3D tomographic imaging of skyrmionic cocoons using HERALDO

Abstract

Uncovering the rich and intricate characteristics of three-dimensional (3D) magnetic textures is essential for functional materials such as magnetic multilayers, where the delicate balance of various magnetic interactions leads to complex 3D spin arrangements. Among these textures, skyrmionic cocoons-tubular 3D magnetic structures characterized by a closed magnetization surface wrapping around a core-have emerged as particularly intriguing. Stabilized by competing magnetic interactions, these textures reside within a fraction of the thickness of the magnetic material and exhibit a typical lateral size of approximately 100 nm. Here, we present a vector tomographic reconstruction of the 3D magnetization in aperiodic Pt/Co/Al chiral multilayers, where skyrmionic cocoons have been recently reported. Using soft X-ray Holography with Extended Reference by Autocorrelation Linear Differential Operator (HERALDO), we acquire tomographic projections of the magnetic configuration and reconstruct the full 3D magnetization vector field with a spatial resolution of approximately 30 nm, as determined by Fourier shell correlation (FSC). This resolution allows us to observe critical features of the cocoons, such as their vertical misalignment and their overall chirality. Our findings demonstrate that HERALDO-based vector tomography is a powerful approach for revealing the internal structure and vertical extent of these nanoscale magnetic textures, offering new experimental insights into their intrinsic behavior.

Figures (5)

• Figure 1: (a) Thickness distribution for the materials that constitute the sample. The cyan background highlights the section with strong perpendicular magnetic anisotropy which contains NiFe as chemical marker for imaging. (b) Schematic configuration of the HERALDO measurement. Four permanent magnets with magnetization along a radial axis set the field at the sample position, using rotation and distance from the $\theta$ rotation axis. The front magnet is made transparent for clarity. The technical drawing is displayed in Fig. \ref{['FigCOMET']}. The zoom-in scanning electron microscopy image present a typical HERALDO mask seen from the back.
• Figure 2: Normalized imaginary part of the HERALDO image reconstruction. (a) 0$^\circ$ and (b) 24$^\circ$ sample rotation angle and 100 mT OOP field at Co L$_3$-Edge (777.4 eV). The insets correspond to a zoomed-in view of regions hosting magnetic cocoons. The same magnetic objects are highlighted for both rotation angles. (c) Image taken near the Ni L$_3$-Edge (852 eV). The cyan circle surrounds the area shown in (a) and (b).
• Figure 3: (a) Three-dimensional imaging of the double gradient structure. The reconstructed region corresponds to a cylindrical volume of radius 60 voxels $\approx$ 936 nm. The isosurfaces represent $m_z=0$, highlighting domain walls. The color gradient indicates the position of the corresponding feature in $z$. The sample end touching the substrate is displayed in cyan and the opposite end in yellow. The green volume inside features a double cocoon. The magenta and blue cylinders surround artificially joined cocoons. The $z$ dimension was oversampled from 13 to 50 voxels for better visualization, which does not change the features of the reconstruction. (b) Spatial resolution for each component of the magnetization estimated by Fourier shell correlation using the 1/2-bit criteria (dashed line).
• Figure 4: Comparison between three-dimensional tomographic reconstruction and relaxed micromagnetic simulation starting from the reconstructed state. The top row images show the isosurface $m_z=0$ in gray. A section of the reconstructed volume is shown in (a). The zoomed-in volume shows a double cocoon and its magnetization vector field for a given $yz$-plane. After relaxing the reconstructed state, the same region is shown in (b). The normalized sum of the magnetization vector field along $z$ for (c) the reconstructed and (d) relaxed state is depicted following the color wheel. The section of the reconstruction volume in (a) has an oversampling in the $z$ dimension from 14 to 50 voxels for better visualization while no resampling was applied for the zoomed-in region. For the cocoons in (a) and (c), the magnetization vectors are shown for the plane passing through the middle of the cocoons in both cases. The area shown in (c)-(d) corresponds to a circle with radius 780 nm, lower than the simulated state to not consider the edge effects. The simulated state for (d) was subsampled after the relaxation process to match the in-plane pixel dimension of the reconstruction (d).
• Figure 5: Drawings of the COMET endstation in the 3D tomographic imaging configuration. X-rays arrive from the left, the sample holder is shown surrounded by the 4 permanents magnets (Cryostat not used in the experiment). The sCMOS detector is also highlighted.