Magnetism in systems that do not contain transition metal or rare earth ions was recently observed or predicted to exist in a wide variety of systems. We summarize both experimental and theoretical results obtained for ideal bulk II-V and II-IV compounds, molecular crystals containing O(2) or N(2) molecules as structural units, as well as for carbon-based materials such as graphite and graphene nanoribbons. Magnetism can be an intrinsic property of a perfect crystal, or it can be induced by non-magnetic dopants or defects. In the case of vacancies, spin polarization is local and results in their high spin states. The non-vanishing spin polarization is shown to originate in the strong spin polarization of the 2p shell of light atoms from the second row of the periodic table.

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Electronic structure of the Mn and Fe ions and of the gallium vacancy V(Ga) in GaN was analysed within the GGA + U approach. First, the +U term was treated as a free parameter, and applied to p(N), d(Mn), and d(Fe). The band gap of GaN is reproduced for U(N) ≈ 4 eV. The electronic structure of defect states was found to be more sensitive to the value of U than that of the bulk states. Both the magnitude and the sign of the U-induced energy shifts of levels depend on occupancies, and thus on the defect charge state. The energy shifts also depend on the hybridization between defect and host states, and thus are different for different level symmetries. In the case of V(Ga), these effects lead to stabilization of spin polarization and the "negative-U(eff)" behavior. The values of Us were also calculated using the linear response approach, which gives U(Fe) ≈ U(Mn) ≈ 4 eV. This reproduces well the results of previous hybrid functionals calculations. However, the best agreement with the experimental data is obtained for vanishing or even negative U(Fe) and U(Mn).