Driven dynamic mode splitting of the magnetic vortex translational resonance

A magnetic vortex in a restricted geometry possesses a nondegenerate translational excitation that corresponds to circular motion of its core at a characteristic frequency. For 40-nm thick, micron-sized permalloy elements, we find that the translational-mode microwave absorption peak splits into two peaks that differ in frequency by up to 25% as the driving field is increased. An analysis of micromagnetic equations shows that for large driving fields two stable solutions emerge.