  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.
