Probing Electron Spin Resonance in Monolayer Graphene

The precise value of the $g$ factor in graphene is of fundamental interest for all spin-related properties and their application. We investigate monolayer graphene on a $\mathrm{Si}/{\mathrm{SiO}}_2$ substrate by resistively detected electron spin resonance. Surprisingly, the magnetic moment and corresponding $g$ factor of $1.952\pm 0.002$ is insensitive to charge carrier type, concentration, and mobility.

Figure 1

The charge carrier density (red) and mobility (blue) versus the gate voltage $V_g$. The values are obtained by performing magnetoresistance measurements at the displayed values for $V_g$. Points are connected by $B$-spline curves. Inset: A schematic of the Hall bar, which is $200\mu \mathrm{m}$ long and $22\mu \mathrm{m}$ wide.

Figure 2

(a) Measurements of longitudinal resistance both with (red, below) and without (black, above) applied rf at 15 GHz and 23 dBm, before subtraction. Inset: Diagram of experimental setup. The solenoid magnetic field is perpendicular to the plane of the Hall bar. Microwave radiation is applied in the plane of the sample and perpendicular to the applied current, supplied by a coaxial cable connected to a loop antenna. (b) $\mathrm{\Delta }{R}_{xx}$ for 15 GHz rf signal at different applied rf power levels, with a back gate voltage of $V_g=-5.0\mathrm{V}$. Power levels are, from top to bottom, 9 to 23 dBm in steps of 2 dBm. Note that the peaks remain stationary with increasing rf power, which implies that there is no measurable temperature dependence for the $g$ factor. Resistance and temperature are inversely related due to effects that arise from the existence of charge puddles [26].

Figure 3

(a) $\mathrm{\Delta }{R}_{xx}$ for different frequencies with the back gate set to $V_g=-4\mathrm{V}$. The measurements are offset to emphasize ESR peak shift due to $g$ factor. Nearly identical graphs can be seen at each measured CNP, though the ESR signal weakens as one moves away from the CNP. (b) Calculated $g$ factor at different charge carrier densities. Negative numbers represent holes. Red dashed line shows the mean value of $g$-factor measurements. Blue dashed line indicates the $g$ factor of free electrons.