Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore

Gao, Bin; Chen, Tong; Tam, David W.; Huang, Chien -Lung; Sasmal, Kalyan; Adroja, Devashibhai T.; Ye, Feng; Cao, Huibo; Sala, Gabriele; Stone, Matthew B.; Baines, Christopher; Verezhak, Joel A. T.; Hu, Haoyu; Chung, Jae -Ho; Xu, Xianghan; Cheong, Sang -Wook; Nallaiyan, Manivannan; Spagna, Stefano; Maple, M. Brian; Nevidomskyy, Andriy H.; Morosan, Emilia; Chen, Gang; Dai, Pengcheng

doi:10.1038/s41567-019-0577-6

Title: Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce₂Zr₂O₇ pyrochlore

Abstract

A quantum spin liquid is a state of matter where unpaired electrons’ spins, although entangled, do not show magnetic order even at the zero temperature. The realization of a quantum spin liquid is a long-sought goal in condensed-matter physics. Although neutron scattering experiments on the two-dimensional spin-1/2 kagome lattice ZnCu₃(OD)₆Cl₂ and triangular lattice YbMgGaO₄ have found evidence for the hallmark of a quantum spin liquid at very low temperature (a continuum of magnetic excitations), the presence of magnetic and non-magnetic site chemical disorder complicates the interpretation of the data. Recently, the three-dimensional Ce³⁺ pyrochlore lattice Ce₂Sn₂O₇ has been suggested as a clean, effective spin-1/2 quantum spin liquid candidate, but evidence of a spin excitation continuum is still missing. Furthermore, we use thermodynamic, muon spin relaxation and neutron scattering experiments on single crystals of Ce₂Zr₂O₇, a compound isostructural to Ce₂Sn₂O₇, to demonstrate the absence of magnetic ordering and the presence of a spin excitation continuum at 35 mK. With no evidence of oxygen deficiency and magnetic/non-magnetic ion disorder seen by neutron diffraction and diffuse scattering measurements, Ce₂Zr₂O₇ may be a three-dimensional pyrochlore lattice quantum spin liquid material with minimum magnetic and non-magnetic chemical disorder.

Authors:

Gao, Bin ^[1]; Chen, Tong ^[1];

^[1];

^[1]; Sasmal, Kalyan ^[2]; Adroja, Devashibhai T. ^[3];

^[4];

^[4]; Baines, Christopher ^[5]; Verezhak, Joel A. T. ^[5]; Hu, Haoyu ^[1]; Chung, Jae -Ho ^[1]; Xu, Xianghan ^[6]; Cheong, Sang -Wook ^[6]; Nallaiyan, Manivannan ^[7]; Spagna, Stefano ^[7]; Maple, M. Brian ^[2]; Nevidomskyy, Andriy H. ^[1] more »

Rice Univ., Houston, TX (United States)
Univ. of California, San Diego, CA (United States)
STFC Rutherford-Appleton Lab, Didcot (United Kingdom)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Paul Scherrer Inst. (PSI), Villigen (Switzerland)
Rutgers Univ., Piscataway, NJ (United States)
Quantum Design Inc., San Diego, CA (United States)
The Univ. of Hong Kong, Hong Kong (China); Fudan Univ., Shanghai (China)

Publication Date:: 2019-07-15

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1558477

Alternate Identifier(s):: OSTI ID: 1661263

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Nature Physics

Additional Journal Information:: Journal Volume: 15; Journal Issue: 7; Journal ID: ISSN 1745-2473

Publisher:: Nature Publishing Group (NPG)

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats


                    Gao, Bin, Chen, Tong, Tam, David W., Huang, Chien -Lung, Sasmal, Kalyan, Adroja, Devashibhai T., Ye, Feng, Cao, Huibo, Sala, Gabriele, Stone, Matthew B., Baines, Christopher, Verezhak, Joel A. T., Hu, Haoyu, Chung, Jae -Ho, Xu, Xianghan, Cheong, Sang -Wook, Nallaiyan, Manivannan, Spagna, Stefano, Maple, M. Brian, Nevidomskyy, Andriy H., Morosan, Emilia, Chen, Gang, and Dai, Pengcheng. Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore.  United States: N. p., 2019. 
Web.  doi:10.1038/s41567-019-0577-6.

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                    Gao, Bin, Chen, Tong, Tam, David W., Huang, Chien -Lung, Sasmal, Kalyan, Adroja, Devashibhai T., Ye, Feng, Cao, Huibo, Sala, Gabriele, Stone, Matthew B., Baines, Christopher, Verezhak, Joel A. T., Hu, Haoyu, Chung, Jae -Ho, Xu, Xianghan, Cheong, Sang -Wook, Nallaiyan, Manivannan, Spagna, Stefano, Maple, M. Brian, Nevidomskyy, Andriy H., Morosan, Emilia, Chen, Gang, & Dai, Pengcheng. Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore.  United States.  https://doi.org/10.1038/s41567-019-0577-6

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                    Gao, Bin, Chen, Tong, Tam, David W., Huang, Chien -Lung, Sasmal, Kalyan, Adroja, Devashibhai T., Ye, Feng, Cao, Huibo, Sala, Gabriele, Stone, Matthew B., Baines, Christopher, Verezhak, Joel A. T., Hu, Haoyu, Chung, Jae -Ho, Xu, Xianghan, Cheong, Sang -Wook, Nallaiyan, Manivannan, Spagna, Stefano, Maple, M. Brian, Nevidomskyy, Andriy H., Morosan, Emilia, Chen, Gang, and Dai, Pengcheng. Mon .  
"Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore".  United States.  https://doi.org/10.1038/s41567-019-0577-6.  https://www.osti.gov/servlets/purl/1558477.

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@article{osti_1558477,

  title        = {Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore},

  author       = {Gao, Bin and Chen, Tong and Tam, David W. and Huang, Chien -Lung and Sasmal, Kalyan and Adroja, Devashibhai T. and Ye, Feng and Cao, Huibo and Sala, Gabriele and Stone, Matthew B. and Baines, Christopher and Verezhak, Joel A. T. and Hu, Haoyu and Chung, Jae -Ho and Xu, Xianghan and Cheong, Sang -Wook and Nallaiyan, Manivannan and Spagna, Stefano and Maple, M. Brian and Nevidomskyy, Andriy H. and Morosan, Emilia and Chen, Gang and Dai, Pengcheng},

  abstractNote = {A quantum spin liquid is a state of matter where unpaired electrons’ spins, although entangled, do not show magnetic order even at the zero temperature. The realization of a quantum spin liquid is a long-sought goal in condensed-matter physics. Although neutron scattering experiments on the two-dimensional spin-1/2 kagome lattice ZnCu3(OD)6Cl2 and triangular lattice YbMgGaO4 have found evidence for the hallmark of a quantum spin liquid at very low temperature (a continuum of magnetic excitations), the presence of magnetic and non-magnetic site chemical disorder complicates the interpretation of the data. Recently, the three-dimensional Ce3+ pyrochlore lattice Ce2Sn2O7 has been suggested as a clean, effective spin-1/2 quantum spin liquid candidate, but evidence of a spin excitation continuum is still missing. Furthermore, we use thermodynamic, muon spin relaxation and neutron scattering experiments on single crystals of Ce2Zr2O7, a compound isostructural to Ce2Sn2O7, to demonstrate the absence of magnetic ordering and the presence of a spin excitation continuum at 35 mK. With no evidence of oxygen deficiency and magnetic/non-magnetic ion disorder seen by neutron diffraction and diffuse scattering measurements, Ce2Zr2O7 may be a three-dimensional pyrochlore lattice quantum spin liquid material with minimum magnetic and non-magnetic chemical disorder.},

  doi          = {10.1038/s41567-019-0577-6},

  journal      = {Nature Physics},

  number       = 7,

  volume       = 15,

  place        = {United States},

  year         = {2019},

  month        = {7}

}

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Figure 1: Summary of crystal structure, CEF levels, direct-current (dc) susceptibility, and specific heat of Ce₂Zr₂O₇. a, Schematic structure of Ce₂Zr₂O₇ with lattice parameters a = b = c = 10.71 Å. The blue ions are magnetic Ce³⁺ (A site) and the red ions are nonmagnetic Zr⁴⁺ (B site). b,more »

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Spectroscopic insight into the interplay between structural disorder and oxidation degree in melt‐grown Ce _0.5 Zr _0.5 O _{2‐ y} compounds
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A quantum liquid of magnetic octupoles on the pyrochlore lattice
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A quantum liquid of magnetic octupoles on the pyrochlore lattice

Journal Article Sibille, Romain ; Gauthier, Nicolas ; Lhotel, Elsa ; ... - Nature Physics

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles. Theories define such states using gauge fields and deconfined quasiparticle excitations that emerge from a local constraint governing the 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. However,more »« less
Cited by 5
https://doi.org/10.1038/s41567-020-0827-7

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Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO₄

Journal Article Paddison, Joseph A.Â M. ; Daum, Marcus ; Dun, Zhiling ; ... - Nature Physics

A quantum spin liquid (QSL) is an exotic state of matter in which electrons’ spins are quantum entangled over long distances, but do not show magnetic order in the zero-temperature limit. The observation of QSL states is a central aim of experimental physics, because they host collective excitations that transcend our knowledge of quantum matter; however, examples in real materials are scarce. We report neutron-scattering experiments on YbMgGaO₄, a QSL candidate in which Yb³⁺ ions with effective spin-1/2 occupy a triangular lattice. Furthermore, our measurements reveal a continuum of magnetic excitations—the essential experimental hallmark of a QSL7—at very low temperaturemore »« less
Cited by 36
https://doi.org/10.1038/nphys3971

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Hydrothermal Crystal Growth of Rare Earth Tin Cubic Pyrochlores, RE₂Sn₂O₇ (RE = La–Lu): Site Ordered, Low Defect Single Crystals

Journal Article Powell, Matthew ; Sanjeewa, Liurukara D. ; McMillen, Colin D. ; ... - Crystal Growth and Design

A hydrothermal route to single crystals of rare earth stannates RE₂Sn₂O₇ (RE = La–Lu) in the cubic pyrochlore structure is reported. Growth reactions were performed in aqueous fluids at 700 °C and 200 MPa with CsF mineralizers in concentrations ranging from 0 to 30 M, with 20 M CsF providing the most consistent results. Single crystals of the entire range of lanthanides were grown and characterized by single crystal X-ray diffraction and found to be isostructural in the Fdmore »« less
Cited by 5
https://doi.org/10.1021/acs.cgd.8b01889

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Title: Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore

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Spin-Glass Ground State in a Triangular-Lattice Compound YbZnGaO 4 journal, February 2018

Continuum of quantum fluctuations in a three-dimensional S = 1 Heisenberg magnet journal, October 2018

Spin Ice, Fractionalization, and Topological Order journal, March 2012

Spinon Fermi surface U ( 1 ) spin liquid in the spin-orbit-coupled triangular-lattice Mott insulator YbMgGaO 4 journal, August 2017

Implementation of cross correlation for energy discrimination on the time-of-flight spectrometer CORELLI journal, March 2018

Physical realization of a quantum spin liquid based on a complex frustration mechanism journal, July 2016

Quantum spin liquids: a review journal, November 2016

Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate journal, December 2016

Experimental Insights into Ground-State Selection of Quantum XY Pyrochlores journal, March 2018

Recent advances in magnetic structure determination by neutron powder diffraction journal, October 1993

Quantum spin liquid states journal, April 2017

Gapless Spin Liquid Ground State in the S = 1 / 2 Vanadium Oxyfluoride Kagome Antiferromagnet [ NH 4 ] 2 [ C 7 H 14 N ] [ V 7 O 6 F 18 ] journal, May 2013

Magnetic anisotropy of the spin-ice compound Dy2Ti2O7 journal, January 2002

Four-circle single-crystal neutron diffractometer at the High Flux Isotope Reactor journal, May 2011

Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice journal, August 2012

Evidence for spin liquid ground state in SrDy 2 O 4 frustrated magnet probed by μ SR journal, April 2017

Coulomb spin liquid in anion-disordered pyrochlore Tb2Hf2O7 journal, October 2017

Spin Correlations in Ho 2 Ti 2 O 7 : A Dipolar Spin Ice System journal, July 2001

Fluctuations and All-In–All-Out Ordering in Dipole-Octupole Nd 2 Zr 2 O 7 journal, November 2015

Colloquium : Herbertsmithite and the search for the quantum spin liquid journal, December 2016

Experimental signatures of emergent quantum electrodynamics in Pr2Hf2O7 journal, April 2018

Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores journal, April 2014

Magnetization process in the spin-ice compound Ho 2 Ti 2 O 7 journal, July 2003

The Resonating Valence Bond State in La2CuO4 and Superconductivity journal, March 1987

Spin Fluctuations in Frustrated Kagomé Lattice System Sr Cr 8 Ga 4 O 19 Studied by Muon Spin Relaxation journal, December 1994

Quantum Spin Ice Dynamics in the Dipole-Octupole Pyrochlore Magnet Ce 2 Zr 2 O 7 journal, May 2019

Symmetry enriched U(1) topological orders for dipole-octupole doublets on a pyrochlore lattice journal, January 2017

Anyons in an exactly solved model and beyond journal, January 2006

Spin liquids in frustrated magnets journal, March 2010

Topography of Spin Liquids on a Triangular Lattice journal, May 2018

Magnetic pyrochlore oxides journal, January 2010

Synthesis and full characterization of the phase-pure pyrochlore Ce2Zr2O7 and the κ-Ce2Zr2O8 phases journal, November 2016

DEMAND, a Dimensional Extreme Magnetic Neutron Diffractometer at the High Flux Isotope Reactor journal, December 2018

Unbound spinons in the S =1/2 antiferromagnetic chain KCuF 3 journal, June 1993

Ising versus X Y Anisotropy in Frustrated R 2 Ti 2 O 7 Compounds as “Seen” by Polarized Neutrons journal, July 2009

Gapless quantum spin liquid ground state in the two-dimensional spin-1/2 triangular antiferromagnet YbMgGaO4 journal, November 2015

Special temperatures in frustrated ferromagnets journal, May 2018

Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4 journal, December 2016

Quantum Spin Ices and Topological Phases from Dipolar-Octupolar Doublets on the Pyrochlore Lattice journal, April 2014

Spin Liquid State in the S = 1 / 2 Triangular Lattice Ba 3 CuSb 2 O 9 journal, April 2011

Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6 journal, October 2018

Quantum spin liquid in the spin- 1 ∕ 2 triangular antiferromagnet Et Me 3 Sb [ Pd ( dmit ) 2 ] 2 journal, March 2008

Magnetic Ground State of an Experimental S = 1 / 2 Kagome Antiferromagnet journal, April 2008

Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet journal, December 2012

Resonating valence bonds: A new kind of insulator? journal, February 1973

Fault-tolerant quantum computation by anyons journal, January 2003

Generic quantum spin ice journal, September 2012

Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets journal, May 2014

Doping a Mott insulator: Physics of high-temperature superconductivity journal, January 2006

Candidate Quantum Spin Liquid in the Ce 3 + Pyrochlore Stannate Ce 2 Sn 2 O 7 journal, August 2015

Site Specific X-ray Anomalous Dispersion of the Geometrically Frustrated Kagomé Magnet, Herbertsmithite, ZnCu 3 (OH) 6 Cl 2 journal, November 2010

Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice journal, September 2003

Spin Ice, Fractionalization and Topological Order text, January 2011

Generic quantum spin ice text, January 2012

Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice text, January 2013

Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice text, January 2016

Quantum Spin Liquid States text, January 2016

Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4 text, January 2016

Coulomb spin liquid in anion-disordered pyrochlore Tb$_2$Hf$_2$O$_7$ text, January 2016

Evidence for spin liquid ground state in SrDy$_2$O$_4$ frustrated magnet probed by muSR text, January 2017

Continuum of quantum fluctuations in a three-dimensional $S\!=\!1$ Heisenberg magnet text, January 2017

Special temperatures in frustrated ferromagnets text, January 2018

Anyons in an exactly solved model and beyond text, January 2005

Fault-tolerant quantum computation by anyons text, January 1997

Spectroscopic insight into the interplay between structural disorder and oxidation degree in melt‐grown Ce 0.5 Zr 0.5 O 2‐ y compounds journal, November 2019

A quantum liquid of magnetic octupoles on the pyrochlore lattice journal, March 2020

Crystal fields and magnetic structure of the Ising antiferromagnet Er 3 Ga 5 O 12 journal, November 2019

Topological thermal Hall effect of magnetic monopoles in the pyrochlore U(1) spin liquid journal, January 2020

Pyrochlore U(1) spin liquid of mixed-symmetry enrichments in magnetic fields journal, March 2020

A quantum liquid of magnetic octupoles on the pyrochlore lattice text, January 2019

Title: Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce₂Zr₂O₇ pyrochlore

Spin-Glass Ground State in a Triangular-Lattice Compound ${YbZnGaO}_{4}$
journal, February 2018

Continuum of quantum fluctuations in a three-dimensional S = 1 Heisenberg magnet
journal, October 2018

Spin Ice, Fractionalization, and Topological Order
journal, March 2012

Spinon Fermi surface $U (1)$ spin liquid in the spin-orbit-coupled triangular-lattice Mott insulator ${YbMgGaO}_{4}$
journal, August 2017

Implementation of cross correlation for energy discrimination on the time-of-flight spectrometer CORELLI
journal, March 2018

Physical realization of a quantum spin liquid based on a complex frustration mechanism
journal, July 2016

Quantum spin liquids: a review
journal, November 2016

Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate
journal, December 2016

Experimental Insights into Ground-State Selection of Quantum XY Pyrochlores
journal, March 2018

Recent advances in magnetic structure determination by neutron powder diffraction
journal, October 1993

Quantum spin liquid states
journal, April 2017

Gapless Spin Liquid Ground State in the $S = 1 / 2$ Vanadium Oxyfluoride Kagome Antiferromagnet $[{NH}_{4}]_{2} [C_{7} H_{14} N] [V_{7} O_{6} F_{18}]$
journal, May 2013

Magnetic anisotropy of the spin-ice compound Dy2Ti2O7
journal, January 2002

Four-circle single-crystal neutron diffractometer at the High Flux Isotope Reactor
journal, May 2011

Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice
journal, August 2012

Evidence for spin liquid ground state in SrDy ₂ O ₄ frustrated magnet probed by μ SR
journal, April 2017

Coulomb spin liquid in anion-disordered pyrochlore Tb2Hf2O7
journal, October 2017

Spin Correlations in ${Ho}_{2} {Ti}_{2} O_{7}$ : A Dipolar Spin Ice System
journal, July 2001

Fluctuations and All-In–All-Out Ordering in Dipole-Octupole ${Nd}_{2} {Zr}_{2} O_{7}$
journal, November 2015

Colloquium : Herbertsmithite and the search for the quantum spin liquid
journal, December 2016

Experimental signatures of emergent quantum electrodynamics in Pr2Hf2O7
journal, April 2018

Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores
journal, April 2014

Magnetization process in the spin-ice compound ${Ho}_{2} {Ti}_{2} O_{7}$
journal, July 2003

The Resonating Valence Bond State in La2CuO4 and Superconductivity
journal, March 1987

Spin Fluctuations in Frustrated Kagomé Lattice System Sr ${Cr}_{8}$ ${Ga}_{4}$ $O_{19}$ Studied by Muon Spin Relaxation
journal, December 1994

Quantum Spin Ice Dynamics in the Dipole-Octupole Pyrochlore Magnet ${Ce}_{2} {Zr}_{2} O_{7}$
journal, May 2019

Symmetry enriched U(1) topological orders for dipole-octupole doublets on a pyrochlore lattice
journal, January 2017

Anyons in an exactly solved model and beyond
journal, January 2006

Spin liquids in frustrated magnets
journal, March 2010

Topography of Spin Liquids on a Triangular Lattice
journal, May 2018

Magnetic pyrochlore oxides
journal, January 2010

Synthesis and full characterization of the phase-pure pyrochlore Ce2Zr2O7 and the κ-Ce2Zr2O8 phases
journal, November 2016

DEMAND, a Dimensional Extreme Magnetic Neutron Diffractometer at the High Flux Isotope Reactor
journal, December 2018

Unbound spinons in the S =1/2 antiferromagnetic chain ${KCuF}_{3}$
journal, June 1993

Ising versus $X Y$ Anisotropy in Frustrated $R_{2} {Ti}_{2} O_{7}$ Compounds as “Seen” by Polarized Neutrons
journal, July 2009

Gapless quantum spin liquid ground state in the two-dimensional spin-1/2 triangular antiferromagnet YbMgGaO4
journal, November 2015

Special temperatures in frustrated ferromagnets
journal, May 2018

Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
journal, December 2016

Quantum Spin Ices and Topological Phases from Dipolar-Octupolar Doublets on the Pyrochlore Lattice
journal, April 2014

Spin Liquid State in the $S = 1 / 2$ Triangular Lattice ${Ba}_{3} {CuSb}_{2} O_{9}$
journal, April 2011

Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6
journal, October 2018

Quantum spin liquid in the spin- $1 ∕ 2$ triangular antiferromagnet $Et {Me}_{3} Sb {[Pd {(dmit)}_{2}]}_{2}$
journal, March 2008

Magnetic Ground State of an Experimental $S = 1 / 2$ Kagome Antiferromagnet
journal, April 2008

Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet
journal, December 2012

Resonating valence bonds: A new kind of insulator?
journal, February 1973

Fault-tolerant quantum computation by anyons
journal, January 2003

Generic quantum spin ice
journal, September 2012

Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets
journal, May 2014

Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006

Candidate Quantum Spin Liquid in the ${Ce}^{3 +}$ Pyrochlore Stannate ${Ce}_{2} {Sn}_{2} O_{7}$
journal, August 2015

Site Specific X-ray Anomalous Dispersion of the Geometrically Frustrated Kagomé Magnet, Herbertsmithite, ZnCu ₃ (OH) ₆ Cl ₂
journal, November 2010

Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice
journal, September 2003

Spin Ice, Fractionalization and Topological Order
text, January 2011

Generic quantum spin ice
text, January 2012

Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice
text, January 2013

Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice
text, January 2016

Quantum Spin Liquid States
text, January 2016

Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
text, January 2016

Coulomb spin liquid in anion-disordered pyrochlore Tb$_2$Hf$_2$O$_7$
text, January 2016

Evidence for spin liquid ground state in SrDy$_2$O$_4$ frustrated magnet probed by muSR
text, January 2017

Continuum of quantum fluctuations in a three-dimensional $S\!=\!1$ Heisenberg magnet
text, January 2017

Special temperatures in frustrated ferromagnets
text, January 2018

Anyons in an exactly solved model and beyond
text, January 2005

Fault-tolerant quantum computation by anyons
text, January 1997

Spectroscopic insight into the interplay between structural disorder and oxidation degree in melt‐grown Ce _0.5 Zr _0.5 O _{2‐ y} compounds
journal, November 2019

A quantum liquid of magnetic octupoles on the pyrochlore lattice
journal, March 2020

Crystal fields and magnetic structure of the Ising antiferromagnet ${Er}_{3} {Ga}_{5} O_{12}$
journal, November 2019

Topological thermal Hall effect of magnetic monopoles in the pyrochlore U(1) spin liquid
journal, January 2020

Pyrochlore U(1) spin liquid of mixed-symmetry enrichments in magnetic fields
journal, March 2020

A quantum liquid of magnetic octupoles on the pyrochlore lattice
text, January 2019