Theory of Layered Iron Oxide on Frustrated Geometry: Electric Polarization, Magnetoelectric Effect and Orbital State

A layered iron oxide \rfeo ($R$: rare-earth elements) is an exotic dielectric material with charge-order (CO) driven electric polarization and magnetoelectric effect caused by spin-charge coupling. In this paper, a theory of electronic structure and dielectric property in \rfeo is presented. Charge frustration in paired-triangular lattices allows a charge imbalance without inversion symmetry. Spin frustration induces reinforcement of this polar CO by a magnetic ordering. We also analyze an orbital model for the Fe ion which does not show a conventional long-range order.