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Three-dimensional magnetization textures: Discovery and control on the nanoscale

Periodic Reporting for period 2 - 3D MAGiC (Three-dimensional magnetization textures: Discovery and control on the nanoscale)

Reporting period: 2022-01-01 to 2023-06-30

The primary goal of the 3D MAGiC project is the study of the physical properties of intriguing novel magnetic texctures that are referred to as three-dimensional (3D) magnetic solitons. Magnetic solitons are localised in space, emerge in extended magnetic crystals and, to a large extent, behave like classical particles that can move and interact with each other. Their motion, creation and annihilation can be controlled by external stimuli, providing opportunities to use them as information carriers in spintronic devices. Within the framework of this project, the fundamental properties of magnetic solitons are addressed, with the aim of providing guidelines about how to make practical applications feasible.

A major challenge in the study of magnetic solitons is that they are very difficult to detect. Although different methods allow the presence of solitons to be detected, only a few of them have the required resolution to image them directly, while retaining the ability to apply external stimuli. The transmission electron microscope (TEM) is the main tool for the study of magnetic solitons in this project. One of the technical challenges is the need to fine tune the conditions inside the electron microscope. A fundamental issue is that the magnetic states of interest are excitations of the magnetisation vector field that correspond to higher energies of the system. Although similar problems are encountered when studying the physics of elementary particles, the energy levels of magnetic solitons are not as high as for elementary particles. As a result, they have long lifetimes, which allow them to be used in memory devices. The strategy for observing magnetic solitons is different from that used in high-energy physics, where researchers work with stable particles accelerated to high speed and force them to collide and split into smaller entities. In the case of magnetic solitons, a specific protocol is required, involving the careful design of the shape and size of the sample and a suitable choice of external stimuli (e.g. temperature, external magnetic field, electric current or laser excitation).

Earlier research focused on the study of 2D magnetic solitons in thin films and plates of magnetic materials. One of the objectives of the 3D MAGiC project is to study magnetic solitons that can move in all three spatial directions. According to theoretical predictions, the most promising objects are so-called magnetic hopfions, which are topological objects whose stability is increased by the fact that their decay or collapse requires the formation of magnetic singularities, where the locally averaged magnetisation tends to zero.
Experimental magnetic imaging of skyrmions and direct comparisons with theoretical modelling have led to several unexpected observations, including skyrmion braiding and the formation of skyrmionium and skyrmion/antiskyrmion pairs in chiral magnetic FeGe, which was previously only known to host Bloch-type skyrmions and helical structures.

The fabrication and three-dimensional characterisation of FeGe nanostructures that host single Bloch-type skyrmions have revealed the importance of geometry and surface states in isotropic chiral magnets. Tomographic experiments and theoretical modelling have shown that skyrmion structures with magnetic singularities (Bloch points) can be stabilised at well-define values of temperature and magnetic field.

Néel-type skyrmions possess magnetic field distributions that are difficult to study using electron microscopy. However, they can form in sizes down to 10 nm in multilayer heterostructures and can be manipulated using electrical currents. The visibility of Néel-skyrmion in simple Fresnel defocus images has been optimised, allowing for their accurate size determination.

Two-dimensional van der Waals type ferromagnets have been studied using electron magnetic chiral dichroism in the electron microscope. In addition, skyrmionic spin structures in Fe5GeTe have been studied close to room temperature.

Highly complex modifications to scientific instruments have been initiated with the active contribution of all project partners to realise vector magnetic field control of skyrmions under cryogenic conditions in the presence of a highly flexible laser illumination system installed in an aberration-corrected transmission electron microscope. These modifications are essential to stabilise and control unconventional magnetic soliton structures that are predicted theoretically but not yet observed experimentally. A proof-of-principle study has been performed to demonstrate picosecond temporal resolution imaging of magnetization processes in a transmission electron microscope using a delay line detector.

In nanodisk samples, three-dimensional magnetic states known as dipole strings, magnetic globules or torons have been revealed. Dipole strings are remarkable in that their stable magnetic configuration contains a pair of magnetic singularities. Whereas such objects were expected in magnetic multilayer systems, they have been observed in confined geometrical samples of isotropic chiral magnets.

First applications of magnetic topological particles in non-conventional computing schemes have been explored. Different non-conventional computing schemes are being studied to determine which of them lend themselves most naturally to the 3-dimensional spin structures that are being developed in this project. Optical control of magnetic structures and their applications in neuromorphic computing are also being investigated. Results include all-optical spin switching in Tb/Co multilayers, the observation of laser-induced nucleation and guided motion of a topological phase and a demonstration of training and pattern recognition by an opto-magnetic neural network.

Furthermore, machine learning techniques are being applied to address and solve complex problems, such as the dynamics of antiferromagnetic spins. The main results are the discovery of supermagnonic propagation in two-dimensional antiferromagnets, parametrically-driven magnon pairs and ultrafast dynamics of entanglement in antiferromagnets. The energy efficiency of computational approaches is also being assessed.

In parallel, control over 3-dimensional magnetic particles is explored to offer more internal degrees of freedom. Interfacial-DMI-stabilized skyrmions can be prepared and controlled in sputter-deposited magnetic multilayer films. One route, which is directed towards ultra-low power computing, makes use of the thermal diffusion of skyrmions in a low-pinning stack that can be modified by extremely low electrical currents via spin-Hall effect induced spin–orbit torques. Systematic studies of thermally activated skyrmion diffusion have been carried out and the effects of lateral confinement and commensurability have been investigated to optimize geometries. Work has been performed to demonstrate spatially multiplexed Brownian reservoir computing, stochastic computing and token-based computing.
Collaborations between partners in the 3D MAGiC project have allowed the combined use of micromagnetic modelling, calculations of electron optical phase shift images and experimental magnetic imaging of skyrmions using Lorentz microscopy and off-axis electron holography. This correlative approach allows 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 allow for the discovery of topologically-stable magnetic solitons and the investigation of their dynamic properties.

An example of the synergetic collaboration between the partners in this project is the establishment of full 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 nontrivial magnetic states 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 damaged surface layers whose magnetic properties differ from the properties of the internal volumes of the same samples. Even though the thickness of this layer is only a few nanometers, its presence affects the energy balance of the magnetic states significantly and is most relevant for geometrically confined samples of small size. Current work is focused in the discovery of one of the most exotic 3D magnetic solitons – a hopfion - in isotropic chiral magnets. As soon as the protocol for hopfion nucleation is accessible, a systematic study of their properties will be performed to assess their practical applications. The protocol for hopfion nucleation in other magnetic systems will also be explored, in order 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 could be demonstrated in this device after appropriate training of the output weights. Three-input logical operations have also been shown. Due to excitations by thermal fluctuations, little additional electrical energy is needed to drive the device.

Beyond conventional thin film multilayers, 2D materials have been explored. Ferromagnetic skyrmionic bubbles have been observed in the van der Waals magnet Fe5GeTe2 up to room temperature, opening the door for potential applications of this material class.

In order to stabilise 3D structures, approaches to tune the interlayer DMI have been developed. The experimental discovery of a new effect, current-induced interlayer DMI, is an important step towards nucleating and manipulating 3-dimensional magnetic solitons. Interlayer DMI favours the non-collinear, chiral alignment of adjacent layers in a multilayer stack and can therefore be used to stabilise 3-dimensional objects in multilayer films. Whereas the previously-discovered static interlayer DMI 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 in the quest for exploring three-dimensional magnetic textures with local control.

Furthermore, a demonstration of energy-efficient opto-magnetic neural networks is planned, including the development of an understanding of the path to realise the most energy efficient computational approaches.
Snapshot of a simulation of a topological fluctuation phase in which (anti)skyrmions are highlighted
Simulation results of the propagation of spin correlations (vertical axis: time)
(Left) Micromagnetic simulation and Lorentz TEM image of an isotropic chiral magnet that supports a