Orbital and spin physics in LiNiO₂ and NaNiO₂

We derive a spin–orbital Hamiltonian for a triangular lattice of e_g orbital degenerate (Ni³⁺) transition-metal ions interacting via 90° 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.