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In a combined theoretical and experimental study, we investigate the critical current densities for vortex domain walls in magnetic nanowires. We systematically determine the critical current densities for continuous motion of vortex walls as a function of the wire width for different wire thicknesses and we find that the critical current density increases monotonously with decreasing wire width. Theoretically we present a mechanism that predicts a threshold current density based on wall transformations and this leads to a scaling of the critical current density ${j}_{c}\ensuremath{\propto}1/\text{width}$. The origin of this scaling is found to be the different dependence of the spin torque energy and the vortex nucleation energy on the wire width and good agreement with the experimental observations is found.

Geometry-dependent scaling of critical current densities for current-induced domain wall motion and transformations