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Resonant inelastic X-ray scattering

Nature Reviews Methods Primers volume 4, Article number: 45 (2024) Cite this article

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Abstract

Resonant inelastic X-ray scattering (RIXS) is a powerful technique that combines spectroscopy and inelastic scattering to probe the electronic structure of materials. RIXS is based on the interaction of X-rays with matter in which the dependence on energy, momentum and polarization is introduced. The RIXS spectra can be approximated as a combination of X-ray absorption and X-ray emission. A 2D RIXS plane can be measured as a function of excitation and emission energies. Using RIXS, collective excitations — such as magnons, phonons, plasmons and orbitons — can be probed in quantum materials, for example, cuprates, nickelates and iridates, with complex low-energy physics and exotic phenomena in energy and momentum space. In addition, RIXS with hard X-rays enables detailed experiments under operando conditions. Spectral broadening owing to short core hole lifetime can be reduced to produce X-ray absorption spectra with high resolution. This Primer gives an overview of RIXS experimentation, data analysis and applications, finishing with a look to the future, where new experimental stations at X-ray free electron lasers promise to revolutionize the understanding of femtosecond processes and non-linear interactions of X-rays with matter.

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Fig. 1: Electronic structure of a transition metal oxide.
Fig. 2: Graphical overviews of the resonant inelastic X-ray scattering processes of a transition metal oxide.
Fig. 3: Excitations in a 2p3d resonant inelastic X-ray scattering process.
Fig. 4: Overview of resonant inelastic X-ray scattering experiments on systems with an open 2p, 3d, 4d, 5d and 4f shell.
Fig. 5: Overview of the 1s2p resonant inelastic X-ray scattering map.
Fig. 6: Momentum dependence in cuprates.
Fig. 7: Magnetism applications.

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References

  1. Kunnus, K. et al. Anti-Stokes resonant X-ray Raman scattering for atom specific and excited state selective dynamics. New J. Phys. 18, 103011 (2016).

    Article  ADS  Google Scholar 

  2. de Groot, F., Vankó, G. & Glatzel, P. The 1s X-ray absorption pre-edge structures in transition metal oxides. J. Phys. Condens. Matter 21, 104207 (2009).

    Article  ADS  Google Scholar 

  3. de Groot, F. M. F. X-ray absorption and dichroism of transition metals and their compounds. J. Electron. Spectros. Relat. Phenom. 67, 529 (1994).

    Article  ADS  Google Scholar 

  4. van den Brink, J. & van Veenendaal, M. Theory of indirect resonant inelastic X-ray scattering. J. Phys. Chem. Solids 66, 2145–2149 (2005).

    Article  ADS  Google Scholar 

  5. van den Brink, J. & van Veenendaal, M. Correlation functions measured by indirect resonant inelastic X-ray scattering. Europhys. Lett. 73, 121–127 (2006).

    Article  ADS  Google Scholar 

  6. Hunault, M. O. J. Y. et al. Direct observation of Cr3+ 3d states in ruby: toward experimental mechanistic evidence of metal chemistry. J. Phys. Chem. A 122, 4399–4413 (2018).

    Article  Google Scholar 

  7. Ghiringhelli, G. et al. SAXES, a high resolution spectrometer for resonant X-ray emission in the 400–1,600 eV energy range. Rev. Sci. Instrum. 77, 113108 (2006). Improvements in resonant inelastic X-ray scattering instruments.

    Article  ADS  Google Scholar 

  8. Brookes, N. B. et al. The beamline ID32 at the ESRF for soft X-ray high energy resolution resonant inelastic X-ray scattering and polarisation dependent X-ray absorption spectroscopy. Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrom. Detect. Assoc. Equip. 903, 175–192 (2018).

    Article  ADS  Google Scholar 

  9. Zhou, K. J. et al. 121: an advanced high-resolution resonant inelastic X-ray scattering beamline at diamond light source. J. Synchrotron Radiat. 29, 563–580 (2022).

    Article  Google Scholar 

  10. Dvorak, J., Jarrige, I., Bisogni, V., Coburn, S. & Leonhardt, W. Towards 10 meV resolution: the design of an ultrahigh resolution soft X-ray RIXS spectrometer. Rev. Sci. Instrum. 87, 115109 (2016).

    Article  ADS  Google Scholar 

  11. Singh, A. et al. Development of the soft X-ray AGM-AGS RIXS beamline at the Taiwan photon source. J. Synchrotron Radiat. 28, 977–986 (2021).

    Article  Google Scholar 

  12. Braicovich, L. et al. The simultaneous measurement of energy and linear polarization of the scattered radiation in resonant inelastic soft X-ray scattering. Rev. Sci. Instrum. 85, 115104 (2014).

    Article  ADS  Google Scholar 

  13. Sala, M. M. et al. A high-energy-resolution resonant inelastic X-ray scattering spectrometer at ID20 of the European Synchrotron Radiation Facility. J. Synchrotron Radiat. 25, 580–591 (2018).

    Article  Google Scholar 

  14. Kramers, H. A. & Heisenberg, W. On the dispersal of radiation by atoms. Z. Fur Phys. 31, 681–708 (1925).

    Article  ADS  Google Scholar 

  15. Kubo, R. Statistical-mechanical theory of irreversible processes. 1. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 12, 570–586 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  16. Kubo, R., Yokota, M. & Nakajima, S. Statistical-mechanical theory of irreversible processes. 2. Response to thermal disturbance. J. Phys. Soc. Jpn. 12, 1203–1211 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  17. de Groot, F. & Kotani, A. Core Level Spectroscopy of Solids. Core Level Spectroscopy of Solids (CRC Press, 2008).

  18. Winfried, S. Electron Dynamics by Inelastic X-Ray Scattering (Oxford Univ. Press, 2007).

  19. Schlappa, J. et al. Collective magnetic excitations in the spin ladder Sr14Cu24O41 measured using high-resolution resonant inelastic X-ray scattering. Phys. Rev. Lett. 103, 047401 (2009).

    Article  ADS  Google Scholar 

  20. Braicovich, L. et al. Dispersion of magnetic excitations in the cuprate La2CuO4 and CaCuO2 compounds measured using resonant X-ray scattering. Phys. Rev. Lett. 102, 167401 (2009).

    Article  ADS  Google Scholar 

  21. Le Tacon, M. et al. Intense paramagnon excitations in a large family of high-temperature superconductors. Nat. Phys. 7, 725–730 (2011).

    Article  Google Scholar 

  22. Kim, J. et al. Magnetic excitation spectra of Sr2IrO4 probed by resonant inelastic X-ray scattering: establishing links to cuprate superconductors. Phys. Rev. Lett. 108, 177003 (2012). Hard X-ray resonant inelastic X-ray scattering experiment on iridates.

    Article  ADS  Google Scholar 

  23. Zhou, K.-J. et al. Persistent high-energy spin excitations in iron-pnictide superconductors. Nat. Commun. 4, 1470 (2013).

    Article  ADS  Google Scholar 

  24. Haverkort, M. W. Theory of resonant inelastic X-ray scattering by collective magnetic excitations. Phys. Rev. Lett. 105, 167404 (2010).

    Article  ADS  Google Scholar 

  25. Glawion, S. et al. Two-spinon and orbital excitations of the spin-Peierls system. Phys. Rev. Lett. 107, 107402 (2011).

    Article  ADS  Google Scholar 

  26. Schlappa, J. et al. Spin-orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3. Nature 485, 82–85 (2012). Low-energy excitations in cuprates (spinons and orbitons).

    Article  ADS  Google Scholar 

  27. Benckiser, E. et al. Orbital superexchange and crystal field simultaneously at play in YVO3: resonant inelastic X-ray scattering at the V L edge and the O K edge. Phys. Rev. B 88, 205115 (2013).

    Article  ADS  Google Scholar 

  28. Nomura, T. et al. Resonant inelastic X-ray scattering study of entangled spin-orbital excitations in superconducting PrFeAsO0.7. Phys. Rev. B 94, 035134 (2016).

    Article  ADS  Google Scholar 

  29. Wang, R. P. et al. Excitonic dispersion of the intermediate spin state in LaCoO3 revealed by resonant inelastic X-ray scattering. Phys. Rev. B 98, 1–6 (2018).

    Google Scholar 

  30. Moser, S. et al. Electron–phonon coupling in the bulk of anatase TiO2 measured by resonant inelastic X-ray spectroscopy. Phys. Rev. Lett. 115, 096404 (2015).

    Article  ADS  Google Scholar 

  31. Ament, L. J. P., van Veenendaal, M. & van den Brink, J. Determining the electron–phonon coupling strength from resonant inelastic X-ray scattering at transition metal L-edges. epl 95, 27008 (2011).

    Article  ADS  Google Scholar 

  32. Bieniasz, K., Johnston, S. & Berciu, M. Theory of dispersive optical phonons in resonant inelastic X-ray scattering experiments. Phys. Rev. B 105, L180302 (2022).

    Article  ADS  Google Scholar 

  33. Ueda, H. et al. Chiral phonons in quartz probed by X-rays. Nature 618, 946 (2023).

    Article  ADS  Google Scholar 

  34. Chaix, L. et al. Dispersive charge density wave excitations in Bi2Sr2CaCu2O8+δ. Nat. Phys. 13, 952 (2017).

    Article  Google Scholar 

  35. da Silva Neto, E. H. et al. Coupling between dynamic magnetic and charge-order correlations in the cuprate superconductor Nd2−xCexCuO4. Phys. Rev. B 98, 161114(R) (2018).

    Article  ADS  Google Scholar 

  36. Boschini, F. et al. Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane. Nat. Commun. 12, 597 (2021).

    Article  ADS  Google Scholar 

  37. Tam, C. C. et al. Charge density waves and Fermi surface reconstruction in the clean overdoped cuprate superconductor Tl2Ba2CuO6+δ. Nat. Commun. 13, 570 (2022).

    Article  ADS  Google Scholar 

  38. Miao, H. et al. Charge density waves in cuprate superconductors beyond the critical doping. npj Quantum Mater. 6, 31 (2021).

    Article  ADS  Google Scholar 

  39. Porter, Z. et al. Spin–orbit excitons and electronic configuration of the 5d4 insulator Sr3Ir2O7F2. Phys. Rev. B 106, 115140 (2022).

    Article  ADS  Google Scholar 

  40. Das, L. et al. Spin–orbital excitations in Ca2RuO4 revealed by resonant inelastic X-ray scattering. Phys. Rev. X 8, 011048 (2018).

    Google Scholar 

  41. Hill, J. P. et al. Observation of a 500 meV collective mode in La2−xSrxCuO4 and Nd2CuO4 using resonant inelastic X-ray scattering. Phys. Rev. Lett. 100, 097001 (2008).

    Article  ADS  Google Scholar 

  42. Nag, A. et al. Many-body physics of single and double spin-flip excitations in NiO. Phys. Rev. Lett. 124, 067202 (2020).

    Article  ADS  Google Scholar 

  43. Li, J. et al. Single- and multimagnon dynamics in antiferromagnetic α-Fe2O3 thin films. Phys. Rev. X 13, 011012 (2023).

    Google Scholar 

  44. Elnaggar, H. et al. Magnetic excitations beyond the single- and double-magnons. Nat. Commun. 14, 2749 (2023).

    Article  ADS  Google Scholar 

  45. Betto, D. et al. Multiple-magnon excitations shape the spin spectrum of cuprate parent compounds. Phys. Rev. B 103, 011012 (2021).

    Article  Google Scholar 

  46. Savchenko, V. et al. Vibrational resonant inelastic X-ray scattering in liquid acetic acid: a ruler for molecular chain lengths. Sci. Rep. 11, 4098 (2021).

    Article  ADS  Google Scholar 

  47. Pietzsch, A. et al. Cuts through the manifold of molecular H2O potential energy surfaces in liquid water at ambient conditions. Proc. Natl Acad. Sci. USA 119, e2118101119 (2022).

    Article  Google Scholar 

  48. Gel’mukhanov, F. & Agren, H. Resonant X-ray Raman scattering. Phys. Rep. Rev. Sect. Phys. Lett. 312, 87–330 (1999).

    Google Scholar 

  49. Butorin, S. M. et al. Resonant X-ray fluorescence spectroscopy of correlated systems: a probe of charge-transfer excitations. Phys. Rev. Lett. 77, 574–577 (1996).

    Article  ADS  Google Scholar 

  50. Luo, J., Trammell, G. T. & Hannon, J. P. Scattering operator for elastic and inelastic resonant X-ray-scattering. Phys. Rev. Lett. 71, 287–290 (1993).

    Article  ADS  Google Scholar 

  51. Ament, L. J. P., Ghiringhelli, G., Moretti Sala, M., Braicovich, L. & van den Brink, J. 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).

    Article  ADS  Google Scholar 

  52. Haverkort, M. W., Hollmann, N., Krug, I. P. & Tanaka, A. Symmetry analysis of magneto-optical effects: the case of X-ray diffraction and X-ray absorption at the transition metal L2,3 edge. Phys. Rev. B Condens. Matter Mater. Phys. 82, 094403 (2010).

    Article  ADS  Google Scholar 

  53. Lu, Y. & Haverkort, M. W. Nonperturbative series expansion of Green’s functions: the anatomy of resonant inelastic X-ray scattering in the doped Hubbard model. Phys. Rev. Lett. 119, 256401 (2017).

    Article  ADS  Google Scholar 

  54. Kang, M. et al. Resolving the nature of electronic excitations in resonant inelastic X-ray scattering. Phys. Rev. B 99, 045105 (2019).

    Article  ADS  Google Scholar 

  55. Jia, C., Wohlfeld, K., Wang, Y., Moritz, B. & Devereaux, T. P. Using RIXS to uncover elementary charge and spin excitations. Phys. Rev. X 6, 021020 (2016).

    Google Scholar 

  56. Jiménez-Mier, J. et al. Dynamical behavior of X-ray absorption and scattering at the L edge of titanium compounds: experiment and theory. Phys. Rev. B 59, 2649–2658 (1999).

    Article  ADS  Google Scholar 

  57. de Groot, F., Sawatzky, G. & Kuiper, P. Local spin-flip spectral distribution obtained by resonant X-ray Raman scattering. Phys. Rev. B Condens. Matter Mater. Phys. 57, 14584–14587 (1998). Prediction of magnetic excitations.

    Article  ADS  Google Scholar 

  58. Lee, S., Zhai, H. & Chan, G. K.-L. An ab initio correction vector restricted active space approach to the L-edge XAS and 2p3d RIXS spectra of transition metal complexes. J. Chem. Theory Comput. 19, 7753–7763 (2023).

    Article  Google Scholar 

  59. Werner, P., Johnston, S. & Eckstein, M. Nonequilibrium-DMFT based RIXS investigation of the two-orbital Hubbard model. epl 133, 57005 (2021).

    Article  ADS  Google Scholar 

  60. Hariki, A., Winder, M., Uozumi, T. & Kunes, J. LDA plus DMFT approach to resonant inelastic X-ray scattering in correlated materials. Phys. Rev. B 101, 115130 (2020).

    Article  ADS  Google Scholar 

  61. Haverkort, M. W. Quanty for core level spectroscopy — excitons, resonances and band excitations in time and frequency domain. J. Phys. Conf. Ser. 712, 12001 (2016).

    Article  Google Scholar 

  62. Wang, S.-X. & Zhu, L.-F. Non-resonant inelastic X-ray scattering spectroscopy: a momentum probe to detect the electronic structures of atoms and molecules. Matter Radiat. Extrem. 5, 054201 (2020).

    Article  Google Scholar 

  63. Schülke, W. Electronic excitations investigated by inelastic X-ray scattering spectroscopy. J. Phys. Condens. Matter 13, 7557–7591 (2001).

    Article  ADS  Google Scholar 

  64. Krisch, M. & Sette, F. Inelastic X-ray scattering from phonons. in Light Scattering in Solids IX: Novel Materials and Techniques Vol. 108 (eds Cardona, M. & Merlin, R.) 317–369 (Springer, 2007).

  65. Nelayah, J. et al. Mapping surface plasmons on a single metallic nanoparticle. Nat. Phys. 3, 348–353 (2007).

    Article  Google Scholar 

  66. Pintschovius, L. Electron–phonon coupling effects explored by inelastic neutron scattering. Phys. Status Sol. B Basic Solid State Phys. 242, 30–50 (2005).

    Article  ADS  Google Scholar 

  67. Rossatmignod, J. et al. Investigation of the spin dynamics in YBa2Cu3O6+x by inelastic neutron-scattering. Phys. B 169, 58–65 (1991).

    Article  ADS  Google Scholar 

  68. Damascelli, A. Probing the electronic structure of complex systems by ARPES. Phys. Scr. T109, 61–74 (2004).

    Article  ADS  Google Scholar 

  69. Cuk, T. et al. A review of electron–phonon coupling seen in the high-Tc superconductors by angle-resolved photoemission studies (ARPES). Phys. Status Sol. B Basic Solid State Phys. 242, 11–29 (2005).

    Article  ADS  Google Scholar 

  70. Abanov, A. & Chubukov, A. V. A relation between the resonance neutron peak and ARPES data in cuprates. Phys. Rev. Lett. 83, 1652–1655 (1999).

    Article  ADS  Google Scholar 

  71. Kotani, A. Resonant inelastic X-ray scattering in d and f electron systems. Eur. Phys. J. B 47, 3–27 (2005).

    Article  ADS  Google Scholar 

  72. Hepting, M., Dean, M. P. M. & Lee, W. S. Soft X-ray spectroscopy of low-valence nickelates. Front. Phys. 9, 808683 (2021).

    Article  Google Scholar 

  73. Cao, Y. et al. Ultrafast dynamics of spin and orbital correlations in quantum materials: an energy- and momentum-resolved perspective. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 377, 20170480 (2019).

    Article  ADS  Google Scholar 

  74. Baker, M. L. et al. K- and L-edge X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) determination of differential orbital covalency (DOC) of transition metal sites. Coord. Chem. Rev. 345, 182–208 (2017).

    Article  Google Scholar 

  75. Monney, C., Patthey, L., Razzoli, E. & Schmitt, T. Static and time-resolved resonant inelastic X-ray scattering: recent results and future prospects. X-Ray Spectrom. 52, 216–225 (2023).

    Article  ADS  Google Scholar 

  76. Ament, L. J. P., van Veenendaal, M., Devereaux Thomas, P., Hill, J. P. & van den Brink, J. Resonant inelastic X-ray scattering studies of elementary excitations. Rev. Mod. Phys. 83, 705 (2011).

    Article  ADS  Google Scholar 

  77. Glatzel, P. & Bergmann, U. High resolution 1s core hole X-ray spectroscopy in 3d transition metal complexes — electronic and structural information. Coord. Chem. Rev. 249, 65–95 (2005).

    Article  Google Scholar 

  78. Glatzel, P., de Groot, F. M. F. & Bergmann, U. Hard X-ray photon-in photon-out spectroscopy. Synchrotron Radiat. News 22, 12–16 (2009).

    Article  ADS  Google Scholar 

  79. De Groot, F. High-resolution X-ray emission and X-ray absorption spectroscopy. Chem. Rev. 101, 1779–1808 (2001).

    Article  Google Scholar 

  80. Gel’mukhanov, F. Theory of resonant inelastic X-ray scattering (RIXS) spectra. J. Electron. Spectros. Relat. Phenom. 156, XXI (2007).

    Google Scholar 

  81. Gel’mukhanov, F., Odelius, M., Polyutov, S. P., Foehlisch, A. & Kimberg, V. Dynamics of resonant X-ray and Auger scattering. Rev. Mod. Phys. 93, 035001 (2021).

    Article  ADS  Google Scholar 

  82. Kotani, A. & Shin, S. Resonant inelastic X-ray scattering spectra for electrons in solids. Rev. Mod. Phys. 73, 203–246 (2001).

    Article  ADS  Google Scholar 

  83. Huotari, S. et al. Improving the performance of high-resolution X-ray spectrometers with position-sensitive pixel detectors. J. Synchrotron Radiat. 12, 467–472 (2005).

    Article  Google Scholar 

  84. Gretarsson, H. et al. IRIXS: a resonant inelastic X-ray scattering instrument dedicated to X-rays in the intermediate energy range. J. Synchrotron Radiat. 27, 538–544 (2020).

    Article  Google Scholar 

  85. Bertinshaw, J. et al. IRIXS spectrograph: an ultra high-resolution spectrometer for tender RIXS. J. Synchrotron Radiat. 28, 1184–1192 (2021).

    Article  Google Scholar 

  86. Kuiper, P. et al. Resonant X-ray Raman spectra of Cu dd excitations in Sr(2)CuO(2)Cl(2). Phys. Rev. Lett. 80, 5204–5207 (1998).

    Article  ADS  Google Scholar 

  87. Chuang, Y. D. et al. High-resolution soft X-ray emission spectrograph at advanced light source. J. Phys. Chem. Solids 66, 2173–2178 (2005).

    Article  ADS  Google Scholar 

  88. Wray, L. A., Yang, W. L., Eisaki, H., Hussain, Z. & Chuang, Y. D. Multiplet resonance lifetimes in resonant inelastic X-ray scattering involving shallow core levels. Phys. Rev. B 86, 195130 (2012).

    Article  ADS  Google Scholar 

  89. Chiuzbaian, S. G. et al. Localized electronic excitations in NiO studied with resonant inelastic X-ray scattering at the Ni M threshold: evidence of spin flip. Phys. Rev. Lett. 95, 197402 (2005).

    Article  ADS  Google Scholar 

  90. Bauer, K. et al. The meV XUV-RIXS facility at UE112-PGM1 of BESSY II. J. Synchrotron Radiat. 29, 908–915 (2022).

    Article  Google Scholar 

  91. Ellis, D. S. et al. Electronic structure of doped lanthanum cuprates studied with resonant inelastic X-ray scattering. Phys. Rev. B 83, 075120 (2011).

    Article  ADS  Google Scholar 

  92. Kim, Y.-J. et al. Observations on the resonant inelastic X-ray scattering cross section in copper oxide compounds. Phys. Rev. B 76, 155116 (2007).

    Article  ADS  Google Scholar 

  93. Chabot-Couture, G. et al. Polarization dependence and symmetry analysis in indirect K-edge RIXS. Phys. Rev. B 82, 035113 (2010).

    Article  ADS  Google Scholar 

  94. Kotani, A., Kvashnina, K. O., Butorin, S. M. & Glatzel, P. Spectator and participator processes in the resonant photon-in and photon-out spectra at the Ce L-3 edge of CeO2. Eur. Phys. J. B 85, 257 (2012).

    Article  ADS  Google Scholar 

  95. Kas, J. J., Rehr, J. J., Soininen, J. A. & Glatzel, P. Real-space Green’s function approach to resonant inelastic X-ray scattering. Phys. Rev. B 83, 235114 (2011).

    Article  ADS  Google Scholar 

  96. Bagger, A. et al. 1s2p resonant inelastic X-ray scattering combined dipole and quadrupole analysis method. J. Synchrotron Radiat. 24, 296–301 (2017).

    Article  Google Scholar 

  97. Caliebe, W., Kao, C., Hastings, J., Taguchi, M. & Kotani, A. Resonant inelastic X-ray scattering. Phys. Rev. B 58, 13452–13458 (1998).

    Article  ADS  Google Scholar 

  98. Kurian, R., van Schooneveld, M. M., Zoltán, N., Vankó, G. & de Groot, F. M. F. Temperature-dependent 1s2p resonant inelastic X-ray scattering of CoO. J. Phys. Chem. C 117, 2976–2981 (2013).

    Article  Google Scholar 

  99. Rubensson, J., Eisebitt, S., Nicodemus, M., Boske, T. & Eberhardt, W. Exchange-split Ca 3s-13d states in CaF2 observed in threshold excited core-to-core fluorescence. Phys. Rev. B 49, 1507–1510 (1994).

    Article  ADS  Google Scholar 

  100. Rubensson, J. E., Eisebitt, S., Nicodemus, M., Boske, T. & Eberhardt, W. Electron correlation in CaF2 studied in threshold-excited soft-X-ray fluorescence. Phys. Rev. B 50, 9035–9045 (1994).

    Article  ADS  Google Scholar 

  101. de Groot, F. 3s2p inelastic X-ray scattering. Phys. Rev. B Condens. Matter Mater. Phys. 53, 7099 (1996).

    Article  ADS  Google Scholar 

  102. Kurian, R. et al. Intrinsic deviations in fluorescence yield detected X-ray absorption spectroscopy: the case of the transition metal L2,3 edges. J. Phys. Condens. Matter 24, 452201 (2012).

    Article  Google Scholar 

  103. Hamalainen, K., Siddons, D. P., Hastings, J. B. & Berman, L. E. Elimination of the inner-shell lifetime broadening in X-ray-absorption spectroscopy. Phys. Rev. Lett. 67, 2850–2853 (1991). Removal of lifetime broadening in resonant inelastic X-ray scattering.

    Article  ADS  Google Scholar 

  104. Carra, P., Fabrizio, M. & Thole, B. T. High resolution X-ray resonant Raman scattering. Phys. Rev. Lett. 74, 3700–3703 (1995).

    Article  ADS  Google Scholar 

  105. Glatzel, P. et al. Reflections on hard X-ray photon-in/photon-out spectroscopy for electronic structure studies. J. Electron. Spectros. Relat. Phenom. 188, 17–25 (2013).

    Article  ADS  Google Scholar 

  106. Kvashnina, K. O. & Butorin, S. M. High-energy resolution X-ray spectroscopy at actinide M4,5 and ligand K edges: what we know, what we want to know, and what we can know. Chem. Commun. 58, 327–342 (2022).

    Article  Google Scholar 

  107. Kvashnina, K. O. et al. Chemical state of complex uranium oxides. Phys. Rev. Lett. 111, 253002 (2013). Resonant inelastic X-ray scattering application to actinides.

    Article  ADS  Google Scholar 

  108. Blachucki, W. et al. High energy resolution off-resonant spectroscopy for X-ray absorption spectra free of self-absorption effects. Phys. Rev. Lett. 112, 173003 (2014).

    Article  ADS  Google Scholar 

  109. Glatzel, P., Jacquamet, L., Bergmann, U., De Groot, F. M. F. & Cramer, S. P. Site-selective EXAFS in mixed-valence compounds using high-resolution fluorescence detection: a study of iron in Prussian blue. Inorg. Chem. 41, 3121–3127 (2002).

    Article  Google Scholar 

  110. De Groot, F. M. F. et al. Local-spin-selective X-ray absorption and X-ray magnetic circular dichroism of MnP. Phys. Rev. B 51, 1045 (1995).

    Article  ADS  Google Scholar 

  111. Hämäläinen, K. et al. Spin-dependent X-ray absorption of MnO and MnF2. Phys. Rev. B 46, 14274–14277 (1992).

    Article  ADS  Google Scholar 

  112. Pirngruber, G. D. et al. On the presence of Fe(IV) in Fe-ZSM-5 and FeSrO3−x — unequivocal detection of the 3d(4) spin system by resonant inelastic X-ray scattering. J. Phys. Chem. B 110, 18104–18107 (2006).

    Article  Google Scholar 

  113. Braicovich, L. et al. Magnetic circular dichroism in resonant Raman scattering in the perpendicular geometry at the L edge of 3d transition metal systems. Phys. Rev. Lett. 82, 1566–1569 (1999).

    Article  ADS  Google Scholar 

  114. Sikora, M. et al. Strong K-edge magnetic circular dichroism observed in photon-in–photon-out spectroscopy. Phys. Rev. Lett. 105, 037202 (2010).

    Article  ADS  Google Scholar 

  115. Miyawaki, J. et al. Dzyaloshinskii–Moriya interaction in alpha-Fe2O3 measured by magnetic circular dichroism in resonant inelastic soft X-ray scattering. Phys. Rev. B 96, 214420 (2017).

    Article  ADS  Google Scholar 

  116. Zhang, W. et al. Unraveling the nature of spin excitations disentangled from charge contributions in a doped cuprate superconductor. npj Quantum Mater. 7, 123 (2022).

    Article  ADS  Google Scholar 

  117. Sikora, M. et al. 1s2p resonant inelastic X-ray scattering-magnetic circular dichroism: a sensitive probe of 3d magnetic moments using hard X-ray photons. J. Appl. Phys. 111, 123 (2012).

    Article  Google Scholar 

  118. Lafuerza, S. et al. New reflections on hard X-ray photon-in/photon-out spectroscopy. Nanoscale 12, 16270–16284 (2020).

    Article  Google Scholar 

  119. Daffe, N. et al. Bad neighbour, good neighbour: how magnetic dipole interactions between soft and hard ferrimagnetic nanoparticles affect macroscopic magnetic properties in ferrofluids. Nanoscale 12, 11222–11231 (2020).

    Article  Google Scholar 

  120. Elnaggar, H. et al. Possible absence of trimeron correlations above the Verwey temperature in Fe3O4. Phys. Rev. B 101, 085107 (2020).

    Article  ADS  Google Scholar 

  121. Elnaggar, H. et al. Magnetic contrast at spin-flip excitations: an advanced X-ray spectroscopy tool to study magnetic-ordering. ACS Appl. Mater. Interfaces 11, 36213–36220 (2019).

    Article  Google Scholar 

  122. Minola, M. et al. Collective nature of spin excitations in superconducting cuprates probed by resonant inelastic X-ray scattering. Phys. Rev. Lett. 114, 217003 (2015).

    Article  ADS  Google Scholar 

  123. Fumagalli, R. et al. Polarization-resolved Cu L3-edge resonant inelastic X-ray scattering of orbital and spin excitations in NdBa2Cu3O7−δ. Phys. Rev. B 99, 134517 (2019).

    Article  ADS  Google Scholar 

  124. Inami, T. Magnetic circular dichroism in X-ray emission from ferromagnets. Phys. Rev. Lett. 119, 137203 (2017).

    Article  ADS  Google Scholar 

  125. Ghiringhelli, G. & Braicovich, L. Magnetic excitations of layered cuprates studied by RIXS at Cu L3 edge. J. Electron. Spectros. Relat. Phenom. 188, 26–31 (2013).

    Article  ADS  Google Scholar 

  126. Ghiringhelli, G. et al. Low energy electronic excitations in the layered cuprates studied by copper L3 resonant inelastic X-ray scattering. Phys. Rev. Lett. 92, 117406 (2004).

    Article  ADS  Google Scholar 

  127. Moretti Sala, M. et al. Energy and symmetry of dd excitations in undoped layered cuprates measured by Cu L3 resonant inelastic X-ray scattering. New J. Phys. 13, 043026 (2011).

    Article  ADS  Google Scholar 

  128. Braicovich, L. et al. Magnetic excitations and phase separation in the underdoped La2−xSrxCuO4 superconductor measured by resonant inelastic X-ray scattering. Phys. Rev. Lett. 104, 077002 (2010). Resonant inelastic X-ray scattering experiment showing magnetic excitations.

    Article  ADS  Google Scholar 

  129. Dean, M. P. M. et al. Persistence of magnetic excitations in La2−xSrxCuO4 from the undoped insulator to the heavily overdoped non-superconducting metal. Nat. Mater. 12, 1019–1023 (2013).

    Article  ADS  Google Scholar 

  130. Braicovich, L. et al. Momentum and polarization dependence of single-magnon spectral weight for Cu L3-edge resonant inelastic X-ray scattering from layered cuprates. Phys. Rev. B Condens. Matter Mater. Phys. 81, 174533 (2010).

    Article  ADS  Google Scholar 

  131. Dean, M. P. M. Insights into the high temperature superconducting cuprates from resonant inelastic X-ray scattering. J. Magn. Magn. Mater. 376, 3–13 (2015).

    Article  ADS  Google Scholar 

  132. Peng, Y. Y. et al. Influence of apical oxygen on the extent of in-plane exchange interaction in cuprate superconductors. Nat. Phys. 13, 1201 (2017).

    Article  Google Scholar 

  133. Wang, L. et al. Paramagnons and high-temperature superconductivity in a model family of cuprates. Nat. Commun. 13, 3163 (2022).

    Article  ADS  Google Scholar 

  134. Schlappa, J. et al. Probing multi-spinon excitations outside of the two-spinon continuum in the antiferromagnetic spin chain cuprate Sr2CuO3. Nat. Commun. 9, 5394 (2018).

    Article  ADS  Google Scholar 

  135. Bisogni, V. et al. Bimagnon studies in cuprates with resonant inelastic X-ray scattering at the O K edge. I. Assessment on La2CuO4 and comparison with the excitation at Cu L3 and Cu K edges. Phys. Rev. B 85, 214527 (2012).

    Article  ADS  Google Scholar 

  136. Kumar, U. et al. Unraveling higher-order contributions to spin excitations probed using resonant inelastic X-ray scattering. Phys. Rev. B 106, L060406 (2022).

    Article  ADS  Google Scholar 

  137. Martinelli, L. et al. Fractional spin excitations in the infinite-layer cuprate CaCuO2. Phys. Rev. X 12, 021041 (2022).

    Google Scholar 

  138. Comin, R. & Damascelli, A. Resonant X-ray scattering studies of charge order in cuprates. Annu. Rev. Condens. Matter Phys. 7, 369–405 (2016).

    Article  ADS  Google Scholar 

  139. Arpaia, R. et al. Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high-Tc superconductor. Science 365, 906 (2019).

    Article  ADS  Google Scholar 

  140. Ghiringhelli, G. et al. Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O6+x. Science 337, 821–825 (2012). Low-energy excitations in cuprates (charge fluctuations).

    Article  ADS  Google Scholar 

  141. Arpaia, R. et al. Signature of quantum criticality in cuprates by charge density fluctuations. Nat. Commun. 14, 7198 (2023).

    Article  ADS  Google Scholar 

  142. Lee, W. S. et al. Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate. Nat. Phys. 17, 53 (2021).

    Article  Google Scholar 

  143. Li, J. M. et al. Multiorbital charge-density wave excitations and concomitant phonon anomalies in Bi2Sr2LaCuO6+δ. Proc. Natl Acad. Sci. USA 117, 16219–16225 (2020).

    Article  ADS  Google Scholar 

  144. Singh, A. et al. Unconventional exciton evolution from the pseudogap to superconducting phases in cuprates. Nat. Commun. 13, 7906 (2022).

    Article  ADS  Google Scholar 

  145. Hepting, M. et al. Three-dimensional collective charge excitations in electron-doped copper oxide superconductors. Nature 563, 374 (2018).

    Article  ADS  Google Scholar 

  146. Nag, A. et al. Detection of acoustic plasmons in hole-doped lanthanum and bismuth cuprate superconductors using resonant inelastic X-ray scattering. Phys. Rev. Lett. 125, 257002 (2020).

    Article  ADS  Google Scholar 

  147. Lin, J. et al. Doping evolution of the charge excitations and electron correlations in electron-doped superconducting La2−xCexCuO4. npj Quantum Mater. 5, 4 (2020).

    Article  ADS  Google Scholar 

  148. Singh, A. et al. Acoustic plasmons and conducting carriers in hole-doped cuprate superconductors. Phys. Rev. B 105, 235105 (2022).

    Article  ADS  MathSciNet  Google Scholar 

  149. Hepting, M. et al. Evolution of plasmon excitations across the phase diagram of the cuprate superconductor La2−xSrxCuO4. Phys. Rev. B 107, 214516 (2023).

    Article  ADS  Google Scholar 

  150. Hepting, M. et al. Gapped collective charge excitations and interlayer hopping in cuprate superconductors. Phys. Rev. Lett. 129, 047001 (2022).

    Article  ADS  Google Scholar 

  151. Saitoh, E. et al. Observation of orbital waves as elementary excitations in a solid. Nature 410, 180–183 (2001).

    Article  ADS  Google Scholar 

  152. Kim, C. et al. Observation of spin-charge separation in one-dimensional SrCuO2. Phys. Rev. Lett. 77, 4054–4057 (1996).

    Article  ADS  Google Scholar 

  153. Martinelli, L. et al. Collective nature of orbital excitations in layered cuprates in the absence of apical oxygens. Phys. Rev. Lett. 132, 066004 (2024).

    Article  ADS  Google Scholar 

  154. Ge, J.-F. et al. Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3. Nat. Mater. 14, 285–289 (2015).

    Article  ADS  Google Scholar 

  155. Yang, W. L. et al. Evidence for weak electronic correlations in iron pnictides. Phys. Rev. B 80, 014508 (2009).

    Article  ADS  Google Scholar 

  156. Pelliciari, J. et al. Intralayer doping effects on the high-energy magnetic correlations in NaFeAs. Phys. Rev. B 93, 134515 (2016).

    Article  ADS  Google Scholar 

  157. Pelliciari, J. et al. Magnetic moment evolution and spin freezing in doped BaFe2As2. Sci. Rep. 7, 8003 (2017).

    Article  ADS  Google Scholar 

  158. Lu, X. et al. Spin-excitation anisotropy in the nematic state of detwinned FeSe. Nat. Phys. 18, 806 (2022).

    Article  ADS  Google Scholar 

  159. Pelliciari, J. et al. Evolution of spin excitations from bulk to monolayer FeSe. Nat. Commun. 12, 3122 (2021).

    Article  ADS  Google Scholar 

  160. Alonso, J. A., Martínez-Lope, M. J., Casais, M. T., Aranda, M. A. G. & Fernández-Díaz, M. T. Metal–insulator transitions, structural and microstructural evolution of RNiO3 (R = Sm, Eu, Gd, Dy, Ho, Y) perovskites: evidence for room-temperature charge disproportionation in monoclinic HoNiO3 and YNiO3. J. Am. Chem. Soc. 121, 4754–4762 (1999).

    Article  Google Scholar 

  161. Cheong, S. W. et al. Charge-ordered states in (La,Sr)2NiO4 for hole concentrations n(h) = 1/3 and n(h) = 1/2. Phys. Rev. B 49, 7088–7091 (1994).

    Article  ADS  Google Scholar 

  162. Freeman, P. G. et al. Spin dynamics of half-doped La3/2Sr1/2NiO4. Phys. Rev. B 71, 174412 (2005).

    Article  ADS  Google Scholar 

  163. Li, D. et al. Superconducting dome in Nd1-xSrxNiO2 infinite layer films. Phys. Rev. Lett. 125, 027001 (2020).

    Article  ADS  Google Scholar 

  164. Li, D. et al. Superconductivity in an infinite-layer nickelate. Nature 572, 624 (2019).

    Article  ADS  Google Scholar 

  165. Sun, H. et al. Signatures of superconductivity near 80 K in a nickelate under high pressure. Nature 621, 493 (2023).

    Article  ADS  Google Scholar 

  166. Fabbris, G. et al. Doping dependence of collective spin and orbital excitations in the spin-1 quantum antiferromagnet La2−xSrxNiO4 observed by X rays. Phys. Rev. Lett. 118, 156402 (2017).

    Article  ADS  Google Scholar 

  167. Bisogni, V. et al. Ground-state oxygen holes and the metal–insulator transition in the negative charge-transfer rare-earth nickelates. Nat. Commun. 7, 13017 (2016).

    Article  ADS  Google Scholar 

  168. Lu, Y. et al. Site-selective probe of magnetic excitations in rare-earth nickelates using resonant inelastic X-ray scattering. Phys. Rev. X 8, 031014 (2018).

    Google Scholar 

  169. Hepting, M. et al. Electronic structure of the parent compound of superconducting infinite-layer nickelates. Nat. Mater. 19, 381 (2020).

    Article  ADS  Google Scholar 

  170. Lu, H. et al. Magnetic excitations in infinite-layer nickelates. Science 373, 213–216 (2021).

    Article  ADS  Google Scholar 

  171. Rossi, M. et al. Universal orbital and magnetic structures in infinite-layer nickelates. Phys. Rev. B 109, 024512 (2024).

    Article  ADS  Google Scholar 

  172. Lin, J. Q. et al. Strong superexchange in a d9−δ nickelate revealed by resonant inelastic X-ray scattering. Phys. Rev. Lett. 126, 087001 (2021).

    Article  ADS  Google Scholar 

  173. Shen, Y. et al. Role of oxygen states in the low valence nickelate La4Ni3O8. Phys. Rev. X 12, 011055 (2022).

    Google Scholar 

  174. Shen, Y. et al. Electronic character of charge order in square-planar low-valence nickelates. Phys. Rev. X 13, 011021 (2023).

    Google Scholar 

  175. Tam, C. C. et al. Charge density waves in infinite-layer NdNiO2 nickelates. Nat. Mater. 21, 1116 (2022).

    Article  ADS  Google Scholar 

  176. Krieger, G. et al. Charge and spin order dichotomy in NdNiO2 driven by the capping layer. Phys. Rev. Lett. 129, 027002 (2022).

    Article  ADS  Google Scholar 

  177. Rossi, M. et al. A broken translational symmetry state in an infinite-layer nickelate. Nat. Phys. 18, 869 (2022).

    Article  Google Scholar 

  178. Parzyck, C. T. et al. Absence of 3a0 charge density wave order in the infinite-layer nickelate NdNiO2. Nat. Mater. 23, 440 (2024).

    Article  ADS  Google Scholar 

  179. Chen, X. et al. Electronic and magnetic excitations in La3Ni2O7. Preprint at https://arxiv.org/abs/2401.12657 (2024).

  180. Nag, A. et al. Quadrupolar magnetic excitations in an isotropic spin-1 antiferromagnet. Nat. Commun. 13, 2327 (2022).

    Article  ADS  Google Scholar 

  181. Bernevig, B. A., Felser, C. & Beidenkopf, H. Progress and prospects in magnetic topological materials. Nature 603, 41–51 (2022).

    Article  ADS  Google Scholar 

  182. Yin, J.-X., Lian, B. & Hasan, M. Z. Topological kagome magnets and superconductors. Nature 612, 647–657 (2022).

    Article  ADS  Google Scholar 

  183. Nag, A. et al. Correlation driven near-flat band Stoner excitations in a Kagome magnet. Nat. Commun. 13, 7317 (2022).

    Article  ADS  Google Scholar 

  184. Brookes, N. B. et al. Spin waves in metallic iron and nickel measured by soft X-ray resonant inelastic scattering. Phys. Rev. B 102, 064412 (2020).

    Article  ADS  Google Scholar 

  185. Poelchen, G. et al. Long-lived spin waves in a metallic antiferromagnet. Nat. Commun. 14, 5422 (2023).

    Article  ADS  Google Scholar 

  186. Pelliciari, J. et al. Tuning spin excitations in magnetic films by confinement. Nat. Mater. 20, 188 (2021).

    Article  ADS  Google Scholar 

  187. von Arx, K. et al. Resonant inelastic X-ray scattering study of Ca3Ru2O7. Phys. Rev. B 102, 235104 (2020).

    Article  ADS  Google Scholar 

  188. Lebert, B. W. et al. Resonant inelastic X-ray scattering study of α-RuCl3: a progress report. J. Phys. Condens. Matter 32, 144001 (2020).

    Article  ADS  Google Scholar 

  189. Occhialini, C. A. et al. Local electronic structure of rutile RuO2. Phys. Rev. Res. 3, 033214 (2021).

    Article  Google Scholar 

  190. Yang, Z. et al. Resonant inelastic X-ray scattering from electronic excitations in α-RuCl3 nanolayers. Phys. Rev. B 108, L041406 (2023).

    Article  ADS  Google Scholar 

  191. Suzuki, H. et al. Spin waves and spin-state transitions in a ruthenate high-temperature antiferromagnet. Nat. Mater. 18, 563–567 (2019). Tender X-ray resonant inelastic X-ray scattering experiment on spin transitions.

    Article  ADS  Google Scholar 

  192. Takahashi, H. et al. Nonmagnetic J = 0 state and spin–orbit excitations in K2RuCl6. Phys. Rev. Lett. 127, 227201 (2021).

    Article  ADS  Google Scholar 

  193. Qamar, A. et al. Experimental and theoretical characterization of X-ray induced excitons, magnons, and dd transitions in MoO3 nanosheets. Phys. Rev. Mater. 6, 074003 (2022).

    Article  Google Scholar 

  194. Biasin, E. et al. Revealing the bonding of solvated Ru complexes with valence-to-core resonant inelastic X-ray scattering. Chem. Sci. 12, 3713–3725 (2021).

    Article  Google Scholar 

  195. Kim, J. et al. Excitonic quasiparticles in a spin–orbit Mott insulator. Nat. Commun. 5, 4453 (2014).

    Article  ADS  Google Scholar 

  196. Paris, E. et al. Strain engineering of the charge and spin–orbital interactions in Sr2IrO4. Proc. Natl Acad. Sci. USA 117, 24764–24770 (2020).

    Article  ADS  Google Scholar 

  197. Gretarsson, H. et al. Crystal-field splitting and correlation effect on the electronic structure of A(2)IrO(3). Phys. Rev. Lett. 110, 076402 (2013).

    Article  ADS  Google Scholar 

  198. Kim, J. et al. Large spin-wave energy gap in the bilayer iridate Sr3Ir2O7: evidence for enhanced dipolar interactions near the Mott metal–insulator transition. Phys. Rev. Lett. 109, 157402 (2012).

    Article  ADS  Google Scholar 

  199. Yuan, B. et al. Determination of Hund’s coupling in 5d oxides using resonant inelastic X-ray scattering. Phys. Rev. B 95, 235114 (2017).

    Article  ADS  Google Scholar 

  200. Ament, L. J. P., Khaliullin, G. & van den Brink, J. Theory of resonant inelastic X-ray scattering in iridium oxide compounds: probing spin–orbit-entangled ground states and excitations. Phys. Rev. B 84, 020403 (2011).

    Article  ADS  Google Scholar 

  201. Revelli, A. et al. Resonant inelastic x-ray incarnation of Young’s double-slit experiment. Sci. Adv. 5, 4020 (2019).

    Article  ADS  Google Scholar 

  202. Lu, X. et al. Dispersive magnetic and electronic excitations in iridate perovskites probed by oxygen K-edge resonant inelastic X-ray scattering. Phys. Rev. B 97, 041102 (2018).

    Article  ADS  Google Scholar 

  203. Sala, M. M. et al. Orbital occupancies and the putative jeff = 1/2 ground state in Ba2IrO4: a combined oxygen K-edge XAS and RIXS study. Phys. Rev. B 89, 121101(R) (2014).

    Article  ADS  Google Scholar 

  204. Zimmermann, V. et al. Coherent propagation of spin–orbit excitons in a correlated metal. npj Quantum Mater. 8, 53 (2023).

    Article  ADS  Google Scholar 

  205. van Veenendaal, M., Carra, P. & Thole, B. T. X-ray resonant Raman scattering in the rare earths. Phys. Rev. B 54, 16010–16023 (1996).

    Article  ADS  Google Scholar 

  206. van Veenendaal, M. & Benoist, R. X-ray absorption and resonant inelastic X-ray scattering in the rare earths. Phys. Rev. B 58, 3741–3749 (1998).

    Article  ADS  Google Scholar 

  207. Butorin, S. M. Resonant inelastic X-ray scattering as a probe of optical scale excitations in strongly electron-correlated systems: quasi-localized view. J. Electron. Spectros. Relat. Phenom. 110, 213–233 (2000).

    Article  ADS  Google Scholar 

  208. Amorese, A. et al. Resonant inelastic X-ray scattering investigation of the crystal-field splitting of Sm3+ in SmB6. Phys. Rev. B 100, 241107 (2019).

    Article  ADS  Google Scholar 

  209. Amorese, A. et al. Orbital selective coupling in CeRh3B2: coexistence of high Curie and high Kondo temperatures. Phys. Rev. B 107, 115164 (2023).

    Article  ADS  Google Scholar 

  210. Zatsepin, D. A. et al. Strong anisotropy of resonant inelastic X-ray scattering from charge-transfer excitations in UO3. J. Phys. Condens. Matter 14, 2541–2546 (2002).

    ADS  Google Scholar 

  211. Butorin, S. M. & Shuh, D. K. Electronic structure of americium sesquioxide probed by resonant inelastic X-ray scattering. Phys. Rev. B 108, 195152 (2023).

    Article  ADS  Google Scholar 

  212. Kvashnina, K. O. et al. Resonant inelastic X-ray scattering of curium oxide. Phys. Rev. B 75, 115107 (2007).

    Article  ADS  Google Scholar 

  213. Kvashnina, K. O. et al. Trends in the valence band electronic structures of mixed uranium oxides. Chem. Commun. 54, 9757–9760 (2018).

    Article  Google Scholar 

  214. Polly, R., Schacherl, B., Rothe, J. & Vitova, T. Relativistic multiconfigurational ab initio calculation of uranyl 3d4f resonant inelastic X-ray scattering. Inorg. Chem. 60, 18764–18776 (2021).

    Article  Google Scholar 

  215. Vitova, T. et al. The role of the 5f valence orbitals of early actinides in chemical bonding. Nat. Commun. 8, 1–9 (2017).

    Article  Google Scholar 

  216. Butorin, S. M. 3d-4f resonant inelastic X-ray scattering of actinide dioxides: crystal-field multiplet description. Inorg. Chem. 59, 16251–16264 (2020).

    Article  Google Scholar 

  217. Kvashnina, K. O., Walker, H. C., Magnani, N., Lander, G. H. & Caciuffo, R. Resonant X-ray spectroscopy of uranium intermetallics at the M4,5 edges of uranium. Phys. Rev. B 95, 245103 (2017).

    Article  ADS  Google Scholar 

  218. Marino, A. et al. Singlet magnetism in intermetallic UGa2 unveiled by inelastic X-ray scattering. Phys. Rev. B 108, 045142 (2023).

    Article  ADS  Google Scholar 

  219. Lander, G. H. et al. Resonant inelastic X-ray spectroscopy on UO2 as a test case for actinide materials. J. Phys. Condens. Matter 33, 06LT01 (2021).

    Article  Google Scholar 

  220. Piancastelli, M. N. et al. Hard X-ray spectroscopy and dynamics of isolated atoms and molecules: a review. Rep. Prog. Phys. 83, 016401 (2020).

    Article  ADS  Google Scholar 

  221. Guillemin, R. et al. Angular and dynamical properties in resonant inelastic X-ray scattering: case study of chlorine-containing molecules. Phys. Rev. A 86, 039903 (2012).

    Article  ADS  Google Scholar 

  222. Püttner, R. et al. Si 1s−1, 2s−1 and 2p−1 lifetime broadening of SiX4 (X = F, Cl, Br, CH3) molecules: SiF4 anomalous behaviour reassessed. Phys. Chem. Chem. Phys. 21, 8827–8836 (2019).

    Article  Google Scholar 

  223. Marchenko, T. et al. Ultrafast nuclear dynamics in the doubly-core-ionized water molecule observed via Auger spectroscopy. Phys. Rev. A 98, 063403 (2018).

    Article  ADS  Google Scholar 

  224. Travnikova, O. et al. Subfemtosecond control of molecular fragmentation by hard X-ray photons. Phys. Rev. Lett. 118, 213001 (2017).

    Article  ADS  Google Scholar 

  225. Fohlisch, A. et al. Direct observation of electron dynamics in the attosecond domain. Nature 436, 373–376 (2005).

    Article  ADS  Google Scholar 

  226. Piancastelli, M. N. et al. Core-hole-clock spectroscopies in the tender X-ray domain. J. Phys. B At. Mol. Opt. Phys. 47, 124031 (2014).

    Article  ADS  Google Scholar 

  227. Marchenko, T. et al. Electron dynamics in the core-excited CS2 molecule revealed through resonant inelastic X-ray scattering spectroscopy. Phys. Rev. X 5, 031021 (2015).

    Google Scholar 

  228. Lundberg, M. et al. Metal-ligand covalency of iron complexes from high-resolution resonant inelastic X-ray scattering. J. Am. Chem. Soc. 135, 17121–17134 (2013).

    Article  Google Scholar 

  229. Braun, A. et al. X-ray spectroscopic study of the electronic structure of a trigonal high-spin Fe(IV) = O complex modeling non-heme enzyme intermediates and their reactivity. J. Am. Chem. Soc. 145, 18977–18991 (2023).

    Article  Google Scholar 

  230. Glatzel, P. et al. The electronic structure of Mn in oxides, coordination complexes, and the oxygen-evolving complex of photosystem II studied by resonant inelastic X-ray scattering. J. Am. Chem. Soc. 126, 9946–9959 (2004).

    Article  Google Scholar 

  231. Kroll, T. et al. Effect of 3d/4p mixing on 1s2p resonant inelastic X-ray scattering: electronic structure of oxo-bridged iron dimers. J. Am. Chem. Soc. 143, 4569–4584 (2021).

    Article  Google Scholar 

  232. Hall, E. R. et al. Valence-to-core-detected X-ray absorption spectroscopy: targeting ligand selectivity. J. Am. Chem. Soc. 136, 10076–10084 (2014).

    Article  Google Scholar 

  233. Gallo, E. et al. Preference towards five‐coordination in Ti silicalite‐1 upon molecular adsorption. ChemPhysChem 14, 79–83 (2013).

    Article  Google Scholar 

  234. Glatzel, P. et al. In situ characterization of the 5d density of states of Pt nanoparticles upon adsorption of CO. J. Am. Chem. Soc. 132, 2555–2557 (2010).

    Article  Google Scholar 

  235. Kunnus, K. et al. Quantifying the steric effect on metal–ligand bonding in Fe carbene photosensitizers with Fe 2p3d resonant inelastic X-ray scattering. Inorg. Chem. 61, 1961–1972 (2022).

    Article  Google Scholar 

  236. House, R. A. et al. Covalency does not suppress O2 formation in 4d and 5d Li-rich O-redox cathodes. Nat. Commun. 12, 2975 (2021).

    Article  ADS  Google Scholar 

  237. House, R. A. et al. First-cycle voltage hysteresis in Li-rich 3d cathodes associated with molecular O(2) trapped in the bulk. Nat. Energy 5, 777–785 (2020).

    Article  ADS  Google Scholar 

  238. House, R. A. et al. Delocalized electron holes on oxygen in a battery cathode. Nat. Energy 8, 351–360 (2023).

    Article  ADS  Google Scholar 

  239. House, R. A. et al. Superstructure control of first-cycle voltage hysteresis in oxygen-redox cathodes. Nature 577, 502 (2020). Resonant inelastic X-ray scattering application to battery systems showing molecular oxygen.

    Article  ADS  Google Scholar 

  240. Wernet, P. et al. Orbital-specific mapping of the ligand exchange dynamics of Fe(CO)(5) in solution. Nature 520, 78–81 (2015). Time-resolved resonant inelastic X-ray scattering experiment.

    Article  ADS  Google Scholar 

  241. Schreck, S. et al. Dynamics of the OH group and the electronic structure of liquid alcohols. Struct. Dyn. 1, 054901 (2014).

    Article  Google Scholar 

  242. Jay, R. M. et al. Tracking C–H activation with orbital resolution. Science 380, 955–960 (2023).

    Article  ADS  Google Scholar 

  243. Wang, R.-P. et al. Saturation and self-absorption effects in the angle-dependent 2p3d resonant inelastic X-ray scattering spectra of Co 3+. J. Synchrotron Radiat. 27, 1–9 (2020).

    Article  Google Scholar 

  244. Titus, C. J. et al. L-edge spectroscopy of dilute, radiation-sensitive systems using a transition-edge-sensor array. J. Chem. Phys. 147, 214201 (2017).

    Article  ADS  Google Scholar 

  245. Lee, S. J. et al. Soft X-ray spectroscopy with transition-edge sensors at Stanford Synchrotron Radiation Lightsource beamline 10-1. Rev. Sci. Instrum. 90, 113101 (2019).

    Article  ADS  Google Scholar 

  246. Vig, S. et al. Measurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS). SciPost Phys. 3, 026 (2017).

    Article  ADS  Google Scholar 

  247. Higley, D. J. et al. Stimulated resonant inelastic X-ray scattering in a solid. Commun. Phys. 5, 83 (2022).

    Article  Google Scholar 

  248. Kroll, T. et al. Observation of seeded Mn Kβ stimulated X-ray emission using two-color X-ray free-electron laser pulses. Phys. Rev. Lett. 125, 037404 (2020).

    Article  ADS  Google Scholar 

  249. Bahrdt, J. et al. First observation of photons carrying orbital angular momentum in undulator radiation. Phys. Rev. Lett. 111, 034801 (2013).

    Article  ADS  Google Scholar 

  250. van Veenendaal, M. & McNulty, I. Prediction of strong dichroism induced by X rays carrying orbital momentum. Phys. Rev. Lett. 98, 157401 (2007).

    Article  ADS  Google Scholar 

  251. Elnaggar, H. et al. Noncollinear ordering of the orbital magnetic moments in magnetite. Phys. Rev. Lett. 123, 207201 (2019).

    Article  ADS  Google Scholar 

  252. Li, Z. X., Wang, Z. Y., Cao, Y. S. & Yan, P. Generation of twisted magnons via spin-to-orbital angular momentum conversion. Phys. Rev. B 105, 174433 (2022).

    Article  ADS  Google Scholar 

  253. Zhou, K. J., Matsuyama, S. & Strocov, V. N. hv(2)-concept breaks the photon-count limit of RIXS instrumentation. J. Synchrotron Radiat. 27, 1235–1239 (2020).

    Article  Google Scholar 

  254. Kokkonen, E. et al. Upgrade of the SPECIES beamline at the MAX IV laboratory. J. Synchrotron Radiat. 28, 588–601 (2021).

    Article  Google Scholar 

  255. Chiuzbaian, S. G. et al. Design and performance of AERHA, a high acceptance high resolution soft X-ray spectrometer. Rev. Sci. Instrum. 85, 043108 (2014).

    Article  ADS  Google Scholar 

  256. Boots, M., Muir, D. & Moewes, A. Optimizing and characterizing grating efficiency for a soft X-ray emission spectrometer. J. Synchrotron Radiat. 20, 272–285 (2013).

    Article  Google Scholar 

  257. Miyawaki, J. et al. A compact permanent-magnet system for measuring magnetic circular dichroism in resonant inelastic soft X-ray scattering. J. Synchrotron Radiat. 24, 449–455 (2017).

    Article  Google Scholar 

  258. Nowak, S. H. et al. A versatile Johansson-type tender X-ray emission spectrometer. Rev. Sci. Instrum. 91, 033101 (2020).

    Article  ADS  Google Scholar 

  259. Rovezzi, M. et al. TEXS: in-vacuum tender X-ray emission spectrometer with 11 Johansson crystal analyzers. J. Synchrotron Radiat. 27, 813–826 (2020).

    Article  Google Scholar 

  260. Glatzel, P. et al. The five-analyzer point-to-point scanning crystal spectrometer at ESRF ID26. J. Synchrotron Radiat. 28, 362–ID371 (2021).

    Article  Google Scholar 

  261. Ablett, J. M. et al. The GALAXIES inelastic hard X-ray scattering end-station at Synchrotron SOLEIL. J. Synchrotron Radiat. 26, 263–271 (2019).

    Article  Google Scholar 

  262. Weinhardt, L. et al. X-SPEC: a 70 eV to 15 keV undulator beamline for X-ray and electron spectroscopies. J. Synchrotron Radiat. 28, 609–617 (2021).

    Article  Google Scholar 

  263. Szlachetko, J. et al. In situ hard X-ray quick RIXS to probe dynamic changes in the electronic structure of functional materials. J. Electron. Spectros. Relat. Phenom. 188, 161–165 (2013).

    Article  ADS  Google Scholar 

  264. Cai, Y. Q. et al. Optical design and performance of the Taiwan inelastic X‐ray scattering beamline (BL12XU) at SPRING‐8. AIP Conf. Proc. 705, 340–343 (2004).

    Article  ADS  Google Scholar 

  265. Alonso-Mori, R. et al. A multi-crystal wavelength dispersive X-ray spectrometer. Rev. Sci. Instrum. 83, 073114 (2012).

    Article  ADS  Google Scholar 

  266. Shvyd’ko, Y. V. et al. MERIX — next generation medium energy resolution inelastic X-ray scattering instrument at the APS. J. Electron. Spectros. Relat. Phenom. 188, 140–149 (2013).

    Article  ADS  Google Scholar 

  267. Glatzel, P. et al. Electronic structural changes of Mn in the oxygen-evolving complex of photosystem II during the catalytic cycle. Inorg. Chem. 52, 5642–5644 (2013).

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Diamond Light Source, Harwell Campus, Didcot, UK

    Frank M. F. de Groot & Ke-Jin Zhou

  2. Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, the Netherlands

    Frank M. F. de Groot

  3. Heidelberg University, Heidelberg, Germany

    Maurits W. Haverkort

  4. Institute of Mineralogy, Physics of Materials and Cosmochemistry, CNRS, Sorbonne University, Paris, France

    Hebatalla Elnaggar & Amélie Juhin

  5. European Synchrotron Radiation Facility, Grenoble, France

    Pieter Glatzel

Authors
  1. Frank M. F. de Groot
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  2. Maurits W. Haverkort
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  3. Hebatalla Elnaggar
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  4. Amélie Juhin
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  5. Ke-Jin Zhou
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  6. Pieter Glatzel
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Contributions

Introduction (F.M.F.d.G., M.W.H., H.E., A.J., K.-J.Z. and P.G.); Experimentation (F.M.F.d.G., H.E., A.J., K.-J.Z. and P.G.); Results (F.M.F.d.G., M.W.H., H.E., A.J., K.-J.Z. and P.G.); Applications (F.M.F.d.G., M.W.H., H.E., A.J., K.-J.Z. and P.G.); Reproducibility and data deposition (F.M.F.d.G., H.E., A.J., K.-J.Z. and P.G.); Limitations and optimizations (F.M.F.d.G., M.W.H., H.E., A.J., K.-J.Z. and P.G.); Outlook (F.M.F.d.G., M.W.H., H.E., A.J., K.-J.Z. and P.G.); overview of the Primer (all authors).

Corresponding authors

Correspondence to Frank M. F. de Groot or Ke-Jin Zhou.

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The authors declare no competing interests.

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Peer review information

Nature Reviews Methods Primers thanks Myron Huzan, who co-reviewed with Michael Baker; Shiyu Fan, who co-reviewed with Jonathan Pelliciari; and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Related links

6-2a: https://www-ssrl.slac.stanford.edu/content/beam-lines/bl6-2a

15-2: https://www-ssrl.slac.stanford.edu/content/beam-lines/bl15-2

20-ID: https://www.aps.anl.gov/Spectroscopy/Beamlines/20-ID

41A: https://tpsbl.nsrrc.org.tw/bd_page.aspx?lang=en&port=41A&pid=1044

ADRESS: https://www.psi.ch/en/sls/adress

AMBER: https://als.lbl.gov/beamlines/6-0-1/

Beamline 8.0.1: https://als.lbl.gov/beamlines/8-0-1/

BL11XU: http://www.spring8.or.jp/wkg/BL11XU/instrument/lang-en

BL12XU: https://www.spring8.or.jp/wkg/BL12XU/instrument/lang-en/

BM20-ROBL: https://www.esrf.fr/UsersAndScience/Experiments/CRG/BM20

BM30-FAME: https://www.esrf.fr/home/UsersAndScience/Experiments/CRG/BM30.html

ChemRIXS qRIXS: https://lcls.slac.stanford.edu/instruments/neh-2-2

ESRF data policy: https://www.esrf.fr/datapolicy

FURKA: https://www.psi.ch/en/swissfel/furka

GALAXIES: https://www.synchrotron-soleil.fr/en/beamlines/galaxies

hRIXS: https://www.xfel.eu/facility/instruments/scs/index_eng.html

I20: https://www.diamond.ac.uk/Instruments/Spectroscopy/I20.html

I21: https://www.diamond.ac.uk/Instruments/Magnetic-Materials/I21.html

ID20: https://www.esrf.fr/home/UsersAndScience/Experiments/EMD/ID20.html

ID26: https://www.esrf.fr/id26

ID32: https://www.esrf.fr/ID32

IPÊ: https://lnls.cnpem.br/grupos/ipe-en/

IRIXS: https://photon-science.desy.de/facilities/petra_iii/beamlines/p01_dynamics/

MARS: https://www.synchrotron-soleil.fr/en/beamlines/mars

QERLIN: https://als.lbl.gov/beamlines/6-0-2/

REIXS: https://reixs.lightsource.ca/

SEXTANTS: https://www.synchrotron-soleil.fr/en/beamlines/sextants

SIX: https://www.bnl.gov/nsls2/beamlines/beamline.php?r=2-ID

SPECIES: https://www.maxiv.lu.se/beamlines-accelerators/beamlines/species/

SUPERXAS: https://www.psi.ch/en/sls/superxas

U41-PEAXIS: https://www.wayforlight.eu/beamline/26510

VERITAS: https://www.maxiv.lu.se/beamlines-accelerators/beamlines/veritas/

X-SPEC: https://www.ips.kit.edu/2786_6092.php

Supplementary information

Glossary

Brillouin zone

Primitive cell in reciprocal space that captures all unique wave vectors.

Core RIXS

Resonant inelastic X-ray scattering (RIXS) involving the decay from a shallow core state to a deeper core state.

Direct RIXS

Decay of another electron after initial X-ray excitation.

Electron energy loss spectroscopy

(EELS). Experimental technique that measures the inelastic scattering of electrons.

Free electron lasers

Linear accelerators coupled to a long undulator yielding coherent X-ray pulses on femtosecond timescales.

High-energy resolution fluorescence detection

(HERFD). Detection of the X-ray emission with an ~100–500 meV fluorescence detector giving, in a first approximation, an X-ray absorption spectroscopy spectrum in which the lifetime broadening of the deep core hole is replaced by the lifetime broadening of a shallow core hole.

Indirect RIXS

Excitation and decay of the same electron with an electronic reorganization in the intermediate state.

Inelastic neutron scattering

(INS). Experimental technique that measures the inelastic scattering of neutrons.

Inelastic X-ray scattering

(IXS). The experimental technique that measures the inelastic scattering of X-rays away from a core resonance, also known as X-ray Raman scattering or non-resonant inelastic X-ray scattering.

Magnons

Collective excitation of the spin structure in a solid.

Orbitons

Collective excitation of the orbital configuration (dd excitation) in a solid.

Phonons

Collective excitation of vibration energy in a solid.

Plasmon

Collective charge excitation in a solid.

Resonant inelastic X-ray scattering

(RIXS). The experimental technique that measures the inelastic scattering of X-rays over the energy range of an X-ray absorption spectrum.

Spinons

Collective excitation of a spin-1/2 quasiparticle.

Valence RIXS

Resonant inelastic X-ray scattering (RIXS) involving the decay from a valence state to a core state.

X-ray absorption spectroscopy

The experimental technique based on the excitation of a core electron by the absorption of X-ray, measured as a function of energy.

X-ray emission spectroscopy

The experimental technique based on the emission of an X-ray owing to the decay of an electron to fill a core hole.

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de Groot, F.M.F., Haverkort, M.W., Elnaggar, H. et al. Resonant inelastic X-ray scattering. Nat Rev Methods Primers 4, 45 (2024). https://doi.org/10.1038/s43586-024-00322-6

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