Pauli-limited superconductivity and antiferromagnetism in the heavy-fermion compound ${\mathrm{CeCo}(\mathrm{In}}_{1-x}{\mathrm{Zn}}_x{)}_5$

We report on the anisotropic properties of Pauli-limited superconductivity (SC) and antiferromagnetism (AFM) in the solid solutions $\text{CeCo}{\left({\text{In}}_{1-x}{\text{Zn}}_x\right)}_5$ $\left(x\le 0.07\right)$. In $\text{CeCo}{\left({\text{In}}_{1-x}{\text{Zn}}_x\right)}_5$, the SC transition temperature $T_c$ is continuously reduced from 2.3 K $\left(x=0\right)$ to $\sim 1.4$ K $\left(x=0.07\right)$ by doping Zn, and then the AFM order with the transition temperature of $T_N\sim 2.2\text{K}$ develops for $x$ larger than $\sim 0.05$. The present thermal, transport, and magnetic measurements under magnetic field $B$ reveal that the substitution of Zn for In yields little change of low-temperature upper critical field ${\mu }_0{H}_{c2}$ for both the tetragonal $a$ and $c$ axes, while it monotonically reduces the SC transition temperature $T_c$. In particular, the magnitudes of ${\mu }_0{H}_{c2}$ at the nominal Zn concentration of $x=0.05$ (measured Zn amount of $\sim 0.019)$ are 11.8 T for $B\left|\right|a$ and 4.8 T for $B\left|\right|c$, which are as large as those of pure compound though $T_c$ is reduced to 80% of that for $x=0$. We consider that this feature originates from a combination of both an enhanced AFM correlation and a reduced SC condensation energy in these alloys. It is also clarified that the AFM order differently responds to the magnetic field, depending on the field directions. For $B\left|\right|c$, the clear anomaly due to the AFM transition is observed up to the AFM critical field of $\sim 5$ T in the thermodynamic quantities, whereas it is rapidly damped with increasing $B$ for $B\left|\right|a$. We discuss this anisotropic response on the basis of a rich variety of AFM modulations involved in the Ce115 compounds.

Figure 1

Temperature variations of (a) the $a$-axis electrical resistivity $\rho$ normalized by the magnitude at 280 K, (b) the $a$- and $c$-axis magnetization divided by magnetic field of $B=0.1\text{T}$ and the $a$-axis ac susceptibility ${\chi }_{ac}$, and (c) the specific heat divided by temperature for $\text{CeCo}{\left({\text{In}}_{0.93}{\text{Zn}}_{0.07}\right)}_5$. In (a) and (b), the $\rho$ and ${\chi }_{\mathrm{ac}}$ data taken from various samples are shown for comparison.

Figure 2

Isothermal magnetization curves at 0.27 K for $\text{CeCo}{\left({\text{In}}_{1-x}{\text{Zn}}_x\right)}_5$ $(x=0.025$, 0.05, and 0.07), measured under $B$ with the directions of (a) $B\left|\right|a$ and (b) $B\left|\right|c$. Note that the offsets of $0.025{\mu }_{\text{B}}/\text{Ce}$ and $0.05{\mu }_{\text{B}}/\text{Ce}$ are added to the magnetization data at $x=0.05$ $\left(y\sim 0.019\right)$ and 0.$07\left(y\sim 0.025\right)$ for clarity. Solid lines are the average of the magnetization curves between increasing and decreasing field variations. Shown in the inset of (a) are the raw capacitance data $\left(B\left|\right|a\right)$ for $x=0.025$ measured without applying a gradient field. The enlargement of the $c$-axis $M/B$ curve for $x=0.05$ is shown in the inset of (b).

Figure 3

(a) The $a$- and $c$-axis upper critical fields $H_{c2}$ at 0.27 K for $\text{CeCo}{\left({\text{In}}_{1-x}{\text{Zn}}_x\right)}_5$ plotted as a function of a nominal Zn concentration $x$. (b) The zero-field $x$ vs $T$ phase diagram for $\text{CeCo}{\left({\text{In}}_{1-x}{\text{Zn}}_x\right)}_5$ obtained from the temperature variations of the ac susceptibility, magnetization, electrical resistivity, and specific heat [34].

Figure 4

Temperature variations of the $a$-axis electrical resistivity $\rho \left(T\right)$ for $\text{CeCo}{\left({\text{In}}_{0.93}{\text{Zn}}_{0.07}\right)}_5$, measured under various $B$ with the directions of (a) $B\left|\right|a$ and (b) $B\left|\right|c$. Note that the magnetic field is applied perpendicular to the sample current $j$ in both (a) and (b). The $\rho \left(T\right)$ data taken under the different field strengths are vertically shifted in a step of $10\mu \mathrm{\Omega }\text{cm}$ for clarity. The arrows indicate the positions of the kink originating from the AFM order.

Figure 5

Temperature variations of the specific heat divided by temperature, $C/T\equiv (C_p-C_{\text{nucl}})/T$, for $\text{CeCo}{\left({\text{In}}_{0.93}{\text{Zn}}_{0.07}\right)}_5$, measured under various $B$ with the directions of (a) $B\left|\right|a$ and (b) $B\left|\right|c$. The nuclear Schottky contribution $C_{\text{nucl}}$ is subtracted using the calculations based on the natural abundance of nuclear spins in the samples. The baseline of the $C/T$ values obtained at each field is shifted in a step of 0.$4{\text{J/K}}^2\text{mol}$ from that at 14 T for clarity. The open and closed arrows indicate $T_c$ and $T_N$, respectively. $C/T$ versus $B$ at $T\sim 3.8\text{K}$ is shown in the inset of (a). The inset of (b) is the $logT$ plot of $C/T$ at 9 T for $B\left|\right|c$.

Figure 6

The entropy change divided by the gas constant, $S/R$, for $\text{CeCo}{\left({\text{In}}_{0.93}{\text{Zn}}_{0.07}\right)}_5$ with (a) $B\left|\right|a$ and (b) $B\left|\right|c$, plotted as a function of temperature. The entropy change is evaluated by integrating $(C_p-C_{\text{nucl}})/T$ above 0.5 K. The initial values of $S/R$ at 0.5 K are modified so that the $S/R$ values at 3.8 K coincide to each other.

Figure 7

Low-temperature $B$ vs $T$ phase diagram of $\text{CeCo}{\left({\text{In}}_{1-x}{\text{Zn}}_x\right)}_5$ $\left(x=0.07,y\sim 0.025\right)$ with (a) $B\left|\right|a$ and (b) $B\left|\right|c$, derived from the anomalies seen in the specific heat, electrical resistivity, and isothermal magnetization. The horizontal error bars indicate the broadening of the AFM and SC transitions estimated from the derivative of the heat capacity as a function of temperature. The insets show the slope of ${\mu }_0{H}_{c2}\left(T\right)$ at $\sim T_c$ for $x=0$, 0.025, 0.05, and 0.07 derived from the specific-heat and magnetization data. The lines on the phase boundaries are guides to the eye.