  Ferromagnetic Nickel is the most celebrated iron group metal with pronounced
discrepancies between the experimental electronic properties and predictions of
density functional theories. In this work, we show in detail that the recently
developed multi-band Gutzwiller theory provides a very good description of the
quasi-particle band structure of nickel. We obtain the correct exchange
splittings and we reproduce the experimental Fermi-surface topology. The
correct (111)-direction of the magnetic easy axis and the right order of
magnitude of the magnetic anisotropy are found. Our theory also reproduces the
experimentally observed change of the Fermi-surface topology when the magnetic
moment is oriented along the (001)-axis. In addition to the numerical study, we
give an analytical derivation for a much larger class of variational
wave-functions than in previous investigations. In particular, we cover cases
of superconductivity in multi-band lattice systems.
