Magnetic properties
Hole doping causes a very rapid destruction of AF order. However, there are magnetic correlations that survive.
Zhang and Rice [1] proposed that each hole forms a bound singlet state with a Cu2+ ion, effectively creating a nonmagnetic site. This bound hole impacts the magnetic correlations in two ways: 1) it reduces the density of magnetic moments, and 2) the motion of the hole can stir up the spins.
The dilution effect leads to destruction of long range AF order at the classical percolation threshold. This effect is observed in, e.g., La2CuO4 where magnetic Cu atoms are replaced by non-magnetic Zn or Mg [2], as well as by Li.
When mobile holes are introduced in the CuO2 planes, the effect is more complex. Even though static magnetism is rapidly suppressed at about 2% hole content, neutron scattering and $\mu$SR indicate presence of residual fluctuating magnetism. $\mu$SR finds that for different families of cuprates, there is a doping-dependent spin-freezing ("spin-glass") temperature that remains finite up to at least 12% doping. In the same range of dopings, inelastic neutron scattering is consistent with the presence of incommensurate magnetic "order," which can be either static (near 1/8 doping) or fluctuating. Incommensurate magnetic "order" correlates with charge "order" of half the spatial period. ("." indicate that order is not necessarily static).