Possible Observation of the Quadrupolar Kondo Effect in Dilute Quadrupolar System ${\mathrm{Pr}}_x{\mathrm{La}}_{1-x}{\mathrm{Pb}}_3$ for $x\le 0.05$

We have studied non-Fermi-liquid (NFL) behavior in ${\mathrm{Pr}}_x{\mathrm{La}}_{1-x}{\mathrm{Pb}}_3$ with ${\Gamma }_3$ quadrupolar moments in the crystalline-electric-field ground state. The specific heat $C/T$ shows NFL behavior in the very dilute region for $x\le 0.05$, which is scaled by a characteristic temperature $T^{*}$ in each Pr concentration. The application of a magnetic field leads to a sharp increase of $C/T$, demonstrating the shift of the entropy existing in the lower temperature region at $H=0\mathrm{T}$. Moreover, Fermi-liquid behavior emerges at higher fields, in contrast with NFL behavior at lower fields. The observed features indicate that NFL behavior is caused by the quadrupolar Kondo effect.

Figure 1

$C_{\mathrm{el}}/T$ at $H=0\mathrm{T}$ plotted on a logarithmic temperature scale measured in a single crystal for $x=0.05$ and polycrystals for $x=0.1$, 0.03, and 0.01. $C_{\mathrm{el}}/T$ for $x=0.1$ is almost constant at low temperatures, while that for $x\le 0.05$ shows NFL behavior (see text). Inset: $C_{\mathrm{el}}$$T^{*}/T$ versus log $(T/T^{*})$ at $H=0\mathrm{T}$. $T^{*}$ is taken to be 1 K for $x=0.05$, 0.65 K for $x=0.03$, and 0.40 K for $x=0.01$.

Figure 2

(a) Temperature dependence of the specific heat for the single crystal in $H\parallel [100]$ at representative magnetic fields. The data from bottom to top at $T=1\mathrm{K}$ correspond to the results for $H=0$, 2, 6, and 4 T, respectively. The dashed line shows the phonon contribution $C_{\mathrm{ph}}$ for $H\ge 1\mathrm{T}$ estimated from the specific heat of ${\mathrm{LaPb}}_3$. (b) Magnetic field dependence of $A_n^{1/2}$ in the nuclear specific heat obtained by the fitting from Eq. (1) and that calculated from the magnetization at $T=2\mathrm{K}$ for $x=0.05$.

Figure 3

(a) Magnetic field dependences of $C_{\mathrm{el}}/T$ in $H\parallel [100]$ in the single crystal. Inset: The magnetic field dependence of $C_{\mathrm{el}}/T$ at representative temperatures. The dashed lines are guides for eyes. (b) Magnetic field dependences of $C_{\mathrm{el}}/T$ in the polycrystal. The inset shows the magnetic field dependence of $C_{\mathrm{el}}/T$ at representative temperatures.