  In this study, we investigate the isolated magnetic interactions between two
identical Fe atoms divacantly-substituted into graphene. Using density
functional theory, we simulated the electronic and magnetic properties for a
supercell of graphene with spatial variation of the Fe atoms along either the
armchair or zig-zag directions. Overall, we find that the exchange interaction
between the two Fe atoms fluctuates from ferromagnetic to antiferromagnetic as
a function of the spatial distance in the armchair direction. Given the induced
magnetic moment and increased density of states at the Fermi level by the
surrounding carbon atoms, we conclude that an RKKY-like interaction may
characterize the exchange interactions between the Fe atoms. Furthermore, we
examined the same interactions for Fe atoms along the zig-zag direction in
graphene and found no evidence for an RKKY interaction as this system shows
standard superexchange between the transition-metal impurities. Therefore, we
determine that Fe-substituted graphene produces a directional-dependent spin
interaction, which may provide stability to spintronic and multifunctional
devices and applications for graphene.
