Effect of electron-lattice coupling on charge and magnetic order in rare-earth nickelates

We investigate the impact of electron-lattice coupling on the stability of various magnetic orders in rare-earth nickelates. We use the Hartree-Fock approximation, at zero temperature, to study an effective two-band model with correlations characterized by a Hubbard U and a Hund's J. This is coupled to breathing-mode distortions of the octahedral oxygen cages, described semiclassically with a Holstein term. We analyze the effect of the various parameters on the resulting phase diagram, in particular, on the degree of charge disproportionation and on the magnetic order. We confirm that the coupling to the lattice cooperates with Hund's coupling and thus encourages charge disproportionation. We also find that it favors the four-site periodic magnetic order of type double up arrow 0 double down arrow 0. Other convergent magnetic phases, such as the collinear up arrow up arrow down arrow down arrow and noncollinear up arrow ->down arrow <- states, do not couple to the lattice because of their lack of charge disproportionation. Novel phases, e.g., with charge disproportionation but no magnetic order, are found to be stabilized in specific conditions.