-10 -5 0 5 -1 0 1 PDOS (a.u.) -10 -5 0 5 -1 0 1 -10 -5 0 5 E - E$_{F}$  (eV) -0.3 0 0.3 PDOS (a.u.) -10 -5 0 5 -0.3 0 0.3 s p d -10 -5 0 5 E - E$_{F}$  (eV) -1 0 1 PDOS (a.u.) O O Sn Sn C (a) (b) 2 -10 -5 0 5 -1 0 1 PDOS (a.u.) -10 -5 0 5 -1 0 1 -10 -5 0 5 -0.3 0 0.3 PDOS (a.u.) -10 -5 0 5 -0.3 0 0.3 s p d -10 -5 0 5 E - E$_{F}$  (eV) -1 0 1 PDOS (a.u.) -10 -5 0 5 E - E$_{F}$  (eV) -1 0 1 C O O O Sn Sn C (c) (a) (b) FIG. 3: PDOS on the surface (a) and subsurface (b) atoms when the C atom is located below the surface. Solid, dashed and dashed-dotted dotted lines represent s and p and d or- bitals, respectively. The positive (negative) PDOS shows ma- jority (minority) spin states. FIG. 2: PDOS on the surface (a) and subsurface (b) atoms when the C atom is located on the surface. Solid, dashed and dashed-dotted lines represent s , p and d orbitals, respectively. The positive (negative) PDOS shows majority (minority) spin states. Panel (c) shows the PDOS of C and the nearest O in bulk C-doped SnO 2 . minority spin states are nearly empty, leading to a sig- nificant spin splitting. The impurity bands introduced by the C atom have then a large weight and are rather localized below and above the valence band maximum so that E$_{F}$ is just between the majority and minority spin states(Fig 2(a)). Similar behavior was also observed in other C-doped bulk systems. 16,18,26 Surface states near E$_{F}$ at the Sn and O atoms which have strong bonding with the C surface atom can also be seen. functional theory within the local spin density approximation 23 were performed using the SIESTA code 24 with a double-zeta polarized basis set. The Hamiltonian matrix elements were calculated on a real space grid defined with a plane-wave energy cutoff of 400 Ry. A 5 × 5 × 1 Monkhorst-Pack mesh was used for k -point sampling. All atomic positions were fully relaxed until all atomic forces were smaller than 0.05 eV/ ˚ A. For all calculations, the optimized lattice parameters 12 were used. Non-magnetic (NM) and spin-polarized (SP) calcula- tions were performed for bulk C-doped SnO$_{2}$. The cal- culated atom projected density of states (PDOS) of C and O are shown in panel (c) of Fig. 2. The bulk PDOS shows no exchange splitting, which signals that C does not induce magnetism in bulk SnO$_{2}$. We found however that N can induce magnetism in bulk SnO$_{2}$, in agreement with previous studies. 20 It was also confirmed that the O vacancy at the surface 25 and in bulk 12 does not show any magnetism. The calculated magnetic moment is 2 . 00 µ$_{B}$ /cell. The C atom contributes about 1 . 75 µ$_{B}$ , according to the Mul- liken populations given by SIESTA. The induced mag- netic moments at the surface Sn(1) and O(I) atoms are 0 . 002 and 0 . 077 µ$_{B}$ , respectively. The magnetic moments of the atoms in the slab have the same direction, indicat- ing that there is a FM coupling between the C atom and the neighboring surface atoms. The PDOS on the subsurface atoms is shown in Fig. 2(b). The subsurface atoms (O(II), Sn(2)) are also polarized and contribute partially to magnetism. The induced magnetic moments at the subsurface Sn(2) and both the O(II) atoms are 0 . 002 µ$_{B}$ and 0 . 068 µ$_{B}$ , respectively. In both cases (sur- face and subsurface), the O atoms have larger magnetic moments than the Sn atoms because their p orbitals have larger weight near E$_{F}$ , where the C spin-split p orbitals are localized. We discuss now the case where the C atom is located at the subsurface O site, i.e., at O(II); this configuration resembles the case where the C atom is covered by lay- ers of SnO$_{2}$, which is NM. Now the surface layer SnO$_{2}$ screens the C atom and therefore the system is expected Figure 2(a) shows the PDOS on the orbitals of the surface atoms when the C atom is located at the surface O position, i.e., at O (I). Clearly, the C atom induces magnetism at the (001) surface of SnO$_{2}$. The low ly- ing s orbitals of C are spin-polarized and strongly hy- bridized with the surface sp orbitals of Sn. The Fermi energy ( E$_{F}$ ) is mainly dominated by the p orbitals of C, which indicates that magnetism is mainly induced by the p orbitals and localized at the C atom. Majority p spin states of the C atom are completely occupied and