Long-range supercurrents through a chiral non-collinear antiferromagnet in lateral Josephson junctions

The proximity-coupling of a chiral non-collinear antiferromagnet (AFM)1–5 with a singlet superconductor allows spin-unpolarized singlet Cooper pairs to be converted into spin-polarized triplet pairs6–8, thereby enabling non-dissipative, long-range spin correlations9–14. The mechanism of this conversion derives from fictitious magnetic fields that are created by a non-zero Berry phase15 in AFMs with non-collinear atomic-scale spin arrangements1–5. Here we report long-ranged lateral Josephson supercurrents through an epitaxial thin film of the triangular chiral AFM Mn3Ge (refs. 3–5). The Josephson supercurrents in this chiral AFM decay by approximately one to two orders of magnitude slower than would be expected for singlet pair correlations9–14 and their response to an external magnetic field reflects a clear spatial quantum interference. Given the long-range supercurrents present in both single- and mixed-phase Mn3Ge, but absent in a collinear AFM IrMn16, our results pave a way for the topological generation of spin-polarized triplet pairs6–8 via Berry phase engineering15 of the chiral AFMs.

where red and black circles (blue and grey) represent Mn and Ge atoms lying in the z = c/2 (z = 0) planes, respectively. The probable antiferromagnetic configurations are presented in c when an external magnetic field is applied along [2110] (left) and [0110] (right). In each layer, Mn atoms form a Kagome-type lattice and their magnetic moments (blue or red arrows) constitute a 120° antiferromagnetic structure. The orange arrows indicate a weak uncompensated magnetization.

NATure MATerIAls
and how to avoid stray-field-driven screening supercurrents and Abrikosov vortex nucleation in adjacent superconductors when patterned to submicron lateral dimensions.
We demonstrate this radically different approach by fabricating Josephson junctions (JJs), in which several superconducting Nb electrodes are laterally separated by an epitaxial thin film of the triangular chiral antiferromagnetic Mn 3 Ge (refs. 4 [3][4][5]20 ), Mn magnetic moments in the x-y Kagome plane form triangular spin structures and lead to a non-collinear AFM configuration with a uniform negative vector chirality 3,4 caused by the Dzyaloshinskii-Moriya interaction.
Unlike Mn 3 Sn (ref. 2 ), the chiral AFM phase in Mn 3 Ge is robust to low temperature 3-5 (T), which allows one to investigate the transport properties of Josephson supercurrents associated with Berry curvature in this chiral non-collinear AFM. Crucially, the observed decay length of the Josephson supercurrents through the Mn 3 Ge is far beyond the predicted singlet coherence length ξ AFM singlet (refs. [9][10][11][12][13][14] ) and such long-ranged supercurrents are absent in JJs with a collinear AFM IrMn (ref. 15 ), providing an experimental indication of topologically generated triplet pairing states. Figure 2a,c,e shows zero-field current-voltage I-V curves of the Nb/Mn 3 Ge/Nb JJs with several edge-to-edge separation distances, d s = 28, 80 and 119 nm, across the superconducting transition of the Nb electrodes. All the JJs exhibit clear Josephson I-V characteristics that are not strongly hysteretic and which are thus in the overdamped regime, indicating a low resistance-capacitance product 21 . The T-dependent Josephson critical current can be approximately described by 22 Ic (T) ≈ Ic (0) (1 − T Tc ) α (black lines in Fig. 2b,d,f), where T c is the superconducting transition temperature at the Nb/Mn 3 Ge interfaces. Using α = 0.50-0.55, we obtain the zero-temperature critical currents |I c (0)| = 2.27, 0.90 and 0.43 mA for d s = 28, 80 and 119 nm, respectively. Note that these values are 1-2 orders of magnitude smaller than the depairing critical current in superconducting microbridges formed from Nb thin films 23 .
With increasing d s , the normal-state zero-bias resistance R n increases linearly whereas I c decays strongly (Fig. 2g), as expected from the diminishment of proximity-induced Cooper pairs in a longer Mn 3 Ge   , where we take the dirty junction regime 21 in which the mean free path is shorter than any other characteristic lengths. Note that in case of the AFM spacer, the proximity-induced pair correlations decay monotonically without an oscillatory behaviour (0-π phase transition, that is, characteristic of ferromagnet spacers) due to the microscopic cancellation of phase shifts through alternating up and down magnetic moments [24][25][26] . The estimated ξ = 155-160 nm is significantly longer than the exchange-field-driven pair breaking and decay of spin-unpolarized singlet supercurrents in the AFM, ξ AFM singlet ≈ √h D 2Eex = 1-3 nm. Here D =h 2 (3π 2 ) 2/3 3mne 2 n 1/3 ρ is the diffusion coefficient, e is the electric charge, m n is the effective electron mass that is assumed to be the free-electron m 0 = 9.1 × 10 −31 kg, n is the electron carrier density (1 × 10 19 cm −3 at T = 2 K) 27 and ρ is the resistivity (50-90 µΩ cm at T = 2 K) 3-5,27 of the Mn 3 Ge. E ex ≅ 2πk B T Néel is the AFM exchange energy of the Mn 3 Ge. In contrast, provided that spin-flip scattering and spin-orbit scattering are frozen 12,13 , spin-polarized triplet supercurrents can decay over a much longer length scale 9-14 that is limited by a thermal coherence length, ξ AFM triplet ≈ √h D 2πk B T = 33-46 nm at T = 2 K, which is in reasonable agreement with what we obtain. This long-range nature is one of the strongest indications of proximity-generated triplet pairing states [6][7][8][9][10][11][12][13][14] .
It is also worth noting that the values of ξ = 155-160 nm that we find in our system are two orders of magnitude larger than typical values (few nanometres) of the spin-diffusion length of chiral AFM Mn 3 X (X = Ge (ref. 28 ) or Sn (ref. 29 )) thin films, quantifying how far out-of-equilibrium spin polarization propagates. This suggests that in such a particular class of antiferromagnetic topological semimetals, the transfer and relaxation mechanisms of equilibrium spin carried by triplet Cooper pairs 6,17,30 may differ fundamentally from those of non-equilibrium spin by normal unpaired electrons. Further experimental and theoretical studies are required for a detailed understanding.
We next measure the magnetic field interference pattern I c (μ 0 H) in Fig. 3a-f, from which one can evaluate the transverse uniformity 21 of I c across the Mn 3 Ge barrier. For all d s = 28, 80 and 119 nm devices, I c is strongly modulated by applying a small (modest) external field μ 0 H ⊥ < 15 mT ( μ 0 H || < 150 mT) perpendicular (parallel) to the interface plane of Nb electrodes. This excludes a short circuit between the neighbouring Nb electrodes and confirms a genuine Josephson effect 21 . Note that if a short exists, I c would be almost independent of μ 0 H ⊥ ( μ 0 H || ) for such a small (modest) field range, as presented in the Supplementary Text. The zero-order maximum of I c is obtained around zero applied field μ 0 H ⊥ = μ 0 H || = 0 without a detectable hysteresis, which indicates a vanishingly small spontaneous magnetization and is consistent with features of the AFM spacer 25,26 .
For a single rectangular JJ, taking into account a non-uniform supercurrent density distribution from structural fluctuations 21 of the barrier, the sinusoidal position-dependent

NATure MATerIAls
superconducting phase by the enclosed magnetic flux Φ under application of μ 0 H gives rise to a characteristic modulation of I c (ref. 21 ). often referred to as a single-slit Fraunhofer diffraction . Here Φ = μ 0 HA eff flux and A eff flux is the effective junction area of magnetic flux penetration that is given by (2λ L + ds) w for μ 0 H ⊥ (bottom inset of Fig. 3a) or (2λ L + ds) t for μ 0 H || (bottom inset of Fig. 3b) and λ L is the London penetration depth (130 nm at 2 K) 31 of 50 nm thick Nb electrodes. w(t) is the width (effective thickness) of the Mn 3 Ge spacer and Φ 0 = h 2e is the magnetic flux quantum. γ is a measure of the supercurrent non-uniformity 21 . Best fits to the Ic (μ 0 H ⊥ ) and Ic ( μ 0 H || ) data using this formula give γ = 0.110 − 0.138, (2λ L + ds) w = 0.40-0.46 µm 2 and (2λ L + ds) t = 0.040-0.047 µm 2 , respectively. We then find w = 1.2-1.4 µm and t = 120-140 nm, which are close to the actual dimensions of our devices. Rather, monotonic I c (μ 0 H) interference patterns with less clear minima (Fig. 3a-f) for our JJs are likely because the position-dependent phase modulation deviates from the sinusoidal form due to the complicated magnetization reversal process 32 of cluster octupole domains of the chiral AFM 33 , each of which induces a tiny uncompensated magnetization, and thereby the locally varying µ 0 H-dependent internal phase 32 .
To prove that the chiral non-collinear antiferromagnetic structure, directly linked to the Berry curvature in k-space, is responsible for the observed long-range supercurrents, we replace the single-phase hexagonal D0 19 -Mn 3 Ge spacer with either a mixed phase of tetragonal D0 22 -and hexagonal D0 19 -Mn 3 Ge (Fig. 4a-c), or a polycrystalline collinear AFM IrMn (Fig. 4d-f). As presented in the Supplementary Text, the mixed-phase Mn 3 Ge reveals a large zero-field anomalous Hall effect (AHE) comparable to the bulk single crystal 3,4 , ensuring that it still hosts, to a large extent, triangular chiral antiferromagnetic domains relevant to a non-trivial topology [1][2][3][4][5] . In contrast, no AHE is detected in the polycrystalline IrMn, as expected for topologically trivial antiferromagnetic ground states 16 .
The most noteworthy result is that in the presence of chiral non-collinearity (equivalently, non-zero Berry phase), long-ranged Josephson supercurrents are established even in the mixed-phase Mn 3 Ge (Fig. 4b,c) whereas this long-range effect almost disappears when the spin arrangements of the AFM spacer are topologically trivial (Fig. 4e,f). This points unambiguously to a topological origin of Josephson coupling in the chiral AFM Mn 3 Ge, which should

NATure MATerIAls
be robust against structural disorder and impurity scattering. Note that the ξ value for the IrMn spacer is estimated to first order to be 3-5 nm (left inset of Fig. 4f and Supplementary Text) and this short-ranged Josephson coupling through the collinear AFM IrMn is in good agreement with previous reports on vertical JJs with γ−Fe 50 Mn 50 (ref. 25 ) or Cr (ref. 26 ) spacers. An intuitive explanation of these results is as follows. The 120° non-collinear arrangements of Mn magnetic moments on the atomic-scale in real-space convert spin-unpolarized singlet Cooper pairs (S = 0) to spin-zero triplets (S = 1, m s = 0). The converted spin-zero triplets (S = 1, m s = 0) in motion then experience fictitious magnetic fields (as large as roughly 100 tesla) 2-4 associated with the Berry curvature 14 in k-space and rotate to form spin-polarized triplets (S = 1, m s = ±1), which are able to penetrate much deeper [6][7][8] . Here, the fictitious magnetic fields rooted in the chiral non-collinear spin texture 2-4 play a crucial role in changing the quantization axis of the spin-zero triplets (S = 1, m s = 0) to be converted into the spin-polarized triplets (S = 1, m s = ±1). None of the above are present in the IrMn spacer, accounting for its short-range nature of Josephson coupling [6][7][8]24,25 . The essential ingredient for the realization of the long-range spin-triplet proximity effect [6][7][8] is the presence of a magnetically inhomogeneous ferromagnet/superconductor interface (often called a spin-active interface), which results in subsequent spin-mixing and spin-rotation processes [9][10][11][12][13][14] , and so far, the spin-triplet proximity effect has been experimentally observed in various JJs with half-metallic ferromagnet (CrO 2 ) 13 , intrinsically inhomogeneous conical ferromagnet (Ho) 11 and non-collinear magnetic heterostructures (PdNi or CuNi) 12 . The CrO 2 -based lateral JJs have revealed an exceptionally long decay length of 0.3-1 µm (ref. 13 ), which is supported by its half-metallicity, albeit uncertainty in the nature of the magnetic inhomogeneity. The notable aspect of the present study is that instead of the nanometre-scale inhomogeneity of ferromagnetic materials, an atomic-scale non-collinear AFM (in combination with fictitious magnetic fields) is exploited to generate the spin-triplet correlation that can extend over 155-160 nm, comparable to the CrO 2 -based JJs 13 .
We have experimentally demonstrated that lateral Josephson supercurrents through a triangular chiral AFM Mn 3 Ge (refs. [3][4][5] are long-ranged, which is a key aspect of proximity-induced spin-polarized triplet pairing states [6][7][8][9][10][11][12][13][14] . Although detailed theories, covering the triplet superconductivity and Berry curvature, need to be developed for a quantitative description, our results provide the experimental indication of topologically generated triplet pairing states via a chiral non-collinear AFM, which can potentially resolve the outstanding issues raised in conventional ferromagnet-based triplet JJs 6-14 . Last but not least, the characteristic decay length of Josephson supercurrents in our chiral AFM is found, not to be limited by hitherto believed spin-diffusion lengths, but rather hinting at topologically protected triplet supercurrents.

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41563-021-01061-9.