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Extremely long-range, high-temperature Josephson coupling across a half-metallic ferromagnet - Nature Materials
Abstract . The Josephson effect results from the coupling of two superconductors across a spacer such as an insulator, a normal metal or a ferromagnet to yield a phase coherent quantum state. However, in junctions with ferromagnetic spacers, very long-range Josephson effects have remained elusive. Here we demonstrate extremely long-range (micrometric) high-temperature (tens of kelvins) Josephson coupling across the half-metallic manganite La 0.7 Sr 0.3 MnO 3 combined with the superconducting cuprate YBa 2 Cu 3 O 7 . These planar junctions, in addition to large critical currents, display the hallmarks of Josephson physics, such as critical current oscillations driven by magnetic flux quantization and quantum phase locking effects under microwave excitation (Shapiro steps). The latter display an anomalous doubling of the Josephson frequency predicted by several theories. In addition to its fundamental interest, the marriage between high-temperature, dissipationless quantum coherent transport and full spin polarization brings opportunities for the practical realization of superconducting spintronics, and opens new perspectives for quantum computing. You have full access to this article via your institution. Download PDF Download PDF Main . The antagonism between ferromagnetism, in which the exchange field tends to spin-polarize the conduction electrons, and singlet superconductivity, in which electrons form Cooper pairs with opposite spins, makes their coexistence challenging 1 . In bulk samples, this has been observed only recently in a P-doped EuFe 2 As 2 compound with extremely weak exchange interaction between electrons and localized moments 2 . Contrarily, equal-spin triplet superconductivity can survive in strong ferromagnets, although only rare bulk materials are considered triplet superconductors 3 . Seminal theoretical studies 4 , 5 , 6 , 7 , 8 , 9 , 10 showed that triplet correlations can be generated at the interface between a ferromagnet (F) and a superconductor (S). Triplets allowed the explanation of the observation of supercurrents across very thick (tens or even hundreds of nanometres) ferromagnets combined with conventional low-temperature (few kelvin) superconductors 11 , 12 , 13 , 14 . Despite many hints of triplet superconductivity, very long-range Josephson effects have remained elusive, especially in the intriguing case of unconventional high-temperature superconductors combined with half-metal ferromagnets 15 , 16 , 17 , 18 , 19 . Much work has followed to identify various mechanisms that can lead to the opposite-spin singlet to equal-spin triplet conversion. Generally, these include spin-mixing, which leads to the generation of an opposite-spin ( S z ?=?0) triplet component out of the singlet one, and spin-flip, which produces the equal-spin ( S z ?=?±1) triplet component (where S z is the expectation value of the z component of the spin operator). At the microscopic level, those processes result from spin-dependent scattering at interfaces with strong ferromagnets 5 and from the presence of an inhomogeneous magnetization 4 , 6 , 8 , 9 , 20 , 21 or a momentum-dependent exchange field due to the spin–orbit interaction 22 , 23 . A number of experiments based on conventional ( s -wave) low-temperature superconductors have found critical currents across S–F–S junctions for F thickness in the tens of nanometre range 12 , 14 , 19 , 24 , 25 , which is much larger than expected for the singlet S–F proximity effect, and therefore supports the triplet scenario. In these vertical junctions, the triplet generation was engineered through the artificial design of a magnetic inhomogeneity at the interface with the superconductor, for example, by intercalating various ferromagnetic layers with different magnetic anisotropy or spin texture 12 , 14 , 19 , 24 , 25 . Experiments on lateral (planar) devices, particularly based on the half-metallic ferromagnet CrO 2 , found critical currents that decay over even longer distances—up to a few hundred nanometres 11 , 13 . Because in half-metals the conduction electrons are fully spin-polarized, and consequently the penetration of opposite-spin singlet correlations is forbidden, that experimental observation was considered evidence for the generation of triplet superconductivity, which was explained 10 by the presence of strong spin-dependent scattering at the S–F interface combined with intrinsic magnetic inhomogeneities 26 . Because of their fundamental and technological interest, heterostructures of unconventional ( d -wave) high-temperature cuprate superconductors combined with half-metallic manganites have attracted much attention, and hints for a triplet proximity effect have accumulated over the years: an unexpected superconducting proximity effect 15 , an induced superconducting gap 16 , 18 and Andreev reflection and coherent transport 17 , 27 , as well as supercurrents 19 over length scales on the order of a few tens of nanometres have been experimentally observed in vertical junctions (although at relatively low temperatures, ~10?K). Notwithstanding, the demonstration of long-range Josephson effects has remained elusive. Proving Josephson coupling requires evidencing the macroscopic phase coherent state. A first signature is the observation of flux quantization effects in the critical current: in principle, the Josephson current must vanish for an integer number of flux quanta, giving rise to the well-known Fraunhofer diffraction pattern. While realized in triplet Josephson junctions based on low-temperature superconductors 25 , 28 , flux quantization effects have never been observed in cuprate–manganite junctions. They are clearly demonstrated in the present experiments. The second signature is the so-called Shapiro steps in the I ( V ) characteristics measured under microwave radiation 29 . These originate from the current–phase relation I ?=? I 0 sin φ ( I 0 , equilibrium critical current of the junction), where the phase φ difference between the electrode evolves in time ( t ) under application of a d.c. voltage bias ( V ) according to \(\frac{{\partial \varphi }}{{\partial t}} = \frac{{2\uppi }}{{{{{\mathrm{{\varPhi}}}}}_0}}V\) , with \({{{{{\varPhi}}}}}_0 = \frac{h}{{2e}}\) being the flux quantum ( h , Planck’s constant; e , electron charge), yielding an a.c. current with the Josephson frequency \(f_{\mathrm{J}} = \frac{V}{{{{{{{\varPhi}}}}}_0}}\) . Resonant absorption of microwave radiation occurs when the Josephson frequency is a multiple of the microwave’s frequency, yielding steps in the I ( V ) curve measured under microwave illumination at voltages given in the conventional case by V ?=? nΦ 0 f ( f , microwave’s frequency), with n ?=?0, 1, 2…. To the best of our knowledge, these phase locking effects have never been reported for triplet Josephson junctions. They are very clear in the present experiments, and they present the anomalous periodicity expected in the context of triplet Josephson effects 23 , 30 . We have fabricated planar S–F–S Josephson junctions (Fig. 1a ) in which two YBa 2 Cu 3 O 7 (YBCO) electrodes are separated a micrometre apart by a La 0.7 Sr 0.3 MnO 3 (LSMO) wire. These microstructures were fabricated from oxide films grown epitaxially on SrTiO 3 by a high-pressure pure oxygen sputtering technique. LSMO layers (30?nm thick) were first patterned into a wire (20 or 25?μm wide) using electron beam lithography (the green layout in the optical image of Fig. 1a ). Amorphous alumina (a-Al 2 O 3 , hereafter ALO) templates fabricated with electron beam lithography were used to define the YBCO contacts (yellow pattern in Fig. 1a ) separated by micrometre-size gaps. The YBCO (50?nm thick) was grown on top of the alumina templates using the same high-pressure sputtering technique as for the manganite. Holes in the ALO template allow epitaxial growth of YBCO in the contacts, while the barrier area was protected by the thick ALO on top of which the YBCO is known to grow, amorphous and highly insulating 31 (below). The spacing between YBCO contacts was ~1?μm (Fig. 1b ). An enlarged view of the portion of LSMO wire protected by the ALO stripe separating the YBCO contacts and thus defining the width of the Josephson barrier is shown in Fig. 1c . Fig. 1: Device structure. a , Optical image of the device. Amorphous Al 2 O 3 and YBCO are on top of the LSMO microwire. b , Atomic force microscopy image of the device before YBCO deposition. The Al 2 O 3 stripe between YBCO electrodes is continuous all along the LSMO. c , Atomic force microscopy image of the Al 2 O 3 stripe separating the YBCO electrodes and defining the width of the barrier (before YBCO deposition). d , Low-magnification STEM-HAADF image of a LSMO–YBCO bilayer grown ex situ on an (001) SrTiO 3 (STO) substrate. e , High-resolution STEM-HAADF image of the same interface. f , Left: atomic resolution HAADF image where atomic positions of each element are indicated by arrows in the different atomic columns. Right: Ba M 4,5 (red), Mn L 2,3 (blue) and La M 4,5 (yellow) elemental EELS map in a colour mix of a spectrum image of a region of interest from the same HAADF image. g , XMCD image of the LSMO nanowire between the two YBCO contacts measured at the Mn L 3 edge (640.3?eV) at 50?K. Black line separates two XMCD images of uniformly magnetized LSMO taken at remanence. Full size image The ex situ growth of the YBCO on top of the manganite wires did not degrade the structure nor the chemistry of the interfaces as compared to vertical structures grown in situ. A demonstration of the high quality of the YBCO–LSMO interface grown ex situ is shown in the scanning transmission electron microscopy (STEM) images displayed in Fig. 1d–f . A low-magnification high-angle annular dark-field (HAADF) image in Fig. 1d shows that the sample grows flat and continuous over long lateral distances. In Fig. 1d,e , the high-resolution image displays the YBCO–LSMO interface, which appears epitaxial, atomically smooth and free of disorder with the same crystalline quality as the interfaces grown in situ. As it turns out, the growth at 900?°C in a pure oxygen plasma has the effect of reconditioning the surface after exposure to the atmosphere or processing. Figure 1f displays an atomic resolution electron energy loss spectroscopy (EELS) chemical map of the interface alongside a high-resolution HAADF image. While the HAADF image indicates which atom corresponds to each atomic column, the coloured map presents a colour mixing of Ba M 4,5 (red), La M 4,5 (yellow) and Mn L 2,3 (blue) elemental EELS maps, where the interface is observed to be chemically sharp with no intermixing detected (M 4,5 and Mn L 2,3 : atomic absorption edges). The interfacial termination planes between YBCO and LSMO are also evidenced and, as in the in situ samples, correspond to BaO facing MnO 2 planes with missing CuO chains at the interface 32 , 33 . The Cu–O–Mn superexchange path across the interface induces a magnetic state in the Cu that may play a central role in the triplet generation 17 , 27 . To ascertain the magnetic properties of the LSMO nanowire, and particularly within the gap in between the two YBCO electrodes, we examine the magnetic domain structure of LSMO–YBCO hybrids with the same geometry of our devices via spatially resolved photoemission electron microscopy (PEEM) using X-ray magnetic circular dichroism (XMCD) as the magnetic contrast mechanism. XMCD was measured at the Mn L 3 edge (640.3?eV) as the normalized difference in absorption of circular polarized radiation with left and right helicity. The colour code in Fig. 1g is set by the projection of the sample magnetization along the direction of propagation of the beam. Coloured arrows in the figure mark the direction of the magnetization. PEEM images of Fig. 1g show that the LSMO bridge can be homogeneously magnetized along the [110] directions corresponding to the biaxial easy axes of the manganite, although in some situations, states with coexisting micrometre-size domains were observed at remanence. In all cases, the domain geometry ensures that there are wide regions with homogeneous magnetization connecting the YBCO contacts where the triplet pairs can propagate freely. The main panel of Fig. 2a shows resistance curves of three different samples with YBCO contacts of similar size separated by 1?μm on LSMO wires of different widths (20 or 25?μm). Transport was measured by injecting current between the two neighbouring YBCO contacts while voltage was measured along the LSMO wire with contacts at its ends (as shown in the schematic displayed in Fig. 2b ). From room temperature down to the transition temperature of the YBCO (90?K), the (four-probe) resistance is dominated by the LSMO wire. This is illustrated by Fig. 2c , which shows that the temperature dependence of the resistance of the devices (the blue curve is, in example, taken from Fig. 2a ) is qualitatively similar to that of a single LSMO film of the same thickness (black curve in Fig. 2c ). Control devices consisting of YBCO deposited on the ALO mask and without the LSMO microwire had resistances at least four orders of magnitude higher, with the resistance exceeding in most cases the measurement limit (10?MΩ) at the temperatures of the experiment. These large resistance values correspond to the YBCO grown on top of amorphous ALO. Similarly to other oxide perovskites grown on amorphous oxides 34 , YBCO grown on the amorphous ALO is amorphous and strongly insulating 31 (orange curve in Fig. 2c corresponds to a device with no LSMO wire and YBCO electrodes separated by 1?μm). This insulating behaviour, found in each of the numerous control devices we fabricated, rules out the presence of conducting paths across ALO that may yield a short between YBCO contacts. Fig. 2: Superconducting characterization. a , Resistance versus temperature of three different devices. Separation between YBCO contacts is 1?μm. Width of the LSMO wire electrodes is 20?μm (red) and 25?μm (blue and green). Current level is 1?μA (red and green) and 20?μA (blue). b , Schematic of the planar devices and wiring used. c , Resistance versus temperature of a 30-nm-thick LSMO single layer (black) to be compared with that of a junction device (blue). The orange curve corresponds to a control sample with no LSMO wire and YBCO electrodes separated 1??m. d , I ( V ) curves at different temperatures between 18?K and 40?K. Inset: Critical current as a function of temperature as extracted from the I ( V ) curves with the criterion shown in panel e . e , I ( V ) curves in double logarithmic scale. Notice that the critical current is attained at very low voltages, shown by the vertical line. Full size image The YBCO–LSMO devices (Fig. 2a ) display a broad resistive transition where different steps can be observed (inset in Fig. 2a ) when the temperature is decreased below ~90?K. This is because a proximity effect is established gradually and, given the planar geometry of the device (sketches in Figs. 2b and 3c ), contributions from different sample regions are concurrently measured. First, the transition of the YBCO electrodes is detected. Thus, a first step in the R ( T ) curve ( R , resistance; T , temperature) is observed around 90?K. Due to the very short YBCO coherence length (~1?nm along the a axis), the onset of superconductivity can occur at ~90?K, far from the interface with the LCMO, while, within a few unit cells from it, the proximity effect depresses critical temperature ( T C ), and the transition is completed at a much lower temperature, ~60–65?K. Below this temperature, the resistance of the LSMO lying directly underneath the YBCO electrodes gradually decreases with decreasing temperature, due to the proximity effect. However, in order to observe zero resistance and a faster drop to zero resistance, Josephson coupling needs to be established between the ‘proximitized LSMO banks’ across the ~1-?m-long LSMO wire that is not covered by superconducting YBCO. In the R ( T ) curve, the onset of Josephson coupling shows as a shoulder at ~40?K. To determine the critical current of the devices, I ( V ) curves were measured as a function of temperature (Fig. 2d ). Figure 2d displays selected I ( V ) curves, while a full set is presented in Supplementary Fig. 1 . Linear scale I ( V ) plots show considerable rounding as recently observed in other Josephson junctions with ferromagnetic barriers 35 . Double logarithmic scale plots of I ( V ) (Fig. 2d ) show that the critical current is indeed much lower than anticipated from the linear scale plots, and that a rather restrictive voltage criterion (around hundreds of nanovolts) is necessary to reach the critical current regime. As discussed in Supplementary Section 2, fits of the low-voltage portion of I ( V ) curves to the Ivachenko–Zil’berman model 36 showed that the critical current is limited by thermal fluctuations, and that the higher voltage regime of I ( V ) is dominated by the contribution of parts of the planar device (YBCO electrodes and proximitized LSMO lying directly underneath YBCO) having higher resistance and critical current than the bare LSMO wire that bridges the YBCO electrodes and plays the role of the Josephson barrier. The dominance of those elements’ contribution, which as discussed above is evident also in R ( T ) at sufficiently high temperatures, is unavoidable in this type of planar geometry, as discussed earlier 35 . Yet the analysis of the lower voltage range (below a few microvolts) allows us to estimate the critical current (Supplementary Section 2), which is shown in Fig. 2e . Values in the range of 10 2 –10 3 ?A?cm –2 are found, that is, much lower than the critical current (a few 10 7 ?A?cm –2 ) typically found in YBCO wires at the same temperatures. The temperature dependence of the critical current was analysed in the framework of the theory of mesoscopic diffusive superconductor–normal–superconductor (SNS) junctions 37 to obtain the Thouless energy E Th , the energy scale for the mesoscopic proximity effect. Details can be found in Supplementary Sections 2 and 3. The Thouless energy was found to be E Th ?=?95?±?10?μeV, not far from the E Th ?=?54?μeV reported in proximity effect experiments with CrO 2 (refs. 13 , 38 ). Since the CrO 2 sample had a 700?nm gap, if we scale the 54?μeV CrO 2 Thouless energy to a sample length of 1?μm, it would be reduced by half, so we should compare 95?μeV for LSMO with 27?μeV for CrO 2 , values that are still reasonably close. This similarity is not surprising since both materials are half-metal oxides with rather similar electronic properties. Measurements on devices with shorter ( L ?=?750?nm) and longer ( L ?=?2?μm) LSMO spacing ( L ) were in agreement with the expected 1/ L 2 scaling of the Thouless energy (Supplementary Section 3), further demonstrating the robustness of this analysis. Measurements of the junction resistance R as a function of the magnetic field H applied in the plane of the LSMO microwire allowed for the observation of quantum interference effects demonstrative of Josephson coupling. At low temperatures (below the critical temperature of the proximitized LSMO) and sufficiently high injected current I , the junction’s resistance periodically oscillates as a function of the applied field. This is shown in the example displayed in Fig. 3a , which corresponds to a R ( H ) measured at T ?=?30?K with I ?=?25?μA and different angles θ between the applied in-plane magnetic field and the LSMO wire (geometry shown in Fig. 3b ). As can be seen, the oscillations’ period depends on the angle between the in-plane magnetic field and the LSMO wire. This is further evidenced in Fig. 3c , which displays a contour plot of the resistance (colour scale) as a function of the magnetic field magnitude and angle θ with respect to the LSMO wire (geometry shown in Fig. 3b ). The contour plot is obtained from a large set of R ( H ) values, measured for varying θ (every 2° for 0°?≤? θ ?≤?360°) at constant T ?=?30?K and I ?=?25?μA. In this plot, the magnetoresistance oscillations show as a ‘wavy pattern’ with mirror symmetry around θ ?=?0°, 90°, 180° and 270°. The pattern results from the oscillations’ period being the shortest when the magnetic field is perpendicular to the LSMO wire (around θ ?=?90° and θ ?=?270°) and gradually increasing as the magnetic field is rotated towards the direction of the LSMO wire ( θ ?=?0° and θ ?=?180°). The periodic magnetoresistance oscillations (Fig. 3a ) result from the Fraunhofer oscillation of the critical current as a function of the magnetic flux Φ threading the junction. The angular ( θ ) dependence of the oscillations (Fig. 3c ) results from the junction’s geometry, more specifically from the angular dependence of the magnetic flux across the junction, \({\varPhi}\left( {H,\theta } \right) = \mu _0HA_{{\mathrm{eff}}}\left {\sin \left( \theta \right)} \right\) ( μ 0 , magnetic vacuum permeability), with A eff an effective junction area as shown in Fig. 3b . The resistance oscillation pattern comes from the critical current oscillation when a magnetic flux is applied (Fraunhofer pattern). We show in Fig. 3d the calculated critical current \(I_{\mathrm{c}}\left( {H,\theta } \right) = I_{{\mathrm{c}}0}\left {\frac{{{\mathrm{sin}}\uppi \frac{{{{{{\varPhi}}}}}}{{{{{{{\varPhi}}}}}_0}}}}{{\uppi \frac{{{{{{\varPhi}}}}}}{{{{{{{\varPhi}}}}}_0}}}}} \right\) , with I c0 being the maximum critical current, Φ 0 the flux quantum (2.07?×?10 ?15 ?Wb) and Φ ( H , θ ) as described above, for a rectangular Josephson junction, which qualitatively reproduces the experimental pattern (Fig. 3c ). The period of resistance oscillations as a function of magnetic field ~0.036?T corresponds to an effective area A eff ?≈?0.101?μm 2 . Considering that the vertical dimension of the wire is limited by the LSMO thickness ( w ?=?30?nm) and that the effective junction area is given by A eff ?=? L eff ?×? w , we extract an effective junction width L eff ?≈?3.4?μm, which is in excess of the distance between the YBCO electrodes (1?μm). The origin of this L eff will be discussed below. Fig. 3: Flux quantization effects. a , Resistance oscillations as a function of magnetic field (?0.4?T?different directions with LSMO wire. Notice the disappearance of the oscillations when the field is applied parallel to the junction. Curves are shifted in resistance for clarity. b , Schematic illustrating the orientation of the magnetic field. Blue shaded areas in the LSMO wire show the proximitized regions. c , Contour plot of the resistance as a function of magnetic field (?0.4?T?different orientations relative to the LSMO wire. The angle θ is varied in steps of 2°. d , Simulation of the oscillation pattern of the I c / I 0 assuming a Fraunhofer dependence of the critical current of the magnetic flux. Full size image Confirmation of the phase-locked response of the Josephson coupling is obtained from the irradiation of the sample with microwaves at different powers while the I ( V ) curves were recorded at a temperature close to the onset of the supercurrent in LSMO. The resonant absorption of the microwave signal by the a.c. Josephson current produced characteristic interference patterns showing phase coherence. This is clearly seen in Fig. 4a , which displays the differential resistance d R ?≡?d V / dI (colour scale) as a function of the bias current I and microwave power, with f ?=?9.997?GHz and measured at T ?=?37?K. The same data can be plotted as a function of the voltage across the junction V (Fig. 4b ), which reveals the presence of Shapiro steps at constant voltages that appear as vertical lines in the interference pattern. This resonant response constitutes direct evidence of the sinusoidal current–phase relationship of the Josephson junction. Strikingly, though, steps appear at half-integer factors of the Josephson voltage V Josephson ?=? Φ 0 f , showing a doubling of the Josephson frequency and thus the preponderance of the second harmonic term in the current–phase relation. Half-integer Shapiro steps have been predicted 23 , 30 , 39 , 40 and experimentally observed in S–F–S vertical (tunnel) junctions with weak ferromagnets at the verge of the 0–π transition 41 , 42 . The half-integer Shapiro steps observed in our junctions constitute a fingerprint of a proximity effect governed by a slowly decaying second harmonic, which is one of the expected scenarios for the long-range propagation of triplet superconductivity in ferromagnets 30 . Interestingly, from the observation of second harmonic dominance in the Shapiro steps, one expects a halving of the period of Fraunhofer oscillations, that is, \(\mu _0{\Delta}H = \phi _0/2A_{{\mathrm{eff}}}\) . Considering this, the period of the Fraunhofer pattern (Fig. 3 ) yields accordingly an effective junction length of L eff ?≈?1.7??m (instead of the L eff ?≈?3.4??m obtained with an analysis in terms of the first harmonic of the current–phase relation). This effective length of the Josephson junction, L eff ?=? L ?+?2 λ ( λ , London penetration depth), is in much better agreement with the actual length of the junction, L ?=?1??m, and yields a value of ~350?nm for the YBCO penetration depth. This value, somewhat larger than the 140?nm of YBCO single crystals, is expected for a thin film in proximity with LSMO. A more accurate quantitative description of the above observations will require future theoretical studies of the proximity effect between unconventional superconductors and half-metals in a planar geometry. Fig. 4: The a.c. Josephson effect. a , Shapiro steps pattern of the differential resistance as a function of current for different microwave power levels for a frequency of 9.997?GHz. dBm, decibel-milliwatt. b , Shapiro steps as a function of voltage normalized to the Josephson voltage \(\left( {V_{{\mathrm{Josephson}}} = \frac{{hf}}{{2e}}} \right)\) for microwave radiation of 9.997?GHz. Dashed lines correspond to half-integer Shapiro steps. Full size image The demonstration of extremely long-range (micrometric) triplet Josephson coupling between d -wave, high-temperature superconducting electrodes across half-metallic ferromagnets is important at various levels. Fundamentally, it brings up various questions. For example, which is the mechanism governing the singlet to triplet conversion (which seems to be very efficient in view of the quantitative agreement obtained with the predictions of theories of SNS junctions 37 ), especially considering the planar geometry, or what is the induced pairing symmetry in the LSMO, that is, is nodal pairing preserved or does a conversion into an s -wave occur 43 ? In addition, the present findings have much relevance in the field of superconducting spintronics 44 , 45 thanks to the pairing of (1) the very high temperature (tens of kelvins), for which triplet Josephson effects are observed, and (2) the very long (micrometric) distance over which phase coherence is preserved in the half-metal in a planar device. Moreover, the fact that triplet supercurrents are necessarily fully spin-polarized in a half-metal, and that both a.c. and d.c. triplet Josephson effects are demonstrated, opens unprecedented opportunities as these condition pave the way to novel logic gates 46 , full superconducting switches, non-volatile random access memories 47 and quantum computing 48 , 49 . Furthermore, the half-metallic Josephson junctions should reveal an anomalous Josephson effect with a non-zero phase difference ? 0 at the ground state, which is determined by the mutual orientation of the magnetization in the half-metal and interface magnetizations 10 , 50 . Such an unusual ? 0 junction could serve as an important building block of a ‘quiet qubit’ 48 , and may provide a unique mechanism of direct coupling between magnetism and phase dynamics in Josephson junctions 49 . Methods . LSMO was grown on (001)-oriented SrTiO 3 single crystals in a high-O 2 -pressure (3.2?mbar) d.c. sputtering system at 900?°C. In situ annealing was done at 800?°C with 900?mbar O 2 pressure for 1?hour. Electron beam lithography was performed in a Raith50 module mounted on a Zeiss EVO 50 scanning electron microscopy instrument to obtain LSMO microwires and to define amorphous alumina patterns. Amorphous alumina was grown in a d.c. sputtering system at 7.3?×?10 ?3 ?mbar atmosphere (argon/oxygen, 2:1) at room temperature. YBCO was grown on top of LSMO and the a-ALO template in a high-O 2 -pressure (3.4?mbar) d.c. sputtering system at 900?°C. In-situ annealing was done at 800?°C with 900?mbar O 2 pressure for 1?hour. R ( T ), R ( H ) and I ( V ) measurements were performed in a helium closed-cycle cryostat down to 15?K applying a maximum current of 800?uA and magnetic field up to 4,000?Oe while measuring the voltage. Voltage contacts were placed at the ends of the LSMO wire (sketch in Fig. 1b ), although we used control experiments with all four contacts on the YBCO wires to check that the normal state resistance R n is not limited by the interface resistance (Supplementary Fig. 1 ). The magnetic domain structure of the ferromagnet superconducting hybrids was examined by means of PEEM using XMCD as the magnetic contrast mechanism. Experiments have been done at the spatially resolved PEEM station at the UE49/PGMa beam line of the synchrotron radiation source BESSY II at Helmholtz-Zentrum Berlin. The angle of incidence of the incoming radiation with respect to the sample surface was 16°. The sample was mounted on a sample holder that allowed application of in-plane magnetic field pulses up to ±1,000?Oe. Magnetic imaging was done in remanence after applying the desired magnetic field value. Images with a 10??m field of view were collected at the Mn L 3 edge (640.3?eV) for circularly polarized radiation with clockwise ( σ +) and counterclockwise ( σ ?) helicities. The data has been normalized to a background image and drift corrected before their averaging. The XMCD images were calculated as ( σ ? ??? σ + )/( σ ? ?+? σ + ). Measurements were conducted at 50?K. Four-probe R ( H ) measurements were carried out in a closed-cycle refrigerator, equipped with an electromagnet and a sample rotating stage. The d.c. resistance R ?=? V / I was measured by injecting an electrical current I with a d.c. source and measuring the voltage V with a nanovoltmeter. The voltage offsets were removed by measuring both current polarities. 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Work (J.S., C.L., F.M. and M.G.-H.) was supported by the Spanish AEI through grants MAT2015-72795-EXP, MAT2017-87134-C02 and PID2020-118078RB-I00. J.S. thanks the scholarship programme Alembert funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02. Work at CNRS and the Thales lab (J.E.V.) was supported by ERC grant no. 647100 ‘SUSPINTRONICS’; J.E.V., A.I.B. and J.L. thank the French ANR grant ANR-15-CE24-0008-01 ‘SUPERTRONICS’, and J.E.V. and J.S. thank the COST action ‘Nanocohybri’. We (J.S., C.L. and J.-E.V.) acknowledge funding from the Flag ERA ERA-NET To2Dox project. We thank Helmholtz-Zentrum Berlin for the allocation of neutron/synchrotron radiation beamtime. This project received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 730872. J.S. thanks E. Strambini and F. Giazotto for collaboration in the early stages of this project. J.E.V. thanks C. Ulysse and L. Vila for collaboration in related projects. A.I.B. acknowledges support by the Ministry of Science and Higher Education of the Russian Federation within the framework of state funding for the creation and development of the world-class research center ‘Digital Biodesign and Personalized Healthcare’, no. 075-15-2020-926. Author information . Author notes M. Rocci Present address: Instituto Nanoscienze, Consiglio Thales Alenia Space Italia, L’Aquila, Italy Affiliations . GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain D. Sanchez-Manzano,?F. A. Cuellar,?V. Rouco,?G. Orfila,?M. Rocci,?F. Gallego,?J. Tornos,?A. Rivera,?C. Leon?&?J. Santamaria Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France S. Mesoraca,?X. Palermo,?A. Balan,?A. Sander?&?Javier E. Villegas IMDEA Nanoscience Institute, Universidad Autonoma, Cantoblanco, Spain M. Cabero Centro Nacional de Microscopia Electronica, Universidad Complutense, Madrid, Spain M. Cabero?&?J. M. Gonzalez-Calbet Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany L. Marcano?&?S. Valencia Characterization Facility, University of Minnesota, Minneapolis, MN, USA J. Garcia-Barriocanal Instituto de Ciencia de Materiales de Madrid (ICMM, CSIC), Cantoblanco, Spain F. Mompean?&?M. Garcia-Hernandez Laboratorio de Heteroestructuras con Aplicación en Spintrónica, Unidad Asociada (UCM-CSIC), Madrid, Spain F. Mompean,?M. Garcia-Hernandez?&?J. Santamaria Departamento Química Inorgánica, Facultad de Química, Universidad Complutense, Madrid, Spain J. M. Gonzalez-Calbet Laboratoire de Physique et d’Etude des Matériaux, ESPCI Paris, CNRS, PSL Research University, Sorbonne University, Paris, France C. Feuillet-Palma,?N. Bergeal?&?J. Lesueur LOMA, CNRS, Université Bordeaux, Talence, France A. I. Buzdin Digital Biodesign and Personalized Healthcare, Sechenov First Moscow State Medical University, Moscow, Russia A. I. Buzdin Authors D. Sanchez-Manzano View author publications You can also search for this author in PubMed ? Google Scholar S. Mesoraca View author publications You can also search for this author in PubMed ? Google Scholar F. A. Cuellar View author publications You can also search for this author in PubMed ? Google Scholar M. Cabero View author publications You can also search for this author in PubMed ? Google Scholar V. Rouco View author publications You can also search for this author in PubMed ? Google Scholar G. Orfila View author publications You can also search for this author in PubMed ? Google Scholar X. Palermo View author publications You can also search for this author in PubMed ? Google Scholar A. Balan View author publications You can also search for this author in PubMed ? Google Scholar L. Marcano View author publications You can also search for this author in PubMed ? Google Scholar A. Sander View author publications You can also search for this author in PubMed ? Google Scholar M. Rocci View author publications You can also search for this author in PubMed ? Google Scholar J. Garcia-Barriocanal View author publications You can also search for this author in PubMed ? Google Scholar F. Gallego View author publications You can also search for this author in PubMed ? Google Scholar J. Tornos View author publications You can also search for this author in PubMed ? Google Scholar A. Rivera View author publications You can also search for this author in PubMed ? Google Scholar F. Mompean View author publications You can also search for this author in PubMed ? Google Scholar M. Garcia-Hernandez View author publications You can also search for this author in PubMed ? Google Scholar J. M. Gonzalez-Calbet View author publications You can also search for this author in PubMed ? Google Scholar C. Leon View author publications You can also search for this author in PubMed ? Google Scholar S. Valencia View author publications You can also search for this author in PubMed ? Google Scholar C. Feuillet-Palma View author publications You can also search for this author in PubMed ? Google Scholar N. Bergeal View author publications You can also search for this author in PubMed ? Google Scholar A. I. Buzdin View author publications You can also search for this author in PubMed ? Google Scholar J. Lesueur View author publications You can also search for this author in PubMed ? Google Scholar Javier E. Villegas View author publications You can also search for this author in PubMed ? Google Scholar J. Santamaria View author publications You can also search for this author in PubMed ? Google Scholar Contributions . D.S.-M. and F.A.C. grew the samples and performed resistance and critical current measurements. D.S.-M. and S.M. measured angle-dependent transport with contributions from A.S., X.P. and A.B.; D.S.-M., L.M. and S.V. measured X-ray absorption. D.S.-M. and S.M. measured Shapiro steps with the guidance and analysis of C.F.-P., N.B. and J.L.; A.I.B. contributed to the theoretical understanding and modelling. G.O., V.R., J.G.-B., M.R., F.G., J.T., A.R., F.M. and M.G.-H. worked on the sample growth and characterization in different stages of the project. M.C. and J.M.G.-C. performed the microscopy. J.S. designed the overall experiment, and J.E.V. contributed with the design of the Josephson characterization. J.S. and J.E.V. wrote the manuscript with the input and help of J.L., A.I.B., S.M., D.S.-M. and C.L. All authors discussed the results and revised the manuscript. Corresponding authors . Correspondence to Javier E. Villegas or J. Santamaria . Ethics declarations . Competing interests . The authors declare no competing interests. Additional information . Peer review information Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Supplementary information . Supplementary Information . Supplementary Figs. 1–8 and Discussion on the temperature and barrier thickness dependence of the critical current. Rights and permissions . Reprints and Permissions About this article . Cite this article . Sanchez-Manzano, D., Mesoraca, S., Cuellar, F.A. et al. Extremely long-range, high-temperature Josephson coupling across a half-metallic ferromagnet. Nat. Mater. (2021). https://doi.org/10.1038/s41563-021-01162-5 Download citation Received : 21 September 2020 Accepted : 21 October 2021 Published : 02 December 2021 DOI : https://doi.org/10.1038/s41563-021-01162-5 Share this article . Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not currently available for this article. 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