We formulate a microscopic model describing the combined effect of the Hund coupling and the local Coulomb repulsion on the ground-state properties of the layered perovskite compound ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. Considering that the properties of this compound are mainly determined by the electron dynamics in the ruthenium-oxygen planes, we have performed an exact diagonalization study on small planar Ru-O clusters, based on the use of the Lanczos algorithm. We show that the minimum value of the Hund coupling $J$ needed to have on each ruthenium atom a local triplet spin state, is a rapidly decreasing function of the intra-orbital $d$-electron Coulomb repulsion $U$. In addition, from the analysis of the off-site spin-spin correlation function, ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ is found to behave as a paramagnetic metal, in agreement with the experiments.

• Received 15 September 1997

DOI:https://doi.org/10.1103/PhysRevB.57.11989