Doping-induced enhancement of anomalous Hall coefficient in Fe-Sn nanocrystalline films for highly sensitive Hall sensors

Magnetic-field sensing^1,2 is one of the core technologies for ubiquitous sensor networks. In widely used semiconductor Hall sensors, a magnetic field (μ₀H, where μ₀ is the vacuum permeability and H is the magnetic field strength) is detected as a transverse Hall voltage (V_yx) generated by the ordinary Hall effect.^3–5 By using high-mobility semiconductors such as GaAs, InAs, and InSb, highly sensitive devices have been developed. With the surging demand for Hall sensors toward the Internet of Things, magnetic materials exhibiting the anomalous Hall effect (AHE)⁶ have garnered attention as a new material resource. While the AHE in conventional ferromagnetic metals^6–8 does not still compete the ordinary Hall effect on the output V_yx, some candidate materials have emerged from recent investigations, including Heusler^9,10 and Fe-Pt alloys,^11–13 Fe₃N,¹⁴ and diluted magnetic semiconductors.^15,16 In our recent study, we reported that ferromagnetic Fe-Sn nanocrystalline films sputtered at room temperature are particularly appealing for AHE-type Hall sensors.¹⁷ The Fe-Sn nanocrystalline films have an in-plane magnetic easy axis; the out-of-plane magnetization increases in proportion to the out-of-plane μ₀H, resulting in the AHE with a large, linear, and nonhysteretic V_yx response against the applied μ₀H up to the saturation field (μ₀H_sat, where H_sat is the strength of saturation magnetic field) as high as 0.5 T. Unlike semiconductors that strongly show temperature (T) dependent conduction, the metal-based material is much less influenced by T variation. These unique characteristics, which are rarely satisfied in other ferromagnetic materials studied to date, allow for practically useful Hall sensor operation with a large V_yx and high thermal stability. Furthermore, the device fabrication on a polymer substrate at room temperature leads to a flexible Hall sensor that is operable under bending conditions. One current challenge toward the applications in AHE-type Hall sensors is to further improve the device performance by controlling the fundamental material’s properties such as the AHE characteristics and magnetism.

In an ideal Hall sensor with a negligibly small contact resistance, the output V_yx is given by $Vyx=ρyxtIin=WLρyxρxxVin$⁠, with I_in being the input (bias) current, V_in being the voltage, ρ_xx being the longitudinal resistivity, ρ_yx being the Hall resistivity, W being the channel width, L being the length (L ≫ W), and t being the thickness.^3–5 When the μ₀H dependence of ρ_xx (i.e., magnetoresistance) is weak in a channel material, the slope of ρ_yx vs μ₀H curves, $dρyxdμ0H$⁠, determines V_yx as per the applied μ₀H when the material is used as a Hall sensor, corresponding to the sensitivity of the Hall sensor. In semiconductor Hall sensors based on the ordinary Hall effect, the above relation is rewritten as $Vyx=RHtμ0HIin=WLμμ0HVin$⁠,^3–5 where R_H is the Hall coefficient and μ is the mobility: the current-related sensitivity $SI=RHt$ (in the unit of V/A/T) and the voltage-related sensitivity $SV=WLμ$ (in the unit of V/V/T = T⁻¹).⁵ Because the T dependence of μ is weaker than that of R_H in narrow bandgap semiconductors used for highly sensitive devices, the V_in-driven mode gives better thermal stability in terms of sensitivity;⁵ however, an external circuit that compensates the strongly T-dependent transport characteristics is unavoidable to guarantee the actual device operation over a wide T range. By contrast, in AHE-type Hall sensors utilizing materials with ρ_yx predominantly contributed by the AHE, V_yx is determined directly by AHE-related parameters since ρ_yx is empirically expressed as ρ_yx = R₀μ₀H + R_AM, where R₀ is the ordinary Hall coefficient, R_A is the anomalous Hall coefficient, and M is the magnetization.^18,19 In metallic materials where ρ_yx and ρ_yx/ρ_xx are insensitive to T like Fe-Sn nanocrystalline films,¹⁷ device operation over a wide T range is feasible either by the I_in-driven mode or the V_in-driven mode without an external circuit.

A noticeable feature found in Fe_0.6Sn_0.4 nanocrystalline films is that the AHE bears a close resemblance to that of bulk single crystals of Fe₃Sn₂, which is isocompositional to Fe_0.6Sn_0.4 but is a crystalline intermetallic compound.^20–22 It has been proposed for Fe₃Sn₂ that a specific topology of the Fe kagome lattices, in combination with spin-orbit coupling (SOC), creates linearly dispersed spin-split bands near the Fermi level, giving rise to the large AHE at room temperature.²² The electrical transport and photoemission spectroscopy measurements as well as the tight-binding band calculation point that the SOC-induced band anticrossing near the Fermi level makes the intrinsic AHE contribution prominent.²² In such AHE of intrinsic origin, anomalous Hall conductivity $σxy=ρyxρxx2+ρyx2$ takes a constant value of the order of 10²–10³ Ω⁻¹ cm⁻¹, while longitudinal conductivity $σxx=ρxxρxx2+ρyx2$ varies from mid-10³ to nearly 10⁶ Ω⁻¹ cm⁻¹.^6,8 As reported previously, σ_xy and σ_xx of Fe_0.6Sn_0.4 nanocrystalline films are within the intrinsic AHE regime.¹⁷ Given that the intrinsic contribution prevails even in the AHE of Fe_0.6Sn_0.4 nanocrystalline films, these AHE-related parameters could be increased by modification of the electronic structure and/or the Fermi level as well as control of magnetic properties. In this study, by doping impurities into Fe-Sn nanocrystalline films, we aimed to control the intrinsic AHE and increase $dρyxdμ0H$ for highly sensitive AHE-type Hall sensors. Through exploratory experiments using various dopants, we found that some heavy transition elements substantially increase ρ_yx and also $dρyxdμ0H$⁠, especially at low field. The concomitant decrease in M suggested the increased R_A in the doped Fe-Sn nanocrystalline films. On the basis of these results, we propose that the tuning of SOC by impurity doping is the key to improving the device performance of Fe-Sn based AHE-type Hall sensors.

Fe-Sn films were grown on Al₂O₃ (0001) substrates at room temperature by radio-frequency magnetron sputtering using Fe-Sn mosaic targets.¹⁷ Doping was performed by adding Ta, W, Pt, Mo, Mn, In, and Ge chips on the Fe-Sn target surface. The crystallinity and t of the films were evaluated by X-ray diffraction (XRD) and X-ray reflectivity measurements using Cu K_α radiation (see supplementary material Fig. S1 for typical XRD patterns of doped Fe-Sn films). The composition was analyzed by energy-dispersive X-ray spectroscopy (EDX). For the microstructural analysis, cross-sectional transmission electron microscopy (TEM) and EDX elemental mapping were carried out. The electrical properties were measured with a VersaLab (Quantum Design, Inc.). μ₀H was applied perpendicular to the film plane. To cancel thermoelectric and geometric contributions, the measured V_yx was antisymmetrized against the applied μ₀H. M was measured with a vibrating sample magnetometer in the VersaLab.

The t and compositions of doped Fe-Sn films, together with nondoped Fe_xSn_1−x films with varied x (Ref. 17), are listed in Table I. In nondoped Fe_xSn_1−x films, ρ_yx in the saturated state peaks around x = 0.6–0.7 at T = 300 K.¹⁷ Using Fe_0.602Sn_0.398 (Sample N2) that shows the largest ρ_yx = 8.8 µΩ cm at μ₀H = 1 T (≫μ₀H_sat) among nondoped Fe_xSn_1−x films as the reference, we study the doping effect on the AHE characteristics. As the dopant (X) elements had different deposition rates at a given sputtering condition, we first checked the composition of Fe-Sn-X films with each preliminary target configuration. Subsequently, by modifying the target configurations, we regulated the supplies of Fe, Sn, and X and obtained the Fe-Sn-X films with (Fe + X)/Sn and Fe/(Sn + X) atomic ratios of approximately 0.6–0.7 for X = Ta, W, Pt, Mo, and Mn and for X = In and Ge. Here, we assume that transition elements (typical elements) are substituted for Fe (Sn) in both nanocrystalline and amorphouslike regions in Fe-Sn films,¹⁷ because of comparable atomic radii: Fe 1.26 Å, Ta 1.46 Å, W 1.40 Å, Pt 1.38 Å, Mo 1.39 Å, Mn 1.30 Å, Sn 1.58 Å, In 1.66 Å, and Ge 1.39 Å.²³ Accordingly, the nominal doping level is defined as X/(Fe + X) for X = Ta, W, Pt, Mo, and Mn and X/(Sn + X) for X = In and Ge. In a general sense of impurity doping, the doping level studied in this work is rather high. Because no qualitative differences were recognized in the structural characterization between nondoped and Fe-Sn films with high impurity contents, we use the term of doping for the present results.

Figure 1(a) shows ρ_yx vs μ₀H curves of nondoped Fe_0.602Sn_0.398 (N2) and Ta-doped (T4, T5, T7, T8, and T9) Fe-Sn films at T = 300 K. In the nondoped Fe_0.602Sn_0.398 film, ρ_yx increases linearly until being saturated at μ₀H_sat = 0.54 T. As indicated by the arrow, μ₀H_sat is determined from the intersection of two linear fits to the low-field (0–0.2 T) and high-field (2–3 T) data. This saturation behavior corresponds to the completion of magnetization rotation from the in-plane easy axis to the out-of-plane hard axis [see Fig. S2(a) for M vs μ₀H curves]. As can be found from the subtle change in ρ_yx above μ₀H_sat, the measured ρ_yx is governed by R_AM (≫R₀μ₀H). By doping a moderate level of Ta, ρ_yx is clearly increased (T4 and T5), whereas the small ordinary Hall contribution does not change much. The increased ρ_yx, together with the unchanged or slightly decreased μ₀H_sat, makes $dρyxdμ0H$ much larger than that in the nondoped Fe_0.602Sn_0.398 film. As the Ta doping level is increased (T7), the saturated ρ_yx value is decreased while the large $dρyxdμ0H$ at relatively low field is maintained. In heavily Ta-doped Fe-Sn films (T8 and T9), ρ_yx vs μ₀H curves become nonlinear in the whole field range. Figures 1(b)–1(d) display the results for the other dopants. The W-doped (W1 and W2) and Mo-doped (O1) Fe-Sn films show the increased $dρyxdμ0H$ at low field as well. However, ρ_yx decreases drastically at the Mo doping level of 0.18 (O2), which is very low as compared to the Ta doping level of about 0.35 in Ta-doped Fe-Sn films [also see Fig. 3(b)]. The Pt, Mn, and Ge doping (P1, M1, and G1) are not effective for the increase in ρ_yx and $dρyxdμ0H$⁠. The Mn-doped Fe-Sn film (M1) behaves like the Fe-poor Fe_0.497Sn_0.503 film (N1). This Fe-poor film is regarded as a disordered form of the antiferromagnetic FeSn crystal (Fe:Sn = 1:1).^24,25 We speculate from the much decreased M [Fig. S2(a)] that 3d Mn might favor antiferromagnetic interactions. In Fig. 1(d), the In doping keeps ρ_yx and $dρyxdμ0H$ as large as those in the nondoped Fe_0.602Sn_0.398 film at the low In doping level (I1 as compared to I2). These results illuminate the distinct contributions of dopants to the AHE of Fe-Sn nanocrystalline films.

Before going into detailed characterization of the AHE characteristics, we inspect the film structure of Ta-doped Fe-Sn films where the large increase in ρ_yx was observed. From the microstructure observation by TEM, Ta-doped Fe-Sn films were found to have crystallized nanodomains in the disordered amorphous matrix [Figs. S3(a) and S3(b)], as those observed for the nondoped Fe_0.602Sn_0.398 film.¹⁷ Using EDX elemental mapping, we analyzed the spatial distribution of doped Ta atoms (T4). Figures 2(a)–2(f) display a high-angle annular dark-field scanning TEM image and the corresponding elemental mapping data taken around the film/substrate interface, respectively. The O-rich surface region [Fig. 2(c)] is presumably due to the natural oxidation layer by air exposure. In the film region, Fe, Sn, and Ta are detected. Although their intensities differ a little according to location, it is obvious that Ta atoms distribute over the film without appreciable segregation. Because of the limited spatial resolution of EDX mapping, it is difficult to directly confirm the existence of Ta atoms in the crystallized nanodomains. However, taking into account quenching-like effect by the room-temperature sputtering process, we speculate that Ta atoms are incorporated both in the crystallized nanodomains and disordered amorphous matrix. It is therefore reasonable to consider that the Ta-doped Fe-Sn film is an Fe-Sn-Ta alloy rather than a phase-separated composite of Fe-Sn and Ta nanoclusters.

In Figs. 3(a) and 3(b), ρ_xx and ρ_yx of Ta-doped Fe-Sn films at T = 300 K and μ₀H = 1 T (≫μ₀H_sat) are plotted as functions of the Ta doping level, Ta/(Fe + Ta). ρ_xx is increased by the Ta doping, albeit with some fluctuations. On the other hand, ρ_yx varies more systematically. At the Ta doping level around 0.33 (T4 and T5), ρ_yx marks 11.7 µΩ cm, which is by 33% larger than the original ρ_yx value of 8.8 µΩ cm (N2). ρ_yx turns to decrease with further increasing the Ta doping level. In the triangular-based Fe kagome-lattice planes, impurity doping into over 1/3 of Fe sites should disrupt in-plane ferromagnetic interactions. In fact, M of the optimally Ta-doped Fe-Sn film (T5) is reduced by approximately 60% [Fig. S2(a)] despite the Ta doping level of 0.34. This also supports our naive assumption that Ta is substituted for Fe. It is noted here that the observed changes in ρ_xx and ρ_yx have no particular relevance to t (Table I). In the nondoped Fe_0.602Sn_0.398 film, both ρ_xx and ρ_yx reach constant values above t of about 10 nm.¹⁷ Hence, in the much thicker Ta-doped Fe-Sn films used (t = 37–65 nm), the t dependences are negligible. Figures 3(c) and 3(d) show the Ta doping level dependences of μ₀H_sat and $dρyxdμ0H$ calculated for μ₀H ≤ 0.2 T, respectively. Although μ₀H_sat and M [Fig. S2(a)] get smaller with the Ta doping, $dρyxdμ0H$ increases up to the Ta doping level of 0.39 (T7). At the relatively low Ta doping level (T1–4), the increase in ρ_yx [Fig. 3(b)] is responsible for the increased $dρyxdμ0H$⁠. At the higher Ta doping level (T5–7), ρ_yx does not increase, but μ₀H_sat in turn decreases probably by the reduction in M (and/or the weakening of magnetic anisotropy), making $dρyxdμ0H$ even larger. These results demonstrate that $dρyxdμ0H$ in the low field region can be twice as large as that in the nondoped Fe_0.602Sn_0.398 film by doping Ta impurities.

Figure 4(a) shows ρ_yx vs μ₀H curves measured for the optimally Ta-doped Fe-Sn film (T5) at T = 400–50 K. In the linear Hall response region at low field, the curves show almost identical traces, namely, with the constant $dρyxdμ0H$ value. In Figs. 4(b)–4(e), the T dependences of ρ_xx and ρ_yx at μ₀H = 1 T, μ₀H_sat, and M at μ₀H = 1 T [Fig. S2(a)] are displayed, respectively. While ρ_xx only weakly depends on T, ρ_yx and μ₀H_sat as well as the M increase gradually with decreasing T. The T dependences of these ferromagnetism-related parameters (ρ_yx, μ₀H_sat, and M) can be understood as being due to the decrease in Curie temperature T_C by Ta impurities. Although the actual T_C in the nondoped Fe_0.602Sn_0.398 film (N2) has yet to be determined because of the difficulty of high-T M measurement, a T_C of ≫400 K is inferred from the very weak T-dependent AHE characteristics¹⁷ and the analogy to Fe₃Sn₂ with T_C = 657 K.^20–22 The substitution of Ta for Fe, which is responsible for the ferromagnetic interactions in Fe-Sn nanocrystalline films, could lower M [Fig. S2(a)] and thus T_C. As a result, the T dependences of M and ρ_yx and μ₀H_sat become stronger than in the nondoped Fe_0.602Sn_0.398 film. However, we should stress here that $dρyxdμ0H$ at low field remains to be nearly independent of T; the sensitivity of an AHE-type Hall sensor is unchanged in the measured wide T range. Similar tendencies were observed for W-doped and Mo-doped Fe-Sn films [Figs. S4(a)–S4(j)]. However, M, ρ_yx, and μ₀H_sat were decreased more rapidly at elevated T despite the comparable M at T = 300 K [Fig. S2(a)]. For further addressing these dopant-dependent magnetic and AHE properties, it will be important to understand the electronic structure of Fe-Sn nanocrystalline films and local atomic environment around dopants.

Having observed the distinct effects of dopants on the AHE, we discuss the possible mechanisms. Judging from the overall tendency, adding heavy transition elements as impurities increases ρ_yx and $dρyxdμ0H$⁠. One feature generic to 5d Ta and W and 4d Mo is strong SOC. According to the critical role of SOC in the large intrinsic AHE of Fe₃Sn₂,²² the additive SOC derived from these impurities might assist the enhancement of intrinsic AHE in Fe-Sn nanocrystalline films. In fact, as presented in Fig. 5(a), σ_xx and σ_xy of doped Fe-Sn films stay in the intrinsic regime, and the relationship is not simply explained by the scaling behavior known for the extrinsic AHE systems.^6–8 Moreover, the much decreased M in doped Fe-Sn films [Fig. S2(b)] points that the increased ρ_yx stems primarily from the enhancement of R_A, which is linked to the topological character of electronic bands. Besides, ρ_yx driven by the intrinsic AHE²² must also depend on the Fermi level. Although quantitative discussion of the Fermi level only with R_H is not easy for such semimetallic systems, we estimate R_H by assuming that the ordinary Hall effect is predominant at high field (μ₀H ≥ 2 T) [Fig. S5(a)]. R_H in the nondoped Fe-Sn film is 1.1 × 10⁻³ cm³ C⁻¹. In In-doped Fe-Sn films, R_H is decreased to 0.66 × 10⁻³ cm³ C⁻¹ (I1) and 0.54 × 10⁻³ cm³ C⁻¹ (I2) and σ_xx is increased with increasing the In doping level [Fig. 5(a)]. In a consistent manner, R_H is increased in Ta-doped, W-doped, and Mo-doped Fe-Sn films that show the decreased σ_xx. Also, σ_xy/σ_xx tends to increase in the small-R_H (high-σ_xx) region [Fig. S5(b)]. The relatively large σ_xy/σ_xx in In-doped Fe-Sn films (0.042 for N2, 0.047 for I1, and 0.060 for I2) implies the enhanced intrinsic AHE in the small-R_H condition. These features are consistent with the expected contribution of the intrinsic AHE, which should be sensitive to the strength of SOC and the Fermi level.

Figure 5(b) summarizes the relationship between $dρyxdμ0H$ and μ₀H_sat at T = 300 K for nondoped Fe_xSn_1−x and doped Fe-Sn films. This plot manifests the main point of this work in that Fe-Sn films doped with Ta, W, and Mo impurities offer the substantially increased $dρyxdμ0H$⁠. Such a high $dρyxdμ0H$ value is not attainable only with varying x in nondoped Fe_xSn_1−x films, corroborating the effectiveness of impurity doping for improving the sensitivity in an AHE-type Hall sensor. Although a slight decrease in μ₀H_sat takes place concomitantly, the increased output V_yx, at least for μ₀H ≤ 0.2 T, should have advantages in practical applications. Notably, in the optimally Ta-doped Fe-Sn film (T5), the improved sensitivity retains the nearly T-independent behavior at low field [Fig. 4(a)], which enables efficient and thermally stable generation of the output V_yx in the I_in-driven mode. In-doped Fe-Sn films with large σ_xy/σ_xx (=ρ_yx/ρ_xx) may have certain merits in the V_in-driven mode. On the basis of the plausible contribution of intrinsic AHE, the simultaneous control of SOC and the Fermi level by codoping, e.g., Fe_1−xTa_xSn_1−yIn_y, is worth considering for further enhancing the Hall sensor performance.

By doping heavy transition elements into ferromagnetic Fe-Sn nanocrystalline films, we have successfully increased ρ_yx and $dρyxdμ0H$⁠. In Ta-doped Fe-Sn films with optimal doping levels of about 0.33, $dρyxdμ0H$ nearly doubled at low field, as compared to that in the nondoped Fe_0.602Sn_0.398 film. W-doped and Mo-doped Fe-Sn films also showed the increased $dρyxdμ0H$ at the low doping levels, but the Pt-doped one failed to increase it. These results suggest that some heavy transition elements are preferentially doped into the Fe sites in the kagome-lattice Fe-Sn nanocrystalline region to enhance the intrinsic AHE by additional contributions due to the strong SOC. These improved AHE characteristics can offer highly sensitive AHE-type Hall sensors with large output V_yx. The easy-to-use doping technique is expected to add a degree of freedom toward the development of superior AHE-type Hall sensors.

See the supplementary material for XRD patterns of Ta-doped, W-doped, and Mo-doped Fe-Sn films (Fig. S1), M vs μ₀H curves and ρ_yx vs M plot (Fig. S2), high-resolution TEM and electron diffraction data (Fig. S3), T dependence of ρ_yx vs μ₀H curves, ρ_xx, ρ_yx, μ₀H_sat, and M for W-doped and Mo-doped Fe-Sn films (Fig. S4), and $dρyxdμ0H$ vs R_H and σ_xy/σ_xx vs R_H plots (Fig. S5).

The authors thank S. Ito for his experimental assistance. This work was supported by JST CREST (Grant No. JPMJCR18T2).