The ordinary Hall effect is due to the Lorentz force acting on the charge carriers.^[1] In ferromagnetic materials, an extra contribution arises from spin–orbit coupling, which is proportional to the spontaneous magnetization, termed the anomalous Hall effect (AHE).^[2,3] The origins of AHE are separated into intrinsic^[4] and extrinsic (skew scattering and side jump) mechanisms.^[5–7] The intrinsic mechanism has been attributed to the Berry curvature in momentum space.^[8–11] Furthermore, in a non-coplanar spin configuration, the Berry phase arising from the real-space scalar spin chirality X_ijk = S_i · (S_j × S_k) can generate a fictitious magnetic field and hence give rise to the topological Hall effect (THE).^[12,13] It is widely known that THE is commonly observed in metallic magnets hosting magnetic skyrmions, which are topologically protected whirling spin textures in nanoscale.^[14] The noncentrosymmetric B20 magnets with skyrmions, such as MnSi,^[15–17] MnGe,^[18] FeGe,^[19,20] and Mn_1−xFe_xSi,^[21] as well as centrosymmetric magnets MnNiGa^[22] and MnPdGa^[23] with biskyrmions are identified to exhibit THE.

Recently, the THE has been observed in frustrated magnetic systems, such as Pr₂Ir₂O₇ and Nd₂Mo₂O₇ with pyrochlore structure,^[24,25] PdCrO₂, Fe_1.3Sb, Fe₃GeTe₂, and Gd₂PdSi₃ with triangular lattice,^[26–29] Mn₃Sn and Mn₃Ga with kagome lattice,^[30,31] and Mn₅Si₃ with noncollinear spin structure.^[32] The THE in these systems has attracted much attention. Especially for frustrated centrosymmetric triangular lattice magnet Gd₂PdSi₃, it shows large THE due to the field induced skyrmion lattice. Meanwhile, the magnetic skyrmions in the frustrated centrosymmetric magnetic system have also been studied theoretically.^[33–36] These experimental and theoretical results suggest that the magnetic skyrmions can also be stabilized in a centrosymmetric lattice via magnetic frustration without Dzyaloshinskii–Moriya (DM) interaction. Hence geometrically frustrated magnets are also an important material system for the generation of magnetic skyrmions. More importantly, the coexistence of skyrmion state and non-collinear magnetic structure both of which originate from magnetic frustration could result in giant THE.

Frustrated kagome lattice ferromagnet Fe₃Sn₂ has attracted much attention in recent years. It shows a large AHE at temperature below Curie temperature T_C (641 K).^[37,38] Moreover, angle resolved photoemission spectroscopy (ARPES) studies confirm the existence of the massive Dirac fermions and flat band.^[38,39] Lorentz transmission electron microscopy (LTEM) studies observe skyrmionic bubbles in Fe₃Sn₂ in a wide temperature range above 100 K.^[40,41] It is also found that the Fe moments rotate from the c axis to the ab plane with non-collinear magnetic structures.^[42] Stimulated by the above results, in this work, we further investigate the THE of Fe₃Sn₂ in detail. There is a giant topological Hall response in the low-field region and the maximum topological Hall resistivity is about −2.01 µΩ·cm at 300 K and 0.76 T. At high field, the THE disappears due to the fully polarized Fe moments. The giant THE can be related to the field-induced skyrmion structure and the non-collinear spin configuration.

Fe₃Sn₂ single crystals were grown by the Fe flux method.^[37] The x-ray diffraction (XRD) of a single crystal was performed using a Bruker D8 x-ray machine with Cu K_α radiation. Magnetization and electrical transport measurements were carried out in Quantum Design MPMS3 and PPMS-14T, respectively. The longitudinal and Hall electrical resistivities were measured using a four-probe configuration.

The crystal structure of Fe₃Sn₂ is presented in Fig. 1(a), where the Fe–Sn bilayer and Sn layer stack along the c axis alternatively. In an Fe–Sn monolayer, the Fe atoms form a kagome lattice, with the Sn atoms sitting at the centers of the hexagons of the Fe atoms. The Fe–Sn bilayer is composed of two Fe–Sn monolayers shifting from each other by r = a/3 − b/3 − c/8. Then, a graphene-like Sn layer is located between two Fe–Sn bilayers. Figure 1(b) shows the longitudinal resistivity ρ_xx(T ) as a function of temperature at zero field, clearly indicating the metallic behavior of Fe₃Sn₂.

Fig. 1.

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	Fig. 1. (a) Crystal structure of Fe3Sn2 and top view of one Fe–Sn kagome layer. (b) Temperature dependence of ρxx(T ) at zero field.

Figure 2(a) shows the magnetic induction B dependence of magnetization M(B) for the Fe₃Sn₂ single crystal at various temperatures with the field along the c axis. The B is calculated by using formula B = µ₀(H_eff + M) = µ₀(H + (1 − N_d)M), where µ₀H_eff is the effective magnetic field, and N_d (∼ 0.4) is the demagnetizing factor. When the temperature is far below ferromagnetic transition temperature T_C (∼ 641 K),^[37] magnetization M(B) curve of Fe₃Sn₂ increases significantly at the low-field region and then saturates above 1 T because of the complete alignment of Fe moments along the field direction. Moreover, the saturation magnetization M_s increases gradually with decreasing temperature, a typical behavior of ferromagnet due to the suppressed excitation of spin waves. Furthermore, the M_s at 5 K is about 2.19 µ_B/Fe for B||c, well consistent with the values reported in the literature.^[37,42–45]

Fig. 2.

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Fig. 2. (a) Magnetization M(B) as a function of magnetic field B at various temperatures with B||c. (b) Field dependence of Hall resistivity ryx(B) at various temperatures. The color code is the same as in (a). (c) The relationship between ρyx/B and M/B at various temperatures. (d) Field dependence of different components of the Hall resistivity at 220 K. The blue, green, black, and red lines represent the measured ρyx(B), (B), (B), and (B), respectively.

Figure 2(b) presents the B-field dependence of Hall resistivity ρ_yx(B) at various temperatures when the field is applied parallel to the c axis. The ρ_yx(B) curves share similar shape features with M(B), however, there is a key difference between the slopes of the M(B) and ρ_yx(B) curves at the low-field region, implying that there might be a THE contribution to ρ_yx(B). Above the saturated field, the ρ_yx(B) is a linear function of B and decreases slightly, indicating that the dominant carriers in Fe₃Sn₂ are electron-type. As the temperature increases, the saturated value of ρ_yx(B) increases and these saturated values at each temperature are well consistent with those in the previous work.^[37]

To analysis the THE in Fe₃Sn₂ at the low-field region, the Hall resistivity ρ_yx can be expressed as the sum of three different contributions^[14,46]

where the first term is the ordinary Hall resistivity induced by the Lorentz force with the ordinary Hall coefficient R₀, the second term is the intrinsic anomalous Hall resistivity and S_H corresponds to the anomalous Hall coefficient with S_H being field independent.^[47] The last term represents the topological Hall resistivity arising from scalar spin chirality. When the applied field is strong enough, is supposed to be zero due to the disappearance of chiral spin texture. Hence, using the formula , the R₀ and S_H can be determined from the y-axis intercept and slope of the linear fit of ρ_yx/B vs. curve in the high-field region, as shown in Fig. 2(c). Here, the fitting range is between 1.4 T and 5.5 T, below this region the curves deviate from linearity, implying the emergence of THE. The R₀ determined from this scaling is negative at various temperatures, confirming that the electron-type carrier is dominant in Fe₃Sn₂. The magnitude of R₀ is about 1×10⁻⁸ Ω·cm·T⁻¹, well consistent with the reported value.^[37] The S_H is almost a constant (∼ 0.033–0.039 V⁻¹) and it turns out that the intrinsic mechanism makes a dominant contribution to the anomalous Hall resistivity for all temperatures at high field.^[47]

Then the values of can be obtained by extracting the calculated and from the total ρ_yx. As shown in Fig. 2(d), at a selected temperature T = 220 K, (green line) and (black line) are calculated by using the fitted R₀ and S_H values. Accordingly, we obtain the field dependence of (red line). It can be clearly seen that the curve shows a hump-like shape and the maximum value is −1.06 µΩ·cm at 0.77 T (B_max), which is taken as the evidence of THE.^[15,17] The derived at various temperatures from 5 K to 300 K is presented in Fig. 3(a). A sizable can be observed over the whole temperature range and the sign of is negative at all temperatures. The absolute value of increases firstly, then goes through a maximum with increasing field. Finally, it disappears when the field is higher than 1.3 T, possibly due to the fully alignment of Fe moments along the field direction. This result is well consistent with the saturated field of the M(B) curve. Although the B_max is almost temperature independent (∼ 0.8 T), the amplitude of increases monotonically with increasing temperature, as shown in Fig. 3(b). The largest (∼ 2.01 µΩ·cm at B = 0.76 T) appears at 300 K, much larger than those of other skyrmion hosting materials such as MnSi (4 nΩ·cm),^[15] FeGe (0.16 µΩ·cm),^[20] and MnNiGa (0.15 µΩ·cm).^[22]

Fig. 3.

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	Fig. 3. (a) Magnetic field dependence of extracted from total Hall resistivity ρyx(B) at various temperatures. (b) Maximum values of topological Hall resistivity as a function of temperature.

According to the phase diagram of magnetic structure in a previous work,^[40] the B_max seems to be very close to the boundary area of the transition from magnetic bubbles to skyrmionic bubbles, and the corresponding filed of vanished is located in the region in which skyrmionic bubbles have disappeared. It seems that the THE might be related to the skyrmion state. If so, in the skyrmion state, the can be written as , where P denotes the local spin polarization of the conduction electron, is the fictitious effective field, and z is the corresponding direction of the applied field.^[15] The polarization P is determined by the ratio between the ordered magnetic moment µ_spo in the Skyrmion phase and the saturated moment µ_sat taken from the Curie– Weiss moment in the paramagnetic state or the free Fe moment in form of P = µ_spo/µ_sat.^[15] For Fe₃Sn₂, the µ_spo at 300 K is 1.764 µ_B/Fe at 0.76 T and the µ_sat (300 K) is 1.996 µ_B/Fe if taken the saturated moment at 5.48 T as an approximate value. Hence, the estimated value of P is 0.88. Taking R₀ = −4.98(1) × 10⁻⁴ cm³/C and , the evaluated is 45.8 T. In the triangular skyrmion crystal,^[40] the emergent magnetic field , where ϕ₀ (=h/|e| = 4.14×10⁻¹⁵ J/A) is the flux quantum for a single electron with h the Planck constant, and λ is the helical period.^[14] Hence, the calculated λ is ∼ 8.8 nm, much smaller than the periodicity of skyrmionic bubbles (∼ 500 nm) at the same field,^[40] indicating that the giant THE can not be ascribed solely to the field-induced skyrmion structure. In addition, the skyrmionic bubble phase only appears above 100 K. But here, the THE can be still observed when the temperature is below 100 K. According to previous results of powder neutron diffraction,^[42] there is a spin reorientation transition from the c axis to the ab plane with decreasing temperature and the moments still do not completely lie in the ab plane at 6 K. During this process, it gives rise to a non-collinear spin configuration,^[42] possibly leading to a nonzero scalar spin chirality. Thus, both of skyrmion state and non-collinear spin structure will contribute to the extremely large THE in Fe₃Sn₂, especially when T > 100 K.

In summary, Fe₃Sn₂ shows a giant THE which is observed below 1.3 T at various temperatures. The reaches a maximum value ∼ 2.01 µΩ·cm at 300 K and 0.76 T. When the field is larger than 1.3 T, the THE disappears as the Fe moments are fully polarized. Detailed analysis suggests that the THE results from the topological magnetic structure in real space. This study will not only deepen our understanding on THE in frustrated magnets, but also help to explore novel frustrated materials with exotic physical properties.