  To calculate the magnetic ground state of nanoparticles we present a
self-consistent first principles method in terms of a fully relativistic
embedded cluster multiple scattering Green's function technique. Based on the
derivatives of the band energy, a Newton-Raphson algorithm is used to find the
ground state configuration. The method is applied to a cobalt nanocontact that
turned out to show a cycloidal domain wall configuration between oppositely
magnetized leads. We found that a wall of cycloidal spin-structure is about 30
meV lower in energy than the one of helical spin-structure. A detailed analysis
revealed that the uniaxial on-site anisotropy of the central atom is mainly
responsible to this energy difference. This high uniaxial anisotropy energy is
accompanied by a huge enhancement and anisotropy of the orbital magnetic moment
of the central atom. By varying the magnetic orientation at the central atom,
we identified the term related to exchange couplings (Weiss-field term),
various on-site anisotropy terms, and also those due to higher order
spin-interactions.
