SINGLE H-VACANCY DEFECT INTRODUCTION arXiv:1001.0919v2 [cond-mat.mtrl-sci] 14 May 2010 Sustained ferromagnetism induced by H-vacancies in graphane Julia Berashevich and Tapash Chakraborty Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada, R3T 2N2 The electronic and magnetic properties of graphane with H-vacancies were investigated using the quantum-chemistry methods. The hybridization of the edges is found to be absolutely crucial in defining the size of the bandgap, which is increased from 3.04 eV to 7.51 eV when the hybridization is changed from the sp 2 to the sp 3 type. The H-vacancy defects also influence the size of the gap that depends on the number of defects and their distribution between the two sides of the graphane plane. Further, the H-vacancy defects induced on one side of the graphane plane and placed on the neighboring carbon atoms are found to be the source of ferromagnetism which is distinguished by the high stability of the state with a large spin number in comparison to that of the singlet state and is expected to persist even at room temperatures. However, the ferromagnetic ordering of the spins is obtained to be limited by the concentration of H-vacancy defects and ordering would be preserved if number of defects do not exceed eight. Graphene is the carbon-based wonder material which has gained wide attention due to its many unique elec- tronic and magnetic properties. Despite the high mo- bility of the charge carriers in graphene resulting from its zero effective mass [1–3], the absence of gap hin- ders its application in nanoelectronics. The magnetic properties of graphene arising from spin ordering of the localized states at the zigzag edges [4] or by the pres- ence of defects [6–10] might facilitate its application in carbon-based spintronics. If the localized states occupy the same sublattice then they can induce the sublattice imbalance and according to Lieb’s theorem [5] that can lead to the ground state being ferromagnetic [6, 7]. The room-temperature ferromagnetism in graphene has been obtained experimentally [11]. However, there are some issues involved in maintaining the ferromagnetic state whose stability depends on the concentration of the lo- calized states, distance between states and size of the graphene flakes through the size of the band gap [6–10]. Therefore, disappearance of the gap in bulk graphene brings some inconsistencies in applying Lieb’s theorem [8]. Recently discovered graphane [15–18] – hydrogenated graphene – has brought new impetus in the investiga- tion of carbon-based materials due to the predicted ad- vantages in its application in nanoelectronics and spin- tronics. Termination of the carbon atoms by hydrogens leads to the generation of sp 3 carbon network removing the π bands from its band structure thereby generating a gap. It was theoretically predicted that fully hydro- genated graphane is non-magnetic and a wide band gap semiconductor [15, 19]. However, H-vacancy defects in graphane generate localized states characterized by non- zero magnetic moments (each defect has µ = 1 . 0 µ$_{B}$ [20], where µ$_{B}$ is the Bohr magneton [Fig. ]). As graphane is characterized by a wide gap and the value of the charge transfer integral ( t$_{σ}$ ∼ -7.7 eV [14]) is higher than that in graphene ( t$_{π}$ ∼ -2.4 eV [14]), according to the Hub- The size of the band gap of graphane nanoribbons de- creases exponentially with increasing nanoribbon width as a result of vanishing of the confinement effect [12] sim- ilarly to that in graphene [13]. Therefore, for graphane flakes confined by the edges from all sides of size 10 ˚ A × 16 ˚ A suggesting strong confinement effect, the large band gap in comparison to that obtained for nanorib- bons [12, 15, 19] is expected. Defect-free graphane flakes We report here on our investigation of the electronic and magnetic properties of graphane and their modi- fication once the H-vacancy defects are introduced in the lattice. Our study is performed via the quantum- chemistry methods using the spin-polarized density func- tional theory with the semilocal gradient corrected func- tional (UB3LYP/6-31G) in the Jaguar 7.5 program [21]. The H-vacancies are introduced in the originally opti- mized structure of defect-free graphane in the chair con- formation (for the size of the graphane flake see Fig. ), whose carbon atoms at the edges are terminated by two hydrogen atoms thereby preserving the sp 3 network over the whole lattice. bard model [6, 7] these should stabilize ferromagnetism in graphane (for example through an increase of the crit- ical value of the on-site repulsion term [9]). FIG. 1: The spin density for a single H-vacancy defect in graphane plotted with isovalues of ± 0 . 001 e/ ˚ A $^{3}$.