Session Z2: Resonant Inelastic X-ray Scattering in Complex Oxides

Resonant Inelastic X-ray Scattering in Correlated Electron Systems

Extremely bright photons generated at the new generation of synchrotron light sources have made a huge impact on various scientific disciplines ranging from biology to materials science. One of the exciting new developments is the use of x-rays in the field of solid-state spectroscopy. Inelastic x-ray scattering, analogous to the well-known inelastic neutron scattering, is a powerful tool for studying momentum-dependent electronic excitations and phonons. In particular, resonant inelastic x-ray scattering in the hard x-ray regime has been widely utilized to study the momentum dependence of various electronic excitations in strongly correlated electron systems. For example, by tuning the incident photon energy to the Cu K-edge, one can gain a large intensity enhancement as well as element specific knowledge of the electronic excitations in various copper oxide compounds. Most of the work to date has been focused on the charge-transfer excitation between the bonding and antibonding molecular orbitals, the excitation across the Mott gap, and crystal field excitations between the d-orbitals. Recent improvements in instrumentation have allowed us to observe a new mode in the mid-infrared frequency region. We will discuss the momentum dependence of these excitations in prototypical cuprate superconductors, La$_{2-x}$Sr$_x$CuO$_4$, and also examine the evolution of such excitations as charge carriers are doped into the system.   

Intermediate-Energy Charge-Transfer Excitations in the Cuprate Superconductors and the Photon Energy Dependence of the RIXS process

We present a study of the charge-transfer excitations of the structurally simple high-Tc superconductor HgBa$_2$CuO$_4+\delta$ and of the Mott insulator La$_2$CuO$_4$ using the burgeoning experimental technique of resonant inelastic X-ray scattering (RIXS). Our measurements address the 1-7 eV spectral range and place particular emphasis on the incident photon energy dependence of the cross section. Our results reveal clear evidence for a group of weakly-dispersing excitations \footnote{ L. Lu et al., \textit{Phys. Rev. Lett.} \textbf{95}, 217003 (2005).} \footnote{J. N. Hancock et al., unpublished.}. Collectively, these results call for the use of a multi-band theoretical approach for the description of the charge dynamics of high-Tc cuprate superconductors in this intermediate-energy regime.   

Momentum Dependence of Charge Excitations in YBa$_{2}$Cu$_{3}$O$_{7-\delta }$ and Nd$_{2-x}$Ce$_{x}$CuO$_{4}$

Resonant inelastic x-ray scattering (RIXS) studies at Cu $K$-edge on high-$T_{c}$ superconducting cuprates, YBa$_{2}$Cu$_{3}$O$_{7-\delta }$ and Nd$_{2-x}$Ce$_{x}$CuO$_{4}$ are presented. The superconductivity occurs in the vicinity of the Mott insulating state and it is important to clarify the nature of the Mott gap and its doping dependence. Because RIXS has an advantage that we can measure charge excitation in a wide energy-momentum space, it gives a unique opportunity to study the electronic structure of materials. We apply this technique to high-$T_{c}$ superconducting cuprates. In particular the electronic structure of strongly correlated metals is in the focus of our RIXS study. The experiments were performed at BL11XU of SPring-8, Japan, where a specially designed spectrometer for inelastic x-ray scattering is installed. In optimally doped YBa$_{2}$Cu$_{3}$O$_{7-\delta }$, anisotropic spectra are observed in the ab plane of a twin-free crystal. The Mott gap excitation from the one-dimensional CuO chain is enhanced at 2 eV near the zone boundary of the chain direction, while the excitation from the CuO$_{2}$ plane is broad at 1.5-4 eV and almost independent of momentum. Theoretical calculation based on the one-dimensional and two-dimensional Hubbard model reproduces the observed features in the RIXS spectra when smaller values of the on-site Coulomb energy of the chain than that of the plane are assumed. This means that the charge transfer gap of the chain is smaller than that of the plane. On the other hand, both interband excitation across the Mott gap and intraband excitation in the upper Hubbard band are observed in the electron-doped Nd$_{2-x}$Ce$_{x}$CuO$_{4}$. The intensity of the interband excitation is concentrated at $\sim $ 2 eV near the zone boundary while a dispersion relation with a momentum-dependent width emerges in the intraband excitation. The author would like to acknowledge to his collaborators, K. Tsutsui, Y. Endoh, T. Tohyama, K. Kuzushita, T. Inami, K. Ohwada, M. Hoesch, M. Tsubota, Y. Murakami, J. Mizuki, S. Maekawa, T. Masui, S. Tajima, and K. Yamada. The crystal growth of YBa$_{2}$Cu$_{3}$O$_{7-\delta }$ was supported by the New Energy and Industrial Technology Development Organization (NEDO) as the Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.   

Low-Energy Electronic Excitations in the Layered Cuprates Studied by Copper L$_{3}$ Resonant Inelastic X-Ray Scattering

Resonant inelastic x-ray scattering (RIXS) can be effectively used to measure the energy and symmetry of neutral electronic excitations in solids. In the soft x-ray range it is particularly powerful for strongly correlated electron systems based on 3$d$ transition metals, because at the L$_{2,3}$ edges it involves directly the 3$d$ states. In those systems it can be considered as a chemically selective, bulk sensitive alternative to optical absorption and electron energy loss spectroscopy in the study of low energy electronic excitations. The reduced intensity and the instrumental energy resolution usually hinder the detection of very detailed spectral features, but the recent progress in the energy resolving power of our RIXS apparatus has opened new exciting possibilities in the 400-1000 eV range. We present spectra measured using the AXES spectrometer, installed at the beam line ID08 of the ESRF, France. The combined resolution ranges from 240 meV to 650 meV going from the Ti to the Cu L$_{3}$ edges. We have measured the \textit{dd} excitations in cuprates [1,2,3,4] and other interesting systems where electronic correlation plays a central role [5]. In the specific case of cuprate superconductors, L$_{3}$ RIXS can be used to estimate the energy of the \textit{xy}, \textit{yz}, \textit{zx} and $z^{2}$ excited states. We report the examples of La$_{2}$CuO$_{4}$, CaCuO$_{2}$, Tl2212 and Nd$_{1.2}$Ba$_{1.8}$Cu$_{3}$O$_{7}$, where the different coordination and Cu-O distances result in a variety of \textit{dd} excitation spectra.\newline \newline [1] G. Ghiringhelli, N. B. Brookes, \textit{et al}, Phys. Rev. Lett. \textbf{92}, 117406 (2004). \newline [2] W.A. Little, G. Ghiringhelli, \textit{et al}, unpublished. \newline [3] M. Salluzzo, G. Ghiringhelli, \textit{et al}, unpublished \newline [4]. C. Aruta, P.G. Medaglia, G. Balestrino, G. Ghiringhelli, \textit{et al}, unpublished. \newline [5] G. Ghiringhelli, \textit{et al}, J. Phys. Cond. Matter \textbf{17}, 5397 (2005).   

Asymmetric evolution of low-energy electron-hole pair modes and the Mott pseudogap in doped cuprates

A central issue in the universal Mott behavior in a variety of complex systems is to understand the nature of the electron- hole pair excitation modes. Using high resolution resonant x- ray scattering we resolve the momentum dependence of low-energy electron-hole pair modes in two major classes of doped copper oxides which reveals the momentum structure of the Mott pseudogap over the entire phase diagram including the superconducting states. The pair bandwidth and zone-boundary velocity renormalize on either sides of the phase diagram at different rates indicating strong doping asymmetries observed in the momentum resolved particle-hole collective channels for the first time. The measured asymmetry of modes is qualitatively consistent with Hubbard model.