On the Hidden Order in URu$_{2}$Si$_{2}$ --- Antiferro Hexadecapole Order and its Consequences

Abstract

An antiferro ordering of an electric hexadecapole moment is discussed as a promising candidate for the long standing mystery of the hidden order phase in URu 2 Si 2 . Based on localized f -electron picture, we discuss the rationale of the selected multipole and the consequences of the antiferro hexadecapole order of xy(x 2 − y 2 ) symmetry. The mean-field solutions and the collective excitations from them explain reasonably significant experimental observations: the strong anisotropy in the magnetic susceptibility, characteristic behavior of pressure versus magnetic field or temperature phase diagrams, disappearance of inelastic neutron-scattering intensity out of the hidden order phase, and insensitiveness of the NQR frequency at Ru-sites upon ordering. A consistency with the strong anisotropy in the magnetic responses excludes all the multipoles in two-dimensional representations, such as (O yz , O zx ). The expected azimuthal angle dependences of the resonant X-ray scattering amplitude are given. The (x 2 −y 2 )-type antiferro quadrupole should be induced by an in-plane magnetic field along [110], which is reflected in the thermal expansion and the elastic constant of the transverse (c 11 − c 12 )/2 mode. The (x 2 − y 2 )-type [(xy)-type] antiferro quadrupole is also induced by applying the uniaxial stress along [110] direction [[100] direction]. A detection of these induced antiferro quadrupoles under the in-plane magnetic field or the uniaxial stress using the resonant X-ray scattering provides a direct redundant test for the proposed order parameter.

Hexadecapolar Kondo Effect inURu2Si2?

“…Recent experiments have definitely ruled out quadrupolar order [8], whereas another might implicitly hint at it [9]. On the other hand, the hypothesis of active Uranium hexadecapolar degrees of freedom provides a natural explanation for numerous experiments [10]. In this Letter, we generalize the work of ref.…”

High-order Ho multipoles in HoB2C2observed with soft resonant x-ray diffraction

“…For example, ordering of the electromagnetic anapole has been observed recently in CuO [3] and may be relevant to both its multiferroic properties and the superconductivity of related compounds. Ordered states of higher rank multipole moments appear in selected compounds, such as octupoles in Ce 1−x La x B 6 [4,5], hexadecapoles (or triakontadipoles) in NpO 2 [6,7], and hexadecapoles in URu 2 Si 2 [8,9]. We have investigated the interplay between the magnetic and quadrupolar order of the 4f electrons in HoB 2 C 2 using resonant x-ray diffraction (RXD).…”