Orbital and spin exchange in LiNiO2

We derive an effective orbital and spin exchange Hamiltonian using a perturbative approach to study the compound LiNiO2. We show that the inclusion of the trigonal crystal field splitting at the oxygen sites leads to the appearance of antiferromagnetic exchange integrals in deviation from the Goodenough-Kanamori-Anderson rules for this 90 degree bond. That gives a microscopic foundation for the recently observed coexistence of ferromagnetic and antiferromagnetic couplings in the orbitally frustrated state of LiNiO2.