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.
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