From chaos to selective ordering of vortex cores in interacting mesomagnets

Magnetic vortex: fundamental physics, developments, and device applications

A magnetic vortex is one of the fundamental and topologically nontrivial spin textures in condensed matter physics. Magnetic vortices are usually the ground states in geometrically restricted ferromagnets with zero magnetocrystalline anisotropy. Magnetic vortices have recently been proposed for use in a variety of spintronics applications due to their resistance to thermal perturbations, flexibility in changing core polarity, simple patterning procedure, and potential uses in magnetic data storage with substantial density, sensors for the magnetic field, devices for logic operations, and other related fields. The data storage and computing capabilities of vortex-based devices are highly integrated and energy-efficient, with low drive current requirements. Thus, a comprehensive understanding ranging from basic physics to real-world applications is necessary to realize these devices. This article provides an overview of the recent developments in our knowledge of magnetic vortices and computing and data storage technologies that are based on them. This thorough analysis aims to advance knowledge and awareness of the possibilities of vortex-based spintronic devices in modern technologies.

Ultrastrong magnon-magnon coupling and chiral spin-texture control in a dipolar 3D multilayered artificial spin-vortex ice

Strongly-interacting nanomagnetic arrays are ideal systems for exploring reconfigurable magnonics. They provide huge microstate spaces and integrated solutions for storage and neuromorphic computing alongside GHz functionality. These systems may be broadly assessed by their range of reliably accessible states and the strength of magnon coupling phenomena and nonlinearities. Increasingly, nanomagnetic systems are expanding into three-dimensional architectures. This has enhanced the range of available magnetic microstates and functional behaviours, but engineering control over 3D states and dynamics remains challenging. Here, we introduce a 3D magnonic metamaterial composed from multilayered artificial spin ice nanoarrays. Comprising two magnetic layers separated by a non-magnetic spacer, each nanoisland may assume four macrospin or vortex states per magnetic layer. This creates a system with a rich 16N microstate space and intense static and dynamic dipolar magnetic coupling. The system exhibits a broad range of emergent phenomena driven by the strong inter-layer dipolar interaction, including ultrastrong magnon-magnon coupling with normalised coupling rates ofΔ f ν = 0.57 , GHz mode shifts in zero applied field and chirality-control of magnetic vortex microstates with corresponding magnonic spectra.

Dzyaloshinskii-Moriya-Interaction-Like Behavior in Confined Permalloy Nanostructures via Coupled Magnetic Vortices

Dzyaloshinskii-Moriya interaction (DMI), one of antisymmetric exchanges, originates from the combination of low structural symmetry and large spin-orbit coupling and favors magnetization rotations with fixed chirality. Herein, this work reports a DMI-like behavior in permalloy via coupled vortices in confined structures. Under the in-plane magnetic fields, continuous reversals of different coupled vortices are directly observed by in situ Lorentz transmission electron microscopy, and reproduced by complementary micromagnetic simulations. The statistical results show that coupled vortices with opposite chirality appear more frequently with the frequency up to about 60%. Such an asymmetric phenomenon mainly arises from a DMI-like behavior, associated with the increased total energy difference between different ground-state coupled vortices. Moreover, in the reversal process, the junction between disks accelerates the annihilation of vortices moving toward it and is also the starting point of vortex nucleation. These results provide an effective method to generate a DMI-like behavior in magnetic systems with symmetry breaking surface and benefit the future development of vortex-based spintronic devices.

Ballistic Hall Photovoltammetry of Magnetic Resonance in Individual Nanomagnets

We report on ballistic Hall photovoltammetry as a contactless probe of localized spin excitations. Spins resonating in the near field of a two-dimensional electron system are shown to induce a long range electromotive force that we calculate. We use this coupling mechanism to detect the spin wave eigenmodes of a single ferromagnet of sub-100 nm size. The high sensitivity of this detection technique, 380 spins/sqrt[Hz], and its noninvasiveness present advantages for probing magnetization dynamics and spin transport.

Magnonic crystals: towards terahertz frequencies

This topical review presents an overview of the recent experimental and theoretical attempts on designing magnonic crystals for operation at different frequencies. The focus is put on the microscopic physical mechanisms involved in the formation of the magnonic band structure, allowed as well as forbidden magnon states in various systems, including ultrathin films, multilayers and artificial magnetic structures. The essential criteria for the formation of magnonic bandgaps in different frequency regimes are explained in connection with the magnon dynamics in such structures. The possibility of designing small-size magnonic crystals for operation at ultrahigh frequencies (terahertz and sub-terahertz regime) is discussed. Recently discovered magnonic crystals based on topological defects and using periodic Dzyaloshinskii-Moriya interaction, are outlined. Different types of magnonic crystals, capable of operation at different frequency regimes, are put within a rather unified picture.

Collective modes in three-dimensional magnonic vortex crystals

Collective modes in three-dimensional crystals of stacked permalloy disks with magnetic vortices are investigated by ferromagnetic resonance spectroscopy and scanning transmission X-ray microscopy. The size of the arrangements is increased step by step to identify the different contributions to the interaction between the vortices. These contributions are the key requirement to understand complex dynamics of three dimensional vortex crystals. Both vertical and horizontal coupling determine the collective modes. In-plane dipoles strongly influence the interaction between the disks in the stacks and lead to polarity-dependent resonance frequencies. Weaker contributions discern arrangements with different polarities and circularities that result from the lateral coupling of the stacks and the interaction of the core regions inside a stack. All three contributions are identified in the experiments and are explained in a rigid particle model.

Nanoscale switch for vortex polarization mediated by Bloch core formation in magnetic hybrid systems

Vortices are fundamental magnetic topological structures characterized by a curling magnetization around a highly stable nanometric core. The control of the polarization of this core and its gyration is key to the utilization of vortices in technological applications. So far polarization control has been achieved in single-material structures using magnetic fields, spin-polarized currents or spin waves. Here we demonstrate local control of the vortex core orientation in hybrid structures where the vortex in an in-plane Permalloy film coexists with out-of-plane maze domains in a Co/Pd multilayer. The vortex core reverses its polarization on crossing a maze domain boundary. This reversal is mediated by a pair of magnetic singularities, known as Bloch points, and leads to the transient formation of a three-dimensional magnetization structure: a Bloch core. The interaction between vortex and domain wall thus acts as a nanoscale switch for the vortex core polarization.

Magnetic vortices in thin ferromagnetic films possess a core with out-of-plane magnetization whose polarity can be manipulated by magnetic fields or currents for technological applications. Here, the authors demonstrate local control of the core polarity in NiFe films via an imprinted maze domain pattern.

Asymmetry in Time Evolution of Magnetization in Magnetic Nanostructures

Strong interest in nanomagnetism stems from the promise of high storage densities of information through control of ever smaller and smaller ensembles of spins. There is a broad consensus that the Landau-Lifshitz-Gilbert equation reliably describes the magnetization dynamics on classical phenomenological level. On the other hand, it is not so evident that the magnetization dynamics governed by this equation contains built-in asymmetry in the case of broad topology sets of symmetric total energy functional surfaces. The magnetization dynamics in such cases shows preference for one particular state from many energetically equivalent available minima. We demonstrate this behavior on a simple one-spin model which can be treated analytically. Depending on the ferromagnet geometry and material parameters, this asymmetric behavior can be robust enough to survive even at high temperatures opening simplified venues for controlling magnetic states of nanodevices in practical applications. Using micromagnetic simulations we demonstrate the asymmetry in magnetization dynamics in a real system with reduced symmetry such as Pacman-like nanodot. Exploiting the built-in asymmetry in the dynamics could lead to practical methods of preparing desired spin configurations on nanoscale.

Magnetization reversal using excitation of collective modes in nanodot matrices

The large arrays of magnetic dots are the building blocks of magnonic crystals and the emerging bit patterned media for future recording technology. In order to fully utilize the functionalities of high density magnetic nanodots, a method for the selective reversal of a single nanodot in a matrix of dots is desired. We have proposed a method for magnetization reversal of a single nanodot with microwave excitation in a matrix of magneto-statically interacting dots. The method is based on the excitation of collective modes and the spatial anomaly in the microwave power absorption. We perform numerical simulations to demonstrate the possibility of switching a single dot from any initial state of a 3 by 3 matrix of dots, and develop a theoretical model for the phenomena. We discuss the applicability of the proposed method for introducing defect modes in magnonic crystals as well as for future magnetic recording.

Higher order vortex gyrotropic modes in circular ferromagnetic nanodots

Magnetic vortex that consists of an in-plane curling magnetization configuration and a needle-like core region with out-of-plane magnetization is known to be the ground state of geometrically confined submicron soft magnetic elements. Here magnetodynamics of relatively thick (50–100 nm) circular Ni₈₀Fe₂₀ dots were probed by broadband ferromagnetic resonance in the absence of external magnetic field. Spin excitation modes related to the thickness dependent vortex core gyrotropic dynamics were detected experimentally in the gigahertz frequency range. Both analytical theory and micromagnetic simulations revealed that these exchange dominated modes are flexure oscillations of the vortex core string with n = 0,1,2 nodes along the dot thickness. The intensity of the mode with n = 1 depends significantly on both dot thickness and diameter and in some cases is higher than the one of the uniform mode with n = 0. This opens promising perspectives in the area of spin transfer torque oscillators.

Magnetic vortex based transistor operations

Transistors constitute the backbone of modern day electronics. Since their advent, researchers have been seeking ways to make smaller and more efficient transistors. Here, we demonstrate a sustained amplification of magnetic vortex core gyration in coupled two and three vortices by controlling their relative core polarities. This amplification is mediated by a cascade of antivortex solitons travelling through the dynamic stray field. We further demonstrated that the amplification can be controlled by switching the polarity of the middle vortex in a three vortex sequence and the gain can be controlled by the input signal amplitude. An attempt to show fan-out operation yielded gain for one of the symmetrically placed branches which can be reversed by switching the core polarity of all the vortices in the network. The above observations promote the magnetic vortices as suitable candidates to work as stable bipolar junction transistors (BJT).

Propagation of magnetic vortices using nanocontacts as tunable attractors

Magnetic vortices in thin films are in-plane spiral spin configurations with a core in which the magnetization twists out of the film plane. Vortices result from the competition between atomic-scale exchange forces and long-range dipolar interactions. They are often the ground state of magnetic dots, and have applications in medicine, microwave generation and information storage. The compact nature of the vortex core, which is 10-20 nm wide, makes it a suitable probe of magnetism at the nanoscale. However, thus far the positioning of a vortex has been possible only in confined structures, which prevents its transport over large distances. Here we show that vortices can be propagated in an unconstrained system that comprises electrical nanocontacts (NCs). The NCs are used as tunable vortex attractors in a manner that resembles the propelling of space craft with gravitational slingshots. By passing current from the NCs to a ferromagnetic film, circulating magnetic fields are generated, which nucleate the vortex and create a potential well for it. The current becomes spin polarized in the film, and thereby drives the vortex into gyration through spin-transfer torques. The vortex can be guided from one NC to another by tuning attractive strengths of the NCs. We anticipate that NC networks may be used as multiterminal sources of vortices and spin waves (as well as heat, spin and charge flows) to sense the fundamental interactions between physical objects and fluxes of the next-generation spintronic devices.

Wave modes of collective vortex gyration in dipolar-coupled-dot-array magnonic crystals

Lattice vibration modes are collective excitations in periodic arrays of atoms or molecules. These modes determine novel transport properties in solid crystals. Analogously, in periodical arrangements of magnetic vortex-state disks, collective vortex motions have been predicted. Here, we experimentally observe wave modes of collective vortex gyration in one-dimensional (1D) periodic arrays of magnetic disks using time-resolved scanning transmission x-ray microscopy. The observed modes are interpreted based on micromagnetic simulation and numerical calculation of coupled Thiele equations. Dispersion of the modes is found to be strongly affected by both vortex polarization and chirality ordering, as revealed by the explicit analytical form of 1D infinite arrays. A thorough understanding thereof is fundamental both for lattice vibrations and vortex dynamics, which we demonstrate for 1D magnonic crystals. Such magnetic disk arrays with vortex-state ordering, referred to as magnetic metastructure, offer potential implementation into information processing devices.