Intrinsic topological Weyl phase transition induced by a magnetostructural transformation in a kagome magnet

Domain: neuroscience
Published: 2026-04-11
Editorial outcome: minor_revision

Abstract
Topological phase transitions provide a unique window into the interplay between structure, magnetism, and Weyl physics in magnetic Weyl semimetals. However, realizing an intrinsic Weyl phase transition between two distinct Weyl states near room temperature remains challenging. Here, we demonstrate that a magnetostructural transition effectively induces such a transition in the kagome magnet Mn3Ga. High-resolution neutron diffraction, magnetization characterizations and first-principles calculations reveal that Mn3Ga undergoes a chiral antiferromagnetic transition below 485 K, followed by a magnetostructural transition to a monoclinic structure with highly canted antiferromagnetic order near room temperature. These cooperative changes in lattice and magnetic symmetries reorganize Weyl nodes, driving a transition from a primary type-II Weyl state to a distinct Weyl state, accompanied by dramatic variations in the anomalous Hall effect and appearance of topological Hall effect. Our findings open a new pathway for discovering novel topological Weyl states and potential spintronic applications.

Introduction
The discovery of topological quantum materials has led to transformative insights into condensed matter physics, with Weyl semimetals emerging as a particularly intriguing class due to their gapless excitations associated with Weyl nodes, band crossings which act as monopoles of Berry curvature in momentum space [1, 2, 3, 4, 5, 6]. While early realizations focused on nonmagnetic systems with broken inversion symmetry, magnetic Weyl semimetals have recently garnered significant interest, as the time-reversal symmetry breaking by magnetic order offers additional control over the topological band structure [7, 8, 9, 10]. Exploring topological phase transitions provides an excellent opportunity to investigate the intricate coupling among structure, magnetism, and Weyl physics. To date, only a limited number of compounds have been identified to undergo topological phase transitions from one non-Weyl topological state to a Weyl state, primarily driven by external stimuli such as magnetic fields or pressure [11, 12, 13]. For example, an applied magnetic field induces the transformation from an antiferromagnetic (AFM) topological insulator to an ideal type-II Weyl state in Mn(Bi1−xSbx)2Te4 [11]. A pressure-induced transition from a magnetic topological insulator to a trivial insulator, and then to a Weyl semimetal was reported in EuCd2As2 [13]. From the perspective of both fundamental and applied research, it is particularly intriguing yet challenging to explore strategies for inducing intrinsic topological phase transitions between two distinct Weyl states without external stimuli, especially under conditions near room temperature.

The kagome magnets Mn3Sn and Mn3Ge, which share the same hexagonal structure as Mn3Ga shown in Fig. 1a, have attracted significant attention [7, 14, 15, 16, 17, 18, 19, 20] due to their recent identification as magnetic Weyl semimetals exhibiting chiral magnetic order and remarkable quantum transport properties. In Mn3Sn, the interplay between the noncollinear antiferromagnetic order and strong spin-orbit coupling gives rise to significant anomalous and topological Hall effects (AHE and THE) [7, 14]. Futhermore, a magnetic inverse spin Hall effect [19] and large anomalous Nernst effect [16] have been discovered in Mn3Sn. While in Mn3Ge, a similar chiral spin structure combined with Weyl points lying closer to the Fermi level produces an even larger AHE despite its moderate spin–orbit coupling [15]. Compared to the more extensively studied Mn3Sn and Mn3Ge, which show topological behavior within a high-symmetry hexagonal structure, Mn3Ga is distinguished by a temperature-dependent magnetostructural transition (MST) [21, 22, 23, 24], i.e., a coupled crystal and magnetic transition, as shown in Fig. 1b, c. Mn3Ga is isostructural with Mn3Sn and Mn3Ge at high temperatures and has been reported to exhibit a 120◦ chiral antiferromagnetic order below TN1 ≈ 470 K [21]. Upon cooling to the lower MST temperature TN2 ≈ 120 K [24] or 170 K [22, 23], Mn3Ga undergoes a structural transition, reported as either orthorhombic [22, 24] or monoclinic [23], accompanied by a magnetic reconfiguration that gives rise to a substantial net ferromagnetic moment [24, 25, 22, 23]. Previous studies have revealed AHE and THE signatures [25, 24] on polycrystalline Mn3Ga, associated with the distinct crystalline and magnetic states in the temperature range TN2 < T < TN1 and T < TN2, respectively, suggesting a strong correlation between structural changes and topological properties. However, determining the true ground-state structure and spin configuration remains challenging due to the subtlety of simultaneous crystalline and magnetic symmetry lowering. These difficulties have hindered the identification of precise topological states below and above MST in Mn3Ga.

In this work, we report that Mn3Ga exhibits an intrinsic topological Weyl phase transition between two distinct Weyl states, driven by a magnetostructural transition. Using a combination of high-resolution neutron diffraction, magnetization measurements, with first-principles density functional theory (DFT) calculations, we have determined and validated the distinct crystal and magnetic structures in TN2 < T < TN1 and T < TN2 in Mn3Ga. The MST temperature in our Mn3Ga (x = 2.94(1)) (hereafter referred to as Mn3Ga for simplicity), was enhanced to near room temperature (TN2 ≈ 295 K). Furthermore, we find that two distinct crystalline and magnetic ordered phases can each host Weyl nodes. More importantly, the MST fundamentally alters both the multiplicity and distribution of Weyl nodes, thereby driving a topological Weyl phase transition to a distinct Weyl state accompanied by a modification of the anomalous Hall conductivity (AHC) with the emergence of non-zero σyz component near room temperature. Transport measurements reveal a sign reversal of the anomalous Hall conductivity alongside a significant enhancement in its magnitude below the MST, providing experimental proof on the redistribution of the Berry curvature and a corresponding reconstruction of the Weyl-node manifold. The emerged THE, coexisting with AHE below a lower temperature ≈ 150 K, highlights a wonderful unification of the real-space Berry phase arising from spin chirality and k-space Berry curvature inherent to the band topology. Our results thus demonstrate that the MST provides a compelling pathway for inducing a topological Weyl phase transition in correlated magnetic materials.

Results
2.1 Chiral Antiferromagnetic Ordering at TN1
We begin by investigating the magnetic structure of Mn3Ga using temperature-dependent neutron diffraction and magnetic characterization measurements (Fig. 2). As shown in Fig. 2a, the color map presents the overview of phase transitions. At TN1 = 485 K, the crystal structure retains hexagonal symmetry, but shows a reduced structural symmetry below TN2 = 295 K, as indicated by the splitting of Bragg peaks. Lattice parameters were extracted from a series of Rietveld refinements against the diffraction data, and Fig. 2b shows that the lattice parameter (aH = bH) exhibits a pronounced anomaly at TN1, despite the absence of any symmetry-breaking structural transition. The observed TN1 is slightly higher than those [21, 22] (<470 K) in previous reports. Magnetic susceptibility measurement on a polycrystalline sample (Fig. 2c) shows a distinct anomaly at 485 K, indicating a magnetic transition. Consistently, the intensity of the hexagonal 101 Bragg peak increases gradually upon cooling below TN1, indicating the feature of a second-order magnetic phase transition, as shown in Fig. 2c. These results collectively indicate strong spin-lattice coupling at TN1, even in the absence of a crystallographic symmetry change.

Rietveld refinements against powder neutron diffraction patterns measured above and below TN1 are presented in Fig. 2d, e. For temperatures above TN1, the refinements indicate the presence of approximately 5.5 wt% MnO impurity, which was held constant in all subsequent refinements. The nominal Mn3Ga phase adopts a hexagonal crystal structure with space group P63/mmc (No. 194), and the refined chemical composition yields Mn3Ga (x = 2.94(1)), indicating a 2.3(3)% of manganese deficiency relative to ideal stoichiometry. Upon cooling into the intermediate temperature range, TN2 < T < TN1, the symmetry analysis and refinements confirm the Cm′cm′ (BNS 63.464) magnetic structure with magnetic propagation vector k = 0. The refined magnetic structure shows noncollinear spins confined to the kagome planes, resulting in a nearly zero net magnetic moment per unit cell (not symmetry-constrained). In each triangular unit, the three Mn moments are oriented ⊥ aH, ⊥ bH, and ∥ (bH − aH), forming a 120◦ chiral antiferromagnetic order as shown in the insert of Fig. 2e and Fig. 1b. The ordered moment per Mn site is refined to be 2.06(25) µB at 350 K. The refined atomic positions and magnetic moments are listed in Table 1.

This magnetic structure differs from the 120◦ antiferromagnetic order previously reported in Mn3Ga where the moment direction is parallel to the crystalline axes [23]. Refinements using Cm′cm′ (BNS 63.464) magnetic model provide improved agreement with our neutron diffraction data compared to the previously reported P63/m′mc′ (BNS 194.269) magnetic model based on the early neutron powder diffraction study [23]. The comparison is shown in Supplementary Fig. 2. It is worthwhile pointing out that to determine (k = 0) magnetic order, the high-resolution neutron diffraction data with wide Q coverage is essential to obtain the reliable structural parameters, such as the scale factor, atomic positions, thermal parameters, occupancy, etc., for separating the nuclear and magnetic contributions to the same peak and distinguishing different magnetic models [26]. Our DFT calculations reveal that the energy of Cm′cm′ configuration is −30.002 eVf.u.−1, which is lower than −29.996 eVf.u.−1 calculated for the previously proposed P63/m′mc′ configuration. This energy difference further validates Cm′cm′ magnetic structure. Furthermore, we observe weak spontaneous magnetization and a small hysteresis loop for TN2 < T < TN1, as discussed below. This indicates the presence of a small uncompensated component to the moment in Mn3Ga, analogous to the small in-plane net moment along the aH axis in Mn3Sn [7] and Mn3Ge [15]. Note that this minuscule moment is undetectable by neutron diffraction yet is allowed by the magnetic symmetry Cm′cm′ (see Table 1). Consequently, the magnetic order in the TN2 < T < TN1 range is described as a nearly 120◦ triangular AFM structure (SCm′cm′) with a slight canting that produces a weak net moment along the aH axis. This configuration is identical to that of iso-structural Mn3Ge [27, 28] and aligns with previous DFT reports [29].

2.2 Magnetostructural Phase Transition at TN2
As shown in Fig. 2a, upon further cooling , high-resolution neutron diffraction reveals a clear splitting of Bragg peaks below TN2 = 295 K, indicating a symmetry-lowering distortion. High resolution neutron diffraction is critical to distinguish between the previously reported orthorhombic [22, 24] or monoclinic [23] models for the low temperature structure. In the case of orthorhombic distortion, the hexagonal 300 peak is expected to split into two reflections (orthorhombic 330 and 060). In contrast, monoclinic symmetry results in three distinct peaks (monoclinic 300, 30¯3 and 003) due to its lower symmetry and additional peak splitting. As shown in Fig. 3b, the observed peak splitting to three peaks at 260 K confirms the formation of a monoclinic unit cell below TN2. It is worth noting that the reflection from the MnO impurity phase near Q = 4 ˚A−1 is negligible and is expected to be less than 1% of the intensity of the hexagonal 300 reflection from Mn3Ga. We performed pseudo-Voigt function fits on the hexagonal 300 Bragg peak above and below TN2 (Fig. 3a, b). The full width at half maximum (FWHM) and mixing parameter (η) obtained from the fit at 300 K are used as constraints for fitting the 260 K data. Fig. 3c, d show the temperature dependence of lattice parameters. Clear splitting of the in-plane lattice parameters (aM and cM) is observed, accompanied by a deviation of β from 120◦. The Rietveld analysis on the neutron diffraction data below TN2 reveals a space group P2/m (No. 11), which shows a better refinement quality than the orthorhombic model Cmcm (No. 63) (see Supplementary Fig. 3). Symmetry analysis, based on the refined crystal structures and structural relationships determined using the Bilbao Crystallographic Server [30, 31, 32], reveals that two distortion modes, Γ+2 and Γ+5, contribute to this monoclinic distortion. These modes involve atomic displacements of both Mn and Ga restricted in the Kagome plane, as shown in Fig. 3e.

It is worth noting that our Mn3Ga sample shows a substantially higher MST temperature TN2 (295 K) compared with the 120 K [24] and 170 K [22, 23] for samples with 70–74 at% Mn, and this value is slightly higher than the transition temperature of ≈ 285 K reported for Mn2.95Ga with the 74.7 at% Mn in recent study [23]. This enhancement is likely attributed to the combined effects of improved crystallinity, variations in synthesis methods and stoichiometry of our sample. Indeed, as shown in Supplementary Fig. 1, changing the processing conditions of the Mn3Ga ingot used in this study can increase TN2 to near 320 K.

Concurrent with this structural distortion, a new magnetic ground state emerges at TN2, as indicated by the onset of increasing magnetization upon cooling as shown in Fig. 4a and changes of the magnetic peak intensities (see Fig. 2a). The rapid increase of the magnetization and the pronounced deviation from linear M(H) behavior below TN2 in Fig. 4b indicate the emergence of a ferromagnetic component below TN2. Our neutron diffraction results shows that the propagation vector remains zero (k = 0). We found neutron powder diffraction alone cannot unambiguously determine the magnetic structure due to overlapping nuclear and magnetic peaks and the subtlety of the simultaneous lowering of crystalline and magnetic symmetry. Only two magnetic models (A and H), shown in Supplementary Fig. 7, yielded excellent yet comparable refinement quality. To identify the correct magnetic structure, we combined the refinement results with our first-principles calculations including spin-orbit coupling (DFT+SOC). The DFT results validated magnetic model A since it exhibits the lowest energy among nine different magnetic orders in the monoclinic phase (see more details in Supplementary information and Supplementary Figs. 6 and 7). The Rietveld refinement against the neutron diffraction data at 30 K using the magnetic model A (P2/m′ (BNS 11.54)) is presented in Fig. 4c. The fitted atomic positions and magnetic moments are listed in Table 2. As shown in the inset of Fig. 4c and Fig. 1c, it is a canted AFM structure with substantial net moment (≈ 0.71 µB per Mn). The moments of Mn(1) and Mn(2) nearly cancel each other, and the net moment arises primarily from Mn(3), oriented nearly perpendicular to aM in the monoclinic aM cM plane, which elucidates the origin of the ferromagnetic component observed in the magnetization. The ordered moment per Mn site at 30 K is refined to be ≈ 2.56 µB. Note that this magnetic structure differs significantly from that proposed in the previous report [23]. In addition, the decrease of the magnetization in Fig. 4a below ≈ 110 K is associated with the AFM transition of impurity phase MnO, as evidenced by the the appearance of AFM peak 111 of MnO below its N´eel temperature TN = 110 K (see Fig. 2a and Supplementary Fig. 4), consistent with previous reports [33, 34].

2.3 Anomalous Hall effects and Weyl states above/below MST
With the established crystal and magnetic symmetries, we carried out first-principles calculations to locate potential Weyl nodes, determine their symmetry characteristics, and evaluate the associated anomalous Hall effect (AHE). The electronic band structure in the intermediate-temperature phase (TN2 < T < TN1) is shown in Fig. 5a. Since Mn3Ga shares the same symmetry as Mn3Sn and Mn3Ge above TN2, their band structures are correspondingly similar. However, reflecting the smaller number of total electrons, the Fermi level in Mn3Ga is lower by ∼ 0.4 eV. This result is fully consistent with that in Ref. [29] (Fig. 3(a)). Because of the spatial inversion symmetry (I) as well as the combined symmetry involving the mirror reflection with respect to a kagome plane and the time reversal (MzT), all bands on the kz = 2π/c plane have twofold degeneracy (see A–H–L–H–L’–H–A line in Fig. 5a). The anomalous Hall conductivity for the hexagonal phase is shown in Fig. 5b. Mirror reflection symmetry about the y axis (My) forbids both σxy and σyz, allowing only σzx. The current σzx in the hexagonal phase is slightly different from the previous theoretical result [29] due to minor variations in the lattice parameters, while the overall range remains consistent. The I and MzT symmetries also exist in the low-temperature monoclinic phase, leading to the twofold degeneracy in the dispersion relation on the kz = 2π/c plane as shown in Fig. 5c (see Z–M–C–M–E–M–Z line). The corresponding AHC is shown in Fig. 5d. Although the My is broken in monoclinic symmetry, the combined symmetry MzT still remains, which prohibits only σxy, allowing σzx and an emergence of non-zero σyz.

Before going into the detailed analysis of Weyl points, we summarize the symmetry of Weyl points dictated by the magnetic and lattice symmetries of the system. For Mn3Sn and Mn3Ge with 120◦ ordering with the net magnetic moment along the y direction, there exist four important symmetries, a mirror reflection with respect to the (010) plane My and a half-lattice translation (c/2), a mirror reflection with respect to the (100) plane combined with the time reversal MxT, a mirror reflection with respect to the (001) plane combined with the time reversal MzT, as well the spatial inversion I. When there is a Weyl point at (kx, ky, kz) with the chirality χ, because of My, MxT, and MzT, there exist other Weyl points at (kx, −ky, kz), (kx, −ky, −kz), and (−kx, −ky, kz) with the opposite chirality −χ. Furthermore, I guarantees the existence of four additional Weyl points at (−kx, −ky, −kz) with the chirality −χ, as well as at (−kx, ky, −kz), (−kx, ky, kz), and (kx, ky, −kz) with the chirality χ. As shown in Fig. 6a, Weyl points in the high-temperature hexagonal phase of Mn3Ga based on our calculations clearly follow this rule.

In the low-temperature monoclinic phase of Mn3Ga, however, My and MxT symmetries are absent, and only MzT and I symmetries remain. As a consequence of this lower symmetry, Weyl points appear as quartets at (kx, ky, kz) and (kx, ky, −kz) with the chirality χ and (−kx, −ky, −kz) and (−kx, −ky, kz) with the chirality −χ, as shown in Fig. 6c. Therefore, our results suggest two distinct Weyl states with different AHEs below and above MST.

2.4 Transport Signatures of the Topological Phase Transition
To seek for the experimental proof supporting our theoretically predicted topological Weyl state transition, we performed field-dependent transport measurements on longitudinal resistivity ρxx and total Hall resistivity ρyx, as well as M(H) measurements across TN2. Figure 7a shows the longitudinal magnetoresistance, MR = [ρxx(H)−ρxx(0)]/ρxx(0), which undergoes a distinct change in slope (∝ d(MR)/dH) across the MST at TN2. At 350 K (TN2 < T < TN1), d(MR)/dH is positive and increases with magnetic fields in the 0–50 kOe region. However, upon cooling to 300 K near TN2, the positive d(MR)/dH becomes pronounced at low fields but decreases at higher fields. At lower temperatures, the positive d(MR)/dH evolves to negative sign and MR changes to negative over the whole measurement range. This sign change in MR was not observed in previously reported polycrystalline Mn3Ga samples [25, 24]. Both the positive and negative MR from 350 K down to 5 K display nearly linear behavior without saturation, which is typical in Weyl semimetals [36, 37, 38].

The temperature dependence of the magnetization M(H) curves is presented in Fig. 7b. In the TN2 < T < TN1 regime, the magnetization exhibits a weak magnetic hysteresis loop at low fields (< 5 kOe) due to weak net component. At 350 K, we observe a small spontaneous magnetization of 0.008 µB per Mn and a coercive field of ≈ 1 kOe. At higher fields, M(H) shows a linear dependence on H and reaches a magnitude of only ≈ 0.03 µB per Mn at 50 kOe (350 K), suggesting that the nearly 120◦ chiral AFM order remains robust against the external field. Below TN2, the spontaneous magnetization increases sharply at low fields, indicating a significant net ferromagnetic component within the distorted AFM phase. While the magnetization continues to rise at higher fields, it only reaches approximately 0.25 µB per Mn at 50 kOe (5 K) which is an order of magnitude lower than the ordered moment of 2.56 µB per Mn determined by neutron diffraction. This discrepancy indicates that the applied field of 50 kOe is insufficient to fully polarize the distorted AFM order into a collinear ferromagnetic state.

The temperature dependence of the total Hall resistivity is shown in Fig. 7c. The total Hall resistivity [7, 39] is composed of the ordinary Hall resistivity (ρN) and the anomalous Hall effect (ρA), such that:
ρyx = ρN + ρA = R0H + SAρxx2M (1)
where R0 is the ordinary Hall coefficient, SA is a field-independent parameter, SAρxx2 is the conventional AHE coefficient proportional to magnetization. Note that the intrinsic ρA reflects the integral of the Berry curvature over the entire Brillouin Zone for all occupied states.

At 350 K (TN2 < T < TN1), the AHE exhibits a negative (positive) sign for positive (negative) fields. A prominent sign reversal, accompanied by a distinct low-field hysteresis loop, is observed in ρyx. As the field increases, the magnitude of the Hall signal decreases linearly. As further illustrated in Fig. 8a, the low-field nonlinearity and sign reversal of ρyx vs M are attributed to an additional, unconventional AHE component, ρAF, which is intrinsically coupled to the nearly 120◦ triangular AFM order. The R0 and SA coefficients are determined using the method described in previous studies on Mn3Sn [7] and Mn3Ge [39]. We then isolate the individual SAρxx2M, ρAF, and ρA = SAρxx2M + ρAF components as a function of M and H, as shown in Fig. 8a and b, respectively. While the conventional AHE component SAρxx2M is weak due to very low magnetization at 350 K and follows the standard proportionality to M, the much stronger ρAF dominants ρA and remains nearly independent with M or H in high field regions. Note that the ρyx profile of Mn3Ga at 350 K bears some similarity to the averaged Hall response based on the single crystal results on the isostructural Mn3Sn [7] and Mn3Ge [15, 39], and that on polycrystalline Mn3Ga [25]. The magnetic structure in this region involving a weak ferromagnetic component is characterized by the orthorhombic magnetic space group Cm′cm′ in Fig. 1b, which explicitly breaks time-reversal symmetry, a fundamental requirement for the Weyl points and AHE. By using the the hexagonal structure and Cm′cm′ magnetic configuration, our DFT calculations have showed a robust AHE with σzx tensor driven by a significant enhancement of the Berry curvature localized around Weyl nodes near the Fermi level. The observed ρA, encompassing both conventional SAρxx2M and unconventional ρAF, provides experimental evidence to support our theoretical predictions.

Upon cooling below TN2, ρyx shows pronounced change in the nonlinearity, indicating a distinct shift in the AHE (ρA) contribution that deviates from the linear field dependence characteristic of the ρN. This occurs near room temperature in our nearly stoichiometric Mn3Ga, significantly higher than the approximately 140 K observed in previous report on Mn3Ga [25]. In addition, in sharp contrast to the high-temperature region, the ρyx becomes positive (negative) under positive (negative) fields at low temperatures, indicating a global sign reversal of the ρA. Notably, a pronounced hump-like feature emerges at moderate fields (< 10 kOe) below ∼ 150 K and vanishes at higher fields (see Fig. 8d and Supplementary Fig. 5c)—both of which are characteristic hallmark of the topological Hall effect (THE) [40, 41, 42]. Although THE was previously reported in polycrystalline Mn3Ga [25], it was associated with a different orthorhombic structure and occurred at a lower temperature, around 100 K.

Since the high-field region can be well described by R0H + SAρxx2M, we determine the coefficients R0 and SA by fitting the high-field data to the linear relation ρyx/H = R0 + SA(ρxx2M/H) [25] (see Supplementary Fig. 5d). The subtracted component ρyx − R0H − SAρxx2M is shown in Fig. 8c-d, which is predominantly dominated by THE showing a clear hump at low fields that vanishes at high fields. Consequently, the Hall resistivity at low temperatures is modeled as ρyx = R0H + ρA + ρT = R0H + SAρxx2M + ρT where the ρA is well-described by the conventional AHE mechanism (SAρxx2M). As shown in Fig. 8c-d, there is a dramatic increase of the SAρxx2M component at 100 K compared to 350 K, which correlates with a significantly increased net moment. In addition to the emergence of a distinct ρT, the AHE (ρA) at 100 K exhibits an opposite sign and different magnitudes from those at 350 K (see Fig. 8a-b).

To further demonstrate the topological contribution to the Hall response, we track the temperature evolution of the Hall conductivity, σxy = −ρyx/ρxx2 (ρxx >> ρyx, see Supplementary Fig. 5a). As shown in Fig. 7d, σxy, which represents the average anomalous Hall conductivity across the three tensor components of the theoretical AHC, shows a significant change in nonlinearity and a sign reversal below TN2, attributed to the topological Weyl transition. In comparison to the maximum σA magnitude of 13.7 (Ωcm)−1 observed at 350 K (above TN2), the AHC increased significantly to 25.8 (Ωcm)−1 at 100 K (below TN2), as shown in Supplementary Fig. 5b. This behavior is consistent with the calculated enhancement of the AHC resulting from the appearance of extra σyz tensor (Fig. 5d), which is originated from the simultaneous structural and magnetic structural transformation at TN2. Therefore, our results on ρyx and σxy provides transport evidence that the MST reorganizes the Berry-curvature distribution and reconstructs the Weyl-node manifold in Mn3Ga.

Methods
4.1 Sample preparation
High-purity manganese (99.95%) and gallium (99.9999%) were combined in a 3:1 molar ratio and arc-melted to form an initial alloy. The resulting ingot was sealed in an evacuated fused silica ampoule and annealed at 673 K for 10 days, resulting in the formation of Mn3Ga in the tetragonal phase. To obtain the hexagonal phase, the ingot was resealed under vacuum, heated to 873 K for 2 hours, and subsequently quenched in room-temperature water.

Further preparation for the powder neutron diffraction sample involved grinding part of the ingot into powder using a percussion mortar and pestle, followed by ball milling in a tungsten carbide-lined crucible with tungsten carbide balls. The powder was annealed (873 K) for 17 hours and quenched in room-temperature water, resulting in well-crystallized hexagonal Mn3Ga powder.

To investigate the impact of ball milling on the magnetic transition temperature (TN2), a separate bulk fragment was cut from the ingot and annealed directly at 873 K for 17 hours without prior milling. Magnetization measurements revealed an increased transition temperature of TN2 ≈ 320 K, as shown in Supplementary Fig. 1.

Further preparation for the electrical transport measurements involved cutting and grinding part of the ingot into rectangular parallelepiped samples. To relieve surface strain and damage induced during the shaping process, these samples underwent an initial annealing at 873 K for 17 hours followed by a water quench. A subsequent annealing step was performed at 873 K for 6 hours. The resulting TN2 was approximately 310 K, close to the transition temperature observed in the powder samples used for neutron diffraction.

4.2 Neutron diffraction
Neutron powder diffraction measurements were carried out using the high-resolution neutron diffractometer POWGEN at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory. A 3.5 g powder sample of Mn3Ga was loaded into a vanadium can, which was subsequently mounted in a cryofurnace (JANIS) to cover temperature region from 30 K to 600 K. An orange cryostat was also used for complementary data collection from 2 K to 300 K. Isothermal neutron diffraction measurements were conducted at 30, 200, 350, and 600 K using the neutron frame 1 (center wavelength: 0.8 ˚A) to cover wide Q region from 1 to 14 ˚A−1. To specially check the small distortion, the high-resolution setup with neutron frame 2 (center wavelength: 1.5 ˚A) and neutron frame 3 (center wavelength: 2.665 ˚A) were also used for the measurements. At each measured temperature, sufficient waiting time was allowed to ensure thermal stability. Continuous temperature-dependent measurements from 30 to 600 K were conducted using a cryofurnace (JANIS) to capture the evolution of structural and magnetic Bragg peaks across two phase transitions.

Neutron powder diffraction data were used to refine the crystal and magnetic structures of Mn3Ga using the GSAS-II software package [65]. |M| represents the size of the ordered magnetic moment vector M = (mx, my, mz). It was calculated based on the (mx, my, 0) components for the hexagonal phase or the (mx, 0, mz) components for the monoclinic phase, incorporating the respective inter-component angles. The GSAS-II software computed these values directly, which were subsequently extracted from the refinement output (.lst) files. To obtain the average net moment per Mn, the vector sum of all Mn moments in the magnetic unit cell was normalized by the six Mn atoms contained within one magnetic unit cell.

The Bilbao Crystallographic Server [30, 31, 32] and Isodistort [66] were used to determine the structural distortion modes and symmetry-allowed magnetic space groups.

4.3 Magnetic characterization and transport measurements
Magnetization measurements were performed using a Magnetic Property Measurement System (MPMS-XL) from Quantum Design. For measurements between 5 and 395 K, 46 mg of powder sample was loaded into gelcaps and mounted into a plastic drinking straw. For measurements between 300 and 550 K, 30 mg of powder sample was loaded in a fused silica tube.

Electrical transport measurements were carried out in a Quantum Design Physical Property Measurement System (PPMS) and Quantum Design Dyancool using the Electrical Transport Option (ETO). Two samples were measured and showed consistent results. Magnetic field dependent measurements in the longitudinal resistivity (ρxx) and Hall (ρyx) configurations were collected under isothermal conditions by stepping the applied field from 50 kOe to –50 kOe then back to 50 kOe. For ρxx, data from a sample with leads attached in a longitudinal configuration was symmetrized by averaging the results from the decreasing-field scan and the increasing-field scan (to remove Hall contributions arising from lead misalignment). For ρyx, data from a sample with leads attached in a transverse configuration were antisymmetrized by taking one half of the difference between the resistance measured on decreasing and on increasing the field (to remove longitudinal contributions arising from lead misalignment). Note that in Fig. 7 full loops of symmetrized and antisymmetrized transport data are shown. Since they were determined from a single loop of raw data, the branches in the full loops of processed data are related and do not represent independent data collected on increasing and decreasing the field. Corresponding isothermal magnetization curves were measured on a piece cut from the Mn3Ga ingot and heat treated in the same way as the transport samples.

4.4 Density functional theory
To gain insight into the magnetic ordering and potential Weyl physics in the regimes TN2 < T < TN1 and T < TN2, we carried out DFT calculations for Mn3Ga using the hexagonal and monoclinic structures obtained from neutron diffraction measurements at 350 K and 30 K, respectively. The projector augmented wave method [67, 68] is used with the generalized gradient approximation in the parametrization of Perdew, Burke, and Enzerhof [69] for exchange-correlation as implemented in the Vienna ab initio simulation package (VASP) [70, 71]. For Mn, we used a potential in which the p states are treated as a valence states (Mn_pv in the VASP distribution), and for Ga, a potential in which d states are treated as valence states (Ga_d). For the electronic self-consistent calculations, we use a 12×12×12 k-point grid and an energy cutoff of 500 eV. Spin-orbit coupling (SOC) is included, whereas the +U correction is omitted because Mn3Ga is an itinerant magnetic system. To investigate the ground-state magnetic structure, we consider nine initial spin configurations that conform to the lattice symmetry, and let them relax to stable configurations.

Subsequently, the topological properties of Mn3Ga are investigated using an effective tight-binding model. We employed the Wannier90 code [72] to derive the maximally localized Wannier functions for both the hexagonal and monoclinic phases of Mn3Ga. The effective tight-binding models were refined utilizing the WannSymm package [73]. The locations and chiralities of the Weyl points were then analyzed using these effective tight-binding models with the WannierTools package [74]. For the calculations on AHC, we used a fixed laboratory frame with x ∥ aH ∥ cM, z ∥ cH ∥ bM and y is set by the right-hand rule (gray axes in Fig. 1b).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Tsung-Han Yang, et al in their manuscript NCOMMS-25-70324 “Intrinsic Topological Weyl Phase Transition Induced by a\nMagnetostructural Transformation in a Kagome Magnet”, employing high-resolution neutron diffraction and magnetization\ncharacterization experiments as well as first-principles calculations, demonstrated that Mn3Ga undergoes a chiral\nantiferromagnetic transition below TN1 = 485 K, followed by a magnetostructural transition (MST) to a monoclinic structure\nwith highly canted antiferromagnetic order at a temperature TN2 = 290 K. These changes in both the crystal structure and\nmagnetic symmetries result in an intrinsic transition between two distinct Weyl states, namely from a type-II Weyl semimetal\nstate to another Weyl state, where the two topological states exhibit substantially different anomalous Hall conductivities.\nPrevious experiments [Refs. 21-24] have reported the MST transition of Mn3Ga from the high-temperature 120 chiral\nantiferromagnetic order below TN1 = 480 K to either the orthorhombic structure at TN2 = 120 K [Ref. 24] or the monoclinic\nstructure at TN2 =170 K. These previous reports have also discussed the MST are accompanied by a magnetic\nreconfiguration that results in a substantial ferromagnetic moment [Refs. 22-25]. The current work identifies that in the\ntemperature range TN2 < T < TN1 the structure is indeed monoclinic and the type of magnetic ordering of this phase. On the\nother hand, all results on the distinct anomalous Hall effect (AHE) of these structures are based solely on density functional\ntheory calculations and not experiment.\nOverall, the AHE results and the intrinsic transition between two distinct Weyl phases which can be tuned with temperature\nare novel and interesting. However, I am bit skeptical whether the manuscript in its current form warrants publication in high\nimpact journal such as Nature Communications. Below I list a number of concerns and points that need to be addressed and\nthe manuscript be revised, before any further consideration.\n1. Very little is discussed on the origin of the MST. In Fig. 3E the authors state that the two distortion modes (Γ+2 and Γ+5) drive the structural transition from hexagonal to the monoclinic. How was this determined? From experiment or theoretical\ncalculations? Is the MST transition associated only with the phonons or do the magnetic degrees of freedom play a role?\n2. As a follow up of point #1 the theoretical calculations can help address the above question. Namely, they can calculate\nthe phonon entropy contribution to the free energy as a function of temperature for both the hexagonal and monoclinic\nstructures and investigate whether there is a structural transition between the two phases at a critical temperature. In the next\nstep, one can add the contributions to the temperature-dependent free energy from the magnetic degrees of freedom and\nexamine whether the critical temperature of the structural transition coincides with the corresponding of the magnetic\nreconfiguration.\n3. In addition, since the Mn concentration is 2.94, the presence of vacancies (different annealing temperatures) and hence\ncharge doping might affect the structural and magnetic transition temperatures and the MST. Perhaps this may be a\npossibility on the different value of TN2 compared to the values in Refs. 24 and 22,23. Presumably, TN2 decreases with\nincreasing Mn deficiency?\n4. The manuscript would be substantially strengthened if in addition to the magnetization measurements there were\ntransport measurement to corroborate the different anomalous Hall effect in the two structures. The fact that there is a net\nmagnetic moment in the monoclinic structure that would enhance the AHE.\n5. Similarly, ARPES measurements can confirm the difference of location of Fermi arcs and Weyl points between the two\nstructures.\n6. The density functional theory calculations should not have assumed the structural parameters (lattice constant, angles,\netc.) determined from experiment for the two structures. It would be more interesting to predict the lattice parameters from\nscratch for the two structures. This will also provide valuable information on the energy difference between the two structures\nat zero temperature.\n7. How did the authors choose the nine magnetic structures shown in Fig. S4 in the supplement?\n8. How do the calculated values of AHC for the hexagonal structure compare with those of previous calculations?", "reviewer_2": "This manuscript presents neutron diffraction, magnetization, and DFT studies on Mn3Ga, claiming the discovery of an\nintrinsic topological Weyl phase transition induced by a magnetostructural transformation near room temperature. While the\nexperimental determination of the structural and magnetic transitions is technically solid and of high quality, the central\ntopological claim is not substantiated by direct experimental evidence. My main concerns are as follows:\n1. The main outcome of the study is the refinement of a magnetostructural transition from a chiral antiferromagnetic\nhexagonal phase to a canted antiferromagnetic monoclinic phase, accompanied by theoretical predictions of changes in\nWeyl-node topology and anomalous Hall conductivity. However, similar magnetostructural transitions (Refs. 22-24) and\nanomalous or topological Hall responses (Refs. 24, 25) in Mn3Ga have already been reported. The present work provides a\nmore refined structural model but does not reveal fundamentally new physical phenomena.\n2. The claimed Weyl phase transition is entirely based on theoretical calculations and remains speculative in nature. No\ntransport or spectroscopic measurements (such as AHE or ARPES) are presented to validate the proposed topological\nreconstruction.\nTherefore, while the study is technically sound and of interest to the condensed-matter community, it does not reach the level\nof novelty or impact expected for publication in Nature Communications. In addition, I have several further technical\nquestions and concerns as outlined below:\n3. The temperature dependence of the lattice parameters shown in Fig. 2B and Fig. 3C is not very intuitive. It is unclear what\nthe y-axis label “ΔI/I0” represents. In Fig. 2B, the authors show that the lattice parameter aH = bH exhibits an anomaly\naround TN1, while in Fig. 3C the parameters aM and bM begin to deviate near TN2.\n4. The evidence supporting the choice of the magnetic space group Cm’cm’ (BNS 63.464) over the previously reported\nP63’/m’mc’ (BNS 194.269) model appears insufficient. The authors state that refinements using Cm’cm’ provide better\nagreement with the neutron diffraction data, but this seems to rely mainly on minor differences in the fitting intensity (Fig. S1).\nIn contrast, the structural distinction discussed later---where the hexagonal 300 peak splits into two reflections in the\northorhombic model and three in the monoclinic model---is more definitive. The observation of three peaks therefore favors\nthe monoclinic model. Stronger and more direct evidence is needed to justify the assignment of Cm’cm’.\n5. The significant increase of TN2 to 290 K compared with earlier reports (120–170 K) is intriguing. The authors attribute this\nto improved crystallinity and stoichiometry. However, it is unclear why TN1 (~480 K) remains largely unchanged within the\nframework of dilute magnetic moments.", "reviewer_3": "This manuscript shows an intrinsic magnetostructural transition (MST) between two distinct Weyl states occurs in MnGa3 at\nMST between these Weyl states in MnGa3 occurs without the need for external stimuli. Overall, I think the manuscript is very\nwell presented and written, it is clear the authors have performed very good experiments and analysed their data thoroughly.\nI have only a few comments and questions which I think would help clarify some points.\n1. As highlighted by the authors, their MnGa3 sample has a significantly higher MST than others reported previously. The\nauthors do make some suggestions as to why including crystallinity, variations in synthesis method and stoichiometry. I find\nit unlikely to be stoichiometry as the sample from Ref. 23 also has 74 % Mn but only a TN of 120 K. I’m particularly interested\nin ball-milling, do the authors have a comparison of a sample annealed with and without ball-milling (eg. magnetisation),\nthat could be included in the supplementary information? I think ultimately this is a really important part of this paper (partly\nbecause the sample used in this study puts the MST near room-temperature) and previous studies of MnGa3 have shown\nthat even if the MST occurs at the same temperature, eg. 170 K, then the low-temperature nuclear structure can be different.\n2. Additionally, ball-milling the sample has been known to decrease the particle size, which in turn can cause strain and\nsignificantly increase the peak width in diffraction – did the authors see any evidence for peak broadening and if so how did\nthey account for this in their refinements?\n3. In Figure 2, there is a star above the main peak in panels d and e. I’m assuming that’s the 101 peak, but if it could be\nclarified in the caption that would be helpful. There is also a star used in panel a for MnO, which I think adds to the\nconfusion, so perhaps the authors could use a different symbol for the impurity.\n4. On page 9, table 1 and page 13, table 2, it is not clear to me how the authors have calculated |M|. Please could the\nauthors add an explanation to the methods section.\n5. On page 11, from the Rietveld refinement at 30 K, it first says there is a substantial net moment of 2.14 μB, and then later\non in the paragraph, it says the ordered moment per Mn site is 2.56 μB. What is the reason for this discrepancy?"}, "author_response": "Response letter for #NCOMMS-25-70324\nReply to the referees’ comments on manuscript # NCOMMS-25-70324\nWe express our sincere appreciation for all the referees’ very constructive comments. We have taken these comments\ninto account fully and have revised our manuscript accordingly.\nHere are our responses and the corresponding revisions for each of the comments:\nReviewer #1 (Remarks to the Author):\nComment:\nTsung-Han Yang, et al in their manuscript NCOMMS-25-70324 “Intrinsic Topological Weyl Phase Transition\nInduced by a Magnetostructural Transformation in a Kagome Magnet”, employing high-resolution neutron\ndiffraction and magnetization characterization experiments as well as first-principles calculations,\ndemonstrated that Mn Ga undergoes a chiral antiferromagnetic transition below T = 485 K, followed by a\nmagnetostructural transition (MST) to a monoclinic structure with highly canted antiferromagnetic order at a\ntemperature T = 290 K. These changes in both the crystal structure and magnetic symmetries result in an\nN2\nintrinsic transition between two distinct Weyl states, namely from a type-I Weyl semimetal state to another\nWeyl state, where the two topological states exhibit substantially different anomalous Hall conductivities.\nPrevious experiments [Refs. 21-24] have reported the MST transition of Mn Ga from the high-temperature 120\n3\nchiral antiferromagnetic order below T = 480 K to either the orthorhombic structure at T = 120 K [Ref. 24]\nN1 N2\nor the monoclinic structure at T =170 K. These previous reports have also discussed the MST are accompanied\nN2\nby a magnetic reconfiguration that results in a substantial ferromagnetic moment [Refs. 22-25]. The current\nwork identifies that in the temperature range T < T < T the structure is indeed monoclinic and the type of\nN2 N1\nmagnetic ordering of this phase. On the other hand, all results on the distinct anomalous Hall effect (AHE) of\nthese structures are based solely on density functional theory calculations and not experiment.\nOverall, the AHE results and the intrinsic transition between two distinct Weyl phases which can be tuned with\ntemperature are novel and interesting. However, I am bit skeptical whether the manuscript in its current form\nwarrants publication in high impact journal such as Nature Communications. Below I list a number of concerns\nand points that need to be addressed and the manuscript be revised, before any further consideration.\nReply:\nWe thank the reviewer for recognizing the novel and interesting results in the manuscript and for providing very\nconstructive comments to help us improve our work. Following the reviewer’s comments, we have added new\ntransport and magnetization hysteresis loop experiments, added two new sections, and made major revisions to the\nmanuscript, as detailed below. These revisions not only provide experimental evidence of topological reconstruction\nbut also identify an emergent anomalous phase driven by spin chirality at low temperatures and fields.\nIn addition, we would like to explain that determining the correct crystal and magnetic structures below T in Mn Ga\nN2 3\nwas a challenge and the low-T magnetic structure below in T<T presented in our manuscript differs significantly\nN2\nfrom that proposed in previous reports. We found that neutron powder diffraction alone cannot unambiguously\ndetermine the magnetic structure in Mn Ga due to overlapping nuclear and magnetic peaks and the subtlety of the\n3\nsimultaneous lowering of crystalline and magnetic symmetry. Two magnetic models A and H shown in Fig. S7 of SI\nyield similar refinement quality on the neutron data. To resolve this, we combined high-resolution neutron diffraction\nwith DFT calculations on the energies to determine the correct magnetic structure. Additionally, the crystal structure\nof Mn Ga has been controversial, with debates between orthorhombic and monoclinic configurations. Although Ref.\n3\n23 claimed a monoclinic structure, only a splitting into two peaks (consistent with orthorhombic symmetry) was\nobserved, and there was no evidence for the three-peak splitting expected from a monoclinic distortion. This likely\nexplains why subsequent studies, such as Ref. 25 in Scientific Reports, continued to adopt an orthorhombic model. To\nresolve this, we employed a high-resolution setup of neutron diffraction that revealed a three-peak splitting from the\nhexagonal 300 peak, with excellent refinement quality, providing strong evidence for a transition to a monoclinic\nstructure.\nThus, determining the correct crystal and magnetic structures below T in Mn Ga was difficult. We think the crystal\nN2 3\nand magnetic structures presented in our manuscript are new and important, forming a crucial foundation for exploring\nthe topological Weyl states and the anomalous Hall effect in Mn Ga. In particular, the specific magnetic symmetry\n3\nbelow T is required to protect the Type-I Weyl nodes shown in our DFT calculations, directly linking the structural\nN2\nsolution to the new topological physics.\nWe apologize that this was not clear in previous manuscript and we have clarified this in page 12 of the revised\nmanuscript.\n1. Very little is discussed on the origin of the MST. In Fig. 3E the authors state that the two distortion modes\n(Γ+2 and Γ+5) drive the structural transition from hexagonal to the monoclinic. How was this determined?\nFrom experiment or theoretical calculations? Is the MST transition associated only with the phonons or do the\nmagnetic degrees of freedom play a role?\nReply:\nThanks for the insightful comments. The specific distortion modes (Γ2+ and Γ5+) were determined through a rigorous\ngroup-theoretical analysis of our experimental diffraction data, using the STRUCTURE RELATIONS tool available\non the Bilbao Crystallography Server (BCS).\nWe provided the experimentally determined crystal structures of the high-temperature hexagonal (parent) phase and\nthe low-temperature monoclinic (child) phase as input. The STRUCTURE RELATIONS tool on the BCS then\ndecomposes the total structural distortion into its symmetry-allowed irreducible representations (irreps) and calculates\ntheir respective amplitudes. This analysis unambiguously identified Γ2+ and Γ5+ as the active modes responsible for\nthe transition.\nThis directly addresses the second part of the question. The fact that this structural transition coincides precisely with\nthe magnetic transition at T is strong evidence that this is a magnetostructural transition (MST). The magnetic\nN2\ndegrees of freedom are not just involved; they are the likely primary driving force. The structural distortion (via the\nΓ2+ and Γ5+ modes) acts as a secondary order parameter that couples to the primary magnetic order. This is a classic\ncase of strong spin-lattice (or magnetoelastic) coupling, where the lattice distorts to accommodate the new magnetic\nground state, likely to relieve magnetic frustration present in the high-symmetry hexagonal phase.\nWe have made the revisions in page 10 in the main text to clarify that the distortion modes were obtained from\nsymmetry analysis based on experimentally refined model.\n2. As a follow up of point #1 the theoretical calculations can help address the above question. Namely, they can\ncalculate the phonon entropy contribution to the free energy as a function of temperature for both the\nhexagonal and monoclinic structures and investigate whether there is a structural transition between the two\nphases at a critical temperature. In the next step, one can add the contributions to the temperature-dependent\nfree energy from the magnetic degrees of freedom and examine whether the critical temperature of the\nstructural transition coincides with the corresponding of the magnetic reconfiguration.\nReply:\nWe thank the reviewer very much for this comment, which is related to comment 6. Since we use experimental lattice\nparameters for both the low-temperature monoclinic phase and the high-temperature hexagonal phase, the computed\nforce constants are not reliable to evaluate phonon dispersions and the phonon contribution to the temperature-\ndependent free energy. Instead, in the revised manuscript, we have included the calculated total energy difference\nbetween the two relevant phases in page 22: the low-temperature monoclinic structure with its stable magnetic\nordering is approximately 0.041 eV ~ 475 K lower in energy than the high-temperature hexagonal structure (also with\nits stable ordering). Thermal effects, such as the reduction in ordered magnetic moments and lattice fluctuation,\nmay reasonably account for the experimentally observed magnetostructural transition between the two phases.\n3. In addition, since the Mn concentration is 2.94, the presence of vacancies (different annealing temperatures)\nand hence charge doping might affect the structural and magnetic transition temperatures and the MST.\nPerhaps this may be a possibility on the different value of T compared to the values in Refs. 24 and 22,23.\nN2\nPresumably, T decreases with increasing Mn deficiency?\nN2\nReply:\nWe thank the reviewer for this comparison. Our samples have a higher Mn concentration (~74.6 at%) compared to the\n70–74 at% reported in Refs. 22–24. This higher Mn content correlates with a substantial increase in T to 295 K, up\nN2\nfrom the previously reported ~150 K. This confirms the trend that T decreases with increasing Mn deficiency as the\nN2\nreviewer pointed out, likely due to the dilution of magnetic exchange interactions.\n4. The manuscript would be substantially strengthened if in addition to the magnetization measurements there\nwere transport measurement to corroborate the different anomalous Hall effect in the two structures. The fact\nthat there is a net magnetic moment in the monoclinic structure that would enhance the AHE.\nReply:\nWe fully agree with reviewer that the experimental evidence of the anomalous Hall effects in both structures is\nimportant. Following reviewer’s comment, we have performed comprehensive transport measurements including the\nanomalous Hall effect 𝜌 and longitudinal resistivity 𝜌 . New results have been added in Figs 7, 8 and\nyx xx\nSupplementary Fig. 5, along with a detailed discussion in the newly added section titled “Transport Signatures of the\nTopological Phase Transition” in page 16–21. We observed a very distinct Anomalous Hall Effect (AHE) between the\ntwo crystalline and magnetic phases, with opposite signs and different magnitudes below T , accompanied by the\nN2\nemergence of topological Hall effect (THE) below ~ 150 K.\nAs pointed out by the referee, the net magnetic moment in the monoclinic structure indeed enhanced the AHE,\nleading to a two-fold increase in the maximum anomalous Hall conductivity (AHC). Since the change in the AHC is closely\nrelated to the change of integrated Berry curvature with the redistribution of Weyl nodes, these transport signatures\nprovide robust experimental evidence supporting our theoretically predicted topological reconstruction in the absence\nof ARPES-grade crystals.\nFurthermore, an anomalous phase characterized by spin chirality is identified at low fields below approximately 150\nK as indicated by the appearance of THE. A new discussion section titled “Emergent Anomalous Phase at Low\nTemperatures and Fields” has been added in page 22-23. Additionally, revisions have been made to the “Discussion”\nsection on pages 21–23.\n5. Similarly, ARPES measurements can confirm the difference of location of Fermi arcs and Weyl points\nbetween the two structures.\nReply:\nWe fully agree that ARPES would provide direct visualization of the Fermi arcs. However, it requires single crystal\nform of Mn Ga for such measurements. We have only succeeded in synthesizing polycrystalline samples exhibiting\n3\nhigh T near room temperature. Getting nearly stoichiometric Mn Ga single crystal with comparably high T is very\nN2 3 N2\nchallenging. Nevertheless, we believe our results on polycrystalline samples will motivate single crystal growth and\nsubsequent ARPES measurements.\n6. The density functional theory calculations should not have assumed the structural parameters (lattice\nconstant, angles, etc.) determined from experiment for the two structures. It would be more interesting to\npredict the lattice parameters from scratch for the two structures. This will also provide valuable information\non the energy difference between the two structures at zero temperature.\nReply:\nWe appreciate the reviewer's suggestion regarding a comprehensive search over all lattice and magnetic degrees of\nfreedom.\nWe fully agree that the suggested procedure is ideal for a global search. Nevertheless, , its application to this material\nis computationally very challenging. First, a high degree of freedom could induce multiple local energy minima.\nIdentifying the true global ground state (the most stable structure) in the resulting complex energy landscape would\nbe exceedingly difficult and computationally expensive. Second, the relative stability of different structural and\nmagnetic orderings can be highly sensitive to specific details of the DFT calculation, such as the chosen exchange-\ncorrelation functional or the application of the +U correction. Considering these constraints, we adopted a pragmatic\nand experimentally validated approach. We utilized the experimentally determined low-temperature monoclinic\ncrystal structure as our starting point. We then systematically examined the stability of nine distinct initial magnetic\nconfigurations within this fixed structure. Although this approach does not guarantee finding the absolute global\nminimum, the most stable magnetic ordering we identified is consistent with our experimental observations. This\nagreement provides significant confidence in the reliability and physical relevance of our DFT results.\nWe have made the revisions in page 22 in the main text and SI to provide more details.\n7. How did the authors choose the nine magnetic structures shown in Fig. S4 in the supplement?\nReply:\nWe thank the reviewer for this comment. We revised the corresponding paragraph in the supplementary information\nby providing the schematics of initial magnetic configurations. A new Supplementary Fig. 6 was added.\n8. How do the calculated values of AHC for the hexagonal structure compare with those of previous calculations?\nReply:\nTo the best of our knowledge, there are no previous reports on the calculated anomalous Hall conductivity (AHC) for\nthe hexagonal structure of Mn Ga.\n3\nReviewer #2 (Remarks to the Author):\nThis manuscript presents neutron diffraction, magnetization, and DFT studies on Mn Ga, claiming the\n3\ndiscovery of an intrinsic topological Weyl phase transition induced by a magnetostructural transformation near\nroom temperature. While the experimental determination of the structural and magnetic transitions is\ntechnically solid and of high quality, the central topological claim is not substantiated by direct experimental\nevidence. My main concerns are as follows:\nReply:\nWe thank the referee for summarizing the main message of our work and agreeing on the high quality of our\nexperimental determination of the structural and magnetic transitions. We fully agree with the referee that lacking\ndirect experimental evidence supporting the topological claim was the weakness of our original manuscript. Following\nthe referee’s comments, we have added transport measurements for both anomalous hall effect 𝜌 and longitudinal\nyx\nresistivity 𝜌 , as well as corresponding magnetization hysteresis loops at the same temperatures. These revisions not\nxx\nonly provide experimental evidence of topological reconstruction but also identify an emergent anomalous phase\ndriven by spin chirality at low temperatures and fields.\n1. The main outcome of the study is the refinement of a magnetostructural transition from a chiral\nantiferromagnetic hexagonal phase to a canted antiferromagnetic monoclinic phase, accompanied by\ntheoretical predictions of changes in Weyl-node topology and anomalous Hall conductivity. However, similar\nmagnetostructural transitions (Refs. 22-24) and anomalous or topological Hall responses (Refs. 24, 25) in\nMn Ga have already been reported. The present work provides a more refined structural model but does not\n3\nreveal fundamentally new physical phenomena.\nReply:\nWe thank the reviewer for the comment on the novelty of our work. After considering the referee’s comments, we\nhave added new transport experiments, data analysis and discussion in the revised manuscript. We believe that the\nrevised manuscript has been improved significantly. Below, we explain the advances and novel aspects of our revised\nmanuscript compared to previous reports.\n(1) We discovered Mn Ga as the first example exhibiting an intrinsic topological Weyl phase transition between two\n3\ndistinct Weyl states, driven by a magnetostructural transition. This has never been reported in Mn Ga or other materials.\ncalculations on both AHE and Weyl states, we have not only validated the topological reconstruction but also identified\nan anomalous phase driven by spin chirality at low temperatures and fields. The emerging topological Hall effect,\ncoexisting with the AHE at low temperatures, highlights a remarkable unification between the real-space Berry phase\nfrom spin chirality and the k-space Berry curvature inherent in the band topology.\nAlthough anomalous Hall Effect have been reported in their samples in Refs. 24, 25, they were not correlated to\ntopological Weyl states. Furthermore, there are key differences between our work and previous results:\na) Below T , while Refs. 24 and 25 report the AHE in an orthorhombic structure, our results indicate that both the\nN2\nAHE and THE are associated with a distinct monoclinic structure.\nb) A sign change in the longitudinal magnetoresistance (MR) was observed only in our sample.\nc) We extracted distinct contributions from the anomalous Hall effect (AHE) with opposite signs and different\nmagnitudes to support the topological reconstruction, with the effect occurring near room temperature—significantly\nhigher than the approximately 140 K reported in Ref. 25. No sign change of the AHE was observed in Ref. 24.\nd) The topological Hall effect (THE) was found at a higher temperature of ~150 K in our study compared to ~100 K\nin Ref. 25.\n(2) Determining the correct crystal and magnetic structures below T in Mn Ga was a significant challenge, which\nN2 3\nwe resolved by combining neutron diffraction and DFT calculations. The crystal structure of Mn Ga has been\n3\ncontroversial, with debates between orthorhombic and monoclinic configurations. Although Ref. 23 claimed a\nmonoclinic structure, only a splitting into two peaks (consistent with orthorhombic symmetry) was observed, and there\nwas no evidence for the three-peak splitting expected from a monoclinic distortion. This likely explains why\nsubsequent studies, such as Ref. 25 in Scientific Reports, continued to adopt an orthorhombic model. To resolve this,\nwe employed a high-resolution setup of neutron diffraction that revealed a three-peak splitting from the hexagonal\n300 peak, with excellent refinement quality, providing strong evidence for a transition to a monoclinic structure.\nFurthermore, we solved a new magnetic structure and determined the net moment direction. This magnetic structure\ndiffers significantly from that proposed in Ref. 23. Note that neutron powder diffraction alone cannot unambiguously\ndetermine the magnetic structure in Mn Ga overlapping nuclear and magnetic peaks and the subtlety of the\n3\nsimultaneous lowering of crystalline and magnetic symmetry. Two magnetic models, A and H shown in Fig.S7 of SI\nyield similar excellent refinement quality. To resolve this, we combined high-resolution neutron diffraction with DFT\ncalculations to determine the correct magnetic structure. Thus, it turns out that determining the correct crystal and\nmagnetic structures below T in Mn Ga was a challenging task. In particular, the low-T magnetic structure below in\nN2 3\nT<T presented in our manuscript differs significantly from that proposed in previous reports. This specific magnetic\nN2\nsymmetry is required to protect the Type-I Weyl nodes shown in our DFT calculations, directly linking the structural\nsolution to the new topological physics. We therefore think the crystal and magnetic structures presented in our\nmanuscript are new and important, providing a crucial foundation for exploring the topological Weyl states and the\nanomalous Hall effect in Mn Ga.\nmanuscript.\n(3) Room-Temperature Functionality: Our stoichiometric control stabilizes the Weyl phase transition near room\ntemperature, facilitating the exploration of potential spintronic applications through the manipulation of two distinct\nWeyl states.\n2. The claimed Weyl phase transition is entirely based on theoretical calculations and remains speculative in\nnature. No transport or spectroscopic measurements (such as AHE or ARPES) are presented to validate the\nproposed topological reconstruction.\nReply:\nWe thank the reviewer for these important comments. We agree that experimental validation of topological\nreconstruction is essential. To address this, we have performed comprehensive temperature-dependent transport\nmeasurements for both anomalous Hall effect 𝜌 and longitudinal resistivity 𝜌 , as well as corresponding\nyx xx\nmagnetization hysteresis loops at the same temperatures. By combining experimental AHE and DFT calculations on\nAHE and Weyl states, we are able to validate the proposed topological reconstruction.\nWe observed a very distinct Anomalous Hall Effect (AHE)–with opposite signs and different magnitudes—between\nthe two crystalline and magnetic phases, together with the emergence of topological Hall effect below T .\nN2\nThese\ntransport signatures provide strong experimental evidence for the proposed topological transition. Furthermore, our\nDFT calculations [Fig. 5] show that the high-symmetry hexagonal phase restricts the Hall tensor (only σ ≠0),\nzx\nwhereas the low-symmetry monoclinic phase allows additional components (e.g., σ ) related to the reorganization of\nyz\nWeyl nodes from Type-II to Type-I, resulting in an enhanced anomalous Hall conductivity (AHC). The observed two-fold\nincrease of the AHC at low temperatures below T is consistent with this theoretical prediction. In addition, an\nN2\nanomalous phase due to spin chirality is identified at low fields below approximately 150 K, as indicated by the\nappearance of THE.\nWe agree that ARPES would provide direct visualization of the Fermi arcs. However, it requires single crystal form\nof Mn Ga for such measurements. We have only succeeded in synthesizing polycrystalline samples exhibiting high\nN2 3 N2\nchallenging. We are sorry that we are unable to present the ARPES measurements. Nevertheless, we believe that the\ndramatic changes in the experimental AHE and THE are sufficient to evidence our theoretically predicted topological\nreconstruction in the absence of ARPES-grade crystals.\nWe have added two sections of “Transport Signatures of the Topological Phase Transition” and ““Emergent anomalous\nphase at low temperatures and fields” in pages 17-21, two new Figs. 7 and 8 in page 17 and 19, as well as\nSupplementary Fig. 5. Additionally, major revisions have been made to the “Discussion” section on pages 21–23.\nComments: Therefore, while the study is technically sound and of interest to the condensed-matter community,\nit does not reach the level of novelty or impact expected for publication in Nature Communications. In addition,\nI have several further technical questions and concerns as outlined below:\nReply:\nTo address the referee’s concern regarding the novelty of the original manuscript, we have made extensive efforts by\nadding new experiments and performing major revisions to significantly enhance the quality of our work, as detailed\nabove. We have also provided point-by-point responses to the other technical questions and concerns raised by the\nreferee below. Hopefully, the referee could be convinced that our revised manuscript is now suitable for publication\nin Nature Communications.\n3. The temperature dependence of the lattice parameters shown in Fig. 2B and Fig. 3C is not very intuitive. It\nis unclear what the y-axis label “Δl/l ” represents. In Fig. 2B, the authors show that the lattice parameter a =\nb exhibits an anomaly around T , while in Fig. 3C the parameters a and b begin to deviate near T .\nH N1 M M N2\nReply:\nWe thank the reviewer for pointing out this ambiguity.\n(1) Clarification of y-axis label: The y-axis represents the relative change in lattice parameters, defined as [l(T)–\nl(300K)]/l(300K). We have added the description of the definition in the caption of Fig. 3 (C–D).\n(2) Relationship between Fig. 2(B) and Fig. 3(C): In Fig. 2(B), the hexagonal cell parameters (a = b ) show an\nH H\nanomaly at T . But the structure remains hexagonal across T In contrast,below T the lattice constant a\nN1 N1. N2, H\nsplits into distinct a and c values, indicating a structural transition from hexagonal to monoclinic symmetry.\nM M\nWe have clarified this in the figure caption and text to make the relationship between the two representations\nexplicit.\n4. The evidence supporting the choice of the magnetic space group Cm’cm’ (BNS 63.464) over the previously\nreported P63’/m’mc’ (BNS 194.269) model appears insufficient. The authors state that refinements using\nCm’cm’ provide better agreement with the neutron diffraction data, but this seems to rely mainly on minor\ndifferences in the fitting intensity (Fig. S1). In contrast, the structural distinction discussed later---where the\nhexagonal 300 peak splits into two reflections in the orthorhombic model and three in the monoclinic model---\nis more definitive. The observation of three peaks therefore favors the monoclinic model. Stronger and more\ndirect evidence is needed to justify the assignment of Cm’cm’.\nReply:\nWe appreciate the reviewer’s comment and the comparison to the structural analysis. We combined both Rietveld\nanalysis and DFT calculations to distinguish Cm’cm’ and P63’/m’mc’.\n(1) To determine (k = 0) magnetic order, the high-resolution neutron diffraction data with wide Q coverage is essential\nto obtain the reliable structural parameters, such as the scale factor, atomic positions, thermal parameters,\noccupancy, etc., for separating the nuclear and magnetic contributions to the same peak and distinguishing\ndifferent magnetic models. Our neutron data covered a wide d spacing so that we can get reliable structural\nparameters by the fits to a lot of middle-d and high-d parts of the neutron data with negligible contribution from\nmagnetic peaks as shown in the new Fig. S2(B) figure (only high-Q data shown for clarity). Then, we fixed these\nstructural parameters and only refined magnetic moments for these two magnetic models and compare the relative\nintensities of the characteristic magnetic peaks. As shown in Fig. S2(a,c), the refinement quality for the\ncharacteristic ratio I(100)/I(110) is well reproduced using the Cm’cm’, but not by the P63’/m’mc’.\n(2) Our DFT calculations reveal that the energy for the Cm′cm′ configuration is −30.002 eV /f.u., which is lower than\nthe -29.996 eV /f.u obtained for the P 63′ /m′mc′ configuration.\nThe consistency between our neutron diffraction and DFT calculations validated the Cm’cm’ spin configuration.\nWe have made the revisions in page 7–9 in the main text, and Supplementary Fig. S2 in the Supporting Information.\n5. The significant increase of T to 290 K compared with earlier reports (120–170 K) is intriguing. The authors\nN2\nattribute this to improved crystallinity and stoichiometry. However, it is unclear why T (~480 K) remains\nN1\nlargely unchanged within the framework of dilute magnetic moments.\nReply:\nWe really appreciate the reviewer for this insightful comment, which motivated us to do a more thorough review of\nprevious reports on T . In earlier studies (Ref. 21 and 22), T was reported to be approximately 460 K and 470 K,\nN1 N1\nrespectively. To be more accurate, the T in previous reports was below ~470 K, while our sample exhibits a slight\nN1\nincrease of approximately 15 K. The Néel temperature in Mn X (X=Ga, Sn or Ge) is governed by strong Mn–Mn\n3\nexchange interactions. Variations in stoichiometry typically lead to modifications in the lattice constants and Mn–Mn\nbond lengths, which is expected to modify Mn–Mn exchange interactions and therefore, induces a slight change of\nT .\nN1\nIn contrast, T corresponds to a magnetostructural transition where both the crystal structure and magnetic order\nN2\nchange simultaneously and are intimately coupled. Consequently, even small variations in lattice parameters/magnetic\ninteractions can induce a much larger shift in T . This high sensitivity to perturbations such as composition and\nN2\npreparation conditions has been observed in not only Mn Ga but other samples undergoing magnetostructural\n3\ntransitions, as discussed in the section “Engineering Magnetostructural Transitions” in page 24-25.\nWe have updated the previously reported T from 480 K to a more accurate 470 K in the “Introduction” part and\nN1\nadded one sentence on page 6-7 of the main text to comment on the difference in T .\nN1\nReviewer #3 (Remarks to the Author):\nThis manuscript shows an intrinsic magnetostructural transition (MST) between two distinct Weyl states\noccurs in Mn Ga at 290 K using a combination of neutron diffraction, magnetisation and first-principle\n3\ncalculations. The novel aspect is that the MST between these Weyl states in MnGa3 occurs without the need for\nexternal stimuli. Overall, I think the manuscript is very well presented and written, it is clear the authors have\nperformed very good experiments and analysed their data thoroughly. I have only a few comments and\nquestions which I think would help clarify some points.\nReply:\nWe thank the reviewer for recognizing the novelty of our manuscript and for the valuable comments very much. We\nhave responded to these comments one-by-one and made corresponding revisions to the manuscript.\n1. As highlighted by the authors, their Mn Ga sample has a significantly higher MST than others reported\n3\npreviously. The authors do make some suggestions as to why including crystallinity, variations in synthesis\nmethod and stoichiometry. I find it unlikely to be stoichiometry as the sample from Ref. 23 also has 74 % Mn\nbut only a T of 120 K. I’m particularly interested in ball-milling, do the authors have a comparison of a sample\nN\nannealed with and without ball-milling (eg. magnetisation), that could be included in the supplementary\ninformation? I think ultimately this is a really important part of this paper (partly because the sample used in\nthis study puts the MST near room-temperature) and previous studies of Mn Ga have shown that even if the\nReply:\nWe thank the reviewer for this incisive observation. As suggested, we have performed a direct comparative study,\nnow presented in the new Figure S1 of the Supplementary Information, which contrasts the magnetization of samples\nsynthesized with and without ball-milling. It seems that the sample with additional ball-milling process shows a lower\ntransition temperature by approximately 20 K, whereas the sample without ball milling exhibits a higher T ~ 320 K.\nN2\nThe reviewer’s comment motivated us to do more thorough literature reviews and experiments. For example, In Ref.\n22, a sample with 71.4 at% Mn shows a T of 170 K. In Ref. 23, the composition of the sample is Mn Ga (~74 %\nN2 2.9\nMn) showing a low T of 120 K as the referee pointed out. We noticed that Ref. 23 also mentioned another\nN2\ncomposition, Mn Ga (~74.7 at % Mn) exhibiting a high T of ~285 K, which is close to our study (Mn Ga,~74.6\n2.95 N2 2.94\nat % Mn; T : 295-320 K). All these results indicate that T is highly sensitive to the stoichiometry in the region ~71\nN2 N2\n-75 am% Mn.\nHowever, we agree that the stoichiometry alone is not sufficient to account for the increase of T in our\nN2\nsample. Factors such as synthesis methods, annealing temperature, crystallinity, and other processing conditions also\nplay some role. Our new test showed that additional round of annealing period of 6 hours after the quenching process\nreduced T by around 10 K.\nN2\nWe have added more information in page 10, 26 of the main text and added new S1 figure in the Supporting\nInformation (SI).\n2. Additionally, ball-milling the sample has been known to decrease the particle size, which in turn can cause\nstrain and significantly increase the peak width in diffraction – did the authors see any evidence for peak\nbroadening and if so how did they account for this in their refinements?\nReply:\nWe thank the reviewer for raising this important point regarding sample microstructure. We agree that ball-milling\ntypically induces mechanical strain and reduces particle size, which can lead to significant peak broadening.\nTo avoid this, we did not use a high-energy ball milling process. Instead, we employed a low-energy ball milling\ntechnique solely to pulverize the ingots into powder. A critical post-milling annealing step was then performed at 873\nK for 17 hours followed by a quenching process. This procedure effectively relieved the mechanical strain and\npromoted grain growth/recrystallization. Consequently, the neutron diffraction patterns exhibit very sharp Bragg peaks,\nas shown in Fig.2(d-e). The peak widths are dominated by instrumental resolution, and we did not observe clear\nbroadening beyond instrument resolution. In our GSAS-II refinements, instrumental resolution parameters were\nsufficient to model the peak shapes, and no additional microstrain term was required.\n3. In Figure 2, there is a star above the main peak in panels d and e. I’m assuming that’s the 101 peak, but if it\ncould be clarified in the caption that would be helpful. There is also a star used in panel a for MnO, which I\nthink adds to the confusion, so perhaps the authors could use a different symbol for the impurity.\nReply:\nWe apologize for the confusion in Fig. 2. We have revised it and now use a different symbol to clearly distinguish the\nMnO impurity phase.\n4. On page 9, table 1 and page 13, table 2, it is not clear to me how the authors have calculated |M|. Please could\nthe authors add an explanation to the methods section.\nand\n5. On page 11, from the Rietveld refinement at 30 K, it first says there is a substantial net moment of 2.14 μB,\nand then later on in the paragraph, it says the ordered moment per Mn site is 2.56 μB. What is the reason for\nthis discrepancy?\nReply:\n|M| is the absolute ordered moment and defined from the vector M=(m , m , m). Thus, |M| in Mn Ga was calculated\nx y z 3\nbased on the two moment components of (mx, my, 0) in the hexagonal phase or (mx, 0, mz) in the monoclinic phase,\nincorporating the respective inter-component angles. And the GSAS-II software computed |M| automatically, which\ncan be found in the output .lst file.\nThe net moment and ordered moment per Mn site refer to different quantities. The ordered moment of 2.56 μB/Mn\nsite was obtained from the magnetic Rietveld refinement. In sharp contrast, the value of 2.14 μB is the total net moment\nin one triangular Mn lattice, i.e., the vector sum of all the three Mn-site moments. To avoid confusion, we change to\nuse average net moment on a per-Mn basis as 2.14/3≈0.71 μB/Mn. Because the refined structure is non-collinear,\nthe individual Mn moments partially cancel, so this value is smaller than the ordered moment per Mn.\nIn addition, we have added a couple sentences on page 27 explaining how |M| and net moment are obtained and\nclarified the difference between net moment and ordered moment in the methods section.\nList of main changes:\n1. Revised Abstract, Introduction and Conclusion parts to add new findings.\n2. Page 6, Figure 2(A): Changed the symbol of MnO for clarity.\n3. Page 8, Figure 3(C–D): Added the description of the definition of normalized lattice constants and the cell\nangle for clarity.\n4. Page 7-9: Added the DFT results and discussion on the two magnetic magnetic structures in T <T<T .\nN2 N1\n5. Page 10: Added the detail of symmetry analysis for clarity.\n6. Page 10: Added the influence of ball-milling on the transition temperature.\n7. Page 12: Clarified the net moment for the monoclinic phase, and SI figure labels.\n8. Page 12: Revised the part to explain how the low-T magnetic structure in T<T was determined by a\nN1\ncombined use of neutron diffraction and DFT calculations.\n9. Page 16-21: Added a new section titled “Transport Signatures of the Topological Phase Transition”, along\nwith new Figs 7, 8 and Supplementary Fig. 5.\n10. Page 21-22: Added discussion on the driving force of the magnetostructural transition based on DFT results.\n11. Page 22-23: Added a new discussion subsection titled “Emergent Anomalous Phase at Low Temperatures\nand Fields”.\n12. Page 23-24: Added discussion and new insight in section “MST-Driven Topological Weyl phase transition”.\n13. Page 26: Sample preparation: Added more details for sample preparation for the transport measurements.\n14. Page 27: Added how |M| and net moment are obtained and clarified the difference between net moment and\nordered moment.\n15. Page 27-28: Add the description of the details of the new transport measurements.\n16. In SI, Added new Fig. 1, 5, 6.\n17. In SI: Improved Fig. 2.\n18. In SI: Added how the nine magnetic configurations were chosen.\n11"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors responded satisfactorily to all my comments and criticisms and have revised the manuscript accordingly. They\nhave performed additional comprehensive transport measurements of the anomalous Hall effect (AHE) and the longitudinal\nresistivity which revealed very distinct AHE between the two crystalline and magnetic phases with opposite signs and\ndifferent magnitudes below TN2. These additional results have strengthened the manuscript immensely.\nConsequently, the manuscript warrants publication in Nature Communications in its present form.", "reviewer_2": "The authors have made extensive efforts to address the previous concerns by performing major revisions and adding\ncomprehensive transport measurements. I am satisfied with these revisions. The manuscript is now significantly\nstrengthened and presents a more complete and convincing study combining neutron diffraction, transport experiments, and\nDFT calculations. The magnetostructural transition from a chiral antiferromagnetic hexagonal phase to a canted\nantiferromagnetic monoclinic phase is well established. Moreover, the electronic band structure calculations reveal distinct\nWeyl states in the two phases, which are accompanied by pronounced changes in the anomalous Hall effect and the\nemergence of a topological Hall effect in the transport measurements. These new experimental results provide strong\nsupport for the claimed topological Weyl phase transition. Therefore, I recommend that this work be published in Nature\nCommunications.", "reviewer_3": "I would like to thank the authors for making the changes I suggested. I support the manuscript for publication in Nature\nCommunications."}, "author_response": ""}]

Decision letter