Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model

TL;DR

This paper models arrays of magnetic spin torque oscillators using the Kuramoto model, revealing finite size effects on synchronization, the impact of dipolar coupling limits, and the formation of topological defects affecting collective behavior.

Contribution

It introduces a Kuramoto model-based framework for understanding STO synchronization, highlighting finite size effects and topological defect formation in these systems.

Findings

Synchronization is a finite size effect in STO arrays.

Critical coupling scales with the number of oscillators.

Dipolar coupling limits the maximum synchronized oscillators.

Abstract

The collective dynamics in populations of magnetic spin torque oscillators (STO) is an intensely studied topic in modern magnetism. Here, we show that arrays of STO coupled via dipolar fields can be modeled using a variant of the Kuramoto model, a well-known mathematical model in non-linear dynamics. By investigating the collective dynamics in arrays of STO we find that the synchronization in such systems is a finite size effect and show that the critical coupling-for a complete synchronized state-scales with the number of oscillators. Using realistic values of the dipolar coupling strength between STO we show that this imposes an upper limit for the maximum number of oscillators that can be synchronized. Further, we show that the lack of long range order is associated with the formation of topological defects in the phase field similar to the two-dimensional XY model of ferromagnetism. Our results shed new light on the synchronization of STO, where controlling the mutual synchronization of several oscillators is considered crucial for applications.