Native defect-induced multifarious magnetism in nonstoichiometric cuprous oxide: First-principles study of bulk and surface properties of Cu _2-δO

Native defects in cuprous oxide Cu₂O are investigated by using first-principles calculations based on density-functional theory. Considering the formation of copper and oxygen vacancies, antisites and interstitials, and a copper split-vacancy complex defect, we analyze the electronic structure and calculate their respective formation energies as a function of the change in Fermi level under both copper-rich and oxygen-rich conditions. We find that, under both growth conditions, the defect with the lowest formation energy is the simple copper vacancy, followed by the copper split-vacancy complex. Both low-energy copper defects produce hole states at the top of the valence band, largely accounting for the p -type conductivity in this material. In spite of the creation of dangling bonds at the nearest-neighbor O atoms, these copper defects are found to be spin neutral. Under oxygen-rich conditions, oxygen interstitials have low formation energies and are found to exhibit a ferromagnetic ordering with a total magnetic moment of 1.38 μ_B and 1.36 μ_B at the octahedral and tetrahedral sites, respectively. Considering the possibility of native defect formation at the surface of this material, we investigate the relative stability of both low- and high-index copper-oxide surfaces by comparing their surface free energies as a function of the change in oxygen chemical potential. Using the technique of ab initio atomistic thermodynamics, we then correlate the dependence of the calculated Gibbs free-surface energy as a function of oxygen pressure and temperature via the oxygen chemical potential. We identify two low-energy surface structures, namely, Cu₂O (110): CuO and Cu₂O (111) -Cu_CUS, with the former marginally more stable for oxygen-rich conditions and the latter more stable for oxygen-lean (or copper-rich) conditions. Cu₂O (110): CuO is calculated to be nonmagnetic and Cu₂O (111) -Cu_CUS is calculated to be a ferromagnetic ordering, with a total magnetic moment of 0.91 μ_B per defect. With the results for both bulk and surface native defects, we find that under oxygen-lean conditions, a ferromagnetic behavior could be attributed mainly to copper vacancy formation in the (111) surface of Cu₂O while under oxygen-rich conditions, low-energy bulk oxygen interstitial defects induce a ferromagnetic character in the same material. This highlights the complementary role of bulk and surface native magnetic defects under different pressure and temperature conditions, especially at the nanoparticle scale where surface properties dominate.