Coupling between dynamic magnetic and charge-order correlations in the cuprate superconductor ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$

Charge order has now been observed in several cuprate high-temperature superconductors. We report a resonant inelastic x-ray scattering experiment on the electron-doped cuprate ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_4$ that demonstrates the existence of dynamic correlations at the charge-order wave vector. Upon cooling we observe a softening in the electronic response, which has been predicted to occur for a $d$-wave charge order in electron-doped cuprates. At low temperatures, the energy range of these excitations coincides with that of the dispersive magnetic modes known as paramagnons. Furthermore, measurements where the polarization of the scattered photon is resolved indicate that the dynamic response at the charge-order wave vector primarily involves spin-flip excitations. Overall, our findings indicate a coupling between dynamic magnetic and charge-order correlations in the cuprates.

Figure 1

(a) Cu-$L_3$ RIXS spectra for selected values of in-plane momentum transfer $H$. The curves are vertically offset for clarity. (b) Energy-momentum color map of RIXS excitations. (c) EI-RXS momentum dependence obtained from the integrated RIXS spectra in the $(-0.06,10)$ eV range. The measurements were performed on the non-SC sample, at 25 K, in $\sigma$ scattering geometry. The color scale in (b) is logarithmic and in the same units as (a).

Figure 2

Energy-momentum structure of the excitations in NCCO 0.106 measured with $\sigma$ scattering at (a) 25 and (b) 300 K. The dashed line in (a) marks $Q_{\mathrm{CO}}$ obtained from the energy-integrated data in Fig. 1 [41]. The variable pixel size in (a) and (b) reflects the values of $H$ and $E$ for which the raw data were acquired.

Figure 3

(a) 25-K RIXS signal integrated over different energy ranges showing that the peak at $Q_{\mathrm{CO}}$ originates from energies below 900 meV. (b), Energy-integrated RIXS for 25 and 300 K in the energy ranges marked on the figure. The line for the $(0.9,10)$ eV data in (a) and the line for $(-60,60)$ meV, 300-K data in (b) are polynomial fits to the data. All the other lines represent a fit to the data using a polynomial for the background plus a Gaussian function for the peak. The data are vertically offset for clarity. All data on the non-SC sample in $\sigma$ geometry.

Figure 4

(a) 25-K high-energy-resolution (35 meV) spectra taken on the non-SC NCCO, with incoming $\sigma$ polarization, for two $H$ values, on and off $Q_{\mathrm{CO}}$. (b) Energy-momentum structure for the excitations in the non-SC NCCO in the $\sigma {\pi }^{\prime }$ channel, which is primarily composed of single spin-flip processes. The color plot in (b) was generated from eight polarization-resolved spectra [41].