  We present results of density-functional calculations on the magnetic
properties of Cr, Mn, Fe and Co nano-clusters (1 to 9 atoms large) supported on
Cu(001) and Cu(111). The inter-atomic exchange coupling is found to depend on
competing mechanisms, namely ferromagnetic double exchange and
antiferromagnetic kinetic exchange. Hybridization-induced broadening of the
resonances is shown to be important for the coupling strength. The cluster
shape is found to weaken the coupling via a mechanism that comprises the
different orientation of the atomic d-orbitals and the strength of
nearest-neighbour hopping. Especially in Fe clusters, a correlation of binding
energy and exchange coupling is also revealed.
