Correlated Electron State in ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{CoIn}}_5$ Stabilized by Cooperative Valence Fluctuations

X-ray diffraction, electrical resistivity, magnetic susceptibility, and specific heat measurements on ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{CoIn}}_5$ ($0\le x\le 1$) reveal that many of the characteristic features of the $x=0$ correlated electron state are stable for $x\le 0.775$ and that phase separation occurs for $x>0.775$. The stability of the correlated electron state is apparently due to cooperative behavior of the Ce and Yb ions, involving their unstable valences. Low-temperature non-Fermi liquid behavior is observed and varies with $x$, even though there is no readily identifiable quantum critical point. The superconducting critical temperature $T_c$ decreases linearly with $x$ towards 0 K as $x\to 1$, in contrast with other HF superconductors where $T_c$ scales with $T_{\mathrm{coh}}$.

Figure 1

(a) Lattice parameters $a$ (filled black squares) and $c$ (filled black circles) vs Yb concentration $x$ for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{CoIn}}_5$. Phase separation occurs for $x\ge 0.8$, and two sets of lattice constants are observed, as shown by the red open symbols that correspond to the lattice constants expected for ${\mathrm{YbCoIn}}_5$. Inset: Representative XRD profile and Rietveld fit for $x=0.5$. (b) Measured Yb concentration $x_{\mathrm{meas}}$ from EDX vs nominal $x$. Inset: Comparison of the XRD profiles for $x=0.05$ and 0.8, illustrating the phase separation. The arrows highlight the splitting of the Bragg reflections (see the text).

Figure 2

(a) Electrical resistivity $\rho$ normalized to its value at 300 K, $\rho /\rho (300\mathrm{K})$, vs temperature $T$ for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{CoIn}}_5$ with $0\le x\le 1.0$. (b) Power law fits for $T_c<T<\sim 25$. (c) Low $T$ resistive superconducting transition curves.

Figure 3

(a) Coherence temperature $T_{\mathrm{coh}}$, where $\rho (T)$ exhibits a maximum (or knee) vs $x$. The error bars represent the width of the maximum, defined as the $T$ $\rho =0.95{\rho }_{\mathrm{coh}}$. (b) Circles: $T_c$ determined from $\rho (T)$ measurements vs $x$ for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{CoIn}}_5$. The vertical bars correspond to the 90% and 10% values of the superconducting transitions. Triangles: $T_c$, determined from $C(T)$ measurements vs $x$. The solid line shows the suppression of $T_c$ as reported for other rare earth substitutions [12]. (c) Fit parameters $n_{\rho }$, extracted from power law $\rho ={\rho }_0+A{T}^{n_{\rho }}$ fits to the normal-state resistivity vs $x$. (d) Fit parameters $n_{\chi }$, determined from fits of ${\chi }_c={\chi }_c(0)+a/T^{n_{\chi }}$ to the normal-state $\chi (T)$ vs $x$. The light gray shading represents the region of phase separation.

Figure 4

(a) Magnetic susceptibility along the $ab$ plane ${\chi }_{ab}$ vs temperature $T$ for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{CoIn}}_5$. Inset: Ratio of ${\chi }_{ab}$ to ${\chi }_c$ at $T=2.3\mathrm{K}$. (b) Magnetic susceptibility along the $c$ axis ${\chi }_c$ vs $T$ for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{CoIn}}_5$. Data for $x=0$ are from Ref. 23.

Figure 5

Specific heat $C$ divided by temperature $T$ vs $T$ for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{CoIn}}_5$.