Three-dimensional (3D) topological magnetic textures, such as skyrmions, vortices, and merons, hold significant promise for spintronic applications due to their exotic properties. While 2D skyrmion dynamics have been extensively studied, particularly concerning spin-transfer torques and spin waves, the dynamics of their 3D counterparts, including skyrmion tubes (SkTs) and chiral bobbers (ChBs), remain largely unexplored, especially under spin-wave excitation. This is a crucial area of research because spin-wave-driven dynamics offer ultralow energy consumption and ease of implementation, particularly in insulating systems, which avoids the high current densities and associated heating issues of current-driven methods. The ability to distinguish between SkTs and ChBs is also challenging, as many imaging techniques only reveal their surface similarities. This paper addresses these gaps by utilizing micromagnetic simulations to investigate the spin-wave-driven dynamics of SkTs and ChBs, aiming to reveal their distinct behaviors and potential for experimental differentiation.

The paper reviews existing literature on topological magnetic textures, highlighting the recent surge in interest in 3D textures like hopfions, torons, and chiral bobbers. It notes the challenges in differentiating SkTs and ChBs using standard magnetic imaging techniques and mentions the potential of X-ray ptychography to resolve their 3D structures. The limitations of electrical manipulation via spin-transfer or spin-orbit torques due to high current densities and heating are discussed, emphasizing the advantages of spin-wave-driven dynamics for low-power applications. Previous work on spin-wave-driven skyrmion dynamics in 2D systems is also reviewed, setting the stage for the current study's focus on 3D textures.

The study employs micromagnetic simulations to model the dynamics of SkTs and ChBs in a thick magnetic film. The simulations solve the Landau-Lifshitz-Gilbert equation, incorporating parameters such as stiffness constant (A), anisotropy constant (K₁), saturation magnetization (Ms), and bulk Dzyaloshinskii-Moriya interaction (DMI) coefficient (D). Spin waves are introduced by an AC magnetic field applied to a thin region of the film. Absorbing boundary conditions are used to avoid reflection at the lateral boundaries, while free boundary conditions are applied to the upper and lower surfaces. The dynamics of topological centers are tracked using a calculation involving the topological density. The simulations explore the impact of varying driving field strength and out-of-plane exchange strength on the motion of both SkTs and ChBs. The penetration length of ChBs is also varied to investigate its influence on the dynamics. The software used is MUMAX3, an open-source micromagnetic simulation tool.

The simulations reveal distinct dynamic behaviors for SkTs and ChBs driven by spin waves. SkTs exhibit a velocity proportional to the driving field power, while ChBs show a threshold in the driving power for motion, linearly dependent on their penetration length. Both SkTs and ChBs display tornado-like dynamics, characterized by a rotation of their topological centers along the thickness direction. The rotation centers form a distorted profile in the y-z plane (perpendicular to the spin-wave propagation direction) for SkTs, a feature absent in ChBs. This distortion is attributed to the non-uniform spin-wave intensity distribution in the thickness direction caused by the bulk DMI, leading to a force imbalance between skyrmions in different layers. The lateral rotation of topological centers is shown to be dissipative in nature and is strongly influenced by the out-of-plane exchange strength, which dictates the attractive interaction between skyrmions in neighboring layers. Finally, the scattering of spin waves by SkTs and ChBs is analyzed, revealing significant deviations from the Rutherford-like scattering pattern predicted for individual Bloch points, highlighting the influence of neighboring skyrmions.

The findings provide crucial insights into the distinct dynamic behaviors of SkTs and ChBs under spin-wave excitation. The threshold behavior observed in ChB motion, directly related to its penetration length, offers a promising avenue for experimental differentiation between SkTs and ChBs. The tornado-like dynamics and the unique scattering patterns observed further enhance the understanding of the interaction between 3D topological magnetic textures and spin waves. The results suggest potential applications in novel spin-wave devices and other spintronics applications.

This study demonstrates spin-wave driven dynamics of 3D topological magnetic textures (SkTs and ChBs), revealing distinct behaviors useful for experimental differentiation. The tornado-like dynamics, driven by non-uniform spin wave intensity due to bulk DMI, and the threshold behavior for ChB motion based on penetration length are key findings. Future research could explore the influence of other material parameters and explore applications in novel spin-wave devices.

The study is based on micromagnetic simulations, which involve inherent approximations and simplifications of real material systems. The influence of temperature and other factors not explicitly included in the model might affect the observed dynamics. Experimental verification of the predicted behaviors is necessary to fully validate the simulation results.