Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14

Dun, Zhiling; Bai, Xiaojian; Paddison, Joseph A. M.; Hollingworth, Emily; Butch, Nicholas P.; Cruz, Clarina D.; Stone, Matthew B.; Hong, Tao; Demmel, Franz; Mourigal, Martin; Zhou, Haidong

doi:10.1103/PhysRevX.10.031069

Title: Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice ${Ho}_{3} {Mg}_{2} {Sb}_{3} O_{14}$

Abstract

A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice material Ho3Mg2Sb3O14 unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho3+ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at T*≈0.32 K to a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down to T≈0.12 K. These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. In Ho3Mg2Sb3O14, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight themore »« less

Authors:

; Bai, Xiaojian; Paddison, Joseph A. M.; Hollingworth, Emily; Butch, Nicholas P.; Cruz, Clarina D.; Stone, Matthew B.; Hong, Tao; Demmel, Franz; Mourigal, Martin; Zhou, Haidong

Publication Date:: 2020-09-29

Research Org.:: Georgia Institute of Technology, Atlanta, GA (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; National Science Foundation (NSF)

OSTI Identifier:: 1668450

Alternate Identifier(s):: OSTI ID: 1673167; OSTI ID: 1798626

Grant/Contract Number:: SC0018660; AC05-00OR22725; DMR-2003117

Resource Type:: Published Article

Journal Name:: Physical Review. X

Additional Journal Information:: Journal Name: Physical Review. X Journal Volume: 10 Journal Issue: 3; Journal ID: ISSN 2160-3308

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Frustrated magnetism; Quantum spin liquid; Kagome lattice; Polycrystalline materials; Spin ice; Mean field theory; Neutron scattering; Random phase approximation; Semiclassical methods; Specific heat measurements; Time-of-flight neutron spectroscopy

Citation Formats


                    Dun, Zhiling, Bai, Xiaojian, Paddison, Joseph A. M., Hollingworth, Emily, Butch, Nicholas P., Cruz, Clarina D., Stone, Matthew B., Hong, Tao, Demmel, Franz, Mourigal, Martin, and Zhou, Haidong. Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevX.10.031069.

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                    Dun, Zhiling, Bai, Xiaojian, Paddison, Joseph A. M., Hollingworth, Emily, Butch, Nicholas P., Cruz, Clarina D., Stone, Matthew B., Hong, Tao, Demmel, Franz, Mourigal, Martin, & Zhou, Haidong. Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14.  United States.  https://doi.org/10.1103/PhysRevX.10.031069

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                    Dun, Zhiling, Bai, Xiaojian, Paddison, Joseph A. M., Hollingworth, Emily, Butch, Nicholas P., Cruz, Clarina D., Stone, Matthew B., Hong, Tao, Demmel, Franz, Mourigal, Martin, and Zhou, Haidong. Tue .  
"Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14".  United States.  https://doi.org/10.1103/PhysRevX.10.031069.

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@article{osti_1668450,

  title        = {Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14},

  author       = {Dun, Zhiling and Bai, Xiaojian and Paddison, Joseph A. M. and Hollingworth, Emily and Butch, Nicholas P. and Cruz, Clarina D. and Stone, Matthew B. and Hong, Tao and Demmel, Franz and Mourigal, Martin and Zhou, Haidong},

  abstractNote = {A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice material Ho3Mg2Sb3O14 unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho3+ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at T*≈0.32 K to a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down to T≈0.12 K. These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. In Ho3Mg2Sb3O14, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight the crucial role played by hyperfine interactions in frustrated quantum magnets and motivate further investigations of the role of quantum fluctuations on partially ordered magnetic states.},

  doi          = {10.1103/PhysRevX.10.031069},

  journal      = {Physical Review. X},

  number       = 3,

  volume       = 10,

  place        = {United States},

  year         = {2020},

  month        = {9}

}

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FIG. 1: Classical spin fragmentation (CSF) process in a model of dipolar kagome ice displaying emergent-charge order, based on Ref. [39]. The expectation values of spinsmore »

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Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field
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Moessner, R.; Sondhi, S. L.; Chandra, P.
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Order-by-Disorder and Quantum Coulomb Phase in Quantum Square Ice
journal, July 2014

Henry, Louis-Paul; Roscilde, Tommaso
Physical Review Letters, Vol. 113, Issue 2
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Disorder and Quantum Spin Ice
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Martin, N.; Bonville, P.; Lhotel, E.
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Wen, J. -J.; Koohpayeh, S. M.; Ross, K. A.
Physical Review Letters, Vol. 118, Issue 10
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Bramwell, S. T.
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Magnitude of quantum effects in classical spin ices
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Rau, Jeffrey G.; Gingras, Michel J. P.
Physical Review B, Vol. 92, Issue 14
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Tuning the two-step melting of magnetic order in a dipolar kagome spin ice by quantum fluctuations
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Physical Review B, Vol. 101, Issue 13
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A new approximation for the dynamics of the transverse ising model
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Lhotel, E.; Petit, S.; Ciomaga Hatnean, M.
Nature Communications, Vol. 9, Issue 1
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Magnetic monopoles in spin ice
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Figures / Tables found in this record:

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Title: Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14

Abstract

Citation Formats

Figures / Tables:

Relaxation-coupled order-parameter oscillation in a transverse Ising system journal, February 1988

The Disk Chopper Spectrometer at NIST: a new instrument for quasielastic neutron scattering studies journal, August 2003

Tunneling-induced restoration of classical degeneracy in quantum kagome ice journal, April 2019

SEQUOIA: A Newly Operating Chopper Spectrometer at the SNS journal, November 2010

Emergent order in the kagome Ising magnet Dy3Mg2Sb3O14 journal, December 2016

Observation of magnetic fragmentation in spin ice journal, April 2016

Determination of the neutron absorption cross section for hydrogen as a function of wavelength with a pulsed neutron source journal, April 1987

Dynamics of the Iongitudinal spin for the three-dimensional, spin-½ Ising model in a transverse field journal, March 1975

Colorings of odd or even chirality on hexagonal lattices journal, February 2017

A two-dimensional spin liquid in quantum kagome ice journal, June 2015

Field dependent specific heat study of the dipolar Ising ferromagnet LiHoF4 journal, September 1984

Rods of Neutron Scattering Intensity in Yb 2 Ti 2 O 7 : Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide journal, May 2011

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

Tetragonal distortion yielding a two-singlet spin liquid in pyrochlore Tb 2 Ti 2 O 7 journal, November 2011

Ising model in a transverse field. I. Basic theory journal, August 1973

Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb 2 Ti 2 O 7 pyrochlore antiferromagnet journal, November 2004

Power-Law Spin Correlations in the Pyrochlore Antiferromagnet Tb 2 Ti 2 O 7 journal, July 2012

Single-ion anisotropy and magnetic field response in the spin-ice materials Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 journal, October 2015

Nuclear spin ordering observed by neutron diffraction (invited) journal, April 1985

Spin Dynamics of a Model Singlet Ground-State System journal, December 1982

Quantum Ice: A Quantum Monte Carlo Study journal, February 2012

Acoustic-Phonon Instability and Critical Scattering in Nb 3 Sb journal, December 1971

Spin liquids in frustrated magnets journal, March 2010

DAVE: A Comprehensive Software Suite for the Reduction, Visualization, and Analysis of Low Energy Neutron Spectroscopic Data journal, November 2009

Dipolar-octupolar Ising antiferromagnetism in Sm 2 Ti 2 O 7 : A moment fragmentation candidate journal, September 2018

Magnetic Coulomb Phase in the Spin Ice Ho2Ti2O7 journal, September 2009

Two-Stage Ordering of Spins in Dipolar Spin Ice on the Kagome Lattice journal, May 2011

Quantum Dimer Model on the Kagome Lattice: Solvable Dimer-Liquid and Ising Gauge Theory journal, September 2002

Collective Excitations and Magnetic Ordering in Materials with Singlet Crystal-Field Ground State journal, August 1968

Numerical Evidence of Quantum Melting of Spin Ice: Quantum-to-Classical Crossover journal, August 2015

Instabilities of a U(1) Quantum Spin Liquid in Disordered Non-Kramers Pyrochlores journal, July 2018

Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays journal, October 2009

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

Correlated Quantum Tunneling of Monopoles in Spin Ice journal, August 2019

Geometrical Frustration in the Ferromagnetic Pyrochlore Ho 2 Ti 2 O 7 journal, September 1997

Quantum origins of moment fragmentation in Nd 2 Zr 2 O 7 journal, September 2016

High-temperature dynamics of the Ising model in a transverse field journal, February 1984

The high-resolution powder diffractometer at the high flux isotope reactor journal, March 2010

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

Are Multiphase Competition and Order by Disorder the Keys to Understanding Yb 2 Ti 2 O 7 ? journal, December 2015

Tunnelling and collective excitations in a microscopic model of ferroelectricity journal, October 1966

Internal Magnetic Field in Rare Earth Metals journal, September 1961

The nuclear heat capacity of HoF 3 journal, April 1994

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

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

Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb 2 Ti 2 O 7 in a Magnetic Field journal, August 2017

Spin liquid correlations, anisotropic exchange, and symmetry breaking in Tb 2 Ti 2 O 7 journal, November 2012

Treating crystal field parameters in lower than cubic symmetries journal, January 1984

Observation of Magnetic Monopoles in Spin Ice journal, October 2009

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

Structural and magnetic properties of two branches of the tripod-kagome-lattice family A 2 R 3 Sb 3 O 14 ( A = Mg, Zn; R = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb) journal, March 2017

Quantum Phase Transition of a Magnet in a Spin Bath journal, April 2005

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

Dynamic structure factor of the transverse Ising model journal, February 1995

Structural and magnetic characterization of Ho 3 SbO 7 and Dy 3 SbO 7 journal, December 2001

Magnetic Ground States of the Rare-Earth Tripod Kagome Lattice Mg 2 RE 3 Sb 3 O 14 ( RE = Gd , Dy , Er ) journal, April 2016

Crystal-field parameters of the rare-earth pyrochlores R 2 Ti 2 O 7 ( R = Tb , Dy, and Ho) journal, July 2016

Candidate quantum spin ice in the pyrochlore Pr 2 Hf 2 O 7 journal, July 2016

Theory of multiple-phase competition in pyrochlore magnets with anisotropic exchange with application to Yb 2 Ti 2 O 7 , Er 2 Ti 2 O 7 , and Er 2 Sn 2 O 7 journal, March 2017

Fragmentation in spin ice from magnetic charge injection journal, August 2017

Crystal field levels and magnetic anisotropy in the kagome compounds Nd 3 Sb 3 Mg 2 O 14 , Nd 3 Sb 3 Zn 2 O 14 , and Pr 3 Sb 3 Mg 2 O 14 journal, October 2018

Coulombic Quantum Liquids in Spin- 1 / 2 Pyrochlores journal, January 2012

Disorder-Induced Quantum Spin Liquid in Spin Ice Pyrochlores journal, February 2017

Pyrochlore photons: The U ( 1 ) spin liquid in a S = 1 2 three-dimensional frustrated magnet journal, February 2004

Theory of the kagome lattice Ising antiferromagnet in weak transverse fields journal, January 2005

Random-Phase Approximation in the Theory of Superconductivity journal, December 1958

Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7 journal, September 2009

Dynamic Spin Ice: Pr 2 Sn 2 O 7 journal, November 2008

Quantum Excitations in Quantum Spin Ice journal, October 2011

Fragmentation of magnetism in artificial kagome dipolar spin ice journal, May 2016

Calorimetric Investigation of Hyperfine Interactions in Metallic Ho and Tb journal, January 1969

SIMPRE: A software package to calculate crystal field parameters, energy levels, and magnetic properties on mononuclear lanthanoid complexes based on charge distributions journal, June 2013

Dynamical crossover in hot spin ice journal, December 2002

Atomic structure study of the pyrochlore Y b 2 T i 2 O 7 and its relationship with low-temperature magnetic order journal, March 2017

Magnetic-Moment Fragmentation and Monopole Crystallization journal, January 2014

Monte Carlo studies of the dipolar spin ice model journal, October 2004

Title: Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice ${Ho}_{3} {Mg}_{2} {Sb}_{3} O_{14}$

Relaxation-coupled order-parameter oscillation in a transverse Ising system
journal, February 1988

The Disk Chopper Spectrometer at NIST: a new instrument for quasielastic neutron scattering studies
journal, August 2003

Tunneling-induced restoration of classical degeneracy in quantum kagome ice
journal, April 2019

SEQUOIA: A Newly Operating Chopper Spectrometer at the SNS
journal, November 2010

Emergent order in the kagome Ising magnet Dy3Mg2Sb3O14
journal, December 2016

Observation of magnetic fragmentation in spin ice
journal, April 2016

Determination of the neutron absorption cross section for hydrogen as a function of wavelength with a pulsed neutron source
journal, April 1987

Dynamics of the Iongitudinal spin for the three-dimensional, spin-½ Ising model in a transverse field
journal, March 1975

Colorings of odd or even chirality on hexagonal lattices
journal, February 2017

A two-dimensional spin liquid in quantum kagome ice
journal, June 2015

Field dependent specific heat study of the dipolar Ising ferromagnet LiHoF4
journal, September 1984

Rods of Neutron Scattering Intensity in ${Yb}_{2} {Ti}_{2} O_{7}$ : Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide
journal, May 2011

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

Tetragonal distortion yielding a two-singlet spin liquid in pyrochlore Tb $_{2}$ Ti $_{2}$ O $_{7}$
journal, November 2011

Ising model in a transverse field. I. Basic theory
journal, August 1973

Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the ${Tb}_{2} {Ti}_{2} O_{7}$ pyrochlore antiferromagnet
journal, November 2004

Power-Law Spin Correlations in the Pyrochlore Antiferromagnet ${Tb}_{2} {Ti}_{2} O_{7}$
journal, July 2012

Single-ion anisotropy and magnetic field response in the spin-ice materials ${Ho}_{2} {Ti}_{2} O_{7}$ and ${Dy}_{2} {Ti}_{2} O_{7}$
journal, October 2015

Nuclear spin ordering observed by neutron diffraction (invited)
journal, April 1985

Spin Dynamics of a Model Singlet Ground-State System
journal, December 1982

Quantum Ice: A Quantum Monte Carlo Study
journal, February 2012

Acoustic-Phonon Instability and Critical Scattering in ${Nb}_{3}$ Sb
journal, December 1971

Spin liquids in frustrated magnets
journal, March 2010

DAVE: A Comprehensive Software Suite for the Reduction, Visualization, and Analysis of Low Energy Neutron Spectroscopic Data
journal, November 2009

Dipolar-octupolar Ising antiferromagnetism in ${Sm}_{2} {Ti}_{2} O_{7}$ : A moment fragmentation candidate
journal, September 2018

Magnetic Coulomb Phase in the Spin Ice Ho2Ti2O7
journal, September 2009

Two-Stage Ordering of Spins in Dipolar Spin Ice on the Kagome Lattice
journal, May 2011

Quantum Dimer Model on the Kagome Lattice: Solvable Dimer-Liquid and Ising Gauge Theory
journal, September 2002

Collective Excitations and Magnetic Ordering in Materials with Singlet Crystal-Field Ground State
journal, August 1968

Numerical Evidence of Quantum Melting of Spin Ice: Quantum-to-Classical Crossover
journal, August 2015

Instabilities of a U(1) Quantum Spin Liquid in Disordered Non-Kramers Pyrochlores
journal, July 2018

Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays
journal, October 2009

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

Correlated Quantum Tunneling of Monopoles in Spin Ice
journal, August 2019

Geometrical Frustration in the Ferromagnetic Pyrochlore ${Ho}_{2} {Ti}_{2} O_{7}$
journal, September 1997

Quantum origins of moment fragmentation in ${Nd}_{2} {Zr}_{2} O_{7}$
journal, September 2016

High-temperature dynamics of the Ising model in a transverse field
journal, February 1984

The high-resolution powder diffractometer at the high flux isotope reactor
journal, March 2010

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

Are Multiphase Competition and Order by Disorder the Keys to Understanding ${Yb}_{2} {Ti}_{2} O_{7}$ ?
journal, December 2015

Tunnelling and collective excitations in a microscopic model of ferroelectricity
journal, October 1966

Internal Magnetic Field in Rare Earth Metals
journal, September 1961

The nuclear heat capacity of HoF ₃
journal, April 1994

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

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

Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore ${Yb}_{2} {Ti}_{2} O_{7}$ in a Magnetic Field
journal, August 2017

Spin liquid correlations, anisotropic exchange, and symmetry breaking in Tb $_{2}$ Ti $_{2}$ O $_{7}$
journal, November 2012

Treating crystal field parameters in lower than cubic symmetries
journal, January 1984

Observation of Magnetic Monopoles in Spin Ice
journal, October 2009

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

Structural and magnetic properties of two branches of the tripod-kagome-lattice family $A_{2} R_{3} {Sb}_{3} O_{14}$ ( $A$ = Mg, Zn; $R$ = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb)
journal, March 2017

Quantum Phase Transition of a Magnet in a Spin Bath
journal, April 2005

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

Dynamic structure factor of the transverse Ising model
journal, February 1995

Structural and magnetic characterization of Ho ₃ SbO ₇ and Dy ₃ SbO ₇
journal, December 2001

Magnetic Ground States of the Rare-Earth Tripod Kagome Lattice ${Mg}_{2} {RE}_{3} {Sb}_{3} O_{14}$ ( $RE = Gd, Dy, Er$ )
journal, April 2016

Crystal-field parameters of the rare-earth pyrochlores $R_{2} {Ti}_{2} O_{7}$ ( $R = Tb$ , Dy, and Ho)
journal, July 2016

Candidate quantum spin ice in the pyrochlore $\Pr_{2} {Hf}_{2} O_{7}$
journal, July 2016

Theory of multiple-phase competition in pyrochlore magnets with anisotropic exchange with application to ${Yb}_{2} {Ti}_{2} O_{7}, {Er}_{2} {Ti}_{2} O_{7}$ , and ${Er}_{2} {Sn}_{2} O_{7}$
journal, March 2017

Fragmentation in spin ice from magnetic charge injection
journal, August 2017

Crystal field levels and magnetic anisotropy in the kagome compounds ${Nd}_{3} {Sb}_{3} {Mg}_{2} O_{14}$ , ${Nd}_{3} {Sb}_{3} {Zn}_{2} O_{14}$ , and $\Pr_{3} {Sb}_{3} {Mg}_{2} O_{14}$
journal, October 2018

Coulombic Quantum Liquids in Spin- $1 / 2$ Pyrochlores
journal, January 2012

Disorder-Induced Quantum Spin Liquid in Spin Ice Pyrochlores
journal, February 2017

Pyrochlore photons: The $U (1)$ spin liquid in a $S = \frac{1}{2}$ three-dimensional frustrated magnet
journal, February 2004

Theory of the kagome lattice Ising antiferromagnet in weak transverse fields
journal, January 2005

Random-Phase Approximation in the Theory of Superconductivity
journal, December 1958

Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7
journal, September 2009

Dynamic Spin Ice: $\Pr_{2} {Sn}_{2} O_{7}$
journal, November 2008

Quantum Excitations in Quantum Spin Ice
journal, October 2011

Fragmentation of magnetism in artificial kagome dipolar spin ice
journal, May 2016

Calorimetric Investigation of Hyperfine Interactions in Metallic Ho and Tb
journal, January 1969

SIMPRE: A software package to calculate crystal field parameters, energy levels, and magnetic properties on mononuclear lanthanoid complexes based on charge distributions
journal, June 2013

Dynamical crossover in hot spin ice
journal, December 2002

Atomic structure study of the pyrochlore $Y b_{2} T i_{2} O_{7}$ and its relationship with low-temperature magnetic order
journal, March 2017

Magnetic-Moment Fragmentation and Monopole Crystallization
journal, January 2014

Monte Carlo studies of the dipolar spin ice model
journal, October 2004

Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E ₈ Symmetry
journal, January 2010

Crystal-field interaction in the pyrochlore magnet Ho2Ti2O7
journal, May 2000

Effect of frustration near the magnetic-nonmagnetic transition
journal, July 1992