Fe-Sn nanocrystalline films for flexible magnetic sensors with high thermal stability

The interplay of magnetism and spin-orbit coupling on an Fe kagome lattice in Fe3Sn2 crystal produces a unique band structure leading to an order of magnitude larger anomalous Hall effect than in conventional ferromagnetic metals. In this work, we demonstrate that Fe-Sn nanocrystalline films also exhibit a large anomalous Hall effect, being applicable to magnetic sensors that satisfy both high sensitivity and thermal stability. In the films prepared by a co-sputtering technique at room temperature, the partial development of crystalline lattice order appears as nanocrystals of the Fe-Sn kagome layer. The tangent of Hall angle, the ratio of Hall resistivity to longitudinal resistivity, is maximized in the optimal alloy composition of close to Fe3Sn2, implying the possible contribution of the kagome origin even though the films are composed of nanocrystal and amorphous-like domains. These ferromagnetic Fe-Sn films possess great advantages as a Hall sensor over semiconductors in thermal stability owing to the weak temperature dependence of the anomalous Hall responses. Moreover, the room-temperature fabrication enables us to develop a mechanically flexible Hall sensor on an organic substrate. These demonstrations manifest the potential of ferromagnetic kagome metals as untapped reservoir for designing new functional devices.

Iron-based alloys and compounds have constituted the outstanding basis for applications, particularly with judicious utilization of their rich magnetism and magneto-transport characteristics [1][2][3][4] . To enrich their functionality further, extensive investigations have continued on iron-based ferromagnetic materials including ordered alloys 5 , oxides 6, and nitrides 7 . In this study, we exemplify magnetic sensor functions in a ferromagnetic iron-tin alloy that is fabricated to harness massive Dirac bands of the kagome metal Fe 3 Sn 2 (ref. 8 ). Magnetic sensors are capable of electrically detecting a magnetic field 9 and are becoming increasingly important towards the acceleration of Internet of Things. Their applications include monitoring of electric current via the Oersted field, electronic compasses and motion detection of mechanical parts in microdevices. In conventional semiconductor Hall sensors, the detection of a magnetic field B (termed instead of magnetic induction, hereafter) relies on the ordinary Hall effect, which converts a flow of electric current to the transverse Hall voltage V yx (ref. 10 ). Since the output V yx is proportional to B and the injection current, good sensor performance under a constant input voltage is achieved in III-V semiconductors such as GaAs, InAs, and InSb with a high carrier mobility 10 . These semiconductor devices are constructed essentially on highly crystalline films with a low carrier density precisely tuned by high-temperature growth. Their bandgaps are, however, inevitably accompanied by substantial temperature (T) dependences of device characteristics. To ensure the stable operation in a wide T range, an external circuit that compensates the T dependence needs to be implemented.
Without changing the basic device structure, the semiconductor can be replaced by a ferromagnetic material if the anomalous Hall effect (AHE) is sufficiently large and provides a linear response to the applied B. V yx induced by AHE is a nominal function of magnetization M and is proportional to tangent of Hall angle, the ratio of Hall resistivity to longitudinal resistivity; materials design is thus better guided with tangent of Hall angle rather than mobility and carrier density. However, conventional ferromagnetic metals such as Fe, Co, and Ni show low tangent of Hall angle values of less than approximately 0.01 (ref. 11 ), and are not suited to AHE-type Hall sensors. In the past two decades, significant progress has been made in the development of AHE materials and understanding of their physical origins 11 . Of particular interest is the intrinsic AHE where Berry curvature arising from electronic band topology acts as an effective magnetic field and can produce a large tangent of Hall angle and V yx .
In this context, a ferromagnetic Fe-Sn compound, Fe 3 Sn 2 (Curie temperature T C = 657 K), is attracting attention because of its very large AHE at room temperature 8,12,13 . The crystal structure consists of alternate stacking of stanene and a bilayer of Fe 3 Sn with a kagome network of Fe, as illustrated in Fig. 1a. A recent angle-resolved photoemission spectroscopic study proposed that an interplay of the kagome lattice, which in analogy to graphene produces linearly dispersed bands and Dirac points, and spin-orbit coupling yields massive Dirac bands that concentrate Berry curvature 8 . By positioning the Fermi level within the gap, e.g. with electrostatic gating and impurity doping, quantized AHE 14,15 may be realized at room temperature. Fe 3 Sn 2 is, however, the high-temperature phase stable above 607 °C; the bulk crystal is formed by a quenching technique 8,12,13,16,17 . Recognizing the uniqueness of Fe 3 Sn 2 , we focus on the thin film of Fe-Sn kagome compounds 18,19 as a candidate for AHE-type Hall sensors (Fig. 1b). Here we demonstrate magnetic sensor functions of nanocrystalline Fe-Sn alloy films prepared by room-temperature sputtering. Despite the lack of macroscopic lattice order, these films clearly bear characteristics of the crystalline Fe-Sn phase diagram and exhibit large and linear AHE responses as in the Fe 3 Sn 2 bulk. This metal-based Hall device can outperform conventional semiconductor Hall sensors in thermal stability. The integration on a bendable polymer sheet thanks to the room-temperature fabrication is demonstrated for potential use in flexible electronics. These findings should accelerate challenges to exploitation of exotic physics hosted by iron and other transition-metal kagome compounds [20][21][22][23] .

Results
Fe-Sn nanocrystalline films grown by co-sputtering at room temperature. Fe x Sn 1−x alloy films were fabricated by a co-sputtering technique 18,19 . The two elements were supplied from a single magnetron cathode by mounting Fe chips on a Sn target (Fig. 1c inset and also see Methods section). In the Fe-Sn binary members 16 , antiferromagnetic FeSn (Néel temperature T N = 368 K) and ferromagnetic Fe 3 Sn (T C = 743 K, refs 24,25 ) also exist, in which the Fe 3 Sn kagome layers are accommodated with different stacking sequences (Fig. 1a). To cover these kagome www.nature.com/scientificreports www.nature.com/scientificreports/ compounds widely, the Fe content x in the films was varied by the Fe chip number as displayed in Fig. 1c. The in-plane distribution of x was as small as a few atomic percent. Figure 1d shows X-ray diffraction (XRD) patterns of films with various x, grown on single-crystalline sapphire (0001) substrates at a growth temperature T g of 500 °C. Nearly equimolar mixture of Fe and Sn (x = 0.54) yields a single phase of FeSn (see Fig. S1 in the Supplementary Information for peak identification). For x = 0.62, diffuse reflections of Fe 3 Sn 2 are recognized though FeSn still remains. For x = 0.78, the Fe 3 Sn phase grows in addition to FeSn. Of the three kagome metals, FeSn is thermodynamically stable and the other two are easily decomposed into FeSn and Sn-rich α-Fe on cooling after high-temperature crystallization 16 ; the above XRD results are consistent with the bulk behavior. As shown in Fig. 1e, the formation of FeSn is found to be suppressed by room-temperature sputtering. Also, macroscopically, the room-temperature grown films do not have crystalline character. Cross-sectional transmission electron microscopy, however, reveals the presence of nanocrystalline domains with typical sizes of as small as a few nanometers, as displayed in Fig. 1f (scale bar, 5 nm). Although d-spacing values calculated from the selected-area electron diffraction pattern (Fig. 1f inset) are not uniquely indexed with one of the three compounds, the clearly visible layered lattice, together with the detailed characterization (Fig. S2 in the Supplementary Information), suggests the existence of Fe 3 Sn 2 -like domains in the nanocrystalline film with x = 0.60. Considering that further characterization is required for the comprehensive phase analysis, we hereafter focus on composition dependent AHE characteristics in these mixed-phase films rather than quantifying physical properties of each phase.

Comparison of anomalous Hall responses in nanocrystalline and polycrystalline films. Contrary
to a naive expectation that the large AHE driven by band topology of the kagome lattice should smear out in such nanocrystalline films, we observed a clear AHE in the room-temperature grown nanocrystalline Fe x Sn 1−x . Figure 2a,b show Hall resistivity ρ yx and magnetization M plots, respectively, measured at 300 K under the out-of-plane B application. It is obvious that ρ yx mirrors M-AHE is mainly responsible for ρ yx . The linear ρ yx response at low magnetic fields and virtually closed hysteresis loops reflect the magnetization vector rotation from the in-plane easy axis to out-of-plane hard axis (Fig. S3 in the Supplementary Information). The wide-range linearity up to about ±0.5 T is beneficial for AHE-type Hall sensors.
The x dependence of saturation ρ yx differs from that of the saturation M (Fig. 2a). To get insights into these composition dependences, we performed control experiments using high-temperature grown polycrystalline Fe x Sn 1−x films (T g = 500 °C), shown in Fig. 2c,d. In the polycrystalline films with x = 0.62 and 0.78, the overall anomalous Hall responses and saturation magnetic fields are similar to those of the nanocrystalline ones. In contrast, AHE and M are considerably small for x = 0.54 in which antiferromagnetic FeSn is dominant as revealed by XRD. In Fig. 2e, these x-dependent AHE properties are summarized using tangent of Hall angle, ρ yx /ρ xx (ρ xx : longitudinal resistivity). As a consequence of a sharp ρ yx peak around x = 0.60 and ρ xx slightly changing with x ( Fig. 2e inset), ρ yx /ρ xx takes a broad maximum around x = 0.60-0.75 in the nanocrystalline films. A weaker but www.nature.com/scientificreports www.nature.com/scientificreports/ similar trend is also seen for the polycrystalline films that partly contain FeSn, Fe 3 Sn 2 , and Fe 3 Sn (Fig. 1d). Note that such a composition dependence is not expected for mere Sn-rich α-Fe.
In Fig. 2f, T dependence of Hall conductivity σ xy = ρ yx /(ρ xx 2 + ρ yx 2 ) is compared for nanocrystalline and polycrystalline films with x ~ 0.6 and also bulk Fe 3 Sn 2 in literature 8 . The occurrence of nearly T-independent σ xy in the polycrystalline films, which resembles the intrinsic behavior in Fe 3 Sn 2 single crystals 8,13 , but with a much smaller σ xy than the bulk value suggests a small fraction of Fe 3 Sn 2 domains crystalized by high-temperature sputtering (T g = 500 °C). Antiferromagnetic FeSn that persistently exists in the polycrystalline film, as found in the decreased M and ρ yx (Fig. 2b,d, and also see Fig. S4 in the Supplementary Information), does not give positive contributions to the AHE. In stark contrast, σ xy in the nanocrystalline film rivals the bulk data in the entire T range. One obvious reason for this is the suppression of FeSn by room-temperature sputtering. Although it is not clear whether the mechanism of the large AHE discussed for Fe 3 Sn 2 single crystals (ref. 8 ) is valid for such nanocrystalline Fe-Sn films, these observations demonstrate that the AHE in the Fe-Sn alloy system is maximized at specific compositions. The large ρ yx and ρ yx /ρ xx observed for x = 0.77 may suggest that ferromagnetic Fe 3 Sn (refs 24,25 ) is also a large AHE material, though the transport properties have not been clarified yet.
Thermal stability of the AHE in room-temperature deposited films. Having confirmed the large AHE in the nanocrystalline Fe x Sn 1−x , we now turn to the characterization as a magnetic sensor element. Taking advantages of room-temperature sputtering, we extend our investigation to more commercially available substrates, glass and flexible polyethylene naphthalate (PEN) sheet (Fig. 3a, also see Fig. 1e for their XRD patterns). T-dependent AHE characteristics of Fe 0.60 Sn 0.40 films with thicknesses d~40 nm, displayed in Fig. 3b, are essentially similar on the three substrates, demonstrating that specific substrates are not required to achieve the large AHE. Magnetic-field sensing can be performed in the almost linear ρ yx − B region, and the differential coefficient, α = dρ yx /dΒ, corresponds to the sensitivity for B via V yx . As displayed in Fig. 3c and inset, α is nearly constant to a large B of approximately 0.5 T, and is rather insensitive to the T variation (red colored regions in the inset). This is more clearly seen in the upper panel of Fig. 3d, where the temperature stability of α is tracked, defined as Δα = (α (T) − α (T = 300 K))/α (T = 300 K). In a general operation range of T = 200-400 K, Δα is within a few percent, corresponding to approximately 0.02%/K. The small variation in ρ xx , shown in the lower panel, gives an advantage over semiconductor devices that are restricted by inherent thermally activated transport 26 .

Characterization of Hall sensor responses and flexibility.
To enhance V yx further in view of the film thickness d (V yx = Ι × ρ yx /d), we examined the lower bound of d. Judging from the d dependences of ρ xx , ρ yx , and ρ yx /ρ xx at B = 2 T (Fig. 4a) and also V yx versus B curves (Fig. 4b), we determine that the applicable large AHE persists down to d = 4 nm. The d decrease to 2 nm is possible for ρ yx , but is accompanied by a sharp rise in ρ xx and the drop of ρ yx /ρ xx . These increase power consumption when supplying a constant excitation current (I). In other www.nature.com/scientificreports www.nature.com/scientificreports/ words, at the fixed input voltage, V yx is reduced by the decreased I. The 1-nm-thick device was no longer conductive; d of approximately 2 nm may be the critical thickness where island-like domains start to coalesce and form conduction paths. As presented in Fig. 4c, by injecting I = 10 mA into the 4-nm-thick device, a large V yx exceeding 0.1 V is generated from a magnetic field of B = 0.5 T.
We would like to here note some specific features, which are potentially utilized for three-dimensional magnetic-field sensing. Figure 4d shows out-of-plane magnetic field angle dependences of R yx under various B, measured for the 4-nm-thick Fe 0.60 Sn 0.40 film on sapphire (0001) (the inset: the schematic measurement configuration). At B = 9 T, R yx obeys a cosθ relation (black dotted curve) as expected from M eff ∝ B eff = Bcosθ with M eff and B eff being the out-of-plane components of magnetization and magnetic field, respectively. As B is decreased, because of the in-plane magnetic easy axis (see Fig. S3 in the Supplementary information), the actual direction of M vector becomes not to fully follow that of B vector, resulting in a deviation from the cosθ relation. Also, the in-plane magnetoresistance R sheet vs φ, shown in Fig. 4e, indicates an anisotropic magnetoresistance effect even at low B = 0.25 T (the inset: the schematic measurement configuration). By combining these anisotropic responses of R yx and R sheet , the magnetic field vector B(θ, φ) could be detected with a simple Hall-bar device.
Nanocrystalline Fe x Sn 1−x as demonstrated above can be served as a Hall-type magnetic sensor. In particular, the capability of sensor integration onto a flexible substrate is appealing, potentially finding applications in flexible electronics 27 . We examined the mechanical bending effect on a nanocrystalline Fe x Sn 1−x device using flexible PEN substrates. Figure 4f demonstrates that, even under severe bending conditions (see Fig. 4g for the definition of bending geometries), the nanocrystalline Fe 0.60 Sn 0.40 device on PEN offers a reversible operation with an almost unchanged sensor performance (Fig. S5 in the Supplementary Information). Such new functionality enabled by nanocrystalline Fe x Sn 1−x films, in combination with its economically and environmentally friendly ingredients, would offer a new type of magnetic sensor design utilizing AHE.

Discussion and Conclusions
Large ρ yx at room temperature has also been obtained in ferromagnetic semiconductors 28 and metal-insulator composites 29 . According to the established classification of AHE origins 11,30,31 , those highly resistive materials, however, are in the poorly conductive region (σ xx < ~3 × 10 3 Ω −1 cm −1 ). Our nanocrystalline Fe x Sn 1−x is essentially a metal with σ xx as high as mid -10 3 -10 4 Ω −1 cm −1 , being in a different category called the intrinsic region (Fig. S6 in the Supplementary Information). In fact, it is observed in nanocrystalline Fe x Sn 1−x films that σ xy is rather independent of σ xx , as being consistent with intrinsic mechanisms. At present, the sensitivity of our device is about one order of magnitude lower than those of the state-of-the-art GaAs and Si Hall sensors 32 . If the Berry curvature mechanism 8 holds for the AHE in nanocrystalline Fe x Sn 1−x films, the device performance could be further improved by Fermi-level tuning into the gap at the Dirac point 8 . Such an intrinsic approach, in addition  Fig. 4g for the definition of x-bent and y-bent. The sample was first measured without bending (flat, black curves), and subsequently characterized under x-bent (red) and y-bent (blue) conditions. After these cycles, the device recovered back to the initial flat state (Fig. S5). (g) Photographs of the x-bent and y-bent devices. 4-nm-thick films on PEN sheet substrates were mounted on the surface of a 4.9-mm-radius semicircular jig in two different geometries.
www.nature.com/scientificreports www.nature.com/scientificreports/ to its critical importance for the next-generation of Hall sensors, may also lead to devices that incorporate exotic quantum transport phenomena, e.g., quantized AHE. We believe that the thin-film structure would be the key enabler for exploration of new functionality that emerges on the kagome lattice.

Methods
Thin-film growth. Fe x Sn 1−x alloy films were fabricated by RF magnetron sputtering. The RF power was 50 W, and Ar gas pressure was 0.5 Pa for x < 0.87 and 0.8 Pa for x = 0.87. The typical growth rate was approximately 4 nm/min as checked by X-ray reflectivity measurement and also with a surface profiler. For films with d ≤ 4 nm, the surface was covered with a 15-nm-thick SiO x insulating layer to prevent oxidation. The SiO x layer was formed by RF magnetron sputtering using a SiO 2 target at an Ar gas pressure of 0.5 Pa. Compositional analysis of the films was performed with energy-dispersive X-ray spectroscopy and inductively coupled plasma atomic emission spectroscopy.
AHE and magnetization measurements. Electrical transport properties were measured with a VersaLab, a Physical Property Measurement System (Quantum Design) and a source-measure unit. Films were patterned into a Hall-bar structure (1b), and electrical contacts were made with an indium solder. The aspect ratio of electrode-electrode distance for V xx versus that for V yx was approximately unity. To remove thermoelectric and geometric effects, the measured data were symmetrized for V xx and anti-symmetrized for V yx against B as widely adopted to these measurements. Magnetization measurements were carried out using a vibrating sample magnetometry mode of VersaLab.