Long-range Supercurrents In Chiral Non-collinear Antiferromagnetic Junctions – Nature Materials

Spin-polarized triplet Cooper pairs^6,7,8 can carry a non-dissipative spin angular momentum over an extended distance^{9,10,11,12,13,14} and are a key ingredient for superconducting spintronics. This nascent analysis area goals to develop new varieties of system the place spin and cost levels of freedom are controllable by superconducting part coherence^6,7,8. Notably, latest experiments and theories have established that inhomogeneous change fields^9,10 in real-space and/or spin-orbit fields^17,18,19 in reciprocal/okay-space at engineered superconductor/ferromagnet interfaces can proximity-generate spin-polarized triplet pairing states through spin-mixing and spin-rotation processes^{6,7,8,9,10,11,12,13,14}. There stay, nevertheless, a number of excellent technical points, particularly, easy methods to simplify the mandatory a number of ferromagnet parts, easy methods to create the specified non-collinear alignment of their magnetization instructions beneath the change size scales (just a few nanometres) and easy methods to keep away from stray-field-driven screening supercurrents and Abrikosov vortex nucleation in adjoining superconductors when patterned to submicron lateral dimensions.

To handle these points, we think about right here chiral non-collinear antiferromagnets (AFMs)^1,2,3,4,5 whose whole web magnetization is actually zero and thereby lack stray fields. The primary idea is that the chiral non-collinear atomic-scale spin preparations in real-space and the ensuing fictitious magnetic fields (as giant as roughly 100 tesla, refs. ^2,3,4,5) from a non-vanishing Berry part¹⁵ in okay-space, successfully fulfil the spin-mixing and spin-rotation mechanisms^{6,7,8,9,10,11,12,13,14} required for singlet-to-triplet pair conversion.

We reveal this radically completely different method by fabricating Josephson junctions (JJs), by which a number of superconducting Nb electrodes are laterally separated by an epitaxial skinny movie of the triangular chiral antiferromagnetic Mn₃Ge (refs. ^4,5; Fig. 1a, see Methods for system fabrication) and by probing long-ranged Josephson supercurrents^{6,7,8,9,10,11,12,13,14} that present a transparent magnetic area interference. The D0₁₉-Mn₃Ge (ref. ²⁰) epitaxial movie used on this examine (see Supplementary Text for structural evaluation and magnetic properties) has a hexagonal lattice with magnetic Mn atoms forming Kagome-type sublattices stacked alongside the c axis (// z axis // [0001] in Fig. 1b), isostructural with Mn₃Sn (ref. ²). Below the Néel temperature T_Néel of roughly 380 Ok (refs. ^3,4,5,20), Mn magnetic moments within the x–y Kagome airplane type triangular spin constructions and result in a non-collinear AFM configuration with a uniform destructive vector chirality^3,4 attributable to the Dzyaloshinskii–Moriya interplay. Unlike Mn₃Sn (ref. ²), the chiral AFM part in Mn₃Ge is strong to low temperature^3,4,5 (T), which permits one to research the transport properties of Josephson supercurrents related to Berry curvature on this chiral non-collinear AFM. Crucially, the noticed decay size of the Josephson supercurrents by means of the Mn₃Ge is much past the anticipated singlet coherence size (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), offering an experimental indication of topologically generated triplet pairing states.

Fig. 1: Chiral non-collinear AFM JJs.

a, Scanning electron micrographs of the fabricated JJs, consisting of a triangular chiral antiferromagnetic Mn₃Ge (40-nm-thick) spacer and a number of superconducting Nb (50-nm thick) electrodes. These Nb electrodes are laterally edge-to-edge separated by 28–119 nm from one another (backside). The higher scale bar is 3 µm, decrease scale bars are 0.5 µm. Note that the 5-nm-ultrathin Ru underlayer serves as a buffer layer (Methods). b,c, Crystal construction (b) and 120^o chiral antiferromagnetic configuration (c) of D0₁₉-Mn₃Ge. Two layers of Mn and Ge atoms are stacked alongside the c axis (// z axis) the place purple and black circles (blue and gray) symbolize Mn and Ge atoms mendacity within the z = c/2 (z = 0) planes, respectively. The possible antiferromagnetic configurations are offered in c when an exterior magnetic area is utilized alongside ([{2bar 1bar 10}]) (left) and ([{0bar 110}]) (proper). In every layer, Mn atoms type a Kagome-type lattice and their magnetic moments (blue or purple arrows) represent a 120° antiferromagnetic construction. The orange arrows point out a weak uncompensated magnetization.

Figure 2a,c,e exhibits zero-field present–voltage I–V curves of the Nb/Mn₃Ge/Nb JJs with a number of edge-to-edge separation distances, d_s = 28, 80 and 119 nm, throughout the superconducting transition of the Nb electrodes. All the JJs exhibit clear Josephson I–V traits that aren’t strongly hysteretic and that are thus within the overdamped regime, indicating a low resistance-capacitance product²¹. The T-dependent Josephson important present might be roughly described by²²(I_{mathrm{c}}left( T proper) approx I_{mathrm{c}}left( 0 proper)( {1 – frac{T}{{T_{mathrm{c}}}}})^alpha) (black traces in Fig. 2b,d,f), the place T_c is the superconducting transition temperature on the Nb/Mn₃Ge interfaces. Using α = 0.50–0.55, we acquire the zero-temperature important 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 important present in superconducting microbridges shaped from Nb skinny movies²³.

Fig. 2: Long-ranged supercurrents by means of a chiral non-collinear AFM.

a,c,e, Zero-field present–voltage I–V traits of Nb/Mn₃Ge/Nb JJs with completely different edge-to-edge separations d_s = 28 (a), 80 (c) and 119 nm (e), taken above (gray) and beneath (purple) the superconducting transition of the Nb electrodes. The black stable traces are becoming curves to find out the Josephson important present I_c. b,d,f, Associated temperature T dependence of I_c with d_s = 28 (b), 80 (d) and 119 nm (f). The black stable traces are theoretical matches to estimate the zero-temperature I_c. g, Normal-state zero-bias resistance R_n (high) and I_c (backside) of the JJs versus d_s. From R_n(d_s), we extract the resistance-area product of Nb/Mn₃Ge interfaces to be 1 mΩ µm² and the efficient resistivity for the Mn₃Ge (40 nm)/Ru (5 nm) observe to be 26 µΩ cm, utilizing an ordinary transmission line (TL) concept (black line, see Supplementary Text for comparability with Hall-bar gadgets). h, Characteristic voltage V_c = I_cR_n as a perform of d_s, from which the decay size of the Josephson coupling by means of the Mn₃Ge spacer is decided utilizing an exponential decay perform (black curves).

With growing d_s, the normal-state zero-bias resistance R_n will increase linearly whereas I_c decays strongly (Fig. 2g), as anticipated from the diminishment of proximity-induced Cooper pairs in an extended Mn₃Ge spacer. To quantify the decay size ξ of the supercurrents, we match the d_s-dependent attribute voltage (V_{mathrm{c}}left( {d_{mathrm{s}}} proper) = I_{mathrm{c}}R_{mathrm{n}}left( {d_{mathrm{s}}} proper)) at T = 2 Ok (Fig. 2h) utilizing an exponential decay perform, ({{mathrm{exp}}}left( { – frac{{d_{mathrm{s}}}}{xi }} proper))^24,25,26, the place we take the soiled junction regime²¹ by which the imply free path is shorter than another attribute lengths. Note that in case of the AFM spacer, the proximity-induced pair correlations decay monotonically with out an oscillatory behaviour (0–π part transition, that’s, attribute of ferromagnet spacers) as a result of microscopic cancellation of part shifts by means of alternating up and down magnetic moments^24,25,26. The estimated ξ = 155–160 nm is considerably longer than the exchange-field-driven pair breaking and decay of spin-unpolarized singlet supercurrents within the AFM, (xi _{mathrm{{singlet}}}^{mathrm{{AFM}}} approx sqrt {frac{{hbar D}}{{2E_{mathrm{{ex}}}}}}) = 1–3 nm. Here (D = frac{{hbar ^2left( {3pi ^2} proper)^{2/3}}}{{3m_ne^2n^{1/3}rho }}) is the diffusion coefficient, e is the electrical cost, m_n is the efficient electron mass that’s assumed to be the free-electron m₀ = 9.1 × 10⁻³¹ kg, n is the electron provider density (1 × 10¹⁹ cm⁻³ at T = 2 Ok)²⁷ and ρ is the resistivity (50–90 µΩ cm at T = 2 Ok)^3,4,5,27 of the Mn₃Ge. E_ex ≅ (2pi k_{mathrm{B}}T_{{{{rm{N}}{acute{{rm{e}}}}{rm{el}}}}}) is the AFM change vitality of the Mn₃Ge. In distinction, offered that spin-flip scattering and spin-orbit scattering are frozen^12,13, spin-polarized triplet supercurrents can decay over a for much longer size scale^{9,10,11,12,13,14} that’s restricted by a thermal coherence size, (xi _{mathrm{{triplet}}}^{mathrm{{AFM}}} approx sqrt {frac{{hbar D}}{{2pi k_{mathrm{B}}T}}}) = 33–46 nm at T = 2 Ok, which is in affordable settlement with what we acquire. This long-range nature is likely one of the strongest indications of proximity-generated triplet pairing states^{6,7,8,9,10,11,12,13,14}.

It can be value noting that the values of ξ = 155–160 nm that we discover in our system are two orders of magnitude bigger than typical values (few nanometres) of the spin-diffusion size of chiral AFM Mn₃X (X = Ge (ref. ²⁸) or Sn (ref. ²⁹)) skinny movies, quantifying how far out-of-equilibrium spin polarization propagates. This means that in such a specific class of antiferromagnetic topological semimetals, the switch and leisure mechanisms of equilibrium spin carried by triplet Cooper pairs^6,17,30 might differ essentially from these of non-equilibrium spin by regular unpaired electrons. Further experimental and theoretical research are required for an in depth understanding.

We subsequent measure the magnetic area interference sample I_c (μ₀H) in Fig. 3a–f, from which one can consider the transverse uniformity²¹ of I_c throughout the Mn₃Ge barrier. For all d_s = 28, 80 and 119 nm gadgets, I_c is strongly modulated by making use of a small (modest) exterior area (mu _0H_ bot) < 15 mT ((mu _0H_) < 150 mT) perpendicular (parallel) to the interface airplane of Nb electrodes. This excludes a brief circuit between the neighbouring Nb electrodes and confirms a real Josephson impact²¹. Note that if a brief exists, I_c can be nearly impartial of (mu _0H_ bot) ((mu _0H_)) for such a small (modest) area vary, as offered within the Supplementary Text. The zero-order most of I_c is obtained round zero utilized area (mu _0H_ bot) = (mu _0H_) = 0 with out a detectable hysteresis, which signifies a vanishingly small spontaneous magnetization and is according to options of the AFM spacer^25,26.

Fig. 3: Magnetic area interference patterns reflecting spatial quantum interference.

a,c,e, Josephson important present I_c versus magnetic area (mu _0H_ bot) plots for the d_s = 28 (a), 80 (c) and 119 nm (e) Nb/Mn₃Ge/Nb junctions, taken at a set T = 2 Ok. In these measurements, (mu _0H_ bot) is utilized perpendicular to the interface airplane of the Nb electrodes. The high inset shows the present–voltage I–V curve of every junction round zero-order minimal of I_c((mu _0H_ bot)). The backside inset in a schematically illustrates the efficient junction space (A_{mathrm{{flux}}}^{mathrm{{eff}}}) of magnetic flux penetration, given by (left( {2lambda _L + d_{mathrm{s}}} proper)w). Here λ_L is the London penetration depth of the Nb electrodes and w is the width of the Mn₃Ge spacer. b,d,f, Data equal to a,d,e however for the magnetic area (mu _0H_) utilized parallel to the interface airplane of the Nb electrodes for d_s = 28 (b), 80 (d) and 119 nm (f). Note that, accordingly, (A_{mathrm{{flux}}}^{mathrm{{eff}}}) adjustments to (left( {2lambda _L + d_{mathrm{s}}} proper)t) the place t is the efficient thickness of the Mn₃Ge spacer.

For a single rectangular JJ, bearing in mind a non-uniform supercurrent density distribution from structural fluctuations²¹ of the barrier, the sinusoidal position-dependent superconducting part by the enclosed magnetic flux Φ beneath utility of μ₀H provides rise to a attribute modulation of I_c (ref. ²¹). sometimes called a single-slit Fraunhofer diffraction sample, (I_{mathrm{c}}left( {mu _0H} proper) = I_{mathrm{c}}sqrt {{mathrm{sinc}}left( {frac{{Phi}}{{{Phi}_0}}} proper)^2 + gamma ^2left[ {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 efficient junction space of magnetic flux penetration that’s given by (left( {2lambda _L + d_{mathrm{s}}} proper)w) for (mu _0H_ bot) (backside inset of Fig. 3a) or (left( {2lambda _L + d_{mathrm{s}}} proper)t) for (mu _0H_) (backside inset of Fig. 3b) and λ_L is the London penetration depth (130 nm at 2 Ok)³¹ of fifty nm thick Nb electrodes. w(t) is the width (efficient 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 matches to the (I_{mathrm{c}}left( {mu _0H_ bot } proper)) and (I_{mathrm{c}}left( mu _0H_ proper)) knowledge utilizing this components give (gamma = 0.110 – 0.138), (left( {2lambda _L + d_{mathrm{s}}} proper)w) = 0.40–0.46 µm² and (left( {2lambda _L + d_{mathrm{s}}} proper)t) = 0.040–0.047 µm², respectively. We then discover w = 1.2–1.4 µm and t = 120–140 nm, that are near the precise dimensions of our gadgets. Rather, monotonic I_c(μ₀H) interference patterns with much less clear minima (Fig. 3a–f) for our JJs are seemingly as a result of the position-dependent part modulation deviates from the sinusoidal type as a result of sophisticated magnetization reversal course of³² of cluster octupole domains of the chiral AFM³³, every of which induces a tiny uncompensated magnetization, and thereby the domestically various µ₀H-dependent inside part³².

To show that the chiral non-collinear antiferromagnetic construction, immediately linked to the Berry curvature in okay-space, is answerable for the noticed long-range supercurrents, we substitute the single-phase hexagonal D0₁₉-Mn₃Ge spacer with both a combined part of tetragonal D0₂₂– and hexagonal D0₁₉-Mn₃Ge (Fig. 4a–c), or a polycrystalline collinear AFM IrMn (Fig. 4d–f). As offered within the Supplementary Text, the mixed-phase Mn₃Ge reveals a big zero-field anomalous Hall impact (AHE) akin to the majority single crystal^3,4, guaranteeing that it nonetheless hosts, to a big extent, triangular chiral antiferromagnetic domains related to a non-trivial topology^1,2,3,4,5. In distinction, no AHE is detected within the polycrystalline IrMn, as anticipated for topologically trivial antiferromagnetic floor states¹⁶.

Fig. 4: Dependence of Josephson supercurrents on the diploma of chiral non-collinearity.

a, Scanning electron micrograph of the fabricated Nb/Mn₃Ge/Nb lateral JJ, the place the Mn₃Ge spacer is a combined part of tetragonal D0₂₂ and hexagonal D0₁₉ (Supplementary Text). The scale bar (a,d) signifies 0.5 µm. b, Magnetic area interface sample I_c((mu _0H_ bot)) when the magnetic area (mu _0H_ bot) is utilized perpendicular to the interface airplane of Nb electrodes (backside inset). The high left and proper insets show the present–voltage I–V curves of the JJ, taken round zero-order most and zero-order minimal of I_c((mu _0H_ bot)), respectively. c, Data equal to b however for the magnetic area (mu _0H_) utilized parallel to the interface airplane of the Nb electrodes (backside inset). d,e,f, Data equal to a,b,c however for the Nb/IrMn/Nb junction with a a lot shorter d_s = 5–16 nm, by which the IrMn spacer is polycrystalline (Supplementary Text). Scanning electron micrograph (d), magnetic area interface patterns (e,f) and knowledge equal to b,c. The left inset in f reveals the attribute voltage V_c = I_cR_n as a perform of d_s, from which the decay size scale of the Josephson coupling by means of the IrMn spacer is decided to the primary order (see Supplementary Text for particulars).

The most noteworthy result’s that within the presence of chiral non-collinearity (equivalently, non-zero Berry part), long-ranged Josephson supercurrents are established even within the mixed-phase Mn₃Ge (Fig. 4b,c) whereas this long-range impact nearly disappears when the spin preparations of the AFM spacer are topologically trivial (Fig. 4e,f). This factors unambiguously to a topological origin of Josephson coupling within the chiral AFM Mn₃Ge, which ought to be sturdy in opposition to structural dysfunction and impurity scattering. Note that the ξ worth 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 by means of the collinear AFM IrMn is in good settlement with earlier reviews on vertical JJs with γ−Fe₅₀Mn₅₀ (ref. ²⁵) or Cr (ref. ²⁶) spacers. An intuitive clarification of those outcomes is as follows. The 120° non-collinear preparations 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 transformed spin-zero triplets (S = 1, m_s = 0) in movement then expertise fictitious magnetic fields (as giant as roughly 100 tesla)^2,3,4 related to the Berry curvature¹⁴ in okay-space and rotate to type spin-polarized triplets (S = 1, m_s = ±1), that are capable of penetrate a lot deeper^6,7,8. Here, the fictional magnetic fields rooted within the chiral non-collinear spin texture^2,3,4 play an important position in altering the quantization axis of the spin-zero triplets (S = 1, m_s = 0) to be transformed into the spin-polarized triplets (S = 1, m_s = ±1). None of the above are current within the IrMn spacer, accounting for its short-range nature of Josephson coupling^6,7,8,24,25.

The important ingredient for the belief of the long-range spin-triplet proximity impact^6,7,8 is the presence of a magnetically inhomogeneous ferromagnet/superconductor interface (typically known as a spin-active interface), which ends up in subsequent spin-mixing and spin-rotation processes^{9,10,11,12,13,14}, and up to now, the spin-triplet proximity impact has been experimentally noticed in varied 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 lengthy decay size of 0.3‒1 µm (ref. ¹³), which is supported by its half-metallicity, albeit uncertainty within the nature of the magnetic inhomogeneity. The notable facet of the current examine is that as a substitute of the nanometre-scale inhomogeneity of ferromagnetic supplies, an atomic-scale non-collinear AFM (together with fictitious magnetic fields) is exploited to generate the spin-triplet correlation that may prolong over 155‒160 nm, akin to the CrO₂-based JJs¹³.

We have experimentally demonstrated that lateral Josephson supercurrents by means of a triangular chiral AFM Mn₃Ge (refs. ^3,4,5) are long-ranged, which is a key facet of proximity-induced spin-polarized triplet pairing states^{6,7,8,9,10,11,12,13,14}. Although detailed theories, protecting the triplet superconductivity and Berry curvature, should be developed for a quantitative description, our outcomes present the experimental indication of topologically generated triplet pairing states through a chiral non-collinear AFM, which might doubtlessly resolve the excellent points raised in typical ferromagnet-based triplet JJs^{6,7,8,9,10,11,12,13,14}. Last however not least, the attribute decay size of Josephson supercurrents in our chiral AFM is discovered, to not be restricted by hitherto believed spin-diffusion lengths, however reasonably hinting at topologically protected triplet supercurrents.