Stress-induced modification of gyration dynamics in stacked double-vortex structures studied by micromagnetic simulations

V Iurchuk,A M Deac,L Körber,J Lindner,J Faßbender,A Kákay

doi:10.1088/1361-6463/ac2333

Abstract

In this paper, using micromagnetic simulations, we investigate the stress-induced frequency tunability of double-vortex nano-oscillators comprising magnetostrictive and non-magnetostrictive ferromagnetic layers separated vertically by a non-magnetic spacer. We show that the relative orientations of the vortex core polarities p 1 and p 2 have a strong impact on the eigen-frequencies of the dynamic modes. When the two vortices with antiparallel polarities have different eigen-frequencies and the magnetostatic coupling between them is sufficiently strong, the stress-induced magnetoelastic anisotropy can lead to the single-frequency resonant gyration mode of the two vortex cores. Additionally, for the case of parallel polarities, we demonstrate that for sufficiently strong magnetostatic coupling, the magnetoelastic anisotropy leads to the coupled vortex gyration in the chaotic regime and to the lateral separation of the vortex core trajectories. These findings offer a path for achieving a fine control over gyration frequencies and trajectories in vortex-based oscillators via adjustable elastic stress, which can be easily generated and tuned electrically, mechanically or optically.

Highlights

The ground state of nanoscale circular magnetic disks of certain geometric aspect ratios is a spontaneously forming stable vortex configuration with circulating in-plane magnetization and a vortex core pointing out-of-plane
We show that, when the two vortices with anti-paralel polarities have different eigen-frequencies and the magnetostatic coupling between them is sufficiently strong, the stress-induced magnetoelastic anisotropy can lead to the single-frequency gyration mode of the two vortex cores
Simulations details In this paper, we report on the simulations of the vortex dynamics in double-vortex structure in the presence of magnetostatic coupling and stress-induced magnetoelastic anisotropy

Summary

Introduction

The ground state of nanoscale circular magnetic disks of certain geometric aspect ratios is a spontaneously forming stable vortex configuration with circulating in-plane magnetization and a vortex core pointing out-of-plane. It was shown both theoretically [13] and experimentally [14] that introducing an additional magnetoelastic anisotropy term to the vortex core dynamics leads to the softening of the restoring force constants and to the gyrotropic frequency decrease This enables the stress-induced controlling of the vortex eigen-frequency e.g. via bending of the flexible membranelike substrate [14], an application of an electric field to the piezoelectric substrate [15,16] or even using optically generated deformation of photostrictive materials [17,18]. For the case of parallel vortex core polarities, the stress-induced magnetoelastic anisotropy affects considerably the resonant frequencies and the vortex core gyration trajectories leading to the stochastic dynamics of the magnetostaically coupled vortex pair These findings offer a frequency tunability of double-vortex-based oscillators via elastic stress, which can be generated and controlled electrically, mechanically, or optically. We show that in such double-vortex structure, the resonance frequencies of the individual and coupled modes, which in general are defined by the vortex polarities and the spacer thickness (i.e. magnetostatic coupling strength), can be modified by introducing the magnetoelastic energy Kσ

Results and discussion

Conclusions and outlook

Acknowle dgments