Charge-Transfer and $dd$ excitations in ${\mathrm{AgF}}_2$

Charge-transfer insulators are the parent phase of a large group of today's unconventional high-temperature superconductors. Here we study experimentally and theoretically the interband excitations of the charge-transfer insulator silver fluoride ${\mathrm{AgF}}_2$, which has been proposed as an excellent analog of oxocuprates. Optical conductivity and resonant inelastic x-ray scattering on ${\mathrm{AgF}}_2$ polycrystalline sample show a close similarity with that measured on undoped ${\mathrm{La}}_2{\mathrm{CuO}}_4$. While the former shows a charge-transfer gap $\sim 3.4$ eV, larger than in the cuprate, $dd$ excitations are nearly at the same energy in the two materials. Density functional theory and exact diagonalization cluster computations of the multiplet spectra show that ${\mathrm{AgF}}_2$ is more covalent than the cuprate, in spite of the larger fundamental gap. Furthermore, we show that ${\mathrm{AgF}}_2$ is at the verge of a charge-transfer instability. The overall resemblance of our data on ${\mathrm{AgF}}_2$ to those published previously on ${\mathrm{La}}_2{\mathrm{CuO}}_4$ suggests that the underlying charge-transfer insulator physics is the same, while ${\mathrm{AgF}}_2$ could also benefit from a proximity to a charge density wave phase as in ${\mathrm{BaBiO}}_3$. Therefore, our work provides a compelling support to the future use of fluoroargentates for materials' engineering of novel high-temperature superconductors.

Figure 1

The central gray octahedron shows the ${\mathrm{AgF}}_6$ cluster used in the computations. The surrounding atoms are implicitly taken into account in the definition of diagonal energies. Some key bond angles are indicated for clarity.

Figure 2

Real part of optical conductivity for ${\mathrm{AgF}}_2$ (this work). The top panel presents ${\sigma }_1$ (blue line with circles) as obtained from direct calculation of the pseudodielectric function using ellipsometry parameters ${\mathrm{\Psi }}_{\mathrm{ellip}}$ and ${\mathrm{\Delta }}_{\mathrm{ellip}}$ for two angles of incidence as measured at a base temperature of 8 K. ${\sigma }_1$ as was obtained by near normal incidence reflectivity measurements in the far infrared is shown in red. The shaded gray area represents the result of a fit to ${\mathrm{\Psi }}_{\mathrm{ellip}}$ and ${\mathrm{\Delta }}_{\mathrm{ellip}}$ data separately (see Appendix pp2), which reflects the confidence boundaries of our model with respect to the experimental data. Our data is compared with optical conductivity data adopted from Falck et al. [27, 28] on undoped ${\mathrm{La}}_2{\mathrm{CuO}}_4$. The optical conductivity in the ${\mathrm{AgF}}_2$ sample shows an onset at about 1.75 eV with high-energy band transition associated with the charge-transfer gap (${\mathrm{\Delta }}_{\mathrm{peak}}\approx 3.4$ eV). The data on ${\mathrm{AgF}}_2$ is compared with a charge-transfer excitation peaking at ${\mathrm{\Delta }}_{\mathrm{peak}}\approx 2.2$ eV with an onset of $\approx 1.6$ eV in the equivalent oxocuprates compound ${\mathrm{La}}_2{\mathrm{CuO}}_4$. In addition, the ${\mathrm{AgF}}_2$ data shows a low spectral weight subgap absorption suggesting negligible doping as intended [28]. Bottom panel shows a comparison with data at 300 K showing slight modifications of the different excitations in the charge-transfer sector and the subgap sector.

Figure 3

Top panel: Comparison of F $K$-XAS on ${\mathrm{AgF}}_2$ and O $K$-XAS on ${\mathrm{La}}_2{\mathrm{CuO}}_4$ [29]. ${\mathrm{AgF}}_2$ and ${\mathrm{La}}_2{\mathrm{CuO}}_4$ XAS energies correspond to the bottom and the top $x$ axes, respectively. Bottom panel: Orbital projected unoccupied density of states (DOS) of ${\mathrm{AgF}}_2$ from the unpolarized DFT computations. The Fermi level has been shifted to 681.8 eV to facilitate comparison with F $K$-XAS (red line). The total unoccupied DOS, includes contributions from the shown symmetries above the edge as well as Ag $4d$, which will be shown later [Fig. 5]. For the band at the Fermi level, it is nearly equal to the difference of the total and F 2p contribution.

Figure 4

Left panel: Comparison of F $K$-RIXS on ${\mathrm{AgF}}_2$ and O $K$-RIXS on ${\mathrm{La}}_2{\mathrm{CuO}}_4$ [33]. Middle panel: F $K$-RIXS on ${\mathrm{AgF}}_2$ fitted with multiple components: black, elastic peak; red, green, and blue, phonons and their overtones; cyan, bimagnon; magenta, yellow, and dark yellow, $dd$ excitations; navy and purple, charge-transfer excitations (see text for further description). Insets show the low-energy inelastic features and $dd$ excitations with fitted profiles in different colors as noted before. Right panel: F $K$-RIXS incident energy map on ${\mathrm{AgF}}_2$ showing Raman and fluorescence features.

Figure 5

(a) DOS of ${\mathrm{AgF}}_2$ projected on Ag $d$ orbitals from the unpolarized DFT computations. (curves have been shifted by 2 eV for clarity). The Fermi level is at zero energy. (b) Joint DOS between the unoccupied DOS of $d_{x^2-y^2}$ character and occupied DOS of different character representing $dd$ transitions of a hole from the half-filled $d_{x^2-y^2}$ to a final state (labeled by the final state) character. The thin black line is the average of the different contributions. The dotted line is the experimental RIXS data.

Figure 6

Energy level diagram for one hole states in the clusters considered for (a) ${\mathrm{AgF}}_2$ with $\mathrm{\Delta }=1.29$ eV and parameters from Table 1 with a 20% increase of the $T_{pd}$ matrix elements and $J=70\mathrm{meV}$ as stabilization energy [46]. (b) ${\mathrm{La}}_2{\mathrm{CuO}}_4$ with $\mathrm{\Delta }=2.45$ eV and $J=130\mathrm{meV}$. Dashed lines correspond to energies before hybridization in the $d^9$ configuration (left) and $d^{10}\underline{L}$ (right). Hybridization yields bonding and antibonding states (full lines). The ground state corresponds to the half-filled antibonding $d_{x^2-y^2}$, which was placed at zero energy so the vertical scale represent energies of transitions to states of majority $d^9$ character (i.e., $dd$ transitions) around 2 eV and $d^{10}\underline{L}$ (i.e., charge-transfer transitions) at higher energy. RIXS spectra has been superposed for comparison. (c) shows the Tanabe-Sugano diagram for $dd$ (lower lines set) and charge-transfer transitions (higher lines set). The position of excited states is measured with respect to the $x^2\text{−}{y}^2$ ground state and are plotted as a function of the renormalization of the $T_{pd}$ matrix element with respect to the DFT value. The vertical line at $T_{pd}/T_{pd}^{DFT}=1.2$ represents the value that was taken in our analysis to fit the experimental data. The magnetic stabilization energy of the $d_{x^2-y^2}$ state mentioned in the text has been omitted.

Figure 7

Charge-transfer processes within the ${\mathrm{AgF}}_6$ cluster (gray region) and to a distant fluorine.

Figure 8

Experimental setup for explosive compaction. 1 - electric detonator, 2 - plane wave generator, 3 - PVC tube, 4 - explosive, 5 - upper plug together with conical hat, 6 - container with compacted sample, 7 - compacted sample, 8 - short circuit sensors for measuring the detonation velocity, 9 - momentum trap. Dimensions are given in mm on the left-hand side.

Figure 9

The ellipsometric parameters ${\mathrm{\Psi }}_{\mathrm{ellip}}$ and ${\mathrm{\Delta }}_{\mathrm{ellip}}$ as measured at temperature of 8 K for AOI of 61 (black spheres) and 63 (red spheres) degrees. The corresponding model fit as explained in the Appendix is shown in dashed lines.