An Origin of Dzyaloshinskii-Moriya Interaction at Graphene-Ferromagnet Interfaces Due to the Intralayer RKKY/BR Interaction.

We present a theory of both the itinerant carrier-mediated RKKY interaction and the virtual excitations-mediated Bloembergen-Rowland (BR) interaction between magnetic moments in graphene induced by proximity effect with a ferromagnetic film. We show that the RKKY/BR interaction consists of the Heisenberg, Ising, and Dzyaloshinskii-Moriya (DM) terms. In the case of the nearest distance, we estimate the DM term from the RKKY/BR interaction is about 0.13 meV for the graphene/Co interface, which is consistent with the experimental result of DM interaction $0.16 \pm 0.05$ meV. Our calculations indicate that the intralayer RKKY/BR interaction may be a possible physical origin of the DM interaction in the graphene-ferromagnet interface. This work provides a new perspective to comprehend the DM interaction in graphene/ferromagnet systems.