Defect Engineering for Stabilizing Magnetic and Topological Properties in Mn(Bi_1-xSb_x)_2Te_4

Domain: physics
Published: 2025-12-18
Editorial outcome: major_revision

Abstract
MnBi2Te4 is a versatile platform for exploring diverse topological quantum states, yet its potential is hampered by intrinsic antisite defects. While Sb substitution has been employed to tune the Fermi level towards the charge neutrality point, it exacerbates the formation of Mn-Sb antisite defects. Here, we address this challenge by combining first-principles calculations with strategic synthesis to systematically investigate and control antisite defects in Mn(Bi1-xSbx)2Te4. Our calculations reveal that increasing antisite defect density progressively destroys the field-forced magnetic Weyl state, eventually driving the system into a trivial magnetic insulator. Motivated by these findings, we develop an optimized chemical vapor transport method, yielding high-quality Mn(Bi1-xSbx)2Te4 crystals with significantly reduced antisite defect density.

The emergence of strong Shubnikov-de Haas oscillations in the forced ferromagnetic state and a pronounced anomalous Hall effect near charge neutrality, with opposite signs for n- and p-type samples, confirms the type-II Weyl semimetal nature. These findings underscore the critical role of antisite defects in determining the magnetic and topological properties of Mn(Bi1-xSbx)2Te4 and establish defect engineering via optimized synthesis as a crucial strategy for realizing its exotic magnetic topological states.

Introduction
MnBi2Te4 represents a unique material platform that facilitates comprehensive investigation of diverse topological quantum states and emergent quantum phenomena1–3, spanning from antiferromagnetic (AFM) topological insulators4–6 to ferromagnetic (FM) Weyl semimetals7–10, and even theoretically predicted Möbius insulators within the canted antiferromagnetic (cAFM) phase11. In reduced dimensions, exfoliated MnBi2Te4 layers can host quantum anomalous Hall states12,13, axion insulator states14,15, as well as cAFM Chern insulator states16, contingent on layer thickness and magnetic configuration17. Its inherent tunability, coupled with readily accessible magnetic transitions, positions it as an ideal system for probing the interplay between magnetism and topology. Indeed, the relatively low critical field of MnBi2Te4 enables facile transitions into field-forced FM Weyl semimetal states with a minimal set of Weyl points, approaching the long-sought paradigm of ideal Weyl semimetals4,6.

Despite this promise, experimental progress has been limited by the presence of antisite defects, particularly Mn atoms occupying Bi sites and the reverse scenario18–22. These defects introduce additional intralayer AFM coupling, suppressing the saturation magnetization and disrupting the ideal Mn moment distribution within the lattice22–26. In the AFM topological insulator ground state, the misplaced Mn moments profoundly affect surface magnetic coupling, leading to a substantial and often debated reduction in the Dirac point gap size20,21,27,28. This has led to conflicting angle-resolved photoemission spectroscopy (ARPES) observations with both gapped and gapless surface states with significant sample-dependent variations5,21,27,29–33. Furthermore, antisite defects contribute to electron over-doping and reduced carrier mobility, shifting the Fermi level away from the desired topological regime and complicating the detection of Weyl points and Fermi arc states in transport measurements.

To mitigate these issues, Sb substitution has been widely adopted to form Mn(Bi1-xSbx)2Te4, with the goal of lowering the Fermi level towards the energy window of the Weyl nodes7,8,10,18,29,34. However, this approach introduces a critical challenge: the chemical similarity between Sb and Mn unfortunately exacerbates the formation of Mn-Sb antisite defects18. Consequently, while Sb doping can optimize carrier density, the resulting increase in antisite concentration may simultaneously degrade both magnetic and topological properties. This trade-off obscures the intrinsic characteristics of Mn(Bi1-xSbx)2Te4, hindering unambiguous interpretation of its fundamental properties. A central question thus remains: can the benefits of Fermi level tuning be retained while suppressing the detrimental effects of defect-induced disorder? Addressing this requires a clear understanding of how antisite defects influence magnetic and topological behavior, along with effective methods to control their formation during synthesis.

In this work, we systematically investigate the role of antisite defects in Mn(Bi1-xSbx)2Te4 through first-principles calculations and targeted materials synthesis. Our calculations reveal that increasing defect concentrations progressively degrade the Weyl cone, ultimately leading to a trivial magnetic insulating phase. Given the intimate interplay between band topology and magnetism in this system, we attribute the topological degradation to the antisite-induced suppression of the field-forced FM state (Weyl semimetal), also the AFM ground state (topological insulator). This finding emphatically underscores the imperative to minimize antisite defects to access the intrinsic topological properties of this material. Motivated by these findings, we develop an optimized chemical vapor transport (OCVT) growth method that enables precise control of growth conditions, including temperature profiles adapted to Sb content and an excess of Mn and Te precursors. This approach yields high-quality, stoichiometric Mn(Bi1-xSbx)2Te4 crystals with markedly improved quality, representing a significant advancement over conventional self-flux and solid-state reaction approaches.

Experimental characterizations of OCVT-grown samples confirm the success of this strategy. Magnetization measurements show enhanced AFM order in the ground state, characterized by elevated Néel temperature and enhanced saturation magnetization, indicative of a significant reduction in antisite defect density. ARPES and transport studies reveal a systematic tuning of the Fermi level from n- to p-type with increasing Sb content. Notably, at an optimized doping level of x=0.20, we achieve a minimum carrier density (7×1017 cm−3) and a record-high carrier mobility (2519 cm2/V·s). In the field-forced FM state, strong Shubnikov-de Haas oscillations appear, with oscillation frequencies tracking carrier density. A pronounced anomalous Hall effect (AHE) emerges as the Fermi level nears charge neutrality, with opposite anomalous Hall conductivity signs for n- and p-type samples, further corroborating the type-II Weyl semimetal character. Together, these results emphasize the critical and previously underappreciated role of antisite defects in determining the magnetic and topological properties of Mn(Bi1-xSbx)2Te4. By combining theoretical insights with advanced synthesis, this work establishes defect engineering as an essential strategy for realizing and stabilizing exotic magnetic topological phases in this material family.

Results
Antisite defects drive degradation of magnetism and band topology

MnBi2Te4 crystallizes in the space group R-3m (No. 166)35, consisting of stacked septuple layers (SLs) that are weakly bonded through van der Waals interaction along the c axis. Within each SL, atoms are arranged in a Te-Bi-Te-Mn-Te-Bi-Te sequence (Fig. 1a), forming a triangular lattice in the ab plane with C3 rotation symmetry.

During crystal growth, MnBi2Te4 inevitably forms point defects, including vacancies (denoted as Vi), interstitials (Ai), and crucially, antisites (AB, denoting A occupying B site), where A and B represent different atomic species18,20. These defects act as electron acceptors or donors, significantly modulating the Fermi level. While ideal MnBi2Te4 is predicted to be a topological insulator with a Fermi level within the band gap, as-grown crystals consistently exhibit pronounced n-type doping, as confirmed by Hall effect and ARPES5,8,14,24,27,29. First-principles calculations suggest that the antisites BiMn and MnBi, arising from lattice mismatch between Bi2Te3 and MnTe building blocks, possess the lowest formation energies, making them the most prevalent defects18,20. The predominant presence of MnBi and BiMn antisites in MnBi2Te4 has been further verified experimentally24,36–39. Vacancies, interstitials and BiTe antisites, having higher formation energies, are comparatively less abundant. Schematics of these defect types are illustrated in Fig. 1a. Notably, MnBi antisites act as electron-acceptors, introducing holes, while the BiMn antisites are electron donors18. Quantitative analysis (see Supplementary Table 1) indicates that non-stoichiometric crystals typically contain more BiMn than MnBi, resulting in the observed heavy n-doped conduction in MnBi2Te4, with the electron density of approximately 1020 cm−3 8,14,24,29.

Furthermore, these prevalent antisite defects (BiMn and MnBi) exert a substantial influence on the magnetic configuration of MnBi2Te4 across varying magnetic fields. Below the Néel temperature (TN), Mn spins are expected to adopt an A-type AFM ground state5. In the idealized scenario, Mn atoms are localized exclusively within the central Mn layer of each SL, denoted as MnMn, with their moments exhibiting intralayer ferromagnetic order. These ferromagnetic SLs couple antiferromagnetically with one another along the c axis (denoted by the red arrows in Fig. 1b). However, excessive MnBi antisites result in a redistribution of spin moments into the nominally non-magnetic Bi layers (the orange arrows in Fig. 1b), where MnBi antisites develop an antiparallel ordering relative to the MnMn moments. This induces a partially compensated net magnetization and establishes a ferrimagnetic (FiM) order for the whole SL, attributable to the strong AFM coupling between the non-equivalent Mn moments24,26. Meanwhile, BiMn antisites introduce magnetic dilution within the Mn layers. Upon application of an external magnetic field exceeding the saturation field, the MnMn moments are forced to align with the field, establishing a FM order. The MnBi antisites, however, continue to compensate the magnetic moments due to the strong AFM intralayer coupling26. Consequently, the saturation magnetization Msat at moderate fields (~9 T) is suppressed owing to both compensation by MnBi antisites and dilution from BiMn antisites (Fig. 1c), causing the value inconsistencies in experimentally obtained Msat 8,26,29,34. Overcoming intralayer AFM coupling, thereby achieving full alignment of all Mn moments across all layers, necessitates much higher magnetic fields, experimentally demonstrated to be around 50 T (Fig. 1d)26.

Beyond their impact on magnetic ordering, MnBi and BiMn antisites fundamentally alter the band topology. While prior theoretical calculations primarily focused on idealized ferromagnetic order, assuming perfect Mn moment alignment in defect-free crystals, these investigations predicted a single pair of type-II Weyl points in field-forced FM MnBi2Te4 4,6,7,10,40,41. They also suggested potential topological phase transitions to type-I Weyl semimetal or trivial magnetic insulator states with minor strain or lattice parameter variations (~1%)6. The susceptibility of the Weyl structure in MnBi2Te4 indicates the necessity of investigating the defect-induced topological transitions. Standard magnetotransport measurements, typically conducted below 12 T, operate in a regime where antisite defects induce a FiM order and introduce additional magnetic sites (Fig. 1c), rendering the idealized FM state assumption questionable. We calculated the band structure as a function of antisite density (Fig. 1e–g), considering the coexistence of MnBi and BiMn antisites. At an antisite density of 6.25% MnBi and 12.5% BiMn (Fig. 1f), band crossing is lifted, opening a gap that further enlarges with the increase of defect concentration (Fig. 1g). Calculation details and defective crystal structures are summarized in Supplementary Figs. 1 and 2. A schematic of defect-induced band topology evolution is shown in Fig. 1h, demonstrating a topological phase degeneration from ideal Weyl semimetals to trivial insulators.

OCVT synthesis

As these defects are inherent to the crystal growth process and their concentration is intimately linked to growth dynamics, optimizing synthesis methods is critical for defect reduction, thereby unlocking the intrinsic magnetic and topological properties of Mn(Bi1-xSbx)2Te4. While the conventional chemical vapor transport approach has shown promise for improving chemical stoichiometry in MnBi2Te4 growth39,42, its application to Mn(Bi1-xSbx)2Te4 may paradoxically result in higher defect densities compared to self-flux grown crystals42. Here, we introduce an optimized chemical vapor transport (OCVT) methodology (Fig. 2a) meticulously engineered to synthesize stoichiometric Mn(Bi1-xSbx)2Te4 with substantially suppressed antisite defects, directly addressing the limitations of conventional methods. This approach achieves precise control of Fermi level and carrier density through systematic compositional tuning of Sb content; in the meantime, the remarkable reduction in antisite density effectively stabilizes both the intrinsic magnetic structure and nontrivial band topology in Mn(Bi1-xSbx)2Te4.

In detail, recognizing the inherent non-stoichiometry of Mn observed in self-flux samples and the slow transportation efficiency of Mn, our OCVT strategy hinges on maintaining a precise excess of Mn in the starting materials, coupled with rigorous pre-heating protocols to ensure stoichiometric Mn incorporation. Critically, introducing additional Mn necessitates a corresponding increase in Te to create a Te-rich growth environment. This Te-rich condition is instrumental in minimizing the formation of BiMn and BiTe defects18, while the merely controlled Mn excess preferentially lead to the benign precipitation of MnTe. Based on this strategy, we mixed Mn, Bi, Sb and Te elements in a ratio of MnTe:(Bi,Sb)2Te3 = y:1 (y ranging from 2 to 3). The raw material mixture was then flame-sealed in vacuum quartz ampules with I2 as the transport agent and placed in a two-zone tube furnace. Considering the elevated melting point and crystallization temperature of Mn(Bi1-xSbx)2Te4 with higher Sb content, it is crucial to use higher temperatures at both the hot and cold ends of the quartz ampule (Fig. 2b). With a small temperature gradient of approximately 1 °C/cm, I2 agent transport the material towards the cold ends. Detailed growth conditions are listed in Supplementary Table 6. After a 14-day reaction, we obtained shiny hexagonal or rectangular plate-shaped crystals at the cold ends (the optical images are shown in Supplementary Fig. 5).

To assess the structural impact of Sb doping, X-ray diffraction (XRD) measurements were performed on the (001)-oriented crystal across a range of Sb concentrations (x = 0 to 0.26), as shown in Supplementary Fig. 6a. Analysis of the XRD peak positions reveals a largely invariant c-lattice parameter across the doping range (see Supplementary Fig. 6b), consistent with prior reports on lightly Sb-doped MnBi2Te4 29,34 and indicating that modest Sb substitution effectively preserves the parent crystal structure. Energy-dispersive X-ray (EDX) spectroscopy confirmed the near-stoichiometric elemental composition of these OCVT-grown crystals (see Table 1 and Supplementary Figs. 7, 8), demonstrating the efficacy of our optimized synthesis. All the x values in this work are the actual Sb content, determined through EDX by x = Sb%/(Bi% + Sb%). Scanning transmission electron microscopy (STEM) and scanning tunneling microscopy (STM) measurements were also performed on the OCVT-grown crystals (see Supplementary Figs. 10, 11), confirming a high-quality crystallinity.

Enhanced magnetism properties due to reduced defect density

To rigorously assess the impact of our OCVT synthesis on mitigating defect-induced magnetic degradation (shown in Fig. 1b–d), we performed comprehensive magnetization measurements to both qualitatively and quantitatively evaluate defect concentrations in OCVT-grown Mn(Bi1-xSbx)2Te4 crystals. Figure 3a presents temperature-dependent magnetic susceptibility curves, χ(T), of Mn(Bi1-xSbx)2Te4 across the doping range x = 0 to 0.26, acquired under field-cooled (FC) conditions with H//c. The near-perfect overlap between zero-field-cooled (ZFC) and FC curves (see Supplementary Fig. 12a) signifies the homogeneity and high quality of our OCVT-grown crystals. All χ(T) curves exhibit consistent AFM behavior, characterized by a distinct peak corresponding to TN. Below TN, the magnetization sharply decreases towards zero upon further cooling, unequivocally evidencing robust long-range AFM ordering. The absence of any signature indicative of FiM behavior in all χ(T) curves underscore the successful suppression of magnetic defects or phase impurity such as Mn-doped (Bi, Sb)2Te3 24,43. As anticipated, TN systematically decreases with increasing Sb content x, reflecting the weakening of interlayer AFM coupling due to the increasing, albeit minimized, density of MnBi and BiMn antisites even in optimized growth.

Figure 3c illustrates representative magnetization versus magnetic field M(H) for x = 0.04. As the magnetic field increases, the AFM order transitions to cAFM state via spin-flopping at μ0Hc1 ~ 3.8 T. Upon further field increase, the cAFM phase transitions to a FM state at the saturation field μ0Hc2 ~ 8.2 T. The magnetization saturates to Msat within 9 T (Msat refers to the magnetization value in the configuration of Fig. 1c). Critical fields Hc1 and Hc2, identified by peak and valley positions in the first and second derivatives of magnetization (dM/dH and d2M/dH2, detailed in Supplementary Fig. 13) respectively, are shown to decrease at elevated temperatures, with M(H) behavior approaches the paramagnetic limit (Fig. 3c). A comprehensive magnetic phase diagram summarizing these transitions is presented in Fig. 3e. M(H) curves at 2 K for each composition are presented in Fig. 3b, revealing a consistent magnetization trend (AFM→cAFM→FM). Both spin-flop and saturation critical fields exhibit a systematic decrease with increasing Sb content (Fig. 3d). Detailed analysis of M(H) across different temperatures and Sb concentrations allows us to construct a three-dimensional magnetic phase diagram (Fig. 3f), mapping distinct magnetic phases across the entire doping range and temperature domains. Additional magnetization curves at various temperatures and torque magnetometry for samples from OCVT are shown in Supplementary Figs. 14 and 15, respectively.

Figure 4a compares TN as a function of Sb content x from this study and previously reported values. TN values, extracted from kinks of χ(T) and longitudinal resistivity ρxx(T) curves (see Supplementary Fig. 13), reflect the strength of interlayer AFM coupling among SLs against thermal fluctuations as a fundamental indicator. Higher TN suggests a more robust AFM ground state with fewer antisite defects. However, with increasing Sb content and consequently, a higher density of MnBi and BiMn antisites (even in optimized growth), the interlayer AFM interaction weakens, lowering the energy barrier towards FiM ground states. In the Sb-rich limit of MnSb2Te4, both FiM and AFM ground states have been observed depending on the Mn concentration, resulting from different growth conditions, with Curie temperatures (TC) ranging from 24 K to 58 K or a lower TN of around 19 K19,22,23,34,44–46.

As shown in Fig. 4b, Msat decreases nearly linearly with a rising Sb content due to the compensation between nonequivalent Mn moments caused by increasing MnBi antisites, while the BiMn antisites act as effective magnetic vacancies within Mn layers, diluting magnetic ion concentration and thereby reducing overall magnetization. In Mn(Bi1-xSbx)2Te4, Mn exists in a high-spin Mn2+ state (S = 5/2), yielding an expected saturation magnetization of 5.0 μB/Mn2+ according to the Hund’s rule (μB being the Bohr magneton). Previous neutron diffraction, high-field magnetization, and theoretical calculations for MnBi2Te4 consistently report a local magnetic moment of 4.04~4.7 μB/Mn2+ 5,24–26,34,47, with minor deviations potentially arising from orbital hybridization26. Importantly, within a 9 T field, the sublattices of MnMn and MnBi form FM configuration respectively yet remain antiparallel to each other (see Fig. 1c). Consequently, the Msat observed at 9 T is reduced by the MnBi moments and can be effectively used to estimate the concentration of Mn-Bi/Sb mixing26,39.

To quantify defect concentrations, we set the amount percentage of MnMn and MnBi/Sb in corresponding atom layers as a and b, respectively. Considering the different FM configurations shown in Figs. 1c and 1d, we write:

a + 2b = MnEDX (1)

a - 2b = Msat / M0 (2)

where MnEDX is the normalized Mn proportion obtained from experiments with Te as a reference value of 4. M0 denotes the local magnetic moment of Mn2+, which can be approximated to be 4.6 μB/Mn2+, the fully saturated magnetization in experiments at 50 T26. Neglecting high-energy vacancies VMn, the concentration of Bi/SbMn can be approximated as (1 - a) × 100%. Calculations based on Eqs. (1) and (2) yield Sb-dependent defect concentrations summarized in Table 1. Compared to Mn(Bi1-xSbx)2Te4 synthesized via other methods, our OCVT-grown crystals show fewer MnBi/Sb and Bi/SbMn defects, directly correlating with the observed enhancement in magnetic properties and the potential for realizing intrinsic topological states. The clear negative correlation between band Msat further underscores the low defect density achieved in our samples, corroborated by the Msat data from other works shown in Fig. 4b.

Tuning the Fermi level by Sb doping

Beyond magnetic property refinement, substituting Bi with Sb in MnBi2Te4 provides a potent means to precisely tune the Fermi level, promoting a transition from n- to p-type conduction. Controlled doping into topological insulators is a crucial strategy for positioning the Fermi level within the bulk band gap while preserving topologically protected surface states, as exemplified by Sn-doped Bi1.1Sb0.9Te2S48. This Fermi level tunability arises from the dopant role in compensating intrinsic defects by introducing counter-doping carriers.

To experimentally visualize this carrier-type transition, we performed ARPES measurements on OCVT-grown Mn(Bi1-xSbx)2Te4 with x ranging from 0.14 to 0.26. Figure 5a, b present the ARPES spectra and their second derivative images, respectively. Sample cleavage and signal detection were both performed at 10 K below TN. Higher than typically used for detecting topological surface states, the utilized photon energy of 13 eV reveals primarily the dispersion of bulk bands, to access optimal signal clarity29. Subtle indications of Dirac-like surface states appear only in the second derivative spectra. This limited surface signal is likely due to a Sb-induced gap opening at the Dirac point49,50, as well as the surface inhomogeneity-induced scattering51. Unlike the minimal surface gap in MnBi2Te4, a recent work showed that the surface gap continuously grows with increasing Sb content, reaching 104 meV at 10 K for x = 0.1, comparable to the non-trivial bulk gap49. It may cause bulk and fully gapped surface states to overlap in the spectra. In our result, a clear downward shift of the Fermi level EF occurs as x rises. At x = 0.14, EF is well above the bulk band gap (E-EF ~ -160 meV), indicating n-type carriers. At x = 0.20, EF approaches the conduction band minimum (CBM), while at x = 0.22, it enters the valence band and locates near the valence band maximum (VBM), signaling a shift to p-type conduction. At x = 0.26, a second valence band becomes visible. Notably, to confirm the band edge proximity of the Fermi level, two samples with x = 0.20 were measured, exhibiting few differences in the EF. Indeed, the almost insulating bulk state at x ~ 0.20 makes the EF more sensitive to even minor carrier variations.

Collectively, ARPES data demonstrate a monotonic downward shifting of EF from the conduction band to the valence band with increasing Sb doping, indicating the n-to-p carrier transition, with a charge neutrality point (CNP) at x ~ 0.20.

Transport properties of Mn(Bi1-xSbx)2Te4

To further investigate the n-p carrier evolution, we performed electrical transport measurements of OCVT-grown Mn(Bi1-xSbx)2Te4 crystals. Temperature-dependent longitudinal resistivity ρxx(T) curves, measured from 300 K down to 2 K, exhibit semimetallic behavior across all doping (Fig. 6a). Notably, samples with x = 0.19 to 0.21, corresponding to Fermi level proximity to the band edge, show elevated resistivity values across the entire temperature range, consistent with reduced carrier density near the charge neutrality point. The x = 0.20 sample, closest to the CNP, displays a nonmonotonic ρxx(T) behavior with a distinct upturn around 165 K. A kink in ρxx(T) near 24.5~26 K marks the Néel temperature, indicative of a sharp change in spin scattering as magnetic moments order below TN34.

Field-dependent magnetoresistance (MR) and Hall resistivity (ρyx) measurements at 2 K (Fig. 6b–c) reveal further transport characteristics (magnetic field applied along the c axis). MR, defined as [ρxx(H) - ρxx(0)]/ρxx(0) × 100%, exhibits distinct slope changes at critical fields Hc1 and Hc2, corresponding to magnetic phase transitions. Here, ρxx(0) refers to the zero-field resistivity. Hall resistivity variations across magnetic phases demonstrate an AHE contribution, suggesting the coupling between band structure and magnetism. Beyond Hc2, where magnetization saturates, the anomalous Hall term stabilizes. To quantitatively determine carrier density, we analyzed Hall data exclusively in FM states by extracting the linear slope of ρyx versus magnetic field, defined as RH = dρyx/dμ0H, where n = 1/(e·RH) (negative values for electrons, positive for holes). As x increases from 0 to 0.23, RH shifts from negative to positive, directly confirming the n-to-p carrier type transition. Pronounced nonlinearity in the ρyx curve for x = 0.20, contrasting sharply with the near-linear behavior for slightly n-doped (x = 0.19) and p-doped (x = 0.21) samples, suggests two-band conduction with significant contributions from both electrons and holes near CNP. To extract reliable carrier densities, we employed a two-band model to fit the nonlinear Hall data. Due to the limit of ±12 T field range in our experiments, fitting FM state Hall signals may be error-prone, as only a limited range (~4 T) is suitable for fitting. To minimize errors, we used nonlinear Hall data above TN for more reliable fits, where the magnetization-related anomalous Hall contributions are negligible in the paramagnetic state. This approach yields a carrier density down to around 7 × 1017 cm−3 through fitting (details in Supplementary Fig. 16).

Carrier mobility μ, another important transport metric, calculated as μ = RH/ρxx(0), exhibits a clear correlation with carrier density (Fig. 6d). Samples with lower carrier densities exhibit higher mobilities, with mobility peak and density valley coinciding around x = 0.20, further corroborating the n-p transition near the CNP observed in ARPES. Remarkably, the maximum mobility reaches 2519 cm2/V·s, significantly exceeding previously reported values for both pristine MnBi2Te4 and Mn(Bi1-xSbx)2Te4 (comparison shown in Table 2), underscoring the efficacy of our OCVT synthesis for high-quality Mn(Bi1-xSbx)2Te4. Carrier densities and mobilities of all measured samples via OCVT are summarized in Supplementary Fig. 17, indicating an overall enhancement of carrier mobilities.

Crucially, the Sb doping level corresponding to the charge neutrality point is not a fixed material parameter but rather synthesis-dependent, varying significantly across growth methods. Prior studies report CNP compositions mostly ranging from x = 0.25 to 0.357–10,29,34,43,52,53, whereas OCVT-grown crystals exhibit a pronounced leftward shift of the CNP to a lower Sb content, around x = 0.20 (see Supplementary Fig. 18). This CNP shift is a compelling consequence of the reduced defect density achieved via OCVT synthesis. As evidenced by magnetization data in Table 1, the lower MnBi/Sb concentration in OCVT-grown crystals effectively stabilizes the intrinsic AFM order and, simultaneously, shifts the Fermi level upward. Compared to samples grown via other methods, OCVT-grown ones exhibit fewer electron-donating Bi/SbMn, whose quantity reduces even more than MnBi/Sb (see Table 1 and Supplementary Table 1), thereby generally enhancing p-doping efficiency for a given Sb concentration and resulting in a CNP at lower Sb doping levels. This capability to reach the CNP at a reduced Sb concentration directly translates to a significant suppression of antisite defects as the Fermi level approaches towards Weyl points. As directly visualized in Fig. 6e, at the optimal doping contents close to the CNP, samples from OCVT exhibit superior stability of the intrinsic magnetic order against antisite-induced disturbance, characterized by concurrent maxima in both Msat and TN. The optimized magnetism profoundly suppresses the defect-induced degradation on the intrinsic band topology, thereby preserving the pristine topological characteristics while facilitating reliable access to key emergent phenomena governed by Weyl points or nontrivial surface states inherent to stoichiometric Mn(Bi1-xSbx)2Te4.

Quantum oscillations and anomalous Hall effect in Sb-doping driven electronic structure evolution

Pronounced Shubnikov-de Haas (SdH) oscillations emerge in both ρxx and ρyx when Mn(Bi1-xSbx)2Te4 bulks are driven into forced FM states by a magnetic field along the c axis. After subtracting the background with polynomial fitting, the oscillation term Δρ as a function of 1/μ0H is shown in Fig. 7a. For visual clarity, oscillations are separated by 0.2 mΩ·cm increments across samples with the carrier density ranging from n- to p-type. The frequency of oscillations FS, derived through fast Fourier transform (FFT) analysis, is shown in Fig. 7b. The FS values, linearly related to the Fermi pocket size AF perpendicular to the field direction via Onsager’s relation, FS = ℏ/2πe AF, reflect the Fermi level position and align with the observed carrier density values. Figure 7c shows the relationship between FS and carrier density n, where FS decreases as carrier density declines on both electron and hole-doped sides. Notably, these SdH oscillations originate from bulk FM-state bands rather than topological surface states. Previous high-field SdH oscillations up to 60 T confirmed that the ferromagnetic Mn(Bi1-xSbx)2Te4 realizes an ideal type-II Weyl semimetal, with a pronounced difference in the three-dimensional Fermi pocket shape between highly n-doped and p-doped samples7,10. To analyze the Fermi surface shape and anisotropy in n- and p-doped Mn(Bi1-xSbx)2Te4, we approximate the Fermi pocket as an ellipsoid with axes ka = kb = γkc and apply Onsager’s relation to estimate the carrier density across three-dimensional ellipsoidal Fermi surfaces using the following formula:

FS = ℏ/2πe AF = ℏ/2πe γ2kc2 (3)

n3D = (2π2)3 4/3 π ka kb kc = 3π 1/2 γ2kc3 (4)

Thus, the relationship between FS and carrier density n can be expressed as:

FS = ℏ/2e (3π2nγ) 2/3 (5)

The factor γ can be extracted from the fitting procedure, which reflects the Fermi surface anisotropy. We can get ka = kb = 0.37kc for the electron-doped regions and ka = kb = 0.107kc for the hole-doped regions. This pronounced difference in Fermi surface anisotropy between conduction and valence bands is fully consistent with the characteristic tilted Weyl cone dispersion of a type-II Weyl semimetal.

Temperature-dependent SdH oscillations (Fig. 7d) persist up to temperatures exceeding TN, with their amplitude diminishing upon warming, attributable to spin fluctuations that allow the magnetic field to induce a moderate alignment of Mn2+ moments even within the paramagnetic phase, consistent with the previous SdH oscillations and electron spin resonance (ESR) characterizations5,8–10,54. From the thermal damping of SdH oscillations, we estimate the effective mass value m* = 0.06m0 (where m0 is the electron mass) by fitting the temperature dependence of FFT amplitude with Lifshitz-Kosevich (LK) formula (Inset in Fig. 7d):

RT = αTm*/B / sinh(αTm*/B) (6)

where RT refers to the amplitude of oscillations at particular 1/B or the amplitude of FFT analysis, and α = 2π2kBm0/eℏ. The magnetic field value in Eq. (6) is taken as 1/B = (1/B1 + 1/B2)/2, where B1 and B2 are the starting and ending fields of FFT analysis. Additionally, as temperature increases, shifts in SdH peak and valley positions reflect the strong coupling between the band structure and magnetic states (Fig. 7d and Supplementary Fig. 20).

The AHE, characterized by corresponding conductivity σAHE, provides further compelling transport evidence for the Weyl cone topology. The presence of a single Weyl point pair in ferromagnetic Mn(Bi1-xSbx)2Te4 simplifies AHE analysis, avoiding complexities arising from multiple Weyl pairs or trivial bands. Theory predicts that type-I Weyl semimetals with broken time-reversal-symmetry exhibit Fermi level-independent σAHE due to the complete compensation of Berry curvature from free carriers, only determined by the Weyl point separation Δk in momentum space55. In contrast, type-II Weyl semimetals, characterized by tilted Weyl cones, generate a non-zero Berry curvature integral, yielding significant free-carrier contributions to AHE along with the Δk-related contributions56. The sign reversal of the Berry-curvature-induced term in σAHE, occurring as the Fermi level traverses Weyl points accompanied by shrinkage or emergence of electron/hole pockets, serves as the key criterion distinguishing type-II from type-I Weyl semimetals7,8.

Figure 7e presents field-dependent anomalous Hall resistivity ρAHE for samples with varied carrier densities, extracted via subtracting the ordinary Hall background from total ρyx. Across all samples, the ρAHE values exhibit distinct evolution among different magnetic phases and gradually saturate in the FM state. Notably, ρAHE changes its sign from negative to positive with Fermi level down shifting due to Sb doping. Furthermore, in both electron and hole doping regions, |ρAHE| increases as Fermi level moving towards CNP. Converted into conductivity σAHE (Fig. 7f), the values are strongly determined by the carrier type and density. Figure 7g shows the anomalous Hall angle ΘAHE = σAHE/σxx as a function of carrier density. Similar to the behavior of σAHE, ΘAHE increases with carrier density in both electron and hole doping regions, and abruptly reverses its sign as the Fermi level crosses the CNP. This characteristic evolution of ΘAHE aligns closely with the expectations for an ideal type-II Weyl semimetal7,8,56. Moreover, the remarkably large ΘAHE (~33.6%) observed near the CNP, along with the enhanced carrier mobility, underscore the dominant role of Weyl fermions in bulk transport. This enhanced anomalous Hall angle, arising from the intrinsic tilted Weyl cone and minimized contributions from irrelevant electronic states due to Fermi level tuning near charge neutrality, further solidifies the type-II Weyl semimetal nature in Mn(Bi1-xSbx)2Te4 and the superior quality of OCVT-grown crystals in revealing these exotic quantum phenomena.

Methods
Single crystal growth

High-quality single crystals were synthesized by the OCVT method. Starting materials, including Mn (piece, 99.98%), Bi (grain, 99.999%), Sb (lump, 99.99%), and Te (lump, 99.99%), were mixed in the molar ratio of MnTe:(Bi,Sb)2Te3 = y:1, with y selected between 2 and 3. For enhanced reactivity, Mn pieces were ground into fine powders. For Sb-doped crystals, a slightly higher Sb content than the target substitution level x was used, where x = Sb%/(Sb%+Bi%). The raw materials (1~2 g) were sealed in a quartz ampule under vacuum. The ampule was first heated at 600~630 °C as a pre-reaction for a uniform mixture. Subsequently, I2 granule of around 20 mg was added with the precursors as the transport agent. The re-sealed ampule was then placed into a two-zone tube furnace (OTF-1200X-II, Kejing) with a slight elevation at the cold end, and exposed to a temperature difference of 20 °C between the hot and cold zones. For higher Sb-doping levels, the temperature difference was increased to 30 °C. The reaction temperature was adjusted depending on the doping level (details in Supplementary Note 4). After a two-week reaction and natural cooling, shiny crystals measuring several millimeters were obtained at the cold end.

Component and structural characterization

Elemental composition and atomic percentages of the single crystals were determined by energy dispersive spectroscopy (EDX, Oxford X-Max), utilizing an electron beam energy of 10 keV and an integral spectrum energy range of 20 keV. X-ray diffraction (XRD) measurements were carried out using a diffractometer (Bruker, D8 Discover) equipped with Cu Kα radiation (λ = 1.5418 Å). A 2-bounce crystal monochromator was installed in the beam path to remove the Kα2 component and get a monochromatic Kα1 X-ray (λ = 1.54056 Å) irradiating on the (001) surface of the crystals. The scanning transmission electron microscopy (STEM) imaging was performed on a double aberration corrected field emission transmission electron microscope (Themis Z, Thermo Fisher Scientific) operated at 300 kV. The probe forming semi-convergent angle is 21.4 mrad, and the semi-collection angle of High-angle annular dark field (HAADF) detector is 79–200 mrad. Scanning tunneling microscopy (STM) was performed on an OCVT-grown Mn(Bi0.8Sb0.2)2Te4 single crystal. The (001) surface, prepared by in situ cleavage under a pressure of 1.9 × 10−10 mbar, was imaged in atomic resolution with a bias voltage of −0.75 V and tunneling current of 230 pA at 77 K.

Magnetic measurements

Temperature- and field-dependent magnetization measurements were conducted using a vibrating sample magnetometer (VSM) equipped in a physical property measurement system (PPMS, EverCool II, Quantum Design, ±9 T) and VSM mode in SQUID (MPMS3, Quantum Design, ±7 T). Standard quartz sample holders were used. For temperature-dependent magnetization, an external field of 500 Oe was applied under both zero-field-cooled (ZFC) and field-cooled (FC) conditions.

ARPES measurements

The ARPES measurements were performed at beamline BL13U of the National Synchrotron Radiation Laboratory (NSRL) in Hefei, China. The samples were cleaved and measured in situ under ultra-high vacuum conditions with a base pressure better than 6 × 10−11 Torr, at a temperature of 10 K. The photon energy was set to hv = 13 eV, which allowed for clear detection of the band dispersions, and the energy resolution was better than 20 meV.

Electrical transport measurements

Electrical transport measurements were performed in a commercial variable temperature insert with a Cryogenic superconducting magnet (1.6~300 K, ±12 T). Clean, flat surfaces were cleaved from the as-grown bulk crystals, and aluminum wires were bonded to the surface using silver paste (DuPont, 4929N) to form a standard six-wire Hall configuration. A voltage-controlled current source (Stanford Research System, CS580) was used to provide an alternating current at 17.777 Hz, and the voltage signals were recorded by several lock-in amplifiers (Stanford Research System, SR865).

Theoretical calculations

The first-principles calculations were performed using the projector augmented-wave (PAW)68 pseudopotential method as implemented in the VASP code69. The Perdew-Burke-Ernzerhof generalized gradient approximation (GGA-PBE)70 is employed to describe the exchange and correlation functional. The plane-wave energy cutoff was set to 550 eV, with a total energy convergence criterion of 10−6 eV. All atoms in the unit cell were allowed to relax until the Hellmann-Feynman force on each atom was less than 0.001 eV/Å. The GGA+U method71 with an effective Hubbard U value of 3.0 eV was used to address the correction effects of d electrons of Mn atoms6. The Brillouin zone integral is implemented on a Γ-centered grid mesh of 9 × 9 × 5. Supercells that correspond to 2 × 2 × 1 of the original unit cells of MnBi2Te4 and Mn(Bi1-xSbx)2Te4 were used to simulate the influence of magnetic antisites or Sb substitutions at various densities.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript presents the optimization of a chemical vapor transport (CVT) method to synthesize high-quality Sb-doped MnBi₂Te₄ crystals. The authors demonstrate a significant reduction in antisite defects and nearly achieve charge neutrality at low Sb concentrations. These improvements are promising for exploring the topological properties of MnBi₂Te₄. The study is well-designed to validate the advantages of the OCVT method and its corresponding enhancement of material performance. However, the manuscript is limited by the absence of mechanistic insights into the role of Sb dopants, despite its potential significance. In my opoion, the manuscript does not meet the publication standards of Nature Communications and requires major revision before further consideration.\n\nMajor concerns regarding the results:\n1. Sb-doped MnBi2Te4 is denoted Mn(Bi1-xSbx)2Te4, where x represents the Sb content. This value is crucial for comparing magnetic properties with prior reports and demonstrating the superiority of the OCVT method. However, the manuscript does not clarify how x is determined. While it appears to be derived from EDX analysis, the distinction between the nominal and actual Sb content remains unclear. The authors must specify whether x refers to xnominal or xactual and ensure that the reported values are directly comparable to those in the literature.\n2. Table 1 reports the elemental composition and defect concentrations across different Sb contents. When x ranges from 0.16 to 0.24, the Mn-Bi/Sb percentage significantly deviates from half of the Bi-Sb-Mn concentration. This deviation suggests possible vacancies in the Bi-Sb sites (the second and sixth layers of the septuple layer). The authors should clarify if these vacancies are considered and if they influence the magnetic or electronic transport properties.\n3. Figures 1 and 8 present electronic band structures seemingly obtained from 4×4 and 2×2 supercells, respectively. However, the manuscript lacks details about the DFT models used. Supercell modeling can induce artificial band folding. Therefore, the authors should explicitly address whether the chosen supercell models affect the identification and interpretation of Weyl points in this system.\n4. The main conclusion is that Sb doping suppresses antisite defects; however, the discussion lacks depth. There are four possible antisite defect types: MnBi, MnSb, BiMn, and SbMn. It is crucial to determine which types are predominant, how their populations fluctuate with Sb concentration, and which defect suppressions are associated with improved magnetic properties (e.g., Néel temperature or saturation magnetization).\nMinor concerns:\n5. The use of MnMn is confusing without an explanatory apparatus in the main text of the manuscript, particularly in the context of its discussion with antisite defects, such as MnBi and MnSb. Please add the explanation shown in Table 1 to the first instance of MnMn.\n6. The order of the figures in the manuscript is confusing. For example, Fig. 3a and Fig. S6a are depicted in the second paragraph on page 6, followed by Fig. 3c and Fig. S5 in the third paragraph. Please adjust the text or figures to ensure they are depicted in the correct order.", "reviewer_2": "This study convincingly demonstrates the pivotal role of antisite defects in governing the magnetic and topological properties of ferromagnetic Mn(Bi₁₋ₓSbₓ)₂Te₄ (MBST), through a synergistic approach combining first-principles calculations and comprehensive experimental investigations. To mitigate the detrimental effects of antisite defects, the authors developed an optimized chemical vapor transport (OCVT) method, enabling the growth of stoichiometric MBST crystals with significantly reduced defect densities. The OCVT-grown samples exhibit a well-defined charge neutrality point (CNP) near x = 0.20, as confirmed by both angle-resolved photoemission spectroscopy (ARPES) and Hall effect measurements. These crystals also show a record-high carrier mobility of 2519 cm²/V·s, surpassing all previously reported values for this material system. Furthermore, the observation of Shubnikov–de Haas (SdH) oscillations and pronounced anomalous Hall conductivity in the field-aligned ferromagnetic state—both strongly dependent on carrier type and density—provides compelling evidence for the realization of a type-II Weyl semimetal phase in MBST.\n\nOverall, the study offers a well-integrated theoretical and experimental framework for controlling material quality and accessing intrinsic topological phases. It not only deepens our understanding of the role of antisite defects but also establishes a new materials platform for exploring magnetically induced topological quantum phenomena.\n\nI recommend its publication in Nature Communications, provided that the following comment is adequately addressed.\n\n1.The authors should provide real-space structural characterization of the MBST crystals, such as transmission electron microscopy (TEM) images, to directly confirm the reduction in defect density."}, "author_response": "Response to Reviewers’ Comments\nDear Reviewers,\nWe sincerely thank you for taking the time to carefully review our manuscript “Defect\nEngineering for Stabilizing Magnetic and Topological Properties in Mn(Bi Sb ) Te ”. Your\n1-x x 2 4\nconstructive and valuable feedback has significantly contributed to refining our manuscript. In the\nfollowing, we have included your comments in their entirety (in blue) and numbered them for clarity,\nand we will address the comments on a point-by-point basis:\nReviewer #1 Comments:\n“This manuscript presents the optimization of a chemical vapor transport (CVT) method to\nsynthesize high-quality Sb-doped MnBi₂Te₄ crystals. The authors demonstrate a significant\nreduction in antisite defects and nearly achieve charge neutrality at low Sb concentrations. These\nimprovements are promising for exploring the topological properties of MnBi₂Te₄. The study is well-\ndesigned to validate the advantages of the OCVT method and its corresponding enhancement of\nmaterial performance. However, the manuscript is limited by the absence of mechanistic insights\ninto the role of Sb dopants, despite its potential significance. In my opinion, the manuscript does\nnot meet the publication standards of Nature Communications and requires major revision before\nfurther consideration.”\nResponse:\nWe thank the reviewer for providing insightful comments on our manuscript. It is important\nto note that Sb doping, although essential for tuning the Fermi level toward Weyl physics,\ninadvertently introduces additional Mn and Bi/Sb antisite defects. These increased antisites,\nBi/Sb\nin turn, degrade the magnetic properties and band topology in Sb-rich Mn(Bi Sb ) Te .\n1-x x 2 4\nOur OCVT\nmethod directly targets this issue by effectively reducing antisite densities in both MnBi Te and\n2 4\nMn(Bi Sb ) Te at given Sb contents than previously reported.\n1-x x 2 4\nIn response to your comments, we have conducted further theoretical calculations and\ndiscussions to clarify the antisite-related mechanism and its influence on the band structure and\nmagnetic orders. We also revised a few statements per your suggestions. We believe that the current\nversion of the manuscript has been significantly improved with your helpful comments.\nReviewer #1 Comment 1:\n“Sb-doped MnBi Te is denoted Mn(Bi Sb ) Te , where x represents the Sb content. This value\n2 4 1-x x 2 4\nis crucial for comparing magnetic properties with prior reports and demonstrating the superiority\nof the OCVT method. However, the manuscript does not clarify how x is determined. While it\nappears to be derived from EDX analysis, the distinction between the nominal and actual Sb content\nremains unclear. The authors must specify whether x refers to x or x and ensure that the\nnominal actual\nreported values are directly comparable to those in the literature.”\nResponse:\nWe thank the reviewer for providing insightful comments and nice suggestions.\nAll doping levels x reported in this manuscript correspond to experimentally determined\ncomposition x from energy-dispersive X-ray spectroscopy (EDX). In the single crystal\nactual\nsynthesis process, the starting materials including Bi and Sb were mixed with a nominal ratio of Bi:\nSb = (1-x ): x , where x = Sb% / (Bi% + Sb%). The value of x was determined by\nnominal nominal nominal actual\nEDX on cleaved surfaces using the formula x = Sb % / (Bi % + Sb %).\nThe minor\nactual EDX EDX EDX\ndeviation between x and x results from different transport efficiency of Bi and Sb during\nnominal actual\ncrystal growth.\nHere, we also clarify the definition of x in the manuscript. The values of Sb content x in Mn(Bi\n1-\nSb ) Te presented in this work, both from our results and prior reports, are mostly based on\nx x 2 4\nexperimental results x , obtained primarily through EDX analysis1–11 or diffraction refinement12.\nactual\nThe only exception is the data extracted from Ma et al.13 (Ref. 49 in the main text, corresponding to\nred half-filled circles in Fig. 4a), where the nominal doping level x instead of x was used\nnominal actual\nin their original article.\nRevision:\nIn response to your comment, we have added clarifications regarding the definition of x in the\nmain text (Page 6) and Supplementary Information (Page 16).\nReviewer #1 Comment 2:\n“Table 1 reports the elemental composition and defect concentrations across different Sb\ncontents. When x ranges from 0.16 to 0.24, the Mn-Bi/Sb percentage significantly deviates from half\nof the Bi-Sb-Mn concentration. This deviation suggests possible vacancies in the Bi-Sb sites (the\nsecond and sixth layers of the septuple layer). The authors should clarify if these vacancies are\nconsidered and if they influence the magnetic or electronic transport properties.”\nResponse:\nWe thank the reviewer for the constructive suggestion. We wish to clarify that a strict twofold\nrelationship between Mn % and Bi/Sb % is not expected in Mn(Bi Sb ) Te .\nThe observed\nBi/Sb Mn 1-x x 2 4\ndeviations (in Table 1) directly stem from intrinsic compositional non-stoichiometry of real Mn(Bi\n1-\nSb ) Te crystals, rather than indicating the presence of Bi/Sb site vacancies (V ). Combined\nx x 2 4 Bi/Sb\ntheoretical calculations and experimental evidence confirm that V defects are energetically\nBi/Sb\nunfavorable and have not been detected. Below, we provide a detailed discussion on the origin of\nthe defect concentration deviation and the role of V defects:\nBi/Sb\n(1) Non-stoichiometry and antisite imbalance.\nCrucially, isolated Mn and Bi/Sb defects can form independently, not limited by equal-\nBi/Sb Mn\nquantity Mn–Bi/Sb exchange. Systematic deviations between Mn % and half of Bi/Sb % have\nBi/Sb Mn\nbeen commonly reported across the entire doping range (x = 0 to 1)12,14–17, with half of Bi/Sb %\nMn\ntypically exceeding Mn %.\nThis trend can be understood from both experimental and theoretical\nBi/Sb\nperspectives.\nExperimentally, Mn(Bi Sb ) Te single crystals commonly exhibit off-stoichiometry in\n1-x x 2 4\nelemental compositions. In particular, the actual Mn:(Bi/Sb) ratio often deviates from the ideal 1:2,\ntypically exhibiting an excess of Bi/Sb content, as confirmed by elemental analysis, structural\nrefinements7,12–14,16,18,19, and our EDX data (Table 1). Given the negligible V density, this excess\nMn\nBi/Sb content promotes Bi/Sb occupation on Mn sites, significantly increasing Bi/Sb defects to\nMn\ncompensate for Mn deficiency. Conversely, Mn-rich compositions (Mn:(Bi/Sb) > 1:2) would\n2 / 24\nenhance Mn defect formation.\nBi/Sb\nMoreover, the inequality of these antisite concentrations is further supported by theoretical\ncalculations in stoichiometric systems. These reveal a formation energy hierarchy follows Bi <\nMn\nMn–Bi < Mn in MnBi Te 20,21 and Mn < Mn–Sb < Sb in MnSb Te 20. This formation energy\nBi 2 4 Sb Mn 2 4\ndifference drives the systematic imbalance between Mn % and half of Bi/Sb % rather than\nBi/Sb Mn\nequilibrating.\nThus, the inequality observed in Table 1 is reasonable, based on both formation energetics in\nstoichiometric systems and the actual non-stoichiometry in real crystals.\n(2) Energetic unfavorability and experimental absence of V defects.\nBi/Sb\nV defects cannot explain the observed deviations due to their vanishingly low\nBi/Sb\nconcentration. Theoretical studies consistently show that V defects possess considerably higher\nBi/Sb\nformation energies than the dominant antisite defects (Mn and Bi/Sb ) in Mn(Bi Sb ) Te 20–\nBi/Sb Mn 1-x x 2 4\n23, suggesting a very low probability of formation.\nTo date, no V defects have been experimentally detected in Mn(Bi Sb ) Te through X-\nBi/Sb 1-x x 2 4\nray or neutron diffraction refinements12,14,16,24,25, and by atomic-resolution techniques such as\nscanning transmission electron microscopy (STEM)16,21,26–28. We further performed large-scale\nSTEM imaging on OCVT-grown MnBi Te and Mn(Bi Sb ) Te crystals. As shown in Figs. R1a–\n2 4 0.8 0.2 2 4\nb, the septuple-layer (SL) structures are well-ordered and separated by van der Waals gaps,\nconfirming high crystallinity. All Bi/Sb sites (the second and sixth atomic layers in each SL) are\nfully occupied, with no detectable V defects.\nBi/Sb\nIn summary, the observed deviation between Mn % and half of Bi/Sb % naturally arises\nBi/Sb Mn\nfrom non-stoichiometry in real crystals and does not imply a significant presence of V .\nThe\nBi/Sb\ninterpretation is robustly supported by the consistently high theoretical formation energies of V\nBi/Sb\nand their persistent absence across all experimental investigations of Mn(Bi Sb ) Te .\n1-x x 2 4\na b\n5 nm 5 nm\nFigure R1. STEM characterizations of OCVT-grown MnBi Te and Mn(Bi Sb ) Te .\n2 4 0.8 0.2 2 4\na, b Atomic-resolution HAADF-STEM images of the cross-sectional OCVT-grown MnBi Te in (a)\n2 4\nand Mn(Bi Sb ) Te in (b), viewed from the [110] direction.\n0.8 0.2 2 4\n(3) Potential influence of V defects. Although the concentration of V defects is\nBi/Sb Bi/Sb\nnegligible, we have considered their potential presence and evaluated possible impacts on magnetic\n3 / 24\nand transport properties. As electron acceptors, V defects introduce hole doping; however, the\nBi/Sb\noverall carrier density and Fermi energy are primarily dominated by the non-equivalent populations\nof Mn and Bi/Sb antisites. Regarding the band structures, theoretical studies on an AFM-\nBi/Sb Mn\nMnBi Te monolayer show that introducing isolated V defects preserves the overall band topology\n2 4 Bi\nand bandgap, introducing only minor defect states compared to the defect-free system22. In contrast,\nMn and Bi antisites strongly modulate the gap size at the Dirac point, with higher defect\nBi Mn\ndensities leading to significant reduction or even closure of the Dirac gap15,22. Magnetically, V\nBi/Sb\ndefects do not directly alter the Mn2+ moment distribution or cause magnetic dilution within the Mn\nlayers. Thus, their impact on magnetic coupling (whether intralayer or interlayer) is expected to be\nminimal. The specific magnetic orders and the resulting magnetic properties in Mn(Bi Sb ) Te\n1-x x 2 4\nare primarily determined by the configuration and concentration of Mn and Bi/Sb antisites,\nBi/Sb Mn\nas further discussed below in our Response to Comment 4.\nRevision:\nWe have added clarifying statements of the density deviations in the main text (Page 26) as\nsuggested.\nReviewer #1 Comment 3:\n“Figures 1 and 8 present electronic band structures seemingly obtained from 4×4 and 2×2\nsupercells, respectively. However, the manuscript lacks details about the DFT models used.\nSupercell modeling can induce artificial band folding. Therefore, the authors should explicitly\naddress whether the chosen supercell models affect the identification and interpretation of Weyl\npoints in this system.”\nResponse:\nThank you for the comment. Firstly, we would like to clarify that the DFT models used for the\nband structure calculations in Figures 1 and 8 are a 2×2 lateral expansion supercell, as we discussed\nbelow. To accurately capture magnetic-order-dependent energies and band structures, our\ncalculation models incorporate two septuple layers (SLs), each containing a Mn layer, so as to model\ninterlayer magnetic coupling (AFM or FM). The non-expanded unit cell with 2 SLs was referred to\nas “1×1” with a total of 14 atoms, as illustrated in the structural schematic in Fig. R2a (highlighted\nby the blue solid box). Different from the minimized primitive cell, we use this conventional cell to\neasily construct the supercell, which is necessary to understand the influence of antisites or Sb\nsubstitutions at various densities. The 2×2 supercell was created by doubling the in-plane lattice\nparameters a and b while keeping c unchanged, resulting in a total of 56 atoms (Figs. R2b–c).\nTo rule out artificial band folding effects due to supercell construction, we compare the band\nstructures of antisite-free FM-MnBi Te calculated using the 2-SL 1×1 unit cell (Fig. R2e) and the\n2 4\n2-SL 2×2 supercell (Fig. R2f). The FM- MnBi Te is predicted to be an ideal type-II Weyl semimetal\n2 4\nwith a single pair of Weyl nodes along Γ–Z path29,30. Apart from minor deviations, both models\nconsistently reproduce the key low-energy features, including a pair of Weyl nodes along Γ–Z and\nthe in-plane band gap, confirming that the supercell expansion preserves the intrinsic electronic\nstructure. Moreover, since the supercell expansion is confined only in the ab-plane, the k dispersion\nz\nand Weyl point identification are almost unaffected. Thus, the identification of Weyl points results\nfrom an intrinsic electronic feature, rather than a supercell-induced artifact.\n4 / 24\nFigure R3 shows the 2-SL 2×2 supercells of defective FM-MnBi Te with increasing antisite\n2 4\ndensities, corresponding to the band structures in Fig. 1 of the main text. For Sb-doped cases, the\nband structures in Figure 8 of the main text were also obtained using 2-SL 2×2 supercells with\ndifferent Sb substitution concentrations, as shown in Fig. R4.\na b c\nb\nc a\nd\nb\nTe c L H\nb Γ\nBi\na b\ne f\n0.4\n0.2\nV)\ne\n(\nF\n0.0\nE\nE- Γ Z Γ Z\n-0.2\n-0.4\nΓZ HK Γ ML H Γ ΓZ HK Γ ML H Γ\ng h\n0.8\n0.4\nV)\ne\n(\nF\n0.0\nE\nE-\n-0.4\n-0.8\nΓZ HK Γ ML H Γ ΓZ HK Γ ML H Γ\nFigure R2. DFT calculated band structures of MnBi Te using different models.\n2 4\na Crystal structure of MnBi Te . The blue solid box marks the 1×1 unit cell consisting of two SLs,\n2 4\ndenoted as a 2-SL 1×1 unit cell. The model incorporates a total of 14 atoms.\nb, c Schematics side view (b) and top view (c) of the 2-SL 2×2 supercell model. The in-plane\ndimensions are doubly enlarged to introduce antisites or dopants, with a total of 56 atoms.\nd Illustration of Brillouin zone utilized in the calculations.\n5 / 24\ne, f Band structures of ferromagnetic MnBi Te with SOC calculated using the 2-SL 1×1 unit cell\n2 4\n(e) and 2-SL 2×2 supercell (f). The calculations were performed using the antisite-free lattice under\ninterlayer FM coupling. Insets highlight the Weyl points along the Γ–Z path.\ng, h Band structures of ferromagnetic MnBi Te without SOC, corresponding to the same models\n2 4\nin (e) and (f), respectively.\na b c\nMn Mn\nH Bi Bi\nBi Bi\nMn Mn\nMn\nTe\nBi\nMn\nBi\nBi\nc Mn\na b\nFigure R3. Schematics of defective MnBi Te for band calculations. The calculations were based\n2 4\non the FM-interlayer-coupled MnBi Te lattice using 2-SL 2×2 supercell models with fully relaxed\n2 4\nlattices (blue solid box). Varying antisite densities were considered, including the ideal lattice in (a),\n6.25% Mn and 12.5% Bi in (b), and 12.5% Mn and 25% Bi in (c). The orientations of Mn\nBi Mn Bi Mn Mn\nand Mn moments were denoted as the red and orange arrows, respectively, showing an AFM\nBi\nintralayer order.\na b c d\nx= 0 x= 0.25 x= 0.50 x= 0.75\nH\nMn\nTe\nc\nSb\nBi\na b\nFigure R4. Schematics of FM-Mn(Bi Sb ) Te for band calculations.\n1-x x 2 4\na, b, c, d Band structures were calculated using defect-free 2-SL 2×2 supercell models (blue solid\n6 / 24\nbox) with fully relaxed lattices. Panels (a) to (d) show structures with Sb contents of x = 0, 0.25,\n0.50, and 0.75, respectively. Mn magnetic moments are indicated by red arrows.\nRevision:\n1. We have provided more detailed descriptions of calculation models in the main text (Page 5),\nMethods (Page 14) and Supplementary Information (Page 5–8). We revised the misleading\nschematics of MnBi Te lattice in original Supplementary Fig. 16, which incorrectly suggest a 4×4\n2 4\nsupercell. We also included the calculation supercell models for the band structure in Figs. 1 and 8\nin the SI.\n2. We have re-calculated the band structures in Figs. 1e–g using the same 2-SL 2×2 supercell models\nwith improved numerical accuracy and rechoosing of reciprocal lattice vectors, which remain\nconsistent with the original ones.\n3. We have re-calculated the energy difference in Supplementary Fig. 16c with SOC using the 2-SL\n2×2 supercell model.\n4. We have revised a few sentences in the main text and Figs. 1b, c, d and h to include the Bi\nMn\ndefects, which were considered in the calculations.\nReviewer #1 Comment 4:\n“The main conclusion is that Sb doping suppresses antisite defects; however, the discussion\nlacks depth. There are four possible antisite defect types: MnBi, MnSb, BiMn, and SbMn. It is crucial\nto determine which types are predominant, how their populations fluctuate with Sb concentration,\nand which defect suppressions are associated with improved magnetic properties (e.g., Néel\ntemperature or saturation magnetization).”\nResponse:\nThank you for your constructive suggestions. Our study confirms that Sb doping in Mn(Bi\n1-\nSb ) Te significantly increases Mn–Bi/Sb antisite densities. These four possible antisite defects\nx x 2 4\nare grouped into two categories: Mn and Bi/Sb , based on their properties and impacts. In\nBi/Sb Mn\nMnBi Te , the predominance in quantity of Bi -type defects is commonly reported12,14,15,17,\n2 4 Mn\nconsistent with observed n-type conduction. Increasing Sb content augments both defect\nconcentrations, with Mn type exhibiting a more pronounced increase, thereby narrowing the\nBi/Sb\ninitial density difference.\nCritically, both antisite types disrupt the intrinsic magnetic order by strengthening intralayer\nAFM coupling and promoting interlayer AFM-to-FM transitions. This degradation affects both the\nAFM ground state and field-forced FM state. Consequently, all four antisites predominantly govern\nthe magnetic properties, making their suppression imperative for enhancing key magnetic\nparameters. Specifically, reducing antisite densities can elevate the Néel temperature (T ) and\nN\ncritical fields by restoring robust AFM interlayer coupling, while simultaneously improving\nsaturation magnetization (M ) through the elimination of detrimental AFM intralayer coupling.\nsat\nIn the following, we discuss the evolution of antisite densities with Sb concentration and their\ninfluence on magnetic properties based on DFT calculations:\n(1) Population trends of antisites with Sb content. Substituting Bi with Sb promotes the\nspontaneous formation of Mn antisites due to the closer electronegativity and ionic radii between\nSb\nMn2+ and Sb3+ compared to Mn2+ and Bi3+, as evidenced by the negative formation energies of Mn\nSb\n7 / 24\ndefects in MnSb Te 20,23. Consequently, higher Sb content increases Mn -type antistites,\n2 4 Bi/Sb\nconsistent with our observations (Table 1 in the main text). Despite relatively high formation energy\nfor isolated Sb defects in MnSb Te 20,23, paired Mn–Sb exchange defects have substantially lower\nMn 2 4\nformation energies than Mn–Bi exchanges in MnBi Te 20,31, indicating a corresponding increase in\n2 4\nBi/Sb -type defects. This trend reveals that both Mn and Bi/Sb antisites become more\nMn Bi/Sb Mn\nabundant at higher x, with Mn showing a larger increment. This population trend is consistent\nBi/Sb\nwith previous reports, with a higher antisite density (around 15% Mn and 30% Sb ) reported in\nSb Mn\nMnSb Te compared to about 5% Mn and 20% Bi in MnBi Te 12,14–16,24,25,31,32.\n2 4 Bi Mn 2 4\n(2) Antisite role on magnetic properties. As noted, the four antisite defect types (Mn , Mn ,\nBi Sb\nBi , and Sb ) can be categorized according to structural, charge, and magnetic properties as\nMn Mn\nfollows:\n Mn and Mn : Mn2+ ions replace Bi/Sb sites, introducing additional magnetic moments into\nBi Sb\noriginally non-magnetic layers, thereby complicating interactions among Mn moments at\ndifferent sites.\n Bi and Sb : Bi/Sb defects act as effective magnetic vacancies within the Mn layers by\nMn Mn Mn\nsubstituting non-magnetic Bi3+/Sb3+ ions, diluting magnetic ion concentration and inducing\nspatial moment inhomogeneity, which reduces overall magnetization.\nThe presence of Mn antisites leads to multiple magnetic layers within a single SL,\nBi/Sb\nnecessitating analysis of intralayer interactions between Mn and Mn moments. DFT\nMn Bi/Sb\ncalculations reveal that isolated Mn defects couple ferromagnetically to Mn moments in\nBi Mn\nMnBi Te , while introducing correlated Bi defects promotes AFM intralayer coupling, resulting\n2 4 Mn\nin a ferrimagnetic SL31. A similar trend is evident in MnSb Te , underscoring the role of Sb in\n2 4 Mn\nstabilizing AFM intralayer order12,31.\nTo further corroborate these findings, we calculated the energy difference ΔE between\nIntra\nintralayer FM and AFM configurations in interlayer FM-coupled MnBi Te , with varying antisite\n2 4\ndensities (Table R1). Results confirm the energetic preference for AFM intralayer order in both\ncases. In the more defective system, the larger ΔE indicates stronger AFM intralayer coupling.\nIntra\nThis trend aligns with the progressive reduction in M at moderate fields as x increases, and the\nsat\nrequirement for higher fields to achieve complete FM alignment (e.g., 50 T for MnBi Te and 60–\n2 4\n2 4\nMn(Bi Sb ) Te , these results underscore the coexistence of Mn and Bi/Sb and their joint\n1-x x 2 4 Bi/Sb Mn\ninfluence on intralayer coupling.\nAntisite types EIntra, FM (eV) EIntra, AFM (eV) ΔEIntra (meV)\nInterlayer\nFM-coupled 6.25% MnBi, 12.5% BiMn -258.28693 -258.30866 21.73\nMnBi2Te4\n12.5% MnBi, 25% BiMn -257.91407 -257.94750 33.43\nTable R1. Energy calculations for MnBi Te with different intralayer couplings and Mn–Bi\n2 4\nantisite concentrations. The calculations were performed under interlayer FM interaction using the\n2-SL 2×2 supercell without SOC.\nAdditionally, we performed band calculations for interlayer-FM-coupled MnBi Te with\n2 4\ndifferent intralayer orders (the same conditions in Table R1), corresponding to defective MnBi Te\n2 4\nat moderate fields (intralayer AFM) and high fields (intralayer FM). For the model with 6.25% Mn\nBi\n8 / 24\nand 12.5% Bi , the bandgap near the Γ point is suppressed from AFM- (Fig. R5a) to FM-intralayer\nMn\ncoupling (Fig. R5b). A Similar trend is observed at higher defect density (12.5% Mn and 25%\nBi\nBi ) in Figs. R5c–d. These results suggest that a fully developed FM state facilitates bandgap\nMn\nclosure, promoting band crossing and Weyl point formation. However, excessive antisites impede\nthe realization of complete FM states, hindering the pursuit of Weyl physics.\na b\n0.4\n0.2\nV)\ne\n(\nF\n0.0\nE\nE-\n-0.2\n-0.4\nΓZ HK Γ ML H Γ ΓZ HK Γ ML H Γ\nc d\n0.4\n0.2\nV)\ne\n(\nF\n0.0\nE\nE-\n-0.2\n-0.4\nΓZ HK Γ ML H Γ ΓZ HK Γ ML H Γ\nIntralayer Intralayer\nH > 50 T\nAFM FM\nFigure R5. Band structures of FM-interlayer-coupled MnBi Te .\n2 4\na, b Band structures of ferromagnetic MnBi Te with SOC calculated using the 2-SL 2×2 supercell\n2 4\nwith 6.25% Mn and 12.5% Bi defects. The calculations were performed considering the AFM\nBi Mn\n(a) or FM (b) intralayer orders.\nc, d Band structures of ferromagnetic MnBi Te with SOC calculated using the 2-SL 2×2 supercell\n2 4\nwith 12.5% Mn and 25% Bi defects. The calculations were performed considering the AFM (c)\nBi Mn\nor FM (d) intralayer orders.\nMaterials Antisite types EInter, FM (eV) EInter, AFM (eV) ΔEInter (meV)\nIdeal -258.69521 -258.71206 16.85\nBiMn 12.5% -254.39341 -254.40435 10.94\nMnBi2Te4\nBiMn 25% -250.11539 -250.12538 9.99\nBiMn 37.5% -245.89780 -245.88983 -7.97\n9 / 24\nBiMn 50% -241.70149 -241.69648 -5.01\nIntralayer MnBi 6.25% -261.77202 -261.72513 -46.89\nAFM-coupled\nMnBi2Te4 MnBi 12.5% -264.82210 -264.77208 -50.02\nTable R2. Energy calculations for MnBi Te with different interlayer couplings and densities\n2 4\nof isolated Mn or Bi antisites. The calculations were performed under intralayer AFM\nBi Mn\ninteraction (for Mn defects) using the 2-SL 2×2 supercell without SOC.\nBi\nIn addressing interlayer magnetic coupling, we calculated the energy difference ΔE between\nInter\ninterlayer FM and AFM states in MnBi Te . The models contain only one defect type at a time\n2 4\n(either Bi or Mn ) to isolate their individual effects. As shown in Table R2, the positive ΔE in\nMn Bi Inter\nideal MnBi Te confirms its AFM ground state. Introducing isolated Bi defects, which place non-\n2 4 Mn\nmagnetic atoms at Mn sites, strongly suppresses the interlayer AFM coupling, as reflected by the\ndecreasing ΔE . High Bi concentrations (37.5% and 50%) induce a transition from AFM to FM\nInter Mn\ninterlayer ordering (negative ΔE ). This magnetic dilution effect, which reduces the T and critical\nInter N\nfields, aligns with reports on Mn A Bi Te (A = Ge, Sn, Pb)33–37. Similarly, increasing Mn density\n1-y y 2 4 Bi\nalone under AFM intralayer coupling also suppresses interlayer AFM order and promotes FM\ncoupling (Table R2). While the single-defect-type models used may introduce deviations in lattice\nparameters and severe non-stoichiometry relative to actual crystals, where both defect types coexist,\nthe overall AFM-to-FM trend with increasing defect density remains valid.\nFurthermore, we computed the interlayer coupling energy under fixed intralayer AFM coupling\nwith coexisting Mn and Bi/Sb antisites to elucidate their concurrent effects. The models\nBi/Sb Mn\nincorporate paired Mn–Bi exchange antisites in MnBi Te , along with Mn–Bi and Mn–Sb antisites\n2 4\nin Mn(Bi Sb ) Te . Results in Table R3 show that increasing the density of both antisite types\n0.75 0.25 2 4\nmarkedly reduces ΔE in MnBi Te and Mn(Bi Sb ) Te , signaling a pronounced weakening\nInter 2 4 0.75 0.25 2 4\nof AFM order and a shift to FM interlayer coupling.\nThese results collectively reveal that Mn and Bi/Sb antisites progressively degrade the\nBi/Sb Mn\nintrinsic interlayer AFM coupling between SLs, serving as the primary origin of the reduced T and\nN\ncritical fields (H and H ).\nc1 c2\nMaterials Antisite types EInter, FM (eV) EInter, AFM (eV) ΔEInter (meV)\nIdeal -258.69521 -258.71206 16.85\nIntralayer\nAFM-coupled 6.25% MnBi, 12.5% BiMn -258.30866 -258.31530 6.64\nMnBi2Te4\n12.5% MnBi, 25% BiMn -257.94750 -257.95045 2.95\nIdeal -258.06706 -258.08499 17.93\nIntralayer\n6.25% MnBi, 12.5% BiMn -257.76152 -257.76960 8.08\nAFM-coupled\nMn(Bi0.75Sb0.25)2Te4\n12.5% MnBi, 25% BiMn -257.40185 -257.38519 -16.66\n6.25% MnSb, 12.5% SbMn -257.73726 -257.74512 7.86\n10 / 24\n12.5% MnSb, 25% SbMn -257.43927 -257.44282 3.55\nTable R3. Energy calculations for MnBi Te and Mn(Bi Sb ) Te with varied interlayer\n2 4 0.75 0.25 2 4\ncouplings and increasing Mn–Bi/Sb antisites. The calculations were performed under intralayer\nAFM interaction using a 2-SL 2×2 supercell without SOC. For Mn(Bi Sb ) Te (x = 0.25, near\n0.75 0.25 2 4\nthe upper doping limit in this work), both Mn–Bi and Mn–Sb antisites were considered.\nIn conclusion, Sb-doping progressively deteriorates intrinsic magnetic properties of Mn(Bi\n1-\nSb ) Te through elevated antisite densities, with both Mn and Bi/Sb types increasing with x\nx x 2 4 Bi/Sb Mn\n(Mn rising more rapidly). While magnetism primarily arises from Mn moments, both Mn\nBi/Sb Mn Bi/Sb\nand Bi/Sb critically influence the specific magnetic orders. Their coexistence introduces\nMn\nundesired intralayer antiparallel alignment, reducing M at moderate fields, deviating the band\nsat\nstructure from the ideal FM state, and requiring higher fields for full FM alignment.\nSimultaneously, these antisites weaken the intrinsic AFM interlayer coupling, lowering T and\nN\ncritical fields. Therefore, suppressing both antisite types is essential for optimizing magnetic\nproperties, including enhancing T and M .\nN sat\nRevision:\nIn response to your comments, we have revised the manuscript by adding descriptions of the\npopulation evolutions and magnetic effects of the Mn and Bi/Sb antisites in the main text\nBi/Sb Mn\n(Page 3–5, 7). Moreover, detailed discussions on the role of antisite defects in governing magnetic\norders, along with the energy calculation results, are added in Supplementary Information (Page 9–\n12).\nReviewer #1 Comment 5:\n“The use of Mn is confusing without an explanatory apparatus in the main text of the\nMn\nmanuscript, particularly in the context of its discussion with antisite defects, such as Mn and Mn .\nBi Sb\nPlease add the explanation shown in Table 1 to the first instance of Mn .”\nMn\nResponse and Revision:\nThank you for the nice input. In this manuscript, the notation of Mn is used to denote Mn\nMn\natoms occupying their original Wyckoff positions (3a) in the Mn(Bi Sb ) Te crystal structure,\n1-x x 2 4\nwhich corresponds to defect-free Mn atoms within the primary Mn layer of a SL. We have now\nadded explanatory text in the revised manuscript (Page 4).\nReviewer #1 Comment 6:\n“The order of the figures in the manuscript is confusing. For example, Fig. 3a and Fig. S6a\nare depicted in the second paragraph on page 6, followed by Fig. 3c and Fig. S5 in the third\nparagraph. Please adjust the text or figures to ensure they are depicted in the correct order.”\nResponse and Revision:\nWe have adjusted the orders of figures and descriptions in the Supplementary Information to\navoid the confusing figure numbers in the main text.\n11 / 24\nOverall, we would like to take this opportunity to thank the reviewer for the insightful\ncomments and valuable suggestions. We hope that our revisions based on your comments are\nsatisfactory. Thank you very much for your consideration.\nReviewer #2 Comments:\n“This study convincingly demonstrates the pivotal role of antisite defects in governing the\nmagnetic and topological properties of ferromagnetic Mn(Bi₁₋ₓSbₓ)₂Te₄ (MBST), through a\nsynergistic approach combining first-principles calculations and comprehensive experimental\ninvestigations. To mitigate the detrimental effects of antisite defects, the authors developed an\noptimized chemical vapor transport (OCVT) method, enabling the growth of stoichiometric MBST\ncrystals with significantly reduced defect densities. The OCVT-grown samples exhibit a well-defined\ncharge neutrality point (CNP) near x = 0.20, as confirmed by both angle-resolved photoemission\nspectroscopy (ARPES) and Hall effect measurements. These crystals also show a record-high\ncarrier mobility of 2519 cm²/V·s, surpassing all previously reported values for this material system.\nFurthermore, the observation of Shubnikov–de Haas (SdH) oscillations and pronounced anomalous\nHall conductivity in the field-aligned ferromagnetic state—both strongly dependent on carrier type\nand density—provides compelling evidence for the realization of a type-II Weyl semimetal phase in\nMBST.\nOverall, the study offers a well-integrated theoretical and experimental framework for\ncontrolling material quality and accessing intrinsic topological phases. It not only deepens our\nunderstanding of the role of antisite defects but also establishes a new materials platform for\nexploring magnetically induced topological quantum phenomena.\nI recommend its publication in Nature Communications, provided that the following comment\nis adequately addressed.”\nResponse:\nThank you for your positive comments and recommendation. We hope that the new\nexperimental results can address your concerns and solidate our conclusions.\nReviewer #2 Comment 1:\n“The authors should provide real-space structural characterization of the MBST crystals, such\nas transmission electron microscopy (TEM) images, to directly confirm the reduction in defect\ndensity.”\nResponse:\nThank you very much for your nice comments and critical suggestions. In response, we have\nperformed real-space structural characterization of OCVT-grown Mn(Bi Sb ) Te using scanning\n1-x x 2 4\ntransmission electron microscopy (STEM) and scanning tunneling microscopy (STM), to directly\nevidence the antisite suppression.\nThe in-plane crystallographic orientation was detected by Laue X-ray diffraction. Figure R6\nshows the Laue pattern from the (001) surface of OCVT-grown MnBi Te , where the diffraction\n2 4\nspots correspond to the high-symmetry directions. Blue and red arrows mark the normal directions\nof (100) and (110) planes, respectively. Cross-sectional specimens for STEM investigations were\nprepared by focused ion beam (FIB) milling with all the normals aligned parallel to the [110] axis.\n12 / 24\n(110)\n(100)\nFigure R6. Laue diffraction pattern from the (001) plane of OCVT-grown MnBi Te .The\n2 4\ndiffraction spots correspond to the high-symmetry directions of the crystal. Blue and red arrows\nmark the normal directions of the (100) and (110) planes, respectively.\nThe STEM imaging was performed on a double aberration corrected field emission\ntransmission electron microscope (Themis Z, Thermo Fisher Scientific) operated at 300 kV. The\nprobe forming semi-convergent angle is 21.4 mrad, and the semi-collection angle of High-angle\nannular dark field (HAADF) detector is 79–200 mrad. HAADF-STEM images of OCVT-MnBi Te\n2 4\n(Figs. R7a–c, at varying magnifications) reveal well-ordered septuple layer (SL) structures\nseparated by vdW gaps. A line intensity profile taken across the SL sequence Te–Bi–Te–Mn–Te–\nBi–Te (green box in Fig. R7c) in Fig. R7d shows clear intensity oscillation. According to the Z-\ncontrast of HAADF-STEM imaging mechanism, atomic sites with higher atomic number Z exhibit\nbrighter image contrast. The observed intensities follow the expected order: Mn < Te < Bi. However,\nthe presence of Mn and Bi antisites would modify this contrast by increasing intensity at Mn\nBi Mn\ncolumns (due to Bi replacement) and decreasing it at Bi columns (due to Mn replacement).\nMn Bi\n13 / 24\na b\n20 nm 5 nm\nc d\nTe Bi Te Mn Te Bi Te\nu.)\na.\ny\n(\nsit\nn\ne\nnt\nI\n1 nm\n0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6\nLocation (nm)\nFigure R7. STEM characterizations of OCVT-grown MnBi Te .\n2 4\na HAADF-STEM image of the cross-sectional OCVT-grown MnBi Te crystal, observed along the\n2 4\n[110] zone axis with large field of view.\nb Atomic-resolution HAADF-STEM image exhibiting well-ordered SLs separated by vdW gaps.\nc Magnified HAADF-STEM image of the region highlighted by the white box in panel (b). The\nbrightness variations among atomic columns reflect different elements and defect densities. The\ninset shows the corresponding crystal model of MnBi Te , consistent with the observed structure in\n2 4\nHAADF-STEM images.\nd Line intensity profile along the green box in panel (c), showing the intensity distribution across\natomic columns averaged within a single septuple-layer.\nFor comparison, HAADF-STEM images of flux-grown MnBi Te are also presented. Figure\n2 4\nR8b displays a magnified SL structure, with each atom site reflects an integrated scattering intensity\nalong the intensity along the atomic column. A representative line profile across Bi, Te, and Mn\natomic layers in the SL (marked by arrows in Fig. R8b) is shown in Fig. R8c. Here, certain Mn\ncolumns display higher brightness than the surrounding Te or even Bi atoms, suggesting Bi\nMn\nantisites. Conversely, the intensities of some Bi columns are suppressed, indicating Mn defects.\nBi\nCompared to the pronounced intensity fluctuations in Bi and Mn atomic layers, Te atomic layers\n14 / 24\nexhibit minimal variation in the line intensity profile, confirming that Te-related defects are\nnegligible. Since the observed intensity fluctuations in atomic resolution HAADF-STEM images\nare not entirely attributed to antisite defects; variations in the electrons dynamical scattering along\nthe atomic columns can also cause small intensity differences at single atomic site, we then introduce\nthe normalized intensity ratio (I -I )/(I -I ) in each SL, for OCVT-grown (Fig. R7b) and flux-\nMn dark Te dark\ngrown MnBi Te (Fig. R8a) to qualitatively compare antisite densities. For each SL, (I -I ) was\n2 4 Mn dark\nobtained by subtracting the dark intensity from peak intensity of individual Mn column, and then\nthe value was averaged across ~47 atomic columns within the Mn layer, while the background-\nsubtracted Te intensity (I -I ) was averaged across four Te atomic layers as a reference due to\nTe dark\nnegligible defects in Te layers. We similarly calculated (I -I )/(I -I ) by averaging across two\nBi dark Te dark\nBi atomic layers (~94 Bi columns) in each SL. As summarized in Fig. R8d, the OCVT-grown sample\ngenerally shows lower (I -I )/(I -I ) and higher (I -I )/(I -I ) values than flux-grown one,\nMn dark Te dark Bi dark Te dark\nwhich may correspond to fewer Bi and Mn antisites in OCVT-grown MnBi Te , respectively.\nMn Bi 2 4\nHowever, we note that quantitative analysis of the HAADF-STEM intensity requires careful\ncalibration of electron optical parameters and imaging conditions.\na d\nSL1\nS\nS\nL\nL\n3\n2\n-I )\nI\n-I )\n/(\nM\nd\nT\nd\na\na\ne\nn\nr\nr\nk\nk\n1\n1\n1\n.\n.\n.\n1\n2\n3\n(I OCVT-MnBi2Te4\n1.0 Flux-MnBi2Te4\n-I )\nI\n-I )\n/(\nB\nd\nT\nd\na\na\ne\ni\nr\nr\nk\nk\n1\n1\n.\n.\n4\n5\n(I OCVT-MnBi2Te4\nFlux-MnBi2Te4\nSL12 5 nm 0 2 4 6 8 10 12\nSL Number\nb\n2 nm\nc\nMn Te Bi\nu.)\na.\ny\n(\nsit\nn\ne\nnt\nI\n0 3 6 9 12 15 18\nLocation (nm)\nFigure R8. STEM characterizations of flux-grown MnBi Te .\n2 4\na Atomic-resolution HAADF-STEM image of the cross-sectional flux-grown MnBi Te crystal.\n2 4\nb Magnified atomic-resolution HAADF-STEM image of a representative SL structure from the\nregion highlighted by the orange dashed box in panel (a).\nc Line intensity profiles taken across the Bi, Te, and Mn atomic layers in the SL, as marked by\n15 / 24\ncorresponding colored arrows in panel (b). The Bi and Mn profiles exhibit pronounced intensity\nfluctuations, indicating Mn and Bi antisites, whereas the Te profile shows minimal variation.\nBi Mn\nThe intensity profiles were offset for clarity.\nd Intensity ratio (I -I )/(I -I ) in upper and (I -I )/(I -I ) in lower panels across multiple\nMn dark Te dark Bi dark Te dark\nSLs extracted from STEM images of OCVT-grown and flux-grown MnBi Te . The SL numbers are\n2 4\nlabeled as 1 to 12 from top to bottom, shown in the left side of panel (a).\nFurthermore, we present the HAADF-STEM images of an OCVT-grown Mn(Bi Sb ) Te\n0.8 0.2 2 4\ncrystal (Figs. R9a–b), where the x~0.20 is the CNP doping level. Figure R9c shows the intensity\nprofile across the SL structure along the SL structure as highlighted by green box in Fig. R9b. The\nnormalized intensity ratios (I -I )/(I -I ) and (I -I )/(I -I ) are plotted in Figs. R9d and\nMn dark Te dark Bi/Sb dark Te dark\nR9e. However, Sb doping (Z = 51) in the Bi atomic layers reduces the intensities of the Bi columns.\nIt also slightly diminishes the intensity enhancement typically observed at Mn sites due to\nBi/Sb antisite defects. Consequently, both (I -I )/(I -I ) and (I -I )/(I -I ) ratios\nMn Mn dark Te dark Bi/Sb dark Te dark\ndecrease due to Sb-doping, complicating direct comparisons on the antisite densities with MnBi Te\n2 4\nand rendering them inconclusive. To circumvent this issue, we calculated the ratio (I -I )/(I -\nBi/Sb dark Mn\nI ) in Fig. R9f. A higher value of (I -I )/(I -I ) may result from fewer Mn and Bi/Sb\ndark Bi/Sb dark Mn dark Bi/Sb Mn\nantisites, where the total density of two antisite types are considered. Assuming the antisite density\nremains unchanged at a low or moderate level, partial substitution of Bi with Sb would lower the\n(I -I )/(I -I ) ratio compared to that of MnBi Te . Therefore, the higher ratio values in\nBi/Sb dark Mn dark 2 4\nOCVT-grown Mn(Bi Sb ) Te crystal indicates a lower antisite density than in the flux-grown\n0.8 0.2 2 4\nMnBi Te (Fig. R9d), even though Sb-rich samples generally exhibit higher antisite densities. These\n2 4\nresults consistently demonstrate the high crystal quality and minimal antisite density in OCVT-\ngrown samples.\nHowever, it should also be noted that the comparative approach illustrated in Figs. R8 and R9\nprovides only a rough, qualitative assessment. HAADF-STEM images represent complex two-\ndimensional projections of atomic arrangements within three-dimensional space, and the formation\nof HAADF-STEM image contrast is accompanied by the multiple dynamical scattering of electrons\nwithin crystals. Consequently, the site-mixing of Mn and Bi atoms cannot be quantitatively\ndetermined solely based on image intensity variations. Rigorous quantification of STEM image\nintensity among different samples is inherently complex, requiring consideration of numerous\nfactors including localized specimen thickness, specific electron optical parameters (such as probe\nconvergent angle and detector collection angle and lens aberrations), the influence of surface\namorphous layers, often introduced during FIB sample milling, modelling atomic vibrations, the\ndetector response quantification and dark current subtraction38,39.\n16 / 24\na b c\nTeBi/Sb Te Mn Te Bi/SbTe\nIntensity\n(a.u.)\n5 nm 1 nm\n0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6\nLocation (nm)\nd e f\n(I -I ) I -I ) /( M d T d a a e n r r k k\n0\n1 1 1 1\n.\n. . . .\n9\n0 1 2 3\n2\n- T M - n M B n i ( 2 B T i e 0 4 .8S\n4\nb0.2)2Te4\n6 8 10 12\n(I -I ) I -I ) /( B d T d a a e i/ r r S k k b\n1\n1 1\n.\n.\n2\n3 4\n2\n- T M - n M B n i ( 2 B T i e 0 4 .8S\n4\nb0.2)2Te4\n6 8 10 12\n(I -I ) I -I ) /( B d M d a a i n / r r S k k b\n1\n1 1 1 1\n.\n. . . .\n0\n1 2 3 4\n0 2 4\nO Fl C u\n6\nx V - T M - n M B n i ( 2 B T i e 0 4 .\n8\n8Sb0.2)2Te4\n10 12\nSL number SL Number SL Number\nFigure R9. STEM characterizations of OCVT-grown Mn(Bi Sb ) Te .\n0.8 0.2 2 4\na Atomic-resolution HAADF-STEM image of the cross-sectional OCVT-grown Mn(Bi Sb ) Te .\n0.8 0.2 2 4\nb Magnified atomic-resolution STEM image of the region highlighted by the white box in panel (a).\nc Line intensity profile along the green box in panel (b), showing the intensity distribution across\natomic columns within a single septuple-layer.\nd, e, f Intensity ratios (I -I )/(I -I ), (I -I )/(I -I ) and (I -I )/(I -I ) in panels\nMn dark Te dark Bi/Sb dark Te dark Bi/Sb dark Mn dark\n(d), (e), and (f), respectively.\nWe also attempted to collect atomic-resolution STEM-EDX mapping on the SL structure of\nOCVT-grown MnBi Te (Fig. R10) using a super-X four segment EDX detector. The blue and red\n2 4\ndashed lines represent the expected atomic layers of Bi and Mn, respectively. The atomic-resolution\nEDX mapping show weak Mn signals within the Bi atomic layers (Fig. R10b), and Bi signals within\nthe Mn atomic layers (Fig. R10c), while Te signals almost remain at their expected sites. The\ndetection of intermixed Bi and Mn signals indicates the presence of Bi and Mn antisite defects.\nMn Bi\nHowever, it is very challenging to count defect density from atomic resolution EDX\nquantification. To achieve sufficient signal-to-noise ratio, high beam current and long exposure were\napplied for the EDX mapping. Significant electron beam damage was observed during EDX\nacquisition, in the mapped region of Fig. R10a, prolonged integration times necessary for clear\nmapping resulted in pronounced structural damage to the lattice, causing a penetration of the thin\nSTEM cross-sectional specimen and creating a hole. Consequently, beam-induced atomic migration\nand diffusion likely occurred within this region, potentially generating artificial element intermixing\nsignals. The structural damage under beam-irradiation effect was also observed in another two\nspecimens, precluding the acquisition of precise atomic-scale EDX data. Furthermore, quantifying\nelemental concentration at the atomic scale remains challenging due to numerous factors. These\ninclude the double channeling effect - the dynamical scattering of electrons both before and after\nthe X-ray emission, as well as uncertainties in the X-ray yield ratio, absorption of X-rays by the\nsample and holder, and the specific geometry of the X-ray detector40,41. Therefore, quantification of\n17 / 24\nantisite defect densities across different specimens is not reliable from current atomic resolution\nEDX analysis.\na b c d\ne\n5 nm\nFigure R10. STEM-EDX mapping of SL structures in OCVT-grown MnBi Te .\n2 4\na Atomic-resolution HAADF-STEM image of SL structure in OCVT-grown MnBi Te before\n2 4\nSTEM-EDX measurements.\nb, c, d Corresponding atomic-resolution STEM-EDX mappings for individual elements of Mn, Bi,\nand Te, shown in panels (a), (b), and (c), respectively. The atomic layers of Mn, Bi, and Te are\ndenoted by the red, blue, and brown arrows.\ne HAADF-STEM image of the lattice in panel (a) after STEM-EDX measurements, exhibiting a\npronounced structural damage.\nFigure R11 presents STEM electron energy-loss spectroscopy (EELS) line scans acquired\nacross the SL structure. Similar beam-induced damage (Figs. R11d–e) critically compromised these\nmeasurements, significantly hindering antisite defect identification by obscuring elemental\ncomposition signals.\n18 / 24\na b c\nHAADF Te Mn\n0.5 nm 0.5 nm 0.5 nm\nd e\n2 n m 2 n m\nFigure R11. STEM-EELS mapping of SL structures in OCVT-grown MnBi Te .\n2 4\na, b, c Cross-sectional HAADF-STEM image of OCVT-grown MnBi Te and the corresponding\n2 4\nEELS mapping of the Te and Mn-L edge.\nd, e HAADF-STEM image of the OCVT-grown MnBi Te lattice before and after the EELS\n2 4\nmeasurements, shown in panels (d) and (e), respectively, exhibiting a pronounced structural damage.\nIn summary, HAADF-STEM characterization was performed on OCVT-grown Mn(Bi\n1-\nSb ) Te (x = 0, 0.21), and a flux-grown MnBi Te for comparison. Qualitative analysis of the image\nx x 2 4 2 4\nintensity generally supports the conclusion of suppression of antisite defects in OCVT-grown\ncrystals. However, rigorous quantification of image intensity remains problematic for determining\nantisite densities. Critically, prolonged high-energy electron beam irradiation induced severe\nstructural damage, preventing reliable spatial analysis of elemental composition via atomic-\nresolution EDX and EELS.\nTo further visualize the defect distribution in Mn(Bi Sb ) Te crystal, STM measurements\n1-x x 2 4\nwere performed on an OCVT-grown Mn(Bi Sb ) Te sample. The crystal was cleaved at room\n0.8 0.2 2 4\ntemperature under a pressure of 1.9×10−10 mbar and immediately transferred into the STM. Atomic\nsurface morphology was conducted using a low-temperature STM operating at 77 K. Figure R12\nshows representative atomic-resolution topographies of the Mn(Bi Sb ) Te (001) surface,\n0.8 0.2 2 4\nexhibiting a hexagonal lattice structure of the topmost Te layer with an in-plane parameter a = b ~\n4.3 Å, in agreement with previous reports9,15,42. Large-scale STM image is difficult to achieve due\nto the fast contamination of the cleaved surface. Topographic STM images exhibited characteristic\nscattering patterns associated with defects, indicated by blue dashed triangles. These dark triangular\n19 / 24\nregions of reduced topographic height represent the scattering signatures of dominant Mn\nBi/Sb\nantisite defects. These defects arise from Mn atoms substituting Bi/Sb sites in the second atomic\nlayer, causing the three covalently bonded Te atoms directly above the substitution site to appear\nlower in height9.\na b\nc\nMn\nBi/Sb\nFigure R12. STM characterizations of OCVT-grown Mn(Bi Sb ) Te .\n0.8 0.2 2 4\na, b Atomically resolved topographic images (bias voltage = −0.75 V, tunneling current = 230 pA)\nfrom different regions. Blue dashed triangles mark characteristic small triangular depressions,\nindicative of Mn antisite defects.\nBi/Sb\nc Enlarged view of a triangular depression corresponding to a Mn antisite defect (left), alongside\nBi/Sb\nits structural model (right). Purple, blue, and brown spheres represent Mn, Bi, and Te atoms,\nrespectively. The grey region in the model denotes the defect position.\nSuch defects are commonly observed on cleaved bulk MnBi Te by STM, with typical Mn\n2 4 Bi\nantisite densities ranging from 3.0% to 8.7%15,18,42–44. As the Mn -type antisite concentration\nBi/Sb\nincreases with Sb content x, a previous STM study on Mn(Bi Sb ) Te reported an estimated\n0.68 0.32 2 4\nMn % of 9.1%9.\nBi/Sb\nSurveying of individual defects in the topography, normalized to the number of atoms in the\nrespective atomic layers, yields Mn densities of approximately 4.6% and 6.5% in Figs. R12a\nBi/Sb\nand R12b, respectively. Analysis of multiple areas indicates an average Mn antisite density of\nBi/Sb\n~5.2%. These values are consistent with the calculated values of 4.95% and 5.32% (for x = 0.20 and\n0.21, respectively) presented in Table 1 of the main text, which are based on the saturation\nmagnetization and EDX data, further confirming the effective suppression of antisites through\nOCVT method.\nRevision:\nIn response to your comments, we have provided STEM and STM results on OCVT-grown\nMn(Bi Sb ) Te in the Supplementary Information (Page 18–21), and added descriptions in the\n1-x x 2 4\nmain text (Page 6) and Methods (Page 13), to directly evidence the antisite suppression.\nFinally, we would like to thank all the reviewers once again for their helpful comments.\n20 / 24\nWe hope that the incorporation of new calculations and experimental data on the mechanism\nand characterization of antisites, along with additional band structure calculations, will\naddress all your concerns satisfactorily. Indeed, we have significantly benefited from all your\nsuggestions and comments. Thank you very much for your consideration.\nAdditional Changes to the manuscript:\n1. We have updated the author list by adding two authors (Wenhao He and Prof. Changlin Zheng\nfrom Fudan University) for their contributions in the STEM measurements in response to Reviewer\n#2’s suggestion.\n2. We have added several brief descriptions of the Supplementary Information contents in the main\ntext.\n3. We have added the terms “Bi/Sb ” or “Bi ” at several locations in the main text to emphasize\nMn Mn\ntheir concurrent influence on the magnetic properties together with Mn antisites.\nBi/Sb\n4. Figure 3a in the main text has been revised. The Sb content (x) labels for the χ(T) curves\nwere incorrectly ordered. This has been corrected by reversing the order of the x labels (decreasing\nfrom top to bottom now) while keeping the curves unchanged.\n5. We have provided a comparison among several techniques for characterizing antisite defects in\nthe Supplementary Information (Page 3).\n6. The reference list of Supplementary Information has been updated.\n21 / 24\nReferences\n1. Yan, J.-Q. et al. Evolution of structural, magnetic, and transport properties in MnBi Sb Te .\n2-x x 4\nPhys. Rev. B 100, 104409 (2019).\n2. Chen, B. et al. Intrinsic magnetic topological insulator phases in the Sb doped MnBi Te bulks\n2 4\nand thin flakes. Nat Commun 10, 4469 (2019).\n3. Lee, S. H. et al. Evidence for a Magnetic-Field-Induced Ideal Type-II Weyl State in\nAntiferromagnetic Topological Insulator Mn(Bi Sb ) Te . Phys. Rev. X 11, 031032 (2021).\n1-x x 2 4\n4. Lee, S. H. et al. Evidence of magnetic fluctuation induced Weyl semimetal state in the\nantiferromagnetic topological insulator Mn(Bi Sb ) Te . Phys. Rev. B 107, 205105 (2023).\n1−x x 2 4\n5. Robinson, R. A. et al. Possible evidence of Weyl fermion enhanced thermal conductivity under\nmagnetic fields in the antiferromagnetic topological insulator Mn(Bi Sb ) Te . Phys. Rev. B 107,\n1-x x 2 4\n235140 (2023).\n6. Wang, H. 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Controllable and Continuous Quantum Phase Transitions in Intrinsic Magnetic\nTopological Insulator. Preprint at https://doi.org/10.48550/arXiv.2503.06044 (2025).\n38. LeBeau, J. M., Findlay, S. D., Allen, L. J. & Stemmer, S. Quantitative Atomic Resolution\nScanning Transmission Electron Microscopy. Phys. Rev. Lett. 100, 206101 (2008).\n39. Dwyer, C. et al. Sub-0.1 nm-resolution quantitative scanning transmission electron microscopy\nwithout adjustable parameters. Applied Physics Letters 100, 191915 (2012).\n40. Lugg, N. R., Kothleitner, G., Shibata, N. & Ikuhara, Y. On the quantitativeness of EDS STEM.\nUltramicroscopy 151, 150–159 (2015).\n41. Chen, Z. et al. Energy dispersive X-ray analysis on an absolute scale in scanning transmission\nelectron microscopy. Ultramicroscopy 157, 21–26 (2015).\n42. Yan, J.-Q. et al. Crystal growth and magnetic structure of MnBi Te . Phys. Rev. Mater. 3,\n2 4\n064202 (2019).\n23 / 24\n43. Yuan, Y. et al. Electronic States and Magnetic Response of MnBi Te by Scanning Tunneling\n2 4\nMicroscopy and Spectroscopy. Nano Lett. 20, 3271–3277 (2020).\n44. Lüpke, F. et al. Defect-induced displacement of topological surface state in quantum magnet\nMnBi Te . Preprint at https://doi.org/10.48550/arXiv.2507.05161 (2025).\n2 4\n24 / 24"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed all my concerns and comments. I believe the manuscript is now suitable for publication.", "reviewer_2": "The authors revised the paper based on the comments by the referees. The revised manuscript is much understandable and persuasive. I recommend the publication."}, "author_response": "Response to Reviewers’ Comments\nDear Reviewers,\nWe would like to sincerely thank you for taking the time and effort to review our resubmitted\nmanuscript “Defect Engineering for Stabilizing Magnetic and Topological Properties in\nMn(Bi Sb ) Te ”. Your insightful suggestions have been instrumental in substantially enhancing\n1-x x 2 4\nthe quality of this work. In the following, we will address the comments on a point-by-point basis:\nReviewer #1 Comments:\n“The authors have addressed all my concerns and comments. I believe the manuscript is now\nsuitable for publication.”\nResponse:\nWe deeply appreciate the reviewer’s acknowledgment of our revisions. The constructive\nfeedback we received has helped to strengthen the manuscript’s scientific rigor and readability.\nReviewer #2 Comments:\n“The authors revised the paper based on the comments by the referees. The revised manuscript\nis much understandable and persuasive. I recommend the publication.”\nResponse:\nWe are grateful for the reviewer’s substantive suggestions and positive recommendations,\nwhich have improved the completeness and persuasiveness of our manuscript.\n1 / 1"}]

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