Fig. 2: Atomic structures of the Ni/HfO2 interfaces with different stoichiometries.

The interfaces with polarization pointing away from (into) the Ni layer are displayed on bottom (top) panels and derived from respective Ni/HfO2/Ni heterostructures with polarization pointing up (indicated by black arrow). a The defect-free Ni/HfO2 interfaces (SDF). The oxygen atoms at the two interfaces are labeled by O1−O8. O1, O3, O5, and O7 belong to the O atoms which are three-fold coordinated in HfO2 bulk and responsible for the ferroelectric displacements. O2, O4, O6, and O8 belong to the O atoms which are four-fold coordinated in HfO2 bulk. b−e The most stable structures with one oxygen vacancy at each interface (SV-1), with two oxygen vacancies at each interface (SV-2), with one interfacial oxygen atom diffused into Ni (SD-1) and with two interfacial oxygen atoms diffused into Ni (SD-2), respectively. Red dashed circles indicate the sites of oxygen vacancies.