Charge transfer and Mott-Hubbard excitations in FeBO${}_3$: An Fe $K$-edge resonant inelastic x-ray scattering study

Momentum-resolved resonant inelastic x-ray scattering (RIXS) spectroscopy has been carried out successfully at the Fe $K$-edge for the first time. The RIXS spectra of a FeBO${}_3$ single crystal reveal a wealth of information on $\simeq$ 1–10 eV electronic excitations. The IXS signal resonates when the incident photon energy approaches the pre-edge (1$\mathrm{s̄}$-3$d$) and the main-edge (1$\mathrm{s̄}$-4$p$) of the Fe $K$-edge absorption spectrum. The RIXS spectra measured at the pre-edge and the main-edge show quantitatively different dependences on the incident photon energy, momentum transfer, photon polarization, and temperature. We present a multielectron analysis of the Mott-Hubbard (MH) and charge transfer (CT) excitations, and calculate their energies. Electronic excitations observed in the pre-edge and main-edge RIXS spectra are interpreted as MH and CT excitations, respectively. We propose the electronic structure around the chemical potential in FeBO${}_3$ based on the experimental data.

Figure 1

Schematic of an Fe $K$-edge RIXS process in FeBO${}_3$. In the initial state, five 3$d$ electrons fill $t_{2g}$ and $e_g$ crystal-field levels in the high-spin configuration. Two absorption transitions can be used for RIXS measurement: the pre-edge 1$\mathrm{s̄}$-3$d$ and the main-edge 1$\mathrm{s̄}$-4$p$. Various valence electronic excitations are left behind after the decay of the excited electron back into the 1$s$ core level: on-site $\mathit{dd}$, charge transfer, and Mott-Hubbard excitations. On-site $\mathit{dd}$ excitations are forbidden because of spin-selection rule.

Figure 2

Schematic of the scattering geometry in the RIXS experiment. The FeBO${}_3$ sample is mounted in such a way that the momentum transfer $\overrightarrow{\mathit{Q}}={\overrightarrow{\mathit{Q}}}_f-{\overrightarrow{\mathit{Q}}}_i$ is parallel to the crystal $c$ axis.

Figure 3

(a) Fe $K$-edge x-ray absorption spectroscopy (XAS) data measured at different angles of incidence $\alpha$ to the crystal surface (solid lines) and integrated intensities of the Fig. 4a RIXS spectra (red filled dots). (b) XAS data in the region of the pre-edge peak.

Figure 4

(a) RIXS spectra (vertically shifted for clarity) measured for different incident photon energies $7112\hspace{0.5em}\mathrm{eV}⩽E_i⩽7140$ eV with $\overrightarrow{\mathit{Q}}=$ (0 0 9) are plotted as a function of energy loss $\varepsilon =E_i-E_f$. Self-absorption corrections for the scattered photon have been made (see the text). (b) 2D plot of the RIXS spectra shown in (a).

Figure 5

Representative RIXS spectra measured at the (a) main-edge ($E_i=7131.0$ eV) and (b) pre-edge ($E_i=7113.5$ eV). Raw and self-absorption corrected spectra are shown in red and black, respectively. Gaussian functions are used to fit inelastic peaks. Fit curves for the main-edge (M1, M2, M3) and pre-edge (P1, P2, P3) RIXS spectra are shown in (c) and (d), respectively.

Figure 6

RIXS spectra measured at the (a) main-edge ($E_i=7131$ eV), and (c) pre-edge ($E_i=7113.5$ eV) as a function of ${\overrightarrow{\mathit{Q}}}_f=$(0 0 L), $2<L<11.5$. 2D plots of the corresponding RIXS data are shown in (b) and (d), respectively.

Figure 7

(a) and (b) show peak energies and widths, respectively, of M1 and M2 as a function of $\overrightarrow{\mathit{Q}}$. Peak energies and widths of the P1 and P2 are shown in (c) and (d), respectively.

Figure 8

Intensity of the (a) elastic line, (b) the RIXS peaks (M1, M2, M3), and (c) (P1, P2, P3) as a function of $\overrightarrow{\mathit{Q}}$ or 2$\theta$.

Figure 9

Temperature dependence of main-edge RIXS [$E_i=7131$ eV, $\overrightarrow{\mathit{Q}}=$ (0 0 9)] spectra (a) in the wide energy range and (b) in the region of the M1 peak.

Figure 10

Temperature dependence of pre-edge RIXS [$E_i=7113.5$ eV, $\overrightarrow{\mathit{Q}}=$ (0 0 9)] spectra (a) in the wide energy range and (b) in the region of the P1 peak.

Figure 11

$E_i$-independent RIXS response function $S[\varepsilon ,\overrightarrow{\mathit{Q}}=$(0 0 9)] derived from main-edge RIXS spectra and Eqs. (1) and (2) (see the text).

Figure 12

Comparison between $S(\varepsilon ,{\overrightarrow{\mathit{Q}}}_f)$ extracted from measurement at ${\overrightarrow{\mathit{Q}}}_f=$ (0 0 6) and (0 0 9) and the loss functions from the literature (Ref. 47).

Figure 13

Scheme of Mott-Hubbard excitations $d_i^5{d}_j^5\to d_i^4{d}_j^6$, associated with (a) P1, (b) P2, and (c) P3 RIXS features. The ground-state levels $d^5({}^6{A}_{1g})$ are marked by a cross.

Figure 14

Two types of the CT excitations (solid line and dotted lines), and the MH excitation (dashed-dotted lines).

Figure 15

Schematic of the electronic structure around the chemical potential ($\mu$) in FeBO${}_3$. Energies are in the unit of eV, based on the presented RIXS measurements.