Observation of superconducting vortex clusters in S/F hybrids

While Abrikosov vortices repel each other and form a uniform vortex lattice in bulk type-II superconductors, strong confinement potential profoundly affects their spatial distribution eventually leading to vortex cluster formation. The confinement could be induced by the geometric boundaries in mesoscopic-size superconductors or by the spatial modulation of the magnetic field in superconductor/ferromagnet (S/F) hybrids. Here we study the vortex confinement in S/F thin film heterostructures and we observe that vortex clusters appear near magnetization inhomogeneities in the ferromagnet, called bifurcations. We use magnetic force microscopy to image magnetic bifurcations and superconducting vortices, while high resolution scanning tunneling microscopy is used to obtain detailed information of the local electronic density of states outside and inside the vortex cluster. We find an intervortex spacing at the bifurcation shorter than the one predicted for the same superconductor in a uniform magnetic field equal to the thermodynamical upper critical field Hc2. This result is due to a local enhanced stray field and a competition between vortex-vortex repulsion and Lorentz force. Our findings suggest that special magnetic topologies could result in S/F hybrids that support superconductivity even when locally the vortex density exceeds the thermodynamic critical threshold value beyond which the superconductivity is destroyed.


Results
Samples. Several magnetically coupled S/F heterostructures, made by Nb/Py and Pb/[Co/Pd] n multilayers, were fabricated for MFM and STM/STS investigations. A thin insulating layer of 10 nm SiO 2 or Al 2 O 3 was used to electrically decouple the superconductor from the ferromagnet. This allows to study the effect of the spatially inhomogeneous stray field on the superconductivity without any interference from proximity coupling between the superconducting and magnetic layers 9 .
The thick Py films and Co/Pd multilayers are designed to have stripe magnetic domain pattern, with local magnetization vector alternating its projection along the out-of-plane direction between the adjacent magnetic stripes. In the Py, the in-plane easy magnetization axis is such that the canting angle of the magnetization vector is very small and magnetic stripe domains are formed only above the critical thickness of t c ≈ 200-300 nm. Above this threshold, the magnetic stripe width w grows as square root of the film thickness d m , ∝ w d m 56,57 . On the other hand, Co/Pd multilayers have a much stronger perpendicular anisotropy. The appearance of an out-of-plane stripe configuration of magnetic domains is a consequence of the competition between the perpendicular magnetic anisotropy and the thin-film shape anisotropy. Moreover, materials with low and medium perpendicular anisotropy, such as Py, always show twisted structure at the surface (closure domains) with an in-plane orientation of the magnetization, perpendicular to the domain wall, able to confine part of the out-of-plane magnetic flux and lower the magnetostatic energy 58 . The resulting domain structure consists of partially closed magnetic loops with alternating clockwise and counterclockwise orientation. In films with a strong perpendicular magnetic anisotropy the formation of closure domains becomes energetically unfavorable. However, recent magnetic simulations, based on the measured magnetic hysteresis loops, show the appearance of closure domains in a twin Co/Pd multilayers as well 59 . In general, closure domains are difficult to observe because the majority of the conventional magnetic imaging techniques rely on the detection of the out-of-plane stray fields. They could be detected by using Kerr microscopy technique, which is sensitive to the in-plane magnetic field component 60 .
It is worth noticing that the magnetic domain size and configuration in both ferromagnets are insensitive to the low magnetic fields applied during the field cooling processes performed in the MFM and STM/STS experiments here.
Twin superconducting films have been fabricated and characterized to derive the fundamental superconducting parameters. Twin Nb films have been magneto-electrically characterized, showing ξ Nb (0) ≈ 12 nm and λ Nb (0) ≈ 61 nm 50,53 . In such a case, Py films with thickness in the range of 1 ÷ 1.5 μ m (and stripe widths w ≈ 500÷ 700 nm 53 ) are good candidates for low temperature MFM experiments on Nb/Py hybrids. Indeed, being λ Nb (6K) ≈ 68 nm 53 at the operational temperature of T = 6 K, vortices can be widely accommodated within the Py(1 ÷ 1.5 μ m) stripe domains.
On the other hand, it is well known that bulk Pb exhibits type-I superconductivity (with ξ Pb,bulk (0) ≈ 83nm and λ Pb,bulk (0) ≈ 38 nm 61 ). However, due to renormalization of the coherence length, Pb thin films behave as type-II superconductors and magnetic field penetrates in form of flux quanta. Moreover, in a twin 30-nm Pb film a Scientific RepoRts | 6:38557 | DOI: 10.1038/srep38557 ξ Pb (0) ≈ 48 nm 11 has been measured using STM vortex imaging, in agreement with values of 40 ÷ 50 nm reported in literature for ultrathin Pb films 62 .
Different combination of superconductor and ferromagnet pairs were used in the S/F bilayers studied by MFM and STM/STS. For the superconducting materials, when limiting the choice to the simplest elemental superconductors, Nb and Pb are the best options. Indeed, due to their low intrinsic pinning, vortex arrangement can only be addressed to the ferromagnetic template. However, Nb is not a good candidate material for STM/ STS investigation due to surface oxidation and difficulty to remove the oxide layer (possible only by annealing at temperatures higher than 1000 °C, which is not compatible with the underlying ferromagnet). On the other hand, Pb is not suitable for the MFM experiments, because of its low critical temperature that is too close to the minimum operational temperature of our instrument. Another important parameter to consider is the available scanning area. While STM provides the highest spatial resolution it does not allow large scanning areas since this compromises the stability of the tip-sample gap. Therefore, the largest STM scanning area of around 500 nm × 500 nm at T = 1.5 K requires a choice of ferromagnet with small stripe width and strong stray field, such as Co/Pd multilayers, to be able to visualize at least a few magnetic stripe domains within a single scan area and allow us to properly tune the intervortex distance with the applied magnetic field. However, Co/Pd multilayers are not suitable for MFM experiments, because of their relatively high out-of-plane stray magnetic fields inducing dense vortex arrangements that overlap on scale of λ . In

MFM observation of vortex clusters.
Low temperature MFM measurements were performed on Nb/Py bilayers. Figure 1 shows the effect of the bifurcations on the vortex configurations in different situations. MFM maps acquired above and below the Nb critical temperature (T s = 8.9K 53 ) in samples with three different Nb layer thicknesses (150 nm, 200 nm, 100 nm) while keeping the Py layer 1 μ m thick, are shown in Fig. 1. Above T s , at T = 13 K, the images show the stripe-like domain pattern of Py, with a stripe width w ≈ 500 nm, each of them containing dislocations of the regular magnetic structure. The significant increase of the magnetic contrast at the core of the bifurcation is representative of a stronger local stray field. Below the Nb T s , superconducting vortices are favored to nucleate at the bifurcation. Moreover, vortices always appear on a partially shielded magnetic stripe contrast. Indeed, the Nb thin films do not completely shield Py magnetic stray field, allowing the MFM visualization of the magnetic stripe domains even below T s . Nevertheless, a suppression of the magnetic contrast of the Py stripes due to the Nb diamagnetism, is confirmed by the comparison of the frequency span scale, above and below T s . Figure 1(d) shows the MFM image acquired on Nb(150 nm)/Py(1 μ m) at T = 6 K after a field cooling in the magnetic tip's field, which is a non-uniform local dipole field (as shown in the Supplementary Fig. S1). This sample's stripe magnetization is below the threshold for spontaneous formation of vortices and antivortices. Therefore, an external magnetic field is needed to facilitate nucleation of Abrikosov vortices. While cooling down below T s , the tip was kept in the bottom-left corner of the image, spaced by only a few nanometers from the sample surface. In such a case, vortices of the same magnetic polarity as the tip are induced within few microns around the tip's apex. As shown in Fig. 1(d), a vortex is present in the middle of the dislocation, separated from its nearest neighbors by a distance sensibly smaller than the spacing between the vortices in the upper-right area of the image. Indeed, an average intervortex distance of about 1.2 μ m is measured between flux quanta around the dislocation, whereas the intervortex spacing on the top of the bifurcation is reduced by 35% to about 780 nm. We infer that such effect is driven by the bifurcation topology and by the local enhancement of the Py stray field.
On the other hand, MFM maps acquired at T = 6 K in Nb(200 nm)/Py(1 μ m) ( Fig. 1(e)) and Nb(100 nm)/ Py(1 μ m) ( Fig. 1(f)) show a strong magnetic contrast at the bifurcation site, surrounded by individual vortices nucleated in the presence of applied field of H = 30 Oe and in zero field cooling respectively. Line profile analysis performed on Nb(200 nm)/Py(1 μ m) below T s ( Fig. 1(e)), confirms that superconducting vortices induced by the external field are mostly separated by a distance of (920 ± 105)nm, close to the expected value of 890 nm, derived by using = , where H is the applied field, Φ 0 is the flux quantum and d is the distance between vortices. Far from the dislocation area, a vortex cluster formed by two separate vortices, spaced by a distance of around 150 nm, appears in the map in Fig. 1(e) (outlined by a dark blue dotted circle). We infer that in this specific case the intrinsic pinning in the Nb layer causes a non-uniform vortex distribution.
On the other hand, spontaneous V/AV formation in Nb(100 nm)/Py(1 μ m) is observed in Fig. 1(f), with vortices and antivortices induced by the stray fields of the Py stripes. The vortices are confined in blue and white dotted circles corresponding to vortex and antivortex confined to stripes with opposite magnetization polarity. Besides the vortices at the dislocation area, few spontaneous vortices populate the imaged area, being the out-of-plane magnetization of Py(1 μ m) very close to the threshold value for spontaneous flux quanta nucleation in Nb(100 nm)/Py(1 μ m) 53 . Careful analysis of the magnetic contrast at the dislocation is required to distinguish whether the observed magnetic profile represents a vortex clusters or a giant vortex.
In Fig. 2, the 3D zoom-in of the MFM maps acquired on the top of the bifurcations in Nb(200 nm)/Py(1 μ m) ( Fig. 2 (a)-(b)) and Nb(100 nm)/Py(1 μ m) (Fig. 2 (d)-(e)), above and below T s , are compared. Keeping the same tip-sample separation, the magnetic contrast of Nb(200 nm)/Py(1 μ m) above and below the Nb superconducting transition appears quite different ( Fig. 2(a,b)). A comparison of line profiles extracted from Fig. 2(a,b), above and below T s is presented in Fig. 2(c). One observes significant change in the magnetic modulation. Indeed, two maxima of the magnetic roughness are clearly present below T s , while two more kinks can be observed closer to the borders (marked by arrows), which might suggests the presence of a more complex vortex cluster. The average intervortex spacing is about 200 nm, whereas the average distance far from the dislocation is about (920 ± 105) nm. Similar analysis performed on Nb(100 nm)/Py(1 μ m), (Fig. 2(e)) does not show any drastic change in the magnetic roughness at the bifurcation core, compared to Fig. 2(d), acquired above T s at the same tip-sample separation. The line profile comparison, reported on Fig. 2(f) and extracted from the white dotted profiles of Fig. 2(d)-(e), only confirms a reduction of the frequency shift below T s , due to Nb diamagnetism. However the formation of a superconducting vortex (giant or cluster) below T s is determined from its interaction with the MFM tip when it moves closer to the Nb surface ( Supplementary Fig. S2).
The MFM experiments performed on a S/F sample having a thicker Py layer, Nb(150 nm)/Py(1.5 μ m), did not show any occurrence of spontaneous V-AV formation, proving that the equilibrium value of Py(1.5 μ m) out-of-plane magnetization has to be lower than the threshold required to nucleate spontaneous vortices in Nb(150 nm) 53,64,65 . However, a strongly localized superconducting vortex nucleation can still be induced at the dislocation site, as shown in Fig. 3. Here, we present a patchwork made of two MFM maps of Nb(150 nm)/ Py(1.5 μ m) bilayer at T = 6 K after zero field cooling. In addition to the vortex nucleation on the top of the bifurcation, a vortex of opposite polarity (antivortex) is induced on the adjacent oppositely magnetized stripe and only a third red vortex appears in proximity of the dislocation. No other vortices (or antivortices) populate the imaged areas, confirming the magnetic influence of the dislocations on vortex nucleation. Indeed, not only that  the vortex nucleation is favored at the bifurcation whenever the sample is over-threshold ( Fig. 1(f)) or it is field cooled (Fig. 1(d)-(e)), but vortices could be locally induced by the dislocation even when no other spontaneous vortices are present. This also proves that the out-of-plane magnetization is under threshold everywhere except for the dislocation site, where a local enhancement of the stray field always occurs. ). Indeed, after the field cooling, vortices nucleate on the underlying magnetic domains of the same polarity as the external field. Wherever the magnetic stripe pattern is straight and regular, as in the left half-image of Fig. 4, the hexagonal arrangement of vortex lattice occurs with an average intervortex spacing of 1.2 μ m, close to the expected value of 1.12 μ m. In the right half-image the regularity of the hexagonal array is lost and an inhomogeneous distribution of flux quanta with a higher vortex density is observed. The intervortex spacing in this area is reduced by 40% to 700 nm. Such irregular vortex arrangement is driven by the presence of two dislocations of the magnetic stripe structure. The curvature of two stripes converging at the bifurcation acts as a vortex accumulation area increasing the local vortex density.

STM/STS study of vortex clusters.
Scanning tunneling microscopy and spectroscopy measures the local electronic density of states and could be used to discriminate between presence of Abrikosov vortex cluster and giant vortex. Despite the lack of magnetic field sensitivity, STM/STS allows vortex imaging with high lateral resolution up to very high magnetic fields. With STM one can infer the domain pattern in ferromagnetic layer in an indirect way: the nucleation sites of superconducting flux quanta after field-cooling the sample below T s in opposite polarity magnetic fields, provides a unique fingerprint of the magnetic domains in the underlying ferromagnet 11 .
Low temperature STM/STS experiments were performed on Pb(30 nm)/[Co(2 nm)/Pd(2 nm)] 200 . As shown in Fig. 5(a) room temperature MFM on [Co(2 nm)/Pd(2 nm)] 200 confirms a stripe-like configuration of magnetic domains with occasional dislocation defects. Figure 5(b) shows the position of spontaneous superconducting vortices in Pb(30 nm)/[Co(2 nm)/Pd(2 nm)] 200 superimposed to a cartoon of the magnetic domains. This is a patchwork of five conductance maps of 438 nm × 438 nm in size, acquired at the Fermi energy at T = 1.5 K after zero field cooling. Vortices and antivortices appear as red spots with higher zero bias conductance (ZBC) compared to the superconducting background, which is here masked by the cartoon of the magnetic texture. An agglomeration of spontaneous flux quanta appears at the bifurcation core, where the vortex nucleation is favored because of the local stray field enhancement. The conductance map at the dislocation, in the green dotted square, at T = 1.5 K and in zero field cooling, is enlarged in Fig. 5(c). Three hot spots of conductance are present inside the cluster, which is surrounded by other two individual and isolated vortices. This strongly inhomogeneous vortex distribution is an evidence of the strong influence of magnetic defects on vortex arrangement.
In Fig. 6(a),(b) we show ZBC maps acquired at T = 1.5 K in the yellow dotted area of Fig. 5(b) (just below the bifurcation) after a field cooling in H = − 300 Oe and H = 300 Oe, respectively. A conductance distribution of individual and well-separated vortices appears in Fig. 6(a), while, in the opposite field antivortices agglomerate at the end point of the interrupted stripe ( Fig. 6(b)). Here, spectroscopic analysis confirms the nucleation of a vortex cluster, formed by three individual flux quanta. The plot of Fig. 6(c) shows the evolution of the superconducting density of states (DOS) along the black dotted line of Fig. 6(b). The tunneling spectra gradually evolve while approaching the vortex cluster and they are characterized by an increase in the zero bias conductance and a decrease of the coherence peaks' height. Clearly the superconductivity is fully suppressed in three separate locations, where a zero bias peak is observed (red dotted curves in Fig. 6(c)). The presence of a pronounced zero-bias peak in the conductance spectra at the vortex core is a clear evidence of the superconducting clean limit regime 67,68 . Finally, superconducting DOS features are completely recovered outside of the cluster. The plot of the normalized ZBC as a function of position, reported in Fig. 6(d), shows three ZBC peaks inside the cluster (indicated as A, B and C), separated by 105 nm (A and B) and 109 nm (B and C). Surprisingly, the resulting intervortex separation is about 1.4 times smaller than the minimum value possible, achievable at the second critical field  Fig. 6(d)) resulting in ξ(1.5K) ≈ 50 nm, which is in good agreement with previous estimates on our twin samples 11 .
It is worth noticing that the size of the cluster that occupies the top of the bifurcation (Fig. 5(c)) is fully consistent with an agglomeration of three flux quanta, each of them having ξ(1.5K) ≈ 50 nm (Supplementary Fig. S3).

Discussion
Direct observation of superconducting vortex cluster and vortex accumulation as a consequence of topological defects of the stripe magnetic structure in S/F thin film hybrids, made by Nb/Py and Pb/[Co/Pd] n, has been carried out by using MFM and STM/STS techniques.
In general in S/F hybrids, with S in the mixed state, the position-dependent Lorentz force due to the screening currents above the magnetic domains, pushes the vortices to the center of the magnetic domains, thus minimizing the interaction energy between the superconducting vortices and the magnetic template 65,69 . In the presence of more than one flux quantum, the vortex-vortex repulsive interaction 0 . On the other hand in S/F hybrids with F in the stripe regime, the strong confinement exerted by the magnetic template leads to a chain-like distribution of vortices that eventually exhibit zig-zag displacement at high fields in wide stripes 50 . In such a scenario, vortex clusters can be explained as a consequence of several factors: a local stray field enhancement, a local reduction of the intervortex repulsive force as well as a local change in the Lorentz force action.
MFM measurements clearly show that a bifurcation, where two magnetic stripe domains converge and coalesce in a single one, leads to a local enhancement of the out-of-plane stray field. In Fig. 7(a),(b) a front view and a 3D sketch of an ideal magnetic stripe arrangement is shown. Blue and red stripes are representative of magnetic domains with opposite out-of-plane polarization. Closure domains in the shape of triangular structures with an in-plane orientation of the magnetization (yellow dotted arrows) are at the sample surface depicted in purple. Such a magnetization distribution is consistent with the magnetic configuration of Co/Pd multilayers, whereas in Py an additional strong in-plane component of the magnetization along the stripes needs to be considered. Magnetic configuration around the bifurcation is presented in Fig. 7(c). The closure domains, indicated by the yellow dotted arrows, are forced to follow the domain wall curvature. As a consequence, an in-plane magnetic flux surplus (resulting from closure domains in Co/Pd multilayers and from closure domains and in-plane stripe magnetization in Py) needs to be expelled by flowing out from the sample surface via the out-of-plane stray field. This gives rise to the enhancement of the out-of-plane magnetization at the bifurcation core which leads to the enhancement of the local stray field that in-turn induces vortex clusters, as demonstrated by MFM and STM experiments.
Moreover, STS measurements on Pb/[Co/Pd] n provided evidence for the existence of a vortex cluster spaced by a distance shorter than the minimum value achievable at the second critical field d(H c2 ) ≈ 2.8 × ξ . We infer that such a condition can be explained by taking into account the role of the bifurcation as topologically induced confinement. Indeed, while each vortex inside an infinite chain would feel the same net repulsive force, which leads to a constant intervortex distance, an unbalanced force is felt by vortices close to magnetic channel interruptions (stripe endpoint or bifurcation core). For instance, the vortex at the stripe endpoint feels a long-range repulsive interaction due to the semi-infinite vortex chain on one side, while on the other side only the Lorentz force would keep it away from the domain wall. In such a case a reduction of the intervortex distance close to the magnetic stripe endpoint is expected.
The bifurcation topology indirectly affects the vortex distribution at the nearest neighbor domains as well. As clearly shown in Fig. 4, hexagonal vortex lattice with an average lattice parameter of about 1.2 μ m is achieved at the matching field 66 wherever the stripes are straight and regular. On the other hand, around the dislocations the intervortex distance is affected by the stripe curvature, leading to a vortex-vortex spacing of about 700 nm. In the presence of straight magnetic domains, the Lorentz force vectors, being always normal to the domain walls where supercurrents flow, push vortices to the middle of the stripes. In such a case, the vortex distribution along the stripe is set by their repulsive interaction producing uniform intervortex spacing determined by the net magnetic field present -sum of the ferromagnet stray field and the external applied field. Instead, whenever there is a curvature of the domain walls, the Lorentz force vectors are locally not parallel, causing modulations of intervortex distance. At the bifurcation region the local bending of the stripes is extreme, leading to strong bending of the Lorentz force vectors that results in effective topological vortex confinement.
In conclusion, we have shown that randomly distributed defects in underlying magnetic structures, such as bifurcations, act as strong pinning sites that induce the nucleation of vortex clusters. Such dislocations strongly affect superconducting vortex distribution because of the magnetic confinement power coming from the local enhancement of the stray field and magnetic domain intrinsic topology. The topology of the magnetization at the bifurcation points in the ferromagnetic layer facilitates creation of vortex clusters in the superconductor, with vortices confined by the strong local Meissner currents while at the same time experiencing mutual repulsion.

Methods
Sample preparation. Nb/SiO 2 /Py were fabricated ex-situ by sputtering deposition and moved to the UHV chamber where the MFM experiments were performed. Py films were deposited by dc sputtering from a Ni 80 Fe 20 target onto a Si substrate at a base pressure of 1.5 × 10 −7 Torr, followed by a 10-nm SiO 2 layer, in order to decouple the F from the S layer, suppressing proximity effects 9 . Nb films were deposited by dc sputtering at room temperature in a dedicated system with a base pressure of 2 × 10 −8 Torr.
Samples for STM studies were fabricated in a different way to preserve their high surface quality. The [Co/Pd] n multilayers (where n is the number of bilayers in the stack) were deposited ex-situ on Si substrates by dc sputtering in a dedicated system and in the presence of an applied in-plane magnetic field, favoring a stripe-like magnetic domain pattern. A 10-nm Al 2 O 3 film was made by RF sputtering deposition from an Al target, in order to insulate the F from the S layer and suppress the proximity effect 9 . The 30-nm Pb film was deposited in-situ via e-beam evaporation at low temperature (120 K) and base pressure of 10 -11 Torr, followed by a room temperature annealing. This procedure guaranties flat and clean surfaces, suitable for STM studies. The UHV chamber, where Pb films were made is linked to the STM chamber where the experiments were performed, in order to avoid surface contamination due to the exposure of the films to the air.
Magnetic Force Microscopy. MFM experiments on Nb/Py where performed at T = 6 K using an Omicron cryogenic ultra-high vacuum (UHV) scanning force microscope, operating in frequency modulation-MFM mode. A commercial Si cantilever, equipped with a magnetic tip and having a resonance frequency f 0 ≈ 75 kHz and elastic constant k ≈ 2.8 N/m, was used. The tip, coated by a ferromagnetic Co/Cr film, was characterized by nominal low moment μ ≈ 0.3 × 10 −13 emu and measured coercivity H c,tip ≈ 550 ÷ 600 G. The magnetic imaging was done by scanning in non-contact regime and by mapping line by line the frequency shift df = f− f 0 of the resonating cantilever, due to the stray field coming out from the sample (f is the oscillation frequency measured during tip-sample interaction and f 0 is the force free resonant frequency of the cantilever). MFM maps were obtained by scanning at constant tip-sample heights, between 110 ÷ 180 nm, and the attractive/repulsive tip-sample interaction was mapped using color contrast. MFM spatial resolution is determined by the lift height used during the scanning and limited by the large magnetic volume of the tip.
Scanning Tunneling Microscopy and Spectroscopy. STM/STS experiments were performed at T = 1.5 K by using a cryogenic UHV Unisoku USM-1300 system, equipped with RHK electronics. Tunneling spectroscopy was performed by using a standard lock-in technique with an alternating current modulation of 0.2 mV at 373 Hz. The conductance maps were acquired by scanning the tip over the sample surface at high voltage (20 mV), acquiring the lock-in signal at the Fermi energy in each location. Conductance maps reveal therefore, vortices by tracking the difference of the electronic density of states inside and outside the vortex cores. Topography was always acquired simultaneously to check the location where the spectroscopic information was recorded. All differential conductance spectra dI/dV were taken with the same tunneling parameters, with the junction stabilized at V = 10 mV, I = 100 pA.