Ruderman-Kittel-Kasuya-Yosida interaction in Weyl semimetals

TL;DR

This paper theoretically investigates the RKKY interaction mediated by Weyl fermions in Weyl semimetals, revealing multiple interaction terms with specific spatial and directional dependencies, including analytical expressions and decay behaviors.

Contribution

It provides a detailed theoretical analysis of the RKKY interaction in Weyl semimetals, identifying four distinct interaction terms and their spatial and directional characteristics.

Findings

Four interaction terms: Heisenberg, Dzyaloshinsky-Moriya, spin-frustrated, Ising.

Interaction decays as R^{-5} with distance at Weyl points.

Beating behavior in interaction depending on impurity separation direction.

Abstract

We theoretically demonstrate the Ruderman-Kittel-Kasuya-Yosida interaction between magnetic impurities that is mediated by the Weyl fermions embedded inside a three-dimensional Weyl semimetal (WSM). The WSM is characterized by a pair of Weyl points separated in the momentum space. Using the Green's function method and a two-band model, we show that four terms contribute to the magnetic impurity interaction in the WSM phase: the Heisenberg, Dzyaloshinsky-Moriya, spin-frustrated and Ising terms. Except the last term which is vanishingly small in the plane perpendicular to the line connecting two Weyl points, all the other interaction terms are finite. Furthermore, the magnetic spins of the Dzyaloshinsky-Moriya and spin-frustrated terms lie in the plane perpendicular to the line connecting two Weyl points, but in this plane, the magnetic spins of the Ising term have no components. For each contribution, an analytical expression is obtained, falling off with a spatial dependence as $R^{-5}$ at Weyl points and showing beating behavior that depends on the direction between two magnetic impurities.