Crystal field and magnetic structure of UO${}_2$

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