A. Hubert

Thermodynamically stable magnetic vortex states in magnetic crystals

Abstract Magnetic vortices can be stabilized in magnetic materials by a so-called Dzyaloshinsky interaction. Their structure is calculated systematically for uniaxial ferromagnetic materials of the easy-axis type by numerically solving the differential equations in the circular cell approximation. In reduced units two external parameters are left over: the value of an external field parallel to the crystal axis and the relative strength of the Dzyaloshinsky interaction. A phase diagram in these variables consists of three thermodynamically stable phases: a uniform state at high field values, a one-dimensionally modulated spiral state at low fields and the new vortex state in an intermediate field range. The corresponding calculated magnetization curves clearly show the transitions between these states.

Enhancement of magneto-optical domain observation by digital image processing

An electronic system is described which allows to subtract contrast of non-magnetic origin from a magneto-optic image. At the same time image noise can be reduced to such a degree that the contrast visibility limit in domain observation is expanded by at least an order of magnitude. The system is demonstrated for a number of applications in which domain analysis was not possible before. These include magnetostriction-free metallic glasses, non-oriented silicon-iron steel and polycrystalline Ni-Fe samples. For the first time the internal wall structure could be made visible on metallic samples with magneto-optical means.

Magnetic states of small cubic particles with uniaxial anisotropy

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).

Corners and nucleation in Micromagnetics

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 SQRT(A/Kd). The singularity in the stray field remains only visible in the torque balance where it is compensated by an exchange torque.

Quantitative observation of magnetic domains with the magneto-optical Kerr effect

Abstract A new method for the quantitative determination of the magnetization direction at every point of a sample surface is presented. The method uses our digitally enhanced Kerr microscope and is based on a combination of the longitudinal and the transverse Kerr effect. The information from both effects is digitally combined with pictures taken in different saturated states. The resulting map of magnetization directions is displayed by arrows and additionally with the help of a colour code. Examples taken from complicated stress-governed domain structures on a metallic glass show pictures which are clearly easier to interpret than conventional qualitative Kerr images.

Domain observations on CoCr-layers with a digitally enhanced Kerr-microscope☆

Abstract The domain structures of different CoCr-layers have been studied magneto-optically by means of a digital image processing system in order to determine the nature of the magnetization processes in these media. All studied samples clearly show the characteristic behaviour of a continous medium. A quantitative analysis of the observed domain patterns as a function of applied fields yields characteristic values of the samples in addition to those derivable from magnetization curves. An observation of written traces indicates how information is recorded by modulation of the domain pattern.

The stability of vortex-like structures in uniaxial ferromagnets

Abstract 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.

First domain observations with the magneto-optical Kerr effect on Ti-ferrites in rocks and their synthetic equivalents

Abstract Ti-ferrites of the composition around Fe 2.4 Ti 0.6 O 4 are commonly found in basaltic rocks. They carry most of the information about the ancient earth magnetic field. For the first time, the magneto-optical Kerr effect could be applied on natural and synthetic Ti-ferrites. The experimental success is based on 1. - the achievement of a sufficiently smooth and stressfree surface obtained by polishing with amorphous SiO 2 suspension and 2. - the use of digital image processing. The results support earlier conclusions that, despite the cubic crystallographic structure, the true intrinsic anisotropy is uniaxial showing domain patterns similar to metallic glasses due to dominating internal stress. The application of the Kerr technique offers new perspectives to investigate the magnetic structure and the magnetization processes of the Ti-ferrites.

Anisotropy pinning of domain walls in a soft amorphous magnetic material

Ribbons were annealed in the demagnetized state with one wall along the ribbon middle. This wall becomes pinned during the heat treatment. Reentrant reversal occurs when reverse domains are nucleated at the ribbon edge with a threshold field larger than the demagnetizing field; this wall does not annihilate when it meets the pinned wall but leaves a line of reverse domains stabilized by ripple in the anisotropy. These domains permit a regular smooth reversal for the demagnetization process until the ribbon returns to the pinned configuration. The regular loop appears when the ribbon has been completely saturated by a large field. Mobile walls are nucleated on both sides of the pinned wall so that the ribbon does not return to the pinned configuration. Reversal now follows the usual demagnetization curve over the entire cycle. Kerr magnetooptical domain and domain wall observations are used in this investigation. All of the possible wall structures predicted by the model of asymmetric flux closed Bloch walls were identified. >

Optimizing stray field computations in finite-element micromagnetics

Abstract Different algorithms to investigate the problems connected with the magnetic stray field in micromagnetic computations for soft magnetic materials were explored. The various interpolation concepts are compared with respect to their required computing resources, their behaviour as the discretization is refined and their aptness to certain types of configurations. Vast differences were discovered between different schemes, all of which are equivalent in the limit of an infinitely fine mesh. Choosing the best method rather than the conventional one can save several orders of magnitude in computation time.