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We have investigated the magnetic ordering in the ultrathin c(10$times$2) CoO(111) film supported on Ir(100) on the basis of ab-initio calculations. We find a close relationship between the local structural properties of the oxide film and the induce d magnetic order, leading to alternating ferromagnetically and anti-ferromagnetically ordered segments. While the local magnetic order is directly related to the geometric position of the Co atoms, the mismatch between the CoO film and the Ir substrate leads to a complex long-range order of the oxide.
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