Skyrmionic Cocoons in Magnetic Multilayers

• Skyrmionic cocoons are ellipsoidal 3D magnetic solitons confined to select layers in chiral multilayers, featuring a reversed-magnetization core with finite vertical extent.
• They are stabilized by spatial variations in magnetic anisotropy and Dzyaloshinskii–Moriya interaction, resulting in nontrivial 2D skyrmion numbers per penetrated layer without Bloch points.
• Advanced imaging methods like MFM and soft X-ray tomography, alongside micromagnetic simulations, validate their unique structure and promise for 3D spintronic device integration.

A skyrmionic cocoon is a three-dimensional (3D), ellipsoidal topological magnetic soliton confined within a subset of layers inside a chiral magnetic multilayer. In contrast to columnar skyrmion tubes—which span the entire multilayer thickness with an approximately constant cross-section—a skyrmionic cocoon exhibits a reversed-magnetization core that is vertically truncated: its core extends over only a finite fraction of the stack, resulting in a characteristic ellipsoidal geometry with typical lateral diameters of 50–130 nm and heights corresponding to 5–7 layers out of 13 in experimental systems. Cocoons are stabilized by spatial variation in the magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI) across the multilayer, ensuring vertical confinement of the skyrmion-like texture. Their topological nature is characterized by a nontrivial 2D skyrmion number in each penetrated layer, but in contrast to other 3D solitons like bobbers, cocoons are devoid of Bloch points at their terminations. State-of-the-art experimental techniques, including magnetic force microscopy (MFM) and soft X-ray vector tomography, have directly visualized the 3D structure and internal spin topology of skyrmionic cocoons, revealing features such as their chirality, vertical misalignment, and ability to pair laterally due to dipolar interactions. Theoretical frameworks within the generalized Skyrme model and micromagnetic simulations underpin their energetic stabilization and provide insight into their role as building blocks for 3D topological magnetism in spintronic devices (Grelier et al., 2022, Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026, Gudnason et al., 2014).

1. Physical Structure and Stabilization

Skyrmionic cocoons arise as vertically confined, ellipsoidal 3D magnets within metallic multilayers engineered for spatially modulated interfacial DMI and perpendicular magnetic anisotropy (PMA). Their geometry emerges from the competition between exchange energy, DMI, uniaxial anisotropy, the Zeeman effect, and magnetostatic (dipolar) energy:

$$E_\text{total} = \int_V \big[A(\nabla \mathbf{m})^2 + D\,\mathbf{m}\cdot(\nabla\times\mathbf{m}) - K_u(z)\,m_z^2 - \mu_0 M_s\,\mathbf{m}\cdot\mathbf{H}_\text{ext}\big]\,dV + E_\text{demag}$$

Here, $A$ is the exchange stiffness ($18\,\text{pJ/m}$), $D$ the DMI constant ($D_s = 2.34\,\text{pJ/m}$ scaled by the local Co thickness $t_\text{Co,\,i}$), $K_u(z)$ the layer-resolved uniaxial anisotropy, and $M_s$ the saturation magnetization ($1.2\,\text{MA/m}$). Gradient engineering is achieved via controlled variation of Co layer thickness $X_i$ across the stack, typically ranging from $1.7\,\text{nm}$ up to $2.3\,\text{nm}$ and back. This anisotropy landscape energetically favors core reversal (skyrmion formation) in central or gradient blocks where PMA is reduced, thus trapping the cocoon to a subset of layers. The resulting cocoon occupies typically 5–7 layers out of 13 in single-gradient stacks, with a lateral diameter $<100\,\text{nm}$ at room temperature (Grelier et al., 2022, Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026).

2. Topological and Micromagnetic Characterization

Cocoons are characterized by their 2D skyrmion number in each horizontal slice:

$$N_\text{sk} = \frac{1}{4\pi}\int m\cdot(\partial_x m \times \partial_y m)\,dx\,dy$$

For every layer crossed by the cocoon, $N_\text{sk} \approx \pm1$, matching the value for a classical skyrmion. Cocoons differ from bobbers and dipole strings by lacking Bloch points at their ends and as their magnetic texture closes within the stack. Micromagnetic simulations (cell size $2\times2\times2\,\text{nm}^3$) confirm the continuous reversal of $m_z$ across the cocoon, its ellipsoidal aspect, and confinement to specific layers at intermediate bias fields (e.g., $\mu_0H \approx 275\,\text{mT}$), with outer layers reverting to uniform $m_z=+1$. The radius $R_i$ where $m_z=0$ vanishes in outer layers for cocoons, demarcating their truncation (Grelier et al., 2022, Chiliquinga-Jacome et al., 21 Jan 2026).

3. Experimental Realization and Imaging

Metallic multilayers for cocoon stabilization are typically of the type:

• Single-Gradient Stack: $\mathrm{SiO}_2|$Ta(5 nm)|Pt(3 nm)|[Co $X_i$/Al(1.4 nm)/Pt(3 nm)]$_{i=1\dots13}$, with $X_i$ stepped as described.
• Aperiodic Gradient Stack: [Pt/Co/Al] × 121 trilayer with Co thickness $t_\text{Co}$ steered “up” over 15 bottom layers, constant in the central block, then “down” over 15 top layers.

Magnetic force microscopy (MFM) at room temperature distinguishes cocoons from tubes by their reduced stray field: tubes produce strong-contrast signals, while cocoons yield weaker, gray-level dots, correlating with their vertical localization beneath the multilayer surface. Soft X-ray holography, using HERALDO and Fourier-transform holography (FTH) at the Co $L_3$ edge, maps the out-of-plane magnetization with $\lesssim 15$ nm lateral and $\sim30$ nm tomographic resolution, directly visualizing vertically confined cocoons, their lateral dimensions (FWHM at $300$ K: $50$–$130$ nm), and vertical misalignment. X-ray contrast intensity scales with cocoon occupancy fraction, enabling discrimination between single, paired, and columnar cocoons or skyrmions (Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026).

4. Tomographic Reconstruction and 3D Mapping

Vector tomography using HERALDO enables full 3D reconstruction of the cocoon spin structure. This method relies on acquiring multiple XMCD projections under variable sample tilt, extracting three orthogonal components of $\mathbf{m}$ via differential processing with extended reference slits. The reconstruction algorithm (based on Donnelly et al., New J. Phys. 20, 083009 (2018), as implemented in MAGTOPY) minimizes $\sum_j \|p_j - \mathcal{P}_j\{\mathbf{m}\}\|^2$ over all angles, imposing $|\mathbf{m}|=1$.

Resolution analysis by Fourier shell correlation (FSC) confirms $\sim30$ nm real-space resolution in all axes. Tomography reveals the vertical fraction of the film occupied by cocoons ($\sim30$\%) and direct measurements of chirality: most cocoons show a Néel-type in-plane flux closure, in agreement with micromagnetic theory. Vertical misalignments in paired cocoons are typically a few nanometers, attributed to local grain pinning (Chiliquinga-Jacome et al., 21 Jan 2026).

5. Interactions, Evolution, and Magneto-Transport Detection

Field and temperature cycling modulate cocoon nucleation, growth, and coupling. As the perpendicular magnetic field is decreased from positive saturation, cocoons nucleate sequentially in gradient blocks ($\mu_0H\approx280\,\text{mT}$), grow in diameter ($D$ up to $120$ nm near zero field), and can “pair” horizontally due to attractive dipole-dipole interactions (dipolar energy minimization). Paired cocoons at different block heights generate a near-doubling of X-ray contrast.

Magneto-resistive measurements in Hall bar geometries (20 µm × 100 µm) quantitatively track cocoon and tube evolution. The resistivity model,

$$R_{xx} = R_{xx}^0 + R_\mathrm{SMR}\,m_y^2 + R_\mathrm{AMR}\,m_x^2$$

$R_{xy} = R_{xy}^0 + R_\mathrm{AHE}\,m_z$

combined with 3D micromagnetic simulation outputs, enables the electrical detection and distinction of cocoons from tubes (fitting data within a few mΩ). This direct electrical observability underscores their potential in spintronic device applications (Grelier et al., 2022).

6. Theoretical Context: Skyrmionic Cocoons in Field Theory

Beyond micromagnetics, skyrmionic cocoons correspond to 3D Skyrmions localized inside lower-dimensional host solitons in generalizations of the Skyrme model. Analytical work formalizes their emergence as “baby-Skyrmions” on domain walls, or as sine-Gordon kinks confining Skyrmion charge inside vortices. Twisted vortex rings (vorton-like, stabilized by the sixth-order term in the Skyrme Lagrangian) provide a continuum analogy for closed, finite-radius cocoons. In each case, their stability requires balance between kinetic, Skyrme (fourth-order), and higher-derivative (sixth-order) terms and, where necessary, a small symmetry-breaking potential. The 3D topological charge (baryon number) decomposes as the product of vortex (or domain wall) and kink (or baby-Skyrmion) charges (Gudnason et al., 2014).

7. Implications and Prospects

The 3D depth-resolved, element-specific imaging of skyrmionic cocoons validates the theoretical concept of vertically confined, topologically nontrivial magnetic solitons in engineered multilayers (Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026). Their chirality, confinement, and misalignment sensitivities indicate pronounced dependence on local growth and anisotropy profiles, making them versatile for multilayer device engineering. Their direct electrical and tomographic signatures, as well as the possibility of vertical multiplexing (distinct cocoons at different heights), point toward their integration in racetrack memories, multi-level nonvolatile logic, and devices harnessing 3D topological magnetism.

A plausible implication is that, by developing advanced imaging and tomographic methodologies, it is now possible to directly correlate the micromagnetic textures with their topological invariants and functional device responses, providing experimentally grounded design criteria for future 3D spintronic architectures (Grelier et al., 2022, Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026).