Calculation of orbital polarization effects in small Co clusters

The effects of orbital polarizations on the magnetic properties of small Co clusters are investigated in the framework of a self-consistent electronic model Hamiltonian including local Coulomb interactions at three different levels of approximation: (i) full orbital dependence of the direct and exchange Coulomb interactions U-mm' and J(mm') as given by atomic symmetry, (ii) orbital-independent interactions U = U-mm' over bar and J = J(mm') over bar and (iii) orbital polarization (OP) approximation of the form H-OP = -(B/2) Sigma(i)(L) over cap (2)(i delta), where (L) over cap (i delta) refers to the orbital momentum operator at atom i and B to the Racah coefficient. Results are given for the orbital magnetic moments < L-delta > along high-symmetry magnetization directions delta and for the corresponding magnetic anisotropy energy Delta E. A compact five-fold symmetric CO7 cluster is considered as representative example. It is shown that with an appropriate choice of B the OP approximation yields a very good agreement with the rigorous orbital-dependent calculations. Moreover, one observes that the orbital-independent approach accounts qualitatively for the main general trends in < L-delta > and MAE. Advantages and limitations of the various approaches are discussed. (c) 2005 Elsevier B.V. All rights reserved.