Synthetic Antiferromagnetic Skyrmions (SAFsk)

• Synthetic Antiferromagnetic Skyrmions (SAFsk) are composite topological spin textures formed by paired skyrmions in adjacent ferromagnetic layers coupled antiferromagnetically.
• Key material platforms and stabilization mechanisms include DMI, perpendicular anisotropy, and Ru-mediated RKKY coupling, enabling room-temperature and zero-field operation.
• Their dynamics suppress the skyrmion Hall effect, allowing efficient, straight-track current-driven motion ideal for racetrack memory, logic, and oscillator devices.

Synthetic antiferromagnetic skyrmions (SAFsk) are topological spin textures hosted in synthetic antiferromagnets, namely multilayers in which ferromagnetic sublayers are coupled antiparallel by interlayer exchange such as RKKY coupling through a spacer. In the canonical bilayer realization, a SAFsk is a bound pair of skyrmions residing in two ferromagnetic layers with opposite magnetization and opposite gyrotropic response, so the composite object has nearly zero net magnetization and, in the ideal compensated limit, zero net topological charge. This suppresses the skyrmion Hall effect and underlies the use of SAFsk as prospective carriers for racetrack, logic, oscillator, and magnonic architectures (Juge et al., 2021, Loreto et al., 2018, Haltz et al., 2023). Subsequent work has expanded the concept beyond a single mirrored-tube picture to include layer-selective textures, non-coaxial heterochiral pairs, collective crystal phases, and chain excitations in confined geometries (Fallon et al., 29 Apr 2026, Menezes et al., 19 Dec 2025, Zulfiqar et al., 4 Jun 2026).

1. Definition, topology, and distinction from related skyrmions

A SAFsk is formed in a synthetic antiferromagnet rather than in a single ferromagnetic film. The basic construction is a pair of ferromagnetic skyrmions in separate magnetic layers, antiferromagnetically locked through interlayer exchange, often Ru-mediated RKKY coupling. In the standard Néel-type case, the layers host antiparallel skyrmions with opposite core polarities and opposite topological response, so the total gyrovector vanishes in the balanced limit and the composite moves without the transverse deflection characteristic of a ferromagnetic skyrmion (Loreto et al., 2018, Kechrakos et al., 2024).

The layer-resolved topological charge is conventionally written as

$$Q=\frac{1}{4\pi}\int \mathbf{m}\cdot\left(\frac{\partial \mathbf{m}}{\partial x}\times\frac{\partial \mathbf{m}}{\partial y}\right)\,dx\,dy,$$

with the continuous-model value $Q=\pm 1$ for an isolated skyrmion and approximate values in discretized simulations (Loreto et al., 2018). In multilayer SAF racetracks an odd-even effect follows directly from summing the layer charges: for $N=1,2,3,4$, the total charge is $Q_{\text{tot}}=1,0,1,0$, respectively. Even-layer stacks therefore eliminate the skyrmion Hall effect, whereas odd-layer stacks retain a reduced Hall angle that scales as $1/N$ in the generalized Thiele description (Zhang et al., 2016).

SAFsk are distinct from intrinsic antiferromagnetic skyrmions. In intrinsic systems, the antiferromagnetic character arises from internal sublattice ordering within one magnetic monolayer, as in the row-wise antiferromagnetic Cr monolayer on PdFe/Ir(111), whereas SAFsk rely on separate ferromagnetic layers coupled across a spacer (Aldarawsheh et al., 2023). They are also distinct from ordinary ferromagnetic skyrmions, which carry nonzero net magnetization and a finite gyrovector, and from ferrimagnetic or compensated ferrimagnetic textures where the two magnetic sublattices are not spatially separated in the same way (Haltz et al., 2023).

2. Materials platforms and stabilization mechanisms

The experimentally established SAFsk platforms are multilayers in which interfacial DMI, perpendicular magnetic anisotropy, and antiferromagnetic interlayer exchange are co-engineered. A fully compensated sputtered SAF of the form $$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$, with $$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$ and $\mathrm{FM}_2=\mathrm{Co}(1.35)$, supported isolated SAF skyrmions at room temperature and zero external field. In representative images the skyrmion diameters were about $107$ nm and $239$ nm, with an average diameter of $Q=\pm 1$0 nm and a standard deviation of $Q=\pm 1$1 nm across multiple nucleation events (Juge et al., 2021).

A later bias-engineered SAF introduced a compensated or partially compensated SAF bias layer as an internal exchange-field source, replacing the role of an external stabilizing field. In that architecture, quantitative high-sensitivity MFM combined with micromagnetic modeling identified room-temperature, zero-field SAFsk below $Q=\pm 1$2 nm, including a true diameter of $Q=\pm 1$3 nm, described as the smallest SAF skyrmions reported to date (Darwin et al., 8 May 2026). In a separate [Pt/Co/Ru]$Q=\pm 1$4 platform, zero-field SAF skyrmions were observed in both non-compensated and compensated samples, with characteristic sizes of about $Q=\pm 1$5 nm and $Q=\pm 1$6 nm, respectively (Geng et al., 21 May 2025).

Several stabilization routes coexist within the SAF literature. In the standard DMI-based route, Pt/Co interfaces provide DMI and PMA, while Ru acts as the spacer responsible for RKKY coupling (Geng et al., 21 May 2025). A second route uses a patterned synthetic antiferromagnet in which antiferromagnetic interlayer exchange coupling, rather than DMI, fulfills the role of nucleation and stabilization; in the demonstrated half-etched geometry, a skyrmion forms in the bottom continuous film beneath a top nanodot and remains field-tunable once nucleated (Li et al., 2019). A third route exploits local coupling nonuniformity: in compensated [Pt/Co/Ru]$Q=\pm 1$7, micromagnetic simulations found that introducing a region covering about $Q=\pm 1$8 of the model area with different RKKY coupling strength caused skyrmion formation under zero field (Geng et al., 21 May 2025).

The microscopic origin of zero-field stabilization can therefore differ across platforms. In [Pt/Co/Ru]$Q=\pm 1$9, first-principles calculations and micromagnetics linked SAFsk formation to nonuniform RKKY coupling associated with proximity-induced magnetic moments in Pt and Ru; the compensated $N=1,2,3,4$0 model yielded asymmetric induced moments in Pt and Ru and a residual net atomic magnetic moment of $N=1,2,3,4$1 for the whole stack (Geng et al., 21 May 2025). This suggests that the experimentally relevant “synthetic antiferromagnet” may involve topological textures extending into nominally nonmagnetic spacer or interface layers rather than only the primary ferromagnetic sublayers.

3. Static phenomenology and geometric variants

The simplest static SAFsk picture is a coaxial pair of Néel skyrmions extending through both ferromagnetic layers. That picture remains central, but it is no longer exhaustive. In a chemically asymmetric CoB/CoFeB synthetic antiferromagnet, two skyrmion families were identified in different field regimes: conventional-polarity skyrmions at higher fields and inverse-polarity skyrmions at lower fields. Correlative microscopy, element-resolved x-ray magnetometry, and matched micromagnetic modeling showed that the textures reside only in the CoFeB layers, while the CoB layers remain laterally uniform and act through an effective RKKY exchange field (Fallon et al., 29 Apr 2026). This directly departs from the conventional SAF “tube” picture.

Frustrated interlayer energetics generate additional topological manifolds. In a SAF combining isotropic DMI in one layer and anisotropic DMI in the other, six metastable elliptical textures were stabilized at intermediate antiferromagnetic RKKY coupling, namely $N=1,2,3,4$2, $N=1,2,3,4$3, $N=1,2,3,4$4, $N=1,2,3,4$5, $N=1,2,3,4$6, and $N=1,2,3,4$7, with a threefold degeneracy for $N=1,2,3,4$8, $N=1,2,3,4$9, and $Q_{\text{tot}}=1,0,1,0$0, and a twofold degeneracy for $Q_{\text{tot}}=1,0,1,0$1 and $Q_{\text{tot}}=1,0,1,0$2 (Bhukta et al., 2020). These states include skyrmion-like, antiskyrmion-like, and $Q_{\text{tot}}=1,0,1,0$3 textures, showing that synthetic antiferromagnetic coupling can stabilize topological sectors unavailable in a single DMI symmetry class.

In extended bilayers, SAF skyrmions also form crystalline phases with nontrivial lattice geometry. Monte Carlo simulations of a synthetic antiferromagnetic bilayer with DMI found that the skyrmion-lattice structure switches from triangular or hexagonal to square as the antiferromagnetic interlayer coupling becomes stronger, because skyrmions in opposite layers repel one another and tend to occupy each other’s dual lattice (Walsem et al., 2018). In a centrosymmetric bilayer triangular lattice with layer-dependent DMI, easy-plane anisotropy, antiferromagnetic interlayer exchange, and an in-plane field, simulated annealing stabilized an antiferro skyrmion crystal with $Q_{\text{tot}}=1,0,1,0$4, $Q_{\text{tot}}=1,0,1,0$5, and therefore $Q_{\text{tot}}=1,0,1,0$6, together with ferri-type skyrmion crystals in which only one layer carries nontrivial skyrmion number (Hayami, 2023).

Localized material inhomogeneity provides yet another degree of static control. In a synthetic antiferromagnetic racetrack of size $Q_{\text{tot}}=1,0,1,0$7 nm$Q_{\text{tot}}=1,0,1,0$8 per magnetic layer, separated by a $Q_{\text{tot}}=1,0,1,0$9-nm Ru spacer, a $1/N$0-nm-long locally modified region created either by changing the perpendicular magnetic anisotropy or by modifying the local thickness can attract, repel, or trap the bilayer skyrmion pair (Loreto et al., 2018). The qualitative rule is asymmetric between layers: a higher-PMA or thinner region attracts and pins the top-layer skyrmion while repelling the bottom-layer one, whereas a lower-PMA or thicker region reverses those roles. If the interlayer antiferromagnetic coupling is sufficiently strong, decoupling need not occur (Loreto et al., 2018).

4. Dynamics, collective modes, and transport kinematics

The chief dynamical attraction of SAFsk is the suppression of Hall deflection together with enhanced or reconfigured mobility. In a balanced SAF, the summed gyrovector vanishes while dissipation is retained, so current-driven motion proceeds along the drive direction without the ferromagnetic skyrmion Hall angle. Micromagnetic simulations and a two-layer Thiele model showed that balanced SAFs exhibit somewhat smaller skyrmion radii than single ferromagnetic layers, the bubble phase disappears from the phase diagram, and the current-driven velocity can approach a factor close to two larger than that of a ferromagnetic single layer; by contrast, angular imbalance reintroduces a finite Hall angle, whereas geometrical imbalance can alter size and speed without necessarily restoring transverse deflection (Haltz et al., 2023).

For multilayer racetracks, finite-temperature dynamics sharpen this contrast. In OOMMF simulations of a $1/N$1 nm $1/N$2 nm $1/N$3 nm-per-layer racetrack under CPP drive, a monolayer ferromagnetic skyrmion at $1/N$4 MA cm$1/N$5 moved at about $1/N$6 m s$1/N$7 but was destroyed once thermal fluctuations and edge deflection became appreciable; in the same study, a bilayer SAF skyrmion at $1/N$8 MA cm$1/N$9 moved straight along the track center at about $$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$0 m s$$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$1 and remained stable up to room temperature, $$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$2 K (Zhang et al., 2016). The straight-path result also appears in frustrated SAF bilayers driven by current-in-plane, where $$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$3 and $$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$4 bilayer skyrmions move with $$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$5, while current-perpendicular-to-plane instead produces circular trajectories with helicity rotation and can split a $$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$6 bilayer into two $$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$7 bilayers (Xia et al., 2018).

A finite interlayer coupling changes the transient dynamics qualitatively. Two coupled Thiele equations for the two skyrmions,

$$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$8

predict that a moving SAF pair reaches its stationary regime only after developing a finite lateral separation orthogonal to the velocity. The associated transient time constant scales inversely with the antiferromagnetic coupling constant, and the coupling force has a maximum at finite separation, which imposes a maximum stable velocity beyond which the bound pair cannot be maintained (Panigrahy et al., 2022). This identifies an intrinsic inertial regime absent in the usual ferromagnetic rigid-skyrmion picture.

The internal-mode spectrum is likewise reorganized by the antiferromagnetic bilayer structure. In confined square SAF geometry, micromagnetic eigenvalue and ringdown calculations found two nearly degenerate gyrotropic modes at $$[\mathrm{Pt}(0.5)/\mathrm{FM}_1/\mathrm{Ru}(0.85)/\mathrm{Pt}(0.5)/\mathrm{FM}_2/\mathrm{Ru}(0.85)]_{\times 2}$$9 GHz and $$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$0 GHz, with common rotation sense within each mode, and two breathing modes at $$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$1 GHz and $$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$2 GHz corresponding to in-phase and out-of-phase layer breathing (Zulfiqar et al., 4 Jun 2026). In a rectangular $$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$3 confinement, opposite gyration sense in the two layers converts the low-frequency response into nearly linear translation along the long or short axis. In chains of $$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$4 SAF skyrmions, the translational and breathing bands follow a standing-wave-like envelope

$$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$5

for horizontal translation and breathing modes, and a 25-skyrmion chain supports signal propagation at about $$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$6 m s$$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$7, approximately $$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$8 faster than a comparable ferromagnetic skyrmion chain with $$\mathrm{FM}_1=\mathrm{Co}(0.3)/\mathrm{Ni}_{80}\mathrm{Fe}_{20}(1.45)/\mathrm{Co}(0.3)$$9 m s$\mathrm{FM}_2=\mathrm{Co}(1.35)$0 (Zulfiqar et al., 4 Jun 2026).

Field-driven motion can also exploit these internal modes. In mumax3 simulations, a static in-plane field of $\mathrm{FM}_2=\mathrm{Co}(1.35)$1 T plus an out-of-plane microwave field of amplitude $\mathrm{FM}_2=\mathrm{Co}(1.35)$2 mT drove a SAF skyrmion by asymmetric spin-wave emission. The decisive resonance was the intrinsic out-of-phase breathing mode at about $\mathrm{FM}_2=\mathrm{Co}(1.35)$3 GHz for $\mathrm{FM}_2=\mathrm{Co}(1.35)$4, whereas the in-phase mode near $\mathrm{FM}_2=\mathrm{Co}(1.35)$5 GHz produced insufficient radius variation to sustain motion. The resulting average $\mathrm{FM}_2=\mathrm{Co}(1.35)$6-velocity saturated near $\mathrm{FM}_2=\mathrm{Co}(1.35)$7 m s$\mathrm{FM}_2=\mathrm{Co}(1.35)$8, with a wiggle-like trajectory and an empirical threshold radius variation of about $\mathrm{FM}_2=\mathrm{Co}(1.35)$9 nm, or $107$0 of the static radius (Barker et al., 12 Feb 2025).

5. Detection, spectroscopy, and topological transport

Because compensation suppresses net magnetization and stray field, SAFsk detection is intrinsically more subtle than ferromagnetic skyrmion detection. Layer-selective x-ray methods provided the first direct proof of their bilayer character. In the fully compensated sputtered SAF described above, XMCD-STXM at the Co and Fe $107$1 edges, together with ptychographic reconstruction, showed the same skyrmion profile in the two magnetic blocks with opposite contrast, thereby establishing antiparallel alignment across layers. XMCD-PEEM further identified the domain-wall sequence $107$2, consistent with a left-handed Néel wall in the visible top layer and with homochiral SAF skyrmions set by the sign of the Pt/Co DMI (Juge et al., 2021).

Quantitative MFM has become a second major route, especially for very small compensated textures. In the bias-engineered SAF system, high-vacuum MFM at about $107$3 mbar, with quality factor up to $107$4 million and tip radius below $107$5 nm, was combined with background subtraction, tip calibration, and quantitative modeling. The measured SAFsk contrast was weak, typically $107$6–$107$7 Hz, but fitted reliably to asymmetric top and bottom trilayer skyrmions with radii such as $107$8 nm and $107$9 nm in the modeled state (Darwin et al., 8 May 2026). Dynamic fingerprints provide a third route: broadband ferromagnetic resonance simulations of SAF nanodisks found that single SAF skyrmions show a dominant anti-phase breathing mode around $239$0 GHz in a representative example, while skyrmion clusters produce spectra whose resonance content depends on skyrmion number and confinement, making the internal-mode spectrum a sensing observable (Lonsky et al., 2022).

Transport signatures have developed along two lines. A 2017 semiclassical SU(2) transport theory for Fe/Cu/Fe trilayers argued that the natural signal of antiferromagnetically ordered skyrmions is a topological spin Hall effect rather than the conventional topological Hall effect: the transverse charge conductivity vanishes, but a pure transverse spin current survives and is highly sensitive to spacer thickness, band filling, and the overlap parameter $239$1 (Buhl et al., 2017). Later experiment complicated the earlier expectation that a perfectly compensated SAF should have negligible Hall response. In [Pt/Co/Ru]$239$2 bilayers, the Hall resistivity was decomposed through

$239$3

and a nonzero topological Hall effect was observed in both non-compensated and fully compensated SAF skyrmion systems. Sample 1, with $239$4 nm and $239$5 nm, showed a signal of about $239$6 n%%%%12$1/N$12%%%%8cm, while the compensated Sample 2, with $239$9 nm, still showed about $Q=\pm 1$00 n$Q=\pm 1$01$Q=\pm 1$02cm; in both cases the field window of the topological Hall effect coincided with MFM and NV-center MFM imaging of SAF skyrmions, and $Q=\pm 1$03 remained nonzero at zero field (Geng et al., 21 May 2025).

A common misconception is therefore that compensation necessarily eliminates any topological electrical signature. The $Q=\pm 1$04 results show that this need not be true once proximity-induced moments in Pt and Ru and broken inversion symmetry are included, and the element-resolved CoB/CoFeB work further shows that the topological texture need not be distributed symmetrically across all magnetic sublattices (Geng et al., 21 May 2025, Fallon et al., 29 Apr 2026).

6. Device concepts, manipulation schemes, and stability limits

The principal application target is racetrack memory. The local-modification study on a synthetic antiferromagnetic racetrack demonstrated that a current pulse of $Q=\pm 1$05 A m$Q=\pm 1$06 moves the SAF skyrmion about $Q=\pm 1$07 nm in $Q=\pm 1$08 ns, after which a $Q=\pm 1$09-nm locally modified region can stop, pin, or repel it. In the lower-PMA case, the top-layer skyrmion is repelled by about $Q=\pm 1$10 nm in $Q=\pm 1$11 ns while the bottom-layer skyrmion is pinned; multiple $Q=\pm 1$12-nm bit regions separated by $Q=\pm 1$13 nm were proposed for controlled placement and MTJ readout (Loreto et al., 2018). This suggests a bit-addressing strategy in which static anisotropy or thickness engineering replaces dynamic edge steering.

Ring geometries convert Hall suppression into periodic signal generation. In PETASPIN simulations of a SAF nanoring with external diameter $Q=\pm 1$14 nm and track width $Q=\pm 1$15 nm, a current-perpendicular-to-plane Thiele model with $Q=\pm 1$16 predicted uniform tangential motion and a circulation frequency linear in current density. Micromagnetics confirmed GHz-range operation at $Q=\pm 1$17 MA/cm$Q=\pm 1$18, with performance about $Q=\pm 1$19 better than a bilayer ferromagnetic-heavy-metal nanoring of the same geometry, and introduced a three-phase AC alternator based on three MTJ detectors separated by $Q=\pm 1$20. The optimal reported signal balance occurred near $Q=\pm 1$21 and detector width $Q=\pm 1$22 nm (Kechrakos et al., 2024).

Signal-processing concepts extend from rings to chains. The 25-skyrmion SAF chain described above transmitted a breathing-band pulse with average speed about $Q=\pm 1$23 m s$Q=\pm 1$24 (Zulfiqar et al., 4 Jun 2026). More generally, a 2025 experimental study summarized prior work reporting SAFsk velocities up to $Q=\pm 1$25 m s$Q=\pm 1$26 under current-induced spin-orbit torque, and emphasized that the combination of high driving velocity, nanoscale size, and suppression of the skyrmion Hall effect is the reason these textures are repeatedly proposed for high-density spintronic devices (Geng et al., 21 May 2025).

The practical bottleneck is stability of the bound pair rather than stability of one skyrmion in isolation. Atomistic minimum-energy-path calculations identified two generic destruction channels: decoupling of the two layer skyrmions, and sequential collapse into the homogeneous antiferromagnetic state. The relevant activation energy is set by the smaller barrier. In homochiral systems, increasing interlayer exchange stabilizes the pair; in heterochiral systems, stronger interlayer exchange can instead destabilize the non-coaxial bound state, while reducing the anisotropy constant effectively stabilizes heterochiral SAFsk (Menezes et al., 19 Dec 2025). Combined with the inertial time constant and maximum-velocity limit from the coupled-Thiele analysis, this yields a consistent engineering rule: strong coupling is favorable for conventional homochiral racetrack pairs, but heterochiral or active non-coaxial pairs require a more delicate balance among $Q=\pm 1$27, DMI asymmetry, anisotropy, and field (Panigrahy et al., 2022, Menezes et al., 19 Dec 2025).

Taken together, the literature presents SAFsk not as a single object with one canonical realization, but as a multilayer topological design space. The recurring invariants are antiferromagnetic interlayer binding, compensation of gyrovector-driven Hall deflection, and strong sensitivity to geometry, anisotropy, DMI symmetry, and vertical asymmetry. The result is a class of spin textures that can be stabilized at room temperature and zero field, manipulated by current, field, anisotropy, or local thickness engineering, detected by layer-resolved microscopy or topological transport, and organized into crystals, chains, and oscillator geometries with experimentally relevant dynamical bandwidths (Juge et al., 2021, Darwin et al., 8 May 2026, Zulfiqar et al., 4 Jun 2026).