Magnetic-Moment Fragmentation and Monopole Crystallization

Abstract

The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of frustrated magnets. The emergent Coulomb phase of lattice-based systems has been associated with divergence-free fields and the absence of long-range order. Here, we go beyond this paradigm, demonstrating that a Coulomb phase can emerge naturally as a persistent fluctuating background in an otherwise ordered system. To explain this behavior, we introduce the concept of the fragmentation of the field of magnetic moments into two parts, one giving rise to a magnetic monopole crystal, the other a magnetic fluid with all the characteristics of an emergent Coulomb phase. Our theory is backed up by numerical simulations, and we discuss its importance with regard to the interpretation of a number of experimental results.

References in corpus (21)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Electron fractionalization in two-dimensional graphenelike structures
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Why spin ice obeys the ice rules
• Theory of the [111] magnetization plateau in spin ice
• Lightly stuffed pyrochlore structure of single-crystalline Yb2Ti2O7 grown by the optical floating zone technique
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• Interacting classical dimers on the square lattice
• Is the Yb2Ti2O7 pyrochlore a quantum spin ice?
• Pinch Points and Kasteleyn Transitions: How Spin Ice Changes its Entropy
• A Three Dimensional Kasteleyn Transition: Spin Ice in a [100] Field
• Magnetoelastic excitations in the pyrochlore spin liquid Tb${}_2$Ti${}_2$O${}_7$
• Magnetization process of spin ice in a [111] magnetic field
• Brownian Motion and Quantum Dynamics of Magnetic Monopoles in Spin Ice
• Antiferromagnetic Spin Ice Correlations at (1/2,1/2,1/2) in the Ground State of the Pyrochlore Magnet Tb2Ti2O7
• Topological Sector Fluctuations and Curie Law Crossover in Spin Ice
• Charge ordering in a pure spin model: dipolar spin-ice
• Classical Topological Order in Kagome Ice
• Low temperature dynamic freezing and the fragility of ordering in Tb2Sn2O7
• Soft dipolar spin ice physics and the ordered phase of the frustrated Tb2Sn2O7 pyrochlore magnet

Cited by in corpus (108)

• A Field Guide to Spin Liquids
• Extensive degeneracy, Coulomb phase and magnetic monopoles in an artificial realization of the square ice model
• Fragmentation of magnetism in artificial kagome dipolar spin ice
• 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
• Investigation of the magnetic structure and crystal field states of pyrochlore antiferromagnet Nd2Zr2O7
• Fluctuations and all-in$-$all-out ordering in dipole-octupole Nd2Zr2O7
• Emergent Order in the Kagome Ising Magnet Dy3Mg2Sb3O14
• Are multiphase competition & order-by-disorder the keys to understanding Yb2Ti2O7?
• Magnetic Charge Propagation upon a 3D Artificial Spin-ice
• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
• The quantum origins of moment fragmentation in Nd2Zr2O7
• Nd2Sn2O7: an all-in-all-out pyrochlore magnet with no divergence-free field and anomalously slow paramagnetic spin dynamics
• Continuous magnetic phase transition in artificial square ice
• Experimental signatures of quantum and topological states in frustrated magnetism
• Coexistence of magnetic order and persistent spin dynamics in a quantum kagome antiferromagnet with no intersite mixing
• Magnetic diffuse scattering in artificial kagome spin ice
• Fragmentation in Frustrated Magnets -- A review
• Topological aspects of symmetry breaking in triangular-lattice Ising antiferromagnets
• When opposites repel: from metastability to extended chiral spin textures in spin ice with short-range topological-defect interactions
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Ground-State Candidate for the Dipolar Kagome Ising Antiferromagnet
• Emergent Electrochemistry in Spin Ice: Debye-Hückel Theory and Beyond
• Quantum versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho3Mg2Sb3O14
• Dipolar-Octupolar Ising Antiferromagnetism in Sm${}_2$Ti${}_2$O${}_7$: A Moment Fragmentation Candidate
• Fragmented monopole crystal, dimer entropy and Coulomb interactions in Dy${}_2$Ir${}_2$O${}_7$
• Clustering of Topological Charges in a Kagome Classical Spin Liquid
• Half moons are pinch points with dispersion
• Spin dynamics of the ordered dipolar-octupolar pseudospin-${}^1{/}_2$ pyrochlore Nd${}_2$Zr${}_2$O${}_7$ probed by muon spin relaxation
• Multiferroicity in spin ice: towards a magnetic crystallography of Tb2Ti2O7 in a field
• Spin Ice Thin Film: Surface Ordering, Partial Magnetic Wetting and Emergent Square Ice
• Dynamic quantum kagome ice
• Field-tuned order by disorder in Ising frustrated magnets with antiferromagnetic interactions
• Monopole ordered phases in dipolar and nearest-neighbours Ising pyrochlore: from spin ice to the "all-in--all-out" antiferromagnet
• Quantum spin ice under a [111] magnetic field: from pyrochlore to kagomé
• Muon spin relaxation and inelastic neutron scattering investigations of all-in/all-out antiferromagnet Nd2Hf2O7
• Spin dynamics and unconventional Coulomb phase in Nd${}_2$Zr${}_2$O${}_7$
• Proposal to recover an extensive ground state degeneracy in a two-dimensional square array of nanomagnets
• Evolution of antiferromagnetic domains in the all-in-all-out ordered pyrochlore Nd${}_2$Zr${}_2$O${}_7$
• Identification of hidden order and emergent constraints in frustrated magnets using tensorial kernel methods
• Exploring the phases of 3D artificial spin ice: From Coulomb phase to magnetic monopole crystal
• Phonon-mediated spin-flipping mechanism in the spin ices Dy${}_2$Ti${}_2$O${}_7$ and Ho${}_2$Ti${}_2$O${}_7$
• Gd pyrochlore under a staggered molecular field in Gd${}_2$Ir${}_2$O${}_7$
• Monopolar and dipolar relaxation in spin ice Ho${}_2$Ti${}_2$O${}_7$
• Long-range dynamical magnetic order and spin tunneling in the cooperative paramagnetic states of the pyrochlore analogous spinel antiferromagnets CdYb2X4 (X = S, Se)
• The multiple symmetry sustaining phase transitions of spin ice
• Spin ice thin films: Large-N theory and Monte Carlo simulations
• Magnetic fragmentation and fractionalized Goldstone modes in a bilayer quantum spin liquid
• Physical properties of the trigonal binary compound Nd${}_2$O${}_3$
• Beyond magnons in Nd2ScNbO7: An Ising pyrochlore antiferromagnet with all in all out order and random fields
• Dipolar Spin Ice Under Uniaxial Pressure
• Topological-sector fluctuations and ergodicity breaking at the Berezinskii-Kosterlitz-Thouless transition
• Absence of moment fragmentation in the mixed $B$-site pyrochlore Nd${}_2$GaSbO${}_7$
• Charge and spin correlations in the Monopole Liquid
• Ferromagnetic Coulomb phase in classical spin ice
• Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum Annealer
• Giant Magnetoelastic-Coupling Driven Spin-Lattice Liquid State in Molybdate Pyrochlores
• Signatures of long range dipolar interactions in artificial square ice
• Coexistence of magnetic fluctuations and long-range orders in the one-dimensional $J_1-J_2$ zigzag chains materials BaDy${}_2$O${}_4$ and BaHo${}_2$O${}_4$
• The Polarized Monopole Liquid: a Coulomb phase in a fluid of magnetic charges
• Evaluating the Effects of Structural Disorder on the Magnetic Properties of Nd${}_2$Zr${}_2$O${}_7$
• Ordered ground states of kagome magnets with generic exchange anisotropy
• Slow spin tunneling in the paramagnetic phase of the pyrochlore Nd2Sn2O7
• Effects of uniaxial pressure on the spin ice Ho2Ti2O7
• Homogenous reduced moment in a gapful scalar chiral kagome antiferromagnet
• Violation of the fluctuation-dissipation theorem and effective temperatures in spin ice
• Field-Induced Ordering in Dipolar Spin Ice
• The Classical Heisenberg Model on the Centred Pyrochlore Lattice
• Doping-induced quantum cross-over in Er${}_2$Ti${}_{2-x}$Sn${}_x$O${}_7$
• Dynamical Axions in $U(1)$ Quantum Spin Liquids
• Screening and the Pinch Point Paradox in Spin Ice
• The Concept of Spin Ice Graphs and a Field Theory for their Topological Monopoles and Charges
• Exactly solvable spin-1/2 XYZ models with highly-degenerate, partially ordered, ground states
• Electric activity at magnetic moment fragmentation in spin ice
• Quadrupole moments and their interactions in the triangular lattice antiferromagnet FeI${}_2$
• Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets
• Tunable critical correlations in kagome ice
• 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
• Pinch points and half-moons in dipolar-octupolar Nd${}_2$Hf${}_2$O${}_7$
• Monte Carlo study on the detection of classical order by disorder in real antiferromagnetic Ising pyrochlores
• Vison crystal in quantum spin ice on the breathing pyrochlore lattice
• The Future of the Correlated Electron Problem
• Perfectly hidden order and Z2 confinement transition in a fully packed monopole liquid
• Interplay of symmetry breaking and deconfinement in 3D quantum vertex models
• Field-temperature phase diagram of the enigmatic Nd${}_2$(Zr${}_{1-x}$Ti${}_x$)${}_2$O${}_7$ pyrochlore magnets
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Neutron scattering from fragmented frustrated magnets
• Symmetry, Superposition and Fragmentation in Classical Spin Liquids: A General Framework and Applications to Square Kagome Magnets
• Gauge-Free Duality in Pure Square Spin Ice: Topological Currents and Monopoles
• Emergent tri-criticality in magnetic metamaterials
• Emergent Snake Magnetic Domains in Canted Kagome Ice
• Pinch points and half moons encode Berry curvature
• Coulombic antiferromagnet in spin-1/2 pyrochlores with dipole-octupole doublets
• Magnetic charge injection in spin ice: a new way to fragmentation
• Algebraic Hastatic Order in One-Dimensional Two-Channel Kondo Lattice
• An electric-field representation of the harmonic XY model
• Square ice Coulomb phase as a percolated vertex lattice
• Spin textures in chiral magnetic monolayers with suppressed nearest-neighbor exchange
• Mean-field theory for confinement transitions and magnetization plateaux in spin ice
• Ferromagnetic fragmented state in the pyrochlore Ho${}_2$Ru${}_2$O${}_7$
• Coupling quantum spin ice to matter on the centered pyrochlore lattice
• Observation of magnetic fragmentation in spin ice
• Unusual Coulomb phase physics in the arctic square ice
• Realizing Blume-Capel Degrees of Freedom with Toroidal Moments in a Ruby Artificial Spin Ice
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• 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