Electric Quadrupolar Contributions in the Magnetic Phases of UNi 4 B

We present acoustic signatures of the electric quadrupolar degrees of freedom in the honeycomb-layer compound ${\mathrm{UNi}}_{4}\mathrm{B}$. The transverse ultrasonic mode ${C}_{66}$ shows softening below 30 K both in the paramagnetic phase and antiferromagnetic phases down to $\ensuremath{\sim}0.33\text{ }\text{ }\mathrm{K}$. Furthermore, we traced magnetic field-temperature phase diagrams up to 30 T and observed a highly anisotropic elastic response within the honeycomb layer. These observations strongly suggest that ${\mathrm{\ensuremath{\Gamma}}}_{6}({E}_{2\mathrm{g}})$ electric quadrupolar degrees of freedom in localized $5{f}^{2}$ ($J=4$) states are playing an important role in the magnetic toroidal dipole order and magnetic-field-induced phases of ${\mathrm{UNi}}_{4}\mathrm{B}$, and evidence some of the U ions remain in the paramagnetic state even if the system undergoes magnetic toroidal ordering.