Ferromagnetism induced by excessive oxygen in lead-apatite Pb10(PO4)6O

The Cu-doped lead-apatite samples reported recently take on the ferromagnetic behavior but the mechanism is unknown. Based on the first-principles calculations, we investigate the magnetic properties of pure and Cu-doped lead apatite with excessive oxygen and copper contents. Three kinds of ferromagnetic compounds are found, including Pb10(PO4)6O2, Pb9Cu(PO4)6O2 with Cu in the 4 f site, and Pb8Cu2(PO4)6O with Cu in the 4 f site. In the first compound ferromagnetism is triggered by the extra O atom, while in the latter two compounds ferromagnetism is enhanced by the incorporation of extra oxygen or copper atoms. Because of the higher energy of Pb9Cu(PO4)6O2 or Pb8Cu2(PO4)6O with Cu in the 4 f site, there is a relatively low probability of them existing in the samples from the viewpoint of energy. Therefore, the ferromagnetic behaviors reported should mainly arise from the oxygen-overdoped lead-apatite Pb10(PO4)6O2.