In a vortex-state magnetic nanodisc [1][2][3] , the static magnetization curls in the plane, except in the core region, where it points out of plane 4,5 , either up or down, leading to two possible stable states of opposite core polarity p. Dynamical reversal of p by large-amplitude motion of the vortex core [6][7][8][9] has recently been demonstrated experimentally [10][11][12][13][14] , raising the prospect of practical applications, in particular in magnetic-storage devices
15. Here we demonstrate coherent control of p by singleand double-microwave-pulse sequences, taking advantage of the resonant vortex dynamics in a perpendicular-bias magnetic field 16 . Experimental optimization of the microwave-pulse duration required for switching p also yields information about the characteristic decay time of the vortex core in the largeoscillation regime. This time is found to be less than half the length seen in the small-oscillation regime, suggesting a nonlinear behaviour of magnetic dissipation.Magnetic vortices are topological solitons with rich dynamical properties. The lowest-energy excitation of the vortex ground state is the so-called gyrotropic mode 3 , corresponding to the gyration of the vortex core around its equilibrium position with a frequency in the sub-gigahertz range 17,18 . It is now established experimentally 14 that the excitation of this gyrotropic motion leads to a dynamical distortion of the vortex-core profile, as predicted by micromagnetic simulations and theoretical analysis 8 . This distortion increases with the linear velocity of the vortex core and opposes the core polarity, until the critical velocity V c 1.66γ √ A ex (γ is the gyromagnetic ratio of the magnetic material and A ex its exchange constant) is reached and the vortex-core polarity is reversed 9 . In zero magnetic field, dynamical control of the polarity is difficult owing to the degeneracy of the gyrotropic frequencies associated with opposite polarities p = ±1, which can lead to multiple core switching 7,11 . Still, selective core-polarity reversal is possible using a circularly polarized microwave magnetic field because the sense of the core rotation is linked by a right-hand rule to its polarity 12 . Control of polarity switching can also be achieved by precise timing of non-resonant magnetic-field pulses 13,19 , in a similar fashion as domain-wall propagation in magnetic nanowires 20 . Resonant amplification 21 of the vortex gyrotropic motion enables us to reverse the core polarity with minimum excitation power 12,14,15 , as it enables us to concentrate the energy in a narrow frequency band. In this scheme, the damping ratio is an important parameter because it controls the minimum amplitude of the resonant excitation required to switch the core 9 . Here, it is shown that the damping ratio close to the reversal threshold is significantly larger than that measured in the small-oscillation regime. We associate this with the nonlinear nature of the reversal process 6,8 .