Magnetic Domain Structures in Thin Uniaxial Plates with Perpendicular Easy Axis

We present a convenient formulation of the single-domain energy in the wall-energy model and minimize the total energy of a lattice of cylindrical domains and of a parallel-stripe array in an infinite plate. The latter structure is shown to have the lower energy for external transverse fields Hex<H1 while the lattice is favored for H1≤Hex<H2. The critical domain sizes and fields bounding these structures are calculated as functions of the plate thickness and the material parameters. The factors which affect the evolution of the domain structures in finite and nearly defect-free plates are discussed and the following conclusions drawn: Domain nucleation is favored by the presence of nonuniformities such as cracks or mounds. Stripes nucleated at cracks or boundaries expand and contract with one end tied to the nucleation point and there may be only as many stripes as nucleation centers. An energy barrier inhibits the separation of a domain from (or the joining to) a free edge boundary or another domain. Closed domains are repelled by boundaries and alternate between stripe- and bubble-domain configurations as the local field varies below and above the critical stripe-bubble instability value. The qualitative conclusions can be quantified to some extent in the wall-energy model and provide a satisfactory explanation of the domain structures observed in a high-mobility garnet film.