Two configurations are, a priori, favorable for a possible magnetic gr
ound state of rhodium: small clusters and very thin films. In both cas
es, the reduction of the average coordination number could allow the o
nset of magnetism. For clusters, experimental works indicate that Rh,
clusters with N similar or equal to 60 have a non-zero average magneti
c moment. By using a d-band Hubbard Hamiltonian, the size and the geom
etric dependence of the magnetic properties of Rh clusters is studied.
Different structures and atomic relaxations are considered. Significa
nt magnetic moments are found up to N similar or equal to 50. For thin
films of rhodium on silver, the Ag/Rh interdiffusion inhibits a long
range magnetic order. The only favorable case is to consider a magneti
c substrate. For thin Rh layers on Fe(001) only mono- and bi-layers ar
e polarized. For larger thicknesses, only an interfacial polarization
remains. Finally, in agreement with other studies, the Rh semi-infinit
e crystal does not display a local magnetic moment.