The paper investigates the skyrmion formation process in a model of a magnetoelectric bilayer film consisting of ferroelectric and ferromagnetic monolayers. The effect of a defect in a ferroelectric layer on the formation of a skyrmion phase, including a phase with a single skyrmion in a ferromagnetic layer, have been investigated, and ground-state phase diagrams have been constructed. The conditions for the formation of a single skyrmion on a ferromagnetic layer in the region under the defect of the ferroelectric layer have been determined. The possibility of skyrmion stabilization in the ground state at zero external magnetic fields is shown employing the steepest-descent method.
Abdrakhmanov et al. (Mon,) studied this question.