Reduced dimensionality and strong electronic correlations, which are among the most important ingredients for cupratelike high-$T_{\text{c}}$ superconductivity, characterize also the physics of nickelate-based heterostructures. Starting from the local-density approximation we arrive at a simple two-band model for quasi-two-dimensional (2D) ${\text{LaNiO}}_3/{\text{LaAlO}}_3$ heterostructures and extend it by introducing an appropriate hopping in the $z$ direction to describe the dimensional crossover to three dimensions (3D). Using dynamical mean-field theory, we study the effects of electronic correlations with increasing interaction strength along the crossover from 2D to 3D. Qualitatively, the effects of electronic correlations are surprisingly similar, albeit quantitatively larger interaction strengths are required in three dimensions for getting a Mott-Hubbard insulating state. The exchange parameters of an effective Kugel-Khomskii-type spin-orbital model are also derived and reveal strong antiferromagnetic tendencies.

• Received 9 September 2010

DOI:https://doi.org/10.1103/PhysRevB.82.235123