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

TL;DR

This study uncovers the role of electric quadrupolar degrees of freedom in the magnetic phases of UNi4B through ultrasonic measurements, revealing anisotropic elastic responses and phase diagram features.

Contribution

It provides the first evidence of electric quadrupolar contributions influencing magnetic ordering and field-induced phases in UNi4B.

Findings

Ultrasonic mode C66 softens below 30 K in multiple phases.

Highly anisotropic elastic response observed in magnetic field-temperature phase diagrams.

Electric quadrupolar degrees of freedom are key to understanding magnetic toroidal order in UNi4B.

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 $\sim0.33$ 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$_{\rm 2g}$) 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.