Charge order, frustration relief, and spin-orbit coupling in U3O8

Research efforts on the description of the low-temperature magnetic order and electronic properties of ${\mathrm{U}}_{3}{\mathrm{O}}_{8}$ have been inconclusive so far. Reinterpreting neutron scattering results, we use group representation theory to show that the ground state presents collinear out-of-plane magnetic moments, with antiferromagnetic coupling both in-layer and between layers. Charge order relieves the initial geometric frustration, generating a slightly distorted honeycomb sublattice with N\'eel-type order. The precise knowledge of the characteristics of this magnetic ground state is then used to explain the fine features of the band gap. In this system, spin-orbit coupling (SOC) is of critical importance, as it strongly affects the electronic structure, narrowing the gap by $\ensuremath{\sim}38%$, compared to calculations neglecting SOC. The predicted electronic structure actually explains the salient features of recent optical absorption measurements, further demonstrating the excellent agreement between the calculated ground state properties and experiment.