Sulfur adatom adsorption on $\alpha $-Fe$_{\mathrm{2}}$O$_{\mathrm{3}}$~(0001) film studied by DFT$+$U method*

The geometric and electronic properties of a sulfur (S) atom adsorption on the hematite~$\alpha $-Fe$_{\mathrm{2}}$O$_{\mathrm{3}}$~(0001) film with have been investigated systematically by calculations based on the density functional theory. The most stable hematite~$\alpha $-Fe$_{\mathrm{2}}$O$_{\mathrm{3}}$~(0001) film with an anti-ferromagnetic arrangement is identified. The S adatom prefers to bond with three O atoms, in the center of a triangle formed by the three O atoms. The S acts as a cation at this site. The sulfur adsorption has introduced two gap states, in addition to the unoccupied surface states. Furthermore, with the most stable S-adsorption configuration, the diffusion of the S adatom from the surface to the inside is searched and the transition state along the minimum-energy pathway is also identified. The isovalent doping of S inside of the film has also been studied.