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Complex trend of magnetic order in Fe clusters on 4$d$ transition-metal surfaces

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.