Effective dimensionality of the indirect interaction on the edges of MoS$_{2}$ triangular flakes

Oscar Ávalos-Ovando, Diego Mastrogiuseppe, Sergio E. Ulloa

Published 2016-07-28Version 1

We study the Ruderman-Kittel-Kasuya-Yosida interaction between two magnetic impurities connected to the edges of zigzag-terminated transition-metal dichalcogenide triangular flakes. When the impurities lie on the edges of the flake, the effective exchange configuration is helical, showing a sizable noncollinear Dzyaloshinskii-Moriya interaction. We analyze the interaction decay exponent for doping levels inside the band gap of the infinite layer, corresponding to edge states for the flake. The exponents show a sub-2D behavior for different band fillings, with a decay that is slower than quadratic. Remarkably, the noncollinear component can feature positive exponents, signaling an interaction that grows with the impurity separation. This effect can be attributed to the presence of an envelope with a wavelength longer than the size of the flake.