Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx(Bi0.1Sb0.9)2-xTe3

Tunable Magnetic Domains in Ferrimagnetic MnSb2Te4

Highly tunable properties make Mn(Bi,Sb)2Te4 a rich playground for exploring the interplay between band topology and magnetism: On one end, MnBi2Te4 is an antiferromagnetic topological insulator, while the magnetic structure of MnSb2Te4 (MST) can be tuned between antiferromagnetic and ferrimagnetic. Motivated to control electronic properties through real-space magnetic textures, we use magnetic force microscopy (MFM) to image the domains of ferrimagnetic MST. We find that magnetic field tunes between stripe and bubble domain morphologies, raising the possibility of topological spin textures. Moreover, we combine in situ transport with domain manipulation and imaging to both write MST device properties and directly measure the scaling of the Hall response with the domain area. This work demonstrates measurement of the local anomalous Hall response using MFM and opens the door to reconfigurable domain-based devices in the M(B,S)T family.

Imaging the Breakdown and Restoration of Topological Protection in Magnetic Topological Insulator MnBi2 Te4

Quantum anomalous Hall (QAH) insulators transport charge without resistance along topologically protected chiral 1D edge states. Yet, in magnetic topological insulators to date, topological protection is far from robust, with zero-magnetic field QAH effect only realized at temperatures an order of magnitude below the Néel temperature TN , though small magnetic fields can stabilize QAH effect. Understanding why topological protection breaks down is therefore essential to realizing QAH effect at higher temperatures. Here a scanning tunneling microscope is used to directly map the size of exchange gap (Eg,ex ) and its spatial fluctuation in the QAH insulator 5-layer MnBi2 Te4 . Long-range fluctuations of Eg,ex are observed, with values ranging between 0 (gapless) and 70 meV, appearing to be uncorrelated to individual surface point defects. The breakdown of topological protection is directly imaged, showing that the gapless edge state, the hallmark signature of a QAH insulator, hybridizes with extended gapless regions in the bulk. Finally, it is unambiguously demonstrated that the gapless regions originate from magnetic disorder, by demonstrating that a small magnetic field restores Eg,ex in these regions, explaining the recovery of topological protection in magnetic fields. The results indicate that overcoming magnetic disorder is the key to exploiting the unique properties of QAH insulators.

Topological spin textures in electronic non-Hermitian systems

Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium. Recent experimental progress is much from optical, cold-atomic, and classical platforms due to the vast tunability and clear identification of observables. However, their counterpart in solid-state electronic systems in equilibrium remains unmasked although highly desired, where a variety of materials are available, calculations are solidly founded, and accurate spectroscopic techniques can be applied. We demonstrate that, in the surface state of a topological insulator with spin-dependent relaxation due to magnetic impurities, highly nontrivial topological soliton spin textures appear in momentum space. Such spin-channel phenomena are delicately related to the type of non-Hermiticity and correctly reveal the most robust non-Hermitian features detectable spectroscopically. Moreover, the distinct topological soliton objects can be deformed to each other, mediated by topological transitions driven by tuning across a critical direction of doped magnetism. These results not only open a solid-state avenue to exotic spin patterns via spin- and angle-resolved photoemission spectroscopy, but also inspire non-Hermitian dissipation engineering of spins in solids.

Progress on the antiferromagnetic topological insulator MnBi2Te4

Topological materials, which feature robust surface and/or edge states, have now been a research focus in condensed matter physics. They represent a new class of materials exhibiting nontrivial topological phases, and provide a platform for exploring exotic transport phenomena, such as the quantum anomalous Hall effect and the quantum spin Hall effect. Recently, magnetic topological materials have attracted considerable interests due to the possibility to study the interplay between topological and magnetic orders. In particular, the quantum anomalous Hall and axion insulator phases can be realized in topological insulators with magnetic order. MnBi2Te4, as the first intrinsic antiferromagnetic topological insulator discovered, allows the examination of existing theoretical predictions; it has been extensively studied, and many new discoveries have been made. Here we review the progress made on MnBi2Te4 from both experimental and theoretical aspects. The bulk crystal and magnetic structures are surveyed first, followed by a review of theoretical calculations and experimental probes on the band structure and surface states, and a discussion of various exotic phases that can be realized in MnBi2Te4. The properties of MnBi2Te4 thin films and the corresponding transport studies are then reviewed, with an emphasis on the edge state transport. Possible future research directions in this field are also discussed.

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.

Gate-tunable Intrinsic Anomalous Hall Effect in Epitaxial MnBi2Te4 Films

The anomalous Hall effect (AHE) is an important transport signature revealing topological properties of magnetic materials and their spin textures. Recently, MnBi2Te4 has been demonstrated to be an intrinsic magnetic topological insulator. However, the origin of its intriguing AHE behaviors remains elusive. Here, we demonstrate the Berry curvature-dominated intrinsic AHE in wafer-scale MnBi2Te4 films. By applying back-gate voltages, we observe an ambipolar conduction and n-p transition in ∼7-layer MnBi2Te4, where a quadratic relation between the AHE resistance and longitudinal resistance suggests its intrinsic AHE nature. In particular, for ∼3-layer MnBi2Te4, the AHE sign can be tuned from pristine negative to positive. First-principles calculations unveil that such an AHE reversal originated from the competing Berry curvature between oppositely polarized spin-minority-dominated surface states and spin-majority-dominated inner bands. Our results shed light on the underlying physical mechanism of the intrinsic AHE and provide new perspectives for the unconventional sign-tunable AHE.

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.

Manipulating Topological Phases in Magnetic Topological Insulators

Magnetic topological insulators (MTIs) are a group of materials that feature topological band structures with concurrent magnetism, which can offer new opportunities for technological advancements in various applications, such as spintronics and quantum computing. The combination of topology and magnetism introduces a rich spectrum of topological phases in MTIs, which can be controllably manipulated by tuning material parameters such as doping profiles, interfacial proximity effect, or external conditions such as pressure and electric field. In this paper, we first review the mainstream MTI material platforms where the quantum anomalous Hall effect can be achieved, along with other exotic topological phases in MTIs. We then focus on highlighting recent developments in modulating topological properties in MTI with finite-size limit, pressure, electric field, and magnetic proximity effect. The manipulation of topological phases in MTIs provides an exciting avenue for advancing both fundamental research and practical applications. As this field continues to develop, further investigations into the interplay between topology and magnetism in MTIs will undoubtedly pave the way for innovative breakthroughs in the fundamental understanding of topological physics as well as practical applications.

Layer-Dependent Magnetic Structure and Anomalous Hall Effect in the Magnetic Topological Insulator MnBi4Te7

The intrinsic antiferromagnetic topological insulator (TI) MnBi₄Te₇ provides a capacious playground for the realization of topological quantum phenomena, such as the axion insulator states and quantum anomalous Hall (QAH) effect. In addition to nontrivial band topology, magnetism is another necessary ingredient for realizing these quantum phenomena. Here, we investigate signatures of thickness-dependent magnetism in exfoliated MnBi₄Te₇ thin flakes. We observe an obvious odd-even layer-number effect in few-layer MnBi₄Te₇. Noticeably, we show that in monolayer MnBi₄Te₇ the anomalous Hall effect exhibits a sign reversal. Compared with the case of MnBi₂Te₄, interlayer antiferromagnetic exchange coupling, which is essential for the realization of the QAH effect, is greatly suppressed in MnBi₄Te₇. The demonstration of thickness-dependent magnetic properties is helpful to further explore the topological quantum phenomena in MnBi₄Te₇.

Electrical Manipulation of Topological Phases in a Quantum Anomalous Hall Insulator

Quantum anomalous Hall phases arising from the inverted band topology in magnetically doped topological insulators have emerged as an important subject of research for quantization at zero magnetic fields. Though necessary for practical implementation, sophisticated electrical control of molecular beam epitaxy (MBE)-grown quantum anomalous Hall matter have been stymied by growth and fabrication challenges. Here, a novel procedure is demonstrated, employing a combination of thin-film deposition and 2D material stacking techniques, to create dual-gated devices of the MBE-grown quantum anomalous Hall insulator, Cr-doped (Bi,Sb)₂ Te₃ . In these devices, orthogonal control over the field-induced charge density and the electric displacement field is demonstrated. A thorough examination of material responses to tuning along each control axis is presented, realizing magnetic property control along the former and a novel capability to manipulate the surface exchange gap along the latter. Through electrically addressing the exchange gap, the capabilities to either strengthen the quantum anomalous Hall state or suppress it entirely and drive a topological phase transition to a trivial state are demonstrated. The experimental result is explained using first principle theoretical calculations, and establishes a practical route for in situ control of quantum anomalous Hall states and topology.

Superlattices of Gadolinium and Bismuth Based Thallium Dichalcogenides as Potential Magnetic Topological Insulators

Using relativistic spin-polarized density functional theory calculations we investigate magnetism, electronic structure and topology of the ternary thallium gadolinium dichalcogenides TlGdZ2 (Z= Se and Te) as well as superlattices on their basis. We find TlGdZ2 to have an antiferromagnetic exchange coupling both within and between the Gd layers, which leads to frustration and a complex magnetic structure. The electronic structure calculations reveal both TlGdSe2 and TlGdTe2 to be topologically trivial semiconductors. However, as we show further, a three-dimensional (3D) magnetic topological insulator (TI) state can potentially be achieved by constructing superlattices of the TlGdZ2/(TlBiZ2)n type, in which structural units of TlGdZ2 are alternated with those of the isomorphic TlBiZ2 compounds, known to be non-magnetic 3D TIs. Our results suggest a new approach for achieving 3D magnetic TI phases in such superlattices which is applicable to a large family of thallium rare-earth dichalcogenides and is expected to yield a fertile and tunable playground for exotic topological physics.

Graphene and Beyond: Recent Advances in Two-Dimensional Materials Synthesis, Properties, and Devices

Since the isolation of graphene in 2004, two-dimensional (2D) materials research has rapidly evolved into an entire subdiscipline in the physical sciences with a wide range of emergent applications. The unique 2D structure offers an open canvas to tailor and functionalize 2D materials through layer number, defects, morphology, moiré pattern, strain, and other control knobs. Through this review, we aim to highlight the most recent discoveries in the following topics: theory-guided synthesis for enhanced control of 2D morphologies, quality, yield, as well as insights toward novel 2D materials; defect engineering to control and understand the role of various defects, including in situ and ex situ methods; and properties and applications that are related to moiré engineering, strain engineering, and artificial intelligence. Finally, we also provide our perspective on the challenges and opportunities in this fascinating field.

Measured Potential Profile in a Quantum Anomalous Hall System Suggests Bulk-Dominated Current Flow

Ideally, quantum anomalous Hall systems should display zero longitudinal resistance. Yet in experimental quantum anomalous Hall systems elevated temperature can make the longitudinal resistance finite, indicating dissipative flow of electrons. Here, we show that the measured potentials at multiple locations within a device at elevated temperature are well described by solution of Laplace's equation, assuming spatially uniform conductivity, suggesting nonequilibrium current flows through the two-dimensional bulk. Extrapolation suggests that at even lower temperatures current may still flow primarily through the bulk rather than, as had been assumed, through edge modes. An argument for bulk current flow previously applied to quantum Hall systems supports this picture.

Intrinsic Magnetic (EuIn)As Nanowire Shells with a Unique Crystal Structure

In the pursuit of magneto-electronic systems nonstoichiometric magnetic elements commonly introduce disorder and enhance magnetic scattering. We demonstrate the growth of (EuIn)As shells, with a unique crystal structure comprised of a dense net of Eu inversion planes, over InAs and InAs_1-xSb_x core nanowires. This is imaged with atomic and elemental resolution which reveal a prismatic configuration of the Eu planes. The results are supported by molecular dynamics simulations. Local magnetic and susceptibility mappings show magnetic response in all nanowires, while a subset bearing a DC signal points to ferromagnetic order. These provide a mechanism for enhancing Zeeman responses, operational at zero applied magnetic field. Such properties suggest that the obtained structures can serve as a preferred platform for time-reversal symmetry broken one-dimensional states including intrinsic topological superconductivity.

Visualizing the interplay of Dirac mass gap and magnetism at nanoscale in intrinsic magnetic topological insulators

In intrinsic magnetic topological insulators, Dirac surface-state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however. Here, we use molecular beam epitaxy to grow intrinsic MnBi₂Te₄ thin films. Using scanning tunneling microscopy/spectroscopy, we directly visualize the Dirac mass gap and its disappearance below and above the magnetic order temperature. We further reveal the interplay of Dirac mass gaps and local magnetic defects. We find that, in high defect regions, the Dirac mass gap collapses. Ab initio and coupled Dirac cone model calculations provide insight into the microscopic origin of the correlation between defect density and spatial gap variations. This work provides unambiguous identification of the Dirac mass gap in MnBi₂Te₄ and, by revealing the microscopic origin of its gap variation, establishes a material design principle for realizing exotic states in intrinsic magnetic topological insulators.

Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics^1,2. The quantum spin Hall phase^3-6 is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature quantum spin Hall edge state on the surface of the higher-order topological insulator Bi₄Br₄. We find that the atomically resolved lattice exhibits a large insulating gap of over 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical hybridization of such edge states, which not only supports the Z₂ topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Our results further encourage the exploration of high-temperature transport quantization of the putative topological phase reported here.

Direct Probe of the Ferromagnetic Proximity Effect at the Interface of SnTe/Fe Heterostructure by Polarized Neutron Reflectometry

Introducing magnetic order into a topological insulator (TI) system has attracted much attention with an expectation of realizing exotic phenomena such as the quantum anomalous Hall effect (QAHE) and axion insulator states. The magnetic proximity effect (MPE) is one of the promising schemes to induce the magnetic order on the surface of a TI without introducing disorder accompanied by doping magnetic impurities in the TI. In this study, we investigate the MPE at the interface of a heterostructure consisting of the topological crystalline insulator (TCI) SnTe and Fe by employing polarized neutron reflectometry. The ferromagnetic order penetrates ∼2.2 nm deep into the SnTe layer from the interface with Fe, which persists up to room temperature. This is induced by the MPE on the surface of the TCI preserving the coherent topological states without introducing the disorder by doping magnetic impurities. This would open up a way for realizing next-generation spintronics and quantum computational devices.

Electronic Structure of Pb Adsorbed Surfaces of Intrinsic Magnetic Topological Insulators

Recently discovered intrinsic magnetic topological insulators (IMTIs) constitute a unique class of quantum materials that combine magnetism and nontrivial topology. One of the most promising applications of these materials is Majorana fermion creation; Majorana fermions are expected to arise when a superconductor is in contact with the surface of an IMTI. Here we study the adsorption of Pb ultrathin films on top of IMTIs of various stoichiometries. By means of XPS we figure out the formation of the Pb wetting layer coupled to the surface atoms for low coverages and overlayer growth on top upon further deposition. Investigation of the adsorbed surfaces by means of ARPES shows the Dirac cone survival, its shift in a binding energy, and the Pb electronic states appearance. The obtained results allow the Pb/IMTI interfaces to be constructed for the understanding of the proximity effect and provide an important step toward quantum device engineering based on IMTIs.

Chern Number Tunable Quantum Anomalous Hall Effect in Monolayer Transitional Metal Oxides via Manipulating Magnetization Orientation

Although much effort has been made to explore quantum anomalous Hall effect (QAHE) in both theory and experiment, the QAHE systems with tunable Chern numbers are yet limited. Here, we theoretically propose that NiAsO_{3} and PdSbO_{3}, monolayer transitional metal oxides, can realize QAHE with tunable Chern numbers via manipulating their magnetization orientations. When the magnetization lies in the x-y plane and all mirror symmetries are broken, the low-Chern-number (i.e., C=±1) phase emerges. When the magnetization exhibits nonzero z-direction component, the system enters the high-Chern-number (i.e., C=±3) phase, even in the presence of canted magnetization. The global band gap can approach the room-temperature energy scale in monolayer PdSbO_{3} (23.4 meV), when the magnetization is aligned to z direction. By using Wannier-based tight-binding model, we establish the phase diagram of magnetization induced topological phase transition. Our work provides a high-temperature QAHE system with tunable Chern number for the practical electronic application.

Large Magnetic Gap in a Designer Ferromagnet-Topological Insulator-Ferromagnet Heterostructure

Combining magnetism and nontrivial band topology gives rise to quantum anomalous Hall (QAH) insulators and exotic quantum phases such as the QAH effect where current flows without dissipation along quantized edge states. Inducing magnetic order in topological insulators via proximity to a magnetic material offers a promising pathway toward achieving the QAH effect at a high temperature for lossless transport applications. One promising architecture involves a sandwich structure comprising two single-septuple layers (1SL) of MnBi₂ Te₄ (a 2D ferromagnetic insulator) with ultrathin few quintuple layer (QL) Bi₂ Te₃ in the middle, and it is predicted to yield a robust QAH insulator phase with a large bandgap greater than 50 meV. Here, the growth of a 1SL MnBi₂ Te₄ /4QL Bi₂ Te₃ /1SL MnBi₂ Te₄ heterostructure via molecular beam epitaxy is demonstrated and the electronic structure probed using angle-resolved photoelectron spectroscopy. Strong hexagonally warped massive Dirac fermions and a bandgap of 75 ± 15 meV are observed. The magnetic origin of the gap is confirmed by the observation of the exchange-Rashba effect, as well as the vanishing bandgap above the Curie temperature, in agreement with density functional theory calculations. These findings provide insights into magnetic proximity effects in topological insulators and reveal a promising platform for realizing the QAH effect at elevated temperatures.

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.

Elemental Topological Dirac Semimetal α-Sn with High Quantum Mobility

α-Sn provides an ideal avenue to investigate novel topological properties owing to its rich diagram of topological phases and simple elemental material structure. Thus far, however, the realization of high-quality α-Sn remains a challenge, which limits the understanding of its quantum transport properties and device applications. Here, epitaxial growth of α-Sn on InSb (001) with the highest quality thus far is presented. The studied samples exhibit unprecedentedly high quantum mobilities of both the surface state (30 000 cm² V^-1 s^-1 ), which is ten times higher than the previously reported values, and the bulk heavy-hole state (1800 cm² V^-1 s^-1 ), which is never obtained experimentally. These excellent features allow quantitative characterization of the nontrivial interfacial and bulk band structure of α-Sn via a thorough investigation of Shubnikov-de Haas oscillations combined with first-principles calculations. The results firmly identify that α-Sn grown on InSb (001) is a topological Dirac semimetal (TDS). Furthermore, a crossover from the TDS to a 2D topological insulator and a subsequent phase transition to a trivial insulator when varying the thickness of α-Sn are demonstrated. This work indicates that α-Sn is an excellent model system to study novel topological phases and a prominent material candidate for topological devices.

Non-Hermitian indirect exchange interaction in a topological insulator coupled to a ferromagnetic metal

We theoretically demonstrate non-Hermitian indirect interaction between two magnetic impurities placed at the interface between a 3D topological insulator and a ferromagnetic metal. The coupling of topological insulator and the ferromagnet introduces not only Zeeman exchange field on the surface states but also broadening to transfer the charge and spin between the surface states of the topological insulator and the metallic states of the ferromagnet. While the former provides bandgap at the charge neutrality point, the latter causes non-Hermiticity. Using the Green's function method, we calculate the range functions of magnetic impurity interactions. We show that the charge decay rate provides a coupling between evanescent modes near the bandgap and traveling modes near the band edge. However, the spin decay rate induces a stronger coupling than the charge decay rate so that higher energy traveling modes can be coupled to lower energy evanescent ones. This results in a non-monotonic behavior of the range functions in terms of distance and decay rates in the subgap regime. In the over gap regime, depending on the type of decay rate and on the distance, the amplitude of spatial oscillations would be damped or promoted.

Magnetic Topological Insulator Heterostructures: A Review

Topological insulators (TIs) provide intriguing prospects for the future of spintronics due to their large spin-orbit coupling and dissipationless, counter-propagating conduction channels in the surface state. The combination of topological properties and magnetic order can lead to new quantum states including the quantum anomalous Hall effect that was first experimentally realized in Cr-doped (Bi,Sb)₂ Te₃ films. Since magnetic doping can introduce detrimental effects, requiring very low operational temperatures, alternative approaches are explored. Proximity coupling to magnetically ordered systems is an obvious option, with the prospect to raise the temperature for observing the various quantum effects. Here, an overview of proximity coupling and interfacial effects in TI heterostructures is presented, which provides a versatile materials platform for tuning the magnetic and topological properties of these exciting materials. An introduction is first given to the heterostructure growth by molecular beam epitaxy and suitable structural, electronic, and magnetic characterization techniques. Going beyond transition-metal-doped and undoped TI heterostructures, examples of heterostructures are discussed, including rare-earth-doped TIs, magnetic insulators, and antiferromagnets, which lead to exotic phenomena such as skyrmions and exchange bias. Finally, an outlook on novel heterostructures such as intrinsic magnetic TIs and systems including 2D materials is given.

Mn-Rich MnSb2 Te4 : A Topological Insulator with Magnetic Gap Closing at High Curie Temperatures of 45-50 K

Ferromagnetic topological insulators exhibit the quantum anomalous Hall effect, which is potentially useful for high-precision metrology, edge channel spintronics, and topological qubits.  The stable 2+ state of Mn enables intrinsic magnetic topological insulators. MnBi2 Te4 is, however, antiferromagnetic with 25 K Néel temperature and is strongly n-doped. In this work, p-type MnSb2 Te4 , previously considered topologically trivial, is shown to be a ferromagnetic topological insulator for a few percent Mn excess. i) Ferromagnetic hysteresis with record Curie temperature of 45-50 K, ii) out-of-plane magnetic anisotropy, iii) a 2D Dirac cone with the Dirac point close to the Fermi level, iv) out-of-plane spin polarization as revealed by photoelectron spectroscopy, and v) a magnetically induced bandgap closing at the Curie temperature, demonstrated by scanning tunneling spectroscopy (STS), are shown. Moreover, a critical exponent of the magnetization β ≈ 1 is found, indicating the vicinity of a quantum critical point. Ab initio calculations reveal that Mn-Sb site exchange provides the ferromagnetic interlayer coupling and the slight excess of Mn nearly doubles the Curie temperature. Remaining deviations from the ferromagnetic order open the inverted bulk bandgap and render MnSb2 Te4 a robust topological insulator and new benchmark for magnetic topological insulators.

Crossover from 2D Ferromagnetic Insulator to Wide Band Gap Quantum Anomalous Hall Insulator in Ultrathin MnBi2Te4

Intrinsic magnetic topological insulators offer low disorder and large magnetic band gaps for robust magnetic topological phases operating at higher temperatures. By controlling the layer thickness, emergent phenomena such as the quantum anomalous Hall (QAH) effect and axion insulator phases have been realized. These observations occur at temperatures significantly lower than the Néel temperature of bulk MnBi₂Te₄, and measurement of the magnetic energy gap at the Dirac point in ultrathin MnBi₂Te₄ has yet to be achieved. Critical to achieving the promise of this system is a direct measurement of the layer-dependent energy gap and verification of a temperature-dependent topological phase transition from a large band gap QAH insulator to a gapless TI paramagnetic phase. Here we utilize temperature-dependent angle-resolved photoemission spectroscopy to study epitaxial ultrathin MnBi₂Te₄. We directly observe a layer-dependent crossover from a 2D ferromagnetic insulator with a band gap greater than 780 meV in one septuple layer (1 SL) to a QAH insulator with a large energy gap (>70 meV) at 8 K in 3 and 5 SL MnBi₂Te₄. The QAH gap is confirmed to be magnetic in origin, as it becomes gapless with increasing temperature above 8 K.

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.

Controllable quantum point junction on the surface of an antiferromagnetic topological insulator

Engineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.

Charge transport in magnetic topological ultra-thin films: the effect of structural inversion asymmetry

We study the effect of structural inversion asymmetry, induced by the presence of substrates or by external electric fields, on charge transport in magnetic topological ultra-thin films. We consider general orientations of the magnetic impurities. Our results are based on the Boltzmann formalism along with a modified relaxation time scheme. We show that the structural inversion asymmetry enhances the charge transport anisotropy induced by the magnetic impurities and when only one conduction subband contributes to the charge transport a dissipationless charge current is accessible. We demonstrate how a substrate or gate voltage can control the effect of the magnetic impurities on the charge transport, and how this depends on the orientation of the magnetic impurities.

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.

A non-volatile cryogenic random-access memory based on the quantum anomalous Hall effect

The interplay between ferromagnetism and topological properties of electronic band structures leads to a precise quantization of Hall resistance without any external magnetic field. This so-called quantum anomalous Hall effect (QAHE) is born out of topological correlations, and is oblivious of low-sample quality. It was envisioned to lead towards dissipation-less and topologically protected electronics. However, no clear framework of how to design such an electronic device out of it exists. Here we construct an ultra-low power, non-volatile, cryogenic memory architecture leveraging the QAHE phenomenon. Our design promises orders of magnitude lower cell area compared with the state-of-the-art cryogenic memory technologies. We harness the fundamentally quantized Hall resistance levels in moiré graphene heterostructures to store non-volatile binary bits (1, 0). We perform the memory write operation through controlled hysteretic switching between the quantized Hall states, using nano-ampere level currents with opposite polarities. The non-destructive read operation is performed by sensing the polarity of the transverse Hall voltage using a separate pair of terminals. We custom design the memory architecture with a novel sensing mechanism to avoid accidental data corruption, ensure highest memory density and minimize array leakage power. Our design provides a pathway towards realizing topologically protected memory devices.

Severe Dirac Mass Gap Suppression in Sb2Te3-Based Quantum Anomalous Hall Materials

The quantum anomalous Hall (QAH) effect appears in ferromagnetic topological insulators (FMTIs) when a Dirac mass gap opens in the spectrum of the topological surface states (SSs). Unaccountably, although the mean mass gap can exceed 28 meV (or ∼320 K), the QAH effect is frequently only detectable at temperatures below 1 K. Using atomic-resolution Landau level spectroscopic imaging, we compare the electronic structure of the archetypal FMTI Cr_0.08(Bi_0.1Sb_0.9)_1.92Te₃ to that of its nonmagnetic parent (Bi_0.1Sb_0.9)₂Te₃, to explore the cause. In (Bi_0.1Sb_0.9)₂Te₃, we find spatially random variations of the Dirac energy. Statistically equivalent Dirac energy variations are detected in Cr_0.08(Bi_0.1Sb_0.9)_1.92Te₃ with concurrent but uncorrelated Dirac mass gap disorder. These two classes of SS electronic disorder conspire to drastically suppress the minimum mass gap to below 100 μeV for nanoscale regions separated by <1 μm. This fundamentally limits the fully quantized anomalous Hall effect in Sb₂Te₃-based FMTI materials to very low temperatures.

Highly Tunable Spin-Orbit Torque and Anisotropic Magnetoresistance in a Topological Insulator Thin Film Attached to Ferromagnetic Layer

We investigate spin-charge conversion phenomena in hybrid structures of topological insulator thin films and magnetic insulators. We find an anisotropic inverse spin-galvanic effect that yields a highly tunable spin-orbit torque. Concentrating on the quasiballistic limit, we also predict a giant anisotropic magnetoresistance at low dopings. These effects, which have no counterparts in thick topological insulators, depend on the simultaneous presence of the hybridization between the surface states and the in-plane magnetization. Both the inverse spin-galvanic effect and anisotropic magnetoresistance exhibit a strong dependence on the magnetization and the Fermi level position and can be used for spintronics and spin-orbit-torque-based applications at the nanoscale.

Magnetized topological insulator multilayers

We discuss the magnetic and topological properties of bulk crystals and quasi-two-dimensional (quasi-2D) thin films formed by stacking intrinsic magnetized topological insulator (for example, Mn ([Formula: see text])2X4 with X = Se,Te) septuple layers and topological insulator quintuple layers in arbitrary order. Our analysis makes use of a simplified model that retains only Dirac cone degrees of freedom on both surfaces of each septuple or quintuple layer. We demonstrate the model's applicability and estimate its parameters by comparing with ab initio density-functional theory (DFT) calculations. We then employ the coupled Dirac cone model to provide an explanation for the dependence of thin-film properties, particularly the presence or absence of the quantum anomalous Hall effect, on film thickness, magnetic configuration, and stacking arrangement, and to comment on the design of Weyl superlattices.

Large non-reciprocal charge transport mediated by quantum anomalous Hall edge states

The topological nature of the quantum anomalous Hall effect (QAHE) causes a dissipationless chiral edge current at the sample boundary^1,2. Of fundamental interest is whether the chirality of the band structure manifests itself in charge transport properties. Here we report the observation of large non-reciprocal charge transport³ in a magnetic topological insulator, Cr-doped (Bi,Sb)₂Te₃. When the surface massive Dirac band is slightly carrier doped by a gate voltage, the edge state starts to dissipate and exhibits a current-direction-dependent resistance with a directional difference as large as 26%. The polarity of this diode effect depends on the magnetization direction as well as on the carrier type, electrons or holes. The correlation between the non-reciprocal resistance and the Hall resistance indicates that the non-reciprocity originates from the interplay between the chiral edge state and the Dirac surface state.

Coexistence of Surface Ferromagnetism and a Gapless Topological State in MnBi_{2}Te_{4}

Surface magnetism and its correlation with the electronic structure are critical to understanding the topological surface state in the intrinsic magnetic topological insulator MnBi_{2}Te_{4}. Here, using static and time resolved angle-resolved photoemission spectroscopy (ARPES), we find a significant ARPES intensity change together with a gap opening on a Rashba-like conduction band. Comparison with a model simulation strongly indicates that the surface magnetism on cleaved MnBi_{2}Te_{4} is the same as its bulk state. The inability of surface ferromagnetism to open a gap in the topological surface state uncovers the novel complexity of MnBi_{2}Te_{4} that may be responsible for the low quantum anomalous Hall temperature of exfoliated MnBi_{2}Te_{4}.

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.

Probing the low-temperature limit of the quantum anomalous Hall effect

Quantum anomalous Hall effect has been observed in magnetically doped topological insulators. However, full quantization, up until now, is limited within the sub-1 K temperature regime, although the material's magnetic ordering temperature can go beyond 100 K. Here, we study the temperature limiting factors of the effect in Cr-doped (BiSb)2Te3 systems using both transport and magneto-optical methods. By deliberate control of the thin-film thickness and doping profile, we revealed that the low occurring temperature of quantum anomalous Hall effect in current material system is a combined result of weak ferromagnetism and trivial band involvement. Our findings may provide important insights into the search for high-temperature quantum anomalous Hall insulator and other topologically related phenomena.

Electronic States and Magnetic Response of MnBi2Te4 by Scanning Tunneling Microscopy and Spectroscopy

Exotic quantum phenomena have been demonstrated in recently discovered intrinsic magnetic topological insulator MnBi₂Te₄. At its two-dimensional limit, the quantum anomalous Hall effect and axion insulator state were observed in odd and even layers of MnBi₂Te₄, respectively. Here, we employ low-temperature scanning tunneling microscopy to study the electronic properties of MnBi₂Te₄. The quasiparticle interference patterns indicate that the electronic structures on the topmost layer of MnBi₂Te₄ are different from those of the expected out-of-plane A-type antiferromagnetic phase. The topological surface states may be embedded in deeper layers beneath the topmost surface. Such novel electronic structure is presumably related to the modification of crystalline structure during sample cleaving and reorientation of the magnetic moment of Mn atoms near the surface. Mn dopants substituted at the Bi site on the second atomic layer are observed. The electronic structures fluctuate at atomic scale on the surface, which can affect the magnetism of MnBi₂Te₄.

Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4

In a magnetic topological insulator, nontrivial band topology combines with magnetic order to produce exotic states of matter, such as quantum anomalous Hall (QAH) insulators and axion insulators. In this work, we probe quantum transport in MnBi2Te4thin flakes—a topological insulator with intrinsic magnetic order. In this layered van der Waals crystal, the ferromagnetic layers couple antiparallel to each other; atomically thin MnBi2Te4, however, becomes ferromagnetic when the sample has an odd number of septuple layers. We observe a zero-field QAH effect in a five–septuple-layer specimen at 1.4 kelvin, and an external magnetic field further raises the quantization temperature to 6.5 kelvin by aligning all layers ferromagnetically. The results establish MnBi2Te4as an ideal arena for further exploring various topological phenomena with a spontaneously broken time-reversal symmetry.

Intrinsic quantized anomalous Hall effect in a moiré heterostructure

The quantum anomalous Hall (QAH) effect combines topology and magnetism to produce precisely quantized Hall resistance at zero magnetic field. We report the observation of a QAH effect in twisted bilayer graphene aligned to hexagonal boron nitride. The effect is driven by intrinsic strong interactions, which polarize the electrons into a single spin- and valley-resolved moiré miniband with Chern number C = 1. In contrast to magnetically doped systems, the measured transport energy gap is larger than the Curie temperature for magnetic ordering, and quantization to within 0.1% of the von Klitzing constant persists to temperatures of several kelvin at zero magnetic field. Electrical currents as small as 1 nanoampere controllably switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory.

Prediction and observation of an antiferromagnetic topological insulator

Magnetic topological insulators are narrow-gap semiconductor materials that combine non-trivial band topology and magnetic order¹. Unlike their nonmagnetic counterparts, magnetic topological insulators may have some of the surfaces gapped, which enables a number of exotic phenomena that have potential applications in spintronics¹, such as the quantum anomalous Hall effect² and chiral Majorana fermions³. So far, magnetic topological insulators have only been created by means of doping nonmagnetic topological insulators with 3d transition-metal elements; however, such an approach leads to strongly inhomogeneous magnetic⁴ and electronic⁵ properties of these materials, restricting the observation of important effects to very low temperatures^2,3. An intrinsic magnetic topological insulator-a stoichiometric well ordered magnetic compound-could be an ideal solution to these problems, but no such material has been observed so far. Here we predict by ab initio calculations and further confirm using various experimental techniques the realization of an antiferromagnetic topological insulator in the layered van der Waals compound MnBi₂Te₄. The antiferromagnetic ordering  that MnBi₂Te₄  shows makes it invariant with respect to the combination of the time-reversal and primitive-lattice translation symmetries, giving rise to a ℤ₂ topological classification; ℤ₂ = 1 for MnBi₂Te₄, confirming its topologically nontrivial nature. Our experiments indicate that the symmetry-breaking (0001) surface of MnBi₂Te₄ exhibits a large bandgap in the topological surface state. We expect this property to eventually enable the observation of a number of fundamental phenomena, among them quantized magnetoelectric coupling^6-8 and axion electrodynamics^9,10. Other exotic phenomena could become accessible at much higher temperatures than those reached so far, such as the quantum anomalous Hall effect² and chiral Majorana fermions³.

Topological phase transition induced by magnetic proximity effect in two dimensions

We study the magnetic proximity effect on a two-dimensional topological insulator in a CrI₃/SnI₃/CrI₃ trilayer structure. From first-principles calculations, the BiI₃-type SnI₃ monolayer without spin-orbit coupling has Dirac cones at the corners of the hexagonal Brillouin zone. With spin-orbit coupling turned on, it becomes a topological insulator, as revealed by a non-vanishing Z ₂ invariant and an effective model from symmetry considerations. Without spin-orbit coupling, the Dirac points are protected if the CrI₃ layers are stacked ferromagnetically, and are gapped if the CrI₃ layers are stacked antiferromagnetically, which can be explained by the irreducible representations of the magnetic space groups [Formula: see text] and [Formula: see text], corresponding to ferromagnetic and antiferromagnetic stacking, respectively. By analyzing the effective model including the perturbations, we find that the competition between the magnetic proximity effect and spin-orbit coupling leads to a topological phase transition between a trivial insulator and a topological insulator.

Cr2Te3 Thin Films for Integration in Magnetic Topological Insulator Heterostructures

Chromium telluride compounds are promising ferromagnets for proximity coupling to magnetic topological insulators (MTIs) of the Cr-doped (Bi,Sb)₂(Se,Te)₃ class of materials as they share the same elements, thus simplifying thin film growth, as well as due to their compatible crystal structure. Recently, it has been demonstrated that high quality (001)-oriented Cr₂Te₃ thin films with perpendicular magnetic anisotropy can be grown on c-plane sapphire substrate. Here, we present a magnetic and soft x-ray absorption spectroscopy study of the chemical and magnetic properties of Cr₂Te₃ thin films. X-ray magnetic circular dichroism (XMCD) measured at the Cr L_2,3 edges gives information about the local electronic and magnetic structure of the Cr ions. We further demonstrate the overgrowth of Cr₂Te₃ (001) thin films by high-quality Cr-doped Sb₂Te₃ films. The magnetic properties of the layers have been characterized and our results provide a starting point for refining the physical models of the complex magnetic ordering in Cr₂Te₃ thin films, and their integration into advanced MTI heterostructures for quantum device applications.

Large Anomalous Hall Effect in Topological Insulators with Proximitized Ferromagnetic Insulators

We report a proximity-driven large anomalous Hall effect in all-telluride heterostructures consisting of the ferromagnetic insulator Cr_{2}Ge_{2}Te_{6} and topological insulator (Bi,Sb)_{2}Te_{3}. Despite small magnetization in the (Bi,Sb)_{2}Te_{3} layer, the anomalous Hall conductivity reaches a large value of 0.2e^{2}/h in accord with a ferromagnetic response of the Cr_{2}Ge_{2}Te_{6}. The results show that the exchange coupling between the surface state of the topological insulator and the proximitized Cr_{2}Ge_{2}Te_{6} layer is effective and strong enough to open the sizable exchange gap in the surface state.

Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states

Quantum-relativistic materials often host electronic phenomena with exotic spatial distributions. In particular, quantum anomalous Hall (QAH) insulators feature topological boundary currents whose chirality is determined by the magnetization orientation. However, understanding the microscopic nature of edge vs. bulk currents has remained a challenge due to the emergence of multidomain states at the phase transitions. Here we use microwave impedance microscopy (MIM) to directly image chiral edge currents and phase transitions in a magnetic topological insulator. Our images reveal a dramatic change in the edge state structure and an unexpected microwave response at the topological phase transition between the Chern number [Formula: see text] and [Formula: see text] states, consistent with the emergence of an insulating [Formula: see text] state. The magnetic transition width is independent of film thickness, but the transition pattern is distinct in differently initiated field sweeps. This behavior suggests that the [Formula: see text] state has 2 surface states with Hall conductivities of [Formula: see text] but with opposite signs.

Unique Thickness-Dependent Properties of the van der Waals Interlayer Antiferromagnet MnBi_{2}Te_{4} Films

Using density functional theory and Monte Carlo calculations, we study the thickness dependence of the magnetic and electronic properties of a van der Waals interlayer antiferromagnet in the two-dimensional limit. Considering MnBi_{2}Te_{4} as a model material, we find it to demonstrate a remarkable set of thickness-dependent magnetic and topological transitions. While a single septuple layer block of MnBi_{2}Te_{4} is a topologically trivial ferromagnet, the thicker films made of an odd (even) number of blocks are uncompensated (compensated) interlayer antiferromagnets, which show wide band gap quantum anomalous Hall (zero plateau quantum anomalous Hall) states. Thus, MnBi_{2}Te_{4} is the first stoichiometric material predicted to realize the zero plateau quantum anomalous Hall state intrinsically. This state has been theoretically shown to host the exotic axion insulator phase.

Multiple Chiral Majorana Fermion Modes and Quantum Transport

The chiral Majorana fermion is a massless self-conjugate fermionic particle that could arise as the quasiparticle edge state of a two-dimensonal topological state of matter. Here we propose a new platform for a chiral topological superconductor (TSC) in two dimensions with multiple N chiral Majorana fermions from a quantized anomalous Hall insulator in proximity to an s-wave superconductor with nontrivial band topology. A concrete example is that a N=3 chiral TSC is realized by coupling a magnetic topological insulator to the ion-based superconductor such as FeTe_{0.55}Se_{0.45}. We further propose the electrical and thermal transport experiments to detect the Majorana nature of three chiral edge fermions. A smoking gun signature is that the two-terminal electrical conductance of a quantized anomalous Hall-TSC junction obeys a unique distribution averaged to (2/3)e^{2}/h, which is due to the random edge mode mixing of chiral Majorana fermions and is distinguished from possible trivial explanations. The homogenous system proposed here provides an ideal platform for studying the exotic physics of chiral Majorana fermions.

Magnetic and defect probes of the SmB6 surface state

The impact of nonmagnetic and magnetic impurities on topological insulators is a central focus concerning their fundamental physics and possible spintronics and quantum computing applications. Combining scanning tunneling spectroscopy with transport measurements, we investigate, both locally and globally, the effect of nonmagnetic and magnetic substituents in SmB₆, a predicted topological Kondo insulator. Around the so-introduced substitutents and in accord with theoretical predictions, the surface states are locally suppressed with different length scales depending on the substituent's magnetic properties. For sufficiently high substituent concentrations, these states are globally destroyed. Similarly, using a magnetic tip in tunneling spectroscopy also resulted in largely suppressed surface states. Hence, a destruction of the surface states is always observed close to atoms with substantial magnetic moment. This points to the topological nature of the surface states in SmB₆ and illustrates how magnetic impurities destroy the surface states from microscopic to macroscopic length scales.