Magnetism induced by single carbon vacancies in a three-dimensional graphitic network R. Faccio, 1 H. Pardo, 1 P. A. Denis, 1 R. Yoshikawa Oeiras, 2 F. M. Araújo-Moreira, 2 M. Veríssimo-Alves, 3 and A. W. Mombrú 1 1 Crystallography, Solid State and Materials Laboratory (Cryssmat-Lab), DETEMA, Facultad de Química, Universidad de la República, P.O. Box 1157, Montevideo 11800, Uruguay 2 Departamento de Física, Universidade Federal de São Carlos, Caixa Postale 676, São Carlos, São Paulo CEP 13565-905, Brazil 3 The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Main Building, Trieste I-34014, Italy Received 18 December 2006; revised manuscript received 12 September 2007; published 15 January 2008 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 3D 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, 2005; D. C. Mattis, Phys. Rev. B 71, 144424 2005; Y. Kobayashi et al., ibid. 73, 125415 2006; R. Yoshikawa Oeiras et al., ibid. to be pub- lished; P. O. Lehtinen et al., Phys. Rev. Lett. 93, 187202 2004. 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  3  1 supercell and that the highly diluted 5  5  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. DOI: 10.1103/PhysRevB.77.035416 PACS numbers: 81.05.Uw, 71.15.Ap, 71.15.Mb, 75.50.Dd I. INTRODUCTION Carbon-based materials have attracted the attention of the scientific community due to their many potential technologi- cal applications. For this reason, novel properties induced on graphite by chemical or physical modifications have become a subject of great interest. 1–5 Many theoretical articles focus not only on the defects of nanostructured materials but also in the contour edges or in the presence of other atoms. 2–5 In most of them, the system was modeled as an interaction among atoms within a graphene single graphite layer. In this paper, we are studying the effect of the presence of single atom vacancies in a three-dimensional graphitic net- work, bulk graphite, with different supercells, with emphasis on the metallic nature and the magnetic response of this modified material. II. METHODOLOGY The ab initio calculations were performed within the den- sity functional theory DFT framework using full potential, all electron, spin polarized electronic structure calculations utilizing the augmented plane wave APW + local orbital lo method within the WIEN2K code. 6 For the exchange- correlation potential, we used generalized-gradient approxi- mation GGA in the Perdew-Burke-Ernzerhoff PBE scheme. 7 Scalar relativistic effects were included, but spin- orbit coupling was neglected. The convergence of the basis set is controlled by a cutoff parameter expressed as the product between the smallest muffin-tin radius in the unit cell R MT  and the magnitude of the maximum reciprocal lattice vector K max . The muffin-tin radii for carbon atoms were selected as R MT = 1.25 a.u., achieving convergence for a cutoff value of R MT K max = 5.5. The 1s state was selected as a core state, while the 2s and 2p states were treated as valence states. In all the cases, the valence charge densities were expanded up to a G max value of 20.0 a.u. -1 , equivalent to kinetic energy E cut =400 Ry, in order to increase the accuracy in the determination of the topology of the electronic density. Finally, the k-point sam- pling in the first Brillouin zone was determine specifically for each supercell Table I, studying convergence for differ- ent numbers of density points. In the case of pristine graph- ite, we obtain a convergence in total energy with 16 000 points in the entire first Brillouin zone. Layered materials present strong corrugation of the crys- tal potential in the direction perpendicular to the layers. Since this is the case of bulk graphite, the local-density- approximation LDA exchange-correlation potential does not accurately reproduce the crystal potential of this system. For example, it is known that LDA tends to overestimate interlayer interactions in graphite, leading to slightly short distances along its c direction or, in some cases, leading by chance close to the experimental one. For this reason, some reports support that the GGA exchange-correlation xc po- tential is more adequate in systems with important in- homogeneities on their charge densities along the direction perpendicular to the c axis 8–10 and for the reconstruction in the a-b plane. They postulate the use of this potential instead of a LDA approach, since they find it more appropriate for carbon structures. Although the van der Waals forces are to- tally neglected 11 for both xc potentials, GGA leads to an increase of the interlayer distances, which causes that some authors prefers to use the LDA potential. 5–10,12 We present here the results of the supercell series using the GGA poten- tial and compare the results extracted from calculations using LDA and GGA for the 3  3  1 supercell, in order to support the reliability of the conclusions presented in this paper. Graphite is a nonmagnetic semimetal that displays a very weak dispersion along the c axis. We started from the hex- agonal graphite cell in the P6 3 / mmc space group, A-B stack- PHYSICAL REVIEW B 77, 035416 2008 1098-0121/2008/773/0354166 ©2008 The American Physical Society 035416-1