Collaborations between the partners in the 3D MAGiC project have resulted in the combined use of micromagnetic modelling, experimental magnetic imaging of skyrmions using Lorentz microscopy and off-axis electron holography and calculations of electron optical phase images. Such a correlative approach has allowed for the direct and efficient discovery of novel magnetic spin structures and the prediction of their properties. Together with instrumentation development, these synergistic cooperations between the project partners have resulted in the discovery of topologically-stable magnetic solitons and the investigation of their dynamic properties.
An example of the synergetic collaboration between the partners is the establishment of fully quantitative agreement between experimental and theoretical magnetic contrast observed using off-axis electron holography. The success of this cooperative work has been achieved by the systematic study of different non-trivial magnetic textures using both electron microscopy and advanced numerical methods in micromagnetic software. The ability to obtain quantitative agreement between experiment and theoretical modeling has resulted in the discovery of magnetic skyrmion braids and antiskyrmions in FeGe, as well as in the development of an understanding of the physical properties of samples prepared by focused ion beam milling, which have been shown to have damaged surface layers whose magnetic properties differ from the internal volumes of the same samples. Even though the thickness of this damaged layer is only a few nanometers, its presence affects the energy balance significantly and is highly relevant for geometrically-confined samples of small size. When studying hopfion rings, a specific magnetic field protocol as employed for their nucleation, which was highly dependent on the shape and size of the sample. Currently, an enhanced nucleation protocol is being developed that will enable the study of hopfion rings in larger samples. This advancement opens new possibilities for investigating both dynamic properties and interactions of hopfion rings. It which will be assisted by the use of current pulses, in order to increase the probability of hopfion ring nucleation. It may also facilitate the nucleation of other topological textures, such as heliknotons - hopfions that re embedded and stabilized within a helical spin spiral state. Hopfion formation in other magnetic systems will also be explored, for example to realise their formation under ambient conditions that are suitable for technological applications.
The study of thermal skyrmion diffusion in geometrically-confined elements has led to the experimental demonstration of a simple three-terminal device that is capable of spatially-multiplexed Brownian reservoir computing using a magnetic skyrmion as an information carrier. Six different two-input Boolean functions were demonstrated in this device after appropriate training of the output weights. Three-input logical operations were also shown. As a result of excitations by thermal fluctuations, little additional electrical energy is needed to drive the device. Such a device can be trained to recognize human hand gestures (e.g. push, swipe left, right, no action) encoded in the form of range-Doppler radar data. This simple, energy-efficient device, made from a single topological magnetic quasiparticle in confinement, already outperforms energy-intensive software-based neural networks.
Whereas multi-local electrical readout of 3D magnetic quasiparticles should ultimately be implemented in non-conventional computing applications, readout is presently performed using magnetic imaging for flexibility. By following the trajectories of up to hundreds of, e.g. magnetic skyrmions using Kerr microscopy, huge amounts of video data are recorded and need to be analysed. A convolutional neural network has been developed and trained to automatically extracts the position and sizes of such nanoparticles, while suppressing defects, structural boundaries and imaging artefacts. This tool and the image dataset use in training has been made publicly available via Zenodo. In a step towards efficient and meaningful electrical readout, it has been demonstrated that collective 4-skyrmion dynamics in such a structure can be coarse grained, indicating optimized positions to locate readout contacts.
Beyond conventional thin film multilayers, two-dimensional materials have been explored. Ferromagnetic skyrmionic bubbles have been observed in the van der Waals magnet Fe5GeTe2 up to room temperature, opening the door to potential applications of this material class.
The experimental discovery of a new effect, the current-induced interlayer Dzyaloshinskii-Moriya interaction, is an important step towards nucleating and manipulating three-dimensional magnetic solitons. Interlayer Dzyaloshinskii-Moriya interaction favours non-collinear, chiral alignment of adjacent layers in a multilayer stack. Whereas the previously discovered static interlayer Dzyaloshinskii-Moriya interaction was realised by structural in-plane symmetry breaking, which is not well understood and cannot be controlled once the material is deposited, the new current-induced effect demonstrates tuning in time and position by directing electrical currents in patterned leads on a sample. This effect is expected to be a game changer for exploring three-dimensional magnetic textures with local control. Layered synthetic antiferromagnets, consisting of pairwise antiferromagnetically coupled ferromagnetic layers, have been investigated as a new class of multilayer systems to host three-dimensional magnetic textures. Magnetic skyrmions in such multilayers show ten-times-increased mobility due to the mutual compensation of topological damping. When not only the magnetization but also anisotropy in a synthetic antiferromagnet is compensated, room-temperature-stable homochiral merons, antimerons and coupled pairs of these, called bimerons, can be realized. More complicated three-dimensional structures are also able to form in these layers, as a result of the formation of vertical spin spirals, providing the first step towards more complex spin structures that vary in all three directions in space.
The use of hopfion spin structures in three dimensions for unconventional computing has also been explored. Theoretical calculations of hopfions and how to use magnon scattering from them for meta-learning have been performed. The dynamics of hopfios in all directions in space and encoding information in the frequency distribution of magnon scattering has been explored, in order to realize a meta-learning device, with the aim of using three-dimensional spin structures for unconventional computing.
A demonstration of energy-efficient opto-magnetic neural networks is planned for the future, including the development of an understanding of the path to realise the most energy-efficient computational approaches.
