Abstract
The proximity-coupling of a chiral non-collinear antiferromagnet (AFM)1,2,3,4,5 with a singlet superconductor allows spin-unpolarized singlet Cooper pairs to be converted into spin-polarized triplet pairs6,7,8, thereby enabling non-dissipative, long-range spin correlations9,10,11,12,13,14. 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 arrangements1,2,3,4,5. Here we report long-ranged lateral Josephson supercurrents through an epitaxial thin film of the triangular chiral AFM Mn3Ge (refs. 3,4,5). The Josephson supercurrents in this chiral AFM decay by approximately one to two orders of magnitude slower than would be expected for singlet pair correlations9,10,11,12,13,14 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 pairs6,7,8 via Berry phase engineering15 of the chiral AFMs.
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Main
Spin-polarized triplet Cooper pairs6,7,8 can carry a non-dissipative spin angular momentum over a long distance9,10,11,12,13,14 and are a key ingredient for superconducting spintronics. This nascent research field aims to develop new types of device where spin and charge degrees of freedom are controllable by superconducting phase coherence6,7,8. Notably, recent experiments and theories have established that inhomogeneous exchange fields9,10 in real-space and/or spin-orbit fields17,18,19 in reciprocal/k-space at engineered superconductor/ferromagnet interfaces can proximity-generate spin-polarized triplet pairing states via spin-mixing and spin-rotation processes6,7,8,9,10,11,12,13,14. There remain, however, several outstanding technical issues, in particular, how to simplify the necessary multiple ferromagnet elements, how to create the desired non-collinear alignment of their magnetization directions below the exchange length scales (a few nanometres) and how to avoid stray-field-driven screening supercurrents and Abrikosov vortex nucleation in adjacent superconductors when patterned to submicron lateral dimensions.
To address these issues, we consider here chiral non-collinear antiferromagnets (AFMs)1,2,3,4,5 whose total net magnetization is essentially zero and thereby lack stray fields. The main concept is that the chiral non-collinear atomic-scale spin arrangements in real-space and the resulting fictitious magnetic fields (as large as roughly 100 tesla, refs. 2,3,4,5) from a non-vanishing Berry phase15 in k-space, effectively fulfil the spin-mixing and spin-rotation mechanisms6,7,8,9,10,11,12,13,14 required for singlet-to-triplet pair conversion.
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 Mn3Ge (refs. 4,5; Fig. 1a, see Methods for device fabrication) and by probing long-ranged Josephson supercurrents6,7,8,9,10,11,12,13,14 that show a clear magnetic field interference. The D019-Mn3Ge (ref. 20) epitaxial film used in this study (see Supplementary Text for structural analysis and magnetic properties) has a hexagonal lattice with magnetic Mn atoms forming Kagome-type sublattices stacked along the c axis (// z axis // [0001] in Fig. 1b), isostructural with Mn3Sn (ref. 2). Below the Néel temperature TNéel of roughly 380 K (refs. 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 chirality3,4 caused by the Dzyaloshinskii–Moriya interaction. Unlike Mn3Sn (ref. 2), the chiral AFM phase in Mn3Ge is robust to low temperature3,4,5 (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 Mn3Ge is far beyond the predicted singlet coherence length \(\xi _{\mathrm{{singlet}}}^{\mathrm{{AFM}}}\) (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/Mn3Ge/Nb JJs with several edge-to-edge separation distances, ds = 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 product21. The T-dependent Josephson critical current can be approximately described by22 \(I_{\mathrm{c}}\left( T \right) \approx I_{\mathrm{c}}\left( 0 \right)( {1 - \frac{T}{{T_{\mathrm{c}}}}})^\alpha\) (black lines in Fig. 2b,d,f), where Tc is the superconducting transition temperature at the Nb/Mn3Ge interfaces. Using α = 0.50–0.55, we obtain the zero-temperature critical currents |Ic(0)| = 2.27, 0.90 and 0.43 mA for ds = 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 films23.
With increasing ds, the normal-state zero-bias resistance Rn increases linearly whereas Ic decays strongly (Fig. 2g), as expected from the diminishment of proximity-induced Cooper pairs in a longer Mn3Ge spacer. To quantify the decay length ξ of the supercurrents, we fit the ds-dependent characteristic voltage \(V_{\mathrm{c}}\left( {d_{\mathrm{s}}} \right) = I_{\mathrm{c}}R_{\mathrm{n}}\left( {d_{\mathrm{s}}} \right)\) at T = 2 K (Fig. 2h) using an exponential decay function, \({{\mathrm{exp}}}\left( { - \frac{{d_{\mathrm{s}}}}{\xi }} \right)\)24,25,26, where we take the dirty junction regime21 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 moments24,25,26. 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, \(\xi _{\mathrm{{singlet}}}^{\mathrm{{AFM}}} \approx \sqrt {\frac{{\hbar D}}{{2E_{\mathrm{{ex}}}}}}\) = 1–3 nm. Here \(D = \frac{{\hbar ^2\left( {3\pi ^2} \right)^{2/3}}}{{3m_ne^2n^{1/3}\rho }}\) is the diffusion coefficient, e is the electric charge, mn is the effective electron mass that is assumed to be the free-electron m0 = 9.1 × 10−31 kg, n is the electron carrier density (1 × 1019 cm−3 at T = 2 K)27 and ρ is the resistivity (50–90 µΩ cm at T = 2 K)3,4,5,27 of the Mn3Ge. Eex ≅ \(2\pi k_{\mathrm{B}}T_{{{{\rm{N}}{\acute{{\rm{e}}}}{\rm{el}}}}}\) is the AFM exchange energy of the Mn3Ge. In contrast, provided that spin-flip scattering and spin-orbit scattering are frozen12,13, spin-polarized triplet supercurrents can decay over a much longer length scale9,10,11,12,13,14 that is limited by a thermal coherence length, \(\xi _{\mathrm{{triplet}}}^{\mathrm{{AFM}}} \approx \sqrt {\frac{{\hbar D}}{{2\pi k_{\mathrm{B}}T}}}\) = 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 states6,7,8,9,10,11,12,13,14.
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 Mn3X (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 pairs6,17,30 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 Ic (μ0H) in Fig. 3a–f, from which one can evaluate the transverse uniformity21 of Ic across the Mn3Ge barrier. For all ds = 28, 80 and 119 nm devices, Ic is strongly modulated by applying a small (modest) external field \(\mu _0H_ \bot\) < 15 mT (\(\mu _0H_{||}\) < 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 effect21. Note that if a short exists, Ic would be almost independent of \(\mu _0H_ \bot\) (\(\mu _0H_{||}\)) for such a small (modest) field range, as presented in the Supplementary Text. The zero-order maximum of Ic is obtained around zero applied field \(\mu _0H_ \bot\) = \(\mu _0H_{||}\) = 0 without a detectable hysteresis, which indicates a vanishingly small spontaneous magnetization and is consistent with features of the AFM spacer25,26.
For a single rectangular JJ, taking into account a non-uniform supercurrent density distribution from structural fluctuations21 of the barrier, the sinusoidal position-dependent superconducting phase by the enclosed magnetic flux Φ under application of μ0H gives rise to a characteristic modulation of Ic (ref. 21). often referred to as a single-slit Fraunhofer diffraction pattern, \(I_{\mathrm{c}}\left( {\mu _0H} \right) = I_{\mathrm{c}}\sqrt {{\mathrm{sinc}}\left( {\frac{{\Phi}}{{{\Phi}_0}}} \right)^2 + \gamma ^2\left[ {1 - {\mathrm{sinc}}\left( {\frac{{\Phi}}{{{\Phi}_0}}} \right)^2} \right]}\). Here \({\Phi} = \mu _0HA_{\mathrm{{flux}}}^{\mathrm{{eff}}}\) and \(A_{\mathrm{{flux}}}^{\mathrm{{eff}}}\) is the effective junction area of magnetic flux penetration that is given by \(\left( {2\lambda _L + d_{\mathrm{s}}} \right)w\) for \(\mu _0H_ \bot\) (bottom inset of Fig. 3a) or \(\left( {2\lambda _L + d_{\mathrm{s}}} \right)t\) for \(\mu _0H_{||}\) (bottom inset of Fig. 3b) and λL 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 Mn3Ge spacer and \({\Phi}_0 = \frac{h}{{2e}}\) is the magnetic flux quantum. γ is a measure of the supercurrent non-uniformity21. Best fits to the \(I_{\mathrm{c}}\left( {\mu _0H_ \bot } \right)\) and \(I_{\mathrm{c}}\left( {\mu _0H_{||}} \right)\) data using this formula give \(\gamma = 0.110 - 0.138\), \(\left( {2\lambda _L + d_{\mathrm{s}}} \right)w\) = 0.40–0.46 µm2 and \(\left( {2\lambda _L + d_{\mathrm{s}}} \right)t\) = 0.040–0.047 µm2, 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 Ic(μ0H) 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 process32 of cluster octupole domains of the chiral AFM33, each of which induces a tiny uncompensated magnetization, and thereby the locally varying µ0H-dependent internal phase32.
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 D019-Mn3Ge spacer with either a mixed phase of tetragonal D022- and hexagonal D019-Mn3Ge (Fig. 4a–c), or a polycrystalline collinear AFM IrMn (Fig. 4d–f). As presented in the Supplementary Text, the mixed-phase Mn3Ge reveals a large zero-field anomalous Hall effect (AHE) comparable to the bulk single crystal3,4, ensuring that it still hosts, to a large extent, triangular chiral antiferromagnetic domains relevant to a non-trivial topology1,2,3,4,5. In contrast, no AHE is detected in the polycrystalline IrMn, as expected for topologically trivial antiferromagnetic ground states16.
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 Mn3Ge (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 Mn3Ge, which should 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−Fe50Mn50 (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, ms = 0). The converted spin-zero triplets (S = 1, ms = 0) in motion then experience fictitious magnetic fields (as large as roughly 100 tesla)2,3,4 associated with the Berry curvature14 in k-space and rotate to form spin-polarized triplets (S = 1, ms = ±1), which are able to penetrate much deeper6,7,8. Here, the fictitious magnetic fields rooted in the chiral non-collinear spin texture2,3,4 play a crucial role in changing the quantization axis of the spin-zero triplets (S = 1, ms = 0) to be converted into the spin-polarized triplets (S = 1, ms = ±1). None of the above are present in the IrMn spacer, accounting for its short-range nature of Josephson coupling6,7,8,24,25.
The essential ingredient for the realization of the long-range spin-triplet proximity effect6,7,8 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 processes9,10,11,12,13,14, and so far, the spin-triplet proximity effect has been experimentally observed in various JJs with half-metallic ferromagnet (CrO2)13, intrinsically inhomogeneous conical ferromagnet (Ho)11 and non-collinear magnetic heterostructures (PdNi or CuNi)12. The CrO2-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 CrO2-based JJs13.
We have experimentally demonstrated that lateral Josephson supercurrents through a triangular chiral AFM Mn3Ge (refs. 3,4,5) are long-ranged, which is a key aspect of proximity-induced spin-polarized triplet pairing states6,7,8,9,10,11,12,13,14. 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 JJs6,7,8,9,10,11,12,13,14. 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.
Methods
Sample preparation and characterization
All the thin films were grown by d.c. magnetron sputtering in a homemade ultra-high vacuum system with a base pressure of 1 × 10−9 Torr. The single-phase hexagonal D019-Mn3Ge(0001) thin film was grown epitaxially on a Ru-buffered Al2O3(0001) substrate. A 5 nm thick Ru buffer layer was first sputtered at 450 °C with a sputter power of 15 W and at an Ar pressure of 3 mTorr. The Mn and Ge were subsequently codeposited from elemental sputter targets on the Ru(0001) buffer layer at 500 °C and at an Ar pressure of 3 mTorr. The optimized sputter powers were 31 and 10 W for Mn and Ge, respectively. The final composition was determined ex situ by Rutherford backscattering spectrometry to be Mn3.2Ge, where the excess Mn helps to stabilize the hexagonal D019 phase28. To study the ground-state chiral non-collinearity dependence (Fig. 4), the mixed phase of tetragonal D022- and hexagonal D019-Mn3Ge(\(11\bar 20\)) film was prepared using the same growth procedure but on a Ru-buffered sapphire Al2O3\((1\bar 102)\) substrate and the polycrystalline thin film of collinear AFM IrMn was sputtered at 27 °C on a SiO2(25 nm)/Si substrate. The used sputter powers were 15 and 30 W for Ir and Mn, respectively. We note here that the thickness of Mn3Ge and IrMn films was fixed at 40 nm that is much larger than their singlet coherence length (a few nanometres)24,25,26. So the singlet-pair-mediated Josephson coupling through the ultrathin Ru buffer layer of Nb/Mn3Ge/Nb junctions is unlikely (see the main text for a detailed discussion). Using these unpatterned films, we performed magneto-transport measurements in a Van der Pauw geometry to investigate the Berry curvature-driven AHE1,2,3,4,5 (Supplementary Text). To probe AFM ordering, indirectly from exchange-biased magnetic hysteresis curve measurements (Supplementary Text), a 10 nm thick Ni8Fe2 layer was sputtered on top of the Mn3Ge and IrMn film. All these films were capped with a 1 nm thick AlOx layer to prevent oxidation.
Device fabrication
To fabricate the lateral JJs (Fig. 1a), we first defined a central AFM track with a lateral dimension of 1.5 × 50 μm2 using optical lithography and Ar-ion beam etching. We then defined Au (80 nm)/Ru (2 nm) electrical leads and bonding pads, which were deposited by Ar-ion beam sputtering. Subsequently, we defined multiple Nb electrodes with an active lateral dimension of 1.0 × 1.5 μm2 on top the AFM track via electron-beam lithography and lift-off steps. The 50-nm thick Nb electrodes were grown by Ar-ion beam sputtering at a pressure of 1.5 × 10–4 mbar and they were edge-to-edge separated by 28–119 nm from each other. Before sputtering the Nb electrodes, the Al2O3 capping layer and Au surface were Ar-ion beam etched away to make possible direct metallic electrical contacts.
Transport measurement
We measured current–voltage I–V curves of the fabricated JJs (Fig. 1a) with a four-probe configuration in a Quantum Design Physical Property Measurement System using a Keithley 6221 current source and a Keithley 2182A nanovoltmeter. The zero-field I–V curves (Fig. 2a–f) were measured across the superconducting transition of Nb electrodes. The Josephson critical current Ic and the normal-state zero-bias resistance Rn of each JJ (Fig. 2g) were determined by fitting the measured I–V curves with the standard formula for overdamped junctions21, \(V(I) = \frac{I}{{|I|}}R_{\mathrm{n}}\sqrt {I^2 - I_{\mathrm{c}}^2}\). As the I–V curves were slightly shifted horizontally, we defined Ic values in positive and negative current directions. We obtained the magnetic field interference patterns Ic (μ0H) (Figs. 3a–f and 4b,c) by repeating the I–V measurements at T = 2 K at the applied magnetic field \(\mu _0H_ \bot\) (\(\mu _0H_{||}\)) perpendicular (parallel) to the interface plane of Nb electrodes. We note here that no significant change in the magnetic interference patterns between zero-field-cooled and field-cooled (1 T) conditions for our JJs with the single-phase Mn3Ge(0001) spacer has been observed. This supports that the chiral non-collinear atomic-scale AFM spin arrangements (as strong as a few hundred tesla at least) are indeed responsible for the observed long-range Josephson coupling in our system. For the same reason, asymmetric hysteretic behaviour in R-\(\mu _0H_ \bot\) curves of our chiral AFM JJs, reflecting a link between the magnetic ordering and the superconducting state, is weak, but evident, further supporting the spin-polarized triplet pairing interpretation (Supplementary Text).
Data availability
The data used in this paper are available from the corresponding authors upon reasonable request.
Change history
02 November 2021
In the version of this article initially published online, the following metadata was omitted and has now been included: “Open access funding provided by Max Planck Institute of Microstructure Physics (2)”
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Acknowledgements
This work was supported by the Alexander von Humboldt Foundation. We are grateful to S. Komori and J. W. A. Robinson at the University of Cambridge for useful discussions, and to K. Mohseni at the Max Planck Institute of Microstructure Physics for the XRD data analysis.
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K.-R.J. and S.S.P.P. conceived and designed the experiments with the help of T.K. B.K.H. prepared thin films of the chiral non-collinear AFM Mn3Ge and the collinear AFM IrMn, and characterized their crystallinity and magnetic properties. H.L.M. and H.H. contributed to the structural analysis. K.-R.J. fabricated the lateral JJs with help from K.C., A.C. and J.-C.J., and carried out the transport measurements with the help of J.-C.J. K.-R.J. performed the data analysis with help from T.K. S.S.P.P. supervised the project. K.-R.J., B.K.H. and S.S.P.P. wrote the manuscript with input from all the other co-authors.
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Jeon, KR., Hazra, B.K., Cho, K. et al. Long-range supercurrents through a chiral non-collinear antiferromagnet in lateral Josephson junctions. Nat. Mater. 20, 1358–1363 (2021). https://doi.org/10.1038/s41563-021-01061-9
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DOI: https://doi.org/10.1038/s41563-021-01061-9
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