Resonant inelastic x-ray scattering spectra for electrons in solids

Abstract

Resonant inelastic x-ray scattering (RIXS) has recently been a subject of remarkable progress due to the advent of high-brilliance synchrotron radiation sources. The authors present a review of both experimental and theoretical investigations of electrons in solids using this second-order optical process, in which there is coherent absorption and emission of x rays at resonance with electronic excitations. The review starts with some of the fundamental aspects of RIXS, after which are presented typical experimental data and their theoretical interpretation for various materials. The first class of materials considered is semiconductors and insulators (Si, C, and BN), which are typical systems with weak electron correlation, and the data are interpreted based on electronic states described by an energy-band model. Effects of symmetry of electronic states and electron momentum conservation are discussed. At the opposite extreme are rare-earth systems (metals and oxides), in which the 4f electrons are almost localized with strong electron correlation. The observations are interpreted based on the effects of intra-atomic multiplet coupling and weak interatomic electron transfer, which are well described with an Anderson impurity model or a cluster model. In this context a narrowing of spectral width in the excitation spectrum, polarization dependence, and the magnetic circular dichroism in ferromagnetic materials are discussed. The authors then consider transition-metal compounds, materials with electron correlation strengths intermediate between semiconductors and rare-earth systems. In these interesting cases there is an interplay of intra-atomic and interatomic electronic interactions that leads to limitations of both the band model and the Anderson impurity model. Finally, other topics in resonant x-ray emission studies of solids are described briefly. CONTENTS I. Introduction 203 II. Fundamental Aspects of Resonant Inelastic X-ray Scattering 205 A. Basic description of RIXS 205 B. Experimental measurements 206 C. Theoretical models 208 1. Energy-band model 208 2. Anderson impurity model 208 3. Momentum selection rule 210 4. Normal XES 210 III. RIXS in Semiconductors and Insulators 211 A. Experimental data 211 B. Silicon and graphite 211 C. Effects of core exciton and phonon relaxation 213 IV. Rare-Earth Systems 217 A. Experimental data for rare-earth metals and compounds 217 B. Effect of intra-atomic multiplet coupling 218 C. Effect of interatomic hybridization 221 D. Narrowing of spectral width in the excitation spectrum 223 E. Polarization dependence and magnetic circular dichroism 225 V. Transition-Metal Compounds 228 A. Crystal-field level excitation and charge-transfer excitation in copper oxide systems 228 B. Multiplet coupling effect and spin-dependent excitation spectra in Mn compounds 230 C. Early transition-metal compounds and the effect of carrier doping 232 D. Limitations of the band model and the Anderson impurity model 235 VI. Other Topics 238 A. Simple metals 238 B. Transition metals 239 C. Oxygen...

Lifetime-Broadening-Suppressed Selective XAFS Spectroscopy

“…However, it was later suggested that PFY spectra cannot be viewed as genuine LBS-XAFS 16,17 (although for wide-band materials, where core-electron interactions are small, they can be a good approximation to LBS-XAFS). 6,16,18 Partially because of this indication, there were very few reports on succeeding PFY measurements. 19 An alternative method to obtain LBS-XAFS by using RIXS has been theoretically suggested by Tulkki and Åberg, 20 even before the proposition of the PFY spectroscopy (at 1982).…”

“…10 Here, the ground state is the initial state, 1s-excited state (same as the final state of absorption) is the intermediate state, and the hole in the intermediate state is filled by an electron in the 2p state, resulting in the emission of a photon with energy w2 (in atomic unit). This resonant process is described by the well-known Kramers-Heisenberg equation, 3,6,7,12 …”

“…[5][6][7][8][9][10][11][12] Here we loosely define RIXS as x-ray emissions excited with x-ray energies near an absorption edge. 6,7 Wide applications of RIXS have been so far hindered by its low intensity.However, the intensity problem in RIXS measurements is now being solved by developing highly sensitive emission spectrometers with high resolution, optimized for the use at third-generation synchrotron sources. [12][13][14][15] In the present review, we survey this novel technique, lifetimebroadening-suppressed (LBS) selective XAFS spectroscopy, while paying attention to basic aspects.…”

“…[5][6][7][8][9][10][11][12] Here we loosely define RIXS as x-ray emissions excited with x-ray energies near an absorption edge. 6,7 Wide applications of RIXS have been so far hindered by its low intensity.…”

Electronic structure of InN studied using soft x-ray emission, soft x-ray absorption, and quasiparticle band structure calculations

“…The measured emission or absorption spectrum can then be interpreted in terms of the density of occupied valence band or unoccupied conduction band states, respectively. 7,8 Dipole selection rules ()l ± 1) govern the optical transition to or from the core-level, 7 and in the present case N K-edge XES and XAS measurements yield information on the N 2p PDOS. Unlike photoemission spectroscopy, these techniques are relatively insensitive to the quality of the sample surface and atomic cleaning is not necessary.…”