Electron spin dynamics and electron spin resonance in graphene

A theory of spin relaxation in graphene including intrinsic, Bychkov-Rashba, and ripple spinorbit coupling is presented. We find from spin relaxation data by Tombros et al. (Nature, 448 (2007) 571) that intrinsic spin-orbit coupling dominates over other contributions with a coupling constant of 3.7 meV. Although it is 1–3 orders of magnitude larger than those obtained from first principles, we show that comparable values are found for other honeycomb systems, MgB2 and LiC6; the latter is studied herein by electron spin resonance (ESR). We assess the feasibility of bulk electron spin resonance spectroscopy on graphene and identify experimental conditions where such experiments are realizable. DOI: https://doi.org/10.1209/0295-5075/92/17002 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-45280 Accepted Version Originally published at: Dóra, B; Murányi, F; Simon, F (2010). Electron spin dynamics and electron spin resonance in graphene. EPL (Europhysics Letters), 92(1):17002. DOI: https://doi.org/10.1209/0295-5075/92/17002 ar X iv :1 00 4. 02 10 v1 [ co nd -m at .s tr -e l] 1 A pr 2 01 0 Electron spin dynamics and electron spin resonance in graphene Ferenc Simon,1, 2, ∗ Ferenc Murányi,3 and Balázs Dóra1 Budapest University of Technology and Economics, Institute of Physics and Condensed Matter Research Group of the Hungarian Academy of Sciences, H-1521 Budapest, Hungary Fakultät für Physik, Universität Wien, Strudlhofgasse 4, 1090 Wien, Austria Physik-Institut der Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland A theory of spin relaxation in graphene including intrinsic, Bychkov-Rashba, and ripple spin-orbit coupling is presented. We find from spin relaxation data by Tombros et al. [Nature 448, 571 (2007).] that intrinsic spin-orbit coupling dominates over other contributions with a coupling constant of 3.7 meV. Although it is 1-3 orders of magnitude larger than those obtained from first principles, we show that comparable values are found for other honeycomb systems, MgB2 and LiC6; the latter is studied herein by electron spin resonance (ESR). We predict that spin coherence is longer preserved for spins perpendicular to the graphene plane, which is beneficial for spintronics. We identify experimental conditions when bulk ESR is realizable on graphene. PACS numbers: 74.70.Ad, 74.25.Nf, 76.30.Pk, 74.25.Ha Introduction. The discovery of graphene [1] stimulated enormous interest due its fundamentally and technologically important properties. One potential application is in spintronics [2], i.e. when the electron spin degree of freedom is utilized as information carrier. The principal parameter governing spintronic usability is the spin relaxation time (also referred to as spin-lattice relaxation time), τs, which characterizes how an injected non-thermal equilibrium spin state decays. For realistic applications, τs longer than 10-100 ns is required. A general, often cited concept is that ”pure materials made of light elements” can reach this limit. The huge mobility of charge carriers in graphene (approaching 10 cm/Vs [3]), the light nature of carbon, and the low-dimensionality of this material are the reasons for the high expectations for its spintronic applications. This is supported by the long spin relaxation time in light metals such as e.g. Li [4] or in lowdimensional conductors [5]. Therefore it came as a surprise that τs as short as 60-150 ps are observed in spin transport experiments on graphene [6, 7], which renders it unusable for such applications. The understanding of this experimental result is therefore of great importance. Theory of spin relaxation are split into two different classes: materials with inversion symmetry (e.g. Na or Si) and to materials where the inversion symmetry is broken either in the bulk (e.g. III-V semiconductors such as GaAs) or in two-dimensional heterostructures. The Elliott-Yafet (EY) theory [8, 9] explains the former case, where only intrinsic (i.e. atomic) spin-orbit coupling (SOC) is present, Li, and predicts that spin (Γs = ~/τs) and momentum relaxation rates (Γ = ~/τ , τ is the momentum relaxation time) are proportional: Γs = αi L2i ∆2Γ. Here αi = 1..10 is band structure dependent [4], ∆ is the energy separation of a neighboring and the conduction band. The relaxation for broken inversion symmetry is explained by the Dyakonov-Perel (DyP) theory. It applies either when the symmetry breaking is in the bulk, (the Dresselhaus SOC [10], LD) or when it happens for a heterolayer structure (the Bychkov-Rashba SOC [11, 12], LBR). The DyP theory shows that the spin and momentum relaxation rates are inversely proportional: Γs = αD/BRLD/BR/Γ, where αD/BR ≈ 1. A link between the EY and the DyP was found recently [13]: for metals with inversion symmetry but rapid momentum scattering, the generalization of the EY theory leads to Γs = αi L2i ∆2+Γ2Γ, which gives a DyP like spin relaxation when Γ > ∆. Three sources of SOC are present in graphene: intrinsic, BR type (due to the symmetry breaking by a perpendicular electric field), and the ripple related (which is due to the inevitable ripples in graphene). However, the role and magnitude of these SOC parameters is a debated issue. Estimates for the intrinsic SOC ranges two orders of magnitude; 0.9200 μeV [14–16], whereas value of the BR SOC appears to be settled to 10-36 μeV per V/nm (Refs. [15] and [14], respectively). The effect of the substrate for the spin relaxation is also unsettled [17]. Given this debate, a description is required which enables comparison with the spin transport data. Here, we present the theory of spin relaxation in graphene including intrinsic, BR, and ripple spin-orbit coupling. We analyze the spin transport data from Refs. [6, 7, 18] and we find that the intrinsic SOC dominates the relaxation with a large, unexpected magnitude. We discuss two similar honeycomb systems; MgB2 and LiC6, and show that they exhibit similar intrinsic SOC. The result predicts a strong anisotropy of the spin relaxation time. We study the feasibility of bulk electron spin resonance (ESR) spectroscopy on graphene and pinpoint experimental conditions when it is possible. ESR would allow a direct, spectroscopic measurement of τs (Ref. [19]), which underlines its importance [20]. Experimental. We prepared Li intercalated HOPG graphite by the ”immersion into molten Li” method [21]. The golden color of the samples attested the LiC6 intercalation level [22]. Freshly cleaved samples were sealed under He in quartz tubes for the ESR experiment. Spin relaxation in graphene. Low energy excitations around the K point of the Brillouin zone are described by a two-dimensional Dirac equation: H = vF(σxpx + σypy), (1)