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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Two-Dimensional Lattices of VN: Emergence of Ferromagnetism and Half-Metallicity at Nanoscale Artem V. Kuklin, Svetlana A. Shostak, and Alexander A Kuzubov J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b03276 • Publication Date (Web): 05 Mar 2018 Downloaded from http://pubs.acs.org on March 5, 2018

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The Journal of Physical Chemistry Letters

Two-Dimensional Lattices of VN: Emergence of Ferromagnetism and HalfMetallicity at Nanoscale Artem V. Kuklin§,‡,*, Svetlana A. Shostak‡, Alexander A. Kuzubov† §

Siberian Federal University, 79 Svobodny pr., Krasnoyarsk 660041, Russia

‡

Department of Chemistry, Kyungpook National University, 80 Daehakro, Bukgu, Daegu

41566, Republic of Korea †

Deceased December 31, 2016.

*

E-mail: [email protected]

ABSTRACT: Two-dimensional (2D) ferromagnets with high spin-polarization ratio and high Curie temperature are crucial for developing next-generation spintronic nanodevices. Here, using first-principles calculations, we predict two polymorphic modifications (t-VN and h-VN) of 2D VN lattices that have robust intrinsic ferromagnetic properties and high Curie temperatures. While t-VN has 99.9% of spin polarization at the Fermi level, h-VN possesses half-metallic type of conductivity and keep it after contact with semiconducting 2D MoS2 that can be used as the substrate for h-VN synthesis and valley polarized contacts. Magnetocrystalline anisotropy energy of 2D VN polymorphs is found to be at least an order larger than those of Fe and Ni bulks. The phonon spectra and ab initio molecular dynamic simulation prove that 2D VN lattices have a high thermodynamic stability. These advantages demonstrate that the VN monolayers should be promising candidates for low dimensional spintronic devices.

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While great efforts during recent decade were made to study graphene1 and 2D semiconductors,2 two-dimensional magnetic materials remain largely unexplored. Only a few two-dimensional materials have been predicted to be intrinsic magnets and only some of them were successfully synthesized,3–5 attracting much attention to develop more efficient magnetic materials at nanoscale. Magnetic materials that exhibit half-metallic properties and therefore act as sources of fully spin-polarized electrons are promising electrodes for high-efficiency spintronic devices. They can provide large magnetoresistance (MR) effect used in hard disks or magnetic tunnel junctions in which magnetic field is applied to switch the state of electrodes.6 One of the family that can manifest such properties is transition metal nitrides (TMNs). Recently, a number of TMNs-based 2D structures have been demonstrated unexpected properties like half-metallicity,7,8 auxeticity,9 piezoelectricity10 and photocatalytic properties,9,10 contributing significantly to the existing pool of 2D materials. ScN and YN nanosheets are found to be indirect band gap semiconductors.11 Quantum spin Hall effect revealed in structural analogs of MC (M = Ti, Zr, Hf) monolayers.12,13 These unusual properties appear due to the presence of unpaired electrons in those nanosheets. It was shown that unsaturated p-orbitals may introduce intrinsic ferromagnetism in vanadium trihalide monolayers. 14 Moreover, we previously reported electronic properties of possible VN hexagonal monolayer within the framework of GGA PBE level.15 However, several key aspects like stability, possible polymorphism and enhanced reproducing of the electronic structure were missed. These findings are very encouraging, and the researches of 2D VN should be extended. Among a number of techniques developed nowadays, the “bottom-up” approach provides on-surface self-assembly of the nanosheets that existed before only within the framework of theory,16,17 enabling possibility to discover monolayers not only van der Waals crystal but also bulk compounds. Polymorphism is one of the unique features of some 2D materials like MoS2,18 phosphorene19 that can be stabilized using different substrates. Structural difference in the same compound can significantly change its properties and therefore is potentially interesting. In this work, based on first-principle calculations, we demonstrate existence of 2D VN polymorphic lattices in either tetragonal (t-VN, coordination number (CN) =4) or honeycomb (h-VN, CN=3) forms, which are associated with (100) and (111) planes of their bulk rock salt structure. Our calculations suggest that both VN monolayers possess ferromagnetic properties with very high rates of spin polarization and high Curie temperatures. Moreover, the electronic 2 ACS Paragon Plus Environment

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structure of h-VN exhibits half-metallic type of conductivity that is essential for spintronic applications. The atomic and electronic structures were calculated using density functional theory (DFT) within PBE and HSE06 exchange-correlation functionals and Grimme D3 correction of weak interactions as implemented in the VASP code. The self-consistent GW calculation was performed by iterating only G, but keeping W fixed (GW0 approximation). The reciprocal space in the Brillouin zone was sampled using Monkhorst-Pack scheme by 20 × 20 × 1 and 24 × 24 × 1 k-points for t-VN and h-VN respectively. Full details of the computational setup are given in the electronic supplementary information (ESI). 2D VN lattices can be obtained by extraction of one stoichiometric layer from the bulk VN crystal, which has NaCl-type structure with Fm3m group of symmetry at ambient conditions (The details are given in SI). The relaxed structures of extracted monolayers are shown in Figure 1(a,b). During the simulation, perfectly planar structures as well as structures with out-of-plane displacements are considered. The unit cell of tetragonal VN contains two vanadium and two nitrogen atoms and refers to (100) plane of its bulk crystal. As the result of energy minimization, the buckled lattice of t-VN (a = 3.653 Å) is more stable in comparison with perfect planar one. Each atom in the lattice has four immediate neighbors. The vanadium atoms have in-plane location (same position along z-axis) whereas nitrogen ones are displaced out of the plane by 0.65 Å (Figure 1(a)). One can identify t-VN monolayer possesses P4/nmm space group which is associated with D4h point group of symmetry and corresponds to the 2D structure of FeSe, which has been recently synthesized.20 The honeycomb VN monolayer is assembled of its bulk (111) plane. The unit cell of h-VN consists of one vanadium and one nitrogen atom in its planar honeycomb lattice (a = 3.231 Å) and has D3h point group (P-62m space group) of symmetry (Figure 1b). Each V atom is three-coordinated with N atoms (h-BN like structure). It is clearly seen that structures have distinct coordination numbers and structural symmetries. The perfect and buckled sheets of VN (110) were also considered. However, minimization of interatomic forces lead to barrier-free transformation into t-VN. The structural parameters are summarized in Table 1. The V-N distances (d) or bond lengths of both two-dimensional sheets are less than its bulk analogues due to lowering of coordination numbers in 2D structures.



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Figure 1. (a, b) Top and side views of two-dimensional t-VN and h-VN respectively. The solid lines denote the unit cells. The separation between nitrogen sublattices perpendicular to the plane Δ = 1.3 Å. (c, d) The phonon spectra of t-VN and h-VN. Γ, X, and K correspond to the (0, 0, 0), (0, 1/2, 0) and (1/3, 1/3, 0) specific points of the Brillouin zone Brillouin zone, respectively. The M points are (1/2, 1/2, 0) and (1/2, 0, 0) for t-VN and h-VN respectively. (e, f) Snapshots of top and side views of t-VN and h-VN sheets after AIMD simulation at 300 K (7 ps) and at 1500 K (5 ps) within the NVT ensemble. The optimized 5×5×1 and 8×8×1 supercells are used as the initial structures.

Two-dimensional materials can be obtained by “bottom-up” and “top-down” approaches. The first path provides on-surface deposition from the gas phase (PVD, CVD, ALD) while the “top-down” approach is associated with mechanical exfoliation of a monolayer from its bulk crystal and the possibility of this can be estimated as: E form _ 3 D  Ebulk / u  E ML

(1)

where Ebulk and EML are the total energies of the monolayer and the bulk VN structure respectively, u is the number of formula units. The cohesive energy helps to understand the magnitude of bonding in a solid. The cohesive energies relative to separated atoms can be calculated by the following formula:

Ecoh  (nEV  nEN  EVN ) / u

(2)

where EVN is the total energy of 2D or 3D VN crystal, EV and EN are the energies of isolated V and N atoms, n – the number of certain atoms in the cell, u – is the number of formula units. 4 ACS Paragon Plus Environment

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The stability of the monolayers in the first approximation can be judged relatively to its simple components (crystalline vanadium and molecular nitrogen): E form  EVN  nEVbulk  nE Nmol (3)

where EVN is the total energies of VN structures, EVbulk – the energy of one vanadium atom in its crystalline unit cell, ENmol is the energy of one nitrogen atom in its molecule, n – the number of certain atoms in the cell. The lower energy indicates an easier structure formation. All calculated energies are listed in Table 1.

Table 1. Structural parameters of V-N distance (d), cell vector (a) and the energies of formation with respect to the bulk (Eform_3D), cohesive energy (Ecoh) and formation energy with respect to simple compounds (Eform) d, Å a, Å Eform_3D, eV Ecoh, eV/VN pair Eform, eV t-VN

1.941

3.653

-1.68

2.91

-1.10

h-VN

1.866

3.231

-1.47

2.25

-0.47

bulk VN

2.060

4.120

-

3.12

-1.94

The first method of production (via mechanical exfoliation) seems to be the less possible according to the high Eform_3D of t-VN and h-VN that are two orders of magnitude higher than graphene (-0.03 eV) and h-BN (-0.09 eV),21 although lower those energies of germanene and silicene.22 The cohesive energies are higher than those of silicene (1.99 eV/Si pair), germanene (1.63 eV/Ge pair)23 but lower than graphene (3.95 eV/C pair) and h-BN (3.53 eV/BN pair), that were calculated by the same way as t-VN and h-VN. The stability of two-dimensional structures cannot be estimated by comparison cohesive energies due to different atomic nature. However, it can be concluded the bonding must be rather strong that will contribute to the monolayers stability. Taking into account formation energies with respect to simple compounds, both 2D polymorphs can be defined as stable due to the preference of formation 2D structures instead of pure components. Phonon dispersions of tetragonal and honeycomb lattices in Figure 1(c,d) reveal no imaginary modes, exhibiting that both polymorphic phases are dynamically stable. The highest frequencies in the monolayers are around 20 THz, which is compared to the honeycomb ZnO structure.24 The lowest optical modes (6 THz for t-VN and 8.5 THz for h-VN) correspond to out-of-plane vibrations, while the highest, doubly degenerated optical modes (19 THz and 20.5 THz) correspond to in-plane vibrations. Finite cluster calculations can also be used to prove 5 ACS Paragon Plus Environment


stability of 2D materials. The relaxation of extended finite nanoclusters consisted of 192 and 186 atoms in t-VN and h-VN respectively was performed at the Γ-point (1 × 1 × 1 k-point mesh) using OpenMX code. The nanoclusters retain their original 2D structures without any serious corrugations demonstrating absent of uncompensated internal mechanical stresses. The thermal stability of VN monolayers is examined by ab initio molecular dynamics (AIMD) simulations using NVT ensemble and the Nose-Hoover heat bath approach (Figure 1(e,f)). The optimized 5×5×1 and 8×8×1 supercells for t-VN and h-VN respectively are used as the initial structures to reduce the constraint of periodic boundary conditions and explore possible reconstruction of monolayers. After simulation at 300 K for 7 ps with the time step of 1 fs and at 1500 K for 5 ps with the same time step, no signs of destruction like large number of dangling bonds or significant amplitude of atomic fluctuations (more than ± 10%) are found that verify high thermal stability of the nanosheets. Therefore, both structures can be considered as stable. The chemical bonding in monolayers can be explained by the spatial distributions and deformations of electron density (Figure 2(a,b)). According to the Bader analysis,25 2.0 and 1.9 electrons are transferred from V to N in t-VN and h-VN respectively. The spatial distribution of charge density in Figures 2(a) shows that charge is mainly distributed over N atoms. The shape of distribution in the case of h-VN refers to in-plane orbitals that participate in σ-bonds formation. The electron density responsible for the formation of bonds is shifted towards nitrogen atoms. Figure 2(b) shows holes in the deformation electron density near vanadium positions while electron concentration is observed around in-plane orbitals of nitrogen especially along V-N bonds. The electron localization functions (ELF) (Figure 2c) show that electrons in both monolayers are localized at N atoms, whereas V atoms reveal electrons deficiency. The form of electron localization in h-VN shows sp2 hybridization of nitrogen atomic orbitals that participate in construction of σ bonds, whereas N atoms in t-VN are sp3 hybridized. ELF of t-VN in the plane of vanadium (Figure 2c right panel) close to 0.5 indicates delocalized π bonds of nitrogen. It is also clearly seen that small part of electron density locates in the interstitial regions revealing a feature of metalloid bonding. This type of bonding is inherent part of transition metal nitrides and carbides where TM donates electrons to the metalloid with following transfer a part of charge from a metalloid to interstitial region. Crystal orbital Hamilton population (COHP) analysis for t-VN and h-VN (Figure S1) shows intersection of occupied (bonding) and unoccupied (antibonding) bands confirming metallic bonding


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between two elements. The bonding and antibonding states are formed by hybridized nitrogen p and metal d orbitals that correspond to metal-nonmetal bonds.

Figure 2. Electronic properties of 2D VN monolayers. (a) Spatial distribution of electron density in t-VN (top) and h-VN (bottom) sheets. (b) 2D plots of electronic density deformation (с) The electron localization function of t-VN (top) and h-VN (bottom) sheets, renormalized between 0.0 and 1.0. The values of 1.0 and 0.5 characterize the totally localized and delocalized electrons, respectively. The band structures and DOS calculated at the PBE level are given in Figure S2. Here we discuss the results calculated within the HSE06 hybrid functional because it provides more accurate electronic structure than PBE and, for some 2D materials than GW.27,28 The band structures and DOS of t-VN and h-VN are shown in Figure 3. The Fermi level is crossed in the Γ–M interval and K point for spin-up electrons. The spin-down valence band of t-VN also crosses the Fermi level in the whole path of the k-vector. One important feature of h-VN is the Dirac-like cone with the small gap of 0.1 eV located at the K-point. The minimum of the conductivity band also located at the K-point of the Brillouin zone with the energy of −0.27 eV. Both 2D polymorphic forms are found to be ferromagnetic. The monolayer of t-VN possesses metallic conductivity in both spin channels whereas h-VN has a large band gap of 4.79 eV for spin-down electrons demonstrating its half-metallic nature. The rates of spin polarization in monolayers estimated via the formula (4) equal to 99.9% and 100% for t-VN and h-VN



respectively. These findings are exiting with respect to nonmagnetic superconducting bulk VN and they bring great advantages in spintronics application.

 

    100%   

(4)

where   and   are numbers of states of spin-up and spin-down electrons at the Fermi level. The electronic structure of h-VN calculated within many-body GW0 method is in very good agreement to the HSE level theory that proves relevance of our results (Figure S3). Such high rates of spin polarization in both polymorphs are resulted from redistribution of the vanadium d states and suggest that the nanosheets are promising candidates for spintronic devices. 2D materials with large spin-gaps can form desirable contacts with efficient spin injection. The spin-down band gap of h-VN is in the range of -1.67 : -6.46 eV that cover major part of two-dimensional materials like MoS2 (-4.28 : -6.27 eV)29, phosphorene (-3.9 : -5.4 eV)30 and graphene. Therefore, efficient spin injection is expected in h-VN-based composites.

Figure 3. Spin-up (in red) and spin-down (in blue) band structures and DOS of (a) t-VN and (b) h-VN sheets calculated at the HSE06 level. The Fermi energy level is shifted to 0.0 eV. Overlaps in orbital-projected DOS (Figure S4) constitute a well-known indicator of hybridization. Perfect resonance in atomic orbital DOS of nitrogen reveals sp3 in t-VN and sp2 8 ACS Paragon Plus Environment

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in h-VN hybridization types. The peaks in V orbital DOS of t-VN suggest the formation of p2d2 hybrid orbital, which is compatible with tetragonal lattice symmetry. This hybrid orbital overlaps with the 𝑠𝑝3 one of nitrogen resulting in bond formation. The V s, dxy and 𝑑𝑥2 −𝑦2 states of h-VN forms rare sd2 hybrid localized in the same energy range as N sp2 hybrid orbitals, revealing a strong overlap between them and formation of sigma bonds lying in the plane of the sheet. The delocalized π bonds in h-VN are formed by N-pz orbitals, which are overlapped with dxz and dyz orbitals of V atoms, while nonbonding states arise from 𝑑𝑧 2 orbitals. The bonding in VN monolayers is similar to their bulk analogs and can be described as the mixture of metallic, covalent, and ionic components. The ionic contribution comes from the charge transfer and electron localization resulting in strong interaction between metal and nonmetal. The metallic character is manifested in their electrical conductivity, which is also observed in bulk VN. Overlaps in projected orbital DOS between N p-states and V d-states can be interpreted as covalently shared electrons. Considering various magnetic states (FM and AFM) of VN nanosheets, it is found that both monolayers are ferromagnets at their ground states. Intrinsic magnetism is generated by uncompensated excess charge. FM configurations are 0.18 eV and 0.96 eV lower in energy than the AFM ones for t-VN and h-VN respectively. The local magnetic moments on metal atoms are 1.46 µB and 2.1 µB for t-VN and h-VN respectively. To estimate the Curie temperature Tc, we use Ising model Hamiltonian Hˆ   i ,l Jmˆ i mˆ j where mˆ j - is the spin magnetic moment per chemical formula and 𝐽 is the nearest-neighbor Heisenberg exchange parameter J

1 Eex / 2m 2 , where Eex  E AFM  EFM and n is number of exchange pairs. Factor 1/2 is n

double counting of exchange pairs. J exchange parameters are 10.56 meV and 18.14 meV for tVN and h-VN respectively. The analytical solution of the square and triangular 2D Ising lattices26 can be evaluated as: kBTc/J = 2.269 (square) and kBTc/J = 3.65 (triangular). Estimated Curie temperatures of t-VN and h-VN are about 278 K and 768 K. Therefore, magnetism can be detected experimentally under ambient or near ambient conditions. Magnetic anisotropy energy (MAE) is an important parameter of magnetic materials and their applications. Following the Mermin-Wagner theorem,31 it is directly related to the thermal stability of 2D magnetic lattices. The MAE of 2D VN polymorphs are calculated using the HSE06 functional and spin-orbit coupling (SOC). The results indicate that the easy axis for both materials is in-plane direction and corresponding values of MAE are 21 and 100 μeV per V atom 9 ACS Paragon Plus Environment


for t-VN and h-VN respectively. It should be noted that MAE values observed via the HSE06 method are usually 2-3 times smaller than those obtained with PBE method. 32,33 MAEs of 2D VN lattices are orders larger than those of ferromagnetic materials such as bulk Fe (1.4 µeV/per atom), and Ni (2.7 µeV/per atom)34 that make 2D VN suitable for magnetoelectronic applications. As far as a synthesis of two-dimensional structures is one of the key steps, the search for possible substrates is necessary. The main criteria for such substrates is small lattice mismatch. According to close cell parameters, such materials as Ni and Cu etc. may be used to synthesize t-VN. These materials have been used successfully to obtain large-scale graphene sheets.35,36 Moreover, the aspect of devices miniaturization is actual for nowadays. For example, the design of 2D nanodevices that have half-metallic properties is one of the most interesting fields of modern spintronics. Moreover, half-metallic materials can be used for spin injection and valley polarization in such material like MoS2. The MoS2 lattice mismatch is ~1% that makes possible to utilize it as the substrate for h-VN synthesis and the effective valley polarized device. To find the most energetically stable configuration, six possible geometries of h-VN/MoS2 composites are designed by different arrangements of the h-VN monolayer on the top of 2H-MoS2 monolayer (Figure S5). The D3 Grimme correction of dispersion interaction is included during energy minimization and further calculations of the heterostructure. The direct location of V above S atoms and N above Mo atoms is the most favorable configuration that demonstrate binding energy of -0.93 eV. The band structure and density of states of the lowest in energy configuration are shown in Figure 4(a). Although the band structure of the composite is drastically changed due to strong interaction with MoS2, ferromagnetic properties and 100% spin polarization at the Fermi level are retained. The h-VN/MoS2 composite has a direct band gap of 2.11 eV in spin-down electrons and metallic conductivity in spin-up demonstrating its half-metallic nature. The interaction of the monolayers leads to the formation of electronic states at the Fermi level of MoS2 for spin-up electrons, whereas the spin-down band gap of h-VN is decreased. The short interlayer distance measured as V-S bond length (2.36 Å) can be explained by strong electrostatic interaction between positive vanadium and negative sulfur atoms. The spatial distributions of electron and spin densities are presented in Figure 4(b). According to the Bader analysis, charge transfer of total 0.3 electrons occurs from h-VN to the MoS2 monolayer. Redistribution of charge induces the magnetic moment of 0.28 µB at Mo atoms and decreases to 1.72 µB at V atoms resulting in the emergence of spin-polarized states at the Fermi level of 10 ACS Paragon Plus Environment

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MoS2. Hence, using an appropriate substrate one can effectively vary spin-down band gap keeping half-metallic conductivity and high rate of spin polarization. These results suggest the possibility of using not only h-VN monolayer but also its composites for construction of spinpolarized optoelectronic and valleytronics devices.37,38

Figure 4. Electronic structure of the h-VN/MoS2 composite in energetically favorable configuration. (a) Band structure and DOS calculated at the HSE06 hybrid functional level. The Fermi energy level is shifted to 0.0 eV. (b) Spatial distribution of electronic (left panel) and spin (right panel) densities.

Furthermore, the extremely high mobility of electrons together with the long spin diffusion length in graphene,39,40 combined with highly spin-polarized materials like h-VN and t-VN, allows one to provide components of logic devices with high magnetoresistance.41 In conclusion, we presented thermodynamically stable 2D VN lattices with two possible polymorphic modifications: tetragonal (t-VN, CN=4, buckled) and honeycomb (h-VN, CN=3, planar), which are associated with (100) and (111) planes of their bulk rock salt structure. High stability of both monolayers revealed from phonon dispersion calculations, AIMD simulations, finite cluster approach and formation energies. The bonding type in VN monolayers can be described as a mixture of metallic, covalent, and ionic components. Our results demonstrate rare p2d2 and sd2 hybridization types of V atoms in t-VN and h-VN respectively. Spin-polarized calculations at the HSE06 hybrid functional level indicate ferromagnetic properties of both monolayers with very high rate of spin polarization at the Fermi level and high Curie temperature. Magnetocrystalline anisotropy energy of 2D VN polymorphs is found to be at least 11 ACS Paragon Plus Environment


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an order larger than those of Fe and Ni bulks. Moreover, h-VN demonstrates half-metallic nature and keep it after contact with semiconducting 2D MoS2 that can be used as a substrate for h-VN synthesis. Our results suggest that tetragonal and honeycomb 2D VN lattices are suitable for low dimensional spintronic technologies.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Details of computational methods, VN unit cell calculation, COHP plots, PBE band structure, GW0 calculation of h-VN DOS, orbital-projected atomic densities of states and some results of h-VN/MoS2 simulation.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS This work is supported by the government contract of the Ministry of Education and Science of the

Russian Federation to Siberian

Federal

University (Grant

No.

16.1455.2017/PCh). The authors would like to thank Joint Supercomputer Center of RAS, Moscow; Information Technology Centre, Novosibirsk State University and Siberian Supercomputer Center (SSCC) of SB RAS, Novosibirsk; HPC-cluster «Academician V.M. Matrosov» for providing the access to their supercomputers. AVK acknowledges National Research Foundation of the Republic of Korea Grant No. NRF-2017R1A2B4004440. Authors greatly acknowledge Prof. Sergei G. Ovchinnikov and Dr. Felix N. Tomilin at the Kirensky Institute of Physics, KSC SB RAS, Krasnoyarsk for valuable discussions.

DEDICATION This paper is dedicated to the memory of Dr. Alexander Kuzubov, whose ideas contributed greatly to the study but who sadly passed away before it was completed. 12 ACS Paragon Plus Environment

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REFERENCES (1)

Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6, 183–191.

(2)

Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Single-Layer MoS2 Transistors. Nat. Nanotechnol. 2011, 6, 147–150.

(3)

Huang, B.; Clark, G.; Navarro-Moratalla, E.; Klein, D. R.; Cheng, R.; Seyler, K. L.; Zhong, D.; Schmidgall, E.; McGuire, M. A.; Cobden, D. H.; et al. Layer-Dependent Ferromagnetism in a van Der Waals Crystal down to the Monolayer Limit. Nature 2017, 546, 270–273.

(4)

Gong, C.; Li, L.; Li, Z.; Ji, H.; Stern, A.; Xia, Y.; Cao, T.; Bao, W.; Wang, C.; Wang, Y.; et al. Discovery of Intrinsic Ferromagnetism in Two-Dimensional van Der Waals Crystals. Nature 2017, 546, 265–269.

(5)

Gao, D.; Xue, Q.; Mao, X.; Wang, W.; Xu, Q.; Xue, D. Ferromagnetism in Ultrathin VS2 Nanosheets. J. Mater. Chem. C 2013, 1, 5909.

(6)

Sinova, J.; Žutić, I. New Moves of the Spintronics Tango. Nat. Mater. 2012, 11, 368– 371.

(7)

Kuklin, A. V.; Kuzubov, A. A.; Kovaleva, E. A.; Mikhaleva, N. S.; Tomilin, F. N.; Lee, H.; Avramov, P. V. Two-Dimensional Hexagonal CrN with Promising Magnetic and Optical Properties: A Theoretical Prediction. Nanoscale 2017, 9, 621–630.

(8)

Zhang, S.; Li, Y.; Zhao, T.; Wang, Q. Robust Ferromagnetism in Monolayer Chromium Nitride. Sci. Rep. 2014, 4, 5241.

(9)

Zhou, L.; Zhuo, Z.; Kou, L.; Du, A.; Tretiak, S. Computational Dissection of TwoDimensional Rectangular Titanium Mononitride TiN: Auxetics and Promises for Photocatalysis. Nano Lett. 2017, 17, 4466–4472.

(10) Anand, S.; Thekkepat, K.; Waghmare, U. V. Two-Dimensional Rectangular and Honeycomb Lattices of NbN: Emergence of Piezoelectric and Photocatalytic Properties at Nanoscale. Nano Lett. 2016, 16, 126–131. (11) Liu, J.; Li, X.-B.; Zhang, H.; Yin, W.-J.; Zhang, H.-B.; Peng, P.; Liu, L.-M. Electronic Structures and Optical Properties of Two-Dimensional ScN and YN Nanosheets. J. Appl. Phys. 2014, 115, 93504. (12) Zhou, L.; Shao, B.; Shi, W.; Sun, Y.; Felser, C.; Yan, B.; Frauenheim, T. Prediction of the Quantum Spin Hall Effect in Monolayers of Transition-Metal Carbides MC (M = Ti, Zr, Hf). 2D Mater. 2016, 3, 35022. (13) Zhang, Z.; Liu, X.; Yakobson, B. I.; Guo, W. Two-Dimensional Tetragonal TiC Monolayer Sheet and Nanoribbons. J. Am. Chem. Soc. 2012, 134, 19326–19329. (14) He, J.; Ma, S.; Lyu, P.; Nachtigall, P. Unusual Dirac Half-Metallicity with Intrinsic Ferromagnetism in Vanadium Trihalide Monolayers. J. Mater. Chem. C 2016, 4, 2518– 2526. (15) Kuklin, A. V.; Kuzubov, A. A.; Eliseeva, N. S.; Tomilin, F. N.; Fedorov, A. S.; Krasnov, P. O. Theoretical Investigation of the Structure and Properties of the VN(111) Monolayer on the MgO(111) Surface. Phys. Solid State 2014, 56, 229–234. 13 ACS Paragon Plus Environment


(16) Mannix, A. J.; Zhou, X.-F.; Kiraly, B.; Wood, J. D.; Alducin, D.; Myers, B. D.; Liu, X.; Fisher, B. L.; Santiago, U.; Guest, J. R.; et al. Synthesis of Borophenes: Anisotropic, Two-Dimensional Boron Polymorphs. Science 2015, 350, 1513–1516. (17) Zhu, F.; Chen, W.; Xu, Y.; Gao, C.; Guan, D.; Liu, C.; Qian, D.; Zhang, S.-C.; Jia, J. Epitaxial Growth of Two-Dimensional Stanene. Nat. Mater. 2015, 14, 1020–1025. (18) Eda, G.; Fujita, T.; Yamaguchi, H.; Voiry, D.; Chen, M.; Chhowalla, M. Coherent Atomic and Electronic Heterostructures of Single-Layer MoS2. ACS Nano 2012, 6, 7311–7317. (19) Kou, L.; Chen, C.; Smith, S. C. Phosphorene: Fabrication, Properties, and Applications. J. Phys. Chem. Lett. 2015, 6, 2794–2805. (20) He, S.; He, J.; Zhang, W.; Zhao, L.; Liu, D.; Liu, X.; Mou, D.; Ou, Y.-B.; Wang, Q.-Y.; Li, Z.; et al. Phase Diagram and Electronic Indication of High-Temperature Superconductivity at 65 K in Single-Layer FeSe Films. Nat. Mater. 2013, 12, 605–610. (21) Zhuang, H. L.; Hennig, R. G. Electronic Structures of Single-Layer Boron Pnictides. Appl. Phys. Lett. 2012, 101, 153109. (22) Cahangirov, S.; Topsakal, M.; Aktürk, E.; Şahin, H.; Ciraci, S. Two- and OneDimensional Honeycomb Structures of Silicon and Germanium. Phys. Rev. Lett. 2009, 102, 236804. (23) Yang, L.-M.; Bačić, V.; Popov, I. A.; Boldyrev, A. I.; Heine, T.; Frauenheim, T.; Ganz, E. Two-Dimensional Cu 2 Si Monolayer with Planar Hexacoordinate Copper and Silicon Bonding. J. Am. Chem. Soc. 2015, 137, 2757–2762. (24) Topsakal, M.; Cahangirov, S.; Bekaroglu, E.; Ciraci, S. First-Principles Study of Zinc Oxide Honeycomb Structures. Phys. Rev. B. 2009, 80, 235119. (25) Sanville, E.; Kenny, S. D.; Smith, R.; Henkelman, G. Improved Grid-Based Algorithm for Bader Charge Allocation. J. Comput. Chem. 2007, 28, 899–908. (26) Fisher, M. E.; Burford, R. J. Theory of Critical-Point Scattering and Correlations. I. The Ising Model. Phys. Rev. 1967, 156, 583–622. (27) Berseneva, N.; Gulans, A.; Krasheninnikov, A. V.; Nieminen, R. M. Electronic Structure of Boron Nitride Sheets Doped with Carbon from First-Principles Calculations. Phys. Rev. B 2013, 87, 35404. (28) Ramasubramaniam, A. Large Excitonic Effects in Monolayers of Molybdenum and Tungsten Dichalcogenides. Phys. Rev. B 2012, 86, 115409. (29) Kang, J.; Tongay, S.; Zhou, J.; Li, J.; Wu, J. Band Offsets and Heterostructures of TwoDimensional Semiconductors. Appl. Phys. Lett. 2013, 102, 12111. (30) Cai, Y.; Zhang, G.; Zhang, Y. W. Layer-Dependent Band Alignment and Work Function of Few-Layer Phosphorene. Sci. Rep. 2014, 4, 6677. (31) Mermin, N. D.; Wagner, H. Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models. Phys. Rev. Lett. 1966, 17, 1133–1136. (32) Zhang, W.-B.; Qu, Q.; Zhu, P.; Lam, C.-H. Robust Intrinsic Ferromagnetism and Half Semiconductivity in Stable Two-Dimensional Single-Layer Chromium Trihalides. J. Mater. Chem. C 2015, 3, 12457–12468. 14 ACS Paragon Plus Environment

Page 14 of 29

Page 15 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(33) Sun, Y.; Zhuo, Z.; Wu, X.; Yang, J. Room-Temperature Ferromagnetism in TwoDimensional Fe 2 Si Nanosheet with Enhanced Spin-Polarization Ratio. Nano Lett. 2017, 17, 2771–2777. (34) Daalderop, G. H. O.; Kelly, P. J.; Schuurmans, M. F. H. First-Principles Calculation of the Magnetocrystalline Anisotropy Energy of Iron, Cobalt, and Nickel. Phys. Rev. B 1990, 41, 11919–11937. (35) Li, X.; Cai, W.; An, J.; Kim, S.; Nah, J.; Yang, D.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E.; et al. Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils. Science 2009, 324, 1312–1314. (36) Reina, A.; Jia, X.; Ho, J.; Nezich, D.; Son, H.; Bulovic, V.; Dresselhaus, M. S.; Kong*, J. Layer Area, Few-Layer Graphene Films on Arbitrary Substrates by Chemical Vapor Deposition. Nano Lett. 2009, 9, 3087–3087. (37) Sanchez, O. L.; Ovchinnikov, D.; Misra, S.; Allain, A.; Kis, A. Valley Polarization by Spin Injection in a Light-Emitting van Der Waals Heterojunction. Nano Lett. 2016, 16, 5792–5797. (38) Zhong, D.; Seyler, K. L.; Linpeng, X.; Cheng, R.; Sivadas, N.; Huang, B.; Schmidgall, E.; Taniguchi, T.; Watanabe, K.; McGuire, M. A.; et al. Van Der Waals Engineering of Ferromagnetic Semiconductor Heterostructures for Spin and Valleytronics. Sci. Adv. 2017, 3, e1603113. (39) Han, W.; Kawakami, R. K. Spin Relaxation in Single-Layer and Bilayer Graphene. Phys. Rev. Lett. 2011, 107, 47207. (40) Dlubak, B.; Martin, M.-B.; Deranlot, C.; Servet, B.; Xavier, S.; Mattana, R.; Sprinkle, M.; Berger, C.; De Heer, W. A.; Petroff, F.; et al. Highly Efficient Spin Transport in Epitaxial Graphene on SiC. Nat. Phys. 2012, 8, 557–561. (41) Asshoff, P. U.; Sambricio, J. L.; Rooney, A. P.; Slizovskiy, S.; Mishchenko, A.; Rakowski, A. M.; Hill, E. W.; Geim, A. K.; Haigh, S. J.; Fal’ko, V. I.; et al. Magnetoresistance of Vertical Co-Graphene-NiFe Junctions Controlled by Charge Transfer and Proximity-Induced Spin Splitting in Graphene. 2D Mater. 2017, 4, 31004.



Supporting Information for

Two-Dimensional Lattices of VN: Polymorphism, Room-Temperature Ferromagnetism and High Transmittance at Nanoscale Artem V. Kuklin§,‡,*, Svetlana A. Shostak‡, Alexander A. Kuzubov† §

Siberian Federal University, 79 Svobodny pr., Krasnoyarsk 660041, Russia

‡

Department of Chemistry, Kyungpook National University, 80 Daehakro, Bukgu, Daegu

41566, Republic of Korea †

Deceased December 31, 2016.

We carried out first-principles spin-polarized plane-wave electronic-structure calculations within density functional theory (DFT) in form of generalized gradient approximation as implemented in the Vienna Ab-initio Simulation Package (VASP) code.1,2 The projector augmented wave (PAW)3 method with a cutoff energy of 500 eV for plane-wave expansions and Perdew-Burke-Ernzerhof (PBE)4 exchange functional were employed. The screened exchange hybrid density functional proposed by Heyd-Scuseria-Ernzerhof (HSE06)5 was adopted to solve electronic structure of the monolayers. The self-consistent GW calculation was performed by iterating only G, but keeping W fixed (GW0 approximation).6 D3 Grimme correction of van-der-Waals - London dispersion was included for multilayer systems. 7 A vacuum region of >12 Å set to avoid artificial interaction between neighboring images. The reciprocal space in the Brillouin zone was sampled using Monkhorst-Pack scheme by 20 × 20 × 1 and 24 × 24 × 1 k-points for t-VN and h-VN respectively. The convergence tolerances for the force and electronic minimizations set to 10 -6 eV/Å and 10-8 eV, respectively. The phonon calculations were carried out using the PHONOPY code.8 COHP was obtained using LOBSTER code.9 The geometries and charge densities were visualized by VESTA software.10 The relaxation of extended finite nanoclusters consisted of 192 and 186 atoms in t-VN and h-VN respectively was performed at the Γ-point (1 × 1 × 1 k-point mesh) using OpenMX code.11–13 To simulate isolated atoms and N2 molecule, spin-polarized calculations at the Г-point using the box of 15 × 15 × 15 Å to avoid any interaction between images were employed. The energy of vanadium unit cell was obtained using 12 × 12 × 12 k-points mesh. 16 ACS Paragon Plus Environment

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In the search of 2D VN lattices, at the initial stage, we used the most stable bulk form of VN at ambient conditions, which is NaCl-type (B1)14 and then determined the equilibrium geometry of VN unit cell. The unit cell of B1 vanadium nitride consists of eight atoms. The results of calculation at 12 × 12 × 12 k-point grid and 500 eV cutoff energy revealed very good agreement of the lattice constant (

Two-Dimensional Lattices of VN: Emergence of ... - ACS Publications

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