Spin Helix of Magnetic Impurities in Two-dimensional Helical Metal

TL;DR

This paper investigates the RKKY interaction in helical metals on topological insulators, revealing a significant Dzyaloshinskii-Moriya interaction that induces a controllable spin helix structure influenced by the Fermi velocity.

Contribution

It demonstrates the emergence of a spin helix due to DM interaction in helical metals and shows how impurity spin polarization can be electrically controlled.

Findings

Dzyaloshinskii-Moriya interaction induces spin helix formation.

Spin helix handedness is linked to Fermi velocity sign.

Electric voltage can control impurity spin polarization.

Abstract

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.