Electric control of a canted-antiferromagnetic Chern insulator

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.

Exchange-Driven Chern States in High-Mobility Intrinsic Magnetic Topological Insulators

The layer-dependent Chern number (C) in MnBi_{2}Te_{4} is characterized by the presence of a Weyl semimetal state in the ferromagnetic coupling. However, the influence of a key factor, namely, the exchange coupling, remains unexplored. This study focuses on characterizing the C=2 state in MnBi_{2}Te_{4}, which is classified as a higher C state resulting from the anomalous n=0 Landau levels (LLs). Our findings demonstrate that the exchange coupling parameter strongly influences the formation of this Chern state, leading to a competition between the C=1 and 2 states. Moreover, the emergence of odd-even LL sequences, resulting from the breaking of LL degeneracy, provides compelling evidence for the strong exchange coupling strength. These findings highlight the significance of the exchange coupling in understanding the behavior of Chern states and LLs in magnetic quantum systems.

Layer Control of Magneto-Optical Effects and Their Quantization in Spin-Valley Splitting Antiferromagnets

Magneto-optical effects (MOE), interfacing the fundamental interplay between magnetism and light, have served as a powerful probe for magnetic order, band topology, and valley index. Here, based on multiferroic and topological bilayer antiferromagnets (AFMs), we propose a layer control of MOE (L-MOE), which is created and annihilated by layer-stacking or an electric field effect. The key character of L-MOE is the sign-reversible response controlled by ferroelectric polarization, the Néel vector, or the electric field direction. Moreover, the sign-reversible L-MOE can be quantized in topologically insulating AFMs. We reveal that the switchable L-MOE originates from the combined contributions of spin-conserving and spin-flip interband transitions in spin-valley splitting AFMs, a phenomenon not observed in conventional AFMs. Our findings bridge the ancient MOE to the emergent realms of layertronics, valleytronics, and multiferroics and may hold immense potential in these fields.

Unveiling the Anomalous Hall Response of the Magnetic Structure Changes in the Epitaxial MnBi2Te4 Films

Recently discovered as an intrinsic antiferromagnetic topological insulator, MnBi2Te4 has attracted tremendous research interest, as it provides an ideal platform to explore the interplay between topological and magnetic orders. MnBi2Te4 displays distinct exotic topological phases that are inextricably linked to the different magnetic structures of the material. In this study, we conducted electrical transport measurements and systematically investigated the anomalous Hall response of epitaxial MnBi2Te4 films when subjected to an external magnetic field sweep, revealing the different magnetic structures stemming from the interplay of applied fields and the material's intrinsic antiferromagnetic (AFM) ordering. Our results demonstrate that the nonsquare anomalous Hall loop is a consequence of the distinct reversal processes within individual septuple layers. These findings shed light on the intricate magnetic structures in MnBi2Te4 and related materials, offering insights into understanding their transport properties and facilitating the implementation of AFM topological electronics.

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.

Quantized anomalous Hall resistivity achieved in molecular beam epitaxy-grown MnBi2Te4 thin films

The intrinsic magnetic topological insulator MnBi2Te4 provides a feasible pathway to the high-temperature quantum anomalous Hall (QAH) effect as well as various novel topological quantum phases. Although quantized transport properties have been observed in exfoliated MnBi2Te4 thin flakes, it remains a big challenge to achieve molecular beam epitaxy (MBE)-grown MnBi2Te4 thin films even close to the quantized regime. In this work, we report the realization of quantized anomalous Hall resistivity in MBE-grown MnBi2Te4 thin films with the chemical potential tuned by both controlled in situ oxygen exposure and top gating. We find that elongated post-annealing obviously elevates the temperature to achieve quantization of the Hall resistivity, but also increases the residual longitudinal resistivity, indicating a picture of high-quality QAH puddles weakly coupled by tunnel barriers. These results help to clarify the puzzles in previous experimental studies on MnBi2Te4 and to find a way out of the big difficulty in obtaining MnBi2Te4 samples showing quantized transport properties.

Crossover from gapped-to-gapless Dirac surface states in magnetic topological insulator MnBi2Te4

Intrinsic magnetic topological insulators (MTIs) host exotic topological phases such as quantized anomalous Hall insulating phase, arising due to the large magnetic exchange gap. However, the interplay of magnetism and topology in these systems in different temperature regimes remains elusive. In this work, we present the logarithmic temperature-dependence of conductivity for sub-100 nm thick exfoliated flakes of MTI MnBi2Te4in the presence of out-of-plane magnetic fields and extracted the linear slope,κ. We observed a characteristic change,Δκ∼-0.5in the low-temperature regime, indicating the gapped Dirac surface state according to Lu-Shen theory. We also report the recovery of topological properties in the system via the weak-antilocalization effect in the vicinity of antiferromagnetic to paramagnetic transition and in the paramagnetic regime. Hikami-Larkin-Nagaoka analysis suggested the presence of topological surface states. Therefore, our study helps in understanding how intrinsic magnetism masks topological properties in an MTI as long as magnetic ordering persists.

Quantum-metric-induced nonlinear transport in a topological antiferromagnet

The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor, which characterizes the topology of quantum states1. The Berry curvature is known to generate a number of important transport phenomena, such as the quantum Hall effect and the anomalous Hall effect2,3; however, the consequences of the quantum metric have rarely been probed by transport measurements. Here we report the observation of quantum-metric-induced nonlinear transport, including both a nonlinear anomalous Hall effect and a diode-like non-reciprocal longitudinal response, in thin films of a topological antiferromagnet, MnBi2Te4. Our observations reveal that the transverse and longitudinal nonlinear conductivities reverse signs when reversing the antiferromagnetic order, diminish above the Néel temperature and are insensitive to disorder scattering, thus verifying their origin in the band-structure topology. They also flip signs between electron- and hole-doped regions, in agreement with theoretical calculations. Our work provides a means to probe the quantum metric through nonlinear transport and to design magnetic nonlinear devices.

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.

Switchable Anomalous Hall Effects in Polar-Stacked 2D Antiferromagnet MnBi2Te4

van der Waals (vdW) assembly of two-dimensional (2D) materials allows polar layer stacking to realize novel properties switchable by the induced electric polarization. Here, based on symmetry analyses and density-functional calculations, we explore the emergence of the anomalous Hall effect (AHE) in antiferromagnetic MnBi₂Te₄ films assembled by polar layer stacking. We demonstrate that breaking P̂T̂ symmetry in an MnBi₂Te₄ bilayer produces a magnetoelectric effect and a spontaneous AHE switchable by electric polarization. We find that reversible polarization at one of the interfaces in a three-layer MnBi₂Te₄ film drives a metal-insulator transition, as well as switching between the AHE and quantum AHE (QAHE). Finally, we predict that engineering interlayer polarization in a three-layer MnBi₂Te₄ film allows converting MnBi₂Te₄ from a trivial insulator to a Chern insulator. Overall, our work emphasizes the topological properties in 2D vdW antiferromagnets induced by polar layer stacking, which do not exist in a bulk material.

Axion optical induction of antiferromagnetic order

Using circularly polarized light to control quantum matter is a highly intriguing topic in physics, chemistry and biology. Previous studies have demonstrated helicity-dependent optical control of chirality and magnetization, with important implications in asymmetric synthesis in chemistry; homochirality in biomolecules; and ferromagnetic spintronics. We report the surprising observation of helicity-dependent optical control of fully compensated antiferromagnetic order in two-dimensional even-layered MnBi₂Te₄, a topological axion insulator with neither chirality nor magnetization. To understand this control, we study an antiferromagnetic circular dichroism, which appears only in reflection but is absent in transmission. We show that the optical control and circular dichroism both arise from the optical axion electrodynamics. Our axion induction provides the possibility to optically control a family of [Formula: see text]-symmetric antiferromagnets ([Formula: see text], inversion; [Formula: see text], time-reversal) such as Cr₂O₃, even-layered CrI₃ and possibly the pseudo-gap state in cuprates. In MnBi₂Te₄, this further opens the door for optical writing of a dissipationless circuit formed by topological edge states.

Distinct Magnetic Gaps between Antiferromagnetic and Ferromagnetic Orders Driven by Surface Defects in the Topological Magnet MnBi_{2}Te_{4}

Many experiments observed a metallic behavior at zero magnetic fields (antiferromagnetic phase, AFM) in MnBi_{2}Te_{4} thin film transport, which coincides with gapless surface states observed by angle-resolved photoemission spectroscopy, while it can become a Chern insulator at field larger than 6 T (ferromagnetic phase, FM). Thus, the zero-field surface magnetism was once speculated to be different from the bulk AFM phase. However, recent magnetic force microscopy refutes this assumption by detecting persistent AFM order on the surface. In this Letter, we propose a mechanism related to surface defects that can rationalize these contradicting observations in different experiments. We find that co-antisites (exchanging Mn and Bi atoms in the surface van der Waals layer) can strongly suppress the magnetic gap down to several meV in the AFM phase without violating the magnetic order but preserve the magnetic gap in the FM phase. The different gap sizes between AFM and FM phases are caused by the exchange interaction cancellation or collaboration of the top two van der Waals layers manifested by defect-induced surface charge redistribution among the top two van der Waals layers. This theory can be validated by the position- and field-dependent gap in future surface spectroscopy measurements. Our work suggests suppressing related defects in samples to realize the quantum anomalous Hall insulator or axion insulator at zero fields.

Room-Temperature Magnetoelectric Coupling in Atomically Thin ε-Fe2 O3

2D multiferroics with magnetoelectric coupling combine the magnetic order and electric polarization in a single phase, providing a cornerstone for constructing high-density information storages and low-energy-consumption spintronic devices. The strong interactions between various order parameters are crucial for realizing such multifunctional applications, nevertheless, this criterion is rarely met in classical 2D materials at room-temperature. Here an ingenious space-confined chemical vapor deposition strategy is designed to synthesize atomically thin non-layered ε-Fe₂ O₃ single crystals and disclose the room-temperature long-range ferrimagnetic order. Interestingly, the strong ferroelectricity and its switching behavior are unambiguously discovered in atomically thin ε-Fe₂ O₃ , accompanied with an anomalous thickness-dependent coercive voltage. More significantly, the robust room-temperature magnetoelectric coupling is uncovered by controlling the magnetism with electric field and verifies the multiferroic feature of atomically thin ε-Fe₂ O₃ . This work not only represents a substantial leap in terms of the controllable synthesis of 2D multiferroics with robust magnetoelectric coupling, but also provides a crucial step toward the practical applications in low-energy-consumption electric-writing/magnetic-reading devices.

Anomalous Second Harmonic Generation from Atomically Thin MnBi2Te4

MnBi₂Te₄ is a van der Waals topological insulator with intrinsic intralayer ferromagnetic exchange and A-type antiferromagnetic interlayer coupling. Theoretically, it belongs to a class of structurally centrosymmetric crystals whose layered antiferromagnetic order breaks inversion symmetry for even layer numbers, making optical second harmonic generation (SHG) an ideal probe of the coupling between the crystal and magnetic structures. Here, we perform magnetic field and temperature-dependent SHG measurements on MnBi₂Te₄ flakes ranging from bulk to monolayer thickness. We find that the dominant SHG signal from MnBi₂Te₄ is unexpectedly unrelated to both magnetic state and layer number. We suggest that surface SHG is the likely source of the observed strong SHG, whose symmetry matches that of the MnBi₂Te₄-vacuum interface. Our results highlight the importance of considering the surface contribution to inversion symmetry-breaking in van der Waals centrosymmetric magnets.

Topological current divider in a Chern insulator junction

A Chern insulator is a two-dimensional material that hosts chiral edge states produced by the combination of topology with time reversal symmetry breaking. Such edge states are perfect one-dimensional conductors, which may exist not only on sample edges, but on any boundary between two materials with distinct topological invariants (or Chern numbers). Engineering of such interfaces is highly desirable due to emerging opportunities of using topological edge states for energy-efficient information transmission. Here, we report a chiral edge-current divider based on Chern insulator junctions formed within the layered topological magnet MnBi₂Te₄. We find that in a device containing a boundary between regions of different thickness, topological domains with different Chern numbers can coexist. At the domain boundary, a Chern insulator junction forms, where we identify a chiral edge mode along the junction interface. We use this to construct topological circuits in which the chiral edge current can be split, rerouted, or switched off by controlling the Chern numbers of the individual domains. Our results demonstrate MnBi₂Te₄ as an emerging platform for topological circuits design.

Superconducting Proximity in Intrinsic Magnetic Topological Insulator MnBi2Te4-NbN Hybrid Device Modulated by Coulomb Blockade Effect

The combination of nontrivial topology, magnetism, and superconductivity could offer the potential to realize exotic excitations of quasiparticles. MnBi₂Te₄, as an intrinsic magnetic topological insulator, may be a good platform to create Majorana fermions if coupled to an s-wave superconductor. Here, we report the transport properties of a MnBi₂Te₄-NbN hybrid device. This device exhibits clear Coulomb blockade oscillations. We observe a large zero-bias conductance peak that exists over considerable changes in gate voltage, magnetic field, and temperature, which is interpreted as a not fully developed supercurrent. The zero-bias peak shows a nonmonotonic evolution with a magnetic field and an abrupt π phase shift with changing temperature. Zero-energy bound states and a topological phase transition may exist in this hybrid system. Our results provide the first experimental investigation into the properties of the intrinsic magnetic topological insulator/superconductor hybrid structures modulated by the Coulomb blockade effect.

Magnons and magnetic fluctuations in atomically thin MnBi2Te4

Electron band topology is combined with intrinsic magnetic orders in MnBi₂Te₄, leading to novel quantum phases. Here we investigate collective spin excitations (i.e. magnons) and spin fluctuations in atomically thin MnBi₂Te₄ flakes using Raman spectroscopy. In a two-septuple layer with non-trivial topology, magnon characteristics evolve as an external magnetic field tunes the ground state through three ordered phases: antiferromagnet, canted antiferromagnet, and ferromagnet. The Raman selection rules are determined by both the crystal symmetry and magnetic order while the magnon energy is determined by different interaction terms. Using non-interacting spin-wave theory, we extract the spin-wave gap at zero magnetic field, an anisotropy energy, and interlayer exchange in bilayers. We also find magnetic fluctuations increase with reduced thickness, which may contribute to a less robust magnetic order in single layers.

MnBi2Te4, referred to as MBT, is a van der Waals material combining topological electron bands with magnetic order. Here, Lujan et al study collective spin excitations in MBT, and show that magnetic fluctuations increase as samples reduce in thickness, implying less robust magnetic order.