Large-scale structure prediction of near-stoichiometric magnesium oxide based on a machine-learned interatomic potential: Crystalline phases and oxygen-vacancy ordering

Using a fast and accurate neural network potential, we are able to systematically explore the energy landscape of large unit cells of bulk magnesium oxide with the minima hopping method. The potential is trained with a focus on the near-stoichiometric compositions, in particular on suboxides, i.e., ${\mathrm{Mg}}_{x}{\mathrm{O}}_{1\ensuremath{-}x}$ with $0.50<x<0.60$. Our extensive exploration demonstrates that for bulk stoichiometric compounds, there are several new low-energy rock-salt-like structures in which Mg atoms are octahedrally six-coordinated and form trigonal prismatic motifs with different stacking sequences. Furthermore, we find a dense spectrum of novel nonstoichiometric crystal phases of ${\mathrm{Mg}}_{x}{\mathrm{O}}_{1\ensuremath{-}x}$ for each composition of $x$. These structures are mostly similar to the rock-salt structure with octahedral coordination and five-coordinated Mg atoms. Due to the removal of one oxygen atom, the energy landscape becomes more glasslike with oxygen-vacancy type structures that all lie very close to each other energetically. For the same number of magnesium and oxygen atoms, our oxygen-deficient structures are lower in energy if the vacancies are aligned along lines or planes than rock-salt structures with randomly distributed oxygen vacancies. We also found the putative global minima configurations for each composition of the nonstoichiometric suboxide structures. These structures are predominantly composed of $\mathrm{MgO}(111)$ layers of the rock-salt structure which are terminated with Mg atoms at the top and bottom and are stacked in different sequences along the $z$ direction. Like for other materials, these Magn\'eli-type phases have properties that differ considerably from their stoichiometric counterparts such as high electrical conductivity.