The properties of UO${}_2$ result from rich $f$-electron physics, including electronic Coulomb interactions, spin-orbit and crystal-field effects, as well as interionic multipolar coupling. We present a comprehensive theoretical study of the electronic structure of UO${}_2$ using a combined application of self-consistent $\text{DFT}+U$ calculations and a model Hamiltonian. The ${\Gamma }_5$ ground state of ${\mathrm{U}}^{4+}$ and the energies of crystal-field excitations ${\Gamma }_5\to {\Gamma }_{3,4,1}$ are reproduced in very good agreement with experiment. We also investigate competing noncollinear magnetic structures and confirm 3k as the $T=0$ K ground-state magnetic structure of UO${}_2$.

• Received 6 January 2011

DOI:https://doi.org/10.1103/PhysRevB.83.085106