Absence of magnetic field effect on the cerium valence in $\mathrm{Ce}{\mathrm{Cu}}_2{\mathrm{Si}}_2$ at its optimum superconducting critical temperature

The archetypical heavy-fermion superconductor $\mathrm{Ce}{\mathrm{Cu}}_2{\mathrm{Si}}_2$ is known to present two distinct superconducting phases under pressure. In the low-pressure region, the superconductivity is mediated by spin fluctuations while the superconducting phase observed in the high-pressure region could be associated with a first-order valence transition (FOVT). However, the critical end point (CEP) of the FOVT was shown to be located at negative temperature and only a continuous valence change (crossover regime) was so far observed at 14 K, i.e., far above the optimal superconducting temperature $\left(T_c=2.3\mathrm{K}\right)$. Here we present x-ray absorption measurements under pressure and applied magnetic field at the Ce $L_3$ edge at 2.7 K, i.e., close to the optimal $T_{\mathrm{c}}$. It was expected that the applied magnetic field could shift the CEP to positive temperature with the possibility to observe a FOVT. Our data indicate the valence of Ce increases continuously (crossover regime) from 3.11 at ambient pressure up to 3.20 at 8.5 GPa likewise for any applied magnetic field up to 6 T.

Figure 1

Schematic P-T phase diagram of $\mathrm{Ce}{\mathrm{Cu}}_2{\mathrm{Si}}_2$ showing the critical pressure $P_{\mathrm{C}}$ and $P_{\mathrm{V}}$ where the superconductivity is mediated either by antiferromagnetic fluctuations (SCI) or critical valence fluctuations. (SCII). $P_{\mathrm{C}}$ where $T_{\mathrm{N}}$ goes to zero appears to be at slightly negative pressure for $\mathrm{Ce}{\mathrm{Cu}}_2{\mathrm{Si}}_2$ samples with tiny Cu excess. The negative pressure where AFM order sets in has been explored by substituting Si by Ge. The VCO line (blue) and the location of the CEP at about 8 K and $4.5\mathrm{GPa}\sim P_{\mathrm{V}}$ are obtained from resistivity measurements (adapted from Ref. [4]).

Figure 2

(a) XANES spectra in $\mathrm{Ce}{\mathrm{Cu}}_2{\mathrm{Si}}_2$ as a function of pressure at 2.7 K. The arrows show the evolution of the $f^1\left({\mathrm{Ce}}^{3+}\right)$ and $f^0\left({\mathrm{Ce}}^{4+}\right)$ features with increasing pressure. The broad bump centered at about 5757 eV is attributed to the extended x-ray absorption fine structure (EXAFS) contribution. (b) Typical fit (red curve) of $\mathrm{Ce}{\mathrm{Cu}}_2{\mathrm{Si}}_2$ XANES spectra (black line) with the combination of Gaussians (white lines) and arctangent functions for ${\mathrm{Ce}}^{3+}\left(4f^1\right)$ and ${\mathrm{Ce}}^{4+}\left(4f^0\right)$ contributions. The couples of G1–G2 and G3–G4 Gaussians are attributed to the ${\mathrm{Ce}}^{3+}$ and ${\mathrm{Ce}}^{4+}$ contributions, respectively.

Figure 3

Pressure dependence of the weight of the ${\mathrm{Ce}}^{3+}$, $4f^1/\left(4f^1+4f^0\right)$, contribution at 2.7 K, i.e., close to the superconducting temperature $T_{\mathrm{C}}$ for different applied fields. The inset represents the pressure dependence at zero applied field of the Ce valence at 14 K obtained previously from the analysis of the x-ray absorption spectra taken in the partial fluorescence mode within the Anderson impurity model [14].

Figure 4

(a) XANES spectra recorded at 1.1 and 5.0 GPa and 2.7 K for zero field and 6 T together with the result of the subtraction. (b) Pressure dependence of the weight of the ${\mathrm{Ce}}^{3+}$, $4f^1/\left(4f^1+4f^0\right)$, contribution at 2.7 K, i.e., close to the superconducting temperature $T_{\mathrm{C}}$ for different applied fields.

Figure 5

Schematic ground-state diagram in the $U_{\mathrm{fc}}\text{−}{E}_{\mathrm{f}}$ plane. The bold solid lines represent the first-order valence transition lines and the filled circles stand for the critical end point. The shaded line connects the CEP under magnetic field. The filled square stands for the location of $\mathrm{Ce}{\mathrm{Cu}}_2{\mathrm{Si}}_2$ in the phase diagram. The point-dashed line mimics the pressure dependence of its location (adapted from Refs. [16, 17]).