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We present ab initio calculations of the orbital moments and magnetocrystalline anisotropy energies for 3d, 4d, and 5d transition-metal adatoms and for some selected small clusters on the (001) surfaces of Ag and Au. The calculations are based on the local density approximation of density functional theory and apply a fully relativistic Koringa-Kohn-Rostoker Green's function method. Due to the reduced coordination of the adatoms and the weak hybridization with the substrate, we find fairly large orbital moments, in particular for the elements towards the end of the series. The general trend can be understood from a simple tight-binding model. The orbital moments are connected with very large anisotropy energies. While the orbital moments are on the Ag substrate somewhat larger than on Au, the magnetic anisotropy has about the same size for both substrates. Calculations for small clusters of Fe, Ru, and Os adatoms show, that due to interaction effects the orbital moments are strongly reduced, e.g., by 50% for the dimer atoms. The size of the reduction correlates well with the coordination number. Similar reductions also occur for the magnetic anisotropy energies

Orbital magnetism of transition-metal adatoms and clusters on the Ag and Au(001) surfaces