Electron-Hole Asymmetry of Spin Injection and Transport in Single-Layer Graphene

Spin-dependent properties of single-layer graphene (SLG) have been studied by nonlocal spin valve measurements at room temperature. Gate voltage dependence shows that the nonlocal magnetoresistance (MR) is proportional to the conductivity of the SLG, which is the predicted behavior for transparent ferromagnetic-nonmagnetic contacts. While the electron and hole bands in SLG are symmetric, gate voltage and bias dependence of the nonlocal MR reveal an electron-hole asymmetry in which the nonlocal MR is roughly independent of bias for electrons, but varies significantly with bias for holes.

Figure 1

(a) Schematic diagram of the single-layer graphene (SLG) spin valve. $E1$, $E2$, $E3$, are $E4$ are four cobalt electrodes. The Si substrate acts as a back gate. Detail: A MgO layer deposited by angle evaporation to reduce the width of the contact area to $\sim 50\mathrm{nm}$. (b) Raman spectroscopy of SLG and bulk graphite. (c) SEM image of a completed device. The darker region corresponds to the SLG.

Figure 2

Electrical characteristics and nonlocal magnetoresistance (MR) scans of sample $A$ and sample $B$. (a),(b) SLG resistivity vs gate voltage of sample $A$ and sample $B$. (c),(d) $I\mathrm{\text{−}}V$ curves between electrodes $E1$ and $E2$ of sample $A$ and sample $B$. (e) Nonlocal MR scans of sample $A$ at three different gate voltages ($V_g=0\mathrm{V}$, $-30\mathrm{V}$, and $-70\mathrm{V}$), as the magnetic field is swept up (black curve) and swept down (red curve). A constant background is subtracted and the curves are offset for clarity. (f) Nonlocal MR scans of sample $B$ at $V_g=10\mathrm{V}$, $-30\mathrm{V}$, and $-60\mathrm{V}$. A constant background is subtracted and the curves are offset for clarity.

Figure 3

(a) Nonlocal MR at zero bias (circles) and conductivity (solid line) vs gate voltage for sample $A$. (b) Nonlocal MR at zero bias (circles) and conductivity (solid line) vs gate voltage for sample $B$. (c) The dependence of nonlocal MR on the gate voltage for sample $A$ at bias current $300\mu \mathrm{A}$ (squares), $0\mu \mathrm{A}$ (circles), $-300\mu \mathrm{A}$ (triangles). (d) The dependence of nonlocal MR on the gate voltage for sample $B$ at bias current $300\mu \mathrm{A}$ (squares), $0\mu \mathrm{A}$ (circles), $-300\mu \mathrm{A}$ (triangles).

Figure 4

(a) Nonlocal MR as a function of dc bias current for sample $A$ at $V_g=0\mathrm{V}$ (electrons, solid squares) and $-70\mathrm{V}$ (holes, open squares). (b) Nonlocal MR as a function of gate voltage and dc bias current for sample $A$. (c) Nonlocal MR as a function of dc bias current for sample $B$ at $V_g=10\mathrm{V}$ (electrons, solid squares) and $-60\mathrm{V}$ (holes, open squares). (d) Nonlocal MR as a function of gate voltage and dc bias current for sample $B$.