Crystalline electric field effects in $\text{Ce}3d$ core-level spectra of heavy-fermion systems: Hard x-ray photoemission spectroscopy on ${\text{CeNi}}_{1-x}{\text{Co}}_x{\text{Ge}}_2$

High-resolution hard x-ray photoemission measurements have been performed to clarify the electronic structure originating from the strong correlation between electrons in bulk $\text{Ce}3d$ core-level spectra of ${\text{CeNi}}_{1-x}{\text{Co}}_x{\text{Ge}}_2$ $\left(0\le x\le 1\right)$. In the $\text{Ce}3d_{5/2}$ core-level spectra, the variation in satellite structures ($f^2$ peaks) shows that the hybridization strength between $\text{Ce}4f$ and conduction electrons gradually increases with Co concentration in good agreement with the results of $\text{Ce}3d\text{−}4f$ and $4d\text{−}4f$-resonant photoemission spectroscopies. Particularly, in $\text{Ce}3d_{3/2}$ core-level spectra the multiplet structures of $f^1$ peaks systematically change with the degeneracy of $f$ states which originates from crystalline electric field effects.

Figure 1

(Color online) $\text{Ce}3d$ core-level photoemission spectra of ${\text{CeNi}}_{1-x}{\text{Co}}_x{\text{Ge}}_2$ ($x=0$, 0.4, and 0.8, 1) measured at 20 K using $hv=7941.5\text{eV}$.

Figure 2

(Color online) (a) $\text{Ce}3d_{5/2}$ core-level photoemission spectra of ${\text{CeNiGe}}_2$. The spectrum is well deconvoluted into the $f^1$ and $f^2$ configurations by Lorentzian fitting. (b) Comparison of $I_2=I\left(f^2\right)/\left[I\left(f^1\right)+I\left(f^2\right)\right]$, where $I\left(f^{1\left(2\right)}\right)$ is the intensity of $f^{1\left(2\right)}$ peak, and the bulk hybridization strength obtained from the valence-band resonant photoemission ($\rho V^2$, where $\rho$ is the density of states of conduction band and $V$ is the hybridization between $\text{Ce}4f$ and conduction electrons).

Figure 3

(Color online) (a) The $\text{Ce}3d_{3/2}$ core-level photoemission spectra of ${\text{CeNi}}_{1-x}{\text{Co}}_x{\text{Ge}}_2$ $\left(x=0,0.4,1\right)$ without offset. Fine structures of $f^1$ peak are labeled as A and B. (b) Differences between the spectrum of ${\text{CeNiGe}}_2$ $\left(x=0\right)$ and those of the other samples $\left(x=0.4,0.8,1\right)$. Thick solid lines are obtained from the smoothing of the thin dashed line.

Figure 4

(Color online) Differences of the A peaks (solid circle) and those of the $f^2$ peaks (open circle) obtained from the differences of $\text{Ce}3d_{3/2}$ core-level spectra between ${\text{CeNiGe}}_2$ $\left(x=0\right)$ and the other samples $\left(x=0.4,0.8,1\right)$. Each value exhibits the different tendencies; while $f^2$ peaks gradually change, A peaks suddenly change between $x=0.4$ and 0.8. The degeneracy $\left(N_f\right)$ and total angular momentum of $f$ electrons $\left(j\right)$ are depicted above the panel.