Robust negative longitudinal magnetoresistance and spin–orbit torque in sputtered Pt3Sn and Pt3SnxFe1-x topological semimetal

Contrary to topological insulators, topological semimetals possess a nontrivial chiral anomaly that leads to negative magnetoresistance and are hosts to both conductive bulk states and topological surface states with intriguing transport properties for spintronics. Here, we fabricate highly-ordered metallic Pt3Sn and Pt3SnxFe1-x thin films via sputtering technology. Systematic angular dependence (both in-plane and out-of-plane) study of magnetoresistance presents surprisingly robust quadratic and linear negative longitudinal magnetoresistance features for Pt3Sn and Pt3SnxFe1-x, respectively. We attribute the anomalous negative longitudinal magnetoresistance to the type-II Dirac semimetal phase (pristine Pt3Sn) and/or the formation of tunable Weyl semimetal phases through symmetry breaking processes, such as magnetic-atom doping, as confirmed by first-principles calculations. Furthermore, Pt3Sn and Pt3SnxFe1-x show the promising performance for facilitating the development of advanced spin-orbit torque devices. These results extend our understanding of chiral anomaly of topological semimetals and can pave the way for exploring novel topological materials for spintronic devices.

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 fields (13~16,25~28).
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 magnetization (31)(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 PtSn 4 single crystal, which has already been demonstrated experimentally to be a nodal line Dirac semimetal (47), a more interesting Pt 3 Sn alloy has been predicted theoretically to be a promising three-dimensional weak topological insulator hosting type-II Dirac fermion (48).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 industrialcompatible Pt 3 Sn is less challenging compared to some topological materials (e.g.Bi 2 Se 3 (10) and WTe 2 (20,23)).
In this work, we successfully fabricate highly ordered Pt 3 Sn with/without seed layers and Fe-doped Pt 3 Sn (Pt 3 Sn x Fe 1-x ) thin films through sputtering deposition that provides seamless integration with the industry development of memory devices for CMOS technology integration.The Pt 3 Sn with/without seed layers and Pt 3 Sn x Fe 1-x samples show a surprising robust quadratic and linear NLMR, respectively.These results are consistent with the topological semimetal phases of the Pt 3 Sn and Pt 3 Sn x Fe 1-x samples with and without TRS, respectively, which is further corroborated by our DFT calculations.
θ SH of the Pt 3 Sn and Pt 3 Sn x Fe 1-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 PtTe 2 (~ 0.1) (21) and WTe 2 (~ 0.2) (19) with the same thickness.

Crystalline structure of Pt 3 Sn and Pt 3 Sn x Fe 1-x
The crystallinity and microstructure are investigated for the Pt 3 Sn, Pt 3 Sn x Fe 1-x , Ptseeded and Mo-seeded Pt 3 Sn thin films deposited on (001) single-crystal MgO substrates with substrate heating at 350 ℃. Figure 1(a) shows the crystalline structure of Pt 3 Sn and Pt 3 Sn x Fe 1-x samples by x-ray diffraction (XRD).We can clearly observe the (111) textured growth for Pt 3 Sn and Pt 3 Sn x Fe 1-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 Pt 3 Sn 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 (4.212Å), by XRD, as shown in Fig. 1(b).Both (111) and (002) diffraction patterns can be seen for Pt 3 Sn and Pt 3 Sn x Fe 1-x samples, confirming highordered phase.For Pt 3 Sn thin films with seed layers, Pt seed layer can maintain the (111) texture with certain (002) orientated grains, the same as Pt 3 Sn and Pt 3 Sn x Fe 1-x .However, a Mo seed layer induces the (002) texture, as shown in Figs.S1(a) and S1(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 Pt 3 Sn, Pt 3 Sn x Fe 1-x , and Mo-seeded Pt 3 Sn samples (Figs.1(c), 1(d), and Fig. S2).From the atomic-resolution STEM images, it was confirmed that both Pt 3 Sn and Pt 3 Sn x Fe 1-x samples show primarily (111) textured grains with in-plane twist between them as well as some grains with a (002) texture (Fig. 1(c)).Mo-seeded Pt 3 Sn sample exhibits only (002) growth (see Fig. S2 for details).STEM-energy dispersive X-ray (EDX) analysis was performed (Fig. 1(d)).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 Pt 3 Sn x Fe 1-x and Pt 3 Sn samples (see Fig. S2(b)), where a relative increase of Fe K peaks and decrease of Sn L peaks in Pt 3 Sn x Fe 1-x can be seen.

Robust negative magnetoresistance of Pt 3 Sn and Pt 3 Sn x Fe 1-x
To investigate the topological properties, the Pt 3 Sn and Pt 3 Sn x Fe 1-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. 2 This behavior can be ascribed to the presence of at least two competing contributions, whose strength is associated with the polar angle θ between I c and H ext .
Positive contribution of MR is commonly observed in metallic systems that depend only on out-of-plane H ext , which can be easily understood from the electron localization induced by magnetic cyclotron orbits (50).On the other hand, negative contribution of MR in 2-dimentional electron gas (2DEG) metallic system is rare, albeit only observed in semiconductor system (41,42).We note that there exist various explanations for the NMR effect, such as the suppression of spin fluctuation under H ext , 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 (H ext I c ) (29,51).To distinguish the contribution between these two components, we further measured MR xx of the Pt 3 Sn Hall bar devices with in-plane rotating H ext with different φ, as plotted in Fig. 2(d).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 Pt

Physical origin of robust NLMR
To better understand the robust NLMR phenomena observed in Pt 3 Sn and Pt 3 Sn x Fe 1- x , a three-resistor model is applied to fit the measured MR results as shown in Fig. 2(b).
The resistance of trivial metallic state can be well described by the Drude model  45).We can easily see that with the increase of SM R , the system has higher tendency to yield negative MR [see Fig. S7 Note that though Pt 3 Sn 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. 3(c)), leading to the formation of a "weak topological insulator" (WTI) or topological semimetal (48).The coexistence of topological surface states, Dirac fermion, and metallic bulk states in Pt 3 Sn 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 systems (34).
The calculated band structure of Pt 3 Sn x Fe 1-x in the TRS-broken scenario is shown in Fig. 3 S12).We note that there is no significant difference of the SOT efficiency between Pt 3 Sn and Pt 3 Sn x Fe 1-x , which could possibly be due to the small change of the band structure between the two (more discussion in Supplementary Note 5).
We conclude that the high crystallinity, industrial-compatible topological semimetals, Pt 3 Sn and Pt 3 Sn x Fe 1-x , have been fabricated via the sputtering method for the advanced SOT devices.In combination with first-principles calculation and threetransistor model study, we thoroughly study the robust quadratic and linear NLMR features of Pt 3 Sn and Pt 3 Sn x Fe 1-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 Pt 3 Sn and Pt 3 Sn x Fe 1-x thin films can inspire us to explore more novel topological semimetals for practicable spintronic applications.

Sample preparation and characterization
The Pt 3 Sn and Pt 3 Sn x Fe 1-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 Pt 3 Sn thin films were deposited using PtSn 4 and Pt targets, and the Pt 3 Sn x Fe 1-x thin films are prepared using PtSn 4 , Pt and Fe targets with substrate temperature of 350 o 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

Device fabrication and electrical testing
The samples with the stack of MgO (001) sub./Pt 3 Sn (60.0 nm)/MgO (6.0 nm)/Ta 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 firstprinciples methods based on DFT.The generalized gradient approximation exchangecorrelation potentials plus the projector augmented wave method for the electron-ion interaction was used (55), as implemented in Vienna ab initio simulation package code (56).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 Pt 3 Sn alloys (57).Fe doping is performed using the virtual crystal approximation method with a doping ratio of 5%, as suggested from experiments.
(a).The resistivity (ρ xx ) is measured and calculated to be 162 μΩ.cm and 114 μΩ.cm for Pt 3 Sn and Pt 3 Sn x Fe 1-x at room temperature, respectively (see Fig. S3(a) in SI).With decreasing temperature, ρ xx exhibits a metallic behavior, reaching at 1.9 K a residual value ρ 0 of about 83 μΩ.cm and 79 μΩ.cm for Pt 3 Sn and Pt 3 Sn x Fe 1-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 (MR xx ) vs. external magnetic field (H ext ) and Hall resistivity (R xy ) vs. H ext of these Pt 3 Sn and Pt 3 Sn x Fe 1-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 H ext and the z-axis; φ denotes the in-plane azimuthal angle between H ext and the x-axis (see Fig. 2(a)) where the electric current (I c ) is applied along the x-axis], as plotted in Figs.2(c)-2(f).As shown in Fig. 2(c), we can clearly see that the measured MR xx is surprisingly negative when θ < 15 o and becomes positive while θ > 15 o for the Pt 3 Sn Hall bar device with a wide range of H ext .

3
Sn system, we tested the transport properties of Pt-seeded Pt 3 Sn and Mo-seeded Pt 3 Sn that possess different orientation with high crystallinity, as shown in Figs.S3(b)-S3(e).Pt-seeded Pt 3 Sn and Mo-seeded Pt 3 Sn have similar nontrivial NLMR behavior as that of Pt 3 Sn without a seed layer.There is only a slight shape difference in the MR xx curve among Pt 3 Sn samples, which can be attributed to sample variations such as doping or crystallinity.It is rather enthralling to observe such robust NLMR in our Pt 3 Sn 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 Pt 3 Sn doped by magnetic element (Pt 3 Sn x Fe 1-x ).With a small amount of Fe dopant (3.8%), Pt 3 Sn x Fe 1-x presents weak ferromagnetic properties below 25 K (see Supplementary Note 2 and Fig.S4in SI).Surprisingly, the MR measurement of Pt 3 Sn x Fe 1-x with rotating H ext (both θ and φ) reveals a very different behavior compared to Pt 3 Sn.As summarized in Figs.2(e) and 2(f), we observe a nearly angle-independent negative MR phenomenon with a clear linear H ext dependence.The negative MR shows the linear behavior within the applied H ext , which could potentially become non-linear when the magnetic field is larger(52).Unlike positive linear MR that is more commonly observed, linear NLMR has been proposed for WSMs with broken TRS(31)(32)(33), see more discussion in SI.In addition, the results of zoomed-in MR xx vs. H ext curves and Hall resistance (R xy ) vs. H ext curves measured at 1.9 K are presented in Fig.S5, in which the weak anti-localization behavior is clearly observed for these Pt 3 Sn and Pt 3 Sn x Fe 1-x samples.Furthermore, the Pt 3 Sn samples show the typical Hall Effect, except for Pt 3 Sn x Fe 1-x with the anomalous contribution, which can be associated to anomalous Hall effect (AHE) (see Figs. S5(e)-S5(i)).The AHE of Pt 3 Sn x Fe 1-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.
(a)], while with the increase of either s c R or p c R , the total MR tends to be more positive [see Figs.S7(a) and S7(c)].This model captures the experimental φ-dependent MR feature of Pt 3 Sn.For the inplane φ-dependent measurement, there will be only contributions from SM R , whose sign remains negative but magnitude changes with the angle between I c and H ext , as shown in the insert of Figs.2(c)-2(d) and S8.However, unlike the ideal theoretical model, the experimental MR does not disappear even for I c ⊥H ext , possibly due to the polycrystalline nature of the sputtered Pt 3 Sn 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 Pt 3 Sn, Pt 3 Sn x Fe 1-x exhibits almost angle-independent linear negative MR behavior [shown in Figs.2(e) and 2(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 H ext in TRS-broken WSMs (see Supplementary Note 4 in SI).Meanwhile, Pt 3 Sn x Fe 1-x sample shows relatively low crystal quality that have different crystalline orientations, as suggested from Figs. 1(a) and S2(b).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 anomaly (31-33), which agrees with our DFT calculations (see Supplementary Note 4 in SI).Therefore, we fitted the experimental results using a linear model ext MR H   , which perfectly reproduces experimental results, as shown in the insert of Figs.2(e) and 2(f) (see details in Supplementary Note 3).To explore the physical origin of the NLMR behavior, we carried out firstprinciples calculations of Pt 3 Sn and Pt 3 Sn x Fe 1-x (see Figs. 3(a) and 3(d) for corresponding crystalline structures).The band structure of pristine Pt 3 Sn is shown in Fig. 3(b).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).
Figs.4(e) and 4(f), the θ SH of Pt 3 Sn and Pt 3 Sn x Fe 1-x is estimated to be 0.4 and 0.38,

2. 1
mTorr for all the layers.The structural features of Pt 3 Sn 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 Pt 3 Sn and Pt 3 Sn x Fe 1-x samples were patterned into Hall bar devices by photolithography and Ar ion milling.And the electrical transport of Pt 3 Sn and Pt 3 Sn x Fe 1-x Hall bar devices was tested through DC setup measurement by utilizing a Physical Property Measurement System (Quantum Design, DynaCool).

Fig. 1 .
Fig. 1.Crystalline structure of the Pt 3 Sn samples.(a) Specular (θ-2θ scans) XRD patterns of the Pt reference, Pt 3 Sn and Pt 3 Sn x Fe 1-x thin films.(b) Reciprocal space maps (RSM) around the (002) Bragg reflection of the MgO substrate of the Pt 3 Sn and Pt 3 Sn x Fe 1-x thin films.Both the Pt reference and the Pt 3 Sn and Pt 3 Sn x Fe 1-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 Pt 3 Sn thin film on the MgO substrate.Low-magnification image (top panel) shows the Pt 3 Sn 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) Atomicresolution HAADF-STEM image and EDX elemental maps of the Pt 3 Sn x Fe 1-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.

Fig. 2 .
Fig. 2. Characterization and physical origin of robust NLMR.(a) The photo image of Hall bar devices used for electric-transport measurements.Where the current (I c ) is applied along x-axis, the external magnetic field (H ext ) rotates along xz plane with angle θ (out-of-plane magnetoresistance (MR xx )) and xy plane with angle φ (in-plane MR xx ), respectively.(b) Schematic of three-resistor model with conventional resistor (color blue) each connected in series ( s c R ) and in parallel ( p c R ) with the topological semimetal SM R (color red).The red areas represent contributions from topological semimetal (both DSM and WSM) and the blue areas denote normal metallic contribution.(c) and (d) The experimental measured and theoretically-fitted MR xx vs. H ext curves of Pt 3 Sn for θ-angle dependence and φ-angle dependence, respectively.The theoretically-fitted MR xx vs. H ext curves based on three-resistor model are shown in the insert of (c) and (d).(e) and (f) The

Fig. 3 .
Fig. 3. Theoretical calculation of topological properties.(a) and (b) The crystal structure of pristine Pt 3 Sn and the band structure of pristine Pt 3 Sn 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) and (e) The crystal structure of pristine Pt 3 Sn x Fe 1-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.