Electronic structure calculations were performed for the rare-earth (RE) nitrides in the rocksalt structure using density functional theory calculations within the $\mathrm{LSDA}+U$ approach (local spin density approximation with Hubbard-$U$ corrections). The $\mathrm{LSDA}+U$ method is implemented in the full-potential linearized muffin-tin orbital method and applied to the $4f$ as well as $5d$ states. Parameters $U$ and $J$ were determined from atomic calculations complemented with experimental photoemission and inverse photoemission data and optical absorption data for Gd pnictides. The solution for the density matrix of $f$ electrons is not unique and thus several configurations need to be investigated to determine the lowest energy state. A trivalent solution is found to have the lowest energy in all cases except $\mathrm{CeN}$, which was found to be tetravalent. Hund’s second rule requires maximizing the orbital momentum component $L_z$, which breaks the cubic symmetry and lowers the total energy. We find Hund’s second rule to be obeyed in all cases except $\mathrm{EuN}$ and $\mathrm{YbN}$, where a cubic symmetry solution has lower energy. In these cases, the divalent solution is also in competition with the trivalent solution. The symmetry breaking in most cases lowers the total energy and in some cases, those with two electrons or holes away from a closed or half-filled shell, is essential to remove $f$ states from the Fermi level. The spin magnetic moments are nearly integer, defined by the number of filled $4f$ states. The orbital magnetic moment is of comparable magnitude to the spin moment. Hund’s third rule, according to which the orbital and spin moment are opposite to each other in the first half of the series but parallel to each other in the second half, is also found to be obeyed. Interestingly, this leads to zero net magnetic moment for $\mathrm{SmN}$.Apart from the few cases where $f$ states remain close to the Fermi level, the band structure is borderline semiconductor to semimetallic in most cases, a RE $5d$ conduction band minimum at $X$, and a $\mathrm{N}2p$ valence band maximum at $\Gamma$. The early members of the series before $\mathrm{GdN}$ (with the exception of $\mathrm{NdN}$) are slightly semimetallic in the majority spin channel only and are thus half-metals, while the later members after Gd have a small indirect gap. In $\mathrm{EuN}$ a complicated hybridization occurs between an $f$ level pinned at $E_F$ and the $\mathrm{N}2p$ states, leading to a metallic band structure. Above the Curie temperature of these ferromagnets, in the paramagnetic state, one expects an average of majority and minority spin gaps and thus an increase in the gap.

• Received 22 August 2006

DOI:https://doi.org/10.1103/PhysRevB.75.045114