Resonant inelastic x-ray scattering study of electronic excitations in insulating ${\mathrm{K}}_{0.83}{\mathrm{Fe}}_{1.53}{\mathrm{Se}}_2$

We report an Fe $K$-edge resonant inelastic x-ray scattering study of ${\mathrm{K}}_{0.83}{\mathrm{Fe}}_{1.53}{\mathrm{Se}}_2$. This material is an insulator, unlike many parent compounds of iron-based superconductors. We found a sharp excitation around 1 eV, which is resonantly enhanced when the incident photon energy is tuned near the pre-edge region of the absorption spectrum. The spectral weight and lineshape of this excitation exhibit clear momentum dependence. In addition, we observe momentum-independent broad interband transitions at higher excitation energies of 3–7 eV. Calculations based on a 70-band $dp$ orbital model, using a moderate $U_{\mathrm{eff}}\approx 2.5\mathrm{eV}$, indicate that the $\sim 1\mathrm{eV}$ feature originates from the correlated Fe $3d$ electrons, with a dominant $d_{xz}$ and $d_{yz}$ orbital character. We find that a moderate $U_{\mathrm{eff}}$ yields a satisfying agreement with the experimental spectra, suggesting that the electron correlations in the insulating and metallic iron-based superconductors are comparable.

Figure 1

(a) Fe $K$-edge XANES taken in the partial fluorescence yield (PFY) mode by monitoring the intensity of $K{\beta }_{1,3}$ emission line $(3p\to 1s)$ as a function of incident energy ($E_i$). Ticks represent the incident energies used for our energy dependence in panel (b) and the blue triangle is our resonance energy. (b) RIXS spectra as a function of the incident energy. Measurements were carried out at at $T=15$ K. The spectra have been shifted vertically for clarity (horizontal ticks).

Figure 2

(a) The evolution of the integrated intensity of both the Fe $4p$ interband transition and the 1 eV features around the pre-edge. (b) Peak position of the Fe $4p$ interband transition as a function of $E_i$. Numbers were derived from fit (see text).

Figure 3

(a) Momentum dependence of the low-energy RIXS spectra of ${\mathrm{K}}_{0.83}{\mathrm{Fe}}_{1.53}{\mathrm{Se}}_2$ obtained at $T=15$ K. Contribution from the elastic line has been subtracted. The spectra have been shifted vertically for clarity (horizontal ticks) and the solid lines are three-point-smoothed spectra. Superimposed as a dashed red line is the smoothed spectrum taken at the $\mathrm{\Gamma }$ point. In panel (b) a schematic diagram of the (HK0) reciprocal space is shown. The Brillouin zone (BZ) corresponding to the tetragonal unit cell (with two Fe per lattice point) is shown as a solid line. The filled circles are the points where RIXS spectra in panel (a) are taken. (c) Wide-range RIXS spectrum at $\mathrm{\Gamma }, X$, and $M$ points.

Figure 4

(a) Fe $3d$, Fe $4p$, and Se $4p$ partial density of state in the nonmagnetic state. Data was obtained by the 102-orbital model (see the text). The Fermi level is set to 0 eV. Arrows indicate the considered RIXS processes. (b) Calculated momentum-resolved ($\mathrm{\Gamma }$ and $M$ points) RIXS spectra using the 102-orbital model. For comparison we also include the experimental data. The spectra were shifted vertically for clarity (horizontal ticks).

Figure 5

Contribution from Fe $3d$ and Se $4p$ states to the RIXS spectrum shown over a wide energy range, as derived from the 70-orbital model. Calculations are presented for different transferred momentum and $U_{\mathrm{eff}}$. Note that the intensity scale used in this figure is the same as for Fig. 4.

Figure 6

(a) Contribution from Fe $3d$ and Se $4p$ states at different transferred momentum. (b) Orbital-resolved contribution of the Fe $3d$ states at $M$ point. The lighter-shaded area represents the total contribution from the Fe $3d$ states while the darker-shaded area transition into only the $d_{xz}$ and $d_{yz}$ orbitals. The plot demonstrates that the 0.9 eV feature consists mostly of excitation into the $d_{xz}$ and $d_{yz}$ orbitals. (c) Difference between the calculated RIXS spectra at momentum $\mathbf{q}$ and the $\mathrm{\Gamma }$ point. (d) Difference between the experimental RIXS spectra from Fig. 3 and the $\mathrm{\Gamma }$-point spectrum [dashed red line in Fig. 3].