Twisted exchange interaction between localized spins embedded in a one- or two-dimensional electron gas with Rashba spin-orbit coupling

TL;DR

This paper theoretically investigates how Rashba spin-orbit coupling induces a twisted RKKY interaction between localized spins in 1D and 2D electron gases, revealing a combination of Heisenberg, Dzyaloshinsky-Moriya, and Ising interactions.

Contribution

It introduces a model showing the twisted RKKY interaction caused by Rashba spin-orbit coupling and derives the effective spin Hamiltonian with rotated spin axes.

Findings

Rashba SO coupling causes a twisted RKKY interaction.

The interaction includes Heisenberg, Dzyaloshinsky-Moriya, and Ising terms.

The effective Hamiltonian reduces to a rotated RKKY form.

Abstract

We study theoretically the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in one- and two-dimensions in presence of a Rashba spin-orbit (SO) coupling. We show that rotation of the spin of conduction electrons due to SO coupling causes a twisted RKKY interaction between localized spins which consists of three different terms: Heisenberg, Dzyaloshinsky-Moriya, and Ising interactions. We also show that the effective spin Hamiltonian reduces to the usual RKKY interaction Hamiltonian in the twisted spin space where the spin quantization axis of one localized spin is rotated.