  We have studied Josephson tunneling through a circularly polarized micron or
submicron-size disk of a soft ferromagnetic material. Such a disk contains a
vortex that exhibits rich classical dynamics and has recently been proposed as
a tool to study quantum dynamics of the nanoscale vortex core. The change in
the Josephson current that is related to a tiny displacement of the vortex core
has been computed analytically and plotted numerically for permalloy disks used
in experiments. It is shown that a Josephson junction with a magnetic disk in
the vortex state can be an interesting physical system that may be used to
measure the nanoscale motion of the magnetic vortex.
