Synchronization in linear chains of non-identical vortex-based spin-torque oscillators

Abstract

Arrays of interacting oscillators having different individual frequencies can exhibit transitions to synchronization depending on array and individual oscillator parameters. In particular, vortex-based spin-torque nanopillar oscillators have gyrotropic frequencies depending inversely on the free layer disk radius. Here the effect of random distribution of radii on synchronization for chains of oscillators is investigated, since in actual systems of spin torque oscillator’s radii will be non-identical owing to fabrication control limitations. The vortex dynamics of linear chains interacting through the dipolar interaction are modeled by the Thiele equations with the free layer radii given by a random distribution about a mean. It is shown that there are two critical current densities for each chain: first, the onset of synchronized gyrotropic motion of the largest radius free layer oscillator, and second, the loss of synchronization as the individual oscillator amplitudes increase. The second critical current density is strongly dependent on the free layer radii of the particular chain. However, the synchronized frequency only weakly depends on the mean radius of each chain, and it is shown to be practically independent of the radii distribution.