There is by now significant theoretical and experimental evidence that the defects such as vacancies (missing carbon atoms) or adsorbates such as hydrogen can induce localized or itinerant (delocalized) magnetic moments in this otherwise nonmagnetic material. Nevertheless, the realization of the defect-induced ferromagnetic graphene at room temperature remains elusive and highly contentious experimentally while the key theoretical issues have yet to be addressed. One of the main theoretical challenges is the inadequate treatment of the interaction between the induced magnetic moment and graphene electrons, hence the possibility of the Kondo effect leading to the quenching of the magnetic moment. Moreover, a complete understanding of the magnetic ordering requires an effective simulation of the collective interactions between random distributions of such defects mediated by interacting graphene electrons. This demonstrates the paramount need for a theoretical method that offers not only an explicit treatment of electron correlations, but also a controlled simulation of realistically large systems.
In this talk I will present the current status of the defect-induced magnetism in carbon-based materials and, in particular, discuss the origins of the controversies in the Kondo problem and magnetic ordering in graphene. Then, I will present my contributions to our understanding of the nature of the defect-induced magnetic moments in disordered graphene, and the magnetic interactions between the localized moments in the material, namely the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction. I will then briefly introduce a robust, nonperturbative correlation-calculation method known as the Gutzwiller variational method and argue how it meets both the above-mentioned requirements. Finally, I outline my proposal for a comprehensive addressing of the defect-induced ferromagnetic graphene based on using the Gutzwiller method, which may open a promising chapter in our quest for the sought after FerroGraphene.