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Abstract
We derive a spin–orbital Hamiltonian for a triangular lattice of eg 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.
Highlights
The low-temperature magnetic behaviour of LiNiO2 has remained puzzling ever since its peculiar properties were discovered [1]
The above analysis demonstrates that the qualitative properties which follow from orbital and spin correlations within triangular Ni planes with 90◦ Ni–O–Ni bonds can be understood within a realistic spin-orbital SE model
This model demonstrates, in agreement with the SE model of Mostovoy and Khomskii [2] and with experiment [10], that the orbital SE Jτ is stronger by one order of magnitude than any other interaction, because all magnetic dependence for the SE along Ni–O–Ni bonds originates from the singlet-triplet splitting of the oxygen 2p4 configuration, and is smaller by at least a factor Jp/Up ∼ 0.1, where Up (Jp) is the interorbital Coulomb (Hund’s exchange) interaction on oxygen
Summary
The low-temperature magnetic behaviour of LiNiO2 has remained puzzling ever since its peculiar properties were discovered [1]. The issue was addressed by Mostovoy and Khomskii (MK) in an important paper [2] in which they proposed a realistic spin-and-orbital model for the Ni plane, which includes the Coulomb repulsion and the Hund’s rule exchange splitting on oxygen They arrived at the conclusion that there is a huge degeneracy in the orbital sector, which is not resolved at the mean-field (MF) level. A conclusion concerning the nature of the magnetic interactions and the origin of the peculiar properties of LiNiO2 had better be drawn only after the theoretical prediction for the intrinsic in-plane behaviour is fully established We believe that this is not the case and reanalyze the situation in this paper. Technical details of the derivation of the model are presented in Appendix A
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