Ferroelectric Metal in Tetragonal BiCoO3/BiFeO3 Bilayers and Its Electric Field Effect

By first-principles calculations we investigate the electronic structure of tetragonal BiCoO3/BiFeO3 bilayers with different terminations. The multiferroic insulator BiCoO3 and BiFeO3 transform into metal in all of three models. Particularly, energetically favored model CoO2-BiO exhibits ferroelectric metallic properties, and external electric field enhances the ferroelectric displacements significantly. The metallic character is mainly associated to eg electrons, while t2g electrons are responsible for ferroelectric properties. Moreover, the strong hybridization between eg and O p electrons around Fermi level provides conditions to the coexistence of ferroelectric and metallic properties. These special behaviors of electrons are influenced by the interfacial electronic reconstruction with formed Bi-O electrovalent bond, which breaks OA-Fe/Co-OB coupling partially. Besides, the external electric field reverses spin polarization of Fe/Co ions efficiently, even reaching 100%.

Multiferroics with ferroelectricity, ferromagnetism or ferroelasticity simultaneously have great potential applications in information storage, electronic devices and sensors [1][2][3] . Particularly, magneto-electric multiferroics, where the spontaneous ferroelectric polarization can be controlled by an external magnetic field or vice versa, are found in perovskite-type transition metal oxides providing bright prospect for novel spintronic devices [4][5][6][7][8] . Oxide heterostructures exhibit unique properties absent in the corresponding isolated parent compounds, therefore it is an effective means to study emergent physics of correlated electrons, such as, metal-insulator transition 9 , two-dimensional electron gas and sharp interfaces at LaAlO 3 /SrTiO 3 interfaces 10-13 , orientation-dependent magnetism and so on 14 . Besides, recent technology advances in oxide synthesis at the atomic level make artificially designing heterostructures feasible 15 . We attempt to combine two perovskite-like multiferroics into bilayers aimed at inducing novel electronic and magnetic states, providing theoretical support for new multifunction devices as well. We pay attention upon Bi-based perovskite materials, whose ferroelectric properties originates from a lone pair of (6s) 2 electrons [16][17][18] , and select tetragonal BiFeO 3 (BFO) and BiCoO 3 (BCO) as multiferroics candidates.
The perovskite BFO is the only known room-temperature single-phase magneto-electric multiferroic material, which is intensively studied in the last decade, with a high ferroelectric Curie temperature of 1103 K and antiferromagnetic Neel temperature of 643 K [19][20][21][22][23] , exhibiting weak magnetism at room temperature due to a residual moment from a canted spin structure 24 . Notablely, tetragonal BFO has much higher spontaneous polarization of 150 μ C/cm 2 and charge transfer excitations than rhombohedral phase, and gets considerable high resistance changes in ferroelectric tunnel junctions [25][26][27][28][29] . The resistance changes in ferroelectric tunnel junctions based on tetragonal BFO are considerably high (OFF/ON ratio >10000) among known ferroelectric tunnel junctions 30 . BCO has been suggested to be a promising multiferroic material, which is predicted to exhibit a giant polarization and extremely high transition temperature 31,32 . The ferroelectricity of BCO is found to be primarily driven by the lone-pair activity of Bi 3+ , and magnetism being driven by the high-spin state of Co 3+ in a C-type antiferromagnetic structure below a Neel temperature of 420 K 33,34 . And, BFO and BCO with large spontaneous ferroelectric polarization have great potential application in electrically controllable devices [35][36][37][38][39] . Besides, compounding BFO with BCO is accessible experimentally in the form of epitaxial thin film 40 and the BFO/BCO multiferroic solid solutions are studied theoretically 41 . Previous studies show that the antiferromagnetic insulator BiFeO 3 can exhibit ferromagnetism in BiFeO 3 /La 2/3 Sr 1/3 MnO 3 interface 42,43 and two-dimensional electron gas in BiFeO 3 /SrTiO 3 interface 44 , demonstrating that heterointerface is significant in BiFeO 3 -based bilayers. However, the heterostructures by constructing BiFeO 3 with another multiferroic BiCoO 3 may present some fantastic properties based on its multiferroic characteristics.
In this paper, we study the electronic structure of BCO/BFO bilayers with different terminations and investigate the external electric field effect on the bilayers by first-principles calculations. We find that energetically favored model CoO 2 -BiO exhibits ferroelectric metallic properties due to the division of e g and t 2g electrons as well as e g -p hybridization. Additional, external electric field enhances the ferroelectric displacements markedly. These special behaviors of electrons are influenced by the interfacial electronic reconstruction with formed Bi-O electrovalent bond, which breaks O A -Fe/Co-O B coupling partially. Our results indicate that interfacial coupling and electric field play key roles on the novel ferroelectric metallic properties of model CoO 2 -BiO, which provides opportunities for developing functional nanoelectronic devices.

Calculation Details
Our first-principle calculations are performed using density functional theory (DFT) within the local spin-density approximation (LSDA), based on the projector augment wave (PAW) pseudo-potentials. The energy cutoff for plane wave basis set is 500 eV and the Brillouin zone is sampled with Γ -centered 5 × 5 × 5 and 5 × 5 × 1 k point meshes for bulk compounds and bilayers respectively, providing numerical convergence of 10 −5 eV. All the structures are fully relaxed until the maximum Hellmann-Feynman forces on each atom are less than 0.02 eV/Å. Aimed at getting reasonable results, we include an on-site Coulomb repulsion of U = 6 eV for Co 3d states 45 , and U = 4.5 eV for Fe 3d states 46,47 , which are sufficient to describe the related bulk properties.
Tetragonal phase of the multiferroic BFO used in this work has a perovskite-type structure with a lattice constant of a = 3.770 Å and c/a = 1.233 in space group P4 mm 47 33 . Bi ions locate in the corner sites, yet Fe (or Co) ions and O ions which ought to occupy the body and face centered sites respectively move from center sites in the z direction owing to ferroelectric spontaneous polarization. In the supercells of BCO/BFO studied here, a 28 Å vacuum space in z direction is used to separate the interaction between periodic images and the supercells are built by placing five BCO atomic layers on the top of five BFO atomic layers within p( × 2 2) periodicity giving altering layers of Bi 2 O 2 and Co 2 O 4 (Fe 2 O 4 ) along the [001] direction. In experiments, the thin films must present one surface that is exposed in the vacuum, even though the sample is a multilayered structure. Hence, the bilayer geometry with vacuum should be calculated. Meanwhile, the difference of optimized geometry and atomic position can affect the multiferroics of the sample. In superlattice structure, there are two interfaces which might influence the relaxation of the atoms, so that each atomic position should be different from the case of bilayer with vacuum. Meanwhile, in order to study the effect of external electric field, the bilayer with vacuum is necessary. We apply external electric field for the bilayers in z direction and switch on the potential correction mode. The calculated in-plane lattice mismatch between BFO(001) and BCO(001) is 1.1%, indicating a good lattice match. We set up three BCO/BFO bilayers with different terminations to investigate the interfacial properties, as shown in Fig. 1(a-c).
The stable pattern is determined by calculating the work of separation, i.e., the cohesive energy between BCO and BFO, BCO BFO , where E BCO/BFO is the total energy of the bilayers, E BCO and E BFO represent the energies of the same supercell containing either the BCO or BFO parts (i.e., we keep the equilibrium structure obtained for the bilayers). For illustrating the nature of the charge transfer at BCO/BFO interface, we calculate the charge density difference by subtracting the charge densities of isolated BFO and BCO parts from the charge density of bilayers as shown in Fig. 1(d-l). The electronic structures of isolated BFO and BCO are calculated by freezing the atoms of the respective component at the supercell positions.

Results and Discussion
First, we analyze the total and projected densities of states (DOS) of fully relaxed bulk BFO and BCO shown in Fig. 2. For BFO, the charge transfer gap is determined by the filled oxygen 2p band and the unoccupied 3d band of Fe, and the calculated band gap of 1.93 eV is in good agreement with previous calculations 49 , but inconsistent with the experimental value of 3.10 eV 50 , as a result of using the LSDA approximation. The Fe spins are antiparallel and the corresponding DOS is symmetrical, so we only show one. The calculated Fe magnetic moments are ± 4.107 μ B per atom. For BCO, the calculated total DOS is similar with previous calculations 45 , and the Co ions are in high-spin state which is consistent with the experimental result 33 , as shown in Fig. 2(a,d). The spin-up and spin-down band structures are completely compatible, so we only show spin-up structure in Fig. 2(e). We find that the strong correlated effect of Co 3d is well described with a band gap of 1.52 eV and the Co magnetic moments are ± 3.035 μ B per atom, which are in good agreement with the experimental values of 1.7 eV and 3.24 μ B 33,51 . These bulk results reveal that the used parameters in the present work are reasonable. We carry out the electronic band structures of three models and separate out the BCO's contribution to demonstrate the changes of the electronic states in BCO by comparing with bulk BCO states in same path, as shown in Fig. 3. Obviously, both BCO and BFO transforms into metal in all of three interfacial models and BCO undergoes a dramatic change, revealing that interfacial compound probably is an efficient method to explore emergent physics as well. The strong interfacial effect is also reflected by the remarkable accumulation and depletion of electrons at interfaces, as shown in Fig. 1(d-l). Bi and O ions combine with each other in the form of electrovalent bond with Bi depleting and O accumulating electrons in the interfacial regions of model CoO 2 -BiO and BiO-FeO 2 , see Fig. 2(d,j). For model CoO 2 -FeO 2 , apparent accumulation of electrons between Co and Fe occurs at the interfacial regions revealing that Co and Fe ions combine via metallic bond we propose, as shown in Fig. 2(g). The calculated cohesive energies demonstrate that model CoO 2 -BiO is the most stable structure with a considerably large value of 11.474 eV and model CoO 2 -FeO 2 is very unstable with a negative value, as listed in Table 1, which is reasonable since the interfaces in model  Fig. 4 indicate that the displacements of model CoO 2 -BiO is larger than the other two models and we list the average values in Table 1. It is obvious that the displacements in model CoO 2 -BiO is almost 50% larger than model CoO 2 -FeO 2 and model BiO-FeO 2 and nearly three quarters of correspond bulks. Therefore, model CoO 2 -BiO exhibit metallic properties with remarkable ferroelectric structures since tetragonal BCO and BFO are typical displacive ferroelectrics originating from relative displacement of positive and negative ions 27,48,52,53 . To further investigate its ferroelectric properties, we add an electric field to all of three bilayers considering the strong electric field effect on ferroelectrics owing to the spontaneous polarization. Based on the experimental study on bulk 52,54 , we add the electric field of 6 and 10 mV/Å (i.e., 600 and 1000 kV/cm) respectively and calculated the relative displacements of positive and negative ions in same layer along z axis, as shown in Fig. 4. We find that

Structure
CoO2-BiO the polarization displacements in model CoO 2 -FeO 2 and model BiO-FeO 2 with electric field (see red and blue lines) are close to the situation without electric field (see black lines) shown in Fig. 4(b,c), but the polarization shifts in model CoO 2 -BiO are enhanced greatly on the condition of applied electric field, particularly at the interfacial regions as shown in Fig. 4(a). This result further confirms the ferroelectric metallic properties of model CoO 2 -BiO and demonstrates that external electric field can modulate the ferroelectric polarization. Figure 1(d) reveals the strong interfacial coupling by Bi-O electrovalent bonds in the interfacial regions of model CoO 2 -BiO, and we further notice that the interfacial Bi-O bonds exist even in applied electric field, as shown in Fig. 1(e,f). This short-range pair interaction makes the ferroelectric polarization properties of bulks preserved in bilayers and lowers the electrostatic energy further stabilize the bilayers structure.  On the other hand, the structure of models CoO 2 -BiO and BiO-FeO 2 contains two asymmetry surfaces and might be as polar as LaAlO 3 /SrTiO 3 interface within a large "internal" electric field 9,55 , which automatically gives rise to the metallicity of the system. We check the same asymmetry geometry in pure BFO and BCO, which possesses the form (BiO-MO 2 ) n within 15 Å vacuum space in z direction (M = Fe/Co, n = 2, 3, 4). The calculated band structures indicate that such pure BFO is insulating when n = 2/3 but exhibits metallic in n = 4, while the pure BCO is metallic and not affected by n. Hence, the asymmetry structure is important for the metallic characters in CoO 2 -BiO model. Furthermore, such pure metallic properties in BFO and BCO are distinguished from the metallic characters in model CoO 2 -BiO. Firstly, both uppermost valence band (UVB) and lowest conduction band (LCB) approach the Fermi level in (BiO-FeO 2 ) 4 , while the LCB of isolated BFO in model CoO 2 -BiO is far away from the Fermi level (see Fig. 3a). Secondly, the UVB in pure BCO overlaps with the Fermi level heavily, while the UVB of isolated BiCoO 3 in CoO 2 -BiO model only approach the Fermi level (see Fig. 3a). It is obvious that the strong interfacial couplings have a great effect on the metallic characters in CoO 2 -BiO model.
Next, we analyze the electronic DOS distribution of ions in the interfacial regions of model CoO 2 -BiO in detail shown in Fig. 5. We find that, for BCO, I-Co d electrons hybridize with II-O p electrons distinctly but interact weakly with I-O p electrons in the energy range from − 3 eV to Fermi level (E F ) as indicated in Fig. 5(a). Similarly, for BFO, II-Fe d electrons hybridize obviously with II-O p electrons while lightly with I-O p electrons in the energy window from − 1.2 to − 0.3 eV as shown in Fig. 5(b). The label "I-Co" represents the Co ions in layer I as shown in Fig. 1(a), and this kind of definition is used in the whole letter. For bulk BCO and BFO, Fe/Co ions hybridize with O A and O B , along with clear O alignment as shown in Fig. 2(b,c).   Then, we analyze the Fe/Co DOS in each layer in different on the condition of electric field or not, as shown in Fig. 6. The Fe electronic distribution varies gently as indicated by Fig. 6(a-c), while Co ions change heavily shown in Fig. 6(d-f). We define spin polarization = ( ( ) ( ))/( ( ) + ( )) F F F in terms of the total DOS in the spin-up N ↑ and spin-down N ↓ channels respectively, and find that the spin polarization of I-Co is reversed from 70% to − 89% on the condition of E = 6 mV/Å by comparing Fig. 6(d) with Fig. 6(e). Besides, the spin polarization of III-Co and V-Co are reversed from 49% to − 82% and 54% to − 62% respectively on the condition of   Fig. 6(d,f). The apparent positive-negative spin polarization reverse in Co ions demonstrates that electric field not only can be used to induce magnetic moments via magneto-electric effect as previous report 2 , but also can reverse spin polarization. The Fe/Co magnetic moments are listed in Table 2, which are influenced heavily by interfacial effect and electric field. The numbers of Fe/Co magnetic moments in same layer are equal but with different signs, so we only list the positive numbers in Table 2. In addition, the Co magnetic moments are changed easily, which is reasonable since the Co ions possess flexible possibilities of high, intermediate and low spin states. The electronic rearrangements of Co caused by interfacial coupling are also reflected by   charge density difference since electrons with different orbital contours increase or decrease, shown in Fig. 1(d-l).
Although it is widely believed that metals cannot exhibit ferroelectricity since the static internal electric fields are screened by conduction electrons 56 , the ferroelectric metal is theoretically proposed by Anderson and Blount in 1965 57 . Recently LiOsO 3 is identified as the first typical example 58 , and the microscopic mechanism for the ferroelectric-like structural transition in a metal are investigate widely 59,60 . The Mott multiferroic based on LiOsO 3 is predicted by compounding with LiNbO 3 as well 61 . However, in our model CoO 2 -BiO, the ferroelectrics are transformed into metal from insulator via interfacial coupling, which is opposite the LiOsO 3 -type metal into ferroelectric transition. The itinerant d electrons can screen the electric fields and inhibit the electrostatic forces, so we analyze the d electron states of Fe/Co ions in each layer of model CoO 2 -BiO on purpose as shown in Fig. 7. We find that the metallic property is associated to the electrons in e g orbitals (i.e., d z 2 and − d x y 2 2 ), and these electrons hybridize with O p electrons around E F according to Fig. 5. However, the electrons in t 2g orbitals (i.e., d xy , d xz , and d yz ) have no contribution to the metallic character, which are responsible for the ferroelectric properties as shown in Figs 2(d) and 7. Therefore, although the specific e g electrons exhibit metallic property, they simultaneously hybridize with O p electrons, which makes ferroelectric and metallic features coexist. And we argue that this special electron occupation is tightly associated with the interfacial coupling as mentioned above.
On the other hand, the ferroelectric displacements are not sensitive to external electric field in model BiO-FeO 2 as shown in Fig. 4(c), and we believe that the different behavior of models CoO 2 -BiO and BiO-FeO 2 is a result of termination effect. It is also found in model BiO-FeO 2 that the electric field reverses spin polarization of Fe/Co ions. Figure 8(d-f) indicate that the spin polarization of IV-Co are reversed from − 73% to 100% upon E = 6 and 10 mV/Å, While V-Fe are reversed from − 100% to 53% upon E = 10 mV/Å according to Fig. 8(a,c). These results show that electric field can not only reverse the positive and negative of spin polarization, but also reach a considerable value even 100%. In addition, the synthesis technology of oxides has beem improved significantly, such as MBE MOCVD, etc., which can fabricate high-quality epitaxial films and heterostructures. We take the La 0. 7 63 . Therefore, the energetically unfavored termination can be achieved by inserting specific monolayer in the stable termination. The prediction of ferroelectric metallic characteristics in BiFeO 3 /BiCoO 3 bilayers is meaningful for the expertimental research, which can provide opportunities for developing novel functional electronic devices.

Conclusion
In summary, we investigate the electronic structure of BCO/BFO(001) bilayers with different terminations based on first-principles calculations. The multiferroic insulator BCO and BFO transform into metal in all of three models. Particularly, energetically favored model CoO 2 -BiO exhibits ferroelectric metallic properties and external electric field enhances the ferroelectric displacements markedly. The metallic character is mainly associated to the e g electrons of Fe/Co ions and these electrons simultaneously hybridize with O p electrons around E F , yet the t 2g electrons are responsible for ferroelectric properties. Therefore, the division of e g and t 2g electrons as well as e g -p hybridization provide conditions to the coexistence of ferroelectric and metallic properties. These special behaviors of electrons are influenced by the interfacial electronic reconstruction with formed Bi-O electrovalent bond, which breaks O A -Fe/Co-O B coupling partially. Besides, strong interfacial coupling changes the Fe/Co magnetic moments and external electric field reverses spin polarization of Fe/Co ions efficiently, reaching a maximum of 100%. Our results demonstrate that interfacial coupling and electric field play key roles on the novel ferroelectric metallic properties of model CoO 2 -BiO, which provides opportunities for developing functional nanoelectronic devices. We hope that our theoretical prediction on the ferroelectric metallic properties and corresponding electric field effect can stimulate further experimental study.