Crystalline and magnetic anisotropy of the 3d-transition metal monoxides MnO, FeO, CoO, and NiO

The magnetic-ordering and orbital-occupancy induced distortions of the rocksalt structure below the N\'eel temperature are computed for antiferromagnetic MnO, FeO, CoO, and NiO by means of spin-polarized density functional theory including generalized-gradient corrections and an on-site Coulomb repulsion $U$. The important role of the occupation of the ${t}_{2g}$ minority-spin states is studied in detail for the occurring rhombohedral and monoclinic distortions. The magnetic anisotropy energy is calculated to determine the orientation of the local magnetic moments in the antiferromagnetic crystals. We take into account both the influence of spin-orbit coupling and the transverse electron interaction. The spin-orbit interaction drives the magnetic anisotropy in CoO and FeO due to the partially filled ${t}_{2g}$ subshell while transverse electron interaction plays an important role for the magnetic anisotropy in MnO and NiO due to the completely empty or filled ${t}_{2g}$ subshell. The results for the structural and magnetic anisotropies are discussed in the light of the available experimental data.