Emergent giant topological Hall effect in twisted Fe_3GeTe_2 metallic system

Domain: chemistry
Published: 2026-02-19
Editorial outcome: accept

Abstract
The topological Hall effect, driven by the exchange interaction between conduction electrons and topological magnetic textures such as skyrmions, is a powerful probe for investigating the topological properties of magnetic materials. Typically, this phenomenon arises in systems with broken global inversion symmetry, where Dzyaloshinskii-Moriya interactions stabilize such textures. Here, we report the discovery of an emergent giant topological Hall effect in the twisted Fe3GeTe2 metallic system, which notably preserves the general global inversion symmetry. This effect manifests exclusively within a narrow window of “magic” twist angles ranging from 0.45° to 0.75°, while it is absent outside of that range, highlighting its unique and emergent nature. Micromagnetic simulations reveal that this topological Hall effect originates from a skyrmion lattice induced by alternating in-plane and layer-contrasting Dzyaloshinskii-Moriya interactions that result from local inversion symmetry breaking. Our findings underscore twisted Fe3GeTe2 as a versatile platform for engineering and controlling topological magnetic textures in metallic twisted van der Waals magnets, thereby opening up new avenues for next-generation spintronic devices.

Introduction
In non-centrosymmetric magnetic materials with broken global inversion symmetry, the interplay among Heisenberg exchange interaction, symmetry-enabled Dzyaloshinskii-Moriya interaction (DMI), and the uniaxial magnetic anisotropy can stabilize chiral spin textures such as skyrmions1. These topological magnetic structures hold great potential for achieving high-density storage and low-power computing2. Skyrmions can provide an effective gauge field that exerts a Lorentz-like force on moving electrons, giving rise to a transverse Hall current-a phenomenon known as the topological Hall effect (THE)3,4. This effect is a key signature for identifying and investigating the topological magnetic textures.

On the other hand, in centrosymmetric magnetic materials preserving global inversion symmetry, skyrmions could also emerge through mechanisms such as magnetic frustration5,6 the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction7, etc., hence giving rise to the THE. This phenomenon has been observed across various materials, including ferromagnetic semiconductors8,9, oxides10–15, transition metals16–20, magnetic topological insulators12,21,22, magnetic heterostructure23–25, etc. Additionally, the global inversion symmetry in such centrosymmetric systems does not preclude local inversion symmetry breaking that allows for alternating DMIs on the atomic scale, hence the formation of skyrmions and the ensuing THE26,27. Despite these theoretical predictions, direct experimental observation of such intrinsic electronic responses in centrosymmetric systems remains elusive.

This article reports a giant THE in a centrosymmetric Fe3GeTe2 (FGT) twisted lattice respecting a global inversion symmetry, observed almost without an external magnetic field. As a representative member of the developing van der Waals (vdW) magnets28–35, FGT36–39 is a ferromagnetic metal with magnetic iron atoms arranged on a triangular lattice, preserving the spatial inversion symmetry. Twisting FGT to form an FGT/FGT homostructure creates a twisted lattice exhibiting alternating AA and AB stacking regions. Our calculation by using the Levy and Fert’s model shows that twisting FGT can induce very strong intralayer DMI. This twisted FGT system introduces an excellent platform for studying emergent magnetic orderings driven by the competition among the exchange interaction, DMI, RKKY interaction, Coulomb interaction, and others40,41.

Moreover, the itinerant electrons in FGT allow for exploring the topological nature of the emergent non-coplanar magnetic ordering through transport measurement. Unlike magnetic insulators such as CrI3 42–45 and CrSBr46,47, however, the strong metallic bonds in FGT pose a significant challenge for fabricating twisted lattices using conventional tear-and-stack techniques. To overcome this difficulty, we developed a novel PCL-hBN tear-and-stack method48–50, leveraging the extreme stickiness of PCL to pick up the specific region of target materials like FGT while avoiding adhesion to hBN. This technique successfully fabricated a twisted FGT system with a twist angle from 0° to 5° (see Methods).

When the twist angle falls within the range of 0.45° to 0.75°, we observe a giant THE that is entirely absent at other angles, signaling the emergence of skyrmions. This effect is more pronounced in thinner FGT twisted systems, highlighting the strong interfacial influence at play. Furthermore, our micromagnetic simulations confirm that THE arises from intralayer DMI induced by twisting, which stabilizes the FGT twisted system into a skyrmion lattice within the specific twist angle range of 0.45° to 0.75°.

Our simulations further indicate that different magnetic ground states, including ferromagnetic metal and magnetic stripe phases, can be stabilized depending on the twist angle and the interlayer thickness. The twist-angle-dependent THE demonstrated in this work provides a compelling example of how topological spin texture can be created and manipulated using vdW ferromagnets. This discovery holds significant potential for various spintronics applications, such as employing a twisted FGT system as a magnetic quantum simulator or in high-density data storage.

Results
Twisted device fabrications and emergent topological Hall effect

In light of the strong adhesion between PCL and FGT and the weaker interaction between hBN and FGT, we developed a combined PCL-hBN method to fabricate twisted FGT devices through an optimized tear-and-stack process, as illustrated in Fig. 1a-d. The process begins with preparing the PCL/hBN stamp (Fig. 1a), which picked up the h-BN nanoflake from a SiO2/Si substrate.

Next, the PCL/hBN stamp is aligned with a selected FGT nanoflake on a separate SiO2/Si substrate, ensuring that the hBN covers only half of the FGT nanoflake. Gradually increasing the temperature of the substrate to 62 °C allows the PCL polymer fringe to cross the entire FGT nanoflake fully. Then, the PCL/hBN stamp is lifted after the temperature has decreased to 30 °C to tear the FGT nanoflake. After this process, half of the FGT nanoflake covered by hBN remains on the SiO2 substrate due to the weak adhesion of FGT to hBN. In contrast, the uncovered half FGT adheres to the PCL stamp due to the strong adhesive force of PCL (Fig. 1b). This results in the half FGT nanoflake (top FGT layer) being attached to the PCL stamp adjacent to the hBN. In contrast, the last half of the FGT nanoflake (bottom FGT layer) remains on the original SiO2/Si substrate, completing the tear process.

The next step involves finely rotating the substrate to introduce a twist angle between the top FGT layer on the stamp and the bottom FGT layer on the SiO2/Si substrate. Finally, the top FGT layer is carefully aligned on the bottom FGT layer and is gradually attached to the bottom FGT layer to complete the stacking process. Then, the temperature is increased above the melting point of PCL to detach the top FGT layer from the PCL stamp. After successful detachment, the substrate with FGT homostructure is dipped into tetrahydrofuran for 10 minutes to remove the PCL residual. As a result, the top FGT layer is well stacked onto the bottom FGT layer (Fig. 1c). This innovative technique overcomes the limitations of the conventional PC tear-and-stack method for rigid vdW metals, offering a significant advancement for the 2D vdW materials community.

Finally, Hall electrodes are patterned onto the overlapping region to facilitate the investigation of the transverse Hall response in the twisted region (Fig. 1d), forming the central focus of this study. Figure 1e, 1f present the schematic of the twisted FGT homostructure and the typical optical image of fabricated devices, respectively. The white scale bar represents approximately 5 μm.

In general, the transverse Hall resistance Rxy consists of three components Rxy = r0B + rsM + RTHE. The first term represents the normal Hall effect arising from the Lorentz force induced by the magnetic field. The second term corresponds to the anomalous Hall effect (AHE), originating from spin-orbit coupling, where r0 and rs are their respective coefficients. The third term RTHE is the THE, which results from the Berry phase accumulation in real space and is a hallmark of topological magnetic textures. When itinerant electrons traverse a topologically nontrivial spin texture, their spins undergo adiabatic evolution, acquiring an additional Berry phase due to the local spin configuration51,52. This Berry phase acts as an effective magnetic flux, giving rise to an anomalous velocity component transverse to the direction of electron motion. Consequently, the scalar spin chirality—defined as χijk = Si · (Sj × Sk)—produces a fictitious magnetic field that deflects the itinerant electrons, resulting in the observable topological Hall response. Since the normal Hall effect is linearly proportional to the applied magnetic field and the AHE can be determined from the magnetization, RTHE can, therefore, be extracted from the experimental data.

FGT is a hard ferromagnet of perpendicular magnetic anisotropy (See Supplementary Note 4 36,37,39). As shown in Fig. 1g, a single pristine FGT nanoflake exhibits only a typical AHE at low temperatures, characterized by a ferromagnetic hysteresis loop in the magnetic field-dependent transverse resistance (Rxy-H curve)53,54. In contrast, a twisted FGT device with a twist angle of 0.6° (Fig. 1h) strikingly displays two asymmetric humps in addition to the typical anomalous Hall loop. These Rxy humps are phenomenologically identical to the THE observed in the topological spin texture of a single magnetic system. This emergent THE is exclusive to metallic magnets, as it relies on electronic conduction, which is detectable through transport measurements. In the following sections, we systematically investigate this emergent quantum effect experimentally and elucidate its underlying mechanism induced by twisting.

Twist angle dependence of the emergent giant topological Hall effect

Next, we investigate the dependence of the exotic THE on the twist angle. Figure 2 presents the normalized Rxy (scaled by its maximum) as a function of the magnetic field (H) for various twisted FGT devices with different twist angles. All samples were fabricated under identical conditions, with the twist angle being the only controlled variable among the devices. As shown in Fig. 2a, the sample with a zero-twist angle exhibits the typical anomalous Hall loop at 20 K, consistent with the behavior of a pristine FGT nanoflake. Similarly, samples with twist angles of 0.15° and 0.3° display no topological Hall signals. Remarkably, however, a distinct topological Hall hump emerges in devices with twist angles of 0.45°, 0.6°, and 0.75°. As the twist angle increases beyond this range, the topological Hall hump disappears, and the pristine anomalous Hall loop reappears. Figure 2b demonstrates the same behavior even more prominently at a temperature of 60 K, confirming that the observed THE is indeed induced by twisting.

Before going further, we would like to discuss several important physical quantities for the THE in our twisted FGT system. Firstly, the supercell lattice Lm(θ) is related to the lattice constant a and a twist angle θ. It can be expressed in the following formula: Lm(θ) = a / 2sin(θ/2). For θ = 0.45°, 0.6°, and 0.75°, this yields a supercell lattice of approximately 50.8, 38.1, and 30.5 nm, respectively. Secondly, the topological Hall resistivity ρTHExy can be related to the carrier density and the effective filed generated by the skyrmion lattice. Within this framework, ρTHExy can be written as ρTHExy = R0 PΦ0 Nsk, where R0 is the ordinary Hall coefficient, P the spin polarization, Φ0 the magnetic flux quantum, and Nsk the skyrmion density24,55. Although this relation is oversimplified for thin-film magnetic layers with interfacial DMI, it remains useful for order-of-magnitude estimates24,56. In our twisted FGT with θ = 0.45°, the magnitude of ρTHExy at 60 K is 0.71 μΩ∙cm, and the corresponding R0 is estimated to be 1.51 × 10−9 m3/C. Using the reported spin polarization of FGT, P is 0.53 at 60 K57. Then skyrmion density Nsk is expected to be 2.15 × 1015 m−2. For a triangular skyrmion lattice, this density is related to the skyrmion lattice constant D via Nsk = 1 / (sqrt(3)D^2/2), from which we estimate D to be about 23 nm. These characteristics emerging on top of the ground-state magnetic configuration suggest a specific microscopic mechanism behind THE, which will be discussed in our theoretical analysis and calculation section afterwards.

To provide a concise representation, we define THE peak ratio as (topological Hall hump)/(topological Hall hump + anomalous Hall magnitude) × 100 %. This ratio is plotted as a color map in Fig. 2c, showing its dependence on temperature and twist angle. The THE peak ratio reaches values as high as 50 %, indicating a giant THE, even comparable in magnitude to the colossal AHE37,38,58 previously reported for FGT. The latter arises from the large Berry curvatures associated with its topological nodal-line band structures38,39,59. As highlighted in the inset, we extended our examination of the twist angle up to 5°, comparable to the twist angle range adopted in the previous study of vdW magnetic insulators42–44.

Notably, the twist-angle-dependent THE persists across a wide temperature range from 20 to 70 K (Fig. 2c). These results not only confirm the universal dependence of the emergent THE on the twist-angle dependence but also demonstrate its reproducibility across different temperatures and individual devices at small twist angles.

Thickness dependence of topological Hall effect

The observed dependence on the twist angle suggests that this extraordinary THE is closely tied to the interfacial effect created by twisting. This inspires us to examine the thickness dependence of such behavior to investigate further the interfacial nature of the underlying interactions driving this phenomenon. We successfully achieved twisted FGT devices as thin as ~6 nm using our current fabrication method. Figure 3d illustrates the normalized Rxy (scaled by its maximum) as a function of an out-of-plane magnetic field for several twisted FGT devices with the same twist angle of 0.75° but varying thicknesses, all measured at 50 K. The data clearly show a pronounced THE in the ~6 nm-thick device, consistent with the results in Fig. 2. However, as the thickness increases, the topological Hall hump becomes weaker in the ~10 nm-thick device before vanishing entirely in a ~20 nm-thick sample.

This behavior aligns with the intuitive expectation that the interfacial twist effect dominates (diminishes) in thinner (thicker) homostructures and is substantially suppressed in thick samples. The thickness dependence observed in Fig. 3d supports this hypothesis, with the disappearance of THE in the thickest 20 nm device, where the Hall response reverts to the typical AHE seen in pristine single FGT nanoflakes. Figure 3a–c, 3e, f display the same thickness-dependent trend across different temperatures.

Considering that the out-of-plane magnetic interaction in FGT expands to ~5 nm36, this suppression of THE with increasing thickness highlights the critical role of the interfacial effect at the twisting interface. These observations shed significant light on the physical mechanism underlying this intriguing twist-induced THE, which we will further explore in the next section.

Theoretical analysis

To theoretically explain the emergent THE in the twisted FGT lattice, we analyze its underlying physical mechanism from an energy perspective. Since the THE is observed over a continuous twist angle range rather than at the discretized “magic angles” (Fig. 2c), electron-electron interactions that dominate when the kinetic energy quenches at “magic angles”, can be excluded as the primary mechanism for the skyrmion formation. Moreover, the absence of THE in pristine FGT as shown in Fig. 1g rules out the possibility of the superimposition of two ferromagnet with different coercive field. As detailed in the Supplementary Information, this twisted FGT lattice allows both intralayer and interlayer DMIs, which can be obtained by an analytical derivation based on the Lévy–Fert model within the perturbation theory framework (Supplementary Note 1). Our calculation shows that the intralayer DMI is about four orders of magnitude larger than the interlayer one. Meanwhile, the magnitude of the intralayer DMI is almost a constant independent of position inside the twisted FGT. Figure 4a shows the magnitude of the interlayer DMI as a function of twisting angle θ for three different thicknesses. It turns out that this intralayer DMI is significantly enhanced by twisting. Mathematically, this intralayer DMI can be expressed as Dij · Si × Sj where Dij = D0(θ)(−1)^l z^ × eij with l = 1 or 2 referring to the top or bottom layers, z^ being the unit vector of the plane normal, and eij the lattice vector connecting site i and j.

In the presence of the DMI, the twisted FGT lattice can be modeled using the continuum free energy (Supplementary Note 2):

H = ∫ dr^2 [J a0^2 (∇ml)^2 - K(mzl)^2 + Jt m1 · m2 + D0(θ) a0 (-1)^l [y^ · (ml × ∂x ml) - x^ · (ml × ∂y ml)]] (1)

where Ja0^2 is the exchange stiffness with a0 the lattice constant, K is the uniaxial anisotropy, Jt is the interlayer exchange interaction, and D0(θ) is the intralayer DMI constant obtained using the Lévy and Fert’s model (Supplementary Note 1), which flips signs between layers and depends on the twisting angle θ. Given the ferromagnetic nature of FGT, we resort to micromagnetic simulations to determine the ground-state magnetic configuration. Specifically, we discretize the energy in Eq. (1) on a triangular superlattice and numerically minimize the total energy at finite temperatures (see Methods). Figure 4b presents the phase diagram of the twisted FGT lattice representing by the skyrmion density inside the entire simulated region versus twisting angle θ and thickness d, with the spin configurations at some representative θ and d plotted in Fig. 4c. Generally, we identify three different phases on the θ-d plane, e.g., the magnetic stripe phase at small twisting angles, the ferromagnetic (FM) phase at large twisting angles, and the skyrmion lattice (SKX) phase interpolating the two. Meanwhile, we also find the magnetic stripe can coexist with the skyrmion lattice at some region.

When d = 6 nm, the system is a skyrmion lattice at 0.45 ≤ θ ≤ 0.75. In principle, the topological Hall resistance is proportional to the spatial topological charge of the magnetic configuration: ρTHExy = PQ = en, where P is the electron polarization, Q is the topological charge of the magnetic ground state, and e and n are the electron charge and density, respectively9,16. Moreover, the THE peaks are typically proportional to the skyrmion density inside the skyrmion lattice. This phase diagram aligns quantitatively with the color map of the THE peak ratio shown in Fig. 2c. Although the spins in opposite layers rotate oppositely due to the reversed DMI, the topological charges in different layers are identical27. Moreover, the high density of the skyrmion lattice provides evidence for the giant THE peaks in the experimental data. Our simulations thus confirm that the giant THE can be ascribed to the emergence of skyrmion lattice at specific twisting angles.

Notably, the DMI plays a crucial role in facilitating the formation of skyrmions and spin stripes at small twist angles. Since the DMI depends heavily on the interlayer coupling induced by twisting, increasing the thickness of the twisted FGT system overall reduces the DMI as shown in Fig. 4a, thereby suppressing THE. Consequently, the THE only appears at a small twisting angle region indicated by the SKX in the phase diagram (Fig. 4b). Furthermore, competitions among the exchange interactions, uniaxial anisotropy, and DMI underpin the formation of skyrmions. Thermal agitations at high temperatures effectively reduce the uniaxial anisotropy, potentially enhancing the THE and broadening the range for the skyrmion formation, as observed in Fig. 2c.

Methods
FGT single-crystal growth
High-quality FGT single crystals were grown using the chemical vapour transport (CVT) method, following our previous work63. High-purity chemical elements were purchased from Thermo Fisher (Fe 99.9%, Ge 99.999%, and Te 99.999%). These elements were placed into a quartz tube with low water and oxygen concentrations (below 1 ppm); all processes were carried out inside a glove box. Iodine was used as the transport agent for the CVT method. After all the chemical powders were placed into the quartz tube, the tube was evacuated and sealed. The sealed tube was then placed in the middle of a two-zone furnace. The temperatures of the cold and hot zones of the two-zone furnace were raised to 700 and 750°C, respectively. After two weeks, high-quality FGT single crystals were synthesized.

Twisted FGT homostructure fabrication
The detailed descriptions of the fabricating method have been presented in the main text and Fig. 1. Here, we would like to elaborate on the development history of the combined PCL-hBN technique for ease of understanding of the experimental technical part. The best method to fabricate a twisted homostructure is the so-called tear-and-stack technique. Unlike CrI3, FGT is difficult to be exfoliated and picked up by a traditional PC transfer polymer, not to mention tearing it apart and stacking it with fine control. To address these problems, we develop a strongly adhesive dry transfer technique based on the newly invented PCL polymer48, which can pick up many vdW magnets effectively with nearly 100% probability under a very low operation temperature of around 60°C.

Adopting this PCL technique to FGT led to our first attempt to access twisted FGT homostructure in 202049, where a plateau-like magnetoresistance was observed in this twisted FGT homostructure, even with no spacer in between. In this paper, PCL polymer gradually attaches to an FGT nanoflake, with the polymer fringe stopping in the middle of the nanoflake. Then, it picks up half of the nanoflake and drops it down on the remaining half after rotation. Although doable, there is still a low possibility of success, and it is difficult to control the whole process finely regarding the stopping fringe in the middle of FGT, preventing a further efficient and systematic investigation. More seriously, this rough tear-and-stack method can only be applied to a large-area exfoliated nanoflake, which generally hosts a large thickness, e.g., 40 nm. This, thus, would smear out the intriguing quantum effects of a twisting interface effect, if any.

The PCL method is further developed into a PCL and hBN combined technique, enabling the reliable fabrication of different twisted homostructures of diverse materials with fine control50. Such a new twisted fabrication method realizes the tear-and-stack process by taking advantage of the uniqueness of PCL, which is extremely sticky and can pick up the target material like FGT, for example. At the same time, it is more challenging for hBN: we used commercial hBN for this work. Most importantly, one can readily achieve fine angle control with a resolution of 0.015° and twisted fabrication on a small nanoflake of several micrometres wide and several nanometers thin. These long-lasting technique developments48–50 eventually allow us to confidently investigate the emergent quantum phenomena in twisted metallic FGT homostructures for the first time. This new universal twisting fabrication method developed for diverse vdW magnets is extremely suitable for making twisted metallic vdW magnets such as twisted FGT homostructures.

Transport measurement
The substrate with twisted FGT is coated with poly(methyl methacrylate) (PMMA) through a spin coating process. A pattern of electrodes is drawn on the PMMA using electron beam lithography. For the electrodes, an electron beam evaporator is used to deposit titanium and gold, with thicknesses of 10 and 85 nm, respectively. Magnetoresistance and Hall resistance of twisted FGT are measured using the standard lock-in technique with SR830 (Stanford Research System). The device is placed inside a cryostat to maintain cryogenic temperatures. The magnetic field is applied perpendicular to the surface of the twisted FGT sample.

Magnetic simulations
To perform the micromagnetic simulations, we discretize the free energy in Eq. 1 on a triangular lattice with the lattice constant A0 = 2 nm, and the system size is taken as Lx = 200 A0, Ly = 100 sqrt(3) A0. The intralayer DMI at different twisting angles is calculated by using the Lévy and Fert’s model as detailed in the Supplementary Note 1. The other parameters are taken as J = 2.0 × 10^-21 Joule, Jt = 3.2 × 10^-23 Joule, K = 1 × 10^-24 Joule, which are fitted from experimental data.

Subsequently, the magnetic ground state can be calculated by numerically minimizing the total energy, which can be implemented by different methods, such as the steepest descent. In this work, the magnetic ground state at different twist angles is obtained using VAMPIRE under the field-cool program (B = 0.1 Tesla) and Monte Carlo integrator. During the simulation, the cooling time is set to 100 picoseconds with a time-step of 1 femtosecond, and the temperature is fixed at 20 K.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors discovered giant topological Hall effect in twisted FGT homojunction. In addition to the twisted angle of Hall resistances, the influences of temperature and thickness are discussed. The atomistic spin dynamics simulations are also performed. The magic angle and twisted 2D material are one of hot topics. The work is interesting. I think is it is timely to the scientific community. However, I have several problems before I recommend the publication of the present work in Nature communications.\n1. This work lacks of the basic inputs of physical properties such as characterization of the quality of single crystals (XRD, EDS), measurements of longitudinal resistances (versus temperature) both for isolated nanoflakes and homojunctions for different thickness.\n2. In general, the coercive field is a bit lower compared with others. It is only less than 0.1 T. What is the thickness of sample in Fig. 1? Is there still the hysteresis loop when the magnetic field is directed along the in-plane direction?\n3. In Figure 1, the pristine FGT is just an isolated FGT or it comprises the homojunction with the other piece of FGT? How do authors determine the twisted angle? Why does the peak disappear at 80 K?\n4. In Figure 2, assuming that the “asymmetric humps” in resistances stem from the topological spin textures, why it disappears at 20 K and is present at 60 K when the twisted angle is 0.75? Why it originates from skyrmion instead of others nonlinear topological magnetic textures?\n5. Are the coercive field and remanent resistances for the different nanoflakes identical at the fixed thickness? How to distinguish it if the humps in Hall resistances originate from the divergence of FGT itself instead of twisted angle in Fig. 3?\n6. For the caption of figure 4, it is atomistic spin dynamics simulations instead of “micromagnetic simulations”. When one talks about twisted angle, the nearest neighbor interlayer exchange J would varied with the twisted angle. In addition, is there any influence for the second nearest neighbor exchange for both J and D?\n7. In the caption of supplemental materials S1, the authors mentioned that “A few droplets of PCL solution, which is made by mixing THF and PCL with a 15% mass ratio, are dropped onto the top of PDMS, and the PCL droplets fully cover the top of PDMS”. It seems to be not consistent with the main text. Does the PCL touch with scotch tape or PDMS? What the role of scotch tape? During the transfer process of FGT, the PCL is just leave on top of FGT/BN or not? Is there any annealing process? How to separate the PCL on top of FGT and FGT in the homojunction？", "reviewer_2": "The manuscript reports the discovery of an emergent giant THE in the twisted Fe3GeTe2 metallic system. This effect manifests exclusively within a narrow window of “magic” twist angles ranging from 0.45 to 0.75 degrees while it is absent identically outside of that range, highlighting its unique and emergent nature. Micromagnetic simulations reveal that this THE originates from a Skyrmion lattice induced by alternating in-plane and layer-contrasting DMI that result from local inversion symmetry breaking.\nThe results are highly interesting and important, while some important information is lacking in text as follows. I recommend after revision of these issues.\n1. There are no sample images for single and integrated thin layers; e.g., cross-sectional AFM images to confirm FGT thickness. In particular, the authors present thickness dependence in Fig.3 and compare between 6nm and 10nm. It may be difficult to fabricate each two uniform flakes with 6nm thickness and 10 nm thickness, and integrate within this narrow angle. Thus, the information for upper and lower FGT layers is indispensable.\n2. For T dependence shown in Fig.2c, THE peak ratio is the highest around 50K. Why is this? Conventionally, THE is stronger at lower T. The authors argue that “thermal agitations at high T effectively reduce the uniaxial anisotropy, potentially enhancing the topological Hall effect and broadening the range for the Skyrmion formation”. But there is no such evidence.\n3. I cannot understand the origin of TH hump and its correlation to Skyrmion. The simulation result actually shows the appearance of Skyrmion around the 0.6 degree-twist angle, while it is not clear how the Skyrmion forms the TH hump.\n4. In my understanding, the simulation is for monolayer FGT. The 6nm-devices correspond to this??", "reviewer_3": "The current manuscript reports the observation of the electrical Hall effect anomalies in twisted magnetic bilayers of metallic Fe3GeTe2 (FGT). Based on the originally developed fabrication technique, twisted FGTs are successfully produced and the Hall transport is investigated, demonstrating an excessive Hall signal (humps) that deviates from the simple hysteresis loop-behavior of the anomalous Hall effect (AHE). These anomalies are attributed to the topological Hall effect (THE) and to the formation of skyrmion crystals at specific twist angles, which is then corroborated by theoretical analysis of the emerging magnetic phases based on micromagnetic simulations. What’s interesting about this particular material platform (FGT bilayer) is that even though there is no global breaking of the inversion symmetry, the formation of skyrmions with a layer-dependent helicity but equal topological number is still allowed. Such a magnetic configuration makes the THE electronic response possible even despite there is no global breaking of the inversion symmetry.\nFirst, I would like to point out the successful device fabrication based on originally developed methods, allowing one to access transport in metallic bilayer at different twisting angles. Second, the experimental data unambiguously reveals the twist-angle and temperature dependent humps in the Hall resistivity. This clearly indicates some reconstruction towards chiral (or even skyrmion) magnetic phases accompanied by the enhancement of the Hall effect and strongly suggests the vital role of the twisting effects for establishing magnetic order and emerging electronic responses in FGT magnetic bilayers.\nI believe that these accomplishments are solid and deserve attention of a broad audience.\nAt the same moment, there are some questions about the interpretation of the observed data and theory analysis that should be resolved before I could make any assessments on the suitability of this work for the Nature Communication.\nIn brief, the manuscript lacks an important discussion (both from experimental and theory/modelling perspectives) about the interplay between relevant spatial scales: Twisted bilayer supercell and skyrmion lattice constants. What is the relation between them? Is an effective skyrmion density, Nsk, determined by twisted bilayer Moire superlattice periodicity or by some other parameters? If the skyrmion configurations have spatial scales larger than the FGT supercell constant, does this imply that twisted Moire pattern and skyrmion lattice are incommensurate? Are the estimations of Nsk consistent for experimental data and modelling? Without this analysis, there is no accurate identification of the possible THE. I expand this question below in more detail:\n1. What are the magnitudes of AHE and THE in real units? The Hall data presented both in the main text and in supplementary is given in its normalized version. The term “giant” (or colossal) THE in the manuscript is used from a comparative perspective: THE reaches 50% of the observed AHE magnitudes. However, if a material has a weak AHE, the THE of 50% magnitude could in fact remain small.\nAnalyzing the real magnitudes of the THE is an additional tool allowing one to derive some information behind its formation. For instance, in case of magnetic multilayers hosting magnetic skyrmions, the “colossal” THE reported in [Raju, Nat.Comm. 12 2758 (2021)] emphasizes a large excess in the estimation of the effective skyrmion density from THE-measurements compared to its estimation from direct magnetic microscopy surface visualization. This extra skyrmion density can be attributed to the thermal chiral fluctuations emerging on top of the ground-state magnetic configuration, suggesting a specific microscopic mechanism behind THE.\nWhat is the situation with the actual THE magnitudes in this work? Is it possible to make an independent check if the observed THE magnitude in real units is consistent with the THE predicted from micromagnetic simulations? For instance, as a simple estimate of THE one can use R = R0 P phi0 Nsk, where R0 is the ordinary Hall effect coefficient (probably known experimentally?), P is the spin polarization, phi0 is a magnetic flux quantum and Nsk is the density of skyrmions (phi0 Nsk being the topological density). What is the corresponding Nsk (in real units) required to realize the observed THE magnitudes? How is the extracted Nsk comparable with the Moire superlattice density, is it larger or smaller? In any case, claiming the \"giant\" THE should be better justified.\n2. Furthermore, the interpretation of THE in terms of an effective magnetic field from real-space chiral spin textures (e.g. implying R = R0 P phi0 Nsk) is valid for sufficiently large-scale skyrmion configurations: It requires an electron mean free path to be much smaller than skyrmion crystal lengths. In the opposite case, the skyrmiom lattice sets the electronic superlattice minibands. Here, the situation can be even more complex as the electronic minibands should be appearing simply from a twisted Moire potential of the FGT bilayer (again, how are these two periods related?). To this end, the introduction of the electronic subbands in a twisted bilayer superlattice can be accompanied by the production of topological bands and enhanced Berry curvatures (e.g. due to topological nodal lines or Weyl points), which potentially modifies the AHE via the anomalous velocity contribution. The scenario of topological bands formation with enhanced Berry curvatures is currently well recognized in twisted TMD bilayers and its quantum anomalous Hall effect. In this regard, what are the spatial lengths of the emerging Moire structures, can the mean free path be estimated experimentally and what are the arguments allowing us to exclude the role of miniband formation for electronic transport in a twisted FGT?\n3a. What is the relation between real lattice unit supercell and the simulated skyrmion diameters in Fig.4d? Are these two scales compatible?\n3b. The presentation of the micromagnetic simulations in the main text should be improved and clarified. According to Fig4a (right side), the DMI vector rotates within a single unit supercell. However, this is not encoded in a magnetic Hamiltonian of Eq.1: Where is the explicit r-dependence of the DMI vector orientation here? The technical explanations given after Eq.1 and in the method section do not help much. Do I understand correctly that instead of evaluating spatially periodic magnetic configurations in a twisted magnetic bilayer with a r-dependent and rotating DMI vector the simulations are performed for some fixed, spatially homogeneous DMI vector and with twisting effects included only in the positions of the lattice sites of Eq.1?\nIf the obtained skyrmion configurations have spatial scales larger than a FGT supercell constant, why should we be safe with using a simplified analysis with DMI vector independent of r? In this case, I would expect the effect of the DMI vector full rotation inside a single supercell to be crucial for establishing magnetic phases.\nThe stability condition of single skyrmions in a material with constant DMI is not exactly the same as for skyrmion lattices, and is not the same when additionally embedded in a spatially inhomogeneous magnetic environment. Of course, the good agreement between modelled twisting angles and the experimental data is appealing (and even convincing), but how strongly is this result protected against skyrmion-skyrmion interactions in a real superlattice of a twisted FGT?\n4. How robust is the modelled range of twisting angles supporting magnetic skyrmions against some perturbations in the mean DMI magnitude, intra- and interlayer exchange interactions? Since the analysis does not rely on first-principles calculations, I wonder if the obtained phase diagram requires any fine tuning in the above-mentioned parameters or if it shows some stability?\nMinor questions:\n5. The line at Page 7:\n“Since the THE is observed over a continuous twist angle range rather than at the discretized “magic angles” (Fig.2c), electron-electron interaction can be excluded as the primary mechanism for the Skyrmion formation” .\nIt is not well clear what is implied, could this statement be clarified in more detail?\n6. How to control and what determines the thickness (distance between two FGT layers) of the fabricated devices?\n7. It is argued that Fig4b presents the phase diagram versus twist angle and the temperature. However, there is no temperature dependence in this diagram.\n8. It would be useful to comment more on the magnetic interactions in FGT materials and on the microscopic origins behind locally-induced DMI and interlayer exchange interaction. Does the RKKY of itinerant electrons play any role in establishing the magnetic order? Should we expect its thickness dependence?", "reviewer_4": "Review Report: NCOMMS 25-39819-T\nIntroductory comment:\nKim et al. discussed “Emergent giant topological Hall effect in twisted Fe3GeTe2 metallic system” in this article. In the article the author discussed the emergent magnetic field and topological Hall conductivity in twisted Fe3GeTe2 metallic system. They provided the 2 evidences for the presence of topological spin tetxures (1) Experimental: Topological Hall effect (2) Micromagnetic simulations.\nSince in literature now its established that topological Hall effect is not enough to show the presence of topological spin texture and often the micromagnetic simulation can be effectively used to get the desired spin textures so these two results in article are not enough to show the presence of topological spin textures. Experimentally in ordered to show the reasoning for topological Hall effect signal (additional Hall effect signal) its necessary to show the real space imaging like MFM and LTEM. As the field of Skyrmion need industrial application direct imaging is always required for topological spin texture in any new systems. Also micromagnetic simulation are not enough, these simulation can be accepted if the reasoning for spin orbit coupling in the presence non collinear magnetism is provided with some additional calculations like DFT etc. Saying broken inversion symmetry is not enough.\nSo these two evidence are not enough to show the presence of Skyrmion or other types of topological spin textures especially when there is Giant emergent magnetic field and Topological Hall effect. So, it should not be accepted as an article in Nature Communications.\nComment 1: The extra hump can be associated with two channel Hall effects or topological Hall effects. Often for Giant topological Hall effect the size of Skyrmion should be very small and density of Skyrmion should be very large. If there is no evidence of these two facts, then these giant topological Hall effects are the results of two channel Hall effects. See article “Distinguishing the Two-Component Anomalous Hall Effect from the Topological Hall Effect” Communications Materials (2022), 3, 19. Especially in Bilayer materials there is huge probability of having different switching fields. What is the proof that these two layers have the same switching fields?\nComment 2: When measuring topological Hall effect the way author did it’s always helpful to provide the magnetization data, so that the reader can compare the magnetization and understand the origin of topological Hall effect and behavior of magnetization when Skyrmion appear. The author needs to show both types of magnetization data i.e. pristine and non-pristine so that one can differentiate between two channel Hall effect and topological Hall effect. It will also help to understand whether there is any two channel Hall effect or topological Hall effect.\nComment 3: It’s very necessary to provide the real space imaging of the Skyrmions for all or different cases twisted angles to prove the presence of topological spin textures, Skyrmions and stripe domains. The author need to compare images at different field for both pristine and non-pristine samples. The real space imaging like MFM or LTEM can be enough to show the presence of a giant topological Hall effect and topological spin texture. Giant topological Hall effect will only apear when the size of skyrmion is very small and density of skyrmion is very high.\nComment 4: How did the author assume the current value of DMI constant in the articles? In micromagnetic simulation providing the DMI constant in simulations will eventually give rise to non-coplanar and non collinear spin textures. The author need to provide evidence how the spin orbit coupling originate and gives rise to DMI interaction and its zero in pristine sample. What type of DMI interaction was used in the article ? What’s the space group ?\nComment 5: What is the size of simulated Skyrmion? As the author mentioned, does it mean that 40*40-unit cell? Again, this size can be artificially changed by changing the DMI constant. So, need to provide proof of the presence of DMI by first principal calculation. As VAMPIRE is not suitable for first-principles (ab initio) calculations of the Dzyaloshinskii–Moriya interaction (DMI) constant.\nThe author need to do Density Functional Theory (DFT) (VASP, Quantum ESPRESSO, WIEN2k, OpenMX) calculations which need spin-orbit coupling and noncollinear magnetism. Or otherwise, they can provide real space imaging like MFM or LTEM for the evidence of topological nature."}, "author_response": "Responses to Reviewers’ Reports\n(Manuscript NCOMMS-25-39819-T by Hyuncheol Kim et al.)\nWe thank all four reviewers for their careful and constructive comments, which have helped us\nto improve the manuscript substantially. In response to their suggestions, we have performed\nadditional experiments, theoretical simulations, analyses, and discussions. These new results\nsignificantly improve the quality of our work, including its novelty, importance, and thorough\nunderstanding. We believe that we have thoroughly addressed all points raised by the reviewers\nin the revised manuscript and accompanying point-by-point response. We hope the revised\nmanuscript is now suitable for publication in Nature Communications.\n----------------------------------------------------------------------------------------------------------------\nDetailed responses to Reviewer #1:\nGeneral Comment: The authors discovered giant topological Hall effect in twisted FGT\nhomojunction. In addition to the twisted angle of Hall resistances, the influences of temperature\nand thickness are discussed. The atomistic spin dynamics simulations are also performed. The\nmagic angle and twisted 2D material are one of hot topics. The work is interesting. I think it is\ntimely to the scientific community. However, I have several problems before I recommend the\npublication of the present work in Nature communications.\nReply: We thank the reviewer for their careful review and their appreciation of our work\nregarding its research interest, importance and timeliness to the scientific community. In the\nfollowing pages, we carefully address your comments point by point, adding new data and\nclarifications.\nComment 1: This work lacks of the basic inputs of physical properties such as characterization\nof the quality of single crystals (XRD, EDS), measurements of longitudinal resistances (versus\ntemperature) both for isolated nanoflakes and homojunctions for different thickness.\nReply 1: Thanks for the helpful comment. We apologize for not providing these physical\nproperties of our samples in the previous manuscript. Following your suggestions, we have\nadded these results in the revised Fig. R1, which includes all the requested information: a single\ncrystal image, XRD, EDS, and typical longitudinal resistances versus temperature for both\nisolated nanoflake and homojunction. These characterizations demonstrate normal behaviors\nas reported in many previous studies. Crucially, we did not see any topological Hall effect in\nisolated nanoflakes, which has only been observed in the twisted FGT/FGT devices within the\nmagic angle region.\nWe have added related information in the revised Supplementary Information (Fig. S13 and\nSupplementary Note 3).\ncrystal, along with XRD and EDS data. b, c Temperature-dependent resistance of pristine and\ntwisted FGT samples, respectively.\nComment 2: In general, the coercive field is a bit lower compared with others. It is only less\nthan 0.1 T. What is the thickness of sample in Fig. 1? Is there still the hysteresis loop when the\nmagnetic field is directed along the in-plane direction?\nReply 2: Thanks for the comment. The thickness of the sample shown in Fig. 1f is\n2\napproximately 5.5 nm. Regarding your second question, we newly performed transport\nmeasurements with the magnetic field applied along the in-plane direction. As shown in Fig.\nR2, the FGT sample used in this work still exhibits a clear hysteresis loop when the magnetic\nfield is directed along the in-plane direction, demonstrating a normal perpendicular\nferromagnetism as reported in previous literature [Nature 563, 94 (2018); Adv. Mater. 33,\n2004110 (2021)]. The lower coercive field can be attributed to a specific Fe deficiency in our\nFe GeTe single crystals, which is consistent with a previous report [Nano Letters 20, 95\n2.89 2\n(2020)]. It ought to be noted that the topological Hall effect only emerges in the twisted\nFGT/FGT devices within the magic angle region, and has never been observed in isolated FGT\ndevices. This strongly supports our conclusion that our central finding, the topological Hall\neffect, is due to twisting, rather than the smaller coercive field.\nFig. R2 | Hysteresis loops of an isolated FGT nanoflake. a Hysteresis loop measured at 30\nK with the magnetic field applied perpendicular to the plane. b Hysteresis loop measured at 30\nK with the magnetic field applied parallel to the plane.\nIn response to the reviewer’s comment, we have added Fig. R2 and related discussions in the\nrevised Supplementary Information (Fig. S14 and Supplementary Note 4).\nComment 3: In Figure 1, the pristine FGT is just an isolated FGT or it comprises the\nhomojunction with the other piece of FGT? How do authors determine the twisted angle? Why\ndoes the peak disappear at 80 K?\nReply 3: Thanks for the comment. In Figure 1, the pristine FGT refers to an isolated FGT\nnanoflake obtained from the mechanical exfoliation process, which shows the typical behavior\nof a pristine FGT nanoflake.\nRegarding the control of the twisted angle, we utilized a combination of a high-precision\nrotation stage and the tear-and-stack method, which we developed in-house and reported\nrecently [Giung Park et al., 2D Mater. 11 025021 (2024)]. In this method, a single FGT\nnanoflake is torn into two layers—designated as the top and bottom layers—before stacking.\nThis ensures that the lattice orientations of the two layers are initially aligned. Subsequently,\n3\nby rotating one of the layers using the rotation stage, we can introduce a well-defined twist\nangle between them. Owing to the fine angular resolution of the rotation stage (as small as\n0.015°), precise control over the twist angle was achieved.\nThe topological spin texture originates from the competition among the exchange\ninteractions, uniaxial anisotropy, and the Dzyaloshinskii–Moriya interaction (DMI). When\nelectrons move around this topological spin texture, they acquire an additional phase, resulting\nin the topological Hall effect and the associated peak in the R -H curve. At higher temperatures,\nxy\nsuch as 80 K, all magnetic ground states and interactions are greatly destroyed, and so is the\nresulting topological spin texture. Consequently, the topological Hall effect and the associated\npeak disappear at high temperatures, such as 80 K.\nWe have added related discussions in the revised Supplementary Information (Supplementary\nNote 5).\nComment 4: In Figure 2, assuming that the “asymmetric humps” in resistances stem from the\ntopological spin textures, why it disappears at 20 K and is present at 60 K when the twisted\nangle is 0.75? Why it originates from skyrmion instead of others nonlinear topological\nmagnetic textures?\nReply 4: Thank you for the interesting question. As discussed in our manuscript, the formation\nof topological spin textures is governed by the interplay between magnetic anisotropy,\nexchange interaction, and the Dzyaloshinskii–Moriya interaction (DMI). At low temperatures\nsuch as 20 K in Fig.2, the ferromagnetic ground state is more stable due to the dominance of\nmagnetic anisotropy, which suppresses the emergence of topological spin textures. In such a\nregime, the DMI is typically insufficient to overcome the energy barrier required to stabilize\ntopological spin textures, thereby reducing the likelihood of observing a topological Hall effect.\nAt relatively high temperatures like 60 K, magnetic anisotropy has been reduced, and thus the\ntopological Hall effect is present due to the comparatively stronger DMI. Our magnetic simulation results further support our conclusion that a skyrmion phase becomes energetically\nfavorable at specific twist angles, forming a typical noncoplanar topological spin texture. These\nresults consistent between theory and experiments highlight the importance of both\ngeometrical and interaction-based tuning parameters in stabilizing topological spin textures in\ntwisted FGT systems.\nTogether with the above Reply 3 and Reply 4, we have added related discussions in the revised\nSupplementary Information (Supplementary Note 5).\nComment 5: Are the coercive field and remanent resistances for the different nanoflakes\nidentical at the fixed thickness? How to distinguish it if the humps in Hall resistances originate\nfrom the divergence of FGT itself instead of twisted angle in Fig. 3?\nReply 5: Thanks for the question. To address your comment more precisely, we show R -H\nxy\ncurves for two FGT nanoflakes with a similar thickness of about 6 nm in Fig. R3. The two\ndevices have similar coercive field and remnant resistance in general (but generally coercive\nfield or magnetic anisotropy is more stable than remnant resistance against sample degradation).\nIn addition, for the twisted FGT sample, we adopt the tear-and-stack method so that the twisted\nFig. R3 | Hysteresis loops of FGT nanoflakes with identical thickness. a, b Hysteresis loops\nof two FGT devices at 30 K, where the coercive field is similar for both samples, with a\nthickness of approximately 6 nm.\nMost importantly, we emphasize that the observed humps cannot originate from the\ndivergence of FGT if any, based on the following reasons. First, according to numerous FGT\nliteratures and over 100 FGT devices we measured in our lab (FGT nanotransport is a\nmandatory training for any new student joining our lab), the topological Hall effect has never\nbeen observed in pristine FGT nanoflake devices, regardless of FGT divergences, including Fe\ncompositions, FGT single crystal batches grown by different people, thickness, etc. Secondly,\nin our current work, the topological Hall effect only appears within specific magic angle\nregimes; such twisted angle dependence supports its tight relevance to twisted angle physics\nrather than trivial origins. These two experimental facts point to a nontrivial intrinsic physical\nsource to the rare case of “twisting-enabled topological Hall effect in magically twisted FGT\ndevices.”\nComment 6: For the caption of figure 4, it is atomistic spin dynamics simulations instead of\n“micromagnetic simulations”. When one talks about twisted angle, the nearest neighbor\ninterlayer exchange J would varied with the twisted angle. In addition, is there any influence\nfor the second nearest neighbor exchange for both J and D?\nReply 6: Thank you for bringing this point to our attention. We have thoroughly revised our\nsimulations, as shown in the manuscript, which includes a micromagnetic simulation. Indeed,\nas shown in Ref.[ Proc. Natl. Acad. Sci. U.S.A. 117, 10721 (2020)], in twisted moiré systems,\nthe interlayer exchange interaction varies with the twisted angle in the form of\n, where are the reciprocal vectors connecting three nearest\n𝐽𝐽( 𝑟𝑟⃗) =\nneig3hbori𝑖𝑖n𝑞𝑞⃗𝑗𝑗g( 𝜃𝜃K)⋅ 𝑟𝑟⃗points, and is a constant characterizing the interlayer exchange interaction.\n𝐽𝐽𝑡𝑡∑𝑗𝑗=1𝑒𝑒 𝑞𝑞⃗1,2,3(𝜃𝜃)\nIn this case, the interlayer exchange is maximised at AA stacking points and vanishes at AB\nstacking points. However, s𝐽𝐽i 𝑡𝑡 nce FGT is a van der Waals material whose interlayer exchange\n5\ninteraction is much weaker than the intralayer one, we can thus safely neglect the special\nvariation and approximate it with a constant value. We have checked that this approximation is\nvalid since different does not bring in any sizable quantitative difference in our result, as\nshown in the Figure below. By virtue of the same reason, the second nearest neighbor and\nare also much w𝐽𝐽e 𝑡𝑡 aker compared to the and . Consequently, to keep our model\nconcise, we only consider the necessary exchange interaction and DMI between the first\nn𝐽𝐽2\nearest\nn𝐷𝐷e 2 ighbors. 𝐽𝐽1 𝐷𝐷1\nFig. R4 | Spin configurations at different twisting angles with different interlayer\nexchange interactions. meV in the top panels (a-c) while meV in the\nbottom panels (d-f)\n𝐽𝐽𝑡𝑡 = 0.2 𝐽𝐽𝑡𝑡 = 0.1\nWe have added related discussions in the revised Main Text (Fig. 4) and Supplementary\nInformation (Fig. S12 and Supplementary Note 2).\nComment 7: In the caption of supplemental materials S1, the authors mentioned that “A few\ndroplets of PCL solution, which is made by mixing THF and PCL with a 15% mass ratio, are\ndropped onto the top of PDMS, and the PCL droplets fully cover the top of PDMS”. It seems\nto be not consistent with the main text. Does the PCL touch with scotch tape or PDMS? What\nthe role of scotch tape? During the transfer process of FGT, the PCL is just leave on top of\nFGT/BN or not? Is there any annealing process? How to separate the PCL on top of FGT and\nFGT in the homojunction？\nReply 7: Thank you for your interest in our newly developed tear-and-stack technique for\ndiverse materials, including vdW metals with strong bonds. We apologize for the confusion\ncaused by the lack of a detailed explanation in the original manuscript. Initially, the PDMS\nlayer on the slide glass is covered with transparent tape prior to the deposition of PCL droplets.\nsurface directly. The transparent tape serves two primary functions: (1) it secures the position\nof the PDMS on the slide glass, and (2) it induces curvature in the PCL film. This curvature is\nessential for the selective pickup of the target nanoflake; without it, effective detachment and\nretrieval are difficult to achieve.\nDuring the transfer process of FGT, a h-BN nanoflake is first detached from the substrate\nusing the PCL adhesive. The h-BN partially covers the target FGT nanoflake. The PCL\nadhesive cannot lift the region of FGT covered by h-BN, as the h-BN blocks direct contact and\nprevents the underlying FGT from detaching. Consequently, the bottom FGT layer remains on\nthe substrate. In contrast, the uncovered portion of the FGT nanoflake, which is in direct contact\nwith the PCL adhesive, is successfully detached. As a result, the top FGT layer and the h-BN\nflake are transferred together onto the PCL surface.\nThe top FGT layer is then aligned with the bottom FGT layer and slowly stacked to form\na homojunction. The temperature is subsequently raised above the melting point of the PCL,\nallowing the FGT homojunction to be transferred and adhered to the substrate upon removal of\nthe PCL adhesive. As a result of the melting of PCL for removal, the FGT homojunction is\ncovered with residual PCL. Residual PCL is then removed by immersing the sample in\ntetrahydrofuran for more than 10 minutes.\nIn response to this comment, we have made necessary changes to the revised Main Text (the\n4th-6th paragraphs on page 4 and the first paragraph on page 5) and Supplementary Information\n(Materials and Methods) to clarify the technical details better.\n7\n----------------------------------------------------------------------------------------------------------------\nDetailed responses to Reviewer #2:\nGeneral comment: The manuscript reports the discovery of an emergent giant THE in the\ntwisted Fe3GeTe2 metallic system. This effect manifests exclusively within a narrow window of\n“magic” twist angles ranging from 0.45 to 0.75 degrees while it is absent identically outside\nof that range, highlighting its unique and emergent nature. Micromagnetic simulations reveal\nthat this THE originates from a Skyrmion lattice induced by alternating in-plane and layer-\ncontrasting DMI that result from local inversion symmetry breaking.\nThe results are highly interesting and important, while some important information is lacking\nin text as follows. I recommend after revision of these issues.\nReply: Thank you for the careful review of our manuscript and the encouraging comments. We\nare pleased to learn that the reviewer finds our work highly interesting and important. As\ndetailed in the next pages, we address your comments and add the lacking information with\ndue respect.\nComment 1: There are no sample images for single and integrated thin layers; e.g., cross-\nsectional AFM images to confirm FGT thickness. In particular, the authors present thickness\ndependence in Fig.3 and compare between 6nm and 10nm. It may be difficult to fabricate each\ntwo uniform flakes with 6nm thickness and 10 nm thickness, and integrate within this narrow\nangle. Thus, the information for upper and lower FGT layers is indispensable.\nReply 1: Thanks for the comment. We agree with the reviewer that it is indeed not easy to\nfabricate the thin twisted FGT devices, whose experimental obstacles have been eventually\nresolved by developing the powerful new “tear-and-stack” method for the present manuscript.\nFor the sample image and thickness information, we have now included them in the\nSupplementary Information. Please see an example in Fig. R5.\nFig. R5 | Hysteresis loops of twisted FGT/FGT homostructures with different thicknesses.\n8\na, b Optical images of twisted FGT/FGT homostructures with FGT thickness of (a) 6 nm and\n(b) 10 nm. Both devices share the same twisted angle of 0.75°. c, d AFM height profiles\nconfirming the thickness of the corresponding devices. e, f Hysteresis loops of the two twisted\nFGT/FGT homostructures, where the thinner device exhibits a larger topological Hall effect.\nIn addition, we want to emphasize the importance of technical development in our present work:\nOur new “tear-and-stack” method enables both handling vdW materials with strong bonds and\nfabricating twisting devices from the same single piece of nanoflake, naturally enhancing the\nuniformity of sample properties and characteristics. Therefore, this concern from the reviewer\ncan be better relieved.\nComment 2: For T dependence shown in Fig.2c, THE peak ratio is the highest around 50K.\nWhy is this? Conventionally, THE is stronger at lower T. The authors argue that “thermal\nagitations at high T effectively reduce the uniaxial anisotropy, potentially enhancing the\ntopological Hall effect and broadening the range for the Skyrmion formation”. But there is no\nsuch evidence.\nReply 2: Thank you for the valuable comment. The reviewer is correct that the topological\nHall effect (THE) is often more pronounced at lower temperatures. However, there are notable\nexceptions in which THE becomes stronger at elevated temperatures, depending on the material\nsystem. One such example is the α-phase of MnSi. As shown in Fig. 2 and Fig. 3 of [Phys. Rev.\nLett. 102, 186602 (2009)], the magnitude of THE in MnSi increases slightly with temperature\nwithin a certain range. Furthermore, Fig. 4 of the same work demonstrates that the temperature\nwindow over which the α-phase exhibits a topological Hall signal becomes broader at higher\ntemperatures.\nThese observations suggest that the temperature dependence of THE is highly material-\nspecific and can be influenced by several factors such as magnetic anisotropy, exchange\ninteractions, and thermal stability of the topological spin textures. In our study, the twisted FGT\nsystem exhibits a similar trend to MnSi, where the THE becomes more prominent at slightly\nhigher temperatures, reinforcing the idea that this behavior is not universal but rather material-\ndependent.\nIn particular for twisted FGT, the formation of topological spin textures is governed by\nthe interplay between magnetic anisotropy, exchange interaction, and the Dzyaloshinskii–\nMoriya interaction (DMI). When electrons move around this topological spin texture, they\nacquire an additional phase, leading to the topological Hall effect.\nIt is well known that the magnetic anisotropy of ferromagnet FGT is large at low\ntemperatures but decreases with rising temperature. At low temperatures, the ferromagnetic\nground state of FGT is more stable due to the dominance of strong magnetic anisotropy, which\nsuppresses the emergence of topological spin textures. In such a regime, the DMI is typically\ninsufficient to overcome the energy barrier required to stabilize topological spin textures,\nthereby reducing the likelihood of observing a topological Hall effect. At relatively high\ntemperatures, magnetic anisotropy has been reduced, and thus the topological Hall effect is\npresent due to the comparatively stronger DMI. Our magnetic simulation results further support\nthis picture, indicating that skyrmion formation becomes energetically favorable at specific\ntwist angles, which highlights the importance of competitive magnetic interactions at play.\nThese consistent results between theory and experiments highlight the importance of both\n9\ngeometrical and interaction-based tuning parameters in stabilizing topological spin textures in\ntwisted FGT systems.\nWe have added related discussions on such temperature dependence in the revised\nSupplementary Information (Supplementary Note 5).\nComment 3: I cannot understand the origin of TH hump and its correlation to Skyrmion. The\nsimulation result actually shows the appearance of Skyrmion around the 0.6 degree-twist angle,\nwhile it is not clear how the Skyrmion forms the TH hump.\nReply 3: We appreciate the reviewer's insightful comment. The articles [Rev. Mod. Phys. 82,\n1539 (2010); Rev. Mod. Phys. 97, 031001 (2025)"}]

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