A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling

Abstract

Magnetic topological insulators (TI) provide an important material platform to explore quantum phenomena such as quantized anomalous Hall effect and Majorana modes, etc. Their successful material realization is thus essential for our fundamental understanding and potential technical revolutions. By realizing a bulk van der Waals material MnBi₄Te₇ with alternating septuple [MnBi₂Te₄] and quintuple [Bi₂Te₃] layers, we show that it is ferromagnetic in plane but antiferromagnetic along the c axis with an out-of-plane saturation field of ~0.22 T at 2 K. Our angle-resolved photoemission spectroscopy measurements and first-principles calculations further demonstrate that MnBi₄Te₇ is a Z₂ antiferromagnetic TI with two types of surface states associated with the [MnBi₂Te₄] or [Bi₂Te₃] termination, respectively. Additionally, its superlattice nature may make various heterostructures of [MnBi₂Te₄] and [Bi₂Te₃] layers possible by exfoliation. Therefore, the low saturation field and the superlattice nature of MnBi₄Te₇ make it an ideal system to investigate rich emergent phenomena.

Emergent quantum phenomena such as quantized anomalous Hall effect may be realized in magnetic topological materials. Here, Hu et al. discovered an intrinsic natural heterostructural Z₂ antiferromagnetic topological insulator MnBi₄Te₇ with low out-of-plane saturation fields.

Introduction

Magnetic topological insulators (MTIs), including Chern insulators with a Z-invariant and antiferromagnetic (AFM) topological insulators (TIs) with a Z₂-invariant, provide fertile ground for the exploration of emergent quantum phenomena such as the quantum anomalous Hall (QAH) effect, Majorana modes, the topological magnetoelectric effect, the proximity effect, etc^1,2. In the two-dimensional (2D) limit of ferromagnetic (FM) TIs, the QAH effect arising from chiral edge states exists under zero external magnetic fields, which has been experimentally observed in doped FM TI Cr_0.15(Bi_0.1Sb_0.9)_1.85Te₃ thin films³. However, the unavoidable sample inhomogeneity in doped materials restrains the investigation of associated emergent phenomena below temperatures of hundreds of mK². Stoichiometric MTIs are expected to have homogeneous electronic and magnetic properties, which may provide new opportunities to study the QAH effect. Recently, MnBi₂Te₄ was discovered to be an intrinsic AFM TI^4–24. In its 2D limit, quantized Hall conductance originating from the topological protected dissipationless chiral edge states was realized in few-layer slabs^15,16. However, probably because the uncompensated AFM spin configuration cannot provide enough Zeeman field to realize the band inversion in only one spin channel, to observe such a QAH effect, a high magnetic field of 12 T at 4.5 K or 6 T at 1.5 K is required to fully polarize the AFM spins into a forced FM state¹⁵.

A FM state is crucial to realize the QAH effect experimentally¹⁵; however, as we await an ideal candidate that has both TI and FM properties, an intrinsic AFM TI with low saturation fields and clean band structure where only non-trivial bands cross the Fermi level can also provide a good material platform. By this, the QAH effect may be realized with higher temperatures and reasonably low magnetic fields, which allows us to study their associated emergent phenomena at more accessible conditions. How can we realize such intrinsic AFM TIs? Recall that MnBi₂Te₄ crystalizing in the GeBi₂Te₄ structure with septuple layers (SL) of [MnBi₂Te₄] is an AFM material with in-plane FM and out-of-plane AFM exchange interaction. Hence, based on the SL building block, one strategy to achieve AFM with small saturation fields or even FM is to reduce the interlayer Mn-Mn exchange interaction by increasing the interlayer distance with extra spacer layers added. Structurally, SL blocks have great compatibility with [Bi₂Te₃] quintuple layers (QL), whose bulk form is a TI with a preserved time-reversal symmetry. As an example, GeBi₄Te₇ with alternating [GeBi₂Te₄] and [Bi₂Te₃] building blocks has been synthesized²⁵. This superior compatibility provides us with flexible structural control to achieve our goal. Furthermore, not only can such superlattices manifest weak interlayer magnetic coupling, but they can also serve as natural heterostructures by exfoliation, which may enable the realization of various topological states.

The exploration of the MnTe–Bi₂Te₃ ternary system²⁶ has shown that MnBi_2nTe_3n+1 (n = 1, 2, and 3) series exist with alternating [MnBi₂Te₄] and (n−1)[Bi₂Te₃] layers. In this work, we focus on MnBi₄Te₇ (n = 2) with a hexagonal superlattice crystal structure of alternate stackings of one [MnBi₂Te₄] SL and one [Bi₂Te₃] QL. Through our transport, thermodynamic, angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations, we discovered that MnBi₄Te₇ is a Z₂ AFM TI with an out-of-plane saturation field as low as 0.22 T at 2 K, 40 times lower than that of MnBi₂Te₄. Furthermore, the natural-heterostructure-like construction of MnBi₄Te₇ can host two distinct (001) surface states. For the [Bi₂Te₃] termination, clean gapped surface states are observed as has long been desired; while for the [MnBi₂Te₄] termination, nearly gapless surface Dirac cone is observed, similar to the case of the MnBi₂Te₄ compound^20–23. Our finding provides a superior new material realization to explore the QAH effect, quantum spin Hall (QSH) effect and associated phenomena²⁷.

Results

A-type antiferromagnetism in MnBi₄Te₇ with strong FM fluctuations and weak interlayer exchange interaction

Figure 1b shows the (00l) X-ray diffraction peaks of a piece of representative single crystal, which can be well indexed by the MnBi₄Te₇ crystal structure²⁶. The Rietveld refinement of the powder X-ray diffraction pattern agrees well the MnBi₄Te₇ structure model²⁶ and suggests Bi₂Te₃ is the only impurity inside with a molar ratio of 14% (Supplementary Fig. 1). The refined lattice parameters are a = 4.3454(5) Å, and c = 23.706(4) Å, indicating the distance between two adjacent Mn layers in MnBi₄Te₇ is 23.706(4) Å, much longer than the 13.8 Å of MnBi₂Te₄. The inset of Fig. 1b shows a picture of a MnBi₄Te₇ single crystal against a 1-mm scale, where the shiny cleaved ab surface can be seen.

Fig. 1. Magnetic and transport properties of bulk AFM MnBi₄Te₇.

a The view of the crystal structure of MnBi₄Te₇ from the [110] directions. Red arrow: Mn spins in the A-type AFM state. Blue block: edge-sharing BiTe₆ octahedra; Pink block: edge-sharing MnTe₆ octahedra, which are connected to the blue block via edge-sharing. J_⊥ is the interlayer exchange coupling. b The (00l) X-ray diffraction peaks of the cleaved ab plane of MnBi₄Te₇. Inset: A piece of MnBi₄Te₇ against 1-mm scale. c The temperature dependent field-cooled susceptibility and inverse susceptibility taken at H = 0.1 T for H || ab and H || c. Average χ is calculated by ${\chi }^{\mathrm{ave}}=\left(2{\chi }^{\mathrm{ab}}+{\chi }^{\mathrm{c}}\right)∕3$. d and e: Full magnetic hysteresis loop of isothermal magnetization taken at various temperatures for: d H || c and e H || ab. f The temperature dependent ρ_xx (I || ab) and ρ_zz (I || c). g Transverse magnetoresistance with I || ab and H || c at various temperatures.

The magnetic properties are depicted in Fig. 1c–e. Figure 1c presents the field-cooled (FC) magnetic susceptibility data of x^ab (H || ab) and x^c (H || c) measured at 0.1 T. The abrupt halt in the rise of x^c on cooling suggests the onset of AFM ordering, similar to that seen in other vdW antiferromagnets MnBi₂Te₄ and CrCl₃,^9,28 but different from the FM one²⁹, suggesting that long range AFM ordering takes place at 13 K. This is consistent with the specific heat measurement in Supplementary Fig. 2, where a specific heat anomaly associated with the AFM transition emerges at 13 K. As seen from Fig. 1c, fitting the inverse susceptibilities up to 80 K to the Curie-Weiss law results in Weiss temperatures of ${\theta }_{\mathrm{w}}^{\mathrm{ab}}$ = 11.5 K, ${\theta }_{\mathrm{w}}^{\mathrm{c}}$ = 12.2 K, ${\theta }_{\mathrm{w}}^{\mathrm{ave}}$ = 11.7 K, and effective moments of ${\mu }_{\mathrm{eff}}^{\mathrm{ab}}$ = 5.4μ_B/Mn, ${\mu }_{\mathrm{eff}}^{\mathrm{c}}$ = 5.1μ_B/Mn and ${\mu }_{\mathrm{eff}}^{\mathrm{ave}}$ = 5.3μ_B/Mn. These values indicate magnetic isotropy above T_N and thus negligible single ion anisotropy in the material. Despite the fact that MnBi₄Te₇ is AFM below 13 K, the positive ${\theta }_{\mathrm{w}}^{\mathrm{ave}}$ of 11.7 K suggests strong ferromagnetic (FM) exchange interactions. Recall that MnBi₂Te₄ has a much higher T_N of 25 K and a much lower θ_w of 3–6 K^9,18, this may indicate that the energy scales of the FM and AFM exchange interaction are much closer in MnBi₄Te₇. This is consistent with the fact that the extra insulating [Bi₂Te₃] layer reduces the interlayer exchange interaction between adjacent Mn layers as we initially designed. The AFM orders of both MnBi₂Te₄ and MnBi₄Te₇ are formed under the superexchange scenario, where the magnetic interaction between the adjacent Mn layers is mediated by the electrons of the common neighbors. Despite the long distance between the adjacent Mn layers (23.7 Å), our DFT calculation reveals an A-type AFM configuration in MnBi₄Te₇ with the interlayer exchange coupling about −0.15 meV/Mn, which is about one order of magnitude smaller than the counterpart of MnBi₂Te₄. More details are given in Supplementary Note 2.

Figure 1d, e present the hysteresis loops of isothermal magnetization data for M^c(H) (H || c) and M^ab(H) (H || ab), respectively. As shown in Fig. 1d, in sharp contrast to MnBi₂Te₄ where a spin-flop transition takes place at 3.5 T and saturates at 8 T in M^c(H)^9,17,18, MnBi₄Te₇ undergoes a first-order spin-flip transition with hysteresis starting at a much lower field of H_f = 0.15 T. It quickly enters the forced FM state and saturates at H_c = 0.22 T. The small saturation field again indicates weaker interlayer AFM exchange interactions than in MnBi₂Te_4. Upon warming up to 10 K, the hysteresis area is gradually reduced to zero, but H_c remains little changed, indicating a sharp triggering of the spin-flipping between 10 K and T_N. With H || ab, the saturation field is 1.0 T, indicating the c axis as the magnetic easy axis and likely Ising form. As shown in Fig. 1e, the saturation moment is 3.5μ_B/Mn at 7 T, which is very similar to the value of 3.6μ_B/Mn¹⁸ in MnBi₂Te₄ but smaller than the DFT calculated value of 4.6μ_B/Mn. The reduced Mn saturation moments in this family may arise from Mn disorders, which were observed in MnBi₂Te₄¹⁰.

Figure 1f shows the temperature dependent in-plane (ρ_xx) and out-of-plane resistivity (ρ_zz). Above 20 K, both ρ_xx and ρ_zz decrease nearly linearly upon cooling with ρ_zz/ρ_xx~53 at 300 K (Supplementary Fig. 3), suggesting a large transport anisotropy that is consistent with its vdW nature. With further cooling, ρ_xx and ρ_zz increase slightly, which is likely caused by the enhanced scattering from spin fluctuations, a phenomenon frequently observed in low dimensional magnetic materials^30,31. Then at 13 K, a sudden drop of ρ_xx and a sharp increase of ρ_zz are observed. This is in agreement with the A-type magnetic structure shown in Fig. 1a since the antiparallel alignment of Mn moments can reduce the conductivity via spin-slip scattering, while parallel alignment of the Mn moments will eliminate such scattering and thus enhance the conductivity³⁰.

Figure 1g shows the transverse magnetoresistance (TMR), defined as MR = (ρ_xx(H)-ρ_xx(0))/ρ_xx(0). The main feature of the figure is the overall W shape of the TMR. The W shape becomes deeper upon warming, with the largest negative TMR of 8% appearing at 12 K, which is close to T_N. Above T_N, it starts to become shallower and finally transforms into an ordinary parabolic shape at 50 K. The overall W shape can be understood in the framework of FM fluctuations. Above 50 K, the lack of magnetic fluctuations leads to the parabolic TMR. Upon cooling, FM fluctuations begin to appear and become increasingly stronger with maxima around T_N. As a result, the summation of the positive parabolic TMR and the negative TMR arising from the FM fluctuations under fields leads to a progressively deeper W shape of TMR upon cooling. Below T_N, the FM fluctuations are reduced, but still with a strong presence, leading to the shallower W shape under field.

The spin-flip transition strongly affects the transport properties, as shown in Fig. 2. ρ_xx(H), ρ_zz(H) and ρ_xy(H) follow the same hysteresis as that in M(H). With H || c, the transverse magnetoresistivity of ρ_xx with I || ab (Fig. 2a) and the longitudinal magnetoresistivity of ρ_zz with I || c (Fig. 2b) slightly change between 0 T to H_f. Then up to H_c, since the system enters the forced FM state and the loss of spin scattering occurs, ρ_xx drops by 3.8% whereas ρ_zz decreases by 34%. With H || ab, up to the saturation field of 1.0 T, ρ_zz (Fig. 2e) decreases by 39% whereas ρ_xx (Fig. 2f) drops by 2.6%. Our data show that the transition from AFM to FM spin alignment along the c axis has much stronger effect on ρ_zz than ρ_xx. MnBi₄Te₇ displays evident anomalous Hall effect (AHE) as seen in the bottom panel of Fig. 2a. Our ρ_xy(H) is linear up to 9 T above 50 K (Supplementary Fig. 3), suggesting single band transport here. Using n = H/eρ_xy, our 50 K data corresponds to an electron carrier density of 2.84 × 10²⁰ cm⁻³, similar to that of MnBi₂Te₄^17,18,32. Our Hall resistivity below 13 K can be described by ${\rho }_{\mathrm{xy}}=R_{0}H+{\rho }_{\mathrm{xy}}^{\mathrm{A}}$, where the R₀H is the trivial linear contribution and ${\rho }_{\mathrm{xy}}^{\mathrm{A}}$ represents the anomalous Hall resistivity. At 2 K, ${\rho }_{\mathrm{xy}}^{\mathrm{A}}$ is extracted to be 3.3 μΩ cm, which is half of the one in MnBi₂Te₄¹⁷. Consequently, the anomalous Hall conductivity ${\sigma }_{\mathrm{xy}}^{\mathrm{A}}\left(={\rho }_{\mathrm{xy}}^{\mathrm{A}}∕{\rho }_{\mathrm{xx}}^2\right)$ is 25.5 Ω⁻¹ cm⁻¹ and the anomalous Hall angle (AHA ~ ${\rho }_{\mathrm{xy}}^{\mathrm{A}}∕{\rho }_{\mathrm{xx}}$) is ~1%.

Fig. 2. Magnetotransport of bulk AFM MnBi₄Te₇.

a The field dependent magnetization M, transverse magnetoresistivity of ρ_xx, and Hall resistivity ρ_xy at 2 K with I || ab and H || c. b The longitudinal magnetoresistivity of ρ_zz, at 2 K with I || H || c. c The field dependent magnetization M with H || ab at 2 K. d The longitudinal magnetoresistivity of ρ_xx, at 2 K with I || H || ab. e The transverse magnetoresistivity of ρ_zz, at 2 K with I || c and H || ab.

Z₂ AFM TI predicted by theoretical calculation

MnBi₄Te₇ crystalizes in the space group (G) P-3m1 (No. 164). By taking into account the A-type AFM, the primitive cell doubles along the c axis, rendering a magnetic space group P_c-3c1 (No. 165.96) under the Belov–Neronova–Smirnova notation³³, as shown in Fig. 1a. This magnetic space group is derived from its nonmagnetic space group by adding an extra sublattice generated by an operation that combines time-reversal T with a fractional translation τ_1/2. Then the full magnetic group is built as G_M = G + GS, where S is a combinatory symmetry S = Tτ_1/2 with τ_1/2 the half translation along the c axis of the AFM primitive cell. Although the explicit T-symmetry is broken, the S-symmetry (also referred to nonsymmorphic time-reversal³⁴) still exists in bulk MnBi₄Te₇. In addition, MnBi₄Te₇ has inversion symmetry P, while the square of the symmetry operator PS equals −1 at an arbitrary k in momentum space. Therefore, analogous to TI with T-symmetry where Kramer’s degeneracy is induced by T² = −1, in MnBi₄Te₇ the existence of the PS symmetry ensures an equivalent Kramer’s degeneracy in the whole Brillion zone, and thus a Z₂ topological classification.

Figure 3a shows the calculated band structure of bulk AFM MnBi₄Te₇ with the presence of spin–orbit coupling (SOC). The conduction band minimum is located at the Γ point, while the valence band maximum in the vicinity of Γ shows a slightly curved feature. The calculated bulk band gap is about 160 meV. The projection of band eigenstates onto the p-orbitals of Bi and Te (as indicated by the blue and red coloring) clearly indicates an inverted order between several conduction and valence bands around the Γ point, which is strong evidence of the possible nontrivial topological nature. On the other hand, the Mn-3d⁵ states form nearly flat bands far away from the Fermi level (Supplementary Fig. 6), indicating that the main effect of Mn is to break T-symmetry by introducing staggered Zeeman field into the low-energy Hamiltonian.

Fig. 3. Topological properties of bulk AFM MnBi₄Te₇ predicted by first-principles calculations.

a Band structure with the projection of Bloch eigenstates onto Bi-p (blue) and Te-p (red) orbitals. SOC is included. b Evolution of Wannier charge centers (WCCs) for k_z = 0, indicating a nontrivial topological invariant Z₂ = 1. c Surface spectra of (010) side surface, showing a gapless Dirac cone protected by S-symmetry.

To determine the topological properties of AFM MnBi₄Te₇, we first apply the Fu-Kane formula³⁵ to calculate the Z₂ invariant. The topological insulator phase of AFM materials is protected by S-symmetry, under which there are only four invariant k-points forming a 2D plane in the momentum space. Thus, analogous to weak Z₂ indices in nonmagnetic materials, the S-symmetry indeed protects weak Z₂ topological phases in AFM materials. In AFM MnBi₄Te₇, four TRIM points, including Γ(0, 0, 0) and three equivalent M(π, 0, 0), need to be considered here with k τ_1/2 = nπ. Due to the abovementioned band inversion at the Γ point, we find that the parities for the occupied bands at Γ are opposite to that of the other three M points, indicating a nontrivial Z₂ = 1. To verify our results, we also calculate the evolution of Wannier charge centers (WCCs) using the Wilson loop approach³⁶. As show in Fig. 3b, the largest gap function and the WCCs line cross each other an odd number of times through the evolution, confirming that MnBi₄Te₇ is indeed a Z₂ AFM topological insulator. Compared with TIs with T-symmetry, the protection of gapless surface states in AFM TIs requires that the cleaved surface respects S-symmetry that contains translation along the c axis. Figure 3c clearly shows the gapless surface Dirac cone at the Γ point for the (010) surface, partially validating the bulk-surface correspondence of MnBi₄Te₇ as an AFM TI. The easy-cleaved (001) plane, where the S-symmetry is broken, are measured by ARPES and compared with our theoretical calculations, as discussed in the following.

Surface and bulk states measured by ARPES

In contrast to the recently discovered AFM TI MnBi₂Te₄ where only one type of surface termination exists, MnBi₄Te₇ can terminate on two different sub-lattice surfaces on the (001) plane, i.e., the [Bi₂Te₃] QL termination and the [MnBi₂Te₄] SL termination, resulting in different surface states. ARPES with 47 eV, linear horizontal polarized light and a small beam spot reveals two different types of E-k maps by scanning across different parts of the sample in real space, as plotted in Fig. 4d, e and Fig. 4h, i. There are several distinguishing features between the two types of surface spectra: Fig. 4h, i appear to show a gap with massive quasiparticles while Fig. 4d, e show a sharp Dirac-like crossing, possibly with a small gap. The spectra of Fig. 4d, e are reminiscent of recent high resolution ARPES spectra of the MnBi₂Te₄ compound^20–23 that show Dirac-like spectra, and we assign these states to the [MnBi₂Te₄] SL termination, while we assign the other set of surface states to the [Bi₂Te₃] QL termination.

Fig. 4. Comparison between ARPES-measured and DFT-calculated surface states.

a–c The DFT-calculated k-E map along $\overline{\mathrm{K}}\leftarrow \overline{\mathrm{\Gamma }}\to \overline{\mathrm{K}}$ on the [MnBi₂Te₄] SL termination: a surface and bulk (S+B) spectrum, b bulk only, and c surface only. d, e The experimental ARPES spectrum on the [MnBi₂Te₄] SL termination obtained with 47 eV, linear horizontal light: d along Μ←Γ→Μ, e along Κ←Γ→Κ high symmetry direction. f, g The DFT-calculated k-E map along $\overline{\mathrm{K}}\leftarrow \overline{\mathrm{\Gamma }}\to \overline{\mathrm{K}}$ on the [Bi₂Te₃] QL termination: f surface and bulk (S+B) spectrum, g surface only. h, i The experimental ARPES spectrum on the [Bi₂Te₃] QL termination obtained with 47 eV, linear horizontal light: h along Μ←Γ→Μ, i along Κ←Γ→Κ high symmetry direction. j The EDC plot at the Γ point (blue-line cut in i) showing three main peaks corresponding to the bulk conduction band, surface conduction band, and mixed surface/bulk valence band. The green curve shows the fitted Voigt profile peaks which sum to the blue curve.

On these two terminations, symmetry operations combined with τ_1/2 are not preserved. In the ideal case that the surface magnetic structure perfectly inherits the bulk property, due to the A-type out-of-plane magnetization of the Mn sublayers, the gapped surface states are described by adding an exchange term to the ordinary Rashba-type surface Hamiltonian for TI with T-symmetry, i.e., $H_{\mathrm{surf}}\left(\mathbf{k}\right)=\left({\sigma }_{\mathrm{x}}{k}_{\mathrm{y}}-{\sigma }_{\mathrm{y}}{k}_{\mathrm{x}}\right)+m_{\mathrm{S}∕\mathrm{Q}}{\sigma }_{\mathrm{z}}$, where σ is the Pauli matrix for spin, and m_S/Q the surface exchange field that distinguishes the [MnBi₂Te₄] SL and [Bi₂Te₃] QL surfaces. Our calculation shows that the surface state terminated at the [Bi₂Te₃] QL has a massive Dirac cone with a surface gap around 60 meV (Fig. 4f, g), and an overall structure that agrees very well with the experimental data of Fig. 4h, i, confirming the assignment of the experimental data as arising from the [Bi₂Te₃] QL termination. When comparing Fig. 4i with the bulk states calculated by DFT (Fig. 4b), we can easily distinguish the surface states from the bulk states. To measure gap sizes in Fig. 4i, we extract an energy distribution curve (EDC) at the Γ point and fit it to several Voigt profiles, as shown in Fig. 4j. We find that despite the appearance of some spectral weight in the gapped region in Fig. 4i, the EDC does not show any signature of a peak in the gapped region, indicating that the surface state is gapped by ~100 meV while the bulk gap is nearly 225 meV.

The equivalent calculation on the [MnBi₂Te₄] SL termination is shown in Fig. 4a, c and does not agree well with the experimental data of Fig. 4d, e. While the theory shows that surface states merge with the bulk valence bands, the experiment suggests a Dirac-like structure inside the gap. By taking full account of experimental resolution functions in both momentum directions and in energy, the ARPES data are consistent with either no gap or a maximum gap size of 10 meV. More details are given in Supplementary Note 3. A similar feature, i.e., nearly gapless surface Dirac cone at the SL termination, was observed recently in MnBi₂Te₄ single crystals^20–23, where the deviation between ARPES and DFT calculation is suggested to be due to the surface-mediated spin reconstruction at the top layers of the [MnBi₂Te₄] SL termination.

Figure 5a, b shows stacks of measured isoenergy surfaces for the [MnBi₂Te₄] SL and [Bi₂Te₃] QL terminations over a wide range of energies both above and below the Dirac point, while Fig. 5c shows equivalent DFT calculations for the [Bi₂Te₃] QL termination. The six-fold symmetric isoenergy surfaces are seen in all cases, including the hexagonal warping or snow-flake effect³⁷. We comment that while both terminations collapse to a single resolution-limited point in k-space in the middle panels in Fig. 5a, b, this is expected whether or not there is a gapless or gapped Dirac point, due to the broad energy band width of the nearby valence and conduction bands (Fig. 4j).

Fig. 5. Experimental and theoretical constant energy slices.

a, b ARPES constant energy surfaces sliced at every 50 meV. c The same contours calculated by DFT for the [Bi₂Te₃] QL termination. The six-fold symmetric snowflake-like surfaces are seen in all cases.

Discussion

The vdW AFM TI MnBi₄Te₇ single crystal reported here is in fact a 1:1 superlattice composing the building blocks of AFM TI [MnBi₂Te₄] and T-invariant TI [Bi₂Te₃]. Our realization of the superlattice design has three advantages. First, as discussed above, it serves as a “buffer layer” that separates and thus effectively decreases the AFM coupling between the two neighboring [MnBi₂Te₄] SLs, leading to a weaker magnetic field to trigger the QAH. Second, by interlayer coupling between [Bi₂Te₃] QL and the adjacent [MnBi₂Te₄] SLs, the SOC-induced nontrivial topology of [Bi₂Te₃] ensures the band inversion in the 2D limit. As a result, QAH is well expected in few-layer MnBi₄Te₇. Third, when MnBi₄Te₇ is exfoliated into the 2D limit, natural heterostructures are made, which provides more 2D configurations than MnBi₂Te₄ or Bi₂Te₃ single crystal since the latter ones are only stacked by one type of building block. One can exfoliate MnBi₄Te₇ with designed termination and different film thickness. For example, two types of three-layer systems with distinct topological properties, [MnBi₂Te₄]/[Bi₂Te₃]/[MnBi₂Te₄] and [Bi₂Te₃]/[MnBi₂Te₄]/[Bi₂Te₃], should be easily obtained by exfoliation. Recent calculations²⁷ show that [MnBi₂Te₄]/[Bi₂Te₃]/[MnBi₂Te₄] is a QAH insulator if a small magnetic field around 0.2 T is applied to stabilize the forced FM phase. On the other hand, [Bi₂Te₃]/[MnBi₂Te₄]/[Bi₂Te₃] is suggested to be a QSH insulator with time-reversal-symmetry breaking²⁷ which cannot be achieved from the thin films of either MnBi₂Te₄ or Bi₂Te₃. Therefore, the 2D version exfoliated from bulk vdW TI MnBi₄Te₇ paves an avenue to chase the long-sought emergent properties such as QAH effect and QSH effect. As the foundation of engineering 2D heterostructures, such topological vdW materials could open up unprecedented opportunities in discovering novel fundamental physics as well as making new quantum devices³⁸.

Methods

Sample growth and characterization

Single crystals of MnBi₄Te₇ were grown using self-flux¹¹. Mn, Bi and Te elements are mixed so the molar ratio of MnTe: Bi₂Te₃ is 15:85. The mixtures are loaded in a 2 mL crucibles, sealed in quartz tube, heated to and held at 900 °C for 5 h. After a quick cooling to 595 °C, the mixtures are slowly cooled down to 582 °C over one to three days, where sizable single crystals are obtained after centrifuging. Although Bi₂Te₃ is the inevitable side product, we can differentiate MnBi₄Te₇ pieces by measuring their (00l) diffraction peaks. In each growth, a few sizable plate-like MnBi₄Te₇ single crystals with typical dimensions of 3 × 3 × 0.5 mm³ were obtained.

To confirm the phase, X-ray diffraction data were collected using a PANalytical Empyrean diffractometer (Cu Kα radiation). Samples used for powder X-ray diffraction were ground into powder inside acetone to reduce the preferred orientation. Electric resistivity and heat capacity data were measured in a Quantum Design (QD) DynaCool Physical Properties Measurement System (DynaCool PPMS). The magnetization data were measured in a QD Magnetic Properties Measurement System (QD MPMS). All magnetic data were calculated assuming the molar ratio between MnBi₄Te₇ and Bi₂Te₃ impurity is 86:14 in the sample suggested by powder X-ray refinement (Supplementary Fig. 1). Magnetic data measured for H || c were corrected with a demagnetization factor.

ARPES measurements

ARPES measurements on single crystals of MnBi₄Te₇ were carried out at the Advanced Light Source beamline 7.0.2 with photon energies between 40 and 55 eV with linear horizontal polarization. Single crystal samples were top-posted on the (001) surface, and cleaved in-situ in an ultra-high vacuum better than 4 × 10⁻¹¹ Torr and a temperature of 15 K. ARPES spectra were taken at 12 K, slightly smaller than T_N. As the cleaved terrain is expected to consist of patches of exposed [Bi₂Te₃] QL and [MnBi₂Te₄] SL, to eliminate the effect of possible QL and SL mixing on the ARPES data, we scanned a 1 mm square surface of the sample in 50 μm steps with a 50 μm beam spot and collected spectra from over 200 different spots on the sample. We looked at each spectrum, finding many regions with clear, sharp features. We also narrowed the beam spot down to 20 μm × 20 μm and scanned more finely, in 15 µm steps, in smaller regions of interest. We found that there were regions on the order of 50 × 50 μm that were spectroscopically stable, meaning the ARPES spectra were not changing from spot to spot. We then took our data with a 20 μm × 20 μm beam spot and studied the centroid of the spectroscopically stable regions, which we believe will minimize any contamination due to another surface.

First-principles calculations

We apply density functional theory (DFT) by using the projector-augmented wave (PAW) pseudopotentials³⁹ with the exchange-correlation of Perdew–Burke–Ernzerhof (PBE) form⁴⁰ and GGA + U⁴¹ approach within the Dudarev scheme⁴² as implemented in the Vienna ab-initio Simulation Package (VASP)⁴³. The energy cutoff is chosen 1.5 times as large as the values recommended in relevant pseudopotentials. The U value is set to be 5 eV⁶. The k-points-resolved value of BZ sampling is 0.02 × 2π Å⁻¹. The total energy minimization is performed with a tolerance of 10⁻⁶ eV. The crystal structure and atomic position are fully relaxed until the atomic force on each atom is <10⁻² eV Å. SOC is included self-consistently throughout the calculations. We constructed Wannier representations^44,45 by projecting the Bloch states from the DFT calculations of bulk materials onto the Mn-3d, Bi-6p, and Te-5p orbitals. The band spectra of the surface states are calculated in the tight-binding models constructed by these Wannier representations and by the iterative Green’s function technique as implemented in WannierTools package⁴⁶.

Author contributions

N.N. conceived the idea and organized the research. N.N., Q.L., and D.D. supervised the research. C.H., J.L., E.E., H.B., and N.N. grew the bulk single crystal and carried out X-ray and transport measurements. A.R. and C.H. performed magnetic measurements. K.G., X.Z., P.H., D.N., and D.D. carried out the ARPES measurements and data analysis. Q.L., P.L., H.S., and Y.L. performed the first-principles calculations. H.C., L.D. and C.H. carried out structure determination. N.N., Q.L., D.D., and K.G. prepared the manuscript with contributions from all authors.

Data availability

Data supporting the findings in this study are available from the corresponding authors on reasonable request.

Competing interests

The authors declare no competing interests.

Supplementary information

Supplementary information is available for this paper at 10.1038/s41467-019-13814-x.