Calculation of the magnetic anisotropy energy in small clusters

The magnetic anisotropy of small FeN clusters is studied in the framework of a d-electron tight-binding Hamiltonian including hopping, Coulomb and spin-orbit interactions on the same electronic level. Results for the magnetic anisotropy energy (MAE), the orbital angular moment and the spin magnetic moment are given as a function of cluster size and bond length. In particular we show that the MAE may be qualitatively related to the projections of the orbital angular moment along the magnetization directions, and that the in plane anisotropy can be of the same order of magnitude as the perpendicular anisotropy.