  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.
