Generation of a superconducting vortex via Néel skyrmions

Baumard, J.; Cayssol, Jérôme; Bergeret, F. S.; Buzdin, A. I.

doi:10.1103/physrevb.99.014511

Cited by 39 publications

(32 citation statements)

References 53 publications

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“…The inclusion of intrinsic and Rashba spin-orbit couplings would require another in-depth study due to the loss of rotational symmetry, and due to the non-trivial interplay of different effective spin-triplet pairings introduced by these couplings. In the limit that we consider in this work, in absence of skyrmion the spin-orbit length in the superconductor l so = 1/(mα), with α a spin-orbit amplitude, is much larger than the typical lengthscale of the skyrmion, so that the magnetoelectric coupling and appearance of vortices can also be neglected [41][42][43][44][45] .…”

Section: Resultsmentioning

confidence: 99%

Topological superconductivity with deformable magnetic skyrmions

2019

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Magnetic skyrmions are nanoscale spin configurations that are efficiently created and manipulated. They hold great promises for next-generation spintronics applications. In parallel, the interplay of magnetism, superconductivity and spin-orbit coupling has proved to be a versatile platform for engineering topological superconductivity predicted to host non-abelian excitations, Majorana zero modes. We show that topological superconductivity can be induced by proximitizing skyrmions and conventional superconductors, without need for additional ingredients. Apart from a previously reported Majorana zero mode in the core of the skyrmion, we find a more universal chiral band of Majorana modes on the edge of the skyrmion. We show that the chiral Majorana band is effectively flat in the physically relevant parameter regime, leading to interesting robustness and scaling properties. In particular, the number of Majorana modes in the (nearly-)flat band scales with the perimeter length of the system, while being robust to local disorder. 1 arXiv:1904.03005v3 [cond-mat.supr-con] 23 Oct 2019 8 where all energies are in units of the bandwidth t, all distances are in units of the lattice spacing a (see Supplementary Note 1 and Supplementary Figure 1 for details). For precisely |m J | = |m * J | the wire is at the topological transition and has a gapless spectrum, giving our model a bulk-gap-closing point as shown in Fig. 2c.The MFB found here has a protection by a chiral symmetry, as MFB's were found to have in models with translational symmetries 39,40,51 . Note that the wire Hamiltonian and its MFB become a correct model for our texture Eq. (1) if we choose q = 0 and thereby nullify the H slope m J (r) term. Physically, this is a special case where instead of the skyrmion shape the texture becomes coplanar (in the xz-plane, see Eq. (1)), and the orthogonal direction provides a chiral operator Ξ = τ y σ ythat anticommutes with the Hamiltonian (see Eq. (2)). Since all the MFB states have the same chirality, they cannot hybridize among themselves. It is difficult to remove the MFB states 51 , namely, a perturbation must have energy larger than the effective gap; or, it should hybridize the MFB with low energy bulk states at |m J | ≈ |m * J |, which are few; or, chirality symmetry must be broken (out-of-xz-plane exchange field). We note that the proof of existence of the MFB rests on the rotational symmetry of the q = 0 coplanar texture, since this symmetry provides the m J quantum number. Consider now deformations of the shape of the edge imposed on our q = 0 coplanar texture. These geometric deformations would generally mix the m J sectors, yet the described stability of the MFB implies that the deformations would be inefficient in removing the MFB states.We can now proceed to the relevant model for a skyrmion with arbitrary q = 0:The single term H slope m J (r) breaks the chiral symmetry Ξ, and there are no other chiral operators. The term H slope m J (r) exactly contributes an energy ε edgestate (m J ) ∼ m J to an MFB state ...

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Section: Resultsmentioning

confidence: 99%

Topological superconductivity with deformable magnetic skyrmions

2019

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“…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…”

Section: Majorana Criterion In a Skyrmion-vortex Pairmentioning

confidence: 99%

“…As we focus on d F δ, where d F may correspond to monoatomic layer thickness [48] whereas δ will be on the order of 10 -100 nanometers, we can expect that J max is insignificant in the thin-film limit. In this limit, vortices may not form spontaneously, but can still be induced by an external out-of-plane magnetic field [67]. When skyrmions and vortices coexist, vortex pinning to the skyrmion center is energetically favorable [54,67,68].…”

Section: Majorana Criterion In a Skyrmion-vortex Pairmentioning

confidence: 99%

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Majorana bound states in magnetic skyrmions imposed onto a superconductor

2019

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We consider a superconducting film exchange-coupled to a close-by chiral magnetic layer and study how magnetic skyrmions can induce the formation of Majorana bound states (MBS) in the superconductor. Inspired by a proposal by Yang et al. [Phys. Rev. B 93, 224505 (2016)], which suggested MBS in skyrmions of even winding number, we explore whether such skyrmions could result from a merger of ordinary skyrmions. We conclude that the formation of higher-winding skyrmions is not realistic in chiral magnets. Subsequently, we present a possibility to obtain MBS from realistic skyrmions of winding number one, if a skyrmion-vortex pair is formed instead of a bare skyrmion. Specifically, we show that MBS are supported in a pair of a circular skyrmion and a vortex which both have a winding number of one. We back up our analytical prediction with results from numerical diagonalization and obtain the spatial profile of the MBS. In light of recent experimental progress on the manipulation of skyrmions, such systems are promising candidates to achieve direct spatial control of MBS. arXiv:1904.04177v2 [cond-mat.supr-con]

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“…We consider an ultrathin FM film, such that the DMI, induced in the FM-HM interface, and the magnetic field induced by the vortex, are considered to be uniform across the film thickness. Notice that in this work we do not consider the creation of vortex-antivortex pairs in the superconductor due to the stray field of the skyrmion 25,27 , since such a stray field emanating from an ultrathin FM film is insufficient to strongly perturb the superconducting film separated by a thick insulating layer.…”

Section: A Stray Field Of a Single Vortexmentioning

confidence: 99%

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

et al. 2019

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Dynamics of magnetic skyrmions in hybrid ferromagnetic films harbors novel physical phenomena and holds promise for technological applications. In this work, we discuss the behavior of magnetic skyrmions when coupled to superconducting vortices in a ferromagnet-superconductor heterostructure. We use numerical simulations and analytic arguments to reveal broader possibilities for manipulating the skyrmion-vortex dynamic correlations in the hybrid system, that are not possible in its separated constituents. We explore the thresholds of particular dynamic phases, and quantify the phase diagram as a function of the relevant material parameters, applied current and induced magnetic torques. Finally, we demonstrate the broad and precise tunability of the skyrmion Hallangle in presence of vortices, with respect to currents applied to either or both the superconductor and the ferromagnet within the heterostructure.

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Generation of a superconducting vortex via Néel skyrmions

Cited by 39 publications

References 53 publications

Topological superconductivity with deformable magnetic skyrmions

Topological superconductivity with deformable magnetic skyrmions

Majorana bound states in magnetic skyrmions imposed onto a superconductor

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

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