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The YNiO$_3$ nickelate is a paradigm d-electron oxide that manifests theintriguing temperature-mediated sequence of three phases transitions from (i)magnetically ordered insulator to (ii) paramagnetic (PM) insulator and then to(iii) PM metal. Such phenomena raised the question of the nature of theassociation of magnetism and structural symmetry breaking with the appearancein (i) and (ii) and disappearance in (iii) of insulating band gaps. It isdemonstrated here that first-principles mean-field-like density functionaltheory (DFT), driven by molecular dynamics temperature evolution, can describenot only the origin of the magnetically long-range ordered insulating phase(i), but also the creation of an insulating paramagnet (ii) that lacksspin-long-range order, and of a metallic paramagnet (iii) as temperature rises.This approach provides the patterns of structural and magnetic symmetrybreaking at different temperatures, in parallel with band gaps obtained whenthe evolving geometries are used as input to DFT electronic band structurecalculations. This disentangles the complex interplay among spin, charge andorbital degrees of freedom. Analysis shows that the success in describing therise and fall of the insulating band gaps along the phase transition sequenceis enabled by allowing sufficient flexibility in describing diverse localstructural and magnetic motifs as input to DFT. This entails using sufficientlylarge supercells that allow expressing structural disproportionation ofoctahedra, as well as a description of PM phases as a distribution of localmagnetic moments. It appears that the historic dismissal of mean-field-like DFTas being unable to describe such Mott-like transitions was premature, as it wasbased on consideration of averaged crystallographic unit cells, a descriptionthat washes out local symmetry-breaking motifs.

The rise and fall of Mott insulating gaps in YNiO$_3$ paramagnets as a reflection of symmetry breaking and remaking