Orbital and spin physics in LiNiO2 and NaNiO2
  We derive a spin-orbital Hamiltonian for a triangular lattice of e_g orbital degenerate (Ni^{3+}) transition metal ions interacting via 90 degree superexchange involving (O^{2-}) anions, taking into account the on-site Coulomb interactions on both the anions and the transition metal ions. The derived interactions in the spin-orbital model are strongly frustrated, with the strongest orbital interactions selecting different orbitals for pairs of Ni ions along the three different lattice directions. In the orbital ordered phase, favoured in mean field theory, the spin-orbital interaction can play an important role by breaking the U(1) symmetry generated by the much stronger orbital interaction and restoring the threefold symmetry of the lattice. As a result the effective magnetic exchange is non-uniform and includes both ferromagnetic and antiferromagnetic spin interactions. Since ferromagnetic interactions still dominate, this offers yet insufficient explanation for the absence of magnetic order and the low-temperature behaviour of the magnetic susceptibility of stoichiometric LiNiO_2. The scenario proposed to explain the observed difference in the physical properties of LiNiO_2 and NaNiO_2 includes small covalency of Ni-O-Li-O-Ni bonds inducing weaker interplane superexchange in LiNiO_2, insufficient to stabilize orbital long-range order in the presence of stronger intraplane competition between superexchange and Jahn-Teller coupling. 
Albert J. W. Reitsma, Louis F. Feiner and Andrzej M. Oles'