The behavior of antiferromagnetic domain wall (ADW) against the background of a periodic ferroelectric domain structure has been investigated. It has been shown that the structure and the energy of ADW change due to the interaction with a ferroelectric domain structure. The ferroelectric domain boundaries play the role of pins for magnetic spins, the spin density changes in the vicinity of ferroelectric walls. The ADW energy becomes a periodical function on a coordinate which is the position of ADW relative to the ferroelectric domain structure. It has been shown that the energy of the magnetic domain wall attains minimum values when the center of the ADW coincides with the ferroelectric wall and the periodic ferroelectric structure creates periodic coercitivity for the ADW. The neighbouring equilibrium states of the ADW are separated by a finite potential barrier.
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