Mutual Synchronization of Spin-Torque Oscillators within a Ring Array

TL;DR

This study investigates the synchronization behavior of spin-torque nano-oscillator arrays arranged in a ring, analyzing phase patterns, locking ranges, and the effects of current mismatch to inform magnetic device development.

Contribution

It provides a combined numerical and analytical analysis of phase modes and locking ranges in ring-arranged STNO arrays, highlighting the effects of array size and current mismatch.

Findings

Identifies in-phase and out-of-phase modes for N ≥ 6.

Shows locking range depends on array size and separation.

Demonstrates current mismatch induces additional phase shifts.

Abstract

An array of spin torque nano-oscillators (STNOs), coupled by dipolar interaction and arranged on a ring, has been studied numerically and analytically. The phase patterns and locking ranges are extracted as a function of the number $N$, their separation, and the current density mismatch between selected subgroups of STNOs. If $N\geq 6$ for identical current densities through all STNOs, two degenerated modes are identified an in-phase mode (all STNOs have the same phase) and an out-of-phase mode (the phase makes a 2$\pi$ turn along the ring). When inducing a current density mismatch between two subgroups, additional phase shifts occur. The locking range (maximum current density mismatch) of the in-phase mode is larger than the one for the out-of-phase mode and depends on the number $N$ of STNOs on the ring as well as on the separation. These results can be used for the development of magnetic devices that are based on STNO arrays.