Skyrmion-number dependence of spin-transfer torque on magnetic bubbles

We theoretically study the skyrmion-number dependence of spin-transfer torque acting on magnetic bubbles. The skymrion number of magnetic bubbles can take any integer value depending on the magnetic profile on its circumference and the size of the bubble. We find that the transverse motion of a bubble with respect to the charge current is greatly suppressed as the absolute value of the skyrmion number departs from unity, whereas the longitudinal motion is less sensitive.