arXiv:1001.2443v2 [cond-mat.mtrl-sci] 13 Feb 2010 Gul Rahman 1, ∗ and V´ıctor M. Garc´ıa-Su´ arez 2,3, † $^{1}$Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, Pohang 790-834, Republic of Korea $^{2}$Departamento de F´ısica, Universidad de Oviedo & CINN, 33007 Oviedo, Spain $^{3}$Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom The magnetism of C-doped SnO 2 (001) surfaces is studied using first-principles calculations. It is found that carbon does not induce magnetism in bulk SnO 2 when located at the oxygen site, but shows a large magnetic moment at the SnO 2 (001) surface. The magnetic moment is mainly contributed by the carbon atoms due to empty minority spins of p orbitals and is localized at the surface and subsurface atoms. No magnetism is observed when the carbon atom is located at the subsurface oxygen sites. The origin of magnetism is discussed in the context of surface bonding. Surface-induced magnetism in C-doped SnO$_{2}$ In search of spintronic materials, many materials, which are non-magnetic but can show magnetism with transition-metal (TM) doping $^{1,2}$, have been discovered. The best example is GaAs, which is a semiconductor, but exibits interesting magnetic properties when doped with Mn. 3 The search for spintronic materials has also produced magnetic compounds with transition tempera- tures ( T$_{C}$ ) higher than room temperature (RT). Among these high T$_{C}$ compounds, a promising but less studied material is TM doped-SnO$_{2}$, which evoked a lot of at- tention when S. B. Ogale et.al 4 found a giant magnetic moment (GMM) in Co-doped SnO$_{2}$. Following this dis- covery, TM doped-SnO$_{2}$ has been extensively studied ex- perimentally 5–7 and theoretically. 8–11 Very recently, 12 we investigated the origin of GMM in doped SnO$_{2}$. Our calculations showed that Sn vacan- cies are responsible for magnetism in this material. This allowed us to classify SnO$_{2}$ into a class of magnetic ma- terials where magnetism is made possible without mag- netic impurities. Therefore, intrinsic defects in SnO$_{2}$ can play an important role to explain magnetism or even opti- cal conductivity. 13 Recent theoretical calculations further showed that magnetism can be induced with nonmag- netic impurities. 14,15 A good example of non-magnetic impurity is carbon, which has been recently predicted to induce magnetism in bulk materials. 16–18 All previous investigations focused mainly on bulk magnetism. However, there are no reports on the surface magnetism of SnO$_{2}$. The questions that will be addressed here are: what is the role played by the surface and is it possible to induce magnetism at the surface without TM impurities? We, therefore, go beyond bulk magnetism and show that a surface can also induce magnetism in SnO$_{2}$ without TM impurities, which proves that impuri- ties that are non-magnetic in bulk can become magnetic on the surface. This is not a general rule because the electronic and magnetic properties depend strongly on the combination of host and impurity 18–20 (e.g. other sp elements are magnetic in bulk SnO$_{2}$ $^{14,15,20}$) but demon- strates the feasibility of such effect. Bulk SnO$_{2}$ has a tetragonal unit cell with two SnO$_{2}$ units (layers) per cell. Each Sn atom is coordinated to FIG. 1: Stoichiometric supercell of SnO 2 used in the calcu- lations for the (001) surface. Big and small balls represent tin and oxygen atoms, respectively. Surface oxygen and tin atoms are represented by O(I) and Sn(1), respectively. The immediate subsurface atoms are represented by O(II) and Sn(2). Note that O(II) is surrounded by three Sn atoms, Sn(2), Sn(3), and Sn(4). The surface O(I) is surrounded only by two Sn atoms, Sn(1) and Sn(2). six O atoms situated at the vortices of a distorted octa- hedron. Each O atom is coordinated to three Sn atoms (labeled Sn(2), Sn(3), and Sn(4) in Fig. 1) and all three O-Sn bonds lie on the same plane. To study the bulk properties of C-doped SnO$_{2}$, a 2 × 2 × 2 supercell was considered and a C atom was lo- cated at the O site. For surface magnetism, we consid- ered a (001) surface of SnO$_{2}$ and used different numbers of layers. We constructed free stoichiometric slabs with total compositions of Sn$_{6}$O$_{12}$(six layers), Sn$_{7}$O$_{14}$ (seven layers, see Fig. 1), and Sn$_{10}$O$_{20}$ (ten layers) separated by a vacuum region of 10 ˚ A. Note that six layers are already enough to converge the SnO$_{2}$ surface. 21,22 To include the C atom different O sites, i.e., O(I), O(II), O(III), and O(IV), were considered for all layers. We will only focus on two cases, O(I) and O(II), because O(III) and O(IV) are similar to O(II). First-principles calculations based on density 1 2 3 4 I II III IV APPLIED PHYSICS LETTERS 96 , 052508 (2010)