Preferential antiferromagnetic coupling of vacancies in graphene on ${\mathrm{SiO}}_2$: Electron spin resonance and scanning tunneling spectroscopy

Monolayer graphene grown by chemical vapor deposition and transferred to ${\mathrm{SiO}}_2$ is used to introduce vacancies by ${\mathrm{Ar}}^{+}$ ion bombardment at a kinetic energy of 50 eV. The density of defects visible in scanning tunneling microscopy is considerably lower than the ion fluence, implying that most of the defects are single vacancies as expected from the low ion energy. The vacancies are characterized by scanning tunneling spectroscopy on graphene and highly oriented pyrolytic graphite (HOPG). A peak close to the Dirac point is found within the local density of states of the vacancies similar to the peak found previously for vacancies on HOPG. The peak persists after air exposure up to 180 min, such that electron spin resonance (ESR) at 9.6 GHz can probe the vacancies exhibiting such a peak. After an ion flux of $10/{\mathrm{nm}}^2$, we find an ESR signal corresponding to a $g$ factor of 2.001–2.003 and a spin density of $1–2\text{spins}/{\mathrm{nm}}^2$. The peak width is as small as 0.17 mT indicating exchange narrowing. Consistently, the temperature-dependent measurements reveal antiferromagnetic correlations with a Curie-Weiss temperature of $-10$ K. Thus, the vacancies preferentially couple antiferromagnetically, ruling out a ferromagnetic graphene monolayer at ion induced spin densities of $1–2{\mathrm{nm}}^2$.

Figure 1

${\mathrm{Ar}}^{+}$ bombardment on HOPG. $E_{\mathrm{kin}}=50$ eV; fluence, $7.4\times {10}^{-3} \mathrm{ions}/{\mathrm{nm}}^2$. (a) STM image with arrow marking the position where the dark blue $dI/dV$ curve in panel (b) is recorded ($I=0.5$ nA, $V=700$ mV). Left inset: STM image of single defect with arrows marking the positions where the $dI/dV$ curves displayed with identical color in panel (b) are recorded and green line marking the profile line displayed in the right inset ($I=1$ nA, $V=700$ mV). Right inset: Profile line across a single defect along the line marked in the left inset. (b) $dI/dV$ curves recorded on the positions marked in panel (a). Pink, black, and light blue curves: $I_{\mathrm{stab}}=1$ nA, $V_{\mathrm{stab}}=700$ mV, and $V_{\mathrm{mod}}=8$ mV. Dark blue curve: $I_{\mathrm{stab}}=0.5$ nA, $V_{\mathrm{stab}}=700$ mV, and $V_{\mathrm{mod}}=8$ mV. (c) $dI/dV$ image recorded within a different area than panel (a) ($I=0.015$ nA, $V=-10$ mV). (d) $dI/dV$ image of the same area as in panel (c) ($I=0.08$ nA, $V=-160$ mV). (e) STM image after 10 min of air exposure with arrows marking the positions of $dI/dV$ curves in panel (f) ($I=0.7$ nA, $V=600$ mV). (f) $dI/dV$ curves recorded at the positions marked in panel (e). Red curve: $I_{\mathrm{stab}}=0.7$ nA, $V_{\mathrm{stab}}=600$ mV, and $V_{\mathrm{mod}}=10$ mV. Green curve: $I_{\mathrm{stab}}=0.8$ nA, $V_{\mathrm{stab}}=600$ mV, and $V_{\mathrm{mod}}=10$ mV. Light blue curve: $I_{\mathrm{stab}}=1$ nA, $V_{\mathrm{stab}}=700$ mV, and $V_{\mathrm{mod}}=10$ mV. (g) STM image after 3 h of air exposure with arrows marking the positions of $dI/dV$ curves in panel (h) ($I=0.2$ nA, $V=500$ mV). (h) $dI/dV$ curves recorded at the positions marked in panel (g). Blue and green curve: $I_{\mathrm{stab}}=0.2$ nA, $V_{\mathrm{stab}}=500$ mV, and $V_{\mathrm{mod}}=10$ mV. Pink curve: $I_{\mathrm{stab}}=0.1$ nA, $V_{\mathrm{stab}}=-100$ mV, and $V_{\mathrm{mod}}=10$ mV.

Figure 2

Atomically resolved STM image of two defects after ${\mathrm{Ar}}^{+}$ bombardment at $E_{\mathrm{kin}}=50$ eV; fluence, $3\times {10}^{-3} \mathrm{ions}/{\mathrm{nm}}^2$; $I=0.05$ nA; and $V=-50$ mV. Inset: Higher resolution image of a single defect exhibiting the $\sqrt{3}\times \sqrt{3}$ superstructure around the defect more clearly: $I=0.2$ nA and $V=700$ mV.

Figure 3

Graphene on ${\mathrm{SiO}}_2$. (a) STM image prior to ion bombardment with arrow marking the position of the $dI/dV$ curve in panel (b) ($I=0.1$ nA, $V=-900$ mV). (b) $dI/dV$ curve (blue curve) recorded at the arrow in panel (a) with linear guides to the eye (orange lines) ($I_{\mathrm{stab}}=0.1$ nA, $V_{\mathrm{stab}}=-900$ mV, $V_{\mathrm{mod}}=20$ mV). (c) STM image after ${\mathrm{Ar}}^{+}$ bombardment at $E_{\mathrm{kin}}=50$ eV with fluence: $8\times {10}^{-3} \mathrm{ions}/{\mathrm{nm}}^2$, $I=0.1$ nA, and $V=-800$ mV. (d) STM image after ${\mathrm{Ar}}^{+}$ fluence: $1.0 \mathrm{ions}/{\mathrm{nm}}^2$, $E_{\mathrm{kin}}=50$ eV, $I=0.04$ nA, and $V=-120$ mV. Arrows mark positions of $dI/dV$ curves in panels (e) and (f). (e), (f) $dI/dV$ curves recorded at the points marked by arrows with the same color in panel (d). The blue curve in panel (e) is a Lorentzian fit to the red curve used to determine peak energy and width. $I_{\mathrm{stab}}=0.04$ nA, $V_{\mathrm{stab}}=-120$ mV, and $V_{\mathrm{mod}}=20$ mV.

Figure 4

ESR spectra after ${\mathrm{Ar}}^{+}$ bombardment on graphene ($E_{\mathrm{kin}}=50$ eV). (a) Sample without ${\mathrm{Ar}}^{+}$ bombardment. Gaussian fit curve (blue line) is added, which is used as an offset for the fit curves in panels (b)–(e) ($f=9.5720$ GHz, $B_{\mathrm{mod}}=0.8$ mT). (b) Sample at ${\mathrm{Ar}}^{+}$ fluence of 10 $\mathrm{ions}/{\mathrm{nm}}^2$, $f=9.5726$ GHz, and $B_{\mathrm{mod}}=0.5$ mT. (c) Sample at ${\mathrm{Ar}}^{+}$ fluence of 10 $\mathrm{ions}/{\mathrm{nm}}^2$, $f=9.5619$ GHz, and $B_{\mathrm{mod}}=0.05$ mT with fit curves as marked (see text). (d) Sample at ${\mathrm{Ar}}^{+}$ fluence of 10 $\mathrm{ions}/{\mathrm{nm}}^2$ with $B$ field applied perpendicular and parallel to the sample plane as indicated and mixed fit curves, $f=9.5611$ GHz ($f=9.5622$ GHz) for in-plane (out-of-plane) field, $B_{\mathrm{mod}}=0.1$ mT. Due to the different measurement frequencies for the two curves, $g$-values are given on the abscissa. (e) Sample at different ${\mathrm{Ar}}^{+}$ fluence as indicated after optimizing the sample contacts by heating to 200 ${}^{\circ }\mathrm{C}$ in Ar atmosphere and additional air exposure of about 60 min. Lorentzian fit curves (lines) are added (10 $\mathrm{ions}/{\mathrm{nm}}^2$: $f=9.5716$ GHz, $B_{\mathrm{mod}}=0.5$ mT; 100 $\mathrm{ions}/{\mathrm{nm}}^2$: $f=9.5760$ GHz, $B_{\mathrm{mod}}=0.8$ mT). (f) Temperature-dependent inverse peak area of the ESR curves calibrated by a ruby standard (see text) in comparison with fit curves $a(T-{\theta }_{\mathrm{cw}})$ revealing ${\theta }_{\mathrm{cw}}=-12$ K and ${\theta }_{\mathrm{cw}}=-5$ K, respectively.

Figure 5

Sheet resistance of monolayer graphene on ${\mathrm{SiO}}_2$ as a function of ion fluence measured at 300 K.