Relay-Like Exchange Mechanism through a Spin Radical between TbPc₂ Molecules and Graphene/Ni(111) Substrates

We investigate the electronic and magnetic properties of TbPc₂ single ion magnets adsorbed on a graphene/Ni(111) substrate, by density functional theory (DFT), ab initio complete active space self-consistent field calculations, and X-ray magnetic circular dichroism (XMCD) experiments. Despite the presence of the graphene decoupling layer, a sizable antiferromagnetic coupling between Tb and Ni is observed in the XMCD experiments. The molecule-surface interaction is rationalized by the DFT analysis and is found to follow a relay-like communication pathway, where the radical spin on the organic Pc ligands mediates the interaction between Tb ion and Ni substrate spins. A model Hamiltonian which explicitly takes into account the presence of the spin radical is then developed, and the different magnetic interactions at play are assessed by first-principle calculations and by comparing the calculated magnetization curves with XMCD data. The relay-like mechanism is at the heart of the process through which the spin information contained in the Tb ion is sensed and exploited in carbon-based molecular spintronics devices.