Interplay between breathing mode distortion and magnetic order in rare-earth nickelates $R$NiO$_3$ within DFT+$U$

TL;DR

This study uses DFT+$U$ to analyze how magnetic order, rare-earth ion substitution, and Hubbard $U$ influence structural and magnetic properties in $R$NiO$_3$ nickelates, aligning well with experimental data.

Contribution

It systematically investigates the effects of magnetic order and Hubbard $U$ on structural trends and magnetic stability in rare-earth nickelates using DFT+$U$, highlighting the sensitivity of bond disproportionation to these parameters.

Findings

Structural parameters match experimental data well.

Bond-length disproportionation depends strongly on $U$ and magnetic order.

Realistic antiferromagnetic order is favored at small $U$, but ferromagnetic stability is overestimated.

Abstract

We present a systematic density functional theory (DFT) plus Hubbard $U$ study of structural trends and the stability of different magnetically ordered states across the rare-earth nickelate series, $R$NiO$_3$, with $R$ from Lu to La. In particular, we investigate how the magnetic order, the change of the rare-earth ion, and the Hubbard interaction $U$ are affecting the bond-length disproportionation between the nickel sites. Our results show that structural parameters can be obtained that are in very good agreement with present experimental data, and that DFT+$U$ is in principle able to capture the most important structural trends across the nickelate series. However, the amplitude of the bond-length disproportionation depends very strongly on the specific value used for the Hubbard $U$ parameter and also on the type of magnetic order imposed in the calculation. Regarding the relative stability of different magnetic orderings, a realistic antiferromagnetic order, consistent with the experimental observations, is favored for small $U$ values, and becomes more and more favorable compared to the ferromagnetic state towards the end of the series (i.e., towards $R$=Pr). Nevertheless, it seems that the stability of the ferromagnetic state is generally overestimated within the DFT+$U$ calculations. Our work provides a profound starting point for more detailed experimental investigations, and also for future studies using more advanced computational techniques such as, e.g., DFT combined with dynamical mean-field theory.