Giant unusual anisotropic magnetoresistance enabled by hole-electron resonance in van der Waals heterostructures

Abstract

The hole-electron resonance in two-dimensional WTe₂ dynamically screens the built-in electric field, disrupting the scattering equilibrium constraints of conventional electron transport. Here, we propose utilizing the hole-electron resonance to achieve Coulomb force-unconstrained spin angular momentum transfer across the WTe₂/Fe₃GaTe₂ interface, offering a novel platform for exploring unconventional spin transport phenomena. A clear signature of this mechanism is the observation of an unusual anisotropic magnetoresistance of 289%, which far exceeds conventional spin Hall magnetoresistance and cannot be explained by standard spin absorption or scattering models. Its angular profile deviates from the simple cosine-squared form but realigns after accounting for magnetization and field orientation, reflecting the interplay between hole-electron resonance and magnetization dynamics. Furthermore, chiral transverse transport with distinct symmetry transitions emerges within the hole-active temperature regime, originating from interfacial symmetry breaking and the inhomogeneous spin-orbital coupling. These findings highlight the essential roles of both electrons and holes in spin transport.

Introduction

Spin transport phenomena, such as spin pumping^1,2, spin injection^3,4,5,6, spin Hall effect^7,8,9,10,11, and spin-orbit torque^{12,13,14,15,16}, constitute the fundamental basis for spintronics research and applications. While current studies in these areas predominantly focus on electron carriers, the role of hole-electron interactions has received comparatively less attention despite its fundamental importance.

Recent advancements in two-dimensional (2D) van der Waals (vdW) materials have provided rich opportunities for exploring transport phenomena. In particular, 2D WTe₂ has emerged as a prototypical system for realizing hole-electron resonance¹⁷, where both electron and hole bands coexist at the Fermi level, as illustrated in Fig. 1a, b. Under the influence of a magnetic field or spin-orbit coupling (SOC), electron and hole displacements effectively neutralize the total charge, suppressing the formation of an internal electric field, as depicted in Fig. 1c. This charge compensation mechanism, combined with enhanced carrier scattering, leads to a remarkably large and unsaturated magnetoresistance (MR)^{17,18,19,20,21,22}. This phenomenon was experimentally observed¹⁷ and confirmed to arise from the nearly perfect hole-electron compensation in WTe₂²². Subsequent studies have extensively explored the electrical transport properties of WTe₂, including its band structure characteristics¹⁹, anisotropic MR^20,23,24, planar Hall effect^25,26, and nonlinear Hall effects^27,28,29. Importantly, while these phenomena produce large MR, they are largely independent of magnetic moments, limiting their direct applicability in spintronic devices.

Fig. 1: Carriers motion and their interactions with the FM interface.

a Crystal structure and b band structure of WTe₂ obtained through first-principles calculations (see Supplementary Information for details). c Carrier dynamics in a NM material and an FM/NM heterostructure under an external magnetic field B. c Electron-dominant systems: In the NM layer, B-induced electron deflection generates interfacial charge accumulation and a counteractive field (E), suppressing further scattering. At the FM/NM interface, E drives spin-exchange saturation. Hole-electron resonance-dominant systems: In the NM layer, synchronized deflection of electrons and holes under B achieves dynamic charge neutrality, effectively nullifying the built-in electric field, which enables persistent carrier scattering without Coulombic screening. At the FM/NM interface, the absence of net charge accumulation allows unrestricted spin-angular-momentum transfer between carriers and the FM layer, yielding a net spin current (J_S) transport across the FM/NM interface.

Incorporating a hole-electron resonance system into a heterojunction with a ferromagnetic (FM) material introduces carrier accumulation and interfacial scattering, fundamentally altering spin transport dynamics. In this context, charge compensation suppresses the internal electric field, facilitating Coulomb force-unconstrained spin angular momentum transfer at the interface, as illustrated in Fig. 1c. WTe₂/FM interface thus serves as an ideal platform to explore these unconventional spin transport processes. In magnetic heterostructures, interfacial effects such as spin absorption/reflection and interfacial electric fields give rise to magnetoresistance phenomena. These include spin Hall magnetoresistance (SMR)^30,31,32 and unusual anisotropic magnetoresistance (UAMR). The concept of UAMR is defined by the two-vector MR theory^33,34,35,36. It closely resembles classical AMR but includes the effect of an interfacial electric field that reflects interfacial interactions. In WTe₂-based magnetic heterostructures within the hole-electron resonance regime, the interplay between hole-electron resonance and interfacial magnetization can further modulate the magnetoresistance, offering a strategy to harness the large MR of WTe₂ for non-volatile spintronic applications.

Here, we investigate how hole-electron resonance interacts with the FM interface in an all-vdW WTe₂/Fe₃GaTe₂ heterostructure. Our findings demonstrate a large UAMR in the plane perpendicular to the charge current, which directly correlates with both the magnetization and hole-electron resonance. Furthermore, within the temperature regime dominated by hole-electron resonance, a chiral transverse transport response is observed. These results highlight the crucial role of both electron and hole carriers in governing spin transport, providing valuable insights for the design of spintronic memory devices based on hole-electron resonance materials.

Results

Hole-electron resonance and UAMR

The vdW heterostructure WTe₂/Fe₃GaTe₂ is prepared via mechanical exfoliation. Fe₃GaTe₂ is a 2D vdW FM material with a bulk Curie temperature of ~350 K^37,38,39 (see Supplementary Information S1). According to atomic force microscopy (AFM), the thicknesses of WTe₂ and Fe₃GaTe₂ are determined to be 9 nm and 26 nm, respectively (see Supplementary Information S2). The schematic of the electrical transport measurements is shown in Fig. 2a. A DC current of 10 μA is applied along the a-axis of WTe₂, corresponding to a current density of ~2.38 × 10³A/cm², where Joule heating effects are negligible⁴⁰ (Fig. S3). A 9T magnetic field is then rotated in the yz-plane (H⊥I) to minimize H–I angle effects and highlight magnetization-induced contributions. To better analyze the sources of the magnetoresistances, we also fabricated WTe₂ devices and Fe₃GaTe₂ devices for comparison with the WTe₂/Fe₃GaTe₂ heterostructure. Details of the sample structures are listed in the Supplementary Information S2.

Fig. 2: Magnetization-dependent large UAMR in WTe₂/Fe₃GaTe₂.

a The schematic of the electrical transport measurements. b Magnetoresistance of WTe₂ and WTe₂/Fe₃GaTe₂ measured at 5 K. Inset is the optical micrograph of WTe₂/Fe₃GaTe₂ device. UAMR of the c WTe₂/Fe₃GaTe₂ d WTe₂ and e Fe₃GaTe₂ obtained in the yz-plane and H = 9T. Solid lines denote the experimental data, while dashed lines represent fits to a cos²β dependence.

The temperature dependence of the WTe₂/Fe₃GaTe₂ heterostructure resistance is depicted in Fig. S4 in Supplementary Information. By analyzing the temperature-dependent resistivities, ρ_W and ρ_F, of WTe₂ and Fe₃GaTe₂ devices under H = 9T, we determine the current distribution ratio I_F/I_W between Fe₃GaTe₂ and WTe₂ layers within the heterostructure. The I_F/I_W ratio exhibits a minimum of ~12 at around 60 K. Below this temperature, I_F/I_W increases with decreasing temperature, approaching 14 at 5 K, suggesting that the majority of the current flows through the Fe₃GaTe₂ layer.

Figure 2b presents the nonsaturating MR in both WTe₂ and WTe₂/Fe₃GaTe₂ heterostructure at 5 K. Nonsaturating MR can originate from several mechanisms, including charge-carrier compensation, open-orbit transport, or other effects related to Fermi surface topology^41,42,43. Among these, charge-carrier compensation, in which nearly equal volumes of electron and hole pockets lead to a continuous increase of resistance with magnetic field, has been identified as the dominant mechanism in systems such as WTe₂¹⁷, LaSb⁴⁴, ReO₃⁴⁵, and GdBi⁴⁶. In the WTe₂, the hole-electron compensation is confirmed by two-band model fitting¹⁸ (Supplementary Information S5). Upon the integration of Fe₃GaTe₂, the field-induced growth of MR becomes less pronounced at high magnetic fields. Nevertheless, a substantial nonsaturating MR persists up to 9 T, suggesting that the hole-electron resonance remains active, albeit potentially modified by the magnetic interface. To elucidate this interplay, we examined the angular dependence of the longitudinal resistance, as shown in Fig. 2c. Given that UAMR provides a mathematical framework encompassing all possible angular dependencies of magnetoresistance, we adopt the term UAMR to describe the angular-dependent magnetoresistance (ADMR) measured in our experiments. Below 80 K, R_xx varies strongly with the angle β between the magnetic field and the z-axis in the yz-plane, producing a pronounced UAMR. Its amplitude is defined as $\frac{{{R}_{{xx},\perp }-R}_{{xx},//}}{{R}_{{xx},//}}\times 1$00 %, where ${R}_{{xx},//}$ and ${R}_{{xx},\perp }$ denote the longitudinal resistance with the magnetic field applied in the ab-plane and along the c-axis, respectively. This UAMR is also observed in isolated WTe₂ and Fe₃GaTe₂, as shown in Fig. 2d, e, respectively. The former is attributed to the hole-electron resonance in WTe₂, while the latter is likely related to interfacial fields in 2D layered systems ^33,34,35,36.

By comparing these three devices, it is evident that the UAMR in the WTe₂/Fe₃GaTe₂ device distinctly differs from that in the WTe₂ and Fe₃GaTe₂ devices. Although WTe₂ itself exhibits appreciable UAMR below 80 K, it is not directly correlated with the magnetic moments and follows a cos²β angular dependence, as indicated by dashed fitting lines in Fig. 2c, d, e. In contrast, the angular dependence in the WTe₂/Fe₃GaTe₂ device deviates significantly from cos²β, exhibiting a sharp peak near H⊥c, reminiscent of the behavior observed in the Fe₃GaTe₂ device. This may arise from the strong perpendicular magnetic anisotropy (PMA) competing with the Zeeman energy, leading to a misalignment between the magnetic moment orientation and the magnetic field direction^39,47. However, contrary to the WTe₂/Fe₃GaTe₂ device, Fe₃GaTe₂ device shows a much lower UAMR when the magnetic field is along the c-axis compared to when it is perpendicular. We further compare the WTe₂/hBN/Fe₃GaTe₂ device, as presented in Supplementary Information S6. With the insertion of an hBN spacer, the interfacial coupling between magnetization and charge carriers is effectively suppressed. Under this condition, the observed UAMR recovers a cos²β dependence, characteristic of the bulk response of WTe₂. This comparison indicates that the UAMR in the WTe₂/Fe₃GaTe₂ heterostructure incorporates contributions from both WTe₂ and Fe₃GaTe₂ yet cannot be regarded as a simple superposition of the two. While the bulk effects associated with hole–electron resonance and the Fermi surface of WTe₂ make an important contribution, the interfacial interplay between magnetizations and both electron and hole carriers in the WTe₂/Fe₃GaTe₂ heterostructure constitutes the decisive factor in shaping the UAMR (Supplementary Information S10). This behavior in the WTe₂/Fe₃GaTe₂ heterostructure has been consistently reproduced across multiple devices (Supplementary Information S11).

Magnetic orientation dependence

To further clarify the contribution of magnetic moments to the UAMR in the WTe₂/Fe₃GaTe₂ device, we perform a correction on the orientations between the magnetization m and the applied magnetic field H using the Fe₃GaTe₂ device. This correction is based on the fact that the anomalous Hall effect (AHE) signal of the Fe₃GaTe₂ device is positively correlated with the z-component of its magnetic moments. Figure 3a shows the transverse magnetoresistance R_xy of the Fe₃GaTe₂ device as a function of β. The normalized polar plot is shown in Fig. 3b. From these results, it is evident that the magnetic moments prefer to maintain an orientation near the c-axis rather than fully aligning with the applied magnetic field, as illustrated in the inset of Fig. 3c. When H is applied at an angle β, the actual angle β_m between the magnetic moments and the z-direction can be expressed as^39,47

$${\,\beta }_{m}=arccos \left[\frac{{R}_{{xy}}\left(\beta \right)}{{R}_{{xy}}\left(\beta=0\right)}\right]$$

(1)

Fig. 3: Correction of magnetization and magnetic field Orientations using AHE of Fe₃GaTe₂.

a The transverse magnetoresistance R_xy of the Fe₃GaTe₂ device as a function of β and b the corresponding polar plot. c The relationship between β_m and β obtained from Fe₃GaTe₂ device. d R_xx of WTe₂/Fe₃GaTe₂ with the corrected β_m at 5 K. Green dots are original data detected at 5 K while orange dots are data variation after β_m correction. Green line is fitted using higher-order terms related to m, and orange line is fitted using cos²β.

The resulting relationship between β_m and β is shown in Fig. 3c. It is clear that m and H are nearly collinear near the c-axis, while there is a significant deviation when approaching the ab-plane, particularly at low temperatures. We introduced the corrected β_m into the WTe₂/Fe₃GaTe₂ device, and the results are shown in Fig. 3d. It is evident that the UAMR of the WTe₂/Fe₃GaTe₂ device now aligns more closely with the cos²β angular dependence. Some deviations from the cos²β dependence remain after the correction is due to the high sensitivity of the PMA of Fe₃GaTe₂ to thickness, making it challenging to achieve a perfect match between the corrected angles in the parallel device and those in the heterostructure device. This indicates that the magnetization in Fe₃GaTe₂ plays a crucial role in the UAMR of the WTe₂/Fe₃GaTe₂ device. Additionally, the UAMR of the WTe₂/Fe₃GaTe₂ device at low temperatures can also be fitted using higher-order terms related to m (green curve in Fig. 3d), which is also a characteristic feature of non-collinearity between the magnetization and the magnetic field, as discussed in the Supplementary Information S7.

Relationship between the UAMR and the hole-electron resonance

Next, we examine the relationship between the UAMR and the hole-electron resonance by analyzing its temperature dependence. The UAMR of WTe₂/Fe₃GaTe₂ exhibits similar temperature trend as pristine WTe₂, as shown in Fig. 4a. Although the current flowing in Fe₃GaTe₂ layer is much larger than that in WTe₂ layer, the heterostructure device exhibits an exceptionally high UAMR of 288.78%. This large value may include bulk contributions from individual WTe₂ and Fe₃GaTe₂ layers, which can be estimated to be ~31.48% based on a parallel-circuit model. The estimated contributions of this bulk effect in WTe₂/Fe₃GaTe₂ device at different temperatures are shown as the green dashed line in Fig. 4a, which are far smaller than the UAMR observed here. Furthermore, control experiments reveal that the UAMR is significantly reduced when the interface is disrupted or weakened, for instance by inserting an hBN spacer (Supplementary Information S6) or by increasing the thickness of the heterostructure (Supplementary Information S11), indicating the important role of the magnetic interface.

Fig. 4: Hole-electron resonance related large UAMR.

a Temperature dependence of UAMR in WTe₂/Fe₃GaTe₂ heterostructure and WTe₂ devices. The inset shows the ratio of electron and hole carrier density (n_e/n_h) in WTe₂, and the black dashed line is guide to the eye. b Temperature dependence of UAMR in Fe₃GaTe₂ and WTe₂/Fe₃GaTe₂ devices. Solid lines represent fits using a generalized logistic function, while green-dashed line denotes the estimated bulk contributions from individual WTe₂ and Fe₃GaTe₂ layers.

The inset of Fig. 4a shows the ratio of electron to hole carrier densities (n_e/n_h) in WTe₂ (Supplementary Information S5). By correlating this ratio with the temperature evolution of UAMR, we find that higher UAMR values occur in the temperature range where the electron and hole carrier densities are nearly balanced. As the temperature increases, the UAMR gradually decreases. Once the system moves out of the hole-electron compensation regime, it approaches the magnitude of UAMR typically observed in magnetic heterostructures (Table S2 in the Supplementary Information). At higher temperatures, thermal fluctuations increasingly suppress the long-range magnetic order in Fe₃GaTe₂, leading to the attenuation of interfacial interaction-related magnetoresistance⁴⁸. Consequently, the UAMR in WTe₂/Fe₃GaTe₂ converges toward that of the Fe₃GaTe₂ device, as shown in Fig. 4b. The temperature-dependent UAMR in both WTe₂/Fe₃GaTe₂ and pristine WTe₂ devices can be well described by an empirical generalized logistic function, UAMR(T) = ${U}_{2}+\frac{{U}_{1}-{U}_{2}}{1+{\left(T/{T}_{0}\right)}^{p}}$, which, while not derived from a microscopic theory, provides an accurate description of the observed temperature dependence (solid lines in Fig. 4a). Here, U₁ and U₂ represent the low- and high- temperature limits of UAMR, respectively, T₀ characterizes the approximate transition temperature, and p determines the sharpness of the temperature dependence. For WTe₂/Fe₃GaTe₂ (WTe₂), the extracted parameters are U₁ = 288.62 (491.97) %, U₂ = −0.62 (0.65) %, T₀ = 27.54 (27.35) K, p = 2.68 (2.64). By contrast, Fe₃GaTe₂ exhibits only a small negative UAMR (not exceeding –1.1%) across its entire magnetically ordered regime, making the logistic description inapplicable.

We further analyze the possible physical sources of the large UAMR in WTe₂/Fe₃GaTe₂. First, we analyze the data within the framework of the SMR model³², with the results shown in Fig. S11. In the hole–electron resonance regime, the conventional SMR framework fails to capture the experimental data, as it leads to an unphysical negative spin-mixing conductance. In contrast, at around 150 K, where electron–hole compensation is lifted while Fe₃GaTe₂ still maintains long-range magnetic order, the SMR model provides a reasonable fit, giving a spin-mixing conductance on the order of 10¹⁴ Ω⁻¹m⁻². This value is consistent with typical experimental reports in conventional systems^49,50. Second, we perform the ADMR measurements in other planes are presented in the Supplementary Information S13, where R_xx for the yz- and xz-planes is found to be comparable and significantly larger than that for the xy-plane. These angular dependencies can be generally described by the two vector MR theory, which posits that the ADMR is determined by the relationships among vectors including the charge current, magnetization, and the interfacial electric field^33,34,35,36. According to the two-vector MR theory, the sum of the expansion coefficients of R_xx for the yz- and xz-planes is comparable and can be much larger than that for the xy-plane, consistent with our experimental observations. In general, these different physical mechanisms may coexist in our system. However, the key point here is that the UAMR formalism itself is a vector-based analytical framework rather than a description of the actual microscopic origin. In our case, the large UAMR mainly arise from the interaction between the charge carriers and the magnetic interface, which may already be implicitly included within the two-vector MR framework and warrants further investigation.

Based on these observations, we propose that the large UAMR in the WTe₂/Fe₃GaTe₂ device is closely associated with the interplay between the magnetic interface and charge carriers under hole–electron balance condition. Specifically, under the hole-electron resonance state, electrons and holes shift and accumulate to one side under the magnetic field due to the Lorentz force. This suppresses the formation of a built-in electric field that balance the transverse migration of carriers. Therefore, the transverse scattering continues to increase, the longitudinal carrier mean free path decreases, ultimately leading to a huge, unsaturated longitudinal resistance. When a magnetic interface is present, the sustained interaction between carriers and the magnetic interface allows the generation of large UAMR. This interaction has often been neglected in prior studies of magneto-electric transport, but our results highlight its critical significance. It is therefore essential to reevaluate the role of hole carriers within the existing theoretical frameworks of spin transport, particularly the SHE and SOT^14,15,51,52. We believe this to be a highly significant and urgently needed direction for theoretical development, as it emphasizes the profound influence of hole carriers on spin-related phenomena and challenges the current paradigms of spin transport.

Evolution of transverse magnetoelectric transport

We now direct our attention to the transverse transport characteristics in WTe₂/Fe₃GaTe₂ heterostructure. Figure 5a, b display the transverse magnetoresistance R_xy as a function of the magnetic field angle in the yz-plane at various temperatures. It is important to note that the R_xy signal may contain contributions from the longitudinal resistance R_xx. We attempted to antisymmetrize the data with respect to the magnetic field direction (see Supplementary Information S12 for details). However, in the WTe₂/Fe₃GaTe₂ bilayer, the even component of R_xy does not correspond to the even part of the measured R_xx, and the odd component of R_xx fails to reproduce the odd part of R_xy. This discrepancy indicates that the even contribution in R_xy cannot be attributed solely to longitudinal mixing, but instead reflects intrinsic interfacial effects. Accordingly, we retained the raw data without performing antisymmetrization. At 5 K, with the magnetic field H aligned along the c-axis, R_xy encompasses contributions from both the AHE in the Fe₃GaTe₂ layer and the ordinary Hall effect in the WTe₂ layer, as shown in Fig.5c. Analysis using the two-band model (Supplementary Information S5) indicates that electron and hole carriers remain comparable at low temperatures, highlighting the critical role of hole carriers in this regime^18,21,22. Figure 5d shows the R_xy-H loop obtained in the ab-plane. The enhanced coercivity for the in-plane field arises from the complex magnetization switching in Fe₃GaTe₂, resulting from the interplay of strong PMA, thermal fluctuations, and domain dynamics^47,53,54. Previous studies have reported in-plane topological Hall effect (THE)-like signals in Fe₃GaTe₂ and Fe₃GeTe₂^55,56,57, which bear some resemblance to the hump-like anomaly around ~3 T observed in Fig. 5d. However, given that the heterostructure may host multiple non-topological contributions, such as the planer Hall effect in Fe₃GaTe₂, and the multiband transport in WTe₂, the presence of a true THE in this system remains to be established.

Fig. 5: Transverse magneto-electric transport properties of WTe₂/Fe₃GaTe₂.

The transverse magnetoresistance R_xy of WTe₂/Fe₃GaTe₂ at a 5–80 K and b 90–350 K. The R_xy versus H loop at 5 K with c H//c and d H⊥c. e The polar plot of |R_xy| obtained after removing the contribution of the longitudinal resistance at different temperatures.

To reveal the intrinsic symmetry of R_xy, we isolate the target signal in the WTe₂/Fe₃GaTe₂ device using a linear least-squares method, which removes the spurious contribution from R_xx while preserving the potential even-symmetric component in R_xy (see Supplementary Information S12 for details). The resulting R_xy is plotted in polar coordinates after taking its absolute value, as shown in Fig. 5e and Fig. S22. With increasing temperature, the angular dependence of R_xy undergoes three characteristic transformations: (a) In the low-temperature regime below 80 K, corresponding to the hole-electron resonance region of WTe₂, R_xy exhibits a complex angular dependence that deviates from the conventional symmetric trigonometric relationships. It breaks the mirror symmetry with respect to the ab-plane, revealing the chiral nature of the transverse current, which is distinct from that observed in conventional electron-dominant magnetic heterostructures or in isolated Fe₃GaTe₂ and WTe₂ (see Fig. 3 and Fig. S16). (b) In the intermediate temperature regime around 150 K, referred to as the competition region, additional extrema in R_xy emerge near angles ~20° away from the y-axis, in contrast to conventional systems where R_xy extrema typically occur at 0° and 180°, indicating a significant change in the spatial symmetry of transverse transport. (c) In high-temperature regime near 300 K, known as the electron-dominant regime, R_xy resembles that observed in Fig. 3 for Fe₃GaTe₂, dominated by the conventional AHE with a cosβ relationship. The detailed evolution of the R_xy symmetry is presented in Fig. S22.

In order to gain deeper insights into the interfacial coupling between hole-electron resonance and magnetic moments, we performed first-principles calculations to map the SOC distribution in WTe₂^58,59,60,61. The calculated band structure with projecting different orbitals for the W and Te atoms in reciprocal space are shown in Fig. 6a, b, respectively. These results reveal that the SOC in WTe₂ primarily arises from the hybridization between the d-orbital of W and the p-orbital of Te. Notably, near the Fermi level, the SOC associated with W d-orbitals exhibits pronounced anisotropy in momentum space, giving rise to a spatially inhomogeneous SOC landscape. This anisotropic SOC distribution can modulate the interfacial interactions with adjacent FM layers, influencing spin-dependent scattering and the coupling between hole-electron resonance and magnetic moments. Such modulation provides a plausible mechanism for the observed chiral transverse transport.

Fig. 6: Theoretical analysis of the origin of chirality.

a The SOC distribution of W atoms and b Te atoms in WTe₂. Purple, red, and green points correspond to s-, p-, and d-orbitals, respectively, with the size and the color intensity of the data points indicating the relative SOC strength. c Crystal structure and symmetry of the WTe₂/Fe₃GaTe₂ interface. The upper panel shows a top view along the c-axis, while the lower panel presents the cross-sectional view.

Considering the decisive role of crystal symmetry in determining the band structure and thereby the spin transport, we performed a symmetry-based quantitative analysis. The constructed WTe₂/Fe₃GaTe₂ interface structure is shown in Fig. 6c. Beyond the intrinsic symmetry breaking of WTe₂, the Fe₃GaTe₂ interface further enhances the spatial asymmetry, placing the system in the point group C_3v(No. 156), characterized by a threefold rotational axis and three mirror planes. According to point group analysis, the Hall current along the y direction can be expressed as

$${j}_{H}^{y}={p}_{1}\cos \beta+{p}_{3}\cos 3\beta+{p}_{5}\cos 5\beta+{q}_{1}\sin \beta+{q}_{3}\sin 3\beta+{q}_{5}\sin 5\beta$$

(2)

where p_n and q_n (n = 1, 3, 5) are coefficients determined by the crystal structure and intrinsic properties of the materials. In addition to the conventional cosβ term, higher-order harmonics and sine terms are symmetry-allowed. The sine terms are even functions with respect to the ab plane, while the cosine terms are odd. Their coexistence yields ${j}_{H}^{y}\left(m\right)\ne -{j}_{H}^{y}\left(-m\right)$, indicating that the Hall current intrinsically reflects the broken ab-plane symmetry⁶². The first-order terms are mainly associated with the dipole moment (net magnetization), whereas the higher-order terms primarily originate from multipole moments contributing to the Hall current^63,64. Details are provided in Supplementary Information S14. Around 150 K, fitting results reveal that higher-order coefficients increase significantly relative to the first-order terms. This enhancement is likely driven by temperature-dependent variations in carrier concentration. In this regime, the electron carrier density rises rapidly while the hole fraction decreases sharply (see inset of Fig. 4a), accompanied by evolving phonon and magnon scattering. These changes alter the Berry curvature, thereby enhancing the multipole effect and accounting for the pronounced contribution to the Hall resistance ⁶³.

In conclusion, we have demonstrated a significant UAMR (~289 %) and the chiral transverse transport properties in an all-vdW heterostructure WTe₂/Fe₃GaTe₂, enabled by the interplay of hole-electron resonance and FM interface. The UAMR observed in the WTe₂/Fe₃GaTe₂ heterostructure is notably influenced by the magnetization orientation of the Fe₃GaTe₂ layer. Despite the current mainly passing through Fe₃GaTe₂, the UAMR shows a WTe₂-like temperature dependence, highlighting the crucial carrier-magnetization interaction enhanced at the hole-electron resonance. Furthermore, when hole and electron carriers are nearly balanced, chiral transverse transport is clearly observed. In the intermediate regime, where electrons gradually dominate but hole carriers remain active, higher-order symmetry components of the Hall resistivity emerge. Theoretical analyses indicate that these unconventional transport responses originate from interfacial symmetry breaking, which permits chiral Hall currents and higher-order symmetry terms. The broken symmetry also induces an inhomogeneous SOC distribution, further modulating the symmetry of the magnetoresistance. These findings underscore the potential limitations of previous magnetic-electric transport models that have primarily considered electron carriers, suggesting the urgency of expanding theoretical frameworks that incorporate hole carriers in spintronics.

Methods

Single crystals growth

Single crystals of Fe₃GaTe₂ are grown by the standard high-temperature self-flux technique. A mixture of iron (Fe, 99.98%), gallium (Ga, 99.99%), and tellurium (Te, 99.99%) powders in a molar ratio of 1:1:2 is placed in an alumina crucible, and another empty alumina crucible is kept on top of it with quartz wool separation. The whole crucible assembly is sealed in an evacuated quartz ampoule after a few purges with Ar. The ampoule is first heated to 1273 K and held at this temperature for 24 h to obtain a homogeneous solution. Subsequently, the temperature is rapidly decreased to 1153 K within 1 h, followed by a slow cooling process to 1053 K in 100 h and remained for 12 h at 1053 K for the annealing of the crystals. The ampoule is then quickly taken out of the furnace and centrifuged to separate the crystals from the fluxes. WTe₂ single crystals are prepared by chemical vapor transport method using Br as transport agent. High-purity tungsten (W, 99.999%) and tellurium (Te, 99.999%) powders are precisely weighed in stoichiometric ratio and placed into a quartz ampoule with transport agent Br (3 mg/ml volume). The sealed ampoule was placed in a two-zone furnace with a temperature gradient. The source zone is gradually heated to 1093 K, while the growth zone is maintained at 993 K, held at this temperature for 7–10 days. After the growth process, the furnace is slowly cooled to room temperature.

Device fabrication

First, a six-electrode Hall bar is prepatterned on a SiO₂ (285 nm)/Si substrate using electron-beam lithography, with Ti/Au (5/15 nm) electrodes deposited by thermal evaporation. Then, thin flakes of Fe₃GaTe₂ and WTe₂ are mechanically exfoliated from bulk crystals using adhesive tape. The exfoliated flakes are transferred onto polydimethylsiloxane stamps, which are adhered to a glass slide. Finally, under optical microscope, the Fe₃GaTe₂ flake with appropriate thickness and shape is chosen and transferred onto the electrodes. Using the same method, a WTe₂ flake is precisely stacked onto the Fe₃GaTe₂ to form the WTe₂/Fe₃GaTe₂ heterostructure. To prevent oxidation, the heterostructure is encapsulated with an hBN layer. Both mechanical exfoliation and transfer process are operated inside an argon-filled glovebox maintaining oxygen and water levels below 0.1 ppm. The obtained WTe₂/Fe₃GaTe₂ heterostructure device is baked at 120 °C for 10 min to enhance interfacial contact.

Measurements

The accurate thickness of each flake is determined by an AFM in a tapping mode. Magnetic and electrical transport measurements are performed using a Physical Property Measurement System (PPMS DynaCool, Quantum Design, USA). During the measurements, an excitation current of 10 μA is applied along the x-direction within the ab-plane of WTe₂ and Fe₃GaTe₂. ADMR measurements are performed by rotating a 9 T magnetic field within the yz-plane while simultaneously recording the longitudinal resistance (R_xx) and transverse resistance (R_xy) as functions of the field orientation.