Research ArticlePHYSICS

Ultrafast dynamics of vibrational symmetry breaking in a charge-ordered nickelate

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Science Advances  24 Nov 2017:
Vol. 3, no. 11, e1600735
DOI: 10.1126/sciadv.1600735
  • Fig. 1 Equilibrium optical conductivity around the Ni–O bending mode of La1.75Sr0.25NiO4.

    (A) In-plane optical conductivity σ1(ω) of LSNO at different temperatures (dots) and best fits (lines) with the multi-oscillator model described in the text and the Materials and Methods. Curves are offset vertically for clarity, and the inset shows an expanded range conductivity with additional data in fig. S4. (B and C) Temperature dependence of the frequency and peak strength from the multi-oscillator fits. Lines are guide to eyes. Error bars are 1 SD. arb. units, arbitrary units. (D) Dispersion of the Ni–O bending mode, as obtained from density functional theory (DFT) calculations (see the Materials and Methods). Charge ordering reduces the size of the Brillouin zone, which corresponds to the zone folding of both the transverse optical (TO) and longitudinal optical (LO) modes from qCO = (0.55,0,1) back to Γ, with coordinates given in an orthorhombic notation (see the Materials and Methods). Solid dots indicate the zone-folded modes at qCO. Open dots mark second-order modes corresponding to an in-plane momentum 2qCO = (1.1,0,0), with some uncertainty on the TO energy due to the strong dispersion. Dotted line indicates LO dispersion including long-range Coulomb interactions, accounting for the observed bulk LO-TO splitting in Fig. 4D. The charge and spin stripe arrangements of LSNO are shown schematically.

  • Fig. 2 Photoinduced terahertz response.

    (A) Spectrum of the terahertz probe along with the optical conductivity of the Ni–O bending mode at 30 K. (B) Reference terahertz field E(t) (blue) reflected off the unexcited crystal, along with photoinduced field changes ΔE(t) at different pump-probe delays Δt. The LSNO crystal was excited at 800-nm wavelength with ≈0.5-mJ/cm2 incident pump fluence corresponding to 15-J/cm3 absorbed energy density (see section S1). The electro-optically sampled fields are plotted as a function of the field delay time t, with curves offset vertically for clarity. The oscillations at long delay times—ringing structures—indicate sharp features in the reflected fields. The reference field presents such oscillations only at low temperatures, where sharp resonances appear in the reflectivity spectrum (see fig. S4).

  • Fig. 3 Transient optical conductivity changes and model fits.

    (A) Two-dimensional plot of the photoinduced change of the real part of optical conductivity, Δσ1(ω), in the stripe phase of LSNO, as a function of pump-probe delay time Δt and probe frequency. (B) Photoinduced conductivity change at 1.8 ps (dots) along with the thermal difference from below to above TCO (lines). (C and D) Transient changes of the real parts of the optical conductivity and dielectric function at several pump-probe delays (dots). The black lines represent the best fit from the differential multi-oscillator model, with corresponding parameters shown in Fig. 4 (A to C) and figs. S7 and S8.

  • Fig. 4 Electronic conductivity and vibrational symmetry-breaking dynamics.

    Dynamics of the multi-oscillator model parameters: (A) electronic spectral weight, (B) peak strengths of the zone-folded phonon resonances, normalized to their equilibrium values, along with (C) their energy shifts. Error bars are 1 SD. Lines indicate the best fit of the data in (A) and (B) with a dynamic coupling model (see the Materials and Methods). The same model (rescaled) is shown for comparison also in (C), where it reproduces the transient energy shifts. (D) Imaginary part of the dielectric function Im(ε) and energy-loss function Im(−1/ε) in equilibrium at 30 K (lines) and upon excitation at Δt = 0 (open circles), with the bulk LO-TO splitting indicated (arrow). The multiscale dynamics is illustrated on the right-hand side: LO lattice distortions react quickly to the charge-order melting due to strong coupling via polar Coulomb interactions, whereas electric fields vanish along the stripes, resulting in a delayed reaction of the TO distortions.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/11/e1600735/DC1

    section S1. Thermal heating and excitation transport

    section S2. Time and frequency resolution in the optical-pump terahertz probe experiments

    fig. S1. Optical-pump terahertz-probe scheme.

    fig. S2. Energy level scheme and couplings used in the simulation.

    fig. S3. Simulated transient terahertz spectra resulting from different probe schemes.

    fig. S4. Equilibrium optical reflectivity around the bending mode of La1.75Sr0.25NiO4.

    fig. S5. Temperature dependence of the sharp modes below TCO.

    fig. S6. Fluence dependence of the mid-IR pseudogap dynamics.

    fig. S7. Dynamics of the ω3 zone-folded vibrational mode.

    fig. S8. Dynamics of the q = 0 bending phonon mode.

    fig. S9. Model comparison for the TO mode dynamics.

    References (3846)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Thermal heating and excitation transport
    • section S2. Time and frequency resolution in the optical-pump terahertz probe experiments
    • fig. S1. Optical-pump terahertz-probe scheme.
    • fig. S2. Energy level scheme and couplings used in the simulation.
    • fig. S3. Simulated transient terahertz spectra resulting from different probe schemes.
    • fig. S4. Equilibrium optical reflectivity around the bending mode of La1.75Sr0.25NiO4.
    • fig. S5. Temperature dependence of the sharp modes below TCO.
    • fig. S6. Fluence dependence of the mid-IR pseudogap dynamics.
    • fig. S7. Dynamics of the ω3 zone-folded vibrational mode.
    • fig. S8. Dynamics of the q = 0 bending phonon mode.
    • fig. S9. Model comparison for the TO mode dynamics.
    • References (38–46)

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