Structural, electronic and magnetic properties of the surfaces of tetragonal and cubic HfO2

We present ab initio density-functional theory (DFT) calculations of the structure and stability of the monoclinic (m), tetragonal (t) and cubic (c) phases of HfO2 and of the stability and the structural, electronic, and magnetic properties of the polar (001) surface of t-HfO2 and the (100) and (111) surfaces of c-HfO2. We show that on all three surfaces, a termination by Hf leads to a metallic and non-magnetic surface, while surfaces covered by a full monolayer of O are predicted to be half-metallic and ferromagnetic, the magnetisms being induced by the Coulomb repulsion between p-holes in the O-2p valence band. In contrast, the partially reduced surfaces terminated by half a monolayer of oxygen are found to be insulating and non-magnetic. Ab initio statistical mechanics in combination with the DFT total-energy calculations show that the partially reduced surfaces are stable over the entire range of admissible values of the chemical potential of oxygen. Investigations of the formation of Hf vacancies on the Hf- and O-terminated surfaces of tetragonal HfO2 demonstrate that under oxidizing conditions, the formation of Hf subsurface vacancies is energetically favored on the partially reduced O-terminated surface. The formation of Hf vacancies causes the creation of holes in the O-2p valence band and of magnetic moments on the surrounding O atoms. That the formation of near-surface Hf vacancies on the O-terminated surface is energetically favored is in contrast to a high formation energy for neutral Hf vacancies in bulk HfO2 and suggests a cooperative mechanism between surface- and vacancy-formation. We discuss our findings in relation to recent reports on ferromagnetism in ultrathin HfO2 films and other models for the formation of p-wave ferromagnetism.