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We study the effective spin-orbital model derived for the d9 ions in athree-dimensional perovskite lattice, as in KCuF_3, where at each site thedoubly degenerate eg orbitals contain a single hole. The model describes thesuperexchange interactions that depend on the pattern of orbitals occupied. Wepresent the ground state properties of this model, depending on the splittingbetween the eg orbitals E_z, and the Hund's rule coupling in the excited d8states, J_H. The classical phase diagram consists of six magnetic phases whichall have different orbital ordering: two antiferromagnetic (AF) phases withG-AF order and either x2-y2 or 3z2-r2 orbitals occupied, two phases with mixedorbital (MO) patterns and A-AF order, and two other MO phases with either C-AFor G-AF order. All of them become degenerate at the multicritical pointM=(E_z,J_H)=(0,0). Using a generalization of linear spin-wave theory we studyboth the transverse excitations which are spin-waves andspin-and-orbital-waves, as well as the longitudinal (orbital) excitations. Thetransverse modes couple to each other, and the spin-and-orbital-wave turns intoa soft mode near the M point. Therefore, quantum corrections to thelong-range-order parameter are drastically increased near the orbitaldegeneracy, and classical order is suppressed in a crossover regime between theG-AF and A-AF phases in the (E_z,J_H) plane. This behavior is reminiscent ofthat found in frustrated spin models, and we conclude that orbital degeneracyprovides a new and physically realizable mechanism which stabilizes a spinliquid ground state due to inherent frustration of magnetic interactions. Wealso point out that such a disordered magnetic phase is likely to be realizedin LiNiO_2.Comment: 33 pages, 19 figure

Quantum melting of magnetic long-range order near orbital degeneracy: Classical phases and Gaussian fluctuations