We present an ab initio density functional theory study of the magnetic moments that arise in graphite by creating single carbon vacancies in a three-dimensional ͑3D͒ graphite network using full potential, all electron, spin polarized electronic structure calculations. In previous reports, the appearance of magnetic moments was explained in a two-dimensional graphene sheet just through the existence of the vacancies itself ͓Carbon-Based Magnetism, edited by F. Palacio and T. Makarova ͑Elsevier, Amsterdam, 2005͒; D. C. Mattis, Phys. Rev. B 71, 144424 ͑2005͒; Y. Kobayashi et al., ibid. 73, 125415 ͑2006͒; R. Yoshikawa Oeiras et al., ibid. ͑to be pub-lished͒; P. O. Lehtinen et al., Phys. Rev. Lett. 93, 187202 ͑2004͔͒.The dependence of the arising magnetic moment on the nature and geometry of the vacancies for different supercells is reported. We found that the highest value of magnetic moment is obtained for a 3 ϫ 3 ϫ 1 supercell and that the highly diluted 5 ϫ 5 ϫ 1 supercell shows no magnetic ordering. The results obtained in this paper are indicative of the importance of interlayer interactions present in a 3D stacking. We conclude that this should not be underestimated when vacancy-based studies on magnetism in graphitic systems are carried out.
Carbon linear atomic chains attached to graphene have experimentally been produced. Motivated by these results, we study the nature of the carbon bonds in these nanowires and how it affects their electrical properties. In the present study we investigate chains with different numbers of atoms and we observe that nanowires with odd number of atoms present a distinct behavior than the ones with even numbers. Using graphene nanoribbons as leads, we identify differences in the quantum transport of the chains with the consequence that even and odd numbered chains have low and high electrical conduction, respectively. We also noted a dependence of current with the wire size. We study this unexpected behavior using a combination of first principles calculations and simple models based on chemical bond theory. From our studies, the electrons of carbon nanowires present a quasi-free electron behavior and this explains qualitatively the high electrical conduction and the bond lengths with unexpected values for the case of odd nanowires. Our study also allows the understanding of the electric conduction dependence with the number of atoms and their parity in the chain. In the case of odd number chains a proposed π-bond (MpB) model describes unsaturated carbons that introduce a mobile π-bond that changes dramatically the structure and transport properties of these wires. Our results indicate that the nature of bonds plays the main role in the oscillation of quantum electrical conduction for chains with even and odd number of atoms and also that nanowires bonded to graphene nanoribbons behave as a quasi-free electron system, suggesting that this behavior is general and it could also remain if the chains are bonded to other materials.
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