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We introduce a topological gauge vector potential which influences spin waveexcitations over arbitrary non-uniform, slowly moving magnetizationdistribution. The time-component of the gauge potential plays a principal rolein magnetization dynamics, whereas its spatial components can be oftenneglected for typical magnetic nanostructures. As an example, we consider spinmodes excited in the vortex state magnetic dots. It is shown that the vortex/spin wave interaction can be described as a consequence of the gauge fieldarising due to non uniform moving vortex magnetization distribution. Thecoupled equations of motion of the vortex and spin waves are solved withinsmall excitation amplitude approximation. The model yields a giant frequencysplitting of the spin wave modes having non-zero overlapping with the vortexmode as well as a finite vortex mass of dynamical origin.

A topological gauge field in nanomagnets: spin wave excitations over a slowly moving magnetization background