  The orbital contribution to the magnetic properties of Fe in systems of
decreasing dimensionality (bulk, surfaces, wire and free clusters) is
investigated using a tight-binding hamiltonian in an $s, p,$ and $d$ atomic
orbital basis set including spin-orbit coupling and intra-atomic electronic
interactions in the full Hartree-Fock (HF) scheme, i.e., involving all the
matrix elements of the Coulomb interaction with their exact orbital dependence.
Spin and orbital magnetic moments and the magnetocrystalline anisotropy energy
(MAE) are calculated for several orientations of the magnetization. The results
are systematically compared with those of simplified hamiltonians which give
results close to those obtained from the local spin density approximation. The
full HF decoupling leads to much larger orbital moments and MAE which can reach
values as large as 1$\mu_B$ and several tens of meV, respectively, in the
monatomic wire at the equilibrium distance. The reliability of the results
obtained by adding the so-called Orbital Polarization Ansatz (OPA) to the
simplified hamiltonians is also discussed. It is found that when the spin
magnetization is saturated the OPA results for the orbital moment are in
qualitative agreement with those of the full HF model. However there are large
discrepancies for the MAE, especially in clusters. Thus the full HF scheme must
be used to investigate the orbital magnetism and MAE of low dimensional
systems.
