Dégénérescence orbitale et ordre magnétique sur le réseau triangulaire

Compounds made of transition metal ions on a triangular lattice may have orbitally degenerate eg states. This is the case for LiNiO2 and NaNiO2 : the Ni3+ ions are in a low-spin state, leaving the last electron of the d-shell in the eg orbitals. In order to understand the magnetic behavior of such systems, we investigate a spin-orbital effective hamiltonian. Using exact diagonalization algorithms of finite clusters and variational approaches we have investigated the phase diagram as a function of the hopping integrals between eg orbitals and of the magnitude of the Hund's rule coupling. We show the existence of intermediate phases lying between a ferromagnetic state and the SU(4)-symmetric point. In particular we show that different types of spin arrangements can be realized ranging from dimer coverings to antiferromagnetic chains or 2D structures. In order to have a better characterization of the dimer-covering phase corresponding to LiNiO2, we derived an effective quantum dimer model adapted to the Kugel-Khomskii model we started with. The relevant terms for this quantum dimer hamiltonian are kinetic ones. A systematic investigation of this model has been carried out with exact diagonalizations and quantum Monte-Carlo. We show that a competition between two kinetic terms can lead to a resonating valence bond (RVB) state for a finite range of parameters. On the basis of the available experiments we argue that this RVB phase gives a correct description of LiNiO2. Another phase that lies nearby in parameter space, ferro-orbitally ordered, has been investigated by spin-wave calculations. The magnetization curves of NaNi02 showed the caracteristic feature of a spin-flop transition. We show that we can reproduce such a behavior in the frame of a spin-orbital model.