Interplay Between Magnetic Order and Lattice Distortions in Rare-Earth Nickelates

We study the magnetic order appearing in the rare-earth nickelates at low temperatures, the exact nature of which is still debated vigorously in the literature. While there is an established link between the metal-insulator transition and lattice distortions in the nickelates, to our knowledge there has been little work on the impact of lattice distortions on the magnetic order, e.g. whether they favor some orders over others. To address this, we consider a two-band Hubbard model for the nickelates, coupled to the lattice distortions (which are treated semiclassically), and use the Hartree-Fock approximation to find the resulting phase diagram. Aside from quantitatively demonstrating how lattice distortions drive bond disproportionation, we find that a variety of 4-site magnetic orders are self-consistent within the model, including both collinear and non-collinear orders. However, in our model a magnetic order can only couple to the lattice distortions if there is an asymmetry in average charge occupation of neighbouring sites. As a result, we find that coupling to the lattice distortions broadly favors the collinear ↑-o-↓-o order in large sectors of the parameter space.