  We consider a spin Hamiltonian describing $d$-$d$ exchange interactions
between localized spins $d$ of a finite antiferromagnet as well as $p$-$d$
interactions between a conducting hole ($p$) and localized spins. The spin
Hamiltonian is solved numerically with use of Lanczos method of
diagonalization. We conclude that $p$-$d$ exchange interaction leads to
localization of magnetic polarons. Quantum fluctuations of the antiferromagnet
strengthen this effect and make the formation of polarons localized in one site
possible even for weak $p$-$d$ coupling. Total energy calculations, including
the kinetic energy, do not change essentially the phase diagram of magnetic
polarons formation. For parameters reasonable for high-$T_c$ superconductors
either a polaron localized on one lattice cell or a small ferron can form. For
reasonable values of the dielectric function and $p$-$d$ coupling, the
contributions of magnetic and phonon terms in the formation of a polaron in
weakly doped high-$T_c$ materials are comparable.
