Magnetic Skyrmion Interacting with Optical Skyrmion

Magnetic skyrmions (MSks) and optical skyrmions (OSks) embody topology in matter and in light, respectively. Here we investigate the interaction between a single MSk and an OSk beam. Three distinct nonlinear dynamical modes are identified: rotation, skipping, and trochoidal motion. By decomposing the optical driving force into gradient, orbital-angular-momentum, and spin-angular-momentum contributions, we clarify their respective roles of radial confinement, azimuthal drift, and precessional modulation. The skipping motion arises from the azimuthal asymmetry of the OSk beam and exhibits spatial selectivity originating from the magnetization-polarization coupling between the MSk and OSk. In three dimensions, the coupling acquires a propagation-dependent phase dominated by the differential Gouy phase, which yields $z$-asymmetric skipping trajectories. These results bridge topological particles and topological fields within a unified framework, offering helicity-selective and phase-programmable routes to optomagnonic control.