BiIrO3 (X=Fe, Mn

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Tunable Valley and Spin Polarizations in BiXO3/ BiIrO3 (X=Fe, Mn) Ferroelectric Superlattices Li Yin, Xiaocha Wang, and Wenbo Mi ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b18379 • Publication Date (Web): 11 Jan 2018 Downloaded from http://pubs.acs.org on January 13, 2018

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ACS Applied Materials & Interfaces

Tunable Valley and Spin Polarizations in BiXO3/BiIrO3 (X=Fe, Mn) Ferroelectric Superlattices

Li Yin1, Xiaocha Wang2, Wenbo Mi1,*

1

Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparation Technology,

School of Science, Tianjin University, Tianjin 300354, China

2

School of Electrical and Electronic Engineering, Tianjin University of Technology, Tianjin 300384,

China

*

Author to whom all correspondence should be addressed. E-mail: [email protected]

1

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ABSTRACT

The generation and modulation on valley and spin degrees of freedom are essential to multifunctional electronic devices. Herewith, the electronic structures in BiXO3/BiIrO3 (X=Fe, Mn) ferroelectric superlattices are studied by first-principles calculations with spin-orbital coupling. Different from previous BiAlO3/BiIrO3 system, both valley and spin polarizations in bilayered BiIrO3 are achieved in BiXO3/BiIrO3 superlattices, where the spin polarization in the valley can be engineered by the spin orientation of Fe or Mn owing to the xy-plane orbitals. Especially, the relatively parallel and antiparallel directions of ferroelectric polarization in BiFeO3 and BiIrO3 can switch the valley injection in BiFeO3/BiIrO3 superlattices. Overall, the tunable valley and spin polarizations in BiFeO3/BiIrO3 ferroelectric superlattices pave a way for developing the nonvolatile data memories and valley-spin devices.

Keywords: BiIrO3, BiFeO3, Valley polarization, Spin polarization, Honeycomb

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INTRODUCTION

Emergent phenomena have been induced at oxide heterostructures due to the interplay between charge, spin, lattice and orbital degrees of freedom (DOF).1 Recently, the generation and control of the valley DOF have been the hot topics due to the various valleytronic physics and devices, such as the valley Hall effect,2,3 valley filter and valley valve.4 The valley polarization and valley-spin coupling provide the conditions for the integration of valleytronic,2 spintronic and optoelectronic devices.5-9 Therefore, the novel valley DOF in oxide heterostructures may advances the next-generation oxide-based electronic devices. Meanwhile, the valley DOF induced in the oxides-based heterostructures probably shows special characteristics, which are absent in commonly studied two-dimensional graphene or group VI transition metal dichalcogenides (TMDCs).2,3,6,10 The inversion symmetry has been demonstrated to be broken in the ferroelectric Rashba semiconductors,11 which reminds the nonvolatile ferroelectric control of the valley index. In analogy to ferroelectric(ferromagnetic) materials with the spontaneous charge(spin) polarization, a novel ferrovalley material with the spontaneous valley polarization, 2H-VSe2, is proposed.12 Especially, the strong spin-valley coupling is indeed achieved in ferroelectric heterostructures BiAlO3/BiIrO3,13 where the Ir ions with large atomic spin-orbital coupling sits on the corrugated honeycomb lattice in bilayered BiIrO3. However, in BiAlO3/BiIrO3, the dispersion of the valence band maximum (VBM) in bilayered BiIrO3 is nearly flat, which is not suited for the practical applications in the valleytronic and spintronic devices. In the two-dimensional valley studies, the valley polarization can be induced by the external magnetic field or proximity to the ferromagnet.7,14-17 Especially, bulk BiIrO3 shows 3



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the BiFeO3-type rhombohedral structure in R3c space group. So, we attempt to enhance the valley effects in bilayered BiIrO3 via proximity to antiferromagnetic BiFeO3 or half-metallic ferromagnetic BiMnO3.18-20 Moreover, the magnetic field probably could modulate the induced valley and spin characteristics in BiIrO3 due to the introduced magnetic materials. Rhombohedral BiFeO3 is the only known room-temperature single phase multiferroic material with a large ferroelectric polarization of ~90 µC/cm2 and the G-type antiferromagnetic order.18,21,22 The parallel and antiparallel directions of ferroelectric polarizations between BiFeO3 and BiIrO3 may have distinct influences on the induced valley DOF, which is meaningful to the valleytronic and ferroelectric applications. Besides, the advanced fabrication methods on (111)-oriented perovskite oxide superlattices have reached the atomic-scale precision, such as the (111)-oriented (Ca0.5Sr0.5IrO3)n/(SrTiO3)2 (n=2, 4 or 6) superlattices grown by the pulsed laser deposition and (111)-oriented (LaNiO3)n/(LaMnO3)m superlattices

fabricated

by

off-axis

radiofrequency

magnetron

sputtering.23,24

The

(BiFeO3)2/(SrTiO3)4 superlattices have also been prepared by pulsed laser deposition.18 These developed fabrication method lay the playground for future experimental researches on the valley physics in transition-metal oxide superlattices. In this work, the electronic structures in BiXO3/BiIrO3 (X=Fe, Mn) ferroelectric superlattices are investigated by first-principles calculations with spin-orbital coupling. Both valley and spin polarizations in the bilayered BiIrO3 appear in BiXO3/BiIrO3 superlattices. Especially, the achieved valley and spin polarizations in BiFeO3/BiIrO3 superlattices can be switched by the ferroelectric polarization and spin orientation respectively, where the xy-plane orbitals play a decisive role in the 4


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spin polarization. The tunable valley and spin polarizations in BiFeO3/BiIrO3 ferroelectric superlattices lay the foundations for developing nonvolatile ferroelectric and valleytronic devices.

CALCULATION DETAILS AND MODELS

The first-principle calculations are implemented in Vienna Ab initio Simulation Package with the density functional theory.25 The Perdew-Burke-Ernzerhof flavor of spin-polarized generalized gradient approximation (GGA) and projector augment wave pseudo-potentials are used.26 Such theoretical calculations were commonly used in the study of valley and spin polarizations in magnetic system.17 In magnetic VSe2 system,12 the normal first-principles were also able to get consistent results as compared with the k·p perturbation theory.27 So, the studies on valley and spin polarizations in this work should be reasonable. The tested on-site Coulomb repulsion of U=4.0 eV, J=0.0 eV for Fe and U=5.0 eV, J=1.0 eV for Mn is applied to reflect the localized 3d orbitals in BiFeO3 and BiMnO3.20,21 The energy cutoff for plane wave basis set is 500 eV.13 The convergence criteria for the energy and atomic forces are 10-5 eV and 0.02 eV/Å, respectively. The Brillouin Zone is sampled with Γ-centered 5×5×1 k point meshes for fully relaxed BiXO3/BiIrO3 superlattices. The charge density differences are calculated by subtracting the charge densities of the isolated BiIrO3 and BiXO3 parts from the superlattices with GGA+U calculations. Two unit cells in BiXO3 and two unit cells in BiIrO3 are included in BiXO3/BiIrO3 superlattices (see Fig. 1), without the thick vacuum space. The cohesive energy is defined as Wcoh = E BIO + E BXO -E BXO / BIO , where EBXO / BIO is the total energy of heterostructures, E BIO and EBXO represent the energies of the same 5



superlattices containing BiIrO3 or BiXO3 respectively. The structure with a larger Wcoh is more stable. In order to achieve the energy valley, the (111)-plane bilayered structure is considered in either BiIrO3 or BiXO3, where the transition metal Ir, Fe or Mn ions form the graphene-like buckled honeycomb lattice (see Fig. 1). The [111] direction in bulk structures corresponds to the z direction in the BiXO3/BiIrO3 superlattices. Additionally, the Γ-centered 6×6×1 and 12×12×1 k meshes have been checked in BFO/OIB model (Fig. S1), where the contours and gap of the band structures are highly similar to the applied 5×5×1 case in this work.

Figure 1. The geometry for (a) bulk BiFeO3. The band structures with (b) GGA+U and (c) GGA+U+SOC calculations for bulk BiIrO3. The spin-up band structures in (b) coincide with spin-down case. The spin projection in (c) is depicted as the color scale. Structures for (d) BFO/BIO, (e) BMO/BIO, (f) BFO/OIB, (g) BMO/OIB superlattices. The hexagonal Brillouin zone and high-symmetry points are shown in (d). The inside Ir(Fe, Mn) circles in specific layers for heterostructures are shown in (d). 6


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RESULTS AND DISCUSSION

Properties of bulk BiIrO3, BiFeO3 and BiMnO3. In Fig. 1(a), Ir atoms in bulk BiIrO3 form a quasi honeycomb structure along the [111] direction, which is similar to the structures of graphene and TMDCs.28,29 The Ir3+-5d6 electrons are in a low-spin occupation, which cause the nonmagnetic state in BiIrO3. In Figs. 1(b) and 1(c), the band structures with or without SOC calculations are consistent with previous study on bulk BiIrO3.13 Especially, in Fig. 1(c), the VBM and next VBM at K high-symmetry point are mainly occupied by the spin-up and spin-down electrons respectively, which is compatible with the previous spin distributions in bulk BiIrO3.13

Table 1. The relaxed lattice constants in bulk and heterostructures at specific U(J) are listed. E is the free energy (eV) of bulk. M indicates the magnetic moments (µB) of Fe(Mn, Ir) in bulk BiFeO3(BiMnO3, BiIrO3) and Ir in heterostructures. Wcoh (eV) is the cohesive energy. U 4.00 4.50 5.00

J 0.00 0.00 0.00

E -189.58 -188.59 -187.64

a 5.61 5.61 5.61

b 5.61 5.61 5.61

c α β γ M 14.01 90.00 90.00 120.00 ±4.1480 14.00 90.00 90.00 120.00 ±4.1900 13.99 90.00 90.00 120.00 ±4.2310

BiMnO3

5.00 5.20

1.00 0.00

-198.04 -195.16

5.63 5.65

5.63 5.65

14.04 90.00 90.00 120.00 14.09 90.00 90.00 120.00

4.0610 4.1800

– –

BiIrO3

0.00

0.00

-189.40

5.85

5.85

12.77 90.00 90.00 120.00

0.0000

–

BFO/BIO BMO/BIO BFO/OIB BMO/OIB

4.00 5.00 4.00 5.00

0.00 1.00 0.00 1.00

– – – –

5.71 5.71 5.76 7.74

5.71 5.71 5.77 5.73

12.54 13.32 10.00 10.21

0.0030 0.0015 0.0230 0.0140

0.45 0.10 5.12 4.12

BiFeO3

90.00 90.00 85.99 90.02

7


90.00 90.00 93.31 90.00

120.00 120.00 120.01 120.00

Wcoh – – –


In recent study,20 the low-energy alternative structure of BiMnO3 is stabilized in the rhombohedral R3c structure, analogy to the ground state of BiFeO3. In Table 1, the on-site Coulomb repulsions of U(J) for Fe and Mn 3d states are tested in bulk BiFeO3 and BiMnO3. At different values of U(J), the relaxed bulk lattice constants and Fe(Mn) moments in bulk BiFeO3(BiMnO3) are consistent. In Table 1, the U=4.0 eV, J=0.0 eV for Fe 3d and U=5.0 eV, J=1.0 eV for Mn 3d are chosen,20,21 which produce the lowest free energy for bulk BiFeO3 and BiMnO3 respectively. Meanwhile, the calculated Fe(Mn) moments of 4.15(4.06) µB at the chosen U(J) are similar to the previously calculated value of 4.00(3.90) µB in bulk BiFeO3(BiMnO3) and experimental value of 4.34 µB in bulk BiFeO3.20,30 Especially, the half-metallicity in bulk BiMnO3 is guaranteed with a gap of 3.07 eV in the spin-down channel, which is consistent with the value of 3.25 eV in the previous study.20 The calculated results in bulk BiIrO3, BiFeO3 and BiMnO3 demonstrate that the used calculation parameters in this work are reasonable. The electronic structures in BiXO3/BiIrO3 ferroelectric superlattices are analyzed next. Valley and spin polarizations in BFO/OIB and BMO/OIB models. In Figs. 1(d)-1(g), the interfacial Ir, Fe or Mn ions are labeled as IrII, FeII or MnII, respectively. Two types of BiXO3/BiIrO3 superlattices are characterized by the direction of ferroelectric polarization in the bilayered BiIrO3, which points away from the FeII or MnII ions in BFO/BIO and BMO/BIO models [Figs. 1(d) and 1(e)], but points toward the FeII or MnII in BFO/OIB and BMO/OIB [Figs. 1(f) and 1(g)]. The polarized direction of ferroelectric BIO can be tunable by the electric field in future experimental studies.19 In Figs. 2(a) and 2(b), BiIrO3 in BFO/BIO and BMO/BIO models show the indirect band gap and flat dispersion of VBM, which is in analogy to BiAlO3/BiIrO3 case.13 8


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Figure 2. Band structures for (a, e) BiFeO3/BiIrO3 and (b, f) BiMnO3/BiIrO3 superlattices with GGA+U+SOC calculations. The circle represents BiIrO3. The spin projection is depicted as the color scale. In (c) and (d), the dashed red(blue) lines represent the spin-up(spin-down) band without SOC, while the solid black lines indicate the band with SOC. The schematic diagram for SOC-induced spin-splitting in TMDCs is depicted near (d). 9



However, in Figs. 2(e) and 2(f), the dispersion of VBM in BiIrO3 is obviously lifted in the BFO/OIB and BMO/OIB models, where the large spin-up and spin-down polarizations appear at K’ and K respectively. Herewith, different U=1, 2 or 3 eV, J=0 eV for Ir d state have been tested in BFO/OIB model (Fig. S2),31 which produces highly similar valley and spin characteristics as compared with the applied U=0 eV case. Especially, in the BFO/OIB and BMO/OIB models, both valley and spin polarizations appear in the bilayered BiIrO3, which is explained next. In Fig. 2(e), the conduction band minimum in BiIrO3 locates near K’ point, which forms a quasi-direct band gap at K’ point but an indirect band gap at K point. For BiIrO3 in BFO/OIB model, electrons at K’ will be easier to emit than K due to the extra moment transformation.32 Moreover, in Fig. 2(e), electrons at K’ are transformed in the spin-up polarized channel, while electrons at K are transformed from spin-down to spin-up polarized channel. So, the different moment and spin characteristics at K’ and K points will form a valley polarization in BiIrO3 at BFO/OIB model. The apparent valley and spin characteristics in BiIrO3 at BFO/OIB model benefit the generation of spinand valley- polarized carriers by optical or electric means in the oxide heterostructures. Besides, the valley height in VBM is characterized by ∆Eh [Figs. 2(a) and 2(e)]. In the BFO-BIO and BFO-OIB models, the valley height ∆Eh in BiIrO3 increases from 56 meV to 220 meV as the relative directions of ferroelectric polarization in BiFeO3 and BiIrO3 transform from parallel to antiparallel. Hence, the valley height and valley polarization in BiFeO3/BiIrO3 superlattices are dependent on the ferroelectric directions in BiFeO3 and BiIrO3, which reminds the electric field modulation on the valley index.19,33 Such ferroelectric-based control on the valley is absent in pure TMDCs.

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In Fig. 2(f), BiIrO3 at BMO/OIB model becomes metallic, where the electrons near Fermi level accumulate at the K’(K) energy valley with the spin-up(spin-down) polarizations. Especially, in Fig. 2(f), the valley maxima at K’ and K points show an energy difference ∆Ep of 33 meV. The different energies and spin polarizations at K and K’ points demonstrate the valley polarization in BiIrO3. Such valley-polarized metallic BiIrO3 at BMO/OIB model is a proper candidate for investigating the anomalous Hall effect in oxide-based valleytronics.34 Besides, in Fig. 2(f), BMO/OIB model becomes metallic due to the SOC, which should be associated with the SOC-lifted VBM and the small band gap of 0.22 eV without SOC. The similar SOC-induced insulator-metal transition also appears in previous Ba2NaOsO6 and Ba2YOsO6 studies with a small gap of 0.1~0.5 eV.35 Notably, the spin-orbital coupling (SOC) has the localized character,5 which breaks the inversion symmetry but preserve the time-reversal symmetry. However, the symmetry is crucial to the electronic structures in (111)-oriented perovskite structures.36-38 In Fig. 2(c), both the inversion symmetry and time-reversal symmetry are broken in BFO/OIB model without SOC, where the energy levels of spin-up and spin-down bands are very close to each other. However, the strong SOC in Ir ions leads to the energy splitting of spin-up and spin-down bands, which lifts the valley height in BiIrO3. Hence, in the magnetic BFO-OIB model, although the broken of inversion and time-reversal symmetries is not dependent on the SOC, the lifted valley relies on the SOC. Moreover, for BiIrO3 in BFO/OIB and BMO/OIB models, the mode of SOC-induced valley-degeneracy splitting at K’ and K points is different from the TMDCs.39 In Figs. 2(c) and 2(d), two SOC-split bands in BiIrO3 move in opposite directions, one toward Fermi level and another away from it, which results in two distinct band shapes. However, in TMDCs, two SOC-split bands 11



have a similar band shape,39 as depicted in Figs. 2(c) and 2(d). Meanwhile, bilayered BiIrO3 and BiXO3 holds distinct honeycomb structure as compared with the two-dimensional graphene or TMDCs (Fig. 3(d)). In graphene,10 the honeycomb consists of C atoms in the same layer. In typical TMDCs MoS2, the honeycomb is made up of the Mo and S trigonal layers.2 However, in bilayered BiIrO3 and BiXO3, two X trigonal layers form the main X honeycomb lattice and the O atoms form another honeycomb (Fig. 3(d)), which surrounds one of the X trigonal layer. For BiXO3/BiIrO3 superlattices, the special two-sets-honeycomb makes its mode of SOC-induced valley-degeneracy splitting different from the commonly studied graphene or TMDCs. Orientation-dependent spin injections. In two-dimensional graphene, the magnetic direction can easily switch the valley injection in a ferromagnet-covered graphene junction.40 Considering the valley and spin polarizations in bilayered BiIrO3 are stimulated by antiferromagnetic BiFeO3 and ferromagnetic BiMnO3, the magnetic field probably modulate the induced valley and spin characteristics. Especially, although the magnetic field cannot change the antiferromagnetic order in BiFeO3, the spin orientation in BiFeO3 is tunable via the magnetic field in previous experiments.41,42 So, in either antiferromagnetic BiFeO3 or ferromagnetic BiMnO3, the magnetic field can modulate the inner spin orientations of Fe or Mn. Hence, in BFO/OIB (BMO/OIB) superlattices, the valley and spin characteristics are further investigated at [100] and [001] spin orientations of Fe(Mn) respectively (please see Figs.3(a) and 3(b)). Herewith, the [100] and [001] spin orientations are parallel and perpendicular to the honeycomb plane, respectively. In Figs. 3(a) and 3(b), for BiIrO3 in BFO/OIB (BMO/OIB) superlattices, the high spin polarization at the enhanced valley is apparently modulated by the spin orientations in Fe and Mn. In 12


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Figure 3. (a) Band structures in BFO/OIB model at [100]- and [001]-oriented Fe spins, respectively. (b) Band structures in BMO/OIB model at [100]- and [001]-oriented Mn spins, respectively. (c) The

O1=pz + dz2 , O2=dxz +d yz and O3=px +py +dxy + dx2 -y2 orbital-decomposed band structures in BFO/OIB model. The circle represents BiIrO3. The spin projection is depicted as the color scale. (d) The top view of graphene, monolayer MoS2 and bilayered BiFeO3.

Fig. 3(a), the [001]-oriented spin polarization in the VBM of BiIrO3 is apparently larger than the [100] case. In Fig. 3(b), the spin polarization near Fermi level in BiIrO3 is also decreased when the spin orientation varies from [001] to [100]. So, in BiIrO3, the high and low spin polarizations at the energy valley are highly dependent on the spin orientations of Fe and Mn. Especially, in Figs. 3(a) and 3(b), BiIrO3 shows the apparent valley and similar response to the spin orientation in BFO/OIB and BMO/OIB models. However, the Fermi level is distinct in the two models. Such phenomenon reminds that doping Fe(Mn) in BiMnO3/BiIrO3 (BiFeO3/BiIrO3) might engineer the Fermi level. 13



In order to analyze the increased spin polarizations in [001] case, the orbital-decomposed band structures are analyzed next. The orbitals O1=pz + dz2 , O2=dxz +d yz and O3=px +py +d xy + dx2 -y2 are defined. In Fig. 3(c), for BFO-OIB model at [001] case, the orbital-decomposed spin polarizations in BiIrO3 increase in the order of O1, O2 and O3 orbitals, which is also suitable for the BMO-OIB model at [001] case. Hence, for BiIrO3 in BFO/OIB and BMO/OIB models, the enlarged spin polarizations at [001] case mainly come from the xy-plane orbitals, which should be associated with the xy-plane honeycomb lattice in the bilayered BiIrO3. The detailed O-p, Fe-d, Mn-d and Ir-d decomposed spin polarizations in BFO/OIB and BMO/OIB models are provided in Fig. S3, where the resolved spin polarizations in the valley at OIB-models increase in the order of Fe d (Mn d), O p and Ir d states. Interactions between BiIrO3 and BiXO3 (X=Fe, Mn). In Fig. 2, the valley and spin characteristics in BFO/OIB and BMO/OIB models are advantaged to the BFO/BIO and BMO/BIO models, which is associated with the different interactions between BiIrO3 and BiXO3 in four heterostructures. The DOS distributions of the Ir, Fe and Mn atoms in four models are displayed in Figs. 4(a)-4(d), where the DOS hybridization between Ir and Fe(Mn) appears in all of the four models, such as the MnII-IrII hybridization near EF-0.5 eV in the BMO/OIB model. However, the charge differences reveal the different interacting means in the four models. In Figs. 4(e) and 4(f), the interfacial IrII, FeII, MnII atoms in BFO/BIO and BMO/BIO models gain the charge, along with the charge-losed Bi atoms. However, for BFO/OIB and BMO/OIB models in Figs. 4(g) and 4(h), Ir, Fe and Mn ions play different roles, where the interfacial IrII gain the charge while FeII and MnII lose the charge. The different interfacial effects in the two kinds of models result in their different valley 14


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Figure 4. (a-d) The DOS for Fe, Mn and Ir d electrons in BiXO3/BiIrO3 superlattices with GGA+U+SOC calculations. (e-h) The charge density differences (isosurface value 0.006e/Å3) for BiXO3/BiIrO3 superlattices with GGA+U calculations. The yellow and blue isosurfaces represent the charge accumulation and depletion, respectively. The symbol II corresponds to Figs. 1(d)-1(g).

and spin characteristics in BiIrO3. Besides, considering the O honeycomb structure (Fig. 3(d)), evident O charge differences (Figs. 4(g) and 4(h)) and p-orbital occupations in the valley (Fig. S3), O atoms shall play an irreplaceable role in the gained valley and spin characteristics of BFO/BIO and BFO/OIB models. Notably, in Fig. S3, the spin polarization at the valley in BFO/OIB and BMO/OIB models are mainly provided by the Ir d resolved states, rather than the O p states. Hence, in later 15



experiments, the possible O vacancies caused by the fabrication method shall influence the spin characteristic but could not collapse the spin polarization in BFO/OIB and BMO/OIB structures. Herewith, in Figs. 2(c) and 2(d), the splitting of bands is induced by the strong SOC in Ir atoms, where the spin polarizations in the valley are mainly provided by the Ir atoms, rather than the Fe/Mn atoms with magnetic orders. However, in Figs. 3(a) and 3(b), the spin polarization in Ir is significantly depend on the spin orientation in Fe(Mn), which should be owing to the IrII-FeII (IrII-MnII) interactions. These results come from the magnetic proximity effect between BiFeO3 and BiIrO3. Besides, the BFO/OIB and BMO/OIB models with larger Wcoh (Table 1) are more stable than the BFO/BIO and BMO/BIO models, which benefits to the experimental realization of valley and spin polarized BiXO3/BiIrO3 superlattices. Predicted valley-spin component with multilevel resistances. As shown in Figs. 2(a) and 2(e), the parallel and antiparallel directions of ferroelectric polarization in BiFeO3 and BiIrO3 can modulate the energy valley and resultant valley polarization in the BiFeO3/BiIrO3 superlattices. However, the ferroelectric states in the BiFeO3/BiIrO3 superlattices can be tuned by the electric field due to the different coercive fields in BiFeO3 and BiIrO3.19,43,44 Hence, the electric field could switch the valley injection in BiFeO3/BiIrO3 superlattices, where the parallel (E↓↓) and antiparallel (E↓↑) states correspond to the flat valley and evident valley polarization respectively. Meanwhile, for BiIrO3 in BFO/OIB superlattices (Fig. 3(a)), the spin polarizations at the valley are relied on the spin orientations of Fe, which can be tuned by the external magnetic field with the remained antiferromagnetic order in BiFeO3.41 So, in BiFeO3/BiIrO3 superlattices, the spin injection at the valley of bilayered BiIrO3 will be controllable via the magnetic field as diagramed in Fig. 5(a). 16


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Considering the large differences between [100]- and [001]-oriented spin polarizations in BFO/OIB models, the magnetic fields parallel(Min-plane) and perpendicular(Mout-of-plane) to the honeycomb plane might produce distinct spin polarizations in the valley of BiFeO3/BiIrO3 superlattices. Besides, in Fig. 3(a), the SOC-induced band splitting is consistent in [100] and [001] cases, where the prominent difference is the spin polarization at the valley. So, the external magnetic field will not influence the SOC-split bands and the resultant valley characteristic, where the varied property will be the spin polarization in the valley. More importantly, the electric-field-switched valley polarization and the magnetic-field-tuned spin polarization in lifted valley will correspond to three states of [E↓↓], [E↓↑, Min-plane] and [E↓↑, Mout-of-plane], which can produce the multilevel resistances in corresponding ferroelectric random access memory.19 Besides, the BiFeO3/BiIrO3 superlattices can be applied in the valley filter,17 where the electric field could switch the parallel (E↓↓) state with flat valley and the antiparallel (E↓↑)

Figure 5. (a) The schematic diagram for valley-spin component based on the BiFeO3/BiIrO3 superlattices. (b-e) The geometries of specific (BiFeO3)2/(BiIrO3)N superlattices with different thickness N of BiIrO3. (f) Band structures for BiFeO3/(BiIrO3)N (N=4) superlattices with GGA+U+SOC calculations. The circle represents BiIrO3. 17



ferroelectric state with evident valley polarization. Meanwhile, the spin-polarized valley in BiIrO3 at BFO/OIB model (Fig. 2(e)) can be used to study the spin and valley physics,33 such as the valley Hall and spin Hall effects,2,3,6 which is urgent in oxide systems. Additionally, the thickness effect on the valley has been recognized in previous TMDCs and (111)-oriented Ca0.5Sr0.5IrO3-based superlattices.23,45 In this work, BiIrO3 with different thickness N (N=2, 4, 6 and 8) is further tested in BFO/IOB and BMO/OIB models [Figs. 5(b)-5(e)], where N also indicates the numbers of unit cells in BiIrO3. The geometry of (BiFeO3)2/(BiIrO3)N is similar to (BiMnO3)2/(BiIrO3)N, where the N=2 cases correspond to the BFO/OIB and BMO/OIB models in Figs. 1(f) and 1(g). In (BiXO3)2/(BiIrO3)N superlattices, the large valley height and high spin polarizations disappear in N=4, 6 and 8 cases, where the band structure in (BiFeO3)2/(BiIrO3)4 is shown in Fig. 5(f) as an example. Herewith, the perovskite ABO3(111) bilayer with honeycomb can reduce the symmetry of the crystalline field from octahedral to trigonal,46 which provides the foundation for generating the energy valley. So, the lifted valley in BFO/OIB and BMO/OIB models are limited to the bilayered structure (i.e., the N=2 case), which is similar to the bilayered limitation in the topological phase of ABO3(111) transition metal oxides.46 The thickness-dependent spin and valley polarizations in BiIrO3 should be noticed in later studies.

CONCLUSION

In summary, the electronic structures in BiXO3/BiIrO3 ferroelectric superlattices are studied by first-principles calculations with the spin-orbital coupling. Both valley and spin polarizations in 18


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bilayered BiIrO3 are achieved in BFO/OIB and BMO/OIB models, where the spin polarization in the valley is highly dependent on the spin orientation of Fe or Mn owing to the xy-plane orbitals. Particularly, the relatively parallel and antiparallel directions of ferroelectric polarization in BiFeO3 and BiIrO3 can modulate the valley injection in BiFeO3/BiIrO3 superlattices. These special characteristics are based on the Ir and X honeycomb lattice and surrounding O honeycomb structure in bilayered BiIrO3 and BiXO3. The tunable valley and spin polarizations in BiFeO3/BiIrO3 ferroelectric superlattices could develop a valley-spin component with multilevel resistances, which paves a way for developing the nonvolatile data memories and valleytronic devices.

ASSOCIATED CONTENT

Supporting Information Band structures in BFO/OIB superlattices at different K meshes; band structures in BFO/OIB superlattices at different U on Ir d state; the O p, Fe d, Mn d and Ir d contributions in BFO/OIB and BMO/OIB superlattices (PDF)

AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected]

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Author Contributions L.Y. and W.M. designed the outline of the manuscript and wrote the main manuscript text. X.W. contributed detailed discussions and revisions. All the authors reviewed the manuscript.

Notes The authors declare no competing ﬁnancial interest.

ACKNOWLEDGEMENTS

This work is supported by National Natural Science Foundation of China (51671142 and U1632152), Key Project of Natural Science Foundation of Tianjin (16JCZDJC37300). It is also supported by High Performance Computing Center of Tianjin University, China.

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Table of Contents Graphic (TOC)

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BiIrO3 (X=Fe, Mn

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