Analysis of a finite spin cluster indicates a possibility of the formation of purely magnetic polarons in low-dimensional antiferromagnets. It is shown that for parameters characteristic of CuO_{2} based superconductors a strong antiferromagnetic polaron can occur. The destruction of antiferromagnetic order by the presence of a magnetic polaron is discussed.
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Diagonalization of Hamiltonian composed from d-d exchange interactions between localized d spins of antiferromagnetic cluster and p-d interaction with the spin of carriers indicates a possibility of formation of pure magnetic polarons. The most energetically favorable solution occurs when the carrier density in CuO_{2} planes is distributed on every second spin. These "comb-like" polarons have a tendency to bind into pairs (bipolarons) "glued" by the antiferromagnetic medium.
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