Inelastic Nuclear Resonant Scattering

Abstract

Soon after the discovery of the M⊙ssbauer effect it became clear that nuclear resonant absorption would be a very sensitive tool for the investigation of atomic motion. The influence of lattice dynamics on the absorption of γ-quanta by nuclei was extensively studied by Singwi & & Sj⊙lander [1]. Visscher predicted that lattice vibrations should manifest as sidebands of the absorption line [2]. However, in a conventional M⊙ssbauer experiment it is very difficult to observe such vibrational sidebands. One reason is that Doppler velocities of hundreds of m/s are necessary to tune the energy of the probing photon by typical phonon energies¹. Another limit results from the broadening of the resonance line due to the finite lifetime of the vibrational excitations. This reduces the peak absorption cross section by 6 to 7 orders of magnitude compared to the elastic peak. Despite of these difficulties a first experiment confirming the ideas of Visscher was performed in 1979, where the phonon spectrum and localized modes in TbO_x were measured [4, 5, 6] by using the 58-keV radiation of the ¹⁵⁹Tb M⊙ssbauer isotope. Doppler shifts of up to 30 meV were achieved by employing high-speed rotational motion of the radioactive source. The phonon density of states of TbO_x obtained by this method is shown in Fig. 5.1. However, due to the low count rates in such experiments, this technique could not compete with the upcoming method of inelastic neutron scattering and the idea was neglected for a long time. Instead, lattice dynamics using nuclear resonant absorption was studied indirectly via the Lamb-M⊙ssbauer factor and the second-order Doppler shift, see e.g. [7, 8]. The situation changed drastically with the advent of a) synchrotron radiation sources that surpassed the brilliance and spectral flux of radioactive sources by several orders of magnitude and b) x-ray optics that allowed for an energy tuning around the resonance with a resolution in the meV range. It was in 1995 when three groups almost simultaneously reported the first phonon spectra recorded by inelastic nuclear resonant absorption [9, 10, 11]. The experiments were performed at undulator-based beamlines with energy resolutions in the range of 6 meV. Since then the technique has made an impressive progress and nowadays phonon spectra are routinely recorded with sub-meV energy resolution [12]. It soon also became clear that the enormous brilliance of undulator radiation at third-generation synchrotrons renders this technique sensitive to very small sample volumes. In the following, the basic features of inelastic nuclear resonant scattering will be described and applications of this method to study vibrational properties of thin films and nanostructures will be demonstrated.