Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7

Abstract

The family of magnetic rare-earth pyrochlore oxides R2M2O7 plays host to a diverse array of exotic phenomena, driven by the interplay between geometrical frustration and spin-orbit interaction, which leads to anisotropy in both magnetic moments and their interactions. In this article we establish a general, symmetry--based theory of pyrochlore magnets with anisotropic exchange interactions. Starting from a very general model of nearest-neighbour exchange between Kramers ions, we find four distinct classical ordered states, all with q=0, competing with a variety of spin-liquids and unconventional forms of magnetic order. The finite-temperature phase diagram of this model is determined by Monte Carlo simulation, supported by classical spin-wave calculations. We pay particular attention to the region of parameter space relevant to the widely studied materials Er2Ti2O7, Yb2Ti2O7, and Er2Sn2O7. We find that many of the most interesting properties of these materials can be traced back to the "accidental" degeneracies where phases with different symmetries meet. These include the ordered ground state selection by fluctuations in Er2Ti2O7, the dimensional-reduction observed in Yb2Ti2O7, and the lack of reported magnetic order in Er2Sn2O7. We also discuss the application of this theory to other pyrochlore oxides.

Long-paper version of "Living on the Edge", arXiv:1311.3501. 41 pages, 27 figures. Accepted for publication in Physical Review B

References in corpus (37)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model
• Is the Yb2Ti2O7 pyrochlore a quantum spin ice?
• Rods of Neutron Scattering Intensity in Yb2Ti2O7: Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide
• Magnetic ordering in Gd2Sn2O7: the archetypal Heisenberg pyrochlore antiferromagnet
• Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice
• Magnetic Frustration in Lead Pyrochlores
• Experimental Realization of a Quantum Breathing Pyrochlore Antiferromagnet
• Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet
• Magnetic order, magnetic correlations and spin dynamics in the pyrochlore antiferromagnet Er2Ti2O7
• The quantum origins of moment fragmentation in Nd2Zr2O7
• Bosonic Many-body Theory of Quantum Spin Ice
• Antiferromagnetic Spin Ice Correlations at (1/2,1/2,1/2) in the Ground State of the Pyrochlore Magnet Tb2Ti2O7
• Structural and Magnetic Investigations of Single-Crystals of the Neodymium Zirconate Pyrochlore, Nd2Zr2O7
• Low Energy Electrodynamics of Novel Spin Excitations in the Quantum Spin Ice Yb${}_2$Ti${}_2$O${}_7$
• Quantum spin configurations in Tb2Ti2O7
• Novel Phase Transitions in the Breathing Pyrochlore Lattice: 7Li-NMR on LiInCr4O8 and LiGaCr4O8
• Evidence for gapped spin-wave excitations in the frustrated Gd2Sn2O7 pyrochlore antiferromagnet from low-temperature specific heat measurements
• Order by Disorder and Energetic Selection of the Ground State in the XY Pyrochlore Antiferromagnet Er2Ti2O7. An Inelastic Neutron Scattering Study
• Low-Energy Excitations and Ground State Selection in Quantum Breathing Pyrochlore Antiferromagnet Ba${}_3$Yb${}_2$Zn${}_5$O${}_{11}$
• Ising Like Order by Disorder In The Pyrochlore Antiferromagnet with Dzyaloshinskii-Moriya Interactions
• Order from structural disorder in $XY$ pyrochlore antiferromagnet $\mathrm{E}{\mathrm{r}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$
• 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
• Order Induced by Dilution in Pyrochlore XY Antiferromagnets
• Incipient Ferromagnetism in Tb2Ge2O7: Application of Chemical Pressure to the Enigmatic Spin Liquid, Tb2Ti2O7
• Relief of Frustration in the Heisenberg Pyrochlore Antiferromagnet Gd${}_2$Pt${}_2$O${}_7$
• Ising versus XY anisotropy in frustrated R${}_2$Ti${}_2$O${}_7$ compounds as seen by polarized neutrons
• Nature of Partial Magnetic Order in the Frustrated Antiferromagnet Gd2Ti2O7
• Effective spin-1/2 exchange interactions in Tb${}_2$Ti${}_2$O${}_7$
• Soft dipolar spin ice physics and the ordered phase of the frustrated Tb2Sn2O7 pyrochlore magnet
• Pyrochlore antiferromagnet with antisymmetric exchange interactions: critical behavior and order from disorder

Cited by in corpus (96)

• Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO${}_4$
• Frustrated quantum rare-earth pyrochlores
• Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra
• Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb${}_2$Ti${}_2$O${}_7$ in Magnetic Field
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Experimental Insights into Ground State Selection of Quantum XY Pyrochlores
• Rank-2 $U(1)$ spin liquid on the breathing pyrochlore lattice
• Probing hidden spin order with interpretable machine learning
• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
• Learning multiple order parameters with interpretable machines
• Multiphase Magnetism in Yb2Ti2O7
• Single-ion properties of the $S_{eff}$ = 1/2 XY antiferromagnetic pyrochlores, Na$A^{\prime }$Co${}_2$F${}_7$ ($A^{\prime }=$ Ca${}^{2+}$, Sr${}^{2+}$)
• Reentrant Phase Diagram of $\mathrm{Y}{\mathrm{b}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ in $⟨111⟩$ Magnetic Field
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• The Spectral Periodicity of Spinon Continuum in Quantum Spin Ice
• Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classification
• Fragmentation in Frustrated Magnets -- A review
• Cluster-glass phase in pyrochlore XY antiferromagnets with quenched disorder
• Effect of Chemical Pressure on the Crystal Electric Field States of Erbium Pyrochlore Magnets
• Role of defects in determining the magnetic ground state of ytterbium titanate
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Magnon interactions in the frustrated pyrochlore ferromagnet Yb${}_2$Ti${}_2$O${}_7$
• Quantum versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho3Mg2Sb3O14
• Order out of a Coulomb phase and Higgs transtion: frustrated transverse interactions of Nd2Zr2O7
• Long range order in the dipolar XY antiferromagnet Er${}_2$Sn${}_2$O${}_7$
• Fragmented monopole crystal, dimer entropy and Coulomb interactions in Dy${}_2$Ir${}_2$O${}_7$
• Competing phases and topological excitations of spin-one pyrochlore antiferromagnets
• Unravelling competing microscopic interactions at a phase boundary: a single crystal study of the metastable antiferromagnetic pyrochlore Yb${}_2$Ge${}_2$O${}_7$
• Low energy structure of spiral spin liquids
• Competing orders in pyrochlore magnets from a ${\mathbb{Z}}_2$ spin liquid perspective
• Phase Competition in the Palmer-Chalker XY Pyrochlore Er${}_2$Pt${}_2$O${}_7$
• Dipolar spin ice regime proximate to an all-in-all-out Néel ground state in the dipolar-octupolar pyrochlore Ce${}_2$Sn${}_2$O${}_7$
• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
• Projective symmetry group classification of chiral ${\mathbb{Z}}_2$ spin liquids on the pyrochlore lattice: application to the spin-$1/2$ XXZ Heisenberg model
• Identification of hidden order and emergent constraints in frustrated magnets using tensorial kernel methods
• Magnetic properties of triangular lattice antiferromagnets Ba3RB9O18 (R = Yb, Er)
• Theory of magnetostriction for multipolar quantum spin ice in pyrochlore materials
• Magnetic Excitations in the Ground State of $\mathrm{Y}{\mathrm{b}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$
• Spin freezing in the disordered pyrochlore magnet NaCaCo${}_2$F${}_7$: NMR studies and Monte-Carlo simulations
• Gd pyrochlore under a staggered molecular field in Gd${}_2$Ir${}_2$O${}_7$
• Generation of modulated magnetic structure based on cluster multipole: Application to $\alpha$-Mn and Co$M_3$S${}_6$
• Long-range dynamical magnetic order and spin tunneling in the cooperative paramagnetic states of the pyrochlore analogous spinel antiferromagnets CdYb2X4 (X = S, Se)
• Frustrated magnetism in the Heisenberg pyrochlore antiferromagnets $A$Yb${}_2$$X$${}_4$ ($A$ = Cd, Mg, $X$ = S, Se)
• Fingerprints of quantum spin ice in Raman scattering
• Understanding Reentrance in Frustrated Magnets: the Case of the Er${}_2$Sn${}_2$O${}_7$ Pyrochlore
• Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores
• Strong quantum fluctuations due to competition between magnetic phases in a pyrochlore iridate
• Competing quantum spin liquids, gauge fluctuations, and anisotropic interactions in a breathing pyrochlore lattice
• Beyond magnons in Nd2ScNbO7: An Ising pyrochlore antiferromagnet with all in all out order and random fields
• Topological thermal Hall effect of "magnetic monopoles" in pyrochlore U(1) spin liquid
• Realization of fractonic quantum phases in the breathing pyrochlore lattice
• Magnetic Order with Fractionalized Excitations: Applications to ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$
• Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules
• Frustration on a centred pyrochlore lattice in metal-organic frameworks
• Dynamical scaling as a signature of multiple phase competition in Yb${}_2$Ti${}_2$O${}_7$
• State selection in frustrated magnets
• Ordered ground states of kagome magnets with generic exchange anisotropy
• Field induced phase diagram of the XY pyrochlore antiferromagnet Er${}_2$Ti${}_2$O${}_7$
• The complex non-collinear magnetic orderings in Ba2YOsO6: A new approach to tuning spin-lattice interactions and controlling magnetic orderings in frustrated complex oxides
• Order-by-disorder without quantum zero-point fluctuations in the pyrochlore Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions
• Orientation Dependence of the Magnetic Phase Diagram of Yb${}_2$Ti${}_2$O${}_7$
• Multi-phase competition in quantum $XY$ pyrochlore antiferromagnet CdYb${}_2$Se${}_4$: zero and applied magnetic field study
• Doping-induced quantum cross-over in Er${}_2$Ti${}_{2-x}$Sn${}_x$O${}_7$
• Effects of "stuffing" on the atomic and electronic structure of the pyrochlore Yb${}_2$Ti${}_2$O${}_7$
• Magnetic interactions and spin dynamics in the bond-disordered pyrochlore fluoride NaCaCo${}_2$F${}_7$
• Exchange interactions in two-state systems: rare earth pyrochlores
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets
• Long-wavelength correlations in ferromagnetic titanate pyrochlores as revealed by small angle neutron scattering
• Quantum effects on pyrochlore higher-rank U(1) spin liquids: Pinch-line singularities, spin nematics, and connections to oxide materials
• Frustrated Magnetism of Pharmacosiderite Comprising Tetrahedral Clusters Arranged in the Primitive Cubic Lattice
• Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln${}_2$InSbO${}_7$ family
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Thermodynamics of the dipole-octupole pyrochlore magnet Ce${}_2$Hf${}_2$O${}_7$ in applied magnetic fields
• Ground state properties of the Heisenberg-compass model on the square lattice
• Pulling order back from the brink of disorder: Observation of a nodal line spin liquid and fluctuation stabilized order in K${}_2$IrCl${}_6$
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• Absence of long-range order in an $XY$ pyrochlore antiferromagnet Er${}_2$AlSbO${}_7$
• Interplay of uniform U(1) quantum spin liquid and magnetic phases in rare earth pyrochlore magnets : a fermionic parton approach
• Analytical theory of pyrochlore cooperative paramagnets
• Symmetry, Superposition and Fragmentation in Classical Spin Liquids: A General Framework and Applications to Square Kagome Magnets
• Electron quasi-itinerancy intertwined with quantum order by disorder in pyrochlore iridate magnetism
• Pinch-line spin liquids as layered Coulomb phases and applications to cubic models
• Spin and quadrupole correlations by three-spin interaction in the frustrated pyrochlore magnet Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Anomalous Proximitized Transport in Metal/Quantum Magnet Heterostructure $\mathrm{B}{\mathrm{i}}_2\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7/Y{\mathrm{b}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$
• Quantum Spin Liquids in Pyrochlore Magnets With Non-Kramers Local Moments
• Intertwined Magnetic Dipolar and Electric Quadrupolar Correlations in the Pyrochlore Tb${}_2$Ge${}_2$O${}_7$
• Quantum Spin Liquids Stabilized by Disorder in Non-Kramers Pyrochlores
• Uncommon magnetic ordering in the quantum magnet Yb${}_3$Ga${}_5$O${}_{12}$
• Theta electromagnetism in quantum spin ice: Microscopic analysis of improper symmetries
• Spin amplitude wave due to dipole-quadrupole hybridization in spin-1 pyrochlore magnets
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Analytic description of spin waves in dipolar/octupolar pyrochlore magnets
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Quantum Coulomb Liquids of Different Rank in the Breathing Pyrochlore Antiferromagnet
• Constructing Emergent U(1) Symmetries in the Gamma-prime $\left({\mathbf{\Gamma }}^{\prime }\right)$ model