Scanning Tunneling Microscopy of the $\pi$ Magnetism of a Single Carbon Vacancy in Graphene

Pristine graphene is strongly diamagnetic. However, graphene with single carbon atom defects could exhibit paramagnetism. Theoretically, the $\pi$ magnetism induced by the monovacancy in graphene is characteristic of two spin-split density-of-states (DOS) peaks close to the Dirac point. Since its prediction, many experiments have attempted to study this $\pi$ magnetism in graphene, whereas only a notable resonance peak has been observed around the atomic defects, leaving the $\pi$ magnetism experimentally elusive. Here, we report direct experimental evidence of $\pi$ magnetism by using a scanning tunneling microscope. We demonstrate that the localized state of the atomic defects is split into two DOS peaks with energy separations of several tens of meV. Strong magnetic fields further increase the energy separations of the two spin-polarized peaks and lead to a Zeeman-like splitting. Unexpectedly, the effective $g$ factor around the atomic defect is measured to be about 40, which is about 20 times larger than the $g$ factor for electron spins.

Figure 1

Graphene with atomic defects on a Rh foil. (a) $46\mu \mathrm{m}\times 46\mu \mathrm{m}$ Raman mapping of the $D$ band (peak at $1350{\mathrm{cm}}^{-1}$ of Raman spectrum) of graphene on Rh foil. (b) $10\mathrm{nm}\times 10\mathrm{nm}$ STM topographic image of graphene region with high density of defects on Rh foil. (c) Atomic resolution STM image of a single carbon vacancy in the topmost graphene sheet. (d) Zoom-in STM image of a single carbon vacancy in the underlying graphene. The atomic structure of graphene with a single carbon vacancy is overlaid onto the STM image to determine the position of the vacancy.

Figure 2

Spin-split states of single carbon vacancy in graphene. (a) STS spectra recorded at different distances away from a single carbon vacancy. The two peaks reflect the DOS with opposite spin polarizations. Inset: Schematic structure of a single carbon vacancy. The first and second spectra are measured on the nearest-neighbor and the next-nearest-neighbor of the monovacancy. (b) Representative STS spectra of five different monovacancies. The energy separations of the two peaks $\mathrm{\Delta }E$ vary from about 20 to about 60 meV.

Figure 3

Landau quantization around the monovacancy in graphene. (a) Tunneling spectra recorded at position 2.6 nm away from a monovacancy under different magnetic fields. LL peak indices are labeled and the data are offset in the $Y$ axis for clarity. A slight splitting of ${\mathrm{LL}}_0$ and ${\mathrm{LL}}_{\pm 1}$ can be observed in the field of 7 T. (b) The energies of LLs show a linear dependence against $\mathrm{sgn}(n){(|n|B)}^{1/2}$, as expected for massless Dirac fermions in the graphene monolayer. The dashed curves are linear fits of the data with Eq. (1). (c) Tunneling spectra recorded at position $\sim 0.2\mathrm{nm}$ away from the monovacancy under various magnetic fields. The energy separations of the two peaks increase with the magnetic fields.

Figure 4

Energy separations of the two spin-split peaks of the monovacancy as a function of magnetic fields. A linear fit of the energy separations versus magnetic field yields an effective $g$ factor of 40 around the monovacancy. Inset: schematic of the energy level split of the two spin-split states in high magnetic fields.