  The development of future spintronic applications requires a thorough and
fundamental understanding of the magnetisation dynamics. Of particular interest
are magnetic nanodisks, in which the vortex state emerges as a stable spin
configuration. Here, we focus on how the vortex core polarisation can be
reversed periodically by an oscillating magnetic field, applied perpendicularly
to the disk's surface. By means of micromagnetic simulations, we demonstrate
the presence of several subharmonic switching modes, i.e., the commensurate
ratio between the switching frequency of the core and the driving frequency.
The underlying mechanism of this periodic behaviour depends on the disk
thickness. For thin disks, the core switches periodically due to resonant
excitation of radial spin wave modes, while it is due to the breathing mode in
the case of thick disks. However, overlap of both modes impedes periodic vortex
core switching. For thin disks, the threshold field amplitude required for
periodic switching can be lowered to about 30~mT by increasing the disk
diameter. For thick disks, in contrast, the minimal field is largely unaffected
by the disk diameter, as only the energy density of a central region around the
vortex core is relevant to excite the breathing mode. Our results contribute to
the understanding of the switching mechanisms in magnetic nanodisks, which are
of technological interest due to their potential in non-volatile memory
devices.
