Session L37: Focus Session: Graphene Structure, Dopants, and Defects: Magnetism

Missing atom as a source of carbon magnetism

Introducing vacancies in graphene-like systems by irradiation has been shown to be an efficient method to vary its mechanical behavior, tune its electronic properties and even to induce magnetism in otherwise non-magnetic samples [1-2]. While the role played by these vacancies as single entities has been extensively addressed by theory [3-6], experimental data available refer to statistical properties of the whole heterogeneous collection of vacancies generated in the irradiation process. Here, by artificially generating isolated vacancies on a graphite surface and measuring their local density of states on the atomic scale, we have shown how single vacancies modify the electronic properties of this graphene-like system [7]. Our scanning tunneling microscopy experiments, complemented by tight binding calculations, reveal the presence of a sharp electronic resonance at the Fermi energy around each single graphite vacancy, which implies a dramatic reduction of the charge carriers' mobility and can be associated with the formation of local magnetic moments. Finally, we have extended our investigations to other graphene systems. \\[4pt] [1] P. Esquinazi, D. Spemann, R. H\"{o}hne, A. Setzer, K.-H. Han and T. Butz, \textit{Phys. Rev. Lett.} \textbf{91}, 227201 (2003).\\[0pt] [2] A. V. Krasheninnikov and F. Banhart, \textit{Nature Materials} \textbf{6}, 723 (2007)\\[0pt] [3] V. M. Pereira, F. Guinea, J. M. Lopes dos Santos, N. M. R. Peres and A. H. Castro Neto, \textit{Phys. Rev. Lett.} \textbf{96}, 036801 (2006)\\[0pt] [4] P. O. Lehtinen, A. S. Foster, Y. C. Ma, A. V. Krasheninnikov and R. M. Nieminen , \textit{Phys. Rev. Lett.} \textbf{93}, 187202 (2004).\\[0pt] [5] J. J. Palacios, J. Fern\'{a}ndez-Rossier and L. Brey, \textit{Phys Rev. B} \textbf{77}, 195428 (2008)\\[0pt] [6]. O. V.Yazyev, \textit{Phys}.\textit{ Rev. Lett.} \textbf{101}, 037203 (2008).\\[0pt] [7] M. M. Ugeda I. Brihuega, F. Guinea and J. M. G\'{o}mez Rodr\'{\i}guez, \textit{Phys. Rev. Lett }\textbf{104}, 096804 (2010)   

Kondo quantum criticality in graphene

Graphene fits in a large class of ``pseudogap'' materials which are allowed to exhibit quantum criticality as a result of the interplay of strong correlations and a vanishing density of states near the Fermi points. In the presence of magnetic impurities, we show there is a symmetry class of localized orbitals which, in combination with quantum interference effects inbuilt in the honeycomb lattice, can lead to a novel class of Kondo quantum criticality in graphene [1]. In this class, graphene effectively screens the local spin as a super-ohmic dissipative environment and the RKKY interaction decays spatially with a fast power-law $\sim 1/R^7$, rather than the standard $1/R^3$ decay expected for Dirac fermions. We also show that unlike metals, the exchange coupling between the localized and itinerant spins can be controlled across the quantum critical region with the application of an external gate voltage. This effect may permit the first experimental observation of quantum criticality in graphene at zero magnetic field, directly with scanning tunneling probes and gating. \\[4pt] [1] B. Uchoa et al., arXiv:1006.2512 (2010)   

Kondo effect in graphene in the presence of Rashba spin-orbit interaction

We present an exact solution for the Anderson model of a single-orbital magnetic impurity on graphene in the Kondo regime. Different positions for the impurity are considered: on top of a carbon atom, substitutional or interstitial (middle of the hexagon cell). We show that regardless of the impurity position, the effective exchange Hamiltonian always describes a single- channel Kondo problem. The inclusion of the Rashba spin-orbit interaction changes the linear energy dispersion to a quadratic one near the Dirac points with the corresponding change in the density of states. This in turn, modifies the value of the critical Kondo coupling as compared to the case where the spin-orbit is absent. Moreover, spin-orbit interactions, introduce a Dzyaloshinsky-Moriya (DM) term in the Kondo Hamiltonian away from particle-hole symmetry. Although still in the single channel region, the effective exchange coupling is augmented by the DM term and the Kondo temperature shows an exponential increase. Supported by NSF-PIRE and MWN/CIAM   

Transport in irradiated graphene: Kondo and charge fluctuation effects

Observation of an upturn in resistance at low temperatures in irradiated graphene has renewed the interest in the nature of the Kondo effect in systems with linear density of states. The vanishing density of states near the Dirac point leads to a much wider local moment regime but a cross over to the charge fluctuation at very low carrier densities indeed occurs. In this talk I will show how the Kondo scale and the resistance versus temperatures evolves from one regime to the other, and compare our results with experimental data. Our chief conclusion is that a good agreement with data can be achieved only if one posits that the energy of the impurity level varies linearly with the chemical potential.   

Spin and Transport Properties of Doped Graphene

Graphene is an ideal system to investigate the interplay of magnetic moments and conduction electrons. Electrostatic gates are able to tune the electron and holes concentrations substantially, and localized magnetic moments can form, in principle, through a variety of methods including vacancies, edges, and adsorbed impurities. Theory predicts a coupling of the localized moments and the conduction electrons, leading to gate tunable indirect coupling between moments which can be ferromagnetic or antiferromagnetic. In this study, we perform magnetotransport measurements on graphene devices where the graphene surface is modified inside an ultrahigh vacuum chamber through a variety of methods including hydrogen adsorption, Ar sputtering, and molecular beam deposition of transition metals [1]. Both /in situ/ and /ex situ/ magnetotransport measurements are performed, where the latter involves the air-free transfer to a low temperature (1.6 - 300 K), high field (7 T) cryostat. We will report results on the temperature-dependent, high-field magnetotransport characteristics of doped graphene. \\[4pt] [1] K. Pi, K. M. McCreary, W. Bao, W. Han, Y. F. Chiang, Y. Li, S.-W. Tsai, C. N. Lau, and R. K. Kawakami, Phys. Rev. B 80, 075406 (2009).   

Can Carbon Be Ferromagnetic?

The existence of long range magnetic order at room temperature in carbon based structures without magnetic elements is very unexpected. Theoretical results from different groups suggest that the existence of long range magnetic order in a graphite structure is possible, if one takes the effects of defects and/or the incorporation of hydrogen atoms into account. SQUID results provided first systematic hints for the existence of magnetic order at room temperature in virgin as well as irradiated highly oriented pyrolytic graphite (HOPG) samples. We present a x-ray dichroism study of graphite surfaces [1] that addresses the origin and magnitude of ferromagnetism in metal-free carbon. Using element specific x-ray microscopy we can show that metallic impurities do not play a role in the ferromagnetism of carbon and that carbon can be ferromagnetic without ferromagnetic impurities. A detailed spectroscopic study shows that in addition to carbon \textit{pi-}states, also hydrogen-mediated electronic states exhibit a net magnetization with magnetic remanence at room temperature. The observed magnetism is restricted to the top \textit{$\sim $}10 nm of the sample where the actual magnetization reaches a value similar to classic ferromagnetic materials like e.g. Nickel. [1] H. Ohldag et al., Phys. Rev. Lett. \textbf{98, }187204 (2007) and submitted to NJP (2010)   

Extinction of ferromagnetism in HOPG by thermal annealing

Observations of ferromagnetism (FM) in highly ordered pyrolytic graphite (HOPG) have generated vigorous research activity to clarify its origin, especially when transition metals are known to be absent. We report that the ferromagnetism of pristine HOPG samples as measured by hysteretic magnetization loops can be diminished and eventually extinguished with sufficiently long high vacuum anneals at temperatures greater than 2000\r{ }C. Concomitant with the extinction of ferromagnetism, we observe an anneal-induced increase in grain size (accompanied by possible edge reconstruction) confirmed by XRD measurement and improved transport properties, including lower in-plane and out-of-plane resistance, higher electron and hole mobility and improved charge compensation. The implied anneal-induced reduction of defects and vacancies suggests that the FM of pristine HOPG is correlated with localized states located at zigzag edges, vacancies and related defects.   

Local Moment Formation of an Anderson Impurity on Graphene

We study the effect of a magnetic impurity on a single layer of graphene within an Anderson impurity model. Due to the vanishing local density of state at the Fermi level in graphene, the impurity spin cannot be effectively screened out. Treating the problem within the Gutzwiller approximation, we found a region in the parameter space of $U$-$E^f$ where the impurity electron is in the local moment state, which is characterized by a zero effective hybridization between the bath electron and magnetic impurity. Here $U$ is the onsite Coulomb repulsion of the impurity and $E^f$ is its energy level with respect to the Fermi energy. The competition between $U$ and $E^f$ is also discussed. While larger $U$ reduces double occupation and favors local moment formation, a deeper impurity level prefers double occupation and a nonzero hybridization and thus a Kondo screened state. For a fixed $U$, by continuously lowering the impurity level, the impurity first enters from a Kondo screened state to a local moment state and then departs from this state and re-enters into the Kondo screened state.   

Spin-dependent scattering from gated potential obstacles in graphene systems

We study the scattering of Dirac fermions in a sheet of graphene from potential obstacles created by external gates in the presence of both intrinsic and extrinsic Spin-Orbit(SO) interactions [1]. Obtaining an analytical solution in real-space representation for the eigenvectors allows us to calculate the phase shifts generated by a finite-size obstacle in the presence of SO interactions [2]. These states take into account the total angular momentum of the Hamiltonian, which includes spin, pseudo-spin and orbital angular momentum. We find an interesting interplay of both SO interactions, which results in oscillations of the spin-flip cross sections with energy; this also generates a difference between both cross sections for different interaction ranges. These results may open a possibility of obtaining spin-polarized currents that are of importance in the field of spintronics.\\[4pt] [1] C. L. Kane and E. J. Mele, PRL 95, 226801 (2005).\\[0pt] [2] A. H. Castro Neto and F. Guinea, PRL 103, 026804 (2009).   

Ferromagnetically coupled local moments along an extended line defect in graphene

Recently an extended line defect was observed composed of octagonal and pentagonal carbon rings embedded in a graphene sheet [Nat. Nanotech. 5, 326 (2010)]. We report results of studies we have made of this defect using both first-principles and semi-empirical methods. Two types of boundary-localized states arising from the defect are identified. The first (second) type has eigenstates with wavefunctions that are anti- symmetric (symmetric) with respect to a mirror plane that is perpendicular to the graphene sheet and passes through the line defect center line. The boundary-localized anti-symmetric states are shown to be intimately connected to the zigzag edge states of semi-infinite graphene. They exhibit little dispersion along the defect line and lie close to the Fermi level giving rise to a spontaneous spin polarization along the defect once electron-electron interactions are included at the level of a mean field approximation to a Hubbard Model. Within this approach, symmetry requires that the principal moments couple ferromagnetically both along and across the line defect leading to approximately 2/3 more up than down spin electrons per defect repeat unit.   

Correlating Magnetotransport and Diamagnetism of sp2-Bonded Carbon Networks Through the Metal-Insulator Transition

Titanium carbide-derived carbons (TiC-CDCs) are porous sp2-bonded networks synthesized by exposing TiC to chlorine gas at an elevated temperature. The latter ``chlorination temperature'' adjusts the size of graphitic domains within this material. We perform magnetoresistance, temperature dependent resistance, and SQUID magnetization measurements on TiC-CDC samples prepared at different chlorination temperatures. Transport reveals a metal-insulator transition where high (low) chlorination temperature samples are on the metallic (insulating) side of the transition. Magnetoresistance measurements are consistent with electronic transport in the weak and strong localization regimes for metallic and insulating samples, respectively. The diamagnetic contribution to the total magnetization increases with chlorination temperature, suggesting that the metal-insulator transition is associated with the expansion of graphitic domains. We also discuss a magnetoresistance anomaly observed in insulating samples. This work supported by NSF DMR-0907266 and NSF MRSEC DMR-05-20020.