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Interplay of frustration, magnetism, charge ordering, and covalency in a model of Na0.5CoO2

We investigate an effective Hamiltonian for Na0.5CoO2 that includes the electrostatic potential due to the ordered Na ions and strong electronic correlations. This model displays a subtle interplay between metallic and insulating phases and between charge and magnetic order. For realistic parameters, the model predicts an insulating phase with similarities to a covalent insulator. We show that this interpretation gives a consistent explanation of experiments on Na0.5CoO2, including the small degree of charge ordering, the small charge gap, the large moment, and the optical conductivity.