Electronic structure of doped lanthanum cuprates studied with resonant inelastic x-ray scattering

We report a comprehensive Cu $K$-edge resonant inelastic x-ray scattering (RIXS) investigation of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO) for $0⩽x⩽0.35$, stripe-ordered ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ (LBCO), and ${\mathrm{La}}_2{\mathrm{Cu}}_{0.96}{\mathrm{Ni}}_{0.04}{\mathrm{O}}_4$ (LCNO) crystals. The RIXS spectra measured at three high-symmetry momentum-transfer (q) positions are compared as a function of doping and for the different dopants. The spectra in the energy range 1–6 eV can be described with three broad peaks, which evolve systematically with increased doping. The most systematic trend was observed for $\mathbf{q}=(\pi ,0)$ corresponding to the zone boundary. As hole doping increased, the spectral weight transfer from high energies to low energies is nearly linear with $x$ at this q. We interpret the peaks as interband transitions in the context of existing band models for this system, assigning them to Zhang-Rice band$\to$upper Hubbard band, lower-lying band$\to$upper Hubbard band, and lower-lying band$\to$Zhang-Rice band transitions. The spectrum of stripe-ordered LBCO was also measured, and found to be identical to the correspondingly doped LSCO, except for a relative enhancement of the near-infrared peak intensity at $~$1.5–1.7 eV. The temperature dependence of this near-infrared peak in LBCO was more pronounced than for other parts of the spectrum, continuously decreasing in intensity as the temperature was raised from 25 to 300 K. Finally, we find that 4% Ni substitution in the Cu site has a similar effect on the spectra as does Sr substitution in the La site.

Figure 1

Progression of RIXS spectra of LSCO at momentum transfers, corresponding to (a) near-zone center, (b) the zone boundary $\mathbf{q}=(\pi ,0)$, and (c) zone boundary $\mathbf{q}=(\pi ,\pi )$, as the sample doping is increased. The curves are vertically shifted with respect to each other for clarity. For $x=0.12$, the bigger orange circles with black outlines, with less point density at higher energy loss, are from the higher-resolution measurement, as described in the text. The insets show the combined, unshifted curves overlayed with each other. The data for $x=0.30$ and $x=0.25$ are from Ref. 31 while the $x=0$ data are from Ref. 29. The data were normalized as specified in the text. The solids lines in (b) are fits to two Lorentzians.

Figure 2

Comparison of the effect of light doping for LSCO and LCNO at three momentum transfers: (a) near-zone center, (b) $\mathbf{q}=(\pi ,0)$, and (c) $\mathbf{q}=(\pi ,\pi )$.

Figure 3

The spectral weight for $\mathbf{q}=(\pi ,0)$ as a function of doping, where the RIXS intensity has been integrated in the low-energy (1–2 eV) and high-energy ranges (2.5–6 eV).

Figure 4

The (a) center energy and (b) peak intensity of the 3.3-eV peak at $\mathbf{q}=(\pi ,0)$, obtained from the fitting procedure described in the text. The lines are guides for the eye.

Figure 5

The low-energy part of the RIXS spectra for momentum transfers of (a) $q⩽0.1\pi$ and (b) $q=(\pi ,0)$. The spectra are displaced along the $y$ axis for clarity, and the solid lines are Lorentzian fits.

Figure 6

(Filled circles) Fit parameters of NIR excitation peak vs doping for momentum transfers of $q~0$ (left-hand side) and $q=(\pi ,0)$ (right-hand side). The parameters are center energy of the NIR peak (top) and full width at half maximum (bottom). See text for details of the fitting procedure. Also shown in (a) and (c) is a curve of the undoped center energy, shifted by the chemical potential obtained from photoemission measurements of Ino et al. (Ref. 41) (unfilled squares). The line in graphs (b) and (d) is a guide for the eye.

Figure 7

(a) Comparison of ${\mathrm{La}}_{1.88}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_4$ and ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ spectra measured at $\mathbf{q}=(\pi ,0)$ and $T=28$ K. (b) Temperature dependence of the ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ $\mathbf{q}=(\pi ,0)$ spectra, after subtraction of elastic line. The inset shows the intensity of the NIR component as obtained from fits described in the text.

Figure 8

(a) Rigid-band model density of states vs energy profile, showing the lower-lying bands (LLB), Zhang-Rice band (ZRB), and the upper Hubbard band (UHB). Gray filling represents the occupied states. The lower Hubbard band (LHB) is also shown for completeness. Transitions between these bands, which we assign to peaks in the RIXS spectra and signified by the arrows, are labeled by numbers: LLB$\to$ ZRB (1), ZRB$\to$UHB (2), LLB$\to$UHB (3). The corresponding transitions in the spectra are shown in (b), for $x=0$ and $x=0.30$ at $\mathbf{q}=(\pi ,0)$. For $x=0$, $E_F$, as shown by the dashed line in (a), would be shifted to the right-hand side, past the edge of the ZRB, while $x=0.30$ would correspond to $E_F$ being near the left edge of the ZRB.