  We study theoretically the RKKY interaction between magnetic impurities on
the surface of three-dimensional topological insulators, mediated by the
helical Dirac electrons. Exact analytical expression shows that the RKKY
interaction consists of the Heisenberg-like, Ising-like and DM-like terms. It
provides us a new way to control surface magnetism electrically. The gap opened
by doped magnetic ions can lead to a short-range Bloembergen-Rowland
interaction. The competition among the Heisenberg, Ising and DM terms leads to
rich spin configurations and anomalous Hall effect on different lattices.
