In this thesis multidomain states in magnetically ordered systems with competing long-range and short range interactions are under consideration. In particular, in antiferromagnetically coupled multilayers with perpendicular anisotropy unusual multidomain textures can be stabilized due to a close competition between long-range demagnetization fields and short-range interlayer exchange coupling. These spatially inhomogeneous magnetic textures of regular multidomain configurations and irregular networks of topological defects as well as complex magnetization reversal processes are described in the frame of the phenomenological theory of magnetic domains. Using a modified model of stripe domains it is theoretically shown that the competition between dipolar coupling and antiferromagnetic interlayer exchange coupling causes an instability of ferromagnetically ordered multidomain states and results in three possible ground states: ferromagnetic multidomain state, antiferromagnetic homogeneous and antiferromagnetic multidomain states. The presented theory allows qualitatively to define the area of existence for each of these states depending on geometrical and material parameters of multilayers. In antiferromagnetically coupled superlattices with perpendicular anisotropy an applied magnetic bias field stabilizes specific multidomain states, so-called metamagnetic domains. A phenomenological theory developed in this thesis allows to derive the equilibrium sizes of metamagnetic stripe and bubble domains as functions of the antiferromagnetic exchange, the magnetic bias field, and the geometrical parameters of the multilayer. The magnetic phase diagram includes three different types of metamagnetic domain states, namely multidomains in the surface layer and in internal layers, and also mixed multidomain states may arise. Qualitative and quantitative analysis of step-like magnetization reversal shows a good agreement between the theory and experiment. Analytical equations have been derived for the stray field components of these multidomain states in perpendicular multilayer systems. In particular, closed expressions for stray fields in the case of ferromagnetic and antiferromagnetic stripes are presented. The theoretical approach provides a basis for the analysis of magnetic force microscopy (MFM) images from this class of nanomagnetic systems. Peculiarities of the MFM contrast have been calculated for realistic tip models. These characteristic features in the MFM signals can be employed for the investigations of the different multidomain modes. The methods developed for stripe-like magnetic domains are employed to calculate magnetization processes in twinned microstructures of ferromagnetic shape-memory materials. The remarkable phenomenon of giant magnetic field induced strain transformations in such ferromagnetic shape memory alloys as Ni-Mn-Ga, Ni-Mn-Al, or Fe-Pd arises as an interplay of two physical effects: (i) A martensitic transition creating competing phases, i.e. crystallographic domains or variants, which are crystallographically equivalent but have different orientation. (ii) High uniaxial magnetocrystalline anisotropy that pins the magnetization vectors along certain directions of these martensite variants. Then, an applied magnetic field can drive a microstructural transformation by which the martensitic twins, i.e. the different crystallographic domains, are redistributed in the martensitic state. Within the phenomenological (micromagnetic) theory the equilibrium parameters of multivariant stripe patterns have been derived as functions of the applied field for an extended single-crystalline plate. The calculated magnetic phase diagram allows to give a detailed description of the magnetic field-driven martensitic twin rearrangement in single crystals of magnetic shape-memory alloys. The analysis reveals the crucial role of preformed twins and of the dipolar stray-field energy for the magnetic-field driven transformation process in magnetic shape-memory materials. This work has been done in close collaboration with a group of experimentalists from Institute of Metallic Materials of IFW Dresden, Germany and San Jose Research Center of Hitachi Global Storage Technologies, United States. Comparisons between theoretical and experimental data from this cooperation are presented throughout this thesis as vital part of my work on these different subjects.

In this thesis multidomain states in magnetically ordered systems with competing long-range and short range interactions are under consideration. In particular, in antiferromagnetically coupled multilayers with perpendicular anisotropy unusual multidomain textures can be stabilized due to a close competition between long-range demagnetization fields and short-range interlayer exchange coupling. These spatially inhomogeneous magnetic textures of regular multidomain configurations and irregular networks of topological defects as well as complex magnetization reversal processes are described in the frame of the phenomenological theory of magnetic domains. Using a modified model of stripe domains it is theoretically shown that the competition between dipolar coupling and antiferromagnetic interlayer exchange coupling causes an instability of ferromagnetically ordered multidomain states and results in three possible ground states: ferromagnetic multidomain state, antiferromagnetic homogeneous and antiferromagnetic multidomain states. The presented theory allows qualitatively to define the area of existence for each of these states depending on geometrical and material parameters of multilayers. In antiferromagnetically coupled superlattices with perpendicular anisotropy an applied magnetic bias field stabilizes specific multidomain states, so-called metamagnetic domains. A phenomenological theory developed in this thesis allows to derive the equilibrium sizes of metamagnetic stripe and bubble domains as functions of the antiferromagnetic exchange, the magnetic bias field, and the geometrical parameters of the multilayer. The magnetic phase diagram includes three different types of metamagnetic domain states, namely multidomains in the surface layer and in internal layers, and also mixed multidomain states may arise. Qualitative and quantitative analysis of step-like magnetization reversal shows a good agreement between the theory and experiment. Analytical equations have been derived for the stray field components of these multidomain states in perpendicular multilayer systems. In particular, closed expressions for stray fields in the case of ferromagnetic and antiferromagnetic stripes are presented. The theoretical approach provides a basis for the analysis of magnetic force microscopy (MFM) images from this class of nanomagnetic systems. Peculiarities of the MFM contrast have been calculated for realistic tip models. These characteristic features in the MFM signals can be employed for the investigations of the different multidomain modes. The methods developed for stripe-like magnetic domains are employed to calculate magnetization processes in twinned microstructures of ferromagnetic shape-memory materials. The remarkable phenomenon of giant magnetic field induced strain transformations in such ferromagnetic shape memory alloys as Ni-Mn-Ga, Ni-Mn-Al, or Fe-Pd arises as an interplay of two physical effects: (i) A martensitic transition creating competing phases, i.e. crystallographic domains or variants, which are crystallographically equivalent but have different orientation. (ii) High uniaxial magnetocrystalline anisotropy that pins the magnetization vectors along certain directions of these martensite variants. Then, an applied magnetic field can drive a microstructural transformation by which the martensitic twins, i.e. the different crystallographic domains, are redistributed in the martensitic state. Within the phenomenological (micromagnetic) theory the equilibrium parameters of multivariant stripe patterns have been derived as functions of the applied field for an extended single-crystalline plate. The calculated magnetic phase diagram allows to give a detailed description of the magnetic field-driven martensitic twin rearrangement in single crystals of magnetic shape-memory alloys. The analysis reveals the crucial role of preformed twins and of the dipolar stray-field energy for the magnetic-field driven transformation process in magnetic shape-memory materials. This work has been done in close collaboration with a group of experimentalists from Institute of Metallic Materials of IFW Dresden, Germany and San Jose Research Center of Hitachi Global Storage Technologies, United States. Comparisons between theoretical and experimental data from this cooperation are presented throughout this thesis as vital part of my work on these different subjects.