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Destruction of Magnetic Long-Range Order by Hole-Induced Skyrmions in Two-Dimensional Heisenberg Model

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.