Electric Quadrupolar Contributions in the Magnetic Phases of UNi${}_4$B

Abstract

We present acoustic signatures of the electric quadrupolar degrees of freedom in the honeycomb-layer compound UNi${}_4$B. The transverse ultrasonic mode $C_{66}$ shows softening below 30 K both in the paramagnetic phase and antiferromagnetic phases down to $\sim 0.33$ 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 ${\Gamma }_6$(E${}_{2g}$) electric quadrupolar degrees of freedom in localized $5f^2$ ($J=4$) states are playing an important role in the magnetic toroidal dipole order and magnetic-field-induced phases of UNi${}_4$B, and evidence some of the U ions remain in the paramagnetic state even if the system undergoes magnetic toroidal ordering.

6 pages, 4 figures + Supplemental Materials (11 pages, 9 figures)

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