Sensitivity to hole doping of Cu $L_3$ resonant spectroscopies: Inelastic x-ray scattering and photoemission of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$

We present Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS) and resonant x-ray photoemission spectroscopy (RXPS) of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ ($x=0.0$, 0.13, and 0.27). RIXS is found to be much more sensitive to the hole doping level than resonant photoemission. RIXS allows us to determine the average energy of $dd$ excitations of both undoped and hole doped sites. The trade-off between the Raman and non-Raman spectral features depends on the doping level strongly in RIXS but weakly in RXPS. These experimental findings are consistently interpreted within a cluster model: The role of nonlocal core hole screening in the intermediate state is shown to be crucial. Nonlocal screening has an impact also on the interpretation of the $L_3$ x-ray absorption spectra in cuprates.

Figure 1

(Color online) A selection of the RIXS spectra for the three samples. The full circles refer to the $L_3$ main peak excitation, and the open circles to the $L_3+3\mathrm{eV}$ excitation. The spectra are as measured: one data point every $110\mathrm{meV}$. For LCO and $x=0.13$, the accumulation time was $8\min$ at $L_3$ and $16\min$ at $L_3+3\mathrm{eV}$. For $x=0.27$, the accumulation time was doubled.

Figure 2

(Color online) An overview of all experimental results. In all cases, the spectra are normalized to the intensity of the main peak visible in the given energy range. (a) Cu $L_3$ absorption spectra of LCO and LSCO. (b) RIXS measurements of LCO. (c) RIXS measurements of LSCO samples. (d) RXPS measurements of LSCO (the expanded green spectrum shows the Fermi level cut).

Figure 3

(Color online) (a) An expansion of RIXS spectra of LSCO with $x=0.13$). (b) An expansion of the comparison between two dopings in RIXS.

Figure 4

(Color online) Comparison, for the two doped LSCO samples, of the RXPS spectra excited above the main $L_3$ peak. The spectra are normalized to the same intensity at an $8\mathrm{eV}$ binding energy, different from Fig. 2. The $x=0.27$ sample gives a clearly lower Raman peak with respect to the $x=0.13$ one, whereas the peak positions are identical in the two samples (above $L_3+1.5\mathrm{eV}$, where the peak can be distinguished).

Figure 5

(Color online) [(a) and (b)] The conventional schematic representation of a resonant inelastic process leading to Raman (a) and non-Raman (b) behaviors of the spectral features. [(c) and (d)] The schematic representation of RIXS (c) and RXPS (d) at an undoped (left) and hole doped site (right). The line of the transition to the $3d^8\underset{̱}{L}$ set of final states is dashed to indicate that this path is not considered in our discussion because it does not give a sharp peak in RXPS.

Figure 6

(Color online) The experimental relative spectral weight of the non-Raman component in RIXS plotted as function of the incident photon energy for the three LSCO samples.