Optimizing magnetodipolar interactions for synchronizing vortex based spin-torque nano-oscillators

Abstract

We report on a theoretical study of the magnetodipolar coupling and synchronization between two vortex-based spin-torque nano-oscillators (STVOs). In this work we study the dependence of the coupling efficiency on the relative magnetization parameters of the vortices in the system. This study is performed in order to propose an optimized configuration of the vortices for synchronizing STVOs. For this purpose, we combine micromagnetic simulations, the Thiele equation approach, and the analytical macrodipole approximation model to identify the optimized configuration for achieving phase-locking between neighboring oscillators. Notably, we compare vortices configurations with parallel (P) core polarities and with opposite (AP) core polarities. We demonstrate that the AP core configuration exhibits a coupling strength about three times higher than in the P core configuration.

Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators

“…To establish a model, we consider a system composed of the two thick layers’ vortices, interacting through the mutual dipolar fields created by their rotating in-plane net magnetizations 29 30 32 50 51 52 53 . Contributions of the out-of-plane components of the magnetization to the coupling are neglected because of the small volume of the vortex cores.…”

“…While the vortex is gyrating, its net in-plane magnetization describes a 360° rotation. To model the dipolar coupling between the two vortices, we consider a simple model of two rotating in-plane macro-dipoles and at the disks’ centre positions 29 30 32 . The interaction energy can then be expressed as:…”

“…Following the approach described in (Ref. 29 , 30 , 32 ) we extracted the effective coupling coefficient μ eff , defined as , as a function of the centre-to-centre distance. The result is presented in Fig.…”

“…To establish a model, we consider a system composed of the two thick layers' vortices, interacting through the mutual dipolar fields created by their rotating in-plane net magnetizations. 29,30,32,[50][51][52][53] Contributions of the out-of-plane components of the magnetization to the coupling are neglected because of the small volume of the vortex cores. Given the large positive current flowing through each pillar, the two vortices have identical chiralities following the direction of the current-induced Oersted field.…”

“…However, these approaches to couple STNOs might be arduous for reaching synchronized states in large arrays of STNOs. Two other strategies have been recently investigated theoretically in order to achieve mutual synchronization of a large number of STNOs, namely the electric coupling by self-modulation of the current flowing through each device 28 and the magnetic coupling between the oscillators arising from the dipolar influence of closely packed STNOs 29 30 31 32 . Our main objective is to propose a complete study combining experimental results and numerical as well as theoretical investigation of the mutual synchronization through dipolar coupling of two adjacent vortex-based STNOs.…”