Figure 1

(a) Resonant inelastic x-ray scattering spectra of ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_4$ as a function of energy loss at some representative incident x-ray energies $E_i$. The scattering vector is fixed at $\mathbf{Q}=(0.5,0,12)$. The strong intensity in the spectra of $E_i=8986\mathrm{eV}$ at high excitation energy comes from the Cu $K{\beta }_5$ fluorescence. (b) X-ray absorption spectra measured by the fluorescence method. The polarization of the x rays ($\epsilon$) is parallel to the $a$ or $c$ axes of the crystal. The thick arrow indicates the energy used for momentum-dependent RIXS measurements.Reuse & Permissions

Figure 2

Momentum dependence in ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_4$ along (a) the $c^{*}$ axis and (b) $(\pi ,0)$ and (c) $(\pi ,\pi )$ directions. $E_i=8991\mathrm{eV}$. The solid symbols are raw data, and the open ones in (b) and (c) are data from which the quasielastic tail and the scattering at higher energy (dashed lines) are subtracted. (d) Contour plot of the RIXS intensity. After subtraction of the quasielastic and high-energy contributions [open symbols in (b) and (c)] the data are normalized for the maximum intensity at each momentum and interpolated smoothly. (e) Comparison of the RIXS spectra to ${\mathrm{Nd}}_{1.925}{\mathrm{Ce}}_{0.075}{\mathrm{CuO}}_4$. The inset of (a) shows a schematic view of the experimental condition with scattering vector ($\mathbf{Q}$), wave vector of the incident (${\mathbf{k}}_i$) and scattered (${\mathbf{k}}_f$) photons, and polarization of the incident photon (${\epsilon }_i$). The direction to the right is $[100]$ for the scan of $\mathbf{Q}=(h,0,l)$ or $[110]$ for the scan of $\mathbf{Q}=(h,h,l)$. The thick arrows correspond to the configuration of $\mathbf{Q}=(0.5,0,12.5)$.Reuse & Permissions

Figure 3

(a) The RIXS spectrum of an electron-doped $4\times 4$ Hubbard cluster with long-range hopping terms. The electron density is $18/16=1.125$, and the model parameters are $t^{\prime }/t=-0.25$, $t^{\prime \prime }/t=0.12$, $U/t=8$, $U_c/t=10$, and $\Gamma /t=3$ with $t=0.3\mathrm{eV}$. The $\delta$ functions are convoluted with a Lorentzian broadening of $0.8t$. Dashed lines: $N(\mathbf{q},\omega )$ for the same cluster. (b) The calculated $1s-4p_{\sigma }$ x-ray absorption spectrum (XAS) with a Lorentzian broadening of $3t$. The vertical arrow denotes $E_i$ for RIXS. (c) Momentum dependence of the peak positions of RIXS (squares), together with those of $N(\mathbf{q},\omega )$ for $4\times 4$ (circles) and $\sqrt{18}\times \sqrt{18}$ (crosses) clusters.Reuse & Permissions