Indirect exchange interaction between magnetic adatoms in monolayer MoS2

Abstract

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in a monolayer MoS2. We show that the rotation of the itinerant electron spin due to the spin-orbit coupling causes a twisted interaction between two magnetic adatoms which consists of different RKKY coupling terms, the Heisenberg, Dzyaloshinsky-Moriya and Ising interactions. We find that the interaction terms are very sensitive to the Fermi energy values and change dramatically from doped to undoped systems. A finite doping causes that all parts of the interaction oscillate with the distance of two magnetic impurities, R and the interaction behaves like R −2 for the long distance between two localized spins. We explore a beating pattern of oscillations of the RKKY interaction which occurs for the doped system.

RKKY interaction and intervalley processes inp-doped transition-metal dichalcogenides

“…21, 22 Parhizgar et al report that the spin-spin interaction can be seen to include three different terms: Ising, XY and Dzyaloshinskii-Moriya components, 21 all found to decay as r −2 . In contrast, Hatami et al finds that, while the out-of-plane component decays as r −2 , the in-plane interaction decays as r −5/2 , a disagreement perhaps produced by their disregard of intervalley scattering.…”

Topological phase and edge states dependence of the RKKY interaction in zigzag silicene nanoribbon

“…We find that the equilibrium direction of the vectors of the magnetic moments is θ 1,2 = 0, π or θ 1 = θ 2 = π/2, where θ is the polar angle and it is defined as an angle between the spin direction with the unit vector normal to the ZSNR surface (ẑ). Also, we find that the impurity moments shall be located inside the plane with a relative azimuthal angle of φ = tan D 2 are quantities of the Hessian matrix introduced in Ref [25)]. Otherwise, the magnetic moment of impurities will be perpendicular to the plane and will form a FM structure when J H + J I < 0 or an AFM structure for the case when J H + J I > 0.…”

“…Following Ref. [25], we assume magnetic impurities as classical spin vectors and rewrite the RKKY interaction Hamiltonian in the spherical coordinate. We find that the equilibrium direction of the vectors of the magnetic moments is θ 1,2 = 0, π or θ 1 = θ 2 = π/2, where θ is the polar angle and it is defined as an angle between the spin direction with the unit vector normal to the ZSNR surface (ẑ).…”

Effect of the Rashba splitting on the RKKY interaction in topological-insulator thin films

“…As one can see in this figure, for the long range distances, all interaction terms decay as R −2 as like as other two-dimensional structures. 4,12 For the intra-surface pairing and in the short distance limit which plays a more prominent role at higher densities of impurities, the RKKY interaction has much higher values. In contrast to the intra-surface pairing between impurities, the RKKY interaction multiplied by R 2 behaves in a more strange way for the inter-surface pairing.…”

“…This interaction is proportional to the spin susceptibility of the host material and so gives the spin information of the system. 4,5 Depending on the spin structure of the host material, different types of couplings can occur between magnetic adatoms via the RKKY interaction. While in spin-degenerate systems, such as graphene, [6][7][8][9] two localized magnetic impurities couple to each other in the form of isotropic collinear Heisenberg-like term, the anisotropic collinear Ising-like term with different coefficients in different spin-directions can be appeared in spin-polarized systems.…”