Topological gauge field in nanomagnets: Spin-wave excitations over a slowly moving magnetization background

We introduce a topological gauge vector potential which influences spin-wave excitations over arbitrary nonuniform, slowly moving magnetization background. The time component of the gauge potential plays a principal role in the magnetization dynamics of typical magnetic nanostructures. As an example, we consider spin modes excited in the vortex-state magnetic dots. The vortex---spin-wave interaction is described as a consequence of the gauge field arising due to the moving vortex magnetization. The approach yields a giant frequency splitting of the spin waves having nonzero overlapping with the vortex background mode as well as a finite vortex mass of dynamical origin.