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 ⇑ 0 ⇓ 0. Other convergent magnetic phases, such as the collinear ↑↑↓↓ and non-collinear ↑→↓← 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.

Motivated by the potential for cuprate-like superconductivity in monolayer rare-earth nickelate superlattices, we study the effects of crystal field splitting, lattice distortions and strain on the charge, magnetic, and orbital order in undoped two-dimensional (2D) nickelate monolayers RNiO3. We use a two-band Hubbard model to describe the low-energy electron states, with correlations controlled by a effective Hubbard U and Hund's J. The electrons are coupled to the octahedral breathing-mode lattice distortions. Treating the lattice semiclassically, we apply the Hartree-Fock approximation to obtain the phase diagram for the ground-state as a function of the various parameters. We find that the 2D confinement leads to strong preference for the planar d x 2 −y 2 orbital even in the absence of a crystal-field splitting. The d x 2 −y 2 polarization is enhanced by adding a crystal field splitting, whereas coupling to breathing-mode lattice distortions weakens it. However, the former effect is stronger, leading to d x 2 −y 2 orbital and antiferromagnetic (AFM) order at reasonable values of U, J and thus to the possibility to realize cuprate-like superconductivity in this 2D material upon doping. We also find that the application of tensile strain enhances the cuprate-like phase and phases with orbital polarization in general, by reducing the t2/t1 ratio of next-nearest to nearest neighbour hopping. On the contrary, systems with compressive stress have an increased hopping ratio and consequently show a preference for ferromagnetic (FM) phases, including, unexpectedly, the out-of-plane d 3z 2 −r 2 FM phase.

No abstract

Motivated to understand phonon spectrum renormalization in the ground state of the half-filled Su-Schrieffer-Heeger model, we use the Born-Oppenheimer approximation together with the harmonic approximation to evaluate semi-analytically the all-to-all real-space ionic force constants generated through both linear and quadratic electron-phonon coupling. We then compute the renormalized phonon spectrum and the corresponding lattice zero-point energy as a function of the lattice dimerization. Crucially, the latter is included in the system's total energy, and thus has a direct effect on the equilibrium dimerization. We find that inclusion of a small quadratic coupling leads to very significant changes in the predicted equilibrium dimerization, calling into question the use of the linear approximation for this model. We also argue that inclusion of the zero-point energy is key for systems with comparable lattice and electronic energies, and/or for finite size chains. Our method can be straightforwardly generalized to study similar problems in higher dimensions.