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Description
The existence of 3D magnetic textures with particle-like properties (3D solitons) is known as intriguing theoretical prediction during four decades. However, despite the successful studies of recent years, 3D magnetic textures still remain a little studied area, which makes it difficult to introduce such newmaterials for technological employment.In order to bring the creation of new devices based on 3D textures closer, in the 3DMATEX project a comprehensive theoretical study of statical and dynamical properties of such magnetic systemswill be performed. The priority issues to explore are: createstate diagrams of the 3D magnetic configurations in cylindrical nanowires, describe resonant motion of 3D solitonsin cylindrical geometries, investigate3D solitons inside of the cylindrical magnetic wires inordered arrayandconsiderthis structure as aversatile green magnetic storage unit with a three-dimensional architecture, study Bloch point and vortex oscillation frequencies in cylindrical nanowire. As a result, the project will answer the principal questionsregarding physics and properties of stable 3D magnetization textures in confined structures:What materials can produce non-trivial 3D magnetization textures? What is their topology? What is their dynamics? How we can control and determined their oscillations? What is detailed magnetization configuration, in particular of the Bloch-point 3D domain wall in cylindrical geometry?With basic knowladge about the physical properties of 3D magnetization textures developed in the project,the important step towardtheirtechnological applications will be done, towards the long-term vision of versatile green magnetic storage units with a 3D architecture, openning a new routefor spintronics which promiseslow energy consuming computations.
Summary of project results
Three-dimensional (3D) magnetic textures, such as hopfions, Bloch points (magnetic hedgehogs), and other topological solitons, were predicted theoretically about forty years ago. Now, after their successful experimental observation, they are considered as promising carriers in data storage and processing devices. In addition to possible applications in information storage, new spintronic and magnonic devices are envisioned, and they are of fundamental interest for the study of fascinating physical phenomena and nonlinear field theories. However, the study of such textures still presents considerable difficulties, both theoretically and experimentally. To overcome the existing challenges and bring closer the creation of new devices based on 3D magnetization textures, we dedicated our project to solving the problems of their statics and dynamics.
We studied the magnetic and geometrical parameters of magnetic nanostructures in which three-dimensional magnetic solitons can be stabilized. One of the main points was hopfion gyrotropic and translational dynamics. In these considerations it is necessary to avoid the unwanted effects of deviations from a given trajectory of hopfions under the action of electric current in spintronic devices (so-called "skyrmion Hall effect").
The next important area of research became the spectrum of spin-wave modes of hopfions, which knowledge helps in experimental identification of hopfions, understanding of hopfion dynamics and stability, answering the question how we can control and determine their oscillations, as well as use of hopfions in spintronic and magnonic applications. Both goals of the project are based on the physical reason that the interaction of hopfions with magnons and conduction electrons cannot destroy the hopfion itself as a topologically stable object, but can sufficiently influence its motion.
Fast switching of nanomagnets is one of the main challenges in the development of magnetic memories. In this context, one of the challenges of the project was to increase the functionality of magnetic memory elements based on nanowires with the Bloch point vortex domain wall.
The question of the magnitude of the gyrovector of the magnetic hopfion became of practical importance. In this project, we present a direct analytical calculation of the gyrovector of the toroidal hopfion, prove that it does not vanish as a whole, and show which of its components are nonzero. The possible nonzero values of the gyrovector components affect both the current-induced translational motion of the hopfion and the dynamics of spin waves over the background of the hopfion. This result is particularly important for choosing the geometry of the driving forces applied to the hopfion to avoid undesired skyrmion Hall effect. It is also useful for understanding the interaction between the magnetic hopfions and elementary excitations (spin waves) on their background. Calculations are presented for bulk samples, cylindrical dots, and ferromagnetic films.
The study of spin-wave modes is of great importance, since these elementary excitations characterize the magnetic systems, reflect the existing symmetries and provide information about fundamental magnetic properties. We consider a ferromagnetic FeGe dot with a diameter of 200 nm and a thickness of 70 nm and show that hopf ion can be stabilized in such nanoparticles. Our numerical calculations proved that the spectrum of spin-wave modes of hopfion is much richer than previously reported. We identified four groups of modes that differ in the sense of rotation (clockwise or counterclockwise) and in the position of an average amplitude localization. The full spectra of the spin waves provide deep insight into the richness and complexity of the spin wave dynamics in the 3D topological magnetic solitons. Our study points to interesting physics and potential applications of the dynamics in hopfion, but now with 3D magnetic objects.
Using both micromagnetic simulations and analytical theory, we carry out a detailed investigation of the stability and dynamics of the Bloch point vortex domain wall in relatively short (up to 3 times the length of the diameter) cylindrical nanowires. As a result, a practical implementation of the method in a device is proposed, involving microwave excitation and the generation of opposite spin currents. This implies the creation of a topological magnetic memory based on short cylindrical nanowires with fine frequency tuning and a latency of less than 1 nanosecond.
The results of the project were published in the 6 research papers and presented in 26 conferences, seminars and other dissemination activities.
The results of the project have a high scientific and technological impact. Indeed, it addresses new physics in magnetism related to many novel effects such as the appearance of topologically protected magnetization textures (e.g., Bloch point domain walls and hopfions). The project results in the study of the gyrotropic and translational dynamics of hopfions, the spin-wave dynamics in the 3D topological magnetic solitons, as well as the stability and dynamics of the Bloch-point vortex domain walls in nanowires could be very useful for technological applications, since they aim at the creation of versatile green magnetic storage devices with 3D architecture and promise low energy consumption. They also make progress in understanding the physics of 3D topological solitons and point out further research directions, although our theoretical results are still awaiting their experimental confirmation and application.
In summary, we can identify the following groups of project beneficiaries
1. Developers of new technologies, to whom we offer new ways to create spintronic and magnonic devices based on 3D spin structures.
2. Experimental physicists, for whom our project will substantiate the geometry of experiments and the properties of materials for the experimental study of 3D magnetic textures.
3. Theoretical physicists involved in both fundamental physics and special problems of magnetism.
4. Teachers of physics courses in higher education institutions, since some of the results of our research are fundamental in nature and can be included in physics and mathematical physics courses at senior university levels.