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

## Abstract

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.

## Introduction

Fundamental symmetry breaking and relativistic spin–orbit coupling give rise to interesting phenomena in quantum materials1,2. For over 60 years, the interplay between ferromagnetism and superconductivity, has offered a wealth of intriguing phenomena in ferromagnet (FM)/superconductor (SC) heterostructures3,4,5,6. 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 spintronics5,6,7, and probing quantum materials8, as well as for realizing elusive Majorana bound states to implement topological quantum computing9,10. The common expectation that spin-triplet pairing in superconducting spintronics requires complex FM multilayers, typically relying on noncollinear/spiral magnetization or half metals3,4,5,6,11.

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 heterostructures12. Our results pave the way for future studies on spin-triplet superconductivity13,14 and the formation on Majorana bound states9,10, as well as many normal-state spintronic applications15.

## Results and discussion

### Spin-triplet Andreev reflection and spin-triplet MR

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 SOC16,17, spin-rotation symmetry is broken for the superconducting pairing (Fig. 1c), which acts as a spin-mixing described in conventional FM/SC heterostructures5,6. 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 field14,19. 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 process5. For example, for FM magnetization along z axis (perpendicular to the interface), unpolarized spin-triplet Cooper pairs component $$\big(|S=1,{S}_{{{{{{\rm{y}}}}}}}=0\rangle \,{{{{{\rm{and}}}}}}\,|S=1,{S}_{{{{{{\rm{x}}}}}}}=0\rangle$$ can be projected to the spin quantization axis as $$|S=1,{S}_{{{{{{\rm{z}}}}}}}=1{\rangle }$$ due to the spin rotation process ($${S}_{{{{{{\mathrm{y}}}}}}}$$, $${{S}}_{{{{{{\mathrm{x}}}}}}}$$, and $${{S}}_{{{{{{\mathrm{z}}}}}}}$$ are the spin quantum numbers along y, x, and z direction, respectively). Thus, both the $${|S}=1,{S}_{{{{{{\mathrm{y}}}}}}}=0{\rangle}$$ and $${|S}=1,{S}_{{{{{{\mathrm{x}}}}}}}=0{\rangle}$$ 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 ($$|S=1,{S}_{{{{{{\mathrm{y}}}}}}}=1{{\rangle }}$$) can only be projected from unpolarized spin-triplet pairing component $$|S=1,{S}_{{{{{{\mathrm{x}}}}}}}=0{\rangle }$$, since $$\left[{S}_{{{{{{\mathrm{x}}}}}}},{S}_{{{{{{\mathrm{y}}}}}}}\,\right]\ne\, 0$$. 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-resistance (high-resistance) state for M out-of-plane (in-plane) (Fig. 1d, e). Hence, the spin-triplet Andreev reflection can lead to the tunneling anisotropic magnetoresistance (MR) at the FM/SC interface, a proposed hallmark of the interfacial SOC and spin-triplet superconductivity in FM/SC heterostructures14,19.

To experimentally probe the anisotropic spin-triplet Andreev reflection and spin-triplet MR, we fabricate the FM/SC devices (see “Methods” section 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° 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 see “Methods” section). 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 ($${\Theta }_{{{{{{\rm{yz}}}}}}}$$) at T = 2 K and B = 9 T. The observed MR shows a strong correlation with B-controlled 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 and 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 SOC14. Figure 2c shows the MR results measured on the device B as a function of $${\Theta }_{{{{{{\rm{yz}}}}}}}$$ at T = 2 K and B = 9 T. The MR ratio can be defined as:

$${{{{{\rm{MR}}}}}}({\Theta }_{{{{{{\rm{yz}}}}}}})\,=\,\frac{R({\Theta }_{{{{{{\rm{yz}}}}}}})\,-\,R({\Theta }_{{{{{{\rm{yz}}}}}}}\,=\,0)}{R({\Theta }_{{{{{{\rm{yz}}}}}}}\,=\,0)}\times 100 \%.$$
(1)

The $$R({\Theta }_{{{{{{\rm{yz}}}}}}}=0)$$ and $$R({\Theta }_{{{{{{\rm{yz}}}}}}}=90)$$ 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 SOC16,17.

### Temperature evolution of spin-triplet MR

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 ($${\Theta }_{{{{{{\rm{yz}}}}}}}$$) 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 negligible21,22.

### Voltage dependence of spin-triplet MR

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 transmissions14, 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 $${\Theta }_{{{{{{\rm{yz}}}}}}}\,=\,0$$ (V3T_0) is used to qualitatively show the interface voltage dependence of the spin-triplet MR. Figure 4b, c 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 $${k}_{{{{{{\rm{B}}}}}}}T$$ ~ 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 correlated to the sub-gap properties, and is completely different form B-induced spin-splitting density of states at the gap edges of SC electrodes23.

### Interface barrier dependence of spin-triplet MR

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 μm2, resulting in the FM/SC heterostructures with very different Z-values. Figure 5 shows 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 μm2. The strong correlation of the MR ratio and RJS reveals the important role of the Z-value in the spin-triplet MR.

This surprising nonmonotonic MR dependence on RJS agrees well with the theoretical expectations14,25. The effective barrier strength is modified by SOC and depends on the helicity (outer/inner Rashba bands, Fig. 1b), $${Z}_{\pm }=Z\pm {\bar{\gamma }k}_{\parallel }$$, where $$\bar{\gamma }$$ is the SOC parameter25 and $${k}_{\parallel }$$ is the component of the wave vector along the interface (Fig. 5 inset). At zero $${k}_{\parallel }$$, the vanishing of Rashba SOC does not support spin-triplet component. At nonzero $${{k}}_{\parallel },$$ increasing $$Z$$ can reduce $${{|Z}}_{+}|$$ or $${{|Z}}_{-}{|}$$ and thus enhance such a transmission for a given helicity. For much larger $$Z$$, 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. 24) are all 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 systems14,25, 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.

### Summary and outlook

Our experimental obervation of a large tunneling anisotropic MR in quasi-2D vdW FM/s-wave 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 layer16,17. 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 fields26,27,28,29. This tantalizing opportunity to implement FM/SC heterostructures to design and probe interfacial SOC offers an important boost for superconducting spintronics36,30,31 and Majorana bounds states9,32. Furthermore, our quasi-2D platform of proximity-induced spin-triplet superconductivity, combined with the gate-controlled 2D vdW ferromagnetism28,29,33 could provide tunable magnetic textures to create synthetic SOC34 and braid Majorana bound states35.

## Methods

### Device fabrication

The quasi-2D vdW Fe0.29TaS2/SC spin-triplet MR devices were fabricated as follows. 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 substrates20. 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.

### Spin-triplet MR measurement

The MR measurement of the quasi-2D vdW Fe0.29TaS2/SC devices was performed in a Physical Properties Measurement System (PPMS; Quantum Design). A bias (Vbias) was applied between the SC electrode and one normal Pt electrode using a Keithley K2400, the source–drain current (Isd) was measured using the same K2400, and the voltage (V3T) between the SC electrode and the other Pt electrode was measured using a Keithley 2002. The interfacial resistance was obtained via dividing the three-terminal voltage by the source–drain current (R3T = V3T/Isd). During the measurement of each spin-triplet MR curve, the quasi-2D vdW Fe0.29TaS2/SC device was rotated from 0 to 360 degrees under the external static magnetic field in the PPMS.

## Data availability

The data that support the findings of this study are available from the corresponding authors upon request.

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## Acknowledgements

We thank E. I. Rashba for valuable discussions. R.C., Y.Y., Y.M., W.X., B.L., Y.J., H.Z., S.J., X.C.X., Q.-F.S., and W.H. acknowledge the financial support from National Basic Research Programs of China (Nos. 2019YFA0308401, 2017YFA0303301, and 2018YFA0305601), National Natural Science Foundation of China (Nos. 11974025, 11921005, 11947053, 11774007, and U1832214), Beijing Natural Science Foundation (No. 1192009), and the Key Research Program of the Chinese Academy of Sciences (Grant No. XDB28000000). P.L. also acknowledges the financial support from Hubei Provincial Natural Science Foundation of China (No. 2019CFB218). C.S. and I.Z. acknowledge the support from U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE- SC0004890.

## Author information

Authors

### Contributions

R.C., W.X., and B.L. prepared the 2D van der Waals ferromagnet Fe0.29TaS2 flakes and fabricated the devices. R.C., Y.Y., Y.M., and Y.J. performed the MR measurements. P.L., C.S., X.C.X., I.Z., and Q.-F.S. performed the theoretical analysis. H.Z. and S.J. synthesized the bulk Fe0.29TaS2 single crystals. W.H. supervised the experiments and wrote the manuscript with contributions from all authors. All the authors discussed the results and contributed to the final version of the manuscript.

### Corresponding author

Correspondence to Wei Han.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Cai, R., Yao, Y., Lv, P. et al. Evidence for anisotropic spin-triplet Andreev reflection at the 2D van der Waals ferromagnet/superconductor interface. Nat Commun 12, 6725 (2021). https://doi.org/10.1038/s41467-021-27041-w

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• DOI: https://doi.org/10.1038/s41467-021-27041-w

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