Long-range exchange interaction between magnetic impurities in graphene

Abstract

The effective spin exchange coupling between impurities (adatoms) on graphene mediated by conduction electrons is studied as a function of the strength of the potential part of the on-site energy U of the electron-adatom interaction. With increasing U , the exchange coupling becomes long-range, determined largely by the impurity levels with energies close to the Dirac points. When adatoms reside on opposite sublattices, their exchange coupling, normally antiferromagnetic, becomes ferromagnetic and resonantly enhanced at a specific distance where an impurity level crosses the Dirac point.

Dilute magnetism in graphene

“…Finally, we note that the spatial decay of the effective magnetic interaction also depends on the local potential induced by the impurities, as shown recently in Ref. [40]. In certain cases, the coupling between the impurities becomes even more long-raged.…”

“…Magnetic moments have been observed in graphene, either associated with structural defects [10][11][12][13][14], or with the presence of certain adatoms, such as H [15][16][17][18], F [13,19], S [20], Au [21], or even certain molecules [9,22]. The theory describing magnetic moment formation in graphene and/or the coupling to magnetic adatoms has also been studied at length [16,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. Although much harder to establish than the presence of magnetic moments, the observation of magnetic long range order has been reported in several experiments related to the presence of adatoms or molecules [9,15,17,20,22].…”

“…The RKKY interaction in graphene has been studied extensively [40,[48][49][50][51][52][53][54][55]. It couples magnetic moments on the same sublattice ferromagnetically, and antiferromagnetically on different sublattices.…”

Kondo effect due to a hydrogen impurity in graphene: A multichannel Kondo problem with diverging hybridization

“…In that case, it has been shown to be ferromagnetic between impurities on the same sublattice, and antiferromagnetic between impurities on different sublattices. Nevertheless, antiferromagnetic RKKY interactions have also been reported between same-sublattice magnetic impurities when other non-magnetic impurities are present [92], or when a large on-site potential energy is associated with the magnetic impurities [93].…”

Potential and spin-exchange interaction between Anderson impurities in graphene

“…It is instructive to begin our analysis of the Andersontype impurities with a discussion of potential impurities. Recent studies of impurity-impurity interaction in the case of substitution impurities with an onsite potential U have obtained an analytical expression exact in U 15,16,33 . In particular, in the large U limit, interaction between impurities on the same sublattice is long range, ∝ 1/R (up to logarithmic factors), and is repulsive, in contrast to the weak U limit where it decays as 1/R 3 and is attractive.…”