Hybridization driving distortions and multiferroicity in rare-earth nickelates

For decades transition-metal oxides have generated a huge interest due to the multitude of physical phenomena they exhibit. In this class of materials, the rare-earth nickelates, $R{\mathrm{NiO}}_{3}$, stand out for their rich phase diagram stemming from complex couplings between the lattice, electronic, and magnetic degrees of freedom. Here, we present a first-principles study of the low-temperature phase for two members of the $R{\mathrm{NiO}}_{3}$ series, with $R=$ Pr, Y. We employ density-functional theory with Hubbard corrections accounting not only for the onsite localizing interactions among the Ni-$3d$ electrons ($U$), but also the intersite hybridization effects between the transition metals and the ligands ($V$). All the $U$ and $V$ parameters are calculated from first principles using density-functional perturbation theory, resulting in a fully ab initio methodology. Our simulations show that the inclusion of the intersite interaction parameters $V$ is necessary to simultaneously capture the features well-established by experimental characterizations of the low-temperature state: insulating character, antiferromagnetism, and bond disproportionation. On the contrary, for some magnetic orderings the inclusion of onsite interaction parameters $U$ alone completely suppresses the breathing distortion occurring in the low-temperature phase and produces an erroneous electronic state with a vanishing band gap. In addition---only when both the $U$ and $V$ are considered---we predict a polar phase with a magnetization-dependent electric polarization, supporting recent experimental observations that suggest a possible occurrence of type-II multiferroicity for these materials.