Partial dissociation of water on Fe$_{3}$O$_{4}$(001): adsorbate induced charge and orbital order

The interaction of water with Fe$_3$O$_4$(001) is studied by density functional theory (DFT) calculations including an on-site Coulomb term. For isolated molecules dissociative adsorption is strongly promoted at surface defect sites, while at higher coverages a hydrogen-bonded network forms with alternating molecular and dissociated species. This mixed adsorption mode and a suppression of the $(\sqrt{2}\times \sqrt{2})R45^{\circ}$-reconstruction are confirmed by a quantitative low energy electron diffraction (LEED) analysis. Adsorbate induced electron transfer processes add a new dimension towards understanding the catalytic activity of magnetite(001).

The interaction of water with Fe3O4(001) is studied by density functional theory (DFT) calculations including an on-site Coulomb term. For isolated molecules dissociative adsorption is strongly promoted at surface defect sites, while at higher coverages a hydrogen-bonded network forms with alternating molecular and dissociated species. This mixed adsorption mode and a suppression of the ( √ 2 × √ 2)R45 • -reconstruction are confirmed by a quantitative low energy electron diffraction (LEED) analysis. Adsorbate induced electron transfer processes add a new dimension towards understanding the catalytic activity of magnetite(001). Magnetite has attracted continued interest in the past decades due to its fascinating properties: The high temperature phase is predicted to be a half-metallic ferrimagnet [1] with high magnetic ordering temperature. At around 120 K it undergoes the so called Verwey transition [2]. Both the type of transition (metal-to-insulator vs. semiconductor-to-semiconductor [3,4]) and the type of charge (CO) and orbital ordering (OO) at the octahedral iron sites in the low temperature phase are subject of an ongoing debate [5,6,7,8].
Besides its applications in magnetic recording and as a prospective material for spintronics, magnetite acts as a catalyst e.g. in environmental redox reactions [9,10], or in the water gas phase shift reaction [11]. Typically these reactions take place in an aqueous environment prompting the need to understand how water interacts with the Fe 3 O 4 -surface. Water can bind to a surface in different modes (e.g. molecular or dissociative) leading to a variety of functional groups that can affect significantly the surface properties and availability of reaction sites and result in a complex surface chemistry [12,13].
The catalytic activity of magnetite is typically related to the presence of both ferrous and ferric iron in its inverse spinel structure. In the [001]-direction two types of layers alternate: A-layers with tetrahedral iron (Fe A 3+ ) and B-layers containing oxygen and octahedral iron (Fe B 2+,3+ ). Both bulk truncations of Fe 3 O 4 (001), either with an A-or a B-layer are polar of type three according to the classification of Tasker [14]. To explain the origin of the ( √ 2 × √ 2)R45 • -reconstruction previous surface models proposed an ordering of surface defects (e.g. [15,16]). Recently, DFT calculations [17,18] have shown that the symmetry lowering at Fe 3 O 4 (001) is achieved rather by a distorted B-layer, supported also by surface x-ray diffraction [17], LEED [19] and scanning tunneling microscopy (STM) [20]. * Electronic address: pentcheva@lrz.uni-muenchen.de Despite its importance, only a few studies have addressed the interaction of water with Fe 3 O 4 (001). While initial adsorption was related to surface defect sites, an extensive hydroxylation was reported from x-ray photoemission experiments (XPS) beyond a threshold pressure of 10 −3 − 10 −4 mbar [21]. Both this study and temperature programmed desorption (TPD) measurements [22] indicate multiple adsorbate sites on the surface. Molecular dynamics simulations with empirical potentials [23,24] point towards a dissociative adsorption. However, such studies cannot provide reliable information on the energetics and underlying electronic phenomena.
Here we address these fundamental questions within a combined DFT and LEED approach. By varying the coverage and adsorbate configuration of water molecules we compile a surface phase diagram in the framework of ab initio thermodynamics. The results show that isolated molecules dissociate on the clean Fe 3 O 4 (001) surface. This process is strongly favored at oxygen vacancies. With increasing coverage a crossover to a mixed adsorption (both molecular and dissociative) takes place that is confirmed in a quantitative LEED analysis. LEED shows also a strong suppression of the ( √ 2 × √ 2)R45 • surface reconstruction. Furthermore we find that the adsorbed species invoke electron transfer processes in the subsurface layers resulting in an unique charge and orbital order that may have important implications on the catalytic activity of the surface.
DFT calculations were performed using the full potential linear augmented plane wave method in the WIEN2K [25] implementation. The generalised gradient approximation (GGA-PBE) [26] of the exchangecorrelation potential is used. Systematic studies [27,28] show that the PBE functional gives a good description of hydrogen bonding w.r.t. equilibrium geometries. The error of overbinding which can be as large as 20 meV/bond will not affect our conclusions. Because magnetite is a strongly correlated material we have explored the influence of electronic correlations within LDA/GGA+U [29] using U = 5 eV and J = 1 eV [30], similar to values used for bulk Fe 3 O 4 [6,7,31]. The surfaces were modelled in the supercell geometry with slabs containing seven Blayers and six A-layers separated by a vacuum region of 10-12Å[32]. The positions of adsorbates and the atoms in the outer two BA-layers were relaxed.
We have compared the stability of more than 30 different configurations using ab initio thermodynamics [33].
The surface energy, γ(T, p) depends on the Gibbs free energy and the chemical potentials of the constituents. The Gibbs free energy can be expressed through the total energy from the DFT-calculations [33]. Because there are two species in the gas phase, O 2 and H 2 O, the surface phase diagram is three dimensional. Fig. 1 displays a two dimensional projection with the most stable configurations for given µ O , µ H2O . We first consider the termination of the clean surface as a function of oxygen pressure. As discussed previously, a modified B-layer (denoted as B) showing lateral and vertical distortions in the surface layer with a wave-like pattern is favored over a broad range of oxygen pressures. However, at oxygen poor conditions a B-layer with oxygen vacancies (B+V O ) is stabilized. This defective surface, previously proposed in a STM study [16], shows dramatic relaxations where the oxygen opposite the vacancy moves towards the Fe B -row by ∼0.8Å. Starting from these two terminations [34], we have adsorbed water molecules, varying their concentration and geometry. We find a strong tendency for isolated molecules to dissociate in surface oxygen vacancies (V O +OH) whereby a proton diffuses to a surface oxygen (O S ) further away and forms a surface OH-group (O S +H). Thus, even at very low water vapor pressures, all surface defects are expected to be filled with OH-groups, consistent with XPS results [21]. The dissociation of water in the defect sites invokes significant changes in the electronic structure as shown in Fig. 2a and c, involving the 1π and 3σ molecular orbitals of the OH groups and a switching from Fe 3+ to Fe 2+ of Fe B S-1 underneath O S +H.
The adsorbate-adsorbate interaction that sets in, when a second molecule is adsorbed within the ( √ 2 × √ 2)R45 • unit cell, leads to a mixed adsorption mode: One molecule dissociates protonating a surface oxygen, while the intact molecule forms a hydrogen bond with the OH-group. The main part of the phase diagram is dominated by a mixed adsorption mode of four water molecules where all surface Fe B -sites (Fe B S) are saturated (B+4H 2 O(M)). Full dissociation is 12 meV/Å 2 less stable. Full hydroxylation of the surface is also not likely to occur as the formation of a surface OH-group neighboring a subsurface Fe A is extremely unfavorable.
The electron density redistribution with respect to the B-layer in Fig. 2b indicates a weak charge accumulation between Fe B S and the water molecule (O w ), but the strongest charge rearrangement takes place between Fe B and the OH-group (O OH ) of the dissociated molecule, in- volving depletion of 3σ and accumulation in 1π molecular orbitals of OH along with depletion of the d z 2 orbital at Fe B S. The main actuator of partial dissociation appears to be the formation of strong intermolecular hydrogen bonds. As a result both H 2 O and OH tilt from the ontop position towards each other and O w -H elongates from 0.95Å (gas phase) to 1.10Å, resulting in an O w -H···O OH of 2.47Å. A fingerprint of the mixed adsorption are the two distinct bond lengths between Fe B -O w and Fe B -O OH of 2.09Å and 1.97Å respectively. This feature is confirmed by the LEED analysis described below.
LEED measurements were performed on a synthetic magnetite sample. The clean surface, prepared by Ar +ion sputtering and subsequent annealing at 900-1000 K at p O2 = 5 × 10 −7 mbar for 2-3 h, exhibited a ( √ 2 × √ 2)R45 • -LEED pattern with sharp superstructure reflections and low background (Fig. 3 a). Water was adsorbed at 273 K for 2 min at a water vapor pressure of 2×10 −6 mbar, resulting in a (1×1)-LEED pattern with an enhanced background (Fig. 3b). While annealing up to 770 K restores the superstructure spots, the shape of the the LEED I(V ) curves cannot be recovered [37], indicating some residual hydroxylation of the surface, as observed by Kendelewicz et al. [21]. Seven LEED I(V ) curves of the (1 × 1)-surface were measured in the energy range 50 -300 eV at 100 K. An increase of the background current during the measurement is attributed to uncorrelated defects induced by the electron beam [38]. However, no changes were observed in the LEED I(V ) curves during repeated measurements over periods of several hours.
LEED calculations were performed with the layer doubling method and a least squares optimization [35] using constraints for bond lengths. The crystal potential was calculated from a superposition of atomic potentials using optimized muffin-tin radii [36] which led to reliable structural determination of the clean Fe 3 O 4 (001)surface [19]. 10 phase shifts were used. All positions and occupation numbers within the adsorbate and top B-A-B substrate layers were optimized in a ( √ 2 × √ 2)R45 • -unit cell, while thermal parameters were kept fixed. The best fit (R P = 0.27) was obtained for a model where all Fe B S sites have adsorbed oxygen on top. Both the surface Fe B -and adsorbate sites are occupied by ∼ 80% possibly due to defect creation during the preparation procedure.  will be published elsewhere [37].
We turn next to the surface and adsorbate induced electronic effects on Fe 3 O 4 (001). The electron density plot in Fig. 4 displays the minority t 2g occupancies at the Fe B -sites, thus allowing to distinguish between sites with predominant Fe 2+ or Fe 3+ -character [30]. The notation Fe 2+ and Fe 3+ is used here for simplicity, but the difference in total 3d occupation within the muffintin sphere is much smaller (0.2-0.4e) consistent with XRD- [5] and LDA+U studies for the low temperature bulk phase [6,7]. The magnetic moments allow a clearer discrimination: M Fe 2+ = 3.54 − 3.75µ B , M Fe 3+ = 3.90 − 4.10µ B , respectively. For most of the stable systems we find that the surface layer contains exclusively Fe 3+ while a unique charge and orbitally ordered state emerges in the deeper layers depending on the type of termination [39]. In B+V O (Fig. 4a) [31]. Here the presence of a surface and adsorbates imposes a unique CO/OO state for each ter- cubes in the surface and subsurface layer are predominantly electron poor (3Fe 3+ +1Fe 2+ ), while those in S-1 and S-2-layer are electron rich (1Fe 3+ +3Fe 2+ ). Evidence for orbital ordering in thin magnetite films was reported recently from resonant soft x-ray diffraction [8].
The charge ordered state in the B-layer leads to the opening of a band gap of 0.3 eV as shown in Fig. 2d, consistent with previous calculations [18] and scanning tunneling spectroscopy measurements [40]. However the adsorption of water on the surface and the formation of surface hydroxyl groups leads to half-metallic behavior.
We have shown that on Fe 3 O 4 (001) water tends to dissociate in oxygen vacancies or partially dissociate on the nondefective surface in contrast to the full dissociation found on Fe 3 O 4 (111) [21,41]. This adsorption mode is triggered by the presence of both Lewis acid and base sites on the surface and the intermolecular interaction as reported also on rutile(110) [42], anatase(001) [43] and MgO(001)-surfaces [44]. The hydrogen bonded OH and H 2 O can easily rearrange and thus provide adsorption sites for further species (e.g. heavy metal complexes).
Our results indicate a pathway to manipulate e.g. the catalytic properties of transition metal oxide surfaces by triggering electron transfer processes and inducing new charge and orbitally ordered states via adsorbates.