Pseudospin-driven spin relaxation mechanism in graphene

Journal name:
Nature Physics
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Published online


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.

At a glance


  1. Spin dynamics in disordered graphene.
    Figure 1: Spin dynamics in disordered graphene.

    a, Ball-and-stick model of a random distribution of adatoms on top of graphene. b, Top view of the gold adatom sitting above the centre of a hexagon. c,d, Time-dependent projected spin polarization Sz(E, t) of charge carriers (symbols) initially prepared in an out-of-plane polarization (at Dirac point (red curves) and at E = 150 meV (blue curves)). Analytical fits are given as solid lines (see text). Parameters are VI = 0.007γ0, VR = 0.0165γ0, μ = 0.1γ0, ρ = 0.05% (c) and ρ = 8% (d).

  2. Spin relaxation times and transport mechanisms.
    Figure 2: Spin relaxation times and transport mechanisms.

    a,b, Spin relaxation times (τs) for ρ = 0.05% (a) and ρ = 8% (b). Black (red) solid symbols indicate τs for μ = 0.1γ0 (μ = 0.2γ0).T versus E is also shown (open symbols). τp (dotted line in b) is shown over a wider energy range (top horizontal axis) to stress the divergence around E = 0 (μ = 0.2γ0). c,d, Time-dependent diffusion coefficient D(t) for ρ = 0.05% (c) and ρ = 8% (d) with μ = 0.2γ0.

  3. Spin relaxation times deduced from the continuum and microscopic models.
    Figure 3: Spin relaxation times deduced from the continuum and microscopic models.

    a, Spin relaxation times (τs) for varying ρ between 0.05% and 8% extracted from the microscopic model (with μ = 0.1γ0). Inset: τs values using the continuum model for ρ = 1% and 8% (filled symbols). A comparison with the microscopic model (with μ = 0) is also given for ρ = 8% (open circles). b, Scaling behaviour of T and τs versus 1/ρ. The T values obtained with the microscopic (resp. continuum) model are given by red diamonds (resp. red solid lines). τs values for the microscopic model (blue squares) and the continuum model (black circles) are shown for two selected energies E = 150 meV (solid symbols) and E = 0 (open symbols). Solid lines are here guides to the eye.

  4. Spin and pseudospin dynamics in graphene with [rho] = 8% of adatoms.
    Figure 4: Spin and pseudospin dynamics in graphene with ρ = 8% of adatoms.

    ac, Time dependence of spin-polarization Sz (blue) and pseudospin polarization σz (green) in the z projection for energies E = 130 meV (a), E = 0 (b), and E = − 5 meV (c). Note that all quantities are normalized to their maximum value to better contrast them in the same scale. Middle panels show the time evolution for both spin (from blue to pink) and pseudospin (from green to orange). The snapshots are taken at different times from t1 to t4, sampling the shaded regions in ac. d, Fourier transform of Sz(t) plotted over oscillation period, and showing non-dispersive spectra at high energy (between E = 125 meV, 130 meV and 135 meV). Low-energy spectra (for E = − 5 meV, 0 and 5 meV) change strongly with energy (dispersive), showing a gradual reduction and blue shift of the original Rashba peak at approximately 0.19 ps and the appearance of additional features.


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  1. ICN2—Institut Catala de Nanociencia i Nanotecnologia, Campus UAB, 08193 Bellaterra (Barcelona), Spain

    • Dinh Van Tuan,
    • Frank Ortmann,
    • David Soriano,
    • Sergio O. Valenzuela &
    • Stephan Roche
  2. Department of Physics, Universitat Autónoma de Barcelona, Campus UAB, 08193 Bellaterra, Spain

    • Dinh Van Tuan
  3. Institute for Materials Science and Max Bergmann Center of Biomaterials, Technische Universität Dresden, 01062 Dresden, Germany

    • Frank Ortmann
  4. Dresden Center for Computational Materials Science, TU Dresden, 01062 Dresden, Germany

    • Frank Ortmann
  5. ICREA, Institució Catalana de Recerca i Estudis Avançats, 08070 Barcelona, Spain

    • Sergio O. Valenzuela &
    • Stephan Roche


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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