  We present an experimental study of spin-torque driven vortex
self-oscillations in magnetic nanocontacts. We find that above a certain
threshold in applied currents, the vortex gyration around the nanocontact is
modulated by relaxation oscillations, which involve periodic reversals of the
vortex core. This modulation leads to the appearance of commensurate but also
more interestingly here, incommensurate states, which are characterized by
devil's staircases in the modulation frequency. We use frequency- and
time-domain measurements together with advanced time-series analyses to provide
experimental evidence of chaos in incommensurate states of vortex oscillations,
in agreement with theoretical predictions.
