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 30K both in the paramagnetic phase and antiferromagnetic phases down to ∼0.33 K. Furthermore, we traced magnetic field-temperature phase diagrams up to 30T and observed a highly anisotropic elastic response within the honeycomb layer. These observations strongly suggest that Γ_{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.
Highlights
The multipole formulation and its foundational concept in solid-state physics have been developed by intensive research on f-electron systems [1,2]
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 Γ6ðE2gÞ electric quadrupolar degrees of freedom in localized 5f2 (J 1⁄4 4) states are playing an important role in the magnetic toroidal dipole order and magnetic-field-induced phases of UNi4B, and evidence some of the U ions remain in the paramagnetic state even if the system undergoes magnetic toroidal ordering
A major experimental challenge is to demonstrate odd-parity multipole ordering by observing cross-correlation phenomena and spontaneous spatial inversion-symmetry breaking in a suitable compound [5,8]
Summary
Remain in a paramagnetic (PM) state. [13,15,16] Assuming a hexagonal crystal structure (P6=mmm, D16h, No 191), an exotic magnetic structure was proposed from neutron scattering experiments in earlier studies [16]. The theory deals with the tetragonal point group C4v, and the contribution of the orbital degrees of freedom such as even-parity electric multipolar moments to the noncollinear magnetic order in UNi4B has not been investigated. Another fascinating point and an open question for this compound is a specific-heat anomaly at TÃ ∼ 0.33 K of unknown origin [22]. The elastic constants reflect the coupling of the strain field caused by the ultrasonic wave to the electric multipolar moments, which are described by orbital degrees of freedom of the CEF state. In the first stage of the analysis, we consider the conventional localized 5f-electronic states with even-parity CEF levels and
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