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The magnetic state of UO$_2$ was determined experimentally to beanti-ferromagnetic. Starting from this experimental fact, researchers havecalculated other properties within the Hubbard-corrected density-functionaltheory, DFT+U. Up to now, the Hubbard parameters for UO$_2$ were usually sochosen that the calculations give good results for some experimental data.Also, to our knowledge there exists no valid theoretical research report on theenergetically stable magnetic state of this system. In present work, employingthe new method which is based on density-functional perturbation theory, wehave determined self-consistently the Hubbard parameters and ground-stateenergies for UO$_2$ crystal in both ferromagnetic and anti-ferromagneticconfigurations, and the calculated results show that UO$_2$ crystalenergetically favors an anti-ferromagnetic state with a small energydifference. In all the calculations the PBE-sol approximation was used for theexchange-correlation energy functional.

Prediction of Magnetic State of UO2 within Hubbard-corrected Density-Functional Theory: A self-consistent approach