Polarity-tunable field-free room-temperature spin orbit torque switching via topological symmetry breaking in an all-vdW heterostructure for spin logic applications

Domain: chemistry
Published: 2026-03-12
Editorial outcome: minor_revision

Abstract
Two-dimensional ferromagnetic materials hold great promise for advancing low-power, high-integrated spintronic devices due to their atomic flat surfaces and versatile interfacial modulation. However, achieving a combination of room-temperature, field-free spin-orbit torque switching with tunable polarity in wafer-scale vdW heterostructures remain a significant challenge. Here, we demonstrate polarity-tunable, field-free spin-orbit torque switching in an all-vdW Bi2Te3/Fe4GeTe2 heterostructure, grown by molecular beam epitaxy. Interfacial coupling induces perpendicular magnetic anisotropy in Bi2Te3/Fe4GeTe2 interface, while the rest in-plane magnetic anisotropy component of Fe4GeTe2 breaks the inversion symmetry, enabling field-free switching. By modulating the direction of in-plane component, magnetic switching with different polarity could be achieved at low current density (~1.55×106 A/cm2). This allows for 16 reconfigurable Boolean logic functions in a single device, paving a pathway for energy-efficient 2D spintronic memory and logic systems. Our findings highlight the potential of all-vdW spin-orbit torque devices to revolutionize spintronics with scalable, room-temperature electronic control.

Introduction
The emergence of spin-orbit torque (SOT) devices offers a transformative platform for constructing energy-efficient, high speed, and non-volatile memory and logic systems, addressing the growing demands of modern information technology1-4. To enhance the performance of SOT spintronic devices, researchers have conducted extensive investigations based on heavy metals and conventional ferromagnetic material systems5-7. However, the difficulty in achieving smooth interface roughness with traditional materials results in SOT heterostructures exhibiting low spin transparency, which subsequently impacts the power consumption of SOT devices. Recently, the utilization of all-van der Waals (vdW) heterostructures has been regarded as a promising avenue to overcome the bottlenecks of power consumption and physical size limitations in integrated circuits, owing to their significant improvements in device integration and spin transparency at the interfaces8-14, including demonstrations in Bi2Te3/Fe3GeTe2 heterostructure15, (Bi,Sb)2Te3/Fe3GeTe2 heterostructure16, etc. However, an external magnetic field is still needed to break symmetry for deterministic switching, which hinders the integration of SOT devices on semiconductor chips. Therefore, the exploration of all-vdW field-free SOT heterostructures holds significant importance for further improving the performance of SOT devices and advancing their applications.

Recent studies have demonstrated field-free switching using various methods, including asymmetric wedge structures17,18, out-of-plane spin currents19, exchange bias20-22, and tilted magnetic anisotropy23. Within all-vdW structures, researchers have combined the unique vdW material WTe2, which exhibits out-of-plane spin currents, with exfoliated vdW ferromagnetic materials Fe3GeTe2, successfully achieving field-free switching24. Later, by mechanically exfoliating Fe3GaTe2 25and pairing it with WTe2 26 and TaIrTe4 27, researchers have fabricated heterostructures that enable deterministic field-free switching at room temperature. However, these material systems may face limitations in achieving wafer-scale fabrication of all-vdW structures, which hinders their potential for large-scale applications. Furthermore, these approaches primarily focus on realizing field-free switching through specialized SOT sources, while overlooking the critical role of the ferromagnetic layer in this process. This oversight further diminishes the scalability of SOT spintronic devices.

Previous studies have demonstrated that combining two magnetic layers, PMA and IMA, not only enables the IMA layer to provide an in-plane effective field to assist switching but also allows for further control over the polarity of field-free switching. The tunable polarity of field-free switching, as it enables the realization of complete spin logic within a single nonvolatile memory, holds significant promise in application of spin logic devices28. Therefore, integrating magnetic layers with PMA and IMA into a heterostructure, while ensuring the moderate coupling between the two layers, is crucial for enabling logic functionalities in SOT spintronic devices. In conventional materials, an interlayer with precisely controlled thickness must be inserted between the IMA and PMA layer to ensure that both maintain their magnetic anisotropy29. However, the naturally present vdW gap between monolayers inherently resolved this issue for vdW material systems. Moreover, one of the key features of 2D vdW ferromagnetic materials is that their magnetic properties can be easily modulated through applying external physical fields30.

Research has shown that interface engineering can modulate the Curie temperature and magnetic anisotropy of two-dimensional magnetic materials12,31-33. Therefore, it paves a fascinating and convenient way to construct the IMA and PMA coexisted 2D vdW ferromagnet through interface engineering for achieving polarity-tunable and field-free SOT switching12,34. Notably, unlike Fe3GeTe2 15, Fe4GeTe2 exhibits a uniquely tunable magnetic anisotropy35, enabling the coexistence of PMA and IMA within a single layer. This PMA–IMA coexistence gives rise to an internal symmetry-breaking exchange field, eliminating the need for any external in-plane magnetic field. However, such all-vdW structure has not yet been reported, and SOT devices based on this system hold significant potential for realizing low-power, highly integrated spin logic devices.

Here, we report the polarity-tunable field-free SOT-driven magnetic switching at room temperature in a wafer-scale all-vdW Bi2Te3/Fe4GeTe2 heterostructure grown by MBE. The magnetic behavior of the heterostructure could be deconvoluted into the coexistence of IMA and PMA component, in which the IMA component provides an equivalent assisting field for field-free switching. More importantly, the polarity in field-free SOT switching can be flexibly manipulated by modulating the unidirectional IMA layer with a low switching current density of ~1.55×106 A/cm2 at 300 K. The PMA in Fe4GeTe2 was confirmed from the interfacial coupling with the Bi2Te3, while the IMA was from its intristinc anisotropy. Micromagnetic simulations revealed the magneto dynamics process of polarity-controlled SOT switching. Subsequently, based on the device characteristics, we demonstrate 16 reconfigurable Boolean logic functions in a single device. Our results open a new way for the construction of field-free and polarity-controlled all-vdW SOT devices at room temperature and promote the development of 2D spintronic memory and spin logic for practical applications.

Results
In this study, we employed molecular beam epitaxy (MBE) to grow thin films on (0001) sapphire substrates, utilizing reflection high-energy electron diffraction (RHEED) for in situ monitoring during the growth process. The result of X-ray diffraction (XRD) confirmed the high-quality single-crystal character of Bi2Te3(12)/Fe4GeTe2(4) heterostructures shown in Supplementary Fig. S1, in which the number represents the film thickness with unit of nm. The high-angle annular dark field (HAADF) cross-section image in the inset (left) in Fig. 1a distinctly delineates two regions: Bi2Te3 and Fe4GeTe2, with evident a clean interface with no inter-diffusion between the layers and no secondary phases are detected36. Figure 1b presents a typical VSM measurement of M as a function of the out-of-plane (OOP) magnetic field. The sharp reversal and hysteretic behavior observed around μ0Hz = 0 are indicative of the PMA component. The increase in M at higher field suggests a gradual transition of magnetization from in-plane (IP) to OOP orientation, affirming the presence of an IMA component. This M-H loop distinctly demonstrates the coexistence of both IMA and PMA components within the Fe4GeTe2 layer37. The M-H curve can be decomposed into a hysteresis loop attributable to Fe4GeTe2 (PMA, adjacent to Bi2Te3) and a hard axis loop corresponding to Fe4GeTe2 (IMA, away from Bi2Te3), as shown in the inset. In contrast, the Fe4GeTe2 film, shown in Supplementary Fig. S2, exhibits only IMA at 300 K. Hall bar devices were fabricated using standard photolithography and ion beam etching, with dimensions of 100 μm (length) × 16 μm (width), as shown in Fig. 1c, where Vxx and Vxy represent the longitudinal voltage and Hall voltage, respectively.

The Rxx-T curve for the Bi2Te3(12)/Fe4GeTe2(4) device, shown in Fig. 1a, demonstrates a metallic behavior. As comparison, 12 nm Bi2Te3 was also grown on a sapphire substrate, and the magnetotransport results, shown in Supplementary Fig. S3, reveal that the Hall resistance exhibits a negative slope under an out-of-plane magnetic field, confirming the n-type Bi2Te3. To elucidate the magnetic properties of the heterostructure, temperature-dependent magnetic transport measurements are conducted. Figure 1d illustrates the anomalous Hall resistance (Rxy) curves of the Bi2Te3(12)/Fe4GeTe2(4) heterostructure with an out-of-plane magnetic field from 100 K to 300 K. Throughout the entire temperature range, the Rxy measurements yielded hysteresis loops with pronounced remanence and relatively sharp switching, and they reach saturation under modest perpendicular magnetic fields. These features clearly indicate the presence of regions where the magnetization vector is perpendicular to the film plane, meaning the existence of components with strong PMA38. Temperature dependence of normalized remnant Rxy and coercivity of Bi2Te3/Fe4GeTe2, shown in Fig. 1e, the ordinary Hall resistance have been deducted, reveals that both the remnant Rxy and Rcoercivity decrease with increasing temperature. Unlike previously reported IMA in pure Fe4GeTe2 at room temperature, the heterostructure maintains notable PMA feature at room temperature, retaining approximately 70% remnant Rxy and a coercivity of 140 Oe at 300 K. Figure 1f shows the hysteresis loop of Bi2Te3/Fe4GeTe2 with in-plane magnetic field from 150 K to 300 K, which confirms its strong PMA characteristic. Leveraging these distinguished properties, we will conduct room-temperature spin-orbit torque-driven magnetic moment switching based on this material system.

The SOT-driven measurement was conducted in above heterostructures, and a schematic diagram of the dynamics in SOT-driven magnetic switching is illustrated in Fig. 2a. When a writing current (Iwrite) is applied to the Bi2Te3 layer, a spin current is generated, which propagates perpendicularly to the direction of the applied current and is subsequently injected into the adjacent Fe4GeTe2 layer. Once the injected spin current exceeds a critical writing current density, it induces the switching of the magnetization (M) within the Fe4GeTe2 layer through SOT. Here, the writing current density can be defined as 𝐽 = 𝐼 /[𝑤 ∗ (𝑡 +𝑡 )], where 𝑤 =16 μm is the width of the Hall bar, t and t is the thickness of Bi2Te3 and Fe4GeTe2, respectively. The magnetization of the Fe4GeTe2 layer can tilt up or down under the effective spin-orbit field induced by spin current, generating positive or negative Z components (Mz). For PMA samples with predominantly out-of-plane magnetic components, an additional external magnetic field along the x-axis is required during the measurement process to break symmetry and enable deterministic SOT switching. Therefore, the magnetization switching could be achieved in the Fe4GeTe2 by the charge-spin conversion induced SOT from the current applied in Bi2Te3 with an external x-axis magnetic field.

To investigate the SOT switching in the Bi2Te3/Fe4GeTe2 heterostructure, we applied a series of magnetic fields along the long axis of the Hall bar at different temperatures with a 1 ms pulse writing current. A small sensing current was applied after each pulse writing current to detect the magnetization state via Rxy. Here, we define the critical current as the sign of Rxy changes. This switching behavior is robust at low temperature, as shown in Supplementary Fig. S4. The critical current of SOT switching as a function of applied external magnetic field at 250 K are shown in Fig. 2b. The formula for the critical currents under different external magnetic fields is expressed as39:

𝐼 = (𝑒𝑡 𝑀 𝑆 / 𝜂ℏ𝜃 ) (𝐻 −√2𝐻 ) (1)
𝑤𝑟𝑖𝑡𝑒 𝐹 𝑆 𝐶 𝑆𝐻 𝑥 𝐾,𝑒𝑓𝑓

where 𝑒 represents the elementary charge, 𝜂 represents the shunt coefficient,ℏ is the reduced Planck constant, 𝜃 refers to the spin Hall angle, 𝑆 indicates the cross-sectional area, 𝐻 is the applied external magnetic field and 𝑀 , 𝑡 , and 𝐻 correspond to the saturation magnetization, thickness, and effective anisotropy field of the ferromagnetic layer, respectively. It can be seen that as the external magnetic field increases, the critical current required for switching gradually decreases, as shown in Fig. 2b, which perfectly follows the formular.

To quantitatively evaluate the efficiency of the SOT, harmonic Hall measurements were subsequently performed on the Bi2Te3/Fe4GeTe2 heterostructure at various temperatures, and the results are shown in Fig. S5. A small alternating current was applied along the x-axis to the device, and in the measurement, the frequency is fixed at 133.33 Hz through the lock-in amplification. The alternating effective field generated by SOT can generate magnetization oscillations around the equilibrium position, so we can get the first and second harmonic signals. The second-harmonic Hall resistance (𝑅2𝜔) was analyzed and the 𝐻 was extracted using the following formula40：

𝑅2𝜔 = 𝑅2𝜔 +𝑅2𝜔 +𝑅 𝑥 +𝑅
𝑥𝑦 𝐴𝐻𝐸 𝑃𝐻𝐸 𝐴𝑁𝐸|𝐻 | 𝑜𝑓𝑓𝑠𝑒𝑡

𝑅2𝜔 = (𝑅 𝐻 𝐻 / |𝐻 |−𝐻 ) +𝑅 𝐻 +𝑅 𝐻 +𝑅 (2)
𝑥𝑦 𝐴 𝐷𝐿 𝐹𝐿 𝑥 𝑘 𝑥 𝑝|𝐻 | 𝐴𝑁𝐸|𝐻 | 𝑜𝑓𝑓𝑠𝑒𝑡

where 𝐻 and 𝐻 represent the damping-like effective field (∝ 𝑚×𝜎) and the field-like effective field (∝ 𝜎), respectively. 𝑅 and 𝑅 refer to the planar Hall resistance and anomalous Hall resistance, respectively, while 𝑅 indicates the resistance offset. 𝑅 is the transverse resistance arising from the anomalous Nernst effect and other spin-related thermoelectric effects. The damping-like effective term decreases as the external field increases. In contrast, the thermal-related term reverses its sign when the direction of the external field changes, but its magnitude remains constant. Typically, 𝑅 is significantly smaller than its anomalous Hall counterpart, which means that 𝑅2𝜔 primarily originates from the damping-like effective field term and the thermal effect term. Here, we define 𝑅 = (𝑅 − 𝑅 )/2 to represent the thermal contribution, where 𝑅 and 𝑅 correspond to the maximum and minimum values of the second-harmonic Hall resistance under a saturated magnetic field. Based on above analysis, we extracted 𝐻 and displayed its dependence on current at 300 K in Fig. 2c. The SOT efficiency (𝜉 ) can be obtained using the following formula41:

𝜉 = (2𝑒𝑡 𝑀 𝑆 𝐻 ) / (ℏ 𝜂𝐼 )
𝐷𝐿 𝐹 𝑆 𝐶 𝐷𝐿 𝑤𝑟𝑖𝑡𝑒 (3)

Accordingly, taking into account the 28% current shunting in the Bi2Te3 layer (Fig. S3), the value of the 𝜉 is determined to be ~0.8 in Bi2Te3(12)/Fe4GeTe2(4) heterostructure at 300 K, demonstrating a superior charge-spin conversion in all-vdW heterostructure.

Room-temperature SOT-induced magnetic switching is critical for the potential application. Hence, the current-driven variations of Rxy under an external magnetic field H along the x-axis are shown in Figs. 2d and 2e, where the Hx alternates with the sequence from positive to negative and negative back to positive, respectively. As the applied write current sweeps from positive to negative, obvious magnetization switching behavior of Fe4GeTe2 could be observed, and the polarity of deterministic switching is significantly affected by the direction of the in-plane external field. Notably, the switching amplitude varies with the applied in-plane field. The maximum switching ratios, calculated from the data in Figs. 2d and 2e, are approximately 22% for field-assisted switching and 16.8% for field-free switching. These values are consistent with reported SOT efficiencies in other two-dimensional magnetic systems (e.g., ~20%42) and reflect the practical challenge of achieving full magnetization reversal in the two-dimensional limit. Interestingly, careful examination could find that field-free switching could be achieved with its polarity adjusted by the sequence of the external field. For instance, as the external field was applied from positive to negative, as shown in Fig. 2d, the switching shows a Up to Down polarity at positive external field. When the applied field decreases to 0, the polarity of field-free switching maintains the same characteristic as the initial condition and does not change with the applied field reversed to a relatively small value. However, when the magnetic field exceeds a certain threshold, the switching polarity of the device changes, becoming dominated by the direction of the external field. Vice versa, a Down to Up polarity field-free switching was observed, when the applied field was applied from negative to positive, as shown in Fig. 2e. Such polarity-tunable field-free switching behavior may arise from the unique magnetic configuration combing both IMA and PMA components together in the heterostructure. The IMA component breaks the symmetry during the switching process, which facilitates the field-free switching. In addition, it could be calculated that the critical switching current density in the Bi2Te3/Fe4GeTe2 at 300 K is ~1.55×106 A/cm2, which is significantly smaller than that in the FGT/Pt heterostructure42, and it corroborates the high charge-spin conversion efficiency in TI non-trivial origin and the high-quality interfaces of our sample15. Figure 2f further elaborates on polarity-tunable field-free switching observed at different temperatures (250 K, 270 K, 280 K and 300 K), showcasing the device’s ability to switch magnetization without an external magnetic field.

Research in the previous section has confirmed that the polarity of field-free switching in the Bi2Te3/Fe4GeTe2 heterostructure is determined by the direction of the initially applied in-plane magnetic field. To further explore the effects of the direction and magnitude of this preset field (Hpre) on field-free SOT switching, the pulse current was applied under zero field condition following initialization with different Hpre values and the switching behaviors are shown in Fig. 3a. To prevent any remanent magnetic field effects, the sample was physically removed from the magnet for each field-free measurement. The results demonstrate that field-free switching cannot be achieved without the initialization provided by the preset magnetic field. Specifically, in the absence of a preset magnetic field, the device resistance remains largely unchanged even as the write current increases, indicating the absence of deterministic magnetization switching. However, when the preset field reaches 0.5 T, distinct field-free switching is observed. Furthermore, as the preset field is progressively increased to 1 T, 1.5 T, and 2 T, the switching polarity remains unchanged. Critically, when the direction of the preset field is reversed (e.g., increased to -0.5 T), the switching polarity also reverses. Similarly, increasing the magnitude of the negative preset field does not alter this reversed switching polarity. Therefore, the preset magnetic field not only enables field-free switching but also controls its polarity. Furthermore, the switching amplitude after applying a +2 T preset magnetic field is slightly smaller than that after a –2 T preset field, a phenomenon observed at both 250 K and 270 K (Fig. S6). The underlying mechanism of this phenomenon lies in the difference in the magnitude of the interlayer exchange coupling field under the two opposite preset field directions. This difference originates from the canted layers situated between our PMA and IMA components that are insensitive to the in-plane magnetic field and their orientation is defined by the out-of-plane magnetic field. To clarify this, we performed comparative experiments, and the results are shown in Fig. S7.

To further investigate the effect of the preset field on SOT switching amplitude, we performed field-free magnetization switching under different preset fields at 250 K, 270 K, and 300 K, and the results are shown in Fig. 3b. At room temperature, the switching amplitude under a -2T preset field increases 2 times compared to that at -0.5 T preset field. And, this trend was maintained in other temperatures. To further examine the effect of higher preset field on switching behavior, we performed SOT switching at 250 K with the preset field of -2 T and -3 T, and the results are shown in Fig. 3c. It is noteworthy that the shape of the magnetization reversal curves is nearly identical under both conditions, indicating that once the preset field exceeds a critical threshold, additional increases have negligible impact on the switching window. The summary results of the switching amplitude are shown in Fig. 3d, clearly demonstrating the switching amplitude kept enlarging with higher preset field across different temperatures. We summarized the switching ratio (Rswitch/RAHE) versus preset magnetic field at 300 K, as shown in Fig. S8. According to calculations, the switching ratio increases with increasing preset in-plane magnetic field and the maximum value of the switching ratio is around 25% at 300 K. Additionally, to evaluate the device's resilience to external perturbations, reverse magnetic fields were applied after establishing the preset field. Figure 3e demonstrates that as the reverse magnetic field increases, the switching window progressively narrows and ultimately disappears at 0.6T. This highlights the excellent anti-interference capability of the preset-field-induced magnetic state, reinforcing the critical role of the preset field in enabling stable, field-free switching.

As mentioned above, the magnetic behavior of the Bi2Te3(12)/Fe4GeTe2(4) heterostructure exhibited coexistence of IMA and PMA components. To understand such fascinating phenomena, different layer configurations: Fe4GeTe2(4), Bi2Te3(8)/Fe4GeTe2(4), and Bi2Te3(12)/Fe4GeTe2(6) were fabricated, and anomalous Hall resistance measurements were performed for magnetic analysis. Figure 4a shows the results of 4 nm Fe4GeTe2, which exhibits a temperature-dependent transition from PMA to IMA with increasing temperature, consistent with previous reports31. In contrast, the Bi2Te3(8)/Fe4GeTe2(4), as shown in Fig. 4b, maintain the same strong PMA characteristics across all temperatures as Bi2Te3(12)/Fe4GeTe2(4) heterostructures in Fig. 1d, which highlights the effect of Bi2Te3 for enhancing the PMA property in Fe4GeTe2. Furthermore, when the Fe4GeTe2 layer is thickened (Bi2Te3(12)/Fe4GeTe2(6)), the anisotropy gradually shifts towards IMA, indicating a weakening of the PMA, as shown in Fig. 4c. In addition, as shown in Fig. S9, the results from the X-ray Magnetic Resonance Reflectivity (XRMR) measurements indicate that the distribution of IMA and PMA is related to the distance from Bi2Te3, specifically their spatial distribution along the Z-axis. The possibility that the observed magnetic behavior originates from the Bi2Te3 layer is ruled out. Fe doping into Bi2Te3 has been reported to induce only weak ferromagnetism below 14 K, with no observable magnetic order at room temperature43. Regarding the proximity effect, previous study indicates that the resulting Curie temperatures are typically very low44. Even in the limited number of reports claiming a Curie temperature near 300 K45, the induced magnetic moment remains orders of magnitude smaller than that of intrinsic magnetic materials. Therefore, neither Fe doping nor proximity-induced magnetism in Bi2Te3 can account for the room-temperature, robust magnetic anisotropy in this work. These observations strongly suggest that the topological insulator interface contributes to the enhancement of PMA in Fe4GeTe2 itself, giving rise to the coexistence of PMA and IMA components with no evidence of measurable magnetic contribution from the Bi2Te3 layer. It has been reported that the PMA of magnetic films containing iron atoms such as Y3Fe5O12 and Tm3Fe5O12, can be greatly strengthened by the adjacent TI layer46,47. These changes are due to the topological surface states (TSS), which can strengthen exchange coupling between Fe ions. Furthermore, theoretical calculations show that modifying the chemical potential of topological insulators can effectively tune the magnetic anisotropy of ferromagnets48. For our experiments we propose that the enhanced PMA may originate from the strengthened exchange coupling between Fe ions in Fe4GeTe2 mediated by the TSS electrons of the Bi2Te3. As shown in Fig. S10, we have also ruled out the influence of strain on the magnetic anisotropy of Fe4GeTe2 49.

Subsequently, we conducted micromagnetic simulations to reveal the dynamics of the polarity-tunable field-free switching, and these simulations were performed using Mumax3. The above results indicate that Bi2Te3 introduced a PMA component into Fe4GeTe2 at 300 K. In addition, it was noted earlier that the Fe4GeTe2 layer in the heterostructure contains both IMA and PMA components at this temperature. Therefore, we constructed a three-layer magnetic model to simulate the magnetic distribution of the experimental samples, as shown in Fig. 4d. Due to interfacial engineering, the layer adjacent to the topological insulator exhibits dominant PMA, while the top layer transitions into IMA.

Based on this model, the IMA layer serves as a symmetry-breaking element required for deterministic switching of the PMA layer through interlayer exchange coupling50, while the direction of the in-plane magnetic anisotropy determines the polarity of the field-free switching. As shown in Fig. 4e, we initially set the magnetization of the IMA layer by applying an external in-plane magnetic field in two opposite directions. Following the removal of this field, current-induced switching measurements revealed distinct hysteresis loops, indicating two opposing polarities depending on the initial magnetization state. The important switching points during field-free switching under initial positive and negative 1 T preset magnetic field are marked in the figure, where TA and TE represent the starting and ending points, corresponding to the positions of the maximum positive pulse current, TB and TD represent the magnetic moment switching points, while TC corresponds to the maximum negative pulse current. The magnetic moment schematics of the three important switching points during field-free switching (TA, TC and TE) are shown in Fig. S11. We observe that when the magnetization direction of the in-plane layer is reversed, the polarity of the PMA layer, which is the main source of the anomalous Hall resistance, also reverses under the same current polarity. This demonstrates that the effective field generated by the multilayer magnetic structure itself is the origin of the polarity-tunable field-free switching. In addition, the inset of Fig. 4e shows field-free switching after applying 0.5 T and 1 T preset magnetic fields, and a comparison of the two curves shows that the switching amplitude increases with increasing preset magnetic field. This may be due to the fact that the in-plane magnetic moments of the ferromagnetic layers become more homogeneous as the preset magnetic field increases, resulting in an increase in the strength of the interlayer exchange coupling and hence a larger equivalent field. Fig. 4f displays the time-resolved evolution of the in-plane magnetization component throughout the magnetization switching process, the Mx under a -1 T preset magnetic field exhibits a marked enhancement compared to the -0.5 T condition, thereby generating a stronger equivalent field to facilitate magnetization switching. In addition, the results reveal that the applied pulse current is insufficient to change the polarity of the in-plane magnetization component, allowing the in-plane layer to stably provide an effective field that facilitates field-free switching.

Reconfigurable logic design offers advantages such as enhanced hardware resource utilization, reduced transistor resource consumption, and more. Below, we demonstrate the implementation of 16 reconfigurable Boolean logic functions in a single Bi2Te3/Fe4GeTe2 heterostructure device. In this scheme, the preset magnetic field and input currents are defined as binary logic inputs. The magnetization strength of Fe4GeTe2 during the writing process is characterized by different magnetic moment states, and the final output is represented by the anomalous Hall voltage. High and low voltages correspond to logical outputs "1" and "0", respectively.

The device structure is shown in Fig. 5a. Owing to the interfacial engineering, the Fe4GeTe2 layer adjacent to Bi2Te3 exhibits PMA properties (lower Fe4GeTe2), while the other layers maintain IMA properties (upper Fe4GeTe2).

The device operates with four binary inputs: one preset magnetic field (H) and three input currents (IA, IB, IC) applied along the x-direction. The logic output "L" is determined by the anomalous Hall voltage. As shown in Fig. 5b, each input can assume only two distinct states, representing the binary logic values "0" and "1", with the specific configuration for the NAND function indicated in parentheses. It should be noted that the absolute values of current IA and the sum of currents IB and IC are each 15 mA. This current magnitude is chosen to ensure the switching of the PMA components in Fe4GeTe2.

Figure 5c illustrates the entire process of the NAND logic operation in the device for different inputs. As shown in Fig. 5b, four distinct states are involved in one logic operation and the inputs H, A(IA), B(IB), and C(IC) are set to "1", "p", "q", and "0", respectively. In this setup, "p" and "q" represent two input variables of the Boolean logic gates (each being "0" or "1") for the logic operation, while H and C are held constant at "1" and "0", respectively. Specifically, in the initial state, the Fe4GeTe2 magnetization is uncertain, with the upper Fe4GeTe2 magnetic moment along either the +x or -x direction, and the lower Fe4GeTe2 magnetic moment oriented along either the +z or -z direction. In the second state (step 1), when a 1 T magnetic field of H (H=1) is applied along the +x axis, the upper Fe4GeTe2 magnetization is set to +x direction, following the Up to Down polarity of field-free SOT switching. Thus, in the third state (step 2), when IA is set to −15 mA (A = p= 0), the magnetization is aligned along the +z direction, corresponding to logic output L = 1. Conversely, when IA is set to +15 mA (A = p= 1), the magnetization is directed towards the -z direction, resulting in a logic output L = 0. In the fourth state (step3), IB and IC are applied simultaneously. Since IC is fixed at -7 mA (C = 0) in the NAND logic function, the total current applied in the third step is −15 mA (with B = q= 0) or 1 mA (with B = q = 1). For the -15 mA (B = q= 0, C = 0) case, the magnetization is switched to the +z direction, giving Boolean results of p = 0, q = 0, L = 1 and p = 1, q = 0, L = 1, as shown in the first and third columns of Fig. 5c. For the 1 mA (B = q= 1, C = 0) case, the magnetization remains aligned as in the third state (step 2), because the current is insufficient to switch the magnetization. Thus, it will give Boolean results of p = 0, q = 1, L = 1 and p = 1, q = 1, L = 0, as shown in the second and fourth columns of Fig. 5c. The implementation of the remaining 15 Boolean logic functions is depicted in Supplementary Fig. S13–S17.

In summary, the single Bi2Te3/Fe4GeTe2 device is capable of implementing the complete set of 16 Boolean logic functions. This is achieved by systematically varying the input preset magnetic field H and the three input currents IA, IB, and IC in three sequential steps. The ability to fully control spin logic electrically within a single nonvolatile memory device paves the way for energy-efficient, compact, and adaptable spintronic devices.

In conclusion, we have successfully fabricated wafer-scale vdW Bi2Te3/Fe4GeTe2 heterostructure by MBE and achieved polarity-tunable field-free current-driven SOT switching at room temperature. With an exceptionally high SOT efficiency of ~0.8 at 300 K, Bi2Te3 enables highly energy-efficient magnetic switching, achieving a critical switching current density as low as ~1.55 × 106 A/cm2 in the Bi2Te3/Fe4GeTe2 heterostructure. Through interfacial exchange coupling effect between Bi2Te3 and Fe4GeTe2, the ferromagnet layer shows both IMA and PMA components, leading to controllable magnetic switching polarity depending on direction of the IMA component. In addition, the effect of preset magnetic field on field-free switching is experimentally demonstrated and verified by micromagnetic simulations. Based on the device characteristics, we demonstrate the practical application of polarity-controlled switching by realizing 16 reconfigurable Boolean logic functions in a single device. Our results provide the feasibility for the construction of all-electric, room-temperature vdW SOT devices and promote the development of 2D spintronic memory and spin logic system for future practical applications.

Methods
Sample growth
The samples were prepared by MBE system, and the films were grown on (0001) sapphire substrates. The substrates were annealed at 600 °C for 1 h prior to growth to obtain a clean surface, followed by cooling to 220 ℃. High-purity Bi, Fe, Ge, and Te were evaporated from standard Knudsen cells, and the growth rate was ~3 nm/min. Crystal quality was monitored in situ by RHEED during growth. After growth, Te was deposited on the films as the protection layer.

Crystal characterizations
The phase and crystal structure characterization of Bi2Te3/Fe4GeTe2 heterostructure were characterised by XRD and TEM. XRD analysis was performed using a PANalytical X’Pert PRO MRD diffractometer equipped with Cu Kα radiation. Cross-section TEM sample prepared by focused ion beam, then a JEOL-ARM 200 F Cold Field Emission Gun TEM was employed to examine the atomic structure of the samples.

Electrical measurements.
Hall bar devices were fabricated by standard lithography and ion beam etching, achieving Hall bar dimensions of 100 μm (length) × 16 μm (width). The electrical measurements were carried out in Cryogenic physical property measurement system.

Data availability
The data that support the findings of this study are provided in the paper and Supplementary Information file. Additional data related to this study are available from the corresponding author upon reasonable request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript presents an experimental demonstration of field-free spin-orbit torque (SOT) switching in an epitaxial Bi₂Te₃/Fe₄GeTe₂ van der Waals heterostructure. The authors achieve deterministic SOT switching at room temperature and demonstrate its potential for reconfigurable spin logic applications. The key innovation here is the wafer-scale epitaxial growth of Bi₂Te₃/Fe₄GeTe₂ films, where Bi₂Te₃/Fe₄GeTe₂ interface induces perpendicular magnetic anisotropy (PMA) in Fe₄GeTe₂, while the intrinsic in-plane magnetic anisotropy (IMA) in thicker Fe₄GeTe₂ layers (away from the Bi₂Te₃/Fe₄GeTe₂ interface) provides in-plane symmetry-breaking exchange field necessary for field-free SOT operation of the PMA Fe₄GeTe₂. The heterostructure quality appears high, and the experimental characterization is reasonably comprehensive.\nThe integration of in-plane exchange bias with PMA in Fe₄GeTe₂ at wafer scale via MBE is a significant advance. While similar ideas have been demonstrated in sputtered synthetic antiferromagnetic systems (e.g. Nature Mater 16, 94–100 (2017)) or in exfoliated 2D AFM/FM heterostructures (Adv. Mater. 2024, 36, 2305739), this work represents the first implementation of both features in a large-area, 2D epitaxial systemAlthough MBE integration of Bi₂Te₃ with FeₓGeTe₂ has been previously reported, to my knowledge, this is the first demonstration of room-temperature, field-free switching enabled by controllably synthesizing a Fe₄GeTe₂ phase. This represents a notable step forward, especially given the longstanding difficulty in controllably growing single-phase FeₓGeTe₂ by MBE (PhysRevMaterials.7.104004, Nat Commun 14, 5173 (2023), etc). I suggest authors incorporate relevant prior work to better contextualize the broader impact and novelty of this work.\nOne open question is the purity of the Fe₄GeTe₂ phase. Could the observed coexistence of PMA and IMA be partially explained by the possible presence of mixed FeₓGeTe₂ phases (e.g., Fe₃GeTe₂ exhibiting PMA)? Clarification on this point would be helpful.\nAnother central question regarding the main claim of this work concerning the origin of PMA. The author attribute it to the Bi₂Te₃/Fe₄GeTe₂ interface. However, Fe₄GeTe₂ itself has been shown to exhibit temperature dependent spin reorientation transition (Sci. Adv.6,eaay8912(2020)). How do the authors rule out this possibility? Alternatively, Bi₂Te₃ can also be doped with Fe ions and/or become magnetized due to proximity effect, how do authors exclude these possibilities?\nMy primary concerns focus on the interpretation of the switching behavior and the underlying physical mechanisms, which I will illustrate point-by-point below:\n1. The switching shown in Figs. 2d and 2e does not appear to be complete. The amplitude of the switching varies with the applied in-plane magnetic field, suggesting partial switching. The authors should quantify the switching ratio and clarify whether full magnetization reversal is achieved.\n2. about the interpretation of the quenching points and in-plane magnetic anisotropy (IMA), The authors attribute the field-free switching to IMA-assisted symmetry breaking, which I have no issues with. However, the details of the switching behavior in Fig. 2d/e is intriguing and unexplained. Switching quenches near −3 mT (Fig. 2d) and +4 mT (Fig. 2e), suggesting apparent changes in the effective IMA field depending on sweep direction.\n- Why do these quenching points differ in magnitude and polarity?\n- If internal IMA cancels the applied field at those points, why would the IMA value switch sign depending on the field sweep sequence? The authors hinted yes at this question in the discussion for Fig.3 but not fully explained. I can think of in-plane domains follows applied in-plane field and thus give rise to sweep-direction dependent field-free switching. What’s authors’ interpretation in this? If authors agree, then one can extract the in-plane anisotropy field based on the applied field value where switching reaches maximum.\n3. The logic and added value of Fig. 2f are unclear in its current form. The ability to control switching chirality using the sign of the in-plane magnetic field has already been clearly demonstrated in Figs. 2d and 2e. It is not obvious what additional physical insight is gained from Fig. 2f as presented. To make this figure more informative, I suggest the authors reframe it to explicitly explore how chirality control evolves with temperature. For example, Does the switching window become more or less symmetric with temperature? Is there evidence of temperature-dependent in-plane magnetic anisotropy (IMA)? Can temperature-dependent chirality response be used to extract information about thermal stability or symmetry breaking in the system? It would be highly valuable if the authors could explore how different in-plane field initialization histories (e.g., varying magnitude, direction, or duration of preset field) affect the chirality and amplitude of switching at different temperatures. Such measurements could provide insight into the temperature dependence of domain alignment, IMA strength, and interlayer coupling.\n4. In Fig. 3, the switching amplitude increases with increasing preset field. However, it remains unclear how these values compare to full out-of-plane (OOP) magnetization switching measured in Fig. 1d. Are the field-free SOT-induced changes in Rxy comparable in magnitude? A normalized comparison (e.g., % of full Rxy jump) would be helpful to assess the degree of reversal and the strength of the SOT effective field.\n5. possible Typo: Line 238, ‘Bi2Te3(12)/Fe4GeTe2(4)’ should be ‘Bi2Te3(12)/Fe4GeTe2(6)’?\n6. The use of “chirality-tunable” as a distinguishing concept is questionable. The reversal of switching polarity with applied in-plane field is a well-established hallmark of SOT-driven deterministic switching and is widely reported in both 2D and conventional systems. While the presence of coexisting PMA and IMA in a vdW system is novel, the underlying mechanism is not fundamentally new. I recommend the authors align their terminology with established SOT literature to avoid confusion.\n7. The changing of switching chirality w.r.t. to opposite initialization field in Fig. 4e can be explained by initialization of opposite IMA, can the authors extract the magnitude or distribution of the IMA field from the switching curves? Is there any evidence of hysteresis, field training, or domain effects, such as MOKE imaging, MFM, or STXM, either from authors’ measurements or literature that could help distinguish between uniform IMA and inhomogeneous in-plane domain alignment?\n8. The authors wrote that ‘the switching amplitude increases with increasing preset magnetic field. This may be due to the fact that the in-plane magnetic moments of the ferromagnetic layers become more homogeneous as the preset magnetic field increases, resulting in an increase in the strength of the interlayer exchange coupling and hence a larger equivalent field’ Authors seems to hint at the alignment of in-plane domains plays a critical role in the switching amplitude. Can the authors estimate the effective IMA strength by identifying the in-plane field that gives maximum switching amplitude? Such analysis could help to provide a more rigorous physical picture.", "reviewer_2": "Gao et al. report the growth and characterization of a Fe₄GeTe₂/Bi₂Te₃ van der Waals ferromagnet/topological insulator heterostructure, demonstrating field-free switching of the out-of-plane magnetization component of Fe₄GeTe₂. This study demonstrates several firsts, including the demonstration of tunable IP to OOP magneto-anisotropy driven by proximity to a topological insulator, possibly due to interactions between topological surface states and the magnetism, as well as field-free switching enabled by the coexistence of IP and OOP magneto-anisotropy without additional antiferromagnetic bias layers.\nThe manuscript is well organized and contains a comprehensive set of control experiments to quantify the mechanism behind the field-free switching. The observation of tunable field-free switching and topological insulator induced magneto-anisotropy will be of interest to both the spintronics field as well as the broader community studying topological and magnetic heterostructures. However, among other concerns, the main mechanism of topological surface state induced magneto-anisotropy requires more support and clarification. Overall, I am in support of the publication of this work in Nature Communications following revisions to answer the following questions.\nKey Comments:\n1) The main claim of anisotropy tuning through topological surface states (TSS) is exciting as there are not many conclusive experimental works reported so far especially in a vdW heterostructure. As this is a key point of novelty for this work, this manuscript would be greatly strengthened if it can be definitively demonstrated that the anisotropy tuning comes from TSS enhancement. The authors cite the example of TSS enhanced PMA in insulating iron garnets coupled with Bi2Se3, where theoretical calculations by Semenov et al. (Phys. Rev. B 86), 161406(R) show that anisotropy varies between PMA and IMA when the chemical potential is gated towards or away from the Dirac point. However, besides proposing a TSS mediated exchange mechanism, the authors do not further support this claim with experimental evidence or calculations.\nGiven that distinct system from the insulating iron garnets is being considered here, at a minimum, first principles theory would be needed to show that in the Fe₄GeTe₂/Bi₂Te₃ system, (i) The TSS-driven interaction is indeed the dominant contributor to the PMA and (ii) The PMA depends systematically on the chemical potential about the Dirac point. Establishing a systematic dependence of the magnetic anisotropy on the TSS would not only substantiate the mechanism proposed here but also expand the impact of this work, with implications extending well beyond field-free switching. In this context, could the authors also comment on possible experimental approaches to tune the chemical potential closer to or further from the Dirac point, by for example, adjusting the Bi₂Te₃ stoichiometry via growth conditions?\n2) On a related note, magneto-anisotropy can also be tuned by strain, (see Y. Wang et al. Adv. Mater. 2020, 32, 2004533). Would the authors be able to compare from RHEED data the lattice parameters of the Fe₄GeTe₂/Bi₂Te₃ versus Fe₄GeTe₂ and comment on lattice reconstruction effects if any?\n3) The authors use the second-harmonic Hall method to characterize the spin-orbit torque efficiency in the Fe₄GeTe₂(4)/Bi₂Te₃(12) which is a widely used technique for measuring spin-orbit torques developed by Hayashi, M. et al. PRB. 2014, 89(14), 144425. This method assumes small angle approximations of a uniform magnetic layer. However, the heterostructures considered in this work have a coexistence of regions with IMA/PMA and an intermediate canted region (Figure 4) which would mean that the anisotropy parameter Hk in the denominator of equation (2) would not be uniform across the Fe₄GeTe₂ layers. It would be helpful if the authors can show that that the uncertainty from this non-uniformity is sufficiently small as when considering only the high-field regime claimed in the supplementary, or if any other modifications to the conventional second-harmonic Hall equations are required to account for non-uniform Hk in similar tilted systems.\n4) In Figure 3d, the authors show that the switching amplitude increases with the magnitude of the preset field, starting from 0 field and saturating near -2 T. However, in Figure 3e, a +1 T field after a -3 T preset field only suppresses the switching without switching its sign. In addition, it appears from figure 3a that the switching amplitude at 2T is slightly smaller than that for a -2T preset field. This appears to also be the case at 250 K and 270 K (Figure S6). Could the authors comment on the origins of this asymmetry for +ve vs -ve preset fields and whether there could be additional exchange bias effects contributing to this?\nIt would be helpful if the authors could include the in-plane magnetization hysteresis loops as well (analogous to figure 1b), to clarify the relationship between switching amplitude and the in-plane magnetic state. Does the observed saturation behavior in the preset field correspond to the saturation of the in-plane magnetization at each temperature? Is there an offset in the in-plane magnetization hysteresis to explain the asymmetry between +ve and -ve fields?\n5) The authors perform substantial control experiments to show that the field-free switching enabled by the preset field shows the same hysteresis amplitude after applying 100 mT in the opposite direction (figure 3e). However, the in-plane symmetry breaking field enabling field-free switching can be cancelled out by much smaller fields of -3 mT and +4 mT (figure 2e, 2d). The authors should consider clarifying that the stability to external fields is different for setting the polarity of the switching versus the field-free switching operation of the device. Otherwise, broad claims of magnetic interference resistance should be avoided.\nMinor comments, questions:\n1) The term “delamination” on page 6 line 104 may be misinterpreted as describing a failure mode where the layers are peeling apart from each other, consider using an alternative phrasing such as “clean interface with no inter-diffusion.”\n2) Do the authors observe any sign of increased Curie temperature in the Fe₄GeTe₂/Bi₂Te₃ heterostructure versus the Fe₄GeTe₂?\n3) The authors mention that the 28% of the current is in the Bi₂Te₃ layer, is this accounted for in Iwrite (equation 3) for the SOT efficiency?", "reviewer_3": "Review of 626669_0_merged_1751871409\nThe authors have investigated an all-vdW heterostructure (HS) Bi2Te3/Fe4GeTe2 and demonstrated the spin-orbit torque (SOT) switching application and some Boolean logic operations with this HS device. The topic is interesting and consistent with the recent trend of spintronics applications but there is a serious point to mention.\nFrom the same (some of them) cluster of collaborative universitites and institutes, there is a similar work done on Bi2Te3/Fe3GeTe2, demonstrating the SOT switching application of the HS, which was published in Nat. Comm. (Nat Comm. 14 5173 (2023)). The initial part of the currently submitted manuscript has a huge resemblance with this work, except for the chirality dependence and Boolean functions. The initial main studies of magnetization, anomalous Hall, harmonic Hall are exactly similar. Since the main idea/concept and the followed pathway of investigations were already published in the same journal just a couple of years back, the novelty of the presently submitted work does not match the criteria of acceptance in Nat. Comm. Moreover, I found it a bit surprisingly unethical of not having a mention of this earlier work at least once in detail, where almost all the initial studies are just the same. They have only casually mentioned this earlier work from the similar cluster of collaborating institutes as reference number 34, while mentioning the sample without any detail. Although the first authors of these two works are not the same, but the communicating author(s) are the same. This is not a good scientific practice/protocol and the authors should rectify it before proceeding any further.\nI do not endorse publication of this work in Nature Communications. Below I am mentioning some more points, which I found unclear while reading this work.\n1) The authors could have mentioned the earlier work and then compare that with the current one, since the FGT material is different. F4GT (Fe4GeTe2) is far more complicated as well as interesting material in comparison to F3GT (Fe3GeTe2). F4GT has a spin-reorientation transition at 100K, beyond which temperature, the spontaneous magnetization of the system is oriented in-plane and the value of the in-plane magnetic anisotropy is not negligible. In-fact, the temperatures at which the HS is studied here are all above 100K. So, the demand of the authors that the F4GT layer in proximity of Bi2Te3 will acquire a perpendicular orientation of magnetization, may not be so simple.\n2) F4GT is far more isotropic than F3GT (S.R. Kim et al. ACS Appl. Nano Mater. 5, 10341 (2022)). Is the slightly lower value of critical current (1.55 X 106) in F4GT in comparison to 2.2 X 106 in F3GT HS related to this lesser anisotropy? How will be the impact of the lesser anisotropy on the SOT performance?\n3) F4GT is a very complex chiral material where the different vertically alligned Fe planes have commensurate spin-spirals with different pitch (Phys. Rev. B 111 134449 (2025)). Defining this system as the in-plane magnetic anisotropic (IMA) component of the HS is an oversimplified statement. The authors should describe the physics of this system after taking into account these complicated magnetic texture. It is not a simple ferromagnet.\n5) Is there any experimental reference which has proved the perpendicular magnetic anisotropy (PMA) of Bi2Te3 ultrathin films? It may so happen that in both of the component layers, the magnetization directions are canted and are composed of complex spin textures. What are the expected impacts of chiral magnetism on the SOT performance?\n6) The origin of spin-reorientation transition in F4GT is strongly related to the strong inherent spin-phonon or magnon-phonon coupling present in this material. Does it have any impact on the SOT performance?\n7) In line number 106, while describing Fig 1(b), it is just mentioned that the results indicate the presence of both PMA and IMA components. The authors should clearly describe here that what are those indications? Just by looking at the hysteresis loops, it is impossible to know it.\n8) In a similar manner, while describing Fig 1d (line number 116), they state that the anomalous Hall resistance curves demonstrated “excellent PMA feature”. Here too, the features are unclear and the analysis is needed to be more descriptive.\n9) Almost all equations used for the F3GT and F4GT papers are very similar.\n10) The SOT efficiency in F4GT device is more the F3GT ones. What could be the possible reason for this?\n11) The authors described the chirality of the deterministic switching in affected by the in-plane external field. What defines this chirality?\n12) The whole portion of the text where the authors are describing chirality after application of some preset field is extremely unclear. The authors should rewrite this portion after keeping the general readership of the work into account.\n13) Another unclear portion of the manuscript is the analysis of Boolean operations. Although a lot of texts and figures are added both in the main manuscript and supplementary, this is the most confusing part of the manuscript. This portion should be modified with simplified and understandable descriptions."}, "author_response": "ANSWER TO REVIEWER #1\nThis manuscript presents an experimental demonstration of field-free spin-orbit torque (SOT)\nswitching in an epitaxial Bi₂Te₃/Fe₄GeTe₂ van der Waals heterostructure. The authors achieve\ndeterministic SOT switching at room temperature and demonstrate its potential for reconfigurable spin\nlogic applications. The key innovation here is the wafer-scale epitaxial growth of Bi₂Te₃/Fe₄GeTe₂\nfilms, where Bi₂Te₃/Fe₄GeTe₂ interface induces perpendicular magnetic anisotropy (PMA) in Fe₄GeTe₂,\nwhile the intrinsic in-plane magnetic anisotropy (IMA) in thicker Fe₄GeTe₂ layers (away from the\nBi₂Te₃/Fe₄GeTe₂ interface) provides in-plane symmetry-breaking exchange field necessary for field-\nfree SOT operation of the PMA Fe₄GeTe₂. The heterostructure quality appears high, and the\nexperimental characterization is reasonably comprehensive.\nThe integration of in-plane exchange bias with PMA in Fe₄GeTe₂ at wafer scale via MBE is a\nsignificant advance. While similar ideas have been demonstrated in sputtered synthetic\nantiferromagnetic systems (e.g. Nature Mater 16, 94–100 (2017)) or in exfoliated 2D AFM/FM\nheterostructures (Adv. Mater. 2024, 36, 2305739), this work represents the first implementation of both\nfeatures in a large-area, 2D epitaxial system. Although MBE integration of Bi₂Te₃ with FeₓGeTe₂ has\nbeen previously reported, to my knowledge, this is the first demonstration of room-temperature, field-\nfree switching enabled by controllably synthesizing a Fe₄GeTe₂ phase. This represents a notable step\nforward, especially given the longstanding difficulty in controllably growing single-phase FeₓGeTe₂\nby MBE (PhysRevMaterials.7.104004, Nat Commun 14, 5173 (2023), etc). I suggest authors\nincorporate relevant prior work to better contextualize the broader impact and novelty of this work.\nResponse: We are grateful that the Referee recognize the importance and impact of our findings. We\nalso thank the reviewer for the valuable feedback, which has greatly improved the manuscript's\nreadability and scientific rigor. Following the reviewer's suggestion, we have added these references\nto the revised manuscript introduction to better describe the novelty and impact of our study. All\ncomments have been addressed point-by-point in our responses below.\nIMA be partially explained by the possible presence of mixed FeₓGeTe₂ phases (e.g., Fe₃GeTe₂\nexhibiting PMA)? Clarification on this point would be helpful.\nResponse:\nPrat1. XRMR measurement of the Bi Te /Fe GeTe heterostructure\n2 3 4 2\nWe thank the reviewers for their constructive comments. Indeed, the coexistence of perpendicular\nmagnetic anisotropy (PMA) and in-plane magnetic anisotropy (IMA) and their origins are the core\nissues of this study. We believe that the source of PMA is attributed to the interfacial effect between\nthe topological insulator and Fe GeTe , which enhances the PMA characteristics of the ferromagnetic\n4 2\nlayer adjacent to Bi Te , allowing it to retain PMA properties even at room temperature. In contrast,\n2 3\nthe ferromagnetic layers farther away from Bi Te still exhibit IMA characteristics. We have provided\n2 3\nthe overall magnetic data and decomposed signal of the sample in Figure 1b of the main text,\ndemonstrating the coexistence of both IMA and PMA components. To further confirm that the\ndistribution of IMA and PMA is related to the distance from Bi Te , specifically their spatial\n2 3\ndistribution along the Z-axis, we conducted X-ray Magnetic Resonance Reflectivity (XRMR)\nmeasurement.\nXRMR is a synchrotron radiation-based material characterization technique. By precisely tuning the\nX-ray energy to the absorption edge of specific elements and utilizing the magnetic circular dichroism\neffect, it can non-destructively probe the spatial distribution of magnetization inside magnetic thin film\nmaterials with elemental specificity and sub-nanoscale depth resolution1,2. Using this technique, the x-\nray reflectivity curves of the sample at different incident angles can be precisely measured near the\nresonance energy3-5. In this study, we employed this technique to focus on observing and analyzing\ninformation from both the surface and deeper layers of the sample, thereby investigating the spatial\ndistribution of the sample's magnetic properties.\nThe measurements were carried out at SEXTANTS beamline of the synchrotron SOLEIL using the\nRESOXS end-stations6. XRMR was measured in θ − 2θ scattering geometry, with a fixed energy and\n2\nfixed helicity of the circular polarized incident x-rays. The energy was chosen to be 1eV below the\npeak of the Fe L absorption edge. In order to magnetize the samples and generate a magnetic contrast\n3\nfor the measurements. The in-plane magnetic field was switched between parallel and antiparallel\norientation with respect to the x-ray beam propagation, with a maximum applied magnetic field of\n±150 mT. For out-of-plane measurements, the magnetic field was applied normal to the sample surface\nand reversed between positive and negative directions, with a maximum field of ±300 mT. For each\nincident angle, the magnetic field was reversed between positive and negative at each point during the\nXRMR measurements. The reflected intensity signals are recorded as 𝐼 and 𝐼 for opposite applied\n(cid:2878) (cid:2879)\nmagnetic field, and the asymmetry ratio is defined as 𝑅 = (𝐼 −𝐼 )/(𝐼 +𝐼 ). Figure R1 presents\n(cid:2878) (cid:2879) (cid:2878) (cid:2879)\nthe reflectivity curve and the asymmetry ratio, demonstrating the relationship between signal intensity\nand detection angle. By varying the incident angle in XRMR, the depth sensitivity of the measurement\nis modified through angle-dependent interference and penetration effects1,2. Consequently, in a rough\napproximation small angles preferentially weight the near-surface magnetization, while larger angles\nincrease sensitivity to deeper regions of the film. Measurements were conducted under out-of-plane\nand in-plane magnetic fields respectively, with all signals collected using the circular left polarized\n(CL) x-ray during testing.\nAs shown in Fig. R1a and Fig. R1c, it can be observed that under an out-of-plane magnetic field, I\n+\nand I overlap, and the asymmetry ratio R remains nearly zero at small angles (0-10°). In contrast, as\n-\nshown in Fig. R1b and Fig. R1d, under an in-plane magnetic field, the two measurement curves show\nclear separation, revealing a significant asymmetry ratio R. By combining the penetration depth at\ngrazing incidence with the observed magnetic asymmetry and hysteresis loop measured at 9.5° under\nan in-plane magnetic field (Fig. R1e), it can be concluded that the surface layer consists\npredominantly of IMA components. As the incident angle increases, the XRMR signal becomes\nincreasingly sensitive to magnetization contributions from deeper regions of the sample, rather than\nbeing dominated solely by the near-surface layer. Field-sweep measurements were performed using\nCL at 50° under both in-plane (Fig. R1f) and out-of-plane magnetic fields (Fig. R1g). Analysis of the\nhysteresis loops reveals that during in-plane field sweeps, the sample saturates rapidly at low magnetic\nfields, suggesting that IMA behavior still dominates at this detection angle. However, as the field\n3\nincreases, the signal exhibits a gradual saturation trend, indicating the presence of components with\nin-plane hard axes—i.e., a contribution from PMA components. On the other hand, the out-of-plane\nmagnetic field sweep test shows an overall gradual saturation trend, with a small remanence observed\nat zero magnetic field, indicating the presence of PMA components. Overall, these XRMR results\nprovide strong evidence of the co-existence IMA and PMA components in the sample indeed\nexhibit a spatial distribution characteristic correlated along the Z-axis. It also strongly indicates\nthat the IMA is located near the Fe GeTe surface, meanwhile the PMA is more deep and close\n4 2\nto the Bi Te layer. Meanwhile it could exclude the possibility of PMA from the Fe GeTe impurity\n2 3 x 2\nphases, which would provide random magnetic distribution.\nFigure R1. XRMR measurement of the Bi Te /Fe GeTe heterostructure measure close to Fe L\n2 3 4 2 3\nedge. a, b, XRMR reflectivity curve under out-of-plane (a) and in-plane (b) magnetic fields. c, d,\nCorresponding asymmetry ratios calculated from the normalized difference of the two measurements\nwith opposite magnetic fields. e, f, g, Hysteresis loop of the Bi Te /Fe GeTe heterostructure measured\n2 3 4 2\nat 9.5° under in-plane magnetic fields (e), at 50° under in-plane magnetic fields (f) and out-of-plane\n4\nmagnetic fields (g).\nPart2. Comparison of the crystal structures of Fe GeTe and Fe GeTe .\n4 2 3 2\nTo further exclude the existence of Fe GeTe phases (e.g. Fe GeTe ), we carefully examined crystal\nx 2 3 2\nphase in our Bi Te /Fe GeTe heterostructure by the XRD and HAADF measurement, and pure\n2 3 4 2\nFe GeTe thin film was fabricated as a comparison. From the XRD data as shown in Fig. R2a, there is\n3 2\nno any observable Fe GeTe phase in our Bi Te /Fe GeTe heterostructure. Moreover, the HAADF\n3 2 2 3 4 2\nimages in Fig. R2b clearly reveal the Bi Te and Fe GeTe atomic structure, without any Fe GeTe\n2 3 4 2 3 2\nphase. Usually, the atomic structures of Fe GeTe and Fe GeTe could be easily distinguished, as\n4 2 3 2\nshown in the right side of Fig. R2b. Therefore, together with the XRMR results, it could be\nconfirmed that the coexistence of PMA and IMA components does not come from the possible\npresence of mixed Fe\nx\nGeTe\n2\nphases.\nFigure R2. Comparison of the crystal structures of the Bi Te /Fe GeTe and Fe GeTe . a, XRD result\n2 3 4 2 3 2\nof Bi Te /Fe GeTe and Fe GeTe . b, HAADF image of Bi Te /Fe GeTe and Fe GeTe .\n2 3 4 2 3 2 2 3 4 2 3 2\nIn summary,\n(1) We confirm that the distribution of the PMA and IMA components in the prepared\nBi Te /Fe GeTe exhibits distinct spatial characteristics along the Z-axis through XRMR\n2 3 4 2\nmeasurement.\n(2) Using XRD and atomic-resolution HAADF imaging, we demonstrate that the primary constituent\nin the heterostructure is indeed Fe GeTe . We acknowledge the possibility of the presence of\n4 2\nundetectable trace amounts of Fe GeTe . However, it should be noted that any such impurities\n3 2\n5\nwould be randomly distributed and thus cannot give rise to a distinct PMA+IMA spatial magnetic\ndistribution.\nTherefore, it confirms that the emergence of the PMA component at room temperature is attributed to\nthe interface effect of Bi Te . We hope that the additional experimental data can enhance the scientific\n2 3\nrigor of this study and fully address the reviewers' concerns.\nAnother central question regarding the main claim of this work concerning the origin of PMA. The\nauthor attribute it to the Bi₂Te₃/Fe₄GeTe₂ interface. However, Fe₄GeTe₂ itself has been shown to exhibit\ntemperature dependent spin reorientation transition (Sci. Adv.6,eaay8912(2020)). How do the authors\nrule out this possibility? Alternatively, Bi₂Te₃ can also be doped with Fe ions and/or become\nmagnetized due to proximity effect, how do authors exclude these possibilities?\nResponse: We sincerely thank the reviewer for their valuable suggestions.\nPart.1 Discussion on the spin reorientation transition in Bi Te /Fe GeTe\n2 3 4 2\nIndeed, studies on Fe GeTe have indicated that this material exhibits a temperature-dependent spin\n4 2\nreorientation transition. In our prepared Bi Te /Fe GeTe heterostructure, the top layer of Fe GeTe\n2 3 4 2 4 2\nkeeps a low spin reorientation transition temperature (T )similar to the reference report, while the\nSR\nbottom layer gives a high T due to interfacial effect. Thus, with increasing temperature, the magnetic\nSR\nbehavior gradually shifts from fully PMA to a mixed state of PMA+IMA, and eventually transforms\ncompletely into IMA. The temperature-dependent anomalous Hall effect (AHE) measurements under\na perpendicular magnetic field are shown in Fig. R3. At 100 K, the AHE loop of the sample exhibits a\nfully square shape. As the temperature rises, the shape of the AHE curve changes, displaying a\ncombination of PMA and IMA characteristics at 150 K and above. The sharp reversal and hysteretic\nbehavior observed around μ H = 0 are indicative of the PMA component. The increase in R at higher\n0 z xy\nfield strengths suggests a gradual transition of magnetization pulled from IMA to PMA orientation,\naffirming the presence of an IMA component. This R-H loop distinctly demonstrates the coexistence\nof both IMA and PMA components within the Fe GeTe layer, which is consistent with our XRMR\n4 2\nmeasurement results. The R-H curve can be decomposed into a hysteresis loop attributable to Fe GeTe\n4 2\n(PMA, adjacent to Bi Te ) and a hard axis loop corresponding to Fe GeTe (IMA, away from Bi Te ),\n2 3 4 2 2 3\n6\nas shown in the Fig. R3b. With further increasing temperature, as shown in Fig. R3c, the remanent\nmagnetization at zero field gradually decreases with a transition temperature around 325 K. Therefore,\nfor the Fe GeTe in our heterostructure sample, the magnetic anisotropy transition characteristic\n4 2\nis still preserved, but the transition temperature of Fe GeTe near the Bi Te increases.\n4 2 2 3\nFigure R3. The anomalous Hall resistance under out-of-plane field (H ) at different temperatures in\nz\nBi Te /Fe GeTe heterostructure. a, R as a function of out-of-plane magnetic field measured at\n2 3 4 2 xy\ntemperatures from 100 K to 300 K. At low temperatures, the anomalous Hall hysteresis loops show\nclear remanence at zero field, demonstrating the coexistence of PMA and IMA components. b,\nVariation and decomposition of R under out-of-plane magnetic field at 300 K. c, R as a function of\nxy xy\nout-of-plane magnetic field measured at temperatures from 325 K to 425 K, the vanishing remanence\nindicates a complete transition to IMA-dominated behavior, preceding the paramagnetic transition at\nthe Curie temperature (~425 K). This series of measurements conclusively demonstrates the\ntemperature-driven reorientation of magnetic anisotropy in Fe GeTe₂, revealing a distinct transition\n4\nfrom PMA/IMA coexistence to pure IMA configuration before the eventual loss of magnetic order at\nT .\nc\n2 3\nEffect\nIndeed, as the reviewer pointed out, current research has introduced magnetism into topological\ninsulators through approaches such as doping and the magnetic proximity effect. However, the\nmagnetic properties introduced in topological insulators differ substantially from those of intrinsic\nmagnetic materials. Therefore, the potential contribution of magnetized Bi Te in this study can be\n2 3\nruled out.\nFirstly, regarding Fe doping, there have been no reports so far demonstrating the achievement of room-\ntemperature PMA through doping. As reported in the work of Arévalo-López, E.P., et al. (J. Alloys\nCompd. 899, 163297 (2022)7), magnetic characterization of Fe-doped Bi Te (Fe Bi Te , x = 0, 0.1,\n2 3 x 2-x 3\n0.2) revealed that \"however, for the doped sample with x = 0.2, a weak ferromagnetic behavior (WFM)\nbelow 14 K is observed.\" This clearly indicates that Fe doping does not affect the magnetic properties\nof the samples at 300 K.\nAs for the introduction of magnetism into Bi Te through proximity effect, the resulting Curie\n2 3\ntemperatures usually remain very low (Nano Lett. 14, 3459-3465 (2014))8. Even in the limited report\nclaiming a Curie temperature near 300 K, it exhibits significant differences compared to intrinsic\nmagnetic materials, particularly in its substantially smaller magnetic moments. Taking the work of\nFerhat Katmis et al. (Nature. 533, 513-516 (2016))9 as an example, while their study successfully\nintroduced room-temperature magnetism into Bi Se via proximity coupling, the magnetic moment\n2 3\nshowed strong temperature dependence and was extremely small at room temperature—differing by\ntwo orders of magnitude from the experimental results presented in our study.\nTherefore, based on the above analysis, although Bi Te could potentially be magnetized through Fe\n2 3\nion doping or proximity effect, the characteristics of such magnetization are distinctly different from\nour experimental data and thus do not affect the conclusions drawn in this work.\nCollectively, our analysis reveals that the spin-reorientation transition of Fe GeTe is significantly\n4 2\nenhanced by interfacial effect of Bi Te , which hence gives rise to a unique coexistence of PMA and\n2 3\nIMA magnetic structure. Crucially, it could effectively exclude the magnetic contribution from Bi Te\n2 3\n8\nlayer.We believe these findings comprehensively address the reviewers’ concerns. We again thank the\nreviewer for the insightful comments, which has substantially improved the rigor of this work.\nMy primary concerns focus on the interpretation of the switching behavior and the underlying physical\nmechanisms, which I will illustrate point-by-point below:\nQ1. The switching shown in Figs. 2d and 2e does not appear to be complete. The amplitude of the\nswitching varies with the applied in-plane magnetic field, suggesting partial switching. The authors\nshould quantify the switching ratio and clarify whether full magnetization reversal is achieved.\nResponse: We thank the reviewer for pointing this out. We confirm that the switching observed in Figs.\n2d and 2e corresponds to partial magnetization reversal, rather than full switching. The maximum\nswitching ratio for field-assisted switching reaches approximately 22%, while for field-free switching,\nthe switching ratio is about 16.8%. Full field-free switching could not be realized in the present system.\nIn fact, such incomplete SOT switching is generally characteristic of two-dimensional magnetic\nmaterials. As noted in a previous report (Sci. Adv. 5, eaaw8904 (2019))10, calculations based on the\nprovided data show that the switching ratio at 110 K is approximately 20%. Furthermore, several recent\nstudies on SOT-driven switching in two-dimensional magnetic materials, such as (Nano Lett. 25, 7276-\n7282 (2025))11 and (Sci. Adv. 10, eadk8669 (2024))12, have documented switching ratios of comparable\nmagnitude.\nThis is because in the two-dimensional limit, the magnetization becomes highly susceptible to thermal\nfluctuations. Meanwhile, achieving spin-orbit torque switching typically requires the use of extremely\nhigh current densities. In atomically thin materials, this induces significant localized Joule heating.\nThe generated heat reduces or even destroys the magnetic anisotropy of the material, making magnetic\nmoments more prone to random fluctuations. This can lead to non-uniform, thermally driven domain\nnucleation instead of deterministic SOT-controlled switching, ultimately resulting in a multi-domain\nstate that macroscopically manifests as low switching efficiency. We have explicitly added this\nquantitative clarification to the revised manuscript to avoid any ambiguity.\nOn page 10, the following description has been added: “The maximum switching ratios, calculated\nfrom the data in Figs. 2d and 2e, are approximately 22% for field-assisted switching and 16.8% for\n9\nfield-free switching. These values are consistent with reported SOT efficiencies in other two-\ndimensional magnetic systems and reflect the practical challenge of achieving full magnetization\nreversal in the two-dimensional limit.”\nQ2. About the interpretation of the quenching points and in-plane magnetic anisotropy (IMA), The\nauthors attribute the field-free switching to IMA-assisted symmetry breaking, which I have no issues\nwith. However, the details of the switching behavior in Fig. 2d/e is intriguing and unexplained.\nSwitching quenches near −3 mT (Fig. 2d) and +4 mT (Fig. 2e), suggesting apparent changes in the\neffective IMA field depending on sweep direction.\n- Why do these quenching points differ in magnitude and polarity?\n- If internal IMA cancels the applied field at those points, why would the IMA value switch sign\ndepending on the field sweep sequence? The authors hinted yes at this question in the discussion for\nFig.3 but not fully explained. I can think of in-plane domains follows applied in-plane field and thus\ngive rise to sweep-direction dependent field-free switching. What’s authors’ interpretation in this? If\nauthors agree, then one can extract the in-plane anisotropy field based on the applied field value\nwhere switching reaches maximum.\nResponse: Thank you for raising the insightful questions, especially pointing out the fascinating\nphenomenon of the asymmetry in the quenching points in Figs 2d and 2e. The core of this\nphenomenon lies in the difference in the magnitude of the interlayer exchange coupling field\ngenerated under the two scanning sequences, which consequently leads to the asymmetry in the\napplied field of quenching point and the size of the field-free switching window in Figs 2d and 2e. The\ndetailed experiments are as follows, in which we have conducted a deeper investigation into the\nasymmetric switching behavior noted by the reviewer.\nTo verify its repeatability of such phenomenon and rule out the coincidence, a new sample was\nprepared for the SOT measurement. Before that, it is important to clarify that, in addition to the testing\nsequence affecting the chirality of field-free switching, the magnitude of the initially applied magnetic\nfield also influences the characteristics of field-free switching. As demonstrated in Fig. 3 of the main\ntext, the magnitude of the preset magnetic field affects the switching amplitude during field-free\nswitching. To eliminate its influence, we conducted experiments after applying the same value of preset\n10\nfield, and the results are shown in Figs. R4a and R4b. It can be observed that, even when the positive\nand negative preset fields are controlled to be identical, the magnitudes corresponding to the switching\nquenches of the two magnetic fields remain different, with a difference of 1 mT. Comparing the field-\nfree switching curves under the two scanning sequences (Fig. R4c), aside from the reversal of\nswitching polarity, there is a noticeable difference in the sizes of the two switching windows.\nTo clarify this mechanism, we need to describe detailly our experimental procedure, as this may be a\nkey for understanding this phenomenon. Before applying any in-plane preset field (H ), we first apply\npre\na strong perpendicular initialization field. This is done to set a uniform starting state for the PMA layer\nand simultaneously reset the underlying IMA layer into a consistent multi-domain state, ensuring the\nsubsequent H is applied to a reproducible magnetic texture. In current measurement, the initially\npre\napplied out-of-plane magnetic field was in the +Z direction, as denoted in Fig. R4c.\nWhen the H is sufficiently large (e.g., ±2.5 T), it saturates the IMA layer, creating a single domain.\npre\nThis saturated IMA layer provides an internal effective field, H , via interlayer exchange coupling.\neff,IMA\nTheoretically, H should be equal in magnitude and opposite in sign for symmetric ±H , which\neff,IMA pre\nwould lead to symmetric SOT switching loops. However, our observation of asymmetric windows\nclearly conflicts with this ideal case. This strongly implies the existence of an additional, stable in-\nplane \"ghost\" field, H , which is not reversed by the in-plane preset field. We attribute this H to\nghost ghost\nthe transition layer in our Bi Te / F GT (PMA) / F GT (canted) / F GT (IMA) structure (as shown in\n2 3 4 4 4\nFig. 4d of the main text), in which the in-plane component of the 'canted' layer provides the H .\nghost\nTo prove this hypothesis, we carried out a critical control experiment: we reversed the initial perpendicular\ninitialization field (to -Z) and repeated the SOT preset measurements. As shown in Fig. R4d, it shows\nthat the SOT window asymmetry disappeared. This conclusively demonstrates that the H is set by\nghost\nthe initial perpendicular field, which determines the \"canted-up\" or \"canted-down\" orientation of the\ncanted layer.\nTo further probe the magnetic rigidity of this canted layer, we performed the supplementary experiment\nshown in Fig. R4e. The in-plane AHE loop was carried out after +Z and -Z initialization, respectively.\nAs shown in the plot, while the curves merge at high fields, they exhibit a clear vertical offset in R\nxy\nat low fields. This offset provides direct evidence of a stable, remnant perpendicular magnetization\n11\ncomponent whose sign depends on the initial Z-field. Crucially, for a canted layer with uniaxial\nanisotropy, a pinned M component necessarily implies a pinned M component. This pinned M\nZ X X\nwould contribute to the H . Therefore, the total effective field acting on the switching PMA layer is\nghost\nH = H + H , as illustrated in the schematic diagram in Fig. R5.\neff eff,IMA ghost\nThe high magnetic rigidity of this canted layer might be an intrinsic physical consequence of its graded\nmagnetic anisotropy. Our system exhibits a self-assembled exchange-spring magnet structure (Phys.\nRev. B. 58, 12193 (1998)13). The Fe GeTe (PMA) layer (near the TI) acts as the \"hard\" layer, while\n4 2\nthe Fe GeTe (IMA) (far the TI) acts as the \"soft\" layer. The Fe GeTe (canted) layer is the transition\n4 2 4 2\nregion, or \"spring\". The physical origin of its high rigidity stems from the intense competing\nanisotropies in this specific region. Theoretical work on graded anisotropy media confirms that such\ntransition regions, where anisotropy gradients are sharpest, can exhibit complex, non-uniform reversal\nmodes and significantly higher effective coercivity than the uniform phases (Appl. Phys. Lett. 87,\n012504 (2005)14; IEEE Trans. Magn. 41, 537 (2005)15). The existence of such distinct interface layers with unique\nmagnetic properties is also well proved in an epitaxial magnetic heterostructures (Rep.\nProg. Phys. 59, 1409 (1996)16). While the aforementioned inference has been supported by some\ntheoretical and experimental reports, direct observation of this transition layer may prove extremely\nchallenging in our system, given that it likely operates at the atomic scale. Nevertheless, our current\nexperiments clearly elucidate the origin of asymmetry in the SOT switching. This asymmetry cannot\nbe accounted for by a single homogeneous magnetism but is highly consistent with the complex non-\nuniform magnetization switching process within an exchange-spring system featuring gradient\nanisotropy.\nTherefore, our system contains two distinct in-plane fields acting on the switching layer:\n(1) A tunable effective field H from the IMA layer, set by the external H . This field determines\neff,IMA pre\nthe SOT switching polarity.\n(2) A fixed internal bias H from the canted layer, set by the initial Z-field. This H adds to or\nghost ghost\nsubtracts from H , causing the SOT switching window asymmetry.\neff,IMA\nThis explanation, where a fixed internal bias field creates asymmetric SOT loops, is fully consistent\nwith established SOT physics (Nature Mater. 15, 535 (2016)17; Nat. Commun. 7, 13367 (2016)18).\nin-plane field, which leads to different alignment of the IMA component under different in-plane preset\nfields. This results in interlayer exchange coupling fields of different directions, ultimately causing the\nquenching points to differ in polarity. However, it should be further added that the quenching points\ndiffer in magnitude because the initial out-of-plane (Z-direction) magnetic field defines the orientation\nof the canted interfacial layer, thereby leading to asymmetry in the switching behavior. Regarding the\npreset field mentioned that maximizes the switching amplitude, I infer that under this in-plane\nmagnetic field, the in-plane magnetic domains achieve their most homogeneous state.\nFigure R4. Origin of the asymmetry quenching points. a, b, SOT-driven magnetization switching\nin Bi Te /Fe GeTe at 250 K under different in-plane magnetic fields along the x-axis (after +z\n2 3 4 2\ninitialization), showing differ quenching points. c, Asymmetric switching windows observed with +x\n(red) and -x (blue) preset fields after +z initialization. d, Symmetric switching windows obtained by\ncomparing the “+z init / +x preset” state with the “-z init / -x preset” state, confirming the asymmetry\nfollows the initialization field. e, In-plane AHE loops after +z and -z initialization. The zero-field\nvertical offset evidences a pinned canted layer, whose in-plane component acts as the static ghost field\n(H ).\nghost\nswitching. It illustrates six different magnetic moment configurations. The diagram depicts the\ninterplay between H and H . The direction of H is determined by the in-plane preset field\neff,IMA ghost eff,IMA\n(+x or -x), while H is pinned by the initial vertical field (e.g., +z). When a +x preset field is applied,\nghost\nH aligns parallel to H , enhancing H and resulting in a larger switching window. Conversely,\neff,IMA ghost eff\na -x preset field aligns H antiparallel to H , reducing the total field and leading to a smaller\neff,IMA ghost\nswitching window. This model consistently explains the experimentally observed asymmetry.\nQ3. The logic and added value of Fig. 2f are unclear in its current form. The ability to control switching\n14\nchirality using the sign of the in-plane magnetic field has already been clearly demonstrated in Figs.\n2d and 2e. It is not obvious what additional physical insight is gained from Fig. 2f as presented. To\nmake this figure more informative, I suggest the authors reframe it to explicitly explore how chirality\ncontrol evolves with temperature. For example, Does the switching window become more or less\nsymmetric with temperature? Is there evidence of temperature-dependent in-plane magnetic anisotropy\n(IMA)? Can temperature-dependent chirality response be used to extract information about thermal\nstability or symmetry breaking in the system? It would be highly valuable if the authors could explore\nhow different in-plane field initialization histories (e.g., varying magnitude, direction, or duration of\npreset field) affect the chirality and amplitude of switching at different temperatures. Such\nmeasurements could provide insight into the temperature dependence of domain alignment, IMA\nstrength, and interlayer coupling.\nResponse: Thank you very much for the insightful suggestion. We fully agree that the ability to control\nfield-free switching chirality using the sign of the in-plane magnetic field has already been clearly\ndemonstrated in Figs. 2d and 2e. The purpose of Fig. 2f, however, is not to introduce new physical\nmechanisms but rather to verify the robustness and temperature persistence of field-free polarity\nswitching. By presenting field-free switching curves across a wide temperature range, Fig. 2f could\nconfirm that the polarity-tunable field-free switching observed at 300 K is not an isolated phenomenon\nbut a general characteristic of the heterostructure.\nWe appreciate the reviewer’s suggestion to probe temperature-dependent switching amplitude and\nIMA strength in greater depth. In our manuscript, the analysis of how temperature and in-plane field\ninitialization histories influence the switching characteristics is already placed in Fig. 3. There, we\nsystematically study the evolution of the switching window as a function of pre-set field magnitude\nand temperature (e.g., Fig. 3d), revealing that the switching window first enlarges and later saturates\nwith increasing preset field—consistent with progressive homogenization of the IMA domain\nconfiguration. Additionally, an analysis of temperature-dependent equivalent effective field has been\nincluded in response to Question 8. These results could address the reviewer’s questions regarding\ntemperature-dependent symmetry breaking and IMA evolution.\nAcross the manuscript, we clearly state that the field-free switching characteristics are sensitive to the\npreset in-plane field history. However, Fig. 2 was deliberately designed to illustrate the basic\nphenomenology—namely, the reversibility and temperature robustness of chirality control—without\nembedding the more complex dependencies on preset field history. The deeper physical insight\nproposed by the reviewer is therefore presented in Fig. 3, which focuses specifically on the magnitude\nand direction of preset fields governing the switching characteristics.\nFor these reasons, and to maintain a clear and non-redundant narrative structure between Figs. 2 and\n3, we keep Fig. 2f. We hope our explanation could addressed the reviewer’s concerns.\nQ4. In Fig. 3, the switching amplitude increases with increasing preset field. However, it remains\nunclear how these values compare to full out-of-plane (OOP) magnetization switching measured in\nFig. 1d. Are the field-free SOT-induced changes in Rxy comparable in magnitude? A normalized\ncomparison (e.g., % of full Rxy jump) would be helpful to assess the degree of reversal and the strength\nof the SOT effective field.\nResponse: We thank the reviewer for the insightful question. To clarify the relationship between the\nswitching amplitudes in Fig. 3 and the full out-of-plane (OOP) magnetization reversal shown in Fig.\n1d, we summarized the switching ratio (R /R ) versus preset magnet field at 300 K, as shown in\nswitch AHE\nFig. R6. The results show that the switching ratio increases with increasing preset in-plane magnetic\nfield. This trend reflects a progressive alignment of the in-plane magnetic domain, resulting in an\nenhancement of SOT effective field. The maximum value of the switching ratio is around 25%, and\nsuch incomplete SOT switching is similar to the reported results in two-dimensional magnetic\nmaterials, as already discussed in Question 1.\nTaken together, the normalized comparison in Fig. R6 provides a comprehensive understanding of how\nthe preset field influences the degree of reversal and the effectiveness of SOT-driven switching.\nWe have added the discussion in our revised manuscript (Page 16): “We summarized the switching\nratio (R /R ) versus preset magnetic field at 300 K, as shown in Fig. S8. According to\nswitch AHE\n16\ncalculations, the switching ratio increases with increasing preset in-plane magnetic field and the\nmaximum value of the switching ratio is around 25% at 300(cid:3031)K.”\nFigure R6. Field-Free Switching Ratio versus Preset Magnetic Field at Different Temperatures.\nQ5. Possible Typo: Line 238, ‘Bi Te (12)/Fe GeTe (4)’ should be ‘Bi Te (12)/Fe GeTe (6)’?\n2 3 4 2 2 3 4 2\nResponse: We thank the reviewer for pointing this out. The original wording could indeed be\nambiguous. The heterostructure Bi Te (12)/Fe GeTe (4) is the primary sample discussed throughout\n2 3 4 2\nthe main manuscript, whereas Bi Te (12)/Fe GeTe (6) is an additional comparison sample introduced\n2 3 4 2\nlater in the study.\nTo eliminate this ambiguity, we have revised the description of this part in the main text (Page 13)\nfrom: “In contrast, the Bi Te (8)/Fe GeTe (4) and Bi Te (12)/Fe GeTe (4) heterostructures, as shown\n2 3 4 2 2 3 4 2\nin Fig. 4b and Fig. 1d, maintain the same strong PMA characteristics across all temperatures, which\nhighlights the effect of Bi Te for enhancing the PMA property in Fe GeTe .”\n2 3 4 2\nto the clarified version:\n“In contrast, the Bi Te (8)/Fe GeTe (4), as shown in Fig. 4b, maintain the same strong PMA\n2 3 4 2\ncharacteristics across all temperatures as Bi Te (12)/Fe GeTe (4) heterostructures in Fig. 1d, which\n2 3 4 2\nhighlights the effect of Bi Te for enhancing the PMA property in Fe GeTe .”\n2 3 4 2\nQ6. The use of “chirality-tunable” as a distinguishing concept is questionable. The reversal of\nswitching polarity with applied in-plane field is a well-established hallmark of SOT-driven\ndeterministic switching and is widely reported in both 2D and conventional systems. While the\npresence of coexisting PMA and IMA in a vdW system is novel, the underlying mechanism is not\nfundamentally new. I recommend the authors align their terminology with established SOT literature\nto avoid confusion.\nResponse: We would like to thank the reviewer again for the helpful suggestion. Your comments have\nundoubtedly contributed to improving the scientific rigor and clarity of the manuscript. Following the\nreviewer, we have changed “chirality-tunable” to “polarity-tunable” in the manuscript to align with the\nstandard terminology in the existing literature.\nQ7. The changing of switching chirality with respect to opposite initialization field in Fig. 4e can be\nexplained by initialization of opposite IMA, can the authors extract the magnitude or distribution of\nthe IMA field from the switching curves? Is there any evidence of hysteresis, field training, or domain\neffects, such as MOKE imaging, MFM, or STXM, either from authors’ measurements or literature that\ncould help distinguish between uniform IMA and inhomogeneous in-plane domain alignment?\nResponse: We thank the reviewer for this insightful comment. We agree that the core mechanism for\nthe polarity control is the initialization of the net magnetization of the IMA component. We also fully\nconcur with the reviewer's astute suggestion that a model based on the alignment of inhomogeneous\nin-plane domains, rather than a uniform single-domain IMA, provides a more accurate and self-\nconsistent description of our experimental observations.\nWith respect to whether the magnitude or distribution of the IMA field can be extracted from the\nswitching curves, we note that the switching amplitude reflects the net IMA contribution, which is\ndetermined by the statistical imbalance between oppositely oriented in-plane domains. Therefore, the\nswitching curves allow us to identify the trend and saturation behavior of the effective IMA field but\ndo not yield a single intrinsic value for the IMA strength. The net IMA should be a domain-weighted\nquantity that evolves continuously with the preset field due to domain realignment.\ngathered a combination of direct and indirect evidence:\n1. Transport evidence for domain-dependent IMA\nOur transport results in Fig. 3d provide the strongest indirect evidence. The SOT switching amplitude\nsystematically increases with the magnitude of the preset field and eventually saturates. This\n\"trainable\" switching amplitude is perfectly consistent with a progressive alignment of in-plane\ndomains under increasing preset field. This alignment leads to a stronger and more uniform effective\ninterlayer exchange field (H ) that facilitates a more complete switching of the PMA layer. In\neff,IMA\ncontrast, a uniform single-domain IMA would simply produce one fixed H , and its switching\neff,IMA\namplitude would not exhibit such a strong dependence on the preset field magnitude.\n2. Direct magnetic imaging revealing multi-domain IMA\nWe performed Magneto-optic Kerr Effect (MOKE) imaging to probe the remanent domain state that\nexists after the preset field is removed. For atomically thin two-dimensional magnetic layers, the\nlongitudinal MOKE signal generated by their in-plane magnetization is already near the detection\nlimit. Specifically for our few-layer samples fabricated on a transparent Al O substrate, light\n2 3\nundergoes multiple reflections and interference at various interfaces within this layered structure. This\nseverely perturbs or even masks the already weak longitudinal MOKE signal, making it unstable and\ndifficult to decouple from pure optical interference effects (Nat. Nanotechnol. 14, 408-419 (2019)19 ,\nAIP Advances 9, 125116 (2019)20). In contrast, polar MOKE is far less sensitive to such multilayer\ninterference effects. Therefore, for our samples, polar MOKE can provide more stable and reliable\nsignals.\nThe results in Fig. R7 show a significant difference between the two magnetic phases. Figure R7a\nshows the MOKE image of Fe GeTe film in its IMA state at 150 K under the hard-axis probe field. It\n4 2\nclearly reveals a complex, wavy, ripple-like texture, which is the characteristic signature of an in-\nplane multi-domain state probed via its vertical susceptibility components. This interpretation is\nstrongly supported by established literature(e.g., Phys. Rev. B. 77, 024405 (2008)21). While our MOKE\ntechnique probes magnetization rather than stray fields, the resulting topological texture is\n19\nphenomenologically consistent. Furthermore, this observation aligns with MOKE imaging reported by\nTang et al. (Nat. Electron. 6, 28-36 (2023)22) on the similar vdW ferromagnet Fe GeTe , which also\n5 2\nexhibited large-scale in-plane multi-domains with comparable features. To aid visualization, we have\nhighlighted representative regions containing these distinct domain wall signals with red dashed boxes\nin Fig. R7a. In sharp contrast, Fig. R7b shows the MOKE image of the heterostructure in its PMA state\nat 50 K, displaying a characteristic densely-packed bubble or maze-like domain texture, which is\nfundamentally different from the ripple texture of the IMA phase.\n3. Micromagnetic simulations quantitatively supporting the multi-domain IMA model\nWe performed micromagnetic simulations to provide a rigorous physical picture which quantitatively\nlinks the inhomogeneous IMA state to our experimental results. In this simulation, we modeled the\nIMA layer as an inhomogeneous collection of domains with two opposing in-plane magnetizations\n(+X and -X). We then varied the Domain Ratio (e.g., from 3:1 to 15:1) to simulate the effect of an\nincreasingly strong preset field, which would align more domains in one direction and thus increase\nthe net IMA magnetization.\nThe simulation results, shown in Figs. R7c-d, perfectly reproduce our experimental findings. The\nsimulated SOT switching loops (Fig. R7c) show that as the domain ratio becomes more skewed (i.e.,\nthe net IMA magnetization increases), the resulting SOT switching window becomes systematically\nlarger. Plotting this extracted \"Switching Ratio\" versus the \"Domain Ratio\" (Fig. R7d) reveals a clear\ntrend of increasing amplitude that begins to saturate at high ratios. This simulation precisely matches\nour experimental observation in Fig. 3d.\nConclusion\nIn summary, the combination of our transport data (Fig. 3d), the clear difference in MOKE imaging\nbetween the two phases (Figs. R7a-b), literature consistency, and micromagnetic simulations (Fig.\nR7c-d) provide overwhelming evidence for the inhomogeneous multi-domain IMA model. This model\nconfirms that the \"magnitude\" of the effective IMA field is not a single fixed value, but a tunable\nparameter directly proportional to the net alignment of the in-plane domains, which can be controlled\nby the preset field.\na pure Fe GeTe film in the IMA state, exhibiting a characteristic wavy texture indicative of in-plane\n4 2\ndomain walls; representative regions containing clear domain wall signals are highlighted by red\ndashed boxes. b, Magneto-optic Kerr image of the heterostructure in the PMA state at 50 K, displaying\na distinct dense multi-domain pattern. c, Micromagnetic simulations of SOT switching loops for\nvarying ratios of antiparallel in-plane domains (from 3:1 to 15:1), simulating the alignment effect of\nthe preset field. d, Simulated switching ratio as a function of the domain ratio, reproducing the\nincreasing and saturating trend observed experimentally in Fig. 3d.\nQ8. The authors wrote that ‘the switching amplitude increases with increasing preset magnetic field.\nThis may be due to the fact that the in-plane magnetic moments of the ferromagnetic layers become\nmore homogeneous as the preset magnetic field increases, resulting in an increase in the strength of\nthe interlayer exchange coupling and hence a larger equivalent field’ Authors seems to hint at the\nalignment of in-plane domains plays a critical role in the switching amplitude. Can the authors estimate\n21\nthe effective IMA strength by identifying the in-plane field that gives maximum switching amplitude?\nSuch analysis could help to provide a more rigorous physical picture.\nResponse: We fully agree with the reviewer’s observation that the alignment of in-plane domains plays\na critical role in determining the switching amplitude. As previously discussed in Question 7 regarding\nthe multi-domain characteristics of the IMA component, a large preset magnetic field facilitates more\nuniform alignment of magnetic domains, thereby resulting in a larger SOT effective field.\nTo provide a more rigorous and quantitative physical picture, we performed a detailed analysis on how\nthe preset magnetic field influences the field-free switching behavior, and extracted the magnitudes of\nthe SOT equivalent fields. As shown in Fig. R8a, we extracted the equivalent field values at 250 K and\nonce the preset field exceeds approximately 2 T. Subsequently, we extracted the maximum equivalent\nfields achievable under saturated preset fields at different temperatures. As shown in Fig. R8b, the\nmaximum equivalent field decreases with increasing temperature. This reduction should arise from the\nthermal suppression of both the magnetization M and the interlayer exchange coupling coefficient J ,\ns ex\nwhich collectively weakens the SOT equivalent field.\nWe believe that this expanded analysis addresses the reviewer’s concerns and provides the rigorous\nphysical picture requested.\nFigure R8. Dependence of the equivalent field on preset magnetic field and temperature. a, Plot\n22\nof the equivalent field as a function of the preset magnetic field at 250 K and 275 K, the equivalent\nfield increases with the preset magnetic field. b, Plot of the maximum equivalent field as a function of\ntemperature under.\nGao et al. report the growth and characterization of a Fe₄GeTe₂/Bi₂Te₃ van der Waals\nferromagnet/topological insulator heterostructure, demonstrating field-free switching of the out-of-\nplane magnetization component of Fe₄GeTe₂. This study demonstrates several firsts, including the\ndemonstration of tunable IP to OOP magneto-anisotropy driven by proximity to a topological insulator,\npossibly due to interactions between topological surface states and the magnetism, as well as field-free\nswitching enabled by the coexistence of IP and OOP magneto-anisotropy without additional\nantiferromagnetic bias layers.\nThe manuscript is well organized and contains a comprehensive set of control experiments to quantify\nthe mechanism behind the field-free switching. The observation of tunable field-free switching and\ntopological insulator induced magneto-anisotropy will be of interest to both the spintronics field as\nwell as the broader community studying topological and magnetic heterostructures. However, among\nother concerns, the main mechanism of topological surface state induced magneto-anisotropy requires\nmore support and clarification. Overall, I am in support of the publication of this work in Nature\nCommunications following revisions to answer the following questions.\nResponse: We sincerely thank reviewer for the thorough and constructive evaluation of our manuscript.\nWe are grateful for the reviewer’s recognition of the significance of our work, including the\ndemonstration of interface-engineered tunable magnetic anisotropy in a van der Waals heterostructure\nand field-free SOT switching with chirality control. At the same time, we deeply appreciate the\nreviewer’s insightful questions and critical comments, which have substantially strengthened the\nscientific depth, clarity, and rigor of our manuscript. We have addressed every major and minor point\nraised by the reviewer with detailed explanations, new data, revised manuscript, and expanded\ndiscussions. We are confident that the revised manuscript presents a much clearer physical picture,\nstronger supporting evidence, and significantly improved exposition.\nKey Comments:\nQ1. The main claim of anisotropy tuning through topological surface states (TSS) is exciting as there\nare not many conclusive experimental works reported so far especially in a vdW heterostructure. As\n24\nthis is a key point of novelty for this work, this manuscript would be greatly strengthened if it can be\ndefinitively demonstrated that the anisotropy tuning comes from TSS enhancement. The authors cite\nthe example of TSS enhanced PMA in insulating iron garnets coupled with Bi Se , where theoretical\n2 3\ncalculations by Semenov et al. (Phys. Rev. B 86), 161406(R) show that anisotropy varies between\nPMA and IMA when the chemical potential is gated towards or away from the Dirac point. However,\nbesides proposing a TSS mediated exchange mechanism, the authors do not further support this claim\nwith experimental evidence or calculations.\nGiven that distinct system from the insulating iron garnets is being considered here, at a minimum,\nfirst principles theory would be needed to show that in the Fe₄GeTe₂/Bi₂Te₃ system, (i) The TSS-driven\ninteraction is indeed the dominant contributor to the PMA and (ii) The PMA depends systematically\non the chemical potential about the Dirac point. Establishing a systematic dependence of the magnetic\nanisotropy on the TSS would not only substantiate the mechanism proposed here but also expand the\nimpact of this work, with implications extending well beyond field-free switching. In this context,\ncould the authors also comment on possible experimental approaches to tune the chemical potential\ncloser to or further from the Dirac point, by for example, adjusting the Bi Te stoichiometry via growth\n2 3\nconditions\nResponse: Thank you for this insightful comment that significantly strengthens our manuscript. We\nfully agree that the mechanism of topological surface state (TSS)-mediated anisotropy tuning requires\nrobust theoretical support. Following the suggestions, we have performed additional first-principles\ncalculations to compare the magnetic anisotropy energy (MAE) of an isolated Fe GeTe system and a\n4 2\nBi Te /Fe GeTe heterostructure. In the following section, we provide an overview of the calculation\n2 3 4 2\nmethods and results:\nThe DS-PAW (Device Studio-Projector Augmented Wave) package was used to perform the density\nfunctional theory (DFT) calculations. The Perdew-Burke-Ernzerhof (PBE) functional within the\ngeneralized gradient approximation (GGA) was used to describe the exchange-correlation functional23.\nThe core-valence electron interaction was represented by the project-augmented wave (PAW) method24,\nand the cutoff energy of plane-wave basis was set to 500 eV. The DFT-D3 method was used to describe\n25\nthe dispersion interactions25. A k-points mesh of 7×4×1 was used in the optimization. To account for\nstrong correlations, an effective Hubbard U = 3.5eV (U = 3.5 eV and J = 0.5 eV) was applied to the\neff\n3d electrons of Fe atoms. During optimization, all atoms were fully relaxed until the maximum force\non each atom was less than 0.05 eV/Å.\nFig. R9 shows the calculated MAEs of these two material systems. The easy and hard magnetic axes\nwere identified as the orientations corresponding to the global minimum and maximum, respectively,\non the angular-dependent energy profile E(θ). For both the isolated Fe GeTe and the Bi Te /Fe GeTe\n4 2 2 3 4 2\nheterostructure, the MAE was calculated as MAE = E(θ=0°) - E(θ=90°), where θ represents the angle\nbetween the magnetization direction and the plane normal. Here, a negative MAE value indicates\nperpendicular magnetic anisotropy, while a positive value indicates in-plane anisotropy.\nThe calculations reveal a fundamental reorientation of the magnetic easy axis driven by interfacial\ncoupling with the topological insulator. For isolated Fe GeTe , a positive MAE shown in Fig. R9a\n4 2\nconfirms in-plane anisotropy, consistent with previous first-principles studies (ACS Appl. Electron.\nMater. 7, 9305-9319 (2025)26). In contrast, the Bi Te /Fe GeTe heterostructure exhibits a negative\n2 3 4 2\nMAE (Fig. R9b), clearly indicating the emergence of strong perpendicular magnetic anisotropy (PMA)\ninduced by the topological interface. This distinct MAE signature demonstrates that the topological\ninsulator layer substantially enhances PMA in the Fe GeTe system, even before any deliberate tuning\n4 2\nof the chemical potential is applied. The robust PMA, quantitatively reflected in the MAE value,\ntheoretically validates the central hypothesis of our work concerning TSS-mediated anisotropy\nenhancement.\nWe also appreciate the reviewer’s request to comment on how the chemical potential may be\nexperimentally controlled in our system. Several approaches are, in principle, viable. For instance,\ntuning the Bi/Te flux ratio can shift the Fermi level through modification of native defects (e.g., Bi\nvacancies, Te antisites). However, such off-stoichiometric Bi Te would lead to other impurities in the\n2 3\nsubsequent epitaxy Fe GeTe which obscures the interpretation of magnetic anisotropy. Therefore,\n4 2,\nalthough stoichiometry control is conceptually attractive, it requires careful optimization of growth\nparameters to avoid unwanted disorder and chemical reactions at the interface. Electrostatic gating is\nalso an effective way to shift the Fermi level without modifying the chemical structure. However, our\n26\ncurrent heterostructure is grown on Al O substrate, which is not suitable for back-gate operation.\n2 3\nOverall, while several tuning routes exist, their execution in our epitaxial TI/FM heterostructure\nrequires significant materials-engineering development. We are currently pursuing these approaches,\nand we hope to report systematic chemical-potential–dependent anisotropy studies in future work.\nIn addition, we thank the reviewer for providing the theoretical calculation of MAE on chemical\npotential. However, such calculations require a well-established correspondence with experimentally\naccessible Fermi-level shifts, and these experiments (stoichiometry tuning, gating) have not yet been\nfully realized in the present study. Therefore, we believe that producing a fully quantitative MAE–E\nf\nphase diagram would be more valuable after matching experimental conditions. Systematic theoretical\nand experimental validation will be the subject of future work.\nWe thank the reviewer again for this thoughtful and impactful suggestion, which has significantly\nstrengthened both the scientific context and future outlook of our work.\nFigure R9. First-principles calculation of the magnetic energy anisotropy for Fe GeTe and\n4 2\nBi Te /Fe GeTe .\n2 3 4 2\nQ2. On a related note, magneto-anisotropy can also be tuned by strain, (see Y. Wang et al. Adv. Mater.\n2020, 32, 2004533). Would the authors be able to compare from RHEED data the lattice parameters\nof the Fe₄GeTe₂/Bi₂Te₃ versus Fe₄GeTe₂ and comment on lattice reconstruction effects if any?\nthe growth process of the Bi Te /Fe GeTe heterostructure in situ using reflection high-energy electron\n2 3 4 2\ndiffraction (RHEED), and calculated the in-plane lattice constant from the RHEED stripe spacing. In\nthe calculation, the lattice constant of the sapphire (Al O ) substrate was taken as a reference value of\n2 3\na=4.75(cid:3031)A˚. The variation of the lattice constant with film thickness is shown in Fig. R10. It can be\nobserved that the bottom Fe GeTe layer experiences a very small tensile strain of approximately 0.7%,\n4 2\nwhich relaxes to the bulk lattice constant (a=4.04(cid:3031)A˚) within a few vdW layers.\nFurthermore, comparison with previously reported results also indicates that tensile strain does\nnot enhance the PMA of Fe GeTe . In the work by Y. Wang et al. (Adv. Mater. 32, 2004533 (2020))27,\n4 2\nthe coercive field of FGT was modulated via a flexible substrate, allowing for tunable magnetic\nanisotropy energy without altering its sign. In a more recent study by Hu et al. (Phys. Rev. B. 110,\n184418 (2024))28, the effect of strain on the magnetic anisotropy of FGT was investigated theoretically.\nThis study clearly demonstrated that compressive strain drives a transition of the easy magnetization\naxis from in-plane to out-of-plane: specifically, a 1% compressive strain induces this transition, while\na 4% compressive strain further enhances the perpendicular magnetic anisotropy. In our\nBi Te /Fe GeTe system, however, the Fe GeTe layer experiences only a minute tensile strain,\n2 3 4 2 4 2\nindicating that strain is not responsible for the observed change in magnetic anisotropy of FGT.\n2 3 2\na, The variation of the lattice constant with film thickness. b, RHEED images of Al O , Bi Te and\n2 3 2 3\nFe GeTe .\n4 2\nQ3. The authors use the second-harmonic Hall method to characterize the spin-orbit torque efficiency\nin the Fe₄GeTe₂(4)/Bi₂Te₃(12) which is a widely used technique for measuring spin-orbit torques\ndeveloped by Hayashi, M. et al. PRB. 2014, 89(14), 144425. This method assumes small angle\napproximations of a uniform magnetic layer. However, the heterostructures considered in this work\nhave a coexistence of regions with IMA/PMA and an intermediate canted region (Figure 4) which\nwould mean that the anisotropy parameter H in the denominator of equation (2) would not be uniform\nk\nacross the Fe₄GeTe₂ layers. It would be helpful if the authors can show that the uncertainty from this\nnon-uniformity is sufficiently small as when considering only the high-field regime claimed in the\nsupplementary, or if any other modifications to the conventional second-harmonic Hall equations are\nrequired to account for non-uniform Hk in similar tilted systems.\nResponse: We sincerely thank the reviewer for this insightful and professional question regarding the\napplicability of the conventional second-harmonic Hall analysis method to our complex\nheterostructure.\nWe concur with the reviewer that the standard model, developed for uniform magnetic layers, is indeed\nan approximation when applied to our system which exhibits coexisting PMA/IMA regions and an\nintermediate canted layer, implying a non-uniform anisotropy field. However, we argue that this\napproximation is reasonable and provides reliable results for our study based on the following\njustifications:\n(1) High-field 2ω fitting suppresses errors arising from non-uniform anisotropy\nFor our analysis, we employed the high-field approximation model developed by Hayashi et al.\n(Phys. Rev. B. 89, 144425 (2014)29). The fitting equation for the second-harmonic resistance 𝑅(cid:2870)(cid:3104)\n(cid:3051)(cid:3052)\nis given by:\n29\n𝑅 𝐻 𝐻 𝐻\n𝑅(cid:2870)(cid:3104) = (cid:3002) (cid:3005)(cid:3013) +𝑅 (cid:3007)(cid:3013) +𝑅 (cid:3051) +𝑅\n(cid:3051)(cid:3052) 2 |𝐻 |−𝐻 (cid:3017)|𝐻 | (cid:3020)(cid:3020)(cid:3006)(cid:2878)(cid:3002) |𝐻 | (cid:3042)(cid:3033)(cid:3033)(cid:3046)(cid:3032)(cid:3047)\n(cid:3051) (cid:3038) (cid:3051) (cid:3051)\nCrucially, this method is valid when the applied in-plane field |𝐻 | is sufficiently large compared\n(cid:3051)\nto the anisotropy field 𝐻 , or when the magnetization is aligned close to the in-plane direction.\n(cid:3038)\nUnder high in-plane magnetic fields in our measurement, the strong external field (|𝐻 | )\n(cid:3051)\ndominates the denominator terms, suppressing the influence of local variations in the internal\nanisotropy field (𝐻 ) across the non-uniform Fe GeTe layers. As discussed in similar itinerant\n(cid:3038) 4 2\nvan der Waals ferromagnetic systems like Fe GeTe , a sufficiently high field effectively drives the\n3 2\nentire sample into a single-domain configuration regardless of local anisotropy variations (“The\nhigh field aligns the domains at all tilt angles..., so the whole sample is effectively a single\ndomain.”) (Nature. 563, 94-99 (2018)30). Thus, this ensures that the small-angle oscillation\napproximation assumed in the formula is satisfied, making the extraction of the damping-like\neffective field (𝐻 ) reliable.\n(cid:3005)(cid:3013)\n(2) AHE-based GST extraction of 𝑯 naturally filters out contributions from IMA regions\n𝒌\nRegarding the sensitivity of AHE and the analysis method used, the AHE is predominantly\nsensitive to the out-of-plane magnetization component (M ). Consequently, the second-harmonic\nZ\nHall signal we measure primarily originates from the oscillations of the perpendicular\nmagnetization components within the PMA layer and potentially the canted interface region.\nFurthermore, our extraction of the anisotropy parameters (K , K ) utilizes the generalized\n1 2\nSucksmith-Thompson (GST) method applied to the AHE data, which is explicitly formulated as:\n2𝐾 (𝑇)+4𝐾 (𝑇)∙(1−𝑚 (𝑇)(cid:2870)) = 𝛼(𝑇)∙𝐻 ∙𝑀 (𝑇)\n(cid:2869) (cid:2870) (cid:3053) (cid:3046)\nwhere 𝛼 is a geometric factor related to the field angle 𝜃 :\n(cid:3009)\n𝑚 sin𝜃 −(cid:3493)1−𝑚(cid:2870)cos𝜃\n(cid:3053) (cid:3009) (cid:3053) (cid:3009)\n𝛼 =\n𝑚 (cid:3493)1−𝑚(cid:2870)\n(cid:3053) (cid:3053)\nAs shown in these equations (exemplified in AIP Adv. 7 (2017) 31), the analysis relies entirely on\nthe behavior of the normalized vertical magnetization component 𝑚 under an external field.\n(cid:3053)\nCrucially, this method inherently filters out the influence of the IMA layer. By fitting the 𝑚 data,\n(cid:3053)\nwe extract the effective perpendicular anisotropy field 𝐻 ≈ 2𝐾 ⁄𝑀 . This confirms that our\n(cid:3038) (cid:3032)(cid:3033)(cid:3033) (cid:3046)\n30\ncharacterization inherently focuses on the perpendicular magnetic anisotropy energy landscape\nthat governs the AHE dynamics.\n(3) Consistency with TI-based SOT literature validates the approach\nBased on our analysis method, the efficiency we obtained (𝜉 ≈0.8) is remarkably high and\n(cid:3005)(cid:3013)\nquantitatively consistent with the efficiencies reported in other high-performing topological\ninsulator-based SOT systems (e.g., 𝜉 values reported in Phys. Rev. Lett. 123, 207205 (2019)32).\n(cid:3005)(cid:3013)\nThis agreement provides strong empirical validation that the conventional high-field analysis\ncontributes a reliable and meaningful torque estimate for our system.\nIn summary, although our heterostructure exhibits spatially non-uniform magnetic anisotropy, the\napplication of the conventional second-harmonic method under high-field conditions provides a\nreliable and valid estimation of the SOT efficiency, sufficient for the main conclusions drawn in this\nwork.\nQ4. In Figure 3d, the authors show that the switching amplitude increases with the magnitude of the\npreset field, starting from 0 field and saturating near -2 T. However, in Figure 3e, a +1 T field after a -\nfigure 3a that the switching amplitude at 2T is slightly smaller than that for a -2T preset field. This\nappears to also be the case at 250 K and 270 K (Figure S6). Could the authors comment on the origins\nof this asymmetry for +ve vs -ve preset fields and whether there could be additional exchange bias\neffects contributing to this?\nIt would be helpful if the authors could include the in-plane magnetization hysteresis loops as well\n(analogous to figure 1b), to clarify the relationship between switching amplitude and the in-plane\nmagnetic state. Does the observed saturation behavior in the preset field correspond to the saturation\nof the in-plane magnetization at each temperature? Is there an offset in the in-plane magnetization\nhysteresis to explain the asymmetry between +ve and -ve fields?\nResponse: We thank the reviewer for this very insightful question and careful observation of the\n31\nasymmetric behavior associated with positive and negative preset in-plane magnetic fields. The\nreviewer accurately identifies related phenomena, and we agree they are all manifestations of the same\nunderlying physics. We will address them one by one.\nFor the first question, regarding the behavior in Fig. 3e, where a +1 T field after a -3 T preset field only\nsuppresses switching without reversing its sign, this is a result of the robust magnetic stability of the\npreset IMA state. For well understanding, we must clarify our experimental procedure: before any in-\nplane preset field (H ), a strong perpendicular initialization field is applied to uniformly set the PMA\npre\nand canted layers. Then, a strong -3 T in-plane preset field is applied to align the IMA layer, which in\nturn provides a strong effective field (H ) in the -x direction via interlayer exchange coupling.\neff,IMA\nTo\nreverse this state, an opposing field must overcome the total energy barrier holding the IMA layer's\nmagnetization. A +1 T field is insufficient to overcome this robust, coupled energy barrier and reverse\nthe entire IMA layer's magnetization. Instead, it only introduces disorder into the IMA layer, which\nweakens H and thus “suppresses” the SOT switching loop, exactly as observed.\neff,IMA\nIn response to this phenomenon, we repeated the experiment in a new prepared sample. The results,\nas shown in Fig. R11a, are consistent with our earlier observations. For the new device, with weaker anti-\ninterference capability, the IMA state was disrupted after applying a reverse field of -0.5 T. However,\nas the field was further increased, chirality-reversed was achieved at -1 T, albeit with a slightly smaller\nswitching window compared to directly applying a -1 T field (Fig. R11b). The overall trend during the\nreverse field application was consistent with the original paper. This indicates that a larger magnetic\nfield is required to uniformly align the IMA layer in the opposite direction once they are stabilized,\nfurther confirming our theory.\nafter applying an opposite magnetic field to the direction of the preset magnetic field. b, Comparison\nof field-free switching amplitudes after different preset magnetic fields.\nRegarding the second question, we thank the reviewer for raising this important question and for their\nkeen observation. We agree with the reviewer that a slight asymmetry in the switching amplitude is\nindeed present between the +2 T and -2 T preset magnetic fields in Fig. 3a and Fig. S6. Upon careful\nconsideration, we attribute the origin of this phenomenon primarily to differences in the initial state of\nthe magnetic system prepared by the oppositely directed vertical preset magnetic fields.\nIn direct response to this query, we performed additional experiments. As clearly shown in Fig. R12a-\nb, when we applied in-plane preset fields with the same magnitude but in two opposite directions, we\nobserved that the switching window for one direction was significantly narrower than for the other\nacross all preset fields. Comparing the field-free switching curves after the ±2.5 T preset field (Fig.\nR12c), aside from the reversal of switching polarity, there is a noticeable difference in the sizes of the\ntwo switching windows. This finding provides direct evidence that the asymmetry is a reproducible\nand systematic phenomenon.\npre\nfirst apply a strong perpendicular initialization field. This is done to set a uniform starting state for the\nPMA layer and simultaneously reset the underlying IMA layer into a consistent multi-domain state,\nensuring the subsequent H is applied to a reproducible magnetic texture.\npre\nIn this measurement, the initially applied out-of-plane magnetic field was in the +Z direction. When\nthis H is sufficiently large (e.g., ±2.5 T), it saturates the IMA layer, creating a single domain.\npre\nThis saturated IMA layer provides an internal effective field, H , via interlayer exchange coupling to\neff,IMA\nadjacent PMA layer. Theoretically, H should be equal in magnitude and opposite in sign for\neff,IMA\nsymmetric ±H , which would lead to symmetric SOT switching loops. However, our observation of\npre\nasymmetric windows clearly conflicts with this ideal picture. This strongly implies the existence of an\nadditional, stable in-plane “ghost” field, H , which is not reversed by the in-plane preset field.\nghost\nWe attribute this H to the transition layer in our Bi Te /Fe GeTe (PMA)/Fe GeTe\nghost 2 3 4 2 4 2\n(canted)/Fe GeTe (IMA) structure (as shown in Fig. 4d). We hypothesized that the in-plane\n4 2\ncomponent of this ’canted’ magnetic layer provides the H . To verify this, we performed a critical\nghost\ncontrol experiment: we reversed the initial perpendicular initialization field (to -Z) and repeated the\nSOT preset measurements. As shown in Fig. R12d, we observed that the SOT window asymmetry\ndisappeared. This conclusively demonstrates that the H is set by the initial perpendicular field,\nghost\nwhich determines the “canted-up” or “canted-down” orientation of the canted layer.\nTo further probe the magnetic rigidity of this canted layer, we performed the supplementary experiment\nshown in Fig. R12e. We measured the in-plane AHE loop after both +Z and -Z initialization. As seen\nin the plot, while the curves merge at high fields, they exhibit a clear vertical offset in R at low fields.\nxy\nThis offset is direct evidence of a stable, remnant perpendicular magnetization component whose sign\ndepends on the initial Z-field. Crucially, for a canted layer with uniaxial anisotropy, a pinned M\nZ\ncomponent necessarily implies a pinned M component. This pinned M is the H . Therefore, the\nx x ghost\ntotal effective field acting on the switching PMA layer is H = H + H , as illustrated in the\neff eff,IMA ghost\nschematic diagram in Fig. R13.\nThe high magnetic rigidity of this canted layer is an intrinsic physical consequence of its graded\n34\nmagnetic anisotropy. Our system is a self-assembled exchange-spring magnet (Phys. Rev. B. 58, 12193-\n12200 (1998)13). The Fe GeTe (PMA) layer (near the TI) acts as the “hard” layer, while the Fe GeTe\n4 2 4 2\n(IMA) (far the TI) acts as the “soft” layer. The Fe GeTe (canted) layer is the transition region, or\n4 2\n“spring”. The physical origin of its high rigidity stems from the intense competing anisotropies in this\nspecific region. Theoretical work on graded anisotropy media confirms that such transition regions,\nwhere anisotropy gradients are sharpest, can exhibit complex, non-uniform reversal modes and\nsignificantly higher effective coercivity than the uniform phases (Appl. Phys. Lett. 87 (2005)14; IEEE\nTrans. Magn. 41, 537-542 (2005)15). The existence of such distinct interface layers with unique\nmagnetic properties is a well-established phenomenon in epitaxial magnetic heterostructures (Rep.\nProg. Phys. 59, 1409 (1996)16). While the aforementioned inference has been supported by some\ntheoretical and experimental reports, direct observation of this transition layer may prove extremely\nchallenging in our system, given that it likely operates at the atomic scale. Nevertheless, our current\nexperiments clearly elucidate the origin of asymmetry in the SOT switching. This asymmetry cannot\nbe accounted for by a single homogeneous magnetism but is highly consistent with the complex non-\nuniform magnetization switching process within an exchange-spring system featuring gradient\nanisotropy.\nTherefore, our system contains two distinct in-plane fields acting on the switching layer:\n1) a tunable effective field H from the IMA layer, set by the external H . This field determines\neff,IMA pre\nthe SOT switching polarity.\n2) a fixed internal bias H from the canted layer, set by the initial Z-field. This H adds to or\nghost ghost\nsubtracts from H , causing the SOT switching window asymmetry.\neff,IMA\nThis explanation, where a fixed internal bias field creates asymmetric SOT loops, is fully consistent\nwith established SOT physics (Nature Mater. 15, 535 (2016)17; Nat. Commun. 7, 13367 (2016)18).\nAlthough this behavior is reminiscent of an exchange-bias effect, its physical origin is fundamentally\ndifferent. The internal bias here arises from a ferromagnetic exchange-spring structure with graded\nmagnetic anisotropy, rather than from interfacial coupling to an antiferromagnet. Therefore, we\ndescribe it as an exchange-bias-like internal field intrinsic to the heterostructure. Overall, the\nasymmetry between positive and negative preset fields are all consistent manifestations of the same\n35\ngraded-anisotropy, exchange-coupled magnetic structure, rather than evidence of extrinsic exchange\nbias or measurement artifacts.\nRegarding in-plane magnetization hysteresis loops and their possible connection to preset field for the\nswitching behavior, it is really correct that the preset field required for the saturation of the switching\namplitude could saturate the total in-plane magnetic moment, with its saturated value that has been\nwell documented in the wafer-scale MBE-grown F GeTe films (Nat. Commun. 14, 2483 (2023)33).\n4 2\nHowever, we believe the two “saturations” correspond to different physical quantities. As mentioned\nabove, the saturation of the switching amplitude reflects the establishment of a maximal effective\nsymmetry-breaking field acting on the PMA layer. This effective field depends on the detailed\nexchange coupling between the IMA, canted, and PMA regions, including the degree of domain\nhomogeneity and the strength of interlayer coupling, rather than solely on whether the magnitude of\nthe in-plane magnetization is saturated. If we carefully check the in-plane statured magnetic field for\nPMA layer, as shown in Fig. 1f, its value of ~2T is almost the same as the statured preset field for\nswitching amplitude. This result proves well with our hypothesis for the origin of the effective field\nfrom a combined effect. As mentioned above, Since the internal H from the pinned canted layer is\nghost\nrelatively small for the asymmetry with a value about 1mT, it is unlikely to produce a resolvable offset\nby conventional hysteresis loops, which include IMA, canted, and PMA signals together.\nWe hope our explanation could well address the concerns from the reviewer.\nmagnetization switching in Bi Te /Fe GeTe at 250 K after different in-plane magnetic fields along the\n2 3 4 2\nx-axis (after +z initialization). c, Asymmetric switching windows observed with +x (red) and -x (blue)\npreset fields after +z initialization. d, Symmetric switching windows obtained by comparing the “+z\ninit / +x preset” state with the “-z init / -x preset” state, confirming the asymmetry follows the\ninitialization field. e, In-plane AHE loops after +z and -z initialization. The zero-field vertical offset\nevidences a pinned canted layer, whose in-plane component acts as the static ghost field (H )\nghost\nswitching. It illustrates six different magnetic moment configurations. The diagram depicts the\ninterplay between H and H . The direction of H is determined by the in-plane preset field\neff,IMA ghost eff,IMA\n(+x or -x), while H is pinned by the initial vertical field (e.g., +z). When a +x preset field is applied,\nghost\nH aligns parallel to H , enhancing H and resulting in a larger switching window. Conversely,\neff,IMA ghost eff\na -x preset field aligns H antiparallel to H , reducing the total field and leading to a smaller\neff,IMA ghost\nswitching window. This model consistently explains the experimentally observed asymmetry.\nQ5. The authors perform substantial control experiments to show that the field-free switching enabled\n38\nby the preset field shows the same hysteresis amplitude after applying 100 mT in the opposite direction\n(figure 3e). However, the in-plane symmetry breaking field enabling field-free switching can be\ncancelled out by much smaller fields of -3 mT and +4 mT (figure 2e, 2d). The authors should consider\nclarifying that the stability to external fields is different for setting the polarity of the switching versus\nthe field-free switching operation of the device. Otherwise, broad claims of magnetic interference\nresistance should be avoided.\nResponse: We sincerely thank the reviewer for this insightful and crucial observation. We fully agree\nthat the effective field stability associated with setting the switching polarity should be clearly\ndistinguished from the external field for canceling field-free switching.\nFor deterministic switching, an in-plane field from either eternal field or intrinsic effective field is\nnecessary for breaking the symmetry. In our sample, the intrinsic effective field (−3 mT and +4 mT)\nis weak, and the total in-plane field for deterministic switching could be cancered by simultaneously\napplying a small external field. This feature is quite common (Adv. Funct. Mater. 31, 2105359 (2021)34)\nin field-free SOT systems. However, such intrinsic effective field is hard to destroy by external field.\nThis intrinsic effective field arises from the preset-field-induced magnetic configuration. The large\npreset field modifies and stabilizes the in-plane domain configuration, resulting in a remanent magnetic\nstate with a substantially higher energy barrier. Disrupting this preset configuration requires much\nlarger external fields, showing a strong magnetic interference resistance. Therefore, the robustness\ndiscussed above refers specifically to the stability of the preset magnetic configuration that is hard to\ndestroy, rather than to the weak effective field responsible for symmetry breaking.\nFollowing the reviewer, we have revised the description of this part in the main text (Page 13): “This\nhighlights the excellent anti-interference capability of the preset-field-induced magnetic state,\nreinforcing the critical role of the preset field in enabling stable, field-free switching.”\nMinor comments, questions:\nQ1. The term “delamination” on page 6 line 104 may be misinterpreted as describing a failure mode\nwhere the layers are peeling apart from each other, consider using an alternative phrasing such as\n“clean interface with no inter-diffusion.”\nthat the reviewer’s suggestion will effectively help prevent potential misunderstandings and therefore\nrepresent a valuable improvement to the manuscript.\nFollowing the reviewer, we have revised the text on page 6, line 104 accordingly. The original phrase\n“delamination between the layers” has been replaced with “a clean interface with no inter-diffusion\nbetween the layers” to accurately describe the high-quality interface of our heterostructure.\nQ2. Do the authors observe any sign of increased Curie temperature in the Fe₄GeTe₂/Bi₂Te₃\nheterostructure versus the Fe₄GeTe₂?\nResponse: We thank the reviewer for this insightful question. A significant enhancement of the Curie\ntemperature (T ) in the Fe GeTe /Bi Te heterostructure is also one of the key findings observed in this\nc 4 2 2 3\nwork.\nThrough variable-temperature anomalous Hall effect (AHE) measurements, as shown in Fig. R14, we\ndetermined that the T of our Fe GeTe /Bi Te heterostructure exceeds 400 K. This value represents a\nc 4 2 2 3\nsubstantial increase compared to the T values typically reported for isolated Fe GeTe flakes in the\nc 4 2\nliterature.\nZ\nBi Te /Fe GeTe heterostructure. a, R as a function of out-of-plane magnetic field measured at\n2 3 4 2 xy\ntemperatures from 100 to 300 K, showing well-defined ferromagnetic hysteresis loops. b, The\nevolution of R from 325 to 425 K, where the hysteresis loop gradually weakened.\nxy\nQ3. The authors mention that the 28% of the current is in the Bi₂Te₃ layer, is this accounted for in\nIwrite (equation 3) for the SOT efficiency?\nResponse: We thank the reviewer for raising this important point. In our calculations, the 28% current\nshunting into the Bi Te layer has been fully included in the SOT efficiency presented in Equation 3.\n2 3\nHowever, the Iwrite values shown in Fig. 2 correspond to the total applied current before shunting\ncorrection, consistent with the convention used in most prior studies.\nThe current I used in Equation (3) refers specifically to the effective current flowing through the\nwrite\nBi Te layer, rather than the total applied current, and is obtained by explicitly correcting for the 28%\n2 3\ncurrent shunting.\nEquation (3). The text surrounding Equation (3) now states:\nAccordingly, taking into account the 28% current shunting in the Bi Te layer (Fig. S3), the value of\n2 3\nthe 𝜉 is determined to be ~0.8 in Bi Te (12)/Fe GeTe (4) heterostructure at 300 K, demonstrating\n(cid:3005)(cid:3013) 2 3 4 2\na superior charge-spin conversion in all-vdW heterostructure.\nThe authors have investigated an all-vdW heterostructure (HS) Bi Te /Fe GeTe and demonstrated the\n2 3 4 2\nspin-orbit torque (SOT) switching application and some Boolean logic operations with this HS device.\nThe topic is interesting and consistent with the recent trend of spintronics applications but there is a\nserious point to mention.\nFrom the same (some of them) cluster of collaborative universitites and institutes, there is a similar\nwork done on Bi Te /Fe GeTe , demonstrating the SOT switching application of the HS, which was\n2 3 3 2\npublished in Nat. Comm. (Nat Comm. 14 5173 (2023)). The initial part of the currently submitted\nmanuscript has a huge resemblance with this work, except for the chirality dependence and Boolean\nfunctions. The initial main studies of magnetization, anomalous Hall, harmonic Hall are exactly similar.\nSince the main idea/concept and the followed pathway of investigations were already published in the\nsame journal just a couple of years back, the novelty of the presently submitted work does not match\nthe criteria of acceptance in Nat. Comm. Moreover, I found it a bit surprisingly unethical of not having\na mention of this earlier work at least once in detail, where almost all the initial studies are just the\nsame. They have only casually mentioned this earlier work from the similar cluster of collaborating\ninstitutes as reference number 34, while mentioning the sample without any detail. Although the first\nauthors of these two works are not the same, but the communicating author(s) are the same. This is not\na good scientific practice/protocol and the authors should rectify it before proceeding any further.\nI do not endorse publication of this work in Nature Communications. Below I am mentioning some\nmore points, which I found unclear while reading this work.\nResponse: We sincerely thank the Reviewer for raising this important concern. We acknowledge that\nour previous work on the Bi Te /Fe GeTe heterostructure (Nat. Commun. 14, 5173 (2023)35)\n2 3 3 2\nconstitutes a direct foundation for the present study, and we appreciate the opportunity to clarify both\nthe continuity and the essential distinctions between the two works.\nFirst, we would like to state explicitly that the present manuscript is part of a coherent research line\nthat builds upon our earlier Bi Te /Fe GeTe study. In that work, we demonstrated that a topological\n2 3 3 2\n43\ninsulator could serve as an efficient spin source to enable room-temperature SOT switching in an all–\nvan der Waals heterostructure. We agree with the Reviewer that the initial magnetic, anomalous Hall,\nand harmonic Hall characterizations follow a similar experimental pathway, which reflects\nmethodological continuity rather than simply repeating prior results. However, the central scientific\nquestion addressed in the present work is fundamentally different from that of the 2023 study. The\nearlier Bi Te /Fe GeTe system demonstrated highly efficient SOT-driven switching but still required\n2 3 3 2\nan external in-plane assist field, as the heterostructure itself did not provide an intrinsic symmetry-\nbreaking mechanism. In contrast, the present work is specifically designed to resolve this long-\nstanding limitation by achieving intrinsic, field-free SOT switching at room temperature.\nIn magnetic random-access memory (MRAM), perpendicular magnetic anisotropy (PMA) magnetic\nlayers exhibit great application potential owing to their higher integration density and switching\nefficiency. However, SOT-induced switching in PMA layers typically requires an external in-plane\nassist field to break the symmetry, which poses a significant obstacle for device applications. Therefore,\nachieving field-free switching in PMA layers is a necessary step toward the realization of practical\nspintronic devices.\nSeveral previously reported material systems—such as WTe / Fe GeTe (Nat. Mater. 21, 1029-1034\n2 3 2\n(2022)36) and TaIrTe /Fe GaTe (Nat. Commun. 16, 8722 (2025)37)—have utilized special out-of-plane\n4 3 2\nspin-polarized SOT sources to achieve field-free switching. Meanwhile, Yun et al. demonstrated that\nan asymmetric device geometry in Pt/ Fe GaTe enables field-free switching at room temperature (Sci.\n3 2\nAdv. 9, eadj3955 (2023)38). However, these material systems may face limitations in achieving wafer-\nscale fabrication of all-vdW structures, which hinders their potential for large-scale applications.\nFurthermore, these approaches primarily focus on realizing field-free switching through specialized\nSOT sources, while overlooking the critical role of the ferromagnetic layer in this process. This\noversight further diminishes the scalability of SOT spintronic devices.\nUnlike Fe GeTe and Fe GaTe , Fe GeTe exhibits a uniquely tunable magnetic anisotropy. Through\n3 2 3 2 4 2\nour deliberate design, we integrate magnetic layers with both PMA and in-plane magnetic anisotropy\n(IMA) into a single layer. The PMA in Fe GeTe was confirmed from the interfacial coupling with the\n4 2\nBi Te , while the IMA was from its intristinc anisotropy. This PMA–IMA coexistence gives rise to an\n2 3\n44\ninternal symmetry-breaking exchange field, eliminating the need for any external in-plane magnetic\nfield. Especially, we realized flexible control of the chirality in field-free SOT switching through tuning\nof the IMA layer. Such a mechanism is physically inaccessible in our previous Bi Te /Fe GeTe\n2 3 3 2\nsystem and represents a qualitative change in the switching physics rather than an incremental\nimprovement in performance.\nBased on this intrinsic field-free switching mechanism, the present work further implements\nreconfigurable Boolean logic operations within a single device. These functionalities are not intended\nas standalone novelties, but rather as direct consequences and validations of the newly introduced\ninternal symmetry-breaking degree of freedom, which does not exist in the earlier system.\nRegarding the Reviewer’s concern about scientific practice and citation, we take this point very\nseriously. We emphasize that there was no intention to downplay or obscure the contribution of our\nprevious work. When considering their totally different points of innovation, we did not expand for\ndetailed description of previous work. Nevertheless, for greater clarity, it is better to discuss the\nrelationship between the two studies more explicitly. In the revised manuscript, we have substantially\nrevised the Introduction to (i) clearly point to the novelty and limitations of the Bi Te /Fe GeTe work,\n2 3 3 2\n(ii) explicitly identify the unresolved problem of field-free switching, and (iii) articulate how the\npresent Bi Te /Fe GeTe system addresses this problem through a fundamentally different physical\n2 3 4 2\nmechanism.\nIn summary, while the two studies employ similar experimental methods and research lineage, they\naddress distinct physical challenges. The present work goes beyond the earlier demonstration of SOT\nswitching by introducing an intrinsic, materials-enabled route to field-free and chirality-reconfigurable\nswitching in a wafer-scale all–vdW system. We hope that this clarification, together with the revised\nmanuscript, adequately addresses the Reviewer’s concerns and clearly delineates the novelty and scope\nof the present study.\nFollowing the reviewer, we have added the following description on main text:\n“…including demonstrations in Bi Te /Fe GeTe heterostructure15, (Bi,Sb) Te /Fe GeTe\n2 3 3 2 2 3 3 2\nheterostructure16, etc. However, an external magnetic field is still needed to break symmetry for\n45\ndeterministic switching, which hinders the integration of SOT devices on semiconductor chips.” (Page\n3)\n“Notably, unlike Fe GeTe 15, Fe GeTe exhibits a uniquely tunable magnetic anisotropy, enabling the\n3 2 4 2\ncoexistence of PMA and IMA within a single layer36. This PMA–IMA coexistence gives rise to an\ninternal symmetry-breaking exchange field, eliminating the need for any external in-plane magnetic\nfield.” (Page 5)\nQ1. The authors could have mentioned the earlier work and then compare that with the current one,\nsince the FGT material is different. F GT (Fe GeTe ) is far more complicated as well as interesting\n4 4 2\nmaterial in comparison to F GT (F GT). F GT has a spin-reorientation transition at 100K, beyond\n3 3 2 4\nwhich temperature, the spontaneous magnetization of the system is oriented in-plane and the value of\nthe in-plane magnetic anisotropy is not negligible. In-fact, the temperatures at which the HS is studied\nhere are all above 100K. So, the demand of the authors that the F GT layer in proximity of Bi Te will\n4 2 3\nacquire a perpendicular orientation of magnetization, may not be so simple.\nResponse: We thank the reviewer for the important reminder regarding the spin-reorientation\ntemperature of F GT. As the reviewer correctly points out, this unique spin reorientation is a key\n4\ncharacteristic of F GT and represents a major distinction from F GT. However, in our work, we focus\n4 3\non maintaining the PMA in F GT/Bi Te heterostructure up to room temperature through interface\n4 2 3\nengineering, rather than on the intrinsic spin reorientation behavior of F GT itself. To avoid any\n4\npossible misunderstanding, please allow us to provide a more detailed clarification of these two aspects:\n(1) Fe GeTe away from the Bi Te retains its intrinsic IMA. In our heterostructure, the F GT layer\n4 2 2 3 4\naway from the Bi Te interface indeed exhibits IMA at the measured temperatures (>100(cid:3031)K),\n2 3\nconsistent with previous reports (Appl. Phys. Lett. 127, 082402 (2025)39). This IMA component\ncontributes to the interlayer exchange coupling field that enables field-free switching and chirality\ncontrol in the device. However, the F GT in close proximity to the Bi Te interface retains\n4 2 3\nPMA above 100(cid:3031)K, implying that the topological interface effectively elevates the spin-\nreorientation temperature. This interfacial effect will be discussed in the following section,\nincluding the simultaneous presence of both IMA and PMA signatures as further demonstrated\nin Question(cid:3031)4.\n46\n(2) Interface-Induced Elevation of the spin-reorientation temperature: In our work, we\nmodulated the magnetism of F GT through the interfacial engineering of Bi Te , as confirmed by\n4 2 3\nour temperature-dependent AHE measurements (Fig. R14). The AHE measurements reveal a clear\ntransition from PMA to IMA with increasing temperature. A large remanence could be observed\nat 300 K, indicating strong PMA (Nature 563, 94-99 (2018)30). Upon heating to 325 K, 350 K,\nand 375 K, the distinct but diminishing loops mark the progressive suppression of PMA and the\nemergence of IMA-dominated behavior (Phys. Rev. B. 111, 224420 (2025)40). The results show\nthat the spin-reorientation transition of F GT is significantly elevated in the F GT/Bi Te\n4 4 2 3\nheterostructure compared to F GT. This shift demonstrates that the topological interfacial effect\n4\nis effectively competing with and overcoming the intrinsic in-plane anisotropy, stabilizing the\nperpendicular magnetization state to a higher temperature range, ultimately achieving room-\ntemperature operation.\nWe hope that the above explanation clearly illustrates the fact that interfacial engineering in our work\nenables the stabilization of high-temperature PMA, and we believe that this clarification could\nadequately address the reviewer’s concerns.\n.\nz\nBi Te /Fe GeTe heterostructure. a, R as a function of out-of-plane magnetic field measured at\n2 3 4 2 xy\ntemperatures from 100 K to 300 K, reveals clear PMA feature. b, R as a function of out-of-plane\nxy\nmagnetic field measured at temperatures from 325 K to 425 K, reveals the characteristic signatures of\nspin-reorientation transition in Fe GeTe . The systematic vanishing of remanence with increasing\n4 2\ntemperature demonstrates the gradual rotation of magnetic moments, confirming the persistence of\nspin-reorientation behavior in this material.\nQ2. F GT is far more isotropic than F GT (S.R. Kim et al. ACS Appl. Nano Mater. 5, 10341 (2022)).\n4 3\nIs the slightly lower value of critical current (1.55 X 106) in F4GT in comparison to 2.2 X 106 in F GT\nperformance?\nResponse: We thank the reviewer for raising this important point regarding the relationship between\nmagnetic anisotropy and the critical switching current.\n3 2 3 4\nthe robustness of data retention. In fact, by comparing the field-assisted switching of our F GT with\n4\npreviously reported F GT systems (e.g., Haiyu Wang et al., Nat. Commun. 14, 5173 (2023)35), we\n3\nfound that the effective anisotropy field (𝐻 ) at 300 K is slightly larger in our F GT system.\n(cid:3038) 4\nThis\nconfirms that our F GT device maintains a robust thermal stability barrier (∆= 𝐾 𝑉⁄𝑘 𝑇) sufficient\n4 (cid:3048) (cid:3003)\nfor non-volatile applications (Nat. Mater. 9, 721-724 (2010)41).\nSecond, the intrinsic spin-reorientation characteristic of F GT is, in fact, a significant advantage for\n4\nour work. This tunable anisotropy allows us to engineer the sophisticated PMA/Canted/IMA coexisting\nstructure. This structure provides the intrinsic symmetry-breaking field necessary to make F GT a\n4\nperfect platform for field-free SOT switching (Adv. Funct. Mater. 31, 2105359 (2021)34), a capability\nthat is difficult to achieve in materials with rigid, single-phase anisotropy.\nRegarding the lower critical current density (𝐽 ), our analysis indicates that it is not primarily driven\n(cid:3030)\nby the weaker anisotropy. According to the established analytical model for SOT switching, 𝐽 is\n(cid:3030)\ngiven by:\n𝛼𝑀 𝐻\n(cid:3046) (cid:3038)\n𝐽 ∝\n(cid:3030) 𝜃\n(cid:3020)(cid:3009)\n(e.g., Appl. Phys. Lett. 102 (2013)42)\nAs shown in the equation, while 𝐽 is indeed proportional to the anisotropy field 𝐻 , it is also\n(cid:3030) (cid:3038)\ninversely proportional to the SOT efficiency (𝜃 ). While a moderate 𝐻 contributes to lowering the\n(cid:3020)(cid:3009) (cid:3038)\nswitching barrier, we argue that the primary driver for the significantly reduced 𝐽 in our work is the\n(cid:3030)\ndenominator term—the remarkably enhanced SOT efficiency. Our Bi Te /F GT heterostructure\n2 3 4\nbenefits from superior interfacial spin injection and more favorable band alignment compared to the\nF GT system, leading to a much higher charge-to-spin conversion efficiency (𝜃 ≈ 0.8).\n3 (cid:3020)(cid:3009)\nTherefore, the superior performance of our system stems from an optimal balance: a high SOT\nefficiency that drastically reduces energy consumption, combined with a robust magnetic anisotropy\nthat ensures thermal stability.\n4\ncommensurate spin-spirals with different pitch (Phys. Rev. B 111 134449 (2025)). Defining this system\nas the in-plane magnetic anisotropic (IMA) component of the HS is an oversimplified statement. The\nauthors should describe the physics of this system after taking into account these complicated magnetic\ntexture. It is not a simple ferromagnet.\nResponse: We sincerely appreciate the reviewer’s insightful reminder regarding the complex chiral\nmagnetic textures in F GT, which undoubtedly strengthens the scientific rigor of our work. As the\n4\nreviewer correctly pointed out, the magnetic state of F GT is indeed complex and non-trivial at low\n4\ntemperatures, and the definition of the IMA component in our heterostructure must fully account for\nthis complexity. This is an important point, and we appreciate the opportunity to clarify the physical\npicture adopted in our work.\nThe key distinction lies in the relevant temperature and energy scales. The chiral spin textures\ndiscussed in Ref. (Phys. Rev. B. 111, 134449 (2025)43) are stabilized at relatively low temperatures\n(typically below ~150 K), where interlayer exchange frustration and weak thermal fluctuations allow\ncommensurate spin spirals with layer-dependent pitch to form. In contrast, the central experiments in\nour study are performed at elevated temperatures (250–300 K), where strong thermal fluctuations\nsubstantially suppress long-range non-collinear order. Under these conditions, fine magnetic textures\nare effectively thermally averaged and do not act as stable order parameters governing the macroscopic\nmagnetic response.\nIn this high-temperature regime, the magnetic behavior of F GT is dominated by its spin-reorientation\n4\ntransition and is well described by an effective in-plane magnetic response, as consistently observed\nin bulk and thin-film experiments (Appl. Phys. Lett. 127, 082402 (2025)39, Phys. Rev. B. 111, 224420\n(2025)40, Sci. Adv. 6, eaay8912 (2020)44). Importantly, in our manuscript, the term “IMA component”\ndoes not imply a rigid, single-domain collinear ferromagnet. Rather, it refers to an effective in-plane\nmagnetic contribution that produces a net in-plane magnetization or susceptibility, which can be biased\nby a preset in-plane field and coupled to the PMA component through interlayer exchange.\nFrom the perspective of spin-orbit torque switching, the decisive factor is not the microscopic\n50\ncollinearity of the spin texture, but the existence of a finite, trainable in-plane magnetic component\nthat breaks symmetry and generates an effective in-plane exchange field acting on the PMA layer. This\neffective description remains valid even if the underlying magnetic structure is spatially non-uniform\nor contains residual short-range non-collinear correlations. Indeed, the gradual saturation of the\nswitching amplitude with increasing preset field observed in our experiments is more naturally\nexplained by such a non-rigid, multi-component magnetic response rather than by an idealized single-\ndomain IMA ferromagnet.\nWe therefore acknowledge the intrinsic magnetic complexity of F GT, while emphasizing that, under\n4\nthe temperature and measurement conditions relevant to this work, its magnetic response can be\nappropriately captured by an effective in-plane magnetic component. This description is sufficient to\nexplain the observed field-free SOT switching and does not rely on assuming a simple collinear\nferromagnetic ground state.\nWe thank the reviewer again for raising this important point, which has helped us clarify the physical\nscope and validity of the effective magnetic picture used in this study.\nQ4. Is there any experimental reference which has proved the perpendicular magnetic anisotropy\n(PMA) of Bi Te ultrathin films? It may so happen that in both of the component layers, the\n2 3\nmagnetization directions are canted（ IMA＋PMA） and are composed of complex spin textures. What\nare the expected impacts of chiral magnetism on the SOT performance?\nResponse: We thank the reviewer for raising this important point. We address this issue in three parts\nand provide a detailed response to each.\nPart.1: Discussion on excluding the possibility of magnetism in Bi Te within our heterostructure\n2 3\n(1) Bi Te is intrinsically a non-magnetic material. As reported in the previous literatures (J. Alloys\n2 3\nCompd. 899, 163297 (2022)7, New J. Phys. 15, 103016 (2013)45, Appl. Phys. Lett. 105 (2014)46),\npristine Bi Te does not exhibit any magnetic ordering. Consistently, Bi Te -only control devices\n2 3 2 3\nin our study show no signs of an anomalous Hall effect (AHE) or magnetic hysteresis, confirming\n51\nits intrinsic non-magnetic character.\n(2) The reported potential external magnetism in topological insulators shows a significant\ndifference from our experimental results. As for the introduction of magnetism into Bi Te\n2 3\nthrough proximity effect, the resulting Curie temperatures usually remain very low (Nano Lett.\n14, 3459-3465 (2014))8. Even in the extremely limited report claiming a Curie temperature near\nmagnetic materials, particularly in its magnetic moments with two orders of magnitude smaller\nfrom the experimental results presented in our study.\nIn summary, the robust PMA signal observed in our heterostructure unequivocally not from the Bi Te\n2 3\nlayer itself.\nPart2: Discussion on the magnetic moment configuration in the ferromagnetic layer.\nWe thank the reviewers for their constructive comments. We appreciate the opportunity to clarify that\nour results are better explained by a depth-dependent transition from IMA to PMA rather than\nuniformly canted moments throughout the layers. Indeed, the coexistence of PMA and IMA and their\norigins are the core issues of this study. We believe that the source of PMA is attributed to the interfacial\neffect between the topological insulator and Fe GeTe , which enhances the PMA characteristics of the\n4 2\nferromagnetic layer adjacent to Bi Te , allowing it to retain PMA properties even at room temperature.\n2 3\nIn contrast, the ferromagnetic layers farther away from Bi Te still exhibit IMA characteristics. This\n2 3\npicture was corroborated by the decomposed signal of the sample in Fig. 1b of the main text,\ndemonstrating the coexistence of both IMA and PMA components. To further confirm that the\ndistribution of IMA and PMA is related to the distance from Bi Te , specifically their spatial\n2 3\ndistribution along the Z-axis, we conducted X-ray Magnetic Resonance Reflectivity (XRMR)\nmeasurement.\nXRMR is a synchrotron radiation-based material characterization technique. By precisely tuning the\nX-ray energy to the absorption edge of specific elements and utilizing the magnetic circular dichroism\neffect, it can non-destructively probe the spatial distribution of magnetization inside magnetic thin film\nmaterials with elemental specificity and sub-nanoscale depth resolution1,2. Using this technique, the x-\nray reflectivity curves of the sample at different incident angles can be precisely measured near the\nresonance energy3-5. In this study, we employed this technique to focus on observing and analyzing\ninformation from both the surface and deeper layers of the sample, thereby investigating the spatial\ndistribution of the sample's magnetic properties.\nThe measurements were carried out at SEXTANTS beamline of the synchrotron SOLEIL using the\nRESOXS end-stations6. XRMR was measured in θ − 2θ scattering geometry, with a fixed energy and\nfixed helicity of the circular polarized incident x-rays. The energy was chosen to be 1eV below the\npeak of the Fe L absorption edge. In order to magnetize the samples and generate a magnetic contrast\n3\nfor the measurements. The in-plane magnetic field was switched between parallel and antiparallel\norientation with respect to the x-ray beam propagation, with a maximum applied magnetic field of\n±150 mT. For out-of-plane measurements, the magnetic field was applied normal to the sample surface\nand reversed between positive and negative directions, with a maximum field of ±300 mT. For each\nincident angle, the magnetic field was reversed between positive and negative at each point during the\nXRMR measurements. The reflected intensity signals are recorded as 𝐼 and 𝐼 for opposite applied\n(cid:2878) (cid:2879)\nmagnetic field, and the asymmetry ratio is defined as 𝑅 = (𝐼 −𝐼 )/(𝐼 +𝐼 ). Figure R15 presents\n(cid:2878) (cid:2879) (cid:2878) (cid:2879)\nthe reflectivity curve and the asymmetry ratio, demonstrating the relationship between signal intensity\nand detection angle. By varying the incident angle in XRMR, the depth sensitivity of the measurement\nis modified through angle-dependent interference and penetration effects1,2. Consequently, a rough\napproximation small angles preferentially weight the near-surface magnetization, while larger angles\nincrease sensitivity to deeper regions of the film. Measurements were conducted under out-of-plane\nand in-plane magnetic fields respectively, with all signals collected using the circular left polarized\n(CL) x-ray during testing.\nAs shown in Fig. R15a and Fig. R15c, it can be observed that under an out-of-plane magnetic field, I\n+\nand I overlap, and the asymmetry ratio R remains nearly zero at small angles (0-10°). In contrast, as\n-\nshown in Fig. R15b and Fig. R15d, under an in-plane magnetic field, the two measurement curves\nshow clear separation, revealing a significant asymmetry ratio R. By combining the penetration depth\nat grazing incidence with the observed magnetic asymmetry and hysteresis loop measured at 9.5° under\nan in-plane magnetic field (Fig. R15e), it can be concluded that the surface layer consists\npredominantly of IMA components. As the incident angle increases, the XRMR signal becomes\nincreasingly sensitive to magnetization contributions from deeper regions of the sample, rather than\nbeing dominated solely by the near-surface layer. Field-sweep measurements were performed using\nCL at 50° under both in-plane (Fig. R15f) and out-of-plane magnetic fields (Fig. R15g). Analysis of\nthe hysteresis loops reveals that during in-plane field sweeps, the sample saturates rapidly at low\nmagnetic fields, suggesting that IMA behavior still dominates at this detection angle. However, as the\nfield increases, the signal exhibits a gradual saturation trend, indicating the presence of components\nwith in-plane hard axes—i.e., a contribution from PMA components. On the other hand, the out-of-\nplane magnetic field sweep test shows an overall gradual saturation trend, with a small remanence\nobserved at zero magnetic field, indicating the presence of PMA components. Overall, these results\nconfirm that the IMA and PMA components in the sample indeed exhibit a spatial distribution\ncharacteristic correlated along the Z-axis. Meanwhile it could exclude the possibility of\nrepresenting a uniform canting of magnetic moments throughout the layers.\n2 3 4 2 3\nedge. a, b, XRMR reflectivity curve under out-of-plane (a) and in-plane (b) magnetic fields. c, d,\nCorresponding asymmetry ratios calculated from the normalized difference of the two measurements\nwith opposite magnetic fields. e, f, g, Hysteresis loop of the Bi Te /Fe GeTe heterostructure measured\n2 3 4 2\nat 9.5° under in-plane magnetic fields (e), at 50° under in-plane magnetic fields (f) and out-of-plane\nmagnetic fields (g).\nPart3: Expected impacts of chiral magnetism on the SOT performance.\nWe acknowledge that Fe GeTe can host complex non-collinear or chiral magnetic textures under\n4 2\ncertain conditions, particularly at low temperatures, as stated in Q3. However, the SOT switching\nexperiments in this work are performed at elevated temperatures (250–300 K), well above the stability\nwindow where such long-range chiral order is expected to persist. Under these experimental conditions,\nthermal fluctuations strongly suppress fine magnetic textures, and transport-based SOT measurements\nprobe an effective, spatially averaged magnetic response. The IMA-PMA structure proved above\nexplains our chirality-tunable field free SOT switching behavior.\nIn summary, Bi Te does not possess intrinsic PMA, and the PMA observed in this work arises from\n2 3\ninterface-modified Fe GeTe . The heterostructure is best described by a depth-dependent anisotropy\n4 2\nprofile rather than a uniformly canted magnetic state. We thank the reviewer again for this insightful\ncomment, which has helped us clarify the physical assumptions and scope of our analysis.\nQ5. The origin of spin-reorientation transition in F GT is strongly related to the strong inherent spin-\n4\nphonon or magnon-phonon coupling present in this material. Does it have any impact on the SOT\nperformance?\nResponse: We thank the reviewer for this insightful physical question, which touches upon the crucial\nrelationship between the intrinsic magnetic properties of F GT and the SOT performance.\nanisotropy of the F GT. This temperature dependence is fundamentally governed by intrinsic many-\n4\nbody effects, such as the spin-phonon or magnon-phonon couplings mentioned. These interactions\n55\nrenormalize the magnetic free energy landscape of the material, leading to a change in the anisotropy\nconstants as a function of temperature (J. Phys. Chem. Solids. 27, 1271-1285 (1966)47, J. Magn. Magn.\nMater. 565, 170257 (2023)48). The SRT occurs when the balance of these competing anisotropy\nenergies shifts, causing the magnetic easy axis to reorient.\nTo clarify how this mechanism impacts SOT performance, it is essential to consider the governing\nequation of motion for the magnetization, the Landau-Lifshitz-Gilbert (LLG) equation, which is\nmodified to include the SOT torque (𝜏 ) (IEEE Trans. Magn. 40, 3443-3449 (2004)49):\n(cid:3020)(cid:3016)(cid:3021)\n𝑑𝑀 𝛼 𝑑𝑀\n= −𝛾 (cid:3435)𝑀×𝐻 (cid:3439)+ (cid:3436)𝑀× (cid:3440)+𝜏\n𝑑𝑡 (cid:2868) (cid:3032)(cid:3033)(cid:3033) 𝑀 𝑑𝑡 (cid:3020)(cid:3016)(cid:3021)\n(cid:3020)\nHere, the dynamics of 𝑀 are dictated by two physically distinct sets of mechanisms.\nFirst, the internal stability of 𝑀 is described by the precession and damping terms, which depend on\nthe effective magnetic field 𝐻 . This 𝐻 is the sum of the external field, the demagnetization\n(cid:3032)(cid:3033)(cid:3033) (cid:3032)(cid:3033)(cid:3033)\n(cid:3032)(cid:3033)(cid:3033)\nfield, and, most importantly, the effective anisotropy field (𝐻 ). The spin-phonon coupling\n(cid:3038)\n(cid:3032)(cid:3033)(cid:3033)\nmechanism described by the reviewer is precisely what determines the value of 𝐻 and its strong\n(cid:3038)\ndependence on temperature.\nSecond, the external 𝜏 is the mechanism we use to manipulate 𝑀. This torque is generated by the\n(cid:3020)(cid:3016)(cid:3021)\nspin source and the interface, originating from the Spin Hall Effect or Rashba-Edelstein Effect (Rev.\nMod. Phys. 87, 1213-1260 (2015)50, Rev. Mod. Phys. 91, 035004 (2019)51). The “SOT performance”\nis a measure of the efficiency (𝜃 ) of this generation process, which is an intrinsic parameter within\n(cid:3020)(cid:3009)\nthe 𝜏 term (e.g., 𝜏 ∝ 𝜃 𝐽 ).\n(cid:3020)(cid:3016)(cid:3021) (cid:3005)(cid:3013) (cid:3020)(cid:3009) (cid:3032)\nTherefore, the intrinsic spin-phonon coupling mechanism does have an impact, but not on the 𝜃 .\n(cid:3020)(cid:3009)\n(cid:3032)(cid:3033)(cid:3033)\nInstead, the spin-phonon coupling defines the magnetic stability of the F GT layer (the 𝐻 it\n4 (cid:3038)\n(cid:3032)(cid:3033)(cid:3033)\nexperiences). This anisotropy 𝐻 sets the energy barrier for reversal, which in turn determines the\n(cid:3038)\nthreshold or 𝐽 required to successfully switch the magnetization (Appl. Phys. Lett. 102 (2013)42).\n(cid:3004)\nIn summary, the mechanism of SOT generation (quantified by 𝜃 ) and the mechanism of F GT's\n(cid:3020)(cid:3009) 4\n56\nmagnetic stability (determined by 𝐻\n(cid:3032)(cid:3033)(cid:3033)(𝑇)\nvia spin-phonon coupling) are physically decoupled. The\n(cid:3038)\nlatter only affects the threshold needed for the former to act, not the fundamental efficiency of the act\nitself.\nQ6. In line number 106, while describing Fig 1(b), it is just mentioned that the results indicate the\npresence of both PMA and IMA components. The authors should clearly describe here that what are\nthose indications? Just by looking at the hysteresis loops, it is impossible to know it.\nResponse: We sincerely apologize for the not sufficiently detailed statement in our manuscript. To\naddress this issue, we have revised the description in the manuscript to explicitly connect the features\nobserved in the hysteresis loop to the presence of both perpendicular magnetic anisotropy (PMA) and\nin-plane magnetic anisotropy (IMA) components. The original sentence: “The results of the vibrating\nsample magnetometer (VSM) measurement of Bi Te (12)/Fe GeTe (4) heterostructures under out-of-\n2 3 4 2\nplane magnetic field are shown in Fig. 1b, which indicate that the heterostructures contain both PMA\nand IMA components.” has been replaced with the following more detailed explanation: “Figure 1b\npresents a typical VSM measurement of M as a function of the out-of-plane (OOP) magnetic field. The\nsharp reversal and hysteretic behavior observed around μ H = 0 are indicative of the PMA component.\n0 z\nThe increase in M at higher field strengths suggests a gradual transition of magnetization from in-plane\n(IP) to OOP orientation, affirming the presence of an IMA component. This M-H loop distinctly\ndemonstrates the coexistence of both IMA and PMA components within the Fe GeTe layer. The M-H\n4 2\ncurve can be decomposed into a hysteresis loop attributable to Fe GeTe (PMA, adjacent to Bi Te )\n4 2 2 3\nand a hard axis loop corresponding to Fe GeTe (IMA, away from Bi Te ), as shown in the inset.”\n4 2 2 3\n(Page 6)\nWe believe this revised text now clearly specifies the \"indications\" within the hysteresis loop, as\nrequested by the reviewer, making our interpretation unambiguous for the reader.\n2 3 4 2\nunder out-of-plane magnetic field at 300 K. The inset shows the separation of the curve.\nQ7. In a similar manner, while describing Fig 1d (line number 116), they state that the anomalous Hall\nresistance curves demonstrated “excellent PMA feature”. Here too, the features are unclear and the\nanalysis is needed to be more descriptive.\nResponse: We apologize again for the not sufficiently clear statement in the text. To clarify the\nindicating “excellent PMA feature” in Fig. 1d, we have revised the manuscript accordingly. The\noriginal sentence has been replaced with the following more descriptive analysis: “Figure 1d illustrates\nthe anomalous Hall resistance (R ) curves of the Bi Te (12)/Fe GeTe (4) heterostructure with an out-\nxy 2 3 4 2\nof-plane magnetic field from 100 K to 300 K. Throughout the entire temperature range, the R\nxy\nmeasurements yielded hysteresis loops with pronounced remanence and relatively sharp switching,\nand they reach saturation under modest perpendicular magnetic fields. These features clearly indicate\nthe presence of regions where the magnetization vector is perpendicular to the film plane, meaning the\nexistence of components with strong PMA.” (Page 7) This revision explicitly links the specific shape\nof the R curves to the conclusion of strong perpendicular magnetic anisotropy.\nxy\nQ8. Almost all equations used for the F GT and F GT papers are very similar.\n3 4\nResponse: We thank the reviewer for their careful examination of our manuscript. The reviewer is\ncorrect that the analytical equations used in this work are similar to those in the previous study on\n2 3 3\ncommunity-accepted analytical framework in spin–orbit torque (SOT) research.\nThe equations used to extract key quantities such as the critical switching current density (𝐼 ) and\n(cid:3050)(cid:3045)(cid:3036)(cid:3047)(cid:3032)\nthe SOT efficiency (𝜉 ) are not system-specific, but rather constitute the established methodology for\n(cid:3005)(cid:3013)\ncharacterizing SOT-driven switching in perpendicularly magnetized systems. Employing the same\nanalytical framework is essential to ensure quantitative consistency and to enable meaningful\ncomparison across different material platforms, including between the F GT- and F GT-based\n3 4\nheterostructures.\nThe formula for critical current density (our Eq. 1) is a fundamental model for describing SOT\nswitching in perpendicular systems, as established in foundational works such as Appl. Phys. Lett. 102\n(2013)42 and Nat. Nanotechnol. 11, 621-625 (2016)52.\nThe harmonic Hall fitting equation (our Eq. 2) and the SOT efficiency formula (our Eq. 3) are based\non the widely accepted methodology developed by Hayashi et al. and further refined in works like\nPhys. Rev. Lett. 123, 207205 (2019)32, which has become the standard for accurately measuring SOT\neffective fields.\nUsing this standardized analytical framework is a necessary prerequisite for ensuring that our results\ncan be meaningfully and directly compared to prior work, including our own study on F GT and other\n3\nreports in the literature53-57. Adopting a different or non-standard set of equations would obscure the\ndirect comparison of performance and physical parameters.\nTherefore, the novelty of our current work does not lie in the development of a new analytical\nformalism. Rather, it lies in the application of this established framework to a new and physically\ndistinct material system, which reveals the fundamentally different physics of polarity-tunable field-\nfree switching—a key focus of this work, distinct from the previous study. Specifically, the consistent\nuse of these equations allows us to unambiguously demonstrate that the critical switching current\ndensity in our F GT system is substantially lower than in the F GT system, and the SOT efficiency is\n4 3\nmarkedly higher. Most importantly, this framework allows us to analyze and understand the novel\nphysical mechanism responsible for this enhanced performance—namely, the field-free switching\n59\nenabled by the intrinsic coexistence of PMA and IMA components within the F GT layer itself.\nfundamentally new physical insights and device functionalities. We believe that the methodological\ncontinuity strengthens, rather than diminishes, the significance of the present results.\nQ9. The SOT efficiency in F GT device is more the F GT ones. What could be the possible reason for\n4 3\nthis?\nResponse: We thank the reviewer for this crucial question. The enhanced SOT efficiency (≈ 0.8) in\nour Bi Te /F GT heterostructure, which is higher than that reported for the Bi Te /F GT system,\n2 3 4 2 3 3\nis indeed a notable finding of our work.\nIt should be emphasized that the measured SOT efficiency is an effective quantity influenced by\nmultiple factors. Based on these considerations, we discuss below several plausible mechanisms that\nmay contribute to the higher efficiency in the Bi Te /F GT device.\n2 3 4\n(cid:3032)(cid:3033)(cid:3033)\nFirst, the effective SOT efficiency (𝜉 ) is critically dependent on the spin transparency of the TI/FM\n(cid:3005)(cid:3013)\ninterface (𝑇 ), which governs how much of the generated spin current is transmitted. A disordered\n(cid:3036)(cid:3041)(cid:3047)\ninterface, often resulting from large lattice mismatch or intermixing, can act as a spin-scattering center\nand cause “spin memory loss” (SML), which depolarizes the spin current before it can exert a torque\n(Phys. Rev. Lett. 112, 106602 (2014)58). In this work, the MBE growth conditions were meticulously\noptimized for the Bi Te /Fe GeTe heterostructure. We hypothesize that the closer lattice match of\n2 3 4 2\nF GT (a ≈ 4.04 Å) to Bi Te (a ≈ 4.38 Å), compared to that of F GT (a ≈ 3.99 Å), facilitates a\n4 2 3 3\nmore coherent epitaxial interface with lower defect density. This higher-quality interface reduces SML,\nthereby enhancing the spin transparency 𝑇 and allowing a larger fraction of the spin angular\n(cid:3036)(cid:3041)(cid:3047)\nmomentum from the TI to be effectively transferred to the F GT layer.\ntwo materials at the Fermi level (E ). The SOT relies on the transfer of angular momentum from the\nF\nTI’s conduction electrons (specifically the spin-polarized topological surface states) to the FGT's local\nmagnetic moments (dominated by 3d orbitals). The efficiency of this transfer is highly dependent on\n60\nthe overlap in density of states (DOS) and orbital/spin texture between the two materials at E (Phys.\nF\nRev. B. 98, 020406 (2018))59. As distinct vdW magnets, F GT and F GT possess different 3d orbital\n4 3\nDOS and symmetries at the Fermi level. It is plausible that the band alignment between Bi Te and\n2 3\nF GT provides a more favorable overlap in momentum space. This improved “spin-impedance\n4\nmatching” would allow the spin current to be absorbed more efficiently by the F GT layer, resulting\n4\nin a larger SOT efficiency.\nIn conclusion, we believe the significantly higher SOT efficiency in our Bi Te /F GT system is most\n2 3 4\nlikely dominated by the combination of an improved interface quality (enhancing spin transparency)\nand a more favorable band alignment (enhancing spin absorption).\nWhile the enhanced SOT efficiency is an encouraging and relevant metric, the central contribution of\nthis study is the demonstration of a robust strategy for field-free and chirality-tunable SOT switching\nin an all–van der Waals heterostructure. We believe that this mechanism-level advance provides a\nversatile platform for future optimization of efficiency and device performance.\nQ10. The authors described the chirality of the deterministic switching in affected by the in-plane\nexternal field. What defines this chirality?\nResponse: We sincerely thank the reviewer for this insightful question and for the opportunity to\nclarify the meaning of “chirality” as used in this work. Achieving field-free SOT switching with\ntunable chirality is indeed the central focus of our work. Below, we provide a detailed explanation of\nthe underlying mechanism.\nIn the present manuscript, chirality refers to an operational and device-level sense to denote the\ndeterministic polarity of current-induced magnetization switching, i.e., whether a given current\ndirection drives the perpendicular magnetization from zz or from -z+z. It should be noted that,\nto align with the well-established hallmark characteristic feature of deterministic SOT-driven\nswitching, where the switching polarity is modulated by changing the direction of the in-plane external\nfield in the field-assisted SOT switching. We have replaced the terminology “chirality” with\n61\n“polarity” throughout the main text and in the following responses, although we use this term to define\nthe switching polarity in our unique IMA/PMA structure for field-free case. This revision ensures\nconsistency with the terminology used in the existing literature.\nThe physical quantity that defines this switching polarity is the in-plane symmetry-breaking field\nacting on the PMA layer during SOT switching. In conventional PMA systems, such symmetry\nbreaking is typically provided by an externally applied in-plane magnetic field. In our heterostructure,\nthis role is instead played by an internal effective field arising from interlayer exchange coupling with\nthe IMA component, which thus enables field-free SOT switching (Nat. Commun. 10, 233 (2019)60).\nSpecifically, the magnetization direction of the IMA layer can be preset by an external in-plane\nmagnetic field during initialization. Once preset, the IMA layer generates a remanent interlayer\nexchange field with a well-defined in-plane direction, which breaks the in-plane symmetry of the PMA\nlayer. The sign of this effective field, relative to the current direction, uniquely determines the\ndeterministic switching polarity. Consequently, reversing the preset in-plane magnetization of the IMA\nlayer reverses the direction of this internal effective field and, correspondingly, reverses the switching\npolarity.\nTherefore, the polarity discussed in this work is a field-defined and controllable switching polarity,\ndetermined by the preset orientation of the IMA magnetization through interlayer exchange coupling,\nrather than a manifestation of chiral magnetism.\nQ11. The whole portion of the text where the authors are describing chirality after application of some\npreset field is extremely unclear. The authors should rewrite this portion after keeping the general\nreadership of the work into account.\nResponse: We sincerely thank the reviewer for this suggestion. In the original manuscript, the\ndescription of the switching polarity after applying a preset magnetic field may not be sufficiently clear,\nparticularly for a general readership.\nTo provide a clearer and more concise description of the effect of the preset field on the switching\npolarity, we have revised the first paragraph of the subsection “Influence of preset field on field-free\nswitching” to clarify the effect of the preset field on the switching polarity. The original text,\nwhich\nstated “The results reveal that field-free switching cannot occur without the initialization provided by\nthe preset field. Notably, when the preset field reached +0.5 T, distinct field-free switching was\nobserved. The switching chirality mirrored the characteristic behavior observed under an externally\napplied +x magnetic field, and the chirality could be reversed by flipping the direction of the preset\nfield”, has been modified to: “The results demonstrate that field-free switching cannot be achieved\nwithout the initialization provided by the preset magnetic field. Specifically, in the absence of a preset\nmagnetic field, the device resistance remains largely unchanged even as the write current increases,\nindicating the absence of deterministic magnetization switching. However, when the preset field\nreaches 0.5 T, distinct field-free switching is observed. Furthermore, as the preset field is progressively\nincreased to 1 T, 1.5 T, and 2 T, the switching polarity remains unchanged. Critically, when the\ndirection of the preset field is reversed (e.g., increased to -0.5 T), the switching polarity also reverses.\nSimilarly, increasing the magnitude of the negative preset field does not alter this reversed switching\npolarity. Therefore, the preset magnetic field not only enables field-free switching but also controls its\npolarity.” (Page 12)\nWe believe that this restructured presentation significantly improves clarity and ensures that the role\nof the preset magnetic field in defining the switching polarity is transparent and accessible to a broad\naudience.\nQ12.Another unclear portion of the manuscript is the analysis of Boolean operations. Although a lot\nof texts and figures are added both in the main manuscript and supplementary, this is the most\nconfusing part of the manuscript. This portion should be modified with simplified and understandable\ndescriptions.\nResponse: We sincerely thank the reviewer for their valuable feedback and agree that the original\npresentation of the Boolean logic operations may not be sufficiently clear for a broad readership.\nTo address this issue, we have substantially revised and simplified the description of the Boolean\noperation analysis. In the revised manuscript, we establish a minimal and intuitive mapping: the preset\n63\nin-plane magnetic field and the write current serves as the data input, and the resulting anomalous Hall\nsignal represents the logic output. Based on this simple and unified framework, we then present\nrepresentative Boolean functions as proof-of-concept demonstrations, rather than as a comprehensive\nlogic architecture. Specifically, the ability to program the switching polarity through a preset magnetic\nfield allows a single physical device to be reconfigured into different logic behaviors without any\nstructural modification. This feature directly stems from the field-free, polarity-tunable SOT switching\nmechanism demonstrated in this work and is fundamentally different from conventional fixed-function\nspintronic logic elements.\nWe have revised the section analyzing Boolean logic operations to enhance its clarity and accessibility\nthrough more concise and clear descriptions. This restructuring significantly reduces redundancy and\nimproves readability, allowing the reader to focus on the central message: that polarity-tunable, field-\nfree switching enables reconfigurable logic functionality within a single device.\nWe believe that these revisions greatly enhance the clarity and accessibility of this section and\nadequately address the reviewer’s concern.\n1. Gibert, M. et al. 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The additional\nexperiments, particularly the XRMR measurements, extended switching characterization, and control\nanalyses, represent a nontrivial experimental investment and significantly strengthen the empirical\nfoundation of the manuscript. In this regard, I find the breadth of new data largely satisfactory.\nResponse: We thank the reviewer for the positive assessment of our revision efforts and for\nacknowledging that the additional experiments have significantly strengthened the manuscript’s\nempirical foundation.\nMy remaining concerns are not about the sufficiency of the data, but rather about how firmly some\nconclusions are framed relative to what the experiments directly establish. In several places, the\nmanuscript presents interpretations in a way that feels more definitive than necessary. I believe the\npaper would be strengthened by a more matter-of-fact tone that explicitly acknowledges alternative\ninterpretations and explains why the authors favor the scenario they propose.\nFor example, the XRMR measurements provide strong evidence for the coexistence of in-plane and\nperpendicular magnetic components and for a depth-dependent weighting of these contributions.\nHowever, statements suggesting that these data exclude impurity phases or uniquely define a sharp\nspatial separation along the film normal seem overstated. A more accurate description would\nemphasize that the data are consistent with a graded magnetic structure, with near-surface regions\ncontributing more strongly to the in-plane signal and deeper regions showing enhanced perpendicular\nsensitivity, while acknowledging the limits of angular averaging and depth resolution. Similarly,\nclarifying whether the applied in-plane and out-of-plane fields are sufficient to fully polarize the\nrespective components would help readers assess the robustness of the interpretation.\nResponse: We appreciate the insightful comment regarding the interpretation of our XRMR data. We\nagree that our original phrasing was overly definitive. In the revised manuscript and Supplementary\nInformation, we have adopted a more measured tone. Specifically, we now describe the data as being\nconsistent with a graded magnetic structure, where IMA contributions are dominant near the surface\nand PMA contributions increase with depth toward the interface, rather than claiming a sharp spatial\nseparation. Furthermore, we have clarified that the applied in-plane (±150 mT) and out-of-plane (±300\nmT) magnetic fields are sufficient to fully polarize the respective components, ensuring the robustness\nof our analysis. We believe these revisions significantly enhance the clarity and rigor of our\ninterpretation.\nThese revisions have been made in Supplementary Information S9:\n“For out-of-plane measurements, the magnetic field was applied normal to the sample surface and\nreversed between positive and negative directions, with a maximum field of ±300 mT. These applied\nfield are expected to be sufficient to fully polarize the respective components, thereby ensuring a robust\nmagnetic contrast for the XRMR analysis……By combining the penetration depth at grazing incidence\nwith the observed magnetic asymmetry and hysteresis loop measured at 9.5° under an in-plane\nmagnetic field (Fig. S9e), the data are most consistent with a model in which the near-surface region\nis dominated by IMA components……The data support a picture of a graded magnetic structure where\nIMA contributions are stronger near the Fe GeTe surface, while PMA contributions increase with\n4 2\ndepth toward the Bi Te interface.”\n2 3\nThe temperature-dependent transport measurements convincingly demonstrate enhanced PMA\nstability in the heterostructure compared to bare Fe GeTe . At the same time, transport remains a global\n4 2\nprobe, and the manuscript should avoid language that implies unambiguous spatial localization of this\neffect within the Fe GeTe layer. Framing the results as consistent with an interfacial enhancement,\n4 2\nrather than as direct proof of where within the layer the transition temperature is modified, would be\nmore precise.\nResponse: We thank the reviewer for this critical point. We fully acknowledge that temperature-\ndependent transport is a global probe and cannot unambiguously resolve the spatial localization of the\nenhanced PMA within the Fe GeTe layer. Accordingly, we have reviewed the manuscript to avoid any\n4 2\nphrasing that implies unambiguous spatial localization and have framed the results as being consistent\nwith an interfacial enhancement effect.\nI also appreciate the detailed discussion excluding Fe doping and proximity-induced magnetism in\nBi Te . This is an important part of the story and would benefit from being presented more openly in\n2 3\nthe main text, rather than largely confined to the response or supplementary discussion. Explicitly\nlaying out these alternative scenarios and explaining why they are unlikely would strengthen the\nmanuscript’s credibility.\nResponse: We sincerely thank the reviewer for this valuable suggestion. We agree that explicitly\naddressing alternative scenarios in the main text significantly strengthens the manuscript’s credibility.\nWe have integrated this discussion into the revised manuscript (Page 14). Specifically, we detail why\nneither Fe doping nor proximity-induced magnetism in Bi Te can account for the observed robust\n2 3\nroom-temperature PMA, citing the low Curie temperatures and weak magnetic moments reported in\nliterature. This explicitly rules out these alternative mechanisms and supports our conclusion that the\ntopological insulator interface enhances the intrinsic PMA of the Fe GeTe layer.\n4 2\n“The possibility that the observed magnetic behavior originates from the Bi Te layer is ruled out. Fe\n2 3\ndoping into Bi Te has been reported to induce only weak ferromagnetism below 14 K, with no\n2 3\nobservable magnetic order at room temperature. Regarding the proximity effect, previous study\nindicates that the resulting Curie temperatures are typically very low. Even in the limited number of\nreports claiming a Curie temperature near 300 K, the induced magnetic moment remains orders of\nmagnitude smaller than that of intrinsic magnetic materials. Therefore, neither Fe doping nor\nproximity-induced magnetism in Bi Te can account for the room-temperature, robust magnetic\n2 3\nanisotropy in this work. These observations strongly suggest that the topological insulator interface\ncontributes to the enhancement of PMA in Fe GeTe itself, giving rise to the coexistence of PMA and\n4 2\nIMA components with no evidence of measurable magnetic contribution from the Bi Te layer.”\n2 3\nWe believe this addition makes the discussion more transparent and complete. We again thank the\nreviewer for the insightful comment, which has helped us significantly improve the manuscript.\nThe clarification that the observed SOT switching is partial is helpful. However, the statement that\nincomplete switching is generally characteristic of two-dimensional magnets is too broad. The\nconditions under which switching is partial or near-complete remain an open and actively studied\nquestion, and Fe GeTe is a comparatively underexplored system in this context. Framing the observed\n4 2\nbehavior as part of this broader, unresolved landscape would be more accurate and more interesting.\nResponse: We thank the reviewer for correcting our previous over-generalization. We agree that\ncharacterizing partial switching as a \"general feature\" of 2D magnets was imprecise. In the revised\nmanuscript, we have refined this statement to reflect that achieving full magnetization reversal remains\na significant practical challenge in the 2D limit, consistent with reported efficiencies in similar systems.\nThe relevant sentence in the main text now reads: “These values are consistent with reported SOT\nefficiencies in other two-dimensional magnetic systems (e.g., ~20%) and reflect the practical challenge\nof achieving full magnetization reversal in the two-dimensional limit.” This revision places our\nobservations within the broader context of current research on switching completeness in emerging 2D\nmagnetic systems.\nFinally, the proposed exchange-spring-like picture is intriguing and plausible, but it remains a model\nrather than a directly proven mechanism. Presenting it explicitly as such, and incorporating the new\ncontrol data and schematics into the supplementary information, would make the argument clearer and\nmore transparent.\nResponse:We thank the reviewer for the constructive suggestion to clarify the nature of the exchange-\nspring-like picture. Accordingly, we have revised the relevant section in Supplementary Information\nS7. The text now explicitly presents this concept as a plausible and self-consistent physical model that\nis consistent with our data, rather than a directly proven mechanism. The supporting control data and\nschematics have been incorporated therein to enhance the clarity and transparency of the argument.\nOverall, I am supportive of publication after moderate revisions focused on interpretive tone and clarity\nrather than additional experiments. Adopting a more open and explicitly comparative narrative would\nsignificantly strengthen the manuscript.\nResponse:We appreciate the reviewer's support for publication and the valuable guidance to improve\nthe manuscript’s clarity and narrative. We will revise the text to ensure a more open and comparative\ntone as suggested.\nANSWER TO REVIEWER #2\nI thank the authors for their detailed follow up measurements and calculations. I am satisfied with their\nedits and am happy to recommend publication to Nature communications.\nResponse: We are grateful for the reviewer's encouraging comments and thank the reviewer for the\nconsiderable effort invested in reviewing our work.\nANSWER TO REVIEWER #3\nThe authors have satisfactorily addressed the comments and concerns of all the reviewers. I have no\nobjection in endorsing its acceptance.\nResponse: We are gratified to receive this positive assessment and thank the reviewer for the\nconfirmation that our revisions have satisfactorily addressed all previous comments. We appreciate the\nendorsement for acceptance."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have made a substantial effort in response to the first-round reviews. The additional experiments, particularly the XRMR measurements, extended switching characterization, and control analyses, represent a nontrivial experimental investment and significantly strengthen the empirical foundation of the manuscript. In this regard, I find the breadth of new data largely satisfactory.\nMy remaining concerns are not about the sufficiency of the data, but rather about how firmly some conclusions are framed relative to what the experiments directly establish. In several places, the manuscript presents interpretations in a way that feels more definitive than necessary. I believe the paper would be strengthened by a more matter-of-fact tone that explicitly acknowledges alternative interpretations and explains why the authors favor the scenario they propose.\nFor example, the XRMR measurements provide strong evidence for the coexistence of in-plane and perpendicular magnetic components and for a depth-dependent weighting of these contributions. However, statements suggesting that these data exclude impurity phases or uniquely define a sharp spatial separation along the film normal seem overstated. A more accurate description would emphasize that the data are consistent with a graded magnetic structure, with near-surface regions contributing more strongly to the in-plane signal and deeper regions showing enhanced perpendicular sensitivity, while acknowledging the limits of angular averaging and depth resolution. Similarly, clarifying whether the applied in-plane and out-of-plane fields are sufficient to fully polarize the respective components would help readers assess the robustness of the interpretation.\nThe temperature-dependent transport measurements convincingly demonstrate enhanced PMA stability in the heterostructure compared to bare Fe₄GeTe₂. At the same time, transport remains a global probe, and the manuscript should avoid language that implies unambiguous spatial localization of this effect within the Fe₄GeTe₂ layer. Framing the results as consistent with an interfacial enhancement, rather than as direct proof of where within the layer the transition temperature is modified, would be more precise.\nI also appreciate the detailed discussion excluding Fe doping and proximity-induced magnetism in Bi₂Te₃. This is an important part of the story and would benefit from being presented more openly in the main text, rather than largely confined to the response or supplementary discussion. Explicitly laying out these alternative scenarios and explaining why they are unlikely would strengthen the manuscript’s credibility.\nThe clarification that the observed SOT switching is partial is helpful. However, the statement that incomplete switching is generally characteristic of two-dimensional magnets is too broad. The conditions under which switching is partial or near-complete remain an open and actively studied question, and Fe₄GeTe₂ is a comparatively underexplored system in this context. Framing the observed behavior as part of this broader, unresolved landscape would be more accurate and more interesting.\nFinally, the proposed exchange-spring-like picture is intriguing and plausible, but it remains a model rather than a directly proven mechanism. Presenting it explicitly as such, and incorporating the new control data and schematics into the supplementary information, would make the argument clearer and more transparent.\nOverall, I am supportive of publication after moderate revisions focused on interpretive tone and clarity rather than additional experiments. Adopting a more open and explicitly comparative narrative would significantly strengthen the manuscript.", "reviewer_2": "I thank the authors for their detailed follow up measurements and calculations. I am satisfied with their edits and am happy to recommend publication to Nature communications.", "reviewer_3": "The authors have satisfactorily addressed the comments and concerns of all the reviewers. I have no objection in endorsing its acceptance."}, "author_response": "ANSWER TO REVIEWER #1\nThe authors have made a substantial effort in response to the first-round reviews. The additional\nexperiments, particularly the XRMR measurements, extended switching characterization, and control\nanalyses, represent a nontrivial experimental investment and significantly strengthen the empirical\nfoundation of the manuscript. In this regard, I find the breadth of new data largely satisfactory.\nResponse: We thank the reviewer for the positive assessment of our revision efforts and for\nacknowledging that the additional experiments have significantly strengthened the manuscript’s\nempirical foundation.\nMy remaining concerns are not about the sufficiency of the data, but rather about how firmly some\nconclusions are framed relative to what the experiments directly establish. In several places, the\nmanuscript presents interpretations in a way that feels more definitive than necessary. I believe the\npaper would be strengthened by a more matter-of-fact tone that explicitly acknowledges alternative\ninterpretations and explains why the authors favor the scenario they propose.\nFor example, the XRMR measurements provide strong evidence for the coexistence of in-plane and\nperpendicular magnetic components and for a depth-dependent weighting of these contributions.\nHowever, statements suggesting that these data exclude impurity phases or uniquely define a sharp\nspatial separation along the film normal seem overstated. A more accurate description would\nemphasize that the data are consistent with a graded magnetic structure, with near-surface regions\ncontributing more strongly to the in-plane signal and deeper regions showing enhanced perpendicular\nsensitivity, while acknowledging the limits of angular averaging and depth resolution. Similarly,\nclarifying whether the applied in-plane and out-of-plane fields are sufficient to fully polarize the\nrespective components would help readers assess the robustness of the interpretation.\nResponse: We appreciate the insightful comment regarding the interpretation of our XRMR data. We\nagree that our original phrasing was overly definitive. In the revised manuscript and Supplementary\nInformation, we have adopted a more measured tone. Specifically, we now describe the data as being\nconsistent with a graded magnetic structure, where IMA contributions are dominant near the surface\nand PMA contributions increase with depth toward the interface, rather than claiming a sharp spatial\nseparation. Furthermore, we have clarified that the applied in-plane (±150 mT) and out-of-plane (±300\nmT) magnetic fields are sufficient to fully polarize the respective components, ensuring the robustness\nof our analysis. We believe these revisions significantly enhance the clarity and rigor of our\ninterpretation.\nThese revisions have been made in Supplementary Information S9:\n“For out-of-plane measurements, the magnetic field was applied normal to the sample surface and\nreversed between positive and negative directions, with a maximum field of ±300 mT. These applied\nfield are expected to be sufficient to fully polarize the respective components, thereby ensuring a robust\nmagnetic contrast for the XRMR analysis……By combining the penetration depth at grazing incidence\nwith the observed magnetic asymmetry and hysteresis loop measured at 9.5° under an in-plane\nmagnetic field (Fig. S9e), the data are most consistent with a model in which the near-surface region\nis dominated by IMA components……The data support a picture of a graded magnetic structure where\nIMA contributions are stronger near the Fe GeTe surface, while PMA contributions increase with\n4 2\ndepth toward the Bi Te interface.”\n2 3\nThe temperature-dependent transport measurements convincingly demonstrate enhanced PMA\nstability in the heterostructure compared to bare Fe GeTe . At the same time, transport remains a global\n4 2\nprobe, and the manuscript should avoid language that implies unambiguous spatial localization of this\neffect within the Fe GeTe layer. Framing the results as consistent with an interfacial enhancement,\n4 2\nrather than as direct proof of where within the layer the transition temperature is modified, would be\nmore precise.\nResponse: We thank the reviewer for this critical point. We fully acknowledge that temperature-\ndependent transport is a global probe and cannot unambiguously resolve the spatial localization of the\nenhanced PMA within the Fe GeTe layer. Accordingly, we have reviewed the manuscript to avoid any\n4 2\nphrasing that implies unambiguous spatial localization and have framed the results as being consistent\nwith an interfacial enhancement effect.\nI also appreciate the detailed discussion excluding Fe doping and proximity-induced magnetism in\nBi Te . This is an important part of the story and would benefit from being presented more openly in\n2 3\nthe main text, rather than largely confined to the response or supplementary discussion. Explicitly\nlaying out these alternative scenarios and explaining why they are unlikely would strengthen the\nmanuscript’s credibility.\nResponse: We sincerely thank the reviewer for this valuable suggestion. We agree that explicitly\naddressing alternative scenarios in the main text significantly strengthens the manuscript’s credibility.\nWe have integrated this discussion into the revised manuscript (Page 14). Specifically, we detail why\nneither Fe doping nor proximity-induced magnetism in Bi Te can account for the observed robust\n2 3\nroom-temperature PMA, citing the low Curie temperatures and weak magnetic moments reported in\nliterature. This explicitly rules out these alternative mechanisms and supports our conclusion that the\ntopological insulator interface enhances the intrinsic PMA of the Fe GeTe layer.\n4 2\n“The possibility that the observed magnetic behavior originates from the Bi Te layer is ruled out. Fe\n2 3\ndoping into Bi Te has been reported to induce only weak ferromagnetism below 14 K, with no\n2 3\nobservable magnetic order at room temperature. Regarding the proximity effect, previous study\nindicates that the resulting Curie temperatures are typically very low. Even in the limited number of\nreports claiming a Curie temperature near 300 K, the induced magnetic moment remains orders of\nmagnitude smaller than that of intrinsic magnetic materials. Therefore, neither Fe doping nor\nproximity-induced magnetism in Bi Te can account for the room-temperature, robust magnetic\n2 3\nanisotropy in this work. These observations strongly suggest that the topological insulator interface\ncontributes to the enhancement of PMA in Fe GeTe itself, giving rise to the coexistence of PMA and\n4 2\nIMA components with no evidence of measurable magnetic contribution from the Bi Te layer.”\n2 3\nWe believe this addition makes the discussion more transparent and complete. We again thank the\nreviewer for the insightful comment, which has helped us significantly improve the manuscript.\nThe clarification that the observed SOT switching is partial is helpful. However, the statement that\nincomplete switching is generally characteristic of two-dimensional magnets is too broad. The\nconditions under which switching is partial or near-complete remain an open and actively studied\nquestion, and Fe GeTe is a comparatively underexplored system in this context. Framing the observed\n4 2\nbehavior as part of this broader, unresolved landscape would be more accurate and more interesting.\nResponse: We thank the reviewer for correcting our previous over-generalization. We agree that\ncharacterizing partial switching as a \"general feature\" of 2D magnets was imprecise. In the revised\nmanuscript, we have refined this statement to reflect that achieving full magnetization reversal remains\na significant practical challenge in the 2D limit, consistent with reported efficiencies in similar systems.\nThe relevant sentence in the main text now reads: “These values are consistent with reported SOT\nefficiencies in other two-dimensional magnetic systems (e.g., ~20%) and reflect the practical challenge\nof achieving full magnetization reversal in the two-dimensional limit.” This revision places our\nobservations within the broader context of current research on switching completeness in emerging 2D\nmagnetic systems.\nFinally, the proposed exchange-spring-like picture is intriguing and plausible, but it remains a model\nrather than a directly proven mechanism. Presenting it explicitly as such, and incorporating the new\ncontrol data and schematics into the supplementary information, would make the argument clearer and\nmore transparent.\nResponse:We thank the reviewer for the constructive suggestion to clarify the nature of the exchange-\nspring-like picture. Accordingly, we have revised the relevant section in Supplementary Information\nS7. The text now explicitly presents this concept as a plausible and self-consistent physical model that\nis consistent with our data, rather than a directly proven mechanism. The supporting control data and\nschematics have been incorporated therein to enhance the clarity and transparency of the argument.\nOverall, I am supportive of publication after moderate revisions focused on interpretive tone and clarity\nrather than additional experiments. Adopting a more open and explicitly comparative narrative would\nsignificantly strengthen the manuscript.\nResponse:We appreciate the reviewer's support for publication and the valuable guidance to improve\nthe manuscript’s clarity and narrative. We will revise the text to ensure a more open and comparative\ntone as suggested.\nANSWER TO REVIEWER #2\nI thank the authors for their detailed follow up measurements and calculations. I am satisfied with their\nedits and am happy to recommend publication to Nature communications.\nResponse: We are grateful for the reviewer's encouraging comments and thank the reviewer for the\nconsiderable effort invested in reviewing our work.\nANSWER TO REVIEWER #3\nThe authors have satisfactorily addressed the comments and concerns of all the reviewers. I have no\nobjection in endorsing its acceptance.\nResponse: We are gratified to receive this positive assessment and thank the reviewer for the\nconfirmation that our revisions have satisfactorily addressed all previous comments. We appreciate the\nendorsement for acceptance."}]

Decision letter