5 ( AA -distribution) and located on the neighboring car- bon atoms belonging to the same sublattice will gen- erate a stable state characterized by a large spin num- ber (ferromagnetic ordering). For a better stabilization of this state, the reorganization of the graphane lattice in response to the occurrence of defects should be mini- mized. Deformation of the graphane lattice can be mini- mized for free standing graphane in the low-temperature regime and through interaction of graphane with a sub- strate under the condition that the sp 3 hybridization of graphane lattice is preserved. If the rigidity of graphane on a substrate could be achieved, graphane containing H-vacancies on one side of the plane can even become a room-temperature ferromagnet, that obviously has enor- mous potentials for application in nanoelectronics and spintronics. Because each defect forms a perpendicu- lar p$_{z}$ orbital possessing unpaired spin and, therefore, its contribution to the magnetization is 1 µ$_{B}$ , the magnitude of magnetization of such room temperature ferromagnet can ideally be regulated by the number of H-vacancy de- fects. However, the number of defects to achieve the stable ferromagnetism at room temperature should be limited because above a critical value the ferromagnetic ordering of spins would be unstable. The work was supported by the Canada Research Chairs Program. References [1] Abergel D S L, Apalkov V, Berashevich J, Ziegler K, Chakraborty T Advances in Physics . in press. FIG. 3: Spin density for the AA -distribution of H-vacancies (a) 8 H-vacancies ( E 0 ( 8 $_{2}$; 1 $_{2}$) = − 6 . 36 eV), (b) 4 H-vacancies in the singlet state ( E 0 ( 4 $_{2}$; 1 $_{2}$) = 4 . 81 × 10 − 5 eV). Spin densities are plotted with isovalues of ± 0 . 005 e/ ˚ A $^{3}$. [2] Novoselov K S, Geim, A K, Morozov S V, Jiang D, Kat- snelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197. [3] Ando T in Nano-Physics & Bio-Electronics: A New Odyssey , edited by Chakraborty T, Peeters F, and Sivan U (Elsevier, Amsterdam, 2002), Chap 1. [4] Berashevich J, Chakraborty T 2009 Phys. Rev. B 80 033404. [5] Lieb E H 1989 Phys. Rev. Lett. 62 1201. [6] Palacois J J, Fernan´ andez-Rossier J, Brey L 2008 Phys. Rev. B 77 195428. [7] Pereira V M, Guinea F, Lopes dos Santos J M B, Peres N M R, Castro Neto A H 2006 Phys. Rev. Lett. 96 036801. [8] Huang B-L, Mou C-Y 2009 EPL 88 68005. [9] Peres N M R, Ara´ ujo M A N, Bozi D 2004 Phys. Rev. B 70 195122. [10] Zhang Y, Talapatra S, Kar S, Vajtai R, Nayak S K, Ajayan P M 2007 Phys. Rev. Lett. 99 107201. [11] Wang Y, Huang Y, Song Y, Zhang X, Ma Y, Liang J, Chen Y 2009 Nano Lett. 9 220. [12] Li Y, Zhou Z, Shen P, Chen Z 2009 J. Phys. Chem. C 113 15043. [13] Han M Y, ¨ Ozyilmaz B, Zhang Y, and Kim P 2007 Phys. Rev. Lett. 98 206805. [14] Tang M S, Wang C Z, Chan C T, Ho K M 1996 Phys.Rev. B 53 979. [15] Sofo J O, Chaudhari A S, Barber G D 2007 Phys. Rev. B 75 153401. [16] Ryu S, Han M Y, Maultzsch J, Heinz T F, Kim P, Steiger- wald M L, Brus L E 2008 Nano Lett. 8 4597. [17] Elias D C, Nair R R, Mohiuddin T M G, Morozov S V, Blake P, Halsall M P, Ferrari A C, Boukhvalov D W, Katsnelson M I, Geim A K, Novoselov K S 2009 Science 323 610. [18] Flores M Z S, Autreto P A S, Legoas S B, Galvao D S 2009 Nanotechnology 20 465704. [19] Leb`egue S, Klintenberg M, Eriksson O, Katsnelson M I 2009 Phys. Rev. B 79 245117. [20] S¸ahin H, Ataca C, Ciraci S 2009 Appl. Phys. Lett. 95 222510. [21] Jaguar, version 7.5. Schr¨ odinger 2007 . LLC: New York, NY. [22] Lee H, Son Y-W, Park N, Han S, Yu, J 2005 Phys. Rev. B 72 174431. [23] Yazyev O V, Wang W L, Meng S, Kaxiras E 2008 Nano Lett. 8 766. [24] Zhou J, Wang Q, Sun Q, Chen X S, Kawazoe Y, Jena P 2009 Nano Lett. 9 3867.