Spin effects and magnetism

After general discussion of itinerant-electron magetism, Hubbard model and Lieb theorem, we discuss magnetic moments at different types of defects in graphene and supposed ferromagnetism at zigzag edges. We consider various mechanisms for determining spin-orbit coupling, with especial emphasis on the importance of full band structure, and the effect of spin-orbit interaction on electronic structure. In this respect, we briefly discuss the difference between graphene, silicene, and germanene, and Kane–Mele model, which initiated development of the field of topological insulators. At the end, we consider the effect of magnetic edges on spin relaxation in graphene nanoribbons