Destruction of long-range antiferromagnetic order by hole doping

Abstract

We study the renormalization of the staggered magnetization of a two-dimensional antiferromagnet as a function of hole doping, in the framework of the $t\ensuremath{-}J$ model. It is shown that the motion of holes generates decay of spin waves into ``particle-hole'' pairs, which causes the destruction of the long-range magnetic order at a small hole concentration. This effect is mainly determined by the coherent motion of holes. The value obtained for the critical hole concentration, of a few percent, is consistent with experimental data for the doped copper oxide high-${T}_{c}$ superconductors.