We consider a superexchange Hamiltonian, $H=-\Sigma {〈i,j〉}^{}(2{\mathbf{S}}_i̇{\mathbf{S}}_j-\frac{1}{2})(2{\mathbf{T}}_i̇{\mathbf{T}}_j-\frac{1}{2})$, which describes systems with orbital degeneracy and strong electron-phonon coupling in the limit of large on-site repulsion. In an $\mathrm{SU}\left(4\right)$ Schwinger boson representation, a reduced spin-orbital interaction is derived exactly, and a mean field theory has been developed. In one dimension, a spin-orbital liquid state with a finite gap is obtained. On a two-dimensional square lattice a novel type of spin-orbital ferromagnetically ordered state appears, while spin and orbital are antiferromagnetic. An important relation has been found, relating the spin and orbital correlation functions to the combined spin-orbital ones.

• Received 25 May 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.157201