Magnetic skyrmions, nanoscale spin textures stabilized by competing magnetic interactions, have shown promise as next-generation computing elements due to their ability to be manipulated by electrical currents. The spin-orbit torque (SOT) generated at heavy metal-ferromagnet interfaces allows for efficient electrical control of skyrmion motion, leading to device proposals utilizing current-driven skyrmion motion in a wire architecture for applications in memory, logic, and synaptic computing. Achieving deterministic, efficient, and high-throughput skyrmion motion is crucial. While initial demonstrations showed impressive speeds, challenges remain regarding intrinsic, extrinsic, and collective effects. One key challenge is the skyrmion Hall effect (SkHE), a transverse deflection caused by the Magnus force acting on the skyrmionic topological charge. SkHE's magnitude, saturation value, and dependence on skyrmion size remain unresolved, with conflicting experimental results. Extrinsic effects, such as material granularity, defects, and interactions with wire edges, also influence skyrmion dynamics. Furthermore, high-throughput devices necessitate much higher skyrmion densities than previously studied, where sparse configurations were examined. This research aims to address these limitations by investigating the ensemble dynamics of densely packed skyrmions in Pt/Co/MgO multilayer wires. Using magnetic force microscopy (MFM), the study examines the motion of individual skyrmions across a wide range of currents and fields, aiming to clarify the interplay between intrinsic properties, extrinsic effects, and collective behavior to establish a robust framework for high-throughput skyrmion motion in wire devices.

The discovery of room-temperature magnetic skyrmions in chiral multilayer films has spurred significant research into their potential for spintronic applications. Early studies demonstrated efficient SOT manipulation and impressive skyrmion speeds. However, the understanding of skyrmion dynamics is far from complete, with unresolved aspects concerning the skyrmion Hall effect (SkHE), extrinsic influences, and the behavior of dense skyrmion arrays. Previous work has explored SkHE's material dependence, saturation, and size dependence, yielding conflicting results. The effects of geometric confinement and disorder on skyrmion motion have also been investigated, showing varying degrees of pinning, annihilation, and expulsion. Finally, most experiments have focused on sparse skyrmion configurations, leaving the behavior of dense arrays largely unexplored. This paper builds upon this existing literature by focusing on the high-density regime and by systematically investigating the influence of skyrmion size, edge effects, and disorder.

The study utilized [Pt(3)/Co(1.2)/MgO(1.5)]₁₅ multilayer films sputtered on Si/SiO₂ substrates and patterned into 2 µm wide wire devices. A custom-designed setup enabled in situ current pulse injection and MFM imaging. Skyrmion configurations were stabilized in the wires, achieving a wide range of densities (2–13 µm⁻²) and sizes (80–200 nm). Current pulses of varying magnitude and polarity were applied, and the motion of individual skyrmions was tracked from sequential MFM images. Over 20,000 instances of skyrmion motion were analyzed, spanning three dynamic regimes: stochastic creep, deterministic creep, and plastic flow. Statistical analysis was employed to quantify skyrmion velocity and angular deflection (SkHE). To investigate the effect of wire geometry, skyrmions were binned by their distance from the wire edge. Similarly, to study the effect of skyrmion size, skyrmions were binned based on their diameter. Micromagnetic simulations and particle model simulations were used to complement experimental findings and explore the underlying mechanisms driving the observed behavior.

The study's key findings demonstrate several crucial aspects of skyrmion dynamics: 1. **High-Speed Skyrmion Motion:** Skyrmion speeds reached up to 24 m/s in the plastic flow regime, demonstrating the potential for high-throughput devices. 2. **Robust Velocity:** Skyrmion velocity showed remarkable robustness to variations in skyrmion size and position within the wire, indicating that the velocity is surprisingly insensitive to disorder and geometric constraints within the plastic flow regime. 3. **Reshaped Skyrmion Hall Effect (SkHE):** The SkHE saturated at approximately 22°, significantly lower than values reported in other studies. The SkHE was strongly reshaped by the proximity to the wire edge, displaying a parabolic profile across the width of the wire. Importantly, SkHE increased weakly with skyrmion size, contradicting theoretical predictions for defect-free rigid skyrmions. 4. **Interplay of Intrinsic and Extrinsic Effects:** Micromagnetic simulations in a grain-free environment showed that the intrinsic SkHE decreased with increasing skyrmion size, while particle model simulations, incorporating disorder, demonstrated that the interplay of intrinsic and pinning-driven effects can explain the experimentally observed weak increase of the SkHE with increasing skyrmion size. Smaller skyrmions were more strongly affected by pinning, reducing their transverse deflection. 5. **Demarcation of Dynamic Regimes:** Clear transitions between stochastic creep, deterministic creep, and plastic flow regimes were identified, enabling a more thorough understanding of skyrmion motion under different driving conditions.

These findings challenge several established notions about skyrmion dynamics in multilayers. The relatively small SkHE magnitude suggests that material design efforts should not solely focus on compensated systems; conventional ferromagnets still hold potential. The weak inelasticity of skyrmion-edge interactions offers opportunities for device design. The influence of material granularity and skyrmion-skyrmion interactions on size effects underscores the need to incorporate these factors into theoretical models. The observed size-dependent behavior of the SkHE indicates that material microstructure can be used as a tuning parameter to tailor skyrmion dynamics in racetrack devices. The individual behavior of skyrmions within dense arrays is promising for applications like stochastic spiking neurons in synaptic computing.

This study provides a comprehensive investigation of skyrmion dynamics in densely packed arrays within multilayer wire devices. The findings highlight the importance of considering both intrinsic and extrinsic factors in predicting and controlling skyrmion motion. The surprisingly high speeds, robustness of velocity, and the unique size and edge dependence of the SkHE pave the way for future high-throughput skyrmion-based devices. Future research should focus on incorporating the observed effects into advanced theoretical models and exploring novel materials for optimizing skyrmion-based technologies.

The study's limitations include the use of a specific material system (Pt/Co/MgO) and a particular wire geometry. The conclusions may not be universally applicable to other materials or device designs. While efforts were made to minimize Joule heating, its potential influence on skyrmion dynamics was not directly quantified. The particle model simulations simplified the complex interactions within the skyrmion array, and a more sophisticated approach might provide further insights.