Competing orders in pyrochlore magnets from a Z2 spin liquid perspective

doi:10.1103/PhysRevB.100.075125

Title: Competing orders in pyrochlore magnets from a $Z_{2}$ spin liquid perspective

Abstract

We report that the pyrochlore materials have long been predicted to harbor a quantum spin liquid, an intrinsic long-rangeentangled state supporting fractionalized excitations. Existing pyrochlore experiments, on the other hand, have discovered several weakly ordered states and a tendency of close competition amongst them. Motivated by these facts, we give a complete classification of spin-orbit-coupled $Z_{2}$ spin-liquid states on the pyrochlore lattice by using the projective symmetry group (PSG) approach for bosonic spinons. For each spin liquid, we construct a mean-field Hamiltonian that can be used to describe phase transitions out of the spin liquid via spinon condensation. Studying these phase transitions, we establish phase diagrams for our mean-field Hamiltonians that link magnetic orders to specific spin liquids. In general, we find that seemingly unrelated magnetic orders are intertwined with each other and that the conventional spin orders seen in the experiments are accompanied by more exotic hidden orders. Our critical theories are categorized into z = 1 and z = 2 types, based on their spinon dispersion and Hamiltonian diagonalizability, and are shown to give distinct signatures in the heat capacity and the spin structure factor. Lastly, this study provides a clear map of pyrochlore phases for future experiments and variational Monte Carlo studies in pyrochlore materials.

Authors:

^[1]; Halász, Gábor B. ^[2]; Balents, Leon ^[3]

Univ. of California, Santa Barbara, CA (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of California, Santa Barbara, CA (United States)
Univ. of California, Santa Barbara, CA (United States) ; Canadian Inst.for Advanced Research, Toronto, ON (Canada)

Publication Date:: 2019-08-12

Research Org.:: Univ. of California, Santa Barbara, CA (United States). Kavli Institute for Theoretical Physics

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

OSTI Identifier:: 1556863

Alternate Identifier(s):: OSTI ID: 1556842

Grant/Contract Number:: FG02-08ER46524

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 100; Journal Issue: 7; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats


                    Liu, Chunxiao, Halász, Gábor B., and Balents, Leon. Competing orders in pyrochlore magnets from a Z2 spin liquid perspective.  United States: N. p., 2019. 
        Web.  doi:10.1103/PhysRevB.100.075125.

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                    Liu, Chunxiao, Halász, Gábor B., & Balents, Leon. Competing orders in pyrochlore magnets from a Z2 spin liquid perspective.  United States.  doi:10.1103/PhysRevB.100.075125.

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                    Liu, Chunxiao, Halász, Gábor B., and Balents, Leon. Mon .  
        "Competing orders in pyrochlore magnets from a Z2 spin liquid perspective".  United States.  doi:10.1103/PhysRevB.100.075125.  https://www.osti.gov/servlets/purl/1556863.

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@article{osti_1556863,

  title        = {Competing orders in pyrochlore magnets from a Z2 spin liquid perspective},

  author       = {Liu, Chunxiao and Halász, Gábor B. and Balents, Leon},

  abstractNote = {We report that the pyrochlore materials have long been predicted to harbor a quantum spin liquid, an intrinsic long-rangeentangled state supporting fractionalized excitations. Existing pyrochlore experiments, on the other hand, have discovered several weakly ordered states and a tendency of close competition amongst them. Motivated by these facts, we give a complete classification of spin-orbit-coupled Z2 spin-liquid states on the pyrochlore lattice by using the projective symmetry group (PSG) approach for bosonic spinons. For each spin liquid, we construct a mean-field Hamiltonian that can be used to describe phase transitions out of the spin liquid via spinon condensation. Studying these phase transitions, we establish phase diagrams for our mean-field Hamiltonians that link magnetic orders to specific spin liquids. In general, we find that seemingly unrelated magnetic orders are intertwined with each other and that the conventional spin orders seen in the experiments are accompanied by more exotic hidden orders. Our critical theories are categorized into z = 1 and z = 2 types, based on their spinon dispersion and Hamiltonian diagonalizability, and are shown to give distinct signatures in the heat capacity and the spin structure factor. Lastly, this study provides a clear map of pyrochlore phases for future experiments and variational Monte Carlo studies in pyrochlore materials.},

  doi          = {10.1103/PhysRevB.100.075125},

  journal      = {Physical Review B},

  number       = 7,

  volume       = 100,

  place        = {United States},

  year         = {2019},

  month        = {8}

}

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DOI: 10.1103/PhysRevB.100.075125

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Title: Competing orders in pyrochlore magnets from a Z 2 spin liquid perspective

Abstract

Citation Formats

Quantum spin liquids: a review journal, November 2016

Spin liquids in frustrated magnets journal, March 2010

Correlated Quantum Phenomena in the Strong Spin-Orbit Regime journal, March 2014

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

Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials journal, March 2016

Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice journal, January 2018

Magnetic pyrochlore oxides journal, January 2010

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

Quantum Excitations in Quantum Spin Ice journal, October 2011

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

Large thermal Hall conductivity of neutral spin excitations in a frustrated quantum magnet journal, April 2015

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

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

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

Reentrant Phase Diagram of Yb 2 Ti 2 O 7 in a ⟨ 111 ⟩ Magnetic Field journal, September 2017

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

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

Discovery of Emergent Photon and Monopoles in a Quantum Spin Liquid journal, June 2018

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

Role of defects in determining the magnetic ground state of ytterbium titanate journal, February 2019

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

Quantum orders and symmetric spin liquids journal, April 2002

Classification of spin liquids on the square lattice with strong spin-orbit coupling journal, November 2014

Symmetric Z 2 spin liquids and their neighboring phases on triangular lattice journal, April 2016

Z 2 spin liquids in the S = 1 2 Heisenberg model on the kagome lattice: A projective symmetry-group study of Schwinger fermion mean-field states journal, June 2011

Doping a spin-orbit Mott insulator: Topological superconductivity from the Kitaev-Heisenberg model and possible application to (Na 2 /Li 2 )IrO 3 journal, August 2012

Classification of quantum phases for the star-lattice antiferromagnet via a projective symmetry group analysis journal, August 2009

Interplay of nonsymmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na 4 Ir 3 O 8 journal, February 2017

Ordering in a frustrated pyrochlore antiferromagnet proximate to a spin liquid journal, April 2006

“Magnetic monopole” condensation of the pyrochlore ice U(1) quantum spin liquid: Application to Pr 2 Ir 2 O 7 and Yb 2 Ti 2 O 7 journal, November 2016

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

Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons journal, June 1992

Spin-liquid states on the triangular and Kagomé lattices: A projective-symmetry-group analysis of Schwinger boson states journal, November 2006

Schwinger boson mean field theories of spin liquid states on a honeycomb lattice: Projective symmetry group analysis and critical field theory journal, July 2010

Schwinger boson spin-liquid states on square lattice journal, July 2016

Time reversal symmetry breaking chiral spin liquids: Projective symmetry group approach of bosonic mean-field theories journal, March 2013

Monopole flux state on the pyrochlore lattice journal, April 2009

Three-dimensional nematic spin liquid in a stacked triangular lattice 6 H -B structure journal, June 2013

Interplay of uniform U (1) quantum spin liquid and magnetic phases in rare-earth pyrochlore magnets: A fermionic parton approach journal, April 2019

Bose-Einstein condensation in quantum magnets journal, May 2014

Order in the Heisenberg pyrochlore: The magnetic structure of Gd 2 Ti 2 O 7 journal, September 2001

Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple- k Partial Order on the Pyrochlore Lattice journal, April 2015

Breathing Pyrochlore Lattice Realized in A -Site Ordered Spinel Oxides LiGaCr 4 O 8 and LiInCr 4 O 8 journal, February 2013

Experimental realization of a quantum breathing pyrochlore antiferromagnet journal, August 2014

Anisotropic Exchange within Decoupled Tetrahedra in the Quantum Breathing Pyrochlore Ba 3 Yb 2 Zn 5 O 11 journal, June 2016

Putting competing orders in their place near the Mott transition journal, April 2005

Putting competing orders in their place near the Mott transition. II. The doped quantum dimer model journal, April 2005

A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd 2 Re 2 O 7 journal, April 2017

High-pressure synthesis and characterization of the effective pseudospin S = 1 / 2 XY pyrochlores R 2 P t 2 O 7 ( R = Er , Yb ) journal, January 2016

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

Ordering due to disorder in a frustrated vector antiferromagnet journal, April 1989

Order by Quantum Disorder in Er 2 Ti 2 O 7 journal, October 2012

Phase transition and thermal order-by-disorder in the pyrochlore antiferromagnet Er 2 Ti 2 O 7 : A high-temperature series expansion study journal, December 2013

Order-by-disorder near criticality in X Y pyrochlore magnets journal, May 2015

Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets journal, May 2016

XY antiferromagnetic ground state in the effective S = 1 2 pyrochlore Yb 2 Ge 2 O 7 journal, March 2016

Gapless quantum excitations from an icelike splayed ferromagnetic ground state in stoichiometric Yb 2 Ti 2 O 7 journal, February 2016

Dynamical Splayed Ferromagnetic Ground State in the Quantum Spin Ice Yb 2 Sn 2 O 7 journal, March 2013

Universal dynamic magnetism in Yb pyrochlores with disparate ground states journal, March 2016

Projective symmetry group classification of chiral spin liquids journal, March 2016

Chiral Spin Liquid on a Kagome Antiferromagnet Induced by the Dzyaloshinskii-Moriya Interaction journal, June 2017

Quantum spin ice on the breathing pyrochlore lattice journal, August 2016

Three-dimensional topological magnon systems journal, October 2019

Title: Competing orders in pyrochlore magnets from a $Z_{2}$ spin liquid perspective

Quantum spin liquids: a review
journal, November 2016

Spin liquids in frustrated magnets
journal, March 2010

Correlated Quantum Phenomena in the Strong Spin-Orbit Regime
journal, March 2014

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

Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
journal, March 2016

Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice
journal, January 2018

Magnetic pyrochlore oxides
journal, January 2010

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

Quantum Excitations in Quantum Spin Ice
journal, October 2011

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

Large thermal Hall conductivity of neutral spin excitations in a frustrated quantum magnet
journal, April 2015

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

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

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

Reentrant Phase Diagram of ${Yb}_{2} {Ti}_{2} O_{7}$ in a $⟨ 111 ⟩$ Magnetic Field
journal, September 2017

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

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

Discovery of Emergent Photon and Monopoles in a Quantum Spin Liquid
journal, June 2018

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

Role of defects in determining the magnetic ground state of ytterbium titanate
journal, February 2019

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

Quantum orders and symmetric spin liquids
journal, April 2002

Classification of spin liquids on the square lattice with strong spin-orbit coupling
journal, November 2014

Symmetric $Z_{2}$ spin liquids and their neighboring phases on triangular lattice
journal, April 2016

$Z_{2}$ spin liquids in the $S = \frac{1}{2}$ Heisenberg model on the kagome lattice: A projective symmetry-group study of Schwinger fermion mean-field states
journal, June 2011

Doping a spin-orbit Mott insulator: Topological superconductivity from the Kitaev-Heisenberg model and possible application to (Na $_{2}$ /Li $_{2}$ )IrO $_{3}$
journal, August 2012

Classification of quantum phases for the star-lattice antiferromagnet via a projective symmetry group analysis
journal, August 2009

Interplay of nonsymmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to ${Na}_{4} {Ir}_{3} O_{8}$
journal, February 2017

Ordering in a frustrated pyrochlore antiferromagnet proximate to a spin liquid
journal, April 2006

“Magnetic monopole” condensation of the pyrochlore ice U(1) quantum spin liquid: Application to $\Pr_{2} {Ir}_{2} O_{7}$ and ${Yb}_{2} {Ti}_{2} O_{7}$
journal, November 2016

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

Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons
journal, June 1992

Spin-liquid states on the triangular and Kagomé lattices: A projective-symmetry-group analysis of Schwinger boson states
journal, November 2006

Schwinger boson mean field theories of spin liquid states on a honeycomb lattice: Projective symmetry group analysis and critical field theory
journal, July 2010

Schwinger boson spin-liquid states on square lattice
journal, July 2016

Time reversal symmetry breaking chiral spin liquids: Projective symmetry group approach of bosonic mean-field theories
journal, March 2013

Monopole flux state on the pyrochlore lattice
journal, April 2009

Three-dimensional nematic spin liquid in a stacked triangular lattice 6 $H$ -B structure
journal, June 2013

Interplay of uniform $U$ (1) quantum spin liquid and magnetic phases in rare-earth pyrochlore magnets: A fermionic parton approach
journal, April 2019

Bose-Einstein condensation in quantum magnets
journal, May 2014

Order in the Heisenberg pyrochlore: The magnetic structure of ${Gd}_{2} {Ti}_{2} O_{7}$
journal, September 2001

Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple- $k$ Partial Order on the Pyrochlore Lattice
journal, April 2015

Breathing Pyrochlore Lattice Realized in $A$ -Site Ordered Spinel Oxides ${LiGaCr}_{4} O_{8}$ and ${LiInCr}_{4} O_{8}$
journal, February 2013

Experimental realization of a quantum breathing pyrochlore antiferromagnet
journal, August 2014

Anisotropic Exchange within Decoupled Tetrahedra in the Quantum Breathing Pyrochlore ${Ba}_{3} {Yb}_{2} {Zn}_{5} O_{11}$
journal, June 2016

Putting competing orders in their place near the Mott transition
journal, April 2005

Putting competing orders in their place near the Mott transition. II. The doped quantum dimer model
journal, April 2005

A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd ₂ Re ₂ O ₇
journal, April 2017

High-pressure synthesis and characterization of the effective pseudospin $S = 1 / 2$ XY pyrochlores $R_{2} P t_{2} O_{7} (R = Er, Yb)$
journal, January 2016

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

Ordering due to disorder in a frustrated vector antiferromagnet
journal, April 1989

Order by Quantum Disorder in ${Er}_{2} {Ti}_{2} O_{7}$
journal, October 2012

Phase transition and thermal order-by-disorder in the pyrochlore antiferromagnet Er $_{2}$ Ti $_{2}$ O $_{7}$ : A high-temperature series expansion study
journal, December 2013

Order-by-disorder near criticality in $X Y$ pyrochlore magnets
journal, May 2015

Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
journal, May 2016

XY antiferromagnetic ground state in the effective $S = \frac{1}{2}$ pyrochlore ${Yb}_{2} {Ge}_{2} O_{7}$
journal, March 2016

Gapless quantum excitations from an icelike splayed ferromagnetic ground state in stoichiometric ${Yb}_{2} {Ti}_{2} O_{7}$
journal, February 2016

Dynamical Splayed Ferromagnetic Ground State in the Quantum Spin Ice ${Yb}_{2} {Sn}_{2} O_{7}$
journal, March 2013

Universal dynamic magnetism in Yb pyrochlores with disparate ground states
journal, March 2016

Projective symmetry group classification of chiral spin liquids
journal, March 2016

Chiral Spin Liquid on a Kagome Antiferromagnet Induced by the Dzyaloshinskii-Moriya Interaction
journal, June 2017

Quantum spin ice on the breathing pyrochlore lattice
journal, August 2016

Three-dimensional topological magnon systems
journal, October 2019