Dynamic structure of electrons in Li metal: Inelastic synchrotron x-ray scattering results and interpretation beyond the random-phase approximation

Abstract

The dynamic structure factor S(q, tv) of electrons in Li-metal single crystals for q~~ [100], q~~[ 110],and q~~[ 111]with 0.28 a.u. & q & 1.4 a.u. was measured with 1-eV resolution by using inelastic scattering of synchrotron x radiation from DORIS II (Doppel-Ring Speicheranlage). Mainly for q & q, (q, is the plasmon cutoff vector) the fine structure of S(q, co) exhibits a strong dependence on the direction of the momentum transfer q. This crystal-lattice-induced peak structure is connected with minima of the combined density of states as due to band gaps across Bragg planes and can be interpreted as zone-boundary collective states within the limits of a two-band approximation.Comparison of the experimental results with model calculations of S(q,co), going beyond the random-phase approximation (RPA) by means of local-field corrections and also taking into account momentum-dependent lifetime effects for the inhomogeneous case (including band-structure effects) led to the following conclusions: (1) Most of the fine structure of S(q,co) is induced by the interaction of electrons with the ion lattice. (2) The overall shape of the S(q, co) spectra, mainly their strong deviation from corresponding homogeneous RPA results, is dominated by the momentum dependence of the inverse lifetime of quasiparticles with a steep rise at momentum po which makes possible decay of quasiparticle states into a plasmon. (3) The influence of exchange and correlation on S(q, co) via a local-field correction factor is found to be appreciable.A second source of experimental evidence for the dynamical structure factor is inelastic x-ray scattering.Thus further difficulties on the experimental side of the problem with S(q, to} of simple metals arise from the limitations of conventional x-ray source experiments, which are connected both with low photon flux in the scattered beam and low-energy resolution of the x-ray measurements compared with electron-energy-loss experiments. Even when using high-power rotating-anode generators, both the energy resolution of inelastic x-ray scattering ex-1986 The American Physical Society 33 DYNAMIC STRUCTURE OF ELECTRONS IN Li METAL: periments performed so far and the signal-to-background ratio are limited by the requirement of using unmonochromatized characteristic x-ray lines with rather large natural width and contaminated by bremsstrahlung.On the other hand, the x-ray measurements are much less influenced by multiscattering events, so that the spectra can give dirmt evidence of the full shape of S(q,co). , is a fine structure with at least two peaks (double-peak structure), where one peak exhibits nearly no dispersion and the other one follows roughly the free-electron RPA peak. This "universal double peak structure, " which has been interpreted by Platzman and Eisenbergers as an indication of an incipient Wigner electron lattice, has prompted much theoretical

Inelastic X-Ray Scattering as a Probe of the Many-Body Local-Field Factor in Metals

“…However, recent x-ray measurements [3] and firstprinciples evaluations of the dynamical density response of Al [4,5] and Be [5] have shown that band structure effects cannot be neglected. Unfortunately, calculations of the effects of dynamical correlations for electrons propagating in the actual band structure of Al-or any other metal-are not yet available.…”

X-ray absorption spectroscopy investigations on radioactive matter using MARS beamline at SOLEIL synchrotron

“…The incident X-ray beam is inelastically scattered (Compton scattering), a part of the incident photons energy is transferred to the sample through electronic transitions. Under certain experimental conditions, the same XAS features are seen in the Compton scattering profile peak when the transferred energy equals the binding energy of the probed element [36,37]. The use of hard X-ray with a large penetrating power can offer then a good alternative to soft X-ray XAS to probe low energy edges in samples with high absorbing environmental set-up such as confinements in case of radioactive samples, cryostat, high-pressure, high-temperature cells.…”

Ultrahigh-Energy-Resolution Inelastic X-Ray Scattering Spectroscopy

“…The broken lines give the range of intraband transitions of a free-electron gas in a weak lattice potential. The results are compared with the experimental results of [16]. The calculated dispersion curves of the zone-boundary collective states are shown according to [17] with the parameters for (a) taken from [18] and for (b) from [19].…”

“…These are excitations that lie in the energy interval that is accessible with the instrument INELAX. The excitations were investigated with an energy resolution of 38 meV [3,5,15] compared to earlier performed experiments [16]. The dispersion curve of the zone-boundary collective states in lithium in [001] direction derived from INELAX data is shown in Figure 8.…”