Localized Character of $4f$ Electrons in ${\mathrm{C}\mathrm{e}\mathrm{R}\mathrm{h}}_x$ $(x=2,3)$ and ${\mathrm{C}\mathrm{e}\mathrm{N}\mathrm{i}}_x$ $(x=2,5)$

We have measured Ce $4f$ spectral weights of extremely $\alpha$-like Ce transition metal intermetallic compounds ${\mathrm{C}\mathrm{e}\mathrm{R}\mathrm{h}}_x$ ($x=2,3$) and ${\mathrm{C}\mathrm{e}\mathrm{N}\mathrm{i}}_x$ ($x=2,5$) by using the bulk-sensitive resonant photoemission technique at the Ce $M_5$($3d_{5/2}\to 4f$) edge. High energy resolution and longer escape depth of photoemitted electron at this photon energy enabled us to distinguish the sharp Kondo resonance tails at the Fermi level, which can be well described by the Gunnarsson-Schönhammer calculation based on the Anderson impurity Hamiltonian. On the other hand, the itinerant $4f$ band description shows big discrepancies, which implies that Ce $4f$ electrons retain localized characters even in extremely $\alpha$-like compounds.

Figure 1

The Ce $M_5$ XAS spectra (dots) of ${\mathrm{C}\mathrm{e}\mathrm{N}\mathrm{i}}_x$ ($x=2,5$). Solid lines are AIM fits with configuration interaction [23] using the same parameters as in Table  (see below). The inset shows off- and on-resonance photoemission data on ${\mathrm{C}\mathrm{e}\mathrm{N}\mathrm{i}}_5$.

Figure 2

Comparison between the experimental Ce $4f$ spectral weights (dots) with band structure calculations (dashed line) and with GS fits (thick solid line) for ${\mathrm{C}\mathrm{e}\mathrm{N}\mathrm{i}}_x$ ($x=2,5$). The thin solid line in the top panel is the spectral function calculated using the self-energy and the thin solid line in the bottom panel is another band calculation by Harima [26].

Figure 3

The comparisons of experimentally extracted bulk-sensitive $4f$ weights of ${\mathrm{C}\mathrm{e}\mathrm{R}\mathrm{h}}_2$ and ${\mathrm{C}\mathrm{e}\mathrm{R}\mathrm{h}}_3$ with the one-electron band calculations and the GS fit.