Ruderman–Kittel–Kasuya–Yosida Mechanism for Magnetic Ordering of Sparse Fe Adatoms on Graphene

First-principles calculations are carried out to elucidate the mechanism of the exchange interaction among magnetic adatoms on graphene, using Fe–graphene as an example. By fitting the calculated spin wave spectra of different sparse adsorption configurations to the Heisenberg Hamiltonian, the exchange parameters between different neighbors (Ji) were found to follow a single Ruderman–Kittel–Kasuya–Yosida (RKKY)-type function, indicating that the RKKY mechanism plays the dominant role in governing the magnetic order in these systems. Furthermore, calculated formation energies suggest that the 3 × 3 structure can be a metastable state for the growth of Fe on graphene, which otherwise may easily form clusters.