Recent ab initio calculations without spin [P. Koskinen et al., Phys. Rev. Lett. 101, 115502 (2008)] predict that the zigzag edges of graphene should be reconstructed, albeit with an energy barrier to be overcome. After verifying that spin-polarized calculations give qualitatively the same result, we study the mechanism and the free energy of the reconstruction of the zigzag edges from a periodic hexagon structure (zz) to an alternate pentagon-heptagon structure [zz(57)] using the empirical long-range carbon bond order potential II (LCBOPII) potential. The zz(57) edges are stabilized by an almost triple bond similar to that of the armchair edges, and we propose a way to account for this quantum mechanical effect in the LCBOPII potential. Aside from that, the reconstructed edge is flat as a result of tensile edge stress. The reconstruction occurs spontaneously in molecular dynamics simulations at high temperature, leading to the identification of a reaction coordinate for the reconstruction that allows us to calculate the free-energy barrier by using Monte Carlo simulations and umbrella sampling. At room temperature, we find a free-energy barrier of 0.83 eV for the first transformations of two hexagons to a pentagon-heptagon pair that is higher than the one for a fully reconstructed edge and increasing with temperature.

Grain boundaries with dangling bonds (DBGB) in graphene are studied by atomistic Monte Carlo and molecular dynamics simulations in combination with density functional (SIESTA) calculations. The most stable configurations are selected and their structure is analyzed in terms of grain boundary dislocations. It is shown that the grain boundary dislocation with the core consisting of pentagon, octagon and heptagon (5-8-7 defect) is a typical structural element of DBGB with relatively low energies. Electron energy spectrum and magnetic properties of the obtained DBGB are studied by density functional calculations. It is shown that the 5-8-7 defect is magnetic and that its magnetic moment survives after hydrogenation. The effects of hydrogenation and of out of plane deformations on the magnetic properties of DBGB are studied.Comment: 10 pages, 11 figures, 4 tables, the final version accepted in pr

We study, by density functional and large-scale tight-binding transport calculations, the electronic structure, magnetism and transport properties of the recently proposed graphene ribbons with edges rolled to form nanotubes. Edges with armchair nanotubes present magnetic moments localized either in the tube or the ribbon and of metallic or half-metallic character, depending on the symmetry of the junction. These properties have potential for spin valve and spin filter devices with advantages over other proposed systems. Edges with zigzag nanotubes are either metallic or semiconducting without affecting the intrinsic mobility of the ribbon. Varying the type and size of the nanotubes and ribbons offers the possibility to tailor the magnetic and transport properties, making these systems very promising for applications.

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Motivated by the observation of ferromagnetism in carbon foams, we perform a massive search for (meta)stable disordered structures of elemental carbon by a generate and test approach. We use the density functional based program SIESTA to optimize the structures and calculate the electronic spectra and spin densities. About 1% of the 24,000 optimized structures present magnetic moments, a necessary but not sufficient condition for intrinsic magnetic order. We analyse the results using elements of graph theory. Although the relation between the structure and the occurrence of magnetic moments is not yet fully clarified, we give some minimal requirements for this possibility, such as the existence of three-fold coordinated atoms surrounded by four-fold coordinated atoms. We discuss in detail the most promising structures.