Animation of the evolution of the spin response function in the single-band Hubbard model over a wide range of hole and electron doping values. Note the dramatic changes with hole doping confined to the region near momentum (π,π) and the dramatic increase in the spin-response energy scale with electron doping. This behavior is born-out in a combination of recent resonant inelastic x-ray scattering (RIXS) measurements. These results helped to reconcile seemingly disparate results between RIXS and inelastic neutron scattering, appearing in C.J. Jia et al, Nature Communications 5, 3314 (2014).

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 finite-order perturbation theory or Hartree-Fock approximation, where correlation effects are poorly treated, or methods based on cluster configuration interaction or numerical Lanczos techniques in which the Hilbert space is truncated and the intermediate state profiles are in general not captured. One way to proceed to tackle this problem is to use numerically exact, full diagonalization for multi-orbital models 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 be constructed, and resonance profiles can then be characterized (see the listed references).

References and Suggested Reading

1. Akio Kotani and Shik Shin, Rev. Mod. Phys. 73, 203 (2001).
2. L. J. P. Ament et al, Rev. Mod. Phys. 83, 705 - 767 (2011)
3. F. Vernay et al, Phys. Rev. B 77, 104519 (2008).
4. C.-C. Chen et al, Phys. Rev. Lett. 105, 177401 (2010)
5. C.J. Jia et al, New J. Phys. 14, 113038 (2012)
6. C.J. Jia et al, Nature Communications 5, 3314 (2014)

The ADRESS Beamline, PSI, SLS
Abbamonte Group, UIUC
Young-June Kim Group, U-Toronto

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