Tracking the local order parameter through the Hubbard exciton decoherence time in the Mott-Hubbard insulator LaVO3

Abstract

The prototypical Mott-Hubbard insulator LaVO3 undergoes a structural phase transition accompanied by the onset of spin and orbital ordering below 140 K. By combining ultrafast optical pump-probe spectroscopy and two-dimensional electronic spectroscopy, we investigate the interplay between fluctuations of the local spin and orbital order parameter and the lifetime of high-energy electron-hole excitations. Specifically, we demonstrate that the pump-induced perturbation of the order parameter leads to a change of the Hubbard exciton decoherence time and, consequently, of its homogeneous linewidth. Dynamical mean-field theory calculations confirm that the exciton scattering rate is crucially affected by the degree of order of the spin and orbital lattices in LaVO3. Our results demonstrate that multi-dimensional ultrafast optical spectroscopy can be used to track the dynamics of the order parameter, thus opening new routes in the study of correlated quantum materials characterized by intertwined orders.

Figures (5)

• Figure 1: a) Spin and orbital ordered structure of LaVO_3 for $T < T_c$. b) Equilibrium optical conductivity (real part $\sigma_1$) of LaVO_3 for light polarization parallel to the $c$-axis at three different temperatures across $T_c$ (from Ref. miyasaka2002), fitted using a multi-peak Drude-Lorentz model. The lowest energy component, highlighted by the filled area in the graph, is associated with a Hubbard exciton resonance. c) Sketch of a pump-probe experiment: the pump pulse generates an out-of-equilibrium state, whose time-evolution is detected by the probe (delayed by $\Delta t$) that measures the pump-induced changes in the reflectivity of the sample. d) Optical pump-probe measurements in reflection geometry at different temperatures, above (left panel) and below (right panel) $T_c$. The measurements have been performed with 1.65 eV photon energy pump, 1.77 eV photon energy probe, and 0.1 mJ/cm$^2$ excitation fluence.
• Figure 2: Broadband pump-probe measurements performed with 1.4 eV photon energy pump and supercontinuum probe in reflection geometry. The transient reflectivity spectra are plotted as a function of pump-probe time delay (horizontal axis) and probe photon energy (vertical axis) in a) and c), for sample temperatures of 110 K and 40 K, respectively. The pump incident fluence is 1 mJ/cm$^2$. The white lines plotted on top represent the time evolution of the signal at 1.77 eV and display the same behavior described in Fig. \ref{['fig1: LaVO3 intro']}d. Panels b) and d) report the transient reflectivity spectra at two selected delays, highlighted in a) and c) by black dashed (30 ps) and dotted (250 ps) lines. Red and blue solid lines are differential fits of the $\Delta R/R$ spectra, performed as described in Appendix C.
• Figure 3: a,b) Time evolution of the parameters describing the out-of-equilibrium state of the HE component, retrieved from the fitting analysis of the $\Delta R/R$ data in Fig. \ref{['fig3: dRR_maps']}. In panel a), the variation of Hubbard exciton's plasma frequency, $\omega_{p,HE}-\omega_{p,HE}^{eq}$ ($\omega_{p,HE}^{eq}$ being the equilibrium value), is plotted as light blue and orange dots (left $y$-axis) for the two measured temperatures (40 K and 110 K, respectively), and is compared to the decay of the number of electronic excitations $n_{exc}$ (red and blue solid lines, right $y-$axis). Similarly, in panel b), the variation of Hubbard exciton's width $\Gamma_{HE}-\Gamma_{HE}^{eq}$ (light blue and orange dots, left $y$-axis), $\Gamma_{HE}^{eq}$ being the equilibrium linewidth, is compared to the dynamics of the order parameter $\epsilon$ (red and blue solid lines, right $y-$axis), obtained from numerical integration of Eq. \ref{['eq: eps time evo']} with $g = 0.6$, $\alpha = 5$, $\gamma = 0.01$ ps$^{-1}$. c) Sketch of the free energy for a first-order phase transition as a function of the order parameter $\epsilon$ and its pump-induced perturbation. The photoexcited electronic population couples to the order parameter, whose dynamics is governed by the free energy potential. d) Cartoon of the Hubbard exciton in the spin and orbital ordered background. Disruption of the ordered background due to pump excitation leads to a reduction of the intrinsic lifetime (decoherence time).
• Figure 4: a) Sketch of a multi-dimensional spectroscopy experiment, employing two phase-coherent pump pulses, delayed by a variable time delay $t_1$, and a probe pulse delayed by $t_2$. b) 2DES measurement performed at $T = 140$ K, $t_2$ = 40 ps and excitation fluence 1.4 mJ/cm$^2$. The 2D spectrum (arb. units) is normalized over both the probe and pump spectra. c) Anti-diagonal profiles of 2D spectra at two different time delays $t_2$ (red and blue lines); they are obtained from a line-cut along the direction indicated by the black dashed line in b) and are integrated over 25 meV width. The plotted values are normalized in intensity for comparison purposes. d) The top panel reports the pump-probe dynamics (grey line) measured in the same experimental configuration of the 2DES data in b) and c), with broadband (1.45-1.9 eV) and degenerate pump and probe beams at $T = 140$ K and 1.4 mJ/cm$^2$ excitation fluence. The colored dots indicate the $t_2$ delays where 2D spectra are collected. In the bottom panel, the relative variation of the anti-diagonal linewidth ($\Gamma_{hom}$, FWHM) extracted from 2D spectra is plotted as a function of $t_2$. It is estimated as $\Delta \Gamma_{hom} / \Gamma_{hom,0} = [\Gamma_{hom}(t_2)-\Gamma_{hom}(t_2 = 100 ~\text{fs})]/\Gamma_{hom}(t_2 = 100 ~\text{fs})$, where the value obtained at the shortest time delay, $t_2$ = 100 fs, is used as reference ($\Gamma_{hom,0} = \Gamma_{hom}(t_2 = 100 ~\text{fs})$).
• Figure 5: Blue markers (left $y$-axis) show the temperature dependence of the variation in the scattering rate - obtained by DFMT calculation as $\text{Im}(\Sigma)$ (Fig. S9 Supplemental Material) - upon suppression of spin and orbital orders. The red solid line (right $y$-axis) shows the temperature-dependence of the order parameter $\epsilon_{eq}$, estimated as the position of the minimum of the free energy in Eq. \ref{['eq: free energy eq']} with $\alpha = 5$, plotted in the inset.