Antiferromagnetism of Cu${\mathrm{O}}_2$ layers

Based on symmetry arguments and supported by electronic structure calculations, we show that an important possible antiferromagnetic state of Cu${\mathrm{O}}_2$ planes has the moments on the O, rather than the Cu, sites. This and other proposed "broken-symmetry" orderings are a direct result of correlation effects and argue for holes on oxygen. In addition, calculations of the core-level shift between ${\mathrm{La}}_2$Cu${\mathrm{O}}_4$ and the extreme doping limit of Cu${\mathrm{O}}_2$ show that the Cu charge state remains unchanged. These results should have important implications for the symmetry of models of the high-$T_c$ copper oxide superconductors.