Magnetisation oscillations by vortex-antivortex dipoles

A vortex-antivortex dipole can be generated due to current with in-plane spin-polarisation, flowing into a magnetic element, which then behaves as a spin transfer oscillator. Its dynamics is analysed 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 stabilise the vortex dipole at a definite vortex-antivortex separation distance. In contrast to a free vortex dipole, the rotating pair under spin-polarised current is an attractor of the motion, therefore a stable state. The details of the rotating magnetisation configurations are analysed theoretically and numerically. The asymptotic behaviour of the rotating configurations provide results on their expected stability. Extensive numerical simulations reveal three types of vortex-antivortex pairs which are obtained as we vary the external field and spintorque strength. We give a guide for the frequency of rotation based on analytical relations. (C) 2014 Elsevier B.V. All rights reserved.