2D FeO: a New Member in 2D Metal Oxide Family

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

2D FeO: a New Member in 2D Metal Oxide Family Konstantin V Larionov, Dmitry G. Kvashnin, and Pavel B. Sorokin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06054 • Publication Date (Web): 03 Jul 2018 Downloaded from http://pubs.acs.org on July 3, 2018

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The Journal of Physical Chemistry

2D FeO: a new member in 2D metal oxide family K.V. Larionov, †,┴ D.G. Kvashnin, †,‡ P.B. Sorokin †,┴,‡,* †

National University of Science and Technology MISiS, 4 Leninskiy prospekt, Moscow, 119049, Russian Federation

┴

Technological Institute for Superhard and Novel Carbon Materials, 7a Centralnaya Street, Troitsk, Moscow, 108840, Russian Federation

‡

Emanuel Institute of Biochemical Physics RAS, 4 Kosigina Street, Moscow, 119334, Russian Federation

* [email protected]

ABSTRACT. Here we report a comprehensive theoretical investigation of ultrathin FeO films as well as principally novel 2D FeO monolayer with uncommon orthorhombic lattice structure. It was shown that 2D FeO is a semiconductor with a robust antiferromagnetic spin ordering. Interface energy of 2D FeO/graphene planar heterostructures was derived analytically and optimal shape of 2D FeO spot in graphene was predicted. Close correspondence between simulated data and reference experiment supports the proposed model.

INTRODUCTION. Isolation and comprehensive investigation of graphene 1,2 established new family of materials with formally two-dimensional structure. This family contains dozens of members, however only graphene and h-BN can be considered as monolayers of atomic thickness whereas other 2D films might be represented as number of chemically bounded atomic ACS Paragon Plus Environment

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layers. Recently published remarkable paper by Zhao et al. 3 has shown possibility of formation of new type of iron film with square lattice of one atom thickness. Being aligned with the previous result, another paper considering 2D metal films was published. It was reported 4,5 that copper atoms can also form two-dimensional square net, but such structure should be stabilized by uniformly arranged oxygen atoms located in the centers of Cu squares. This result correlates with proposal

6

that reported stable configuration of two-

dimensional iron might be iron carbide in fact. Another variant might include an introduction of oxygen that can also stabilize the iron lattice with formation of 2D iron oxide. Possible existence of 2D transition metal oxide family of materials can be conjugated with early proposed “ionic graphitization” effect of splitting of atomically thin zinc blende 7 and rock salt 8–10 films (with dominant ionic bonding contribution) into layered phase. In the latter case the possible formation of 2D monolayered hexagonal phases of NaCl, MgO was proposed. The main reason of cubic structure instability is the charge transfer from the outermost anions to the cations resulted in huge dipole moment, normally oriented to polar surface, leading to divergence of the surface energy that makes the whole film structure intrinsically unstable. 11,12 Such effect can play crucial role in case of FeO ultrathin films that also have rock salt lattice structure leading to formation of new member of 2D monolayers of atomic thickness. Present paper is devoted to the detailed investigation of possible layered phase of FeO. In the first part of the work, we show energy favorability of formation of the stack of 2D FeO monolayers with orthorhombic lattice in comparison with ultrathin rocksalt FeO films. We predict that FeO films with polar (111) surface below critical thickness tend to be split into pack of orthorhombic 2D FeO monolayers. Next, we discuss the electronic and magnetic properties of the films. Further part of the paper we devoted to the study of stability of such structures and their planar heterojunction with graphene matrix. We combined crystal growth theory and atomistic computations to predict the energetically favorable structure of FeO/graphene 2D

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composite. Final part of the paper is devoted to the comparison of our data with reference experiment. METHODS. All calculations of atomic structure and stability were performed with DFT+U method 13 describing transition metal compounds within the local density approximation (LDA) functional. 14 Ueff parameter (Ueff = U – J = 4.0 eV) was set in accordance with Refs. 15–17. Spin-orbital coupling was taken into account in order to break the degeneracy of the d orbitals at the Fermi level and properly describe electronic properties of bulk FeO.

18,19

We used the

projector augmented wave method 20 approximation with the periodic boundary conditions implemented in Vienna Ab-initio Simulation Package. 21–24 The plane-wave energy cut-off was set to 500 eV. To calculate the equilibrium atomic structure of bulk FeO, the Brillouin zone was sampled according to the Monkhorst–Pack scheme 25 with a 10×10×10 grid in the k-space. The structural relaxation was performed until the forces acting on each atom became less than 10-4 eV/Å. To avoid interaction between the neighboring FeO layers, the translation vector along non-periodic direction was set to be greater than 15 Å. To calculate edge energies of graphene and 2D FeO ribbons as well as energies of 2D FeO/graphene interface Monkhorst–Pack scheme with the k-point spacing smaller than 0.2 Å-1 was used. RESULTS AND DISCUSSIONS. Dominant contribution of surface atoms in ultrathin films of nanometer thickness governs the specific behavior of the atomic structure which can be sufficiently changed due to the large-scale surface reconstruction. Most evident example of such effect is graphitization of diamond nanofilms 26 and “ionic graphitization” predicted for films with zincblende 7 and rocksalt 9,10 structures with prevalent ionic contribution to the bonding. Recent experimental results about formation of iron 3 and copper 4,5 based 2D films have risen the question about the extending of the ionic graphitization theory to 2D metal compounds family which we exemplified by the iron oxide ultrathin films. The same rocksalt atomic



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structure of FeO and ionic interatomic bonding allow to propose realization of similar effect on the nanoscale level. N

N The energy balance ∆Ehex = EN hex – ERS is presented in Figure 1a by red line, where Ehex is

energy of the AA stack of N monolayers (0001) with graphene-like hexagonal structure and EN RS is energy of N-layered rocksalt FeO film oriented by polar surface (111). One can see that below critical thickness ∆EN hex changes sign from positive to negative value which can indicate further energy favorability of film splitting. However, in contrast to previously studied two-dimensional salts, 9 it was shown that energetically favorable atomic structure of 2D FeO not hexagonal one, but orthorhombic one N

(a = 2.76 Å, b = 2.80 Å, see Figure 1b, AFM2). Energy difference ∆Eort = EN ort – ERS is presented in Figure 1a by blue line, where EN ort is energy of the AA stack of N monolayers (001) with orthorhombic structure and EN RS is energy of N-layered rocksalt FeO film oriented by polar surface (111). In addition to the absence of energy barrier between hexagonal and orthorhombic structures (see inset in Figure 1a), one can observe that ∆Eort values are lower than ∆Ehex , which means that below critical thickness (~9-10 layers) rocksalt polar FeO film will irreversibly change its structure to the stack of orthorhombic 2D FeO monolayers with interlayered distance equaled to 3.16 Å and interlayer binding energy ~0.1 eV/FeO. The latter corresponds to the vander-Waals interaction and comparable with the values for graphite

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which manifests relative

independence of monolayers in films. The result of formation of 2D FeO with orthorhombic structure is particularly notable in the light of early prediction of formation of hexagonal phase of 2D FeO on the metal surfaces 28,29, which makes especially important the proper choice of substrate which can dictate the final structure of 2D film. In addition, we have compared energy of nonpolar (001) N-layered FeO film with the energy of a stack of N monolayers (001) with orthorhombic structure (Figure S1). We found that pack of orthorhombic monolayered FeO films is more energetically favorable (or at least equally favorable) than (001) N-layered FeO film with rocksalt structure for the thickness of 1-4 atomic ACS Paragon Plus Environment

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layers, which means that once “graphitized” from polar (111) film the resulted orthorhombic film remains in split state below such number of layers. We investigated the properties of orthorhombic 2D FeO by calculation of electronic spectrum (see Supplementary materials) and spin ordering (Figure 1b). It was shown that 2D FeO has semiconducting properties with a band gap of ~2.12 eV and major contributions of Fe states at the bottom of the conduction band and the top of the valence band (Figure S2) whereas bulk FeO is a semiconductor with a band gap of ∼2.05 eV. Furthermore, 2D iron oxide displays strong antiferromagnetic spin ordering with spin values same to bulk FeO (3.6 µB). The ground state of spin configuration is alternation of the spin-up and spin-down in the neighboring rows of the Fe atoms (Figure 1b, AFM2 configuration). Existence of such kind of magnetic ordering is directly linked with the orthorhombic symmetry of the lattice, since Fe atoms with the same spin orientation are repulsed from each other, whereas atoms with alternate spin ordering are attracted. The energy difference between NM and AFM states of bulk FeO is about 1.5 eV per FeO pair, whereas in the two-dimensional case this energy difference is even larger, 1.7 eV per FeO pair, which suggests the high robustness of magnetic properties in 2D FeO, for example, in comparison with 2D CuO 4.



Figure 1. a) Cohesive energy difference ∆E of N-layered stack of FeO monolayers and N-layered rocksalt FeO film, with ∆E < 0 indicating energetic preference for ionic graphitization. Hexagonal (square) symbols illustrate difference in the energy between stack of monolayers with hexagonal (orthorhombic) structure and rocksalt film with polar (111) surface. Solid and open symbols represent structures with locally stable and unstable cubic phase, respectively. Inset demonstrates pathway from hexagonal to orthorhombic structure with no energy barrier; b) energetically favorable spin ordering in 2D FeO monolayer. AFM1, AFM2 are antiferromagnetic spin ordering, FM is ferromagnetic spin state, NM is nonmagnetic configuration. Lattice parameters are shown for the most favorable case of AFM2 configuration. For the investigation of lattice stability we applied bending analysis 30 which reveals the tendency of monolayer curving (see Figure S3). It was found that energetically favorable layer is crumbled one represented in the analysis by nanotube with diameter 7.5 Å. Such high curvature suggests the instability of the infinite flat 2D monolayer. This result gives a clue that twoACS Paragon Plus Environment

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dimensional structure can exist only in the supported state. The possible realization of such idea has been already demonstrated by observation of stable heterostructures such as Fe/graphene 3,31, FeO/Pt 28,32, CuO/graphene 5 and MgO/Ag 8 junctions. We considered atomic geometry of possible FeO/graphene in-plane heterostructures in details. The energetically favorable shape of the 2D FeO spot in graphene can be estimated by using crystal growth theory, in particular, Wulff construction approach. Such method has been already successfully applied for the description of the thermodynamically favorable atomic structure of graphene33, h-BN34, MoS235 GaSe36 flakes. Interface energy per unit length Γ(χ) (where χ is mutual angle of the connected FeO and graphene edges) is used as input parameter for Wulff construction. This method at first sight is intuitively clear and simple to be implemented for some discrete variants. However, in the case of arbitrary angle χ the time-consuming problem linked with the vast sizes of atomic models describing various 2D FeO/graphene grain boundaries has to be solved. One of the way to do that is to represent an arbitrary direction as a linear combination of lattice vectors defining our structure. It was shown 34 that interface energy might be calculated as a sum of independent constituent edge energies and some additional term defining their binding energy:

Γχ = γgraphene χ + γFeO χ + Ebind,

(1)

where Γ is interface energy; γgraphene and γFeO are the edge energies of graphene and FeO, respectively; Ebind is the energy of binding of FeO and graphene components. Continuous functions γgraphene and γFeO can be represented by linear combination of two basic directions (e.g. zigzag (ZZ) and armchair (AC) edge energies for graphene in Ref. 37). Thus, calculation of only such two values (as well as binding energy between them) allows to define interface energy for any arbitrary angle χ. In the case of graphene, edge energy can be calculated as: 37 π

γgraphene χ = 2γZZ sinχ + 2γAC sin( – χ), 6


(2)


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π

where γZZ = γgraphene and γAC = γgraphene 0 are the energies of zigzag and armchair edges, 6

respectively. Edge energies of basic directions γX (X = AC, ZZ) for graphene can be directly obtained using procedure developed for the evaluation of surface energy 38,39 but reduced to two-dimensional case, where instead of slabs of finite thickness, the graphene ribbons with two identical opposite edges should be used. Based on that, we can find edge energy from the following dependence: γX =

1 2L

Eribbon – NµC .

(3)

Here, Eribbon is the energy of the graphene ribbon oriented along direction X; N is number of constituents C atoms and µC is their energy in graphene monolayer. While such approach is already developed for the graphene case, 37 the orthorhombic lattice as well as presence of two sorts of atoms in 2D FeO require some modifications of the edge energy definition. Due to orthogonal orientation of the lattice vectors (Figure 2a), FeO film edges can be named in a way that was previously used for the description of 2D square lattices. 40 The edges oriented parallel to the lattice vectors and consisted of two sorts of atoms were defined as linear type (LN) according to their geometric structure. For the same reason, the edges including only one atomic type could be named as zigzag. It should be noted that the latter could be terminated by iron and oxygen which type we denote in the parentless (e.g. ZZ(O) for zigzag edge terminated by oxygen). Possible configurations of basic 2D FeO/graphene interfaces are presented at Figure 2b. Having introduced the necessary notations, 2D FeO edge energy in case of arbitrary direction might be defined in a way similar to equation (2) (see Supplementary Materials): π

γFeO χ = √2 γZZ sinχ + √2 γLN sin – χ, 4

(4)

π

where γZZ = γFeO and γLN = γFeO 0 are zigzag and linear edge energies, respectively. 4

Two types of termination of 2D FeO can also lead to a problem of non-equality of iron and oxygen atoms in FeO ribbon with zigzag edges (see Figure 2b) used for the calculation of the


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energy. Thus, we have to take into account the contribution from extra-atoms (Fe or O) into total edge energy. One can obtain FeO zigzag edge energy from the following dependence (see Supplementary Materials): γZZ =

1 2L

Eribbon – NFeO µFeO ±

Nextµ 2L

(5)

,

where Eribbon is the energy of FeO zigzag ribbon; NFeO is the number of FeO pairs; Next is the number of extra iron or oxygen atoms in the case of iron and oxygen terminated edges, respectively; µFeO is the energy of infinite 2D FeO monolayer per FeO unit which allows 1

formally express chemical potential for individual species as µFe,O = µ

2 FeO

± µ. Sign “+” in the

equation (5) corresponds to O-terminated (Next = NO extra atoms of oxygen) ZZ edge, while “–“ corresponds to Fe-terminated one (Next = NFe extra atoms of iron). On the other hand, since the number of iron and oxygen atoms in linear (LN) FeO edge are equal, its energy can be calculated similarly to (3) but only with µFeO instead of µC. Both equations (2) and (4) display the obvious fact of periodicity of edge energy since the crystallographic directions in 2D FeO as well as in graphene lattices are repetitive with a period π

and , respectively. 3


π 2


Figure 2. a) Scheme of atomic structure of the orthorhombic lattice of 2D FeO monolayer. Dashed lines denote two high-symmetry directions: zigzag (a = b) and linear (a ≠ 0, b = 0; a = 0, b ≠ 0); b) atomic structure of studied interfaces between zigzag (ZZ) and armchair (AC) graphene edges and linear (LN) and zigzag (ZZ) (with oxygen (O) and iron (Fe) terminations) FeO edges; c) interface energy Г (black line) calculated for µ = 4.5 eV case as sum of graphene (gray line) and the energetically favorable iron terminated FeO (red line) edge energies depending on mutual angle χ. In addition, less favorable (for chosen µ) dependence of edge energy of oxygen terminated FeO on χ is presented (yellow line). In order to clarify the results, main types of edges (ZZ, AC, LN) are marked by empty circles. In (a) and (b) carbon, iron and oxygen atoms are colored by grey, orange and red, respectively.


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It was found that the most and less energetically favorable edges in graphene are armchair (1.12 eV/Å) and zigzag (1.45 eV/Å), respectively, which is in a good agreement with Ref. 37. As for 2D FeO, its edge energy function is limited by LN (0.29 eV/Å) and ZZ edges. The latter one depends not only on mutual angle but also on chemical potential µ (Eq. (5)). As an example, 2D FeO edge energies are presented for the case of µ = 4.5 eV (see Figure 2c) as functions of mutual angle χ. For this particular µ-value, the most energetically favorable edge of 2D FeO is zigzag type with iron termination. All this data can be resulted in total 2D FeO/graphene interface energy (black line) that displays the optimal angle between its constituents and, in fact, describes the equilibrium shape of 2D FeO embedded in graphene as will be discussed later. It should be noted that since χ = 0 is just relative starting value and formally could be chosen in arbitrary manner, it was decided to correspond graphene AC and FeO ZZ(Fe) points because particularly this case means the global minimum of total energy as follows from calculations. Therefore we observe the minimal possible interface energy (0.36 eV/Å) for χ = 0, as well as two local minimums (0.41 eV/Å) at π/3 and 2π/3. This trend is repeated with a period equaled to π as follows from the lowest common denominator of π/3 (period of graphene) and π/2 (period of 2D FeO). One should note that found minimal points do not have to correspond to “pure” basic directions (LN, ZZ, AC). For instance, while χ = 0 corresponds to combination of exact graphene AC and FeO ZZ(Fe) edges, at χ = π/3 we observe a combination of graphene AC and some intermediate FeO point which is 15° more than LN edge.



Figure 3. Energies of ZZ(Fe) (red), ZZ(O) (yellow) and LN (blue) 2D FeO edges as well as armchair (green solid) and zigzag (green dashed) edges of graphene as functions of chemical potential µ. Some equilibrium shapes of 2D FeO/graphene interface for particular µ values are presented below: external and internal boarders correspond to graphene and FeO edges, respectively. Energies of different edges types in graphene and FeO as functions of chemical potential µ are presented at Figure 3. One can see the evolution of equilibrium shape of 2D FeO/graphene interface with increasing the µ value. For instance, change of dominant type of zigzag FeO from ZZ(O) (yellow) to ZZ(Fe) (red) is being observed. Another result is almost zero contribution of graphene zigzag edge (green dashed) within all sequence of µ values because of its relatively high edge energy (1.45 eV/Å) in comparison with graphene armchair edge (1.12 eV/Å). Thus,


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variation of the external conditions represented by changing of chemical potential of constituent elements (Fe and O) can influence on the shape of 2D FeO spot in graphene. In particular, experimentally observed 2D Fe in graphene

3

has the pronounced shape.

Remarkably that 2D FeO can also repeat this contour in the case of µ = 4.5 eV (Figure 4a). Moreover, the resulted model of iron oxide has number of other important similarities with experimental image. Both 2D FeO model (Figure 4b) and experimental data (Figure 4c) demonstrate clear presence of LN and ZZ(Fe) edges. At the same time, Fe-Fe bond length in presented model (2.76 – 2.8 Å) has a better correspondence with experimental values (2.65 Å) than in “pure Fe” model, where Fe-Fe bond length is claimed to be 2.35 Å. 3 Finally, simulated TEM (Figure 4d) shows that large contrast difference between Fe and O, caused by the high mass ratio, can hide the presence of intermediate oxygen atoms in the experiment. Moreover, authors of Ref. 3 claimed that some small amount of reference atoms (other than Fe) may lie beyond the detection limits of the EELS measurements which probably requires additional analysis in order to fully exclude the possibility of the membranes consisting of iron oxide. Therefore, close correspondence between two sets of data allows to propose that in experiment 3 another member of 2D metal oxide family with orthorhombic lattice (in addition to 2D CuO 4) could be obtained.



Figure 4. a) Equilibrium shape and b) atomic model of 2D FeO spot in graphene for µ = 4.5 eV; c) experimental TEM image from Ref. 3 (Reprinted with permission from AAAS) and d) simulated TEM image. CONCLUSIONS. In the course of the current work, comprehensive ab initio study of ultrathin FeO films as well as principally novel 2D FeO monolayer was carried out. The effect of FeO films splitting into monolayers with an orthorhombic two-dimensional lattice was studied and the critical film thickness of such transition was determined as well. Further electronic properties calculations shown that 2D FeO is a semiconductor with Eg = 2.12 eV, apart from bulk structure with Eg = 2.05 eV. Moreover, 2D FeO demonstrates a robust antiferromagnetic ground state which is 1.7 eV lower than non-magnetic state. Being forced by results of bending analysis showing the instability of free-standing FeO monolayer, we investigated its possible stabilization in graphene. Interface energy of arbitrary 2D FeO/graphene heterostructure as a function of mutual angle and chemical potential of Fe/O was derived analytically. It was shown that variation of chemical potential, which in fact depends on experimental conditions, could change


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the shape of 2D FeO spot in graphene matrix. Such effect might become a promising way of controllable synthesis of metallic graphene with semiconducting “islands” demonstrating AFM ground state that further could be used for spintronics needs. 41 Thus, the obtained results on the structure of two-dimensional iron oxide and its antiferromagnetic and semiconducting properties not only expand the underinvestigated class of planar compounds with an orthorhombic lattice from theoretical point of view, but also provide the reasonable expectation of its possible synthesis. ACKNOWLEDGEMENTS. The analysis of energy difference between stack of monolayers and rocksalt film of different structure was supported by the RFBR (16-32-60138 mol_a_dk). The rest of the work was supported by Russian Science Foundation (Project identifier: 17-7220223). Authors acknowledge Dr. Péter Vancsó (KFKI MFA) and Prof. Boris P. Sorokin (TISNCM) for fruitful discussions. We are grateful to the supercomputer cluster provided by the Materials Modelling and Development Laboratory at NUST "MISIS" (supported via the Grant from the Ministry of Education and Science of the Russian Federation No. 14.Y26.31.0005), and to the Joint Supercomputer Center of the Russian Academy of Sciences.

Supporting Information: Energy difference between stack of monolayers and rocksalt film of different structure. Electronic properties of 2D and bulk FeO. Bending analysis of 2D FeO stability. Derivation of 2D FeO edge energy. Derivation of 2D FeO zigzag edge energy as a function of chemical potential µ. Determination of elastic strain. Determination of binding energy in 2D FeO/graphene interface. REFERENCES (1) (2) (3)

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2D FeO: a New Member in 2D Metal Oxide Family

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