Search for Multipolar Instability in URu$_2$Si$_2$ Studied by Ultrasonic Measurements under Pulsed Magnetic Field

The elastic properties of URu$_2$Si$_2$ in the high-magnetic field region above 40 T, over a wide temperature range from 1.5 to 120 K, were systematically investigated by means of high-frequency ultrasonic measurements. The investigation was performed at high magnetic fields to better investigate the innate bare 5$f$-electron properties, since the unidentified electronic thermodynamic phase of unknown origin, so called `hidden order(HO) and associated hybridization of conduction and $f$-electron ($c$-$f$ hybridization) are suppressed at high magnetic fields. From the three different transverse modes we find contrasting results; both the $Gamma_4$(B$_{rm 2g}$) and $Gamma_5$(E$_{rm g}$) symmetry modes $C_{66}$ and $C_{44}$ show elastic softening that is enhanced above 30 T, while the characteristic softening of the $Gamma_3$(B$_{rm 1g}$) symmetry mode $(C_{11}-C_{12})/2$ is suppressed in high magnetic fields. These results underscore the presence of a hybridization-driven $Gamma_3$(B$_{rm 1g}$) lattice instability in URu$_2$Si$_2$. However, the results from this work cannot be explained by using existing crystalline-electric field (CEF) schemes applied to the quadrupolar susceptibility in a local $5f^2$ configuration. Instead, we present an analysis based on a band Jahn-Teller effect.