A vortex-antivortex (VA) dipole may be generated due to a spin-polarized current flowing through a nano-aperture in a magnetic element. We study the vortex dipole dynamics using the Landau-Lifshitz equation in the presence of an in-plane applied magnetic field and a Slonczewski spin-torque term with in-plane polarization. We establish that the vortex dipole is set in steady state rotational motion. The frequency of rotation is due to two independent forces: the interaction between the two vortices and the external magnetic field. The nonzero skyrmion number of the dipole is responsible for both forces giving rise to rotational dynamics. The spin-torque acts to stabilize the vortex dipole motion at a definite vortex-antivortex separation distance. We give analytical and numerical results for the angular frequency of rotation and VA dipole features as functions of the parameters.
تحميل البحث