This thesis presents the theoretical studies of chiral magnetic structures, which exist or are affected by antisymmetric Dzyaloshinskii-Moriya interactions. The theoretical approach is based on the phenomenological model of ferromagnetic materials lacking inversion symmetry. Equilibrium magnetic states are described as static structures in the micromagnetic low temperature limit with a fixed magnitude of the magnetization. The studies are focused on two cases: (i) magnetization structures that are affected by chiral exchange so that a particular chirality of these structures is selected, and (ii) novel solitonic states that are called chiral Skyrmions and only exist because of the chiral exchange. Vortex states in magnetic nanodisks provide the simplest example of a handed magnetization structure, where effects of the chiral couplings may become noticeable. A chiral exchange here favours one chirality of such a vortex state over the other. This effect can stem from surface-induced or other defect-related chiral Dzyaloshinskii-Moriya exchange. The different chiral versions of the vortex states are shown to display strong dependencies on the materials properties of such nanodisks. Within a micromagnetic model for these effects, numerical calculations of the shape, size, and stability of the vortices in equilibrium as functions of magnetic field and the material and geometrical parameters provide a general analysis of the influence of the broken mirror symmetry caused by the surface/interfaces or structural defect on their properties. The Dzyaloshinskii-Moriya interactions impose differences in the energies and sizes of vortices with different chirality: these couplings can considerably increase sizes of vortices with one sense of rotation and suppress vortices with opposite sense of rotation. Torsions related to lattice defects can cause similar to the surface-induced chiral couplings. A general phenomenological magneto-elastic formulation for this torsional chirality selection is given. It is applied to calculate similar effects on vortex states in magnetic disks with a screw dislocation at their center. In systems with strong chiral exchange the magnetic equilibrium states themselves become chiral twisted structures. The most interesting structures in this context are the two-dimensional solitonic states that are now known as chiral Skyrmions. The properties and stability of multiply twisted states composed of these particle-like units are the subject of the second part of this thesis. These states compete with the well known onedimensionally modulated helical states in non-centrosymmetric magnetic systems. Studies of modulated states in cubic helimagnets have shown, that in absence of additional effects, the only thermodynamically stable state is a cone helix. Uniaxial distortions, that can be caused by uniaxial stresses in the bulk samples or arise due to surface effects in thin films, suppress the helical states and stabilize Skyrmion lattices in a broad range of thermodynamical parameters. Using the phenomenological theory for modulated and localized states in chiral magnets, the equilibrium parameters of the Skyrmion and helical states have been derived as functions of applied magnetic field and induced uniaxial anisotropy. These results show that due to a combined effect of induced uniaxial anisotropy and an applied magnetic field, Skyrmion lattices can be formed as thermodynamically stable states. The theoretical results provide a comprehensive description of the evolution of modulated states in an applied magnetic field depending on type of anisotropy. The cases of a uniaxial anisotropy of easy axis and easy plane type with fields applied along its axis are investigated in detail. Existence of Skyrmion-lattice states in the easy axis case as thermodynamic field-induced phase is demonstrated. The results explain recent observation of Skyrmion lattices by magnetic Lorentz microscopy in thin foils of cubic chiral magnets. In systems with easy plane type of anisotropy, Skyrmion states do not form thermodynamic phases in applied fields along the axis. However, distorted Skyrmion phases can exist in fields applied perpendicularly to the axis. In this configuration of anisotropy axis and fields, both the helical states and the Skyrmions display elliptical distortions. The investigated micromagnetic model maps out the basic helical and Skyrmionic states expected to exist in cubic and nearly cubic chiral magnets.

This thesis presents the theoretical studies of chiral magnetic structures, which exist or are affected by antisymmetric Dzyaloshinskii-Moriya interactions. The theoretical approach is based on the phenomenological model of ferromagnetic materials lacking inversion symmetry. Equilibrium magnetic states are described as static structures in the micromagnetic low temperature limit with a fixed magnitude of the magnetization. The studies are focused on two cases: (i) magnetization structures that are affected by chiral exchange so that a particular chirality of these structures is selected, and (ii) novel solitonic states that are called chiral Skyrmions and only exist because of the chiral exchange. Vortex states in magnetic nanodisks provide the simplest example of a handed magnetization structure, where effects of the chiral couplings may become noticeable. A chiral exchange here favours one chirality of such a vortex state over the other. This effect can stem from surface-induced or other defect-related chiral Dzyaloshinskii-Moriya exchange. The different chiral versions of the vortex states are shown to display strong dependencies on the materials properties of such nanodisks. Within a micromagnetic model for these effects, numerical calculations of the shape, size, and stability of the vortices in equilibrium as functions of magnetic field and the material and geometrical parameters provide a general analysis of the influence of the broken mirror symmetry caused by the surface/interfaces or structural defect on their properties. The Dzyaloshinskii-Moriya interactions impose differences in the energies and sizes of vortices with different chirality: these couplings can considerably increase sizes of vortices with one sense of rotation and suppress vortices with opposite sense of rotation. Torsions related to lattice defects can cause similar to the surface-induced chiral couplings. A general phenomenological magneto-elastic formulation for this torsional chirality selection is given. It is applied to calculate similar effects on vortex states in magnetic disks with a screw dislocation at their center. In systems with strong chiral exchange the magnetic equilibrium states themselves become chiral twisted structures. The most interesting structures in this context are the two-dimensional solitonic states that are now known as chiral Skyrmions. The properties and stability of multiply twisted states composed of these particle-like units are the subject of the second part of this thesis. These states compete with the well known onedimensionally modulated helical states in non-centrosymmetric magnetic systems. Studies of modulated states in cubic helimagnets have shown, that in absence of additional effects, the only thermodynamically stable state is a cone helix. Uniaxial distortions, that can be caused by uniaxial stresses in the bulk samples or arise due to surface effects in thin films, suppress the helical states and stabilize Skyrmion lattices in a broad range of thermodynamical parameters. Using the phenomenological theory for modulated and localized states in chiral magnets, the equilibrium parameters of the Skyrmion and helical states have been derived as functions of applied magnetic field and induced uniaxial anisotropy. These results show that due to a combined effect of induced uniaxial anisotropy and an applied magnetic field, Skyrmion lattices can be formed as thermodynamically stable states. The theoretical results provide a comprehensive description of the evolution of modulated states in an applied magnetic field depending on type of anisotropy. The cases of a uniaxial anisotropy of easy axis and easy plane type with fields applied along its axis are investigated in detail. Existence of Skyrmion-lattice states in the easy axis case as thermodynamic field-induced phase is demonstrated. The results explain recent observation of Skyrmion lattices by magnetic Lorentz microscopy in thin foils of cubic chiral magnets. In systems with easy plane type of anisotropy, Skyrmion states do not form thermodynamic phases in applied fields along the axis. However, distorted Skyrmion phases can exist in fields applied perpendicularly to the axis. In this configuration of anisotropy axis and fields, both the helical states and the Skyrmions display elliptical distortions. The investigated micromagnetic model maps out the basic helical and Skyrmionic states expected to exist in cubic and nearly cubic chiral magnets.