Magnetization oscillations by vortex-antivortex dipoles

A vortex-antivortex dipole can be generated due to current with in-plane spin-polarization, flowing into a magnetic element, which then behaves as a spin transfer oscillator. Its dynamics is analyzed using the Landau-Lifshitz equation including a Slonczewski spin-torque term. We establish that the vortex dipole is set in steady state rotational motion due to the interaction between the vortices, while an external in-plane magnetic field can tune the frequency of rotation. The rotational motion is linked to the nonzero skyrmion number of the dipole. The spin-torque acts to stabilize the vortex dipole at a definite vortex-antivortex separation distance. In contrast to a free vortex dipole, the rotating pair under spin-polarized current is an attractor of the motion, therefore a stable state. Three types of vortex-antivortex pairs are obtained as we vary the external field and spin-torque strength. We give a guide for the frequency of rotation based on analytical relations.