Competing orders in pyrochlore magnets from a ${\mathbb{Z}}_2$ spin liquid perspective

Abstract

The pyrochlore materials have long been predicted to harbor a quantum spin liquid, an intrinsic long-range-entangled 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 ${\mathbb{Z}}_2$ 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. This study provides a clear map of pyrochlore phases for future experiments and variational Monte Carlo studies in pyrochlore materials.

arXiv comment29 pages, 4 figures

References in corpus (57)

• Quantum Spin Liquids
• Magnetic Pyrochlore Oxides
• Correlated quantum phenomena in the strong spin-orbit regime
• Quantum Orders and Symmetric Spin Liquids
• Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Quantum Excitations in Quantum Spin Ice
• Coulombic Quantum Liquids in Spin-1/2 Pyrochlores
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Thermal Hall conductivity in the frustrated pyrochlore magnet Tb2Ti2O7
• Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3
• Putting competing orders in their place near the Mott transition
• Z2 spin liquid in S=1/2 Heisenberg model on Kagome lattice: A projective symmetry group study of Schwinger-fermion mean-field states
• A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd${}_2$Re${}_2$O${}_7$
• Order in the Heisenberg Pyrochlore: The Magnetic Structure of Gd2Ti2O7
• Quantum Spin Ice Dynamics in the Dipole-Octupole Pyrochlore Magnet Ce${}_2$Zr${}_2$O${}_7$
• Breathing Pyrochlore Lattice Realized in A-Site Ordered Spinel Oxides LiGaCr4O8 and LiInCr4O8
• Living on the edge : ground-state selection in quantum spin-ice pyrochlores
• Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7
• Schwinger Boson Mean Field Theories of Spin Liquid States on Honeycomb Lattice: Projective Symmetry Group Analysis and Critical Field Theory
• Candidate Quantum Spin Liquid in the Ce\textsuperscript{3+} Pyrochlore Stannate Ce${}_2$Sn${}_2$O${}_7$
• Projective symmetry group classification of chiral spin liquids
• Fluctuations and all-in$-$all-out ordering in dipole-octupole Nd2Zr2O7
• Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb${}_2$Ti${}_2$O${}_7$ in Magnetic Field
• Experimental signatures of emergent quantum electrodynamics in Pr${}_2$Hf${}_2$O${}_7$
• Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice
• Experimental Insights into Ground State Selection of Quantum XY Pyrochlores
• Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories
• Experimental Realization of a Quantum Breathing Pyrochlore Antiferromagnet
• Anisotropic exchange within decoupled tetrahedra in the quantum breathing pyrochlore Ba3Yb2Zn5O11
• Candidate quantum spin ice in the pyrochlore Pr${}_2$Hf${}_2$O${}_7$
• Magnetic monopole condensation in pyrochlore ice quantum spin liquid: application to Pr2Ir2O7 and Yb2Ti2O7
• Gapless quantum excitations from an Ice-like Splayed Ferromagnetic ground state in stoichiometric Yb2Ti2O7
• Chiral spin liquid on kagome antiferromagnet induced by Dzyaloshinskii-Moriya interaction
• Phase Transition and Thermal Order-by-Disorder in the Pyrochlore Quantum Antiferromagnet Er2Ti2O7: a High-Temperature Series Expansion Study
• Symmetric $Z_2$ spin liquids and their neighboring phases on triangular lattice
• Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice
• Reentrant Phase Diagram of $\mathrm{Y}{\mathrm{b}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ in $⟨111⟩$ Magnetic Field
• Monopole Flux State on the Pyrochlore Lattice
• Ordering in a frustrated pyrochlore antiferromagnet proximate to a spin liquid
• Competing orders II: the doped quantum dimer model
• Quantum spin ice on the breathing pyrochlore lattice
• Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
• Universal Dynamic Magnetism in Yb-Pyrochlores with Disparate Ground States
• Order-by-disorder near criticality in $XY$ pyrochlore magnets
• XY Antiferromagnetic Ground State in the Effective S=1/2 Pyrochlore Yb2Ge2O7
• Role of defects in determining the magnetic ground state of ytterbium titanate
• Schwinger boson spin liquid states on square lattice
• Interplay of non-symmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na${}_4$Ir${}_3$O${}_8$
• Classification of spin liquids on the square lattice with strong spin-orbit coupling
• Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: the Case of Multiple-k Partial Order on the Pyrochlore Lattice
• Discovery of Emergent Photon and Monopoles in a Quantum Spin Liquid
• Classification of quantum phases for the star-lattice antiferromagnet via a projective symmetry group analysis
• Three-dimensional nematic spin liquid in the stacked triangular lattice 6H-B structure
• Interplay of uniform U(1) quantum spin liquid and magnetic phases in rare earth pyrochlore magnets : a fermionic parton approach

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