Symmetries and hybridization in the indirect interaction between magnetic moments inMoS2nanoflakes

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.

Introducing Magnetism into 2D Nonmagnetic Inorganic Layered Crystals: A Brief Review from First-Principles Aspects

“…positioned on the edge of the LTMDs [96]. A similar oscillation trend from RKKY was also found between the distance of impurities and the interaction strength in the p-doped LTMD monolayer [97]. Therefore, the symmetry of the whole system also affects the final magnetism.…”

“…A magnetic dipole is formed, and the polarization decays in oscillations based on the distance from the dopant. Such a trend is well reproduced in the dually doped ILC systems [97,98]. On the other hand, in a dilute-doped system, the local magnet is strong enough, but the couplings from the neighboring supercells are general neglected.…”

Long range of indirect exchange interaction on the edges of MoS2flakes

“…Although we had found 2D behavior for the interaction between impurities in the interior of flakes before [47], and some evidence of long range interaction for hybridization near the edges [48], we present here the full systematics.…”

“…We use 2λ = 150 meV, in good agreement with DFT calculations [5,45] and experimental values (152 meV [53], 138 meV [54] and 145 meV [55]). With this Hamiltonian and the right choice of boundaries, one can construct a flake like the triangle we consider [48,47,52]. Others TMDs can be similarly modeled, taking the onsite, hopping and SOC parameters from Tables II and III in [45].…”

“…The total effective interaction is a competition between in-plane J XX (= J Y Y ), Ising J ZZ , and DzyaloshinskiiMoriya J DM terms. In TMDs the Ising and DM terms are generated by the SOC; their competition has been recently discussed for bulk samples [31,33] and flakes [48,47]. To calculate the effective J's in our finite sample, we take the difference of triplet and singlet configurations of impurities in the electronic ground state [58,59] as…”