Self-consistent domain theory in soft-ferromagnetic media. II. Basic domain structures in thin-film objects

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Abstract
A construction method for determining the domain structure in ideally soft-ferromagnetic cylindrical objects with plane-parallel top and bottom surfaces of arbitrary shape is presented. The self-consistent theory is confined to two-dimensional solenoidal dipole distributions in which the dipoles are parallel to the top and bottom surfaces. It is proved that the basic domain structure is uniquely defined in simply connected objects, while an extra criterion has to be added in order to guarantee the uniqueness in the multiply connected ones. The treatment is based on differential geometrical principles. The object edge is partitioned into segments, in which each segment is situated in between two adjacent edge points where the radii of curvature of convex edge segments are locally minimal. To each edge segment, a region is attributed, in which M is uniquely specified by the course of M along that edge segment. In the cross section of regions corresponding to different edge segments, domain walls provide an adequate separation of the dipole distribution imposed by these segments. The extremities of these domain walls are found in the singular points of the evolute corresponding to the extremities of the edge segments and in the points where a number of walls meet. It is proved that the basic domain structure is the locus of centers of all circles inside the object that touch the object edge at at least two points. A number of experimentally observed basic structures are given, and the relevance of the definition of basic structures in multiply connected objects is examined. OFF