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 Umm′ and Jmm′ as given by atomic symmetry, (ii) orbital-independent interactions U = U mm ′ ¯ and J = J mm ′ ¯ , and (iii) orbital polarization (OP) approximation of the form H OP = - ( B / 2 ) ∑ i L ˆ i δ 2 , where L ˆ i δ refers to the orbital momentum operator at atom i and B to the Racah coefficient. Results are given for the orbital magnetic moments 〈Lδ〉 along high-symmetry magnetization directions δ and for the corresponding magnetic anisotropy energy ΔE. 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 〈Lδ〉 and MAE. Advantages and limitations of the various approaches are discussed.