Abstract
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.
Highlights
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
The analysis of the layer-resolved densities of states (DOSs) demonstrates that the effects leading to surfaceferromagnetism on the fully O-covered surfaces are the same as those discussed for tetragonal HfO2: the stable O-terminated surface is insulating and non-magnetic due to the complete filling of the O-2p states of the atoms in the surface layer, while for the OO-terminated surface the formation of holes in the valence band induces an exchange-splitting and the formation of a half-metallic and ferromagnetic surface
Ab initio statistical mechanics in combination with DFT total energy calculations have been used to determine the stable surface terminations. For both polymorphs we find that on these polar surfaces, a partially reduced surface covered by half a monolayer of oxygen is lower in energy than the Hf- and fully O-terminated surfaces at all realistic values of the chemical potential of oxygen
Summary
The calculations have been performed using the Vienna ab initio simulation package (VASP) [29]–[31]4, which performs a variational solution of the Kohn–Sham equations in a plane-wave basis set. The plane-wave basis set contained components with a kinetic energy of up to Ecut = 354 eV—with this cut-off, a good convergence of the structural energy differences between the cubic, tetragonal and. For the tetragonal and monoclinic phases, we used a cell containing four formula units, BZ integrations were performed over a 6 × 6 × 6 mesh. The BZ integrations have been performed on 4 × 4 × 1 k-point meshes, convergence has been verified by test-calculations using 8 × 8 × 1 grids. Both non-stoichiometric symmetric Hf- and O-terminated slabs and polar asymmetric stoichiometric slabs (in this case including dipolar energy corrections) have been used. We have verified that the reduction of the cut-off energy does not affect the accuracy of our results in any significant way
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