Electronic structure of the heavy-fermion caged compound ${\text{Ce}}_3{\text{Pd}}_{20}{X}_6(X=\text{Si,}\text{Ge})$ studied by density functional theory and photoelectron spectroscopy

The electronic structure of ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{X}_6(X=\text{Si,}\text{Ge})$ has been studied using detailed density functional theory (DFT) calculations and high-resolution photoelectron spectroscopy (PES) measurements. The orbital decomposition of the electronic structure by DFT calculations indicates that Ce atoms at the (8c) site surrounded by 16 Pd atoms have a tendency to be magnetic. Ce atoms at the (4a) site surrounded by 12 Pd and 6 $X$ atoms, on the other hand, are more localized and paramagnetic. The $4d\text{−}4f$ resonance PES measurements clearly indicate the Ce $4f$ contribution in the valence band in these compounds. The spectral weight of Ce $4f^0$ is stronger than that of Ce $4f^1$, indicating the localized nature of Ce $4f$ electrons. Near the Fermi level, the Ce $4f^1$ weight of ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$ is stronger than that of ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Ge}}_6$, suggesting stronger $c\text{−}f$ hybridization in the former.

Figure 1

(a) Schematic image of the cubic ${\mathrm{Cr}}_{22}{\mathrm{C}}_6$-type crystal structure of ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{X}_6(X=\text{Si,}\text{Ge})$. (b) ${\mathrm{Ce}}_{4a}$ at site (4a) is surrounded by a cage of 12 ${\mathrm{Pd}}_{\mathrm{mix}}$ and 6 Si/Ge atoms. (c) ${\mathrm{Ce}}_{8c}$ at site (8c) is inside a cage of 4 ${\mathrm{Pd}}_{8\mathrm{c}}$ and 12 ${\mathrm{Pd}}_{8\mathrm{c}}$ atoms.

Figure 2

(a) Main contributions to the density of states of ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$ from Ce $f$, Pd $d$, and Si $p$ orbitals. (b–d) Partial density of states calculated within density functional theory for each species in ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$. (e) Main contributions to the density of states of ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Ge}}_6$ from Ce $f$, Pd $d$, and Ge $p$ orbitals. (f–h) Partial density of states calculated within density functional theory for each species in ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Ge}}_6$.

Figure 3

(a) Spin- and site-resolved Pd $d$ partial density of states for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$. (b) Spin- and site-resolved Ce $f$ partial density of states for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$.

Figure 4

Band dispersion in the $c\text{−}f$ hybridization of ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$ weighted by the (a) ${\mathrm{Ce}}_{8\mathrm{c}}f$ states, (b) ${\mathrm{Pd}}_{8\mathrm{c}}d$ states, (c) ${\mathrm{Ce}}_{4\mathrm{a}}f$ states, and (d) ${\mathrm{Pd}}_{\mathrm{mix}}d$ states.

Figure 5

Band dispersion in the $c\text{−}f$ hybridization of ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$ (black lines) and ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Ge}}_6$ [gray (green) lines].

Figure 6

(a) Valence-band spectra near the Fermi edge at 8–9.5 K and $h\nu =9.9$, 12.2, 20.1, 30.3, 40, and 110 eV for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$. (b) Partial density of states calculated within DFT for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$.

Figure 7

(a) Temperature dependence of the valence-band spectra at $h\nu =12.2$ eV for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$. (b) Enlarged view of the valence-band spectra in (a) near the Fermi edge. The direction of the arrows corresponds to the change in intensity at the given binding energy when the temperature decreases.

Figure 8

(a) Temperature dependence of the valence-band spectra at $h\nu =122$ eV for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$. (b) Contour intensity map of the temperature dependence of the valence-band spectra in (a). (c) Enlarged view of the valence-band spectra in (a) near the Fermi edge. The direction of the arrows corresponds to the change in intensity at the given binding energy when the temperature decreases.

Figure 9

(a) Valence-band spectra at 10 and 100 K and $h\nu =122$ eV for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Ge}}_6$. (b) Enlarged view of the valence-band spectra in (a) near $E_F$.

Figure 10

(a) Resonant photoelectron spectra of the valence band for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$ at 8 K in the incident energy range $h\nu =110.5$–130.1 eV. (b) Resonant photoelectron spectra of the valence band for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Ge}}_6$ at 10 K in the incident energy range $h\nu =110$-130 eV. (c) Contour intensity map of the resonant spectra in (a) as a function of the incident photon energies. (d) Contour intensity map of the resonant spectra in (b) as a function of the incident photon energies. (e) Comparison of the spectra at 110 eV (off resonance) and 122 eV (on resonance) for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$ and ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Ge}}_6$. On-resonance spectra are normalized at 7 eV. The off-resonant spectra intensity is normalized to the intensity at 4 eV for on-resonance spectra. (f) Difference in the intensity between on- and of-resonant spectra for ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Si}}_6$ and ${\mathrm{Ce}}_3{\mathrm{Pd}}_{20}{\mathrm{Ge}}_6$.