Intrinsic magnetic moment on (0001) surfaces of rhombohedral graphite

We study electronic structure of the (0001) surfaces of graphite with a rhombohedral stacking arrangement by performing the first-principles total-energy calculations based on the density functional theory. We find that ferrimagnetic spin polarization occurs on the (0001) surfaces of rhombohedral graphite. Detailed analyses of energy bands, spin densities, and wave-function distribution unequivocally reveal the nature of the ferrimagnetic spin polarization, which is associated with the peculiar surface-localized state that possesses the same characteristics as the edge-localized states of graphite flakes.

Figure 1

(a) Reciprocal lattice of rhombohedral graphite with (0001) surfaces. Edge states appear at the shadowed region when ${\gamma }_1/{\gamma }_0=0.1$. (b) Expanded figure around the $K$ point.

Figure 2

(a) Electronic energy band of a rhombohedral graphite slab made of eight graphene layers. The energy is measured from the Fermi level. (b) The electronic energy band near the Fermi level in the vicinity of the $K$ point.

Figure 3

(Color online) Contour plots of spin density $\Delta \rho ={\rho }_{\uparrow }\left(\mathbf{r}\right)-{\rho }_{\downarrow }\left(\mathbf{r}\right)$ of rhombohedral graphite. The solid circles denote the position of C atoms. Positive and negative values of the spin density are shown by black and red lines, respectively. Each contour represents twice (or half) the density of the adjacent contour lines.

Figure 4

Contour plots of squared wave functions of rhombohedral graphite at the $K$ point for (a) the lower and (b) higher branches of the flat-band state at the vicinity of the $K$ point along the $K\text{−}\Gamma$ line for (c) the lower and (d) higher branches. The solid circles denote the position of C atoms. Each contour represents twice (or half) the density of the adjacent contour lines.