Orbital Polarization, Surface Enhancement and Quantum Confinement in   Nano-cluster Magnetism
  Within a rather general tight-binding framework, we studied the magnetic properties of Ni$_{n}$ clusters with $n=9$ through 60. In addition to usual hopping, exchange, and spin-orbit coupling terms, our Hamiltonian also included orbital correlation and valence orbital shift of surface atoms. We show that orbital moment not only contributes appreciably to the total moment in this range of cluster size, but also dominates the oscillation of total moment with respect to the cluster size. Surface enhancement is found to occur not only for spin but, even stronger, also for orbital moment. The magnitude of this enhancement depends mainly on the coordination deficit of surface atoms, well described by a simple interpolation. For very small clusters ($n \leq 20$), quantum confinement of 4s electrons has drastic effects on 3$d$ electron occupation, and thus greatly influences both spin and orbital magnetic moments. With physically reasonable parameters to account for orbital correlation and surface valence orbital shift, our results are in good quantitative agreement with available experiments, evidencing the construction of a unified theoretical framework for nano-cluster magnetism. 
Xiangang Wan, Lei Zhou, Jinming Dong, T.K. Lee and Ding-sheng Wang