Interaction-Induced Spiral Motion and Breathing Dynamics of Neel Skyrmions in Ferromagnetic Thin Films

Abstract

Magnetic skyrmions exhibit particle-like stability and rich dynamical behaviour arising from their topological nature, making them promising building blocks for future spintronic devices. In this work, we investigate the interaction dynamics of two Neel-type skyrmions in an ultrathin ferromagnetic film through a combined analytical and numerical approach. Full micromagnetic simulations reveal that when the initial separation exceeds twice the skyrmion radius, the pair undergoes a repulsive interaction leading to an outward spiral trajectory whose radial and angular components depend sensitively on the Gilbert damping, consistent with particle-like models of skyrmion motion. The simulations further show a two-component oscillatory behaviour in the out-of-plane magnetization: a fast intrinsic breathing mode superimposed on a slower interaction-induced modulation. Using Thiele collective-coordinate model, an expression for the radial drift, angular decay, and logarithmic growth of the separation distance is derived. The analytical predictions show excellent agreement with numerical results, confirming the exponential form of the long-range interaction potential. A continuum micromagnetic analysis of the skyrmion tail explains the origin of the exponential decay and its role in governing the interaction strength. Together, these findings provide a unified framework for understanding spiral motion, breathing dynamics, and long-range repulsion in interacting skyrmion systems, offering insights relevant for multi-skyrmion information carriers and collective skyrmion-based devices.