A magnetic heterostructure of topological insulators as a candidate for an axion insulator

Quantum-Confined Tunable Ferromagnetism on the Surface of a Van der Waals Antiferromagnet NaCrTe2

The surface of three-dimensional materials provides an ideal and versatile platform to explore quantum-confined physics. Here, we systematically investigate the electronic structure of Na-intercalated CrTe2, a van der Waals antiferromagnet, using angle-resolved photoemission spectroscopy and ab initio calculations. The measured band structure deviates from the calculation of bulk NaCrTe2 but agrees with that of ferromagnetic monolayer CrTe2. Consistently, we observe unexpected exchange splitting of the band dispersions, persisting well above the Néel temperature of bulk NaCrTe2. We argue that NaCrTe2 features a quantum-confined 2D ferromagnetic state in the topmost surface layer due to strong ferromagnetic correlation in the CrTe2 layer. Moreover, the exchange splitting and the critical temperature can be controlled by surface doping of alkali-metal atoms, suggesting the feasibility of tuning the surface ferromagnetism. Our work not only presents a simple platform for exploring tunable 2D ferromagnetism but also provides important insights into the quantum-confined low-dimensional magnetic states.

Chiral edge transport along domain walls in magnetic topological insulator nanoribbons

Quantum anomalous Hall insulators are topologically characterized by non-zero integer Chern numbers, the sign of which depends on the direction of the exchange field that breaks time-reversal symmetry. This feature allows the manipulation of the conducting chiral edge states present at the interface of two magnetic domains with opposite magnetization and opposite Chern numbers. Motivated by this broad understanding, the present study investigates the quantum transport properties of a magnetizedBi2Se3topological insulator nanoribbon with a domain wall (DW) oriented either parallel or perpendicular to the transport direction. Employing an atomistic tight-binding model and a non-equilibrium Green's function formalism, we calculate the quantum conductance and explore the nature of the edge states. We elucidate the conditions leading to exact conductance quantization and identify the origin of deviations from this behavior. Our analysis shows that although the conductance is quantized in the presence of the horizontal DW, the quantization is absent in the perpendicular DW case. Furthermore, the investigation of the spin character of the edge modes confirms that the conductance in the horizontal DW configuration is spin polarized. This finding underscores the potential of our system as a simple three dimensional spin-filter device.

High spin axion insulator

Axion insulators possess a quantized axion field θ = π protected by combined lattice and time-reversal symmetry, holding great potential for device applications in layertronics and quantum computing. Here, we propose a high-spin axion insulator (HSAI) defined in large spin-s representation, which maintains the same inherent symmetry but possesses a notable axion field θ = (s + 1/2)2π. Such distinct axion field is confirmed independently by the direct calculation of the axion term using hybrid Wannier functions, layer-resolved Chern numbers, as well as the topological magneto-electric effect. We show that the guaranteed gapless quasi-particle excitation is absent at the boundary of the HSAI despite its integer surface Chern number, hinting an unusual quantum anomaly violating the conventional bulk-boundary correspondence. Furthermore, we ascertain that the axion field θ can be precisely tuned through an external magnetic field, enabling the manipulation of bonded transport properties. The HSAI proposed here can be experimentally verified in ultra-cold atoms by the quantized non-reciprocal conductance or topological magnetoelectric response. Our work enriches the understanding of axion insulators in condensed matter physics, paving the way for future device applications.

Fabrication-induced even-odd discrepancy of magnetotransport in few-layer MnBi2Te4

The van der Waals antiferromagnetic topological insulator MnBi2Te4 represents a promising platform for exploring the layer-dependent magnetism and topological states of matter. Recently observed discrepancies between magnetic and transport properties have aroused controversies concerning the topological nature of MnBi2Te4 in the ground state. In this article, we demonstrate that fabrication can induce mismatched even-odd layer dependent magnetotransport in few-layer MnBi2Te4. We perform a comprehensive study of the magnetotransport properties in 6- and 7-septuple-layer MnBi2Te4, and reveal that both even- and odd-number-layer device can show zero Hall plateau phenomena in zero magnetic field. Importantly, a statistical survey of the optical contrast in more than 200 MnBi2Te4 flakes reveals that the zero Hall plateau in odd-number-layer devices arises from the reduction of the effective thickness during the fabrication, a factor that was rarely noticed in previous studies of 2D materials. Our finding not only provides an explanation to the controversies regarding the discrepancy of the even-odd layer dependent magnetotransport in MnBi2Te4, but also highlights the critical issues concerning the fabrication and characterization of 2D material devices.

Electrically Controlled Anomalous Hall Effect and Orbital Magnetization in Topological Magnet MnBi_{2}Te_{4}

We propose an intrinsic mechanism to understand the even-odd effect, namely, opposite signs of anomalous Hall resistance and different shapes of hysteresis loops for even and odd septuple layers (SLs), of MBE-grown MnBi_{2}Te_{4} thin films with electron doping. The nonzero hysteresis loops in the anomalous Hall effect and magnetic circular dichroism for even-SLs MnBi_{2}Te_{4} films originate from two different antiferromagnetic (AFM) configurations with different zeroth Landau level energies of surface states. The complex form of the anomalous Hall hysteresis loop can be understood from two magnetic transitions, a transition between two AFM states followed by a second transition to the ferromagnetic state. Our model also clarifies the relationship and distinction between axion parameter and magnetoelectric coefficient, and shows an even-odd oscillation behavior of magnetoelectric coefficients in MnBi_{2}Te_{4} films.

Layer Hall effect induced by hidden Berry curvature in antiferromagnetic insulators

The layer Hall effect describes electrons spontaneously deflected to opposite sides at different layers, which has been experimentally reported in the MnBi2Te4 thin films under perpendicular electric fields. Here, we reveal a universal origin of the layer Hall effect in terms of the so-called hidden Berry curvature, as well as material design principles. Hence, it gives rise to zero Berry curvature in momentum space but non-zero layer-locked hidden Berry curvature in real space. We show that, compared to that of a trivial insulator, the layer Hall effect is significantly enhanced in antiferromagnetic topological insulators. Our universal picture provides a paradigm for revealing the hidden physics as a result of the interplay between the global and local symmetries, and can be generalized in various scenarios.

Topological magnetoelectric response in ferromagnetic axion insulators

The topological magnetoelectric effect (TME) is a hallmark response of the topological field theory, which provides a paradigm shift in the study of emergent topological phenomena. However, its direct observation is yet to be realized due to the demanding magnetic configuration required to gap all surface states. Here, we theoretically propose that axion insulators with a simple ferromagnetic configuration, such as the MnBi2Te4/(Bi2Te3)n family, provide an ideal playground to realize the TME. In the designed triangular prism geometry, all the surface states are magnetically gapped. Under a vertical electric field, the surface Hall currents give rise to a nearly half-quantized orbital moment, accompanied by a gapless chiral hinge mode circulating in parallel. Thus, the orbital magnetization from the two topological origins can be easily distinguished by reversing the electric field. Our work paves the way for direct observation of the TME in realistic axion-insulator materials.

Magneto-optical Effects of an Artificially Layered Ferromagnetic Topological Insulator with a TC of 160 K

Magnetic topological insulators are a fertile platform for studying the interplay between magnetism and topology. The unique electronic band structure can induce exotic transport and optical properties. However, a comprehensive optical study at both near-infrared and terahertz frequencies has been lacking. Here, we report magneto-optical effects from a heterostructure of a Cr-incorporated topological insulator, CBST. By measuring the magneto-optical Kerr effect, we observe a high temperature ferromagnetic transition (160 K) in the CBST film. We also use time-domain terahertz polarimetry to reveal a terahertz Faraday rotation of 1.5 mrad and a terahertz Kerr rotation of 3.6 mrad at 2 K. The calculated terahertz Hall conductance is 0.42 e2/h. Our work shows the optical responses of an artificially layered magnetic topological insulator, paving the way toward a high-temperature quantum anomalous Hall effect via heterostructure engineering.

Epitaxial Growth and Characterization of Nanoscale Magnetic Topological Insulators: Cr-Doped (Bi0.4Sb0.6)2Te3

The exploration initiated by the discovery of the topological insulator (BixSb1-x)2Te3 has extended to unlock the potential of quantum anomalous Hall effects (QAHEs), marking a revolutionary era for topological quantum devices, low-power electronics, and spintronic applications. In this study, we present the epitaxial growth of Cr-doped (Bi0.4Sb0.6)2Te3 (Cr:BST) thin films via molecular beam epitaxy, incorporating various Cr doping concentrations with varying Cr/Sb ratios (0.025, 0.05, 0.075, and 0.1). High-quality crystalline of the Cr:BST thin films deposited on a c-plane sapphire substrate has been rigorously confirmed through reflection high-energy electron diffraction (RHEED), X-ray diffraction (XRD), and high-resolution transmission electron microscopy (HRTEM) analyses. The existence of a Cr dopant has been identified with a reduction in the lattice parameter of BST from 30.53 ± 0.05 to 30.06 ± 0.04 Å confirmed by X-ray diffraction, and the valence state of Cr verified by X-ray photoemission (XPS) at binding energies of ~573.1 and ~583.5 eV. Additionally, the influence of Cr doping on lattice vibration was qualitatively examined by Raman spectroscopy, revealing a blue shift in peaks with increased Cr concentration. Surface characteristics, crucial for the functionality of topological insulators, were explored via Atomic Force Microscopy (AFM), illustrating a sevenfold reduction in surface roughness as the Cr concentration increased from 0 to 0.1. The ferromagnetic properties of Cr:BST were examined by a superconducting quantum interference device (SQUID) with a magnetic field applied in out-of-plane and in-plane directions. The Cr:BST samples exhibited a Curie temperature (Tc) above 50 K, accompanied by increased magnetization and coercivity with increasing Cr doping levels. The introduction of the Cr dopant induces a transition from n-type ((Bi0.4Sb0.6)2Te3) to p-type (Cr:(Bi0.4Sb0.6)2Te3) carriers, demonstrating a remarkable suppression of carrier density up to one order of magnitude, concurrently enhancing carrier mobility up to a factor of 5. This pivotal outcome is poised to significantly influence the development of QAHE studies and spintronic applications.

Antisite-Defects Control of Magnetic Properties in MnSb2Te4

The intrinsic magnetic topological materials Mn(Sb/Bi)2n+2Te3n+4 have attracted extensive attention due to their topological quantum properties. Although, the Mn-Sb/Bi antisite defects have been frequently reported to exert significant influences on both magnetism and band topology, their formation mechanism and the methods to manipulate their distribution and concentration remain elusive. Here, we present MnSb2Te4 as a typical example and demonstrate that Mn-Sb antisite defects and magnetism can be tuned by controlling the crystal growth conditions. The cooling rate is identified as the primary key parameter. Magnetization and chemical analysis demonstrate that a slower cooling rate would lead to a higher Mn concentration, a higher magnetic transition temperature, and a higher saturation moment. Further analysis indicates that the Mn content at the original Mn site (MnMn, 3a site) varies more significantly with the cooling rate than the Mn content at the Sb site (MnSb, 6c site). Based on experimental observations, magnetic phase diagrams regarding MnMn and MnSb concentrations are constructed. With the assistance of first-principles calculations, it is demonstrated that the Mn-Sb mixing states primarily result from the mixing entropy and the growth kinetics. The present findings offer valuable insights into defects engineering for preparation of two-dimensional quantum materials.

Phase Separation Prevents the Synthesis of VBi2Te4 by Molecular Beam Epitaxy

Intrinsic magnetic topological insulators (IMTIs) have a non-trivial band topology in combination with magnetic order. This potentially leads to fascinating states of matter, such as quantum anomalous Hall (QAH) insulators and axion insulators. One of the theoretically predicted IMTIs is VBi2Te4, but experimental evidence of this material is lacking so far. Here, we report on our attempts to synthesise VBi2Te4 by molecular beam epitaxy (MBE). X-ray diffraction reveals that in the thermodynamic phase space reachable by MBE, there is no region where VBi2Te4 is stably synthesised. Moreover, scanning transmission electron microscopy shows a clear phase separation to Bi2Te3 and VTe2 instead of the formation of VBi2Te4. We suggest the phase instability to be due to either the large lattice mismatch between VTe2 and Bi2Te3 or the unfavourable valence state of vanadium.

3D Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred-Nanometer Thickness

Magnetic topological states refer to a class of exotic phases in magnetic materials with the non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state, which is a zero magnetic field manifestation of the quantum Hall effect. Current research in this direction focuses on QAH insulators with a thickness of less than 10 nm. Here, molecular beam epitaxy (MBE) is employed to synthesize magnetic TI trilayers with a thickness of up to ≈106 nm. It is found that these samples exhibit well-quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field. By varying the magnetic dopants, gate voltages, temperature, and external magnetic fields, the properties of these thick QAH insulators are examined and the robustness of the 3D QAH effect is demonstrated. The realization of the well-quantized 3D QAH effect indicates that the nonchiral side surface states of the thick magnetic TI trilayers are gapped and thus do not affect the QAH quantization. The 3D QAH insulators of hundred-nanometer thickness provide a promising platform for the exploration of fundamental physics, including axion physics and image magnetic monopole, and the advancement of electronic and spintronic devices to circumvent Moore's law.

Topological phase transition in the antiferromagnetic topological insulator MnBi[Formula: see text]Te[Formula: see text] from the point of view of axion-like state realization

This work aims to study the conditions of topological phase transition (TPT) between the topological and trivial states in the antiferromagnetic topological insulator (AFM TI) MnBi[Formula: see text]Te[Formula: see text] and propose some theory about the relationship of this TPT with the possibility of axion-like state realization in this material. Using the density functional approach we have analyzed the changes in the electronic and spin structure of topological surface states (TSSs) and the nearest conduction and valence bands (CB and VB) including the changes in the bulk band gap as well as the Dirac point (DP) gap in TSSs under variation of the spin-orbit coupling strength in the region of the TPT for infinite crystal and slab with a surface both. We have shown that in both cases the TPT occurs with inversion of the contributions of the Bi-[Formula: see text] and Te-[Formula: see text] states of different parity at the gap edges related to change in the gap sign. In the case of surface calculations, the Bi-[Formula: see text] and Te-[Formula: see text] states at the edges of the bulk band gap and their inversion at the TPT point are transformed into the TSSs with an energy gap at the DP. In this case the TPT takes place without closing the band gap, i.e. with a "jump" through zero and the formation of the nonzero gap during such a transition. Our calculations show that the TPT point is also characterized by an inversion of the out-of-plane spin polarization [Formula: see text] at the [Formula: see text] point for lower and upper parts of the Dirac cone and a significant spatial redistribution of the TSSs between the surface and the bulk. We suppose that the nonzero Dirac gap can have some relationship with the formation of the axion-like state, which presumably couples nonmagnetic spin-orbit and magnetic contributions at the boundary between the topological and trivial phases for a system with parameters close to the TPT conditions. A practically realized system is proposed - the AFM TI with a stoichiometry close to that of MnBi[Formula: see text]Te[Formula: see text]Se[Formula: see text] with partial (about 50%) substitution of Te atoms for Se atoms in MnBi[Formula: see text]Te[Formula: see text] which can be an experimental platform for the implementation and experimental analysis of the TPT and the corresponding possibility of the axion-like state realization in Condensed Matter. Besides, such system could serve as a good platform for studying the dynamic axion effect, where the axion field fluctuations are maximised when a small external field is applied to the system which state is close to the TPT.

Quantized resistance revealed at the criticality of the quantum anomalous Hall phase transitions

In multilayered magnetic topological insulator structures, magnetization reversal processes can drive topological phase transitions between quantum anomalous Hall, axion insulator, and normal insulator states. Here we report an examination of the critical behavior of two such transitions: the quantum anomalous Hall to normal insulator (QAH-NI), and quantum anomalous Hall to axion insulator (QAH-AXI) transitions. By introducing a new analysis protocol wherein temperature dependent variations in the magnetic coercivity are accounted for, the critical behavior of the QAH-NI and QAH-AXI transitions are evaluated over a wide range of temperature and magnetic field. Despite the uniqueness of these different transitions, quantized longitudinal resistance and Hall conductance are observed at criticality in both cases. Furthermore, critical exponents were extracted for QAH-AXI transitions occurring at magnetization reversals of two different magnetic layers. The observation of consistent critical exponents and resistances in each case, independent of the magnetic layer details, demonstrates critical behaviors in quantum anomalous Hall transitions to be of electronic rather than magnetic origin. Our finding offers a new avenue for studies of phase transition and criticality in QAH insulators.

Half-quantized helical hinge currents in axion insulators

Fractional quantization can emerge in noncorrelated systems due to the parity anomaly, while its condensed matter realization is a challenging problem. We propose that in axion insulators (AIs), parity anomaly manifests a unique fractional boundary excitation: the half-quantized helical hinge currents. These helical hinge currents microscopically originate from the lateral Goos-Hänchen (GH) shift of massless side-surface Dirac electrons that are totally reflected from the hinges. Meanwhile, due to the presence of the massive top and bottom surfaces of the AI, the helical current induced by the GH shift is half-quantized. The semiclassical wave packet analysis uncovers that the hinge current has a topological origin and its half quantization is robust to parameter variations. Lastly, we propose an experimentally feasible six-terminal device to identify the half-quantized hinge channels by measuring the nonreciprocal conductances. Our results advance the realization of the half-quantization and topological magnetoelectric responses in AIs.

Macroscopic Quantum Tunneling of a Topological Ferromagnet

The recent advent of topological states of matter spawned many significant discoveries. The quantum anomalous Hall (QAH) effect is a prime example due to its potential for applications in quantum metrology, as well as its influence on fundamental research into the underlying topological and magnetic states and into axion electrodynamics. Here, electronic transport studies on a (V,Bi,Sb)₂ Te₃ ferromagnetic topological insulator nanostructure in the QAH regime are presented. This allows access to the dynamics of an individual ferromagnetic domain. The domain size is estimated to be in the 50-100 nm range. Telegraph noise resulting from the magnetization fluctuations of this domain is observed in the Hall signal. Careful analysis of the influence of temperature and external magnetic field on the domain switching statistics provides evidence for quantum tunneling (QT) of magnetization in a macrospin state. This ferromagnetic macrospin is not only the largest magnetic object in which QT is observed, but also the first observation of the effect in a topological state of matter.

Giant nonlocal edge conduction in the axion insulator state of MnBi2Te4

The recently discovered antiferromagnetic (AFM) topological insulator (TI) MnBi₂Te₄ represents a versatile material platform for exploring exotic topological quantum phenomena in nanoscale devices. It has been proposed that even-septuple-layer (even-SL) MnBi₂Te₄ can host helical hinge currents with unique nonlocal behavior, but experimental confirmation is still lacking. In this work, we report transport studies of exfoliated MnBi₂Te₄ flakes with varied thicknesses down to the few-nanometer regime. We observe giant nonlocal transport signals in even-SL devices when the system is in the axion insulator state but vanishingly small nonlocal signal in the odd-SL devices at the same magnetic field range. In conjunction with theoretical calculations, we demonstrate that the nonlocal transport is via the helical edge currents mainly distributed at the hinges between the side and top/bottom surfaces. The helical edge currents in the axion insulator state may find unique applications in topological quantum devices.

Controlling the Zero Hall Plateau in a Quantum Anomalous Hall Insulator by In-Plane Magnetic Field

We investigate the quantum anomalous Hall plateau transition in the presence of independent out-of-plane and in-plane magnetic fields. The perpendicular coercive field, zero Hall plateau width, and peak resistance value can all be systematically controlled by the in-plane magnetic field. The traces taken at various fields almost collapse into a single curve when the field vector is renormalized to an angle as a geometric parameter. These results can be explained consistently by the competition between magnetic anisotropy and in-plane Zeeman field, and the close relationship between quantum transport and magnetic domain structure. The accurate control of zero Hall plateau facilitates the search for chiral Majorana modes based on the quantum anomalous Hall system in proximity to a superconductor.

Direct visualization of edge state in even-layer MnBi2Te4 at zero magnetic field

Being the first intrinsic antiferromagnetic (AFM) topological insulator (TI), MnBi₂Te₄ is argued to be a topological axion state in its even-layer form due to the antiparallel magnetization between the top and bottom layers. Here we combine both transport and scanning microwave impedance microscopy (sMIM) to investigate such axion state in atomically thin MnBi₂Te₄ with even-layer thickness at zero magnetic field. While transport measurements show a zero Hall plateau signaturing the axion state, sMIM uncovers an unexpected edge state raising questions regarding the nature of the "axion state". Based on our model calculation, we propose that the edge state of even-layer MnBi₂Te₄ at zero field is derived from gapped helical edge states of the quantum spin Hall effect with time-reversal-symmetry breaking, when a crossover from a three-dimensional TI MnBi₂Te₄ to a two-dimensional TI occurs. Our finding thus signifies the richness of topological phases in MnB₂Te₄ that has yet to be fully explored.

Spontaneous Ferromagnetism Induced Topological Transition in EuB_{6}

The interplay between various symmetries and electronic bands topology is one of the core issues for topological quantum materials. Spontaneous magnetism, which leads to the breaking of time-reversal symmetry, has been proven to be a powerful approach to trigger various exotic topological phases. In this Letter, utilizing the combination of angle-resolved photoemission spectroscopy, magneto-optical Kerr effect microscopy, and first-principles calculations, we present the direct evidence on the realization of the long-sought spontaneous ferromagnetism induced topological transition in soft ferromagnetic EuB_{6}. Explicitly, we reveal the topological transition is from Z_{2}=1 topological insulator in paramagnetic state to χ=1 magnetic topological semimetal in low temperature ferromagnetic state. Our results demonstrate that the simple band structure near the Fermi level and rich topological phases make EuB_{6} an ideal platform to study the topological phase physics.

Gate-Tunable Anomalous Hall Effect in a 3D Topological Insulator/2D Magnet van der Waals Heterostructure

We demonstrate advantages of samples made by mechanical stacking of exfoliated van der Waals materials for controlling the topological surface state of a three-dimensional topological insulator (TI) via interaction with an adjacent magnet layer. We assemble bilayers with pristine interfaces using exfoliated flakes of the TI BiSbTeSe₂ and the magnet Cr₂Ge₂Te₆, thereby avoiding problems caused by interdiffusion that can affect interfaces made by top-down deposition methods. The samples exhibit an anomalous Hall effect (AHE) with abrupt hysteretic switching. For the first time in samples composed of a TI and a separate ferromagnetic layer, we demonstrate that the amplitude of the AHE can be tuned via gate voltage with a strong peak near the Dirac point. This is the signature expected for the AHE due to Berry curvature associated with an exchange gap induced by interaction between the topological surface state and an out-of-plane-oriented magnet.

Transport Theory of Half-Quantized Hall Conductance in a Semimagnetic Topological Insulator

Recently, a half-quantized Hall conductance (HQHC) plateau was experimentally observed in a semimagnetic topological insulator heterostructure. However, the heterostructure was metallic with a nonzero longitudinal conductance, which contradicts the common belief that quantized Hall conductance is usually observed in insulators. In this work, we systematically study the surface transport of a semimagnetic topological insulator with both gapped and gapless Dirac surfaces in the presence of dephasing process. In particular, we reveal that the HQHC is directly related to the half-quantized chiral current along the edge of a strongly dephasing metal. The Hall conductance keeps a half-quantized value for large dephasing strengths, while the longitudinal conductance varies with Fermi energies and dephasing strengths. Furthermore, we evaluate both the conductance and resistance as a function of the temperature, which is consistent with the experimental results. Our results not only provide the microscopic transport mechanism of the HQHC, but also are instructive for the probe of the HQHC in future experiments.

Evolution of the Electronic Structure of Ultrathin MnBi2Te4 Films

Ultrathin films of intrinsic magnetic topological insulator MnBi₂Te₄ exhibit fascinating quantum properties such as the quantum anomalous Hall effect and the axion insulator state. In this work, we systematically investigate the evolution of the electronic structure of MnBi₂Te₄ thin films. With increasing film thickness, the electronic structure changes from an insulator type with a large energy gap to one with in-gap topological surface states, which is, however, still in drastic contrast to the bulk material. By surface doping of alkali-metal atoms, a Rashba split band gradually emerges and hybridizes with topological surface states, which not only reconciles the puzzling difference between the electronic structures of the bulk and thin-film MnBi₂Te₄ but also provides an interesting platform to establish Rashba ferromagnet that is attractive for (quantum) anomalous Hall effect. Our results provide important insights into the understanding and engineering of the intriguing quantum properties of MnBi₂Te₄ thin films.

Light-Driven Topological and Magnetic Phase Transitions in Thin Layer Antiferromagnets

We theoretically study the effect of low-frequency light pulses in resonance with phonons in the topological and magnetically ordered two-septuple layer (2-SL) MnBi₂Te₄ (MBT) and MnSb₂Te₄ (MST). These materials share symmetry properties and an antiferromagnetic ground state in pristine form but present different magnetic exchange interactions. In both materials, shear and breathing Raman phonons can be excited via nonlinear interactions with photoexcited infrared phonons using intense laser pulses that can be attained in the current experimental setups. The light-induced transient lattice distortions lead to a change in the sign of the effective interlayer exchange interaction and magnetic order accompanied by a topological band transition. Furthermore, we show that moderate antisite disorder, typically present in MBT and MST samples, can facilitate such an effect. Therefore, our work establishes 2-SL MBT and MST as candidate platforms for achieving non-equilibrium magneto-topological phase transitions.

Progress and prospects in magnetic topological materials

Magnetic topological materials represent a class of compounds with properties that are strongly influenced by the topology of their 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 recent theoretical progress that has resulted in the tabulation of, for the first time, 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, and we survey future perspectives.

Thickness-Driven Quantum Anomalous Hall Phase Transition in Magnetic Topological Insulator Thin Films

The quantized version of the anomalous Hall effect realized in magnetic topological insulators (MTIs) has great potential for the development of topological quantum physics and low-power electronic/spintronic applications. Here we report the thickness-tailored quantum anomalous Hall (QAH) effect in Cr-doped (Bi,Sb)₂Te₃ thin films by tuning the system across the two-dimensional (2D) limit. In addition to the Chern number-related QAH phase transition, we also demonstrate that the induced hybridization gap plays an indispensable role in determining the ground magnetic state of the MTIs; namely, the spontaneous magnetization owing to considerable Van Vleck spin susceptibility guarantees the zero-field QAH state with unitary scaling law in thick samples, while the quantization of the Hall conductance can only be achieved with the assistance of external magnetic fields in ultrathin films. The modulation of topology and magnetism through structural engineering may provide useful guidance for the pursuit of other QAH-based phase diagrams and functionalities.

Layer-Number-Dependent Antiferromagnetic and Ferromagnetic Behavior in MnSb_{2}Te_{4}

MnBi_{2}Te_{4}, an intrinsic magnetic topological insulator, has shown layer-number-correlated magnetic and topological phases. More interestingly, in the isostructural material MnSb_{2}Te_{4}, the antiferromagnetic (AFM) and ferromagnetic (FM) states have been both observed in the bulk counterparts, which are also predicted to be topologically nontrivial. Revealing the layer-number-dependent magnetic properties of MnSb_{2}Te_{4} down to a single septuple layer (SL) is of great significance for exploring the topological phenomena. However, this is still elusive. Here, using the polar reflective magnetic circular dichroism spectroscopy, both the A-type AFM and FM behaviors are observed and comprehensively studied in MnSb_{2}Te_{4} down to a single SL limit. In A-type AFM MnSb_{2}Te_{4} flakes, an obvious odd-even layer-number effect is observed. An additional surface spin-flop (SSF) transition occurs in even-SL flakes with the number of layers larger than 2. With the AFM linear-chain model, we identify that the even-SL flakes stabilize in a collinear state between the SSF transition and the spin-flop transition due to their appropriate energy ratio between the magnetic-field-scale anisotropy and interlayer interaction. In FM MnSb_{2}Te_{4} flakes, we observe very different magnetic behaviors with an abrupt spin-flipping transition and very small saturation fields, indicating a weakened interlayer interaction. By revealing the rich magnetic states of few-SL MnSb_{2}Te_{4} on the parameter space of the number of layers, external magnetic field, and temperature, our findings pave the way for further quantum transport studies of few-SL MnSb_{2}Te_{4}.

Topological spintronics and magnetoelectronics

Topological electronic materials, such as topological insulators, are distinct from trivial materials in the topology of their electronic band structures that lead to robust, unconventional topological states, which could bring revolutionary developments in electronics. This Perspective summarizes developments of topological insulators in various electronic applications including spintronics and magnetoelectronics. We group and analyse several important phenomena in spintronics using topological insulators, including spin-orbit torque, the magnetic proximity effect, interplay between antiferromagnetism and topology, and the formation of topological spin textures. We also outline recent developments in magnetoelectronics such as the axion insulator and the topological magnetoelectric effect observed using different topological insulators.

Epitaxial Growth and Structural Characterizations of MnBi2Te4 Thin Films in Nanoscale

The intrinsic magnetic topological insulator MnBi₂Te₄ has attracted much attention due to its special magnetic and topological properties. To date, most reports have focused on bulk or flake samples. For material integration and device applications, the epitaxial growth of MnBi₂Te₄ film in nanoscale is more important but challenging. Here, we report the growth of self-regulated MnBi₂Te₄ films by the molecular beam epitaxy. By tuning the substrate temperature to the optimal temperature for the growth surface, the stoichiometry of MnBi₂Te₄ becomes sensitive to the Mn/Bi flux ratio. Excessive and deficient Mn resulted in the formation of a MnTe and Bi₂Te₃ phase, respectively. The magnetic measurement of the 7 SL MnBi₂Te₄ film probed by the superconducting quantum interference device (SQUID) shows that the antiferromagnetic order occurring at the Néel temperature 22 K is accompanied by an anomalous magnetic hysteresis loop along the c-axis. The band structure measured by angle-resolved photoemission spectroscopy (ARPES) at 80 K reveals a Dirac-like surface state, which indicates that MnBi₂Te₄ has topological insulator properties in the paramagnetic phase. Our work demonstrates the key growth parameters for the design and optimization of the synthesis of nanoscale MnBi₂Te₄ films, which are of great significance for fundamental research and device applications involving antiferromagnetic topological insulators.

Quantum anomalous Hall edge channels survive up to the Curie temperature

Achieving metrological precision of quantum anomalous Hall resistance quantization at zero magnetic field so far remains limited to temperatures of the order of 20 mK, while the Curie temperature in the involved material is as high as 20 K. The reason for this discrepancy remains one of the biggest open questions surrounding the effect, and is the focus of this article. Here we show, through a careful analysis of the non-local voltages on a multi-terminal Corbino geometry, that the chiral edge channels continue to exist without applied magnetic field up to the Curie temperature of bulk ferromagnetism of the magnetic topological insulator, and that thermally activated bulk conductance is responsible for this quantization breakdown. Our results offer important insights on the nature of the topological protection of these edge channels, provide an encouraging sign for potential applications, and establish the multi-terminal Corbino geometry as a powerful tool for the study of edge channel transport in topological materials.

The quantum anomalous Hall effect has so far been limited to temperature of the order of 20 mK. Here, Fijalkowski et al. report the existence of chiral edge channels up to the Curie temperature of bulk ferromagnetism of the magnetic topological insulator with a multi-terminal Corbino geometry.

Recent Progress in Proximity Coupling of Magnetism to Topological Insulators

Inducing long-range magnetic order in 3D topological insulators can gap the Dirac-like metallic surface states, leading to exotic new phases such as the quantum anomalous Hall effect or the axion insulator state. These magnetic topological phases can host robust, dissipationless charge and spin currents or unique magnetoelectric behavior, which can be exploited in low-energy electronics and spintronics applications. Although several different strategies have been successfully implemented to realize these states, to date these phenomena have been confined to temperatures below a few Kelvin. This review focuses on one strategy: inducing magnetic order in topological insulators by proximity of magnetic materials, which has the capability for room temperature operation, unlocking the potential of magnetic topological phases for applications. The unique advantages of this strategy, the important physical mechanisms facilitating magnetic proximity effect, and the recent progress to achieve, understand, and harness proximity-coupled magnetic order in topological insulators are discussed. Some emerging new phenomena and applications enabled by proximity coupling of magnetism and topological materials, such as skyrmions and the topological Hall effect, are also highlighted, and the authors conclude with an outlook on remaining challenges and opportunities in the field.

Spacer-Layer-Tunable Magnetism and High-Field Topological Hall Effect in Topological Insulator Heterostructures

Controlling magnetic order in magnetic topological insulators (MTIs) is a key to developing spintronic applications with MTIs and is commonly achieved by changing the magnetic doping concentration, which inevitably affects the spin-orbit coupling strength and the topological properties. Here, we demonstrate tunable magnetic properties in topological heterostructures over a wide range, from a ferromagnetic phase with a Curie temperature of around 100 K all the way to a paramagnetic phase, while keeping the overall chemical composition the same, by controlling the thickness of nonmagnetic spacer layers between two atomically thin magnetic layers. This work showcases that spacer-layer control is a powerful tool to manipulate magneto-topological functionalities in MTI heterostructures. Furthermore, the interaction between the MTI and the Cr₂O₃ buffer layers also leads to a robust topological Hall effect surviving up to a record-high 6 T of magnetic field, shedding light on the critical role of interfacial layers in thin-film topological materials.

Synthesis, Magnetic Properties, and Electronic Structure of Magnetic Topological Insulator MnBi2Se4

The intrinsic magnetic topological insulators MnBi₂Te₄ and MnBi₂Se₄ support novel topological states related to symmetry breaking by magnetic order. Unlike MnBi₂Te₄, the study of MnBi₂Se₄ has been inhibited by the lack of bulk crystals, as the van der Waals (vdW) crystal is not the thermodynamic equilibrium phase. Here, we report the layer-by-layer synthesis of vdW MnBi₂Se₄ crystals using nonequilibrium molecular beam epitaxy. Atomic-resolution scanning transmission electron microscopy and scanning tunneling microscopy identify a well-ordered vdW crystal with septuple-layer base units. The magnetic properties agree with the predicted layered antiferromagnetic ordering but disagree with its predicted out-of-plane orientation. Instead, our samples exhibit an easy-plane anisotropy, which is explained by including dipole-dipole interactions. Angle-resolved photoemission spectroscopy reveals the gapless Dirac-like surface state, which demonstrates that MnBi₂Se₄ is a topological insulator above the magnetic-ordering temperature. These studies show that MnBi₂Se₄ is a promising candidate for exploring rich topological phases of layered antiferromagnetic topological insulators.

Spectral signatures of the surface anomalous Hall effect in magnetic axion insulators

The topological surface states of magnetic topological systems, such as Weyl semimetals and axion insulators, are associated with unconventional transport properties such as nonzero or half-quantized surface anomalous Hall effect. Here we study the surface anomalous Hall effect and its spectral signatures in different magnetic topological phases using both model Hamiltonian and first-principles calculations. We demonstrate that by tailoring the magnetization and interlayer electron hopping, a rich three-dimensional topological phase diagram can be established, including three types of topologically distinct insulating phases bridged by Weyl semimetals, and can be directly mapped to realistic materials such as MnBi2Te4/(Bi2Te3)n systems. Among them, we find that the surface anomalous Hall conductivity in the axion-insulator phase is a well-localized quantity either saturated at or oscillating around e2/2h, depending on the magnetic homogeneity. We also discuss the resultant chiral hinge modes embedded inside the side surface bands as the potential experimental signatures for transport measurements. Our study is a significant step forward towards the direct realization of the long-sought axion insulators in realistic material systems.

Critical Behavior and Universal Signature of an Axion Insulator State

Recently, the search for an axion insulator state in the ferromagnetic-3D topological insulator (TI) heterostructure and MnBi_{2}Te_{4} has attracted intense interest. However, its detection remains difficult in experiments. We systematically investigate the disorder-induced phase transition of the axion insulator state in a 3D TI with antiparallel magnetization alignment surfaces. It is found that there exists a 2D disorder-induced phase transition on the surfaces of the 3D TI which shares the same universality class with the quantum Hall plateau to plateau transition. Then, we provide a phenomenological theory which maps the random mass Dirac Hamiltonian of the axion insulator state into the Chalker-Coddington network model. Therefore, we propose probing the axion insulator state by investigating the universal signature of such a phase transition in the ferromagnetic-3D TI heterostructure and MnBi_{2}Te_{4}. Our findings not only show a global phase diagram of the axion insulator state, but also stimulate further experiments to probe it.

Monoclinic EuSn_{2}As_{2}: A Novel High-Pressure Network Structure

The layered crystal of EuSn_{2}As_{2} has a Bi_{2}Te_{3}-type structure in rhombohedral (R3[over ¯]m) symmetry and has been confirmed to be an intrinsic magnetic topological insulator at ambient conditions. Combining ab initio calculations and in situ x-ray diffraction measurements, we identify a new monoclinic EuSn_{2}As_{2} structure in C2/m symmetry above ∼14  GPa. It has a three-dimensional network made up of honeycomblike Sn sheets and zigzag As chains, transformed from the layered EuSn_{2}As_{2} via a two-stage reconstruction mechanism with the connecting of Sn-Sn and As-As atoms successively between the buckled SnAs layers. Its dynamic structural stability has been verified by phonon mode analysis. Electrical resistance measurements reveal an insulator-metal-superconductor transition at low temperature around 5 and 15 GPa, respectively, according to the structural conversion, and the superconductivity with a T_{C} value of ∼4  K is observed up to 30.8 GPa. These results establish a high-pressure EuSn_{2}As_{2} phase with intriguing structural and electronic properties and expand our understandings about the layered magnetic topological insulators.

Enhanced negative magnetoresistance near the charge neutral point in Cr doped topological insulator

Negative magnetoresistance (MR) is not only of great fundamental interest for condensed matter physics and materials science, but also important for practical applications, especially magnetic data storage and sensors. However, the microscopic origin of negative MR is still elusive and the nature of the negative MR in magnetic topological insulators has still not been completely elucidated. Here, we report magnetotransport studies on Cr doped (Bi1-x Sb x )2Te3 topological insulator thin films grown by magnetron sputtering. At the temperature of 2 K, a giant negative MR reaching 61% is observed at H = 2 T. We show that the negative MR is closely related to the position of the Fermi level, and it reaches the maximum when the Fermi level is gated near the charge neutral point. We attribute these results to the Coulomb potential due to the random composition fluctuations in Cr doped (Bi1-x Sb x )2Te3. Our results provide a deeper insight into the mechanism of negative MR, and are helpful to realize the quantum anomalous Hall effect in the sputtered Cr-(Bi1-x Sb x )2Te3 thin-film systems by tuning the Fermi level and reducing disorder effects.

Current-induced switching of proximity-induced ferromagnetic surface states in a topological insulator

Electrical manipulation of magnetization could be an essential function for energy-efficient spintronics technology. A magnetic topological insulator, possessing a magnetically gapped surface state with spin-polarized electrons, not only exhibits exotic topological phases relevant to the quantum anomalous Hall state but also enables the electrical control of its magnetic state at the surface. Here, we demonstrate efficient current-induced switching of the surface ferromagnetism in hetero-bilayers consisting of the topological insulator (Bi_1-xSb_x)₂Te₃ and the ferromagnetic insulator Cr₂Ge₂Te₆, where the proximity-induced ferromagnetic surface states play two roles: efficient charge-to-spin current conversion and emergence of large anomalous Hall effect. The sign reversal of the surface ferromagnetic states with current injection is clearly observed, accompanying the nearly full magnetization reversal in the adjacent insulating Cr₂Ge₂Te₆ layer of an optimal thickness range. The present results may facilitate an electrical control of dissipationless topological-current circuits.

Electrical manipulation of magnetization in devices made of topological materials may be an essential route towards future spintronics technology. Here, Mogi et al. show efficient current-induced switching of surface ferromagnetism in hetero-bilayers of topological insulator (Bi_1-xSb_x)₂Te₃ and ferromagnetic insulator Cr₂Ge₂Te₆.

Superconductivity in topological insulator-PdBi2under pressure

The topological insulator PdBi2exhibits two different crystal phases at ambient pressure, i.e., 'α-PdBi2' and ' -PdBi2'. The pressure dependence of crystal structure and superconductivity of α-PdBi2has been fully elucidated thus far. However, the physical properties of β-PdBi2crystals under pressure have not been sufficiently investigated. In this study, we fully investigate the crystal structure and superconductivity of β-PdBi2under pressure based on synchrotron x-ray diffraction (XRD) patterns. The temperature dependence of β-PdBi2indicates its superconductivity with a superconducting transition temperature (Tc) as high as 4.10 K, and its crystal structure is tetragonal [space group ofI4/mmm(no. 139)]. The XRD patterns at 0-22.0 GPa indicate no structural phase transitions, and the unit cell volume shrinks monotonically with pressure, unlike the behavior of α-PdBi2. Furthermore, α-PdBi2transformed to β-PdBi2under pressure. This suggests that β-PdBi2is stable under pressure. The superconductivity is clearly observed at 0-11.8 GPa, and the value ofTcis almost constant at ∼4.4 K. The temperature dependence of the upper critical field at ambient pressure and 10.7 GPa indicates that the superconductivity is not attributed to a simples-wave dirty limit but ans-wave clean orp-wave polar model. This is the first systematic study of superconductivity of topological insulator β-PdBi2under pressure.

Topological Hall Effect in a Topological Insulator Interfaced with a Magnetic Insulator

A topological insulator (TI) interfaced with a magnetic insulator (MI) may host an anomalous Hall effect (AHE), a quantum AHE, and a topological Hall effect (THE). Recent studies, however, suggest that coexisting magnetic phases in TI/MI heterostructures may result in an AHE-associated response that resembles a THE but in fact is not. This Letter reports a genuine THE in a TI/MI structure that has only one magnetic phase. The structure shows a THE in the temperature range of T = 2-3 K and an AHE at T = 80-300 K. Over T = 3-80 K, the two effects coexist but show opposite temperature dependencies. Control measurements, calculations, and simulations together suggest that the observed THE originates from skyrmions, rather than the coexistence of two AHE responses. The skyrmions are formed due to a Dzyaloshinskii-Moriya interaction (DMI) at the interface; the DMI strength estimated is substantially higher than that in heavy metal-based systems.

Te-Vacancy-Induced Surface Collapse and Reconstruction in Antiferromagnetic Topological Insulator MnBi2Te4

MnBi₂Te₄ is an antiferromagnetic topological insulator that has stimulated intense interest due to its exotic quantum phenomena and promising device applications. The surface structure is a determinant factor to understand the magnetic and topological behavior of MnBi₂Te₄, yet its precise atomic structure remains elusive. Here we discovered a surface collapse and reconstruction of few-layer MnBi₂Te₄ exfoliated under delicate protection. Instead of the ideal septuple-layer structure in the bulk, the collapsed surface is shown to reconstruct as a Mn-doped Bi₂Te₃ quintuple layer and a Mn_xBi_yTe double layer with a clear van der Waals gap in between. Combined with first-principles calculations, such surface collapse is attributed to the abundant intrinsic Mn-Bi antisite defects and the tellurium vacancy in the exfoliated surface, which is further supported by in situ annealing and electron irradiation experiments. Our results shed light on the understanding of the intricate surface-bulk correspondence of MnBi₂Te₄ and provide an insightful perspective on the surface-related quantum measurements in MnBi₂Te₄ few-layer devices.

Demonstration of Dissipative Quasihelical Edge Transport in Quantum Anomalous Hall Insulators

Doping a topological insulator (TI) film with transition metal ions can break its time-reversal symmetry and lead to the realization of the quantum anomalous Hall (QAH) effect. Prior studies have shown that the longitudinal resistance of the QAH samples usually does not vanish when the Hall resistance shows a good quantization. This has been interpreted as a result of the presence of possible dissipative conducting channels in magnetic TI samples. By studying the temperature- and magnetic-field-dependence of the magnetoresistance of a magnetic TI sandwich heterostructure device, we demonstrate that the predominant dissipation mechanism in thick QAH insulators can switch between nonchiral edge states and residual bulk states in different magnetic-field regimes. The interactions between bulk states, chiral edge states, and nonchiral edge states are also investigated. Our Letter provides a way to distinguish between the dissipation arising from the residual bulk states and nonchiral edge states, which is crucial for achieving true dissipationless transport in QAH insulators and for providing deeper insights into QAH-related phenomena.

Observation of Quantum Anomalous Hall Effect and Exchange Interaction in Topological Insulator/Antiferromagnet Heterostructure

Integration of a quantum anomalous Hall insulator with a magnetically ordered material provides an additional degree of freedom through which the resulting exotic quantum states can be controlled. Here, an experimental observation is reported of the quantum anomalous Hall effect in a magnetically-doped topological insulator grown on the antiferromagnetic insulator Cr₂ O₃ . The exchange coupling between the two materials is investigated using field-cooling-dependent magnetometry and polarized neutron reflectometry. Both techniques reveal strong interfacial interaction between the antiferromagnetic order of the Cr₂ O₃ and the magnetic topological insulator, manifested as an exchange bias when the sample is field-cooled under an out-of-plane magnetic field, and an exchange spring-like magnetic depth profile when the system is magnetized within the film plane. These results identify antiferromagnetic insulators as suitable candidates for the manipulation of magnetic and topological order in topological insulator films.

A new protocol for the preparation of superconducting KBi2

A superconducting KBi2 sample was successfully prepared using a liquid ammonia (NH3) technique. The temperature dependence of the magnetic susceptibility (M/H) showed a superconducting transition temperature (T c) as high as 3.6 K. In addition, the shielding fraction at 2.0 K was evaluated to be 87%, i.e., a bulk superconductor was realized using the above method. The T c value was the same as that reported for the KBi2 sample prepared using a high-temperature annealing method. An X-ray diffraction pattern measured based on the synchrotron X-ray radiation was analyzed using the Rietveld method, with a lattice constant, a, of 9.5010(1) Å under the space group of Fd3̄m (face-centered cubic, no. 227). The lattice constant and space group found for the KBi2 sample using a liquid NH3 technique were the same as those reported for KBi2 through a high-temperature annealing method. Thus, the superconducting behavior and crystal structure of the KBi2 sample obtained in this study are almost the same as those for the KBi2 sample reported previously. Strictly speaking, the magnetic behavior of the superconductivity was different from that of a KBi2 sample reported previously, i.e., the KBi2 sample prepared using a liquid NH3 technique was a type-II like superconductor, contrary to that prepared using a high-temperature annealing method, the reason for which is fully discussed. These results indicate that the liquid NH3 technique is effective and simple for the preparation of a superconducting KBi2. In addition, the topological nature of the superconductivity for KBi2 was not confirmed.

Exchange Bias in Magnetic Topological Insulator Superlattices

Magnetic doping and proximity coupling can open a band gap in a topological insulator (TI) and give rise to dissipationless quantum conduction phenomena. Here, by combining these two approaches, we demonstrate a novel TI superlattice structure that is alternately doped with transition and rare earth elements. An unexpected exchange bias effect is unambiguously confirmed in the superlattice with a large exchange bias field using magneto-transport and magneto-optical techniques. Further, the Curie temperature of the Cr-doped layers in the superlattice is found to increase by 60 K compared to a Cr-doped single-layer film. This result is supported by density-functional-theory calculations, which indicate the presence of antiferromagnetic ordering in Dy:Bi2Te3 induced by proximity coupling to Cr:Sb2Te3 at the interface. This work provides a new pathway to realizing the quantum anomalous Hall effect at elevated temperatures and axion insulator state at zero magnetic field by interface engineering in TI heterostructures.

Changes of Magnetism in a Magnetic Insulator due to Proximity to a Topological Insulator

We report the modification of magnetism in a magnetic insulator Y_{3}Fe_{5}O_{12} thin film by topological surface states (TSS) in an adjacent topological insulator Bi_{2}Se_{3} thin film. Ferromagnetic resonance measurements show that the TSS in Bi_{2}Se_{3} produces a perpendicular magnetic anisotropy, results in a decrease in the gyromagnetic ratio, and enhances the damping in Y_{3}Fe_{5}O_{12}. Such TSS-induced changes become more pronounced as the temperature decreases from 300 to 50 K. These results suggest a completely new approach for control of magnetism in magnetic thin films.

Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures

The quantum anomalous Hall (QAH) effect is a consequence of non-zero Berry curvature in momentum space. The QAH insulator harbours dissipation-free chiral edge states in the absence of an external magnetic field. However, the topological Hall (TH) effect, a hallmark of chiral spin textures, is a consequence of real-space Berry curvature. Here, by inserting a topological insulator (TI) layer between two magnetic TI layers, we realized the concurrence of the TH effect and the QAH effect through electric-field gating. The TH effect is probed by bulk carriers, whereas the QAH effect is characterized by chiral edge states. The appearance of the TH effect in the QAH insulating regime is a consequence of chiral magnetic domain walls that result from the gate-induced Dzyaloshinskii-Moriya interaction and occurs during the magnetization reversal process in the magnetic TI sandwich samples. The coexistence of chiral edge states and chiral spin textures provides a platform for proof-of-concept dissipationless spin-textured spintronic applications.

The Material Efforts for Quantized Hall Devices Based on Topological Insulators

A topological insulator (TI) is a kind of novel material hosting a topological band structure and plenty of exotic topological quantum effects. Achieving quantized electrical transport, including the quantum Hall effect (QHE) and the quantum anomalous Hall effect (QAHE), is an important aspect of realizing quantum devices based on TI materials. Intense efforts are made in this field, in which the most essential research is based on the optimization of realistic TI materials. Herein, the TI material development process is reviewed, focusing on the realization of quantized transport. Especially, for QHE, the strategies to increase the surface transport ratio and decrease the threshold magnetic field of QHE are examined. For QAHE, the evolution history of magnetic TIs is introduced, and the recently discovered magnetic TI candidates with intrinsic magnetizations are discussed in detail. Moreover, future research perspectives on these novel topological quantum effects are also evaluated.

Toward 2D Magnets in the (MnBi2 Te4 )(Bi2 Te3 )n Bulk Crystal

2D magnets and their engineered magnetic heterostructures are intriguing materials for both fundamental physics and application prospects. On the basis of the recently discovered intrinsic magnetic topological insulators (MnBi₂ Te₄ )(Bi₂ Te₃ )_n , here, a new type of magnet, in which the magnetic layers are separated by a large number of non-magnetic layers and become magnetically independent, is proposed. This magnet is named as a single-layer magnet, regarding the vanishing interlayer exchange coupling. Theoretical calculations and magnetization measurements indicate that, the decoupling of the magnetic layers starts to emerge from n = 2 and 3, as revealed by a unique slow-relaxation behavior below a ferromagnetic-type transition at T_c = 12-14 K. Magnetization data analysis shows that the proposed new magnetic states have a strong uniaxial anisotropy along the c-axis, forming an Ising-type magnetic structure, where T_c is the ordering temperature for each magnetic layer. The characteristic slow relaxation, which exists only along the c-axis but is absent along the ab plane, can be ascribed to interlayer coherent spin rotation and/or intralayer domain wall movement. The present results will stimulate further theoretical and experimental investigations for the prototypical magnetic structures, and their combination with the topological surface states may lead to exotic physical properties.