Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures

Abstract

We investigate the formation of a new type of composite topological excitation -the skyrmionvortex pair (SVP) -in hybrid systems consisting of coupled ferromagnetic and superconducting layers. Spin-orbit interaction in the superconductor mediates a magnetoelectric coupling between the vortex and the skyrmion, with a sign (attractive or repulsive) that depends on the topological indices of the constituents. We determine the conditions under which a bound SVP is formed, and characterize the range and depth of the effective binding potential through analytical estimates and numerical simulations. Furthermore, we develop a semiclassical description of the coupled skyrmion-vortex dynamics and discuss how SVPs can be controlled by applied spin currents. PACS numbers:Advances in materials and fabrication capabilities in recent years have opened many possibilities for modifying and harnessing the properties of matter in a variety of interesting and powerful ways. In particular, hybrid systems comprised of layers of two or more materials of very different character provide new opportunities to study important fundamental phenomena -such as magnetism and superconductivity [1][2][3][4], or optical and electronic properties [5] -in new regimes and in new combinations of coexistence.Often, the range of phenomena exhibited by a hybrid system is much richer than that of its parts [6]. For example, it was recently demonstrated that hybrid systems comprised of superconductors and semiconductors yield exquisite new levels of fully-electrical control over Josephson-based quantum devices [7]. It has also been proposed that the exchange field of a magnetic layer proximity-coupled to a 3D topological insulator surface may open the possibility to realize a new quantum phase of matter with an intriguing quantized magnetoelectric response [8]. Moreover, the possibilities afforded by the trifold combination of magnetic, superconducting, and semiconducting systems is at the heart of the intense wave of recent activity aimed at realizing topological superconductivity and associated Majorana bound states [9-16] -a key step in the development of topological quantum information processing [17].In this work, we investigate a novel type of composite topological excitation in hybrid systems. Specifically, we investigate the coupling between magnetic skyrmions and superconducting vortices in a two-dimensional (2D) layered ferromagnet-superconductor heterostructure (see Fig. 1). The combination of spin-orbit coupling (SOC) in the superconductor and the lack of inversion symmetry of the heterostructure leads to a magnetoelectric coupling that mediates an interaction between textures of the magnetic and superconducting order parameters. In isolation, both the superconductor and the 2D ferromagnet may host a variety of robust topological excitationsvortices and anti-vortices for the superconductor [18] and The exchange field of a ferromagnetic thin film is induced into a thin film superconductor by proximity coupling. The spatially varying exchange f...

Manipulation of magnetic skyrmions by superconducting vortices in ferromagnet-superconductor heterostructures

“…Similar expression has been obtained in Ref. 24 by a different approach, where Lorentz force due to currents applied into the superconductor was not considered. At this point, we call for attention to three different scenarios in Eq.…”

“…Particularly, ferromagnetsuperconductor (FM-SC) heterostructures have received much attention in recent years [9][10][11][12] , either for their possible applications in spintronics 13 and Josephson devices [14][15][16][17] , or for the rich emergent physics in such systems [18][19][20][21][22] . Recently, theoretical works on chiral FM-SC heterostructures have demonstrated that the stray magnetic field of superconducting vortices may be able to create 23 magnetic skyrmions in the ferromagnetic layer, also to trap or repel the preexisting skyrmions 24,25 , depending on vortex polarity. First insights in the dynamic properties of such hybrid systems were recently provided in Ref.…”

Magnetically induced anisotropy of flux penetration into strong-pinning superconductor/ferromagnet bilayers

“…A protection layer of 10 nm MgO is furthermore deposited between superconductor and ferromagnet to reduce pair-breaking effects. As previously reported, the interaction across the interface is dominated by magnetic dipolar coupling [18][19][20].…”

Majorana bound states in magnetic skyrmions imposed onto a superconductor

“…The superconducting order parameter is spatially dependent to account for the vortex, ∆(r) = e ibϕ ∆(r) with integer b and ∆(r) = ∆(1 − e −r/Rv ), where the vortex and the skyrmion cores are both located at the origin. This configuration can be energetically stable [54,67,68]. Then, the modified angular momentum operator…”

“…47 in order to cirumvent the requirement of a DWS, by combining an SWS with a vortex in the superconductor. Such skyrmion-vortex pairs have been shown to be stable under suitable conditions [54]. MBS being bound to vortex cores is a concept that has been known for many years [55] for two-dimensional p-wave superconductors.…”