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

TL;DR

This paper proposes that antiferro hexadecapole order explains the hidden order phase in URu$_{2}$Si$_{2}$, aligning with various experimental observations and predicting specific responses to external stimuli.

Contribution

It introduces the antiferro hexadecapole order as a novel candidate for the hidden order in URu$_{2}$Si$_{2}$, with detailed theoretical analysis and experimental predictions.

Findings

Explains anisotropic magnetic susceptibility and phase diagram behaviors.

Accounts for neutron scattering and NQR experimental results.

Predicts induced quadrupole moments under magnetic field and stress.

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.