Interatomic Spin Coupling in Manganese Clusters Registered on Graphene

Different interatomic spin interactions in graphene-regulated Mn atomic clusters are investigated by low-temperature scanning tunneling microscopy and magnetic-field-dependent inelastic spin excitation spectroscopy. All dimers observed exhibit an antiferromagnetic (AFM) singlet ground state and spin transition from the singlet to triplet states, but their AFM coupling strength shows a unique dependence on their site registration on the graphene. Intriguing spin coupling can be found in the graphene-mediated Mn trimers, which manifest multilevel spin excitations. In combination with Heisenberg spin modeling and first-principles numerical simulation, an exclusive noncollinear spin configuration of the Mn trimer regulated by the graphene template can be determined, and our observed experimental exchange energies cannot be understood by a direct spin exchange mechanism, but suggest a nonlocal Ruderman-Kittel-Kasuya-Yosida indirect spin exchange mechanism through substrate modulation, which has not yet been achieved in graphene so far.