Indirect exchange interaction between magnetic adatoms in graphene

Abstract

We present a theoretical study of indirect exchange interaction between magnetic adatoms in graphene. The coupling between the adatoms to a graphene sheet is described in the framework of tunneling Hamiltonian. We account for the possibility of this coupling being of resonant character if a bound state of the adatom effectively interacts with the continuum of 2D delocalized states in graphene. In this case the indirect exchange between the adatoms mediated by the 2D carriers appears to be substantially enhanced compared to the results known from Ruderman-Kittel-KasuyaYosida (RKKY) theory. Moreover, unlike the results of RKKY calculations in the case of resonant exchange the magnetic coupling between the adatoms sitting over different graphene sublattices do not cancel each other. Thus, for a random distribution of the magnetic adatoms over graphene surface a non-zero magnetic interaction is expected. We also suggest an idea of controlling the magnetism by driving the tunnel coupling in and out of resonance by a gate voltage.

Long-range exchange interaction between magnetic impurities in graphene

“…In Ref. 30 the indirect exchange between resonant Anderson impurities in graphene was studied numerically with the emphasis on the short-distance behavior. No analytic dependence has been reported, however, in the strong coupling limit.…”

Enhanced Electrochemical CO2 Reduction of Cu@CuxO Nanoparticles Decorated on 3D Vertical Graphene with Intrinsic sp3‐type Defect

“…[ 45 ] This indicates that the distance between unpaired electrons is increased due to the decreased amount of unpaired electrons. [ 46 ] In addition to the qualitative analysis of EPR spectra, semiquantitative EPR analysis was also conducted using 2,2‐diphenyl‐1‐picrylhydrazyl (DPPH) as reference (Figure S13, Supporting Information). The EPR spectra of VG materials were doubly integrated and compared with the double integration of the DPPH reference spectrum (which possessed 1.40 × 10 8 spins) to calculate the spin density (Table S5, Supporting Information).…”

Gate-tunable magnetism of C adatoms on graphene

“…(5) are in agreement with the conventional RKKY theory results for graphene, [26][27][28][29][30][31][32] the difference in the prefactor is due to the details of the model where the bound state level exists also in a non-resonant case. 33 As a consequence of Eqs. (5), the AA interaction is FM while AB is AFM.…”

“…If the bound impurity state lies above E D , the indirect exchange is mediated by electron-like states of graphene and the indirect exchange is FM at a small distance between the adatoms, whereas if 0 < E D , it is AFM at a small distance as it is mediated by graphene hole-like states. 33 In the case of carbon adatoms, the ψ p,⊥ state is located below E D , therefore, we expect the C adatoms to interact antiferromagnetically when E F is tuned above 0 by gate voltage, which we refer to as resonant region.…”

“…However, the problem can be solved using a different approach. 33,81,82 This generalized theory of indirect exchange considers the following Hamiltonian:…”