1
|
Georgiou R, Sahle CJ, Sokaras D, Bernard S, Bergmann U, Rueff JP, Bertrand L. X-ray Raman Scattering: A Hard X-ray Probe of Complex Organic Systems. Chem Rev 2022; 122:12977-13005. [PMID: 35737888 DOI: 10.1021/acs.chemrev.1c00953] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
This paper provides a review of the characterization of organic systems via X-ray Raman scattering (XRS) and a step-by-step guidance for its application. We present the fundamentals of XRS required to use the technique and discuss the main parameters of the experimental set-ups to optimize spectral and spatial resolution while maximizing signal-to-background ratio. We review applications that target the analysis of mixtures of organic compounds, the identification of minor spectral features, and the spatial discrimination in heterogeneous systems. We discuss the recent development of the direct tomography technique, which utilizes the XRS process as a contrast mechanism for assessing the three-dimensional spatially resolved carbon chemistry of complex organic materials. We conclude by exposing the current limitations and provide an outlook on how to overcome some of the existing challenges and advance future developments and applications of this powerful technique for complex organic systems.
Collapse
Affiliation(s)
- Rafaella Georgiou
- Université Paris-Saclay, CNRS, Ministère de la Culture, UVSQ, MNHN, IPANEMA, F-91192 Saint-Aubin, France.,Synchrotron SOLEIL, L'Orme des Merisiers, Saint Aubin BP 48, 91192, Gif-sur-Yvette, France
| | | | - Dimosthenis Sokaras
- SLAC National Accelerator Laboratory, Stanford Synchrotron Radiation Lightsource, Menlo Park, California 94025, United States
| | - Sylvain Bernard
- Muséum National d'Histoire Naturelle, Sorbonne Université, CNRS, UMR 7590, Institut de Minéralogie, Physique des Matériaux et Cosmochimie, 75005 Paris, France
| | - Uwe Bergmann
- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
| | - Jean-Pascal Rueff
- Synchrotron SOLEIL, L'Orme des Merisiers, Saint Aubin BP 48, 91192, Gif-sur-Yvette, France.,Laboratoire de Chimie Physique-Matière et Rayonnement, Sorbonne Université, CNRS, 75005 Paris, France
| | - Loïc Bertrand
- Photophysique et Photochimie Supramoléculaires et Macromoléculaires, Université Paris-Saclay, ENS Paris-Saclay, CNRS, 91190 Gif-sur-Yvette, France
| |
Collapse
|
2
|
Kvashnina KO, Butorin SM. High-energy resolution X-ray spectroscopy at actinide M 4,5 and ligand K edges: what we know, what we want to know, and what we can know. Chem Commun (Camb) 2022; 58:327-342. [PMID: 34874022 PMCID: PMC8725612 DOI: 10.1039/d1cc04851a] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2021] [Accepted: 11/15/2021] [Indexed: 12/20/2022]
Abstract
In recent years, scientists have progressively recognized the role of electronic structures in the characterization of chemical properties for actinide containing materials. High-energy resolution X-ray spectroscopy at the actinide M4,5 edges emerged as a promising direction because this method can probe actinide properties at the atomic level through the possibility of reducing the experimental spectral width below the natural core-hole lifetime broadening. Parallel to the technical developments of the X-ray method and experimental discoveries, theoretical models, describing the observed electronic structure phenomena, have also advanced. In this feature article, we describe the latest progress in the field of high-energy resolution X-ray spectroscopy at the actinide M4,5 and ligand K edges and we show that the methods are able to (a) provide fingerprint information on the actinide oxidation state and ground state characters (b) probe 5f occupancy, non-stoichiometry, defects, and ligand/metal ratio and (c) investigate the local symmetry and effects of the crystal field. We discuss the chemical aspects of the electronic structure in terms familiar to chemists and materials scientists and conclude with a brief description of new opportunities and approaches to improve the experimental methodology and theoretical analysis for f-electron systems.
Collapse
Affiliation(s)
- Kristina O Kvashnina
- The Rossendorf Beamline at ESRF, The European Synchrotron, CS40220, 38043 Grenoble Cedex 9, France.
- Institute of Resource Ecology, Helmholtz Zentrum Dresden-Rossendorf (HZDR), PO Box 510119, 01314 Dresden, Germany
- Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
| | - Sergei M Butorin
- Condensed Matter Physics of Energy Materials, X-ray Photon Science, Department of Physics and Astronomy, Uppsala University, P.O. Box 516, SE-751 20 Uppsala, Sweden.
| |
Collapse
|
3
|
Caciuffo R, Lander GH. X-ray synchrotron radiation studies of actinide materials. JOURNAL OF SYNCHROTRON RADIATION 2021; 28:1692-1708. [PMID: 34738923 PMCID: PMC8570219 DOI: 10.1107/s1600577521009413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 09/09/2021] [Indexed: 06/13/2023]
Abstract
By reviewing a selection of X-ray diffraction (XRD), resonant X-ray scattering (RXS), X-ray magnetic circular dichroism (XMCD), resonant and non-resonant inelastic scattering (RIXS, NIXS), and dispersive inelastic scattering (IXS) experiments, the potential of synchrotron radiation techniques in studying lattice and electronic structure, hybridization effects, multipolar order and lattice dynamics in actinide materials is demonstrated.
Collapse
Affiliation(s)
- Roberto Caciuffo
- European Commission, Joint Research Centre, Postfach 2340, D-76125 Karlsruhe, Germany
| | - Gerard H. Lander
- European Commission, Joint Research Centre, Postfach 2340, D-76125 Karlsruhe, Germany
- Interface Analysis Centre, School of Physics, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| |
Collapse
|
4
|
Abstract
The application of core-to-core (3d-to-4f) resonant inelastic x-ray scattering (RIXS) and high-energy-resolution fluorescence-detected x-ray absorption (HERFD-XAS) at actinide M4,5 edges, as techniques with the enhanced sensitivity to changes in the chemical state, was analyzed for trivalent actinide compounds. As an example, a series of actinide chlorides AnCl3 (An = U, Np, Pu, Am, Cm, Bk, and Cf) was used. The crystal-field multiplet formalism was applied to calculate the 3d-4f RIXS maps, and the HERFD-XAS spectra were extracted as cuts of these RIXS maps along the incident energy axis at the constant emitted energy, corresponding to the maximum of the RIXS intensity. A relation between HERFD and conventional XAS methods was also examined. Despite some differences between profiles of the An M5 HERFD and conventional XAS spectra of trivalent actinides, the results of calculations indicate that the HERFD method can be used at the An M5 edge for monitoring even small variations in the An chemical state. As a whole, better agreement between the HERFD and XAS spectra was found for the An M4 edges as compared to the An M5 edges. By using the point charge electrostatic model, the dependence of the An M4,5 HERFD-XAS spectra on the An coordination number was studied, which indicates the significant sensitivity of the distribution of the An 5f states to the ligand structural arrangement around the An sites.
Collapse
Affiliation(s)
- Sergei M Butorin
- Condensed Matter Physics of Energy Materials, X-ray Photon Science, Department of Physics and Astronomy, Uppsala University, P.O. Box 516, SE-75120 Uppsala, Sweden
| |
Collapse
|
5
|
Lander GH, Sundermann M, Springell R, Walters AC, Nag A, Garcia-Fernandez M, Zhou KJ, van der Laan G, Caciuffo R. Resonant inelastic x-ray spectroscopy on UO 2 as a test case for actinide materials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:06LT01. [PMID: 33325375 DOI: 10.1088/1361-648x/abc4d2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Resonant inelastic x-ray spectroscopy at the uranium N4 absorption edge at 778 eV has been used to reveal the excitations in UO2 up to 1 eV. The earlier (1989) studies by neutron inelastic scattering of the crystal-field states within the 3H4 multiplet are confirmed. In addition, the first excited state of the 3F2 multiplet at ∼520 meV has been established, and there is a weak signal corresponding to the next excited state at ∼920 meV. This represents a successful application of soft x-ray spectroscopy to an actinide sample, and resolves an open question in UO2 that has been discussed for 50 years. The technique is described and important caveats are drawn about possible future applications.
Collapse
Affiliation(s)
- G H Lander
- European Commission, Joint Research Centre (JRC), Postfach 2340, D-76125 Karlsruhe, Germany
- Interface Analysis Centre, School of Physics, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
| | - M Sundermann
- Institute of Physics II, University of Cologne, Zülpicher Straße 77, D-50937 Cologne, Germany
- Max Planck Institute for Chemical Physics of Solids, Nöthnizer Straße 40, 01187 Dresden, Germany
| | - R Springell
- Interface Analysis Centre, School of Physics, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
| | - A C Walters
- Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0DE, United Kingdom
| | - A Nag
- Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0DE, United Kingdom
| | - M Garcia-Fernandez
- Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0DE, United Kingdom
| | - K J Zhou
- Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0DE, United Kingdom
| | - G van der Laan
- Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0DE, United Kingdom
| | - R Caciuffo
- European Commission, Joint Research Centre (JRC), Postfach 2340, D-76125 Karlsruhe, Germany
| |
Collapse
|
6
|
Amorese A, Sundermann M, Leedahl B, Marino A, Takegami D, Gretarsson H, Gloskovskii A, Schlueter C, Haverkort MW, Huang Y, Szlawska M, Kaczorowski D, Ran S, Maple MB, Bauer ED, Leithe-Jasper A, Hansmann P, Thalmeier P, Tjeng LH, Severing A. From antiferromagnetic and hidden order to Pauli paramagnetism in U M 2Si 2 compounds with 5 f electron duality. Proc Natl Acad Sci U S A 2020; 117:30220-30227. [PMID: 33203673 PMCID: PMC7720184 DOI: 10.1073/pnas.2005701117] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022] Open
Abstract
Using inelastic X-ray scattering beyond the dipole limit and hard X-ray photoelectron spectroscopy we establish the dual nature of the U [Formula: see text] electrons in U[Formula: see text] (M = Pd, Ni, Ru, Fe), regardless of their degree of delocalization. We have observed that the compounds have in common a local atomic-like state that is well described by the U [Formula: see text] configuration with the [Formula: see text] and [Formula: see text] quasi-doublet symmetry. The amount of the U 5[Formula: see text] configuration, however, varies considerably across the U[Formula: see text] series, indicating an increase of U 5f itineracy in going from M = Pd to Ni to Ru and to the Fe compound. The identified electronic states explain the formation of the very large ordered magnetic moments in [Formula: see text] and [Formula: see text], the availability of orbital degrees of freedom needed for the hidden order in [Formula: see text] to occur, as well as the appearance of Pauli paramagnetism in [Formula: see text] A unified and systematic picture of the U[Formula: see text] compounds may now be drawn, thereby providing suggestions for additional experiments to induce hidden order and/or superconductivity in U compounds with the tetragonal body-centered [Formula: see text] structure.
Collapse
Affiliation(s)
- Andrea Amorese
- Institute of Physics II, University of Cologne, 50937 Cologne, Germany
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - Martin Sundermann
- Institute of Physics II, University of Cologne, 50937 Cologne, Germany
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - Brett Leedahl
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - Andrea Marino
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - Daisuke Takegami
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - Hlynur Gretarsson
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
- Positron-Elektron-Tandem-Ring-Anlage III (PETRA III), Deutsches Elektronen-Synchrotron, 22607 Hamburg, Germany
| | - Andrei Gloskovskii
- Positron-Elektron-Tandem-Ring-Anlage III (PETRA III), Deutsches Elektronen-Synchrotron, 22607 Hamburg, Germany
| | - Christoph Schlueter
- Positron-Elektron-Tandem-Ring-Anlage III (PETRA III), Deutsches Elektronen-Synchrotron, 22607 Hamburg, Germany
| | - Maurits W Haverkort
- Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg, Germany
| | - Yingkai Huang
- van der Waals-Zeeman Institute, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
| | - Maria Szlawska
- Institute of Low Temperature & Structure Research, Polish Academy of Science, 50-950 Wroclaw, Poland
| | - Dariusz Kaczorowski
- Institute of Low Temperature & Structure Research, Polish Academy of Science, 50-950 Wroclaw, Poland
| | - Sheng Ran
- Department of Physics, University of California San Diego, La Jolla, CA 92093
| | - M Brian Maple
- Department of Physics, University of California San Diego, La Jolla, CA 92093
| | - Eric D Bauer
- MPA-Q, Los Alamos National Laboratory, Los Alamos, NM 87545
| | | | - Philipp Hansmann
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
- Department of Physics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany
| | - Peter Thalmeier
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - Liu Hao Tjeng
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - Andrea Severing
- Institute of Physics II, University of Cologne, 50937 Cologne, Germany;
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| |
Collapse
|
7
|
Mydosh JA, Oppeneer PM, Riseborough PS. Hidden order and beyond: an experimental-theoretical overview of the multifaceted behavior of URu 2Si 2. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:143002. [PMID: 31801118 DOI: 10.1088/1361-648x/ab5eba] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This topical review describes the multitude of unconventional behaviors in the hidden order, heavy fermion, antiferromagnetic and superconducting phases of the intermetallic compound URu2Si2 when tuned with pressure, magnetic field, and substitutions for all three elements. Such 'perturbations' result in a variety of new phases beyond the mysterious hidden order that are only now being slowly understood through a series of state-of-the-science experimentation, along with an array of novel theoretical approaches. Despite all these efforts spanning more than 30 years, hidden order (HO) remains puzzling and non-clarified, and the search continues in 2019 into a fourth decade for its final resolution. Here we attempt to update the present situation of URu2Si2 importing the latest experimental results and theoretical proposals. First, let us consider the pristine compound as a function of temperature and report the recent measurements and models relating to its heavy Fermi liquid crossover, its HO and superconductivity (SC). Recent experiments and theories are surmized that address four-fold symmetry breaking (or nematicity), Isingness and unconventional excitation modes. Second, we review the pressure dependence of URu2Si2 and its transformation to antiferromagnetic long-range order. Next we confront the dramatic high magnetic-field phases requiring fields above 40 T. And finally, we attempt to answer how does random substitutions of other 5f elements for U, and 3d, 4d, and 5d elements for Ru, and even P for Si affect and transform the HO. Commensurately, recent theoretical models are summarized and then related to the intriguing experimental behavior.
Collapse
Affiliation(s)
- J A Mydosh
- Institute Lorentz and Kamerlingh Onnes Laboratory, Leiden University, NL-2300 RA Leiden, The Netherlands
| | | | | |
Collapse
|
8
|
Miao L, Basak R, Ran S, Xu Y, Kotta E, He H, Denlinger JD, Chuang YD, Zhao Y, Xu Z, Lynn JW, Jeffries JR, Saha SR, Giannakis I, Aynajian P, Kang CJ, Wang Y, Kotliar G, Butch NP, Wray LA. High temperature singlet-based magnetism from Hund's rule correlations. Nat Commun 2019; 10:644. [PMID: 30733441 PMCID: PMC6367396 DOI: 10.1038/s41467-019-08497-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2018] [Accepted: 01/10/2019] [Indexed: 11/24/2022] Open
Abstract
Uranium compounds can manifest a wide range of fascinating many-body phenomena, and are often thought to be poised at a crossover between localized and itinerant regimes for 5f electrons. The antiferromagnetic dipnictide USb2 has been of recent interest due to the discovery of rich proximate phase diagrams and unusual quantum coherence phenomena. Here, linear-dichroic X-ray absorption and elastic neutron scattering are used to characterize electronic symmetries on uranium in USb2 and isostructural UBi2. Of these two materials, only USb2 is found to enable strong Hund’s rule alignment of local magnetic degrees of freedom, and to undergo distinctive changes in local atomic multiplet symmetry across the magnetic phase transition. Theoretical analysis reveals that these and other anomalous properties of the material may be understood by attributing it as the first known high temperature realization of a singlet ground state magnet, in which magnetism occurs through a process that resembles exciton condensation. Electrons in uranium-based materials are often on the border between localised and itinerant behaviour, which can lead to unusual magnetic behaviour. Here the authors combine experiment and theory to show that USb2 may be an unusually high temperature example of a singlet-ground-state magnet.
Collapse
Affiliation(s)
- Lin Miao
- Department of Physics, New York University, New York, NY, 10003, USA.,Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Rourav Basak
- Department of Physics, New York University, New York, NY, 10003, USA
| | - Sheng Ran
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA
| | - Yishuai Xu
- Department of Physics, New York University, New York, NY, 10003, USA
| | - Erica Kotta
- Department of Physics, New York University, New York, NY, 10003, USA
| | - Haowei He
- Department of Physics, New York University, New York, NY, 10003, USA
| | - Jonathan D Denlinger
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Yi-De Chuang
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Y Zhao
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA.,Department of Materials Science and Engineering, University of Maryland, College Park, MD, 20742, USA
| | - Z Xu
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA
| | - J W Lynn
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA
| | - J R Jeffries
- Materials Science Division, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - S R Saha
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA.,Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - Ioannis Giannakis
- Department of Physics, Applied Physics and Astronomy, Binghamton University, Binghamton, NY, 13902, USA
| | - Pegor Aynajian
- Department of Physics, Applied Physics and Astronomy, Binghamton University, Binghamton, NY, 13902, USA
| | - Chang-Jong Kang
- Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, 08854-8019, USA
| | - Yilin Wang
- Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - Gabriel Kotliar
- Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, 08854-8019, USA
| | - Nicholas P Butch
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA.,Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - L Andrew Wray
- Department of Physics, New York University, New York, NY, 10003, USA.
| |
Collapse
|
9
|
Sundermann M, Yavaş H, Chen K, Kim DJ, Fisk Z, Kasinathan D, Haverkort MW, Thalmeier P, Severing A, Tjeng LH. 4f Crystal Field Ground State of the Strongly Correlated Topological Insulator SmB_{6}. PHYSICAL REVIEW LETTERS 2018; 120:016402. [PMID: 29350947 DOI: 10.1103/physrevlett.120.016402] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Revised: 09/25/2017] [Indexed: 06/07/2023]
Abstract
We investigated the crystal-electric field ground state of the 4f manifold in the strongly correlated topological insulator SmB_{6} using core-level nonresonant inelastic x-ray scattering. The directional dependence of the scattering function that arises from higher multipole transitions establishes unambiguously that the Γ_{8} quartet state of the Sm f^{5} J=5/2 configuration governs the ground-state symmetry and, hence, the topological properties of SmB_{6}. Our findings contradict the results of density functional calculations reported so far.
Collapse
Affiliation(s)
- M Sundermann
- Institute of Physics II, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
| | - H Yavaş
- PETRA III, Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, 22607 Hamburg, Germany
| | - K Chen
- Institute of Physics II, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany
| | - D J Kim
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - Z Fisk
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - D Kasinathan
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
| | - M W Haverkort
- Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, 69120 Heidelberg, Germany
| | - P Thalmeier
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
| | - A Severing
- Institute of Physics II, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
| | - L H Tjeng
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
| |
Collapse
|