Metallization and spin fluctuations in Cu-doped lead apatite

An electronic structure and magnetic properties analysis of the recently proposed Cu-doped lead apatite is performed. We show that electronic structures of differently Cu-substituted structures are characterized by localized molecular Cu-O bands at or near the Fermi level. The Cu substitutions can happen at both Pb1 and Pb2 sites, leading to metallic and semiconducting states differently. The electronic states in these bands are highly unstable magnetically and form clusters of rigidly ferromagnetically coupled magnetic moments on Cu and neighboring oxygen atoms with a total moment of about 1 $\mu_B$. The ground state of uniformly Cu-doped lead apatite appears to be magnetic and semiconducting. The non-uniform distribution of two Cu atoms at the nearest Pb2 sites leads to an antiferromagnetic semiconducting state with formation energy close to uniformly distributed Cu configurations. The inclusion of quantum spin fluctuations confirms the stability of magnetic Cu-O clusters. Our calculations revealed the absence of the long-range magnetic order between uniformly distributed Cu-O clusters, creating the spin glass type of system.