Magnetic skyrmions: Basic properties and potential applications

Magnetic skyrmions are particle‐like topological magnetic textures that are potential information carriers in future spintronics. An enormous body of research confirms their existence in a broad range of magnetic materials since their first discovery in 2009. To date, magnetic skyrmions can not only be found in asymmetric systems but also in centrosymmetric ones. Notably, engineered magnetic multilayers are promising structures for skyrmion‐based spintronics because they can stabilize small‐sized skyrmions at room temperature and facilitate their electric manipulation. In this overview, we introduce the topological nature, their special properties, and nucleation methods of skyrmions, and show their potential for applications. Perspectives on skyrmionic devices and developments toward other, more three‐dimensional particle‐like magnetic nanostructures, are discussed at the end.


| INTRODUCTION
In field theory, a skyrmion is a topological stable configuration of a certain class of nonlinear sigma models. It was originally introduced by Tony Skyrme, who proposed a topological soliton stabilized by the topology of a spatial field to describe a nucleon. [1] Although skyrmions turned out not to be elementary particles, their particle-like properties still attract much attention, in particular in condensed matter physics. With swirling vortex-like structures, skyrmions have been demonstrated in different systems, for instance, in a Bose-Einstein condensate, [2] liquid crystals, [3] acoustic systems, [4] and photonic systems. [5] The topic of this review, magnetic skyrmions, are two-dimensional (2D) topological structures comprised of localized spin vectors varying smoothly from their cores to their edges with fixed helicities ( Figure 1A), which were for the first time experimentally demonstrated in a chiral magnet in 2009. [10] The Dzyaloshinskii-Moriya interaction (DMI or antisymmetric exchange interaction) plays a key role in stabilizing skyrmions in materials with asymmetric crystal structures [11] and at interfaces with natural broken inversion symmetry, [12] despite the few exceptions in some centrosymmetric materials. [13][14][15][16] Compared to other magnetic nanostructures like chiral domain walls (DWs), which have been studied for their potential applications in efficient spintronic devices, [17,18] their nontrivial topological structures grant skyrmions intrinsic stability while their low energy-cost currentdriven motion opens perspectives for their applications. [19][20][21][22][23] At present, magnetic skyrmions are emerging candidates for data storage applications due to their stability, small sizes, and controllable responses to external perturbations. Intensive studies for over a decade have demonstrated promising architectures like ferromagnet/heavy metal (FM/HM) interfaces, ferrimagnet/HM interfaces, and synthetic antiferromagnets (SAFs), while current-driven skyrmion dynamics [24][25][26][27][28][29] have further enlarged the application possibilities of skyrmions. The fast development of this field has already led to many excellent reviews centered on their topological properties, [30,31] the various hosting crystals and multilayers, [11,12] and the progress in their applications. [32][33][34][35][36][37][38][39][40] The scope of this review is to describe the most important recent findings and achievements in this rapidly developing field, in particular the recent developments in their manipulation, [29, the move to more three-dimensional (3D) structures [67] and the emergence of new materials [11] and new applications. [68] We start this review with the topological and mathematical descriptions of skyrmions and other nontrivial topological structures. We present a detailed classification of skyrmion hosting materials up to now, from chiral magnets to novel interfaces and 2D van der Waals systems and from ferromagnetic materials to ferri-or antiferromagnetic systems. The mechanisms of stabilizing magnetic skyrmions discovered up to now will be elucidated, followed by discussions about their static and dynamic properties as well as their nucleation. Recent findings on the topological Hall effect in skyrmions and the current-driven dynamics focused on the skyrmion Hall effect are included. Regarding novel methods for manipulating skyrmions, we highlight the role of ultrafast laser pulses in particular. Based on all the aspects above, the future prospects for skyrmions and emerging 3D structures and new materials will be addressed at the end.

| TOPOLOGICAL AND MATHEMATICAL DESCRIPTIONS
At first, some topological concepts should be discussed to help us understand the basics of skyrmions. [69] A manifold is a special n-dimensional space (S n ) that is locally homeomorphic to an n-dimensional Euclidean space (R n ). For instance, connecting two endpoints of a real line R gives a closed loop, which is a type of 1D manifold and denoted S 1 , while attaching the edges of a 2D R 2 plane produces a 2D surface of a sphere, which is a kind of 2D manifold and denoted by S 2 . A specific field that is used to depict a physical system can be viewed as a shaped vector space. The topological winding number was introduced to classify these fields. This mathematical parameter is an integer describing the continuous mapping of a real space (field) on the target manifold, which indicates the number of times a field wraps around the established topological space. Objects or real spaces with different winding numbers cannot transform into each other continuously. [69] A 2D skyrmion structure with disk-like spin textures can be transformed into a hedgehog-like sphere with spins seated on its surface (an S 2 manifold as mentioned above) [30,32] through a stereographic projection. The skyrmion topological number N (the winding number in essence, topologically denoted π S ( ) 2 2 ) can be obtained by integrating over the entire solid angle of all spins and finally be expressed by the following equation: Here, n is a unit vector referring to the direction of the local spin vector, while i and j form the orthogonal basis of the 2D space which is used to indicate each spin unit of the skyrmion.
Mathematically, [11,31,32] more detailed parameters about skyrmions can be obtained by analyzing this integral equation. Each unit spin vector can be defined by spherical coordinates as where r = r(cos(φ), sin(φ)) is the vector describing the location of the spin unit in polar coordinates. From this, Equation (1) can be simplified to ( ) and the vorticity is embedded in this equation. We can then define the azimuthal angle ω γ Φ = φ + , where γ is the helicity that can be viewed as a phase factor. Vorticity together with the boundary conditions (the direction of the spins in the core and at the edge) determine the topological number N (N = ω or N = −ω), and the helicity γ modulates the in-plane spin orientations.
Skyrmions (N = ±1) can be further subdivided depending on these parameters (N, ω, γ) as shown in Figure 1A. [11] We can distinguish antiskyrmions and skyrmions because they have negative and positive vorticity numbers, respectively. [32] The Néel-type skyrmion with radial-shaped spin textures possesses zero helicity. The helicity of Bloch-type skyrmions is π ± /2, which leads to chirality and forms a vortex-like topological structure. Accordingly, spin arrangements in a cross-sectional view are distinct for different skyrmions. [70] In a Néel-type skyrmion, the endpoints of the spins along a cross section form a cycloid, while the spins reveal a helicoidal propagation in a Bloch-type skyrmion. It follows that antiskyrmions take on helicoidal or cycloidal modulations in opposite directions.
Apart from skyrmions, other particle-like nontrivial structures with nonzero topological numbers are shown in Figure 1. Merons and antimerons (N = ±1/2) are halfskyrmion-like spin textures with in-plane magnetization, except at the singularity where the direction of spins is normal to the plane ( Figure 1B). [6,71] They have recently been observed in a chiral magnetic thin plate. [72] Pairs of skyrmions with opposite helicities are called biskyrmions (N = ±2) and can be driven with low current density compared with conventional DWs (see schematics in Figure 1C). [7,73] In 3D space, hedgehogs and antihedgehogs (N = ±1) are topological spin structures behaving like emergent magnetic monopoles and antimonopoles ( Figure 1D). [8,74] Specifically, when skyrmions with opposite topological numbers centrally coincide with each other, a skyrmionium is created as an intriguing nontopological soliton with zero net topological number ( Figure 1E), thus showing no skyrmion Hall effects. [9] Such structures have been experimentally achieved in a thin ferrimagnetic film with the help of ultrafast laser pulses. [55] The topological numbers of nontrivial spin structures are robust unless singularities are introduced with external stimuli, [30] in the same way that one cannot turn a Mobius ring into an undistorted strip without a cut. Changing topological numbers generally costs so much energy that objects like skyrmions are topologically protected and remain robust against perturbations.
Topological objects often appear in assemblies and arrange themselves in a lattice. The first discovered Bloch-type skyrmion lattice in a chiral magnet has been shown to have sixfold symmetry by neutron scattering, with helical wave vectors perpendicular to the magnetic field. This suggests a triple-Q state where the localized spin vectors can be seen as the superposition of three coplanar helical spin waves. [10] This triple-Q state is also observed in a centrosymmetric system hosting a Blochtype skyrmion lattice. [13] The formation of a hedgehog lattice, however, can be attributed to three orthogonal spin waves instead of coplanar ones. Double-Q states manifest themselves as ultrasmall square lattices due to effective four-spin interactions. [14,75] Pairs of biskyrmion lattices and meron-antimeron lattices are also observed in real space. [72,73] Topology not only endows skyrmions with intriguing spin textures but also guides us to emergent properties and current-driven dynamics, [19,20,[22][23][24]31,76,77] that facilitate their future applications. In the next section, we are going to discuss the stabilization mechanisms of skyrmions.

| Stabilization mechanisms for magnetic skyrmions
Here, we are going to describe the underlying physics of magnetic skyrmions. The energy contributions for stabilizing complex magnetic systems include the symmetric Heisenberg exchange interaction, the asymmetric exchange interaction (the Dzyaloshinskii-Moriya interaction [DMI]), the Zeeman energy exerted by an applied magnetic field, the anisotropy energy associated with the crystal lattice, and the long-range dipolar interaction. The competition among these ingredients stabilizes the specific spin textures. [78] For instance, the dipolar interaction fractionalizes a ferromagnetic state sustained by exchange interactions into small domains where magnetic moments have identical directions. [78] Boundaries between these domains are the well-known DWs, a fundamental type of spin texture.
The total energy connected with Heisenberg exchange interactions is expressed as  E J S S = · ij i j J ( < 0 for ferromagnetic coupling and J > 0 for antiferromagnetic coupling), [79] so that it favors parallel or antiparallel alignment (↑↑↑↑ or ↑↓↑↓) between adjacent spins, respectively. This basic but symmetric exchange interaction cannot by itself form noncollinear magnetic structures. The asymmetric DMI which requires symmetry breaking, however, tilts neighboring spins to form chiral structures and magnetic skyrmions. It was first proposed by Dzyaloshinskii in 1958 when studying weak ferromagnetism in certain antiferromagnetic crystals. [80] The Hamiltonian for the DMI is H where D denotes the so-called DM vector whose direction can be determined following the Moriya rules, [81] as shown in Figure 2A. To describe it in spatial coordinates, different Lifshitz invariants, which are linear combinations of the components of magnetization vectors with their first spatial derivatives are combined to indicate the free energy contributions of the DMI based on the lattice symmetry. [11,82,83] Typically, for the widely studied interfacial DMI for a ferromagnetic film on top of a nonmagnetic substrate with strong spinorbit coupling, the DM vector points perpendicularly to the triangle plane formed by two spins and one neighboring nonmagnetic atom ( Figure 2B) and has a large value. [21] The effective range of the DMI can extend beyond the vicinity of the interface via the mediation by conduction electrons. [84] In addition, spin-orbit-induced magnetocrystalline anisotropy also plays an important role in defining spin textures. Single-ion easy-plane or easy-axis anisotropy has been taken into consideration in studies elucidating stabilizing mechanisms for skyrmions, merons, and other multiple periodic states. [85][86][87] The dipolar interaction, when competing with the magnetic anisotropy, can give rise to nontrivial skyrmion bubbles in some centrosymmetric systems, [88][89][90][91][92][93][94] including the recently emerging 2D van der Waals magnets. [95,96] Long-range dipolar interaction can stabilize micrometer-size skyrmions. [11] Apart from these, the size of the discovered skyrmions mostly ranges from several 10 nm down to several nanometers, governed by the key ingredients for their stabilization. [12] The DMI is usually the dominant part for submicrometer skyrmions and relatively weaker in bulk materials than at interfaces with intrinsic asymmetry. It was conjectured that smaller skyrmions could be realized by an enhanced DMI. [11,12] In this sense, to achieve large skyrmion densities as required for future applications, one needs to measure and control the magnitude of the DMI typically at the interfaces of a multilayer structure. Techniques such as Brillouin light scattering and observations of asymmetric propagation of DWs have been used for quantitative analysis of the DMI. [97][98][99] By manipulating the multilayer structure, one can thus achieve larger additive DMI and stabilize sub-100-nm and even sub-50-nm skyrmions at room temperature. [100,101] Additional components such as higher-order interactions and magnetic frustration may be significant for generating skyrmions in some cases. [11] For instance, the emergence of a skyrmions lattice in Fe/Ir(111) was ascribed to the higher-order four-spin interaction. [75] It has also been demonstrated in an itinerant magnet that the four-spin interaction can lead to a noncollinear multi-Q state. [102] Magnetic frustration, due to competing exchange interactions, is another potential ingredient for stabilizing skyrmions, especially in centrosymmetric materials without DMI. [103] Theoretical predictions show the potential existence of skyrmions stabilized by competing exchange interactions between nearest and next-nearest neighbor spins. [86,104] The effects of these competing interactions have been recently confirmed by experimental discoveries of ultrasmall (few nanometers) skyrmions in rare-earth-based centrosymmetric materials. [13][14][15][16] In addition to the interactions mentioned above, artificial geometric confinement can bring skyrmions into the ground state by nanofabrication techniques with high controllability. [105,106] With these factors in mind, we can better understand typical experimental discoveries of skyrmions described in the next subsections, which are summarized in Table 1.

| Skyrmions in single-phase systems
Potential skyrmion hosting materials come in large varieties. Here, we will describe different types of skyrmions stabilized in asymmetric and centrosymmetric single-phase materials, while interface-based systems will be addressed in Section 3.3.
Noncentrosymmetric magnetic materials can display intrinsic DMI in bulk or thin film forms. The first experimental identification of the existence of skyrmions was carried out in the chiral itinerant-electron magnet MnSi using neutron scattering. [10] A magnetic phase diagram was inferred from magnetic susceptibility measurements, where a skyrmion ground state was found to be confined in a narrow B-T range of the phase diagram as shown in Figure 3A. Neutron scattering results showed a sixfold symmetry intensity distribution which could be attributed to three helical spin-waves forming the skyrmion structure ( Figure 3A). A real space observation through Lorentz transmission electron microscopy (LTEM) ( Figure 3B) was then carried out in a Fe 0.5 Co 0.5 Si thin film, another material that belongs to the B20 compounds. [107] After these pioneering works, materials with similar lattice structures (P2 1 3 space group) were reported to host Bloch-type skyrmions, F I G U R E 2 (A) Schematics of Moriya rules for directions of DM vectors: when a mirror plane α normal to ij passes through the midpoint of two spins, then D is parallel to α; when ij lies in α, then D is perpendicular to α; when a two fold axis C 2 normal to ij passes through the midpoint of two spins, then D is perpendicular to C 2 ; when an n-fold axis C n is along ij, then D is parallel to C n ; when there is inversion symmetry between i and j, then D = 0. [81] (B) Schematic of interfacial DMI in which the DM vector (D 12 ) points perpendicularly to the triangle formed by two spins and one neighboring atom with large spin-orbit coupling at the interface. Reproduced with permission, [21] Copyright 2013, Springer Nature.

Materials
The temperature dependence, skyrmion size, and detection methods are summarized.
a This research studies a series of films with varying thicknesses and the selected data corresponds to one with a thickness of 15 nm. b The magnetic periodicity is related to the thickness of the sample.
c For skyrmions that are stabilized in the form of lattices, the skyrmion size refers to the skyrmion lattice constant which is usually identical to the periodicity of the helical or stripe states. d The size of skyrmions can be controlled by the applied magnetic field.
for instance, FeGe and Mn 1−x Fe x Ge helimagnets and Cu 2 OSeO 3 insulators. [108,109,127] Moreover, β-Mn-type Co-Zn-Mn alloys with a different chiral lattice structure (P4 1 32 space group) were demonstrated to host skyrmions even at room temperature. [110,111] The helicity of the skyrmions in this special type of material can be tuned by varying the concentration of the different elements. [128] In addition to a skyrmion lattice, a meron F I G U R E 3 Representative discoveries of skyrmions in single-phase materials: (A) magnetic phase diagram for B20-type MnSi (top) and a sixfold intensity pattern obtained through SANS in the A phase (bottom), reproduced with permission, [10] Copyright 2009, The American Association for the Advancement of Science; (B) an analyzed LTEM (overfocus) image for Fe 0.5 Co 0.5 Si at 25 K under a 50 mT magnetic field normal to the plane, reproduced with permission, [107] Copyright 2010, Springer Nature; (C) real-space observation of the (anti)meron lattice in a Co 8 Zn 9 Mn 3 thin plate, reproduced with permission, [72] Copyright 2018, Springer Nature; (D) an AFM image of a Néel-type skyrmion lattice in the polar magnet GaV 4 S 8 , reproduced with permission, [114] Copyright 2015, Springer Nature; (E) MFM measurement for a hexagonal skyrmion lattice in a 128-nm-thick (Fe 0.5 Co 0.5 ) 5 GeTe 2 nanoflake (scale bar, 2 μm), reproduced with permission, [115] Copyright 2022, The American Association for the Advancement of Science; (F) an under-focused LTEM image showing an antiskyrmion lattice (left) in the Heusler compound and a simulation of an antiskyrmion lattice in an oblique field, reproduced with permission, [70] Copyright 2017, Springer Nature; (G) a nanometer skyrmion lattice in a centrosymmetric material, reproduced with permission, [14] Copyright 2020, Springer Nature. and antimeron square lattice ( Figure 3C) was also observed in a Co 8 Zn 9 Mn 3 thin film with in-plane magnetic anisotropy. It was demonstrated that in this material skyrmions possess better topological stabilities than merons and antimerons. [72] However, skyrmions discovered in these chiral systems are limited to narrow regions where applied magnetic fields are indispensable. Note that, compared to bulk samples, thin film specimens with smaller thicknesses are likely to hold a skyrmion phase in a wider B-T range. [108] A field-cooling technique can create metastable skyrmions beyond the supposed phase regions, which extends the phase area to some extent. [111] Besides Bloch-type skyrmion lattices extensively studied in chiral magnets, Néel-type skyrmions which usually exist at interfaces and multilayers, also appear in bulk polar magnetic materials which are distinct from chiral systems. [87,114,115,129] Polar magnets with C nv symmetry lead to specific orientations of the DMI; thus, they can host a Néel skyrmion lattice composed of three spin cycloids in a relatively broad temperature range, for instance in the magnetic semiconductor GaV 4 S 8 . [114] Very recently, the observation of Néel-type skyrmions at zero magnetic fields and the room temperature was demonstrated in a singlephase layered 2D magnet (Fe 0.5 Co 0.5 ) 5 GeTe 2 . [115] A realspace observation of a Néel-type skyrmion lattice can be seen in Figure 3D,E.
Antiskyrmions with varying helical and cycloidal modulations were first observed via LTEM ( Figure 3F) in a tetragonal Mn-Pt-Sn inverse Heusler compound, which has D 2d crystal symmetry. [70] Antiskyrmions in this material remain robust across a very wide temperature range (100-400 K) and stable below 200 K after the initially applied magnetic field is removed. [70] Lattices of square-shaped antiskyrmions were later discovered in this D 2d Heusler compound and in a new material Fe 1.9 Ni 0.9 Pd 0.2 P with S 4 symmetry, by careful manipulation of external conditions. [112,113] For systems without broken symmetry, the dipolar interaction together with magnetic anisotropy can not only generate skyrmion bubbles, topologically equivalent to magnetic skyrmions in materials such as the perovskite La 1−x Sr x MnO 3 , [88] the frustrated magnet Fe 3 Sn 2 , [89][90][91][92][93] the Kagomé crystal Mn 4 Ga 2 Sn, [94] the 2D vdW magnets Fe 3 GeTe 2 , and Cr 2 Ge 2 Te 6 , [95,96] but also in the ferrimagnetic TbFeCo. [55] It should be noted that unlike DMI-stabilized skyrmions, which reflect the chirality of the crystal lattice, these skyrmion bubbles possess random helicity, which can be electrically manipulated. [91] The movability of their constituent Bloch lines allows the transformation between these skyrmion bubbles and nontopological bubbles via tuning the applied magnetic field [89,93] or the density of applied current pulses. [92] In another scenario, magnetic frustration and higher-order interactions can also realize skyrmion lattice states in centrosymmetric materials. This was demonstrated in the centrosymmetric triangular-lattice magnet Gd 2 PdSi 3 , where a hexagonal lattice of skyrmions with a short wavelength spin modulation (~2.5 nm) was created by applying a magnetic field perpendicularly to the triangular plane. [13] Similarly, Gd 3 Ru 4 Al 12 with a breathing Kagomé lattice, stabilizes a topological skyrmion lattice like that in chiral systems, but due to geometric frustration instead of DMI. [15] A square skyrmion lattice (double-Q state) was imaged by LTEM in the tetragonal magnet GdRu 2 Si 2 without geometrically frustrated lattices as shown in Figure 3G, which can be ascribed to a four-spin interaction mediated by itinerant electrons. [14] Apart from Gd-based crystals, a single-phase binary compound EuAl 4 was reported to host nanometric skyrmions, potentially with similar forming mechanisms. [16] Skyrmions found in these highly symmetric systems are characterized by ultra-small sizes, usually leading to a large topological Hall effect. [13,15]

| Skyrmions at interfaces
Apart from the broken symmetry in crystal lattices as described above, natural asymmetric structures are established at interfaces of designed bilayers and multilayers, where Néel-type skyrmions are preferred due to an appreciable interfacial DMI.
The experimental work was initially focused on ultrathin epitaxial ferromagnetic films with a nonmagnetic HM substrate (FM/HM structure). In a Fe monolayer on Ir (111), ultrasmall skyrmions down to several nanometers were observed using spin-polarized scanning tunneling microscopy. [75] Later, the transition from a spin spiral phase to a nanoskyrmion lattice state was discovered in FePd/Ir(111) at 8 K by increasing the external magnetic field before getting saturated into a ferromagnetic ground state. The applied magnetic field dependence of the size and shape of isolated skyrmions generated by tunneling currents at 4.2 K was demonstrated. [41,116] These intriguing results exploit the existence of DMI at interfaces, stemming from the indirect coupling between two magnetic atoms and a nonmagnetic atom with strong spin-orbit coupling (SOC), which form a triangle to which the DM vector is perpendicular. [84] The large DMI, comparable to the exchange interaction, gives rise to emergent skyrmions with small sizes at a high density, beneficial for skyrmionic applications.
In this sense, a better understanding of the origin of interfacial DMI can guide us to choose appropriate combinations of ferromagnetic materials and HM substrates. Proximity-induced magnetic moments (PIMs) in the HM layers are introduced to explain the origin of interfacial DMI. [130] But this model was doubted because first-principle calculations on a Co/Pt system demonstrated that the DMI here is determined by the interfacial Co layer and bears little relation to PIMs in the Pt substrate. [131] After that, HM-FM hybridization was highlighted in controlling the strength of interfacial DMI at 3d-5d interfaces. [132] To summarize these discussed mechanisms, it was recently concluded that the size of DMI at FM/HM interfaces depends on both HM-FM hybridization and HM spin mixing terms, while the sign is controlled by the orbital contributions from the HM layer. [133] Great efforts have been devoted to moving from lowtemperature interfacial skyrmions at epitaxial monolayer thin films to room temperature (RT) skyrmions in stacks of (more industry-compatible) sputtered multilayers containing many FM/HM interfaces. [100,101,117] Boulle et al. reported the stabilization of RT skyrmions with zero magnetic fields in Pt/Co/MgO thin films exhibiting large DMI (D = 2.05 ± 0.3 mJ m −2 ) which originates both from the Pt/Co and the Co/MgO interfaces. [117] Similar results for attaining additive DMI are achieved by sandwiching a magnetic layer between two HM layers ( Figure 4A,B), such as the [Ir/Co/Pt] 10 multilayer and the [Ir/Fe/Co/ Pt] n stacks with varying Fe/Co composition. [100,101] The combined interfacial DMI at opposite interfaces of the magnetic layer compresses stable skyrmions to sub-100 nm sizes. Note that repetitions of the sandwich-like structures can help stabilize skyrmions against thermal fluctuations. [100] The [Pt/Co/Ta] 15 multilayer structure with not additive but partially canceled DMI can still host skyrmions, which can be easily controlled electrically thanks to the enhanced spin-orbit torque in Pt/Co/ Ta heterostructures. [118] To balance the stability and drivability of interfacial skyrmions, it has been indicated that multilayers with additive DMI and spin-orbit torques might be the most promising choice for putting skyrmions into applications. [12] Furthermore, magnetism and strong SOC in novel 2D vdW materials can be building blocks for skyrmion-hosting heterostructures with interfacial DMI. Wu et al. constructed WTe 2 / Fe 3 GeTe 2 vdW heterostructures with a large DMI (1.0 mJ m −2 ) for stabilizing Néel-type skyrmions. [120] Wu et al. demonstrated another heterostructure composed of two vdW magnets Cr 2 Te 2 Ge 6 and Fe 3 TeGe 2 which mutually support each other to form two groups of skyrmions ( Figure 4C). [121] The surface oxidation in vdW materials during sample fabrication may contribute to another interface with broken symmetry, for instance, Fe 3 GeTe 2 /O x -Fe 3 GeTe 2 interfaces. [134] A skyrmion ground state can also be obtained through interlayer exchange coupling in multilayers. Chen et al. reported a Fe/Ni/Cu/Ni/Cu(001) structure in which Cu/Ni/Cu(001) layers with perpendicular magnetic anisotropy (PMA) are designed to modify the ground state in Fe/Ni bilayers. [119] By manipulating the thickness of the Cu interlayer, the interlayer coupling strength can be tuned to drive the ground state from a stripe phase to a skyrmion phase in the top magnetic bilayers ( Figure 4D). [119] Likewise, skyrmions can be created in the itinerant vdW FM Fe 3 GeTe 2 due to its coupling to the [Co/Pd] 10 superlattice underlayer ( Figure 4E). [122] Actually, apart from interfacial DMI, other material parameters like the exchange stiffness A and the magnetic anisotropy K should be balanced to stabilize skyrmions in multilayer nanostructures. A theoretical study demonstrated the widely accepted criterion that the condition πD AK > 4 should be satisfied to thermodynamically stabilize skyrmions. [135] Therefore, approaches such as varying the thickness or composition of magnetic layers and inserting a wedge-shaped interlayer are used because they can modulate these parameters. [25,101] In conclusion, FM/HM interfaces are convenient sources of strong DMI. Based on appropriate choices of magnetic and substrate materials, special coupled structures can be designed and one can engineer different parameters to optimize the conditions for stabilizing skyrmions at room temperature in complicated multilayer systems.

| Skyrmions in ferrimagnets and antiferromagnets
Besides the skyrmions in ferromagnetic materials, the stabilization and manipulation of skyrmions in ferrimagnets and antiferromagnets have also been theoretically predicted and recently also observed. [26,27,[123][124][125][126]136] In magnetic systems with antiferromagnetically aligned spins, antiferromagnetic skyrmions (AFSKs) can be stabilized and seen as a combination of skyrmions generated in each sublattice ( Figure 5A). [136] In comparison with ferromagnetic skyrmions, antiferromagnetic ones tend to be smaller in size because of the vanishing long-range dipolar interactions in antiferromagnetic systems. [124] However, the nearly canceled effective magnetic moment hinders their detection. To tackle this, X-ray imaging techniques that are sensitive to specific elements can be utilized to detect the exchange-coupled Reproduced with permission, [121] Copyright 2022, John Wiley and Sons. (D) RT skyrmions observed by spin-polarized low-energy electron microscopy in a Fe/Ni bilayer which is exchange-coupled to a single-domain Ni layer in a multilayer structure. Reproduced with permission, [119] Copyright 2015, AIP Publishing. (E) Schematic of a multilayer structure where a Pd wedge interlayer controls the coupling strength between van der Waals Fe 3 GeTe 2 flakes and [Co/Pd] 10 multilayers. Strip domains in flakes break into skyrmions as the thickness of the Pd space layer decreases. Reproduced with permission, [122] Copyright 2020, The American Association for the Advancement of Science. skyrmions, thus confirming the existence of AFSKs or similar topological structures in real space. [26,126] From the perspective of applications, AFSKs can be driven straight along the injected current flows, which is a great advantage over ferromagnetic skyrmions that also have a transverse motion (due to the skyrmion Hall effect) while being transported along the driving force. [136] AFSKs have already been experimentally observed in compensated ferrimagnetic materials. [Pt/Gd 25 Fe 65.6 Co 9.4 / MgO] 20 and Pt/Gd 44 Co 56 /TaO x ferrimagnetic multilayer structures are reported to host AFSKs due to interfacial DMI with good electrical controllability. [26,123] For example, Figure 5B shows a schematic of an AFSK in GdFeCo and images of skyrmions in different sublattices obtained by F I G U R E 5 (A) Schematic of an AFSK with top and side views. Reproduced with permission, [136] Copyright 2016, American Physical Society. (B) Schematic of an AFSK in a GdFeCo ferrimagnet and element-specific STXM images of skyrmions in different sublattices with opposite contrast. Reproduced with permission, [26] Copyright 2018, Springer Nature. (C) Schematic of a SAF multilayer and antiferromagnetic skyrmions observed by a MOKE microscopy due to uncompensated magnetization. Reproduced with permission, [27] Copyright 2019, Springer Nature. (D) Néel-vector mapped obtained from PEEM excited by horizontally polarized X-rays (LH-PEEM) where the color ring represents orientations of the in-plane Néel-vectors and schematics of skyrmion analogs marked on the mapping. Reproduced with permission, [126] Copyright 2021, Springer Nature.
scanning transmission X-ray microscopy (STXM). [26] AFSKs have also been observed in SAFs composed of ferromagnetic layers which are separated by nonmagnetic spacers and display antiparallel coupling of their magnetizations due to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. [27,124,125,137] Figure 5C shows an example of a SAF and an antiferromagnetic skyrmion observed in this specific structure, where the skyrmion Hall effect nearly vanishes and efficient control of AFSKs is achieved. [27] By meticulous manipulation of the SAF structure, individual AFSKs can be stabilized at RT without magnetic fields. [124] Also, high-density AFSKs at RT are demonstrated in an uncompensated SAF structure. [125] Very recently, antiferromagnetic half-skyrmions (merons) are experimentally discovered in the natural antiFM α-Fe 2 O 3 capped with Pt. An in-plane Néel vector map obtained by XLMD-PEEM shows the existence of vortexlike skyrmion analogs whose control may be facilitated by the Pt capping layer ( Figure 5D). [126] These findings will further guide the research on skyrmions for antiferromagnetic spintronics which is momentarily a hot topic. [138]

| STATIC AND DYNAMIC PROPERTIES OF MAGNETIC SKYRMIONS
To exploit magnetic skyrmions for applications, we must be capable of generating, detecting, manipulating, and processing them in efficient ways. Fortunately, skyrmions with noncoplanar spin distributions can interact with optical and X-ray photons as well as electrons, which facilitates their real-space detection. The nontrivial spin textures also provide ways for electrical readout through the topological Hall effect (THE). Magnetic skyrmions deflect conducting electrons like emergent electromagnetic fields and inversely can be electrically driven by injected current pulses. High-frequency dynamics are also an intriguing characteristic of magnetic skyrmions. Both static and dynamic properties of skyrmions will be discussed in this section.

| Experimental imaging of skyrmions
With modulated spin structures, skyrmions can be indirectly detected with the help of scattering experiments, for instance, neutron scattering and resonant X-ray scattering. [10,13] On the other hand, direct observation of skyrmions not only helps identify their sizes but also serves as a powerful tool for studying their creation processes and dynamical transport properties.
Due to its high resolution, LTEM has been extensively used to characterize skyrmion spin textures, [14,15,70,72,73,92,[94][95][96][107][108][109][110]112,120,127,134] although it is limited to electron-transparent thin specimens. One can use LTEM to reconstruct the in-plane spin distribution of skyrmions by analyzing the defocused images because the incident electrons experience a Lorentz force exerted by the local spins in the skyrmions and then diverge or converge correspondingly to form dark or bright contrasts in the mapping ( Figure 6A). [107,127] With higher spatial resolution, spinpolarized scanning tunneling microscopy (SP-STM) is a powerful tool for investigating ultrasmall skyrmion structures with both in-plane and out-of-plane sensitive modes as shown in Figure 6B. [41,75,116] Moreover, magnetic force microscopy (MFM) can probe spin textures by quantifying the magnetostatic force between the sample and the tip, which has been extended to observe skyrmion patterns on the surface or in thin magnetic multilayers. [113,114,124] By analyzing the MFM information with a quantitative physical model, Néeltype and Bloch-type skyrmions can be distinguished from each other. [139] With lower resolution subject to the diffraction limit but easy accessibility, magneto-optical Kerr effect (MOKE) microscopy is widely used for detecting larger skyrmions (see Figure 6C for an example) and studying skyrmion dynamics. [24,25,27,42,140] X-ray-based microscopy is featured by its element specificity arising from the characteristic binding energies of the core electrons. With the help of X-ray magnetic dichroism (both XMCD and XMLD), magnetic materials show strong X-ray absorption contrasts for different polarizations at resonance thresholds. [141,142] By detecting the absorption of X-rays or the yielded photoelectrons, the local magnetization proportional to the contrast is obtained. X-ray magnetic circular dichroism assisted-photoemission electron microscopy (XMCD-PEEM) with high resolution (~20 nm) has been used to observe interfacial skyrmions in Pt/Co/MgO thin films ( Figure 6D) where in-plane and out-of-plane magnetizations contribute distinctively, depending on the angle between the sample and the X-ray beam. [117] Zhang et al. summarized the advantages of the aforementioned imaging techniques. [32] It is obvious that, for studies of AFSKs which are relatively hard to detect, the element-sensitive X-ray-based microscopies are most attractive because they can visualize coupled ferromagnetic skyrmions belonging to different sublattices. For instance, XMLD-PEEM was used to visualize skyrmion analogs in a natural antiferromagnetic system. [126] STXM can show ferromagnetic skyrmions in different sublattices and facilitate the study of current-driven behavior for skyrmions in ferrimagnetic systems ( Figure 6E). [26,29] Scanning nitrogen-vacancy (NV) magnetometry is another suitable approach to studying skyrmion structures. [49,51,[143][144][145] This method provides a noninvasive detection of magnetic stray fields produced by skyrmions by measuring the induced Zeeman splitting effect in a single NV center. [144] It has been used to observe skyrmions in Ta/CoFeB/MgO thin films, [144] Pt/Co 2 FeAl/MgO heterostructures, [49] Pt/Co/Ta multilayer stacks, [143] and Y 3 Fe 5 O 12 /Tm 3 Fe 5 O 12 /Pt ferrimagnetic trilayers. [51] Apart from static stray fields, Finco et al. demonstrated that NV magnetometry can visualize noncollinear antiferromagnetic textures by probing the magnetic noise from the samples. [145] They successfully imaged AFSKs in SAF systems by this means and point out their ability to study domain structures in low-moment magnetic materials such as 2D vdW magnets. [145] F I G U R E 6 (A) Schematic of how skyrmions can be visualized by LTEM. Reproduced with permission, [127] Copyright 2013, Springer Nature. (B) SP-STM images of ultrasmall skyrmions in PdFe/Ir(111) measured with out-of-plane (left) and in-plane (right) sensitive magnetic tips. Reproduced with permission, [116] Copyright 2015, American Physical Society. (C) MOKE microscopy for visualizing the current-driven skyrmion generation in a Ta/CoFeB/TaO x sputtered trilayer. Reproduced with permission, [42] Copyright 2015, The American Association for the Advancement of Science. (D) XMCD-PEEM image of an individual skyrmion in a Pt/Co/MgO thin film. Reproduced with permission, [117] Copyright 2016, Springer Nature. (E) Schematic of STXM microscopy geometry and its application to observe the current-driven skyrmion motion in a Pt/GdFeCo/MgO ferrimagnetic multilayer (images taken at Fe edge). Reproduced with permission, [26] Copyright 2018, Springer Nature.

| Topological Hall effect and skyrmion Hall effect
Nontrivial skyrmion structures in solids give rise to a topological Hall effect (THE) because they behave like emergent electromagnetic fields, deflecting the motion of conducting electrons. [11,20,31,77] Likewise, the skyrmion Hall effect (SkHE) describes the deflected motion of skyrmions with topological charges like that guided by the Hall effect for electrons. [24] Skyrmions with topological charges can also be driven by currents due to the generated spin-transfer torque (STT), as depicted in Figure 7. [31] For multilayer structures, the spin-orbit torque (SOT) generated by injected spin currents that originate from adjacent HM layers plays an important role in skyrmion kinetics. [22,146]

| Topological Hall effect related to skyrmions
The topological Hall effect offers a tool for studying the transport of skyrmions. An electron traveling through a skyrmion is coupled to the local spins due to Hund's rule. [31] As a result, it gains a quantum-mechanical Berry phase which accounts for the emergent magnetic field that an electron feels. [11,20,31,77] The Berry phase depends on the solid angle covered by a closed trajectory of an electron while the corresponding emergent magnetic field (EMF) for an infinitesimal loop is written as [20]   where n is the normalized spin vector and ϵ ijk an asymmetric tensor. By integrating the EMF over the area of a skyrmion where spins spread out over the solid angle π 4 , a skyrmion can be seen as a quantized emergent magnetic flux ϕ 0 with a fixed value. [11,20] The smaller a skyrmion, the stronger the local EMF will be. The total Hall effect is usually illustrated by the transverse Hall resistivity which has three contributions: The first term is the normal Hall resistivity proportional to the magnetic field. The second term is the anomalous Hall resistivity proportional to the magnetization. The last term is the topological Hall resistivity which can be extracted reliably to serve as an indication of a nontrivial topological ground state. [13,147] The THE signal of skyrmions has been detected in bulk materials and magnetic heterostructures. [13,120,121,148]  ) from the skyrmion phase in MnSi which is absent in other phases ( Figure 8A). [148] In 2019, a giant THE (∆  ρ 2.6μΩcm yx ) was found in the skyrmion state of the frustrated magnet Gd 2 PdSi 3 which has a much shorter modulated length ( Figure 8B). [13] In 2020, Néeltype skyrmions were observed by LTEM in WTe 2 /Fe 3 GeTe 2 heterostructures which display THE signals below 100 K ( Figure 8C). [120] In 2022, clear THE signals versus temperature helped to identify two groups of skyrmions at the interface of two vdW magnets ( Figure 8D). [121] For sputtered magnetic multilayers which can stabilize individual skyrmions, the Hall resistivity contribution from emergent skyrmions was studied. [149,150] Although it has F I G U R E 7 Schematic of deflected motion of an electron (THE) and a skyrmion (skyrmion Hall effect). Reproduced with permission, [31] Copyright 2013, Springer Nature. been demonstrated that the Hall signal change in a Pt/Co/ Ir multilayer due to a single skyrmion bears little relationship to the THE signal, it did facilitate the electric detection of skyrmions. [149] Static Hall resistivity measurements together with diffraction and real-space observation techniques can facilitate research on topological structures.

| Current-driven dynamics and skyrmion Hall effect
The current-driven dynamic of skyrmions can be derived from the Landau-Lifshitz-Gilbert (LLG) equation: (8) in which the former two terms on the right-hand side of the equation are torques exerted by the effective magnetic field (γ is the gyromagnetic ratio) and intrinsic damping (α is the damping parameter) while the latter two terms are contributions from STT and SOT. The STT originates from the angular momentum exchange between spin-polarized currents and local spins [151,152] and the SOT is generated by vertical spin currents thanks to the spin Hall effect (SHE). [153,154] F I G U R E 8 Topological Hall resistivity variation with temperature due to skyrmion phase in (A) MnSi, reproduced with permission, [148] Copyright 2009, American Physical Society, (B) Gd 2 PdSi 3 , reproduced with permission, [13] Copyright 2019, The American Association for the Advancement of Science. Hall hysteresis loops in (C) WTe 2 /Fe 3 GeTe 2 heterostructures showing peaks and dips near the transition edge before saturation which is the sign of the THE, reproduced with permission, [120] Copyright 2020, Springer Nature, and in (D) Cr 2 Te 2 Ge 6 / Fe 3 TeGe 2 vdW heterostructures where peaks and dips (denoted with blue and orange circles) appear below 60 K due to the emergence of skyrmions at interfaces, signifying the existence of a THE, reproduced with permission, [121] Copyright 2022, John Wiley and Sons.
In bulk systems, STT can be created in a chiral magnet by currents with an ultralow threshold (~10 6 Am −2 ), which makes skyrmions a powerful choice of information carriers. [19] Considering the skyrmions as rigid entities, their motion driven by STT can be described by the Thiele equation: [20,76,[155][156][157] where G is the gyrocoupling vector with respect to the topological number N,  is the dissipative tensor, and v d and v s are the skyrmion drift and current velocity, respectively. The potential term V r ( ) is connected to the existence of boundaries and defects. From Equation (9) and considering no boundaries or defects, the additional transverse velocity of skyrmions can be deduced: [76]  (10) where N refers to the topological number and e z is the unit vector along the z-axis. Zang et al. describe the bending of a skyrmion trajectory as the SkHE. [158] This kind of motion has been observed in real space by LTEM in a FeGe thin film ( Figure 9A) which shows the collective motion of skyrmion bundles. [159] The SkHE is shown to be dependent on the topological number of these bundles. [23,159] Typically, skyrmioniums (N = 0 skyrmion bundles) propagate with a zero skyrmion Hall angle. [159] For multilayer structures, vertical spin currents can be generated by injecting currents into a HM layer with strong SOC, [154] which is theoretically shown to be the most efficient driving source for skyrmions. [22,146] The Thiele equation is modified to describe skyrmion motion driven by SOT [24,146,155] : Here, j hm is the electrical current density in the HM, and v = (v , v ) x y is the velocity of a skyrmion containing a transverse component. The direct observation of SkHE by MOKE was carried out in Ta/CoFeB/TaO x multilayers ( Figure 9B). In the low-current-density regime (j e < 1.5 × 10 6 A cm −2 ), skyrmions migrate stochastically along the direction of the current. Only in the high-current-density regime (j e > 1.5 × 10 6 A cm −2 ) the transverse motion of skyrmions can be observed and the Hall angle is found to depend linearly on the current density until saturation. [24] This can be attributed to the pinning potential associated with randomly distributed defects. [160][161][162] Also, after being pushed near the edge of a track, skyrmions are observed to take on "oscillatory" motions due to the competition of the driving force and the repulsive force exerted by the edge. [24] These findings may help to explain the absence of a transverse skyrmion motion driven by currents in an early study on sputtered multilayers. [118] To elucidate the dependence of the skyrmion Hall angle on the current density, which was discovered by time-resolved X-ray microscopy, Litzius et al. proposed that internal excitations of skyrmions should be considered. [163] That implies that the skyrmions should not be described as rigid bodies and also that a field-like SOT plays an important role. [163] Consequently, the SkHE, causing the accumulation of skyrmions at edges, is detrimental for skyrmionic devices because it may reduce the drift velocity, stop skyrmions or even annihilate them. [24,76] In this sense, AFSKs may be more promising candidates for applications because of the cancellation of the opposite Magnus forces on the skyrmions from different sublattices. [136,164] Experimentally, a suppressed SkHE has been achieved in ferrimagnets and SAF structures ( Figure 9C-E). [26,27,29] A reduced SkHE (~20°) is observed in a ferrimagnetic multilayer which was not totally compensated compared to their ferromagnetic counterparts. [26] Very recently, fast skyrmion motion accompanied by very small SkHE (~3°) was achieved in ferrimagnetic Pt/CoGd/(W or Ta) films. [29] AFSKs in exchange coupled multilayers can also be driven by SOT with increased efficiency and negligible SkHE. [27] It is likely that the SkHE can vanish completely by varying material compositions or adjusting the temperature to the critical compensation temperature, but more research is needed here. [26,28]

| Microwave and laser-induced spin excitations of skyrmions
Skyrmions maintain intrinsic spin excitation modes in which they undergo deformations or rotations upon external stimuli, namely the clockwise (CW) and counterclockwise (CCW) gyration modes and the breathing mode ( Figure 10A). [165,168] These GHz-range spin modes of skyrmions can help to explain some intriguing phenomena such as the relationship between the skyrmion Hall angle and the current density [163] and are also the basis for skyrmion devices in need of dynamically manipulating magnetic orders. [169] Sophisticated microwave absorption experiments carried out in the insulating chiral magnet Cu 2 OSeO 3 have identified spin excitations of skyrmions with eigenfrequencies in the microwave regime. [165,170] The real-space tracking of the skyrmion motion in a magnetic disk induced by a magnetic field gradient via pump-probe X-ray F I G U R E 9 (A) Current-driven motion of a skyrmion bundle (N = 18) in a FeGe thin plate at a current density of  j 4.0 × 10 10 A m −2 and the dependence of the position on the pulse number, the average velocities on the current density and the skyrmion Hall angle on the current density. Reproduced with permission, [159] Copyright 2021, Springer Nature. (B) MOKE snapshots of skyrmion motion at low current density (  j 1.3 × 10 6 A cm −2 ) showing no SkHE and that at high current density (  j 2.8 × 10 6 A cm −2 ) showing SkHE. Below is the summarized dependence of the skyrmion Hall angle on the current density and the sign of the topological number. Reproduced with permission, [24] Copyright 2016, Springer Nature. (C) Experimental and simulated dependence of skyrmion Hall angle on the current density for a ferrimagnetic multilayer. Reproduced with permission, [26] Copyright 2018, Springer Nature. (D) Experimental results of skyrmion Hall angle versus skyrmion velocity in a ferrimagnetic thin film of Pt/CoGd/(Ta or W). Reproduced with permission, [29] Copyright 2022, American Chemical Society. (E) Dependence of skyrmion Hall angle on velocity for AFSKs and ferromagnetic skyrmions. Reproduced with permission, [27] Copyright 2019, Springer Nature.
holography also demonstrates the superposition of a CW higher-frequency mode and a CCW lower-frequency mode ( Figure 10B). [166] In addition, ultrafast optical pump-probe techniques serve as powerful tools for driving and detecting highfrequency dynamics of skyrmions. [167,169,171] In general, optical pump laser pulses manipulate magnetic order via thermal effects, the energy transferring initially from photons to electrons and then to spins through subsequent electron-phonon and spin-lattice interactions, or via nonthermal effects, the direct coupling between photons and spins through optomagnetic and photomagnetic processes, which strongly depend on the polarization state of the excitation light. [172] Probe pulses at finite time intervals with respect to the pump light can dynamically measure the transient spin orientation through magnetooptical Faraday or Kerr effects. [172] Ogawa et al. demonstrated the excitation of skyrmions in the insulating magnet Cu 2 OSeO 3 by circularly-polarized laser pulses which generate effective magnetic fields along the light kvector through the inverse Faraday effect. Eigenfrequencies can be deduced from the decaying spin precession signals (Faraday rotations) obtained by time-resolved magneto-optics. [167] With a 165 Oe in-plane field at F I G U R E 10 (A) Schematics of spin excitation modes of skyrmions. Reproduced with permission, [165] Copyright 2013, Springer Nature. (B) Evolution of displacements of skyrmion cores in the x and y coordinate (up), both of which cannot be fitted with a single-frequency mode but a CW higher-frequency mode together with a CCW lower frequency mode, and the global trajectory (down) in a magnetic disk. Reproduced with permission, [166] Copyright 2015, Springer Nature. (C) Time-resolved Faraday rotation in the SkX phase, which can be fitted with two sinusoidal functions, referring to the superposition of CW and CCW modes (top), and one that can be fitted with a sinusoidal function referring to the breathing mode (bottom). Reproduced with permission, [167] Copyright 2015, Springer Nature. 56.5 K, the observed signal which contained two sinusoidal waves with distinct frequencies suggests the coexistence of CW and CCW modes in the skyrmion phase ( Figure 10C). [167] With a 198 Oe out-of-plane field at 58 K, the skyrmion breathing mode was identified ( Figure 10C). [167] Similarly, Padmanabhan et al. observed the CCW mode and breathing mode in the Néel-type skyrmion host GaV 4 S 8 with time-resolved MOKE spectroscopy. [171] This can be attributed to the laser-induced quench of the magnetocrystalline anisotropy and the efficiency of such kind of optical excitation is enhanced in the skyrmion phase. [169] The specific frequencies of the skyrmion excitations, distinct from that in other phases, provide a fingerprint of the skyrmion phase state in their hosting materials. [167,169,171] 5 | NUCLEATION OF SKYRMIONS FOR FUTURE APPLICATIONS

| Nucleation of skyrmions by current and electric field pulses
The prerequisite for skyrmionic applications is to write skyrmion bits readily into potential devices. As discussed in Section 3, one can naturally apply magnetic fields to encode skyrmions. Besides this, skyrmions can be generated with electric current, electric field, and laser pulses.
Many experiments have demonstrated that spin torque can not only be used to transport skyrmions but also to facilitate the creation of skyrmions. [29,[41][42][43][44][45][46][47][48][49][50][51][52] Therefore, the FM/HM structures capable of generating SOT by injecting currents in HM layers are potential candidates for skyrmion applications due to their convenience of both creating and manipulating skyrmions. Current flows with inhomogeneous density due to geometric confinement in tracks and specially engineered injector structures can be used to create skyrmions in multilayer thin films. [42,43,47,48,52] For example, Jiang et al. nucleated skyrmions by electrically pushing DWs through a confined narrow neck in their Ta/CoFeB/TaO x trilayer device. [42] Büttner et al. observed controllable skyrmion nucleation near a custom-defined constriction in their multilayer device [43] (Figure 11A). On the other hand, homogeneous currents but with bipolar injection have also been used to create skyrmions. [45] By performing time-resolved measurements on skyrmion writing and deleting, Woo et al. demonstrated that pinning sites in sputtered films may serve as skyrmion generation sources. [44] Although the existence of external magnetic fields may hinder applications for skyrmions, [48] tilted magnetic fields have been shown to improve the skyrmion nucleation efficiency by SOT. [49] The successful deletion of skyrmion bits with tunneling currents and normal current pulses are also important steps toward their application in skyrmionic devices. [41,50] Although beneficial, writing new skyrmion bits with current pulses may lead to the subsequent displacement of the written skyrmions according to Section 4.2, which is unwanted for some applications. [61,62] Moreover, the heat produced by the injected currents is also a threat to skyrmion stability. [60] Utilizing electric fields can avoid the aforementioned disadvantages and provide another way to generate skyrmions. [59][60][61][62][63][64][65][66] Skyrmions can be generated by applying electric fields in multilayer heterostructures, which can probably be attributed to electric field induced modification of the exchange interaction, [61] magnetic anisotropy [63,66] and DMI [65] due to an interfacial charge redistribution. Recently, FM/ ferroelectric (FE) multiferroic heterostructures were used to demonstrate voltage-induced skyrmion nucleation via the effect of induced strain on interfacial DMI and magnetic anisotropy. [59,60] Based on the nonvolatile electric-field-driven switching of topological structures ( Figure 11B), Wang et al. proposed a random access memory device based on a FM/FE heterostructure. [60] Likewise, skyrmions can also be annihilated [59,61,62,66] or switched into other states [60] through electric fields.

| Nucleation of skyrmions by optical laser pulses
Ultrafast laser pulses have been demonstrated to be powerful tools for manipulating magnetization in (engineered) magnetic materials. [172,173] The generation of skyrmions by ultrashort laser pulses yields a faster and potentially more efficient way compared to that driven by currents. [52][53][54][55][56][57][58] By tuning the magnetic field and incident laser fluence, spatially distributed skyrmions can be encoded in the illuminated area of targeted materials. [53,54,56,58] The density and topological structure of optically generated skyrmions can be controlled by laser fluence. [54,56] Generally, such processes can be understood by laser-induced local heating which helps to overcome the energy barrier for nucleation. [52] Alternatively, laser excitation of itinerant electrons has recently been proposed as a microscopic mechanism for skyrmion photoexcitation. [174] Büttner et al. performed time-resolved X-ray scattering experiments and revealed that femtosecond laser pulses can drive Pt/Co-based materials into a high-temperature topological fluctuation state after which skyrmions are nucleated in picoseconds as illustrated in Figure 11C. [53] Efforts are still needed for studying the dynamics of laser-induced topological transitions and their sensitivity to laser wavelength and fluence. [53] Note LI ET AL.
| 279 that vortex laser beams with intrinsic angular momentum may also contribute to skyrmion generation. [175,176] From an applicational point of view, randomly distributed skyrmions are unwanted, so tailoring laser-induced skyrmion generation via ways such as tight focusing or near-field effects should be considered. [58] To achieve that, Kern et al. proposed an approach by patterning backside reflective masks to create skyrmions in well-defined regions and successfully demonstrated localized skyrmions in chains and arrays, which provides a nice application concept for all-optical skyrmion nucleation. [58] 5.3 | Potential applications for skyrmions

| Memory devices
After the magnetic domain-wall racetrack memory was put forward, [18] Fert et al. proposed a similar device but with magnetic skyrmion as information carriers. [21] Due to their topological stability, small sizes, and low-cost drivability, a skyrmion racetrack memory where skyrmions are transported in stripes of magnetic materials has been analyzed as a new method for ultra-dense storage. [21,22,93,146,164,[177][178][179][180][181] The FM/HM structure provides an ideal framework with the ease of nucleating and driving skyrmions in all-electrical ways. However, possible interference between these two procedures can cause problems as the nucleating currents may also shift existing skyrmions. [61,62] Although this can be tackled by using currents under nucleation threshold, [43] it correspondingly limits the skyrmion transport velocity. On the other hand, large driving currents aiming at high shifting speed may disturb existing magnetic information by nucleating unwanted skyrmions near a pinning site due to large SOT. [44,146] While the presence ("1") or absence ("0") of skyrmions on the racetrack can be used to store binary information, skyrmions with other magnetic topologies F I G U R E 11 (A) Current-induced skyrmion nucleation near a constriction is controlled by the number and direction of applied current pulses (indicated by red arrows). Reproduced with permission, [43] Copyright 2017, Springer Nature. (B) The electric-field-induced topological transition between stripe (Q = 0), vortex (Q = 0.5), and skyrmion (Q = 1), observed by MFM. Reproduced with permission, [60] Copyright 2020, Springer Nature. (C) Schematic of a typical magnetic hysteresis with different magnetic states depicted alongside, which contain a laser-accessible skyrmion phase. The inset shows the laser-induced skyrmion nucleation (denoted 3) from a uniform state (denoted 1) mediated by a topological fluctuation state (denoted 2). Reproduced with permission, [53] Copyright 2020, Springer Nature.
can also represent data bits for memory. [93,179,182] Siegl et al. introduced a strategy for racetrack devices by controlled creation, annihilation, and motion of densely packed skyrmions ("0") and antiskyrmions ("1") in the same sample. [179] Wu et al. proposed another method via magnetic-field-controlled coexistence of topological skyrmions ("1") and nontopological bubbles ("0") in a Fe 3 Sn 2 nanostripe, constituting a skyrmion-bubble-based memory. [93] Zheng et al. discussed the concept of constructing data streams by skyrmion tubes ("1") and chiral bobbers ("0"). [182] Critical properties for a skyrmion racetrack memory are data stability and reliability, which are susceptible to skyrmion-skyrmion and skyrmion-defect interactions. [178,183] To achieve them, it will be beneficial to use a modification of material parameters, like magnetic anisotropy ( Figure 12A), and to create artificial pinning sites ( Figure 12B) to trap skyrmion bits and therefore enhance their stability. [93,180,181] The aforementioned SkHE is another barrier to overcome. It was experimentally shown that this issue could probably be addressed by using AFSKs in ferrimagnets and SAFs. [26,27,29] Instead of suppressing it, Göbel et al. showed that the SkHE can even be favorable by driving skyrmion ratchet propagation in mirror-asymmetric racetracks via alternating currents. [186] The geometric constrictions along one side of the racetrack will also trap skyrmions after the currents are turned off, thus enhancing the position stability. [186] Yet, their propagation speed should be further improved to satisfy the needs for high-speed racetrack memory devices. [186] 5.3.2 | Other applications: Logic and magnonic devices Compared to complementary metal oxide semiconductor (CMOS) devices nowadays, nanomagnetic logic devices are candidate alternatives with potential higher efficiency. [187] Logic gates carried out by manipulating F I G U R E 12 (A) Schematic of a multiplexed gate architecture with voltage-controlled anisotropy gradient to create stage-like potential wells for propelling (indicated by green arrows) and trapping skyrmions. Reproduced with permission, [180] Copyright 2018, The Royal Society of Chemistry. (B) Schematic of a skyrmion-based memory device with artificial pinning sites to suppress the interruption induced by skyrmion movement whose magnetization is indicated by color wheels. Reproduced with permission, [93] Copyright 2021, AIP Publishing. (C) Schematic of a reconfigurable skyrmion logic gate based on FM/HM structure with magnetic tunnel junctions for inputs and outputs. The logic functions controlled by three voltages (V K1 , V K2 , V M ) are listed in the table. Reproduced with permission, [184] Copyright 2018, American Chemical Society. (D) Schematic of a cascaded one-bit fuller adder by skyrmion logic gates. Reproduced with permission, [185] Copyright 2019, American Physical Society. magnetic skyrmions have also been proposed in recent years. [184,185,[188][189][190][191][192] Zhang et al. were the first to propose a device with "Y"-shaped junction channels connecting inputs and outputs to control the duplication and merging of skyrmions and further constructed logic AND and OR gates. [188] Luo et al. reported an architecture for reconfigurable skyrmion logic gates ( Figure 12C) implementing SOT, SkHE, skyrmion-edge interactions, and skyrmion-skyrmion interactions. [184] Cascaded skyrmionic logic gates to execute complex logic functions, for instance, a one-bit full adder ( Figure 12D), are promising. [185,189] Replacing ferromagnetic skyrmions and logic gates using AFSKs structures with better stability and mobility as information carriers were also designed. [190,191] Besides conventional binary computing, stochastic computing implemented by skyrmionic logic devices is also possible. [192] In addition, particlelike skyrmions with noncolinear spin nature and internal excitation modes contribute to future magnonic devices for manipulating spin waves. Skyrmions can also be used for constructing magnonic crystals with high-tunability to adjust the magnonic band structure, [193] while the concept of using 3D skyrmion tubes as magnonic waveguides for spin-wave channeling was also proposed. [194] Recently, it was theoretically predicted that a magnonic frequency comb consisting of discrete and equally spaced frequencies can be obtained by nonlinear magnon-skyrmion scattering, [195] offering a new way for combining skyrmions and magnonics.

| SUMMARY AND PERSPECTIVES
The emergence of magnetic skyrmions in various materials and the expanding toolbox for their characterization have introduced intriguing topological phenomena in the field of magnetism that offer a broad platform for research of their exotic static and dynamic properties and their potential applications.
First, as discussed and classified in this review, the family of skyrmion hosting materials keeps expanding, from single-phase crystals to multilayer structures, from ferromagnets to ferrimagnets and antiferromagnets and from asymmetric systems to centrosymmetric systems. From the scientific point of view, it leads us to the question of whether other ingredients apart from the asymmetric DMI are essential factors for skyrmion stabilization, especially after the recent demonstration of ultrasmall skyrmions in some centrosymmetric crystals. It will also be interesting to see whether magnetic skyrmions can exist in the recently proposed nonrelativistic altermagnets, which present a new class of magnetically ordered materials beyond the conventional ferromagnets, ferrimagnets, and antiferromagnets. [196,197] From the application point of view, apart from the well-established FM/HM structures suitable for CMOS applications, the search for other material architectures to create skyrmions with smaller sizes and higher thermal stability, or which provide other avenues for skyrmion manipulation are of interest, for instance, the FM/FE multiferroic interfaces facilitating voltage-controlled effects. Recent discoveries of magnetic order in 2D magnets make them potential building blocks for functional hybrid heterostructures as skyrmion hosts. Their atomically thin nature, high integrability, and available proximity effects at interfaces might pave new routes for exploring novel skyrmionic devices. It will become even more attractive if these can be realized with room-temperature stability.
Second, for skyrmion applications in memory and computing, reliable and reproducible nucleation and manipulation are essential. This brings challenges for manufacturing high-quality skyrmion hosting materials free from natural defects. In addition, the controlled local nucleation requires modifying material parameters to create potential wells or introducing artificial constrictions, for example, via focused ion beams. Other potential approaches include vertical current injection, local electric fields, and tailored laser illumination. Among them, the first two are more compatible with electronic devices. Compared to them, optical skyrmion nucleation may potentially increase the speed of information coding but requires further research on the energy transfer from photons to electrons and the topological fluctuations emerging during ultrafast laser-induced heating and subsequent cooling processes. Regarding the stability of dynamical skyrmion bits flow, it is worth thinking about how to further suppress the SkHE without compensation of drift speeds or instead utilize it for specific functions.
Third, to meet the requirements of our modern information society the present, so-called "Von Neumann architecture," based on the separation of processing and storage units in a 2D architecture, will be insufficient. Alternative approaches to store and process data beyond Von Neumann are inspired by the most efficient computational architecture known, the human brain. They make use of the huge interconnectivity in a massively parallel integrated processing and storage neural network and potentially offer energy savings of six orders of magnitude. [198] This emerging field of braininspired or neuromorphic computing is strongly growing and exploring various material platforms in the search for more energy-efficient data processing concepts. [199][200][201] Neuromorphic spintronics is emerging as one of the promising approaches, in particular for applications that involve big data, with a much higher energy efficiency compared to conventional computing schemes. [202][203][204][205] It has been demonstrated that skyrmion accumulation and dissipation in ferrimagnets controlled by electrical pulses can imitate synaptic weights and skyrmion-based artificial neural networks can execute the task of pattern recognition. [206] Furthermore, skyrmions have been investigated for 2D reservoir computing. [207,208] Recently, we demonstrated that Co/Pt films can be used as artificial synapses by controlling their magnetization state using ultrashort laser pulses. [209] In addition, an efficient implementation of supervised perceptron learning and pattern recognition was demonstrated experimentally in an opto-magnetic neural network built from such magnetic synapses. [210] These optical-magnetic methods might be integrated with skyrmions to build more sophisticated neural networks in the future. However, so far all these developments have been in 2D systems. As objects in 2D can only be connected by graphs with a crossing number of zero, limiting connections to four sites or four neurons. Thus going to 3D geometries would be a disruptive game-changer that could achieve similar interconnectivity as the brain. The potential of these very first implementations is enormous: a simple estimate shows that the realization of the Landauer limit [211] for 1 trillion binary synapses, adopted at a rate of 10 Hz, yields an energy cost as low as 3 µW, which is nearly six orders of magnitude lower than that of the human brain. Hence, even partially reaching this estimated limit offers an enormous gain in energy efficiency. What remains is the formidable challenge of developing 3D spin structures and a real 3D magnetic architecture, something that might be achieved with 3D skyrmion-like structures such as hopfions (Figure 13). [212] The latter is a kind of 3D loop-like solitons formed by twisted skyrmion strings displaying exotic dynamics, [212,213] which are experimentally created and observed in a magnetic multilayer only recently. [214] Research on such 3D topological solitons will be further facilitated by recent advances in 3Dmagnetization-reconstruction techniques such as X-ray tomography, [215][216][217] X-ray laminography, [218,219] and spin-resolved electron microscopy. [220] To conclude, magnetic skyrmions are a still strongly growing field of fundamental research with great potential for future energy-efficient information technologies. In particular, new developments beyond Von Neumann might bring new opportunities for applications of skyrmions and other 3D topological spin textures in the coming years.