Low Energy Electronic Excitations in the Layered Cuprates Studied by Copper $L_3$ Resonant Inelastic X-Ray Scattering

We have measured the resonant inelastic x-ray scattering (RIXS) spectra at the Cu $L_3$ edge in a variety of cuprates. Exploiting a considerably improved energy resolution (0.8 eV) we recorded significant dependencies on the sample composition and orientation, on the scattering geometry, and on the incident photon polarization. The RIXS final states correspond to two families of electronic excitations, having local ($dd$ excitations) and nonlocal (charge-transfer) character. The $dd$ energy splitting can be estimated with a simple crystal field model. The RIXS at the $L_3$ edge demonstrates here a great potential, thanks to the resonance strength and to the large $2p$ spin-orbit splitting.

Figure 1

The RIXS spectra measured at the Cu $L_3$ peak on three insulating and three superconducting cuprates at grazing incidence and V polarization [GI,V]. The energy scale is given in relative scattered photon energy, having aligned the highest energy peak to zero, by implicitly assigning it to an elastic peak. All the spectra are as measured. The topmost curve shows the Cu $L_3$ absorption peak of ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_4$. Inset: the local $D_{4h}$ crystal field symmetry used in the calculations.

Figure 2

Upper panel: measured RIXS spectra for CuO, ${\mathrm{La}}_2{\mathrm{CuO}}_4$, and ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_4$ in [GI,V] geometry. Bottom panel: calculated RIXS spectra in $D_{4h}$ crystal field symmetry. The spectra are given with a 0.05 eV Lorentzian broadening in the final state solid lines) and after a 0.8 eV Gaussian broadening (dashed lines). CuO and ${\mathrm{La}}_2{\mathrm{CuO}}_4$ are calculated, with the energy parameters of Table , for a randomly oriented ${\mathrm{Cu}}^{2+}$ ion, ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_4$ in the oriented [GI,V] geometry.

Figure 3

Upper panel: RIXS spectra of ${\mathrm{Sr}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$ measured at grazing and normal incidence with V and H polarizations ([GI,V], [NI,V], [NI,H]). Bottom panel: calculated spectra for the same scattering geometries. Inset: experimental geometry, where $\beta =70°$ is the scattering angle and $\alpha =0°$ ($80°$) is the incidence angle in the NI (GI) configuration.