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.
We discuss the structural and electronic properties of tetragonal CuO grown on SrTiO3(100) by means of hybrid density functional theory. Our analysis explains the anomalously large Cu-O vertical distance observed in the experiments (~2.7 A) in terms
of a peculiar frustration between two competing local Cu-O environments characterized by different in-plane and out-of-plane bond lengths and Cu electronic populations. The proper inclusion of substrate effects is crucial to understand the tetragonal expansion and to reproduce correctly the measured valence band spectrum for a CuO thickness of 3-3.5 unit cells, in agreement with the experimentally estimated thickness.
