Capturing the ground state of uranium dioxide from first principles: crystal distortion, magnetic structure, and phonons

TL;DR

This study uses advanced first-principles calculations to accurately model the complex electronic, magnetic, and structural properties of uranium dioxide, achieving good agreement with experimental phonon data and revealing the importance of spin-orbit coupling and Hubbard U.

Contribution

The paper introduces a novel approach to identify the ground state of UO$_2$ by controlling $f$-orbital occupations in DFT+$U$, capturing crystal distortions, magnetic structure, and phonons.

Findings

Oxygen cage distortion matches experimental data

Spin-orbit coupling and Hubbard U are essential for accurate modeling

Phonon modes show U-dependent behavior

Abstract

Uranium dioxide (UO$_2$) remains a formidable challenge for first-principles approaches, due to the complex interplay among spin-orbit coupling, Mott physics, magnetic ordering, and crystal distortions. Here we use DFT+$U$ to explore UO$_2$ at zero temperature, incorporating all the aforementioned phenomena. The technical challenge is to navigate the many metastable electronic states produced by DFT+$U$, which is acomplished using $f$-orbital occupation matrix control to search for the ground state. We restrict our search to the high-symmetry ferromagnetic phase, including spin-orbit coupling, which produces a previously unreported occupation matrix. This newfound occupation matrix is then used as an initialization to explore the broken symmetry phases. We find the oxygen cage distortion of the 3k antiferromagnetic state to be in excellent agreement with experiments, and both the spin-orbit coupling and the Hubbard $U$ are critical ingredients. We demonstrate that only select phonon modes have a strong dependence on the Hubbard $U$, whereas magnetic ordering has only a small influence overall. We perform measurements of the phonon dispersion curves using inelastic neutron scattering, and our calculations show good agreement when using reasonable values of $U$. The quantitative success of DFT+$U$ warrants exploration of thermal transport and other observables within this level of theory.