Local modes around the ferromagnetic impurities in the two-dimensional Heisenberg antiferromagnets

The behaviors of the spin-wave excitations around the ferromagnetic impurities in the two-dimensional spin-1/2 Heisenberg antiferromagnets are investigated for the cases with one, two and four impurities respectively. By means of the double-time Green's function numerical procedure, it is found that, in the two impurity case, two ferromagnetic impurities prefer to form an effective singlet. While in the four impurity case we obtained that, two nearest-neighbor ferromagnetic domains with contrary spin directions are formed in the antiferromagnetic background, and thus the whole system has the lowest energy.