Recent experiments on isolated Co clusters have shown huge orbital magnetic moments in comparison with their bulk and surface counterparts. These clusters hence provide the unique possibility to study the evolution of the orbital magnetic moment with respect to the cluster size and how competing interactions contribute to the quenching of orbital magnetism. We investigate here different theoretical methods to calculate the spin and orbital moments of Co clusters, and assess the performances of the methods in comparison with experiments. It is shown that density-functional theory in conventional local density or generalized gradient approximations, or even with a hybrid functional, severely underestimates the orbital moment. As natural extensions/corrections, we considered the orbital polarization correction, the LDA+U approximation as well as the LDA+DMFT method. Our theory shows that of the considered methods, only the LDA+DMFT method provides orbital moments in agreement with experiment, thus emphasizing the importance of dynamic correlations effects for determining fundamental magnetic properties of magnets in the nanosize regime.

From microscopic point-dipole model calculations of the screening of the Coulomb interaction in non-polar systems by polarizable atoms, it is known that screening strongly depends on dimensionality. For example, in one dimensional systems the short range interaction is screened, while the long range interaction is anti-screened. This anti-screening is also observed in some zero dimensional structures, i.e. molecular systems. By means of ab-initio calculations in conjunction with the random-phase approximation (RPA) within the FLAPW method we study screening of the Coulomb interaction in FexOy clusters. For completeness these results are compared with their bulk counterpart magnetite. It appears that the onsite Coulomb interaction is very well screened both in the clusters and bulk. On the other hand for the intersite Coulomb interaction the important observation is made that it is almost contant throughout the clusters, while for the bulk it is almost completely screened. More precisely and interestingly, in the clusters anti-screening is observed by means of ab-initio calculations.

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