Magnetic topological textures could serve as powerful tools in the development of next-generation spintronics devices, especially in terms of stability and energy consumption. Two-dimensional (2D) magnetic solitons such as chiral domain walls or skyrmions were mostly under focus for the last decade. Beyond these 2D textures, a new interest has risen for more complex quasi-particles that display variations over the thickness, i.e., three-dimensional (3D) objects. Examples include different skyrmion phases [1], bobbers [2] or even hopfions [3]. In this work, we show how by engineering Pt/Co/Al based multilayers with variable Co thickness, we observe the signature of new textures, called skyrmionic cocoons [4] that are only present in a fraction of the magnetic layers. Interestingly, these cocoons can coexist with more standard ‘tubular’ skyrmions going through all the multilayer as evidenced by the existence of two very different contrasts in the magnetic force microscopy (MFM) images recorded at room temperature (Fig. 1a). Moreover, the field dependence of skyrmionic cocoons has also been studied with Fourier transform holography measurements (FTH) with similar observations (Fig. 1b). FTH additionally puts forward various magnetic phase transitions as well as the existence of an attractive interaction between cocoons. The presence of these novel skyrmionic textures has also been investigated by micromagnetic simulations (Fig. 1c). The relaxed states can easily be identified with the different experimental contrasts: the columnar skyrmion tubes (resp. cocoons) corresponds to the strong contrast (resp. weak contrast). Thus, this coexistence of various magnetic textures in multilayers and the discovery of a novel magnetic texture are particularly interesting as they can open new paths for three-dimensional spintronics. 
**References** [1] A.O. Mandru et al. Nature communications 11,1 (2020)
[2] F. Zheng et al. Nature Nanotechnology 13, 451 (2018)
[3] N. Kent et al. Nature communications 12, 1 (2021)
[4] M. Grelier et al. arXiv: 2205.01172 (2022). 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/b8a97625e75c0927f841711b49e2982a.png)

Skyrmionic 3D cocoons in magnetic multilayers

In the fields of magnetism and spintronics, magnetic multilayers continue to thrive as pivotal structures to functionalize magnetic interactions, including the interfacial Dzyaloshinskii-Moriya interaction (DMI), and to engineer complex non-trivial spin textures [1-3]. However, previous research has focused almost exclusively on 2D structures. The challenge in studying 3D textures is in obtaining the necessary spatial resolution and sensitivity to resolve them. Here we show that this challenge can be met by reference-aided coherent diffractive x-ray imaging combining the robust Fourier Transform Holography with phase retrieval algorithms [4,5]. Based on this amplified wide-angle scattering, we achieve 5 nm spatial resolution for spin textures in Pt/Co/Cu magnetic multilayers, which allows us to clearly resolve fine domain walls (Fig.1c). Surprisingly, while conventional low-resolution images only show the well-known stripe domain state characteristic of such multilayers, our high-resolution images additionally reveal several small, mostly circular features of much weaker contrast (Fig. 1a,b), indicating a reduced net magnetization in the out-of-plane direction. Interestingly, while these features are clearly magnetic in nature and interact with the domain walls, they do not annihilate at the largest fields available in our system (220 mT). We associate the features to a localized increased surface roughness, leading to a local loss of perpendicular magnetic anisotropy promoting in-plane spin alignment and of 3D magnetic textures.

Revealing 3D Magnetic Textures in [Pt/Co/Cu]15 Multilayers by Coherent X ray Imaging with 5 nm Resolution

Fluctuations are ubiquitous in nanometer-scale systems, spanning orders of magnitude in space and time. Real-space access to fluctuating states is impeded by a dilemma
between spatial and temporal resolution. Averaging over an extended period of time (or repetitions) is key for the majority of high-resolution imaging experiments, especially in weak
contrast systems. If, by lack of better knowledge, averaging is indiscriminate, it leads to a loss of temporal resolution and to motion-blurred images. We present coherent correlation imaging (CCI) – a high-resolution, full-field imaging technique that realizes multi-shot, time-resolved imaging of stochastic processes. The key of CCI is
the classification of camera frames that correspond to the same physical state (Fig. 1) even at low photon count, where imaging is not possible. CCI combines a correlation-based similarity
metric with powerful classification algorithm developed for genome research [1] realizing informed, non-sequential signal averaging while maintaining single frame temporal resolution. We apply CCI to study previously inaccessible magnetic fluctuations in a highly degenerate magnetic stripe domain state. Our material is a Co-based chiral ferromagnetic multilayer with
magnetic pinning low enough to exhibit stochastically recurring dynamics that resemble thermally-induced Barkhausen jumps near room temperature. CCI reconstructs sharp, high-contrast
images of all domain states by phase retrieval [2] and, unlike previous approaches, also tracks the time when these states occur. The spatiotemporal imaging reveals an intrinsic transition
network between the states and unprecedented details of the magnetic pinning landscape (Fig. 2). 
**References** 
[1] G. Sherlock, et. al., Current Opinion in Immunology 12, 201-205 (2000)
[2] Flewett, S. et al., Optics Express 20, 29210–29216, 2012 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/575255bbb0f7b8891a22722531593fa6.png) 
Principle of time-resolved coherent correlation imaging. Top: Sequence of camera frames showing Fourier-space coherent scattering patterns. Coherent correlation imaging classifies
scattering frames by their underlying domain state, as indicated by the colors. Bottom: Real-space images reconstructed from an informed average of same-state frames. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/c06609f11a71267f63b9f1a35eff95c7.png) 
Map of attractive (blue dots) and repulsive (red areas) pinning sites. The background shows the position of the domain walls and their relative occurrence observed in the experiment.

Coherent Correlation Imaging: Resolving fluctuating states of matter

Fluctuations are ubiquitous in magnetically and charge ordered systems. Spanning multiple orders of magnitude in space and time, they often lead to a wealth of fascinating physical effects. Recent examples of such dynamics are fluctuations of spin- and charge density waves in antiferromagnets [1], diffusion-like motion of magnetic skyrmions in low pinning magnetic multilayer or spontaneous fluctuations between ordered stripe and skyrmion lattices phases [2]. High-resolution real-space imaging can resolve the spatial information. However, due to insufficient signal on a timescale faster than the relevant dynamics, averaging over an extended period of time (or repetitions) is key for the majority of high-resolution imaging experiments. So far, averaging has been performed blindly and continuously, leading to a trade-off between extracting either spatial or temporal information, especially in weak contrast systems. Here, we present coherent correlation imaging (CCI) – a high-resolution, full-field imaging technique that realizes multi-shot, time-resolved imaging of stochastic processes. The key of CCI is the classification of camera frames that correspond to that same physical state by combining a correlation-based similarity metric with powerful classification algorithm developed for nanoparticle tomography and genome research (see Fig. 1) [3]. CCI extends these algorithms to the temporal domain, realizing informed, non-sequential signal averaging while maintaining single frame temporal resolution. CCI does not require prior knowledge of the imaged system, rendering it the first time-resolved x-ray imaging technique capable of accessing systems with entirely unknown dynamics. To develop and demonstrate CCI, we study thermal hopping of magnetic domain walls – a prototypical example of stochastic nanometer-scale dynamics – on timescales ranging from sub-seconds to hours under equilibrium conditions. Our material is [Pt (2.7 nm)/Co60Fe20B20 (0.8 nm)/MgO (1.5 nm)]15, a chiral ferromagnet with magnetic pinning low enough to exhibit stochastically recurring dynamics that resemble thermally induced Barkhausen jumps near room temperature [4]. Imaging is performed through Fourier-transform x-ray holography with contrast provided by the x-ray magnetic circular dichroism [5]. CCI reconstructs sharp, high-contrast images of all domain states and, unlike previous approaches, also tracks the time when these states occur (see Fig. 2). This uniquely reveals not only the occupation probabilities of all states, but further, the complex network of stochastic transition trajectories between states. The full potential of this technique will manifest at the next generation of pulsed high-coherence x-ray sources, where it promises to resolve a wealth of previously hidden dynamic processes, such as the nucleation dynamics of externally-induced phase transitions and the intrinsic fluctuations of weakly pinned textures in spin and charge ordered systems.

**References:**

[1] - Shpyrko, O. G. et al. Direct measurement of antiferromagnetic domain fluctuations. Nature 447, 68–71 (2007) [2] - Seaberg, M. H. et al. Nanosecond X-Ray Photon Correlation Spectroscopy on Magnetic Skyrmions. Physical Review Letters 119, 067403 (2017) [3] - Eisen, M. B. et al. Cluster analysis and display of genome-wide expression patterns. Proceedings of the National Academy of Sciences 95, 14863–14868 (1998) [4] - Lemesh, I. et al. Current-Induced Skyrmion Generation through Morphological ThermalTransitions in Chiral Ferromagnetic Heterostructures. Advanced Materials 30, 1805461 (2018) [5] - Eisebitt, S. et al. Lensless imaging of magnetic nanostructures by X-ray spectro-holoraphy. Nature 432, 885–888 (2004)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/02c68b10457f8b0b09df682b3321c147.jpg)
Figure 1| Single-frame correlation and single-frame imaging. a, CCI two-time correlation 
analysis showing the similarity between the states recorded at different times. b, Cross-section of the two-time correlation function at t2 = 28 s (red line in (a)). The colored shades define frames that correspond to the same physical state of the system. c, Image corresponding to the blind average of all frames. High-contrast regions indicate stationary behavior of the local out-of-plane magnetization mz, while seemingly semi-transparent features correspond to a superposition of two different magnetic states. d,e, Images obtained by selectively averaging the blue and yellow shaded regions in (b), respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/d7e9df838294c2b83f25a91cbc1552ab.jpg)
Figure 2| CCI-resolved dynamics in our sample. a, Real-space images of all domain states. Field of view is 720 nm in diameter. b, Temporal evolution of the states. The horizontal axis indicates the measurement time. The vertical axis shows which state has existed at the given time.

Coherent Correlation Imaging: High-resolution imaging of stochastic dynamics INVITED

Magnetic skyrmions are long-lived topological excitations in a small subset of magnetic materials, including some heavy-metal / ferromagnet multilayers with strong interfacial spin-orbit interactions. Skyrmions are a rare example of a compact, unbound, and switchable topological state of matter. Here, “compact” means that each skyrmion is confined to a very small area of the sample. Thanks to this property, even micrometer-sized samples can host a very large number of such topological objects and thereby acquire a very large topological charge. “Unbound” means that skyrmions, unlike vortices or hedgehogs, can exist without their topological counterpart, the antiskyrmion. In fact, skyrmions are often found in pure form, such as ordered (crystalline) or disordered (amorphous) arrays. These dense skyrmion states can be considered a topological phase, with the order parameter being the topological charge. Finally, “switchable” means that, due to the discrete nature of the lattice, skyrmions can be nucleated and annihilated, leading to a change of the global topological charge. Switching from a topological trivial state to a skyrmion state is a topological phase transition. Such a phase transition requires the overcoming of strong energy barriers—the same energy barriers that also allow skyrmions to exist at room temperature [1]. Topological phase transitions are therefore expected to be of first order, with a transition dynamic characterized by slow and heterogeneous nucleation, as known, e.g., from the freezing of water. In fact, heterogeneous nucleation is the underlying principle of electrical skyrmion nucleation, which crucially relies on material defects to break the translational symmetry [2]. Surprisingly, however, we find picosecond homogeneous nucleation of an extended topological phase, comprising a dense array of nanometer-scale magnetic skyrmions, after a single femtosecond laser pulse in metallic ferromagnetic multilayers. Lorentz transmission electron microscopy and skyrmion Hall effect measurements confirm that only skyrmions, and not antiskyrmions, are nucleated by the light pulse, even in an achiral Pt/Co/Pt material. This presentation will focus on the nucleation dynamics of this all-optical topological phase transition, which we were able to follow in real time during the early user operation of beamline SCS at the European XFEL [3]. Using time-resolved small angle x-ray scattering, we discovered that rapid, homogeneous nucleation of the skyrmion phase is mediated by a previously undisclosed transient fluctuation state. This state, which is characterized by high spatial frequency magnetic fluctuations, persists for approximately 100 ps after exciting our magnetic multilayer with a femtosecond, infrared laser pulse. The topological phase emerges from these fluctuations by nucleation and coalescence, a mechanism that goes beyond existing theories of topological phase transitions such as the Kibble–Zurek mechanism and the Berezinskii–Kosterlitz–Thouless transition. The process is completed on a time scale of 300 ps. Using atomistic spin dynamics simulations, we confirm that the fluctuation state is key to the ultrafast increase of the global topological charge, enabled by an almost complete elimination of the topological energy barrier in this transient state of matter.

**References:**

[1] F. Büttner, I. Lemesh, and G. S. D. Beach, Theory of isolated magnetic skyrmions: From fundamentals to room temperature applications. Scientific Reports 8, 4464 (2018). [2] F. Büttner, I. Lemesh, M. Schneider, B. Pfau, C. M. Günther, P. Hessing, J. Geilhufe, L. Caretta, D. Engel, B. Krüger, J. Viefhaus, S. Eisebitt, and G. S. D. Beach, Field-free deterministic ultrafast creation of magnetic skyrmions by spin–orbit torques. Nature Nanotechnology 12, 1040 (2017). [3] F. Büttner, B. Pfau, M. Böttcher, M. Schneider, G. Mercurio, C. M. Günther, P. Hessing, C. Klose, A. Wittmann, K. Gerlinger, L.-M. Kern, C. Strüber., C. von Korff Schmising, J. Fuchs , D. Engel, A. Churikova, S. Huang, D. Suzuki, I. Lemesh, M. Huang, L. Caretta, D. Weder, J. H. Gaida, M. Möller, T. R. Harvey, S. Zayko, K. Bagschik, R. Carley, L. Mercadier, J. Schlappa, A. Yaroslavtsev, L. Le Guyarder, N. Gerasimova , A. Scherz, C. Deiter, R. Gort, D. Hickin, J. Zhu, M. Turcato, D. Lomidze, F. Erdinger, A. Castoldi, S. Maffessanti, M. Porro, A. Samartsev, J. Sinova, C. Ropers, J. H. Mentink, B. Dupé, G. S. D. Beach, and S. Eisebitt, Observation of fluctuation-mediated picosecond nucleation of a topological phase. Nature Materials 20, 30 (2021).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/32457bd794a7357a1245dc6e188b51db.jpg)
Magnetic state of the sample before (left) and after (right) exposure with a single fs laser pulse. The circle (1.5 µm diameter) indicates our field of view. Black (white) indicates magnetization pointing up (down).

![](https://assets.underline.io/uploads/markdown_image/1/image/97b56242ca4e46e74620e4de652ae946.jpg)
Schematic of the process of all-optical topological switching. Starting with a uniform state (1), the sample is heated to a transient fluctuations state (2) by the laser. The fluctuations remove the topological energy barrier and allow skyrmion seeds to nucleate. The final state (3) is a skyrmion state obtained after coalescence and growth of the skyrmion nuclei.

 Colossal Topological Hall Effect at the Transition Between Isolated and Lattice-Phase Interfacial Skyrmions

EOD: Skyrmions II

technical paper

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Skyrmionic 3D cocoons in magnetic multilayers

Revealing 3D Magnetic Textures in [Pt/Co/Cu]15 Multilayers by Coherent X ray Imaging with 5 nm Resolution

Coherent Correlation Imaging: Resolving fluctuating states of matter

Coherent Correlation Imaging: High-resolution imaging of stochastic dynamics INVITED

Colossal Topological Hall Effect at the Transition Between Isolated and Lattice-Phase Interfacial Skyrmions

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