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 Δ/|t| and on the sign of the hopping amplitude t. We find a Mott insulator for Δ⪢U⪢|t|; a charge-transfer insulator for U⪢Δ⪢|t|; and a correlated covalent insulator for U⪢Δ∼|t|, 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⪢Δ∼|t| and t<0 is relevant to Na_0.5CoO₂. The calculated optical conductivity and the spectral density are discussed in the light of recent experiments on Na_0.5CoO₂.