Resonant inelastic x-ray scattering study of charge excitations in superconducting and nonsuperconducting PrFeAsO${}_{1-y}$

We report the first observation by momentum-resolved resonant inelastic x-ray scattering of charge excitations in an iron-based superconductor and its parent compound, PrFeAsO${}_{0.7}$ and PrFeAsO, respectively, with two main results. First, using calculations based on a 16-band $dp$ model, we show that the energy of the lowest-lying excitations, identified as $dd$ interband transitions of dominant $xz,yz$ orbital character, exhibits a dramatic dependence on electron correlation. This enables us to estimate the Coulomb repulsion $U$ and Hund's coupling $J$, and to highlight the role played by $J$ in these peculiar orbital-dependent electron correlation effects. Second, we show that short-range antiferromagnetic correlations, which are a prerequisite to the occurrence of these excitations at the $\Gamma$ point, are still present in the superconducting state.

Figure 1

(a) Incident energy dependence of the RIXS spectrum measured on PrFeAsO at $q=(\pi ,\pi )$. The top and bottom panels are, respectively, centered around the resonance of the CT and $dd$ features. The vertical shift between the spectra in the top panel is half of that in the bottom panel. (b) Fe $K$ edge measured in the partial fluorescence yield on PrFeAsO and PrFeAsO${}_{0.7}$ for both $\varepsilon //a$ and $\varepsilon //c$ incident photon polarization conditions. (c) Fe $3d$ and As $4p$ density of states calculated for LaFeAsO.

Figure 2

(a) Two-dimensional folded Brillouin zone. The colored dots correspond to the color of the plots in panels (c) and (d). (b) Scattering geometry with the incident photon polarization $\varepsilon$ parallel to the $ac$ plane. Momentum dependence of the RIXS spectrum of PrFeAsO (c) and PrFeAsO${}_{0.7}$ (d). The circles are the raw data and the lines are three-point smoothed spectra. Data are shifted vertically for clarity. Vertical ticks indicate the energy position of the $dd$ feature at (0,0) and ($\pi$,$\pi$).

Figure 3

(a) RIXS spectra calculated at $q=(0,0)$, ($\pi$,0), and ($\pi$,$\pi$) for $U=2$, 3, and 4 eV and $J=0.2\times U$. (b) $U$ and $J$ dependencies of the RIXS spectrum calculated at $q=(0,0)$. (c) Diagonal orbital excitations calculated for $U=3$ eV. (d) Difference between the momentum-resolved, area-normalized spectra calculated for $U=2$ and 4 eV (white line) and intensity ratio of the diagonal transitions of $xz,yz$ orbitals to the sum of the diagonal transitions of all five $d$ orbitals for $U=3$ eV (color bars).

Figure 4

(a) RIXS spectra calculated for the antiferromagnetic (solid line) and the paramagnetic (dashed line) ground states, for $U=2.4$ eV and bandwidth renormalized by a factor of 0.8. (b) Experimental RIXS spectra for PrFeAsO after subtraction of the elastic line. The spectrum measured at $q=(\pi ,\pi )$ (dashed magenta) is overlaid with the spectra measured at other momenta. In both panels, vertical ticks indicate the energy position of the $dd$ feature at (0,0) and ($\pi$,$\pi$).