  We present a detailed theoretical investigation on the magnetic properties of
small single-layered Fe, Co and Ni clusters deposited on Ir(111), Pt(111) and
Au(111). For this a fully relativistic {\em ab-initio} scheme based on density
functional theory has been used. We analyse the element, size and geometry
specific variations of the atomic magnetic moments and their mutual exchange
interactions as well as the magnetic anisotropy energy in these systems. Our
results show that the atomic spin magnetic moments in the Fe and Co clusters
decrease almost linearly with coordination on all three substrates, while the
corresponding orbital magnetic moments appear to be much more sensitive to the
local atomic environment. The isotropic exchange interaction among the cluster
atoms is always very strong for Fe and Co exceeding the values for bulk bcc Fe
and hcp Co, whereas the anisotropic Dzyaloshinski-Moriya interaction is in
general one or two orders of magnitude smaller when compared to the isotropic
one. For the magnetic properties of Ni clusters the magnetic properties can
show quite a different behaviour and we find in this case a strong tendency
towards noncollinear magnetism.
