Orbital and spin physics in LiNiO2 and NaNiO2

We derive a spin-orbital Hamiltonian for a triangular lattice of eg orbital degenerate (Ni3+) transition-metal ions interacting via 900 superexchange involving (O2-) anions, taking into account the onsite 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 three-fold 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 LiNiO2. The scenario proposed to explain the observed difference in the physical properties of LiNiO2 and NaNiO2 includes small covalency of Ni-O-Li-O-Ni bonds inducing weaker interplane superexchange in LiNiO2, insufficient to stabilize orbital long-range order in the presence of stronger intraplane competition between superexchange and Jahn-Teller coupling