Evidence for anisotropic spin-triplet Andreev reflection at the 2D van der Waals ferromagnet/superconductor interface

Fundamental symmetry breaking and relativistic spin–orbit coupling give rise to fascinating phenomena in quantum materials. Of particular interest are the interfaces between ferromagnets and common s-wave superconductors, where the emergent spin-orbit fields support elusive spin-triplet superconductivity, crucial for superconducting spintronics and topologically-protected Majorana bound states. Here, we report the observation of large magnetoresistances at the interface between a quasi-two-dimensional van der Waals ferromagnet Fe0.29TaS2 and a conventional s-wave superconductor NbN, which provides the possible experimental evidence for the spin-triplet Andreev reflection and induced spin-triplet superconductivity at ferromagnet/superconductor interface arising from Rashba spin-orbit coupling. The temperature, voltage, and interfacial barrier dependences of the magnetoresistance further support the induced spin-triplet superconductivity and spin-triplet Andreev reflection. This discovery, together with the impressive advances in two-dimensional van der Waals ferromagnets, opens an important opportunity to design and probe superconducting interfaces with exotic properties.

Fundamental symmetry breaking and relativistic spin-orbit coupling give rise to interesting phenomena in quantum materials 1,2 .For over sixty years, the interplay between ferromagnetism and superconductivity, has offered a wealth of intriguing phenomena in ferromagnet (FM)/superconductor (SC) heterostructures [3][4][5][6] .However, to overcome a strong suppression of spin-singlet superconductivity by the FM's exchange field the platforms supporting spin-triplet pairing are sought.They are desirable for dissipationless spin currents in superconducting spintronics [5][6][7] , and probing quantum materials 8 , as well as for realizing elusive Majorana bound states to implement topological quantum computing 9,10 .The common expectation that spin-triplet pairing in superconducting spintronics requires complex FM multilayers, typically relying on noncollinear/spiral magnetization or half metals [3][4][5][6]11 .
Here, we report the possible experimental evidence for the spin-triplet Andreev reflection and induced spin-triplet superconductivity at the interface of a quasi-2D van der Waals (vdW) FM and a conventional s-wave SC with Rashba spin-orbit coupling (SOC).Such vdW heterostructures offer a great versatility in exploring the interplay between ferromagnetism and superconductivity, beyond the lattice-matching constraints of all-epitaxial FM/SC heterostructures 12 .Our results pave the way for future studies on spin-triplet superconductivity 13,14 and the formation on Majorana bound states 9,10 , as well as many normal-state spintronic applications 15 .
In contrast to the conventional Andreev reflection at the FM/SC interface (Fig. 1a), an incident spin-up electron forms a spin-singlet Cooper pair in the ordinary SC with a reflected spin-down hole in the FM, spin-triplet Andreev reflection generates the spin-up hole with an injection of an equal-spin triplet Cooper pair in the spin-triplet SC (Fig. 1b).Due to Rashba SOC 16,17 , spin-rotation symmetry is broken for the superconducting pairing (Fig. 1c), which acts as a spin-mixing described in conventional FM/SC heterostructures 5,6 .The broken spin-rotation symmetry leads to the spin-singlet paring (m = 0, S = 0) (S is the total spin quantum number, and m is magnetic quantum number) with an unpolarized spin-triplet component (m = 0, S = 1) 18 .The spin-triplet component results in the interface spin-triplet Andreev reflection at the FM/SC interface which is highly anisotropic (Supplementary Note 1 and Supplementary Fig. 1), depending on the relative orientation between the magnetization (M) in the FM and the interfacial spin-orbit field 14,19 .M sets the spin-quantization axis, and unpolarized spin-triplet component (m = 0, S = 1) is projected onto the spin-quantization axis to generate the equal-spin-triplet component (m = 1, S = 1), which can be considered as a spin-rotation process 5 .For example, for FM magnetization along z axis (perpendicular to the interface), unpolarized spin-triplet Cooper pairs component (| = 1,  y = 0 ⟩ and | = 1,  x = 0 ⟩ can be projected to the spin quantization axis as | = 1,  z = 1 ⟩ due to the spin rotation process (   ,   , and   are the spin quantum numbers along y, x, and z direction, respectively).Thus, both the | = 1,   = 0 ⟩ and | = 1,   = 0 ⟩ components will contribute to the interface conductance when M is perpendicular to interface, as illustrated in Fig. 1d.On the other hand, when the M is parallel to the interface along y direction, the equal-spin triplet Cooper pairs (| = 1,   = 1 ⟩) can only be projected from unpolarized spin-triplet pairing component | = 1,   = 0 ⟩, since [  ,   ] ≠ 0. Consequently, spin-triplet Andreev reflection conductance channel is suppressed when M is parallel to interface, as illustrated in Fig. 1e.As a result of the anisotropic spin-triplet Andreev reflection processes, there is a low-(high-) resistance state for M out-of-plane (in-plane) (Figs.1d and 1e).Hence, the spin-triplet Andreev reflection can lead to the tunnelling anisotropic magnetoresistance (MR) at the FM/SC interface, a proposed hallmark of the interfacial SOC and spin-triplet superconductivity in FM/SC heterostructures 14,19 .
To experimentally probe the anisotropic spin-triplet Andreev reflection and spin-triplet MR, we fabricate the FM/SC devices (see Methods for details), which consist of a quasi-2D vdW Fe0.29TaS2 flake, several s-wave superconducting NbN electrodes, and two normal metal Pt electrodes (Fig. 2a and Supplementary Fig. 2).At the interface between the quasi-2D vdW Fe0.29TaS2 flake and s-wave NbN electrode, the Cooper pairing consists of both spin-singlet (m = 0, S = 0) and spin-triplet components (m = 0, S = 1) due to the spin-rotation symmetry breaking by the interfacial Rashba SOC (right panel of Fig. 2a).The superconducting critical temperature of the NbN electrode is TSC ~ 12.5 K (Supplementary Fig. 3a) characterized by standard four-probe electrical measurement.Fe0.29TaS2 flakes are typical quasi-2D vdW FM, with a Curie temperature, TCurie, ~ 90 K, characterized by anomalous Hall effect (Supplementary Fig. 4) 20 .The magnetic easy axis is perpendicular to the sample plane, and M of Fe0.29TaS2 can be controlled by a large external magnetic field (B) (Supplementary Note 2 and Supplementary Fig. 5).For an in-plane B = 9 T, M is almost in plane, 83 o from the z direction.Under B = 9 T, the current-voltage characteristics of the NbN electrode are measured, with critical currents of ~ 50 μA at T = 2 K (Supplementary Fig. 4b).Typical dI/dV curves of the Fe0.29TaS2/SC junctions as a function of T and B are shown in Supplementary Note 3 and Supplementary Fig. 6.
To characterize the expected MR arising from anisotropic spin-triplet Andreev reflection, the interfacial resistance between the quasi-2D vdW FM Fe0.29TaS2 and SC electrode is measured using the three-terminal geometry (Fig. 2a and Methods).Figure 2b shows the typical MR curve (blue) measured (device A; Supplementary Fig. 2) as a function of the magnetic field angle in the yz plane (Θ yz ) at T = 2 K and B = 9 T. The observed MR shows a strong correlation with Bcontrolled M (Supplementary Fig. 7).In contrast to this large MR at T = 2 K, the normal-state interfacial resistance exhibits little variation at T = 20 K.A possible important contribution of vortices in type-II SC to the observed MR has been ruled out from our control measurements on normal metal/SC heterostructures at T = 2 K (orange curve in Fig. 2b; Supplementary Note 4 and Supplementary Fig. 8).We have also fabricated the control devices of Fe0.29TaS2/Al2O3/normal metal (Al), where no MR could be observed at T = 2 K (Supplementary Fig. 9), which further indicates the critical role of SC for the observed MR.Furthermore, the π-periodic oscillation further supports that the observed MR results from the anisotropic feature of spin-triplet Andreev reflection at the interface with Rashba SOC 14 .Figure 2c shows the MR results measured on the device B as a function of Θ yz at T = 2 K and B = 9 T. The MR ratio can be defined as: The (Θ yz = 0) and (Θ yz = 90) are the interfacial resistances for magnetic field that is perpendicular and parallel (along z and y directions in Fig. 2a) to the FM/SC interface, respectively.
Interestingly, the observed MR ratio is ~ 37% ± 2% for device A, and ~ 103% ± 4% for device B, which are much larger than previous reports on the tunneling anisotropic MR in FM/semiconductor heterostructures arising from the Rashba and Dresselhaus SOC 16,17 .
Next, we investigate the temperature evolution of the MR to distinguish the contributions from the spin-triplet Andreev reflection and spin-dependent scattering by Bogoliubov quasiparticles under large magnetic field.Figure 3a shows the MR (Θ yz ) for device B at T = 2, 4, 8, and 9 K, respectively, under the magnetic field of B = 5 T. Figure 3b summarizes temperature dependence of the MR ratio for device B measured at B = 9, 7, and 5 T, respectively.The MR appears for T < TC, and starts to saturate below the temperature of ~ 5 K.The MR is no longer observable for T ~ TC at B = 9, 7, and 5 T (Supplementary Fig. 10).Clearly, there is no enhancement or any anomaly of the MR observed at the temperature slightly below TC, which further confirms that contribution from spin-dependent scattering by Bogoliubov quasiparticles is negligible 21,22 .
To further investigate the MR at the quasi-2D vdW FM Fe0.29TaS2/SC interface, we systematically vary the bias voltage (Vbias), which also affect the junction voltage (V3T) across the interface.At the interface, the induced SC energy gap (ΔIn) by SC proximity effect with spin-triplet component is smaller compared to the SC gap (ΔNbN) of bulk NbN electrode, as illustrated in Fig. 4a.When the potential (eV3T) of the incoming electrons is considerably smaller than the interface spin-triplet superconducting energy gap (ΔIn) (Fig. 4a), the charge transport channel is dominated by the anisotropic spin-triplet Andreev reflection.Hence, the spin-triplet MR exhibits little variation with the eV3T within the ΔIn.As the V3T increases, other isotropic transport processes, such as electron-like and hole-like tunneling transmissions 14 , also contribute to the interface conductance.As these transport processes are M-independent, the spin-triplet MR ratio is expected to decrease significantly.Since the change of V3T is much smaller than Vbias during the rotation of the external magnetic field, the junction voltage for Θ yz = 0 (V3T_0) is used to qualitatively show the interface voltage dependence of the spin-triplet MR.Figures 4b and 4c summarize these results measured on devices B and C. For small V3T_0, the MR exhibit little variation as the voltage changes.However, when V3T_0 is higher than a critical value, MR strongly decreases as V3T increases.The critical junction voltage is obtained to be ~ 0.15 mV (~ 0.2 mV) for device B (C).
We note that at 2 K the thermal energy is  B  ~ 0.17 meV, comparable to the critical electron potential from the bias-dependent results.Therefore, an accurate value of the proximity-induced superconducting gap is not able to be clearly resolved here, which will need future studies.
Additionally, the bias dependence of the spin-triplet MR further confirms that the observed MR is This surprising nonmonotonic MR dependence on RJS agrees well with the theoretical expectations 14,25 .The effective barrier strength is modified by SOC and depends on the helicity (outer/inner Rashba bands, Fig. 1b),  ± =  ±  ̅ ∥ , where ̅ is the SOC parameter 25 and  ∥ is the component of the wave vector along the interface (Fig. 5  or | − | and thus enhance such a transmission for a given helicity.For much larger , all of the conduction channels, including spin-triplet Andreev reflection, are suppressed due to the low interface transparency.As a result, the spin-triplet Andreev reflection and spin-triplet MR will also be nonmonotonic in Z. Taken together, the observed nonmonotonic MR dependence with RJS (Fig. 5) and MR decrease with T or an applied voltage (Figs.2-4) are all possible experimental evidence for the spin-triplet Andreev reflection in our vdW heterostructures.We note that the spin-triplet MR theory is developed using an idealized model of ballistic systems 14,25 , the role of disorder, which could induce reflectionless tunneling, is expected to reduce the MR amplitude.To the best of our understanding, the spin-triplet Andreev reflection is the major cause for the observation of large MR up to ~103% ± 4%, and can qualitatively explain the bias and temperature dependence of the MR.Given the growing interest in systems that could support spin-triplet superconductivity, in the future studies, it would be important to generalize our description and also include the effects of disorder and diffusive transport on spin-triplet MR.
Our experimental obervation of a large tunneling anisotropic MR in quasi-2D vdW FM/swave SC heterostructures up to ~103% ± 4% is already promising for spintronic applications and much larger than for the normal-state transport in previously measured heterostructures with a single FM layer 16,17 .More importantly, this result also reveals an emergent spin-triplet superconductivity which, through spin-triplet Andreev reflection, is a sensitive probe of interfacial Rashba SOC.With the advances towards high-quality vdW heterostructures, we anticipate that the magnitude of such spin-triplet MR can be further enhanced and strongly modulated using different 2D vdW FMs due to their highly-tunable Rashba SOC by electric fields [26][27][28][29] .This tantalizing opportunity to implement FM/SC heterostructures to design and probe interfacial SOC offers an important boost for superconducting spintronics [3][4][5][6]30,31 and Majorana bounds states 9,32 .
Furthermore, our quasi-2D platform of proximity-induced spin-triplet superconductivity, combined with the gate-controlled 2D vdW ferromagnetism 28,29,33 could provide tunable magnetic textures to create synthetic SOC 34 and braid Majorana bound states 35 .

Device fabrication
The quasi-2D vdW Fe0.29TaS2/SC spin-triplet MR devices were fabricated as follows.symmetry.After solving the standard Gor'kov equations 2,3 , the corresponding pairing correlations can be written as

Spin-triplet MR measurement
where  0 (, ) =  + (, ) characterizes the spin-singlet part, (, ) =  − (, ) ̂ characterizes the spin-triplet part, E is the energy eigenvalue,   = (    +     , −(    +     ),0) is the SOC field with unit vector  ̂ =   /|  |, and In the absence of the SOC field (i.e., |  | = 0), the spin-triplet part (, ) =  − (, ) ̂ vanishes, and the system exhibits conventional s-wave superconductivity.On the other hand, in the presence of the SOC with the nonzero   , the system supports mixed s-wave and p-wave superconductivity, with the spin-triplet part being linearly proportional to |  | for small SOC field.It is important to note that in the basis where the spin-quantization axis is along the out-ofplane direction (-direction, see Fig. 2a in the main text), only   ,   components of the spintriplet part (, ) are nonzero, and all the spin-triplet Cooper pairs are formed by electrons with equal spins (Table.S1).Hence, besides conventional Andreev reflection, spin-triplet Andreev reflection also occur at the FM/SC interface, as shown in Fig. S1a.Here, we emphasize that √  2 +   2 is nonzero for arbitrary in-plane wave vector (  ,   ), which indicates that the spintriplet Andreev reflection can occur without any constraint if the spins of the incident electrons are along the out-of-plane direction.
For incident electrons with spins pointing along the xy plane, the spin-triplet Andreev reflection can be suppressed for certain in-plane wave vectors.For example, considering the spins of incident electrons being along the  axis, √  2 +   2 = |    +     | can be zero at some special wave vectors (  ,   ), leading to the disappearance of the spin-triplet Andreev reflection.
To see this more clearly, we introduce an angle  to denote the strength ratio between Dresselhaus and Rashba SOC, with   = cos ,   = sin ,  = √  2 +   2 .We also introduce an angle  to denote the azimuth of in-plane wave vector  ∥ , with Then the SOC field   can be simplified to ( ∥ sin( + ), − ∥ cos( − ),0) .By defining sin = sin( + )/ , cos = cos( − )/ ,  = √1 + sin2sin2, the pairing correlations in Eq. ( S3) can be rewritten as ) , (6)   where  is the angle between the spin-quantization axis and the  axis.The spin-triplet Andreev reflection arises from the diagonal part of the paring correlations, which vanishes if and reaches a maximum if Note that the parameter  encodes the in-plane wave vector (  ,   ) of the spin-polarized electrons, which means that for certain in-plane wave vectors, the spin-triplet Andreev reflection SC NbN electrode, we fabricate control devices that use ~20 nm Al as a NM to replace the quasi-2D vdW FM Fe0.29TaS2.As seen in Fig. S8, The only difference between the spin-triplet MR device (Fig. S8a) and control device (Fig. S8b) is the bottom layer; NM Al vs. quasi-2D vdW FM Fe0.29TaS2.These two devices are chosen for the comparision due to similar values of the interface resistance area product (RJS) of 29.7 and 45.6 Ω μm 2 for spin-triplet MR device and control device, respectively.
Using the same measurement geomery and under the same conditions (T = 2 K, B = 9 T, and Vbias = 1 mV) as the spin-triplet MR device, the angle dependence of the interfacial resistance between the Al electrode and the NbN electrode is measured.Clearly, the vortex-induced MR in control device (red symbols in Fig. S8c) is significantly smaller compared to the spin-triplet MR (blue symbols in Fig. S8c).Furthermore, the MR in the control device is within the noise level of ~3% (Fig. S8d).To rule out any significant contribution from vortex in SC, the control devices   b, c, For incident electrons with spins along the x axis, the spin-triplet Andreev reflection cannot occur for in-plane wave vector (0, ky), but is significant for in-plane wave vector (kx, 0).
possible experimental evidence for the spin triplet Andreev reflection and induced spintriplet superconductivity at ferromagnet/superconductor interface arising from Rashba spin-orbit coupling.The temperature, voltage, and interfacial barrier dependences of the magnetoresistance further support the induced spin-triplet superconductivity and spintriplet Andreev reflection.This discovery, together with the impressive advances in twodimensional van der Waals ferromagnets, opens an important opportunity to design and probe superconducting interfaces with exotic properties.
correlated to the sub-gap properties,, and is completely different form B-induced spin-splitting density of states at the gap edges of SC electrodes 23 .As the spin-triplet Andreev reflection depends strongly on the FM and SC wave-function overlap, it is expected that the dimensionless interface barrier strength (Z) plays an important role in the spin-triplet MR24,25  .To explore the influence of interface barrier strength on the observed spin-triplet MR, we investigate more than dozen devices that are fabricated with Al2O3 layer of different thickness (~ 1 -2.5 nm) between the quasi-2D vdW FM Fe0.29TaS2 and NbN SC electrodes.This process leads to a large range of interface resistance area product (RJS) from ~ 10 to ~ 2000 Ω μm 2 , resulting in the FM/SC heterostructures with very different Z-values.Figure5shows the measured MR ratio as a function of the RJS at T = 2 K and B = 9 T (Note: the MR is not observable for very large RJS and not plotted in this figure).The largest MR is observed with RJS ~ 48.4 Ω μm 2 .The strong correlation of the MR ratio and RJS reveals the important role of the Zvalue in the spin-triplet MR.
First, bulk single crystalline Fe0.29TaS2 were grown by the iodine vapor transport method.Then the quasi-2D vdW Fe0.29TaS2 flakes were mechanical exfoliated from the bulk single crystal onto the SiO2 (~ 300 nm)/Si substrates18  .Second, a first-step electron-beam lithography was used to define the SC electrodes on the quasi-2D vdW Fe0.29TaS2 flakes.The SC electrodes consist of ~ 5 nm thick Nb and ~ 60 nm thick NbN, which were grown in a DC magneton sputtering system with a base pressure of ~ 1.2 × 10 -4 Pa.Prior to the growth of SC electrodes, a thin Al2O3 layer (~ 1 -2.5 nm) is deposited as the barrier to tune the interface coupling strength between the quasi-2D vdW Fe0.29TaS2 flakes and the SC electrodes.The Al2O3 layer was grown by DC magnetron sputtering with Al target under the oxygen atmosphere.Then, a second-step electron-beam lithography was used to define the two normal Pt electrodes (~ 80 nm) on the quasi-2D vdW Fe0.29TaS2 flakes.The Pt electrodes were deposited by RF magneton sputtering in a system with a base pressure lower than 6.5 × 10 -4 Pa.The optical images of three typical devices (A, B, and C) are shown in Fig.S2.

Figure 1 .
Figure 1.Schematic of the spin-triplet Andreev reflection at FM/SC interface.a, Conventional Andreev reflection at the FM/spin-singlet SC interface.b, The spin-triplet Andreev reflection at the FM/spin-triplet SC interface.c, Schematic of the spin-triplet Andreev reflection resulting from Rashba SOC at the interface between a FM and a conventional s-wave SC.The arrows in Rashba SOC band indicate spin-momentum locking and the red arrows represent the spin-polarization direction of equal-spin-triplet pairs.d-e, Anisotropic spin-triplet Andreev reflection at the FM/SC interface and the low/high interfacial resistance states that depend on the FM magnetization direction, M (green arrow).Red arrows at the interface denote the spin direction of equal-spintriplet pairs.For M along the interface the spin-triplet Andreev reflection can be suppressed.

Figure 2 .
Figure 2. Large magnetoresistance of the quasi-2D vdW Fe 0.29 TaS 2 /SC junction.a, Illustration of the quasi-2D vdW Fe0.29TaS2/SC MR device and the measurement geometry.The right panel shows the schematic of the spin-triplet pairing component resulting from Rashba SOC at the FM/SC interface.b, The interfacial resistance (R3T = V3T/Isd) and MR ratio as a function of the magnetic field angle measured on the typical quasi-2D vdW Fe0.29TaS2/SC device (device A) under B = 9 T. The orange curve represents the resistance measured on a typical control device (Al/Al2O3/NbN) under B = 9 T. c, The interfacial resistance and MR ratio as a function of the magnetic field angle on device B under B = 9 T. The solid lines in b and c are guides to the eye.

Figure 3 .
Figure 3.The temperature dependence of MR at Fe 0.29 TaS 2 /SC interface.a, The interfacial resistance as a function of Θyz measured on device B at T = 2 K (blue), 4 K (yellow) 8 K (olive), and 9 K (black), respectively.These results were obtained under B = 5 T and Vbias = 1 mV, which correspond to V3T ~ 0.40 mV for T = 2 and 4 K, and V3T ~ 0.25 mV for T = 8 and 9 K. b, The temperature dependence of MR ratio of device B at B = 9 T, 7 T, and 5 T, respectively.The error bars correspond to one standard deviation.The open circles represent the absence of obvious MR.

Figure 4 .
Figure 4.The voltage dependence of MR at Fe 0.29 TaS 2 /SC interface.a, Schematic of the incident spin-polarized electrons with chemical potentials inside and above the interface spintriplet superconducting energy gap.ΔIn and ΔNbN indicate the superconducting energy gaps of the interface SC and the bulk NbN.b, The voltage dependence (V3T_0) of the MR ratio of device B measured at T = 2 K and B = 9 T. V3T_0 represents V3T when an applied magnetic field is perpendicular to the FM/SC interface.The error bars correspond to one standard deviation.Inset: The typical MR curve at V3T_0 = 0.10 mV.c, The voltage dependence (V3T_0) of the MR ratio of device C measured at T = 2 K and B = 9 T. The error bars correspond to one standard deviation.Inset: The typical MR curve at V3T_0 = 0.17 mV.

Figure 5 .
Figure 5.The interface barrier dependence of MR at Fe 0.29 TaS 2 /SC interface.The MR ratio as a function of the interface resistance area product (RJS) measured on various devices in the low voltage bias region.Inset: Schematic of the incident spin-polarized electrons into the interfacial spin-triplet SC via interface barrier with Rashba SOC.The Rashba SOC modifies the interface barrier strength (Z) to be  ± =  ± ̅  ∥ , where ̅ is the SOC parameter and  ∥ is the in-plane wave vector 25 .The blue, red, and green dots represent the MR of devices A, B, and C, respectively.The error bars correspond to one standard deviation.
Table S1: A summary list of the pairing functions of mixed s-and p-wave superconductivity.The spins of incident electrons are chosen to be along the z axis.The singlet part d0 and the triplet part dz are formed by electrons with opposite spins along the z direction, while dx and dy are formed by electrons with equal spins.The nonzero dx or dy gives rise to unconventional spin-triplet Andreev reflection (AR).

Figure S1 .
Figure S1.The schematic diagram of the spin-triplet Andreev reflection at the FM/SC interface.a, For incident electrons with out-of-plane spins, the spin-triplet Andreev reflection can occur for arbitrary in-plane wave vector (kx, ky), due to the formation of equal-spin Cooper pairs.

Figure S2 .
Figure S2.The optical images of the representative devices.a, Illustration of the quasi-2D vdW Fe0.29TaS2/SC MR device and the measurement geometry.Between the SC and the Fe0.29TaS2 flake, a thin Al2O3 layer (~ 1 -2.5 nm) is used to tune the interface coupling strength.b, The optical image of Device A. Three SC NbN electrodes are fabricated onto the central part of the Fe0.29TaS2 flake, and two normal metal Pt electrodes are contacted on the two ends of the Fe0.29TaS2 flake.The thickness of the Fe0.29TaS2 flake is estimated to be ~ 20 nm.c, The optical image of device B. The thickness of the Fe0.29TaS2 flake is estimated to be ~ 15 nm.d, The optical image of device C.The thickness of the Fe0.29TaS2 flake is estimated to be ~ 20 nm.

Figure S3 .
Figure S3.Characterization of the SC electrodes.a, The resistance of the NbN electrode as a function of the temperature.The superconducting critical temperature (TSC) is determined to be ~ 12.5 K. Inset: The characterization of the SC electrode's resistance on a typical device using the standard four-probe measurement geometry.b, The current-voltage characteristics of the NbN electrode measured at T = 2 K under the in-plane (red) and out-of-plane (black) magnetic fields (B = 9 T), respectively.

Figure 4 .
Figure 4. Magnetic properties of quasi-2D vdW Fe 0.29 TaS 2 .a, The side view of the crystal structure of itinerant quasi-2D vdW FM Fe0.29TaS2 flakes.The Fe atoms are located between the TaS2 layers, which are stacked together via vdW interaction with an interlayer distance of ~ 6 Å. b, The optical image of the Fe0.29TaS2 anomalous Hall effect (AHE) device and the measurement geometry.The thickness of the quasi-2D vdW Fe0.29TaS2 is ~ 14 nm determined via atomic force microscopy.c, The transverse resistance (Rxy) as a function of the out-of-plane magnetic field measured on the Fe0.29TaS2AHE device at T = 2 K. d, The temperature-dependent anomalous Hall resistivity of the quasi-2D vdW Fe0.29TaS2 flake.The Curie temperature (TCurie) is ~ 90 K, indicated by the black arrow.

Figure S6 .
Figure S6.Bias dependence of the conductance (dI/dV) at the Fe 0.29 TaS 2 /SC interface.a, The dI/dV curves at temperatures from T = 2 K to T = 20 K at B = 0 T. b, The dI/dV curves at magnetic fields from B = 0 T to B = 9 T at T = 2 K.The results were obtained on the device C.

Figure S7 .
Figure S7.The MR of Fe 0.29 TaS 2 /NbN as a function of the external magnetic field.The red dots represent the MR measured on the device B at T = 2 K and V3T ~ 0.4 mV, and the open black squares represent the magnetization angle as a function of the in-plane magnetic field at T = 2 K.

Figure S8 .
Figure S8.Comparison of spin-triplet MR and SC vortex-induced MR. a, b, The optical images of the spin-triplet MR device (device A) and the control device that measures the vortexinduced MR and their measurement geometry.For the control device, everything is the same as the spin-triplet MR device except that the 2D vdW FM Fe0.29TaS2 flake is replaced by a 20 nm Al electrode.c, The comparison of the spin-triplet MR (blue symbols) and vortex-induced MR (red

Figure S9 .
Figure S9.Results of control devices of Fe 0.29 TaS 2 /Al 2 O 3 /normal metal (Al).a, The optical images of a typical control device Fe0.29TaS2/Al2O3/Al, where the SC NbN electrode is replaced with ~ 50 nm Al. b, The MR results of the control device Fe0.29TaS2/ Al2O3/Al-1 measured at B = 9 T and T = 2, 4, and 8 K, respectively.c, The comparison of the spin-triplet MR (blue symbols) and control device Fe0.29TaS2/Al2O3/Al (black symbols; RJS: 59.4 Ω μm 2 ) as a function of temperature measured at B = 9 T. Inset: The MR curves of control device and the spin-triplet MR device B with similar RJS.d, e, The absence of MR signals on two other control devices Fe0.29TaS2/Al2O3/Al-2, and Fe0.29TaS2/Al2O3/Al-3 with RJS of 33.8 and 1626.2Ω μm 2 , respectively, measured at B = 9 T and T = 2 K.The blue symbols represent the MR curves on spintriplet MR devices with similar RJS.

Figure S10 .
Figure S10.The T SC of the NbN electrode and the correlation with the temperaturedependent MR. a, The temperature dependence of the resistance measured on a typical NbN electrode under the perpendicular B = 0, 5, 7, and 9 T, respectively.b-d, The temperature dependence of MR and the resistance of the NbN electrode (dashed lines) measured at B = 9, 7, and 5 T, respectively.