# Maghemite surface termination variations: Influence of models and Pt substrate

Amit Sahu, Céline Dupont

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To cite this version:

Amit Sahu, Céline Dupont. Maghemite surface termination variations: Influence of models and Pt substrate. Surfaces and Interfaces, 2024, 55, pp.105377. 10.1016/j.surfin.2024.105377. hal-05344398

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# Maghemite surface termination variations: Influence of models and Pt substrate

Amit Sahu, Céline Dupont*

Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS, Université de Bourgogne, BP 47870, Dijon Cedex, 21078, France

## ARTICLE INFO

**Keywords:**

- Maghemite structure
- Tetragonal and cubic models
- Substrate influence
- Density functional theory

## ABSTRACT

In spite of the growing interest in maghemite, its structure is not accurately known, and numerous uncertainties remain. The ongoing debate centers on its crystalline structure, whether cubic or tetragonal, and its implications for stable surface terminations. This study explores the crystalline nature of maghemite — cubic versus tetragonal — and its effects on surface stability. Using density functional theory (DFT) with Hubbard corrections, we evaluated the stability and electronic properties of maghemite's (001) and (111) surfaces under both cubic and tetragonal configurations, while also considering the influence of a Pt substrate and strain arising from lattice mismatch. Our findings indicate that native cubic (001) surfaces are inherently more stable than tetragonal ones. However, the presence of a Pt substrate shifts this stability, favoring the cubic (111) surface presenting a higher adhesion energy. We examined the electronic properties of various cases to provide a rationalization of the observed stability order. Our study provides crucial insights into the impact of crystalline structure and Pt substrate on the stability and favored terminations of maghemite surfaces, emphasizing their prospective utility as water oxidation catalysts.

## 1. Introduction

Iron oxides belong to a family of compounds presenting great interest thanks to their numerous advantages like their abundance, and thus their low-cost, their non-toxicity and also their various properties, like magnetism, allowing numerous potential applications. If hematite or magnetite are the most studied and well-known iron oxides, defective magnetite, namely maghemite, also deserves attention, among others, thanks to its magnetic and catalytic properties. Among a wide range of possibilities, maghemite nanoparticles are often used as clean catalysts, in particular for the removal of pollutants [1–4]. Their magnetic properties are also used in medical applications for specific delivery of drugs [5,6]. Finally, catalysis and especially the energy domain is certainly one of the most important fields of applications of maghemite [7–11], for either carbon fuel cells [12] or water-splitting processes [7,13–16]. For all these applications, the exact nature and structure of these systems can play a fundamental role in their activity. For example, it has been demonstrated that the size of the nanoparticles, and thus the available facets, influence significantly their activity [8,11]. It thus appears critical to know exactly the structure of maghemite. The general structure, namely the spinel structure of magnetite with vacancies in some cation positions, has been set down many years ago [17]. However, due to its high complexity, experimental studies do not agree on the order of the

vacancies and, thus, on the global symmetry. Basically, two models coexist in the literature, namely the cubic one associated with a random distribution of vacancies and the tetragonal one in which vacancies are fully ordered. Indeed, some experiments [18,19] have concluded to a tetragonal symmetry in the P4₁₃₁₂ group, related to a full vacancies ordering. On the contrary, other studies have evidenced the cubic symmetry [20–22]. Finally, some works also mention the evolution from tetragonal to cubic (or conversely), linked with a decrease of particles' size and vacancies ordering [23–26]. From the theoretical point of view, Grau-Crespo et al. [27] have demonstrated that the tetragonal bulk with a full vacancies ordering occurs to be the most stable. On the contrary, for slabs' studies, as far as we know, the non-stoichiometric (Fe₂O₃) cubic system has always been considered [28,29] to reduce the computational cost, with no evidence that this system is the most stable. As mentioned by Grau-Crespo et al. [27] themselves, surfaces' effects can impact the vacancies ordering, so that the highest stability of tetragonal bulk does not give any information on the relative stabilities of the slabs. For instance, Takei and Chiba [30] demonstrated that vacancies are not ordered in epitaxial layers of maghemite, which indicates a cubic symmetry. It thus appears critical to determine the exact structure of slab systems. In practice, thin iron oxide surfaces are usually deposited on a substrate, such as MgO [31,32], Pt [33–38], or

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: celine.dupont@u-bourgogne.fr (C. Dupont).</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. (a) (001) termination of tetragonal model. Lateral view of layers' succession of (001) plane. Layer A consists of two $Fe_{Th}$, layer B of eight O and four $Fe_{O_h}$, and layer C is the same as B but with one vacancy at an octahedral iron site. (b) (111) termination of tetragonal model. Lateral view of layers' succession of (111) plane. Layer A is the same as in (001) case with 8 $Fe_{Th}$, layer D consists of 8 $Fe_{O_h}$, layer E contains 32 O, layers F1 and F2 contain 20 and 16 $Fe_{O_h}$, with 4 and 8 vacancies on octahedral sites, respectively. $Fe_{Th}$ are reported in green, $Fe_{O_h}$ in bronze and O in red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

Fe [39], to enhance stability and promote the development of a specific surface termination. Pt(111) [33,35,37,38] and Pt(100) [32,40] stand out as the primary substrates employed for the epitaxial growth of iron oxides. On Pt(100) surfaces, the resulting iron oxides typically exhibit oxygen deficiency [32,40], therefore, consequently may augment water adsorption on the surface.

In this study, we thus compare the cubic and tetragonal models. Following experimental literature, we made the choice to investigate (001) and (111) slabs. Indeed, several studies have evidenced the growth of $\gamma$-Fe$_2$O$_3$ (001) on MgO(001) slabs [41–43], while the (111) surface has been observed standing alone [44,45]. This stability of the (111) has also been evidenced by Baetzold and Yang [46], who have demonstrated that the (111) surface has the lowest attachment energy, while several other low indices surfaces are polar and unstable. We will thus search to better understand the stability of maghemite (001) and (111) slabs. Previous research has often overlooked the distinct terminations of these surfaces due to presumptions of similarity between magnetite and maghemite structures. We aim to address this gap by exploring the thermodynamic stability of different surface terminations and systematically investigating vacancy distributions. Additionally, we consider the effects of strain and electronic interactions with a platinum substrate to mimic experimental conditions.

## 2. Methods

### 2.1. Computational details

All calculations have been performed using the Vienna ab-initio simulation package (VASP 5.4.4) [47,48] based on plane-wave density functional theory (DFT). As maghemite displays a ferrimagnetic nature, spin-polarized calculations are performed. The interaction between iron-oxygen ions is modeled using the projector-augmented plane-wave (PAW) method [49]. In this method, we explicitly account for eight valence electrons for Fe ($3d^74s^1$), six for O ($2s^22p^4$), and ten for Pt ($5d^96s^1$). The Perdew, Burke and Ernzerhof (PBE) exchange-correlation functional is applied within the framework of the general gradient approximation (GGA) [50]. To consider the long-range interactions, Grimme D3 (DFT-D3) dispersion correction is used with zero damping [51]. Given issues of DFT to properly describe the band-gap due to the excessive electron delocalization typical of transition metal oxides, the Hubbard correction has been applied to the 3d levels of the iron atoms, in the framework of the DFT+U Dudarev approximation [52]. A value of 4.3 eV has been selected for $U_{eff}$ [53,54], leading to a bandgap of 2.1 eV for both cubic and tetragonal models. This value is in good agreement with the experimental bulk bandgap of maghemite ranging from 2.0 to 2.3 eV [55–57].

The Brillouin zone sampling is done by a Monkhorst-Pack k-point mesh of 8 × 8 × 1 for termination (001) as cell size for native system is 8.39 × 8.39 × 42.13 Å, while a 2 × 4 × 1 is used for (111) surface as the

cell size of native surface is 20.59 × 11.89 × 29.55 Å. Gaussian smearing with a width of 0.1 is employed to improve convergence and minimize electronic energy. This is combined with a mixture of the blocked-Davidson scheme and the residual minimization method. The kinetic energy cutoff is set at 550 eV, and convergence thresholds for energy and forces are established at 10⁻⁵ eV and 0.01 eV/Å, respectively. For the pristine maghemite surface, all atoms are allowed to relax. However, in the case of composite structure comprising maghemite/Pt(001), the bottom two layers of the Pt substrate remain fixed. Surface terminations are described using a slab model derived from the bulk, and a 15 Å vacuum is included to prevent unintended interactions with periodic images along the z-direction.

### 2.2. Models

As mentioned above, there exist basically two distinct types of models to describe maghemite: cubic and tetragonal. The cubic model is obtained through its parent structure, magnetite, with a random distribution of the vacancies on iron octahedral sites ($Fe_{O_h}$). By removing 1/3 Fe atoms out of 8a and 16d Wyckoff Fe sites in the Fd3 m space group from the magnetite structure, the maghemite structure can be constructed. It is known that these vacancies (noted as □ in the following) are located on iron octahedral sites. The unit cell configuration of magnetite changes from $Fe_8^{3+}$[$Fe^{2.5+}]_{16}O_{32}$ to $Fe_8^{3+}$[$Fe^{3+}]_{16}O_{32}$ for maghemite, which can be approximated to cubic unit cell as $Fe_8^{3+}$[$Fe^{3+}]_{12}O_{32}$. Therefore, this 8 layers cubic model exhibits a slight excess of vacancies, with three Fe vacancies present in a cubic unit cell. In contrast, a perfectly stoichiometric cell, following a tetragonal model, would entail 8 vacancies of Fe atoms, corresponding to three times the cubic cell, rather than the 9 vacancies observed in the current cubic cell. However, using this cubic model reduces the computational cost by avoiding the large tetragonal supercell, necessary to keep the exact stoichiometry.

Cell parameters for tetragonal model will thus be of 8.39×8.39×25.17 Å, namely the succession of three cubic (8.39 × 8.39 × 8.39 Å) units, consisting of 24 layers. To help the reader, all unit cells used in this study are fully described in Table S1.

### 2.3. Surface terminations and strain

Finally, the constraint due to the lattice mismatch between Pt substrate and maghemite has to be considered for composite structures. This constraint differs significantly between the models and termination planes. Firstly, one has to mention that the (001) orientation of platinum has to be considered to allow the growth of maghemite. Indeed, the use of Pt(111) for example would lead to formation of hematite [58,59], while maghemite can be obtained with Pt(001) [60]. For the tetragonal model cut along the (001) plane, with a cell size of 8.39 × 8.39 Å, a weak strain of about 0.84% is observed in both x and y directions, as we use a 3 × 3 supercell of 8.32 × 8.32 Å for the Pt(001) substrate. However, if maghemite is cut along (111) plane, with a 2 × 2 supercell corresponding to 20.58×11.88 Å, the strain increases to 7.78% along the x-axis and 6.65% along the y-axis as we use a 8 × 4 supercell of 22.19 × 11.09 Å for the Pt(001) substrate. Similarly, for the earlier investigated cubic model [29], (001) terminations have a constraint of 6.65% along both axis, while it is of 4.64% along x and 0.86% along y for (111) terminations.

### 2.4. Energetics

To examine the surface stability, we have calculated the cleavage surface energy with respect to the bulk counterpart. The following formula has been used:

$$ \gamma_{cleav} = \frac{1}{S} \times (E_{slab} - m \times E_{bulk}), \qquad (1) $$
<figure><img src="image_5.png" /><figcaption>Fig. 2. Most stable optimized native surface structures of (001) termination: (a) AB, (b) AC1, and (c) AC2. (TOP row) side views - For the sake of clarity, only some of top and bottom layers are displayed, separated by a dotted blue line. Letters on right correspond to the labels of the top and bottom layers. (MIDDLE row) Top views from the top side. (BOTTOM row) Top views from the bottom side. Full structures are given in SI. Fe<sub>Th</sub> are reported in green, Fe<sub>Oh</sub> in bronze and O in red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

where E<sub>slab</sub> and E<sub>bulk</sub> are the energies of the slab and bulk structures, respectively, while m corresponds to the number of bulk units in the slab and S to the area of the slab unit cell. Cleavage energy is twice the surface energy: γ<sub>cleav</sub> = 2×γ<sub>S</sub> for symmetric slabs and γ<sub>cleav</sub> = γ<sub>S1</sub> + γ<sub>S2</sub> for asymmetric ones.

To analyze growth on platinum, we have separated the impact of Pt induced strain due to lattice mismatch from the interaction between maghemite surfaces and Pt substrate. Firstly, to determine the impact of lattice mismatch, we have calculated the strain energy per unit area defined as follows:

$$ \Delta E_{\text{strain}} = \frac{E_{\gamma-\text{Fe}_2\text{O}_3}^{\text{strained}} - E_{\gamma-\text{Fe}_2\text{O}_3}^{\text{unstrained}}}{S^{\text{strained}}}, \quad (2) $$

where E<sub>unstrained</sub> and E<sub>strained</sub> are the total energy of the maghemite slab, native and strained, respectively, and S<sup>strained</sup> is the area of the strained unit cell. Secondly, to understand the strength of the interaction between Pt(001) and strained maghemite, we have computed the interaction energy per surface unit with the following equation:

$$ \Delta E_{\text{int}} = \frac{E_{\gamma-\text{Fe}_2\text{O}_3/\text{Pt}} - E_{\gamma-\text{Fe}_2\text{O}_3}^{\text{strained}} - E_{\text{Pt}}}{S^{\text{strained}}}. \quad (3) $$

where E<sub>γ-Fe<sub>2</sub>O<sub>3</sub>/Pt</sub> is the total energy of the whole system, E<sub>γ-Fe<sub>2</sub>O<sub>3</sub></sub><sup>strained</sup> is the total energy of strained maghemite surface and E<sub>Pt</sub> is the total energy of the Pt(001) substrate.

In the following, we will also discuss the adhesion energy, which takes into account the combined effect of strain and interaction with Pt substrate, defined as the sum of strain and interaction energies, namely:

$$ \Delta E_{\text{adh}} = \frac{E_{\gamma-\text{Fe}_2\text{O}_3/\text{Pt}} - E_{\gamma-\text{Fe}_2\text{O}_3}^{\text{unstrained}} - E_{\text{Pt}}}{S^{\text{strained}}}. $$

that is to say:

$$ \Delta E_{\text{adh}} = \Delta E_{\text{strain}} + \Delta E_{\text{int}} \quad (4) $$

Adhesion energy considers the destabilization caused by lattice constraints and the stabilization on the Pt substrate, but overlooks the energy required to construct the surface from its bulk counterpart. To address this and evaluate the relative stability of the surface grown on a Pt substrate, we have also analyzed the formation energy of the surface in relation to the bulk structures of maghemite:

$$ E_{\text{form}} = \frac{E_{\gamma-\text{Fe}_2\text{O}_3/\text{Pt}} - E_{\text{Pt}} - E_{\gamma-\text{Fe}_2\text{O}_3}^{\text{bulk}}}{S^{\text{strained}}}. \quad (5) $$

## 3. Results

### 3.1. Stability of (001) and (111) surfaces of tetragonal model

The stability of native (001) surface is first analyzed. When cutting tetragonal bulk along the (001) plane with a thickness of 24 layers, three different combinations of terminations (AB, AC1, and AC2) are obtained (see Fig. 2). In this model, layer A consists of two tetrahedral iron (Fe<sub>Th</sub>), layer B of eight oxygen and four octahedral iron (Fe<sub>Oh</sub>), and layer C contains one vacancy at an octahedral iron site (see Fig. 1). Here, AC1 and AC2 only differ due to ordering differences in underlying layers below the terminal layers. Comparing cleavage energies shows that these surfaces exhibit different stabilities, with AB (γ<sub>cleav</sub> = 155 meV/Å<sup>2</sup>) being the most stable, followed by AC2 (γ<sub>cleav</sub> = 186.5 meV/Å<sup>2</sup>) and then AC1 (γ<sub>cleav</sub> = 194 meV/Å<sup>2</sup>) as native surfaces. The AB termination does not have any vacancies on the surface and consists of Fe<sub>Th</sub> and Fe<sub>Oh</sub> atoms. Conversely, AC1 and AC2 terminations involve Fe<sub>Th</sub> and vacancies within the Fe<sub>Oh</sub> atomic positions. This observation is in line with earlier findings [29,61] that highlight the destabilizing influence of surface vacancies.

The impact of compressive strain due to lattice mismatch with the Pt substrate is now considered. As the strain is only of 0.84%, it induces
<figure><img src="image_6.png" /><figcaption>Fig. 3. Most stable optimized native surface structures of (111) termination: (a) AD and (b) EF1. (TOP row) side views - For the sake of clarity, only some of top and bottom layers are displayed, separated by a dotted blue line. Letters on right correspond to the labels of the top and bottom layers. (MIDDLE row) Top views from the top side. (BOTTOM row) Top views from the bottom side. Full structures are given in SI. Fe<sub>Th</sub> are reported in green, Fe<sub>Oh</sub> in bronze and O in red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

a slight destabilization of surfaces by about 2–4 meV/Å², leaving the
relative order of stability unchanged (see Fig. 5a).

Cutting surfaces along (111) direction is not as straightforward as the case of (001), due to the substantial size of the supercell and the in-plane angle different from 90°. A C-centered transformation matrix has thus been used to transform the lattice vectors and make them orthogonal. To address the size issue, we adopt a magnetite structure to construct the (111) surface with randomly distributed vacancies. We systematically investigate the most stable configuration for distributing Fe<sub>Oh</sub> vacancies on this surface as detailed in SI. Starting from the obtained configurations, surfaces cut along (111) consists of 18 layers from five different types: layer A contains 8 Fe<sub>Th</sub>, layer D contains 8 Fe<sub>Oh</sub>, layer E consists of 32 O and layers F1 and F2 have 20, or 16, Fe<sub>Oh</sub> with four or eight vacancies on octahedral sites, respectively. Several combinations of these layers terminations have been investigated, but only the two most stable, namely EF1 and AD (see Fig. 3), will be detailed. Interestingly, the two native AD and EF1 surfaces have very close cleavage energies, with γ<sub>cleav</sub>(AD) = 279 meV/Å<sup>2</sup> and γ<sub>cleav</sub>(EF1) = 281 meV/Å<sup>2</sup>. When strain (7.78% and 6.65% along x and y, respectively) is applied, the situation evolves: both terminations are destabilized, but the destabilization is twice larger for EF1 (ΔE<sub>strain</sub> = 56 meV/Å<sup>2</sup>) than for AD (ΔE<sub>strain</sub> = 29 meV/Å<sup>2</sup>) (see Table 1). As a consequence, in presence of strain, AD (γ<sup>strain</sup><sub>cleav</sub> = 308 meV/Å<sup>2</sup>) is finally more stable than EF1 (γ<sup>strain</sup><sub>cleav</sub> = 335 meV/Å<sup>2</sup>).

Finally, as mentioned in the introduction, ultimate goal is to de-
termine the structure of the epitaxial film of maghemite preferentially
grown on platinum. To do so, we compute the formation energy, re-
flecting the cost for the obtention of epitaxial film from bulk maghemite
and platinum. If all classical relative positions (top, bridge and hollow)
between maghemite and platinum have been probed (see Table S2),

<figure><img src="image_7.png" /><figcaption>Fig. 4. Pt supported (001) and (111) terminations of tetragonal model. (TOP row) three terminations (AB, AC1, and AC2) of the (001) plane on Pt. (BOTTOM row) both terminations (AD and EF1) of the (111) plane on Pt. Full structures as well as corresponding top views are given in SI. Fe<sub>Th</sub> are reported in green, Fe<sub>Oh</sub> in bronze and O in red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

only most stable cases are discussed and reported in Fig. 4, while
associated formation energies can be obtained on Fig. 6. When ad-
sorbed on platinum, the tetragonal AB(001) surface occurs to be the
most favorable with E<sub>form</sub> = 51 meV/Å<sup>2</sup>, followed by AC2(001) (E<sub>form</sub>
= 59 meV/Å<sup>2</sup>), EF1(111) (E<sub>form</sub> = 85 meV/Å<sup>2</sup>), AC1(001) (E<sub>form</sub>
= 103 meV/Å<sup>2</sup>), and AD(111) (E<sub>form</sub> = 136 meV/Å<sup>2</sup>) (see Fig. 6 -
Left). One can note the crucial influence of the substrate. While native
and constrained tetragonal (111) surfaces were significantly less stable
<figure><img src="image_8.png" /><figcaption>Fig. 5. Results for (Left) tetragonal model and (Right) cubic one. Cleavage energy in meV/Å² for (001) surface termination in the top row (a and b) and (111) surface termination in the bottom row (c and d) are presented. Values for unconstrained systems are reported with crosses, while diamonds stand for constrained ones.</figcaption></figure>

Source: Values for cubic model are taken from [29].

<figure><img src="image_9.png" /><figcaption>Fig. 6. Formation energy in meV/Å² for (Left) tetragonal model and (Right) cubic of (001) and (111) surface termination. Circles stand for (001) termination, while triangles correspond to the (111).</figcaption></figure>

Source: Values for cubic model are taken from [29].

than their (001) counterparts, when grown on platinum, EF1(111) is significantly stabilized and becomes more stable than AC1(001). This behavior can be explained by the relationship with Pt substrate. Indeed, the constraint differs significantly between the (001) and (111) surfaces. Specifically, the (001) surface experiences a minor constraint (0.84% in both directions) compared to the (111) surface (7.78% along the x-axis and 6.65% along the y-axis). This lower amount of strain puts up by (001) surfaces gives them a higher stability compared to (111) ones. On the contrary, interaction between (111) terminations and Pt substrate is widely favored compared to (001) terminations (see Fig. S8).

In summary, tetragonal model native slabs of γ-Fe₂O₃(001) predominantly demonstrate higher stability in contrast with (111). Under strain, the surfaces are destabilized in proportion to the applied strain. Pt substrate considerably stabilizes (111) termination in comparison with (001), leading to competing (111) surfaces on Pt with (001) terminations.

## 3.2. Density of states (DOS) for (001) and (111) surfaces of tetragonal model

To examine the electronic characteristics of these surfaces, we have generated projected density of states (PDOS) plots for the most stable configurations (see Figs. 7 and 8 for (001) and (111) surfaces, respectively). To avoid confusion, we exclusively depict the states related to Fe<sub>Th</sub>, Fe<sub>Oh</sub>, and O, while DOS including Pt states are reported in SI (Fig. S10). The energy reference point is set to the respective Fermi energy of each surface. The valence bands are primarily composed of O-p states with a minor contribution from Fe<sub>Th</sub> or Fe<sub>Oh</sub> states, while the conduction bands are predominantly populated by Fe-d states as observed earlier [28,29]. Notably, the bandgap of these surface layers is narrower and lower than their corresponding bulk counterparts [62,

<caption>Table 1</caption>

Strain energies, interaction energies, and adhesion energies of AB, AC, AC2, AD, and EF1 for tetragonal model.

<table><thead><tr><th>Surface</th><th>Strain energy (meV/Å<sup>2</sup>)</th><th>Interaction energy (meV/Å<sup>2</sup>)</th><th>Adhesion energy (meV/Å<sup>2</sup>)</th></tr></thead><tbody><tr><td>AB(001)</td><td>3</td><td>-115</td><td>-113</td></tr><tr><td>AC1(001)</td><td>2</td><td>-101</td><td>-99</td></tr><tr><td>AC2(001)</td><td>2</td><td>-138</td><td>-135</td></tr><tr><td>AD(111)</td><td>29</td><td>-172</td><td>-143</td></tr><tr><td>EF1(111)</td><td>56</td><td>-251</td><td>-195</td></tr></tbody></table>

[63]. In some instances, a few states appear within the bandgap region, primarily originating from unsaturated Fe/O species present on the surfaces (see bandgap region of Fig. 7).

In the case of the (001) surface, AB and AC2 configurations exhibit a larger bandgap than AC1 which presents some states crossing the Fermi energy for the bare surface. When these (001) surfaces are put on Pt substrate, the Fermi energy experiences a slight shift towards the center of the band gap. A minor change is observed in the Fe or O atoms states, which depends on the nature of the interaction layer of the (001) surface with Pt. Additionally, the appearance of a limited number of states within the bandgap region decreases upon placement on Pt substrate, consistent with our earlier findings for the cubic model (see Ref. [29] for DOS of cubic model). These observations also hold true for (111) surfaces (see Fig. 8). Furthermore, the bandgap is much smaller in the case of (111) native surfaces due to a higher number of states in the bandgap region. The bandgap increases when placed on Pt substrate, and almost no states are present in the bandgap region due to the saturation surface atoms by Pt.

## 3.3. Comparison between cubic and tetragonal models

In this study, we thoroughly examined the behavior of (001) and (111) terminations obtained from the tetragonal model, while the cubic one has already been investigated in an earlier work [29]. A comparison of surfaces coming from both models appears now as essential. Among native surfaces, cubic (001) is the most stable termination, followed by tetragonal (001), cubic (111), and tetragonal (111) as the least stable one (see Fig. 5). This is mainly due to the intrinsic stability of the slabs, as there is no external factor of strain or substrate influence. One can note that the slight over vacancy of Fe<sub>Oh</sub> in cubic model has some stabilizing influence on the relative behavior of (001) and (111) terminations. This stabilizing effect is particularly important for (111) surfaces, as native (111) surfaces are nearly 96 meV/Å² less stable for tetragonal (γ<sub>cleav</sub><sup>AD</sup> = 279 meV/Å²) than for cubic model (γ<sub>cleav</sub><sup>AD</sup> = 183 meV/Å²). However, this effect is slightly moderate on (001) surfaces, with an energy difference of 18 meV/Å² between AB cubic (001) and AB tetragonal (001) surfaces (see Fig. 5).

Under compressive strain, (001) surfaces are destabilized for both cubic and tetragonal models, with a lower impact for tetragonal one, due to a weaker strain of 0.84% compared to 6.65% for cubic case. Under strain, (111) surfaces of both tetragonal and cubic models get destabilized, but destabilization is higher on the tetragonal model due to the larger strain. Moreover, destabilization caused by strain is different between the two surfaces (AD and EF1) of tetragonal model, which is not the case in cubic model. Strain destabilizes the EF1 surface twice as much as AD one (see Fig. 5b and d). The distinct behavior exhibited by AD and EF1 results from alterations in electronic properties induced by strain. As one side of EF1 is terminated by O-atoms, these unsaturated O-atoms are further destabilized by the constraint. This is reflected by an augmentation in oxygen states within the bandgap region for EF1 under strain, whereas AD shows minimal change (see Fig. 7).

Finally, when these surfaces are grown on Pt substrate, they undergo certain structural modifications as a consequence of Pt-O or
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Density of states (DOS) of AB, AC1, AC2 terminations of (001) surface of tetragonal model. (TOP row) Native (001) surface. (BOTTOM row) (001) surface on Pt substrate. Positive scale states are Spin Up, and negative scale state represents Spin Down.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Density of states (DOS) of AD and EF1 terminations of (111) surface of tetragonal model. (TOP row) Native (111) surface. (BOTTOM row) (111) surface on Pt substrate. Positive scale states are Spin Up, and negative scale state represents Spin Down.</figcaption></figure>

Pt-Fe interactions. To assess their relative stability, we compare their respective formation energy (Fig. 6). For tetragonal model, AB and AC2 of (001) terminations are more stable (about more than 30 meV/Å²) than (111). However, the inverse holds true for cubic model where (111) termination is more stable than (001). In overall stability order, EF of cubic (111) is the most stable surface termination, followed by AB of tetragonal (001), AD of cubic (111), AC2 of tetragonal (001), and EF1 of tetragonal (111). Here, the stability order of various surfaces is predominantly driven by interaction at maghemite/Pt interface and the strain effect, without any straightforward link with the considered model or termination. A higher amount of strain gives rise to higher strain energy. Moreover, the interaction energy is higher when there are more Pt-O bonds at the interface over Pt-Fe bonds ($\Delta E_{int}(\text{AD}) = -172$ meV/Å² vs. $\Delta E_{int}(\text{EF1}) = -251$ meV/Å²) (see Table 1); therefore, each heterostructure maximizes the possibility of having more Pt-O bonds. The relative stability of (001) termination for tetragonal and cubic models can thus be explained by the strain difference between the two models and the number of Pt-O bonds present in each system.

On the contrary, the two EF and EF1 structures of the (111) surfaces, from cubic and tetragonal models respectively, have similar density of Pt-O bonds, as seen by similar interaction energies, namely $\Delta E_{int}(\text{EF}) = -266$ meV/Å² and $\Delta E_{int}(\text{EF1}) = -251$ meV/Å². The difference in their stability thus comes from the higher strain felt by the EF1 (tetragonal) compared to the EF (cubic) structure. The destabilization of 33 meV/Å² in EF1 (tetragonal) with respect to EF (cubic), which thus comes from higher strain energy. To confirm this point, we compared the adhesion energy, which combines strain and interaction energy. Interestingly,

due to the very high strain energy for EF1, almost four times higher than for EF (14 meV/Å² vs. 56 meV/Å²), the adhesion energy of EF1 (-195 meV/Å²) is considerably lower than the one of EF (-251 meV/Å²). Therefore, the higher stability of EF in comparison to EF1 is due to its lower strain energy and higher adhesion energy. Furthermore, the presence of slight overvacancy of $Fe_{Oh}$ in the cubic model, in contrast with the tetragonal model, could also play a role in stability. This can be clearly seen by the huge difference between the AD surface of the two models, where strain and vacancy both play a role.

In summary, when it comes to native surfaces, the (001) surfaces of cubic and tetragonal structures are more stable compared to the (111) termination. However, when placed on a Pt substrate, the stability order shifts, cubic (111) demonstrates the lowest formation energy, similar as tetragonal (001). Nevertheless, one has to note that cubic (111) presents an adhesion energy two times higher than tetragonal (001), which will certainly favor the starting growth of cubic (111) over a Pt substrate. Cubic (111) and tetragonal (001) are then followed by tetragonal (111), and finally, cubic (001). This shift is attributed to variations in the number and in the strength of Pt-O bonds, as well as to the level of strain. All stability orders for various models and terminations have been summarized in Table S1. Thus, according to our results, maghemite should grow with the cubic (111) structure when put on Pt(001) substrate. This result fully agrees with experimental works. Firstly, Takei and Chiba [30] have evidenced that, when epitaxially grown on MgO(001), layers of $\gamma$-Fe$_2$O$_3$ present a cubic structure, excluding vacancies ordering. More recently, Paparoni et al. [60] have obtained the (111) facet, when Ni-doped maghemite is epitaxially grown on Pt(001).

## 4. Conclusion

In this study, we conducted a comprehensive comparison of two distinct maghemite models, each featuring their most prominent surface terminations, specifically the (001) and (111) orientations. This comparative analysis encompassed structural and electronic properties, including DOS, providing valuable insights into the behavior of these models.

From an energetic perspective, when considering the surface energies of bare surfaces, the (001) surface exhibits greater thermodynamic stability than the (111) surface. Among (001) surfaces on one side and (111) on the other side, cubic structures are always favored over tetragonal ones.

When these surfaces are placed on Pt substrate, some (111) surfaces gain huge stability with several Pt-O and/or Pt-Fe bonds and become competitive or even more stable with respect to (001). Energetically, when considering the formation energies, EF(111) termination from the cubic model appears to be the most favorable, in close competition with tetragonal AB(001) followed by cubic AD(111), tetragonal AC2(001), and tetragonal EF1(111) terminations. Therefore, overall, the stability
order of various surfaces on Pt substrate compared is the following: cubic (111) ≈ tetra (001) > tetra (111) > cubic (001). Besides, our results demonstrate the competitiveness between cubic and tetragonal models and thus justify that both can be experimentally obtained, depending on preparation conditions. This comprehensive study allows to better know structure of epitaxially grown maghemite and thus paves the way for further investigations and a better understanding of reactivity of maghemite surfaces.

## CRediT authorship contribution statement

**Amit Sahu:** Writing – original draft, Data curation. **Céline Dupont:** Writing – review & editing, Supervision, Funding acquisition, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

This work was financially supported by Agence Nationale de la Recherche (ANR), France project OPTYMAL grant number ANR-20-CE42-0015-02 and ANR-17-EURE-0002 (EIPHI Graduate School). The calculations were performed at Centre de Calcul de l'Université de Bourgogne (CCuB) and IDRIS. We are thankful to HPC resources from IDRIS under allocation of A0130811108. We are also grateful to Prof. Bruno Domenichini for his insight and fruitful discussion on this work.

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.surfin.2024.105377. In supporting information, we have reported full representations of all structures discussed in the main text. We have detailed the study of vacancies location for tetragonal (111) termination. A summary of the relative energies of all considered systems is also reported. Data related to various electronic properties such as magnetic moment, workfunction, and charge transfer, are also given in SI. Finally, all coordinates of relevant structures have been given in the final section of supporting information.

## Data availability

Data will be made available on request.

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