Abstract
Natural superlattice structures MnBi2Te4(Bi2Te3)n (nâ=â1, 2, ...), in which magnetic MnBi2Te4 layers are separated by nonmagnetic Bi2Te3 layers, hold band topology, magnetism and reduced interlayer coupling, providing a promising platform for the realization of exotic topological quantum states. However, their magnetism in the two-dimensional limit, which is crucial for further exploration of quantum phenomena, remains elusive. Here, complex ferromagnetic-antiferromagnetic coexisting ground states that persist down to the 2-septuple layers limit are observed and comprehensively investigated in MnBi4Te7 (nâ=â1) and MnBi6Te10 (nâ=â2). The ubiquitous Mn-Bi site mixing modifies or even changes the sign of the subtle interlayer magnetic interactions, yielding a spatially inhomogeneous interlayer coupling. Further, a tunable exchange bias effect, arising from the coupling between the ferromagnetic and antiferromagnetic components in the ground state, is observed in MnBi2Te4(Bi2Te3)n (nâ=â1, 2), which provides design principles and material platforms for future spintronic devices. Our work highlights a new approach toward the fine-tuning of magnetism and paves the way for further study of quantum phenomena in MnBi2Te4(Bi2Te3)n (nâ=â1, 2) as well as their magnetic applications.
Similar content being viewed by others
Introduction
The interplay between magnetism and topology inaugurates a new horizon in exploring exotic quantum phenomena, such as the quantum anomalous Hall effect (QAHE), axion insulators and magnetic Weyl semimetals1,2,3,4,5,6. Recently, MnBi2Te4 (MBT) was discovered to be an intrinsic stoichiometric antiferromagnetic (AFM) topological insulator (TI)7,8,9,10,11,12,13,14. The intertwined band topology and magnetic order in A-type AFM MnBi2Te4 pose great challenges to the realization of its exotic topological physics and subsequent devices, because either the layer number of the material needs to be strictly controlled, or a high magnetic field (~6â8âT) is required11,12,13,14. Therefore, there is an urgent need to develop a magnetic topological insulator of the MBT family that is magnetically insensitive to the number of layers and has a small saturation field, in which engineering of the interlayer magnetic interaction is the key. Now, the natural superlattice structure MnBi2Te4(Bi2Te3)n (nâ=â1, 2, ...) provides an opportunity to modify the interlayer exchange coupling using nonmagnetic Bi2Te3 (BT) quintuple layer (QL) as spacer layers15,16,17,18,19,20. With the increase of n, the interlayer AFM coupling gradually weakens, while the global spin-orbit coupling strength gradually increases with the increase of Bi content16,17,18,19,20,21. For MnBi4Te7 (nâ=â1) and MnBi6Te10 (nâ=â2), neutron scattering experiments and theoretical calculations show that they possess weak interlayer magnetic coupling, but still maintain the A-type AFM structure19,20,21,22,23, that is, in each MBT septuple layer (SL), the Mn magnetic moments are ferromagnetically aligned, while the adjacent SLs are antiferromagnetically aligned. Although tremendous efforts have been devoted to studying the magnetic properties of the MnBi4Te7 and MnBi6Te10, most studies have only focused on their bulk phase16,17,18,19,20,24,25,26,27. However, the magnetic property and topological phase in MBT family often exhibit intricate thickness dependence, posing a significant influence for the realization of exotic topological physics11,12,13,14,28,29,30. Therefore, determining the magnetism of MnBi2Te4(Bi2Te3)n (nâ=â1, 2) at their two-dimensional (2D) limit is crucial, but has so far remained elusive.
In this work, we systematically investigate the magnetic properties of MnBi4Te7 and MnBi6Te10 thin flakes down to 1âSL by employing polar reflective magnetic circular dichroism (RMCD) spectroscopy. We demonstrate that the odd-even-layer oscillation of compensated and uncompensated AFM states, a common effect in ideal A-type AFM materials13,30,31,32, vanishes in atomically thin MnBi4Te7 and MnBi6Te10. In all the measured samples above 1âSL, in addition to the AFM spin-flip transition, a significant ferromagnetic (FM) hysteresis loop centered at zero field is observed. We reveal that the peculiar hysteresis loop arises from the complex FM-AFM coexisting ground state. Atomic-resolution electron energy loss spectroscopy (EELS) mapping as well as single-crystal X-ray diffraction (SC-XRD) reveal the ubiquitous Mn-Bi site mixing in the crystals. The spins of the randomly distributed MnBi antisite defects in each SL are antiferromagnetically coupled to the spins of the main Mn layer23,24,33, that further modify or even change the sign of the subtle inter-SL magnetic interactions, yielding a spatially inhomogeneous interlayer coupling. As a result, the energy gained through the formation of magnetic domains compensates for the energy cost in the appearance of domain walls, yielding a complex FM-AFM coexisting ground state. Furthermore, a tunable exchange bias effect is observed in MnBi4Te7 and MnBi6Te10, arising from the coupling between the FM and AFM components in the ground state. The direction of this exchange bias can be easily tuned by the historical polarization field and does not require warming and field cooling processes. Our results reveal the nontrivial magnetic ground states in MnBi4Te7 and MnBi6Te10, keeping the promise for further investigation of exotic topological quantum states.
Results
FM-AFM coexisting ground states of MnBi4Te7 and MnBi6Te10
High-quality MnBi4Te7 and MnBi6Te10 bulk crystals are grown by flux method34 and confirmed by XRD results (Supplementary Fig. S1). The field-cooled (FC) and zero-field-cooled (ZFC) magnetic susceptibilities of Hâ¥c (Ïc) of MnBi4Te7 and MnBi6Te10 crystals show that their long-range AFM orders occur at Néel temperature (TN) of 12.1âK and 10.9âK, respectively (Supplementary Fig. S2). Compared with MnBi2Te47,22 (TN of ~24.5âK), the reduction of TN in MnBi4Te7 and MnBi6Te10 manifests the weakened interlayer coupling. Scrutiny of the MâH curve at 2âK under Hâ¥c, we find that MnBi4Te7 (MnBi6Te10) undergoes a spin transition at a very low magnetic field and quickly enters the forced FM state with a field of about 0.25âT (0.21âT). This is in sharp contrast to MnBi2Te4, where the spin-flop transition occurs at about 3.5âT and its magnetic moment eventually saturates under external magnetic fields larger than 8âT11,12,13,30 (Supplementary Fig. S3a). We can estimate the interlayer antiferromagnetic coupling Jc and single-ion anisotropy D based on the StonerâWohlfarth model35, giving SJcâââ0.0127âmeV and SDâââ0.0440âmeV in MnBi4Te7 and SJcâââ0.0037âmeV and SDâââ0.0417âmeV in MnBi6Te10 (see details in Supplementary Note I). The anisotropy energy of MnBi4Te7 and MnBi6Te10 are of the same order of magnitudes as that of MnBi2Te4, but the interlayer coupling values of MnBi4Te7 and MnBi6Te10 are almost 1â2 orders of magnitude smaller than that of MnBi2Te419,30,33,36, indicating a greatly reduced interlayer coupling from MnBi2Te4 to MnBi4Te7 and MnBi6Te10.
To explore how the weakened interlayer exchange coupling affects the magnetic ground order, we investigated the layer-number-dependent magnetism of MnBi4Te7 and MnBi6Te10 using the RMCD spectroscopy. Atomically thin flakes down to 1âSL are mechanically exfoliated from their bulk crystals onto gold substrates using the standard Scotch tape method37 (Fig. 1a). The number of layers is confirmed by atomic force microscopy characterizations (see Supplementary Fig. S4 for MnBi4Te7 samples and Fig. S5 for MnBi6Te10 samples). Typical height line profiles of the stepped MnBi6Te10 flakes indicate SL and QL thicknesses of approximately 1.4 and 1.0ânm, respectively (Fig. 1b), consistent with previous reports29,38. The layer-number-dependent magnetic behavior in MnBi4Te7 and MnBi6Te10 is very similar, so here we show 1â4 SLs MnBi6Te10 as examples, and provide the full set of other samples in Supplementary Figs. S6 and S7. 1-SL MnBi6Te10 shows a distinct RMCD signal at zero field and a clear hysteresis loop (Fig. 1c), confirming its FM nature. With increasing temperature, the hysteresis loop shrinks and disappears at 10âK, indicating an FM to paramagnetic phase transition (Supplementary Fig. S8a). Compared with the intrinsic 1-SL MnBi2Te4 (TCâ=â14.5âK)30, the decreased TC may be due to the increased BiMn sites, as the intralayer exchange coupling decreases with the increase of the average distance between the Mn sites. Surprisingly, with increasing thickness, no odd-even layer-number oscillation occurs, which is a typical feature of ideal A-type AFM materials. Instead, both FM and AFM signals (confirmed by the following discussions) are present in all the measured samples with SL number Nâ>â1 (Fig. 1c). In the 2-SL sample, there is a distinct residual magnetic moment after spin-flipping near zero field during the descending field, indicating the existence of additional FM component. Here we denote the transition fields of the AFM and FM components as Hf and Hc, respectively. With increasing thickness, the magnetic reversal curve evolves into two AFM and one FM spin-flip transitions with different magnetic moment amplitudes (Fig. 1c).
As the temperature increases, the value of the spin-flip field \({H}_{{{{{{{{\rm{f-}}}}}}}}}^{1}\) in the 3-SL sample changes from negative to positive, and then slowly decreases to approach zero (Fig. 1d, e). A positive value of \({H}_{{{{{{{{\rm{f-}}}}}}}}}^{1}\) again signifies the AFM nature of this spin-flip process, since interlayer AFM coupling prefers to make the magnetic moment in adjacent layers be antiparallel, while the Zeeman energy tends to keep the magnetic moment parallel to the magnetic field. Since the AFM interlayer coupling is stronger in the MnBi4Te7 samples, \({H}_{{{{{{{{\rm{f-}}}}}}}}}^{1}\) usually occurs at larger positive values (see Supplementary Figs. S6 and S9). The FM spin-flip field Hcâ of the MnBi6Te10 samples increase monotonically from a negative value and approach zero with increasing temperature (Fig. 1d, e and Supplementary Fig. S8b). However, in some MnBi4Te7 samples (Supplementary Fig. S9d), Hcâ first increases from negative to positive and then jumps back to negative with increasing temperature, signifying the correlated coupling between the FM and AFM components.
Specifically, we build a five-layer macrospin model to interpret the hysteresis loops in the MnBi4Te7 and MnBi6Te10 samples (Supplementary Fig. S10), which captures the main features. But in fact, the FM and AFM distributions and proportions can be very complex due to the spatial inhomogeneity. We denote the proportions of FM and AFM components by \({f}_{{{{{{{{\rm{FM}}}}}}}}}=\frac{{{\mbox{RMCD(FM flip height)}}}}{{{\mbox{RMCD(up-saturation)}}}-{{\mbox{RMCD(down-saturation)}}}}\) and fAFMâ=â1âââfFM, respectively. As expected, fAFMâ~â0 (fFMâ~â1) in the 1-SL sample (Fig. 1f). The fAFM (fFM) of MnBi6Te10 samples increases (decreases) as the number of layers increases. In most samples, the values of fAFM do not coincide with those expected for single-domain case (cross marks in Fig. 1f), indicating a multi-domain configuration within the laser spot size. The values of fFM and fAFM are nearly temperature independent over the entire measurement temperature range (Fig. 1g).
After confirming the FM-AFM coexistence ground states, the puzzling magnetism of bulk MnBi4Te7 and MnBi6Te10 can also be well explained. It is worth noting that at low temperatures, the MnBi4Te7 and MnBi6Te10 crystals exhibit non-zero magnetization at zero field8,16,17,18,19,22,29, and the magnetic reversal completes through three sluggish spin-flip transitions (marked by the arrows in Supplementary Fig. S3). The non-zero magnetization at the zero field suggests that there may be some residual FM components in the AFM sate. The FM-AFM coexisting magnetic order is also confirmed by the bifurcations of the ZFC and FC curves at temperatures slightly below the Néel temperature (Supplementary Fig. S2). The large difference in the values of fAFM between thin flakes and bulk crystals suggests that the FM-AFM coexisting magnetic order is possibly a thickness-related effect. The complex multi-domain structure in the bulk samples smears the distinct signatures of the FM-AFM coexisting ground state, resulting in sluggish changes in the magnetic moment, which also masks the potential applications of this unique magnetic order.
Origin of the FM-AFM coexisting ground state
Due to the weak interlayer coupling, the energy difference between the AFM and FM spin configurations is very small19,20, providing a breeding ground for the magnetism tuning39,40. Cross-sectional atomic-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image along the [100] direction shows that two Bi2Te3 layers are inserted between MnBi2Te4 layers in MnBi6Te10 (Fig. 2a, b). The crystal structure and stacking remain intact all the way to the surface, and no stacking disorders are observed (Supplementary Fig. S11). However, the experimental and simulated integrated HAADF intensity profiles along the c-axis show clear discrepancy, showing BiMn antisite defects in SL (red arrow in Fig. 2a) and MnTe in QL (gray arrow in Fig. 2a). In addition, atomic EELS mapping shows clear Mn signals in the Bi layers in SL and also QL (Fig. 2b), demonstrating the existence of the MnBi antisite defects (see Supplementary Fig. S11 for more details).
Below TN, the spins of Mn atoms are ferromagnetically coupled (âJ1) within the SL, but antiferromagnetically coupled (J4) with those of Mn atoms in the adjacent SL. The spins of MnBi in SL are ferromagnetically coupled (âJ2) within the sublayer, but antiferromagnetically coupled (J3) to the main Mn layer33, forming a ferrimagnetic SL configuration (Fig. 2c). Flipping the spins of MnBi in SL to align with those in the Mn layer requires a magnetic field above 50âT33, so all spins in SL flip together under a small magnetic field. This stable ferrimagnetic SL configuration results in a reduced measured saturation magnetic moment than the theoretically value19 (Supplementary Fig. S3), and determines that the magnetic moment change at low magnetic fields (from â0.2 to 0.2âT) comes only from that of the main Mn layer. Considering that Mn atoms doped into the Bi2Te3 always tend to be ferromagnetically coupled41,42,43, the spins of MnBi are expected to be ferromagnetically coupled (âJ5) in the adjacent SLs and within QLs. The magnetic moment in the QL to flip to align with the magnetic field requires a magnetic field of about 8 and 6âT in MnBi4Te7 and MnBi6Te1024, respectively (marked by the arrows in Supplementary Fig. S3). For simplification, we do not additionally consider the coupling in QL and accommodate it in J5, which effectively strengthens the FM coupling between the MnBi antisites in the two neighboring SLs. Then, the Hamiltonian of the 2-SL system can be expressed as:
where m and M are the magnetic moments at each Bi and Mn lattice sites, superscripts 1 and 2 represent the SL layer indices, and the sum is over all the nearest-neighboring lattice sites. In the presence of MnBi antisite defects, the energy difference per unit cell between the AFM and FM configurations (Fig. 2c, d) can be expressed as:
This energy difference increases with the amount of Mn-Bi site mixing (the summation of M at Mn layer decreases and the summation of m at Bi layer increases), eventually leading to a change in the sign of the interlayer magnetic coupling (from AFM to FM). The randomly distributed MnBi antisites lead to a spatially inhomogeneous interlayer coupling. As a result, the FM-AFM coexisting ground states are expected to emerge when the energy gain from forming FM domains exceeds the energy cost from forming domain walls. In general, the lattice defect concentration of the MBT family is difficult to precisely control due to the narrow growth temperature window and the large size difference between Mn and Bi ions. Then, in the isostructural MnSb2Te4 with a larger growth temperature window44, we observe the evolution of A-type AFM to FM-AFM coexistence and finally to the FM ground state with varying growth temperature (Supplementary Fig. S12).
Domain size and distribution characterizations
To further evaluate the domain sizes of the FM and AFM components, we characterize the magnetic spatial homogeneity by RMCD mapping. In the typical RMCD-μ0H curve of a 3-SL MnBi6Te10 sample (Fig. 3a), we map the RMCD signals in a selected area (Fig. 3b) under four selected magnetic fields (0.1, 0, â0.05, and â0.1âT, respectively) corresponding to four different spin configurations (see Supplementary Fig. S13 for MnBi4Te7 sample). Changes in the RMCD signal at the two AFM spin-flip transitions (Fig. 3c, e) and the FM spin-flip transition (Fig. 3d) are uniform across the scanned sample area, indicating homogeneous FM-AFM coexistence at a spatial resolution limited by the laser spot size of ~2âμm. The small domain size of the FM and AFM components is consistent with the large number of Mn-Bi site mixing characterized by SC-XRD (see Tables I and II in Supplementary Note VIII). It should be noted that these spin-flip transitions, especially for the FM spin-flip transition at Hc, are quite sharp despite the FM-AFM spatial inhomogeneity. In an inhomogeneous system, the sharp transition field suggests that its magnetic reversal is dominated by the nucleation of reverse domain and the subsequent domain wall motion processes (see detailed discussions in Supplementary Note VII and Supplementary Fig. S14).
Tunable exchange bias effect
The FM-AFM coexisting ground state provides us with a unique system to study exchange bias effects. The large-field full hysteresis loops at 4âK (gray data in Fig. 4aâd) are plotted as references for the minor hysteresis loops of the FM components. Historically polarized by a positive saturation magnetic field, the minor hysteresis loop of the FM component shifts to the right side in MnBi4Te7 sample, namely a positive exchange bias (blue data in Fig. 4a). By contrast, polarized by a negative saturation magnetic field, then the minor hysteresis loop of the FM component shifts to the left, indicating a negative exchange bias (orange data in Fig. 4a). The direction of this exchange bias can be easily tuned by the historical polarization field and does not require warming and field cooling processes. Moreover, this exchange bias is rather stable under multiple back-and-forth magnetic field sweeps, with no training effect (Supplementary Fig. S15). The exchange bias effect observed in MnBi6Te10 is opposite to that of MnBi4Te7 (Fig. 4b), possibly due to the different magnetic interactions at the FM/AFM interfaces because of the different interlayer coupling strengths (see discussion following Supplementary Fig. S10).
As the temperature increases, the coercive field Hc for the biased hysteresis loop, defined as 1/2(Hc+âââHcâ), gradually shrinks and the exchange bias field HE, defined as 1/2(Hc+â+âHcâ), slightly increases (Fig. 4câf). The Hc shows an abnormal increase at 10âK for MnBi4Te7 and 8âK for MnBi6Te10, respectively, accompanied by the vanishment of the exchange bias effect. In typical AFM and FM heterostructure systems, the exchange bias effect occurs only when (KAFMtAFM)/Jintââ¥â1, where KAFM is the anisotropy energy of the AFM component, tAFM is the thickness of the AFM component, and Jint is the exchange coupling between the AFM and FM components. As the temperature increase, the KAFM in the MBT system decreases, and eventually, the AFM pinning layer flips collectively with the FM spins, resulting in the vanishment of the exchange bias and the abnormal increase in the coercive field. At high temperatures, the two AFM spin-flip transitions lead to identical RMCD signal changes, also confirming the collective flipping of the AFM and FM components during the FM spin-flip transition. The EB effect can be used reliably when the temperature, number of layers, and especially defect concentration are precisely controlled.
Discussion
In summary, we systematically study the magnetism of atomically thin MnBi4Te7 and MnBi6Te10 flakes in the parameter space of layer number, temperature and applied magnetic field using RMCD spectroscopy. The complex FM-AFM coexisting ground state is observed and verified. The weakened interlayer coupling and inhomogeneously distributed ubiquitous Mn-Bi site mixing have been attributed to result in such a unique magnetic ground state. A tunable exchange bias effect without the assistance of field cooling process is observed in MnBi4Te7 and MnBi6Te10, arising from the coupling between the FM and AFM components. Instead of fabricating heterostructures with magnetically ordered systems, such as AFM and FM45,46,47,48, we obtained the magnetic ground state of FM-AFM coexistence in a single material by a simple exfoliation process, while the crystal structure remained intact. This FM-AFM coexisting ground state expands EB phenomenon and provides design principles and materials for spintronic devices. The EB effect observed in the MnBi4Te7 and MnBi6Te10 system may not have a high enough critical temperature for spintronics in the near future, but the mechanism we learn from them actually helps us understand the principle and therefore design material systems with higher critical temperatures. Using sophisticated techniques, synthetic antiferromagnets composed of two or more ferromagnetic layers separated by nonmagnetic spacers can be precisely prepared49. Due to the weak interlayer exchange coupling in synthetic antiferromagnets, introducing spatial inhomogeneity in thickness of the spacer layer or disorders can therefore tune the interaction and form an FM-AFM coexisting ground state, allowing for precise manipulation of the exchange bias effect in this system. By unraveling the puzzling magnetic states in MnBi4Te7 and MnBi6Te10 flakes, our findings pave the way for further investigation of quantum phenomena intertwined with the magnetic orders.
Methods
Crystal growth and magnetic characterizations
MnBi2Te4(Bi2Te3)n (nâ=â1, 2) single crystals were grown by flux method34. Mn powder, Bi lump and Te lump were weighed with the ratio of Mn:Bi:Teâ=â1:8:13 (MnTe:Bi2Te3â=â1:4). The mixture was loaded into a corundum crucible sealed into a quartz tube. The tube was then placed into a furnace and heated to 1100â°C for 20âh to allow sufficient homogenization. After a rapid cooling to 600â°C at 5â°C/h, the mixture was cooled slowly to 585â°C (581â°C) at 0.5â°C/h for MnBi4Te7 (MnBi6Te10) and kept at this temperature for 2 days. Finally, the single crystals were obtained after centrifuging. The centimeter-scale plate-like MnBi4Te7 and MnBi6Te10 single crystals can be easily exfoliated. Magnetic measurements of MnBi4Te7 and MnBi6Te10 single crystals were measured by the vibrating sample magnetometer (VSM) option in a Quantum Design Physical Properties Measurement System (PPMS-9 T). The temperature-dependent magnetization measurements are described in detail in Supplementary Note I.
Preparation of the ultra-thin samples
The MnBi4Te7 and MnBi6Te10 flakes with different thicknesses were first mechanically exfoliated on a polydimethylsiloxane (PDMS) substrate by the Scotch tape method. The exfoliated samples on PDMS substrates were then dry-transferred onto 285ânm SiO2/Si substrates with evaporated gold films. Then, a layer of PMMA was spin-coated on the thin flakes for protection.
AFM characterization
The thickness of the ultra-thin samples was verified by the atomic force microscopy characterization using the Oxford Cypher S system in tapping mode. According to the height line profiles, the MnBi4Te7 and MnBi6Te10 were confirmed to possess an alternated lattice structure of BT (1ânm) + MBT (1.4ânm) and BT (1ânm) + BT (1ânm) + MBT (1.4ânm). See more details in Supplementary Note II.
RMCD measurements
The RMCD measurements were performed based on the Attocube closed-cycle cryostat (attoDRY2100) down to 1.6âK and up to 9âT in the out-of-plane direction. The linearly polarized light of 633ânm HeNe laser was modulated between left and right circular polarization by a photoelastic modulator (PEM) and focused on the sample through a high numerical aperture (0.82) objective. The reflected light was detected by a photomultiplier tube (THORLABS PMT1001/M). The magnetic reversal under external magnetic field was detected by the RMCD signal determined by the ratio of the a.c. component of PEM at 50.052âkHz and the a.c. component of chopper at 779âHz (dealt by a two-channel lock-in amplifier Zurich HF2LI). The errors of ratio of FM and AFM components are determined by the instability of the data acquired during RMCD measurements.
STEM characterization
Samples for cross-sectional investigations were prepared by standard lift-out procedures using an FEI Helios NanoLab G3 CX-focused ion beam system. To minimize sidewall damage and make the samples sufficiently thin to be electronically transparent, final milling was carried out at a voltage of 5âkV and a fine milling at 2âkV. Aberration-corrected STEM imaging was performed using a Nion HERMES-100 operating at an acceleration voltage of 60âkV and a probe forming semi-angle of 32âmrad. HAADF images were acquired using an annular detector with a collection semi-angle of 75â210âmrad. EELS measurements were performed using a collection semi-angle of 75âmrad, an energy dispersion of 0.3âeV per channel, and a probe current of ~20âpA. The Mn-L (640âeV) and Te-M (572âeV) absorption edges were integrated for elemental mapping after background subtraction. The original spectrum images were processed to reduce random noise using a principal component analysis (PCA) tool. HAADF image simulations were computed using the STEM_CELL software simulation package matching the microscope experimental settings described above and using a supercell with a thickness ~20ânm.
Data availability
The source data generated in this study have been deposited in the Zenodo database under the accession code https://zenodo.org/badge/latestdoi/541886998. Source Data are provided with this paper.
References
Tokura, Y., Yasuda, K. & Tsukazaki, A. Magnetic topological insulators. Nat. Rev. Phys. 1, 126â143 (2019).
Nomura, K. & Nagaosa, N. Surface-quantized anomalous hall current and the magnetoelectric effect in magnetically disordered topological insulators. Phys. Rev. Lett. 106, 166802 (2011).
Chang, C.-Z. et al. Experimental observation of the quantum anomalous hall effect in a magnetic topological insulator. Science 340, 167â170 (2013).
Li, R., Wang, J., Qi, X.-L. & Zhang, S.-C. Dynamical axion field in topological magnetic insulators. Nat. Phys. 6, 284â288 (2010).
Liu, E. et al. Giant anomalous hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125â1131 (2018).
Liu, D. F. et al. Magnetic Weyl semimetal phase in a kagomé crystal. Science 365, 1282â1285 (2019).
Yan, J.-Q. et al. Crystal growth and magnetic structure of MnBi2Te4. Phys. Rev. Mater. 3, 064202 (2019).
Li, J. et al. Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials. Sci. Adv. 5, eaaw5685 (2019).
Otrokov, M. M. et al. Prediction and observation of an antiferromagnetic topological insulator. Nature 576, 416â422 (2019).
Deng, H. et al. High-temperature quantum anomalous hall regime in a MnBi2Te4/Bi2Te3 superlattice. Nat. Phys. 17, 36â42 (2021).
Deng, Y. et al. Quantum anomalous hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science 367, 895â900 (2020).
Liu, C. et al. Robust axion insulator and chern insulator phases in a two-dimensional antiferromagnetic topological insulator. Nat. Mater. 19, 522â527 (2020).
Ovchinnikov, D. et al. Intertwined topological and magnetic orders in atomically thin chern insulator MnBi2Te4. Nano Lett. 21, 2544â2550 (2021).
Ge, J. et al. High-chern-number and high-temperature quantum hall effect without Landau levels. Natl. Sci. Rev. 7, 1280â1287 (2020).
Wu, J. et al. Toward 2D magnets in the (MnBi2Te4) (Bi2Te3)n bulk crystal. Adv. Mater. 32, 2001815 (2020).
Hu, C. et al. Realization of an intrinsic ferromagnetic topological state in MnBi8Te13. Sci. Adv. 6, eaba4275 (2020).
Wu, J. et al. Natural van der Waals heterostructural single crystals with both magnetic and topological properties. Sci. Adv. 5, eaax9989 (2019).
Roychowdhury, S. et al. Giant topological hall effect in the noncollinear phase of two-dimensional antiferromagnetic topological insulator MnBi4Te7. Chem. Mater. 33, 8343â8350 (2021).
Hu, C. et al. A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling. Nat. Commun. 11, 1â8 (2020).
Xie, H. et al. The mechanism exploration for zero-field ferromagnetism in intrinsic topological insulator MnBi2Te4 by Bi2Te3 intercalations. Appl. Phys. Lett. 116, 221902 (2020).
Vidal, R. C. et al. Orbital complexity in intrinsic magnetic topological insulators MnBi4Te7 and MnBi6Te10. Phys. Rev. Lett. 126, 176403 (2021).
Ding, L. et al. Crystal and magnetic structures of magnetic topological insulators MnBi2Te4 and MnBi4Te7. Phys. Rev. B 101, 020412(R) (2020).
Yan, J.-Q. et al. A-type antiferromagnetic order in MnBi4Te7 and MnBi6Te10 single crystals. Phys. Rev. Mater. 4, 054202 (2020).
Hu, C. et al. Tuning magnetism and band topology through antisite defects in Sb-doped MnBi4Te7. Phys. Rev. B 104, 054422 (2021).
Shi, M. Z. et al. Magnetic and transport properties in the magnetic topological insulators MnBi2Te4 (Bi2Te3)n(n= 1, 2). Phys. Rev. B 100, 155144 (2019).
Chen, B. et al. Coexistence of ferromagnetism and topology by charge carrier engineering in the intrinsic magnetic topological insulator MnBi4Te7. Phys. Rev. B 104, 075134 (2021).
Tan, A. et al. Metamagnetism of weakly coupled antiferromagnetic topological insulators. Phys. Rev. Lett. 124, 197201 (2020).
Vidal, R. C. et al. Topological electronic structure and intrinsic magnetization in MnBi4Te7: a Bi2Te3 derivative with a periodic Mn sublattice. Phys. Rev. X 9, 041065 (2019).
Xu, L. et al. Persistent surface states with diminishing gap in MnBi2Te4/Bi2Te3 superlattice antiferromagnetic topological insulator. Sci. Bull. 65, 2086â2093 (2020).
Yang, S. et al. Odd-even layer-number effect and layer-dependent magnetic phase diagrams in MnBi2Te4. Phys. Rev. X 11, 011003 (2021).
Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270â273 (2017).
Zang, Z. et al. Layer-number-dependent antiferromagnetic and ferromagnetic behavior in MnSb2Te4. Phys. Rev. Lett. 128, 017201 (2022).
Lai, Y., Ke, L., Yan, J., McDonald, R. D. & McQueeney, R. J. Defect-driven ferrimagnetism and hidden magnetization in MnBi2Te4. Phys. Rev. B 103, 184429 (2021).
Aliev, Z. S. et al. Novel ternary layered manganese bismuth tellurides of the MnTe-Bi2Te3 system: synthesis and crystal structure. J. Alloys Compd. 789, 443â450 (2019).
Stoner, E. C. & Wohlfarth, E. A mechanism of magnetic hysteresis in heterogeneous alloys. Philos. Trans. Royal Soc. A 240, 599â642 (1948).
Klimovskikh, I. I. et al. Tunable 3d/2d magnetism in the MnBi2Te4 (Bi2Te3)m topological insulators family. NPJ Quantum Mater. 5, 1â9 (2020).
Huang, Y. et al. Universal mechanical exfoliation of large-area 2D crystals. Nat. Commun. 11, 1â9 (2020).
Wu, X. et al. Distinct topological surface states on the two terminations of MnBi4Te7. Phys. Rev. X 10, 031013 (2020).
Shao, J. et al. Pressure-tuned intralayer exchange in superlattice-like MnBi2Te4/(Bi2Te3)n topological insulators. Nano Lett. 21, 5874â5880 (2021).
Xie, H. et al. Charge carrier mediation and ferromagnetism induced in MnBi6Te10 magnetic topological insulators by antimony doping. J. Phys. D. 55, 104002 (2021).
Hor, Y. S. et al. Development of ferromagnetism in the doped topological insulator Bi2âxMnxTe3. Phys. Rev. B 81, 195203 (2010).
Henk, J. et al. Topological character and magnetism of the dirac state in Mn-doped Bi2Te3. Phys. Rev. Lett. 109, 076801 (2012).
Zimmermann, S. et al. Spin dynamics and magnetic interactions of Mn dopants in the topological insulator Bi2Te3. Phys. Rev. B 94, 125205 (2016).
Liu, Y. et al. Site mixing for engineering magnetic topological insulators. Phys. Rev. X 11, 021033 (2021).
Nogués, J. & Schuller, I. K. Exchange bias. J. Magn. Magn. Mater. 192, 203â232 (1999).
Zhu, R. et al. Exchange bias in van der Waals CrCl3/Fe3GeTe2 heterostructures. Nano Lett. 20, 5030â5035 (2020).
Dai, H. et al. Enhancement of the coercive field and exchange bias effect in Fe3GeTe2/MnPX3 (X = S and Se) van der Waals heterostructures. ACS Appl. Mater. Interfaces 13, 24314â24320 (2021).
Albarakati, S. et al. Electric control of exchange bias effect in FePS3-Fe5GeTe2 van der Waals heterostructures. Nano Lett. 22, 6166â6172 (2022).
Chen, B. et al. All-oxideâbased synthetic antiferromagnets exhibiting layer-resolved magnetization reversal. Science 357, 191â194 (2017).
Acknowledgements
This work was supported by the National Key R&D Program of China (Grants Nos. 2018YFA0306900, 2019YFA0308602, 2019YFA0308000, 2018YFA0305800, 2022YFA1403800, and 2018YFE0202600), the National Natural Science Foundation of China (Grants Nos. 62022089, 12074425, 11874422, 12274459, 62274010, 11975035, 92163206, and 52272135), Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB33000000), Beijing Natural Science Foundation (Grant Nos. JQ21018 and Z200005), the Beijing Outstanding Young Scientist Program (Grant No. BJJWZYJH01201914430039), and the Fundamental Research Funds for the Central Universities (E1E40209).
Author information
Authors and Affiliations
Contributions
Y.Y., S.Y., and X.X. conceived the project, designed the experiments, analyzed the results and wrote the manuscript. S.Y. and X.X. conducted the RMCD measurements. H.W. and T.X. grew the MnBi4Te7 and MnBi6Te10 bulk crystals. M.X., S.T., and H.L. grew the MnSb2Te4 bulk crystal. Y.H. prepared the few-layer samples with Y.W.. Y.P. and J.Y. performed the magnetic characterizations of the bulk crystals. R.G. performed the STEM characteristics under the supervision of W.Z.. Y.G., Y.Z., and Z.L. helped with the results analysis. All authors discussed the results and contributed to the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Communications thanks Nicodemos Varnava, Zhe Wang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Additional information
Publisherâs note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Source data
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the articleâs Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the articleâs Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Xu, X., Yang, S., Wang, H. et al. Ferromagnetic-antiferromagnetic coexisting ground state and exchange bias effects in MnBi4Te7 and MnBi6Te10. Nat Commun 13, 7646 (2022). https://doi.org/10.1038/s41467-022-35184-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41467-022-35184-7
This article is cited by
-
Intrinsic exchange biased anomalous Hall effect in an uncompensated antiferromagnet MnBi2Te4
Nature Communications (2024)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.