Topological Aspects of Antiferromagnets

Abstract

The long fascination antiferromagnetic materials have exerted on the scientific community over about a century has been entirely renewed recently with the discovery of several unexpected phenomena including various classes of anomalous spin and charge Hall effects and unconventional magnonic transport, but also homochiral magnetic entities such as skyrmions. With these breakthroughs, antiferromagnets standout as a rich playground for the investigation of novel topological behaviors, and as promising candidate materials for disruptive low-power microelectronic applications. Remarkably, the newly discovered phenomena are all related to the topology of the magnetic, electronic or magnonic ground state of the antiferromagnets. This review exposes how non-trivial topology emerges at different levels in antiferromagnets and explores the novel mechanisms that have been discovered recently. We also discuss how novel classes of quantum magnets could enrich the currently expanding field of antiferromagnetic spintronics and how spin transport can in turn favor a better understanding of exotic quantum excitations.

77 pages, 47 figures

References in corpus (77)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Topological Crystalline Insulators
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Spin Transfer Torques
• Titanic Magnetoresistance in WTe2
• Direct electronic measurement of the spin Hall effect
• Spin Seebeck insulator
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Observation of the Magnon Hall Effect
• Antiferromagnetic topological insulators
• The space group classification of topological band insulators
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Scattering Continuum and Possible Fractionalized Excitations in $\alpha$-RuCl${}_3$
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Theoretical prediction of rotating magnon wavepacket in ferromagnets
• Electrical Manipulation of a Topological Antiferromagnetic State
• Structure determination and coexistence of superconductivity and antiferromagnetic order in (Li0.8Fe0.2)OHFeSe
• Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Topological Magnon Insulator in Insulating Ferromagnet
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Cluster multipole theory for anomalous Hall effect in antiferromagnets
• Properties of an algebraic spin liquid on the kagome lattice
• Spin Oscillations in Antiferromagnetic NiO Triggered by Circularly Polarized Light
• 17O NMR study of the intrinsic magnetic susceptibility and spin dynamics of the quantum kagome antiferromagnet ZnCu3(OH)6Cl2
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Extensive degeneracy, Coulomb phase and magnetic monopoles in an artificial realization of the square ice model
• Low Temperature Spin Freezing in Dy2Ti2O7 Spin Ice
• Monolayer FeSe on SrTiO${}_3$
• Electric control of Dirac quasiparticles by spin-orbit torque in an antiferromagnet
• Observation of spin current in quantum spin liquid
• Giant thermal Hall conductivity from neutral excitations in the pseudogap phase of cuprates
• Antiferromagnetic skyrmion crystals: generation, topological Hall and topological spin Hall effect
• Tunable magnon Weyl points in ferromagnetic pyrochlores
• Propulsion of a domain wall in an antiferromagnet by magnons
• Signature of magnon Nernst effect in an antiferromagnetic insulator
• Unconventional Anomalous Hall Effect in the Metallic Triangular-Lattice Magnet PdCrO2
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Discretized Topological Hall Effect Emerging from Skyrmions in Constricted Geometry
• Fractionalization, topological order, and quasiparticle statistics
• Spin-order dependent anomalous Hall effect and magneto-optical effect in noncollinear antiferromagnets Mn${}_{3}X$N ($X$ = Ga, Zn, Ag, and Ni)
• Multipole expansion for magnetic structures: A generation scheme for symmetry-adapted orthonormal basis set in crystallographic point group
• Anisotropic spin Hall effect from first principles
• Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model
• Weyl spin liquids
• One-Third Magnetization Plateau with a Preceding Novel Phase in Volborthite
• Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics
• Barlowite: A Spin-1/2 Antiferromagnet with a Geometrically Perfect Kagome Motif
• Topological and Transport Properties of Dirac Fermions in Antiferromagnetic Metallic Phase of Iron-Based Superconductors
• Anomalous Hall Conductivity of a Non-Collinear Magnetic Antiperovskite
• Brownian Motion and Quantum Dynamics of Magnetic Monopoles in Spin Ice
• Spin current noise of the spin Seebeck effect and spin pumping
• Low Energy Electrodynamics of Novel Spin Excitations in the Quantum Spin Ice Yb${}_2$Ti${}_2$O${}_7$
• Topological antiferromagnetic phase in a correlated Bernevig-Hughes-Zhang model
• Topological spin Hall effects and tunable skyrmion Hall effects in uniaxial antiferromagnetic insulators
• Antiferromagnetic Dirac Semimetals in Two Dimensions
• Dynamics of ferromagnetic bimerons driven by spin currents and magnetic fields
• Disentangling the magnetoelectric and thermoelectric transport in topological insulator thin films
• Anomalous Hall Effect in $t_{2g}$ Orbital Kagome Lattice due to Non-collinearity:Significance of Orbital Aharonov-Bohm Effect
• Bulk Rashba Effect in Multiferroics: a theoretical prediction for BiCoO3
• Quantum Anomalous Hall Effect in Kagome Ice
• Two-dimensional Massless Dirac Fermions in Antiferromagnetic AFe2As2 (A = Ba, Sr)
• Anomalous Hall Effect due to Non-collinearily in Pyrochlore Compounds: Role of Orbital Aharonov-Bohm Effect
• Realization of the Chern insulator and Axion insulator phases in antiferromagnetic $MnTe$-$B{i}_2(Se,Te{)}_3$-$MnTe$ heterostructures
• Intrinsic non-adiabatic topological torque in magnetic skyrmions and vortices
• Laser control of magnonic topological phases in antiferromagnets
• Orbital magnetization and its effect in antiferromagnets on the distorted fcc lattice
• Chiral phase transition and thermal Hall effect in an anisotropic spin model on the kagome lattice