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Pseudospin-driven spin relaxation mechanism in graphene


The prospect of transporting spin information over long distances in graphene, possible because of its small intrinsic spin–orbit coupling (SOC) and vanishing hyperfine interaction, has stimulated intense research exploring spintronics applications. However, measured spin relaxation times are orders of magnitude smaller than initially predicted, while the main physical process for spin dephasing and its charge-density and disorder dependences remain unconvincingly described by conventional mechanisms. Here, we unravel a spin relaxation mechanism for non-magnetic samples that follows from an entanglement between spin and pseudospin driven by random SOC, unique to graphene. The mixing between spin and pseudospin-related Berry’s phases results in fast spin dephasing even when approaching the ballistic limit, with increasing relaxation times away from the Dirac point, as observed experimentally. The SOC can be caused by adatoms, ripples or even the substrate, suggesting novel spin manipulation strategies based on the pseudospin degree of freedom.

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Figure 1: Spin dynamics in disordered graphene.
Figure 2: Spin relaxation times and transport mechanisms.
Figure 3: Spin relaxation times deduced from the continuum and microscopic models.
Figure 4: Spin and pseudospin dynamics in graphene with ρ = 8% of adatoms.


  1. 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, 109–162 (2009).

    Article  ADS  Google Scholar 

  2. Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chiral tunnelling and the Klein paradox in graphene. Nature Phys. 2, 620–625 (2006).

    Article  ADS  Google Scholar 

  3. McCann, E. et al. Weak localisation magnetoresistance and valley symmetry in graphene. Phys. Rev. Lett. 97, 146805 (2006).

    Article  ADS  Google Scholar 

  4. Novoselov, K. S. et al. Room-temperature quantum Hall effect in graphene. Science 315, 1379 ( 2007).

    Article  ADS  Google Scholar 

  5. Rycerz, A., Tworzydlo, J. & Beenakker, C. W. J. Valley filter and valley valve in graphene. Nature Phys. 3, 172–175 (2007).

    Article  ADS  Google Scholar 

  6. San-Jose, P., Prada, E., McCann, E. & Schomerus, H. Pseudospin valve in bilayer graphene: Towards graphene-based pseudospintronics. Phys. Rev. Lett. 102, 247204 (2009).

    Article  ADS  Google Scholar 

  7. Rashba, E. I. Graphene with structure-induced spin–orbit coupling: Spin-polarized states, spin zero modes, and quantum Hall effect. Phys. Rev. B 79, 161409 (2009).

    Article  ADS  Google Scholar 

  8. Zutic, I., Fabian, J. & Das Sarma, S. Spintronics: Fundamentals and applications. Rev. Mod. Phys. 76, 323–410 (2004).

    Article  ADS  Google Scholar 

  9. 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, 713–716 (2002).

    Article  ADS  Google Scholar 

  10. Lou, X. et al. Electrical detection of spin transport in lateral ferromagnet–semiconductor devices. Nature Phys. 3, 197–202 (2007).

    Article  ADS  Google Scholar 

  11. Avsar, A. et al. Towards wafer scale fabrication of graphene based spin valve devices. Nano Lett. 11, 2363–2368 (2011).

    Article  ADS  Google Scholar 

  12. Han, W. & Kawakami, R. K. Spin relaxation in single-layer and bilayer graphene. Phys. Rev. Lett. 107, 047207 (2011).

    Article  ADS  Google Scholar 

  13. Zomer, P. J., Guimaraes, 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(R) (2012).

    Article  ADS  Google Scholar 

  14. Dlubak, B. et al. Highly efficient spin transport in epitaxial graphene on SiC. Nature Phys. 8, 557–561 (2012).

    Article  ADS  Google Scholar 

  15. Ochoa, H., Castro Neto, A. H. & Guinea, F. Elliot-Yafet mechanism in graphene. Phys. Rev. Lett. 108, 206808 (2012).

    Article  ADS  Google Scholar 

  16. Zhang, Z. & Wu, M. W. Electron spin relaxation in graphene with random Rashba field: Comparison of the Dyakonov-Perel’ and Elliot-Yafet-like mechanisms. New J. Phys. 14, 033015 (2012).

    Article  ADS  Google Scholar 

  17. 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, 571–574 (2007).

    Article  ADS  Google Scholar 

  18. Min, H. et al. Intrinsic and Rashba spin–orbit interactions in graphene sheets. Phys. Rev. B 74, 165310 (2006).

    Article  ADS  Google Scholar 

  19. Ertler, C., Konshush, S., Gmitra, M. & Fabian, J. Electron spin relaxation in graphene: The role of substrate. Phys. Rev. B 80, 045405(R) (2009).

    Article  Google Scholar 

  20. Castro Neto, A. H. & Guinea, F. Impurity-induced spin–orbit coupling in graphene. Phys. Rev. Lett. 103, 026804 (2009).

    Article  ADS  Google Scholar 

  21. Guimaraes, M. H. D. et al. Spin transport in high-quality suspended graphene device. Nano Lett. 12, 3512–3517 (2012).

    Article  ADS  Google Scholar 

  22. Neumann, I. et al. Electrical detection of spin precession in freely suspended graphene spin valves on cross-linked poly(methyl methacrylate). Small 9, 156–160 (2013).

    Article  Google Scholar 

  23. Dery, H. & Song, Y. Transport theory of monolayer transition-metal dichalcogenides through symmetry. Phys. Rev. Lett. 111, 026601 (2013).

    Article  ADS  Google Scholar 

  24. Pi, K. et al. Manipulation of spin transport in graphene by surface chemical doping. Phys. Rev. Lett. 104, 187201 (2010).

    Article  ADS  Google Scholar 

  25. Kochan, D., Gmitra, M. & Fabian, J. Spin relaxation mechanism in graphene: Resonant scattering by magnetic impurities. Phys. Rev. Lett. 112, 116602 (2014).

    Article  ADS  Google Scholar 

  26. Roche, S. & Valenzuela, S. O. Graphene spintronics: Puzzling controversies and challenges for spin manipulation. J. Phys. D 47, 094011 (2014).

    Article  ADS  Google Scholar 

  27. 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).

    Google Scholar 

  28. Dedkov, Y. S., Fonin, M., Rudiger, U. & Laubschat, C. Rashba effect in the graphene/Ni(111) system. Phys. Rev. Lett. 100, 107602 (2008).

    Article  ADS  Google Scholar 

  29. Marchenko, D. et al. Giant Rashba splitting in graphene due to hybridization with gold. Nature Commun. 3, 1232 (2012).

    Article  ADS  Google Scholar 

  30. Roche, S. et al. Quantum transport in disordered graphene: A theoretical perspective. Solid State Commun. 152, 1404–1410 (2012).

    Article  ADS  Google Scholar 

  31. Nikolic, B. K. & Souma, S. Decoherence of transported spin in multichannel spin–orbit-coupled spintronic devices: Scattering approach to spin-density matrix from the ballistic to the localized regime. Phys. Rev. B 71, 195328 (2005).

    Article  ADS  Google Scholar 

  32. Dery, H. et al. Nanospintronics based on magnetologic gates. IEEE Trans. Electron Devices 59, 259–262 (2012).

    Article  ADS  Google Scholar 

  33. Foa Torres, L. E. F., Roche, S. & Charlier, J. C. Introduction to Graphene-Based Nanomaterials: From Electronic Structure to Quantum Transport (Cambridge Univ. Press, 2014).

    Google Scholar 

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We thank A. Cummings for a critical reading of the manuscript. The research leading to these results has received funding from the European Union Seventh Framework Programme under grant agreement number 604391 Graphene Flagship. This work was also funded by Spanish Ministry of Economy and Competitiveness under contracts MAT2012-33911 and MAT2010-18065. S.O.V. acknowledges ERC Grant agreement 308023 SPINBOUND.

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D.V.T., D.S. and F.O. designed the models and performed the calculations. D.V.T., F.O., S.O.V. and S.R. carried out analyses and interpretation. F.O., S.O.V. and S.R. wrote the text and all authors contributed to the manuscript and Supplementary Information.

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Correspondence to Stephan Roche.

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The authors declare no competing financial interests.

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Tuan, D., Ortmann, F., Soriano, D. et al. Pseudospin-driven spin relaxation mechanism in graphene. Nature Phys 10, 857–863 (2014).

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