Control of the local magnetic states in graphene with voltage and gating

Magnetism of graphene can be created by atomic defects, either hydrogen adsorption or single-carbon vacancy formation, owing to the unpaired $\pi$ electrons around the defects. Here we explore, based on rigorous first principles calculations, the possibility of voltage manipulation of two such types of $\pi$ magnetism in graphene via a scanning tunneling microscope tip. We find a remarkably different behavior. For the hydrogen, the magnetic moment can be switched on and off with voltage-induced doping, whereas, for the carbon vacancy, the spin splitting of the $\pi$ bands persists, almost independent of the extent of doping, due to the coupling between the $\pi$ and the $\sigma$ bonds. Furthermore, the local atomic structures near the vacancy can be reversibly manipulated by a coordination mechanism between an intermediate tip-defect distance and a moderate tip voltage, consequently leading to the reversal of spin polarization of the $\pi$ bands. Voltage control of the local magnetic states may open a new avenue for potential applications in spintronics.

Figure 1

Doping modulation in defects on graphene lattice. (a) Schematic diagram of a hydrogen adsorbate on graphene (H) and a single-carbon vacancy (CV) in graphene. (b) Density of states of H and CV systems with and without doping. Red and blue lines represent spin-up and spin-down states, respectively. The sharp $\sigma$ peak in the right column locates on carbon atom 1, which is labeled in panel (a).

Figure 2

Hydrogen adsorbate on graphene. (a) Schematic diagram of the three-terminal graphene device. The light gray and yellow spheres indicate left, right, and tip electrodes, respectively. Periodic boundary conditions are applied transverse to the left-right (L-R) direction in the graphene. The notation ${\mu }_{\text{T}}$ and ${\mu }_{\text{G}}$ stands for the chemical potential of the gold tip and graphene, respectively. The inset shows electrostatic potential profile at 0.4 V with $g=0$ gating. (b) Magnetic moment as a function of applied voltage. (c) Density of states projected onto the $p_z$ orbitals. Red and blue lines represent spin-up and spin-down states, respectively. (d) Spin-density distribution (isosurface values of $\pm 0.005e/{\text{bohr}}^{\text{3}}$), red and blue surfaces correspond to the densities of spin-up and spin-down states, respectively.

Figure 3

The ground state, i.e., the high spin state (HS) and metastable state (LS) of monovacancy graphene. (a) Energy difference ($E_{\text{diff}}=E_{\text{HS}}-E_{\text{LS}}$) between HS and LS with and without doping. (b) Top view of charge-density difference after doping. Isosurfaces values of $\pm 0.001e/{\text{bohr}}^{\text{3}}$ are shown. Red and blue clouds correspond to electron accumulation and depletion, respectively.

Figure 4

Carbon vacancy. (a) The magnetic moment as a function of applied voltage for the three different vacancy spin states and conformations, HS, LS, and NS, respectively. (b) The density of states projected on the $p_z$ orbitals. The red and blue lines represent the spin-up and spin-down states. (c) Charge-induced force in the LS state at $\pm 0.4$ V. The absolute force on the C1 atom is 0.24 nN at $-0.4$ V.