Complete phase diagram of rare-earth nickelates from first-principles

The structural, electronic and magnetic properties of AMO(3) perovskite oxides, where M is a 3d transition metal, are highly sensitive to the geometry of the bonds between the metal-d and oxygen-p ions (through octahedra rotations and distortions) and to their level of covalence. This is particularly true in rare-earth nickelates RNiO3 that display a metal-insulator transition with complex spin orders tunable by the rare-earth size, and are on the border line between dominantly ionic (lighter elements) and covalent characters (heavier elements). Accordingly, computing their ground state is challenging and a complete theoretical description of their rich phase diagram is still missing. Here, using first-principles simulations, we successfully describe the electronic and magnetic experimental ground state of nickelates. We show that the insulating phase is characterized by a split of the electronic states of the two Ni sites (i.e., resembling low-spin 4+ and high-spin 2+) with a concomitant shift of the oxygen-2p orbitals toward the depleted Ni cations. Therefore, from the point of view of the charge, the two Ni sites appear nearly identical whereas they are in fact distinct. Performing such calculations for several nickelates, we built a theoretical phase diagram that reproduces all their key features, namely a systematic dependence of the metal-insulator transition with the rare-earth size and the crossover between a second to first order transition for R = Pr and Nd. Finally, our results hint at strategies to control the electronic and magnetic phases of perovskite oxides by fine tuning of the level of covalence.