Kinetics and intermediate phases in epitaxial growth of Fe₃O₄ films from deposition and thermal reduction

Magnetite (Fe₃O₄), as one of the phases of iron oxides, has been of wide usage in, e.g., pigments, magnetic recording, and catalysis, due to their useful optical, magnetic, and chemical properties and the low cost. Additional applications are constantly being explored in Fe₃O₄, particularly in molecular biology and spintronics, because of its bio-compatibility and special electronic structures, respectively.^1–6 

In the thermodynamic standard conditions, Fe₃O₄ is a metastable phase of iron oxide, which has an inverse spinel structure (space group Fd-3 m).⁷ In Fe₃O_4, the cubic unit cell contains eight formula units that can be written as (Fe³⁺)₈[Fe³⁺Fe²⁺]₈O₃₂. The Fe²⁺ and Fe³⁺ cations are located in the interstitial sites of oxygen anions sub-lattice. One cation site, occupied only by Fe³⁺ ions, is tetrahedrally coordinated to oxygen. The other site, occupied by equal numbers of Fe²⁺ and Fe³⁺ ions, is octahedrally coordinated to oxygen. Below T_N ≈ 860 K, Fe₃O₄ is ferrimagnetic, in which the magnetic moments of the Fe³⁺ in two different sites cancel each other while the moments of the Fe²⁺ are aligned and form a spontaneous magnetization.⁸ The resistivity of Fe₃O₄ decreases when temperature increases, with a rapid change at T_V ≈ 120 K, noted as the Verwey transition, which is often considered as a signature of the Fe₃O₄ phase.^9–13 

Great efforts have been devoted to preparing epitaxial Fe₃O₄ thin films using pulsed laser depositions (PLDs), with a variety of target materials to begin with, including metal Fe,¹⁴ Fe₃O₄,^9,15–18 and Fe₂O₃.^9–12,19 The structural phase and the oxygen stoichiometry of the films are sensitive to the growth conditions, especially temperature and background O₂ pressure.¹⁵ Therefore, thermodynamics and chemical reactions on the substrate are the key for the growth of Fe₃O₄ films, as also indicated by many studies on the transitions between iron oxide phases using surface characterizations.^20–30 The surface structures, including termination, reconstruction, and morphology, have been the focus of study.^20–23,26 On the other hand, the kinetics of the transitions (time scale as a function of conditions) have seldom been systematically investigated, although the important energetic information can be extracted from the kinetics, and the time scale itself is a critical factor both for studying and for applying these transitions.

In this work, we studied the growth of Fe₃O₄ thin films using thermal reduction from the deposited Fe₂O₃ layers on Al₂O₃ (001) substrates. The time-resolved transitions between different phases of iron oxide were measured, using the reflection high energy electron diffraction (RHEED), around the phase boundaries. In particular, the transition from an α-Fe₂O₃ (001) layer to an Fe₃O₄ (111) layer shows a long temperature-dependent time constant that follows the Arrhenius law with an activation energy of 2.3 ± 0.6 eV; the activation energy does not change significantly with the O₂ pressure while the time constant decreases with increasing pressure. These studies on kinetics of transitions between iron oxide phases at the surface are important for advancing our understanding on the response of the iron oxide surfaces to oxidation and reduction environments, which is critical in the application of iron oxides in heterogeneous catalysis, spintronics, and biomedicine.

The film deposition was carried out on 0.2° miscut and one side polished sapphire Al₂O₃ (001) substrates using pulsed laser deposition (PLD), in 5 × 10⁻³Torr O₂, with 600 °C substrate temperature. The substrates temperature was controlled by an infrared laser by heating an absorber mechanically attached to the back. Both the temperature of the absorber and the temperature of the substrate were monitored using two separate pyrometers. The uncertainty of the temperature measurements was about 50 °C. Before deposition, the substrates were annealed in base pressure (lower than 1 × 10⁻⁷ Torr) at 600 °C for 30 min. Each deposition corresponds to 500 laser shots and to an epilayer of approximately 2.5 nm. The target used for the deposition is Fe₂O₃ pellet prepared from high purity Fe₂O₃ powder, sintered at 1400 °C for 24 h. An excimer laser (KrF, λ = 248 nm) was used at a fluence of 1.8 J/cm² and a repetition rate of 2 Hz. The target to substrate distance was kept at 5 cm. Thermal reduction of the α-Fe₂O₃ epilayers was carried out by heating the sample to a high temperature in a low O₂ pressure after the deposition of the target material. The transition between the iron oxide phases were studied using a time-resolved RHEED in which the images were taken automatically every 15 s. X-ray diffractions (XRD) were measured (θ–2θ scan) using a Rigaku D/Max-B diffractometer, with a cobalt K-$α$ source (⁠$λ=1.79$ Å). The rocking curves were measured using a Rigaku SmartLab with a copper K-$α$ source (⁠$λ=1.54$ Å). Magneto optical Kerr effect (MOKE) on the iron oxide films was measured using a He-Ne laser (632.8 nm) and a photoelastic modulator, in a longitudinal geometry. Atomic force microscopy (AFM) was studied using a Bruker Dimension ICON at room temperature. Temperature dependent resistivity was measured in a Janis cryostat using a Van der Pauw geometry.

First, we examine the different iron oxide phases that appeared during the growth, including hematite (α-Fe₂O₃), maghematite (γ-Fe₂O₃), and magnetite (Fe₃O₄) (Fig. 1). Figure 2 shows the RHEED patterns of the iron oxide layers as well as the Al₂O₃ (001) substrate, where Figs. 2(a), 2(c), 2(e), and 2(g) correspond to the condition in which the electron beam points along the Al₂O₃ ⟨001⟩ direction, while Figs. 2(b), 2(d), 2(f), and 2(h) correspond to the condition in which the electron beam points along the Al₂O₃ ⟨120⟩ direction; the two directions are perpendicular to each other. These phases, as well as their epitaxial relations with the Al₂O₃ (001) substrate, are identified, according to the RHEED pattern, condition of appearance, and ex-situ characterizations. The structure of these phases and the epitaxial relations are depicted using models in Fig. 3 and summarized in Table I.^7,31–33 Below, we show a more detailed analysis.

Direct deposition of the target material onto the Al₂O₃ (001) surface resulted in the RHEED patterns displayed in Figs. 2(c) and 2(d), which are similar to those of the Al₂O₃ (001) surface, indicating a similar in-plane lattice structure. Using the pattern separation of the Al₂O₃ (001) as the calibration, one can calculate the in-plane lattice constant as 5.07 ± 0.1 Å, which matches the lattice constant of the α-Fe₂O₃ (001) surface (see Table I) within the experimental error. Since Al₂O₃ and Fe₂O₃ are isomorphic (R-3c corundum structure), it is understandable that the most stable iron oxide epilayer on Al₂O₃ (001) without thermal reduction is α-Fe₂O₃ (001). Therefore, we assign the structural phase that shows the RHEED patterns in Figs. 2(c) and 2(d) as α-Fe₂O₃ (001). The epitaxial relation is Al₂O₃ (001)//α-Fe₂O₃ (001) and Al₂O₃ [100]//α-Fe₂O₃ [100]), as shown in Fig. 3(a). The corresponding reciprocal indices are marked accordingly.

The Fe₃O₄ (111) layer was obtained by thermally reducing the deposited Fe₂O₃ epilayer at high temperature. After the Fe₂O₃ epilayer underwent thermal reduction, we observed the RHEED patterns in Figs. 2(g) and 2(h), which also indicate a surface of triangular lattice. Assuming that a Fe₃O₄ (111) epilayer is on top of the Al₂O₃ (001) substrates and that the RHEED patterns observed in Figs. 2(g) and 2(h) are from the bulk reciprocal space projected onto the (111) surface, one can calculate the in-plane lattice constant as 5.93 ± 0.05 Å. For a normal Fe₃O₄ (111) surface, the in-plane lattice constant is 5.924 Å, which is close to the observed value. Therefore, we assign the structural phase that shows these patterns as Fe₃O₄ (111). The epitaxial relation is Al₂O₃ (001)//Fe₃O₄ (111) and Al₂O₃ [100]//Fe₃O₄ [−211], as shown in Fig. 2. There is no obvious match between the in-plane lattice constant of Al₂O₃ (001) and Fe₃O₄ (111), since the difference is more than 10%. To understand this epitaxial relation, we projected the Al₂O₃ unit cell and the Fe₃O₄ onto the (001) and (111) planes, respectively, and overlapped the two unit cells, as shown in Fig. 3(b). The oxygen network appears to be overlapping well, which may be the reason for the epitaxial relation. The reciprocal indices of Fe₃O₄ (111) layer are marked in Figs. 2(g) and 2(h). Note that Fe₃O₄ has a face centered cubic (fcc) structure, so the lattice constant of the primitive cell of the (111) epilayer is $12$ of the cubic lattice. Because of the fcc structure of the Fe₃O₄, only the reciprocal indices that have all-odd or all-even indices using the cubic indices are present, as shown in Figs. 2(g) and 2(h). Further verification of the Fe₃O₄ phase is found from ex-situ characterizations, such as X-ray diffraction, electric transport measurements, and magneto optical Kerr effect measurements (see Characterization of the Fe₃O₄ and γ-Fe₂O₃ films).

The γ-Fe₂O₃ (111) epilayers were observed after deposition of the target material onto the Fe₃O₄ (111) surface. Among the iron oxide structural phases, γ-Fe₂O₃, another metastable phase of iron oxide at the thermodynamic standard conditions, has a similar structure with Fe₃O₄, as shown in Fig. 3(c). This structure can be represented as: (Fe³⁺)₈[Fe³⁺_40/3◻_8/3]O₃₂ where ◻ denotes vacancy, in which eight Fe³⁺ atoms occupy tetrahedral sites while the remainder occupies octahedral sites.³⁴ In other words, it is a cation deficient spinel structure (space group P4₃32). Figures 2(g) and 2(h) show the RHEED pattern of the epilayers after the deposition of target material onto the Fe₃O₄ (111) surface. Interestingly, these patterns differ dramatically from those in Figs. 2(e) and 2(f), suggesting that the surface structure has a determinant effect on the structure of the epilayer. Since the target is Fe₂O₃ which contains only Fe³⁺, we expect mostly Fe³⁺ in the epilayer after the direct deposition. Based on the structural similarity and valence consideration, a γ-Fe₂O₃ (111) epilayer is expected after the direct deposition of the target material onto the Fe₃O₄ (111) surface.^15,35 This is confirmed using combined characterizations: in-situ RHEED and ex-situ X-ray diffractions (see Characterization of the Fe₃O₄ and γ-Fe₂O₃ films).

Having identified the γ-Fe₂O₃ phase, we also note that the RHEED patterns of the γ-Fe₂O₃ (111) epilayer are not consistent with the bulk reciprocal space projected onto the (111) plane. The structure of γ-Fe₂O₃ has similar lattice constants with those of Fe₃O₄. But because the lattice is simple cubic, the primitive cell is actually smaller; one expects no systematic extinction for the diffraction. This means that the RHEED patterns of the γ-Fe₂O₃ (111) epilayer are supposed to have more streaks than those of the Fe₃O₄ (111) epilayers. In contrast, the observed RHEED patterns of the γ-Fe₂O₃ (111) in fact show less streaks. As shown in Fig. 2(e), in the ⟨01-1⟩ direction (Fig. 2(f)), there appears to be no (022), (0-2-2) streaks for the γ-Fe₂O₃ (111) surface. In addition, along the ⟨-211⟩ direction, the (02-2) and (0-22) streaks are much weaker than the other diffraction streaks (marked as red arrow). In fact the RHEED patterns of the γ-Fe₂O₃ (111) epilayer is more consistent with a FeO (111) surface, which suggests a significant reconstruction at the γ-Fe₂O₃ (111) surface, as also observed in γ-Fe₂O₃ (001) films deposited on MgO substrates.¹⁵ 

The dependence of the structural phase of the thin epilayer on the structure of the beginning surface can be understood in terms of the interfacial energy. Since α-Fe₂O₃ and Al₂O₃ are isomorphic, the energy of the α-Fe₂O₃/Al₂O₃ interface is expected to be relatively lower than that of the γ-Fe₂O₃/Al₂O₃ interface. On the other hand, since γ-Fe₂O₃ and Fe₃O₄ have similar structures, the γ-Fe₂O₃/Fe₃O₄ interface is expected to have lower energy than that of the α-Fe₂O₃/Fe₃O₄ interface. Therefore, after the direct deposition, the α-Fe₂O₃/Al₂O₃ interface and the γ-Fe₂O₃/Fe₃O₄ interface are formed. In fact, a continuous change of epilayer structure from γ-Fe₂O₃ to Fe₃O₄ has been observed previously by changing the growth conditions.^15,26,35 The effect of substrate is expected to diminish when the film thickness is much larger. Using growth conditions (target material, substrate temperature, background O₂ pressure, and laser fluence) that are similar to the deposition conditions used in this work, Tiwari et al. has obtained an Fe₃O₄ (111) film on an Al₂O₃ (001) substrate when the deposition thickness is 200 nm. In this case, the structure is determined by the bulk thermodynamics rather than by the energetics at the film/substrate interface.

In order to study the kinetics of the Fe₂O₃ → Fe₃O₄ transition, we first examined the boundary conditions between the phases using thermodynamic analysis. For both α-Fe₂O₃ (001) and γ-Fe₂O₃ (111) epilayers, the conversion to a Fe₃O₄ (111) layer at high temperature involves not only a change of crystal structure but also a loss of oxygen, which can also be treated as thermal reduction. The condition for the Fe₂O₃ → Fe₃O₄ transition can be estimated according to change of Gibbs free energy (⁠$ΔrG$⁠) in the following reaction:

The $ΔrG$ for this reaction at certain temperature (⁠$T$⁠) and pressure (⁠$P$⁠) can be calculated from the Gibbs free energy at standard condition (⁠$ΔG0$⁠) of Fe₂O₃ and Fe₃O₄, using the relation $ΔrG=23ΔfGFe3O40−ΔfGFe2O30+16RT ln(PP0)$(see the supplementary material), where $P$ is the oxygen pressure and $T$ is the temperature. The standard formation Gibbs free energy (⁠$ΔfGFe2O30$ and $ΔfGFe3O40$⁠) can be calculated using the corresponding formation enthalpy (⁠$ΔfH0$⁠) and formation entropy (⁠$ΔfS0$⁠), which can be assumed as constants. Tables II and III^,36 show the values of $ΔfH0$ and $ΔfS0$⁠. The boundary between the α-Fe₂O₃ and the Fe₃O₄ phases is found by setting $ΔrG=$ 0 and solving the relation between $P$ and $T$⁠. As shown in Fig. 4(c), the solid line is the calculated phase boundary of the Fe₂O₃ and Fe₃O₄, according to the data in Tables II and III, which are in fair agreement with the phase boundaries calculated previously using a different set of data.^28,37

For the high pressure and low temperature region, α-Fe₂O₃ phase is stable, while for the low pressure and high temperature region, the Fe₃O₄ phase is stable. The above thermodynamic analysis provides the information on the boundary between the bulk α-Fe₂O₃ and Fe₃O₄ phases, but not the rate of the transition (kinetics). Various time scales have been mentioned during the studies on the transition between iron oxide phases;^{20–24,26–30} however, a systematic study is lacking. Using the phase boundary in Fig. 4(c) as a guidance, we studied the kinetics of the α-Fe₂O₃ → Fe₃O₄ transition for an epilayer on the Al₂O₃ (001) substrate, by measuring the time evolution of the structure during the thermal reduction using the time-resolved RHEED.

Starting from the Al₂O₃ (001) substrate, we deposited the target material (∼2.5 nm), which generates an α-Fe₂O₃ (001) epilayer (see Figs. S1 and S2 in the supplementary material). During the thermal reduction of α-Fe₂O₃, we monitor the RHEED pattern with the incident electron along the ⟨100⟩ direction of the Al₂O₃. Images of the RHEED patterns were saved every 15 s and integrated along the longer dimension of the diffraction streaks (see Figs. S1 and S2 in the supplementary material). The evolution of the intensities of diffraction streaks is then plotted as a function of time. Figure 4(a) shows an example of RHEED intensity evolution at 930 °C in 9.2 × 10⁻⁸Torr O₂. We found that the Fe₃O₄ (02-2) diffraction streaks slowly emerged between the diffraction streaks of α-Fe₂O₃ (01) and (02), indicating the α-Fe₂O₃ → Fe₃O₄ transition. The intensity of the Fe₃O₄ streaks increases and starts to saturate after a certain time (see Fig. 4(b)). We fit the intensity (⁠$I$⁠) of the Fe₃O₄ streaks using the formula $I=I0(1−e−t/τ)$⁠, where t is time, $I0$ is a saturation intensity, and τ is the time constant of the transition.

The time constant τ has been measured at different temperatures and the dependence is plotted in Fig. 4(d). When the temperature increases, τ decreases dramatically. We fit the temperature dependence of τ using the Arrhenius law, $τ=τ0eEakT$⁠, where $Ea$ is the activation energy and $k$ is the Boltzmann constant. We repeated this study of time constant τ and activation energy at different O₂ pressure; the results are shown in Fig. 4(d). It is interesting that the activation energies do not change significantly considering the experimental uncertainty (see Table IV), while $τ0$ depends on the O₂ pressure dramatically.

In principle, the activation energy corresponds to the minimum energy barrier for the transition. For the Fe₂O₃ → Fe₃O₄ transition, this energy barrier is related to breaking of the Fe-O bonds. The dissociation energy for a typical Fe-O bond is 4.2 eV, however,³⁸ which is about twice as much as the measured $Ea$ (2.3 ± 0.6 eV on average). Therefore, it appears that at the surface, there are weaker Fe-O bonds that actually determine the $Ea$⁠. In fact, the measured $Ea$ value is close to the band gap energy of α-Fe₂O₃.^39,40 The band gap energy of α-Fe₂O₃ corresponds to the energy to excite an electron from O back to Fe, which can be understood as the breaking of the weakest possible link between the Fe and O atoms.

The observation that the activation energy is not significantly affected by the pressure is not surprising, since the change of O₂ pressure is not supposed to affect the Fe-O bond energy significantly. On the other hand, the experimental observations show that higher O₂ pressure actually makes the thermal reduction faster. We speculate a “fall-off” scenario of pressure dependent kinetics:⁴¹ because the α-Fe₂O₃ → Fe₃O₄ is exothermic, when the pressure is lower, the heat transfer is expected to be slower, causing a local O₂ temperature that is higher than that of the solid phase; the higher O₂ temperature may speed up the reversed transition Fe₃O₄ → α-Fe₂O₃ and slow down the rate of the net α-Fe₂O₃ → Fe₃O₄ transition.

The Fe₃O₄ → Fe₂O₃ transition is more complex. At high temperature, the time constant is much smaller for the transition. After the thermal reduction, we decreased the substrate temperature to 600 °C and increased the background O₂ pressure to 5 × 10⁻³Torr. The Fe₃O₄ → α-Fe₂O₃ transition occurred within seconds, indicating a much smaller activation energy. Therefore, the rate of oxidation is not determined by the energy scale to break the O-O bonds (5.2 eV),⁴² which is not untypical for reactions on transition metal oxide surfaces.⁴³ On the other hand, at lower temperature, the transition is not only slow, but with different direct product (γ-Fe₂O₃). We carried out the annealing of the Fe₃O₄ films in one atmosphere O₂ at 250 °C for 4 h. The RHEED pattern after that turned out to be similar to the ones in Figs. 2(e) and 2(f) (see Fig. S3 in the supplementary material). Ex-situ X-ray diffraction and magneto optical Kerr effect measurements indicate that the structure phase is γ-Fe₂O₃ (see Characterization of the Fe₃O₄ and γ-Fe₂O₃ films).

To confirm the structural analysis of the epitaxial layer, we have characterized the Fe₃O₄ films (∼30 nm) ex-situ using X-ray diffraction, atomic force microscopy, electric transport, and magneto-optical Kerr effect.

Figure 5(a) shows the θ-2θ scan of the Fe₃O₄ film grown by repeating the deposition/thermal reduction cycles. No impurity phases can be identified from the diffraction spectrum. Figure 5(b) is the close-up view of the (111) peaks, where the Laue oscillation is obvious, indicating a flat surface of the film. Fitting the Laue oscillation with the consideration of background,⁴⁴ one can find the film thickness as 25 ± 1 nm. The inset shows the rocking curve of Fe₃O₄ (111) peak, for which the full-width-half-maximum (FWHM) is 0.14°, indicating a high crystallinity. One can estimate the size of the crystallites of the film using the peak width of the rocking curve and the θ-2θ scans; the results show a size of 57 ± 1 nm along in-plane direction and 26 ± 1 nm along the out of plane direction (see Figs. S4 and S5 in the supplementary material).

Figure 6(a) shows the surface morphology of a Fe₃O₄ film measured using the atomic force microscopy. The surface of the film consists of domains separated by grooves of 1–2 nm deep. Despite this feature, the root mean square roughness of this film is 0.3 nm (Fig. S1(b)), confirming the flat surface indicated by the Laue oscillation observed in X-ray diffraction. Within the domains, the atomic terraces are observed (Fig. 6(c)), indicating again the high crystallinity. One of the origin of these grooves may be the unavoidable grain boundaries of the Fe₃O₄ films, when the epilayer has a larger unit cell than that of the substrate and the film nucleation occurs at different positions.^45–47 For example, when a Fe₃O₄ film is deposited on a MgO substrate, similar mechanism generates anti-phase boundary because the lattice constant of Fe₃O₄ is about twice as much as that of MgO.^45–47 The large domains on the surface of the Fe₃O₄ films may be due to the thermal reduction at high temperature. According to the broad streaky RHEED patterns in Figs. 2(c) and 2(d), before the thermal reduction, the α-Fe₂O₃ layer consists of small crystallites; the surface also has no grooves (see Fig. S6 in the supplementary material). The high temperature thermal reduction not only converted the α-Fe₂O₃ layer into the Fe₃O₄ layer, but also merged the small crystallites into much larger ones, as indicated by the large domains observed in the AFM images (Fig. 6), as well as by the much sharper RHEED patterns in Figs. 2(g) and 2(h).

To verify the Verwey transition in the Fe₃O₄ films, temperature dependence of the electrical resistance has been measured between 50 and 300 K, as shown in Fig. 7(a). The Verwey transition temperature around 120 K is visible but not as clear as that in bulk,^10,12,13,47 consistent with the significant domain boundaries.^45–47 To highlight the Verwey transition, we have calculated effective activation energy (⁠$Eaeff$⁠) using the relation $Eaeff=dlnRd(1kT)$⁠, where $R$ is the resistance, and $k$ is the Boltzmann constant; the result is shown in Fig. 7(b). A clear anomaly is observed at 114 K, which is attributed to the Verwey transition.

Using the magneto-optical Kerr (MOKE) effect, we have measured the in-plane hysteretic behavior of the magnetization of the Fe₃O₄ films at room temperature, as shown in Fig. 8. The coercivity of the Fe₃O₄ films here (∼270 Oe, see also Fig. S7 in the supplementary material) is comparable with the bulk value (∼310 Oe).⁴⁸ The saturation field appears to be ∼1000 Oe, which is smaller than the bulk value (∼2500 Oe).⁴⁵ On the other hand, previous studies revealed that the magnetization of the Fe₃O₄ films deposited on MgO substrates does not saturate even in a 70 kOe magnetic field. It is possible that the larger structural domains (∼200 nm, see Fig. 6) generated in the high temperature thermal reduction makes the contribution of the domain boundaries less important. In contrast, for the Fe₃O₄ films deposited at lower temperature (500 °C), the smaller structural domains (∼25 nm) make the effect of the antiphase boundary more significant.⁴⁵ 

To verify the observation of the γ-Fe₂O₃ as an intermediate phase in the deposition, we annealed a Fe₃O₄ film (∼30 nm) in one atmosphere O₂ at 250 °C for 4 h.⁴⁹ The RHEED patterns of the annealed film turn from those in Figs. 2(g) and 2(h) to those in Figs. 2(e) and 2(f), indicating a phase transition (see Fig. S3 in the supplementary material). As shown in Fig. 5(a), the X-ray diffraction spectrum of the annealed film is similar to that of the Fe₃O₄ film, except that the angles are systematically larger. The lattice constants calculated from the X-ray diffraction is 8.338 Å for the Fe₃O₄ film and 8.222 Å for the annealed Fe₃O₄ film, respectively (see Fig. S8 in the supplementary material), in agreement with the difference between the bulk values of Fe₃O₄ and γ-Fe₂O₃. Therefore, it appears that the annealed Fe₃O₄ film, as well as the layer observed in Figs. 2(e) and 2(f), are in fact the γ-Fe₂O₃ phase.

By studying the growth of Fe₃O₄ (111)/Al₂O₃ (001) films using pulsed laser deposition and thermal reduction and studying the kinetics of the transitions between the iron oxide phases, we have found that the activation energy for the α-Fe₂O₃ → Fe₃O₄ transition is 2.3 ± 0.6 eV, corresponding to the weakest Fe-O bond to break at the surface. While the α-Fe₂O₃ → Fe₃O₄ transition is slow due to the high activation energy, the Fe₃O₄ → Fe₂O₃ transition is in general much faster and more complex. At high temperature, the oxidation of Fe₃O₄ is quick and results directly in the α-Fe₂O₃ phase; at lower temperature, the oxidation of Fe₃O₄ is much slower and generates the intermediate γ-Fe₂O₃ phase. The Fe₃O₄ (111) films grown from thermal reduction show high crystallinity, even though films contain significant grain boundaries due to the larger mismatch between the in-plane unit cells of Al₂O₃ (001) and Fe₃O₄ (111).

See supplementary material for more detailed information.

This project was primarily supported by the National Science Foundation (NSF), DMR, under Award No. DMR-1454618. Additional support (X.Z.) was from NSF, DMR, under Award No. DMREF: SusChEM 1436385. Z.M.Y. and S.Y. acknowledge the support from the National Science Foundation of China (NSFC Nos. 51272209, 51471125, and 51501140) and the Shaanxi Province Science and Technology Innovation Team Project (2013KCT-05). X.Z. is grateful for the help from Jack Rodenburg and Shi Cao on the MOKE measurements.