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Resonant inelastic X-ray Scattering (RIXS) is one of the most important experimental probes for studying strongly correlated materials. RIXS is a photon-in photon-out process, and by observing the frequency shift and polarization change of the outgoing photon compared to the incoming photon, properties of the material's electronic structure can be measured. A schematic representation of the RIXS scattering process is shown below:

RIXS has the ability to highlight momentum-dependent many-body excitations essential for understanding the material properties of strongly-correlated systems. This second-order RIXS process may be described in two steps such that starting from the ground state an optical excitation accesses the intermediate state where a localized core-hole is created and photoelectron gets promoted to a higher energy band. The de-excitation from the intermediate state to final state proceeds via the emission of a scattered photon, leaving the system in an excited state with energy and momentum transferred from the incident photon. While ARPES reveals the momentum resolved single-particle spectral function of occupied states, the momentum-depednent RIXS process involves both occupied and unoccupied states such that one readily obtains information regarding the electron or charge transfer dynamics involving multi-particle excitations.

Many exciting RIXS measurements have already been reported, and it is generally believed that RIXS can be a new powerful tool to probe the interplay between charge, spin, orbital, and lattice degrees of freedom. However, these experiment results are not fully understood. Previous theoretical RIXS studies include methods based on some approximations such as fine-order perturbation theory or Hartree-Fock approximation where correlation effects are poorly treated, or methods based on cluster configuration interaction or numerical Lanczos techniqe in which the Hilbert space is truncated and the intermediate state profiles are in general not captured. The way we proceed to tackle down this problem is to use numerically full exact diagonalization for a multi-orbital Hubbard model on small clusters, form which one has direct accesses to the eigenvalues and eigenvectors of the initial, intermediate, and final states. In combination with the information for the valence band density of states provided by density functional theory, the momentum-dependent RIXS spectra can therefore be constructed, and their resonance profiles can then be characterized (see the listed references).

The low x-ray emission efficiency problem has been improved with the advances in high brilliant undulator light sources as well as the use of highly efficient detectors. Nowadays the RIXS energy resolution has reached 100 meV, and further improvements in the near future are highly expected. At the same time, the development in theory is crucial to provide understandings toward the new physics revealed from RIXS measurements.

**References and Suggested Reading**

- Akio Kotani and Shik Shin,
*Rev. Mod. Phys.***73**, 203 (2001). - L. J. P. Ament
*et al*,*Rev. Mod. Phys.***83**, 705 - 767 (2011) - F. Vernay
*et al*,*Phys. Rev. B***77**, 104519 (2008). - C.-C. Chen
*et al*,*Phys. Rev. Lett.***105**, 177401 (2010) - S. Wang
*et al*,*Phys. Rev. B***82**, 144428 (2010) - J. N. Hancock
*et al*,*Phys. Rev. B***80**, 092509 (2009)

Abbamonte Group, UIUC

Young-June Kim Group, U-Toronto

The ADRESS Beamline, PSI, SLS