Electrical resistivity, magnetism and electronic structure of the intermetallic 3d/4f Laves phase compounds ErNi2Mnx

The non-stoichiometric intermetallic compounds RENi2Mnx (RE = rare earth) with the cubic MgCu2-type structure display a large variety of magnetic properties which is due to a complex interplay between the degrees of freedom of the 3d and 4f electrons and their interactions. We performed a comprehensive study of the electrical resistivity, magnetic properties and the electronic structure of ErNi2Mnx (x =0, 0.25, 0.5, 0.75, 1, 1.25) compounds by employing a suitable set of complementary experimental approaches. We find an increase in electrical resistance compared to ErNi2 upon Mn doping, the residual resistivity ratio decreases with increasing manganese content. The Curie temperature exhibits a sharp increase to around 50 K for Mn concentrations x 0.5, whereas the saturation magnetization decreases with growing Mn content x 0.5. Valence band X-ray photoelectron spectroscopy reveals an increasing intensity of Mn 3d states near Fermi energy in dependence of Mn concentration and Curie temperature. Resonant photoelectron spectroscopy of ErNi2Mn0.75 reveals that the photoemission decay channels dominate the valence band spectra across the Er N5 and Mn L3 X-ray absorption maxima, whereas the L3VV Auger dictates the resonant valence band spectra close to and at the Ni L3 X-ray absorption edge

From Fe3O4/NiO bilayers to NiFe2O4-like thin films through Ni interdiffusion

Ferrites with (inverse) spinel structure display a large variety of electronic and magnetic properties, making some of them interesting for potential applications in spintronics. We investigate the thermally induced interdiffusion of Ni$^{2+}$ ions out of NiO into Fe$_3$O$_4$ ultrathin films, resulting in off-stoichiometric nickel ferrite–like thin layers. We synthesized epitaxial Fe$_3$O$_4$ bilayers on Nb-doped SrTiO$_3$(001) substrates by means of reactive molecular beam epitaxy. Subsequently, we performed an annealing cycle comprising three steps at temperatures of 400$^\circ$C, 600$^\circ$C, and 800$^\circ$C under an oxygen background atmosphere. We studied the changes of the chemical and electronic properties as result of each annealing step with help of hard x-ray photoelectron spectroscopy and found a rather homogeneous distribution of Ni and Fe cations throughout the entire film after the overall annealing cycle. For one sample we observed a cationic distribution close to that of the spinel ferrite NiFe$_2$O$_4$. Further evidence comes from low-energy electron diffraction patterns indicating a spinel-type structure at the surface after annealing. Site- and element-specific hysteresis loops performed by x-ray magnetic circular dichroism uncovered the antiferrimagnetic alignment between the octahedral coordinated Ni$^{2+}$ and Fe$^{3+}$ ions and the Fe$^{3+}$ ion in tetrahedral coordination. We find a quite low coercive field of 0.02 T, indicating a rather low defect concentration within the thin ferrite films

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Behavioral Economics and the Public Sector

This thesis consists of four essays dealing with topics that are relevant for the public sector. The essays cover diverse issues of economics partly overlapping with political science. The topics reach from the taxation of labor over monetary policy to preferences over voting institutions. Throughout this thesis it is, in contrast to classical economics, not assumed that humans are necessarily fully rational. Once full rationality is no longer assumed, experiments become an important tool to learn about human behavior. Consequently, most of the work in this thesis makes use of economic experiments