Analysis of ultrafast X-ray diffraction data in a linear-chain model of the lattice dynamics
We present ultrafast X-ray diffraction (UXRD) experiments which sensitively probe impulsively excited acoustic phonons propagating in a SrRuO3/SrTiO3 superlattice and further into the substrate. These findings are discussed together with previous UXRD results (Herzog et al. in Appl. Phys. Lett. 96, 161906, 2010; Woerner et al. in Appl. Phys. A 96, 83, 2009; v. Korff Schmising in Phys. Rev. B 78, 060404(R), 2008 and in Appl. Phys. B 88, 1, 2007) using a normal-mode analysis of a linear-chain model of masses and springs, thus identifying them as linear-response phenomena. We point out the direct correspondence of calculated observables with X-ray signals. In this framework the complex lattice motion turns out to result from an interference of vibrational eigenmodes of the coupled system of nanolayers and substrate. UXRD in principle selectively measures the lattice motion occurring with a specific wavevector, however, each Bragg reflection only measures the amplitude of a delocalized phonon mode in a spatially localized region, determined by the nanocomposition of the sample or the extinction depth of X-rays. This leads to a decay of experimental signals although the excited modes survive.
KeywordsAcoustic Phonon Strain Wave Substrate Peak Coherent Phonon Heat Expansion
We thank Chris Milne, Renske van der Veen and Steve Johnson for their help with the experiments at the FEMTO-slicing beamline (XOSLA) of the Swiss Light Source at the PSI, Villigen, Switzerland and Ionela Vrejoiu from Max-Planck Institute for Microstructure Physics in Halle for fruitful discussions and for providing the sample experimentally investigated. M.B. would like to thank Dr. Michael Woerner (MBI Berlin) for very fruitful discussions on the model and simulations using “spacer sticks”. We gratefully acknowledge the financial support by the BMBF via grant No. 03WKP03A and the Deutsche Forschungsgemeinschaft via grant No. BA2281/3-1.
- 3.C. v. Korff Schmising, A. Harpoeth, N. Zhavoronkov, Z. Ansari, C. Aku-Leh, M. Woerner, T. Elsaesser, M. Bargheer, M. Schmidbauer, I. Vrejoiu, D. Hesse, M. Alexe, Ultrafast magnetostriction and phonon-mediated stress in a photoexcited ferromagnet. Phys. Rev. B 78, 060404(R) (2008) ADSCrossRefGoogle Scholar
- 11.Bauer, Multilayers, 2nd edn. (Springer, Berlin, 1998) Google Scholar
- 13.A.M. Lindenberg, I. Kang, S.L. Johnson, T. Missalla, P.A. Heimann, Z. Chang, J. Larsson, P.H. Bucksbaum, H.C. Kapteyn, H.A. Padmore, R.W. Lee, J.S. Wark, R.W. Falcone, Time-resolved X-ray diffraction from coherent phonons during a laser-induced phase transition. Phys. Rev. Lett. 84(1), 111–114 (2000) ADSCrossRefGoogle Scholar
- 17.A. Cavalleri, C.W. Siders, F.L.H. Brown, D.M. Leitner, C. Tóth, J.A. Squier, C.P.J. Barty, K.R. Wilson, K. Sokolowski-Tinten, M. Horn von Hoegen, D. von der Linde, M. Kammler, Anharmonic lattice dynamics in germanium measured with ultrafast X-ray diffraction. Phys. Rev. Lett. 85(3), 586–589 (2000) ADSCrossRefGoogle Scholar
- 20.P. Beaud, S.L. Johnson, A. Streun, R. Abela, D. Abramsohn, D. Grolimund, F. Krasniqi, T. Schmidt, V. Schlott, G. Ingold, Spatiotemporal stability of a femtosecond hard–X-ray undulator source studied by control of coherent optical phonons. Phys. Rev. Lett. 99(17), 174801 (2007) ADSCrossRefGoogle Scholar