Ordered valence bond states in symmetric two-dimensional spin-orbital systems

Abstract

We consider a superexchange Hamiltonian, $H=-{\sum }_{<i,j>}(2{\mathbf{S}}_i\cdot {\mathbf{S}}_j-\frac{1}{2})(2{\mathbf{T}}_i\cdot {\mathbf{T}}_j-\frac{1}{2})$, which describes systems with orbital degeneracy and strong electron-phonon coupling in the limit of large on-site repulsion. In an SU(4) Schwinger boson representation, a reduced spin-orbital interaction is derived {\it exactly}, and a mean field theory has been developed by introducing a symmetric valence bond pairing order parameter. 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. Moreover, an important relation has been found, relating the spin and orbital correlation functions to the combined spin-orbital ones.

four pages in Revtex, no figures, accepted for publication in Physical Review Letters

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