Absence of hyperfine effects in ${}^{13}$C-graphene spin-valve devices

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Absence of hyperfine effects in $^{13}$ C-graphene spin-valve devices

M. Wojtaszek, I. J. Vera-Marun, E. Whiteway, M. Hilke, and B. J. van Wees

Phys. Rev. B 89, 035417 – Published 14 January 2014

Abstract

The carbon isotope $^{13}$ C, in contrast to $^{12}$ C, possesses a nuclear magnetic moment and can induce electron spin dephasing in graphene. This effect is usually neglected due to the low abundance of $^{13}$ C in natural carbon allotropes ( $\sim$ 1%). Chemical vapor deposition (CVD) allows for artificial synthesis of graphene solely from a $^{13}$ C precursor, potentially amplifying the influence of the nuclear magnetic moments. In this work we study the effect of hyperfine interactions in pure $^{13}$ C-graphene on its spin transport properties. Using Hanle precession measurements we determine the spin relaxation time and observe a weak increase of $τ_{s}$ with doping and a weak change of $τ_{s}$ with temperature, as in natural graphene. For comparison we study spin transport in pure $^{12}$ C-graphene, also synthesized by CVD, and observe similar spin relaxation properties. As the signatures of hyperfine effects can be better resolved in oblique spin-valve and Hanle configurations, we use finite-element modeling to emulate oblique signals in the presence of a hyperfine magnetic field for typical graphene properties. Unlike in the case of GaAs, hyperfine interactions with $^{13}$ C nuclei influence electron spin transport only very weakly, even for a fully polarized nuclear system. Also, in the measurements of the oblique spin-valve and Hanle effects no hyperfine features could be resolved. This work experimentally confirms the weak character of hyperfine interactions and the negligible role of $^{13}$ C atoms in the spin dephasing processes in graphene.

Received 20 November 2013

DOI:https://doi.org/10.1103/PhysRevB.89.035417

Authors & Affiliations

M. Wojtaszek^1,*, I. J. Vera-Marun¹, E. Whiteway², M. Hilke², and B. J. van Wees¹

¹Physics of Nanodevices, Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands
²Department of Physics, McGill University, Montreal, Quebec, Canada H3A 0G4

^*m.wojtaszek@rug.nl

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Vol. 89, Iss. 3 — 15 January 2014

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Images

Figure 1
(a) Raman spectrum of CVD graphene on SiO $_{2}$ of pure $^{12}$ C (black) and pure $^{13}$ C (red) isotopic content. The ratios of the Raman shift $ν$ for graphene G and 2D bands reflect the difference in the mass of these isotopes: $ν_{^{12} C} / ν_{^{13} C} = \sqrt{13 / 12}$ . (b) The typical curve of $^{13}$ C-graphene sheet resistivity as a function of gate voltage at room temperature (black) and at $T = 4.2$ K (red).
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Figure 2
(a) Nonlocal detection scheme in a graphene spin-valve device. The arrows on the inner contacts mark their magnetization (here parallel). We measure signals for three different configurations of external field: in-plane $B = (B, 0, 0)$ for the spin-valve effect, normal to the plane $B = (0, 0, B)$ for the regular Hanle effect, and at an angle $θ$ , $B = (B sin θ, 0, B cos θ)$ for the oblique Hanle effect. (b) Spin-valve and Hanle measurements in $^{13}$ C-graphene at room temperature (black) and at $T = 4.2$ K (red). The distance between ferromagnetic injector and detector is $L = 2.7 μ$ m and the contact magnetization is parallel.
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Figure 3
Comparison of spin properties at different carrier concentrations $n$ between pure $^{13}$ C- and pure $^{12}$ C-graphene at room temperature. The coefficients are obtained from fitting Hanle measurements to the solution of Eq. (1). For $^{13}$ C we analyze data for injector-detector spacing $L = 2.7 μ$ m and for $^{12}$ C $L = 4 μ$ m.
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Figure 4
(a) Simulation of the nonlocal spin-valve signal at fixed $B_{z}$ = 2 mT under the influence of a nuclear field $B_{n}$ for different injection currents $I_{dc}$ at $L = 1 μ$ m in $↑ ↑$ alignment. Values of $I_{dc} = 10, 50, 100 μ$ A correspond to the graphene polarization $β = 2 %, 10 %, 20 %$ , respectively. The values of $σ$ , $D_{s}$ , and $τ_{s}$ used in the model are determined experimentally for CVD graphene. (b) Simulation of the Hanle effect for magnetic field at the oblique angle $θ = 10^{\circ}$ under the influence of nuclear field $B_{n}$ for different polarization currents $I_{dc}$ at $L = 5 μ$ m. The inset presents full Hanle curves for all $I_{dc}$ , and the main figure zooms to the region where the curves for each $I_{dc}$ do differ.
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Figure 5
(a) Measurements of the nonlocal spin-valve signal with varying polarization currents $I_{dc}$ at fixed $B_{z} = 1$ mT at $L = 1.5 μ$ m. The inset presents a zoom into region around $B_{x} = 0$ . No dip around zero could be observed for any strength of polarization current $I_{dc}$ . (b) Measurements of the Hanle effect for magnetic field at an oblique angle $θ = 5^{\circ}$ upon varying polarization currents $I_{dc}$ at $L = 4 μ$ m ( $↑ ↑$ ). No asymmetry in the Hanle line shape could be clearly resolved. The linear background present for all $I_{dc}$ comes from the Ohmic (not spin-dependent) contribution to the nonlocal signal.
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