Calculations using the $\text{LSDA}+\text{U}$ (local spin-density approximation corrected by Hubbard Coulomb terms for the $d$ electrons) approach show that CrN is close to a charge-transfer insulator transition. The values of $U$ are estimated in various ways, including the recently developed linear-response approach. With reasonable values of $U$ in the range of 3–5 eV it is found that the density of states near the Fermi level is strongly depleted by the spin separation of the states. In the case of the antiferromagnetic (AFM)-${\left[110\right]}_2$ configuration a small gap actually opens even for $U$ as small as 3 eV. Furthermore a smallest direct gap of about 1 eV can be seen in these band structures and could be responsible for the onset of strong optical absorption observed to occur at 0.7 eV. The tendency of opening the gap is found to be strongest in the actually observed AFM-${\left[110\right]}_2$ structure below the Néel temperature. The widely varying transport data in the literature are critically examined. They indicate a gap smaller than 0.1 eV, consistent with the present calculations, a strong influence of N-vacancy-induced doping carriers and possibly localization effects associated with the distortions accompanying the loss of antiferromagnetic ordering above the Néel temperature.

• Received 23 June 2008

DOI:https://doi.org/10.1103/PhysRevB.79.035125