Introduction

Van der Waals materials provide an interesting platform to study the intertwined magnetism and band topology1,2, and a series of exotic states of matter emerge. Among them, quantum anomalous Hall effect (QAHE) attracted a lot of attention. For QAHE, the most interesting part would be quantized plateau of Hall conductance as well as the dissipationless chiral edge transport channels that emerge at the Chern insulator states. Besides, the chirality of the edge transport, as well as the magnetization, play an essential role in dissipative transport regimes, for instance, non-reciprocal charge transport behaviors2,3,4,5,6.

Non-reciprocal response, manifesting as the resistance difference between positive and negative current, is the central process to convert an oscillating electromagnetic field to a direct current, in other words, rectification. The demand of low-power, high-frequency rectifiers inspires studies on non-reciprocal charge transport in new material systems, such as non-centrosymmetric crystals7,8,9,10,11,12, topological insulators13,14,15,16,17, magnet/superconductor interfaces18,19, topological insulator/superconductor interfaces20 and magnet/topological insulator interfaces3,21,22. Especially, a large non-reciprocal charge transport mediated by quantum anomalous Hall edge states has been observed in magnetically doped topological insulator14. As compared to traditional magnetically doped topological insulators, the intrinsic magnetic topological insulator MnBi2Te4 provides more robust QAHE, since it does not introduce magnetic impurities and remove the need of precise control of element species. Due to the ferromagnetic intralayer coupling and antiferromagnetic interlayer coupling, MnBi2Te4 also hosts rich magnetic phases, including fully compensated antiferromagnetic, uncompensated antiferromagnetic and spin-aligned ferromagnetic states. External magnetic field turns out to be an effective tool to manipulate such magnetic states as well as the charge transport. Besides, the van der Waals nature of MnBi2Te4 makes it possible to realize more attractive phenomena by changing stacking sequence or assembling heterostructure23,24,25,26,27,28,29,30.

In our current manuscript, we have demonstrated controllable large non-reciprocal charge transport in an intrinsic magnetic topological insulator MnBi2Te4. Due to its unique antiferromagnetic van-der-Waals structure, the large non-reciprocal charge transport in MnBi2Te4 can be manipulated by gate voltage, magnetic field and septuple layer numbers. The observation of tunable non-reciprocal resistance may help to develop multifunctional spintronic devices, such as magnetic switchable diodes and high-frequency rectification.

Results

Chiral edge states revealed by quantum anomalous Hall effect

First, we show the characterization of MnBi2Te4 devices. The device structure is shown in Fig. 1a. In details, MnBi2Te4 thin flakes are obtained by Al2O3-assisted exfoliation31,32. The sample thickness is determined by optical contrast as shown in Supplementary Fig. 1. We have chosen four 5-SL (Device 1, Device 2, Device 4, and Device 5) and one 4-SL (Device 3) MnBi2Te4 in our measurements. In the main text, we show the results from Device 1 and Device 3. Au electrodes are thermally deposited through stencil masks, which avoids the degradation from the chemical or ambient exposure and ensures the high device quality. The Si/SiO2 bottom gate or the graphite/hBN top gate works as gate. We measure the longitudinal resistance of a 5-SL MnBi2Te4 as a function of temperature as shown in Fig. 1b. The Néel temperature is around 23 K, which is indicated by the resistance peak. The temperature dependent resistance of other two devices are shown in Supplementary Fig. 2a, b. Three devices display similar Néel temperature.

Fig. 1: The characterization of MnBi2Te4 devices.
figure 1

a The schematic structure of the MnBi2Te4 device. The MnBi2Te4 thin flakes are obtained by Al2O3-assisted exfoliation method. Au electrodes are thermally deposited through stencil masks. Si/SiO2 and graphite/hBN work as bottom and top gate, respectively. b The temperature-dependent resistance of a 5-SL MnBi2Te4 (Device 1) device. The Néel temperature (TN) is indicated by a resistance peak around 23 K. c, d The transverse and longitudinal resistance as a function of the magnetic field at 1.7 K for Device 1. A top gate voltage of −2 V is applied to tune the Fermi energy to the charge neutrality point.

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To reveal the chiral edge states in MnBi2Te4, we tune the Fermi level to the charge neutrality point (CNP). 5-SL MnBi2Te4 owns uncompensated magnetic moments under zero external magnetic field when temperature below the Néel temperature, as shown in Fig. 1c, d. We also show the fully compensated antiferromagnetic states of a 4-SL MnBi2Te4 device in Supplementary Fig. 4d. We note that in the ideal quantum anomalous Hall state, only chiral edge states contribute to the charge transport and the longitudinal resistance becomes zero. However, longitudinal resistance in our MnBi2Te4 samples does not vanish. For our Device 2 and Device 3, the nearly quantized Hall resistance of 0.977 h/e2 and 0.945 h/e2 have been achieved (Supplementary Fig. 2 and Supplementary Fig. 3).

Large non-reciprocal resistance in MnBi2Te4

Next, we study the non-reciprocal charge transport in MnBi2Te4 devices. As shown in Fig. 2a, when the current is injected in opposite directions, charge carriers at the same edge are scattered by the chiral state in different ways. This leads to a difference in resistance under current reversal, so-called non-reciprocal charge transport behaviors. Here, we adopt the phenomenological model33 to describe the current relevant resistance:

$${V}_{xx}=i{R}_{{xx}}={{iR}}_{0}+\gamma {R}_{0}{i}^{2}\left(\hat{M}\times \hat{P}\right)\cdot \hat{i},$$
(1)

where R0 is the resistance that does not change with the current, γ is the constant that characterizes the strength of the non-reciprocal charge transport effect, \(\hat{M}\) is the magnetization direction of the MnBi2Te4, \(\hat{P}\) is the edge charge dipole which is opposite on two edges, and \(\hat{i}\) is the current direction. We study the non-reciprocal charge transport by measuring the resistance difference between positive and negative currents in a 5-SL MnBi2Te4 as described in Fig. 2a. The 10 μA and −10 μA DC current is injected to the device respectively, and we measure the longitudinal resistance at the right edge at 11 K. A top gate voltage of −2 V is applied, at which the Fermi level is around the CNP. In Fig. 2b, we plot the resistance difference as a function of the magnetic field. The resistance difference ∆R is defined as RL(10 μA) − RL(−10 μA) and the value is antisymmetrized for M. The raw data are shown in Supplementary Fig. 5. A large resistance difference is observed, reaching the magnitude of 100 Ω. Such a resistance difference cannot originate from thermal effect as we discuss in Supplementary Note 5. We then compare the non-reciprocity in MnBi2Te4 and Cr-doped (Bi,Sb)2Te3 by \(\triangle R/{R}_{0}/I\). Under 7 T magnetic field, the \(\triangle R/{R}_{0}/I\) reaches 2911 A−1 in MnBi2Te4, which is comparable to 2600 A−1 in Cr-doped (Bi,Sb)2Te314.

Fig. 2: Non-reciprocal charge transport in a 5-SL MnBi2Te4.
figure 2

a Schematic illustrations of current direction dependent backscattering of edge transport. The chiral edge states are indicated by green arrows. b Resistance difference between positive and negative current as a function of the magnetic field. The measurement is performed at 11 K with top gate voltage of −2 V. c, d The non-reciprocal resistance measured at the right edge and left edge, respectively. The injected current IRMS is 5 μA. The measurements are performed at 11 K with top gate voltage of −2 V. Insets show schematic illustrations of the interplay between chiral edge states and 2D bulk transport channels (e.g., surface states) at different magnetic states.

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Since the non-reciprocal response are originated from the quadratic term of current, we adopt the second-harmonic voltage measurements with small AC driven current IRMS =5 μA to obtain better signal-to-noise ratio and rule out other high-order effects. With the base frequency of the driven current set as 17.777 Hz, the voltage drop is written as:

$${V}_{{xx}}=\sqrt{2}{{\sin }}\left(\omega t\right){R}_{0}+\gamma {R}_{0}{i}^{2}\left(1-{{\cos }}\left(2\omega t\right)\right)\left(\hat{M}\times \hat{P}\right)\cdot \hat{i}.\,$$
(2)

The voltage with the frequency of 35.554 Hz reveals the strength of the non-reciprocal charge transport effect. Here, the non-reciprocal resistance is defined as \({R}_{{xx}}^{2\omega }={V}_{{xx}}^{2\omega }/{I}^{{{{{{{\rm{RMS}}}}}}}}\), where \({V}_{{xx}}^{2\omega }\) is the second-harmonic voltage measured by the lock-in amplifier. In Fig. 2c, we show the non-reciprocal resistance as a function of magnetic field, which is antisymmetrized for M. The magnitude of γ is estimated by \(\gamma=\sqrt{2}{R}_{{xx}}^{2\omega }/({R}_{0}\cdot {I}^{{{{{{{\rm{RMS}}}}}}}})\). At 11 K, the γ is 4.5 × 103 A−1 under the magnetic field of 7 T, and 1.4 × 103 A−1 without the external magnetic field. We also study the current magnitude dependent non-reciprocal resistance as shown in Supplementary Fig. 8. The non-reciprocal resistance scales linearly with the AC current magnitude, which agrees well with our phenomenological model.

Remarkably, the A-type antiferromagnetic order unlocks complicated magnetic states and it deeply influences the non-reciprocal resistance. Applying the magnetic field aligns magnetic moments along with the external field. By controlling the magnetization, the bulk/edge conduction ratio is manipulated. Meanwhile, the chirality of the edge transport can be switched by reversing magnetic moments, leading to opposite non-reciprocity at opposite magnetic states. The finite non-reciprocal resistance is observed without external magnetic field and shows the sign reversal under magnetic states ↑↓↑↓↑ and ↓↑↓↑↓ due to the uncompensated magnetic moments in the 5-SL MnBi2Te4. Multiple non-reciprocal resistance plateaus under magnetic field are also revealed including fully spin polarized states ↑↑↑↑↑ and ↓↓↓↓↓. The abundant magnetic field controlled non-reciprocal resistance states are absent in other non-reciprocal system, such as magnetically doped topological insulator. We show the non-reciprocal resistance in Device 2 in Supplementary Fig. 6. Apart from magnetic field, non-reciprocal resistance in MnBi2Te4 is edge position sensitive. In Fig. 2d, we show the non-reciprocal resistance as a function of magnetic field measured at the left edge of the device. Non-reciprocal resistance that measured at two different edges shows the close magnitude, but the sign is reversed. This behavior indicates the broken inversion symmetry of the edge transport and the edge–charge dipole \(\hat{P}\) at two edges is opposite.

Magnetic moments of 4-SL MnBi2Te4 are fully compensated under zero magnetic field, for which the non-reciprocal charge transport in 4-SL MnBi2Te4 shows different behaviors compared with that in 5-SL MnBi2Te4. In Fig. 3a, b, we show the field dependent non-reciprocity γ of 5-SL and 4-SL MnBi2Te4 devices, respectively. The non-reciprocal resistance for both devices are measured at the right edge with slightly electron doping. We find in high-magnetic-field regime, non-reciprocity of 5-SL MnBi2Te4 and 4-SL exhibit the same order of magnitude. However, under zero magnetic field, non-reciprocal resistance nearly vanishes in 4-SL MnBi2Te4 devices. This is consistent with the phenomenological model for M = 0 and the current relevant term vanishes. The vanished non-reciprocity with zero magnetization can be further confirmed by measuring the non-reciprocal resistance at paramagnetic states. Increasing the temperature above the Néel temperature results in the breakdown of chiral edge states even under high magnetic field, leading to vanished non-reciprocal resistance, which is shown in Supplementary Fig. 9.

Fig. 3: Non-reciprocal charge transport in 5-SL MnBi2Te4 and 4-SL MnBi2Te4.
figure 3

a Magnetic field dependent non-reciprocity for a 5-SL MnBi2Te4 device. A top gate voltage of 3 V is applied, and the sample is slightly electron doped. Insets show the schematic illustrations of two magnetic states under zero magnetic field. b Magnetic field dependent non-reciprocity for a 4-SL MnBi2Te4 device. The AC driven current IRMS = 1 μA is adopted in measurements. The measurements are performed at the temperature of 11 K. A top gate voltage of 3 V is applied, and the sample is slightly electron doped. Insets show schematic illustrations of two magnetic states under zero magnetic field.

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Gate tunability of non-reciprocal charge transport

Finally, we demonstrate the gate tunability of the non-reciprocal charge transport in MnBi2Te4. In Fig. 4, we show the gate dependent \({R}_{{{{{{\rm{L}}}}}}}^{2\omega }\) and \({R}_{{{{{{\rm{R}}}}}}}^{2\omega }\) at 11 K with various top gate voltage. We find that both the magnitude and sign of the \({R}_{{{{{{\rm{L}}}}}}/{{{{{\rm{R}}}}}}}^{2\omega }\) can be tuned by applying gate voltage. In high field regime, \({R}_{{{{{{\rm{L}}}}}}}^{2\omega }\) at the spin state ↑↑↑↑↑ is tuned from positive to negative when gate voltage is scanned from −5 V to 5 V, while \({R}_{{{{{{\rm{R}}}}}}}^{2\omega }\) shows the opposite trend. The gate tunability is also valid under zero magnetic field, where the loop chirality is switched while scanning top gate voltage from −5 to 5 V. We note the gate voltage does not switch the ↑↓↑↓↑ and ↓↑↓↑↓ states as we discussed in Supplementary Note 9. Besides, optical magnetic circular dichroism (MCD) reveals the magnetization is gate voltage independent in the field regime of −1 to 1 T. Therefore, it is the change of Fermi energy that affects the non-reciprocal charge transport.

Fig. 4: Non-reciprocal resistance at various top gate voltages.
figure 4

a Non-reciprocal resistance as a function of magnetic field measured at the left edge. b Non-reciprocal resistance as a function of magnetic field measured at the right edge.

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To provide more insights into the effect of gate voltage on the non-reciprocal charge transport, we summarize the gate dependence of longitudinal resistance and non-reciprocal resistance in Fig. 5. As shown in Fig. 5a, the longitudinal resistance under zero magnetic field shows the maximum at the top gate voltage of −2 V. We also show sign reversal of the \({R}_{{{{{{\rm{L}}}}}}}^{2\omega }\) and \({R}_{{{{{{\rm{R}}}}}}}^{2\omega }\) while scanning gate voltage at different magnetic states in Fig. 4b, c. Further study about magnetic-field-direction dependent non-reciprocal charge transport is shown in Supplementary Fig. 13. A dip of \({R}_{{{{{{\rm{R}}}}}}}^{2\omega }\) when the Rxy reaches the maximum value under an out-of-plane magnetic field is observed in Device 4, indicating that the coexistence of chiral edge transport and bulk transport plays an important role in the non-reciprocal charge transport.

Fig. 5: Gate tunability of non-reciprocal resistance at different magnetic states in 5-SL MnBi2Te4.
figure 5

a Longitudinal resistance of the 5-SL MnBi2Te4 as a function of the top gate voltage under zero magnetic field. The measurement is carried out at 11 K. The resistance shows a maximum at the charge neutrality point (CNP) with the top gate voltage of −2 V. b, c Non-reciprocal resistance measured at left edge and right edge of the 5-SL MnBi2Te4, respectively. Different curves show the non-reciprocal resistance at spin states of ↓↓↓↓↓, ↓↑↓↓↓ and ↓↑↓↑↓.

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Discussion

The remarkable features of non-reciprocal resistance can be rationalized by a simple band structure scenario on the QAHE edge. At the CNP, we should note that our devices deviate slightly from the fully insulating state and Rxy being smaller than h/e2 (see Fig. 1c). Therefore, one chiral edge state and trivial edge states (including subbands from the 2D bulk) coexist, from which the local edge transport is detected by two voltage electrodes. Apart from MnBi2Te4, prior studies on magnetically doped topological insulators show the small finite longitudinal resistance in presence of nonchiral edge states and residual bulk states34. In the ideal QAHE case, the pure chiral edge state would not lead to non-reciprocal transport, since its Rxx = 0. In the weakly doped QAHE which is the case in present work, chiral edge state hybridizes strongly with trivial edge states, leading to asymmetric dispersion between opposite momenta, i.e., different magnitudes of Fermi velocities along opposite directions. This velocity asymmetry coincides with the fact that both inversion symmetry and time-reversal symmetry are broken on the edge. Suppose a finite relaxation time, the direction-dependent mean free path comes with direction-dependent Fermi velocity and eventually leads to direction-dependent resistance. Moreover, the induced resistance change is maximized near the band edge of trivial states, explaining the large non-reciprocal effect near the CNP6. Further, the velocity asymmetry flips order between conduction and valence bands, or when reversing the magnetism or changing edge sides, rationalizing related experimental sign changes.

In summary, we have demonstrated the non-reciprocal charge transport in an intrinsic magnetic topological insulator MnBi2Te4. The broken inversion symmetry and broken time-reversal symmetry in the dissipative charge transport regime are key components of the non-reciprocity in our study. By manipulating the symmetry breaking, the septuple layer dependent non-reciprocity turns out to be magnetically controllable and edge position sensitive. Meanwhile, the observed non-reciprocal resistance can be tuned by gate voltage. We ascribe the observed non-reciprocal resistance to the interaction between chiral edge states and dissipative states. Our finding paves the way to build next-generation spintronic devices though chirality engineering.

Methods

Device fabrication

High-quality MnBi2Te4 crystals are grown by flux methods. MnBi2Te4 thin flakes are obtained by Al2O3 assisted exfoliation method. We determine the thickness of MnBi2Te4 thin flakes by optical contrast of captured optical images of MnBi2Te4/Al2O3 on PDMS stamps. MnBi2Te4 thin flakes, as well as the Al2O3 film are then transferred on Si/SiO2 substrates. Au electrodes are thermally deposited through stencil masks. Finally, the hBN and graphite are transferred on top of the selected MnBi2Te4 flake. The fabrication processes before covering hBN and graphite are performed in a N2-filled glove box.

Electrical measurements

DC transport measurements are performed by a current source (Keithley 6221) and a nanovoltmeter (Keithley 2182A). The top gate voltage and bottom gate voltage are applied by a dual-channel sourcemeter (Keithley 2636B). AC transport measurements are performed by a current source (Keithley 6221) and a lock-in amplifier (Zurich MFLI). All measurements are carried out with a Cryomagnetic cryostat.