Room temperature observation of the anomalous in-plane Hall effect in a Weyl ferromagnet

Domain: physics
Published: 2025-12-04
Editorial outcome: major_revision

Abstract
Topologically nontrivial electronic states can lead to novel anomalous Hall effects, with room temperature manifestations promising for applications in magnetic sensing, spintronics, and energy harvesting. The anomalous in-plane Hall effect is expected in topological magnetic materials under an in-plane magnetic field, but its detection has been challenging because of strict symmetry requirements. Here, we combine molecular beam epitaxy of the kagome metal Fe3Sn, electric Hall effect measurements, and theoretical calculations to propose and demonstrate that the kagome lattice motif combined with spin-orbit coupling and canted ferromagnetism induces the anomalous in-plane Hall effect at room temperature via topological Weyl points. Additionally, we synthesize a topological thin-film heterostructure with Fe3Sn and ferromagnetic CoFeB, showing enhanced anomalous in-plane Hall effect amplitude due to CoFeB’s magnetic stray field. This work establishes a design framework for topological magnets and heterostructures aimed at discovering and controlling anomalous Hall effects for technological applications.

Introduction
Topologically nontrivial electronic states can give rise to novel electric transport phenomena, such as anomalous Hall effects (AHE)1–5. These phenomena provided deep insight into the fundamental properties of topological quantum materials and have garnered increasing attention for their applications in magnetic sensing, spintronics, and energy harvesting technology6–8. The conventional AHE requires the breaking of the time-reversal symmetry T resulting in a finite Berry curvature of the occupied electronic states. Therefore, AHE can be experimentally detected in magnetic materials and heterostructures, where T is broken by long-range magnetic order1,9,10. As long as the energy scale of this T-breaking mechanism, such as the magnetic exchange interaction J, is sufficiently large, Berry curvature-induced AHEs can be detected even at and above room temperature5,11–16. This favors their potential integration into technological applications and motivates the search for new classes of topological magnetic materials and heterostructures, which can be manufactured using scalable synthesis methods, to discover and control Hall effects at room temperature.

Novel Hall effects can arise by the additional breaking of crystalline symmetries, such as inversion and rotation symmetries. Governed by distinct symmetry restrictions, these Hall effects can be qualitatively distinguished from the conventional AHE9,10,17, and their unique experimental characteristics are attracting an increasing amount of interest. For example, breaking of inversion symmetry permits the observation of the second-order nonlinear anomalous Hall effect that appears as a Hall voltage at the second harmonic of a longitudinal a.c. current drive2–4,9. It has also been predicted that breaking of out-of-plane rotation symmetries17,18 can give rise to an anomalous in-plane Hall effect (IPHE). The IPHE describes the appearance of an electric Hall voltage when an external magnetic field is applied within the sample plane. Because of this rigorous restriction with respect to rotation symmetries, the observation of the anomalous IPHE has proven challenging. To date, IPHEs are mostly field-induced, where the breaking of the relevant crystalline symmetries is realized by an external magnetic field19–21; moreover, a temperature-independent anomalous IPHE, resulting from topological electronic states, has not yet been reported22.

In this study, we overcome this challenge by combining electric Hall measurements of epitaxially grown thin films of the Weyl ferromagnet Fe3Sn with systematic theoretical calculations. We propose and experimentally demonstrate that the interplay of the kagome lattice motif with spin-orbit coupling and canted in-plane ferromagnetism with large exchange interactions J≈40meV23 breaks the relevant crystalline symmetries and gives rise to the anomalous IPHE at room temperature.

Results
Prediction of the anomalous in-plane Hall effect in the Weyl ferromagnet Fe3Sn

The kagome metal Fe3Sn (a=b=5.487Å and c=4.3Å, space group P6/mmc) belongs to the class of binary kagome metals X3Yp, which attracts a lot of interest due to its topological and flat band electronic states (X=Fe, Co, Ni, Y=Sn, In, Ge, with chemical stoichiometry p, q)5,11,24–30. Common among this material class are strong nearest-neighbor magnetic exchange interactions between transition metal atoms arranged on the kagome lattice, as seen in Fig. 1a that can result in a long-range magnetic order much above room temperature11,23,31. In Fe3Sn, the Fe ions form a kagome lattice in the crystallographic ab plane, and a Sn ion occupies the honeycomb center, as seen in Fig. 1a. The primitive unit cell of Fe3Sn is composed of kagome bilayers stacked along the crystallographic [0001]-direction. For simplicity, we introduce the Cartesian coordinates x, y, and z corresponding to the crystalline directions [2\bar{1}\bar{1}0], [01\bar{1}0], and [0001], respectively. An easy-plane magneto-crystalline anisotropy imparts in-plane ferromagnetism with the magnetization M pointing along the x direction, where large ferromagnetic exchange interactions J≈40meV23 favor a Curie temperature TC≈705K above room temperature31–35.

Ferromagnetism combined with spin-orbit coupling profoundly influences the electronic structure and topology of kagome metals5,11,26. In Fe3Sn, it has been shown that this combination imparts a set of Weyl points when the magnetization vector points along the x direction32. An additional magnetization component along the z direction, such as resulting from a canting of the magnetic moments of Fe, further lifts characteristic degeneracies of the electronic band structure of the kagome lattice, such as occurring at the crystallographic Γ and K points of the hexagonal Brillouin zone. This results in a set of Weyl points near the Fermi energy32. Using symmetry analyses and ab-initio model calculations, we show that these Weyl points give rise to an anomalous in-plane Hall conductivity σIPHE in spin-canted Fe3Sn.

Given that the magnetization vector is oriented along the x direction, the magnetic space group (MSG) of Fe3Sn is Cmc0m0, which consists of three mirror (glide-mirror) symmetries Mx, MytT, and MztT, where t is a fractional translation. Note that Mz=I\timesC2z, where I and C2z correspond to the inversion and two-fold rotation symmetry, respectively. Since the Berry curvature is invariant under I, Mz and C2z are equivalent in symmetry analysis. Determined by all the symmetries in the MSG, the total Berry curvature (as seen in Fig. 1b, d) and thus the anomalous Hall conductivity σxy within the sample xy-plane vanishes; only an out-of-plane component σyz is permitted (see Section I of the Supplementary Materials for more details). On the other hand, an out-of-plane magnetic field or out-of-plane canting of the magnetization along the z-direction breaks Mx and MztT and results in a finite total Berry curvature Ωz (as seen in Fig. 1c, e).

This understanding is also consistent with our results of ab-initio calculations of the electronic band structure of Fe3Sn (see the “Methods” section for calculation details). While the total Berry curvature vanishes in the absence of canting (as seen in Fig. 1d), the presence of canting M=(Mx, 0, Mz) results in a finite Berry curvature that is induced by Weyl points near the Fermi energy, as seen in Fig. 1e. The detailed analysis of the electronic structure, Weyl point chirality, and resulting Berry curvature is shown in Section II of the Supplementary Materials.

An externally applied in-plane magnetic field B\parallel=B(cosϕB, sinϕB, 0) can further modulate the associated anomalous in-plane Hall conductivity σIPHE through the exchange coupling between B\parallel and the spin of the itinerant electrons. Here, ϕB is defined as the azimuthal angle between Mx and B\parallel within the xy-plane, as illustrated in Fig. 1f. We have analyzed this effect using a Wannier tight-binding model of the electronic band structure of Fe3Sn (see the “Methods” section for details). The resulting σIPHE(ϕB) is shown in Fig. 1f. Our calculations establish that B\parallel modulates σIPHE with 2π periodicity in the presence of canting. The cos(ϕB) dependence arises because the preserved MytT symmetry requires σIPHE to be an even function of the magnetic field angle ϕB (see details in Section III of the Supplementary Materials). Therefore, our symmetry analysis and model calculations propose that Fe3Sn should allow the observation of the anomalous IPHE when finite spin canting in the z direction is present. Note that the anomalous IPHE is odd under magnetic field reversal and exhibits an antisymmetric conductivity tensor. It should thus be invariant under a rotation of the current direction within the xy-plane.

Classification of Hall effects

This distinct dependence on the relative angle between B\parallel and Mx (seen in Fig. 1f), as well as the magnetic-field-reversal symmetry of σIPHE enables us to separate the anomalous IPHE from possible other contributions to the measured transverse voltage Vxy that can occur in the presence of an in-plane magnetic field B\parallel and canted ferromagnetism with M=(Mx, 0, Mz), namely the symmetric transverse resistivity (STR), the planar Hall effect (PHE), the AHE, and the ordinary Hall effect (OHE). To this end, it is instructive to briefly introduce these effects and discuss their properties. The detailed characteristics of these phenomena are summarized in Table 1. The STR is an anisotropy effect that originates from the breaking of the C3z-rotation symmetry by the in-plane magnetization component Mx. Therefore, it only depends on the azimuthal angle ϕE between the longitudinal electric field E, which lies in the xy-plane of the sample and is always parallel to the longitudinal current direction, and Mx36. The associated conductivity is symmetric under magnetic field reversal and follows the relation σSTR\propto sin(2ϕE) (also see Section IV of the Supplementary Materials for a detailed derivation of the STR effect). The PHE arises when both B\parallel and E lie within the sample plane. It results from a field-induced anisotropic magnetoresistance and its conductivity σPHE\propto sin(2ϕB-2ϕE) exhibits a sinusoidal dependence on the relative angle between B\parallel and E36. Critically, PHE displays a symmetric conductivity tensor, classifying it as an anisotropic magnetoresistance effect rather than a true Hall signal. The AHE results from a finite out-of-plane magnetization Mz. Hence, the anomalous Hall conductivity is independent of ϕB and ϕE and the AHE is isotropic within the xy-plane1. Moreover, its conductivity tensor is odd under magnetization reversal, σxy(Mz)=−σxy(−Mz).

Finally, a slight misalignment of the sample xy-plane with the direction of B\parallel results in a finite out-of-plane component Bz of the magnetic field, which can give rise to the OHE. The OHE arises from the Bz-induced Lorentz force acting on the moving charge carriers, and its conductivity tensor is odd under magnetic field reversal. There are two possible misalignment configurations, which are described in detail in Section V of the Supplementary Materials: When the surface normal of the sample xy-plane is parallel to the rotation axis of B\parallel, the associated Hall conductivity σH is independent of both ϕB and ϕE due to a fixed Bz. When additionally the surface normal of the sample xy-plane is misaligned with the rotation axis of B\parallel, the associated Hall conductivity exhibits a sinusoidal dependence as σH/sin(ϕB), since the in-plane rotation modulates the relative orientation between B\parallel and the surface normal. Overall, this classification shows that different contributions to the transverse voltage Vxy can be distinguished by their distinct angle dependence and by using suitable symmetrization operations with respect to the externally applied magnetic field.

Experimental detection of spin-canted in-plane ferromagnetism in Fe3Sn thin films

We developed the molecular beam epitaxy on Fe3Sn thin films (typical thicknesses 30–60nm) on the (0001) surface of sapphire substrates using a Pt(111) buffer layer of 5nm thickness to facilitate layer-by-layer growth of continuous films (see the “Methods” section and Section VI of the Supplementary Materials for results of the chemical and structural characterization). Transmission electron microscopy measurements reveal a defined Pt(111)-Fe3Sn interface and confirm the characteristic bilayer stacking of the Fe3Sn kagome layers along the z direction, as seen in Fig. 2a. Measurements of the temperature (T) dependent longitudinal resistivity shown in Fig. 2b demonstrate the metallic character of the Fe3Sn thin films. The residual ρxx≈72×10−6Ωcm at T=2K agrees well with previously reported values for single crystals31,32,35, indicating a high crystalline quality and a low defect density of our samples. Note that the Pt(111) buffer layer is metallic and could shunt the electric conduction through the Fe3Sn layer in current-biased measurements. Our analysis of this shunt effect, discussed in Section VII of the Supplementary Materials, shows that electric conduction through the Pt(111) buffer layer enhances the transverse voltage Vxy,Fe3Sn=ζVxy across the Fe3Sn layer over the measured transverse voltage Vxy by a shunt factor ζ≤1.19 that is nearly temperature independent. All transverse resistivities and voltages across the Fe3Sn layer shown in the main text and Supplementary Materials are corrected for this shunt effect.

The results of our magnetization measurements (see “Methods” section) at T=300K as a function of an externally applied magnetic field B are shown in Fig. 2c. In agreement with previous results on sputtered thin films and bulk crystals31–33, we detect an anisotropic response to an externally applied magnetic field B; the saturation field is smaller when B is applied within the xy-plane than when B is applied along the z-axis. This result is consistent with the presence of in-plane ferromagnetism along the x-axis. The detected magnetic moment of ≈2.3μB/Fe atom matches well with previous reports31–33 and is dominated by the spin moment of the Fe atoms31. A closer examination of the magnetization curve at small out-of-plane fields further reveals the presence of a narrow hysteresis loop with remnant out-of-plane magnetization Mz≈0.11μB/Fe atom at B=0. This observation indicates the presence of a finite out-of-plane canting of the magnetic easy plane of Fe in our thin films. Note that the absence of an in-plane hysteresis, as seen in Fig. 2c could result from the combination of small energy barriers for magnetization reversal within the ab-plane31 and finite size effects. These factors could enable nearly reversible magnetization processes through coherent spin rotation37 or free domain wall motion at small fields sweep rates38.

Fe3Sn films were shaped into circular Hall bar devices with 12 terminals, as seen in Fig. 2d (see “Methods” section for details of the device fabrication). As discussed above, this device geometry enables us to identify and extract the different contributions to measured transverse voltage Vxy, when an externally applied magnetic field B\parallel=B(cosϕB, sinϕB, 0) is rotated within the xy-plane of the sample and when a longitudinal electric field E, which is parallel to the direction of the applied bias current I, is applied between different terminal pairs. In our experiment, we define the Cartesian coordinate system, shown in Fig. 2d, such that the in-plane magnetization component Mx points along the +x-direction. Moreover, ϕB=ϕE=0 when both B\parallel and E are aligned in parallel to the +x-direction. For example, ϕE=0 and ϕE=π/2 correspond to I applied from contacts 1 to 7 and 4 to 10, respectively. The azimuthal angle ϕB can be independently controlled by rotating the circular Hall bar sample within a static magnetic field applied within the xy-plane of the sample (also see “Methods” section for measurement details).

We first characterize the conventional Hall response of a Fe3Sn thin film (thickness d1=60nm) at room temperature when the magnetic field B is applied in the out-of-plane direction along the z-direction. The Hall resistivity ρH(B, ϕE=0) is shown in Fig. 2e and corresponds to the magnetic field-antisymmetric contribution to the transverse resistivity tensor ρxy. Specifically, it can be obtained by using the symmetrization operation ρH(B)=(ρxy(B)−ρxy(−B))/2. The magnetic-field symmetric contribution to ρxy that depends on ϕE is discussed in Section IV of the Supplementary Materials. As can be seen, ρH(B)\propto B in small fields and saturates at ρH(B)≈6×10−6Ωcm at B>1T, consistent with the results of magnetization measurements (c.f. Fig. 1c). These observations agree well with previous results31–33. This saturation effect was reported to be associated with the magnetic field-induced reorientation of Fe magnetic moments from the x-axis to the z-axis31. Examining ρxy over a smaller field range for upward and downwards sweeps of Bz reveals the presence of a hysteresis loop, as seen in Fig. 2f. The observation of hysteresis in both the electric Hall and magnetization measurements experimentally indicates an out-of-plane canting of the Fe magnetic moments at zero applied magnetic field. As suggested by our symmetry analysis and model calculation, the presence of this canting should permit the observation of the anomalous IPHE by breaking the MztT symmetry.

Observation of the in-plane Hall effect at room temperature

In the next step, we characterize the Hall response of Fe3Sn at T=300K when the magnetic field is applied within the sample plane. To this end, we record the transverse resistivity ρxy(ϕB, ϕE, B\parallel) as a function of ϕE and ϕB at T=300K and B\parallel=±20mT. Using symmetrization operations ρIPHE(ϕB, ϕE)=(ρxy(ϕB, ϕE, B\parallel)−ρxy(ϕB, ϕE, −B\parallel))/2 and ρsym(ϕB, ϕE)=(ρxy(ϕB, ϕE, B\parallel)+ρxy(ϕB, ϕE, −B\parallel))/2, we obtain the magnetic field-antisymmetric and symmetric contributions to ρxy(ϕB, ϕE, B\parallel), respectively. Representative raw data of ρxy are presented in Section VIII of the Supplementary Materials.

We first consider the antisymmetric part ρIPHE, which is a true Hall effect, because it is odd under magnetic field reversal. In Fig. 3a, we plot the angular dependence of ρIPHE(ϕB) for device D1 recorded at ϕE=0, and ϕE=π. The complete 4π angle dependence of ρIPHE within the (ϕB, ϕE)-plane is shown in Fig. 3b. We detect a characteristic 2π-periodicity of ρIPHE(ϕB, ϕE) with respect to ϕB. Moreover, as clearly seen in Fig. 3a, ρIPHE(ϕB, ϕE) is independent of ϕE. We can accurately describe the ϕB-dependence of ρIPHE using ρIPHE(ϕB)=ρ0+ρ0IPHE cos(ϕB+δ) in a least square fit; the fit parameters are listed in Section VIII of the Supplementary Materials. The phase factor δ accounts for small angular offsets, which possibly arise from small misalignment of ϕB and ϕE with Mx in our measurements and give rise to the curved contour of ρIPHE along the ϕE-axis, as seen in Fig. 3b. Also note that these fits reveal the absence of a sizable vertical offset ρ0, as shown in the inset of Fig. 3a (ρ0/max(ρIPHE)<1%). Hence, our experimental observations indicate that ρIPHE only depends on the relative angle ϕB between the in-plane magnetic field B\parallel and the in-plane magnetization Mx and exhibits a characteristic cos(ϕB) dependence. These findings are in excellent agreement with our theoretical predictions shown in Fig. 1f (also see Sections I–III of the Supplementary Materials) and suggest the experimental detection of anomalous IPHE in our measurements.

Before we discuss this key result of our work in a broader context, we also consider the full 4π angle dependence of the magnetic-field symmetric resistivity ρsym(ϕB, ϕE). To this end, we plot its angular dependence in the (ϕB−ϕE, ϕE)-plane, as shown in Fig. 3c. The circular Hall bar geometry allows us to decompose ρsym(ϕB, ϕE) into two separate contributions, ρSTR(ϕE) and ρPHE(ϕB−ϕE) through their separate dependencies on ϕE and ϕB−ϕE, respectively, as seen in Fig. 3c. Here, ρSTR(ϕE), shown in Fig. 3d, only depends on ϕE and exhibits a π-periodicity with respect to ϕE. These observations indicate the presence of the symmetric transverse resistivity effect in our measurements (see Section IV of Supplementary Materials for a detailed analysis of STR), which describes the projection of the anisotropic magnetoresistance effect into transverse resistivity36. On the other hand, ρPHE exhibits a sinusoidal dependence on (ϕB−ϕE) with π-periodicity. It can be accurately fitted using ρPHE(ϕB−ϕE)=ρPHE0 sin(2ϕB−2ϕE), as seen in Fig. 3e, indicating the underlying AMR origin of PHE. More broadly, the detection and characteristics of the STR and PHE in our measurements are consistent with theoretical expectations for a ferromagnetic metal with an in-plane magnetization component, as discussed above. Finally, the regular periodicity of ρIPHE(ϕB, ϕE) and ρsym(ϕB−ϕE, ϕE) suggests that the effect of magnetic domains, if present, on the in-plane Hall response is negligible.

Discussion

Origin of the in-plane Hall effect

The observation of the anomalous IPHE in spin-canted Fe3Sn in our measurements agrees with our theoretical analyses, which predict a finite in-plane Hall response induced by topological Weyl points in the kagome band structure when the relevant magnetic symmetry (MztT) is broken. Performing measurements as a function of the magnetic field amplitude, we can detect a 2π-periodic IPHE in fields as small as B\parallel=5mT, as shown in Fig. 4a. Moreover, we find that the IPHE amplitude remains nearly field independent at B\parallel<100mT. This observation is consistent with our theoretical proposal, shown in Fig. 1f, that B\parallel only modulates ρIPHE(ϕB) through Zeeman coupling as a function of ϕB, while MztT is already broken by the canting of the magnetic moments rather than by a strong in-plane magnetic field. Indeed, we also detect a finite transverse resistivity at zero magnetic field, such as ρxy≈140nΩcm at ϕB=π where ρIPHE has the maximum amplitude. Note that the quantitative assessment of the IPHE contribution to this value is challenging. An unavoidable, yet small, misalignment of our Hall bar electrodes with the direction of the magnetization Mx results in a finite contribution of the symmetric transverse resistivity to ρxy. Therefore, a symmetrization with respect to the magnetic field at B≠0 is needed to extract the contributions of ρIPHE(ϕB) (antisymmetric in B), as well as ρSTR(ϕE) and ρPHE(ϕB, ϕE) (both symmetric in B) from ρxy.

In the presence of a small misalignment of the sample plane with the direction of B\parallel, the OHE Hall effect can generally contribute to ρIPHE, because both the IPHE and the OHE are odd under magnetic field reversal, as discussed above (also see Table 1 for a detailed comparison). Given an alignment accuracy of our sample plane with respect to the magnetic field axis of equal or better than 2°, an in-plane magnetic field amplitude B\parallel=20mT could cause an out-of-plane component of the magnetic field Bz<0.7mT. However, we can safely exclude measurable contributions of the OHE to the experimentally detected ρIPHE(ϕB) for two key reasons. First, temperature (T)-dependent measurements show that the anomalous in-plane Hall conductivity σIPHE(T) is temperature independent over a wide temperature range from 100K to 300K, as seen in Fig. 4b. This observation is inconsistent with a temperature dependence reported on the Hall coefficient of Fe3Sn within the same temperature range35. Second, the small Hall coefficient of Fe3Sn at 300K, R0≈−1×10−4cm3C−135 would result in a vanishing voltage signal VH<10nV of the OHE in our measurements when Bz<0.7mT; by comparison, the voltage signal of the anomalous IPHE is on the order of microvolts, as seen in Fig. 4d.

Moreover, the out-of-plane magnetization Mz of the canted moments breaks the mirror symmetry Mx and permits a finite out-of-plane Berry curvature Ωz, which is isotropic within the xy-plane. Hence, Mz can give rise to the conventional AHE with resistivity ρAHE that is independent of ϕB and ϕE (also see Table 1 for a detailed overview of the AHE properties). If the out-of-plane component of the magnetic field Bz is smaller than the coercive field of ≈50mT, as seen in Fig. 2f, it cannot switch the out-of-plane magnetization and ρAHE(B)=ρAHE(−B). In our measurements Bz<0.7mT. Therefore, the conventional AHE would thus appear as a ϕB and ϕE-independent contribution to the magnetic field-symmetric part ρsym(ϕB, ϕE). Note that it is difficult to quantitatively determine and separate the contribution of ρAHE to ρsym due to the large amplitude of ρSTR and the scarce point density along the ϕE-axis limited by the number of Hall bar terminals.

Berry curvature contributions to the Hall conductivity are generally independent of the charge carrier scattering time. They can thus be distinguished from other contributions, such as skew scattering and side jumps1,39–41, which depend on the scattering time. Accordingly, Berry curvature contributions to the Hall effect can be identified by analyzing the temperature dependence of the anomalous Hall conductivity. To examine this relation, we characterize the IPHE as a function of the temperature. The resulting anomalous in-plane Hall conductivity σIPHE(T, ϕB=0, ϕE=π), as well as the longitudinal conductivity σxx(T) are shown in Fig. 4b. As can be seen, the amplitude of σIPHE is temperature independent at T≥100K but increases at T<100K. These characteristics contrast with those of σxx(T), which depends on T throughout the examined temperature range. The experimental observation of a temperature-independent contribution |σ0IPHE|≈0.68Scm−1 to the IPHE suggests that the Hall response at T≥100K is dominated by an intrinsic Berry curvature contribution1, consistent with our expectations from symmetry analyses and model calculations. Moreover, the experimentally detected |σ0IPHE|≈0.7Scm−1 is also in relatively good quantitative agreement with the calculated in-plane Hall conductivity |σcalcIPHE|≈1.5Scm−1, as shown in Fig. 1f. At lower temperatures, the scaling σIPHE(T) ∝ σxx, as seen in Fig. 4c, indicates that the Hall conductivity is dominated by skew-scattering contributions1,39,40.

Breaking inversion symmetry at the Fe3Sn/Pt(111) interface could induce a canting of the Fe magnetic moments near the interface via the Dzyaloshinskii-Moriya (DM) interaction42. To test whether the experimentally observed canting in our samples originates from this effect, we examined in the in-plane Hall response of thin films with a smaller thickness (d2=30nm). If the IPHE arises from interfacial symmetry-breaking effects, the corresponding antisymmetric part VIPHE(ϕB) of the Hall voltage Vxy(ϕB) is independent of the film thickness. The VIPHE(ϕB, ϕE=0) of devices D1 (d1=60nm) and D2 (d2=30nm) are shown in Fig. 4d. Applying a sine function fit as before, we find VIPHE(30nm)/VIPHE(60nm)≈2.5, i.e., VIPHE scales approximately with the thickness of the film. Since ρxy∝Vxy/d (d is the thickness of the film), it follows that ρIPHE(ϕB, ϕE) and ρsym(ϕB, ϕE) of devices D1 and D2 are in qualitative and approximate quantitative agreement (ρIPHE(ϕB, ϕE) and ρsym(ϕB, ϕE−ϕB) of device D2 are shown in Section IX of the Supplementary Materials).

Our results suggest that the IPHE is independent of the film thickness, and thus arises from spin canting within the bulk of the film. Since our films are comparably thick (d≤60nm), it is difficult to reconcile the fact that epitaxial strain at the Pt(111)-Fe3Sn interface gives rise to the detected canting effect. Although it remains an interesting question to what extent this canting is generally present in Fe3Sn31,35, it has been reported that the magnetization of the isostructural ferromagnet Fe3Ge undergoes a reorientation from an out-of-plane to an in-plane magnetization via a second-order transition below 380K43,44. It is conceivable that such a transition is present in Fe3Sn, leading to finite out-of-plane canting at finite temperatures. Thus, it would be desirable to conduct more temperature-dependent neutron scattering measurements on bulk crystals to obtain more detailed information on the magnetic structure of Fe3Sn.

Tuning the in-plane Hall effect in a topological heterostructure

The amplitude of a Hall effect induced by Berry curvature generally depends on the magnitude of the underlying mechanism of symmetry breaking1. Tuning the spin-canting in Fe3Sn through external control parameters would thus allow the control of the anomalous IPHE. We will show that the magnetic stray field of ferromagnetic CoFeB layers augments the IPHE amplitude via the coupling to the magnetic moments of Fe. To this end, we realize a topological heterostructure structure comprising of TiO2 (3nm)/CoFeB (20nm)/Al2O3 (20nm)/Fe3Sn (30nm)/Pt(111) (5nm) layers deposited on sapphire(0001), as schematically shown in Fig. 5a (see “Methods” section for fabrication details). The electrically isolating Al2O3 spacer prevents electric shunting of Fe3Sn by the metallic CoFeB. The successful fabrication of the topological heterostructure is confirmed by scanning transmission electron microscopy and energy-dispersive X-ray spectroscopy measurements shown in Fig. 5b–d (see “Methods” section for measurement details). In addition, we performed a detailed characterization of the crystallographic and magnetic properties of the CoFeB films, as shown in Section X of the Supplementary Materials. These measurements indicate that CoFeB exhibits an amorphous crystal structure with a tilted easy-plane magnetic anisotropy. Hence, the CoFeB films of device D2hs are expected to have a magnetic stray field with a component in the z direction.

To maintain direct comparability of the measured IPHE amplitudes, we deposited the (TiO2/CoFeB/Al2O3)-layer structure directly on the circular Hall bar device D2 using a two-step lithography process. We then recorded the electric in-plane Hall response of device D2hs (hs-heterostructure). The resulting ρIPHE(ϕB) of the devices D2hs and D2 at ϕE=0 are shown in Fig. 5e. We find that the amplitude of the IPHE is increased by approximately 38% after the deposition of the CoFeB film whereas the angular characteristics of the IPHE remain unchanged, as can be seen from the full angle dependence of ρIPHE and ρsym shown in Section X.D of the Supplementary Materials. On the other hand, the symmetric part ρsym(ϕB−ϕE, ϕE) of the Hall resistivity of device D2hs and D2 are in qualitative and quantitative agreement. At a basic level and disregarding effects from the microscopic magnetic structure of CoFeB, these observations suggest that the CoFeB layer leaves the in-plane magnetic structure of Fe3Sn invariant, but enhances the out-of-plane canting effect through the coupling of the magnetic moments of Fe to its magnetic stray field. Note that such enhanced canting could increase the amplitude of the conventional AHE. However, we do not detect a measurable ϕB- and ϕE-independent background of ρsym(ϕB−ϕE, ϕE). We anticipate that further optimization of the heterostructure layers and the use of other kagome materials11,45 could enhance the IPHE amplitude even further beyond what was detected in this proof-of-concept experiment.

To conclude, we report the experimental observation of the anomalous IPHE in epitaxially grown thin films of the Weyl ferromagnet Fe3Sn at room temperature. The combination of the kagome lattice motif with spin-orbit coupling and ferromagnetism imparts a topological electronic structure32 and canting of the magnetic moments of Fe breaks the relevant crystalline symmetry for the anomalous IPHE to appear. Meanwhile, strong ferromagnetic exchange interactions J≈40meV between the transition metal atoms arranged on the kagome lattice23 enable the room temperature observation of this phenomenon. The temperature-independent anomalous in-plane Hall conductivity detected over a wide temperature range (100–300K) provides strong evidence for the topological origin of the anomalous IPHE, consistent with the presence of topological Weyl points near the Fermi energy. Our work also presents a technical advance. We demonstrate that the combination of circular Hall bar structures with magnetic field-angle-dependent measurements and suitable symmetrization operations can be used to distinguish different contributions to the transverse voltage, such as IPHE, AHE, OHE, and anisotropy effects (PHE and STR). More broadly, establishing the thin-film heteroepitaxy of topological kagome magnets and heterostructures, our work establishes a design paradigm to examine new electric Hall effects2–5,9,10 that result from crystalline symmetry breaking toward their use in technological applications, such as magnetic sensing, spintronics, and energy harvesting.

Methods
Molecular beam epitaxy of Fe3Sn films

Epitaxial Fe3Sn films were grown on top of a 5nm thick Pt(111) buffer layer on [0001]-oriented 5mm×5mm×0.5mm sized sapphire substrates (from CrysTec GmbH) using a home-build molecular beam epitaxy (MBE) system (effusion cells from MBE Komponenten GmbH). The as-received sapphire substrates were chemically cleaned using sonication in acetone and isopropyl alcohol (IPA) for 5min each. Atomically flat surfaces with single-step height terraces were obtained by thermal annealing in air at 1300K for 1h using a tube furnace. Prior to the thin-film deposition, the substrates were degassed inside the MBE chamber at 900K at a base pressure p≤5×10−10mbar. Adopting the recipe of Cheng et al.46, high purity Pt(99.999%) was evaporated using an electron beam evaporator (EFM4 from Focus GmbH) at an approximate rate of 0.2Å/min to obtain a 5nm thick Pt layer oriented along the [111]-direction. The initial 6Å of Pt were deposited at a substrate temperature of 740K. The remaining 4.4Å were deposited while the substrate temperature was reduced from 440K to 380K, followed by annealing at 600K for 10min. Onward, high-purity Fe(99.999%) and Sn(99.999%) were co-evaporated using effusion cells at an approximate growth rate of 1.2Å/min to obtain Fe3Sn films. The structural and chemical characterization of the fabricated thin films is described in Section V of the Supplementary Materials.

Device fabrication and deposition of a topological heterostructure

The as-grown Fe3Sn thin films were shaped into 12-terminal circular Hall bar devices using Ar+ ion milling and optical UV lithography. The electrical contacts to the Hall bars were fabricated by evaporating 5nm/100nm titanium/gold electrodes. The heterostructure device D2hs was prepared directly on top of the Fe3Sn circular hall bars of device D2 using a UV lithography mask. An e-beam evaporator (Innovative Vacuum System) was used to deposit 20nm of amorphous Al2O3. In the next step, a 20nm thick amorphous CoFeB layer was deposited using DC magnetron-sputtering (AJA International Ltd.) at a base pressure of 1×10−8torr with a 3mtorr partial pressure of argon and a d.c. power of 60W. Following CoFeB deposition, a 3nm thick titanium (Ti) capping layer was sputter-deposited to protect the heterostructure from oxidation, where the Ti layer naturally oxidizes into TiO2 via exposure to an ambient atmosphere. The material characterization of the CoFeB films is described in Section IX of the Supplementary Materials.

Electric transport measurements

All electric transport measurements were carried out in a Quantum Design PPMS6000 system using a four-probe contact geometry. The circular Hall bar devices were wire bound to the chip holder using 25μm thick aluminum wire. An a.c. bias current of I=I0 sin(ωt) with a peak amplitude of I0=1.1mA at a frequency of f=ω/2π=19.375Hz was applied by using an a.c. current source (6221A, Keithley). Two lock-in amplifiers (SRS 830, Stanford Research Systems), which are phase-matched to the bias current output, were used to record the longitudinal Vxx and transverse Vxy voltages as a function of the azimuthal angles ϕE and ϕB. As illustrated in Fig. 2d, ϕE and ϕB are defined as the angles between the direction of the electric field E and the x-axis and the direction of the in-plane magnetic field B\parallel and the x-axis, respectively. Within this definition, ϕE can be varied by applying the bias current along different contact pairs of the circular Hall bar, and ϕB can be independently tuned from ϕB=0° to ϕB=350° by rotating the sample within an externally applied uniaxial field using a commercial rotator probe by Quantum Design. The travel limitation of the rotator probe to ϕB≤350° prevents a complete 2π rotation of ϕB and causes the missing data points seen in Fig. 3. The longitudinal and transverse resistivities were obtained by using the relations ρxx=(d1,2 L/L) (Vxx/Ix) and ρxy=(d1,2 L/L) (Vxy/Ix) with the device dimension, L=L=200μm and thicknesses d1=60nm and d2=30nm, respectively.

Magnetization measurements

Measurements of sample magnetization were performed using a vibrating sample magnetometer (MPMS3 from Quantum Design, resolution <10−8emu). The samples were attached to standard quartz or brass holders using GE varnish. All measurements were performed at a temperature of 300K. The magnetic moment per Fe atom was calculated considering the film thickness, as determined from X-ray reflection measurements, and the effective sample area A0. A0 is smaller by 4mm2 than the actual surface area A=5×5mm2 of the sapphire substrate due to the four corner clamps used to mount the substrate to the sample holder of the molecular beam epitaxy system. A linear diamagnetic background, as seen in the inset of Fig. 2c, caused by the sapphire substrate, was subtracted from the magnetization data. Note that this diamagnetic contribution (magnetic moment m≈1.5×10−4emu at B=1T) dominates over the paramagnetic contribution of the Pt(111) buffer layer, which is estimated to be on the order of 10−8emu at B=1T.

Scanning transmission electron microscopy measurements

Lamellas suitable for carrying out scanning transmission electron microscopy (STEM) measurements were prepared using a focused ion beam system (FEI Helios G4 UX). To protect the heterostructure from potential damage caused by the Ga+ ion beam, an amorphous platinum (Pt) layer was deposited on the surface of the sample. Following the ion milling process, the as-prepared lamella was transferred to a copper grid. Cross-sectional STEM measurements were performed using a commercial JEOL JEM-ARM200F system. Using an acceleration voltage of 60kV and a probe corrector, an image resolution below 0.1nm was achieved. Energy-dispersive X-ray spectroscopy measurements were performed to map out the elemental distribution in an area measuring 100μm×100μm.

Density functional theory calculations

Density functional theory (DFT) calculations of the electronic structure of Fe3Sn were performed using the density functional theory framework as implemented in the Vienna ab initio simulation package47,48. The projector-augmented wave potential was adopted with the plane-wave energy cutoff set to 600eV (convergence criteria 10−6eV). The exchange-correlation functional of the Perdew-Burke-Ernzerhof type was used49 with a 11×11×13 gamma-centered Monkhorst-Pack mesh. We constructed the Hamiltonian of a Wannier tight-binding model using the WANNIER90 interface50, including the Fe d- and Sn p-orbitals. We then calculated the anomalous Hall conductivity from this Wannier model using a 131×131×141 k-mesh and the WannierBerri code51. The surface states are calculated with the surface Green’s function for the semi-infinite system52.

Anomalous in-plane Hall effect calculated using the Wannier tight-binding model

To analyze the characteristics of in-plane Hall effect (IPHE) under an in-plane magnetic field B\parallel, we computed the anomalous in-plane Hall conductivity σIPHE using the Wannier tight-binding model projected by DFT calculations. The effective Hamiltonian is given by:

H=H0+gB\parallel\cdotσ, (1)

where H0 refers to the Wannier Hamiltonian of Fe3Sn with or without canting, the second term denotes the Zeeman coupling with B\parallel=B(cosϕB, sinϕB, 0), with ϕB as the angle between the in-plane magnetization of Fe3Sn and B\parallel, g as the effective coupling factor, and σ as the Pauli matrices for spin. We calculate σxy≡σIPHE using the effective model through the Kubo formula1,53:

σxy=e2/ℏ \sum_n \int_BZ d3k/(2π)3 f(k) Ωn,xy(k), (2)

Ωn,xy(k)=2iℏ2 \sum_{m≠n} (\langleψnk|v^x|ψmk\rangle \langleψmk|v^y|ψnk\rangle − \langleψnk|v^y|ψmk\rangle \langleψmk|v^x|ψnk\rangle) / (Enk−Emk)2, (3)

where f(k) denotes the Fermi-Dirac distribution, ψnk and Enk refer to the Bloch wave functions and eigenvalues of band n, respectively, and v^ is the velocity operator. The calculated σIPHE using gB\parallel=0.001eV is shown in Fig. 1f. As expected from our symmetry analysis, σIPHE vanishes without canting, while it exhibits a finite amplitude with 2π periodicity with respect to ϕB when canting is included. Specifically, in the absence of canting, the magnetic space group symmetry MztT is preserved under an in-plane magnetic field, resulting in opposite values of Ωn,xy(k) at symmetry-related reciprocal points: Ωn,xy(k)=−Ωn,xy(MztT k). Thus, σIPHE vanishes without canting, as it involves integrating Ωxy over the reciprocal space for all symmetry-determined relations of the Berry curvature (see Section I of Supplementary Materials). Meanwhile, when canting is present, MztT is broken, allowing for a non-zero σIPHE based on symmetry considerations.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Sankar et al. report a room-temperature anomalous in-plane Hall effect (IPHE) in the Kagome magnet Fe₃Sn, grown using the molecular beam epitaxy method. Through measurements with varying magnetic fields and current orientations, the authors successfully separate the IPHE from other effects—such as the planar Hall effect (PHE), symmetric transverse resistivity (STR), and anomalous Hall effect (AHE). Their findings are consistent with calculations based on canted ferromagnetism and topological Weyl points.\n\nThe IPHE is distinct from the planar Hall effect observed in topological materials, and its presence in Fe₃Sn thin films at room temperature will be of broad interest. The data and theoretical analysis are of high quality. I recommend the manuscript for publication after addressing the following technical and presentation issues to enhance overall readability:\n1. On Page 1, the authors state, \"To date, the observation of novel anomalous Hall effects remains often limited to cryogenic temperatures. This motivates the search for a new class of topological materials and heterostructures, which can be manufactured using scalable synthesis methods, to discover and control Hall effects at room temperatures.\" This claim may be an overstatement. The anomalous Hall effect has recently been observed in several Mn/Fe-based materials near or at room temperature in both bulk and thin-film forms, such as Mn3Sn/Ge, YbMnBi2, RMn6Sn6, Fe3GeTe2, Fe3Sn2, and FeS. The authors should revise this statement to acknowledge these recent discoveries.\n2. In Figure 1(d) and (e), the caption states that (d) corresponds to the calculation with canting and (e) without canting. However, the Berry curvature appears to be zero in (d) and nonzero in (e), which contradicts the claim in the text. The authors should clarify their claim or improve their figures.\n3. In the IPHE fitting, the authors assume that the anomalous Hall effect contribution is independent of the angle (θ). They should clarify why this must be the case, particularly considering the possibility of misalignment. Based on the amplitude shown in Fig. 2(f) and Fig. 3(a), even slight misalignment could induce an anomalous Hall effect comparable to the IPHE (an out-of-plane component of B ~ 3 mT).\n4. In Fig. 3 and Fig. 4, the IPHE appears small compared to the raw signal. It would be beneficial to include figures displaying the raw signal alongside the separated signals (IPHE, AHE, and STR) to illustrate the robustness of the IPHE better.\n5. The IPHE is significantly stronger (by three orders of magnitude) in Fig. 4(a) compared to Fig. 3(a). Additionally, the unit in the inset of Fig. 4(a) is incorrect (should be cm not cm^-1).\n6. The magnetic field values span a large range in Fig. 4(a), making it difficult to track the values corresponding to each curve. The authors should consider adding field values next to each curve or incorporating a color bar to improve readability.\n7. In addition to the coupling to the Fe moment, the stray field from CoFeB might enhance the AHE. The authors should discuss this possibility in the context of the IPHE.\n8. On Page 9, the authors state, \"we find VIPHE(60nm)/VIPHE(30nm) ≈ 2.5.\" This seems a typo, as a thicker film should yield a smaller voltage. Furthermore, this contradicts Fig. S7.", "reviewer_2": "My full report is given by the word file attached.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_4": "The authors present essential results, where they report observation of the anomalous in-plane Hall effect in the thin films of a Weil ferromagnet at room temperature. The reported findings (in the case of their correctness) are exciting and may draw further attention. Nevertheless, I do not believe this article is suitable for publication in its current form in Nature Communications. The discussions are weak and lack clear explanations. The theoretical support is very limited. Therefore, I do not recommend this article in its current form for publication."}, "author_response": "We thank the reviewer for the positive evaluation of our work. The reviewer’s constructive comments on our manuscript have provided us with an opportunity to further broaden the discussion and improve the presentation of our data. Point-by-point responses are presented below, and changes to the manuscript are highlighted in red text color. We hope that the reviewer will recommend the revised manuscript for publication in Nature Communication.\n1. On page 1, the authors state, \"To date, the observation of novel anomalous Hall effects remains often limited to cryogenic temperatures. This motivates the search for a new class of topological materials and heterostructures, which can be manufactured using scalable synthesis methods, to discover and control Hall effects at room temperatures.\" This claim may be an overstatement. The anomalous Hall effect has recently been observed in several Mn/Fe-based materials near or at room temperature in both bulk and thin-film forms, such as Mn3Sn/Ge, YbMnBi2, RMn6Sn6, Fe3GeTe2, Fe3Sn2, and FeS. The authors should revise this statement to acknowledge these recent discoveries.\nResponse and changes made: We thank the referee for pointing out previous work on room temperature anomalous Hall effects. We have included additional relevant publications as refs. 13-16 and revised the introductory paragraph accordingly.\n2. In Figure 1(d) and (e), the caption states that (d) corresponds to the calculation with canting and (e) without canting. However, the Berry curvature appears to be zero in (d) and nonzero in (e), which contradicts the claim in the text. The authors should clarify their claim or improve their figures.\nResponse: We thank the referee for pointing out this mistake which must have occurred in the final steps of rearranging the figures. Indeed, the panel assignment in the figure caption is incorrect.\nChanges made: We have revised the caption of Fig.1 accordingly.\n3. In the IPHE fitting, the authors assume that the anomalous Hall effect contribution is independent of the angle (θ). They should clarify why this must be the case, particularly considering the possibility of misalignment. Based on the amplitude shown in Fig. 2(f) and Fig. 3(a), even slight misalignment could induce an anomalous Hall effect comparable to the IPHE (an out-of-plane component of B ~ 3 mT).\nResponse: We thank the referee for raising the important question of how to distinguish different contributions to the magnetic-field asymmetric part of the Hall resistivity, such as the ordinary Hall effect (OHE) induced by an out-of-plane magnetic field, the conventional anomalous Hall effect (AHE) induced by an out-of-plane magnetization, and the anomalous in-plane Hall effect (IPHE) induced by Berry curvature. The circular Hall bar structure used in our experiment enables us to exclude the OHE and AHE as the origin of the observed Hall effect, when the magnetic field is applied within the sample plane, as follows.\nFirst, we recall that the in-plane Hall measurements presented in Fig.3 are carried out with a magnetic field of amplitude B = 20 mT applied within the sample plane. The alignment accuracy of our sample plane with respect to the magnetic field is equal or better than 2°. The presence of a 2° misalignment would thus cause an out-of-plane component of the magnetic field of less than 0.7 mT. The presence of such out-of-plane component is unable to switch the out-of-plane component of the magnetization, since the coercive field is on the order of 50 mT, as shown in Fig.2(f).\nOrdinary Hall effect: The presence of an out-of-plane component of the externally applied magnetic field can cause an OHE with Hall resistivity ρ_OHE. Moreover, under an in-plane rotation of the sample, this misalignment would result in a sinusoidal dependence ρ_OHE(θ) ∝ sin(θ) with respect to the angle θ. The angle θ is defined as the angle between the electric field E, which is parallel to the direction of the applied bias current within the sample plane, and the in-plane magnetic field B_||. However, ρ_OHE(θ) does not depend on the angle between E and the in-plane component of the magnetization M_||. In other words, ρ_OHE(θ) is independent of the angle φ. Even though ρ_OHE(θ) exhibits the same sinusoidal θ-dependence as ρ_IPHE(θ,φ), it cannot account for the experimentally detected φ-dependence of ρ_IPHE(θ,φ) as seen in Fig.3, (a) and (b).\nAnomalous Hall effect: The presence of an out-of-plane spin canting in Fe3Sn breaks the mirror-x symmetry M_x of Fe3Sn. Breaking of M_x permits a finite out-of-plane component of the Berry curvature Ω_z that can give rise to an anomalous contribution ρ_AHE to the Hall effect within the xy-plane. This contribution is isotropic within the xy-plane and it follows that ρ_AHE is independent of θ and φ. Moreover, in the presence of a small angular misalignment ≤2°, the application of an in-plane magnetic field of ±20 mT does not affect the direction of the out-of-plane spin canting. Therefore, ρ_AHE(B) = ρ_AHE(-B) and the AHE would appear as a θ and φ -independent contribution in the magnetic field-symmetric part ρ_sym(θ,φ) if the out-of-plane component of the magnetic field is smaller than the coercive field of ~50 mT. This understanding is consistent with the absence of a sizable θ-independent offset to ρ_IPHE(θ,φ), as seen in Fig.3a, which is antisymmetric with respect to B.\nTherefore, the OHE and AHE cannot account for the experimentally detected θ and φ dependence of ρ_IPHE(θ,φ). Instead, by combining symmetry analyses and electronic structure calculations, we can explain all salient features of ρ_IPHE(θ,φ) in terms of a Berry curvature induced anomalous in-plane Hall effect induced.\nChanges made: We have included an extended discussion on how to exclude the OHE and AHE as the origin of the observed ρ_IPHE(θ,φ) based on the respective angle dependencies of the OHE and AHE in the first three paragraphs of the section ‘Origin of the in-plane Hall effect’ of the revised manuscript.\n4. In Fig. 3 and Fig. 4, the IPHE appears small compared to the raw signal. It would be beneficial to include figures displaying the raw signal alongside the separated signals (IPHE, AHE, and STR) to illustrate the robustness of the IPHE better.\nResponse and changes made: We thank the referee for this valuable suggestion. To illustrate the robustness of our analysis, we now also present representative data of the θ-dependence of the measured ρ_xy(θ) at φ = 0 for B = ±20 mT before the field symmetrization in Sec.V.A of the revised Supplementary Materials and included a corresponding comment in the main text.\n5. The IPHE is significantly stronger (by three orders of magnitude) in Fig. 4(a) compared to Fig. 3(a). Additionally, the unit in the inset of Fig. 4(a) is incorrect (should be cm not cm^-1).\nResponse and changes made: We sincerely apologize for the typos in Fig.4(a). The referee is of course correct that the unit in Fig.4(a) should be nΩ not µΩ and that the unit of the inset is wrong. We have revised the units of Fig.4(a) and the inset accordingly.\n6. The magnetic field values span a large range in Fig. 4(a), making it difficult to track the values corresponding to each curve. The authors should consider adding field values next to each curve or incorporating a color bar to improve readability.\nResponse and changes made: We thank the referee for this valuable suggestion to improve the presentation of our data. In response to the referee’s comment, we have added a color bar to Fig.4(a).\n7. In addition to the coupling to the Fe moment, the stray field from CoFeB might enhance the AHE. The authors should discuss this possibility in the context of the IPHE.\nResponse: We appreciate this insightful comment by the referee. Indeed, the enhancement of the out-of-plane spin canting in Fe3Sn by the stray field of CoFeB can enhance the out-of-plane Berry curvature Ω_z resulting in an enhanced AHE contribution ρ_AHE to the Hall resistivity ρ_xy. However, as we argue in response to comment 3, ρ_AHE is independent of the angles φ and θ and would appear in the magnetic-field symmetric part ρ_sym of the transverse resistivity ρ_xy. Therefore, the AHE cannot account for the observed amplitude enhancement of the anomalous IPHE (as shown in Fig.5e).\nChanges made: We discuss the role of the AHE for the detected amplitude enhancement of the IPHE in the topological heterostructure in the second paragraph of page 11 of the revised manuscript.\n8. On Page 9, the authors state, \"we find VIPHE(60nm)/VIPHE(30nm) ≈ 2.5.\" This seems a typo, as a thicker film should yield a smaller voltage. Furthermore, this contradicts Fig. S7.\nResponse and changes made: We thank the referee for the careful review of our manuscript. We apologize for this typo, which we missed in the final proof-reading stage. Indeed, the correct statement is V_IPHE(30nm)/V_IPHE(60nm) ≈2.5, and we have revised the manuscript accordingly."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The manuscript is much improved, especially the discussion of OHE, AHE and IPHE. However, they must discuss their results in the context of all the other AHE recent reports mentioned in the review (Mn3Sn/Ge, YbMnBi2, RMn6Sn6 and the other Fe compounds). Juts adding the references is not enough. The bigger point here is the question about the novelty of the present results, in which case the authors need to make a convincing case that the current study is suitable for Nature Communications by distinguishing it from all these other reports.\nDepending on the outcome of such a discussion, I may recommend the publication of the manuscript, but not in the current form.", "reviewer_2": "my report is given in the word file.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_5": "In this article the authors demonstrate an in-plane anomalous Hall effect in Fe$_3$Sn, which can even be detected at room temperature and that is induced by the electronic topology. Other ingredients accompanying the effect of topology are the spin canting and the spin orbit interaction. Besides, this signal can be tunable by the magnetic stray field of CoFeB. The paper has good quality and the experimental results are interesting, but I am not satisfied with the theoretical explanation of the effect. Because of this reason, I do not recommend this article to be published in Nature in its present form. Nevertheless, and to help them with the quality of the work, there are a few important points that the authors need to solve before trying to submit again or looking for another journal:\n1. In page 7, you claim that the planar Hall effect is $\\phi$ invariant. If you are trying to say that it does not depend on the electric field angle, then I strongly disagree. The planar Hall effect is typically connected to the Fermi surface contribution to the transverse conductivity, and I would expect an angular dependence similar to $\\sin(2\\phi_E-2\\phi_B)$. Here, $\\phi_E$ and $\\phi_B$ are the electric and magnetic field angles, respectively. Could you further give more arguments about this to confirm your statement?\n2. In page 8, which evidences do you have to attribute the in-plane Hall effect to the Weyl points? In my view, I can simply rule out the Berry curvature as a possible explanation of this effect, because the related conductivity is independent of the electric field angle. Instead, you claim that the in-plane Hall effect can be fit to $\\sin(\\phi_E+\\phi_B)$. I also do not see that this origin should change upon increasing temperature. In the same spirit, are you sure that the Weyl points survive in the high temperature limit?\n3. In the same spirit as the previous question, I do not believe that the DFT is wrong, but rather cannot capture the effect measured by the authors in the experiment. Could you show the angular dependence of the conductivity, when computed with the Berry curvature formula, in terms of the electric field angle, please? I would expect a constant as a function of $\\phi_E$, and thus not consistent with Fig.3(a).\n4. Could the authors check the behavior of the in-plane Hall effect when reversing $\\mathrm{M}_z$ to $-\\mathrm{M}_z$, please? It would be also instrumental to reverse all the magnetic components together, so you can better explain whether the unconventional conductivity arises on the Berry curvature at high temperature or not."}, "author_response": "We thank the referees for their careful review of our work. We appreciate the overall positive assessment of our revised manuscript by the referees who find our manuscript interesting and acknowledge the high quality of our work. At the same time, the referees raise several concerns that they would like to have addressed before they can recommend publication in Nature Communications.\n\nPreamble\nBefore presenting point-by-point responses to the comments by each referee, we would like to address two consolidated comments in an answer to all referees. We are convinced that our answers to these two comments and pertinent revisions are of general relevance and significantly improve the quality and clarify of our manuscript.\n\nChanges to the manuscript are highlighted in red text color.\n\nComment 1: The comments of referees two and five illustrate that we must present an even more detailed discussion of the different types of Hall effects and their properties, namely the symmetric transverse resistivity (STR), the planar Hall effect (PHE), the anomalous Hall effect (AHE), the ordinary Hall effect (OHE) and the anomalous in-plane Hall effect (IPHE), that can occur in the combined presence of an in-plane magnetic field B_|| and in-plane ferromagnetism with out-of-plane canting M = (M_x, 0, M_z).\n\nResponse: Therefore, we now present a detailed discussion on their general properties, origins, magnetic field dependence, and angle dependence in an in-plane measurement geometry. To this end, we have added a new section ‘Classification of Hall effects’, which introduces and discusses the properties of these different types of Hall effects, to the revised manuscript. We here list the key definitions and properties of these different types of Hall effects that we have also summarized in new Table 1 in the main manuscript. This table is reproduced as Table R1 below.\n\n1. Anomalous in-plane Hall effect (IPHE): The anomalous IPHE arises from finite Berry curvature in the electronic structure. In the presence of canted in-plane ferromagnetism M = (M_x, 0, M_z), the IPHE is modulated by B_|| through the Zeeman coupling between the magnetic field and the conduction electrons. As predicted by our model calculations shown in Fig.1(f) of our manuscript, the IPHE conductivity only depends on the azimuthal (in-plane) angle φ_B between the direction of B_|| and the in-plane component of magnetization M_x via a sinusoidal relation σ_IPHE ∝ cos(φ_B); see Fig.R1 for an illustration of the angle definition. The cosine dependence on φ_B arises because the preserved M_y tT symmetry (M_y, t, and T correspond to the mirror-y, fractional translation, and time-reversal symmetry, respectively) requires σ_IPHE to be an even function of φ_B. A detailed symmetry analysis of σ_IPHE is provided in the new Sec. II of the revised Suppl. Materials. Moreover, the IPHE is defined by an antisymmetric conductivity tensor and is thus odd under magnetic field reversal B_|| → -B_|| with φ_B → φ_B +π.\n\n2. Symmetric transverse resistivity (STR): The STR is an anisotropy effect that originates from the breaking of the C_2-rotation symmetry by the in-plane magnetization M_x. In the presence of C_2, it enforces an isotropic conductivity in xy -plane. Therefore, STR only depends on the azimuthal angle φ_E between the longitudinal electric field E and M_x, as defined in Fig.R1 and Fig.2(d) of the revised manuscript, and exhibits the dependence σ_STR ∝ sin(2φ_E) that is π-periodic in φ_E. Note that the longitudinal electric field E lies in the xy-plane of the sample and is always parallel to the longitudinal current direction. The occurrence of the STR only requires a finite in-plane magnetization. Therefore, the associated conductivity is independent of B_|| and is naturally symmetric under magnetic field reversal B_|| → -B_||. A detailed derivation of the STR effect is shown in Sec.III of the revised Suppl. Materials.\n\n3. Planar Hall effect (PHE): The PHE is very similar to the STR. However, the PHE arises from the anisotropic magnetoresistance due to an in-plane magnetic field instead of an in-plane magnetization. Therefore, its conductivity is σ_PHE ∝ sin(2φ_E - 2φ_B) and exhibits a sinusoidal dependence on the relative angle between φ_B and φ_E with π-periodicity. The angle φ_B (φ_E) is defined as the azimuthal angle between B_|| (E) and the x-axis. Hence, the observation of the PHE requires both an in-plane magnetic field (B_||) and a deviation between the current and magnetic field direction (φ_E ≠ φ_B). Critically, PHE displays a symmetric conductivity tensor, and hence it is more suitable to describe it as an anisotropic magnetoresistance effect rather than a true Hall effect. Note that the existence of PHE does not depend on the presence nor direction of an in-plane magnetization.\n\n4. Anomalous Hall effect (AHE): The AHE results from a finite out-of-plane magnetization M_z and is anisotropic within the xy-plane. Critically, the AHE conductivity is independent of φ_E owing to the antisymmetric nature of the AHE tensor. Moreover, M_z keeps invariant under rotating in-plane magnetic field, thus, the AHE is independent of φ_B and φ_E. Note that the conductivity tensor of AHE is odd under magnetization reversal, σ_AHE(M_z) = -σ_AHE(-M_z).\n\n5. Ordinary Hall effect (OHE): A slight misalignment of the sample xy-plane with the direction of B_|| results in a finite out-of-plane component B_z of the magnetic field, which can give rise to the OHE. The OHE arises from the B_z-induced Lorentz force acting on the moving charge carriers, and its conductivity tensor is odd under magnetic field reversal. Two possible misalignment scenarios exist, as illustrated in Fig.R2: If B_|| is not aligned with the sample plane, the associated Hall conductivity σ_OHE is independent of both φ_B and φ_E. If, in addition, the surface normal of the sample xy-plane is misaligned with the rotation axis of B_||, our geometric analysis shows that the associated Hall conductivity can exhibit a sinusoidal dependence as σ_OHE ∝ sin(φ_B). Here, the misalignment between sample normal and rotation axis of B_|| periodically modulates the relative orientation between B_z and the surface normal under an in-plane rotation of B_|| with 2π periodicity.\n\nIn summary, these distinct properties of the different Hall effects allow us to separate their contributions to the measured transverse voltage V_xy based on their specific angle dependence in an in-plane measurement geometry and their symmetry with respect to magnetic field reversal B_|| → -B_|| with φ_B → φ_B +π. Following this spirit, our combined experimental and theoretical study in this work establishes that the combination of a circular Hall bar geometry, rotations of an in-plane magnetic field B_||, and suitable symmetrization operations facilitates the unambiguous identification and separation of these different contributions in measurements of the electric Hall effect. We are confident that this systematic methodology will be adopted by future studies of electric Hall effects in in-plane measurement geometries.\n\nChanges made: We have included a new section ‘Classification of Hall effects’ to the revised manuscript and summarized the properties of different Hall effects in new Table 1.\n\nComment 2: The combined comments of referee five show us that the angle definitions of the angles between the in-plane magnetic field, the longitudinal electric field, and the sample magnetization used in our previous manuscript version are not ideally suited to display the unique angle dependence of the anomalous IPHE and could cause confusion for the reader.\n\nResponse: In our previous manuscript version, we chose to display the magnetic field antisymmetric ρ_IPHE and magnetic field symmetric ρ_sym contributions to the transverse resistivity ρ_xy as a function of φ and θ = φ_E - φ_B, as seen in Fig.3, (a) and (c); φ effectively corresponds to φ_B but was referenced to the y-axis of our sample. We intended to follow previous convention used in the study of planar Hall responses where the PHE is commonly displayed as function of θ owing to its dependence on φ_E - φ_B, as introduced above. However, we acknowledge that this choice is not best suited to display the angle dependence of the anomalous IPHE. Specifically, as described in the above classification of Hall effects, the anomalous IPHE only depends on φ_B and is independent of φ_E. Accordingly, to improve the data presentation and enhance the clarity of our manuscript, we decided to drop the use of φ and θ and instead display and analyze all Hall effect data as a function of φ_B and φ_E, as illustrated in Fig.R1. Specifically, in our revised manuscript, φ_B and φ_E are defined as the angles between the direction of B_|| and the in-plane component of magnetization M_x and as the angle between the direction of the longitudinal electric field E and the in-plane component of magnetization M_x, respectively. We also define our Cartesian coordinate system such that M_x is oriented along the +x-direction, and φ_B = 0 and φ_E = 0 when B_|| and E are aligned parallel to the +x-direction, respectively.\n\nFollowing this definition, we have taken great care to revise all angle definitions and values in the main text and supplementary information as well as the figures, tables, and captions thereof. We reproduce Fig.3, (b) and (c) using the old and the updated angle definition in Fig.R3 to illustrate the changes to the data representation.\n\nThe choice of φ_B and φ_E provides us with the most suitable framework to analyze the measured transverse resistivity ρ_xy in the context of the angle dependencies of the different Hall effects, as described in the classification of Hall effects described above. As shown in Fig.3, (a) and (b) of the revised manuscript, we now display analyze the anomalous in-plane Hall resistivity ρ_IPHE as a function of φ_B and φ_E. The magnetic field-symmetric part ρ_sym is displayed and analyzed as a function of φ_E - φ_B and φ_E, as shown in Fig.3, (c)-(e). Using this updated angle definition, the ρ_IPHE ∝ cos(φ_B) dependence of the anomalous IPHE, the ρ_STR ∝ sin(2φ_E) dependence of the STR, and the ρ_PHE ∝ sin(2φ_E - 2φ_B) dependence of the PHE are clearly visible in the new Fig.3 and in excellent agreement with theoretical expectations, as described in the preamble of this response letter. Hence, we are convinced that the use of this updated angle definition, as suggested by referee 5, significantly improves the clarity and quality of our manuscript.\n\nChanges made: We have adopted the angle definitions for φ_B and φ_E suggested by referee 5 for the presentation and analysis of our experimental data throughout the revised manuscript. The updated angle definitions are illustrated in Fig.2(d) of the revised manuscript and reproduced in Fig.R1 of this response letter.\n\nReferee 1\nThe manuscript is much improved, especially the discussion of OHE, AHE and IPHE. However, they must discuss their results in the context of all the other AHE recent reports mentioned in the review (Mn3Sn/Ge, YbMnBi2, RMn6Sn6 and the other Fe compounds). Just adding references is not enough. The bigger point here is the question about the novelty of the present results, in which case the authors need to make a convincing case that the current study is suitable for Nature Communications by distinguishing it from all these other reports.\nDepending on the outcome of such a discussion, I may recommend the publication of the manuscript, but not in its current form.\n\nResponse: We thank the referee for providing us with another opportunity to clarify the novelty of our work over previous studies on the anomalous Hall effect (AHE). We agree with the referee that the Berry curvature induced conventional AHE has been observed at room temperature in various material realization. The observation of this conventional AHE requires breaking of time-reversal symmetry (T) which, for example, can be realized through ferromagnetism. The additional breaking of crystalline symmetries, such as inversion and rotation symmetries, can further give rise to new types of Hall effects. They can be qualitatively distinguished from the conventional AHE by symmetry arguments and their unique experimental characteristics are attracting an increasing amount of interest. For example, breaking of inversion symmetry permits the observation of the second order nonlinear anomalous Hall effect (Ref.9) with potential applications in high-frequency electronics and energy harvesting, as reported in Nature by Ma and co-authors (Ref.2). It has also been predicted that breaking of out-of-plane rotation symmetries can give rise to an anomalous in-plane Hall effect (IPHE) (refs. 17, 18), whose spatial anisotropic Hall response could, for example, facilitate sensitive magnetic field sensors. Because such rotation symmetries are present in most crystalline materials, the observation of the anomalous IPHE has proven challenging. To date, recently published reports of the IPHE still require the presence of an externally applied magnetic field to break these crystalline symmetries and are constrained to cryogenic conditions (refs. 19-21) or exhibit a temperature-dependent anomalous Hall conductivity, which is inconsistent with an intrinsic Berry curvature origin (Ref. 22).\n\nThe key novelty of our work is the prediction and experimental observation of the anomalous IPHE in the kagome ferromagnet Fe3Sn. Spin-canting of the magnetic moments of iron breaks the relevant M_y tT symmetry, where M_y, t, and T correspond to the mirror-z, fractional translation, and time-reversal symmetry, respectively and enable the observation of the IPHE on symmetry grounds. Topological Weyl points in the electronic band structure provide the non-zero Berry curvature distribution, which can be further modulated by an in-plane magnetic field. Hence, the resulting anomalous IPHE is temperature independent if the long-range ferromagnetic order persists. Moreover, strong magnetic exchange terms between the Fe ions on the kagome lattice permit high Curie temperature and hence the observation of this effect at room temperature.\n\nIn addition, to our knowledge, our work also presents technical novelty. Various mechanisms, such as the ordinary Hall effect, Berry curvature induced Hall effects, anisotropic effects, and the planar Hall effect can contribute to the transverse resistivity, as we describe above and in the new section ‘Classification of Hall effects’. Hence, it can be challenging to separate these different contributions from each other, preventing reliable analysis of experimental data. We establish that the combination of a circular Hall bar device with rotations of the in-plane magnetic field and symmetrization procedures can be used to identify, separate, and extract these various contributions, based on their unique magnetic field and angle dependencies.\n\nWe are confident that this systematic methodology will be adopted by future studies of electric Hall effects in in-plane measurement geometries.\n\nRegarding the broader impact of our study, by observing and tuning the anomalous IPHE in epitaxial thin films and heterostructures of topological kagome magnets at room temperature, our study establishes a credible pathway toward exploring the use of this and other Berry curvature-induced Hall effects in technologically relevant concepts, such as magnetic sensing applications.\n\nChanges made: We have revised the introduction and conclusion section of the manuscript to better highlight the novelty of our study over previous published work. We have also included a new section ‘Classification of Hall effects’ in the revised manuscript to better distinguish our results from previous reports on other Hall effects, such as the AHE. We hope the referee can recommend our revised work for publication in Nature Communications."}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have made extensive changes in response to the comments from all reviewers in the previous round. They have shown that the anomalous in-plane Hall effect (IPHE) is clearly distinct from the anomalous Hall effect (AHE) based on the required broken symmetries. In Table 1 and in the section “Classification of Hall effects”, they present a complete classification of the different possible contributions to the Hall signal and explain how these contributions can be distinguished based on their magnetic-field and electric-field dependence. In addition, they have adopted a new definition of the angles φ_B and φ_E (instead of φ and θ), which is easier to follow and improves the readability of the corresponding sections compared to the previous version.\nOverall, the quality of the manuscript has been greatly improved by these changes. Therefore, I recommend publication in Nature Communications.", "reviewer_2": "I thank the authors for the excessive revision and explaining in detail the different contributions to their measured signal. It is much helpful for understanding the manuscript. With this said, I still have concerns regarding the data acquisition and analysis of the thin films. As the authors said in their response, they do agree that their method does not exclude contacts contribution and possible anisotropy effect. This raises more questions than answer.\n1. Why is there a factor of 10 between the amplitude of the same device, as seen in Fig S9 and Figure 3a (main results of the paper)?\n2. Also, all their data is taken on a single device, why no other devices shown?\n3. Same thing with D2, in Figure S9 and Figure S10 the amplitude is 9 ueV, 36ueV respectively, while in Figure 5e its 60 ueV, a factor of 6, and 2.\n4. Also Figure S9 show that D2 and D1 have different contribution from the bulk as the authors claim, so why use D2 in a heterostructure device?\nCould it come from degradation of the contacts? Such a scenario with the authors method which does not exclude contribution from the contacts (as they also said in the response) makes the entire data analysis debatable.\nThe paper is interesting and well written, but more data in the form of other devices, reproducing the same results, and using a more accepted technique of measuring the Hall effect is required. If any such data exist to show reproducibility, I think that the manuscript can be accepted while adding the data to the Supplementary data section. The manuscript, as it is, relies on a single device with a problem in the data acquisition method, and therefore I cannot recommend it for publication as it is.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_5": "Dear authors,\nI believe that mostly all of the questions have been properly answered in the reply letter. Nevertheless, I decided to not recommend it for publication in its present form because I am not convinced about the microscopic origin of the Hall effect described in the paper. I think the role of the Weyl points is not fully clear, so I suggest you to do the following to clarify this question:\n- Plotting your version of the band structure, indicating the location of the Weyl points explicitly.\n- You should display the surface states and the Fermi arcs as a complementary figure.\n- For the maximum value of the Hall effect into discussion, compute the conductivity as a function of the energy and then conclude directly whether the maximum of the conductivity corresponds to a Weyl feature of the band structure."}, "author_response": "We appreciate the feedback and acknowledgment of our efforts by the referee. However, it seems that the referee has misunderstood our response to comment 1 in the previous round of review. In paragraph 1 of this response, we clearly state that the various Hall resistivities were obtained by using a symmetrization operation based on flipping the magnetic field direction to avoid contact resistance effects. Contrary to the referee’s statement, we do neither agree nor state that this procedure results in possible contributions from contact resistance and anisotropy effects. In summary, our data acquisition and analysis are technically robust and up to standard practice in this field.\n\n1. Why is there a factor of 10 between the amplitude of the same device, as seen in Fig S9 and Figure 3a (main results of the paper)?\nResponse: We thank the referee for this careful observation. In Fig.S9 of the previous manuscript version, we display the in-plane Hall voltage V_IPHE(φ_B, φ_E), as indicated in the supplementary text and related figure caption. However, the color bars of Fig.S9 were accidentally double labelled with both ρ_IPHE and V_IPHE. This oversight occurred during our comprehensive revision in response to the second round of review and is limited to this specific figure. We sincerely apologize for this error. This double-labelling explains the seeming disagreement with Fig.3a, which displays ρ_IPHE(φ_B).\nChanges Made: We have removed the label ρ_IPHE from the color bars in Fig.S13 of the revised manuscript (Fig.S9 of the previous manuscript version).\n\n2. Also, all their data is taken on a single device, why no other devices shown?\nThe referee seems to have overlooked that our manuscript and supplementary information present experimental data recorded on two devices, which are clearly labelled ‘D1’ and ‘D2’. Data recorded on D1 are presented in Fig.3 of the main text and Sec.VIII of the Suppl. Materials. Data recorded on D2 are presented in Fig.5 and Sec.IX of the Suppl. Materials and are in both qualitative and good quantitative agreement with the data of device D1. This establishes the robustness of our observations.\n\n3. Same thing with D2, in Figure S9 and Figure S10 the amplitude is 9 ueV, 36ueV respectively, while in Figure 5e its 60 ueV, a factor of 6, and 2.\nWe thank the referee for this technical question. Referring to our answer to question 1, Fig.S9 displays V_IPHE whereas Fig.S10 and Fig.5 display ρ_IPHE. The data of ρ_IPHE of device D2 shown in Fig.5e are extracted from Fig.S10 and exhibit identical amplitude. The referee may be referring to ρ_IPHE recorded on the heterostructure device D2hs, which exhibits an enhanced amplitude owing to the presence of the ferromagnetic CoFeB film, as described in the main text.\n\n4. Also Figure S9 show that D2 and D1 have different contribution from the bulk as the authors claim, so why use D2 in a heterostructure device?\nWe appreciate the referee's insightful question, which perhaps results from the double-labelled color bar of Fig.S9 in the previous manuscript version. We have intentionally fabricated devices from films of different thicknesses to evaluate the contributions of the surface and bulk to the anomalous in-plane Hall response.\nWe find that devices D1 and D2 display V_IPHE signals of different amplitude attributed to their differing thicknesses, as seen in Fig.S9 of the previous manuscript version. However, taking the film thicknesses into account, the resulting anomalous in-plane Hall resistivities of devices D1 and D2 are in good quantitative agreement, ρ_IPHE(D1) ≈ ρ_IPHE(D2). As discussed in detail in paragraphs 3 and 4 on page 10 of the manuscript, this finding unambiguously excludes surface effects are the origin of the observed in-plane Hall effect and suggests that the anomalous IPHE is facilitated by spin canting within the bulk of the sample.\n\n5. Could it come from degradation of the contacts? Such a scenario with the authors method which does not exclude contribution from the contacts (as they also said in the response) makes the entire data analysis debatable.\nAs described in our response to the previous question, we observe a qualitative and quantitative agreement of ρ_IPHE measured on devices D1 and D2 in terms of their amplitude and specific dependence on the electric and magnetic field angles φ_B and φ_E, respectively. This establishes the robustness of our experimental observations.\nMoreover, all data were obtained using a standard 4-probe geometry and symmetrization using a flipped magnetic field geometry to exclude contact resistance effects.\n\nThe paper is interesting and well written, but more data in the form of other devices, reproducing the same results, and using a more accepted technique of measuring the Hall effect is required. If any such data exist to show reproducibility, I think that the manuscript can be accepted while adding the data to the Supplementary data section. The manuscript, as it is, relies on a single device with a problem in the data acquisition method, and therefore I cannot recommend it for publication as it is.\nWe thank the referee for their suggestions. We are convinced that our clarifications regarding the double-labelling of the color bars in old Fig.S9 resolves the technical concerns brought forward in comments 1, 3, 4, and 5. The quantitative and qualitative reproduction of our results on devices D1 and D2 establish the robustness and reproducibility of our observations of the anomalous in-plane Hall effect. As we already stated in our response to comment 1 from the previous round of review, our data acquisition and analysis based on magnetic field-symmetrized transverse voltages obtained using 4-probe measurements are technically robust and up to standard practice in this field. Since all technical concerns raised by the referee have been refuted, we hope that the referee can now recommend publication of our manuscript in Nature Communications.\n\nChanges to the main text and supplementary information are highlighted in red text color."}, {"round": 4, "reviewer_comments": {"reviewer_2": "I am thankful for the authors for their response and clarification.\nI do agree that I may have been confused by the author comment regarding the flipping of the magnetic field in measuring the Hall signal.\nRegarding the different scale bars in the figures I appreciate their correction.\nTherefore, I recommend publication in Nature Communications.", "reviewer_5": "Dear authors,\nThe current version of the paper is appropriate to be considered for publication in Nature.\nBest regards."}, "author_response": ""}]

Decision letter
Peer Review File
Room temperature observation of the anomalous in-plane
Hall effect in a Weyl ferromagnet
Corresponding Author: Dr Berthold Jäck
This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
Attachments originally included by the reviewers as part of their assessment can be found at the end of this file.
Version 0:
Reviewer comments:
Reviewer #1
(Remarks to the Author)
Sankar et al. report a room-temperature anomalous in-plane Hall effect (IPHE) in the Kagome magnet Fe₃Sn, grown using
the molecular beam epitaxy method. Through measurements with varying magnetic fields and current orientations, the
authors successfully separate the IPHE from other effects—such as the planar Hall effect (PHE), symmetric transverse
resistivity (STR), and anomalous Hall effect (AHE). Their findings are consistent with calculations based on canted
ferromagnetism and topological Weyl points.
The IPHE is distinct from the planar Hall effect observed in topological materials, and its presence in Fe₃Sn thin films at
room temperature will be of broad interest. The data and theoretical analysis are of high quality. I recommend the manuscript
for publication after addressing the following technical and presentation issues to enhance overall readability:
1. On Page 1, the authors state, "To date, the observation of novel anomalous Hall effects remains often limited to cryogenic
temperatures. This motivates the search for a new class of topological materials and heterostructures, which can be
manufactured using scalable synthesis methods, to discover and control Hall effects at room temperatures." This claim may
be an overstatement. The anomalous Hall effect has recently been observed in several Mn/Fe-based materials near or at
room temperature in both bulk and thin-film forms, such as Mn3Sn/Ge, YbMnBi2, RMn6Sn6, Fe3GeTe2, Fe3Sn2, and FeS.
The authors should revise this statement to acknowledge these recent discoveries.
2. In Figure 1(d) and (e), the caption states that (d) corresponds to the calculation with canting and (e) without canting.
However, the Berry curvature appears to be zero in (d) and nonzero in (e), which contradicts the claim in the text. The
authors should clarify their claim or improve their figures.
3. In the IPHE fitting, the authors assume that the anomalous Hall effect contribution is independent of the angle (θ). They
should clarify why this must be the case, particularly considering the possibility of misalignment. Based on the amplitude
shown in Fig. 2(f) and Fig. 3(a), even slight misalignment could induce an anomalous Hall effect comparable to the IPHE
(an out-of-plane component of B ~ 3 mT).
4. In Fig. 3 and Fig. 4, the IPHE appears small compared to the raw signal. It would be beneficial to include figures
displaying the raw signal alongside the separated signals (IPHE, AHE, and STR) to illustrate the robustness of the IPHE
better.
5. The IPHE is significantly stronger (by three orders of magnitude) in Fig. 4(a) compared to Fig. 3(a). Additionally, the unit in
the inset of Fig. 4(a) is incorrect (should be cm not cm^-1).
6. The magnetic field values span a large range in Fig. 4(a), making it difficult to track the values corresponding to each
curve. The authors should consider adding field values next to each curve or incorporating a color bar to improve readability.
7. In addition to the coupling to the Fe moment, the stray field from CoFeB might enhance the AHE. The authors should
discuss this possibility in the context of the IPHE.
8. On Page 9, the authors state, "we find VIPHE(60nm)/VIPHE(30nm) ≈ 2.5." This seems a typo, as a thicker film should
yield a smaller voltage. Furthermore, this contradicts Fig. S7.
Reviewer #2
(Remarks to the Author)
My full report is given by the word file attached.
Reviewer #3
(Remarks to the Author)
I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature
Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career
Researchers who co-review manuscripts.
Reviewer #4
(Remarks to the Author)
The authors present essential results, where they report observation of the anomalous in-plane
Hall effect in the thin films of a Weil ferromagnet at room temperature. The reported
findings (in the case of their correctness) are exciting and may draw further attention.
Nevertheless, I do not believe this article is suitable for publication in its current form in
Nature Communications. The discussions are weak and lack clear explanations. The theoretical support is very limited.
Therefore, I do not recommend this article in its current form for publication.
Version 1:
Reviewer comments:
Reviewer #1
(Remarks to the Author)
The manuscript is much improved, especially the discussion of OHE, AHE and IPHE. However, they must discuss their
results in the context of all the other AHE recent reports mentioned in the review (Mn3Sn/Ge, YbMnBi2, RMn6Sn6 and the
other Fe compounds). Juts adding the references is not enough. The bigger point here is the question about the novelty of
the present results, in which case the authors need to make a convincing case that the current study is suitable for Nature
Communications by distinguishing it from all these other reports.
Depending on the outcome of such a discussion, I may recommend the publication of the manuscript, but not in the current
form.
Reviewer #2
(Remarks to the Author)
my report is given in the word file.
Reviewer #3
(Remarks to the Author)
I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature
Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career
Researchers who co-review manuscripts.
Reviewer #5
(Remarks to the Author)
In this article the authors demonstrate an in-plane anomalous Hall effect in Fe$_3$Sn, which can even be detected at room
temperature and that is induced by the electronic topology. Other ingredients accompanying the effect of topology are the
spin canting and the spin orbit interaction. Besides, this signal can be tunable by the magnetic stray field of CoFeB. The
paper has good quality and the experimental results are interesting, but I am not satisfied with the theoretical explanation of
the effect. Because of this reason, I do not recommend this article to be published in Nature in its present form. Nevertheless,
and to help them with the quality of the work, there are a few important points that the authors need to solve before trying to
submit again or looking for another journal:
1. In page 7, you claim that the planar Hall effect is $\phi$ invariant. If you are trying to say that it does not depend on the
electric field angle, then I strongly disagree. The planar Hall effect is typically connected to the Fermi surface contribution to
the transverse conductivity, and I would expect an angular dependence similar to $\sin(2\phi_E-2\phi_B)$. Here, $\phi_E$ and $\phi_B$ are the electric and magnetic field angles, respectively. Could you further give more arguments about this to confirm your statement?
2. In page 8, which evidences do you have to attribute the in-plane Hall effect to the Weyl points? In my view, I can simply
rule out the Berry curvature as a possible explanation of this effect, because the related conductivity is independent of the
electric field angle. Instead, you claim that the in-plane Hall effect can be fit to $\sin(\phi_E+\phi_B)$. I also do not see that
this origin should change upon increasing temperature. In the same spirit, are you sure that the Weyl points survive in the
high temperature limit?
3. In the same spirit as the previous question, I do not believe that the DFT is wrong, but rather cannot capture the effect
measured by the authors in the experiment. Could you show the angular dependence of the conductivity, when computed
with the Berry curvature formula, in terms of the electric field angle, please? I would expect a constant as a function of
$\phi_E$, and thus not consistent with Fig.3(a).
4. Could the authors check the behavior of the in-plane Hall effect when reversing $\mathrm{M}_z$ to $-\mathrm{M}_z$,
please? It would be also instrumental to reverse all the magnetic components together, so you can better explain whether
the unconventional conductivity arises on the Berry curvature at high temperature or not.
Version 2:
Reviewer comments:
Reviewer #1
(Remarks to the Author)
The authors have made extensive changes in response to the comments from all reviewers in the previous round. They
have shown that the anomalous in-plane Hall effect (IPHE) is clearly distinct from the anomalous Hall effect (AHE) based on
the required broken symmetries. In Table 1 and in the section “Classification of Hall effects”, they present a complete
classification of the different possible contributions to the Hall signal and explain how these contributions can be
distinguished based on their magnetic-field and electric-field dependence. In addition, they have adopted a new definition of
the angles φ_B and φ_E (instead of φ and θ), which is easier to follow and improves the readability of the corresponding
sections compared to the previous version.
Overall, the quality of the manuscript has been greatly improved by these changes. Therefore, I recommend publication in
Nature Communications.
Reviewer #2
(Remarks to the Author)
I thank the authors for the excessive revision and explaining in detail the different contributions to their measured signal. It is
much helpful for understanding the manuscript. With this said, I still have concerns regarding the data acquisition and
analysis of the thin films. As the authors said in their response, they do agree that their method does not exclude contacts
contribution and possible anisotropy effect. This raises more questions than answer.
1. Why is there a factor of 10 between the amplitude of the same device, as seen in Fig S9 and Figure 3a (main results of the
paper)?
2. Also, all their data is taken on a single device, why no other devices shown?
3. Same thing with D2, in Figure S9 and Figure S10 the amplitude is 9 ueV, 36ueV respectively, while in Figure 5e its 60
ueV, a factor of 6, and 2.
4. Also Figure S9 show that D2 and D1 have different contribution from the bulk as the authors claim, so why use D2 in a
heterostructure device?
Could it come from degradation of the contacts? Such a scenario with the authors method which does not exclude
contribution from the contacts (as they also said in the response) makes the entire data analysis debatable.
The paper is interesting and well written, but more data in the form of other devices, reproducing the same results, and using
a more accepted technique of measuring the Hall effect is required. If any such data exist to show reproducibility, I think that
the manuscript can be accepted while adding the data to the Supplementary data section. The manuscript, as it is, relies on a
single device with a problem in the data acquisition method, and therefore I cannot recommend it for publication as it is.
Reviewer #3
(Remarks to the Author)
I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature
Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career
Researchers who co-review manuscripts.
Reviewer #5
(Remarks to the Author)
Dear authors,
I believe that mostly all of the questions have been properly answered in the reply letter. Nevertheless, I decided to not
recommend it for publication in its present form because I am not convinced about the microscopic origin of the Hall effect
described in the paper. I think the role of the Weyl points is not fully clear, so I suggest you to do the following to clarify this
question:
- Plotting your version of the band structure, indicating the location of the Weyl points explicitly.
- You should display the surface states and the Fermi arcs as a complementary figure.
- For the maximum value of the Hall effect into discussion, compute the conductivity as a function of the energy and then
conclude directly whether the maximum of the conductivity corresponds to a Weyl feature of the band structure.
Version 3:
Reviewer comments:
Reviewer #2
(Remarks to the Author)
I am thankful for the authors for their response and clarification.
I do agree that I may have been confused by the author comment regarding the flipping of the magnetic field in measuring
the Hall signal.
Regarding the different scale bars in the figures I appreciate their correction.
Therefore, I recommend publication in Nature Communications.
Reviewer #5
(Remarks to the Author)
Dear authors,
The current version of the paper is appropriate to be considered for publication in Nature.
Best regards.