Nanoscale magnetic skyrmions and target states in confined geometries

Cortés‐Ortuño, David; Romming, Niklas; Beg, Marijan; Bergmann, Kirsten; Kubetzka, André; Hovorka, Ondřej; Fangohr, Hans; Wiesendanger, R.

doi:10.1103/physrevb.99.214408

Cited by 54 publications

(42 citation statements)

References 51 publications

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“…This is due to the fact that stability induced by topological charge only applies to structures with non trivial topological charge; target skyrmions are either topologically trivial, or have a single skyrmion surrounded by a topologically trivial structure. This collapse is in agreement with simulations of pure DMI stabilized target skyrmions [35], even though in general the dynamic properties of skyrmions depend on the energies that stabilize them.…”

Section: Please Cite This Article As Doi: 101063/15099991supporting

confidence: 87%

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Generation and stability of structurally imprinted target skyrmions in magnetic multilayers

Kent

Streubel

Lambert

et al. 2019

Applied Physics Letters

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Target Skyrmions (TSks) are extended topological spin textures with a constant chirality where the rotation of the z component of the magnetization is larger than π. TSks have topological charge 1 or 0, if the z component of the magnetization Mz goes through a rotation of nπ where n is an odd or even integer, respectively. TSks with a rotation of the z component of up to 4π have been imaged via high spatial resolution element-specific x-ray imaging. The TSks were generated by weakly coupling 30 nm thin Permalloy (Ni80Fe20, PY) disks with a 1 μm diameter to asymmetric (Ir 1 nm/Co 1.5 nm/Pt 1 nm) × 7 multilayers that exhibit Dzyaloshinskii-Moriya interaction. The PY disks stabilize the TSks in the multilayers due to reduced stray field energy and enforced circular symmetry from pinning of domain walls at the edges of the disks. Upon applying external magnetic fields, it is the skyrmion core at the center that ensures stability of the TSk, whereas the collapse of the extended structures in the TSk does not depend on the topological charge.

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Section: Please Cite This Article As Doi: 101063/15099991supporting

confidence: 87%

“…The classic skyrmion spans one Bloch sphere, corresponding to a rotation of one-π. Recent experiments have found TSks [17], [18], [35] at low temperatures and/or in confined structures. However, thus far, there have been no observations of target skyrmion states with more than 2π rotations of Mz.…”

Section: Introductionmentioning

confidence: 99%

Generation and stability of structurally imprinted target skyrmions in magnetic multilayers

Kent

Streubel

Lambert

et al. 2019

Applied Physics Letters

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“…An alternative platform to consider would be thick permalloy (Ni 81 Fe 19 ) disks 64 , since the existence of skyrmions with p up to 3 was recently shown in them, although this would require a different setup. High-p skyrmions were also recently observed in Pd/Fe/Ir(111) magnetic islands 65 . These systems, albeit metallic, naturally provide an edge to localize the CMEM and remove the need to grow a superconducting island.…”

Section: Discussionmentioning

confidence: 64%

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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“…For a sample of 300nm × 300nm × 0.4nm with A = 10pJ/m, D = 6mJ/m 2 , K = 0.49M J/m 3 , and M s = 0.58M A/m that are typical values for those chiral magnets supporting skyrmion crystals [17,20,21], κ > 1, so that single domain and isolated circular skyrmion are not stable any more [18]. We will start from a small nucleation magnetic domain with sharp domain wall to speed up skyrmion formation dynamics although stripe skyrmions will appear spontaneously due to thermal or other fluctuations in reality.…”

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confidence: 98%

“…A one dimensional model [16] was used to describe the rotation of spins perpendicular to stripes. To date, the general belief is that those stripes are not skyrmions and have zero skyrmion numbers [17].…”

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confidence: 99%

Stripe Skyrmions and Skyrmion Crystals

Wang

2020

Preprint

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Skyrmions are important in topological quantum field theory for being soliton solutions of nonlinear sigma model and magnetics for their attractive applications in information technology. Either isolated skyrmions or skyrmion crystals may exist in a given chiral magnet, but not both at the same time. When skyrmion crystals, in which skyrmions often arrange themselves into triangular lattices, can be observed in a chiral magnet, stripy spin textures in various forms appear also and even mix with skyrmion crystals. People believe that skyrmions are circular objects and stripy spin textures have zero skyrmion number. Those stripy spin textures are called anything such as spiral, helical, and cycloid spin orders, but not skyrmions. Here we present convincing evidences showing that those stripy spin textures are skyrmions, ``siblings" of circular skyrmions in skyrmion crystals and ``cousins" of isolated circular skyrmions. Specifically, isolated skyrmions are excitations of chiral magnetic films whose ground states are ferromagnetic and skyrmion formation energy is positive. When the skyrmion formation energy is negative (relative to the single domain state), condensed skyrmions are the ground states and stripe skyrmions appear spontaneously. The density of skyrmion number determines the morphology of condensed skyrmion states. At the extreme of one skyrmion in the whole sample, the skyrmion has a ramified stripe structure that maximizes the skyrmion wall length in order to lower system energy. As the skyrmion number density increases, individual skyrmion shapes gradually change from ramified stripes to rectangular stripes, and eventually to disk-like objects due to the competition between negative formation energy and stripe-stripe or skyrmion-skyrmion repulsion. At a low skyrmion number density, the natural width of stripes is proportional to the ratio between the exchange stiffness constant and Dzyaloshinskii-Moriya interaction coefficient. At a high skyrmion number density, skyrmion crystals are the preferred states. Our findings reveal the nature and properties of stripy spin texture, and open a new avenue for manipulating skyrmions, especially condensed skyrmions such as skyrmion crystals.

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Nanoscale magnetic skyrmions and target states in confined geometries

Cited by 54 publications

References 51 publications

Generation and stability of structurally imprinted target skyrmions in magnetic multilayers

Generation and stability of structurally imprinted target skyrmions in magnetic multilayers

Topological superconductivity with deformable magnetic skyrmions

Stripe Skyrmions and Skyrmion Crystals

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