  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.
