Long range of indirect exchange interaction on the edges of MoS$_{2}$ flakes

TL;DR

This paper investigates the long-range indirect exchange interactions between magnetic impurities on the edges of MoS₂ flakes, revealing significant noncollinear Dzyaloshinskii-Moriya effects and sub-2D decay behavior, with implications for impurity phase studies.

Contribution

It provides the first analysis of edge-mediated exchange interactions in MoS₂ flakes, highlighting the coexistence of Ising and Dzyaloshinskii-Moriya interactions with tunable long-range behavior.

Findings

Edge impurities exhibit strong noncollinear Dzyaloshinskii-Moriya interactions.

Decay of interactions shows sub-2D behavior, slower than quadratic.

Long-range interactions enable potential for stable helical impurity phases.

Abstract

We study the Ruderman-Kittel-Kasuya-Yosida interaction between two magnetic impurities connected to the edges of zigzag-terminated MoS$_{2}$ flakes. When the impurities lie on the edges of the flake, the effective exchange interaction exhibits sizable noncollinear Dzyaloshinskii-Moriya character that competes with a strong Ising coupling. We analyze the characteristic decay exponent for doping levels inside the band gap of the infinite layer, corresponding to edge states of the flake at the Fermi level. The characteristic exponents show sub-two-dimensional (sub-2D) behavior for these band fillings, with decays much slower than quadratic. The Ising interaction has effectively one-dimensional (1D) long range, while the noncollinear component that grows for short impurity separation becomes comparable in magnitude. The resulting tunable exchange interaction on these systems opens the way for the study of interesting phases of impurity arrays with long-range stable helical order.