  Motivated by the rapid destruction of antiferromagnetic long-range order in
hole-doped cuprate high-temperature superconductors, we study the effect of
skyrmions on the magnetic long-range order (MLRO). Here we assume that either a
skyrmion or antiskyrmion is introduced by a doped hole. Our numerical
simulation indicates that in the case of isolated skyrmions, there is an abrupt
disappearance of MLRO for doping concentration $x < 1.0\times 10^{-4}$. In the
case of skyrmion-antiskyrmion pairs, the critical doping concentration $x_c$
for the suppression of MLRO is given as a function of the separation of the
pairs. For a moderate separation of $3 - 4$ lattice constants, we find that the
critical doping is consistent with the experimental value.
