Probing magnetic-field-induced multipolar ordering through field-angle-resolved magnetostriction and thermal expansion in PrIr$_2$Zn$_{20}$

Abstract

We performed field-angle-resolved magnetostriction and thermal-expansion measurements on PrIr$_2$Zn$_{20}$, a cubic non-Kramers compound exhibiting antiferroquadrupolar order below $T_{\rm Q}=0.125$ K. Thermal expansion exhibits two qualitatively different anomalies under magnetic fields applied along the $[001]$ direction, providing experimental support for the existence of an intermediate A phase previously reported. Furthermore, comparison between the experimental results and theoretical modeling indicates a strong anisotropic coupling of the $O_{20}$ quadrupolar moment, which plays a key role in stabilizing the A phase. These findings demonstrate that multipolar states in non-Kramers systems can be effectively tuned by magnetic-field orientation, providing insights into the anisotropic nature of quadrupolar interactions.

Figures (5)

• Figure 1: Field-angle $\phi$ dependence of $\Delta L/L=(L-L_0)/L$ at 0.12 K under magnetic fields of 1 and 2 T rotated within the $(1\bar{1}0)$ plane. Here, $\phi$ is the magnetic-field angle measured from the $[001]$ axis. The solid lines show a phenomenological expression for the effective quadrupolar field component, proportional to $B^2(3\cos^2\phi-1)$, which couples to the $O_{20}$ moment (see text for details). The inset shows the magnetostriction coefficient $\lambda=(\partial L/\partial B)/L$ at 0.12 K for $B \parallel [001]$ (at $\phi=0^\circ$).
• Figure 2: (a) Thermal expansion coefficient $\alpha=(\partial L/\partial T)/L$ measured at several magnetic fields applied parallel to the $[001]$ axis. (b) Selected field data highlighting the emergence of a double transition. Each set of data is shifted vertically by $3 \times 10^{-5}$ K$^{-1}$ for clarity. Triangles indicate the positions of the anomalies.
• Figure 3: (a) Thermal expansion coefficient $\alpha(T)$ measured at several magnetic fields applied parallel to the $[112]$ axis. (b) The $\alpha(T)$ data under a magnetic field of 2.9 T rotated in $0^\circ \le \phi \le 30^\circ$. Each set of data is shifted vertically by $3 \times 10^{-5}$ K$^{-1}$ for clarity. Triangles indicate the positions of the anomalies.
• Figure 4: Thermal expansion coefficient $\alpha(T)$ measured at several magnetic fields applied parallel to the (a) $[110]$ and (b) $[111]$ axes. Each set of data is shifted vertically by $3 \times 10^{-5}$ K$^{-1}$ for clarity. Triangles indicate the positions of the anomalies.
• Figure 5: Field-temperature phase diagram of PrIr$_2$Zn$_{20}$ for magnetic fields applied along the (a) $[001]$, (b) $[112]$, (c) $[111]$, and (d) $[110]$ axes. Circles and squares indicate peak and dip anomalies observed in $\alpha(T)$, respectively. (e) Field-angle $\phi$ dependence of the critical fields obtained from previous specific-heat measurements at 0.12 K Kittaka2024PRB. The solid lines represent theoretically predictions of $B_{\rm c}(\phi)$ (see text for details) with $B_{\rm c}(0)=1.9$ and $3.0$ T.