Finite-temperature ordering of dilute graphene antiferromagnets

Abstract

We employ large-scale quantum Monte Carlo simulations to study the magnetic ordering transition among dilute magnetic moments randomly localized on the graphene honeycomb lattice, induced by long-ranged RKKY interactions at low charge carrier concentration. In this regime the effective exchange interactions are ferromagnetic within each sublattice, and antiferromagnetic between opposite sublattices, with an overall cubic decay of the interaction strength with the separation between the moments. We verify explicitly, that this commensurability leads to antiferromagnetic order among the magnetic moments below a finite transition temperature in this two-dimensional system. Furthermore, the ordering temperature shows a crossover in its power-law scaling with the moments' dilution from a low-to a high-concentration regime.that pair-wise interactions are ferromagnetic (antiferromagnetic) among the same (different) sublattice on the bipartite honeycomb lattice of graphene.This means for the exchange couplings in Eq.(1), thatwith J > 0 and ǫ ij = −1 (+1) if i and j belong to the same (different) sublattice [10,11]. Here, r i denotes the (random) position of the i-th magnetic moment S i on the honeycomb lattice, which we consider to be spin-1 2

Critical temperature of two-dimensional hydrogenated multilayer graphene-based diluted ferromagnet

“…Let us note that, in general, the integral approximation is valid for low p (see also Refs. [35,36]).…”

The physics of Kondo impurities in graphene

“…Thus, an inhomogeneous but unfrustrated antiferromagnetic ground state can be expected for randomly placed moments. Such order is predicted to persist at finite temperature even in this 2d situation due to the long-range nature of the RKKY interaction [81]. Departing from charge neutrality, a crossover to standard metallic behaviour is expected.…”

EPR evidence of antiferromagnetic ordering in single‐layer graphene

“…Theoretical studies suggest that the crucial role in determining the magnetic properties of graphene is played by the the localized electron states. Exchange between them is realized by the longranged Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions mediated by conducting electrons [2][3][4][5][6]. For the centres localized on the same sublattice, ferromagnetic order is expected, whereas interactions between centres localized on two various sublattices lead to antiferromagnetic ordering analogous to the state of a diluted antiferromagnet [2][3][4].…”

“…Exchange between them is realized by the longranged Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions mediated by conducting electrons [2][3][4][5][6]. For the centres localized on the same sublattice, ferromagnetic order is expected, whereas interactions between centres localized on two various sublattices lead to antiferromagnetic ordering analogous to the state of a diluted antiferromagnet [2][3][4]. Several authors have demonstrated the importance of the edge states and single-atom point defects [5][6][7][8].…”