Natural van der Waals heterostructural single crystals with both magnetic and topological properties

RESULTS

MnBi₂Te₄ was recently reported to be the first intrinsic van der Waals antiferromagnet showing topological nontrivial SS (10–13). It shares a similar crystal structure with Bi₂Te₃, a typical TI. Along the c axis, Bi₂Te₃ is composed of Te-Bi-Te-Bi-Te quintuple atomic layers (QLs) held together by van der Waals forces, while MnBi₂Te₄ is composed of Te-Bi-Te-Mn-Te-Bi-Te septuple atomic layers (SLs), where each layer is equal to a QL intercalated by a MnTe layer (Fig. 1, A, B, E, and F, and fig. S1, A and B). As the two van der Waals materials have similar lattice constants in the a-b plane (the lattice mismatch is only around 1.3%), it would be interesting to check the possibility of synthesizing a natural heterostructure with alternating QL and SL following a new periodicity along the c axis (17).

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Following this assumption, were prepared polycrystalline samples of (MnBi₂Te₄)_m(Bi₂Te₃)_n using a solid-state reaction route, and their crystal structures are shown in fig. S1 and table S1. MnBi₄Te₇ (m = n = 1) and MnBi₆Te₁₀ (m = 1 and n = 2) are identified as natural van der Waals heterostructures (fig. S1F) in which SLs are separated by one or two QLs, respectively, as spacers (Fig. 1, C and D). As with Bi₂Te₃ and MnBi₂Te₄, MnBi₆Te₁₀ adopts a trigonal structure with a space group of R3¯m, while MnBi₄Te₇ adopts a space group of P3¯m1. The direct evidence of heterostructures is obtained by high-angle annular dark-field (HAADF)–STEM measurements (for polycrystalline samples), as shown in Fig. 1, E to H and fig. S2. The atomic resolution images are highly consistent with crystal structures obtained through XRD measurements and the proposed model (Fig. 1, A to D), showing QL and SL as well as van der Waals gaps. The high degree of crystallinity of the prepared samples can also be confirmed by the selected-area electron diffraction (SAED) patterns (Fig. 1, I to L) and the fast Fourier transform patterns of the obtained HAADF-STEM images (fig. S2). The distinct SAED patterns are mainly the results of different atomic stacking sequences and periodicity along the c axis of these compounds.

To check the physical properties, we grew single crystals of MnBi₂Te₄ and MnBi₄Te₇ using a flux-assisted method, and found that it is difficult to synthesize these phases because they evolve only at a very narrow temperature range, similar to recent reports on the synthesis of single-crystalline MnBi₂Te₄ (18–21). The selected pieces of single crystals show shining surfaces and high quality, as indicated by the XRD patterns (Fig. 2). Compared to MnBi₂Te₄, MnBi₄Te₇ has more complex diffraction peaks due to its more complex structure containing both QL and SL. The diffraction peak positions and intensities are in agreement with SAED results shown in Fig. 1, J and K. The fresh surfaces of the samples were checked by Auger electron spectroscopy and x-ray photoelectron spectroscopy under high vacuum (around 10⁻¹⁰ torr), and the results show that the samples are very clean and contain all the proposed elements, i.e., Mn, Bi, and Te (fig. S3). The content of Mn, which is the magnetic center in MnBi₄Te₇, is about half of the content in MnBi₂Te₄ (fig. S3D). This is consistent with the results that the former contains half QL and half SL, while the latter contains SL only.

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Note that the preparation of (MnBi₂Te₄)_m(Bi₂Te₃)_n with larger values of m (>2) and n (>1) would be rather challenging. The degree of difficulty for synthesis increases greatly from MnBi₂Te₄ to MnBi₄Te₇ and to MnBi₆Te₁₀, and we observed only a trace amount of m = 3, n = 1 phase in our solid-state reaction route for polycrystalline samples. For single-crystal growth, MnBi₂Te₄ evolves only at a narrow temperature interval (around 10°C from 590° to 600°C) (18–20), MnBi₄Te₇ evolves only within 2°C near 588°C, and the growth temperature for MnBi₆Te₁₀ is even narrower. Therefore, precise temperature controlling would be the most difficult point for growing the compounds with greater m and n values. Alternatively, on the basis of the present findings, deposition or transfer method might be feasible to prepare (MnBi₂Te₄)_m(Bi₂Te₃)_n with any combination of m and n, although it is also challenging in skills.

The structural modifications are strongly indicative of modulations of the magnetic properties. We first measured the magnetization of polycrystalline MnBi₂Te₄ and a mixture of MnBi₄Te₇ and MnBi₆Te₁₀. The magnetization of MnBi₂Te₄ is consistent with a previous report (18), showing an AFM transition at T_N = 25 K and a spin-flop transition at 3.54 T (fig. S4, A and B). For the mixture of MnBi₄Te₇ and MnBi₆Te₁₀, magnetic susceptibility demonstrates an FM transition at T_C = 12.1 K for fields greater than 0.1 T (fig. S4, C to H). However, for fields that are less than 0.1 T, there are two magnetic transitions: an AFM transition (T_N1 ≅ 13 K) attributed to MnBi₄Te₇ and a spin glass-like transition (T_N2 ≅ 6.5 K) probably attributed to MnBi₆Te₁₀ or amorphous phases (inhomogeneous QL and SL heterostructures). This field-dependent magnetization displays a saturation value at high fields and magnetic hysteresis at low fields below 5 K, indicating the arising of FM states.

To make the magnetic structures clear, we conducted magnetization measurements on single-crystalline MnBi₂Te₄ and MnBi₄Te₇. The two compounds show remarkably different magnetic structures (Fig. 3). For MnBi₂Te₄, the results are consistent with those for the polycrystalline sample, additionally demonstrating that the magnetization easy axis is along the c direction (10, 11, 19, 20). While the interlayer exchange coupling (IEC; which favors AFM states) of MnBi₂Te₄ is at an intermediate strength, the IEC of MnBi₄Te₇ becomes much weaker. For MnBi₄Te₇, at a field of 1 T, the AFM transition disappears and an FM transition occurs at T_C = 12.5 K (Fig. 3D). The magnetization is saturated above 1 T for fields along either the c axis or the a-b plane (Fig. 3, E and F), indicating that the spin orientation can easily be realigned by an external field irrespective of the crystal orientation. However, similar to MnBi₂Te₄, MnBi₄Te₇ also exhibits a magnetization easy axis along the c direction (fig. S5A).

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Note that the AFM-IEC can still play an important role at small fields as shown in Fig. 3G and that an AFM transition takes place at T_N = 12.7 K. However, AFM-IEC seems not to be the only interaction that determines the magnetic order, because an obvious upturn was observed below T_N, especially for fields applied along the a-b plane. The first derivative of magnetic susceptibility over temperature also suggests that there might be another magnetic transition near 2 K (fig. S6, A to F). The field-dependent magnetization when a field is applied along the a-b plane shows a nonlinear curve below 5 K and a small hysteresis at 2 K (Fig. 3H), suggesting an additional magnetic interaction (AMI) that tends to cant the spins away from their out-of-plane direction and favors an FM state. When the field is applied along the z axis, we observed much higher hysteresis at 2 K with spin-flip transitions connecting FM phase at high fields and AFM phase at the critical field (H_c). The FM states can be maintained even at 0 T, indicating again the existence of AMI. However, the AMI decays rapidly with increasing thermal energy, and the magnetic hysteresis disappears above 5 K. Figure S6 provides a detailed analysis of the magnetic structure. We also observed the AFM transitions in MnBi₂Te₄ and MnBi₄Te₇ in their low-temperature heat capacities (figs. S5B and S7A). Note that because of the weak IEC, the magnetic properties of MnBi₄Te₇ can be modified by controlling the applied magnetic field (strength and direction). In addition, the IEC can be modified by controlling the spacers (QL), and it gradually decreases from MnBi₂Te₄ to MnBi₄Te₇ and to MnBi₆Te₁₀. In view of these features, we regard the magnetic properties of (MnBi₂Te₄)_m(Bi₂Te₃)_n as “tunable.”

To gain insight into the electronic structure and topology of MnBi₄Te₇, we carried out first-principles DFT calculations based on the hybrid functional (HSE06) method, which is used widely for the study of small bandgap materials. The obtained band structures, with and without spin-orbit coupling (SOC), of bulk MnBi₄Te₇ are shown in Fig. 4 (A and B, respectively). When SOC is turned off, Te-5p states (valence bands) and Bi-6p states (conduction bands) are separated by a direct gap of 633 meV at Γ point (Fig. 4A), consistent with their balanced charge states, [Bi³⁺]₂[Te²⁻]₃. However, this simple chemical picture breaks down when SOC is taken into account (Fig. 4B) with Te-5p bands and Bi-6p bands hybridizing near the Fermi level to cause band inversion (bandgap, 247 meV). This band inversion induced by strong SOC suggests that the material is topologically nontrivial (22). According to Mong et al. (23), AFM insulators breaking both time-reversal symmetry (Θ) and a primitive lattice translation symmetry (T_1/2) but preserving their combination S = ΘT_1/2 (MnBi₄Te₇ is one such material) can be classified by ℤ₂ topology. We carried out a Wilson loop calculation (24, 25) for MnBi₄Te₇ and confirmed that it is an AFM TI with ℤ₂ = 1.

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TIs are known to have SSs associated with their bulk topology (22). Figure 4 (C and D) shows the electronic structures of MnBi₄Te₇ slabs with two surface terminations, QL-terminated and SL-terminated, respectively. Distinct from the gapless SS in Bi₂Te₃, the SSs of MnBi₄Te₇ are gapped with a gap of 11 meV (indirect) and 62 meV (direct) for the QL-terminated and SL-terminated surface, respectively. The nonvanishing gap is consistent with the broken time-reversal symmetry, presumably reflecting the interaction between the SSs and the FM layer near the surface, similar to the gapped SS of MnBi₂Te₄ (another AFM TI) (10, 19).

We measured the SS of MnBi₄Te₇ using ARPES at 20 and 300 K with an excitation photon energy of 48 eV (Fig. 5), which had been used for the experimental confirmation of the SS of Bi₂Te₃, a prototypical three-dimensional TI (26). Closely resembling the SS of Bi₂Te₃ while having a finite energy gap, the observed bands were confirmed to be SS, for which the Γ¯ point was confirmed through measurements of the Fermi surface in the k_x-k_y plane (fig. S3, G and H). Compared with the calculation results (Fig. 4, C and D), the measured SSs (Fig. 5A) were found to come mainly from the SL-terminated surface as indicated by the bump (or cusp) at the valence band maximum. However, at the present stage, we cannot exclude the contributions from the QL-terminated surface, as it should be equally exposed on the mechanically cleaved surface (there are steps connecting QL and SL). Considering that the QL/SL surface domain size may be much smaller than the photon beam spot size in the present measurements, we speculate that both surfaces were measured. There are several possible reasons that the observed SSs look more like the contributions from SL, such as the self-protecting behavior of the topological states as proposed in a previous report (27) or a notably larger cross section of SL-SS than that of QL-SS. According to Fig. 4 (C and D), the contribution from the SL-terminated surface is much larger than that from the QL-terminated surface at the Γ point near the gap. This may be another reason that we cannot resolve the two different types of surfaces, and the observed SS at the Γ point near the gap is mostly from SL. Given that the photon beam is only focused on QL, its SS would be largely enhanced and observable.

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MnBi₄Te₇ exhibits surface bandgaps of 120 ± 10 and 90 ± 10 meV at 20 and 300 K, respectively (Fig. 5, B and D), similar to the reported data for MnBi₂Te₄ (10, 19). The opening of the surface bandgap above T_N (12.7 K) indicates that the time-reversal invariance is broken even in the paramagnetic (PM) phase for MnBi₄Te₇. Similar phenomena have been frequently observed in intrinsic magnetic TIs (10, 19) and magnetically doped TIs (28–31), but no consensus has been reached on the mechanism. Rader and co-workers (28) proposed that impurity-induced resonance states may destroy the Dirac point and explain the nonmagnetic gap, while this mechanism was excluded as the primary factor in MnBi₂Te₄ (a system similar to ours) (10). Mao and co-workers ascribed the PM gap to strong FM-type spin fluctuations (19). Actually, we have also observed FM spin fluctuations in MnBi₄Te₇ above T_N as indicated by the positive Curie-Weiss temperature (fig. S6, B and E); therefore, the present results may also suggest spin fluctuations as a possible reason for the SS gap. However, this is an open question requiring further investigations. A theory for the SS when the material is in the PM phase would be very helpful. Note that the SSs of MnBi₄Te₇ are more complex than those of MnBi₂Te₄, as indicated by a flattening of the conduction band and a cusp in the valence band near the Γ¯ point (Fig. 5A), reminiscent of the more sophisticated SSs of PbBi₄Te₇ than that of PbBi₂Te₄ (27, 32). With gapped nontrivial SSs and tunable magnetic properties, magnetic heterostructures of (MnBi₂Te₄)_m(Bi₂Te₃)_n will be an ideal platform for exploring tunable quantized magnetoelectric phenomena such as QAHE and axion insulator states.

The electrical transport properties of MnBi₄Te₇ single crystals are shown in Fig. 6, and they are notably different from those of MnBi₂Te₄ (fig. S7). The compound has a metallic conductivity (fig. S5C), and the Hall effect shows that the carrier is n-type with a carrier concentration (n) of 2.85 × 10²⁰ cm⁻³ at 2 K (fig. S5D), consistent with the ARPES results that the Fermi level is not located in the SS Zeeman gap but in the conduction band (Fig. 5). The Hall resistivity has a linear field dependence at high fields (Fig. 6A), suggesting a single carrier in the present compound. The derived AH resistivity (Fig. 6A) is well coupled with the magnetization curves (Fig. 3I) and shows hysteresis at low temperatures, which is strongly indicative of the possibility of observing QAHE if the Fermi level is tuned in the SS Zeeman gap (6, 7, 14). The AH conductivity, which can be expressed as σxyA=ρyxA/ρxx2 (33), is shown to be virtually temperature independent below 2 K, while its temperature dependence above 2 K follows the same trend as magnetic susceptibility (Fig. 6, B and C). Here, ρyxA and ρ_xx represent the AH resistivity and longitudinal resistivity, respectively. In general, there are three main mechanisms accounting for the AH effect, intrinsic Berry’s phase curvature in the momentum space, side jump, and skew scattering (33). In the present study, the temperature-independent σxyA and the scaling factor S_H (σxyA=SHM, M is the magnetization; Fig. 6C) and σ_xx-independent σxyA (fig. S5F) exclude skew scattering as the primary reason and suggest that the intrinsic Berry’s phase curvature is the major contribution to the AH effect (33–36). More studies are necessary for elucidation of the details. Note that a small nonlinear coupling of ρyxA with M was observed below 5 K near the spin-flip transition (fig. S8) and the discrepancy (ΔρHA) is n independent and probably due to the intrinsic contribution from the net Berry’s curvature of a noncollinear spin texture (19, 37).

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The spin-flip transitions can also be reflected in magnetoresistance (ρ_xx), as shown in Fig. 6 (D and E) and fig. S9. At higher temperatures (5 to 12 K), there are two peaks in ρ_xx at H_c1 and H_c2, which are critical fields for spin-flip transitions with H_c2 = −H_c1 (note that H_c1 and H_c2 are essentially the same and their signs only depend on the definition of the sign of the applied magnetic field). The sample is in AFM phase at a field between H_c1 and H_c2 and in FM phase at higher fields (Fig. 6F). At lower temperatures (50 mK to 2 K), H_c1 and H_c2 are on the same side (corresponding to the magnetic hysteresis of ρyxA), either positive or negative, depending on the sweep direction of the field (Fig. 6F and fig. S5I), indicating that the sample turns into a spin valve–like state (1–3). H_c1 and H_c2 are nearly merged from 0.35 to 2 K (Fig. 6F), demonstrating that AFM states can survive only within a very narrow range of fields near the critical field. There are plateaus (high-resistance state) in ρ_xx between H_c1 and H_c2 at temperatures lower than 0.3 K (Fig. 6E), indicating that electrons suffer a higher scattering rate than they do at a lower or higher field. This implies that, different from the FM states at high fields (larger than H_c2), the material is now in an AFM state, similar to the phenomenon frequently observed for spin valves (1–3). However, the magnetoresistance plateaus cannot survive at higher temperatures (≥0.35 K), where thermal activation may destroy the AFM ordering quickly and the system enters an FM state. Although the FM state at a field between H_c1 and H_c2 should be more stable (in a lower energy level), it seems that the transition from AFM to FM cannot automatically happen (below 0.3 K) without sufficient thermal energy to overcome an energy barrier. This is supported by fig. S9E, where thermal activation for the transition from the high-resistance state (AFM) to the low-resistance state (FM) can be clearly observed (the resistance from 70 mK to 1 K at 0.15 T). Note that the plateaus are also shown in AH conductivity (Fig. 6B), resembling axion insulating states (8, 12, 14). Therefore, the present system is also a potential platform for creating axion insulators if the Fermi level is tuned into the SS Zeeman gap. In addition, when current flows across the magnetic and nonmagnetic layers, the magnetoresistance effect seems much stronger (fig. S5H), similar to materials that show giant magnetoresistance (1, 4).