Enhanced Valley Splitting of Transition-Metal Dichalcogenide by

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Enhanced valley splitting of transition metal dichalcogenide by vacancies in robust ferromagnetic insulating chromium trihalides Changqing Lin, Yiran Li, Qilin Wei, Qian Shen, Yingchun Cheng, and Wei Huang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 30 Apr 2019 Downloaded from http://pubs.acs.org on April 30, 2019

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ACS Applied Materials & Interfaces

Enhanced Valley Splitting of Transition Metal Dichalcogenide by Vacancies in Robust Ferromagnetic Insulating Chromium Trihalides Changqing Lin,1 Yiran Li,1 Qilin Wei,1 Qian Shen,1* Yingchun Cheng,1* and Wei Huang1,2 1Key

Laboratory of Flexible Electronics & Institute of Advanced Materials, Jiangsu National

Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, 30 South Puzhu Road, Nanjing 211816, China 2Shaanxi

Institute of Flexible Electronics (SIFE), Northwestern Polytechnical University (NPU),

127 West Youyi Road, Xi’an, 710072 Shaanxi, China *To

whom

correspondence

should

be

addressed.

E-mail:

[email protected];

[email protected]

Keywords: valley splitting; CrI3; transition metal dichalcogenide; point defect; ferromagnetism.

Abstract Recently, single-layer CrI3, one member of the chromium trihalides CrX3 (where X=Cl, Br, or I), has been exfoliated and experimentally demonstrated as an atomically thin material suitable for two-dimensional spintronics. Valley splitting due to the magnetic proximity effect has been demonstrated in a WSe2/CrI3 van der Waals heterojunction. However, the understanding of the mechanisms behind the favorable performance of CrI3 is still limited. Here, we systematically study the carrier mobility and the intrinsic point defects in CrX3, and assess their influence on valley splitting in WSe2/CrI3 by first-principles calculations. The flat-band nature induces extremely large carrier mass and ultra-low carrier mobility. In addition, intrinsic point defects—localized states in the middle of the band gap—show deep transition energy levels and act as carrier recombination centers, further lowering the carrier mobility. Moreover, vacancies in CrI3 can enhance ferromagnetism and valley splitting in a WSe2/CrI3

heterojunction,

proving

that

chromium

trihalides

ferromagnetic insulators for spintronic and valleytronic applications.

1

ACS Paragon Plus Environment

are

excellent

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I. INTRODUCTION Since the discovery of graphene in 2004,1 two-dimensional (2D) materials have attracted significant attention due to their broad applications in ultra-thin electronic, spintronic, and optoelectronic devices. Many other 2D materials have been extensively studied, such as h-BN,2 transitional metal dichalcogenides (TMDs),3 and MXene.4 Because single-layer TMDs have spin-valley coupling, they are considered to be a promising 2D material for spintronics and valleytronics.5-8 The magnetic proximity effect is theoretically proposed9, 10 and experimentally demonstrated on an EuO substrate11 to control the spin and valley in TMDs. Since 2017, single-layer chromium trihalides, CrX3 (where X=Cl, Br, or I),12-14 Fe3GeTe215 and Cr2Ge2Te616 have been experimentally synthesized and verified as 2D ferromagnetic materials. CrX3 has been used in 2D spintronic devices, showing excellent performance.15,

17

Multilayer CrI3 has been used as a magnetic substrate to promote valley splitting in TMDs such as WSe218 because of proximity effect.19-22 Though the research development of CrX3 is fast, there are still some arguments about the fundamental properties of CrX3. For example, some researchers regard CrX3 as an insulator,12,

14

while others classify it as a semiconductor.13,

23, 24

Defects can

have significant influence on the properties of semiconductors, insulators, and magnetic materials. As a novel family of ferromagnetic materials, studies about the defect influence, such as the effect of point defects to the magnetism, for CrX3 are very limited.24 Moreover, how defects in CrX3 can affect valley splitting in TMDs remains unknown and deserves investigation. In this work, we have investigated the carrier mobility of CrX3, explored the influence of the intrinsic point defects on the electronic properties of CrX3 and on the valley splitting of a WSe2/CrI3 heterojunction by first-principles calculations. The band edges of CrX3 are flat, inducing large carrier mass and low mobility. The formation energies of intrinsic point defects in CrX3 are large, indicating a low concentration. Some point defects, such as Cr-vacancy (VCr), I-vacancy (VI), and I-interstitial (iI), have relatively low formation energies, which induces deep level 2


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states and further reduces electron mobility. Therefore, CrX3 is a robust ferromagnetic insulator. VCr and VI can significantly improve the valley splitting of the WSe2/CrI3 van der Waals heterojunction by interlayer interaction enhancement. For defect engineering, we can create vacancies by electron or ion irradiation to enhance the ferromagnetism of CrI3. We demonstrate robust ferromagnetism of insulating chromium trihalides against point defects, showing great potential for spintronic and valleytronic applications.

II. CALCULATION METHOD First-principles calculations based on density functional theory were performed using the plane-wave pseudopotential method, which is implemented in the QUANTUM-ESPRESSO code.25 The generalized gradient approximation (GGA)26 with Perdew–Burke–Ernzerhof (PBE) parameterization for the exchange and correlation functional was used.27 Ultra-soft pseudopotentials were utilized for elements Cr, Cl, Br, and I. A kinetic energy cutoff of 544 eV and a Monkhorst–Pack k-mesh of 4 × 4 × 1 were set. The energy convergence threshold ion optimization was 2.72×10-3 eV. The vacuum was set to 20 Å for single-layer CrX3 to prevent interaction between images of slab models. The inplane lattice parameters of WSe2 and CrI3 are 3.32 and 6.85 Å, respectively. A 4 × 4 supercell was used for WSe2 and a 2 × 2 was used for CrI3 to build the WSe2/CrI3 van der Waals heterostructure with 3.3% lattice mismatch. To calculate the band structure of WSe2/CrI3, the spin-orbit coupling effect was taken into account.

III. RESULTS AND DISCUSSION

3



Figure 1. (a) Unit cell and (b) Brillouin zone of single-layer CrX3. (c) 3 × 3 × 1 supercell CrX3 model with 72 atoms. Structure: The unit cell of single-layer CrX3 is a honeycomb lattice where Cr atoms are sandwiched between two atomic planes of X, as shown in Fig. 1. The unit cell of CrX3 contains eight atoms as shown in Fig. 1(a). The in-plane lattice parameters of CrCl3, CrBr3, and CrI3 are 6.07, 6.39, and 6.86 Å, respectively. To simulate point defects, we first constructed a 3 × 3 × 1 supercell containing 72 atoms. Then, a series of intrinsic point defects were created, including two vacancies (VCr and VX), two interstitials (iCr and iX), and two substitutions (CrX and XCr). All the defect-containing supercells are optimized to the ground state.

Figure 2. Band structures of (a) CrCl3, (b) CrBr3, and (c) CrI3.

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Effective mass and carrier mobility: Figure 2(a–c) shows the band structures of single-layer CrCl3, CrBr3, and CrI3. All band structures show indirect band gaps, which are 1.70, 1.49, and 1.44 eV for CrCl3, CrBr3, and CrI3, respectively. The valence band maximum (VBM) of CrX3 is found at the M point and conduction band minimum (CBM) is at the Γ point in the first Brillouin zone. The band edges are very flat, indicating large carrier mass. By taking the second-order partial differential of the energy band near VBM and CBM, we obtain the effective mass of holes (mh) and electrons (me). The carrier mobility can be evaluated by using the deformation potential approximation with formula28 𝜇2𝐷 =

2ⅇℏ3𝐶2𝐷 2

3𝑘𝐵𝑇|𝑚 ∗ | 𝐸21

, where m* is the effective

mass, T is the temperature, E1 is the deformation potential constant, which represents the shift of the band edges (VBM for holes and CBM for electrons) induced by the strain, and C2D is the elastic modulus of 2D system, C2D = [∂2E/∂δ2]/S0, where E is the total energy of the supercell, δ is the applied uniaxial strain, and S0 is the area of the optimized supercell. Table I. Properties of CrX3: band gap Eg, electron and hole effective masses me and mh, electron mobility μe, and hole mobility μh. Parameters of MoS2 are also listed for comparison. Eg /eV me / m0 mh / m0 μe / cm2/Vs μh / cm2/Vs

CrCl3

CrBr3

CrI3

MoS2a

MoS2b

MoS2c

1.70 6.02 5.33 0.02 0.05

1.49 3.76 3.47 4.41 5.63

1.44 26.92 7.16 0.11 0.64

1.64a 0.48a 0.60a 53.78a 119.55a

1.64 0.48 0.60 60.32 152.18

1.57 0.48 0.57 -

a

present work ref. 28 c ref. 29 b

The effective mass and mobility of CrX3 are shown in Table I. For CrCl3, CrBr3, or CrI3, the effective masses of the hole are always smaller than those of the electrons and the mobilities of holes are higher, indicating that holes are more favorable to be driven by an electric field. We take a typical 2D semiconductor, MoS2, for comparison. The effective masses of electrons and holes of single-layer MoS2 are 0.48 5



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m0 and 0.60 m0, respectively, which is consistent with previous reports.28,

29

The

effective masses of electrons or holes of three kinds of CrX3 are greater than 3.00 m0, which is greater than those of MoS2. Of all three kinds of CrX3, CrI3 has the largest me and mh. Because of the large effective masses, the carrier mobilities are rather small. The mobility of holes/electrons are 0.02/0.05, 4.41/5.63, and 0.11/0.64 cm2/Vs for CrCl3, CrBr3, and CrI3, respectively. The carrier mobilities of CrX3 are 2–3 orders smaller than those of MoS2 (119.55/53.78 cm2/Vs). Therefore, chromium trihalides are more like an insulator than a semiconductor as claimed.13,

23, 24

CrI3 is the

best-performing of the three kinds of CrX3.

Figure 3. Calculated stable chemical potential ranges for (a) CrCl3, (b) CrBr3, and (c) CrI3. The purple area surrounded by points A, C, and D. Region of chemical potential for CrX3 growth: For crystal growth, it is important to control the elemental chemical potentials. From a database search, we have obtained all binary compounds containing Cr and X, CrX2, and CrX3.30 The chemical potentials of Cr and X should obey the equation ∆𝜇Cr + 3∆𝜇X = ∆Hf(CrX3) to form CrX3. ∆𝜇𝑖, which equals 𝜇i-𝜇isolid, expresses the relative chemical potential referenced to the chemical potential of its elemental solid (𝜇isolid). For simplicity, we labeled ∆𝜇i as the chemical potential of element i in our manuscript. To avoid the formation of elemental crystals of Cr, Cl2, Br2, and I2 in the process of growth, the conditions of ∆𝜇Cr < 0 and ∆𝜇X2 < 0 should be satisfied. Meanwhile, in order to prevent the synthesis of CrX2, the ∆𝜇Cr + 2∆𝜇X < ∆Hf(CrX2) constraint also needs to be satisfied. The stable chemical potential regions for CrCl3, CrBr3, and CrI3 growth can be determined, as shown in Fig. 3(a–c). In experiments, Cr powder and elementary 6


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substance Cl2/Br2/I2 are used for synthesis. Based on the phase diagram in Fig. 3, byproduct CrX2 may also be synthesized. Taking CrCl3 in Fig. 3(a) as an example, CrCl2 will form when the (∆μCr, ∆μCl) point is on the left-hand side of the A–D line. It is important therefore to control the stoichiometric proportion of Cr and X2 when synthesizing CrX3. From Fig. 3, we obtain the stable areas for CrCl3, CrBr3, and CrI3 growth: 21.34%, 19.33%, and 9.96% of the entire area, respectively. In other words, the size of the stable chemical potential region becomes smaller with increasing atomic number of X. It is known that the oxidation capacity of halogen decreases with increasing atomicity. Therefore, the growth of CrCl3 and CrBr3 is easier than that of CrI3. It has already been demonstrated that the growth of CrX3 can be achieved by using a chemical vapor transport method with appropriate temperature gradient.31 Formation energies of point defects: To simulate the formation of point defects in CrX3, the formation energies of a series of defects are calculated using supercell methods. The formation energy of a defect 𝛼 ionized to the charge state 𝑞 is defined as ∆𝐻f(𝛼,𝑞) = 𝐸(𝛼,𝑞) − 𝐸(perfect) − ∑𝑖𝑛𝑖∆𝜇𝑖 + 𝑞(𝐸F + 𝐸VBM), where the formation energy ∆𝐻f(𝛼,𝑞) is a function of both the electron Fermi energy 𝐸F and the chemical potential ∆𝜇𝑖 of the species i involved in the defects. (𝛼,q) represents the total energy of the supercell with defect 𝛼 in the charge state 𝑞. The total energy of the perfect crystal supercell is defined as (perfect) and 𝑛𝑖 represents the number of atoms i added (𝑛𝑖 > 0) or removed (𝑛𝑖 < 0). The energy of VBM EVBM is taken as reference to determine the Fermi energy EF. When the Fermi level is located at the VBM, the value of 𝐸F is zero. Different chemical potential conditions have significant influence on the formation energies of defects, determining the defect concentrations in CrX3. Three typical positions in the stable chemical potential region of CrX3 are considered, as shown in Fig. 3. At point A, the value of ∆𝜇Cr is the smallest, corresponding to a Cr-rich/X-poor condition. At point C, ∆𝜇X is close to the elemental substance halogen, corresponding to a Cr-poor/X-rich condition. Point B is in the middle of the stable 7



chemical potential region, thus corresponding to a moderate growth condition.

Figure 4. Calculated defect formation energies as a function of the Fermi level for various intrinsic point defects in (a–c) CrCl3, (d–f) CrBr3, and (g–i) CrI3 under different conditions: (a,d,g) Cr-rich (point A), (b,e,h) Cr-moderate (point B), and (c,f,i) Cr-poor (point C). Figure 4 shows the defect formation energies of various point defects of CrX3 as a function of Fermi level under different chemical potential conditions (Cr-rich, moderate, and poor). From Fig. 4, we can see that most point defects are energetically unfavorable to form under the three different conditions due to their positive formation energies, except VCr in CrCl3 under Cr-poor condition (see Fig. 4(c)). This indicates that most point defects are difficult to form with the exception of VCr in CrCl3, which can be formed under electron-rich conditions. Though intrinsic point defects are difficult to form in CrX3 during the synthesis process, the defects can be engineered afterwards by various methods, such as pulsed laser deposition,32 chemical 8


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doping,33 and plasma treatment.34 In addition, it has been predicted that defect engineering will improve the magnetic properties of CrX3. For example, the Curie temperatures of CrX3 can be tuned by hole doping.35 Recently, it has been predicted that I-vacancy (VI) in CrI3 can enhance the intrinsic ferromagnetism and induce switchable electric polarization.24 According to the formation energies of various defects in Fig. 4, the most promising defects are iX, VCr, and VX. Therefore, it is important to investigate the effect of intrinsic point defects (iX, VCr, and VX) on the electronic properties of CrX3.

Figure 5. Spin-polarized partial density of states of (a) pristine CrI3, (b) VCr, (c) VI, and (d) iI, respectively. Top views of (e) VCr and (f) VI. (g) Top view and (h) side 9



view of iI. Effect of defects on electronic and magnetic properties. Figure 5 shows the spin-polarized density of states (DOS) of pristine CrI3 and CrI3 with VCr, VI, and iI defects. From Fig. 5(a) we can see that the valence band and conduction band edges are fully spin-polarized, which is consistent with the band structure of CrI3 in Fig. 2(c). For CrI3 with VCr defects, there is only one empty state in the band gap, which is shown in Fig. 5(b). The spin-polarized DOS of CrI3 with VI in Fig. 5(c) shows that there are two localized defect states in the middle of the band gap, which is consistent with previous work.24 Both the states are in the middle band gap, indicating the deep level defect nature of VI. There are also two empty localized defect states in the middle of the band gap for iI, as shown in Fig. 5(d). The interstitial position of I for iI can be found in Fig. 5(g, h). From the top and side views, we find that iI is close to I atoms and the two defect states are therefore mainly attributed to I atoms, which is consistent with the partial DOS of I p orbitals in Fig. 5(d). By using Löwdin charge analysis, we obtain the magnetic moment of a unit cell for CrX3 to be 3.00 𝜇B and the local magnetic moment of Cr/I to be 3.34/-0.12 𝜇B, indicating that the origin of the ferromagnetism is from Cr atoms. The localized states induced by intrinsic defects will alter the spin density distribution. We studied the local magnetic moments of Cr and I atoms near the intrinsic defects. For a VI defect, the magnetic moment of nearby Cr/I changes to 3.72/-0.10 𝜇B, which is close to that of pristine CrI3. However, for VCr, the change of magnetic moment of nearby Cr is reduced to 3.19 𝜇B and that of nearby I is enhanced to -0.34. Because the interstitial I atom of iI is close to one I atom in CrI3, there is strong interaction between the two I atoms. The magnetic moments of interstitial and nearby I atoms are -0.12 and 0.12 𝜇B, while that of nearby Cr is reduced to 0.60 𝜇B. Therefore, we claim that CrI3 with defects remains a robust ferromagnetic insulator, even though there is spin density redistribution. Here, we only discussed CrI3, but most conclusions are also valid for CrCl3 and CrBr3.

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Figure 6. (a) Scheme of WSe2/CrI3 van der Waals heterostructure. The red dotted circles represent Cr-vacancy and I-vacancy, respectively. (b) and (c) Schemes of conduction and valence band edges around the +K/‒K point for pristine WSe2 and WSe2/CrI3, respectively. Spin-resolved band structures from WSe2 contribution for (d) WSe2/CrI3, (e) WSe2/VCr-CrI3, and (f) WSe2/VI-CrI3. Valley splitting of WSe2 on CrI3 with defects. One application of CrI3 is to induce valley splitting in single-layer transition metal dichalcogenides.18 WSe2 and single-layer CrI3 van der Waals heterojunctions (WSe2/CrI3) are shown in Fig. 6(a). Figure 6(b) shows the scheme of band edges around K valleys for pristine single-layer transition metal dichalcogenide. Due to a magnetic field or magnetic exchange field induced by the proximity effect or magnetic doping, the energy of band edges around K valleys in WSe2 will split, as shown in Fig. 6(c). This is generally called “valley splitting”. The value of valley splitting Δ can be evaluated by considering the transition energy difference between the conduction band edge and the valence band edge with the same spin, as shown in Fig. 6(c). The value of Δ is 1.28 meV for WSe2/CrI3, found by analyzing the band structure, as shown in Fig. 6(d). The positions of VCr and VI are shown in Fig. 6(a). It has been reported that the electric field36 and stacking order37 will affect the value of valley splitting in WSe2/CrI3. Here we focus on the effect of defects on the valley splitting. The valley splitting is reported to be 3.5 meV for WSe2 on multilayer CrI3 at 5 K.18 Our predicted splitting value is of the same order of magnitude. The difference between calculated and experimental values can be attributed to the following reasons. Firstly, multilayer CrI3 is used in experiments, while single-layer CrI3 is used 11



in our calculation—layer thickness may play a role in interlayer interaction. Secondly, mechanical exfoliation and dry transfer methods are employed to build a WSe2/CrI3 heterojunction18—there may be some defects generated on the CrI3 surface. Thirdly, stacking order38 and twist angle between layers39, 40 are crucial factors affecting the electronic properties of a van der Waals heterojunction—the stacking order and twist angle are not controlled and are therefore unknown in the experiment.18 There may also be inconsistencies between our WSe2/CrI3 model and experimental samples. Figures 6(e) and 6(f) show that the valley splitting remains for WSe2 on CrI3 with VCr (VCr-CrI3) and VI (VI-CrI3), with the values of Δ increasing to 8.61 meV and 11.38 meV, respectively. This indicates that the existence of vacancies not only retains the ferromagnetic contribution from CrI3 but also enhances valley splitting. The interlayer distance d of WSe2/CrI3 is defined as the distance between the Se and I plane, as shown in Fig. 6(a). The d reduces from 3.71 Å for WSe2/CrI3 to 3.64 Å, and 3.69 Å for WSe2/VCr-CrI3 and WSe2/VI-CrI3, respectively, indicating an increase in layer–layer interaction. From the discussion of defect states shown in Fig. 5, we conclude that vacancies lead to interlayer electron density and spin density redistribution. Therefore, the increase in valley splitting induced by vacancies can be attributed to an increased interaction and electron redistribution between WSe2 and CrI3. The vacancy density is an important factor in experiments. If the vacancy density is high, then interaction of vacancies will occur, altering the electronic structure of the heterojunction. Also, the effect of vacancy disorder on magnetic properties has not been considered in our prediction. We only considered VCr and VI at the interface of WSe2/CrI3 in the present work. Due to iI increasing the d, the WSe2/CrI3 interaction would be reduced, which may not enhance valley splitting. Therefore, we have not studied iI in WSe2/CrI3 in our present work. It is expected that the significant enhancement of valley splitting induced by vacancies can stimulate experimental development.

IV. CONCLUSION 12


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In conclusion, we have applied first-principles calculations to study the physics of intrinsic defects in CrX3. Comparing the chemical potential phase diagrams, we find that all three kinds of CrX3 are easy to grow. The concentration of most point defects in CrX3 are very low because of their high formation energies. Due to the large effective carrier mass and low carrier mobility, we claim that CrX3 is a family of insulators rather than semiconductors. From the defect physics study, we studied the effect of VI, VCr, and iI point defects on the electronic properties of CrI3 and conclude that CrI3 is a robust ferromagnetic insulator against defects. Moreover, VCr and VI at the interfaces between the WSe2/CrI3 van der Waals heterojunction can strongly improve the valley splitting in WSe2 due to the enhancement of interlayer interaction.

ACKNOWLEDGEMENT This work was supported by the National Natural Science Foundation of China (Nos. 61575094, 21673118 and 91833302). This work was also sponsored by Qing Lan Project and the Jiangsu Specially-Appointed Professor programme. We are grateful to the High Performance Computing Center of Nanjing Tech University for supporting the computational resources.

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