Covalent versus localized nature of $4f$ electrons in ceria: Resonant angle-resolved photoemission spectroscopy and density functional theory

We have conducted resonant angle-resolved photoemission spectroscopy of well-defined ${\mathrm{CeO}}_2$(111) and $c–{\mathrm{Ce}}_2{\mathrm{O}}_3$(111) model surfaces, revealing distinct $f$ contributions in the valence band of the two compounds. In conjunction with density functional theory calculations, we show that the $f$ contribution in ${\mathrm{CeO}}_2$ is of a covalent nature, arising from hybridization with the $\mathrm{O}2p$ bands. In contrast, $c–{\mathrm{Ce}}_2{\mathrm{O}}_3$ exhibits an almost nondispersive $f$ state at 1.3 eV, which is indicative of almost negligible c-f hybridization.

Figure 1

Partial density of states (pDOS) of ${\mathrm{CeO}}_2$ and $c–{\mathrm{Ce}}_2{\mathrm{O}}_3$ as calculated using the HSE06 exchange-correlation functional and measured by photoelectron spectroscopy (PES). The pDOS has been calculated for the ground state of ${\mathrm{CeO}}_2$ and $c–{\mathrm{Ce}}_2{\mathrm{O}}_3$ and for an intermediate state with a $\mathrm{Ce}4d$ electron excited into the $\mathrm{Ce}4f$ level. The PES spectra are shown as measured off (dashed black lines, $h\nu =115$ eV) and on (solid black lines, $h\nu =125$ and 121 eV for ${\mathrm{CeO}}_2$ and $c–{\mathrm{Ce}}_2{\mathrm{O}}_3$, respectively) the $\mathrm{Ce}4d\to 4f$ resonance. The calculated DOS is shifted to coincide with the experimental data (the actual Fermi energy of the DOS plots in the figure is at 2.9 and 1.55 eV for ${\mathrm{CeO}}_2$ and $c–{\mathrm{Ce}}_2{\mathrm{O}}_3$, respectively). The $c–{\mathrm{Ce}}_2{\mathrm{O}}_3$ pDOS has been scaled down by a factor of 32 to account for the higher number of Ce atoms in the unit cell in comparison with ${\mathrm{CeO}}_2$.

Figure 2

Dispersion of the valence band in ${\mathrm{CeO}}_2$ and $c–{\mathrm{Ce}}_2{\mathrm{O}}_3$ in the $\overline{M}-\overline{\mathrm{\Gamma }}-\overline{M}$ direction of the surface Brillouin zone followed by resonant angle-resolved photoelectron spectroscopy. (a) Valence band of ${\mathrm{CeO}}_2$ ($h\nu =115$ eV); (b) and (c) dispersion of the resonant feature at the $4d\to 4f$ photoabsorption threshold in ${\mathrm{CeO}}_2$ ($h\nu =125$ eV) and $c–{\mathrm{Ce}}_2{\mathrm{O}}_3$ ($h\nu =121$ eV), respectively. The areas of the energy-dispersive curves were normalized to 1 prior to plotting the maps. The bottom and upper parts of (c) were normalized separately in order to highlight the $\mathrm{O}2p$ bands.

Figure 3

(a) Band structure of ${\mathrm{CeO}}_2$ calculated along $X-\mathrm{\Gamma }-L$ for the ground state (black) and the intermediate $4d^{9}4f^1$ state (red). The extra $4f^1$ band of the intermediate state is at 5 eV at $\mathrm{\Gamma }$. The calculated band structure has been shifted by 2.9 eV to coincide with the experimental data. Calculated Kohn-Sham wave functions at the $\mathrm{\Gamma }$ point of ${\mathrm{CeO}}_2$ in the intermediate state are shown as cyan contours (corresponding to a probability density of $2^{-5}$; higher probability densities are shown in warmer colors as visible in cutout areas) in (b) the topmost $\mathrm{O}2p$ band, (c) the second $\mathrm{O}2p$ band (the third has the same symmetry and is not shown), (d) $4f^1$, and (e) a representation of the bottom three $\mathrm{O}2p$ bands. There are four cerium atoms and two oxygen atoms in the corners and in the middle of the displayed cut through the ${\mathrm{CeO}}_2$ lattice, respectively. Periodic portions of the wave functions have been eliminated for clarity.