Abstract
Effective spin Hamiltonians with t 2g orbital degeneracy have been investigated theoretically. We assume that a d electron occupies one of doubly degenerate d z x and d y z orbitals which have the lowest energy in atomic level. The orbital degrees of freedom are represented as Ising iso-spin operators because of the symmetry of the orbital characters. We apply the Hamiltonians to a ladder and a chain lattices and investigate the models using the exact diagonalization. For the ladder model, a spin gap opens above a finite value of the spin exchange coupling on rung, which is qualitatively different from the ladder model with single orbital. For the chain model, the spin gap behavior is observed in the uniform spin correlation at low temperature. Origin of the spin gap is a spin-dimer triggered by the occurrence of the ferromagnetic orbital ordering, which suggests a new mechanism of the spin gap formation.
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