Magnetic skyrmions, localized and stable topological magnetic textures, exhibit particle-like behavior when stimulated externally. Their motion control using spin-polarized currents has opened avenues for skyrmionic devices like racetrack memory and neuromorphic computing. The coexistence of skyrmions with high topological charges within a single system further enhances potential technological applications. Skyrmion stabilization occurs through two primary mechanisms: short-range interactions (e.g., in chiral magnets, stemming from the interplay between Heisenberg exchange and Dzyaloshinskii-Moriya interaction), and long-range dipolar interactions competing with short-range exchange interactions in thin ferrimagnetic films with perpendicular magnetic anisotropy. While chiral magnets often exhibit skyrmions with Q = -1, some systems demonstrate skyrmion bundles and bags of arbitrary charge, theoretically and experimentally. However, these systems typically require cryogenic temperatures, and their fabrication methods may hinder industrial scalability. Dipolar-stabilized skyrmions in thin ferrimagnetic films offer a room-temperature, readily accessible fabrication method using magnetron sputtering. By tuning material parameters like saturation magnetization and anisotropy constant, the coexistence of skyrmions (Q = -1), type-II bubbles (Q = 0), and antiskyrmions (Q = 1) has been previously observed. Studies on high-order antiskyrmions, featuring extra Bloch and Néel wall iterations, are limited, and their size often exceeds typical dipolar-skyrmion dimensions. This work focuses on the direct observation and characterization of small, dipolar-stabilized skyrmions and antiskyrmions of arbitrary topological charge at room temperature, paving the way for new applications.

The literature extensively covers topological magnetic textures with particle-like properties, quantifiable by their topological charge Q. Integer Q values signify topologically protected structures, with magnetic skyrmions (SKs) being a prominent example. SK stabilization mechanisms include short-range interactions in chiral magnets (competing Heisenberg exchange and Dzyaloshinskii-Moriya interaction), resulting mostly in Q = -1 SKs, and the competition between long-range dipolar and short-range exchange interactions in thin ferrimagnetic films with perpendicular magnetic anisotropy. The latter allows for room-temperature fabrication and stability, offering advantages over chiral magnets. Previous work has demonstrated the coexistence of SKs (Q=-1), type-II bubbles (Q=0), and ASKs (Q=1) in such systems, and even a rare Q=2 ASK in Fe/Gd multilayers. Theoretical descriptions of additional Bloch and Néel wall segments in dipolar-stabilized hard magnetic bubbles are scarce. While similar structures (VBLs) were reported in bubble domain materials, their size was significantly larger. This paper builds upon this prior work by directly observing and characterizing small, room-temperature stable high-order SKs and ASKs with arbitrary topological charge.

The study employed a series of [Co(0.2 nm)/Ni(0.7 nm)]n multilayers (n = 4–11) deposited on Si(100) substrates and Si3N4 membranes for Lorentz transmission electron microscopy (LTEM). Magnetic properties were characterized using superconducting quantum interference device – vibrating sample magnetometry (SQUID-VSM), yielding saturation magnetization (Ms) values. Ferromagnetic resonance (FMR) measurements determined uniaxial magnetic anisotropy (K) values. LTEM imaging, performed at room temperature, was sensitive to in-plane magnetic induction, revealing the magnetic textures. Magnetic induction maps were generated by solving the transport-of-intensity equation. Micromagnetic simulations, using the GPU-accelerated code magnum.np, were performed to model the magnetic configurations, topological charge calculation, energy dependence on topological charge and external field, and current-induced motion. The simulations considered demagnetization, exchange, uniaxial magnetic anisotropy, and external field energy contributions. A crucial aspect was the selection of an appropriate cell size in the simulations to resolve vertical Bloch lines (VBLs) accurately. Current-driven motion simulations utilized the Zhang-Li model to incorporate spin-transfer torque effects. The stability phase diagrams were generated by varying M_s and K_u while keeping other parameters constant in the simulations. The SK Hall angle was calculated from the final positions of SKs and ASKs after a current pulse.

The study directly observed dipolar-stabilized skyrmions (SKs) and antiskyrmions (ASKs) with topological charges ranging from Q = -5 to 5 in Co/Ni multilayers at room temperature. Higher-order SKs and ASKs, distinguished from SK bags or bundles in chiral magnets, were observed and characterized. These high-order (A)SKs are enclosed by a single domain boundary, containing an arbitrary number of Bloch and Néel segments. The energy of (A)SKs generally increases with increasing topological charge, with SKs and ASKs of the same |Q| having nearly identical energies. A variety of high-order (A)SKs were found to coexist. The size of these objects increases with topological charge, but remains below 500 nm. Experimentally, SKs and ASKs with |Q| up to 6 were observed by LTEM, while Extended Data Fig 4 shows |Q| values up to 10. The symmetry of ASKs in LTEM contrasts is one order higher than their topological charge. Micromagnetic simulations revealed that high-order spin objects nucleate from domain walls containing VBLs, with the topological charge depending on the number of VBLs. A stability phase diagram was created based on the saturation magnetization (Ms) and uniaxial magnetic anisotropy (Ku), showing a clear parameter range where high-order (A)SKs are stable, with the magnetic quality factor Ku/Ka (Ku/(0.5µ0Ms^2)) around 1 being crucial. Current-driven motion simulations demonstrated that the SK Hall effect is reduced with increasing topological charge, providing a route to minimize this effect in future skyrmionic devices. The decay of topological charge, observed in both experimental and simulation data, showed a preference for odd number decay for SKs.

The findings directly address the research question of observing and characterizing high-order SKs and ASKs at room temperature. The observation of these structures with topological charges up to 10, significantly larger than previously reported, expands the understanding of topological spin textures and their stability. The room-temperature stability and simple fabrication method make this system particularly promising for technological applications. The coexistence of a large number of different spin objects opens up possibilities for unconventional computing applications like reservoir computing, which can benefit from the nonlinear interactions of diverse spin objects. The reduction of the SK Hall effect with increasing topological charge is significant for future skyrmionic devices, as it allows for more efficient control of their movement. The nucleation process from domain walls with VBLs provides insights into the formation mechanism of these high-order structures.

This work presents the first observation of high-order skyrmions and antiskyrmions with topological charges up to 10 in Co/Ni multilayers at room temperature. These structures are stable, readily fabricated, and exhibit tunable properties. Their coexistence within the same system offers potential for advanced computing architectures. The demonstrated current-driven motion with reduced SK Hall effect paves the way for efficient skyrmionic devices. Future research may focus on exploring the limits of topological charge, detailed theoretical understanding of energetic stability, and the development of specific applications leveraging the unique properties of these high-order spin textures.

While the study successfully demonstrates the existence and properties of high-order skyrmions and antiskyrmions, there are some limitations. The precise classification of some complex spin objects remained challenging due to limitations of the LTEM technique. Further theoretical studies are needed to fully understand the energy landscape and dynamic behavior of these high-order structures. The simulations employed an effective temperature-dependent material parameter approach, which might not capture all aspects of thermal fluctuations. This warrants further study. More detailed characterization is required to elucidate the roles of material parameters, in particular the impact of different layers and their thickness on the formation of high order spin objects.