[en] This thesis comprises three parts, which are each associated with a separate chapter and a brief introduction to those topics addressed in depth: First, spin-orbit coupling in the magnetic and superconducting phase is taken into account and its effect on the corresponding order parameters is studied. Second, multi-orbital effects are shown to determine the Cooper pairing, which is analyzed by using the example of the iron-based compound LiFeAs and CaKFe₄As₄. In a final step, the importance of spin-orbit coupling and orbital effects for the understanding of the spin-space anisotropy and the ordering of magnetic moments in the magnetic phases is revealed.

[en] We analyze the spin susceptibility in LiFeAs and NaFeAs by using the ten-orbital tight-binding model that we fitted to the electronic band structure measured by recent ARPES experiments. We identify an effective five-band model for a weak k_z-dependence. Besides we present the bare and RPA-susceptibility and its q_z dependencies to study the magnetic instabilities and estimate the strength of intra-orbital and inter-orbital nesting.

[en] Measurements on optimally electron doped LaFeAsO_1_-_xF_x samples under pressure up to ∝23 kbar reveal a clear mutual independence between the critical temperature T_c and the ratio of superfluid density over effective band mass of Cooper pairs n_s/m*. The ratio increases about ∝30 % at the maximum pressure whereas T_c remains constant, which clearly implies a breakdown of the Uemura relation in LaFeAsO_1_-_xF_x. Here we analyze theoretically this effect by taking into account the effect of nonmagnetic impurities in a multi-band superconductor. We show that the ratio between intra-band and inter-band scattering rates can explain the behaviour of the observables under pressure by only acting on structural parameters while the amount of chemical disorder is still constant.

[en] We analyze the competition of SDW and SC orders in the iron-based superconductors, taking into account the orbital matrix elements. We find that the SDW order necessarily possesses the nodal structure as a result of angular dependence of the Fermi-liquid interactions. To obtain the phase diagram we solve the system of coupled mean-field gap equations, which describes the competition between SDW and s++ or s+- superconductivity. We revisit the result, obtained previously, for the constant SDW gap. We further discuss the role played by the spin-orbit coupling.

[en] We study the interplay of SDW and iCDW order in iron-based superconductors and find that both orders couple to each other due to spin-orbit coupling. Most importantly, we analyze the influence of the CDW formation on the competition between various magnetic phases in iron-based superconductors.

[en] Using 10-orbital model Hamiltonian we present quasiparticle interference (QPI) calculations in the spin density wave phase (SDW) of Fe-based superconductors (FeSc). We find that the QPI structure can be regarded as a robust way of studying the orbital driven effects on the magnetically ordered phase. In particular, we study the phase-relevant changes induced by the SDW order parameters with orbital structure starting from two-band model up to ab initio based band structure calculation using a realistic model Hamiltonian. We provide the detailed insight for the one dimensional QPI maps seen by STM experiment.

[en] Motivated by recent experimental reports on sizeable spin-orbit coupling (SOC) in the iron pnictides, we study the SOC induced mixing of the spin singlet and the spin triplet pairing for the leading s- and d-wave superconducting instabilities. We focus on highly electron doped systems where only electron d${}_{yz}$/d${}_{xz}$/d${}_{xy}$ pockets are present at the M-point of the two-iron unit cell. Using a orbitally projected effective low energy model for the iron pnictides with pairing driven by atomic onsite interactions, we present the gap structure close to Fermi level and discuss consequences of the induced triplet pairing to experiment.

[en] We analyze and compare the structure of the pairing interaction and superconducting gaps in LiFeAs and Co-doped NaFeAs by using the ten-orbital tight-binding model, derived from ab initio LDA calculations with hopping parameters extracted from the fit to ARPES experiments. We discuss the phase diagram and experimental probes to determine the structure of the superconducting gap in these systems with special emphasis on the quasiparticle interference, computed using the T-matrix approximation. In particular, we analyze how the superconducting state with opposite sign of the gaps on the two inner hole pockets in LiFeAs evolve upon changing the parameters towards NaFeAs compound.

[en] We analyze the magnetic ordering in the iron-based superconductors in presence of spin-orbit coupling. Based on several tight-binding parametrizations of the 3d electron states we show how the spin-orbit coupling introduces the anisotropy of the magnetization of the striped antiferromagnetic state by lifting the degeneracy of all three components of the magnetization m_x, m_y and m_z. The orientation of the magnetic moment is determined by the contribution of the xy, xz, and yz orbitals to the electronic states near the Fermi level of the electron and hole bands and is determined by the electron filling. We find that within an itinerant approach the magnetic ordering is most favorable along the wavevector of the striped AF state. This appears to be a natural consequence of the spin-orbit coupling in the striped AF state where the ferro-orbital order of the xz and yz orbitals is only a consequence of the striped AF order. We further analyze the role of spin-orbit coupling for the C_4 magnetic structure where SDW order parameters with both wavevectors, Q_x = (π,0) and Q_y = (0,π), coexist.

[en] We report on the effect of nearly-hydrostatic pressure P ≤ 23 kbar in an optimally-doped LaFeAsO_1_-_xF_x sample. Our results of muon spin rotation show no dependence of T_c on P and, at the same time, a remarkable enhancement of the superfluid density (n_s). This is a dramatic effect, the saturation value of n_s being increased by ∝ 30 % at the maximum P value. We provide evidence from density-functional theory (DFT) calculations that this increase should not be associated to an induced change in the fermiology of LaFeAsO_1_-_xF_x. Accordingly, we suggest that the experimental data can be explained by assuming a modification of the ratio between intra- and inter-band impurity scattering, only possible in multi-band SC.