Orbital degeneracy as a source of frustration inLiNiO2

Motivated by the absence of cooperative Jahn-Teller effect and of magnetic ordering in ${\mathrm{LiNiO}}_2$, a layered oxide with triangular planes, we study a general spin-orbital model on the triangular lattice. A mean-field approach reveals the presence of several singlet phases between the $\mathrm{SU}\left(4\right)$ symmetric point and a ferromagnetic phase, a conclusion supported by exact diagonalizations of finite clusters. We argue that one of the phases, characterized by a large number of low-lying singlets associated to dimer coverings of the triangular lattice, could explain the properties of ${\mathrm{LiNiO}}_2$, while a ferro-orbital phase that lies nearby in parameter space leads to a new prediction for the magnetic properties of ${\mathrm{NaNiO}}_2$.