Introduction

Topological materials provide a promising platform for exploring intriguing physics and designing new materials1,2,3. Given the unique chiral topological surface/edge states in topological materials4,5,6, they have been proposed to be used to design  novel spin-orbit torque (SOT) memory and logic devices with large spin-torque efficiency (θSH)7,8,9,10,11,12. Most notable technological advancements are the demonstration of θSH >10 with the switching current density (Jc) lower than 106 A/cm2 in sputtered topological insulators at room temperature10,11,12. Most recent efforts, however, have shifted to the exploration of novel topological semimetals, which possess the exotic physics of the topological bulk states with conduction and valence bands touching at points (WSM/DSM) or lines (nodal line semimetals)6,13,14,15,16, which could benefit more energy-efficient and industry-compatible SOT memory and logic devices. Recently, a relatively large θSH and SOT magnetization switching through several topological semimetals have indeed been experimentally demonstrated17,18,19,20,21,22,23,24, hence ushering in their exploration for topological spintronic applications.

One of the most intriguing transport phenomena in topological semimetals is the chiral (Adler-Bell-Jackiw) anomaly, which predicts the transfer of Weyl Fermions with opposite chirality in the presence of parallel electric and magnetic fields13,14,15,16,25,26,27,28. Negative longitudinal magnetoresistance (NLMR) is one of the manifestations of chiral anomaly and commonly considered as an experimental signature of topological semimetals29,30,31,32,33,34, as reported in Na3Bi13,27, TaAs14,15,16, WTe235, ZrTe536, Cd3As237,38, TaP39, among many others. However, the exact origin of NLMR is still an open debate as there are alternative thin film material systems showing NLMR absence of chiral anomaly, such as topological insulators or disordered semiconductors, whose origin are attributed to Berry curvature induced anomalous velocity and its derivative orbital moment or Zeeman effect on percolating current pathways in disordered bulk40,41,42,43,44,45,46.

Recent theoretical works also predict a linear NLMR in time-reversal symmetry (TRS) breaking WSM instead of quadratic NLMR in the TRS counterpart based on Onsager’s relations, where electric current depends linearly on the magnetization31,32,33. Contrary to typical magneto-transport experiments, the NLMR associated with chiral anomaly in a thin film semimetal relies only on the in-plane magnetic field. This effect should be accompanied by additional contributions of the conventional positive magnetoresistance (MR) due to carrier localization induced by the out-of-plane magnetic field. Systematic angle dependent (both in-plane azimuthal and out-of-plane polar angles) magneto-transport study of topological semimetals with/without TRS breaking would allow us to validate and reconcile these different contributions.

Recently, binary Pt-Sn alloys have been identified as a new family of topological materials, which have five known stable phases of different compositions that show rich topological properties. Besides the PtSn4 single crystal, which has already been demonstrated experimentally to be a nodal line Dirac semimetal47, a more interesting Pt3Sn alloy has been predicted theoretically to be a promising three-dimensional weak topological insulator hosting type-II Dirac fermion48. However, there is no experimental investigation of its topological properties and application in spintronic devices to-date. Meanwhile, fabrication process of a high-ordered and industrial-compatible Pt3Sn is less challenging compared to some topological materials (e.g. Bi2Se310 and WTe220,23).

In this work, we successfully fabricate highly ordered Pt3Sn with/without seed layers and Fe-doped Pt3Sn (Pt3SnxFe1−x) thin films through sputtering deposition that provides seamless integration with the industry development of memory and logic devices for CMOS technology integration. The Pt3Sn with/without seed layers and Pt3SnxFe1−x samples show a surprising robust quadratic and linear NLMR, respectively. These results are consistent with the topological semimetal phases of the Pt3Sn and Pt3SnxFe1−x samples with and without TRS, respectively, which is further corroborated by our DFT calculations. Meanwhile, both azimuthal and polar angular sweepings of the magnetic field reveal a NLMR behavior that is commensurate with the phenomenon of chiral anomaly and can be reliably reproduced within a simple model. Furthermore, we calculate the spin Hall conductivity to be ~4.34 × 105 ℏ/2e (Ω ⋅ m)−1 for Pt3Sn, which is two times larger than that of DSM PtTe2 (0.2–2 × 105 ℏ/2e (Ω ⋅ m)−1) and WSM WTe2 (2.04 × 105 ℏ/2e (Ω ⋅ m)−1)21,49. θSH of the Pt3Sn and Pt3SnxFe1-x thin films is evaluated to be ~ 0.4 and 0.38, respectively, as characterized by spin-torque ferromagnetic resonance (ST-FMR) measurement, which is several times larger than that of PtTe2 (~0.1)21 and WTe2 (~0.2)19 with the same thickness.

Results

Crystalline structure of Pt3Sn and Pt3SnxFe1-x

The crystallinity and microstructure are investigated for the Pt3Sn, Pt3SnxFe1−x, Pt-seeded Pt3Sn, and Mo-seeded Pt3Sn thin films deposited on (001) single-crystal MgO substrates with substrate heating at 350 °C. Figure 1a shows the crystalline structure of Pt3Sn and Pt3SnxFe1−x samples by x-ray diffraction (XRD). We can clearly observe the (111) textured growth for Pt3Sn and Pt3SnxFe1−x samples with the (111) peak, which is like the Pt reference sample on MgO substrate. We also observe a small (002) peak for both samples, indicating that these Pt3Sn thin films have (002) orientated grains only in some regions while the dominant texture is along the (111) direction. To further confirm the crystalline orientation, we carried out reciprocal space mapping (RSM) measurements, in units of the MgO lattice (4.212 Å), by XRD, as shown in Fig. 1b. Both (111) and (002) diffraction patterns can be seen for Pt3Sn and Pt3SnxFe1−x samples, confirming high-ordered phase. For Pt3Sn thin films with seed layers, Pt seed layer can maintain the (111) texture with certain (002) orientated grains, the same as Pt3Sn and Pt3SnxFe1−x. However, a Mo seed layer induces the (002) texture, as shown in Fig. S1a, b in Supplemental Information (SI). To further investigate the microstructure and chemical composition of the samples, scanning transmission electron microscopy (STEM) measurements were conducted for Pt3Sn, Pt3SnxFe1−x, and Mo-seeded Pt3Sn samples (Figs. 1c, d, and S2). From the atomic-resolution STEM images, it was confirmed that both Pt3Sn and Pt3SnxFe1−x samples show primarily (111) textured grains with in-plane twist between them as well as some grains with a (002) texture (Fig. 1c). Mo-seeded Pt3Sn sample exhibits only (002) growth (see Fig. S2 for details). STEM-energy dispersive X-ray (EDX) analysis was performed (Fig. 1d). Atomic-resolution EDX elemental maps show that the atomic positions of Sn and Fe are overlapping, which directly demonstrates that the Fe atoms are located at the Sn sites. The Fe atoms substituting Sn atoms is also evidenced from comparison of two EDX spectra from Pt3SnxFe1−x and Pt3Sn samples (see Fig. S2b), where a relative increase of Fe K peaks and decrease of Sn L peaks in Pt3SnxFe1−x can be seen.

Fig. 1: Crystalline structure of the Pt3Sn samples.
figure 1

a Specular (θ−2θ scans) XRD patterns of the Pt reference, Pt3Sn and Pt3SnxFe1-x thin films. b Reciprocal space maps (RSM) around the (002) Bragg reflection of the MgO substrate of the Pt3Sn and Pt3SnxFe1−x thin films. Both the Pt reference and the Pt3Sn and Pt3SnxFe1-x thin films grow epitaxially on the MgO substrate along the (111) direction. The XRD experiments show a small amount of (001) oriented grains. c HAADF-STEM images of the Pt3Sn thin film on the MgO substrate. Low-magnification image (top panel) shows the Pt3Sn film and capping layers with relatively uniform thicknesses. Atomic-resolution HAADF-STEM images obtained from (111) oriented (bottom-left) and (002) oriented (bottom-right) grains demonstrate their crystalline orientations. Fast Fourier transforms (FFTs) from the (111) and (002) oriented grains are also displayed (bottom-middle). d Atomic-resolution HAADF-STEM image and EDX elemental maps of the Pt3SnxFe1−x. Schematic of the atomic structure is illustrated along with elemental line profiles, extracted from the region in the yellow-dashed line on the HAADF-STEM image.

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Robust negative magnetoresistance of Pt3Sn and Pt3SnxFe1-x

To investigate the topological properties, the Pt3Sn and Pt3SnxFe1−x samples were patterned into Hall bar devices with 12-μm width and 144-μm length by using an optical lithography process. The electric-transport properties were tested by a physical property measurement system, as illustrated in Fig. 2a. The resistivity (ρxx) is measured and calculated to be 162 μΩ.cm and 114 μΩ.cm for Pt3Sn and Pt3SnxFe1−x at room temperature, respectively (see Fig. S3a in SI). With decreasing temperature, ρxx exhibits a metallic behavior, reaching at 1.9 K a residual value ρ0 of ~83 μΩ.cm and 79 μΩ.cm for Pt3Sn and Pt3SnxFe1−x, respectively, due to carrier scattering with impurities or lattice defects. The residual resistivity ratio RRR = ρ(300 K)/ρ(0) ~ 1−2 signals high quality of the studied thin film materials. Meanwhile, the magnetoresistance (MRxx) vs. external magnetic field (Hext) and Hall resistivity (Rxy) vs. Hext of these Pt3Sn and Pt3SnxFe1-x Hall bar devices were measured at 1.9 K for different angles θ and φ [θ represents the out-of-plane polar angle between Hext and the z-axis; φ denotes the in-plane azimuthal angle between Hext and the x-axis (see Fig. 2a) where the electric current (Ic) is applied along the x-axis], as plotted in Fig. 2c−f. As shown in Fig. 2c, we can clearly see that the measured MRxx is surprisingly negative when θ < 15° and becomes positive while θ > 15° for the Pt3Sn Hall bar device with a wide range of Hext.

Fig. 2: Characterization and physical origin of robust NLMR.
figure 2

a The photo image of Hall bar devices used for electric-transport measurements. Where the current (Ic) is applied along x-axis, the external magnetic field (Hext) rotates along xz plane with angle θ [out-of-plane magnetoresistance (MRxx)] and xy plane with angle φ (in-plane MRxx), respectively. b Schematic of three-resistor model with conventional resistor (color blue) each connected in series (\({R}_{c}^{s}\)) and in parallel (\({R}_{c}^{p}\)) with the topological semimetal \({R}_{SM}\)(color red). The red areas represent contributions from topological semimetal (both DSM and WSM) and the blue areas denote normal metallic contribution. c, d The experimental measured and theoretically-fitted MRxx vs. Hext curves of Pt3Sn for θ-angle dependence and φ-angle dependence, respectively. The theoretically-fitted MRxx vs. Hext curves based on three-resistor model are shown in the insert of c, d. e, f The experimental measured and theoretically-fitted MRxx vs. Hext curves of Pt3SnxFe1-x for θ-angle dependence and φ-angle dependence, respectively. The theoretically-fitted MRxx vs. Hext curves based on three-resistor model are shown in the insert of e, f.

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This behavior can be ascribed to the presence of at least two competing contributions, whose strength is associated with the polar angle θ between Ic and Hext. Positive contribution of MR is commonly observed in metallic systems that depend only on out-of-plane Hext, which can be easily understood from the electron localization induced by magnetic cyclotron orbits50. On the other hand, negative contribution of MR in 2-dimentional electron gas (2DEG) metallic system is rare, albeit only observed in semiconductor system41,42. We note that there exist various explanations for the NMR effect, such as the suppression of spin fluctuation under Hext, or the weak localization effect, however, most of those effects cannot explain the experimentally observed angle dependence of the NMR (more discussion in Supplementary Note 3). A defining characteristic of the chiral anomaly in topological semimetals is that it only relies on the magnetic field component parallel to the applied electric field (Hext || Ic)29,51. To distinguish the contribution between these two components, we further measured MRxx of the Pt3Sn Hall bar devices with in-plane rotating Hext with different φ, as plotted in Fig. 2d. We can clearly observe NLMR for all azimuthal angles φ whose magnitude decreases when φ changes from 0 degree to 90 degree. Such robust NLMR phenomenon unequivocally confirms the anomaly contribution from the topological semimetal.

To further investigate the intriguing phenomena of Pt3Sn system, we tested the transport properties of Pt-seeded Pt3Sn and Mo-seeded Pt3Sn that possess different orientation with high crystallinity, as shown in Fig. S3b–e. Pt-seeded Pt3Sn and Mo-seeded Pt3Sn have similar nontrivial NLMR behavior as that of Pt3Sn without a seed layer. There is only a slight shape difference in the MRxx curve among Pt3Sn samples, which can be attributed to sample variations such as doping or crystallinity. It is rather enthralling to observe such robust NLMR in our Pt3Sn thin films regardless of their different orientations with/without seed layers, strongly suggesting the existence of robust topological semimetal states.

Meanwhile, we also investigated the topological properties of Pt3Sn doped by magnetic element (Pt3SnxFe1−x). With a small amount of Fe dopant (3.8%), Pt3SnxFe1−x presents weak ferromagnetic properties below 25 K (see Supplementary Note 2 and Fig. S4 in SI). Surprisingly, the MR measurement of Pt3SnxFe1−x with rotating Hext (both θ and φ) reveals a very different behavior compared to Pt3Sn. As summarized in Fig. 2e, f, we observe a nearly angle-independent negative MR phenomenon with a clear linear Hext dependence. The negative MR shows the linear behavior within the applied Hext, which could potentially become non-linear when the magnetic field is larger52. Unlike positive linear MR that is more commonly observed, linear NLMR has been proposed for WSMs with broken TRS31,32,33, see more discussion in SI. In addition, the results of zoomed-in MRxx vs. Hext curves and Hall resistance (Rxy) vs. Hext curves measured at 1.9 K are presented in Fig. S5, in which the weak anti-localization behavior is clearly observed for these Pt3Sn and Pt3SnxFe1−x samples. Furthermore, the Pt3Sn samples show the typical Hall Effect, except for Pt3SnxFe1−x with the anomalous contribution, which can be associated to anomalous Hall effect (AHE) (see Fig. S5e–i). The AHE of Pt3SnxFe1−x can be related to a spin-split band structure due to magnetic dopants, and thus further supports the presence of topologically nontrivial electronic structure in our materials.

Physical origin of robust NLMR

To better understand the robust NLMR phenomena observed in Pt3Sn and Pt3SnxFe1-x, a three-resistor model is applied to fit the measured MR results as shown in Fig. 2b. The resistance of trivial metallic state can be well described by the Drude model \({R}_{c}({H}_{ext})={R}_{c,0}[1+\alpha {({H}_{ext}\cdot sin(\theta ))}^{2}]\), contributing to positive MR when Hext ⊥ Ic. While that of the topological semimetal states is assumed to be \({R}_{SM}({H}_{ext})={R}_{SM,0}[1+\beta {({H}_{ext}\cdot \cos (\theta )\cos (\varphi ))}^{2}]\), inducing negative MR for Hext ∥ Ic (see details in Supplementary Note 3 and Fig. S6).\({R}_{c,0}\) and \({R}_{SM,0}\) represent the initial resistance without Hext, which can be extracted from experimental measurements. The total resistance can be simplified using a three-resistor model with one conventional resistor each connected in series and in parallel with \({R}_{SM}\) that is described as \(R({H}_{ext})=1/[\frac{1}{({R}_{SM}+{R}_{c}^{s})}+\frac{1}{{R}_{c}^{p}}]\)45. We can easily see that with the increase of RSM, the system has higher tendency to yield negative MR (Fig. S7a), while with the increase of either \({R}_{c}^{s}\) or \({R}_{c}^{p}\), the total MR tends to be more positive (Fig. S7a, c).

This model captures the experimental φ-dependent MR feature of Pt3Sn. For the in-plane φ-dependent measurement, there will be only contributions from \({R}_{SM}\), whose sign remains negative but magnitude changes with the angle between Ic and Hext, as shown in the insert of Figs. 2c, d and S8. However, unlike the ideal theoretical model, the experimental MR does not disappear even for Hext ⊥ Ic, possibly due to the polycrystalline nature of the sputtered Pt3Sn that hosts various pairs of Weyl fermions along different directions. Additionally, certain weak localization and weak anti-localization effects, that may cause the deviation between theory and experiments, are not considered. Contrary to Pt3Sn, Pt3SnxFe1-x exhibits almost angle-independent linear negative MR behavior (shown in Fig. 2e, f). Such distinction is possibly related to the distinct nature of the Weyl nodes of TRS-broken WSMs. In time reversal topological semimetal systems, the Weyl pairs are oriented along certain spatial orientations, while the Weyl pairs are locked to Hext in TRS-broken WSMs (see Supplementary Note 4 in SI).

Meanwhile, Pt3SnxFe1−x sample shows relatively low crystal quality that have different crystalline orientations, as suggested from Figs. 1a and S2b. Hence, we attribute the azimuthal angle independence to the random crystalline orientations. On the other hand, linear NLMR has indeed been predicted for TRS-broken WSMs when the type-I Weyl nodes are further tilted to form a one-dimensional chiral anomaly31,32,33, which agrees with our DFT calculations (see Supplementary Note 4 in SI). Therefore, we fitted the experimental results using a linear model\(MR\cong \alpha+\beta {H}_{ext}\), which perfectly reproduces experimental results, as shown in the insert of Fig. 2e, f (see details in Supplementary Note 3).

To explore the physical origin of the NLMR behavior, we carried out first-principles calculations of Pt3Sn and Pt3SnxFe1−x (see Figs. 3a, d for corresponding crystalline structures). The band structure of pristine Pt3Sn is shown in Fig. 3b. For the pristine phase without SOC, Dirac nodes can be clearly seen at Γ and R points, which become completely gapped when considering SOC, suggesting the topological insulator phase, as also confirmed from our topological edge state calculations (see Fig. S9 in SI). Note that though Pt3Sn has features of topological insulators, there is a type-II Dirac node and significant bulk states appearing near the Fermi level around R point (Fig. 3c), leading to the formation of a “weak topological insulator” (WTI) or topological semimetal48. The coexistence of topological surface states, Dirac fermion, and metallic bulk states in Pt3Sn constitutes a physical picture as it is consistent with our previous analysis of the competing contributions to MR that are associated with the angle between electric current and magnetic field. The Dirac fermions contribute to the NLMR due to chiral anomaly while the metallic bulk states contribute to positive MR. It is important to mention that although the Dirac node is not located exactly at the Fermi level, theories have demonstrated that NLMR is robust despite departure from the ideal semimetal systems34.

Fig. 3: Theoretical calculation of topological properties.
figure 3

a, b The crystal structure of pristine Pt3Sn and the band structure of pristine Pt3Sn that shows weak topological features. Blue and red lines represent band structures with and without spin–orbit coupling, respectively. c Enlarged band structure with the Dirac nodes around the R point. d, e The crystal structure of pristine Pt3SnxFe1−x and its band structure that shows clear spin-splitting and formation of TRS-broken WSM. Blue, black (spin up), and red (spin down) lines represent band structures with/without spin–orbit coupling, respectively. f Enlarged band structure with the Weyl nodes around the R point that shows formation of TRS-broken WSM.

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The calculated band structure of Pt3SnxFe1−x in the TRS-broken scenario is shown in Fig. 3e. The band structure without SOC shows a clear spin-splitting due to magnetic doping with each spin channel [spin up (black curve) and spin down (red curve)] hosting a set of bands identical to that of pristine Pt3Sn. When SOC effect is considered, one can clearly see the formation of various pairs of Weyl nodes near the R (Fig. 3f) and \(\Gamma\) points, confirming the formation of TRS-broken WSM phase. Therefore, we have established the topological transition between topological Dirac semimetal and WSM through time-reversal symmetry breaking for the Pt3Sn and demonstrate the robustness of topological semimetal states against magnetic doping. Considering the possibility of small perturbations of strain or structural defects due to lattice mismatch during sputtering using various seed layers, we also calculated Pt3Sn with different structural variations, which shows the robustness of topological semimetal states against structural perturbation (see Supplementary Note 4 and Fig. S10 in SI).

Spin torque efficiency (θ SH)

After confirming the topological features, we investigate θSH of the Pt3Sn and Pt3SnxFe1-x samples utilizing the ST-FMR technique53,54. The schematic of the sample stack and testing configuration are illustrated in Fig. 4a, b. To precisely evaluate the spin torque efficiency, we fix the thickness of the Pt3Sn layer and change the thickness of the CoFeB layer (tCoFeB = 3.0–6.0 nm). Figure 4c, d show the room-temperature ST-FMR spectra of Pt3Sn (10.0 nm)/CoFeB (5.0 nm) and Pt3SnxFe1−x (10.0 nm)/CoFeB (5.0 nm) devices, respectively, excited at microwave frequency of 9 GHz. The experimental data (black) is fitted to separate the contribution of symmetric Lorentzian (blue) and antisymmetric Lorentzian (pink) curves. The (τFL + τOe)/τDL vs. tCoFeB is plotted in Fig. 4e, f for Pt3Sn and Pt3SnxFe1−x, respectively, where the slope contains the information for damping-like torque (τDL), the intercept contains the information for field-like torque (τFL) and the Oersted field contribution (τOe, see Supplementary Note 5).

Fig. 4: Spin torque efficiency.
figure 4

a, b The schematic of the ST-FMR measurement and experimental setup with the microscopy of the device. c, d the room-temperature ST-FMR spectra for the Pt3Sn (10.0 nm)/CoFeB (5.0 nm) and Pt3SnxFe1−x (10.0 nm)/CoFeB (5.0 nm) devices. e, f The ratio (τFL + τOe)/τAD plotted against the thickness of the CoFeB layer. Through the linear fitting, spin torque efficiencies θSH of ~0.4 and ~0.38 are obtained for Pt3Sn (10.0 nm) and Pt3SnxFe1−x (10.0 nm), respectively.

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The thickness-dependent measurement estimates the θSH more reliably by determining the slope of the (τFL + τOe)/τDL ratio over film thickness in Fig. 4e, f, as shown by equation \(\frac{{J}_{s}}{{J}_{c}}=\frac{e{\mu }_{0}{M}_{s}}{\hslash }\times \frac{{\tau }_{AD}}{{\tau }_{Oe}/({t}_{CoFeB}{d}_{P{t}_{3}Sn})}\)53. From linear curve fitting of Fig. 4e, f, the θSH of Pt3Sn and Pt3SnxFe1-x is estimated to be 0.4 and 0.38, respectively. These values are larger than that of the Pt reference (θSH ~ 0.1) with the same experimental process and testing method (Fig. S11). Such high θSH could originate from the high spin Hall conductivity of the Pt3Sn. A spin Hall conductivity up to ~4.34 × 105 ℏ/2e (Ω ⋅ m)−1 for Pt3Sn is predicted, which is two times larger than that of WSM WTe2 (Fig. S12). We note that there is no significant difference of the SOT efficiency between Pt3Sn and Pt3SnxFe1−x, which could possibly be due to the small change of the band structure between the two (more discussion in Supplementary Note 5).

Discussion

In this study, the high crystallinity, industrial-compatible topological semimetals, Pt3Sn and Pt3SnxFe1−x, have been fabricated via the sputtering method for the advanced SOT devices. In combination with first-principles calculation and three-transistor model study, we thoroughly study the robust quadratic and linear NLMR features of Pt3Sn and Pt3SnxFe1−x thin films, which can not only extend the understanding of chiral anomaly in sputtered topological semimetal systems, but also demonstrate the feasibility to design and/or control the topological properties through seed layers or dopants. Meanwhile, the promising SOT performance of the Pt3Sn and Pt3SnxFe1−x thin films can inspire us to explore more novel topological semimetals for practicable spintronic applications.

Methods

Sample preparation and characterization

The Pt3Sn and Pt3SnxFe1−x samples studied in this work were prepared on single crystal (001) MgO substrates by magnetron sputtering under an ultrahigh vacuum (base pressure < 5.0 × 10−8 Torr). The Pt3Sn thin films were deposited using PtSn4 and Pt targets, and the Pt3SnxFe1-x thin films are prepared using PtSn4, Pt, and Fe targets with substrate temperature of 350 °C. The Pt thin film was also grown with the same experimental condition as a reference. The MgO (6.0 nm)/Ta (5.0 nm) capping layer was grown after the substrate was cooled down to room temperature. The pressure of Ar working gas is 2.1 mTorr for all the layers. The structural features of Pt3Sn thin films were characterized by out-of-plane (θ−2θ scan) x-ray diffraction (XRD) with Co-Kα radiation (λ = 0.179 nm) using a Bruker D8 Discover system and by analytical electron microscopy using aberration-corrected FEI Titan G2 60-300 STEM equipped with super-X EDX detector. Cross-sectional samples for the STEM study were prepared by using a FEI focused-ion beam (FIB) system. The Pt3Sn and Pt3SnxFe1-x samples were patterned into Hall bar devices by photolithography and Ar ion milling. And the electrical transport of Pt3Sn and Pt3SnxFe1-x Hall bar devices was tested through DC setup measurement by utilizing a Physical Property Measurement System (Quantum Design, DynaCool).

Device fabrication and electrical testing

The samples with the stack of MgO (001) sub./Pt3Sn (60.0 nm)/MgO (6.0 nm)/Ta (5.0 nm), MgO (001) sub./Pt (Mo) (2.0 nm)/Pt3Sn (60.0 nm)/MgO (6.0 nm)/Ta (5.0 nm), and MgO (001) sub./Pt3SnxFe1−x (60.0 nm)/MgO (6.0 nm)/Ta (5.0 nm) (numbers indicate the thickness in nm, same below), were prepared and patterned into Hall bar devices with 4–12-μm width and 144-μm length using an optical lithography process. The electrode with Ti (10.0 nm)/Au (150.0 nm) was deposited by CHA evaporator after etching the MgO (6.0 nm)/Ta (5.0 nm). Then temperature-dependent magnetoresistance, resistance, and Hall effect were tested by a physical property measurement system (PPMS) with a dc setup with Keithley’s 2182 nanovoltmeter and 6221 current source.

The Pt3Sn (10.0 nm)/CoFeB (3.0–6.0 nm), Mo (2.0 nm)/Pt3Sn (10.0 nm)/CoFeB (3.0–6.0 nm), Pt3SnxFe1−x (10.0 nm)/CoFeB (3.0–6.0 nm) and Pt (5.0 nm)/CoFeB (3.0–6.0 nm) samples were patterned into rectangular-shaped microstrips with dimensions of 5–20-μm width and 30-μm length by optical lithography and Ar ion milling. The electrode with Ti (10.0 nm)/Au (150.0 nm) was deposited by CHA evaporator. Symmetric coplanar waveguides in the ground-signal-ground (GSG) form were utilized for microwave injection into the Pt3Sn (Pt3SnxFe1-x)/CoFeB microstrips. A bias tee was used to inject microwave current and measure the resulting dc voltage at the same time. During the measurement, a microwave current with constant frequency (6–15 GHz) is injected while a magnetic field is swept at an angle of 45° with respect to the microstrips, and the output dc voltage is measured at each magnetic field with Keithley’s 2182 nanovoltmeter.

DFT calculations

The total-energy electronic structure calculations were carried out using first-principles methods based on DFT. The generalized gradient approximation exchange-correlation potentials plus the projector augmented wave method for the electron-ion interaction was used55, as implemented in Vienna ab initio simulation package code56. All self-consistent calculations were performed with a plane-wave cutoff of 500 eV. The geometric optimizations were carried out without any constraint until the force on each atom is less than 0.01 eV/A and the change of energy per cell is smaller than 10-5 eV. The Brillouin zone k-point sampling was set with a 21 × 21 × 21 Γ-centered Monkhorst-Pack grids. Wannier 90 package was used to fit the DFT band structures and calculate the SHC of Pt3Sn alloys57. Fe doping is performed using the virtual crystal approximation method with a doping ratio of 5%, as suggested from experiments.