128
H. Elnaggar et al.
4.3 Conclusion
We have expressed the XAS cross section using Green’s function formalism and
spherical tensors, which allows a tractable investigation of the different types of
dichroism: on the one hand experimentally, by allowing the experimentalist to predict the smallest set of measurements required to recover the full spectroscopic
information and therefore to optimize beamtime; on the other hand theoretically,
using modern core level spectroscopy codes, by allowing a more efficient calculation rather than a point-by-point time-consuming treatment. In a forthcoming work,
we intend to use a similar approach for resonant inelastic X-ray scattering (RIXS)
spectroscopy, whose richness lies in the large number of possible spectra that can
be obtained by varying the energy, direction, and polarization state of the incident
and scattered beams [28]. But as a matter of fact, there is so much information in
the spectra that it is difficult to know whether a specific set of experiments measures
all potential information. In our opinion, the possibilities offered by angular and
polarization dependent RIXS measurements have not yet been exploited to the best
of their potential. Nevertheless, the technique has now become mature and popular
and will benefit from the huge instrumentation progress achieved in the last years,
which open new doors for the exploration of dichroims in materials.
References
1. C. Brouder, Angular dependence of X-ray absorption spectra. J. Phys.: Condens. Matter 2, 701
(1990). https://doi.org/10.1088/0953-8984/2/3/018
2. A. Juhin, S.P. Collins, Y. Joly, M. Diaz-Lopez, K. Kvashnina, P. Glatzel, C. Brouder, F.M.F. de
Groot, Measurement of f orbital hybridization in rare earths through electric dipole-octupole
interference in X-ray absorption spectroscopy. Phys. Rev. Mater. 3, 120801(R) (2019). https://
doi.org/10.1103/PhysRevMaterials.3.120801
3. S. Sugano, T. Tanabe, H. Kamimura, Multiplets of Transition Metal Ions in Crystals (Academic,
New York, 1970)
4. J.S. Griffith, The Theory of Transition-Metal Ions (Cambridge University Press, Cambridge,
1961)
5. E. König, S. Kremer, Ligand Field Energy Diagrams (Springer Science+Business Media, New
York, 2013). https://doi.org/10.1007/978-1-4757-1529-3
6. R.D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press,
Berkeley, 1981)
7. M.W. Haverkort, Y. Lu, S. Macke, R. Green, M. Brass, S. Heinze, Quanty – a quantum many
body script language, http://www.quanty.org/doku.php?id=start&rev=1522759229
8. M. Baer, Multipole expansion package, https://github.com/maroba/multipoles
9. M.W. Haverkort, M. Zwierzycki, O.K. Andersen, Multiplet ligand-field theory using Wannier
orbitals. Phys. Rev. B 85, 165113 (2012). https://doi.org/10.1103/PhysRevB.85.165113
10. Y. Lu, M. Höppner, O. Gunnarsson, M.W. Haverkort, Efficient real-frequency solver for dynamical mean-field theory. Phys. Rev. B 90, 085102 (2014). https://doi.org/10.1103/PhysRevB.90.
085102
11. M.W. Haverkort, G. Sangiovanni, P. Hansmann, A. Toschi, Y. Lu, S. Macke, Bands, resonances,
edge singularities and excitons in core level spectroscopy investigated within the dynamical
H. Elnaggar et al.
4.3 Conclusion
We have expressed the XAS cross section using Green’s function formalism and
spherical tensors, which allows a tractable investigation of the different types of
dichroism: on the one hand experimentally, by allowing the experimentalist to predict the smallest set of measurements required to recover the full spectroscopic
information and therefore to optimize beamtime; on the other hand theoretically,
using modern core level spectroscopy codes, by allowing a more efficient calculation rather than a point-by-point time-consuming treatment. In a forthcoming work,
we intend to use a similar approach for resonant inelastic X-ray scattering (RIXS)
spectroscopy, whose richness lies in the large number of possible spectra that can
be obtained by varying the energy, direction, and polarization state of the incident
and scattered beams [28]. But as a matter of fact, there is so much information in
the spectra that it is difficult to know whether a specific set of experiments measures
all potential information. In our opinion, the possibilities offered by angular and
polarization dependent RIXS measurements have not yet been exploited to the best
of their potential. Nevertheless, the technique has now become mature and popular
and will benefit from the huge instrumentation progress achieved in the last years,
which open new doors for the exploration of dichroims in materials.
References
1. C. Brouder, Angular dependence of X-ray absorption spectra. J. Phys.: Condens. Matter 2, 701
(1990). https://doi.org/10.1088/0953-8984/2/3/018
2. A. Juhin, S.P. Collins, Y. Joly, M. Diaz-Lopez, K. Kvashnina, P. Glatzel, C. Brouder, F.M.F. de
Groot, Measurement of f orbital hybridization in rare earths through electric dipole-octupole
interference in X-ray absorption spectroscopy. Phys. Rev. Mater. 3, 120801(R) (2019). https://
doi.org/10.1103/PhysRevMaterials.3.120801
3. S. Sugano, T. Tanabe, H. Kamimura, Multiplets of Transition Metal Ions in Crystals (Academic,
New York, 1970)
4. J.S. Griffith, The Theory of Transition-Metal Ions (Cambridge University Press, Cambridge,
1961)
5. E. König, S. Kremer, Ligand Field Energy Diagrams (Springer Science+Business Media, New
York, 2013). https://doi.org/10.1007/978-1-4757-1529-3
6. R.D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press,
Berkeley, 1981)
7. M.W. Haverkort, Y. Lu, S. Macke, R. Green, M. Brass, S. Heinze, Quanty – a quantum many
body script language, http://www.quanty.org/doku.php?id=start&rev=1522759229
8. M. Baer, Multipole expansion package, https://github.com/maroba/multipoles
9. M.W. Haverkort, M. Zwierzycki, O.K. Andersen, Multiplet ligand-field theory using Wannier
orbitals. Phys. Rev. B 85, 165113 (2012). https://doi.org/10.1103/PhysRevB.85.165113
10. Y. Lu, M. Höppner, O. Gunnarsson, M.W. Haverkort, Efficient real-frequency solver for dynamical mean-field theory. Phys. Rev. B 90, 085102 (2014). https://doi.org/10.1103/PhysRevB.90.
085102
11. M.W. Haverkort, G. Sangiovanni, P. Hansmann, A. Toschi, Y. Lu, S. Macke, Bands, resonances,
edge singularities and excitons in core level spectroscopy investigated within the dynamical