Unraveling the Nature of Charge Excitations in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ with Momentum-Resolved Cu $K$-Edge Resonant Inelastic X-Ray Scattering

The results of model calculations using exact diagonalization reveal the orbital character of states associated with different Raman loss peaks in Cu $K$-edge resonant inelastic x-ray scattering (RIXS) from ${\mathrm{La}}_2{\mathrm{CuO}}_4$. The model includes electronic orbitals necessary to highlight the nonlocal Zhang-Rice singlet, charge transfer, and $d\mathrm{\text{−}}d$ excitations, as well as states with apical oxygen $2p_z$ character. The dispersion of these excitations is discussed with prospects for resonant final state wave-function mapping. A good agreement with experiments emphasizes the substantial multiorbital character of RIXS profiles in the energy transfer range 1–6 eV.

Figure 1

Theoretical RIXS spectra at the $\Gamma$ point for (a) planar ${\mathrm{Cu}}_4{\mathrm{O}}_8$, and (b) planar ${\mathrm{Cu}}_8{\mathrm{O}}_{16}$ cluster (with the elastic resonance removed). The red dashed rectangle in (a) indicates the energy range of the RIXS plot in (b) (intensity $\times {10}^5$). The spectra are broadened with a 0.1 eV Lorentzian in energy loss and a core-hole lifetime of 1.0 eV.

Figure 2

Theoretical RIXS spectra at the $\Gamma$ point for (a) octahedral ${\mathrm{Cu}}_4{\mathrm{O}}_{16}$ with apical O, (b) planar ${\mathrm{Cu}}_4^{*}{\mathrm{O}}_8$ (with Cu $3d_{3z^2-r^2})$, and (c) octahedral ${\mathrm{Cu}}_4^{*}{\mathrm{O}}_{16}$ (with both Cu $3d_{3z^2-r^2}$ and apical O). (d)–(f) Schematic of the nonlocal intersite $d\mathrm{\text{−}}d$ excitation pathway for the results in (b) and (c): (d) $d^9$ ground state configuration, (e) intermediate ligand occupation on both plaquettes, and (f) final state configuration highlighting the intersite $d\mathrm{\text{−}}d$ excitation.

Figure 3

Theoretical RIXS spectra for ${\mathrm{Cu}}_4{\mathrm{O}}_8$ at $\Delta \mathbf{Q}=$ (a) (0,0), (b) ($\pi$, 0), and (c) ($\pi$, $\pi$). (d), (e), and (f) represent the same momentum points for ${\mathrm{Cu}}_4^{*}{\mathrm{O}}_{16}$. The dispersions of local molecular orbital and interplaquette apical CT excitations are indicated, respectively, by the blue and green dashed lines.

Figure 4

(a) Experimental [6] and (b) theoretical RIXS spectra for different $\Delta \mathbf{Q}$ at incident photon energy 8992.5 eV. The elastic part for $\Delta \mathbf{Q}=(0,0)$ is removed. The spectra in (b) are broadened with an energy-dependent Lorentzian increasing linearly with energy loss from 0.1 to 0.4 eV, 0.2 to 0.5 eV, and 0.3 to 0.6 eV, for $\Delta \mathbf{Q}=(0,0)$, ($\pi$, 0), and ($\pi$, $\pi$), respectively. (c) Experimental and (d) theoretical RIXS spectra convolved with $4p_z$ DOS at $\Delta \mathbf{Q}=(\pi ,\pi )$.