Periodic Reporting for period 3 - 3D MAGiC (Three-dimensional magnetization textures: Discovery and control on the nanoscale)
Okres sprawozdawczy: 2023-07-01 do 2024-12-31
The 3D MAGiC project aims to study the physical properties of intriguing novel magnetic textures that are referred to as three-dimensional magnetic solitons and to use them for unconventional energy-efficient computing applications. 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 magnetic 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 is the primary tool for the study of magnetic solitons in this project. One of the technical challenges is the need to fine-tune the conditions in 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 two-dimensional magnetic solitons in thin films and plates of magnetic materials. One of the main objectives of the 3D MAGiC project is to study magnetic solitons that can move in all three spatial directions. According to theoretical predictions, some of the most promising objects are so-called magnetic hopfions, 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.
A major challenge in the study of magnetic solitons is that they are very difficult to detect. Although different methods allow the presence of magnetic 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 is the primary tool for the study of magnetic solitons in this project. One of the technical challenges is the need to fine-tune the conditions in 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 two-dimensional magnetic solitons in thin films and plates of magnetic materials. One of the main objectives of the 3D MAGiC project is to study magnetic solitons that can move in all three spatial directions. According to theoretical predictions, some of the most promising objects are so-called magnetic hopfions, 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 imaging of magnetic skyrmions and direct comparisons with theoretical modelling have led to many unexpected and interesting observations, some of which are listed here:
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-type skyrmions in Fresnel defocus images has been optimised, allowing for the accurate determination of their sizes.
Layered van-der-Waals-type ferromagnets have been studied using both electron magnetic chiral dichroism and phase contrast techniques in the electron microscope, reealing skyrmionic spin structures in FeGeTe close to room temperature.
In nanodisk samples, Bloch points and three-dimensional magnetic states known as dipole strings, magnetic globules or torons have been revealed. Dipole strings are remarkable as their stable magnetic configuration contains a pair of magnetic singularities. Whereas such objects were expected in magnetic multilayer systems, they have now 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 presently being studied to determine which of them lend themselves most naturally to the three-dimensional spin structures that are being developed in the 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 topological phases and the demonstration of training and pattern recognition by opto-magnetic neural networks. Optical creation and magnetic force microscopy observations of stochastic domain networks have been achieved and first attempts at modelling them have been completed.
Machine learning techniques have been 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.
Control over three-dimensional magnetic particles is being explored to offer more internal degrees of freedom 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.
By fabricating nanoscale samples of B20-type FeGe and using a specific external magnetic field protocol in a transmission electron microscope, the direct observation of magnetic hopfions - an exotic type of three-dimensional topological soliton – has been achieved. Hopfion rings were found to be stable when linked to skyrmion strings that penetrate through the hopfion rings. The coexistence of hopfions and skyrmion strings represents a breakthrough discovery. A protocol has been developed to reproduce these observations reliably. In addition to the direct observation of magnetic hopfions, several other fundamental discoveries have been made, including a skyrmion braiding effect, the coexistence of skyrmions and antiskyrmions and the direct observation of skyrmion bags.
From a theoretical standpoint, the possibility of finding single hopfions in magnetic materials that exhibit competing magnetic interactions has been explored. An elegant micromagnetic field model has been developed and it has been shown that hopfion solutions indeed exist. A relationship between hopfion number and hopfion energy has been found. The stability of toroidal hopfions against decay into a ferromagnetic state has been investigated and it has been shown that the stability of a hopfion increases with its size.
Highly complex modifications to scientific instruments have been made with the active contribution of all project partners, in order to realise magnetic vector 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, which have been 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.
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-type skyrmions in Fresnel defocus images has been optimised, allowing for the accurate determination of their sizes.
Layered van-der-Waals-type ferromagnets have been studied using both electron magnetic chiral dichroism and phase contrast techniques in the electron microscope, reealing skyrmionic spin structures in FeGeTe close to room temperature.
In nanodisk samples, Bloch points and three-dimensional magnetic states known as dipole strings, magnetic globules or torons have been revealed. Dipole strings are remarkable as their stable magnetic configuration contains a pair of magnetic singularities. Whereas such objects were expected in magnetic multilayer systems, they have now 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 presently being studied to determine which of them lend themselves most naturally to the three-dimensional spin structures that are being developed in the 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 topological phases and the demonstration of training and pattern recognition by opto-magnetic neural networks. Optical creation and magnetic force microscopy observations of stochastic domain networks have been achieved and first attempts at modelling them have been completed.
Machine learning techniques have been 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.
Control over three-dimensional magnetic particles is being explored to offer more internal degrees of freedom 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.
By fabricating nanoscale samples of B20-type FeGe and using a specific external magnetic field protocol in a transmission electron microscope, the direct observation of magnetic hopfions - an exotic type of three-dimensional topological soliton – has been achieved. Hopfion rings were found to be stable when linked to skyrmion strings that penetrate through the hopfion rings. The coexistence of hopfions and skyrmion strings represents a breakthrough discovery. A protocol has been developed to reproduce these observations reliably. In addition to the direct observation of magnetic hopfions, several other fundamental discoveries have been made, including a skyrmion braiding effect, the coexistence of skyrmions and antiskyrmions and the direct observation of skyrmion bags.
From a theoretical standpoint, the possibility of finding single hopfions in magnetic materials that exhibit competing magnetic interactions has been explored. An elegant micromagnetic field model has been developed and it has been shown that hopfion solutions indeed exist. A relationship between hopfion number and hopfion energy has been found. The stability of toroidal hopfions against decay into a ferromagnetic state has been investigated and it has been shown that the stability of a hopfion increases with its size.
Highly complex modifications to scientific instruments have been made with the active contribution of all project partners, in order to realise magnetic vector 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, which have been 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.
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.
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.