  We demonstrate the occurrence of compensated spin configurations in Fe
clusters and monolayers on Ru(0001) and Rh(111) by a combination of X-ray
magnetic circular dichroism experiments and first-principles calculations. Our
results reveal complex intra-cluster exchange interactions which depend
strongly on the substrate 4$d$-band filling, the cluster geometry as well as
lateral and vertical structural relaxations. The importance of substrate
4$d$-band filling manifests itself also in small nearest-neighbor exchange
interactions in Fe dimers and in an nearly inverted trend of the
Ruderman-Kittel-Kasuya-Yosida coupling constants for Fe adatoms on the Ru and
Rh surface.
