Charge and Orbital Ordering in the Triangular-Lattice t_2g-Orbital System in One Dimension: A Possible Ground State of Bi_xV₈O₁₆

Abstract

We consider the possible charge and orbital ordering in a Hollandite compound Bi_xV₈O₁₆, which is a new one-dimensional triangular-lattice t_2g-orbital system. Using the strong-coupling perturbation theory, we derive the effective spin-orbit Hamiltonian in the approximation neglecting the small off-diagonal hopping parameters or orbital fluctuation, whereby we obtain the spin Hamiltonians in the partial space of each orbital-ordering pattern. We then apply an exact-diagonalization technique on small clusters to these spin Hamiltonians and calculate the ground-state phase diagram. We find that a variety of orbital-ordering patterns appear in the parameter space, which include the state characterized by the partial spin-singlet formation consistent with recent NMR experiment.