Triferroic Material and Electrical Control of Valley Degree of Freedom

Research Article Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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Triferroic Material and Electrical Control of Valley Degree of Freedom Qi Pei,† Baozeng Zhou,‡ Wenbo Mi,*,† and Yingchun Cheng*,§ †

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Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparation Technology, School of Science, Tianjin University, Tianjin 300354, China ‡ School of Electrical and Electronic Engineering, Tianjin University of Technology, Tianjin 300384, China § Key Laboratory of Flexible Electronics (KLOFE) & Institute of Advanced Materials (IAM), Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), Nanjing Tech University, Nanjing 211816, China S Supporting Information *

ABSTRACT: The generation and manipulation of valley polarization in controllable ways are important for the valley-related physics and devices. In analogy to multiferroic materials with more than one ferromagnetic, ferroelectric, and ferroelastic orders, a new triferroic system with ferromagnetism, ferroelectricity, and ferrovalley is proposed, namely, the monolayer AgBiP2Se6/CrI3 van der Waals heterostructure. Using density functional theory, we further predict that the electrical control on the valley degree of freedom could be realized in this triferroic system. The mechanism of electrically controlled valley is elucidated as an intermediate coupling between lattice and ferroelectricity. The coupling of three ferroic orders in triferroic material paves the way for electrically controlled valleytronic devices.

KEYWORDS: AgBiP2Se6, CrI3, triferroic material, valleytronics, electrical control

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INTRODUCTION To date, the valley degree of freedom (DOF) has attracted much attention due to many distinctive quantum phenomena including valley Hall effect1 and valley-dependent orbital magnetic moment.2 Analogous to the charge DOF in electronics and spin DOF in spintronics, valleytronics relies on the utilization of valley DOF.3−5 Many systems have been proposed as candidates for valleytronic materials, such as graphene,6 silicon,7 bismuth thin films,8 and transition-metal dichalcogenide (TMDC) monolayers.9,10 To utilize the valley DOF, it is necessary to generate the valley polarized state, where several strategies have been proposed including optical pumping,11−13 magnetic doping,14−16 and magnetic proximity.17−19 Since optical pumping is a dynamic process, it is not suitable for data storage. Meanwhile, the magnetic doping makes the electronic transport suffer from impurity scattering. A comparison of with the above approaches shows that magnetic proximity is superior to achieving valley polarization. The proximity effect of magnetic semiconducting EuO (EuS) substrate can induce a large valley splitting in the monolayer MoTe2 (WSe2).17−19 The sign of valley splitting and net valley/spin-polarized Hall current could be switched by reversing the magnetization of the substrate by an external magnetic field. However, from the view point of practical application, this is somewhat inconvenient because the generation of magnetic field in an electronic device will enlarge the device size and increase the © XXXX American Chemical Society

energy consumption. Thus, the generation and manipulation of the valley DOF by means of electrical approach are highly desired. In addition, the exploration for new valleytronic materials is also a great impetus to the development of valleytronic devices. Recently, the spontaneous valley polarization has been predicted in monolayer 2H-VSe2, and a new member of ferroic family has been proposed, called ferrovalley materials.20 For the two-dimensional (2D) material, the monolayer AgBiP2Se6 has been predicted to have an outplane ferroelectricity by the first-principles calculations,21 whereas the possibility of monolayer AgBiP2Se6 as a new valleytronic material remains to be explored. In this work, we predict the ferroelectric monolayer AgBiP2Se6 as a new valleytronic material with a large spin− orbit splitting (∼472 meV) at the conduction band minimum (CBM) by first-principles calculations. Then, the monolayer AgBiP2Se6/CrI3 van der Waals (vdW) heterostructure is constructed, which has ferromagnetism, ferroelectricity, and ferrovalley simultaneously, named as a new triferroic system. The three ferroic orders in triferroic materials provide the conditions for the electrical control of the valley DOF. The perpendicular magnetic anisotropy (PMA) of monolayer CrI3 in AgBiP2Se6/CrI3 vdW heterostructure can be tailored by Received: January 31, 2019 Accepted: March 14, 2019 Published: March 14, 2019 A

DOI: 10.1021/acsami.9b02095 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces

Figure 1. Collinear spin-polarized BS of the monolayer CrI3 calculated by (a) PBE and (b) HSE06. The blue and red curves represent the spin-up and spin-down bands, respectively. (c) Noncollinear spin-polarized BS of monolayer CrI3 obtained by PBE + SOC. The arrows indicate the locations of the CBM and VBM.

SOC is treated as a perturbation in non-self-consistent calculations at different magnetization directions. Finally, MAE is obtained by taking the total energy differences between in-plane and out-of-plane magnetization orientations as MAE = E∥ − E⊥, where E∥ and E⊥ are the energies with the magnetization in the (100) and (001) directions, respectively. Correspondingly, the positive or negative MAE indicates that the easy magnetization axis is perpendicular or parallel to the interface of the heterostructures.

ferroelectric polarization of the monolayer AgBiP2Se6, which offers new attempts for high-density data storage at a nanoscale.

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CALCULATION DETAILS AND MODELS The structure relaxation, band structure (BS), and density of states (DOS) calculations are performed using Vienna ab initio simulation package22,23 based on the density functional theory (DFT) with generalized gradient approximation by Perdew, Burke, and Ernzerhof (PBE).24 Kohn−Sham single-particle wave functions are expanded in the plane wave basis set with a kinetic energy cutoff at 500 eV. A 9 × 9 × 1 k-point grid centered at Γ point is used for both monolayers and heterostructures. A 20 Å thick vacuum layer is adopted in the (001) direction to obtain the 2D structures under the periodic boundary condition. During the geometry optimization, all of the atomic positions are free to relax until the energy difference between two successive ionic steps is converged to 10−5 eV and the force is less than 10−2 eV/Å. Spin−orbit coupling (SOC) is considered in the electronic structure calculations. To take into account the interlayer vdW force, the DFT-D2 method is used,25 which has been evidenced to give accurate descriptions for various vdW systems, such as graphene/CrI3 heterostructure.26 The lattice constant of bulk CrI3 calculated using PBE and DFT-D2 are given in Table S1. To describe Cr 3d electrons, the onsite Coulomb and exchange interaction for Cr 3d are set as U = 2.7 eV and J = 0.7 eV.27,28 It should be mentioned that the exchange energies of monolayer CrI3 with or without DFT + U show similar results.27 Therefore, the simulation is performed at U = 0. The phonon properties of monolayer AgBiP2Se6/CrI3 heterostructure are calculated by the finite-displacement method implemented in Phonopy.29 Since PBE functional always underestimates the band gap, the BSs of monolayer AgBiP2Se6 and CrI3 are further calculated with more accurate hybrid functional developed by Heyd, Scuseria, and Ernzerhof (HSE06).30 The tight-binding Hamiltonian is constructed based on maximally localized Wannier functions (MLWFs) from the calculated bands by DFT, as implemented in the Wannier90 code.31,32 The calculation of Berry curvature is carried out with a denser k-mesh (101 × 101 × 1). The magnetic anisotropy energy (MAE) is calculated from the force theorem by considering the SOC,33 which is obtained by performing a two-step procedure. First, the charge density is acquired by a fully self-consistent calculation for the collinear case.34 Second, by freezing the potential charge density, the

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RESULTS AND DISCUSSION Monolayer CrI3 is the first 2D ferromagnet that has been successfully fabricated in experiments.35 In our calculations, the relaxed lattice constant of monolayer CrI3 is 7.000 Å, slightly larger than its experimental bulk lattice constant of 6.867 Å,36 which is the same as the previous theoretical results.37,38 The above results indicate that the optimized geometry structure is reliable. In Figure 1a,b, the band gaps calculated by PBE and HSE06 methods are 1.19 and 1.94 eV, respectively, in accordance with 1.19 and 1.93 eV reported by Zhang et al.26 Both functionals show a 2D ferromagnetic ground state, where the magnetic moment per unit cell is approximately 6.0 μB. The calculated magnetic characteristics are consistent with previous results.35,36 In Figure 1c, the noncollinear spin-polarized BS shows that the monolayer CrI3 has a direct band gap with both CBM and valence band maximum (VBM) located at Γ point. The band gap obtained by PBE + SOC method is 0.88 eV. Bulk AgBiP2Se6 with a lamellar structure was reported to be an antiferroelectric semiconductor with an intralayer ferrielectric ordering.39 When it was exploited to the 2D form, monolayer AgBiP2Se6 was predicted to be an atomically thin ferroelectric semiconductor.21 However, the ground state of monolayer AgBiP2Se6 was not purely ferroelectric because the out-of-plane ferroelectricity came from the compensated ferrielectric state owing to the off-centering antiparallel displacements of Ag+ and Bi3+.21 In Figure 2a, the off-centering antiparallel displacements of Ag+ and Bi3+ can induce an outof-plane ferroelectricity. The paraelectric phase of monolayer AgBiP2Se6 is unstable, where the Ag+ and Bi3+ are located in the same plane.21 When Ag+ and Bi3+ shift away from the plane along the z-axis in opposite directions, the structure turns to a stable polar phase, where the total energy decreases by 6.2 meV/f.u.21 The off-centering of Ag+ is much greater than that of Bi3+. Hence, a spontaneous polarization appears, which is perpendicular to the monolayer. B


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K+ and K− points are opposite due to the protection of timereversal symmetry, which gives rise to K+ and K− valleys. The carriers at K± valleys are Dirac fermions. In the presence of an in-plane electric field, the carriers will acquire a transverse velocity proportional to Berry curvature, which can give rise to an intrinsic contribution to Hall conductivity.10 To confirm the above analysis, the Berry curvature and anomalous Hall conductivity are calculated based on the first-principles methods. Figure 4a shows the band structure of AgBiP2Se6 calculated by MLWFs method with SOC, which is in well agreement with DFT results. The Berry curvature is defined as Ω(k) = ± Figure 2. (a, b) Structure of the most stable monolayer AgBiP2Se6/ CrI3 heterostructure. The blue and purple arrows indicate the offcentering antiparallel displacements of Ag+ and Bi3+, respectively. The ferroelectric polarization of AgBiP2Se6 pointed to and pointed away from the interface is indicated by green arrows. (c) Hexagonal Brillouin zone and high symmetry points.

2τa 2t 2(Δ − τszλ) [(Δ − τszλ)2 + 4a 2t 2k 2]3/2

(1)

where + and − signs represent the valence and conduction bands, respectively. a, t, Δ, and 2λ are the lattice constant, effective hopping integral, energy band gap, and SOC strength, respectively. ŝz is the spin operator. τ is the valley index, which has opposite signs for the two valleys due to the opposite spin splitting direction with SOC.40 Hence, the signs of the Berry curvature have a strong correlation with the valley index τ. The integral of the Berry curvature over the occupied states gives contributes to Hall conductivity

After structural optimization, the lattice parameter of monolayer AgBiP2Se6 is 6.754 Å, which is consistent with previous result.21 Owing to the lack of inversion symmetry, the ferroelectric monolayer AgBiP2Se6 with a space group of P3 is expected to have a spin splitting just like in the H-phase monolayer TMDCs.9 In Figure 3a, the BS of monolayer AgBiP2Se6 obtained with PBE functional predicts an indirect band gap of 1.46 eV, in accordance with previous study.21 The VBM is located between K and Γ points, whereas CBM is located at Γ point. The more accurate HSE06 also gives an intrinsically semiconducting property with an indirect band gap of 2.33 eV (Figure S1). The BS of monolayer AgBiP2Se6 calculated by PBE + SOC is shown in Figure 3b. Notably, CBM moves to K point by considering SOC, and the band gap decreases to 1.22 eV by comparing with the value obtained with PBE. By considering SOC, the spin-split bands appear along M−K+−Γ−K−−M high-symmetry path. In the orbitalresolved BS shown in Figure 3a, it is clear that some higher valence bands are mainly contributed from Ag orbitals, whereas some lower conduction bands are mainly from Bi orbitals. Hence, the conduction bands present a larger spin splitting due to a stronger SOC strength of Bi. In Figure 3b, the splitting of CBM at K± points is 472 meV. The splittings at

σH =

e2 ℏ

∑∫

d 2k f (k , τ , sz)Ω(k , τ , sz) (2π )2

(2)

where f is the Fermi−Dirac distribution function. In monolayer AgBiP2Se6, the splittings at K+ and K− points are opposite, so the values at K+ and K− points are similar with opposite signs, which means the carriers at K+ and K− valleys will be deflected along the opposite transverse directions under a longitudinal electric field. The results remain valid as an exchange field decouples the spin-up and spin-down bands.17 Without the disturbance of exchange field, the carrier dynamics give rise to pure spin and valley Hall effects. In Figure 4c, the total integral amount of the anomalous Hall conductance in different spin directions is approximately zero. Under the broken timereversal symmetry, the valley splitting appears. A valley- and spin-polarized anomalous Hall effect can be induced, where a net charge Hall current could be achieved by a longitudinal electric voltage. Hence, the K+ and K− points of monolayer AgBiP2Se6 are exactly valley indexes, which can be used to store and process information.

Figure 3. (a) BS of monolayer AgBiP2Se6 obtained by PBE. The open circles and squares represent the contributions from Bi and Ag orbitals, respectively. (b) BS with SOC. (c, d) BS of the most stable AgBiP2Se6/CrI3 vdW heterostructure. The ferroelectric polarization in (c) and (d) points to and away from the interface, respectively. The circles represent the AgBiP2Se6 component. The size of the circles is proportional to the spin projection along the (001) direction. The blue/red denotes the positive/negative value. The black arrows indicate the spin splitting of the CBM at K± points. C


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Figure 4. Calculated (a, b) BS, (c, d) anomalous Hall conductivity, and (e, f) Berry curvature of monolayer AgBiP2Se6 and the most stable AgBiP2Se6/CrI3 vdW heterostructure with polarization pointing away from interface by MLWFs method with SOC. The upper and lower panels represent the monolayer AgBiP2Se6 and AgBiP2Se6/CrI3 vdW heterostructure, respectively.

The AgBiP2Se6/CrI3 heterostructure is built with the primitive cells. The lattice mismatch between the two monolayers is 3.6%, which is in an acceptable range and accessible in experimental synthesis. Usually, the lattice constant of vdW heterostructure is significantly influenced by the strain effect from substrate. However, in our theoretical simulation, the lattice constants of the heterostructure are fixed at the average value due to the absence of substrate, where the moderate strains are applied to both the monolayers. This approach has been widely used in theoretical studies on vdW heterostructures.41 Owing to the sensitivity of low-dimensional materials to external strain, the strain effect originating from the lattice mismatch between AgBiP2Se6 and CrI3 is carefully checked and shown in Figure S2, which confirms that the appearance of valley polarized states in heterostructure is independent of the strain but only related to the interaction between the two monolayers. Five representative interfacial configurations with different relative positions are built, and two ferroelectric polarizations of AgBiP2Se6 are considered to construct the vertical vdW heterostructures. The top views of the different interfacial configurations are given in Figures 2b and S3a−d. After structure relaxation, the model in Figure S3d transforms into the model in Figure S3c. Hence, this configuration is not involved in the following discussion. The binding energy Eb of the heterostructure is calculated as Eb = EA + EC − Eh, where EA, EC, and Eh are the total energies of the pristine monolayer AgBiP2Se6, the pristine monolayer CrI3 and the heterostructure, respectively. In Table 1, the obtained binding energies are in the range of 543−651 meV. The positive values indicate the exothermic formation process and the stability of geometry configuration. Our predicted AgBiP2Se6/CrI3 heterostructure is more stable than many vdW heterostructures, such as the bilayer graphene (Eb = 100 meV)42 and phosphorene/graphene vdW heterostructure (Eb

Table 1. Binding Energies Eb (meV), Equilibrium Interlayer Distances d0 (Å), Total Magnetic Moments Mtotal (μB), and MAE (μeV/f.u.) for the Configurations in Figures 2b and S3a−ca 2b Eb d0 Mtotal MAE a

S3a

S3b

S3c

↑

↓

↑

↓

↑

↓

↑

↓

651 3.18 5.74 557

618 3.22 5.74 573

611 3.26 5.74 576

543 3.32 5.74 591

544 3.34 5.74 518

561 3.28 5.74 557

621 3.21 5.73 594

577 3.25 5.73 619

The arrows indicate the opposite ferroelectric polarizations.

= 120 meV).43 Previous reports proved the absent imaginary frequency in the whole Brillouin zone for monolayer ferroelectric AgBiP2Se6 and monolayer CrI3, indicating that these monolayers are dynamically stable and can exist as freestanding 2D crystals.21,44 To further check the stability of AgBiP2Se6/CrI3 heterostructure, the phonon dispersion curve of heterostructure with polarization pointing away from the interface is calculated based on the supercell. In Figure S4, a very small imaginary frequency at Γ point appears in the phonon band dispersion, which may be ascribed to the residual stress due to the lattice mismatch. Besides, the heat of formation energy is another important parameter to check the thermodynamic stability of the system, whereas the evaluation of the heat of formation in a heterostructure with a weak vdW force is complicated. There are various literatures using binding energy instead of heat of formation energy to evaluate the stability of the vdW heterostructures.45,46 Hence, the fabrication of AgBiP2Se6/CrI3 heterostructure is predicted to be feasible in experiments. The equilibrium interlayer distances d0 between monolayer AgBiP2Se6 and CrI3 are also given in Table 1. To some extent, this distance can reflect the strength of interfacial interaction. D


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Figure 5. Partial DOS of Ag, Bi, Seup (upper plane), Sedn (lower plane), Idn (lower plane), and Cr with ferroelectric polarization (a) pointed to and (b) pointed away from the interface. The gray region indicates the pz orbital hybridization between Seup and Idn near the energy of −0.75 eV. The insets are the corresponding relaxed geometries of heterostructures. In a trigonal crystal field, the d orbital splits into one singlet a1 (dz2) and two doublets e1 (dxz, dyz) and e2 (dxy, dx2−y2).

Hence, the obtained smallest d0 together with the highest Eb indicates that the heterostructure in Figure 2b is the most stable stacking configuration, which will serve as the typical model to investigate the electronic properties of AgBiP2Se6/ CrI3 heterostructure. Notably, the CrI3 monolayer bonds to AgBiP2Se6 by weak vdW interaction. Furthermore, the schematic of the energy levels of the monolayer AgBiP2Se6 and CrI3 before and after contacts are plotted in Figure S5. The work function WF (the energy difference between Evac and Ef), the electron affinity χ (the energy difference between Evac and the CBM), and the ionization potential η (the energy difference between Evac and the VBM) of monolayer AgBiP2Se6 and CrI3 calculated with PBE + SOC are listed in Table S2. Figure 3c,d shows the BS of the most stable AgBiP2Se6/CrI3 heterostructure with two different ferroelectric polarizations. The proximity effect of ferromagnetic CrI3 will induce the exchange field in monolayer AgBiP2Se6. Owing to the opposite original splittings at K+ and K− points,14 when the ferroelectric polarization points to the interface, the spin splitting at CBM of AgBiP2Se6 component is enhanced to 551 meV at K+ point and reduced to 395 meV at K− point (black arrows in Figure 3c). Hence, the robust valley splitting exists in monolayer AgBiP2Se6, i.e., ferrovalley. At this time, the CBM of the heterostructure is located at Γ point and comes only from CrI3 orbitals, which is a blunting in the valley DOF of the heterostructure. When the ferroelectric polarization reverses, the CBM transfers to K− point (Figure 3d). Now, the CBM is contributed by both AgBiP2Se6 and CrI3 orbitals. It is reasonable to speculate that the K− valley of the heterostructure could afford the anomalous valley Hall effect. Figure 4b,d,f shows the BS, anomalous Hall conductivity, and Berry curvature of the most stable AgBiP2Se6/CrI3 heterostructure, respectively, with ferroelectric polarization pointing away from the interface. Due to the broken timereversal symmetry, a nonzero anomalous Hall conductivity appears. The direction of spin splitting at valleys is unchanged, but the intensity difference appears. So, the value at K+ and K− points are nondegenerate with opposite signs in Berry curvature, which agrees with the analysis that the valley splitting appears under the broken time-reversal symmetry. Besides, the ferromagnetism of monolayer CrI3 is not be influenced by the weak vdW interaction, so the magnetism of

AgBiP2Se6/CrI3 heterostructures is almost entirely from the magnetic Cr ions. In Table 1, the total magnetic moments of heterostructures are close to that of the monolayer CrI3. Therefore, the system with simultaneous ferromagnetism, ferroelectricity, and ferrovalley is proposed as a triferroic material. The electrical control of valley DOF using triferroic system is demonstrated for the first time, where the valley DOF can be switched on and off by the ferroelectricity of AgBiP2Se6. The modulation on valley characteristics by ferroelectric polarization is also observed in the less stable configurations, as shown in Figure S6. To gain more physical insights on the interplay of the orbitals, the partial DOS of the most stable heterostructure is given in Figure 5. In a trigonal crystal field, the d orbital splits into one singlet a1 (dz2) and two doublets e1 (dxz, dyz) and e2 (dxy, dx2−y2). It shows that the out-of-plane a1 orbital of Ag is sensitive to ferroelectric polarization, which is consistent with the large displacement in the (001) direction. On the contrary, the states of Bi are insensitive to the ferroelectric polarization with a relatively small displacement. The relaxed geometries of AgBiP2Se6 in the heterostructures are given in the insets. In Figure 5a, Ag is closer to the upper Se(Seup). Strong hybridizations between Ag a1 and Seup pz, Ag e1 and Seup px, and Ag e2 and Seup py orbitals are observed, which can be recognized from the identical shape and energy range. However, the orbitals of Se in a lower plane (Sedn) show the weak hybridizations with Ag. When the ferroelectric polarization is reversed, the antiparallel displacements of the Ag and Bi change the sign, where Ag is closer to Sedn, as shown in Figure 5b. The hybridizations between Ag a1 and Sedn pz, Ag e1 and Sedn py, and Ag e2 and Sedn px orbitals become more distinct. In addition, it should be noted that the DOS of Cr and lower I (Idn) in the heterostructure is not sensitive to the ferroelectric polarization. Hence, the mechanism of electrically controlled valley is elucidated as an intermediate coupling between lattice and ferroelectricity. If the Fermi level is tuned to the vicinity of CBM, e.g., by electron doping, the longitudinal valley- and spin-polarized transport will be switched on/off through an external electric field. Different from the valley filter model proposed before,17,47 it utilizes an electric field than a magnetic field to modulate the valley characteristics rather, which reduces the energy consumption and the device complexity. Moreover, it E


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monolayer CrI3, the obtained MAE is about 737 μeV/f.u., which is quantitatively consistent with the previous result of 0.69 meV/f.u. reported by Zhang et al.44 The easy axis is along the out-of-plane direction. After contacting with AgBiP2Se6, MAE varies in the range of 518−619 μeV/f.u., which is still of considerable magnitude compared with monolayer CrSnTe348 and also comparable to 2D Fe2Si naonosheets.49 Figure 7 shows the orbital-resolved MAE of Cr and Idn atoms in monolayer CrI3 and AgBiP2Se6/CrI3 heterostructure. For Cr atom in isolated monolayer CrI3, the hybridization between Cr dyz and dz2 gives the largest PMA contribution, and the second largest PMA contribution originates from the hybridization between Cr dyz and dx2−y2, as well as the hybridization between Cr dxy and dxz orbitals. The matrix element differences between Cr dxy and dx2−y2 orbitals favor a comparable large in-plane magnetic anisotropy (IMA). For Idn atom, the PMA and IMA contributions are mainly from the matrix element differences between I px and py orbitals and between I py and pz orbitals, respectively. When the monolayer CrI3 interacts with AgBiP2Se6, a small increment of PMA contributions and a relatively big increment of IMA contributions appear simultaneously for both Cr and I atoms. The resultant overall MAE in the heterostructure is decreased. As mentioned in Figure 5, the DOS of Cr d and I p orbitals in AgBiP2Se6/CrI3 heterostructure are inert to ferroelectric polarization. However, different MAE values are related to ferroelectric polarization. When the ferroelectric polarization of AgBiP2Se6 points to the interface, an obvious pz orbital hybridization appears between Seup and Idn near the energy of −0.75 eV, implying the orbital overlapping. Since Lado et al. demonstrated that the MAE in monolayer CrI3 originates from the ferromagnetic superexchange interaction with the Cr−I−Cr bond angle of about 90°, predominantly from the SOC in the heavy iodine atoms,27 the interfacial hybridization will have further influence the anisotropic exchange interaction. Besides, Figure 7g, the charge density differences show charge redistribution around Seup, Cr, and Idn,

switches on and off the valley DOF to store information rather than using the two valley indexes. The Schematic of electrically controlled valley characteristics by using triferroic materials is depicted in Figure 6. G+/− is the gate electrode used to switch

Figure 6. (a, b) Electrical switch of valley degree in triferroic system. S, D, A, and C represent the source, drain, AgBiP2Se6, and CrI3, respectively. The gate electrode G+/− is used to switch the ferroelectric polarization. The ferroelectric polarization direction is depicted by red arrows.

the ferroelectric polarization. The basic electronic element proposed here has the potential applications in valleytronics. Notably, since the monolayer CrI3 interacts with monolayer AgBiP2Se6 mainly through weak vdW force, the interlayer modulation effect is limited. However, the mechanism of electrically controlled valley demonstrated here is valid, which can also be extended into other systems, such as TMDC/ multiferroic heterostructures. The detection of MAE in low-dimensional materials is of great importance for fabricating novel spintronic devices. Hence, the MAE of monolayer AgBiP2Se6/CrI3 heterostructures with different stacking patterns is calculated. For

Figure 7. Orbital-resolved MAE for Cr and I ions in monolayer CrI3 and the most stable AgBiP2Se6/CrI3 heterostructure. (a) and (d) The AgBiP2Se6/CrI3 heterostructure with ferroelectric polarization pointing to the interface. (b) and (e) The monolayer CrI3 and (c) and (f) the AgBiP2Se6/CrI3 heterostructure with ferroelectric polarization pointing away from the interface. (g) Charge density differences of AgBiP2Se6/CrI3 heterostructures. The isosurface value is 0.25 e/nm3. Yellow and blue regions represent charge gain and loss, respectively. F



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which can affect the bonding and hybridization between the two monolayers. Hence, the variation of MAE may be ascribed to the intermediate coupling between lattice and ferroelectricity. An electrical field could change the ferroelectric polarization direction, i.e., the atomic structure of AgBiP2Se6 and electron density distribution. The tunable PMA of monolayer CrI3 in AgBiP2Se6/CrI3 vdW heterostructure by ferroelectric polarization of monolayer AgBiP2Se6 offers new attempts for high-density data storage in 2D devices.

CONCLUSIONS By density functional theory, the monolayer AgBiP2Se6/CrI3 vdW heterostructure is predicted as a triferroic system, where ferromagnetism, ferroelectricity, and ferrovalley exist simultaneously. First, ferroelectric monolayer AgBiP2Se6 presents two degenerate valleys at K+ and K− points. Then, the proximity effect of the ferromagnetic CrI3 induces a robust valley splitting. Finally, the spontaneous ferroelectricity modulates the valley DOF in the heterostructure, which can make the anomalous valley Hall effect switchable. On account of this effect, the triferroic systems has potential applications in electrically controlled valleytronic devices. Moreover, tunable PMA in AgBiP2Se6/CrI3 heterostructure paves the way for developing low-dimensional magnetoelectronic devices. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.9b02095.

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REFERENCES

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Research Article

DFT-D2 test; BS of monolayer AgBiP2Se6 obtained with different functionals; BS of the monolayer AgBiP2Se6 at different tensile strains; top views of the less stable stacking patterns; phonon band dispersion of the most stable heterostructure with polarization pointing away from the interface; work function, electron affinity, ionization potential, band gap, and schematic of the energy levels of monolayer AgBiP2Se6 and CrI3; BS for the less stable heterostructures (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (W.M.). *E-mail: [email protected] (Y.C.). ORCID

Baozeng Zhou: 0000-0003-3568-701X Wenbo Mi: 0000-0002-9108-9930 Yingchun Cheng: 0000-0002-8495-9184 Author Contributions

Q.P. and W.M. designed the outline of the manuscript and wrote the main manuscript text; B.Z. and Y.C. contributed detailed discussions and revisions. All the authors reviewed the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Prof. W.M. thanks the National Natural Science Foundation of China (51871161, 51671142, and U1632152) and Key Project of Natural Science Foundation of Tianjin City (16JCZDJC37300) for financial support. G


Research Article


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Triferroic Material and Electrical Control of Valley Degree of Freedom

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