Diversity of chiral magnetic solitons

This thesis is devoted to the theoretical study of chiral ferromagnets [1]. The main properties of any ferromagnet are usually defined by the competition of Heisenberg exchange interaction with the other energy terms, e.g., anisotropy or demagnetizing fields. In the case of chiral ferromagnets, the key energy term is the Dzyaloshinskii-Moria interaction (DMI). The interplay between exchange interaction and DMI leads to many exciting properties distinguishing chiral magnets from many other magnetic systems. One of the most thrilling properties of chiral magnets is their ability to host an extraordinary wide diversity of stable well-localized vortex-like spin textures, also known as skyrmions (Sk). They are magnetic solitons - solutions of the corresponding non-linear model of chiral magnet which is akin to a similar model in nuclear physics developed by Tony Skyrme. Currently, Sks are under intensive study by different scientific groups and are the "hot topic" of modern magnetism. The high attention to Sks is heated up by their possible utilization in computational devices. For instance, Sks have excellent potential for application in neuromorphic and reservoir computing. Additionally, investigation of Sks is of academic interest, allowing us to extend our knowledge about non-linear models and solitons in general. In this work, I study the various properties of chiral magnetic Sks by combining wellestablished analytical methods and different advanced numerical methods. A significant part of the presented work is devoted to investigating the static properties of Sks, such as stability regions, inter-solitonic interactions, and homotopy transformations. The most intriguing part of these studies is related to the role of the tilted magnetic field on Sks. As it turned out, one can learn a lot about Sks in experimental and theoretical studies by manipulating the direction of the external magnetic field. Among the dynamic properties of Sks, I pay the most attention to the current-induced motion and thermal generation of Sks. The results for Sk motion induced by electric current are based on a quite general analysis of the symmetry and topology of Sks, and thus are general for all possible solutions allowed by this model. In the chapter devoted to the thermal generation of Sks, I present an approach for the generation of a new type of Sks solution which has not been experimentally observed so far. The presented approach allows moving further in constructing more complicated magnetic textures and can be thought of as a guideline for experimental verification of the theoretical prediction. Besides the static and dynamic properties of magnetic solitons in chiral magnets, in this thesis, I have also considered other interesting problems related to the properties of chiral magnets themselves. The first one is related to the problem of an analytically solvable model for the dynamics of the cone phase in the presence of an electric current. The second problem is related to the equilibrium magnetization distribution when the free sample boundaries are taken into account. I found that under certain conditions, this problem has a fully analytical solution. The final part of my thesis is related to a new type of 3D solitons in chiral magnets. The discovery of these solutions, to a certain extent, was motivated by the analysis of homotopies of 2D Sk solutions. However, the central results of this chapter can be obtained even without referring to 2D systems. I strongly believe that the results presented in thesis will motivate further study of chiral magnets and trigger other researchers' interest in this topic.