Orbital contribution to the magnetic properties of iron as a function of dimensionality

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 1B 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.