Defect-Mediated Spin Relaxation and Dephasing in Graphene

A principal motivation to develop graphene for future devices has been its promise for quantum spintronics. Hyperfine and spin-orbit interactions are expected to be negligible in single-layer graphene. Spin transport experiments, on the other hand, show that graphene’s spin relaxation is orders of magnitude faster than predicted. We present a quantum interference measurement that disentangles sources of magnetic and nonmagnetic decoherence in graphene. Magnetic defects are shown to be the primary cause of spin relaxation, masking any potential effects of spin-orbit interaction.

Figure 1

(a) Simplified device geometry and measurement setup (see Supplemental Material [22] for device and measurement details). Dark purple regions are graphene, gold indicates leads, and light-shaded regions have been etched away. (b) Conductance as a function of gate voltage; the shaded region indicates the studied interval (${ϵ}_F\approx 200\mathrm{meV}$). (c) A typical UCF trace in perpendicular field. (d) A typical autocorrelation function (solid curve) and its derivative (dotted curve, no vertical scale plotted). The vertical spike in the dotted curve corresponds to the noise peak in the autocorrelation. The dashed line indicates the inflection point, used as a measure of coherence through Eq. (1).

Figure 2

Dependence of the rate ${\tau }_{\mathrm{UCF}}^{-1}$ on temperature for $B_{\parallel }=0$ (open circles) and $B_{\parallel }=6\mathrm{T}$ (filled circles). Dotted lines have slope $9.0{\mathrm{ns}}^{-1}/\mathrm{K}$ and offsets ${\tau }_{\mathrm{UCF}}^{-1}(T=0)=10.9{\mathrm{ns}}^{-1}$ (upper line), ${\tau }_{\mathrm{UCF}}^{-1}(T=0)=6.2{\mathrm{ns}}^{-1}$ (middle line). The lower, dashed line shows how ${\tau }_{\mathrm{UCF}}^{-1}$ would appear without saturation [${\tau }_{\mathrm{UCF}}^{-1}(T=0)=0$].

Figure 3

Dependence of ${\tau }_{\mathrm{UCF}}^{-1}$ on rms total magnetic field $B_{\mathrm{tot}}=(B_{\parallel }^2+\overline{B_{\perp }^2}{)}^{1/2}$, for various $T$. Curves show the theoretical crossover for a scattering rate ${\tau }_{\mathrm{mag}}^{-1}=5{\mathrm{ns}}^{-1}$ from spin-$\frac{1}{2}$ magnetic defects with $g=2$ (solid lines) or $g=1$ (dotted lines).

Figure 4

(a) Conductance, averaged over the same $V_{\mathrm{BG}}$ range as used in Fig. 2. (b) Comparison of characteristic rates ${\tau }_{\mathrm{WL}}^{-1}$ [square, extracted from (a)] and ${\tau }_{\mathrm{UCF}}^{-1}$ (open circles, from Fig. 2) at $B_{\parallel }=0$. The dotted lines are WL and UCF rates expected for electron-electron parameter $9.0{\mathrm{ns}}^{-1}/\mathrm{K}$, collision rate ${\tau }_{\mathrm{mag}}^{-1}=4.7{\mathrm{ns}}^{-1}$ with slow magnetic defects, and nonmagnetic offsets of $3.5{\mathrm{ns}}^{-1}$ (WL), $6.2{\mathrm{ns}}^{-1}$ (UCF). (c) Dependence of ${\tau }_{\mathrm{WL}}^{-1}$ on $B_{\parallel }^2$ (same $V_{\mathrm{BG}}$ range as used in Fig. 3). The solid line is ${\tau }_{\mathrm{TRS}}^{-1}(B_{\parallel })=4.3{\mathrm{ns}}^{-1}+(4.0{\mathrm{ns}}^{-1}/{\mathrm{T}}^2)B_{\parallel }^2$, a fit to the $B_{\parallel }\ge 1\mathrm{T}$ data. Inset: The same data at low field, plotted linearly in $B_{\parallel }$.