Spin helix of magnetic impurities in two-dimensional helical metal

The surface state of a topological insulator dubbed as helical metal is a unique metallic system, which exhibits one single Dirac cone and spin-momentum locking. We show that the behaviors of magnetic impurities embedded in this kind of surface states manifest the uniqueness of helical metals among other conventional Dirac materials such as graphene. We find there is a significant Dzyaloshinskii-Moriya (DM) term among the effective interactions between impurity spins mediated by the conduction electrons. For a chain of impurity spins, we show that such a DM interaction gives rise to a single-handed spin helix state, the handedness of which is locked with the sign of the Fermi velocity of the emergent Dirac fermions. We also point out that the polarization of impurity spins can be controlled via electric voltage for dilute magnetic-impurity concentration. Copyright (C) EPLA, 2010