Spontaneous switching dynamics of magnetic soliton structures in two-dimensional spin systems

This research focuses on the nonlinear wave self-excitation in two-dimensional anisotropic ferromagnets. Starting from the Lax pair of the (2+1)-dimensional Heisenberg ferromagnet spin equation, the exact magnetic soliton solutions are successfully obtained by constructing the iterative N-fold Darboux transformation (DT). Building upon these solutions, we identify three critical parameters that govern magnetic state self-switching, enabling transitions between various soliton configurations. According to three key parameters, we propose two practical strategies—localized wave packet control and weak periodic perturbation—for inducing magnetic state transitions and soliton structure conversions. Notably, the weak periodic perturbation presents a dynamic, continuous process capable of both amplification and attenuation. Meanwhile, we also determine the conditions for the generation of this process and analyze the time interval for weak periodic perturbation. Finally, we deeply analyze the core differences between the initial state field, the final state field and the ground state. At the same time, we explore the dependence of the field along the y direction of the channel in the two practical strategies, and verify the dynamic characteristics of the two physical phenomena proposed in this paper through the magnetization structure. These results provide meaningful insights into the control of magnetic states, offering a fresh perspective on the nonlinear dynamics of Heisenberg ferromagnets and laying a theoretical foundation for future advancements in magnetic switching and soliton engineering.