  We investigate the dynamics of a magnetic vortex driven by spin-transfer
torque due to spin current in the adiabatic case. The vortex core represented
by collective coordinate experiences a transverse force proportional to the
product of spin current and gyrovector, which can be interpreted as the
geometric force determined by topological charges. We show that this force is
just a reaction force of Lorentz-type force from the spin current of conduction
electrons. Based on our analyses, we propose analytically and numerically a
possible experiment to check the vortex displacement by spin current in the
case of single magnetic nanodot.
