Planar spin exchange in LiNiO₂

We study the planar spin exchange couplings in LiNiO2 using a perturbative approach. 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. (F. Reynaud et al, Phys. Rev. Lett. 86, 3638 (2001))