Abstract
The one-magnon states localized near the different types of the two-dimensional defects in Heisenberg ferromagnets with the long-range exchange interaction between spins arranged along one of the crystallographic axis are investigated. We consider the case when this axis is parallel to the defect plane and the interaction between its spins is either ferromagnetic, or alternating with the distance ferro- and antiferromagnetic type. In all other directions only the nearest-neighbour spin interactions are considered. The energies, eigenfunctions and the conditions of the formation of the localized states are obtained in an analytical form. It appears that the obtained characteristics strongly depend on the type of the long-range potential. The long-range interaction is also found to be essential for the stability of the ferromagnetic ordering in the defect plane in the case of alternating potential. Thus, the instability which can emerge in the finite number of neighbours approximation never appears if the long-range interaction is taken into acount.
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