Skyrmion-(Anti)Vortex Coupling in a Chiral Magnet-Superconductor Heterostructure

We report experimental coupling of chiral magnetism and superconductivity in [IrFeCoPt]/Nb heterostructures. The stray field of skyrmions with radius ~50nm is sufficient to nucleate antivortices in a 25nm Nb film, with unique signatures in the magnetization, critical current and flux dynamics, corroborated via simulations. We also detect a thermally-tunable Rashba-Edelstein exchange coupling in the isolated skyrmion phase. This realization of a strongly interacting skyrmion-(anti)vortex system opens a path towards controllable topological hybrid materials, unattainable to date.

Introduction.-Chiral magnets and superconductors host topological excitations known as skyrmions and vortices, whose duality was recognised in the 1980s [1]. Recently, skyrmion-vortex pairing in heterostructures [2][3][4][5][6] has been proposed as a method of coupling chiral magnetism and superconductivity: a combination anticipated to deliver novel hybrid behavior [7,8]. For example, one can envisage changing the superconducting order parameter symmetry by imprinting non-collinear exchange fields from skyrmions or spin helices onto Cooper pairs. Such fields are gauge-equivalent to a Zeeman field combined with spin-orbit coupling (SOC) and may hence create a topological superconductor hosting Majorana fermions at its boundaries and vortex cores [9][10][11][12][13][14][15][16]. Controlling the nucleation and dynamics of vortices in the presence of skyrmions is the key to unlocking the potential of chiral magnet-superconductor hybrids for topological quantum computation [17,18] and fluxonics [19].
Skyrmions and vortices interact via two mechanisms. The first originates from the Rashba-Edelstein effect [20]: the skyrmion exchange field combines with interfacial SOC to induce circulating spin-polarized supercurrents, which interfere with vortex currents [2,3,[21][22][23]. This interaction ("exchange coupling") requires contact between superconductor and magnet, and depends on the sign and magnitude of the SOC and exchange field. The second mechanism -stray field coupling -allows skyrmionvortex interaction without electronic contact at distances greater than the exchange length [4]. The sign and magnitude of this interaction are determined by the current profile induced in the superconductor, which depends on the magnetic layer thickness d m , skyrmion chirality and skyrmion-vortex separation [24]. The skyrmion core polarization is antiparallel to the applied magnetic field H and hence repels vortices. However, a sufficiently large skyrmion can nucleate an antivortex in a nearby super-conductor, creating a bound pair of topological solitons experimentally unexplored to date.
These interactions can be modulated by adjusting the skyrmion/vortex lengthscales. Stray field coupling is enhanced by increasing skyrmion size, whereas exchange coupling requires Rashba-Edelstein and (anti)vortex currents to circulate with similar radii. This corresponds to the condition ξ < r sk < λ ( Fig. 1(a), [3]), where ξ, λ are the superconducting coherence and penetration lengths, and r sk is the skyrmion radius. Minimizing H (and hence the vortex density) also favours antivortex formation -but aside from Co/Ru(0001) monolayers [25], stabilizing skyrmions at low temperature in thin films has typically required H 1 T [26,27]. This exceeds the upper critical field H c2 of many s-wave superconductors, precluding skyrmion-(anti)vortex coupling. Here we present the first chiral magnet-superconductor heterostructures to host stable skyrmions at low fields and temperatures below the superconducting transition T c . Experiments and simulations both indicate that skyrmion stray fields create antivortices in the superconductor, strongly coupling spin and flux topologies. We also detect signatures of skyrmion-antivortex exchange coupling and identify routes to optimize this effect.
Superconducting layer.-Knowing r sk , we can tune the Nb layer thickness to optimize skyrmion-vortex coupling. In films of thickness d s < λ, Meissner screening is weak and λ is replaced by the Pearl depth Λ = λ 2 /d s [31]. To ensure long-range vortex interactions and negligible Nb bulk pinning, we select d s = 25 nm, resulting in Λ 200 nm (SM III). Figure 1(j-l) display the low-field vortex matter in a 25 nm Nb film with T c = 6.05 K, imaged by scanning tunneling spectroscopy (STS). The spatial evolution of the zero-bias conductance suggests a coherence length ξ ef f (0.4K) ≈ 36 nm (SM IV), far exceeding the Ginzburg-Landau (GL) ξ(0) ≈ 10 nm (SM III). This disparity likely originates from vortex core expansion in the Pt layer encapsulating the Nb against oxidation [32]. Our heterostructures thus satisfy ξ < ξ ef f < r sk < Λ. The saturation magnetization of our chiral film µ 0 M s = 1.82 T exceeds the lower critical field of the Nb film H c1 ≈ 0.012 T at 2 K (SM III, [33]), indicating that magnetic textures may form (anti)vortices in the su-perconductor [3]. Spontaneous vortex formation is wellestablished in superconductor-ferromagnet hybrids [34][35][36][37], but far more challenging to achieve using chiral magnets since r sk can be orders of magnitude smaller than typical ferromagnetic domains. Modelling the radial spin evolution as m z ∼ tanh π(r−r sk ) r sk [38], we estimate an upper limit of -4.44 Φ 0 for the flux through our 50 nm Néel skyrmions. Although the skyrmion stray field decays rapidly outside the magnetic layer, the flux piercing the adjacent superconductor remains sufficient to cre- ate antivortices in all our heterostructures (SM VI A). A threshold M s ≥ Φ 0 ln(Λ/ξ)/(0.86π 2 d m r sk ) was derived in ref. 4 for vortex formation by zero-field skyrmions, which our heterostructures exceed by 34% at 2 K. As a definite proof of antivortex nucleation in our experiments, we combine micromagnetic simulations of the [Ir 1 Fe 0.5 Co 0.5 Pt 1 ] 10 stray field (SM VI A) with GL simulations of the superfluid (|Ψ| 2 ) and supercurrent densities in an adjacent 25 nm Nb film (SM VI B,C). Figure 2(d) shows the supercurrent and |Ψ| 2 profiles above two Néel skyrmions stabilized at H = 125 mT, confirming the coexistence of skyrmion-induced antivortices (blue arrows) with vortices parallel to H (red arrows), separated by screening currents (grey arrows) above the skyrmion domain walls. In Fig. 2(e,f) we present large simulations of vortex-antivortex states at H = 25, 125 mT, visualized using the supercurrent-induced field h. At all fields, skyrmions and stripe domains [solid lines in Fig. 2(e,f)] robustly generate antivortices.
As H falls, the simulated antivortex density N AVx rises [ Fig. 2(g)]. MS heterostructures develop a higher N AVx than MIS samples, since they experience a stronger stray field (as the Nb layer is 7 nm closer to the magnetic film). This higher N AVx is visible in experiments [ Fig. 2(c)] as a larger drop in M super below H nuc for the MS sample. Raising the temperature also increases N AVx , since H c1 falls. For T < T c , M super (H) in all our heterostructures collapse onto a single curve between 0.04-0.14 T following a linear aM super + b scaling [ Fig. 2(h)]. N AVx (H, T ) can be similarly rescaled onto a single curve (Fig. 2(h) inset), confirming that antivortex nucleation driven by evolving spin topology is responsible for the magnetic response of the superconductor.  Skyrmion impact on vortex dynamics.-The critical current density J c (H) measured by electrical transport (SM VII) is plotted in Fig. 3(a). MS and MIS heterostructures both exhibit an enhanced J c (H nuc →H ann ) relative to a bare Nb film. This behaviour is mirrored by an emergent time-dependent magnetization [ Fig. 3(b)]. M super (H nuc →H ann ) relaxes towards increasingly negative magnetizations over several minutes after every reduction in H, leading to a measurable drop ∆M super . This relaxation and the rise in J c are caused by the chiral magnet inducing supercurrents which impede vortex motion. Just below H nuc , the skyrmion/antivortex density is low and the initial rise in J c (H) originates from longrange vortex-antivortex attraction. Reducing the field increases the skyrmion density, obliging vortices moving in a flux gradient or applied current to cross chiral domains. Vortices are repelled by skyrmion screening currents [ Fig. 2(d)]; however the presence of an antivortex reduces the barrier height, enabling vortices to cross the skyrmion/stripe in a process analogous to Klein tunneling. Flux-flow simulations are shown in Fig. 3 Fig. 3(a,b)]. Around zero field, a sharp maximum in J c and ∆M super originates from strong vortex pinning by labyrinthine stripes (SM II C, [39]). This phenomenon also causes the upturn and scaling failure in M super (H) below 0.04 T [ Fig. 2(c,h)]. However, the J c , ∆M super maxima in MS heterostructures are > 50% lower than in MIS samples, confirming the crucial role of antivortices in facilitating vortex motion. Skyrmion-vortex exchange coupling.-Our STS data ( Fig. 1(j-l), SM IV) suggest ξ ef f (0.4K) ≈ 36 nm in the 2 nm Pt separating Nb from [Ir 1 Fe 0.5 Co 0.5 Pt 1 ] 10 . This corresponds to ξ ef f (2 K) ≈ 43 nm, close to r sk ≈ 50 nm. Exchange coupling will consequently be weak, since the induced Rashba-Edelstein currents centred at r = r sk scarcely interact with antivortex currents which peak at r ≈ 2ξ ef f . However, MFM images close to H nuc show larger skyrmions with r sk up to ∼ 60 nm (Fig.1(e), SM II B). Since any increase in r sk should enhance exchange coupling, we search for differences between MS and MIS heterostructures at high fields. Figure 4(a) shows that the field at which M super first responds to skyrmion formation (denoted H Sc ) is ∼ 20 mT higher in MS versus MIS samples at 2 K. This pattern is repeated in the critical current [ Fig. 4(b)], where MS samples exhibit an earlier and larger J c (H) enhancement in the 0.16 → 0.12 T field range. Since the flux lattice stray field has negligible influence on skyrmion formation (SM IX), we interpret these data as exchange coupling assisting antivortex creation at high fields, by inducing supercurrents rotating in the same sense as antivortex currents. As the temperature rises the difference in H Sc between MS and MIS heterostructures is suppressed [ Fig. 4(c)], due to the divergence in ξ which only enables the r sk > ξ ef f condition to be fulfilled at low temperature. Exchange coupling can be strengthened in future hybrids by minimizing ξ ef f at the superconductor/chiral magnet interface.
Summary.-We have shown that skyrmion stray fields can nucleate stable antivortices in engineered chiral magnet-superconductor heterostructures. This process is independent of SOC, thus simplifying the task of building a topological superconductivity platform from (anti)vortices coupled to chiral spin textures. Coexistence of these hybrid magnetic solitons with superconducting vortices creates a complex yet controllable environment for exploring unique emergent flux dynamics.