Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

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:
ORCiD logo [1];  [2];  [3]
+ Show Author Affiliations
  1. Univ. of California, Santa Barbara, CA (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of California, Santa Barbara, CA (United States)
  3. Univ. of California, Santa Barbara, CA (United States) ; Canadian Inst.for Advanced Research, Toronto, ON (Canada)
Publication Date:
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.
Copy to clipboard
Liu, Chunxiao, Halász, Gábor B., & Balents, Leon. Competing orders in pyrochlore magnets from a Z2 spin liquid perspective. United States. https://doi.org/10.1103/PhysRevB.100.075125
Copy to clipboard
Liu, Chunxiao, Halász, Gábor B., and Balents, Leon. Mon . "Competing orders in pyrochlore magnets from a Z2 spin liquid perspective". United States. https://doi.org/10.1103/PhysRevB.100.075125. https://www.osti.gov/servlets/purl/1556863.
Copy to clipboard
@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}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevB.100.075125
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Figures / Tables:

TABLE I TABLE I: Most important characteristics of the 15 critical “paraphases” corresponding to phase transitions between the six 0-flux $\mathbb{Z}_2$ spin-liquid phases [labeled as 0-($n_\bar{C_6S}$ $n_{ST_1}$ <$n_\bar{C_6}$)] and a rich variety of magnetically ordered phases. Each paraphase is labeled by the condensation momenta (see Table IV for notation) where the spinonsmore » become gapless and condense at the phase transition. For each critical theory, experimental signatures are given in terms of the dynamical critical exponent, the low-temperature behavior of the heat capacity, and the low-energy features of the dynamic spin structure factor (see Fig. 4). For each magnetically ordered phase obtained by spinon condensation, it is specified whether various orders are generically present (+) or absent (0), including conventional spin orders, such as all-in-all-out (AIAO) order, XY antiferromagnetic (AFM) order [Ψ2,3], ferromagnetic (FM) order, and Palmer-Chalker (PC) order [Ψ4], as well as inversion-breaking “hidden” orders.« less
All figures and tables (15 total)
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

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

  • Gardner, Jason S.; Gingras, Michel J. P.; Greedan, John E.
  • Reviews of Modern Physics, Vol. 82, Issue 1
  • DOI: 10.1103/RevModPhys.82.53

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

  • Tokiwa, Yoshifumi; Yamashita, Takuya; Terazawa, Daiki
  • Journal of the Physical Society of Japan, Vol. 87, Issue 6
  • DOI: 10.7566/JPSJ.87.064702

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

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

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

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

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

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

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

Role of defects in determining the magnetic ground state of ytterbium titanate.
text, January 2019

  • Bowman, Df; Cemal, E.; Lehner, T.
  • Apollo - University of Cambridge Repository
  • DOI: 10.17863/cam.37263

Monopole Flux State on the Pyrochlore Lattice
text, January 2008

Correlated quantum phenomena in the strong spin-orbit regime
text, January 2013

Classification of spin liquids on the square lattice with strong spin-orbit coupling
text, January 2014

Order-by-disorder near criticality in $XY$ pyrochlore magnets
text, January 2015

Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
text, January 2015

Schwinger boson spin liquid states on square lattice
text, January 2015

Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
text, January 2015

Quantum spin ice on the breathing pyrochlore lattice
text, January 2015

Projective symmetry group classification of chiral spin liquids
text, January 2015

Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice
text, January 2017

Discovery of Emergent Photon and Monopoles in a Quantum Spin Liquid
text, January 2018

Ordering in a frustrated pyrochlore antiferromagnet proximate to a spin liquid
text, January 2005

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Three-dimensional topological magnon systems
    journal, October 2019

    Three-dimensional topological magnon systems
    text, January 2019

      Sort by:
      [ × clear filter / sort ]

      Figures / Tables found in this record:

      TABLE I (p. 3)table
      TABLE II (p. 8)table
      FIG. 1 (p. 9)figure
      TABLE III (p. 9)table
      TABLE IV (p. 10)table
      TABLE V (p. 11)table
      FIG. 2 (p. 13)figure
      TABLE VI (p. 14)table
      FIG. 3 (p. 15)figure
      FIG. 4 (p. 15)figure
      TABLE VII (p. 16)table
      TABLE VIII (p. 17)table
      TABLE IX (p. 18)table
      TABLE X (p. 23)table
      TABLE XI (p. 25)table
        [ × clear filter / sort ]
        Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

        Similar Records in DOE PAGES and OSTI.GOV collections: