Polarization Direction Dependence of Thermodynamic Stability of

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Polarization-Direction Dependence of Thermodynamic Stability of Ferroelectric BiAlO(0001) Polar Surfaces 3

Jian-Qing Dai, Xiao-Wei Wang, and Jie-Wang Xu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08148 • Publication Date (Web): 06 Dec 2018 Downloaded from http://pubs.acs.org on December 7, 2018

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The Journal of Physical Chemistry

Polarization-Direction Dependence of Thermodynamic Stability of Ferroelectric BiAlO3(0001) Polar Surfaces Jian-Qing Dai,* Xiao-Wei Wang, and Jie-Wang Xu Faculty 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). ORCID: 0000-0003-4352-0789 (Jian-Qing Dai) Abstract: Polar surfaces of ferroelectric oxides are of great importance for both fundamental and practical interest. In this report, we present a theoretical study to determine the thermodynamic stability and electronic properties of ferroelectric BiAlO3(0001) surfaces. According to the calculated surface phase diagram, we predict that the equilibrium stoichiometries are distinct for the oppositely polarized BiAlO3 surfaces under the same chemical conditions. In addition to nonstoichiometry of the surface chemical compositions, we find that anomalous filling of the surface states can also result in surface metallization in order to compensate the remarkable surface polarity. Besides providing atomic-scale understanding of the BiAlO3(0001) surfaces, we also put forward the practical implications in novel magnetoelectric devices and advanced surface chemistry.

1. Introduction It is the switchable spontaneous polarization of ferroelectric oxides which leads to their numerous industrial applications including pyroelectric and piezoelectric devices as well as ferroelectric memory technology.1 Considering the potential future applications in nanoscale devices such as ferroelectric/multiferroic tunnel junctions2,3 and advanced surface chemistry,4,5 atomic-scale understanding of the surface and interface properties is of crucial importance. Previous theoretical and experimental reports demonstrated that the surface physical and chemical properties of ferroelectric

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oxides show strong dependence on the polarization direction.6,7,8,9,10 Polar oxide surfaces almost always tend to screen their surface polarity by various atomic reconstructions rather than by purely electronic reconstruction.6,11,12,13,14,15 A representative example is the comprehensively studied LiNbO3(0001) polar surfaces. According to Ref. [6,12,16,17], the local chemical compositions of the LiNbO3(0001) surfaces are characterized by an unique nonstoichiometric feature which is different between the oppositely polarized surfaces under the same conditions. In contrast to the thermodynamically preferred negative surface with -Li-O termination, the energetically favourable positive surface is terminated with Li2-O3-Nb- layer consisting of more oxygen and lithium ions.6,16 Another example is the multiferroic BiFeO3(0001) surfaces. Our recent theoretical work18 showed that, under the thermodynamically allowed chemical conditions, there exist three kinds of surface terminations (-Bi-O3-Fe, -Bi-O2, and -Bi-O3) for the negative surface and two kinds of terminations (-Fe-O3-Bi and -Fe-O3) for the positive surface. The predicted difference in oxygen content between the oppositely polarized BiFeO3(0001) surfaces is in agreement with experimental observations at the BiFeO3/metal interfaces.19,20 In addition, theoretical studies13,14 for PbTiO3 and BaTiO3 (001) polar surfaces also predicted that the surface polarity prefers to be canceled by adjusting the surface stoichiometry, which therefore results in distinct surface terminations depending on the specific chemical conditions. BiAlO3 (BAO), as an intriguing novel ferroelectric perovskite,21,22,23 has the same R3c space group as LiNbO3 and BiFeO3. The theoretical value of spontaneous polarization is about 80 μC/cm2 and the direction is along the [0001] direction in the four-index Bravais-Miller notation, which is equivalent to the [111] direction in the pseudo-cubic representation.16 Similar to BiFeO3, the ferroelectricity comes from off-center displacement of the Bi cations with respect to the O octahedral driven by the 6s2 lone pair on the A-site Bi ion.24,25 Due to the high-performance of ferroelectricity and piezoelectricity, BAO is regarded as an appealing alternative to the widely used Pb-based piezoelectric materials.21,23,25,26 Furthermore, recent relativistic first-principles calculations27 predicted that bulk BAO shows a coexistence of ferroelectricity and 2


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Rashba-Dresselhaus spin-orbit coupling (SOC) effect, which leads to the full reversal of the spin texture with ferroelectric polarization switching and might offer intriguing perspectives for novel magnetoelectric and spintronic devices. The R3c BAO can be viewed as -Al-O3-Bi- trilayers stacking along the [0001] crystallographic direction, which is the direction of ferroelectric polarization and usually denoted as z-direction or c-axis. We define the BAO(0001) as the positive surface (Z+) and BAO (0001) as the negative surface (Z−), which is consistent with previous reports on the (0001) polar surfaces of R3c LiNbO3 and BiFeO3.6,16,18 As regard to the BAO(0001) polar surfaces, our previous report28 only focused on the stoichiometric surface terminations. In this work, we present a first-principles density functional theory (DFT) study predicting the relative thermodynamic stability of BAO(0001) polar surfaces with different stoichiometry. Similar to the theoretical investigations on LiNbO3(0001) and BiFeO3(0001) surfaces,6,16,18 we focus on the (1×1) surface unit cell. Our results demonstrate that the surface structure and stoichiometry of BAO(0001) surfaces display significant dependence on the ferroelectric polarization direction. According to the calculated surface phase diagram, we predict that the thermodynamically preferred positive (Z+) surface is only terminated with -Al-O3-Bi trilayer, while the attainable negative (Z) surface is characterized by three types of terminations (-Bi2-O3, -Bi-O2, and -O3), depending on the particular chemical conditions.

2. Methodology Our first-principles DFT calculations were performed by using the Vienna ab initio simulation package (VASP).29,30 The projector augmented wave (PAW) potentials were used to describe the electron core-valence interactions,31,32 and reference states were set as 5d106s26p3, 3s23p1 and 2s22p4 for Bi, Al and O, respectively. The revised Perdew-Burke-Ernzerhof (PBEsol) exchange-correlation functional of generalized gradient approximation (GGA) was employed.33 The wave functions were expanded by plane wave at a kinetic-energy cutoff of 500 eV, and the Fermi energy was smeared by Gaussian method using a width of 0.1 eV. Sampling of Brillouin zone was performed 3



by 5×5×1, and 9×9×1 Г-centered Monkhorst-Pack mesh for self-consistent and density of states (DOS) calculations, respectively. The structural relaxations were carried out until the Hellmann-Feynman forces  0.01 eV/Å and the precision of total energy calculation is 10-6 eV. In addition, the dipole correction34 was used to avoid the artificial electric field created by slab images. To simulate the BAO(0001) surfaces, slabs consisting of ten -Al-O3-Bi- (for Z+ surfaces) or -Bi-O3-Al- (for Z surfaces) trilayers (50 atoms) plus surface termination and a vacuum layer of ~15Å were considered, which are similar to the BiFeO3(0001) surfaces.18 The Z+ and Z surface terminations were considered with -Al-Ox-Biy and -Bij-Oi terminations (x, i = 0, 1, 2, 3; y, j = 0, 1, 2), respectively. Due to the nonequivalence of the two oppositely polarized BAO(0001) surfaces, the surface phase diagram of the Z+ and Z surfaces should be determined separately. For the BAO Z+ surfaces, except for the surface terminations (-Al-Ox-Biy), all the initial slabs consist of ten same Al-O3-Bi- trilayers fixed at their bulk positions. As regard to BAO Z- surfaces, in addition to the -Bij-Oi terminations, the initial slabs are composed of ten same Bi-O3-Al- trilayers which are located at the bulk atomic positions. During surface structure optimization, all the termination atoms and the outer three trilayers (-Al-O3-Bifor Z+ and -Bi-O3-Al- for Z-) were allowed to fully relax, while the rest of atomic layers are fixed. In other words, all the BAO Z+ surfaces have the same backside and vice versa for all the Z- surfaces. For the surface terminations, all possible combinations and different starting geometries were included in order to determine their relative stabilities. The details to construct various surface atomic configurations can be found in our previous report.18 To ensure the atoms were not relaxed to the possible saddle-point positions, we broke slightly the threefold rotation symmetry and employed no symmetry restrictions.

3. Results and discussion 3.1 Range of chemical potentials and surface phase diagram We start from determining the range of chemical potentials within which the clean BAO(0001) surfaces are thermodynamically permissible. For this purpose, we should 4


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first obtain the formation energies of relative compounds including BAO, Bi2O3, Al2O3, and O2. The theoretical and experimental values35-38 of the formation energies are listed in Table 1. It can be seen that our calculated formation energies are in good agreement with previous theoretical and experimental results. To the best of our knowledge, the experimental value of the formation energy for BAO is not available. As we know, the GGA functional tends to overestimate the binding energy of molecules,6 which is O2 in our case. To prevent this effect, we employed the experimental values for all of the available formation energies in our calculations. In Fig. 1, we show the calculated ternary chemical potential mapping for BAO, Bi2O3, and Al2O3. Details of determining the range of chemical potentials can be found in the Supporting Information. The triangle ABC represents the range of chemical potentials within which the formation of bulk BAO phase is thermodynamically preferred. The region enveloped in triangle ADE determines the chemical potential space without the formation of Al2O3, while the space spanned by points B, F, G, and C indicates the region without the formation of Bi2O3. Therefore, we can identify that the red trapezoid of DFGE is the chemical potential region within which only the bulk BAO phase is stable, i.e., the clean BAO(0001) surfaces are thermodynamically preferred in this region. Out of this region, the BAO(0001) surfaces should be covered with other condensed phases. We note that our result is consistent with previous theoretical prediction.35 To identify the relative stability of BAO(0001) surfaces with different stoichiometry, the surface grand potential should be employed and therefore various growth conditions can be represented by the chemical potentials of different atomic species.6,15,16 In our case, the chemical potentials of Bi, Al, and O are denoted as Bi, Al, and O, respectively. By adopting the relationship of BiAlO3  Bi  Al  3O and using Bi, Al, and O as the variations of chemical potentials relative to the reference phases (rhombohedral Bi and fcc Al bulk structure as well as the free isolated O2 molecule), the surface grand potential can be expressed in terms of Bi and O because both of them are more controllable in experiments. From the formation energies of the above mentioned phases, we can determine the lower and upper bounds of Bi 5



and O. Details of the surface grand potential and the boundary limits of the chemical potentials are described in the Supporting Information. In addition, it should be pointed out that, in our first-principles thermodynamic approach, we approximate the free energy by the DFT total energy and the effects of surface formation entropy Ss (which contributes a -TSs term to surface energy16) and lattice vibration are not taken into account. Next, we evaluate the relative stability of the BAO(0001) Z+ and Z surfaces with different stoichiometries and the calculated surface phase diagram is shown in Fig. 2. As we know, the surface can reach equilibrium much faster than the bulk phase, so the chemical potentials of Bi and O were not restricted to the trapezoid region restricted by Fig. 1. It is clear that the oppositely polarized BAO(0001) surfaces show different stoichiometries under the same chemical conditions, i.e., the thermodynamic stability strongly depends on the direction of ferroelectric polarization. According to previous reports,6,16,18 for LiNbO3(0001) and BiFeO3(0001) surfaces, the ferroelectric polarization also plays an important role in determining the thermodynamically preferred surface configurations. For the BAO(0001) Z surface (Fig. 2a), there are three types of thermodynamically allowable surface terminations. Within the region where only bulk BAO is stable, as the chemical conditions change from the upper-left (Bi-rich and O-moderate) to the lower-right (O-rich and Bi-moderate) region, the preferred surface termination follows the sequence of -Bi2-O3, -Bi-O2, and -O3. It should be pointed out that all the thermodynamically allowed BAO(0001) Z surface terminations are nonstoichiometric. As regard to the BAO(0001) Z+ surface (Fig. 2b), we find that the -Al-O3-Bi trilayer is the only thermodynamically preferred termination and that the local chemical composition is stoichiometric.28 As the first step to study thermodynamic stability of the BAO(0001) surfaces, the surface reconstructions other than 11 surface unit-cell are not taken into account, although it may be necessary in order to determine the exact stoichiometry of the real BAO(0001) surfaces. For larger surface unit-cells, there are two possible effects on the thermodynamic stability of the BAO(0001) surfaces. One possible influence relates to 6


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the surface stoichiometry. Since the larger surface unit-cell expands the scope of the surface compositions, the surface terminations with chemical composition out of the range of 11 surface unit-cell may occur in the surface phase diagram. Another potential consequence is the long-period surface reconstruction, which is an effective way to compensate the surface polarity and cannot be included in the 11 surface unit-cell. In fact, for the LiNbO3(0001) surfaces, these two effects have been demonstrated by first-principles calculations on the 33 and 77 surface unit-cells39,40and the experimental observations.39 This implies that the influence of larger surface unit-cells on the thermodynamic stability of the BAO(0001) surfaces deserves to be further investigated. 3.2 Surface geometries and surface polarity compensation The side-view of surface terminations for BAO(0001) Z and Z+ surfaces are shown in Fig. 3 (top-view of surface terminations are shown in Fig. S1 of the Supporting Information). Meanwhile, the interlayer distances of different surface terminations are listed in Table 2. The results demonstrate that structural relaxations mainly occurred in the outer atomic layers. For the BAO(0001) Z+ surface terminated with -Al-O3-Bi trilayer, the distance between the outmost Bi layer and the second O3 layer is expanded by 86% with respect to the bulk value, and the outer O3 atomic layers exhibit considerable in-plane rotational reconstructions.28 For the BAO(0001) Z surface with -Bi2-O3 termination, one Bi is relaxed beyond the top O3 atomic layer, while the other Bi remains below the O3 layer (denoted as Bi′ as shown in Fig. 3a). As regard to the -Bi-O2 terminated Z surface, the Bi layer is located between the two atomic planes composed of the outmost O2 termination (one denoted as O and the other denoted as O′ as shown in Fig. 3b). In case of the -O3 terminated Z surface, the outmost O3 atomic layer is characterized by significant rumpling as large as 0.79 Å, and the surface configuration indicates the formation of peroxo groups,15,41 which is demonstrated by the electron localization function shown in Fig. S2c of the Supporting Information. The surface charge redistribution can be roughly estimated by the Bader’s 7



topological charge analysis.42 As we know, the calculated static atomic charges strongly differ from their formal values and show dependence on the actual theoretical and computational scheme.42 Although there are debates on strategies to determine the static atomic charges, the total static charge distribution is often decomposed into atomic contributions in order to provide insight for polar character of the surface termination.11 The changes of atomic charge, ΔQ, at the BAO Z and Z+ surfaces with respect to the bulk values are shown in Table 3. In addition, the summation of Q (labeled as  in Table 3) for the topmost six atomic layers is also listed (the counterpart at the backside of each slab is not shown). It is clear that variations of atomic charges are mainly restricted to several outer atomic layers regardless of the polarization direction and the surface stoichiometry.18,43 For the BAO(0001) surfaces with Bi as the topmost layer (-Bi2-O3 terminated Z− surface and -Al-O3-Bi terminated Z+ surface), remarkable electronic charge accumulation occurs at the topmost atomic layer. Taking the Bi2-O3 terminated Z− surface as the example, the values of ΔQ for the topmost Bi and the second Bi layer are is -0.30 |e| and -0.10 |e|, respectively. On the other hand, the BAO(0001) surfaces with oxygen atoms as the topmost termination are characterized by electronic charge depletion at the topmost O atomic layer. For example, the topmost O at the -O3 terminated Z− surface shows a significant loss of electronic charge by +1.21 |e| with respect to the bulk value. Taking into account the Bader’s atomic charge of O in bulk BAO (-1.45 |e|), we find that the atomic charge of topmost O is only -0.24 |e|. As we know, the accumulation/depletion of electronic charges at the surface termination will inevitably shift the relative positions of the Fermi level, which leads to reduction of the band gap and, in extreme cases, to surface metallization. We will return this issue in the next section. Due to the polarity compensation by atomic and/or electronic reconstructions, all the realistic BAO(0001) surfaces should display nearly vanishing total surface charges in spite of their different surface terminations. In fact, the summations of Q (labeled as ) should be defined as the surface compensating charges, which compensate the intrinsic polarities of the R3c BAO(0001) surfaces. As we know, the intrinsic surface polarity

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can be represented by the surface charge of the bulk-truncated stoichiometric BAO(0001)

surface, which had been determined in our previous report.28 For the

relevant bulk-truncated BAO(0001) Z+ and Z- surfaces, we listed in Table 4 their intrinsic surface polarities, which can be taken as the reference values to identify the screening efficiency of the surface compensating charges shown in Table 3. For the BAO(0001) Z+ surfaces with -Al-O3-Bi and -Al-O3 termination, which are stoichiometric surfaces and can be directly compared with their bulk-truncated analogues. We find that the intrinsic surface polarities of the bulk-truncated -Al-O3-Bi and -Al-O3 termination are the -0.58 |e| and -2.40 |e|, respectively. From Table 3, the values of compensating charge for the relaxed -Al-O3-Bi and -Al-O3 terminated surfaces are respectively +0.52 |e| and +2.29 |e|, which can almost completely compensate their intrinsic surface polarities and result in the nearly vanishing total surface charges. For the BAO(0001) surfaces with nonstoichiometric terminations, we can assign the intrinsic surface polarity by using the chemical composition difference between the nonstoichiometric and stoichiometric terminations and the Bader’s atomic charges of the bulk BAO (+1.86|e|, +2.49|e|, and -1.45 |e| for Bi, Al, and O, respectively). The third BAO(0001) Z+ surface in our present study is the nonstoichiometric -Al-O2 atomic layer, which is characterized by one less O as compared to the stoichiometric -Al-O3 termination. By using the bulk Bader charge of O (-1.45 |e|) and the intrinsic surface polarity (-2.40 |e|) of the bulk-truncated -Al-O3 Z+ surface, we estimate the intrinsic surface polarity of the nonstoichiometric -Al-O2 Z+ surface is -0.95|e|, which is completely canceled out by the surface compensating charge of +0.95|e| listed in Table 3. As regard to the BAO(0001) Z- surfaces, all of them are nonstoichiometric terminations, the estimation of surface polarities can also be successfully made by the intrinsic surface polarity of the stoichiometric bulk-truncated BAO(0001) Z- surfaces. Based on the intrinsic surface polarity of +0.56|e| for the bulk-truncated Z- surface with -Bi-O3-Al termination, the intrinsic surface polarities of the nonstoichiometric Zsurfaces with additional -Bi2-O3, -Bi-O2, and -O3 layers should be changed by -0.63|e|, -1.04|e|, and -4.35|e|, respectively. Therefore, the necessary surface compensating

9



charges are respectively +0.07|e|, +0.48|e|, and +3.79|e|, which are well consistent with the values of  listed in Table 3. In addition, if the bulk-truncated -Al-Bi-O3 Ztermination is taken as the reference surface, we can still obtain very similar results. 3.3 Surface electronic properties To further shed light on the electronic properties of the BAO(0001) surfaces with different terminations, we plot in Fig. 4 the surface and atomic-resolved DOS. In our case, the surface DOS means the partial DOS including the surface termination plus one underlying Al-O3-Bi trilayer. For the -Bi2-O3 terminated Z surface (Fig. 4a), it shows that the Fermi level lies in the conduction band minimum (CBM), which indicates the weak n-type conducting behavior. Such an n-type surface metallization is in good agreement with the remarkable accumulation of electronic charges at the topmost Bi layer as shown in Table 3. From the atomic-resolved partial DOS, we find that the CBM contains mainly the Bi 6p orbitals and some contributions from Bi 6s and O 2p orbitals, while the valence band maximum (VBM) is dominated by the Bi 6s states. The energy gap between CBM and VBM is about 1.9 eV, which is reduced by 0.8 eV as compared with the bulk value.28 As regard to the Z surfaces terminated with -Bi-O2 and -O3 (Fig. 4b and 4c, respectively), the Fermi level is located above the VBM. It is important to note that, across the Fermi energy, there is a sharp peak arising predominantly from the O 2p states. The resulting O 2p holes and therefore the p-type weak conducting feature are consistent with the Bader’s charge analysis that the surface oxygen atoms are characterized by considerable depletion of electrons (Table 3). This indicates that, in addition to non-stoichiometry, p-type surface metallization also occurs at these two Z surfaces in order to screen the intrinsic surface polarities. As discussed above, the surface compensating charges are mainly located at the topmost oxygen terminations, which are characterized by significant depletion of electronic charges. Due to the equivalence between loss of electrons and gain of holes, the surface DOS displays a sharp O 2p peak across the Fermi level. For the -Bi-O2 terminated Z surface (Fig. 4b), the CBM is contributed from the Bi 6s, 6p, and O 2p states. In case of the Z surface with -O3 termination (Fig. 4c), the weight of Bi 6s states is centered around -0.6 eV

10


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below the Fermi energy and has negligible contribution to the CBM. For the Z+ surface with -Al-O3-Bi termination (Fig. 4d), which is the only thermodynamically preferred surface termination, the surface DOS implies the insulating behavior and the band gap shows the same value of 1.9 eV as the -Bi2-O3 terminated Z surface. As reported in Ref. [28], the -Al-O3-Bi Z+ termination is stoichiometric. In contrast to the bulk BAO (Fig. 3 in Ref. [28]), most of the weight of Bi 6s and O 2p at the VBM is transferred to the CBM, therefore the -Al-O3-Bi Z+ surface displays significantly reduced DOS at the VBM. This variation is mainly due to the remarkable in-plane rotation reconstruction of the outer O3 atomic layer,28 which changes the hybridization between the Bi 6s and O 2p orbitals. As for the thermodynamically unfavorable Z+ surfaces terminated with -Al-O3 (Fig. 4e) and -Al-O2 (Fig. 4f), we find that the anomalous filling of surface states leads to the surface metallization. For -Al-O3 terminated Z surface, the sharp peak across the Fermi energy is originated from O 2p states. In case of the Z surface with -Al-O2 termination, however, both O 2p and Bi 6s orbitals contribute to the sharp peak across the Fermi level. Finally, from the weight distribution of Bi 6s states in the VBM and CBM for both BAO Z and Z+ surfaces DOS, we expect that the stereo-chemical activity of Bi 6s lone pair electrons will manifest itself in the surface physical and chemical properties. 3.4 Implications As mentioned above, the thermodynamic stability of ferroelectric perovskite R3c LiNbO3(0001) and BiFeO3(0001) polar surfaces has been determined from first-principles DFT calculations.6,16,18 Taking into account the current BAO(0001) surfaces, we find that the equilibrium stoichiometry of R3c ferroelectric (0001) surfaces display a more stronger dependence on the polarization direction than the P4mm ferroelectric (001) surfaces such as PbTiO3(001) and BaTiO3(001).13,14 In contrast to LiNbO3(0001), the BiFeO3(0001) is a more suitable analogue of the BAO(0001) surface due to the same constituent of Bi as well as the same formal valence of Fe and Al. However, the thermodynamically stable terminations of BiFeO3(0001) and BAO(0001) 11



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surfaces are dissimilar. For the Z+ surface, BiFeO3(0001) has two possible surface terminations of -Fe-O3-Bi and -Fe-O3,18 while the BAO(0001) surface possesses only one thermodynamically allowed termination of -Al-O3-Bi. As regard to the Z surface, although both (0001) surfaces have three types of terminations, the equilibrium surface stoichiometries are different. The results indicate that the thermodynamically preferred (0001) surfaces of R3c ferroelectric perovskites differ from one to the other, which therefore provides us variety of platforms for novel surface/interface-based functionalities. As an intriguing lead-free ferroelectric material, BAO has the potential application as tunneling barrier in ferroelectric or multiferroic tunnel junctions.2,3 More recently, a remarkable

negative

magneto-resistivity

response

has

been

observed

in

BiAlO3/La0.67Sr0.33MnO3 (BAO/LSMO) heterostructure.44 In order to reduce the switching voltage, the device size should be minimized to nano-scale. Therefore, the physical and chemical properties of the ferroelectric/metal interfaces are of great importance for the device performances. Our present work provides the atomic-scale understanding of the BAO(0001) surfaces and hence has practical implications for designing/improving the BAO-based nanoelectronic and spintronic devices. On the other hand, the ferroelectric control of Rashba SOC enables an unique possibility to manipulate the spin degrees of freedom in the absence of an external magnetic field.45,46,47 We have mentioned that, due to the Rashba-Dresselhaus SOC effect, the spin texture of bulk BAO is reversible by switching the ferroelectric polarization.27 As we know, the strong SOC effect occurs in the systems containing heavy elements, such as Bi. For the thermodynamically preferred BAO(0001) surfaces, we find that most of the surface configurations are Bi-containing terminations (the -Al-O3-Bi terminated Z+ surface, and the Z surfaces terminated with -Bi2-O3 and -Bi-O2), which may lead to giant Rashba-Dresselhaus SOC effect at the BAO(0001) surfaces. For example, the experimentally observed enhancement of ferromagnetic characteristic in the BAO/LSMO system is ascribed to the SOC effect at the interface.44 Obviously, the Rashba-Dresselhaus effect at the BAO(0001)-based surfaces/interfaces is an appealing

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and important issue deserving of further theoretical and experimental efforts. In present work, for the surface electronic properties of the thermodynamically preferred BAO(0001) Z+ and Z− surfaces, we did not take into account the SOC effect, which is left out for future investigations. Our results predict that both the atomic configurations and the electronic properties are quite different for the oppositely polarized BAO(0001) surfaces. This polarization-direction dependent behavior will inevitably result in modification of the surface chemical properties, which is intriguing for switchable surface chemistry and catalysis.4,5 The well-known Sabatier principle48 pointed out that, to get maximum catalytic efficiency, an intermediate interaction strength of molecules with heterocatalysis surface is necessary because of the compromise between forcing the reaction forward and allowing the products desorption. According to the switchable ferroelectric surface chemistry, a so-called cyclic catalytic strategy has been proposed by Kakekhani et. al.49 It is the switching of ferroelectric polarization by external applied electric field that circulates the two oppositely polarized surfaces, of which rapid reaction occurs at one surface with strong binding strength while the products can be effectively desorbed at the other surface with weak adsorption strength.5,49 By employing the cyclic catalytic method, it is expected that the limitations of Sabatier principle could be circumvented and therefore the catalytic efficiency will be remarkably improved. This kind of dynamical control of surface chemical properties has been experimentally demonstrated at the LiNbO3(0001) surfaces by heterogeneous catalysis,50

photocatalysis/photosynthesis,9

and

reversible

fragmentation

and

self-assembling of nematic liquid crystals.10 For the BAO(0001) polar surfaces, our results provide the theory foundation for future experimental studies.

4. Conclusions To summarize, the relative thermodynamic stabilities of ferroelectric BAO(0001) surfaces with different stoichiometries have been determined by using first-principles DFT calculations. The results demonstrate that the surface structure and equilibrium stoichiometry are directly related to the ferroelectric polarization direction and the

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chemical conditions. Within the thermodynamics-allowed region, -Al-O3-Bi is the only preferred termination for the BAO(0001) Z+ surface. In case of the BAO(0001) Z surface, there are three possible surface terminations (-Bi2-O3, -Bi-O2, and -O3) depending on the specially appointed chemical conditions. According to the surface electronic structure, the BAO(0001) Z+ surface remains insulating behavior. For the BAO(0001) Z surfaces, both surface non-stoichiometry and surface metallization make contributions to compensating the surface polarity and the carrier type (n- or p-type) shows dependence on the surface termination. We hope that the atomic-scale understanding of BAO(0001) surfaces will stimulate relevant theoretical and experimental investigations to further explore this novel ferroelectric material.

Supporting Information. Further details on formula derivation of surface grand-potential of BAO(0001) surfaces and the range of chemical potential for Bi and O atoms, top-view of atomic configurations and electron localization functions (ELF) of the BAO(0001) surfaces with different terminations.

Conflicts of interest There are no conflicts of interest to declare.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No.51762030 and 51462019). Table 1. Theoretical and experimental formation energy (in eV) per formula unit for relevant compounds. System BiAlO3 Bi2O3 Al2O3 O2 a

This work

Other theory

Exp.

-11.90 -6.38 -17.44 -5.84

-12.62a

 -6.01c -17.24d -5.12e

-5.73a -17.22a -6.40b

Ref. [35]; b Ref. [6]; c Ref. [36]; d Ref. [37]; e Ref. [38]. 14


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Table 2. Distances (in unit of Å) between the atomic layers of different surface terminations. Note that negative value refers to rearrangement of the atomic layer sequence. The corresponding bulk values are d (Al, O) = 0.96 Å, d(O, Bi) = 0.43 Å and d (Bi, Al) = 0.82 Å, respectively. The symbols of Bi′ and O′ are shown in Fig. 3. For -O3 terminated Z surface, the rumpling of outmost O3 layer is as large as 0.79 Å. The increase of number indicates the atomic layer changing from outer to the inner surface. Z 1-2 2-3 3-4 4-5 5-6 Z+ 1-2 2-3 3-4 4-5 5-6

-Bi2-O3

-Bi-O2

-O3

Interlayer

d(Å)

Interlayer

d(Å)

Interlayer

d(Å)

Bi-O3 O3-Bi′ Bi′-Al Al-O3 O3-Bi

1.24 0.48 0.64 1.04 0.45

O-Bi Bi-O′ Bi-Al Al-O3 O3-Bi

0.35 0.45 1.21 0.92 0.38

O3-Al Al-O3 O3-Bi Bi-Al Al-O3

1.79 0.64 0.41 0.68 1.08

-Al-O3-Bi

-Al-O3

-Al-O2

Interlayer

d(Å)

Interlayer

d(Å)

Interlayer

d(Å)

Bi-O3 O3-Al Al-Bi Bi-O3 O3-Al

0.80 0.98 0.55 0.70 0.92

O3-Al Al-Bi Bi-O3 O3-Al Al-Bi

0.86 -0.04 1.39 0.78 0.85

O2-Al Al-Bi Bi-O3 O3-Al Al-Bi

1.08 0.09 1.21 0.93 0.85

Table 3. Changes of atomic charge Q (in unit of |e|) relative to the bulk values. The atomic charges for bulk BAO are +1.86 |e| for the Bi atom, +2.49 |e| for the Al atom, and -1.45 |e| for the O atom, respectively. The increase of number indicates the atomic layer changing from outer to the inner surface. For the Ox (x = 2 or 3) layer, the product of Q×x represents the total change of Bader’s charge for the whole Ox atomic layer.

Z 1 2 3 4 5

-Bi2-O3 Atom Bi O3 Bi′ Al O3

ΔQ -0.30 0.15×3 -0.10

Polarization Direction Dependence of Thermodynamic Stability of

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