Intrinsic magnetic topological insulator phases in the Sb doped MnBi2Te4 bulks and thin flakes

Rules for dissipationless topotronics

Topological systems hosting gapless boundary states have attracted huge attention as promising components for next-generation information processing, attributed to their capacity for dissipationless electronics. Nevertheless, recent theoretical and experimental inquiries have revealed the emergence of energy dissipation in precisely quantized electrical transport. Here, we present a criterion for the realization of truly no-dissipation design, characterized as Nin = Ntunl + Nbs, where Nin, Ntunl, and Nbs represent the number of modes participating in injecting, tunneling, and backscattering processes, respectively. The key lies in matching the number of injecting, tunneling, and backscattering modes, ensuring the equilibrium among all engaged modes inside the device. Among all the topological materials, we advocate for the indispensability of Chern insulators exhibiting higher Chern numbers to achieve functional devices and uphold the no-dissipation rule simultaneously. Furthermore, we design the topological current divider and collector, evading dissipation upon fulfilling the established criterion. Our work paves the path for developing the prospective topotronics.

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.

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.

Lossless Spin-Orbit Torque in Antiferromagnetic Topological Insulator MnBi_{2}Te_{4}

We formulate and quantify the spin-orbit torque (SOT) in intrinsic antiferromagnetic topological insulator MnBi_{2}Te_{4} of a few septuple-layer thick in charge-neutral condition, which exhibits pronounced layer-resolved characteristics and even-odd contrast. Contrary to traditional current-induced torques, our SOT is not accompanied by Ohm's currents, thus being devoid of Joule heating. We study the SOT-induced magnetic resonances, where in the tri-septuple-layer case we identify a peculiar exchange mode that is blind to microwaves but can be exclusively driven by the predicted SOT. As an inverse effect, the dynamical magnetic moments generate a pure adiabatic current, which occurs concomitantly with the SOT and gives rise to an overall reactance for the MnBi_{2}Te_{4}, enabling a lossless conversion of electric power into magnetic dynamics.

Revealing Fermi surface evolution and Berry curvature in an ideal type-II Weyl semimetal

In type-II Weyl semimetals (WSMs), the tilting of the Weyl cones leads to the coexistence of electron and hole pockets that touch at the Weyl nodes. These electrons and holes experience the Berry curvature generated by the Weyl nodes, leading to an anomalous Hall effect that is highly sensitive to the Fermi level position. Here we have identified field-induced ferromagnetic MnBi2-xSbxTe4 as an ideal type-II WSM with a single pair of Weyl nodes. By employing a combination of quantum oscillations and high-field Hall measurements, we have resolved the evolution of Fermi-surface sections as the Fermi level is tuned across the charge neutrality point, precisely matching the band structure of an ideal type-II WSM. Furthermore, the anomalous Hall conductivity exhibits a heartbeat-like behavior as the Fermi level is tuned across the Weyl nodes, a feature of type-II WSMs that was long predicted by theory. Our work uncovers a large free carrier contribution to the anomalous Hall effect resulting from the unique interplay between the Fermi surface and diverging Berry curvature in magnetic type-II WSMs.

The Case for a Defect Genome Initiative

The Materials Genome Initiative (MGI) has streamlined the materials discovery effort by leveraging generic traits of materials, with focus largely on perfect solids. Defects such as impurities and perturbations, however, drive many attractive functional properties of materials. The rich tapestry of charge, spin, and bonding states hosted by defects are not accessible to elements and perfect crystals, and defects can thus be viewed as another class of "elements" that lie beyond the periodic table. Accordingly, a Defect Genome Initiative (DGI) to accelerate functional defect discovery for energy, quantum information, and other applications is proposed. First, major advances made under the MGI are highlighted, followed by a delineation of pathways for accelerating the discovery and design of functional defects under the DGI. Near-term goals for the DGI are suggested. The construction of open defect platforms and design of data-driven functional defects, along with approaches for fabrication and characterization of defects, are discussed. The associated challenges and opportunities are considered and recent advances towards controlled introduction of functional defects at the atomic scale are reviewed. It is hoped this perspective will spur a community-wide interest in undertaking a DGI effort in recognition of the importance of defects in enabling unique functionalities in materials.

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.

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.

ARPES investigation of the electronic structure and its evolution in magnetic topological insulator MnBi2+2nTe4+3n family

In the past 5 years, there has been significant research interest in the intrinsic magnetic topological insulator family compounds MnBi2+2nTe4+3n (where n = 0, 1, 2 …). In particular, exfoliated thin films of MnBi2Te4 have led to numerous experimental breakthroughs, such as the quantum anomalous Hall effect, axion insulator phase and high-Chern number quantum Hall effect without Landau levels. However, despite extensive efforts, the energy gap of the topological surface states due to exchange magnetic coupling, which is a key feature of the characteristic band structure of the system, remains experimentally elusive. The electronic structure measured by using angle-resolved photoemission (ARPES) shows significant deviation from ab initio prediction and scanning tunneling spectroscopy measurements, making it challenging to understand the transport results based on the electronic structure. This paper reviews the measurements of the band structure of MnBi2+2nTe4+3n magnetic topological insulators using ARPES, focusing on the evolution of their electronic structures with temperature, surface and bulk doping and film thickness. The aim of the review is to construct a unified picture of the electronic structure of MnBi2+2nTe4+3n compounds and explore possible control of their topological properties.

Recent progress in MnBi2nTe3n+1 intrinsic magnetic topological insulators: crystal growth, magnetism and chemical disorder

The search for magnetic topological materials has been at the forefront of condensed matter research for their potential to host exotic states such as axion insulators, magnetic Weyl semimetals, Chern insulators, etc. To date, the MnBi2nTe3n+1 family is the only group of materials showcasing van der Waals-layered structures, intrinsic magnetism and non-trivial band topology without trivial bands at the Fermi level. The interplay between magnetism and band topology in this family has led to the proposal of various topological phenomena, including the quantum anomalous Hall effect, quantum spin Hall effect and quantum magnetoelectric effect. Among these, the quantum anomalous Hall effect has been experimentally observed at record-high temperatures, highlighting the unprecedented potential of this family of materials in fundamental science and technological innovation. In this paper, we provide a comprehensive review of the research progress in this intrinsic magnetic topological insulator family, with a focus on single-crystal growth, characterization of chemical disorder, manipulation of magnetism through chemical substitution and external pressure, and important questions that remain to be conclusively answered.

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.

Antiferromagnetic topological insulator with selectively gapped Dirac cones

Antiferromagnetic (AF) topological materials offer a fertile ground to explore a variety of quantum phenomena such as axion magnetoelectric dynamics and chiral Majorana fermions. To realize such intriguing states, it is essential to establish a direct link between electronic states and topology in the AF phase, whereas this has been challenging because of the lack of a suitable materials platform. Here we report the experimental realization of the AF topological-insulator phase in NdBi. By using micro-focused angle-resolved photoemission spectroscopy, we discovered contrasting surface electronic states for two types of AF domains; the surface having the out-of-plane component in the AF-ordering vector displays Dirac-cone states with a gigantic energy gap, whereas the surface parallel to the AF-ordering vector hosts gapless Dirac states despite the time-reversal-symmetry breaking. The present results establish an essential role of combined symmetry to protect massless Dirac fermions under the presence of AF order and widen opportunities to realize exotic phenomena utilizing AF topological materials.

Surface Electronic Structure Engineering of Manganese Bismuth Tellurides Guided by Micro-Focused Angle-Resolved Photoemission

Modification of the electronic structure of quantum matter by ad atom deposition allows for directed fundamental design of electronic and magnetic properties. This concept is utilized in the present study in order to tune the surface electronic structure of magnetic topological insulators based on MnBi2 Te4 . The topological bands of these systems are typically strongly electron-doped and hybridized with a manifold of surface states that place the salient topological states out of reach of electron transport and practical applications. In this study, micro-focused angle-resolved photoemission spectroscopy (microARPES) provides direct access to the termination-dependent dispersion of MnBi2 Te4 and MnBi4 Te7 during in situ deposition of rubidium atoms. The resulting band structure changes are found to be highly complex, encompassing coverage-dependent ambipolar doping effects, removal of surface state hybridization, and the collapse of a surface state band gap. In addition, doping-dependent band bending is found to give rise to tunable quantum well states. This wide range of observed electronic structure modifications can provide new ways to exploit the topological states and the rich surface electronic structures of manganese bismuth tellurides.

Anomalous Landau quantization in intrinsic magnetic topological insulators

The intrinsic magnetic topological insulator, Mn(Bi1-xSbx)2Te4, has been identified as a Weyl semimetal with a single pair of Weyl nodes in its spin-aligned strong-field configuration. A direct consequence of the Weyl state is the layer dependent Chern number, [Formula: see text]. Previous reports in MnBi2Te4 thin films have shown higher [Formula: see text] states either by increasing the film thickness or controlling the chemical potential. A clear picture of the higher Chern states is still lacking as data interpretation is further complicated by the emergence of surface-band Landau levels under magnetic fields. Here, we report a tunable layer-dependent [Formula: see text] = 1 state with Sb substitution by performing a detailed analysis of the quantization states in Mn(Bi1-xSbx)2Te4 dual-gated devices-consistent with calculations of the bulk Weyl point separation in the doped thin films. The observed Hall quantization plateaus for our thicker Mn(Bi1-xSbx)2Te4 films under strong magnetic fields can be interpreted by a theory of surface and bulk spin-polarised Landau level spectra in thin film magnetic topological insulators.

Tuning electronic and phononic states with hidden order in disordered crystals

Disorder in crystals is rarely random, and instead involves local correlations whose presence and nature are hidden from conventional crystallographic probes. This hidden order can sometimes be controlled, but its importance for physical properties of materials is not well understood. Using simple models for electronic and interatomic interactions, we show how crystals with identical average structures but different types of hidden order can have very different electronic and phononic band structures. Increasing the strength of local correlations within hidden-order states can open band gaps and tune mode (de)localisation-both mechanisms allowing for fundamental changes in physical properties without long-range symmetry breaking. Taken together, our results demonstrate how control over hidden order offers a new mechanism for tuning material properties, orthogonal to the conventional principles of (ordered) structure/property relationships.

Intrinsic and extrinsic dopings in epitaxial films MnBi2Te4

The intrinsic antiferromagnetic topological insulator MnBi₂Te₄and members of its family have been the subject of theoretical and experimental research, which has revealed the presence of a variety of defects and disorders that are crucial in determining the topological and magnetic properties. This also brings about challenges in realizing the quantum states like the quantum anomalous Hall and the axion insulator states. Here, utilizing cryogenic magnetoelectric transport and magnetic measurements, we systematically investigate the effects arising from intrinsic doping by antisite defects and extrinsic doping by Sb in MnBi₂Te₄epitaxial films grown by molecular beam epitaxy. We demonstrate that the nonequilibrium condition in epitaxy allows a wide growth window for optimizing the crystalline quality and defect engineering. While the intrinsic antisite defects caused by the intermixing between Bi and Mn can be utilized to tune the Fermi level position as evidenced by a p-to-n conductivity transition, the extrinsic Sb-doping not only compensates for this doping effect but also modifies the magnetism and topology of the film, during which a topological phase transition is developed. Conflicting reports from the theoretical calculations and experimental measurements in bulk crystals versus epitaxial films are addressed, which highlights the intimate correlation between the magnetism and topology as well as the balance between the Fermi-level positioning and defect control. The present study provides an experimental support for the epitaxial growth of the intrinsic topological insulator and underlines that the topology, magnetism, and defect engineering should be revisited for enabling a steady and reliable film production.

Intermixing-Driven Surface and Bulk Ferromagnetism in the Quantum Anomalous Hall Candidate MnBi6 Te10

The recent realizations of the quantum anomalous Hall effect (QAHE) in MnBi₂ Te₄ and MnBi₄ Te₇ benchmark the (MnBi₂ Te₄ )(Bi₂ Te₃ )_n family as a promising hotbed for further QAHE improvements. The family owes its potential to its ferromagnetically (FM) ordered MnBi₂ Te₄ septuple layers (SLs). However, the QAHE realization is complicated in MnBi₂ Te₄ and MnBi₄ Te₇ due to the substantial antiferromagnetic (AFM) coupling between the SLs. An FM state, advantageous for the QAHE, can be stabilized by interlacing the SLs with an increasing number n of Bi₂ Te₃ quintuple layers (QLs). However, the mechanisms driving the FM state and the number of necessary QLs are not understood, and the surface magnetism remains obscure. Here, robust FM properties in MnBi₆ Te₁₀ (n = 2) with T_c ≈ 12 K are demonstrated and their origin is established in the Mn/Bi intermixing phenomenon by a combined experimental and theoretical study. The measurements reveal a magnetically intact surface with a large magnetic moment, and with FM properties similar to the bulk. This investigation thus consolidates the MnBi₆ Te₁₀ system as perspective for the QAHE at elevated temperatures.

Topological Phase Transitions Driven by Sn Doping in (Mn1−xSnx)Bi2Te4

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 its topologically nontrivial nature and a number of fundamental phenomena. At the same time, the possibility to control the electronic and magnetic properties of this system can provide new effective ways for its application in devices. One of the approaches to manipulate MnBi2Te4 properties is the partial substitution of magnetic atoms in the compound with atoms of non-magnetic elements, which inevitably affect the interplay of magnetism and band topology in the system. In this work, we have carried out theoretical modelling of changes in the electronic structure that occur as a result of increasing the concentration of Sn atoms at Mn positions in the (Mn1−xSnx)Bi2Te4 compound both using Korringa–Kohn–Rostoker (KKR) Green’s function method as well as the widespread approach of using supercells with impurity in DFT methods. The calculated band structures were also compared with those experimentally measured by angle-resolved photoelectron spectroscopy (ARPES) for samples with x values of 0, 0.19, 0.36, 0.52 and 0.86. We assume that the complex hybridization of Te-pz and Bi-pz orbitals with Sn and Mn ones leads to a non-linear dependence of band gap on Sn content in Mn positions, which is characterized by a plateau with a zero energy gap at some concentration values, suggesting possible topological phase transitions in the system.

Large Exchange Bias Effect and Coverage-Dependent Interfacial Coupling in CrI3/MnBi2Te4 van der Waals Heterostructures

Igniting interface magnetic ordering of magnetic topological insulators by building a van der Waals heterostructure can help to reveal novel quantum states and design functional devices. Here, we observe an interesting exchange bias effect, indicating successful interfacial magnetic coupling, in CrI₃/MnBi₂Te₄ ferromagnetic insulator/antiferromagnetic topological insulator (FMI/AFM-TI) heterostructure devices. The devices originally exhibit a negative exchange bias field, which decays with increasing temperature and is unaffected by the back-gate voltage. When we change the device configuration to be half-covered by CrI₃, the exchange bias becomes positive with a very large exchange bias field exceeding 300 mT. Such sensitive manipulation is explained by the competition between the FM and AFM coupling at the interface of CrI₃ and MnBi₂Te₄, pointing to coverage-dependent interfacial magnetic interactions. Our work will facilitate the development of topological and antiferromagnetic devices.

Delicate Ferromagnetism in MnBi6Te10

Tailoring magnetic orders in topological insulators is critical to the realization of topological quantum phenomena. An outstanding challenge is to find a material where atomic defects lead to tunable magnetic orders while maintaining a nontrivial topology. Here, by combining magnetization measurements, angle-resolved photoemission spectroscopy, and transmission electron microscopy, we reveal disorder-enabled, tunable magnetic ground states in MnBi₆Te₁₀. In the ferromagnetic phase, an energy gap of 15 meV is resolved at the Dirac point on the MnBi₂Te₄ termination. In contrast, antiferromagnetic MnBi₆Te₁₀ exhibits gapless topological surface states on all terminations. Transmission electron microscopy and magnetization measurements reveal substantial Mn vacancies and Mn migration in ferromagnetic MnBi₆Te₁₀. We provide a conceptual framework where a cooperative interplay of these defects drives a delicate change of overall magnetic ground state energies and leads to tunable magnetic topological orders. Our work provides a clear pathway for nanoscale defect-engineering toward the realization of topological quantum phases.

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.

Large Exchange Coupling Between Localized Spins and Topological Bands in MnBi2 Te4

Magnetism in topological materials creates phases exhibiting quantized transport phenomena with potential technological applications. The emergence of such phases relies on strong interaction between localized spins and the topological bands, and the consequent formation of an exchange gap. However, this remains experimentally unquantified in intrinsic magnetic topological materials. Here, this interaction is quantified in MnBi₂ Te₄ , a topological insulator with intrinsic antiferromagnetism. This is achieved by optically exciting Bi-Te p states comprising the bulk topological bands and interrogating the consequent Mn 3d spin dynamics, using a multimodal ultrafast approach. Ultrafast electron scattering and magneto-optic measurements show that the p states demagnetize via electron-phonon scattering at picosecond timescales. Despite being energetically decoupled from the optical excitation, the Mn 3d spins, probed by resonant X-ray scattering, are observed to disorder concurrently with the p spins. Together with atomistic simulations, this reveals that the exchange coupling between localized spins and the topological bands is at least 100 times larger than the superexchange interaction, implying an optimal exchange gap of at least 25 meV in the surface states. By quantifying this exchange coupling, this study validates the materials-by-design strategy of utilizing localized magnetic order to manipulate topological phases, spanning static to ultrafast timescales.

Two-Dimensional Van Der Waals Topological Materials: Preparation, Properties, and Device Applications

Over the past decade, 2D van der Waals (vdW) topological materials (TMs), including topological insulators and topological semimetals, which combine atomically flat 2D layers and topologically nontrivial band structures, have attracted increasing attention in condensed-matter physics and materials science. These easily cleavable and integrated TMs provide the ideal platform for exploring topological physics in the 2D limit, where new physical phenomena may emerge, and represent a potential to control and investigate exotic properties and device applications in nanoscale topological phases. However, multifaced efforts are still necessary, which is the prerequisite for the practical application of 2D vdW TMs. Herein, this review focuses on the preparation, properties, and device applications of 2D vdW TMs. First, three common preparation strategies for 2D vdW TMs are summarized, including single crystal exfoliation, chemical vapor deposition, and molecular beam epitaxy. Second, the origin and regulation of various properties of 2D vdW TMs are introduced, involving electronic properties, transport properties, optoelectronic properties, thermoelectricity, ferroelectricity, and magnetism. Third, some device applications of 2D vdW TMs are presented, including field-effect transistors, memories, spintronic devices, and photodetectors. Finally, some significant challenges and opportunities for the practical application of 2D vdW TMs in 2D topological electronics are briefly addressed.

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.

Doping-driven topological polaritons in graphene/α-MoO3 heterostructures

Control over charge carrier density provides an efficient way to trigger phase transitions and modulate the optoelectronic properties of materials. This approach can also be used to induce topological transitions in the optical response of photonic systems. Here we report a topological transition in the isofrequency dispersion contours of hybrid polaritons supported by a two-dimensional heterostructure consisting of graphene and α-phase molybdenum trioxide. By chemically changing the doping level of graphene, we observed that the topology of polariton isofrequency surfaces transforms from open to closed shapes as a result of doping-dependent polariton hybridization. Moreover, when the substrate was changed, the dispersion contour became dominated by flat profiles at the topological transition, thus supporting tunable diffractionless polariton propagation and providing local control over the optical contour topology. We achieved subwavelength focusing of polaritons down to 4.8% of the free-space light wavelength by using a 1.5-μm-wide silica substrate as an in-plane lens. Our findings could lead to on-chip applications in nanoimaging, optical sensing and manipulation of energy transfer at the nanoscale.

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.

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.

Observation of Ultrastrong Coupling between Substrate and the Magnetic Topological Insulator MnBi2Te4

The intrinsic magnetic topological insulator MnBi₂Te₄ has attracted significant interest recently as a promising platform for exploring exotic quantum phenomena. Here we report that, when atomically thin MnBi₂Te₄ is deposited on a substrate such as silicon oxide or gold, there is a very strong mechanical coupling between the atomic layer and the supporting substrate. This is manifested as an intense low-frequency breathing Raman mode that is present even for monolayer MnBi₂Te₄. Interestingly, this coupling turns out to be stronger than the interlayer coupling between the MnBi₂Te₄ atomic layers. We further found that these low-energy breathing modes are highly sensitive to sample degradation, and they become drastically weaker upon ambient air exposure. This is in contrast to the higher energy optical phonon modes which are much more robust, suggesting that the low-energy Raman modes found here can be an effective indicator of sample quality.

Defect-gradient-induced Rashba effect in van der Waals PtSe2 layers

Defect engineering is one of the key technologies in materials science, enriching the modern semiconductor industry and providing good test-beds for solid-state physics. While homogenous doping prevails in conventional defect engineering, various artificial defect distributions have been predicted to induce desired physical properties in host materials, especially associated with symmetry breakings. Here, we show layer-by-layer defect-gradients in two-dimensional PtSe₂ films developed by selective plasma treatments, which break spatial inversion symmetry and give rise to the Rashba effect. Scanning transmission electron microscopy analyses reveal that Se vacancies extend down to 7 nm from the surface and Se/Pt ratio exhibits linear variation along the layers. The Rashba effect induced by broken inversion symmetry is demonstrated through the observations of nonreciprocal transport behaviors and first-principles density functional theory calculations. Our methodology paves the way for functional defect engineering that entangles spin and momentum of itinerant electrons for emerging electronic applications.

Materials with strong Rashba-type spin-orbit coupling hold promise for spintronic applications and the investigation of topological phases of matter. Here, the authors report a method to generate layer-by-layer defect gradients in a van der Waals material, inducing broken spatial inversion symmetry and Rashba effect in the engineered layers.

Topological surface currents accessed through reversible hydrogenation of the three-dimensional bulk

Hydrogen, the smallest and most abundant element in nature, can be efficiently incorporated within a solid and drastically modify its electronic and structural state. In most semiconductors interstitial hydrogen binds to defects and is known to be amphoteric, namely it can act either as a donor (H⁺) or an acceptor (H⁻) of charge, nearly always counteracting the prevailing conductivity type. Here we demonstrate that hydrogenation resolves an outstanding challenge in chalcogenide classes of three-dimensional (3D) topological insulators and magnets — the control of intrinsic bulk conduction that denies access to quantum surface transport, imposing severe thickness limits on the bulk. With electrons donated by a reversible binding of H⁺ ions to Te(Se) chalcogens, carrier densities are reduced by over 10²⁰cm⁻³, allowing tuning the Fermi level into the bulk bandgap to enter surface/edge current channels without altering carrier mobility or the bandstructure. The hydrogen-tuned topological nanostructures are stable at room temperature and tunable disregarding bulk size, opening a breadth of device platforms for harnessing emergent topological states.

Hydrogen can be incorporated within a solid and drastically modify its electronic and structural state. Here, the authors report reversible binding of H⁺ ions to chalcogens in the Bi₂Te₃ class of topological insulators and magnets, allowing Fermi level tuning into the bulk gap without altering carrier mobility or the bandstructure.

Interlayer magnetophononic coupling in MnBi2Te4

The emergence of magnetism in quantum materials creates a platform to realize spin-based applications in spintronics, magnetic memory, and quantum information science. A key to unlocking new functionalities in these materials is the discovery of tunable coupling between spins and other microscopic degrees of freedom. We present evidence for interlayer magnetophononic coupling in the layered magnetic topological insulator MnBi₂Te₄. Employing magneto-Raman spectroscopy, we observe anomalies in phonon scattering intensities across magnetic field-driven phase transitions, despite the absence of discernible static structural changes. This behavior is a consequence of a magnetophononic wave-mixing process that allows for the excitation of zone-boundary phonons that are otherwise ‘forbidden’ by momentum conservation. Our microscopic model based on density functional theory calculations reveals that this phenomenon can be attributed to phonons modulating the interlayer exchange coupling. Moreover, signatures of magnetophononic coupling are also observed in the time domain through the ultrafast excitation and detection of coherent phonons across magnetic transitions. In light of the intimate connection between magnetism and topology in MnBi₂Te₄, the magnetophononic coupling represents an important step towards coherent on-demand manipulation of magnetic topological phases.

Tunable coupling between magnetism and the lattice is important for on-demand manipulation of magnetic phases. Here, the authors demonstrate that lattice vibrations can coherently modulate the interlayer magnetic exchange coupling in the magnetic topological insulator MnBi₂Te₄.

Understanding Heterogeneities in Quantum Materials

Quantum materials are usually heterogeneous, with structural defects, impurities, surfaces, edges, interfaces, and disorder. These heterogeneities are sometimes viewed as liabilities within conventional systems; however, their electronic and magnetic structures often define and affect the quantum phenomena such as coherence, interaction, entanglement, and topological effects in the host system. Therefore, a critical need is to understand the roles of heterogeneities in order to endow materials with new quantum functions for energy and quantum information science applications. In this article, several representative examples are reviewed on the recent progress in connecting the heterogeneities to the quantum behaviors of real materials. Specifically, three intertwined topic areas are assessed: i) Reveal the structural, electronic, magnetic, vibrational, and optical degrees of freedom of heterogeneities. ii) Understand the effect of heterogeneities on the behaviors of quantum states in host material systems. iii) Control heterogeneities for new quantum functions. This progress is achieved by establishing the atomistic-level structure-property relationships associated with heterogeneities in quantum materials. The understanding of the interactions between electronic, magnetic, photonic, and vibrational states of heterogeneities enables the design of new quantum materials, including topological matter and quantum light emitters based on heterogenous 2D materials.

Soft-Magnetic Skyrmions Induced by Surface-State Coupling in an Intrinsic Ferromagnetic Topological Insulator Sandwich Structure

A magnetic skyrmion induced on a ferromagnetic topological insulator (TI) is a real-space manifestation of the chiral spin texture in the momentum space and can be a carrier for information processing by manipulating it in tailored structures. Here, a sandwich structure containing two layers of a self-assembled ferromagnetic septuple-layer TI, Mn(Bi_1-xSb_x)₂Te₄ (MnBST), separated by quintuple layers of TI, (Bi_1-xSb_x)₂Te₃ (BST), is fabricated and skyrmions are observed through the topological Hall effect in an intrinsic magnetic topological insulator for the first time. The thickness of BST spacer layer is crucial in controlling the coupling between the gapped topological surface states in the two MnBST layers to stabilize the skyrmion formation. The homogeneous, highly ordered arrangement of the Mn atoms in the septuple-layer MnBST leads to a strong exchange interaction therein, which makes the skyrmions "soft magnetic". This would open an avenue toward a topologically robust rewritable magnetic memory.

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.

2D Bi2Se3 materials for optoelectronics

2D layered materials with diverse exciting properties have recently attracted tremendous interest in the scientific community. Layered topological insulator Bi2Se3 comes into the spotlight as an exotic state of quantum matter with insulating bulk states and metallic Dirac-like surface states. Its unique crystal and electronic structure offer attractive features such as broadband optical absorption, thickness-dependent surface bandgap and polarization-sensitive photoresponse, which enable 2D Bi2Se3 to be a promising candidate for optoelectronic applications. Herein, we present a comprehensive summary on the recent advances of 2D Bi2Se3 materials. The structure and inherent properties of Bi2Se3 are firstly described and its preparation approaches (i.e., solution synthesis and van der Waals epitaxy growth) are then introduced. Moreover, the optoelectronic applications of 2D Bi2Se3 materials in visible-infrared detection, terahertz detection, and opto-spintronic device are discussed in detail. Finally, the challenges and prospects in this field are expounded on the basis of current development.

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.

Light-Tunable Surface State and Hybridization Gap in Magnetic Topological Insulator MnBi8Te13

MnBi₈Te₁₃ is an intrinsic ferromagnetic (FM) topological insulator with different complex surface terminations. Resolving the electronic structures of different termination surfaces and manipulation of the electronic state are important. Here, by using micrometer spot time- and angle-resolved photoemission spectroscopy (μ-TrARPES), we resolve the electronic structures and reveal the ultrafast dynamics upon photoexcitation. Photoinduced filling of the surface state hybridization gap is observed for the Bi₂Te₃ quintuple layer directly above MnBi₂Te₄ accompanied by a nontrivial shift of the surface state, suggesting light-tunable interlayer interaction. Relaxation of photoexcited electrons and holes is observed within 1-2 ps. Our work reveals photoexcitation as a potential control knob for tailoring the interlayer interaction and surface state of MnBi₈Te₁₃.

Pressure-Tuned Intralayer Exchange in Superlattice-Like MnBi2Te4/(Bi2Te3)n Topological Insulators

The magnetic structures of MnBi₂Te₄(Bi₂Te₃)_n can be manipulated by tuning the interlayer coupling via the number of Bi₂Te₃ spacer layers n, while the intralayer ferromagnetic (FM) exchange coupling is considered too robust to control. By applying hydrostatic pressure up to 3.5 GPa, we discover opposite responses of magnetic properties for n = 1 and 2. MnBi₄Te₇ stays at A-type antiferromagnetic (AFM) phase with a decreasing Néel temperature and an increasing saturation field. In sharp contrast, MnBi₆Te₁₀ experiences a phase transition from A-type AFM to a quasi-two-dimensional FM state with a suppressed saturation field under pressure. First-principles calculations reveal the essential role of intralayer exchange coupling from lattice compression in determining these magnetic properties. Such magnetic phase transition is also observed in 20% Sb-doped MnBi₆Te₁₀ because of the in-plane lattice compression.

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.

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.

Multiple Magnetic Topological Phases in Bulk van der Waals Crystal MnSb_{4}Te_{7}

The magnetic van der Waals crystals MnBi_{2}Te_{4}/(Bi_{2}Te_{3})_{n} have drawn significant attention due to their rich topological properties and the tunability by external magnetic field. Although the MnBi_{2}Te_{4}/(Bi_{2}Te_{3})_{n} family have been intensively studied in the past few years, their close relatives, the MnSb_{2}Te_{4}/(Sb_{2}Te_{3})_{n} family, remain much less explored. In this work, combining magnetotransport measurements, angle-resolved photoemission spectroscopy, and first principles calculations, we find that MnSb_{4}Te_{7}, the n=1 member of the MnSb_{2}Te_{4}/(Sb_{2}Te_{3})_{n} family, is a magnetic topological system with versatile topological phases that can be manipulated by both carrier doping and magnetic field. Our calculations unveil that its A-type antiferromagnetic (AFM) ground state stays in a Z_{2} AFM topological insulator phase, which can be converted to an inversion-symmetry-protected axion insulator phase when in the ferromagnetic (FM) state. Moreover, when this system in the FM phase is slightly carrier doped on either the electron or hole side, it becomes a Weyl semimetal with multiple Weyl nodes in the highest valence bands and lowest conduction bands, which are manifested by the measured notable anomalous Hall effect. Our work thus introduces a new magnetic topological material with different topological phases that are highly tunable by carrier doping or magnetic field.

Intrinsic magnetic topological insulators

Introducing magnetism into topological insulators breaks time-reversal symmetry, and the magnetic exchange interaction can open a gap in the otherwise gapless topological surface states. This allows various novel topological quantum states to be generated, including the quantum anomalous Hall effect (QAHE) and axion insulator states. Magnetic doping and magnetic proximity are viewed as being useful means of exploring the interaction between topology and magnetism. However, the inhomogeneity of magnetic doping leads to complicated magnetic ordering and small exchange gaps, and consequently the observed QAHE appears only at ultralow temperatures. Therefore, intrinsic magnetic topological insulators are highly desired for increasing the QAHE working temperature and for investigating topological quantum phenomena further. The realization and characterization of such systems are essential for both fundamental physics and potential technical revolutions. This review summarizes recent research progress in intrinsic magnetic topological insulators, focusing mainly on the antiferromagnetic topological insulator MnBi₂Te₄ and its family of materials.

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van der Waals material MnBi₂Te₄ is an intrinsic antiferromagnetic topological insulator

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Under moderate magnetic field, MnBi₂Te₄ may become a magnetic Weyl semimetal

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MnBi₂Te₄ and its family of materials have brought great progress in studying novel topological quantum states

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Quantum anomalous Hall effect above the liquid-nitrogen temperature can be expected in MnBi₂Te₄-related systems

Topological Magnetic Materials of the (MnSb2Te4)·(Sb2Te3)n van der Waals Compounds Family

Using density functional theory, we propose the (MnSb₂Te₄)·(Sb₂Te₃)_n family of stoichiometric van der Waals compounds that harbor multiple topologically nontrivial magnetic phases. In the ground state, the first three members of the family (n = 0, 1, 2) are 3D antiferromagnetic topological insulators, while for n ≥ 3 a special phase is formed, in which a nontrivial topological order coexists with a partial magnetic disorder in the system of the decoupled 2D ferromagnets, whose magnetizations point randomly along the third direction. Furthermore, due to a weak interlayer exchange coupling, these materials can be field-driven into the FM Weyl semimetal (n = 0) or FM axion insulator states (n ≥ 1). Finally, in two dimensions, we reveal these systems to show intrinsic quantum anomalous Hall and AFM axion insulator states, as well as quantum Hall state, achieved under external magnetic field. Our results demonstrate that MnSb₂Te₄ is not topologically trivial as was previously believed that opens possibilities of realization of a wealth of topologically nontrivial states in the (MnSb₂Te₄)·(Sb₂Te₃)_n family.

Orbital Complexity in Intrinsic Magnetic Topological Insulators MnBi_{4}Te_{7} and MnBi_{6}Te_{10}

Using angle-resolved photoelectron spectroscopy (ARPES), we investigate the surface electronic structure of the magnetic van der Waals compounds MnBi_{4}Te_{7} and MnBi_{6}Te_{10}, the n=1 and 2 members of a modular (Bi_{2}Te_{3})_{n}(MnBi_{2}Te_{4}) series, which have attracted recent interest as intrinsic magnetic topological insulators. Combining circular dichroic, spin-resolved and photon-energy-dependent ARPES measurements with calculations based on density functional theory, we unveil complex momentum-dependent orbital and spin textures in the surface electronic structure and disentangle topological from trivial surface bands. We find that the Dirac-cone dispersion of the topologial surface state is strongly perturbed by hybridization with valence-band states for Bi_{2}Te_{3}-terminated surfaces but remains preserved for MnBi_{2}Te_{4}-terminated surfaces. Our results firmly establish the topologically nontrivial nature of these magnetic van der Waals materials and indicate that the possibility of realizing a quantized anomalous Hall conductivity depends on surface termination.

Persistent surface states with diminishing gap in MnBi2Te4/Bi2Te3 superlattice antiferromagnetic topological insulator

Magnetic topological quantum materials (TQMs) provide a fertile ground for the emergence of fascinating topological magneto-electric effects. Recently, the discovery of intrinsic antiferromagnetic (AFM) topological insulator MnBi₂Te₄ that could realize quantized anomalous Hall effect and axion insulator phase ignited intensive study on this family of TQM compounds. Here, we investigated the AFM compound MnBi₄Te₇ where Bi₂Te₃ and MnBi₂Te₄ layers alternate to form a superlattice. Using spatial- and angle-resolved photoemission spectroscopy, we identified ubiquitous (albeit termination dependent) topological electronic structures from both Bi₂Te₃ and MnBi₂Te₄ terminations. Unexpectedly, while the bulk bands show strong temperature dependence correlated with the AFM transition, the topological surface states with a diminishing gap show negligible temperature dependence across the AFM transition. Together with the results of its sister compound MnBi₂Te₄, we illustrate important aspects of electronic structures and the effect of magnetic ordering in this family of magnetic TQMs.

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.

Fabrication of a novel magnetic topological heterostructure and temperature evolution of its massive Dirac cone

Materials that possess nontrivial topology and magnetism is known to exhibit exotic quantum phenomena such as the quantum anomalous Hall effect. Here, we fabricate a novel magnetic topological heterostructure Mn₄Bi₂Te₇/Bi₂Te₃ where multiple magnetic layers are inserted into the topmost quintuple layer of the original topological insulator Bi₂Te₃. A massive Dirac cone (DC) with a gap of 40–75 meV at 16 K is observed. By tracing the temperature evolution, this gap is shown to gradually decrease with increasing temperature and a blunt transition from a massive to a massless DC occurs around 200–250 K. Structural analysis shows that the samples also contain MnBi₂Te₄/Bi₂Te₃. Magnetic measurements show that there are two distinct Mn components in the system that corresponds to the two heterostructures; MnBi₂Te₄/Bi₂Te₃ is paramagnetic at 6 K while Mn₄Bi₂Te₇/Bi₂Te₃ is ferromagnetic with a negative hysteresis (critical temperature  ~20 K). This novel heterostructure is potentially important for future device applications.

Magnetic topological heterostructures are promising devices to manipulate emergent quantum effects. Here, Hirahara et al. fabricate a novel magnetic topological heterostructure with a massive Dirac cone which becomes a massless one tuned by temperature.

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}.