Robust Paramagnon and Acoustic Plasmon in a Photo-excited Electron-doped Cuprate Superconductor

TL;DR

Using time-resolved resonant inelastic X-ray scattering at the Cu $L_3$ edge, this work tracks the concurrent dynamics of spin (paramagnon) and charge (acoustic plasmon) excitations in optimally electron-doped Nd1-xCexCuO4 under femtosecond photoexcitation. The pump induces an anti-Stokes population of paramagnons and modest softening of the paramagnon dispersion near the zone center, while the acoustic plasmon loses energy and spectral weight, signaling a light-driven redistribution of charge carriers. Remarkably, the paramagnon and plasmon responses are temporally locked on a sub-100 fs timescale, revealing robust spin–charge intertwining in a non-equilibrium state. Time-dependent exact-diagonalization of a single-band Hubbard model and trRIXS simulations reproduce the qualitative trends, supporting a picture of light-induced spin scrambling and possible photo-induced charge-transfer effects that modulate the plasmon response. These findings demonstrate the resilience of coupled spin and charge collective modes under ultrafast excitation and open avenues for manipulating emergent phases in cuprates on ultrafast timescales.

Abstract

Characterizing the spin and charge degrees of freedom in high-temperature superconducting cuprates under non-equilibrium conditions provides new insights into their electronic correlations. However, their collective dynamics have been largely unexplored due to experimental challenges. Here, we use time-resolved resonant inelastic X-ray scattering (trRIXS) at the Cu $L_3$-edge to simultaneously track the collective spin (paramagnon) and charge (acoustic plasmon) dynamics in an optimally electron-doped cuprate driven out-of-equilibrium by a femtosecond pump laser pulse. Upon pumping, we observed an anti-Stokes signal associated with paramagnon generation, which modifies the paramagnon dispersion near the zone center, though the bandwidth remained unchanged, suggesting no significant alteration to spin exchange interactions. Simultaneously, in the charge sector, the acoustic plasmon's energy and spectral weight decreased, suggesting a light-induced redistribution of charge carriers. The variations of both the paramagnon and the plasmon were locked in time, demonstrating a robust intertwining between the spin and charge degrees of freedom on a femtosecond timescale, even in this non-equilibrium state.

Figures (12)

• Figure 1: Probing the paramagnon and plasmon in an electron-doped cuprate. a, A sketch for information of spin and charge degrees of freedom in a photoexcited cuprate, which can be deduced from paramagnon and acoustic plasmon dispersion. J, E$_p$, and $n_e$ represent the spin superexchange interaction, plasmon energy at a given momentum, and charge carrier density, respectively. b, Energy-momentum RIXS intensity map (left) taken before time zero ($\Delta t$= -2.0 ps). The waterfall plot of RIXS spectra are shown in the right panel. The red and blue markers indicate the paramagnon and plasmon peaks, respectively.
• Figure 1: Scattering and Pump-probe Geometry and NCCO reflectivity to 400 nm.a.$k_{in}$ and $k_{out}$ represent the momenta of the incident and outgoing x-ray, respectively. The scattering angle is 125$^{\circ}$. The ac plane of the crystal is in the scattering plane, as sketched. $q$ and $q_{\parallel}$ represent the magnitude of the momentum transfer and the projected in-plane momentum along the a-axis (i.e. $h$-direction). The $q_{\parallel}$ is defined to be positive when $\theta > 62.5^{\circ}$ (i.e. on the branch of grazing x-ray emission). The polarization of the incident x-ray lies in the scattering plane (i.e.$\pi$ polarization). The 400 nm pump is collinear with the incident x-ray with a $\sigma$ polarization b. Angle-dependent reflectivity for $\sigma$- and $\pi$-polarized 400 nm light. $\alpha_i$ denotes the angle-of-incidence as measured from the surface normal. Global fits of the Fresnel equations are shown as solid lines. Dashed lines are extrapolation of the fits.
• Figure 2: Light-driven variations in trRIXS spectra.a, Differential RIXS intensity map obtained by subtracting the RIXS map taken at $\Delta t=0.25$ ps from that taken at -2.0 ps. The red and blue markers indicated the peak positions of paramagnon and plasmon, same as those shown in Fig. \ref{['fig:Equilibrium']}b. b, Waterfall plot of the differential RIXS spectra shown in panel a. The red and blue ticks in the b indicate the variations associated near the peaks of paramagnon and plasmon, respectively. c, Differential spectral at $q_{\parallel} = -0.125 r.l.u.$ taken at different $\Delta t$. d, Time traces of quasi-elastic peak intensity for four representative $q_{\parallel}$s, obtained by integrating the intensity within an energy window of $\pm$ 60 meV with respect to the zero energy loss, as indicated by the gray shaded area in panel c.
• Figure 2: Illustration of energy gain spectrum in thermal equilibrium condition. When a finite population of bosonic modes exists, anti-Stokes scattering becomes detectable, resulting in an energy gain spectral weight in the dynamical structure factor ($S(q,\omega)$), which can be measured using inelastic neutron and X-ray scattering experiments. In the thermal equilibrium condition, modes are excited by thermal energy with a population following the Bose-Einstein statistics. Using the dissipation-fluctuation theorem, $S(q,\omega) = (1 + n(\omega, T)) \cdot \chi(q,\omega)"$, where $n(\omega, T)$ and $\chi(q,\omega)"$ are the Bose-Einstein distribution function and dynamical susceptibility $\chi(q,\omega)"$, respectively. In this simulation, we use the damped harmonic oscillator function to generate $\chi(q,\omega)"$ for three different scenarios: a sharp mode (a, $\omega > 2\Gamma$)), a damped mode ($\omega \sim 2\Gamma$), and an overdamped mode ($\omega < 2\Gamma$). Only in the situation of a sharp mode, a distinct peak can be resolved in the energy gain spectrum, which is the commonly known anti-Stoke peak. In the situations of a broad mode (b, c), the anti-Stoke peak is not resolvable, instead the $S(q,\omega)$ manifests as a broadened peak with significant spectral weight in the negative energy loss (energy gain). Regarding the case of photoexcitation, the dissipation-fluctuation theorem cannot be applied due to the non-equilibrium nature near time zero. Nevertheless, we expect a qualitative similarity for the spectral lineshape in the presence of photo-excited mode population. Since the paramagnon and plasmon are heavily damped in the optimally-doped electron-doped cuprates, we believe that a Gaussian function is a realistic and simplest model to fit the time dependence of the paramagnon and plasmon.
• Figure 3: Photo-induced variation in Paramagnon. a RIXS spectra at $q_{\parallel}=0.33$ r.l.u. before and after time-zero with the differential spectrum shown in the lower panel. b, Time traces of the integrated intensity within windows (i) and (ii) indicated in panel a. The error bars were estimated from the noise level of the RIXS spectrum. c. RIXS spectra at a representative moment near the Brillouin zone center. The fitted paramagnon is shown as the red-shaded area. The vertical line indicates the peak position of the fitted paramagnon excitation. d. Summary of the fitted paramagnon positions E$_{p}$ before (black markers) and after (red markers) time zero. e Momentum dependence of the normalized change of the paramagnon spectral weight (area of the fitted paramagnon) $\Delta A = {A^{(0.25 \text{ps})}} - {A^o}$, where ${A^o} = {A^{(-2.0 \text{ps})}}$. Shaded area are guide-to-the-eye. The error bars were estimated via standard propagation of uncertainty from the 95% confidence level from the fit of the peak parameter.