The relative stability of multiferroic BiFeO (0001) surfaces, which is the (111) facet in the pseudocubic notation, with different stoichiometry is systematically studied by using ab initio thermodynamic approach in order to obtain insights into the stable surface terminations. We predict that under most chemical potential conditions the thermodynamically favored terminations for the negative and positive surfaces are -Bi-O and -Fe-O-Bi, respectively. The predicted difference in oxygen content between the negative and positive surfaces is consistent with experimental observations at the BiFeO/metal interfaces ( Nat. Mater. , 2014 , 13 , 1019 , DOI: 10.1038/nmat4058 ; Adv. Mater. , 2015 , 27 , 6934 , DOI: 10.1002/adma.201502754 ). We determine the atomic geometries and electronic states as well as the magnetic properties for the negatively and positively polarized stable surfaces. Our results demonstrate that not only the stoichiometry and atomic geometries but also the electronic and magnetic properties of the BiFeO (0001) surfaces show strong dependence on the ferroelectric polarization direction. Therefore, we expect that the surface physical and chemical properties of the BiFeO (0001) surfaces can be easily tuned by an external electric field.

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For graphene/ferroelectric hybrid structures, the atomistic and electronic details of the interfaces are of crucial importance for charge doping in graphene. In this paper, we choose thermodynamically stable BiFeO(0001) surfaces to explore the adsorption behavior and charge doping effect in a graphene/BiFeO system. By performing first-principles calculations, we find that both the adsorption behavior and charge doping effect show distinct characteristics for graphene adsorbed on the oppositely polarized BiFeO(0001) surfaces. We predict that n-type doping and p-type charge doping occur in graphene on the positive and negative BiFeO(0001) surfaces, respectively. The carrier density is estimated to be 10 cm orders of magnitude. Our results reveal that the graphene/BiFeO hybrid system is an intriguing candidate to make graphene-based field-effect transistors, whose p-n junctions can be made by patterning the domain structure of the BiFeO substrate. Moreover, the graphene/BFO hybrid structure may display an outstanding photovoltaic effect due to the combination of the bulk photovoltaic effect of the BFO substrate and the optical transparency of the graphene electrode.