Anisotropic RKKY interaction in spin-polarized graphene

Abstract

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in the presence of spin polarized two dimensional Dirac fermions. We show that a spin polarization along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. For undoped graphene, while the x part of interaction keeps its constant ferromagnetic sign, its z part oscillates with the distance of magnetic impurities, R. A finite doping causes that both parts of the interaction oscillate with R. We explore a beating pattern of oscillations of the RKKY interaction along armchair and zigzag lattice directions, which occurs for some certain values of the chemical potential. The two characteristic periods of the beating are determined by inverse of the difference and the sum of the chemical potential and the spin polarization.

Indirect exchange interaction between magnetic adatoms in monolayer MoS2

“…To first order in momenta, the first part of Hamiltonian describes the dynamics of massive Dirac fermions which are studied from the graphene committees. It is commonly known that the RKKY interaction in massless graphene is quite different [15][16][17] from that of a shcrödinger 2D electron liquid. The second part of the Hamiltonian illustrates the spin-orbit interaction which leads to coupled spin and valley physics in the monolayer MoS 2 .…”

Long range of indirect exchange interaction on the edges of MoS2flakes

“…However, the spin and orbital content of the conduction states involved can result in unusual interaction features. For instance, in graphene, the interaction is found to decay as r −3 at the Dirac point, while in doped or spin-polarized graphene it decays as r −2 [29], as in conventional 2D materials. As we will see, TMD edges result in unusual decay with |d| < 2, which we call sub-2D behavior.…”

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

“…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.…”

“…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. 5,10 Moreover in materials with Rashba spin-orbit coupling [11][12][13] as well as materials with spin-valley coupling, 4,14,15 it has been shown that twisting RKKY interaction is possible by the anti-symmetric noncollinear Dzyaloshinskii-Moria-like term. 16,17 In general, the RKKY is a long-ranged interaction, (it decays with R −D , D the dimension of the system) which oscillates with respect to the distance between impurities and electron's Fermi wavevector.…”