Direct probe of Mott-Hubbard to charge-transfer insulator transition and electronic structure evolution in transition-metal systems

We report the most direct experimental verification of Mott-Hubbard and charge-transfer insulators through x-ray emission spectroscopy in transition-metal (TM) fluorides. The p-d hybridization features in the spectra allow a straightforward energy alignment of the anion-2$p$ and metal-3$d$ valence states, which visually shows the difference between the two types of insulators. Furthermore, in parallel with the theoretical Zaanen-Sawatzky-Allen diagram, a complete experimental systematics of the 3$d$ Coulomb interaction and the 2$p$-3$d$ charge-transfer energy is reported and could serve as a universal experimental trend for other TM systems including oxides.

Figure 1

Schematic of (top) C-T and (bottom) M-H insulators. The lower intensity d-p and p-d humps are hybridization features in d- and p-partial DOS, respectively. Such features are evident in an $M$F${}_2$ system, enabling a straightforward alignment of the experimental partial DOS of TM-3$d$ with F-2$p$.

Figure 2

Experimental metal-3$d$ and anion-2$p$ valence states in $M$F${}_2$ aligned by EATH. (a) XES spectra of TM-Lα in red (gray) and F-Kα in blue (black) displays the partial 3d- and 2p-DOS, respectively. The arbitrary intensity of the TM-Lα and F-Kα spectra are scaled to the same maximum value for each component. Bars are LHBs indicated by the highest-energy TM-3$d$ peaks from top valence states. From CrF${}_2$ to CuF${}_2$, TM-3$d$ LHBs shifts toward lower energy, in parallel with the shrinking of the hybridization shoulder in F-Kα spectra.[29] ZnF${}_2$ is the only C-T or intermediate insulator with Zn-3$d$ under F-2$p$ valence states. (b)–(d) show three amplified examples on the energy alignments.[29] The leading edges of F-$K$ and TM-Lα, the emission peaks of TM-Lα (F-$K$), and the hybridization features of F-$K$ (TM-Lα), respectively, are aligned.

Figure 3

Fluorine-$K$ XES and XAS experimental data plotted on a common energy scale. Red (gray) bars indicate LHBs from Fig. 2a. Black bars indicate the highest-energy F-2$p$ valence states. The TM-3$d$ UHBs are defined by the lowest-energy intensity peaks in XAS data, the so-called in-gap states (dashed bars). The data exhibit monotonic energy shift on occupied F-2$p$ and LHB states contrasting very irregular energies of unoccupied UHBs.

Figure 4

Systematics of $U_{\mathit{dd}}$ and Δ${}_{\mathrm{C}\text{−}\mathrm{T}}$ generated from experiments on TM fluorides and their extension to oxides. (a) Experimental $U_{\mathit{dd}}$ from Fig. 3 in comparison with theoretical Zaanen-Sawatzky (ZS) analysis. (b) Experimental and theoretical Δ${}_{\mathrm{C}\text{−}\mathrm{T}}$ basically follow the same trend as that of $U_{\mathit{dd}}$. (c) Direct comparison of experimental $U_{\mathit{dd}}$ with Δ${}_{\mathrm{C}\text{−}\mathrm{T}}$ in difluorides and oxides. Δ${}_{\mathrm{C}\text{−}\mathrm{T}}$ were decreased by 3 eV for oxides to compensate the difference in electronegativity between F and ${\mathrm{O}}^2$.