Structure and energetics of FeO/Fe(001) interfaces

We report results of density functional theory calculations of structure and properties of 1–5 monolayer thin FeO(001) films and their interactions with the Fe(001) surface. It is found that deposition of an iron-oxide film affects weakly geometry of the Fe(001) support, causing small < 2% expansion of the first interplanar distance compared to clean iron surface. Analysis of the electronic structure of the FeO/Fe system shows that after interface formation, the oxide layer remains semiconducting and the substrate metallic. Electronic structure of the FeO(001) layer in direct contact with the Fe(001) surface exhibits metallic character. Magnetism of the metal/semiconductor interface is only slightly disturbed compared to that of isolated components. The FeO adlayers preserve antiferromagnetic (AFM) nature of the oxide and the sharp boundary between higher AFM phase of FeO and lower ferromagnetic phase of Fe is observed at the interface.


Introduction
Iron and iron compounds are strongly present in daily life and different areas of industry. Oxidation of iron surfaces and formation of stable oxide films attract substantial interest of researchers for several decades [1], for its importance in catalysis, corrosion and passivation processes. The knowledge of structure and electronic properties of the oxide/metal interfaces is significant for different areas of materials engineering including spintronics. Formation and growth of ironoxides on different substrates and oxide/metal interfaces have * Author to whom any correspondence should be addressed.
Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. been investigated both experimentally [2][3][4][5][6][7][8][9][10] and theoretically [11][12][13][14][15][16][17][18][19][20][21][22]. Adsorption and interaction of oxygen atoms on the Fe(001) surface have been studied both experimentally [3][4][5] and theoretically [19][20][21]. Experimental studies showed coverage dependence of the on-surface oxygen structure and FeO islands formation [7,8]. The composition of thin oxide films grown on Fe(001) at room temperature was found to be FeOlike [6]. In contrast to that, combined experimental and density functional theory (DFT) study determined the oxide film stoichiometry to be Fe 3 O 4 [9]. However, more recent experimental work revealed that upon annealing at 800 K in an ultra-high vacuum, the magnetite film transforms reversibly to FeO [10]. Also molecular dynamics simulations of early stages of oxidation process at differently oriented iron surfaces [14] indicated formation of an ultrathin layer of iron monoxide (FeO) in the oxidized part of the substrate. It is not stable and during further oxidation it transforms into other iron oxides (magnetite Fe 3 O 4 and hematite α-Fe 2 O 3 ). However, at the buried iron/iron-oxide interface the FeO region still remains. Therefore, it is interesting to explore the interfacial bonding interactions and their dependence on the thickness of this region. Exposed to vacuum the FeO(001) surface is non-polar and stoichiometric, and is the second most stable surface of FeO [23]. Some informations on the structure of the FeO/Fe(001) interface were revealed by previous DFT investigations [21,22]. First of these studies [21] discussed oxygen adsorption on the Fe (110) and (100) surfaces. Results for the Fe(100) surface covered with a monolayer (ML) of on-surface oxygen or a ML of adsorbed on-surface oxygen together with an ML of subsurface oxygen atoms can be interpreted as formation of one or two MLs of FeO at the Fe surface. Similar properties of the FeO/Fe(001) interface were discussed in [22]. However, none of these two studies [21,22] took into account antiferromagnetism of FeO layers. At ambient pressure and low temperature, FeO (wüstite) crystallizes in the distorted B1 structure which transforms into the cubic rock-salt structure above the Néel temperature (198 K) [24]. Below this temperature FeO exhibits antiferromagnetic (AFM) ordering in the [111] direction [25,26]. It means, that the magnetic moments of Fe cations are aligned perpendicularly to the ferromagnetically ordered (111) planes, thus reversing their orientation from one to another neighboring iron plane.
The purpose of this study is to supplement and extend existing knowledge on the onset of oxide formation on iron surfaces and oxide/metal interfaces not only for detailed analysis of structural, electronic and magnetic characteristics of the systems but also to contribute to understanding of mechanisms responsible for the bonding and structure of the interfaces. Besides, from electronic structure point of view, by forming the FeO/Fe system we are dealing with semiconductor/metal interface which may exhibit very interesting and useful properties resulting from electron charge transfer and changes in the geometry and stoichiometric composition at the interface.
The outline of the paper is as follows. In section 2 we briefly describe methodology applied. Section 3 reports results of our calculations of Fe(001) and FeO(001) surfaces and the FeO(001)/Fe(001) interfacial atomic and electronic structure and discusses them. In section 4 we summarize the study.

Methods
Calculations presented in this work were performed using the spin-dependent DFT as implemented in the Vienna ab initio simulation package (VASP) [27,28]. The electron ion-core interactions were described by projector augmented-wave (PAW) potentials [29,30] supplied with VASP with Fe 4s 1 3d 7 , and O 2s 2 2p 4 states treated as valence states. The electron exchange and correlation interactions were treated using the generalized gradient approximation (GGA) functional of the Perdew-Burke-Ernzerhof form [31]. However, a realistic description of the electronic structure of FeO (an insulating transition-metal monoxide) requires consideration of strong correlations of the Fe 3d electrons. It was realized within the framework of GGA+U by using the rotationally invariant approach of Dudarev et al [32], with the effective U eff = U − J = 4 eV. The U eff has been included only for iron atoms from the FeO part and its choice was based on the results of previous calculations of iron-oxides [23,33] and in order to provide a consistent comparison with energetic properties of other iron oxides calculated in our previous works [34]. Solutions of the Kohn-Sham equations were represented by the plane-wave-basis with kinetic energy cutoff of 500 eV. The integrations over the Brillouin zone were performed using the k-point sampling method with a 12 × 12 × 12 Monkhorst-Pack [35] grid for the bulk calculations. The second order Methfessel-Paxton method [36] was used to treat fractional occupancies with a smearing width of 0.2 eV.
The FeO/Fe(001) interface was modeled by a periodic supercell built of a slab consisting of nine Fe(001) atomic layers, with the 2 × 2 surface periodicity, and the FeO(001) overlayer, separated from its periodic images in the direction perpendicular to the surface by a vacuum region of about 27 Å. The 4 × 4 × 1 special k-points mesh was used for the Brillouin zone sampling during relaxation of the systems, whereas for postprocessing, electronic properties calculations, the k-points mesh was increased to 12 × 12 × 1. The equilibrium lattice parameter of bcc iron (a Fe = 2.830 Å) calculated in our previous work [37] was used to model the (001) oriented Fe substrate slab. The atoms of the top six Fe layers were relaxed whereas those of the bottom three Fe layers were frozen in their bulk positions. Positions of atoms in the relaxed layers were optimized in all directions until the forces on each atom were smaller than 0.01 eV Å −1 . The supercell size was kept fixed during deposition of FeO overlayers (on one side of the slab), which resulted in a minimum width of the vacuum layer of about 14 Å for a thickest FeO adlayer. In order to compensate an asymmetry of the slab, and to calculate accurate work functions, a dipole correction has been applied [38]. GGA+U calculations of the rock-salt structure of bulk FeO, with the interpenetrating Fe and O face-centered cubic sublattices, yielded the lattice parameter of 4.35 Å, which is in good agreement both with theory (4.35 Å [39]) and experiment The main parameter characterizing energetics of the interface, which describes strength of adhesion, is the adhesion energy, W adh . In case of the FeO/Fe interface it can be defined as the total energy difference: where E FeO is the energy of the compressed free-standing FeO(001) layer relaxed in the same cell as the Fe(001) surface slab, E Fe(001) is the energy of the bare, relaxed Fe(001) surface slab, and E FeO/Fe(001) is the energy of relaxed Fe(001) surface slab covered with FeO. A is the area of the computational surface cell. A related quantity is the work of separation [42] which, however, neglects dissipative processes of lattice relaxation in the E FeO and E Fe(001) components.
The stability of different interfaces can be calculated from the interface energy which is defined as where N Fe and N O denote the number of Fe and O species, and µ Fe and µ O are their chemical potentials (in a bcc bulk for Fe and gas phase for O atoms). The µ Fe is equal to the total energy per Fe atom in bcc, ferromagnetic iron bulk, and µ O is the half energy of the O 2 molecule in large supercell.

Fe(001) and FeO(001) surfaces
Before studying the FeO/Fe(001) interfaces we have optimized structures of the Fe(001) and FeO(001) surface slabs. The (001) facet is the second most stable surface of bcc iron [43]. The interplanar distances between surface layers of an ideal iron crystal have relaxed during optimization process. Magnitude of the relaxed separation of two subsequent layers i, j was calculated as  [43]. The magnetic moments on deeper layer atoms approach the bulk value of 2.18 µ B [37].
To study effect of the film thickness on adhesive energies and electronic properties we considered the FeO(001) slab built of one to five atomic layers. The Fe atoms of FeO(001) films exhibit AFM configuration resulting from the AFM ordering of the FeO layers in the [111] direction. It means that each FeO(001) layer is composed of antiferromagnetically arranged rows of ferromagnetically oriented Fe atoms, separated by the rows of oxygen atoms, which is reflected in our results. In the FeO bulk crystal, half of the edge length of the (001) surface unit cell measures 2.175 Å. This is only a little more (≈8%) than half of the diagonal of the Fe(001) surface unit cell (2.001 Å). It suggests a possibility of growing of FeO(001) layers on the Fe(001) surface, with the fcc sublattice of the iron-oxide rotated by 45 • around the [001] direction and compressed compared with its natural geometry. The calculated lattice parameters of bulk FeO and bcc Fe crystals (a FeO(001) and a Fe , respectively) resulted in the FeO(001) and Fe(001) lattice mismatch of about 8%. The lattice mismatch is defined  [47] which showed that compared to the bulk, the FeO lattice is laterally compressed by about 5%-6%. Therefore, in this study we consider free-standing FeO(001) films of 1-5 ML compressed to match the surface unit cell of Fe(001). The compressive stress induced in the system is reduced by expansion of interplanar distances in the [001] direction and the rumpling, ∆z i , of the FeO(001) planes. The magnitude of rumpling was calculated as the difference between the lowest and highest vertical positions of the atoms of the ith layer of the FeO(001) film.
The calculated interplanar distances are presented in table 1. Final geometries of free-standing FeO(001) films are given in figure S1 of the supplementary material. Interestingly, a compressed ML of a free-standing FeO remains flat and does not show any rumpling during relaxation process. For a 2 ML oxide film corrugation of the atomic planes remains small and amounts about 0.05 Å. In contrast, the relaxed FeO films of 3-5 ML exhibit quite a substantial rumpling which for the outermost layers varies in the range 0.73-0.83 Å. It is even stronger for a inner oxide layers and reaches 0.93-1.01 Å. In the thicker FeO films, each plane is disturbed in the way that half of the atoms of the film is shifted up and half of them is shifted down. The interlayer distance is much increased in comparison to its bulk magnitude (2.175 Å). The longest (3.61 Å) is for the 2 ML film. For thicker FeO(001) films the distances are distinctly reduced and range from 2.81 to 2.99 Å.
A nonmonotonic dependence of the interplanar distances in the FeO overlayers as a function of FeO thickness is observed. A shorter distances are observed for odd than even numbers of layers. Its quite large decrease from 3.61 to 2.84 Å by the transition from 2 to 3 MLs can be understood from a comparison between the total energy for the 1-5 MLs of the free standing FeO slabs and their relaxed geometries (shown in figure S1) without Fe(001) buffer. From the comparison follows that the FeO film thicker than 2 MLs starts to reconstruct which results in observed higher changes in geometry. These reduce the total energy by more than 0.1 eV per formula unit. The total energy of a free standing 3 ML FeO film is by 0.11 eV f.u. −1 lower than for 2 ML. Interesingly, the lowest energy per formula unit is observed for 4 ML of FeO (lower by 0.16 and by 0.03 eV f.u. −1 than for 2ML and for 5 ML of FeO, respectively).
For all the considered FeO films, the magnitudes of magnetic moments on Fe atoms differ not very much from that calculated for Fe in the bulk FeO (± 3.69 µ B ). Depending on the oxide film thickness and position of the atom, the magnetic moments on Fe atoms are in the range from ±3.65 to ±3.71 µ B . Free standing FeO preserved its antiferromagnetism. An easy magnetization direction of FeO bulk is [111]. It means, that in (001) plane the in-plane antiferromagnetism is present, our results for free-standing FeO(001) slabs reflect such AFM structure. Interestingly, thickness of the FeO slabs as well as a broken symmetry (e.g. a surface presence) affect very weakly the magnetization of FeO films.

FeO/Fe(001) interface
The FeO/Fe(001) interfaces were constructed using the same relaxed 9-layer Fe(001) slab and the free-standing 1-5 ML FeO(001) films. The films have been compressed and positions of atoms fully optimized to fit a supercell of the same size as that applied for the Fe(001) surface slabs. Next, the relaxed FeO(001) film was placed above the relaxed Fe(001) surface at the initial optimum distance that was determined from static calculations for FeO and Fe(001) slabs frozen in their relaxed configurations and placed at different separations. The lowest total energy configuration was used as a starting point for further relaxation of the FeO/Fe systems. It is worth noting, that data from such static calculations show a good fit to the universal binding energy relation (UBER) curve [48] (cf figure S2 in supplemental material). However, for thicker oxide films the UBER procedure applied, without relaxation of the interface layer, underestimates the equilibrium oxide-metal separation. The above model introduces 8% compressive strain in the FeO overlayer and no strain in the Fe(001) surface. One could also think of an alternative model with no strain in the FeO layer and 8% tensile strain on the Fe(001) surface or a model in which the strain due to the lattice mismatch is shared by the Fe(001) surface and the FeO(001) overlayer in a different proportion. In order to check the effect of tensile strain on the Fe(001) surface we have also calculated the energy of Fe(001) surface slabs built by using an FeO lattice constant. Results show that the energy of the FeO/Fe(001) system, calculated with the FeO lattice parameter is by ∼5-6 eV less favorable than that with Fe parameter. Moreover, the adhesion energy became negative that suggests that the system with the adopted FeO lattice parameter is not possible to be realized in experiment.
The calculated adhesive energies, W adh , and the equilibrium oxide-metal separations, d eq , for different oxide thicknesses are displayed in table 2. The phase diagram presented in figure 1 shows stability of the FeO films as a function of the film thickness and oxygen chemical potential. As is seen,   The observed rumpling of adsorbed 3 ML of FeO and the accompanying charge transfer (discussed below), lead to a similar effect as that reported in [49], where it was shown that rumpling of the supported oxide film is manifestation of a structural response to the interfacial electron charge transfer. We observe the dipole moments rumpling and electron transfer compensating each other. Interestingly, such an effect appears for thicker FeO films for which a higher dipole moments appear exactly at the interface layer.
It is worth noting, that presented here results for the geometry and energetics of the one ML oxide film adhered to the Fe(001) surface are in perfect agreement with those obtained for an ML of oxygen atoms adsorbed in the four-fold coordinated hollows. The structural changes in the system correspond well with results of other DFT calculations reported for oxygen adsorption at this iron facet [21,22]. However, both of these calculations [21,22] applied a smaller 1 × 1 surface unit cell which did not allow to set AFM configuration of Fe atoms in a topmost substrate layer, which is (by about 0.24 eV) energetically more stable than a ferromagnetic one. Besides, application of a small 1 × 1 cell did not allow to observe a surface rumpling that was revealed in this study. Nonetheless, analysis of the geometry of the FeO/Fe(001) interface shows changes of the interlayer distances in the Fe substrate slab of magnitude similar to that observed in iron bulk after oxygen adsorption. If Fe atoms from the oxide part are treated as a topmost layer of the substrate, then the relaxations of the interlayer distance are: ∆ 12 = 31.6%, ∆ 23 = 1.1%, and ∆ 34 = 0.18%, compared to 15.6%, 0.33% and 2.96% which were reported in [21] and 15%, 0.6% and 0.6%, as calculated in [22], respectively. It is obvious that both results of [21,22]  and the present results show that an ML of FeO is formed, as evidenced by a large expansion of the first interlayer distance. Similar conclusions can be drawn for a 2 ML FeO films adhered to the Fe(001) as considered in this work, and for adsorption of 2 ML of O atoms, with one of them incorporated into subsurface layer, as discussed in [21]. It was shown that a very big relaxation leads to separation of the topmost layer and eventually to formation of a two-layer FeO film at the Fe(001) surface. Although the calculations in [21] have been done in p(1 × 1) surface unit cell, and their results cannot be directly compared with the present ones, however the observed trends are the same.
The FeO(001)/Fe(001) interface is characterized by a rather strong adhesion energy (table 2) which ranges from 1.12 to 1.31 J m −2 . A strongest bound to the Fe(001) surface is seen for a 4 ML oxide film. Interestingly, the adhesion energy increases with the oxide film thickness increased from 1 to 4 MLs, and decreases by almost 20% for 5 ML FeO film. This may suggest an easier peeling of the oxide layer from the iron substrate. The adhesive bond at the FeO/Fe(001) interface is much weaker than an intrinsic adhesion of the Fe(001) slabs to themselves. According to the calculations performed in [12], by using a computational setup similar to ours, W adh is 4.69 J m −2 , and the equilibrium separation, d 0 = 1.39 Å. This agrees also well with the adhesion energy estimated roughly as twice the surface energy of the Fe(001) facet and ranges from 4.40 to 5.00 J m −2 [12,43,46,50] In order to analyze the FeO-Fe bond after interface formation we have calculated the redistribution of electronic charge at the interface defined by the following difference: where ρ FeO/Fe is the total electronic charge density of the total system FeO/Fe, and the ρ FeO and ρ Fe are the electronic charge densities of parts, FeO and Fe in the same frozen geometry. The calculated surfaces of constant electron charge density difference for the FeO/Fe(001) interface are presented in figure 4. Inspection of the figure shows that the highest charge redistribution occurs for 4 ML of FeO at the substrate. This is most likely related to the greater reconstruction of the oxide due to its interaction with the substrate. Eventually, the 4 ML FeO film is the strongest bound to the Fe(001) surface.
We have also performed analysis of Bader charge differences on atoms of the FeO/Fe(001) interface, clean Fe(001) surface, and free-standing FeO(001) slabs. For all atoms the Bader charge changes, ∆Q, have been determined, with respect to their values for the same atoms of noninteracting parts from the expression: Here, Q FeO/Fe is the electron charge on atoms of the total FeO/Fe(001) system, while Q FeO and Q Fe represent electronic charges on atoms of the noninteracting FeO film and Fe(001) substrate slab calculated in the configuration corresponding to that of the relaxed FeO/Fe(001) system. Analysis of the Bader charge differences presented in figure 2 shows that after the interface formation electronic charge transfer from the substrate to the oxide occurs. The largest changes are observed on atoms of the FeO-Fe interface layer. The differences are quite distinct and reach even ±0.3-0.4e. For atoms further from the interface, the differences in electron charge are much smaller or negligible. From the analysis of the total Bader charge difference on substrate atoms, and separately on oxide atoms, follows that the electronic charge transfer from the surface to the oxide ranges from 0.50 to 0.68 e. A presence of the FeO film on the Fe(001) surface reduces work function of the system by 0.03-0.57 eV (table 2). This decrease is larger for thicker FeO films. Similar effect was observed for experimentally investigated ultrathin FeO films on the Pt(111) surface [51]. However, a small deviation from a monotonic variation is observed for the system of 2 ML of oxide at the Fe(001), for which work function is increased by about 0.09 eV, i.e. more than for one ML. This can be explained by a transition between the system which in fact consists of an ML of oxygen on the Fe(001) and the true FeO/Fe(001) interface which is observed for thicker oxide films. Eventually, the relaxed ML of FeO at the Fe(001) surface gives the same structure as that obtained for an ML of oxygen adsorbed on the Fe(001) surface. The system with 2 MLs of FeO marks the onset of formation of the true FeO/Fe(001) interface. For oxide films thicker than 2 ML the geometry and electronic structure of oxide/iron interface are stabilized. Figure 5 presents partial density of states (PDOSs) for 4 ML of FeO at Fe(001), projected on successive layers of the Fe(001) surface and the FeO oxide atoms. For comparison PDOS of a clean Fe(001) substrate, and free-standing FeO films are also drawn. For the interface, density of states of the oxide films are shifted into direction of the occupied states, whereas for the iron substrate they are shifted into the direction of unoccupied states. These agree with the electron charge transfer discussed above. Moreover, it is observed that after the interface formation additional states on the FeO appear near the Fermi level, which eliminate a gap in the density of states of free-standing FeO slabs. The changes in the electronic structure appear only locally, near the FeO-Fe(001) interface. It is clearly visible, that changes in the electronic structure affect only the interface layers. A disappearance of the band gap in FeO is observed only for the oxide layer directly interacting with the iron surface ( figure 5). The other FeO layers, I + 2 to I + 4, preserve their semiconducting character. Similarly, the changes in density of states at the Fe substrate atoms are limited to the topmost Fe (interface) layer. As can be seen from figure 5, the I−1 and deeper (not shown) layers preserve the PDOS character of the bulk Fe layers. This is in line with Bader charge analysis which shows that electron charge transfer is predominantly limited to the interface layers. A similar effect is observed for other thicknesses of the FeO at Fe(001). Detailed PDOS' on atoms of the interface layers compared with a free standing FeO and pure Fe(001) surface for all FeO thicknesses are presented in figure S3 of the supplementary material.
Magnetic properties of the oxide and of the Fe support are preserved after the interface formation. The substrate remains ferromagnetic with magnetic moments, in general, lowered by 0.1-0.4 µ B . The magnetic moments on Fe atoms of the oxide are almost the same as for a free-standing FeO film. Only at the interface, magnetic moments of some atoms are reduced, however, not more than by 0.15 µ B . The changes are related to the redistribution of the electron charge after the formation of the interface. Moreover, the atomic coordination of FeO/Fe(001) interface atoms is higher than that of the surfaces of a freestanding FeO or bare Fe(001) surface. Generally, the magnetic moments on Fe substrate atoms are lower than on Fe atoms from the oxide part. Moreover, the FeO film retains its AFM character. The in-plane atniferromagnetism as well as anitferromagnetic stacking of successive FeO planes (as it is for free-standing slabs and FeO bulk) is preserved. Therefore, eventually a sharp boundary between lower magnetization of ferromagnetic Fe and higher magnetization of AFM FeO is observed at the interface.

Summary
We have presented results of DFT+U study of the structure and energetics of thin FeO(001) films deposited on the Fe(001) surface and formation of the FeO(001)/Fe(001) interfaces for different film thickness. We found that an ML of a free-standing FeO(001) has to be compressed in order to match the Fe unit cell but it remains flat. Thicker oxide layers exhibit substantial rumpling which increases with film thickness. After formation of the FeO/Fe(001) interface, the geometry of the system changes only weakly. Adsorption of thicker oxide films induces small rumpling of the topmost substrate layers. The strongest bound to the surface is observed for the 4 ML FeO film, for which the strongest adhesion energy is found. Oxide films deposited on iron surface cause lowering of the work function with oxide film thickness. For 2 ML of FeO(001) a small deviation from a monotonic change of the work function is observed, which can be explained by a transition between system with oxygen at the surface and a system with real FeO/Fe interface. Analysis of the calculated density of states of the system shows that FeO adlayers, except for the first layer at the FeO/Fe(001) interface, preserve its semiconducting character and eventually metal/semiconductor interface is formed. The magnetism of the system turns out to be only slightly disturbed by the interface formation, and a sharp boundary between the higher AFM phase of FeO(001) and lower ferromagnetic phase of Fe(001) is observed at the interface.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).