Resonant scattering by magnetic impurities as a model for spin relaxation in bilayer graphene

We propose that the observed spin-relaxation in bilayer graphene is due to resonant scattering by magnetic impurities. We analyze a resonant scattering model due to adatoms on both dimer and non-dimer sites, finding that only the former give narrow resonances at the charge neutrality point. Opposite to single-layer graphene, the measured spin-relaxation rate in graphene bilayer increases with carrier density. Although it has been commonly argued that a different mechanism must be at play for the two structures, our model explains this behavior rather naturally in terms of different broadening scales for the same underlying resonant processes. Not only our results---using robust and first-principles inspired parameters---agree with experiment, they also predict an experimentally testable sharp decrease of the spin-relaxation rate at high carrier densities.Comment: 6 pages, 3 figures + 2 pages Suppl. Materia

Theoretical investigations of orbital and spin-orbital effects in functionalized graphene

Functionalization of graphene with adsorbants offers the possibility to tailor existing properties of graphene and also to introduce new desirable features in the system. The ultimate goal is to increase graphene's potential for future spintronics applications. The focus of this thesis is theoretical investigation of orbital and spin-orbital properties of functionalized graphene. The first part of the thesis presents the development of effective spin-orbit coupling (SOC) model Hamiltonians from simple symmetry arguments. Within the tight-binding framework SOC is investigated in graphene systems subject to global minimal structural modifications. In particular, the emergence of SOC terms is explained in systems such as pristine graphene, graphene miniripple, planar graphene with inequivalent sublattices, graphene in an external electric field, and graphene on a transition-metal dichalcogenide. Based on the experience for these global modifications to graphene's point group symmetries, SOC is studied in the vicinity of single adsorbates in the adsorption positions hollow, top, and bridge. The derived SOC Hamiltonians are tested on density functional theory calculations of the methyl group, fluorine, and the copper adatom. A strong local enhancement of SOC in graphene by a factor of 100 is observed for the methyl group, while fluorine and copper increase SOC locally by about 1000 times. The second part comprises a study of the orbital impact of hollow, top, and bridge adsorbates on scattering resonances in graphene using the T-matrix formalism. The influence of the adsorption position, the impurity's orbital character, and the orbital parameters on the resonance characteristics is emphasized. The distinctive features arising in the momentum relaxation rate reveal the difference between general adsorbates and their oversimplified nature in vacancy models. Connecting to the resonance level formation due to adsorbates in graphene, the third part of the thesis considers spin relaxation in graphene due to resonant scattering off adsorbate induced magnetic moments. This mechanism offers a possible explanation for experimentally observed spin relaxation rates in bilayer graphene with a small amount of residual strong scatterers. Also shown are the successes and failures of the model in comparison to experimental data on fluorinated single layer and bilayer graphene. The theoretical analysis was aimed to test the experimental hypothesis that fluorine induces local magnetic moments in graphene

Spin-orbit coupling in methyl functionalized graphene

We present first-principles calculations of the electronic band structure and spin-orbit effects in graphene functionalized with methyl molecules in dense and dilute limits. The dense limit is represented by a 2$\times$2 graphene supercell functionalized with one methyl admolecule. The calculated spin-orbit splittings are up to $0.6$ meV. The dilute limit is deduced by investigating a large, 7$\times$7, supercell with one methyl admolecule. The electronic band structure of this supercell is fitted to a symmetry-derived effective Hamiltonian, allowing us to extract specific hopping parameters including intrinsic, Rashba, and PIA (pseudospin inversion asymmetry) spin-orbit terms. These proximity-induced spin-orbit parameters have magnitudes of about 1 meV, giant compared to pristine graphene whose intrinsic spin-orbit coupling is about 10 $\mu$eV. We find that the origin of this giant local enhancement is the $sp^3$ corrugation and the breaking of local pseudospin inversion symmetry, as in the case of hydrogen adatoms. Also similar to hydrogen, methyl acts as a resonant scatterer, with a narrow resonance peak near the charge neutrality point. We also calculate STM-like images showing the local charge densities at different energies around methyl on graphene.Comment: 9 pages, 10 figure

Resonant scattering due to adatoms in graphene: Top, bridge, and hollow positions

We present a theoretical study of resonance characteristics in graphene from adatoms with s or p(z) character binding in top, bridge, and hollow positions. The adatoms are described by two tight-binding parameters: on-site energy and hybridization strength. We explore a wide range of different magnitudes of these parameters by employing T-matrix calculations in the single adatom limit and by tight-binding supercell calculations for dilute adatom coverage. We calculate the density of states and the momentum relaxation rate and extract the resonance level and resonance width. The top position with a large hybridization strength or, equivalently, small on-site energy, induces resonances close to zero energy. The bridge position, compared to top, is more sensitive to variation in the orbital tight-binding parameters. Resonances within the experimentally relevant energy window are found mainly for bridge adatoms with negative on-site energies. The effect of resonances from the top and bridge positions on the density of states and momentum relaxation rate is comparable and both positions give rise to a power-law decay of the resonant state in graphene. The hollow position with s orbital character is affected from destructive interference, which is seen from the very narrow resonance peaks in the density of states and momentum relaxation rate. The resonant state shows no clear tendency to a power-law decay around the impurity and its magnitude decreases strongly with lowering the adatom content in the supercell calculations. This is in contrast to the top and bridge positions. We conclude our study with a comparison to models of pointlike vacancies and strong midgap scatterers. The latter model gives rise to significantly higher momentum relaxation rates than caused by single adatoms

Model spin-orbit coupling Hamiltonians for graphene systems

We present a detailed theoretical study of effective spin-orbit coupling (SOC) Hamiltonians for graphene-based systems, covering global effects such as proximity to substrates and local SOC effects resulting, for example, from dilute adsorbate functionalization. Our approach combines group theory and tight-binding descriptions. We consider structures with global point group symmetries D-6h, D-3d, D-3h, C-6v, and C-3v that represent, for example, pristine graphene, graphene miniripple, planar boron nitride, graphene on a substrate, and free standing graphone, respectively. The presence of certain spin-orbit coupling parameters is correlated with the absence of the specific point group symmetries. Especially in the case of C-6v -graphene on a substrate, or transverse electric field-we point out the presence of a third SOC parameter, besides the conventional intrinsic and Rashba contributions, thus far neglected in literature. For all global structures we provide effective SOC Hamiltonians both in the local atomic and Bloch forms. Dilute adsorbate coverage results in the local point group symmetries C-6v, C-3v, and C-2v, which represent the stable adsorption at hollow, top and bridge positions, respectively. For each configuration we provide effective SOC Hamiltonians in the atomic orbital basis that respect local symmetries. In addition to giving specific analytic expressions for model SOC Hamiltonians, we also present general (no-go) arguments about the absence of certain SOC terms

Spin-orbit coupling in fluorinated graphene

We report on theoretical investigations of the spin-orbit coupling effects in fluorinated graphene. First-principles density functional calculations are performed for the dense and dilute adatom coverage limits. The dense limit is represented by the single-side semifluorinated graphene, which is a metal with spin-orbit splittings of about 10 meV. To simulate the effects of a single adatom, we also calculate the electronic structure of a $10 \times 10$ supercell, with one fluorine atom in the top position. Since this dilute limit is useful to study spin transport and spin relaxation, we also introduce a realistic effective hopping Hamiltonian, based on symmetry considerations, which describes the supercell bands around the Fermi level. We provide the Hamiltonian parameters which are best fits to the first-principles data. We demonstrate that, unlike for the case of hydrogen adatoms, fluorine's own spin-orbit coupling is the principal cause of the giant induced local spin-orbit coupling in graphene. The $sp^3$ hybridization induced transfer of spin-orbit coupling from graphene's $\sigma$ bonds, important for hydrogenated graphene, contributes much less. Furthermore, the magnitude of the induced spin-orbit coupling due to fluorine adatoms is about $1000$ times more than that of pristine graphene, and 10 times more than that of hydrogenated graphene. Also unlike hydrogen, the fluorine adatom is not a narrow resonant scatterer at the Dirac point. The resonant peak in the density of states of fluorinated graphene in the dilute limit lies 260 meV below the Dirac point. The peak is rather broad, about 300 meV, making the fluorine adatom only a weakly resonant scatterer.Comment: 11 pages, 14 figure

Copper adatoms on graphene: Theory of orbital and spin-orbital effects

We present a combined DFT and model Hamiltonian analysis of spin-orbit coupling in graphene induced by copper adatoms in the bridge and top positions, representing isolated atoms in the dilute limit. The orbital physics in both systems is found to be surprisingly similar, given the fundamental difference in the local symmetry. In both systems the Cu p and d contributions at the Fermi level are very similar. Based on the knowledge of orbital effects we identify that the main cause of the locally induced spin-orbit couplings are Cu p and d orbitals. By employing the DFT+U formalism as an analysis tool we find that both the p and d orbital contributions are equally important to spin-orbit coupling, although p contributions to the density of states are much higher. We fit the DFT data with phenomenological tight-binding models developed separately for the top and bridge positions. Our model Hamiltonians describe the low-energy electronic band structure in the whole Brillouin zone and allow us to extract the size of the spin-orbit interaction induced by the local Cu adatom to be in the tens of meV. By application of the phenomenological models to Green's function techniques, we find that copper atoms act as resonant impurities in graphene with large lifetimes of 50 and 100 fs for top and bridge, respectively