Multi-orbital physics in Fermi liquids prone to magnetic order

The interplay of spin-orbit-coupling and strong electronic correlations is studied for the single-layer and the bilayer compound of the strontium ruthenate Ruddlesden-Popper series by a combination of first-principles band-structure theory with mean-field rotationally invariant slave bosons. At equilibrium strongly renormalized (spin-orbit-split) quasiparticle bands are traced and a thorough description of the low-energy regime for the nearly ferromagnetic bilayer system in accordance with experimental data is presented. The metamagnetic response of Sr$_3$Ru$_2$O$_7$ in finite magnetic field $H$ is verified and a detailed analysis of the underlying correlated electronic structure provided. Intriguing multi-orbital physics on both local and itinerant level, such as e.g. competing paramagnetic and diamagnetic contributions, is observed with important differences depending on the magnetic-field angle $\theta$ with the crystallographic c axis.