We experimentally investigated the contribution of intrinsic anomalous Hall effect (AHE) in ferromagnetic Fe-Sn nanocrystalline films by means of impurity doping. We found that some heavy transition elements such as Ta, W, and Mo are effective for increasing the anomalous Hall resistivity of Fe-Sn films. The concomitant decrease in magnetization of the Fe-Sn matrix indicated that the increased anomalous Hall resistivity arises from the enhancement of the anomalous Hall coefficient. The increased anomalous Hall resistivity, in combination with the moderately decreased saturation field, substantially increased the derivative of anomalous Hall resistivity with respect to applied magnetic field in the linear Hall response region at low field, which corresponds to the sensitivity in an AHE-type Hall sensor. In particular, optimally Ta-doped Fe-Sn films showed nearly doubled sensitivity in comparison with nondoped Fe-Sn films, while the virtually temperature-independent behavior of the sensitivity was maintained between 400 and 50 K. These improved AHE characteristics enable sensitive detection of magnetic field over a wide temperature range. We discuss that strong spin-orbit coupling inherent to these heavy transition elements contributes to the modification of electronic structure, inducing the large intrinsic AHE. The doping technique demonstrated will be a fundamental strategy for exploiting the performance of Fe-Sn metal-based AHE-type Hall sensors.
Magnetic-field sensing1,2 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 (Vyx) 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 metals6–8 does not still compete the ordinary Hall effect on the output Vyx, some candidate materials have emerged from recent investigations, including Heusler9,10 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 Vyx response against the applied μ0H up to the saturation field (μ0Hsat, where Hsat 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 Vyx 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 Vyx is given by , with Iin being the input (bias) current, Vin being the voltage, ρxx being the longitudinal resistivity, ρyx 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 ρxx (i.e., magnetoresistance) is weak in a channel material, the slope of ρyx vs μ0H curves, , determines Vyx 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 ,3–5 where RH is the Hall coefficient and μ is the mobility: the current-related sensitivity (in the unit of V/A/T) and the voltage-related sensitivity (in the unit of V/V/T = T−1).5 Because the T dependence of μ is weaker than that of RH in narrow bandgap semiconductors used for highly sensitive devices, the Vin-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 ρyx predominantly contributed by the AHE, Vyx is determined directly by AHE-related parameters since ρyx is empirically expressed as ρyx = R0μ0H + RAM, where R0 is the ordinary Hall coefficient, RA is the anomalous Hall coefficient, and M is the magnetization.18,19 In metallic materials where ρyx and ρyx/ρxx are insensitive to T like Fe-Sn nanocrystalline films,17 device operation over a wide T range is feasible either by the Iin-driven mode or the Vin-driven mode without an external circuit.
A noticeable feature found in Fe0.6Sn0.4 nanocrystalline films is that the AHE bears a close resemblance to that of bulk single crystals of Fe3Sn2, which is isocompositional to Fe0.6Sn0.4 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 takes a constant value of the order of 102–103 Ω−1 cm−1, while longitudinal conductivity varies from mid-103 to nearly 106 Ω−1 cm−1.6,8 As reported previously, σxy and σxx of Fe0.6Sn0.4 nanocrystalline films are within the intrinsic AHE regime.17 Given that the intrinsic contribution prevails even in the AHE of Fe0.6Sn0.4 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 for highly sensitive AHE-type Hall sensors. Through exploratory experiments using various dopants, we found that some heavy transition elements substantially increase ρyx and also , especially at low field. The concomitant decrease in M suggested the increased RA 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 Kα 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 Vyx 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 FexSn1−x films with varied x (Ref. 17), are listed in Table I. In nondoped FexSn1−x films, ρyx in the saturated state peaks around x = 0.6–0.7 at T = 300 K.17 Using Fe0.602Sn0.398 (Sample N2) that shows the largest ρyx = 8.8 µΩ cm at μ0H = 1 T (≫μ0Hsat) among nondoped FexSn1−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.
Thicknesses and compositions of nondoped FexSn1−x (Ref. 17) and doped Fe-Sn films (dopant X = Ta, W, Pt, Mo, Mn, In, and Ge).
. | . | Thickness . | Fe:Sn:X . | X/(Fe + X) . | X/(Sn + X) . |
---|---|---|---|---|---|
Sample . | Dopant X . | t (nm) . | (at. ratio) . | (at. ratio) . | (at. ratio) . |
N1 (Ref. 17) | None | 43 | 0.497:0.503:0 | 0 | 0 |
N2 (Ref. 17) | None | 42 | 0.602:0.398:0 | 0 | 0 |
N3 (Ref. 17) | None | 45 | 0.670:0.330:0 | 0 | 0 |
N4 (Ref. 17) | None | 33 | 0.774:0.226:0 | 0 | 0 |
N5 (Ref. 17) | None | 41 | 0.871:0.129:0 | 0 | 0 |
T1 | Ta | 46 | 0.537:0.346:0.117 | 0.18 | … |
T2 | Ta | 41 | 0.524:0.337:0.139 | 0.21 | … |
T3 | Ta | 38 | 0.498:0.323:0.179 | 0.26 | … |
T4 | Ta | 37 | 0.491:0.278:0.231 | 0.32 | … |
T5 | Ta | 50 | 0.446:0.326:0.228 | 0.34 | … |
T6 | Ta | 53 | 0.434:0.313:0.253 | 0.37 | … |
T7 | Ta | 63 | 0.381:0.379:0.240 | 0.39 | … |
T8 | Ta | 58 | 0.386:0.309:0.305 | 0.44 | … |
T9 | Ta | 65 | 0.346:0.293:0.361 | 0.51 | … |
W1 | W | 40 | 0.551:0.349:0.100 | 0.15 | … |
W2 | W | 41 | 0.541:0.325:0.134 | 0.20 | … |
P1 | Pt | 48 | 0.589:0.345:0.066 | 0.10 | … |
O1 | Mo | 42 | 0.575:0.347:0.078 | 0.12 | … |
O2 | Mo | 54 | 0.518:0.370:0.112 | 0.18 | … |
M1 | Mn | 48 | 0.409:0.360:0.231 | 0.36 | … |
I1 | In | 41 | 0.611:0.308:0.081 | … | 0.21 |
I2 | In | 42 | 0.608:0.291:0.101 | … | 0.26 |
G1 | Ge | 47 | 0.583:0.300:0.117 | … | 0.28 |
. | . | Thickness . | Fe:Sn:X . | X/(Fe + X) . | X/(Sn + X) . |
---|---|---|---|---|---|
Sample . | Dopant X . | t (nm) . | (at. ratio) . | (at. ratio) . | (at. ratio) . |
N1 (Ref. 17) | None | 43 | 0.497:0.503:0 | 0 | 0 |
N2 (Ref. 17) | None | 42 | 0.602:0.398:0 | 0 | 0 |
N3 (Ref. 17) | None | 45 | 0.670:0.330:0 | 0 | 0 |
N4 (Ref. 17) | None | 33 | 0.774:0.226:0 | 0 | 0 |
N5 (Ref. 17) | None | 41 | 0.871:0.129:0 | 0 | 0 |
T1 | Ta | 46 | 0.537:0.346:0.117 | 0.18 | … |
T2 | Ta | 41 | 0.524:0.337:0.139 | 0.21 | … |
T3 | Ta | 38 | 0.498:0.323:0.179 | 0.26 | … |
T4 | Ta | 37 | 0.491:0.278:0.231 | 0.32 | … |
T5 | Ta | 50 | 0.446:0.326:0.228 | 0.34 | … |
T6 | Ta | 53 | 0.434:0.313:0.253 | 0.37 | … |
T7 | Ta | 63 | 0.381:0.379:0.240 | 0.39 | … |
T8 | Ta | 58 | 0.386:0.309:0.305 | 0.44 | … |
T9 | Ta | 65 | 0.346:0.293:0.361 | 0.51 | … |
W1 | W | 40 | 0.551:0.349:0.100 | 0.15 | … |
W2 | W | 41 | 0.541:0.325:0.134 | 0.20 | … |
P1 | Pt | 48 | 0.589:0.345:0.066 | 0.10 | … |
O1 | Mo | 42 | 0.575:0.347:0.078 | 0.12 | … |
O2 | Mo | 54 | 0.518:0.370:0.112 | 0.18 | … |
M1 | Mn | 48 | 0.409:0.360:0.231 | 0.36 | … |
I1 | In | 41 | 0.611:0.308:0.081 | … | 0.21 |
I2 | In | 42 | 0.608:0.291:0.101 | … | 0.26 |
G1 | Ge | 47 | 0.583:0.300:0.117 | … | 0.28 |
Figure 1(a) shows ρyx vs μ0H curves of nondoped Fe0.602Sn0.398 (N2) and Ta-doped (T4, T5, T7, T8, and T9) Fe-Sn films at T = 300 K. In the nondoped Fe0.602Sn0.398 film, ρyx increases linearly until being saturated at μ0Hsat = 0.54 T. As indicated by the arrow, μ0Hsat 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 ρyx above μ0Hsat, the measured ρyx is governed by RAM (≫R0μ0H). By doping a moderate level of Ta, ρyx is clearly increased (T4 and T5), whereas the small ordinary Hall contribution does not change much. The increased ρyx, together with the unchanged or slightly decreased μ0Hsat, makes much larger than that in the nondoped Fe0.602Sn0.398 film. As the Ta doping level is increased (T7), the saturated ρyx value is decreased while the large at relatively low field is maintained. In heavily Ta-doped Fe-Sn films (T8 and T9), ρyx 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 at low field as well. However, ρyx 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 ρyx and . The Mn-doped Fe-Sn film (M1) behaves like the Fe-poor Fe0.497Sn0.503 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 ρyx and as large as those in the nondoped Fe0.602Sn0.398 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.
(a) ρyx vs μ0H curves measured at T = 300 K for nondoped (N2)17 and Ta-doped (T4, T5, T7, T8, and T9) Fe-Sn films. The sample information is given in Table I. The two fitting lines (black broken lines) are used for the determination of μ0Hsat (black arrow). (b) W-doped (W1 and W2) and Mo-doped (O1 and O2) Fe-Sn films. (c) Pt-doped (P1) and Mn-doped (M1) Fe-Sn films. An Fe-poor Fe0.496Sn0.504 film (N1) is also included for comparison. (d) In-doped (I1 and I2) and Ge-doped (G1) Fe-Sn films.
(a) ρyx vs μ0H curves measured at T = 300 K for nondoped (N2)17 and Ta-doped (T4, T5, T7, T8, and T9) Fe-Sn films. The sample information is given in Table I. The two fitting lines (black broken lines) are used for the determination of μ0Hsat (black arrow). (b) W-doped (W1 and W2) and Mo-doped (O1 and O2) Fe-Sn films. (c) Pt-doped (P1) and Mn-doped (M1) Fe-Sn films. An Fe-poor Fe0.496Sn0.504 film (N1) is also included for comparison. (d) In-doped (I1 and I2) and Ge-doped (G1) Fe-Sn 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 ρyx 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 Fe0.602Sn0.398 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.
(a) High-angle annular dark-field scanning TEM image of a Ta-doped Fe-Sn film on Al2O3 (0001) (T4). Elemental mapping images using EDX (count mode): (b) Al, (c) O, (d) Fe, (e) Sn, and (f) Ta.
(a) High-angle annular dark-field scanning TEM image of a Ta-doped Fe-Sn film on Al2O3 (0001) (T4). Elemental mapping images using EDX (count mode): (b) Al, (c) O, (d) Fe, (e) Sn, and (f) Ta.
In Figs. 3(a) and 3(b), ρxx and ρyx of Ta-doped Fe-Sn films at T = 300 K and μ0H = 1 T (≫μ0Hsat) are plotted as functions of the Ta doping level, Ta/(Fe + Ta). ρxx is increased by the Ta doping, albeit with some fluctuations. On the other hand, ρyx varies more systematically. At the Ta doping level around 0.33 (T4 and T5), ρyx marks 11.7 µΩ cm, which is by 33% larger than the original ρyx value of 8.8 µΩ cm (N2). ρyx 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 ρxx and ρyx have no particular relevance to t (Table I). In the nondoped Fe0.602Sn0.398 film, both ρxx and ρyx 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 μ0Hsat and calculated for μ0H ≤ 0.2 T, respectively. Although μ0Hsat and M [Fig. S2(a)] get smaller with the Ta doping, increases up to the Ta doping level of 0.39 (T7). At the relatively low Ta doping level (T1–4), the increase in ρyx [Fig. 3(b)] is responsible for the increased . At the higher Ta doping level (T5–7), ρyx does not increase, but μ0Hsat in turn decreases probably by the reduction in M (and/or the weakening of magnetic anisotropy), making even larger. These results demonstrate that in the low field region can be twice as large as that in the nondoped Fe0.602Sn0.398 film by doping Ta impurities.
Ta doping level dependences of (a) ρxx and (b) ρyx at T = 300 K and μ0H = 1 T for nondoped17 (N2 shown by the black square) and Ta-doped (T1–9 by the red circles) Fe-Sn films. The Ta doping level is defined as Ta/(Fe + Ta) (Table I). Ta doping level dependences of (c) μ0Hsat and (d) calculated for μ0H ≤ 0.2 T (N2 and T1–7).
Ta doping level dependences of (a) ρxx and (b) ρyx at T = 300 K and μ0H = 1 T for nondoped17 (N2 shown by the black square) and Ta-doped (T1–9 by the red circles) Fe-Sn films. The Ta doping level is defined as Ta/(Fe + Ta) (Table I). Ta doping level dependences of (c) μ0Hsat and (d) calculated for μ0H ≤ 0.2 T (N2 and T1–7).
Figure 4(a) shows ρyx 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 value. In Figs. 4(b)–4(e), the T dependences of ρxx and ρyx at μ0H = 1 T, μ0Hsat, and M at μ0H = 1 T [Fig. S2(a)] are displayed, respectively. While ρxx only weakly depends on T, ρyx and μ0Hsat as well as the M increase gradually with decreasing T. The T dependences of these ferromagnetism-related parameters (ρyx, μ0Hsat, and M) can be understood as being due to the decrease in Curie temperature TC by Ta impurities. Although the actual TC in the nondoped Fe0.602Sn0.398 film (N2) has yet to be determined because of the difficulty of high-T M measurement, a TC of ≫400 K is inferred from the very weak T-dependent AHE characteristics17 and the analogy to Fe3Sn2 with TC = 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 TC. As a result, the T dependences of M and ρyx and μ0Hsat become stronger than in the nondoped Fe0.602Sn0.398 film. However, we should stress here that 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, ρyx, and μ0Hsat 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.
(a) ρyx vs μ0H curves of a Ta-doped Fe-Sn film (T5) measured at T = 400, 350, 300, 250, 200, 150, 100, and 50 K. The T dependences of (b) ρxx and (c) ρyx at μ0H = 1 T, (d) μ0Hsat, and (e) M at μ0H = 1 T.
(a) ρyx vs μ0H curves of a Ta-doped Fe-Sn film (T5) measured at T = 400, 350, 300, 250, 200, 150, 100, and 50 K. The T dependences of (b) ρxx and (c) ρyx at μ0H = 1 T, (d) μ0Hsat, and (e) M at μ0H = 1 T.
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 ρyx and . 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), σxx and σxy 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 ρyx stems primarily from the enhancement of RA, which is linked to the topological character of electronic bands. Besides, ρyx driven by the intrinsic AHE22 must also depend on the Fermi level. Although quantitative discussion of the Fermi level only with RH is not easy for such semimetallic systems, we estimate RH by assuming that the ordinary Hall effect is predominant at high field (μ0H ≥ 2 T) [Fig. S5(a)]. RH in the nondoped Fe-Sn film is 1.1 × 10−3 cm3 C−1. In In-doped Fe-Sn films, RH is decreased to 0.66 × 10−3 cm3 C−1 (I1) and 0.54 × 10−3 cm3 C−1 (I2) and σxx is increased with increasing the In doping level [Fig. 5(a)]. In a consistent manner, RH is increased in Ta-doped, W-doped, and Mo-doped Fe-Sn films that show the decreased σxx. Also, σxy/σxx tends to increase in the small-RH (high-σxx) region [Fig. S5(b)]. The relatively large σxy/σxx 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-RH 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.
(a) σxy vs σxx plot at T = 300 K and μ0H = 1 T (≫μ0Hsat). The dashed lines represent σxy/σxx values of 0.10 and 0.01. (b) vs μ0Hsat plot for nondoped FexSn1−x (Ref. 17) and doped Fe-Sn films at T = 300 K.
(a) σxy vs σxx plot at T = 300 K and μ0H = 1 T (≫μ0Hsat). The dashed lines represent σxy/σxx values of 0.10 and 0.01. (b) vs μ0Hsat plot for nondoped FexSn1−x (Ref. 17) and doped Fe-Sn films at T = 300 K.
Figure 5(b) summarizes the relationship between and μ0Hsat at T = 300 K for nondoped FexSn1−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 . Such a high value is not attainable only with varying x in nondoped FexSn1−x films, corroborating the effectiveness of impurity doping for improving the sensitivity in an AHE-type Hall sensor. Although a slight decrease in μ0Hsat takes place concomitantly, the increased output Vyx, 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 Vyx in the Iin-driven mode. In-doped Fe-Sn films with large σxy/σxx (=ρyx/ρxx) may have certain merits in the Vin-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., Fe1−xTaxSn1−yIny, 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 ρyx and . In Ta-doped Fe-Sn films with optimal doping levels of about 0.33, nearly doubled at low field, as compared to that in the nondoped Fe0.602Sn0.398 film. W-doped and Mo-doped Fe-Sn films also showed the increased 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 Vyx. 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 ρyx vs M plot (Fig. S2), high-resolution TEM and electron diffraction data (Fig. S3), T dependence of ρyx vs μ0H curves, ρxx, ρyx, μ0Hsat, and M for W-doped and Mo-doped Fe-Sn films (Fig. S4), and vs RH and σxy/σxx vs RH plots (Fig. S5).
The authors thank S. Ito for his experimental assistance. This work was supported by JST CREST (Grant No. JPMJCR18T2).