We study in this paper the jet schemes of the closure of nilpotent orbits in a finite-dimensional complex reductive Lie algebra. For the nilpotent cone, which is the closure of the regular nilpotent orbit, all the jet schemes are irreducible. This wa
s first observed by Eisenbud and Frenkel, and follows from a strong result of Mustau{t}c{a} (2001). Using induction and restriction of little nilpotent orbits in reductive Lie algebras, we show that for a large number of nilpotent orbits, the jet schemes of their closure are reducible. As a consequence, we obtain certain geometrical properties of these nilpotent orbit closures.
Two magnetic ordering transitions are found in InMnO3, the paramagnetic to antiferromagnetic transition near ~118 K and a lower possible spin rotation transition near ~42 K. Multiple length scale structural measurements reveal enhanced local distorti
on found to be connected with tilting of the MnO5 polyhedra as temperature is reduced. Strong coupling is observed between the lattice and the spin manifested as changes in the structure near both of the magnetic ordering temperatures (at ~42 K and ~ 118 K). External parameters such as pressure are expected to modify the coupling.
Detailed structural measurements were conducted on a new perovskite, ScMnO3, and on orthorhombic LuMnO3. Complementary density functional theory (DFT) calculations were carried out, and predict that ScMnO3 possesses E-phase magnetic order at low temp
erature with displacements of the Mn sites (relative to the high temperature state) of ~0.07 {AA}, compared to ~ 0.04 {AA} predicted for LuMnO3. However, detailed local, intermediate and long-range structural measurements by x-ray pair distribution function analysis, single crystal x-ray diffraction and x-ray absorption spectroscopy, find no local or long- range distortions on crossing into the low temperature E-phase of the magnetically ordered state. The measurements place upper limits on any structural changes to be at most one order of magnitude lower than density functional theory predictions and suggest that this theoretical approach does not properly account for the spin-lattice coupling in these oxides and may possibly predict the incorrect magnetic order at low temperatures. The results suggest that the electronic contribution to the electrical polarization dominates and should be properly treated in theoretical models.
Single crystal synthesis, structure, electric polarization and heat capacity measurements on hexagonal InMnO3 show that this small R ion in the RMnO3 series is ferroelectric (space group P63cm). Structural analysis of this system reveals a high degre
e of order within the MnO5 polyhedra but significant distortions in the R-O bond distributions compared to the previously studied materials. Point-charge estimates of the electric polarization yield an electrical polarization of approximately 7.8 micro C/cm^2, 26% larger than the well-studied YMnO3 system. This system with enhanced room temperature polarization values may serve as a possible replacement for YMnO3 in device application.
Knotty structures of Herbig-Haro jets are common phenomena, and knowing the origin of these structures is essential for understanding the processes of jet formation. Basically, there are two theoretical approaches: different types of instabilities in
stationary flow, and velocity variations in the flow. We investigate the structures with different radial velocities in the knots of the HL Tau jet as well as its unusual behaviour starting from 20 arcsec from the source. Collation of radial velocity data with proper motion measurements of emission structures in the jet of HL Tau makes it possible to understand the origin of these structures and decide on the mechanism for the formation of the knotty structures in Herbig-Haro flows. We present observations obtained with a 6 m telescope (Russia) using the SCORPIO camera with scanning Fabry-Perot interferometer. Two epochs of the observations of the HL/XZ Tau region in Halpha emission (2001 and 2007) allowed us to measure proper motions for high and low radial velocity structures. The structures with low and high radial velocities in the HL Tau jet show the same proper motion. The point where the HL Tau jet bents to the north (it coincides with the trailing edge of so-called knot A) is stationary, i.e. does not have any perceptible proper motion and is visible in Halpha emission only. We conclude that the high- and low- velocity structures in the HL Tau jet represent bow-shocks and Mach disks in the internal working surfaces of episodic outflows. The bend of the jet and the brightness increase starting some distance from the source coincides with the observed stationary deflecting shock. The increase of relative surface brightness of bow-shocks could be the result of the abrupt change of the physical conditions of the ambient medium as well as the interaction of a highly collimated flow and the side wind from XZ Tau.
The local structure of superconducting single crystals of K0.8Fe1.6+xSe2 with Tc = 32.6 K was studied by x-ray absorption spectroscopy. Near-edge spectra reveal that the average valence of Fe is 2+. The room temperature structure about the Fe, K and
Se sites was examined by iron, selenium and potassium K-edge measurements. The structure about the Se and Fe sites shows a high degree of order in the nearest neighbor Fe-Se bonds. On the other hand, the combined Se and K local structure measurements reveal a very high level of structural disorder in the K layers. Temperature dependent measurements at the Fe sites show that the Fe-Se atomic correlation follows that of the Fe-As correlation in the superconductor LaFeAsO0.89F0.11 - having the same effective Einstein temperature (stiffness). In K0.8Fe1.6+xSe2, the nearest neighbor Fe-Fe bonds has a lower Einstein temperature and higher structural disorder than in LaFeAsO0.89F0.11. The moderate Fe site and high K site structural disorder is consistent with the high normal state resistivity seen in this class of materials. For higher shells, an enhancement of the second nearest neighbor Fe-Fe interaction is found just below Tc and suggests that correlations between Fe magnetic ion pairs beyond the first neighbor are important in models of magnetic order and superconductivity in these materials.
