By means of three-dimensional numerical calculations we studied possible micromagnetic configurations in a rectangular Permalloy-like thin-film element. The parameters were chosen to be compatible with the so-called micromagnetic standard problem 1. We demonstrate that for these parameters a diamond domain pattern is the lowest energy state that replaces cross-tie patterns favorable in larger elements. Only at smaller sizes does the originally envisaged Landau pattern form the ground state. The transition to high-remanence structures (or what would be comparable to a "single-domain" state) is found for lateral sizes that are an order of magnitude smaller than the benchmark parameters. The transitions among the different domain patterns become plausible in view of the energy of symmetric Neel walls in extended thin films. The features of the high-remanence structures can be derived from the principle of uniform charge distribution.

Two-dimensional localized states in the form of isolated vortices are studied systematically in uniaxial ferromagnets with an antisymmetric `Dzyaloshinsky’ exchange interaction. In addition to previously investigated π-vortices, new types of localized solutions were found. Their structure and equilibrium parameters were calculated by numerically solving the differential equations. We studied the stability of all solutions with respect to small radial distortions by solving the eigenvalue problem for the perturbation energy. It turned out that single vortices as well as multiple vortices with a magnetization rotation kπ(k=2,3,…) are stable in certain parameter regions, while other solutions of the differential equations such as vortices with nodes and large or blown-up vortices are always radially unstable. The stability analysis also answered the question of the decay modes of the stable solutions at their stability limits.

Models of uniaxial hard magnetic particles show that irregularly shaped grains possess a considerable equilibrium remanence due to domain imbalance. This remanence decreases approximately as L-1 with grain size L and is very stable with respect to alternating field and thermal demagnetization. It is therefore likely to be a major source of pseudo-single-domain remanence in rocks. Using the methods of domain theory, the range of possible remanences in irregularly shaped uniaxial particles with less than five domains is investigated. Even for slightly asymmetric particle geometries the remanence decreases monotonically with grain size. Most two-domain remanences lie above 0.3 M-s. The behaviour of the domain imbalance moments seems to be largely independent of details of the shape asymmetry. Since domain imbalance is a global equilibrium remanence, local remanences due to wall pinning effects can be superimposed without destroying it. This can explain the fact that the remanence of pseudo-single-domain particles appears to be a mixture of independent single- and multidomain-like components.

The character of closure domains was investigated by numerical micromagnetic methods for different anisotropy functionals. Closure domain walls are undefined in the classical sense, but sharp wall-like transitions can be formed if the anisotropy functional is stationary in the center of the closure domains.

As in a soft magnetic material the stray field energy dominates over anisotropy, domain structures are formed which tend to avoid stray fields. Their details depend on the anisotropy, the surface orientation relative to the easy axes, and the dimensions of the specimen. Based on magnetooptical domain studies, the fundamentals and characteristics of magnetic microstructures in soft magnetic materials are exemplarily reviewed in this presentation. In-situ experiments using applied magnetic fields and mechanical stresses help in understanding complex magnetic microstructures and in assessing their role in hysteresis properties.

Guided by the properties of the Stoner-Wohlfarth model, the switching behavior of general inhomogeneous micromagnetic configurations is investigated. In most cases the extrapolation of a suitably defined local susceptibility to infinity is demonstrated to lead to the switching point. Only conventional tools of numerical micromagnetics are needed in this calculation. For certain, symmetric classes of switching events we have to resort to indirect methods to determine the switching fields. Examples for the successful application of the proposed methods to various switching phenomena in cube-shaped particles with uniaxial anisotropy are given to validate the procedures.

The stray-field-free, curling type magnetization configuration proposed by Arrott et al. (IEEE Trans. Magn. 15 (1979) 1228) for an ideally soft-magnetic finite cylinder is re-evaluated. Because this magnetization pattern represents an important example for micromagnetic configurations in compact bodies, the examination of the foundations of this model is considered important. Two insufficiencies of the original proposal are pointed out while confirming the general correctness of the idea.

The wall width of asymmetrical Bloch walls was calculated numerically over a wide thickness range. Careful extrapolation was used to eliminate numerical finite size effects. On the surface a larger wall width as in the interior was expected and found due to the asymmetrical character of the wall. However, no saturation of the surface wall width with increasing thickness was observed. Instead we found a power law for the surface wall width δw as a function of the reduced thickness D of the form δw∝D0.14 within the investigated thickness range.

The lowest energy states in small cubic particles with uniaxial anisotropy are explored as a function of anisotropy strength and particle size. The investigations result in a phase diagram which contains the boundaries between the regions of one, two and three domains (flower, vortex and double vortex states). While the general features of the phase diagram are derived from energy estimates based on domain theory, the details are obtained using numerical micromagnetics. The two-domain and the three-domain phase can be subdivided into subphases. The comparison between different configurations revealed that a twisted vortex configuration with an S-shaped domain wall replaces the symmetric vortex with a straight wall at larger sizes. The three-domain phase contains two subphases which are symmetric with respect to (1 0 0) and (1 1 0) mirror planes, respectively. The transition from two to three domains occurs into the (1 1 0)-three-domain-state (diagonal state). This structure can be described as a configuration with two (quarter-) circular domain walls in two opposing corners. However, this configuration is energetically favored only in a small region within the phase diagram relative to the (1 0 0)-symmetry three-domain state with straight walls (sandwich state).

The divergence of the stray field in corners and its consequence for micromagnetic calculations was studied numerically in two dimensions for high-anisotropy materials. The results show that no atomistic theory has to be invoked because the singularity is smoothed out already within micromagnetics. The magnetic configurations and its deduced critical quantity, the coercivity, are determined correctly if the configurations are well approximated on the exchange length A/Kd. The singularity in the stray field remains only visible in the torque balance where it is compensated by an exchange torque.

A model that combines an analytical and a numerical approach allows fast calculation of the enhanced remanence of an assembly of exchange-coupled, nanocrystalline, hard magnetic grains. It makes use of the short-range characteristic of the exchange coupling by dividing each grain of the distribution into a core and a boundary region and treating only the relevant energy terms in the different parts. Exchange coupling across the grain boundary is described as a domain wall function between two limiting angles and explains the increase of remanence with decreasing grain size. Magnetostatic interactions are treated in a mean-field approximation and are found to contribute a further small, grain size-independent effect.

Magnetic force microscopy images of NdFeB crystals of different crystallographic orientation are directly compared with magneto-optical Kerr images. This comparison facilitates the analysis of contrast mechanisms in the MFM images. Different contributions to the contrast arise from the Zeeman interaction energy between (unperturbed) tip and sample on the one hand and the mutual reaction of their magnetizations to the stray fields. These contributions are separated by forming sum and difference images from pictures taken with opposite tip magnetization. This technique yields complementary images of the surface charge pattern of the sample and its local susceptibility.

This paper collects the explicit results for linear magneto-optical effects including all interference effects in arbitrary, laterally uniform thin film systems, and also including diffraction effects from an arbitrary three-dimensional magnetization distribution. New contributions are: (1) A convenient representation of the final result in terms of amplitude transfer functions for the primary and the refracted light, making use of previously noticed reciprocity relations. (2) A generalization applicable to systems containing optically uniaxial films with the axis along the film normal (as in most cases of growth- or stress-induced anisotropies). (3) A general formula for the case of ultrathin magnetic layers. (4) A systematic analysis of domain boundary contrast phenomena including the magneto-optical gradient effect. Further applications explore the case of thin film mirror systems and their potential to reach the theoretical optimum magneto-optical signal for a given magneto-optical material.

A magnetic force sensor was integrated into the objective revolver of an optical polarization microscope. The instrument was tested on a wedge-shaped Co single crystal and on branched NdFeB domains. The combination of force and Kerr microscopy on identical domains gives access to a new interpretation of MFM contrasts. Three contrast mechanisms are proposed to interpret the observations.

We prepared NiFeCo-Cu-NiFeCo GMR sensor structures with crossed anisotropy. The ferromagnetic layers are weakly coupled. The measured GMR ratio is about 1.2%-smaller than the ratio derived from measurements on similar spin-valve structures. To explain the poor performance we studied the domains in the coupled ferromagnetic layers by Kerr microscopy. The magnetization processes are strongly influenced by the remaining weak ferromagnetic coupling and the occurrence of compensated wall structures. These irregularities lead to reduced GMR ratios. Also the formation of 360/spl deg/-walls can be observed.