Structure and magnetism of disordered carbon

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. (paper)