Our knowledge of matter in all its different states of aggregation is incomplete if we only investigate the average arrangement of its constituents, the nuclei and the electrons. The atoms can vibrate as a whole, different types of localised oscillations can occur, phonon waves can propagate through matter. The frequencies of these degrees of freedom correspond to an energy spectrum of excitations.

Inelastic X-ray scattering with energy resolution down to 1.5 meV and well-defined momentum transfer is the method to investigate these elementary resonances. In many respects this method supplements the existing technique of inelastic neutron scattering to higher energy. Much smaller samples are accessible to investigations, and momentum resolution, which reveals the spatial extension of the excitation mode, is increased.

In a similar way electrons have dynamic degrees of freedom which manifest themselves in the form of plasma or interband transitions. Again inelastic X-ray scattering is a method which serves to investigate these excitations. The momentum of these excitations can be widely varied and, among other dynamic properties of electronic excitations, complete dispersion curves can be obtained. 

Another method is photoelectron spectroscopy, which is applied for the investigation of band structures at low-energy storage rings. At the ESRF, a beamline (ID12B) provides unique circular polarised radiation between 550 eV and 1.6 keV for experiments of this type in which also the spin state (magnetic state) of photoelectrons is analysed.

Further, Compton scattering is a well-established method using an inelastic process to investigate the ground state momentum distribution of electronic states.


Direct observation of Zhang-Rice singlets in CuO

CuO is often seen as a model compound for high temperature superconductors, since in comparing it with the insulating parent compounds of the superconductors, the magnitude of the insulating gap, the anti-ferromagnetic superexchange interactions, the basic structural unit (CuO4), the Cu-O distances, as well as the Cu valence, appear to be quite similar. Therefore, the characteristics of the first ionisation states in CuO (two hole final state in photoemission) may be representative for the behaviour of the doped holes in cuprates (ground state).

The top panel of Figure 41 shows the valence band photoemission spectra of CuO using circularly polarised X-rays at ID12B, with the photon energy tuned at the Cu 2p3/2 (L3) white line (h = 931.5 eV). The thick solid line is the sum of the spectra taken with parallel (+ + - ) and anti-parallel ( + + - ) alignment of the photon spin and electron spin. The spectrum reveals primarily the Cu 3d8 final states, and the peaks at 16.2 and 12.5 eV binding energy are states derived from the typical atomic-like 1S and 1G states, respectively. The thin line with open circles is the difference between the spectra taken with parallel and anti-parallel alignment of the photon and electron spins. After taking into account the spin detector sensitivity and the degree of circular polarisation, we observe that this difference is very large, up to 41% of the sum spectrum, which is quite remarkable since we are studying a system with randomly oriented local moments.

Figure 41 also shows that the difference spectrum has a different lineshape from the sum spectrum. For further analysis, we represent in the bottom panel of Figure 41 the data in terms of the degree of spin polarisation defined as the ratio between the difference and the sum spectrum.

The states assigned as 1S and 1G like have a polarisation of about +35% and +41%, respectively, and this compares very well with an analysis of the selection rules in which the polarisation for a 3d9 ion, neglecting the small 3d spin-orbit interaction, is found to be + 5/12 (+42%) for the singlet and -1/3 x 5/12 (-14%) for the triplet final states.

While for 12 eV and higher binding energies only singlet states are present, between 1 and 12 eV the polarisation is much reduced but not negative, indicating the presence of both singlet and triplet states as proposed in earlier studies. Quite remarkable is that the polarisation is high again for states located at the top of the valence band, suggesting strongly that they are singlets, i.e. the Zhang-Rice singlets in cuprates.

With a value of +35%, one is tempted to make a comparison with the polarisation of the high energy 1S state (also +35%) and suggest a common origin. In fact, model calculations showed that both the first ionisation state and the high energy 1S state belong to the 1A1 irreducible representation of the D4h point group, and that the first ionisation state, which is mainly 3d9L like, acquires some (~ 7%) 3d8 character which is now being probed in this resonant photoemission experiment (L denotes an oxygen ligand hole).

The calculations also showed that it is the strongly non-cubic environment, present in all cuprates, that makes the first ionisation state a singlet. In CuO, the stability of this singlet with respect to other states can be estimated from the width of the high polarisation region, which is about 1 eV.

Figure 42 shows a breakdown of the 3d8 final states in terms of singlets and triplets, using the above-mentioned selection rules. The results demonstrate clearly that this type of experiments can unravel the different spin states of the valence band of transition metal materials. A quantitative analysis that includes Auger matrix elements could provide a much more accurate modelling of the complicated electronic structure of such strongly correlated systems.

In our case, a qualitative analysis is more than sufficient to establish that the first 1 eV of the valence band consists of singlets only, as can be seen from the inset of Figure 42. While much theoretical work has been carried out in the past, our study provides the direct experimental support for a meaningful identification of Zhang-Rice singlets in cuprates.

In summary, we demonstrate the feasibility of spin-resolved valence band photoemission on macroscopically non-magnetic transition metal materials, i.e. antiferromagnets, paramagnets and materials with disordered magnetic structure, and show that a very high degree of spin polarisation can be obtained. The combined use of circularly polarised light, electron spin detection and 2p3/2 (L3) resonance condition is essential. We have been able to unravel the different spin states in the single particle excitation spectrum of CuO [1] and show that the top of the valence band is of pure singlet character, which provides strong support for the existence and stability of Zhang-Rice singlets in high temperature superconductors.



[1] L. H. Tjeng (a), B. Sinkovic (b), N. B. Brookes (c), J. B. Goedkoop (c), R. Hesper (a), E. Pellegrin (a), F. M. F. de Groot (a), S. Altieri (a), S. L. Hulbert (d), E. Shekel (b), and G. A. Sawatzky (a), Phys. Rev. Lett. 78, 1126 (1997).

(a) Materials Science Centre, University of Groningen (The Netherlands)
(b) Physics Department, New York University (USA)
(c) ESRF
(d) NSLS, Upton (USA)




Electron momentum densities in high-Tc superconductors

High-Tc superconductors were discovered ten years ago and since then have been intensively studied. However, a theory explaining the fundamental mechanisms of high-Tc superconductivity has yet to be formulated.

One of the keys to this step is understanding normal-state (above the critical temperature) properties of these materials. Unusual behaviour in the normal state reflects strong structural anisotropies.

Other characteristic properties (for example the linear behaviour of the d.c. resistivity and a temperature dependent Hall coefficient) indicate that it may not be possible to describe this state as a Fermi liquid.

Many theories have been put forward, some generalising the concept of the Fermi liquid, while others attempt to describe coulombic interactions and possible highly correlated behaviour using Hubbard or t-J models.

In this context, it is important to study the electron momentum density of these materials, which, when compared to predictions of theoretical models, can give an indication of their correctness or applicability. Detecting the energy of inelastically scattered photons at a fixed angle in back-scattering geometry from a mono-energetic beam incident on the sample, gives access to the Compton profile. This is a projection onto one dimension of the true electron momentum density.

YBa2Cu3O7 (YBCO) belongs to the category of high-Tc superconductors with Tc ~ 92 K and other members of this class are formed when most rare-earth elements are substituted for yttrium. An exception is praseodymium: PrBa2Cu3O7 (PrBCO) is an insulator macroscopically, even though isostructural with YBCO (lately there have been reports of superconducting PrBCO crystals but those used in this experiment were insulators). This is one reason to study both materials since understanding the absence of superconductivity in PrBCO may lead to an insight into high-Tc superconductivity.

In this experiment we measured the difference of profiles between two crystallographic directions for both samples (100/010 - 110, the samples were twinned), and compared it to the theoretical prediction. The incident energy, 60 keV, was enough to provide a reasonable signal from these highly absorbing materials. The scanning spectrometer used at beamline ID15B is designed such that the detector has a narrow receiving slit so as to minimise background. This is crucial for these samples as the background is very high due to Y, Pr and Ba fluorescence. High quality samples are small in size, and we used a stacking arrangement with three crystals mounted in a configuration where the full beam size, 0.2 mm x 6 mm, could be used, optimising the count rate.

Figure 43 shows the results of the measurement. The theoretical prediction is from a FLAPW calculation and has been scaled to the typical variation in the data. It reproduces most features in the measured difference profile for YBCO, the biggest deviations being at low momentum. Quantitative comparisons will be made later when a more complete calculation with the full core component is available.

There is also a remarkable difference between the PrBCO and YBCO data. This is an important fact because calculated band structures for these are very similar. The unit cell in both can be thought of as containing two different structural entities composed of copper and oxygen atoms: one-dimensional chains and two-dimensional planes. Earlier Cu-O chain momentum density measurements in these two materials using optical reflectivity and positron annihilation have shown very similar behaviour in YBCO and PrBCO. The difference seen now probably originates in the Cu-O planes which are also the seat of superconductivity.

Further efforts at ID15B will centre around trying to pinpoint the origin of these differences and performing other experiments to check the veracity of theoretical predictions concerning these materials.


A. Shukla (a), V. Honkimäki (a), T. Buslaps (a), P. Suortti (a), A. Erb (b), A.A. Manuel (b), D. Vasumathi (b), B. Barbiellini (c), to be published.

(a) ESRF
(b) DPMC, University of Geneva (Switzerland)
(c) Solid State Group, University of California, Los Angeles (USA)




High frequency dynamics of glass forming liquids at the glass transition

The study of the high frequency density fluctuations in glass-forming liquids has received great attention, and one of its aims is to improve our understanding of the microscopic mechanisms responsible for the liquid-glass transition. Whether the liquid-glass transition must be considered as a classical phase transition is, in fact, still a highly-debated topic.

For example, the glass transition temperature Tg, associated with the macroscopic structural arrest, cannot be considered as a critical transition temperature because certain quantities of the system show an anomalous behaviour at temperatures different from Tg: among others, the time scale dependence of the structural relaxations and the ergodicity of the system. Similarly, an order parameter in the classical sense has not yet been identified and there are properties that depend on the cooling rate. These issues have been the object of many theoretical models, extending from thermodynamic descriptions of the transition [Kivelson et al.], to pure dynamical approaches as the mode coupling theory (MCT) [Bengtzelius et al.].

The high frequency dynamics of three glass-forming systems (glycerol (GLY), o-terphenyl (OTP) and n-butyl-benzene (NBB)) was studied in the glass transition region using inelastic X-ray scattering (IXS) to determine their dynamic structure factor, S (Q,). The experiment has been carried out at the very high energy resolution inelastic X-ray scattering beamline ID16. In these three systems, we find a propagating longitudinal collective dynamics in a temperature range extending from the glass to the liquid phase well above Tg, and up to Q-transfers approaching the inverse of the interparticle separation. This result confirms and generalises previous findings obtained in a molecular liquid such as water, and in other glasses such as SiO2, glycerol and LiCl:6H2O. Specifically, it shows that this dynamics is the high-frequency continuation of the acoustic branch detected with ultra-sound and Brillouin light scattering techniques. Moreover, at a given Q, we find that the temperature dependence of the excitation frequency, (Q,T), is more pronounced in the liquid than in the glass, and has a cusp-like behaviour at a temperature Tx which we infer to be higher than Tg. This is shown in Figure 44, reporting excitation frequencies and energy widths derived using a damped harmonic oscillator model to fit the experimental IXS spectra of GLY, OTP and NBB. We associate this behaviour with the liquid-glass transition at the investigated frequencies, which manifests itself in a change of the collective dynamics likely to be due to the freezing of the microscopic diffusional processes. This microscopic structural arrest takes place, therefore, at a temperature higher than Tg. The common behaviour among the considered systems may lead to speculate on a more general origin of this property and therefore also to its validity for other glass-formers.


C. Masciovecchio (a), G. Monaco (b), G. Ruocco (b), F. Sette (a), A. Cunsolo (a), M. Krisch (a), A. Mermet (a), M. Soltwisch (b) and R. Verbeni (a), submitted to Phys. Rev. Lett.

(a) ESRF
(b) Universita di L'Aquila and INFM, L'Aquila (Italy)
(c) Institut für Experimentalphysik, Freie Universität Berlin (Germany)




Mixing of longitudinal and transverse dynamics in liquid water

The investigation of large wavevector excitations in liquid water has been a challenging task since the pioneering computational and experimental studies on its dynamic structure factor, S(Q,). These works revealed the existence of acoustic-like excitations propagating with a speed, = 3300 m/s, corresponding to a value more than twice the hydrodynamic sound uo o ~ 1500 m/s. Many subsequent works studied this issue by molecular dynamics (MD), inelastic neutron-scattering (INS), and inelastic X-ray-scattering (IXS). The high-frequency picture emerging from S(Q,) of H2O can be summarised as follows: i) The acoustic-like mode propagates with in the 4 to 14 nm-1 Q range. ii) For Q larger than 4 nm-1, there is a second, weakly dispersing mode with an energy of ~ 5 meV. iii) Both modes involve the motion of the molecular centre of mass. iv) At Q = 4 nm-1 the energy of the two modes becomes comparable, and in the 1 to 4 nm-1 Q region only one mode is observed; the sound velocity of this mode changes decreasing Q from towards o. This picture indicates the existence of two branches, one strongly- and the other weakly-dispersing with Q. The first one is identified as the sound branch with a bend up in the region below Q = 4 nm-1. The second one, on the basis of MD and of INS and IXS results on ice crystals can be related to a localised motion reminiscent of the transverse dynamics in the crystal and to the bending motion between three hydrogen-bonded water molecules. The most important point, however, is not yet settled: is the physical mechanism responsible for the bending of the sound branch and for the observation of a second mode at Q larger than 4 nm-1 a feature common to a large class of liquids or is it specific to water?

We performed a numerical MD investigation on the symmetry character of the modes observed in liquid water. The MD results in the Q range of the IXS and INS experiments show the existence of two different dynamic regimes. In the small Q limit, Q < 2 ~ nm-1, the dynamics is liquid-like: there are pure longitudinal modes propagating with = o, and the transverse dynamics is relaxational-like. In the opposite limit, at Q larger than 4 ~ nm-1, the dynamics is solid-like: there are two modes with energies close to the longitudinal and transverse phonon branches in ice. Here, however, contrary to ice, both modes have a large mixing of longitudinal and transverse symmetry. A propagating transverse dynamics starts to appear in the same intermediate Q region where the longitudinal branch acquires a transverse component, and its sound velocity changes from o to . The transition between the two regimes is found in the Q - region corresponding to the lengthscale and lifetime of local order in liquid water. Therefore, these results link the anomalies in the high frequency collective dynamics of liquid water to relaxation processes originating from locally ordered molecular assemblies. Moreover, the analysis of the longitudinal and transverse current spectra calculated by MD simulations gives a coherent picture of the previous experimental and MD results on the high frequency dynamics of liquid water, and shows that these dynamics can be described within the same framework used for other molecular liquids.


M. Sampoli (a), G. Ruocco (b), F. Sette (c), Phys. Rev. Lett. 79, 1678 (1997)

(a) Universita di Firenze and INFM, Firenze (Italy)
(b) Universita di L'Aquila and INFM, L'Aquila (Italy)
(c) ESRF




Coherent dynamic structure factor of liquid lithium by inelastic X-ray scattering

Recently, Canales et al. [1] calculated the dynamic structure factor of liquid lithium by means of molecular dynamic simulations using two different pair potentials: the empty core potential derived by Ashcroft and an ab initio calculation for a pair potential deduced from the neutral pseudoatom method (NPA). Although, the shapes of these two potentials are quite different, most of the calculated structural and thermodynamic properties are very similar [1]. However significant differences are observed in the calculations of the coherent part of the dynamic structure factor.

Inelastic neutron experiments on the dynamic structure factor of liquid 7Li were performed by de Jong et al. [2]. These measurements yielded no decision on which one of the two pair-potential approaches is the more favourable. The reason is that an essential part of the coherent structure factor ­ the Brillouin modes ­ could not be observed at small momentum transfers Q. Because of the momentum-energy relation for a classical particle there exists a maximum energy transfer at a momentum transfer Q, which is determined by the flight velocity of the incident neutron. In the neutron experiment the Brillouin excitations were not detectable (Q < 1.2 Å-1). Moreover, the high fraction of incoherent scattering at small Q and the uncertainties in the incoherent cross-section of 7Li makes it difficult to extract the Brillouin modes from the experimental data.

In contrast, these limitations do not appear in an inelastic X-ray scattering experiment with sufficient high-energy resolution. At energy transfers of about a few meV the observed intensity originates dominantly from coherent scattering. The energy-momentum relation of the photon allows an almost unlimited energy transfer at any accessible momentum transfer.

The measured inelastic X-ray scattering spectra I(Q, ) obtained at ID16 are shown in Figure 45 for selected values of momentum transfers. The spectrum is characterised by a central peak component due to quasi-elastic scattering, and the two side components are due to inelastic X-ray scattering (energy loss and gain) from collective atom excitations, generally referred to as Brillouin modes. At low Q values, the dispersion of these lines, and therefore the persistence of a propagating collective behaviour of this excitation, is evident already in the raw data.

The dispersion s(Q) of the Brillouin lines in comparison with results from molecular dynamic simulation and inelastic neutron scattering is shown in Figure 46. The results from the neutral pseudoatom method (solid line) are in good agreement with the dispersion from inelastic X-ray scattering, with respect to the maximum observed frequency.

The discrepancies between X-ray data and the neutron data for Q > 1.2 Å-1, which suggest a lower lying dispersion, is not fully understood. However, for a further investigation, the error bars of the neutron data have to be diminished.

For small Q values, the dispersion observed by inelastic X-ray scattering is steeper than the slope corresponding to the macroscopic sound velocity in the liquid (dashed-dotted line in Figure 46). This so-called positive dispersion was observed before, with X-ray scattering in water and on liquid cesium with neutron scattering. For a monoatomic liquid this effect is associated with the onset of a viscoelastic shear relaxation [3].


H. Sinn (a), F. Sette (b), U. Bergmann (b), Ch. Halcoussis (b), M. Krisch (b), R. Verbeni (b) and E. Burkel (a), Phys. Rev. Lett. 78, 1715 (1997)

(a) Universität Rostock (Germany)
(b) ESRF


[1] M. Canales, L.E. Gonzales, and J.A. Padro, Phys. Rev. E 50, 3656 (1994).
[2] P. H. K. de Jong, P. Verkerk, and L. A. de Graaf, J. NonCryst. Solids 156-158, 48 (1993).
[3] J. B. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980).




High-energy resonant photoemission in CeRh compounds

In many compounds, cerium exhibits unusual physical properties that are connected to its electronic structure: the partial delocalisation of the 4f electrons, which leads to an intermediate-valent ground state. In all the transition metals, lanthanide and actinide compounds, the quite high localisation of the d and f orbitals leads to an intermediate situation and it is still controversial if the bandlike or localised model is the most appropriate. Resonant valence band photoemission and Auger spectroscopy have shown clearly the presence of atomic like features. We present here first results of core level resonant photoemission and Auger spectroscopy. They clearly show that interference effects exist also between core levels.

We have measured 3d resonant photoemission spectra around the L3 absorption edge: we select one 3d photoemission line and measure its intensity sweeping the photon energy. The occurrence of a resonant profile shows evidence for a strong autoionisation process involving core levels (2p and 3d) [1]. The good energy resolution available at ID32 allowed us to isolate, in the CeRh3 photoemission spectra, the satellites corresponding to mainly 4f0, 4f1 and 4f2 character of the final state. The resonance occurs at different energy positions when we select different photoemission lines, allowing to identify unambiguously the main contributions to the different XAS structures to mainly 4f0, 4f1 and 4f2 contributions.

We have also performed resonant Auger measurements on two samples with different valences of Ce: Ce7Rh3 and CeRh3. The study was done on the L3M4,5N4,5 Ce Auger lines, and the spectra, obtained at different photon energies across the Ce L3 edge, are presented on Figure 47.

On the trivalent compound Ce7Rh3 , the spectra can be understood simply with the presence of a Raman-Auger process (double line appearing at constant binding energy), which resonates at the maximum of the white line of the XAS spectrum (5728 eV), and becomes afterwards the classical Auger process (at constant kinetic energy).

The same measurements done on the CeRh3 mixed valent compound are more complex to interpret. Up to 5728 eV (first maximum of XAS spectrum), we observe the Raman-Auger process at constant binding energy, with an increasing intensity. A surprising fact is that this double line still disperses to higher kinetic energies for photon energies between 5728 and 5738 eV, which indicates that the photoelectron created in this energy range (more than 10 eV above the edge) is still located on the absorbing atom. Between 5728 and 5738 eV, a second double line appears at varying kinetic energy, resonates at 5738 eV (second maximum of the XAS spectrum) and becomes afterwards the classical Auger process at constant kinetic energy. Knowing the previous resonant photoemission results, it seems therefore that the first doublet corresponds to 4f1 type final states, and the second doublet to 4f0 type final states. At high energy, the CeRh3 Auger spectra are dominated by the 4f0 final states.

In this work, high-energy resonant photoemission has allowed a better understanding of the absorption edge lines of Ce in mixed-valent compounds. This kind of spectroscopy provides new elements for a global knowledge of the electronic structure in these strongly-correlated systems.


P. Le Fèvre (a), H. Magnan (a) and D. Chandesris (a, b), J. Vogel (c), V. Formoso (d) and F. Comin (d), to be published.

(a) LURE, Orsay (France)
(b) CEA - SRSIM, Saclay (France)
(c) Laboratoire Louis Néel, CNRS, Grenoble (France)
(d) ESRF


[1] J. Vogel, H. Magnan, J.P. Kappler, G. Krill and D. Chandesris, J. Electron Spectrosc. Relat. Phenom. 76 (1995) 735.




Lineshape of X-ray critical scattering in systems with structural defects

In a large number of solids undergoing structural, magnetic or other second-order phase transitions, diffuse X-ray and neutron critical scattering with a puzzling scattering-vector dependence have been reported in the last few years. The surprising feature is that, in some samples, the observed profile S(k) is not at all well reproduced by a simple lorentzian lineshape, with an inverse width proportional to the correlation length at the observation temperature; the lineshape displays an unexpected sharper peak superimposed near the centre of the lorentzian. The sharper peak width seems to scale, as the temperature approaches the critical temperature, with a different critical exponent. Also, this central component does not have a lorentzian profile, but rather a steeper shape, better fitted by a lorentzian square or by a gaussian.

Two years ago, scientists from the ESRF Theory Group proposed an explanation of these "two length-scales" features in terms of a region near the sample surface with a sizeable concentration of structural defects, generating long-range random strain fields. The random strain fields can modify the critical behaviour of the near-surface region, corresponding to the sharp central component, while the bulk of the sample would retain the ordinary critical behaviour (the broader lorentzian component).

This proposal was plausible but some unexplained points remained, and an unambiguous experimental verification was not available.

The main open question was that, even if the strained region belongs to a different universality class of critical behaviour, with fluctuations characterised by a larger length scale, it is not clear why the corresponding S(k) should be non-lorentzian. This question was answered recently by the authors of the original proposal, in terms of an inhomogeneous broadening of the line. The random strain fields correspond to regions with expanded or compressed lattice parameter. This distribution of lattice parameters is characterised by an average value over the whole distorted volume, and by a variance, i.e. a mean quadratic deviation of the averages performed over regions with smaller volume from this value. When critical fluctuations occur, over a length scale corresponding to the correlation length, each fluctuating region has a slightly different average lattice parameter, and produces a lorentzian scattering profile centered at a slightly different value of the scattering vector. The resulting S(k) is therefore a superposition of lorentzians with centres slightly offset from one another. This superposition is better fitted by a lorentzian square lineshape than by a single lorentzian, as shown for a typical case in Figure 48. There is therefore a rather natural explanation for the steeper lineshape.

Finally, the explanation based on strain fields has recently received support by experiments on SrTiO3 (a system undergoing a structural phase transition) establishing a direct correlation between the intensity of the sharp component and the fluctuations of the lattice parameter at different probing depths inside the sample [U. Rütt et al., Hasylab, to be published].

In conclusion, the evidence pointing to structural defects and to related strain fields as the generic explanation for a surprising phenomenon observed with similar features in a wide variety of physical systems has become much more compelling.


M. Papoular (a, b), M.D. Núñez-Regueiro (b) and M. Altarelli (b), Phys. Rev. B, 56, 166 (1997)

(a) CRTBT/CNRS, Grenoble (France)
(b) ESRF




Excitons and the inelastic scattering of soft X-rays in graphite

Energy bands are central in the description of electron states in solids. Imagine injecting an additional electron into a crystal: its energy in this periodic environment is a function of its wavevector, assuming values in characteristic intervals, or "bands", of the energy axis. Likewise, if one imagines to remove an electron from the crystal, the energy of the "hole" left behind depends on the wavevector of the removed electron, defining the occupied "bands" of the system. The conceptual experiments described above find a partial implementation in photoemission and inverse photoemission, with a caveat represented by their sensitivity to surface, rather than bulk, properties and by other limitations.

X-ray experiments, in which the photon transfers an electron from an occupied band to an empty one (see Figure 49a), also attempt to unravel the band structure of materials, i.e. to determine the dependence of electron energies on wavevector. In a sense, this is like adding an extra electron and simultaneously removing another one from an occupied level, with essentially the same wavevector, because the wavevector q1 transferred by the photon is negligible. Recently, third generation synchrotron sources have made resonant inelastic scattering experiments practical, in which, after hitting the sample with X-rays of energy w1, outgoing photons of energy 2, produced by the recombination of a valence electron with the hole in the core level, are detected (see Figure 49c).

One could argue that the energy 1 - 2 transferred to the system corresponds to the energy difference of an empty and a full band at wavevector k (Figure 49c, with k = k').

Interpretations of experiments on graphite performed at the ALS in Berkeley [1] according to this picture were however fraught with difficulties. Why?

The explanation was provided by scientists in the ESRF Theory Group; they pointed out that the electron and the core hole created simultaneously (Figure 49a) interact strongly because they are electrically charged, and their mutual scattering destroys all memory of the initial wavevector before the emission of the 2 photon (see Figure 49b, showing relaxation of the intermediate state particles to wavevectors k' and k'- q1). The strength of the electron-hole interaction in graphite can be inferred by analysing X-ray absorption, in which only the process induced by the 1 photon occurs (or related experiments such as electron energy-loss). These experiments have shown that it is strong enough to produce bound electron-hole pairs (called "excitons"), revealed by a strong absorption peak near the K-edge threshold.

Screening of the long-range part of the Coulomb interaction in semi-metallic graphite reduces the electron-hole interaction to a short-range one; fitting its strength to the absorption results, and computing its effect on the inelastic scattering intensity (see Figure 50), excellent agreement with experiment is recovered. Thus, if on the one hand the direct mapping of the energy bands by inelastic scattering appears problematic, it is comforting to see that the exciton picture produces a consistent, accurate description of both absorption and inelastic scattering.


M. van Veenendaal (a) and P. Carra (a), Phys. Rev. Lett. 78, 2839 (1997).

(a) ESRF


[1] J.A. Carlisle et al., Phys. Rev. Lett. 74, 1234 (1995)