Numerical and analytical investigation of the synchronization of dipolarly coupled vortex spin-torque nano-oscillators

We investigate analytically and numerically the synchronization dynamics of dipolarly coupled vortex based Spin-Torque Nano Oscillators with different pillar diameters. We identify the critical interpillar distances on which synchronization occurs as a function of their diameter mismatch. We obtain numerically a phase diagram showing the transition between unsynchronized and synchronized states and compare it to analytical predictions we make using the Thiele approach. Our study demonstrates that for relatively small diameter differences the synchronization dynamics can be described qualitatively using Adler equation. However, when the diameters difference increases significantly, the system becomes strongly non-Adlerian