CeO2 films were epitaxially grown on Si(111) substrates by reactive sputtering following the single-crystal CeO2 seed layer formation by oxygen-reactive solid-phase epitaxy. Formation of metallic Ce layers and oxidation of the layers prior to reactive sputtering was found to be the key process for epitaxial growth of CeO2 on Si substrates. An Auger electron spectroscopy depth profiling analysis showed that the Ce–Si interlayer was formed after the Ce metal deposition. Reflection high-energy electron diffraction and transmission electron microscopy proved that epitaxial CeO2 films were grown by reactive sputtering on the seed layers formed by oxidation of Ce metal layers with thickness of 5 to 10 nm. Crystalline quality of the films depended on the sputtering conditions, especially on total sputtering pressure and oxygen concentration. The optimization of the conditions for seed layer formation by oxygen-reactive solid-phase epitaxy and reactive sputtering was an important factor for improving the crystalline quality of epitaxially grown CeO2 film.
Epitaxial Fe–Si(111) monolayer films and [Fe–Si(111)/Cr(111)]4 multilayer films were grown on Si(111) substrates by dc facing-targets sputtering. The thickness dependence of the Fe–Si layer and the Cr layer on the crystallinity and the magnetic properties was studied. In the case of Fe-7.2 wt% Si(111) monolayer films, excellent soft magnetic properties were observed in films thinner than 200 nm. The sudden deterioration of soft magnetic properties was observed at the thickness of 200 nm. Torque measurements of the films revealed that the increase of effective anisotropy energy caused the deterioration of soft magnetic properties. In the [Fe-7.2 wt% Si(111)/Cr(111)]4 multilayer films, permeability increased with increase of the Cr layer thickness, and excellent soft magnetic properties of multilayer films were obtained with a Cr layer thickness of 20 nm. Soft magnetic characteristics were improved in the multilayered structure compared with the monolayer film with identical total thickness of magnetic layers.
We present a cohomological method for obtaining the non-abelian Seiberg-Witten map for any gauge group and to any order in θ. By introducing a ghost field, we are able to express the equations defining the Seiberg-Witten map through a coboundary operator, so that they can be solved by constructing a corresponding homotopy operator.
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