How repulsive are holes to local antiferromagnetic order in cuprates?

The superexchange interaction and antiferromagnetic order are investigated in the cuprate cluster model M2Cu4O4. The stability of antiferromagnetic order to geometric distortions, M ionic charge, oxygen holes doping and Ni and Zn impurities is quantified. The interplay between the Cu 3dx2−y2 band and oxygen holes is proposed to produce a fluctuating electronic superlattice in cuprates. Singlet coupling of hole clusters is proposed to restore global antiferromagnetic order.