Anomalous magnetism in hydrogenated graphene

Abstract

We revisit the problem of local moment formation in graphene due to chemisorption of individual atomic hydrogen or other analogous sp 3 covalent functionalizations. We describe graphene with the single-orbital Hubbard model, so that the H chemisorption is equivalent to a vacancy in the honeycomb lattice. To circumvent artifacts related to periodic unit cells, we use either huge simulation cells of up to 8 × 10 5 sites, or an embedding scheme that allows the modeling of a single vacancy in an otherwise pristine infinite honeycomb lattice. We find three results that stress the anomalous nature of the magnetic moment (m) in this system. First, in the noninteracting (U = 0) zero-temperature (T = 0) case, the m(B) is a continuous smooth curve with divergent susceptibility, different from the stepwise constant function found for single unpaired spins in a gapped system. Second, for U = 0 and T > 0, the linear susceptibility follows a power law ∝ T −α with an exponent of α = 0.77 different from the conventional Curie law. For U > 0, in the mean-field approximation, the integrated moment is smaller than m = 1μ B , in contrast with results using periodic unit cells. These three results highlight the fact that the magnetic response of the local moment induced by sp 3 functionalizations in graphene is different from that of local moments in gapped systems, for which the magnetic moment is quantized and follows a Curie law, and from Pauli paramagnetism in conductors, for which linear susceptibility can be defined at T = 0.

Electrical spin manipulation in graphene nanostructures

“…This has been established using either density functional theory (DFT) and/or mean field Hubbard model calculations in the case of infinitely long graphene ribbons with zigzag edges [24,35] as well as the small nanoribbons considered here [18,40] and for hydrogenated graphene [26,30,38,50]. The emergence of local moments in the case of undoped topological junctions is explored here.…”

“…For the nanographenes considered here, we make use of the so-called mean-field approximation [24,28,34,35,37,38] where the exact four-fermion operator is replaced by…”

“…Their direct experimental observation by means of scanning tunneling microscopy (STM) has been reported both for the edge states of rectangular nanographenes with short zigzag edges [17] as well as for the individual and for pairs of chemisorbed hydrogen atoms in graphene [29,30]. These sublattice polarized zero modes are expected to host unpaired spin electrons, giving rise to the formation of local moments [24,28,[31][32][33][34][35][36][37][38]. Sublattice polarized zero modes have recently been predicted [39] to exist as in-gap topological states at the interface of certain graphene ribbons with armchair edges, shown in Fig.…”

Emergent quantum matter in graphene nanoribbons

“…with different symmetry protected topological indexes Z 2 , defined below, as proposed by Cao et al [12] In addition, zero modes also appear when graphene is functionalized with atomic hydrogen [43][44][45][46] or any other sp 3 functionalization [47]. There are two complementary ways to understand the emergence of these zero modes.…”

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

“…One particularly intensively explored approach to making graphene magnetic is through point defects [10][11][12][13][14][15][16], such as adsorbing adatoms [17][18][19][20][21][22][23][24] and vacancies [25][26][27][28][29][30][31][32][33][34]. While transition metal adatoms with d or f electrons constitute an obvious option, rather amazingly, it has been shown both theoretically and experimentally that hydrogen impurities in graphene are also capable of inducing local magnetic moments [35][36][37][38][39][40][41][42], of the order of one Bohr magneton per defect. An intuitive explanation follows from the strong coupling between the hydrogen impurity and the carbon atom directly below it [43,44].…”