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.

10 pages, 10 figures, 5 tables

References in corpus (6)

• Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2
• Similarity of Fermi Surface in the Hidden Order State and in the Antiferromagnetic State of URu2Si2
• Spin nematic state as a candidate of the hidden order phase of URu${}_2$Si${}_2$
• Neutron Scattering Study on Competition between Hidden Order and Antiferromagnetism in U(Ru_{1-x}Rh_x)_2Si_2 (x <= 0.05)
• Electrical Resistivity and Thermal Expansion Measurements of URu2Si2 under Pressure
• Magnetization, Maxwell's Relations and the Local Physics of the Dilute System Th_{1-x}U_{x}Ru_{2}Si_{2}

Cited by in corpus (49)

• Colloquium: Hidden Order, Superconductivity, and Magnetism -- The Unsolved Case of URu2Si2
• Emergent Rank-5 'Nematic' Order in URu2Si2
• Chirality density wave of the 'hidden order' phase in URu${}_2$Si${}_2$
• Hidden Order Behaviour in URu2Si2 (A Critical Review of the Status of Hidden Order in 2014)
• First-principles theory of magnetic multipoles in condensed matter systems
• Hidden order and beyond: an experimental-theoretical overview of the multifaceted behavior of URu${}_2$Si${}_2$
• Heavy fermions in high magnetic field
• Microscopic theory of the insulating electronic ground states of actinide dioxides AnO2 (An=U, Np, Pu, Am, and Cm)
• Superconductivity in magnetic multipole states
• Details of Sample Dependence and Transport Properties of URu2Si2
• One-Component Order Parameter in URu${}_2$Si${}_2$ Uncovered by Resonant Ultrasound Spectroscopy and Machine Learning
• Spectroscopic determination of the atomic f-electron symmetry underlying hidden order in URu${}_2$Si${}_2$
• Direct bulk sensitive probe of 5f symmetry in URu2Si2
• Interplay of magnetism, Fermi surface reconstructions, and hidden-order in the heavy-fermion material URu${}_2$Si${}_2$
• Symmetry of the Excitations in the Hidden Order State of URu2Si2
• Study of the magnetic properties of URu2Si2 under uniaxial stress by neutron scattering
• Odd-parity multipole fluctuation and unconventional superconductivity in locally noncentrosymmetric crystal
• Untangling the structural, magnetic dipole, and charge multipolar orders in Ba${}_2$MgReO${}_6$
• Superconductivity induced by fluctuations of momentum-based multipoles
• Γ3-type Lattice Instability and the Hidden Order of URu2Si2
• Lattice dynamics of the heavy fermion compound URu${}_2$Si${}_2$
• Hybridization-Driven Orthorhombic Lattice Instability in URu2Si2
• Chiral charge as hidden order parameter in URu${}_2$Si${}_2$
• Magnetic Field Effect on Crossover Temperature from Non-Fermi Liquid to Fermi Liquid Behavior in f^2-Impurity Systems with Crystalline-Electric-Field Singlet State Competing with Kondo-Yosida Singlet State
• Multipole order and global/site symmetry in the hidden order phase of URu2Si2
• Hexadecapolar Kondo effect in URu${}_2$Si${}_2$?
• Local observation of linear-$T$ superfluid density and anomalous vortex dynamics in URu${}_2$Si${}_2$
• Magnetic Exciton Mediated Superconductivity in the Hidden-Order Phase of URu2Si2
• Optical conductivity of URu${}_2$Si${}_2$ in the Kondo Liquid and Hidden-Order Phases
• Search for Multipolar Instability in URu${}_2$Si${}_2$ Studied by Ultrasonic Measurements under Pulsed Magnetic Field
• 3D Modulated Spin Liquid model applied to URu${}_2$Si${}_2$
• On the possibility to detect multipolar order in URu${}_2$Si${}_2$ by the electric quadrupolar transition of resonant elastic X-ray scattering
• Superconducting phase within the hidden-order state of the heavy-fermion material $\mathrm{UR}{\mathrm{u}}_2\mathrm{S}{\mathrm{i}}_2$
• Thermodynamic evidence for broken fourfold rotational symmetry in the hidden-order phase of URu2Si2
• Exceptional Ising Magnetic Behavior of Itinerant Spin-polarized Carriers in URu2Si2
• Modulated Spin Liquid and Magnetic Order from a Kondo-Heisenberg model applied to $UR{u}_{2}S{i}_2$
• Induced order and collective excitations in three-singlet quantum magnets
• Magnetoelastic coupling in URu2Si2: Probing multipolar correlations in the hidden order state
• Tunneling spectroscopy of the superconducting state of URu2Si2
• Ultrasonic Study of the Hidden Order and Heavy-Fermion State in URu${}_2$Si${}_2$ with Hydrostatic Pressure, Rh-doping, and High-Magnetic Fields
• Fe substitution in URu${}_2$Si${}_2$: singlet magnetism in an extended Doniach phase diagram
• Hidden order symmetry and superconductivity in URu2Si2 investigated by quasiparticle interference
• Efficient Method for Prediction of Meta-stable/Ground Multipolar Ordered States and its Application in Monolayer $\alpha$-\ce{RuX3} (X=Cl,I)
• Raman Active High Energy Excitations in URu${}_2$Si${}_2$
• Analysis of Magnetoacoustic Quadrupole Resonance and Application to Probe Quadrupole Degrees of Freedom in Quantum Magnets
• Spin-orbit density wave: A new phase of matter applicable to the hidden order state of URu2Si2
• Phenomenological theory of the superconducting state inside the hidden-order phase of URu${}_2$Si${}_2$
• Ultrasonic Observation of Slowing Down of Multipole Fluctuations in Sr${}_2$RuO${}_4$
• Elastic properties of hidden order in URu${}_{\text{2}}$Si${}_{\text{2}}$ are reproduced by a staggered nematic