Symmetries and hybridization in the indirect interaction between magnetic moments in MoS$_{2}$ nanoflakes

TL;DR

This paper investigates how symmetries and hybridization affect the indirect magnetic interactions in MoS$_{2}$ nanoflakes, revealing anisotropic, tunable interactions influenced by impurity placement and doping levels.

Contribution

It provides a detailed analysis of the symmetry-dependent Ruderman-Kittel-Kasuya-Yosida interaction in MoS$_{2}$ nanoflakes, highlighting the effects of spin-orbit coupling, impurity hybridization, and doping.

Findings

Strong anisotropic interactions due to spin-orbit coupling.

Onsite impurities show similar interaction components; hollow sites favor Ising dominance.

Doping level influences the interaction strength and tunability.

Abstract

We study the Ruderman-Kittel-Kasuya-Yosida interaction between magnetic impurities embedded in $p$-doped transition metal dichalcogenide triangular flakes. The role of underlying symmetries is exposed by analyzing the interaction as a function of impurity separation along zigzag and armchair trajectories, in specific parts of the sample. The large spin-orbit coupling in these materials produces strongly anisotropic interactions, including a Dzyaloshinskii-Moriya component that can be sizable and tunable. We consider impurities hybridized to different orbitals of the host transition-metal and identify specific characteristics for onsite and hollow site adsorption. In the onsite case, the different components of the interaction have similar magnitude, while for the hollow site, the Ising component dominates. We also study the dependence of the interaction with the level of hole doping, which supplies a further degree of tunability. Our results could provide ways of controlling helical long range spin order in magnetic impurity arrays embedded in these materials.