Mutual synchronization of spin-torque oscillators consisting of perpendicularly magnetized free layers and in-plane magnetized pinned layers

TL;DR

This paper theoretically investigates how spin-torque oscillators with perpendicular free layers and in-plane pinned layers synchronize through electrical coupling, revealing conditions for in-phase or antiphase synchronization and identical current-frequency relations.

Contribution

It introduces models for electrical coupling in parallel and series circuits and analyzes synchronization behavior using the Landau-Lifshitz-Gilbert equation.

Findings

In-phase and antiphase synchronization depend on circuit connection

Current-frequency relations are identical to single oscillator case

Synchronization can be achieved through current injection in coupled oscillators

Abstract

A mutual synchronization of spin-torque oscillators coupled through current injection is studied theoretically. Models of electrical coupling in parallel and series circuits are proposed. Solving the Landau-Lifshitz-Gilbert equation, excitation of in-phase or antiphase synchronization, depending on the ways the oscillators are connected, is found. It is also found from both analytical and numerical calculations that the current-frequency relations for both parallel and series circuits are the same as that for a single spin-torque oscillator.