  We present electronic structure calculations in combination with local and
non-local many-body correlation effects for the half-metallic ferromagnet
CrO$_2$. Finite-temperature Dynamical Mean Field Theory results show the
existence of non-quasiparticle states, which were recently observed as almost
currentless minority spin states near the Fermi energy in resonant scattering
experients. At zero temperatures, Variational Cluster Approach calculations
support the half-metallic nature of CrO$_2$ as seen in superconducting point
contact spectroscopy. The combination of these two techniques allowed us to
qualitatively describe the spin-polarization in CrO$_2$.
