Topology-Engineered Orbital Hall Effect in Two-Dimensional Ferromagnets

Recent advances in the manipulation of the orbital angular momentum (OAM) within the paradigm of orbitronics presents a promising avenue for the design of future electronic devices. In this context, the recently observed orbital Hall effect (OHE) occupies a special place. Here, focusing on both the second-order topological and quantum anomalous Hall insulators in two-dimensional ferromagnets, we demonstrate that topological phase transitions present an efficient and straightforward way to engineer the OHE, where the OAM distribution can be controlled by the nature of the band inversion. Using first-principles calculations, we identify Janus RuBrCl and three septuple layers of MnBi2Te4 as experimentally feasible examples of the proposed mechanism of OHE engineering by topology. With our work, we open up new possibilities for innovative applications in topological spintronics and orbitronics.

Magnetization direction-controlled topological band structure in TlTiX (X = Si, Ge) monolayers

The quantum anomalous Hall (QAH) insulator is a vital material for the investigation of emerging topological quantum effects, but its extremely low working temperature limits experiments. Apart from the temperature challenge, effective regulation of the topological state of QAH insulators is another crucial concern. Here, by first-principles calculations, we find a family of stable two-dimensional materials TlTiX (X = Si, Ge) are large-gap QAH insulators. Their extremely robust ferromagnetic (FM) ground states are determined by both the direct- and super-exchange FM coupling. In the absence of spin-orbit coupling (SOC), there exist a spin-polarized crossing point located at eachKandK' points, respectively. The SOC effect results in the spontaneous breaking ofC2symmetry and introduces a mass term, giving rise to a QAH state with sizable band gap. The tiny magnetocrystalline anisotropic energy (MAE) implies that an external magnetic field can be easily used to align magnetization deviating fromzdirection to thex-yplane, thereby leading to a transformation of the electronic state from the QAH state to the Weyl half semimetals state, which indicate monolayers TlTiX (X = Si, Ge) exhibit a giant magneto topological band effect. Finally, we examined the impact of stress on the band gap and MAE, which underlies the reasons for the giant magneto topological band effect attributed to the crystal field. These findings present novel prospects for the realization of large-gap QAH states with the characteristic of easily modifiable topological states.

Tunable quantum anomalous Hall effects in ferromagnetic van der Waals heterostructures

The quantum anomalous Hall effect (QAHE) has unique advantages in topotronic applications, but it is still challenging to realize the QAHE with tunable magnetic and topological properties for building functional devices. Through systematic first-principles calculations, we predict that the in-plane magnetization induced QAHE with Chern numbers C = ±1 and the out-of-plane magnetization induced QAHE with high Chern numbers C = ±3 can be realized in a single material candidate, which is composed of van der Waals (vdW) coupled Bi and MnBi2Te4 monolayers. The switching between different phases of QAHE can be controlled in multiple ways, such as applying strain or (weak) magnetic field or twisting the vdW materials. The prediction of an experimentally available material system hosting robust, highly tunable QAHE will stimulate great research interest in the field. Our work opens a new avenue for the realization of tunable QAHE and provides a practical material platform for the development of topological electronics.

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.

Orbital-Selectivity-Induced Robust Quantum Anomalous Hall Effect in Hund's Metals MgFeP

Ferromagnetic (FM) states with high Curie temperatures (Tc) and strong spin-orbit coupling (SOC) are indispensable for the long-sought room-temperature quantum anomalous Hall (QAH) effects. Here, we propose a two-dimensional (2D) iron-based monolayer MgFeP that exhibits a notably high FM Tc (about 1525 K) along with exceptional structural stabilities. The unique multiorbital nature in MgFeP, where localized d x 2 - y 2 and dxz/yz orbitals coexist with itinerant dxy and dz2 orbitals, renders the monolayer a Hund's metal and in an orbital-selective Mott phase (OSMP). This OSMP triggers an FM double exchange mechanism, rationalizing the high Tc in the Hund's metal. This material transitions to a QAH insulator upon consideration of the SOC effect. By leveraging orbital selectivity, the QAH band gap can be enlarged by more than two times (to 137 meV). Our findings showcase Hund's metals as a promising material platform for realizing high-performance quantum topological electronic devices.

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.

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.

Chern-Insulator Phase in Antiferromagnets

The long-sought Chern insulators that manifest a quantum anomalous Hall effect are typically considered to occur in ferromagnets. Here, we theoretically predict the realizabilities of Chern insulators in antiferromagnets, in which the magnetic sublattices are connected by symmetry operators enforcing zero net magnetic moment. Our symmetry analysis provides comprehensive magnetic layer point groups that allow antiferromagnetic (AFM) Chern insulators, revealing that an in-plane magnetic configuration is required. Followed by first-principles calculations, such design principles naturally lead to two categories of material candidates, exemplified by monolayer RbCr4S8 and bilayer Mn3Sn with collinear and noncollinear AFM orders, respectively. We further show that the Chern number could be tuned by slight ferromagnetic canting as an effective pivot. Our work elucidates the nature of the Chern-insulator phase in AFM systems, paving a new avenue for designing quantum anomalous Hall insulators with the integration of nondissipative transport and the promising advantages of the AFM order.

Spin-Chirality-Driven Quantum Anomalous and Quantum Topological Hall Effects in Chiral Magnets

The quantum anomalous Hall effect (QAHE) is a highly researched topic in condensed matter physics due to its ability to enable dissipationless transport. Previous studies have mainly focused on the ferromagnetic QAHE, which arises from the combination of collinear ferromagnetism and two-dimensional (2D) Z₂ topological insulator phases. In our study, we demonstrate the emergence of the spin-chirality-driven QAHE and the quantum topological Hall effect (QTHE) by sandwiching a 2D Z₂ topological insulator between two chiral kagome antiferromagnetic single-layers synthesized experimentally. The QAHE is surprisingly realized with fully compensated noncollinear antiferromagnetism in contrast to conventional collinear ferromagnetism. The Chern number can be regulated periodically with the interplay between vector- and scalar-spin chiralities, and the QAHE emerges even without spin-orbit coupling, indicating the rare QTHE. Our findings open a new avenue for realizing antiferromagnetic quantum spintronics based on the unconventional mechanisms from chiral spin textures.

Enhanced Quantum Anomalous Hall Effect with an Active Capping Layer

The quantum anomalous Hall effect (QAHE) was discovered a decade ago but is still not utilized beyond a handful of research groups, due to numerous limitations such as extremely low temperature, electric-field-effect gating requirement, small sample sizes, and environmental aging effect. Here, we present a robust platform that provides effective solutions to these problems. Specifically, on this platform, we observe QAH signatures at record-high temperatures, with a Hall conductance of 1.00 e²/h at 2.0 K, 0.98 e²/h at 4.2 K, and 0.92 e²/h at 10 K, on centimeter-scale substrates, without electric-field-effect gating. The key ingredient is an active CrO_x capping layer, which substantially boosts the ferromagnetism while suppressing environmental degradation. With this development, QAHE will now be accessible to much broader applications than before.

Experimental Demonstration of a Magnetically Induced Warping Transition in a Topological Insulator Mediated by Rare-Earth Surface Dopants

Magnetic topological insulators constitute a novel class of materials whose topological surface states (TSSs) coexist with long-range ferromagnetic order, eventually breaking time-reversal symmetry. The subsequent bandgap opening is predicted to co-occur with a distortion of the TSS warped shape from hexagonal to trigonal. We demonstrate such a transition by means of angle-resolved photoemission spectroscopy on the magnetically rare-earth (Er and Dy) surface-doped topological insulator Bi₂Se₂Te. Signatures of the gap opening are also observed. Moreover, increasing the dopant coverage results in a tunable p-type doping of the TSS, thereby allowing for a gradual tuning of the Fermi level toward the magnetically induced bandgap. A theoretical model where a magnetic Zeeman out-of-plane term is introduced in the Hamiltonian governing the TSS rationalizes these experimental results. Our findings offer new strategies to control magnetic interactions with TSSs and open up viable routes for the realization of the quantum anomalous Hall effect.

Floquet Engineering of Nonequilibrium Valley-Polarized Quantum Anomalous Hall Effect with Tunable Chern Number

Here, we propose that Floquet engineering offers a strategy to realize the nonequilibrium quantum anomalous Hall effect (QAHE) with tunable Chern number. Using first-principles calculations and Floquet theorem, we unveil that QAHE related to valley polarization (VP-QAHE) is formed from the hybridization of Floquet sidebands in the two-dimensional family MSi₂Z₄ (M = Mo, W, V; Z = N, P, As) by irradiating circularly polarized light (CPL). Through the tuning of frequency, intensity, and handedness of CPL, the Chern number of VP-QAHE is highly tunable and up to C = ±4, which attributes to light-induced trigonal warping and multiple-band inversion at different valleys. The chiral edge states and quantized plateau of Hall conductance are visible inside the global band gap, thereby facilitating the experimental measurement. Our work not only establishes Floquet engineering of nonequilibrium VP-QAHE with tunable Chern number in realistic materials but also provides an avenue to explore emergent topological phases under light irradiation.

Electrically Tunable Topological Phase Transition in van der Waals Heterostructures

The realization and control of the quantum anomalous Hall (QAH) effect are highly desirable for the development of spintronic and quantum devices. In this work, we propose a van der Waals (vdW) heterostructure of ultrathin MnBi₂Se₄ and Bi₂Se₃ layers and demonstrate that it is an excellent tunable QAH platform by using model Hamiltonian and density functional theory simulations. Its band gap closes and reopens as external electric field increases, manifesting a novel topological phase transition with an electric field of ∼0.06 V/Å. This heterostructure has other major advantageous, such as large topological band gap, perpendicular magnetization, and strong ferromagnetic ordering. Our work provides clear physical insights and suggests a new strategy for experimental realization and control of the QAH effect in real materials.

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.

Controllable Chirality and Band Gap of Quantum Anomalous Hall Insulators

Finding guiding principles to optimize properties of quantum anomalous Hall (QAH) insulators is of pivotal importance to fundamental science and applications. Here, we build a first-principles QAH material database of chirality and band gap, explore microscopic mechanisms determining the QAH material properties, and obtain a general physical picture that can help researchers comprehensively understand the QAH data. Our results reveal that the usually neglected Coulomb exchange is unexpectedly strong in a large class of QAH materials, which is the key to resolve experimental puzzles. Moreover, we identify simple indicators for property evaluation and suggest material design strategies to control QAH chirality and gap by tuning cooperative or competing contributions via magnetic codoping, heterostructuring, spin-orbit proximity, etc. The work is valuable to future research of magnetic topological physics and materials.

Quantum anomalous Hall effect in M2X3honeycomb Kagome lattice

The quantum anomalous Hall (QAH) effect has recently drawn great attention in spintronics with extraordinary property of chiral edge states without dissipation in absence of magnetic field. In M₂X₃honeycomb Kagome lattice, numerous two-dimensional materials are predicted to be QAH insulators including metal oxides/sulfides and metal organic lattice. In this work, we proposed a general model to explain the mechanism of Dirac half metal with absence of spin orbital coupling and the nontrivial topological property with spin orbital coupling, which could be induced by combination of electron counting rule, crystal field effect anddxz,dyzorbitals hybridization. Based on the mechanism, we further predict that triphenyl-metal lattice M₂(C₆H₄)₃(M= V, Nb, Ta) are all QAH insulators with high Curie temperature and large nontrivial band gap for triphenyl-Nb and triphenyl-Ta lattice.

Excited quantum anomalous and spin Hall effect: dissociation of flat-bands-enabled excitonic insulator state

Quantum anomalous Hall effect (QAHE) and quantum spin Hall effect (QSHE) are two interesting physical manifestations of 2D materials that have an intrinsic nontrivial band topology. In principle, they are ground-state equilibrium properties characterized by Fermi level lying in a topological gap, below which all the occupied bands are summed to a non-zero topological invariant. Here, we propose theoretical concepts and models of 'excited' QAHE (EQAHE) and EQSHE generated by dissociation of an excitonic insulator (EI) state with complete population inversion (CPI), a uniquemany-bodyground state enabled by two yin-yang flat bands (FBs) of opposite chirality hosted in a diatomic Kagome lattice. The two FBs have a trivial gap in between, i.e. the system is a trivial insulator in thesingle-particleground-state, but nontrivial gaps above and below, so that upon photoexcitation the quasi-Fermi levels of both electrons and holes will lie in a nontrivial gap achieved by the CPI-EI state, as demonstrated by exact diagonalization calculations. Then dissociation of singlet and triplet EI state will lead to EQAHE and EQSHE, respectively. Realizations of yin-yang FBs in real materials are also discussed.

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

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

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.

Quantum anomalous Hall effect in Cr2Ge2Te6/Bi2Se3/Cr2Ge2Te6heterostructures

Currently, quantum anomalous Hall (QAH) effect can only be observed at very low temperatures, which severely hinders its utilization from spintronics to quantum computation. Finding or predicting new systems supporting QAH effect at high temperatures remains essential and challenging. This work presents first-principles studies on the proximity effect between Bi₂Se₃slabs and Cr₂Ge₂Te₆(CGT) layers, reporting that Chern insulators are available in CGT/Bi₂Se₃/CGT heterostructures. If the sandwiched Bi₂Se₃slab is 4 quintuple layers (QLs) or thicker, the Chern insulating state is robust against the interfacial stacking manner. If the Bi₂Se₃slab is only 2 or 3 QLs, the CrBi- and CrH-aligned heterostructures are also Chern insulators, while the CrSe-aligned ones are trivial. The Chern insulators support the Hall conductivityσ_xy=e²/hand have energy gaps ranging from 3 to 20 meV, implying QAH effect at higher temperatures. An effective model Hamiltonian is introduced to understand the topological phase of the heterostructures.

Light-Induced Quantum Anomalous Hall Effect on the 2D Surfaces of 3D Topological Insulators

Quantum anomalous Hall (QAH) effect generates quantized electric charge Hall conductance without external magnetic field. It requires both nontrivial band topology and time-reversal symmetry (TRS) breaking. In most cases, one can break the TRS of time-reversal invariant topological materials to yield QAH effect, which is essentially a topological phase transition. However, conventional topological phase transition induced by external field/stimulus usually needs a route along which the bandgap closes and reopens. Hence, the transition occurs only when the magnitude of field/stimulus is larger than a critical value. In this work the authors propose that using gapless systems, the transition can happen at an arbitrarily weak (but finite) external field strength. For such an unconventional topological phase transition, the bandgap closing is guaranteed by bulk-edge correspondence and symmetries, while the bandgap reopening is induced by external fields. This concept is demonstrated on the 2D surface states of 3D topological insulators like Bi2 Se3 , which become 2D QAH insulators once a circularly polarized light is turned on, according to the Floquet time crystal theory. The sign of quantized Chern number can be controlled via the chirality of the light. This provides a convenient and dynamic approach to trigger topological phase transitions and create QAH insulators.

Topological Phase and Quantum Anomalous Hall Effect in Ferromagnetic Transition-Metal Dichalcogenides Monolayer 1T-VSe2

Magnetic two-dimensional (2D) van der Waals materials have attracted tremendous attention because of their high potential in spintronics. In particular, the quantum anomalous Hall (QAH) effect in magnetic 2D layers shows a very promising prospect for hosting Majorana zero modes at the topologically protected edge states in proximity to superconductors. However, the QAH effect has not yet been experimentally realized in monolayer systems to date. In this work, we study the electronic structures and topological properties of the 2D ferromagnetic transition-metal dichalcogenides (TMD) monolayer 1T−VSe2 by first-principles calculations with the Heyd–Scuseria–Ernzerhof (HSE) functional. We find that the spin-orbit coupling (SOC) opens a continuous band gap at the magnetic Weyl-like crossing point hosting the quantum anomalous Hall effect with Chern number C=2. Moreover, we demonstrate the topologically protected edge states and intrinsic (spin) Hall conductivity in this magnetic 2D TMD system. Our results indicate that 1T−VSe2 monolayer serves as a stoichiometric quantum anomalous Hall material.

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.

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.

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

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

Investigating and manipulating the molecular beam epitaxy growth kinetics of intrinsic magnetic topological insulator MnBi2Te4within-situangle-resolved photoemission spectroscopy

Intrinsic magnetic topological insulator MnBi2Te4is the key to realizing the quantum anomalous Hall effect and other related quantum phenomena at a sufficiently high temperature for their practical electronic applications. The research progress on the novel material, however, is severely hindered by the extreme difficulty in preparing its high-quality thin films with well-controlled composition and thickness. Combining molecular beam epitaxy (MBE) andin-situangle-resolved photoemission spectroscopy (ARPES), we have systematically studied the growth conditions and kinetics of MnBi2Te4thin films prepared by simple co-evaporation of Mn, Bi and Te. The transition and competition between the Mn-doped Bi2Te3and MnBi2Te4phases under different growth conditions have been mapped, which gives the recipe and the key principles of growing high-quality MnBi2Te4thin films. Particularly, to obtain high quality MnBi2Te4films, it is crucial to raise the growth temperature as high as allowed by the nucleation of the films to minimize density of Mn substitutional atoms on Bi sites. The ARPES data also reveal the kinetic process in the nucleation and ripening of MnBi2Te4islands. These results offer the essential information for designing and optimizing the MBE growth procedure of MnBi2Te4-like compounds to achieve the exotic topological quantum effects.

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.

Spin-Orientation-Dependent Topological States in Two-Dimensional Antiferromagnetic NiTl2S4 Monolayers

The topological states of matter arising from the nontrivial magnetic configuration provide a better understanding of physical properties and functionalities of solid materials. Such studies benefit from the active control of spin orientation in any solid, which is known to take place rarely in the two-dimensional (2D) limit. Here we demonstrate by the first-principles calculations that spin-orientation-dependent topological states can appear in the geometrically frustrated monolayer antiferromagnet (AFM). Different topological states including the quantum anomalous Hall (QAH) effect and time-reversal-symmetry (TRS) broken quantum spin Hall (QSH) effect can be obtained by changing the spin orientation in the NiTl₂S₄ monolayer. Remarkably, the dilated nc-AFM NiTl₂S₄ monolayer gives birth to the QAH effect with the hitherto reported largest number of quantized conducting channels (Chern number [Formula: see text] = -4) in 2D materials. Interestingly, under tunable chemical potential, the nc-AFM NiTl₂S₄ monolayer hosts a novel state supporting the coexistence of QAH and TRS broken QSH effects with a Chern number of [Formula: see text] = 3 and a spin Chern number of [Formula: see text] = 1. This work manifests a promising concept and material realization of topological spintronics in 2D antiferromagnets by manipulating their spin degree of freedom.

Enhancing the Quantum Anomalous Hall Effect by Magnetic Codoping in a Topological Insulator

The quantum anomalous Hall (QAH) effect, which has been realized in magnetic topological insulators (TIs), is the key to applications of dissipationless quantum Hall edge states in electronic devices. However, investigations and utilizations of the QAH effect are limited by the ultralow temperatures needed to reach full quantization-usually below 100 mK in either Cr- or V-doped (Bi,Sb)₂ Te₃ of the two experimentally confirmed QAH materials. Here it is shown that by codoping Cr and V magnetic elements in (Bi,Sb)₂ Te₃ TI, the temperature of the QAH effect can be significantly increased such that full quantization is achieved at 300 mK, and zero-field Hall resistance of 0.97 h/e² is observed at 1.5 K. A systematic transport study of the codoped (Bi,Sb)₂ Te₃ films with varied Cr/V ratios reveals that magnetic codoping improves the homogeneity of ferromagnetism and modulates the surface band structure. This work demonstrates magnetic codoping to be an effective strategy for achieving high-temperature QAH effect in TIs.

Large-Gap Magnetic Topological Heterostructure Formed by Subsurface Incorporation of a Ferromagnetic Layer

Inducing magnetism into topological insulators is intriguing for utilizing exotic phenomena such as the quantum anomalous Hall effect (QAHE) for technological applications. While most studies have focused on doping magnetic impurities to open a gap at the surface-state Dirac point, many undesirable effects have been reported to appear in some cases that makes it difficult to determine whether the gap opening is due to the time-reversal symmetry breaking or not. Furthermore, the realization of the QAHE has been limited to low temperatures. Here we have succeeded in generating a massive Dirac cone in a MnBi₂Se₄/Bi₂Se₃ heterostructure, which was fabricated by self-assembling a MnBi₂Se₄ layer on top of the Bi₂Se₃ surface as a result of the codeposition of Mn and Se. Our experimental results, supported by relativistic ab initio calculations, demonstrate that the fabricated MnBi₂Se₄/Bi₂Se₃ heterostructure shows ferromagnetism up to room temperature and a clear Dirac cone gap opening of ∼100 meV without any other significant changes in the rest of the band structure. It can be considered as a result of the direct interaction of the surface Dirac cone and the magnetic layer rather than a magnetic proximity effect. This spontaneously formed self-assembled heterostructure with a massive Dirac spectrum, characterized by a nontrivial Chern number C = -1, has a potential to realize the QAHE at significantly higher temperatures than reported up to now and can serve as a platform for developing future "topotronics" devices.

Above 400-K robust perpendicular ferromagnetic phase in a topological insulator

The quantum anomalous Hall effect (QAHE) that emerges under broken time-reversal symmetry in topological insulators (TIs) exhibits many fascinating physical properties for potential applications in nanoelectronics and spintronics. However, in transition metal-doped TIs, the only experimentally demonstrated QAHE system to date, the QAHE is lost at practically relevant temperatures. This constraint is imposed by the relatively low Curie temperature (T_c) and inherent spin disorder associated with the random magnetic dopants. We demonstrate drastically enhanced T_c by exchange coupling TIs to Tm₃Fe₅O₁₂, a high-T_c magnetic insulator with perpendicular magnetic anisotropy. Signatures showing that the TI surface states acquire robust ferromagnetism are revealed by distinct squared anomalous Hall hysteresis loops at 400 K. Point-contact Andreev reflection spectroscopy confirms that the TI surface is spin-polarized. The greatly enhanced T_c, absence of spin disorder, and perpendicular anisotropy are all essential to the occurrence of the QAHE at high temperatures.

Two Dimensional Antiferromagnetic Chern Insulator: NiRuCl6

Density functional theory (DFT) and Berry curvature calculations show that quantum anomalous Hall effect (QAHE) can be realized in two-dimensional(2D) antiferromagnetic (AFM) NiRuCl₆. The results indicate that NiRuCl₆ behaves as an AFM Chern insulator and its spin-polarized electronic structure and strong spin-orbit coupling (SOC) are responsible for the QAHE. By tuning SOC, we found that the topological property of NiRuCl₆ arises from its energy band inversion. Considering the compatibility between the AFM and insulators, AFM Chern insulator provides a new way to archive high temperature QAHE in experiments due to its different magnetic coupling mechanism from that of ferromagnetic (FM) Chern insulator.

Thickness Dependence of the Quantum Anomalous Hall Effect in Magnetic Topological Insulator Films

The evolution of the quantum anomalous Hall effect with the thickness of Cr-doped (Bi,Sb)2 Te3 magnetic topological insulator films is studied, revealing how the effect is caused by the interplay of the surface states, band-bending, and ferromagnetic exchange energy. Homogeneity in ferromagnetism is found to be the key to high-temperature quantum anomalous Hall material.

Independent Tuning of Electronic Properties and Induced Ferromagnetism in Topological Insulators with Heterostructure Approach

The quantum anomalous Hall effect (QAHE) has been recently demonstrated in Cr- and V-doped three-dimensional topological insulators (TIs) at temperatures below 100 mK. In those materials, the spins of unfilled d-electrons in the transition metal dopants are exchange coupled to develop a long-range ferromagnetic order, which is essential for realizing QAHE. However, the addition of random dopants does not only introduce excess charge carriers that require readjusting the Bi/Sb ratio, but also unavoidably introduces paramagnetic spins that can adversely affect the chiral edge transport in QAHE. In this work, we show a heterostructure approach to independently tune the electronic and magnetic properties of the topological surface states in (BixSb1-x)2Te3 without resorting to random doping of transition metal elements. In heterostructures consisting of a thin (BixSb1-x)2Te3 TI film and yttrium iron garnet (YIG), a high Curie temperature (∼550 K) magnetic insulator, we find that the TI surface in contact with YIG becomes ferromagnetic via proximity coupling which is revealed by the anomalous Hall effect (AHE). The Curie temperature of the magnetized TI surface ranges from 20 to 150 K but is uncorrelated with the Bi fraction x in (BixSb1-x)2Te3. In contrast, as x is varied, the AHE resistivity scales with the longitudinal resistivity. In this approach, we decouple the electronic properties from the induced ferromagnetism in TI. The independent optimization provides a pathway for realizing QAHE at higher temperatures, which is important for novel spintronic device applications.

Chern half metals: a new class of topological materials to realize the quantum anomalous Hall effect

New topological insulators that demonstrate the quantum anomalous Hall effect (QAHE) are a cutting-edge research topic in condensed matter physics and materials science. So far, the QAHE has been observed only in Cr-doped (Bi,Sb)2Te3 at extremely low temperature. Therefore, it is important to find new materials with large topological band gap and high thermal stability for the realization of the QAHE. On the basis of first-principles and tight-binding model calculations, we discovered a new class of topological phase, Chern half metal, which manifests the QAHE in one spin channel while is metallic in the other spin channel, in Co or Rh deposited graphene. The QAHE is robust in these sytems for the adatom coverage ranging from 2% to 6%. Meanwhile, these systems have large perpendicular magnetic anisotropy energies of 5.3 and 11.5 meV, necessary for the observation of the QAHE at reasonably high temperature.

Quantum anomalous Hall effect in magnetic insulator heterostructure

On the basis of ab initio calculations, we predict that a monolayer of Cr-doped (Bi,Sb)2Te3 and GdI2 heterostructure is a quantum anomalous Hall insulator with a nontrivial band gap up to 38 meV. The principle behind our prediction is that the band inversion between two topologically trivial ferromagnetic insulators can result in a nonzero Chern number, which offers a better way to realize the quantum anomalous Hall state without random magnetic doping. In addition, a simple effective model is presented to describe the basic mechanism of spin polarized band inversion in this system. Moreover, we predict that 3D quantum anomalous Hall insulator could be realized in (Bi2/3Cr1/3)2Te3 /GdI2 superlattice.