Inhomogeneous magnetization of a thin film of a ferromagnetic semiconductor in an electric field

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A theoretical model describing the spontaneous magnetization of a ferromagnetic semiconductor (InMn)As film in the presence of an external electric field directed across the film is considered. It is assumed that the ions of a manganese impurity with spin 5/2 are acceptors, have a uniform spatial distribution inside the semiconductor, and do not change their position under the action of an external field. The motion of holes with spin ½ changes their spatial distribution under the action of the field. The exchange interaction between manganese ions and holes allows the formation of magnetization that is non-uniform across the film thickness.In particular, the existence of a piecewise continuous solution describing the presence of a phase transition boundary for magnetization inside a ferromagnetic semiconductor film is shown.