Three-dimensional skyrmionic cocoons in magnetic multilayers

Three-dimensional spin textures are attracting significant interest as potential information carriers in future spintronic devices. The third dimension offers enhanced control over their properties and broader application possibilities. However, their stabilization and characterization in readily implementable systems remain a challenge. Two-dimensional (2D) spin textures, such as magnetic skyrmions (2D whirling magnetization uniform along the vertical axis), have been extensively studied in chiral magnets and magnetic multilayers. Skyrmion tubes, extending along the vertical axis with minor variations, have also been observed in thicker structures. Recently, 3D nanomagnetism and complex textures exhibiting significant thickness-dependent evolution have garnered attention. Examples include magnetic bobbers (skyrmion strings with one end at a surface and the other at an internal point singularity), torons (dipole strings with two Bloch points), and hopfions (observed in magnetic multilayers). Truncated skyrmions, ending abruptly at an interface, have also been reported. Characterizing such 3D textures typically requires advanced techniques like soft X-ray or electron microscopy to probe magnetization depth profiles. This research presents a less demanding alternative, combining magneto-transport measurements with micromagnetic simulations to detect and resolve the magnetization profiles of 3D objects. The use of multilayers is particularly promising for hosting 3D topological textures due to their resilience, scalability, and tunable magnetic properties. By adjusting film thickness and interface properties, magnetic interactions, such as the Dzyaloshinskii-Moriya interaction (DMI), which favors the stabilization of non-collinear textures, can be controlled. This study introduces novel multilayer architectures enabling the stabilization of skyrmionic cocoons, a new type of 3D spin texture with potential for 3D skyrmionic devices.

The paper reviews existing literature on 2D and 3D magnetic textures. It highlights the extensive research on 2D magnetic skyrmions in chiral magnets and multilayers, referencing key studies on their observation and properties. It then delves into the emerging field of 3D nanomagnetism, mentioning theoretical and experimental work on magnetic bobbers, torons, and hopfions. The challenges in characterizing 3D textures using advanced imaging techniques such as X-ray laminography and tomography are also discussed. Finally, it underscores the potential advantages of using magnetic multilayers for stabilizing 3D topological textures due to their tunability and scalability.

To induce the stabilization of 3D magnetic textures, the researchers engineered magnetic multilayers with variable ferromagnetic layer thicknesses. The multilayers consisted of Pt/Co/Al trilayers, with the Co thickness varying across layers to create an uneven distribution of magnetic interactions. Two architectures were investigated: a Single Gradient (SG) multilayer, where the Co thickness increased and then decreased linearly, and a Double Gradient (DG) multilayer, which incorporated two SG blocks separated by layers of constant Co thickness with strong perpendicular magnetic anisotropy (PMA). Micromagnetic simulations using Mumax3 were performed to model the magnetization distribution and the behavior of the textures under different magnetic fields. Magnetic force microscopy (MFM) was employed to experimentally characterize the magnetic textures, providing phase maps that were compared to the simulated MFM images. Magneto-transport measurements, using Hall bar devices, were conducted to probe the electrical properties of the cocoons. A simple model was developed to fit the experimental data, incorporating contributions from spin Hall magnetoresistance (SMR), anisotropic magnetoresistance (AMR), and anomalous Hall effect (AHE). The parameters for this model were obtained through independent experimental measurements. The simulations used realistic micromagnetic parameters, carefully considering the variable layer thicknesses and their impact on exchange, DMI, and anisotropy. The MFM simulations were performed using a realistic lift height. The magneto-transport simulations involved initializing the magnetization with noise and sweeping the magnetic field. For the DG samples, additional steps were taken to enhance nucleation in the strong PMA layers. The micromagnetic simulations provided data on magnetization components (mx, my, mz) used as input for fitting the magneto-transport data. The analysis of the topological properties of the cocoons involved calculations of the 2D skyrmion number in individual layers and considerations of a 3D generalization of the topological charge.

The research identified a new type of 3D magnetic texture, the skyrmionic cocoon, characterized by its ellipsoidal shape and vertical confinement. These cocoons were observed to coexist with conventional tubular skyrmions in the designed multilayers. Micromagnetic simulations accurately reproduced the experimental MFM observations, confirming the shape, size, and density of the observed textures. Simulations revealed that the skyrmion tubes exhibit a counter-clockwise (CCW) Néel chirality in the bottom layers and a clockwise (CW) Néel chirality in the top layers, due to a balance between interfacial DMI and dipolar fields. In contrast, the skyrmionic cocoons lacked Bloch points at their extremities, differing from similar structures like torons. The analysis of topological properties using 2D skyrmion numbers and a 3D topological charge was discussed, but a complete description in the discretized multilayer structure remains challenging. In more complex Double Gradient (DG) multilayers, the coexistence of skyrmionic cocoons and columnar textures (3D stripes or worms) was demonstrated. The MFM and simulations showed that different magnetic initialization procedures (in-plane, out-of-plane, tilted fields) yielded distinct distributions of these textures. The application of an external magnetic field allowed for the controlled manipulation of the textures. At higher fields, 3D stripes transition into skyrmion tubes, whereas the cocoons exhibited greater resilience. Magneto-transport measurements demonstrated the electrical detection of skyrmionic cocoons, exhibiting clear signatures in both longitudinal (Rxx) and transverse (Rxy) resistance. The measured resistances matched remarkably well with predictions from a model incorporating SMR, AMR, and AHE, without requiring fitting parameters. The analysis of Rxx and Rxy curves, along with their derivatives, allowed for the precise identification of different magnetic phases (uniform, cocoons only, cocoons and 3D worms) and the corresponding transitions. The study confirmed that magneto-transport measurements, combined with micromagnetic simulations, provide a powerful tool for detecting and characterizing 3D magnetic objects in multilayers.

The findings demonstrate the successful stabilization and characterization of a novel 3D magnetic texture, the skyrmionic cocoon. The coexistence of cocoons and other textures, such as columnar stripes and skyrmion tubes, highlights the rich phase space in these multilayer systems. The ability to control the distribution and arrangement of these textures through magnetic field application and different multilayer architectures opens promising avenues for the development of 3D spintronic devices. The excellent agreement between experimental measurements (MFM and magneto-transport) and micromagnetic simulations validates the approach and its accuracy in capturing the complex magnetization configurations. The electrical detectability of cocoons makes them attractive candidates for future devices. The potential for designing multi-state memory devices based on the vertical position and number of cocoons is suggested.

This research successfully demonstrated the existence of skyrmionic cocoons, a new type of 3D topological magnetic texture. These structures were shown to coexist with other magnetic textures and are electrically detectable, making them promising candidates for 3D spintronic devices. Future research could explore different multilayer architectures to further tune the properties of skyrmionic cocoons and investigate their potential in memory applications.

The study focused on a specific set of multilayer parameters. A more comprehensive investigation with broader parameter ranges is needed to fully understand the stability and behavior of skyrmionic cocoons. The topological characterization of the cocoons was limited by the discrete nature of the multilayer structure. More advanced 3D imaging techniques would provide a more detailed understanding of the magnetization distribution. The simplified model used for fitting the magneto-transport data may not fully account for all contributing effects, though the agreement is excellent.