Hard-X-Ray Spectroscopy with a Spectrographic Approach

Aleksandr I. Chumakov, Yuri Shvyd’ko, Ilya Sergueev, Dimitrios Bessas, and Rudolf Rüffer

Phys. Rev. Lett. 123, 097402 – Published 29 August 2019

Abstract

Hard-x-ray spectroscopy relies on a suite of modern techniques for studies of vibrational, electronic, and magnetic excitations in condensed matter. At present, the energy resolution of these techniques can be improved only by decreasing the spectral window of the involved optics—monochromators and analyzers—thereby sacrificing the intensity. Here, we demonstrate hard-x-ray spectroscopy with greatly improved energy resolution without narrowing the spectral window by adapting principles of spectrographic imaging to the hard-x-ray regime. Similar to Newton’s classical prism, the hard-x-ray spectrograph disperses different “colors”—i.e., energies—of x-ray photons in space. Then, selecting each energy component with a slit ensures high energy resolution, whereas measuring x-ray spectra with all components of a broad spectral window keeps the intensity. We employ the principles of spectrographic imaging for phonon spectroscopy. Here the new approach revealed anomalous soft atomic dynamics in $α$ -iron, a phenomenon which was not previously reported in the literature. We argue that hard-x-ray spectrographic imaging also could be a path to discovering new physics in studies of electronic and magnetic excitations.

Received 31 January 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.097402

Physics Subject Headings (PhySH)

Lifetimes & widths

Spectroscopy X-ray techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Aleksandr I. Chumakov^1,*, Yuri Shvyd’ko^2,†, Ilya Sergueev³, Dimitrios Bessas¹, and Rudolf Rüffer¹

¹ESRF–The European Synchrotron, F-38043 Grenoble, France
²Advanced Photon Source, Argonne National Laboratory, Lemont, 60439 Illinois, USA
³Deutsches Elektronen Synchrotron, D-22607 Hamburg, Germany

^*Also at: National Research Center “Kurchatov Institute,” 123182 Moscow, Russia. chumakov@esrf.fr
^†shvydko@anl.gov

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Vol. 123, Iss. 9 — 30 August 2019

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Images

Figure 1
The experimental setup. (a) The beamline layout with the indicated distances of the elements from the source. High-heat-load monochromator (HHLM), compound refractive lenses (CRL), multilayer mirror (ML). (b) Optical scheme of the spectrograph with the parameters of the optical elements and angular dispersion $d θ / d E$ in various points of the scheme. Blue to red colors correspond to photons of highest to lowest energies, respectively.
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Figure 2
The measurements of the energy resolution and of the angular dispersion. (a) The optical scheme. The ${}^{57}{Fe}$ foil and avalanche photodiode (APD) [51] function as a resonance detector with a bandwidth of $\sim 0.50 μ eV$ (see SM [20]). (b) The x-ray intensity recorded by the resonance detector as the function of the mean energy of the spectrograph (see text) without the slit, and for five indicated vertical positions of a $20 − μ m$ -wide slit. (c),(d) The energies (c) and the energy bandwidths (d) of the x-ray components selected by the slit at various vertical positions for the mean energy of the spectrograph at resonance. The values are obtained by fitting Lorentz curves to the data displayed in (b). The error bars are obtained from the fits. For (c), they are within the symbol size. The value and error bar of the angular dispersion are obtained by a linear fit (solid line) to the data displayed in (c). The dashed line in (d) shows the energy resolution averaged over five slit positions. Blue to red colors correspond to photons of highest to lowest energies, respectively.
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Figure 3
(a)–(d) An example of phonon spectroscopy with the gain in quality (energy resolution) but without sacrificing quantity (intensity) from a broad spectral window. (a)–(c) Various parts of the energy spectra of nuclear inelastic scattering measured in parallel with four identical foils of $α$ -iron located at different vertical positions. The data are scaled to the same peak values to facilitate comparison. (d) The net spectrum obtained after the elimination of the relative shift between the spectra shown in (a)–(c) and adding them together (see text). (e) The inelastic spectrum and instrumental function measured for a single foil of $α$ -iron. The data are scaled to the same peak value. The dashed line in (d) and (e) emphasizes the presence of the soft modes. (f) The reduced DOS $g (E) / E^{2}$ , with the central part enlarged in (g). The data at positive and negative energies are derived from the corresponding parts of the inelastic spectrum shown in (e). The black horizontal line in (f) and (g) shows the Debye level—the expected contribution to the reduced DOS from the acoustic modes [20]. The error bars indicate the statistical uncertainty. Only those points are shown where the systematic uncertainty related to the subtraction of the elastic peak is less than the symbol size.
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Figure 4
Example of simultaneous spectroscopy of different hexacyanoferrates samples: $K_{2} Mg {}^{57}{Fe} (CN)_{6}$ and $({NH}_{4})_{2} Mg {}^{57}{Fe} (CN)_{6}$ . The spectra are corrected for the relative energy shift caused by different sample positions (see text). The inserts emphasize the relative energies of the acoustic and optical modes and show the instrumental function of the spectrograph for comparison. The solid lines are to guide the eye.
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