Incident energy and polarization-dependent resonant inelastic x-ray scattering study of ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$

We present a detailed Cu $K$-edge resonant inelastic x-ray scattering (RIXS) study of the Mott insulator ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ in the $1–7\mathrm{eV}$ energy loss range. As initially found for the high-temperature superconductor $\mathrm{Hg}{\mathrm{Ba}}_2\mathrm{Cu}{\mathrm{O}}_{4+\delta }$, the spectra exhibit a multiplet of weakly dispersive electron-hole excitations, which are revealed by utilizing the subtle dependence of the cross section on the incident photon energy. The close similarity between the fine structures for in-plane and out-of-plane polarizations is indicative of the central role played by the $1s$ core hole in inducing charge excitations within the $\mathrm{Cu}{\mathrm{O}}_2$ planes. On the other hand, we observe a polarization dependence of the spectral weight, and careful analysis reveals two separate features near $2\mathrm{eV}$ that may be related to different charge-transfer processes. The polarization dependence indicates that the $4p$ electrons contribute significantly to the RIXS cross section. Third-order perturbation arguments and a shake-up of valence excitations are then applied to account for the final-energy resonance in the spectra. As an alternative scenario, we discuss fluorescence-like emission processes due to $1s\to 4p$ transitions into a narrow continuum $4p$ band.

Figure 1

(Color online) The two scattering geometries used in this study and discussed in the text.

Figure 2

(Color online) RIXS spectra plotted versus final photon energy along with the absorption spectra monitored by total fluorescence yield for photons polarized (a) parallel and (b) perpendicular to the $\mathrm{Cu}{\mathrm{O}}_2$ planes. The shaded areas indicate the incident-energy ranges probed in the present study. All spectra were taken at $\mathbf{Q}=(3,0,0)$ and at different incident energies corresponding to the shaded ranges.

Figure 3

(Color online) (a) RIXS signal versus energy transfer for out-of-plane polarization at three representative incident energies at a momentum transfer of (3,0,0), which corresponds to the two-dimensional zone center (0,0). The lines are the result of a fit, as discussed in the text (reproduced from Ref. 12). (b) Contour plot of all zone-center scans, taken in $500\mathrm{meV}$ increments of $E_i$.

Figure 4

(Color online) Incident-energy dependence of the $\mathbf{E}\Vert c$ RIXS spectra for (a) $(\pi ∕4,0)$, (b) $(\pi ,0)$, (c) $(\pi ∕2,\pi ∕2)$, and (d) $(\pi ,\pi )$. The lines are the result of fits, as discussed in the text.

Figure 5

(Color online) Dispersion of the charge excitations for both in-plane and out-of-plane polarization along the two high-symmetry directions studied in the present work. The dashed lines indicate sinusoidal fits to the dispersion of the three lowest-energy features discerned with out-of-plane polarization. Previous results (Ref. 10), obtained with out-of-plane polarization, are shown for comparison.

Figure 6

(Color online) Five line scans at the zone center obtained with in-plane polarization.

Figure 7

(Color online) RIXS spectra obtained with $\mathbf{E}\Vert ab$ at (a) $(\pi ∕2,0)$ (b) $(\pi ,0)$ (c) $(\pi ∕2,\pi ∕2)$, and (d) $(\pi ,\pi )$.

Figure 8

(Color online) (a) ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ unit cell. In a Cu $K$-edge absorption process, several $4p$ states can be reached, depending on the polarization of the incident photon relative to the crystal axes. (b) $4p_{\sigma }$ configuration created by absorption of a $E_i\sim 8996\mathrm{eV}$ photon with $E\Vert ab$. (c) $4p_z$ configuration created by absorption of a $E_i\sim 8991\mathrm{eV}$ photon with $E\Vert c$. The emissive process discussed in the text corresponds to relaxation from state (b) to state (c).

Figure 9

(Color online) (a) Contour plot of ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ RIXS intensity: incident photon energy vs energy transfer for $\mathbf{E}\Vert c$ (from Ref. 10) and $\mathbf{E}\Vert ab$ (inset; present work). The white dashed lines indicate the two trends with different slope, as discussed in the text. (b) Calculations following third-order perturbation theory, as discussed in the text.