Pt/Co/Al Chiral Multilayers: Skyrmionic Cocoons

• Pt/Co/Al chiral multilayers are engineered magnetic stacks exhibiting confined, ellipsoidal skyrmionic cocoons with distinct topological spin textures.
• The stabilization arises from graded ferromagnetic layer thickness and modulated anisotropy that balance exchange, DMI, and dipolar energies.
• Advanced imaging and simulation techniques confirm these 3D spin configurations, which hold promise for multi-level spintronic information encoding.

A skyrmionic cocoon is a three-dimensional (3D), ellipsoidal, topologically nontrivial spin texture stabilized within magnetic multilayers featuring a spatially modulated ferromagnetic layer thickness. Unlike full skyrmion tubes—which extend through the entire stack—skyrmionic cocoons are spatially confined in the vertical (out-of-plane) direction to only a subset of layers, creating an internal region with reversed magnetization surrounded by a flux-closure surface. Their existence is a direct manifestation of the competition between exchange, Dzyaloshinskii–Moriya (DMI), uniaxial anisotropy, and dipolar energies, further mediated by engineered inhomogeneity in anisotropy and layer thickness. These objects are distinguished by their unique geometry and topological properties, their coexistence with conventional skyrmionic textures, and their potential impact for multi-level spintronic information encoding (Grelier et al., 2022, Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026).

1. Definition, Structure, and Physical Origin

Skyrmionic cocoons are 3D magnetization textures characterized by a closed surface region of reversed core spins wrapping around an inner axis, forming an ellipsoidal or tubular morphology that is truncated along the film's normal. The spins orient in a vortex-like fashion within the interior, leading to a flux-closure (Néel-type) configuration around the core. The core is confined to central regions of the multilayer; this spatial restriction arises because the local energy landscape, shaped by gradients in layer thickness and magnetic anisotropy, destabilizes skyrmion tubes near the surfaces, resulting in "cocoon" formation within energetically favorable gradients (Grelier et al., 2022, Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026).

Topologically, each horizontal cross-section of a cocoon exhibits a 2D skyrmion number $N_{\text{sk}}$,

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

with $N_{\text{sk}} \approx \pm 1$, but the cocoon as a whole does not connect the top and bottom surfaces, and lacks terminal Bloch points (Grelier et al., 2022, Grelier et al., 2023). The vertical extent is typically a fraction of the full thickness, on the order of $5$–$7$ layers of $13$ ($\sim 30\%$), and the lateral diameter is $\sim 100$ nm at room temperature (Grelier et al., 2022, Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026).

2. Micromagnetic Energy Landscape and Theoretical Models

The stabilization of cocoons results from the balanced interplay of the following micromagnetic energy terms: $$E_{\text{total}} = \int_V \left[ A (\nabla m)^2 + D\, m \cdot (\nabla \times m) - K_u(z) m_z^2 - \mu_0 M_s m \cdot H_{\text{ext}} \right] dV + E_{\text{demag}}$$ where $A$ is the exchange constant, $D$ is the DMI constant, $K_u(z)$ is the layer-dependent uniaxial anisotropy, $M_s$ is the saturation magnetization, $H_{\text{ext}}$ is the external field, and $E_{\text{demag}}$ is the magnetostatic energy (Grelier et al., 2022, Chiliquinga-Jacome et al., 21 Jan 2026). Typical parameters: $A = 18$ pJ/m, $M_s = 1.2$ MA/m, $D_s = 2.34$ pJ/m, $K_{u,s} = 1.62$ mJ/m² (Chiliquinga-Jacome et al., 21 Jan 2026).

Cocoons arise when the anisotropy gradient (engineered via Co thickness modulation) yields a region where the skyrmion core is energetically unfavorable near the highest-anisotropy surfaces, confining the chiral core to regions with reduced $K_u$ (Grelier et al., 2022, Chiliquinga-Jacome et al., 21 Jan 2026).

Field-theoretic models, such as those analyzed by Gudnason & Nitta, recast these phenomena in terms of SU(2) Skyrme theory with higher-order (fourth, sixth) derivative terms, supporting stable, localized 3D solitonic configurations when confined by host defects (domain walls, vortices). In general,

$$\mathcal{L} = \frac{f_\pi^2}{16} \operatorname{Tr}(\partial_\mu U^\dagger \partial^\mu U) + \mathcal{L}_4 + \mathcal{L}_6 - V(U)$$

with explicit stabilization achieved through higher-order derivative and symmetry-breaking potential terms (Gudnason et al., 2014).

3. Experimental Realization, Materials Architecture, and Detection

Experimental stabilization of cocoons has used metallic multilayers with engineered thickness profiles. Prototypical architectures include:

Sample Type	Gradient Description	Repeats/Layer Structure
SG (Single-gradient)	$X_1=1.7$ nm, step $S=0.1$ nm to $X_7=2.3$ nm, then back	SiO$_2$
DG (Double-gradient)	SG block, [Co 1.0/Al 1.4/Pt 3]$_{15}$, SG block	Pt 2 instead of Pt 3 in gradient blocks
Aperiodic stack	$t_{\text{Co}}=2.0\to2.5$ nm ($\Delta=0.1$) in bottom 15, 1 nm in 84, $2.5\to2.0$ nm in top 15	[Pt/Co/Al]$_{121}$

(Grelier et al., 2022, Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026)

Imaging and electrical detection methods:

• Magnetic Force Microscopy (MFM): Reveals contrast corresponding to full tubes (strong) and cocoons (weak, grey), with two distinct phase signals at different fields/locations (Grelier et al., 2022, Grelier et al., 2023).
• X-ray Holography (HERALDO, FTH): Resolves the thickness-averaged $m_z$ with lateral resolution down to $\lesssim 15$ nm, and in vector tomography mode down to $\sim 30$ nm spatial resolution; allows direct observation of vertical confinement, lateral size, and pairing phenomena (Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026).
• Magnetoresistive transport: Simultaneous measurement and simulation (via extracted $m_x$, $m_y$, $m_z$ from micromagnetic modeling) of $R_{xx}$ and $R_{xy}$ as function of $H$ reproduce the presence and field-driven evolution of cocoons and tubes in the multilayer (Grelier et al., 2022).

4. 3D Tomographic Imaging and Chirality Determination

Advanced vector tomographic reconstructions using HERALDO provide full 3D maps of the magnetization vector field $\mathbf{m}(x,y,z)$ in these multilayers. By acquiring 58 projections over two perpendicular tilt axes (±45°), all components of $\mathbf{m}$ are reconstructed, subject to the constraint $|\mathbf{m}|=1$ and regularization over a $200 \times 200 \times 200$ voxel volume (diameter ≃936 nm, height ≃234 nm). Resolution analysis by Fourier shell correlation reaches $\sim 30$ nm in all directions (Chiliquinga-Jacome et al., 21 Jan 2026).

Key experimental findings include:

• Lateral size: $\sim 100$ nm diameter, with variability (50–130 nm at 300 K; up to >200 nm at 80 K) (Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026).
• Fractional film occupancy: Cocoons are strictly confined to gradient sections (no extension into central blocks) (Chiliquinga-Jacome et al., 21 Jan 2026).
• Vertical misalignment: Pairs of cocoons in distinct gradient zones are rarely perfectly vertically stacked, showing lateral offsets of several nanometers, likely due to grain pinning (Chiliquinga-Jacome et al., 21 Jan 2026).
• Chirality: The in-plane magnetization shows flux-closure (Néel-type) around each cocoon; the averaged sense of rotation matches micromagnetic predictions for observed field conditions (Chiliquinga-Jacome et al., 21 Jan 2026).

5. Field Dynamics, Pairing Interactions, and Topological Distinctions

Cocoons nucleate at characteristic fields (e.g., $\mu_0 H \approx 280$ mT in the gradient block), with diameter increasing as field decreases, reaching $\sim 120$ nm near zero field (Grelier et al., 2023). Notably, during field cycling, lateral “pairing” of isolated cocoons from different vertical sections is observed; two single-cocoon contrasts in distinct gradient blocks move laterally by $\sim 50$ nm and “lock” into a paired state. This phenomenon is explained by dipolar stray-field energy minimization: $$E_{\text{dip}} = -\frac{\mu_0}{2} \int M(r) \cdot H_{\text{dip}}(r) d^3r$$ when $+z$ and $-z$-pointing caps of distinct cocoons align, reducing surface charge and demagnetizing energy (Grelier et al., 2023). The absence of Bloch points at the truncation boundaries and the robustness of the layer-resolved 2D skyrmion number ($N_{\text{sk}} \approx \pm 1$) distinguish cocoons from 3D bobbers or hopfions (Grelier et al., 2022, Grelier et al., 2023).

6. Theoretical Connections and Generalizations

The mathematical construct of a “skyrmionic cocoon” links to the broader theory of confined or incarnated Skyrmions (Gudnason et al., 2014). In general, a Skyrmion can be confined by a host soliton (domain wall, vortex line, twisted vortex ring), yielding a composite object:

• For a domain wall, the effective action reduces to a “baby-Skyrme” model, supporting a lump localized by the wall, with the total baryon number determined by the moduli on the host soliton.
• For a twisted vortex ring, a cocoon forms as a closed tube with internal twist, stabilized by sixth-order derivatives (BPS extension), with energy and baryon number scaling with the twist and ring size (Gudnason et al., 2014).

This theoretical perspective is consistent with the stabilization and spatial localization of cocoons within multilayer heterostructures, where the magnetic parameters provide the necessary gradient background in which the composite topological texture is confined.

7. Implications for Spintronics and Future Directions

Skyrmionic cocoons, as directly visualized in multilayers, represent a new paradigm for 3D information encoding. Their multi-level spatial organization, vertical misalignment, and controllable chirality offer possibilities for vertically multiplexed spintronic systems, where information is stored not just laterally but across discrete vertical positions in the stack (Grelier et al., 2023, Chiliquinga-Jacome et al., 21 Jan 2026). Detailed understanding of their formation, stability, and interaction with defects is essential for developing advanced racetrack memory, logic, and potential neuromorphic architectures.

Extensions of HERALDO-based vector tomography and advanced micromagnetic modeling enable further studies, including time-resolved dynamics, engineering of other 3D topological textures (e.g., bobbers, hopfions), and the rational design of artificial heterostructures for hosting novel solitonic states.