Localized States Influence Spin Transport in Epitaxial Graphene

We developed a spin transport model for a diffusive channel with coupled localized states that result in an effective increase of spin precession frequencies and a reduction of spin relaxation times in the system. We apply this model to Hanle spin precession measurements obtained on monolayer epitaxial graphene on SiC(0001). Combined with newly performed measurements on quasi-free-standing monolayer epitaxial graphene on SiC(0001) our analysis shows that the different values for the diffusion coefficient measured in charge and spin transport measurements on monolayer epitaxial graphene on SiC(0001) and the high values for the spin relaxation time can be explained by the influence of localized states arising from the buffer layer at the interface between the graphene and the SiC surface.

Figure 1

(a) Sketch of the Hanle precession geometry with a diffusive channel of width $W$ connected to the ferromagnetic spin injector ($F_i$) and detector ($F_d$) on distance $L$. The out-of-plane magnetic field $\overrightarrow{B}$ causes the in-plane injected spins to precess while diffusing through the channel. (b) Extension of the Hanle precession geometry with localized states that are coupled to the channel. The spins can hop into these states and back into the channel while the states are not coupled with each other.

Figure 2

The effective spin relaxation time ${\tau }_S^{\mathrm{eff}}$ (a) and Lamor precession frequency ${\omega }_L^{\mathrm{eff}}$ (b) as a function of the coupling rate $\Gamma$ (black solid curves). The asymptotic values in the limit of strong (red, dashed curves) and weak coupling (blue, dash dotted curves). In the graphs we keep ${\tau }_S=150\mathrm{ps}$ [gray dotted curve in panel (a)], ${\tau }_S^{*}=5\mathrm{ns}$, ${\omega }_L=10\mathrm{GHz}$ [for a magnetic field of $B\approx 50\mathrm{mT}$, gray dotted curve in panel (b)] and $\eta =50$ constant.

Figure 3

RT Hanle precession measurements with aligned ($\uparrow \uparrow$) and antialigned ($\uparrow \downarrow$) inner electrodes. The narrow curves in the middle (light colors, gray fitting curves, scale on the left axis) show a measurement on MLEG with $L=1.2\mu \mathrm{m}$ and $W=0.7\mu \mathrm{m}$ from Ref. 11. The broader measurements enclosing the MLEG measurements (dark colors, black fitting curves, scale on the right axis) were performed on QFMLG with $L=1.5\mu \mathrm{m}$ and $W=1\mu \mathrm{m}$. For both sets of measurements a constant background resistance was subtracted.