Antiferroquadrupolar Ordering in a Pr-Based Superconductor ${\mathrm{PrIr}}_2{\mathrm{Zn}}_{20}$

An antiferroquadrupolar ordering at $T_{\mathrm{Q}}=0.11\mathrm{K}$ has been found in a Pr-based superconductor ${\mathrm{PrIr}}_2{\mathrm{Zn}}_{20}$. The measurements of specific heat and magnetization revealed the non-Kramers ${\Gamma }_3$ doublet ground state with the quadrupolar degrees of freedom. The specific heat exhibits a sharp peak at $T_{\mathrm{Q}}=0.11\mathrm{K}$. The increment of $T_{\mathrm{Q}}$ in magnetic fields and the anisotropic $B-T$ phase diagram are consistent with the antiferroquadrupolar ordered state below $T_{\mathrm{Q}}$. The entropy release at $T_{\mathrm{Q}}$ is only 20% of $R\ln 2$, suggesting that the quadrupolar fluctuations play a role in the formation of the superconducting pairs below $T_{\mathrm{c}}=0.05\mathrm{K}$.

Figure 1

Temperature dependence of the inverse magnetic susceptibility ${\chi }^{-1}(T)$ at a magnetic field of $B=0.1\mathrm{T}$ for $\mathit{B}\Vert [100]$. At $T>30\mathrm{K}$, ${\chi }^{-1}(T)$ follows the Curie-Weiss law with the effective magnetic moment of a free ${\mathrm{Pr}}^{3+}$ ion. The lower inset displays the temperature dependence of the magnetic part of the specific heat divided by the temperature, $C_m/T$. The solid line is the calculation for a CEF level scheme with the ground state of a ${\Gamma }_3$ doublet and an excited state of magnetic ${\Gamma }_4$ triplet lying at 30 K. The upper inset shows the isothermal magnetization in $\mathit{B}\Vert [100]$ and $\mathit{B}\Vert [110]$ at 1.8 K. The lines are the $M(B)$’s calculated for the CEF scheme as shown in the lower inset.

Figure 2

The solid circles and solid line, respectively, show the temperature dependences of the specific heat $C$ (left-hand scale) and the entropy $S$ (right-hand scale) of ${\mathrm{PrIr}}_2{\mathrm{Zn}}_{20}$. $C$ shows a sharp peak at $T_{\mathrm{Q}}=0.11\mathrm{K}$, at which temperature $S$ is only 20% of $R\ln 2$. The inset shows the temperature dependence of $M/B$ at various magnetic fields of $\mathit{B}\Vert [100]=3$, 4, 5, 6, 8, and 10 T.

Figure 3

Temperature dependence of the specific heat of ${\mathrm{PrIr}}_2{\mathrm{Zn}}_{20}$ in $\mathit{B}\Vert [100]$ and $\mathit{B}\Vert [110]$. Each data point in the magnetic field is vertically offset for clarity. In $B=0$, a sharp peak appears at 0.11 K, which splits into two at $T_{Q1}$ and $T_{Q2}$ in $\mathit{B}\Vert [100]\ge 1\mathrm{T}$. The upper temperature $T_{Q1}$ increases with increasing magnetic fields. In $\mathit{B}\Vert [110]$, however, the peak shifts to higher temperatures without being split.

Figure 4

$B-T$ phase diagram of ${\mathrm{PrIr}}_2{\mathrm{Zn}}_{20}$ for $\mathit{B}\Vert [100]$ (open circles) and $\mathit{B}\Vert [110]$ (solid triangles). $T_{\mathrm{c}}$ and SC denote the superconducting transition temperature and the superconducting phase, respectively. The inset shows the temperature dependence of the ac magnetic susceptibility and electrical resistivity.