Progress and prospects in magnetic topological materials

Abstract

Magnetic topological materials represent a class of compounds whose properties are strongly influenced by the topology of the electronic wavefunctions coupled with the magnetic spin configuration. Such materials can support chiral electronic channels of perfect conduction, and can be used for an array of applications from information storage and control to dissipationless spin and charge transport. Here, we review the theoretical and experimental progress achieved in the field of magnetic topological materials beginning with the theoretical prediction of the Quantum Anomalous Hall Effect without Landau levels, and leading to the recent discoveries of magnetic Weyl semimetals and antiferromagnetic topological insulators. We outline the recent theoretical progress that resulted in the tabulation, for the first time, of all magnetic symmetry group representations and topology. We describe several experiments realizing Chern insulators, Weyl and Dirac magnetic semimetals, and an array of axionic and higher-order topological phases of matter as well as survey future perspectives.

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• Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3
• Anomalous Hall effect arising from noncollinear antiferromagnetism
• Magnetic Weyl Semimetal Phase in a Kagome Crystal
• Realization of Quantum Spin Hall State in Monolayer 1T'-WTe2
• Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Large anomalous Nernst effect at room temperature in a chiral antiferromagnet
• Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
• Dirac fermions and flat bands in the ideal kagome metal FeSn
• Experimental realization of an intrinsic magnetic topological insulator
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co3Sn2S2
• Antiferromagnetic topological insulators
• Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions
• Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet $\mathrm{MnB}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$ films
• Evidence for Magnetic Weyl Fermions in a Correlated Metal
• Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal
• The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi
• Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet
• Inversion Symmetric Topological Insulators
• Discovery of a quantum limit Chern magnet TbMn6Sn6
• The development of ferromagnetism in the doped topological insulator Bi2-xMnxTe3
• Negative flat band magnetism in a spin-orbit coupled correlated kagome magnet
• High-throughput calculations of magnetic topological materials
• Hourglass Fermions
• Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal
• Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn
• Hedgehog Spin-texture and Berry's Phase tuning in a Magnetic Topological Insulator
• Non-collinear Antiferromagnets and the Anomalous Hall Effect
• Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys
• High-Chern-Number and High-Temperature Quantum Hall Effect without Landau Levels
• Giant and anisotropic many-body spin-orbit tunability in a strongly correlated kagome magnet
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures
• Heusler, Weyl, and Berry
• Double Dirac Semimetals in Three Dimensions
• Crystal growth and magnetic structure of MnBi2Te4
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Zero-field Nernst effect in a ferromagnetic kagome-lattice Weyl-semimetal Co3Sn2S2
• Anomalous Nernst effect beyond the magnetization scaling relation in the ferromagnetic Heusler compound Co${}_2$MnGa
• Spatial Fluctuations of Helical Dirac Fermions on the Surface of Topological Insulators
• Strong, anisotropic anomalous Hall effect and spin Hall effect in chiral antiferromagnetic compounds Mn${}_{3}X$ ($X$ = Ge, Sn, Ga, Ir, Rh and Pt)
• Anomalous Nernst and Righi-Leduc effects in Mn${}_3$Sn: Berry curvature and entropy flow
• Quantitative mappings between symmetry and topology in solids
• Dirac Fermions in Antiferromagnetic Semimetal
• Magnetic Topological Quantum Chemistry
• Carrier-independent ferromagnetism and giant anomalous Hall effect in magnetic topological insulator
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Large magnetic gap at the Dirac point in a Mn-induced Bi${}_2$Te${}_3$ heterostructure
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Spin scattering and noncollinear spin structure-induced intrinsic anomalous Hall effect in antiferromagnetic topological insulator $\mathrm{MnB}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$
• Imaging Dirac-Mass Disorder from Magnetic Dopant-Atoms in the Ferromagnetic Topological Insulator Cr${}_x$(Bi${}_{0.1}$Sb${}_{0.9}$)${}_{2-x}$Te${}_3$
• Chiral anomaly, Charge Density Waves, and Axion Strings from Weyl Semimetals
• Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects
• Giant room temperature anomalous Hall effect and magnetically tuned topology in the ferromagnetic Weyl semimetal Co2MnAl
• Evidence for an axionic charge density wave in the Weyl semimetal (TaSe4)2I
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Variety of magnetic topological phases in the (MnBi${}_2$Te${}_4$)(Bi${}_2$Te${}_3$)${}_m$ family
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Orbital-selective Dirac fermions and extremely flat bands in frustrated kagome-lattice metal CoSn
• Surface states in bulk single crystal of topological semimetal Co${}_3$Sn${}_2$S${}_2$ towards water oxidation
• Möbius Insulator and Higher-Order Topology in MnBi${}_{2n}$Te${}_{3n+1}$
• Anomalous Hall effect in Weyl semimetal half Heusler compounds RPtBi (R = Gd and Nd)
• Planar Hall effect in the Weyl semimetal GdPtBi
• Rare earth engineering in RMn${}_6$Sn${}_6$ topological kagome magnets
• Topological Quadrupolar Semimetals
• Realization of an intrinsic, ferromagnetic topological state in MnBi8Te13
• Topological Magnetic Phase in the Candidate Weyl Semimetal CeAlGe
• Nernst and magneto-thermal conductivity in a lattice model of Weyl fermions
• Visualization of superparamagnetic dynamics in magnetic topological insulators
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Rotation Anomaly and Topological Crystalline Insulators
• Large-gap magnetic topological heterostructure formed by subsurface incorporation of a ferromagnetic layer
• Large anomalous Nernst effect in a van der Waals ferromagnet Fe${}_3$GeTe${}_2$
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Berry curvature unravelled by the Nernst effect in Mn${}_3$Ge
• Large anomalous Hall effect in ferromagnetic insulator-topological insulator heterostructures
• A Charge-Density-Wave Topological Semimetal
• Dirac semimetal in type IV magnetic space group
• Graph Theory Data for Topological Quantum Chemistry
• A Single Pair of Weyl Fermions in Half-metallic EuCd2As2 Semimetal
• Electronic states and magnetic response of MnBi2Te4 by scanning tunneling microscopy and spectroscopy
• Quantum Anomalous Hall Effect in Time-Reversal-Symmetry Breaking Topological Insulators
• Topological Insulators with Commensurate Antiferromagnetism
• Electronic correlations and flattened band in magnetic Weyl semimetal candidate Co3Sn2S2
• Slater to Mott crossover in the metal to insulator transition of Nd2Ir2O7
• Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Anomalous Hall Effect in Kagome Ferrimagnet GdMn${}_6$Sn${}_6$
• Emerging chiral edge states from the confinement of a magnetic Weyl semimetal in Co${}_3$Sn${}_2$S${}_2$
• Observation of Weyl fermions in a magnetic non-centrosymmetric crystal
• Multifold nodal points in magnetic materials
• The Axion Insulator as a Pump of Fragile Topology
• Fragile Phases As Affine Monoids: Classification and Material Examples
• Topological nodal-line semimetals in ferromagnetic rare-earth-metal monohalides
• Direct determination of the spin structure of Nd${}_2$Ir${}_2$O${}_7$ by means of neutron diffraction
• Competing orders and topology in the global phase diagram of pyrochlore iridates
• Strong anomalous Nernst effect in collinear magnetic Weyl semimetals without net magnetic moments
• Topological semimetal in honeycomb lattice LnSI
• Signature of band inversion in the antiferromagnetic phase of axion insulator candidate EuIn2As2
• Spectroscopic perspective on the interplay between electronic and magnetic properties of magnetically doped topological insulators
• Canonical magnetic insulators with isotropic magnetoelectric coupling
• Model Hamiltonian and Time Reversal Breaking Topological Phases of Anti-ferromagnetic Half-Heusler Materials
• Axion coupling in the hybrid Wannier representation
• A gap-protected zero-Hall effect state in the quantum limit of the nonsymmorphic metal KHgSb

Cited by in corpus (143)

• Topological kagome magnets and superconductors
• Enumeration of spin-space groups: Towards a complete description of symmetries of magnetic orders
• Topological Transformation and Free-Space Transport of Photonic Hopfions
• Topologically controlled multiskyrmions in photonic gradient-index lenses
• Strain-tunable Berry curvature in quasi-two-dimensional chromium telluride
• Monolayer V2MX4: A new family of quantum anomalous Hall insulators
• Progress and Prospects in Two-Dimensional Magnetism of van der Waals Materials
• Theory of optical axion electrodynamics and application to the Kerr effect in topological antiferromagnets
• Ab-initio overestimation of the topological region in Eu-based compounds
• Free-Space Propagation and Skyrmion Topology of Toroidal Electromagnetic Pulses
• Progress and prospects in the quantum anomalous Hall effect
• Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling
• Intrinsic Magnetic Topological Materials
• Transport, refraction and interface arcs in junctions of Weyl semimetals
• Engineering magnetic topological insulators in Eu${}_5{M}_2{X}_6$ Zintls
• Photonic torons, topological phase transition and tunable spin monopoles
• Multi-k magnetic structure and large anomalous Hall effect in candidate magnetic Weyl semimetal NdAlGe
• Towards the Quantized Anomalous Hall effect in AlO${}_x$-capped MnBi${}_2$Te${}_4$
• Space-Time Hopfion Crystals
• Reversible Non-Volatile Electronic Switching in a Near Room Temperature van der Waals Ferromagnet
• New insight into tuning magnetic phases of $R$Mn${}_6$Sn${}_6$ kagome metals
• Signature of weakly coupled $f$ electrons and conduction electrons in magnetic Weyl semimetal candidates PrAlSi and SmAlSi
• Ubiquitous order-disorder transition in the Mn antisite sublattice of the (MnBi${}_2$Te${}_4$)(Bi${}_2$Te${}_3$)${}_n$ magnetic topological insulators
• Quasi-one-dimensional spin transport in altermagnetic $Z^3$ nodal net metals
• Coexistence of Weyl semimetal and Weyl nodal loop semimetal phases in a collinear antiferromagnet
• Even-Odd Layer-Dependent Exchange Bias Effect in MnBi2Te4 Chern Insulator Devices
• MSGCorep: A package for corepresentations of magnetic space groups
• Electrons in helical magnetic field: a new class of topological metals
• Discovering two-dimensional magnetic topological insulators by machine learning
• Optical skyrmion lattices accelerating in free space
• Weyl nodal ring states and Landau quantization with very large magnetoresistance in square-net magnet EuGa${}_4$
• Anatomy of anomalous Hall effect due to magnetic fluctuations
• Monolayer and bilayer PtCl${}_3$: Energetics, magnetism, and band topology
• Large-Gap Quantum Anomalous Hall Insulators in $A$Ti$X$ Class
• Bimerons create bimerons: proliferation and aggregation induced by currents and magnetic fields
• Fermi-arc metals
• Chemical Principles of Intrinsic Topological Superconductors
• Antiferromagnetic topological insulator with selectively gapped Dirac cones
• Two-dimensional ferromagnetic extension of a topological insulator
• Large anomalous Hall, Nernst effect and topological phases in the 3d-4d/5d based oxide double perovskites
• The Layer Hall Effect without External Electric Field
• Integer quantum Hall effect and enhanced g-factor in quantum confined Cd3As2 films
• Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams
• Programmable skyrmions for robust communication and intelligent sensing
• Large magnetoresistance and first-order phase transition in antiferromagnetic single-crystalline EuAg${}_4$Sb${}_2$
• Charge-density wave transition in magnetic topological semimetal EuAl${}_4$
• Evidence for Two-dimensional Weyl Fermions in Air-Stable Monolayer PtTe${}_{1.75}$
• Magnetic hourglass fermions: from exhaustive symmetry conditions to high-throughput materials predictions
• Surface state evolution induced by magnetic order in axion insulator candidate EuIn2As2
• Anomalous Hall effect with plateaus observed in a magnetic Weyl semimetal NdAlGe at low temperatures
• Vibrationally Induced Magnetism in Supramolecular Aggregates
• Engineering axion insulator phase in superlattices with inversion symmetry breaking
• Magnetic Breakdown and Chiral Magnetic Effect at Weyl-Semimetal Tunnel Junctions
• Giant spin-charge conversion in ultrathin films of the MnPtSb half-Heusler compound
• Disorder-Induced Topological Transitions in a Multilayer Topological Insulator
• Chiral Phonons Enhance Ferromagnetism
• Kitaev Interactions Through an Extended Superexchange Pathway in the jeff = 1/2 Ru3+ Honeycomb Magnet, RuP3SiO11
• Multiple superconducting phases driven by pressure in the topological insulator GeSb4Te7
• Fully-gapped superconductivity and topological aspects of the noncentrosymmetric TaReSi superconductor
• Topological electronic bands in crystalline solids
• Lieb-Schultz-Mattis Theorem for 1D Quantum Magnets with Antiunitary Translation and Inversion Symmetries
• ErMn${}_6$Sn${}_6$: A Promising Kagome Antiferromagnetic Candidate for Room-Temperature Nernst Effect-based thermoelectrics
• Absence of metallicity and bias-dependent resistivity in low-carrier-density EuCd2As2
• Topological metals constructed by sliding quantum wire arrays
• Geometrical Nonlinear Hall Effect Induced by Lorentz Force
• Experimental progress in Eu(Al,Ga)${}_4$ topological antiferromagnets
• Incommensurate broken helix induced by nonstoichiometry in the axion insulator candidate EuIn${}_2$As${}_2$
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Uniaxial stress effect on the electronic structure of quantum materials
• Hall-effect in the MnBi_2Te_4 crystal using silicon nitride nanomembrane via contacts
• Quantum Oscillation Signatures of Fermi Arcs in Tunnel Magnetoconductance
• Intrinsic antiferromagnetic topological insulator and axion state in V2WS4
• Spin-Reorientation-Driven Linear Magnetoelectric Effect in Topological Antiferromagnet Cu${}_3$TeO${}_6$
• Exploring Intrinsic Magnetic Topological Insulators: The Case of EuIn${}_2$As${}_2$
• Quantum description of Fermi arcs in Weyl semimetals in a magnetic field
• Boundary and defect criticality in topological insulators and superconductors
• Strain-induced two-dimensional topological crystalline insulator
• Spin-hedgehog-derived electromagnetic effects in itinerant magnets
• Defect Engineering for Stabilizing Magnetic and Topological Properties in Mn(Bi1-xSbx)2Te4
• Doping-tunable Fermi surface with persistent topological Hall effect in axion candidate EuIn${}_2$As${}_2$
• Tight-binding theory of spin-spin interactions, Curie temperatures, and quantum Hall effects in topological (Hg,Cr)Te in comparison to non-topological (Zn,Cr)Te, and (Ga,Mn)N
• Conductance asymmetry in proximitized magnetic topological insulator junctions with Majorana modes
• Many-body Chern insulator in the Kondo lattice model on a triangular lattice
• Controlling topology through targeted composite symmetry manipulation in magnetic systems
• Comparative study of magnetic exchange parameters and magnon dispersions in NiO and MnO from first principles
• Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides
• Doping Topological Dirac Semimetal with magnetic impurities: electronic structure of Mn-doped Cd${}_3$As${}_2$
• Collective excitations in magnetic topological insulators and axion dark matter search
• Magnetic flux induced topological superconductivity in magnetic atomic rings
• Spectroscopic signatures of magnetization-induced band renormalization and strong spin-charge-lattice coupling in EuZn${}_2$As${}_2$
• Incommensurate magnetic order in an axion insulator candidate EuIn${}_2$As${}_2$ investigated by NMR measurement
• Poincaré sphere engineering of dynamical ferroelectric topological solitons
• Field-driven band asymmetry and non-reciprocal transport in a helimagnet
• Interface engineering of van der Waals heterostructures towards energy-efficient quantum devices operating at high temperatures
• Multiband superconductivity in the topological Kramers nodal-line semimetals
• EuAuSb: An odd-parity helical variation on altermagnetism
• Band structure picture for topology in strongly correlated systems with the ghost Gutzwiller ansatz
• I-centered vs F-centered orthorhombic symmetry and negative thermal expansion of the charge density wave of EuAl2Ga2
• Antiferromagnetic order in a layered magnetic topological insulator MnBi${}_2$Se${}_4$ probed by resonant soft x-ray scattering
• Magneto-elastic coupling in a sinusoidal modulated magnet Cr${}_2$GaN
• Interfaces of nodal-line semimetals: drum states, transport and refraction
• Gilbert damping in two-dimensional metallic anti-ferromagnets
• Giant octupole moment in magnetic multilayers
• Spin torques and anomalous velocity in spin textures induced by fast electron injection from topological ferromagnets: The role of gauge fields
• Anisotropic metamagnetism and magnetotransport of heavy rare-earth orthorhombic single-crystal TbAlGe
• Spin order and dynamics in the topological rare-earth germanide semimetals
• Magneto-thermoelectricty of anisotropic two-dimensional materials
• Axionic Instability of Periodic Weyl-Semimetal Superstructures
• Dichotomy of flat bands in the van der Waals ferromagnet Fe${}_5$GeTe${}_2$
• Predicted versatile topological nodal magnons in Tb-based icosahedral quasicrystal 1/1 approximants
• Spin-orbit torque switching of Néel order in band-inverted antiferromagnetic bilayer MnBi${}_2$Te${}_4$
• Conductance oscillations of antiferromagnetic layer tunnel junctions
• Topological Magnetic Phases and Magnon-Phonon Hybridization in the Presence of Strong Dzyaloshinskii-Moriya Interaction
• Giant Spin Transport Anisotropy in Magnetic Topological Insulators
• Enhancement of Curie Temperature in Ferromagnetic Insulator-Topological Insulator Heterostructures
• Ta2Pd3Te5 topological thermometer
• Proximity Magnetism in Mn(Bi,Sb)2Te4-(Bi,Sb)2Te3/MnTe Natural Heterostructures
• Interface controlled Berry phase and anisotropic spin-charge conversion in altermagnet-topological insulator bilayers
• Bulk versus surface: Nonuniversal partitioning of the topological magnetoelectric effect
• Crystalline electric field excitations in Weyl semimetal \textit{R}AlSi (\textit{R} = Ce, Pr and Nd)
• Tunable topological phase in 2D ScV${}_6$Sn${}_6$ kagome material
• Extended Haldane model -- a modern gateway to topological insulators
• Correlated helimagnetic configuration in a nonsymmorphic magnetic nodal semimetal
• Network model for magnetic higher-order topological phases
• Fate of surface gaps in magnetic topological insulators
• Topological analog of the magnetic bit within the Su-Schrieffer-Heeger-Holstein model
• Spontaneous Enhancement of Dzyaloshinskii-Moriya Interaction via Field-Cooling-Induced Interface Engineering in 2D van der Waals Ferromagnetic ternary Tellurides
• Origin of pressure-induced anomalies in the nodal-line ferrimagnet Mn${}_3$Si${}_2$Te${}_6$
• Topological properties of domain walls in antiferromagnetic topological insulators
• Chern insulators in two and three dimensions: A global perspective
• Accelerated Discovery of Topological Conductors for Nanoscale Interconnects
• Triply degenerate nodal line and tunable contracted-drumhead surface state in a tight-binding model
• Topological bands in metals
• Spin order and excitations in the collinear kagome antiferromagnet Y${}_{0.5}$Fe${}_3$Sn${}_3$
• Evolution from Topological Dirac Metal to Flat-band-Induced Antiferromagnet in Layered KxNi4S2 (0<=x<=1)
• Design, synthesis, and physical properties of the intergrowth compound Eu${}_2$CuZn${}_2$As${}_3$
• Type-II Weyl nodes, flat bands, and evidence for a topological Hall-effect in the new ferromagnet FeCr${}_3$Te${}_6$
• Magnetic structure of EuZn${}_2$Sb${}_2$ single-crystal thin-film
• Exact solutions for topological surface states of three-dimensional lattice models
• Superconductivity in the pressure-amorphized topological insulator CrP${}_4$
• Investigating the intrinsic anomalous Hall effect in MnPt3 topological semimetal
• Simple model for the gap in the surface states of the antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Fractal Path Strategies for Efficient 2D DMRG Simulations