Diffraction from Ordered States of Higher Multipoles

Possible ways of identification are discussed of an electronic order of higher multipoles such as octupoles and hexadecapoles. A particularly powerful method is resonant X-ray scattering (RXS) using quadrupolar resonance processes called E2.The characteristic azimuthal angle dependence of Ce$_{0.7}$La$_{0.3}$B$_6$ is interpreted as evidence of antiferro-octupole order. For PrRu$_4$P$_{12}$, eightfold pattern against azimuthal angle is predicted if its metal-insulator transition is a consequence of a hexadecapole order. In non-resonant superlattice Bragg scattering, hexadecapole contribution may also be identified because of absence of quadrupole component.Comment: Invited paper to be published in Proc. Hiroshima Workshop on Novel Functional Materials with Multinary Freedoms (Physica B, 2006

Detection of Neutron Scattering from Phase IV of Ce0.7La0.3B6: A Confirmation of the Octupole Order

We have performed a single crystal neutron scattering experiment on Ce0.7La0.3B6 to investigate the order parameter of phase IV microscopically. Below the phase transition temperature 1.5 K of phase IV, weak but distinct superlattice reflections at the scattering vector (h/2,h/2,l/2) (h, l = odd number) have been observed by neutron scattering for the first time. The intensity of the superlattice reflections is stronger for high scattering vectors, which is quite different from the usual magnetic form factor of magnetic dipoles. This result directly evidences that the order parameter of phase IV has a complex magnetization density, consistent with the recent experimental and theoretical prediction in which the order parameter is the magnetic octupoles Tbeta with Gamma5 symmetry of point group Oh. Neutron scattering experiments using short wavelength neutrons, as done in this study, could become a general method to study the high-rank multipoles in f electron systems.Comment: 4 pages, 4 figure

Evidence for Octupole Order in Ce0.7_{0.7}La0.3_{0.3}B6_6 from Resonant X-ray Scattering

The azimuthal angle dependence observed in the resonant X-ray scattering in phase IV of Ce$_{0.7}$La$_{0.3}$B$_6$ is analyzed theoretically. It is shown that the peculiar angle dependence observed in the E2 channel is consistent with the Gamma_{5u}-type octupole order with principal axis along (111) and equivalent directions. Under the assumption that the four equivalent octupole domains are nearly equally populated in the sample, the observed angle dependences are reproduced by calculation for both sigma-sigma' and sigma-pi' polarizations. The calculation for various symmetries of order parameters excludes unambiguously other order parameters than the Gamma_{5u}-type octupole.Comment: 4 pages, 2 figures, 3 tables, in JPSJ forma

Multipole correlations in low-dimensional f-electron systems

By using a density matrix renormalization group method, we investigate the ground-state properties of a one-dimensional three-orbital Hubbard model on the basis of a j-j coupling scheme. For $B_4^0 \ne 0$, where $B_4^0$ is a parameter to control cubic crystalline electric field effect, one orbital is itinerant, while other two are localized. Due to the competition between itinerant and localized natures, we obtain orbital ordering pattern which is sensitive to $B_4^0$, leading to a characteristic change of $\Gamma_{3g}$ quadrupole state into an incommensurate structure. At $B_4^0 = 0$, all the three orbitals are degenerate, but we observe a peak at $q = 0$ in $\Gamma_{3g}$ quadrupole correlation, indicating a ferro-orbital state, and the peak at $q = \pi$ in $\Gamma_{4u}$ dipole correlation, suggesting an antiferromagnetic state. We also discuss the effect of $\Gamma_{4u}$ octupole on magnetic anisotropy.Comment: 4 pages, 3 figures, Proceedings of ASR-WYP-2005 (September 27-29, 2005, Tokai

Toward Identification of Order Parameters in Skutterudites - a Wonderland of Strong Correlation Physics -

Current status is described toward identifying unconventional order parameters in filled skutterudites with unique ordering phenomena. The order parameters in PrFe$_4$P$_{12}$ and PrRu$_4$P$_{12}$ are discussed in relation to associated crystalline electric field (CEF) states and angular form factors. By phenomenological Landau analysis, it is shown that a scalar order model explains most properties in both PrFe$_4$P$_{12}$ and PrRu$_4$P$_{12}$ with very different magnetic properties. In particular, the highly anisotropic susceptibility induced by uniaxial pressure in PrFe$_4$P$_{12}$ is explained in terms of two types of couplings. In the case of SmRu$_4$P$_{12}$, the main order parameter at low field is identified as magnetic octupoles. A microscopic mechanism is proposed how the dipole and octupole degrees of freedom mix under the point group $T_h$ of skutterudites.Comment: To be published in Proc. International Conference on New Quantum Phenomena in Skutterudite and Related Systems (Suppl. J. Phys. Soc. Jpn 78, 2008

Effect of surface polishing and oxidization induced strain on electronic order at the Verwey transition in Fe3O4

International audienceFollowing the controversy between two previous publications (Lorenzo et al 2008 Phys. Rev. Lett. 101 226401 and Garcia et al 2009 Phys. Rev. Lett. 102 176405), we report on the influence of mechanical polishing, and subsequent sample storage, on the electronic order at the Verwey transition of highly pure magnetite, Fe3O4, by resonant x-ray scattering. Contrary to expectations, mechanically polishing the surface induces an inhomogeneous micron deep dead layer, probably of powdered Fe3O4. In addition, we have found that polishing the sample immediately before the experiment influences and favors the appearance of long range order electronic correlations, whereas samples polished well in advance have their electronic order quenched. Conversely, lattice distortions associated with the Verwey transition appear less affected by the surface state. We conclude that mechanical polishing induces stresses at the surface that may propagate into the core of the single crystal sample. These strains relax with time, which affects the different order parameters, as measured by x-ray resonant diffraction

Groundwater Flow Models of Illinois: Data, Processes, Model Performance, and Key Results

The Illinois State Water Survey (ISWS) has a long history of developing groundwater flow models to simulate water supply and groundwater contamination issues in the state of Illinois. However, past local- and regional-scale models developed by the ISWS have traditionally been project based; thus models are archived when the project is completed and may not be updated for many years. This report presents the first version of the Evolving Network of Illinois Groundwater Monitoring and Modeling Analyses (ENIGMMA), which is the framework of data, procedures, protocols, and scripts that facilitate the development of a single, continuously updated groundwater flow model and other outputs (hydrographs, maps, animations of groundwater potentiometric surfaces). This report focuses on five aspects of ENIGMMA: 1. The archived models and high-resolution datasets that serve as inputs to ENIGMMA 2. The procedures for developing model-ready datasets from these inputs 3. The Illinois Groundwater Flow Model (IGWFM), which serves as the single model that will be continuously updated by ENIGMMA 4. The ISWS Calibration Toolbox, used to facilitate a transient calibration of the IGWFM 5. Animations of groundwater potentiometric surfaces using head-specified models This report is a living document that will be updated periodically. Future updates to this report will focus on additional aspects of ENIGMMA, including the automated development of model-ready inputs and display of model outputs. Updates to this report will also chronicle any additional geologic data added to ENIGMMA, and subsequently, to the Illinois Groundwater Flow Model. Updates will also highlight both local- and regional-scale advancements made with the model, including any key results from these models. The current version of the IGWFM combines and expands on two existing groundwater flow models: 1) the Northeastern Illinois Cambrian-Ordovician Sandstone Aquifer model and 2) the East-Central Illinois Mahomet Aquifer model. In addition, the model incorporates new geologic information developed by the Illinois State Geological Survey in the Middle Illinois Water Supply Planning region. The current model domain covers large portions of Illinois, Wisconsin, Indiana, and Michigan. This large spatial extent is necessary to capture the far-reaching regional head declines in the deep Cambrian-Ordovician sandstone aquifer system, which can extend beyond state boundaries. Depicting some shallow, unconsolidated aquifers also requires a simultaneous simulation of the deep sandstone to account for flow exchange between units. This is because the low-permeable stratigraphic units (aquitards) overlying the sandstone aquifers are absent over large areas of northern Illinois or are locally punctured by wells with long, open intervals. To capture these complex flow pathways, the three-dimensional IGWFM explicitly simulates all geologic materials from the land surface to the impermeable Pre-Cambrian crystalline bedrock. The IGWFM does not currently include a groundwater flow simulation of the southern portion of the state where the deep basin sandstones are highly saline and not used for water supply. Incorporating the shallow aquifers in the southern portion of the state into the IGWFM is a long-term goal. The primary datasets currently incorporated into IGWFM include surface water elevations, annual groundwater withdrawals, well information such as open intervals, geologic 2 surfaces, measured water levels, and aquifer properties inferred from previous modeling studies. These datasets are input at their best available spatial and temporal resolutions, allowing for the development of refined local-scale models. Such local-scale models are essential for simulating groundwater-surface water interactions, well interference, and contaminant transport. Major local-scale models already exist for the Mahomet Aquifer, Kane County, and McHenry County. The IGWFM can address a number of water supply planning questions, particularly the impacts of historic, modern, and future high-capacity groundwater withdrawals on heads and groundwater discharging to surface waters. In addition, where detailed geologic information of the shallow aquifers is available, the IGWFM can also simulate the subsurface migration of point (e.g., volatile organic compounds) and nonpoint (e.g., chloride and nitrate) contaminants.published or submitted for publicationis peer reviewedOpe

An x-ray resonant diffraction study of multiferroic DyMn2O5

X-ray resonant scattering has been used to measure the magnetic order of the Dy ions below 40K in multiferroic DyMn$_{2}$O$_{5}$. The magnetic order has a complex behaviour. There are several different ordering wavevectors, both incommensurate and commensurate, as the temperature is varied. In addition a non-magnetic signal at twice the wavevector of one of the commensurate signals is observed, the maximum intensity of which occurs at the same temperature as a local maximum in the ferroelectric polarisation. Some of the results, which bear resemblence to the behaviour of other members of the RMn$_{2}$O$_{5}$ family of multiferroic materials, may be explained by a theory based on so-called acentric spin-density waves.Comment: 8 pages, 8 figure

Satellite holmium M-edge spectra from the magnetic phase via resonant x-ray scattering

Developing an expression of resonant x-ray scattering (RXS) amplitude which is convenient for investigating the contributions from the higher rank tensor on the basis of a localized electron picture, we analyze the RXS spectra from the magnetic phases of Ho near the $M_{4,5}$ absorption edges. At the $M_5$ edge in the uniform helical phase, the calculated spectra of the absorption coefficient, the RXS intensities at the first and second satellite spots capture the properties the experimental data possess, such as the spectral shapes and the peak positions. This demonstrates the plausibility of the adoption of the localized picture in this material and the effectiveness of the spectral shape analysis. The latter point is markedly valuable since the azimuthal angle dependence, which is one of the most useful informations RXS can provides, is lacking in the experimental conditions. Then, by focusing on the temperature dependence of the spectral shape at the second satellite spot, we expect that the spectrum is the contribution of the pure rank two profile in the uniform helical and the conical phases while that is dominated by the rank one profile in the intermediate temperature phase, so-called spin slip phase. The change of the spectral shape as a function of temperature indicates a direct evidence of the change of magnetic structures undergoing. Furthermore, we predict that the intensity, which is the same order observed at the second satellite spot, is expected at the fourth satellite spot from the conical phase in the electric dipolar transition.Comment: 24 pages, 5 figure