Phonon spectroscopy with sub-meV resolution by femtosecond x-ray diffuse scattering

We present a reconstruction of the transverse acoustic phonon dispersion of germanium from femtosecond time-resolved x-ray diffuse scattering measurements at the Linac Coherent Light Source. We demonstrate an energy resolution of 0.3 meV with a momentum resolution of $0.01{\mathrm{nm}}^{-1}$ using 10-keV x rays with a bandwidth of $\sim 1\mathrm{eV}$. This high resolution was achieved simultaneously for a large section of reciprocal space including regions closely following three of the principal symmetry directions. The phonon dispersion was reconstructed with less than 3 h of measurement time, during which neither the x-ray energy, the sample orientation, nor the detector position were scanned. These results demonstrate how time-domain measurements can complement conventional frequency domain inelastic-scattering techniques.

Figure 1

(a) Schematics of the grazing incidence pump-probe setup. A multishot averaged thermal diffuse scattering pattern is shown in gray scale. Five distinct locations are indicated by the colored dots on the CSPAD detector. (b) The time evolution of the normalized scattering intensity as a function of pump-probe delay [at the five locations indicated by the corresponding colored dots on the scattering pattern in (a)] is shown using the corresponding color scheme. The reduced $\left(hkl\right)$ positions are indicated for each time trace.

Figure 2

Reconstruction of the phonon dispersion relation along the path in reciprocal space indicated in the right inset. Locations of this path close to high-symmetry points in the BZ are labeled with their respective wave vectors in reciprocal lattice units (r.l.u.). The left inset shows the BZ with the high-symmetry points. The right inset shows the multishot averaged diffuse scattering pattern and superimposed path (as indicated by the dashed line) taken to obtain the main plot. The dashed box near ${\mathrm{\Gamma }}_2$ in the main plot indicates the region that is magnified in Fig. 3.

Figure 3

(a) Detailed view of the dispersion relation presented in the dashed box in Fig. 2. This was obtained from a single delay scan over 8 min. (b) Energy line outs for the two wave vectors as indicated in (a) by the dashed and solid lines.