  We analyze the Ruderman-Kettel-Kasuya-Yosida(RKKY) interaction between
magnetic impurities embedded in the helical metal on the surface of
three-dimensional topological insulators. Apart from the conventional RKKY
terms, the spin-momentum locking of conduction electrons also leads to a
significant Dzyaloshinskii-Moriya (DM) interaction between impurity spins. For
a chain of magnetic impurities, the DM term can result in single-handed spin
helix on the surface. The handedness of spin helix is locked with the sign of
Fermi velocity of the emergent Dirac fermions on the surface. We also show the
polarization of impurity spins can be controlled via electric voltage for
dilute magnetic impurity concentration.
