A self-consistent domain theory in ideal soft-magnetic media

A self-consistent domain theory for ideal soft-ferromagnetic specimens is unfolded. The treatment is based on micromagnetic equilibrium and stability equations which are simplified by removing the contributions due to the intrinsic anisotropy and the spatial variation term in the exchange-energy density. Only the solenoidal magnetization distributions in thin film objects are investigated, so that we can confine ourselves to two-dimensional magnetization distributions. Cauchy's method of the characteristics is employed to solve the magnetostatic problem. It is proved that the characteristic base curves are straight lines perpendicular to the magnetization. Moreover, it is demonstrated that domain structure is required to separate the incompatible magnetization distributions imposed by the various segments of the object's edge. The domain structure is explicitly derived for a simple object that is bounded by two circular edge segments and experimental confirmation is given.