Introduction

A Chern insulator is a two-dimensional topological state of matter with quantized Hall resistance of h/Ce2 and vanishing longitudinal resistance1,2, where the Chern number C is an integer that determines the number of topologically protected chiral edge channels1,3,4,5. The formation of the Chern insulator requires time-reversal symmetry breaking, which is usually achieved by magnetic doping or magnetic proximity effect3,6,7. A seminal example is the magnetically-doped topological insulators that realize a ferromagnetic (FM) Chern insulator with the quantum anomalous Hall effect2. Although Chern insulators have now been realized in several systems, little is known about this topological phase in antiferromagnets, which may offer a platform for exploring new physics and control of band topology8,9.

MnBi2Te4, an intrinsic topological magnet, provides a new platform for incorporating band topology with different magnetic states10,11,12,13,14. MnBi2Te4 is a layered van der Waals compound that consists of Te–Bi–Te–Mn–Te–Bi–Te septuple layers (SL) stacked along the crystallographic c-axis. At zero magnetic field, it hosts an A-type antiferromagnetic (AFM) ground state: each SL of MnBi2Te4 individually exhibits ferromagnetism with out-of-plane magnetization, while the adjacent SLs couple antiferromagnetically13,14. By applying an external magnetic field perpendicular to the SLs, the magnetic state evolves from AFM to canted AFM (cAFM) and then to FM8. The Chern insulator state has recently been demonstrated in mechanically exfoliated MnBi2Te4 devices at both zero and high magnetic fields15,16,17,18. However, the topological properties in the cAFM state have not been investigated, where the spin structure can be continuously tuned by a magnetic field. In addition, the electric field effect, which has been demonstrated in 2D magnets19,20, remains to be explored as a means to control the topological states in thin MnBi2Te4 devices.

Here, we demonstrate that MnBi2Te4 is a Chern insulator in the cAFM state and realize the electric field control of the band topology. We employed a combined approach of polar reflective magnetic circular dichroism (RMCD) measurement to identify the magnetic states and magneto-transport measurement to probe the topological property. To distinguish between electric-field and carrier doping effects, we fabricated MnBi2Te4 devices with dual gates. The devices with a single gate were also used for combined transport and RMCD measurements. The transport and optical measurements were carried out at T = 50 mK and 2 K, respectively, unless otherwise specified (see the “Methods” section for fabrication and measurement details).

Results

Formation of Chern insulator phase in the cAFM state

Figure 1a shows the magnetic field dependence of the RMCD signal of a 7-SL MnBi2Te4 device with a single bottom gate (Device 1). Near zero magnetic field, the RMCD signal shows a narrow hysteresis loop due to the uncompensated magnetization in odd layer-number devices17,21. Upon increasing the magnetic field, the sample enters the cAFM state at the spin-flop field μ0HC1 ~ 3.8 T, manifested by the sudden jump of the RMCD signal. Remarkably, as the spin–flop transition occurs, the Hall resistivity ρyx quantizes to about -h/e2 (Fig. 1b), and the longitudinal resistivity ρxx drops from ~100 kΩ to near zero (Fig. 1c, see Supplementary Fig. 1 for a full gate-dependent transport measurement). As the magnetic field further increases, the canted spins rotate towards the out-of-plane direction and eventually become fully polarized at μ0HC2 ~ 7.2 T with saturated RMCD signal (Fig. 1a). Within the field range of about 3.8–7.2 T, where MnBi2Te4 is in the cAFM state, ρyx remains quantized with vanishing ρxx, this demonstrates the formation of C = 1 cAFM Chern insulator state.

Fig. 1: Observation of the canted-antiferromagnetic (cAFM) Chern insulator state.
figure 1

Data is taken from a single gated Device 1. a Reflective circular dichroism (RMCD) signal taken at a temperature of 2 K at Vbg = 0 V. b ρyx, and c, ρxx measurements as a function of magnetic field (μ0H) at optimal gate voltage Vbg = 53 V. RMCD data are acquired at T = 2 K while transport data at T = 50 mK. Green and orange traces correspond to magnetic field sweeping down and up, respectively. The red arrow denotes the spin flop field HC1 and the light blue arrow indicates the critical field HC2 for reaching the field-induced ferromagnetic states. The slight offset of the spin-flop fields between RMCD and transport measurements are due to the different gate voltage and temperature of the measurements. ρyx is antisymmetrized against μ0H while ρxx is symmetrized.

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The cAFM Chern insulator is further supported by exploring the topological phase diagram in dual-gated devices over a broad range of magnetic field. Figure 2a is a 2D color map of ρyx in a 7-SL dual-gated MnBi2Te4 device (Device 2) as a function of both μ0H and gate-induced carrier density nG at electric field D/ε0 = −0.2 V/nm (see corresponding ρxx map and characterization in Supplementary Figs. 2–4). Here nG partly compensates for the residual carrier density in the sample and tunes the Fermi level (see the “Methods” section). The electric field D is defined to be positive when it points from top to bottom gates. Notably, in the range of nG 1.0–2.0 × 1012 cm−2, a sharp phase boundary of the C = 1 state is observed near the spin-flop field | μ0HC1 | ~ 3.6 T. This further supports that the formation of C = 1 state is coupled to the cAFM order. The cAFM Chern insulator has been observed in multiple devices. See a device summary in Supplementary Table 1 and their basic characterization in Supplementary Figs. 5–7.

Fig. 2: Observation of Chern insulator to orbital quantum Hall states phase transition.
figure 2

a Unsymmetrized ρyx as a function of magnetic field μ0H and gate induced carrier density nG at fixed electric field D/ɛ0 = −0.2 V/nm in Device 2. Black, green and red dashed lines enclose C = 1, 2, 3 quantum Hall states, respectively. The dashed lines are contours defined by ρyx = (0.97, 0.47, 0.30) h/e2. Carrier densities n1-3 and critical magnetic fields μ0HC1 and μ0HC2 are marked on the axis. (n1, n2, n3) = (2.23, 1.87, 1.29) × 1012 cm−2. Note that for |μ0H| < |μ0HC1| and nG in the range of −1~1 × 1012 cm−2, since the sample is very insulating (i.e. ρxx > 1 GΩ), the excitation current flowing through the sample is not stable and thus ρyx shows a fluctuating signal with positive and negative values. b–d Anti-symmetrized ρyx as a function of μ0H, under different carrier density n1-3, and e–g The corresponding symmetrized ρxx. Orange and green curves correspond to magntic field sweeping up and down, respectively.

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This intimate relationship between the topological and magnetic phase transitions in MnBi2Te4 can be understood as follows. Due to the easy-axis anisotropy, the transition from the AFM to the cAFM state is a first-order phase transition: at the spin–flop field, the magnetization in each SL suddenly rotates into the cAFM state with a finite canting angle. The abrupt change of the magnetic state is accompanied by the formation of the Chern insulator gap, hence a change in the Chern number. Further increase of the magnetic field results in a continuous rotation of the canted spins, which is expected to cause an adiabatic change in the size of the Chern insulator gap until the system enters the FM state. This understanding naturally connects our observation of cAFM Chern insulator and previously reported C = 1 Chern insulator in the field–induced FM state15,16,17. As the exchange gap in both cAFM and FM states are adiabatically connected, the stability of Chern number ensures a cAFM Chern insulator state as long as the exchange gap is not closed by external disorder or temperature.

When μ0H is above | μ0HC2 | ~ 7.4 T, the sample enters the magnetic field-induced FM state. A rich topological phase diagram is uncovered, in which the topological states with corresponding Chern numbers are identified based on ρyx ~ h/Ce2 and nearly vanishing ρxx. In addition to the C = 1, C = 2 and 3 states, characterized by ρyx ~ h/Ce2, appear at higher nG. Unlike the C = 1 phase, the contours of C = 2 and 3 phases are linearly dependent on magnetic field μ0H (Fig. 2a and its derivative in Supplementary Fig. 2c). This implies that the C = 2 and 3 states are a result of the Landau level (LL) formation coexisting with edge state from band topology22. For the C = 1 phase, there is only a single region present in the phase diagram. So, the C = 1 Chern insulator state in the cAFM is adiabatically connected to the same state in the field-induced FM phase, as discussed above. The phase space of C = 1, 2, and 3 states can also be controlled by the top gate, as shown in Supplementary Figs. 3 and 4.

Figure 2b–g plot the μ0H dependence of ρyx and ρyx at three selected nG. For heavy electron doping n1 ~ 2.23 × 1012 cm−2, ρyx ~ 0 and ρxx ~ 0.005 h/e2 near zero magnetic field. As | μ0H | increases, we see a kink-like feature, namely a sudden increase of both ρyx and ρxx related to the AFM to cAFM transition at HC1 (Fig. 2b, e). For | μ0H | > 10 T, ρyx approaches 0.5 h/e2, indicating a C = 2 Chern insulator state. For n2 ~ 1.87 × 1012 cm−2, upon entering the cAFM phase at | μ0H | ~ 3.6 T, the sample first goes into the C = 1 state with ρyx ~ h/e2 and ρxx = 0.05h/e2. At a higher magnetic field | μ0H | ~ 10 T, it then switches into the C = 2 state with ρyx ~ 0.5h/e2 and ρxx = 0.05h/e2 (Fig. 2c, f). This phase transition from the C = 1 state into a higher Chern number C = 2 state as | μ0H | increases at a fixed carrier density is unusual. Increasing | μ0H | increases the degeneracy of LLs. Therefore, if the quantization is caused by the formation of LLs, then the quantum Hall plateau should always change from higher to lower Chern numbers as the magnetic field increases at a fixed carrier density. The opposite observation here further supports our interpretation that the C = 1 state observed in the cAFM phase is a Chern insulator originating from the intrinsic nontrivial band structure, while the C = 2 state in the FM state is the quantum Hall state due to the formation of LLs23,24. For n3 ~ 1.43 × 1012 cm−2, close to the charge neutral point, the transport data shows an abrupt formation of a C = 1 Chern insulator at spin-flop field HC1, consistent with our discussions above (Fig. 2d, g). The sharp transition exists over a finite doping range, implying that a finite magnetic exchange gap opens suddenly with the spin–flop transition from the AFM to the cAFM phase. This further validates the conclusion that the electronic structure is coupled to the magnetic order17.

We note that similar effects, i.e., the transition from C = 1 to C = 2 states as magnetic field increases, have also been studied in other material systems. For example, in doped magnetic topological insulator quantum well (Mn, Hg) Te23, the increase of magnetic field first leads to a transition from C = 2 to C = 1 due to linear Hall effect, then back to C = 2 state attributed to the effective nonlinear Zeeman effect of Mn ions. A recent theoretical study24 on MnBi2Te4 also suggested that the lowest Landau level, stabilized by Anderson localized state, together with quantum anomalous Hall edge state, can form a C = 2 state. Thus, the increase of magnetic field can give rise to a transition from C = 1 to C = 2 state. Note that Weyl semimetal physics has also been proposed in the FM state of bulk MnBi2Te425,26. So, Landau level could originate either from the surface band in a standard magnetic topological insulator picture15, or from the quantum well states in a confined Weyl semimetal picture18. Considering that the 3D bulk crystal of MnBi2Te4 has not been well established experimentally as a Weyl semimetal, the application of the Weyl physics to the atomically thin flakes needs extra caution. Nevertheless, future studies in the FM state are needed to distinguish these two different physical origins of the high Chern number states.

Electric field control of the cAFM Chern insulator

The association of the formation of C = 1 state with the AFM to cAFM magnetic phase transition suggests the possibility of electric-field control of the Chern number at the cAFM to AFM phase boundary where the magnetic exchange gap should be small. Figure 3a shows ρyx vs. μ0H at nG = 1.0 × 1012 cm−2 and D/ɛ0 = −0.3 V/nm for a dual gated 6-SL MnBi2Te4 device (Device 3), from which we determine the spin–flop field μ0HC1 is about 3 T. The small hysteresis loop in the AFM state is possibly due to magnetic domain effects, as previously reported17. We then map out ρyx (Fig. 3b) and ρxx (Fig. 3c) as a function of nG and D at μ0HC1 = 3 T. The droplet shapes enclosed by the dashed lines in both plots, elongated along the D axis, indicate the C = 1 Chern insulator phases. Figure 3d shows both ρyx and ρxx as a function of D, obtained from line cuts of Fig. 3b and c at nG = 1.1 × 1012 cm−2. As D varies from positive to negative values, the sample starts with small ρyx, enters C = 1 state at optimal Dopt/ɛ0 = −0.3 V/nm supported by the observation of ρyx ~ h/e2 and vanishing ρxx, and finally exits the C = 1 state with reduced ρyx and increased ρxx. The behavior of ρyx and ρxx suggests that the dissipationless chiral edge transport can be switched on and off by an external electric field. The same electric field effect is reproduced in Device 2 (Supplementary Fig. 8).

Fig. 3: Electric control of the cAFM Chern insulator in a dual gated device.
figure 3

a Anti-symmetrized ρyx as a function of magnetic field μ0H near optimal doping in Device 3. μ0HC1 ~ 3 T is identified when ρyx reaches −0.999 h/e2. b, c ρyx and ρxx as functions of gate-induced carrier density nG and electric field D, at fixed magnetic μ0H = 3 T. The droplet shapes enclosed by the black dashed line in b, c show the quantization area where ρyx < −0.9 h/e2 and ρxx < 0.1 h/e2. Insert of b is a schematic of the dual gated device. d, ρyx (blue) and ρxx (red) vs. D at nG = 1.1 × 1012 cm−2, which are linecuts obtained from b, c, indicated by the red arrows. Optimal Dopt/ɛ0 = −0.3 V/nm denoted by black arrow is identified by ρyx ~ h/e2 and vanishing ρxx. ρyx and ρxx in b–d are unsymmetrized.

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The sensitive dependence of the C = 1 state on D near HC1 may be because the electric field directly alters the electronic band structure27,28, or because it affects the magnetic order (e.g., by tuning HC1), which in turn affects the band structure. To distinguish these two mechanisms, we perform gate-dependent RMCD measurements on a 7-SL dual gated device (Device 4). We found that both RMCD signal and spin–flop field are marginally affected by the electric field, but strongly tuned by gate-induced doping (as illustrated in Fig. 4a), consistent with previous reports on 2D magnets19,20. Figure 4b shows the RMCD map as a function of D and nG near spin–flop field HC1. As nG sweeps from electron to hole doping, RMCD significantly increases, i.e., a larger out-of-plane magnetization of the cAFM state at hole doping than electron doping. However, the electric field effect on the magnetic state is marginal, evident by unchanged color along the vertical direction (i.e., parallel to the D axis) in Fig. 4b. The RMCD measurements exclude electric field tuning of the magnetic state as the origin of the electric control of the cAFM Chern insulator state.

Fig. 4: Mechanism of electric control of cAFM Chern insulator.
figure 4

a RMCD as a function of μ0H under selected nG and D. (n1, n2, n3) = (3.1, −3.1, −9.3) × 1012 cm−2, (D1, D2, D3, D4) = (−0.8, 0.3, 0.8, −0.3) V/nm. The data shows that RMCD (n1, D1) = RMCD (n1, D2), and RMCD (n2, D3) = RMCD (n2, D4), i.e. for fixed nG, RMCD signal and spin–flop field has neglibigle dependence on D. The spin–flop field changes significantly when tuning nG. b RMCD map as a function of D and nG at μ0H = 2.75 T. Inset: schematics of cAFM states tuned by nG. The data in (a) and (b) show that the magnetoelectric effect is solely determined by doping. c Illustration of band alignment of top and bottom surfaces under different D. See Maintext for details.

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Discussion

This left us with the explanation that the electric field adjusts the relative energy alignment of the magnetic exchange gaps of the two surfaces, as depicted in Fig. 4c. There is a built-in asymmetry between the top and bottom surfaces, possibly due to the different dielectrics used for top and bottom gates. As D is tuned to the optimal electric field (Dopt), the exchange gaps of top and bottom surfaces are aligned. When the chemical potential is tuned into the exchange gap29,30,31, a well-defined edge state with C = 1 forms. However, when the deviation of D from Dopt is large enough to completely misalign the two magnetic exchange gaps, i.e. the magnetic exchange gap of one surface is aligned to either bulk conduction or valence bands on the other surface, energy dissipative bulk transport is dominant. In the cAFM phase, as the magnetic field increases, the magnetic exchange gap becomes larger as well due to the increase of out-of-plane magnetization. The electric field modulation of the Chern insulator state thus becomes weaker at high field but can be still feasible when the chemical potential is tuned near the band edge (see Supplementary Fig. 9). Our work shows that with the combination of independent control of electric field and carrier doping, as well as intimately coupled magnetic and topological orders, MnBi2Te4 can be a model system for developing on-demand Chern insulator devices and exploring other novel quantum phenomena such as topological magnetoelectric effects.

Methods

Device fabrication

Bulk crystals of MnBi2Te4 were grown out of a Bi–Te flux as previously reported32. Scotch-tape exfoliation onto 285 nm-thick SiO2/p-Si substrates was adopted to obtain MnBi2Te4 from 4 SL to 10 SL, distinguished by combined optical contrast, atomic force microscopy, and RMCD measurements. A sharp tip was used to disconnect thin flakes with the surrounding thick flake. Then the flakes were fabricated into single-gated or dual-gated devices. Single-gated devices were fabricated by electron beam lithography with Polymethyl methacrylate (PMMA) resist and followed by thermal evaporation of Cr (5 nm) and Au (50 nm) and liftoff in anhydrous solvents. Then the devices were covered with PMMA as the capping layer. This fabrication process brought spatial charge inhomogeneity and doped the flake. The measured voltages of charge neutrality points shifted between the thermal cycle from 2 to 300 K. Dual-gated devices were fabricated by stencil mask method33, followed by thermal evaporation of Au (30 nm) and transfer of 30–60 nm h-BN as capping layer by polydimethylsiloxane (PDMS). Standard electron beam lithography (EBL) was adopted to define outer electrodes and metal top gates. Since the highly reflective Au top gate (Device 2 and 3) forbids the RMCD measurements, we also fabricated an optical dual-gated device with graphite top gate (Device 4). Before EBL we transfer a thin graphite (5–20 nm) on top of h-BN with PDMS. For this particular device, a bulk flake which connects to the thin one is used as the contact. In this way, there is no metal underneath or deposited on top of hBN. Thus, Device 4 provided higher doping density than other ones. During the fabrication, MnBi2Te4 was either capped by PMMA/hBN or kept inside an Argon-filled glovebox to avoid surface degradation.

Transport measurements

Transport measurements were conducted in a dilution refrigerator (Bluefors) with low-temperature electronic filters and an out-of-plane 13 T superconductor magnet coil. Four-terminal longitudinal resistance Rxx and Hall resistance Ryx were measured using standard lock-in technique with an a.c excitation of 0.5–10 nA at 13.777 Hz. The a.c. excitation was provided by the SR830 in series with a 100 MΩ resistor, flowed through the device, and was pre-amplified by DL1211 at 1 V/10−6 A sensitivity. Rxx and Ryx signals were pre-amplified by differential-ended mode of SR560 with a 1000 times amplification. All preamplifiers were read out by SR830. A similar amplifier chain provided approximately ±3% uncertainty in the previous study34. We estimated our uncertainty was of the same order. In Figs. 1–4, ρyx overshoot 2.36%, 0.92%, 1.14% and 1.7%, respectively. The sheet resistivity ρxx and ρyx were obtained by ρxx = s × Rxx/l and ρyx = Ryx where s was the width of the current path, l was the length between two voltage probes, estimated from device geometry. Magneto-transport data involved positive and negative magnetic fields was anti-symmetrized/symmetrized by a standard method to avoid geometric mixing of ρxx and ρyx. As this mixing did not affect the topological transport signal, we presented raw data for fixed magnetic field study. To convert top gate voltage Vtg and bottom gate voltage Vbg into gate-induced carrier density nG and electric field D, we used nG = (VtgCtg + VbgCbg)/e and D/ɛ0 = (VtgCtg − VbgCbg)/2ɛ0, where Ctg and Cbg are top and bottom gate capacitance obtained from device geometry, e the electron charge and ɛ0 the vacuum permittivity. This formula is derived from the parallel-plate capacitor model. Fixing D(nG) and sweeping nG(D) monotonically modify the carrier density n2D (external displacement field Dext) and thus the chemical potential (electric field) of the device. To obtain the nG-D maps, we first got Vtg − Vbg maps of transport data by sweeping Vbg from the negative side to the positive for every fixed Vtg. Converting Vtg − Vbg to nG−D leads to the uncovered parameter space, e.g., in Figs. 3b, c and 4b. The n-μ0H (Vbg − μ0H) maps were taken by sweeping dual gates (back gate) quickly, ~4 min per data line back and forth, while sweeping magnetic field slowly, ~0.015 T/min. This method gave digitized noise or unfinished lines near the field limit, e.g., near 0 T of Fig. 2a.

Reflective magnetic circular dichroism measurements

The experiment setup follows our previous RMCD/MOKE study of magnetic order in CrI3. RMCD measurements were performed in an attoDRY cryostat with attocube xyz piezo stage, the base temperature of 1.6 K and 9 T superconducting magnet. The magnetic field was applied perpendicular to the sample plane. Linearly polarized 632.8 nm He–Ne laser with 200 nW power was focused through an aspheric lens to form ~2 µm beam spot on the sample surface. The out-of-plane magnetization of the sample induced magnetic circular dichroism (MCD) ΔR, the amplitude difference between the reflected right- and left-circularly polarized light. To obtain the RMCD ΔR/R signal, two lock-in amplifiers SR830 were used to analyze the output signals from a photomultiplier tube with the chopping frequency p = 1.377 kHz and photoelastic modulator frequency f = 50 kHz. The ratio between p-component signal I1 and f-component signal I2 is proportional to the RMCD signal: ΔR/R = I2/(J1(π/2) × I1) where J1 is the first-order Bessel function.