Comparing the oscillation phase in optical pump-probe spectra to ultrafast x-ray diffraction in the metal-dielectric SrRuO${}_3$/SrTiO${}_3$ superlattice

We measured the ultrafast optical response of metal-dielectric superlattices by broadband all-optical pump-probe spectroscopy. The observed phase of the superlattice mode depends on the probe wavelength, making assignments of the excitation mechanism difficult. Ultrafast x-ray diffraction data reveal the true oscillation phase of the lattice which changes as a function of the excitation fluence. This result is confirmed by the fluence dependence of optical transients. We set up a linear chain model of the lattice dynamics and successfully simulated the broadband optical reflection by unit-cell resolved calculation of the strain-dependent dielectric functions of the constituting materials.

Figure 1

(a) UXRD measurements of the (0 0 116) reflection of the SRO/STO SL recorded at the SLS ${\lambda }_{\mathrm{pump}}=800$ nm for different fluences. (b) Strain amplitude derived from the data in panel (a) by comparison to a dynamical x-ray diffraction simulation (Ref. 20). (c) Oscillation phase extracted from the measured data using the fit function of eq. 1. The error bars correspond to a 68$\%$ confidence interval from fitting the relative phase. The absolute phase is obtained by comparison to the experiments at the laser-based plasma source discussed in Fig. 4.

Figure 2

(a) Measured optical reflectivity ${\lambda }_{\mathrm{probe}}=670$ nm for different fluences. The dotted line indicates the incoherent background contribution which is subtracted from each transient to fit the oscillations and to plot Fig. 3a. The thin dashed line shows the UXRD measurement for comparison. (b) Oscillation amplitude as a function of the fluence. (c) Comparison of the relative oscillation phase of the optical signal (solid circles) to the phase determined by UXRD [open squares reproduced from Fig. 1c]. The error bars of the relative phase are determined from the maximum deviation of phases in two measurement series. The absolute phase is shifted to agree with the UXRD data.

Figure 3

(a) Experimentally measured change of the optical reflectivity from ${\lambda }_{\mathrm{probe}}=500$ to 780 nm at normal incidence after exciting the sample at ${\lambda }_{\mathrm{pump}}=800$ nm as a function of time delay. The electronic response and a slowly varying signal contribution have been subtracted as exemplified in Fig. 2a. (b) Results from the simulation described in the text. The slowly varying background has been subtracted as well. The simulations show that the spectral position of the phase change at 560 and 720 nm is given by an interference of light reflected from the surface and the interface to the substrate.

Figure 4

(a) All-optical response measured in the same configuration for ${\lambda }_{\mathrm{pump}}=800$ nm and ${\lambda }_{\mathrm{probe}}=800$ nm. The schematic shows the combined optical/x-ray pump-probe geometry. Optical (red) and x-ray (green) probe pulses collinearly propagate through a slit towards the sample. Both emerge from the laser focus on the copper tape which generates the x-ray pulses and which is removed for optical probing. (b) UXRD data from the laser-based plasma source (red dots) with removed x-ray optics to precisely determine the zero time delay. The signal is shifted by 250 fs to earlier times with respect to the data as measured, according to the analysis described in the text. For comparison we show the UXRD data measured at the SLS [open circles, reproduced from Fig. 1a]. The blue line is the simulated UXRD signal based on the calculated lattice dynamics. (c) Simulated average strain in STO (solid) and SRO (dashed) pattern which is consistent with the observed x-ray diffraction signal. (d) Simulated optical reflectivity for three selected probe wavelengths. (e) Corresponding color-coded horizontal cuts through Fig. 3a.