Orbital degeneracy as a source of frustration in LiNiO${}_2$

Motivated by the absence of cooperative Jahn-Teller effect and of magnetic ordering in 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 SU(4) 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 LiNiO${}_2$, while a ferro-orbital phase that lies nearby in parameter space leads to a new prediction for the magnetic properties of NaNiO${}_2$.