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.