  In a vortex-state magnetic nano-disk, the static magnetization is curling in
the plane, except in the core region where it is pointing out-of-plane, 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 has
recently been demonstrated experimentally,raising fundamental interest for
potential application in magnetic storage devices. Here we demonstrate coherent
control of p by single and double microwave pulse sequences, taking advantage
of the resonant vortex dynamics in a perpendicular bias magnetic field.
Optimization of the microwave pulse duration required to switch p allows to
experimentally infer the characteristic decay time of the vortex core in the
large oscillation regime. It is found to be more than twice shorter than in the
small oscillation regime, raising the fundamental question of the non-linear
behaviour of magnetic dissipation.
