Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid

Abstract

Quantum matter provides an effective vacuum out of which arise emergent particles not corresponding to any experimentally detected elementary particle. Topological quantum materials in particular have become a focus of intense research in part because of the remarkable possibility to realize Majorana fermions, with their potential for new, decoherence-free quantum computing architectures. In this paper we undertake a study on high-quality single crystal of $\alpha -RuC{l}_3$ which has been identified as a material realizing a proximate Kitaev state, a topological quantum state with magnetic Majorana fermions. Four-dimensional tomographic reconstruction of dynamical correlations measured using neutrons is uniquely powerful for probing such magnetic states. We discover unusual signals, including an unprecedented column of scattering over a large energy interval around the Brillouin zone center which is remarkably stable with temperature. This is straightforwardly accounted for in terms of the Majorana excitations present in Kitaev's topological quantum spin liquid. Other, more delicate, features in the scattering can be transparently associated with perturbations to an ideal model. This opens a window on emergent magnetic Majorana fermions in correlated materials.

10 pages main text with 4 main figures, 13 Supplementary pages with 9 figures

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• Acoustic phonon dispersion of $\alpha$-RuCl${}_3$
• Quantum and classical spin dynamics across temperature scales in the S = 1/2 Heisenberg antiferromagnet
• Neutron spectroscopy evidence for a possible magnetic-field-induced gapless quantum-spin-liquid phase in a Kitaev material $\alpha$-RuCl${}_3$
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• Single-crystal study of the honeycomb XXZ magnet BaCo${}_2$(PO${}_4$)${}_2$ in magnetic fields
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• Reentrant incommensurate order and anomalous magnetic torque in the Kitaev magnet $\beta$-${\text{Li}}_2{\text{IrO}}_3$
• Multiferroic nematic d-wave altermagnetism driven by orbital-order on the honeycomb lattice
• Diffuse Scattering from Correlated Electron Systems
• Two-step growth of high-quality single crystals of the Kitaev magnet $\alpha$-RuCl${}_3$
• Freezing of a disorder induced quantum spin liquid
• Electronic Density of States of a $U\left(1\right)$ Quantum Spin Liquid with Spinon Fermi Surface. II. Zeeman Magnetic Field Effects
• Light-induced magnetization driven by interorbital charge motion in a spin-orbit assisted Mott insulator alpha-RuCl3
• Ground State Magnetic Structure and Magnetic Field Effects in the Layered Honeycomb Antiferromagnet YbOCl
• Signatures for spinons in the quantum spin liquid candidate Ca${}_{10}$Cr${}_7$O${}_{28}$
• Optical magnons with dominant bond-directional exchange interactions in a honeycomb lattice iridate $\alpha$-Li${}_2$IrO${}_3$
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• Hamiltonian inference from dynamical excitations in confined quantum magnets
• Hidden spin-orbital order in the Kitaev hyperhoneycomb $\beta$-Li${}_2$IrO${}_3$
• Quantum magnetism in the frustrated square lattice oxyhalides YbBi2IO4 and YbBi2ClO4
• Magnetism study on a triangular lattice antiferromagnet Cu${}_2$(OH)${}_3$Br
• Oriented propagation of magnetization due to chiral edge modes in Kitaev-type models
• Weak-coupling to strong-coupling quantum criticality crossover in a Kitaev quantum spin liquid $\alpha$-RuCl${}_3$
• Differentiable programming tensor networks for Kitaev magnets
• Phonon Dynamics in the Generalized Kitaev Spin Liquid
• Peering into the darkness: vison-generated photon mass in quantum spin ice
• Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy
• Dynamics of fractionalized mean-field theories: consequences for Kitaev materials
• Magnetic States of Graphene Proximitized Kitaev Materials
• $J=1/2$ Pseudospins and $d$-$p$ Hybridization in the Kitaev Spin Liquid Candidates Ru$X_3$ ($X$ = Cl, Br, I)
• Low-temperature environments for quantum computation and quantum simulation
• Realization and detection of Kitaev quantum spin liquid with Rydberg atoms
• Short-range order and hidden energy scale in geometrically frustrated magnets
• Orbital Magnetic Field Effects in Mott Insulators with Strong Spin-Orbit Coupling
• Antiferromagnetism and Ising Ground States in the Rare-earth Garnet Nd${}_3$Ga${}_5$O${}_{12}$
• Correlation effects on the magnetization process of the Kitaev model
• Emergent quantum Majorana metal from a chiral spin liquid
• Neutron scattering study of the kagome metal Sc3Mn3Al7Si5
• Signatures of non-Loudon-Fleury Raman scattering in the Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• The honeycomb and hyperhoneycomb polymorphs of IrI${}_3$
• Suppression of the antiferromagnetic order by Zn doping in a possible Kitaev material Na${}_2$Co${}_2$TeO${}_6$
• Pyrochlore NaYbO2: A potential Quantum Spin Liquid Candidate
• Confinement transition in a Kitaev-like honeycomb model with bond anisotropy
• Magnetism and field-induced effects in the S = 5/2 honeycomb lattice antiferromagnet FeP3SiO11
• Interplay of magnetic field and trigonal distortion in the honeycomb $\Gamma$ model: Occurrence of a spin-flop phase
• Unconventional anomalous Hall effect in epitaxially stabilized orthorhombic Ru${}^{3+}$ perovskite thin films
• Perturbed Kitaev model: excitation spectrum and long-ranged spin correlations
• Majorana Fermion Mean-Field Theories of Kitaev Quantum Spin Liquids
• Anomalous thermal relaxation and pump-probe spectroscopy of 2D topologically ordered systems
• Probing critical spin fluctuations with a composite magnetoelectric method: A case study on a Kitaev spin liquid candidate Na${}_3$Co${}_2$SbO${}_6$
• Dielectric Evidence for Possible Type-II Multiferroicity in alpha-RuCl3
• Bound states of fractionalized excitations in a modulated Kitaev spin liquid
• Engineering the Kitaev spin liquid in a quantum dot system
• Spin-isotropic continuum of spin excitations in antiferromagnetically ordered Fe${}_{1.07}$Te
• Exactly solvable spin-1/2 XYZ models with highly-degenerate, partially ordered, ground states
• Continuous transition between Ising magnetic order and a chiral spin liquid
• Kinetic Ferromagnetism and Topological Magnons of the Hole-Doped Kitaev Spin Liquid
• Spin Seebeck Effect as a Probe for Majorana Fermions in Kitaev Spin Liquids
• Disentangling spin excitation continua in classical and quantum magnets using 2D nonlinear spectroscopy
• Trimer classical spin liquid from interacting fractional charges
• Multinode quantum spin liquids in extended Kitaev honeycomb models: the view from variational Monte Carlo
• Anisotropic magnetic interactions in a candidate Kitaev spin liquid close to a metal-insulator transition
• Quantum spin liquid from electron-phonon coupling
• Multicomponent magneto-orbital order and magneto-orbitons in monolayer VCl3
• Valence bond fluctuations in the Kitaev spin model
• Direct evidence of intrinsic Mott state and its layer-parity oscillation in a breathing kagome crystal down to monolayer
• Crystalline Splitting of $d$ Orbitals in Regular Optical Lattices
• Dimerization in honeycomb Na2RuO3 under pressure: a DFT study
• Role of disorder in the electronic and magnetic properties of Ag${}_3$LiIr${}_2$O${}_6$
• Excitonic transverse and amplitude fluctuations in the noncollinear and charge-ordered RbFe${}^{2+}$Fe${}^{3+}$F${}_6$
• Projective-symmetry-group analysis of inelastic light scattering in Kitaev spin balls
• Probing emergent QED in quantum spin ice via Raman scattering of phonons: shallow inelastic scattering and pair production
• Theory of quasiparticle interference in Kitaev quantum spin liquids
• Soft-Chemical Synthesis, Structure Evolution, and Insulator-to-Metal Transition in a Prototypical Metal Oxide, λ-RhO${}_2$
• Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids
• Unraveling the magnetic ground-state in alkali-metal lanthanide oxide Na${}_2$PrO${}_3$
• Static and fluctuating zigzag order, and possible signatures of Kitaev physics, in torque measurements of $\alpha$-RuCl${}_3$
• Giant anisotropic magnetoresistance in few-layer α-RuCl3 tunnel junctions
• Gauge symmetry of excited states in projected entangled-pair state simulations
• Magnetic order in the two-dimensional metal-organic framework manganese pyrazinecarboxylate with Mn-Mn dimers
• Drag resistance mediated by quantum spin liquids
• Widely Spaced Planes of Magnetic Dimers in the Ba6Y2Rh2Ti2O17-δ Hexagonal Perovskite
• Chiral excitations and the intermediate-field spin-liquid regime in the Kitaev magnet $\alpha$-RuCl${}_3$
• Dominant Kitaev interaction and field-induced quantum phase transitions in triangular-lattice KCeSe2
• Magnetostriction of α-RuCl3 flakes in the zigzag phase
• Majorana corner states in square and Kagome quantum spin liquids
• Ultrafast spin dynamics in the proximate quantum spin liquid α-RuCl3
• Fracton and topological order in the XY checkerboard toric code
• Emergent Hyper-Magic Manifold in Twisted Kitaev Bilayers
• Computational studies on magnetism and ferroelectricity
• Detection of anyon braiding through pump-probe spectroscopy
• Signatures of a gapless quantum spin liquid in the Kitaev material Na${}_3$Co${}_{2-x}$Zn${}_x$SbO${}_6$
• Effects of magnon-magnon interactions in a noncollinear magnet induced by combination of a symmetric and an antisymmetric exchange interaction
• High temperature dynamics in quantum compass models
• High-field quantum spin liquid transitions and angle-field phase diagram of Kitaev magnet $\alpha$-RuCl${}_3$
• Two-triplon excitations of the Kitaev-Heisenberg-Bilayer
• High-fidelity dimer excitations using quantum hardware
• Ligand Field Exciton Annihilation in Bulk CrCl3
• Exfoliation and Optical Properties of S=1 Triangular Lattice Antiferromagnet NiGa${}_2$S${}_4$
• Temperature dependence of the $(\pi ,0)$ anomaly in the excitation spectrum of the 2D quantum Heisenberg antiferromagnet
• Evidence for distortion-induced local electric polarization in $\alpha$-RuCl${}_3$
• Ground state and magnetic transitions of the orthorhombic antiferromagnet CaCo${}_2$TeO${}_6$
• Emergent Quadrupolar Order in the Spin-$1/2$ Kitaev-Heisenberg Model
• Finite-momentum energy dynamics in a Kitaev magnet
• Sweet spot in the RuCl${}_3$ magnetic system: nearly ideal $j_{\mathrm{eff}}=1/2$ moments and maximized $K/J$ ratio under pressure
• Colossal quasiparticle radiation in the Lifshitz spin liquid phase of a two-dimensional quantum antiferromagnet
• Field-induced quantum phase in a frustrated zigzag-square lattice
• Incommensurate Spiral Spin Order in CaMn${}_2$Bi${}_2$ observed via High Pressure Neutron Diffraction
• Pairing tendencies in the doped Kitaev-Heisenberg model
• Anyon polarons as a window into competing phases of the Kitaev honeycomb model under a Zeeman field
• Phase diagram for Hole-Doped Kitaev System on the Honeycomb Lattice
• First-principles-based calculation of branching ratio for 5$\mathbf{d}$, 4$\mathbf{d}$, and 3$\mathbf{d}$ transition metal systems
• Renormalized density matrix downfolding: A rigorous framework in learning emergent models from ab initio many-body calculations
• Discovery of an ultrastable antiferromagnetic two-dimensional CrF3 phase with anisotropic quasi-one-dimensional mechanical, electronic, and thermal properties
• Mott Gap Softening Coinciding with Spin Correlations Collapse in a-RuCl3
• Bulk excitations in ultraclean $\alpha$-RuCl${}_3$: Quantitative evidence for Majorana dispersions in a Kitaev quantum spin liquid
• Anisotropic Coulomb exchange as source of Kitaev and off-diagonal symmetric anisotropic couplings
• Coupled spin-1/2 antiferromagnetic chain Cs${}_2$LiRuCl${}_6$ with partially disordered crystal lattice
• Direct evidence for anisotropic magnetic interaction in $\alpha$-RuCl${}_3$ from polarized inelastic neutron scattering
• Optical detection of bond-dependent and frustrated spin in the two-dimensional cobalt-based honeycomb antiferromagnet Cu3Co2SbO6
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Assembling Kitaev honeycomb spin liquids from arrays of 1D symmetry protected topological phases
• Pulsed Neutron Spectroscopy of Low Dimensional Magnets: Past, Present, and Future
• Thermal decomposition of the Kitaev material $\alpha$-RuCl${}_3$ and its influence on low-temperature behavior
• Impact of gapped spin-orbit excitons on low energy pseudospin exchange interactions
• Topological Aspects of Antiferromagnets
• Three-dimensional Sandglass Magnet with Non-Kramers ions
• Ground-state phase diagram of anisotropically interacting Heisenberg-$\Gamma$ models on a honeycomb lattice
• Optical contrast analysis of α-RuCl${}_3$ nanoflakes on oxidized silicon wafers
• (H,Li)${}_6$Ru${}_2$O${}_6$ : a possible zero-field Ru${}^{3+}$-based Kitaev Quantum Spin Liquid
• Kitaev interactions in the van der Waals antiferromagnet VBr3
• Ferroelectric switching of interfacial dipoles in $\alpha$-RuCl${}_3$/graphene heterostructure
• KOMPASS: the new cold neutron triple-axis-spectrometer specialized for polarization analysis
• Phenomenological Ginzburg-Landau theory for triple-Q magnetic orders on a hexagonal lattice
• Robustness of Vacancy-Bound Non-Abelian Anyons in the Kitaev Model in a Magnetic Field
• Dipolar and quadrupolar correlations in the $5d^2$ Re-based double perovskites Ba${}_2$YReO${}_6$ and Ba${}_2$ScReO${}_6$
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• Scale-invariant magnetic anisotropy in $\alpha$-RuCl${}_3$: A quantum Monte Carlo study
• Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet
• Spectral damping without quasiparticle decay: The dynamic structure factor of two-dimensional quantum Heisenberg antiferromagnets
• Antiferromagnetic Order and Magnetic Frustration in the Honeycomb Heavy-Fermion System Ce(Pt${}_{1-x}$Pd${}_x$)${}_6$Al${}_3$: ${}^{27}$Al and ${}^{195}$Pt NMR Studies
• Moiré spintronics: Emergent phenomena, material realization and machine learning accelerating discovery
• Field-induced phase transitions in the Kitaev-Heisenberg model: A sign-problem-free quantum Monte Carlo study and possible application to $\alpha$-RuCl3
• Angular-Dependent Thermal Hall Effect in a Honeycomb Magnet: Disentangling Kitaev and Dzyaloshinskii-Moriya Interactions
• Electron correlation effects and spin-liquid state in the Herbertsmithite Kagome lattice
• The Kekulé-Kitaev model: linear and non-linear responses and magnetic field effects
• The Magnetic Ground State of Atacamite Cu${}_2$Cl(OH)${}_3$: The Crucial Role of Frustrated Zigzag Chains Revealed by Inelastic Neutron Scattering
• Using magnetic dynamics to measure the spin gap in a candidate Kitaev material
• Collapse of susceptibility and non-trivial spin dynamics in the hyper-honeycomb magnet $\beta$-Li${}_2$IrO${}_3$ under high pressure
• Spin disorder state induced by Mg${}^{2+}$ doping in a Kitaev material Na${}_3$Co${}_2$SbO${}_6$
• Dynamical Response of the Kitaev Spin Liquid under Third-Nearest-Neighbor Heisenberg Interaction
• Sizable Ligand-Mediated Bond-Dependent Interactions in a Spin-1 Triangular Antiferromagnet NiI${}_2$
• Stabilization of zigzag order in NiPS${}_3$ via positive biquadratic interaction
• Crystal field splittings and magnetic ground state of the square-lattice antiferromagnets YbBi2ClO4 and YbBi2IO4 with Jeff = 1/2
• Magnetic excitations in the Kitaev material Na${}_2$IrO${}_3$ studied by neutron scattering
• Hidden Frustration in Double-Perovskite CaFeTi${}_2$O${}_6$
• Absence of magnetic order and magnetic fluctuations in RuO${}_2$
• Magnetic-field induced melting of long-range magnetic order akin to Kitaev insulators in the metallic compound Tb5Si3
• Dominant Kitaev Interaction and Field-induced Quantum Disordered Phase in the Cobaltate Na${}_2$Co${}_2$TeO${}_6$
• Ground state of the staggered Heisenberg-$\Gamma$ honeycomb model in a magnetic field
• Low-temperature spin dynamics and absence of magnetic order in layered $\alpha$-RuI${}_3$
• Spin sensitive transport in RuCl_3/Pt heterostructures: revealing a field-transverse spin anisotropy in a spin liquid candidate
• Designer quantum matter in van der Waals heterostructures
• An indirect geometry crystal time-of-flight spectrometer for FRM II
• Thermal Properties and Instability of a $U(1)$ Spin Liquid on the Triangular Lattice
• Non-Loudon-Fleury Raman scattering in spin-orbit coupled Mott insulators
• Anomalous and Anisotropic Nonlinear Susceptibility in the Proximate Kitaev Magnet $\alpha$-RuCl${}_3$
• Magnetic and magnetocaloric effect in the stuffed honeycomb antiferromagnet GdInO3 polycrystalline
• The field-angle anisotropy of proximate Kitaev systems under an in-plane magnetic field
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• Phases and Quantum Phase Transitions in Anisotropic Antiferromagnetic Kitaev-Heisenberg-$\Gamma$ magnet