  It is demonstrated that the magnetic interactions can be drastically
different for nano-sized systems compared to those of bulk or surfaces. Using a
real-space formalism we have developed a method to calculate non-collinear
magnetization structures and hence exchange interactions. Our results for
magnetic clusters supported on a Cu(111) surface show that the magnetic
ordering as a rule is non-collinear and can not always be described using a
simple Heisenberg Hamiltonian. We suggest that ab initio calculations allowing
for non-collinear coupling between atomic spins is the best tool for analyzing
nano-sized magnets.
