Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO 4

Zhang, Xinshu; Mahmood, Fahad; Daum, Marcus; Dun, Zhiling; Paddison, Joseph A. M.; Laurita, Nicholas J.; Hong, Tao; Zhou, Haidong; Armitage, N. P.; Mourigal, Martin

doi:10.1103/PhysRevX.8.031001

Title: Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid ${YbMgGaO}_{4}$

Abstract

The spin-1/2 triangular lattice antiferromagnet YbMgGaO₄ has attracted attention recently as a quantum spin-liquid candidate with the possible presence of off-diagonal anisotropic exchange interactions induced by spin-orbit coupling. Whether a quantum spin liquid is stabilized or not depends on the interplay of various exchange interactions with chemical disorder that is inherent to the layered structure of the compound. We combine time-domain terahertz spectroscopy and inelastic neutron scattering measurements in the field-polarized state of YbMgGaO₄ to obtain better insight of its exchange interactions. Terahertz spectroscopy in this fashion functions as a high-field electron spin resonance and probes the spin-wave excitations at the Brillouin zone center, ideally complementing neutron scattering. A global spin-wave fit to all our spectroscopic data at fields over 4 T, informed by the analysis of the terahertz spectroscopy linewidths, yields constraints on the disorder-averaged g factors and exchange interactions. Our results paint YbMgGaO₄ as an easy-plane XXZ antiferromagnet with the combined and necessary presence of subleading next-nearest neighbor and weak anisotropic off-diagonal nearest-neighbor interactions. Moreover, the obtained g factors are substantially different from previous reports. Furthermore, this work establishes the hierarchy of exchange interactions in YbMgGaO₄ from high-field data alone and thus strongly constrains possible mechanisms responsible formore »« less

Authors:: Zhang, Xinshu; Mahmood, Fahad; Daum, Marcus; Dun, Zhiling; Paddison, Joseph A. M.; Laurita, Nicholas J.; Hong, Tao; Zhou, Haidong; Armitage, N. P.; Mourigal, Martin

Publication Date:: Mon Jul 02 00:00:00 EDT 2018

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

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1458603

Alternate Identifier(s):: OSTI ID: 1462902

Grant/Contract Number:: FG02-08ER46544; AC05-00OR22725

Resource Type:: Published Article

Journal Name:: Physical Review. X

Additional Journal Information:: Journal Name: Physical Review. X Journal Volume: 8 Journal Issue: 3; Journal ID: ISSN 2160-3308

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats


                    Zhang, Xinshu, Mahmood, Fahad, Daum, Marcus, Dun, Zhiling, Paddison, Joseph A. M., Laurita, Nicholas J., Hong, Tao, Zhou, Haidong, Armitage, N. P., and Mourigal, Martin. Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO 4.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevX.8.031001.

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                    Zhang, Xinshu, Mahmood, Fahad, Daum, Marcus, Dun, Zhiling, Paddison, Joseph A. M., Laurita, Nicholas J., Hong, Tao, Zhou, Haidong, Armitage, N. P., & Mourigal, Martin. Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO 4.  United States.  https://doi.org/10.1103/PhysRevX.8.031001

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                    Zhang, Xinshu, Mahmood, Fahad, Daum, Marcus, Dun, Zhiling, Paddison, Joseph A. M., Laurita, Nicholas J., Hong, Tao, Zhou, Haidong, Armitage, N. P., and Mourigal, Martin. Mon .  
"Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO 4".  United States.  https://doi.org/10.1103/PhysRevX.8.031001.

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@article{osti_1458603,

  title        = {Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO 4},

  author       = {Zhang, Xinshu and Mahmood, Fahad and Daum, Marcus and Dun, Zhiling and Paddison, Joseph A. M. and Laurita, Nicholas J. and Hong, Tao and Zhou, Haidong and Armitage, N. P. and Mourigal, Martin},

  abstractNote = {The spin-1/2 triangular lattice antiferromagnet YbMgGaO4 has attracted attention recently as a quantum spin-liquid candidate with the possible presence of off-diagonal anisotropic exchange interactions induced by spin-orbit coupling. Whether a quantum spin liquid is stabilized or not depends on the interplay of various exchange interactions with chemical disorder that is inherent to the layered structure of the compound. We combine time-domain terahertz spectroscopy and inelastic neutron scattering measurements in the field-polarized state of YbMgGaO4 to obtain better insight of its exchange interactions. Terahertz spectroscopy in this fashion functions as a high-field electron spin resonance and probes the spin-wave excitations at the Brillouin zone center, ideally complementing neutron scattering. A global spin-wave fit to all our spectroscopic data at fields over 4 T, informed by the analysis of the terahertz spectroscopy linewidths, yields constraints on the disorder-averaged g factors and exchange interactions. Our results paint YbMgGaO4 as an easy-plane XXZ antiferromagnet with the combined and necessary presence of subleading next-nearest neighbor and weak anisotropic off-diagonal nearest-neighbor interactions. Moreover, the obtained g factors are substantially different from previous reports. Furthermore, this work establishes the hierarchy of exchange interactions in YbMgGaO4 from high-field data alone and thus strongly constrains possible mechanisms responsible for the observed spin-liquid phenomenology.},

  doi          = {10.1103/PhysRevX.8.031001},

  journal      = {Physical Review. X},

  number       = 3,

  volume       = 8,

  place        = {United States},

  year         = {Mon Jul 02 00:00:00 EDT 2018},

  month        = {Mon Jul 02 00:00:00 EDT 2018}

}

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In this paper, we report inelastic neutron scattering experiments in Ca₂Y₂Cu₅O₁₀ and map out the full one-magnon dispersion which extends up to a record value of 53 meV for frustrated ferromagnetic (FM) edge-sharing CuO₂ chain (FFESC) cuprates. A homogeneous spin-1/2 chain model with a FM nearest-neighbor (NN), an antiferromagnetic (AFM) next-nearest-neighbor (NNN) inchain, and two diagonal AFM interchain couplings (ICs) analyzed within linear spin-wave theory (LSWT) reproduces well the observed strong dispersion along the chains and a weak one perpendicularly. The ratio α=|J_a2/J_a1| of the FM NN and the AFM NNN couplings is found as ~0.23, close to the critical point α_c=1/4 which separates ferromagnetically and antiferromagnetically correlated spiral magnetic ground states in single chains, whereas α_c>0.25 for coupled chains is considerably upshifted even for relatively weak IC. Although the measured dispersion can be described by homogeneous LSWT, the scattering intensity appears to be considerably reduced at ~11.5 and ~28 meV. The gaplike feature at 11.5 meV is attributed to magnon-phonon coupling whereas based on density matrix renormalization group simulations of the dynamical structure factor the gap at 28 meV is considered to stem partly from quantum effects due to the AFM IC. Another contribution to that gap is ascribed to the intrinsic superstructure from the distorting incommensurate pattern of CaY cationic chains adjacent to the CuO₂ ones. It gives rise to nonequivalent CuO₄ units and Cu-O-Cu bond angles Φ and a resulting distribution of all exchange integrals. The J's fitted by homogeneous LSWT are regarded as average values. The record value of the FM NN integral J₁=24 meV among FFESC cuprates can be explained by a nonuniversal Φ(≠90°) and Cu-O bond length dependent anisotropic mean direct FM Cu-O exchangemore »« less
Cited by 8
https://doi.org/10.1103/PhysRevB.100.104415

Full Text Available
Canted antiferromagnetic order and spin dynamics in the honeycomb-lattice compound ${Tb}_{2} {Ir}_{3} {Ga}_{9}$

Journal Article Ye, Feng ; Morgan, Zachary ; Tian, Wei ; ... - Physical Review B

Single-crystal neutron diffraction, inelastic neutron scattering, bulk magnetization measurements, and first-principles calculations are used to investigate the magnetic properties of the honeycomb lattice Tb2Ir3Ga9. While the R ln 2 magnetic contribution to the low-temperature entropy indicates a J(eff) = 1/2 moment for the lowest-energy crystal-field doublet, the Tb3+ ions form a canted antiferromagnetic structure below 12.5 K. Due to the Dzyaloshinskii-Moriya interactions, the Tb moments in the ab plane are slightly canted towards b with a canted moment of 1.22 mu(B) per formula unit. A minimal xxz spin Hamiltonian is used to simultaneously fit the spin-wave frequencies along the high-symmetrymore »« less
https://doi.org/10.1103/physrevb.103.184413

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Spin order and dynamics in the diamond-lattice Heisenberg antiferromagnets ${CuRh}_{2} O_{4}$ and ${CoRh}_{2} O_{4}$

Journal Article Ge, L. ; Flynn, J. ; Paddison, Joseph A. M. ; ... - Physical Review B

Here, antiferromagnetic insulators on a diamond lattice are candidate materials to host exotic magnetic phenomena ranging from spin-orbital entanglement to degenerate spiral ground states and topological paramagnetism. Compared to other three-dimensional networks of magnetic ions, such as the geometrically frustrated pyrochlore lattice, the investigation of diamond-lattice magnetism in real materials is less mature. In this work, we characterize the magnetic properties of model A-site spinels CoRh₂O₄ (cobalt rhodite) and CuRh₂O₄ (copper rhodite) by means of thermomagnetic and neutron-scattering measurements, and we perform group theory analysis, Rietveld refinement, mean-field theory, and spin-wave theory calculations to analyze the experimental results. Our investigationmore »« less
Cited by 19
https://doi.org/10.1103/PhysRevB.96.064413

Full Text Available
Short-range order in the quantum XXZ honeycomb lattice material ${BaCo}_{2} {({PO}_{4})}_{2}$

Journal Article Nair, Harikrishnan S. ; Brown, J ; Coldren, E. ; ... - Physical Review B

In this paper, we present observations of highly frustrated quasi-two-dimensional (2D) magnetic correlations in the honeycomb lattice layers of the S_eff =1/2 compound γ-BaCo₂(PO₄)₂ (γ-BCPO). Specific heat shows a broad peak comprised of two weak kink features at T_N1~6 K and T_N2~3.5 K, the relative weights of which can be modified by sample annealing. Neutron powder diffraction measurements reveal short range quasi-2D order that is established below T_N1 and T_N2, at which two separate, incompatible, short range magnetic orders onset: commensurate antiferromagnetic correlations with correlation length ξ_c=60±2 Å (T_N1) and in quasi-2D helical domains with ξ_h=350±11 Å (T_N2). The acmore »« less
Cited by 35
https://doi.org/10.1103/PhysRevB.97.134409

Full Text Available
Single-ion properties of the $S_{eff}$ = $\frac{1}{2}$ XY antiferromagnetic pyrochlores $Na A^{'} {Co}_{2} F_{7}$ ( $A^{'} = {Ca}^{2 +}, {Sr}^{2 +}$ )

Journal Article Ross, Kathryn A. ; Brown, J. M. ; Cava, R. J. ; ... - Physical Review B

The antiferromagnetic pyrochlore material NaCaCo₂F₇ is a thermal spin liquid over a broad temperature range (≈140 K down to T_F=2.4 K), in which magnetic correlations between Co²⁺ dipole moments explore a continuous manifold of antiferromagnetic XY states. The thermal spin liquid is interrupted by spin freezing at a temperature that is ~2% of the mean-field interaction strength, leading to short-range static XY clusters with distinctive relaxation dynamics. Here we report the low-energy inelastic neutron scattering response from the related compound NaSrCo₂F₇, confirming that it hosts the same static and dynamic spin correlations as NaCaCo₂F₇. We then present the single-ion levelsmore »« less
Cited by 39
https://doi.org/10.1103/PhysRevB.95.144414

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Title: Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO 4

Abstract

Citation Formats

Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagome Compound ZnCu 3 ( OH ) 6 Cl 2 journal, July 2008

Singlet-Triplet Excitations and Long-Range Entanglement in the Spin-Orbital Liquid Candidate FeSc 2 S 4 journal, May 2015

Electron spin resonance in S = 1 2 antiferromagnetic chains journal, March 2002

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Quasiclassical magnetic order and its loss in a spin- 1 2 Heisenberg antiferromagnet on a triangular lattice with competing bonds journal, January 2015

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Hierarchy of Bound States in the One-Dimensional Ferromagnetic Ising Chain CoNb 2 O 6 Investigated by High-Resolution Time-Domain Terahertz Spectroscopy journal, April 2014

Quantum phase transitions in the Heisenberg J 1 − J 2 triangular antiferromagnet in a magnetic field journal, January 2017

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

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Order by Quenched Disorder in the Model Triangular Antiferromagnet RbFe ( MoO 4 ) 2 journal, July 2017

Quantum spin liquid states journal, April 2017

Spontaneous symmetry breaking in quantum frustrated antiferromagnets journal, April 1993

Helical magnetism and structural anomalies in triangular lattice α-SrCr 2 O 4 journal, May 2011

Evidence for a spinon Fermi surface in the triangular S = 1 quantum spin liquid Ba 3 NiSb 2 O 9 journal, February 2017

Low-energy electrodynamics of novel spin excitations in the quantum spin ice Yb2Ti2O7 journal, September 2014

Probing α − RuCl 3 Beyond Magnetic Order: Effects of Temperature and Magnetic Field journal, February 2018

Magnetic and non-magnetic phases of a quantum spin liquid journal, March 2011

Ground-state properties of the S =1/2 Heisenberg antiferromagnet on a triangular lattice journal, September 1990

Semiclassical ground-state phase diagram and multi- Q phase of a spin-orbit-coupled model on triangular lattice journal, November 2016

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

Spin dynamics in the geometrically frustrated multiferroic CuCrO 2 journal, March 2010

Spin liquid nature in the Heisenberg J 1 − J 2 triangular antiferromagnet journal, April 2016

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

Possible valence-bond condensation in the frustrated cluster magnet LiZn2Mo3O8 journal, May 2012

Magnetic and quantum disordered phases in triangular-lattice Heisenberg antiferromagnets journal, October 1999

Detecting spin fractionalization in a spinon Fermi surface spin liquid journal, August 2017

Nearest-neighbour resonating valence bonds in YbMgGaO4 journal, June 2017

Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain journal, June 2013

Three-sublattice order in triangular- and Kagomé-lattice spin-half antiferromagnets journal, March 1992

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

An End to the Drought of Quantum Spin Liquids journal, September 2008

The new cold neutron chopper spectrometer at the Spallation Neutron Source: Design and performance journal, August 2011

Effect of the pseudodipolar interaction on critical spin dynamics in cubic ferromagnets journal, December 1983

Spin liquids in frustrated magnets journal, March 2010

Static and Dynamical Properties of the Spin- 1 / 2 Equilateral Triangular-Lattice Antiferromagnet Ba 3 CoSb 2 O 9 journal, February 2016

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

Modes of Magnetic Resonance in the Spin-Liquid Phase of Cs 2 CuCl 4 journal, July 2011

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

Spin Disorder on a Triangular Lattice journal, September 2005

A General Theory of Magnetic Resonance Absorption journal, November 1954

Magnetization Process and Collective Excitations in the S = 1 / 2 Triangular-Lattice Heisenberg Antiferromagnet Ba 3 CoSb 2 O 9 journal, June 2013

Effect of spin-orbit coupling on the effective-spin correlation in YbMgGaO 4 journal, March 2018

Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO 4 journal, October 2017

Anisotropic spin model of strong spin-orbit-coupled triangular antiferromagnets journal, July 2016

Do quantum spin liquids exist? journal, August 2016

Neutron scattering in the proximate quantum spin liquid α-RuCl 3 journal, June 2017

A measure of monopole inertia in the quantum spin ice Yb2Ti2O7 journal, December 2015

Measurement of the spin-excitation continuum in one-dimensional KCuF 3 using neutron scattering journal, November 1995

Quantum Excitations in Quantum Spin Ice journal, October 2011

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

Magnetic Soft Modes in the Distorted Triangular Antiferromagnet α − CaCr 2 O 4 journal, September 2012

Antisymmetric Exchange and Exchange-Narrowed Electron-Paramagnetic-Resonance Linewidths journal, July 1971

Constraints on Jones transmission matrices from time-reversal invariance and discrete spatial symmetries journal, July 2014

Mott Physics in Organic Conductors with Triangular Lattices journal, March 2011

Extended Quantum Critical Phase in a Magnetized Spin- 1 2 Antiferromagnetic Chain journal, July 2003

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

Rare-Earth Triangular Lattice Spin Liquid: A Single-Crystal Study of YbMgGaO 4 journal, October 2015

Entanglement entropy as a portal to the physics of quantum spin liquids journal, February 2013

Spin liquid phase of the S = 1 2 J 1 − J 2 Heisenberg model on the triangular lattice journal, July 2015

Spinon Magnetic Resonance of Quantum Spin Liquids journal, January 2018

Quantum fluctuations in the effective pseudospin- 1 2 model for magnetic pyrochlore oxides journal, March 2011

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

String-net condensation: A physical mechanism for topological phases journal, January 2005

Ground-state phase diagram of an anisotropic spin- 1 2 model on the triangular lattice journal, April 2017

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

ESR study of the spin ladder with uniform Dzyaloshinskii-Moriya interaction journal, November 2015

Long-Range Néel Order in the Triangular Heisenberg Model journal, May 1999

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

Theory of a Competitive Spin Liquid State for Weak Mott Insulators on the Triangular Lattice journal, October 2013

Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice journal, July 1999

Finite-temperature behavior of a classical spin-orbit-coupled model for YbMgGaO 4 with and without bond disorder journal, May 2018

Absence of Magnetic Thermal Conductivity in the Quantum Spin-Liquid Candidate YbMgGaO 4 journal, December 2016

Experimental Realization of a 2D Fractional Quantum Spin Liquid journal, February 2001

Disordered Route to the Coulomb Quantum Spin Liquid: Random Transverse Fields on Spin Ice in Pr 2 Zr 2 O 7 journal, March 2017

Muon Spin Relaxation Evidence for the U(1) Quantum Spin-Liquid Ground State in the Triangular Antiferromagnet YbMgGaO 4 journal, August 2016

Title: Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid ${YbMgGaO}_{4}$

Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagome Compound ${ZnCu}_{3} (OH)_{6} {Cl}_{2}$
journal, July 2008

Singlet-Triplet Excitations and Long-Range Entanglement in the Spin-Orbital Liquid Candidate ${FeSc}_{2} S_{4}$
journal, May 2015

Electron spin resonance in $S = \frac{1}{2}$ antiferromagnetic chains
journal, March 2002

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

Quasiclassical magnetic order and its loss in a spin- $\frac{1}{2}$ Heisenberg antiferromagnet on a triangular lattice with competing bonds
journal, January 2015

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

Hierarchy of Bound States in the One-Dimensional Ferromagnetic Ising Chain ${CoNb}_{2} O_{6}$ Investigated by High-Resolution Time-Domain Terahertz Spectroscopy
journal, April 2014

Quantum phase transitions in the Heisenberg $J_{1} - J_{2}$ triangular antiferromagnet in a magnetic field
journal, January 2017

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

On the Anisotropy of Cubic Ferromagnetic Crystals
journal, December 1937

Order by Quenched Disorder in the Model Triangular Antiferromagnet $RbFe ({MoO}_{4})_{2}$
journal, July 2017

Quantum spin liquid states
journal, April 2017

Spontaneous symmetry breaking in quantum frustrated antiferromagnets
journal, April 1993

Helical magnetism and structural anomalies in triangular lattice α-SrCr ₂ O ₄
journal, May 2011

Evidence for a spinon Fermi surface in the triangular $S = 1$ quantum spin liquid ${Ba}_{3} {NiSb}_{2} O_{9}$
journal, February 2017

Low-energy electrodynamics of novel spin excitations in the quantum spin ice Yb2Ti2O7
journal, September 2014

Probing $α - {RuCl}_{3}$ Beyond Magnetic Order: Effects of Temperature and Magnetic Field
journal, February 2018

Magnetic and non-magnetic phases of a quantum spin liquid
journal, March 2011

Ground-state properties of the S =1/2 Heisenberg antiferromagnet on a triangular lattice
journal, September 1990

Semiclassical ground-state phase diagram and $multi- Q$ phase of a spin-orbit-coupled model on triangular lattice
journal, November 2016

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

Spin dynamics in the geometrically frustrated multiferroic ${CuCrO}_{2}$
journal, March 2010

Spin liquid nature in the Heisenberg $J_{1} - J_{2}$ triangular antiferromagnet
journal, April 2016

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

Possible valence-bond condensation in the frustrated cluster magnet LiZn2Mo3O8
journal, May 2012

Magnetic and quantum disordered phases in triangular-lattice Heisenberg antiferromagnets
journal, October 1999

Detecting spin fractionalization in a spinon Fermi surface spin liquid
journal, August 2017

Nearest-neighbour resonating valence bonds in YbMgGaO4
journal, June 2017

Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain
journal, June 2013

Three-sublattice order in triangular- and Kagomé-lattice spin-half antiferromagnets
journal, March 1992

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

An End to the Drought of Quantum Spin Liquids
journal, September 2008

The new cold neutron chopper spectrometer at the Spallation Neutron Source: Design and performance
journal, August 2011

Effect of the pseudodipolar interaction on critical spin dynamics in cubic ferromagnets
journal, December 1983

Spin liquids in frustrated magnets
journal, March 2010

Static and Dynamical Properties of the Spin- $1 / 2$ Equilateral Triangular-Lattice Antiferromagnet ${Ba}_{3} {CoSb}_{2} O_{9}$
journal, February 2016

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

Modes of Magnetic Resonance in the Spin-Liquid Phase of ${Cs}_{2} {CuCl}_{4}$
journal, July 2011

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

Spin Disorder on a Triangular Lattice
journal, September 2005

A General Theory of Magnetic Resonance Absorption
journal, November 1954

Magnetization Process and Collective Excitations in the $S = 1 / 2$ Triangular-Lattice Heisenberg Antiferromagnet ${Ba}_{3} {CoSb}_{2} O_{9}$
journal, June 2013

Effect of spin-orbit coupling on the effective-spin correlation in ${YbMgGaO}_{4}$
journal, March 2018

Disorder-Induced Mimicry of a Spin Liquid in ${YbMgGaO}_{4}$
journal, October 2017

Anisotropic spin model of strong spin-orbit-coupled triangular antiferromagnets
journal, July 2016

Do quantum spin liquids exist?
journal, August 2016

Neutron scattering in the proximate quantum spin liquid α-RuCl ₃
journal, June 2017

A measure of monopole inertia in the quantum spin ice Yb2Ti2O7
journal, December 2015

Measurement of the spin-excitation continuum in one-dimensional ${KCuF}_{3}$ using neutron scattering
journal, November 1995

Quantum Excitations in Quantum Spin Ice
journal, October 2011

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

Magnetic Soft Modes in the Distorted Triangular Antiferromagnet $α − {CaCr}_{2} O_{4}$
journal, September 2012

Antisymmetric Exchange and Exchange-Narrowed Electron-Paramagnetic-Resonance Linewidths
journal, July 1971

Constraints on Jones transmission matrices from time-reversal invariance and discrete spatial symmetries
journal, July 2014

Mott Physics in Organic Conductors with Triangular Lattices
journal, March 2011

Extended Quantum Critical Phase in a Magnetized Spin- $\frac{1}{2}$ Antiferromagnetic Chain
journal, July 2003

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

Rare-Earth Triangular Lattice Spin Liquid: A Single-Crystal Study of ${YbMgGaO}_{4}$
journal, October 2015

Entanglement entropy as a portal to the physics of quantum spin liquids
journal, February 2013

Spin liquid phase of the $S = \frac{1}{2} J_{1} - J_{2}$ Heisenberg model on the triangular lattice
journal, July 2015

Spinon Magnetic Resonance of Quantum Spin Liquids
journal, January 2018

Quantum fluctuations in the effective pseudospin- $\frac{1}{2}$ model for magnetic pyrochlore oxides
journal, March 2011

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

String-net condensation: A physical mechanism for topological phases
journal, January 2005

Ground-state phase diagram of an anisotropic spin- $\frac{1}{2}$ model on the triangular lattice
journal, April 2017

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

ESR study of the spin ladder with uniform Dzyaloshinskii-Moriya interaction
journal, November 2015

Long-Range Néel Order in the Triangular Heisenberg Model
journal, May 1999

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

Theory of a Competitive Spin Liquid State for Weak Mott Insulators on the Triangular Lattice
journal, October 2013

Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice
journal, July 1999

Finite-temperature behavior of a classical spin-orbit-coupled model for ${YbMgGaO}_{4}$ with and without bond disorder
journal, May 2018

Absence of Magnetic Thermal Conductivity in the Quantum Spin-Liquid Candidate ${YbMgGaO}_{4}$
journal, December 2016

Experimental Realization of a 2D Fractional Quantum Spin Liquid
journal, February 2001

Disordered Route to the Coulomb Quantum Spin Liquid: Random Transverse Fields on Spin Ice in $\Pr_{2} {Zr}_{2} O_{7}$
journal, March 2017

Muon Spin Relaxation Evidence for the U(1) Quantum Spin-Liquid Ground State in the Triangular Antiferromagnet ${YbMgGaO}_{4}$
journal, August 2016

Unusual ordered phases of highly frustrated magnets: a review
journal, April 2015

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