Thermodynamic Stability of BiFeO3 (0001) Surfaces from ab Initio

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Thermodynamic stability of BiFeO (0001) surfaces from ab-initio theory Jian-Qing Dai, Jie-Wang Xu, and Jian-Hui Zhu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b14726 • Publication Date (Web): 29 Dec 2016 Downloaded from http://pubs.acs.org on January 2, 2017

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ACS Applied Materials & Interfaces

Thermodynamic Stability of BiFeO3 (0001) Surfaces from Ab-initio Theory Jian-Qing Dai,* Jie-Wang Xu, and Jian-Hui Zhu School of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, P. R. China *Corresponding author. Fax: +86 871 65107922. E-mail address: [email protected] (J.-Q. Dai). Abstract: The relative stability of multiferroic BiFeO3 (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-O2 and -Fe-O3-Bi, respectively. The predicted difference in oxygen content between the negative and positive surfaces is consistent with experimental observations at the BiFeO3/metal interfaces [Nat. Mater. 13, 1019 (2014); Adv. Mater. 27, 6934 (2015)]. 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 BiFeO3 (0001) surfaces show strong dependence on the ferroelectric polarization direction. Therefore, we expect that the surface physical and chemical properties of the BiFeO3 (0001) surfaces can be easily tuned by an external electric field. Keywords: BiFeO3; (0001); polar surfaces; thermodynamic stability; ab-initio calculations.

1.

Introduction Polar oxide surfaces have become a rapidly expanding field of research due to the intriguing

surface physical and chemical properties as well as the potential technological applications.1,2 For ferroelectric oxide materials, along the polarization direction, there are two types of surfaces, i.e. the negatively and positively polarized terminations, which can be quite different in the stoichiometry, atomic geometry, and surface electronic states. Moreover, the ferroelectric polarization direction can be easily switched by an external electric field, which provides the feasibility for reversible conversion between the negative and positive surfaces, and hence a novel avenue for advanced surface chemistry.3 As the first comprehensively investigated ferroelectric polar surfaces, the stoichiometry and

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atomic configuration of LiNbO3 1×1 (0001) surfaces show remarkable dependence on the direction of ferroelectric polarization.4,5,6 In contrast to the stable negative surface (-Li-O termination), the preferred positive surface (Li2-O3-Nb- termination) contains more O and Li atoms with rearrangement of the atomic layer sequence. Furthermore, the LiNbO3 (0001) polar surfaces will undergo a series of surface reconstructions with temperature due to different charge compensation mechanisms.7,8 These results were consistent with the mass-spectrometric measured differences in evaporation rates of LiO, Li, and O2 species from the negative and positive surfaces of LiNbO3 single-domain crystal. 9 The subsequent density functional theory (DFT) investigations 10 , 11 , 12 demonstrated that the adsorption behavior of H2O, CH3OH, and other molecules on the LiNbO3 (0001) surfaces are strongly polarization-dependent. By using DFT calculations and kinetic Monte Carlo (KMC) simulations, Kim et al.13 found that depositing Pd on negative and positive LiNbO3 (0001) surfaces leads to very different adsorption geometries, which can be used to explain the observed difference in catalytic activity for Pd deposited on oppositely polarized LiNbO3 (0001) surfaces. Recently, theoretical and experimental results by Baeumer et al.14 also demonstrated that graphene adsorbed on the oppositely polarized LiNbO3 (0001) surfaces displays remarkable modulation for the spatial carrier density. BiFeO3 (BFO), the only single-phase multiferroics with large polarization (~90 µC/cm2) and G-type antiferromagnetic (AFM) order well above room-temperature,15,16 belongs to the same R3c space group just as LiNbO3. For the BFO (0001) polar surfaces which is the (111) facet in the pseudocubic notation, our previous report17 predicted that the preferred stoichiometric negative and positive surfaces are composed of complete Fe-O3-Bi trilayer. The outermost Fe atomic layer at the negative surface suffers from large inward relaxation while the O3 atomic layers in the positive surface have evident in-plane rotational reconstruction. As for the surface electronic states, the negative surface distinguishes from the positive termination by a gap state though both surfaces remain the insulating character. A relevant study by Zhu et al.18 investigated the BFO pseudocubic (111) surfaces from ab-initio theory and we have commented their results in detail in Ref [17]. However, the calculated surface energy in our previous work17 is only an indication of the surface stability in vacuum without varying the surface stoichiometry. In order to predict the stable negative and positive surfaces under particular environmental conditions, the surface grand potentials are needed and we should use the ab-initio thermodynamic approach19,20 It is just the issue to be addressed in our present work. Based on DFT total energy calculations, we investigate the dependence of thermodynamically favored BFO (0001) surfaces on the chemical potential conditions. Besides the stoichiometry and surface geometries, we determine the electronic states and magnetic properties for the stable negative and positive surfaces. The predicted strong dependence of surface 2


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physical properties on ferroelectric polarization direction indicates that the BFO (0001) surface is an intriguing platform for exploiting the surface chemical and magnetoelectric applications.

2.

Methodology We employ the VASP package 21 to perform ab-initio calculations based on the projector

augmented wave (PAW) potentials22,23 and the Perdew-Burke-Ernzerhof functional revised for solids (PBEsol)24. The valence electrons included in the PAW potentials for Bi, Fe, and O are 5d106s26p3, 3p63d64s, and 2s22p, respectively. A 5×5×1 Γ-centered k-points mesh is used for Brillouin zone sampling. For density of states (DOS) calculation, the k-points mesh is increased to 9×9×1. The cut-off energy of plane wave expansion is 500 eV and the change of total energies in self-consistent calculations is no more than 10-6 eV. We use the DFT+U method25 to treat the on-site Coulomb correlation of Fe 3d electrons and the Hubbard parameter Ueff is set to 2.5 eV, which is the same value as adopted in previous theoretical investigation on the BFO (11 2 0) nonpolar surfaces.26 The spin-orbital coupling (SOC) is not turned on in our present work since it has negligible influence on the thermodynamic stability and atomic geometries of the BFO surfaces. In addition, the two terminations of a BFO (0001) slab could not be equivalent in any case due to ferroelectric polarization. And we use the dipole corrections27 to eliminate the spurious electrostatic interactions between the slab periodic images. To simulate the BFO (0001) polar surfaces, we adopt the similar approach adopted in Refs.[4,5] to construct a slab consisting of ten -Fe-O3-Bi- trilayers plus a surface termination and a vacuum layer of ~15 Å. We follow Refs. [4,5,8] to define the polar BFO (0001) surface, the negative and positive BFO (0001) surfaces are denoted as the ferroelectric polarization direction pointing away and toward the surface terminations, respectively. The details to construct the stoichiometric slabs can be found in our previous report.17 We use -Fe-Ox-Biy as the positive termination and -Fe-Biv-Ou as the negative termination (x, u = 0, 1, 2, 3 and y, v = 0, 1, 2). All the possible combinations and different initial atomic configurations have been considered in the surface calculation, which leads to about 80 different slabs (the methodology to construct distinct surface atomic configurations is illustrated in the Supporting Information for this article). In this way, we believe that all the possible nonstoichiometric surfaces (including the stoichiometric bulk cuts) are included in our simulation. All the termination atoms as well as the outer three trilayers on each surface are allowed to relax in all directions (force threshold 20 meV/Å) while the remaining atomic layers are clamped to simulate the bulk phase of BFO. To avoid the possible saddle point, the threefold rotation symmetry has been slightly broken and no symmetry restrictions are applied during the structural relaxation. As the first step to investigate the BFO (0001) surfaces, we do not consider surface reconstructions other than

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the 1×1 surface unit-cell although large surface unit-cells are required to pinpoint the exact stoichiometry of the real surfaces.

3.

Results

3.1 Surface phase diagrams and atomic geometries We first concentrate on the formation energies of relative compounds since they restrict the thermodynamically stable region of the pure BFO phase. The calculated (the DFT total energy differences) and experimental (T = 0 K and p = 1 atm) formation energies for different compounds are summarized in Table 1. Our theoretical results are in quite good agreement with the experimental values.28,29 Especially for BFO, the experimental formation energy of BFO is only available in a recent report.30 We find that our theoretical value (-7.92 eV) is very close to the experiment measurement (-7.97 eV) and previous calculation (-7.40 eV).31 Based on the calculated formation energies, we find that the thermodynamically stable region of the pure BFO phase is constrained by the boundaries beyond which Bi2O3 and Fe2O3 begin to precipitate on the BFO surfaces (shown as red and black lines in Fig. 1). Our result is consistent with Ref. [31], which also found that other phases such as Fe3O4, Bi2Fe4O9, and Fe2Bi4O9 have no influences on the stability of BFO. The quite narrow region for pure BFO phase as compared to other perovskites such as LiNbO34,5 and SrTiO320 is due to its small formation energy. To compare the relative stability of surfaces with different stoichiometry, we should employ the surface grand potential, in which various growth conditions are represented by the chemical potentials of different atomic species.4,5,19,20 In our case, they are µBi, µFe, and µO, respectively. By utilizing the relationship of µ BiFeO3 = µBi + µFe + 3µO and introducing ∆µBi, ∆µFe, and ∆µO as variations of the chemical potentials with respect to those of the reference phases (rhombohedral Bi and bcc Fe bulk structure as well as the free isolated O2 molecule), we can express the surface grand potential in terms of ∆µBi and ∆µO since they are more easily controlled in experiments. From the formation energies of relative phases, the lower and upper bounds of ∆µBi and ∆µO can also be determined. The derivations of the surface grand potential and the boundary limits of the chemical potentials are detailed in the Supporting Information for this article. According to Ref. [32], the chemical potential of oxygen can be expressed as the experimental conditions of temperature and pressure based on the ideal-gas assumption. The calculated phase diagrams of the negative and positive BFO (0001) surfaces are shown in Fig. 1. We can clearly see that the oppositely polarized surfaces show distinct stoichiometries under the same conditions, which demonstrates the important effect of ferroelectric polarization on the

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surface stabilization. For the negative surface (Fig. 1a), there are three types of surface terminations within the thermodynamically allowed region. In the O-poor and simultaneously Bi-rich chemical environments (top left corner of Fig. 1a), the stable surface termination is the complete -Bi-O3-Fe trilayer, which has been investigated in Ref. [17]. The -Bi-O3 termination becomes the most stable surface corresponding to the O-rich and Bi-poor conditions (lower right corner of Fig. 1a). In contrast to very limited domains for the -Bi-O3-Fe and -Bi-O3 terminations, the nonstoichiometric -Bi-O2 termination is favored under most conditions. In case of the positive surface (Fig. 1b), the complete -Fe-O3-Bi trilayer happens to be the thermodynamically favored termination under most chemical conditions despite the small region for -Fe-O3 termination in the O-rich and Bi-poor environments. Our results show that, under most conditions, the preferred negative and positive surfaces have the nonstoichiometric -Bi-O2 and stoichiometric -Fe-O3-Bi terminations, respectively. In other words, the negative surface contains less oxygen than the positive surface. Although there are no direct measurements on the oppositely polarized BFO (0001) surfaces, our results are consistent with the experimental observations at the BFO/LaxSr1-xMnO3 (LSMO) interface by Kim et al.33 Through a combination of scanning transmission electron microscopy and electron energy-loss spectroscopy, they found that an unexpected lattice expansion and anomalous decrease of Mn valence, as well as a change of oxygen K-edge intensity, occurred at the BFO/LSMO interface with negative polarization of BFO (i.e. the ferroelectric polarization points away the interface).33 They demonstrated that this behavior was a direct evidence for screening by oxygen vacancies. At the same time, for the BFO/LSMO interface with positive polarization of BFO, neither lattice expansion nor oxygen vacancy-controlled screening was observed. In addition, the thermal stability investigation of the BFO/CoFeB heterointerface 34 also confirmed that there exists the BFO polarization direction induced oxygen vacancies difference. The top view of space-filling models of different surface terminations is presented in Fig. 2 while Fig. 3 illustrates the side view of these terminations. Simultaneously, the inter-planar distances of various surface terminations are collected in Table 2. We start with the (0001) surface terminations composed of complete -Bi-O3-Fe or -Fe-O3-Bi trilayers to inspect the surface geometries. According to our previous work17, the atomic configurations of these two negative and positive surfaces are summarized as follows. For the negative -Bi-O3-Fe termination, the outermost Fe atomic layer shows a large inward relaxation (-0.48 Å) which results in the the inter-planar distance between the outmost Fe layer and the O3 layer beneath it contracts by about 50% with respect to the bulk value. In case of the positive -Fe-O3-Bi termination, the outward displacement of the outmost Bi layer (0.20 Å) leads to the inter-planar distance of the outmost Bi layer and the neighboring O3 layer expands by 43% 5



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with respect to the bulk value. In addition to the distinct atomic displacements along the z-direction, another significant feature is that there exists a remarkable in-plane rotational reconstruction of the O3 atomic layer for the positive surface (~15° for the outmost O3 layer) while this behavior is negligible for the negative surface (~2° for the outmost O3 layer). As demonstrated in Ref. [17], at the -Fe-O3-Bi surface termination, the strongly hybridization of the Bi-6p orbitals with the O-2p states needs to reduce the Bi-O bond length, which can be effectively achieved by in-plane rotation of the O3 atomic layer instead of relaxation along the z-axis. Next we focus on the other terminations. Under the O-rich and Bi-poor chemical potential conditions, the stable negative and positive surface terminations are -Bi-O3 and -Fe-O3, respectively. Though the surface terminations are not composed of complete -Bi-O3-Fe or -Fe-O3-Bi trilayer, both of them have no oxygen vacancies. For the negative -Bi-O3 termination, we note that the in-plane rotational reconstruction of the outmost O3 layer remains negligible just like the stoichiometric -Bi-O3-Fe termination. As for the positive -Fe-O3 termination, however, the outmost O3 atomic layer undergoes a significantly suppressed rotation (~5°) as compared with the large value of ~15° for the stoichiometric -Fe-O3-Bi termination. From Fig. 3a and Tab. II, a very notable feature of the negative -Bi-O3 termination is the remarkable contraction of Bi-O3 spacing (0.17 Å and -0.08 Å for the outmost and the secondary outer Bi-O3 layers) with respect to the bulk value of 0.59 Å. In fact, both of them are more suitable to be regarded as one atomic layer with small rumpling. As we know, the spontaneous polarization of BFO is due to large displacement of Bi cation relative to the oxygen octahedral.35 Therefore, the Bi and O3 layers moving into one plane will lead to the vanishing polarization, which hence can be considered as an efficient way to compensate the surface charge. In case of the positive -Fe-O3 termination, the outmost Fe-O3 spacing (0.83 Å) doesn't change much relative to the bulk value (0.90 Å), while the underlaying Fe-Bi spacing (0.33 Å) exhibits significant contraction as compared with the bulk value of 0.80 Å. As demonstrated later, in addition to the atomic relaxation, the charge compensation of the -Fe-O3 surface termination is achieved mainly through the surface electronic reconstruction. The last thermodynamically stable surface is the negative -Bi-O2 termination (the right panel of Fig. 2a and Fig. 3a), which is favored under most chemical potential conditions. A noticeable feature of the -Bi-O2 surface termination is that one O relaxes down into the top Bi plane to form BiO atomic layer, while the other O resides above the Bi plane by 0.65 Å. Due to the nonstoichiometry and the insufficient O content, the top Fe is surrounded by five O atoms and the structure shows a distorted trigonal bipyramidal configuration. At the same time, besides the outmost two O atoms, the top Bi bonds to another O located in the underlaying layer. In addition, from Fig. 2 and Fig.3, it can be seen that the -Bi-O2 termination shows much larger microscopic surface roughness as compared 6


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to other thermodynamically stable surface terminations. 3.2 Surface electronic states and magnetic properties As we know, the real surfaces in the absence of an external electric field should be charge neutral, so the surface charges of polar terminations must be neutralized by different compensation mechanisms.2 The charge redistribution at the surfaces can be inspected by means of Bader’s topological charge analysis, which is summarized in Table 3. First, it can be seen that marked changes ∆Q of the atomic charges are only confined to several outer atomic layers for different surface terminations. Second, the sum of ∆Q of the outer several layers is roughly consistent with the charge compensation criterion estimated by the formal oxidation states of each species (+3e, +3e, and -2e for Bi, Fe, and O, respectively). For the negative and positive surfaces terminated with complete -Bi-O3-Fe or -Fe-O3-Bi trilayers, our previous report17 has pointed out that the surface charges are vanishing because the stacking of the dipole-minimal trilayers leaves the surface region emptyand hence there is no need for polarity compensation.2 According to Table 3, the summations of ∆Q for the negative -Bi-O3-Fe and the positive -Fe-O3-Bi terminations are -0.06 and +0.05, respectively. We can see that the quantitative results based on the Bader’s atomic charges method are in fairly good agreement with the estimations by the ionic formal valence states. On the other hand, for the negative -Bi-O3 and positive -Fe-O3 terminations, based on the ionic formal valence states, both of them show the surface charges of -3/2, which are roughly compensated by the summation of the Bader’s charges of the surface atoms (+1.26 and +1.83 for -Bi-O3 and -Fe-O3 terminations, respectively). In case of the surface terminations with oxygen vacancies, the Bader’s surface charges for the -Bi-O2 and -Fe-O2 terminations are figured up to be +0.45 and +0.68, respectively, which can roughly satisfy the polarity compensation criterion since the formal surface charge of both terminations is -1/2. Third, we note that the Bader’s surface charge of the negative -Fe-On (n = 2, 3) termination is higher than the corresponding positive -Bi-On one. In view of the surface geometries of the -Bi-On terminations where the O atoms relax into the Bi plane suppressing the spontaneous polarization, we can understand that there is no need for additional compensating charges to counteract the surface polarization. The surface electronic DOS for different negative surface terminations are shown in Fig. 4 and Fig. 5. It is clear that all the stable negative (0001) surfaces of BFO show insulating behavior with a band-gap of ~0.7 eV, which decreases by 1 eV with respect to the bulk value (our previous work17 demonstrated that the band-gap of bulk BFO is about 1.7 eV for Ueff = 2.5 eV). The decrease of band-gap for both the -Bi-O3-Fe and -Bi-O2 surface terminations can be considered to be caused by the emergence of a spin-polarized gap state, while the bottom of conduction band for the -Bi-O3 termination is no longer spin-polarized. From the site-resolved partial DOS (Fig. 5), we can see that, 7



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for the -Bi-O3-Fe termination, the spin-polarized gap state is mainly composed of the down-spin Fe 3d orbitals and the sharp peak at the top of the valence band is due to the O2p, Bi 6s, and Fe 3d states. In case of the -Bi-O2 termination, the spin-polarized gap state origins from the O2p and Fe 3d states, as well as small contribution from the Bi 6p orbitals. As for the -Bi-O3 termination, the lowest conduction-band states exhibit noticeable Fe 3d and O 2p characters. For the -Bi-On (n = 2, 3) terminations, the weight of valence band near the Fermi level is shifted down to lower energy as compared with that of the -Bi-O3-Fe termination. In addition, another interesting feature should be mentioned is that the DOS of the Bi 6s lone pair electrons near the Fermi energy is affected remarkably by the different surface terminations. We show in Fig. 6 and Fig. 7 the surface electronic states for the thermodynamically stable positive -Fe-O3-Bi and -Fe-O3 terminations. As displayed in Fig. 6a and Fig. 7a, the band-gap of the -Fe-O3-Bi surface termination is ~1.3 eV and the spin-polarized bottom of the conduction band is made dominantly by the Fe 3d orbitals despite of some contributions from the O 2p and Bi 6p states. The effect of in-plane rotational reconstruction of the O3 atomic layer on the surface electronic structure has been discussed in detail in our previous work.17 In short, we find that hybridization of the outermost Bi with the second O3 layer is achieved by the in-plane rotation of the O3 atomic layer, which can effectively reduce the Bi-O bond length and simultaneously affects the hybridization of the Fe 3d with the O 2p states. In case of the -Fe-O3 termination (Fig. 6b and Fig. 7b), however, a sharp spin-polarized gap state affects the surface electronic structure remarkably, which corresponds to the O 2p and Bi 6s states, as well as some contributions from the Fe 3d and Bi 6p orbitals. Moreover, it is the pseudogap caused by the spin-polarized gap state that makes the surface DOS of the -Fe-O3 termination showing half metal-like character, for which the band-gap of the up-spin electronic states is vanishing while the down-spin DOS exhibits an insulating behavior with a band-gap of ~1 eV. Next we focus on the steric configuration of the Bi 6s lone pair electrons since its weight near the Fermi energy varies notably from one type of surface termination to another. Let’s take the negative -Bi-O2 and positive -Fe-O3-Bi terminations as examples, which are favored under most chemical potential conditions. The calculated electron localization functions (ELF)36,37 are shown in Fig. 8. It can be seen that the O 2p electrons display the same egg-shaped ELFs with different spatial directions for these two surface terminations. For the negative -Bi-O2 termination (Fig. 8a and 8c), the ELF of the Bi 6s lone pair electrons is like a small piece of broken eggshell located over the lateral side of the Bi atom. As for the positive -Fe-O3-Bi termination (Fig. 8b and 8d), the large lobe-shaped 6s lone pair electrons reside on top of the Bi atom. As we know, for Bi-containing bulk materials, the stereochemical activity of the Bi 6s lone pairs is responsible for many functional 8


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properties such as ferroelectric polarization and piezoelectric response, so we expect that its distinct steric configurations for the negative and positive BFO (0001) surfaces will play an important role in determining the surface physical and chemical properties. Finally, we turn our attention to the influence of different terminations on the surface magnetic moments. As we know, for the bulk R3c BFO, the magnetic structure belongs to the G-type AFM order and the preferred orientation of magnetic moments lies in the (0001) plane with small spin-canting, which leads to a uniform weak ferromagnetism (FM).38,39 As reported in our previous paper17, the calculated magnetic moment of Fe atom is ±3.987 µB and the SOC effect leads to the weak ferromagnetism of 0.027 µB/Fe, which are in good agreement with the experimental value38 and other theoretical results.39,40 The SOC effect is not included in our present work since it has negligible influence on the magnitude of magnetic moments. The calculated magnetic moments for upper four Fe atomic layers are collected in Table 4. For the negative -Bi-O3-Fe and positive -Fe-O3-Bi surface terminations, we can clearly see that the changes of magnetic moments relative to the bulk value are very small. However, large deviations from the bulk magnetic moment are observed in the outmost two Fe layers for other surface terminations. In particular, the total change of magnetic moments for the positive -Fe-O3 surface reaches a high value of -1.9 µB per unit-cell area. Viewed in connection with the surface DOS (Fig. 6b and Fig. 7b), we find that the half metal-like electronic structure is responsible for this remarkable surface ferromagnetism, because some weight of the up-spin Fe 3d states is transferred from the valence band to the gap state.

4.

Discussion Our ab-initio calculations confirm that not only the stoichiometry and atomic configurations but

also the electronic and magnetic properties are quite different for the thermodynamically stable negative and positive BFO (0001) surfaces. These polarization dependent behaviors are accompanied by modification of the surface chemical properties which may lead to many exciting applications. As have been demonstrated in the LiNbO3 (0001) surfaces, the dynamical control of heterogeneous catalysis,41 artificial photosynthesis and photocatalysis,42 as well as reversible fragmentation and self-assembling of nematic liquid crystals,43 are also expected to be discovered in the BFO (0001) polar surfaces. Our results indicate that the BFO (0001) polar surfaces will be an intriguing candidate for advanced surface chemistry. Apart from the surface chemical properties, we should reiterate that BFO is known as an important multiferroic material possessing simultaneous ferroelectric and antiferromagnetic ordering that can be altered by application of an external filed. It is the robust ferroelectricity and antiferromagnetism as well as the weak ferromagnetism arising from spin-orbital coupling

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interactions39,44 that make BFO the promising candidate for novel magnetoelectric and spintronic applications such as exchange-bias coupling and spin-dependent tunneling for information storage and processing.45,46 Considering the use of nanodimensional materials in future devices, atomic-scale understanding of the surface and interface properties may become crucial. For instance, the heterointerfaces between ferromagnetic metals and ferroelectric/multiferroic oxides are of particular importance for the next generation of magnetoelectric memories.47,48 As mentioned above, our calculated thermodynamic stability of BFO (0001) surfaces is well consistent with the recent experimental observations,33,34 which demonstrated the existence of oxygen vacancies difference at the metal/BFO interfaces induced by the ferroelectric polarization. This polarization-dependent modulation in oxygen content has detrimental influence on the device performance due to the irreversible fatigue of the interface after limited electric cycles. Therefore, the thermal stability of the metal/BFO interface plays a crucial role in determining the reliability of the interface-based magnetoelectric devices. According to our results, although the oxygen content of the negative BFO (0001) surface is less than the positive surface under most chemical conditions, the calculated phase diagram (Fig. 1) indicates that the difference in oxygen vacancies can be avoided in two chemical potential regions: one is the O-poor and Bi-rich region, the other is the O-rich and Bi-poor region. Our finding casts new insights into the thermal stability of the BFO (0001) polar surfaces and provides feasible strategy in device design with better performance. The influences of epitaxial strain and doping on the thermodynamic stability of BFO polar surfaces are interesting issues deserved further investigations. As we know, BFO is often studied in the form of thin films and therefore the epitaxial constraint has significant effect on its structural, ferroelectric, and magnetic properties. An appealing discovery is that the BFO thin films epitaxially grown on the (001) RAlO3 (R = La and Y) substrates exhibit tetragonal-like structure (c/a ≈ 1.24) and large spontaneous polarization (~130 µC/cm2).49,50,51 The subsequent investigations52,53 revealed that a strain-induced isosymmetric phase transition occurs at the compressive strain of ~4.5% and that the tetragonal-like structure belongs to a monoclinic phase with either the nontilted Cm or titled Cc space group. For the BFO (11 2 0) nonpolar surface, which is (110) plane in the pseudocubic notation, Shimada et. al.

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investigated the strain effect on ferroelectric and magnetic properties at

the most favorable O-terminated surface and found that the strain response of the ferroelectric polarization and the magnetic moment are markedly enhanced at the surface with respect to the bulk. The effect of epitaxial strain on the BFO (0001) polar surfaces may be more complex than the the nonpolar surface due to the tetragonal-like phase occurred at large compressive strain, which leads to the polarization with nonzero in-plane and out-of-plane components and may change the magnetic order from G-type to the C-type.53,54 In addition, it should be noted that the epitaxial thin films can 10


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be grown by the BFO-based solid solutions such as BiFe0.6Ga0.4O3 and Bi0.9La0.1FeO3 in order to enhance the structure stability and the physical properties.55,56 We expect the high doping of Ga (La) to replace Fe (Bi) will affect the BFO polar surfaces, which should be paid adequate attention in future works.

5.

Conclusions To summarize, we have performed ab-initio calculations to investigate the relative

thermodynamic stability of multiferroic BFO (0001) surfaces with different stoichiometry and obtained some valuable understandings about the stable surface terminations. Under chemical environments where the bulk BFO is stable, we predict that there are three types of stable terminations for the negative surface while the positive surface possesses two kinds of thermodynamically preferred terminations. Under most conditions The favored terminations for the negative and positive surfaces are -Bi-O2 and -Fe-O3-Bi, respectively, which indicates that the positive surface contains more oxygen than the negative surface at similar chemical environments. This result is consistent with the experimental observations at the BFO/LSMO33 and BFO/CoFeB34 interfaces, which implies that the oxygen vacancies difference induced by the ferroelectric polarization is a universal phenomenon both at the BFO surfaces and the BFO/metal interfaces and may have important influences on the interface-mediated magnetoelectric performance. Besides the stoichiometry and atomic configurations, our calculations clearly show that there exist remarkable differences in the surface electronic and magnetic properties between the stable negative and positive surface terminations. In view of these strong polarization dependent surface physical properties, we expect that the BFO (0001) surface will prove to be an ideal place for advanced surface chemistry which can be tuned via an external electric field. Furthermore, our findings also provide important implications in the interface-based magnetoelectric applications. Supporting Information. Further details on how to construct the starting surface configurations, expression of the surface grand-potential of BiFeO3, the range of chemical potential for Bi and O, and other restrictive conditions such as formation of Bi2O3, Fe2O3, and FeO.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 51462019 and 51162019).

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Table 1. Theoretical and experimental formation energy (in eV) for relevant compounds. Compounds BiFeO3 Bi2O3 Fe2O3 FeO O2

Theory -7.92 -6.49 -8.45 -2.42 -5.84

Exp. -7.97a -6.01b -8.49c -2.80b -5.12c

a

Ref. [30]; b Ref. [27]; c Ref. [28]. Note that the formation energies for Bi2O3 and FeO are extrapolated from 298.15 K to 0K.

Table 2. Distances (in unit of Å) between atomic layers of the different surface terminations. The corresponding bulk values are d(Bi,O)=0.59 Å, d(O,Fe)=0.90 Å, d(Fe,Bi)=0.80 Å, and d(O, O)=2.29 Å, respectively. Note that the negative value indicates rearrangement of the atomic layer sequence. The symbols of Fe0, FeI, FeII, Bi0, BiI, BiII, OI, OI′, and OII are shown in Fig. 3. For the positive -Fe-O2 termination, the rumpling of OI atomic layer is 0.22 Å. -Bi-O3-Fe d(Fe0,OI) 0.45 d (OI,BiI) 0.62 Distance d (BiI,FeI) 0.56 d (FeI,OII) 1.08 d(OII,BiII) 0.61 Z+ -Fe-O2

-Bi-O3 d (OI,BiI) 0.17 d (BiI,FeI) 0.65 d (FeI,OII) 1.09 d(OII,BiII) -0.08 -Fe-O3

d (OI,FeI) Distance d (FeI,BiI) d (BiI,OII) d(OII,FeII)

d (OI,FeI) d (FeI,BiI) d (BiI,OII) d(OII,FeII)

Z−

1.10 -0.01 1.21 0.85

0.83 0.33 1.02 0.80

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-Bi-O2 0.69 d (OI′, OI) d (OI,BiI) -0.04 d (BiI,FeI) 0.85 d (FeI,OII) 0.94 d(OII,BiII) 0.54 -Fe-O3-Bi d (Bi0,OI) 0.84 d (OI,FeI) 0.95 d (FeI,BiI) 0.51 d (BiI,OII) 0.83 d(OII,FeII) 0.85

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Table 3. Changes of Bader atomic charge ∆Q (in e) with respect to the bulk values. The Bader charges for bulk BFO are +1.856 (Bi), +1.706 (Fe), and -1.188 (O), respectively. The negative and positive surfaces are represented by Z- and Z+, respectively. .

Z−

Z+

-Bi-O3-Fe Atom ∆Q Fe0 -0.243 OI +0.069 -0.033 BiI FeI +0.034 -0.003 OII BiII -0.020 -0.06 Σ -Fe-O2 Atom ∆Q OI FeI BiI OII FeII Σ

+0.295 -0.059 -0.069 +0.066 +0.020 +0.68

-Bi-O3 Atom ∆Q

-Bi-O2 Atom ∆Q +0.232 OI′ OI +0.176 BiI -0.081 FeI -0.030 OII +0.047 BiII +0.013 +0.45 Σ -Fe-O3-Bi Atom ∆Q Bi0 -0.184 OI +0.045 FeI +0.010 BiI +0.041 OII +0.015 FeII +0.002 +0.05 Σ

OI BiI FeI OII BiII Σ

+0.286 +0.024 +0.004 +0.102 +0.063 +1.26 -Fe-O3 Atom ∆Q OI FeI BiI OII FeII Σ

0.441 0.020 0.170 0.098 0.019 +1.83

Table 4. The calculated magnetic moment (in unit of µB) of Fe atom for different negative (Z-) and positive (Z+) terminations. Note that the magnetic moment of Fe for bulk BiFeO3 is 3.99 µB. The Fe atom changes from outer to inner surface as the layer number increases.

Fe Layer 1 2 3 4 Σ

Z- surface -Bi-O3-Fe -Bi-O3 -Bi-O2 3.75 2.45 3.26 -3.99 -3.21 -3.96 4.00 3.97 3.99 -3.99 -3.98 -3.99 -0.23 -0.77 -0.70

-Fe-O2 3.13 -3.99 3.99 -3.99 -0.86

Z+ surface -Fe-O3 -Fe-O3-Bi 2.14 3.99 -4.04 -3.98 3.98 3.99 -3.99 -3.99 -1.91 0.01

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Fig. 1 Stable terminations of (a) the negative and (b) the positive BFO (0001) surfaces. The surface terminations are labeled with hyphens. The black, red, and blue lines denote boundaries beyond which Bi2O3, Fe2O3, and Fe phases start to precipitate on the BFO surfaces, respectively. In the region between the black and red lines, only the bulk BFO phase is stable.

Fig. 2 The space-filling model of BFO (a) negative and (b) positive surface terminations. Purple atoms are Bi, brown atoms are Fe, and red atoms are O.

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Fig. 3 Side view of the (a) negative and (b) positive surface terminations. Bi, Fe, and O atoms are in purple, brown, and red color, respectively. The atom layer changes from outer to inner surface as the layer number increases. For the Bi (Fe) layer located on the outside of OI atomic layer, we denote this atomic layer as Bi0 (Fe0). Not that for -Bi-O3 termination of Fig. 3a, the second Bi layer (BiII) is shaded from the OII atomic layer.

Fig. 4 Surface DOS of the outmost trilayer for the negative (0001) surfaces of BFO. (a) the -Bi-O3-Fe termination, (b) the -Bi-O3 termination, and (c) the -Bi-O2 termination.

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Fig. 5 Site/orbital-resolved partial DOS of the outmost trilayer for the negative the negative (0001) surfaces of BFO. (a) the -Bi-O3-Fe termination, (b) the -Bi-O3 termination, and (c) the -Bi-O2 termination. For the Bi partial DOS, the red dot and black solid curves represent the 6s and 6p orbitals, respectively.

Fig. 6 Surface DOS of the outmost trilayer for the positive (0001) surfaces of BFO. (a) the -Fe-O3-Bi and (b) the -Fe-O3 terminations.

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Fig. 7 Site/orbital-resolved partial DOS of the outmost trilayer for the negative the positive (0001) surfaces of BFO. (a) the -Fe-O3-Bi and (b) the -Fe-O3 terminations. For the Bi partial DOS, the red dot and black solid curves represent the 6s and 6p orbitals, respectively.

Fig. 8 Electron localization functions of (a, c) the negative -Bi-O2 and (b, d) positive -Fe-O3-Bi surfaces of BFO. (a, b) shows the side view while (c, d) illustrates the top view of the surfaces. The threshold for the image of electron localization function image is 0.47.

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Table of Contents Graphic

Brief Summary: Surface phase diagram for the (a) negative Z- and (b) positive Z+ BiFeO3 (0001) surfaces. The surface terminations are labeled with hyphens. The bulk BiFeO3 phase is only stable in the region between the black and red lines.

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Thermodynamic Stability of BiFeO3 (0001) Surfaces from ab Initio

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