A quantum liquid of magnetic octupoles on the pyrochlore lattice

Abstract

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles${}^1$. Theories typically define such states using gauge fields and deconfined quasiparticle excitations that emerge from a simple rule governing the local ground state of a frustrated magnet. For example, the '2-in-2-out' ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores - a state described by a lattice gauge theory of quantum electrodynamics${}^{2-4}$. However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and 'hidden' orders${}^{5-6}$. Here we show that the correlated ground state of a Ce${}^{3+}$-based pyrochlore, Ce${}_2$Sn${}_2$O${}_7$, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with the formation of a fluid-like state of matter, but the intensity distribution is weighted to larger scattering vectors, which indicates that the correlated degrees of freedom have a more complex magnetization density than that typical of magnetic dipoles in a spin liquid. The temperature evolution of the bulk properties in the correlated regime below 1 Kelvin is well reproduced using a model of dipole-octupole doublets on a pyrochlore lattice${}^{7-8}$. The nature and strength of the octupole-octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a '2-plus-2-minus' rule. Our work identifies Ce${}_2$Sn${}_2$O${}_7$ as a unique example of a material where frustrated multipoles form a 'hidden' topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.

References in corpus (35)

• Quantum Spin Liquids
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Quantum Orders and Symmetric Spin Liquids
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• A Field Guide to Spin Liquids
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
• Spin Ice, Fractionalization and Topological Order
• HORACE: software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments
• Seeing the light : experimental signatures of emergent electromagnetism in a quantum spin ice
• Generic quantum spin ice
• Frustrated quantum rare-earth pyrochlores
• Evidence of an odd-parity hidden order in a spin-orbit coupled correlated iridate
• Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore
• Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice
• Quantum Melting of Spin Ice: Emergent Cooperative Quadrupole and Chirality
• Emergent Rank-5 'Nematic' Order in URu2Si2
• Quantum Spin Ice Dynamics in the Dipole-Octupole Pyrochlore Magnet Ce${}_2$Zr${}_2$O${}_7$
• Description of Multipole in f-Electron Systems
• Candidate Quantum Spin Liquid in the Ce\textsuperscript{3+} Pyrochlore Stannate Ce${}_2$Sn${}_2$O${}_7$
• Structural distortion and the spin liquid state in Tb2Ti2O7
• Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice
• Continuum of quantum fluctuations in a three-dimensional $S=1$ Heisenberg magnet
• Electric Toroidal Quadrupoles in Spin-Orbit Coupled Metal Cd${}_2$Re${}_2$O${}_7$
• How quantum are classical spin ices?
• Crystal field states in a Quantum Spin Ice]{Crystal field states of Pr${}^{3+}$ in the candidate quantum spin ice Pr${}_2$Sn${}_2$O${}_7$
• Dynamics of Topological Excitations in a Model Quantum Spin Ice
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• Upgrade to the MAPS neutron time-of-flight chopper spectrometer
• The Spectral Periodicity of Spinon Continuum in Quantum Spin Ice
• Quasi-static magnetoelectric quadrupoles as the order parameter for the pseudo-gap phase in cuprate superconductors
• Pyrochlore U(1) spin liquid of mixed symmetry enrichments in magnetic fields
• Orbital currents, anapoles, and magnetic quadrupoles in CuO
• Spectrum of itinerant fractional excitations in quantum spin ice
• Spectroscopy of spinons in Coulomb quantum spin liquids

Cited by in corpus (72)

• Orbital effects in solids: basics, recent progress and opportunities
• The Chemistry of Quantum Spin Liquids
• The case for a U(1)${}_{\pi }$ Quantum Spin Liquid Ground State in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
• Sleuthing out exotic quantum spin liquidity in the pyrochlore magnet Ce${}_2$Zr${}_2$O${}_7$
• Thermal Hall effects in quantum magnets
• Experimental signatures of quantum and topological states in frustrated magnetism
• Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO${}_4$ and beyond
• Magnetic octupole tensor decomposition and second-order magnetoelectric effect
• Ground state phase diagram of dipolar-octupolar pyrochlores
• Distinguishing dipolar and octupolar quantum spin ices using contrasting magnetostriction signatures
• Collective excitations in the tetravalent lanthanide honeycomb antiferromagnet, Na2PrO3
• Magnetic field effects in an octupolar quantum spin liquid candidate
• Crystal-field states and defect levels in candidate quantum spin ice Ce${}_2$Hf${}_2$O${}_7$
• Competing $U(1)$ and ${\mathbb{Z}}_2$ dipolar-octupolar quantum spin liquids on the pyrochlore lattice: application to Ce${}_2$Zr${}_2$O${}_7$
• Uncovering footprints of dipolar-octupolar quantum spin ice from neutron scattering signatures
• Superconductivity induced by fluctuations of momentum-based multipoles
• Spin liquid state in a rare-earth hyperkagome lattice
• Dipolar spin ice regime proximate to an all-in-all-out Néel ground state in the dipolar-octupolar pyrochlore Ce${}_2$Sn${}_2$O${}_7$
• Quantum Spin Ice Response to a Magnetic Field in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
• Magnetic properties and signatures of moment ordering in triangular lattice antiferromagnet KCeO${}_2$
• Hierarchy of energy scales and field-tunable order by disorder in dipolar-octupolar pyrochlores
• Spectroscopic signatures of fractionalization in octupolar quantum spin ice
• Antiferromagnetism and crystalline-electric field excitations in tetragonal NaCeO2
• Field-angle resolved magnetic excitations as a probe of hidden-order symmetry in CeB6
• Beyond magnons in Nd2ScNbO7: An Ising pyrochlore antiferromagnet with all in all out order and random fields
• Extended Coulomb liquid of paired hardcore boson model on a pyrochlore lattice
• Hidden orders in spin-orbit entangled correlated insulators
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Signatures of hidden octupolar order from nonlinear Hall effects
• Stripe magnetic order and field-induced quantum criticality in the perfect triangular-lattice antiferromagnet CsCeSe${}_2$
• Multipolar exchange interaction and complex order in insulating lanthanides
• Epitaxial stabilization of (111)-oriented frustrated quantum pyrochlore thin films
• Magnetic multipoles and correlation shortage in pyrochlore cerium stannate
• Evaluating the Effects of Structural Disorder on the Magnetic Properties of Nd${}_2$Zr${}_2$O${}_7$
• $\mu$SR Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$
• Emergent photons and fractionalized excitations in a quantum spin liquid
• Energy scales in 4f1 delafossite magnets: crystal-field splittings larger than the strength of spin-orbit coupling in KCeO2
• Quantum spin liquids on the diamond lattice
• Ferroic quadrupolar ordering in CeCoSi revealed using ${}^{59}$Co-NMR measurements
• Distinguishing thermodynamics and spectroscopy for octupolar U(1) spin liquid of Ce-pyrochlores
• Ultrasound detection of emergent photons in generic quantum spin ice
• Classification of Classical Spin Liquids: Topological Quantum Chemistry and Crystalline Symmetry
• A pseudofermion functional renormalization group study of dipolar-octupolar pyrochlore magnets
• Finite Temperature Dynamics in 0-Flux and $\pi$-Flux Quantum Spin Ice: Self-Consistent Exclusive Boson Approach
• Exploiting polarization dependence in two dimensional coherent spectroscopy: examples of Ce${}_2$Zr${}_2$O${}_7$ and Nd${}_2$Zr${}_2$O${}_7$
• Dipolar-octupolar correlations and hierarchy of exchange interactions in Ce${}_2$Hf${}_2$O${}_7$
• Spin ice in a general applied magnetic field: Kasteleyn transition, magnetic torque and rotational magnetocaloric effect
• Hidden phases born of a quantum spin liquid: Application to pyrochlore spin ice
• Thermodynamics of the dipole-octupole pyrochlore magnet Ce${}_2$Hf${}_2$O${}_7$ in applied magnetic fields
• Crystal-field effects competing with spin-orbit interactions in NaCeO${}_2$
• Spin-orbit coupling induced orbital entanglement in a three-band Hubbard model
• Signatures of spinon dynamics and phase structure of dipolar-octupolar quantum spin ices in two-dimensional coherent spectroscopy
• Two-Peak Heat Capacity Accounts for $R\ln (2)$ Entropy and Ground State Access in the Dipole-Octupole Pyrochlore Ce${}_2$Hf${}_2$O${}_7$
• Multipolar spin liquid in an exactly solvable model for $j_{\mathrm{eff}}=\frac{3}{2}$ moments
• Single Crystal Diffuse Neutron Scattering Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$: No Apparent Octupolar Correlations Above $T=0.05$ K
• Magnetic Field Response of Dipolar-Octupolar Quantum Spin Ice
• Inelastic neutron scattering on Ce pyrochlores: Signatures of electric monopoles
• Coulombic antiferromagnet in spin-1/2 pyrochlores with dipole-octupole doublets
• Influence of controlled disorder on the dipolar spin ice state of Ho-based pyrochlores
• Emergent Dispersive Multipolar Excitations in NaErSe${}_2$
• Keldysh pseudo-fermion functional renormalization group for quantum magnetism
• Coupling quantum spin ice to matter on the centered pyrochlore lattice
• AMBER: Algorithm for Multiplexing spectrometer Background Estimation with Rotation-independence
• Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
• Possibility of ferro-octupolar order in Ba${}_2$CaOsO${}_6$ assessed by X-ray magnetic dichroism measurements
• Spinon band flattening by its emergent gauge field in quantum kagome ice
• Bragg diffraction by a magnetic all-in-all-out configuration with application to a cubic cerium pyrochlore oxide
• Disorder-induced proximate quantum spin ice phase in Pr2Sn2O7
• Towards a global phase diagram of Ce-based dipolar-octupolar pyrochlore magnets under magnetic fields
• 5d-mediated indirect exchange and effective spin Hamiltonians in Ce triangular-lattice delafossites
• Classification and correlation signatures of chiral spin liquids on the pyrochlore lattice
• Excitation spectrum and low-temperature magnetism in disordered defect-fluorite Ho2Zr2O7