Abstract
The macroscopic characteristics of a material are determined by its elementary excitations, which dictate the response of the system to external stimuli. The spectrum of excitations is related to fluctuations in the density–density correlations and is typically measured through frequency-domain neutron1 or X-ray2,3,4 scattering. Time-domain measurements of these correlations could yield a more direct way to investigate the excitations of solids and their couplings both near to and far from equilibrium. Here we show that we can access large portions of the phonon dispersion of germanium by measuring the diffuse scattering from femtosecond X-ray free-electron laser pulses. A femtosecond optical laser pulse slightly quenches the vibrational frequencies, producing pairs of high-wavevector phonons with opposite momenta. These phonons manifest themselves as time-dependent coherences in the displacement correlations5 probed by the X-ray scattering. As the coherences are preferentially created in regions of strong electron–phonon coupling, the time-resolved approach is a natural spectroscopic tool for probing low-energy collective excitations in solids, and their microscopic interactions.
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Acknowledgements
The authors thank A. Barty, M. Bionta, J. Defever, S. Edstrom, C. Kenney, T. Huber, S. Nelson and K. Ramsey for their experimental assistance. This work was primarily supported by the US Department of Energy (DOE), Office of Basic Energy Sciences (BES) through the Division of Materials Sciences and Engineering under contract DE-AC02-76SF00515. Measurements were carried out at the LCLS at SLAC National Accelerator Laboratory. LCLS is an Office of Science User Facility operated for DOE Office of Science by Stanford University. M.E.K. was supported by the DOE Office of Science Graduate Fellowship Program. G.N. and S.G. were supported by the AMOS program within the Chemical Sciences, Geosciences, and Biosciences Division, DOE, BES. M.F. acknowledges financial support from the Volkswagen Foundation. F.Q. and K.S-T. acknowledge support by the German Research Council (DFG) through the Collaborative Research Center 616 ‘Energy Dissipation at Surfaces’. J.L. was supported by the Swedish Science Council (VR) A.H. was supported by AWE. J.S.W. is grateful for support from the UK EPSRC under grant no. EP/H035877/1.
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D.A.R. and M.T. conceived the experiment and the framework for the data interpretation, M.T. and M.F. analysed the data, K.G., S.F. and J.S.W. contributed to data interpretation, C.U. and G.W. prepared Bi samples for the precise timing overlap between the X-ray and optical pulses, and M.T. and D.A.R. wrote the manuscript with input from all other authors. The experiment was carried out by M.T., M.F., J.C., M.P.J., M.C., D.M.F., K.G, S.G., A.H., S.L.J., M.E.K., J.L., H.L., A.M.L., G.N., F.Q., K.S-T., D.Z. and D.A.R. The X-ray pump–probe instrument was operated by M.C. D.M.F., H.L. and D.Z.
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Trigo, M., Fuchs, M., Chen, J. et al. Fourier-transform inelastic X-ray scattering from time- and momentum-dependent phonon–phonon correlations. Nature Phys 9, 790–794 (2013). https://doi.org/10.1038/nphys2788
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DOI: https://doi.org/10.1038/nphys2788
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