Kondo ground states and non-Fermi-liquid behavior in $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$

We report measurements of the magnetic susceptibility, specific heat, and electrical resistivity of the heavy fermion alloy series $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$. With increasing $x$, hybridization between the localized $4f$ and conduction band electrons is enhanced. The magnetic order observed at $x=0$ is completely suppressed at $x=0.3$ and non-Fermi-liquid behavior appears at the critical concentration, which is analyzed in terms of two-dimensional antiferromagnetic quantum fluctuations. Specific heat and magnetic susceptibility data are quantitatively explained by the Coqblin-Schrieffer model with degenerate impurity spin $j=1∕2$, $3∕2$, and $5∕2$ for Co concentration range of $x⩽0.6$, $0.7⩽x⩽0.8$, and $x⩾0.9$, respectively.

Figure 1

Lattice parameters $a$, $b$, and $c$ versus Co concentration $x$. Here, $b$ is plotted as divided by 4 for better presentation.

Figure 2

Temperature dependence of the magnetic susceptibility $\chi \left(T\right)$ for $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$.

Figure 3

Temperature dependence of the inverse magnetic susceptibility $1∕\chi \left(T\right)$ for $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$.

Figure 4

(Upper panel) Paramagnetic Curie temperature ${\Theta }_p$. (Lower panel) Kondo temperature $T_K^{\chi }$ and $\chi \left(0\right)$ evaluated from the magnetic susceptibility $\chi \left(T\right)$ and Kondo temperature $T_K^C$ evaluated from $4f$ specific heat $C_{4f}$ as a function of Co concentration $x$ in $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$.

Figure 5

Corrected magnetic susceptibility ${\chi }_c\left(T\right)$ of $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$ by using the method mentioned in the text. The calculated results (solid line) from the Coqblin-Schrieffer model with various $j$ values are also included. The inset in the graph for $x=0.3$ shows a power-law temperature dependence of the susceptibility, $\chi ={\chi }_0(1-a{T}^{1∕2})$, in low temperature region. (See the text.)

Figure 6

Specific heat divided by temperature $C∕T$ for $\mathrm{La}\mathrm{Ni}{\mathrm{Ge}}_2$ and $\mathrm{La}\mathrm{Co}{\mathrm{Ge}}_2$ as well as $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$.

Figure 7

Sommerfeld coefficient $\gamma$ and the $T^2$ resistivity coefficient $A$ as a function of Co concentration $x$ in $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$.

Figure 8

$4f$-electron contribution to the specific heat $C_{4f}$ given by the difference between the specific heats of $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$ and $\mathrm{La}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$. The solid lines indicate $C_{4f}$ calculated from the Coqblin-Schrieffer model with various $j$ values.

Figure 9

$C_{4f}$ data of $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$ and the calculated results (solid line) from the Coqblin-Schrieffer model in the presence of crystalline electric field. The details are mentioned in the text.

Figure 10

Temperature dependence of the electrical resistivity $\rho \left(T\right)$ for $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$. The insets show magnetic contribution to the resistivity for $\mathrm{Ce}\mathrm{Ni}{\mathrm{Ge}}_2$ and $\mathrm{Ce}\mathrm{Co}{\mathrm{Ge}}_2$.

Figure 11

Low-temperature parts of $\rho \left(T\right)$ for $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$. The values are shifted for easy comparison with each other. (Upper panel) The solid line indicates the fitting curve of $\rho ={\rho }_0+\beta T$ and the arrows indicate the antiferromagnetic transition temperature $T_N$. (Lower panel) The solid lines indicate the fitting curves with $\rho ={\rho }_0+A{T}^2$ and the arrows indicate the maximum temperature $T_{FL}$ of the $T^2$ dependence.

Figure 12

(Upper panel) The $T^2$ resistivity coefficient $A$ versus Sommerfeld coefficient in $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$. The slope of $A∕\gamma$ in the logarithmic scale is nearly constant. (Lower panel) The Sommerfeld coefficient $\gamma$ versus zero-temperature susceptibility $\chi \left(0\right)$ in $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$. The slope of $\gamma ∕\chi \left(0\right)$ in the logarithmic scale is nearly constant. Symbols are for our samples.

Figure 13

Dimensionless effective exchange coupling constant $N_{\mathrm{F}}J$ estimated from the equation of $T_K=D\exp (-1∕N_{\mathrm{F}}J)$, assuming $D=5\times {10}^4\mathrm{K}$.

Figure 14

Prefactor $A^{\prime }$ and the temperature exponent $n$ as a function of Co concentration $x$.

Figure 15

Phase diagram as a function of $\Delta T_K=T_K\left(x\right)\text{−}{T}_K(x=0.3)$ in $\mathrm{Ce}{\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{Ge}}_2$.