Orbital Ordering in Frustrated Jahn-Teller Systems with 90° Exchange

We show that superexchange interactions in frustrated Jahn-Teller systems with transition metal ions connected by the 90^∘ metal-oxygen-metal bonds (e.g., NaNiO₂, LiNiO₂, and ZnMn₂O₄) are much different from those in materials with the 180^∘ bonds. In the 90^∘-exchange systems spins and orbitals are decoupled: the spin exchange is much weaker than the orbital one and it is ferromagnetic for all orbital states. Though the mean-field orbital ground state is strongly degenerate, quantum orbital fluctuations select particular ferro-orbital states. We explain the orbital and magnetic ordering observed in NaNiO₂ and show that LiNiO₂ is not a spin-orbital liquid.