1
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Gerasimova N, La Civita D, Samoylova L, Vannoni M, Villanueva R, Hickin D, Carley R, Gort R, Van Kuiken BE, Miedema P, Le Guyarder L, Mercadier L, Mercurio G, Schlappa J, Teichman M, Yaroslavtsev A, Sinn H, Scherz A. The soft X-ray monochromator at the SASE3 beamline of the European XFEL: from design to operation. J Synchrotron Radiat 2022; 29:1299-1308. [PMID: 36073890 PMCID: PMC9455211 DOI: 10.1107/s1600577522007627] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Accepted: 07/26/2022] [Indexed: 06/15/2023]
Abstract
The SASE3 soft X-ray beamline at the European XFEL has been designed and built to provide experiments with a pink or monochromatic beam in the photon energy range 250-3000 eV. Here, the focus is monochromatic operation of the SASE3 beamline, and the design and performance of the SASE3 grating monochromator are reported. The unique capability of a free-electron laser source to produce short femtosecond pulses of a high degree of coherence challenges the monochromator design by demanding control of both photon energy and temporal resolution. The aim to transport close to transform-limited pulses poses very high demands on the optics quality, in particular on the grating. The current realization of the SASE3 monochromator is discussed in comparison with optimal design performance. At present, the monochromator operates with two gratings: the low-resolution grating is optimized for time-resolved experiments and allows for moderate resolving power of about 2000-5000 along with pulse stretching of a few to a few tens of femtoseconds RMS, and the high-resolution grating reaches a resolving power of 10 000 at the cost of larger pulse stretching.
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Affiliation(s)
- N. Gerasimova
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - D. La Civita
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - L. Samoylova
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - M. Vannoni
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - R. Villanueva
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - D. Hickin
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - R. Carley
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - R. Gort
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | | | - P. Miedema
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | | | - L. Mercadier
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - G. Mercurio
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - J. Schlappa
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - M. Teichman
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | | | - H. Sinn
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
| | - A. Scherz
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
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2
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Bühlmann K, Gort R, Fognini A, Däster S, Holenstein S, Hartmann N, Zemp Y, Salvatella G, Michlmayr TU, Bähler T, Kutnyakhov D, Medjanik K, Schönhense G, Vaterlaus A, Acremann Y. Compact setup for spin-, time-, and angle-resolved photoemission spectroscopy. Rev Sci Instrum 2020; 91:063001. [PMID: 32611013 DOI: 10.1063/5.0004861] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 05/16/2020] [Indexed: 06/11/2023]
Abstract
We present a compact setup for spin-, time-, and angle-resolved photoemission spectroscopy. A 10 kHz titanium sapphire laser system delivers pulses of 20 fs duration, which drive a high harmonic generation-based source for ultraviolet photons at 21 eV for photoemission. The same laser also excites the sample for pump-probe experiments. Emitted electrons pass through a hemispherical energy analyzer and a spin-filtering element. The latter is based on spin-polarized low-energy electron diffraction on an Au-passivated iridium crystal. The performance of the measurement system is discussed in terms of the resolution and efficiency of the spin filter, which are higher than those for Mott-based techniques.
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Affiliation(s)
- K Bühlmann
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - R Gort
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - A Fognini
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - S Däster
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - S Holenstein
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - N Hartmann
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Y Zemp
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - G Salvatella
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - T U Michlmayr
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - T Bähler
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - D Kutnyakhov
- Institute of Physics, Johannes Gutenberg University of Mainz, 55128 Mainz, Germany
| | - K Medjanik
- Institute of Physics, Johannes Gutenberg University of Mainz, 55128 Mainz, Germany
| | - G Schönhense
- Institute of Physics, Johannes Gutenberg University of Mainz, 55128 Mainz, Germany
| | - A Vaterlaus
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Y Acremann
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
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3
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Kutnyakhov D, Xian RP, Dendzik M, Heber M, Pressacco F, Agustsson SY, Wenthaus L, Meyer H, Gieschen S, Mercurio G, Benz A, Bühlman K, Däster S, Gort R, Curcio D, Volckaert K, Bianchi M, Sanders C, Miwa JA, Ulstrup S, Oelsner A, Tusche C, Chen YJ, Vasilyev D, Medjanik K, Brenner G, Dziarzhytski S, Redlin H, Manschwetus B, Dong S, Hauer J, Rettig L, Diekmann F, Rossnagel K, Demsar J, Elmers HJ, Hofmann P, Ernstorfer R, Schönhense G, Acremann Y, Wurth W. Time- and momentum-resolved photoemission studies using time-of-flight momentum microscopy at a free-electron laser. Rev Sci Instrum 2020; 91:013109. [PMID: 32012554 DOI: 10.1063/1.5118777] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Accepted: 11/30/2019] [Indexed: 06/10/2023]
Abstract
Time-resolved photoemission with ultrafast pump and probe pulses is an emerging technique with wide application potential. Real-time recording of nonequilibrium electronic processes, transient states in chemical reactions, or the interplay of electronic and structural dynamics offers fascinating opportunities for future research. Combining valence-band and core-level spectroscopy with photoelectron diffraction for electronic, chemical, and structural analyses requires few 10 fs soft X-ray pulses with some 10 meV spectral resolution, which are currently available at high repetition rate free-electron lasers. We have constructed and optimized a versatile setup commissioned at FLASH/PG2 that combines free-electron laser capabilities together with a multidimensional recording scheme for photoemission studies. We use a full-field imaging momentum microscope with time-of-flight energy recording as the detector for mapping of 3D band structures in (kx, ky, E) parameter space with unprecedented efficiency. Our instrument can image full surface Brillouin zones with up to 7 Å-1 diameter in a binding-energy range of several eV, resolving about 2.5 × 105 data voxels simultaneously. Using the ultrafast excited state dynamics in the van der Waals semiconductor WSe2 measured at photon energies of 36.5 eV and 109.5 eV, we demonstrate an experimental energy resolution of 130 meV, a momentum resolution of 0.06 Å-1, and a system response function of 150 fs.
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Affiliation(s)
- D Kutnyakhov
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - R P Xian
- Fritz Haber Institute of the Max Planck Society, 14195 Berlin, Germany
| | - M Dendzik
- Fritz Haber Institute of the Max Planck Society, 14195 Berlin, Germany
| | - M Heber
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - F Pressacco
- Physics Department and Centre for Free-Electron Laser Science (CFEL), University of Hamburg, 22761 Hamburg, Germany
| | - S Y Agustsson
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
| | - L Wenthaus
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - H Meyer
- Physics Department and Centre for Free-Electron Laser Science (CFEL), University of Hamburg, 22761 Hamburg, Germany
| | - S Gieschen
- Physics Department and Centre for Free-Electron Laser Science (CFEL), University of Hamburg, 22761 Hamburg, Germany
| | - G Mercurio
- Physics Department and Centre for Free-Electron Laser Science (CFEL), University of Hamburg, 22761 Hamburg, Germany
| | - A Benz
- Physics Department and Centre for Free-Electron Laser Science (CFEL), University of Hamburg, 22761 Hamburg, Germany
| | - K Bühlman
- Laboratorium für Festkörperphysik, ETH Zürich, 8093 Zürich, Switzerland
| | - S Däster
- Laboratorium für Festkörperphysik, ETH Zürich, 8093 Zürich, Switzerland
| | - R Gort
- Laboratorium für Festkörperphysik, ETH Zürich, 8093 Zürich, Switzerland
| | - D Curcio
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark
| | - K Volckaert
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark
| | - M Bianchi
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark
| | - Ch Sanders
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Harwell OX11 0QX, United Kingdom
| | - J A Miwa
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark
| | - S Ulstrup
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark
| | - A Oelsner
- Surface Concept GmbH, 55124 Mainz, Germany
| | - C Tusche
- Forschungszentrum Jülich GmbH, Peter Grünberg Institut (PGI-6), 52428 Jülich, Germany
| | - Y-J Chen
- Forschungszentrum Jülich GmbH, Peter Grünberg Institut (PGI-6), 52428 Jülich, Germany
| | - D Vasilyev
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
| | - K Medjanik
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
| | - G Brenner
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - S Dziarzhytski
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - H Redlin
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - B Manschwetus
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - S Dong
- Fritz Haber Institute of the Max Planck Society, 14195 Berlin, Germany
| | - J Hauer
- Fritz Haber Institute of the Max Planck Society, 14195 Berlin, Germany
| | - L Rettig
- Fritz Haber Institute of the Max Planck Society, 14195 Berlin, Germany
| | - F Diekmann
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
| | - K Rossnagel
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - J Demsar
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
| | - H-J Elmers
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
| | - Ph Hofmann
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark
| | - R Ernstorfer
- Fritz Haber Institute of the Max Planck Society, 14195 Berlin, Germany
| | - G Schönhense
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
| | - Y Acremann
- Laboratorium für Festkörperphysik, ETH Zürich, 8093 Zürich, Switzerland
| | - W Wurth
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
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4
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Gort R, Bühlmann K, Däster S, Salvatella G, Hartmann N, Zemp Y, Holenstein S, Stieger C, Fognini A, Michlmayr TU, Bähler T, Vaterlaus A, Acremann Y. Early Stages of Ultrafast Spin Dynamics in a 3d Ferromagnet. Phys Rev Lett 2018; 121:087206. [PMID: 30192573 DOI: 10.1103/physrevlett.121.087206] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2018] [Revised: 07/24/2018] [Indexed: 06/08/2023]
Abstract
Prior to the development of pulsed lasers, one assigned a single local temperature to the lattice, the electron gas, and the spins. With the availability of ultrafast laser sources, one can now drive the temperature of these reservoirs out of equilibrium. Thus, the solid shows new internal degrees of freedom characterized by individual temperatures of the electron gas T_{e}, the lattice T_{l} and the spins T_{s}. We demonstrate an analogous behavior in the spin polarization of a ferromagnet in an ultrafast demagnetization experiment: At the Fermi energy, the polarization is reduced faster than at deeper in the valence band. Therefore, on the femtosecond time scale, the magnetization as a macroscopic quantity does not provide the full picture of the spin dynamics: The spin polarization separates into different parts similar to how the single temperature paradigm changed with the development of ultrafast lasers.
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Affiliation(s)
- R Gort
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - K Bühlmann
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - S Däster
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - G Salvatella
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - N Hartmann
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Y Zemp
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - S Holenstein
- Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
- Department of Physics, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - C Stieger
- Department of Information Technology and Electrical Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - A Fognini
- Department of Quantum Nanoscience, TU Delft, 2628 CD Delft, Netherlands
| | - T U Michlmayr
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - T Bähler
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - A Vaterlaus
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Y Acremann
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
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5
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Salvatella G, Gort R, Bühlmann K, Däster S, Vaterlaus A, Acremann Y. Erratum: “Ultrafast demagnetization by hot electrons: Diffusion or super-diffusion?” [Struct. Dyn. 3, 055101 (2016)]. Struct Dyn 2017; 4:019901. [PMID: 28191479 PMCID: PMC5272820 DOI: 10.1063/1.4975037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2017] [Accepted: 01/17/2017] [Indexed: 11/27/2022] Open
Affiliation(s)
- G. Salvatella
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - R. Gort
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - K. Bühlmann
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - S. Däster
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - A. Vaterlaus
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Y. Acremann
- Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
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6
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Salvatella G, Gort R, Bühlmann K, Däster S, Vaterlaus A, Acremann Y. Ultrafast demagnetization by hot electrons: Diffusion or super-diffusion? Struct Dyn 2016; 3:055101. [PMID: 27795975 PMCID: PMC5065576 DOI: 10.1063/1.4964892] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Accepted: 10/04/2016] [Indexed: 05/23/2023]
Abstract
Ultrafast demagnetization of ferromagnetic metals can be achieved by a heat pulse propagating in the electron gas of a non-magnetic metal layer, which absorbs a pump laser pulse. Demagnetization by electronic heating is investigated on samples with different thicknesses of the absorber layer on nickel. This allows us to separate the contribution of thermalized hot electrons compared to non-thermal electrons. An analytical model describes the demagnetization amplitude as a function of the absorber thickness. The observed change of demagnetization time can be reproduced by diffusive heat transport through the absorber layer.
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Affiliation(s)
- G Salvatella
- Laboratory for Solid State Physics , ETH Zurich, 8093 Zurich, Switzerland
| | - R Gort
- Laboratory for Solid State Physics , ETH Zurich, 8093 Zurich, Switzerland
| | - K Bühlmann
- Laboratory for Solid State Physics , ETH Zurich, 8093 Zurich, Switzerland
| | - S Däster
- Laboratory for Solid State Physics , ETH Zurich, 8093 Zurich, Switzerland
| | - A Vaterlaus
- Laboratory for Solid State Physics , ETH Zurich, 8093 Zurich, Switzerland
| | - Y Acremann
- Laboratory for Solid State Physics , ETH Zurich, 8093 Zurich, Switzerland
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7
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Fognini A, Salvatella G, Gort R, Michlmayr T, Vaterlaus A, Acremann Y. The influence of the excitation pulse length on ultrafast magnetization dynamics in nickel. Struct Dyn 2015; 2:024501. [PMID: 26798794 PMCID: PMC4711621 DOI: 10.1063/1.4914891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2015] [Accepted: 03/02/2015] [Indexed: 05/15/2023]
Abstract
The laser-induced demagnetization of a ferromagnet is caused by the temperature of the electron gas as well as the lattice temperature. For long excitation pulses, the two reservoirs are in thermal equilibrium. In contrast to a picosecond laser pulse, a femtosecond pulse causes a non-equilibrium between the electron gas and the lattice. By pump pulse length dependent optical measurements, we find that the magnetodynamics in Ni caused by a picosecond laser pulse can be reconstructed from the response to a femtosecond pulse. The mechanism responsible for demagnetization on the picosecond time scale is therefore contained in the femtosecond demagnetization experiment.
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Affiliation(s)
- A Fognini
- Laboratory for Solid State Physics , Otto-Stern-Weg 1, ETH Zurich, 8093 Zurich, Switzerland
| | - G Salvatella
- Laboratory for Solid State Physics , Otto-Stern-Weg 1, ETH Zurich, 8093 Zurich, Switzerland
| | - R Gort
- Laboratory for Solid State Physics , Otto-Stern-Weg 1, ETH Zurich, 8093 Zurich, Switzerland
| | - T Michlmayr
- Laboratory for Solid State Physics , Otto-Stern-Weg 1, ETH Zurich, 8093 Zurich, Switzerland
| | - A Vaterlaus
- Laboratory for Solid State Physics , Otto-Stern-Weg 1, ETH Zurich, 8093 Zurich, Switzerland
| | - Y Acremann
- Laboratory for Solid State Physics , Otto-Stern-Weg 1, ETH Zurich, 8093 Zurich, Switzerland
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8
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Kutnyakhov D, Lushchyk P, Fognini A, Perriard D, Kolbe M, Medjanik K, Fedchenko E, Nepijko SA, Elmers HJ, Salvatella G, Stieger C, Gort R, Bähler T, Michlmayer T, Acremann Y, Vaterlaus A, Giebels F, Gollisch H, Feder R, Tusche C, Krasyuk A, Kirschner J, Schönhense G. Imaging spin filter for electrons based on specular reflection from iridium (001). Ultramicroscopy 2013; 130:63-9. [PMID: 23639852 DOI: 10.1016/j.ultramic.2013.03.017] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2012] [Revised: 03/15/2013] [Accepted: 03/18/2013] [Indexed: 11/18/2022]
Abstract
As Stern-Gerlach type spin filters do not work with electrons, spin analysis of electron beams is accomplished by spin-dependent scattering processes based on spin-orbit or exchange interaction. Existing polarimeters are single-channel devices characterized by an inherently low figure of merit (FoM) of typically 10⁻⁴-10⁻³. This single-channel approach is not compatible with parallel imaging microscopes and also not with modern electron spectrometers that acquire a certain energy and angular interval simultaneously. We present a novel type of polarimeter that can transport a full image by making use of k-parallel conservation in low-energy electron diffraction. We studied specular reflection from Ir (001) because this spin-filter crystal provides a high analyzing power combined with a "lifetime" in UHV of a full day. One good working point is centered at 39 eV scattering energy with a broad maximum of 5 eV usable width. A second one at about 10 eV shows a narrower profile but much higher FoM. A relativistic layer-KKR SPLEED calculation shows good agreement with measurements.
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Affiliation(s)
- D Kutnyakhov
- Johannes Gutenberg-Universität, Institut für Physik, 55099 Mainz, Germany
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