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

TL;DR

This study explores how electron-lattice interactions influence magnetic and charge ordering in rare-earth nickelates using a two-band model and Hartree-Fock approximation, revealing lattice coupling's role in stabilizing specific magnetic phases.

Contribution

It demonstrates that electron-lattice coupling promotes charge disproportionation and stabilizes certain magnetic orders, providing new insights into phase stability in rare-earth nickelates.

Findings

Lattice coupling encourages charge disproportionation.

It favors the fully disproportionated magnetic order of type ar;0ar;0.

Novel phases with charge disproportionation but no magnetic order are identified.

Abstract

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 semi-classically, with a Holstein term. We analyze the effect of the various parameters on the resulting phase diagram, in particular on the 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 fully disproportionated, 4-site periodic magnetic order of type $\Uparrow 0 \Downarrow 0$. Other convergent magnetic phases, such as the collinear $\uparrow\uparrow\downarrow\downarrow$ and non-collinear $\uparrow\rightarrow\downarrow\leftarrow$ 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 also found to be stabilized in specific conditions.