SU(4) Theory for Spin Systems with Orbital Degeneracy

In many transitional metal oxides, the electron configuration on the metal ions has orbital degeneracy in addition to spin degeneracy. In these systems, the sign and magnitude of the spin-spin couplings depend on the orbital occupancy. This may result in interesting magnetic properties of the Mott insulating phase, and is believed to be relevant to unusual properties of many vanadium, titanium, manganese, and nickel oxides [1–12]. It may be also relevant to the quasi-one-dimensional tetrahis-dimethylaminoethylene (TDAE)-C60 [13], and to artificial quantum dot arrays [14]. Orbitals are much more difficult to measure in experiments than spins. Recent successful measurement of orbitals using a reflection technique in x ray [15] has opened a new avenue in the study of orbitals in spin systems. The Hamiltonian describing spin s ­ 1y2 systems with a twofold orbital degeneracy (isospin t ­ 1y2) was derived by Castellani et al. [2]. The Hamiltonian is generally rotationally symmetric in $ s space, but not in $ t space. The anisotropy of the latter is due to Hund’s rule and the anisotropy in orbital wave functions. In this Letter we study a simplified Hamiltonian, Eq. (1), which has SU(4) symmetry. The insight learned from this higher symmetric model should shed light on our understanding of more realistic systems. The model provides a new possibility for spin liquid ground states in higher dimensions. For the square lattice, using the fermion mean field theory, we find the flavor liquid state to be stable against flavor or generalized spin density wave formation. By comparing the energies of long-ranged ordered states to short-ranged ones on the triangular lattice, we argue the ground state is likely to be a resonant plaquette flavor liquid. In the SU(4) Néel ordered state, the spin-spin correlations can be antiferromagnetic (AF) between two neighboring sites with parallel magnetic moments. The simplest AF quantum spin-1y2 system with twofold degenerate orbitals (t-1y2) and rotational invariance in both $ s and $ t spaces is given by [5]