Electronic and magnetic properties of the ionic Hubbard model on the striped triangular lattice at 3/4 filling

We report a detailed study of a model Hamiltonian which exhibits a rich interplay of geometrical spin frustration, strong electronic correlations, and charge ordering. The character of the insulating phase depends on the magnitude of the onsite energy Delta/vertical bar t vertical bar and on the sign of the hopping amplitude t. We find a Mott insulator for Delta >> U >>vertical bar t vertical bar; a charge- transfer insulator for U >>Delta >>vertical bar t vertical bar; and a correlated covalent insulator for U >>Delta similar to vertical bar t vertical bar, with U the onsite Coulomb repulsion energy. The charge- transfer insulating state is investigated using a strong-coupling expansion. The frustration of the triangular lattice can lead to antiferromagnetism or ferromagnetism depending on the sign of t. We identify the ring exchange process around a triangular plaquette which determines the sign of the magnetic interactions. Exact diagonalization calculations are performed on the model for a wide range of parameters and compared to the strong-coupling expansion. The regime U >>Delta similar to vertical bar t vertical bar and t < 0 is relevant to Na(0.5)CoO(2). The calculated optical conductivity and the spectral density are discussed in the light of recent experiments on Na(0.5)CoO(2).