Graphene spintronics

Journal name:
Nature Nanotechnology
Volume:
9,
Pages:
794–807
Year published:
DOI:
doi:10.1038/nnano.2014.214
Received
Accepted
Published online

Abstract

The isolation of graphene has triggered an avalanche of studies into the spin-dependent physical properties of this material and of graphene-based spintronic devices. Here, we review the experimental and theoretical state-of-art concerning spin injection and transport, defect-induced magnetic moments, spin–orbit coupling and spin relaxation in graphene. Future research in graphene spintronics will need to address the development of applications such as spin transistors and spin logic devices, as well as exotic physical properties including topological states and proximity-induced phenomena in graphene and other two-dimensional materials.

At a glance

Figures

  1. Spin injection and transport in graphene spin valves.
    Figure 1: Spin injection and transport in graphene spin valves.

    a,b, Non-local (a) and local (b) spin transport measurement geometries. Blue symbols indicate spin-polarized carriers. c,d, Typical non-local (c) and local (d) MR curves measured on graphene with Al2O3 barriers. The arrows indicate the magnetization directions of four ferromagnetic electrodes. The green (red) curves are for the up (down) sweep of the magnetic field. Inset: Schematic of the device geometry. e, Large non-local MR measured on graphene spin valves with tunnelling contacts at gate voltage Vg = 0 V. Black/red traces indicate the data measured while sweeping up/down the magnetic field. Inset: Schematic of the device measurement geometry. f, Large local MR measured on epitaxial graphene grown on SiC with highly resistive tunnelling contacts. Figures reproduced with permission from: c,d, ref. 5, 2007 Nature Publishing Group; e, ref. 6, © 2010 American Physical Society; f, ref. 10, 2012 Nature Publishing Group.

  2. Magnetic moment in graphene due to light adatoms and vacancy defects.
    Figure 2: Magnetic moment in graphene due to light adatoms and vacancy defects.

    ac, Theoretical prediction of magnetic moments in graphene due to hydrogen (a) and to vacancy defects (b), and at the graphene edges (c). Red and blue denote the opposite spin polarizations. d, Magnetic moments due to hydrogen doping detected by spin transport measurements at 15 K. The device was measured after 8 s hydrogen doping. Black line is the experimental result, and the red line is a fitted curve based on the spin scattering model due to local magnetic moments. Inset: A schematic of spin (black arrows) scattered by local magnetic moments (green arrow). The grey arrows represent the motion of the spin-polarized conduction electrons. e, Magnetic moments due to vacancy defects detected by SQUID. Error bars indicate the accuracy of determination of the number of spins per vacancy. Inset: Magnetic moment due to vacancies as a function of parallel field H. The solid lines are fitted curves based on a Brillouin function with J = 1/2. Figures reproduced with permission from: d, ref. 50, © 2012 American Physical Society; e, ref. 48, 2012 Nature Publishing Group.

  3. Band structure topologies of graphene with spin-orbit coupling in a transverse electric field.
    Figure 3: Band structure topologies of graphene with spin–orbit coupling in a transverse electric field.

    Touching Dirac cones exist only when spin–orbit coupling is neglected (first from left). As long as it is present, the orbital degeneracy at the Dirac point is lifted and the spin–orbit gap appears (second from left). In an external electric field perpendicular to graphene, due to a gate or a substrate, the Rashba effect lifts the remaining spin degeneracy of the bands (third, fourth and fifth from left). If the intrinsic and Rashba couplings are equal, at a certain value of the electric field, two bands (red) form touching Dirac cones again (fourth from left). If the Rashba coupling dominates (fifth from left), the spin–orbit gap closes. Red and blue denote the opposite spin polarizations.

  4. Experimental studies of spin relaxation in graphene.
    Figure 4: Experimental studies of spin relaxation in graphene.

    a, Schematic of Hanle measurement by applying an out-of-plane magnetic field (B, blue arrow). Black arrows indicate the magnetization direction of the ferromagnetic electrodes. Red arrows indicate the spin orientation precessing due to the existence of the magnetic field. b, Typical Hanle curves in graphene spin valves with tunnelling contacts. Red (black) circles are data for parallel (antiparallel) alignment of the central electrodes. Red and black lines are curve fits based on equation (4). The fitted spin lifetime is 771 ps and diffusion constant is 0.020 m2 s−1. c,d, Spin lifetime (squares) and diffusion coefficients (circles) as a function of gate voltage at 4 K for single-layer graphene (c) and bilayer graphene (d). Error bars represent the 99% confidence interval. e, Hanle curves measured on suspended graphene spin valves. Black curves are the experimental results and the red line is the fitting. Inset: Scanning electron micrograph of a typical suspended graphene device. f, Spin lifetime as a function of carrier densities for same graphene spin valve measured at 10 K with tunable mobility: 4,200 cm2 V−1 s−1, 12,000 cm2 V−1 s−1 and 4,050 cm2 V−1 s−1. Error bars represent the 99% confidence interval. Inset: Geometry of graphene spin-valve device with organic ligand-bound nanoparticles. Figures reproduced with permission from: c,d, ref. 9, © 2011 American Physical Society; e, ref. 40, © 2012 American Chemical Society; f, ref. 107, © 2012 American Chemical Society.

  5. Spin relaxation mechanisms in graphene.
    Figure 5: Spin relaxation mechanisms in graphene.

    An illustrative figure of three possible spin relaxation mechanisms for graphene: Elliott–Yafet, Dyakonov–Perel and resonant scattering by local magnetic moments. The blue dots indicate the electrons/holes with yellow arrows as their spin orientation. The red dots represent the scattering centres. Grey cones with circular arrows represent the spin precession.

  6. Spin logic application of graphene spin valves.
    Figure 6: Spin logic application of graphene spin valves.

    a, Schematic drawing of graphene-based magnetologic gate consisting of a graphene sheet contacted by five ferromagnetic electrodes. Two electrodes (A and D) define the input states, two electrodes (B and C) define the operation of the gate, and one electrode (M) is utilized for read-out; Vdd drives the steady-state current, and IM(t) is the transient current response, which gives the output; CM is a capacitor; IW is the writing current to manipulate the magnetization direction of each ferromagnetic electrode; Ir(t) is the current used to perturb the magnetization of the electrode M. b, 'All-spin logic' proposed by Behin-Aein et al.133. Labels 1, 2, 3, 4 and 5 indicate magnetic-free layer, isolation layer, tunnelling layer, channel/interconnect and the contact, respectively. GND, ground terminal. Panel b reproduced with permission from ref. 133, 2010 Nature Publishing Group.

References

  1. Zutic, I., Fabian, J. & Das Sarma, S. Spintronics: Fundamentals and applications. Rev. Mod. Phys. 76, 323410 (2004).
  2. Dery, H., Dalal, P., Cywinski, L. & Sham, L. J. Spin-based logic in semiconductors for reconfigurable large-scale circuits. Nature 447, 573576 (2007).
  3. Dery, H. et al. Nanospintronics based on magnetologic gates. IEEE Trans. Electron Dev. 59, 259262 (2012).
  4. Datta, S. & Das, B. Electronic analog of the electro-optic modulator. Appl. Phys. Lett. 56, 665667 (1990).
  5. Tombros, N., Jozsa, C., Popinciuc, M., Jonkman, H. T. & van Wees, B. J. Electronic spin transport and spin precession in single graphene layers at room temperature. Nature 448, 571574 (2007).
    This is the first paper to demonstrate spin transport and precession in graphene at room temperature.
  6. Han, W. et al. Tunneling spin injection into single layer graphene. Phys. Rev. Lett. 105, 167202 (2010).
    This is the first paper to demonstrate tunnelling spin injection into graphene, which led to efficient spin injection and enhanced spin lifetimes.
  7. Zomer, P. J., Guimarães, M. H. D., Tombros, N. & van Wees, B. J. Long-distance spin transport in high-mobility graphene on hexagonal boron nitride. Phys. Rev. B 86, 161416 (2012).
  8. Yang, T.-Y. et al. Observation of long spin relaxation times in bilayer graphene at room temperature. Phys. Rev. Lett. 107, 047206 (2011).
    This paper and the next are the first ones to report longer spin lifetimes and a different spin-relaxation mechanism in bilayer graphene.
  9. Han, W. & Kawakami, R. K. Spin relaxation in single layer and bilayer graphene. Phys. Rev. Lett. 107, 047207 (2011).
  10. Dlubak, B. et al. Highly efficient spin transport in epitaxial graphene on SiC. Nature Phys. 8, 557561 (2012).
    This paper presents efficient spin injection into epitaxial graphene on SiC.
  11. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109162 (2009).
  12. Sarma, S. D., Adam, S., Hwang, E. H. & Rossi, E. Electronic transport in two dimensional graphene. Rev. Mod. Phys. 83, 407470 (2011).
  13. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666669 (2004).
  14. Johnson, M. & Silsbee, R. H. Interfacial charge–spin coupling: Injection and detection of spin magnetization in metals. Phys. Rev. Lett. 55, 17901793 (1985).
  15. Jedema, F. J., Filip, A. T. & van Wees, B. J. Electrical spin injection and accumulation at room temperature in an all-metal mesoscopic spin valve. Nature 410, 345348 (2001).
  16. Fert, A. & Lee, S.-F. Theory of the bipolar spin switch. Phys. Rev. B 53, 65546565 (1996).
  17. Muduli, P. K. et al. Large local Hall effect in pin-hole dominated multigraphene spin-valves. Nanotechnology 24, 015703 (2013).
  18. Cho, S., Chen, Y.-F. & Fuhrer, M. S. Gate-tunable graphene spin valve. Appl. Phys. Lett. 91, 123105 (2007).
  19. Nishioka, M. & Goldman, A. M. Spin transport through multilayer graphene. Appl. Phys. Lett. 90, 252505 (2007).
  20. Ohishi, M. et al. Spin injection into a graphene thin film at room temperature. Jpn. J. Appl. Phys. 46, L605L607 (2007).
  21. Jozsa, C., Popinciuc, M., Tombros, N., Jonkman, H. T. & van Wees, B. J. Electronic spin drift in graphene field effect transistors. Phys. Rev. Lett. 100, 236603 (2008).
  22. Han, W. et al. Electron–hole asymmetry of spin injection and transport in single-layer graphene. Phys. Rev. Lett. 102, 137205 (2009).
  23. Han, W. et al. Electrical detection of spin precession in single layer graphene spin valves with transparent contacts. Appl. Phys. Lett. 94, 222109 (2009).
  24. Popinciuc, M. et al. Electronic spin transport in graphene field effect transistors. Phys. Rev. B 80, 214427 (2009).
  25. Schmidt, G., Ferrand, D., Molenkamp, L. W., Filip, A. T. & van Wees, B. J. Fundamental obstacle for electrical spin injection from a ferromagnetic metal into a diffusive semiconductor. Phys. Rev. B 62, 4790(R) (2000).
  26. Rashba, E. I. Theory of electrical spin injecton: Tunnel contacts as a solution of the conductivity mismatch problem. Phys. Rev. B 62, 16267(R) (2000).
  27. Fert, A. & Jaffres, H. Conditions for efficient spin injection from a ferromagnetic metal into a semiconductor. Phys. Rev. B 64, 184420 (2001).
  28. Zhang, C., Wang, Y., Wu, B. & Wu, Y. Enhancement of spin injection from ferromagnet to graphene with a Cu interfacial layer. Appl. Phys. Lett. 101, 022406 (2012).
  29. Yamaguchi, T., Masubuchi, S., Iguchi, K., Moriya, R. & Machida, T. Tunnel spin injection into graphene using Al2O3 barrier grown by atomic layer deposition on functionalized graphene surface. J. Magn. Magn. Mater. 324, 849852 (2012).
  30. Jo, S., Ki, D.-K., Jeong, D., Lee, H-J. & Kettemann, S. Spin relaxation properties in graphene due to its linear dispersion. Phys. Rev. B 84, 075453 (2011).
  31. Avsar, A. et al. Towards wafer scale fabrication of graphene based spin valve devices. Nano Lett. 11, 23632358 (2011).
  32. Pi, K. et al. Manipulation of spin transport in graphene by surface chemical doping. Phys. Rev. Lett. 104, 187201 (2010).
  33. Liu, Y. P. et al. Spin injection properties in trilayer graphene lateral spin valves. Appl. Phys. Lett. 102, 033105 (2013).
  34. Neumann, I. et al. Electrical detection of spin precession in freely suspended graphene spin valves on cross-linked poly(methyl methacrylate). Small 9, 156160 (2013).
  35. Friedman, A. L., van't Erve, O. M. J., Li, C. H., Robinson, J. T. & Jonker, B. T. Homoepitaxial tunnel barriers with functionalized graphene-on-graphene for charge and spin transport. Nature Commun. 5, 3161 (2014).
  36. Volmer, F. et al. Role of MgO barriers for spin and charge transport in Co/MgO/graphene nonlocal spin-valve devices. Phys. Rev. B 88, 161405 (2013).
  37. Yamaguchi, T. et al. Electrical spin injection into graphene through monolayer hexagonal boron nitride. Appl. Phys. Express 6, 073001 (2013).
  38. Hill, E. W., Geim, A. K., Novoselov, K., Schedin, F. & Blake, P. Graphene spin valve devices. IEEE Trans. Magn. 42, 26942696 (2006).
  39. Wang, W. H. et al. Magnetotransport properties of mesoscopic graphite spin valves. Phys. Rev. B 77, 020402(R) (2008).
  40. Guimarães, M. H. D. et al. Spin transport in high-quality suspended graphene devices. Nano Lett. 12, 35123517 (2012).
  41. Drögeler, M. et al. Nanosecond spin lifetimes in single- and few-layer graphene–hBN heterostructures at room temperature. Preprint at http://arXiv.org/abs/1406.2439v1 (2014).
  42. Guimarães, M. H. D. et al. Transverse electric field control of spin relaxation in hBN encapsulated graphene. Phys. Rev. Lett. 113, 086602 (2014).
  43. Patra, A. K. et al. Dynamic spin injection into chemical vapor deposited graphene. Appl. Phys. Lett. 101, 162407 (2012).
  44. Tang, Z. et al. Dynamically generated pure spin current in single-layer graphene. Phys. Rev. B 87, 140401 (2013).
  45. Birkner, B. et al. Annealing-induced magnetic moments detected by spin precession measurements in epitaxial graphene on SiC. Phys. Rev. B 87, 081405 (2013).
  46. Vera-Marun, I. J., Ranjan, V. & van Wees, B. J. Nonlinear detection of spin currents in graphene with non-magnetic electrodes. Nature Phys. 8, 313316 (2012).
  47. Yazyev, O. V. & Helm, L. Defect-induced magnetism in graphene. Phys. Rev. B 75, 125408 (2007).
    This paper predicts magnetic moments induced by point defects including vacancy and hydrogen adatoms.
  48. Nair, R. R. et al. Spin-half paramagnetism in graphene induced by point defects. Nature Phys. 8, 199202 (2012).
    This paper identifies the spin-1/2 paramagnetism in graphene induced by fluorine and vacancy point defects based on SQUID magnetometry.
  49. Cervenka, J., Katsnelson, M. I. & Flipse, C. F. J. Room-temperature ferromagnetism in graphite driven by two-dimensional networks of point defects. Nature Phys. 5, 840844 (2009).
  50. McCreary, K. M., Swartz, A. G., Han, W., Fabian, J. & Kawakami, R. K. Magnetic moment formation in graphene detected by scattering of pure spin currents. Phys. Rev. Lett. 109, 186604 (2012).
    This paper presents the formation of localized magnetic moments and paramagnetism induced by hydrogen and vacancy point defects based on spin transport.
  51. Giesbers, A. J. M. et al. Interface-induced room-temperature ferromagnetism in hydrogenated epitaxial graphene. Phys. Rev. Lett. 111, 166101 (2013).
  52. Boukhvalov, D. W., Katsnelson, M. I. & Lichtenstein, A. I. Hydrogen on graphene: Electronic structure, total energy, structural distortions and magnetism from first-principles calculations. Phys. Rev. B 77, 035427 (2008).
  53. Hong, X., Zou, K., Wang, B., Cheng, S. H. & Zhu, J. Evidence for spin-flip scattering and local moments in dilute fluorinated graphene. Phys. Rev. Lett. 108, 226602 (2012).
  54. Santos, E. J. G., Sánchez-Portal, D. & Ayuela, A. Magnetism of substitutional Co impurities in graphene: Realization of single π vacancies. Phys. Rev. B 81, 125433 (2010).
  55. Zhang, H., Lazo, C., Blügel, S., Heinze, S. & Mokrousov, Y. Electrically tunable quantum anomalous Hall effect in graphene decorated by 5d transition-metal adatoms. Phys. Rev. Lett. 108, 056802 (2012).
  56. Hong, J. et al. Room-temperature magnetic ordering in functionalized graphene. Sci. Rep. 2, 624 (2012).
  57. Nair, R. R. et al. Dual origin of defect magnetism in graphene and its reversible switching by molecular doping. Nature Commun. 4, 2010 (2013).
  58. Son, Y.-W., Cohen, M. L. & Louie, S. G. Half-metallic graphene nanoribbons. Nature 444, 347349 (2006).
  59. Lieb, E. H. Two theorems on the Hubbard model. Phys. Rev. Lett. 62, 12011204 (1989).
  60. Elias, D. C. et al. Control of graphene's properties by reversible hydrogenation: Evidence for graphane. Science 323, 610613 (2009).
  61. Sofo, J. O. et al. Magnetic structure of hydrogen-induced defects on graphene. Phys. Rev. B 85, 115405 (2012).
  62. Rudenko, A. N., Keil, F. J., Katsnelson, M. I. & Lichtenstein, A. I. Exchange interactions and frustrated magnetism in single-side hydrogenated and fluorinated graphene. Phys. Rev. B 88, 081405 (2013).
  63. Kelly, K. F., Mickelson, E. T., Hauge, R. H., Margrave, J. L. & Halas, N. J. Nanoscale imaging of chemical interactions: Fluorine on graphite. Proc. Natl Acad. Sci. USA 97, 1031810321 (2000).
  64. Robinson, J. T. et al. Properties of fluorinated graphene films. Nano Lett. 10, 30013005 (2010).
  65. Wei, W. & Jacob, T. Electronic and optical properties of fluorinated graphene: A many-body perturbation theory study. Phys. Rev. B 87, 115431 (2013).
  66. Nair, R. R. et al. Fluorographene: A two-dimensional counterpart of Teflon. Small 6, 28772884 (2010).
  67. Liu, H. Y., Hou, Z. F., Hu, C. H., Yang, Y. & Zhu, Z. Z. Electronic and magnetic properties of fluorinated graphene with different coverage of fluorine. J. Phys. Chem. C 116, 1819318201 (2012).
  68. Kim, H.-J. & Cho, J.-H. Fluorine-induced local magnetic moment in graphene: A hybrid DFT study. Phys. Rev. B 87, 174435 (2013).
  69. Mori-Sánchez, P., Cohen, A. J. & Yang, W. Localization and delocalization errors in density functional theory and implications for band-gap prediction. Phys. Rev. Lett. 100, 146401 (2008).
  70. Casolo, S., Flage-Larsen, E., Løvvik, O. M., Darling, G. R. & Tantardini, G. F. Role of the self-interaction error in studying chemisorption on graphene from first-principles. Phys. Rev. B 81, 205412 (2010).
  71. Nanda, B. R. K., Sherafati, M., Popović, Z. S. & Satpathy, S. Electronic structure of the substitutional vacancy in graphene: density-functional and Green's function studies. New J. Phys. 14, 083004 (2012).
  72. Ugeda, M. M., Brihuega, I., Guinea, F. & Gómez-Rodríguez, J. M. Missing atom as a source of carbon magnetism. Phys. Rev. Lett. 104, 096804 (2010).
  73. Palacios, J. J. & Ynduráin, F. Critical analysis of vacancy-induced magnetism in monolayer and bilayer graphene. Phys. Rev. B 85, 245443 (2012).
  74. Swartz, A. G., McCreary, K. M., Han, W., Wen, H. & Kawakami, R. K. A systematic approach to interpreting Hanle spin precession data in non-local spin valves. Proc. SPIE 8813, 881328 (2013).
  75. Fabian, J., Matos-Abiague, A., Ertler, C., Stano, P. & Zutic, I. Semiconductor spintronics. Acta Phys. Slov. 57, 565907 (2007).
  76. Balakrishnan, J., Kok Wai Koon, G., Jaiswal, M., Castro Neto, A. H. & Ozyilmaz, B. Colossal enhancement of spin–orbit coupling in weakly hydrogenated graphene. Nature Phys. 9, 284287 (2013).
  77. Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).
    This paper started the field of topological insulators.
  78. Tse, W.-K., Qiao, Z., Yao, Y., MacDonald, A. H. & Niu, Q. Quantum anomalous Hall effect in single-layer and bilayer graphene. Phys. Rev. B 83, 155447 (2011).
  79. Liu, M.-H., Bundesmann, J. & Richter, K. Spin-dependent Klein tunneling in graphene: Role of Rashba spin–orbit coupling. Phys. Rev. B 85, 085406 (2012).
  80. McCann, E. & Fal'ko, V. I. zright arrow-z symmetry of spin–orbit coupling and weak localization in graphene. Phys. Rev. Lett. 108, 166606 (2012).
  81. Scholz, A., López, A. & Schliemann, J. Interplay between spin–orbit interactions and a time-dependent electromagnetic field in monolayer graphene. Phys. Rev. B 88, 045118 (2013).
  82. Kramida, A., Ralchenko, Y., Reader, J. & Team, N. A. NIST Atomic Spectra Database (version 5.1) http://physics.nist.gov/asd (National Institute of Standards and Technology, 2013).
  83. Rashba, E. I. Properties of semiconductors with an extremum loop. 1. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop. Sov. Phys. Solid State 2, 12241238 (1960).
  84. Gmitra, M., Konschuh, S., Ertler, C., Ambrosch-Draxl, C. & Fabian, J. Band-structure topologies of graphene: Spin–orbit coupling effects from first principles. Phys. Rev. B 80, 235431 (2009).
    This paper establishes ab initio values for intrinsic and Rashba spin–orbit coupling in graphene.
  85. Abdelouahed, S., Ernst, A., Henk, J., Maznichenko, I. V. & Mertig, I. Spin-split electronic states in graphene: Effects due to lattice deformation, Rashba effect, and adatoms by first principles. Phys. Rev. B 82, 125424 (2010).
  86. Boettger, J. C. & Trickey, S. B. First-principles calculation of the spin–orbit splitting in graphene. Phys. Rev. B 75, 121402 (2007).
  87. McClure, J. W. & Yafet, Y. Theory of the g-factor of the current carriers in graphite single crystals. Proc. 5th Conf. Carbon 1, 22 (Pergamon, 1962).
  88. Huertas-Hernando, D., Guinea, F. & Brataas, A. Spin–orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps. Phys. Rev. B 74, 155426 (2006).
  89. Jhang, S. H. et al. Spin-orbit interaction in chiral carbon nanotubes probed in pulsed magnetic fields. Phys. Rev. B 82, 041404 (2010).
  90. Ochoa, H., Castro Neto, A. H., Fal'ko, V. I. & Guinea, F. Spin–orbit coupling assisted by flexural phonons in graphene. Phys. Rev. B 86, 245411 (2012).
  91. Song, Y. & Dery, H. Transport theory of monolayer transition-metal dichalcogenides through symmetry. Phys. Rev. Lett. 111, 026601 (2013).
  92. Mayorov, A. S. et al. How close can one approach the Dirac point in graphene experimentally? Nano Lett. 12, 46294634 (2012).
  93. Liu, C.-C., Feng, W. & Yao, Y. Quantum spin Hall effect in silicene and two-dimensional germanium. Phys. Rev. Lett. 107, 076802 (2011).
  94. Qiu, D. Y., da Jornada, F. H. & Louie, S. G. Optical spectrum of MoS2: Many-body effects and diversity of exciton states. Phys. Rev. Lett. 111, 216805 (2013).
  95. Kośmider, K., González, J. W. & Fernández-Rossier, J. Large spin splitting in the conduction band of transition metal dichalcogenide monolayers. Phys. Rev. B 88, 245436 (2013).
  96. Shi, H., Pan, H., Zhang, Y.-W. & Yakobson, B. I. Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2. Phys. Rev. B 87, 155304 (2013).
  97. Min, H. et al. Intrinsic and Rashba spin–orbit interactions in graphene sheets. Phys. Rev. B 74, 165310 (2006).
  98. Konschuh, S., Gmitra, M. & Fabian, J. Tight-binding theory of the spin–orbit coupling in graphene. Phys. Rev. B 82, 245412 (2010).
  99. Konschuh, S., Gmitra, M., Kochan, D. & Fabian, J. Theory of spin–orbit coupling in bilayer graphene. Phys. Rev. B 85, 115423 (2012).
  100. Konschuh, S. Spin–Orbit Coupling Effects: From Graphene to Graphite PhD thesis, Univ. Regensburg (2011).
  101. Kormányos, A. & Burkard, G. Intrinsic and substrate induced spin–orbit interaction in chirally stacked trilayer graphene. Phys. Rev. B 87, 045419 (2013).
  102. Castro Neto, A. H. & Guinea, F. Impurity-induced spin–orbit coupling in graphene. Phys. Rev. Lett. 103, 026804 (2009).
    This paper proposes to use adatoms to increase and manipulate spin–orbit coupling in graphene.
  103. Weeks, C., Hu, J., Alicea, J., Franz, M. & Wu, R. Engineering a robust quantum spin Hall state in graphene via adatom deposition. Phys. Rev. X 1, 021001 (2011).
  104. Gmitra, M., Kochan, D. & Fabian, J. Spin–orbit coupling in hydrogenated graphene. Phys. Rev. Lett. 110, 246602 (2013).
  105. Józsa, C. et al. Linear scaling between momentum and spin scattering in graphene. Phys. Rev. B 80, 241403(R) (2009).
  106. Han, W. et al. Spin transport and relaxation in graphene. J. Magn. Magn. Mater. 324, 369381 (2012).
  107. Han, W. et al. Spin relaxation in single-layer graphene with tunable mobility. Nano Lett. 12, 34433447 (2012).
  108. Jedema, F. J., Heersche, H. B., Filip, A. T., Baselmans, J. J. A. & van Wees, B. J. Electrical detection of spin precession in a metallic mesoscopic spin valve. Nature 416, 713716 (2002).
  109. Zaffalon, M. & van Wees, B. J. Spin injection, accumulation, and precession in a mesoscopic nonmagnetic metal island. Phys. Rev. B 71, 125401 (2005).
  110. Sosenko, E., Wei, H. & Aji, V. Effect of contacts on spin lifetime measurements in graphene. Phys. Rev. B 89, 245436 (2014).
  111. Maassen, T. et al. Localized states influence spin transport in epitaxial graphene. Phys. Rev. Lett. 110, 067209 (2013).
  112. Huertas-Hernando, D., Guinea, F. & Brataas, A. Spin–orbit-mediated spin relaxation in graphene. Phys. Rev. Lett. 103, 146801 (2009).
  113. Dóra, B., Murányi, F. & Simon, F. Electron spin dynamics and electron spin resonance in graphene. Europhys. Lett. 92, 17002 (2010).
  114. Ertler, C., Konschuh, S., Gmitra, M. & Fabian, J. Electron spin relaxation in graphene: The role of the substrate. Phys. Rev. B 80, 041405(R) (2009).
  115. Fratini, S., Gosálbez-Martínez, D., Merodio Cámara, P. & Fernández-Rossier, J. Anisotropic intrinsic spin relaxation in graphene due to flexural distortions. Phys. Rev. B 88, 115426 (2013).
  116. Elliott, R. J. Theory of the effect of spin–orbit coupling on magnetic resonance in some semiconductors. Phys. Rev. 96, 266279 (1954).
  117. Yafet, Y. in Solid State Physics Vol. 14 (eds Seitz F. & Turnbull, D.) 198 (Academic, 1963).
  118. Dyakonov, M. I. & Perel, V. I. Spin relaxation of conduction electrons in noncentrosymmetric semiconductors. Sov. Phys. Solid State 13, 30233026 (1972).
  119. Wu, M. W., Jiang, J. H. & Weng, M. Q. Spin dynamics in semiconductors. Phys. Rep. 493, 61236 (2010).
  120. Tuan, D. V., Ortmann, F., Soriano, D., Valenzuela, S. O. & Roche, S. Pseudospin-driven spin relaxation mechanism in graphene. Nature Phys. http://dx.doi.org/10.1038/nphys3083 (2014).
  121. Maassen, T., Dejene, F. K., Guimaraes, M. H., Jozsa, C. & van Wees, B. J. Comparison between charge and spin transport in few layer graphene. Phys. Rev. B 83, 115410 (2011).
  122. Dugaev, V. K., Sherman, E. Y. & Barnaś, J. Spin dephasing and pumping in graphene due to random spin-orbit interaction. Phys. Rev. B 83, 085306 (2011).
  123. Zhang, P. & Wu, M. W. Electron spin relaxation in graphene with random Rashba field: comparison of the D'yakonov–Perel' and Elliott-Yafet-like mechanisms. New J. Phys. 14, 033015 (2012).
  124. Wojtaszek, M., Vera-Marun, I. J., Whiteway, E., Hilke, M. & van Wees, B. J. Absence of hyperfine effects in 13C-graphene spin-valve devices. Phys. Rev. B 89, 035417 (2014).
  125. Lundeberg, M. B., Yang, R., Renard, J. & Folk, J. A. Defect-mediated spin relaxation and dephasing in graphene. Phys. Rev. Lett. 110, 156601 (2013).
  126. Kochan, D., Gmitra, M. & Fabian, J. Spin relaxation mechanism in graphene: resonant scattering by magnetic impurities. Phys. Rev. Lett. 112, 116602 (2014).
  127. Wojtaszek, M., Vera-Marun, I. J., Maassen, T. & van Wees, B. J. Enhancement of spin relaxation time in hydrogenated graphene spin-valve devices. Phys. Rev. B 87, 081402 (2013).
  128. Kimura, T., Sato, T. & Otani, Y. Temperature evolution of spin relaxation in a NiFe/Cu lateral spin valve. Phys. Rev. Lett. 100, 066602 (2008).
  129. Suzuki, T. et al. Room-temperature electron spin transport in a highly doped Si channel. Appl. Phys. Express 4, 023003 (2011).
  130. Zhou, Y. et al. Electrical spin injection and transport in germanium. Phys. Rev. B 84, 125323 (2011).
  131. Yang, T., Kimura, T. & Otani, Y. Giant spin-accumulation signal and pure spin-current-induced reversible magnetization switching. Nature Phys. 4, 851854 (2008).
  132. Idzuchi, H., Fukuma, Y., Wang, L. & Otani, Y. Spin relaxation mechanism in silver nanowires covered with MgO protection layer. Appl. Phys. Lett. 101, 022415 (2012).
  133. Behin-Aein, B., Datta, D., Salahuddin, S. & Datta, S. Proposal for an all-spin logic device with built-in memory. Nature Nanotech. 5, 266270 (2010).
  134. Lin, C.-C. et al. Spin transfer torque in a graphene lateral spin valve assisted by an external magnetic field. Nano Lett. 13, 51775181 (2013).
  135. Wen, H., Zhu, T., Luo, Y., Amamou, W. & Kawakami, R. K. Current-based detection of nonlocal spin transport in graphene for spin-based logic applications. J. Appl. Phys. 115, 17B741 (2014).
  136. Jaffres, H., George, J.-M. & Fert, A. Spin transport in multiterminal devices: Large spin signals in devices with confined geometry. Phys. Rev. B 82, 140408 (2010).
  137. Qiao, Z. et al. Quantum anomalous Hall effect in graphene proximity coupled to an antiferromagnetic insulator. Phys. Rev. Lett. 112, 116404 (2014).
  138. Jiang, H., Qiao, Z., Liu, H., Shi, J. & Niu, Q. Stabilizing topological phases in graphene via random adsorption. Phys. Rev. Lett. 109, 116803 (2012).
  139. Haugen, H., Huertas-Hernando, D. & Brataas, A. Spin transport in proximity-induced ferromagnetic graphene. Phys. Rev. B 77, 115406 (2008).
  140. Michetti, P., Recher, P. & Iannaccone, G. Electric field control of spin rotation in bilayer graphene. Nano Lett. 10, 44634469 (2010).
  141. Yang, H. X. et al. Proximity effects induced in graphene by magnetic insulators: First-principles calculations on spin filtering and exchange-splitting gaps. Phys. Rev. Lett. 110, 046603 (2013).
  142. Swartz, A. G., Odenthal, P. M., Hao, Y., Ruoff, R. S. & Kawakami, R. K. Integration of the ferromagnetic insulator EuO onto graphene. ACS Nano 6, 1006310069 (2012).
  143. Song, C.-L. et al. Topological insulator Bi2Se3 thin films grown on double-layer graphene by molecular beam epitaxy. Appl. Phys. Lett. 97, 143118 (2010).
  144. Roy, K. et al. Graphene–MoS2 hybrid structures for multifunctional photoresponsive memory devices. Nature Nanotech. 8, 826830 (2013).
  145. Butler, S. Z. et al. Progress, challenges, and opportunities in two-dimensional materials beyond graphene. ACS Nano 7, 28982926 (2013).
  146. Bianco, E. et al. Stability and exfoliation of germanane: A germanium graphane analogue. ACS Nano 7, 44144421 (2013).
  147. Pinchuk, I. V. et al. Epitaxial co-deposition growth of CaGe2 films by molecular beam epitaxy for large area germanane. J. Mater. Res. 29, 410416 (2014).
  148. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: A new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).
  149. Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nature Nanotech. 7, 699712 (2012).
  150. Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).
  151. Xu, Y. et al. Large-gap quantum spin Hall insulators in tin films. Phys. Rev. Lett. 111, 136804 (2013).
  152. Blase, X., Rubio, A., Louie, S. G. & Cohen, M. L. Quasiparticle band structure of bulk hexagonal boron nitride and related systems. Phys. Rev. B 51, 68686875 (1995).
  153. FLEUR: The Jülich FLAPW code family; http://www.flapw.de
  154. Appelbaum, I., Huang, B. & Monsma, D. J. Electronic measurement and control of spin transport in silicon. Nature 447, 295298 (2007).
  155. Lou, X. et al. Electrical detection of spin transport in lateral ferromagnet-semiconductor devices. Nature Phys. 3, 197202 (2007).
  156. Huang, B. & Appelbaum, I. Spin dephasing in drift-dominated semiconductor spintronics devices. Phys. Rev. B 77, 165331 (2008).
  157. Li, P., Li, J., Qing, L., Dery, H. & Appelbaum, I. Anisotropy-driven spin relaxation in germanium. Phys. Rev. Lett. 111, 257204 (2013).
  158. Kikkawa, J. M. & Awschalom, D. D. Resonant spin amplification in n-type GaAs. Phys. Rev. Lett. 80, 4313 (1998).

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Affiliations

  1. International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China

    • Wei Han
  2. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

    • Wei Han
  3. IBM Almaden Research Center, San Jose, California 95120, USA

    • Wei Han
  4. Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA

    • Roland K. Kawakami
  5. Department of Physics and Astronomy, University of California, Riverside, California 92521, USA

    • Roland K. Kawakami
  6. Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany

    • Martin Gmitra &
    • Jaroslav Fabian

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