Proximity Effect Induced Spin Injection in Phosphorene on Magnetic

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Proximity Effect Induced Spin Injection in Phosphorene on Magnetic Insulator Haoqi Chen, Bin Li, and Jinlong Yang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b11454 • Publication Date (Web): 16 Oct 2017 Downloaded from http://pubs.acs.org on October 20, 2017

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ACS Applied Materials & Interfaces

Proximity Effect Induced Spin Injection in Phosphorene on Magnetic Insulator Haoqi Chen,a Bin Li,a,b,* and Jinlong Yanga,b,* a

Hefei National Laboratory of Physical Science at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China b

Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

ABSTRACT: Black phosphorus is a promising candidate for future nano-electronics with moderate electronic band gap and high carrier mobility. Introducing the magnetism into black phosphorus will widely expand its application scope and may present a bright prospect in spintronic nano-devices. Here we report our first-principles calculations of spin-polarized electronic structure of monolayer black phosphorus (phosphorene) adsorbed on a magnetic europium oxide (EuO) substrate. Effective spin injection into the phosphorene is realized by means of interaction with the nearby EuO(111) surface, i.e. proximity effect, which results in spin-polarized electrons in 3p orbitals of phosphorene with the spin polarization at Fermi level is beyond 30%, together with an exchange-splitting energy of ~ 0.184 eV for conduction-band minimum of the adsorbed phosphorene corresponding to an energy region where only one spin channel is conductive. The energy region of these exchange-splitting and spin-polarized band

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gaps of the adsorbed phosphorene can be effectively modulated by in-plane strain. Intrinsically high and anisotropic carrier mobilities at the conduction-band minimum of the phosphorene become also spin-polarized mainly due to spin polarization of deformation potentials and are not depressed significantly after the adsorption. These extraordinary properties would endow black phosphorus with great potentials in the future spintronic nano-devices.

Keywords: black phosphorus, magnetic substrate, proximity effect, spin injection, carrier mobility I. INTRODUCTION Development of the existing silicon-based semiconductor industry is currently is faced with crisis of demise of Moore’s law, so searching for advanced substitutes with lower power and higher performance at nanoscale for the future semiconductor electronics is urgently demanded. Discovery of graphene has presented novel properties and opened up new visions1-4 to realize the above purpose, and intensive investigations have been focused on two-dimensional (2D) atomically thick materials, including graphdiyne,5 silicene,6,7 boron nitride sheet,8 monolayers of transition metal dichalcogenides (TMDCs),9-11 etc. for future electronic applications with intriguing properties.12-16 However, some intrinsic shortcomings become obstacles to utilize these 2D materials as high performance electronic devices. For instance, gapless band dispersion in the graphene and relatively low carrier mobility in the TMDCs limit their practical applications. Recently, a new type of material, i.e. few-layers black phosphorus, has been successfully fabricated in experiment.17,18 It has a direct band gap varying from about 0.3 eV19,20 for bulk black phosphorus to ~ 2.0 eV21 for monolayer, contrast to zero-gap of the graphene, and this tunable band gap possesses broader wave range than the TMDCs.22 The few-layers black


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phosphorus materials have also higher carrier mobility [~1000 cm2/(Vs)]23 than the 2D TMDCs materials [~200 cm2/(Vs) for MoS224 and ~20 cm2/(Vs) for MoTe2],25 comparable to those of some commercial semiconductors [~1500 cm2/(Vs)],26 and good current ON/OFF ratio in fieldeffect transistors.27 Moreover, the few-layers black phosphorus have displayed ambipolar behavior which is contrast to only unipolar (n-type) behavior of the TMDs.26 The above properties suggest that the few-layers black phosphorus materials can avoid many shortcomings of the graphene and TMDCs so as to be considered as an appealing nano-electronic candidate in the future. So far, studies of the few-layers black phosphorus have been concentrated mainly on their mechanical, electrical and optical properties, and reports of exploring possible applications of the few-layers black phosphorus in spintronics, i.e. integrating spin with injection, manipulation, detection and transportation and aiming to design spin logics devices, are yet rare. The spin degree of freedom in the few-layers black phosphorus can be addressed by some ways of material engineering. For example, magnetism has been induced in the few-layers black phosphorus by tailoring into nanoribbons with zigzag edge28 and depositing atomic or molecular adsorbate (such as hydrogen,29 3d metal atoms,29-31 or NO, NO2 and O2 molecules32). But in these cases the magnetism is localized around the defects or dopants and then the possibly enhanced scattering will increase heat dissipation and influence transport performance of the few-layers black phosphorus. Here, we try to employ another practical method of depositing the black phosphorus on magnetic substrates,33,34 which is expected to introduce the magnetism into the few-layers black phosphorus by proximity effect, with advantages of the homogeneous spin polarization in material and preventing its intrinsic properties from being destroyed. Some efforts have been previously devoted to explore the spin injections of 2D materials via the proximity


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effect with the help of theoretical calculation. For example, density functional theory (DFT) calculation of the graphene adsorbed on a ferromagnetic semiconductor EuO(111) surface had shown spin polarization of π orbitals in the graphene by up to 24% and an exchange-splitting band gap of ~ 36 meV.35 It was also found that in the contact formed by nonmagnetic MoS2 or WS2 on ferromagnet VS2, magnetic proximity effect can induce spin injection for the MoS2 or WS2 and the increasing pressure even results in a 100% spin polarization of them.36 Recently, MoTe2 on EuO(111) substrate was examined theoretically by two groups and a large spin-valley polarization was revealed.37,38 In these studies the EuO(111) substrate got more attentions, because an experimental study had shown the deposition of EuO film onto the graphene via reactive molecular beam epitaxy,39 suggesting better integration of EuO substrate with 2D materials. Considering that the induced band gap of the graphene on the EuO(111) substrate is smaller (98 meV and 134 meV for two spin channels)35 and the intrinsic shortcomings of the TMDCs in the nano-electronics, such as relatively lower carrier mobility, it should be important and urgent to explore the spin injection via the proximity effect in the few-layers black phosphorus materials which have many advantages over the graphene and TMDCs as discussed before. In this paper, we employ first-principles calculation to investigate the spin injection of monolayer black phosphorus (phosphorene) deposited on ferromagnetic EuO(111) surface. It is demonstrated that due to the interactions with nearby magnetic semiconductor, the phosphorene is spin-polarized with the polarization at the Fermi level (EF) beyond 30% and an exchangesplitting at the conduction band minimum (CBM) of ~ 0.184 eV which can be tuned effectively by in-plane strain. The exchange-splitting also brings spin polarizations of the anisotropic carrier


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mobilities at the CBM of the phosphorene after the adsorption with the mobilities being not depressed significantly.

II. COMPUTATIONAL METHODS The Vienna Ab initio Simulation Package (VASP)40 is implemented based on spin-polarized DFT where the electron-core interactions are described by the projector augmented wave method41 and the exchange correlation energy is calculated through the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation.42 The plane wave basis is set with a kinetic energy cutoff of 500 eV, and in the structural optimization and total energy calculation the criteria of 105

eV and 0.01 eV/Å for total energy and Hellman-Feymann force acting on ions are used

respectively. The Brillouin zone integration is generated according to the Monkhorst-Pack scheme43 with k points setting depending on the different adsorption matching configurations. In all of the structural models, a vacuum thickness larger than 20 Å along z direction is employed to avoid interaction between the top and bottom surfaces of the adjacent slabs. Accounting for the strong correlations between the Eu 4f electrons, a GGA+U strategy44 is adopted. In order to according with the clear band gap observed in experiments,45,46 the on-site Coulomb repulsion U and exchange interaction JH are set to 8.3 and 0.77 eV for Eu 4f orbitals while for the O 2p orbitals are 4.6 and 1.2 eV respectively.47-50

III. RESULTS AND DISCUSSION Interfacial Structure of Phosphorene on EuO(111) Surface. Bulk EuO is a rock-salt crystal with Fm-3m symmetry with experimental lattice parameter of 5.141 Å. Our optimized lattice constant for the bulk EuO is 5.186 Å, close to the experimental one with ~ 1% deviation.


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And our electronic structure calculation shows that the bulk EuO is a ferromagnetic semiconductor with a direct band gap of 0.96 eV, consistent with the experimental absorption gaps observed below and above the Curio temperature of 0.9 eV and 1.2 eV.51 A hexagonal symmetry is possessed with lattice parameter of 3.667 Å by the EuO(111) surface used in our calculation. For the phosphorene, the calculated lattice constants are =4.627 Å and =3.298 Å and [Fig. 1(a)], in agreement with previous theoretical studies.52,53 To match the phosphorene with EuO(111) surface, we redefine the unit cell of EuO(111) surface in two perpendicular lattice vectors as =3.667 Å and =6.351 Å [Fig. 1(b)]. Thus, we find a reasonable matching relationship of 4×2 supercell of phosphorene with 5×1 supercell of EuO(111) surface [Fig. 1(c)], in which the mismatch in and direction is -0.93% and -3.71% respectively. This mismatch is tolerable because of high elasticity and superior flexibility of the phosphorene.54 In the phosphorene/EuO adsorption system, we fix the lattice to the value of EuO substrate, and the unit cell contains thirty-two phosphorus atoms and six atomic layers (three europium layers plus three oxygen layers) of EuO(111) consisting of thirty europium and thirty oxygen atoms (we have also calculated the case of twelve atomic layers of EuO substrate later for checking). The kmesh applied in the calculation is 3×9×1 in the Brillouin zone. To evaluate stability of the phosphorene on EuO(111) surface, both the europium- and oxygen-terminated surfaces are taken into account and the optimizations show that the phosphorene can exist on Eu-terminated surface stably, while on O-terminated surface the adsorption of phosphorene is much weaker, as will be shown by the adsorption energy calculations later. Thus, we confirm that the phosphorene prefers to adsorb on the Eu-terminated surface of EuO(111) substrate, which is used in our calculations. In addition, the O atoms on the bottom surface of slab are saturated with hydrogen atoms to avoid the dangling bonds and simulate a semi-infinite EuO(111) surface.


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Figure 1. (a) Top (up) and side (down) views of the phosphorene. (b) Top view of EuO(111) surface with four possible adsorption sites (T, H, F and B) labelled. (c) Top and (d) side views of the stable configuration of the phosphorene on top of EuO(111) surface. (e) Spatial distribution of spin density of the phosphorene on top of EuO(111) surface at isosurface value of 0.0007 eÅ3 (the spin density of EuO substrate is hidden for better display of the phosphorene). Gray spheres represent the P atoms, red spheres represent the O atoms, white spheres represent the H atoms, and bright pink, pink and pale pink spheres represent the surface, subsurface and the third-layer Eu atoms respectively. In order to find the lowest energy adsorption configuration of phosphorene on top of EuO(111) surface, different configurations with higher symmetry based on the matching of 4×2 supercell of phosphorene with 5×1 supercell of EuO(111) surface are considered. As showed in Fig. 1(b), one of the P atoms is possibly put at the top site (T), hcp hollow site (H), fcc hollow site (F) or bridge site (B), corresponding to four possible configurations. However, after the structural optimization only one configuration with top adsorption site keeps stable as shown in Figs. 1(c) and 1(d), and all of the others transform to it. The structure of the phosphorene is slightly deformed in this


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stable adsorption configuration. Compared with the freestanding phosphorene, the P-P bond length is contracted from 2.22 Å to about 2.18 Å in intra-layer due to the matching with the substrate, and elongated from 2.25 Å to 2.31 Å in interlayer mainly as a result of the phosphorene-EuO interaction. The equilibrium distance between the lower P plane and the EuO(111) surface is about 2.65 Å, and the nearest distance between the Eu and P atoms is 2.91 Å. The adsorption energy of the phosphorene deposited onto the EuO(111) surface is evaluated by the formula: = / () − () − ,

(1)

where / () , () and are total energies of the joint system, EuO substrate and phosphorene, respectively. The adsorption energy of phosphorene deposited on EuO(111) surface is 0.244 eV per P atom, i.e. 0.488 eV per P atom directly interacting with the EuO substrate. As a comparison, the adsorption energy of phosphorene deposited on the O-terminated surface of the EuO(111) substrate is only 0.036 eV per P atom, meaning a much weaker adsorption. Magnetic Moments and Charge Transfer of Phosphorene on EuO(111) Surface. The spin-polarized calculation informs that the magnetic moment of Eu atom is increased gradually from the bulk value of 7.0 µB to 7.2 µB for the surface atoms, and the O atoms are also spin-polarized with magnetic moments being about -0.03 µB. Particularly, it is remarkable that the nonmagnetic phosphorene becomes spin-polarized as expected by means of the proximity effect from the magnetic substrate, resulting in the magnetic moment of 0.03 µB per P atom. It is found that the phosphorene is more electronegative so that each P atom gains ~ 0.138 electron on average from the EuO substrate as evaluated by Bader charge analysis.55,56 Considering the nonequivalent P atoms in the phosphorene due to its armchair ridges geometry, we simply divide


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them into two parts, i.e. the upper P atoms facing to the vacuum space and the lower P atoms near to the substrate. According to Bader charge analysis, the upper P atoms lose ~ 0.008 electron per atom while the lower P atoms gain ~ 0.146 electron per atom. The spin density of the phosphorene/EuO(111) adsorption system is shown in Fig. 1(e), and our calculation shows that the lower P atoms hold larger magnetic moment of 0.05 µB on average than the upper P atoms of 0.01 µB, which could be related to the more charge carried by the lower P atoms than the upper P atoms. Since the Eu atoms have much larger magnetic moments than the P atoms, the spin density of the substrate is hidden in Fig. 1(e) for better display. It is noted that the magnetic moment of P atoms is small. The magnetic moment of C atom was not mentioned in the study of graphene on EuO substrate,35 but it may be surmised to be very small from the spin-polarized density of states and small exchange-splitting.35 For the case of MoTe2 on EuO substrate, 4d orbitals of Mo atom contributes a larger magnetic moment of 0.43 µB, and the magnetic moments of Te atoms in the top and bottom Te layers are -0.02 µB and 0.01 µB respectively,37 although the bottom Te atoms directly interact with the EuO substrate. So it is maybe difficult to induce larger magnetic moment at the non-metal atoms by proximity effect from the EuO substrate. However, here we will concern difference between densities of states in two spin channels within some energy regions, which have no explicit relationship with the magnetic moment as integral throughout the full energy scale in the occupied states. The smaller atomic magnetic moment will not remarkably affect our concerned application realization of the spin injection in the phosphorene on EuO substrate. Band Structure of Phosphorene on EuO(111) Surface. Next we will analyze band structure characters of the phosphorene/EuO system in detail. The electronic band structures of the phosphorene and bulk EuO are shown in Figs. 2(a) and (b) respectively. The phosphorene is


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a nonmagnetic semiconductor with direct band gap of 0.91 eV, consistent with the previous DFT calculation results.21,57 And the bulk EuO is ferromagnetic with band gaps of 0.96 eV and 3.49 eV in spin up and down channel respectively. When the phosphorene is deposited onto EuO(111) surface, the interaction between them brings obvious variations of the band structures, as shown by the band dispersion of the joint phosphorene/EuO system in Fig. 2(c) where the bands with weight projected on phosphorene are marked by the black circles. As a result of the electron transfer from the substrate to phosphorene, the phosphorene becomes metallic and its intrinsic CBM passes through the EF deep into the EuO gap, similar to the cases of graphene and MoTe2 on EuO(111) surface.35,37,38 Moreover, attributed to the magnetic proximity effect from the EuO substrate, the exchange interaction leads to a spin splitting of ~ 0.014 eV at original valenceband maximum (VBM) of phosphorene and an apparently larger spin splitting of ~ 0.184 eV at CBM as labelled by C1 and C2 in Fig. 2(c). This asymmetrical exchange-splitting should be ascribed to the different orbital hybridizations of the CBM and VBM with the substrate states. The exchange-splitting energy of the CBM of phosphorene on EuO(111) surface is larger than the values (< 0.1 eV) of graphene on EuO,35 and is smaller than the values (0.342 eV and 0.386 eV) of VBM of MoTe2 on EuO.38 Meanwhile, the band gap of the phosphorene is decreased to 0.298 eV and 0.483 eV in spin up and down channel after the adsorption, respectively. It is noted that the EuO substrate also turns to metallic as revealed by the weight-projected bands near the EF in Fig. 2(c).


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Figure 2. (a) Band structure of the phosphorene. (b) Spin-polarized band structure of the ferromagnetic bulk EuO. Red and blue lines are the spin up and down bands respectively. (c) Spin-polarized band structure of the phosphorene/EuO(111) adsorption system. The sizes of black circles are proportional to the weight of phosphorene in the states, and the gray lines are the bands originating from EuO substrate. (d) The top and side views of spatial distribution of the charge density for the spin-polarized CBM with isosurface value of 4×10-7 eÅ-3. In order to avoid the influence of the EuO substrate in transport of the phosphorene, we concentrate on the states in the gap of EuO. In fact, the spin-polarized CBM and VBM of the phosphorene as discussed above are just within this EuO gap. In the energy region of 0.184 eV due to exchange-splitting of CBM, electrons in only one spin channel are allowed for transport (half-metal), suggesting potential applications in spintronics. Although this energy region is


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located around ~ 1.0 eV below the EF, which is higher than that in graphene/EuO(111) (around ~ 1.3 eV below the EF)35 and is lower than that in MoTe2/EuO(111) (from ~ 0 to ~ 0.5 eV below the EF),37,38 in the actual applications the EF can be tuned by some external ways, such as doping the substrate and applying a gate voltage. We also plot the spatial distribution of charge density at C1 and C2. Both the spatial distributions are similar, so we illustrate only the pattern of C1 as example in Fig. 2(d), which displays that the spin-polarized CBM is indeed localized around the phosphorene and its interface with EuO, supporting that the EuO substrate will have little influence on the transport of the adsorbed phosphorene if the EF can be tuned into this energy region. It is also found that after the adsorption the CBM of the phosphorene is still kept at Γ point, which is advantageous to inherit various excellent properties of the phosphorene, contrast to notable variances of the band structure of the monolayer MoTe2 after its adsorption onto the EuO(111) substrate.37,38 Density of States and Spin Polarization of Phosphorene on EuO(111) Surface. We have also scrutinized the spin-polarized projected density of states (PDOS) as illustrated in Fig. 3. Figure 3(a) shows PDOS of fours elements in the phosphorene/EuO(111) adsorption system. The exchange-splitting of CBM of the phosphorene around ~ 1.0 eV below the EF and just into the gap of EuO substrate is distinctly displayed and consistent with the band structure analyzed before. It is deduced from the PDOS of different atomic orbitals of P and Eu [Figs. 3(b) and 3(c)] that the hybridizations between P-3p and Eu orbitals (including 4f, 4d and 6s) lead to the spin injection into the phosphorene that brings the exchange-splitting of its CBM and VBM. This orbital hybridization can be also revealed by the spatial distribution for the spin-polarized CBM shown in Fig. 2(d).


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Figure 3. (a) The spin-polarized PDOS of Eu, O, H and P atoms in the phosphorene/EuO(111) adsorption system. (b) The spin-polarized total density of states and PDOS of s, p orbitals of P atoms in phosphorene/EuO(111). Insert: magnification around ~ 1.0 eV below the EF. (c) The spin-polarized PDOS of s, p, d and f orbitals of Eu atoms in phosphorene/EuO(111). Insert: magnification around ~ 1.0 eV below the EF. (d) The spin-polarized PDOS of the upper P atoms in phosphorene/EuO(111). (e) The spin-polarized PDOS of the lower P atoms in phosphorene/EuO(111). (f) The spin-polarized PDOS calculated within Bader volumes of Eu, O, H and P atoms in the phosphorene/EuO(111) adsorption system.


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A frequently used index for characterizing the magnetism of materials is spin polarization p which is defined as the difference of the majority and minority states divided by total density of states at the EF: p = (n↑ − n↓ )/(n↑ + n↓ ),

(2)

where ↑ and ↓ are the majority and minority electron density states at the EF respectively. From Fig. 3(b), it can be found that the averaged spin polarization of phosphorene reaches ~ 33.9%. The averaged spin polarizations of the upper and lower P atoms are 49.1% and 16.3% respectively [see Figs. 3(d) and (e)], suggesting that the outside surface has much stronger polarization. This spin polarization index is related to the application of the adsorbed phosphorene on EuO(111) substrate in the spin electron transport even without doping the substrate or gating. We have also calculated PDOS within Bader volumes56 to obtain the more precise density of states. The PDOS calculated within Bader volumes shown in Fig. 3(f) are similar to the PDOS in Fig. 3(a), except for small differences between the quantitative values of two kinds of PDOS. These small differences also result in variation of the averaged spin polarization p at the EF: p changes from 33.9% to 30.7% for the whole adsorbed phosphorene; for the upper and lower P atoms, p changes from 49.1% to 22.1% and 16.3% to 32.9% (not shown). It seems that different projection methods for the PDOS may influence contrast between the averaged spin polarizations of the upper and lower P atoms, but will not markedly affect the averaged spin polarization of the whole phosphorene layer. Although Figs. 3(a) and (c) show obvious contributions of the EuO substrate to the states near the EF, which is consistent with the band structure in Fig. 2, our further calculations for the spatial distribution of charge density integrated around the EF and from the EF to the energy of C1 [Figs. 4(a) and (b)] reveal that only the surface Eu and subsurface O atoms are involved in it, and


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this quasi-2D nature makes that the influence of the EuO substrate on the transport of the adsorbed phosphorene in the related energy region is adequately minimized and also avoids short circuit. Of course, the rugged density of states near the EF due to the dense peaks structure could disturb the stability of performance of the related spintronic devices, in contrast to the steady half-metal nature related to the spin-polarized CBM around ~ 1.0 eV below the EF as discussed before. In order to evaluate the feasibility of applying the spin-polarized CBM by doping the substrate or applying a gate voltage, we also make a quantitative estimate of the carrier doping concentration required to tune the EF to C1 by calculating the integral of electron density of states from the EF to C1. The estimated value is 3.475×1014 cm-2 for the hole doping, which may be realized according to previous experimental reports.58,59

Figure 4. The phosphorene/EuO(111) adsorption system: (a) the charge density integrated from 0.01 eV to 0.01 eV relative to the EF at isosurface value of 0.002 eÅ-3; (b) the charge density integrated from the EF to the energy of C1 at isosurface value of 0.003 eÅ-3. Verifications of Spin Injection in Phosphorene on EuO(111) Surface. To confirm the above results, we have also performed calculations for the case of the phosphorene on top of EuO(111) substrate with twelve atomic layers (six Eu layers plus six O layers). The optimized


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structure [Fig. 5(a)] is basically consistent with the stable configuration obtained with the model using six atomic layers for EuO substrate, and the further electronic structure calculation also presents almost the same results with those using six atomic layers for EuO. Figure 5(b) shows spin-polarized PDOS of the phosphorene in the phosphorene/EuO(111) system with twelve atomic layers for EuO. The averaged spin polarization is 41.1%, larger than that using six atomic layers for EuO. And the 100% polarized region, i.e. the exchanged-splitting energy of CBM of the phosphorene, is narrowed a bit to 0.15 eV. So the model using six atomic layers for EuO substrate is enough to present main spin-polarized behaviors for the adsorbed phosphorene, and in the subsequent calculations we still adopt this model for convenience.


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Figure 5. (a) Side view of the stable configuration of the phosphorene on top of EuO(111) surface with twelve atomic layers and (b) spin-polarized PDOS of phosphorene in this adsorption system. Insert: magnification around ~ 1.0 eV below the EF. (c) The spin-polarized total density of states and PDOS of P atoms in the system of the phosphorene on top of EuO(111) surface with six atomic layers in the vdW-DF correction scheme along with (d) the corresponding band structure. The sizes of black circles in (d) are proportional to the weight of phosphorene in the states, and the gray lines are the bands originating from EuO substrate. It should be also noted that dispersive van der Waals (vdW) interaction is not considered in our calculations. Previous calculations on the graphene and MoTe2 on Eu(111) surface did not involve vdW interaction either,35,37,38 and our calculation is performed at the same level as them for the sake of comparison. We have also tested influence of the vdW interaction on our calculation, and the vdW correction scheme proposed by Dion et al.60-62 is used. It is found that inclusion of the vdW correction significantly slower convergence of the structural optimization. After involving the vdW correction, the equilibrium distance between the lower P plane and the EuO(111) surface changes from 2.65 Å to 2.64 Å, and the nearest distance between the Eu and P atoms changes from 2.91 Å to 2.90 Å. The spin polarization of the phosphorene turns to 48.5% [Fig. 5(c)]. The exchange-splitting energy is 0.166 eV for the CBM and 0.011 eV for the VBM of the adsorbed phosphorene, respectively [Fig. 5(d)]. The above results show that the vdW interaction is negligible in this system and will be not involved in the subsequent calculations. In order to testify generality of the spin injection properties in phosphorene on EuO(111) surface, we have further carried out simulations of some different matching configurations. After the optimizations, we are informed that similar with the matching configuration as simulated before, i.e. (4×2) phosphorene matched with (5×1) EuO(111) surface, the lattice structure of the


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phosphorene will keep only when high symmetry directions of the phosphorene and substrate are aligned, for example, the armchair direction of the phosphorene () along the nearest-neighbor Eu-Eu direction on the EuO surface ( ), otherwise the structure of the phosphorene will be destroyed or it is shifted to the high symmetry directions of the substrate. The remaining matching configurations which can be afforded by our computational resources have only two: one is just the matching relationship of (4×2) phosphorene with (5×1) EuO(111) surface as simulated before, and another is a matching relationship of 3×2 supercell of the phosphorene matched with 4×1 supercell of EuO (111) surface [Fig. 6(a)]. In this new matching configuration, the mismatches between the phosphorene and EuO surface along A1 and B1 directions are 5.67% and -3.71%, respectively. The k-point setting employed in the calculation for this configuration is 4×9×1 in the reciprocal space. The calculation shows that each P atom gains 0.147 electron on average from the EuO substrate. The corresponding spin-polarized PDOS of phosphorene in this configuration is illustrated in Fig. 6(b), and its band structure is shown in Fig. 6(c). The main characteristics of the PDOS are analogous to those of the first configuration, with the spin polarization of 39.1% [Fig. 6(b)]. There is still an exchange-splitting of the CBM of the phosphorene around -1.0 eV below the EF [Figs. 6(b) and (c)], but the splitting energy is increased to 0.226 eV, which may be ascribed to its larger strain than the first matching configuration. The above calculation results suggest that in the phosphorene/EuO(111) adsorption system, the spin-dependent properties are qualitatively general and reliable for different matching relationships.


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Figure 6. (a) Lattice matching relationship of another configuration of phosphorene/EuO(111) and (b) the corresponding spin-polarized PDOS of phosphorene along with (c) band structure. The sizes of black circles in (c) are proportional to the weight of phosphorene in the states, and the gray lines are the bands originating from EuO substrate. Strain-dependent Spin Injection in Phosphorene on EuO(111) Surface. In previous studies of the 2D materials, external strain had become a common and effective method for tuning their electronic structures,63-65 and was also used to modulate the spin injection properties of MoTe2 on EuO substrate.37 Here we have explored the strain effect of the phosphorene/EuO(111) adsorption system. We apply the strains in the armchair (x) and zigzag (y) direction to the adsorption system, and focus on the eigen-energies relative to the EF ( and ) of C1 and C2, the exchange-splitting energy λ, and the energy gaps ∆1 and ∆2 below the EF


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in the spin up and down channels of the adsorbed phosphorene. The calculation results are listed in Table. 1. Table 1. Characteristic parameters of the band structure of phosphorene/EuO(111) system under different in-plane strains along the armchair (x) and zigzag (y) directionsa

Strain in x direction (%)

(eV)

(eV)

λ(eV)

∆1(eV)

∆2(eV)

-3

-1.1691

-0.9918

0.1773

0.1920

0.3951

-1

-1.1458

-0.9649

0.1809

0.2809

0.4636

0

-1.1356

-0.9512

0.1844

0.3219

0.4921

1

-1.1252

-0.9375

0.1877

0.3577

0.5183

3

-1.0958

-0.9059

0.1899

0.4199

0.5715

5

-1.0586

-0.8698

0.1888

0.4720

0.6166

λ(eV)

∆1(eV)

∆2(eV)

Strain in y direction (%)

a

(eV)

(eV)

-3

-1.2006

-1.0671

0.1335

0.1795

0.4138

-1.5

-1.2099

-0.9999

0.2100

0.1850

0.4840

-1

-1.1552

-0.9218

0.2334

0.2743

0.5211

-0.5

-1.1970

-0.9598

0.2372

0.2438

0.5102

0

-1.1356

-0.9512

0.1844

0.3219

0.4921

1

-1.1172

-0.9171

0.2001

0.3543

0.5185

3

-1.0797

-0.8509

0.2288

0.3910

0.5765

5

-1.0711

-0.7714

0.2997

0.4307

0.6691

and are the eigen-energies relative to the EF of the spin-polarized CBM C1 and C2

respectively, λ is the exchange-splitting energy, and ∆1 and ∆2 are the energy gaps below the EF in the spin up and down channels of the adsorbed phosphorene on the EuO surface respectively.


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When the lattice is enlarged in both directions, the C1 and C2 are generally shifted upwards a little and approach the EF except for some small fluctuations, which is propitious for the application of the adsorbed phosphorene in the spintronics via doping the substrate or gating. But the exchange-splitting energy λ at the CBM displays complicated and anisotropic response to the strain: λ keeps almost unchanged with the varied strain in the armchair direction; when the strain is applied in the zigzag direction, the compressive strain will make λ increase first and then decrease so that λ reaches a maximum close to 0.24 eV under the strain of ~ -0.5%, in contrast with that the tensile strain can make λ increase monotonously even up to ~ 0.3 eV under the strain of 5%. The anisotropic response of the exchange-splitting energy to the strain could be ascribed to the following reason: previous calculation for the intrinsic phosphorene showed that the CBM has larger energy upshifting under the strain (near zero point) in the zigzag direction than that in the armchair direction (see Figs. 3 and 4 in Ref. 66); the larger energy upshifting of the CBM results in its more strong interaction with the conductive bands of the EuO substrate, so as to bring larger exchange-splitting energy. This increase of λ means expanding of the exchange-splitting energy region, and then is also advantageous to the stable and robust application of the adsorbed phosphorene in the spintronics. The band gaps ∆1 and ∆2 of the adsorbed phosphorene also increase with the enlarged lattice, similar to previous results for the intrinsic phosphorene.66 It is also noted that this increase of the band gap in the spin up channel is more rapid, which should be related to smaller gap below the EF in the spin up channel of the EuO substrate (see Fig. 3a) and then the stronger phosphorene-EuO interactions in this channel. Spin-polarized and Anisotropic Carrier Mobility in Phosphorene on EuO(111) Surface. It is well-known that the few-layers black phosphorus materials have higher carrier mobility among various new types of 2D materials, and one of their interesting properties is


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anisotropy of their carrier mobilities.57,66-68 For the purpose of briefly evaluating transport performance of the phosphorene deposited on EuO substrate and influence of the spin injection on its anisotropic carrier mobilities, we have simply estimated carrier mobilities at the spinpolarized CBM of the phosphorene, i.e. C1 and C2. The carrier mobility of 2D materials can be usually estimated by the following expression:69 μ =

ℏ !"# . $% &'∗( '* (+, )"

(3)

Here -. is elastic modulus in transport direction of longitudinal strain derived from -(∆0⁄0 ) ⁄2 = ( − )⁄3, where 0 is the lattice constant of the propagation direction and ∆0

is the corresponding deformation, and are the total energy and equilibrium energy and 3 is the lattice area at equilibrium, 45∗ is effective mass in the transport direction according to 45∗ = ℏ (6 ⁄67 )

8

and 4 is the effective mass on average determined by 4 =

(49∗ 4:∗ )∕, the term represents deformation potential constant of the CBM for electrons or VBM for holes along the transport direction, defined as = ∆ ⁄(∆0⁄0 ) in which ∆ is energy change of the related band under strain in the transport direction, < is the temperature being always set as 300 K. In the intrinsic phosphorene, the carrier mobility is anisotropic, i.e. close to 151 cm2/(Vs) in zigzag direction and extremely high of 2325 cm2/(Vs) in armchair direction for the electron (corresponding to CBM) at 300 K shown by our calculation (see Table 2), accordant with previous works67,68 on the whole. Table 2. The carrier mobilities of the phosphorene and phosphorene/EuO adsorption system at the CBM and related calculating parametersa

Mobility

49∗

4:∗

9

:

(4 )

(4 )

(eV)

(eV)

=9 . (103cm2/Vs)

=: . (103cm2/Vs)


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phosphorene

CBM

0.138

1.253

1.98

5.29

C1

0.116

1.068

2.53

5.28

2.325

0.151

2.003

0.210

(18.721)

(0.361)

1.113

0.122

(10.403)

(0.210)

phosphorene/EuO C2 a

0.112

1.137

3.43

6.68

4∗ is the anisotropic effective mass, is the deformation potential, and = is the carrier

mobility. The footnotes x and y represent the armchair and zigzag directions respectively. The carrier mobilities out and in the parentheses are obtained by using the elastic modulus of the intrinsic phosphorene and adsorption system respectively. In the phosphorene/EuO(111) system, the exchange-splitting CBM of the phosphorene should bring the spin polarization of its carrier mobility, suggesting that an additional degree of freedom is introduced along with the anisotropy to modulate the carrier mobility. As listed in Table 2, the simulated effective masses of electron corresponding to the spin-polarized CBM (C1 and C2) of the phosphorene along the armchair direction are 0.116 4 and 0.112 4 in the spin up and down channels respectively, while along the zigzag direction they are 1.068 4 and 1.137 4 respectively, a bit smaller than the values of the intrinsic phosphorene of 0.138 4 and 1.253 4 . Although the difference between the effective masses with different spin polarities is smaller for both the directions, we find that the deformation potential constant evaluated from the strain-induced change of the band dispersion has larger spin polarizations for the two directions: 2.53 eV (spin up) vs 3.43 eV (spin down) for the armchair direction (9 ), and 5.28 eV (spin up) vs 6.68 eV (spin down) for the zigzag direction (: ). After all, the deduced carrier mobility at the CBM of the phosphorene after adsorbed on EuO substrate at 300 K is 2003 cm2/(Vs) and 1113 cm2/(Vs) along the armchair direction in the spin up and down channel respectively, and in


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the zigzag direction, the carrier mobility at the CBM in the spin up and down channel is 210 cm2/(Vs) and 122 cm2/(Vs) respectively, i.e. that the carrier mobilities at the CBM in both of two spin channels have larger spin polarizations. It should be noted that the mechanism behind our results is mainly related to the spin polarization of the deformation potential constant which originates from the complicated interactions between the phosphorene and EuO substrate in different spin channels, and has little relationship with the effective mass which was often considered as main factor in influencing transport behaviors of the phosphorene.66,67,70 The coexistence of the spin polarization and anisotropy of the carrier mobility brings more modulations and potential applications in the spintronics for the phosphorene. Moreover, the calculation results also show that after the adsorption onto the EuO substrate the carrier mobility of the phosphorene at the CBM does not significantly decrease, i.e. its excellent transport performance is not depressed markedly by the proximity effect. It is also noted that in the above calculation the spin-independent elastic modulus -. uses the values of the intrinsic phosphorene: 24.56 N/m in the armchair direction, and 103.45 N/m in the zigzag direction. If the elastic modulus values of the adsorption system (177.78 N/m in the armchair direction and 229.55 N/m in the zigzag direction) are used, the above spin-independent conclusions still remain valid (see Table 2), but we think that the former values are more reasonable because the CBM is still mainly localized around the phosphorene after the adsorption. Spin Injection in Bilayer Black Phosphorus on EuO(111) Surface. We have also simulated bilayer black phosphorus adsorbed on the EuO(111) surface in order to check whether the spin injection by the proximity effect can extend to the second phosphorene layer and even farther. Figure 7(a) shows the optimized structure for the bilayer black phosphorus adsorbed on the EuO(111) surface. The calculation result shows the atom averaged magnetic moments of the


24

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lower layer (close to the substrate) and the upper layer (far from the substrate) are 0.03 µB and 0.0002 µB respectively. It is noted that the former is the same as that in the case of monolayer adsorption. The much smaller magnetic moment of the upper phosphorene layer than that of the lower layer seems suggest that the spin injection from the EuO substrate hardly takes effect in the second (upper) layer. This conclusion may be deduced from the spin-polarized PDOS of the two phosphorene layers shown in Fig. 7(b). However, the PDOS also shows that there exist still some small energy regions with larger differences between the densities of states of two spin channels for the upper layer, such as the spin polarization p at EF of -44.4% for the upper layer [Fig. 7(b)], which could be applicable in the spintronics.

Figure 7. (a) Top (upper panel) and side (lower panel) views of the stable configuration of the bilayer black phosphorus adsorbed on the EuO(111) surface. (b) The corresponding spinpolarized PDOS of the two phosphorene layers.

IV. CONCLUSIONS


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In summary, by employing the DFT calculations we have theoretically explored the spin injection of the phosphorene on the magnetic insulator by utilizing proximity effects. On the EuO(111) surface, the adsorbed phosphorene becomes metallic with the band gap shifting below the EF, and has the spin polarization at the EF beyond 30% along with an exchange-splitting of the CBM at Γ point with the splitting energy of ~ 0.184 eV where only one spin channel is conductive. The in-plane strain will effectively modulate the energy region and splitting energy of this exchange-splitting. It is also found that the proximity effect makes the deformation potentials and then anisotropic mobilities at the CBM of the phosphorene become spin-polarized, but it will not significantly weaken the transport performance of the phosphorene. These results may provide a theoretical understanding of the spin injection in the phosphorene on the magnetic insulator, offering phosphorene a promising potential in future spintronic devices.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]. (J. Y.). * E-mail: [email protected]. (B. L.). Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest.


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ACKNOWLEDGMENT This paper is financially supported by the National Key Research & Development Program of China (Grant No. 2016YFA0200604), by the Ministry of Science and Technology of China (Grant No. 2017YFA0204904), by the National Natural Science Foundation of China (NSFC) (Grants No. 21421063, No. 21233007), by the Fundamental Research Funds for the Central Universities (Grant No. WK2340000074). We used computational resources of Super-computing Center of University of Science and Technology of China, Supercomputing Center of Chinese Academy of Sciences, Tianjin and Shanghai Supercomputer Centers.

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TOC Graphic


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Proximity Effect Induced Spin Injection in Phosphorene on Magnetic

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