calculations suggest that this is the consequence of an interplay between the quantum-well states and ferromagnetism.

We present a fully relativistic first-principles-based theoretical approach for the calculation of the spectral properties of magnetic impurities on the surface of a superconducting substrate, providing a material specific framework for the investigation of the Yu-Shiba-Rusinov (YSR) states. By using a suitable orbital decomposition of the local densities of states we discuss in great detail the formation of the YSR states for an Mn adatom and for two kinds of Mn dimers placed on the Nb(110) surface and compare our results to recent experimental findings. In the case of the adatom we find that the spin-orbit coupling slightly shifts some of the YSR peaks and also the local spin polarization on the Nb atoms has marginal effects on their positions. Moreover, by scaling the exchange field on the Mn site we could explain the lack of the d x 2 −y 2 -like YSR state in the spectrum. While our results for a close packed ferromagnetic dimer are in satisfactory agreement with the experimentally observed splitting of the YSR states, in the case of an antiferromagnetic dimer we find that the spin-orbit coupling is not sufficiently large to explain the splitting of the YSR states seen in the experiment. Changing the relative orientation of the magnetic moments in this dimer induces splitting of the YSR states and also shifts their energy, leading even to the formation of a zero bias peak in the case of the deepest YSR state.

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We present combined spin model and first principles electronic structure calculations to study the weak ferromagnetism in bulk Mn 3 Z (Z=Sn, Ge, Ga) compounds. The spin model parameters were determined from a spin-cluster expansion technique based on the relativistic disordered local moment formalism implemented in the screened Korringa-Kohn-Rostoker method. We describe the magnetic ground state of the system within a three-sublattice model and investigate the formation of the weak ferromagnetic states in terms of the relevant model parameters. First, we give a group-theoretical argument how the point-group symmetry of the lattice leads to the formation of weak ferromagnetic states. Then we study the ground states of the classical spin model and derive analytical expressions for the weak ferromagnetic distortions by recovering the main results of the group-theoretical analysis. As a third approach we obtain the weak ferromagnetic ground states from self-consistent density functional calculations and compare our results with previous first principles calculations and with available experimental data. In particular, we demonstrate that the orbital moments follow a decomposition predicted by group theory. For a deeper understanding of the formation of weak ferromagnetism we selectively trace the effect of the spin-orbit coupling at the Mn and Z sites. In addition, for the case of Mn 3 Ga, we gain information on the role of the induced moment of Ga from constrained local density functional calculations.

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