Three-dimensional skyrmionic cocoons in magnetic multilayers

The study targets the stabilization and characterization of three-dimensional (3D) topological magnetic textures in scalable magnetic multilayers, aiming to exploit the third dimension for enhanced control of properties and device functionality. Prior work has focused on two-dimensional skyrmions and skyrmion tubes in chiral magnets and multilayers. Recent interest in 3D nanomagnetism has revealed complex textures such as bobbers, torons, hopfions, and truncated skyrmions, but their characterization often requires advanced X-ray/electron imaging and their implementation typically relies on chiral crystals or nanostructures, limiting scalability. The purpose here is to engineer multilayer architectures that stabilize new 3D textures—"skyrmionic cocoons"—and to develop accessible detection via magneto-transport coupled with micromagnetic simulations, enabling layer-resolved insight into their magnetization, chirality, and topological properties in practical thin-film systems.

- 2D skyrmions were first observed in B20 chiral magnets and have been extensively studied in chiral magnets and magnetic multilayers. In thick structures, skyrmion tubes extend through the film thickness with modest variations. - 3D textures predicted and observed in bulk include bobbers (skyrmion strings terminating in a point singularity) and torons (dipole strings with two Bloch points). Hopfions have been reported in magnetic multilayers, originally predicted in chiral crystals. Truncated skyrmions at interfaces can be stabilized in hybrid ferromagnetic/ferrimagnetic multilayers. - Characterization of 3D textures often relies on advanced techniques such as soft X-ray laminography and X-ray tomography, which can reconstruct 3D magnetization but are resource-intensive. - Dzyaloshinskii–Moriya interaction (DMI) at interfaces in multilayers is key to stabilizing chiral non-collinear textures; tuning layer thickness and interfaces provides a route to engineer DMI and anisotropy for 3D texture stabilization.

- Multilayer design and fabrication: Magnetron sputtering on thermally oxidized Si with 5 nm Ta seed and Pt capping. Architectures based on Pt/Co/Al trilayers with variable Co thickness to create a vertical gradient of magnetic properties. • Single Gradient (SG): Pt 3 nm/Co Xi/Al 1.4 nm repeated with Co thickness evolving by fixed steps S from a starting thickness X1 to a maximum and back, over N layers. Example studied: X1 = 1.7 nm, S = 0.1 nm, N = 13. The reorientation transition thickness ≈ 1.7 nm implies mostly in-plane effective anisotropy; modeled with interfacial uniaxial anisotropy Kus ≈ 1.58±0.08 mJ/m². • Double Gradient (DG): Two SG blocks separated by M repetitions of thin Co layers (Y = 1.0 nm) with strong PMA. Parameters: X1 = 2.0 nm, S = 0.1 nm, Y = 1.0 nm, N = 13, M = 15. - Micromagnetic simulations: Performed with Mumax3. Visualization via isosurfaces of mz = −0.8 (red), mz = 0 (white), and mz = 1 (blue). Simulated relaxed states after various magnetic-field initializations (OOP, IP, tilted). Layer-resolved profiles used to extract chirality (CW/CCW Néel) and topology (2D skyrmion number per layer and discussion of 3D topological charge over closed surfaces). • Representative parameters: A = 18 pJ/m, Ms ≈ 1.2 MA/m, Kus ≈ 1.62 mJ/m² (surfacial), DMI surfacial constant Ds ≈ 2.34 pJ/m. Cell sizes: SG 2×2×2.1 nm³ (512×512×37); DG 2×2×1.8 nm³ (512×512×121). Checks with finer in-plane mesh (1×1 nm²) showed negligible differences. Variable Co thickness handled via dilution factor f = X/Lz; exchange, DMI, Ms scaled by f; anisotropy K = Kuf − μ0Ms(f − f²)/2 with Ku = Kus/Xi. • Field protocols: Initialization along y/z with 50% noise; field sweeps from positive to negative; thermal assistance (T = 500 K for 2 ns, α = 0.01) to aid nucleation. Simulated MFM computed with 50 nm lift. - Magnetic imaging: Magnetic force microscopy (MFM) at room temperature with demagnetization procedures (oscillating field, exponentially decaying amplitude). Tapping mode, lift ~10 nm (effective higher), Gaussian filtering (Gwyddion, 2-pixel FWHM). MFM phase maps compared with simulated MFM for various fields and initializations. - Magneto-transport: Hall bars (20×100 µm²) on DG measured with fields up to 0.65 T (and up to 9 T to extract AMR/SMR). Measured longitudinal Rxx and transverse Rxy versus field orientation θ (angle to film normal). Model includes SMR (∝ mz²), AMR (∝ mx²), and AHE (Rxy ∝ mz): Rxx = Rxx0 + RSMR·mz² + RAMR·mx²; Rxy = Rxy0 + RAHE·mz. Extracted RAMR = −18 mΩ, RSMR = −108 mΩ; other effects (ordinary Hall, GMR, PHE, THE) neglected as negligible. Simulations provide mx,my,mz to predict transport without fitting parameters; experimental Rxy normalized by Rxx for comparison to mz.

- Discovery and definition of skyrmionic cocoons: 3D, vertically confined magnetic textures with deformed ellipsoidal shape residing within a subset of multilayer repeats, distinct from skyrmion tubes that span the full stack. - SG multilayers (X1=1.7 nm, S=0.1 nm, N=13): • At 0 mT: columnar textures form an irregular lattice (skyrmion tubes with circular/elongated shapes), extending through the full thickness. • At 175 mT: objects shrink laterally (Zeeman effect), approaching a lattice of skyrmion tubes with barrel-like vertical profile. • At 275 mT: tubes become vertically confined into skyrmionic cocoons; MFM shows reduced contrast as cocoons are buried below the top surface; simulations reproduce density, shape and size. • Layer-resolved chirality (0 mT): bottom layers (1–6) show CCW Néel, top layers (11–13) CW Néel; middle layers have uniform in-plane wall direction due to near-cancellation of DMI and interlayer dipolar fields. • Layer-resolved state (275 mT): outer layers’ cores disappear (mz>0.99 top layers), with vortex-like, non-singular textures above the cocoon (layers 9–10, mz>0.85). No Bloch points at cocoon ends due to discrete layering and dipolar coupling, distinguishing them from torons. • Topology: non-zero 2D skyrmion number in layers with well-defined Néel chirality; near-zero in middle layers with uniform wall direction. 3D topological charge over closed surfaces is discussed but ill-defined for non-continuous media; dependence on cocoon position/extent analyzed in Supplementary. - DG multilayers (X1=2.0 nm, S=0.1 nm, Y=1.0 nm, N=13, M=15): • After different initializations, MFM and simulations reveal coexistence of columnar 3D stripes (worms) and skyrmionic cocoons; two distinct MFM contrasts correspond to tubes/stripes (strong contrast) and cocoons (weaker contrast). Smallest features reach sub-100 nm at 0 mT. • Tilted-field evolutions: at increasing OOP field, 3D stripes narrow and cocoons proliferate, forming alternating stripes and cocoon chains; at ~350 mT (sim., ~275 mT exp.), stripes transform into skyrmion tubes while cocoons persist; at ~400 mT, strong PMA layers align uniformly and remaining tubes convert to two cocoons (one per gradient block). Simulations often show vertical alignment of cocoons across SG blocks. - Electrical detection and phase mapping: • OOP field (θ=0°): Rxx shows nucleation of cocoons near ~325 mT (state I), leading to increased in-plane components and a negative contribution to Rxx (given negative RAMR, RSMR). As field decreases to 0 mT, Rxx continues decreasing, with coexistence of 3D worms and cocoons (state II). For negative fields, 3D worms vanish leaving only cocoons (state III) before saturation. • Rxy (θ=0°): derivative highlights phase boundaries. Near ~+75 mT a jump indicates nucleation in strong PMA layers (narrow walls, negligible in Rxx); above this field the DG hosts only cocoons in the SG blocks (state I). For negative fields, simulations place the cocoon-only regime between approximately −350 mT and −475 mT, ending near a small derivative peak around −300 mT. • Across multiple field angles (30°, 60°, 90°), simulated transport curves, using micromagnetic mx,my,mz without fit parameters, agree with experiments within a few mΩ. At 0 mT, tilted-field demagnetizations yield states with 3D stripes and cocoons for 30°/60°, and stripes only for 90°. - Practical attributes: skyrmionic cocoons are stabilizable at distinct vertical locations (per SG block), coexist with columnar textures even at remanence, and can be made sub-100 nm. Their presence can be inferred via accessible magneto-transport, not only by advanced 3D imaging.

The work demonstrates that engineering vertical gradients of magnetic properties in Pt/Co/Al multilayers stabilizes a new 3D magnetic texture—skyrmionic cocoons—addressing the challenge of realizing and detecting 3D spin textures in scalable thin-film systems. Micromagnetic simulations elucidate their internal structure, layer-resolved chirality, and absence of Bloch points, distinguishing them from torons. The coexistence of cocoons with 3D stripes and skyrmion tubes and their selective stabilization in different vertical blocks show controllable 3D texture architectures. The strong correlation between simulated and measured magneto-transport enables identification of magnetic phases and transitions (uniform, cocoon-only, and cocoon+worm regimes), validating magnetoresistance as a practical probe for 3D textures. These findings are relevant for 3D spintronic devices where the third dimension encodes information and offers new operational degrees of freedom.

By introducing thickness gradients in magnetic multilayers, the authors discover and characterize skyrmionic cocoons—vertically confined, sub-100 nm 3D textures that can coexist with and transform from columnar textures. Combining MFM and micromagnetic simulations with magneto-transport yields consistent identification of their morphology, chirality, and phase evolution under field, enabling electrical detection. The multilayer platform allows positioning cocoons at distinct z-levels (per gradient block) and tailoring their confinement, suggesting 3D memory concepts encoding information via cocoon number and vertical position. Future directions include: tuning confinement by varying thickness steps; stacking more gradient blocks for multiple addressable vertical positions; elucidating detailed transition mechanisms between 3D textures; and employing advanced 3D imaging (e.g., laminography) to resolve full magnetization distributions.

- The definition and computation of a rigorous 3D topological charge are ill-defined in this discretized, non-continuous multilayer medium; only layer-wise 2D skyrmion numbers are unambiguously evaluated. - MFM primarily senses stray fields from top layers, limiting direct experimental verification of vertical alignment and detailed depth profiles (advanced 3D imaging like laminography is needed). - The exact mechanisms and nature of transitions between stripes, tubes, and cocoons remain to be fully elucidated. - Transport modeling neglects minor contributions (ordinary Hall, GMR, PHE, THE); residual discrepancies of a few mΩ indicate model simplifications and experimental uncertainties. - Simulations rely on effective parameters and discretization (though mesh refinement checks were performed), and thermal/nucleation protocols may influence specific field thresholds.