Resonant inelastic X-ray scattering

"RIXS" redirects here. For the plural of rix, see Rix.

Resonant Inelastic X-ray Scattering (RIXS) is an x-ray spectroscopy technique used to investigate the electronic structure of molecules and materials.

Direct RIXS process. The incoming x-rays excite an electron from a deep-lying core level into the empty valence. The empty core state is subsequently filled by an electron from the occupied states under the emission of an x-ray. This RIXS process creates a valence excitation with momentum k′ − k and energy ħω − ħω′ .

Inelastic X-ray Scattering is a fast developing experimental technique in which one scatters high energy, x-ray photons inelastically off matter. It is a photon-in/photon-out spectroscopy where one measures both the energy and momentum change of the scattered photon. The energy and momentum lost by the photon are transferred to intrinsic excitations of the material under study and thus RIXS provides information about those excitations. The RIXS process can also be described as a Resonant X-ray Raman or Resonant X-ray Emission process.

RIXS is a resonant technique because the energy of the incident photon is chosen such that it coincides with, and hence resonates with, one of the atomic x-ray absorption edges of the system. The resonance can greatly enhance the inelastic scattering cross section, sometimes by many orders of magnitude[1][2][3]

The RIXS event can be thought of as a two-step process. Starting from the initial state, absorption of an incident photon leads to creation of an excited intermediate state, that has a core hole. From this state, emission of a photon leads to the final state. In a simplified picture the absorption process gives information of the empty electronic states, while the emission gives information about the occupied states. In the RIXS experiment these two pieces of information come together in a convolved manner, strongly perturbed by the core-hole potential in the intermediate state.

RIXS studies can be performed using both soft and hard x-rays.

Features

Elementary excitations in condensed matter systems that can be measured by RIXS. The indicated energy scales are the ones relevant for transition metal oxides.

Compared to other scattering techniques, RIXS has a number of unique features: it covers a large scattering phase-space, is polarization dependent, element and orbital specific, bulk sensitive and requires only small sample volumes:

  1. In RIXS one measures both the energy and momentum change of the scattered photon. Comparing the energy of a neutron, electron or photon with a wavelength of the order of the relevant length scale in a solid— as given by the de Broglie equation considering the interatomic lattice spacing is in the order of Ångströms—it derives from the relativistic energy–momentum relation that an x-ray photon has less energy than a neutron or electron. The scattering phase space (the range of energies and momenta that can be transferred in a scattering event) of x-rays is therefore without equal. In particular, high-energy x-rays carry a momentum that is comparable to the inverse lattice spacing of typical condensed matter systems so that, unlike Raman scattering experiments with visible or infrared light, RIXS can probe the full dispersion of low energy excitations in solids.
  2. RIXS can utilize the polarization of the photon: the nature of the excitations created in the material can be disentangled by a polarization analysis of the incident and scattered photons, which allow one, through the use of various selection rules, to characterize the symmetry and nature of the excitations.
  3. RIXS is element and orbital specific: chemical sensitivity arises by tuning to the absorption edges of the different types of atoms in a material. RIXS can even differentiate between the same chemical element at sites with inequivalent chemical bondings, with different valencies or at inequivalent crystallographic positions as long as the x-ray absorption edges in these cases are distinguishable. In addition, the type of information on the electronic excitations of a system being probed can be varied by tuning to different x-ray edges (e.g., K, L or M) of the same chemical element, where the photon excites core-electrons into different valence orbitals.
  4. RIXS is bulk sensitive: the penetration depth of resonant x-ray photons is material and scattering geometry- specific, but typically is on the order of a few micrometre in the hard x-ray regime (for example at transition metal K-edges) and on the order of 0.1 micrometre in the soft x-ray regime (e.g. transition metal L-edges).
  5. RIXS needs only small sample volumes: the photon-matter interaction is relatively strong, compared to for instance the neutron-matter interaction strength. This makes RIXS possible on very small volume samples, thin films, surfaces and nano-objects, in addition to bulk single crystal or powder samples.

In principle RIXS can probe a very broad class of intrinsic excitations of the system under study—as long as the excitations are overall charge neutral. This constraint arises from the fact that in RIXS the scattered photons do not add or remove charge from the system under study. This implies that, in principle RIXS has a finite cross section for probing the energy, momentum and polarization dependence of any type of electron-hole excitation: for instance the electron-hole continuum and excitons in band metals and semiconductors, charge transfer and crystal field excitations in strongly correlated materials, lattice excitations (phonons), orbital excitations,[4] and so on. In addition magnetic excitations are also symmetry-allowed in RIXS, because the angular momentum that the photons carry can in principle be transferred to the electron's spin moment.[5][6] Moreover, it has been theoretically shown that RIXS can probe Bogoliubov quasiparticles in high-temperature superconductors,[7] and shed light on the nature and symmetry of the electron-electron pairing of the superconducting state.[8]

Resolution

The energy and momentum resolution of RIXS do not depend on the core-hole that is present in the intermediate state. In general the natural linewidth of a spectral feature is determined by the life-times of initial and final states. In x-ray absorption and non-resonant emission spectroscopy, the resolution is often limited by the relatively short life-time of the final state core-hole. As in RIXS a high energy core-hole is absent in final state, this leads to intrinsically sharp spectra with energy and momentum resolution determined by the instrumentation.[1][2][3][9] At the same time, RIXS experiments keep the advantages of x-ray probes, e.g., element specificity.

The elemental specificity of the experiments comes from tuning the incident x-ray energy to the binding energy of a core level of the element of interest. One of the major technical challenges in RIXS experiments is selecting the monochromator and energy analyzer which produce, at the desired energy, the desired resolution. Some of the feasible crystal monochromator reflections and energy analyzer reflections have been tabulated. The total energy resolution comes from a combination of the incident x-ray bandpass, the beam spot size at the sample, the bandpass of the energy analyzer (which works on the photons scattered by the sample) and the detector geometry.

Radiative inelastic x-ray scattering is a weak process, with a small cross section. RIXS experiments therefore require a high-brilliance x-ray source, and are only performed at synchrotron radiation sources. In recent years, the use of area sensitive detectors has significantly decreased the counting time needed to collect one spectrum at a given energy resolution.[10]

Direct and Indirect RIXS

Indirect RIXS process. An electron is excited from a deep-lying core level into the valence shell. Excitations are created through the Coulomb interaction Uc between the core hole (and in some cases the excited electron) and the valence electrons.

Resonant Inelastic x-ray Scattering processes are classified as either direct or indirect.[11] This distinction is useful because the cross-sections for each are quite different. When direct scattering is allowed, it will be the dominant scattering channel, with indirect processes contributing only in higher order. In contrast, for the large class of experiments for which direct scattering is forbidden, RIXS relies exclusively on indirect scattering channels.

In direct RIXS, the incoming photon promotes a core-electron to an empty valence band state. Subsequently, an electron from a different state decays and annihilates the core-hole. The hole in the final state may either be in a core level at lower binding energy than in the intermediate state or in the filled valence shell. Some authors refer to this technique as resonant x-ray emission spectroscopy (RXES). The distinction between RIXS, resonance x-ray Raman and RXES in the literature is not strict.

The net result is a final state with an electron-hole excitation, as an electron was created in an empty valence band state and a hole in a filled shell. If the hole is in the filled valence shell, the electron-hole excitation can propagate through the material, carrying away momentum and energy. Momentum and energy conservation require that these are equal to the momentum and energy loss of the scattered photon.

For direct RIXS to occur, both photoelectric transitions—the initial one from core to valence state and succeeding one to fill the core hole—must be possible. These transitions can for instance be an initial dipolar transition of 1s → 2p followed by the decay of another electron in the 2p band from 2p → 1s. This happens at the K-edge of oxygen, carbon and silicon. A very efficient sequence often used in 3d transition metals is a 1s → 3d excitation followed by a 2p → 1s decay.[12]

Indirect RIXS is slightly more complicated. Here, the incoming photon promotes a core-electron to an itinerant state far above the electronic chemical potential. Subsequently, the electron in this same state decays again, filling the core-hole. Scattering of the x-rays occurs via the core-hole potential that is present in the intermediate state. It shakes up the electronic system, creating excitations to which the x-ray photon loses energy and momentum. The number of electrons in the valence sub-system is constant throughout the process.[11][13][14]

Applications

See also

References

  1. 1 2 W. Schuelke, Electron Dynamics by Inelastic X-Ray Scattering, Oxford University Press, Oxford 2007
  2. 1 2 F. De Groot and A. Kotani, Core Level Spectroscopy of Solids, CRC Press, 2008
  3. 1 2 L. Ament, M. van Veenendaal, T. Devereaux, J.P. Hill and J. van den Brink, Resonant Inelastic X-ray Scattering Studies of Elementary Excitations, Rev. Mod. Phys. 83, 705, 2011
  4. 1 2 J. Schlappa, K. Wohlfeld, K. J. Zhou, M. Mourigal, M. W. Haverkort, V. N. Strocov, L. Hozoi, C. Monney, S. Nishimoto, S. Singh, A. Revcolevschi, J.-S. Caux, L. Patthey, H. M. Ronnow, J. van den Brink & T. Schmitt, Spin–orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3, Nature 485, 82–85 (2012)
  5. ↑ L. Ament, G. Ghiringhelli, M. Moretti Sala, L. Braicovich and J. van den Brink, Theoretical demonstration of how the dispersion of magnetic excitations in cuprate compounds can be determined using resonant inelastic x-ray scattering, Phys. Rev. Lett. 103, 117003 (2009).
  6. ↑ L. Braicovich, J. van den Brink, V. Bisogni, M. Moretti Sala, L. Ament, N. Brookes, G. De Luca, M. Salluzzo, T. Schmitt and G. Ghiringhelli, Evidence for Dynamic Phase Separation and High Energy Spin Dynamics in underdoped La2-xSrxCuO4 from Resonant Inelastic X-Ray Scattering, Phys. Rev. Lett. 104, 077002 (2010).
  7. ↑ P. Marra, S. Sykora, K. Wohlfeld, J. van den Brink, Resonant Inelastic X-Ray Scattering as a Probe of the Phase and Excitations of the Order Parameter of Superconductors, Phys. Rev. Lett. 110, 117005 (2013).
  8. ↑ P. Marra, J. van den Brink, S. Sykora, Theoretical approach to resonant inelastic x-ray scattering in iron-based superconductors at the energy scale of the superconducting gap, Scientific Reports 6, Article number: 25386 (2016)
  9. ↑ P. Glatzel, M. Sikora, and M. Fernandez-Garcia, Resonant x-ray spectroscopy to study K absorption pre-edges in 3d transition metal compounds, European Physical Journal-Special Topics, 169 207 (2009).
  10. ↑ , S. Huotari et al., Improving the performance of high-resolution X-ray spectrometers with position-sensitive pixel detectors, J. Synchrotron Radiation, 12 467 (2005).
  11. 1 2 J. van den Brink, and M. van Veenendaal, Correlation functions measured by indirect resonant inelastic x-ray scattering Europhysics Letters, 73 121 (2006).
  12. 1 2 Glatzel, P.; Bergmann, U.; Yano, J.; Visser, H.; Robblee, J. H.; Gu, W. W.; de Groot, F. M. F.; Christou, G.; Pecoraro, V. L.; Cramer, S. P.; Yachandra, V. K. J. Am. Chem. Soc. 2004, 126, 9946-9959.
  13. ↑ J. N. Hancock, G. Chabot-Couture and M. Greven, Lattice coupling and Franck–Condon effects in K-edge resonant inelastic x-ray scattering New Journal of Physics, 12, 033001 (2010)
  14. ↑ F. Vernay, B. Moritz, I. Elfimov, J. Geck, D. Hawthorn, T. P. Devereaux, G. A. Sawatzky, Cu K-edge Resonant Inelastic X-Ray Scattering in Edge-Sharing Cuprates, Physical Review B 77, 104519 (2008)
  15. ↑ Kotani, A.; Okada, K.; Vanko, G.; Dhalenne, G.; Revcolevschi, A.; Giura, P.; Shukla, A. Physical Review B 2008, 77.
  16. ↑ L. Braicovich, L. Ament, V. Bisogni, F. Forte, C. Aruta, G. Balestrinoi, N. Brookes, G. de Luca, P. Medaglia, F. Miletto Granozio, M. Radovic, M. Salluzzo, J. van den Brink and G. Ghiringhelli, Dispersion of Magnetic Excitations in the Cuprate La2CuO4 and CaCuO2 Compounds Measured Using Resonant X-Ray Scattering, Phys. Rev. Lett. 102, 167401 (2009).
  17. ↑ M. Le Tacon, G. Ghiringhelli, J. Chaloupka, M. Moretti Sala, V. Hinkov, M. W. Haverkort, M. Minola, M. Bakr, K. J. Zhou, S. Blanco-Canosa, C. Monney, Y. T. Song, G. L. Sun, C. T. Lin, G. M. De Luca, M. Salluzzo, G. Khaliullin, T. Schmitt, L. Braicovich & B. Keimer, Intense paramagnon excitations in a large family of high-temperature superconductors, Nature Physics 7, 725–730 (2011)
  18. ↑ M. P. M. Dean, R. S. Springell, C. Monney, K. J. Zhou, J. Pereiro, I. Božović, B. Dalla Piazza, H. M. Ronnow, E. Morenzoni, J. van den Brink, T. Schmitt & J. P. Hill, Spin excitations in a single La2CuO4 layer, Nature Materials 11, 850–854 (2012)
  19. ↑ M. P. M. Dean, G. Dellea, R. S. Springell, F. Yakhou-Harris, K. Kummer, N. B. Brookes, X. Liu, Y.-J. Sun, J. Strle, T. Schmitt, L. Braicovich, G. Ghiringhelli, I. Bozovic, J. P. Hill, Persistence of magnetic excitations in La2-xSrxCuO4 from the undoped insulator to the heavily overdoped non-superconducting metal, Nature Materials 12, 1019–1023 (2013)
  20. ↑ J. N. Hancock, R. Viennois, D. van der Marel, H. M. Rønnow, M. Guarise, P.-H. Lin, M. Grioni, M. Moretti Sala, G. Ghiringhelli, V. N. Strocov, J. Schlappa, and T. Schmitt, Evidence for core-hole-mediated inelastic x-ray scattering from metallic Fe1.087Te, Physical Review B 82 020513(R) (2010)
  21. ↑ K. J. Zhou, Y. B. Huang, C. Monney, X. Dai, V. Strocov, N. L. Wang, Z. G. Chen, C. Zhang, P. Dai, L. Patthey, J. van den Brink, H. Ding, and T. Schmitt, Persistent high-energy spin excitations in iron-pnictide superconductors, Nature Communications 4, 1470 (2013)
  22. ↑ Y.-J. Kim, J.P. Hill, H. Yamaguchi, T. Gog and D. Casa, Resonant Inelastic X-Ray Scattering study of the electronic structure of Cu2O, arXiv:0904.3937.
  23. ↑ S. Grenier, J.P. Hill, V. Kiryukhin, W. Ku, Y.-J. Kim, K.J. Thomas, S.-W. Cheong, Y. Tokura, Y. Tomioka, D. Casa and T. Gog, d-d excitations in manganites probed by Resonant Inelastic X-Ray Scattering, Phys. Rev. Letters 94, 047203}, 2005.
  24. ↑ Y. Harada, M. Taguchi, Y. Miyajima, T. Tokushima, Y. Horikawa, A. Chainani, Y. Shiro, Y. Senba, H. Ohashi, H. Fukuyama,S. Shin, "Ligand Energy Controls the Heme-Fe Valence in Aqueous Myoglobins.", Journal of the Physical Society of Japan, 2009. 78(4): p. 044802.
  25. ↑ P. Glatzel, J. Singh, K.O. Kvashnina, and J.A. van Bokhoven, In situ characterization of the 5d density of states of Pt nanoparticles upon adsorption of CO, Journal of the American Chemical Society 132 2555 (2010).
  26. ↑ O. Fuchs, M. Zharnikov, L. Weinhardt, M. Blum, M. Weigand, Y. Zubavichus, M. Bar, F. Maier, J.D. Denlinger, C. Heske, M. Grunze,E. Umbach, "Isotope and Temperature Effects in Liquid Water Probed by X-Ray Absorption and Resonant X-Ray Emission Spectroscopy." Physical Review Letters, 2008. 100(2): p. 027801.
  27. ↑ T. Tokushima, Y. Harada, O. Takahashi, Y. Senba, H. Ohashi, L.G.M. Pettersson, A. Nilsson,S. Shin, "High resolution X-ray emission spectroscopy of liquid water: The observation of two structural motifs." Chemical Physics Letters, 2008. 460(4-6): p. 387-400.
  28. ↑ J. Forsberg, J. Grasjo, B. Brena, J. Nordgren, L.C. Duda,J.E. Rubensson, "Angular anisotropy of resonant inelastic soft x-ray scattering from liquid water.", Physical Review B, 2009. 79(13): p. 132203.
  29. ↑ Z. Yin, I. Rajkovic, K. Kubicek, W. Quevedo, A. Pietzsch, P. Wernet, A. Föhlisch and S. Techert, "Probing the Hofmeister effect with ultrafast core−hole spectroscopy." Journal of Physical Chemistry B, 2014. 118(31):p. 9398-9403
  30. ↑ Y. Horikawa, T. Tokushima, Y. Harada, O. Takahashi, A. Chainani, Y. Senba, H. Ohashi, A. Hiraya,S. Shin, "Identification of valence electronic states of aqueous acetic acid in acid–base equilibrium using site-selective X-ray emission spectroscopy.", Physical Chemistry Chemical Physics, 2009. 11(39): p. 8676-8679.
  31. ↑ J. Grasjo, E. Andersson, J. Forsberg, L. Duda, E. Henke, W. Pokapanich, O. Bjorneholm, J. Andersson, A. Pietzsch, F. Hennies,J.E. Rubensson, "Local Electronic Structure of Functional Groups in Glycine As Anion, Zwitterion, and Cation in Aqueous Solution.", Journal of Physical Chemistry B, 2009. 113(49): p. 16002-16006.
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