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.

Doping properties of Ag in ZnO were analyzed by first-principles calculations within both the local-density and generalized gradient approximations. The ionization energy of ${\text{Ag}}_{\text{Zn}}$, about 0.2 eV, is comparable to that of the commonly used group-V acceptors, and is lower than that of two other ${\text{I}}^{\text{B}}$ species, Cu and Au. Formation energy of Ag in the favorable O-rich conditions is 0.85 eV, which corresponds to the solubility limit of about ${10}^{18}{\text{cm}}^{-3}$ at $700°\text{C}$. Formation of Ag-rich second phases is predicted for high Ag concentrations. Energetics of the onset of this process is analyzed and ${\text{Ag}}_{\text{Zn}}$ display a tendency to form aggregates of AgO with the wurtzite structure. Formation of such nanoinclusions is shown to affect the lattice constant of ZnO:Ag. Two “wrong” incorporation channels, i.e., at the interstitial sites and at the oxygen sites as ${\text{Ag}}_{\text{O}}$, are predicted to be nonefficient due to the high formation energies. The calculated magnetic coupling between Ag ion reveals an unexpected dependence on the Ag-Ag distance; the interaction between the nearest-neighbor ${\text{Ag}}_{\text{Zn}}$ pair vanishes while that for the more distant pairs is weakly ferromagnetic.

Electronic, magnetic, and structural properties of several ${\mathrm{II}}^A\text{−}\mathrm{V}$ compounds are analyzed using ab initio calculations. We consider four crystal structures: zinc-blende, NiAs, rocksalt, and ${\mathrm{Zn}}_3{\mathrm{P}}_2$. Our results indicate that ${\mathrm{II}}^A\text{−}\mathrm{V}$ nitrides in the rocksalt phase are stable ferromagnetic half-metals characterized by the total spin polarization of free holes in the valence band. The previously considered zinc-blende phase of II-V crystals is ferromagnetic as well, but is less stable by about $0.3\mathrm{eV}$/atom. The stability of the ${\mathrm{Zn}}_3{\mathrm{P}}_2$ phase is close to that of the rocksalt, but the spin polarization vanishes in this case. Analysis of the electronic structure shows that ferromagnetism of ${\mathrm{II}}^A\text{−}\mathrm{V}$ compounds originates in the spin polarization of the $p$ shell of anions, as described by Hund’s rule, which persists in solids after formation of bonds. Furthermore, the results for isolated atoms indicate why the spin polarization is the most stable in ${\mathrm{II}}^A\text{−}\mathrm{V}$ nitrides, which are discussed in detail.

High-spin states of cation vacancies in GaP, GaN, AlN, BN, ZnO, and BeO were analyzed by first-principles calculations. The spin-polarized vacancy-induced level is located in the band gap in GaP, ZnO, and BeO. In the nitrides, the stronger exchange coupling forces the vacancy states to be resonant with valence bands, forbids formation of positively charged vacancies in GaN and BN, and allows Al vacancy in p-AlN to assume the highest possible S~=~2 spin state. The shape of the spin density, isotropic in the zinc-blende structure, has a pronounced directional character in the wurtzite structure. Stability of spin polarization of the vacancy states is determined by spin-polarization energies of anions as well as by interatomic distances between the vacancy neighbors and, thus, is given by both the lattice constant of the host and the atomic relaxations around the vacancy. Implications for the experiment are discussed.

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).