Magnetic polarons in weakly doped high-Tcsuperconductors

Abstract

The formation of magnetic polarons in an antiferromagnetic medium is studied numerically in wide range of parameters with special attention to high-${T}_{c}$ superconductors. We consider a Hamiltonian describing $d\ensuremath{-}d$ exchange interactions between d spins of a finite Heisenberg antiferromagnet, $p\ensuremath{-}d$ interactions between a conducting hole p, and d spins, as well as kinetic energy of hole. The decoupling of orbital and spin degrees of freedom allows us to consider the spin Hamiltonian and kinetic energy separately. The spin Hamiltonian is solved exactly with use of the Lanczos method of diagonalization. We conclude that $p\ensuremath{-}d$ exchange interaction favors magnetic polarons localized on one site of the antiferromagnet. Adding the kinetic energy does not change essentially the phase diagram of magnetic polarons formation. For parameters relevant for high-${T}_{c}$ superconductors either a polaron localized on one lattice cell or a small ferron form. However, we find that the contribution of magnetic and phonon terms in the formation of a polaron in weakly doped high-${T}_{c}$ materials can be comparable.