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We use first-principles calculations based on density functional theory toinvestigate the magnetic exchange interaction of Fe clusters on Rh(111) andRu(0001). We consider dimers, trimers, tetramers, and pentamers of differentshape in fcc and hcp stacking as well as infinite atomic and biatomic chains.From the dimer calculations we extract the exchange interaction as a functionof adatom distance by mapping total energies to a Heisenberg model. Thenearest-neighbor (NN) exchange constant is about one order of magnitude smallerthan reported for other substrates due to the strong hybridization between theFe atoms and the partly filled $4d$-band of the surface. We also find atransition from a ferromagnetic NN exchange interaction for Fe dimers onRh(111) to an antiferromagnetic one on Ru(0001). The distance-dependentexchange coupling displays a RKKY-like oscillatory behavior which is nearlyinverted for Fe dimers on the Rh(111) surface compared to those on Ru(0001).Unexpectedly, for Fe clusters beyond dimers, a complex trend of the magneticground state is observed which alternates between ferro- and antiferromagneticconfigurations depending on cluster size and shape. In view of the exchangeconstants obtained for dimers, it is surprising that on both surfaces smallcompact clusters are ferromagnetic while open structures such as linear trimersor tetramers become antiferromagnetic. We demonstrate that both vertical andlateral structural relaxations of the clusters are crucial in order tounderstand this unexpected trend of magnetic order and connected to thecompetition of direct ferromagnetic exchange among Fe atoms in the cluster andthe hybridization with the substrate.

Unexpected trend of exchange interactions in Fe clusters on Rh(111) and Ru(0001)