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2D Intrinsic Ferromagnets from van der Waals Antiferromagnets Naihua Miao, Bin Xu, Linggang Zhu, Jian Zhou, and Zhimei Sun J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b12976 • Publication Date (Web): 05 Feb 2018 Downloaded from http://pubs.acs.org on February 6, 2018
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2D Intrinsic Ferromagnets from van der Waals Antiferromagnets Naihua Miao,†,‡ Bin Xu,¶ Linggang Zhu,†,‡ Jian Zhou,† and Zhimei Sun∗,†,‡ †School of Materials Science and Engineering, Beihang University, Beijing, 100191, China. ‡Center for Integrated Computational Materials Engineering, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, China. ¶Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas, 72701, USA. Received February 2, 2018; E-mail:
[email protected] Abstract: Intrinsically ferromagnetic 2D semiconductors are essential and highly sought for nanoscale spintronics, but they can only be obtained from ferromagnetic bulk crystals, while the possibility to create 2D intrinsic ferromagnets from bulk antiferromagnets remains unknown. Herein on the basis of ab initio calculations, we demonstrate this feasibility with the discovery of intrinsic ferromagnetism in an emerging class of singlelayer 2D semiconductors CrOX (CrOCl and CrOBr monolayers), which show robust ferromagnetic ordering, large spin polarization, and high Curie temperature. These 2D crystals promise great dynamical and thermal stabilities as well as easy experimental fabrication from their bulk antiferromagnets. The Curie temperature of 2D CrOCl is 160 K, which exceeds the record (155 K) of the most-studied dilute magnetic GaMnAs materials, and could be further enhanced by appropriate strains. Our study offers an alternative promising way to create 2D intrinsic ferromagnets from their antiferromagnetic bulk counterparts and also renders 2D CrOX monolayers great platform for future spintronics.
As a fundamental challenge in solid-state chemistry and materials science, spintronics or spin-based electronics, using both charge and spin of electron, offer great opportunities for next generation information technology with the advantage of low energy consumption, fast device operation, and high storage density. 1–3 For spintronic devices at nanoscale, atomically thin two-dimensional (2D) ferromagnetic materials with the combination of large spin polarization and high Curie temperature (TC ) are of particular importance and interest. 4–13 However, although plenty of 2D crystals have been widely explored, most of them are lacking of intrinsic polarization or ferromagnetic ordering, which greatly hinder their direct applications in spintronics. 6,8,14–17 To this end, 2D ferromagnetic materials with desirable magnetic and electronic properties for nanoscale spintronic devices are highly needed. The absence of ferromagnetism in many 2D monolayers has motivated great efforts to artificially introduce spin ordering via defect engineering or magnetic proximity effects. 6,17–20 For instance, the ferromagnetism in graphene nanoribbons can be controlled by external electric field or magnetic defects. 21 While under carrier doping, nonmagnetic 2D semiconductors, including the GaSe, 22 αSnO, 23 and InP3 7 monolayers, become ferromagnetic. However, it is still difficult to induce long-range spin ordering in these 2D materials. Until very recently, the first way to create intrinsically ferromangetic 2D semiconductors, through the inheritance of intrinsic ferromangetism from
their ferromagnetic bulk layered crystals, has been evidenced in atomically-thin 2D CrI3 (TC =45 K) 4 and Cr2 Ge2 Te6 (TC =20 K), 5 opening the door for low-temperature 2D spintronics at atomic thickness. But their TC are much below the liquid-nitrogen temperature (77 K) and thus greatly restrict their practical applications. Nevertheless, despite tremendous efforts, the development of new ferromagnetic 2D crystals with robust long-range spin ordering and high TC is still essential and very challenging. Additionally, whether it is possible to create 2D intrinsically ferromagnetic semiconductors from their antiferromagnetic bulk counterparts remains an open question. Herein by means of ab initio calculations, molecular dynamics, and Monte Carlo simulations, we demonstrate this feasibility in an emerging class of 2D spintronic semiconductors (single-layer CrOCl and CrOBr) with intrinsic ferromagnetism, large spin polarization, and high Curie temperature. We show that the proposed 2D chromium oxyhalides (CrOX; X=Cl or Br) can be easily fabricated from their antiferromagnetic bulk crystals by mechanical exfoliation owing to their ultra-low exfoliation energy. We suggest that both the CrOCl and CrOBr monolayers have great dynamical and thermal stability according to their phonon dispersions and molecular dynamics trajectories. The predicted TC of the CrOCl and CrOBr monolayers are as high as 160 K and 129 K, respectively. Under appropriate strains, the TC could be further increased and exceeds the current record of dilute magnetic semiconductors. Geometry. The bulk 3d transition-metal oxyhalides (MOX; M=Cr/V/Ti, X=Cl/Br) are antiferromagnetic semiconductors with interesting spin-Peierls behaviours. 24–28 They crystallize in an orthorhombic structure (space group #59, P mmn) with 2D networks of rectangle sublattice in the xy plane (Figure 1(a)), while the metal ions form alternated pyramids bounded by the oxygen atoms and the 2D planer layers sandwiched by the Cl layers are stacking along the z direction with large van der Waals (vdW) gaps (Figure 1(b)). The 3d metal ion is coordinated by 4 oxygen and 2 halide ions, leading to a strongly distorted octahedron of MO4 Cl2 . The calculated lattice constants, electronic band gaps, and the magnetic moments of the bulk crystals are shown in Table S1 and S2 of the supporting information (SI) together with the available experimental data. Compared to the experiments, the physical properties of the MOX are better reproduced quantitatively by the GGA+U approaches with careful determinations of U values than the pure GGA technique, indicating the strong correlation effects of the 3d electrons should be considered. 26–28 Therefore, in the following study of the monolayers, the GGA+U approach will be adopted
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ther CrOCl and CrOBr, indicating that 2D CrOX crystals are dynamically stable, while the imaginary frequencies in other MOX monolayers suggest their dynamical instabilities. Therefore, the following study will be focused on 2D CrOX crystals. The highest frequencies of optical modes in singlelayer CrOX are around 700 cm−1 , which is a significant character of strongly covalent O-O bondings. To further confirm the thermal stability of the CrOCl and CrOBr monolayers, we performed ab initio molecular dynamics (AIMD) simulations at 300 K for 20 ps. As indicated by the AIMD snapshots (Figure S2(b) and (d)), the 2D planer networks are well maintained within 20 ps, suggesting the CrOX monolayers are thermally stable. This is further confirmed by the timedependent evolutions of total energies, which shows very small fluctuation. During the AIMD simulations, all atoms in the cell vibrate near their equilibrium positions and no phase transition is observed, demonstrating 2D CrOCl and CrOBr crystals are highly stable at room temperature. Magnetic properties. To study the magnetic properties of 2D CrOCl and CrOBr crystals, we first studied the preferred spin ordering in the lattices. Interestingly, among the six considered magnetic configurations for the MOX monolayers (Figure S3), the ground state with the lowest energy (Table S3 and S4) is ferromagnetic for the single-layer CrOX, while the other oxyhalide monolayers are anti-ferromagnetic. The net magnetic moment is ∼ 3µB /f.u., indicating a large spin polarization in these 2D CrOX crystals. For a further understanding on the fundamental character of ferromagnetic ordering in 2D CrOX at low temperature, the magnetocrystalline anisotropy energy (MAE) were calculated by considering the spin-orbit coupling. As summarized in Table S5, the easy magnetization along the z axis in 2D CrOX crystals suggests a long-range ferromagnetic order. 33 Therefore, the spins in both 2D CrOCl and CrOBr align along the out-of-plane direction. This is consistent with the above discussion on the ferromagnetic ground states of the CrOX monolayers. The calculated MAE of single-layer CrOCl and CrOBr are considerably large (0.03-0.29 meV), which is in the same order of magnitude of the Fe (0.10 ± 0.05 meV) and Co (0.15 ± 0.02 meV) monolayers on the Pt(111) substrates, 34 suggesting the potential applications of the 2D CrOX crystals in magnetic devices. Electronic structures and wave functions. Further insight on the magnetic properties of single-layer CrOX crystals can be disclosed from their electronic structures. The calculated spin-dependent electronic band dispersions and density of states (DOS) are depicted in Figure 2(ac) for the CrOCl monolayer (Figure S4 for 2D CrOBr). One-dimensional-like van Hove singularities with dramatic change in the DOS around the Fermi energy were observed as seen in some other 2D materials. 7,22,23 Obviously, singlelayer CrOCl is a ferromagnetic semiconductor with a band gap of 2.38 eV and a total magnetic moment of 3 µB /f.u.. Both its conduction band minimum and valance band maximum are dominated by the majority spins, which are predominantly contributed by the Cr-3d and Cl-2p orbitals, respectively. This is also confirmed by the up-spin (↑) charge density in Figure 2(d). Regarding the minority spins, the highest occupied bands mainly includes the Cl-2p and O-2p orbitals which are consistently demonstrated by the downspin (↓) charge density (Figure 2(e)). Moreover, we note that most of spin-polarized electrons in the CrOCl monolayer locate around the chromium ions, resulting in a large magnetic moment of 3.22 µB /Cr. The strong magnetization
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for all calculations, unless stated otherwise. As summarized in Table S3, the calculated lattice constants a and b of the oxyhalides monolayers are very close to that of their bulk counterparts, suggesting very weak effects from the inter-layer vdW forces and surface relaxations. Exfoliation energy. To fabricate 2D monolayers from their bulk crystals with weak vdW interactions, the most commonly used approaches are mechanical cleavage and liquid exfoliation. 17,29 We predicted exfoliation energy of MOX as shown in Figure 1(c) by modelling the exfoliation process (Figure S1). Taking graphite as a benchmark, the calculated exfoliation energy is 0.31 J/m2 , which is in excellent agreement with the experimental measurement 30 (0.32±0.03 J/m2 ) and previous theoretical value 31 (0.32 J/m2 ). For transition-metal oxyhalides, the calculated exfoliation energy are much smaller than that of graphite, indicating the MOX monolayers can be easily prepared from their bulk forms using similar expermiental approaches as graphene. Especially, we note that the exfoliation energy of the CrOCl is around 0.208 J/m2 , which is only two-third of graphite, implying its superior experimental feasibility. Owing to the weak vdW interactions in MOX, these monolayers could be great candidates to construct vdW hetrostructures for nanoelectronics. 32 Dynamical and thermal stability. The stability of the MOX monolayers are accessed according to their phonon dispersions and molecular dynamics trajectories. From the calculated phonon dispersion curves (Figure S2) for the MOX monolayers, no imaginary phonon mode is observed for ei-
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Figure 3 (a) Specific heat CV with respective to temperature for the CrOCl and CrOBr monolayers and the inset shows the correspongding magnization. (b) Curie temperature in comparison with 2D CrI3 (45 K), 4 Cr2 Ge2 Te6 (20 K), 5 GaMnAs (155 K), 35 and single-layer CrOCl under 5% biaxial tensile strain. The magnetic transition temperatures TC are denoted by dashed lines. of the Cr ions could be well understood by the localized spin wave functions as illustrated in Figure 2(f). Clearly, the net spin polarization is along the z direction, which also accounts for the easy magnetization axis [001] with long-range ferromagnetic orders in 2D CrOX. Curie temperatures. For practical spintronic applications of 2D CrOX crystals, it is essential to understand the behaviour of magnetism with temperature. To study the spin dynamics, Monte Carlo simulations were performed with the Wolff algorithm. 36 The spin Hamiltonian P based on the 2D Ising model is considered as: H = − i,j Ji,j Szi Szj , where Ji,j is the nearest-neighbour exchange coupling conz stant and Si/j is the spin parallel or anti-parallel to the z direction. Providing the exact solution to the spin Hamiltonians, the Curie temperature can be accurately extracted from the peak of thermodynamic specific heat 35 for the CrOCl and CrOBr monolayers as illustrated in Figure 3(a). We note that the TC of the CrOX monolayers obviously ex-
ceed the liquid nitrogen temperature (77 K) and the CrOCl monolayer shows higher TC than the CrOBr monolayer, owing to the larger energy difference between the ferromagnetic and antiferromagnetic states. Our calculated TC for the 2D CrOCl is 160 K, which is dramatically larger than the recently reported values for 2D CrI3 (45 K) 4 and Cr2 Ge2 Te6 (20 K), 5 approaching the highest known TC (∼155 K) of the most-studied dilute magnetic semiconductors GaMnAs 35 (Figure 3(b)), which can be further enhanced under approximate strains (Figure S5). In summary, we reported a promising alteriative way to creat 2D intrinsic ferromagnetism from bulk van der Waals antiferromagnets, as realized in the CrOX monolayers which can be easily exfoliated from their bulk counterparts. The achieved CrOCl and CrOBr monolayers were identified as intrinsically ferromagnetic semiconductors with band gaps of 2.38 and 1.59 eV, respectively. Both of them are dynamically and thermally stable. Their exfoliation energy are
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much smaller than that of graphite, suggesting 2D CrOX could be fabricated by mechanical cleavage or exfoliation as graphene. We demonstrated that the robust long-range ferromagnetic ordering align in the out-of-plane direction of 2D CrOX, which is the easy magnetization axis with large spin polarization and magnetocrystalline anisotropy energy. The predicted TC are 160 and 129 K for the CrOCl and CrOBr monolayers, respectively, much higher than that of the recently reported TC of 2D CrI3 and Cr2 Ge2 Te6 crystals. 4,5 Under appropriate strains, the TC of the CrOX monolayers can be further enhanced up to 204 K. Our findings on the intrinsic ferromagnetism of 2D CrOX crystals open new pathway to develop 2D semiconducting intrinsic ferromagnets from antiferromagnetic bulk crystals and also provide new opportunities for future spintronic investigations and applications at atomic thickness.
Supporting Information Available The following files are available free of charge. • Computational methodologies. Tables and Figures for the structural and magnetic properties, exfoliation process, phonon dispersions, AIMD evolutions, spin configurations, electronic structures, strain responses, and reliability test.
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