Topological magneto-optical Kerr effect without spin-orbit coupling in spin-compensated antiferromagnet

Domain: chemistry
Published: 2026-03-03
Editorial outcome: major_revision

Abstract
The magneto-optical Kerr effect (MOKE), the differential reflection of oppositely circularly polarized light, has traditionally been associated with relativistic spin-orbit coupling (SOC), which links a particle’s spin with its orbital motion. In ferromagnets, large MOKE signals arise from the combination of magnetization and SOC, while in certain coplanar antiferromagnets, SOC-induced Berry curvature enables MOKE despite zero net magnetization. Theoretically, large MOKE can also arise in a broader class of magnetic materials with compensated spins, without relying on SOC - for example, in systems exhibiting real-space scalar spin chirality. The experimental verification has remained elusive. Here, we demonstrate such a SOC- and magnetization-free MOKE in the noncoplanar antiferromagnet Co TaS . Using a Sagnac interferometer microscope, we image domains of scalar spin chirality and their reversal. Our findings establish experimentally a new mechanism for generating large MOKE signals and position chiral spin textures in compensated magnets as a compelling platform for ultrafast, stray-field-immune opto-spintronic applications.

Introduction
The magneto-optical Faraday 1 and Kerr 2 effects, which reflect the fundamental interactions between circularly polarized light and magnetic materials, have been known for over a century. Among them, the magneto-optical Kerr effect (MOKE) has been extensively utilized for probing magnetic properties 3, visualizing magnetic domains 2, manipulating magnetic order 4, and enabling a variety of magneto-optical technologies 5, even down to the two-dimensional (2D) limit 6,7.

Spin-orbit coupling (SOC) 8,9, a relativistic interaction between a particle’s spin and its orbital motion, has been deemed central in generating large MOKE signals. The presence of MOKE in ferromagnets has been attributed to the interplay between SOC and band exchange splitting (BES) in the band structure 10 induced by either the spontaneous magnetization or an external magnetic field. In non-collinear antiferromagnets with negligible net magnetization 11, large MOKE signals up to 300 μrad have recently been predicted 12 and observed 13, due to a non-zero net Berry curvature in the band structure induced by SOC. This dependence on SOC appears to be a general requirement: although finite MOKE can be observed in systems such as time-reversal symmetry-breaking superconductors 14–16 and orbital Hall materials 17 with negligible SOC, the magnitude of the effect in these cases is typically several orders of magnitude smaller, often in the nanoradian range. With the emergence of novel magnetic materials such as altermagnets 18,19, where SOC and net magnetization are both intrinsically weak or absent, it becomes a question of fundamental significance whether large MOKE signals can be achieved without relying on SOC or net magnetization. This is also of practical importance, as MOKE offers a practical readout for spintronic and opto-spintronic devices based on altermagnets and antiferromagnets of compensated spins, with minimal stray fields, field robustness, and fast switching 20–23.

Theoretically, spin-dependent band splitting, and thus MOKE, can also arise from real-space spin textures of compensated spins without referencing relativistic SOC 24–26. For instance, non-relativistic exchange-driven band splitting occurs in itinerant electron systems, giving rise to phenomena like altermagnetism 18,19. One of the simplest examples is a noncoplanar antiferromagnet, proposed to exhibit a novel topological light-matter interaction 24, inducing a topological MOKE signal due to finite scalar spin chirality without relying on SOC or BES, i.e. without a net magnetization. In its minimal configuration as illustrated in Fig.1a, three noncoplanar twisted spins 𝑆 , 𝑆 , and 𝑆 generate a fictitious U(1) gauge field 𝑏 ∝ 𝑡 χ 𝑛̂, where 𝑡 = 𝑡 𝑡 𝑡 is the product of successive electron hopping integrals around the triangular loop 𝑖 → 𝑗 → 𝑘 → 𝑖, 𝜒 = 𝑆 ∙(𝑆 ×𝑆 ) is the scalar spin chirality representing real-space “spin-winding”, and n̂ is the unit vector normal to the face of the triangle. This fictitious field 𝑏 originates from the orbital motion of electrons: as an electron hops around the triangle, it acquires a geometric Berry phase 27 corresponding to the solid angle subtended by the three spins. This topologically nontrivial Berry phase results in a phase difference ∆𝜑 between left- and right-circularly polarized (LCP and RCP) light upon reflection, manifesting as a Kerr angle 𝜃 = ∆𝜑/2. Notably, this coupling between spin and orbital degrees of freedom (spin-dependent band splitting) arises from Kondo exchange coupling between conduction electrons and a noncoplanar arrangement of localized magnetic moments, without requiring relativistic SOC 25.

Despite the promising potential of this SOC-free mechanism for MOKE in compensated magnetic systems, experimental verification has remained elusive. Proposed candidate systems such as γ-Fe Mn and γ-Na CoO₂ 24 have not exhibited the expected signatures. This absence is partly due to the limited exploration of non-coplanar antiferromagnetic orders and partly because the fictitious magnetic field arising from scalar spin chirality often cancels out due to symmetry, typically requiring external strain to stabilize a net effect 24. Lastly, the choice of the optical wavelength is non-trivial as the theoretically calculated Kerr signal oscillates strongly with the photon energy, crossing zero frequently 24.

In this study, we report the first experimental realization of a large spontaneous MOKE signal of 250 𝜇𝑟𝑎𝑑 at the technologically relevant telecommunication wavelength of 1550 𝑛𝑚 in the triangular lattice compound Co TaS 28–30, despite its negligible net magnetization of 0.01 𝜇 /𝐶𝑜. This result confirms the viability of the SOC-free mechanism for producing technologically relevant MOKE signals. Using MOKE imaging, we visualize scalar spin chirality domains and their switching behavior under applied magnetic fields.

Results
Co TaS belongs to a broader family of magnetic element-intercalated van der Waals transition metal dichalcogenides, which exhibit a wide range of magnetic states depending on the intercalants 31–36. Its crystal structure consists of chiral alternating layers of cobalt, which carry localized magnetic moments, and metallic tantalum disulfide, which hosts itinerant electrons. While neutron scattering studies in the 1980s reported 33 a magnetic modulation vector of 𝑞 = (1/3,1/3,0), leading to interpretations involving a “toroidal” magnetic order 28, recent experiments 30,29 on Co TaS and Co NbS have instead identified 𝑞 = (1/2,0,0). The latter corresponds to a non-coplanar “triple-Q” order 30,29, simultaneously breaking time-reversal and inversion symmetry. Consequently they exhibit anomalous Hall effect 37,30,29 and Nernst effect 38 arising from an uncompensated fictitious magnetic field, even though their net magnetic moments are vanishingly small. A clear correlation between the degree of spin non-coplanarity and the amplitude of spontaneous Hall signal was confirmed by temperature dependence of polarized neutron scattering 30. As illustrated in Fig.1c, the magnetic unit cell in this triple-Q state includes eight triangular plaquettes that generate a strong fictitious field oriented along the crystallographic c-axis. Importantly, this magnetic order in an ideal triple-Q state 29 does not involve any net spin magnetization; rather, the fictitious field couples to the orbital motion of itinerant electrons, producing a small orbital magnetic moment of approximately 0.01 𝜇 per Co2+ ion 29,30. Note that the real material Co TaS may deviate from this ideal triple-Q state, and the observed zero-field magnetization could include some spin contribution.

This spin configuration has non-zero scalar spin chirality and is not associated with any spin rotation symmetry, so non-relativistic spin splitting can occur along any direction. In addition, this spin configuration can have a net magnetization along 𝑐-axis when SOC is included, so it may be considered as an “M-type” altermagnet with magnetic point group of 32' 39.

Upon warming, this triple-Q order transitions at the Néel temperature 𝑇 into a single-Q stripe order as illustrated in Fig.2b with zero scalar spin chirality, and subsequently into a paramagnetic state above 𝑇 29. The Co TaS crystals used in our experiments were synthesized via chemical vapor transport (Methods), as shown in the inset of Fig.1d. Magnetic susceptibility measurements under field-cooled (FC) and zero-field-cooled (ZFC) conditions (Fig.1b) indicate transition temperatures of 𝑇 ~33 𝐾 and 𝑇 ~16 𝐾.

MOKE detection and imaging are performed using a zero-loop Sagnac interferometer microscope 6,14,40,41 in the polar geometry (Fig.1e) operating at the most popular telecommunication wavelength of 1550 𝑛𝑚 (0.80 𝑒𝑉 photon energy). This technique offers exceptional sensitivity, routinely achieving 0.01 𝜇𝑟𝑎𝑑 resolution. This is made possible by its exclusive detection of microscopic time-reversal symmetry breaking (TRSB) while strongly rejecting non-TRSB effects, such as optical birefringence, with a suppression level of 10−6 (Supplementary Information). This distinction is particularly important in Co TaS , where some of the authors have recently observed a birefringent polarization rotation of 600 𝜇𝑟𝑎𝑑𝑠𝑖𝑛(2𝛼) due to a nonvolatile nematic order, with 𝛼 being the incident polarization angle 42. The selective sensitivity to TRSB is achieved by using a single-mode optical fiber as both the source and detector for counter-propagating, time-reversed light beams 43. According to Onsager’s relations 44, this configuration guarantees zero signal in the absence of TRSB.

We now present the results of our MOKE measurements. Fig.1d shows the spontaneous MOKE signal 𝜃 obtained during zero-field warm (ZFW) after 𝐵 = 0.3 𝑇 field cool (FC), measured at a single point with 2 𝜇𝑚 optical beam size. Remarkably, we observe a giant 𝜃 of 250 𝜇𝑟𝑎𝑑, comparable to the 300 𝜇𝑟𝑎𝑑 signal reported in the coplanar non-collinear antiferromagnet Mn₃Sn 13, where the large MOKE arises from relativistic SOC-induced Berry curvature 12. It is important to note that both Co TaS and Mn₃Sn exhibit vanishingly small net magnetic moments, with values of ~0.01 𝜇 /𝐶𝑜 29,30 and ~0.005 𝜇 /𝑀𝑛 45, respectively. This experimental result thus firmly establishes that the SOC-free mechanism driven by the scalar spin chirality can produce MOKE signals on par with those generated by SOC-induced Berry curvature. The pronounced temperature dependence of MOKE in Co TaS stands in sharp contrast to the temperature-invariant behavior we observed in the coplanar non-collinear antiferromagnet Mn₃NiN 46, underscoring their distinct origins. When compared to theoretical predictions, the calculated 𝜃 in the proposed triple-Q state of γ-Fe Mn is even larger, reaching ±10 𝑚𝑟𝑎𝑑 depending on the photon wavelength 24. These observations suggest that the SOC-free mechanism holds substantial promise for approaching the largest reported MOKE of ~10 𝑚𝑟𝑎𝑑 in ferromagnets CoPt 47.

In contrast to the large 𝜃 in the triple-Q state, no measurable MOKE signal was detected during ZFW through 𝑇 into the single-Q phase, or upon further warming above 𝑇 into the paramagnetic phase (Fig.1d). This is consistent with theoretical predictions: both the single-Q and paramagnetic phases lack scalar spin chirality and thus are not expected to support a finite MOKE 24.

We observed negligible spontaneous 𝜃 after zero-field cool (ZFC) (Supplementary Fig. 7b), indicating the formation of oppositely polarized domains smaller than the optical beam size in the absence of a training field. This also confirms that the zero-field MOKES signal does not originate from uncompensated spins at AFM domain walls. If that were the case, ZFC, which produces a higher density of domain walls, would yield a larger MOKE signal than field cooling (FC), contrary to our observations. The negligible magnetic contribution from AFM domain walls is also supported by MFM measurements after ZFC (Supplementary Fig. 8), which show no detectable fringing fields from domain walls.

Fig.2a summarizes the MOKE hysteresis loops across different magnetic phases of Co TaS . At 50 𝐾, in the paramagnetic phase, the Kerr signal 𝜃 exhibits a small linear response to the applied magnetic field 𝐵, consistent with partial alignment of magnetic moments by the external field. At 20 𝐾, in the single-Q phase as illustrated in Fig. 2b, the MOKE signal develops a shallow S-shaped curve but remains zero at zero field, consistent with the absence of scalar spin chirality 𝜒 . Upon cooling to 15 𝐾, as the system enters the non-coplanar triple-Q phase, a small hysteresis loop emerges between ±0.4 𝑇 (cyan curve in Fig. 2a), signaling the onset of a finite 𝜒 and the associated fictitious field 𝑏 . Notably, across ~5 𝑇 magnetic field, there is a smooth change in the Kerr signal, corresponding to a metamagnetic transition into a different magnetic configuration 29,30, referred to here as the triple-Q’ state. Further cooling to 10 𝐾, 5 𝐾, and 2 𝐾 leads to increasingly wide and pronounced hysteresis loops, indicating higher coercive fields required to reverse the chirality domains and stronger fictitious fields at zero applied field. The jump in MOKE signal across 5 𝑇 field also becomes more abrupt at lower temperatures, signifying a sharper metamagnetic transition between the triple-Q and triple-Q′ phases.

The most striking feature of the Kerr hysteresis in the triple-Q phase (Fig.2a) is its field independence: once the sign of 𝜒 is established by the external field, the Kerr signal remains nearly constant between 0 𝑇 and 4 𝑇 fields. A similar plateau is observed in the triple-Q’ phase above 6 𝑇. For clarity, the 2 𝐾 MOKE hysteresis is replotted in Fig. 2d, revealing a stark contrast to the corresponding 2 𝐾 magnetization 𝑀 (Fig. 2c). 𝑀 begins at ~0.01 𝜇 per Co at zero field and increases linearly at a rate of 𝑑𝑀 /𝑑𝐵 ~0.02 𝜇 /𝑇, except for a discrete jump of ~0.07 𝜇 at 5 𝑇 due to the metamagnetic transition. We estimate that the magnetization contribution to the MOKE signal is negligible, less than 1% (see Supplementary Information). This contrasting field dependence between MOKE and 𝑀 confirms their decoupling: while MOKE arises from the fictitious field 𝑏 generated by scalar spin chirality, the magnetization includes both spin and orbital contributions. Specifically, the zero-field 𝑀 and its linear slope 𝑑𝑀 /𝑑𝐵 are due to the orbital moment of itinerant electrons, induced respectively by the fictitious field 𝑏 and the external magnetic field 𝐵. These orbital contributions are not directly coupled to the Kerr signal. In contrast, the metamagnetic transition, which involves a spin reconfiguration, produces simultaneous step-like changes in both 𝑀 and 𝜃 . Importantly the optical reflectivity remained constant to within 0.5% during the entire measurement (Fig. 2g), confirming that the metamagnetic transition represents a change of the spin configuration and has minimum impacts on the electronic structure.

Since the nature of the metamagnetic transition has not been resolved by neutron scattering experiments yet 29,30, we adopt a simplified working assumption: the transition reflects a sudden change in the angle 𝜃 between spins 𝑆 and 𝑆 , as illustrated in the inset of Fig. 2d. Under this assumption, the net spin moment is given by 𝑀 = (−1−3 cos(𝜃)) 𝜇 , assuming a g-factor of -2. And it can be estimated experimentally from magnetization as 𝑀 ~𝑀 −0.02 𝜇 ∙𝐵, accounting for the orbital contribution. The scalar spin chirality 𝜒 is assumed to scale with the bottom triangular plaquette 𝜒 ∝ 𝜒 ∝ − 3 √3 cos(𝜃) sin(𝜃)2 .

Within this simplistic model, we estimate 𝜒 ~− 2(1+2𝑀𝑠𝑝𝑖𝑛)(−2+𝑀𝑠𝑝𝑖𝑛+𝑀𝑠𝑝𝑖𝑛 2) , as plotted in Fig. 2f. Comparing this estimated 𝜒 and the measured 𝜃 (Fig. 2d), the model qualitatively captures the key features of the magnetic-field dependence of MOKE. The quantitative discrepancy across the transition across 5 𝑇 suggests that a more accurate model is required for this metamagnetic transition. This will depend on resolving the spin structure of the triple-Q’ phase in future neutron scattering experiments, beyond the scope of the present work. Lastly, we note the DC Hall effect 𝜎 (Fig. 2e) shows an opposite change across the metamagnetic transition, suggesting a rather complex frequency dependence related to the corresponding change of spin texture across the metamagnetic transition.

Spin chirality can be imaged by MOKE microscopy that provides a powerful, non-contact method for mapping spin chirality domains and their associated dynamics. One immediate application is the assessment of chemical inhomogeneity. Recent neutron scattering and transport studies 48 have reported that even slight variations in cobalt composition can lead to significant changes in the physical properties of 𝐶𝑜 𝑇𝑎𝑆 . It is therefore critical to determine the extent of chemical inhomogeneity, and its impact on the MOKE signal within a single crystal. We found that higher Co content leads to lower red-light reflectivity, an effect which we expect to persist at 1550 𝑛𝑚 in the Sagnac measurements. (Supplementary Fig. 9 c, d).

In Fig.3, we present a combined study of optical reflectivity imaging, MOKE imaging, and single location MOKE hysteresis, all performed at 2 𝐾. The optical reflectivity map (Fig. 3b) is largely uniform with 0.42 < 𝑅 < 0.44, which we use as a convenient proxy for cobalt composition as it is difficult to perform energy dispersive x-ray spectroscopy (EDX) chemical mapping in the same region. MOKE hysteresis loops measured at a few representative locations with varying reflectivity values are shown in Fig. 3a. All locations exhibit nearly identical coercive fields of ~0.8 𝑇, with the primary variation being in the zero-field Kerr signal (200, 202, 160, and 80 𝜇𝑟𝑎𝑑, respectively). To further examine the magnetic inhomogeneity, we performed MOKE imaging at three key points along the hysteresis loop: at zero field (Fig. 3d), and near the switching fields at −1 𝑇 (Fig. 3c) and +0.8 𝑇 (Fig. 3e). Near the switching fields, large variations in both positive and negative Kerr signals are observed (Fig. 3c, e), consistent with the coexistence and reversal of spin chirality domains across the sample. Importantly, the spatial patterns seen in Figs. 3c and 3e do not resemble those in the reflectivity map (Fig. 3b), suggesting that the coercive field and domain switching behavior are not strongly correlated with cobalt composition. Instead, they are likely influenced by local strain, defects, or other extrinsic structural factors.

In stark contrast, a clear correlation emerges between the optical reflectivity (Fig. 3b) and the zero-field MOKE image (Fig. 3d), where the chirality has been uniformly trained to a negative value. This observation implies that cobalt composition primarily affects the magnitude of the MOKE signal in the zero-field state, rather than the switching dynamics. To further test this hypothesis, we investigated a rare inhomogeneous region (see Supplementary Fig. 1) where reflectivity varies significantly from 0.40 to 0.45. In this region, the spontaneous MOKE signal ranges from −40 𝜇𝑟𝑎𝑑 to −180 𝜇𝑟𝑎𝑑. A plot of MOKE vs. reflectivity in Supplementary Fig. 1 reveals an empirical linear relationship within this limited reflectivity range, supporting the idea that local cobalt concentration modulates the amplitude of the Kerr signal.

Having established that most of the sample is magnetically uniform, we now demonstrate the utility of MOKE microscopy in visualizing scalar spin chirality domain reversal under an external magnetic field. These measurements were conducted in magnetically homogeneous regions at an elevated temperature of 10 𝐾, where domain reversal occurs over a broader field range. The results are shown in Fig.4 and Supplementary Fig. 2.

A sequence of MOKE images from a uniform region is presented in Figs. 4b-i, with the corresponding local hysteresis loop taken at a single location shown in Fig. 4a. At 𝐵 = −9 𝑇 (Fig. 4b), the MOKE signal is uniformly negative (𝜃 ~−200 𝜇𝑟𝑎𝑑, shown in blue), except for a few isolated spots that are likely regions of differing Co composition with near-zero Kerr signals (green). At 𝐵 = 0 (Fig. 4c), patches with 𝜃 ~0 begin to emerge. These are interpreted as sub-wavelength domains with mixed positive and negative chiralities, whose contributions average to near zero within the ~2 𝜇𝑚 optical spot size. As the magnetic field increases (Figs. 4d-f), these green regions grow and are joined by new areas exhibiting positive chirality (orange to red). The positive domains progressively expand through domain wall motion, eventually dominating the lower half (Fig. 4g) and finally the entire imaged region (Fig. 4h-i), culminating in a uniform positive Kerr signal of 𝜃 ~200 𝜇𝑟𝑎𝑑.

Notably, even at a low field of 0.1 𝑇 (Fig. 4d), isolated positive domains are already present. This indicates that the coercive field for domain reversal is not fundamentally dictated by the intrinsic non-coplanar magnetic phase but is instead governed by extrinsic factors such as local strain, defects, or pinning centers. This insight suggests that by engineering these extrinsic factors, it may be possible to tailor coercive fields in Co TaS and related materials, either minimizing them for low-power logic switching applications or maximizing them for robust spin memory devices.

Further evidence of this chirality domain reversal dynamics is provided in Supplementary Fig. 2, which presents MOKE images of another region taken at 1 𝑇 intervals across the full field sweep. As in the main data, domain reversal near ±1 𝑇 occurs via domain wall motion, with positive and negative chirality domains coexisting during the transition.

Interestingly, Supplementary Fig. 2 also captures the distinct dynamics of the metamagnetic transition, which occurs gradually between 𝐵 = 4 𝑇 and 6 𝑇. Across the 3 𝑇 → 9 𝑇 → 3 𝑇 cycle, the MOKE signal changes smoothly and uniformly across the field of view, with no evidence of domain wall motion. This behavior resembles a coherent rotation process in ferromagnetic hysteresis, and implies that the critical field for the metamagnetic transition is determined by the intrinsic spin structure transformation. This conclusion is supported by the consistent metamagnetic transition field observed across different samples and temperatures 30,29. Finally, Supplementary Fig. 3 shows a zero-field MOKE image taken at 20 𝐾 in the single-Q phase. The MOKE signal is uniformly zero across the imaged region, consistent with the expectation that scalar spin chirality, hence MOKE, is absent in the single-Q phase.

Methods
Crystal Growth:
Co TaS single crystals were grown by chemical vapor transport method. The powder samples of Co TaS were synthesized first using the solid-state reaction method. High-purity powders of Cr (99.97%), Ta (99.9%), and S (99.999%) were mixed in stoichiometric ratios. The mixed powders were ground, pelletized, and sealed in quartz tubes. The pellets of powder were then sintered at 750 °C for 48 hours at a heating rate of ~15 °C/h, with intermediate grinding. For the single-crystal growth of Co TaS , the resulting black powder samples were sealed in evacuated quartz tubes together with iodine (I2) as a transport agent. The tubes were placed in a two-zone furnace for 10 days, where the hot and cold ends were maintained at 1000 °C and 900 °C, respectively. The resulting crystals are hexagonal plate-like.

Magnetization measurements:
The magnetic susceptibility versus temperature (χ-T) curves were measured using a Cryogenic-Limited Cryogen Free Measurement System (CFMS) with a vibrating sample magnetometer (VSM) option. A magnetic field of 0.1 T was applied along the c-axis of the Co TaS single crystal during the measurements of χ-T curves. The magnetic moment versus magnetic field (M-H) curves were also measured using the VSM option of our CFMS. The crystal was first cooled to base temperature in a zero magnetic field, then the M-H curve was measured by ramping up the magnetic field.

Hall measurements:
The Hall effects of the sample were characterized by a Keithley 2182 Nanovoltmeter and Keithley 6221 Current Source, and the sample temperature and magnetic field were controlled by the CFMS system. During the measurement, an electric current of 1 mA was applied along the ab plane of the crystal, and the magnetic field was applied to the c-axis of the crystal.

Sagnac MOKE measurements:
The MOKE measurements are performed using a zero-loop fiber-optic Sagnac interferometer 43 operating at 1550 𝑛𝑚 wavelength. For MOKE imaging we utilize a scanning Sagnac microscope with 2 𝜇𝑚 lateral spatial resolution installed inside a cryostat with 1.8 𝐾 base temperature and 9 𝑇 magnetic field capability. The operation of the interferometer is described in the Supplementary Information.

Low-temperature magnetic force microscopy (MFM):
After zero-field cooling from room temperature, a freshly-cleaved Co TaS crystal was scanned at 5 𝐾 using a temperature-variable AFM system (Attocube) in a dual pass mode (lift height ~ 35 𝑛𝑚) with commercial Co/Cr-coated magnetic tips.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Farhang et al. report the observation of the so-called topological magneto-optical Kerr effect (MOKE) in a compensated\nantiferromagnet. Using a Sanac interferometer microscope, they discuss a magneto-optical response arising from spin\ntopology and further argue a correlation between Co composition and MOKE. The experiments appear carefully conducted,\nand the discussion on composition is intriguing. Although the topological MOKE must be the important topic, I have several\nconcerns regarding the interpretation of MOKE and its novelty, which should be addressed before the manuscript can be\nreconsidered:\n(i) The authors ascribe the zero-field magnetization to an orbital moment induced by a fictitious field in Line 93. Could you\nclarify why this assignment is justified?\n(ii) The authors emphasize the SOC-free mechanism for the MOKE, but I am not convinced their data provide evidence.\nThey show that a simple spin model can explain the anomaly in the magnetic-field dependence of MOKE, but similar\nanomalies could also arise from SOC-induced MOKE. Whenever the antiferromagnetic structure is modified by an external\nfield, one would expect anomalies in MOKE. Moreover, the field dependence of MOKE differs from that of the topological\nHall effect in their data. If both phenomena share the same microscopic origin, their field dependence should be consistent.\nThis discrepancy is critical, and the authors must clarify why the two responses behave differently.\n(iii) Related to this point, I strongly recommend the authors measure the wavelength dependence. There should be the\nparticular wavelength where the MOKE shows the same field dependence as the Hall conductivity, which is the genuine\ntopological MOKE.\n(iv) The contrast in the optical reflectivity image is attributed to variations in Co composition. Is there direct evidence\nsupporting this assignment? The authors should take an EDX image in the corresponding region.\n(v) The authors argue a clear correlation between Co composition and the magnitude of MOKE. The 5 % change in\nreflectivity results in dramatic change of MOKE signal as shown in Fig. S1. What could be the underlying mechanism? Does\nthe magnetic structure or spin–orbit coupling strength change with Co substitution?\n(vi) Topological MOKE has already been reported in several other systems. If the novelty of the present work lies in\ndemonstrating the SOC-free mechanism, its significance is limited. In addition, the authors should provide a balanced\ndiscussion of prior studies especially in the introduction and clearly highlight what is genuinely new in their results.\n(vii) Even if the MOKE is primarily driven by spin topology, the spin–orbit coupling inevitably plays some role in real\nmaterials. It is therefore misleading to stress a purely SOC-free mechanism.\n(viii) Figure S4 shows that Mn₃Sn exhibits the largest ratio of MOKE to magnetization. Then, what is the specific\nadvantage of the topological MOKE inferred from the present data?", "reviewer_2": "In this study, the authors investigate the magneto-optical Kerr effect (MOKE) in the non-coplanar antiferromagnet\nCo1/3TaS2. They propose that the observed MOKE signal is topological in nature and arises from a mechanism\nindependent of spin–orbit coupling (SOC) and net magnetization. By employing Sagnac interferometry-based MOKE\nmicroscopy, the authors simultaneously resolve chiral domain structures and superparamagnetic transition behavior. The\nwork compellingly argues that, in contrast to the conventional SOC-dependent MOKE mechanisms that require either\nrelativistic spin–orbit coupling or a finite magnetization, the signal here originates from collective topological properties of\ncompensated spins within a real-space spin texture. The findings are intriguing and the data are in high quality. Although the\nexperimental observations are of significant interest, the authors’ conclusions require further substantiation. Several\nconcerns regarding the interpretation and experimental design should be addressed prior to publication.\n1. The authors attribute the MOKE signal in Co1/3TaS2 to a mechanism that does not involve SOC or net magnetization.\nHowever, certain experimental details appear to indicate a correlation between the MOKE signals and magnetic field-\ninduced changes in magnetization. For example, a comparison between Figures 1b and 1d reveals an increase in the\nMOKE signal concomitant with a rise in the magnetization Mz. Moreover, an upturn in Mz is observed as the magnetic field is\nswept from 4 T to 6 T (Figure 2c) due to a transition from a triple-Q to a single-Q state, which is mirrored by a corresponding\nincrease in the MOKE signal (Figure 2d). This suggests that at least part of the MOKE signal may stem from field-induced\nmagnetization. In addition to the data collected during ZFW after 0.3 T FC, could the authors provide MOKE measurements\nafter ZFC?\n2. Unlike SQUID, which probes bulk magnetization, Signac MOKE is a local measurement technique. Thus, the detected\nsignal may originate not only from the intrinsic crystal properties but also from magnetization at domain walls. Owing to the\nhigh sensitivity of Sagnac interferometry microscopy, the authors clearly visualize localized structures in the\nantiferromagnetic material, as shown in Figures 3 and 4. These images reveal the presence of pronounced magnetic\ndomains within Co1/3TaS2. At domain boundaries, even in the absence of an external magnetic field (B=0), uncompensated\nmagnetization can arise due to spontaneous moments, which could contribute to a MOKE signal at B = 0. Therefore, could\npart of the zero-field MOKE signal be attributable to incomplete spin compensation at domain walls, while the field-\ndependent component arises from field-induced magnetization (Mz)? To rule out contributions from both uncompensated\nmoments and field-induced magnetization, it is recommended that the authors perform additional local magnetic\nmeasurements, such as magnetic force microscopy (MFM), to corroborate their interpretations.", "reviewer_3": "This work focuses on realizing a magneto-optical Kerr effect (MOKE) in the spin-compensated noncoplanar antiferromagnet\nCo1/3TaS2 without relying on spin-orbit coupling, thereby addressing a central open question in the fields of magnetism and\nlight–matter interactions. By employing a highly sensitive zero-loop Sagnac interferometer microscope, the authors achieved\ndirect imaging of scalar spin chirality domains and their reversal driven by noncoplanar spin configurations. They report a\ngiant spontaneous Kerr signal of up to 250 μrad under an applied magnetic field, at a technologically relevant\ntelecommunication wavelength, which is comparable in magnitude to SOC-driven MOKE in noncollinear antiferromagnets\n(e.g., Mn3Sn). Importantly, the study also captures the phase transition between 1Q and 3Q magnetic states, revealing that\nthe Kerr signal vanishes in the 1Q phase and emerges robustly in the 3Q phase. Furthermore, the authors provide\ncompelling evidence of chirality domain dynamics, disentangle extrinsic influences such as local strain and defects, and\ncarefully correlate the Kerr response with chemical inhomogeneity. This clear correspondence between spin texture and\nmagneto-optical response underscores the reliability of the experimental observations. The experimental design is\nmeticulous, the methodology is state-of-the-art, and the results constitute the first robust experimental demonstration of the\ntheoretically predicted topological magneto-optical effects.\nThe significance of this work lies in its demonstration that large, macroscopically measurable \"topological\" MOKE signals\ncan arise without relying on either spin–orbit coupling or band exchange splitting, thereby fundamentally broadening the\ncurrent understanding of magneto-optical phenomena. By establishing a direct connection between scalar spin chirality and\nthe optical response—most notably the disappearance of the Kerr signal in the 1Q and paramagnetic phases and its robust\nreemergence in the 3Q phase—the study provides a well-defined benchmark for identifying and manipulating topological\nmagneto-optical effects. These findings mark a milestone in exploring topological light–matter interactions and open\npromising avenues for spintronics and opto-spintronics based on chiral magnets, with potential implications for ultrafast,\nenergy-efficient, and stray-field-immune device technologies.\nBefore publication, I would like to raise two minor comments for the authors’ consideration:\n1) In the estimation of the scalar spin chirality (χ_{ijk}), only the bottom triangular plaquette is considered. However, from the\ncrystal structure, there appear to be two layers of spin textures. How does the top triangular plaquette contribute to the scalar\nspin chirality, and can it qualitatively change the relationship between magnetization and the Kerr signals?\n2) In the Discussion section, line 254, there seems to be a typo: Extended Data Fig. 2 should be corrected to\nExtended Data Fig. 4. In Extended Data Fig. 4, the work on the skyrmion lattice Gd2PdSi2 (Ref. 50) is cited and\ncompared with the present results. However, for topological MOKE emerging in skyrmion lattices, two more recent\nstudies should also be cited and discussed: Nat. Phys. 20, 1145–1151 (2024) and ACS Nano 18, 20055–20064 (2024). As this is a rapidly developing and\ncompetitive field, including these relevant references and, if possible, comparing their magneto-optical data with the present\nwork (e.g., in Fig. 4) would strengthen the completeness and impact of the discussion.\nOverall, this is an outstanding piece of work with high originality and broad implications for the field. I strongly\nrecommend this work for publication in Nature Communications."}, "author_response": "Dear referees:\nThank you for your professional assessments and insightful suggestions. Attached below are the summary\nof changes and point-to-point responses to comments and questions.\n-Jing Xia, on behalf of all authors\nSummary of Changes\nChanges in the manuscript are highlighted in yellow.\n1. Following Nature Communications format, I have moved extended data figs 1-4 from the main text to the\nsupplementary information and renamed them as supplementary figs 1-4, organized the main text in sections of\n“Introduction”, “Results”, and “Discussions”, and removed inserted figures but kept figure captions in the main\ntext.\n2. In the supplementary information, I have added sections “MOKE after Zero-field Cool (ZFC)”, “Magnetic Force\nMicroscopy (MFM)”, “Energy-dispersive X-ray spectroscopy (EDX)”, and “Estimating the Contribution of\nMagnetization to the MOKE Signal”.\n3. In the “Methods”, I have added “Low-temperature magnetic force microscopy (MFM)” and moved the bulk of\n“Sagnac MOKE measurements” to the supplementary information.\n4. In the “Acknowledgements”, I have added “We thank J.-G. Zheng for Energy-dispersive X-ray spectroscopy\n(EDX) at UC Irvine.”.\n5. On page 3, I added “Note that the real material Co1/3TaS2 may deviate from this ideal triple-Q state, and the\nobserved zero-field magnetization could include some spin contribution.”\n6. On page 5, I added “This also confirms that the zero-field MOKE signal does not originate from uncompensated\nspins at AFM domain walls. If that were the case, ZFC, which produces a higher density of domain walls, would\nyield a larger MOKE signal than field cooling (FC), contrary to our observations. The negligible magnetic\ncontribution from AFM domain walls is also supported by MFM measurements after ZFC (Supplementary Fig.\n8), which show no detectable fringing fields from domain walls.”\n7. On page 5, I added “We estimate that the magnetization contribution to the MOKE signal is negligible, less than\n1% (see Supplementary Information).”.\n8. On page 6, I added “We found that higher Co content leads to lower red-light reflectivity, an effect which we\nexpect to persist at 1550 nm in the Sagnac measurements. (Supplementary Fig. 9c, d).”.\n9. On page 9, I added “Similarly, small ratios are found in skyrmion lattices in CrVI6 51 (θ_K~2×10^(-4) rad, M~3\nμ_B/Cr) and graphene/Fe3GeTe2/graphene heterostructure 52 (RMCD~1×10^(-3) rad, M~2.5 μ_B/Fe) primarily\ndue to their large ferromagnetic moments.”.\n10. On page 11, I added “Data availability: Source data are provided with this paper. They have been deposited in a\nfigshare repository with (link TBA).”.\nResponse to Referees\n(Responses are in blue for clarity.)\nReviewer #1 (Remarks to the Author):\nFarhang et al. report the observation of the so-called topological magneto-optical Kerr effect (MOKE) in a\ncompensated antiferromagnet. Using a Sanac interferometer microscope, they discuss a magneto-optical response\narising from spin topology and further argue a correlation between Co composition and MOKE. The experiments\nappear carefully conducted, and the discussion on composition is intriguing. Although the topological MOKE must\nbe the important topic, I have several concerns regarding the interpretation of MOKE and its novelty, which should\nbe addressed before the manuscript can be reconsidered:\nWe thank the reviewer for his/her professional assessments and suggestions, and for acknowledging the importance\nof the topic discussed in our paper.\n(i) The authors ascribe the zero-field magnetization to an orbital moment induced by a fictitious field in Line 93.\nCould you clarify why this assignment is justified?\nThis is a general statement for the tetrahedral triple-Q state, as I quote below from Ref. 29 (Nature Communications,\n14(1):8346 (2023)): \"Notably, this ordering does not have any net spin magnetization. However, the emergent\nmagnetic field couples to the orbital degrees of freedom of the conduction electrons, giving rise to a uniform orbital\nmagnetization and a large topological Hall effect characterized by scalar spin chirality.\"\nThe real material Co TaS , however, could deviate from an ideal tetrahedral triple-Q state, leading to a\n1/3 2\nsmall spin contribution to the zero-field magnetization, but this doesn’t change the discussion or the conclusion of\nthis paper. We have added the following to page 3:\n“Note that the real material Co1/3TaS2 may deviate from this ideal triple-Q state, and the observed zero-field\nmagnetization could include some spin contribution.”\n(ii) The authors emphasize the SOC-free mechanism for the MOKE, but I am not convinced their data provide\nevidence. They show that a simple spin model can explain the anomaly in the magnetic-field dependence of MOKE,\nbut similar anomalies could also arise from SOC-induced MOKE. Whenever the antiferromagnetic structure is\nmodified by an external field, one would expect anomalies in MOKE.\nFor SOC-driven MOKE, the MOKE signal is expected to scale with the product of the SOC strength and the\nmagnetization. However, as shown in our response to point (vii), this SOC-induced contribution is estimated to be\nless than 1% of the observed MOKE change across the 4–6 T metamagnetic transition, and less than 0.5% during the\n0–4 T field sweep. Thus, SOC-induced MOKE can account for at most ~1% of the observed “anomalies.”\nMoreover, the field dependence of MOKE differs from that of the topological Hall effect in their data. If both\nphenomena share the same microscopic origin, their field dependence should be consistent. This discrepancy is\ncritical, and the authors must clarify why the two responses behave differently.\nIndeed, there is an opposite change between MOKE and DC Hall effect across the metamagnetic transition (4-6 T).\nWhile both MOKE and the Hall effect should scale with the fictitious U(1) gauge field 𝑏 ∝𝑡 χ 𝑛&, i.e. 𝜃 =\n! \" #$% &\n𝐴 𝑏 , Hall=𝐵 𝑏 , the proportionality factors 𝐴 and 𝐵 are definitely different due to the frequency\n'(&) ! *+,, ! '(&) *+,,\ndependence. This can be seen when calculating the magneto-optical conductivity using the Kubo formula (Nature\nCommunications, 11(1):118. (2020)).\nWithin a single magnetic phase, one can assume that both 𝐴 and 𝐵 remain unchanged, and expect that\n'(&) *+,,\nMOKE and the Hall effect would scale with each other. However, across a metamagnetic transition into a different\nmagnetic phase, 𝐴 and 𝐵 necessarily change differently as they are at different frequencies ω. As a result,\n'(&) *+,,\nthe changes of 𝜃 and Hall can be different across the metamagnetic transition at 4-6 T. This is why we wrote on\n&\npage 6 the following:\n“Lastly, we note the DC Hall effect σ_xy (Fig. 2e) shows an opposite change across the metamagnetic transition,\nsuggesting a rather complex frequency dependence related to the corresponding change of spin texture across the\nmetamagnetic transition.”\n(iii) Related to this point, I strongly recommend the authors measure the wavelength dependence. There should be\nthe particular wavelength where the MOKE shows the same field dependence as the Hall conductivity, which is the\ngenuine topological MOKE.\nAs discussed above, in the long-wavelength limit, such as at microwave frequencies, the proportionality factors\n𝐴 and 𝐵 are expected to evolve similarly across the metamagnetic transition. Correspondingly, the MOKE\n'(&) *+,,\nresponse at microwave wavelength should exhibit the same relative change as the Hall conductivity between 4 and 6\nT. Unfortunately, we currently lack the capability to perform wavelength-dependent measurements to confirm this\ndirectly.\n(iv) The contrast in the optical reflectivity image is attributed to variations in Co composition. Is there direct\nevidence supporting this assignment? The authors should take an EDX image in the corresponding region.\nOur working knowledge is that the reflectivities of 𝐶𝑜 𝑇𝑎𝑆 crystals with different Co-compositions are different. It\n- .\nis difficult to perform energy dispersive X-ray spectroscopy (EDX) chemical mapping in the same region of Sagnac\nimaging, as (1) both are time-consuming and cover a very small area on the sample surface, and (2) the surface is\nlargely topographically featureless, lacking “landmarks”. This is why we didn’t provide direct evidence in the\noriginal submission for the correlation between optical reflectivity and Co composition.\nDuring the revision, we have found a workaround: Since no known optical transitions exist in Co1/3TaS2\nbetween red light (620 - 750 nm) and 1550 nm, we may assume that the optical reflectivity at 1550 nm qualitatively\nfollows that at red wavelengths. Based on this assumption, we use a faster and wide-field laboratory microscope to\nmeasure red-light reflectivity in the same region where EDX was conducted, and infer qualitatively the\ncorresponding 1550 nm reflectivity. Locating the same region in the lab-microscope after EDX measurements is\nmade possible because there is a triangular pattern of several large pits serving as “landmarks”. We found that\nhigher Co content leads to lower red-light reflectivity, an effect which we expect to persist at 1550 nm in the Sagnac\nmeasurements. (Supplementary Fig. 9c, d).\nIn the supplementary information, we have added a new section “Energy-dispersive X-ray spectroscopy\n(EDX)” to elaborate on the details. And on page 6 of the main text, we have added “We found that higher Co\ncontent leads to lower red-light reflectivity, an effect which we expect to persist at 1550 nm in the Sagnac\nmeasurements. (Supplementary Fig. 9c, d).”.\n(v) The authors argue a clear correlation between Co composition and the magnitude of MOKE. The 5 % change in\nreflectivity results in dramatic change of MOKE signal as shown in Fig. S1. What could be the underlying\nmechanism? Does the magnetic structure or spin–orbit coupling strength change with Co substitution?\nThe anomalous Hall effect (AHE), arising from spin chirality, has only been observed when the Co composition\nfalls below a certain threshold, as reported in Ref. 47 (Physical Review B 109, L060403 (2024)). In our\nmeasurements, regions with low optical reflectivity, corresponding to higher Co composition, exhibit a strongly\nsuppressed MOKE signal. Although I don’t have evidence for a precise mechanism, I suspect that electron or hole\ndoping from varying Co content modifies the electronic structure, which in turn alters both the magnetic ground\nstate and optical reflectivity. As the reviewer correctly pointed out, the MOKE signal changes very abruptly as a\nfunction of reflectivity (or Co composition). Such abruptness is unlikely to arise from a change in the spin-orbit\ncoupling strength, which should vary smoothly with Co composition. Instead, our observation of an abrupt change\nof MOKE is more consistent with a magnetic phase transition driven by varying Co composition.\n(vi) Topological MOKE has already been reported in several other systems. If the novelty of the present work lies in\ndemonstrating the SOC-free mechanism, its significance is limited. In addition, the authors should provide a\nbalanced discussion of prior studies especially in the introduction and clearly highlight what is genuinely new in\ntheir results.\n“Topological MOKE” of the same name has been reported in several ferromagnetic systems that host skyrmion\nlattices, such as Gd2PdSi2 (Ref. 50), CrVI6 (Ref. 51), and graphene/Fe3GeTe2/graphene heterostructure (Ref. 52),\nwhere Ref. 51 and 52 are pointed out by reviewer # 3. Although sharing the same name “Topological MOKE”, these\nare rather different from the “Topological MOKE” in the theory paper Nature Communications, 11(1):118. (2020),\nwhich discusses antiferromagnetic systems instead of ferromagnetic systems and motivated our work. Another\nmajor difference is that the “Topological MOKE” contributions in those skyrmion lattices in ferromagnets only\nappear in a narrow range of magnetic fields, appearing as “bump features”, while in the antiferromagnetic system\n(this work), the “Topological MOKE” is everywhere, including at zero magnetic field.\nIn the “Discussion”, we have included the following, where the change is marked by yellow highlights:\n“The skyrmion lattice phase in Gd PdSi 50 has a topological contribution to MOKE from swirling spins, though\n2 2\nlimited to a narrow field range and a large net moment of 4 𝜇 , resulting in a small ratio ~7×1001 𝑟𝑎𝑑/𝜇 .\n/ /\nSimilarly, small ratios are found in skyrmion lattices in CrVI 51 (𝜃 ~2×1002 𝑟𝑎𝑑, 𝑀~3 𝜇 /𝐶𝑟) and\n6 & /\ngraphene/Fe GeTe /graphene heterostructure 52 (𝑅𝑀𝐶𝐷~1×100\" 𝑟𝑎𝑑, 𝑀~2.5 𝜇 /𝐹𝑒) primarily due to their large\n3 2 /\nferromagnetic moments.”\n(vii) Even if the MOKE is primarily driven by spin topology, the spin–orbit coupling inevitably plays some role in\nreal materials. It is therefore misleading to stress a purely SOC-free mechanism.\nI don’t think it is misleading to stress a SOC-free mechanism, as the SOC-induced contribution, which is\nproportional to the product of SOC and magnetization, is estimated to be less than 1% below:\nThis can be seen by comparing the magnetization Mz (Fig. 2c) and MOKE signal (Fig. 2d, red) during a\nmagnetic field sweep from 0 to 4 T. At zero-field, Mz (0 T) = 0.01 𝜇 , 𝜃 (0 T) = 195 𝜇𝑟𝑎𝑑; at 4 Tesla just below\n/ &\nthe metamagnetic transition, the magnetization increases to Mz (4 T) = 0.10 𝜇 , and MOKE only changes slightly to\n/\n𝜃 (0 T) = 196 𝜇𝑟𝑎𝑑. This indicated that the MOKE due to magnetization is no bigger than (196 -195) 𝜇𝑟𝑎𝑑 / (0.10-\n&\n0.01 𝜇 ) = 11 𝜇𝑟𝑎𝑑/𝜇 . Thus, even at 4 Tesla when the magnetization is 0.10 𝜇 , the MOKE contribution from\n/ / /\nmagnetization is at most 11 𝜇𝑟𝑎𝑑/𝜇 * 0.10 𝜇 = 1.1 𝜇𝑟𝑎𝑑, i.e. only 0.5 % of the total 195(6) 𝜇𝑟𝑎𝑑 signal. A\n/ /\nsimilar argument applies to the field sweep across the metamagnetic transition between 4 T and 6 T (Figs. 2c and\n2d). In this region, both magnetization Mz and MOKE 𝜃 increase sharply, by 0.08 𝜇 and 60 𝜇𝑟𝑎𝑑, respectively,\n& /\ndue to a sudden reconstruction of the spin configuration (i.e., spin chirality). If the MOKE change were driven\nprimarily by the SOC-magnetization mechanism, it would amount to only 11 𝜇𝑟𝑎𝑑/𝜇 * 0.08 𝜇 = 0.9 𝜇𝑟𝑎𝑑 , i.e.,\n/ /\njust 1% of the observed 60 𝜇𝑟𝑎𝑑. Therefore, the dominant origin of MOKE is clearly the change in spin chirality,\nnot the net magnetization Mz during the metamagnetic transition.\nAccordingly, we have added in the supplementary information a section “Estimating the Contribution of\nMagnetization to the MOKE Signal”. And in the main text page 5, we have added a sentence “We estimate that the\nmagnetization contribution to the MOKE signal is negligible, less than 1% (see Supplementary Information).”.\n(viii) Figure S4 shows that Mn₃Sn exhibits the largest ratio of MOKE to magnetization. Then, what is the specific\nadvantage of the topological MOKE inferred from the present data?\nThe MOKE in Mn Sn (non-collinear but coplanar AFM) arises from a very different mechanism requiring SOC, and\n3\nhence also different implications. By contrast, our results demonstrate that large MOKE can arise without requiring\nstrong SOC, possible in materials composed of lighter elements, thus widening the material choice for spintronics.\nNotably, the MOKE/magnetization ratio in Co₁/₃TaS₂ reported here is already 1/3 of that in Mn₃Sn, underscoring\nthe strong potential of this SOC-independent mechanism.\nReviewer #2 (Remarks to the Author):\nIn this study, the authors investigate the magneto-optical Kerr effect (MOKE) in the non-coplanar antiferromagnet\nCo1/3TaS2. They propose that the observed MOKE signal is topological in nature and arises from a mechanism\nindependent of spin–orbit coupling (SOC) and net magnetization. By employing Sagnac interferometry-based\nMOKE microscopy, the authors simultaneously resolve chiral domain structures and superparamagnetic transition\nbehavior. The work compellingly argues that, in contrast to the conventional SOC-dependent MOKE mechanisms\nthat require either relativistic spin–orbit coupling or a finite magnetization, the signal here originates from collective\ntopological properties of compensated spins within a real-space spin texture. The findings are intriguing and the data\nare in high quality. Although the experimental observations are of significant interest, the authors’ conclusions\nrequire further substantiation. Several concerns regarding the interpretation and experimental design should be\naddressed prior to publication.\nWe thank the reviewer for his/her professional assessments and suggestions, and for acknowledging the “significant\ninterest” of our observations.\n1. The authors attribute the MOKE signal in Co1/3TaS2 to a mechanism that does not involve SOC or net\nmagnetization. However, certain experimental details appear to indicate a correlation between the MOKE signals\nand magnetic field-induced changes in magnetization. For example, a comparison between Figures 1b and 1d\nreveals an increase in the MOKE signal concomitant with a rise in the magnetization Mz. Moreover, an upturn in\nMz is observed as the magnetic field is swept from 4 T to 6 T (Figure 2c) due to a transition from a triple-Q to a\nsingle-Q state, which is mirrored by a corresponding increase in the MOKE signal (Figure 2d). This suggests that at\nleast part of the MOKE signal may stem from field-induced magnetization. In addition to the data collected during\nZFW after 0.3 T FC, could the authors provide MOKE measurements after ZFC?\nCertainly! The ZFC data is now presented in Supplementary Fig. 7b in the newly added Supplementary Information\nsection “MOKE after Zero-field Cool (ZFC)”, which shows 100 times smaller MOKE signal compared to both FC\n(Supplementary Fig. 7a blue) and the subsequent ZFW (Supplementary Fig. 7b red), at the same location. The 100\ntimes smaller MOKE signal in ZFC is due to cancellations between oppositely oriented chirality domains. We have\nadded the reference of Supplementary Fig. 7b to the following sentence on page 5 in the main text:\n“We observed negligible spontaneous 𝜃 after zero-field cool (ZFC) (Supplementary Fig. 7b), indicating the\n&\nformation of oppositely polarized domains smaller than the optical beam size in the absence of a training field.”\nWe agree with the reviewer that some portion of the MOKE signal may originate from field-induced\nmagnetization, which is the “conventional mechanism” for MOKE, but we demonstrate below that this contribution\nis extremely small, less than 1% of the full MOKE signal.\nThis can be seen by comparing the magnetization Mz (Fig. 2c) and MOKE signal (Fig. 2d, red) during a\nmagnetic field sweep from 0 to 4 T. At zero-field, Mz (0 T) = 0.01 𝜇 , 𝜃 (0 T) = 195 𝜇𝑟𝑎𝑑; at 4 Tesla just below\n/ &\nthe metamagnetic transition, the magnetization increases to Mz (4 T) = 0.10 𝜇 , and MOKE only changes slightly to\n/\n𝜃 (0 T) = 196 𝜇𝑟𝑎𝑑. This indicated that the MOKE due to magnetization is no bigger than (196 -195) 𝜇𝑟𝑎𝑑 / (0.10-\n&\n0.01 𝜇 ) = 11 𝜇𝑟𝑎𝑑/𝜇 . Thus, even at 4 Tesla when the magnetization is 0.10 𝜇 , the MOKE contribution from\n/ / /\nmagnetization is at most 11 𝜇𝑟𝑎𝑑/𝜇 * 0.10 𝜇 = 1.1 𝜇𝑟𝑎𝑑, i.e. only 0.5 % of the total 195(6) 𝜇𝑟𝑎𝑑 signal.\n/ /\nA similar argument applies to the field sweep across the metamagnetic transition between 4 T and 6 T\n(Figs. 2c and 2d). In this region, both magnetization and MOKE increase sharply, by 0.08 𝜇 and 60 𝜇𝑟𝑎𝑑,\n/\nrespectively, due to a sudden reconstruction of the spin configuration (i.e., spin chirality). If the MOKE change were\ndriven primarily by magnetization, it would amount to only 11 𝜇𝑟𝑎𝑑/𝜇 * 0.08 𝜇 = 0.9 𝜇𝑟𝑎𝑑, i.e., just 1% of the\n/ /\nobserved 60 𝜇𝑟𝑎𝑑. Therefore, the dominant origin of MOKE is clearly the change in spin chirality, not the net\nmagnetization during the metamagnetic transition.\nNow consider the simultaneous increase of magnetic susceptibility (Fig. 1b) and zero-field MOKE (Fig.\n1d) noticed by the reviewer. Both effects reflect the buildup of spin chirality, but one does not cause the other;\ninstead, they are parallel consequences of the same underlying evolution of spin texture.\nWe thank the reviewer for bringing this up, which we didn’t explain clearly in the original submission.\nAccordingly, we have added in the revised supplementary information a section “Estimating the Contribution of\nMagnetization to the MOKE Signal”. And in the main text page 5, we have added the following sentence:\n“We estimate that the magnetization contribution to the MOKE signal is negligible, less than 1% (see\nSupplementary Information).”.\n2. Unlike SQUID, which probes bulk magnetization, Signac MOKE is a local measurement technique. Thus, the\ndetected signal may originate not only from the intrinsic crystal properties but also from magnetization at domain\nwalls. Owing to the high sensitivity of Sagnac interferometry microscopy, the authors clearly visualize localized\nstructures in the antiferromagnetic material, as shown in Figures 3 and 4. These images reveal the presence of\npronounced magnetic domains within Co1/3TaS2. At domain boundaries, even in the absence of an external\nmagnetic field (B=0), uncompensated magnetization can arise due to spontaneous moments, which could contribute\nto a MOKE signal at B = 0. Therefore, could part of the zero-field MOKE signal be attributable to incomplete spin\ncompensation at domain walls, while the field-dependent component arises from field-induced magnetization (Mz)?\nTo rule out contributions from both uncompensated moments and field-induced magnetization, it is recommended\nthat the authors perform additional local magnetic measurements, such as magnetic force microscopy (MFM), to\ncorroborate their interpretations.\nWe thank the reviewer for raising the very important question regarding domain walls. And below, we use Sagnac\ndata and newly added magnetic force microscopy (MFM) data to rule out this scenario. Accordingly, we have added\ntwo sections in the Supplementary Information, “MOKE after Zero-field Cool (ZFC)”, and “Magnetic Force\nMicroscopy (MFM)”. And in the main text on page 5, we have added the following: “This also confirms that the\nzero-field MOKE signal does not originate from uncompensated spins at AFM domain walls. If that were the case,\nZFC, which produces a higher density of domain walls, would yield a larger MOKE signal than field cooling (FC),\ncontrary to our observations. The negligible magnetic contribution from AFM domain walls is also supported by\nMFM measurements after ZFC (Supplementary Fig. 8), which show no detectable fringing fields from domain\nwalls.”.\nSagnac data: in Supplementary Fig. 7b in the newly added Supplementary Information section “MOKE\nafter Zero-field Cool (ZFC)”, we compare Sagnac measurements at the same location between field-cooling (FC)\nand zero-field-cooling (ZFC). The 0.3 T FC (blue) and subsequent zero-field warm (ZFW, red) traces in\nSupplementary Fig. 7a exhibit a large 𝜃 of 180 𝜇𝑟𝑎𝑑. In contrast, the ZFC measurement (blue in Supplementary\n&\nFig. 7b) yields a much smaller 𝜃 of −2 𝜇𝑟𝑎𝑑. If the zero-field MOKE signal is from incomplete spin compensation\n&\nat domain walls, we would expect a much smaller MOKE signal after FC because it has nearly zero domain walls.\nInstead, it shows a 100 times larger signal compared to ZFC, ruling out this scenario.\nMFM data: We have conducted extensive low-temperature MFM measurements under various\nexperimental conditions. The newly added Supplementary Fig. 8 shows a representative scan taken at 5 K after zero-\nfield cooling, where AFM domains are expected to be most abundant. However, no magnetic domains or domain\nwalls were detected within the MFM sensitivity. This indicates that the fringing fields produced by uncompensated\nmoments at AFM domain walls are too weak to be resolved by MFM. This is consistent with the picture that the\nMOKE signal is (dominantly) due to the chirality of AFM domains instead of uncompensated magnetic moments at\nAFM domain walls.\nReviewer #3 (Remarks to the Author):\nThis work focuses on realizing a magneto-optical Kerr effect (MOKE) in the spin-compensated noncoplanar\nantiferromagnet Co1/3TaS2 without relying on spin-orbit coupling, thereby addressing a central open question in the\nfields of magnetism and light–matter interactions. By employing a highly sensitive zero-loop Sagnac interferometer\nmicroscope, the authors achieved direct imaging of scalar spin chirality domains and their reversal driven by\nnoncoplanar spin configurations. They report a giant spontaneous Kerr signal of up to 250 μrad under an applied\nmagnetic field, at a technologically relevant telecommunication wavelength, which is comparable in magnitude to\nSOC-driven MOKE in noncollinear antiferromagnets (e.g., Mn3Sn). Importantly, the study also captures the phase\ntransition between 1Q and 3Q magnetic states, revealing that the Kerr signal vanishes in the 1Q phase and emerges\nrobustly in the 3Q phase. Furthermore, the authors provide compelling evidence of chirality domain dynamics,\ndisentangle extrinsic influences such as local strain and defects, and carefully correlate the Kerr response with\nchemical inhomogeneity. This clear correspondence between spin texture and magneto-optical response underscores\nthe reliability of the experimental observations. The experimental design is meticulous, the methodology is state-of-\nthe-art, and the results constitute the first robust experimental demonstration of the theoretically predicted\ntopological magneto-optical effects.\nThe significance of this work lies in its demonstration that large, macroscopically measurable \"topological\" MOKE\nsignals can arise without relying on either spin–orbit coupling or band exchange splitting, thereby fundamentally\nbroadening the current understanding of magneto-optical phenomena. By establishing a direct connection between\nscalar spin chirality and the optical response—most notably the disappearance of the Kerr signal in the 1Q and\nparamagnetic phases and its robust reemergence in the 3Q phase—the study provides a well-defined benchmark for\nidentifying and manipulating topological magneto-optical effects. These findings mark a milestone in exploring\ntopological light–matter interactions and open promising avenues for spintronics and opto-spintronics based on\nchiral magnets, with potential implications for ultrafast, energy-efficient, and stray-field-immune device\ntechnologies.\nWe thank the reviewer for his/her professional assessments and suggestions, and for acknowledging that our “results\nconstitute the first robust experimental demonstration of the theoretically predicted topological magneto-optical\neffects”, and that they “mark a milestone” in this field.\nBefore publication, I would like to raise two minor comments for the authors’ consideration:\n1) In the estimation of the scalar spin chirality (χ_{ijk}), only the bottom triangular plaquette is considered.\nHowever, from the crystal structure, there appear to be two layers of spin textures. How does the top triangular\nplaquette contribute to the scalar spin chirality, and can it qualitatively change the relationship between\nmagnetization and the Kerr signals?\nWe agree with the reviewer that there is more than one plaquette in the magnetic unit cell. In a “complete”\ntheory, one would ideally perform a vector sum of each plaquette’s chirality multiplied by the corresponding hopping\nintegral, with the direction of the resulting vector being along the normal direction of that plaquette. However, such\na calculation is beyond the scope of this experimental paper, largely due to my lack of skill to calculate the hopping\nintegral. From a symmetry point of view, however, such a vector sum would, to the first order, be proportional to the\ncontribution from the single plaquette considered in this paper. Therefore, one could expect the same qualitative\n(and likely quantitative to the first order) relationship between magnetization and the Kerr signal by considering\nonly one plaquette.\n2) In the Discussion section, line 254, there seems to be a typo: Extended Data Fig. 2 should be corrected to\nExtended Data Fig. 4. In Extended Data Fig. 4, the work on the skyrmion lattice Gd2PdSi2 (Ref. 50) is cited and\ncompared with the present results. However, for topological MOKE emerging in skyrmion lattices, two more recent\nstudies should also be cited and discussed: Nat. Phys. 20, 1145–1151 (2024) and ACS Nano 18, 20055–20064 (2024). As this is a rapidly developing and competitive field, including these relevant references and, if possible,\ncomparing their magneto-optical data with the present work (e.g., in Fig. 4) would strengthen the completeness and\nimpact of the discussion.\nWe thank the reviewer for pointing these out. I have fixed the typo, and have added in the “Discussion” section\n(page 9) the following sentence with these two recent references on topological MOKE in skyrmion lattices:\n“Similarly, small ratios are found in skyrmion lattices in CrVI 51 (𝜃 ~2×1002 𝑟𝑎𝑑, 𝑀~3 𝜇 /𝐶𝑟) and\n6 & /\ngraphene/Fe GeTe /graphene heterostructure 52 (𝑅𝑀𝐶𝐷~1×100\" 𝑟𝑎𝑑, 𝑀~2.5 𝜇 /𝐹𝑒) primarily due to their large\n3 2 /\nferromagnetic moments.”\nOverall, this is an outstanding piece of work with high originality and broad implications for the field. I strongly\nrecommend this work for publication in Nature Communications.\nWe thank the reviewer again for his/her professional assessments."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The revised manuscript and the authors' replies address many of my concerns, but the central issue of the microscopic origin of the observed MOKE remains unresolved. The authors continue to attribute the observed MOKE to a scalar-spin-chirality (topological) mechanism and propose that the different field dependence of the Hall effect and MOKE arises from a change in frequency dependence across the metamagnetic transition — yet no experimental evidence for such frequency dependence is presented. I am seriously concerned that a spin–orbit-coupling (SOC)–driven mechanism, which is discussed for Mn3Sn, not magnetization induced MOKE, may be contributing, either instead of or in addition to a topological MOKE. In the present material, the observed Kerr signal (and even Hall effect) could therefore be a superposition of three contributions: (i) topological MOKE from scalar spin chirality, (ii) Mn3Sn-type MOKE arising from TRS breaking specific to the antiferromagnetic order (but not directly proportional to net magnetization), and (iii) the ordinary magnetization-induced MOKE. The authors must explicitly separate (or convincingly argue why they can be neglected) these contributions. Without such discussion, their main claim that the MOKE is dominated by topological spin chirality is not substantiated.", "reviewer_2": "The authors have performed calculations demonstrating that the contribution of the conventional mechanism to the overall MOKE signal is less than 1%. In addition, they have included new magnetic force microscopy (MFM) data in an effort to rule out any signal contribution from domain walls. It appears that the authors have addressed the issues I raised in a constructive and appropriate manner. Therefore, I have no further questions regarding this paper and recommend it for publication.", "reviewer_3": "I have carefully reviewed the revised manuscript and the authors’ responses to all reviewers. In my opinion, their revisions satisfactorily address the previous concerns. Considering that this work presents the first robust experimental demonstration of topological magneto-optical effects, it fully merits publication in a high-impact journal such as Nature Communications. Therefore, I recommend the manuscript for publication in its current form."}, "author_response": "Dear referees:\nThank you for your professional assessments and insightful suggestions. Attached below are the summary\nof changes and point-to-point responses to comments and questions.\n-Jing Xia, on behalf of all authors\nSummary of Changes\nChanges in the manuscript are highlighted in yellow.\nI have added the following clarifications to the revised manuscript:\nLine 93: A clear correlation between the degree of spin non-coplanarity and the amplitude of spontaneous Hall\nsignal was confirmed by temperature dependence of polarized neutron scattering 30.\nLine 130: The pronounced temperature dependence of MOKE in Co TaS stands in sharp contrast to the\n1/3 2\ntemperature-invariant behavior we observed in the coplanar non-collinear antiferromagnet Mn₃NiN 46, underscoring\ntheir distinct origins.\nResponse to Referees\n(Responses are in blue for clarity.)\nReviewer #1 (Remarks to the Author):\nThe revised manuscript and the authors' replies address many of my concerns, but the central issue of the\nmicroscopic origin of the observed MOKE remains unresolved. The authors continue to attribute the observed\nMOKE to a scalar-spin-chirality (topological) mechanism and propose that the different field dependence of the Hall\neffect and MOKE arises from a change in frequency dependence across the metamagnetic transition — yet no\nexperimental evidence for such frequency dependence is presented. I am seriously concerned that a spin–orbit-\ncoupling (SOC)–driven mechanism, which is discussed for Mn3Sn, not magnetization induced MOKE, may be\ncontributing, either instead of or in addition to a topological MOKE. In the present material, the observed Kerr\nsignal (and even Hall effect) could therefore be a superposition of three contributions: (i) topological MOKE from\nscalar spin chirality, (ii) Mn3Sn-type MOKE arising from TRS breaking specific to the antiferromagnetic order (but\nnot directly proportional to net magnetization), and (iii) the ordinary magnetization-induced MOKE. The authors\nmust explicitly separate (or convincingly argue why they can be neglected) these contributions. Without such\ndiscussion, their main claim that the MOKE is dominated by topological spin chirality is not substantiated.\nWe thank the reviewer for raising the question regarding the separation of the possible contributions (i), (ii), and\n(iii). As clarified in our previous revision, contribution (i) is at least two orders of magnitude larger than (iii). To\nfurther address mechanism (ii) “Mn3Sn-type MOKE arising from TRS breaking specific to the antiferromagnetic\norder (but not directly proportional to net magnetization)”, we now cite two key experimental results, including one\nfrom our group, showing that mechanism (i) dominates while (ii) doesn’t dominate in Co₁/₃TaS₂.\n(1) As the reviewer noted, mechanism (ii) gives rise to MOKE and AHE in coplanar noncollinear\nantiferromagnets such as Mn₃Sn, where the Hall conductivity 𝜎 is given by the Berry curvature integral as\n!\"\n𝜎 = \n#$!\n∫ 𝑑𝑘 Ω(𝑘). Here Ω(𝑘)=∑ 𝑓[𝜖 (𝑘)−𝜇] Ω (𝑘) is the total Berry curvature over the occupied bands\n!\" %&\"ℏ () * * *\nin the Brillouin zone. It is expected that once the AFM phase is fully developed, 𝜎 should be largely temperature\n!\"\nindependent since the Berry curvature is a band structure property. Accordingly, the MOKE signal 𝜃 (𝜔)=\n+\nRe6\n#,#$(.)\n7 is also expected to be temperature invariant if mechanism (ii) dominates.\n,##(.)01234 %\n'\n& 5,##(.)\nFigure 1 adopted from our MOKE measurement\nof coplanar noncollinear AFM Mn3NiN, where\nMOKE is from mechanism (ii).\nFarhang et.al. Temperature-invariant magneto-\noptical Kerr effect in a noncollinear\nantiferromagnet, (arXiv:2510.19709)\nWe have recently reported such behavior in our Sagnac-interferometer MOKE measurements on the coplanar\nnoncollinear antiferromagnet Mn₃NiN (Farhang et al., arXiv:2510.19709), where the spontaneous Kerr signal\nremains nearly constant with temperature, consistent with a Berry-curvature-driven origin, as shown in the adopted\nfigure above. In stark contrast, Co₁/₃TaS₂ exhibits a strong temperature dependence in MOKE (Fig.1d of the main\ntext), clearly indicating that mechanism (ii) is not dominant in this system.\n(2) A quantitative comparison between mechanism (i) and (ii) requires the experimental measurement of\nspin non-coplanarity, which directly corresponds to contribution (i) but is irrelevant to (ii). Such measurements in\nCo₁/₃TaS₂ were reported in Takagi, H. et al., Nat. Phys. 19, 961–968 (2023), where polarized neutron scattering\nconfirmed a clear correlation between the degree of spin non-coplanarity and the amplitude of the spontaneous Hall\nsignal, quote “Supplementary Note IX discusses the temperature dependence of polarized neutron scattering data,\nwhich confirms the clear correlation between the degree of spin non-coplanarity and the amplitude of spontaneous\nHall signal and Supplementary Note X provides a detailed discussion on the mechanism of Hall effect in\nantiferromagnets”. Their result establishes that mechanism (i) dominates the AHE in Co₁/₃TaS₂. Since MOKE is the\noptical-frequency analog of the AHE, it follows that mechanism (i) is also the primary contributor to MOKE in\nCo₁/₃TaS₂.\nAccordingly, we have added the following clarifications to the revised manuscript:\nLine 93: A clear correlation between the degree of spin non-coplanarity and the amplitude of spontaneous Hall\nsignal was confirmed by temperature dependence of polarized neutron scattering 30.\nLine 130: The pronounced temperature dependence of MOKE in Co TaS stands in sharp contrast to the\n1/3 2\ntemperature-invariant behavior we observed in the coplanar non-collinear antiferromagnet Mn₃NiN 46, underscoring\ntheir distinct origins.\nReviewer #2 (Remarks to the Author):\nThe authors have performed calculations demonstrating that the contribution of the conventional mechanism to the\noverall MOKE signal is less than 1%. In addition, they have included new magnetic force microscopy (MFM) data\nin an effort to rule out any signal contribution from domain walls. It appears that the authors have addressed the\nissues I raised in a constructive and appropriate manner. Therefore, I have no further questions regarding this paper\nand recommend it for publication.\nWe thank the reviewer again for his/her professional assessments.\nReviewer #3 (Remarks to the Author):\nI have carefully reviewed the revised manuscript and the authors’ responses to all reviewers. In my opinion, their\nrevisions satisfactorily address the previous concerns. Considering that this work presents the first robust\nexperimental demonstration of topological magneto-optical effects, it fully merits publication in a high-impact\njournal such as Nature Communications. Therefore, I recommend the manuscript for publication in its current form.\nWe thank the reviewer again for his/her professional assessments."}, {"round": 3, "reviewer_comments": {"reviewer_2": "REVIEWERS' COMMENTS\nR#2:\nReviewer 1 disputes the authors' attribution of the observed MOKE signal solely to a scalar spin chirality\n(topological) mechanism. He proposed that the MOKE observed in this study may also comprise two additional\ncomponents: 1) a contribution arising from the time-reversal symmetry breaking specific to the antiferromagnetic\norder, and 2) the conventional magnetization-induced MOKE.\nI had previously raised a similar concern regarding the potential influence of component 2). In their response, the\nauthors provided detailed calculations, concluding that \"we estimate the magnetization contribution to the MOKE\nsignal is negligible, less than 1%.\" This justification satisfactorily addresses and effectively rules out the second\nfactor.\nHowever, Reviewer 1 points out that the MOKE generated via the spin-orbit coupling (SOC) driven mechanism is\nnot directly proportional to the net magnetization, a phenomenon previously documented in Mn3Sn [Nature\nPhotonics 12, 73–78 (2018)]. As a plausible underlying reason for the observed signal, the authors need to provide a\nthorough discussion of this specific issue in their revised manuscript."}, "author_response": "Dear referees:\nThank you for your professional assessments and insightful suggestions. Attached below are the summary\nof changes and point-to-point responses to comments and questions.\n-Jing Xia, on behalf of all authors\nSummary of Changes\nChanges in the manuscript are highlighted in yellow.\nThere is no further change to the manuscript in this revision.\nResponse to Referees\n(Responses are in blue for clarity.)\nREVIEWERS' COMMENTS\nR#2:\nReviewer 1 disputes the authors' attribution of the observed MOKE signal solely to a scalar spin chirality\n(topological) mechanism. He proposed that the MOKE observed in this study may also comprise two additional\ncomponents: 1) a contribution arising from the time-reversal symmetry breaking specific to the antiferromagnetic\norder, and 2) the conventional magnetization-induced MOKE.\nI had previously raised a similar concern regarding the potential influence of component 2). In their response, the\nauthors provided detailed calculations, concluding that \"we estimate the magnetization contribution to the MOKE\nsignal is negligible, less than 1%.\" This justification satisfactorily addresses and effectively rules out the second\nfactor.\nHowever, Reviewer 1 points out that the MOKE generated via the spin-orbit coupling (SOC) driven mechanism is\nnot directly proportional to the net magnetization, a phenomenon previously documented in Mn3Sn [Nature\nPhotonics 12, 73–78 (2018)]. As a plausible underlying reason for the observed signal, the authors need to provide a\nthorough discussion of this specific issue in their revised manuscript.\nWe thank the reviewer again for his/her professional assessment and for raising this crucial point, which echoes a\nquestion from Reviewer 1 in the last revision: whether the observed MOKE signal arises from a Spin-Orbit\nCoupling (SOC) driven mechanism that is non-proportional to net magnetization, similar to the phenomenon\ndocumented in Mn₃Sn [Nature Photonics 12, 73–78 (2018)].\nAs discussed in our response to Reviewer 1 in the last revision, the physical origin of the MOKE in the non-coplanar\nantiferromagnet Co₁/₃TaS₂ (this work) is fundamentally different from that of the coplanar non-collinear\nantiferromagnet such as Mn₃Sn. In Co₁/₃TaS₂, the MOKE arises from the Berry phase associated with the real-space\nscalar spin chirality of the non-coplanar spin arrangement (a topological effect not explicitly reliant on SOC). In\ncontrast, the signal in non-collinear antiferromagnet Mn₃Sn results from the momentum-space Berry curvature of the\nmagnetic band structure driven by SOC. This distinction is supported with two key pieces of evidence that we have\npreviously explained in the last revision:\n(1) Temperature Dependence vs. Invariance: In systems like Mn₃Sn, the intrinsic anomalous Hall effect (AHE)\nand MOKE are band structure properties. Therefore, once the AFM order is established, these signals should be\nlargely temperature-independent. We recently verified this behavior by observing a \"temperature-invariant\" MOKE\nin the non-collinear antiferromagnet Mn₃NiN (Farhang et al., arXiv:2510.19709). In stark contrast, Co₁/₃TaS₂\nexhibits a strong temperature dependence in its MOKE signal. This is because the signal tracks the scalar spin\nchirality, which itself varies significantly with temperature in this system. This distinct behavior strongly suggests a\nchirality-driven origin rather than a purely SOC-driven band structure effect.\nIn the last revision, we have added the following clarifications in Line 93: A clear correlation between the degree of\nspin non-coplanarity and the amplitude of spontaneous Hall signal was confirmed by temperature dependence of\npolarized neutron scattering 30.\n(2) Correlation with Spin Chirality: A quantitative link between spin non-coplanarity and the spontaneous Hall\neffect in Co₁/₃TaS₂ has been established by Takagi et al. [Nat. Phys. 19, 961–968 (2023)]. Their polarized neutron\nscattering results confirmed that the amplitude of the spontaneous Hall signal is directly correlated with the degree\nof spin non-coplanarity, identifying scalar spin chirality as the dominant mechanism for the AHE. Since MOKE is\nthe optical-frequency analog of the AHE, it follows that scalar spin chirality is also the primary contributor to the\nMOKE observed in our work.\nIn the last revision, we have added the following clarifications in Line 130: The pronounced temperature\ndependence of MOKE in Co TaS stands in sharp contrast to the temperature-invariant behavior we observed in the\n1/3 2\ncoplanar non-collinear antiferromagnet Mn₃NiN 46, underscoring their distinct origins."}]

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