We use an exact-diagonalization technique to investigate the phase diagram of correlated $t_{2g}$ electrons within the single-layer Ca-based ruthenates. The interplay between the charge fluctuations, induced by the crystalline field potential, and those due to the Coulomb correlations leads to different magnetic and orbital patterns. We show that the compressive octahedra distortions tend to stabilize an antiferromagnetic state with $C$- or $G$-type structure and different orbital configurations, depending on the degree of flattening. In the case of elongated octahedra, as a consequence of the orbital frustration, a ground state with incomplete ferromagnetism appears, except in the limit of large Coulomb repulsion with respect to the Hund’s rule, where an antiferromagnetic $G$-type state emerges.

• Received 21 July 2006

DOI:https://doi.org/10.1103/PhysRevB.74.195124