Coherence and modality of driven interlayer-coupled magnetic vortices

Abstract

The high-frequency dynamics of mode-coupled magnetic vortices have generated great interest for spintronic technologies, such as spin-torque nano-oscillators. While the spectroscopic characteristics of vortex oscillators have been reported, direct imaging of driven coupled magnetic quasi-particles is essential to the fundamental understanding of the dynamics involved. Here, we present the first direct imaging study of driven interlayer coaxial vortices in the dipolar-and indirect exchange-coupled regimes. Employing in situ highfrequency excitation with Lorentz microscopy, we directly observe the steady-state orbital amplitudes in real space with sub-5 nm spatial resolution. We discuss the unique frequency response of dipolar-and exchange-coupled vortex motion, wherein mode splitting and locking demonstrates large variations in coherent motion, as well as detail the resultant orbital amplitudes. This provides critical insights of the fundamental features of collective vortex-based microwave generators, such as their steady-state amplitudes, tunability and mode-coupled motion.

Spin-Torque and Spin-Hall Nano-Oscillators

“…Frequently, the dimensions of the free layer are such that a magnetic vortex characterized by an in-plane curling of the magnetization with a 10-nm sized out-of-plane vortex core at the center is a stable equilibrium configuration [99]. If so, then the STT will excite the fundamental gyration of the vortex core with frequencies typically less than 2 GHz [100], [101], [61], [62], [102], [103], [104], [105], [106]. However, in a large enough external field, the vortex state will no longer be energetically favorable [107], the magnetization will become more or less uniform, and STT will typically excite highly elliptical clam-shell precession in the case of a free layer magnetized in-plane.…”

Perturbation theory for propagating magnetic droplet solitons

“…Of particular, recent interest is the generation of coherent structures within the magnetization, a vector field describing the magnetic dipole moments of a magnetic material. Coherent structures observed experimentally include those with nontrivial topology such as magnetic vortices Uhlíř et al [2013], Pulecio et al [2014] and skyrmions Nagaosa and Tokura [2013], Fert et al [2013], Yu et al [2014] as well as nontopological droplet solitons Mohseni et al [2013, , Macià et al [2014]. The magnetic droplet soliton (droplet hereafter) is a coherently precessing, nanometer-scale localized wave structure exhibiting strongly nonlinear effects Kosevich et al [1990].…”

Frontiers ofin situelectron microscopy

“…54 In this issue, Li et al present details on in situ measurements of ferroelectric domain switching using in situ biasing, atomic imaging, and displacement mapping. Other methods for probing ferroelectric switching, including off-axis electron holography, are described in References 3 and 14.…”