Experimental Observation of the Gate-Controlled Reversal of the Anomalous Hall Effect in the Intrinsic Magnetic Topological Insulator MnBi2Te4 Device

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.

Sign-flipping intrinsic anomalous Hall conductivity with Berry curvature tunability in a half-metallic ferromagnet NbSe2-VSe2 lateral heterostructure

Single-layer half-metal magnets offer exciting scope in spin electronic quantum applications owing to improved spin transport, reduced interfacial resistance and streamlined device fabrication. Herein, we report the emergence of sign-flipping intrinsic anomalous Hall conductivity (AHC) as a result of changes in Berry curvature under an external electric field and half metallicity in a lateral heterostructure composed of centrosymmetric metallic monolayers 1T-NbSe2 and 1T-VSe2. The metallic monolayers 1T-NbSe2 and 1T-VSe2 laterally interfaced along the zigzag orientation break inversion symmetry at the interface and result in distinctive Berry curvature features. Furthermore, the half-metallic character was prominent with gapped states in the spin-up channel, while the spin-down state remained conductive; we observed the unique manifestation of sign-flipping intrinsic AHC at the Fermi level in addition to the electron- and hole-doped regions. This sign-flipping aspect of AHC at the Fermi level is of fundamental importance from the prospect of real-time device applications as it eliminates the necessity of supplementary actions, such as doping and strain engineering, which are traditionally employed to achieve AHC sign reversal. Additionally, a phase transition from half metal to metal occurs at a field of 0.5 V Å-1 and beyond. Half metallicity with sign switching AHC via external electric field makes the lateral NbSe2-VSe2 heterostructure a potential candidate for real-time energy-efficient low-power spintronic devices.

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

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

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.

Pressure-cycling induced transition behaviors of MnBi2Te4

MnBi2Te4 can generate a variety of exotic topological quantum states, which are closely related to its special structure. We conduct comprehensive multiple-cycle high-pressure research on MnBi2Te4 by using a diamond anvil cell to study its phase transition behaviors under high pressure. As observed, when the pressure does not exceed 15 GPa, the material undergoes an irreversible metal-semiconductor-metal transition, whereas when the pressure exceeds 17 GPa, the layered structure is damaged and becomes irreversibly amorphous due to the lattice distortion caused by compression, but it is not completely amorphous, which presents some nano-sized grains after decompression. Our investigation vividly reveals the phase transition behaviors of MnBi2Te4 under high pressure cycling and paves the experimental way to find topological phases under high pressure.

Magnetic Topological Insulator MnBi2Te4 Nanosheets for Femtosecond Pulse Generation

The van der Waals layered material MnBi2Te4, as a magnetic topological insulator, has attracted tremendous interest for novel physics research in the fields of condensed matter physics and materials science. However, the nonlinear optical properties of MnBi2Te4 and its applications in ultrafast optics have rarely been explored. In this study, high-quality MnBi2Te4 nanosheets have been successfully synthesized by the self-flux method. The morphology, chemical composition, magnetic properties, and nonlinear optical characteristics were systematically investigated. The magnetic transition of MnBi2Te4 was confirmed by a low-temperature spatially resolved spectroscopic technique. The saturable absorption property of MnBi2Te4 was measured by a balanced twin-detector system with a modulation depth of 4.5% and a saturation optical intensity of 2.35 GW/cm2. Furthermore, by inserting the MnBi2Te4-based saturable absorber, a soliton mode-locking laser operating at 1558.8 nm was obtained with a pulse duration of 331 fs. This research will pave the way for applications of the magnetic TI MnBi2Te4 in nonlinear optics and photonics.

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

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

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.

Highly Tunable Beyond-Room-Temperature Intrinsic Ferromagnetism in Cr-Doped Topological Crystalline Insulator SnTe Crystals

The combination of topological phase and intrinsic beyond-room-temperature ferromagnetism is expected to realize the quantum anomalous Hall effect at a high temperature. However, no beyond-room-temperature intrinsic ferromagnetism has been reported in either topological insulator or topological crystalline insulator (TCI) so far. Here, we report Cr-doping in TCI-phase SnTe crystals which possess highly tunable beyond-room-temperature intrinsic ferromagnetism including T_c, magnetic moment, and coercivity by varying Cr contents and crystal thickness. With the increase of the Cr content, the T_c increases by 159 K from 221 to 380 K and the saturation magnetic moments increase by ∼23.6 times from 0.018 to 0.421 μ_B/f.u. This intrinsic beyond-room-temperature ferromagnetism is fully demonstrated by the anomalous Hall effect and magneto-optical Kerr effect in a single Cr_xSn_1-xTe nanosheet. Moreover, the room-temperature tunneling magnetoresistance effect has been realized by using a Cr_xSn_1-xTe flake, a Fe thin film, and a commercially compatible ultrathin AlO_x tunneling barrier. This work indicates a great potential of Cr_xSn_1-xTe crystals in room-temperature magnetoelectronic and spintronic devices.

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.

Epitaxial Growth and Structural Characterizations of MnBi2Te4 Thin Films in Nanoscale

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

Even-Odd Layer-Dependent Anomalous Hall Effect in Topological Magnet MnBi2Te4 Thin Films

Recently, MnBi₂Te₄ has been demonstrated to be an intrinsic magnetic topological insulator and the quantum anomalous Hall (QAH) effect was observed in exfoliated MnBi₂Te₄ flakes. Here, we used molecular beam epitaxy (MBE) to grow MnBi₂Te₄ films with thickness down to 1 septuple layer (SL) and performed thickness-dependent transport measurements. We observed a nonsquare hysteresis loop in the antiferromagnetic state for films with thickness greater than 2 SL. The hysteresis loop can be separated into two AH components. We demonstrated that one AH component with the larger coercive field is from the dominant MnBi₂Te₄ phase, whereas the other AH component with the smaller coercive field is from the minor Mn-doped Bi₂Te₃ phase. The extracted AH component of the MnBi₂Te₄ phase shows a clear even-odd layer-dependent behavior. Our studies reveal insights on how to optimize the MBE growth conditions to improve the quality of MnBi₂Te₄ films.

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.

Magnetic-field-induced robust zero Hall plateau state in MnBi2Te4 Chern insulator

The intrinsic antiferromagnetic topological insulator MnBi2Te4 provides an ideal platform for exploring exotic topological quantum phenomena. Recently, the Chern insulator and axion insulator phases have been realized in few-layer MnBi2Te4 devices at low magnetic field regime. However, the fate of MnBi2Te4 in high magnetic field has never been explored in experiment. In this work, we report transport studies of exfoliated MnBi2Te4 flakes in pulsed magnetic fields up to 61.5 T. In the high-field limit, the Chern insulator phase with Chern number C = -1 evolves into a robust zero Hall resistance plateau state. Nonlocal transport measurements and theoretical calculations demonstrate that the charge transport in the zero Hall plateau state is conducted by two counter-propagating edge states that arise from the combined effects of Landau levels and large Zeeman effect in strong magnetic fields. Our result demonstrates the intricate interplay among intrinsic magnetic order, external magnetic field, and nontrivial band topology in MnBi2Te4.

Layer Hall effect in a 2D topological axion antiferromagnet

Whereas ferromagnets have been known and used for millennia, antiferromagnets were only discovered in the 1930s¹. At large scale, because of the absence of global magnetization, antiferromagnets may seem to behave like any non-magnetic material. At the microscopic level, however, the opposite alignment of spins forms a rich internal structure. In topological antiferromagnets, this internal structure leads to the possibility that the property known as the Berry phase can acquire distinct spatial textures^2,3. Here we study this possibility in an antiferromagnetic axion insulator-even-layered, two-dimensional MnBi₂Te₄-in which spatial degrees of freedom correspond to different layers. We observe a type of Hall effect-the layer Hall effect-in which electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under zero electric field, even-layered MnBi₂Te₄ shows no anomalous Hall effect. However, applying an electric field leads to the emergence of a large, layer-polarized anomalous Hall effect of about 0.5e²/h (where e is the electron charge and h is Planck's constant). This layer Hall effect uncovers an unusual layer-locked Berry curvature, which serves to characterize the axion insulator state. Moreover, we find that the layer-locked Berry curvature can be manipulated by the axion field formed from the dot product of the electric and magnetic field vectors. Our results offer new pathways to detect and manipulate the internal spatial structure of fully compensated topological antiferromagnets^4-9. The layer-locked Berry curvature represents a first step towards spatial engineering of the Berry phase through effects such as layer-specific moiré potential.

Electrical switching of magnetic order in an orbital Chern insulator

Magnetism typically arises from the joint effect of Fermi statistics and repulsive Coulomb interactions, which favours ground states with non-zero electron spin. As a result, controlling spin magnetism with electric fields-a longstanding technological goal in spintronics and multiferroics^1,2-can be achieved only indirectly. Here we experimentally demonstrate direct electric-field control of magnetic states in an orbital Chern insulator^3-6, a magnetic system in which non-trivial band topology favours long-range order of orbital angular momentum but the spins are thought to remain disordered^7-14. We use van der Waals heterostructures consisting of a graphene monolayer rotationally faulted with respect to a Bernal-stacked bilayer to realize narrow and topologically non-trivial valley-projected moiré minibands^15-17. At fillings of one and three electrons per moiré unit cell within these bands, we observe quantized anomalous Hall effects¹⁸ with transverse resistance approximately equal to h/2e² (where h is Planck's constant and e is the charge on the electron), which is indicative of spontaneous polarization of the system into a single-valley-projected band with a Chern number equal to two. At a filling of three electrons per moiré unit cell, we find that the sign of the quantum anomalous Hall effect can be reversed via field-effect control of the chemical potential; moreover, this transition is hysteretic, which we use to demonstrate non-volatile electric-field-induced reversal of the magnetic state. A theoretical analysis¹⁹ indicates that the effect arises from the topological edge states, which drive a change in sign of the magnetization and thus a reversal in the favoured magnetic state. Voltage control of magnetic states can be used to electrically pattern non-volatile magnetic-domain structures hosting chiral edge states, with applications ranging from reconfigurable microwave circuit elements to ultralow-power magnetic memories.

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.

Realization of an intrinsic ferromagnetic topological state in MnBi8Te13

Novel magnetic topological materials pave the way for studying the interplay between band topology and magnetism. However, an intrinsically ferromagnetic topological material with only topological bands at the charge neutrality energy has so far remained elusive. Using rational design, we synthesized MnBi8Te13, a natural heterostructure with [MnBi2Te4] and [Bi2Te3] layers. Thermodynamic, transport, and neutron diffraction measurements show that despite the adjacent [MnBi2Te4] being 44.1 Å apart, MnBi8Te13 manifests long-range ferromagnetism below 10.5 K with strong coupling between magnetism and charge carriers. First-principles calculations and angle-resolved photoemission spectroscopy measurements reveal it is an axion insulator with sizable surface hybridization gaps. Our calculations further demonstrate the hybridization gap persists in the two-dimensional limit with a nontrivial Chern number. Therefore, as an intrinsic ferromagnetic axion insulator with clean low-energy band structures, MnBi8Te13 serves as an ideal system to investigate rich emergent phenomena, including the quantized anomalous Hall effect and quantized magnetoelectric effect.