Emergent ferromagnetism with superconductivity in Fe(Te,Se) van der Waals Josephson junctions

Ferromagnetism and superconductivity are two key ingredients for topological superconductors, which can serve as building blocks of fault-tolerant quantum computers. Adversely, ferromagnetism and superconductivity are typically also two hostile orderings competing to align spins in different configurations, and thus making the material design and experimental implementation extremely challenging. A single material platform with concurrent ferromagnetism and superconductivity is actively pursued. In this paper, we fabricate van der Waals Josephson junctions made with iron-based superconductor Fe(Te,Se), and report the global device-level transport signatures of interfacial ferromagnetism emerging with superconducting states for the first time. Magnetic hysteresis in the junction resistance is observed only below the superconducting critical temperature, suggesting an inherent correlation between ferromagnetic and superconducting order parameters. The 0-π phase mixing in the Fraunhofer patterns pinpoints the ferromagnetism on the junction interface. More importantly, a stochastic field-free superconducting diode effect was observed in Josephson junction devices, with a significant diode efficiency up to 10%, which unambiguously confirms the spontaneous time-reversal symmetry breaking. Our work demonstrates a new way to search for topological superconductivity in iron-based superconductors for future high Tc fault-tolerant qubit implementations from a device perspective.


Introduction
By virtue of its immunity to adiabatic perturbation, the topological quantum computer is deemed a promising paradigm for fault-tolerant quantum information processing.The mainstream hardware approach to implement topological qubits is to utilize non-Abelian quasiparticle excitations -Majorana fermions in topological superconductors (TSCs) [1][2][3] .
Unfortunately, the two key ingredients to create TSCs, ferromagnetism and superconductivity are generally two hostile orderings that compete to arrange electron spins in different configurations.The spins in a ferromagnetic material are aligned in parallel due to exchange interactions.In contrast Cooper pairs in a mundane s-wave superconductor feature singlet-pairing states of two electrons with opposite spins.In carefully engineered heterostructures, the magnetism and superconductivity orderings can be mixed through the proximity effect 4 .Yet, a single material with inherent co-existence of ferromagnetism and superconductivity is rare to encounter in nature, which would favorably ease the fabrication challenge compared to other proposed hybrid topological superconductor implementations [5][6][7][8][9] .
Recently, the iron-based superconductor Fe(Te,Se) (FTS) stands out as a promising intrinsic TSC candidate with the coexistence of topological Dirac surface states, bulk superconductivity, and ferromagnetism.The bulk s-wave superconductivity induces a topological superconducting gap at the Dirac surfaces states below the superconducting Tc 10 , which can be directly visualized by high-resolution angle-resolved photon-emission spectroscopy (ARPES) experiments 11 .Traces of Majorana bound states (MBS) in vortex cores were also detected using tunneling spectroscopy measurements 12,13 .In these earlier works, an external magnetic field was still required to observe MBS.Recently, evidence of the spontaneous time-reversal symmetry breaking on the surface of this material has been reported via several techniques, including ARPES 14 , nitrogen-vacancy (NV) center imaging 15 , surface magneto-optic Kerr effect (MOKE) 16 , and nano superconducting quantum interference device (SQUID) imaging 17 .This superconductivity-compatible surface magnetism is unexpected, and the mechanism is not yet clear.And the current studies of ferromagnetism in superconducting FTS using spectroscopy and imaging techniques are subject to material inhomogeneity, magnetic impurities and other trivial origins, such as Caroli-de Gennes Matricon states 18 .Device level transport measurement is yet to be explored, which can eliminate spatial variations by measuring averaged global topological features.In addition, understanding mesoscopic transport behavior is critical for top-down scalable manufacturing of topological qubits.In this work, we fabricate and characterize FTS van der Waals Josephson junction (vJJ) devices and observed the unconventional interfacial ferromagnetism emerging with superconductivity unambiguously with the following major observations: (1) a magnetic hysteresis loop (R vs. H) below superconducting Tc; (2) a π phase component in the Fraunhofer patterns of the vJJ arising from ferromagnetism; (3) the stochastic supercurrent diode effect without external magnetic field which suggests spontaneous time-reversal symmetry breaking.This is the first time that evidence of time-reversal symmetry breaking superconductivity in FTS has been reported through device transport experiments.Our work provides a unique way of identifying time-reversal symmetry breaking in superconductivity in topological superconductors candidates.

FTS vdW Josephson Junctions
We fabricate Josephson junctions by employing the vdW gap between two homogeneously stacked FTS flakes, as shown in Fig. 1a-1b.Two FTS flakes are exfoliated from a single crystal Fe(Te0.58Se0.42)onto a SiO2/Si substrate, then capped with a hexagonal-boron nitride (h-BN) flake and transferred onto pre-patterned electrodes.More details of material synthesis and device fabrication are available in the Methods section and Supplementary Note 1. Atomic resolution annular dark-field scanning transmission electron microscopy (ADF-STEM) imaging of the cross-sectional sample (Fig 1c and 1d) reveals an interatomic vdW gap of 3.6 Å between the two FTS flakes, as shown in Fig. 1e (see Methods for more details).This vdW gap is sufficient to establish a phase separation between two adjacent superconducting flakes to form a superconductor-vdW-superconductor Josephson junction 19,20 .
The Josephson effect is confirmed by detecting a supercurrent flowing across the junction as demonstrated in the R-T curve in Fig. 2a.The FTS superconducting flakes (blue curves) show a critical temperature Tc of 14.5 K, in accordance with the value reported in the literature 21 .The resistance of superconducting flakes (reservoirs) completely vanishes at 14 K (blue curve in Fig. 2a); therefore, the remnant resistance below 14 K solely comes from the junction.The junction resistance further drops to zero in two stages, as illustrated in the red and blue areas in Fig. 2b, which we conjecture are contributed by the Josephson effect from bulk and surface superconductivity, respectively.In temperature regime (I) from 14 K to 12 K, the rapid resistance drop may be attributed to the Josephson effect from bulk superconductivity.This is evidenced by almost overlapping resistance curves under zero-field cooling (ZFC) and 1 T field cooling (FC).FTS is a type-II superconductor with a large upper critical field Hc2 well above 50 T 22 ; hence in this bulk state-dominated regime, the resistance shows little response to 1 T magnetic field.Below 12 K (temperature regime II in Fig. 2b), the resistance further drops to zero upon zero-field cooling.In contrast, the Josephson supercurrent is suppressed under 1 T field cooling, indicating a different superconducting order with distinctive magnetic response compared to the bulk states in regime I. Hence the lower temperature transition in regime II can be tentatively attributed to the surface superconducting states, as the lower Tc of surface superconductivity is directly confirmed by a smaller superconducting gap on the surface (1.8 meV) versus in the bulk (2.5 meV) through high-resolution ARPES measurements 11 .At a base temperature of 2 K, a critical current Ic of 290 µA is measured.Our device is in the strongly overdamped limit since no apparent hysteresis is observable in the I-V curve.

Concurrent Ferromagnetic and Superconducting Orderings
Fig. 3a shows the magnetic field response of a representative vJJ device, where a magnetic hysteresis behavior is observed in the junction resistance at 2 K, suggesting an unexpected ferromagnetic order arises in this vJJ structure.The junction resistance drops from a finite value to zero only when the field passes zero, and the center of the superconducting window appears around ±30 mT.We define the center of the zero-resistance window as the coercive field of the emerging ferromagnetism.We noticed pronounced resistance jumps and noises during the magnetic field sweeping, which is most likely related to random flux dynamics during the domain switching near the coercive field.Such jumps are suppressed at higher magnetic fields where all the domains are aligned with the external magnetic field.The noises also do not exist in the time domain if we pause the magnetic field at a certain value.
Such magnetic hysteresis behavior is reproducible in other additional devices we fabricated (see additional data in Supplementary Note 2).Another proof of unconventional ferromagnetism amidst superconductivity is the magnetic history dependence on the critical current.The Ic in a zero-field-cooled device will be significantly reduced after applying a "magnetic pulse", i.e., experiencing a sufficiently large magnetic field bias (e.g., 100 mT) and then returning to zero field (See Supplementary Note 3).After removing the magnetic field, the remnant magnetization will suppress the superconducting order parameter Δ  and thus reduce the Ic.Such suppression of Δ  is reversible by elevating the temperature above the Curie temperature of this ferromagnetic ordering to demagnetize the device and then cool it back to the base temperature (See Supplementary Note 3).Here the Curie temperature is roughly estimated from the temperature above which the magnetic hysteresis loop vanishes (see Fig. S6 and Supplementary Note 4).We find the demagnetization temperature around 12 K, which coincides with the superconducting critical temperature Tc, implying that these two orderings may be strongly associated The strong correlation between ferromagnetism and superconductivity in our FTS vJJ substantially differs from heterogeneous vdW magnetic Josephson junctions where ferromagnetism and superconductivity are independent and repulsive [23][24][25] .
Evidence of the spontaneous time-reversal symmetry breaking in the FTS system has been recently reported by the laser ARPES experiment 14 , wide-field nitrogen vacancy imaging 15 , and Sagnac magneto-optic Kerr effect (MOKE) imaging experiments 16 , but has not yet been confirmed through transport measurements in single crystals.By stacking two layers of FTS flakes, the exchange energy of magnetism may be enhanced through the hybridization between the surface states of top and bottom flakes, allowing us to directly measure the magnetic behavior in such vJJ structures.This enhancement of ferromagnetism can be explained by the spin-spin interactions between the two adjacent layers as follows.For a single FTS flake, the in-plane spin polarization direction can be arbitrary due to the (1) × (1) symmetry.However, the non-negligible inter-layer spinspin interactions can further lower the ground state energy by reducing this degeneracy down to a (1) × (2) symmetry.Therefore, the inter-layer coherent spin-polarized state has much stronger magnetism.A detailed analytical understanding on how interlayer spinspin interactions can enhance magnetism from the Ginzburg-Landau theory is discussed in Supplementary Note 5.As a result, the magnetic hysteresis behavior is discernable in such a vJJ device geometry, while it is absent in a bare FTS flake (Supplementary Note 6).We also notice that the hysteresis behavior is only observable with the presence of an in-plane magnetic field (i.e., perpendicular to the c-axis), showing a strong magnetic anisotropy with an in-plane easy axis (Supplementary Note 2).This is consistent with the reported stray field direction in the nitrogen-vacancy center magnetometry measurements 15 .
Our experimental observation of magnetic hysteresis loops can be qualitatively explained by the co-existence of ferromagnetic and superconducting ordering parameters, as shown in Fig. 3b-d.A square-like hysteresis loop describes the magnetization of a ferromagnetic ordering (Fig. 3b), where the Zeeman energy of ferromagnetic ordering Δ  is minimized near the coercive field during magnetic domain switching.In this regime, the superconducting gap energy Δ  exceeds Δ  (Fig. 3c); therefore, the device reaches zeroresistance superconducting states (Fig. 3d).We also propose an effective model Hamiltonian to describe our system.We ignore all the bulk bands that are trivially gapped out by an s-wave pairing potential below Tc, and study the hybridization of top and bottom surface Dirac states at the interface with the inclusion of surface magnetism  ⃗⃗ .The fourby-four Hamiltonian reads: where (Fig. 3g) 26 .In this state, the superconducting nature is preserved locally in the momentum space, whereas the overall sample can exhibit finite resistance due to scattering processes (more discussion on the model Hamiltonian can be found in Supplementary Note 7).While the partial Fermi surface picture can phenomenologically interpret the observed results, we shall acknowledge that additional contributing factor such as nucleation of vortexantivortex pairs may also potentially give rise to a finite resistance 17,27 .

Fraunhofer Pattern and Mixture of 0π Josephson Junctions
We next present prominent Fraunhofer oscillatory features in FTS vJJs with a multidomain texture of mixed 0 and π phase junctions.vdW gap  less than 1 nm, we find   = 28  at 2 K in good agreement with the previously reported value 28,29 .The Josephson penetration depth 23,30  ) (3) 31 .Here  1,2 are real and imaginary parts of the complex coherence length which is very short in magnetic JJs (typically on the order of nm), and   ,   are the thickness of the magnetic layer and magnetically dead layer, respectively.Due to the small superconducting coherence length in magnetic layers, the phase is extremely sensitive to the magnetic layer thickness, hence slight spatial variation (either from inhomogeneous magnetic domains or vdW gap thickness fluctuation) will create mixed domains with 0 and π phase ground states.The major features of the Fraunhofer patterns can be well reproduced by decomposing the critical current into contributions from 0 and π Josephson junctions, as indicated by the solid lines in Fig. 4a and 4b.We shall emphasize that the multi-domain mesoscopic structure provides a natural platform to host 1D chiral Majorana states along domain walls with the π phase difference in superconducting order parameters 32 , as predicted in the Fu-Kane model 7 .
By zooming in on the low-field region in Fig. 4c, it becomes apparent that the Fraunhofer pattern is slightly skewed, and the positive (Ic+) and negative (Ic-) critical currents are bounded by a non-reciprocal field-dependent relationship  + () = − − (−) .This centrosymmetric pattern is highlighted by some highly coinciding features in the opposite quadrants linked by the white solid lines (as shown in Fig. 4c).A similar skewed Fraunhofer pattern is also reported in other ferromagnetic Josephson junctions 23 .This effect is consistent with Fulde-Ferrell (FF) finite-momentum pairing states 33 arising from the ferromagnetic ordering, leading to an imbalance between opposite critical currents.
Unlike traditional Bardeen-Cooper-Schrieffer (BCS) pairing (Fig. 4d), the Zeeman energy will shift the Fermi surface away from the Brillouin zone center and cause a finite centerof-mass momentum pairing (Fig. 4e).We note that the finite-momentum pairing is general in our case and can happen even without a phase transition to FF states 34 .This nonreciprocal critical current is known as superconducting diode effect, which necessitates time-reversal symmetry breaking, and will be further discussed next.

Stochastic Field-free Superconducting Diode Effect
The superconducting diode effect (SDE) refers to imbalanced critical current values of a superconductor in opposite DC current bias directions.SDE is premised on both lack of inversion symmetry and time-reversal symmetry [34][35][36] ; the former is achieved by structural or crystal symmetry breaking, whereas the latter can be realized with either external magnetic field or intrinsic magnetism.So far, the majority of the reported SDEs require applying an external magnetic field.Field-free SDEs are rare to encounter (with very few recent exceptions [37][38][39][40] ) due to the incompatibility of magnetism and superconductivity.In our FTS vJJ devices, the field-free SDE is observed (Fig. 5a), suggesting both inversion symmetry and time-reversal symmetry are broken in this system.The inversion symmetry can be easily broken in this stacked structure, for example, by introducing a relative chemical potential shift between top and bottom Dirac surface states (see Supplementary Note 7).The fact that SDE can be achieved without external magnetic field is a direct manifestation of spontaneous time-reversal symmetry breaking, and the diode behavior can be used to probe the interface ferromagnetism below Tc.More strikingly, the diode polarity can be stochastically switched by performing a thermal cycle above the superconducting Tc which randomizes the spin configurations and generates random net magnetization.Two middle panels in Fig. 5a show two representative dV/dI curves measured at 2K with zerofield before and after a thermal cycle.Here a thermal cycle refers to the procedure of heating the device to 25 K (well above Tc) and cooling back to base temperature of 2 K.
Above Tc the thermal fluctuation renders the spin configuration undetermined without established magnetism.Upon zero-field cooling, the randomized spin will freeze and trap a small but non-zero net magnetization (see Fig. 5b), the direction and amplitude of which will determine the polarity and efficiency ( ) of the SDE.We further notice that by performing a field cooling under a moderate magnetic field of ±10 mT, the diode efficiency enhanced because of the fully aligned spin configuration, and the polarity is deterministic upon the field direction (as shown in top and bottom panels of Fig. 5a and  5b).The stochastic distribution of field-free SDE, as shown by the red curves in Fig. 5c, is statistically investigated by repeating thermal cycling 50 times.In another 50 zero-field current scans without thermal cycling, the diode behavior remains unchanged (blue curves in Fig. 5c).The histograms show that the diode effect is widely distributed between thermal cycles (left panel in Fig. 5d and Supplementary Note 10).In contrast, without thermal cycling, the magnetic domains freeze and do not evolve with time (Fig. 5d, right panel; and Supplementary Note 10).The stochasticity also rules out a trivial mechanism of SDE due to the trapped flux from the superconducting coil, as the magnet was kept in the persistent mode throughout the entire measurement and thus the remnant field is fixed and should not induce such stochasticity (more discussion see Supplementary Note 10).We emphasize that if sample inhomogeneity causes magnetic regions to be completely separated from the superconducting regions across the surface, there will be no superconducting diode effect at zero magnetic field.Thus, our finding of field-free superconducting diode effect not only shows the coexistence, but also the coupling between ferromagnetism and superconductivity in FTS.

Discussion
Here we briefly discuss the relationship between ferromagnetism and superconductivity in our FTS samples.While the previous studies suggest the coexistence of ferromagnetic and superconducting orderings [14][15][16][17] , the correlation between them is yet elusive.It should be acknowledged that a small amount of excess iron atoms may exist in superconducting FTS samples and contribute to the ferromagnetism 41 .However, detailed study revealed that magnetic impurity distribution highly overlaps with non-superconducting region 21 , suggesting the ferromagnetism induced by excessive iron is locally incompatible with superconductivity.In addition, such ferromagnetic ordering from iron atoms should sustain above the superconducting temperature, which is contradictory to our experimental observation and recent MOKE results 16 .This may be indicative of other more complex is the Fermi velocity of surface Dirac states,  0 and  1 describe the hybridization strength between the top and bottom surface Dirac states,  ⃗⃗ = (  ,   ,   ) is the spin magnetization,   is the relative chemical potential shift of the top and bottom Dirac states, and  is the overall chemical potential.Here  and  are Pauli matrices for the spin and layer degrees of freedom.Without magnetization, a superconducting gap is fully open near the Fermi surface, as shown In Fig. 3e.Since the surface Hamiltonian has a continuous rotational symmetry about the z-axis, we choose   = 0.2,   = 0 to turn on magnetization without loss of generality.We also set   = 0 since the experiment result suggests the magnetization mainly concentrates in the x-y plane.The competition between superconductivity and ferromagnetism produces gapless superconducting states, as shown in Fig. 3f, which give rise to an arc-like energy contour, known as partial Fermi surfaces Fig. 4a shows the differential resistance mapping as a function of DC bias current and external magnetic field measured at 2K, where "single-slit" type interference patterns are resolved, confirming the established Josephson phase-current relation in this vJJ structure.An oscillation period Δ = 5.5  is extracted from the diffraction pattern, which can be translated into a junction area of 0.38 µm 2 under the flux quantization condition: Δ •  = Φ 0 = ℎ/2.Here  is the effective junction cross-sectional area perpendicular to the magnetic field.Given that the junction length (that is, the average width over the overlapping area perpendicular to the magnetic field) is ~ 7 µm, we can deduce a junction width  =  + 2  = 56  ( and   denotes the vdW gap size and in-plane London penetration depth of FTS).With a negligible origins, for example, unconventional superconducting pairing mechanisms with spontaneous time-reversal symmetry breaking, are possible given the strongly synchronized behaviors between ferromagnetism and superconductivity.Further investigations combining high-quality transport devices and precise magnetic probes are needed to confirm such a picture.In conclusion, we report an emergent ferromagnetism with superconductivity at the interface of Fe(Te,Se) flakes through transport measurements in the van der Waals Josephson junction device geometry.The concurrency of ferromagnetism and superconductivity suggests the close tie between these two orderings which can arise from unconventional pairing mechanisms with interface coupling.A field-free stochastic superconducting diode effect is further discovered, implying spontaneous time-reversal symmetry breaking in the superconducting states.The stochasticity in the polarity and efficiency of SDE reflects the randomness of net magnetic moment of the surface magnetism without external magnetic field.Our work provides comprehensive understanding of the interplay between superconducting and ferromagnetic orderings and lays a foundation for understanding the TSC nature and related Majorana physics in the iron-based high Tc superconductor platform.flakes parallel to the transmission electron beam.Atomic resolution ADF-STEM images were then taken to measure the physical vdW gap between the two flakes.Transport measurements Magneto-transport measurements were performed in a Quantum Design Physical PropertyMeasurement System (PPMS) with a superconducting coil capable of producing up to 9Tesla magnetic field.The data was taken using the standard low-frequency (< 20 Hz) lockin technique with an AC current excitation of 10 µA at a base temperature of 2 K, unless otherwise specified.For differential resistance measurement, a DC current bias is applied via a Keithley 6221 Current source meter; the AC current/voltages are sourced/measured by SR830 lock-in amplifiers.The critical current is always read off from the outbound branch of the current scan, i.e., from 0 to a large current, to eliminate the Joule heating effect.During the dV/dI measurement, the AC excitation is kept below 0.5% of the full DC scan range.For zero-field cooling procedures, prior to cooling down, the superconducting coil was set to oscillate to 0 field to minimize the trapped flux and therefore the remnant field generated from the coil.

Figure
Figure 1| Fe(Te,Se) van der Waals Josephson junctions (FTS vJJ).a, The device schematic of an FTS vJJ.b, A false-colored scanning electron microscopy image of an FTS vJJ device.c, Low-magnification ADF-STEM image showing the cross-section of a vJJ stack.d, atomic resolution image from the region defined by a red box in (c) showing a van der Waals gap between the two FTS flakes.e, Integrated line intensity from STEM image in (d).An interatomic van der Waals gap of 3.6 Å is determined.

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