Effects of reduced dimensionality, crystal field, electron-lattice coupling, and strain on the ground state of a rare-earth nickelate monolayer

Motivated by the potential for cuprate-like superconductivity in monolayer rare-earth nickelate superlattices, we study effects of crystal field splitting, lattice distortions and strain on charge, magnetic, orbital order undoped two-dimensional (2D) monolayers $R$NiO$_3$. We use a two-band Hubbard model to describe low-energy electron states, with correlations controlled effective $U$ Hund's $J$. The electrons are coupled octahedral breathing-mode distortions. Treating semiclassically, apply Hartree-Fock approximation obtain phase diagram ground-state as function various parameters. find that 2D confinement leads strong preference planar $d_{x^2-y^2}$ even absence crystal-field splitting. polarization is enhanced adding whereas coupling weakens it. However, former effect stronger, leading antiferromagnetic (AFM) at reasonable values $U,J$ thus possibility realize this material upon doping. also application tensile enhances phases general, reducing $t_2 / t_1$ ratio next-nearest nearest neighbour hopping. On contrary, systems compressive stress have an increased hopping consequently show ferromagnetic (FM) phases, including, unexpectedly, out-of-plane $d_{3z^2-r^2}$ FM phase.