Research ArticleCONDENSED MATTER PHYSICS

Ultrafast time-resolved x-ray scattering reveals diffusive charge order dynamics in La2–xBaxCuO4

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Science Advances  16 Aug 2019:
Vol. 5, no. 8, eaax3346
DOI: 10.1126/sciadv.aax3346
  • Fig. 1 Pump-induced suppression and recoil of the charge order in LBCO.

    (A) Sketch of the experiment. Pump pulses of 1.55 eV perturb the charge order, which is then probed by resonant scattering of copropagating soft x-ray FEL pulses resonantly tuned to the Cu L3/2 edge. In this experiment, there is an additional surface miscut of 21° from the ab plane. (B) Time-dependent shift of the charge order wave vector in the H momentum direction for two different azimuthal sample angles, ϕ = 0 and π. Error bars represent the SD of the pseudo-Voigt peak position fit. The dashed line is a fit to the ϕ = 0 data (reflected for comparison to the ϕ = π points) with an exponential function of the type H(t) = H0 + Θ(t)(1 − et0)(δHet + δH) (note S2). (C) Transverse momentum scan in the H direction through the charge order peak for a selection of time delays. Dashed lines are fits using a pseudo-Voigt function (note S2). The fluorescence background has been subtracted. a.u., arbitrary units.

  • Fig. 2 tr-RIXS measurement of charge order in LBCO.

    (A) tr-RIXS spectra taken at a series of delay times, with the momentum tuned to the peak of the charge order, Qco (data are binned in 400-fs time steps to reduce counting noise in the plot). (B) Line plots of the same tr-RIXS spectra for a selection of time delays. Error bars represent Poisson counting error. The quasi-elastic scattering from the charge order appears at zero energy and is the only spectral feature influenced by the pump. The feature at −1.8 eV is a combination of dd excitations and Cu2+ emission, and the features at −6 eV are charge transfer excitations.

  • Fig. 3 Collective modes of charge order in LBCO propagate diffusively.

    (A) Solid lines: Time traces of the energy-integrated charge order scattering for a selection of momenta q=QQCO. The data are scaled to the same height and binned into 200-fs time steps to reduce counting noise in the plot. Dashed lines: Fits using a single exponential function (see note S6) show that the recovery time is highly momentum dependent. (B) Red points: Exponential decay parameter, γ(q), as a function of relative momentum difference, q=sgn(HHCO)QQCO. Error bars represent only the statistical uncertainties in the fits. Dashed line: Fit to the data using Eq. 1. Shaded area: Line shape of the unperturbed charge order reflection in equilibrium.

  • Fig. 4 Demonstration of dynamic scale invariance at long times.

    (A) Scaled momentum profiles (as in Fig. 1C) showing that the data collapse at late times for d = 3. Here, L(t) is taken to be the inverse half-width of the reflection at each time delay, t. The curves have been shifted in H to compensate for the momentum recoil at short times. (B) Compensated plot of the scaling function, L(t), taken to be the inverse half-width 1/g of the order parameter reflection (gray circles) or the cube root of the peak intensity at each time delay, t, i.e., by inverting the dynamical scaling relation S(0, t) = L3(t)F(0) (red line). The data show a power law of 0.03 at long times, indicating a logarithmic behavior.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/8/eaax3346/DC1

    Note S1. Pump-probe cross-correlation

    Note S2. Charge order peak rocking curves fit and background subtraction

    Note S3. Charge order peak rocking curves for ϕ ∼ π

    Note S4. Comparison between tr-RIXS and APD data

    Note S5. Response of the low-temperature tetragonal distortion peak

    Note S6. Raw time-dependent, energy-integrated peak intensities around QCO

    Note S7. Momentum-dependent recovery of the charge-ordered phase

    Fig. S1. Optical pump x-ray probe cross-correlation.

    Fig. S2. Pump-induced CO peak melting.

    Fig. S3. Time-dependent CO peak fit parameters.

    Fig. S4. CO peak shift at ϕ ∼ π.

    Fig. S5. Comparison between tr-RIXS and energy-integrated time dependence at Qco.

    Fig. S6. Dynamics of the low-temperature tetragonal distortion.

    Fig. S7. Raw time-dependent CO peak intensity.

    Fig. S8. Schematic representation of the scattering geometry.

    Table S1. Fit parameters along K projection.

  • Supplementary Materials

    This PDF file includes:

    • Note S1. Pump-probe cross-correlation
    • Note S2. Charge order peak rocking curves fit and background subtraction
    • Note S3. Charge order peak rocking curves for ϕ ∼ π
    • Note S4. Comparison between tr-RIXS and APD data
    • Note S5. Response of the low-temperature tetragonal distortion peak
    • Note S6. Raw time-dependent, energy-integrated peak intensities around QCO
    • Note S7. Momentum-dependent recovery of the charge-ordered phase
    • Fig. S1. Optical pump x-ray probe cross-correlation.
    • Fig. S2. Pump-induced CO peak melting.
    • Fig. S3. Time-dependent CO peak fit parameters.
    • Fig. S4. CO peak shift at ϕ ∼ π.
    • Fig. S5. Comparison between tr-RIXS and energy-integrated time dependence at Qco.
    • Fig. S6. Dynamics of the low-temperature tetragonal distortion.
    • Fig. S7. Raw time-dependent CO peak intensity.
    • Fig. S8. Schematic representation of the scattering geometry.
    • Table S1. Fit parameters along K projection.

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