Interplay between breathing mode distortion and magnetic order in rare-earth nickelates RNiO3 within DFT plus U

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, RNiO3, 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.